LMFDB - Embedded newform 2001.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.312617.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 $ x^5 - 2x^4 - 5x^3 + 11*x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.26093$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31874 q^{2} -1.00000 q^{3} -0.260930 q^{4} +2.51371 q^{5} +1.31874 q^{6} -2.25278 q^{7} +2.98157 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.31874 q^{2} -1.00000 q^{3} -0.260930 q^{4} +2.51371 q^{5} +1.31874 q^{6} -2.25278 q^{7} +2.98157 q^{8} +1.00000 q^{9} -3.31493 q^{10} -0.206934 q^{11} +0.260930 q^{12} -0.720644 q^{13} +2.97083 q^{14} -2.51371 q^{15} -3.41006 q^{16} +2.26093 q^{17} -1.31874 q^{18} -4.58613 q^{19} -0.655902 q^{20} +2.25278 q^{21} +0.272892 q^{22} +1.00000 q^{23} -2.98157 q^{24} +1.31874 q^{25} +0.950341 q^{26} -1.00000 q^{27} +0.587818 q^{28} +1.00000 q^{29} +3.31493 q^{30} -0.615304 q^{31} -1.46618 q^{32} +0.206934 q^{33} -2.98157 q^{34} -5.66284 q^{35} -0.260930 q^{36} +1.84272 q^{37} +6.04791 q^{38} +0.720644 q^{39} +7.49481 q^{40} -3.39931 q^{41} -2.97083 q^{42} -8.50175 q^{43} +0.0539954 q^{44} +2.51371 q^{45} -1.31874 q^{46} +5.89878 q^{47} +3.41006 q^{48} -1.92498 q^{49} -1.73907 q^{50} -2.26093 q^{51} +0.188038 q^{52} +5.61905 q^{53} +1.31874 q^{54} -0.520173 q^{55} -6.71683 q^{56} +4.58613 q^{57} -1.31874 q^{58} +1.23398 q^{59} +0.655902 q^{60} +9.37442 q^{61} +0.811425 q^{62} -2.25278 q^{63} +8.75362 q^{64} -1.81149 q^{65} -0.272892 q^{66} -9.43319 q^{67} -0.589944 q^{68} -1.00000 q^{69} +7.46780 q^{70} +1.35812 q^{71} +2.98157 q^{72} -1.27374 q^{73} -2.43007 q^{74} -1.31874 q^{75} +1.19666 q^{76} +0.466178 q^{77} -0.950341 q^{78} +9.36077 q^{79} -8.57189 q^{80} +1.00000 q^{81} +4.48280 q^{82} -13.4640 q^{83} -0.587818 q^{84} +5.68332 q^{85} +11.2116 q^{86} -1.00000 q^{87} -0.616990 q^{88} -3.61318 q^{89} -3.31493 q^{90} +1.62345 q^{91} -0.260930 q^{92} +0.615304 q^{93} -7.77895 q^{94} -11.5282 q^{95} +1.46618 q^{96} +1.72542 q^{97} +2.53855 q^{98} -0.206934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * 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 $

$2$	−1.31874	−0.932489	−0.466244	−	0.884656i	$-0.654393\pi$
$2$	−1.31874	−0.932489	−0.466244	+	0.884656i	$0.654393\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.260930	−0.130465
$5$	2.51371	1.12417	0.562083	−	0.827081i	$-0.310000\pi$
$5$	2.51371	1.12417	0.562083	+	0.827081i	$0.310000\pi$
$6$	1.31874	0.538373
$7$	−2.25278	−0.851471	−0.425735	−	0.904848i	$-0.639985\pi$
$7$	−2.25278	−0.851471	−0.425735	+	0.904848i	$0.639985\pi$
$8$	2.98157	1.05415
$9$	1.00000	0.333333
$10$	−3.31493	−1.04827
$11$	−0.206934	−0.0623931	−0.0311965	−	0.999513i	$-0.509932\pi$
$11$	−0.206934	−0.0623931	−0.0311965	+	0.999513i	$0.509932\pi$
$12$	0.260930	0.0753240
$13$	−0.720644	−0.199871	−0.0999354	−	0.994994i	$-0.531864\pi$
$13$	−0.720644	−0.199871	−0.0999354	+	0.994994i	$0.531864\pi$
$14$	2.97083	0.793987
$15$	−2.51371	−0.649037
$16$	−3.41006	−0.852514
$17$	2.26093	0.548356	0.274178	−	0.961679i	$-0.411594\pi$
$17$	2.26093	0.548356	0.274178	+	0.961679i	$0.411594\pi$
$18$	−1.31874	−0.310830
$19$	−4.58613	−1.05213	−0.526065	−	0.850444i	$-0.676333\pi$
$19$	−4.58613	−1.05213	−0.526065	+	0.850444i	$0.676333\pi$
$20$	−0.655902	−0.146664
$21$	2.25278	0.491597
$22$	0.272892	0.0581808
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.98157	−0.608611
$25$	1.31874	0.263748
$26$	0.950341	0.186377
$27$	−1.00000	−0.192450
$28$	0.587818	0.111087
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.31493	0.605220
$31$	−0.615304	−0.110512	−0.0552559	−	0.998472i	$-0.517597\pi$
$31$	−0.615304	−0.110512	−0.0552559	+	0.998472i	$0.517597\pi$
$32$	−1.46618	−0.259186
$33$	0.206934	0.0360227
$34$	−2.98157	−0.511336
$35$	−5.66284	−0.957194
$36$	−0.260930	−0.0434883
$37$	1.84272	0.302942	0.151471	−	0.988462i	$-0.451599\pi$
$37$	1.84272	0.302942	0.151471	+	0.988462i	$0.451599\pi$
$38$	6.04791	0.981100
$39$	0.720644	0.115395
$40$	7.49481	1.18503
$41$	−3.39931	−0.530883	−0.265441	−	0.964127i	$-0.585518\pi$
$41$	−3.39931	−0.530883	−0.265441	+	0.964127i	$0.585518\pi$
$42$	−2.97083	−0.458409
$43$	−8.50175	−1.29650	−0.648252	−	0.761426i	$-0.724500\pi$
