LMFDB - Embedded newform 2006.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 13x^{6} + 24x^{5} + 50x^{4} - 50x^{3} - 62x^{2} + 28x + 24 $ x^8 - 3x^7 - 13x^6 + 24x^5 + 50x^4 - 50x^3 - 62x^2 + 28*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.68716$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.82114 q^{3} +1.00000 q^{4} +3.81371 q^{5} -1.82114 q^{6} -0.872031 q^{7} +1.00000 q^{8} +0.316568 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.82114 q^{3} +1.00000 q^{4} +3.81371 q^{5} -1.82114 q^{6} -0.872031 q^{7} +1.00000 q^{8} +0.316568 q^{9} +3.81371 q^{10} +3.34426 q^{11} -1.82114 q^{12} -2.89421 q^{13} -0.872031 q^{14} -6.94532 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.316568 q^{18} +3.14746 q^{19} +3.81371 q^{20} +1.58809 q^{21} +3.34426 q^{22} -0.282862 q^{23} -1.82114 q^{24} +9.54438 q^{25} -2.89421 q^{26} +4.88692 q^{27} -0.872031 q^{28} +5.44261 q^{29} -6.94532 q^{30} +7.49403 q^{31} +1.00000 q^{32} -6.09038 q^{33} -1.00000 q^{34} -3.32567 q^{35} +0.316568 q^{36} +2.03027 q^{37} +3.14746 q^{38} +5.27077 q^{39} +3.81371 q^{40} -11.1496 q^{41} +1.58809 q^{42} -2.99212 q^{43} +3.34426 q^{44} +1.20730 q^{45} -0.282862 q^{46} +11.7026 q^{47} -1.82114 q^{48} -6.23956 q^{49} +9.54438 q^{50} +1.82114 q^{51} -2.89421 q^{52} -7.54064 q^{53} +4.88692 q^{54} +12.7540 q^{55} -0.872031 q^{56} -5.73197 q^{57} +5.44261 q^{58} -1.00000 q^{59} -6.94532 q^{60} +4.58010 q^{61} +7.49403 q^{62} -0.276057 q^{63} +1.00000 q^{64} -11.0377 q^{65} -6.09038 q^{66} -0.136011 q^{67} -1.00000 q^{68} +0.515132 q^{69} -3.32567 q^{70} +10.1868 q^{71} +0.316568 q^{72} -8.99122 q^{73} +2.03027 q^{74} -17.3817 q^{75} +3.14746 q^{76} -2.91630 q^{77} +5.27077 q^{78} -0.381218 q^{79} +3.81371 q^{80} -9.84949 q^{81} -11.1496 q^{82} +12.9494 q^{83} +1.58809 q^{84} -3.81371 q^{85} -2.99212 q^{86} -9.91179 q^{87} +3.34426 q^{88} +12.6471 q^{89} +1.20730 q^{90} +2.52384 q^{91} -0.282862 q^{92} -13.6477 q^{93} +11.7026 q^{94} +12.0035 q^{95} -1.82114 q^{96} -9.34304 q^{97} -6.23956 q^{98} +1.05869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * 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
$3$	−1.82114	−1.05144	−0.525719	−	0.850658i	$-0.676204\pi$
$3$	−1.82114	−1.05144	−0.525719	+	0.850658i	$0.676204\pi$
$4$	1.00000	0.500000
$5$	3.81371	1.70554	0.852771	−	0.522285i	$-0.174920\pi$
$5$	3.81371	1.70554	0.852771	+	0.522285i	$0.174920\pi$
$6$	−1.82114	−0.743479
$7$	−0.872031	−0.329597	−0.164798	−	0.986327i	$-0.552697\pi$
$7$	−0.872031	−0.329597	−0.164798	+	0.986327i	$0.552697\pi$
$8$	1.00000	0.353553
$9$	0.316568	0.105523
$10$	3.81371	1.20600
$11$	3.34426	1.00833	0.504166	−	0.863607i	$-0.331800\pi$
$11$	3.34426	1.00833	0.504166	+	0.863607i	$0.331800\pi$
$12$	−1.82114	−0.525719
$13$	−2.89421	−0.802709	−0.401354	−	0.915923i	$-0.631460\pi$
$13$	−2.89421	−0.802709	−0.401354	+	0.915923i	$0.631460\pi$
$14$	−0.872031	−0.233060
$15$	−6.94532	−1.79327
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.316568	0.0746159
$19$	3.14746	0.722076	0.361038	−	0.932551i	$-0.382422\pi$
$19$	3.14746	0.722076	0.361038	+	0.932551i	$0.382422\pi$
$20$	3.81371	0.852771
$21$	1.58809	0.346551
$22$	3.34426	0.712998
$23$	−0.282862	−0.0589807	−0.0294904	−	0.999565i	$-0.509388\pi$
$23$	−0.282862	−0.0589807	−0.0294904	+	0.999565i	$0.509388\pi$
$24$	−1.82114	−0.371740
$25$	9.54438	1.90888
$26$	−2.89421	−0.567601
$27$	4.88692	0.940488
$28$	−0.872031	−0.164798
$29$	5.44261	1.01067	0.505334	−	0.862924i	$-0.331369\pi$
$29$	5.44261	1.01067	0.505334	+	0.862924i	$0.331369\pi$
$30$	−6.94532	−1.26804
$31$	7.49403	1.34597	0.672984	−	0.739657i	$-0.265012\pi$
$31$	7.49403	1.34597	0.672984	+	0.739657i	$0.265012\pi$
$32$	1.00000	0.176777
$33$	−6.09038	−1.06020
$34$	−1.00000	−0.171499
$35$	−3.32567	−0.562141
$36$	0.316568	0.0527614
$37$	2.03027	0.333774	0.166887	−	0.985976i	$-0.446629\pi$
$37$	2.03027	0.333774	0.166887	+	0.985976i	$0.446629\pi$
$38$	3.14746	0.510585
$39$	5.27077	0.843999
$40$	3.81371	0.603000
$41$	−11.1496	−1.74128	−0.870639	−	0.491923i	$-0.836294\pi$
$41$	−11.1496	−1.74128	−0.870639	+	0.491923i	$0.836294\pi$
$42$	1.58809	0.245048
$43$	−2.99212	−0.456294	−0.228147	−	0.973627i	$-0.573267\pi$
$43$	−2.99212	−0.456294	−0.228147	+	0.973627i	$0.573267\pi$
$44$	3.34426	0.504166
$45$	1.20730	0.179974
$46$	−0.282862	−0.0417057
$47$	11.7026	1.70700	0.853501	−	0.521092i	$-0.174475\pi$
$47$	11.7026	1.70700	0.853501	+	0.521092i	$0.174475\pi$
$48$	−1.82114	−0.262860
$49$	−6.23956	−0.891366
$50$	9.54438	1.34978
$51$	1.82114	0.255011
$52$	−2.89421	−0.401354
$53$	−7.54064	−1.03579	−0.517893	−	0.855445i	$-0.673283\pi$
$53$	−7.54064	−1.03579	−0.517893	+	0.855445i	$0.673283\pi$
$54$	4.88692	0.665025
$55$	12.7540	1.71975
$56$	−0.872031	−0.116530
$57$	−5.73197	−0.759219
$58$	5.44261	0.714650
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−6.94532	−0.896636
$61$	4.58010	0.586421	0.293211	−	0.956048i	$-0.405276\pi$
$61$	4.58010	0.586421	0.293211	+	0.956048i	$0.405276\pi$
$62$	7.49403	0.951743
$63$	−0.276057	−0.0347800
$64$	1.00000	0.125000
$65$	−11.0377	−1.36905
$66$	−6.09038	−0.749674
$67$	−0.136011	−0.0166164	−0.00830822	−	0.999965i	$-0.502645\pi$
$67$	−0.136011	−0.0166164	−0.00830822	+	0.999965i	$0.502645\pi$
$68$	−1.00000	−0.121268
$69$	0.515132	0.0620146
$70$	−3.32567	−0.397494
$71$	10.1868	1.20895	0.604475	−	0.796624i	$-0.293383\pi$
$71$	10.1868	1.20895	0.604475	+	0.796624i	$0.293383\pi$
$72$	0.316568	0.0373079
$73$	−8.99122	−1.05234	−0.526171	−	0.850378i	$-0.676373\pi$
$73$	−8.99122	−1.05234	−0.526171	+	0.850378i	$0.676373\pi$
