LMFDB - Embedded newform 8043.2.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.16260 q^{2} +1.00000 q^{3} +2.67684 q^{4} -4.31110 q^{5} -2.16260 q^{6} +1.00000 q^{7} -1.46374 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16260 q^{2} +1.00000 q^{3} +2.67684 q^{4} -4.31110 q^{5} -2.16260 q^{6} +1.00000 q^{7} -1.46374 q^{8} +1.00000 q^{9} +9.32319 q^{10} -5.80365 q^{11} +2.67684 q^{12} -1.66764 q^{13} -2.16260 q^{14} -4.31110 q^{15} -2.18820 q^{16} -5.76364 q^{17} -2.16260 q^{18} +0.717512 q^{19} -11.5401 q^{20} +1.00000 q^{21} +12.5510 q^{22} +7.08037 q^{23} -1.46374 q^{24} +13.5856 q^{25} +3.60644 q^{26} +1.00000 q^{27} +2.67684 q^{28} -5.54972 q^{29} +9.32319 q^{30} +3.41691 q^{31} +7.65968 q^{32} -5.80365 q^{33} +12.4645 q^{34} -4.31110 q^{35} +2.67684 q^{36} -4.82309 q^{37} -1.55169 q^{38} -1.66764 q^{39} +6.31033 q^{40} +7.18352 q^{41} -2.16260 q^{42} -4.92963 q^{43} -15.5355 q^{44} -4.31110 q^{45} -15.3120 q^{46} +6.49823 q^{47} -2.18820 q^{48} +1.00000 q^{49} -29.3802 q^{50} -5.76364 q^{51} -4.46401 q^{52} -2.72337 q^{53} -2.16260 q^{54} +25.0201 q^{55} -1.46374 q^{56} +0.717512 q^{57} +12.0018 q^{58} +2.46104 q^{59} -11.5401 q^{60} +6.64681 q^{61} -7.38941 q^{62} +1.00000 q^{63} -12.1884 q^{64} +7.18936 q^{65} +12.5510 q^{66} +12.5899 q^{67} -15.4284 q^{68} +7.08037 q^{69} +9.32319 q^{70} +11.4392 q^{71} -1.46374 q^{72} +2.29375 q^{73} +10.4304 q^{74} +13.5856 q^{75} +1.92067 q^{76} -5.80365 q^{77} +3.60644 q^{78} -2.36639 q^{79} +9.43356 q^{80} +1.00000 q^{81} -15.5351 q^{82} -10.1843 q^{83} +2.67684 q^{84} +24.8477 q^{85} +10.6608 q^{86} -5.54972 q^{87} +8.49503 q^{88} -6.15249 q^{89} +9.32319 q^{90} -1.66764 q^{91} +18.9530 q^{92} +3.41691 q^{93} -14.0531 q^{94} -3.09327 q^{95} +7.65968 q^{96} -3.70053 q^{97} -2.16260 q^{98} -5.80365 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * 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 $

$2$	−2.16260	−1.52919	−0.764595	−	0.644511i	$-0.777061\pi$
$2$	−2.16260	−1.52919	−0.764595	+	0.644511i	$0.777061\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.67684	1.33842
$5$	−4.31110	−1.92798	−0.963992	−	0.265932i	$-0.914320\pi$
$5$	−4.31110	−1.92798	−0.963992	+	0.265932i	$0.914320\pi$
$6$	−2.16260	−0.882878
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.46374	−0.517510
$9$	1.00000	0.333333
$10$	9.32319	2.94825
$11$	−5.80365	−1.74987	−0.874933	−	0.484244i	$-0.839095\pi$
$11$	−5.80365	−1.74987	−0.874933	+	0.484244i	$0.839095\pi$
$12$	2.67684	0.772738
$13$	−1.66764	−0.462520	−0.231260	−	0.972892i	$-0.574285\pi$
$13$	−1.66764	−0.462520	−0.231260	+	0.972892i	$0.574285\pi$
$14$	−2.16260	−0.577979
$15$	−4.31110	−1.11312
$16$	−2.18820	−0.547050
$17$	−5.76364	−1.39789	−0.698944	−	0.715176i	$-0.746347\pi$
$17$	−5.76364	−1.39789	−0.698944	+	0.715176i	$0.746347\pi$
$18$	−2.16260	−0.509730
$19$	0.717512	0.164608	0.0823042	−	0.996607i	$-0.473772\pi$
$19$	0.717512	0.164608	0.0823042	+	0.996607i	$0.473772\pi$
$20$	−11.5401	−2.58045
$21$	1.00000	0.218218
$22$	12.5510	2.67588
$23$	7.08037	1.47636	0.738180	−	0.674604i	$-0.235686\pi$
$23$	7.08037	1.47636	0.738180	+	0.674604i	$0.235686\pi$
$24$	−1.46374	−0.298784
$25$	13.5856	2.71712
$26$	3.60644	0.707281
$27$	1.00000	0.192450
$28$	2.67684	0.505876
$29$	−5.54972	−1.03056	−0.515278	−	0.857023i	$-0.672311\pi$
$29$	−5.54972	−1.03056	−0.515278	+	0.857023i	$0.672311\pi$
$30$	9.32319	1.70217
$31$	3.41691	0.613695	0.306847	−	0.951759i	$-0.400726\pi$
$31$	3.41691	0.613695	0.306847	+	0.951759i	$0.400726\pi$
$32$	7.65968	1.35405
$33$	−5.80365	−1.01029
$34$	12.4645	2.13764
$35$	−4.31110	−0.728709
$36$	2.67684	0.446140
$37$	−4.82309	−0.792911	−0.396456	−	0.918054i	$-0.629760\pi$
$37$	−4.82309	−0.792911	−0.396456	+	0.918054i	$0.629760\pi$
$38$	−1.55169	−0.251718
$39$	−1.66764	−0.267036
$40$	6.31033	0.997750
$41$	7.18352	1.12188	0.560939	−	0.827857i	$-0.310440\pi$
$41$	7.18352	1.12188	0.560939	+	0.827857i	$0.310440\pi$
$42$	−2.16260	−0.333697
$43$	−4.92963	−0.751762	−0.375881	−	0.926668i	$-0.622660\pi$
$43$	−4.92963	−0.751762	−0.375881	+	0.926668i	$0.622660\pi$
$44$	−15.5355	−2.34206
$45$	−4.31110	−0.642661
$46$	−15.3120	−2.25763
$47$	6.49823	0.947865	0.473932	−	0.880561i	$-0.342834\pi$
$47$	6.49823	0.947865	0.473932	+	0.880561i	$0.342834\pi$
$48$	−2.18820	−0.315840
$49$	1.00000	0.142857
$50$	−29.3802	−4.15499
$51$	−5.76364	−0.807072
$52$	−4.46401	−0.619047
$53$	−2.72337	−0.374084	−0.187042	−	0.982352i	$-0.559890\pi$
$53$	−2.72337	−0.374084	−0.187042	+	0.982352i	$0.559890\pi$
$54$	−2.16260	−0.294293
$55$	25.0201	3.37371
$56$	−1.46374	−0.195600
$57$	0.717512	0.0950367
$58$	12.0018	1.57592
$59$	2.46104	0.320401	0.160200	−	0.987085i	$-0.448786\pi$
$59$	2.46104	0.320401	0.160200	+	0.987085i	$0.448786\pi$
$60$	−11.5401	−1.48983
$61$	6.64681	0.851036	0.425518	−	0.904950i	$-0.360092\pi$
$61$	6.64681	0.851036	0.425518	+	0.904950i	$0.360092\pi$
$62$	−7.38941	−0.938456
$63$	1.00000	0.125988
$64$	−12.1884	−1.52355
$65$	7.18936	0.891731
$66$	12.5510	1.54492
$67$	12.5899	1.53810	0.769049	−	0.639189i	$-0.220730\pi$
$67$	12.5899	1.53810	0.769049	+	0.639189i	$0.220730\pi$
$68$	−15.4284	−1.87096
$69$	7.08037	0.852376
$70$	9.32319	1.11433
$71$	11.4392	1.35758	0.678790	−	0.734332i	$-0.262505\pi$
$71$	11.4392	1.35758	0.678790	+	0.734332i	$0.262505\pi$
$72$	−1.46374	−0.172503
$73$	2.29375	0.268463	0.134232	−	0.990950i	$-0.457143\pi$
$73$	2.29375	0.268463	0.134232	+	0.990950i	$0.457143\pi$
$74$	10.4304	1.21251
$75$	13.5856	1.56873
$76$	1.92067	0.220315
