LMFDB - Embedded newform 6041.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10602 q^{2} -0.719393 q^{3} +2.43533 q^{4} +1.34496 q^{5} +1.51506 q^{6} -1.00000 q^{7} -0.916817 q^{8} -2.48247 q^{9} +O(q^{10})$	\(q-2.10602 q^{2} -0.719393 q^{3} +2.43533 q^{4} +1.34496 q^{5} +1.51506 q^{6} -1.00000 q^{7} -0.916817 q^{8} -2.48247 q^{9} -2.83252 q^{10} +1.02546 q^{11} -1.75196 q^{12} +0.467718 q^{13} +2.10602 q^{14} -0.967557 q^{15} -2.93982 q^{16} +5.19344 q^{17} +5.22814 q^{18} -7.70274 q^{19} +3.27543 q^{20} +0.719393 q^{21} -2.15963 q^{22} +1.28646 q^{23} +0.659552 q^{24} -3.19108 q^{25} -0.985024 q^{26} +3.94405 q^{27} -2.43533 q^{28} -1.56865 q^{29} +2.03770 q^{30} +6.10742 q^{31} +8.02497 q^{32} -0.737707 q^{33} -10.9375 q^{34} -1.34496 q^{35} -6.04564 q^{36} -7.69092 q^{37} +16.2221 q^{38} -0.336473 q^{39} -1.23308 q^{40} +3.58266 q^{41} -1.51506 q^{42} +0.782202 q^{43} +2.49733 q^{44} -3.33883 q^{45} -2.70930 q^{46} -4.20421 q^{47} +2.11489 q^{48} +1.00000 q^{49} +6.72048 q^{50} -3.73613 q^{51} +1.13905 q^{52} -0.775132 q^{53} -8.30627 q^{54} +1.37920 q^{55} +0.916817 q^{56} +5.54130 q^{57} +3.30362 q^{58} -6.57459 q^{59} -2.35632 q^{60} -5.76820 q^{61} -12.8624 q^{62} +2.48247 q^{63} -11.0211 q^{64} +0.629063 q^{65} +1.55363 q^{66} +8.11799 q^{67} +12.6477 q^{68} -0.925468 q^{69} +2.83252 q^{70} +7.94562 q^{71} +2.27597 q^{72} -7.24631 q^{73} +16.1972 q^{74} +2.29564 q^{75} -18.7587 q^{76} -1.02546 q^{77} +0.708620 q^{78} -14.5374 q^{79} -3.95395 q^{80} +4.61009 q^{81} -7.54517 q^{82} +9.85504 q^{83} +1.75196 q^{84} +6.98498 q^{85} -1.64733 q^{86} +1.12848 q^{87} -0.940156 q^{88} +15.2270 q^{89} +7.03166 q^{90} -0.467718 q^{91} +3.13295 q^{92} -4.39363 q^{93} +8.85415 q^{94} -10.3599 q^{95} -5.77311 q^{96} +9.15583 q^{97} -2.10602 q^{98} -2.54567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.10602	−1.48918	−0.744591	−	0.667521i	$-0.767356\pi$
$2$	−2.10602	−1.48918	−0.744591	+	0.667521i	$0.767356\pi$
$3$	−0.719393	−0.415342	−0.207671	−	0.978199i	$-0.566588\pi$
$3$	−0.719393	−0.415342	−0.207671	+	0.978199i	$0.566588\pi$
$4$	2.43533	1.21767
$5$	1.34496	0.601486	0.300743	−	0.953705i	$-0.402765\pi$
$5$	1.34496	0.601486	0.300743	+	0.953705i	$0.402765\pi$
$6$	1.51506	0.618520
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.916817	−0.324144
$9$	−2.48247	−0.827491
$10$	−2.83252	−0.895722
$11$	1.02546	0.309187	0.154593	−	0.987978i	$-0.450593\pi$
$11$	1.02546	0.309187	0.154593	+	0.987978i	$0.450593\pi$
$12$	−1.75196	−0.505748
$13$	0.467718	0.129722	0.0648608	−	0.997894i	$-0.479340\pi$
$13$	0.467718	0.129722	0.0648608	+	0.997894i	$0.479340\pi$
$14$	2.10602	0.562858
$15$	−0.967557	−0.249822
$16$	−2.93982	−0.734956
$17$	5.19344	1.25959	0.629797	−	0.776760i	$-0.283138\pi$
$17$	5.19344	1.25959	0.629797	+	0.776760i	$0.283138\pi$
$18$	5.22814	1.23229
$19$	−7.70274	−1.76713	−0.883565	−	0.468309i	$-0.844863\pi$
$19$	−7.70274	−1.76713	−0.883565	+	0.468309i	$0.844863\pi$
$20$	3.27543	0.732408
$21$	0.719393	0.156985
$22$	−2.15963	−0.460436
$23$	1.28646	0.268245	0.134122	−	0.990965i	$-0.457179\pi$
$23$	1.28646	0.268245	0.134122	+	0.990965i	$0.457179\pi$
$24$	0.659552	0.134631
$25$	−3.19108	−0.638215
$26$	−0.985024	−0.193179
$27$	3.94405	0.759034
$28$	−2.43533	−0.460234
$29$	−1.56865	−0.291292	−0.145646	−	0.989337i	$-0.546526\pi$
$29$	−1.56865	−0.291292	−0.145646	+	0.989337i	$0.546526\pi$
$30$	2.03770	0.372031
$31$	6.10742	1.09692	0.548462	−	0.836175i	$-0.315213\pi$
$31$	6.10742	1.09692	0.548462	+	0.836175i	$0.315213\pi$
$32$	8.02497	1.41863
$33$	−0.737707	−0.128418
$34$	−10.9375	−1.87577
$35$	−1.34496	−0.227340
$36$	−6.04564	−1.00761
$37$	−7.69092	−1.26438	−0.632190	−	0.774814i	$-0.717844\pi$
$37$	−7.69092	−1.26438	−0.632190	+	0.774814i	$0.717844\pi$
$38$	16.2221	2.63158
$39$	−0.336473	−0.0538788
$40$	−1.23308	−0.194968
$41$	3.58266	0.559518	0.279759	−	0.960070i	$-0.409745\pi$
$41$	3.58266	0.559518	0.279759	+	0.960070i	$0.409745\pi$
$42$	−1.51506	−0.233779
$43$	0.782202	0.119285	0.0596423	−	0.998220i	$-0.481004\pi$
$43$	0.782202	0.119285	0.0596423	+	0.998220i	$0.481004\pi$
$44$	2.49733	0.376486
$45$	−3.33883	−0.497724
$46$	−2.70930	−0.399465
$47$	−4.20421	−0.613247	−0.306623	−	0.951831i	$-0.599199\pi$
$47$	−4.20421	−0.613247	−0.306623	+	0.951831i	$0.599199\pi$
$48$	2.11489	0.305258
$49$	1.00000	0.142857
$50$	6.72048	0.950419
$51$	−3.73613	−0.523162
$52$	1.13905	0.157958
$53$	−0.775132	−0.106473	−0.0532363	−	0.998582i	$-0.516954\pi$
$53$	−0.775132	−0.106473	−0.0532363	+	0.998582i	$0.516954\pi$
$54$	−8.30627	−1.13034
$55$	1.37920	0.185971
$56$	0.916817	0.122515
$57$	5.54130	0.733963
$58$	3.30362	0.433787
$59$	−6.57459	−0.855939	−0.427970	−	0.903793i	$-0.640771\pi$
$59$	−6.57459	−0.855939	−0.427970	+	0.903793i	$0.640771\pi$
$60$	−2.35632	−0.304200
$61$	−5.76820	−0.738542	−0.369271	−	0.929322i	$-0.620393\pi$
$61$	−5.76820	−0.738542	−0.369271	+	0.929322i	$0.620393\pi$
$62$	−12.8624	−1.63352
$63$	2.48247	0.312762
$64$	−11.0211	−1.37764
$65$	0.629063	0.0780257
$66$	1.55363	0.191238
$67$	8.11799	0.991770	0.495885	−	0.868388i	$-0.334844\pi$
$67$	8.11799	0.991770	0.495885	+	0.868388i	$0.334844\pi$
$68$	12.6477	1.53376
$69$	−0.925468	−0.111413
$70$	2.83252	0.338551
$71$	7.94562	0.942971	0.471486	−	0.881874i	$-0.343718\pi$
$71$	7.94562	0.942971	0.471486	+	0.881874i	$0.343718\pi$
$72$	2.27597	0.268226
$73$	−7.24631	−0.848117	−0.424058	−	0.905635i	$-0.639395\pi$
$73$	−7.24631	−0.848117	−0.424058	+	0.905635i	$0.639395\pi$
$74$	16.1972	1.88289
$75$	2.29564	0.265078