$43$	−8.50175	−1.29650	−0.648252	+	0.761426i	$0.724500\pi$
$44$	0.0539954	0.00814011
$45$	2.51371	0.374722
$46$	−1.31874	−0.194437
$47$	5.89878	0.860425	0.430213	−	0.902728i	$-0.358439\pi$
$47$	5.89878	0.860425	0.430213	+	0.902728i	$0.358439\pi$
$48$	3.41006	0.492199
$49$	−1.92498	−0.274997
$50$	−1.73907	−0.245942
$51$	−2.26093	−0.316593
$52$	0.188038	0.0260761
$53$	5.61905	0.771836	0.385918	−	0.922533i	$-0.373885\pi$
$53$	5.61905	0.771836	0.385918	+	0.922533i	$0.373885\pi$
$54$	1.31874	0.179458
$55$	−0.520173	−0.0701401
$56$	−6.71683	−0.897574
$57$	4.58613	0.607448
$58$	−1.31874	−0.173159
$59$	1.23398	0.160651	0.0803253	−	0.996769i	$-0.474404\pi$
$59$	1.23398	0.160651	0.0803253	+	0.996769i	$0.474404\pi$
$60$	0.655902	0.0846766
$61$	9.37442	1.20027	0.600136	−	0.799898i	$-0.295113\pi$
$61$	9.37442	1.20027	0.600136	+	0.799898i	$0.295113\pi$
$62$	0.811425	0.103051
$63$	−2.25278	−0.283824
$64$	8.75362	1.09420
$65$	−1.81149	−0.224688
$66$	−0.272892	−0.0335907
$67$	−9.43319	−1.15245	−0.576224	−	0.817292i	$-0.695474\pi$
$67$	−9.43319	−1.15245	−0.576224	+	0.817292i	$0.695474\pi$
$68$	−0.589944	−0.0715412
$69$	−1.00000	−0.120386
$70$	7.46780	0.892573
$71$	1.35812	0.161179	0.0805896	−	0.996747i	$-0.474320\pi$
$71$	1.35812	0.161179	0.0805896	+	0.996747i	$0.474320\pi$
$72$	2.98157	0.351382
$73$	−1.27374	−0.149080	−0.0745398	−	0.997218i	$-0.523749\pi$
$73$	−1.27374	−0.149080	−0.0745398	+	0.997218i	$0.523749\pi$
$74$	−2.43007	−0.282490
$75$	−1.31874	−0.152275
$76$	1.19666	0.137266
$77$	0.466178	0.0531259
$78$	−0.950341	−0.107605
$79$	9.36077	1.05317	0.526585	−	0.850123i	$-0.323472\pi$
$79$	9.36077	1.05317	0.526585	+	0.850123i	$0.323472\pi$
$80$	−8.57189	−0.958367
$81$	1.00000	0.111111
$82$	4.48280	0.495042
$83$	−13.4640	−1.47786	−0.738932	−	0.673780i	$-0.764670\pi$
$83$	−13.4640	−1.47786	−0.738932	+	0.673780i	$0.764670\pi$
$84$	−0.587818	−0.0641362
$85$	5.68332	0.616443
$86$	11.2116	1.20898
$87$	−1.00000	−0.107211
$88$	−0.616990	−0.0657714
$89$	−3.61318	−0.382996	−0.191498	−	0.981493i	$-0.561335\pi$
$89$	−3.61318	−0.382996	−0.191498	+	0.981493i	$0.561335\pi$
$90$	−3.31493	−0.349424
$91$	1.62345	0.170184
$92$	−0.260930	−0.0272038
$93$	0.615304	0.0638041
$94$	−7.77895	−0.802337
$95$	−11.5282	−1.18277
$96$	1.46618	0.149641
$97$	1.72542	0.175190	0.0875950	−	0.996156i	$-0.472082\pi$
$97$	1.72542	0.175190	0.0875950	+	0.996156i	$0.472082\pi$
$98$	2.53855	0.256432
$99$	−0.206934	−0.0207977
$100$	−0.344098	−0.0344098
$101$	−5.34150	−0.531499	−0.265750	−	0.964042i	$-0.585619\pi$
$101$	−5.34150	−0.531499	−0.265750	+	0.964042i	$0.585619\pi$
$102$	2.98157	0.295220
$103$	−8.03732	−0.791941	−0.395970	−	0.918263i	$-0.629592\pi$
$103$	−8.03732	−0.791941	−0.395970	+	0.918263i	$0.629592\pi$
$104$	−2.14866	−0.210693
$105$	5.66284	0.552636
$106$	−7.41006	−0.719728
$107$	−3.51280	−0.339595	−0.169798	−	0.985479i	$-0.554311\pi$
$107$	−3.51280	−0.339595	−0.169798	+	0.985479i	$0.554311\pi$
$108$	0.260930	0.0251080
$109$	18.5175	1.77366	0.886828	−	0.462100i	$-0.152904\pi$
$109$	18.5175	1.77366	0.886828	+	0.462100i	$0.152904\pi$
$110$	0.685972	0.0654049
$111$	−1.84272	−0.174904
$112$	7.68211	0.725891
$113$	−17.2446	−1.62224	−0.811119	−	0.584882i	$-0.801141\pi$
$113$	−17.2446	−1.62224	−0.811119	+	0.584882i	$0.801141\pi$
$114$	−6.04791	−0.566438
$115$	2.51371	0.234405
$116$	−0.260930	−0.0242267
$117$	−0.720644	−0.0666236
$118$	−1.62730	−0.149805
$119$	−5.09338	−0.466909
$120$	−7.49481	−0.684180
$121$	−10.9572	−0.996107
$122$	−12.3624	−1.11924
$123$	3.39931	0.306505
$124$	0.160551	0.0144179
$125$	−9.25362	−0.827669
$126$	2.97083	0.264662
$127$	14.4331	1.28073	0.640364	−	0.768072i	$-0.278783\pi$
$127$	14.4331	1.28073	0.640364	+	0.768072i	$0.278783\pi$
$128$	−8.61137	−0.761145
$129$	8.50175	0.748537
$130$	2.38888	0.209519
$131$	−9.95272	−0.869573	−0.434787	−	0.900533i	$-0.643176\pi$
$131$	−9.95272	−0.869573	−0.434787	+	0.900533i	$0.643176\pi$
$132$	−0.0539954	−0.00469969
$133$	10.3315	0.895859
$134$	12.4399	1.07464
$135$	−2.51371	−0.216346
$136$	6.74113	0.578047
$137$	−21.7145	−1.85519	−0.927597	−	0.373582i	$-0.878129\pi$
$137$	−21.7145	−1.85519	−0.927597	+	0.373582i	$0.878129\pi$
