LMFDB - Embedded newform 4010.2.a.l.1.10

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			1.10
Root			$0.278065$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.278065 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.278065 q^{6} +4.59715 q^{7} -1.00000 q^{8} -2.92268 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.278065 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.278065 q^{6} +4.59715 q^{7} -1.00000 q^{8} -2.92268 q^{9} +1.00000 q^{10} +0.566591 q^{11} +0.278065 q^{12} +1.45977 q^{13} -4.59715 q^{14} -0.278065 q^{15} +1.00000 q^{16} -0.0142483 q^{17} +2.92268 q^{18} +7.85152 q^{19} -1.00000 q^{20} +1.27831 q^{21} -0.566591 q^{22} +2.81249 q^{23} -0.278065 q^{24} +1.00000 q^{25} -1.45977 q^{26} -1.64689 q^{27} +4.59715 q^{28} -3.55383 q^{29} +0.278065 q^{30} +4.06624 q^{31} -1.00000 q^{32} +0.157549 q^{33} +0.0142483 q^{34} -4.59715 q^{35} -2.92268 q^{36} -0.140122 q^{37} -7.85152 q^{38} +0.405911 q^{39} +1.00000 q^{40} +1.53171 q^{41} -1.27831 q^{42} -1.47795 q^{43} +0.566591 q^{44} +2.92268 q^{45} -2.81249 q^{46} -8.80015 q^{47} +0.278065 q^{48} +14.1338 q^{49} -1.00000 q^{50} -0.00396195 q^{51} +1.45977 q^{52} -0.608900 q^{53} +1.64689 q^{54} -0.566591 q^{55} -4.59715 q^{56} +2.18324 q^{57} +3.55383 q^{58} -14.8356 q^{59} -0.278065 q^{60} +8.63024 q^{61} -4.06624 q^{62} -13.4360 q^{63} +1.00000 q^{64} -1.45977 q^{65} -0.157549 q^{66} +12.2504 q^{67} -0.0142483 q^{68} +0.782055 q^{69} +4.59715 q^{70} +10.1024 q^{71} +2.92268 q^{72} -7.41356 q^{73} +0.140122 q^{74} +0.278065 q^{75} +7.85152 q^{76} +2.60470 q^{77} -0.405911 q^{78} -11.7539 q^{79} -1.00000 q^{80} +8.31009 q^{81} -1.53171 q^{82} +8.77249 q^{83} +1.27831 q^{84} +0.0142483 q^{85} +1.47795 q^{86} -0.988198 q^{87} -0.566591 q^{88} +16.5693 q^{89} -2.92268 q^{90} +6.71077 q^{91} +2.81249 q^{92} +1.13068 q^{93} +8.80015 q^{94} -7.85152 q^{95} -0.278065 q^{96} -0.629215 q^{97} -14.1338 q^{98} -1.65596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.278065	0.160541	0.0802706	−	0.996773i	$-0.474422\pi$
$3$	0.278065	0.160541	0.0802706	+	0.996773i	$0.474422\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.278065	−0.113520
$7$	4.59715	1.73756	0.868779	−	0.495200i	$-0.164905\pi$
$7$	4.59715	1.73756	0.868779	+	0.495200i	$0.164905\pi$
$8$	−1.00000	−0.353553
$9$	−2.92268	−0.974227
$10$	1.00000	0.316228
$11$	0.566591	0.170834	0.0854168	−	0.996345i	$-0.472778\pi$
$11$	0.566591	0.170834	0.0854168	+	0.996345i	$0.472778\pi$
$12$	0.278065	0.0802706
$13$	1.45977	0.404867	0.202434	−	0.979296i	$-0.435115\pi$
$13$	1.45977	0.404867	0.202434	+	0.979296i	$0.435115\pi$
$14$	−4.59715	−1.22864
$15$	−0.278065	−0.0717962
$16$	1.00000	0.250000
$17$	−0.0142483	−0.00345571	−0.00172786	−	0.999999i	$-0.500550\pi$
$17$	−0.0142483	−0.00345571	−0.00172786	+	0.999999i	$0.500550\pi$
$18$	2.92268	0.688882
$19$	7.85152	1.80126	0.900631	−	0.434584i	$-0.143105\pi$
$19$	7.85152	1.80126	0.900631	+	0.434584i	$0.143105\pi$
$20$	−1.00000	−0.223607
$21$	1.27831	0.278950
$22$	−0.566591	−0.120798
$23$	2.81249	0.586444	0.293222	−	0.956044i	$-0.405273\pi$
$23$	2.81249	0.586444	0.293222	+	0.956044i	$0.405273\pi$
$24$	−0.278065	−0.0567599
$25$	1.00000	0.200000
$26$	−1.45977	−0.286284
$27$	−1.64689	−0.316945
$28$	4.59715	0.868779
$29$	−3.55383	−0.659930	−0.329965	−	0.943993i	$-0.607037\pi$
$29$	−3.55383	−0.659930	−0.329965	+	0.943993i	$0.607037\pi$
$30$	0.278065	0.0507676
$31$	4.06624	0.730319	0.365159	−	0.930945i	$-0.381014\pi$
$31$	4.06624	0.730319	0.365159	+	0.930945i	$0.381014\pi$
$32$	−1.00000	−0.176777
$33$	0.157549	0.0274258
$34$	0.0142483	0.00244356
$35$	−4.59715	−0.777060
$36$	−2.92268	−0.487113
$37$	−0.140122	−0.0230359	−0.0115179	−	0.999934i	$-0.503666\pi$
$37$	−0.140122	−0.0230359	−0.0115179	+	0.999934i	$0.503666\pi$
$38$	−7.85152	−1.27369
$39$	0.405911	0.0649978
$40$	1.00000	0.158114
$41$	1.53171	0.239213	0.119607	−	0.992821i	$-0.461837\pi$
$41$	1.53171	0.239213	0.119607	+	0.992821i	$0.461837\pi$
$42$	−1.27831	−0.197247
$43$	−1.47795	−0.225385	−0.112693	−	0.993630i	$-0.535948\pi$
$43$	−1.47795	−0.225385	−0.112693	+	0.993630i	$0.535948\pi$
$44$	0.566591	0.0854168
$45$	2.92268	0.435687
$46$	−2.81249	−0.414678
$47$	−8.80015	−1.28363	−0.641817	−	0.766858i	$-0.721819\pi$
$47$	−8.80015	−1.28363	−0.641817	+	0.766858i	$0.721819\pi$
$48$	0.278065	0.0401353
$49$	14.1338	2.01911
$50$	−1.00000	−0.141421
$51$	−0.00396195	−0.000554784 0
$52$	1.45977	0.202434
$53$	−0.608900	−0.0836388	−0.0418194	−	0.999125i	$-0.513315\pi$
$53$	−0.608900	−0.0836388	−0.0418194	+	0.999125i	$0.513315\pi$
$54$	1.64689	0.224114
$55$	−0.566591	−0.0763991
$56$	−4.59715	−0.614320
$57$	2.18324	0.289177
$58$	3.55383	0.466641
$59$	−14.8356	−1.93143	−0.965714	−	0.259610i	$-0.916406\pi$
$59$	−14.8356	−1.93143	−0.965714	+	0.259610i	$0.916406\pi$
$60$	−0.278065	−0.0358981
$61$	8.63024	1.10499	0.552495	−	0.833516i	$-0.313676\pi$
$61$	8.63024	1.10499	0.552495	+	0.833516i	$0.313676\pi$
$62$	−4.06624	−0.516413
$63$	−13.4360	−1.69278
$64$	1.00000	0.125000
$65$	−1.45977	−0.181062
$66$	−0.157549	−0.0193930
$67$	12.2504	1.49662	0.748312	−	0.663347i	$-0.230865\pi$
$67$	12.2504	1.49662	0.748312	+	0.663347i	$0.230865\pi$
$68$	−0.0142483	−0.00172786
$69$	0.782055	0.0941484
$70$	4.59715	0.549464
$71$	10.1024	1.19894	0.599469	−	0.800398i	$-0.295378\pi$
$71$	10.1024	1.19894	0.599469	+	0.800398i	$0.295378\pi$
$72$	2.92268	0.344441
$73$	−7.41356	−0.867691	−0.433846	−	0.900987i	$-0.642844\pi$
$73$	−7.41356	−0.867691	−0.433846	+	0.900987i	$0.642844\pi$
$74$	0.140122	0.0162888
$75$	0.278065	0.0321082
$76$	7.85152	0.900631
