LMFDB - Embedded newform 4010.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.507814$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.507814 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.507814 q^{6} +1.00840 q^{7} -1.00000 q^{8} -2.74213 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.507814 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.507814 q^{6} +1.00840 q^{7} -1.00000 q^{8} -2.74213 q^{9} +1.00000 q^{10} +1.14369 q^{11} +0.507814 q^{12} -2.05099 q^{13} -1.00840 q^{14} -0.507814 q^{15} +1.00000 q^{16} +6.55597 q^{17} +2.74213 q^{18} -3.91995 q^{19} -1.00000 q^{20} +0.512078 q^{21} -1.14369 q^{22} -2.79831 q^{23} -0.507814 q^{24} +1.00000 q^{25} +2.05099 q^{26} -2.91593 q^{27} +1.00840 q^{28} -3.74610 q^{29} +0.507814 q^{30} +7.43315 q^{31} -1.00000 q^{32} +0.580783 q^{33} -6.55597 q^{34} -1.00840 q^{35} -2.74213 q^{36} -4.68283 q^{37} +3.91995 q^{38} -1.04152 q^{39} +1.00000 q^{40} +11.8154 q^{41} -0.512078 q^{42} +10.3010 q^{43} +1.14369 q^{44} +2.74213 q^{45} +2.79831 q^{46} -8.20270 q^{47} +0.507814 q^{48} -5.98313 q^{49} -1.00000 q^{50} +3.32921 q^{51} -2.05099 q^{52} -8.22595 q^{53} +2.91593 q^{54} -1.14369 q^{55} -1.00840 q^{56} -1.99060 q^{57} +3.74610 q^{58} +7.81254 q^{59} -0.507814 q^{60} +3.18656 q^{61} -7.43315 q^{62} -2.76515 q^{63} +1.00000 q^{64} +2.05099 q^{65} -0.580783 q^{66} +6.44414 q^{67} +6.55597 q^{68} -1.42102 q^{69} +1.00840 q^{70} -15.5631 q^{71} +2.74213 q^{72} +8.43433 q^{73} +4.68283 q^{74} +0.507814 q^{75} -3.91995 q^{76} +1.15330 q^{77} +1.04152 q^{78} +8.56541 q^{79} -1.00000 q^{80} +6.74563 q^{81} -11.8154 q^{82} +0.905124 q^{83} +0.512078 q^{84} -6.55597 q^{85} -10.3010 q^{86} -1.90232 q^{87} -1.14369 q^{88} -1.54275 q^{89} -2.74213 q^{90} -2.06821 q^{91} -2.79831 q^{92} +3.77465 q^{93} +8.20270 q^{94} +3.91995 q^{95} -0.507814 q^{96} +3.83789 q^{97} +5.98313 q^{98} -3.13615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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
$3$	0.507814	0.293186	0.146593	−	0.989197i	$-0.453169\pi$
$3$	0.507814	0.293186	0.146593	+	0.989197i	$0.453169\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.507814	−0.207314
$7$	1.00840	0.381138	0.190569	−	0.981674i	$-0.438967\pi$
$7$	1.00840	0.381138	0.190569	+	0.981674i	$0.438967\pi$
$8$	−1.00000	−0.353553
$9$	−2.74213	−0.914042
$10$	1.00000	0.316228
$11$	1.14369	0.344837	0.172418	−	0.985024i	$-0.444842\pi$
$11$	1.14369	0.344837	0.172418	+	0.985024i	$0.444842\pi$
$12$	0.507814	0.146593
$13$	−2.05099	−0.568842	−0.284421	−	0.958699i	$-0.591801\pi$
$13$	−2.05099	−0.568842	−0.284421	+	0.958699i	$0.591801\pi$
$14$	−1.00840	−0.269506
$15$	−0.507814	−0.131117
$16$	1.00000	0.250000
$17$	6.55597	1.59006	0.795029	−	0.606572i	$-0.207456\pi$
$17$	6.55597	1.59006	0.795029	+	0.606572i	$0.207456\pi$
$18$	2.74213	0.646325
$19$	−3.91995	−0.899299	−0.449649	−	0.893205i	$-0.648451\pi$
$19$	−3.91995	−0.899299	−0.449649	+	0.893205i	$0.648451\pi$
$20$	−1.00000	−0.223607
$21$	0.512078	0.111745
$22$	−1.14369	−0.243836
$23$	−2.79831	−0.583488	−0.291744	−	0.956496i	$-0.594236\pi$
$23$	−2.79831	−0.583488	−0.291744	+	0.956496i	$0.594236\pi$
$24$	−0.507814	−0.103657
$25$	1.00000	0.200000
$26$	2.05099	0.402232
$27$	−2.91593	−0.561171
$28$	1.00840	0.190569
$29$	−3.74610	−0.695634	−0.347817	−	0.937563i	$-0.613077\pi$
$29$	−3.74610	−0.695634	−0.347817	+	0.937563i	$0.613077\pi$
$30$	0.507814	0.0927137
$31$	7.43315	1.33503	0.667517	−	0.744595i	$-0.267357\pi$
$31$	7.43315	1.33503	0.667517	+	0.744595i	$0.267357\pi$
$32$	−1.00000	−0.176777
$33$	0.580783	0.101101
$34$	−6.55597	−1.12434
$35$	−1.00840	−0.170450
$36$	−2.74213	−0.457021
$37$	−4.68283	−0.769853	−0.384926	−	0.922947i	$-0.625773\pi$
$37$	−4.68283	−0.769853	−0.384926	+	0.922947i	$0.625773\pi$
$38$	3.91995	0.635900
$39$	−1.04152	−0.166777
$40$	1.00000	0.158114
$41$	11.8154	1.84525	0.922625	−	0.385698i	$-0.126039\pi$
$41$	11.8154	1.84525	0.922625	+	0.385698i	$0.126039\pi$
$42$	−0.512078	−0.0790153
$43$	10.3010	1.57088	0.785440	−	0.618937i	$-0.212436\pi$
$43$	10.3010	1.57088	0.785440	+	0.618937i	$0.212436\pi$
$44$	1.14369	0.172418
$45$	2.74213	0.408772
$46$	2.79831	0.412589
$47$	−8.20270	−1.19649	−0.598244	−	0.801314i	$-0.704134\pi$
$47$	−8.20270	−1.19649	−0.598244	+	0.801314i	$0.704134\pi$
$48$	0.507814	0.0732966
$49$	−5.98313	−0.854734
$50$	−1.00000	−0.141421
$51$	3.32921	0.466183
$52$	−2.05099	−0.284421
$53$	−8.22595	−1.12992	−0.564961	−	0.825118i	$-0.691109\pi$
$53$	−8.22595	−1.12992	−0.564961	+	0.825118i	$0.691109\pi$
$54$	2.91593	0.396808
$55$	−1.14369	−0.154216
$56$	−1.00840	−0.134753
$57$	−1.99060	−0.263662
$58$	3.74610	0.491887
$59$	7.81254	1.01711	0.508553	−	0.861031i	$-0.330180\pi$
$59$	7.81254	1.01711	0.508553	+	0.861031i	$0.330180\pi$
$60$	−0.507814	−0.0655585
$61$	3.18656	0.407998	0.203999	−	0.978971i	$-0.434606\pi$
$61$	3.18656	0.407998	0.203999	+	0.978971i	$0.434606\pi$
$62$	−7.43315	−0.944011
$63$	−2.76515	−0.348376
$64$	1.00000	0.125000
$65$	2.05099	0.254394
$66$	−0.580783	−0.0714895
$67$	6.44414	0.787277	0.393639	−	0.919265i	$-0.371216\pi$
$67$	6.44414	0.787277	0.393639	+	0.919265i	$0.371216\pi$
$68$	6.55597	0.795029
$69$	−1.42102	−0.171071
$70$	1.00840	0.120527
$71$	−15.5631	−1.84699	−0.923497	−	0.383605i	$-0.874682\pi$
$71$	−15.5631	−1.84699	−0.923497	+	0.383605i	$0.874682\pi$
$72$	2.74213	0.323163
$73$	8.43433	0.987164	0.493582	−	0.869699i	$-0.335687\pi$
$73$	8.43433	0.987164	0.493582	+	0.869699i	$0.335687\pi$
$74$	4.68283	0.544368
$75$	0.507814	0.0586373
$76$	−3.91995	−0.449649