$138$	1.31874	0.112258
$139$	−9.64007	−0.817660	−0.408830	−	0.912610i	$-0.634063\pi$
$139$	−9.64007	−0.817660	−0.408830	+	0.912610i	$0.634063\pi$
$140$	1.47760	0.124880
$141$	−5.89878	−0.496767
$142$	−1.79101	−0.150298
$143$	0.149126	0.0124706
$144$	−3.41006	−0.284171
$145$	2.51371	0.208752
$146$	1.67973	0.139015
$147$	1.92498	0.158770
$148$	−0.480822	−0.0395233
$149$	3.81234	0.312319	0.156159	−	0.987732i	$-0.450089\pi$
$149$	3.81234	0.312319	0.156159	+	0.987732i	$0.450089\pi$
$150$	1.73907	0.141994
$151$	−24.1476	−1.96511	−0.982553	−	0.185983i	$-0.940453\pi$
$151$	−24.1476	−1.96511	−0.982553	+	0.185983i	$0.940453\pi$
$152$	−13.6739	−1.10910
$153$	2.26093	0.182785
$154$	−0.614766	−0.0495393
$155$	−1.54670	−0.124234
$156$	−0.188038	−0.0150551
$157$	13.7130	1.09442	0.547209	−	0.836996i	$-0.315690\pi$
$157$	13.7130	1.09442	0.547209	+	0.836996i	$0.315690\pi$
$158$	−12.3444	−0.982068
$159$	−5.61905	−0.445620
$160$	−3.68555	−0.291368
$161$	−2.25278	−0.177544
$162$	−1.31874	−0.103610
$163$	1.12483	0.0881033	0.0440516	−	0.999029i	$-0.485973\pi$
$163$	1.12483	0.0881033	0.0440516	+	0.999029i	$0.485973\pi$
$164$	0.886981	0.0692616
$165$	0.520173	0.0404954
$166$	17.7555	1.37809
$167$	7.17952	0.555568	0.277784	−	0.960644i	$-0.410400\pi$
$167$	7.17952	0.555568	0.277784	+	0.960644i	$0.410400\pi$
$168$	6.71683	0.518215
$169$	−12.4807	−0.960052
$170$	−7.49481	−0.574826
$171$	−4.58613	−0.350710
$172$	2.21836	0.169148
$173$	3.39322	0.257982	0.128991	−	0.991646i	$-0.458826\pi$
$173$	3.39322	0.257982	0.128991	+	0.991646i	$0.458826\pi$
$174$	1.31874	0.0999733
$175$	−2.97083	−0.224573
$176$	0.705658	0.0531910
$177$	−1.23398	−0.0927517
$178$	4.76483	0.357139
$179$	−12.3767	−0.925078	−0.462539	−	0.886599i	$-0.653061\pi$
$179$	−12.3767	−0.925078	−0.462539	+	0.886599i	$0.653061\pi$
$180$	−0.655902	−0.0488880
$181$	−21.5325	−1.60050	−0.800251	−	0.599666i	$-0.795300\pi$
$181$	−21.5325	−1.60050	−0.800251	+	0.599666i	$0.795300\pi$
$182$	−2.14091	−0.158695
$183$	−9.37442	−0.692977
$184$	2.98157	0.219805
$185$	4.63207	0.340557
$186$	−0.811425	−0.0594966
$187$	−0.467864	−0.0342136
$188$	−1.53917	−0.112255
$189$	2.25278	0.163866
$190$	15.2027	1.10292
$191$	−18.6497	−1.34944	−0.674722	−	0.738072i	$-0.735737\pi$
$191$	−18.6497	−1.34944	−0.674722	+	0.738072i	$0.735737\pi$
$192$	−8.75362	−0.631738
$193$	−8.16030	−0.587391	−0.293696	−	0.955899i	$-0.594885\pi$
$193$	−8.16030	−0.587391	−0.293696	+	0.955899i	$0.594885\pi$
$194$	−2.27538	−0.163363
$195$	1.81149	0.129724
$196$	0.502285	0.0358775
$197$	13.5299	0.963969	0.481984	−	0.876180i	$-0.339916\pi$
$197$	13.5299	0.963969	0.481984	+	0.876180i	$0.339916\pi$
$198$	0.272892	0.0193936
$199$	−3.83619	−0.271941	−0.135970	−	0.990713i	$-0.543415\pi$
$199$	−3.83619	−0.271941	−0.135970	+	0.990713i	$0.543415\pi$
$200$	3.93192	0.278028
$201$	9.43319	0.665366
$202$	7.04404	0.495617
$203$	−2.25278	−0.158114
$204$	0.589944	0.0413043
$205$	−8.54488	−0.596800
$206$	10.5991	0.738476
$207$	1.00000	0.0695048
$208$	2.45744	0.170393
$209$	0.949029	0.0656457
$210$	−7.46780	−0.515327
$211$	−18.0641	−1.24359	−0.621793	−	0.783181i	$-0.713596\pi$
$211$	−18.0641	−1.24359	−0.621793	+	0.783181i	$0.713596\pi$
$212$	−1.46618	−0.100698
$213$	−1.35812	−0.0930569
$214$	4.63246	0.316669
$215$	−21.3709	−1.45749
$216$	−2.98157	−0.202870
$217$	1.38614	0.0940976
$218$	−24.4197	−1.65391
$219$	1.27374	0.0860712
$220$	0.135729	0.00915083
$221$	−1.62933	−0.109600
$222$	2.43007	0.163096
$223$	5.81999	0.389736	0.194868	−	0.980830i	$-0.437572\pi$
$223$	5.81999	0.389736	0.194868	+	0.980830i	$0.437572\pi$
$224$	3.30298	0.220689
$225$	1.31874	0.0879159
$226$	22.7411	1.51272
$227$	−15.3483	−1.01870	−0.509352	−	0.860558i	$-0.670115\pi$
$227$	−15.3483	−1.01870	−0.509352	+	0.860558i	$0.670115\pi$
$228$	−1.19666	−0.0792506
$229$	−15.8178	−1.04527	−0.522634	−	0.852557i	$-0.675050\pi$
$229$	−15.8178	−1.04527	−0.522634	+	0.852557i	$0.675050\pi$
$230$	−3.31493	−0.218580
$231$	−0.466178	−0.0306722
$232$	2.98157	0.195750
$233$	10.8064	0.707951	0.353975	−	0.935255i	$-0.384830\pi$
$233$	10.8064	0.707951	0.353975	+	0.935255i	$0.384830\pi$
$234$	0.950341	0.0621258
$235$	14.8278	0.967260
$236$	−0.321982	−0.0209593