$77$	−5.80365	−0.661387
$78$	3.60644	0.408349
$79$	−2.36639	−0.266239	−0.133120	−	0.991100i	$-0.542499\pi$
$79$	−2.36639	−0.266239	−0.133120	+	0.991100i	$0.542499\pi$
$80$	9.43356	1.05470
$81$	1.00000	0.111111
$82$	−15.5351	−1.71556
$83$	−10.1843	−1.11788	−0.558939	−	0.829209i	$-0.688791\pi$
$83$	−10.1843	−1.11788	−0.558939	+	0.829209i	$0.688791\pi$
$84$	2.67684	0.292067
$85$	24.8477	2.69511
$86$	10.6608	1.14959
$87$	−5.54972	−0.594992
$88$	8.49503	0.905573
$89$	−6.15249	−0.652163	−0.326081	−	0.945342i	$-0.605728\pi$
$89$	−6.15249	−0.652163	−0.326081	+	0.945342i	$0.605728\pi$
$90$	9.32319	0.982751
$91$	−1.66764	−0.174816
$92$	18.9530	1.97599
$93$	3.41691	0.354317
$94$	−14.0531	−1.44946
$95$	−3.09327	−0.317362
$96$	7.65968	0.781763
$97$	−3.70053	−0.375732	−0.187866	−	0.982195i	$-0.560157\pi$
$97$	−3.70053	−0.375732	−0.187866	+	0.982195i	$0.560157\pi$
$98$	−2.16260	−0.218456
$99$	−5.80365	−0.583289
$100$	36.3665	3.63665
$101$	15.5277	1.54506	0.772531	−	0.634977i	$-0.218991\pi$
$101$	15.5277	1.54506	0.772531	+	0.634977i	$0.218991\pi$
$102$	12.4645	1.23417
$103$	18.7888	1.85132	0.925660	−	0.378357i	$-0.123511\pi$
$103$	18.7888	1.85132	0.925660	+	0.378357i	$0.123511\pi$
$104$	2.44099	0.239359
$105$	−4.31110	−0.420720
$106$	5.88957	0.572045
$107$	−15.7392	−1.52157	−0.760783	−	0.649007i	$-0.775185\pi$
$107$	−15.7392	−1.52157	−0.760783	+	0.649007i	$0.775185\pi$
$108$	2.67684	0.257579
$109$	14.8471	1.42209	0.711046	−	0.703146i	$-0.248222\pi$
$109$	14.8471	1.42209	0.711046	+	0.703146i	$0.248222\pi$
$110$	−54.1085	−5.15905
$111$	−4.82309	−0.457788
$112$	−2.18820	−0.206766
$113$	−8.95308	−0.842235	−0.421118	−	0.907006i	$-0.638362\pi$
$113$	−8.95308	−0.842235	−0.421118	+	0.907006i	$0.638362\pi$
$114$	−1.55169	−0.145329
$115$	−30.5242	−2.84640
$116$	−14.8557	−1.37932
$117$	−1.66764	−0.154173
$118$	−5.32226	−0.489953
$119$	−5.76364	−0.528352
$120$	6.31033	0.576051
$121$	22.6823	2.06203
$122$	−14.3744	−1.30140
$123$	7.18352	0.647716
$124$	9.14652	0.821382
$125$	−37.0134	−3.31058
$126$	−2.16260	−0.192660
$127$	7.33023	0.650453	0.325227	−	0.945636i	$-0.394559\pi$
$127$	7.33023	0.650453	0.325227	+	0.945636i	$0.394559\pi$
$128$	11.0393	0.975750
$129$	−4.92963	−0.434030
$130$	−15.5477	−1.36363
$131$	0.159279	0.0139162	0.00695812	−	0.999976i	$-0.497785\pi$
$131$	0.159279	0.0139162	0.00695812	+	0.999976i	$0.497785\pi$
$132$	−15.5355	−1.35219
$133$	0.717512	0.0622162
$134$	−27.2269	−2.35204
$135$	−4.31110	−0.371041
$136$	8.43647	0.723421
$137$	9.03933	0.772282	0.386141	−	0.922440i	$-0.373808\pi$
$137$	9.03933	0.772282	0.386141	+	0.922440i	$0.373808\pi$
$138$	−15.3120	−1.30345
$139$	−20.6387	−1.75055	−0.875274	−	0.483628i	$-0.839319\pi$
$139$	−20.6387	−1.75055	−0.875274	+	0.483628i	$0.839319\pi$
$140$	−11.5401	−0.975320
$141$	6.49823	0.547250
$142$	−24.7384	−2.07600
$143$	9.67840	0.809348
$144$	−2.18820	−0.182350
$145$	23.9254	1.98690
$146$	−4.96047	−0.410531
$147$	1.00000	0.0824786
$148$	−12.9107	−1.06125
$149$	−17.2991	−1.41720	−0.708601	−	0.705610i	$-0.750673\pi$
$149$	−17.2991	−1.41720	−0.708601	+	0.705610i	$0.750673\pi$
$150$	−29.3802	−2.39889
$151$	5.72907	0.466225	0.233113	−	0.972450i	$-0.425109\pi$
$151$	5.72907	0.466225	0.233113	+	0.972450i	$0.425109\pi$
$152$	−1.05025	−0.0851865
$153$	−5.76364	−0.465963
$154$	12.5510	1.01139
$155$	−14.7306	−1.18319
$156$	−4.46401	−0.357407
$157$	−11.7233	−0.935624	−0.467812	−	0.883828i	$-0.654958\pi$
$157$	−11.7233	−0.935624	−0.467812	+	0.883828i	$0.654958\pi$
$158$	5.11755	0.407131
$159$	−2.72337	−0.215978
$160$	−33.0217	−2.61059
$161$	7.08037	0.558011
$162$	−2.16260	−0.169910
$163$	−10.3853	−0.813443	−0.406721	−	0.913552i	$-0.633328\pi$
$163$	−10.3853	−0.813443	−0.406721	+	0.913552i	$0.633328\pi$
$164$	19.2291	1.50154
$165$	25.0201	1.94781
$166$	22.0247	1.70945
$167$	−5.42059	−0.419458	−0.209729	−	0.977760i	$-0.567258\pi$
$167$	−5.42059	−0.419458	−0.209729	+	0.977760i	$0.567258\pi$
$168$	−1.46374	−0.112930
$169$	−10.2190	−0.786075
$170$	−53.7356	−4.12133
$171$	0.717512	0.0548695
$172$	−13.1959	−1.00617
$173$	14.3608	1.09183	0.545914	−	0.837841i	$-0.316182\pi$
$173$	14.3608	1.09183	0.545914	+	0.837841i	$0.316182\pi$
$174$	12.0018	0.909856
$175$	13.5856	1.02697
$176$	12.6996	0.957265
$177$	2.46104	0.184983
$178$	13.3054	0.997280
$179$	17.3459	1.29650	0.648248	−	0.761429i	$-0.275502\pi$
$179$	17.3459	1.29650	0.648248	+	0.761429i	$0.275502\pi$
$180$	−11.5401	−0.860151
$181$	−24.5308	−1.82336	−0.911680	−	0.410900i	$-0.865214\pi$
$181$	−24.5308	−1.82336	−0.911680	+	0.410900i	$0.865214\pi$
$182$	3.60644	0.267327
$183$	6.64681	0.491346
$184$	−10.3638	−0.764030
$185$	20.7928	1.52872
$186$	−7.38941	−0.541818
$187$	33.4502	2.44612
$188$	17.3947	1.26864
$189$	1.00000	0.0727393
$190$	6.68950	0.485307
$191$	−20.0498	−1.45075	−0.725377	−	0.688351i	$-0.758335\pi$
$191$	−20.0498	−1.45075	−0.725377	+	0.688351i	$0.758335\pi$
$192$	−12.1884	−0.879624
$193$	−9.93458	−0.715107	−0.357553	−	0.933893i	$-0.616389\pi$
$193$	−9.93458	−0.715107	−0.357553	+	0.933893i	$0.616389\pi$
$194$	8.00278	0.574566
$195$	7.18936	0.514841
$196$	2.67684	0.191203
$197$	17.0192	1.21257	0.606285	−	0.795247i	$-0.292659\pi$
$197$	17.0192	1.21257	0.606285	+	0.795247i	$0.292659\pi$
$198$	12.5510	0.891959
$199$	17.0640	1.20963	0.604816	−	0.796365i	$-0.293247\pi$
$199$	17.0640	1.20963	0.604816	+	0.796365i	$0.293247\pi$
$200$	−19.8858	−1.40614
$201$	12.5899	0.888022
$202$	−33.5802	−2.36269
$203$	−5.54972	−0.389514
$204$	−15.4284	−1.08020
$205$	−30.9689	−2.16296