$74$	2.03027	0.236014
$75$	−17.3817	−2.00706
$76$	3.14746	0.361038
$77$	−2.91630	−0.332343
$78$	5.27077	0.596797
$79$	−0.381218	−0.0428903	−0.0214452	−	0.999770i	$-0.506827\pi$
$79$	−0.381218	−0.0428903	−0.0214452	+	0.999770i	$0.506827\pi$
$80$	3.81371	0.426386
$81$	−9.84949	−1.09439
$82$	−11.1496	−1.23127
$83$	12.9494	1.42138	0.710690	−	0.703506i	$-0.248383\pi$
$83$	12.9494	1.42138	0.710690	+	0.703506i	$0.248383\pi$
$84$	1.58809	0.173275
$85$	−3.81371	−0.413655
$86$	−2.99212	−0.322649
$87$	−9.91179	−1.06266
$88$	3.34426	0.356499
$89$	12.6471	1.34059	0.670293	−	0.742096i	$-0.266168\pi$
$89$	12.6471	1.34059	0.670293	+	0.742096i	$0.266168\pi$
$90$	1.20730	0.127261
$91$	2.52384	0.264570
$92$	−0.282862	−0.0294904
$93$	−13.6477	−1.41520
$94$	11.7026	1.20703
$95$	12.0035	1.23153
$96$	−1.82114	−0.185870
$97$	−9.34304	−0.948642	−0.474321	−	0.880352i	$-0.657306\pi$
$97$	−9.34304	−0.948642	−0.474321	+	0.880352i	$0.657306\pi$
$98$	−6.23956	−0.630291
$99$	1.05869	0.106402
$100$	9.54438	0.954438
$101$	2.85099	0.283684	0.141842	−	0.989889i	$-0.454698\pi$
$101$	2.85099	0.283684	0.141842	+	0.989889i	$0.454698\pi$
$102$	1.82114	0.180320
$103$	−3.84252	−0.378615	−0.189307	−	0.981918i	$-0.560624\pi$
$103$	−3.84252	−0.378615	−0.189307	+	0.981918i	$0.560624\pi$
$104$	−2.89421	−0.283800
$105$	6.05653	0.591057
$106$	−7.54064	−0.732411
$107$	9.55608	0.923821	0.461910	−	0.886927i	$-0.347164\pi$
$107$	9.55608	0.923821	0.461910	+	0.886927i	$0.347164\pi$
$108$	4.88692	0.470244
$109$	11.8952	1.13935	0.569676	−	0.821869i	$-0.307069\pi$
$109$	11.8952	1.13935	0.569676	+	0.821869i	$0.307069\pi$
$110$	12.7540	1.21605
$111$	−3.69741	−0.350942
$112$	−0.872031	−0.0823992
$113$	10.1593	0.955706	0.477853	−	0.878440i	$-0.341415\pi$
$113$	10.1593	0.955706	0.477853	+	0.878440i	$0.341415\pi$
$114$	−5.73197	−0.536849
$115$	−1.07875	−0.100594
$116$	5.44261	0.505334
$117$	−0.916214	−0.0847041
$118$	−1.00000	−0.0920575
$119$	0.872031	0.0799389
$120$	−6.94532	−0.634018
$121$	0.184063	0.0167330
$122$	4.58010	0.414662
$123$	20.3051	1.83085
$124$	7.49403	0.672984
$125$	17.3309	1.55013
$126$	−0.276057	−0.0245931
$127$	6.90568	0.612780	0.306390	−	0.951906i	$-0.400879\pi$
$127$	6.90568	0.612780	0.306390	+	0.951906i	$0.400879\pi$
$128$	1.00000	0.0883883
$129$	5.44909	0.479765
$130$	−11.0377	−0.968068
$131$	11.3864	0.994830	0.497415	−	0.867513i	$-0.334283\pi$
$131$	11.3864	0.994830	0.497415	+	0.867513i	$0.334283\pi$
$132$	−6.09038	−0.530099
$133$	−2.74468	−0.237994
$134$	−0.136011	−0.0117496
$135$	18.6373	1.60404
$136$	−1.00000	−0.0857493
$137$	−15.0865	−1.28893	−0.644465	−	0.764634i	$-0.722920\pi$
$137$	−15.0865	−1.28893	−0.644465	+	0.764634i	$0.722920\pi$
$138$	0.515132	0.0438510
$139$	−0.301722	−0.0255917	−0.0127958	−	0.999918i	$-0.504073\pi$
$139$	−0.301722	−0.0255917	−0.0127958	+	0.999918i	$0.504073\pi$
$140$	−3.32567	−0.281071
$141$	−21.3121	−1.79481
$142$	10.1868	0.854856
$143$	−9.67898	−0.809397
$144$	0.316568	0.0263807
$145$	20.7565	1.72374
$146$	−8.99122	−0.744119
$147$	11.3631	0.937216
$148$	2.03027	0.166887
$149$	16.5949	1.35951	0.679754	−	0.733440i	$-0.262087\pi$
$149$	16.5949	1.35951	0.679754	+	0.733440i	$0.262087\pi$
$150$	−17.3817	−1.41921
$151$	−19.2901	−1.56980	−0.784902	−	0.619620i	$-0.787287\pi$
$151$	−19.2901	−1.56980	−0.784902	+	0.619620i	$0.787287\pi$
$152$	3.14746	0.255292
$153$	−0.316568	−0.0255930
$154$	−2.91630	−0.235002
$155$	28.5801	2.29561
$156$	5.27077	0.422000
$157$	8.56288	0.683392	0.341696	−	0.939810i	$-0.388999\pi$
$157$	8.56288	0.683392	0.341696	+	0.939810i	$0.388999\pi$
$158$	−0.381218	−0.0303281
$159$	13.7326	1.08907
$160$	3.81371	0.301500
$161$	0.246664	0.0194399
$162$	−9.84949	−0.773849
$163$	−20.9542	−1.64126	−0.820628	−	0.571462i	$-0.806376\pi$
$163$	−20.9542	−1.64126	−0.820628	+	0.571462i	$0.806376\pi$
$164$	−11.1496	−0.870639
$165$	−23.2269	−1.80821
$166$	12.9494	1.00507
$167$	−2.37631	−0.183884	−0.0919421	−	0.995764i	$-0.529307\pi$
$167$	−2.37631	−0.183884	−0.0919421	+	0.995764i	$0.529307\pi$
$168$	1.58809	0.122524
$169$	−4.62356	−0.355658
$170$	−3.81371	−0.292498
$171$	0.996385	0.0761955
$172$	−2.99212	−0.228147
$173$	2.14829	0.163331	0.0816656	−	0.996660i	$-0.473976\pi$
$173$	2.14829	0.163331	0.0816656	+	0.996660i	$0.473976\pi$
$174$	−9.91179	−0.751411
$175$	−8.32299	−0.629159
$176$	3.34426	0.252083
$177$	1.82114	0.136886
$178$	12.6471	0.947938
$179$	−12.3511	−0.923167	−0.461583	−	0.887097i	$-0.652718\pi$
$179$	−12.3511	−0.923167	−0.461583	+	0.887097i	$0.652718\pi$
$180$	1.20730	0.0899868
$181$	16.9661	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$181$	16.9661	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$182$	2.52384	0.187079
$183$	−8.34102	−0.616586
$184$	−0.282862	−0.0208528
$185$	7.74284	0.569265
$186$	−13.6477	−1.00070
$187$	−3.34426	−0.244556
$188$	11.7026	0.853501
$189$	−4.26154	−0.309982
$190$	12.0035	0.870824
$191$	−5.91729	−0.428160	−0.214080	−	0.976816i	$-0.568675\pi$
$191$	−5.91729	−0.428160	−0.214080	+	0.976816i	$0.568675\pi$
$192$	−1.82114	−0.131430
$193$	−20.3361	−1.46383	−0.731913	−	0.681398i	$-0.761372\pi$
$193$	−20.3361	−1.46383	−0.731913	+	0.681398i	$0.761372\pi$
$194$	−9.34304	−0.670791
$195$	20.1012	1.43948
$196$	−6.23956	−0.445683
$197$	−0.0256642	−0.00182850	−0.000914251	−	1.00000i	$-0.500291\pi$
$197$	−0.0256642	−0.00182850	−0.000914251		1.00000i	$0.500291\pi$
$198$	1.05869	0.0752375
$199$	−25.6137	−1.81571	−0.907853	−	0.419288i	$-0.862280\pi$
$199$	−25.6137	−1.81571	−0.907853	+	0.419288i	$0.862280\pi$
$200$	9.54438	0.674889
$201$	0.247696	0.0174712
$202$	2.85099	0.200595
