LMFDB - Embedded newform 8043.2.a.q.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:	$1$
Dimension:	$44$
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)

$f(q)$	$=$	$q-2.03170 q^{2} +1.00000 q^{3} +2.12780 q^{4} -1.52866 q^{5} -2.03170 q^{6} -1.00000 q^{7} -0.259645 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.03170 q^{2} +1.00000 q^{3} +2.12780 q^{4} -1.52866 q^{5} -2.03170 q^{6} -1.00000 q^{7} -0.259645 q^{8} +1.00000 q^{9} +3.10578 q^{10} -4.21000 q^{11} +2.12780 q^{12} +5.16978 q^{13} +2.03170 q^{14} -1.52866 q^{15} -3.72807 q^{16} -3.56003 q^{17} -2.03170 q^{18} -0.432907 q^{19} -3.25268 q^{20} -1.00000 q^{21} +8.55345 q^{22} -0.283065 q^{23} -0.259645 q^{24} -2.66319 q^{25} -10.5034 q^{26} +1.00000 q^{27} -2.12780 q^{28} -0.577908 q^{29} +3.10578 q^{30} +2.46822 q^{31} +8.09361 q^{32} -4.21000 q^{33} +7.23291 q^{34} +1.52866 q^{35} +2.12780 q^{36} +2.97652 q^{37} +0.879537 q^{38} +5.16978 q^{39} +0.396909 q^{40} +5.92982 q^{41} +2.03170 q^{42} +7.13326 q^{43} -8.95802 q^{44} -1.52866 q^{45} +0.575103 q^{46} -8.16293 q^{47} -3.72807 q^{48} +1.00000 q^{49} +5.41079 q^{50} -3.56003 q^{51} +11.0002 q^{52} -2.47811 q^{53} -2.03170 q^{54} +6.43567 q^{55} +0.259645 q^{56} -0.432907 q^{57} +1.17414 q^{58} +8.92991 q^{59} -3.25268 q^{60} +10.0377 q^{61} -5.01468 q^{62} -1.00000 q^{63} -8.98762 q^{64} -7.90285 q^{65} +8.55345 q^{66} +7.80754 q^{67} -7.57502 q^{68} -0.283065 q^{69} -3.10578 q^{70} -5.46582 q^{71} -0.259645 q^{72} +2.46548 q^{73} -6.04739 q^{74} -2.66319 q^{75} -0.921139 q^{76} +4.21000 q^{77} -10.5034 q^{78} -13.5291 q^{79} +5.69897 q^{80} +1.00000 q^{81} -12.0476 q^{82} +8.59324 q^{83} -2.12780 q^{84} +5.44209 q^{85} -14.4926 q^{86} -0.577908 q^{87} +1.09310 q^{88} -10.4943 q^{89} +3.10578 q^{90} -5.16978 q^{91} -0.602306 q^{92} +2.46822 q^{93} +16.5846 q^{94} +0.661770 q^{95} +8.09361 q^{96} -16.4026 q^{97} -2.03170 q^{98} -4.21000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.03170	−1.43663	−0.718314	−	0.695719i	$-0.755086\pi$
$2$	−2.03170	−1.43663	−0.718314	+	0.695719i	$0.755086\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.12780	1.06390
$5$	−1.52866	−0.683639	−0.341820	−	0.939766i	$-0.611043\pi$
$5$	−1.52866	−0.683639	−0.341820	+	0.939766i	$0.611043\pi$
$6$	−2.03170	−0.829437
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.259645	−0.0917982
$9$	1.00000	0.333333
$10$	3.10578	0.982135
$11$	−4.21000	−1.26936	−0.634681	−	0.772774i	$-0.718869\pi$
$11$	−4.21000	−1.26936	−0.634681	+	0.772774i	$0.718869\pi$
$12$	2.12780	0.614242
$13$	5.16978	1.43384	0.716919	−	0.697156i	$-0.245552\pi$
$13$	5.16978	1.43384	0.716919	+	0.697156i	$0.245552\pi$
$14$	2.03170	0.542994
$15$	−1.52866	−0.394699
$16$	−3.72807	−0.932019
$17$	−3.56003	−0.863434	−0.431717	−	0.902009i	$-0.642092\pi$
$17$	−3.56003	−0.863434	−0.431717	+	0.902009i	$0.642092\pi$
$18$	−2.03170	−0.478876
$19$	−0.432907	−0.0993158	−0.0496579	−	0.998766i	$-0.515813\pi$
$19$	−0.432907	−0.0993158	−0.0496579	+	0.998766i	$0.515813\pi$
$20$	−3.25268	−0.727322
$21$	−1.00000	−0.218218
$22$	8.55345	1.82360
$23$	−0.283065	−0.0590232	−0.0295116	−	0.999564i	$-0.509395\pi$
$23$	−0.283065	−0.0590232	−0.0295116	+	0.999564i	$0.509395\pi$
$24$	−0.259645	−0.0529997
$25$	−2.66319	−0.532638
$26$	−10.5034	−2.05989
$27$	1.00000	0.192450
$28$	−2.12780	−0.402116
$29$	−0.577908	−0.107315	−0.0536574	−	0.998559i	$-0.517088\pi$
$29$	−0.577908	−0.107315	−0.0536574	+	0.998559i	$0.517088\pi$
$30$	3.10578	0.567036
$31$	2.46822	0.443306	0.221653	−	0.975126i	$-0.428855\pi$
$31$	2.46822	0.443306	0.221653	+	0.975126i	$0.428855\pi$
$32$	8.09361	1.43076
$33$	−4.21000	−0.732867
$34$	7.23291	1.24043
$35$	1.52866	0.258391
$36$	2.12780	0.354633
$37$	2.97652	0.489337	0.244668	−	0.969607i	$-0.421321\pi$
$37$	2.97652	0.489337	0.244668	+	0.969607i	$0.421321\pi$
$38$	0.879537	0.142680
$39$	5.16978	0.827827
$40$	0.396909	0.0627568
$41$	5.92982	0.926082	0.463041	−	0.886337i	$-0.346758\pi$
$41$	5.92982	0.926082	0.463041	+	0.886337i	$0.346758\pi$
$42$	2.03170	0.313498
$43$	7.13326	1.08781	0.543906	−	0.839146i	$-0.316945\pi$
$43$	7.13326	1.08781	0.543906	+	0.839146i	$0.316945\pi$
$44$	−8.95802	−1.35047
$45$	−1.52866	−0.227880
$46$	0.575103	0.0847944
$47$	−8.16293	−1.19069	−0.595343	−	0.803472i	$-0.702984\pi$
$47$	−8.16293	−1.19069	−0.595343	+	0.803472i	$0.702984\pi$
$48$	−3.72807	−0.538101
$49$	1.00000	0.142857
$50$	5.41079	0.765202
$51$	−3.56003	−0.498504
$52$	11.0002	1.52546
$53$	−2.47811	−0.340395	−0.170198	−	0.985410i	$-0.554441\pi$
$53$	−2.47811	−0.340395	−0.170198	+	0.985410i	$0.554441\pi$
$54$	−2.03170	−0.276479
$55$	6.43567	0.867786
$56$	0.259645	0.0346965
$57$	−0.432907	−0.0573400
$58$	1.17414	0.154171
$59$	8.92991	1.16258	0.581288	−	0.813698i	$-0.302549\pi$
$59$	8.92991	1.16258	0.581288	+	0.813698i	$0.302549\pi$
$60$	−3.25268	−0.419920
$61$	10.0377	1.28519	0.642597	−	0.766204i	$-0.277857\pi$
$61$	10.0377	1.28519	0.642597	+	0.766204i	$0.277857\pi$
$62$	−5.01468	−0.636865
$63$	−1.00000	−0.125988
$64$	−8.98762	−1.12345
$65$	−7.90285	−0.980228
$66$	8.55345	1.05286
$67$	7.80754	0.953843	0.476921	−	0.878946i	$-0.341753\pi$
$67$	7.80754	0.953843	0.476921	+	0.878946i	$0.341753\pi$
$68$	−7.57502	−0.918606
$69$	−0.283065	−0.0340771
$70$	−3.10578	−0.371212
$71$	−5.46582	−0.648673	−0.324337	−	0.945942i	$-0.605141\pi$
$71$	−5.46582	−0.648673	−0.324337	+	0.945942i	$0.605141\pi$
$72$	−0.259645	−0.0305994
$73$	2.46548	0.288563	0.144281	−	0.989537i	$-0.453913\pi$
$73$	2.46548	0.288563	0.144281	+	0.989537i	$0.453913\pi$
$74$	−6.04739	−0.702994
