LMFDB - Embedded newform 4006.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.06520 q^{3} +1.00000 q^{4} +4.19388 q^{5} +3.06520 q^{6} +2.77423 q^{7} -1.00000 q^{8} +6.39547 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.06520 q^{3} +1.00000 q^{4} +4.19388 q^{5} +3.06520 q^{6} +2.77423 q^{7} -1.00000 q^{8} +6.39547 q^{9} -4.19388 q^{10} -1.46071 q^{11} -3.06520 q^{12} +5.16019 q^{13} -2.77423 q^{14} -12.8551 q^{15} +1.00000 q^{16} -2.76462 q^{17} -6.39547 q^{18} -5.73378 q^{19} +4.19388 q^{20} -8.50359 q^{21} +1.46071 q^{22} +0.445728 q^{23} +3.06520 q^{24} +12.5886 q^{25} -5.16019 q^{26} -10.4078 q^{27} +2.77423 q^{28} +2.61472 q^{29} +12.8551 q^{30} -4.88256 q^{31} -1.00000 q^{32} +4.47737 q^{33} +2.76462 q^{34} +11.6348 q^{35} +6.39547 q^{36} +6.83067 q^{37} +5.73378 q^{38} -15.8170 q^{39} -4.19388 q^{40} +4.60213 q^{41} +8.50359 q^{42} +4.71602 q^{43} -1.46071 q^{44} +26.8218 q^{45} -0.445728 q^{46} +1.83762 q^{47} -3.06520 q^{48} +0.696367 q^{49} -12.5886 q^{50} +8.47412 q^{51} +5.16019 q^{52} -0.469054 q^{53} +10.4078 q^{54} -6.12603 q^{55} -2.77423 q^{56} +17.5752 q^{57} -2.61472 q^{58} +11.6882 q^{59} -12.8551 q^{60} -4.43357 q^{61} +4.88256 q^{62} +17.7425 q^{63} +1.00000 q^{64} +21.6412 q^{65} -4.47737 q^{66} -4.75276 q^{67} -2.76462 q^{68} -1.36625 q^{69} -11.6348 q^{70} +12.6008 q^{71} -6.39547 q^{72} -6.74523 q^{73} -6.83067 q^{74} -38.5866 q^{75} -5.73378 q^{76} -4.05235 q^{77} +15.8170 q^{78} -0.365541 q^{79} +4.19388 q^{80} +12.7156 q^{81} -4.60213 q^{82} +0.362040 q^{83} -8.50359 q^{84} -11.5945 q^{85} -4.71602 q^{86} -8.01466 q^{87} +1.46071 q^{88} +8.83637 q^{89} -26.8218 q^{90} +14.3156 q^{91} +0.445728 q^{92} +14.9660 q^{93} -1.83762 q^{94} -24.0467 q^{95} +3.06520 q^{96} -2.40425 q^{97} -0.696367 q^{98} -9.34192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.06520	−1.76970	−0.884848	−	0.465880i	$-0.845738\pi$
$3$	−3.06520	−1.76970	−0.884848	+	0.465880i	$0.845738\pi$
$4$	1.00000	0.500000
$5$	4.19388	1.87556	0.937779	−	0.347232i	$-0.112878\pi$
$5$	4.19388	1.87556	0.937779	+	0.347232i	$0.112878\pi$
$6$	3.06520	1.25136
$7$	2.77423	1.04856	0.524281	−	0.851546i	$-0.324334\pi$
$7$	2.77423	1.04856	0.524281	+	0.851546i	$0.324334\pi$
$8$	−1.00000	−0.353553
$9$	6.39547	2.13182
$10$	−4.19388	−1.32622
$11$	−1.46071	−0.440420	−0.220210	−	0.975452i	$-0.570674\pi$
$11$	−1.46071	−0.440420	−0.220210	+	0.975452i	$0.570674\pi$
$12$	−3.06520	−0.884848
$13$	5.16019	1.43118	0.715590	−	0.698521i	$-0.246158\pi$
$13$	5.16019	1.43118	0.715590	+	0.698521i	$0.246158\pi$
$14$	−2.77423	−0.741445
$15$	−12.8551	−3.31917
$16$	1.00000	0.250000
$17$	−2.76462	−0.670518	−0.335259	−	0.942126i	$-0.608824\pi$
$17$	−2.76462	−0.670518	−0.335259	+	0.942126i	$0.608824\pi$
$18$	−6.39547	−1.50743
$19$	−5.73378	−1.31542	−0.657709	−	0.753272i	$-0.728474\pi$
$19$	−5.73378	−1.31542	−0.657709	+	0.753272i	$0.728474\pi$
$20$	4.19388	0.937779
$21$	−8.50359	−1.85563
$22$	1.46071	0.311424
$23$	0.445728	0.0929407	0.0464704	−	0.998920i	$-0.485203\pi$
$23$	0.445728	0.0929407	0.0464704	+	0.998920i	$0.485203\pi$
$24$	3.06520	0.625682
$25$	12.5886	2.51772
$26$	−5.16019	−1.01200
$27$	−10.4078	−2.00298
$28$	2.77423	0.524281
$29$	2.61472	0.485542	0.242771	−	0.970084i	$-0.421944\pi$
$29$	2.61472	0.485542	0.242771	+	0.970084i	$0.421944\pi$
$30$	12.8551	2.34701
$31$	−4.88256	−0.876934	−0.438467	−	0.898747i	$-0.644478\pi$
$31$	−4.88256	−0.876934	−0.438467	+	0.898747i	$0.644478\pi$
$32$	−1.00000	−0.176777
$33$	4.47737	0.779410
$34$	2.76462	0.474128
$35$	11.6348	1.96664
$36$	6.39547	1.06591
$37$	6.83067	1.12296	0.561478	−	0.827492i	$-0.310233\pi$
$37$	6.83067	1.12296	0.561478	+	0.827492i	$0.310233\pi$
$38$	5.73378	0.930141
$39$	−15.8170	−2.53275
$40$	−4.19388	−0.663110
$41$	4.60213	0.718732	0.359366	−	0.933197i	$-0.382993\pi$
$41$	4.60213	0.718732	0.359366	+	0.933197i	$0.382993\pi$
$42$	8.50359	1.31213
$43$	4.71602	0.719186	0.359593	−	0.933109i	$-0.382916\pi$
$43$	4.71602	0.719186	0.359593	+	0.933109i	$0.382916\pi$
$44$	−1.46071	−0.220210
$45$	26.8218	3.99836
$46$	−0.445728	−0.0657190
$47$	1.83762	0.268044	0.134022	−	0.990978i	$-0.457211\pi$
$47$	1.83762	0.268044	0.134022	+	0.990978i	$0.457211\pi$
$48$	−3.06520	−0.442424
$49$	0.696367	0.0994810
$50$	−12.5886	−1.78030
$51$	8.47412	1.18661
$52$	5.16019	0.715590
$53$	−0.469054	−0.0644295	−0.0322147	−	0.999481i	$-0.510256\pi$
$53$	−0.469054	−0.0644295	−0.0322147	+	0.999481i	$0.510256\pi$
$54$	10.4078	1.41632
$55$	−6.12603	−0.826034
$56$	−2.77423	−0.370722
$57$	17.5752	2.32789
$58$	−2.61472	−0.343330
$59$	11.6882	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$59$	11.6882	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$60$	−12.8551	−1.65958
$61$	−4.43357	−0.567661	−0.283830	−	0.958875i	$-0.591605\pi$
$61$	−4.43357	−0.567661	−0.283830	+	0.958875i	$0.591605\pi$
$62$	4.88256	0.620086
$63$	17.7425	2.23535
$64$	1.00000	0.125000
$65$	21.6412	2.68426
$66$	−4.47737	−0.551126
$67$	−4.75276	−0.580642	−0.290321	−	0.956929i	$-0.593762\pi$
$67$	−4.75276	−0.580642	−0.290321	+	0.956929i	$0.593762\pi$
$68$	−2.76462	−0.335259
$69$	−1.36625	−0.164477
$70$	−11.6348	−1.39062
$71$	12.6008	1.49544	0.747721	−	0.664013i	$-0.231148\pi$
$71$	12.6008	1.49544	0.747721	+	0.664013i	$0.231148\pi$
$72$	−6.39547	−0.753714
$73$	−6.74523	−0.789470	−0.394735	−	0.918795i	$-0.629164\pi$
$73$	−6.74523	−0.789470	−0.394735	+	0.918795i	$0.629164\pi$
$74$	−6.83067	−0.794050
$75$	−38.5866	−4.45560
$76$	−5.73378	−0.657709
$77$	−4.05235	−0.461808