$77$	2.60470	0.296833
$78$	−0.405911	−0.0459604
$79$	−11.7539	−1.32242	−0.661209	−	0.750202i	$-0.729956\pi$
$79$	−11.7539	−1.32242	−0.661209	+	0.750202i	$0.729956\pi$
$80$	−1.00000	−0.111803
$81$	8.31009	0.923344
$82$	−1.53171	−0.169149
$83$	8.77249	0.962906	0.481453	−	0.876472i	$-0.340109\pi$
$83$	8.77249	0.962906	0.481453	+	0.876472i	$0.340109\pi$
$84$	1.27831	0.139475
$85$	0.0142483	0.00154544
$86$	1.47795	0.159371
$87$	−0.988198	−0.105946
$88$	−0.566591	−0.0603988
$89$	16.5693	1.75634	0.878172	−	0.478345i	$-0.158763\pi$
$89$	16.5693	1.75634	0.878172	+	0.478345i	$0.158763\pi$
$90$	−2.92268	−0.308077
$91$	6.71077	0.703480
$92$	2.81249	0.293222
$93$	1.13068	0.117246
$94$	8.80015	0.907667
$95$	−7.85152	−0.805549
$96$	−0.278065	−0.0283799
$97$	−0.629215	−0.0638872	−0.0319436	−	0.999490i	$-0.510170\pi$
$97$	−0.629215	−0.0638872	−0.0319436	+	0.999490i	$0.510170\pi$
$98$	−14.1338	−1.42773
$99$	−1.65596	−0.166431
$100$	1.00000	0.100000
$101$	2.63191	0.261885	0.130942	−	0.991390i	$-0.458200\pi$
$101$	2.63191	0.261885	0.130942	+	0.991390i	$0.458200\pi$
$102$	0.00396195	0.000392292 0
$103$	3.03981	0.299521	0.149761	−	0.988722i	$-0.452150\pi$
$103$	3.03981	0.299521	0.149761	+	0.988722i	$0.452150\pi$
$104$	−1.45977	−0.143142
$105$	−1.27831	−0.124750
$106$	0.608900	0.0591416
$107$	−7.01281	−0.677954	−0.338977	−	0.940795i	$-0.610081\pi$
$107$	−7.01281	−0.677954	−0.338977	+	0.940795i	$0.610081\pi$
$108$	−1.64689	−0.158472
$109$	2.21467	0.212127	0.106064	−	0.994359i	$-0.466175\pi$
$109$	2.21467	0.212127	0.106064	+	0.994359i	$0.466175\pi$
$110$	0.566591	0.0540223
$111$	−0.0389630	−0.00369821
$112$	4.59715	0.434390
$113$	16.0274	1.50774	0.753868	−	0.657026i	$-0.228186\pi$
$113$	16.0274	1.50774	0.753868	+	0.657026i	$0.228186\pi$
$114$	−2.18324	−0.204479
$115$	−2.81249	−0.262266
$116$	−3.55383	−0.329965
$117$	−4.26644	−0.394432
$118$	14.8356	1.36573
$119$	−0.0655014	−0.00600451
$120$	0.278065	0.0253838
$121$	−10.6790	−0.970816
$122$	−8.63024	−0.781346
$123$	0.425916	0.0384036
$124$	4.06624	0.365159
$125$	−1.00000	−0.0894427
$126$	13.4360	1.19697
$127$	−16.1425	−1.43241	−0.716206	−	0.697889i	$-0.754123\pi$
$127$	−16.1425	−1.43241	−0.716206	+	0.697889i	$0.754123\pi$
$128$	−1.00000	−0.0883883
$129$	−0.410967	−0.0361836
$130$	1.45977	0.128030
$131$	−15.5816	−1.36137	−0.680684	−	0.732577i	$-0.738317\pi$
$131$	−15.5816	−1.36137	−0.680684	+	0.732577i	$0.738317\pi$
$132$	0.157549	0.0137129
$133$	36.0946	3.12980
$134$	−12.2504	−1.05827
$135$	1.64689	0.141742
$136$	0.0142483	0.00122178
$137$	8.47503	0.724071	0.362036	−	0.932164i	$-0.382082\pi$
$137$	8.47503	0.724071	0.362036	+	0.932164i	$0.382082\pi$
$138$	−0.782055	−0.0665729
$139$	15.3218	1.29958	0.649788	−	0.760116i	$-0.274858\pi$
$139$	15.3218	1.29958	0.649788	+	0.760116i	$0.274858\pi$
$140$	−4.59715	−0.388530
$141$	−2.44702	−0.206076
$142$	−10.1024	−0.847778
$143$	0.827092	0.0691649
$144$	−2.92268	−0.243557
$145$	3.55383	0.295130
$146$	7.41356	0.613550
$147$	3.93011	0.324150
$148$	−0.140122	−0.0115179
$149$	−8.57222	−0.702264	−0.351132	−	0.936326i	$-0.614203\pi$
$149$	−8.57222	−0.702264	−0.351132	+	0.936326i	$0.614203\pi$
$150$	−0.278065	−0.0227039
$151$	2.17999	0.177405	0.0887025	−	0.996058i	$-0.471728\pi$
$151$	2.17999	0.177405	0.0887025	+	0.996058i	$0.471728\pi$
$152$	−7.85152	−0.636843
$153$	0.0416431	0.00336665
$154$	−2.60470	−0.209893
$155$	−4.06624	−0.326608
$156$	0.405911	0.0324989
$157$	−2.40182	−0.191686	−0.0958431	−	0.995396i	$-0.530555\pi$
$157$	−2.40182	−0.191686	−0.0958431	+	0.995396i	$0.530555\pi$
$158$	11.7539	0.935090
$159$	−0.169314	−0.0134275
$160$	1.00000	0.0790569
$161$	12.9294	1.01898
$162$	−8.31009	−0.652903
$163$	9.67817	0.758053	0.379026	−	0.925386i	$-0.376259\pi$
$163$	9.67817	0.758053	0.379026	+	0.925386i	$0.376259\pi$
$164$	1.53171	0.119607
$165$	−0.157549	−0.0122652
$166$	−8.77249	−0.680877
$167$	−7.82472	−0.605495	−0.302748	−	0.953071i	$-0.597904\pi$
$167$	−7.82472	−0.605495	−0.302748	+	0.953071i	$0.597904\pi$
$168$	−1.27831	−0.0986236
$169$	−10.8691	−0.836083
$170$	−0.0142483	−0.00109279
$171$	−22.9475	−1.75484
$172$	−1.47795	−0.112693
$173$	17.9889	1.36767	0.683837	−	0.729635i	$-0.260310\pi$
$173$	17.9889	1.36767	0.683837	+	0.729635i	$0.260310\pi$
$174$	0.988198	0.0749151
$175$	4.59715	0.347512
$176$	0.566591	0.0427084
$177$	−4.12526	−0.310074
$178$	−16.5693	−1.24192
$179$	−16.1910	−1.21017	−0.605087	−	0.796159i	$-0.706862\pi$
$179$	−16.1910	−1.21017	−0.605087	+	0.796159i	$0.706862\pi$
$180$	2.92268	0.217844
$181$	−12.0848	−0.898258	−0.449129	−	0.893467i	$-0.648266\pi$
$181$	−12.0848	−0.898258	−0.449129	+	0.893467i	$0.648266\pi$
$182$	−6.71077	−0.497436
$183$	2.39977	0.177396
$184$	−2.81249	−0.207339
$185$	0.140122	0.0103020
$186$	−1.13068	−0.0829056
$187$	−0.00807294	−0.000590352 0
$188$	−8.80015	−0.641817
$189$	−7.57101	−0.550710
$190$	7.85152	0.569609
$191$	10.8053	0.781844	0.390922	−	0.920424i	$-0.372156\pi$
$191$	10.8053	0.781844	0.390922	+	0.920424i	$0.372156\pi$
$192$	0.278065	0.0200676
$193$	−13.8645	−0.997988	−0.498994	−	0.866605i	$-0.666297\pi$
$193$	−13.8645	−0.997988	−0.498994	+	0.866605i	$0.666297\pi$
$194$	0.629215	0.0451750
$195$	−0.405911	−0.0290679
$196$	14.1338	1.00955
$197$	17.4084	1.24030	0.620148	−	0.784485i	$-0.287072\pi$
$197$	17.4084	1.24030	0.620148	+	0.784485i	$0.287072\pi$
$198$	1.65596	0.117684
$199$	19.5090	1.38296	0.691479	−	0.722396i	$-0.256959\pi$
$199$	19.5090	1.38296	0.691479	+	0.722396i	$0.256959\pi$
$200$	−1.00000	−0.0707107
$201$	3.40641	0.240270
$202$	−2.63191	−0.185181
$203$	−16.3375	−1.14667
$204$	−0.00396195	−0.000277392 0
