LMFDB - Embedded newform 4015.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.654679 q^{2} +2.96699 q^{3} -1.57140 q^{4} +1.00000 q^{5} -1.94243 q^{6} -1.18438 q^{7} +2.33812 q^{8} +5.80304 q^{9} +O(q^{10})$	\(q-0.654679 q^{2} +2.96699 q^{3} -1.57140 q^{4} +1.00000 q^{5} -1.94243 q^{6} -1.18438 q^{7} +2.33812 q^{8} +5.80304 q^{9} -0.654679 q^{10} +1.00000 q^{11} -4.66232 q^{12} -4.60802 q^{13} +0.775392 q^{14} +2.96699 q^{15} +1.61207 q^{16} -7.77763 q^{17} -3.79913 q^{18} -0.268143 q^{19} -1.57140 q^{20} -3.51406 q^{21} -0.654679 q^{22} -4.92594 q^{23} +6.93717 q^{24} +1.00000 q^{25} +3.01678 q^{26} +8.31658 q^{27} +1.86114 q^{28} -6.92411 q^{29} -1.94243 q^{30} +6.56155 q^{31} -5.73163 q^{32} +2.96699 q^{33} +5.09185 q^{34} -1.18438 q^{35} -9.11886 q^{36} -3.22675 q^{37} +0.175548 q^{38} -13.6720 q^{39} +2.33812 q^{40} -2.94224 q^{41} +2.30058 q^{42} +7.92647 q^{43} -1.57140 q^{44} +5.80304 q^{45} +3.22491 q^{46} -3.76896 q^{47} +4.78301 q^{48} -5.59723 q^{49} -0.654679 q^{50} -23.0762 q^{51} +7.24103 q^{52} +9.37200 q^{53} -5.44469 q^{54} +1.00000 q^{55} -2.76923 q^{56} -0.795579 q^{57} +4.53307 q^{58} -10.8719 q^{59} -4.66232 q^{60} -12.5884 q^{61} -4.29571 q^{62} -6.87303 q^{63} +0.528227 q^{64} -4.60802 q^{65} -1.94243 q^{66} +0.584697 q^{67} +12.2217 q^{68} -14.6152 q^{69} +0.775392 q^{70} +3.89594 q^{71} +13.5682 q^{72} -1.00000 q^{73} +2.11249 q^{74} +2.96699 q^{75} +0.421359 q^{76} -1.18438 q^{77} +8.95075 q^{78} -11.1650 q^{79} +1.61207 q^{80} +7.26612 q^{81} +1.92622 q^{82} -14.4340 q^{83} +5.52197 q^{84} -7.77763 q^{85} -5.18929 q^{86} -20.5438 q^{87} +2.33812 q^{88} -12.4692 q^{89} -3.79913 q^{90} +5.45767 q^{91} +7.74060 q^{92} +19.4681 q^{93} +2.46746 q^{94} -0.268143 q^{95} -17.0057 q^{96} +3.68577 q^{97} +3.66439 q^{98} +5.80304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	−0.654679	−0.462928	−0.231464	−	0.972843i	$-0.574352\pi$
$2$	−0.654679	−0.462928	−0.231464	+	0.972843i	$0.574352\pi$
$3$	2.96699	1.71299	0.856497	−	0.516153i	$-0.172636\pi$
$3$	2.96699	1.71299	0.856497	+	0.516153i	$0.172636\pi$
$4$	−1.57140	−0.785698
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.94243	−0.792992
$7$	−1.18438	−0.447655	−0.223828	−	0.974629i	$-0.571855\pi$
$7$	−1.18438	−0.447655	−0.223828	+	0.974629i	$0.571855\pi$
$8$	2.33812	0.826649
$9$	5.80304	1.93435
$10$	−0.654679	−0.207028
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.66232	−1.34589
$13$	−4.60802	−1.27804	−0.639018	−	0.769192i	$-0.720659\pi$
$13$	−4.60802	−1.27804	−0.639018	+	0.769192i	$0.720659\pi$
$14$	0.775392	0.207232
$15$	2.96699	0.766074
$16$	1.61207	0.403019
$17$	−7.77763	−1.88635	−0.943176	−	0.332293i	$-0.892178\pi$
$17$	−7.77763	−1.88635	−0.943176	+	0.332293i	$0.892178\pi$
$18$	−3.79913	−0.895463
$19$	−0.268143	−0.0615163	−0.0307581	−	0.999527i	$-0.509792\pi$
$19$	−0.268143	−0.0615163	−0.0307581	+	0.999527i	$0.509792\pi$
$20$	−1.57140	−0.351375
$21$	−3.51406	−0.766830
$22$	−0.654679	−0.139578
$23$	−4.92594	−1.02713	−0.513565	−	0.858051i	$-0.671675\pi$
$23$	−4.92594	−1.02713	−0.513565	+	0.858051i	$0.671675\pi$
$24$	6.93717	1.41604
$25$	1.00000	0.200000
$26$	3.01678	0.591638
$27$	8.31658	1.60053
$28$	1.86114	0.351722
$29$	−6.92411	−1.28578	−0.642888	−	0.765960i	$-0.722264\pi$
$29$	−6.92411	−1.28578	−0.642888	+	0.765960i	$0.722264\pi$
$30$	−1.94243	−0.354637
$31$	6.56155	1.17849	0.589244	−	0.807955i	$-0.299426\pi$
$31$	6.56155	1.17849	0.589244	+	0.807955i	$0.299426\pi$
$32$	−5.73163	−1.01322
$33$	2.96699	0.516487
$34$	5.09185	0.873245
$35$	−1.18438	−0.200197
$36$	−9.11886	−1.51981
$37$	−3.22675	−0.530475	−0.265237	−	0.964183i	$-0.585450\pi$
$37$	−3.22675	−0.530475	−0.265237	+	0.964183i	$0.585450\pi$
$38$	0.175548	0.0284776
$39$	−13.6720	−2.18927
$40$	2.33812	0.369689
$41$	−2.94224	−0.459500	−0.229750	−	0.973250i	$-0.573791\pi$
$41$	−2.94224	−0.459500	−0.229750	+	0.973250i	$0.573791\pi$
$42$	2.30058	0.354987
$43$	7.92647	1.20878	0.604388	−	0.796690i	$-0.293418\pi$
$43$	7.92647	1.20878	0.604388	+	0.796690i	$0.293418\pi$
$44$	−1.57140	−0.236897
$45$	5.80304	0.865066
$46$	3.22491	0.475487
$47$	−3.76896	−0.549759	−0.274880	−	0.961479i	$-0.588638\pi$
$47$	−3.76896	−0.549759	−0.274880	+	0.961479i	$0.588638\pi$
$48$	4.78301	0.690368
$49$	−5.59723	−0.799605
$50$	−0.654679	−0.0925856
$51$	−23.0762	−3.23131
$52$	7.24103	1.00415
$53$	9.37200	1.28734	0.643672	−	0.765302i	$-0.277410\pi$
$53$	9.37200	1.28734	0.643672	+	0.765302i	$0.277410\pi$
$54$	−5.44469	−0.740929
$55$	1.00000	0.134840
$56$	−2.76923	−0.370054
$57$	−0.795579	−0.105377
$58$	4.53307	0.595221
$59$	−10.8719	−1.41540	−0.707698	−	0.706515i	$-0.750266\pi$
$59$	−10.8719	−1.41540	−0.707698	+	0.706515i	$0.750266\pi$
$60$	−4.66232	−0.601902
$61$	−12.5884	−1.61178	−0.805890	−	0.592065i	$-0.798313\pi$
$61$	−12.5884	−1.61178	−0.805890	+	0.592065i	$0.798313\pi$
$62$	−4.29571	−0.545555
$63$	−6.87303	−0.865920
$64$	0.528227	0.0660284
$65$	−4.60802	−0.571555
$66$	−1.94243	−0.239096
$67$	0.584697	0.0714321	0.0357161	−	0.999362i	$-0.488629\pi$
$67$	0.584697	0.0714321	0.0357161	+	0.999362i	$0.488629\pi$
$68$	12.2217	1.48210
$69$	−14.6152	−1.75947
$70$	0.775392	0.0926770
$71$	3.89594	0.462363	0.231182	−	0.972911i	$-0.425741\pi$
$71$	3.89594	0.462363	0.231182	+	0.972911i	$0.425741\pi$
$72$	13.5682	1.59903
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	2.11249	0.245572
$75$	2.96699	0.342599
$76$	0.421359	0.0483332
$77$	−1.18438	−0.134973
$78$	8.95075	1.01347
$79$	−11.1650	−1.25616	−0.628078	−	0.778151i	$-0.716158\pi$