$75$	−2.66319	−0.307519
$76$	−0.921139	−0.105662
$77$	4.21000	0.479774
$78$	−10.5034	−1.18928
$79$	−13.5291	−1.52214	−0.761072	−	0.648668i	$-0.775327\pi$
$79$	−13.5291	−1.52214	−0.761072	+	0.648668i	$0.775327\pi$
$80$	5.69897	0.637164
$81$	1.00000	0.111111
$82$	−12.0476	−1.33043
$83$	8.59324	0.943231	0.471615	−	0.881804i	$-0.343671\pi$
$83$	8.59324	0.943231	0.471615	+	0.881804i	$0.343671\pi$
$84$	−2.12780	−0.232162
$85$	5.44209	0.590277
$86$	−14.4926	−1.56278
$87$	−0.577908	−0.0619583
$88$	1.09310	0.116525
$89$	−10.4943	−1.11239	−0.556196	−	0.831051i	$-0.687740\pi$
$89$	−10.4943	−1.11239	−0.556196	+	0.831051i	$0.687740\pi$
$90$	3.10578	0.327378
$91$	−5.16978	−0.541940
$92$	−0.602306	−0.0627947
$93$	2.46822	0.255943
$94$	16.5846	1.71057
$95$	0.661770	0.0678961
$96$	8.09361	0.826051
$97$	−16.4026	−1.66543	−0.832714	−	0.553704i	$-0.813214\pi$
$97$	−16.4026	−1.66543	−0.832714	+	0.553704i	$0.813214\pi$
$98$	−2.03170	−0.205232
$99$	−4.21000	−0.423121
$100$	−5.66672	−0.566672
$101$	−3.74382	−0.372524	−0.186262	−	0.982500i	$-0.559637\pi$
$101$	−3.74382	−0.372524	−0.186262	+	0.982500i	$0.559637\pi$
$102$	7.23291	0.716164
$103$	12.3021	1.21216	0.606080	−	0.795404i	$-0.292741\pi$
$103$	12.3021	1.21216	0.606080	+	0.795404i	$0.292741\pi$
$104$	−1.34231	−0.131624
$105$	1.52866	0.149182
$106$	5.03478	0.489021
$107$	0.772867	0.0747159	0.0373579	−	0.999302i	$-0.488106\pi$
$107$	0.772867	0.0747159	0.0373579	+	0.999302i	$0.488106\pi$
$108$	2.12780	0.204747
$109$	−12.2436	−1.17272	−0.586360	−	0.810050i	$-0.699440\pi$
$109$	−12.2436	−1.17272	−0.586360	+	0.810050i	$0.699440\pi$
$110$	−13.0753	−1.24668
$111$	2.97652	0.282519
$112$	3.72807	0.352270
$113$	0.754989	0.0710234	0.0355117	−	0.999369i	$-0.488694\pi$
$113$	0.754989	0.0710234	0.0355117	+	0.999369i	$0.488694\pi$
$114$	0.879537	0.0823762
$115$	0.432712	0.0403506
$116$	−1.22967	−0.114172
$117$	5.16978	0.477946
$118$	−18.1429	−1.67019
$119$	3.56003	0.326347
$120$	0.396909	0.0362327
$121$	6.72410	0.611282
$122$	−20.3935	−1.84635
$123$	5.92982	0.534674
$124$	5.25188	0.471632
$125$	11.7144	1.04777
$126$	2.03170	0.180998
$127$	1.85998	0.165047	0.0825234	−	0.996589i	$-0.473702\pi$
$127$	1.85998	0.165047	0.0825234	+	0.996589i	$0.473702\pi$
$128$	2.07292	0.183222
$129$	7.13326	0.628049
$130$	16.0562	1.40822
$131$	−9.56274	−0.835500	−0.417750	−	0.908562i	$-0.637181\pi$
$131$	−9.56274	−0.835500	−0.417750	+	0.908562i	$0.637181\pi$
$132$	−8.95802	−0.779696
$133$	0.432907	0.0375378
$134$	−15.8626	−1.37032
$135$	−1.52866	−0.131566
$136$	0.924343	0.0792617
$137$	−5.86961	−0.501475	−0.250737	−	0.968055i	$-0.580673\pi$
$137$	−5.86961	−0.501475	−0.250737	+	0.968055i	$0.580673\pi$
$138$	0.575103	0.0489560
$139$	−3.28599	−0.278714	−0.139357	−	0.990242i	$-0.544504\pi$
$139$	−3.28599	−0.278714	−0.139357	+	0.990242i	$0.544504\pi$
$140$	3.25268	0.274902
$141$	−8.16293	−0.687443
$142$	11.1049	0.931902
$143$	−21.7648	−1.82006
$144$	−3.72807	−0.310673
$145$	0.883427	0.0733646
$146$	−5.00911	−0.414557
$147$	1.00000	0.0824786
$148$	6.33342	0.520604
$149$	15.6897	1.28535	0.642674	−	0.766140i	$-0.277825\pi$
$149$	15.6897	1.28535	0.642674	+	0.766140i	$0.277825\pi$
$150$	5.41079	0.441790
$151$	−15.1397	−1.23205	−0.616026	−	0.787726i	$-0.711259\pi$
$151$	−15.1397	−1.23205	−0.616026	+	0.787726i	$0.711259\pi$
$152$	0.112402	0.00911701
$153$	−3.56003	−0.287811
$154$	−8.55345	−0.689257
$155$	−3.77308	−0.303061
$156$	11.0002	0.880724
$157$	5.20660	0.415532	0.207766	−	0.978179i	$-0.433381\pi$
$157$	5.20660	0.415532	0.207766	+	0.978179i	$0.433381\pi$
$158$	27.4871	2.18675
$159$	−2.47811	−0.196527
$160$	−12.3724	−0.978124
$161$	0.283065	0.0223087
$162$	−2.03170	−0.159625
$163$	20.3027	1.59023	0.795114	−	0.606461i	$-0.207411\pi$
$163$	20.3027	1.59023	0.795114	+	0.606461i	$0.207411\pi$
$164$	12.6174	0.985257
$165$	6.43567	0.501016
$166$	−17.4589	−1.35507
$167$	−4.98351	−0.385636	−0.192818	−	0.981235i	$-0.561763\pi$
$167$	−4.98351	−0.385636	−0.192818	+	0.981235i	$0.561763\pi$
$168$	0.259645	0.0200320
$169$	13.7266	1.05589
$170$	−11.0567	−0.848009
$171$	−0.432907	−0.0331053
$172$	15.1781	1.15732
$173$	−3.77348	−0.286892	−0.143446	−	0.989658i	$-0.545818\pi$
$173$	−3.77348	−0.286892	−0.143446	+	0.989658i	$0.545818\pi$
$174$	1.17414	0.0890110
$175$	2.66319	0.201318
$176$	15.6952	1.18307
$177$	8.92991	0.671213
$178$	21.3212	1.59809
$179$	7.23839	0.541023	0.270511	−	0.962717i	$-0.412807\pi$
$179$	7.23839	0.541023	0.270511	+	0.962717i	$0.412807\pi$
$180$	−3.25268	−0.242441
$181$	13.2249	0.983001	0.491500	−	0.870877i	$-0.336449\pi$
$181$	13.2249	0.983001	0.491500	+	0.870877i	$0.336449\pi$
$182$	10.5034	0.778566
$183$	10.0377	0.742007
$184$	0.0734964	0.00541822
$185$	−4.55009	−0.334530
$186$	−5.01468	−0.367694
$187$	14.9877	1.09601
$188$	−17.3691	−1.26677
$189$	−1.00000	−0.0727393
$190$	−1.34452	−0.0975415
$191$	−5.21342	−0.377230	−0.188615	−	0.982051i	$-0.560400\pi$
$191$	−5.21342	−0.377230	−0.188615	+	0.982051i	$0.560400\pi$
$192$	−8.98762	−0.648626
$193$	2.49960	0.179925	0.0899626	−	0.995945i	$-0.471325\pi$
$193$	2.49960	0.179925	0.0899626	+	0.995945i	$0.471325\pi$
$194$	33.3250	2.39260
$195$	−7.90285	−0.565935
$196$	2.12780	0.151985
$197$	−0.0135469	−0.000965177 0	−0.000482589	−	1.00000i	$-0.500154\pi$
$197$	−0.0135469	−0.000965177 0	−0.000482589		1.00000i	$0.500154\pi$
$198$	8.55345	0.607867
$199$	−19.3662	−1.37284	−0.686418	−	0.727207i	$-0.740818\pi$
$199$	−19.3662	−1.37284	−0.686418	+	0.727207i	$0.740818\pi$
$200$	0.691482	0.0488952
$201$	7.80754	0.550701
$202$	7.60631	0.535178
$203$	0.577908	0.0405612