$78$	15.8170	1.79093
$79$	−0.365541	−0.0411266	−0.0205633	−	0.999789i	$-0.506546\pi$
$79$	−0.365541	−0.0411266	−0.0205633	+	0.999789i	$0.506546\pi$
$80$	4.19388	0.468890
$81$	12.7156	1.41285
$82$	−4.60213	−0.508221
$83$	0.362040	0.0397390	0.0198695	−	0.999803i	$-0.493675\pi$
$83$	0.362040	0.0397390	0.0198695	+	0.999803i	$0.493675\pi$
$84$	−8.50359	−0.927817
$85$	−11.5945	−1.25760
$86$	−4.71602	−0.508541
$87$	−8.01466	−0.859261
$88$	1.46071	0.155712
$89$	8.83637	0.936653	0.468327	−	0.883555i	$-0.344857\pi$
$89$	8.83637	0.936653	0.468327	+	0.883555i	$0.344857\pi$
$90$	−26.8218	−2.82727
$91$	14.3156	1.50068
$92$	0.445728	0.0464704
$93$	14.9660	1.55191
$94$	−1.83762	−0.189536
$95$	−24.0467	−2.46714
$96$	3.06520	0.312841
$97$	−2.40425	−0.244114	−0.122057	−	0.992523i	$-0.538949\pi$
$97$	−2.40425	−0.244114	−0.122057	+	0.992523i	$0.538949\pi$
$98$	−0.696367	−0.0703437
$99$	−9.34192	−0.938899
$100$	12.5886	1.25886
$101$	12.8419	1.27781	0.638906	−	0.769285i	$-0.279387\pi$
$101$	12.8419	1.27781	0.638906	+	0.769285i	$0.279387\pi$
$102$	−8.47412	−0.839063
$103$	16.3897	1.61493	0.807464	−	0.589917i	$-0.200840\pi$
$103$	16.3897	1.61493	0.807464	+	0.589917i	$0.200840\pi$
$104$	−5.16019	−0.505998
$105$	−35.6630	−3.48035
$106$	0.469054	0.0455585
$107$	−10.6985	−1.03426	−0.517130	−	0.855907i	$-0.673000\pi$
$107$	−10.6985	−1.03426	−0.517130	+	0.855907i	$0.673000\pi$
$108$	−10.4078	−1.00149
$109$	3.00583	0.287907	0.143953	−	0.989584i	$-0.454018\pi$
$109$	3.00583	0.287907	0.143953	+	0.989584i	$0.454018\pi$
$110$	6.12603	0.584094
$111$	−20.9374	−1.98729
$112$	2.77423	0.262140
$113$	−15.9389	−1.49940	−0.749701	−	0.661777i	$-0.769802\pi$
$113$	−15.9389	−1.49940	−0.749701	+	0.661777i	$0.769802\pi$
$114$	−17.5752	−1.64607
$115$	1.86933	0.174316
$116$	2.61472	0.242771
$117$	33.0019	3.05102
$118$	−11.6882	−1.07599
$119$	−7.66969	−0.703080
$120$	12.8551	1.17350
$121$	−8.86633	−0.806030
$122$	4.43357	0.401397
$123$	−14.1065	−1.27194
$124$	−4.88256	−0.438467
$125$	31.8257	2.84657
$126$	−17.7425	−1.58063
$127$	16.7747	1.48852	0.744259	−	0.667891i	$-0.232803\pi$
$127$	16.7747	1.48852	0.744259	+	0.667891i	$0.232803\pi$
$128$	−1.00000	−0.0883883
$129$	−14.4556	−1.27274
$130$	−21.6412	−1.89806
$131$	1.72870	0.151037	0.0755186	−	0.997144i	$-0.475939\pi$
$131$	1.72870	0.151037	0.0755186	+	0.997144i	$0.475939\pi$
$132$	4.47737	0.389705
$133$	−15.9068	−1.37930
$134$	4.75276	0.410576
$135$	−43.6491	−3.75671
$136$	2.76462	0.237064
$137$	−1.46454	−0.125124	−0.0625620	−	0.998041i	$-0.519927\pi$
$137$	−1.46454	−0.125124	−0.0625620	+	0.998041i	$0.519927\pi$
$138$	1.36625	0.116303
$139$	−13.7374	−1.16519	−0.582594	−	0.812763i	$-0.697962\pi$
$139$	−13.7374	−1.16519	−0.582594	+	0.812763i	$0.697962\pi$
$140$	11.6348	0.983319
$141$	−5.63267	−0.474357
$142$	−12.6008	−1.05744
$143$	−7.53754	−0.630321
$144$	6.39547	0.532956
$145$	10.9658	0.910662
$146$	6.74523	0.558239
$147$	−2.13451	−0.176051
$148$	6.83067	0.561478
$149$	−17.7442	−1.45366	−0.726832	−	0.686815i	$-0.759008\pi$
$149$	−17.7442	−1.45366	−0.726832	+	0.686815i	$0.759008\pi$
$150$	38.5866	3.15059
$151$	−18.3425	−1.49270	−0.746348	−	0.665556i	$-0.768194\pi$
$151$	−18.3425	−1.49270	−0.746348	+	0.665556i	$0.768194\pi$
$152$	5.73378	0.465071
$153$	−17.6810	−1.42943
$154$	4.05235	0.326547
$155$	−20.4769	−1.64474
$156$	−15.8170	−1.26638
$157$	−21.5026	−1.71609	−0.858047	−	0.513571i	$-0.828322\pi$
$157$	−21.5026	−1.71609	−0.858047	+	0.513571i	$0.828322\pi$
$158$	0.365541	0.0290809
$159$	1.43774	0.114021
$160$	−4.19388	−0.331555
$161$	1.23655	0.0974541
$162$	−12.7156	−0.999035
$163$	−20.9092	−1.63773	−0.818867	−	0.573984i	$-0.805397\pi$
$163$	−20.9092	−1.63773	−0.818867	+	0.573984i	$0.805397\pi$
$164$	4.60213	0.359366
$165$	18.7775	1.46183
$166$	−0.362040	−0.0280997
$167$	24.0145	1.85830	0.929149	−	0.369706i	$-0.120541\pi$
$167$	24.0145	1.85830	0.929149	+	0.369706i	$0.120541\pi$
$168$	8.50359	0.656066
$169$	13.6276	1.04827
$170$	11.5945	0.889255
$171$	−36.6702	−2.80424
$172$	4.71602	0.359593
$173$	11.3209	0.860709	0.430355	−	0.902660i	$-0.358388\pi$
$173$	11.3209	0.860709	0.430355	+	0.902660i	$0.358388\pi$
$174$	8.01466	0.607590
$175$	34.9237	2.63998
$176$	−1.46071	−0.110105
$177$	−35.8267	−2.69290
$178$	−8.83637	−0.662314
$179$	21.6284	1.61658	0.808292	−	0.588782i	$-0.200392\pi$
$179$	21.6284	1.61658	0.808292	+	0.588782i	$0.200392\pi$
$180$	26.8218	1.99918
$181$	18.4548	1.37173	0.685867	−	0.727727i	$-0.259423\pi$
$181$	18.4548	1.37173	0.685867	+	0.727727i	$0.259423\pi$
$182$	−14.3156	−1.06114
$183$	13.5898	1.00459
$184$	−0.445728	−0.0328595
$185$	28.6470	2.10617
$186$	−14.9660	−1.09736
$187$	4.03830	0.295310
$188$	1.83762	0.134022
$189$	−28.8737	−2.10025
$190$	24.0467	1.74453
$191$	19.5310	1.41321	0.706607	−	0.707606i	$-0.250225\pi$
$191$	19.5310	1.41321	0.706607	+	0.707606i	$0.250225\pi$
$192$	−3.06520	−0.221212
$193$	8.07861	0.581511	0.290756	−	0.956797i	$-0.406093\pi$
$193$	8.07861	0.581511	0.290756	+	0.956797i	$0.406093\pi$
$194$	2.40425	0.172615
$195$	−66.3347	−4.75033
$196$	0.696367	0.0497405
$197$	0.626124	0.0446095	0.0223047	−	0.999751i	$-0.492900\pi$
$197$	0.626124	0.0446095	0.0223047	+	0.999751i	$0.492900\pi$
$198$	9.34192	0.663902
$199$	2.19031	0.155267	0.0776336	−	0.996982i	$-0.475264\pi$
$199$	2.19031	0.155267	0.0776336	+	0.996982i	$0.475264\pi$
$200$	−12.5886	−0.890149
$201$	14.5682	1.02756
$202$	−12.8419	−0.903550
$203$	7.25385	0.509120
$204$	8.47412	0.593307
$205$	19.3008	1.34802
$206$	−16.3897	−1.14193