$77$	1.15330	0.131431
$78$	1.04152	0.117929
$79$	8.56541	0.963684	0.481842	−	0.876258i	$-0.339968\pi$
$79$	8.56541	0.963684	0.481842	+	0.876258i	$0.339968\pi$
$80$	−1.00000	−0.111803
$81$	6.74563	0.749514
$82$	−11.8154	−1.30479
$83$	0.905124	0.0993502	0.0496751	−	0.998765i	$-0.484181\pi$
$83$	0.905124	0.0993502	0.0496751	+	0.998765i	$0.484181\pi$
$84$	0.512078	0.0558723
$85$	−6.55597	−0.711095
$86$	−10.3010	−1.11078
$87$	−1.90232	−0.203950
$88$	−1.14369	−0.121918
$89$	−1.54275	−0.163531	−0.0817654	−	0.996652i	$-0.526056\pi$
$89$	−1.54275	−0.163531	−0.0817654	+	0.996652i	$0.526056\pi$
$90$	−2.74213	−0.289045
$91$	−2.06821	−0.216808
$92$	−2.79831	−0.291744
$93$	3.77465	0.391413
$94$	8.20270	0.846044
$95$	3.91995	0.402179
$96$	−0.507814	−0.0518285
$97$	3.83789	0.389679	0.194839	−	0.980835i	$-0.437581\pi$
$97$	3.83789	0.389679	0.194839	+	0.980835i	$0.437581\pi$
$98$	5.98313	0.604388
$99$	−3.13615	−0.315195
$100$	1.00000	0.100000
$101$	15.0709	1.49961	0.749805	−	0.661659i	$-0.230148\pi$
$101$	15.0709	1.49961	0.749805	+	0.661659i	$0.230148\pi$
$102$	−3.32921	−0.329641
$103$	−0.419848	−0.0413689	−0.0206844	−	0.999786i	$-0.506585\pi$
$103$	−0.419848	−0.0413689	−0.0206844	+	0.999786i	$0.506585\pi$
$104$	2.05099	0.201116
$105$	−0.512078	−0.0499737
$106$	8.22595	0.798975
$107$	5.38922	0.520995	0.260498	−	0.965474i	$-0.416113\pi$
$107$	5.38922	0.520995	0.260498	+	0.965474i	$0.416113\pi$
$108$	−2.91593	−0.280585
$109$	−7.44373	−0.712980	−0.356490	−	0.934299i	$-0.616027\pi$
$109$	−7.44373	−0.712980	−0.356490	+	0.934299i	$0.616027\pi$
$110$	1.14369	0.109047
$111$	−2.37801	−0.225710
$112$	1.00840	0.0952846
$113$	7.03637	0.661926	0.330963	−	0.943644i	$-0.392626\pi$
$113$	7.03637	0.661926	0.330963	+	0.943644i	$0.392626\pi$
$114$	1.99060	0.186437
$115$	2.79831	0.260944
$116$	−3.74610	−0.347817
$117$	5.62407	0.519945
$118$	−7.81254	−0.719203
$119$	6.61103	0.606032
$120$	0.507814	0.0463568
$121$	−9.69196	−0.881088
$122$	−3.18656	−0.288498
$123$	6.00000	0.541002
$124$	7.43315	0.667517
$125$	−1.00000	−0.0894427
$126$	2.76515	0.246339
$127$	4.18623	0.371468	0.185734	−	0.982600i	$-0.440534\pi$
$127$	4.18623	0.371468	0.185734	+	0.982600i	$0.440534\pi$
$128$	−1.00000	−0.0883883
$129$	5.23096	0.460561
$130$	−2.05099	−0.179884
$131$	11.3317	0.990052	0.495026	−	0.868878i	$-0.335159\pi$
$131$	11.3317	0.990052	0.495026	+	0.868878i	$0.335159\pi$
$132$	0.580783	0.0505507
$133$	−3.95287	−0.342757
$134$	−6.44414	−0.556689
$135$	2.91593	0.250963
$136$	−6.55597	−0.562170
$137$	5.64994	0.482707	0.241353	−	0.970437i	$-0.422409\pi$
$137$	5.64994	0.482707	0.241353	+	0.970437i	$0.422409\pi$
$138$	1.42102	0.120965
$139$	6.80751	0.577405	0.288703	−	0.957419i	$-0.406776\pi$
$139$	6.80751	0.577405	0.288703	+	0.957419i	$0.406776\pi$
$140$	−1.00840	−0.0852251
$141$	−4.16544	−0.350794
$142$	15.5631	1.30602
$143$	−2.34570	−0.196158
$144$	−2.74213	−0.228510
$145$	3.74610	0.311097
$146$	−8.43433	−0.698030
$147$	−3.03832	−0.250596
$148$	−4.68283	−0.384926
$149$	19.1008	1.56480	0.782399	−	0.622777i	$-0.213996\pi$
$149$	19.1008	1.56480	0.782399	+	0.622777i	$0.213996\pi$
$150$	−0.507814	−0.0414628
$151$	−2.45068	−0.199434	−0.0997168	−	0.995016i	$-0.531794\pi$
$151$	−2.45068	−0.199434	−0.0997168	+	0.995016i	$0.531794\pi$
$152$	3.91995	0.317950
$153$	−17.9773	−1.45338
$154$	−1.15330	−0.0929354
$155$	−7.43315	−0.597045
$156$	−1.04152	−0.0833884
$157$	16.7062	1.33330	0.666648	−	0.745372i	$-0.267728\pi$
$157$	16.7062	1.33330	0.666648	+	0.745372i	$0.267728\pi$
$158$	−8.56541	−0.681428
$159$	−4.17725	−0.331278
$160$	1.00000	0.0790569
$161$	−2.82181	−0.222390
$162$	−6.74563	−0.529987
$163$	16.7232	1.30986	0.654929	−	0.755690i	$-0.272698\pi$
$163$	16.7232	1.30986	0.654929	+	0.755690i	$0.272698\pi$
$164$	11.8154	0.922625
$165$	−0.580783	−0.0452139
$166$	−0.905124	−0.0702512
$167$	−3.16416	−0.244850	−0.122425	−	0.992478i	$-0.539067\pi$
$167$	−3.16416	−0.244850	−0.122425	+	0.992478i	$0.539067\pi$
$168$	−0.512078	−0.0395077
$169$	−8.79344	−0.676419
$170$	6.55597	0.502820
$171$	10.7490	0.821996
$172$	10.3010	0.785440
$173$	13.1339	0.998548	0.499274	−	0.866444i	$-0.333600\pi$
$173$	13.1339	0.998548	0.499274	+	0.866444i	$0.333600\pi$
$174$	1.90232	0.144215
$175$	1.00840	0.0762277
$176$	1.14369	0.0862092
$177$	3.96732	0.298202
$178$	1.54275	0.115634
$179$	−5.99076	−0.447771	−0.223885	−	0.974615i	$-0.571874\pi$
$179$	−5.99076	−0.447771	−0.223885	+	0.974615i	$0.571874\pi$
$180$	2.74213	0.204386
$181$	12.5849	0.935430	0.467715	−	0.883879i	$-0.345077\pi$
$181$	12.5849	0.935430	0.467715	+	0.883879i	$0.345077\pi$
$182$	2.06821	0.153306
$183$	1.61818	0.119619
$184$	2.79831	0.206294
$185$	4.68283	0.344289
$186$	−3.77465	−0.276771
$187$	7.49803	0.548310
$188$	−8.20270	−0.598244
$189$	−2.94042	−0.213884
$190$	−3.91995	−0.284383
$191$	−24.1835	−1.74985	−0.874927	−	0.484255i	$-0.839091\pi$
$191$	−24.1835	−1.74985	−0.874927	+	0.484255i	$0.839091\pi$
$192$	0.507814	0.0366483
$193$	5.76974	0.415315	0.207657	−	0.978202i	$-0.433416\pi$
$193$	5.76974	0.415315	0.207657	+	0.978202i	$0.433416\pi$
$194$	−3.83789	−0.275545
$195$	1.04152	0.0745848
$196$	−5.98313	−0.427367
$197$	2.95108	0.210256	0.105128	−	0.994459i	$-0.466475\pi$
$197$	2.95108	0.210256	0.105128	+	0.994459i	$0.466475\pi$
$198$	3.13615	0.222877
$199$	−11.6718	−0.827393	−0.413696	−	0.910415i	$-0.635762\pi$
$199$	−11.6718	−0.827393	−0.413696	+	0.910415i	$0.635762\pi$
$200$	−1.00000	−0.0707107
$201$	3.27242	0.230819
$202$	−15.0709	−1.06038
$203$	−3.77756	−0.265133
$204$	3.32921	0.233092