$204$	−7.57502	−0.530358
$205$	−9.06469	−0.633106
$206$	−24.9941	−1.74142
$207$	−0.283065	−0.0196744
$208$	−19.2733	−1.33636
$209$	1.82254	0.126068
$210$	−3.10578	−0.214319
$211$	−17.7389	−1.22120	−0.610599	−	0.791940i	$-0.709071\pi$
$211$	−17.7389	−1.22120	−0.610599	+	0.791940i	$0.709071\pi$
$212$	−5.27292	−0.362146
$213$	−5.46582	−0.374512
$214$	−1.57023	−0.107339
$215$	−10.9044	−0.743671
$216$	−0.259645	−0.0176666
$217$	−2.46822	−0.167554
$218$	24.8752	1.68476
$219$	2.46548	0.166602
$220$	13.6938	0.923236
$221$	−18.4046	−1.23803
$222$	−6.04739	−0.405874
$223$	26.3967	1.76765	0.883827	−	0.467814i	$-0.154958\pi$
$223$	26.3967	1.76765	0.883827	+	0.467814i	$0.154958\pi$
$224$	−8.09361	−0.540777
$225$	−2.66319	−0.177546
$226$	−1.53391	−0.102034
$227$	−18.4142	−1.22219	−0.611095	−	0.791557i	$-0.709271\pi$
$227$	−18.4142	−1.22219	−0.611095	+	0.791557i	$0.709271\pi$
$228$	−0.921139	−0.0610039
$229$	7.90445	0.522341	0.261170	−	0.965293i	$-0.415892\pi$
$229$	7.90445	0.522341	0.261170	+	0.965293i	$0.415892\pi$
$230$	−0.879139	−0.0579687
$231$	4.21000	0.276998
$232$	0.150051	0.00985131
$233$	1.48413	0.0972288	0.0486144	−	0.998818i	$-0.484519\pi$
$233$	1.48413	0.0972288	0.0486144	+	0.998818i	$0.484519\pi$
$234$	−10.5034	−0.686631
$235$	12.4784	0.813999
$236$	19.0010	1.23686
$237$	−13.5291	−0.878810
$238$	−7.23291	−0.468840
$239$	−8.72581	−0.564426	−0.282213	−	0.959352i	$-0.591068\pi$
$239$	−8.72581	−0.564426	−0.282213	+	0.959352i	$0.591068\pi$
$240$	5.69897	0.367867
$241$	3.08007	0.198405	0.0992023	−	0.995067i	$-0.468371\pi$
$241$	3.08007	0.198405	0.0992023	+	0.995067i	$0.468371\pi$
$242$	−13.6613	−0.878184
$243$	1.00000	0.0641500
$244$	21.3582	1.36732
$245$	−1.52866	−0.0976627
$246$	−12.0476	−0.768127
$247$	−2.23804	−0.142403
$248$	−0.640860	−0.0406947
$249$	8.59324	0.544575
$250$	−23.8002	−1.50526
$251$	10.7794	0.680391	0.340196	−	0.940355i	$-0.389507\pi$
$251$	10.7794	0.680391	0.340196	+	0.940355i	$0.389507\pi$
$252$	−2.12780	−0.134039
$253$	1.19171	0.0749219
$254$	−3.77892	−0.237111
$255$	5.44209	0.340797
$256$	13.7637	0.860232
$257$	−23.2509	−1.45035	−0.725175	−	0.688564i	$-0.758241\pi$
$257$	−23.2509	−1.45035	−0.725175	+	0.688564i	$0.758241\pi$
$258$	−14.4926	−0.902272
$259$	−2.97652	−0.184952
$260$	−16.8157	−1.04286
$261$	−0.577908	−0.0357716
$262$	19.4286	1.20030
$263$	−7.73885	−0.477198	−0.238599	−	0.971118i	$-0.576688\pi$
$263$	−7.73885	−0.477198	−0.238599	+	0.971118i	$0.576688\pi$
$264$	1.09310	0.0672759
$265$	3.78820	0.232707
$266$	−0.879537	−0.0539279
$267$	−10.4943	−0.642240
$268$	16.6129	1.01479
$269$	15.7343	0.959339	0.479670	−	0.877449i	$-0.340756\pi$
$269$	15.7343	0.959339	0.479670	+	0.877449i	$0.340756\pi$
$270$	3.10578	0.189012
$271$	−7.02767	−0.426900	−0.213450	−	0.976954i	$-0.568470\pi$
$271$	−7.02767	−0.426900	−0.213450	+	0.976954i	$0.568470\pi$
$272$	13.2721	0.804737
$273$	−5.16978	−0.312889
$274$	11.9253	0.720432
$275$	11.2120	0.676110
$276$	−0.602306	−0.0362545
$277$	−8.64955	−0.519701	−0.259851	−	0.965649i	$-0.583673\pi$
$277$	−8.64955	−0.519701	−0.259851	+	0.965649i	$0.583673\pi$
$278$	6.67615	0.400409
$279$	2.46822	0.147769
$280$	−0.396909	−0.0237199
$281$	−23.9588	−1.42926	−0.714630	−	0.699502i	$-0.753405\pi$
$281$	−23.9588	−1.42926	−0.714630	+	0.699502i	$0.753405\pi$
$282$	16.5846	0.987599
$283$	8.96742	0.533058	0.266529	−	0.963827i	$-0.414123\pi$
$283$	8.96742	0.533058	0.266529	+	0.963827i	$0.414123\pi$
$284$	−11.6301	−0.690122
$285$	0.661770	0.0391999
$286$	44.2194	2.61475
$287$	−5.92982	−0.350026
$288$	8.09361	0.476921
$289$	−4.32618	−0.254481
$290$	−1.79486	−0.105398
$291$	−16.4026	−0.961535
$292$	5.24604	0.307001
$293$	−18.1847	−1.06236	−0.531179	−	0.847259i	$-0.678251\pi$
$293$	−18.1847	−1.06236	−0.531179	+	0.847259i	$0.678251\pi$
$294$	−2.03170	−0.118491
$295$	−13.6508	−0.794782
$296$	−0.772837	−0.0449202
$297$	−4.21000	−0.244289
$298$	−31.8767	−1.84657
$299$	−1.46339	−0.0846298
$300$	−5.66672	−0.327168
$301$	−7.13326	−0.411154
$302$	30.7593	1.77000
$303$	−3.74382	−0.215077
$304$	1.61391	0.0925642
$305$	−15.3442	−0.878609
$306$	7.23291	0.413478
$307$	6.73427	0.384345	0.192173	−	0.981361i	$-0.438447\pi$
$307$	6.73427	0.384345	0.192173	+	0.981361i	$0.438447\pi$
$308$	8.95802	0.510431
$309$	12.3021	0.699841
$310$	7.66576	0.435386
$311$	11.2551	0.638217	0.319109	−	0.947718i	$-0.396616\pi$
$311$	11.2551	0.638217	0.319109	+	0.947718i	$0.396616\pi$
$312$	−1.34231	−0.0759931
$313$	5.88276	0.332513	0.166257	−	0.986083i	$-0.446832\pi$
$313$	5.88276	0.332513	0.166257	+	0.986083i	$0.446832\pi$
$314$	−10.5782	−0.596965
$315$	1.52866	0.0861304
$316$	−28.7872	−1.61941
$317$	−9.10720	−0.511511	−0.255756	−	0.966741i	$-0.582324\pi$
$317$	−9.10720	−0.511511	−0.255756	+	0.966741i	$0.582324\pi$
$318$	5.03478	0.282336
$319$	2.43299	0.136222
$320$	13.7390	0.768036
$321$	0.772867	0.0431372
$322$	−0.575103	−0.0320493
$323$	1.54116	0.0857526
$324$	2.12780	0.118211
$325$	−13.7681	−0.763717
$326$	−41.2489	−2.28456
$327$	−12.2436	−0.677071
$328$	−1.53964	−0.0850127
$329$	8.16293	0.450037
$330$	−13.0753	−0.719774
$331$	−24.1187	−1.32568	−0.662842	−	0.748759i	$-0.730650\pi$
$331$	−24.1187	−1.32568	−0.662842	+	0.748759i	$0.730650\pi$
$332$	18.2847	1.00350
$333$	2.97652	0.163112
$334$	10.1250	0.554015
$335$	−11.9351	−0.652084
$336$	3.72807	0.203383
$337$	−6.17412	−0.336326	−0.168163	−	0.985759i	$-0.553783\pi$
$337$	−6.17412	−0.336326	−0.168163	+	0.985759i	$0.553783\pi$
$338$	−27.8883	−1.51693
$339$	0.754989	0.0410054
$340$	11.5797	0.627995
$341$	−10.3912	−0.562716
$342$	0.879537	0.0475599
