LMFDB - Embedded newform 4010.2.a.l.1.8

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			1.8
Root			$-0.103424$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.103424 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.103424 q^{6} +1.84281 q^{7} -1.00000 q^{8} -2.98930 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.103424 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.103424 q^{6} +1.84281 q^{7} -1.00000 q^{8} -2.98930 q^{9} +1.00000 q^{10} +5.58434 q^{11} -0.103424 q^{12} +5.84741 q^{13} -1.84281 q^{14} +0.103424 q^{15} +1.00000 q^{16} -1.40746 q^{17} +2.98930 q^{18} -0.622954 q^{19} -1.00000 q^{20} -0.190592 q^{21} -5.58434 q^{22} -4.53753 q^{23} +0.103424 q^{24} +1.00000 q^{25} -5.84741 q^{26} +0.619440 q^{27} +1.84281 q^{28} -0.233790 q^{29} -0.103424 q^{30} +8.85996 q^{31} -1.00000 q^{32} -0.577557 q^{33} +1.40746 q^{34} -1.84281 q^{35} -2.98930 q^{36} +6.90832 q^{37} +0.622954 q^{38} -0.604765 q^{39} +1.00000 q^{40} -3.42105 q^{41} +0.190592 q^{42} -0.338471 q^{43} +5.58434 q^{44} +2.98930 q^{45} +4.53753 q^{46} +12.2677 q^{47} -0.103424 q^{48} -3.60405 q^{49} -1.00000 q^{50} +0.145566 q^{51} +5.84741 q^{52} +0.244408 q^{53} -0.619440 q^{54} -5.58434 q^{55} -1.84281 q^{56} +0.0644287 q^{57} +0.233790 q^{58} +0.302742 q^{59} +0.103424 q^{60} +8.08067 q^{61} -8.85996 q^{62} -5.50872 q^{63} +1.00000 q^{64} -5.84741 q^{65} +0.577557 q^{66} -12.5965 q^{67} -1.40746 q^{68} +0.469292 q^{69} +1.84281 q^{70} -6.23114 q^{71} +2.98930 q^{72} +0.619738 q^{73} -6.90832 q^{74} -0.103424 q^{75} -0.622954 q^{76} +10.2909 q^{77} +0.604765 q^{78} -10.6948 q^{79} -1.00000 q^{80} +8.90384 q^{81} +3.42105 q^{82} -10.0340 q^{83} -0.190592 q^{84} +1.40746 q^{85} +0.338471 q^{86} +0.0241796 q^{87} -5.58434 q^{88} -8.22681 q^{89} -2.98930 q^{90} +10.7757 q^{91} -4.53753 q^{92} -0.916336 q^{93} -12.2677 q^{94} +0.622954 q^{95} +0.103424 q^{96} +0.417650 q^{97} +3.60405 q^{98} -16.6933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.103424	−0.0597121	−0.0298561	−	0.999554i	$-0.509505\pi$
$3$	−0.103424	−0.0597121	−0.0298561	+	0.999554i	$0.509505\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.103424	0.0422228
$7$	1.84281	0.696517	0.348258	−	0.937399i	$-0.386773\pi$
$7$	1.84281	0.696517	0.348258	+	0.937399i	$0.386773\pi$
$8$	−1.00000	−0.353553
$9$	−2.98930	−0.996434
$10$	1.00000	0.316228
$11$	5.58434	1.68374	0.841871	−	0.539678i	$-0.181454\pi$
$11$	5.58434	1.68374	0.841871	+	0.539678i	$0.181454\pi$
$12$	−0.103424	−0.0298561
$13$	5.84741	1.62178	0.810890	−	0.585198i	$-0.198983\pi$
$13$	5.84741	1.62178	0.810890	+	0.585198i	$0.198983\pi$
$14$	−1.84281	−0.492512
$15$	0.103424	0.0267041
$16$	1.00000	0.250000
$17$	−1.40746	−0.341360	−0.170680	−	0.985327i	$-0.554596\pi$
$17$	−1.40746	−0.341360	−0.170680	+	0.985327i	$0.554596\pi$
$18$	2.98930	0.704586
$19$	−0.622954	−0.142915	−0.0714577	−	0.997444i	$-0.522765\pi$
$19$	−0.622954	−0.142915	−0.0714577	+	0.997444i	$0.522765\pi$
$20$	−1.00000	−0.223607
$21$	−0.190592	−0.0415905
$22$	−5.58434	−1.19059
$23$	−4.53753	−0.946141	−0.473070	−	0.881025i	$-0.656854\pi$
$23$	−4.53753	−0.946141	−0.473070	+	0.881025i	$0.656854\pi$
$24$	0.103424	0.0211114
$25$	1.00000	0.200000
$26$	−5.84741	−1.14677
$27$	0.619440	0.119211
$28$	1.84281	0.348258
$29$	−0.233790	−0.0434136	−0.0217068	−	0.999764i	$-0.506910\pi$
$29$	−0.233790	−0.0434136	−0.0217068	+	0.999764i	$0.506910\pi$
$30$	−0.103424	−0.0188826
$31$	8.85996	1.59130	0.795648	−	0.605760i	$-0.207131\pi$
$31$	8.85996	1.59130	0.795648	+	0.605760i	$0.207131\pi$
$32$	−1.00000	−0.176777
$33$	−0.577557	−0.100540
$34$	1.40746	0.241378
$35$	−1.84281	−0.311492
$36$	−2.98930	−0.498217
$37$	6.90832	1.13572	0.567860	−	0.823125i	$-0.307771\pi$
$37$	6.90832	1.13572	0.567860	+	0.823125i	$0.307771\pi$
$38$	0.622954	0.101057
$39$	−0.604765	−0.0968400
$40$	1.00000	0.158114
$41$	−3.42105	−0.534278	−0.267139	−	0.963658i	$-0.586078\pi$
$41$	−3.42105	−0.534278	−0.267139	+	0.963658i	$0.586078\pi$
$42$	0.190592	0.0294089
$43$	−0.338471	−0.0516163	−0.0258082	−	0.999667i	$-0.508216\pi$
$43$	−0.338471	−0.0516163	−0.0258082	+	0.999667i	$0.508216\pi$
$44$	5.58434	0.841871
$45$	2.98930	0.445619
$46$	4.53753	0.669023
$47$	12.2677	1.78943	0.894716	−	0.446636i	$-0.147378\pi$
$47$	12.2677	1.78943	0.894716	+	0.446636i	$0.147378\pi$
$48$	−0.103424	−0.0149280
$49$	−3.60405	−0.514864
$50$	−1.00000	−0.141421
$51$	0.145566	0.0203833
$52$	5.84741	0.810890
$53$	0.244408	0.0335720	0.0167860	−	0.999859i	$-0.494657\pi$
$53$	0.244408	0.0335720	0.0167860	+	0.999859i	$0.494657\pi$
$54$	−0.619440	−0.0842951
$55$	−5.58434	−0.752993
$56$	−1.84281	−0.246256
$57$	0.0644287	0.00853379
$58$	0.233790	0.0306981
$59$	0.302742	0.0394137	0.0197068	−	0.999806i	$-0.493727\pi$
$59$	0.302742	0.0394137	0.0197068	+	0.999806i	$0.493727\pi$
$60$	0.103424	0.0133520
$61$	8.08067	1.03462	0.517312	−	0.855797i	$-0.326933\pi$
$61$	8.08067	1.03462	0.517312	+	0.855797i	$0.326933\pi$
$62$	−8.85996	−1.12522
$63$	−5.50872	−0.694033
$64$	1.00000	0.125000
$65$	−5.84741	−0.725282
$66$	0.577557	0.0710924
$67$	−12.5965	−1.53891	−0.769455	−	0.638700i	$-0.779472\pi$
$67$	−12.5965	−1.53891	−0.769455	+	0.638700i	$0.779472\pi$
$68$	−1.40746	−0.170680
$69$	0.469292	0.0564961
$70$	1.84281	0.220258
$71$	−6.23114	−0.739500	−0.369750	−	0.929131i	$-0.620557\pi$
$71$	−6.23114	−0.739500	−0.369750	+	0.929131i	$0.620557\pi$
$72$	2.98930	0.352293
$73$	0.619738	0.0725348	0.0362674	−	0.999342i	$-0.488453\pi$
$73$	0.619738	0.0725348	0.0362674	+	0.999342i	$0.488453\pi$
$74$	−6.90832	−0.803076
$75$	−0.103424	−0.0119424
$76$	−0.622954	−0.0714577