$205$	−11.8154	−0.825221
$206$	0.419848	0.0292522
$207$	7.67332	0.533333
$208$	−2.05099	−0.142211
$209$	−4.48323	−0.310111
$210$	0.512078	0.0353367
$211$	−6.34620	−0.436890	−0.218445	−	0.975849i	$-0.570098\pi$
$211$	−6.34620	−0.436890	−0.218445	+	0.975849i	$0.570098\pi$
$212$	−8.22595	−0.564961
$213$	−7.90313	−0.541513
$214$	−5.38922	−0.368399
$215$	−10.3010	−0.702519
$216$	2.91593	0.198404
$217$	7.49557	0.508832
$218$	7.44373	0.504153
$219$	4.28307	0.289423
$220$	−1.14369	−0.0771078
$221$	−13.4462	−0.904492
$222$	2.37801	0.159601
$223$	12.7174	0.851618	0.425809	−	0.904813i	$-0.359990\pi$
$223$	12.7174	0.851618	0.425809	+	0.904813i	$0.359990\pi$
$224$	−1.00840	−0.0673764
$225$	−2.74213	−0.182808
$226$	−7.03637	−0.468052
$227$	13.7313	0.911380	0.455690	−	0.890138i	$-0.349393\pi$
$227$	13.7313	0.911380	0.455690	+	0.890138i	$0.349393\pi$
$228$	−1.99060	−0.131831
$229$	−24.8047	−1.63914	−0.819571	−	0.572977i	$-0.805788\pi$
$229$	−24.8047	−1.63914	−0.819571	+	0.572977i	$0.805788\pi$
$230$	−2.79831	−0.184515
$231$	0.585660	0.0385336
$232$	3.74610	0.245944
$233$	3.15317	0.206571	0.103286	−	0.994652i	$-0.467064\pi$
$233$	3.15317	0.206571	0.103286	+	0.994652i	$0.467064\pi$
$234$	−5.62407	−0.367657
$235$	8.20270	0.535085
$236$	7.81254	0.508553
$237$	4.34963	0.282539
$238$	−6.61103	−0.428529
$239$	−19.9543	−1.29074	−0.645368	−	0.763872i	$-0.723296\pi$
$239$	−19.9543	−1.29074	−0.645368	+	0.763872i	$0.723296\pi$
$240$	−0.507814	−0.0327792
$241$	27.7902	1.79012	0.895061	−	0.445944i	$-0.147132\pi$
$241$	27.7902	1.79012	0.895061	+	0.445944i	$0.147132\pi$
$242$	9.69196	0.623023
$243$	12.1733	0.780918
$244$	3.18656	0.203999
$245$	5.98313	0.382248
$246$	−6.00000	−0.382546
$247$	8.03978	0.511559
$248$	−7.43315	−0.472005
$249$	0.459634	0.0291281
$250$	1.00000	0.0632456
$251$	−7.99454	−0.504611	−0.252306	−	0.967648i	$-0.581189\pi$
$251$	−7.99454	−0.504611	−0.252306	+	0.967648i	$0.581189\pi$
$252$	−2.76515	−0.174188
$253$	−3.20041	−0.201208
$254$	−4.18623	−0.262667
$255$	−3.32921	−0.208483
$256$	1.00000	0.0625000
$257$	−16.0974	−1.00413	−0.502063	−	0.864831i	$-0.667425\pi$
$257$	−16.0974	−1.00413	−0.502063	+	0.864831i	$0.667425\pi$
$258$	−5.23096	−0.325666
$259$	−4.72215	−0.293420
$260$	2.05099	0.127197
$261$	10.2723	0.635838
$262$	−11.3317	−0.700073
$263$	−0.932053	−0.0574728	−0.0287364	−	0.999587i	$-0.509148\pi$
$263$	−0.932053	−0.0574728	−0.0287364	+	0.999587i	$0.509148\pi$
$264$	−0.580783	−0.0357447
$265$	8.22595	0.505316
$266$	3.95287	0.242366
$267$	−0.783428	−0.0479450
$268$	6.44414	0.393639
$269$	−15.2626	−0.930577	−0.465288	−	0.885159i	$-0.654049\pi$
$269$	−15.2626	−0.930577	−0.465288	+	0.885159i	$0.654049\pi$
$270$	−2.91593	−0.177458
$271$	20.7915	1.26299	0.631497	−	0.775378i	$-0.282441\pi$
$271$	20.7915	1.26299	0.631497	+	0.775378i	$0.282441\pi$
$272$	6.55597	0.397514
$273$	−1.05027	−0.0635650
$274$	−5.64994	−0.341325
$275$	1.14369	0.0689673
$276$	−1.42102	−0.0855354
$277$	29.7786	1.78922	0.894612	−	0.446843i	$-0.147452\pi$
$277$	29.7786	1.78922	0.894612	+	0.446843i	$0.147452\pi$
$278$	−6.80751	−0.408287
$279$	−20.3826	−1.22028
$280$	1.00840	0.0602633
$281$	−0.775006	−0.0462330	−0.0231165	−	0.999733i	$-0.507359\pi$
$281$	−0.775006	−0.0462330	−0.0231165	+	0.999733i	$0.507359\pi$
$282$	4.16544	0.248049
$283$	−1.95865	−0.116430	−0.0582150	−	0.998304i	$-0.518541\pi$
$283$	−1.95865	−0.116430	−0.0582150	+	0.998304i	$0.518541\pi$
$284$	−15.5631	−0.923497
$285$	1.99060	0.117913
$286$	2.34570	0.138704
$287$	11.9146	0.703296
$288$	2.74213	0.161581
$289$	25.9808	1.52828
$290$	−3.74610	−0.219979
$291$	1.94893	0.114249
$292$	8.43433	0.493582
$293$	15.5152	0.906405	0.453203	−	0.891408i	$-0.350281\pi$
$293$	15.5152	0.906405	0.453203	+	0.891408i	$0.350281\pi$
$294$	3.03832	0.177198
$295$	−7.81254	−0.454864
$296$	4.68283	0.272184
$297$	−3.33493	−0.193512
$298$	−19.1008	−1.10648
$299$	5.73931	0.331913
$300$	0.507814	0.0293186
$301$	10.3875	0.598723
$302$	2.45068	0.141021
$303$	7.65320	0.439665
$304$	−3.91995	−0.224825
$305$	−3.18656	−0.182462
$306$	17.9773	1.02769
$307$	30.9902	1.76871	0.884353	−	0.466819i	$-0.154600\pi$
$307$	30.9902	1.76871	0.884353	+	0.466819i	$0.154600\pi$
$308$	1.15330	0.0657153
$309$	−0.213205	−0.0121288
$310$	7.43315	0.422175
$311$	−2.72060	−0.154271	−0.0771356	−	0.997021i	$-0.524577\pi$
$311$	−2.72060	−0.154271	−0.0771356	+	0.997021i	$0.524577\pi$
$312$	1.04152	0.0589645
$313$	19.6439	1.11034	0.555169	−	0.831737i	$-0.312653\pi$
$313$	19.6439	1.11034	0.555169	+	0.831737i	$0.312653\pi$
$314$	−16.7062	−0.942783
$315$	2.76515	0.155799
$316$	8.56541	0.481842
$317$	13.1902	0.740836	0.370418	−	0.928865i	$-0.379214\pi$
$317$	13.1902	0.740836	0.370418	+	0.928865i	$0.379214\pi$
$318$	4.17725	0.234249
$319$	−4.28439	−0.239880
$320$	−1.00000	−0.0559017
$321$	2.73672	0.152749
$322$	2.82181	0.157253
$323$	−25.6991	−1.42994
$324$	6.74563	0.374757
$325$	−2.05099	−0.113768
$326$	−16.7232	−0.926210
$327$	−3.78003	−0.209036
$328$	−11.8154	−0.652395
$329$	−8.27158	−0.456027
$330$	0.580783	0.0319711
$331$	11.1139	0.610878	0.305439	−	0.952212i	$-0.401197\pi$
$331$	11.1139	0.610878	0.305439	+	0.952212i	$0.401197\pi$
$332$	0.905124	0.0496751
$333$	12.8409	0.703678
$334$	3.16416	0.173135
$335$	−6.44414	−0.352081
$336$	0.512078	0.0279361
$337$	−0.465789	−0.0253732	−0.0126866	−	0.999920i	$-0.504038\pi$
$337$	−0.465789	−0.0253732	−0.0126866	+	0.999920i	$0.504038\pi$
$338$	8.79344	0.478300
$339$	3.57316	0.194068
$340$	−6.55597	−0.355548
$341$	8.50125	0.460368
$342$	−10.7490	−0.581239
$343$	−13.0922	−0.706910