$343$	−1.00000	−0.0539949
$344$	−1.85211	−0.0998592
$345$	0.432712	0.0232964
$346$	7.66657	0.412157
$347$	2.41133	0.129447	0.0647234	−	0.997903i	$-0.479383\pi$
$347$	2.41133	0.129447	0.0647234	+	0.997903i	$0.479383\pi$
$348$	−1.22967	−0.0659173
$349$	26.4862	1.41777	0.708887	−	0.705322i	$-0.249198\pi$
$349$	26.4862	1.41777	0.708887	+	0.705322i	$0.249198\pi$
$350$	−5.41079	−0.289219
$351$	5.16978	0.275942
$352$	−34.0741	−1.81616
$353$	−18.0081	−0.958474	−0.479237	−	0.877686i	$-0.659087\pi$
$353$	−18.0081	−0.958474	−0.479237	+	0.877686i	$0.659087\pi$
$354$	−18.1429	−0.964284
$355$	8.35540	0.443458
$356$	−22.3297	−1.18347
$357$	3.56003	0.188417
$358$	−14.7062	−0.777248
$359$	−0.356247	−0.0188020	−0.00940099	−	0.999956i	$-0.502992\pi$
$359$	−0.356247	−0.0188020	−0.00940099	+	0.999956i	$0.502992\pi$
$360$	0.396909	0.0209189
$361$	−18.8126	−0.990136
$362$	−26.8690	−1.41221
$363$	6.72410	0.352924
$364$	−11.0002	−0.576569
$365$	−3.76889	−0.197273
$366$	−20.3935	−1.06599
$367$	19.6428	1.02535	0.512673	−	0.858584i	$-0.328655\pi$
$367$	19.6428	1.02535	0.512673	+	0.858584i	$0.328655\pi$
$368$	1.05529	0.0550107
$369$	5.92982	0.308694
$370$	9.24442	0.480594
$371$	2.47811	0.128657
$372$	5.25188	0.272297
$373$	−17.1238	−0.886637	−0.443319	−	0.896364i	$-0.646199\pi$
$373$	−17.1238	−0.886637	−0.443319	+	0.896364i	$0.646199\pi$
$374$	−30.4505	−1.57456
$375$	11.7144	0.604931
$376$	2.11946	0.109303
$377$	−2.98766	−0.153872
$378$	2.03170	0.104499
$379$	2.96205	0.152150	0.0760751	−	0.997102i	$-0.475761\pi$
$379$	2.96205	0.152150	0.0760751	+	0.997102i	$0.475761\pi$
$380$	1.40811	0.0722346
$381$	1.85998	0.0952898
$382$	10.5921	0.541938
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	2.07292	0.105783
$385$	−6.43567	−0.327992
$386$	−5.07844	−0.258486
$387$	7.13326	0.362604
$388$	−34.9013	−1.77185
$389$	14.5664	0.738544	0.369272	−	0.929321i	$-0.379607\pi$
$389$	14.5664	0.738544	0.369272	+	0.929321i	$0.379607\pi$
$390$	16.0562	0.813038
$391$	1.00772	0.0509627
$392$	−0.259645	−0.0131140
$393$	−9.56274	−0.482376
$394$	0.0275232	0.00138660
$395$	20.6815	1.04060
$396$	−8.95802	−0.450158
$397$	−21.4640	−1.07725	−0.538623	−	0.842547i	$-0.681055\pi$
$397$	−21.4640	−1.07725	−0.538623	+	0.842547i	$0.681055\pi$
$398$	39.3463	1.97225
$399$	0.432907	0.0216725
$400$	9.92856	0.496428
$401$	−23.7501	−1.18602	−0.593011	−	0.805194i	$-0.702061\pi$
$401$	−23.7501	−1.18602	−0.593011	+	0.805194i	$0.702061\pi$
$402$	−15.8626	−0.791153
$403$	12.7602	0.635629
$404$	−7.96609	−0.396328
$405$	−1.52866	−0.0759599
$406$	−1.17414	−0.0582713
$407$	−12.5311	−0.621146
$408$	0.924343	0.0457618
$409$	−27.5845	−1.36397	−0.681984	−	0.731367i	$-0.738882\pi$
$409$	−27.5845	−1.36397	−0.681984	+	0.731367i	$0.738882\pi$
$410$	18.4167	0.909537
$411$	−5.86961	−0.289527
$412$	26.1763	1.28962
$413$	−8.92991	−0.439412
$414$	0.575103	0.0282648
$415$	−13.1362	−0.644829
$416$	41.8422	2.05148
$417$	−3.28599	−0.160916
$418$	−3.70285	−0.181112
$419$	13.3210	0.650772	0.325386	−	0.945581i	$-0.394506\pi$
$419$	13.3210	0.650772	0.325386	+	0.945581i	$0.394506\pi$
$420$	3.25268	0.158715
$421$	−14.5857	−0.710862	−0.355431	−	0.934703i	$-0.615666\pi$
$421$	−14.5857	−0.710862	−0.355431	+	0.934703i	$0.615666\pi$
$422$	36.0402	1.75441
$423$	−8.16293	−0.396895
$424$	0.643429	0.0312477
$425$	9.48103	0.459898
$426$	11.1049	0.538034
$427$	−10.0377	−0.485758
$428$	1.64450	0.0794901
$429$	−21.7648	−1.05081
$430$	22.1544	1.06838
$431$	2.19508	0.105733	0.0528666	−	0.998602i	$-0.483164\pi$
$431$	2.19508	0.105733	0.0528666	+	0.998602i	$0.483164\pi$
$432$	−3.72807	−0.179367
$433$	2.37912	0.114333	0.0571666	−	0.998365i	$-0.481793\pi$
$433$	2.37912	0.114333	0.0571666	+	0.998365i	$0.481793\pi$
$434$	5.01468	0.240712
$435$	0.883427	0.0423571
$436$	−26.0518	−1.24766
$437$	0.122541	0.00586194
$438$	−5.00911	−0.239345
$439$	−29.2891	−1.39789	−0.698947	−	0.715174i	$-0.746348\pi$
$439$	−29.2891	−1.39789	−0.698947	+	0.715174i	$0.746348\pi$
$440$	−1.67099	−0.0796612
$441$	1.00000	0.0476190
$442$	37.3925	1.77858
$443$	−2.18256	−0.103696	−0.0518482	−	0.998655i	$-0.516511\pi$
$443$	−2.18256	−0.103696	−0.0518482	+	0.998655i	$0.516511\pi$
$444$	6.33342	0.300571
$445$	16.0422	0.760475
$446$	−53.6301	−2.53946
$447$	15.6897	0.742096
$448$	8.98762	0.424625
$449$	−15.7649	−0.743991	−0.371996	−	0.928234i	$-0.621326\pi$
$449$	−15.7649	−0.743991	−0.371996	+	0.928234i	$0.621326\pi$
$450$	5.41079	0.255067
$451$	−24.9645	−1.17553
$452$	1.60646	0.0755617
$453$	−15.1397	−0.711326
$454$	37.4120	1.75583
$455$	7.90285	0.370491
$456$	0.112402	0.00526371
$457$	−27.8438	−1.30248	−0.651239	−	0.758872i	$-0.725751\pi$
$457$	−27.8438	−1.30248	−0.651239	+	0.758872i	$0.725751\pi$
$458$	−16.0595	−0.750409
$459$	−3.56003	−0.166168
$460$	0.920722	0.0429289
$461$	9.04405	0.421223	0.210612	−	0.977570i	$-0.432454\pi$
$461$	9.04405	0.421223	0.210612	+	0.977570i	$0.432454\pi$
$462$	−8.55345	−0.397942
$463$	12.5708	0.584216	0.292108	−	0.956385i	$-0.405643\pi$
$463$	12.5708	0.584216	0.292108	+	0.956385i	$0.405643\pi$
$464$	2.15449	0.100019
$465$	−3.77308	−0.174972
$466$	−3.01531	−0.139682
$467$	−8.57605	−0.396852	−0.198426	−	0.980116i	$-0.563583\pi$
$467$	−8.57605	−0.396852	−0.198426	+	0.980116i	$0.563583\pi$
$468$	11.0002	0.508486
$469$	−7.80754	−0.360519
$470$	−25.3523	−1.16941
$471$	5.20660	0.239907
$472$	−2.31860	−0.106722
$473$	−30.0310	−1.38083
$474$	27.4871	1.26252
$475$	1.15291	0.0528993
$476$	7.57502	0.347201
$477$	−2.47811	−0.113465
$478$	17.7282	0.810870
$479$	−6.51690	−0.297765	−0.148882	−	0.988855i	$-0.547568\pi$