$76$	−18.7587	−2.15177
$77$	−1.02546	−0.116862
$78$	0.708620	0.0802354
$79$	−14.5374	−1.63558	−0.817792	−	0.575514i	$-0.804802\pi$
$79$	−14.5374	−1.63558	−0.817792	+	0.575514i	$0.804802\pi$
$80$	−3.95395	−0.442066
$81$	4.61009	0.512233
$82$	−7.54517	−0.833224
$83$	9.85504	1.08173	0.540866	−	0.841109i	$-0.318097\pi$
$83$	9.85504	1.08173	0.540866	+	0.841109i	$0.318097\pi$
$84$	1.75196	0.191155
$85$	6.98498	0.757628
$86$	−1.64733	−0.177637
$87$	1.12848	0.120986
$88$	−0.940156	−0.100221
$89$	15.2270	1.61406	0.807029	−	0.590511i	$-0.201074\pi$
$89$	15.2270	1.61406	0.807029	+	0.590511i	$0.201074\pi$
$90$	7.03166	0.741202
$91$	−0.467718	−0.0490302
$92$	3.13295	0.326632
$93$	−4.39363	−0.455599
$94$	8.85415	0.913236
$95$	−10.3599	−1.06290
$96$	−5.77311	−0.589216
$97$	9.15583	0.929633	0.464817	−	0.885407i	$-0.346120\pi$
$97$	9.15583	0.929633	0.464817	+	0.885407i	$0.346120\pi$
$98$	−2.10602	−0.212740
$99$	−2.54567	−0.255849
$100$	−7.77133	−0.777133
$101$	−6.09427	−0.606403	−0.303201	−	0.952926i	$-0.598056\pi$
$101$	−6.09427	−0.606403	−0.303201	+	0.952926i	$0.598056\pi$
$102$	7.86836	0.779084
$103$	−0.691658	−0.0681511	−0.0340756	−	0.999419i	$-0.510849\pi$
$103$	−0.691658	−0.0681511	−0.0340756	+	0.999419i	$0.510849\pi$
$104$	−0.428812	−0.0420484
$105$	0.967557	0.0944239
$106$	1.63245	0.158557
$107$	14.5875	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$107$	14.5875	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$108$	9.60508	0.924249
$109$	16.3802	1.56894	0.784470	−	0.620167i	$-0.212935\pi$
$109$	16.3802	1.56894	0.784470	+	0.620167i	$0.212935\pi$
$110$	−2.90463	−0.276945
$111$	5.53280	0.525150
$112$	2.93982	0.277787
$113$	−8.57005	−0.806203	−0.403101	−	0.915155i	$-0.632068\pi$
$113$	−8.57005	−0.806203	−0.403101	+	0.915155i	$0.632068\pi$
$114$	−11.6701	−1.09300
$115$	1.73023	0.161345
$116$	−3.82019	−0.354696
$117$	−1.16110	−0.107343
$118$	13.8462	1.27465
$119$	−5.19344	−0.476082
$120$	0.887073	0.0809783
$121$	−9.94844	−0.904404
$122$	12.1480	1.09982
$123$	−2.57734	−0.232391
$124$	14.8736	1.33569
$125$	−11.0167	−0.985363
$126$	−5.22814	−0.465760
$127$	2.95927	0.262592	0.131296	−	0.991343i	$-0.458086\pi$
$127$	2.95927	0.262592	0.131296	+	0.991343i	$0.458086\pi$
$128$	7.16079	0.632930
$129$	−0.562711	−0.0495439
$130$	−1.32482	−0.116194
$131$	−15.9882	−1.39689	−0.698447	−	0.715661i	$-0.746125\pi$
$131$	−15.9882	−1.39689	−0.698447	+	0.715661i	$0.746125\pi$
$132$	−1.79656	−0.156370
$133$	7.70274	0.667912
$134$	−17.0967	−1.47693
$135$	5.30461	0.456548
$136$	−4.76143	−0.408289
$137$	4.47188	0.382059	0.191029	−	0.981584i	$-0.438817\pi$
$137$	4.47188	0.382059	0.191029	+	0.981584i	$0.438817\pi$
$138$	1.94906	0.165915
$139$	−16.4102	−1.39190	−0.695949	−	0.718091i	$-0.745016\pi$
$139$	−16.4102	−1.39190	−0.695949	+	0.718091i	$0.745016\pi$
$140$	−3.27543	−0.276824
$141$	3.02448	0.254707
$142$	−16.7337	−1.40426
$143$	0.479624	0.0401082
$144$	7.29804	0.608170
$145$	−2.10978	−0.175208
$146$	15.2609	1.26300
$147$	−0.719393	−0.0593346
$148$	−18.7299	−1.53959
$149$	8.06059	0.660350	0.330175	−	0.943920i	$-0.392892\pi$
$149$	8.06059	0.660350	0.330175	+	0.943920i	$0.392892\pi$
$150$	−4.83467	−0.394749
$151$	16.1653	1.31551	0.657756	−	0.753231i	$-0.271506\pi$
$151$	16.1653	1.31551	0.657756	+	0.753231i	$0.271506\pi$
$152$	7.06200	0.572804
$153$	−12.8926	−1.04230
$154$	2.15963	0.174028
$155$	8.21425	0.659784
$156$	−0.819424	−0.0656064
$157$	−21.4454	−1.71153	−0.855765	−	0.517365i	$-0.826913\pi$
$157$	−21.4454	−1.71153	−0.855765	+	0.517365i	$0.826913\pi$
$158$	30.6161	2.43568
$159$	0.557625	0.0442225
$160$	10.7933	0.853284
$161$	−1.28646	−0.101387
$162$	−9.70896	−0.762808
$163$	18.5087	1.44971	0.724856	−	0.688900i	$-0.241906\pi$
$163$	18.5087	1.44971	0.724856	+	0.688900i	$0.241906\pi$
$164$	8.72497	0.681305
$165$	−0.992188	−0.0772417
$166$	−20.7549	−1.61090
$167$	2.61909	0.202671	0.101336	−	0.994852i	$-0.467688\pi$
$167$	2.61909	0.202671	0.101336	+	0.994852i	$0.467688\pi$
$168$	−0.659552	−0.0508855
$169$	−12.7812	−0.983172
$170$	−14.7105	−1.12825
$171$	19.1218	1.46228
$172$	1.90492	0.145249
$173$	19.4010	1.47503	0.737514	−	0.675332i	$-0.236000\pi$
$173$	19.4010	1.47503	0.737514	+	0.675332i	$0.236000\pi$
$174$	−2.37660	−0.180170
$175$	3.19108	0.241223
$176$	−3.01466	−0.227239
$177$	4.72972	0.355507
$178$	−32.0684	−2.40363
$179$	−2.39920	−0.179325	−0.0896624	−	0.995972i	$-0.528579\pi$
$179$	−2.39920	−0.179325	−0.0896624	+	0.995972i	$0.528579\pi$
$180$	−8.13117	−0.606061
$181$	23.2470	1.72794	0.863968	−	0.503547i	$-0.167972\pi$
$181$	23.2470	1.72794	0.863968	+	0.503547i	$0.167972\pi$
$182$	0.985024	0.0730149
$183$	4.14960	0.306748
$184$	−1.17944	−0.0869498
$185$	−10.3440	−0.760506
$186$	9.25309	0.678470
$187$	5.32564	0.389450
$188$	−10.2386	−0.746729
$189$	−3.94405	−0.286888
$190$	21.8182	1.58286
$191$	22.3360	1.61618	0.808088	−	0.589062i	$-0.200502\pi$
$191$	22.3360	1.61618	0.808088	+	0.589062i	$0.200502\pi$
$192$	7.92852	0.572192
$193$	10.3783	0.747045	0.373523	−	0.927621i	$-0.378150\pi$
$193$	10.3783	0.747045	0.373523	+	0.927621i	$0.378150\pi$
$194$	−19.2824	−1.38439
$195$	−0.452544	−0.0324073
$196$	2.43533	0.173952
$197$	−15.6294	−1.11355	−0.556776	−	0.830663i	$-0.687962\pi$
$197$	−15.6294	−1.11355	−0.556776	+	0.830663i	$0.687962\pi$
$198$	5.36123	0.381006
$199$	3.07147	0.217731	0.108865	−	0.994057i	$-0.465278\pi$
$199$	3.07147	0.217731	0.108865	+	0.994057i	$0.465278\pi$
$200$	2.92563	0.206873
$201$	−5.84003	−0.411924
$202$	12.8347	0.903045
$203$	1.56865	0.110098