$203$	−4.74613	−0.333113
$204$	1.82114	0.127506
$205$	−42.5214	−2.96982
$206$	−3.84252	−0.267721
$207$	−0.0895450	−0.00622381
$208$	−2.89421	−0.200677
$209$	10.5259	0.728092
$210$	6.05653	0.417940
$211$	3.87815	0.266983	0.133491	−	0.991050i	$-0.457381\pi$
$211$	3.87815	0.266983	0.133491	+	0.991050i	$0.457381\pi$
$212$	−7.54064	−0.517893
$213$	−18.5516	−1.27114
$214$	9.55608	0.653240
$215$	−11.4111	−0.778229
$216$	4.88692	0.332513
$217$	−6.53503	−0.443627
$218$	11.8952	0.805644
$219$	16.3743	1.10647
$220$	12.7540	0.859876
$221$	2.89421	0.194686
$222$	−3.69741	−0.248154
$223$	−13.1275	−0.879085	−0.439542	−	0.898222i	$-0.644859\pi$
$223$	−13.1275	−0.879085	−0.439542	+	0.898222i	$0.644859\pi$
$224$	−0.872031	−0.0582650
$225$	3.02145	0.201430
$226$	10.1593	0.675786
$227$	−20.9808	−1.39255	−0.696273	−	0.717777i	$-0.745160\pi$
$227$	−20.9808	−1.39255	−0.696273	+	0.717777i	$0.745160\pi$
$228$	−5.73197	−0.379609
$229$	5.93166	0.391975	0.195988	−	0.980606i	$-0.437209\pi$
$229$	5.93166	0.391975	0.195988	+	0.980606i	$0.437209\pi$
$230$	−1.07875	−0.0711308
$231$	5.31100	0.349438
$232$	5.44261	0.357325
$233$	−15.0799	−0.987918	−0.493959	−	0.869485i	$-0.664451\pi$
$233$	−15.0799	−0.987918	−0.493959	+	0.869485i	$0.664451\pi$
$234$	−0.916214	−0.0598948
$235$	44.6304	2.91136
$236$	−1.00000	−0.0650945
$237$	0.694253	0.0450966
$238$	0.872031	0.0565254
$239$	−5.89116	−0.381068	−0.190534	−	0.981681i	$-0.561022\pi$
$239$	−5.89116	−0.381068	−0.190534	+	0.981681i	$0.561022\pi$
$240$	−6.94532	−0.448318
$241$	−9.27580	−0.597507	−0.298753	−	0.954330i	$-0.596571\pi$
$241$	−9.27580	−0.597507	−0.298753	+	0.954330i	$0.596571\pi$
$242$	0.184063	0.0118320
$243$	3.27659	0.210194
$244$	4.58010	0.293211
$245$	−23.7959	−1.52026
$246$	20.3051	1.29460
$247$	−9.10940	−0.579617
$248$	7.49403	0.475872
$249$	−23.5827	−1.49449
$250$	17.3309	1.09610
$251$	10.5821	0.667936	0.333968	−	0.942584i	$-0.391612\pi$
$251$	10.5821	0.667936	0.333968	+	0.942584i	$0.391612\pi$
$252$	−0.276057	−0.0173900
$253$	−0.945963	−0.0594722
$254$	6.90568	0.433301
$255$	6.94532	0.434933
$256$	1.00000	0.0625000
$257$	13.1875	0.822615	0.411307	−	0.911497i	$-0.365072\pi$
$257$	13.1875	0.822615	0.411307	+	0.911497i	$0.365072\pi$
$258$	5.44909	0.339245
$259$	−1.77045	−0.110011
$260$	−11.0377	−0.684527
$261$	1.72296	0.106648
$262$	11.3864	0.703451
$263$	11.1094	0.685033	0.342517	−	0.939512i	$-0.388721\pi$
$263$	11.1094	0.685033	0.342517	+	0.939512i	$0.388721\pi$
$264$	−6.09038	−0.374837
$265$	−28.7578	−1.76658
$266$	−2.74468	−0.168287
$267$	−23.0321	−1.40954
$268$	−0.136011	−0.00830822
$269$	−12.4105	−0.756683	−0.378341	−	0.925666i	$-0.623505\pi$
$269$	−12.4105	−0.756683	−0.378341	+	0.925666i	$0.623505\pi$
$270$	18.6373	1.13423
$271$	12.9913	0.789166	0.394583	−	0.918860i	$-0.370889\pi$
$271$	12.9913	0.789166	0.394583	+	0.918860i	$0.370889\pi$
$272$	−1.00000	−0.0606339
$273$	−4.59628	−0.278179
$274$	−15.0865	−0.911411
$275$	31.9189	1.92478
$276$	0.515132	0.0310073
$277$	−10.5327	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$277$	−10.5327	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$278$	−0.301722	−0.0180961
$279$	2.37237	0.142030
$280$	−3.32567	−0.198747
$281$	27.3237	1.63000	0.814999	−	0.579462i	$-0.196737\pi$
$281$	27.3237	1.63000	0.814999	+	0.579462i	$0.196737\pi$
$282$	−21.3121	−1.26912
$283$	15.5468	0.924160	0.462080	−	0.886838i	$-0.347103\pi$
$283$	15.5468	0.924160	0.462080	+	0.886838i	$0.347103\pi$
$284$	10.1868	0.604475
$285$	−21.8601	−1.29488
$286$	−9.67898	−0.572330
$287$	9.72281	0.573919
$288$	0.316568	0.0186540
$289$	1.00000	0.0588235
$290$	20.7565	1.21887
$291$	17.0150	0.997438
$292$	−8.99122	−0.526171
$293$	−0.391950	−0.0228980	−0.0114490	−	0.999934i	$-0.503644\pi$
$293$	−0.391950	−0.0228980	−0.0114490	+	0.999934i	$0.503644\pi$
$294$	11.3631	0.662712
$295$	−3.81371	−0.222043
$296$	2.03027	0.118007
$297$	16.3431	0.948324
$298$	16.5949	0.961317
$299$	0.818661	0.0473444
$300$	−17.3817	−1.00353
$301$	2.60922	0.150393
$302$	−19.2901	−1.11002
$303$	−5.19206	−0.298276
$304$	3.14746	0.180519
$305$	17.4672	1.00017
$306$	−0.316568	−0.0180970
$307$	−0.532127	−0.0303701	−0.0151850	−	0.999885i	$-0.504834\pi$
$307$	−0.532127	−0.0303701	−0.0151850	+	0.999885i	$0.504834\pi$
$308$	−2.91630	−0.166171
$309$	6.99779	0.398090
$310$	28.5801	1.62324
$311$	−33.4966	−1.89942	−0.949709	−	0.313134i	$-0.898621\pi$
$311$	−33.4966	−1.89942	−0.949709	+	0.313134i	$0.898621\pi$
$312$	5.27077	0.298399
$313$	−19.2550	−1.08836	−0.544179	−	0.838969i	$-0.683159\pi$
$313$	−19.2550	−1.08836	−0.544179	+	0.838969i	$0.683159\pi$
$314$	8.56288	0.483231
$315$	−1.05280	−0.0593187
$316$	−0.381218	−0.0214452
$317$	−16.4888	−0.926104	−0.463052	−	0.886331i	$-0.653246\pi$
$317$	−16.4888	−0.926104	−0.463052	+	0.886331i	$0.653246\pi$
$318$	13.7326	0.770085
$319$	18.2015	1.01909
$320$	3.81371	0.213193
$321$	−17.4030	−0.971341
$322$	0.246664	0.0137461
$323$	−3.14746	−0.175129
$324$	−9.84949	−0.547194
$325$	−27.6234	−1.53227
$326$	−20.9542	−1.16054
$327$	−21.6629	−1.19796
$328$	−11.1496	−0.615635
$329$	−10.2050	−0.562622
$330$	−23.2269	−1.27860
$331$	28.7122	1.57816	0.789081	−	0.614289i	$-0.210557\pi$
$331$	28.7122	1.57816	0.789081	+	0.614289i	$0.210557\pi$
$332$	12.9494	0.710690
$333$	0.642718	0.0352207
$334$	−2.37631	−0.130026
$335$	−0.518708	−0.0283400
$336$	1.58809	0.0866377
$337$	15.3670	0.837093	0.418547	−	0.908195i	$-0.362540\pi$
$337$	15.3670	0.837093	0.418547	+	0.908195i	$0.362540\pi$
$338$	−4.62356	−0.251488
$339$	−18.5016	−1.00487
$340$	−3.81371	−0.206827
$341$	25.0620	1.35718