$79$	−11.1650	−1.25616	−0.628078	+	0.778151i	$0.716158\pi$
$80$	1.61207	0.180235
$81$	7.26612	0.807347
$82$	1.92622	0.212715
$83$	−14.4340	−1.58433	−0.792167	−	0.610304i	$-0.791047\pi$
$83$	−14.4340	−1.58433	−0.792167	+	0.610304i	$0.791047\pi$
$84$	5.52197	0.602497
$85$	−7.77763	−0.843602
$86$	−5.18929	−0.559576
$87$	−20.5438	−2.20252
$88$	2.33812	0.249244
$89$	−12.4692	−1.32173	−0.660866	−	0.750504i	$-0.729811\pi$
$89$	−12.4692	−1.32173	−0.660866	+	0.750504i	$0.729811\pi$
$90$	−3.79913	−0.400463
$91$	5.45767	0.572119
$92$	7.74060	0.807013
$93$	19.4681	2.01874
$94$	2.46746	0.254499
$95$	−0.268143	−0.0275109
$96$	−17.0057	−1.73564
$97$	3.68577	0.374233	0.187117	−	0.982338i	$-0.440086\pi$
$97$	3.68577	0.374233	0.187117	+	0.982338i	$0.440086\pi$
$98$	3.66439	0.370159
$99$	5.80304	0.583227
$100$	−1.57140	−0.157140
$101$	10.9044	1.08503	0.542516	−	0.840045i	$-0.317472\pi$
$101$	10.9044	1.08503	0.542516	+	0.840045i	$0.317472\pi$
$102$	15.1075	1.49586
$103$	13.8037	1.36012	0.680058	−	0.733159i	$-0.261955\pi$
$103$	13.8037	1.36012	0.680058	+	0.733159i	$0.261955\pi$
$104$	−10.7741	−1.05649
$105$	−3.51406	−0.342937
$106$	−6.13565	−0.595947
$107$	6.18906	0.598319	0.299160	−	0.954203i	$-0.403294\pi$
$107$	6.18906	0.598319	0.299160	+	0.954203i	$0.403294\pi$
$108$	−13.0686	−1.25753
$109$	18.1685	1.74023	0.870113	−	0.492853i	$-0.164046\pi$
$109$	18.1685	1.74023	0.870113	+	0.492853i	$0.164046\pi$
$110$	−0.654679	−0.0624212
$111$	−9.57374	−0.908700
$112$	−1.90932	−0.180413
$113$	9.44149	0.888181	0.444090	−	0.895982i	$-0.353527\pi$
$113$	9.44149	0.888181	0.444090	+	0.895982i	$0.353527\pi$
$114$	0.520849	0.0487820
$115$	−4.92594	−0.459346
$116$	10.8805	1.01023
$117$	−26.7405	−2.47216
$118$	7.11758	0.655227
$119$	9.21170	0.844435
$120$	6.93717	0.633274
$121$	1.00000	0.0909091
$122$	8.24136	0.746138
$123$	−8.72959	−0.787120
$124$	−10.3108	−0.925936
$125$	1.00000	0.0894427
$126$	4.49963	0.400859
$127$	−19.4582	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$127$	−19.4582	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$128$	11.1174	0.982652
$129$	23.5178	2.07062
$130$	3.01678	0.264589
$131$	0.173708	0.0151769	0.00758845	−	0.999971i	$-0.497584\pi$
$131$	0.173708	0.0151769	0.00758845	+	0.999971i	$0.497584\pi$
$132$	−4.66232	−0.405803
$133$	0.317585	0.0275381
$134$	−0.382789	−0.0330679
$135$	8.31658	0.715778
$136$	−18.1850	−1.55935
$137$	3.88243	0.331699	0.165849	−	0.986151i	$-0.446963\pi$
$137$	3.88243	0.331699	0.165849	+	0.986151i	$0.446963\pi$
$138$	9.56828	0.814506
$139$	−13.4937	−1.14452	−0.572259	−	0.820073i	$-0.693933\pi$
$139$	−13.4937	−1.14452	−0.572259	+	0.820073i	$0.693933\pi$
$140$	1.86114	0.157295
$141$	−11.1825	−0.941733
$142$	−2.55059	−0.214041
$143$	−4.60802	−0.385342
$144$	9.35493	0.779577
$145$	−6.92411	−0.575016
$146$	0.654679	0.0541816
$147$	−16.6069	−1.36972
$148$	5.07050	0.416793
$149$	13.5106	1.10684	0.553418	−	0.832904i	$-0.313323\pi$
$149$	13.5106	1.10684	0.553418	+	0.832904i	$0.313323\pi$
$150$	−1.94243	−0.158598
$151$	12.8662	1.04704	0.523518	−	0.852015i	$-0.324619\pi$
$151$	12.8662	1.04704	0.523518	+	0.852015i	$0.324619\pi$
$152$	−0.626951	−0.0508524
$153$	−45.1339	−3.64886
$154$	0.775392	0.0624828
$155$	6.56155	0.527036
$156$	21.4841	1.72010
$157$	6.17185	0.492568	0.246284	−	0.969198i	$-0.420790\pi$
$157$	6.17185	0.492568	0.246284	+	0.969198i	$0.420790\pi$
$158$	7.30946	0.581510
$159$	27.8067	2.20521
$160$	−5.73163	−0.453125
$161$	5.83421	0.459800
$162$	−4.75698	−0.373744
$163$	−5.41929	−0.424471	−0.212236	−	0.977219i	$-0.568074\pi$
$163$	−5.41929	−0.424471	−0.212236	+	0.977219i	$0.568074\pi$
$164$	4.62341	0.361028
$165$	2.96699	0.230980
$166$	9.44962	0.733432
$167$	10.5815	0.818820	0.409410	−	0.912351i	$-0.365735\pi$
$167$	10.5815	0.818820	0.409410	+	0.912351i	$0.365735\pi$
$168$	−8.21628	−0.633900
$169$	8.23388	0.633375
$170$	5.09185	0.390527
$171$	−1.55605	−0.118994
$172$	−12.4556	−0.949732
$173$	13.8283	1.05134	0.525671	−	0.850688i	$-0.323814\pi$
$173$	13.8283	1.05134	0.525671	+	0.850688i	$0.323814\pi$
$174$	13.4496	1.01961
$175$	−1.18438	−0.0895310
$176$	1.61207	0.121515
$177$	−32.2567	−2.42456
$178$	8.16332	0.611867
$179$	−21.8832	−1.63563	−0.817813	−	0.575484i	$-0.804814\pi$
$179$	−21.8832	−1.63563	−0.817813	+	0.575484i	$0.804814\pi$
$180$	−9.11886	−0.679680
$181$	−5.42899	−0.403534	−0.201767	−	0.979434i	$-0.564668\pi$
$181$	−5.42899	−0.403534	−0.201767	+	0.979434i	$0.564668\pi$
$182$	−3.57302	−0.264850
$183$	−37.3497	−2.76097
$184$	−11.5174	−0.849076
$185$	−3.22675	−0.237235
$186$	−12.7453	−0.934533
$187$	−7.77763	−0.568757
$188$	5.92252	0.431944
$189$	−9.85003	−0.716484
$190$	0.175548	0.0127356
$191$	−25.5063	−1.84557	−0.922785	−	0.385315i	$-0.874093\pi$
$191$	−25.5063	−1.84557	−0.922785	+	0.385315i	$0.874093\pi$
$192$	1.56725	0.113106
$193$	14.8984	1.07241	0.536205	−	0.844088i	$-0.319857\pi$
$193$	14.8984	1.07241	0.536205	+	0.844088i	$0.319857\pi$
$194$	−2.41300	−0.173243
$195$	−13.6720	−0.979070
$196$	8.79547	0.628248
$197$	20.2360	1.44175	0.720877	−	0.693063i	$-0.243739\pi$
$197$	20.2360	1.44175	0.720877	+	0.693063i	$0.243739\pi$
$198$	−3.79913	−0.269992
$199$	6.86991	0.486995	0.243497	−	0.969902i	$-0.421705\pi$
$199$	6.86991	0.486995	0.243497	+	0.969902i	$0.421705\pi$
$200$	2.33812	0.165330
$201$	1.73479	0.122363
$202$	−7.13891	−0.502292
$203$	8.20081	0.575584
$204$	36.2618	2.53883
$205$	−2.94224	−0.205495
$206$	−9.03697	−0.629636
$207$	−28.5854	−1.98682
$208$	−7.42847	−0.515072
