LMFDB - Embedded newform 4010.2.a.o.1.4

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:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52966 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.52966 q^{6} +2.69506 q^{7} +1.00000 q^{8} +3.39917 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52966 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.52966 q^{6} +2.69506 q^{7} +1.00000 q^{8} +3.39917 q^{9} -1.00000 q^{10} +0.593915 q^{11} -2.52966 q^{12} -6.28762 q^{13} +2.69506 q^{14} +2.52966 q^{15} +1.00000 q^{16} +6.95580 q^{17} +3.39917 q^{18} -5.09873 q^{19} -1.00000 q^{20} -6.81759 q^{21} +0.593915 q^{22} +1.45729 q^{23} -2.52966 q^{24} +1.00000 q^{25} -6.28762 q^{26} -1.00977 q^{27} +2.69506 q^{28} +9.36235 q^{29} +2.52966 q^{30} -4.09715 q^{31} +1.00000 q^{32} -1.50240 q^{33} +6.95580 q^{34} -2.69506 q^{35} +3.39917 q^{36} -8.75664 q^{37} -5.09873 q^{38} +15.9055 q^{39} -1.00000 q^{40} +6.34639 q^{41} -6.81759 q^{42} +4.00307 q^{43} +0.593915 q^{44} -3.39917 q^{45} +1.45729 q^{46} +1.52226 q^{47} -2.52966 q^{48} +0.263360 q^{49} +1.00000 q^{50} -17.5958 q^{51} -6.28762 q^{52} -2.68563 q^{53} -1.00977 q^{54} -0.593915 q^{55} +2.69506 q^{56} +12.8980 q^{57} +9.36235 q^{58} -10.6776 q^{59} +2.52966 q^{60} -8.19422 q^{61} -4.09715 q^{62} +9.16098 q^{63} +1.00000 q^{64} +6.28762 q^{65} -1.50240 q^{66} +3.50933 q^{67} +6.95580 q^{68} -3.68644 q^{69} -2.69506 q^{70} +8.78008 q^{71} +3.39917 q^{72} +5.86791 q^{73} -8.75664 q^{74} -2.52966 q^{75} -5.09873 q^{76} +1.60064 q^{77} +15.9055 q^{78} +13.4584 q^{79} -1.00000 q^{80} -7.64315 q^{81} +6.34639 q^{82} +5.01714 q^{83} -6.81759 q^{84} -6.95580 q^{85} +4.00307 q^{86} -23.6835 q^{87} +0.593915 q^{88} -0.515316 q^{89} -3.39917 q^{90} -16.9455 q^{91} +1.45729 q^{92} +10.3644 q^{93} +1.52226 q^{94} +5.09873 q^{95} -2.52966 q^{96} +15.5258 q^{97} +0.263360 q^{98} +2.01882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - 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
$3$	−2.52966	−1.46050	−0.730249	−	0.683181i	$-0.760596\pi$
$3$	−2.52966	−1.46050	−0.730249	+	0.683181i	$0.760596\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.52966	−1.03273
$7$	2.69506	1.01864	0.509319	−	0.860578i	$-0.329897\pi$
$7$	2.69506	1.01864	0.509319	+	0.860578i	$0.329897\pi$
$8$	1.00000	0.353553
$9$	3.39917	1.13306
$10$	−1.00000	−0.316228
$11$	0.593915	0.179072	0.0895361	−	0.995984i	$-0.471462\pi$
$11$	0.593915	0.179072	0.0895361	+	0.995984i	$0.471462\pi$
$12$	−2.52966	−0.730249
$13$	−6.28762	−1.74387	−0.871937	−	0.489619i	$-0.837136\pi$
$13$	−6.28762	−1.74387	−0.871937	+	0.489619i	$0.837136\pi$
$14$	2.69506	0.720286
$15$	2.52966	0.653155
$16$	1.00000	0.250000
$17$	6.95580	1.68703	0.843515	−	0.537106i	$-0.180482\pi$
$17$	6.95580	1.68703	0.843515	+	0.537106i	$0.180482\pi$
$18$	3.39917	0.801192
$19$	−5.09873	−1.16973	−0.584864	−	0.811131i	$-0.698852\pi$
$19$	−5.09873	−1.16973	−0.584864	+	0.811131i	$0.698852\pi$
$20$	−1.00000	−0.223607
$21$	−6.81759	−1.48772
$22$	0.593915	0.126623
$23$	1.45729	0.303866	0.151933	−	0.988391i	$-0.451450\pi$
$23$	1.45729	0.303866	0.151933	+	0.988391i	$0.451450\pi$
$24$	−2.52966	−0.516364
$25$	1.00000	0.200000
$26$	−6.28762	−1.23310
$27$	−1.00977	−0.194330
$28$	2.69506	0.509319
$29$	9.36235	1.73854	0.869272	−	0.494333i	$-0.164588\pi$
$29$	9.36235	1.73854	0.869272	+	0.494333i	$0.164588\pi$
$30$	2.52966	0.461850
$31$	−4.09715	−0.735871	−0.367935	−	0.929851i	$-0.619935\pi$
$31$	−4.09715	−0.735871	−0.367935	+	0.929851i	$0.619935\pi$
$32$	1.00000	0.176777
$33$	−1.50240	−0.261535
$34$	6.95580	1.19291
$35$	−2.69506	−0.455549
$36$	3.39917	0.566529
$37$	−8.75664	−1.43958	−0.719791	−	0.694191i	$-0.755762\pi$
$37$	−8.75664	−1.43958	−0.719791	+	0.694191i	$0.755762\pi$
$38$	−5.09873	−0.827123
$39$	15.9055	2.54692
$40$	−1.00000	−0.158114
$41$	6.34639	0.991140	0.495570	−	0.868568i	$-0.334959\pi$
$41$	6.34639	0.991140	0.495570	+	0.868568i	$0.334959\pi$
$42$	−6.81759	−1.05198
$43$	4.00307	0.610463	0.305232	−	0.952278i	$-0.401266\pi$
$43$	4.00307	0.610463	0.305232	+	0.952278i	$0.401266\pi$
$44$	0.593915	0.0895361
$45$	−3.39917	−0.506719
$46$	1.45729	0.214866
$47$	1.52226	0.222044	0.111022	−	0.993818i	$-0.464588\pi$
$47$	1.52226	0.222044	0.111022	+	0.993818i	$0.464588\pi$
$48$	−2.52966	−0.365125
$49$	0.263360	0.0376228
$50$	1.00000	0.141421
$51$	−17.5958	−2.46391
$52$	−6.28762	−0.871937
$53$	−2.68563	−0.368899	−0.184450	−	0.982842i	$-0.559050\pi$
$53$	−2.68563	−0.368899	−0.184450	+	0.982842i	$0.559050\pi$
$54$	−1.00977	−0.137412
$55$	−0.593915	−0.0800835
$56$	2.69506	0.360143
$57$	12.8980	1.70839
$58$	9.36235	1.22934
$59$	−10.6776	−1.39011	−0.695056	−	0.718956i	$-0.744620\pi$
$59$	−10.6776	−1.39011	−0.695056	+	0.718956i	$0.744620\pi$
$60$	2.52966	0.326578
$61$	−8.19422	−1.04916	−0.524581	−	0.851360i	$-0.675778\pi$
$61$	−8.19422	−1.04916	−0.524581	+	0.851360i	$0.675778\pi$
$62$	−4.09715	−0.520339
$63$	9.16098	1.15417
$64$	1.00000	0.125000
$65$	6.28762	0.779884
$66$	−1.50240	−0.184933
$67$	3.50933	0.428733	0.214367	−	0.976753i	$-0.431231\pi$
$67$	3.50933	0.428733	0.214367	+	0.976753i	$0.431231\pi$
$68$	6.95580	0.843515
$69$	−3.68644	−0.443796
$70$	−2.69506	−0.322122
$71$	8.78008	1.04200	0.521002	−	0.853556i	$-0.325558\pi$
$71$	8.78008	1.04200	0.521002	+	0.853556i	$0.325558\pi$
$72$	3.39917	0.400596
$73$	5.86791	0.686786	0.343393	−	0.939192i	$-0.388424\pi$
$73$	5.86791	0.686786	0.343393	+	0.939192i	$0.388424\pi$
$74$	−8.75664	−1.01794
$75$	−2.52966	−0.292100
$76$	−5.09873	−0.584864