$479$	−6.51690	−0.297765	−0.148882	+	0.988855i	$0.547568\pi$
$480$	−12.3724	−0.564720
$481$	15.3879	0.701630
$482$	−6.25777	−0.285033
$483$	0.283065	0.0128799
$484$	14.3075	0.650342
$485$	25.0740	1.13855
$486$	−2.03170	−0.0921597
$487$	18.7118	0.847912	0.423956	−	0.905683i	$-0.360641\pi$
$487$	18.7118	0.847912	0.423956	+	0.905683i	$0.360641\pi$
$488$	−2.60623	−0.117979
$489$	20.3027	0.918118
$490$	3.10578	0.140305
$491$	−15.1294	−0.682779	−0.341390	−	0.939922i	$-0.610898\pi$
$491$	−15.1294	−0.682779	−0.341390	+	0.939922i	$0.610898\pi$
$492$	12.6174	0.568838
$493$	2.05737	0.0926593
$494$	4.54701	0.204580
$495$	6.43567	0.289262
$496$	−9.20172	−0.413169
$497$	5.46582	0.245175
$498$	−17.4589	−0.782351
$499$	19.4236	0.869522	0.434761	−	0.900546i	$-0.356833\pi$
$499$	19.4236	0.869522	0.434761	+	0.900546i	$0.356833\pi$
$500$	24.9259	1.11472
$501$	−4.98351	−0.222647
$502$	−21.9005	−0.977469
$503$	13.1267	0.585292	0.292646	−	0.956221i	$-0.405464\pi$
$503$	13.1267	0.585292	0.292646	+	0.956221i	$0.405464\pi$
$504$	0.259645	0.0115655
$505$	5.72304	0.254672
$506$	−2.42118	−0.107635
$507$	13.7266	0.609621
$508$	3.95767	0.175593
$509$	38.5361	1.70808	0.854042	−	0.520205i	$-0.174144\pi$
$509$	38.5361	1.70808	0.854042	+	0.520205i	$0.174144\pi$
$510$	−11.0567	−0.489598
$511$	−2.46548	−0.109066
$512$	−32.1095	−1.41905
$513$	−0.432907	−0.0191133
$514$	47.2388	2.08361
$515$	−18.8057	−0.828680
$516$	15.1781	0.668180
$517$	34.3659	1.51141
$518$	6.04739	0.265707
$519$	−3.77348	−0.165637
$520$	2.05193	0.0899832
$521$	−36.3877	−1.59417	−0.797087	−	0.603864i	$-0.793627\pi$
$521$	−36.3877	−1.59417	−0.797087	+	0.603864i	$0.793627\pi$
$522$	1.17414	0.0513905
$523$	−19.4894	−0.852212	−0.426106	−	0.904673i	$-0.640115\pi$
$523$	−19.4894	−0.852212	−0.426106	+	0.904673i	$0.640115\pi$
$524$	−20.3476	−0.888887
$525$	2.66319	0.116231
$526$	15.7230	0.685555
$527$	−8.78695	−0.382765
$528$	15.6952	0.683046
$529$	−22.9199	−0.996516
$530$	−7.69648	−0.334314
$531$	8.92991	0.387525
$532$	0.921139	0.0399364
$533$	30.6558	1.32785
$534$	21.3212	0.922660
$535$	−1.18145	−0.0510787
$536$	−2.02719	−0.0875611
$537$	7.23839	0.312360
$538$	−31.9674	−1.37821
$539$	−4.21000	−0.181338
$540$	−3.25268	−0.139973
$541$	5.26909	0.226536	0.113268	−	0.993564i	$-0.463868\pi$
$541$	5.26909	0.226536	0.113268	+	0.993564i	$0.463868\pi$
$542$	14.2781	0.613297
$543$	13.2249	0.567536
$544$	−28.8135	−1.23537
$545$	18.7163	0.801718
$546$	10.5034	0.449505
$547$	35.9729	1.53809	0.769046	−	0.639194i	$-0.220732\pi$
$547$	35.9729	1.53809	0.769046	+	0.639194i	$0.220732\pi$
$548$	−12.4893	−0.533518
$549$	10.0377	0.428398
$550$	−22.7794	−0.971319
$551$	0.250181	0.0106581
$552$	0.0734964	0.00312821
$553$	13.5291	0.575316
$554$	17.5733	0.746617
$555$	−4.55009	−0.193141
$556$	−6.99193	−0.296524
$557$	3.08538	0.130732	0.0653659	−	0.997861i	$-0.479179\pi$
$557$	3.08538	0.130732	0.0653659	+	0.997861i	$0.479179\pi$
$558$	−5.01468	−0.212288
$559$	36.8774	1.55975
$560$	−5.69897	−0.240825
$561$	14.9877	0.632782
$562$	48.6770	2.05331
$563$	−33.7758	−1.42348	−0.711740	−	0.702443i	$-0.752093\pi$
$563$	−33.7758	−1.42348	−0.711740	+	0.702443i	$0.752093\pi$
$564$	−17.3691	−0.731369
$565$	−1.15412	−0.0485544
$566$	−18.2191	−0.765805
$567$	−1.00000	−0.0419961
$568$	1.41917	0.0595470
$569$	20.4792	0.858533	0.429267	−	0.903178i	$-0.358772\pi$
$569$	20.4792	0.858533	0.429267	+	0.903178i	$0.358772\pi$
$570$	−1.34452	−0.0563156
$571$	13.4137	0.561346	0.280673	−	0.959804i	$-0.409442\pi$
$571$	13.4137	0.561346	0.280673	+	0.959804i	$0.409442\pi$
$572$	−46.3110	−1.93636
$573$	−5.21342	−0.217794
$574$	12.0476	0.502857
$575$	0.753856	0.0314380
$576$	−8.98762	−0.374484
$577$	2.98857	0.124416	0.0622079	−	0.998063i	$-0.480186\pi$
$577$	2.98857	0.124416	0.0622079	+	0.998063i	$0.480186\pi$
$578$	8.78950	0.365595
$579$	2.49960	0.103880
$580$	1.87975	0.0780525
$581$	−8.59324	−0.356508
$582$	33.3250	1.38137
$583$	10.4329	0.432085
$584$	−0.640148	−0.0264895
$585$	−7.90285	−0.326743
$586$	36.9457	1.52621
$587$	43.6179	1.80030	0.900152	−	0.435576i	$-0.143455\pi$
$587$	43.6179	1.80030	0.900152	+	0.435576i	$0.143455\pi$
$588$	2.12780	0.0877489
$589$	−1.06851	−0.0440273
$590$	27.7344	1.14181
$591$	−0.0135469	−0.000557245 0
$592$	−11.0967	−0.456071
$593$	4.56471	0.187450	0.0937250	−	0.995598i	$-0.470123\pi$
$593$	4.56471	0.187450	0.0937250	+	0.995598i	$0.470123\pi$
$594$	8.55345	0.350952
$595$	−5.44209	−0.223104
$596$	33.3844	1.36748
$597$	−19.3662	−0.792607
$598$	2.97316	0.121581
$599$	−21.3200	−0.871111	−0.435556	−	0.900162i	$-0.643448\pi$
$599$	−21.3200	−0.871111	−0.435556	+	0.900162i	$0.643448\pi$
$600$	0.691482	0.0282297
$601$	−35.2931	−1.43964	−0.719818	−	0.694163i	$-0.755775\pi$
$601$	−35.2931	−1.43964	−0.719818	+	0.694163i	$0.755775\pi$
$602$	14.4926	0.590676
$603$	7.80754	0.317948
$604$	−32.2142	−1.31078
$605$	−10.2789	−0.417896
$606$	7.60631	0.308985
$607$	15.2787	0.620144	0.310072	−	0.950713i	$-0.399647\pi$
$607$	15.2787	0.620144	0.310072	+	0.950713i	$0.399647\pi$
$608$	−3.50378	−0.142097
$609$	0.577908	0.0234180
$610$	31.1749	1.26223
$611$	−42.2006	−1.70725
$612$	−7.57502	−0.306202
$613$	−8.25106	−0.333257	−0.166629	−	0.986020i	$-0.553288\pi$
$613$	−8.25106	−0.333257	−0.166629	+	0.986020i	$0.553288\pi$
$614$	−13.6820	−0.552161
$615$	−9.06469	−0.365524
$616$	−1.09310	−0.0440424
$617$	−21.0875	−0.848951	−0.424476	−	0.905439i	$-0.639542\pi$
$617$	−21.0875	−0.848951	−0.424476	+	0.905439i	$0.639542\pi$
$618$	−24.9941	−1.00541
$619$	−12.7368	−0.511936	−0.255968	−	0.966685i	$-0.582394\pi$