$206$	−40.6328	−2.83102
$207$	7.08037	0.492120
$208$	3.64913	0.253022
$209$	−4.16419	−0.288043
$210$	9.32319	0.643361
$211$	−23.6075	−1.62521	−0.812604	−	0.582816i	$-0.801951\pi$
$211$	−23.6075	−1.62521	−0.812604	+	0.582816i	$0.801951\pi$
$212$	−7.29004	−0.500682
$213$	11.4392	0.783799
$214$	34.0376	2.32676
$215$	21.2522	1.44939
$216$	−1.46374	−0.0995948
$217$	3.41691	0.231955
$218$	−32.1083	−2.17465
$219$	2.29375	0.154997
$220$	66.9749	4.51545
$221$	9.61168	0.646552
$222$	10.4304	0.700044
$223$	−3.84902	−0.257750	−0.128875	−	0.991661i	$-0.541137\pi$
$223$	−3.84902	−0.257750	−0.128875	+	0.991661i	$0.541137\pi$
$224$	7.65968	0.511784
$225$	13.5856	0.905707
$226$	19.3619	1.28794
$227$	28.8301	1.91352	0.956760	−	0.290877i	$-0.0939471\pi$
$227$	28.8301	1.91352	0.956760	+	0.290877i	$0.0939471\pi$
$228$	1.92067	0.127199
$229$	−13.9777	−0.923674	−0.461837	−	0.886965i	$-0.652809\pi$
$229$	−13.9777	−0.923674	−0.461837	+	0.886965i	$0.652809\pi$
$230$	66.0116	4.35268
$231$	−5.80365	−0.381852
$232$	8.12333	0.533323
$233$	26.2684	1.72090	0.860450	−	0.509534i	$-0.170182\pi$
$233$	26.2684	1.72090	0.860450	+	0.509534i	$0.170182\pi$
$234$	3.60644	0.235760
$235$	−28.0145	−1.82747
$236$	6.58783	0.428831
$237$	−2.36639	−0.153713
$238$	12.4645	0.807951
$239$	3.43864	0.222427	0.111213	−	0.993797i	$-0.464526\pi$
$239$	3.43864	0.222427	0.111213	+	0.993797i	$0.464526\pi$
$240$	9.43356	0.608934
$241$	6.08853	0.392197	0.196098	−	0.980584i	$-0.437173\pi$
$241$	6.08853	0.392197	0.196098	+	0.980584i	$0.437173\pi$
$242$	−49.0528	−3.15324
$243$	1.00000	0.0641500
$244$	17.7925	1.13905
$245$	−4.31110	−0.275426
$246$	−15.5351	−0.990481
$247$	−1.19655	−0.0761347
$248$	−5.00146	−0.317593
$249$	−10.1843	−0.645407
$250$	80.0452	5.06250
$251$	−26.4649	−1.67045	−0.835225	−	0.549908i	$-0.814663\pi$
$251$	−26.4649	−1.67045	−0.835225	+	0.549908i	$0.814663\pi$
$252$	2.67684	0.168625
$253$	−41.0920	−2.58343
$254$	−15.8524	−0.994666
$255$	24.8477	1.55602
$256$	0.503162	0.0314476
$257$	4.00631	0.249907	0.124954	−	0.992163i	$-0.460122\pi$
$257$	4.00631	0.249907	0.124954	+	0.992163i	$0.460122\pi$
$258$	10.6608	0.663714
$259$	−4.82309	−0.299692
$260$	19.2448	1.19351
$261$	−5.54972	−0.343519
$262$	−0.344456	−0.0212806
$263$	−15.3756	−0.948100	−0.474050	−	0.880498i	$-0.657208\pi$
$263$	−15.3756	−0.948100	−0.474050	+	0.880498i	$0.657208\pi$
$264$	8.49503	0.522833
$265$	11.7407	0.721228
$266$	−1.55169	−0.0951403
$267$	−6.15249	−0.376526
$268$	33.7011	2.05862
$269$	−7.21997	−0.440209	−0.220105	−	0.975476i	$-0.570640\pi$
$269$	−7.21997	−0.440209	−0.220105	+	0.975476i	$0.570640\pi$
$270$	9.32319	0.567391
$271$	−26.8021	−1.62811	−0.814055	−	0.580788i	$-0.802745\pi$
$271$	−26.8021	−1.62811	−0.814055	+	0.580788i	$0.802745\pi$
$272$	12.6120	0.764716
$273$	−1.66764	−0.100930
$274$	−19.5485	−1.18097
$275$	−78.8460	−4.75460
$276$	18.9530	1.14084
$277$	−0.0290973	−0.00174829	−0.000874143	−	1.00000i	$-0.500278\pi$
$277$	−0.0290973	−0.00174829	−0.000874143		1.00000i	$0.500278\pi$
$278$	44.6332	2.67692
$279$	3.41691	0.204565
$280$	6.31033	0.377114
$281$	27.6549	1.64975	0.824876	−	0.565313i	$-0.191245\pi$
$281$	27.6549	1.64975	0.824876	+	0.565313i	$0.191245\pi$
$282$	−14.0531	−0.836849
$283$	28.3107	1.68289	0.841447	−	0.540339i	$-0.181704\pi$
$283$	28.3107	1.68289	0.841447	+	0.540339i	$0.181704\pi$
$284$	30.6209	1.81701
$285$	−3.09327	−0.183229
$286$	−20.9305	−1.23765
$287$	7.18352	0.424030
$288$	7.65968	0.451351
$289$	16.2196	0.954094
$290$	−51.7411	−3.03834
$291$	−3.70053	−0.216929
$292$	6.14001	0.359317
$293$	30.2413	1.76672	0.883358	−	0.468698i	$-0.155277\pi$
$293$	30.2413	1.76672	0.883358	+	0.468698i	$0.155277\pi$
$294$	−2.16260	−0.126125
$295$	−10.6098	−0.617727
$296$	7.05975	0.410339
$297$	−5.80365	−0.336762
$298$	37.4112	2.16717
$299$	−11.8075	−0.682846
$300$	36.3665	2.09962
$301$	−4.92963	−0.284139
$302$	−12.3897	−0.712947
$303$	15.5277	0.892042
$304$	−1.57006	−0.0900491
$305$	−28.6551	−1.64078
$306$	12.4645	0.712546
$307$	26.4195	1.50784	0.753921	−	0.656965i	$-0.228160\pi$
$307$	26.4195	1.50784	0.753921	+	0.656965i	$0.228160\pi$
$308$	−15.5355	−0.885214
$309$	18.7888	1.06886
$310$	31.8565	1.80933
$311$	−25.8578	−1.46626	−0.733132	−	0.680087i	$-0.761942\pi$
$311$	−25.8578	−1.46626	−0.733132	+	0.680087i	$0.761942\pi$
$312$	2.44099	0.138194
$313$	−4.81008	−0.271882	−0.135941	−	0.990717i	$-0.543406\pi$
$313$	−4.81008	−0.271882	−0.135941	+	0.990717i	$0.543406\pi$
$314$	25.3529	1.43075
$315$	−4.31110	−0.242903
$316$	−6.33445	−0.356340
$317$	−0.933485	−0.0524297	−0.0262149	−	0.999656i	$-0.508345\pi$
$317$	−0.933485	−0.0524297	−0.0262149	+	0.999656i	$0.508345\pi$
$318$	5.88957	0.330271
$319$	32.2086	1.80334
$320$	52.5456	2.93739
$321$	−15.7392	−0.878476
$322$	−15.3120	−0.853305
$323$	−4.13548	−0.230104
$324$	2.67684	0.148713
$325$	−22.6559	−1.25672
$326$	22.4594	1.24391
$327$	14.8471	0.821045
$328$	−10.5148	−0.580583
$329$	6.49823	0.358259
$330$	−54.1085	−2.97858
$331$	7.20446	0.395993	0.197997	−	0.980203i	$-0.436557\pi$
$331$	7.20446	0.395993	0.197997	+	0.980203i	$0.436557\pi$
$332$	−27.2619	−1.49619
$333$	−4.82309	−0.264304
$334$	11.7226	0.641430
$335$	−54.2763	−2.96543
$336$	−2.18820	−0.119376
$337$	11.7865	0.642054	0.321027	−	0.947070i	$-0.395972\pi$
$337$	11.7865	0.642054	0.321027	+	0.947070i	$0.395972\pi$
$338$	22.0996	1.20206
$339$	−8.95308	−0.486265
$340$	66.5132	3.60719
$341$	−19.8305	−1.07388
$342$	−1.55169	−0.0839059
$343$	1.00000	0.0539949
$344$	7.21570	0.389044
$345$	−30.5242	−1.64337