$77$	1.60064	0.182410
$78$	15.9055	1.80095
$79$	13.4584	1.51419	0.757094	−	0.653306i	$-0.226619\pi$
$79$	13.4584	1.51419	0.757094	+	0.653306i	$0.226619\pi$
$80$	−1.00000	−0.111803
$81$	−7.64315	−0.849238
$82$	6.34639	0.700842
$83$	5.01714	0.550702	0.275351	−	0.961344i	$-0.411206\pi$
$83$	5.01714	0.550702	0.275351	+	0.961344i	$0.411206\pi$
$84$	−6.81759	−0.743860
$85$	−6.95580	−0.754463
$86$	4.00307	0.431663
$87$	−23.6835	−2.53914
$88$	0.593915	0.0633116
$89$	−0.515316	−0.0546234	−0.0273117	−	0.999627i	$-0.508695\pi$
$89$	−0.515316	−0.0546234	−0.0273117	+	0.999627i	$0.508695\pi$
$90$	−3.39917	−0.358304
$91$	−16.9455	−1.77637
$92$	1.45729	0.151933
$93$	10.3644	1.07474
$94$	1.52226	0.157009
$95$	5.09873	0.523118
$96$	−2.52966	−0.258182
$97$	15.5258	1.57640	0.788201	−	0.615418i	$-0.211013\pi$
$97$	15.5258	1.57640	0.788201	+	0.615418i	$0.211013\pi$
$98$	0.263360	0.0266034
$99$	2.01882	0.202899
$100$	1.00000	0.100000
$101$	−10.0014	−0.995174	−0.497587	−	0.867414i	$-0.665781\pi$
$101$	−10.0014	−0.995174	−0.497587	+	0.867414i	$0.665781\pi$
$102$	−17.5958	−1.74224
$103$	−2.84718	−0.280541	−0.140270	−	0.990113i	$-0.544797\pi$
$103$	−2.84718	−0.280541	−0.140270	+	0.990113i	$0.544797\pi$
$104$	−6.28762	−0.616552
$105$	6.81759	0.665328
$106$	−2.68563	−0.260851
$107$	3.00795	0.290789	0.145395	−	0.989374i	$-0.453555\pi$
$107$	3.00795	0.290789	0.145395	+	0.989374i	$0.453555\pi$
$108$	−1.00977	−0.0971650
$109$	16.1226	1.54426	0.772130	−	0.635464i	$-0.219191\pi$
$109$	16.1226	1.54426	0.772130	+	0.635464i	$0.219191\pi$
$110$	−0.593915	−0.0566276
$111$	22.1513	2.10251
$112$	2.69506	0.254659
$113$	8.33026	0.783645	0.391822	−	0.920041i	$-0.371845\pi$
$113$	8.33026	0.783645	0.391822	+	0.920041i	$0.371845\pi$
$114$	12.8980	1.20801
$115$	−1.45729	−0.135893
$116$	9.36235	0.869272
$117$	−21.3727	−1.97591
$118$	−10.6776	−0.982957
$119$	18.7463	1.71847
$120$	2.52966	0.230925
$121$	−10.6473	−0.967933
$122$	−8.19422	−0.741870
$123$	−16.0542	−1.44756
$124$	−4.09715	−0.367935
$125$	−1.00000	−0.0894427
$126$	9.16098	0.816125
$127$	−5.49037	−0.487192	−0.243596	−	0.969877i	$-0.578327\pi$
$127$	−5.49037	−0.487192	−0.243596	+	0.969877i	$0.578327\pi$
$128$	1.00000	0.0883883
$129$	−10.1264	−0.891581
$130$	6.28762	0.551461
$131$	18.2916	1.59814	0.799070	−	0.601238i	$-0.205326\pi$
$131$	18.2916	1.59814	0.799070	+	0.601238i	$0.205326\pi$
$132$	−1.50240	−0.130767
$133$	−13.7414	−1.19153
$134$	3.50933	0.303160
$135$	1.00977	0.0869070
$136$	6.95580	0.596455
$137$	−1.44077	−0.123093	−0.0615465	−	0.998104i	$-0.519603\pi$
$137$	−1.44077	−0.123093	−0.0615465	+	0.998104i	$0.519603\pi$
$138$	−3.68644	−0.313811
$139$	−16.3881	−1.39002	−0.695012	−	0.718998i	$-0.744601\pi$
$139$	−16.3881	−1.39002	−0.695012	+	0.718998i	$0.744601\pi$
$140$	−2.69506	−0.227774
$141$	−3.85080	−0.324296
$142$	8.78008	0.736808
$143$	−3.73431	−0.312279
$144$	3.39917	0.283264
$145$	−9.36235	−0.777501
$146$	5.86791	0.485631
$147$	−0.666210	−0.0549481
$148$	−8.75664	−0.719791
$149$	11.7788	0.964954	0.482477	−	0.875909i	$-0.339737\pi$
$149$	11.7788	0.964954	0.482477	+	0.875909i	$0.339737\pi$
$150$	−2.52966	−0.206546
$151$	−1.12117	−0.0912399	−0.0456199	−	0.998959i	$-0.514526\pi$
$151$	−1.12117	−0.0912399	−0.0456199	+	0.998959i	$0.514526\pi$
$152$	−5.09873	−0.413561
$153$	23.6440	1.91150
$154$	1.60064	0.128983
$155$	4.09715	0.329091
$156$	15.9055	1.27346
$157$	4.73827	0.378155	0.189077	−	0.981962i	$-0.439450\pi$
$157$	4.73827	0.378155	0.189077	+	0.981962i	$0.439450\pi$
$158$	13.4584	1.07069
$159$	6.79372	0.538777
$160$	−1.00000	−0.0790569
$161$	3.92749	0.309529
$162$	−7.64315	−0.600502
$163$	11.0048	0.861962	0.430981	−	0.902361i	$-0.358168\pi$
$163$	11.0048	0.861962	0.430981	+	0.902361i	$0.358168\pi$
$164$	6.34639	0.495570
$165$	1.50240	0.116962
$166$	5.01714	0.389405
$167$	14.1301	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$167$	14.1301	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$168$	−6.81759	−0.525988
$169$	26.5342	2.04109
$170$	−6.95580	−0.533486
$171$	−17.3314	−1.32537
$172$	4.00307	0.305232
$173$	19.4990	1.48248	0.741239	−	0.671241i	$-0.234238\pi$
$173$	19.4990	1.48248	0.741239	+	0.671241i	$0.234238\pi$
$174$	−23.6835	−1.79545
$175$	2.69506	0.203728
$176$	0.593915	0.0447680
$177$	27.0108	2.03026
$178$	−0.515316	−0.0386245
$179$	4.75816	0.355642	0.177821	−	0.984063i	$-0.443095\pi$
$179$	4.75816	0.355642	0.177821	+	0.984063i	$0.443095\pi$
$180$	−3.39917	−0.253359
$181$	21.0239	1.56270	0.781348	−	0.624096i	$-0.214533\pi$
$181$	21.0239	1.56270	0.781348	+	0.624096i	$0.214533\pi$
$182$	−16.9455	−1.25609
$183$	20.7286	1.53230
$184$	1.45729	0.107433
$185$	8.75664	0.643801
$186$	10.3644	0.759955
$187$	4.13116	0.302100
$188$	1.52226	0.111022
$189$	−2.72139	−0.197952
$190$	5.09873	0.369900
$191$	−11.7213	−0.848122	−0.424061	−	0.905634i	$-0.639396\pi$
$191$	−11.7213	−0.848122	−0.424061	+	0.905634i	$0.639396\pi$
$192$	−2.52966	−0.182562
$193$	15.3455	1.10460	0.552298	−	0.833647i	$-0.313751\pi$
$193$	15.3455	1.10460	0.552298	+	0.833647i	$0.313751\pi$
$194$	15.5258	1.11468
$195$	−15.9055	−1.13902
$196$	0.263360	0.0188114
$197$	3.14693	0.224209	0.112105	−	0.993696i	$-0.464241\pi$
$197$	3.14693	0.224209	0.112105	+	0.993696i	$0.464241\pi$
$198$	2.01882	0.143471
$199$	0.439268	0.0311389	0.0155694	−	0.999879i	$-0.495044\pi$
$199$	0.439268	0.0311389	0.0155694	+	0.999879i	$0.495044\pi$
$200$	1.00000	0.0707107
$201$	−8.87741	−0.626164
$202$	−10.0014	−0.703695
$203$	25.2321	1.77095
$204$	−17.5958	−1.23195
