LMFDB - Embedded newform 667.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.445942$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.445942 q^{2} -0.0589774 q^{3} -1.80114 q^{4} +2.46971 q^{5} -0.0263005 q^{6} -2.81741 q^{7} -1.69509 q^{8} -2.99652 q^{9} +O(q^{10})$	\(q+0.445942 q^{2} -0.0589774 q^{3} -1.80114 q^{4} +2.46971 q^{5} -0.0263005 q^{6} -2.81741 q^{7} -1.69509 q^{8} -2.99652 q^{9} +1.10135 q^{10} +4.28934 q^{11} +0.106226 q^{12} +4.41981 q^{13} -1.25640 q^{14} -0.145657 q^{15} +2.84636 q^{16} +6.60695 q^{17} -1.33628 q^{18} +4.20884 q^{19} -4.44829 q^{20} +0.166163 q^{21} +1.91280 q^{22} +1.00000 q^{23} +0.0999718 q^{24} +1.09948 q^{25} +1.97098 q^{26} +0.353659 q^{27} +5.07453 q^{28} -1.00000 q^{29} -0.0649547 q^{30} +3.00347 q^{31} +4.65949 q^{32} -0.252974 q^{33} +2.94632 q^{34} -6.95818 q^{35} +5.39714 q^{36} +0.401833 q^{37} +1.87690 q^{38} -0.260669 q^{39} -4.18638 q^{40} -2.84424 q^{41} +0.0740992 q^{42} +2.53651 q^{43} -7.72567 q^{44} -7.40054 q^{45} +0.445942 q^{46} -11.7062 q^{47} -0.167871 q^{48} +0.937778 q^{49} +0.490303 q^{50} -0.389660 q^{51} -7.96068 q^{52} +7.37978 q^{53} +0.157712 q^{54} +10.5934 q^{55} +4.77575 q^{56} -0.248226 q^{57} -0.445942 q^{58} -1.99814 q^{59} +0.262348 q^{60} +14.6586 q^{61} +1.33937 q^{62} +8.44242 q^{63} -3.61486 q^{64} +10.9157 q^{65} -0.112812 q^{66} -12.4268 q^{67} -11.9000 q^{68} -0.0589774 q^{69} -3.10295 q^{70} -6.86171 q^{71} +5.07937 q^{72} +3.98002 q^{73} +0.179194 q^{74} -0.0648442 q^{75} -7.58069 q^{76} -12.0848 q^{77} -0.116243 q^{78} +17.1580 q^{79} +7.02969 q^{80} +8.96871 q^{81} -1.26837 q^{82} +3.57952 q^{83} -0.299282 q^{84} +16.3173 q^{85} +1.13114 q^{86} +0.0589774 q^{87} -7.27080 q^{88} -7.34060 q^{89} -3.30022 q^{90} -12.4524 q^{91} -1.80114 q^{92} -0.177137 q^{93} -5.22029 q^{94} +10.3946 q^{95} -0.274804 q^{96} +7.56673 q^{97} +0.418195 q^{98} -12.8531 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	0.445942	0.315329	0.157664	−	0.987493i	$-0.449604\pi$
$2$	0.445942	0.315329	0.157664	+	0.987493i	$0.449604\pi$
$3$	−0.0589774	−0.0340506	−0.0170253	−	0.999855i	$-0.505420\pi$
$3$	−0.0589774	−0.0340506	−0.0170253	+	0.999855i	$0.505420\pi$
$4$	−1.80114	−0.900568
$5$	2.46971	1.10449	0.552244	−	0.833682i	$-0.313772\pi$
$5$	2.46971	1.10449	0.552244	+	0.833682i	$0.313772\pi$
$6$	−0.0263005	−0.0107371
$7$	−2.81741	−1.06488	−0.532440	−	0.846468i	$-0.678725\pi$
$7$	−2.81741	−1.06488	−0.532440	+	0.846468i	$0.678725\pi$
$8$	−1.69509	−0.599304
$9$	−2.99652	−0.998841
$10$	1.10135	0.348277
$11$	4.28934	1.29328	0.646642	−	0.762794i	$-0.276173\pi$
$11$	4.28934	1.29328	0.646642	+	0.762794i	$0.276173\pi$
$12$	0.106226	0.0306649
$13$	4.41981	1.22584	0.612918	−	0.790147i	$-0.289996\pi$
$13$	4.41981	1.22584	0.612918	+	0.790147i	$0.289996\pi$
$14$	−1.25640	−0.335787
$15$	−0.145657	−0.0376085
$16$	2.84636	0.711590
$17$	6.60695	1.60242	0.801210	−	0.598383i	$-0.204190\pi$
$17$	6.60695	1.60242	0.801210	+	0.598383i	$0.204190\pi$
$18$	−1.33628	−0.314963
$19$	4.20884	0.965574	0.482787	−	0.875738i	$-0.339625\pi$
$19$	4.20884	0.965574	0.482787	+	0.875738i	$0.339625\pi$
$20$	−4.44829	−0.994667
$21$	0.166163	0.0362598
$22$	1.91280	0.407810
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.0999718	0.0204067
$25$	1.09948	0.219895
$26$	1.97098	0.386541
$27$	0.353659	0.0680617
$28$	5.07453	0.958996
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.0649547	−0.0118590
$31$	3.00347	0.539439	0.269719	−	0.962939i	$-0.413069\pi$
$31$	3.00347	0.539439	0.269719	+	0.962939i	$0.413069\pi$
$32$	4.65949	0.823689
$33$	−0.252974	−0.0440371
$34$	2.94632	0.505289
$35$	−6.95818	−1.17615
$36$	5.39714	0.899524
$37$	0.401833	0.0660609	0.0330305	−	0.999454i	$-0.489484\pi$
$37$	0.401833	0.0660609	0.0330305	+	0.999454i	$0.489484\pi$
$38$	1.87690	0.304473
$39$	−0.260669	−0.0417404
$40$	−4.18638	−0.661924
$41$	−2.84424	−0.444196	−0.222098	−	0.975024i	$-0.571291\pi$
$41$	−2.84424	−0.444196	−0.222098	+	0.975024i	$0.571291\pi$
$42$	0.0740992	0.0114338
$43$	2.53651	0.386814	0.193407	−	0.981119i	$-0.438046\pi$
$43$	2.53651	0.386814	0.193407	+	0.981119i	$0.438046\pi$
$44$	−7.72567	−1.16469
$45$	−7.40054	−1.10321
$46$	0.445942	0.0657506
$47$	−11.7062	−1.70753	−0.853763	−	0.520662i	$-0.825685\pi$
$47$	−11.7062	−1.70753	−0.853763	+	0.520662i	$0.825685\pi$
$48$	−0.167871	−0.0242301
$49$	0.937778	0.133968
$50$	0.490303	0.0693393
$51$	−0.389660	−0.0545634
$52$	−7.96068	−1.10395
$53$	7.37978	1.01369	0.506846	−	0.862037i	$-0.330811\pi$
$53$	7.37978	1.01369	0.506846	+	0.862037i	$0.330811\pi$
$54$	0.157712	0.0214618
$55$	10.5934	1.42842
$56$	4.77575	0.638186
$57$	−0.248226	−0.0328784
$58$	−0.445942	−0.0585551
$59$	−1.99814	−0.260136	−0.130068	−	0.991505i	$-0.541520\pi$
$59$	−1.99814	−0.260136	−0.130068	+	0.991505i	$0.541520\pi$
$60$	0.262348	0.0338690
$61$	14.6586	1.87685	0.938423	−	0.345488i	$-0.112287\pi$
$61$	14.6586	1.87685	0.938423	+	0.345488i	$0.112287\pi$
$62$	1.33937	0.170101
$63$	8.44242	1.06364
$64$	−3.61486	−0.451857
$65$	10.9157	1.35392
$66$	−0.112812	−0.0138862
$67$	−12.4268	−1.51817	−0.759085	−	0.650992i	$-0.774353\pi$
$67$	−12.4268	−1.51817	−0.759085	+	0.650992i	$0.774353\pi$
$68$	−11.9000	−1.44309
$69$	−0.0589774	−0.00710004
$70$	−3.10295	−0.370873
$71$	−6.86171	−0.814335	−0.407168	−	0.913353i	$-0.633484\pi$
$71$	−6.86171	−0.814335	−0.407168	+	0.913353i	$0.633484\pi$
$72$	5.07937	0.598609
$73$	3.98002	0.465827	0.232913	−	0.972498i	$-0.425174\pi$
$73$	3.98002	0.465827	0.232913	+	0.972498i	$0.425174\pi$
$74$	0.179194	0.0208309
$75$	−0.0648442	−0.00748756
$76$	−7.58069	−0.869564
$77$	−12.0848	−1.37719