$204$	−9.09870	−0.637037
$205$	4.81855	0.336542
$206$	1.45665	0.101489
$207$	−3.19359	−0.221970
$208$	−1.37501	−0.0953397
$209$	−7.89882	−0.546373
$210$	−2.03770	−0.140614
$211$	−13.3363	−0.918106	−0.459053	−	0.888409i	$-0.651811\pi$
$211$	−13.3363	−0.918106	−0.459053	+	0.888409i	$0.651811\pi$
$212$	−1.88770	−0.129648
$213$	−5.71602	−0.391656
$214$	−30.7215	−2.10008
$215$	1.05203	0.0717480
$216$	−3.61598	−0.246036
$217$	−6.10742	−0.414598
$218$	−34.4971	−2.33644
$219$	5.21295	0.352258
$220$	3.35881	0.226451
$221$	2.42906	0.163397
$222$	−11.6522	−0.782044
$223$	18.1411	1.21482	0.607408	−	0.794390i	$-0.292209\pi$
$223$	18.1411	1.21482	0.607408	+	0.794390i	$0.292209\pi$
$224$	−8.02497	−0.536191
$225$	7.92176	0.528117
$226$	18.0487	1.20058
$227$	−15.0584	−0.999462	−0.499731	−	0.866181i	$-0.666568\pi$
$227$	−15.0584	−0.999462	−0.499731	+	0.866181i	$0.666568\pi$
$228$	13.4949	0.893721
$229$	−24.0801	−1.59125	−0.795627	−	0.605786i	$-0.792859\pi$
$229$	−24.0801	−1.59125	−0.795627	+	0.605786i	$0.792859\pi$
$230$	−3.64391	−0.240273
$231$	0.737707	0.0485375
$232$	1.43817	0.0944205
$233$	18.2670	1.19671	0.598357	−	0.801230i	$-0.295821\pi$
$233$	18.2670	1.19671	0.598357	+	0.801230i	$0.295821\pi$
$234$	2.44530	0.159854
$235$	−5.65450	−0.368859
$236$	−16.0113	−1.04225
$237$	10.4581	0.679327
$238$	10.9375	0.708973
$239$	10.2811	0.665031	0.332515	−	0.943098i	$-0.392103\pi$
$239$	10.2811	0.665031	0.332515	+	0.943098i	$0.392103\pi$
$240$	2.84445	0.183608
$241$	14.9604	0.963686	0.481843	−	0.876258i	$-0.339968\pi$
$241$	14.9604	0.963686	0.481843	+	0.876258i	$0.339968\pi$
$242$	20.9516	1.34682
$243$	−15.1486	−0.971785
$244$	−14.0475	−0.899297
$245$	1.34496	0.0859265
$246$	5.42794	0.346073
$247$	−3.60271	−0.229235
$248$	−5.59938	−0.355561
$249$	−7.08965	−0.449288
$250$	23.2014	1.46739
$251$	−3.28647	−0.207440	−0.103720	−	0.994607i	$-0.533075\pi$
$251$	−3.28647	−0.207440	−0.103720	+	0.994607i	$0.533075\pi$
$252$	6.04564	0.380840
$253$	1.31920	0.0829376
$254$	−6.23228	−0.391048
$255$	−5.02495	−0.314674
$256$	6.96146	0.435091
$257$	−13.1271	−0.818849	−0.409424	−	0.912344i	$-0.634270\pi$
$257$	−13.1271	−0.818849	−0.409424	+	0.912344i	$0.634270\pi$
$258$	1.18508	0.0737800
$259$	7.69092	0.477890
$260$	1.53198	0.0950092
$261$	3.89414	0.241041
$262$	33.6715	2.08023
$263$	−21.2236	−1.30871	−0.654353	−	0.756189i	$-0.727059\pi$
$263$	−21.2236	−1.30871	−0.654353	+	0.756189i	$0.727059\pi$
$264$	0.676342	0.0416260
$265$	−1.04252	−0.0640417
$266$	−16.2221	−0.994643
$267$	−10.9542	−0.670386
$268$	19.7700	1.20764
$269$	3.27240	0.199522	0.0997608	−	0.995011i	$-0.468192\pi$
$269$	3.27240	0.199522	0.0997608	+	0.995011i	$0.468192\pi$
$270$	−11.1716	−0.679883
$271$	0.794456	0.0482598	0.0241299	−	0.999709i	$-0.492318\pi$
$271$	0.794456	0.0482598	0.0241299	+	0.999709i	$0.492318\pi$
$272$	−15.2678	−0.925746
$273$	0.336473	0.0203643
$274$	−9.41789	−0.568956
$275$	−3.27231	−0.197328
$276$	−2.25382	−0.135664
$277$	−12.7082	−0.763562	−0.381781	−	0.924253i	$-0.624689\pi$
$277$	−12.7082	−0.763562	−0.381781	+	0.924253i	$0.624689\pi$
$278$	34.5603	2.07279
$279$	−15.1615	−0.907695
$280$	1.23308	0.0736909
$281$	−9.12975	−0.544635	−0.272318	−	0.962207i	$-0.587790\pi$
$281$	−9.12975	−0.544635	−0.272318	+	0.962207i	$0.587790\pi$
$282$	−6.36962	−0.379305
$283$	−18.6339	−1.10767	−0.553835	−	0.832626i	$-0.686836\pi$
$283$	−18.6339	−1.10767	−0.553835	+	0.832626i	$0.686836\pi$
$284$	19.3502	1.14822
$285$	7.45284	0.441468
$286$	−1.01010	−0.0597284
$287$	−3.58266	−0.211478
$288$	−19.9218	−1.17390
$289$	9.97180	0.586577
$290$	4.44325	0.260917
$291$	−6.58664	−0.386116
$292$	−17.6472	−1.03272
$293$	−8.89138	−0.519440	−0.259720	−	0.965684i	$-0.583630\pi$
$293$	−8.89138	−0.519440	−0.259720	+	0.965684i	$0.583630\pi$
$294$	1.51506	0.0883600
$295$	−8.84258	−0.514835
$296$	7.05117	0.409841
$297$	4.04446	0.234683
$298$	−16.9758	−0.983381
$299$	0.601698	0.0347971
$300$	5.59064	0.322776
$301$	−0.782202	−0.0450854
$302$	−34.0445	−1.95904
$303$	4.38418	0.251865
$304$	22.6447	1.29876
$305$	−7.75801	−0.444222
$306$	27.1520	1.55218
$307$	24.5314	1.40008	0.700042	−	0.714102i	$-0.253165\pi$
$307$	24.5314	1.40008	0.700042	+	0.714102i	$0.253165\pi$
$308$	−2.49733	−0.142298
$309$	0.497574	0.0283060
$310$	−17.2994	−0.982539
$311$	1.13968	0.0646251	0.0323125	−	0.999478i	$-0.489713\pi$
$311$	1.13968	0.0646251	0.0323125	+	0.999478i	$0.489713\pi$
$312$	0.308484	0.0174645
$313$	30.0121	1.69638	0.848191	−	0.529690i	$-0.177692\pi$
$313$	30.0121	1.69638	0.848191	+	0.529690i	$0.177692\pi$
$314$	45.1645	2.54878
$315$	3.33883	0.188122
$316$	−35.4033	−1.99159
$317$	−26.6462	−1.49660	−0.748299	−	0.663361i	$-0.769129\pi$
$317$	−26.6462	−1.49660	−0.748299	+	0.663361i	$0.769129\pi$
$318$	−1.17437	−0.0658554
$319$	−1.60859	−0.0900636
$320$	−14.8230	−0.828631
$321$	−10.4941	−0.585724
$322$	2.70930	0.150984
$323$	−40.0037	−2.22586
$324$	11.2271	0.623728
$325$	−1.49252	−0.0827903
$326$	−38.9797	−2.15889
$327$	−11.7838	−0.651647
$328$	−3.28464	−0.181364
$329$	4.20421	0.231785
$330$	2.08957	0.115027
$331$	−16.3339	−0.897793	−0.448896	−	0.893584i	$-0.648183\pi$
$331$	−16.3339	−0.897793	−0.448896	+	0.893584i	$0.648183\pi$
$332$	24.0003	1.31719
$333$	19.0925	1.04626
$334$	−5.51586	−0.301814
$335$	10.9184	0.596536
$336$	−2.11489	−0.115377
$337$	−10.6110	−0.578017	−0.289009	−	0.957327i	$-0.593326\pi$
$337$	−10.6110	−0.578017	−0.289009	+	0.957327i	$0.593326\pi$
$338$	26.9176	1.46412
$339$	6.16524	0.334850
$340$	17.0107	0.922537
$341$	6.26289	0.339154
$342$	−40.2710	−2.17761