$205$	−6.34639	−0.443251
$206$	−2.84718	−0.198372
$207$	4.95358	0.344297
$208$	−6.28762	−0.435968
$209$	−3.02821	−0.209466
$210$	6.81759	0.470458
$211$	0.275574	0.0189713	0.00948564	−	0.999955i	$-0.496981\pi$
$211$	0.275574	0.0189713	0.00948564	+	0.999955i	$0.496981\pi$
$212$	−2.68563	−0.184450
$213$	−22.2106	−1.52185
$214$	3.00795	0.205619
$215$	−4.00307	−0.273007
$216$	−1.00977	−0.0687060
$217$	−11.0421	−0.749586
$218$	16.1226	1.09196
$219$	−14.8438	−1.00305
$220$	−0.593915	−0.0400417
$221$	−43.7355	−2.94197
$222$	22.1513	1.48670
$223$	12.4245	0.832009	0.416004	−	0.909363i	$-0.363430\pi$
$223$	12.4245	0.832009	0.416004	+	0.909363i	$0.363430\pi$
$224$	2.69506	0.180071
$225$	3.39917	0.226611
$226$	8.33026	0.554121
$227$	−8.21616	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$227$	−8.21616	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$228$	12.8980	0.854193
$229$	18.3093	1.20991	0.604956	−	0.796259i	$-0.293191\pi$
$229$	18.3093	1.20991	0.604956	+	0.796259i	$0.293191\pi$
$230$	−1.45729	−0.0960908
$231$	−4.04907	−0.266409
$232$	9.36235	0.614668
$233$	−12.2244	−0.800848	−0.400424	−	0.916330i	$-0.631137\pi$
$233$	−12.2244	−0.800848	−0.400424	+	0.916330i	$0.631137\pi$
$234$	−21.3727	−1.39718
$235$	−1.52226	−0.0993013
$236$	−10.6776	−0.695056
$237$	−34.0451	−2.21147
$238$	18.7463	1.21514
$239$	−2.60123	−0.168260	−0.0841299	−	0.996455i	$-0.526811\pi$
$239$	−2.60123	−0.168260	−0.0841299	+	0.996455i	$0.526811\pi$
$240$	2.52966	0.163289
$241$	−0.619296	−0.0398924	−0.0199462	−	0.999801i	$-0.506349\pi$
$241$	−0.619296	−0.0398924	−0.0199462	+	0.999801i	$0.506349\pi$
$242$	−10.6473	−0.684432
$243$	22.3639	1.43464
$244$	−8.19422	−0.524581
$245$	−0.263360	−0.0168254
$246$	−16.0542	−1.02358
$247$	32.0589	2.03986
$248$	−4.09715	−0.260170
$249$	−12.6916	−0.804300
$250$	−1.00000	−0.0632456
$251$	−6.27873	−0.396310	−0.198155	−	0.980171i	$-0.563495\pi$
$251$	−6.27873	−0.396310	−0.198155	+	0.980171i	$0.563495\pi$
$252$	9.16098	0.577087
$253$	0.865506	0.0544139
$254$	−5.49037	−0.344497
$255$	17.5958	1.10189
$256$	1.00000	0.0625000
$257$	19.1931	1.19724	0.598618	−	0.801035i	$-0.295717\pi$
$257$	19.1931	1.19724	0.598618	+	0.801035i	$0.295717\pi$
$258$	−10.1264	−0.630443
$259$	−23.5997	−1.46641
$260$	6.28762	0.389942
$261$	31.8242	1.96987
$262$	18.2916	1.13006
$263$	15.7314	0.970041	0.485021	−	0.874503i	$-0.338812\pi$
$263$	15.7314	0.970041	0.485021	+	0.874503i	$0.338812\pi$
$264$	−1.50240	−0.0924665
$265$	2.68563	0.164977
$266$	−13.7414	−0.842538
$267$	1.30357	0.0797774
$268$	3.50933	0.214367
$269$	22.2823	1.35857	0.679287	−	0.733872i	$-0.262289\pi$
$269$	22.2823	1.35857	0.679287	+	0.733872i	$0.262289\pi$
$270$	1.00977	0.0614526
$271$	−29.3704	−1.78413	−0.892063	−	0.451911i	$-0.850742\pi$
$271$	−29.3704	−1.78413	−0.892063	+	0.451911i	$0.850742\pi$
$272$	6.95580	0.421757
$273$	42.8664	2.59439
$274$	−1.44077	−0.0870399
$275$	0.593915	0.0358144
$276$	−3.68644	−0.221898
$277$	26.0400	1.56459	0.782296	−	0.622907i	$-0.214049\pi$
$277$	26.0400	1.56459	0.782296	+	0.622907i	$0.214049\pi$
$278$	−16.3881	−0.982895
$279$	−13.9269	−0.833784
$280$	−2.69506	−0.161061
$281$	−6.24636	−0.372627	−0.186313	−	0.982490i	$-0.559654\pi$
$281$	−6.24636	−0.372627	−0.186313	+	0.982490i	$0.559654\pi$
$282$	−3.85080	−0.229312
$283$	−0.102084	−0.00606827	−0.00303414	−	0.999995i	$-0.500966\pi$
$283$	−0.102084	−0.00606827	−0.00303414	+	0.999995i	$0.500966\pi$
$284$	8.78008	0.521002
$285$	−12.8980	−0.764014
$286$	−3.73431	−0.220815
$287$	17.1039	1.00961
$288$	3.39917	0.200298
$289$	31.3832	1.84607
$290$	−9.36235	−0.549776
$291$	−39.2749	−2.30233
$292$	5.86791	0.343393
$293$	6.29810	0.367939	0.183969	−	0.982932i	$-0.441105\pi$
$293$	6.29810	0.367939	0.183969	+	0.982932i	$0.441105\pi$
$294$	−0.666210	−0.0388542
$295$	10.6776	0.621677
$296$	−8.75664	−0.508969
$297$	−0.599717	−0.0347991
$298$	11.7788	0.682326
$299$	−9.16289	−0.529903
$300$	−2.52966	−0.146050
$301$	10.7885	0.621841
$302$	−1.12117	−0.0645163
$303$	25.3001	1.45345
$304$	−5.09873	−0.292432
$305$	8.19422	0.469200
$306$	23.6440	1.35164
$307$	5.26894	0.300714	0.150357	−	0.988632i	$-0.451958\pi$
$307$	5.26894	0.300714	0.150357	+	0.988632i	$0.451958\pi$
$308$	1.60064	0.0912048
$309$	7.20238	0.409729
$310$	4.09715	0.232703
$311$	−20.3210	−1.15230	−0.576149	−	0.817345i	$-0.695445\pi$
$311$	−20.3210	−1.15230	−0.576149	+	0.817345i	$0.695445\pi$
$312$	15.9055	0.900474
$313$	−24.1905	−1.36733	−0.683664	−	0.729797i	$-0.739614\pi$
$313$	−24.1905	−1.36733	−0.683664	+	0.729797i	$0.739614\pi$
$314$	4.73827	0.267396
$315$	−9.16098	−0.516163
$316$	13.4584	0.757094
$317$	21.8195	1.22550	0.612752	−	0.790275i	$-0.290063\pi$
$317$	21.8195	1.22550	0.612752	+	0.790275i	$0.290063\pi$
$318$	6.79372	0.380973
$319$	5.56044	0.311325
$320$	−1.00000	−0.0559017
$321$	−7.60908	−0.424697
$322$	3.92749	0.218870
$323$	−35.4657	−1.97337
$324$	−7.64315	−0.424619
$325$	−6.28762	−0.348775
$326$	11.0048	0.609499
$327$	−40.7846	−2.25539
$328$	6.34639	0.350421
$329$	4.10258	0.226183
$330$	1.50240	0.0827045
$331$	6.78917	0.373167	0.186583	−	0.982439i	$-0.440259\pi$
$331$	6.78917	0.373167	0.186583	+	0.982439i	$0.440259\pi$
$332$	5.01714	0.275351
$333$	−29.7653	−1.63113
$334$	14.1301	0.773166
$335$	−3.50933	−0.191735
$336$	−6.81759	−0.371930
$337$	19.3596	1.05459	0.527293	−	0.849684i	$-0.323207\pi$
$337$	19.3596	1.05459	0.527293	+	0.849684i	$0.323207\pi$
$338$	26.5342	1.44327
$339$	−21.0727	−1.14451
$340$	−6.95580	−0.377231
$341$	−2.43336	−0.131774
$342$	−17.3314	−0.937177