$78$	−0.116243	−0.0131620
$79$	17.1580	1.93042	0.965212	−	0.261469i	$-0.0842069\pi$
$79$	17.1580	1.93042	0.965212	+	0.261469i	$0.0842069\pi$
$80$	7.02969	0.785943
$81$	8.96871	0.996523
$82$	−1.26837	−0.140068
$83$	3.57952	0.392903	0.196452	−	0.980514i	$-0.437058\pi$
$83$	3.57952	0.392903	0.196452	+	0.980514i	$0.437058\pi$
$84$	−0.299282	−0.0326544
$85$	16.3173	1.76985
$86$	1.13114	0.121974
$87$	0.0589774	0.00632304
$88$	−7.27080	−0.775070
$89$	−7.34060	−0.778102	−0.389051	−	0.921216i	$-0.627197\pi$
$89$	−7.34060	−0.778102	−0.389051	+	0.921216i	$0.627197\pi$
$90$	−3.30022	−0.347873
$91$	−12.4524	−1.30537
$92$	−1.80114	−0.187781
$93$	−0.177137	−0.0183682
$94$	−5.22029	−0.538432
$95$	10.3946	1.06646
$96$	−0.274804	−0.0280471
$97$	7.56673	0.768285	0.384143	−	0.923274i	$-0.374497\pi$
$97$	7.56673	0.768285	0.384143	+	0.923274i	$0.374497\pi$
$98$	0.418195	0.0422441
$99$	−12.8531	−1.29178
$100$	−1.98030	−0.198030
$101$	−8.93289	−0.888856	−0.444428	−	0.895815i	$-0.646593\pi$
$101$	−8.93289	−0.888856	−0.444428	+	0.895815i	$0.646593\pi$
$102$	−0.173766	−0.0172054
$103$	−17.0586	−1.68083	−0.840415	−	0.541944i	$-0.817689\pi$
$103$	−17.0586	−1.68083	−0.840415	+	0.541944i	$0.817689\pi$
$104$	−7.49197	−0.734648
$105$	0.410375	0.0400485
$106$	3.29096	0.319646
$107$	1.72224	0.166496	0.0832478	−	0.996529i	$-0.473471\pi$
$107$	1.72224	0.166496	0.0832478	+	0.996529i	$0.473471\pi$
$108$	−0.636988	−0.0612942
$109$	−10.6626	−1.02129	−0.510644	−	0.859792i	$-0.670593\pi$
$109$	−10.6626	−1.02129	−0.510644	+	0.859792i	$0.670593\pi$
$110$	4.72406	0.450421
$111$	−0.0236991	−0.00224942
$112$	−8.01935	−0.757757
$113$	16.2113	1.52503	0.762515	−	0.646971i	$-0.223964\pi$
$113$	16.2113	1.52503	0.762515	+	0.646971i	$0.223964\pi$
$114$	−0.110695	−0.0103675
$115$	2.46971	0.230302
$116$	1.80114	0.167231
$117$	−13.2441	−1.22441
$118$	−0.891056	−0.0820283
$119$	−18.6145	−1.70638
$120$	0.246902	0.0225389
$121$	7.39840	0.672582
$122$	6.53691	0.591824
$123$	0.167746	0.0151252
$124$	−5.40965	−0.485801
$125$	−9.63317	−0.861617
$126$	3.76483	0.335398
$127$	6.42264	0.569917	0.284958	−	0.958540i	$-0.408020\pi$
$127$	6.42264	0.569917	0.284958	+	0.958540i	$0.408020\pi$
$128$	−10.9310	−0.966172
$129$	−0.149597	−0.0131713
$130$	4.86776	0.426931
$131$	−14.9726	−1.30817	−0.654083	−	0.756423i	$-0.726945\pi$
$131$	−14.9726	−1.30817	−0.654083	+	0.756423i	$0.726945\pi$
$132$	0.455640	0.0396584
$133$	−11.8580	−1.02822
$134$	−5.54162	−0.478723
$135$	0.873436	0.0751734
$136$	−11.1994	−0.960337
$137$	−0.156153	−0.0133410	−0.00667052	−	0.999978i	$-0.502123\pi$
$137$	−0.156153	−0.0133410	−0.00667052	+	0.999978i	$0.502123\pi$
$138$	−0.0263005	−0.00223885
$139$	−13.5888	−1.15259	−0.576295	−	0.817241i	$-0.695502\pi$
$139$	−13.5888	−1.15259	−0.576295	+	0.817241i	$0.695502\pi$
$140$	12.5326	1.05920
$141$	0.690401	0.0581423
$142$	−3.05993	−0.256783
$143$	18.9581	1.58535
$144$	−8.52918	−0.710765
$145$	−2.46971	−0.205098
$146$	1.77486	0.146889
$147$	−0.0553077	−0.00456170
$148$	−0.723756	−0.0594924
$149$	2.15399	0.176461	0.0882307	−	0.996100i	$-0.471879\pi$
$149$	2.15399	0.176461	0.0882307	+	0.996100i	$0.471879\pi$
$150$	−0.0289168	−0.00236105
$151$	3.13094	0.254792	0.127396	−	0.991852i	$-0.459338\pi$
$151$	3.13094	0.254792	0.127396	+	0.991852i	$0.459338\pi$
$152$	−7.13435	−0.578672
$153$	−19.7979	−1.60056
$154$	−5.38913	−0.434268
$155$	7.41770	0.595804
$156$	0.469500	0.0375901
$157$	16.8952	1.34838	0.674191	−	0.738557i	$-0.264492\pi$
$157$	16.8952	1.34838	0.674191	+	0.738557i	$0.264492\pi$
$158$	7.65147	0.608718
$159$	−0.435240	−0.0345168
$160$	11.5076	0.909755
$161$	−2.81741	−0.222043
$162$	3.99953	0.314233
$163$	−22.1137	−1.73208	−0.866038	−	0.499978i	$-0.833342\pi$
$163$	−22.1137	−1.73208	−0.866038	+	0.499978i	$0.833342\pi$
$164$	5.12287	0.400029
$165$	−0.624772	−0.0486385
$166$	1.59626	0.123894
$167$	2.95049	0.228316	0.114158	−	0.993463i	$-0.463583\pi$
$167$	2.95049	0.228316	0.114158	+	0.993463i	$0.463583\pi$
$168$	−0.281661	−0.0217306
$169$	6.53474	0.502673
$170$	7.27656	0.558086
$171$	−12.6119	−0.964454
$172$	−4.56860	−0.348352
$173$	18.1533	1.38017	0.690085	−	0.723728i	$-0.257573\pi$
$173$	18.1533	1.38017	0.690085	+	0.723728i	$0.257573\pi$
$174$	0.0263005	0.00199384
$175$	−3.09767	−0.234162
$176$	12.2090	0.920287
$177$	0.117845	0.00885778
$178$	−3.27348	−0.245358
$179$	−10.1727	−0.760346	−0.380173	−	0.924915i	$-0.624136\pi$
$179$	−10.1727	−0.760346	−0.380173	+	0.924915i	$0.624136\pi$
$180$	13.3294	0.993514
$181$	21.4731	1.59608	0.798040	−	0.602604i	$-0.205870\pi$
$181$	21.4731	1.59608	0.798040	+	0.602604i	$0.205870\pi$
$182$	−5.55306	−0.411620
$183$	−0.864528	−0.0639078
$184$	−1.69509	−0.124964
$185$	0.992412	0.0729636
$186$	−0.0789927	−0.00579203
$187$	28.3394	2.07238
$188$	21.0845	1.53774
$189$	−0.996401	−0.0724775
$190$	4.63540	0.336287
$191$	21.7372	1.57285	0.786425	−	0.617686i	$-0.211930\pi$
$191$	21.7372	1.57285	0.786425	+	0.617686i	$0.211930\pi$
$192$	0.213195	0.0153860
$193$	−5.77711	−0.415846	−0.207923	−	0.978145i	$-0.566670\pi$
$193$	−5.77711	−0.415846	−0.207923	+	0.978145i	$0.566670\pi$
$194$	3.37433	0.242263
$195$	−0.643777	−0.0461018
$196$	−1.68906	−0.120647
$197$	−16.9138	−1.20506	−0.602529	−	0.798097i	$-0.705840\pi$
$197$	−16.9138	−1.20506	−0.602529	+	0.798097i	$0.705840\pi$
$198$	−5.73174	−0.407337
$199$	−15.4767	−1.09712	−0.548559	−	0.836112i	$-0.684823\pi$
$199$	−15.4767	−1.09712	−0.548559	+	0.836112i	$0.684823\pi$
$200$	−1.86371	−0.131784
$201$	0.732897	0.0516946
$202$	−3.98355	−0.280282
$203$	2.81741	0.197743
$204$	0.701831	0.0491380
$205$	−7.02446	−0.490610
$206$	−7.60713	−0.530014