$205$	−1.53171	−0.106979
$206$	−3.03981	−0.211794
$207$	−8.21999	−0.571329
$208$	1.45977	0.101217
$209$	4.44860	0.307716
$210$	1.27831	0.0882116
$211$	4.04104	0.278197	0.139098	−	0.990279i	$-0.455580\pi$
$211$	4.04104	0.278197	0.139098	+	0.990279i	$0.455580\pi$
$212$	−0.608900	−0.0418194
$213$	2.80914	0.192479
$214$	7.01281	0.479386
$215$	1.47795	0.100795
$216$	1.64689	0.112057
$217$	18.6931	1.26897
$218$	−2.21467	−0.149997
$219$	−2.06145	−0.139300
$220$	−0.566591	−0.0381996
$221$	−0.0207992	−0.00139911
$222$	0.0389630	0.00261503
$223$	−14.4091	−0.964908	−0.482454	−	0.875921i	$-0.660254\pi$
$223$	−14.4091	−0.964908	−0.482454	+	0.875921i	$0.660254\pi$
$224$	−4.59715	−0.307160
$225$	−2.92268	−0.194845
$226$	−16.0274	−1.06613
$227$	19.9234	1.32236	0.661180	−	0.750227i	$-0.270056\pi$
$227$	19.9234	1.32236	0.661180	+	0.750227i	$0.270056\pi$
$228$	2.18324	0.144588
$229$	7.79756	0.515277	0.257639	−	0.966241i	$-0.417056\pi$
$229$	7.79756	0.515277	0.257639	+	0.966241i	$0.417056\pi$
$230$	2.81249	0.185450
$231$	0.724278	0.0476540
$232$	3.55383	0.233321
$233$	2.69921	0.176831	0.0884156	−	0.996084i	$-0.471820\pi$
$233$	2.69921	0.176831	0.0884156	+	0.996084i	$0.471820\pi$
$234$	4.26644	0.278906
$235$	8.80015	0.574059
$236$	−14.8356	−0.965714
$237$	−3.26835	−0.212302
$238$	0.0655014	0.00424583
$239$	−14.1713	−0.916664	−0.458332	−	0.888781i	$-0.651553\pi$
$239$	−14.1713	−0.916664	−0.458332	+	0.888781i	$0.651553\pi$
$240$	−0.278065	−0.0179490
$241$	10.9813	0.707366	0.353683	−	0.935365i	$-0.384929\pi$
$241$	10.9813	0.707366	0.353683	+	0.935365i	$0.384929\pi$
$242$	10.6790	0.686470
$243$	7.25143	0.465179
$244$	8.63024	0.552495
$245$	−14.1338	−0.902973
$246$	−0.425916	−0.0271554
$247$	11.4614	0.729272
$248$	−4.06624	−0.258207
$249$	2.43933	0.154586
$250$	1.00000	0.0632456
$251$	18.3946	1.16106	0.580530	−	0.814239i	$-0.302846\pi$
$251$	18.3946	1.16106	0.580530	+	0.814239i	$0.302846\pi$
$252$	−13.4360	−0.846388
$253$	1.59353	0.100184
$254$	16.1425	1.01287
$255$	0.00396195	0.000248107 0
$256$	1.00000	0.0625000
$257$	4.93374	0.307758	0.153879	−	0.988090i	$-0.450823\pi$
$257$	4.93374	0.307758	0.153879	+	0.988090i	$0.450823\pi$
$258$	0.410967	0.0255857
$259$	−0.644161	−0.0400262
$260$	−1.45977	−0.0905311
$261$	10.3867	0.642921
$262$	15.5816	0.962632
$263$	31.1231	1.91913	0.959566	−	0.281485i	$-0.0908269\pi$
$263$	31.1231	1.91913	0.959566	+	0.281485i	$0.0908269\pi$
$264$	−0.157549	−0.00969649
$265$	0.608900	0.0374044
$266$	−36.0946	−2.21310
$267$	4.60735	0.281966
$268$	12.2504	0.748312
$269$	10.7710	0.656722	0.328361	−	0.944552i	$-0.393504\pi$
$269$	10.7710	0.656722	0.328361	+	0.944552i	$0.393504\pi$
$270$	−1.64689	−0.100227
$271$	−2.02243	−0.122854	−0.0614270	−	0.998112i	$-0.519565\pi$
$271$	−2.02243	−0.122854	−0.0614270	+	0.998112i	$0.519565\pi$
$272$	−0.0142483	−0.000863929 0
$273$	1.86603	0.112938
$274$	−8.47503	−0.511996
$275$	0.566591	0.0341667
$276$	0.782055	0.0470742
$277$	31.7151	1.90557	0.952787	−	0.303641i	$-0.0982023\pi$
$277$	31.7151	1.90557	0.952787	+	0.303641i	$0.0982023\pi$
$278$	−15.3218	−0.918939
$279$	−11.8843	−0.711496
$280$	4.59715	0.274732
$281$	2.63457	0.157166	0.0785828	−	0.996908i	$-0.474961\pi$
$281$	2.63457	0.157166	0.0785828	+	0.996908i	$0.474961\pi$
$282$	2.44702	0.145718
$283$	5.60684	0.333292	0.166646	−	0.986017i	$-0.446706\pi$
$283$	5.60684	0.333292	0.166646	+	0.986017i	$0.446706\pi$
$284$	10.1024	0.599469
$285$	−2.18324	−0.129324
$286$	−0.827092	−0.0489070
$287$	7.04151	0.415647
$288$	2.92268	0.172221
$289$	−16.9998	−0.999988
$290$	−3.55383	−0.208688
$291$	−0.174963	−0.0102565
$292$	−7.41356	−0.433846
$293$	10.0378	0.586415	0.293207	−	0.956049i	$-0.405277\pi$
$293$	10.0378	0.586415	0.293207	+	0.956049i	$0.405277\pi$
$294$	−3.93011	−0.229209
$295$	14.8356	0.863761
$296$	0.140122	0.00814442
$297$	−0.933114	−0.0541448
$298$	8.57222	0.496575
$299$	4.10558	0.237432
$300$	0.278065	0.0160541
$301$	−6.79435	−0.391620
$302$	−2.17999	−0.125444
$303$	0.731843	0.0420433
$304$	7.85152	0.450316
$305$	−8.63024	−0.494166
$306$	−0.0416431	−0.00238058
$307$	10.7817	0.615345	0.307673	−	0.951492i	$-0.400450\pi$
$307$	10.7817	0.615345	0.307673	+	0.951492i	$0.400450\pi$
$308$	2.60470	0.148417
$309$	0.845266	0.0480855
$310$	4.06624	0.230947
$311$	7.40839	0.420091	0.210046	−	0.977692i	$-0.432639\pi$
$311$	7.40839	0.420091	0.210046	+	0.977692i	$0.432639\pi$
$312$	−0.405911	−0.0229802
$313$	−24.3746	−1.37774	−0.688868	−	0.724887i	$-0.741892\pi$
$313$	−24.3746	−1.37774	−0.688868	+	0.724887i	$0.741892\pi$
$314$	2.40182	0.135543
$315$	13.4360	0.757032
$316$	−11.7539	−0.661209
$317$	6.72912	0.377945	0.188972	−	0.981982i	$-0.439484\pi$
$317$	6.72912	0.377945	0.188972	+	0.981982i	$0.439484\pi$
$318$	0.169314	0.00949465
$319$	−2.01357	−0.112738
$320$	−1.00000	−0.0559017
$321$	−1.95002	−0.108840
$322$	−12.9294	−0.720528
$323$	−0.111871	−0.00622465
$324$	8.31009	0.461672
$325$	1.45977	0.0809734
$326$	−9.67817	−0.536024
$327$	0.615824	0.0340552
$328$	−1.53171	−0.0845747
$329$	−40.4556	−2.23039
$330$	0.157549	0.00867281
$331$	−4.01232	−0.220537	−0.110269	−	0.993902i	$-0.535171\pi$
$331$	−4.01232	−0.220537	−0.110269	+	0.993902i	$0.535171\pi$
$332$	8.77249	0.481453
$333$	0.409531	0.0224422
$334$	7.82472	0.428150
$335$	−12.2504	−0.669310
$336$	1.27831	0.0697374
$337$	9.90612	0.539621	0.269810	−	0.962913i	$-0.413039\pi$
$337$	9.90612	0.539621	0.269810	+	0.962913i	$0.413039\pi$
$338$	10.8691	0.591200
$339$	4.45668	0.242054
$340$	0.0142483	0.000772721 0
$341$	2.30390	0.124763
$342$	22.9475	1.24086
$343$	32.7950	1.77076
$344$	1.47795	0.0796857
$345$	−0.782055	−0.0421044