$342$	0.996385	0.0538783
$343$	11.5453	0.623388
$344$	−2.99212	−0.161324
$345$	1.96456	0.105769
$346$	2.14829	0.115493
$347$	−21.4830	−1.15327	−0.576635	−	0.817002i	$-0.695634\pi$
$347$	−21.4830	−1.15327	−0.576635	+	0.817002i	$0.695634\pi$
$348$	−9.91179	−0.531328
$349$	17.9169	0.959069	0.479534	−	0.877523i	$-0.340806\pi$
$349$	17.9169	0.959069	0.479534	+	0.877523i	$0.340806\pi$
$350$	−8.32299	−0.444883
$351$	−14.1438	−0.754938
$352$	3.34426	0.178250
$353$	−20.3338	−1.08226	−0.541131	−	0.840938i	$-0.682004\pi$
$353$	−20.3338	−1.08226	−0.541131	+	0.840938i	$0.682004\pi$
$354$	1.82114	0.0967928
$355$	38.8494	2.06191
$356$	12.6471	0.670293
$357$	−1.58809	−0.0840509
$358$	−12.3511	−0.652778
$359$	9.93024	0.524098	0.262049	−	0.965055i	$-0.415602\pi$
$359$	9.93024	0.524098	0.262049	+	0.965055i	$0.415602\pi$
$360$	1.20730	0.0636303
$361$	−9.09351	−0.478606
$362$	16.9661	0.891719
$363$	−0.335205	−0.0175937
$364$	2.52384	0.132285
$365$	−34.2899	−1.79482
$366$	−8.34102	−0.435992
$367$	−27.9971	−1.46144	−0.730718	−	0.682679i	$-0.760815\pi$
$367$	−27.9971	−1.46144	−0.730718	+	0.682679i	$0.760815\pi$
$368$	−0.282862	−0.0147452
$369$	−3.52961	−0.183744
$370$	7.74284	0.402531
$371$	6.57567	0.341392
$372$	−13.6477	−0.707601
$373$	1.90055	0.0984067	0.0492033	−	0.998789i	$-0.484332\pi$
$373$	1.90055	0.0984067	0.0492033	+	0.998789i	$0.484332\pi$
$374$	−3.34426	−0.172927
$375$	−31.5621	−1.62986
$376$	11.7026	0.603516
$377$	−15.7521	−0.811272
$378$	−4.26154	−0.219190
$379$	−14.4697	−0.743261	−0.371631	−	0.928381i	$-0.621201\pi$
$379$	−14.4697	−0.743261	−0.371631	+	0.928381i	$0.621201\pi$
$380$	12.0035	0.615766
$381$	−12.5762	−0.644300
$382$	−5.91729	−0.302755
$383$	17.8009	0.909583	0.454791	−	0.890598i	$-0.349714\pi$
$383$	17.8009	0.909583	0.454791	+	0.890598i	$0.349714\pi$
$384$	−1.82114	−0.0929349
$385$	−11.1219	−0.566825
$386$	−20.3361	−1.03508
$387$	−0.947210	−0.0481494
$388$	−9.34304	−0.474321
$389$	−36.8684	−1.86930	−0.934650	−	0.355569i	$-0.884287\pi$
$389$	−36.8684	−1.86930	−0.934650	+	0.355569i	$0.884287\pi$
$390$	20.1012	1.01786
$391$	0.282862	0.0143049
$392$	−6.23956	−0.315145
$393$	−20.7362	−1.04600
$394$	−0.0256642	−0.00129295
$395$	−1.45385	−0.0731513
$396$	1.05869	0.0532010
$397$	−25.0078	−1.25510	−0.627552	−	0.778575i	$-0.715943\pi$
$397$	−25.0078	−1.25510	−0.627552	+	0.778575i	$0.715943\pi$
$398$	−25.6137	−1.28390
$399$	4.99846	0.250236
$400$	9.54438	0.477219
$401$	−18.4945	−0.923573	−0.461786	−	0.886991i	$-0.652791\pi$
$401$	−18.4945	−0.923573	−0.461786	+	0.886991i	$0.652791\pi$
$402$	0.247696	0.0123540
$403$	−21.6893	−1.08042
$404$	2.85099	0.141842
$405$	−37.5631	−1.86652
$406$	−4.74613	−0.235546
$407$	6.78973	0.336554
$408$	1.82114	0.0901601
$409$	37.5751	1.85797	0.928983	−	0.370122i	$-0.120684\pi$
$409$	37.5751	1.85797	0.928983	+	0.370122i	$0.120684\pi$
$410$	−42.5214	−2.09998
$411$	27.4748	1.35523
$412$	−3.84252	−0.189307
$413$	0.872031	0.0429098
$414$	−0.0895450	−0.00440090
$415$	49.3852	2.42422
$416$	−2.89421	−0.141900
$417$	0.549479	0.0269081
$418$	10.5259	0.514839
$419$	−33.0176	−1.61301	−0.806507	−	0.591225i	$-0.798645\pi$
$419$	−33.0176	−1.61301	−0.806507	+	0.591225i	$0.798645\pi$
$420$	6.05653	0.295528
$421$	−8.93121	−0.435281	−0.217640	−	0.976029i	$-0.569836\pi$
$421$	−8.93121	−0.435281	−0.217640	+	0.976029i	$0.569836\pi$
$422$	3.87815	0.188785
$423$	3.70468	0.180127
$424$	−7.54064	−0.366206
$425$	−9.54438	−0.462970
$426$	−18.5516	−0.898829
$427$	−3.99399	−0.193282
$428$	9.55608	0.461910
$429$	17.6268	0.851031
$430$	−11.4111	−0.550291
$431$	−33.0181	−1.59043	−0.795214	−	0.606329i	$-0.792641\pi$
$431$	−33.0181	−1.59043	−0.795214	+	0.606329i	$0.792641\pi$
$432$	4.88692	0.235122
$433$	−20.5947	−0.989717	−0.494859	−	0.868973i	$-0.664780\pi$
$433$	−20.5947	−0.989717	−0.494859	+	0.868973i	$0.664780\pi$
$434$	−6.53503	−0.313691
$435$	−37.8007	−1.81240
$436$	11.8952	0.569676
$437$	−0.890295	−0.0425886
$438$	16.3743	0.782395
$439$	−12.1668	−0.580688	−0.290344	−	0.956922i	$-0.593770\pi$
$439$	−12.1668	−0.580688	−0.290344	+	0.956922i	$0.593770\pi$
$440$	12.7540	0.608024
$441$	−1.97525	−0.0940594
$442$	2.89421	0.137663
$443$	−16.3355	−0.776125	−0.388063	−	0.921633i	$-0.626856\pi$
$443$	−16.3355	−0.776125	−0.388063	+	0.921633i	$0.626856\pi$
$444$	−3.69741	−0.175471
$445$	48.2322	2.28643
$446$	−13.1275	−0.621607
$447$	−30.2217	−1.42944
$448$	−0.872031	−0.0411996
$449$	6.96027	0.328476	0.164238	−	0.986421i	$-0.447484\pi$
$449$	6.96027	0.328476	0.164238	+	0.986421i	$0.447484\pi$
$450$	3.02145	0.142432
$451$	−37.2872	−1.75579
$452$	10.1593	0.477853
$453$	35.1300	1.65055
$454$	−20.9808	−0.984679
$455$	9.62519	0.451236
$456$	−5.73197	−0.268424
$457$	−32.6957	−1.52944	−0.764719	−	0.644364i	$-0.777122\pi$
$457$	−32.6957	−1.52944	−0.764719	+	0.644364i	$0.777122\pi$
$458$	5.93166	0.277168
$459$	−4.88692	−0.228102
$460$	−1.07875	−0.0502971
$461$	−27.0210	−1.25849	−0.629247	−	0.777205i	$-0.716637\pi$
$461$	−27.0210	−1.25849	−0.629247	+	0.777205i	$0.716637\pi$
$462$	5.31100	0.247090
$463$	−28.8094	−1.33889	−0.669444	−	0.742863i	$-0.733467\pi$
$463$	−28.8094	−1.33889	−0.669444	+	0.742863i	$0.733467\pi$
$464$	5.44261	0.252667
$465$	−52.0484	−2.41369
$466$	−15.0799	−0.698563
$467$	5.57588	0.258021	0.129011	−	0.991643i	$-0.458820\pi$
$467$	5.57588	0.258021	0.129011	+	0.991643i	$0.458820\pi$
$468$	−0.916214	−0.0423520
$469$	0.118606	0.00547672
$470$	44.6304	2.05864
$471$	−15.5942	−0.718545
$472$	−1.00000	−0.0460287
$473$	−10.0064	−0.460096
$474$	0.694253	0.0318881
$475$	30.0405	1.37835
$476$	0.872031	0.0399695