$207$	−2.99652	−0.208273
$208$	12.5804	0.872292
$209$	18.0531	1.24876
$210$	0.183004	0.0126285
$211$	5.84718	0.402536	0.201268	−	0.979536i	$-0.435494\pi$
$211$	5.84718	0.402536	0.201268	+	0.979536i	$0.435494\pi$
$212$	−13.2920	−0.912897
$213$	0.404686	0.0277286
$214$	0.768022	0.0525009
$215$	6.26445	0.427232
$216$	−0.599483	−0.0407897
$217$	−8.46199	−0.574437
$218$	−4.75489	−0.322042
$219$	−0.234731	−0.0158617
$220$	−19.0802	−1.28639
$221$	29.2015	1.96430
$222$	−0.0105684	−0.000709306 0
$223$	−22.7769	−1.52525	−0.762625	−	0.646840i	$-0.776090\pi$
$223$	−22.7769	−1.52525	−0.762625	+	0.646840i	$0.776090\pi$
$224$	−13.1277	−0.877129
$225$	−3.29460	−0.219640
$226$	7.22930	0.480886
$227$	4.87598	0.323630	0.161815	−	0.986821i	$-0.448265\pi$
$227$	4.87598	0.323630	0.161815	+	0.986821i	$0.448265\pi$
$228$	0.447089	0.0296092
$229$	−10.9661	−0.724661	−0.362330	−	0.932050i	$-0.618019\pi$
$229$	−10.9661	−0.724661	−0.362330	+	0.932050i	$0.618019\pi$
$230$	1.10135	0.0726208
$231$	0.712730	0.0468942
$232$	1.69509	0.111288
$233$	29.0404	1.90250	0.951251	−	0.308418i	$-0.0997996\pi$
$233$	29.0404	1.90250	0.951251	+	0.308418i	$0.0997996\pi$
$234$	−5.90609	−0.386093
$235$	−28.9109	−1.88594
$236$	3.59892	0.234270
$237$	−1.01193	−0.0657321
$238$	−8.30098	−0.538072
$239$	22.0157	1.42408	0.712039	−	0.702140i	$-0.247772\pi$
$239$	22.0157	1.42408	0.712039	+	0.702140i	$0.247772\pi$
$240$	−0.414593	−0.0267618
$241$	−25.2176	−1.62441	−0.812206	−	0.583371i	$-0.801733\pi$
$241$	−25.2176	−1.62441	−0.812206	+	0.583371i	$0.801733\pi$
$242$	3.29926	0.212085
$243$	−1.58993	−0.101994
$244$	−26.4022	−1.69023
$245$	2.31604	0.147966
$246$	0.0748051	0.00476940
$247$	18.6023	1.18363
$248$	−5.09114	−0.323288
$249$	−0.211111	−0.0133786
$250$	−4.29584	−0.271693
$251$	−21.9563	−1.38587	−0.692933	−	0.721002i	$-0.743682\pi$
$251$	−21.9563	−1.38587	−0.692933	+	0.721002i	$0.743682\pi$
$252$	−15.2059	−0.957884
$253$	4.28934	0.269668
$254$	2.86413	0.179711
$255$	−0.962349	−0.0602646
$256$	2.35512	0.147195
$257$	−23.2366	−1.44946	−0.724731	−	0.689032i	$-0.758036\pi$
$257$	−23.2366	−1.44946	−0.724731	+	0.689032i	$0.758036\pi$
$258$	−0.0667115	−0.00415328
$259$	−1.13213	−0.0703469
$260$	−19.6606	−1.21930
$261$	2.99652	0.185480
$262$	−6.67694	−0.412503
$263$	−7.44609	−0.459145	−0.229573	−	0.973292i	$-0.573733\pi$
$263$	−7.44609	−0.459145	−0.229573	+	0.973292i	$0.573733\pi$
$264$	0.428813	0.0263916
$265$	18.2259	1.11961
$266$	−5.28799	−0.324227
$267$	0.432929	0.0264948
$268$	22.3823	1.36721
$269$	17.2475	1.05160	0.525800	−	0.850608i	$-0.323766\pi$
$269$	17.2475	1.05160	0.525800	+	0.850608i	$0.323766\pi$
$270$	0.389502	0.0237043
$271$	3.53709	0.214863	0.107431	−	0.994212i	$-0.465737\pi$
$271$	3.53709	0.214863	0.107431	+	0.994212i	$0.465737\pi$
$272$	18.8057	1.14027
$273$	0.734410	0.0444485
$274$	−0.0696352	−0.00420682
$275$	4.71602	0.284387
$276$	0.106226	0.00639407
$277$	−5.35010	−0.321456	−0.160728	−	0.986999i	$-0.551384\pi$
$277$	−5.35010	−0.321456	−0.160728	+	0.986999i	$0.551384\pi$
$278$	−6.05984	−0.363445
$279$	−8.99995	−0.538813
$280$	11.7947	0.704870
$281$	2.43662	0.145356	0.0726782	−	0.997355i	$-0.476845\pi$
$281$	2.43662	0.145356	0.0726782	+	0.997355i	$0.476845\pi$
$282$	0.307879	0.0183339
$283$	−14.9942	−0.891313	−0.445656	−	0.895204i	$-0.647030\pi$
$283$	−14.9942	−0.891313	−0.445656	+	0.895204i	$0.647030\pi$
$284$	12.3589	0.733364
$285$	−0.613047	−0.0363138
$286$	8.45420	0.499908
$287$	8.01339	0.473016
$288$	−13.9623	−0.822734
$289$	26.6518	1.56775
$290$	−1.10135	−0.0646735
$291$	−0.446266	−0.0261606
$292$	−7.16856	−0.419508
$293$	−9.90190	−0.578475	−0.289238	−	0.957257i	$-0.593402\pi$
$293$	−9.90190	−0.578475	−0.289238	+	0.957257i	$0.593402\pi$
$294$	−0.0246640	−0.00143844
$295$	−4.93483	−0.287317
$296$	−0.681142	−0.0395906
$297$	1.51696	0.0880231
$298$	0.960554	0.0556434
$299$	4.41981	0.255604
$300$	0.116793	0.00674306
$301$	−7.14638	−0.411910
$302$	1.39622	0.0803433
$303$	0.526838	0.0302661
$304$	11.9799	0.687092
$305$	36.2026	2.07296
$306$	−8.82871	−0.504704
$307$	8.06498	0.460293	0.230146	−	0.973156i	$-0.426079\pi$
$307$	8.06498	0.460293	0.230146	+	0.973156i	$0.426079\pi$
$308$	21.7664	1.24025
$309$	1.00607	0.0572333
$310$	3.30787	0.187874
$311$	−16.9600	−0.961714	−0.480857	−	0.876799i	$-0.659674\pi$
$311$	−16.9600	−0.961714	−0.480857	+	0.876799i	$0.659674\pi$
$312$	0.441857	0.0250152
$313$	30.2949	1.71237	0.856185	−	0.516669i	$-0.172828\pi$
$313$	30.2949	1.71237	0.856185	+	0.516669i	$0.172828\pi$
$314$	7.53428	0.425184
$315$	20.8503	1.17478
$316$	−30.9038	−1.73848
$317$	−21.3506	−1.19917	−0.599584	−	0.800312i	$-0.704667\pi$
$317$	−21.3506	−1.19917	−0.599584	+	0.800312i	$0.704667\pi$
$318$	−0.194092	−0.0108841
$319$	−4.28934	−0.240157
$320$	−8.92765	−0.499071
$321$	−0.101573	−0.00566928
$322$	−1.25640	−0.0700165
$323$	27.8076	1.54725
$324$	−16.1539	−0.897436
$325$	4.85948	0.269555
$326$	−9.86143	−0.546174
$327$	0.628850	0.0347755
$328$	4.82124	0.266209
$329$	32.9811	1.81831
$330$	−0.278612	−0.0153371
$331$	0.784375	0.0431131	0.0215566	−	0.999768i	$-0.493138\pi$
$331$	0.784375	0.0431131	0.0215566	+	0.999768i	$0.493138\pi$
$332$	−6.44720	−0.353836
$333$	−1.20410	−0.0659844
$334$	1.31575	0.0719946
$335$	−30.6905	−1.67680
$336$	0.472960	0.0258021
$337$	−22.2511	−1.21209	−0.606047	−	0.795429i	$-0.707246\pi$
$337$	−22.2511	−1.21209	−0.606047	+	0.795429i	$0.707246\pi$
$338$	2.91412	0.158507
$339$	−0.956099	−0.0519282
$340$	−29.3896	−1.59387
$341$	12.8829	0.697647
$342$	−5.62417	−0.304120
$343$	17.0797	0.922219
$344$	−4.29961	−0.231819
$345$	−0.145657	−0.00784192