$209$	−0.268143	−0.0185479
$210$	2.30058	0.158755
$211$	−17.0203	−1.17172	−0.585862	−	0.810411i	$-0.699244\pi$
$211$	−17.0203	−1.17172	−0.585862	+	0.810411i	$0.699244\pi$
$212$	−14.7271	−1.01146
$213$	11.5592	0.792025
$214$	−4.05185	−0.276979
$215$	7.92647	0.540581
$216$	19.4452	1.32308
$217$	−7.77139	−0.527557
$218$	−11.8945	−0.805599
$219$	−2.96699	−0.200491
$220$	−1.57140	−0.105943
$221$	35.8395	2.41083
$222$	6.26773	0.420662
$223$	22.6403	1.51611	0.758054	−	0.652191i	$-0.226150\pi$
$223$	22.6403	1.51611	0.758054	+	0.652191i	$0.226150\pi$
$224$	6.78845	0.453572
$225$	5.80304	0.386869
$226$	−6.18115	−0.411164
$227$	−10.2398	−0.679638	−0.339819	−	0.940491i	$-0.610366\pi$
$227$	−10.2398	−0.679638	−0.339819	+	0.940491i	$0.610366\pi$
$228$	1.25017	0.0827945
$229$	−23.9264	−1.58110	−0.790551	−	0.612396i	$-0.790206\pi$
$229$	−23.9264	−1.58110	−0.790551	+	0.612396i	$0.790206\pi$
$230$	3.22491	0.212644
$231$	−3.51406	−0.231208
$232$	−16.1894	−1.06289
$233$	−16.2596	−1.06520	−0.532601	−	0.846366i	$-0.678785\pi$
$233$	−16.2596	−1.06520	−0.532601	+	0.846366i	$0.678785\pi$
$234$	17.5065	1.14443
$235$	−3.76896	−0.245860
$236$	17.0840	1.11207
$237$	−33.1263	−2.15179
$238$	−6.03071	−0.390913
$239$	7.33025	0.474154	0.237077	−	0.971491i	$-0.423811\pi$
$239$	7.33025	0.474154	0.237077	+	0.971491i	$0.423811\pi$
$240$	4.78301	0.308742
$241$	−22.3137	−1.43735	−0.718674	−	0.695347i	$-0.755251\pi$
$241$	−22.3137	−1.43735	−0.718674	+	0.695347i	$0.755251\pi$
$242$	−0.654679	−0.0420844
$243$	−3.39123	−0.217547
$244$	19.7814	1.26637
$245$	−5.59723	−0.357594
$246$	5.71508	0.364380
$247$	1.23561	0.0786200
$248$	15.3417	0.974197
$249$	−42.8255	−2.71395
$250$	−0.654679	−0.0414055
$251$	−17.4073	−1.09874	−0.549370	−	0.835579i	$-0.685132\pi$
$251$	−17.4073	−1.09874	−0.549370	+	0.835579i	$0.685132\pi$
$252$	10.8002	0.680351
$253$	−4.92594	−0.309691
$254$	12.7388	0.799306
$255$	−23.0762	−1.44509
$256$	−8.33481	−0.520925
$257$	−4.06762	−0.253731	−0.126865	−	0.991920i	$-0.540492\pi$
$257$	−4.06762	−0.253731	−0.126865	+	0.991920i	$0.540492\pi$
$258$	−15.3966	−0.958550
$259$	3.82171	0.237470
$260$	7.24103	0.449069
$261$	−40.1809	−2.48713
$262$	−0.113723	−0.00702581
$263$	−30.8340	−1.90130	−0.950651	−	0.310261i	$-0.899584\pi$
$263$	−30.8340	−1.90130	−0.950651	+	0.310261i	$0.899584\pi$
$264$	6.93717	0.426954
$265$	9.37200	0.575718
$266$	−0.207916	−0.0127482
$267$	−36.9960	−2.26412
$268$	−0.918790	−0.0561240
$269$	0.552399	0.0336804	0.0168402	−	0.999858i	$-0.494639\pi$
$269$	0.552399	0.0336804	0.0168402	+	0.999858i	$0.494639\pi$
$270$	−5.44469	−0.331354
$271$	4.50829	0.273859	0.136930	−	0.990581i	$-0.456277\pi$
$271$	4.50829	0.273859	0.136930	+	0.990581i	$0.456277\pi$
$272$	−12.5381	−0.760235
$273$	16.1929	0.980036
$274$	−2.54175	−0.153553
$275$	1.00000	0.0603023
$276$	22.9663	1.38241
$277$	−15.5527	−0.934470	−0.467235	−	0.884133i	$-0.654750\pi$
$277$	−15.5527	−0.934470	−0.467235	+	0.884133i	$0.654750\pi$
$278$	8.83402	0.529829
$279$	38.0769	2.27960
$280$	−2.76923	−0.165493
$281$	2.61186	0.155811	0.0779054	−	0.996961i	$-0.475177\pi$
$281$	2.61186	0.155811	0.0779054	+	0.996961i	$0.475177\pi$
$282$	7.32093	0.435955
$283$	−19.7876	−1.17625	−0.588124	−	0.808771i	$-0.700133\pi$
$283$	−19.7876	−1.17625	−0.588124	+	0.808771i	$0.700133\pi$
$284$	−6.12207	−0.363278
$285$	−0.795579	−0.0471260
$286$	3.01678	0.178386
$287$	3.48474	0.205698
$288$	−33.2608	−1.95991
$289$	43.4915	2.55832
$290$	4.53307	0.266191
$291$	10.9357	0.641059
$292$	1.57140	0.0919590
$293$	26.9227	1.57284	0.786419	−	0.617693i	$-0.211933\pi$
$293$	26.9227	1.57284	0.786419	+	0.617693i	$0.211933\pi$
$294$	10.8722	0.634081
$295$	−10.8719	−0.632984
$296$	−7.54452	−0.438517
$297$	8.31658	0.482577
$298$	−8.84514	−0.512385
$299$	22.6989	1.31271
$300$	−4.66232	−0.269179
$301$	−9.38798	−0.541114
$302$	−8.42322	−0.484702
$303$	32.3534	1.85865
$304$	−0.432267	−0.0247922
$305$	−12.5884	−0.720810
$306$	29.5482	1.68916
$307$	−14.3423	−0.818559	−0.409280	−	0.912409i	$-0.634220\pi$
$307$	−14.3423	−0.818559	−0.409280	+	0.912409i	$0.634220\pi$
$308$	1.86114	0.106048
$309$	40.9554	2.32987
$310$	−4.29571	−0.243980
$311$	−6.83511	−0.387584	−0.193792	−	0.981043i	$-0.562079\pi$
$311$	−6.83511	−0.387584	−0.193792	+	0.981043i	$0.562079\pi$
$312$	−31.9667	−1.80976
$313$	21.7077	1.22699	0.613497	−	0.789697i	$-0.289762\pi$
$313$	21.7077	1.22699	0.613497	+	0.789697i	$0.289762\pi$
$314$	−4.04058	−0.228023
$315$	−6.87303	−0.387251
$316$	17.5446	0.986958
$317$	16.1290	0.905895	0.452947	−	0.891537i	$-0.350373\pi$
$317$	16.1290	0.905895	0.452947	+	0.891537i	$0.350373\pi$
$318$	−18.2044	−1.02085
$319$	−6.92411	−0.387676
$320$	0.528227	0.0295288
$321$	18.3629	1.02492
$322$	−3.81953	−0.212854
$323$	2.08552	0.116041
$324$	−11.4180	−0.634331
$325$	−4.60802	−0.255607
$326$	3.54789	0.196500
$327$	53.9057	2.98099
$328$	−6.87929	−0.379845
$329$	4.46389	0.246102
$330$	−1.94243	−0.106927
$331$	−9.58667	−0.526931	−0.263466	−	0.964669i	$-0.584866\pi$
$331$	−9.58667	−0.526931	−0.263466	+	0.964669i	$0.584866\pi$
$332$	22.6815	1.24481
$333$	−18.7250	−1.02612
$334$	−6.92748	−0.379055
$335$	0.584697	0.0319454
$336$	−5.66492	−0.309047
$337$	31.3758	1.70915	0.854575	−	0.519328i	$-0.173818\pi$
$337$	31.3758	1.70915	0.854575	+	0.519328i	$0.173818\pi$
$338$	−5.39055	−0.293207
$339$	28.0128	1.52145
$340$	12.2217	0.662816
$341$	6.56155	0.355328
$342$	1.01871	0.0550856
$343$	14.9200	0.805602
$344$	18.5330	0.999233
$345$	−14.6152	−0.786857
$346$	−9.05307	−0.486696