$477$	−2.38713	−0.109299
$478$	−5.89116	−0.269456
$479$	34.8184	1.59090	0.795448	−	0.606022i	$-0.207236\pi$
$479$	34.8184	1.59090	0.795448	+	0.606022i	$0.207236\pi$
$480$	−6.94532	−0.317009
$481$	−5.87601	−0.267923
$482$	−9.27580	−0.422501
$483$	−0.449211	−0.0204398
$484$	0.184063	0.00836648
$485$	−35.6316	−1.61795
$486$	3.27659	0.148629
$487$	36.1327	1.63733	0.818665	−	0.574271i	$-0.194715\pi$
$487$	36.1327	1.63733	0.818665	+	0.574271i	$0.194715\pi$
$488$	4.58010	0.207331
$489$	38.1606	1.72568
$490$	−23.7959	−1.07499
$491$	−0.0887839	−0.00400676	−0.00200338	−	0.999998i	$-0.500638\pi$
$491$	−0.0887839	−0.00400676	−0.00200338	+	0.999998i	$0.500638\pi$
$492$	20.3051	0.915423
$493$	−5.44261	−0.245123
$494$	−9.10940	−0.409851
$495$	4.03752	0.181473
$496$	7.49403	0.336492
$497$	−8.88319	−0.398466
$498$	−23.5827	−1.05677
$499$	2.79786	0.125249	0.0626247	−	0.998037i	$-0.480053\pi$
$499$	2.79786	0.125249	0.0626247	+	0.998037i	$0.480053\pi$
$500$	17.3309	0.775063
$501$	4.32760	0.193343
$502$	10.5821	0.472302
$503$	24.9766	1.11365	0.556826	−	0.830629i	$-0.312019\pi$
$503$	24.9766	1.11365	0.556826	+	0.830629i	$0.312019\pi$
$504$	−0.276057	−0.0122966
$505$	10.8728	0.483835
$506$	−0.945963	−0.0420532
$507$	8.42017	0.373953
$508$	6.90568	0.306390
$509$	3.16970	0.140495	0.0702474	−	0.997530i	$-0.477621\pi$
$509$	3.16970	0.140495	0.0702474	+	0.997530i	$0.477621\pi$
$510$	6.94532	0.307544
$511$	7.84062	0.346849
$512$	1.00000	0.0441942
$513$	15.3814	0.679104
$514$	13.1875	0.581676
$515$	−14.6543	−0.645744
$516$	5.44909	0.239883
$517$	39.1366	1.72122
$518$	−1.77045	−0.0777893
$519$	−3.91234	−0.171733
$520$	−11.0377	−0.484034
$521$	20.3871	0.893177	0.446588	−	0.894740i	$-0.352639\pi$
$521$	20.3871	0.893177	0.446588	+	0.894740i	$0.352639\pi$
$522$	1.72296	0.0754119
$523$	−1.43748	−0.0628568	−0.0314284	−	0.999506i	$-0.510006\pi$
$523$	−1.43748	−0.0628568	−0.0314284	+	0.999506i	$0.510006\pi$
$524$	11.3864	0.497415
$525$	15.1574	0.661522
$526$	11.1094	0.484392
$527$	−7.49403	−0.326445
$528$	−6.09038	−0.265050
$529$	−22.9200	−0.996521
$530$	−28.7578	−1.24916
$531$	−0.316568	−0.0137379
$532$	−2.74468	−0.118997
$533$	32.2693	1.39774
$534$	−23.0321	−0.996698
$535$	36.4441	1.57562
$536$	−0.136011	−0.00587480
$537$	22.4932	0.970653
$538$	−12.4105	−0.535056
$539$	−20.8667	−0.898793
$540$	18.6373	0.802021
$541$	−14.8050	−0.636515	−0.318257	−	0.948004i	$-0.603098\pi$
$541$	−14.8050	−0.636515	−0.318257	+	0.948004i	$0.603098\pi$
$542$	12.9913	0.558025
$543$	−30.8977	−1.32595
$544$	−1.00000	−0.0428746
$545$	45.3648	1.94321
$546$	−4.59628	−0.196702
$547$	24.5654	1.05034	0.525170	−	0.850997i	$-0.324002\pi$
$547$	24.5654	1.05034	0.525170	+	0.850997i	$0.324002\pi$
$548$	−15.0865	−0.644465
$549$	1.44991	0.0618808
$550$	31.9189	1.36102
$551$	17.1304	0.729779
$552$	0.515132	0.0219255
$553$	0.332434	0.0141365
$554$	−10.5327	−0.447490
$555$	−14.1008	−0.598547
$556$	−0.301722	−0.0127958
$557$	0.141153	0.00598086	0.00299043	−	0.999996i	$-0.499048\pi$
$557$	0.141153	0.00598086	0.00299043	+	0.999996i	$0.499048\pi$
$558$	2.37237	0.100431
$559$	8.65982	0.366271
$560$	−3.32567	−0.140535
$561$	6.09038	0.257136
$562$	27.3237	1.15258
$563$	−9.79808	−0.412940	−0.206470	−	0.978453i	$-0.566198\pi$
$563$	−9.79808	−0.412940	−0.206470	+	0.978453i	$0.566198\pi$
$564$	−21.3121	−0.897403
$565$	38.7446	1.63000
$566$	15.5468	0.653480
$567$	8.58906	0.360707
$568$	10.1868	0.427428
$569$	−7.66102	−0.321167	−0.160583	−	0.987022i	$-0.551338\pi$
$569$	−7.66102	−0.321167	−0.160583	+	0.987022i	$0.551338\pi$
$570$	−21.8601	−0.915618
$571$	−25.0096	−1.04662	−0.523310	−	0.852142i	$-0.675303\pi$
$571$	−25.0096	−1.04662	−0.523310	+	0.852142i	$0.675303\pi$
$572$	−9.67898	−0.404698
$573$	10.7762	0.450184
$574$	9.72281	0.405822
$575$	−2.69974	−0.112587
$576$	0.316568	0.0131903
$577$	−6.55880	−0.273047	−0.136523	−	0.990637i	$-0.543593\pi$
$577$	−6.55880	−0.273047	−0.136523	+	0.990637i	$0.543593\pi$
$578$	1.00000	0.0415945
$579$	37.0350	1.53912
$580$	20.7565	0.861869
$581$	−11.2923	−0.468482
$582$	17.0150	0.705295
$583$	−25.2178	−1.04442
$584$	−8.99122	−0.372059
$585$	−3.49418	−0.144466
$586$	−0.391950	−0.0161913
$587$	−13.2122	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$587$	−13.2122	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$588$	11.3631	0.468608
$589$	23.5871	0.971891
$590$	−3.81371	−0.157008
$591$	0.0467383	0.00192256
$592$	2.03027	0.0834434
$593$	36.6680	1.50577	0.752887	−	0.658150i	$-0.228661\pi$
$593$	36.6680	1.50577	0.752887	+	0.658150i	$0.228661\pi$
$594$	16.3431	0.670566
$595$	3.32567	0.136339
$596$	16.5949	0.679754
$597$	46.6462	1.90910
$598$	0.818661	0.0334775
$599$	35.8515	1.46485	0.732426	−	0.680847i	$-0.238388\pi$
$599$	35.8515	1.46485	0.732426	+	0.680847i	$0.238388\pi$
$600$	−17.3817	−0.709605
$601$	18.4556	0.752818	0.376409	−	0.926454i	$-0.377159\pi$
$601$	18.4556	0.752818	0.376409	+	0.926454i	$0.377159\pi$
$602$	2.60922	0.106344
$603$	−0.0430569	−0.00175341
$604$	−19.2901	−0.784902
$605$	0.701961	0.0285388
$606$	−5.19206	−0.210913
$607$	−9.06766	−0.368045	−0.184022	−	0.982922i	$-0.558912\pi$
$607$	−9.06766	−0.368045	−0.184022	+	0.982922i	$0.558912\pi$
$608$	3.14746	0.127646
$609$	8.64339	0.350248
$610$	17.4672	0.707224
$611$	−33.8698	−1.37023
$612$	−0.316568	−0.0127965
$613$	16.5874	0.669958	0.334979	−	0.942226i	$-0.391271\pi$
$613$	16.5874	0.669958	0.334979	+	0.942226i	$0.391271\pi$
$614$	−0.532127	−0.0214749
$615$	77.4376	3.12259
$616$	−2.91630	−0.117501
$617$	−31.2098	−1.25646	−0.628229	−	0.778029i	$-0.716220\pi$
$617$	−31.2098	−1.25646	−0.628229	+	0.778029i	$0.716220\pi$