$346$	8.09533	0.435207
$347$	19.0506	1.02269	0.511344	−	0.859376i	$-0.329148\pi$
$347$	19.0506	1.02269	0.511344	+	0.859376i	$0.329148\pi$
$348$	−0.106226	−0.00569432
$349$	−13.1162	−0.702096	−0.351048	−	0.936357i	$-0.614175\pi$
$349$	−13.1162	−0.702096	−0.351048	+	0.936357i	$0.614175\pi$
$350$	−1.38138	−0.0738380
$351$	1.56311	0.0834325
$352$	19.9861	1.06526
$353$	17.5345	0.933265	0.466633	−	0.884451i	$-0.345467\pi$
$353$	17.5345	0.933265	0.466633	+	0.884451i	$0.345467\pi$
$354$	0.0525521	0.00279311
$355$	−16.9464	−0.899424
$356$	13.2214	0.700733
$357$	1.09783	0.0581034
$358$	−4.53646	−0.239759
$359$	21.0184	1.10931	0.554653	−	0.832082i	$-0.312851\pi$
$359$	21.0184	1.10931	0.554653	+	0.832082i	$0.312851\pi$
$360$	12.5446	0.661157
$361$	−1.28569	−0.0676678
$362$	9.57575	0.503290
$363$	−0.436338	−0.0229018
$364$	22.4285	1.17557
$365$	9.82951	0.514500
$366$	−0.385530	−0.0201520
$367$	22.5736	1.17833	0.589165	−	0.808013i	$-0.299457\pi$
$367$	22.5736	1.17833	0.589165	+	0.808013i	$0.299457\pi$
$368$	2.84636	0.148377
$369$	8.52284	0.443681
$370$	0.442559	0.0230075
$371$	−20.7918	−1.07946
$372$	0.319047	0.0165418
$373$	−28.5809	−1.47986	−0.739931	−	0.672683i	$-0.765142\pi$
$373$	−28.5809	−1.47986	−0.739931	+	0.672683i	$0.765142\pi$
$374$	12.6377	0.653482
$375$	0.568139	0.0293386
$376$	19.8430	1.02333
$377$	−4.41981	−0.227632
$378$	−0.444338	−0.0228543
$379$	−8.35998	−0.429423	−0.214712	−	0.976677i	$-0.568881\pi$
$379$	−8.35998	−0.429423	−0.214712	+	0.976677i	$0.568881\pi$
$380$	−18.7221	−0.960424
$381$	−0.378790	−0.0194060
$382$	9.69355	0.495965
$383$	−1.67118	−0.0853932	−0.0426966	−	0.999088i	$-0.513595\pi$
$383$	−1.67118	−0.0853932	−0.0426966	+	0.999088i	$0.513595\pi$
$384$	0.644681	0.0328988
$385$	−29.8460	−1.52109
$386$	−2.57626	−0.131128
$387$	−7.60071	−0.386366
$388$	−13.6287	−0.691893
$389$	−18.1730	−0.921405	−0.460703	−	0.887554i	$-0.652403\pi$
$389$	−18.1730	−0.921405	−0.460703	+	0.887554i	$0.652403\pi$
$390$	−0.287088	−0.0145372
$391$	6.60695	0.334128
$392$	−1.58962	−0.0802877
$393$	0.883048	0.0445439
$394$	−7.54258	−0.379990
$395$	42.3753	2.13213
$396$	23.1502	1.16334
$397$	11.1359	0.558897	0.279449	−	0.960161i	$-0.409848\pi$
$397$	11.1359	0.558897	0.279449	+	0.960161i	$0.409848\pi$
$398$	−6.90174	−0.345953
$399$	0.699354	0.0350115
$400$	3.12950	0.156475
$401$	36.0633	1.80091	0.900457	−	0.434945i	$-0.143232\pi$
$401$	36.0633	1.80091	0.900457	+	0.434945i	$0.143232\pi$
$402$	0.326830	0.0163008
$403$	13.2748	0.661263
$404$	16.0893	0.800475
$405$	22.1501	1.10065
$406$	1.25640	0.0623541
$407$	1.72360	0.0854355
$408$	0.660509	0.0327000
$409$	−5.09351	−0.251858	−0.125929	−	0.992039i	$-0.540191\pi$
$409$	−5.09351	−0.251858	−0.125929	+	0.992039i	$0.540191\pi$
$410$	−3.13251	−0.154703
$411$	0.00920949	0.000454271 0
$412$	30.7248	1.51370
$413$	5.62958	0.277013
$414$	−1.33628	−0.0656744
$415$	8.84038	0.433957
$416$	20.5941	1.00971
$417$	0.801435	0.0392464
$418$	8.05065	0.393770
$419$	−18.9896	−0.927701	−0.463850	−	0.885914i	$-0.653532\pi$
$419$	−18.9896	−0.927701	−0.463850	+	0.885914i	$0.653532\pi$
$420$	−0.739141	−0.0360664
$421$	−25.9673	−1.26557	−0.632784	−	0.774328i	$-0.718088\pi$
$421$	−25.9673	−1.26557	−0.632784	+	0.774328i	$0.718088\pi$
$422$	2.60750	0.126931
$423$	35.0779	1.70555
$424$	−12.5094	−0.607509
$425$	7.26418	0.352364
$426$	0.180467	0.00874363
$427$	−41.2993	−1.99862
$428$	−3.10200	−0.149941
$429$	−1.11810	−0.0539822
$430$	2.79358	0.134719
$431$	−20.4418	−0.984648	−0.492324	−	0.870412i	$-0.663852\pi$
$431$	−20.4418	−0.984648	−0.492324	+	0.870412i	$0.663852\pi$
$432$	1.00664	0.0484320
$433$	2.43016	0.116786	0.0583930	−	0.998294i	$-0.481402\pi$
$433$	2.43016	0.116786	0.0583930	+	0.998294i	$0.481402\pi$
$434$	−3.77356	−0.181137
$435$	0.145657	0.00698372
$436$	19.2047	0.919739
$437$	4.20884	0.201336
$438$	−0.104677	−0.00500164
$439$	9.08175	0.433448	0.216724	−	0.976233i	$-0.430463\pi$
$439$	9.08175	0.433448	0.216724	+	0.976233i	$0.430463\pi$
$440$	−17.9568	−0.856056
$441$	−2.81007	−0.133813
$442$	13.0222	0.619402
$443$	26.2999	1.24954	0.624772	−	0.780807i	$-0.285192\pi$
$443$	26.2999	1.24954	0.624772	+	0.780807i	$0.285192\pi$
$444$	0.0426852	0.00202575
$445$	−18.1292	−0.859405
$446$	−10.1572	−0.480956
$447$	−0.127036	−0.00600862
$448$	10.1845	0.481173
$449$	−21.0659	−0.994161	−0.497081	−	0.867704i	$-0.665595\pi$
$449$	−21.0659	−0.994161	−0.497081	+	0.867704i	$0.665595\pi$
$450$	−1.46920	−0.0692589
$451$	−12.1999	−0.574472
$452$	−29.1987	−1.37339
$453$	−0.184654	−0.00867582
$454$	2.17441	0.102050
$455$	−30.7539	−1.44176
$456$	0.420765	0.0197041
$457$	−11.7132	−0.547922	−0.273961	−	0.961741i	$-0.588334\pi$
$457$	−11.7132	−0.547922	−0.273961	+	0.961741i	$0.588334\pi$
$458$	−4.89025	−0.228506
$459$	2.33661	0.109063
$460$	−4.44829	−0.207402
$461$	−11.7310	−0.546369	−0.273184	−	0.961962i	$-0.588077\pi$
$461$	−11.7310	−0.546369	−0.273184	+	0.961962i	$0.588077\pi$
$462$	0.317837	0.0147871
$463$	−10.9534	−0.509049	−0.254525	−	0.967066i	$-0.581919\pi$
$463$	−10.9534	−0.509049	−0.254525	+	0.967066i	$0.581919\pi$
$464$	−2.84636	−0.132139
$465$	−0.437476	−0.0202875
$466$	12.9504	0.599914
$467$	−3.23636	−0.149761	−0.0748804	−	0.997193i	$-0.523857\pi$
$467$	−3.23636	−0.149761	−0.0748804	+	0.997193i	$0.523857\pi$
$468$	23.8544	1.10267
$469$	35.0112	1.61667
$470$	−12.8926	−0.594692
$471$	−0.996433	−0.0459132
$472$	3.38702	0.155900
$473$	10.8799	0.500260
$474$	−0.451264	−0.0207272
$475$	4.62751	0.212325
$476$	33.5272	1.53671
$477$	−22.1137	−1.01252
$478$	9.81773	0.449053
$479$	−19.1033	−0.872854	−0.436427	−	0.899740i	$-0.643756\pi$