$77$	10.2909	1.17275
$78$	0.604765	0.0684762
$79$	−10.6948	−1.20326	−0.601628	−	0.798777i	$-0.705481\pi$
$79$	−10.6948	−1.20326	−0.601628	+	0.798777i	$0.705481\pi$
$80$	−1.00000	−0.111803
$81$	8.90384	0.989316
$82$	3.42105	0.377792
$83$	−10.0340	−1.10138	−0.550689	−	0.834711i	$-0.685635\pi$
$83$	−10.0340	−1.10138	−0.550689	+	0.834711i	$0.685635\pi$
$84$	−0.190592	−0.0207952
$85$	1.40746	0.152661
$86$	0.338471	0.0364982
$87$	0.0241796	0.00259232
$88$	−5.58434	−0.595293
$89$	−8.22681	−0.872040	−0.436020	−	0.899937i	$-0.643612\pi$
$89$	−8.22681	−0.872040	−0.436020	+	0.899937i	$0.643612\pi$
$90$	−2.98930	−0.315100
$91$	10.7757	1.12960
$92$	−4.53753	−0.473070
$93$	−0.916336	−0.0950196
$94$	−12.2677	−1.26532
$95$	0.622954	0.0639138
$96$	0.103424	0.0105557
$97$	0.417650	0.0424059	0.0212030	−	0.999775i	$-0.493250\pi$
$97$	0.417650	0.0424059	0.0212030	+	0.999775i	$0.493250\pi$
$98$	3.60405	0.364064
$99$	−16.6933	−1.67774
$100$	1.00000	0.100000
$101$	1.96069	0.195096	0.0975482	−	0.995231i	$-0.468900\pi$
$101$	1.96069	0.195096	0.0975482	+	0.995231i	$0.468900\pi$
$102$	−0.145566	−0.0144132
$103$	11.7954	1.16224	0.581120	−	0.813818i	$-0.302615\pi$
$103$	11.7954	1.16224	0.581120	+	0.813818i	$0.302615\pi$
$104$	−5.84741	−0.573386
$105$	0.190592	0.0185998
$106$	−0.244408	−0.0237390
$107$	−3.70774	−0.358441	−0.179221	−	0.983809i	$-0.557358\pi$
$107$	−3.70774	−0.358441	−0.179221	+	0.983809i	$0.557358\pi$
$108$	0.619440	0.0596057
$109$	7.98563	0.764884	0.382442	−	0.923979i	$-0.375083\pi$
$109$	7.98563	0.764884	0.382442	+	0.923979i	$0.375083\pi$
$110$	5.58434	0.532446
$111$	−0.714489	−0.0678163
$112$	1.84281	0.174129
$113$	3.28552	0.309076	0.154538	−	0.987987i	$-0.450611\pi$
$113$	3.28552	0.309076	0.154538	+	0.987987i	$0.450611\pi$
$114$	−0.0644287	−0.00603430
$115$	4.53753	0.423127
$116$	−0.233790	−0.0217068
$117$	−17.4797	−1.61600
$118$	−0.302742	−0.0278697
$119$	−2.59369	−0.237763
$120$	−0.103424	−0.00944131
$121$	20.1849	1.83499
$122$	−8.08067	−0.731589
$123$	0.353820	0.0319029
$124$	8.85996	0.795648
$125$	−1.00000	−0.0894427
$126$	5.50872	0.490756
$127$	14.6808	1.30271	0.651356	−	0.758772i	$-0.274200\pi$
$127$	14.6808	1.30271	0.651356	+	0.758772i	$0.274200\pi$
$128$	−1.00000	−0.0883883
$129$	0.0350061	0.00308212
$130$	5.84741	0.512852
$131$	−10.9274	−0.954732	−0.477366	−	0.878705i	$-0.658408\pi$
$131$	−10.9274	−0.954732	−0.477366	+	0.878705i	$0.658408\pi$
$132$	−0.577557	−0.0502699
$133$	−1.14799	−0.0995430
$134$	12.5965	1.08817
$135$	−0.619440	−0.0533129
$136$	1.40746	0.120689
$137$	15.6029	1.33305	0.666525	−	0.745483i	$-0.267781\pi$
$137$	15.6029	1.33305	0.666525	+	0.745483i	$0.267781\pi$
$138$	−0.469292	−0.0399488
$139$	−14.2313	−1.20708	−0.603541	−	0.797332i	$-0.706244\pi$
$139$	−14.2313	−1.20708	−0.603541	+	0.797332i	$0.706244\pi$
$140$	−1.84281	−0.155746
$141$	−1.26878	−0.106851
$142$	6.23114	0.522906
$143$	32.6540	2.73066
$144$	−2.98930	−0.249109
$145$	0.233790	0.0194152
$146$	−0.619738	−0.0512899
$147$	0.372747	0.0307436
$148$	6.90832	0.567860
$149$	8.31344	0.681063	0.340532	−	0.940233i	$-0.389393\pi$
$149$	8.31344	0.681063	0.340532	+	0.940233i	$0.389393\pi$
$150$	0.103424	0.00844457
$151$	6.52536	0.531026	0.265513	−	0.964107i	$-0.414459\pi$
$151$	6.52536	0.531026	0.265513	+	0.964107i	$0.414459\pi$
$152$	0.622954	0.0505283
$153$	4.20734	0.340143
$154$	−10.2909	−0.829263
$155$	−8.85996	−0.711649
$156$	−0.604765	−0.0484200
$157$	9.02016	0.719887	0.359944	−	0.932974i	$-0.382796\pi$
$157$	9.02016	0.719887	0.359944	+	0.932974i	$0.382796\pi$
$158$	10.6948	0.850830
$159$	−0.0252778	−0.00200466
$160$	1.00000	0.0790569
$161$	−8.36181	−0.659003
$162$	−8.90384	−0.699552
$163$	−3.69813	−0.289660	−0.144830	−	0.989457i	$-0.546263\pi$
$163$	−3.69813	−0.289660	−0.144830	+	0.989457i	$0.546263\pi$
$164$	−3.42105	−0.267139
$165$	0.577557	0.0449628
$166$	10.0340	0.778791
$167$	22.1308	1.71253	0.856267	−	0.516533i	$-0.172778\pi$
$167$	22.1308	1.71253	0.856267	+	0.516533i	$0.172778\pi$
$168$	0.190592	0.0147045
$169$	21.1922	1.63017
$170$	−1.40746	−0.107948
$171$	1.86220	0.142406
$172$	−0.338471	−0.0258082
$173$	−22.7335	−1.72840	−0.864198	−	0.503153i	$-0.832173\pi$
$173$	−22.7335	−1.72840	−0.864198	+	0.503153i	$0.832173\pi$
$174$	−0.0241796	−0.00183305
$175$	1.84281	0.139303
$176$	5.58434	0.420936
$177$	−0.0313109	−0.00235347
$178$	8.22681	0.616625
$179$	17.6250	1.31735	0.658677	−	0.752426i	$-0.271116\pi$
$179$	17.6250	1.31735	0.658677	+	0.752426i	$0.271116\pi$
$180$	2.98930	0.222810
$181$	0.427412	0.0317693	0.0158847	−	0.999874i	$-0.494944\pi$
$181$	0.427412	0.0317693	0.0158847	+	0.999874i	$0.494944\pi$
$182$	−10.7757	−0.798746
$183$	−0.835739	−0.0617796
$184$	4.53753	0.334511
$185$	−6.90832	−0.507910
$186$	0.916336	0.0671890
$187$	−7.85976	−0.574762
$188$	12.2677	0.894716
$189$	1.14151	0.0830327
$190$	−0.622954	−0.0451938
$191$	2.32607	0.168308	0.0841541	−	0.996453i	$-0.473181\pi$
$191$	2.32607	0.168308	0.0841541	+	0.996453i	$0.473181\pi$
$192$	−0.103424	−0.00746401
$193$	2.51926	0.181341	0.0906703	−	0.995881i	$-0.471099\pi$
$193$	2.51926	0.181341	0.0906703	+	0.995881i	$0.471099\pi$
$194$	−0.417650	−0.0299855
$195$	0.604765	0.0433081
$196$	−3.60405	−0.257432
$197$	−18.6715	−1.33029	−0.665145	−	0.746714i	$-0.731630\pi$
$197$	−18.6715	−1.33029	−0.665145	+	0.746714i	$0.731630\pi$
$198$	16.6933	1.18634
$199$	−22.8015	−1.61635	−0.808176	−	0.588941i	$-0.799545\pi$
$199$	−22.8015	−1.61635	−0.808176	+	0.588941i	$0.799545\pi$
$200$	−1.00000	−0.0707107
$201$	1.30279	0.0918916
$202$	−1.96069	−0.137954
$203$	−0.430830	−0.0302383
$204$	0.145566	0.0101917
$205$	3.42105	0.238936