$618$	6.99779	0.281492
$619$	−15.3115	−0.615419	−0.307710	−	0.951480i	$-0.599563\pi$
$619$	−15.3115	−0.615419	−0.307710	+	0.951480i	$0.599563\pi$
$620$	28.5801	1.14780
$621$	−1.38232	−0.0554707
$622$	−33.4966	−1.34309
$623$	−11.0286	−0.441853
$624$	5.27077	0.211000
$625$	18.3732	0.734930
$626$	−19.2550	−0.769586
$627$	−19.1692	−0.765544
$628$	8.56288	0.341696
$629$	−2.03027	−0.0809520
$630$	−1.05280	−0.0419446
$631$	20.5450	0.817883	0.408942	−	0.912561i	$-0.365898\pi$
$631$	20.5450	0.817883	0.408942	+	0.912561i	$0.365898\pi$
$632$	−0.381218	−0.0151640
$633$	−7.06268	−0.280716
$634$	−16.4888	−0.654854
$635$	26.3362	1.04512
$636$	13.7326	0.544533
$637$	18.0586	0.715507
$638$	18.2015	0.720605
$639$	3.22481	0.127572
$640$	3.81371	0.150750
$641$	−23.2230	−0.917252	−0.458626	−	0.888629i	$-0.651658\pi$
$641$	−23.2230	−0.917252	−0.458626	+	0.888629i	$0.651658\pi$
$642$	−17.4030	−0.686841
$643$	−43.4637	−1.71404	−0.857021	−	0.515282i	$-0.827687\pi$
$643$	−43.4637	−1.71404	−0.857021	+	0.515282i	$0.827687\pi$
$644$	0.246664	0.00971993
$645$	20.7812	0.818260
$646$	−3.14746	−0.123835
$647$	5.78721	0.227519	0.113759	−	0.993508i	$-0.463711\pi$
$647$	5.78721	0.227519	0.113759	+	0.993508i	$0.463711\pi$
$648$	−9.84949	−0.386924
$649$	−3.34426	−0.131274
$650$	−27.6234	−1.08348
$651$	11.9012	0.466446
$652$	−20.9542	−0.820628
$653$	−8.11951	−0.317741	−0.158870	−	0.987299i	$-0.550785\pi$
$653$	−8.11951	−0.317741	−0.158870	+	0.987299i	$0.550785\pi$
$654$	−21.6629	−0.847085
$655$	43.4242	1.69673
$656$	−11.1496	−0.435319
$657$	−2.84634	−0.111046
$658$	−10.2050	−0.397834
$659$	2.86460	0.111589	0.0557946	−	0.998442i	$-0.482231\pi$
$659$	2.86460	0.111589	0.0557946	+	0.998442i	$0.482231\pi$
$660$	−23.2269	−0.904107
$661$	−35.3125	−1.37350	−0.686749	−	0.726895i	$-0.740963\pi$
$661$	−35.3125	−1.37350	−0.686749	+	0.726895i	$0.740963\pi$
$662$	28.7122	1.11593
$663$	−5.27077	−0.204700
$664$	12.9494	0.502533
$665$	−10.4674	−0.405909
$666$	0.642718	0.0249048
$667$	−1.53951	−0.0596100
$668$	−2.37631	−0.0919421
$669$	23.9071	0.924304
$670$	−0.518708	−0.0200394
$671$	15.3170	0.591307
$672$	1.58809	0.0612621
$673$	−32.0766	−1.23646	−0.618230	−	0.785997i	$-0.712150\pi$
$673$	−32.0766	−1.23646	−0.618230	+	0.785997i	$0.712150\pi$
$674$	15.3670	0.591914
$675$	46.6426	1.79527
$676$	−4.62356	−0.177829
$677$	39.3712	1.51316	0.756579	−	0.653902i	$-0.226869\pi$
$677$	39.3712	1.51316	0.756579	+	0.653902i	$0.226869\pi$
$678$	−18.5016	−0.710548
$679$	8.14742	0.312669
$680$	−3.81371	−0.146249
$681$	38.2091	1.46418
$682$	25.0620	0.959673
$683$	1.27266	0.0486969	0.0243484	−	0.999704i	$-0.492249\pi$
$683$	1.27266	0.0486969	0.0243484	+	0.999704i	$0.492249\pi$
$684$	0.996385	0.0380977
$685$	−57.5356	−2.19832
$686$	11.5453	0.440802
$687$	−10.8024	−0.412138
$688$	−2.99212	−0.114074
$689$	21.8242	0.831435
$690$	1.96456	0.0747897
$691$	−44.9584	−1.71030	−0.855148	−	0.518383i	$-0.826534\pi$
$691$	−44.9584	−1.71030	−0.855148	+	0.518383i	$0.826534\pi$
$692$	2.14829	0.0816656
$693$	−0.923207	−0.0350697
$694$	−21.4830	−0.815485
$695$	−1.15068	−0.0436477
$696$	−9.91179	−0.375705
$697$	11.1496	0.422322
$698$	17.9169	0.678164
$699$	27.4627	1.03873
$700$	−8.32299	−0.314580
$701$	6.00335	0.226743	0.113372	−	0.993553i	$-0.463835\pi$
$701$	6.00335	0.226743	0.113372	+	0.993553i	$0.463835\pi$
$702$	−14.1438	−0.533822
$703$	6.39017	0.241010
$704$	3.34426	0.126041
$705$	−81.2783	−3.06112
$706$	−20.3338	−0.765275
$707$	−2.48615	−0.0935013
$708$	1.82114	0.0684428
$709$	39.7808	1.49400	0.746999	−	0.664825i	$-0.231494\pi$
$709$	39.7808	1.49400	0.746999	+	0.664825i	$0.231494\pi$
$710$	38.8494	1.45799
$711$	−0.120681	−0.00452591
$712$	12.6471	0.473969
$713$	−2.11977	−0.0793862
$714$	−1.58809	−0.0594329
$715$	−36.9128	−1.38046
$716$	−12.3511	−0.461583
$717$	10.7287	0.400669
$718$	9.93024	0.370593
$719$	17.2845	0.644604	0.322302	−	0.946637i	$-0.395543\pi$
$719$	17.2845	0.644604	0.322302	+	0.946637i	$0.395543\pi$
$720$	1.20730	0.0449934
$721$	3.35080	0.124790
$722$	−9.09351	−0.338426
$723$	16.8926	0.628242
$724$	16.9661	0.630541
$725$	51.9464	1.92924
$726$	−0.335205	−0.0124406
$727$	11.1060	0.411899	0.205950	−	0.978563i	$-0.433972\pi$
$727$	11.1060	0.411899	0.205950	+	0.978563i	$0.433972\pi$
$728$	2.52384	0.0935397
$729$	23.5813	0.873382
$730$	−34.2899	−1.26913
$731$	2.99212	0.110668
$732$	−8.34102	−0.308293
$733$	9.91867	0.366354	0.183177	−	0.983080i	$-0.441362\pi$
$733$	9.91867	0.366354	0.183177	+	0.983080i	$0.441362\pi$
$734$	−27.9971	−1.03339
$735$	43.3357	1.59846
$736$	−0.282862	−0.0104264
$737$	−0.454857	−0.0167549
$738$	−3.52961	−0.129927
$739$	21.7958	0.801773	0.400886	−	0.916128i	$-0.368702\pi$
$739$	21.7958	0.801773	0.400886	+	0.916128i	$0.368702\pi$
$740$	7.74284	0.284633
$741$	16.5895	0.609432
$742$	6.57567	0.241400
$743$	−19.6089	−0.719380	−0.359690	−	0.933072i	$-0.617118\pi$
$743$	−19.6089	−0.719380	−0.359690	+	0.933072i	$0.617118\pi$
$744$	−13.6477	−0.500350
$745$	63.2882	2.31870
$746$	1.90055	0.0695840
$747$	4.09936	0.149988
$748$	−3.34426	−0.122278
$749$	−8.33319	−0.304488
$750$	−31.5621	−1.15249
$751$	36.1465	1.31900	0.659502	−	0.751703i	$-0.270767\pi$
$751$	36.1465	1.31900	0.659502	+	0.751703i	$0.270767\pi$
$752$	11.7026	0.426750
$753$	−19.2715	−0.702293
$754$	−15.7521	−0.573656
$755$	−73.5668	−2.67737
$756$	−4.26154	−0.154991
$757$	17.0217	0.618664	0.309332	−	0.950954i	$-0.399895\pi$
$757$	17.0217	0.618664	0.309332	+	0.950954i	$0.399895\pi$
$758$	−14.4697	−0.525565
$759$	1.72273	0.0625313
$760$	12.0035	0.435412