$479$	−19.1033	−0.872854	−0.436427	+	0.899740i	$0.643756\pi$
$480$	−0.678688	−0.0309777
$481$	1.77603	0.0809799
$482$	−11.2456	−0.512224
$483$	0.166163	0.00756069
$484$	−13.3255	−0.605706
$485$	18.6877	0.848563
$486$	−0.709016	−0.0321616
$487$	−10.3407	−0.468580	−0.234290	−	0.972167i	$-0.575277\pi$
$487$	−10.3407	−0.468580	−0.234290	+	0.972167i	$0.575277\pi$
$488$	−24.8477	−1.12480
$489$	1.30421	0.0589783
$490$	1.03282	0.0466581
$491$	−5.57488	−0.251591	−0.125795	−	0.992056i	$-0.540148\pi$
$491$	−5.57488	−0.251591	−0.125795	+	0.992056i	$0.540148\pi$
$492$	−0.302133	−0.0136212
$493$	−6.60695	−0.297562
$494$	8.29554	0.373234
$495$	−31.7434	−1.42676
$496$	8.54895	0.383859
$497$	19.3322	0.867169
$498$	−0.0941432	−0.00421866
$499$	−15.7898	−0.706847	−0.353423	−	0.935463i	$-0.614982\pi$
$499$	−15.7898	−0.706847	−0.353423	+	0.935463i	$0.614982\pi$
$500$	17.3506	0.775944
$501$	−0.174012	−0.00777430
$502$	−9.79123	−0.437004
$503$	−33.2833	−1.48403	−0.742015	−	0.670383i	$-0.766130\pi$
$503$	−33.2833	−1.48403	−0.742015	+	0.670383i	$0.766130\pi$
$504$	−14.3106	−0.637447
$505$	−22.0617	−0.981731
$506$	1.91280	0.0850342
$507$	−0.385402	−0.0171163
$508$	−11.5680	−0.513249
$509$	21.2303	0.941015	0.470507	−	0.882396i	$-0.344071\pi$
$509$	21.2303	0.941015	0.470507	+	0.882396i	$0.344071\pi$
$510$	−0.429152	−0.0190032
$511$	−11.2133	−0.496049
$512$	22.9122	1.01259
$513$	1.48849	0.0657186
$514$	−10.3622	−0.457057
$515$	−42.1297	−1.85646
$516$	0.269444	0.0118616
$517$	−50.2118	−2.20831
$518$	−0.504863	−0.0221824
$519$	−1.07063	−0.0469956
$520$	−18.5030	−0.811410
$521$	−31.4014	−1.37572	−0.687860	−	0.725843i	$-0.741450\pi$
$521$	−31.4014	−1.37572	−0.687860	+	0.725843i	$0.741450\pi$
$522$	1.33628	0.0584872
$523$	17.7232	0.774981	0.387491	−	0.921874i	$-0.373342\pi$
$523$	17.7232	0.774981	0.387491	+	0.921874i	$0.373342\pi$
$524$	26.9678	1.17809
$525$	0.182692	0.00797335
$526$	−3.32053	−0.144782
$527$	19.8437	0.864407
$528$	−0.720054	−0.0313363
$529$	1.00000	0.0434783
$530$	8.12772	0.353046
$531$	5.98747	0.259834
$532$	21.3579	0.925981
$533$	−12.5710	−0.544512
$534$	0.193062	0.00835459
$535$	4.25345	0.183893
$536$	21.0644	0.909845
$537$	0.599962	0.0258903
$538$	7.69140	0.331600
$539$	4.02244	0.173259
$540$	−1.57318	−0.0676987
$541$	12.4106	0.533575	0.266788	−	0.963755i	$-0.414038\pi$
$541$	12.4106	0.533575	0.266788	+	0.963755i	$0.414038\pi$
$542$	1.57734	0.0677525
$543$	−1.26643	−0.0543475
$544$	30.7850	1.31990
$545$	−26.3334	−1.12800
$546$	0.327505	0.0140159
$547$	25.4806	1.08947	0.544737	−	0.838607i	$-0.316630\pi$
$547$	25.4806	1.08947	0.544737	+	0.838607i	$0.316630\pi$
$548$	0.281253	0.0120145
$549$	−43.9249	−1.87467
$550$	2.10307	0.0896754
$551$	−4.20884	−0.179302
$552$	0.0999718	0.00425508
$553$	−48.3410	−2.05567
$554$	−2.38584	−0.101364
$555$	−0.0585298	−0.00248445
$556$	24.4754	1.03799
$557$	−3.73579	−0.158291	−0.0791453	−	0.996863i	$-0.525219\pi$
$557$	−3.73579	−0.158291	−0.0791453	+	0.996863i	$0.525219\pi$
$558$	−4.01346	−0.169903
$559$	11.2109	0.474170
$560$	−19.8055	−0.836934
$561$	−1.67138	−0.0705659
$562$	1.08659	0.0458351
$563$	25.6826	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$563$	25.6826	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$564$	−1.24351	−0.0523611
$565$	40.0372	1.68438
$566$	−6.68655	−0.281057
$567$	−25.2685	−1.06118
$568$	11.6312	0.488034
$569$	15.4592	0.648082	0.324041	−	0.946043i	$-0.394958\pi$
$569$	15.4592	0.648082	0.324041	+	0.946043i	$0.394958\pi$
$570$	−0.273384	−0.0114508
$571$	−22.9487	−0.960373	−0.480186	−	0.877166i	$-0.659431\pi$
$571$	−22.9487	−0.960373	−0.480186	+	0.877166i	$0.659431\pi$
$572$	−34.1460	−1.42772
$573$	−1.28200	−0.0535565
$574$	3.57351	0.149156
$575$	1.09948	0.0458513
$576$	10.8320	0.451333
$577$	−8.10729	−0.337511	−0.168755	−	0.985658i	$-0.553975\pi$
$577$	−8.10729	−0.337511	−0.168755	+	0.985658i	$0.553975\pi$
$578$	11.8852	0.494357
$579$	0.340719	0.0141598
$580$	4.44829	0.184705
$581$	−10.0850	−0.418394
$582$	−0.199009	−0.00824919
$583$	31.6544	1.31099
$584$	−6.74649	−0.279172
$585$	−32.7090	−1.35235
$586$	−4.41568	−0.182410
$587$	−21.2223	−0.875938	−0.437969	−	0.898990i	$-0.644302\pi$
$587$	−21.2223	−0.875938	−0.437969	+	0.898990i	$0.644302\pi$
$588$	0.0996166	0.00410812
$589$	12.6411	0.520868
$590$	−2.20065	−0.0905994
$591$	0.997532	0.0410330
$592$	1.14376	0.0470083
$593$	−4.05015	−0.166320	−0.0831599	−	0.996536i	$-0.526501\pi$
$593$	−4.05015	−0.166320	−0.0831599	+	0.996536i	$0.526501\pi$
$594$	0.676478	0.0277562
$595$	−45.9723	−1.88468
$596$	−3.87962	−0.158915
$597$	0.912778	0.0373575
$598$	1.97098	0.0805994
$599$	−35.6449	−1.45641	−0.728205	−	0.685359i	$-0.759645\pi$
$599$	−35.6449	−1.45641	−0.728205	+	0.685359i	$0.759645\pi$
$600$	0.109917	0.00448733
$601$	−34.0859	−1.39039	−0.695196	−	0.718820i	$-0.744683\pi$
$601$	−34.0859	−1.39039	−0.695196	+	0.718820i	$0.744683\pi$
$602$	−3.18687	−0.129887
$603$	37.2370	1.51641
$604$	−5.63924	−0.229457
$605$	18.2719	0.742859
$606$	0.234940	0.00954377
$607$	24.0259	0.975183	0.487592	−	0.873072i	$-0.337876\pi$
$607$	24.0259	0.975183	0.487592	+	0.873072i	$0.337876\pi$
$608$	19.6110	0.795332
$609$	−0.166163	−0.00673327
$610$	16.1443	0.653663
$611$	−51.7392	−2.09315
$612$	35.6586	1.44141
$613$	−10.2325	−0.413285	−0.206643	−	0.978417i	$-0.566254\pi$
$613$	−10.2325	−0.413285	−0.206643	+	0.978417i	$0.566254\pi$
$614$	3.59652	0.145144
$615$	0.414285	0.0167056
$616$	20.4848	0.825356
$617$	21.8083	0.877969	0.438985	−	0.898495i	$-0.355338\pi$
$617$	21.8083	0.877969	0.438985	+	0.898495i	$0.355338\pi$
$618$	0.448649	0.0180473
$619$	3.64506	0.146507	0.0732537	−	0.997313i	$-0.476662\pi$