$346$	−17.9889	−0.967091
$347$	4.78135	0.256676	0.128338	−	0.991730i	$-0.459036\pi$
$347$	4.78135	0.256676	0.128338	+	0.991730i	$0.459036\pi$
$348$	−0.988198	−0.0529730
$349$	−10.1955	−0.545753	−0.272877	−	0.962049i	$-0.587975\pi$
$349$	−10.1955	−0.545753	−0.272877	+	0.962049i	$0.587975\pi$
$350$	−4.59715	−0.245728
$351$	−2.40408	−0.128320
$352$	−0.566591	−0.0301994
$353$	−21.6800	−1.15391	−0.576954	−	0.816777i	$-0.695759\pi$
$353$	−21.6800	−1.15391	−0.576954	+	0.816777i	$0.695759\pi$
$354$	4.12526	0.219255
$355$	−10.1024	−0.536182
$356$	16.5693	0.878172
$357$	−0.0182137	−0.000963970 0
$358$	16.1910	0.855722
$359$	−4.47352	−0.236104	−0.118052	−	0.993007i	$-0.537665\pi$
$359$	−4.47352	−0.236104	−0.118052	+	0.993007i	$0.537665\pi$
$360$	−2.92268	−0.154039
$361$	42.6464	2.24455
$362$	12.0848	0.635165
$363$	−2.96945	−0.155856
$364$	6.71077	0.351740
$365$	7.41356	0.388043
$366$	−2.39977	−0.125438
$367$	−2.55763	−0.133507	−0.0667535	−	0.997769i	$-0.521264\pi$
$367$	−2.55763	−0.133507	−0.0667535	+	0.997769i	$0.521264\pi$
$368$	2.81249	0.146611
$369$	−4.47671	−0.233048
$370$	−0.140122	−0.00728459
$371$	−2.79920	−0.145327
$372$	1.13068	0.0586231
$373$	24.7683	1.28245	0.641226	−	0.767352i	$-0.278426\pi$
$373$	24.7683	1.28245	0.641226	+	0.767352i	$0.278426\pi$
$374$	0.00807294	0.000417442 0
$375$	−0.278065	−0.0143592
$376$	8.80015	0.453833
$377$	−5.18778	−0.267184
$378$	7.57101	0.389411
$379$	−21.6397	−1.11156	−0.555778	−	0.831331i	$-0.687580\pi$
$379$	−21.6397	−1.11156	−0.555778	+	0.831331i	$0.687580\pi$
$380$	−7.85152	−0.402775
$381$	−4.48866	−0.229961
$382$	−10.8053	−0.552847
$383$	19.0022	0.970968	0.485484	−	0.874246i	$-0.338643\pi$
$383$	19.0022	0.970968	0.485484	+	0.874246i	$0.338643\pi$
$384$	−0.278065	−0.0141900
$385$	−2.60470	−0.132748
$386$	13.8645	0.705684
$387$	4.31957	0.219576
$388$	−0.629215	−0.0319436
$389$	−30.9536	−1.56941	−0.784706	−	0.619868i	$-0.787186\pi$
$389$	−30.9536	−1.56941	−0.784706	+	0.619868i	$0.787186\pi$
$390$	0.405911	0.0205541
$391$	−0.0400731	−0.00202658
$392$	−14.1338	−0.713863
$393$	−4.33270	−0.218556
$394$	−17.4084	−0.877022
$395$	11.7539	0.591403
$396$	−1.65596	−0.0832153
$397$	26.5776	1.33389	0.666945	−	0.745107i	$-0.267602\pi$
$397$	26.5776	1.33389	0.666945	+	0.745107i	$0.267602\pi$
$398$	−19.5090	−0.977899
$399$	10.0367	0.502462
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−3.40641	−0.169896
$403$	5.93578	0.295682
$404$	2.63191	0.130942
$405$	−8.31009	−0.412932
$406$	16.3375	0.810816
$407$	−0.0793918	−0.00393530
$408$	0.00396195	0.000196146 0
$409$	21.9682	1.08626	0.543129	−	0.839649i	$-0.317239\pi$
$409$	21.9682	1.08626	0.543129	+	0.839649i	$0.317239\pi$
$410$	1.53171	0.0756459
$411$	2.35661	0.116243
$412$	3.03981	0.149761
$413$	−68.2013	−3.35597
$414$	8.21999	0.403991
$415$	−8.77249	−0.430625
$416$	−1.45977	−0.0715711
$417$	4.26046	0.208635
$418$	−4.44860	−0.217588
$419$	−30.5760	−1.49374	−0.746868	−	0.664972i	$-0.768443\pi$
$419$	−30.5760	−1.49374	−0.746868	+	0.664972i	$0.768443\pi$
$420$	−1.27831	−0.0623750
$421$	30.8913	1.50555	0.752774	−	0.658279i	$-0.228715\pi$
$421$	30.8913	1.50555	0.752774	+	0.658279i	$0.228715\pi$
$422$	−4.04104	−0.196715
$423$	25.7200	1.25055
$424$	0.608900	0.0295708
$425$	−0.0142483	−0.000691143 0
$426$	−2.80914	−0.136103
$427$	39.6745	1.91998
$428$	−7.01281	−0.338977
$429$	0.229986	0.0111038
$430$	−1.47795	−0.0712730
$431$	25.8689	1.24606	0.623030	−	0.782198i	$-0.285902\pi$
$431$	25.8689	1.24606	0.623030	+	0.782198i	$0.285902\pi$
$432$	−1.64689	−0.0792362
$433$	−4.21323	−0.202475	−0.101237	−	0.994862i	$-0.532280\pi$
$433$	−4.21323	−0.202475	−0.101237	+	0.994862i	$0.532280\pi$
$434$	−18.6931	−0.897298
$435$	0.988198	0.0473805
$436$	2.21467	0.106064
$437$	22.0823	1.05634
$438$	2.06145	0.0985001
$439$	29.6216	1.41376	0.706882	−	0.707331i	$-0.250101\pi$
$439$	29.6216	1.41376	0.706882	+	0.707331i	$0.250101\pi$
$440$	0.566591	0.0270112
$441$	−41.3085	−1.96707
$442$	0.0207992	0.000989317 0
$443$	27.0592	1.28562	0.642811	−	0.766024i	$-0.277768\pi$
$443$	27.0592	1.28562	0.642811	+	0.766024i	$0.277768\pi$
$444$	−0.0389630	−0.00184910
$445$	−16.5693	−0.785461
$446$	14.4091	0.682293
$447$	−2.38364	−0.112742
$448$	4.59715	0.217195
$449$	−29.9449	−1.41319	−0.706594	−	0.707619i	$-0.749769\pi$
$449$	−29.9449	−1.41319	−0.706594	+	0.707619i	$0.749769\pi$
$450$	2.92268	0.137776
$451$	0.867855	0.0408657
$452$	16.0274	0.753868
$453$	0.606180	0.0284808
$454$	−19.9234	−0.935050
$455$	−6.71077	−0.314606
$456$	−2.18324	−0.102239
$457$	−16.0764	−0.752021	−0.376010	−	0.926615i	$-0.622704\pi$
$457$	−16.0764	−0.752021	−0.376010	+	0.926615i	$0.622704\pi$
$458$	−7.79756	−0.364356
$459$	0.0234654	0.00109527
$460$	−2.81249	−0.131133
$461$	−20.7818	−0.967905	−0.483952	−	0.875094i	$-0.660799\pi$
$461$	−20.7818	−0.967905	−0.483952	+	0.875094i	$0.660799\pi$
$462$	−0.724278	−0.0336964
$463$	−19.3691	−0.900160	−0.450080	−	0.892988i	$-0.648605\pi$
$463$	−19.3691	−0.900160	−0.450080	+	0.892988i	$0.648605\pi$
$464$	−3.55383	−0.164983
$465$	−1.13068	−0.0524341
$466$	−2.69921	−0.125038
$467$	−6.97825	−0.322915	−0.161457	−	0.986880i	$-0.551619\pi$
$467$	−6.97825	−0.322915	−0.161457	+	0.986880i	$0.551619\pi$
$468$	−4.26644	−0.197216
$469$	56.3169	2.60047
$470$	−8.80015	−0.405921
$471$	−0.667863	−0.0307735
$472$	14.8356	0.682863
$473$	−0.837392	−0.0385033
$474$	3.26835	0.150120
$475$	7.85152	0.360253
$476$	−0.0655014	−0.00300225
$477$	1.77962	0.0814831
$478$	14.1713	0.648179
$479$	−35.5114	−1.62256	−0.811279	−	0.584660i	$-0.801228\pi$
$479$	−35.5114	−1.62256	−0.811279	+	0.584660i	$0.801228\pi$
$480$	0.278065	0.0126919