$344$	−10.3010	−0.555390
$345$	1.42102	0.0765052
$346$	−13.1339	−0.706080
$347$	−5.20212	−0.279265	−0.139632	−	0.990203i	$-0.544592\pi$
$347$	−5.20212	−0.279265	−0.139632	+	0.990203i	$0.544592\pi$
$348$	−1.90232	−0.101975
$349$	−6.43887	−0.344665	−0.172332	−	0.985039i	$-0.555130\pi$
$349$	−6.43887	−0.344665	−0.172332	+	0.985039i	$0.555130\pi$
$350$	−1.00840	−0.0539011
$351$	5.98054	0.319218
$352$	−1.14369	−0.0609591
$353$	−13.8887	−0.739223	−0.369612	−	0.929186i	$-0.620509\pi$
$353$	−13.8887	−0.739223	−0.369612	+	0.929186i	$0.620509\pi$
$354$	−3.96732	−0.210860
$355$	15.5631	0.826001
$356$	−1.54275	−0.0817654
$357$	3.35717	0.177680
$358$	5.99076	0.316622
$359$	−8.41795	−0.444283	−0.222141	−	0.975014i	$-0.571305\pi$
$359$	−8.41795	−0.444283	−0.222141	+	0.975014i	$0.571305\pi$
$360$	−2.74213	−0.144523
$361$	−3.63398	−0.191262
$362$	−12.5849	−0.661449
$363$	−4.92171	−0.258323
$364$	−2.06821	−0.108404
$365$	−8.43433	−0.441473
$366$	−1.61818	−0.0845836
$367$	22.2563	1.16177	0.580884	−	0.813986i	$-0.302707\pi$
$367$	22.2563	1.16177	0.580884	+	0.813986i	$0.302707\pi$
$368$	−2.79831	−0.145872
$369$	−32.3992	−1.68664
$370$	−4.68283	−0.243449
$371$	−8.29503	−0.430656
$372$	3.77465	0.195707
$373$	22.2449	1.15180	0.575899	−	0.817521i	$-0.304652\pi$
$373$	22.2449	1.15180	0.575899	+	0.817521i	$0.304652\pi$
$374$	−7.49803	−0.387714
$375$	−0.507814	−0.0262234
$376$	8.20270	0.423022
$377$	7.68321	0.395706
$378$	2.94042	0.151239
$379$	22.0793	1.13414	0.567070	−	0.823670i	$-0.308077\pi$
$379$	22.0793	1.13414	0.567070	+	0.823670i	$0.308077\pi$
$380$	3.91995	0.201089
$381$	2.12582	0.108909
$382$	24.1835	1.23733
$383$	−20.8700	−1.06641	−0.533204	−	0.845987i	$-0.679012\pi$
$383$	−20.8700	−1.06641	−0.533204	+	0.845987i	$0.679012\pi$
$384$	−0.507814	−0.0259143
$385$	−1.15330	−0.0587775
$386$	−5.76974	−0.293672
$387$	−28.2465	−1.43585
$388$	3.83789	0.194839
$389$	33.1721	1.68189	0.840945	−	0.541120i	$-0.182000\pi$
$389$	33.1721	1.68189	0.840945	+	0.541120i	$0.182000\pi$
$390$	−1.04152	−0.0527394
$391$	−18.3457	−0.927780
$392$	5.98313	0.302194
$393$	5.75437	0.290270
$394$	−2.95108	−0.148673
$395$	−8.56541	−0.430973
$396$	−3.13615	−0.157598
$397$	23.2321	1.16598	0.582992	−	0.812478i	$-0.301882\pi$
$397$	23.2321	1.16598	0.582992	+	0.812478i	$0.301882\pi$
$398$	11.6718	0.585055
$399$	−2.00732	−0.100492
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−3.27242	−0.163214
$403$	−15.2453	−0.759423
$404$	15.0709	0.749805
$405$	−6.74563	−0.335193
$406$	3.77756	0.187477
$407$	−5.35573	−0.265473
$408$	−3.32921	−0.164821
$409$	19.6303	0.970658	0.485329	−	0.874332i	$-0.338700\pi$
$409$	19.6303	0.970658	0.485329	+	0.874332i	$0.338700\pi$
$410$	11.8154	0.583519
$411$	2.86912	0.141523
$412$	−0.419848	−0.0206844
$413$	7.87815	0.387658
$414$	−7.67332	−0.377123
$415$	−0.905124	−0.0444308
$416$	2.05099	0.100558
$417$	3.45694	0.169287
$418$	4.48323	0.219282
$419$	28.0583	1.37074	0.685368	−	0.728197i	$-0.259641\pi$
$419$	28.0583	1.37074	0.685368	+	0.728197i	$0.259641\pi$
$420$	−0.512078	−0.0249868
$421$	−5.49638	−0.267877	−0.133939	−	0.990990i	$-0.542763\pi$
$421$	−5.49638	−0.267877	−0.133939	+	0.990990i	$0.542763\pi$
$422$	6.34620	0.308928
$423$	22.4928	1.09364
$424$	8.22595	0.399488
$425$	6.55597	0.318011
$426$	7.90313	0.382908
$427$	3.21332	0.155504
$428$	5.38922	0.260498
$429$	−1.19118	−0.0575107
$430$	10.3010	0.496756
$431$	−14.2277	−0.685322	−0.342661	−	0.939459i	$-0.611328\pi$
$431$	−14.2277	−0.685322	−0.342661	+	0.939459i	$0.611328\pi$
$432$	−2.91593	−0.140293
$433$	−12.9706	−0.623328	−0.311664	−	0.950192i	$-0.600886\pi$
$433$	−12.9706	−0.623328	−0.311664	+	0.950192i	$0.600886\pi$
$434$	−7.49557	−0.359799
$435$	1.90232	0.0912093
$436$	−7.44373	−0.356490
$437$	10.9692	0.524730
$438$	−4.28307	−0.204653
$439$	11.6366	0.555387	0.277693	−	0.960670i	$-0.410430\pi$
$439$	11.6366	0.555387	0.277693	+	0.960670i	$0.410430\pi$
$440$	1.14369	0.0545235
$441$	16.4065	0.781262
$442$	13.4462	0.639572
$443$	−19.5822	−0.930377	−0.465189	−	0.885212i	$-0.654014\pi$
$443$	−19.5822	−0.930377	−0.465189	+	0.885212i	$0.654014\pi$
$444$	−2.37801	−0.112855
$445$	1.54275	0.0731332
$446$	−12.7174	−0.602185
$447$	9.69965	0.458778
$448$	1.00840	0.0476423
$449$	0.0108722	0.000513089 0	0.000256544	−	1.00000i	$-0.499918\pi$
$449$	0.0108722	0.000513089 0	0.000256544		1.00000i	$0.499918\pi$
$450$	2.74213	0.129265
$451$	13.5132	0.636310
$452$	7.03637	0.330963
$453$	−1.24449	−0.0584712
$454$	−13.7313	−0.644443
$455$	2.06821	0.0969593
$456$	1.99060	0.0932186
$457$	−36.9213	−1.72711	−0.863554	−	0.504256i	$-0.831767\pi$
$457$	−36.9213	−1.72711	−0.863554	+	0.504256i	$0.831767\pi$
$458$	24.8047	1.15905
$459$	−19.1168	−0.892294
$460$	2.79831	0.130472
$461$	−11.8234	−0.550673	−0.275336	−	0.961348i	$-0.588789\pi$
$461$	−11.8234	−0.550673	−0.275336	+	0.961348i	$0.588789\pi$
$462$	−0.585660	−0.0272474
$463$	−7.16221	−0.332856	−0.166428	−	0.986054i	$-0.553223\pi$
$463$	−7.16221	−0.332856	−0.166428	+	0.986054i	$0.553223\pi$
$464$	−3.74610	−0.173908
$465$	−3.77465	−0.175045
$466$	−3.15317	−0.146068
$467$	−3.57157	−0.165273	−0.0826363	−	0.996580i	$-0.526334\pi$
$467$	−3.57157	−0.165273	−0.0826363	+	0.996580i	$0.526334\pi$
$468$	5.62407	0.259973
$469$	6.49825	0.300062
$470$	−8.20270	−0.378362
$471$	8.48362	0.390904
$472$	−7.81254	−0.359601
$473$	11.7811	0.541697
$474$	−4.34963	−0.199785
$475$	−3.91995	−0.179860
$476$	6.61103	0.303016
$477$	22.5566	1.03280
$478$	19.9543	0.912688
$479$	14.4273	0.659198	0.329599	−	0.944121i	$-0.393086\pi$