$206$	−11.7954	−0.821828
$207$	13.5641	0.942767
$208$	5.84741	0.405445
$209$	−3.47879	−0.240633
$210$	−0.190592	−0.0131521
$211$	−4.73586	−0.326030	−0.163015	−	0.986624i	$-0.552122\pi$
$211$	−4.73586	−0.326030	−0.163015	+	0.986624i	$0.552122\pi$
$212$	0.244408	0.0167860
$213$	0.644452	0.0441571
$214$	3.70774	0.253456
$215$	0.338471	0.0230835
$216$	−0.619440	−0.0421476
$217$	16.3272	1.10836
$218$	−7.98563	−0.540855
$219$	−0.0640960	−0.00433121
$220$	−5.58434	−0.376496
$221$	−8.23002	−0.553611
$222$	0.714489	0.0479533
$223$	19.2328	1.28792	0.643962	−	0.765057i	$-0.277289\pi$
$223$	19.2328	1.28792	0.643962	+	0.765057i	$0.277289\pi$
$224$	−1.84281	−0.123128
$225$	−2.98930	−0.199287
$226$	−3.28552	−0.218550
$227$	−0.191081	−0.0126825	−0.00634126	−	0.999980i	$-0.502018\pi$
$227$	−0.191081	−0.0126825	−0.00634126	+	0.999980i	$0.502018\pi$
$228$	0.0644287	0.00426689
$229$	23.7962	1.57250	0.786249	−	0.617910i	$-0.212020\pi$
$229$	23.7962	1.57250	0.786249	+	0.617910i	$0.212020\pi$
$230$	−4.53753	−0.299196
$231$	−1.06433	−0.0700277
$232$	0.233790	0.0153490
$233$	8.35023	0.547042	0.273521	−	0.961866i	$-0.411812\pi$
$233$	8.35023	0.547042	0.273521	+	0.961866i	$0.411812\pi$
$234$	17.4797	1.14268
$235$	−12.2677	−0.800258
$236$	0.302742	0.0197068
$237$	1.10610	0.0718489
$238$	2.59369	0.168124
$239$	11.7813	0.762068	0.381034	−	0.924561i	$-0.375568\pi$
$239$	11.7813	0.762068	0.381034	+	0.924561i	$0.375568\pi$
$240$	0.103424	0.00667602
$241$	−15.3809	−0.990768	−0.495384	−	0.868674i	$-0.664973\pi$
$241$	−15.3809	−0.990768	−0.495384	+	0.868674i	$0.664973\pi$
$242$	−20.1849	−1.29753
$243$	−2.77920	−0.178285
$244$	8.08067	0.517312
$245$	3.60405	0.230254
$246$	−0.353820	−0.0225587
$247$	−3.64267	−0.231778
$248$	−8.85996	−0.562608
$249$	1.03776	0.0657656
$250$	1.00000	0.0632456
$251$	−0.326757	−0.0206247	−0.0103123	−	0.999947i	$-0.503283\pi$
$251$	−0.326757	−0.0206247	−0.0103123	+	0.999947i	$0.503283\pi$
$252$	−5.50872	−0.347017
$253$	−25.3391	−1.59306
$254$	−14.6808	−0.921157
$255$	−0.145566	−0.00911570
$256$	1.00000	0.0625000
$257$	28.9582	1.80636	0.903181	−	0.429260i	$-0.141226\pi$
$257$	28.9582	1.80636	0.903181	+	0.429260i	$0.141226\pi$
$258$	−0.0350061	−0.00217939
$259$	12.7307	0.791048
$260$	−5.84741	−0.362641
$261$	0.698868	0.0432589
$262$	10.9274	0.675097
$263$	7.09764	0.437659	0.218830	−	0.975763i	$-0.429776\pi$
$263$	7.09764	0.437659	0.218830	+	0.975763i	$0.429776\pi$
$264$	0.577557	0.0355462
$265$	−0.244408	−0.0150139
$266$	1.14799	0.0703876
$267$	0.850853	0.0520714
$268$	−12.5965	−0.769455
$269$	22.3362	1.36187	0.680933	−	0.732346i	$-0.261575\pi$
$269$	22.3362	1.36187	0.680933	+	0.732346i	$0.261575\pi$
$270$	0.619440	0.0376979
$271$	13.5780	0.824806	0.412403	−	0.911001i	$-0.364690\pi$
$271$	13.5780	0.824806	0.412403	+	0.911001i	$0.364690\pi$
$272$	−1.40746	−0.0853400
$273$	−1.11447	−0.0674507
$274$	−15.6029	−0.942609
$275$	5.58434	0.336749
$276$	0.469292	0.0282480
$277$	−8.24630	−0.495472	−0.247736	−	0.968828i	$-0.579687\pi$
$277$	−8.24630	−0.495472	−0.247736	+	0.968828i	$0.579687\pi$
$278$	14.2313	0.853536
$279$	−26.4851	−1.58562
$280$	1.84281	0.110129
$281$	−8.35119	−0.498190	−0.249095	−	0.968479i	$-0.580133\pi$
$281$	−8.35119	−0.498190	−0.249095	+	0.968479i	$0.580133\pi$
$282$	1.26878	0.0755549
$283$	19.4605	1.15681	0.578403	−	0.815751i	$-0.303676\pi$
$283$	19.4605	1.15681	0.578403	+	0.815751i	$0.303676\pi$
$284$	−6.23114	−0.369750
$285$	−0.0644287	−0.00381643
$286$	−32.6540	−1.93087
$287$	−6.30434	−0.372134
$288$	2.98930	0.176146
$289$	−15.0190	−0.883473
$290$	−0.233790	−0.0137286
$291$	−0.0431952	−0.00253215
$292$	0.619738	0.0362674
$293$	−1.45627	−0.0850764	−0.0425382	−	0.999095i	$-0.513544\pi$
$293$	−1.45627	−0.0850764	−0.0425382	+	0.999095i	$0.513544\pi$
$294$	−0.372747	−0.0217390
$295$	−0.302742	−0.0176263
$296$	−6.90832	−0.401538
$297$	3.45917	0.200721
$298$	−8.31344	−0.481584
$299$	−26.5328	−1.53443
$300$	−0.103424	−0.00597121
$301$	−0.623737	−0.0359516
$302$	−6.52536	−0.375492
$303$	−0.202784	−0.0116496
$304$	−0.622954	−0.0357289
$305$	−8.08067	−0.462698
$306$	−4.20734	−0.240517
$307$	26.6408	1.52047	0.760234	−	0.649649i	$-0.225084\pi$
$307$	26.6408	1.52047	0.760234	+	0.649649i	$0.225084\pi$
$308$	10.2909	0.586377
$309$	−1.21994	−0.0693998
$310$	8.85996	0.503212
$311$	−0.850180	−0.0482093	−0.0241047	−	0.999709i	$-0.507673\pi$
$311$	−0.850180	−0.0482093	−0.0241047	+	0.999709i	$0.507673\pi$
$312$	0.604765	0.0342381
$313$	25.7403	1.45493	0.727463	−	0.686147i	$-0.240699\pi$
$313$	25.7403	1.45493	0.727463	+	0.686147i	$0.240699\pi$
$314$	−9.02016	−0.509037
$315$	5.50872	0.310381
$316$	−10.6948	−0.601628
$317$	−30.3884	−1.70678	−0.853390	−	0.521272i	$-0.825458\pi$
$317$	−30.3884	−1.70678	−0.853390	+	0.521272i	$0.825458\pi$
$318$	0.0252778	0.00141751
$319$	−1.30556	−0.0730974
$320$	−1.00000	−0.0559017
$321$	0.383471	0.0214033
$322$	8.36181	0.465985
$323$	0.876785	0.0487856
$324$	8.90384	0.494658
$325$	5.84741	0.324356
$326$	3.69813	0.204820
$327$	−0.825909	−0.0456729
$328$	3.42105	0.188896
$329$	22.6071	1.24637
$330$	−0.577557	−0.0317935
$331$	−20.3547	−1.11879	−0.559396	−	0.828900i	$-0.688967\pi$
$331$	−20.3547	−1.11879	−0.559396	+	0.828900i	$0.688967\pi$
$332$	−10.0340	−0.550689
$333$	−20.6511	−1.13167
$334$	−22.1308	−1.21094
$335$	12.5965	0.688222
$336$	−0.190592	−0.0103976
$337$	−1.39241	−0.0758493	−0.0379247	−	0.999281i	$-0.512075\pi$
$337$	−1.39241	−0.0758493	−0.0379247	+	0.999281i	$0.512075\pi$
$338$	−21.1922	−1.15271
$339$	−0.339803	−0.0184556
$340$	1.40746	0.0763304
$341$	49.4770	2.67933
$342$	−1.86220	−0.100696
$343$	−19.5413	−1.05513