$481$	−0.204546	−0.00932648
$482$	−10.9813	−0.500183
$483$	3.59522	0.163588
$484$	−10.6790	−0.485408
$485$	0.629215	0.0285712
$486$	−7.25143	−0.328931
$487$	−24.8341	−1.12534	−0.562670	−	0.826682i	$-0.690226\pi$
$487$	−24.8341	−1.12534	−0.562670	+	0.826682i	$0.690226\pi$
$488$	−8.63024	−0.390673
$489$	2.69116	0.121699
$490$	14.1338	0.638498
$491$	−23.0335	−1.03949	−0.519744	−	0.854322i	$-0.673973\pi$
$491$	−23.0335	−1.03949	−0.519744	+	0.854322i	$0.673973\pi$
$492$	0.425916	0.0192018
$493$	0.0506360	0.00228053
$494$	−11.4614	−0.515673
$495$	1.65596	0.0744300
$496$	4.06624	0.182580
$497$	46.4424	2.08323
$498$	−2.43933	−0.109309
$499$	−28.0686	−1.25652	−0.628260	−	0.778003i	$-0.716233\pi$
$499$	−28.0686	−1.25652	−0.628260	+	0.778003i	$0.716233\pi$
$500$	−1.00000	−0.0447214
$501$	−2.17578	−0.0972069
$502$	−18.3946	−0.820993
$503$	21.2360	0.946868	0.473434	−	0.880829i	$-0.343014\pi$
$503$	21.2360	0.946868	0.473434	+	0.880829i	$0.343014\pi$
$504$	13.4360	0.598486
$505$	−2.63191	−0.117118
$506$	−1.59353	−0.0708410
$507$	−3.02231	−0.134226
$508$	−16.1425	−0.716206
$509$	−5.54967	−0.245985	−0.122992	−	0.992408i	$-0.539249\pi$
$509$	−5.54967	−0.245985	−0.122992	+	0.992408i	$0.539249\pi$
$510$	−0.00396195	−0.000175438 0
$511$	−34.0812	−1.50766
$512$	−1.00000	−0.0441942
$513$	−12.9306	−0.570901
$514$	−4.93374	−0.217618
$515$	−3.03981	−0.133950
$516$	−0.410967	−0.0180918
$517$	−4.98609	−0.219288
$518$	0.644161	0.0283028
$519$	5.00210	0.219568
$520$	1.45977	0.0640151
$521$	39.6792	1.73838	0.869188	−	0.494482i	$-0.164642\pi$
$521$	39.6792	1.73838	0.869188	+	0.494482i	$0.164642\pi$
$522$	−10.3867	−0.454614
$523$	−5.38433	−0.235440	−0.117720	−	0.993047i	$-0.537559\pi$
$523$	−5.38433	−0.235440	−0.117720	+	0.993047i	$0.537559\pi$
$524$	−15.5816	−0.680684
$525$	1.27831	0.0557899
$526$	−31.1231	−1.35703
$527$	−0.0579370	−0.00252377
$528$	0.157549	0.00685646
$529$	−15.0899	−0.656084
$530$	−0.608900	−0.0264489
$531$	43.3596	1.88165
$532$	36.0946	1.56490
$533$	2.23595	0.0968496
$534$	−4.60735	−0.199380
$535$	7.01281	0.303190
$536$	−12.2504	−0.529136
$537$	−4.50216	−0.194283
$538$	−10.7710	−0.464373
$539$	8.00806	0.344932
$540$	1.64689	0.0708710
$541$	14.2482	0.612580	0.306290	−	0.951938i	$-0.400912\pi$
$541$	14.2482	0.612580	0.306290	+	0.951938i	$0.400912\pi$
$542$	2.02243	0.0868709
$543$	−3.36037	−0.144207
$544$	0.0142483	0.000610890 0
$545$	−2.21467	−0.0948662
$546$	−1.86603	−0.0798589
$547$	25.5268	1.09145	0.545723	−	0.837966i	$-0.316255\pi$
$547$	25.5268	1.09145	0.545723	+	0.837966i	$0.316255\pi$
$548$	8.47503	0.362036
$549$	−25.2234	−1.07651
$550$	−0.566591	−0.0241595
$551$	−27.9030	−1.18871
$552$	−0.782055	−0.0332865
$553$	−54.0344	−2.29778
$554$	−31.7151	−1.34744
$555$	0.0389630	0.00165389
$556$	15.3218	0.649788
$557$	26.6954	1.13112	0.565561	−	0.824707i	$-0.308660\pi$
$557$	26.6954	1.13112	0.565561	+	0.824707i	$0.308660\pi$
$558$	11.8843	0.503104
$559$	−2.15746	−0.0912510
$560$	−4.59715	−0.194265
$561$	−0.00224481	−9.47758e−5 0
$562$	−2.63457	−0.111133
$563$	−16.6454	−0.701522	−0.350761	−	0.936465i	$-0.614077\pi$
$563$	−16.6454	−0.701522	−0.350761	+	0.936465i	$0.614077\pi$
$564$	−2.44702	−0.103038
$565$	−16.0274	−0.674280
$566$	−5.60684	−0.235673
$567$	38.2027	1.60436
$568$	−10.1024	−0.423889
$569$	16.7923	0.703968	0.351984	−	0.936006i	$-0.385507\pi$
$569$	16.7923	0.703968	0.351984	+	0.936006i	$0.385507\pi$
$570$	2.18324	0.0914457
$571$	−17.8064	−0.745175	−0.372587	−	0.927997i	$-0.621529\pi$
$571$	−17.8064	−0.745175	−0.372587	+	0.927997i	$0.621529\pi$
$572$	0.827092	0.0345825
$573$	3.00458	0.125518
$574$	−7.04151	−0.293907
$575$	2.81249	0.117289
$576$	−2.92268	−0.121778
$577$	44.0367	1.83327	0.916635	−	0.399726i	$-0.130895\pi$
$577$	44.0367	1.83327	0.916635	+	0.399726i	$0.130895\pi$
$578$	16.9998	0.707098
$579$	−3.85524	−0.160218
$580$	3.55383	0.147565
$581$	40.3284	1.67311
$582$	0.174963	0.00725245
$583$	−0.344997	−0.0142883
$584$	7.41356	0.306775
$585$	4.26644	0.176396
$586$	−10.0378	−0.414658
$587$	−26.3900	−1.08923	−0.544615	−	0.838686i	$-0.683324\pi$
$587$	−26.3900	−1.08923	−0.544615	+	0.838686i	$0.683324\pi$
$588$	3.93011	0.162075
$589$	31.9262	1.31550
$590$	−14.8356	−0.610771
$591$	4.84067	0.199119
$592$	−0.140122	−0.00575897
$593$	10.2022	0.418954	0.209477	−	0.977814i	$-0.432824\pi$
$593$	10.2022	0.418954	0.209477	+	0.977814i	$0.432824\pi$
$594$	0.933114	0.0382861
$595$	0.0655014	0.00268530
$596$	−8.57222	−0.351132
$597$	5.42479	0.222022
$598$	−4.10558	−0.167890
$599$	27.9963	1.14390	0.571949	−	0.820289i	$-0.306187\pi$
$599$	27.9963	1.14390	0.571949	+	0.820289i	$0.306187\pi$
$600$	−0.278065	−0.0113520
$601$	−16.8979	−0.689281	−0.344641	−	0.938735i	$-0.611999\pi$
$601$	−16.8979	−0.689281	−0.344641	+	0.938735i	$0.611999\pi$
$602$	6.79435	0.276917
$603$	−35.8040	−1.45805
$604$	2.17999	0.0887025
$605$	10.6790	0.434162
$606$	−0.731843	−0.0297291
$607$	21.9399	0.890514	0.445257	−	0.895403i	$-0.353112\pi$
$607$	21.9399	0.890514	0.445257	+	0.895403i	$0.353112\pi$
$608$	−7.85152	−0.318421
$609$	−4.54289	−0.184087
$610$	8.63024	0.349428
$611$	−12.8462	−0.519701
$612$	0.0416431	0.00168332
$613$	−36.0970	−1.45795	−0.728973	−	0.684543i	$-0.760002\pi$
$613$	−36.0970	−1.45795	−0.728973	+	0.684543i	$0.760002\pi$
$614$	−10.7817	−0.435115
$615$	−0.425916	−0.0171746
$616$	−2.60470	−0.104946
$617$	28.3241	1.14029	0.570143	−	0.821545i	$-0.306888\pi$
$617$	28.3241	1.14029	0.570143	+	0.821545i	$0.306888\pi$
$618$	−0.845266	−0.0340016
$619$	−9.48185	−0.381108	−0.190554	−	0.981677i	$-0.561028\pi$
$619$	−9.48185	−0.381108	−0.190554	+	0.981677i	$0.561028\pi$