$479$	14.4273	0.659198	0.329599	+	0.944121i	$0.393086\pi$
$480$	0.507814	0.0231784
$481$	9.60444	0.437925
$482$	−27.7902	−1.26581
$483$	−1.43295	−0.0652017
$484$	−9.69196	−0.440544
$485$	−3.83789	−0.174270
$486$	−12.1733	−0.552193
$487$	29.4456	1.33431	0.667154	−	0.744920i	$-0.267512\pi$
$487$	29.4456	1.33431	0.667154	+	0.744920i	$0.267512\pi$
$488$	−3.18656	−0.144249
$489$	8.49225	0.384033
$490$	−5.98313	−0.270290
$491$	−20.7047	−0.934388	−0.467194	−	0.884155i	$-0.654735\pi$
$491$	−20.7047	−0.934388	−0.467194	+	0.884155i	$0.654735\pi$
$492$	6.00000	0.270501
$493$	−24.5593	−1.10610
$494$	−8.03978	−0.361727
$495$	3.13615	0.140960
$496$	7.43315	0.333758
$497$	−15.6937	−0.703960
$498$	−0.459634	−0.0205967
$499$	−4.60205	−0.206016	−0.103008	−	0.994681i	$-0.532847\pi$
$499$	−4.60205	−0.206016	−0.103008	+	0.994681i	$0.532847\pi$
$500$	−1.00000	−0.0447214
$501$	−1.60680	−0.0717866
$502$	7.99454	0.356814
$503$	2.61675	0.116675	0.0583376	−	0.998297i	$-0.481420\pi$
$503$	2.61675	0.116675	0.0583376	+	0.998297i	$0.481420\pi$
$504$	2.76515	0.123170
$505$	−15.0709	−0.670646
$506$	3.20041	0.142276
$507$	−4.46543	−0.198317
$508$	4.18623	0.185734
$509$	9.60634	0.425793	0.212897	−	0.977075i	$-0.431710\pi$
$509$	9.60634	0.425793	0.212897	+	0.977075i	$0.431710\pi$
$510$	3.32921	0.147420
$511$	8.50516	0.376246
$512$	−1.00000	−0.0441942
$513$	11.4303	0.504660
$514$	16.0974	0.710024
$515$	0.419848	0.0185007
$516$	5.23096	0.230280
$517$	−9.38138	−0.412593
$518$	4.72215	0.207480
$519$	6.66955	0.292761
$520$	−2.05099	−0.0899418
$521$	−22.9404	−1.00504	−0.502520	−	0.864566i	$-0.667594\pi$
$521$	−22.9404	−1.00504	−0.502520	+	0.864566i	$0.667594\pi$
$522$	−10.2723	−0.449605
$523$	−0.445663	−0.0194875	−0.00974373	−	0.999953i	$-0.503102\pi$
$523$	−0.445663	−0.0194875	−0.00974373	+	0.999953i	$0.503102\pi$
$524$	11.3317	0.495026
$525$	0.512078	0.0223489
$526$	0.932053	0.0406394
$527$	48.7315	2.12278
$528$	0.580783	0.0252754
$529$	−15.1694	−0.659541
$530$	−8.22595	−0.357313
$531$	−21.4230	−0.929678
$532$	−3.95287	−0.171379
$533$	−24.2332	−1.04966
$534$	0.783428	0.0339022
$535$	−5.38922	−0.232996
$536$	−6.44414	−0.278344
$537$	−3.04219	−0.131280
$538$	15.2626	0.658017
$539$	−6.84288	−0.294744
$540$	2.91593	0.125482
$541$	−5.07718	−0.218285	−0.109142	−	0.994026i	$-0.534810\pi$
$541$	−5.07718	−0.218285	−0.109142	+	0.994026i	$0.534810\pi$
$542$	−20.7915	−0.893072
$543$	6.39079	0.274255
$544$	−6.55597	−0.281085
$545$	7.44373	0.318854
$546$	1.05027	0.0449473
$547$	0.0369043	0.00157792	0.000788958	−	1.00000i	$-0.499749\pi$
$547$	0.0369043	0.00157792	0.000788958		1.00000i	$0.499749\pi$
$548$	5.64994	0.241353
$549$	−8.73796	−0.372927
$550$	−1.14369	−0.0487673
$551$	14.6845	0.625582
$552$	1.42102	0.0604827
$553$	8.63734	0.367297
$554$	−29.7786	−1.26517
$555$	2.37801	0.100941
$556$	6.80751	0.288703
$557$	1.51235	0.0640802	0.0320401	−	0.999487i	$-0.489800\pi$
$557$	1.51235	0.0640802	0.0320401	+	0.999487i	$0.489800\pi$
$558$	20.3826	0.862865
$559$	−21.1271	−0.893583
$560$	−1.00840	−0.0426126
$561$	3.80760	0.160757
$562$	0.775006	0.0326917
$563$	10.0857	0.425060	0.212530	−	0.977155i	$-0.431830\pi$
$563$	10.0857	0.425060	0.212530	+	0.977155i	$0.431830\pi$
$564$	−4.16544	−0.175397
$565$	−7.03637	−0.296022
$566$	1.95865	0.0823284
$567$	6.80227	0.285669
$568$	15.5631	0.653011
$569$	−21.7086	−0.910070	−0.455035	−	0.890474i	$-0.650373\pi$
$569$	−21.7086	−0.910070	−0.455035	+	0.890474i	$0.650373\pi$
$570$	−1.99060	−0.0833773
$571$	22.6745	0.948898	0.474449	−	0.880283i	$-0.342647\pi$
$571$	22.6745	0.948898	0.474449	+	0.880283i	$0.342647\pi$
$572$	−2.34570	−0.0980788
$573$	−12.2807	−0.513033
$574$	−11.9146	−0.497305
$575$	−2.79831	−0.116698
$576$	−2.74213	−0.114255
$577$	−30.9779	−1.28963	−0.644813	−	0.764341i	$-0.723065\pi$
$577$	−30.9779	−1.28963	−0.644813	+	0.764341i	$0.723065\pi$
$578$	−25.9808	−1.08066
$579$	2.92995	0.121765
$580$	3.74610	0.155548
$581$	0.912724	0.0378662
$582$	−1.94893	−0.0807859
$583$	−9.40797	−0.389638
$584$	−8.43433	−0.349015
$585$	−5.62407	−0.232527
$586$	−15.5152	−0.640925
$587$	39.4934	1.63007	0.815033	−	0.579415i	$-0.196719\pi$
$587$	39.4934	1.63007	0.815033	+	0.579415i	$0.196719\pi$
$588$	−3.03832	−0.125298
$589$	−29.1376	−1.20059
$590$	7.81254	0.321637
$591$	1.49860	0.0616441
$592$	−4.68283	−0.192463
$593$	−4.03016	−0.165499	−0.0827494	−	0.996570i	$-0.526370\pi$
$593$	−4.03016	−0.165499	−0.0827494	+	0.996570i	$0.526370\pi$
$594$	3.33493	0.136834
$595$	−6.61103	−0.271026
$596$	19.1008	0.782399
$597$	−5.92710	−0.242580
$598$	−5.73931	−0.234698
$599$	−28.5729	−1.16746	−0.583729	−	0.811949i	$-0.698407\pi$
$599$	−28.5729	−1.16746	−0.583729	+	0.811949i	$0.698407\pi$
$600$	−0.507814	−0.0207314
$601$	24.3943	0.995063	0.497532	−	0.867446i	$-0.334240\pi$
$601$	24.3943	0.995063	0.497532	+	0.867446i	$0.334240\pi$
$602$	−10.3875	−0.423361
$603$	−17.6706	−0.719604
$604$	−2.45068	−0.0997168
$605$	9.69196	0.394034
$606$	−7.65320	−0.310890
$607$	29.8943	1.21337	0.606687	−	0.794941i	$-0.292498\pi$
$607$	29.8943	1.21337	0.606687	+	0.794941i	$0.292498\pi$
$608$	3.91995	0.158975
$609$	−1.91830	−0.0777333
$610$	3.18656	0.129020
$611$	16.8237	0.680612
$612$	−17.9773	−0.726689
$613$	46.5736	1.88109	0.940545	−	0.339669i	$-0.110315\pi$
$613$	46.5736	1.88109	0.940545	+	0.339669i	$0.110315\pi$
$614$	−30.9902	−1.25066
$615$	−6.00000	−0.241944
$616$	−1.15330	−0.0464677
$617$	−42.6735	−1.71797	−0.858985	−	0.512000i	$-0.828905\pi$
$617$	−42.6735	−1.71797	−0.858985	+	0.512000i	$0.828905\pi$
$618$	0.213205	0.00857635