$343$	−18.1557	−0.980314
$344$	4.00307	0.215831
$345$	3.68644	0.198471
$346$	19.4990	1.04827
$347$	27.3040	1.46576	0.732879	−	0.680359i	$-0.238176\pi$
$347$	27.3040	1.46576	0.732879	+	0.680359i	$0.238176\pi$
$348$	−23.6835	−1.26957
$349$	26.8022	1.43469	0.717345	−	0.696718i	$-0.245357\pi$
$349$	26.8022	1.43469	0.717345	+	0.696718i	$0.245357\pi$
$350$	2.69506	0.144057
$351$	6.34904	0.338887
$352$	0.593915	0.0316558
$353$	4.92354	0.262054	0.131027	−	0.991379i	$-0.458173\pi$
$353$	4.92354	0.262054	0.131027	+	0.991379i	$0.458173\pi$
$354$	27.0108	1.43561
$355$	−8.78008	−0.465998
$356$	−0.515316	−0.0273117
$357$	−47.4218	−2.50983
$358$	4.75816	0.251477
$359$	23.7453	1.25323	0.626614	−	0.779330i	$-0.284440\pi$
$359$	23.7453	1.25323	0.626614	+	0.779330i	$0.284440\pi$
$360$	−3.39917	−0.179152
$361$	6.99701	0.368263
$362$	21.0239	1.10499
$363$	26.9339	1.41367
$364$	−16.9455	−0.888187
$365$	−5.86791	−0.307140
$366$	20.7286	1.08350
$367$	−6.48800	−0.338671	−0.169335	−	0.985558i	$-0.554162\pi$
$367$	−6.48800	−0.338671	−0.169335	+	0.985558i	$0.554162\pi$
$368$	1.45729	0.0759665
$369$	21.5725	1.12302
$370$	8.75664	0.455236
$371$	−7.23793	−0.375775
$372$	10.3644	0.537369
$373$	−2.61844	−0.135578	−0.0677888	−	0.997700i	$-0.521594\pi$
$373$	−2.61844	−0.135578	−0.0677888	+	0.997700i	$0.521594\pi$
$374$	4.13116	0.213617
$375$	2.52966	0.130631
$376$	1.52226	0.0785045
$377$	−58.8669	−3.03180
$378$	−2.72139	−0.139973
$379$	−17.4432	−0.895997	−0.447999	−	0.894034i	$-0.647863\pi$
$379$	−17.4432	−0.895997	−0.447999	+	0.894034i	$0.647863\pi$
$380$	5.09873	0.261559
$381$	13.8888	0.711543
$382$	−11.7213	−0.599713
$383$	17.7731	0.908162	0.454081	−	0.890960i	$-0.349968\pi$
$383$	17.7731	0.908162	0.454081	+	0.890960i	$0.349968\pi$
$384$	−2.52966	−0.129091
$385$	−1.60064	−0.0815761
$386$	15.3455	0.781068
$387$	13.6071	0.691690
$388$	15.5258	0.788201
$389$	−20.6606	−1.04753	−0.523766	−	0.851862i	$-0.675473\pi$
$389$	−20.6606	−1.04753	−0.523766	+	0.851862i	$0.675473\pi$
$390$	−15.9055	−0.805408
$391$	10.1366	0.512631
$392$	0.263360	0.0133017
$393$	−46.2714	−2.33408
$394$	3.14693	0.158540
$395$	−13.4584	−0.677165
$396$	2.01882	0.101449
$397$	−14.7486	−0.740212	−0.370106	−	0.928989i	$-0.620679\pi$
$397$	−14.7486	−0.740212	−0.370106	+	0.928989i	$0.620679\pi$
$398$	0.439268	0.0220185
$399$	34.7610	1.74023
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−8.87741	−0.442765
$403$	25.7614	1.28327
$404$	−10.0014	−0.497587
$405$	7.64315	0.379791
$406$	25.2321	1.25225
$407$	−5.20070	−0.257789
$408$	−17.5958	−0.871122
$409$	−35.4849	−1.75461	−0.877307	−	0.479930i	$-0.840662\pi$
$409$	−35.4849	−1.75461	−0.877307	+	0.479930i	$0.840662\pi$
$410$	−6.34639	−0.313426
$411$	3.64465	0.179777
$412$	−2.84718	−0.140270
$413$	−28.7769	−1.41602
$414$	4.95358	0.243455
$415$	−5.01714	−0.246282
$416$	−6.28762	−0.308276
$417$	41.4564	2.03013
$418$	−3.02821	−0.148115
$419$	−16.4639	−0.804312	−0.402156	−	0.915571i	$-0.631739\pi$
$419$	−16.4639	−0.804312	−0.402156	+	0.915571i	$0.631739\pi$
$420$	6.81759	0.332664
$421$	24.8756	1.21236	0.606182	−	0.795326i	$-0.292700\pi$
$421$	24.8756	1.21236	0.606182	+	0.795326i	$0.292700\pi$
$422$	0.275574	0.0134147
$423$	5.17442	0.251589
$424$	−2.68563	−0.130426
$425$	6.95580	0.337406
$426$	−22.2106	−1.07611
$427$	−22.0839	−1.06872
$428$	3.00795	0.145395
$429$	9.44654	0.456083
$430$	−4.00307	−0.193045
$431$	−19.3811	−0.933555	−0.466777	−	0.884375i	$-0.654585\pi$
$431$	−19.3811	−0.933555	−0.466777	+	0.884375i	$0.654585\pi$
$432$	−1.00977	−0.0485825
$433$	18.9177	0.909126	0.454563	−	0.890715i	$-0.349795\pi$
$433$	18.9177	0.909126	0.454563	+	0.890715i	$0.349795\pi$
$434$	−11.0421	−0.530037
$435$	23.6835	1.13554
$436$	16.1226	0.772130
$437$	−7.43032	−0.355440
$438$	−14.8438	−0.709264
$439$	−7.44743	−0.355447	−0.177723	−	0.984080i	$-0.556873\pi$
$439$	−7.44743	−0.355447	−0.177723	+	0.984080i	$0.556873\pi$
$440$	−0.593915	−0.0283138
$441$	0.895205	0.0426288
$442$	−43.7355	−2.08028
$443$	−8.27884	−0.393339	−0.196670	−	0.980470i	$-0.563013\pi$
$443$	−8.27884	−0.393339	−0.196670	+	0.980470i	$0.563013\pi$
$444$	22.1513	1.05125
$445$	0.515316	0.0244283
$446$	12.4245	0.588319
$447$	−29.7963	−1.40931
$448$	2.69506	0.127330
$449$	−38.2882	−1.80693	−0.903467	−	0.428658i	$-0.858987\pi$
$449$	−38.2882	−1.80693	−0.903467	+	0.428658i	$0.858987\pi$
$450$	3.39917	0.160238
$451$	3.76922	0.177485
$452$	8.33026	0.391822
$453$	2.83619	0.133256
$454$	−8.21616	−0.385603
$455$	16.9455	0.794419
$456$	12.8980	0.604006
$457$	−31.8051	−1.48778	−0.743889	−	0.668303i	$-0.767021\pi$
$457$	−31.8051	−1.48778	−0.743889	+	0.668303i	$0.767021\pi$
$458$	18.3093	0.855538
$459$	−7.02375	−0.327841
$460$	−1.45729	−0.0679465
$461$	−27.2217	−1.26784	−0.633921	−	0.773398i	$-0.718555\pi$
$461$	−27.2217	−1.26784	−0.633921	+	0.773398i	$0.718555\pi$
$462$	−4.04907	−0.188380
$463$	1.09144	0.0507233	0.0253617	−	0.999678i	$-0.491926\pi$
$463$	1.09144	0.0507233	0.0253617	+	0.999678i	$0.491926\pi$
$464$	9.36235	0.434636
$465$	−10.3644	−0.480638
$466$	−12.2244	−0.566285
$467$	−28.8369	−1.33441	−0.667207	−	0.744873i	$-0.732510\pi$
$467$	−28.8369	−1.33441	−0.667207	+	0.744873i	$0.732510\pi$
$468$	−21.3727	−0.987954
$469$	9.45787	0.436724
$470$	−1.52226	−0.0702166
$471$	−11.9862	−0.552295
$472$	−10.6776	−0.491479
$473$	2.37749	0.109317
$474$	−34.0451	−1.56374
$475$	−5.09873	−0.233946
$476$	18.7463	0.859236
$477$	−9.12890	−0.417984
$478$	−2.60123	−0.118978
$479$	7.89329	0.360653	0.180327	−	0.983607i	$-0.442285\pi$