$346$	−31.0566	−1.66961
$347$	2.95872	0.158832	0.0794161	−	0.996842i	$-0.474694\pi$
$347$	2.95872	0.158832	0.0794161	+	0.996842i	$0.474694\pi$
$348$	−14.8557	−0.796350
$349$	14.2547	0.763039	0.381519	−	0.924361i	$-0.375401\pi$
$349$	14.2547	0.763039	0.381519	+	0.924361i	$0.375401\pi$
$350$	−29.3802	−1.57044
$351$	−1.66764	−0.0890120
$352$	−44.4541	−2.36941
$353$	−21.7285	−1.15649	−0.578247	−	0.815862i	$-0.696263\pi$
$353$	−21.7285	−1.15649	−0.578247	+	0.815862i	$0.696263\pi$
$354$	−5.32226	−0.282875
$355$	−49.3154	−2.61739
$356$	−16.4692	−0.872868
$357$	−5.76364	−0.305044
$358$	−37.5123	−1.98259
$359$	−20.3906	−1.07618	−0.538089	−	0.842888i	$-0.680853\pi$
$359$	−20.3906	−1.07618	−0.538089	+	0.842888i	$0.680853\pi$
$360$	6.31033	0.332583
$361$	−18.4852	−0.972904
$362$	53.0503	2.78826
$363$	22.6823	1.19051
$364$	−4.46401	−0.233978
$365$	−9.88860	−0.517593
$366$	−14.3744	−0.751361
$367$	22.0886	1.15302	0.576509	−	0.817091i	$-0.304415\pi$
$367$	22.0886	1.15302	0.576509	+	0.817091i	$0.304415\pi$
$368$	−15.4933	−0.807643
$369$	7.18352	0.373959
$370$	−44.9666	−2.33770
$371$	−2.72337	−0.141390
$372$	9.14652	0.474225
$373$	−11.6854	−0.605049	−0.302525	−	0.953142i	$-0.597829\pi$
$373$	−11.6854	−0.605049	−0.302525	+	0.953142i	$0.597829\pi$
$374$	−72.3394	−3.74058
$375$	−37.0134	−1.91136
$376$	−9.51171	−0.490529
$377$	9.25493	0.476653
$378$	−2.16260	−0.111232
$379$	−13.4365	−0.690185	−0.345093	−	0.938569i	$-0.612153\pi$
$379$	−13.4365	−0.690185	−0.345093	+	0.938569i	$0.612153\pi$
$380$	−8.28018	−0.424764
$381$	7.33023	0.375539
$382$	43.3598	2.21848
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	11.0393	0.563349
$385$	25.0201	1.27514
$386$	21.4845	1.09353
$387$	−4.92963	−0.250587
$388$	−9.90575	−0.502888
$389$	−7.49920	−0.380224	−0.190112	−	0.981762i	$-0.560885\pi$
$389$	−7.49920	−0.380224	−0.190112	+	0.981762i	$0.560885\pi$
$390$	−15.5477	−0.787290
$391$	−40.8087	−2.06379
$392$	−1.46374	−0.0739300
$393$	0.159279	0.00803454
$394$	−36.8058	−1.85425
$395$	10.2017	0.513305
$396$	−15.5355	−0.780686
$397$	−19.5022	−0.978787	−0.489393	−	0.872063i	$-0.662782\pi$
$397$	−19.5022	−0.978787	−0.489393	+	0.872063i	$0.662782\pi$
$398$	−36.9025	−1.84976
$399$	0.717512	0.0359205
$400$	−29.7280	−1.48640
$401$	18.6803	0.932849	0.466424	−	0.884561i	$-0.345542\pi$
$401$	18.6803	0.932849	0.466424	+	0.884561i	$0.345542\pi$
$402$	−27.2269	−1.35795
$403$	−5.69817	−0.283846
$404$	41.5651	2.06794
$405$	−4.31110	−0.214220
$406$	12.0018	0.595640
$407$	27.9915	1.38749
$408$	8.43647	0.417667
$409$	−27.8140	−1.37532	−0.687658	−	0.726035i	$-0.741361\pi$
$409$	−27.8140	−1.37532	−0.687658	+	0.726035i	$0.741361\pi$
$410$	66.9733	3.30758
$411$	9.03933	0.445877
$412$	50.2948	2.47784
$413$	2.46104	0.121100
$414$	−15.3120	−0.752544
$415$	43.9057	2.15525
$416$	−12.7736	−0.626277
$417$	−20.6387	−1.01068
$418$	9.00547	0.440472
$419$	−2.89367	−0.141365	−0.0706826	−	0.997499i	$-0.522518\pi$
$419$	−2.89367	−0.141365	−0.0706826	+	0.997499i	$0.522518\pi$
$420$	−11.5401	−0.563101
$421$	−15.8866	−0.774267	−0.387134	−	0.922024i	$-0.626535\pi$
$421$	−15.8866	−0.774267	−0.387134	+	0.922024i	$0.626535\pi$
$422$	51.0536	2.48525
$423$	6.49823	0.315955
$424$	3.98631	0.193592
$425$	−78.3025	−3.79823
$426$	−24.7384	−1.19858
$427$	6.64681	0.321662
$428$	−42.1313	−2.03649
$429$	9.67840	0.467277
$430$	−45.9599	−2.21638
$431$	−25.0198	−1.20516	−0.602580	−	0.798059i	$-0.705860\pi$
$431$	−25.0198	−1.20516	−0.602580	+	0.798059i	$0.705860\pi$
$432$	−2.18820	−0.105280
$433$	−10.0684	−0.483854	−0.241927	−	0.970294i	$-0.577780\pi$
$433$	−10.0684	−0.483854	−0.241927	+	0.970294i	$0.577780\pi$
$434$	−7.38941	−0.354703
$435$	23.9254	1.14713
$436$	39.7433	1.90336
$437$	5.08025	0.243021
$438$	−4.96047	−0.237020
$439$	38.8887	1.85605	0.928027	−	0.372512i	$-0.121503\pi$
$439$	38.8887	1.85605	0.928027	+	0.372512i	$0.121503\pi$
$440$	−36.6229	−1.74593
$441$	1.00000	0.0476190
$442$	−20.7862	−0.988700
$443$	−16.9403	−0.804860	−0.402430	−	0.915451i	$-0.631834\pi$
$443$	−16.9403	−0.804860	−0.402430	+	0.915451i	$0.631834\pi$
$444$	−12.9107	−0.612712
$445$	26.5240	1.25736
$446$	8.32390	0.394148
$447$	−17.2991	−0.818222
$448$	−12.1884	−0.575849
$449$	−4.21042	−0.198702	−0.0993509	−	0.995052i	$-0.531677\pi$
$449$	−4.21042	−0.198702	−0.0993509	+	0.995052i	$0.531677\pi$
$450$	−29.3802	−1.38500
$451$	−41.6906	−1.96314
$452$	−23.9660	−1.12727
$453$	5.72907	0.269175
$454$	−62.3480	−2.92614
$455$	7.18936	0.337043
$456$	−1.05025	−0.0491825
$457$	22.8965	1.07105	0.535527	−	0.844518i	$-0.320113\pi$
$457$	22.8965	1.07105	0.535527	+	0.844518i	$0.320113\pi$
$458$	30.2282	1.41247
$459$	−5.76364	−0.269024
$460$	−81.7084	−3.80968
$461$	−6.99567	−0.325821	−0.162910	−	0.986641i	$-0.552088\pi$
$461$	−6.99567	−0.325821	−0.162910	+	0.986641i	$0.552088\pi$
$462$	12.5510	0.583924
$463$	−28.2642	−1.31355	−0.656774	−	0.754087i	$-0.728080\pi$
$463$	−28.2642	−1.31355	−0.656774	+	0.754087i	$0.728080\pi$
$464$	12.1439	0.563766
$465$	−14.7306	−0.683117
$466$	−56.8081	−2.63158
$467$	−19.5573	−0.905005	−0.452502	−	0.891763i	$-0.649469\pi$
$467$	−19.5573	−0.905005	−0.452502	+	0.891763i	$0.649469\pi$
$468$	−4.46401	−0.206349
$469$	12.5899	0.581347
$470$	60.5843	2.79454
$471$	−11.7233	−0.540183
$472$	−3.60233	−0.165811
$473$	28.6099	1.31548
$474$	5.11755	0.235057
$475$	9.74783	0.447261
$476$	−15.4284	−0.707158
$477$	−2.72337	−0.124695
$478$	−7.43640	−0.340133
$479$	37.6614	1.72079	0.860396	−	0.509626i	$-0.170216\pi$
$479$	37.6614	1.72079	0.860396	+	0.509626i	$0.170216\pi$