$344$	0.338471	0.0182491
$345$	−0.469292	−0.0252658
$346$	22.7335	1.22216
$347$	11.2816	0.605630	0.302815	−	0.953049i	$-0.402074\pi$
$347$	11.2816	0.605630	0.302815	+	0.953049i	$0.402074\pi$
$348$	0.0241796	0.00129616
$349$	7.95625	0.425888	0.212944	−	0.977064i	$-0.431695\pi$
$349$	7.95625	0.425888	0.212944	+	0.977064i	$0.431695\pi$
$350$	−1.84281	−0.0985023
$351$	3.62212	0.193335
$352$	−5.58434	−0.297646
$353$	32.4714	1.72828	0.864140	−	0.503251i	$-0.167863\pi$
$353$	32.4714	1.72828	0.864140	+	0.503251i	$0.167863\pi$
$354$	0.0313109	0.00166416
$355$	6.23114	0.330715
$356$	−8.22681	−0.436020
$357$	0.268251	0.0141973
$358$	−17.6250	−0.931510
$359$	−17.2949	−0.912790	−0.456395	−	0.889777i	$-0.650860\pi$
$359$	−17.2949	−0.912790	−0.456395	+	0.889777i	$0.650860\pi$
$360$	−2.98930	−0.157550
$361$	−18.6119	−0.979575
$362$	−0.427412	−0.0224643
$363$	−2.08761	−0.109571
$364$	10.7757	0.564799
$365$	−0.619738	−0.0324386
$366$	0.835739	0.0436848
$367$	11.9713	0.624898	0.312449	−	0.949935i	$-0.398851\pi$
$367$	11.9713	0.624898	0.312449	+	0.949935i	$0.398851\pi$
$368$	−4.53753	−0.236535
$369$	10.2266	0.532373
$370$	6.90832	0.359146
$371$	0.450398	0.0233835
$372$	−0.916336	−0.0475098
$373$	35.7825	1.85275	0.926374	−	0.376605i	$-0.122908\pi$
$373$	35.7825	1.85275	0.926374	+	0.376605i	$0.122908\pi$
$374$	7.85976	0.406418
$375$	0.103424	0.00534081
$376$	−12.2677	−0.632660
$377$	−1.36706	−0.0704074
$378$	−1.14151	−0.0587130
$379$	−15.3396	−0.787945	−0.393972	−	0.919122i	$-0.628899\pi$
$379$	−15.3396	−0.787945	−0.393972	+	0.919122i	$0.628899\pi$
$380$	0.622954	0.0319569
$381$	−1.51836	−0.0777877
$382$	−2.32607	−0.119012
$383$	9.62976	0.492058	0.246029	−	0.969262i	$-0.420874\pi$
$383$	9.62976	0.492058	0.246029	+	0.969262i	$0.420874\pi$
$384$	0.103424	0.00527786
$385$	−10.2909	−0.524472
$386$	−2.51926	−0.128227
$387$	1.01179	0.0514323
$388$	0.417650	0.0212030
$389$	35.0354	1.77636	0.888182	−	0.459492i	$-0.151969\pi$
$389$	35.0354	1.77636	0.888182	+	0.459492i	$0.151969\pi$
$390$	−0.604765	−0.0306235
$391$	6.38641	0.322975
$392$	3.60405	0.182032
$393$	1.13016	0.0570091
$394$	18.6715	0.940657
$395$	10.6948	0.538112
$396$	−16.6933	−0.838870
$397$	35.3610	1.77472	0.887358	−	0.461081i	$-0.152538\pi$
$397$	35.3610	1.77472	0.887358	+	0.461081i	$0.152538\pi$
$398$	22.8015	1.14293
$399$	0.118730	0.00594393
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.30279	−0.0649772
$403$	51.8078	2.58073
$404$	1.96069	0.0975482
$405$	−8.90384	−0.442436
$406$	0.430830	0.0213817
$407$	38.5784	1.91226
$408$	−0.145566	−0.00720660
$409$	−4.13679	−0.204551	−0.102276	−	0.994756i	$-0.532612\pi$
$409$	−4.13679	−0.204551	−0.102276	+	0.994756i	$0.532612\pi$
$410$	−3.42105	−0.168954
$411$	−1.61373	−0.0795992
$412$	11.7954	0.581120
$413$	0.557896	0.0274523
$414$	−13.5641	−0.666637
$415$	10.0340	0.492551
$416$	−5.84741	−0.286693
$417$	1.47186	0.0720775
$418$	3.47879	0.170153
$419$	−19.0120	−0.928799	−0.464399	−	0.885626i	$-0.653730\pi$
$419$	−19.0120	−0.928799	−0.464399	+	0.885626i	$0.653730\pi$
$420$	0.190592	0.00929992
$421$	5.59225	0.272549	0.136275	−	0.990671i	$-0.456487\pi$
$421$	5.59225	0.272549	0.136275	+	0.990671i	$0.456487\pi$
$422$	4.73586	0.230538
$423$	−36.6719	−1.78305
$424$	−0.244408	−0.0118695
$425$	−1.40746	−0.0682720
$426$	−0.644452	−0.0312238
$427$	14.8911	0.720633
$428$	−3.70774	−0.179221
$429$	−3.37722	−0.163054
$430$	−0.338471	−0.0163225
$431$	−7.71770	−0.371749	−0.185874	−	0.982574i	$-0.559512\pi$
$431$	−7.71770	−0.371749	−0.185874	+	0.982574i	$0.559512\pi$
$432$	0.619440	0.0298028
$433$	−13.4278	−0.645299	−0.322650	−	0.946518i	$-0.604574\pi$
$433$	−13.4278	−0.645299	−0.322650	+	0.946518i	$0.604574\pi$
$434$	−16.3272	−0.783732
$435$	−0.0241796	−0.00115932
$436$	7.98563	0.382442
$437$	2.82667	0.135218
$438$	0.0640960	0.00306263
$439$	26.3252	1.25643	0.628216	−	0.778039i	$-0.283785\pi$
$439$	26.3252	1.25643	0.628216	+	0.778039i	$0.283785\pi$
$440$	5.58434	0.266223
$441$	10.7736	0.513029
$442$	8.23002	0.391462
$443$	21.7024	1.03111	0.515556	−	0.856856i	$-0.327585\pi$
$443$	21.7024	1.03111	0.515556	+	0.856856i	$0.327585\pi$
$444$	−0.714489	−0.0339081
$445$	8.22681	0.389988
$446$	−19.2328	−0.910700
$447$	−0.859812	−0.0406677
$448$	1.84281	0.0870646
$449$	−20.5440	−0.969530	−0.484765	−	0.874644i	$-0.661095\pi$
$449$	−20.5440	−0.969530	−0.484765	+	0.874644i	$0.661095\pi$
$450$	2.98930	0.140917
$451$	−19.1043	−0.899587
$452$	3.28552	0.154538
$453$	−0.674881	−0.0317087
$454$	0.191081	0.00896789
$455$	−10.7757	−0.505171
$456$	−0.0644287	−0.00301715
$457$	19.8374	0.927953	0.463976	−	0.885848i	$-0.346422\pi$
$457$	19.8374	0.927953	0.463976	+	0.885848i	$0.346422\pi$
$458$	−23.7962	−1.11192
$459$	−0.871840	−0.0406940
$460$	4.53753	0.211563
$461$	−37.5681	−1.74972	−0.874861	−	0.484373i	$-0.839048\pi$
$461$	−37.5681	−1.74972	−0.874861	+	0.484373i	$0.839048\pi$
$462$	1.06433	0.0495170
$463$	−1.21270	−0.0563588	−0.0281794	−	0.999603i	$-0.508971\pi$
$463$	−1.21270	−0.0563588	−0.0281794	+	0.999603i	$0.508971\pi$
$464$	−0.233790	−0.0108534
$465$	0.916336	0.0424941
$466$	−8.35023	−0.386817
$467$	29.4819	1.36426	0.682131	−	0.731230i	$-0.261054\pi$
$467$	29.4819	1.36426	0.682131	+	0.731230i	$0.261054\pi$
$468$	−17.4797	−0.807999
$469$	−23.2130	−1.07188
$470$	12.2677	0.565868
$471$	−0.932905	−0.0429860
$472$	−0.302742	−0.0139348
$473$	−1.89014	−0.0869086
$474$	−1.10610	−0.0508049
$475$	−0.622954	−0.0285831
$476$	−2.59369	−0.118881
$477$	−0.730610	−0.0334523
$478$	−11.7813	−0.538863
$479$	−2.58826	−0.118261	−0.0591304	−	0.998250i	$-0.518833\pi$
$479$	−2.58826	−0.118261	−0.0591304	+	0.998250i	$0.518833\pi$