$620$	−4.06624	−0.163304
$621$	−4.63186	−0.185870
$622$	−7.40839	−0.297049
$623$	76.1716	3.05175
$624$	0.405911	0.0162495
$625$	1.00000	0.0400000
$626$	24.3746	0.974207
$627$	1.23700	0.0494011
$628$	−2.40182	−0.0958431
$629$	0.00199649	7.96055e−5 0
$630$	−13.4360	−0.535303
$631$	−24.0751	−0.958416	−0.479208	−	0.877701i	$-0.659076\pi$
$631$	−24.0751	−0.958416	−0.479208	+	0.877701i	$0.659076\pi$
$632$	11.7539	0.467545
$633$	1.12367	0.0446620
$634$	−6.72912	−0.267247
$635$	16.1425	0.640594
$636$	−0.169314	−0.00671373
$637$	20.6320	0.817471
$638$	2.01357	0.0797180
$639$	−29.5262	−1.16804
$640$	1.00000	0.0395285
$641$	4.49247	0.177442	0.0887209	−	0.996057i	$-0.471722\pi$
$641$	4.49247	0.177442	0.0887209	+	0.996057i	$0.471722\pi$
$642$	1.95002	0.0769611
$643$	32.9994	1.30137	0.650684	−	0.759349i	$-0.274482\pi$
$643$	32.9994	1.30137	0.650684	+	0.759349i	$0.274482\pi$
$644$	12.9294	0.509490
$645$	0.410967	0.0161818
$646$	0.111871	0.00440149
$647$	−18.0032	−0.707778	−0.353889	−	0.935287i	$-0.615141\pi$
$647$	−18.0032	−0.707778	−0.353889	+	0.935287i	$0.615141\pi$
$648$	−8.31009	−0.326451
$649$	−8.40570	−0.329953
$650$	−1.45977	−0.0572569
$651$	5.19791	0.203722
$652$	9.67817	0.379026
$653$	8.98189	0.351489	0.175744	−	0.984436i	$-0.443767\pi$
$653$	8.98189	0.351489	0.175744	+	0.984436i	$0.443767\pi$
$654$	−0.615824	−0.0240806
$655$	15.5816	0.608822
$656$	1.53171	0.0598033
$657$	21.6675	0.845328
$658$	40.4556	1.57712
$659$	8.56606	0.333686	0.166843	−	0.985983i	$-0.446643\pi$
$659$	8.56606	0.333686	0.166843	+	0.985983i	$0.446643\pi$
$660$	−0.157549	−0.00613260
$661$	−21.6572	−0.842366	−0.421183	−	0.906976i	$-0.638385\pi$
$661$	−21.6572	−0.842366	−0.421183	+	0.906976i	$0.638385\pi$
$662$	4.01232	0.155943
$663$	−0.00578354	−0.000224614 0
$664$	−8.77249	−0.340439
$665$	−36.0946	−1.39969
$666$	−0.409531	−0.0158690
$667$	−9.99510	−0.387012
$668$	−7.82472	−0.302748
$669$	−4.00668	−0.154907
$670$	12.2504	0.473274
$671$	4.88982	0.188769
$672$	−1.27831	−0.0493118
$673$	−14.5424	−0.560568	−0.280284	−	0.959917i	$-0.590429\pi$
$673$	−14.5424	−0.560568	−0.280284	+	0.959917i	$0.590429\pi$
$674$	−9.90612	−0.381569
$675$	−1.64689	−0.0633889
$676$	−10.8691	−0.418041
$677$	−2.80305	−0.107730	−0.0538650	−	0.998548i	$-0.517154\pi$
$677$	−2.80305	−0.107730	−0.0538650	+	0.998548i	$0.517154\pi$
$678$	−4.45668	−0.171158
$679$	−2.89260	−0.111008
$680$	−0.0142483	−0.000546396 0
$681$	5.54000	0.212293
$682$	−2.30390	−0.0882207
$683$	10.9445	0.418778	0.209389	−	0.977832i	$-0.432853\pi$
$683$	10.9445	0.418778	0.209389	+	0.977832i	$0.432853\pi$
$684$	−22.9475	−0.877419
$685$	−8.47503	−0.323814
$686$	−32.7950	−1.25212
$687$	2.16823	0.0827232
$688$	−1.47795	−0.0563463
$689$	−0.888853	−0.0338626
$690$	0.782055	0.0297723
$691$	−3.65556	−0.139064	−0.0695320	−	0.997580i	$-0.522151\pi$
$691$	−3.65556	−0.139064	−0.0695320	+	0.997580i	$0.522151\pi$
$692$	17.9889	0.683837
$693$	−7.61271	−0.289183
$694$	−4.78135	−0.181497
$695$	−15.3218	−0.581188
$696$	0.988198	0.0374575
$697$	−0.0218243	−0.000826653 0
$698$	10.1955	0.385906
$699$	0.750557	0.0283887
$700$	4.59715	0.173756
$701$	−40.4724	−1.52862	−0.764311	−	0.644848i	$-0.776921\pi$
$701$	−40.4724	−1.52862	−0.764311	+	0.644848i	$0.776921\pi$
$702$	2.40408	0.0907363
$703$	−1.10017	−0.0414937
$704$	0.566591	0.0213542
$705$	2.44702	0.0921601
$706$	21.6800	0.815936
$707$	12.0993	0.455040
$708$	−4.12526	−0.155037
$709$	−39.9460	−1.50020	−0.750102	−	0.661322i	$-0.769996\pi$
$709$	−39.9460	−1.50020	−0.750102	+	0.661322i	$0.769996\pi$
$710$	10.1024	0.379138
$711$	34.3529	1.28833
$712$	−16.5693	−0.620961
$713$	11.4363	0.428291
$714$	0.0182137	0.000681630 0
$715$	−0.827092	−0.0309315
$716$	−16.1910	−0.605087
$717$	−3.94054	−0.147162
$718$	4.47352	0.166950
$719$	−18.6782	−0.696580	−0.348290	−	0.937387i	$-0.613238\pi$
$719$	−18.6782	−0.696580	−0.348290	+	0.937387i	$0.613238\pi$
$720$	2.92268	0.108922
$721$	13.9745	0.520436
$722$	−42.6464	−1.58713
$723$	3.05351	0.113561
$724$	−12.0848	−0.449129
$725$	−3.55383	−0.131986
$726$	2.96945	0.110207
$727$	23.6038	0.875417	0.437709	−	0.899117i	$-0.355790\pi$
$727$	23.6038	0.875417	0.437709	+	0.899117i	$0.355790\pi$
$728$	−6.71077	−0.248718
$729$	−22.9139	−0.848663
$730$	−7.41356	−0.274388
$731$	0.0210582	0.000778867 0
$732$	2.39977	0.0886982
$733$	−31.8588	−1.17673	−0.588366	−	0.808595i	$-0.700229\pi$
$733$	−31.8588	−1.17673	−0.588366	+	0.808595i	$0.700229\pi$
$734$	2.55763	0.0944037
$735$	−3.93011	−0.144964
$736$	−2.81249	−0.103670
$737$	6.94096	0.255674
$738$	4.47671	0.164790
$739$	−45.7639	−1.68345	−0.841727	−	0.539904i	$-0.818461\pi$
$739$	−45.7639	−1.68345	−0.841727	+	0.539904i	$0.818461\pi$
$740$	0.140122	0.00515098
$741$	3.18702	0.117078
$742$	2.79920	0.102762
$743$	−44.1661	−1.62030	−0.810148	−	0.586225i	$-0.800614\pi$
$743$	−44.1661	−1.62030	−0.810148	+	0.586225i	$0.800614\pi$
$744$	−1.13068	−0.0414528
$745$	8.57222	0.314062
$746$	−24.7683	−0.906830
$747$	−25.6392	−0.938089
$748$	−0.00807294	−0.000295176 0
$749$	−32.2389	−1.17798
$750$	0.278065	0.0101535
$751$	−31.6854	−1.15622	−0.578109	−	0.815960i	$-0.696209\pi$
$751$	−31.6854	−1.15622	−0.578109	+	0.815960i	$0.696209\pi$
$752$	−8.80015	−0.320909
$753$	5.11491	0.186398
$754$	5.18778	0.188928
$755$	−2.17999	−0.0793379
$756$	−7.57101	−0.275355
$757$	2.46836	0.0897142	0.0448571	−	0.998993i	$-0.485717\pi$
$757$	2.46836	0.0897142	0.0448571	+	0.998993i	$0.485717\pi$
$758$	21.6397	0.785989
$759$	0.443105	0.0160837
$760$	7.85152	0.284805
$761$	50.0613	1.81472	0.907361	−	0.420352i	$-0.138094\pi$
$761$	50.0613	1.81472	0.907361	+	0.420352i	$0.138094\pi$