$480$	−33.0217	−1.50723
$481$	8.04318	0.366737
$482$	−13.1671	−0.599743
$483$	7.08037	0.322168
$484$	60.7170	2.75987
$485$	15.9534	0.724406
$486$	−2.16260	−0.0980976
$487$	−13.3260	−0.603858	−0.301929	−	0.953330i	$-0.597631\pi$
$487$	−13.3260	−0.603858	−0.301929	+	0.953330i	$0.597631\pi$
$488$	−9.72919	−0.440420
$489$	−10.3853	−0.469641
$490$	9.32319	0.421179
$491$	4.36559	0.197016	0.0985082	−	0.995136i	$-0.468593\pi$
$491$	4.36559	0.197016	0.0985082	+	0.995136i	$0.468593\pi$
$492$	19.2291	0.866917
$493$	31.9866	1.44060
$494$	2.58766	0.116424
$495$	25.0201	1.12457
$496$	−7.47688	−0.335722
$497$	11.4392	0.513117
$498$	22.0247	0.986949
$499$	41.8150	1.87190	0.935948	−	0.352138i	$-0.114545\pi$
$499$	41.8150	1.87190	0.935948	+	0.352138i	$0.114545\pi$
$500$	−99.0790	−4.43095
$501$	−5.42059	−0.242174
$502$	57.2330	2.55443
$503$	−0.115178	−0.00513555	−0.00256777	−	0.999997i	$-0.500817\pi$
$503$	−0.115178	−0.00513555	−0.00256777	+	0.999997i	$0.500817\pi$
$504$	−1.46374	−0.0652001
$505$	−66.9414	−2.97885
$506$	88.8656	3.95056
$507$	−10.2190	−0.453841
$508$	19.6219	0.870580
$509$	37.1812	1.64803	0.824015	−	0.566568i	$-0.191729\pi$
$509$	37.1812	1.64803	0.824015	+	0.566568i	$0.191729\pi$
$510$	−53.7356	−2.37945
$511$	2.29375	0.101470
$512$	−23.1668	−1.02384
$513$	0.717512	0.0316789
$514$	−8.66406	−0.382155
$515$	−81.0006	−3.56931
$516$	−13.1959	−0.580915
$517$	−37.7135	−1.65864
$518$	10.4304	0.458286
$519$	14.3608	0.630368
$520$	−10.5234	−0.461480
$521$	33.5751	1.47095	0.735475	−	0.677552i	$-0.236959\pi$
$521$	33.5751	1.47095	0.735475	+	0.677552i	$0.236959\pi$
$522$	12.0018	0.525305
$523$	5.69919	0.249208	0.124604	−	0.992207i	$-0.460234\pi$
$523$	5.69919	0.249208	0.124604	+	0.992207i	$0.460234\pi$
$524$	0.426363	0.0186258
$525$	13.5856	0.592924
$526$	33.2513	1.44982
$527$	−19.6938	−0.857877
$528$	12.6996	0.552677
$529$	27.1316	1.17964
$530$	−25.3905	−1.10289
$531$	2.46104	0.106800
$532$	1.92067	0.0832714
$533$	−11.9795	−0.518891
$534$	13.3054	0.575780
$535$	67.8533	2.93355
$536$	−18.4283	−0.795981
$537$	17.3459	0.748532
$538$	15.6139	0.673163
$539$	−5.80365	−0.249981
$540$	−11.5401	−0.496608
$541$	9.93259	0.427035	0.213518	−	0.976939i	$-0.431508\pi$
$541$	9.93259	0.427035	0.213518	+	0.976939i	$0.431508\pi$
$542$	57.9622	2.48969
$543$	−24.5308	−1.05272
$544$	−44.1477	−1.89282
$545$	−64.0072	−2.74177
$546$	3.60644	0.154341
$547$	−30.2659	−1.29408	−0.647038	−	0.762458i	$-0.723992\pi$
$547$	−30.2659	−1.29408	−0.647038	+	0.762458i	$0.723992\pi$
$548$	24.1969	1.03364
$549$	6.64681	0.283679
$550$	170.513	7.27068
$551$	−3.98199	−0.169638
$552$	−10.3638	−0.441113
$553$	−2.36639	−0.100629
$554$	0.0629258	0.00267346
$555$	20.7928	0.882607
$556$	−55.2464	−2.34297
$557$	−3.39710	−0.143940	−0.0719699	−	0.997407i	$-0.522929\pi$
$557$	−3.39710	−0.143940	−0.0719699	+	0.997407i	$0.522929\pi$
$558$	−7.38941	−0.312819
$559$	8.22085	0.347705
$560$	9.43356	0.398641
$561$	33.4502	1.41227
$562$	−59.8065	−2.52278
$563$	−8.68245	−0.365921	−0.182961	−	0.983120i	$-0.558568\pi$
$563$	−8.68245	−0.365921	−0.182961	+	0.983120i	$0.558568\pi$
$564$	17.3947	0.732451
$565$	38.5976	1.62382
$566$	−61.2247	−2.57346
$567$	1.00000	0.0419961
$568$	−16.7440	−0.702561
$569$	−15.2756	−0.640386	−0.320193	−	0.947352i	$-0.603748\pi$
$569$	−15.2756	−0.640386	−0.320193	+	0.947352i	$0.603748\pi$
$570$	6.68950	0.280192
$571$	−0.727989	−0.0304654	−0.0152327	−	0.999884i	$-0.504849\pi$
$571$	−0.727989	−0.0304654	−0.0152327	+	0.999884i	$0.504849\pi$
$572$	25.9075	1.08325
$573$	−20.0498	−0.837594
$574$	−15.5351	−0.648422
$575$	96.1911	4.01144
$576$	−12.1884	−0.507851
$577$	−16.2506	−0.676522	−0.338261	−	0.941052i	$-0.609839\pi$
$577$	−16.2506	−0.676522	−0.338261	+	0.941052i	$0.609839\pi$
$578$	−35.0765	−1.45899
$579$	−9.93458	−0.412867
$580$	64.0445	2.65930
$581$	−10.1843	−0.422518
$582$	8.00278	0.331726
$583$	15.8055	0.654597
$584$	−3.35745	−0.138932
$585$	7.18936	0.297244
$586$	−65.3999	−2.70164
$587$	33.6376	1.38837	0.694187	−	0.719795i	$-0.255764\pi$
$587$	33.6376	1.38837	0.694187	+	0.719795i	$0.255764\pi$
$588$	2.67684	0.110391
$589$	2.45167	0.101019
$590$	22.9448	0.944622
$591$	17.0192	0.700078
$592$	10.5539	0.433762
$593$	−12.1101	−0.497302	−0.248651	−	0.968593i	$-0.579987\pi$
$593$	−12.1101	−0.497302	−0.248651	+	0.968593i	$0.579987\pi$
$594$	12.5510	0.514973
$595$	24.8477	1.01865
$596$	−46.3071	−1.89681
$597$	17.0640	0.698381
$598$	25.5349	1.04420
$599$	19.0055	0.776546	0.388273	−	0.921544i	$-0.373072\pi$
$599$	19.0055	0.776546	0.388273	+	0.921544i	$0.373072\pi$
$600$	−19.8858	−0.811833
$601$	−24.5377	−1.00091	−0.500456	−	0.865762i	$-0.666834\pi$
$601$	−24.5377	−1.00091	−0.500456	+	0.865762i	$0.666834\pi$
$602$	10.6608	0.434503
$603$	12.5899	0.512700
$604$	15.3358	0.624006
$605$	−97.7859	−3.97556
$606$	−33.5802	−1.36410
$607$	−23.0518	−0.935645	−0.467823	−	0.883822i	$-0.654961\pi$
$607$	−23.0518	−0.935645	−0.467823	+	0.883822i	$0.654961\pi$
$608$	5.49591	0.222889
$609$	−5.54972	−0.224886
$610$	61.9695	2.50907
$611$	−10.8367	−0.438406
$612$	−15.4284	−0.623655
$613$	−25.6782	−1.03713	−0.518565	−	0.855038i	$-0.673534\pi$
$613$	−25.6782	−1.03713	−0.518565	+	0.855038i	$0.673534\pi$
$614$	−57.1349	−2.30578
$615$	−30.9689	−1.24879
$616$	8.49503	0.342274
$617$	−41.9259	−1.68787	−0.843937	−	0.536443i	$-0.819768\pi$
$617$	−41.9259	−1.68787	−0.843937	+	0.536443i	$0.819768\pi$
$618$	−40.6328	−1.63449
$619$	12.6402	0.508054	0.254027	−	0.967197i	$-0.418245\pi$