$480$	−0.103424	−0.00472066
$481$	40.3958	1.84189
$482$	15.3809	0.700579
$483$	0.864815	0.0393505
$484$	20.1849	0.917495
$485$	−0.417650	−0.0189645
$486$	2.77920	0.126067
$487$	−10.9716	−0.497170	−0.248585	−	0.968610i	$-0.579965\pi$
$487$	−10.9716	−0.497170	−0.248585	+	0.968610i	$0.579965\pi$
$488$	−8.08067	−0.365795
$489$	0.382477	0.0172962
$490$	−3.60405	−0.162814
$491$	16.8735	0.761492	0.380746	−	0.924680i	$-0.375667\pi$
$491$	16.8735	0.761492	0.380746	+	0.924680i	$0.375667\pi$
$492$	0.353820	0.0159514
$493$	0.329050	0.0148197
$494$	3.64267	0.163892
$495$	16.6933	0.750308
$496$	8.85996	0.397824
$497$	−11.4828	−0.515074
$498$	−1.03776	−0.0465033
$499$	−30.8906	−1.38286	−0.691428	−	0.722446i	$-0.743018\pi$
$499$	−30.8906	−1.38286	−0.691428	+	0.722446i	$0.743018\pi$
$500$	−1.00000	−0.0447214
$501$	−2.28887	−0.102259
$502$	0.326757	0.0145839
$503$	−17.2230	−0.767934	−0.383967	−	0.923347i	$-0.625442\pi$
$503$	−17.2230	−0.767934	−0.383967	+	0.923347i	$0.625442\pi$
$504$	5.50872	0.245378
$505$	−1.96069	−0.0872497
$506$	25.3391	1.12646
$507$	−2.19180	−0.0973411
$508$	14.6808	0.651356
$509$	9.05332	0.401281	0.200641	−	0.979665i	$-0.435698\pi$
$509$	9.05332	0.401281	0.200641	+	0.979665i	$0.435698\pi$
$510$	0.145566	0.00644578
$511$	1.14206	0.0505217
$512$	−1.00000	−0.0441942
$513$	−0.385883	−0.0170371
$514$	−28.9582	−1.27729
$515$	−11.7954	−0.519769
$516$	0.0350061	0.00154106
$517$	68.5072	3.01294
$518$	−12.7307	−0.559356
$519$	2.35120	0.103206
$520$	5.84741	0.256426
$521$	−14.5636	−0.638044	−0.319022	−	0.947747i	$-0.603354\pi$
$521$	−14.5636	−0.638044	−0.319022	+	0.947747i	$0.603354\pi$
$522$	−0.698868	−0.0305886
$523$	16.6986	0.730178	0.365089	−	0.930973i	$-0.381038\pi$
$523$	16.6986	0.730178	0.365089	+	0.930973i	$0.381038\pi$
$524$	−10.9274	−0.477366
$525$	−0.190592	−0.00831810
$526$	−7.09764	−0.309472
$527$	−12.4701	−0.543205
$528$	−0.577557	−0.0251350
$529$	−2.41081	−0.104818
$530$	0.244408	0.0106164
$531$	−0.904988	−0.0392731
$532$	−1.14799	−0.0497715
$533$	−20.0043	−0.866482
$534$	−0.850853	−0.0368200
$535$	3.70774	0.160300
$536$	12.5965	0.544087
$537$	−1.82286	−0.0786620
$538$	−22.3362	−0.962984
$539$	−20.1263	−0.866899
$540$	−0.619440	−0.0266565
$541$	−13.8672	−0.596199	−0.298099	−	0.954535i	$-0.596353\pi$
$541$	−13.8672	−0.596199	−0.298099	+	0.954535i	$0.596353\pi$
$542$	−13.5780	−0.583226
$543$	−0.0442049	−0.00189701
$544$	1.40746	0.0603445
$545$	−7.98563	−0.342067
$546$	1.11447	0.0476948
$547$	44.5261	1.90380	0.951899	−	0.306412i	$-0.0991286\pi$
$547$	44.5261	1.90380	0.951899	+	0.306412i	$0.0991286\pi$
$548$	15.6029	0.666525
$549$	−24.1556	−1.03093
$550$	−5.58434	−0.238117
$551$	0.145640	0.00620448
$552$	−0.469292	−0.0199744
$553$	−19.7084	−0.838087
$554$	8.24630	0.350352
$555$	0.714489	0.0303284
$556$	−14.2313	−0.603541
$557$	12.5161	0.530323	0.265162	−	0.964204i	$-0.414575\pi$
$557$	12.5161	0.530323	0.265162	+	0.964204i	$0.414575\pi$
$558$	26.4851	1.12120
$559$	−1.97918	−0.0837103
$560$	−1.84281	−0.0778729
$561$	0.812891	0.0343203
$562$	8.35119	0.352274
$563$	−32.6226	−1.37488	−0.687439	−	0.726242i	$-0.741265\pi$
$563$	−32.6226	−1.37488	−0.687439	+	0.726242i	$0.741265\pi$
$564$	−1.26878	−0.0534254
$565$	−3.28552	−0.138223
$566$	−19.4605	−0.817985
$567$	16.4081	0.689075
$568$	6.23114	0.261453
$569$	−32.7365	−1.37239	−0.686193	−	0.727420i	$-0.740719\pi$
$569$	−32.7365	−1.37239	−0.686193	+	0.727420i	$0.740719\pi$
$570$	0.0644287	0.00269862
$571$	2.26358	0.0947280	0.0473640	−	0.998878i	$-0.484918\pi$
$571$	2.26358	0.0947280	0.0473640	+	0.998878i	$0.484918\pi$
$572$	32.6540	1.36533
$573$	−0.240572	−0.0100500
$574$	6.30434	0.263138
$575$	−4.53753	−0.189228
$576$	−2.98930	−0.124554
$577$	−12.0269	−0.500685	−0.250342	−	0.968157i	$-0.580543\pi$
$577$	−12.0269	−0.500685	−0.250342	+	0.968157i	$0.580543\pi$
$578$	15.0190	0.624710
$579$	−0.260553	−0.0108282
$580$	0.233790	0.00970759
$581$	−18.4908	−0.767128
$582$	0.0431952	0.00179050
$583$	1.36486	0.0565267
$584$	−0.619738	−0.0256449
$585$	17.4797	0.722696
$586$	1.45627	0.0601581
$587$	−44.1957	−1.82415	−0.912075	−	0.410023i	$-0.865521\pi$
$587$	−44.1957	−1.82415	−0.912075	+	0.410023i	$0.865521\pi$
$588$	0.372747	0.0153718
$589$	−5.51935	−0.227421
$590$	0.302742	0.0124637
$591$	1.93109	0.0794345
$592$	6.90832	0.283930
$593$	22.6433	0.929848	0.464924	−	0.885351i	$-0.346082\pi$
$593$	22.6433	0.929848	0.464924	+	0.885351i	$0.346082\pi$
$594$	−3.45917	−0.141931
$595$	2.59369	0.106331
$596$	8.31344	0.340532
$597$	2.35823	0.0965158
$598$	26.5328	1.08501
$599$	−31.2829	−1.27818	−0.639092	−	0.769130i	$-0.720690\pi$
$599$	−31.2829	−1.27818	−0.639092	+	0.769130i	$0.720690\pi$
$600$	0.103424	0.00422228
$601$	−1.89067	−0.0771221	−0.0385610	−	0.999256i	$-0.512277\pi$
$601$	−1.89067	−0.0771221	−0.0385610	+	0.999256i	$0.512277\pi$
$602$	0.623737	0.0254216
$603$	37.6548	1.53342
$604$	6.52536	0.265513
$605$	−20.1849	−0.820632
$606$	0.202784	0.00823752
$607$	4.19582	0.170303	0.0851515	−	0.996368i	$-0.472863\pi$
$607$	4.19582	0.170303	0.0851515	+	0.996368i	$0.472863\pi$
$608$	0.622954	0.0252641
$609$	0.0445583	0.00180559
$610$	8.08067	0.327177
$611$	71.7345	2.90207
$612$	4.20734	0.170071
$613$	−17.5215	−0.707688	−0.353844	−	0.935305i	$-0.615126\pi$
$613$	−17.5215	−0.707688	−0.353844	+	0.935305i	$0.615126\pi$
$614$	−26.6408	−1.07513
$615$	−0.353820	−0.0142674
$616$	−10.2909	−0.414631
$617$	−25.7255	−1.03567	−0.517834	−	0.855481i	$-0.673262\pi$
$617$	−25.7255	−1.03567	−0.517834	+	0.855481i	$0.673262\pi$
$618$	1.21994	0.0490731
$619$	−18.3178	−0.736254	−0.368127	−	0.929776i	$-0.620001\pi$