$347$	31.9214	1.71363	0.856817	−	0.515621i	$-0.172439\pi$
$347$	31.9214	1.71363	0.856817	+	0.515621i	$0.172439\pi$
$348$	32.2824	1.73052
$349$	−5.84868	−0.313073	−0.156536	−	0.987672i	$-0.550033\pi$
$349$	−5.84868	−0.313073	−0.156536	+	0.987672i	$0.550033\pi$
$350$	0.775392	0.0414464
$351$	−38.3230	−2.04553
$352$	−5.73163	−0.305497
$353$	−29.9477	−1.59396	−0.796978	−	0.604008i	$-0.793569\pi$
$353$	−29.9477	−1.59396	−0.796978	+	0.604008i	$0.793569\pi$
$354$	21.1178	1.12240
$355$	3.89594	0.206775
$356$	19.5940	1.03848
$357$	27.3310	1.44651
$358$	14.3265	0.757177
$359$	−27.4269	−1.44754	−0.723768	−	0.690043i	$-0.757591\pi$
$359$	−27.4269	−1.44754	−0.723768	+	0.690043i	$0.757591\pi$
$360$	13.5682	0.715106
$361$	−18.9281	−0.996216
$362$	3.55425	0.186807
$363$	2.96699	0.155727
$364$	−8.57616	−0.449513
$365$	−1.00000	−0.0523424
$366$	24.4521	1.27813
$367$	9.03418	0.471580	0.235790	−	0.971804i	$-0.424232\pi$
$367$	9.03418	0.471580	0.235790	+	0.971804i	$0.424232\pi$
$368$	−7.94098	−0.413952
$369$	−17.0739	−0.888832
$370$	2.11249	0.109823
$371$	−11.1001	−0.576286
$372$	−30.5920	−1.58612
$373$	34.5101	1.78687	0.893433	−	0.449197i	$-0.148290\pi$
$373$	34.5101	1.78687	0.893433	+	0.449197i	$0.148290\pi$
$374$	5.09185	0.263293
$375$	2.96699	0.153215
$376$	−8.81227	−0.454458
$377$	31.9065	1.64327
$378$	6.44861	0.331681
$379$	−9.03625	−0.464161	−0.232081	−	0.972697i	$-0.574553\pi$
$379$	−9.03625	−0.464161	−0.232081	+	0.972697i	$0.574553\pi$
$380$	0.421359	0.0216153
$381$	−57.7322	−2.95771
$382$	16.6984	0.854366
$383$	16.4421	0.840151	0.420075	−	0.907489i	$-0.362004\pi$
$383$	16.4421	0.840151	0.420075	+	0.907489i	$0.362004\pi$
$384$	32.9853	1.68328
$385$	−1.18438	−0.0603618
$386$	−9.75367	−0.496449
$387$	45.9976	2.33819
$388$	−5.79180	−0.294034
$389$	20.7936	1.05428	0.527139	−	0.849779i	$-0.323265\pi$
$389$	20.7936	1.05428	0.527139	+	0.849779i	$0.323265\pi$
$390$	8.95075	0.453239
$391$	38.3121	1.93753
$392$	−13.0870	−0.660993
$393$	0.515389	0.0259979
$394$	−13.2481	−0.667428
$395$	−11.1650	−0.561770
$396$	−9.11886	−0.458240
$397$	−18.1846	−0.912657	−0.456329	−	0.889811i	$-0.650836\pi$
$397$	−18.1846	−0.912657	−0.456329	+	0.889811i	$0.650836\pi$
$398$	−4.49758	−0.225443
$399$	0.942271	0.0471726
$400$	1.61207	0.0806037
$401$	−15.9260	−0.795306	−0.397653	−	0.917536i	$-0.630175\pi$
$401$	−15.9260	−0.795306	−0.397653	+	0.917536i	$0.630175\pi$
$402$	−1.13573	−0.0566451
$403$	−30.2358	−1.50615
$404$	−17.1352	−0.852507
$405$	7.26612	0.361057
$406$	−5.36890	−0.266454
$407$	−3.22675	−0.159944
$408$	−53.9548	−2.67116
$409$	−13.6687	−0.675873	−0.337937	−	0.941169i	$-0.609729\pi$
$409$	−13.6687	−0.675873	−0.337937	+	0.941169i	$0.609729\pi$
$410$	1.92622	0.0951292
$411$	11.5191	0.568197
$412$	−21.6910	−1.06864
$413$	12.8765	0.633609
$414$	18.7143	0.919756
$415$	−14.4340	−0.708536
$416$	26.4115	1.29493
$417$	−40.0356	−1.96055
$418$	0.175548	0.00858632
$419$	0.330454	0.0161437	0.00807186	−	0.999967i	$-0.497431\pi$
$419$	0.330454	0.0161437	0.00807186	+	0.999967i	$0.497431\pi$
$420$	5.52197	0.269445
$421$	24.0104	1.17020	0.585098	−	0.810962i	$-0.301056\pi$
$421$	24.0104	1.17020	0.585098	+	0.810962i	$0.301056\pi$
$422$	11.1428	0.542424
$423$	−21.8714	−1.06342
$424$	21.9128	1.06418
$425$	−7.77763	−0.377270
$426$	−7.56758	−0.366651
$427$	14.9095	0.721522
$428$	−9.72546	−0.470098
$429$	−13.6720	−0.660089
$430$	−5.18929	−0.250250
$431$	−4.24954	−0.204693	−0.102346	−	0.994749i	$-0.532635\pi$
$431$	−4.24954	−0.204693	−0.102346	+	0.994749i	$0.532635\pi$
$432$	13.4070	0.645042
$433$	−37.3354	−1.79422	−0.897112	−	0.441803i	$-0.854339\pi$
$433$	−37.3354	−1.79422	−0.897112	+	0.441803i	$0.854339\pi$
$434$	5.08777	0.244221
$435$	−20.5438	−0.984999
$436$	−28.5499	−1.36729
$437$	1.32086	0.0631852
$438$	1.94243	0.0928127
$439$	36.6754	1.75042	0.875211	−	0.483742i	$-0.160723\pi$
$439$	36.6754	1.75042	0.875211	+	0.483742i	$0.160723\pi$
$440$	2.33812	0.111465
$441$	−32.4810	−1.54671
$442$	−23.4634	−1.11604
$443$	−23.3291	−1.10840	−0.554199	−	0.832384i	$-0.686975\pi$
$443$	−23.3291	−1.10840	−0.554199	+	0.832384i	$0.686975\pi$
$444$	15.0441	0.713963
$445$	−12.4692	−0.591097
$446$	−14.8222	−0.701849
$447$	40.0860	1.89600
$448$	−0.625624	−0.0295580
$449$	2.37424	0.112047	0.0560237	−	0.998429i	$-0.482158\pi$
$449$	2.37424	0.112047	0.0560237	+	0.998429i	$0.482158\pi$
$450$	−3.79913	−0.179093
$451$	−2.94224	−0.138544
$452$	−14.8363	−0.697842
$453$	38.1739	1.79356
$454$	6.70376	0.314623
$455$	5.45767	0.255860
$456$	−1.86016	−0.0871098
$457$	−33.7710	−1.57974	−0.789869	−	0.613275i	$-0.789852\pi$
$457$	−33.7710	−1.57974	−0.789869	+	0.613275i	$0.789852\pi$
$458$	15.6641	0.731937
$459$	−64.6833	−3.01916
$460$	7.74060	0.360907
$461$	−28.0192	−1.30498	−0.652492	−	0.757796i	$-0.726276\pi$
$461$	−28.0192	−1.30498	−0.652492	+	0.757796i	$0.726276\pi$
$462$	2.30058	0.107033
$463$	−27.3891	−1.27288	−0.636439	−	0.771327i	$-0.719593\pi$
$463$	−27.3891	−1.27288	−0.636439	+	0.771327i	$0.719593\pi$
$464$	−11.1622	−0.518191
$465$	19.4681	0.902809
$466$	10.6448	0.493112
$467$	23.8382	1.10310	0.551551	−	0.834141i	$-0.314036\pi$
$467$	23.8382	1.10310	0.551551	+	0.834141i	$0.314036\pi$
$468$	42.0199	1.94237
$469$	−0.692506	−0.0319770
$470$	2.46746	0.113815
$471$	18.3118	0.843765
$472$	−25.4197	−1.17004
$473$	7.92647	0.364459
$474$	21.6871	0.996122
$475$	−0.268143	−0.0123033
$476$	−14.4752	−0.663471
$477$	54.3861	2.49017
$478$	−4.79896	−0.219499
$479$	30.6573	1.40077	0.700384	−	0.713766i	$-0.253012\pi$