$619$	12.6402	0.508054	0.254027	+	0.967197i	$0.418245\pi$
$620$	−39.4316	−1.58361
$621$	7.08037	0.284125
$622$	55.9202	2.24220
$623$	−6.15249	−0.246494
$624$	3.64913	0.146082
$625$	91.6405	3.66562
$626$	10.4023	0.415759
$627$	−4.16419	−0.166302
$628$	−31.3815	−1.25226
$629$	27.7986	1.10840
$630$	9.32319	0.371445
$631$	−16.5961	−0.660680	−0.330340	−	0.943862i	$-0.607163\pi$
$631$	−16.5961	−0.660680	−0.330340	+	0.943862i	$0.607163\pi$
$632$	3.46377	0.137782
$633$	−23.6075	−0.938314
$634$	2.01875	0.0801750
$635$	−31.6014	−1.25406
$636$	−7.29004	−0.289069
$637$	−1.66764	−0.0660743
$638$	−69.6543	−2.75764
$639$	11.4392	0.452527
$640$	−47.5918	−1.88123
$641$	11.1959	0.442212	0.221106	−	0.975250i	$-0.429033\pi$
$641$	11.1959	0.442212	0.221106	+	0.975250i	$0.429033\pi$
$642$	34.0376	1.34336
$643$	−16.3496	−0.644764	−0.322382	−	0.946610i	$-0.604484\pi$
$643$	−16.3496	−0.644764	−0.322382	+	0.946610i	$0.604484\pi$
$644$	18.9530	0.746854
$645$	21.2522	0.836803
$646$	8.94340	0.351873
$647$	−7.96479	−0.313128	−0.156564	−	0.987668i	$-0.550042\pi$
$647$	−7.96479	−0.313128	−0.156564	+	0.987668i	$0.550042\pi$
$648$	−1.46374	−0.0575011
$649$	−14.2830	−0.560658
$650$	48.9956	1.92177
$651$	3.41691	0.133919
$652$	−27.7999	−1.08873
$653$	−10.4990	−0.410857	−0.205429	−	0.978672i	$-0.565859\pi$
$653$	−10.4990	−0.410857	−0.205429	+	0.978672i	$0.565859\pi$
$654$	−32.1083	−1.25553
$655$	−0.686666	−0.0268303
$656$	−15.7190	−0.613723
$657$	2.29375	0.0894878
$658$	−14.0531	−0.547846
$659$	20.6626	0.804901	0.402451	−	0.915442i	$-0.368158\pi$
$659$	20.6626	0.804901	0.402451	+	0.915442i	$0.368158\pi$
$660$	66.9749	2.60699
$661$	−25.8021	−1.00358	−0.501792	−	0.864988i	$-0.667326\pi$
$661$	−25.8021	−1.00358	−0.501792	+	0.864988i	$0.667326\pi$
$662$	−15.5804	−0.605548
$663$	9.61168	0.373287
$664$	14.9072	0.578512
$665$	−3.09327	−0.119952
$666$	10.4304	0.404171
$667$	−39.2940	−1.52147
$668$	−14.5101	−0.561411
$669$	−3.84902	−0.148812
$670$	117.378	4.53470
$671$	−38.5757	−1.48920
$672$	7.65968	0.295479
$673$	16.0557	0.618902	0.309451	−	0.950915i	$-0.399855\pi$
$673$	16.0557	0.618902	0.309451	+	0.950915i	$0.399855\pi$
$674$	−25.4896	−0.981822
$675$	13.5856	0.522910
$676$	−27.3546	−1.05210
$677$	−16.5925	−0.637700	−0.318850	−	0.947805i	$-0.603297\pi$
$677$	−16.5925	−0.637700	−0.318850	+	0.947805i	$0.603297\pi$
$678$	19.3619	0.743591
$679$	−3.70053	−0.142013
$680$	−36.3705	−1.39474
$681$	28.8301	1.10477
$682$	42.8855	1.64217
$683$	36.1036	1.38146	0.690732	−	0.723110i	$-0.257288\pi$
$683$	36.1036	1.38146	0.690732	+	0.723110i	$0.257288\pi$
$684$	1.92067	0.0734385
$685$	−38.9695	−1.48895
$686$	−2.16260	−0.0825685
$687$	−13.9777	−0.533283
$688$	10.7870	0.411252
$689$	4.54161	0.173021
$690$	66.0116	2.51302
$691$	7.66709	0.291670	0.145835	−	0.989309i	$-0.453413\pi$
$691$	7.66709	0.291670	0.145835	+	0.989309i	$0.453413\pi$
$692$	38.4415	1.46133
$693$	−5.80365	−0.220462
$694$	−6.39852	−0.242885
$695$	88.9753	3.37503
$696$	8.12333	0.307914
$697$	−41.4033	−1.56826
$698$	−30.8273	−1.16683
$699$	26.2684	0.993563
$700$	36.3665	1.37452
$701$	13.0559	0.493113	0.246556	−	0.969128i	$-0.420701\pi$
$701$	13.0559	0.493113	0.246556	+	0.969128i	$0.420701\pi$
$702$	3.60644	0.136116
$703$	−3.46062	−0.130520
$704$	70.7374	2.66602
$705$	−28.0145	−1.05509
$706$	46.9901	1.76850
$707$	15.5277	0.583978
$708$	6.58783	0.247586
$709$	24.0242	0.902247	0.451123	−	0.892462i	$-0.351023\pi$
$709$	24.0242	0.902247	0.451123	+	0.892462i	$0.351023\pi$
$710$	106.650	4.00249
$711$	−2.36639	−0.0887465
$712$	9.00564	0.337501
$713$	24.1930	0.906034
$714$	12.4645	0.466471
$715$	−41.7245	−1.56041
$716$	46.4323	1.73526
$717$	3.43864	0.128418
$718$	44.0968	1.64568
$719$	5.08987	0.189820	0.0949101	−	0.995486i	$-0.469744\pi$
$719$	5.08987	0.189820	0.0949101	+	0.995486i	$0.469744\pi$
$720$	9.43356	0.351568
$721$	18.7888	0.699733
$722$	39.9761	1.48775
$723$	6.08853	0.226435
$724$	−65.6651	−2.44042
$725$	−75.3962	−2.80014
$726$	−49.0528	−1.82052
$727$	−23.4689	−0.870414	−0.435207	−	0.900330i	$-0.643325\pi$
$727$	−23.4689	−0.870414	−0.435207	+	0.900330i	$0.643325\pi$
$728$	2.44099	0.0904691
$729$	1.00000	0.0370370
$730$	21.3851	0.791498
$731$	28.4127	1.05088
$732$	17.7925	0.657628
$733$	40.8670	1.50946	0.754729	−	0.656037i	$-0.227769\pi$
$733$	40.8670	1.50946	0.754729	+	0.656037i	$0.227769\pi$
$734$	−47.7689	−1.76318
$735$	−4.31110	−0.159017
$736$	54.2334	1.99907
$737$	−73.0673	−2.69147
$738$	−15.5351	−0.571854
$739$	−0.886167	−0.0325982	−0.0162991	−	0.999867i	$-0.505188\pi$
$739$	−0.886167	−0.0325982	−0.0162991	+	0.999867i	$0.505188\pi$
$740$	55.6591	2.04607
$741$	−1.19655	−0.0439564
$742$	5.88957	0.216213
$743$	−47.1256	−1.72887	−0.864436	−	0.502744i	$-0.832324\pi$
$743$	−47.1256	−1.72887	−0.864436	+	0.502744i	$0.832324\pi$
$744$	−5.00146	−0.183362
$745$	74.5784	2.73234
$746$	25.2709	0.925235
$747$	−10.1843	−0.372626
$748$	89.5408	3.27394
$749$	−15.7392	−0.575098
$750$	80.0452	2.92284
$751$	−46.7834	−1.70715	−0.853575	−	0.520969i	$-0.825571\pi$
$751$	−46.7834	−1.70715	−0.853575	+	0.520969i	$0.825571\pi$
$752$	−14.2194	−0.518530
$753$	−26.4649	−0.964435
$754$	−20.0147	−0.728893
$755$	−24.6986	−0.898875
$756$	2.67684	0.0973558
$757$	−3.26228	−0.118570	−0.0592849	−	0.998241i	$-0.518882\pi$
$757$	−3.26228	−0.118570	−0.0592849	+	0.998241i	$0.518882\pi$
$758$	29.0577	1.05542
$759$	−41.0920	−1.49154
$760$	4.52773	0.164238
$761$	25.1148	0.910412	0.455206	−	0.890386i	$-0.349566\pi$
$761$	25.1148	0.910412	0.455206	+	0.890386i	$0.349566\pi$