$343$	−1.00000	−0.0539949
$344$	−0.717136	−0.0386654
$345$	−1.24472	−0.0670134
$346$	−40.8589	−2.19659
$347$	−0.446437	−0.0239660	−0.0119830	−	0.999928i	$-0.503814\pi$
$347$	−0.446437	−0.0239660	−0.0119830	+	0.999928i	$0.503814\pi$
$348$	2.74822	0.147320
$349$	22.8669	1.22404	0.612019	−	0.790843i	$-0.290358\pi$
$349$	22.8669	1.22404	0.612019	+	0.790843i	$0.290358\pi$
$350$	−6.72048	−0.359225
$351$	1.84471	0.0984631
$352$	8.22926	0.438621
$353$	−35.9824	−1.91515	−0.957575	−	0.288184i	$-0.906949\pi$
$353$	−35.9824	−1.91515	−0.957575	+	0.288184i	$0.906949\pi$
$354$	−9.96089	−0.529416
$355$	10.6866	0.567184
$356$	37.0828	1.96538
$357$	3.73613	0.197737
$358$	5.05277	0.267047
$359$	26.6541	1.40675	0.703375	−	0.710819i	$-0.251675\pi$
$359$	26.6541	1.40675	0.703375	+	0.710819i	$0.251675\pi$
$360$	3.06110	0.161334
$361$	40.3322	2.12274
$362$	−48.9587	−2.57321
$363$	7.15684	0.375637
$364$	−1.13905	−0.0597023
$365$	−9.74602	−0.510130
$366$	−8.73916	−0.456803
$367$	13.7296	0.716678	0.358339	−	0.933591i	$-0.383343\pi$
$367$	13.7296	0.716678	0.358339	+	0.933591i	$0.383343\pi$
$368$	−3.78195	−0.197148
$369$	−8.89386	−0.462996
$370$	21.7847	1.13253
$371$	0.775132	0.0402429
$372$	−10.7000	−0.554767
$373$	30.9902	1.60461	0.802306	−	0.596912i	$-0.203606\pi$
$373$	30.9902	1.60461	0.802306	+	0.596912i	$0.203606\pi$
$374$	−11.2159	−0.579962
$375$	7.92533	0.409262
$376$	3.85449	0.198780
$377$	−0.733688	−0.0377869
$378$	8.30627	0.427228
$379$	4.50802	0.231562	0.115781	−	0.993275i	$-0.463063\pi$
$379$	4.50802	0.231562	0.115781	+	0.993275i	$0.463063\pi$
$380$	−25.2298	−1.29426
$381$	−2.12888	−0.109066
$382$	−47.0401	−2.40678
$383$	19.9675	1.02029	0.510147	−	0.860088i	$-0.329591\pi$
$383$	19.9675	1.02029	0.510147	+	0.860088i	$0.329591\pi$
$384$	−5.15142	−0.262882
$385$	−1.37920	−0.0702906
$386$	−21.8569	−1.11249
$387$	−1.94179	−0.0987070
$388$	22.2975	1.13198
$389$	−6.03188	−0.305828	−0.152914	−	0.988239i	$-0.548866\pi$
$389$	−6.03188	−0.305828	−0.152914	+	0.988239i	$0.548866\pi$
$390$	0.953067	0.0482604
$391$	6.68113	0.337879
$392$	−0.916817	−0.0463063
$393$	11.5018	0.580189
$394$	32.9160	1.65828
$395$	−19.5522	−0.983780
$396$	−6.19954	−0.311539
$397$	3.85977	0.193716	0.0968582	−	0.995298i	$-0.469121\pi$
$397$	3.85977	0.193716	0.0968582	+	0.995298i	$0.469121\pi$
$398$	−6.46859	−0.324241
$399$	−5.54130	−0.277412
$400$	9.38120	0.469060
$401$	−14.5792	−0.728049	−0.364025	−	0.931389i	$-0.618598\pi$
$401$	−14.5792	−0.728049	−0.364025	+	0.931389i	$0.618598\pi$
$402$	12.2992	0.613430
$403$	2.85655	0.142295
$404$	−14.8416	−0.738396
$405$	6.20040	0.308100
$406$	−3.30362	−0.163956
$407$	−7.88670	−0.390929
$408$	3.42534	0.169580
$409$	−20.5007	−1.01369	−0.506846	−	0.862037i	$-0.669189\pi$
$409$	−20.5007	−1.01369	−0.506846	+	0.862037i	$0.669189\pi$
$410$	−10.1480	−0.501172
$411$	−3.21704	−0.158685
$412$	−1.68442	−0.0829853
$413$	6.57459	0.323515
$414$	6.72578	0.330554
$415$	13.2547	0.650646
$416$	3.75342	0.184027
$417$	11.8054	0.578114
$418$	16.6351	0.813649
$419$	24.7535	1.20929	0.604644	−	0.796496i	$-0.293315\pi$
$419$	24.7535	1.20929	0.604644	+	0.796496i	$0.293315\pi$
$420$	2.35632	0.114977
$421$	−22.3014	−1.08690	−0.543452	−	0.839440i	$-0.682883\pi$
$421$	−22.3014	−1.08690	−0.543452	+	0.839440i	$0.682883\pi$
$422$	28.0865	1.36723
$423$	10.4368	0.507456
$424$	0.710654	0.0345124
$425$	−16.5727	−0.803892
$426$	12.0381	0.583247
$427$	5.76820	0.279143
$428$	35.5253	1.71718
$429$	−0.345039	−0.0166586
$430$	−2.21560	−0.106846
$431$	34.4242	1.65816	0.829078	−	0.559133i	$-0.188866\pi$
$431$	34.4242	1.65816	0.829078	+	0.559133i	$0.188866\pi$
$432$	−11.5948	−0.557857
$433$	−22.1074	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$433$	−22.1074	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$434$	12.8624	0.617413
$435$	1.51776	0.0727712
$436$	39.8912	1.91044
$437$	−9.90923	−0.474023
$438$	−10.9786	−0.524577
$439$	−4.72206	−0.225372	−0.112686	−	0.993631i	$-0.535945\pi$
$439$	−4.72206	−0.225372	−0.112686	+	0.993631i	$0.535945\pi$
$440$	−1.26447	−0.0602815
$441$	−2.48247	−0.118213
$442$	−5.11566	−0.243327
$443$	−8.25823	−0.392360	−0.196180	−	0.980568i	$-0.562854\pi$
$443$	−8.25823	−0.392360	−0.196180	+	0.980568i	$0.562854\pi$
$444$	13.4742	0.639457
$445$	20.4797	0.970833
$446$	−38.2055	−1.80908
$447$	−5.79874	−0.274271
$448$	11.0211	0.520699
$449$	22.2271	1.04896	0.524480	−	0.851423i	$-0.324260\pi$
$449$	22.2271	1.04896	0.524480	+	0.851423i	$0.324260\pi$
$450$	−16.6834	−0.786463
$451$	3.67386	0.172995
$452$	−20.8709	−0.981685
$453$	−11.6292	−0.546388
$454$	31.7133	1.48838
$455$	−0.629063	−0.0294909
$456$	−5.08036	−0.237909
$457$	10.6490	0.498138	0.249069	−	0.968486i	$-0.419875\pi$
$457$	10.6490	0.498138	0.249069	+	0.968486i	$0.419875\pi$
$458$	50.7131	2.36967
$459$	20.4832	0.956074
$460$	4.21369	0.196464
$461$	−17.8508	−0.831396	−0.415698	−	0.909503i	$-0.636463\pi$
$461$	−17.8508	−0.831396	−0.415698	+	0.909503i	$0.636463\pi$
$462$	−1.55363	−0.0722813
$463$	12.8076	0.595221	0.297610	−	0.954687i	$-0.403810\pi$
$463$	12.8076	0.595221	0.297610	+	0.954687i	$0.403810\pi$
$464$	4.61157	0.214087
$465$	−5.90927	−0.274036
$466$	−38.4708	−1.78212
$467$	5.74695	0.265937	0.132969	−	0.991120i	$-0.457549\pi$
$467$	5.74695	0.265937	0.132969	+	0.991120i	$0.457549\pi$
$468$	−2.82766	−0.130708
$469$	−8.11799	−0.374854
$470$	11.9085	0.549298
$471$	15.4277	0.710870
$472$	6.02770	0.277447
$473$	0.802114	0.0368812
$474$	−22.0250	−1.01164
$475$	24.5800	1.12781
$476$	−12.6477	−0.579708
$477$	1.92424	0.0881051