$619$	3.64506	0.146507	0.0732537	+	0.997313i	$0.476662\pi$
$620$	−13.3603	−0.536562
$621$	0.353659	0.0141919
$622$	−7.56319	−0.303256
$623$	20.6815	0.828585
$624$	−0.741958	−0.0297021
$625$	−29.2885	−1.17154
$626$	13.5098	0.539960
$627$	−1.06473	−0.0425210
$628$	−30.4305	−1.21431
$629$	2.65489	0.105857
$630$	9.29805	0.370443
$631$	26.2926	1.04669	0.523346	−	0.852120i	$-0.324684\pi$
$631$	26.2926	1.04669	0.523346	+	0.852120i	$0.324684\pi$
$632$	−29.0843	−1.15691
$633$	−0.344851	−0.0137066
$634$	−9.52112	−0.378132
$635$	15.8621	0.629467
$636$	0.783927	0.0310847
$637$	4.14480	0.164223
$638$	−1.91280	−0.0757284
$639$	20.5613	0.813391
$640$	−26.9964	−1.06713
$641$	−0.983922	−0.0388626	−0.0194313	−	0.999811i	$-0.506186\pi$
$641$	−0.983922	−0.0388626	−0.0194313	+	0.999811i	$0.506186\pi$
$642$	−0.0452959	−0.00178769
$643$	4.65539	0.183591	0.0917953	−	0.995778i	$-0.470739\pi$
$643$	4.65539	0.183591	0.0917953	+	0.995778i	$0.470739\pi$
$644$	5.07453	0.199964
$645$	−0.369461	−0.0145475
$646$	12.4006	0.487894
$647$	28.6978	1.12823	0.564114	−	0.825697i	$-0.309218\pi$
$647$	28.6978	1.12823	0.564114	+	0.825697i	$0.309218\pi$
$648$	−15.2027	−0.597220
$649$	−8.57070	−0.336429
$650$	2.16705	0.0849986
$651$	0.499066	0.0195599
$652$	39.8297	1.55985
$653$	9.32695	0.364992	0.182496	−	0.983207i	$-0.441582\pi$
$653$	9.32695	0.364992	0.182496	+	0.983207i	$0.441582\pi$
$654$	0.280431	0.0109657
$655$	−36.9781	−1.44486
$656$	−8.09574	−0.316086
$657$	−11.9262	−0.465286
$658$	14.7077	0.573365
$659$	−27.8179	−1.08363	−0.541816	−	0.840497i	$-0.682263\pi$
$659$	−27.8179	−1.08363	−0.541816	+	0.840497i	$0.682263\pi$
$660$	1.12530	0.0438022
$661$	−4.22069	−0.164166	−0.0820828	−	0.996626i	$-0.526157\pi$
$661$	−4.22069	−0.164166	−0.0820828	+	0.996626i	$0.526157\pi$
$662$	0.349786	0.0135948
$663$	−1.72223	−0.0668857
$664$	−6.06760	−0.235468
$665$	−29.2859	−1.13566
$666$	−0.536960	−0.0208068
$667$	−1.00000	−0.0387202
$668$	−5.31424	−0.205614
$669$	1.34332	0.0519357
$670$	−13.6862	−0.528744
$671$	62.8758	2.42729
$672$	0.774236	0.0298668
$673$	20.7109	0.798348	0.399174	−	0.916875i	$-0.369297\pi$
$673$	20.7109	0.798348	0.399174	+	0.916875i	$0.369297\pi$
$674$	−9.92271	−0.382208
$675$	0.388840	0.0149664
$676$	−11.7700	−0.452691
$677$	32.4382	1.24670	0.623350	−	0.781943i	$-0.285771\pi$
$677$	32.4382	1.24670	0.623350	+	0.781943i	$0.285771\pi$
$678$	−0.426365	−0.0163745
$679$	−21.3186	−0.818131
$680$	−27.6592	−1.06068
$681$	−0.287573	−0.0110198
$682$	5.74502	0.219988
$683$	−30.2595	−1.15785	−0.578923	−	0.815382i	$-0.696527\pi$
$683$	−30.2595	−1.15785	−0.578923	+	0.815382i	$0.696527\pi$
$684$	22.7157	0.868556
$685$	−0.385653	−0.0147350
$686$	7.61658	0.290802
$687$	0.646752	0.0246751
$688$	7.21982	0.275253
$689$	32.6173	1.24262
$690$	−0.0649547	−0.00247278
$691$	32.4824	1.23569	0.617845	−	0.786300i	$-0.288006\pi$
$691$	32.4824	1.23569	0.617845	+	0.786300i	$0.288006\pi$
$692$	−32.6965	−1.24294
$693$	36.2124	1.37559
$694$	8.49545	0.322483
$695$	−33.5605	−1.27302
$696$	−0.0999718	−0.00378942
$697$	−18.7918	−0.711789
$698$	−5.84909	−0.221391
$699$	−1.71273	−0.0647813
$700$	5.57932	0.210879
$701$	7.93803	0.299815	0.149908	−	0.988700i	$-0.452102\pi$
$701$	7.93803	0.299815	0.149908	+	0.988700i	$0.452102\pi$
$702$	0.697056	0.0263087
$703$	1.69125	0.0637867
$704$	−15.5053	−0.584379
$705$	1.70509	0.0642175
$706$	7.81936	0.294286
$707$	25.1676	0.946524
$708$	−0.212255	−0.00797703
$709$	26.4257	0.992438	0.496219	−	0.868197i	$-0.334721\pi$
$709$	26.4257	0.992438	0.496219	+	0.868197i	$0.334721\pi$
$710$	−7.55714	−0.283614
$711$	−51.4143	−1.92819
$712$	12.4430	0.466320
$713$	3.00347	0.112481
$714$	0.489570	0.0183217
$715$	46.8209	1.75100
$716$	18.3225	0.684743
$717$	−1.29843	−0.0484907
$718$	9.37298	0.349796
$719$	−10.2899	−0.383747	−0.191873	−	0.981420i	$-0.561456\pi$
$719$	−10.2899	−0.383747	−0.191873	+	0.981420i	$0.561456\pi$
$720$	−21.0646	−0.785032
$721$	48.0609	1.78988
$722$	−0.573343	−0.0213376
$723$	1.48727	0.0553122
$724$	−38.6759	−1.43738
$725$	−1.09948	−0.0408335
$726$	−0.194582	−0.00722161
$727$	−8.52204	−0.316065	−0.158033	−	0.987434i	$-0.550515\pi$
$727$	−8.52204	−0.316065	−0.158033	+	0.987434i	$0.550515\pi$
$728$	21.1079	0.782312
$729$	−26.8124	−0.993050
$730$	4.38340	0.162237
$731$	16.7586	0.619839
$732$	1.55713	0.0575533
$733$	−44.2153	−1.63313	−0.816566	−	0.577253i	$-0.804125\pi$
$733$	−44.2153	−1.63313	−0.816566	+	0.577253i	$0.804125\pi$
$734$	10.0665	0.371562
$735$	−0.136594	−0.00503835
$736$	4.65949	0.171751
$737$	−53.3025	−1.96342
$738$	3.80070	0.139906
$739$	−12.5582	−0.461959	−0.230980	−	0.972959i	$-0.574193\pi$
$739$	−12.5582	−0.461959	−0.230980	+	0.972959i	$0.574193\pi$
$740$	−1.78747	−0.0657086
$741$	−1.09711	−0.0403035
$742$	−9.27197	−0.340385
$743$	22.9126	0.840580	0.420290	−	0.907390i	$-0.361928\pi$
$743$	22.9126	0.840580	0.420290	+	0.907390i	$0.361928\pi$
$744$	0.300262	0.0110081
$745$	5.31973	0.194900
$746$	−12.7454	−0.466643
$747$	−10.7261	−0.392448
$748$	−51.0431	−1.86632
$749$	−4.85226	−0.177298
$750$	0.253357	0.00925130
$751$	−1.20310	−0.0439018	−0.0219509	−	0.999759i	$-0.506988\pi$
$751$	−1.20310	−0.0439018	−0.0219509	+	0.999759i	$0.506988\pi$
$752$	−33.3201	−1.21506
$753$	1.29492	0.0471896
$754$	−1.97098	−0.0717789
$755$	7.73251	0.281415
$756$	1.79465	0.0652709
$757$	3.23336	0.117518	0.0587592	−	0.998272i	$-0.481286\pi$
$757$	3.23336	0.117518	0.0587592	+	0.998272i	$0.481286\pi$
$758$	−3.72807	−0.135410
$759$	−0.252974	−0.00918237
$760$	−17.6198	−0.639137
$761$	−42.3343	−1.53462	−0.767308	−	0.641279i	$-0.778404\pi$
$761$	−42.3343	−1.53462	−0.767308	+	0.641279i	$0.778404\pi$