$762$	−15.8524	−0.574271
$763$	14.8471	0.537500
$764$	−53.6702	−1.94172
$765$	24.8477	0.898369
$766$	2.16260	0.0781379
$767$	−4.10414	−0.148192
$768$	0.503162	0.0181563
$769$	−6.97292	−0.251450	−0.125725	−	0.992065i	$-0.540126\pi$
$769$	−6.97292	−0.251450	−0.125725	+	0.992065i	$0.540126\pi$
$770$	−54.1085	−1.94994
$771$	4.00631	0.144284
$772$	−26.5933	−0.957114
$773$	−9.19112	−0.330581	−0.165291	−	0.986245i	$-0.552856\pi$
$773$	−9.19112	−0.330581	−0.165291	+	0.986245i	$0.552856\pi$
$774$	10.6608	0.383196
$775$	46.4207	1.66748
$776$	5.41662	0.194445
$777$	−4.82309	−0.173027
$778$	16.2178	0.581435
$779$	5.15426	0.184671
$780$	19.2448	0.689074
$781$	−66.3889	−2.37558
$782$	88.2530	3.15592
$783$	−5.54972	−0.198331
$784$	−2.18820	−0.0781500
$785$	50.5405	1.80387
$786$	−0.344456	−0.0122863
$787$	−51.3295	−1.82970	−0.914850	−	0.403794i	$-0.867691\pi$
$787$	−51.3295	−1.82970	−0.914850	+	0.403794i	$0.867691\pi$
$788$	45.5578	1.62293
$789$	−15.3756	−0.547386
$790$	−22.0623	−0.784941
$791$	−8.95308	−0.318335
$792$	8.49503	0.301858
$793$	−11.0845	−0.393621
$794$	42.1754	1.49675
$795$	11.7407	0.416401
$796$	45.6775	1.61900
$797$	−46.7538	−1.65610	−0.828052	−	0.560651i	$-0.810551\pi$
$797$	−46.7538	−1.65610	−0.828052	+	0.560651i	$0.810551\pi$
$798$	−1.55169	−0.0549293
$799$	−37.4535	−1.32501
$800$	104.061	3.67913
$801$	−6.15249	−0.217388
$802$	−40.3980	−1.42650
$803$	−13.3121	−0.469775
$804$	33.7011	1.18855
$805$	−30.5242	−1.07584
$806$	12.3229	0.434055
$807$	−7.21997	−0.254155
$808$	−22.7285	−0.799585
$809$	−43.6363	−1.53417	−0.767085	−	0.641545i	$-0.778294\pi$
$809$	−43.6363	−1.53417	−0.767085	+	0.641545i	$0.778294\pi$
$810$	9.32319	0.327584
$811$	20.9131	0.734358	0.367179	−	0.930150i	$-0.380324\pi$
$811$	20.9131	0.734358	0.367179	+	0.930150i	$0.380324\pi$
$812$	−14.8557	−0.521333
$813$	−26.8021	−0.939990
$814$	−60.5345	−2.12173
$815$	44.7723	1.56830
$816$	12.6120	0.441509
$817$	−3.53707	−0.123746
$818$	60.1506	2.10312
$819$	−1.66764	−0.0582720
$820$	−82.8988	−2.89495
$821$	16.9627	0.592002	0.296001	−	0.955188i	$-0.404347\pi$
$821$	16.9627	0.592002	0.296001	+	0.955188i	$0.404347\pi$
$822$	−19.5485	−0.681831
$823$	10.2511	0.357332	0.178666	−	0.983910i	$-0.442822\pi$
$823$	10.2511	0.357332	0.178666	+	0.983910i	$0.442822\pi$
$824$	−27.5020	−0.958076
$825$	−78.8460	−2.74507
$826$	−5.32226	−0.185185
$827$	−10.1735	−0.353768	−0.176884	−	0.984232i	$-0.556602\pi$
$827$	−10.1735	−0.353768	−0.176884	+	0.984232i	$0.556602\pi$
$828$	18.9530	0.658663
$829$	−9.53924	−0.331311	−0.165656	−	0.986184i	$-0.552974\pi$
$829$	−9.53924	−0.331311	−0.165656	+	0.986184i	$0.552974\pi$
$830$	−94.9506	−3.29578
$831$	−0.0290973	−0.00100937
$832$	20.3259	0.704674
$833$	−5.76364	−0.199698
$834$	44.6332	1.54552
$835$	23.3687	0.808707
$836$	−11.1469	−0.385522
$837$	3.41691	0.118106
$838$	6.25786	0.216174
$839$	22.9060	0.790802	0.395401	−	0.918508i	$-0.370606\pi$
$839$	22.9060	0.790802	0.395401	+	0.918508i	$0.370606\pi$
$840$	6.31033	0.217727
$841$	1.79934	0.0620463
$842$	34.3565	1.18400
$843$	27.6549	0.952485
$844$	−63.1936	−2.17521
$845$	44.0551	1.51554
$846$	−14.0531	−0.483155
$847$	22.6823	0.779374
$848$	5.95929	0.204643
$849$	28.3107	0.971620
$850$	169.337	5.80822
$851$	−34.1493	−1.17062
$852$	30.6209	1.04905
$853$	−14.5232	−0.497263	−0.248632	−	0.968598i	$-0.579981\pi$
$853$	−14.5232	−0.497263	−0.248632	+	0.968598i	$0.579981\pi$
$854$	−14.3744	−0.491881
$855$	−3.09327	−0.105787
$856$	23.0381	0.787425
$857$	−12.5833	−0.429839	−0.214920	−	0.976632i	$-0.568949\pi$
$857$	−12.5833	−0.429839	−0.214920	+	0.976632i	$0.568949\pi$
$858$	−20.9305	−0.714556
$859$	−24.1287	−0.823261	−0.411631	−	0.911351i	$-0.635041\pi$
$859$	−24.1287	−0.823261	−0.411631	+	0.911351i	$0.635041\pi$
$860$	56.8887	1.93989
$861$	7.18352	0.244814
$862$	54.1077	1.84292
$863$	−44.6253	−1.51906	−0.759531	−	0.650471i	$-0.774571\pi$
$863$	−44.6253	−1.51906	−0.759531	+	0.650471i	$0.774571\pi$
$864$	7.65968	0.260588
$865$	−61.9107	−2.10503
$866$	21.7738	0.739905
$867$	16.2196	0.550846
$868$	9.14652	0.310453
$869$	13.7337	0.465883
$870$	−51.7411	−1.75419
$871$	−20.9954	−0.711402
$872$	−21.7322	−0.735946
$873$	−3.70053	−0.125244
$874$	−10.9865	−0.371626
$875$	−37.0134	−1.25128
$876$	6.14001	0.207452
$877$	−30.6802	−1.03600	−0.517999	−	0.855381i	$-0.673323\pi$
$877$	−30.6802	−1.03600	−0.517999	+	0.855381i	$0.673323\pi$
$878$	−84.1007	−2.83826
$879$	30.2413	1.02001
$880$	−54.7491	−1.84559
$881$	3.43806	0.115831	0.0579157	−	0.998321i	$-0.481555\pi$
$881$	3.43806	0.115831	0.0579157	+	0.998321i	$0.481555\pi$
$882$	−2.16260	−0.0728186
$883$	−56.4741	−1.90051	−0.950253	−	0.311480i	$-0.899175\pi$
$883$	−56.4741	−1.90051	−0.950253	+	0.311480i	$0.899175\pi$
$884$	25.7290	0.865358
$885$	−10.6098	−0.356645
$886$	36.6352	1.23078
$887$	15.9282	0.534815	0.267408	−	0.963583i	$-0.413833\pi$
$887$	15.9282	0.534815	0.267408	+	0.963583i	$0.413833\pi$
$888$	7.05975	0.236910
$889$	7.33023	0.245848
$890$	−57.3608	−1.92274
$891$	−5.80365	−0.194430
$892$	−10.3032	−0.344977
$893$	4.66256	0.156027
$894$	37.4112	1.25122
$895$	−74.7801	−2.49962
$896$	11.0393	0.368799
$897$	−11.8075	−0.394241
$898$	9.10545	0.303853
$899$	−18.9629	−0.632447
$900$	36.3665	1.21222
$901$	15.6966	0.522928
$902$	90.1602	3.00201
$903$	−4.92963	−0.164048
$904$	13.1050	0.435865
$905$	105.755	3.51541
$906$	−12.3897	−0.411620
$907$	−9.18731	−0.305060	−0.152530	−	0.988299i	$-0.548742\pi$
$907$	−9.18731	−0.305060	−0.152530	+	0.988299i	$0.548742\pi$
$908$	77.1736	2.56110