$478$	−21.6523	−0.990352
$479$	10.8213	0.494439	0.247220	−	0.968959i	$-0.420483\pi$
$479$	10.8213	0.494439	0.247220	+	0.968959i	$0.420483\pi$
$480$	−7.76462	−0.354405
$481$	−3.59718	−0.164017
$482$	−31.5070	−1.43510
$483$	0.925468	0.0421102
$484$	−24.2277	−1.10126
$485$	12.3142	0.559161
$486$	31.9034	1.44717
$487$	23.8525	1.08086	0.540430	−	0.841389i	$-0.318262\pi$
$487$	23.8525	1.08086	0.540430	+	0.841389i	$0.318262\pi$
$488$	5.28838	0.239394
$489$	−13.3150	−0.602126
$490$	−2.83252	−0.127960
$491$	21.7307	0.980693	0.490346	−	0.871528i	$-0.336870\pi$
$491$	21.7307	0.980693	0.490346	+	0.871528i	$0.336870\pi$
$492$	−6.27668	−0.282975
$493$	−8.14671	−0.366909
$494$	7.58738	0.341373
$495$	−3.42383	−0.153890
$496$	−17.9547	−0.806191
$497$	−7.94562	−0.356410
$498$	14.9310	0.669072
$499$	−16.4787	−0.737689	−0.368844	−	0.929491i	$-0.620246\pi$
$499$	−16.4787	−0.737689	−0.368844	+	0.929491i	$0.620246\pi$
$500$	−26.8293	−1.19984
$501$	−1.88415	−0.0841778
$502$	6.92138	0.308916
$503$	31.1068	1.38698	0.693491	−	0.720465i	$-0.256072\pi$
$503$	31.1068	1.38698	0.693491	+	0.720465i	$0.256072\pi$
$504$	−2.27597	−0.101380
$505$	−8.19657	−0.364743
$506$	−2.77827	−0.123509
$507$	9.19474	0.408353
$508$	7.20679	0.319750
$509$	9.11182	0.403874	0.201937	−	0.979398i	$-0.435276\pi$
$509$	9.11182	0.403874	0.201937	+	0.979398i	$0.435276\pi$
$510$	10.5827	0.468608
$511$	7.24631	0.320558
$512$	−28.9826	−1.28086
$513$	−30.3800	−1.34131
$514$	27.6461	1.21942
$515$	−0.930255	−0.0409919
$516$	−1.37039	−0.0603279
$517$	−4.31123	−0.189608
$518$	−16.1972	−0.711666
$519$	−13.9569	−0.612641
$520$	−0.576736	−0.0252915
$521$	35.9861	1.57658	0.788289	−	0.615305i	$-0.210967\pi$
$521$	35.9861	1.57658	0.788289	+	0.615305i	$0.210967\pi$
$522$	−8.20115	−0.358955
$523$	18.8077	0.822401	0.411201	−	0.911545i	$-0.365110\pi$
$523$	18.8077	0.822401	0.411201	+	0.911545i	$0.365110\pi$
$524$	−38.9365	−1.70095
$525$	−2.29564	−0.100190
$526$	44.6975	1.94890
$527$	31.7185	1.38168
$528$	2.16873	0.0943818
$529$	−21.3450	−0.928045
$530$	2.19558	0.0953698
$531$	16.3213	0.708282
$532$	18.7587	0.813293
$533$	1.67567	0.0725815
$534$	23.0698	0.998328
$535$	19.6196	0.848228
$536$	−7.44271	−0.321476
$537$	1.72597	0.0744811
$538$	−6.89174	−0.297124
$539$	1.02546	0.0441695
$540$	12.9185	0.555923
$541$	−6.84489	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$541$	−6.84489	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$542$	−1.67314	−0.0718677
$543$	−16.7237	−0.717684
$544$	41.6772	1.78689
$545$	22.0308	0.943695
$546$	−0.708620	−0.0303261
$547$	−2.16025	−0.0923657	−0.0461828	−	0.998933i	$-0.514706\pi$
$547$	−2.16025	−0.0923657	−0.0461828	+	0.998933i	$0.514706\pi$
$548$	10.8905	0.465220
$549$	14.3194	0.611137
$550$	6.89156	0.293857
$551$	12.0829	0.514750
$552$	0.848484	0.0361139
$553$	14.5374	0.618193
$554$	26.7638	1.13708
$555$	7.44140	0.315870
$556$	−39.9644	−1.69487
$557$	27.9839	1.18572	0.592858	−	0.805307i	$-0.298000\pi$
$557$	27.9839	1.18572	0.592858	+	0.805307i	$0.298000\pi$
$558$	31.9305	1.35172
$559$	0.365850	0.0154738
$560$	3.95395	0.167085
$561$	−3.83123	−0.161755
$562$	19.2275	0.811061
$563$	18.6299	0.785156	0.392578	−	0.919719i	$-0.371583\pi$
$563$	18.6299	0.785156	0.392578	+	0.919719i	$0.371583\pi$
$564$	7.36561	0.310148
$565$	−11.5264	−0.484919
$566$	39.2434	1.64952
$567$	−4.61009	−0.193606
$568$	−7.28468	−0.305658
$569$	−10.6372	−0.445935	−0.222968	−	0.974826i	$-0.571574\pi$
$569$	−10.6372	−0.445935	−0.222968	+	0.974826i	$0.571574\pi$
$570$	−15.6958	−0.657427
$571$	41.9841	1.75698	0.878491	−	0.477760i	$-0.158551\pi$
$571$	41.9841	1.75698	0.878491	+	0.477760i	$0.158551\pi$
$572$	1.16804	0.0488384
$573$	−16.0684	−0.671266
$574$	7.54517	0.314929
$575$	−4.10518	−0.171198
$576$	27.3596	1.13998
$577$	26.4988	1.10316	0.551579	−	0.834122i	$-0.314025\pi$
$577$	26.4988	1.10316	0.551579	+	0.834122i	$0.314025\pi$
$578$	−21.0008	−0.873520
$579$	−7.46607	−0.310279
$580$	−5.13802	−0.213345
$581$	−9.85504	−0.408856
$582$	13.8716	0.574997
$583$	−0.794864	−0.0329199
$584$	6.64354	0.274912
$585$	−1.56163	−0.0645655
$586$	18.7254	0.773541
$587$	−23.6772	−0.977263	−0.488631	−	0.872490i	$-0.662504\pi$
$587$	−23.6772	−0.977263	−0.488631	+	0.872490i	$0.662504\pi$
$588$	−1.75196	−0.0722497
$589$	−47.0438	−1.93841
$590$	18.6227	0.766683
$591$	11.2437	0.462505
$592$	22.6100	0.929263
$593$	0.496864	0.0204038	0.0102019	−	0.999948i	$-0.496753\pi$
$593$	0.496864	0.0204038	0.0102019	+	0.999948i	$0.496753\pi$
$594$	−8.51772	−0.349486
$595$	−6.98498	−0.286356
$596$	19.6302	0.804085
$597$	−2.20960	−0.0904327
$598$	−1.26719	−0.0518193
$599$	12.8701	0.525860	0.262930	−	0.964815i	$-0.415311\pi$
$599$	12.8701	0.525860	0.262930	+	0.964815i	$0.415311\pi$
$600$	−2.10468	−0.0859232
$601$	35.0928	1.43147	0.715733	−	0.698374i	$-0.246093\pi$
$601$	35.0928	1.43147	0.715733	+	0.698374i	$0.246093\pi$
$602$	1.64733	0.0671403
$603$	−20.1527	−0.820681
$604$	39.3678	1.60185
$605$	−13.3803	−0.543986
$606$	−9.23318	−0.375072
$607$	−7.14596	−0.290046	−0.145023	−	0.989428i	$-0.546326\pi$
$607$	−7.14596	−0.290046	−0.145023	+	0.989428i	$0.546326\pi$
$608$	−61.8142	−2.50690
$609$	−1.12848	−0.0457283
$610$	16.3385	0.661529
$611$	−1.96638	−0.0795513
$612$	−31.3977	−1.26918
$613$	42.3735	1.71145	0.855724	−	0.517432i	$-0.173112\pi$
$613$	42.3735	1.71145	0.855724	+	0.517432i	$0.173112\pi$
$614$	−51.6638	−2.08498
$615$	−3.46643	−0.139780
$616$	0.940156	0.0378800
$617$	36.2149	1.45796	0.728979	−	0.684536i	$-0.239995\pi$
$617$	36.2149	1.45796	0.728979	+	0.684536i	$0.239995\pi$