$207$	2.85064	0.198133
$208$	5.16019	0.357795
$209$	8.37538	0.579337
$210$	35.6630	2.46098
$211$	16.3183	1.12340	0.561700	−	0.827341i	$-0.310148\pi$
$211$	16.3183	1.12340	0.561700	+	0.827341i	$0.310148\pi$
$212$	−0.469054	−0.0322147
$213$	−38.6241	−2.64648
$214$	10.6985	0.731333
$215$	19.7784	1.34888
$216$	10.4078	0.708162
$217$	−13.5454	−0.919519
$218$	−3.00583	−0.203581
$219$	20.6755	1.39712
$220$	−6.12603	−0.413017
$221$	−14.2660	−0.959632
$222$	20.9374	1.40523
$223$	−20.4102	−1.36677	−0.683386	−	0.730058i	$-0.739493\pi$
$223$	−20.4102	−1.36677	−0.683386	+	0.730058i	$0.739493\pi$
$224$	−2.77423	−0.185361
$225$	80.5101	5.36734
$226$	15.9389	1.06024
$227$	−15.3617	−1.01959	−0.509796	−	0.860296i	$-0.670279\pi$
$227$	−15.3617	−1.01959	−0.509796	+	0.860296i	$0.670279\pi$
$228$	17.5752	1.16395
$229$	25.7159	1.69936	0.849679	−	0.527301i	$-0.176796\pi$
$229$	25.7159	1.69936	0.849679	+	0.527301i	$0.176796\pi$
$230$	−1.86933	−0.123260
$231$	12.4213	0.817259
$232$	−2.61472	−0.171665
$233$	−18.9109	−1.23889	−0.619446	−	0.785039i	$-0.712643\pi$
$233$	−18.9109	−1.23889	−0.619446	+	0.785039i	$0.712643\pi$
$234$	−33.0019	−2.15740
$235$	7.70674	0.502732
$236$	11.6882	0.760836
$237$	1.12046	0.0727816
$238$	7.66969	0.497152
$239$	17.8336	1.15356	0.576780	−	0.816900i	$-0.304309\pi$
$239$	17.8336	1.15356	0.576780	+	0.816900i	$0.304309\pi$
$240$	−12.8551	−0.829792
$241$	7.48099	0.481893	0.240946	−	0.970538i	$-0.422542\pi$
$241$	7.48099	0.481893	0.240946	+	0.970538i	$0.422542\pi$
$242$	8.86633	0.569949
$243$	−7.75260	−0.497330
$244$	−4.43357	−0.283830
$245$	2.92048	0.186582
$246$	14.1065	0.899396
$247$	−29.5874	−1.88260
$248$	4.88256	0.310043
$249$	−1.10973	−0.0703260
$250$	−31.8257	−2.01283
$251$	21.0242	1.32703	0.663516	−	0.748162i	$-0.269063\pi$
$251$	21.0242	1.32703	0.663516	+	0.748162i	$0.269063\pi$
$252$	17.7425	1.11767
$253$	−0.651079	−0.0409330
$254$	−16.7747	−1.05254
$255$	35.5394	2.22556
$256$	1.00000	0.0625000
$257$	−18.2594	−1.13899	−0.569495	−	0.821995i	$-0.692861\pi$
$257$	−18.2594	−1.13899	−0.569495	+	0.821995i	$0.692861\pi$
$258$	14.4556	0.899964
$259$	18.9499	1.17749
$260$	21.6412	1.34213
$261$	16.7224	1.03509
$262$	−1.72870	−0.106799
$263$	−6.79425	−0.418951	−0.209476	−	0.977814i	$-0.567176\pi$
$263$	−6.79425	−0.418951	−0.209476	+	0.977814i	$0.567176\pi$
$264$	−4.47737	−0.275563
$265$	−1.96715	−0.120841
$266$	15.9068	0.975310
$267$	−27.0853	−1.65759
$268$	−4.75276	−0.290321
$269$	−8.65242	−0.527547	−0.263774	−	0.964585i	$-0.584967\pi$
$269$	−8.65242	−0.527547	−0.263774	+	0.964585i	$0.584967\pi$
$270$	43.6491	2.65640
$271$	6.05294	0.367690	0.183845	−	0.982955i	$-0.441146\pi$
$271$	6.05294	0.367690	0.183845	+	0.982955i	$0.441146\pi$
$272$	−2.76462	−0.167630
$273$	−43.8801	−2.65575
$274$	1.46454	0.0884760
$275$	−18.3883	−1.10886
$276$	−1.36625	−0.0822384
$277$	7.59849	0.456549	0.228274	−	0.973597i	$-0.426692\pi$
$277$	7.59849	0.456549	0.228274	+	0.973597i	$0.426692\pi$
$278$	13.7374	0.823913
$279$	−31.2263	−1.86947
$280$	−11.6348	−0.695312
$281$	−8.20210	−0.489296	−0.244648	−	0.969612i	$-0.578672\pi$
$281$	−8.20210	−0.489296	−0.244648	+	0.969612i	$0.578672\pi$
$282$	5.63267	0.335421
$283$	1.35508	0.0805512	0.0402756	−	0.999189i	$-0.487176\pi$
$283$	1.35508	0.0805512	0.0402756	+	0.999189i	$0.487176\pi$
$284$	12.6008	0.747721
$285$	73.7082	4.36610
$286$	7.53754	0.445704
$287$	12.7674	0.753635
$288$	−6.39547	−0.376857
$289$	−9.35689	−0.550405
$290$	−10.9658	−0.643935
$291$	7.36951	0.432008
$292$	−6.74523	−0.394735
$293$	−1.70421	−0.0995610	−0.0497805	−	0.998760i	$-0.515852\pi$
$293$	−1.70421	−0.0995610	−0.0497805	+	0.998760i	$0.515852\pi$
$294$	2.13451	0.124487
$295$	49.0188	2.85399
$296$	−6.83067	−0.397025
$297$	15.2028	0.882155
$298$	17.7442	1.02790
$299$	2.30004	0.133015
$300$	−38.5866	−2.22780
$301$	13.0833	0.754111
$302$	18.3425	1.05549
$303$	−39.3629	−2.26134
$304$	−5.73378	−0.328855
$305$	−18.5938	−1.06468
$306$	17.6810	1.01076
$307$	−21.7810	−1.24311	−0.621553	−	0.783372i	$-0.713498\pi$
$307$	−21.7810	−1.24311	−0.621553	+	0.783372i	$0.713498\pi$
$308$	−4.05235	−0.230904
$309$	−50.2378	−2.85793
$310$	20.4769	1.16301
$311$	−4.67047	−0.264838	−0.132419	−	0.991194i	$-0.542274\pi$
$311$	−4.67047	−0.264838	−0.132419	+	0.991194i	$0.542274\pi$
$312$	15.8170	0.895463
$313$	−18.5828	−1.05036	−0.525181	−	0.850991i	$-0.676002\pi$
$313$	−18.5828	−1.05036	−0.525181	+	0.850991i	$0.676002\pi$
$314$	21.5026	1.21346
$315$	74.4100	4.19253
$316$	−0.365541	−0.0205633
$317$	30.2629	1.69973	0.849866	−	0.526999i	$-0.176683\pi$
$317$	30.2629	1.69973	0.849866	+	0.526999i	$0.176683\pi$
$318$	−1.43774	−0.0806247
$319$	−3.81935	−0.213842
$320$	4.19388	0.234445
$321$	32.7930	1.83033
$322$	−1.23655	−0.0689104
$323$	15.8517	0.882012
$324$	12.7156	0.706425
$325$	64.9596	3.60331
$326$	20.9092	1.15805
$327$	−9.21350	−0.509507
$328$	−4.60213	−0.254110
$329$	5.09798	0.281061
$330$	−18.7775	−1.03367
$331$	12.0552	0.662616	0.331308	−	0.943523i	$-0.392510\pi$
$331$	12.0552	0.662616	0.331308	+	0.943523i	$0.392510\pi$
$332$	0.362040	0.0198695
$333$	43.6854	2.39394
$334$	−24.0145	−1.31402
$335$	−19.9325	−1.08903
$336$	−8.50359	−0.463909
$337$	32.7778	1.78552	0.892760	−	0.450533i	$-0.148766\pi$
$337$	32.7778	1.78552	0.892760	+	0.450533i	$0.148766\pi$
$338$	−13.6276	−0.741242
$339$	48.8558	2.65348
$340$	−11.5945	−0.628798
$341$	7.13200	0.386220
$342$	36.6702	1.98290
$343$	−17.4877	−0.944249
$344$	−4.71602	−0.254271
$345$	−5.72987	−0.308486
$346$	−11.3209	−0.608613