$761$	−33.3095	−1.20747	−0.603734	−	0.797186i	$-0.706321\pi$
$761$	−33.3095	−1.20747	−0.603734	+	0.797186i	$0.706321\pi$
$762$	−12.5762	−0.455589
$763$	−10.3730	−0.375527
$764$	−5.91729	−0.214080
$765$	−1.20730	−0.0436500
$766$	17.8009	0.643172
$767$	2.89421	0.104504
$768$	−1.82114	−0.0657149
$769$	39.0296	1.40744	0.703722	−	0.710475i	$-0.251520\pi$
$769$	39.0296	1.40744	0.703722	+	0.710475i	$0.251520\pi$
$770$	−11.1219	−0.400806
$771$	−24.0164	−0.864929
$772$	−20.3361	−0.731913
$773$	−2.61022	−0.0938832	−0.0469416	−	0.998898i	$-0.514947\pi$
$773$	−2.61022	−0.0938832	−0.0469416	+	0.998898i	$0.514947\pi$
$774$	−0.947210	−0.0340468
$775$	71.5259	2.56929
$776$	−9.34304	−0.335396
$777$	3.22425	0.115669
$778$	−36.8684	−1.32179
$779$	−35.0929	−1.25734
$780$	20.1012	0.719738
$781$	34.0672	1.21902
$782$	0.282862	0.0101151
$783$	26.5976	0.950521
$784$	−6.23956	−0.222842
$785$	32.6563	1.16555
$786$	−20.7362	−0.739636
$787$	40.5188	1.44434	0.722170	−	0.691716i	$-0.243145\pi$
$787$	40.5188	1.44434	0.722170	+	0.691716i	$0.243145\pi$
$788$	−0.0256642	−0.000914251 0
$789$	−20.2318	−0.720270
$790$	−1.45385	−0.0517258
$791$	−8.85922	−0.314998
$792$	1.05869	0.0376188
$793$	−13.2558	−0.470726
$794$	−25.0078	−0.887493
$795$	52.3721	1.85745
$796$	−25.6137	−0.907853
$797$	−32.7569	−1.16031	−0.580154	−	0.814507i	$-0.697007\pi$
$797$	−32.7569	−1.16031	−0.580154	+	0.814507i	$0.697007\pi$
$798$	4.99846	0.176944
$799$	−11.7026	−0.414009
$800$	9.54438	0.337445
$801$	4.00366	0.141462
$802$	−18.4945	−0.653065
$803$	−30.0690	−1.06111
$804$	0.247696	0.00873558
$805$	0.940705	0.0331555
$806$	−21.6893	−0.763973
$807$	22.6014	0.795605
$808$	2.85099	0.100297
$809$	23.2368	0.816962	0.408481	−	0.912767i	$-0.366059\pi$
$809$	23.2368	0.816962	0.408481	+	0.912767i	$0.366059\pi$
$810$	−37.5631	−1.31983
$811$	27.1181	0.952245	0.476123	−	0.879379i	$-0.342042\pi$
$811$	27.1181	0.952245	0.476123	+	0.879379i	$0.342042\pi$
$812$	−4.74613	−0.166556
$813$	−23.6591	−0.829759
$814$	6.78973	0.237980
$815$	−79.9131	−2.79923
$816$	1.82114	0.0637528
$817$	−9.41757	−0.329479
$818$	37.5751	1.31378
$819$	0.798967	0.0279182
$820$	−42.5214	−1.48491
$821$	23.0023	0.802786	0.401393	−	0.915906i	$-0.368526\pi$
$821$	23.0023	0.802786	0.401393	+	0.915906i	$0.368526\pi$
$822$	27.4748	0.958292
$823$	31.7968	1.10837	0.554183	−	0.832395i	$-0.313031\pi$
$823$	31.7968	1.10837	0.554183	+	0.832395i	$0.313031\pi$
$824$	−3.84252	−0.133861
$825$	−58.1289	−2.02379
$826$	0.872031	0.0303418
$827$	−30.1713	−1.04916	−0.524580	−	0.851361i	$-0.675778\pi$
$827$	−30.1713	−1.04916	−0.524580	+	0.851361i	$0.675778\pi$
$828$	−0.0895450	−0.00311191
$829$	21.3128	0.740223	0.370112	−	0.928987i	$-0.379319\pi$
$829$	21.3128	0.740223	0.370112	+	0.928987i	$0.379319\pi$
$830$	49.3852	1.71418
$831$	19.1815	0.665399
$832$	−2.89421	−0.100339
$833$	6.23956	0.216188
$834$	0.549479	0.0190269
$835$	−9.06254	−0.313622
$836$	10.5259	0.364046
$837$	36.6227	1.26587
$838$	−33.0176	−1.14057
$839$	−25.9908	−0.897303	−0.448652	−	0.893707i	$-0.648096\pi$
$839$	−25.9908	−0.897303	−0.448652	+	0.893707i	$0.648096\pi$
$840$	6.05653	0.208970
$841$	0.622049	0.0214500
$842$	−8.93121	−0.307790
$843$	−49.7605	−1.71384
$844$	3.87815	0.133491
$845$	−17.6329	−0.606590
$846$	3.70468	0.127369
$847$	−0.160508	−0.00551513
$848$	−7.54064	−0.258947
$849$	−28.3129	−0.971697
$850$	−9.54438	−0.327369
$851$	−0.574284	−0.0196862
$852$	−18.5516	−0.635568
$853$	40.0257	1.37045	0.685227	−	0.728329i	$-0.259703\pi$
$853$	40.0257	1.37045	0.685227	+	0.728329i	$0.259703\pi$
$854$	−3.99399	−0.136671
$855$	3.79992	0.129955
$856$	9.55608	0.326620
$857$	39.5833	1.35214	0.676071	−	0.736837i	$-0.263681\pi$
$857$	39.5833	1.35214	0.676071	+	0.736837i	$0.263681\pi$
$858$	17.6268	0.601770
$859$	43.9565	1.49978	0.749888	−	0.661565i	$-0.230107\pi$
$859$	43.9565	1.49978	0.749888	+	0.661565i	$0.230107\pi$
$860$	−11.4111	−0.389115
$861$	−17.7066	−0.603441
$862$	−33.0181	−1.12460
$863$	−18.1640	−0.618310	−0.309155	−	0.951012i	$-0.600046\pi$
$863$	−18.1640	−0.618310	−0.309155	+	0.951012i	$0.600046\pi$
$864$	4.88692	0.166256
$865$	8.19294	0.278568
$866$	−20.5947	−0.699836
$867$	−1.82114	−0.0618493
$868$	−6.53503	−0.221813
$869$	−1.27489	−0.0432477
$870$	−37.8007	−1.28156
$871$	0.393645	0.0133382
$872$	11.8952	0.402822
$873$	−2.95771	−0.100103
$874$	−0.890295	−0.0301147
$875$	−15.1131	−0.510916
$876$	16.3743	0.553237
$877$	−36.3281	−1.22671	−0.613356	−	0.789807i	$-0.710181\pi$
$877$	−36.3281	−1.22671	−0.613356	+	0.789807i	$0.710181\pi$
$878$	−12.1668	−0.410608
$879$	0.713798	0.0240758
$880$	12.7540	0.429938
$881$	−31.5642	−1.06342	−0.531712	−	0.846925i	$-0.678451\pi$
$881$	−31.5642	−1.06342	−0.531712	+	0.846925i	$0.678451\pi$
$882$	−1.97525	−0.0665100
$883$	−43.1941	−1.45360	−0.726798	−	0.686851i	$-0.758993\pi$
$883$	−43.1941	−1.45360	−0.726798	+	0.686851i	$0.758993\pi$
$884$	2.89421	0.0973428
$885$	6.94532	0.233464
$886$	−16.3355	−0.548803
$887$	14.9820	0.503045	0.251522	−	0.967851i	$-0.419069\pi$
$887$	14.9820	0.503045	0.251522	+	0.967851i	$0.419069\pi$
$888$	−3.69741	−0.124077
$889$	−6.02197	−0.201970
$890$	48.2322	1.61675
$891$	−32.9392	−1.10351
$892$	−13.1275	−0.439542
$893$	36.8335	1.23258
$894$	−30.2217	−1.01077
$895$	−47.1036	−1.57450
$896$	−0.872031	−0.0291325
$897$	−1.49090	−0.0497797
$898$	6.96027	0.232267
$899$	40.7871	1.36033
$900$	3.02145	0.100715
$901$	7.54064	0.251215
$902$	−37.2872	−1.24153
$903$	−4.75177	−0.158129
$904$	10.1593	0.337893
$905$	64.7038	2.15083
$906$	35.1300	1.16712
$907$	30.1761	1.00198	0.500991	−	0.865453i	$-0.332969\pi$