$479$	7.89329	0.360653	0.180327	+	0.983607i	$0.442285\pi$
$480$	2.52966	0.115463
$481$	55.0584	2.51045
$482$	−0.619296	−0.0282082
$483$	−9.93520	−0.452067
$484$	−10.6473	−0.483967
$485$	−15.5258	−0.704988
$486$	22.3639	1.01445
$487$	−5.74798	−0.260466	−0.130233	−	0.991483i	$-0.541573\pi$
$487$	−5.74798	−0.260466	−0.130233	+	0.991483i	$0.541573\pi$
$488$	−8.19422	−0.370935
$489$	−27.8384	−1.25890
$490$	−0.263360	−0.0118974
$491$	−15.8547	−0.715513	−0.357756	−	0.933815i	$-0.616458\pi$
$491$	−15.8547	−0.715513	−0.357756	+	0.933815i	$0.616458\pi$
$492$	−16.0542	−0.723779
$493$	65.1227	2.93298
$494$	32.0589	1.44240
$495$	−2.01882	−0.0907392
$496$	−4.09715	−0.183968
$497$	23.6629	1.06142
$498$	−12.6916	−0.568726
$499$	−23.2985	−1.04299	−0.521493	−	0.853255i	$-0.674625\pi$
$499$	−23.2985	−1.04299	−0.521493	+	0.853255i	$0.674625\pi$
$500$	−1.00000	−0.0447214
$501$	−35.7444	−1.59694
$502$	−6.27873	−0.280233
$503$	11.9932	0.534751	0.267375	−	0.963592i	$-0.413844\pi$
$503$	11.9932	0.534751	0.267375	+	0.963592i	$0.413844\pi$
$504$	9.16098	0.408062
$505$	10.0014	0.445056
$506$	0.865506	0.0384764
$507$	−67.1225	−2.98101
$508$	−5.49037	−0.243596
$509$	−5.87013	−0.260189	−0.130094	−	0.991502i	$-0.541528\pi$
$509$	−5.87013	−0.260189	−0.130094	+	0.991502i	$0.541528\pi$
$510$	17.5958	0.779155
$511$	15.8144	0.699586
$512$	1.00000	0.0441942
$513$	5.14853	0.227313
$514$	19.1931	0.846573
$515$	2.84718	0.125462
$516$	−10.1264	−0.445790
$517$	0.904093	0.0397620
$518$	−23.5997	−1.03691
$519$	−49.3257	−2.16516
$520$	6.28762	0.275731
$521$	−23.0610	−1.01032	−0.505160	−	0.863026i	$-0.668566\pi$
$521$	−23.0610	−1.01032	−0.505160	+	0.863026i	$0.668566\pi$
$522$	31.8242	1.39291
$523$	−7.07173	−0.309225	−0.154613	−	0.987975i	$-0.549413\pi$
$523$	−7.07173	−0.309225	−0.154613	+	0.987975i	$0.549413\pi$
$524$	18.2916	0.799070
$525$	−6.81759	−0.297544
$526$	15.7314	0.685923
$527$	−28.4990	−1.24144
$528$	−1.50240	−0.0653837
$529$	−20.8763	−0.907666
$530$	2.68563	0.116656
$531$	−36.2952	−1.57508
$532$	−13.7414	−0.595765
$533$	−39.9037	−1.72842
$534$	1.30357	0.0564111
$535$	−3.00795	−0.130045
$536$	3.50933	0.151580
$537$	−12.0365	−0.519415
$538$	22.2823	0.960657
$539$	0.156413	0.00673720
$540$	1.00977	0.0434535
$541$	43.8337	1.88456	0.942280	−	0.334827i	$-0.108678\pi$
$541$	43.8337	1.88456	0.942280	+	0.334827i	$0.108678\pi$
$542$	−29.3704	−1.26157
$543$	−53.1833	−2.28232
$544$	6.95580	0.298228
$545$	−16.1226	−0.690614
$546$	42.8664	1.83451
$547$	5.25683	0.224766	0.112383	−	0.993665i	$-0.464152\pi$
$547$	5.25683	0.224766	0.112383	+	0.993665i	$0.464152\pi$
$548$	−1.44077	−0.0615465
$549$	−27.8536	−1.18876
$550$	0.593915	0.0253246
$551$	−47.7361	−2.03362
$552$	−3.68644	−0.156905
$553$	36.2712	1.54241
$554$	26.0400	1.10633
$555$	−22.1513	−0.940270
$556$	−16.3881	−0.695012
$557$	−1.13967	−0.0482895	−0.0241448	−	0.999708i	$-0.507686\pi$
$557$	−1.13967	−0.0482895	−0.0241448	+	0.999708i	$0.507686\pi$
$558$	−13.9269	−0.589574
$559$	−25.1698	−1.06457
$560$	−2.69506	−0.113887
$561$	−10.4504	−0.441217
$562$	−6.24636	−0.263487
$563$	−34.8904	−1.47045	−0.735227	−	0.677821i	$-0.762924\pi$
$563$	−34.8904	−1.47045	−0.735227	+	0.677821i	$0.762924\pi$
$564$	−3.85080	−0.162148
$565$	−8.33026	−0.350457
$566$	−0.102084	−0.00429092
$567$	−20.5988	−0.865066
$568$	8.78008	0.368404
$569$	18.4896	0.775125	0.387563	−	0.921843i	$-0.373317\pi$
$569$	18.4896	0.775125	0.387563	+	0.921843i	$0.373317\pi$
$570$	−12.8980	−0.540239
$571$	5.31054	0.222239	0.111120	−	0.993807i	$-0.464556\pi$
$571$	5.31054	0.222239	0.111120	+	0.993807i	$0.464556\pi$
$572$	−3.73431	−0.156140
$573$	29.6508	1.23868
$574$	17.1039	0.713904
$575$	1.45729	0.0607732
$576$	3.39917	0.141632
$577$	12.7026	0.528816	0.264408	−	0.964411i	$-0.414823\pi$
$577$	12.7026	0.528816	0.264408	+	0.964411i	$0.414823\pi$
$578$	31.3832	1.30537
$579$	−38.8190	−1.61326
$580$	−9.36235	−0.388750
$581$	13.5215	0.560966
$582$	−39.2749	−1.62800
$583$	−1.59503	−0.0660596
$584$	5.86791	0.242816
$585$	21.3727	0.883653
$586$	6.29810	0.260172
$587$	−7.33750	−0.302851	−0.151426	−	0.988469i	$-0.548386\pi$
$587$	−7.33750	−0.302851	−0.151426	+	0.988469i	$0.548386\pi$
$588$	−0.666210	−0.0274741
$589$	20.8903	0.860769
$590$	10.6776	0.439592
$591$	−7.96066	−0.327458
$592$	−8.75664	−0.359896
$593$	3.36322	0.138111	0.0690555	−	0.997613i	$-0.478001\pi$
$593$	3.36322	0.138111	0.0690555	+	0.997613i	$0.478001\pi$
$594$	−0.599717	−0.0246067
$595$	−18.7463	−0.768524
$596$	11.7788	0.482477
$597$	−1.11120	−0.0454783
$598$	−9.16289	−0.374698
$599$	−21.2423	−0.867937	−0.433968	−	0.900928i	$-0.642887\pi$
$599$	−21.2423	−0.867937	−0.433968	+	0.900928i	$0.642887\pi$
$600$	−2.52966	−0.103273
$601$	26.0160	1.06122	0.530608	−	0.847618i	$-0.321964\pi$
$601$	26.0160	1.06122	0.530608	+	0.847618i	$0.321964\pi$
$602$	10.7885	0.439708
$603$	11.9288	0.485779
$604$	−1.12117	−0.0456199
$605$	10.6473	0.432873
$606$	25.3001	1.02775
$607$	−25.9621	−1.05377	−0.526885	−	0.849937i	$-0.676640\pi$
$607$	−25.9621	−1.05377	−0.526885	+	0.849937i	$0.676640\pi$
$608$	−5.09873	−0.206781
$609$	−63.8286	−2.58647
$610$	8.19422	0.331774
$611$	−9.57139	−0.387217
$612$	23.6440	0.955751
$613$	−30.2914	−1.22346	−0.611730	−	0.791067i	$-0.709526\pi$
$613$	−30.2914	−1.22346	−0.611730	+	0.791067i	$0.709526\pi$
$614$	5.26894	0.212637
$615$	16.0542	0.647368
$616$	1.60064	0.0644915
$617$	−11.0758	−0.445896	−0.222948	−	0.974830i	$-0.571568\pi$
$617$	−11.0758	−0.445896	−0.222948	+	0.974830i	$0.571568\pi$
$618$	7.20238	0.289722