$619$	−18.3178	−0.736254	−0.368127	+	0.929776i	$0.620001\pi$
$620$	−8.85996	−0.355824
$621$	−2.81073	−0.112791
$622$	0.850180	0.0340891
$623$	−15.1604	−0.607391
$624$	−0.604765	−0.0242100
$625$	1.00000	0.0400000
$626$	−25.7403	−1.02879
$627$	0.359792	0.0143687
$628$	9.02016	0.359944
$629$	−9.72320	−0.387690
$630$	−5.50872	−0.219473
$631$	26.2630	1.04551	0.522756	−	0.852482i	$-0.324904\pi$
$631$	26.2630	1.04551	0.522756	+	0.852482i	$0.324904\pi$
$632$	10.6948	0.425415
$633$	0.489803	0.0194679
$634$	30.3884	1.20688
$635$	−14.6808	−0.582591
$636$	−0.0252778	−0.00100233
$637$	−21.0744	−0.834997
$638$	1.30556	0.0516877
$639$	18.6268	0.736864
$640$	1.00000	0.0395285
$641$	−15.0907	−0.596046	−0.298023	−	0.954559i	$-0.596327\pi$
$641$	−15.0907	−0.596046	−0.298023	+	0.954559i	$0.596327\pi$
$642$	−0.383471	−0.0151344
$643$	−5.18335	−0.204411	−0.102206	−	0.994763i	$-0.532590\pi$
$643$	−5.18335	−0.204411	−0.102206	+	0.994763i	$0.532590\pi$
$644$	−8.36181	−0.329501
$645$	−0.0350061	−0.00137837
$646$	−0.876785	−0.0344967
$647$	−36.1888	−1.42273	−0.711365	−	0.702823i	$-0.751922\pi$
$647$	−36.1888	−1.42273	−0.711365	+	0.702823i	$0.751922\pi$
$648$	−8.90384	−0.349776
$649$	1.69062	0.0663625
$650$	−5.84741	−0.229354
$651$	−1.68863	−0.0661828
$652$	−3.69813	−0.144830
$653$	−47.3592	−1.85331	−0.926654	−	0.375914i	$-0.877329\pi$
$653$	−47.3592	−1.85331	−0.926654	+	0.375914i	$0.877329\pi$
$654$	0.825909	0.0322956
$655$	10.9274	0.426969
$656$	−3.42105	−0.133569
$657$	−1.85258	−0.0722762
$658$	−22.6071	−0.881316
$659$	49.2987	1.92040	0.960202	−	0.279307i	$-0.0901048\pi$
$659$	49.2987	1.92040	0.960202	+	0.279307i	$0.0901048\pi$
$660$	0.577557	0.0224814
$661$	−7.84117	−0.304986	−0.152493	−	0.988305i	$-0.548730\pi$
$661$	−7.84117	−0.304986	−0.152493	+	0.988305i	$0.548730\pi$
$662$	20.3547	0.791106
$663$	0.851185	0.0330573
$664$	10.0340	0.389396
$665$	1.14799	0.0445170
$666$	20.6511	0.800212
$667$	1.06083	0.0410754
$668$	22.1308	0.856267
$669$	−1.98914	−0.0769047
$670$	−12.5965	−0.486646
$671$	45.1252	1.74204
$672$	0.190592	0.00735223
$673$	9.49213	0.365895	0.182947	−	0.983123i	$-0.441436\pi$
$673$	9.49213	0.365895	0.182947	+	0.983123i	$0.441436\pi$
$674$	1.39241	0.0536336
$675$	0.619440	0.0238423
$676$	21.1922	0.815086
$677$	−2.19599	−0.0843988	−0.0421994	−	0.999109i	$-0.513436\pi$
$677$	−2.19599	−0.0843988	−0.0421994	+	0.999109i	$0.513436\pi$
$678$	0.339803	0.0130501
$679$	0.769649	0.0295364
$680$	−1.40746	−0.0539738
$681$	0.0197625	0.000757300 0
$682$	−49.4770	−1.89457
$683$	30.8560	1.18067	0.590337	−	0.807157i	$-0.298995\pi$
$683$	30.8560	1.18067	0.590337	+	0.807157i	$0.298995\pi$
$684$	1.86220	0.0712030
$685$	−15.6029	−0.596158
$686$	19.5413	0.746088
$687$	−2.46111	−0.0938972
$688$	−0.338471	−0.0129041
$689$	1.42916	0.0544465
$690$	0.469292	0.0178656
$691$	44.8079	1.70457	0.852286	−	0.523076i	$-0.175216\pi$
$691$	44.8079	1.70457	0.852286	+	0.523076i	$0.175216\pi$
$692$	−22.7335	−0.864198
$693$	−30.7626	−1.16857
$694$	−11.2816	−0.428245
$695$	14.2313	0.539824
$696$	−0.0241796	−0.000916524 0
$697$	4.81500	0.182381
$698$	−7.95625	−0.301148
$699$	−0.863618	−0.0326650
$700$	1.84281	0.0696517
$701$	−10.8313	−0.409094	−0.204547	−	0.978857i	$-0.565572\pi$
$701$	−10.8313	−0.409094	−0.204547	+	0.978857i	$0.565572\pi$
$702$	−3.62212	−0.136708
$703$	−4.30357	−0.162312
$704$	5.58434	0.210468
$705$	1.26878	0.0477851
$706$	−32.4714	−1.22208
$707$	3.61319	0.135888
$708$	−0.0313109	−0.00117674
$709$	−24.1311	−0.906261	−0.453131	−	0.891444i	$-0.649693\pi$
$709$	−24.1311	−0.906261	−0.453131	+	0.891444i	$0.649693\pi$
$710$	−6.23114	−0.233851
$711$	31.9699	1.19897
$712$	8.22681	0.308313
$713$	−40.2023	−1.50559
$714$	−0.268251	−0.0100390
$715$	−32.6540	−1.22119
$716$	17.6250	0.658677
$717$	−1.21847	−0.0455047
$718$	17.2949	0.645440
$719$	−2.32974	−0.0868847	−0.0434423	−	0.999056i	$-0.513832\pi$
$719$	−2.32974	−0.0868847	−0.0434423	+	0.999056i	$0.513832\pi$
$720$	2.98930	0.111405
$721$	21.7368	0.809519
$722$	18.6119	0.692664
$723$	1.59076	0.0591609
$724$	0.427412	0.0158847
$725$	−0.233790	−0.00868273
$726$	2.08761	0.0774785
$727$	−46.6409	−1.72982	−0.864908	−	0.501930i	$-0.832623\pi$
$727$	−46.6409	−1.72982	−0.864908	+	0.501930i	$0.832623\pi$
$728$	−10.7757	−0.399373
$729$	−26.4241	−0.978670
$730$	0.619738	0.0229375
$731$	0.476385	0.0176197
$732$	−0.835739	−0.0308898
$733$	−4.52259	−0.167046	−0.0835228	−	0.996506i	$-0.526617\pi$
$733$	−4.52259	−0.167046	−0.0835228	+	0.996506i	$0.526617\pi$
$734$	−11.9713	−0.441870
$735$	−0.372747	−0.0137490
$736$	4.53753	0.167256
$737$	−70.3433	−2.59113
$738$	−10.2266	−0.376445
$739$	−52.2584	−1.92235	−0.961177	−	0.275931i	$-0.911014\pi$
$739$	−52.2584	−1.92235	−0.961177	+	0.275931i	$0.911014\pi$
$740$	−6.90832	−0.253955
$741$	0.376741	0.0138399
$742$	−0.450398	−0.0165346
$743$	−25.8513	−0.948391	−0.474196	−	0.880419i	$-0.657261\pi$
$743$	−25.8513	−0.948391	−0.474196	+	0.880419i	$0.657261\pi$
$744$	0.916336	0.0335945
$745$	−8.31344	−0.304581
$746$	−35.7825	−1.31009
$747$	29.9947	1.09745
$748$	−7.85976	−0.287381
$749$	−6.83267	−0.249660
$750$	−0.103424	−0.00377653
$751$	46.1498	1.68403	0.842016	−	0.539453i	$-0.181369\pi$
$751$	46.1498	1.68403	0.842016	+	0.539453i	$0.181369\pi$
$752$	12.2677	0.447358
$753$	0.0337946	0.00123154
$754$	1.36706	0.0497856
$755$	−6.52536	−0.237482
$756$	1.14151	0.0415163
$757$	−9.01429	−0.327630	−0.163815	−	0.986491i	$-0.552380\pi$
$757$	−9.01429	−0.327630	−0.163815	+	0.986491i	$0.552380\pi$
$758$	15.3396	0.557161
$759$	2.62068	0.0951248
$760$	−0.622954	−0.0225969
$761$	14.5194	0.526327	0.263164	−	0.964751i	$-0.415234\pi$