$479$	30.6573	1.40077	0.700384	+	0.713766i	$0.253012\pi$
$480$	−17.0057	−0.776200
$481$	14.8689	0.677966
$482$	14.6083	0.665389
$483$	17.3100	0.787634
$484$	−1.57140	−0.0714271
$485$	3.68577	0.167362
$486$	2.22017	0.100709
$487$	26.0502	1.18045	0.590224	−	0.807240i	$-0.299040\pi$
$487$	26.0502	1.18045	0.590224	+	0.807240i	$0.299040\pi$
$488$	−29.4332	−1.33238
$489$	−16.0790	−0.727117
$490$	3.66439	0.165540
$491$	10.8633	0.490255	0.245128	−	0.969491i	$-0.421170\pi$
$491$	10.8633	0.490255	0.245128	+	0.969491i	$0.421170\pi$
$492$	13.7176	0.618439
$493$	53.8532	2.42543
$494$	−0.808928	−0.0363954
$495$	5.80304	0.260827
$496$	10.5777	0.474953
$497$	−4.61429	−0.206979
$498$	28.0369	1.25636
$499$	15.6987	0.702772	0.351386	−	0.936231i	$-0.385711\pi$
$499$	15.6987	0.702772	0.351386	+	0.936231i	$0.385711\pi$
$500$	−1.57140	−0.0702749
$501$	31.3952	1.40263
$502$	11.3962	0.508638
$503$	−37.6237	−1.67756	−0.838780	−	0.544471i	$-0.816731\pi$
$503$	−37.6237	−1.67756	−0.838780	+	0.544471i	$0.816731\pi$
$504$	−16.0699	−0.715812
$505$	10.9044	0.485241
$506$	3.22491	0.143365
$507$	24.4298	1.08497
$508$	30.5764	1.35661
$509$	−27.0004	−1.19677	−0.598385	−	0.801209i	$-0.704191\pi$
$509$	−27.0004	−1.19677	−0.598385	+	0.801209i	$0.704191\pi$
$510$	15.1075	0.668970
$511$	1.18438	0.0523941
$512$	−16.7782	−0.741501
$513$	−2.23004	−0.0984585
$514$	2.66298	0.117459
$515$	13.8037	0.608262
$516$	−36.9557	−1.62688
$517$	−3.76896	−0.165759
$518$	−2.50200	−0.109931
$519$	41.0283	1.80094
$520$	−10.7741	−0.472476
$521$	11.5250	0.504918	0.252459	−	0.967608i	$-0.418761\pi$
$521$	11.5250	0.504918	0.252459	+	0.967608i	$0.418761\pi$
$522$	26.3056	1.15136
$523$	17.4149	0.761499	0.380749	−	0.924678i	$-0.375666\pi$
$523$	17.4149	0.761499	0.380749	+	0.924678i	$0.375666\pi$
$524$	−0.272963	−0.0119245
$525$	−3.51406	−0.153366
$526$	20.1863	0.880166
$527$	−51.0333	−2.22304
$528$	4.78301	0.208154
$529$	1.26490	0.0549955
$530$	−6.13565	−0.266516
$531$	−63.0898	−2.73787
$532$	−0.499051	−0.0216366
$533$	13.5579	0.587257
$534$	24.2205	1.04812
$535$	6.18906	0.267576
$536$	1.36709	0.0590493
$537$	−64.9272	−2.80182
$538$	−0.361644	−0.0155916
$539$	−5.59723	−0.241090
$540$	−13.0686	−0.562385
$541$	5.17467	0.222477	0.111238	−	0.993794i	$-0.464518\pi$
$541$	5.17467	0.222477	0.111238	+	0.993794i	$0.464518\pi$
$542$	−2.95149	−0.126777
$543$	−16.1078	−0.691251
$544$	44.5785	1.91129
$545$	18.1685	0.778253
$546$	−10.6011	−0.453686
$547$	17.5442	0.750135	0.375067	−	0.926998i	$-0.377620\pi$
$547$	17.5442	0.750135	0.375067	+	0.926998i	$0.377620\pi$
$548$	−6.10084	−0.260615
$549$	−73.0510	−3.11774
$550$	−0.654679	−0.0279156
$551$	1.85665	0.0790961
$552$	−34.1721	−1.45446
$553$	13.2236	0.562325
$554$	10.1820	0.432592
$555$	−9.57374	−0.406383
$556$	21.2039	0.899244
$557$	−21.8143	−0.924303	−0.462152	−	0.886801i	$-0.652922\pi$
$557$	−21.8143	−0.924303	−0.462152	+	0.886801i	$0.652922\pi$
$558$	−24.9281	−1.05529
$559$	−36.5254	−1.54486
$560$	−1.90932	−0.0806833
$561$	−23.0762	−0.974276
$562$	−1.70993	−0.0721292
$563$	−2.66904	−0.112486	−0.0562432	−	0.998417i	$-0.517912\pi$
$563$	−2.66904	−0.112486	−0.0562432	+	0.998417i	$0.517912\pi$
$564$	17.5721	0.739918
$565$	9.44149	0.397206
$566$	12.9545	0.544518
$567$	−8.60588	−0.361413
$568$	9.10917	0.382212
$569$	−30.1292	−1.26308	−0.631542	−	0.775342i	$-0.717578\pi$
$569$	−30.1292	−1.26308	−0.631542	+	0.775342i	$0.717578\pi$
$570$	0.520849	0.0218160
$571$	16.8678	0.705897	0.352948	−	0.935643i	$-0.385179\pi$
$571$	16.8678	0.705897	0.352948	+	0.935643i	$0.385179\pi$
$572$	7.24103	0.302763
$573$	−75.6769	−3.16145
$574$	−2.28138	−0.0952231
$575$	−4.92594	−0.205426
$576$	3.06532	0.127722
$577$	36.5004	1.51953	0.759765	−	0.650198i	$-0.225314\pi$
$577$	36.5004	1.51953	0.759765	+	0.650198i	$0.225314\pi$
$578$	−28.4730	−1.18432
$579$	44.2034	1.83703
$580$	10.8805	0.451789
$581$	17.0954	0.709235
$582$	−7.15934	−0.296764
$583$	9.37200	0.388149
$584$	−2.33812	−0.0967520
$585$	−26.7405	−1.10558
$586$	−17.6257	−0.728111
$587$	−9.36145	−0.386388	−0.193194	−	0.981161i	$-0.561885\pi$
$587$	−9.36145	−0.386388	−0.193194	+	0.981161i	$0.561885\pi$
$588$	26.0961	1.07618
$589$	−1.75944	−0.0724963
$590$	7.11758	0.293026
$591$	60.0400	2.46971
$592$	−5.20176	−0.213791
$593$	13.8452	0.568554	0.284277	−	0.958742i	$-0.408246\pi$
$593$	13.8452	0.568554	0.284277	+	0.958742i	$0.408246\pi$
$594$	−5.44469	−0.223398
$595$	9.21170	0.377643
$596$	−21.2306	−0.869638
$597$	20.3830	0.834219
$598$	−14.8605	−0.607689
$599$	2.62350	0.107193	0.0535966	−	0.998563i	$-0.482931\pi$
$599$	2.62350	0.107193	0.0535966	+	0.998563i	$0.482931\pi$
$600$	6.93717	0.283209
$601$	13.5796	0.553923	0.276961	−	0.960881i	$-0.410673\pi$
$601$	13.5796	0.553923	0.276961	+	0.960881i	$0.410673\pi$
$602$	6.14612	0.250497
$603$	3.39302	0.138174
$604$	−20.2179	−0.822653
$605$	1.00000	0.0406558
$606$	−21.1811	−0.860422
$607$	4.99676	0.202812	0.101406	−	0.994845i	$-0.467666\pi$
$607$	4.99676	0.202812	0.101406	+	0.994845i	$0.467666\pi$
$608$	1.53690	0.0623294
$609$	24.3317	0.985972
$610$	8.24136	0.333683
$611$	17.3674	0.702612
$612$	70.9231	2.86690
$613$	4.69964	0.189817	0.0949083	−	0.995486i	$-0.469744\pi$
$613$	4.69964	0.189817	0.0949083	+	0.995486i	$0.469744\pi$
$614$	9.38961	0.378934
$615$	−8.72959	−0.352011
$616$	−2.76923	−0.111575
$617$	25.1246	1.01148	0.505740	−	0.862686i	$-0.331219\pi$
$617$	25.1246	1.01148	0.505740	+	0.862686i	$0.331219\pi$
$618$	−26.8126	−1.07856
$619$	−7.98938	−0.321120	−0.160560	−	0.987026i	$-0.551330\pi$