$347$	−15.0728	−0.809150	−0.404575	−	0.914505i	$-0.632581\pi$
$347$	−15.0728	−0.809150	−0.404575	+	0.914505i	$0.632581\pi$
$348$	−8.01466	−0.429631
$349$	−2.69077	−0.144033	−0.0720167	−	0.997403i	$-0.522943\pi$
$349$	−2.69077	−0.144033	−0.0720167	+	0.997403i	$0.522943\pi$
$350$	−34.9237	−1.86675
$351$	−53.7063	−2.86663
$352$	1.46071	0.0778560
$353$	−22.0267	−1.17236	−0.586182	−	0.810179i	$-0.699370\pi$
$353$	−22.0267	−1.17236	−0.586182	+	0.810179i	$0.699370\pi$
$354$	35.8267	1.90417
$355$	52.8463	2.80479
$356$	8.83637	0.468327
$357$	23.5092	1.24424
$358$	−21.6284	−1.14310
$359$	−25.5491	−1.34843	−0.674214	−	0.738536i	$-0.735517\pi$
$359$	−25.5491	−1.34843	−0.674214	+	0.738536i	$0.735517\pi$
$360$	−26.8218	−1.41363
$361$	13.8762	0.730325
$362$	−18.4548	−0.969963
$363$	27.1771	1.42643
$364$	14.3156	0.750340
$365$	−28.2887	−1.48070
$366$	−13.5898	−0.710350
$367$	38.2674	1.99754	0.998772	−	0.0495408i	$-0.0157758\pi$
$367$	38.2674	1.99754	0.998772	+	0.0495408i	$0.0157758\pi$
$368$	0.445728	0.0232352
$369$	29.4328	1.53221
$370$	−28.6470	−1.48929
$371$	−1.30126	−0.0675583
$372$	14.9660	0.775953
$373$	−0.760855	−0.0393956	−0.0196978	−	0.999806i	$-0.506270\pi$
$373$	−0.760855	−0.0393956	−0.0196978	+	0.999806i	$0.506270\pi$
$374$	−4.03830	−0.208816
$375$	−97.5522	−5.03757
$376$	−1.83762	−0.0947679
$377$	13.4925	0.694898
$378$	28.8737	1.48510
$379$	17.5733	0.902681	0.451340	−	0.892352i	$-0.350946\pi$
$379$	17.5733	0.902681	0.451340	+	0.892352i	$0.350946\pi$
$380$	−24.0467	−1.23357
$381$	−51.4180	−2.63422
$382$	−19.5310	−0.999293
$383$	16.4499	0.840553	0.420276	−	0.907396i	$-0.361933\pi$
$383$	16.4499	0.840553	0.420276	+	0.907396i	$0.361933\pi$
$384$	3.06520	0.156421
$385$	−16.9950	−0.866147
$386$	−8.07861	−0.411191
$387$	30.1612	1.53318
$388$	−2.40425	−0.122057
$389$	−16.0464	−0.813584	−0.406792	−	0.913521i	$-0.633353\pi$
$389$	−16.0464	−0.813584	−0.406792	+	0.913521i	$0.633353\pi$
$390$	66.3347	3.35899
$391$	−1.23227	−0.0623185
$392$	−0.696367	−0.0351718
$393$	−5.29882	−0.267290
$394$	−0.626124	−0.0315436
$395$	−1.53303	−0.0771354
$396$	−9.34192	−0.469449
$397$	20.2834	1.01799	0.508997	−	0.860768i	$-0.330016\pi$
$397$	20.2834	1.01799	0.508997	+	0.860768i	$0.330016\pi$
$398$	−2.19031	−0.109790
$399$	48.7577	2.44094
$400$	12.5886	0.629430
$401$	3.19816	0.159709	0.0798543	−	0.996807i	$-0.474555\pi$
$401$	3.19816	0.159709	0.0798543	+	0.996807i	$0.474555\pi$
$402$	−14.5682	−0.726594
$403$	−25.1950	−1.25505
$404$	12.8419	0.638906
$405$	53.3279	2.64988
$406$	−7.25385	−0.360002
$407$	−9.97762	−0.494572
$408$	−8.47412	−0.419531
$409$	−20.3726	−1.00736	−0.503680	−	0.863890i	$-0.668021\pi$
$409$	−20.3726	−1.00736	−0.503680	+	0.863890i	$0.668021\pi$
$410$	−19.3008	−0.953197
$411$	4.48911	0.221431
$412$	16.3897	0.807464
$413$	32.4258	1.59557
$414$	−2.85064	−0.140101
$415$	1.51835	0.0745329
$416$	−5.16019	−0.252999
$417$	42.1078	2.06203
$418$	−8.37538	−0.409653
$419$	2.56331	0.125226	0.0626130	−	0.998038i	$-0.480057\pi$
$419$	2.56331	0.125226	0.0626130	+	0.998038i	$0.480057\pi$
$420$	−35.6630	−1.74018
$421$	−16.3036	−0.794588	−0.397294	−	0.917691i	$-0.630051\pi$
$421$	−16.3036	−0.794588	−0.397294	+	0.917691i	$0.630051\pi$
$422$	−16.3183	−0.794363
$423$	11.7524	0.571423
$424$	0.469054	0.0227793
$425$	−34.8027	−1.68818
$426$	38.6241	1.87134
$427$	−12.2998	−0.595227
$428$	−10.6985	−0.517130
$429$	23.1041	1.11548
$430$	−19.7784	−0.953799
$431$	−4.15383	−0.200083	−0.100041	−	0.994983i	$-0.531898\pi$
$431$	−4.15383	−0.200083	−0.100041	+	0.994983i	$0.531898\pi$
$432$	−10.4078	−0.500746
$433$	−5.48066	−0.263384	−0.131692	−	0.991291i	$-0.542041\pi$
$433$	−5.48066	−0.263384	−0.131692	+	0.991291i	$0.542041\pi$
$434$	13.5454	0.650198
$435$	−33.6125	−1.61160
$436$	3.00583	0.143953
$437$	−2.55570	−0.122256
$438$	−20.6755	−0.987914
$439$	−21.7058	−1.03596	−0.517980	−	0.855393i	$-0.673316\pi$
$439$	−21.7058	−1.03596	−0.517980	+	0.855393i	$0.673316\pi$
$440$	6.12603	0.292047
$441$	4.45359	0.212076
$442$	14.2660	0.678562
$443$	−0.234150	−0.0111248	−0.00556240	−	0.999985i	$-0.501771\pi$
$443$	−0.234150	−0.0111248	−0.00556240	+	0.999985i	$0.501771\pi$
$444$	−20.9374	−0.993645
$445$	37.0587	1.75675
$446$	20.4102	0.966453
$447$	54.3897	2.57254
$448$	2.77423	0.131070
$449$	8.27860	0.390691	0.195346	−	0.980734i	$-0.437417\pi$
$449$	8.27860	0.390691	0.195346	+	0.980734i	$0.437417\pi$
$450$	−80.5101	−3.79528
$451$	−6.72238	−0.316544
$452$	−15.9389	−0.749701
$453$	56.2236	2.64162
$454$	15.3617	0.720960
$455$	60.0377	2.81461
$456$	−17.5752	−0.823034
$457$	−23.6938	−1.10835	−0.554173	−	0.832401i	$-0.686966\pi$
$457$	−23.6938	−1.10835	−0.554173	+	0.832401i	$0.686966\pi$
$458$	−25.7159	−1.20163
$459$	28.7736	1.34304
$460$	1.86933	0.0871579
$461$	−2.51491	−0.117131	−0.0585656	−	0.998284i	$-0.518653\pi$
$461$	−2.51491	−0.117131	−0.0585656	+	0.998284i	$0.518653\pi$
$462$	−12.4213	−0.577890
$463$	−31.8881	−1.48197	−0.740983	−	0.671523i	$-0.765640\pi$
$463$	−31.8881	−1.48197	−0.740983	+	0.671523i	$0.765640\pi$
$464$	2.61472	0.121385
$465$	62.7658	2.91069
$466$	18.9109	0.876029
$467$	12.2784	0.568177	0.284089	−	0.958798i	$-0.408309\pi$
$467$	12.2784	0.568177	0.284089	+	0.958798i	$0.408309\pi$
$468$	33.0019	1.52551
$469$	−13.1853	−0.608838
$470$	−7.70674	−0.355486
$471$	65.9099	3.03697
$472$	−11.6882	−0.537993
$473$	−6.88873	−0.316744
$474$	−1.12046	−0.0514644
$475$	−72.1802	−3.31186
$476$	−7.66969	−0.351540
$477$	−2.99982	−0.137352
$478$	−17.8336	−0.815690
$479$	40.1439	1.83422	0.917111	−	0.398633i	$-0.130515\pi$