$619$	−12.7368	−0.511936	−0.255968	+	0.966685i	$0.582394\pi$
$620$	−8.02835	−0.322426
$621$	−0.283065	−0.0113590
$622$	−22.8669	−0.916881
$623$	10.4943	0.420445
$624$	−19.2733	−0.771550
$625$	−4.59148	−0.183659
$626$	−11.9520	−0.477698
$627$	1.82254	0.0727852
$628$	11.0786	0.442084
$629$	−10.5965	−0.422510
$630$	−3.10578	−0.123737
$631$	−28.1261	−1.11968	−0.559841	−	0.828600i	$-0.689138\pi$
$631$	−28.1261	−1.11968	−0.559841	+	0.828600i	$0.689138\pi$
$632$	3.51276	0.139730
$633$	−17.7389	−0.705059
$634$	18.5031	0.734851
$635$	−2.84329	−0.112832
$636$	−5.27292	−0.209085
$637$	5.16978	0.204834
$638$	−4.94311	−0.195700
$639$	−5.46582	−0.216224
$640$	−3.16879	−0.125257
$641$	−11.1754	−0.441400	−0.220700	−	0.975342i	$-0.570834\pi$
$641$	−11.1754	−0.441400	−0.220700	+	0.975342i	$0.570834\pi$
$642$	−1.57023	−0.0619721
$643$	−18.8337	−0.742730	−0.371365	−	0.928487i	$-0.621110\pi$
$643$	−18.8337	−0.742730	−0.371365	+	0.928487i	$0.621110\pi$
$644$	0.602306	0.0237342
$645$	−10.9044	−0.429358
$646$	−3.13118	−0.123195
$647$	−1.02767	−0.0404018	−0.0202009	−	0.999796i	$-0.506431\pi$
$647$	−1.02767	−0.0404018	−0.0202009	+	0.999796i	$0.506431\pi$
$648$	−0.259645	−0.0101998
$649$	−37.5949	−1.47573
$650$	27.9726	1.09718
$651$	−2.46822	−0.0967373
$652$	43.1999	1.69184
$653$	−30.8098	−1.20568	−0.602840	−	0.797862i	$-0.705964\pi$
$653$	−30.8098	−1.20568	−0.602840	+	0.797862i	$0.705964\pi$
$654$	24.8752	0.972698
$655$	14.6182	0.571181
$656$	−22.1068	−0.863125
$657$	2.46548	0.0961875
$658$	−16.5846	−0.646535
$659$	−26.0127	−1.01331	−0.506655	−	0.862149i	$-0.669118\pi$
$659$	−26.0127	−1.01331	−0.506655	+	0.862149i	$0.669118\pi$
$660$	13.6938	0.533031
$661$	−5.29436	−0.205927	−0.102963	−	0.994685i	$-0.532832\pi$
$661$	−5.29436	−0.205927	−0.102963	+	0.994685i	$0.532832\pi$
$662$	49.0019	1.90451
$663$	−18.4046	−0.714774
$664$	−2.23119	−0.0865869
$665$	−0.661770	−0.0256623
$666$	−6.04739	−0.234331
$667$	0.163586	0.00633407
$668$	−10.6039	−0.410277
$669$	26.3967	1.02056
$670$	24.2485	0.936802
$671$	−42.2587	−1.63138
$672$	−8.09361	−0.312218
$673$	27.9155	1.07606	0.538032	−	0.842924i	$-0.319168\pi$
$673$	27.9155	1.07606	0.538032	+	0.842924i	$0.319168\pi$
$674$	12.5440	0.483175
$675$	−2.66319	−0.102506
$676$	29.2075	1.12336
$677$	−4.99015	−0.191787	−0.0958935	−	0.995392i	$-0.530571\pi$
$677$	−4.99015	−0.191787	−0.0958935	+	0.995392i	$0.530571\pi$
$678$	−1.53391	−0.0589094
$679$	16.4026	0.629472
$680$	−1.41301	−0.0541864
$681$	−18.4142	−0.705632
$682$	21.1118	0.808413
$683$	−3.48643	−0.133405	−0.0667023	−	0.997773i	$-0.521248\pi$
$683$	−3.48643	−0.133405	−0.0667023	+	0.997773i	$0.521248\pi$
$684$	−0.921139	−0.0352206
$685$	8.97266	0.342828
$686$	2.03170	0.0775706
$687$	7.90445	0.301574
$688$	−26.5933	−1.01386
$689$	−12.8113	−0.488072
$690$	−0.879139	−0.0334683
$691$	−9.58982	−0.364814	−0.182407	−	0.983223i	$-0.558389\pi$
$691$	−9.58982	−0.364814	−0.182407	+	0.983223i	$0.558389\pi$
$692$	−8.02919	−0.305224
$693$	4.21000	0.159925
$694$	−4.89909	−0.185967
$695$	5.02318	0.190540
$696$	0.150051	0.00568766
$697$	−21.1103	−0.799611
$698$	−53.8120	−2.03681
$699$	1.48413	0.0561351
$700$	5.66672	0.214182
$701$	−35.3419	−1.33485	−0.667423	−	0.744678i	$-0.732603\pi$
$701$	−35.3419	−1.33485	−0.667423	+	0.744678i	$0.732603\pi$
$702$	−10.5034	−0.396426
$703$	−1.28856	−0.0485988
$704$	37.8379	1.42607
$705$	12.4784	0.469963
$706$	36.5870	1.37697
$707$	3.74382	0.140801
$708$	19.0010	0.714103
$709$	23.9630	0.899950	0.449975	−	0.893041i	$-0.351433\pi$
$709$	23.9630	0.899950	0.449975	+	0.893041i	$0.351433\pi$
$710$	−16.9756	−0.637084
$711$	−13.5291	−0.507381
$712$	2.72479	0.102116
$713$	−0.698668	−0.0261653
$714$	−7.23291	−0.270685
$715$	33.2710	1.24427
$716$	15.4018	0.575593
$717$	−8.72581	−0.325872
$718$	0.723786	0.0270114
$719$	−5.58936	−0.208448	−0.104224	−	0.994554i	$-0.533236\pi$
$719$	−5.58936	−0.208448	−0.104224	+	0.994554i	$0.533236\pi$
$720$	5.69897	0.212388
$721$	−12.3021	−0.458154
$722$	38.2215	1.42246
$723$	3.08007	0.114549
$724$	28.1399	1.04581
$725$	1.53908	0.0571600
$726$	−13.6613	−0.507020
$727$	13.6563	0.506484	0.253242	−	0.967403i	$-0.418503\pi$
$727$	13.6563	0.506484	0.253242	+	0.967403i	$0.418503\pi$
$728$	1.34231	0.0497491
$729$	1.00000	0.0370370
$730$	7.65724	0.283407
$731$	−25.3946	−0.939254
$732$	21.3582	0.789420
$733$	−29.7814	−1.10000	−0.550001	−	0.835164i	$-0.685373\pi$
$733$	−29.7814	−1.10000	−0.550001	+	0.835164i	$0.685373\pi$
$734$	−39.9083	−1.47304
$735$	−1.52866	−0.0563856
$736$	−2.29102	−0.0844481
$737$	−32.8697	−1.21077
$738$	−12.0476	−0.443478
$739$	3.20127	0.117761	0.0588804	−	0.998265i	$-0.481247\pi$
$739$	3.20127	0.117761	0.0588804	+	0.998265i	$0.481247\pi$
$740$	−9.68167	−0.355905
$741$	−2.23804	−0.0822163
$742$	−5.03478	−0.184832
$743$	−10.7599	−0.394744	−0.197372	−	0.980329i	$-0.563241\pi$
$743$	−10.7599	−0.394744	−0.197372	+	0.980329i	$0.563241\pi$
$744$	−0.640860	−0.0234951
$745$	−23.9842	−0.878714
$746$	34.7904	1.27377
$747$	8.59324	0.314410
$748$	31.8908	1.16604
$749$	−0.772867	−0.0282399
$750$	−23.8002	−0.869060
$751$	−21.3400	−0.778707	−0.389354	−	0.921088i	$-0.627302\pi$
$751$	−21.3400	−0.778707	−0.389354	+	0.921088i	$0.627302\pi$
$752$	30.4320	1.10974
$753$	10.7794	0.392824
$754$	6.07002	0.221057
$755$	23.1435	0.842279
$756$	−2.12780	−0.0773872
$757$	−7.78099	−0.282805	−0.141402	−	0.989952i	$-0.545161\pi$
$757$	−7.78099	−0.282805	−0.141402	+	0.989952i	$0.545161\pi$
$758$	−6.01799	−0.218583
$759$	1.19171	0.0432562
$760$	−0.171825	−0.00623274
$761$	54.3552	1.97037	0.985187	−	0.171486i	$-0.0548568\pi$