$619$	6.35244	0.255326	0.127663	−	0.991818i	$-0.459252\pi$
$619$	6.35244	0.255326	0.127663	+	0.991818i	$0.459252\pi$
$620$	−7.43315	−0.298522
$621$	8.15968	0.327437
$622$	2.72060	0.109086
$623$	−1.55570	−0.0623279
$624$	−1.04152	−0.0416942
$625$	1.00000	0.0400000
$626$	−19.6439	−0.785128
$627$	−2.27664	−0.0909204
$628$	16.7062	0.666648
$629$	−30.7005	−1.22411
$630$	−2.76515	−0.110166
$631$	−17.0865	−0.680203	−0.340101	−	0.940389i	$-0.610461\pi$
$631$	−17.0865	−0.680203	−0.340101	+	0.940389i	$0.610461\pi$
$632$	−8.56541	−0.340714
$633$	−3.22268	−0.128090
$634$	−13.1902	−0.523850
$635$	−4.18623	−0.166125
$636$	−4.17725	−0.165639
$637$	12.2713	0.486208
$638$	4.28439	0.169621
$639$	42.6758	1.68823
$640$	1.00000	0.0395285
$641$	−7.71349	−0.304664	−0.152332	−	0.988329i	$-0.548678\pi$
$641$	−7.71349	−0.304664	−0.152332	+	0.988329i	$0.548678\pi$
$642$	−2.73672	−0.108010
$643$	33.8189	1.33369	0.666843	−	0.745198i	$-0.267645\pi$
$643$	33.8189	1.33369	0.666843	+	0.745198i	$0.267645\pi$
$644$	−2.82181	−0.111195
$645$	−5.23096	−0.205969
$646$	25.6991	1.01112
$647$	39.8048	1.56489	0.782445	−	0.622720i	$-0.213972\pi$
$647$	39.8048	1.56489	0.782445	+	0.622720i	$0.213972\pi$
$648$	−6.74563	−0.264993
$649$	8.93516	0.350736
$650$	2.05099	0.0804464
$651$	3.80635	0.149183
$652$	16.7232	0.654929
$653$	7.72515	0.302308	0.151154	−	0.988510i	$-0.451701\pi$
$653$	7.72515	0.302308	0.151154	+	0.988510i	$0.451701\pi$
$654$	3.78003	0.147811
$655$	−11.3317	−0.442765
$656$	11.8154	0.461313
$657$	−23.1280	−0.902309
$658$	8.27158	0.322460
$659$	−11.3829	−0.443415	−0.221708	−	0.975113i	$-0.571163\pi$
$659$	−11.3829	−0.443415	−0.221708	+	0.975113i	$0.571163\pi$
$660$	−0.580783	−0.0226070
$661$	9.87625	0.384142	0.192071	−	0.981381i	$-0.438480\pi$
$661$	9.87625	0.384142	0.192071	+	0.981381i	$0.438480\pi$
$662$	−11.1139	−0.431956
$663$	−6.82818	−0.265185
$664$	−0.905124	−0.0351256
$665$	3.95287	0.153286
$666$	−12.8409	−0.497575
$667$	10.4828	0.405894
$668$	−3.16416	−0.122425
$669$	6.45805	0.249683
$670$	6.44414	0.248959
$671$	3.64445	0.140693
$672$	−0.512078	−0.0197538
$673$	−30.4374	−1.17328	−0.586638	−	0.809849i	$-0.699549\pi$
$673$	−30.4374	−1.17328	−0.586638	+	0.809849i	$0.699549\pi$
$674$	0.465789	0.0179415
$675$	−2.91593	−0.112234
$676$	−8.79344	−0.338209
$677$	−1.32341	−0.0508629	−0.0254314	−	0.999677i	$-0.508096\pi$
$677$	−1.32341	−0.0508629	−0.0254314	+	0.999677i	$0.508096\pi$
$678$	−3.57316	−0.137227
$679$	3.87012	0.148522
$680$	6.55597	0.251410
$681$	6.97296	0.267204
$682$	−8.50125	−0.325530
$683$	5.37719	0.205753	0.102876	−	0.994694i	$-0.467195\pi$
$683$	5.37719	0.205753	0.102876	+	0.994694i	$0.467195\pi$
$684$	10.7490	0.410998
$685$	−5.64994	−0.215873
$686$	13.0922	0.499861
$687$	−12.5962	−0.480574
$688$	10.3010	0.392720
$689$	16.8713	0.642747
$690$	−1.42102	−0.0540973
$691$	−36.5861	−1.39180	−0.695900	−	0.718139i	$-0.744994\pi$
$691$	−36.5861	−1.39180	−0.695900	+	0.718139i	$0.744994\pi$
$692$	13.1339	0.499274
$693$	−3.16249	−0.120133
$694$	5.20212	0.197470
$695$	−6.80751	−0.258223
$696$	1.90232	0.0721073
$697$	77.4612	2.93405
$698$	6.43887	0.243715
$699$	1.60122	0.0605638
$700$	1.00840	0.0381138
$701$	15.7240	0.593887	0.296944	−	0.954895i	$-0.404033\pi$
$701$	15.7240	0.593887	0.296944	+	0.954895i	$0.404033\pi$
$702$	−5.98054	−0.225721
$703$	18.3565	0.692327
$704$	1.14369	0.0431046
$705$	4.16544	0.156880
$706$	13.8887	0.522710
$707$	15.1974	0.571559
$708$	3.96732	0.149101
$709$	35.7368	1.34212	0.671061	−	0.741402i	$-0.265839\pi$
$709$	35.7368	1.34212	0.671061	+	0.741402i	$0.265839\pi$
$710$	−15.5631	−0.584071
$711$	−23.4874	−0.880848
$712$	1.54275	0.0578169
$713$	−20.8003	−0.778976
$714$	−3.35717	−0.125639
$715$	2.34570	0.0877244
$716$	−5.99076	−0.223885
$717$	−10.1331	−0.378426
$718$	8.41795	0.314155
$719$	−23.8588	−0.889784	−0.444892	−	0.895584i	$-0.646758\pi$
$719$	−23.8588	−0.889784	−0.444892	+	0.895584i	$0.646758\pi$
$720$	2.74213	0.102193
$721$	−0.423374	−0.0157673
$722$	3.63398	0.135243
$723$	14.1122	0.524839
$724$	12.5849	0.467715
$725$	−3.74610	−0.139127
$726$	4.92171	0.182662
$727$	−26.4113	−0.979541	−0.489770	−	0.871851i	$-0.662919\pi$
$727$	−26.4113	−0.979541	−0.489770	+	0.871851i	$0.662919\pi$
$728$	2.06821	0.0766531
$729$	−14.0551	−0.520560
$730$	8.43433	0.312169
$731$	67.5328	2.49779
$732$	1.61818	0.0598097
$733$	−30.7611	−1.13619	−0.568094	−	0.822964i	$-0.692319\pi$
$733$	−30.7611	−1.13619	−0.568094	+	0.822964i	$0.692319\pi$
$734$	−22.2563	−0.821494
$735$	3.03832	0.112070
$736$	2.79831	0.103147
$737$	7.37013	0.271482
$738$	32.3992	1.19263
$739$	45.3589	1.66856	0.834278	−	0.551344i	$-0.185885\pi$
$739$	45.3589	1.66856	0.834278	+	0.551344i	$0.185885\pi$
$740$	4.68283	0.172144
$741$	4.08271	0.149982
$742$	8.29503	0.304520
$743$	8.29697	0.304386	0.152193	−	0.988351i	$-0.451366\pi$
$743$	8.29697	0.304386	0.152193	+	0.988351i	$0.451366\pi$
$744$	−3.77465	−0.138386
$745$	−19.1008	−0.699799
$746$	−22.2449	−0.814444
$747$	−2.48196	−0.0908103
$748$	7.49803	0.274155
$749$	5.43447	0.198571
$750$	0.507814	0.0185427
$751$	43.2207	1.57714	0.788572	−	0.614942i	$-0.210821\pi$
$751$	43.2207	1.57714	0.788572	+	0.614942i	$0.210821\pi$
$752$	−8.20270	−0.299122
$753$	−4.05974	−0.147945
$754$	−7.68321	−0.279806
$755$	2.45068	0.0891894
$756$	−2.94042	−0.106942
$757$	−4.77420	−0.173521	−0.0867606	−	0.996229i	$-0.527652\pi$
$757$	−4.77420	−0.173521	−0.0867606	+	0.996229i	$0.527652\pi$
$758$	−22.0793	−0.801958
$759$	−1.62521	−0.0589915
$760$	−3.91995	−0.142192
$761$	−15.2103	−0.551373	−0.275687	−	0.961248i	$-0.588905\pi$