$237$	−9.36077	−0.608047
$238$	6.71683	0.435388
$239$	−12.4863	−0.807670	−0.403835	−	0.914832i	$-0.632323\pi$
$239$	−12.4863	−0.807670	−0.403835	+	0.914832i	$0.632323\pi$
$240$	8.57189	0.553313
$241$	−3.94214	−0.253935	−0.126968	−	0.991907i	$-0.540524\pi$
$241$	−3.94214	−0.253935	−0.126968	+	0.991907i	$0.540524\pi$
$242$	14.4496	0.928859
$243$	−1.00000	−0.0641500
$244$	−2.44607	−0.156593
$245$	−4.83884	−0.309142
$246$	−4.48280	−0.285813
$247$	3.30497	0.210290
$248$	−1.83457	−0.116496
$249$	13.4640	0.853245
$250$	12.2031	0.771792
$251$	6.79990	0.429206	0.214603	−	0.976701i	$-0.431154\pi$
$251$	6.79990	0.429206	0.214603	+	0.976701i	$0.431154\pi$
$252$	0.587818	0.0370290
$253$	−0.206934	−0.0130099
$254$	−19.0334	−1.19426
$255$	−5.68332	−0.355903
$256$	−6.15109	−0.384443
$257$	−25.4934	−1.59023	−0.795116	−	0.606457i	$-0.792590\pi$
$257$	−25.4934	−1.59023	−0.795116	+	0.606457i	$0.792590\pi$
$258$	−11.2116	−0.698002
$259$	−4.15125	−0.257946
$260$	0.472672	0.0293139
$261$	1.00000	0.0618984
$262$	13.1250	0.810867
$263$	5.87654	0.362363	0.181181	−	0.983450i	$-0.442008\pi$
$263$	5.87654	0.362363	0.181181	+	0.983450i	$0.442008\pi$
$264$	0.616990	0.0379731
$265$	14.1247	0.867671
$266$	−13.6246	−0.835378
$267$	3.61318	0.221123
$268$	2.46140	0.150354
$269$	−3.61181	−0.220216	−0.110108	−	0.993920i	$-0.535120\pi$
$269$	−3.61181	−0.220216	−0.110108	+	0.993920i	$0.535120\pi$
$270$	3.31493	0.201740
$271$	−23.1450	−1.40596	−0.702980	−	0.711209i	$-0.748148\pi$
$271$	−23.1450	−1.40596	−0.702980	+	0.711209i	$0.748148\pi$
$272$	−7.70990	−0.467481
$273$	−1.62345	−0.0982559
$274$	28.6357	1.72995
$275$	−0.272892	−0.0164560
$276$	0.260930	0.0157061
$277$	15.9558	0.958693	0.479346	−	0.877626i	$-0.340874\pi$
$277$	15.9558	0.958693	0.479346	+	0.877626i	$0.340874\pi$
$278$	12.7127	0.762459
$279$	−0.615304	−0.0368373
$280$	−16.8842	−1.00902
$281$	−3.25850	−0.194386	−0.0971928	−	0.995266i	$-0.530986\pi$
$281$	−3.25850	−0.194386	−0.0971928	+	0.995266i	$0.530986\pi$
$282$	7.77895	0.463229
$283$	7.75465	0.460966	0.230483	−	0.973076i	$-0.425969\pi$
$283$	7.75465	0.460966	0.230483	+	0.973076i	$0.425969\pi$
$284$	−0.354374	−0.0210282
$285$	11.5282	0.682872
$286$	−0.196658	−0.0116287
$287$	7.65790	0.452031
$288$	−1.46618	−0.0863954
$289$	−11.8882	−0.699306
$290$	−3.31493	−0.194659
$291$	−1.72542	−0.101146
$292$	0.332356	0.0194497
$293$	23.5594	1.37636	0.688178	−	0.725541i	$-0.258411\pi$
$293$	23.5594	1.37636	0.688178	+	0.725541i	$0.258411\pi$
$294$	−2.53855	−0.148051
$295$	3.10187	0.180598
$296$	5.49422	0.319345
$297$	0.206934	0.0120076
$298$	−5.02747	−0.291234
$299$	−0.720644	−0.0416759
$300$	0.344098	0.0198665
$301$	19.1526	1.10394
$302$	31.8444	1.83244
$303$	5.34150	0.306861
$304$	15.6390	0.896956
$305$	23.5646	1.34930
$306$	−2.98157	−0.170445
$307$	11.0124	0.628509	0.314254	−	0.949339i	$-0.398245\pi$
$307$	11.0124	0.628509	0.314254	+	0.949339i	$0.398245\pi$
$308$	−0.121640	−0.00693107
$309$	8.03732	0.457227
$310$	2.03969	0.115846
$311$	−4.46225	−0.253031	−0.126515	−	0.991965i	$-0.540379\pi$
$311$	−4.46225	−0.253031	−0.126515	+	0.991965i	$0.540379\pi$
$312$	2.14866	0.121644
$313$	11.9157	0.673516	0.336758	−	0.941591i	$-0.390670\pi$
$313$	11.9157	0.673516	0.336758	+	0.941591i	$0.390670\pi$
$314$	−18.0839	−1.02053
$315$	−5.66284	−0.319065
$316$	−2.44250	−0.137402
$317$	−2.70900	−0.152153	−0.0760764	−	0.997102i	$-0.524239\pi$
$317$	−2.70900	−0.152153	−0.0760764	+	0.997102i	$0.524239\pi$
$318$	7.41006	0.415535
$319$	−0.206934	−0.0115861
$320$	22.0041	1.23006
$321$	3.51280	0.196065
$322$	2.97083	0.165558
$323$	−10.3689	−0.576942
$324$	−0.260930	−0.0144961
$325$	−0.950341	−0.0527155
$326$	−1.48335	−0.0821553
$327$	−18.5175	−1.02402
$328$	−10.1353	−0.559628
$329$	−13.2887	−0.732627
$330$	−0.685972	−0.0377615
$331$	−10.9224	−0.600349	−0.300175	−	0.953884i	$-0.597045\pi$
$331$	−10.9224	−0.600349	−0.300175	+	0.953884i	$0.597045\pi$
$332$	3.51316	0.192809
$333$	1.84272	0.100981
$334$	−9.46790	−0.518061
$335$	−23.7123	−1.29554
$336$	−7.68211	−0.419093
$337$	35.6784	1.94353	0.971763	−	0.235960i	$-0.0758235\pi$
$337$	35.6784	1.94353	0.971763	+	0.235960i	$0.0758235\pi$
$338$	16.4587	0.895237