$762$	4.48866	0.162607
$763$	10.1812	0.368584
$764$	10.8053	0.390922
$765$	−0.0416431	−0.00150561
$766$	−19.0022	−0.686578
$767$	−21.6565	−0.781972
$768$	0.278065	0.0100338
$769$	−14.3209	−0.516424	−0.258212	−	0.966088i	$-0.583133\pi$
$769$	−14.3209	−0.516424	−0.258212	+	0.966088i	$0.583133\pi$
$770$	2.60470	0.0938669
$771$	1.37190	0.0494079
$772$	−13.8645	−0.498994
$773$	−23.2324	−0.835613	−0.417806	−	0.908536i	$-0.637201\pi$
$773$	−23.2324	−0.835613	−0.417806	+	0.908536i	$0.637201\pi$
$774$	−4.31957	−0.155264
$775$	4.06624	0.146064
$776$	0.629215	0.0225875
$777$	−0.179119	−0.00642585
$778$	30.9536	1.10974
$779$	12.0263	0.430886
$780$	−0.405911	−0.0145340
$781$	5.72395	0.204819
$782$	0.0400731	0.00143301
$783$	5.85278	0.209161
$784$	14.1338	0.504777
$785$	2.40182	0.0857247
$786$	4.33270	0.154542
$787$	39.4321	1.40560	0.702802	−	0.711385i	$-0.251932\pi$
$787$	39.4321	1.40560	0.702802	+	0.711385i	$0.251932\pi$
$788$	17.4084	0.620148
$789$	8.65425	0.308100
$790$	−11.7539	−0.418185
$791$	73.6805	2.61978
$792$	1.65596	0.0588421
$793$	12.5982	0.447374
$794$	−26.5776	−0.943203
$795$	0.169314	0.00600495
$796$	19.5090	0.691479
$797$	7.31702	0.259182	0.129591	−	0.991568i	$-0.458634\pi$
$797$	7.31702	0.259182	0.129591	+	0.991568i	$0.458634\pi$
$798$	−10.0367	−0.355294
$799$	0.125387	0.00443587
$800$	−1.00000	−0.0353553
$801$	−48.4268	−1.71108
$802$	−1.00000	−0.0353112
$803$	−4.20045	−0.148231
$804$	3.40641	0.120135
$805$	−12.9294	−0.455702
$806$	−5.93578	−0.209079
$807$	2.99505	0.105431
$808$	−2.63191	−0.0925903
$809$	18.6783	0.656694	0.328347	−	0.944557i	$-0.393508\pi$
$809$	18.6783	0.656694	0.328347	+	0.944557i	$0.393508\pi$
$810$	8.31009	0.291987
$811$	39.9588	1.40314	0.701571	−	0.712599i	$-0.252482\pi$
$811$	39.9588	1.40314	0.701571	+	0.712599i	$0.252482\pi$
$812$	−16.3375	−0.573334
$813$	−0.562369	−0.0197231
$814$	0.0793918	0.00278268
$815$	−9.67817	−0.339011
$816$	−0.00396195	−0.000138696 0
$817$	−11.6041	−0.405978
$818$	−21.9682	−0.768101
$819$	−19.6134	−0.685349
$820$	−1.53171	−0.0534897
$821$	16.9205	0.590529	0.295265	−	0.955415i	$-0.404592\pi$
$821$	16.9205	0.590529	0.295265	+	0.955415i	$0.404592\pi$
$822$	−2.35661	−0.0821964
$823$	8.94273	0.311724	0.155862	−	0.987779i	$-0.450185\pi$
$823$	8.94273	0.311724	0.155862	+	0.987779i	$0.450185\pi$
$824$	−3.03981	−0.105897
$825$	0.157549	0.00548516
$826$	68.2013	2.37303
$827$	−37.8709	−1.31690	−0.658449	−	0.752625i	$-0.728787\pi$
$827$	−37.8709	−1.31690	−0.658449	+	0.752625i	$0.728787\pi$
$828$	−8.21999	−0.285665
$829$	−28.9110	−1.00412	−0.502060	−	0.864833i	$-0.667424\pi$
$829$	−28.9110	−1.00412	−0.502060	+	0.864833i	$0.667424\pi$
$830$	8.77249	0.304498
$831$	8.81886	0.305923
$832$	1.45977	0.0506084
$833$	−0.201382	−0.00697746
$834$	−4.26046	−0.147528
$835$	7.82472	0.270786
$836$	4.44860	0.153858
$837$	−6.69666	−0.231471
$838$	30.5760	1.05623
$839$	−44.5787	−1.53903	−0.769514	−	0.638630i	$-0.779501\pi$
$839$	−44.5787	−1.53903	−0.769514	+	0.638630i	$0.779501\pi$
$840$	1.27831	0.0441058
$841$	−16.3703	−0.564492
$842$	−30.8913	−1.06458
$843$	0.732584	0.0252315
$844$	4.04104	0.139098
$845$	10.8691	0.373907
$846$	−25.7200	−0.884273
$847$	−49.0928	−1.68685
$848$	−0.608900	−0.0209097
$849$	1.55907	0.0535070
$850$	0.0142483	0.000488712 0
$851$	−0.394091	−0.0135093
$852$	2.80914	0.0962395
$853$	−10.7141	−0.366842	−0.183421	−	0.983034i	$-0.558717\pi$
$853$	−10.7141	−0.366842	−0.183421	+	0.983034i	$0.558717\pi$
$854$	−39.6745	−1.35763
$855$	22.9475	0.784787
$856$	7.01281	0.239693
$857$	−33.7732	−1.15367	−0.576836	−	0.816860i	$-0.695713\pi$
$857$	−33.7732	−1.15367	−0.576836	+	0.816860i	$0.695713\pi$
$858$	−0.229986	−0.00785158
$859$	48.9037	1.66857	0.834286	−	0.551331i	$-0.185880\pi$
$859$	48.9037	1.66857	0.834286	+	0.551331i	$0.185880\pi$
$860$	1.47795	0.0503976
$861$	1.95800	0.0667285
$862$	−25.8689	−0.881097
$863$	9.57444	0.325918	0.162959	−	0.986633i	$-0.447896\pi$
$863$	9.57444	0.325918	0.162959	+	0.986633i	$0.447896\pi$
$864$	1.64689	0.0560284
$865$	−17.9889	−0.611642
$866$	4.21323	0.143171
$867$	−4.72706	−0.160539
$868$	18.6931	0.634486
$869$	−6.65965	−0.225913
$870$	−0.988198	−0.0335030
$871$	17.8827	0.605934
$872$	−2.21467	−0.0749983
$873$	1.83900	0.0622406
$874$	−22.0823	−0.746945
$875$	−4.59715	−0.155412
$876$	−2.06145	−0.0696501
$877$	−21.1364	−0.713725	−0.356863	−	0.934157i	$-0.616154\pi$
$877$	−21.1364	−0.713725	−0.356863	+	0.934157i	$0.616154\pi$
$878$	−29.6216	−0.999682
$879$	2.79117	0.0941437
$880$	−0.566591	−0.0190998
$881$	−25.4776	−0.858364	−0.429182	−	0.903218i	$-0.641198\pi$
$881$	−25.4776	−0.858364	−0.429182	+	0.903218i	$0.641198\pi$
$882$	41.3085	1.39093
$883$	0.796973	0.0268203	0.0134101	−	0.999910i	$-0.495731\pi$
$883$	0.796973	0.0268203	0.0134101	+	0.999910i	$0.495731\pi$
$884$	−0.0207992	−0.000699553 0
$885$	4.12526	0.138669
$886$	−27.0592	−0.909073
$887$	8.47633	0.284607	0.142304	−	0.989823i	$-0.454549\pi$
$887$	8.47633	0.284607	0.142304	+	0.989823i	$0.454549\pi$
$888$	0.0389630	0.00130751
$889$	−74.2092	−2.48890
$890$	16.5693	0.555405
$891$	4.70842	0.157738
$892$	−14.4091	−0.482454
$893$	−69.0946	−2.31216
$894$	2.38364	0.0797208
$895$	16.1910	0.541206
$896$	−4.59715	−0.153580
$897$	1.14162	0.0381176
$898$	29.9449	0.999275
$899$	−14.4507	−0.481959
$900$	−2.92268	−0.0974227
$901$	0.00867577	0.000289032 0
$902$	−0.867855	−0.0288964
$903$	−1.88927	−0.0628711
$904$	−16.0274	−0.533065
$905$	12.0848	0.401713
$906$	−0.606180	−0.0201390
$907$	−34.7929	−1.15528	−0.577639	−	0.816292i	$-0.696026\pi$
$907$	−34.7929	−1.15528	−0.577639	+	0.816292i	$0.696026\pi$