$618$	−1.04790	−0.0421528
$619$	42.1701	1.69496	0.847479	−	0.530828i	$-0.178119\pi$
$619$	42.1701	1.69496	0.847479	+	0.530828i	$0.178119\pi$
$620$	20.0044	0.803396
$621$	5.07385	0.203607
$622$	−2.40018	−0.0962386
$623$	−15.2270	−0.610057
$624$	0.989172	0.0395986
$625$	1.13834	0.0455336
$626$	−63.2061	−2.52622
$627$	5.68236	0.226932
$628$	−52.2267	−2.08407
$629$	−39.9423	−1.59260
$630$	−7.03166	−0.280148
$631$	41.0642	1.63474	0.817369	−	0.576114i	$-0.195432\pi$
$631$	41.0642	1.63474	0.817369	+	0.576114i	$0.195432\pi$
$632$	13.3281	0.530164
$633$	9.59402	0.381328
$634$	56.1174	2.22871
$635$	3.98010	0.157945
$636$	1.35800	0.0538483
$637$	0.467718	0.0185317
$638$	3.38772	0.134121
$639$	−19.7248	−0.780300
$640$	9.63099	0.380698
$641$	43.5983	1.72203	0.861014	−	0.508581i	$-0.169830\pi$
$641$	43.5983	1.72203	0.861014	+	0.508581i	$0.169830\pi$
$642$	22.1008	0.872251
$643$	14.0596	0.554456	0.277228	−	0.960804i	$-0.410584\pi$
$643$	14.0596	0.554456	0.277228	+	0.960804i	$0.410584\pi$
$644$	−3.13295	−0.123455
$645$	−0.756825	−0.0298000
$646$	84.2487	3.31472
$647$	1.71402	0.0673852	0.0336926	−	0.999432i	$-0.489273\pi$
$647$	1.71402	0.0673852	0.0336926	+	0.999432i	$0.489273\pi$
$648$	−4.22661	−0.166037
$649$	−6.74196	−0.264645
$650$	3.14329	0.123290
$651$	4.39363	0.172200
$652$	45.0748	1.76526
$653$	−31.5747	−1.23561	−0.617807	−	0.786330i	$-0.711979\pi$
$653$	−31.5747	−1.23561	−0.617807	+	0.786330i	$0.711979\pi$
$654$	24.8170	0.970421
$655$	−21.5035	−0.840212
$656$	−10.5324	−0.411221
$657$	17.9888	0.701809
$658$	−8.85415	−0.345171
$659$	40.5115	1.57810	0.789052	−	0.614326i	$-0.210572\pi$
$659$	40.5115	1.57810	0.789052	+	0.614326i	$0.210572\pi$
$660$	−2.41631	−0.0940546
$661$	45.3115	1.76241	0.881207	−	0.472730i	$-0.156732\pi$
$661$	45.3115	1.76241	0.881207	+	0.472730i	$0.156732\pi$
$662$	34.3996	1.33698
$663$	−1.74745	−0.0678654
$664$	−9.03527	−0.350636
$665$	10.3599	0.401739
$666$	−40.2092	−1.55808
$667$	−2.01800	−0.0781375
$668$	6.37834	0.246786
$669$	−13.0506	−0.504564
$670$	−22.9944	−0.888351
$671$	−5.91504	−0.228347
$672$	5.77311	0.222703
$673$	−4.38962	−0.169208	−0.0846038	−	0.996415i	$-0.526962\pi$
$673$	−4.38962	−0.169208	−0.0846038	+	0.996415i	$0.526962\pi$
$674$	22.3470	0.860773
$675$	−12.5858	−0.484427
$676$	−31.1266	−1.19718
$677$	12.2915	0.472401	0.236200	−	0.971704i	$-0.424098\pi$
$677$	12.2915	0.472401	0.236200	+	0.971704i	$0.424098\pi$
$678$	−12.9841	−0.498653
$679$	−9.15583	−0.351368
$680$	−6.40395	−0.245580
$681$	10.8329	0.415118
$682$	−13.1898	−0.505063
$683$	−6.83517	−0.261541	−0.130770	−	0.991413i	$-0.541745\pi$
$683$	−6.83517	−0.261541	−0.130770	+	0.991413i	$0.541745\pi$
$684$	46.5680	1.78057
$685$	6.01452	0.229803
$686$	2.10602	0.0804083
$687$	17.3230	0.660915
$688$	−2.29954	−0.0876690
$689$	−0.362543	−0.0138118
$690$	2.62141	0.0997953
$691$	33.7267	1.28302	0.641512	−	0.767113i	$-0.278308\pi$
$691$	33.7267	1.28302	0.641512	+	0.767113i	$0.278308\pi$
$692$	47.2478	1.79609
$693$	2.54567	0.0967019
$694$	0.940206	0.0356897
$695$	−22.0712	−0.837207
$696$	−1.03461	−0.0392168
$697$	18.6063	0.704765
$698$	−48.1582	−1.82282
$699$	−13.1412	−0.497045
$700$	7.77133	0.293728
$701$	−16.8256	−0.635492	−0.317746	−	0.948176i	$-0.602926\pi$
$701$	−16.8256	−0.635492	−0.317746	+	0.948176i	$0.602926\pi$
$702$	−3.88499	−0.146630
$703$	59.2411	2.23432
$704$	−11.3017	−0.425948
$705$	4.06781	0.153203
$706$	75.7798	2.85201
$707$	6.09427	0.229199
$708$	11.5184	0.432889
$709$	25.4343	0.955205	0.477602	−	0.878576i	$-0.341506\pi$
$709$	25.4343	0.955205	0.477602	+	0.878576i	$0.341506\pi$
$710$	−22.5061	−0.844640
$711$	36.0887	1.35343
$712$	−13.9604	−0.523187
$713$	7.85692	0.294244
$714$	−7.86836	−0.294466
$715$	0.645077	0.0241245
$716$	−5.84285	−0.218358
$717$	−7.39617	−0.276215
$718$	−56.1342	−2.09491
$719$	23.1028	0.861589	0.430794	−	0.902450i	$-0.358233\pi$
$719$	23.1028	0.861589	0.430794	+	0.902450i	$0.358233\pi$
$720$	9.81559	0.365805
$721$	0.691658	0.0257587
$722$	−84.9404	−3.16116
$723$	−10.7624	−0.400259
$724$	56.6141	2.10405
$725$	5.00570	0.185907
$726$	−15.0725	−0.559392
$727$	−11.6692	−0.432786	−0.216393	−	0.976306i	$-0.569429\pi$
$727$	−11.6692	−0.432786	−0.216393	+	0.976306i	$0.569429\pi$
$728$	0.428812	0.0158928
$729$	−2.93245	−0.108609
$730$	20.5253	0.759677
$731$	4.06232	0.150250
$732$	10.1057	0.373516
$733$	−0.836434	−0.0308944	−0.0154472	−	0.999881i	$-0.504917\pi$
$733$	−0.836434	−0.0308944	−0.0154472	+	0.999881i	$0.504917\pi$
$734$	−28.9148	−1.06727
$735$	−0.967557	−0.0356889
$736$	10.3238	0.380539
$737$	8.32465	0.306642
$738$	18.7307	0.689485
$739$	29.8055	1.09641	0.548206	−	0.836343i	$-0.315311\pi$
$739$	29.8055	1.09641	0.548206	+	0.836343i	$0.315311\pi$
$740$	−25.1911	−0.926042
$741$	2.59176	0.0952108
$742$	−1.63245	−0.0599290
$743$	−31.8634	−1.16895	−0.584477	−	0.811410i	$-0.698700\pi$
$743$	−31.8634	−1.16895	−0.584477	+	0.811410i	$0.698700\pi$
$744$	4.02816	0.147679
$745$	10.8412	0.397191
$746$	−65.2661	−2.38956
$747$	−24.4649	−0.895123
$748$	12.9697	0.474219
$749$	−14.5875	−0.533014
$750$	−16.6909	−0.609467
$751$	44.7826	1.63414	0.817071	−	0.576538i	$-0.195597\pi$
$751$	44.7826	1.63414	0.817071	+	0.576538i	$0.195597\pi$
$752$	12.3596	0.450709
$753$	2.36426	0.0861586
$754$	1.54516	0.0562715
$755$	21.7417	0.791262
$756$	−9.60508	−0.349333
$757$	−6.82137	−0.247927	−0.123963	−	0.992287i	$-0.539561\pi$
$757$	−6.82137	−0.247927	−0.123963	+	0.992287i	$0.539561\pi$
$758$	−9.49400	−0.344838
$759$	−0.949027	−0.0344475
$760$	9.49813	0.344533