$761$	−15.2103	−0.551373	−0.275687	+	0.961248i	$0.588905\pi$
$762$	−2.12582	−0.0770104
$763$	−7.50624	−0.271744
$764$	−24.1835	−0.874927
$765$	17.9773	0.649971
$766$	20.8700	0.754064
$767$	−16.0234	−0.578573
$768$	0.507814	0.0183241
$769$	3.64130	0.131309	0.0656543	−	0.997842i	$-0.479087\pi$
$769$	3.64130	0.131309	0.0656543	+	0.997842i	$0.479087\pi$
$770$	1.15330	0.0415620
$771$	−8.17445	−0.294396
$772$	5.76974	0.207657
$773$	−17.2084	−0.618942	−0.309471	−	0.950909i	$-0.600152\pi$
$773$	−17.2084	−0.618942	−0.309471	+	0.950909i	$0.600152\pi$
$774$	28.2465	1.01530
$775$	7.43315	0.267007
$776$	−3.83789	−0.137772
$777$	−2.39797	−0.0860269
$778$	−33.1721	−1.18928
$779$	−46.3157	−1.65943
$780$	1.04152	0.0372924
$781$	−17.7994	−0.636911
$782$	18.3457	0.656040
$783$	10.9234	0.390369
$784$	−5.98313	−0.213683
$785$	−16.7062	−0.596269
$786$	−5.75437	−0.205252
$787$	−18.6554	−0.664994	−0.332497	−	0.943104i	$-0.607891\pi$
$787$	−18.6554	−0.664994	−0.332497	+	0.943104i	$0.607891\pi$
$788$	2.95108	0.105128
$789$	−0.473309	−0.0168502
$790$	8.56541	0.304744
$791$	7.09546	0.252285
$792$	3.13615	0.111438
$793$	−6.53561	−0.232086
$794$	−23.2321	−0.824476
$795$	4.17725	0.148152
$796$	−11.6718	−0.413696
$797$	−14.5759	−0.516306	−0.258153	−	0.966104i	$-0.583114\pi$
$797$	−14.5759	−0.516306	−0.258153	+	0.966104i	$0.583114\pi$
$798$	2.00732	0.0710584
$799$	−53.7767	−1.90248
$800$	−1.00000	−0.0353553
$801$	4.23041	0.149474
$802$	−1.00000	−0.0353112
$803$	9.64630	0.340410
$804$	3.27242	0.115409
$805$	2.82181	0.0994558
$806$	15.2453	0.536993
$807$	−7.75055	−0.272832
$808$	−15.0709	−0.530192
$809$	−48.3998	−1.70165	−0.850824	−	0.525451i	$-0.823896\pi$
$809$	−48.3998	−1.70165	−0.850824	+	0.525451i	$0.823896\pi$
$810$	6.74563	0.237017
$811$	19.6900	0.691409	0.345704	−	0.938344i	$-0.387640\pi$
$811$	19.6900	0.691409	0.345704	+	0.938344i	$0.387640\pi$
$812$	−3.77756	−0.132566
$813$	10.5582	0.370293
$814$	5.35573	0.187718
$815$	−16.7232	−0.585787
$816$	3.32921	0.116546
$817$	−40.3792	−1.41269
$818$	−19.6303	−0.686359
$819$	5.67130	0.198171
$820$	−11.8154	−0.412611
$821$	−48.7718	−1.70215	−0.851075	−	0.525045i	$-0.824049\pi$
$821$	−48.7718	−1.70215	−0.851075	+	0.525045i	$0.824049\pi$
$822$	−2.86912	−0.100072
$823$	3.13893	0.109416	0.0547082	−	0.998502i	$-0.482577\pi$
$823$	3.13893	0.109416	0.0547082	+	0.998502i	$0.482577\pi$
$824$	0.419848	0.0146261
$825$	0.580783	0.0202203
$826$	−7.87815	−0.274116
$827$	−26.3636	−0.916753	−0.458376	−	0.888758i	$-0.651569\pi$
$827$	−26.3636	−0.916753	−0.458376	+	0.888758i	$0.651569\pi$
$828$	7.67332	0.266666
$829$	−34.5724	−1.20075	−0.600375	−	0.799719i	$-0.704982\pi$
$829$	−34.5724	−1.20075	−0.600375	+	0.799719i	$0.704982\pi$
$830$	0.905124	0.0314173
$831$	15.1220	0.524576
$832$	−2.05099	−0.0711053
$833$	−39.2253	−1.35908
$834$	−3.45694	−0.119704
$835$	3.16416	0.109500
$836$	−4.48323	−0.155056
$837$	−21.6745	−0.749182
$838$	−28.0583	−0.969257
$839$	−24.8699	−0.858603	−0.429301	−	0.903161i	$-0.641240\pi$
$839$	−24.8699	−0.858603	−0.429301	+	0.903161i	$0.641240\pi$
$840$	0.512078	0.0176684
$841$	−14.9667	−0.516094
$842$	5.49638	0.189418
$843$	−0.393559	−0.0135549
$844$	−6.34620	−0.218445
$845$	8.79344	0.302504
$846$	−22.4928	−0.773320
$847$	−9.77335	−0.335816
$848$	−8.22595	−0.282480
$849$	−0.994631	−0.0341357
$850$	−6.55597	−0.224868
$851$	13.1040	0.449200
$852$	−7.90313	−0.270757
$853$	−38.2937	−1.31115	−0.655575	−	0.755130i	$-0.727574\pi$
$853$	−38.2937	−1.31115	−0.655575	+	0.755130i	$0.727574\pi$
$854$	−3.21332	−0.109958
$855$	−10.7490	−0.367608
$856$	−5.38922	−0.184200
$857$	11.5975	0.396162	0.198081	−	0.980186i	$-0.436529\pi$
$857$	11.5975	0.396162	0.198081	+	0.980186i	$0.436529\pi$
$858$	1.19118	0.0406662
$859$	20.5466	0.701041	0.350521	−	0.936555i	$-0.386005\pi$
$859$	20.5466	0.701041	0.350521	+	0.936555i	$0.386005\pi$
$860$	−10.3010	−0.351260
$861$	6.05039	0.206197
$862$	14.2277	0.484596
$863$	−22.3193	−0.759758	−0.379879	−	0.925036i	$-0.624034\pi$
$863$	−22.3193	−0.759758	−0.379879	+	0.925036i	$0.624034\pi$
$864$	2.91593	0.0992019
$865$	−13.1339	−0.446564
$866$	12.9706	0.440759
$867$	13.1934	0.448071
$868$	7.49557	0.254416
$869$	9.79621	0.332314
$870$	−1.90232	−0.0644947
$871$	−13.2169	−0.447836
$872$	7.44373	0.252077
$873$	−10.5240	−0.356183
$874$	−10.9692	−0.371040
$875$	−1.00840	−0.0340901
$876$	4.28307	0.144711
$877$	−43.4101	−1.46585	−0.732927	−	0.680307i	$-0.761846\pi$
$877$	−43.4101	−1.46585	−0.732927	+	0.680307i	$0.761846\pi$
$878$	−11.6366	−0.392718
$879$	7.87881	0.265746
$880$	−1.14369	−0.0385539
$881$	8.37198	0.282059	0.141030	−	0.990005i	$-0.454959\pi$
$881$	8.37198	0.282059	0.141030	+	0.990005i	$0.454959\pi$
$882$	−16.4065	−0.552436
$883$	47.3359	1.59298	0.796490	−	0.604652i	$-0.206688\pi$
$883$	47.3359	1.59298	0.796490	+	0.604652i	$0.206688\pi$
$884$	−13.4462	−0.452246
$885$	−3.96732	−0.133360
$886$	19.5822	0.657876
$887$	15.2603	0.512390	0.256195	−	0.966625i	$-0.417531\pi$
$887$	15.2603	0.512390	0.256195	+	0.966625i	$0.417531\pi$
$888$	2.37801	0.0798006
$889$	4.22138	0.141581
$890$	−1.54275	−0.0517130
$891$	7.71493	0.258460
$892$	12.7174	0.425809
$893$	32.1542	1.07600
$894$	−9.69965	−0.324405
$895$	5.99076	0.200249
$896$	−1.00840	−0.0336882
$897$	2.91450	0.0973123
$898$	−0.0108722	−0.000362808 0
$899$	−27.8453	−0.928694
$900$	−2.74213	−0.0914042
$901$	−53.9291	−1.79664
$902$	−13.5132	−0.449939
$903$	5.27489	0.175537
$904$	−7.03637	−0.234026
$905$	−12.5849	−0.418337
$906$	1.24449	0.0413454
$907$	−36.9567	−1.22713	−0.613563	−	0.789646i	$-0.710264\pi$