$761$	54.3552	1.97037	0.985187	+	0.171486i	$0.0548568\pi$
$762$	−3.77892	−0.136896
$763$	12.2436	0.443247
$764$	−11.0931	−0.401334
$765$	5.44209	0.196759
$766$	−2.03170	−0.0734082
$767$	46.1657	1.66695
$768$	13.7637	0.496655
$769$	9.06390	0.326852	0.163426	−	0.986556i	$-0.447745\pi$
$769$	9.06390	0.326852	0.163426	+	0.986556i	$0.447745\pi$
$770$	13.0753	0.471203
$771$	−23.2509	−0.837360
$772$	5.31864	0.191422
$773$	−41.2419	−1.48337	−0.741684	−	0.670750i	$-0.765972\pi$
$773$	−41.2419	−1.48337	−0.741684	+	0.670750i	$0.765972\pi$
$774$	−14.4926	−0.520927
$775$	−6.57334	−0.236121
$776$	4.25883	0.152883
$777$	−2.97652	−0.106782
$778$	−29.5944	−1.06101
$779$	−2.56706	−0.0919745
$780$	−16.8157	−0.602097
$781$	23.0111	0.823402
$782$	−2.04739	−0.0732143
$783$	−0.577908	−0.0206528
$784$	−3.72807	−0.133146
$785$	−7.95914	−0.284074
$786$	19.4286	0.692995
$787$	−15.7706	−0.562162	−0.281081	−	0.959684i	$-0.590693\pi$
$787$	−15.7706	−0.562162	−0.281081	+	0.959684i	$0.590693\pi$
$788$	−0.0288251	−0.00102685
$789$	−7.73885	−0.275510
$790$	−42.0185	−1.49495
$791$	−0.754989	−0.0268443
$792$	1.09310	0.0388417
$793$	51.8926	1.84276
$794$	43.6083	1.54760
$795$	3.78820	0.134354
$796$	−41.2074	−1.46056
$797$	−9.45922	−0.335063	−0.167531	−	0.985867i	$-0.553580\pi$
$797$	−9.45922	−0.335063	−0.167531	+	0.985867i	$0.553580\pi$
$798$	−0.879537	−0.0311353
$799$	29.0603	1.02808
$800$	−21.5548	−0.762078
$801$	−10.4943	−0.370798
$802$	48.2530	1.70387
$803$	−10.3797	−0.366291
$804$	16.6129	0.585890
$805$	−0.432712	−0.0152511
$806$	−25.9248	−0.913162
$807$	15.7343	0.553875
$808$	0.972063	0.0341970
$809$	−7.87743	−0.276956	−0.138478	−	0.990366i	$-0.544221\pi$
$809$	−7.87743	−0.276956	−0.138478	+	0.990366i	$0.544221\pi$
$810$	3.10578	0.109126
$811$	0.208031	0.00730497	0.00365249	−	0.999993i	$-0.498837\pi$
$811$	0.208031	0.00730497	0.00365249	+	0.999993i	$0.498837\pi$
$812$	1.22967	0.0431530
$813$	−7.02767	−0.246471
$814$	25.4595	0.892355
$815$	−31.0359	−1.08714
$816$	13.2721	0.464615
$817$	−3.08804	−0.108037
$818$	56.0434	1.95951
$819$	−5.16978	−0.180647
$820$	−19.2878	−0.673560
$821$	−31.3242	−1.09322	−0.546610	−	0.837387i	$-0.684082\pi$
$821$	−31.3242	−1.09322	−0.546610	+	0.837387i	$0.684082\pi$
$822$	11.9253	0.415942
$823$	−19.1753	−0.668409	−0.334205	−	0.942501i	$-0.608468\pi$
$823$	−19.1753	−0.668409	−0.334205	+	0.942501i	$0.608468\pi$
$824$	−3.19417	−0.111274
$825$	11.2120	0.390353
$826$	18.1429	0.631272
$827$	18.4354	0.641061	0.320530	−	0.947238i	$-0.396139\pi$
$827$	18.4354	0.641061	0.320530	+	0.947238i	$0.396139\pi$
$828$	−0.602306	−0.0209316
$829$	−14.3231	−0.497463	−0.248731	−	0.968573i	$-0.580014\pi$
$829$	−14.3231	−0.497463	−0.248731	+	0.968573i	$0.580014\pi$
$830$	26.6887	0.926380
$831$	−8.64955	−0.300050
$832$	−46.4640	−1.61085
$833$	−3.56003	−0.123348
$834$	6.67615	0.231176
$835$	7.61811	0.263636
$836$	3.87800	0.134123
$837$	2.46822	0.0853142
$838$	−27.0642	−0.934917
$839$	−1.93561	−0.0668245	−0.0334123	−	0.999442i	$-0.510637\pi$
$839$	−1.93561	−0.0668245	−0.0334123	+	0.999442i	$0.510637\pi$
$840$	−0.396909	−0.0136947
$841$	−28.6660	−0.988484
$842$	29.6337	1.02124
$843$	−23.9588	−0.825184
$844$	−37.7448	−1.29923
$845$	−20.9834	−0.721850
$846$	16.5846	0.570191
$847$	−6.72410	−0.231043
$848$	9.23859	0.317254
$849$	8.96742	0.307761
$850$	−19.2626	−0.660702
$851$	−0.842549	−0.0288822
$852$	−11.6301	−0.398442
$853$	50.5951	1.73234	0.866172	−	0.499745i	$-0.166573\pi$
$853$	50.5951	1.73234	0.866172	+	0.499745i	$0.166573\pi$
$854$	20.3935	0.697853
$855$	0.661770	0.0226320
$856$	−0.200671	−0.00685878
$857$	−5.45738	−0.186421	−0.0932103	−	0.995646i	$-0.529713\pi$
$857$	−5.45738	−0.186421	−0.0932103	+	0.995646i	$0.529713\pi$
$858$	44.2194	1.50963
$859$	26.4322	0.901854	0.450927	−	0.892561i	$-0.351093\pi$
$859$	26.4322	0.901854	0.450927	+	0.892561i	$0.351093\pi$
$860$	−23.2022	−0.791190
$861$	−5.92982	−0.202088
$862$	−4.45974	−0.151899
$863$	−21.4827	−0.731279	−0.365639	−	0.930757i	$-0.619150\pi$
$863$	−21.4827	−0.731279	−0.365639	+	0.930757i	$0.619150\pi$
$864$	8.09361	0.275350
$865$	5.76838	0.196131
$866$	−4.83365	−0.164254
$867$	−4.32618	−0.146925
$868$	−5.25188	−0.178260
$869$	56.9575	1.93215
$870$	−1.79486	−0.0608514
$871$	40.3633	1.36766
$872$	3.17898	0.107654
$873$	−16.4026	−0.555142
$874$	−0.248967	−0.00842142
$875$	−11.7144	−0.396020
$876$	5.24604	0.177247
$877$	−13.0506	−0.440688	−0.220344	−	0.975422i	$-0.570718\pi$
$877$	−13.0506	−0.440688	−0.220344	+	0.975422i	$0.570718\pi$
$878$	59.5066	2.00825
$879$	−18.1847	−0.613353
$880$	−23.9927	−0.808793
$881$	48.2234	1.62469	0.812344	−	0.583179i	$-0.198191\pi$
$881$	48.2234	1.62469	0.812344	+	0.583179i	$0.198191\pi$
$882$	−2.03170	−0.0684108
$883$	22.2132	0.747533	0.373766	−	0.927523i	$-0.378066\pi$
$883$	22.2132	0.747533	0.373766	+	0.927523i	$0.378066\pi$
$884$	−39.1612	−1.31713
$885$	−13.6508	−0.458868
$886$	4.43430	0.148973
$887$	−14.9549	−0.502138	−0.251069	−	0.967969i	$-0.580782\pi$
$887$	−14.9549	−0.502138	−0.251069	+	0.967969i	$0.580782\pi$
$888$	−0.772837	−0.0259347
$889$	−1.85998	−0.0623818
$890$	−32.5930	−1.09252
$891$	−4.21000	−0.141040
$892$	56.1668	1.88060
$893$	3.53379	0.118254
$894$	−31.8767	−1.06612
$895$	−11.0651	−0.369864
$896$	−2.07292	−0.0692513
$897$	−1.46339	−0.0488610
$898$	32.0295	1.06884
$899$	−1.42641	−0.0475733
$900$	−5.66672	−0.188891
$901$	8.82216	0.293909
$902$	50.7204	1.68880
$903$	−7.13326	−0.237380
$904$	−0.196029	−0.00651982
$905$	−20.2164	−0.672018
$906$	30.7593	1.02191
$907$	6.85198	0.227516	0.113758	−	0.993508i	$-0.463711\pi$