$908$	19.9234	0.661180
$909$	−7.69223	−0.255135
$910$	6.71077	0.222460
$911$	−30.0304	−0.994952	−0.497476	−	0.867478i	$-0.665740\pi$
$911$	−30.0304	−0.994952	−0.497476	+	0.867478i	$0.665740\pi$
$912$	2.18324	0.0722942
$913$	4.97041	0.164497
$914$	16.0764	0.531759
$915$	−2.39977	−0.0793340
$916$	7.79756	0.257639
$917$	−71.6308	−2.36546
$918$	−0.0234654	−0.000774473 0
$919$	−6.30698	−0.208048	−0.104024	−	0.994575i	$-0.533172\pi$
$919$	−6.30698	−0.208048	−0.104024	+	0.994575i	$0.533172\pi$
$920$	2.81249	0.0927249
$921$	2.99802	0.0987882
$922$	20.7818	0.684412
$923$	14.7472	0.485411
$924$	0.724278	0.0238270
$925$	−0.140122	−0.00460718
$926$	19.3691	0.636509
$927$	−8.88439	−0.291802
$928$	3.55383	0.116660
$929$	−34.6207	−1.13587	−0.567934	−	0.823074i	$-0.692257\pi$
$929$	−34.6207	−1.13587	−0.567934	+	0.823074i	$0.692257\pi$
$930$	1.13068	0.0370765
$931$	110.972	3.63695
$932$	2.69921	0.0884156
$933$	2.06002	0.0674419
$934$	6.97825	0.228335
$935$	0.00807294	0.000264014 0
$936$	4.26644	0.139453
$937$	−36.0198	−1.17672	−0.588358	−	0.808600i	$-0.700226\pi$
$937$	−36.0198	−1.17672	−0.588358	+	0.808600i	$0.700226\pi$
$938$	−56.3169	−1.83881
$939$	−6.77774	−0.221183
$940$	8.80015	0.287029
$941$	−11.7725	−0.383773	−0.191886	−	0.981417i	$-0.561460\pi$
$941$	−11.7725	−0.383773	−0.191886	+	0.981417i	$0.561460\pi$
$942$	0.667863	0.0217602
$943$	4.30792	0.140285
$944$	−14.8356	−0.482857
$945$	7.57101	0.246285
$946$	0.837392	0.0272260
$947$	34.6816	1.12700	0.563500	−	0.826116i	$-0.309454\pi$
$947$	34.6816	1.12700	0.563500	+	0.826116i	$0.309454\pi$
$948$	−3.26835	−0.106151
$949$	−10.8221	−0.351300
$950$	−7.85152	−0.254737
$951$	1.87114	0.0606757
$952$	0.0655014	0.00212291
$953$	9.79661	0.317343	0.158672	−	0.987331i	$-0.449279\pi$
$953$	9.79661	0.317343	0.158672	+	0.987331i	$0.449279\pi$
$954$	−1.77962	−0.0576173
$955$	−10.8053	−0.349651
$956$	−14.1713	−0.458332
$957$	−0.559904	−0.0180991
$958$	35.5114	1.14732
$959$	38.9610	1.25812
$960$	−0.278065	−0.00897452
$961$	−14.4657	−0.466634
$962$	0.204546	0.00659481
$963$	20.4962	0.660481
$964$	10.9813	0.353683
$965$	13.8645	0.446314
$966$	−3.59522	−0.115674
$967$	−39.2675	−1.26276	−0.631379	−	0.775475i	$-0.717511\pi$
$967$	−39.2675	−1.26276	−0.631379	+	0.775475i	$0.717511\pi$
$968$	10.6790	0.343235
$969$	−0.0311074	−0.000999313 0
$970$	−0.629215	−0.0202029
$971$	51.6760	1.65836	0.829181	−	0.558981i	$-0.188807\pi$
$971$	51.6760	1.65836	0.829181	+	0.558981i	$0.188807\pi$
$972$	7.25143	0.232590
$973$	70.4365	2.25809
$974$	24.8341	0.795735
$975$	0.405911	0.0129996
$976$	8.63024	0.276247
$977$	−15.7059	−0.502475	−0.251237	−	0.967925i	$-0.580838\pi$
$977$	−15.7059	−0.502475	−0.251237	+	0.967925i	$0.580838\pi$
$978$	−2.69116	−0.0860539
$979$	9.38803	0.300043
$980$	−14.1338	−0.451486
$981$	−6.47278	−0.206660
$982$	23.0335	0.735029
$983$	−39.5943	−1.26286	−0.631431	−	0.775432i	$-0.717532\pi$
$983$	−39.5943	−1.26286	−0.631431	+	0.775432i	$0.717532\pi$
$984$	−0.425916	−0.0135777
$985$	−17.4084	−0.554677
$986$	−0.0506360	−0.00161258
$987$	−11.2493	−0.358069
$988$	11.4614	0.364636
$989$	−4.15671	−0.132176
$990$	−1.65596	−0.0526300
$991$	15.4742	0.491554	0.245777	−	0.969326i	$-0.420957\pi$
$991$	15.4742	0.491554	0.245777	+	0.969326i	$0.420957\pi$
$992$	−4.06624	−0.129103
$993$	−1.11569	−0.0354053
$994$	−46.4424	−1.47306
$995$	−19.5090	−0.618478
$996$	2.43933	0.0772930
$997$	−3.06942	−0.0972096	−0.0486048	−	0.998818i	$-0.515477\pi$
$997$	−3.06942	−0.0972096	−0.0486048	+	0.998818i	$0.515477\pi$
$998$	28.0686	0.888494
$999$	0.230766	0.00730110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.10	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.278065 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.278065 q^{6} +4.59715 q^{7} -1.00000 q^{8} -2.92268 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.278065 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.278065 q^{6} +4.59715 q^{7} -1.00000 q^{8} -2.92268 q^{9} +1.00000 q^{10} +0.566591 q^{11} +0.278065 q^{12} +1.45977 q^{13} -4.59715 q^{14} -0.278065 q^{15} +1.00000 q^{16} -0.0142483 q^{17} +2.92268 q^{18} +7.85152 q^{19} -1.00000 q^{20} +1.27831 q^{21} -0.566591 q^{22} +2.81249 q^{23} -0.278065 q^{24} +1.00000 q^{25} -1.45977 q^{26} -1.64689 q^{27} +4.59715 q^{28} -3.55383 q^{29} +0.278065 q^{30} +4.06624 q^{31} -1.00000 q^{32} +0.157549 q^{33} +0.0142483 q^{34} -4.59715 q^{35} -2.92268 q^{36} -0.140122 q^{37} -7.85152 q^{38} +0.405911 q^{39} +1.00000 q^{40} +1.53171 q^{41} -1.27831 q^{42} -1.47795 q^{43} +0.566591 q^{44} +2.92268 q^{45} -2.81249 q^{46} -8.80015 q^{47} +0.278065 q^{48} +14.1338 q^{49} -1.00000 q^{50} -0.00396195 q^{51} +1.45977 q^{52} -0.608900 q^{53} +1.64689 q^{54} -0.566591 q^{55} -4.59715 q^{56} +2.18324 q^{57} +3.55383 q^{58} -14.8356 q^{59} -0.278065 q^{60} +8.63024 q^{61} -4.06624 q^{62} -13.4360 q^{63} +1.00000 q^{64} -1.45977 q^{65} -0.157549 q^{66} +12.2504 q^{67} -0.0142483 q^{68} +0.782055 q^{69} +4.59715 q^{70} +10.1024 q^{71} +2.92268 q^{72} -7.41356 q^{73} +0.140122 q^{74} +0.278065 q^{75} +7.85152 q^{76} +2.60470 q^{77} -0.405911 q^{78} -11.7539 q^{79} -1.00000 q^{80} +8.31009 q^{81} -1.53171 q^{82} +8.77249 q^{83} +1.27831 q^{84} +0.0142483 q^{85} +1.47795 q^{86} -0.988198 q^{87} -0.566591 q^{88} +16.5693 q^{89} -2.92268 q^{90} +6.71077 q^{91} +2.81249 q^{92} +1.13068 q^{93} +8.80015 q^{94} -7.85152 q^{95} -0.278065 q^{96} -0.629215 q^{97} -14.1338 q^{98} -1.65596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 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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