$339$	17.2446	0.936599
$340$	−1.48295	−0.0804242
$341$	0.127328	0.00689518
$342$	6.04791	0.327033
$343$	20.1060	1.08562
$344$	−25.3486	−1.36670
$345$	−2.51371	−0.135334
$346$	−4.47477	−0.240565
$347$	11.2710	0.605060	0.302530	−	0.953140i	$-0.402169\pi$
$347$	11.2710	0.605060	0.302530	+	0.953140i	$0.402169\pi$
$348$	0.260930	0.0139873
$349$	−12.9056	−0.690823	−0.345412	−	0.938451i	$-0.612261\pi$
$349$	−12.9056	−0.690823	−0.345412	+	0.938451i	$0.612261\pi$
$350$	3.91774	0.209412
$351$	0.720644	0.0384652
$352$	0.303403	0.0161714
$353$	6.75930	0.359761	0.179881	−	0.983688i	$-0.442429\pi$
$353$	6.75930	0.359761	0.179881	+	0.983688i	$0.442429\pi$
$354$	1.62730	0.0864899
$355$	3.41392	0.181192
$356$	0.942786	0.0499675
$357$	5.09338	0.269570
$358$	16.3216	0.862624
$359$	33.2370	1.75418	0.877091	−	0.480325i	$-0.159481\pi$
$359$	33.2370	1.75418	0.877091	+	0.480325i	$0.159481\pi$
$360$	7.49481	0.395011
$361$	2.03260	0.106979
$362$	28.3958	1.49245
$363$	10.9572	0.575103
$364$	−0.423607	−0.0222031
$365$	−3.20181	−0.167590
$366$	12.3624	0.646193
$367$	12.7646	0.666308	0.333154	−	0.942872i	$-0.391887\pi$
$367$	12.7646	0.666308	0.333154	+	0.942872i	$0.391887\pi$
$368$	−3.41006	−0.177761
$369$	−3.39931	−0.176961
$370$	−6.10849	−0.317565
$371$	−12.6585	−0.657196
$372$	−0.160551	−0.00832419
$373$	−18.6085	−0.963511	−0.481756	−	0.876306i	$-0.660001\pi$
$373$	−18.6085	−0.963511	−0.481756	+	0.876306i	$0.660001\pi$
$374$	0.616990	0.0319038
$375$	9.25362	0.477855
$376$	17.5876	0.907014
$377$	−0.720644	−0.0371151
$378$	−2.97083	−0.152803
$379$	−7.61409	−0.391109	−0.195555	−	0.980693i	$-0.562651\pi$
$379$	−7.61409	−0.391109	−0.195555	+	0.980693i	$0.562651\pi$
$380$	3.00805	0.154310
$381$	−14.4331	−0.739429
$382$	24.5941	1.25834
$383$	−6.30303	−0.322070	−0.161035	−	0.986949i	$-0.551483\pi$
$383$	−6.30303	−0.322070	−0.161035	+	0.986949i	$0.551483\pi$
$384$	8.61137	0.439447
$385$	1.17184	0.0597223
$386$	10.7613	0.547736
$387$	−8.50175	−0.432168
$388$	−0.450214	−0.0228561
$389$	−19.1940	−0.973175	−0.486588	−	0.873632i	$-0.661759\pi$
$389$	−19.1940	−0.973175	−0.486588	+	0.873632i	$0.661759\pi$
$390$	−2.38888	−0.120966
$391$	2.26093	0.114340
$392$	−5.73947	−0.289887
$393$	9.95272	0.502048
$394$	−17.8425	−0.898890
$395$	23.5303	1.18394
$396$	0.0539954	0.00271337
$397$	3.97724	0.199612	0.0998059	−	0.995007i	$-0.468178\pi$
$397$	3.97724	0.199612	0.0998059	+	0.995007i	$0.468178\pi$
$398$	5.05894	0.253582
$399$	−10.3315	−0.517224
$400$	−4.49697	−0.224849
$401$	−7.76968	−0.387999	−0.194000	−	0.981002i	$-0.562146\pi$
$401$	−7.76968	−0.387999	−0.194000	+	0.981002i	$0.562146\pi$
$402$	−12.4399	−0.620446
$403$	0.443415	0.0220881
$404$	1.39376	0.0693420
$405$	2.51371	0.124907
$406$	2.97083	0.147440
$407$	−0.381323	−0.0189015
$408$	−6.74113	−0.333736
$409$	24.8374	1.22813	0.614066	−	0.789255i	$-0.289533\pi$
$409$	24.8374	1.22813	0.614066	+	0.789255i	$0.289533\pi$
$410$	11.2685	0.556509
$411$	21.7145	1.07110
$412$	2.09718	0.103321
$413$	−2.77989	−0.136789
$414$	−1.31874	−0.0648124
$415$	−33.8446	−1.66136
$416$	1.05659	0.0518037
$417$	9.64007	0.472076
$418$	−1.25152	−0.0612138
$419$	2.53323	0.123756	0.0618782	−	0.998084i	$-0.480291\pi$
$419$	2.53323	0.123756	0.0618782	+	0.998084i	$0.480291\pi$
$420$	−1.47760	−0.0720996
$421$	−0.486597	−0.0237153	−0.0118576	−	0.999930i	$-0.503774\pi$
$421$	−0.486597	−0.0237153	−0.0118576	+	0.999930i	$0.503774\pi$
$422$	23.8219	1.15963
$423$	5.89878	0.286808
$424$	16.7536	0.813628
$425$	2.98157	0.144628
$426$	1.79101	0.0867745
$427$	−21.1185	−1.02200
$428$	0.916594	0.0443052
$429$	−0.149126	−0.00719988
$430$	28.1827	1.35909
$431$	17.1122	0.824267	0.412133	−	0.911123i	$-0.364784\pi$
$431$	17.1122	0.824267	0.412133	+	0.911123i	$0.364784\pi$
$432$	3.41006	0.164066
$433$	−25.5910	−1.22982	−0.614912	−	0.788596i	$-0.710808\pi$
$433$	−25.5910	−1.22982	−0.614912	+	0.788596i	$0.710808\pi$
$434$	−1.82796	−0.0877450
$435$	−2.51371	−0.120523
$436$	−4.83177	−0.231400
$437$	−4.58613	−0.219384
$438$	−1.67973	−0.0802604
$439$	−7.57936	−0.361743	−0.180872	−	0.983507i	$-0.557892\pi$
$439$	−7.57936	−0.361743	−0.180872	+	0.983507i	$0.557892\pi$
$440$	−1.55094	−0.0739379
$441$	−1.92498	−0.0916658