$619$	−7.98938	−0.321120	−0.160560	+	0.987026i	$0.551330\pi$
$620$	−10.3108	−0.414091
$621$	−40.9670	−1.64395
$622$	4.47480	0.179423
$623$	14.7683	0.591680
$624$	−22.0402	−0.882315
$625$	1.00000	0.0400000
$626$	−14.2116	−0.568010
$627$	−0.795579	−0.0317724
$628$	−9.69842	−0.387009
$629$	25.0965	1.00066
$630$	4.49963	0.179269
$631$	2.50173	0.0995923	0.0497961	−	0.998759i	$-0.484143\pi$
$631$	2.50173	0.0995923	0.0497961	+	0.998759i	$0.484143\pi$
$632$	−26.1050	−1.03840
$633$	−50.4990	−2.00716
$634$	−10.5593	−0.419364
$635$	−19.4582	−0.772173
$636$	−43.6952	−1.73263
$637$	25.7922	1.02192
$638$	4.53307	0.179466
$639$	22.6083	0.894370
$640$	11.1174	0.439455
$641$	0.968305	0.0382457	0.0191229	−	0.999817i	$-0.493913\pi$
$641$	0.968305	0.0382457	0.0191229	+	0.999817i	$0.493913\pi$
$642$	−12.0218	−0.474462
$643$	45.9274	1.81120	0.905600	−	0.424134i	$-0.139421\pi$
$643$	45.9274	1.81120	0.905600	+	0.424134i	$0.139421\pi$
$644$	−9.16785	−0.361264
$645$	23.5178	0.926011
$646$	−1.36535	−0.0537188
$647$	−30.0036	−1.17956	−0.589782	−	0.807562i	$-0.700786\pi$
$647$	−30.0036	−1.17956	−0.589782	+	0.807562i	$0.700786\pi$
$648$	16.9891	0.667393
$649$	−10.8719	−0.426758
$650$	3.01678	0.118328
$651$	−23.0577	−0.903701
$652$	8.51584	0.333506
$653$	−48.5659	−1.90053	−0.950265	−	0.311443i	$-0.899188\pi$
$653$	−48.5659	−1.90053	−0.950265	+	0.311443i	$0.899188\pi$
$654$	−35.2910	−1.37999
$655$	0.173708	0.00678731
$656$	−4.74310	−0.185187
$657$	−5.80304	−0.226398
$658$	−2.92242	−0.113928
$659$	20.0632	0.781549	0.390775	−	0.920486i	$-0.372207\pi$
$659$	20.0632	0.781549	0.390775	+	0.920486i	$0.372207\pi$
$660$	−4.66232	−0.181480
$661$	−38.0791	−1.48111	−0.740553	−	0.671998i	$-0.765436\pi$
$661$	−38.0791	−1.48111	−0.740553	+	0.671998i	$0.765436\pi$
$662$	6.27619	0.243931
$663$	106.335	4.12973
$664$	−33.7483	−1.30969
$665$	0.317585	0.0123154
$666$	12.2588	0.475020
$667$	34.1078	1.32066
$668$	−16.6277	−0.643345
$669$	67.1737	2.59708
$670$	−0.382789	−0.0147884
$671$	−12.5884	−0.485970
$672$	20.1413	0.776966
$673$	11.4905	0.442925	0.221463	−	0.975169i	$-0.428917\pi$
$673$	11.4905	0.442925	0.221463	+	0.975169i	$0.428917\pi$
$674$	−20.5411	−0.791214
$675$	8.31658	0.320105
$676$	−12.9387	−0.497641
$677$	−11.3696	−0.436970	−0.218485	−	0.975840i	$-0.570111\pi$
$677$	−11.3696	−0.436970	−0.218485	+	0.975840i	$0.570111\pi$
$678$	−18.3394	−0.704321
$679$	−4.36537	−0.167527
$680$	−18.1850	−0.697363
$681$	−30.3813	−1.16421
$682$	−4.29571	−0.164491
$683$	47.5094	1.81790	0.908949	−	0.416908i	$-0.136886\pi$
$683$	47.5094	1.81790	0.908949	+	0.416908i	$0.136886\pi$
$684$	2.44516	0.0934931
$685$	3.88243	0.148340
$686$	−9.76779	−0.372936
$687$	−70.9895	−2.70842
$688$	12.7781	0.487159
$689$	−43.1864	−1.64527
$690$	9.56828	0.364258
$691$	3.98143	0.151461	0.0757304	−	0.997128i	$-0.475871\pi$
$691$	3.98143	0.151461	0.0757304	+	0.997128i	$0.475871\pi$
$692$	−21.7297	−0.826038
$693$	−6.87303	−0.261085
$694$	−20.8983	−0.793289
$695$	−13.4937	−0.511844
$696$	−48.0338	−1.82072
$697$	22.8836	0.866779
$698$	3.82901	0.144930
$699$	−48.2421	−1.82469
$700$	1.86114	0.0703443
$701$	−45.8827	−1.73297	−0.866483	−	0.499206i	$-0.833625\pi$
$701$	−45.8827	−1.73297	−0.866483	+	0.499206i	$0.833625\pi$
$702$	25.0893	0.946934
$703$	0.865232	0.0326328
$704$	0.528227	0.0199083
$705$	−11.1825	−0.421156
$706$	19.6061	0.737887
$707$	−12.9150	−0.485720
$708$	50.6881	1.90497
$709$	24.4858	0.919582	0.459791	−	0.888027i	$-0.347924\pi$
$709$	24.4858	0.919582	0.459791	+	0.888027i	$0.347924\pi$
$710$	−2.55059	−0.0957220
$711$	−64.7906	−2.42984
$712$	−29.1545	−1.09261
$713$	−32.3218	−1.21046
$714$	−17.8931	−0.669631
$715$	−4.60802	−0.172330
$716$	34.3871	1.28511
$717$	21.7488	0.812223
$718$	17.9558	0.670105
$719$	40.5402	1.51190	0.755948	−	0.654632i	$-0.227176\pi$
$719$	40.5402	1.51190	0.755948	+	0.654632i	$0.227176\pi$
$720$	9.35493	0.348637
$721$	−16.3488	−0.608863
$722$	12.3918	0.461176
$723$	−66.2044	−2.46217
$724$	8.53109	0.317056
$725$	−6.92411	−0.257155
$726$	−1.94243	−0.0720902
$727$	8.13113	0.301567	0.150783	−	0.988567i	$-0.451820\pi$
$727$	8.13113	0.301567	0.150783	+	0.988567i	$0.451820\pi$
$728$	12.7607	0.472942
$729$	−31.8601	−1.18000
$730$	0.654679	0.0242308
$731$	−61.6491	−2.28018
$732$	58.6911	2.16929
$733$	−4.76258	−0.175910	−0.0879550	−	0.996124i	$-0.528033\pi$
$733$	−4.76258	−0.175910	−0.0879550	+	0.996124i	$0.528033\pi$
$734$	−5.91449	−0.218308
$735$	−16.6069	−0.612556
$736$	28.2337	1.04071
$737$	0.584697	0.0215376
$738$	11.1779	0.411465
$739$	−13.4696	−0.495487	−0.247743	−	0.968826i	$-0.579689\pi$
$739$	−13.4696	−0.495487	−0.247743	+	0.968826i	$0.579689\pi$
$740$	5.07050	0.186395
$741$	3.66605	0.134676
$742$	7.26697	0.266779
$743$	11.4794	0.421137	0.210568	−	0.977579i	$-0.432469\pi$
$743$	11.4794	0.421137	0.210568	+	0.977579i	$0.432469\pi$
$744$	45.5186	1.66879
$745$	13.5106	0.494992
$746$	−22.5930	−0.827190
$747$	−83.7608	−3.06465
$748$	12.2217	0.446871
$749$	−7.33023	−0.267841
$750$	−1.94243	−0.0709274
$751$	30.6073	1.11688	0.558438	−	0.829547i	$-0.311401\pi$
$751$	30.6073	1.11688	0.558438	+	0.829547i	$0.311401\pi$
$752$	−6.07584	−0.221563
$753$	−51.6474	−1.88214
$754$	−20.8885	−0.760714
$755$	12.8662	0.468248
$756$	15.4783	0.562940
$757$	−48.9421	−1.77883	−0.889415	−	0.457101i	$-0.848888\pi$
$757$	−48.9421	−1.77883	−0.889415	+	0.457101i	$0.848888\pi$
$758$	5.91585	0.214873
$759$	−14.6152	−0.530499
$760$	−0.626951	−0.0227419
$761$	1.36996	0.0496610	0.0248305	−	0.999692i	$-0.492095\pi$
$761$	1.36996	0.0496610	0.0248305	+	0.999692i	$0.492095\pi$