$762$	−0.168919	−0.00611928
$763$	30.0408	1.08755
$764$	−39.1517	−1.41646
$765$	−48.8950	−1.76780
$766$	−0.745249	−0.0269269
$767$	−8.83141	−0.318884
$768$	−0.138899	−0.00501207
$769$	−28.5767	−1.03050	−0.515251	−	0.857040i	$-0.672301\pi$
$769$	−28.5767	−1.03050	−0.515251	+	0.857040i	$0.672301\pi$
$770$	−13.3096	−0.479644
$771$	1.37044	0.0493551
$772$	10.4054	0.374497
$773$	−14.8823	−0.535281	−0.267640	−	0.963519i	$-0.586244\pi$
$773$	−14.8823	−0.535281	−0.267640	+	0.963519i	$0.586244\pi$
$774$	−3.38948	−0.121832
$775$	3.30224	0.118620
$776$	−12.8263	−0.460437
$777$	0.0667699	0.00239536
$778$	−8.10409	−0.290546
$779$	−11.9710	−0.428904
$780$	1.15953	0.0415178
$781$	−29.4322	−1.05317
$782$	2.94632	0.105360
$783$	−0.353659	−0.0126387
$784$	2.66925	0.0953305
$785$	41.7262	1.48927
$786$	0.393788	0.0140460
$787$	−7.61476	−0.271437	−0.135719	−	0.990747i	$-0.543334\pi$
$787$	−7.61476	−0.271437	−0.135719	+	0.990747i	$0.543334\pi$
$788$	30.4640	1.08524
$789$	0.439151	0.0156342
$790$	18.8969	0.672323
$791$	−45.6738	−1.62397
$792$	21.7871	0.774171
$793$	64.7884	2.30070
$794$	4.96599	0.176236
$795$	−1.07492	−0.0381234
$796$	27.8757	0.988029
$797$	31.1708	1.10413	0.552063	−	0.833803i	$-0.313841\pi$
$797$	31.1708	1.10413	0.552063	+	0.833803i	$0.313841\pi$
$798$	0.311872	0.0110401
$799$	−77.3423	−2.73617
$800$	5.12299	0.181125
$801$	21.9963	0.777200
$802$	16.0821	0.567880
$803$	17.0717	0.602446
$804$	−1.32005	−0.0465545
$805$	−6.95818	−0.245244
$806$	5.91978	0.208515
$807$	−1.01721	−0.0358076
$808$	15.1420	0.532695
$809$	−17.5131	−0.615729	−0.307864	−	0.951430i	$-0.599614\pi$
$809$	−17.5131	−0.615729	−0.307864	+	0.951430i	$0.599614\pi$
$810$	9.87768	0.347066
$811$	25.4490	0.893634	0.446817	−	0.894625i	$-0.352558\pi$
$811$	25.4490	0.893634	0.446817	+	0.894625i	$0.352558\pi$
$812$	−5.07453	−0.178081
$813$	−0.208608	−0.00731621
$814$	0.768625	0.0269403
$815$	−54.6144	−1.91306
$816$	−1.10911	−0.0388267
$817$	10.6758	0.373497
$818$	−2.27141	−0.0794181
$819$	37.3139	1.30385
$820$	12.6520	0.441827
$821$	46.7718	1.63235	0.816174	−	0.577807i	$-0.196091\pi$
$821$	46.7718	1.63235	0.816174	+	0.577807i	$0.196091\pi$
$822$	0.00410690	0.000143245 0
$823$	−32.5789	−1.13563	−0.567814	−	0.823157i	$-0.692211\pi$
$823$	−32.5789	−1.13563	−0.567814	+	0.823157i	$0.692211\pi$
$824$	28.9157	1.00733
$825$	−0.278139	−0.00968354
$826$	2.51047	0.0873503
$827$	−39.4266	−1.37100	−0.685499	−	0.728074i	$-0.740416\pi$
$827$	−39.4266	−1.37100	−0.685499	+	0.728074i	$0.740416\pi$
$828$	5.39714	0.187564
$829$	−17.3107	−0.601224	−0.300612	−	0.953746i	$-0.597191\pi$
$829$	−17.3107	−0.601224	−0.300612	+	0.953746i	$0.597191\pi$
$830$	3.94230	0.136839
$831$	0.315535	0.0109458
$832$	−15.9770	−0.553902
$833$	6.19585	0.214673
$834$	0.357394	0.0123755
$835$	7.28686	0.252172
$836$	−32.5161	−1.12459
$837$	1.06220	0.0367151
$838$	−8.46825	−0.292531
$839$	−44.8932	−1.54988	−0.774942	−	0.632032i	$-0.782221\pi$
$839$	−44.8932	−1.54988	−0.774942	+	0.632032i	$0.782221\pi$
$840$	−0.695622	−0.0240012
$841$	1.00000	0.0344828
$842$	−11.5799	−0.399070
$843$	−0.143705	−0.00494947
$844$	−10.5316	−0.362511
$845$	16.1389	0.555196
$846$	15.6427	0.537808
$847$	−20.8443	−0.716219
$848$	21.0055	0.721332
$849$	0.884319	0.0303497
$850$	3.23941	0.111111
$851$	0.401833	0.0137747
$852$	−0.728894	−0.0249715
$853$	10.6947	0.366180	0.183090	−	0.983096i	$-0.441390\pi$
$853$	10.6947	0.366180	0.183090	+	0.983096i	$0.441390\pi$
$854$	−18.4171	−0.630221
$855$	−31.1477	−1.06523
$856$	−2.91936	−0.0997815
$857$	−9.25319	−0.316083	−0.158042	−	0.987432i	$-0.550518\pi$
$857$	−9.25319	−0.316083	−0.158042	+	0.987432i	$0.550518\pi$
$858$	−0.498607	−0.0170222
$859$	0.609581	0.0207986	0.0103993	−	0.999946i	$-0.496690\pi$
$859$	0.609581	0.0207986	0.0103993	+	0.999946i	$0.496690\pi$
$860$	−11.2831	−0.384751
$861$	−0.472609	−0.0161065
$862$	−9.11587	−0.310488
$863$	39.0869	1.33053	0.665267	−	0.746605i	$-0.268318\pi$
$863$	39.0869	1.33053	0.665267	+	0.746605i	$0.268318\pi$
$864$	1.64787	0.0560617
$865$	44.8334	1.52438
$866$	1.08371	0.0368260
$867$	−1.57185	−0.0533829
$868$	15.2412	0.517319
$869$	73.5963	2.49659
$870$	0.0649547	0.00220217
$871$	−54.9239	−1.86103
$872$	18.0740	0.612062
$873$	−22.6739	−0.767395
$874$	1.87690	0.0634871
$875$	27.1406	0.917518
$876$	0.422783	0.0142845
$877$	26.4590	0.893456	0.446728	−	0.894670i	$-0.352589\pi$
$877$	26.4590	0.893456	0.446728	+	0.894670i	$0.352589\pi$
$878$	4.04994	0.136679
$879$	0.583988	0.0196974
$880$	30.1527	1.01645
$881$	14.3959	0.485009	0.242504	−	0.970150i	$-0.422031\pi$
$881$	14.3959	0.485009	0.242504	+	0.970150i	$0.422031\pi$
$882$	−1.25313	−0.0421951
$883$	−31.2893	−1.05297	−0.526485	−	0.850184i	$-0.676490\pi$
$883$	−31.2893	−1.05297	−0.526485	+	0.850184i	$0.676490\pi$
$884$	−52.5958	−1.76899
$885$	0.291043	0.00978332
$886$	11.7282	0.394017
$887$	−2.94486	−0.0988786	−0.0494393	−	0.998777i	$-0.515743\pi$
$887$	−2.94486	−0.0988786	−0.0494393	+	0.998777i	$0.515743\pi$
$888$	0.0401720	0.00134808
$889$	−18.0952	−0.606893
$890$	−8.08456	−0.270995
$891$	38.4698	1.28879
$892$	41.0242	1.37359
$893$	−49.2695	−1.64874
$894$	−0.0566510	−0.00189469
$895$	−25.1237	−0.839794
$896$	30.7970	1.02886
$897$	−0.260669	−0.00870348
$898$	−9.39418	−0.313488
$899$	−3.00347	−0.100171
$900$	5.93403	0.197801
$901$	48.7578	1.62436
$902$	−5.44046	−0.181148
$903$	0.421475	0.0140258
$904$	−27.4796	−0.913956
$905$	53.0323	1.76285
$906$	−0.0823452	−0.00273574
$907$	43.2269	1.43533	0.717663	−	0.696390i	$-0.245212\pi$
$907$	43.2269	1.43533	0.717663	+	0.696390i	$0.245212\pi$
$908$	−8.78230	−0.291451