$442$	2.14866	0.102201
$443$	8.39708	0.398958	0.199479	−	0.979902i	$-0.436075\pi$
$443$	8.39708	0.398958	0.199479	+	0.979902i	$0.436075\pi$
$444$	0.480822	0.0228188
$445$	−9.08248	−0.430551
$446$	−7.67505	−0.363424
$447$	−3.81234	−0.180317
$448$	−19.7200	−0.931681
$449$	30.7310	1.45029	0.725144	−	0.688597i	$-0.241773\pi$
$449$	30.7310	1.45029	0.725144	+	0.688597i	$0.241773\pi$
$450$	−1.73907	−0.0819806
$451$	0.703434	0.0331234
$452$	4.49963	0.211645
$453$	24.1476	1.13455
$454$	20.2404	0.949931
$455$	4.08089	0.191315
$456$	13.6739	0.640339
$457$	1.32954	0.0621932	0.0310966	−	0.999516i	$-0.490100\pi$
$457$	1.32954	0.0621932	0.0310966	+	0.999516i	$0.490100\pi$
$458$	20.8595	0.974700
$459$	−2.26093	−0.105531
$460$	−0.655902	−0.0305816
$461$	−7.33804	−0.341767	−0.170883	−	0.985291i	$-0.554662\pi$
$461$	−7.33804	−0.341767	−0.170883	+	0.985291i	$0.554662\pi$
$462$	0.614766	0.0286015
$463$	−2.68755	−0.124901	−0.0624506	−	0.998048i	$-0.519892\pi$
$463$	−2.68755	−0.124901	−0.0624506	+	0.998048i	$0.519892\pi$
$464$	−3.41006	−0.158308
$465$	1.54670	0.0717263
$466$	−14.2508	−0.660156
$467$	6.84657	0.316821	0.158411	−	0.987373i	$-0.449363\pi$
$467$	6.84657	0.316821	0.158411	+	0.987373i	$0.449363\pi$
$468$	0.188038	0.00869204
$469$	21.2509	0.981276
$470$	−19.5540	−0.901959
$471$	−13.7130	−0.631863
$472$	3.67921	0.169349
$473$	1.75930	0.0808929
$474$	12.3444	0.566997
$475$	−6.04791	−0.277497
$476$	1.32901	0.0609153
$477$	5.61905	0.257279
$478$	16.4661	0.753143
$479$	15.1503	0.692236	0.346118	−	0.938191i	$-0.387500\pi$
$479$	15.1503	0.692236	0.346118	+	0.938191i	$0.387500\pi$
$480$	3.68555	0.168221
$481$	−1.32795	−0.0605493
$482$	5.19865	0.236792
$483$	2.25278	0.102505
$484$	2.85905	0.129957
$485$	4.33721	0.196942
$486$	1.31874	0.0598192
$487$	−2.30603	−0.104496	−0.0522481	−	0.998634i	$-0.516639\pi$
$487$	−2.30603	−0.104496	−0.0522481	+	0.998634i	$0.516639\pi$
$488$	27.9505	1.26526
$489$	−1.12483	−0.0508665
$490$	6.38117	0.288272
$491$	−30.1262	−1.35958	−0.679789	−	0.733408i	$-0.737929\pi$
$491$	−30.1262	−1.35958	−0.679789	+	0.733408i	$0.737929\pi$
$492$	−0.886981	−0.0399882
$493$	2.26093	0.101827
$494$	−4.35839	−0.196093
$495$	−0.520173	−0.0233800
$496$	2.09822	0.0942129
$497$	−3.05955	−0.137239
$498$	−17.7555	−0.795642
$499$	14.1251	0.632328	0.316164	−	0.948705i	$-0.397605\pi$
$499$	14.1251	0.632328	0.316164	+	0.948705i	$0.397605\pi$
$500$	2.41455	0.107982
$501$	−7.17952	−0.320757
$502$	−8.96729	−0.400230
$503$	−28.0963	−1.25275	−0.626377	−	0.779521i	$-0.715463\pi$
$503$	−28.0963	−1.25275	−0.626377	+	0.779521i	$0.715463\pi$
$504$	−6.71683	−0.299191
$505$	−13.4270	−0.597493
$506$	0.272892	0.0121315
$507$	12.4807	0.554286
$508$	−3.76602	−0.167090
$509$	−5.49940	−0.243757	−0.121878	−	0.992545i	$-0.538892\pi$
$509$	−5.49940	−0.243757	−0.121878	+	0.992545i	$0.538892\pi$
$510$	7.49481	0.331876
$511$	2.86945	0.126937
$512$	25.3344	1.11963
$513$	4.58613	0.202483
$514$	33.6191	1.48287
$515$	−20.2035	−0.890273
$516$	−2.21836	−0.0976578
$517$	−1.22066	−0.0536846
$518$	5.47442	0.240532
$519$	−3.39322	−0.148946
$520$	−5.40110	−0.236854
$521$	19.0771	0.835783	0.417892	−	0.908497i	$-0.362769\pi$
$521$	19.0771	0.835783	0.417892	+	0.908497i	$0.362769\pi$
$522$	−1.31874	−0.0577196
$523$	−5.59256	−0.244545	−0.122273	−	0.992497i	$-0.539018\pi$
$523$	−5.59256	−0.244545	−0.122273	+	0.992497i	$0.539018\pi$
$524$	2.59696	0.113449
$525$	2.97083	0.129658
$526$	−7.74961	−0.337899
$527$	−1.39116	−0.0605998
$528$	−0.705658	−0.0307098
$529$	1.00000	0.0434783
$530$	−18.6267	−0.809094
$531$	1.23398	0.0535502
$532$	−2.69581	−0.116878
$533$	2.44969	0.106108
$534$	−4.76483	−0.206195
$535$	−8.83016	−0.381761
$536$	−28.1258	−1.21485
$537$	12.3767	0.534094
$538$	4.76303	0.205349
$539$	0.398345	0.0171579
$540$	0.655902	0.0282255
$541$	12.7925	0.549994	0.274997	−	0.961445i	$-0.411323\pi$
$541$	12.7925	0.549994	0.274997	+	0.961445i	$0.411323\pi$
$542$	30.5222	1.31104
$543$	21.5325	0.924050
$544$	−3.31493	−0.142126
$545$	46.5476	1.99388
$546$	2.14091	0.0916225
$547$	−28.1352	−1.20298	−0.601488	−	0.798882i	$-0.705425\pi$
$547$	−28.1352	−1.20298	−0.601488	+	0.798882i	$0.705425\pi$
$548$	5.66596	0.242038
$549$	9.37442	0.400090