$619$	0.956965	0.0384637	0.0192318	−	0.999815i	$-0.493878\pi$
$619$	0.956965	0.0384637	0.0192318	+	0.999815i	$0.493878\pi$
$620$	4.09715	0.164546
$621$	−1.47152	−0.0590503
$622$	−20.3210	−0.814798
$623$	−1.38881	−0.0556414
$624$	15.9055	0.636731
$625$	1.00000	0.0400000
$626$	−24.1905	−0.966846
$627$	7.66034	0.305924
$628$	4.73827	0.189077
$629$	−60.9094	−2.42862
$630$	−9.16098	−0.364982
$631$	−31.0729	−1.23699	−0.618496	−	0.785788i	$-0.712258\pi$
$631$	−31.0729	−1.23699	−0.618496	+	0.785788i	$0.712258\pi$
$632$	13.4584	0.535346
$633$	−0.697107	−0.0277075
$634$	21.8195	0.866562
$635$	5.49037	0.217879
$636$	6.79372	0.269388
$637$	−1.65591	−0.0656094
$638$	5.56044	0.220140
$639$	29.8450	1.18065
$640$	−1.00000	−0.0395285
$641$	−28.2476	−1.11571	−0.557856	−	0.829938i	$-0.688376\pi$
$641$	−28.2476	−1.11571	−0.557856	+	0.829938i	$0.688376\pi$
$642$	−7.60908	−0.300306
$643$	3.90614	0.154043	0.0770216	−	0.997029i	$-0.475459\pi$
$643$	3.90614	0.154043	0.0770216	+	0.997029i	$0.475459\pi$
$644$	3.92749	0.154765
$645$	10.1264	0.398727
$646$	−35.4657	−1.39538
$647$	41.8236	1.64426	0.822129	−	0.569302i	$-0.192786\pi$
$647$	41.8236	1.64426	0.822129	+	0.569302i	$0.192786\pi$
$648$	−7.64315	−0.300251
$649$	−6.34162	−0.248930
$650$	−6.28762	−0.246621
$651$	27.9327	1.09477
$652$	11.0048	0.430981
$653$	3.40004	0.133054	0.0665269	−	0.997785i	$-0.478808\pi$
$653$	3.40004	0.133054	0.0665269	+	0.997785i	$0.478808\pi$
$654$	−40.7846	−1.59480
$655$	−18.2916	−0.714710
$656$	6.34639	0.247785
$657$	19.9460	0.778168
$658$	4.10258	0.159935
$659$	−14.1025	−0.549356	−0.274678	−	0.961536i	$-0.588571\pi$
$659$	−14.1025	−0.549356	−0.274678	+	0.961536i	$0.588571\pi$
$660$	1.50240	0.0584809
$661$	38.6273	1.50243	0.751213	−	0.660059i	$-0.229469\pi$
$661$	38.6273	1.50243	0.751213	+	0.660059i	$0.229469\pi$
$662$	6.78917	0.263869
$663$	110.636	4.29674
$664$	5.01714	0.194703
$665$	13.7414	0.532868
$666$	−29.7653	−1.15338
$667$	13.6437	0.528284
$668$	14.1301	0.546711
$669$	−31.4298	−1.21515
$670$	−3.50933	−0.135577
$671$	−4.86667	−0.187876
$672$	−6.81759	−0.262994
$673$	32.3872	1.24843	0.624216	−	0.781251i	$-0.285418\pi$
$673$	32.3872	1.24843	0.624216	+	0.781251i	$0.285418\pi$
$674$	19.3596	0.745705
$675$	−1.00977	−0.0388660
$676$	26.5342	1.02055
$677$	13.5371	0.520273	0.260137	−	0.965572i	$-0.416232\pi$
$677$	13.5371	0.520273	0.260137	+	0.965572i	$0.416232\pi$
$678$	−21.0727	−0.809293
$679$	41.8429	1.60578
$680$	−6.95580	−0.266743
$681$	20.7841	0.796448
$682$	−2.43336	−0.0931782
$683$	−30.5448	−1.16877	−0.584383	−	0.811478i	$-0.698663\pi$
$683$	−30.5448	−1.16877	−0.584383	+	0.811478i	$0.698663\pi$
$684$	−17.3314	−0.662684
$685$	1.44077	0.0550489
$686$	−18.1557	−0.693186
$687$	−46.3163	−1.76708
$688$	4.00307	0.152616
$689$	16.8862	0.643313
$690$	3.68644	0.140341
$691$	28.6593	1.09025	0.545126	−	0.838354i	$-0.316482\pi$
$691$	28.6593	1.09025	0.545126	+	0.838354i	$0.316482\pi$
$692$	19.4990	0.741239
$693$	5.44084	0.206681
$694$	27.3040	1.03645
$695$	16.3881	0.621637
$696$	−23.6835	−0.897723
$697$	44.1442	1.67208
$698$	26.8022	1.01448
$699$	30.9236	1.16964
$700$	2.69506	0.101864
$701$	17.2750	0.652468	0.326234	−	0.945289i	$-0.394220\pi$
$701$	17.2750	0.652468	0.326234	+	0.945289i	$0.394220\pi$
$702$	6.34904	0.239629
$703$	44.6477	1.68392
$704$	0.593915	0.0223840
$705$	3.85080	0.145029
$706$	4.92354	0.185300
$707$	−26.9543	−1.01372
$708$	27.0108	1.01513
$709$	32.3820	1.21613	0.608066	−	0.793887i	$-0.291946\pi$
$709$	32.3820	1.21613	0.608066	+	0.793887i	$0.291946\pi$
$710$	−8.78008	−0.329510
$711$	45.7474	1.71566
$712$	−0.515316	−0.0193123
$713$	−5.97074	−0.223606
$714$	−47.4218	−1.77472
$715$	3.73431	0.139655
$716$	4.75816	0.177821
$717$	6.58023	0.245743
$718$	23.7453	0.886166
$719$	−49.5574	−1.84818	−0.924089	−	0.382176i	$-0.875175\pi$
$719$	−49.5574	−1.84818	−0.924089	+	0.382176i	$0.875175\pi$
$720$	−3.39917	−0.126680
$721$	−7.67331	−0.285769
$722$	6.99701	0.260402
$723$	1.56661	0.0582628
$724$	21.0239	0.781348
$725$	9.36235	0.347709
$726$	26.9339	0.999612
$727$	−30.0362	−1.11398	−0.556990	−	0.830519i	$-0.688044\pi$
$727$	−30.0362	−1.11398	−0.556990	+	0.830519i	$0.688044\pi$
$728$	−16.9455	−0.628043
$729$	−33.6435	−1.24605
$730$	−5.86791	−0.217181
$731$	27.8446	1.02987
$732$	20.7286	0.766150
$733$	−22.3358	−0.824993	−0.412496	−	0.910959i	$-0.635343\pi$
$733$	−22.3358	−0.824993	−0.412496	+	0.910959i	$0.635343\pi$
$734$	−6.48800	−0.239476
$735$	0.666210	0.0245735
$736$	1.45729	0.0537164
$737$	2.08425	0.0767742
$738$	21.5725	0.794094
$739$	−25.3793	−0.933594	−0.466797	−	0.884365i	$-0.654592\pi$
$739$	−25.3793	−0.933594	−0.466797	+	0.884365i	$0.654592\pi$
$740$	8.75664	0.321900
$741$	−81.0980	−2.97921
$742$	−7.23793	−0.265713
$743$	15.8810	0.582619	0.291309	−	0.956629i	$-0.405909\pi$
$743$	15.8810	0.582619	0.291309	+	0.956629i	$0.405909\pi$
$744$	10.3644	0.379977
$745$	−11.7788	−0.431541
$746$	−2.61844	−0.0958678
$747$	17.0541	0.623977
$748$	4.13116	0.151050
$749$	8.10660	0.296209
$750$	2.52966	0.0923701
$751$	−31.3595	−1.14433	−0.572163	−	0.820140i	$-0.693895\pi$
$751$	−31.3595	−1.14433	−0.572163	+	0.820140i	$0.693895\pi$
$752$	1.52226	0.0555111
$753$	15.8830	0.578810
$754$	−58.8669	−2.14381
$755$	1.12117	0.0408037
$756$	−2.72139	−0.0989760
$757$	22.7332	0.826253	0.413127	−	0.910674i	$-0.364437\pi$
$757$	22.7332	0.826253	0.413127	+	0.910674i	$0.364437\pi$
$758$	−17.4432	−0.633566
$759$	−2.18943	−0.0794714
$760$	5.09873	0.184950
$761$	38.4057	1.39220	0.696102	−	0.717943i	$-0.254916\pi$