$762$	37.7960	1.36921
$763$	−21.5185	−0.779021
$764$	40.0805	1.45006
$765$	−45.1339	−1.63182
$766$	−10.7643	−0.388929
$767$	50.0978	1.80893
$768$	−24.7293	−0.892342
$769$	51.8261	1.86890	0.934448	−	0.356099i	$-0.115893\pi$
$769$	51.8261	1.86890	0.934448	+	0.356099i	$0.115893\pi$
$770$	0.775392	0.0279432
$771$	−12.0686	−0.434639
$772$	−23.4113	−0.842590
$773$	52.2443	1.87910	0.939548	−	0.342418i	$-0.111246\pi$
$773$	52.2443	1.87910	0.939548	+	0.342418i	$0.111246\pi$
$774$	−30.1137	−1.08241
$775$	6.56155	0.235698
$776$	8.61777	0.309360
$777$	11.3390	0.406784
$778$	−13.6131	−0.488055
$779$	0.788941	0.0282667
$780$	21.4841	0.769253
$781$	3.89594	0.139408
$782$	−25.0822	−0.896936
$783$	−57.5850	−2.05792
$784$	−9.02316	−0.322256
$785$	6.17185	0.220283
$786$	−0.337414	−0.0120352
$787$	−34.6016	−1.23342	−0.616708	−	0.787192i	$-0.711534\pi$
$787$	−34.6016	−1.23342	−0.616708	+	0.787192i	$0.711534\pi$
$788$	−31.7987	−1.13278
$789$	−91.4841	−3.25692
$790$	7.30946	0.260059
$791$	−11.1824	−0.397599
$792$	13.5682	0.482124
$793$	58.0076	2.05991
$794$	11.9051	0.422494
$795$	27.8067	0.986200
$796$	−10.7953	−0.382631
$797$	26.3171	0.932200	0.466100	−	0.884732i	$-0.345659\pi$
$797$	26.3171	0.932200	0.466100	+	0.884732i	$0.345659\pi$
$798$	−0.616885	−0.0218375
$799$	29.3136	1.03704
$800$	−5.73163	−0.202644
$801$	−72.3592	−2.55669
$802$	10.4264	0.368170
$803$	−1.00000	−0.0352892
$804$	−2.72604	−0.0961401
$805$	5.83421	0.205629
$806$	19.7947	0.697239
$807$	1.63896	0.0576942
$808$	25.4959	0.896941
$809$	8.09975	0.284772	0.142386	−	0.989811i	$-0.454523\pi$
$809$	8.09975	0.284772	0.142386	+	0.989811i	$0.454523\pi$
$810$	−4.75698	−0.167143
$811$	−11.1762	−0.392450	−0.196225	−	0.980559i	$-0.562868\pi$
$811$	−11.1762	−0.392450	−0.196225	+	0.980559i	$0.562868\pi$
$812$	−12.8867	−0.452235
$813$	13.3761	0.469119
$814$	2.11249	0.0740426
$815$	−5.41929	−0.189829
$816$	−37.2005	−1.30228
$817$	−2.12543	−0.0743594
$818$	8.94860	0.312881
$819$	31.6711	1.10668
$820$	4.62341	0.161457
$821$	22.5273	0.786210	0.393105	−	0.919494i	$-0.371401\pi$
$821$	22.5273	0.786210	0.393105	+	0.919494i	$0.371401\pi$
$822$	−7.54134	−0.263035
$823$	−6.55933	−0.228644	−0.114322	−	0.993444i	$-0.536470\pi$
$823$	−6.55933	−0.228644	−0.114322	+	0.993444i	$0.536470\pi$
$824$	32.2746	1.12434
$825$	2.96699	0.103297
$826$	−8.42995	−0.293316
$827$	−0.0890257	−0.00309573	−0.00154786	−	0.999999i	$-0.500493\pi$
$827$	−0.0890257	−0.00309573	−0.00154786	+	0.999999i	$0.500493\pi$
$828$	44.9190	1.56104
$829$	−44.9330	−1.56059	−0.780294	−	0.625413i	$-0.784931\pi$
$829$	−44.9330	−1.56059	−0.780294	+	0.625413i	$0.784931\pi$
$830$	9.44962	0.328001
$831$	−46.1446	−1.60074
$832$	−2.43408	−0.0843867
$833$	43.5332	1.50834
$834$	26.2104	0.907593
$835$	10.5815	0.366187
$836$	0.421359	0.0145730
$837$	54.5697	1.88620
$838$	−0.216341	−0.00747338
$839$	29.4691	1.01739	0.508694	−	0.860947i	$-0.330128\pi$
$839$	29.4691	1.01739	0.508694	+	0.860947i	$0.330128\pi$
$840$	−8.21628	−0.283489
$841$	18.9433	0.653218
$842$	−15.7191	−0.541717
$843$	7.74938	0.266903
$844$	26.7456	0.920622
$845$	8.23388	0.283254
$846$	14.3187	0.492289
$847$	−1.18438	−0.0406959
$848$	15.1084	0.518823
$849$	−58.7095	−2.01490
$850$	5.09185	0.174649
$851$	15.8948	0.544866
$852$	−18.1641	−0.622292
$853$	−18.5140	−0.633909	−0.316954	−	0.948441i	$-0.602660\pi$
$853$	−18.5140	−0.633909	−0.316954	+	0.948441i	$0.602660\pi$
$854$	−9.76094	−0.334013
$855$	−1.55605	−0.0532156
$856$	14.4708	0.494600
$857$	39.9333	1.36409	0.682047	−	0.731308i	$-0.261090\pi$
$857$	39.9333	1.36409	0.682047	+	0.731308i	$0.261090\pi$
$858$	8.95075	0.305574
$859$	5.70709	0.194723	0.0973617	−	0.995249i	$-0.468960\pi$
$859$	5.70709	0.194723	0.0973617	+	0.995249i	$0.468960\pi$
$860$	−12.4556	−0.424733
$861$	10.3392	0.352358
$862$	2.78208	0.0947581
$863$	−5.04767	−0.171825	−0.0859124	−	0.996303i	$-0.527381\pi$
$863$	−5.04767	−0.171825	−0.0859124	+	0.996303i	$0.527381\pi$
$864$	−47.6676	−1.62168
$865$	13.8283	0.470175
$866$	24.4427	0.830597
$867$	129.039	4.38239
$868$	12.2119	0.414500
$869$	−11.1650	−0.378745
$870$	13.4496	0.455984
$871$	−2.69430	−0.0912928
$872$	42.4801	1.43856
$873$	21.3887	0.723897
$874$	−0.864738	−0.0292502
$875$	−1.18438	−0.0400395
$876$	4.66232	0.157525
$877$	−2.83181	−0.0956235	−0.0478118	−	0.998856i	$-0.515225\pi$
$877$	−2.83181	−0.0956235	−0.0478118	+	0.998856i	$0.515225\pi$
$878$	−24.0106	−0.810319
$879$	79.8793	2.69426
$880$	1.61207	0.0543430
$881$	−36.0003	−1.21288	−0.606440	−	0.795129i	$-0.707403\pi$
$881$	−36.0003	−1.21288	−0.606440	+	0.795129i	$0.707403\pi$
$882$	21.2646	0.716016
$883$	23.7869	0.800494	0.400247	−	0.916407i	$-0.368924\pi$
$883$	23.7869	0.800494	0.400247	+	0.916407i	$0.368924\pi$
$884$	−56.3180	−1.89418
$885$	−32.2567	−1.08430
$886$	15.2731	0.513108
$887$	1.38914	0.0466426	0.0233213	−	0.999728i	$-0.492576\pi$
$887$	1.38914	0.0466426	0.0233213	+	0.999728i	$0.492576\pi$
$888$	−22.3845	−0.751176
$889$	23.0459	0.772936
$890$	8.16332	0.273635
$891$	7.26612	0.243424
$892$	−35.5769	−1.19120
$893$	1.01062	0.0338191
$894$	−26.2434	−0.877712
$895$	−21.8832	−0.731474
$896$	−13.1673	−0.439889
$897$	67.3473	2.24866
$898$	−1.55437	−0.0518699
$899$	−45.4329	−1.51527
$900$	−9.11886	−0.303962
$901$	−72.8920	−2.42838
$902$	1.92622	0.0641361
$903$	−27.8541	−0.926925
$904$	22.0753	0.734214
$905$	−5.42899	−0.180466
$906$	−24.9916	−0.830291
$907$	51.7497	1.71832	0.859160	−	0.511706i	$-0.170986\pi$
$907$	51.7497	1.71832	0.859160	+	0.511706i	$0.170986\pi$