$550$	0.359874	0.0153451
$551$	−4.58613	−0.195376
$552$	−2.98157	−0.126904
$553$	−21.0878	−0.896743
$554$	−21.0416	−0.893970
$555$	−4.63207	−0.196621
$556$	2.51538	0.106676
$557$	−0.823300	−0.0348843	−0.0174422	−	0.999848i	$-0.505552\pi$
$557$	−0.823300	−0.0348843	−0.0174422	+	0.999848i	$0.505552\pi$
$558$	0.811425	0.0343504
$559$	6.12674	0.259133
$560$	19.3106	0.816021
$561$	0.467864	0.0197532
$562$	4.29710	0.181262
$563$	20.8016	0.876684	0.438342	−	0.898808i	$-0.355566\pi$
$563$	20.8016	0.876684	0.438342	+	0.898808i	$0.355566\pi$
$564$	1.53917	0.0648106
$565$	−43.3480	−1.82366
$566$	−10.2263	−0.429845
$567$	−2.25278	−0.0946079
$568$	4.04934	0.169906
$569$	−8.48857	−0.355859	−0.177930	−	0.984043i	$-0.556940\pi$
$569$	−8.48857	−0.355859	−0.177930	+	0.984043i	$0.556940\pi$
$570$	−15.2027	−0.636770
$571$	1.08653	0.0454698	0.0227349	−	0.999742i	$-0.492763\pi$
$571$	1.08653	0.0454698	0.0227349	+	0.999742i	$0.492763\pi$
$572$	−0.0389115	−0.00162697
$573$	18.6497	0.779102
$574$	−10.0988	−0.421514
$575$	1.31874	0.0549952
$576$	8.75362	0.364734
$577$	39.2324	1.63327	0.816634	−	0.577156i	$-0.195838\pi$
$577$	39.2324	1.63327	0.816634	+	0.577156i	$0.195838\pi$
$578$	15.6774	0.652095
$579$	8.16030	0.339130
$580$	−0.655902	−0.0272348
$581$	30.3314	1.25836
$582$	2.27538	0.0943175
$583$	−1.16278	−0.0481572
$584$	−3.79774	−0.157152
$585$	−1.81149	−0.0748959
$586$	−31.0687	−1.28344
$587$	−13.3533	−0.551152	−0.275576	−	0.961279i	$-0.588869\pi$
$587$	−13.3533	−0.551152	−0.275576	+	0.961279i	$0.588869\pi$
$588$	−0.502285	−0.0207139
$589$	2.82186	0.116273
$590$	−4.09055	−0.168405
$591$	−13.5299	−0.556547
$592$	−6.28379	−0.258262
$593$	11.9242	0.489668	0.244834	−	0.969565i	$-0.421267\pi$
$593$	11.9242	0.489668	0.244834	+	0.969565i	$0.421267\pi$
$594$	−0.272892	−0.0111969
$595$	−12.8033	−0.524883
$596$	−0.994752	−0.0407466
$597$	3.83619	0.157005
$598$	0.950341	0.0388623
$599$	19.6776	0.804004	0.402002	−	0.915639i	$-0.368315\pi$
$599$	19.6776	0.804004	0.402002	+	0.915639i	$0.368315\pi$
$600$	−3.93192	−0.160520
$601$	−2.28447	−0.0931854	−0.0465927	−	0.998914i	$-0.514836\pi$
$601$	−2.28447	−0.0931854	−0.0465927	+	0.998914i	$0.514836\pi$
$602$	−25.2572	−1.02941
$603$	−9.43319	−0.384149
$604$	6.30084	0.256377
$605$	−27.5432	−1.11979
$606$	−7.04404	−0.286145
$607$	35.5364	1.44238	0.721188	−	0.692739i	$-0.243596\pi$
$607$	35.5364	1.44238	0.721188	+	0.692739i	$0.243596\pi$
$608$	6.72408	0.272698
$609$	2.25278	0.0912873
$610$	−31.0755	−1.25821
$611$	−4.25092	−0.171974
$612$	−0.589944	−0.0238471
$613$	−6.04229	−0.244046	−0.122023	−	0.992527i	$-0.538938\pi$
$613$	−6.04229	−0.244046	−0.122023	+	0.992527i	$0.538938\pi$
$614$	−14.5224	−0.586078
$615$	8.54488	0.344563
$616$	1.38994	0.0560024
$617$	12.1271	0.488220	0.244110	−	0.969748i	$-0.421504\pi$
$617$	12.1271	0.488220	0.244110	+	0.969748i	$0.421504\pi$
$618$	−10.5991	−0.426359
$619$	40.4628	1.62634	0.813168	−	0.582028i	$-0.197741\pi$
$619$	40.4628	1.62634	0.813168	+	0.582028i	$0.197741\pi$
$620$	0.403579	0.0162081
$621$	−1.00000	−0.0401286
$622$	5.88453	0.235948
$623$	8.13969	0.326110
$624$	−2.45744	−0.0983763
$625$	−29.8546	−1.19418
$626$	−15.7137	−0.628046
$627$	−0.949029	−0.0379005
$628$	−3.57814	−0.142783
$629$	4.16627	0.166120
$630$	7.46780	0.297524
$631$	−26.9996	−1.07484	−0.537418	−	0.843316i	$-0.680600\pi$
$631$	−26.9996	−1.07484	−0.537418	+	0.843316i	$0.680600\pi$
$632$	27.9098	1.11019
$633$	18.0641	0.717985
$634$	3.57247	0.141881
$635$	36.2806	1.43975
$636$	1.46618	0.0581377
$637$	1.38723	0.0549639
$638$	0.272892	0.0108039
$639$	1.35812	0.0537264
$640$	−21.6465	−0.855653
$641$	−3.52991	−0.139423	−0.0697116	−	0.997567i	$-0.522208\pi$
$641$	−3.52991	−0.139423	−0.0697116	+	0.997567i	$0.522208\pi$
$642$	−4.63246	−0.182829
$643$	−24.7084	−0.974405	−0.487203	−	0.873289i	$-0.661983\pi$
$643$	−24.7084	−0.974405	−0.487203	+	0.873289i	$0.661983\pi$
$644$	0.587818	0.0231633
$645$	21.3709	0.841479
$646$	13.6739	0.537992
$647$	9.56460	0.376023	0.188012	−	0.982167i	$-0.439796\pi$
$647$	9.56460	0.376023	0.188012	+	0.982167i	$0.439796\pi$
$648$	2.98157	0.117127
$649$	−0.255353	−0.0100235
$650$	1.25325	0.0491566
$651$	−1.38614	−0.0543273