$761$	38.4057	1.39220	0.696102	+	0.717943i	$0.254916\pi$
$762$	13.8888	0.503137
$763$	43.4513	1.57304
$764$	−11.7213	−0.424061
$765$	−23.6440	−0.854850
$766$	17.7731	0.642167
$767$	67.1370	2.42418
$768$	−2.52966	−0.0912812
$769$	−49.9226	−1.80026	−0.900128	−	0.435626i	$-0.856527\pi$
$769$	−49.9226	−1.80026	−0.900128	+	0.435626i	$0.856527\pi$
$770$	−1.60064	−0.0576830
$771$	−48.5521	−1.74856
$772$	15.3455	0.552298
$773$	36.7863	1.32311	0.661555	−	0.749897i	$-0.269897\pi$
$773$	36.7863	1.32311	0.661555	+	0.749897i	$0.269897\pi$
$774$	13.6071	0.489098
$775$	−4.09715	−0.147174
$776$	15.5258	0.557342
$777$	59.6991	2.14169
$778$	−20.6606	−0.740717
$779$	−32.3585	−1.15936
$780$	−15.9055	−0.569510
$781$	5.21462	0.186594
$782$	10.1366	0.362485
$783$	−9.45381	−0.337851
$784$	0.263360	0.00940571
$785$	−4.73827	−0.169116
$786$	−46.2714	−1.65045
$787$	27.1062	0.966230	0.483115	−	0.875557i	$-0.339505\pi$
$787$	27.1062	0.966230	0.483115	+	0.875557i	$0.339505\pi$
$788$	3.14693	0.112105
$789$	−39.7951	−1.41674
$790$	−13.4584	−0.478828
$791$	22.4506	0.798250
$792$	2.01882	0.0717356
$793$	51.5222	1.82961
$794$	−14.7486	−0.523409
$795$	−6.79372	−0.240948
$796$	0.439268	0.0155694
$797$	8.23178	0.291585	0.145792	−	0.989315i	$-0.453427\pi$
$797$	8.23178	0.291585	0.145792	+	0.989315i	$0.453427\pi$
$798$	34.7610	1.23053
$799$	10.5885	0.374595
$800$	1.00000	0.0353553
$801$	−1.75165	−0.0618914
$802$	−1.00000	−0.0353112
$803$	3.48504	0.122984
$804$	−8.87741	−0.313082
$805$	−3.92749	−0.138426
$806$	25.7614	0.907405
$807$	−56.3666	−1.98420
$808$	−10.0014	−0.351847
$809$	−49.7857	−1.75037	−0.875187	−	0.483785i	$-0.839262\pi$
$809$	−49.7857	−1.75037	−0.875187	+	0.483785i	$0.839262\pi$
$810$	7.64315	0.268553
$811$	−43.4387	−1.52534	−0.762669	−	0.646789i	$-0.776112\pi$
$811$	−43.4387	−1.52534	−0.762669	+	0.646789i	$0.776112\pi$
$812$	25.2321	0.885474
$813$	74.2971	2.60571
$814$	−5.20070	−0.182284
$815$	−11.0048	−0.385481
$816$	−17.5958	−0.615976
$817$	−20.4106	−0.714076
$818$	−35.4849	−1.24070
$819$	−57.6008	−2.01273
$820$	−6.34639	−0.221626
$821$	21.3550	0.745296	0.372648	−	0.927973i	$-0.378450\pi$
$821$	21.3550	0.745296	0.372648	+	0.927973i	$0.378450\pi$
$822$	3.64465	0.127122
$823$	2.82040	0.0983129	0.0491564	−	0.998791i	$-0.484347\pi$
$823$	2.82040	0.0983129	0.0491564	+	0.998791i	$0.484347\pi$
$824$	−2.84718	−0.0991861
$825$	−1.50240	−0.0523069
$826$	−28.7769	−1.00128
$827$	−14.3111	−0.497646	−0.248823	−	0.968549i	$-0.580044\pi$
$827$	−14.3111	−0.497646	−0.248823	+	0.968549i	$0.580044\pi$
$828$	4.95358	0.172149
$829$	10.7430	0.373118	0.186559	−	0.982444i	$-0.440266\pi$
$829$	10.7430	0.373118	0.186559	+	0.982444i	$0.440266\pi$
$830$	−5.01714	−0.174147
$831$	−65.8723	−2.28508
$832$	−6.28762	−0.217984
$833$	1.83188	0.0634708
$834$	41.4564	1.43552
$835$	−14.1301	−0.488993
$836$	−3.02821	−0.104733
$837$	4.13718	0.143002
$838$	−16.4639	−0.568734
$839$	23.1978	0.800876	0.400438	−	0.916324i	$-0.368858\pi$
$839$	23.1978	0.800876	0.400438	+	0.916324i	$0.368858\pi$
$840$	6.81759	0.235229
$841$	58.6536	2.02254
$842$	24.8756	0.857270
$843$	15.8012	0.544221
$844$	0.275574	0.00948564
$845$	−26.5342	−0.912805
$846$	5.17442	0.177900
$847$	−28.6950	−0.985973
$848$	−2.68563	−0.0922248
$849$	0.258238	0.00886270
$850$	6.95580	0.238582
$851$	−12.7610	−0.437440
$852$	−22.2106	−0.760923
$853$	−14.5802	−0.499215	−0.249608	−	0.968347i	$-0.580302\pi$
$853$	−14.5802	−0.499215	−0.249608	+	0.968347i	$0.580302\pi$
$854$	−22.0839	−0.755696
$855$	17.3314	0.592723
$856$	3.00795	0.102809
$857$	−2.64486	−0.0903468	−0.0451734	−	0.998979i	$-0.514384\pi$
$857$	−2.64486	−0.0903468	−0.0451734	+	0.998979i	$0.514384\pi$
$858$	9.44654	0.322500
$859$	−37.2076	−1.26951	−0.634753	−	0.772715i	$-0.718898\pi$
$859$	−37.2076	−1.26951	−0.634753	+	0.772715i	$0.718898\pi$
$860$	−4.00307	−0.136504
$861$	−43.2671	−1.47454
$862$	−19.3811	−0.660123
$863$	−25.1512	−0.856158	−0.428079	−	0.903741i	$-0.640810\pi$
$863$	−25.1512	−0.856158	−0.428079	+	0.903741i	$0.640810\pi$
$864$	−1.00977	−0.0343530
$865$	−19.4990	−0.662985
$866$	18.9177	0.642849
$867$	−79.3888	−2.69618
$868$	−11.0421	−0.374793
$869$	7.99314	0.271149
$870$	23.6835	0.802947
$871$	−22.0654	−0.747656
$872$	16.1226	0.545979
$873$	52.7747	1.78615
$874$	−7.43032	−0.251334
$875$	−2.69506	−0.0911097
$876$	−14.8438	−0.501525
$877$	−15.4033	−0.520132	−0.260066	−	0.965591i	$-0.583744\pi$
$877$	−15.4033	−0.520132	−0.260066	+	0.965591i	$0.583744\pi$
$878$	−7.44743	−0.251339
$879$	−15.9320	−0.537375
$880$	−0.593915	−0.0200209
$881$	−12.9067	−0.434838	−0.217419	−	0.976078i	$-0.569764\pi$
$881$	−12.9067	−0.434838	−0.217419	+	0.976078i	$0.569764\pi$
$882$	0.895205	0.0301431
$883$	12.2835	0.413374	0.206687	−	0.978407i	$-0.433732\pi$
$883$	12.2835	0.413374	0.206687	+	0.978407i	$0.433732\pi$
$884$	−43.7355	−1.47098
$885$	−27.0108	−0.907958
$886$	−8.27884	−0.278133
$887$	34.1629	1.14708	0.573538	−	0.819179i	$-0.305570\pi$
$887$	34.1629	1.14708	0.573538	+	0.819179i	$0.305570\pi$
$888$	22.1513	0.743349
$889$	−14.7969	−0.496272
$890$	0.515316	0.0172734
$891$	−4.53938	−0.152075
$892$	12.4245	0.416004
$893$	−7.76158	−0.259731
$894$	−29.7963	−0.996536
$895$	−4.75816	−0.159048
$896$	2.69506	0.0900357
$897$	23.1790	0.773923
$898$	−38.2882	−1.27770
$899$	−38.3590	−1.27934
$900$	3.39917	0.113306
$901$	−18.6807	−0.622344
$902$	3.76922	0.125501
$903$	−27.2913	−0.908198
$904$	8.33026	0.277060
$905$	−21.0239	−0.698859
$906$	2.83619	0.0942260
$907$	46.6083	1.54760	0.773802	−	0.633427i	$-0.218352\pi$