$909$	26.7676	0.887825
$910$	−13.7144	−0.454630
$911$	7.76302	0.257200	0.128600	−	0.991697i	$-0.458952\pi$
$911$	7.76302	0.257200	0.128600	+	0.991697i	$0.458952\pi$
$912$	−0.706541	−0.0233959
$913$	15.3538	0.508135
$914$	−5.22343	−0.172776
$915$	−2.13514	−0.0705854
$916$	19.7514	0.652606
$917$	42.1840	1.39304
$918$	1.04199	0.0343909
$919$	−16.8327	−0.555258	−0.277629	−	0.960688i	$-0.589549\pi$
$919$	−16.8327	−0.555258	−0.277629	+	0.960688i	$0.589549\pi$
$920$	−4.18638	−0.138021
$921$	−0.475651	−0.0156732
$922$	−5.23137	−0.172286
$923$	−30.3275	−0.998241
$924$	−1.28372	−0.0422314
$925$	0.441806	0.0145265
$926$	−4.88460	−0.160518
$927$	51.1163	1.67888
$928$	−4.65949	−0.152955
$929$	3.48943	0.114485	0.0572423	−	0.998360i	$-0.481769\pi$
$929$	3.48943	0.114485	0.0572423	+	0.998360i	$0.481769\pi$
$930$	−0.195089	−0.00639723
$931$	3.94695	0.129356
$932$	−52.3057	−1.71333
$933$	1.00026	0.0327469
$934$	−1.44323	−0.0472239
$935$	69.9902	2.28892
$936$	22.4498	0.733796
$937$	−12.1417	−0.396651	−0.198325	−	0.980136i	$-0.563550\pi$
$937$	−12.1417	−0.396651	−0.198325	+	0.980136i	$0.563550\pi$
$938$	15.6130	0.509782
$939$	−1.78672	−0.0583073
$940$	52.0725	1.69842
$941$	−0.794187	−0.0258897	−0.0129449	−	0.999916i	$-0.504121\pi$
$941$	−0.794187	−0.0258897	−0.0129449	+	0.999916i	$0.504121\pi$
$942$	−0.444352	−0.0144778
$943$	−2.84424	−0.0926214
$944$	−5.68743	−0.185110
$945$	−2.46082	−0.0800506
$946$	4.85183	0.157747
$947$	−4.85051	−0.157620	−0.0788102	−	0.996890i	$-0.525112\pi$
$947$	−4.85051	−0.157620	−0.0788102	+	0.996890i	$0.525112\pi$
$948$	1.82263	0.0591962
$949$	17.5910	0.571027
$950$	2.06361	0.0669522
$951$	1.25920	0.0408324
$952$	31.5531	1.02264
$953$	45.0348	1.45882	0.729410	−	0.684077i	$-0.239795\pi$
$953$	45.0348	1.45882	0.729410	+	0.684077i	$0.239795\pi$
$954$	−9.86143	−0.319276
$955$	53.6847	1.73720
$956$	−39.6532	−1.28248
$957$	0.252974	0.00817748
$958$	−8.51899	−0.275236
$959$	0.439946	0.0142066
$960$	0.526529	0.0169937
$961$	−21.9792	−0.709006
$962$	0.792006	0.0255353
$963$	−5.16074	−0.166303
$964$	45.4204	1.46289
$965$	−14.2678	−0.459297
$966$	0.0740992	0.00238410
$967$	12.2318	0.393348	0.196674	−	0.980469i	$-0.436986\pi$
$967$	12.2318	0.393348	0.196674	+	0.980469i	$0.436986\pi$
$968$	−12.5409	−0.403081
$969$	−1.64002	−0.0526850
$970$	8.33362	0.267576
$971$	13.2141	0.424062	0.212031	−	0.977263i	$-0.431992\pi$
$971$	13.2141	0.424062	0.212031	+	0.977263i	$0.431992\pi$
$972$	2.86368	0.0918524
$973$	38.2853	1.22737
$974$	−4.61134	−0.147757
$975$	−0.286599	−0.00917852
$976$	41.7238	1.33554
$977$	−34.4548	−1.10231	−0.551153	−	0.834404i	$-0.685812\pi$
$977$	−34.4548	−1.10231	−0.551153	+	0.834404i	$0.685812\pi$
$978$	0.581601	0.0185976
$979$	−31.4863	−1.00631
$980$	−4.17150	−0.133254
$981$	31.9506	1.02010
$982$	−2.48607	−0.0793338
$983$	6.12679	0.195414	0.0977071	−	0.995215i	$-0.468849\pi$
$983$	6.12679	0.195414	0.0977071	+	0.995215i	$0.468849\pi$
$984$	−0.284344	−0.00906457
$985$	−41.7722	−1.33097
$986$	−2.94632	−0.0938299
$987$	−1.94514	−0.0619145
$988$	−33.5052	−1.06594
$989$	2.53651	0.0806563
$990$	−14.1557	−0.449899
$991$	−51.7917	−1.64522	−0.822609	−	0.568608i	$-0.807482\pi$
$991$	−51.7917	−1.64522	−0.822609	+	0.568608i	$0.807482\pi$
$992$	13.9946	0.444329
$993$	−0.0462604	−0.00146803
$994$	8.62106	0.273443
$995$	−38.2231	−1.21175
$996$	0.380239	0.0120483
$997$	40.0083	1.26708	0.633538	−	0.773711i	$-0.281602\pi$
$997$	40.0083	1.26708	0.633538	+	0.773711i	$0.281602\pi$
$998$	−7.04132	−0.222889
$999$	0.142112	0.00449622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.9	✓	16
3.2	odd	2		6003.2.a.q.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.9	✓	16	1.1	even	1	trivial
6003.2.a.q.1.8		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.445942 q^{2} -0.0589774 q^{3} -1.80114 q^{4} +2.46971 q^{5} -0.0263005 q^{6} -2.81741 q^{7} -1.69509 q^{8} -2.99652 q^{9} +O(q^{10})\)	\(q+0.445942 q^{2} -0.0589774 q^{3} -1.80114 q^{4} +2.46971 q^{5} -0.0263005 q^{6} -2.81741 q^{7} -1.69509 q^{8} -2.99652 q^{9} +1.10135 q^{10} +4.28934 q^{11} +0.106226 q^{12} +4.41981 q^{13} -1.25640 q^{14} -0.145657 q^{15} +2.84636 q^{16} +6.60695 q^{17} -1.33628 q^{18} +4.20884 q^{19} -4.44829 q^{20} +0.166163 q^{21} +1.91280 q^{22} +1.00000 q^{23} +0.0999718 q^{24} +1.09948 q^{25} +1.97098 q^{26} +0.353659 q^{27} +5.07453 q^{28} -1.00000 q^{29} -0.0649547 q^{30} +3.00347 q^{31} +4.65949 q^{32} -0.252974 q^{33} +2.94632 q^{34} -6.95818 q^{35} +5.39714 q^{36} +0.401833 q^{37} +1.87690 q^{38} -0.260669 q^{39} -4.18638 q^{40} -2.84424 q^{41} +0.0740992 q^{42} +2.53651 q^{43} -7.72567 q^{44} -7.40054 q^{45} +0.445942 q^{46} -11.7062 q^{47} -0.167871 q^{48} +0.937778 q^{49} +0.490303 q^{50} -0.389660 q^{51} -7.96068 q^{52} +7.37978 q^{53} +0.157712 q^{54} +10.5934 q^{55} +4.77575 q^{56} -0.248226 q^{57} -0.445942 q^{58} -1.99814 q^{59} +0.262348 q^{60} +14.6586 q^{61} +1.33937 q^{62} +8.44242 q^{63} -3.61486 q^{64} +10.9157 q^{65} -0.112812 q^{66} -12.4268 q^{67} -11.9000 q^{68} -0.0589774 q^{69} -3.10295 q^{70} -6.86171 q^{71} +5.07937 q^{72} +3.98002 q^{73} +0.179194 q^{74} -0.0648442 q^{75} -7.58069 q^{76} -12.0848 q^{77} -0.116243 q^{78} +17.1580 q^{79} +7.02969 q^{80} +8.96871 q^{81} -1.26837 q^{82} +3.57952 q^{83} -0.299282 q^{84} +16.3173 q^{85} +1.13114 q^{86} +0.0589774 q^{87} -7.27080 q^{88} -7.34060 q^{89} -3.30022 q^{90} -12.4524 q^{91} -1.80114 q^{92} -0.177137 q^{93} -5.22029 q^{94} +10.3946 q^{95} -0.274804 q^{96} +7.56673 q^{97} +0.418195 q^{98} -12.8531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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