$908$	16.0907	0.533990
$909$	63.2789	2.09883
$910$	−3.57302	−0.118445
$911$	4.91325	0.162783	0.0813916	−	0.996682i	$-0.474064\pi$
$911$	4.91325	0.162783	0.0813916	+	0.996682i	$0.474064\pi$
$912$	−1.28253	−0.0424689
$913$	−14.4340	−0.477695
$914$	22.1091	0.731305
$915$	−37.3497	−1.23474
$916$	37.5979	1.24227
$917$	−0.205736	−0.00679402
$918$	42.3468	1.39765
$919$	19.3088	0.636940	0.318470	−	0.947933i	$-0.396831\pi$
$919$	19.3088	0.636940	0.318470	+	0.947933i	$0.396831\pi$
$920$	−11.5174	−0.379718
$921$	−42.5535	−1.40219
$922$	18.3436	0.604113
$923$	−17.9526	−0.590917
$924$	5.52197	0.181660
$925$	−3.22675	−0.106095
$926$	17.9311	0.589251
$927$	80.1032	2.63093
$928$	39.6864	1.30277
$929$	−19.1177	−0.627230	−0.313615	−	0.949550i	$-0.601540\pi$
$929$	−19.1177	−0.627230	−0.313615	+	0.949550i	$0.601540\pi$
$930$	−12.7453	−0.417936
$931$	1.50086	0.0491887
$932$	25.5503	0.836927
$933$	−20.2797	−0.663928
$934$	−15.6064	−0.510656
$935$	−7.77763	−0.254356
$936$	−62.5225	−2.04361
$937$	−24.8288	−0.811122	−0.405561	−	0.914068i	$-0.632924\pi$
$937$	−24.8288	−0.811122	−0.405561	+	0.914068i	$0.632924\pi$
$938$	0.453369	0.0148030
$939$	64.4067	2.10183
$940$	5.92252	0.193171
$941$	−10.9974	−0.358503	−0.179252	−	0.983803i	$-0.557368\pi$
$941$	−10.9974	−0.358503	−0.179252	+	0.983803i	$0.557368\pi$
$942$	−11.9884	−0.390602
$943$	14.4933	0.471966
$944$	−17.5263	−0.570431
$945$	−9.85003	−0.320422
$946$	−5.18929	−0.168718
$947$	−43.0541	−1.39907	−0.699535	−	0.714599i	$-0.746609\pi$
$947$	−43.0541	−1.39907	−0.699535	+	0.714599i	$0.746609\pi$
$948$	52.0545	1.69065
$949$	4.60802	0.149583
$950$	0.175548	0.00569552
$951$	47.8546	1.55179
$952$	21.5380	0.698052
$953$	44.1296	1.42950	0.714749	−	0.699382i	$-0.246541\pi$
$953$	44.1296	1.42950	0.714749	+	0.699382i	$0.246541\pi$
$954$	−35.6054	−1.15277
$955$	−25.5063	−0.825364
$956$	−11.5187	−0.372542
$957$	−20.5438	−0.664086
$958$	−20.0707	−0.648455
$959$	−4.59829	−0.148487
$960$	1.56725	0.0505827
$961$	12.0539	0.388835
$962$	−9.73439	−0.313849
$963$	35.9153	1.15736
$964$	35.0636	1.12932
$965$	14.8984	0.479596
$966$	−11.3325	−0.364618
$967$	26.3760	0.848193	0.424097	−	0.905617i	$-0.360592\pi$
$967$	26.3760	0.848193	0.424097	+	0.905617i	$0.360592\pi$
$968$	2.33812	0.0751499
$969$	6.18772	0.198778
$970$	−2.41300	−0.0774767
$971$	21.4536	0.688479	0.344239	−	0.938882i	$-0.388137\pi$
$971$	21.4536	0.688479	0.344239	+	0.938882i	$0.388137\pi$
$972$	5.32896	0.170927
$973$	15.9817	0.512349
$974$	−17.0545	−0.546462
$975$	−13.6720	−0.437853
$976$	−20.2934	−0.649577
$977$	−55.9952	−1.79144	−0.895722	−	0.444615i	$-0.853341\pi$
$977$	−55.9952	−1.79144	−0.895722	+	0.444615i	$0.853341\pi$
$978$	10.5266	0.336603
$979$	−12.4692	−0.398517
$980$	8.79547	0.280961
$981$	105.432	3.36620
$982$	−7.11200	−0.226953
$983$	−14.8536	−0.473755	−0.236877	−	0.971540i	$-0.576124\pi$
$983$	−14.8536	−0.473755	−0.236877	+	0.971540i	$0.576124\pi$
$984$	−20.4108	−0.650673
$985$	20.2360	0.644772
$986$	−35.2565	−1.12280
$987$	13.2443	0.421572
$988$	−1.94163	−0.0617716
$989$	−39.0453	−1.24157
$990$	−3.79913	−0.120744
$991$	20.0048	0.635475	0.317737	−	0.948179i	$-0.397077\pi$
$991$	20.0048	0.635475	0.317737	+	0.948179i	$0.397077\pi$
$992$	−37.6083	−1.19407
$993$	−28.4436	−0.902630
$994$	3.02088	0.0958165
$995$	6.86991	0.217791
$996$	67.2957	2.13235
$997$	29.6488	0.938988	0.469494	−	0.882936i	$-0.344436\pi$
$997$	29.6488	0.938988	0.469494	+	0.882936i	$0.344436\pi$
$998$	−10.2776	−0.325333
$999$	−26.8356	−0.849039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.11	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.11	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.654679 q^{2} +2.96699 q^{3} -1.57140 q^{4} +1.00000 q^{5} -1.94243 q^{6} -1.18438 q^{7} +2.33812 q^{8} +5.80304 q^{9} +O(q^{10})\)	\(q-0.654679 q^{2} +2.96699 q^{3} -1.57140 q^{4} +1.00000 q^{5} -1.94243 q^{6} -1.18438 q^{7} +2.33812 q^{8} +5.80304 q^{9} -0.654679 q^{10} +1.00000 q^{11} -4.66232 q^{12} -4.60802 q^{13} +0.775392 q^{14} +2.96699 q^{15} +1.61207 q^{16} -7.77763 q^{17} -3.79913 q^{18} -0.268143 q^{19} -1.57140 q^{20} -3.51406 q^{21} -0.654679 q^{22} -4.92594 q^{23} +6.93717 q^{24} +1.00000 q^{25} +3.01678 q^{26} +8.31658 q^{27} +1.86114 q^{28} -6.92411 q^{29} -1.94243 q^{30} +6.56155 q^{31} -5.73163 q^{32} +2.96699 q^{33} +5.09185 q^{34} -1.18438 q^{35} -9.11886 q^{36} -3.22675 q^{37} +0.175548 q^{38} -13.6720 q^{39} +2.33812 q^{40} -2.94224 q^{41} +2.30058 q^{42} +7.92647 q^{43} -1.57140 q^{44} +5.80304 q^{45} +3.22491 q^{46} -3.76896 q^{47} +4.78301 q^{48} -5.59723 q^{49} -0.654679 q^{50} -23.0762 q^{51} +7.24103 q^{52} +9.37200 q^{53} -5.44469 q^{54} +1.00000 q^{55} -2.76923 q^{56} -0.795579 q^{57} +4.53307 q^{58} -10.8719 q^{59} -4.66232 q^{60} -12.5884 q^{61} -4.29571 q^{62} -6.87303 q^{63} +0.528227 q^{64} -4.60802 q^{65} -1.94243 q^{66} +0.584697 q^{67} +12.2217 q^{68} -14.6152 q^{69} +0.775392 q^{70} +3.89594 q^{71} +13.5682 q^{72} -1.00000 q^{73} +2.11249 q^{74} +2.96699 q^{75} +0.421359 q^{76} -1.18438 q^{77} +8.95075 q^{78} -11.1650 q^{79} +1.61207 q^{80} +7.26612 q^{81} +1.92622 q^{82} -14.4340 q^{83} +5.52197 q^{84} -7.77763 q^{85} -5.18929 q^{86} -20.5438 q^{87} +2.33812 q^{88} -12.4692 q^{89} -3.79913 q^{90} +5.45767 q^{91} +7.74060 q^{92} +19.4681 q^{93} +2.46746 q^{94} -0.268143 q^{95} -17.0057 q^{96} +3.68577 q^{97} +3.66439 q^{98} +5.80304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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