$907$	46.6083	1.54760	0.773802	+	0.633427i	$0.218352\pi$
$908$	−8.21616	−0.272663
$909$	−33.9964	−1.12759
$910$	16.9455	0.561739
$911$	−21.2634	−0.704489	−0.352244	−	0.935908i	$-0.614581\pi$
$911$	−21.2634	−0.704489	−0.352244	+	0.935908i	$0.614581\pi$
$912$	12.8980	0.427097
$913$	2.97975	0.0986155
$914$	−31.8051	−1.05202
$915$	−20.7286	−0.685266
$916$	18.3093	0.604956
$917$	49.2969	1.62793
$918$	−7.02375	−0.231818
$919$	44.8065	1.47803	0.739015	−	0.673689i	$-0.235291\pi$
$919$	44.8065	1.47803	0.739015	+	0.673689i	$0.235291\pi$
$920$	−1.45729	−0.0480454
$921$	−13.3286	−0.439193
$922$	−27.2217	−0.896499
$923$	−55.2058	−1.81712
$924$	−4.04907	−0.133205
$925$	−8.75664	−0.287916
$926$	1.09144	0.0358668
$927$	−9.67804	−0.317868
$928$	9.36235	0.307334
$929$	21.5954	0.708521	0.354260	−	0.935147i	$-0.384733\pi$
$929$	21.5954	0.708521	0.354260	+	0.935147i	$0.384733\pi$
$930$	−10.3644	−0.339862
$931$	−1.34280	−0.0440085
$932$	−12.2244	−0.400424
$933$	51.4052	1.68293
$934$	−28.8369	−0.943573
$935$	−4.13116	−0.135103
$936$	−21.3727	−0.698589
$937$	40.5805	1.32571	0.662853	−	0.748750i	$-0.269346\pi$
$937$	40.5805	1.32571	0.662853	+	0.748750i	$0.269346\pi$
$938$	9.45787	0.308810
$939$	61.1937	1.99698
$940$	−1.52226	−0.0496506
$941$	40.2207	1.31116	0.655578	−	0.755128i	$-0.272425\pi$
$941$	40.2207	1.31116	0.655578	+	0.755128i	$0.272425\pi$
$942$	−11.9862	−0.390531
$943$	9.24853	0.301173
$944$	−10.6776	−0.347528
$945$	2.72139	0.0885268
$946$	2.37749	0.0772987
$947$	−28.9824	−0.941802	−0.470901	−	0.882186i	$-0.656071\pi$
$947$	−28.9824	−0.941802	−0.470901	+	0.882186i	$0.656071\pi$
$948$	−34.0451	−1.10573
$949$	−36.8952	−1.19767
$950$	−5.09873	−0.165425
$951$	−55.1958	−1.78985
$952$	18.7463	0.607572
$953$	8.92239	0.289025	0.144512	−	0.989503i	$-0.453839\pi$
$953$	8.92239	0.289025	0.144512	+	0.989503i	$0.453839\pi$
$954$	−9.12890	−0.295559
$955$	11.7213	0.379292
$956$	−2.60123	−0.0841299
$957$	−14.0660	−0.454690
$958$	7.89329	0.255020
$959$	−3.88296	−0.125387
$960$	2.52966	0.0816444
$961$	−14.2133	−0.458494
$962$	55.0584	1.77516
$963$	10.2245	0.329481
$964$	−0.619296	−0.0199462
$965$	−15.3455	−0.493991
$966$	−9.93520	−0.319660
$967$	34.2616	1.10178	0.550890	−	0.834578i	$-0.314289\pi$
$967$	34.2616	1.10178	0.550890	+	0.834578i	$0.314289\pi$
$968$	−10.6473	−0.342216
$969$	89.7162	2.88210
$970$	−15.5258	−0.498502
$971$	−19.1516	−0.614604	−0.307302	−	0.951612i	$-0.599426\pi$
$971$	−19.1516	−0.614604	−0.307302	+	0.951612i	$0.599426\pi$
$972$	22.3639	0.717321
$973$	−44.1670	−1.41593
$974$	−5.74798	−0.184177
$975$	15.9055	0.509385
$976$	−8.19422	−0.262291
$977$	−8.56851	−0.274131	−0.137065	−	0.990562i	$-0.543767\pi$
$977$	−8.56851	−0.274131	−0.137065	+	0.990562i	$0.543767\pi$
$978$	−27.8384	−0.890173
$979$	−0.306054	−0.00978152
$980$	−0.263360	−0.00841272
$981$	54.8033	1.74974
$982$	−15.8547	−0.505944
$983$	−46.3236	−1.47749	−0.738747	−	0.673982i	$-0.764582\pi$
$983$	−46.3236	−1.47749	−0.738747	+	0.673982i	$0.764582\pi$
$984$	−16.0542	−0.511789
$985$	−3.14693	−0.100269
$986$	65.1227	2.07393
$987$	−10.3781	−0.330340
$988$	32.0589	1.01993
$989$	5.83364	0.185499
$990$	−2.01882	−0.0641623
$991$	26.3590	0.837321	0.418660	−	0.908143i	$-0.362500\pi$
$991$	26.3590	0.837321	0.418660	+	0.908143i	$0.362500\pi$
$992$	−4.09715	−0.130085
$993$	−17.1743	−0.545010
$994$	23.6629	0.750540
$995$	−0.439268	−0.0139257
$996$	−12.6916	−0.402150
$997$	27.7994	0.880416	0.440208	−	0.897896i	$-0.354905\pi$
$997$	27.7994	0.880416	0.440208	+	0.897896i	$0.354905\pi$
$998$	−23.2985	−0.737503
$999$	8.84218	0.279754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.4	✓	22	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52966 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.52966 q^{6} +2.69506 q^{7} +1.00000 q^{8} +3.39917 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52966 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.52966 q^{6} +2.69506 q^{7} +1.00000 q^{8} +3.39917 q^{9} -1.00000 q^{10} +0.593915 q^{11} -2.52966 q^{12} -6.28762 q^{13} +2.69506 q^{14} +2.52966 q^{15} +1.00000 q^{16} +6.95580 q^{17} +3.39917 q^{18} -5.09873 q^{19} -1.00000 q^{20} -6.81759 q^{21} +0.593915 q^{22} +1.45729 q^{23} -2.52966 q^{24} +1.00000 q^{25} -6.28762 q^{26} -1.00977 q^{27} +2.69506 q^{28} +9.36235 q^{29} +2.52966 q^{30} -4.09715 q^{31} +1.00000 q^{32} -1.50240 q^{33} +6.95580 q^{34} -2.69506 q^{35} +3.39917 q^{36} -8.75664 q^{37} -5.09873 q^{38} +15.9055 q^{39} -1.00000 q^{40} +6.34639 q^{41} -6.81759 q^{42} +4.00307 q^{43} +0.593915 q^{44} -3.39917 q^{45} +1.45729 q^{46} +1.52226 q^{47} -2.52966 q^{48} +0.263360 q^{49} +1.00000 q^{50} -17.5958 q^{51} -6.28762 q^{52} -2.68563 q^{53} -1.00977 q^{54} -0.593915 q^{55} +2.69506 q^{56} +12.8980 q^{57} +9.36235 q^{58} -10.6776 q^{59} +2.52966 q^{60} -8.19422 q^{61} -4.09715 q^{62} +9.16098 q^{63} +1.00000 q^{64} +6.28762 q^{65} -1.50240 q^{66} +3.50933 q^{67} +6.95580 q^{68} -3.68644 q^{69} -2.69506 q^{70} +8.78008 q^{71} +3.39917 q^{72} +5.86791 q^{73} -8.75664 q^{74} -2.52966 q^{75} -5.09873 q^{76} +1.60064 q^{77} +15.9055 q^{78} +13.4584 q^{79} -1.00000 q^{80} -7.64315 q^{81} +6.34639 q^{82} +5.01714 q^{83} -6.81759 q^{84} -6.95580 q^{85} +4.00307 q^{86} -23.6835 q^{87} +0.593915 q^{88} -0.515316 q^{89} -3.39917 q^{90} -16.9455 q^{91} +1.45729 q^{92} +10.3644 q^{93} +1.52226 q^{94} +5.09873 q^{95} -2.52966 q^{96} +15.5258 q^{97} +0.263360 q^{98} +2.01882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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