$479$	40.1439	1.83422	0.917111	+	0.398633i	$0.130515\pi$
$480$	12.8551	0.586752
$481$	35.2476	1.60715
$482$	−7.48099	−0.340750
$483$	−3.79029	−0.172464
$484$	−8.86633	−0.403015
$485$	−10.0831	−0.457851
$486$	7.75260	0.351665
$487$	−31.2967	−1.41819	−0.709094	−	0.705113i	$-0.750896\pi$
$487$	−31.2967	−1.41819	−0.709094	+	0.705113i	$0.750896\pi$
$488$	4.43357	0.200698
$489$	64.0909	2.89829
$490$	−2.92048	−0.131934
$491$	−16.6930	−0.753344	−0.376672	−	0.926347i	$-0.622932\pi$
$491$	−16.6930	−0.753344	−0.376672	+	0.926347i	$0.622932\pi$
$492$	−14.1065	−0.635969
$493$	−7.22871	−0.325565
$494$	29.5874	1.33120
$495$	−39.1789	−1.76096
$496$	−4.88256	−0.219234
$497$	34.9576	1.56806
$498$	1.10973	0.0497280
$499$	23.2012	1.03863	0.519314	−	0.854584i	$-0.326188\pi$
$499$	23.2012	1.03863	0.519314	+	0.854584i	$0.326188\pi$
$500$	31.8257	1.42329
$501$	−73.6093	−3.28862
$502$	−21.0242	−0.938354
$503$	30.8916	1.37739	0.688693	−	0.725053i	$-0.258185\pi$
$503$	30.8916	1.37739	0.688693	+	0.725053i	$0.258185\pi$
$504$	−17.7425	−0.790315
$505$	53.8572	2.39661
$506$	0.651079	0.0289440
$507$	−41.7713	−1.85513
$508$	16.7747	0.744259
$509$	27.0566	1.19926	0.599630	−	0.800277i	$-0.295314\pi$
$509$	27.0566	1.19926	0.599630	+	0.800277i	$0.295314\pi$
$510$	−35.5394	−1.57371
$511$	−18.7128	−0.827807
$512$	−1.00000	−0.0441942
$513$	59.6761	2.63476
$514$	18.2594	0.805387
$515$	68.7365	3.02889
$516$	−14.4556	−0.636370
$517$	−2.68422	−0.118052
$518$	−18.9499	−0.832610
$519$	−34.7008	−1.52319
$520$	−21.6412	−0.949030
$521$	−17.4838	−0.765981	−0.382990	−	0.923752i	$-0.625106\pi$
$521$	−17.4838	−0.765981	−0.382990	+	0.923752i	$0.625106\pi$
$522$	−16.7224	−0.731919
$523$	19.9416	0.871985	0.435992	−	0.899950i	$-0.356397\pi$
$523$	19.9416	0.871985	0.435992	+	0.899950i	$0.356397\pi$
$524$	1.72870	0.0755186
$525$	−107.048	−4.67197
$526$	6.79425	0.296243
$527$	13.4984	0.588001
$528$	4.47737	0.194853
$529$	−22.8013	−0.991362
$530$	1.96715	0.0854477
$531$	74.7515	3.24394
$532$	−15.9068	−0.689648
$533$	23.7479	1.02864
$534$	27.0853	1.17209
$535$	−44.8681	−1.93982
$536$	4.75276	0.205288
$537$	−66.2955	−2.86086
$538$	8.65242	0.373032
$539$	−1.01719	−0.0438134
$540$	−43.6491	−1.87836
$541$	27.3247	1.17478	0.587391	−	0.809303i	$-0.300155\pi$
$541$	27.3247	1.17478	0.587391	+	0.809303i	$0.300155\pi$
$542$	−6.05294	−0.259996
$543$	−56.5677	−2.42755
$544$	2.76462	0.118532
$545$	12.6061	0.539986
$546$	43.8801	1.87790
$547$	1.61605	0.0690974	0.0345487	−	0.999403i	$-0.489001\pi$
$547$	1.61605	0.0690974	0.0345487	+	0.999403i	$0.489001\pi$
$548$	−1.46454	−0.0625620
$549$	−28.3548	−1.21015
$550$	18.3883	0.784079
$551$	−14.9922	−0.638691
$552$	1.36625	0.0581513
$553$	−1.01410	−0.0431238
$554$	−7.59849	−0.322829
$555$	−87.8089	−3.72728
$556$	−13.7374	−0.582594
$557$	−22.6394	−0.959263	−0.479631	−	0.877470i	$-0.659230\pi$
$557$	−22.6394	−0.959263	−0.479631	+	0.877470i	$0.659230\pi$
$558$	31.2263	1.32191
$559$	24.3356	1.02928
$560$	11.6348	0.491660
$561$	−12.3782	−0.522609
$562$	8.20210	0.345985
$563$	−2.65044	−0.111703	−0.0558514	−	0.998439i	$-0.517787\pi$
$563$	−2.65044	−0.111703	−0.0558514	+	0.998439i	$0.517787\pi$
$564$	−5.63267	−0.237178
$565$	−66.8456	−2.81222
$566$	−1.35508	−0.0569583
$567$	35.2762	1.48146
$568$	−12.6008	−0.528719
$569$	40.5640	1.70053	0.850266	−	0.526353i	$-0.176441\pi$
$569$	40.5640	1.70053	0.850266	+	0.526353i	$0.176441\pi$
$570$	−73.7082	−3.08730
$571$	0.397993	0.0166555	0.00832775	−	0.999965i	$-0.497349\pi$
$571$	0.397993	0.0166555	0.00832775	+	0.999965i	$0.497349\pi$
$572$	−7.53754	−0.315160
$573$	−59.8665	−2.50096
$574$	−12.7674	−0.532900
$575$	5.61109	0.233999
$576$	6.39547	0.266478
$577$	2.20213	0.0916758	0.0458379	−	0.998949i	$-0.485404\pi$
$577$	2.20213	0.0916758	0.0458379	+	0.998949i	$0.485404\pi$
$578$	9.35689	0.389195
$579$	−24.7626	−1.02910
$580$	10.9658	0.455331
$581$	1.00438	0.0416688
$582$	−7.36951	−0.305476
$583$	0.685151	0.0283760
$584$	6.74523	0.279120
$585$	138.406	5.72237
$586$	1.70421	0.0704003
$587$	−6.34486	−0.261880	−0.130940	−	0.991390i	$-0.541800\pi$
$587$	−6.34486	−0.261880	−0.130940	+	0.991390i	$0.541800\pi$
$588$	−2.13451	−0.0880255
$589$	27.9955	1.15354
$590$	−49.0188	−2.01807
$591$	−1.91920	−0.0789452
$592$	6.83067	0.280739
$593$	24.2166	0.994458	0.497229	−	0.867619i	$-0.334351\pi$
$593$	24.2166	0.994458	0.497229	+	0.867619i	$0.334351\pi$
$594$	−15.2028	−0.623778
$595$	−32.1658	−1.31867
$596$	−17.7442	−0.726832
$597$	−6.71375	−0.274776
$598$	−2.30004	−0.0940557
$599$	32.6040	1.33216	0.666082	−	0.745879i	$-0.267970\pi$
$599$	32.6040	1.33216	0.666082	+	0.745879i	$0.267970\pi$
$600$	38.5866	1.57529
$601$	−23.1212	−0.943133	−0.471567	−	0.881830i	$-0.656311\pi$
$601$	−23.1212	−0.943133	−0.471567	+	0.881830i	$0.656311\pi$
$602$	−13.0833	−0.533237
$603$	−30.3961	−1.23783
$604$	−18.3425	−0.746348
$605$	−37.1843	−1.51176
$606$	39.3629	1.59901
$607$	−4.40534	−0.178807	−0.0894036	−	0.995995i	$-0.528496\pi$
$607$	−4.40534	−0.178807	−0.0894036	+	0.995995i	$0.528496\pi$
$608$	5.73378	0.232535
$609$	−22.2345	−0.900988
$610$	18.5938	0.752843
$611$	9.48246	0.383619
$612$	−17.6810	−0.714714
$613$	11.7306	0.473794	0.236897	−	0.971535i	$-0.423870\pi$
$613$	11.7306	0.473794	0.236897	+	0.971535i	$0.423870\pi$
$614$	21.7810	0.879008
$615$	−59.1608	−2.38559
$616$	4.05235	0.163274
$617$	−1.67417	−0.0673994	−0.0336997	−	0.999432i	$-0.510729\pi$
$617$	−1.67417	−0.0673994	−0.0336997	+	0.999432i	$0.510729\pi$
$618$	50.2378	2.02086