$761$	−15.2466	−0.552689	−0.276345	−	0.961059i	$-0.589123\pi$
$761$	−15.2466	−0.552689	−0.276345	+	0.961059i	$0.589123\pi$
$762$	4.48346	0.162419
$763$	−16.3802	−0.593004
$764$	54.3956	1.96796
$765$	−17.3400	−0.626930
$766$	−42.0521	−1.51940
$767$	−3.07505	−0.111034
$768$	−5.00803	−0.180712
$769$	41.0884	1.48169	0.740843	−	0.671678i	$-0.234426\pi$
$769$	41.0884	1.48169	0.740843	+	0.671678i	$0.234426\pi$
$770$	2.90463	0.104676
$771$	9.44358	0.340102
$772$	25.2746	0.909651
$773$	−32.5549	−1.17092	−0.585459	−	0.810702i	$-0.699086\pi$
$773$	−32.5549	−1.17092	−0.585459	+	0.810702i	$0.699086\pi$
$774$	4.08946	0.146993
$775$	−19.4892	−0.700074
$776$	−8.39422	−0.301335
$777$	−5.53280	−0.198488
$778$	12.7033	0.455434
$779$	−27.5963	−0.988740
$780$	−1.10209	−0.0394613
$781$	8.14788	0.291554
$782$	−14.0706	−0.503164
$783$	−6.18686	−0.221100
$784$	−2.93982	−0.104994
$785$	−28.8433	−1.02946
$786$	−24.2231	−0.864008
$787$	−31.5949	−1.12624	−0.563118	−	0.826377i	$-0.690398\pi$
$787$	−31.5949	−1.12624	−0.563118	+	0.826377i	$0.690398\pi$
$788$	−38.0629	−1.35593
$789$	15.2681	0.543560
$790$	41.1775	1.46503
$791$	8.57005	0.304716
$792$	2.33391	0.0829319
$793$	−2.69789	−0.0958049
$794$	−8.12877	−0.288479
$795$	0.749985	0.0265992
$796$	7.48005	0.265123
$797$	−38.3864	−1.35971	−0.679857	−	0.733345i	$-0.737958\pi$
$797$	−38.3864	−1.35971	−0.679857	+	0.733345i	$0.737958\pi$
$798$	11.6701	0.413117
$799$	−21.8343	−0.772442
$800$	−25.6083	−0.905390
$801$	−37.8006	−1.33562
$802$	30.7041	1.08420
$803$	−7.43078	−0.262226
$804$	−14.2224	−0.501586
$805$	−1.73023	−0.0609828
$806$	−6.01595	−0.211903
$807$	−2.35414	−0.0828697
$808$	5.58733	0.196562
$809$	−19.9294	−0.700679	−0.350340	−	0.936623i	$-0.613934\pi$
$809$	−19.9294	−0.700679	−0.350340	+	0.936623i	$0.613934\pi$
$810$	−13.0582	−0.458818
$811$	−40.8664	−1.43501	−0.717507	−	0.696552i	$-0.754717\pi$
$811$	−40.8664	−1.43501	−0.717507	+	0.696552i	$0.754717\pi$
$812$	3.82019	0.134063
$813$	−0.571527	−0.0200443
$814$	16.6096	0.582165
$815$	24.8935	0.871981
$816$	10.9836	0.384501
$817$	−6.02509	−0.210791
$818$	43.1748	1.50957
$819$	1.16110	0.0405720
$820$	11.7348	0.409795
$821$	39.3911	1.37476	0.687380	−	0.726298i	$-0.258761\pi$
$821$	39.3911	1.37476	0.687380	+	0.726298i	$0.258761\pi$
$822$	6.77517	0.236311
$823$	−47.3633	−1.65098	−0.825491	−	0.564416i	$-0.809102\pi$
$823$	−47.3633	−1.65098	−0.825491	+	0.564416i	$0.809102\pi$
$824$	0.634124	0.0220908
$825$	2.35408	0.0819585
$826$	−13.8462	−0.481772
$827$	36.8861	1.28266	0.641328	−	0.767267i	$-0.278384\pi$
$827$	36.8861	1.28266	0.641328	+	0.767267i	$0.278384\pi$
$828$	−7.77745	−0.270285
$829$	28.9701	1.00617	0.503086	−	0.864236i	$-0.332198\pi$
$829$	28.9701	1.00617	0.503086	+	0.864236i	$0.332198\pi$
$830$	−27.9146	−0.968930
$831$	9.14220	0.317140
$832$	−5.15478	−0.178710
$833$	5.19344	0.179942
$834$	−24.8625	−0.860917
$835$	3.52257	0.121904
$836$	−19.2362	−0.665299
$837$	24.0880	0.832603
$838$	−52.1314	−1.80085
$839$	−3.26857	−0.112844	−0.0564218	−	0.998407i	$-0.517969\pi$
$839$	−3.26857	−0.112844	−0.0564218	+	0.998407i	$0.517969\pi$
$840$	−0.887073	−0.0306069
$841$	−26.5393	−0.915149
$842$	46.9673	1.61860
$843$	6.56788	0.226210
$844$	−32.4782	−1.11795
$845$	−17.1903	−0.591364
$846$	−21.9802	−0.755695
$847$	9.94844	0.341832
$848$	2.27875	0.0782527
$849$	13.4051	0.460062
$850$	34.9024	1.19714
$851$	−9.89403	−0.339163
$852$	−13.9204	−0.476905
$853$	47.3494	1.62121	0.810606	−	0.585592i	$-0.199138\pi$
$853$	47.3494	1.62121	0.810606	+	0.585592i	$0.199138\pi$
$854$	−12.1480	−0.415695
$855$	25.7182	0.879542
$856$	−13.3740	−0.457115
$857$	−2.10411	−0.0718750	−0.0359375	−	0.999354i	$-0.511442\pi$
$857$	−2.10411	−0.0718750	−0.0359375	+	0.999354i	$0.511442\pi$
$858$	0.726659	0.0248077
$859$	9.20250	0.313985	0.156993	−	0.987600i	$-0.449820\pi$
$859$	9.20250	0.313985	0.156993	+	0.987600i	$0.449820\pi$
$860$	2.56205	0.0873651
$861$	2.57734	0.0878356
$862$	−72.4982	−2.46930
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	31.6509	1.07679
$865$	26.0936	0.887208
$866$	46.5587	1.58213
$867$	−7.17365	−0.243630
$868$	−14.8736	−0.504842
$869$	−14.9075	−0.505701
$870$	−3.19644	−0.108370
$871$	3.79693	0.128654
$872$	−15.0177	−0.508562
$873$	−22.7291	−0.769263
$874$	20.8691	0.705906
$875$	11.0167	0.372432
$876$	12.6953	0.428933
$877$	−38.5682	−1.30235	−0.651177	−	0.758926i	$-0.725724\pi$
$877$	−38.5682	−1.30235	−0.651177	+	0.758926i	$0.725724\pi$
$878$	9.94477	0.335620
$879$	6.39640	0.215745
$880$	−4.05461	−0.136681
$881$	46.2466	1.55809	0.779044	−	0.626970i	$-0.215705\pi$
$881$	46.2466	1.55809	0.779044	+	0.626970i	$0.215705\pi$
$882$	5.22814	0.176041
$883$	−23.9028	−0.804393	−0.402196	−	0.915553i	$-0.631753\pi$
$883$	−23.9028	−0.804393	−0.402196	+	0.915553i	$0.631753\pi$
$884$	5.91557	0.198962
$885$	6.36129	0.213833
$886$	17.3920	0.584297
$887$	28.0853	0.943011	0.471505	−	0.881863i	$-0.343711\pi$
$887$	28.0853	0.943011	0.471505	+	0.881863i	$0.343711\pi$
$888$	−5.07256	−0.170224
$889$	−2.95927	−0.0992506
$890$	−43.1308	−1.44575
$891$	4.72745	0.158375
$892$	44.1795	1.47924
$893$	32.3839	1.08369
$894$	12.2123	0.408440
$895$	−3.22684	−0.107861
$896$	−7.16079	−0.239225
$897$	−0.432858	−0.0144527
$898$	−46.8107	−1.56209
$899$	−9.58043	−0.319525
$900$	19.2921	0.643070
$901$	−4.02560	−0.134112
$902$	−7.73724	−0.257622
$903$	0.562711	0.0187258
$904$	7.85717	0.261326
$905$	31.2663	1.03933
$906$	24.4914	0.813671
$907$	−15.3995	−0.511332	−0.255666	−	0.966765i	$-0.582295\pi$
$907$	−15.3995	−0.511332	−0.255666	+	0.966765i	$0.582295\pi$