$761$	14.5194	0.526327	0.263164	+	0.964751i	$0.415234\pi$
$762$	1.51836	0.0550042
$763$	14.7160	0.532755
$764$	2.32607	0.0841541
$765$	−4.20734	−0.152117
$766$	−9.62976	−0.347937
$767$	1.77026	0.0639203
$768$	−0.103424	−0.00373201
$769$	9.16381	0.330455	0.165228	−	0.986255i	$-0.447164\pi$
$769$	9.16381	0.330455	0.165228	+	0.986255i	$0.447164\pi$
$770$	10.2909	0.370858
$771$	−2.99498	−0.107862
$772$	2.51926	0.0906703
$773$	14.9120	0.536346	0.268173	−	0.963371i	$-0.413580\pi$
$773$	14.9120	0.536346	0.268173	+	0.963371i	$0.413580\pi$
$774$	−1.01179	−0.0363681
$775$	8.85996	0.318259
$776$	−0.417650	−0.0149928
$777$	−1.31667	−0.0472352
$778$	−35.0354	−1.25608
$779$	2.13116	0.0763566
$780$	0.604765	0.0216541
$781$	−34.7968	−1.24513
$782$	−6.38641	−0.228378
$783$	−0.144819	−0.00517540
$784$	−3.60405	−0.128716
$785$	−9.02016	−0.321943
$786$	−1.13016	−0.0403115
$787$	−2.32070	−0.0827242	−0.0413621	−	0.999144i	$-0.513170\pi$
$787$	−2.32070	−0.0827242	−0.0413621	+	0.999144i	$0.513170\pi$
$788$	−18.6715	−0.665145
$789$	−0.734070	−0.0261336
$790$	−10.6948	−0.380503
$791$	6.05459	0.215277
$792$	16.6933	0.593170
$793$	47.2510	1.67793
$794$	−35.3610	−1.25491
$795$	0.0252778	0.000896510 0
$796$	−22.8015	−0.808176
$797$	−34.7709	−1.23165	−0.615825	−	0.787883i	$-0.711177\pi$
$797$	−34.7709	−1.23165	−0.615825	+	0.787883i	$0.711177\pi$
$798$	−0.118730	−0.00420299
$799$	−17.2664	−0.610840
$800$	−1.00000	−0.0353553
$801$	24.5924	0.868931
$802$	−1.00000	−0.0353112
$803$	3.46083	0.122130
$804$	1.30279	0.0459458
$805$	8.36181	0.294715
$806$	−51.8078	−1.82485
$807$	−2.31011	−0.0813198
$808$	−1.96069	−0.0689770
$809$	−44.0979	−1.55040	−0.775200	−	0.631716i	$-0.782351\pi$
$809$	−44.0979	−1.55040	−0.775200	+	0.631716i	$0.782351\pi$
$810$	8.90384	0.312849
$811$	−43.8783	−1.54078	−0.770388	−	0.637576i	$-0.779937\pi$
$811$	−43.8783	−1.54078	−0.770388	+	0.637576i	$0.779937\pi$
$812$	−0.430830	−0.0151192
$813$	−1.40430	−0.0492509
$814$	−38.5784	−1.35217
$815$	3.69813	0.129540
$816$	0.145566	0.00509583
$817$	0.210852	0.00737677
$818$	4.13679	0.144640
$819$	−32.2118	−1.12557
$820$	3.42105	0.119468
$821$	−15.4022	−0.537540	−0.268770	−	0.963204i	$-0.586617\pi$
$821$	−15.4022	−0.537540	−0.268770	+	0.963204i	$0.586617\pi$
$822$	1.61373	0.0562852
$823$	19.0671	0.664637	0.332319	−	0.943167i	$-0.392169\pi$
$823$	19.0671	0.664637	0.332319	+	0.943167i	$0.392169\pi$
$824$	−11.7954	−0.410914
$825$	−0.577557	−0.0201080
$826$	−0.557896	−0.0194117
$827$	−2.06639	−0.0718555	−0.0359277	−	0.999354i	$-0.511439\pi$
$827$	−2.06639	−0.0718555	−0.0359277	+	0.999354i	$0.511439\pi$
$828$	13.5641	0.471384
$829$	−5.87059	−0.203894	−0.101947	−	0.994790i	$-0.532507\pi$
$829$	−5.87059	−0.203894	−0.101947	+	0.994790i	$0.532507\pi$
$830$	−10.0340	−0.348286
$831$	0.852869	0.0295857
$832$	5.84741	0.202723
$833$	5.07257	0.175754
$834$	−1.47186	−0.0509665
$835$	−22.1308	−0.765869
$836$	−3.47879	−0.120316
$837$	5.48821	0.189700
$838$	19.0120	0.656760
$839$	−27.4663	−0.948243	−0.474121	−	0.880459i	$-0.657234\pi$
$839$	−27.4663	−0.948243	−0.474121	+	0.880459i	$0.657234\pi$
$840$	−0.190592	−0.00657603
$841$	−28.9453	−0.998115
$842$	−5.59225	−0.192722
$843$	0.863717	0.0297480
$844$	−4.73586	−0.163015
$845$	−21.1922	−0.729035
$846$	36.6719	1.26081
$847$	37.1969	1.27810
$848$	0.244408	0.00839301
$849$	−2.01269	−0.0690753
$850$	1.40746	0.0482756
$851$	−31.3467	−1.07455
$852$	0.644452	0.0220786
$853$	−5.11974	−0.175297	−0.0876483	−	0.996151i	$-0.527935\pi$
$853$	−5.11974	−0.175297	−0.0876483	+	0.996151i	$0.527935\pi$
$854$	−14.8911	−0.509564
$855$	−1.86220	−0.0636859
$856$	3.70774	0.126728
$857$	−5.25446	−0.179489	−0.0897445	−	0.995965i	$-0.528605\pi$
$857$	−5.25446	−0.179489	−0.0897445	+	0.995965i	$0.528605\pi$
$858$	3.37722	0.115296
$859$	56.9195	1.94207	0.971034	−	0.238942i	$-0.0768007\pi$
$859$	56.9195	1.94207	0.971034	+	0.238942i	$0.0768007\pi$
$860$	0.338471	0.0115418
$861$	0.652023	0.0222209
$862$	7.71770	0.262866
$863$	19.2227	0.654348	0.327174	−	0.944964i	$-0.393904\pi$
$863$	19.2227	0.654348	0.327174	+	0.944964i	$0.393904\pi$
$864$	−0.619440	−0.0210738
$865$	22.7335	0.772962
$866$	13.4278	0.456296
$867$	1.55334	0.0527541
$868$	16.3272	0.554182
$869$	−59.7233	−2.02597
$870$	0.0241796	0.000819764 0
$871$	−73.6571	−2.49578
$872$	−7.98563	−0.270427
$873$	−1.24848	−0.0422547
$874$	−2.82667	−0.0956137
$875$	−1.84281	−0.0622983
$876$	−0.0640960	−0.00216560
$877$	47.8341	1.61524	0.807621	−	0.589701i	$-0.200755\pi$
$877$	47.8341	1.61524	0.807621	+	0.589701i	$0.200755\pi$
$878$	−26.3252	−0.888432
$879$	0.150614	0.00508009
$880$	−5.58434	−0.188248
$881$	40.3090	1.35804	0.679022	−	0.734118i	$-0.262404\pi$
$881$	40.3090	1.35804	0.679022	+	0.734118i	$0.262404\pi$
$882$	−10.7736	−0.362766
$883$	9.97927	0.335829	0.167915	−	0.985802i	$-0.446297\pi$
$883$	9.97927	0.335829	0.167915	+	0.985802i	$0.446297\pi$
$884$	−8.23002	−0.276806
$885$	0.0313109	0.00105251
$886$	−21.7024	−0.729107
$887$	33.0464	1.10959	0.554794	−	0.831988i	$-0.312797\pi$
$887$	33.0464	1.10959	0.554794	+	0.831988i	$0.312797\pi$
$888$	0.714489	0.0239767
$889$	27.0540	0.907361
$890$	−8.22681	−0.275763
$891$	49.7221	1.66575
$892$	19.2328	0.643962
$893$	−7.64223	−0.255737
$894$	0.859812	0.0287564
$895$	−17.6250	−0.589139
$896$	−1.84281	−0.0615640
$897$	2.74414	0.0916242
$898$	20.5440	0.685561
$899$	−2.07137	−0.0690839
$900$	−2.98930	−0.0996434
$901$	−0.343996	−0.0114602
$902$	19.1043	0.636104
$903$	0.0645097	0.00214675
$904$	−3.28552	−0.109275
$905$	−0.427412	−0.0142077
$906$	0.674881	0.0224214
$907$	−0.290957	−0.00966106	−0.00483053	−	0.999988i	$-0.501538\pi$