$619$	31.7118	1.27461	0.637303	−	0.770613i	$-0.280050\pi$
$619$	31.7118	1.27461	0.637303	+	0.770613i	$0.280050\pi$
$620$	−20.4769	−0.822371
$621$	−4.63905	−0.186159
$622$	4.67047	0.187269
$623$	24.5141	0.982139
$624$	−15.8170	−0.633188
$625$	70.5299	2.82120
$626$	18.5828	0.742718
$627$	−25.6722	−1.02525
$628$	−21.5026	−0.858047
$629$	−18.8842	−0.752962
$630$	−74.4100	−2.96456
$631$	−20.6405	−0.821687	−0.410844	−	0.911706i	$-0.634766\pi$
$631$	−20.6405	−0.821687	−0.410844	+	0.911706i	$0.634766\pi$
$632$	0.365541	0.0145404
$633$	−50.0190	−1.98808
$634$	−30.2629	−1.20189
$635$	70.3512	2.79180
$636$	1.43774	0.0570103
$637$	3.59339	0.142375
$638$	3.81935	0.151209
$639$	80.5882	3.18802
$640$	−4.19388	−0.165778
$641$	18.6374	0.736134	0.368067	−	0.929799i	$-0.380020\pi$
$641$	18.6374	0.736134	0.368067	+	0.929799i	$0.380020\pi$
$642$	−32.7930	−1.29424
$643$	−7.01861	−0.276787	−0.138394	−	0.990377i	$-0.544194\pi$
$643$	−7.01861	−0.276787	−0.138394	+	0.990377i	$0.544194\pi$
$644$	1.23655	0.0487270
$645$	−60.6248	−2.38710
$646$	−15.8517	−0.623677
$647$	−31.6708	−1.24511	−0.622554	−	0.782577i	$-0.713905\pi$
$647$	−31.6708	−1.24511	−0.622554	+	0.782577i	$0.713905\pi$
$648$	−12.7156	−0.499518
$649$	−17.0730	−0.670176
$650$	−64.9596	−2.54793
$651$	41.5193	1.62727
$652$	−20.9092	−0.818867
$653$	14.8572	0.581409	0.290705	−	0.956813i	$-0.406110\pi$
$653$	14.8572	0.581409	0.290705	+	0.956813i	$0.406110\pi$
$654$	9.21350	0.360276
$655$	7.24995	0.283279
$656$	4.60213	0.179683
$657$	−43.1389	−1.68301
$658$	−5.09798	−0.198740
$659$	8.86693	0.345407	0.172703	−	0.984974i	$-0.444750\pi$
$659$	8.86693	0.345407	0.172703	+	0.984974i	$0.444750\pi$
$660$	18.7775	0.730915
$661$	49.1387	1.91127	0.955637	−	0.294547i	$-0.0951686\pi$
$661$	49.1387	1.91127	0.955637	+	0.294547i	$0.0951686\pi$
$662$	−12.0552	−0.468541
$663$	43.7281	1.69826
$664$	−0.362040	−0.0140499
$665$	−66.7113	−2.58695
$666$	−43.6854	−1.69277
$667$	1.16546	0.0451266
$668$	24.0145	0.929149
$669$	62.5616	2.41877
$670$	19.9325	0.770059
$671$	6.47616	0.250009
$672$	8.50359	0.328033
$673$	−24.0831	−0.928336	−0.464168	−	0.885747i	$-0.653647\pi$
$673$	−24.0831	−0.928336	−0.464168	+	0.885747i	$0.653647\pi$
$674$	−32.7778	−1.26255
$675$	−131.020	−5.04296
$676$	13.6276	0.524137
$677$	−27.4519	−1.05506	−0.527531	−	0.849536i	$-0.676882\pi$
$677$	−27.4519	−1.05506	−0.527531	+	0.849536i	$0.676882\pi$
$678$	−48.8558	−1.87630
$679$	−6.66994	−0.255969
$680$	11.5945	0.444628
$681$	47.0867	1.80437
$682$	−7.13200	−0.273099
$683$	−11.7886	−0.451079	−0.225539	−	0.974234i	$-0.572414\pi$
$683$	−11.7886	−0.451079	−0.225539	+	0.974234i	$0.572414\pi$
$684$	−36.6702	−1.40212
$685$	−6.14209	−0.234677
$686$	17.4877	0.667685
$687$	−78.8246	−3.00735
$688$	4.71602	0.179797
$689$	−2.42041	−0.0922101
$690$	5.72987	0.218133
$691$	−46.6992	−1.77652	−0.888261	−	0.459340i	$-0.848086\pi$
$691$	−46.6992	−1.77652	−0.888261	+	0.459340i	$0.848086\pi$
$692$	11.3209	0.430355
$693$	−25.9167	−0.984493
$694$	15.0728	0.572156
$695$	−57.6128	−2.18538
$696$	8.01466	0.303795
$697$	−12.7231	−0.481923
$698$	2.69077	0.101847
$699$	57.9656	2.19246
$700$	34.9237	1.31999
$701$	−9.10253	−0.343798	−0.171899	−	0.985115i	$-0.554990\pi$
$701$	−9.10253	−0.343798	−0.171899	+	0.985115i	$0.554990\pi$
$702$	53.7063	2.02701
$703$	−39.1655	−1.47716
$704$	−1.46071	−0.0550525
$705$	−23.6227	−0.889684
$706$	22.0267	0.828987
$707$	35.6263	1.33987
$708$	−35.8267	−1.34645
$709$	21.7821	0.818045	0.409023	−	0.912524i	$-0.365870\pi$
$709$	21.7821	0.818045	0.409023	+	0.912524i	$0.365870\pi$
$710$	−52.8463	−1.98329
$711$	−2.33781	−0.0876747
$712$	−8.83637	−0.331157
$713$	−2.17630	−0.0815029
$714$	−23.5092	−0.879809
$715$	−31.6115	−1.18220
$716$	21.6284	0.808292
$717$	−54.6636	−2.04145
$718$	25.5491	0.953482
$719$	36.9438	1.37777	0.688885	−	0.724870i	$-0.258100\pi$
$719$	36.9438	1.37777	0.688885	+	0.724870i	$0.258100\pi$
$720$	26.8218	0.999590
$721$	45.4689	1.69335
$722$	−13.8762	−0.516418
$723$	−22.9307	−0.852804
$724$	18.4548	0.685867
$725$	32.9157	1.22246
$726$	−27.1771	−1.00864
$727$	−40.3173	−1.49529	−0.747643	−	0.664100i	$-0.768815\pi$
$727$	−40.3173	−1.49529	−0.747643	+	0.664100i	$0.768815\pi$
$728$	−14.3156	−0.530570
$729$	−14.3836	−0.532727
$730$	28.2887	1.04701
$731$	−13.0380	−0.482228
$732$	13.5898	0.502293
$733$	28.1473	1.03964	0.519821	−	0.854275i	$-0.325998\pi$
$733$	28.1473	1.03964	0.519821	+	0.854275i	$0.325998\pi$
$734$	−38.2674	−1.41248
$735$	−8.95185	−0.330194
$736$	−0.445728	−0.0164298
$737$	6.94239	0.255726
$738$	−29.4328	−1.08344
$739$	7.49058	0.275545	0.137773	−	0.990464i	$-0.456006\pi$
$739$	7.49058	0.275545	0.137773	+	0.990464i	$0.456006\pi$
$740$	28.6470	1.05308
$741$	90.6913	3.33163
$742$	1.30126	0.0477709
$743$	0.296959	0.0108944	0.00544719	−	0.999985i	$-0.498266\pi$
$743$	0.296959	0.0108944	0.00544719	+	0.999985i	$0.498266\pi$
$744$	−14.9660	−0.548682
$745$	−74.4171	−2.72643
$746$	0.760855	0.0278569
$747$	2.31542	0.0847166
$748$	4.03830	0.147655
$749$	−29.6801	−1.08449
$750$	97.5522	3.56210
$751$	−5.75904	−0.210150	−0.105075	−	0.994464i	$-0.533508\pi$
$751$	−5.75904	−0.210150	−0.105075	+	0.994464i	$0.533508\pi$
$752$	1.83762	0.0670110
$753$	−64.4433	−2.34844
$754$	−13.4925	−0.491367
$755$	−76.9264	−2.79964
$756$	−28.8737	−1.05013
$757$	25.1288	0.913322	0.456661	−	0.889641i	$-0.349045\pi$
$757$	25.1288	0.913322	0.456661	+	0.889641i	$0.349045\pi$
$758$	−17.5733	−0.638292
$759$	1.99569	0.0724389
$760$	24.0467	0.872267
$761$	−10.7010	−0.387911	−0.193955	−	0.981010i	$-0.562132\pi$