$908$	−36.6722	−1.21701
$909$	15.1289	0.501793
$910$	1.32482	0.0439174
$911$	41.6932	1.38136	0.690679	−	0.723161i	$-0.257312\pi$
$911$	41.6932	1.38136	0.690679	+	0.723161i	$0.257312\pi$
$912$	−16.2904	−0.539431
$913$	10.1059	0.334457
$914$	−22.4270	−0.741818
$915$	5.58106	0.184504
$916$	−58.6429	−1.93762
$917$	15.9882	0.527977
$918$	−43.1381	−1.42377
$919$	−47.4800	−1.56622	−0.783111	−	0.621882i	$-0.786368\pi$
$919$	−47.4800	−1.56622	−0.783111	+	0.621882i	$0.786368\pi$
$920$	−1.58631	−0.0522990
$921$	−17.6478	−0.581514
$922$	37.5942	1.23810
$923$	3.71631	0.122324
$924$	1.79656	0.0591025
$925$	24.5423	0.806946
$926$	−26.9731	−0.886392
$927$	1.71702	0.0563944
$928$	−12.5884	−0.413235
$929$	−41.4334	−1.35939	−0.679693	−	0.733496i	$-0.737887\pi$
$929$	−41.4334	−1.35939	−0.679693	+	0.733496i	$0.737887\pi$
$930$	12.4451	0.408090
$931$	−7.70274	−0.252447
$932$	44.4863	1.45720
$933$	−0.819875	−0.0268415
$934$	−12.1032	−0.396029
$935$	7.16279	0.234248
$936$	1.06451	0.0347947
$937$	14.8045	0.483641	0.241820	−	0.970321i	$-0.422255\pi$
$937$	14.8045	0.483641	0.241820	+	0.970321i	$0.422255\pi$
$938$	17.0967	0.558226
$939$	−21.5905	−0.704579
$940$	−13.7706	−0.449147
$941$	−59.3040	−1.93326	−0.966628	−	0.256184i	$-0.917535\pi$
$941$	−59.3040	−1.93326	−0.966628	+	0.256184i	$0.917535\pi$
$942$	−32.4910	−1.05862
$943$	4.60893	0.150088
$944$	19.3282	0.629078
$945$	−5.30461	−0.172559
$946$	−1.68927	−0.0549229
$947$	−20.0954	−0.653014	−0.326507	−	0.945195i	$-0.605872\pi$
$947$	−20.0954	−0.653014	−0.326507	+	0.945195i	$0.605872\pi$
$948$	25.4689	0.827193
$949$	−3.38923	−0.110019
$950$	−51.7661	−1.67951
$951$	19.1691	0.621600
$952$	4.76143	0.154319
$953$	−12.6847	−0.410899	−0.205450	−	0.978668i	$-0.565866\pi$
$953$	−12.6847	−0.410899	−0.205450	+	0.978668i	$0.565866\pi$
$954$	−4.05250	−0.131205
$955$	30.0411	0.972107
$956$	25.0379	0.809785
$957$	1.15721	0.0374072
$958$	−22.7900	−0.736311
$959$	−4.47188	−0.144405
$960$	10.6636	0.344165
$961$	6.30053	0.203243
$962$	7.57574	0.244252
$963$	−36.2130	−1.16695
$964$	36.4336	1.17345
$965$	13.9584	0.449337
$966$	−1.94906	−0.0627098
$967$	−12.8855	−0.414370	−0.207185	−	0.978302i	$-0.566430\pi$
$967$	−12.8855	−0.414370	−0.207185	+	0.978302i	$0.566430\pi$
$968$	9.12090	0.293157
$969$	28.7784	0.924495
$970$	−25.9341	−0.832693
$971$	60.3232	1.93586	0.967932	−	0.251212i	$-0.0808290\pi$
$971$	60.3232	1.93586	0.967932	+	0.251212i	$0.0808290\pi$
$972$	−36.8919	−1.18331
$973$	16.4102	0.526088
$974$	−50.2339	−1.60960
$975$	1.07371	0.0343863
$976$	16.9575	0.542796
$977$	−28.9363	−0.925755	−0.462878	−	0.886422i	$-0.653183\pi$
$977$	−28.9363	−0.925755	−0.462878	+	0.886422i	$0.653183\pi$
$978$	28.0417	0.896676
$979$	15.6146	0.499046
$980$	3.27543	0.104630
$981$	−40.6634	−1.29828
$982$	−45.7654	−1.46043
$983$	−36.2677	−1.15676	−0.578379	−	0.815768i	$-0.696315\pi$
$983$	−36.2677	−1.15676	−0.578379	+	0.815768i	$0.696315\pi$
$984$	2.36295	0.0753281
$985$	−21.0210	−0.669785
$986$	17.1572	0.546395
$987$	−3.02448	−0.0962702
$988$	−8.77379	−0.279131
$989$	1.00627	0.0319975
$990$	7.21066	0.229170
$991$	40.6558	1.29147	0.645737	−	0.763560i	$-0.276550\pi$
$991$	40.6558	1.29147	0.645737	+	0.763560i	$0.276550\pi$
$992$	49.0118	1.55613
$993$	11.7505	0.372891
$994$	16.7337	0.530759
$995$	4.13101	0.130962
$996$	−17.2656	−0.547083
$997$	−9.12711	−0.289058	−0.144529	−	0.989501i	$-0.546167\pi$
$997$	−9.12711	−0.289058	−0.144529	+	0.989501i	$0.546167\pi$
$998$	34.7046	1.09855
$999$	−30.3334	−0.959707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.19	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.19	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10602 q^{2} -0.719393 q^{3} +2.43533 q^{4} +1.34496 q^{5} +1.51506 q^{6} -1.00000 q^{7} -0.916817 q^{8} -2.48247 q^{9} +O(q^{10})\)	\(q-2.10602 q^{2} -0.719393 q^{3} +2.43533 q^{4} +1.34496 q^{5} +1.51506 q^{6} -1.00000 q^{7} -0.916817 q^{8} -2.48247 q^{9} -2.83252 q^{10} +1.02546 q^{11} -1.75196 q^{12} +0.467718 q^{13} +2.10602 q^{14} -0.967557 q^{15} -2.93982 q^{16} +5.19344 q^{17} +5.22814 q^{18} -7.70274 q^{19} +3.27543 q^{20} +0.719393 q^{21} -2.15963 q^{22} +1.28646 q^{23} +0.659552 q^{24} -3.19108 q^{25} -0.985024 q^{26} +3.94405 q^{27} -2.43533 q^{28} -1.56865 q^{29} +2.03770 q^{30} +6.10742 q^{31} +8.02497 q^{32} -0.737707 q^{33} -10.9375 q^{34} -1.34496 q^{35} -6.04564 q^{36} -7.69092 q^{37} +16.2221 q^{38} -0.336473 q^{39} -1.23308 q^{40} +3.58266 q^{41} -1.51506 q^{42} +0.782202 q^{43} +2.49733 q^{44} -3.33883 q^{45} -2.70930 q^{46} -4.20421 q^{47} +2.11489 q^{48} +1.00000 q^{49} +6.72048 q^{50} -3.73613 q^{51} +1.13905 q^{52} -0.775132 q^{53} -8.30627 q^{54} +1.37920 q^{55} +0.916817 q^{56} +5.54130 q^{57} +3.30362 q^{58} -6.57459 q^{59} -2.35632 q^{60} -5.76820 q^{61} -12.8624 q^{62} +2.48247 q^{63} -11.0211 q^{64} +0.629063 q^{65} +1.55363 q^{66} +8.11799 q^{67} +12.6477 q^{68} -0.925468 q^{69} +2.83252 q^{70} +7.94562 q^{71} +2.27597 q^{72} -7.24631 q^{73} +16.1972 q^{74} +2.29564 q^{75} -18.7587 q^{76} -1.02546 q^{77} +0.708620 q^{78} -14.5374 q^{79} -3.95395 q^{80} +4.61009 q^{81} -7.54517 q^{82} +9.85504 q^{83} +1.75196 q^{84} +6.98498 q^{85} -1.64733 q^{86} +1.12848 q^{87} -0.940156 q^{88} +15.2270 q^{89} +7.03166 q^{90} -0.467718 q^{91} +3.13295 q^{92} -4.39363 q^{93} +8.85415 q^{94} -10.3599 q^{95} -5.77311 q^{96} +9.15583 q^{97} -2.10602 q^{98} -2.54567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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