$909$	15.5277	0.515021
$910$	−15.5477	−0.515402
$911$	−34.7042	−1.14980	−0.574901	−	0.818223i	$-0.694959\pi$
$911$	−34.7042	−1.14980	−0.574901	+	0.818223i	$0.694959\pi$
$912$	−1.57006	−0.0519899
$913$	59.1064	1.95614
$914$	−49.5160	−1.63784
$915$	−28.6551	−0.947307
$916$	−37.4162	−1.23626
$917$	0.159279	0.00525984
$918$	12.4645	0.411388
$919$	−25.8551	−0.852882	−0.426441	−	0.904515i	$-0.640233\pi$
$919$	−25.8551	−0.852882	−0.426441	+	0.904515i	$0.640233\pi$
$920$	44.6794	1.47304
$921$	26.4195	0.870553
$922$	15.1288	0.498242
$923$	−19.0764	−0.627908
$924$	−15.5355	−0.511079
$925$	−65.5246	−2.15443
$926$	61.1242	2.00866
$927$	18.7888	0.617106
$928$	−42.5091	−1.39543
$929$	41.9695	1.37697	0.688487	−	0.725248i	$-0.258275\pi$
$929$	41.9695	1.37697	0.688487	+	0.725248i	$0.258275\pi$
$930$	31.8565	1.04462
$931$	0.717512	0.0235155
$932$	70.3164	2.30329
$933$	−25.8578	−0.846548
$934$	42.2947	1.38392
$935$	−144.207	−4.71608
$936$	2.44099	0.0797862
$937$	9.95329	0.325160	0.162580	−	0.986695i	$-0.448018\pi$
$937$	9.95329	0.325160	0.162580	+	0.986695i	$0.448018\pi$
$938$	−27.2269	−0.888989
$939$	−4.81008	−0.156971
$940$	−74.9905	−2.44592
$941$	0.569521	0.0185659	0.00928293	−	0.999957i	$-0.497045\pi$
$941$	0.569521	0.0185659	0.00928293	+	0.999957i	$0.497045\pi$
$942$	25.3529	0.826042
$943$	50.8620	1.65629
$944$	−5.38526	−0.175275
$945$	−4.31110	−0.140240
$946$	−61.8717	−2.01162
$947$	−31.5213	−1.02430	−0.512152	−	0.858895i	$-0.671151\pi$
$947$	−31.5213	−1.02430	−0.512152	+	0.858895i	$0.671151\pi$
$948$	−6.33445	−0.205733
$949$	−3.82515	−0.124170
$950$	−21.0807	−0.683947
$951$	−0.933485	−0.0302703
$952$	8.43647	0.273428
$953$	16.8943	0.547259	0.273630	−	0.961835i	$-0.411776\pi$
$953$	16.8943	0.547259	0.273630	+	0.961835i	$0.411776\pi$
$954$	5.88957	0.190682
$955$	86.4369	2.79703
$956$	9.20468	0.297701
$957$	32.2086	1.04116
$958$	−81.4465	−2.63142
$959$	9.03933	0.291895
$960$	52.5456	1.69590
$961$	−19.3247	−0.623379
$962$	−17.3942	−0.560811
$963$	−15.7392	−0.507188
$964$	16.2980	0.524924
$965$	42.8290	1.37871
$966$	−15.3120	−0.492656
$967$	−35.8169	−1.15179	−0.575896	−	0.817523i	$-0.695347\pi$
$967$	−35.8169	−1.15179	−0.575896	+	0.817523i	$0.695347\pi$
$968$	−33.2010	−1.06712
$969$	−4.13548	−0.132851
$970$	−34.5008	−1.10775
$971$	2.06847	0.0663803	0.0331901	−	0.999449i	$-0.489433\pi$
$971$	2.06847	0.0663803	0.0331901	+	0.999449i	$0.489433\pi$
$972$	2.67684	0.0858597
$973$	−20.6387	−0.661645
$974$	28.8188	0.923413
$975$	−22.6559	−0.725569
$976$	−14.5446	−0.465560
$977$	−41.5468	−1.32920	−0.664600	−	0.747199i	$-0.731398\pi$
$977$	−41.5468	−1.32920	−0.664600	+	0.747199i	$0.731398\pi$
$978$	22.4594	0.718171
$979$	35.7069	1.14120
$980$	−11.5401	−0.368636
$981$	14.8471	0.474031
$982$	−9.44103	−0.301276
$983$	−58.5883	−1.86868	−0.934338	−	0.356389i	$-0.884008\pi$
$983$	−58.5883	−1.86868	−0.934338	+	0.356389i	$0.884008\pi$
$984$	−10.5148	−0.335200
$985$	−73.3717	−2.33782
$986$	−69.1742	−2.20296
$987$	6.49823	0.206841
$988$	−3.20298	−0.101900
$989$	−34.9036	−1.10987
$990$	−54.1085	−1.71968
$991$	−36.5699	−1.16168	−0.580841	−	0.814017i	$-0.697276\pi$
$991$	−36.5699	−1.16168	−0.580841	+	0.814017i	$0.697276\pi$
$992$	26.1724	0.830975
$993$	7.20446	0.228627
$994$	−24.7384	−0.784653
$995$	−73.5644	−2.33215
$996$	−27.2619	−0.863826
$997$	8.93170	0.282870	0.141435	−	0.989948i	$-0.454828\pi$
$997$	8.93170	0.282870	0.141435	+	0.989948i	$0.454828\pi$
$998$	−90.4291	−2.86248
$999$	−4.82309	−0.152596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.n.1.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.n.1.6	✓	40	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)

\(f(q)\)	\(=\)	\(q-2.16260 q^{2} +1.00000 q^{3} +2.67684 q^{4} -4.31110 q^{5} -2.16260 q^{6} +1.00000 q^{7} -1.46374 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16260 q^{2} +1.00000 q^{3} +2.67684 q^{4} -4.31110 q^{5} -2.16260 q^{6} +1.00000 q^{7} -1.46374 q^{8} +1.00000 q^{9} +9.32319 q^{10} -5.80365 q^{11} +2.67684 q^{12} -1.66764 q^{13} -2.16260 q^{14} -4.31110 q^{15} -2.18820 q^{16} -5.76364 q^{17} -2.16260 q^{18} +0.717512 q^{19} -11.5401 q^{20} +1.00000 q^{21} +12.5510 q^{22} +7.08037 q^{23} -1.46374 q^{24} +13.5856 q^{25} +3.60644 q^{26} +1.00000 q^{27} +2.67684 q^{28} -5.54972 q^{29} +9.32319 q^{30} +3.41691 q^{31} +7.65968 q^{32} -5.80365 q^{33} +12.4645 q^{34} -4.31110 q^{35} +2.67684 q^{36} -4.82309 q^{37} -1.55169 q^{38} -1.66764 q^{39} +6.31033 q^{40} +7.18352 q^{41} -2.16260 q^{42} -4.92963 q^{43} -15.5355 q^{44} -4.31110 q^{45} -15.3120 q^{46} +6.49823 q^{47} -2.18820 q^{48} +1.00000 q^{49} -29.3802 q^{50} -5.76364 q^{51} -4.46401 q^{52} -2.72337 q^{53} -2.16260 q^{54} +25.0201 q^{55} -1.46374 q^{56} +0.717512 q^{57} +12.0018 q^{58} +2.46104 q^{59} -11.5401 q^{60} +6.64681 q^{61} -7.38941 q^{62} +1.00000 q^{63} -12.1884 q^{64} +7.18936 q^{65} +12.5510 q^{66} +12.5899 q^{67} -15.4284 q^{68} +7.08037 q^{69} +9.32319 q^{70} +11.4392 q^{71} -1.46374 q^{72} +2.29375 q^{73} +10.4304 q^{74} +13.5856 q^{75} +1.92067 q^{76} -5.80365 q^{77} +3.60644 q^{78} -2.36639 q^{79} +9.43356 q^{80} +1.00000 q^{81} -15.5351 q^{82} -10.1843 q^{83} +2.67684 q^{84} +24.8477 q^{85} +10.6608 q^{86} -5.54972 q^{87} +8.49503 q^{88} -6.15249 q^{89} +9.32319 q^{90} -1.66764 q^{91} +18.9530 q^{92} +3.41691 q^{93} -14.0531 q^{94} -3.09327 q^{95} +7.65968 q^{96} -3.70053 q^{97} -2.16260 q^{98} -5.80365 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * q^99

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