$907$	−0.290957	−0.00966106	−0.00483053	+	0.999988i	$0.501538\pi$
$908$	−0.191081	−0.00634126
$909$	−5.86111	−0.194401
$910$	10.7757	0.357210
$911$	30.0330	0.995038	0.497519	−	0.867453i	$-0.334244\pi$
$911$	30.0330	0.995038	0.497519	+	0.867453i	$0.334244\pi$
$912$	0.0644287	0.00213345
$913$	−56.0334	−1.85444
$914$	−19.8374	−0.656162
$915$	0.835739	0.0276287
$916$	23.7962	0.786249
$917$	−20.1371	−0.664987
$918$	0.871840	0.0287750
$919$	16.4667	0.543188	0.271594	−	0.962412i	$-0.412449\pi$
$919$	16.4667	0.543188	0.271594	+	0.962412i	$0.412449\pi$
$920$	−4.53753	−0.149598
$921$	−2.75531	−0.0907904
$922$	37.5681	1.23724
$923$	−36.4361	−1.19931
$924$	−1.06433	−0.0350138
$925$	6.90832	0.227144
$926$	1.21270	0.0398517
$927$	−35.2602	−1.15810
$928$	0.233790	0.00767452
$929$	−30.8980	−1.01373	−0.506865	−	0.862025i	$-0.669196\pi$
$929$	−30.8980	−1.01373	−0.506865	+	0.862025i	$0.669196\pi$
$930$	−0.916336	−0.0300478
$931$	2.24516	0.0735821
$932$	8.35023	0.273521
$933$	0.0879294	0.00287868
$934$	−29.4819	−0.964678
$935$	7.85976	0.257042
$936$	17.4797	0.571342
$937$	9.99116	0.326397	0.163198	−	0.986593i	$-0.447819\pi$
$937$	9.99116	0.326397	0.163198	+	0.986593i	$0.447819\pi$
$938$	23.2130	0.757932
$939$	−2.66217	−0.0868767
$940$	−12.2677	−0.400129
$941$	39.8287	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$941$	39.8287	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$942$	0.932905	0.0303957
$943$	15.5231	0.505502
$944$	0.302742	0.00985342
$945$	−1.14151	−0.0371333
$946$	1.89014	0.0614536
$947$	4.47554	0.145436	0.0727178	−	0.997353i	$-0.476833\pi$
$947$	4.47554	0.145436	0.0727178	+	0.997353i	$0.476833\pi$
$948$	1.10610	0.0359245
$949$	3.62386	0.117636
$950$	0.622954	0.0202113
$951$	3.14290	0.101916
$952$	2.59369	0.0840619
$953$	−59.7560	−1.93569	−0.967843	−	0.251556i	$-0.919058\pi$
$953$	−59.7560	−1.93569	−0.967843	+	0.251556i	$0.919058\pi$
$954$	0.730610	0.0236544
$955$	−2.32607	−0.0752697
$956$	11.7813	0.381034
$957$	0.135027	0.00436480
$958$	2.58826	0.0836230
$959$	28.7533	0.928491
$960$	0.103424	0.00333801
$961$	47.4989	1.53222
$962$	−40.3958	−1.30241
$963$	11.0836	0.357163
$964$	−15.3809	−0.495384
$965$	−2.51926	−0.0810980
$966$	−0.864815	−0.0278250
$967$	−7.64288	−0.245778	−0.122889	−	0.992420i	$-0.539216\pi$
$967$	−7.64288	−0.245778	−0.122889	+	0.992420i	$0.539216\pi$
$968$	−20.1849	−0.648767
$969$	−0.0906810	−0.00291309
$970$	0.417650	0.0134099
$971$	28.5679	0.916789	0.458395	−	0.888749i	$-0.348425\pi$
$971$	28.5679	0.916789	0.458395	+	0.888749i	$0.348425\pi$
$972$	−2.77920	−0.0891427
$973$	−26.2256	−0.840753
$974$	10.9716	0.351552
$975$	−0.604765	−0.0193680
$976$	8.08067	0.258656
$977$	8.09895	0.259108	0.129554	−	0.991572i	$-0.458645\pi$
$977$	8.09895	0.259108	0.129554	+	0.991572i	$0.458645\pi$
$978$	−0.382477	−0.0122303
$979$	−45.9413	−1.46829
$980$	3.60405	0.115127
$981$	−23.8715	−0.762157
$982$	−16.8735	−0.538456
$983$	25.2147	0.804223	0.402111	−	0.915591i	$-0.368276\pi$
$983$	25.2147	0.804223	0.402111	+	0.915591i	$0.368276\pi$
$984$	−0.353820	−0.0112794
$985$	18.6715	0.594924
$986$	−0.329050	−0.0104791
$987$	−2.33812	−0.0744233
$988$	−3.64267	−0.115889
$989$	1.53582	0.0488363
$990$	−16.6933	−0.530548
$991$	−17.3009	−0.549580	−0.274790	−	0.961504i	$-0.588608\pi$
$991$	−17.3009	−0.549580	−0.274790	+	0.961504i	$0.588608\pi$
$992$	−8.85996	−0.281304
$993$	2.10517	0.0668055
$994$	11.4828	0.364212
$995$	22.8015	0.722855
$996$	1.03776	0.0328828
$997$	17.4042	0.551196	0.275598	−	0.961273i	$-0.411124\pi$
$997$	17.4042	0.551196	0.275598	+	0.961273i	$0.411124\pi$
$998$	30.8906	0.977826
$999$	4.27929	0.135391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.103424 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.103424 q^{6} +1.84281 q^{7} -1.00000 q^{8} -2.98930 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.103424 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.103424 q^{6} +1.84281 q^{7} -1.00000 q^{8} -2.98930 q^{9} +1.00000 q^{10} +5.58434 q^{11} -0.103424 q^{12} +5.84741 q^{13} -1.84281 q^{14} +0.103424 q^{15} +1.00000 q^{16} -1.40746 q^{17} +2.98930 q^{18} -0.622954 q^{19} -1.00000 q^{20} -0.190592 q^{21} -5.58434 q^{22} -4.53753 q^{23} +0.103424 q^{24} +1.00000 q^{25} -5.84741 q^{26} +0.619440 q^{27} +1.84281 q^{28} -0.233790 q^{29} -0.103424 q^{30} +8.85996 q^{31} -1.00000 q^{32} -0.577557 q^{33} +1.40746 q^{34} -1.84281 q^{35} -2.98930 q^{36} +6.90832 q^{37} +0.622954 q^{38} -0.604765 q^{39} +1.00000 q^{40} -3.42105 q^{41} +0.190592 q^{42} -0.338471 q^{43} +5.58434 q^{44} +2.98930 q^{45} +4.53753 q^{46} +12.2677 q^{47} -0.103424 q^{48} -3.60405 q^{49} -1.00000 q^{50} +0.145566 q^{51} +5.84741 q^{52} +0.244408 q^{53} -0.619440 q^{54} -5.58434 q^{55} -1.84281 q^{56} +0.0644287 q^{57} +0.233790 q^{58} +0.302742 q^{59} +0.103424 q^{60} +8.08067 q^{61} -8.85996 q^{62} -5.50872 q^{63} +1.00000 q^{64} -5.84741 q^{65} +0.577557 q^{66} -12.5965 q^{67} -1.40746 q^{68} +0.469292 q^{69} +1.84281 q^{70} -6.23114 q^{71} +2.98930 q^{72} +0.619738 q^{73} -6.90832 q^{74} -0.103424 q^{75} -0.622954 q^{76} +10.2909 q^{77} +0.604765 q^{78} -10.6948 q^{79} -1.00000 q^{80} +8.90384 q^{81} +3.42105 q^{82} -10.0340 q^{83} -0.190592 q^{84} +1.40746 q^{85} +0.338471 q^{86} +0.0241796 q^{87} -5.58434 q^{88} -8.22681 q^{89} -2.98930 q^{90} +10.7757 q^{91} -4.53753 q^{92} -0.916336 q^{93} -12.2677 q^{94} +0.622954 q^{95} +0.103424 q^{96} +0.417650 q^{97} +3.60405 q^{98} -16.6933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 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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