$907$	30.1761	1.00198	0.500991	+	0.865453i	$0.332969\pi$
$908$	−20.9808	−0.696273
$909$	0.902533	0.0299351
$910$	9.62519	0.319072
$911$	−6.52039	−0.216030	−0.108015	−	0.994149i	$-0.534449\pi$
$911$	−6.52039	−0.216030	−0.108015	+	0.994149i	$0.534449\pi$
$912$	−5.73197	−0.189805
$913$	43.3061	1.43322
$914$	−32.6957	−1.08148
$915$	−31.8102	−1.05161
$916$	5.93166	0.195988
$917$	−9.92925	−0.327893
$918$	−4.88692	−0.161292
$919$	−20.4302	−0.673930	−0.336965	−	0.941517i	$-0.609400\pi$
$919$	−20.4302	−0.673930	−0.336965	+	0.941517i	$0.609400\pi$
$920$	−1.07875	−0.0355654
$921$	0.969080	0.0319323
$922$	−27.0210	−0.889890
$923$	−29.4827	−0.970434
$924$	5.31100	0.174719
$925$	19.3776	0.637132
$926$	−28.8094	−0.946736
$927$	−1.21642	−0.0399525
$928$	5.44261	0.178663
$929$	−17.4788	−0.573460	−0.286730	−	0.958011i	$-0.592568\pi$
$929$	−17.4788	−0.573460	−0.286730	+	0.958011i	$0.592568\pi$
$930$	−52.0484	−1.70674
$931$	−19.6388	−0.643634
$932$	−15.0799	−0.493959
$933$	61.0022	1.99712
$934$	5.57588	0.182448
$935$	−12.7540	−0.417101
$936$	−0.916214	−0.0299474
$937$	19.2640	0.629328	0.314664	−	0.949203i	$-0.398108\pi$
$937$	19.2640	0.629328	0.314664	+	0.949203i	$0.398108\pi$
$938$	0.118606	0.00387263
$939$	35.0662	1.14434
$940$	44.6304	1.45568
$941$	−42.1307	−1.37342	−0.686711	−	0.726931i	$-0.740946\pi$
$941$	−42.1307	−1.37342	−0.686711	+	0.726931i	$0.740946\pi$
$942$	−15.5942	−0.508088
$943$	3.15380	0.102702
$944$	−1.00000	−0.0325472
$945$	−16.2523	−0.528687
$946$	−10.0064	−0.325337
$947$	26.9615	0.876132	0.438066	−	0.898943i	$-0.355664\pi$
$947$	26.9615	0.876132	0.438066	+	0.898943i	$0.355664\pi$
$948$	0.694253	0.0225483
$949$	26.0225	0.844725
$950$	30.0405	0.974643
$951$	30.0285	0.973741
$952$	0.872031	0.0282627
$953$	27.4511	0.889227	0.444614	−	0.895722i	$-0.353341\pi$
$953$	27.4511	0.889227	0.444614	+	0.895722i	$0.353341\pi$
$954$	−2.38713	−0.0772861
$955$	−22.5668	−0.730246
$956$	−5.89116	−0.190534
$957$	−33.1476	−1.07151
$958$	34.8184	1.12493
$959$	13.1559	0.424827
$960$	−6.94532	−0.224159
$961$	25.1605	0.811630
$962$	−5.87601	−0.189450
$963$	3.02515	0.0974841
$964$	−9.27580	−0.298753
$965$	−77.5560	−2.49662
$966$	−0.449211	−0.0144531
$967$	23.4797	0.755056	0.377528	−	0.925998i	$-0.376774\pi$
$967$	23.4797	0.755056	0.377528	+	0.925998i	$0.376774\pi$
$968$	0.184063	0.00591599
$969$	5.73197	0.184138
$970$	−35.6316	−1.14406
$971$	31.1707	1.00032	0.500158	−	0.865934i	$-0.333275\pi$
$971$	31.1707	1.00032	0.500158	+	0.865934i	$0.333275\pi$
$972$	3.27659	0.105097
$973$	0.263111	0.00843494
$974$	36.1327	1.15777
$975$	50.3062	1.61109
$976$	4.58010	0.146605
$977$	10.3931	0.332505	0.166253	−	0.986083i	$-0.446833\pi$
$977$	10.3931	0.332505	0.166253	+	0.986083i	$0.446833\pi$
$978$	38.1606	1.22024
$979$	42.2951	1.35176
$980$	−23.7959	−0.760131
$981$	3.76564	0.120228
$982$	−0.0887839	−0.00283321
$983$	12.5608	0.400626	0.200313	−	0.979732i	$-0.435804\pi$
$983$	12.5608	0.400626	0.200313	+	0.979732i	$0.435804\pi$
$984$	20.3051	0.647302
$985$	−0.0978760	−0.00311859
$986$	−5.44261	−0.173328
$987$	18.5849	0.591562
$988$	−9.10940	−0.289808
$989$	0.846356	0.0269126
$990$	4.03752	0.128321
$991$	30.9967	0.984642	0.492321	−	0.870414i	$-0.336149\pi$
$991$	30.9967	0.984642	0.492321	+	0.870414i	$0.336149\pi$
$992$	7.49403	0.237936
$993$	−52.2890	−1.65934
$994$	−8.88319	−0.281758
$995$	−97.6832	−3.09677
$996$	−23.5827	−0.747246
$997$	−4.95303	−0.156864	−0.0784320	−	0.996919i	$-0.524991\pi$
$997$	−4.95303	−0.156864	−0.0784320	+	0.996919i	$0.524991\pi$
$998$	2.79786	0.0885647
$999$	9.92174	0.313910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.t.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.t.1.2	✓	8	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.82114 q^{3} +1.00000 q^{4} +3.81371 q^{5} -1.82114 q^{6} -0.872031 q^{7} +1.00000 q^{8} +0.316568 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.82114 q^{3} +1.00000 q^{4} +3.81371 q^{5} -1.82114 q^{6} -0.872031 q^{7} +1.00000 q^{8} +0.316568 q^{9} +3.81371 q^{10} +3.34426 q^{11} -1.82114 q^{12} -2.89421 q^{13} -0.872031 q^{14} -6.94532 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.316568 q^{18} +3.14746 q^{19} +3.81371 q^{20} +1.58809 q^{21} +3.34426 q^{22} -0.282862 q^{23} -1.82114 q^{24} +9.54438 q^{25} -2.89421 q^{26} +4.88692 q^{27} -0.872031 q^{28} +5.44261 q^{29} -6.94532 q^{30} +7.49403 q^{31} +1.00000 q^{32} -6.09038 q^{33} -1.00000 q^{34} -3.32567 q^{35} +0.316568 q^{36} +2.03027 q^{37} +3.14746 q^{38} +5.27077 q^{39} +3.81371 q^{40} -11.1496 q^{41} +1.58809 q^{42} -2.99212 q^{43} +3.34426 q^{44} +1.20730 q^{45} -0.282862 q^{46} +11.7026 q^{47} -1.82114 q^{48} -6.23956 q^{49} +9.54438 q^{50} +1.82114 q^{51} -2.89421 q^{52} -7.54064 q^{53} +4.88692 q^{54} +12.7540 q^{55} -0.872031 q^{56} -5.73197 q^{57} +5.44261 q^{58} -1.00000 q^{59} -6.94532 q^{60} +4.58010 q^{61} +7.49403 q^{62} -0.276057 q^{63} +1.00000 q^{64} -11.0377 q^{65} -6.09038 q^{66} -0.136011 q^{67} -1.00000 q^{68} +0.515132 q^{69} -3.32567 q^{70} +10.1868 q^{71} +0.316568 q^{72} -8.99122 q^{73} +2.03027 q^{74} -17.3817 q^{75} +3.14746 q^{76} -2.91630 q^{77} +5.27077 q^{78} -0.381218 q^{79} +3.81371 q^{80} -9.84949 q^{81} -11.1496 q^{82} +12.9494 q^{83} +1.58809 q^{84} -3.81371 q^{85} -2.99212 q^{86} -9.91179 q^{87} +3.34426 q^{88} +12.6471 q^{89} +1.20730 q^{90} +2.52384 q^{91} -0.282862 q^{92} -13.6477 q^{93} +11.7026 q^{94} +12.0035 q^{95} -1.82114 q^{96} -9.34304 q^{97} -6.23956 q^{98} +1.05869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * q^99

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