$907$	−36.9567	−1.22713	−0.613563	+	0.789646i	$0.710264\pi$
$908$	13.7313	0.455690
$909$	−41.3263	−1.37071
$910$	−2.06821	−0.0685606
$911$	27.1108	0.898220	0.449110	−	0.893476i	$-0.351741\pi$
$911$	27.1108	0.898220	0.449110	+	0.893476i	$0.351741\pi$
$912$	−1.99060	−0.0659155
$913$	1.03518	0.0342596
$914$	36.9213	1.22125
$915$	−1.61818	−0.0534954
$916$	−24.8047	−0.819571
$917$	11.4268	0.377347
$918$	19.1168	0.630947
$919$	10.2520	0.338183	0.169092	−	0.985600i	$-0.445917\pi$
$919$	10.2520	0.338183	0.169092	+	0.985600i	$0.445917\pi$
$920$	−2.79831	−0.0922576
$921$	15.7373	0.518560
$922$	11.8234	0.389384
$923$	31.9197	1.05065
$924$	0.585660	0.0192668
$925$	−4.68283	−0.153971
$926$	7.16221	0.235365
$927$	1.15128	0.0378129
$928$	3.74610	0.122972
$929$	−36.2338	−1.18879	−0.594396	−	0.804173i	$-0.702609\pi$
$929$	−36.2338	−1.18879	−0.594396	+	0.804173i	$0.702609\pi$
$930$	3.77465	0.123776
$931$	23.4536	0.768661
$932$	3.15317	0.103286
$933$	−1.38156	−0.0452302
$934$	3.57157	0.116865
$935$	−7.49803	−0.245212
$936$	−5.62407	−0.183828
$937$	14.5227	0.474436	0.237218	−	0.971456i	$-0.423765\pi$
$937$	14.5227	0.474436	0.237218	+	0.971456i	$0.423765\pi$
$938$	−6.49825	−0.212176
$939$	9.97544	0.325536
$940$	8.20270	0.267543
$941$	−21.1840	−0.690578	−0.345289	−	0.938496i	$-0.612219\pi$
$941$	−21.1840	−0.690578	−0.345289	+	0.938496i	$0.612219\pi$
$942$	−8.48362	−0.276411
$943$	−33.0631	−1.07668
$944$	7.81254	0.254277
$945$	2.94042	0.0956517
$946$	−11.7811	−0.383038
$947$	−50.8617	−1.65278	−0.826391	−	0.563097i	$-0.809610\pi$
$947$	−50.8617	−1.65278	−0.826391	+	0.563097i	$0.809610\pi$
$948$	4.34963	0.141270
$949$	−17.2987	−0.561540
$950$	3.91995	0.127180
$951$	6.69817	0.217203
$952$	−6.61103	−0.214265
$953$	40.8934	1.32467	0.662333	−	0.749209i	$-0.269566\pi$
$953$	40.8934	1.32467	0.662333	+	0.749209i	$0.269566\pi$
$954$	−22.5566	−0.730297
$955$	24.1835	0.782559
$956$	−19.9543	−0.645368
$957$	−2.17567	−0.0703295
$958$	−14.4273	−0.466123
$959$	5.69738	0.183978
$960$	−0.507814	−0.0163896
$961$	24.2517	0.782313
$962$	−9.60444	−0.309659
$963$	−14.7779	−0.476211
$964$	27.7902	0.895061
$965$	−5.76974	−0.185734
$966$	1.43295	0.0461045
$967$	−42.5184	−1.36730	−0.683650	−	0.729810i	$-0.739609\pi$
$967$	−42.5184	−1.36730	−0.683650	+	0.729810i	$0.739609\pi$
$968$	9.69196	0.311512
$969$	−13.0504	−0.419238
$970$	3.83789	0.123227
$971$	−11.3096	−0.362942	−0.181471	−	0.983396i	$-0.558086\pi$
$971$	−11.3096	−0.362942	−0.181471	+	0.983396i	$0.558086\pi$
$972$	12.1733	0.390459
$973$	6.86467	0.220071
$974$	−29.4456	−0.943499
$975$	−1.04152	−0.0333553
$976$	3.18656	0.101999
$977$	8.23842	0.263570	0.131785	−	0.991278i	$-0.457929\pi$
$977$	8.23842	0.263570	0.131785	+	0.991278i	$0.457929\pi$
$978$	−8.49225	−0.271552
$979$	−1.76443	−0.0563914
$980$	5.98313	0.191124
$981$	20.4116	0.651694
$982$	20.7047	0.660712
$983$	28.0976	0.896174	0.448087	−	0.893990i	$-0.352105\pi$
$983$	28.0976	0.896174	0.448087	+	0.893990i	$0.352105\pi$
$984$	−6.00000	−0.191273
$985$	−2.95108	−0.0940292
$986$	24.5593	0.782129
$987$	−4.20042	−0.133701
$988$	8.03978	0.255779
$989$	−28.8253	−0.916591
$990$	−3.13615	−0.0996735
$991$	43.7578	1.39001	0.695006	−	0.719004i	$-0.255402\pi$
$991$	43.7578	1.39001	0.695006	+	0.719004i	$0.255402\pi$
$992$	−7.43315	−0.236003
$993$	5.64381	0.179101
$994$	15.6937	0.497775
$995$	11.6718	0.370021
$996$	0.459634	0.0145641
$997$	−21.3406	−0.675864	−0.337932	−	0.941171i	$-0.609727\pi$
$997$	−21.3406	−0.675864	−0.337932	+	0.941171i	$0.609727\pi$
$998$	4.60205	0.145675
$999$	13.6548	0.432019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.11	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.507814 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.507814 q^{6} +1.00840 q^{7} -1.00000 q^{8} -2.74213 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.507814 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.507814 q^{6} +1.00840 q^{7} -1.00000 q^{8} -2.74213 q^{9} +1.00000 q^{10} +1.14369 q^{11} +0.507814 q^{12} -2.05099 q^{13} -1.00840 q^{14} -0.507814 q^{15} +1.00000 q^{16} +6.55597 q^{17} +2.74213 q^{18} -3.91995 q^{19} -1.00000 q^{20} +0.512078 q^{21} -1.14369 q^{22} -2.79831 q^{23} -0.507814 q^{24} +1.00000 q^{25} +2.05099 q^{26} -2.91593 q^{27} +1.00840 q^{28} -3.74610 q^{29} +0.507814 q^{30} +7.43315 q^{31} -1.00000 q^{32} +0.580783 q^{33} -6.55597 q^{34} -1.00840 q^{35} -2.74213 q^{36} -4.68283 q^{37} +3.91995 q^{38} -1.04152 q^{39} +1.00000 q^{40} +11.8154 q^{41} -0.512078 q^{42} +10.3010 q^{43} +1.14369 q^{44} +2.74213 q^{45} +2.79831 q^{46} -8.20270 q^{47} +0.507814 q^{48} -5.98313 q^{49} -1.00000 q^{50} +3.32921 q^{51} -2.05099 q^{52} -8.22595 q^{53} +2.91593 q^{54} -1.14369 q^{55} -1.00840 q^{56} -1.99060 q^{57} +3.74610 q^{58} +7.81254 q^{59} -0.507814 q^{60} +3.18656 q^{61} -7.43315 q^{62} -2.76515 q^{63} +1.00000 q^{64} +2.05099 q^{65} -0.580783 q^{66} +6.44414 q^{67} +6.55597 q^{68} -1.42102 q^{69} +1.00840 q^{70} -15.5631 q^{71} +2.74213 q^{72} +8.43433 q^{73} +4.68283 q^{74} +0.507814 q^{75} -3.91995 q^{76} +1.15330 q^{77} +1.04152 q^{78} +8.56541 q^{79} -1.00000 q^{80} +6.74563 q^{81} -11.8154 q^{82} +0.905124 q^{83} +0.512078 q^{84} -6.55597 q^{85} -10.3010 q^{86} -1.90232 q^{87} -1.14369 q^{88} -1.54275 q^{89} -2.74213 q^{90} -2.06821 q^{91} -2.79831 q^{92} +3.77465 q^{93} +8.20270 q^{94} +3.91995 q^{95} -0.507814 q^{96} +3.83789 q^{97} +5.98313 q^{98} -3.13615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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