$907$	6.85198	0.227516	0.113758	+	0.993508i	$0.463711\pi$
$908$	−39.1816	−1.30029
$909$	−3.74382	−0.124175
$910$	−16.0562	−0.532258
$911$	−24.6069	−0.815262	−0.407631	−	0.913147i	$-0.633645\pi$
$911$	−24.6069	−0.815262	−0.407631	+	0.913147i	$0.633645\pi$
$912$	1.61391	0.0534419
$913$	−36.1775	−1.19730
$914$	56.5702	1.87118
$915$	−15.3442	−0.507265
$916$	16.8191	0.555718
$917$	9.56274	0.315789
$918$	7.23291	0.238721
$919$	−47.2474	−1.55855	−0.779273	−	0.626684i	$-0.784412\pi$
$919$	−47.2474	−1.55855	−0.779273	+	0.626684i	$0.784412\pi$
$920$	−0.112351	−0.00370411
$921$	6.73427	0.221902
$922$	−18.3748	−0.605141
$923$	−28.2571	−0.930093
$924$	8.95802	0.294697
$925$	−7.92703	−0.260639
$926$	−25.5401	−0.839300
$927$	12.3021	0.404053
$928$	−4.67736	−0.153542
$929$	−36.3301	−1.19195	−0.595976	−	0.803002i	$-0.703235\pi$
$929$	−36.3301	−1.19195	−0.595976	+	0.803002i	$0.703235\pi$
$930$	7.66576	0.251370
$931$	−0.432907	−0.0141880
$932$	3.15793	0.103442
$933$	11.2551	0.368475
$934$	17.4239	0.570129
$935$	−22.9112	−0.749276
$936$	−1.34231	−0.0438746
$937$	−31.4037	−1.02592	−0.512958	−	0.858414i	$-0.671450\pi$
$937$	−31.4037	−1.02592	−0.512958	+	0.858414i	$0.671450\pi$
$938$	15.8626	0.517931
$939$	5.88276	0.191977
$940$	26.5514	0.866012
$941$	−16.0184	−0.522186	−0.261093	−	0.965314i	$-0.584083\pi$
$941$	−16.0184	−0.522186	−0.261093	+	0.965314i	$0.584083\pi$
$942$	−10.5782	−0.344658
$943$	−1.67853	−0.0546603
$944$	−33.2914	−1.08354
$945$	1.52866	0.0497274
$946$	61.0140	1.98374
$947$	−30.8725	−1.00322	−0.501611	−	0.865093i	$-0.667259\pi$
$947$	−30.8725	−1.00322	−0.501611	+	0.865093i	$0.667259\pi$
$948$	−28.7872	−0.934965
$949$	12.7460	0.413752
$950$	−2.34237	−0.0759966
$951$	−9.10720	−0.295321
$952$	−0.924343	−0.0299581
$953$	−28.7207	−0.930356	−0.465178	−	0.885217i	$-0.654010\pi$
$953$	−28.7207	−0.930356	−0.465178	+	0.885217i	$0.654010\pi$
$954$	5.03478	0.163007
$955$	7.96956	0.257889
$956$	−18.5668	−0.600492
$957$	2.43299	0.0786475
$958$	13.2404	0.427777
$959$	5.86961	0.189540
$960$	13.7390	0.443426
$961$	−24.9079	−0.803480
$962$	−31.2636	−1.00798
$963$	0.772867	0.0249053
$964$	6.55376	0.211082
$965$	−3.82105	−0.123004
$966$	−0.575103	−0.0185036
$967$	−4.29708	−0.138185	−0.0690923	−	0.997610i	$-0.522010\pi$
$967$	−4.29708	−0.138185	−0.0690923	+	0.997610i	$0.522010\pi$
$968$	−1.74588	−0.0561146
$969$	1.54116	0.0495093
$970$	−50.9428	−1.63567
$971$	−49.4650	−1.58741	−0.793703	−	0.608305i	$-0.791850\pi$
$971$	−49.4650	−1.58741	−0.793703	+	0.608305i	$0.791850\pi$
$972$	2.12780	0.0682491
$973$	3.28599	0.105344
$974$	−38.0167	−1.21813
$975$	−13.7681	−0.440932
$976$	−37.4212	−1.19782
$977$	5.15719	0.164993	0.0824965	−	0.996591i	$-0.473711\pi$
$977$	5.15719	0.164993	0.0824965	+	0.996591i	$0.473711\pi$
$978$	−41.2489	−1.31899
$979$	44.1810	1.41203
$980$	−3.25268	−0.103903
$981$	−12.2436	−0.390907
$982$	30.7383	0.980899
$983$	32.2045	1.02716	0.513582	−	0.858041i	$-0.328318\pi$
$983$	32.2045	1.02716	0.513582	+	0.858041i	$0.328318\pi$
$984$	−1.53964	−0.0490821
$985$	0.0207087	0.000659833 0
$986$	−4.17996	−0.133117
$987$	8.16293	0.259829
$988$	−4.76209	−0.151502
$989$	−2.01918	−0.0642062
$990$	−13.0753	−0.415562
$991$	36.4341	1.15737	0.578683	−	0.815553i	$-0.303567\pi$
$991$	36.4341	1.15737	0.578683	+	0.815553i	$0.303567\pi$
$992$	19.9768	0.634265
$993$	−24.1187	−0.765384
$994$	−11.1049	−0.352226
$995$	29.6045	0.938524
$996$	18.2847	0.579372
$997$	−46.3534	−1.46803	−0.734014	−	0.679135i	$-0.762355\pi$
$997$	−46.3534	−1.46803	−0.734014	+	0.679135i	$0.762355\pi$
$998$	−39.4630	−1.24918
$999$	2.97652	0.0941729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.9	✓	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.03170 q^{2} +1.00000 q^{3} +2.12780 q^{4} -1.52866 q^{5} -2.03170 q^{6} -1.00000 q^{7} -0.259645 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.03170 q^{2} +1.00000 q^{3} +2.12780 q^{4} -1.52866 q^{5} -2.03170 q^{6} -1.00000 q^{7} -0.259645 q^{8} +1.00000 q^{9} +3.10578 q^{10} -4.21000 q^{11} +2.12780 q^{12} +5.16978 q^{13} +2.03170 q^{14} -1.52866 q^{15} -3.72807 q^{16} -3.56003 q^{17} -2.03170 q^{18} -0.432907 q^{19} -3.25268 q^{20} -1.00000 q^{21} +8.55345 q^{22} -0.283065 q^{23} -0.259645 q^{24} -2.66319 q^{25} -10.5034 q^{26} +1.00000 q^{27} -2.12780 q^{28} -0.577908 q^{29} +3.10578 q^{30} +2.46822 q^{31} +8.09361 q^{32} -4.21000 q^{33} +7.23291 q^{34} +1.52866 q^{35} +2.12780 q^{36} +2.97652 q^{37} +0.879537 q^{38} +5.16978 q^{39} +0.396909 q^{40} +5.92982 q^{41} +2.03170 q^{42} +7.13326 q^{43} -8.95802 q^{44} -1.52866 q^{45} +0.575103 q^{46} -8.16293 q^{47} -3.72807 q^{48} +1.00000 q^{49} +5.41079 q^{50} -3.56003 q^{51} +11.0002 q^{52} -2.47811 q^{53} -2.03170 q^{54} +6.43567 q^{55} +0.259645 q^{56} -0.432907 q^{57} +1.17414 q^{58} +8.92991 q^{59} -3.25268 q^{60} +10.0377 q^{61} -5.01468 q^{62} -1.00000 q^{63} -8.98762 q^{64} -7.90285 q^{65} +8.55345 q^{66} +7.80754 q^{67} -7.57502 q^{68} -0.283065 q^{69} -3.10578 q^{70} -5.46582 q^{71} -0.259645 q^{72} +2.46548 q^{73} -6.04739 q^{74} -2.66319 q^{75} -0.921139 q^{76} +4.21000 q^{77} -10.5034 q^{78} -13.5291 q^{79} +5.69897 q^{80} +1.00000 q^{81} -12.0476 q^{82} +8.59324 q^{83} -2.12780 q^{84} +5.44209 q^{85} -14.4926 q^{86} -0.577908 q^{87} +1.09310 q^{88} -10.4943 q^{89} +3.10578 q^{90} -5.16978 q^{91} -0.602306 q^{92} +2.46822 q^{93} +16.5846 q^{94} +0.661770 q^{95} +8.09361 q^{96} -16.4026 q^{97} -2.03170 q^{98} -4.21000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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