$761$	−10.7010	−0.387911	−0.193955	+	0.981010i	$0.562132\pi$
$762$	51.4180	1.86268
$763$	8.33888	0.301888
$764$	19.5310	0.706607
$765$	−74.1521	−2.68097
$766$	−16.4499	−0.594361
$767$	60.3133	2.17779
$768$	−3.06520	−0.110606
$769$	16.2172	0.584807	0.292403	−	0.956295i	$-0.405545\pi$
$769$	16.2172	0.584807	0.292403	+	0.956295i	$0.405545\pi$
$770$	16.9950	0.612459
$771$	55.9687	2.01566
$772$	8.07861	0.290756
$773$	−21.3015	−0.766161	−0.383080	−	0.923715i	$-0.625137\pi$
$773$	−21.3015	−0.766161	−0.383080	+	0.923715i	$0.625137\pi$
$774$	−30.1612	−1.08412
$775$	−61.4647	−2.20788
$776$	2.40425	0.0863074
$777$	−58.0852	−2.08380
$778$	16.0464	0.575291
$779$	−26.3876	−0.945434
$780$	−66.3347	−2.37516
$781$	−18.4061	−0.658623
$782$	1.23227	0.0440658
$783$	−27.2135	−0.972533
$784$	0.696367	0.0248702
$785$	−90.1793	−3.21864
$786$	5.29882	0.189003
$787$	−26.4017	−0.941120	−0.470560	−	0.882368i	$-0.655948\pi$
$787$	−26.4017	−0.941120	−0.470560	+	0.882368i	$0.655948\pi$
$788$	0.626124	0.0223047
$789$	20.8258	0.741417
$790$	1.53303	0.0545429
$791$	−44.2181	−1.57221
$792$	9.34192	0.331951
$793$	−22.8781	−0.812424
$794$	−20.2834	−0.719830
$795$	6.02973	0.213852
$796$	2.19031	0.0776336
$797$	−2.20499	−0.0781046	−0.0390523	−	0.999237i	$-0.512434\pi$
$797$	−2.20499	−0.0781046	−0.0390523	+	0.999237i	$0.512434\pi$
$798$	−48.7577	−1.72600
$799$	−5.08031	−0.179729
$800$	−12.5886	−0.445074
$801$	56.5128	1.99678
$802$	−3.19816	−0.112931
$803$	9.85282	0.347698
$804$	14.5682	0.513780
$805$	5.18595	0.182781
$806$	25.1950	0.887455
$807$	26.5214	0.933598
$808$	−12.8419	−0.451775
$809$	−43.3673	−1.52471	−0.762356	−	0.647158i	$-0.775957\pi$
$809$	−43.3673	−1.52471	−0.762356	+	0.647158i	$0.775957\pi$
$810$	−53.3279	−1.87375
$811$	−44.7538	−1.57152	−0.785759	−	0.618533i	$-0.787727\pi$
$811$	−44.7538	−1.57152	−0.785759	+	0.618533i	$0.787727\pi$
$812$	7.25385	0.254560
$813$	−18.5535	−0.650699
$814$	9.97762	0.349716
$815$	−87.6905	−3.07167
$816$	8.47412	0.296653
$817$	−27.0406	−0.946031
$818$	20.3726	0.712311
$819$	91.5548	3.19918
$820$	19.3008	0.674012
$821$	−9.13165	−0.318697	−0.159348	−	0.987222i	$-0.550939\pi$
$821$	−9.13165	−0.318697	−0.159348	+	0.987222i	$0.550939\pi$
$822$	−4.48911	−0.156576
$823$	−19.8752	−0.692806	−0.346403	−	0.938086i	$-0.612597\pi$
$823$	−19.8752	−0.692806	−0.346403	+	0.938086i	$0.612597\pi$
$824$	−16.3897	−0.570963
$825$	56.3638	1.96234
$826$	−32.4258	−1.12824
$827$	45.8950	1.59593	0.797963	−	0.602706i	$-0.205911\pi$
$827$	45.8950	1.59593	0.797963	+	0.602706i	$0.205911\pi$
$828$	2.85064	0.0990666
$829$	−22.9479	−0.797013	−0.398507	−	0.917165i	$-0.630471\pi$
$829$	−22.9479	−0.797013	−0.398507	+	0.917165i	$0.630471\pi$
$830$	−1.51835	−0.0527027
$831$	−23.2909	−0.807953
$832$	5.16019	0.178897
$833$	−1.92519	−0.0667038
$834$	−42.1078	−1.45808
$835$	100.714	3.48535
$836$	8.37538	0.289668
$837$	50.8168	1.75649
$838$	−2.56331	−0.0885481
$839$	−30.1617	−1.04130	−0.520648	−	0.853771i	$-0.674310\pi$
$839$	−30.1617	−1.04130	−0.520648	+	0.853771i	$0.674310\pi$
$840$	35.6630	1.23049
$841$	−22.1632	−0.764249
$842$	16.3036	0.561859
$843$	25.1411	0.865906
$844$	16.3183	0.561700
$845$	57.1524	1.96610
$846$	−11.7524	−0.404057
$847$	−24.5973	−0.845172
$848$	−0.469054	−0.0161074
$849$	−4.15360	−0.142551
$850$	34.8027	1.19372
$851$	3.04462	0.104368
$852$	−38.6241	−1.32324
$853$	8.86955	0.303688	0.151844	−	0.988404i	$-0.451479\pi$
$853$	8.86955	0.303688	0.151844	+	0.988404i	$0.451479\pi$
$854$	12.2998	0.420889
$855$	−153.790	−5.25952
$856$	10.6985	0.365666
$857$	23.5905	0.805837	0.402918	−	0.915236i	$-0.367996\pi$
$857$	23.5905	0.805837	0.402918	+	0.915236i	$0.367996\pi$
$858$	−23.1041	−0.788760
$859$	40.3158	1.37556	0.687779	−	0.725920i	$-0.258586\pi$
$859$	40.3158	1.37556	0.687779	+	0.725920i	$0.258586\pi$
$860$	19.7784	0.674438
$861$	−39.1346	−1.33370
$862$	4.15383	0.141480
$863$	26.9799	0.918407	0.459203	−	0.888331i	$-0.348135\pi$
$863$	26.9799	0.918407	0.459203	+	0.888331i	$0.348135\pi$
$864$	10.4078	0.354081
$865$	47.4783	1.61431
$866$	5.48066	0.186240
$867$	28.6808	0.974050
$868$	−13.5454	−0.459760
$869$	0.533949	0.0181130
$870$	33.6125	1.13957
$871$	−24.5251	−0.831002
$872$	−3.00583	−0.101790
$873$	−15.3763	−0.520409
$874$	2.55570	0.0864480
$875$	88.2918	2.98481
$876$	20.6755	0.698561
$877$	−20.6191	−0.696259	−0.348129	−	0.937446i	$-0.613183\pi$
$877$	−20.6191	−0.696259	−0.348129	+	0.937446i	$0.613183\pi$
$878$	21.7058	0.732534
$879$	5.22375	0.176193
$880$	−6.12603	−0.206509
$881$	20.1284	0.678141	0.339071	−	0.940761i	$-0.389887\pi$
$881$	20.1284	0.678141	0.339071	+	0.940761i	$0.389887\pi$
$882$	−4.45359	−0.149960
$883$	55.0960	1.85413	0.927064	−	0.374904i	$-0.122324\pi$
$883$	55.0960	1.85413	0.927064	+	0.374904i	$0.122324\pi$
$884$	−14.2660	−0.479816
$885$	−150.253	−5.05069
$886$	0.234150	0.00786642
$887$	49.1273	1.64953	0.824767	−	0.565473i	$-0.191306\pi$
$887$	49.1273	1.64953	0.824767	+	0.565473i	$0.191306\pi$
$888$	20.9374	0.702613
$889$	46.5371	1.56080
$890$	−37.0587	−1.24221
$891$	−18.5739	−0.622248
$892$	−20.4102	−0.683386
$893$	−10.5365	−0.352590
$894$	−54.3897	−1.81906
$895$	90.7069	3.03200
$896$	−2.77423	−0.0926806
$897$	−7.05010	−0.235396
$898$	−8.27860	−0.276261
$899$	−12.7665	−0.425788
$900$	80.5101	2.68367
$901$	1.29675	0.0432011
$902$	6.72238	0.223831
$903$	−40.1031	−1.33455
$904$	15.9389	0.530118
$905$	77.3972	2.57277
$906$	−56.2236	−1.86791
$907$	−37.8655	−1.25730	−0.628651	−	0.777687i	$-0.716393\pi$
$907$	−37.8655	−1.25730	−0.628651	+	0.777687i	$0.716393\pi$
$908$	−15.3617	−0.509796
$909$	82.1297	2.72407
$910$	−60.0377	−1.99023
$911$	−3.62739	−0.120181	−0.0600904	−	0.998193i	$-0.519139\pi$
$911$	−3.62739	−0.120181	−0.0600904	+	0.998193i	$0.519139\pi$
$912$	17.5752	0.581973
$913$	−0.528835	−0.0175019
$914$	23.6938	0.783720
$915$	56.9939	1.88416
$916$	25.7159	0.849679
$917$	4.79581	0.158372
$918$	−28.7736	−0.949671
$919$	3.70868	0.122338	0.0611691	−	0.998127i	$-0.480517\pi$
$919$	3.70868	0.122338	0.0611691	+	0.998127i	$0.480517\pi$
$920$	−1.86933	−0.0616299
$921$	66.7631	2.19992
$922$	2.51491	0.0828242
$923$	65.0226	2.14025
$924$	12.4213	0.408630
$925$	85.9886	2.82729
$926$	31.8881	1.04791
$927$	104.820	3.44274
$928$	−2.61472	−0.0858325
$929$	−48.9057	−1.60454	−0.802271	−	0.596959i	$-0.796375\pi$
$929$	−48.9057	−1.60454	−0.802271	+	0.596959i	$0.796375\pi$
$930$	−62.7658	−2.05817
$931$	−3.99281	−0.130859
$932$	−18.9109	−0.619446
$933$	14.3159	0.468683
$934$	−12.2784	−0.401762
$935$	16.9361	0.553871
$936$	−33.0019	−1.07870
$937$	11.5932	0.378734	0.189367	−	0.981906i	$-0.439356\pi$
$937$	11.5932	0.378734	0.189367	+	0.981906i	$0.439356\pi$
$938$	13.1853	0.430514
$939$	56.9601	1.85882
$940$	7.70674	0.251366
$941$	26.0619	0.849592	0.424796	−	0.905289i	$-0.360346\pi$
$941$	26.0619	0.849592	0.424796	+	0.905289i	$0.360346\pi$
$942$	−65.9099	−2.14746
$943$	2.05130	0.0667995
$944$	11.6882	0.380418
$945$	−121.093	−3.93915
$946$	6.88873	0.223972
$947$	14.7442	0.479122	0.239561	−	0.970881i	$-0.422996\pi$
$947$	14.7442	0.479122	0.239561	+	0.970881i	$0.422996\pi$
$948$	1.12046	0.0363908
$949$	−34.8067	−1.12987
$950$	72.1802	2.34184
$951$	−92.7619	−3.00801
$952$	7.66969	0.248576
$953$	60.5974	1.96294	0.981471	−	0.191610i	$-0.0613710\pi$
$953$	60.5974	1.96294	0.981471	+	0.191610i	$0.0613710\pi$
$954$	2.99982	0.0971227
$955$	81.9106	2.65057
$956$	17.8336	0.576780
$957$	11.7071	0.378436
$958$	−40.1439	−1.29699
$959$	−4.06297	−0.131200
$960$	−12.8551	−0.414896
$961$	−7.16058	−0.230986
$962$	−35.2476	−1.13643
$963$	−68.4218	−2.20486
$964$	7.48099	0.240946
$965$	33.8807	1.09066
$966$	3.79029	0.121951
$967$	−51.9975	−1.67213	−0.836063	−	0.548634i	$-0.815148\pi$
$967$	−51.9975	−1.67213	−0.836063	+	0.548634i	$0.815148\pi$
$968$	8.86633	0.284975
$969$	−48.5887	−1.56089
$970$	10.0831	0.323749
$971$	−44.6545	−1.43303	−0.716516	−	0.697571i	$-0.754264\pi$
$971$	−44.6545	−1.43303	−0.716516	+	0.697571i	$0.754264\pi$
$972$	−7.75260	−0.248665
$973$	−38.1107	−1.22177
$974$	31.2967	1.00281
$975$	−199.114	−6.37676
$976$	−4.43357	−0.141915
$977$	−24.9150	−0.797101	−0.398550	−	0.917146i	$-0.630487\pi$
$977$	−24.9150	−0.797101	−0.398550	+	0.917146i	$0.630487\pi$
$978$	−64.0909	−2.04940
$979$	−12.9074	−0.412521
$980$	2.92048	0.0932912
$981$	19.2237	0.613767
$982$	16.6930	0.532695
$983$	34.6967	1.10665	0.553326	−	0.832965i	$-0.313358\pi$
$983$	34.6967	1.10665	0.553326	+	0.832965i	$0.313358\pi$
$984$	14.1065	0.449698
$985$	2.62589	0.0836677
$986$	7.22871	0.230209
$987$	−15.6263	−0.497392
$988$	−29.5874	−0.941300
$989$	2.10206	0.0668417
$990$	39.1789	1.24519
$991$	1.24280	0.0394788	0.0197394	−	0.999805i	$-0.493716\pi$
$991$	1.24280	0.0394788	0.0197394	+	0.999805i	$0.493716\pi$
$992$	4.88256	0.155022
$993$	−36.9518	−1.17263
$994$	−34.9576	−1.10879
$995$	9.18590	0.291213
$996$	−1.10973	−0.0351630
$997$	−22.6523	−0.717406	−0.358703	−	0.933452i	$-0.616781\pi$
$997$	−22.6523	−0.717406	−0.358703	+	0.933452i	$0.616781\pi$
$998$	−23.2012	−0.734420
$999$	−71.0924	−2.24926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.4	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.4	✓	42	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.06520 q^{3} +1.00000 q^{4} +4.19388 q^{5} +3.06520 q^{6} +2.77423 q^{7} -1.00000 q^{8} +6.39547 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.06520 q^{3} +1.00000 q^{4} +4.19388 q^{5} +3.06520 q^{6} +2.77423 q^{7} -1.00000 q^{8} +6.39547 q^{9} -4.19388 q^{10} -1.46071 q^{11} -3.06520 q^{12} +5.16019 q^{13} -2.77423 q^{14} -12.8551 q^{15} +1.00000 q^{16} -2.76462 q^{17} -6.39547 q^{18} -5.73378 q^{19} +4.19388 q^{20} -8.50359 q^{21} +1.46071 q^{22} +0.445728 q^{23} +3.06520 q^{24} +12.5886 q^{25} -5.16019 q^{26} -10.4078 q^{27} +2.77423 q^{28} +2.61472 q^{29} +12.8551 q^{30} -4.88256 q^{31} -1.00000 q^{32} +4.47737 q^{33} +2.76462 q^{34} +11.6348 q^{35} +6.39547 q^{36} +6.83067 q^{37} +5.73378 q^{38} -15.8170 q^{39} -4.19388 q^{40} +4.60213 q^{41} +8.50359 q^{42} +4.71602 q^{43} -1.46071 q^{44} +26.8218 q^{45} -0.445728 q^{46} +1.83762 q^{47} -3.06520 q^{48} +0.696367 q^{49} -12.5886 q^{50} +8.47412 q^{51} +5.16019 q^{52} -0.469054 q^{53} +10.4078 q^{54} -6.12603 q^{55} -2.77423 q^{56} +17.5752 q^{57} -2.61472 q^{58} +11.6882 q^{59} -12.8551 q^{60} -4.43357 q^{61} +4.88256 q^{62} +17.7425 q^{63} +1.00000 q^{64} +21.6412 q^{65} -4.47737 q^{66} -4.75276 q^{67} -2.76462 q^{68} -1.36625 q^{69} -11.6348 q^{70} +12.6008 q^{71} -6.39547 q^{72} -6.74523 q^{73} -6.83067 q^{74} -38.5866 q^{75} -5.73378 q^{76} -4.05235 q^{77} +15.8170 q^{78} -0.365541 q^{79} +4.19388 q^{80} +12.7156 q^{81} -4.60213 q^{82} +0.362040 q^{83} -8.50359 q^{84} -11.5945 q^{85} -4.71602 q^{86} -8.01466 q^{87} +1.46071 q^{88} +8.83637 q^{89} -26.8218 q^{90} +14.3156 q^{91} +0.445728 q^{92} +14.9660 q^{93} -1.83762 q^{94} -24.0467 q^{95} +3.06520 q^{96} -2.40425 q^{97} -0.696367 q^{98} -9.34192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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