$652$	−0.293501	−0.0114944
$653$	−9.70004	−0.379592	−0.189796	−	0.981824i	$-0.560783\pi$
$653$	−9.70004	−0.379592	−0.189796	+	0.981824i	$0.560783\pi$
$654$	24.4197	0.954888
$655$	−25.0183	−0.977544
$656$	11.5918	0.452585
$657$	−1.27374	−0.0496932
$658$	17.5243	0.683167
$659$	16.1697	0.629881	0.314940	−	0.949111i	$-0.398015\pi$
$659$	16.1697	0.629881	0.314940	+	0.949111i	$0.398015\pi$
$660$	−0.135729	−0.00528323
$661$	15.2278	0.592295	0.296147	−	0.955142i	$-0.404298\pi$
$661$	15.2278	0.592295	0.296147	+	0.955142i	$0.404298\pi$
$662$	14.4038	0.559819
$663$	1.62933	0.0632778
$664$	−40.1439	−1.55788
$665$	25.9705	1.00709
$666$	−2.43007	−0.0941633
$667$	1.00000	0.0387202
$668$	−1.87335	−0.0724821
$669$	−5.81999	−0.225014
$670$	31.2703	1.20808
$671$	−1.93989	−0.0748886
$672$	−3.30298	−0.127415
$673$	−30.1373	−1.16171	−0.580854	−	0.814008i	$-0.697281\pi$
$673$	−30.1373	−1.16171	−0.580854	+	0.814008i	$0.697281\pi$
$674$	−47.0504	−1.81232
$675$	−1.31874	−0.0507583
$676$	3.25658	0.125253
$677$	−4.23918	−0.162925	−0.0814624	−	0.996676i	$-0.525959\pi$
$677$	−4.23918	−0.162925	−0.0814624	+	0.996676i	$0.525959\pi$
$678$	−22.7411	−0.873368
$679$	−3.88699	−0.149169
$680$	16.9452	0.649821
$681$	15.3483	0.588150
$682$	−0.167912	−0.00642967
$683$	−45.8651	−1.75498	−0.877490	−	0.479596i	$-0.840783\pi$
$683$	−45.8651	−1.75498	−0.877490	+	0.479596i	$0.840783\pi$
$684$	1.19666	0.0457554
$685$	−54.5839	−2.08554
$686$	−26.5146	−1.01233
$687$	15.8178	0.603486
$688$	28.9914	1.10529
$689$	−4.04934	−0.154267
$690$	3.31493	0.126197
$691$	32.6070	1.24043	0.620215	−	0.784432i	$-0.287046\pi$
$691$	32.6070	1.24043	0.620215	+	0.784432i	$0.287046\pi$
$692$	−0.885392	−0.0336576
$693$	0.466178	0.0177086
$694$	−14.8635	−0.564212
$695$	−24.2324	−0.919185
$696$	−2.98157	−0.113016
$697$	−7.68560	−0.291113
$698$	17.0192	0.644185
$699$	−10.8064	−0.408735
$700$	0.775177	0.0292990
$701$	−35.5331	−1.34207	−0.671033	−	0.741427i	$-0.734149\pi$
$701$	−35.5331	−1.34207	−0.671033	+	0.741427i	$0.734149\pi$
$702$	−0.950341	−0.0358683
$703$	−8.45097	−0.318735
$704$	−1.81142	−0.0682706
$705$	−14.8278	−0.558448
$706$	−8.91375	−0.335473
$707$	12.0332	0.452556
$708$	0.321982	0.0121008
$709$	−45.4945	−1.70858	−0.854290	−	0.519796i	$-0.826008\pi$
$709$	−45.4945	−1.70858	−0.854290	+	0.519796i	$0.826008\pi$
$710$	−4.50207	−0.168960
$711$	9.36077	0.351056
$712$	−10.7730	−0.403734
$713$	−0.615304	−0.0230433
$714$	−6.71683	−0.251371
$715$	0.374860	0.0140190
$716$	3.22945	0.120690
$717$	12.4863	0.466309
$718$	−43.8309	−1.63575
$719$	−20.5160	−0.765119	−0.382560	−	0.923931i	$-0.624957\pi$
$719$	−20.5160	−0.765119	−0.382560	+	0.923931i	$0.624957\pi$
$720$	−8.57189	−0.319456
$721$	18.1063	0.674315
$722$	−2.68047	−0.0997566
$723$	3.94214	0.146610
$724$	5.61848	0.208809
$725$	1.31874	0.0489767
$726$	−14.4496	−0.536277
$727$	−28.3740	−1.05233	−0.526167	−	0.850382i	$-0.676371\pi$
$727$	−28.3740	−1.05233	−0.526167	+	0.850382i	$0.676371\pi$
$728$	4.84045	0.179399
$729$	1.00000	0.0370370
$730$	4.22234	0.156276
$731$	−19.2219	−0.710946
$732$	2.44607	0.0904092
$733$	50.2037	1.85432	0.927158	−	0.374672i	$-0.122245\pi$
$733$	50.2037	1.85432	0.927158	+	0.374672i	$0.122245\pi$
$734$	−16.8332	−0.621324
$735$	4.83884	0.178483
$736$	−1.46618	−0.0540440
$737$	1.95205	0.0719048
$738$	4.48280	0.165014
$739$	−19.7992	−0.728326	−0.364163	−	0.931335i	$-0.618645\pi$
$739$	−19.7992	−0.728326	−0.364163	+	0.931335i	$0.618645\pi$
$740$	−1.20865	−0.0444307
$741$	−3.30497	−0.121411
$742$	16.6932	0.612828
$743$	−46.4475	−1.70399	−0.851997	−	0.523546i	$-0.824609\pi$
$743$	−46.4475	−1.70399	−0.851997	+	0.523546i	$0.824609\pi$
$744$	1.83457	0.0672588
$745$	9.58311	0.351098
$746$	24.5397	0.898463
$747$	−13.4640	−0.492621
$748$	0.122080	0.00446368
$749$	7.91356	0.289155
$750$	−12.2031	−0.445594
$751$	36.9387	1.34791	0.673956	−	0.738772i	$-0.264594\pi$
$751$	36.9387	1.34791	0.673956	+	0.738772i	$0.264594\pi$
$752$	−20.1152	−0.733525
$753$	−6.79990	−0.247802
$754$	0.950341	0.0346094
$755$	−60.7001	−2.20910
$756$	−0.587818	−0.0213787
$757$	15.5417	0.564872	0.282436	−	0.959286i	$-0.408857\pi$
$757$	15.5417	0.564872	0.282436	+	0.959286i	$0.408857\pi$
$758$	10.0410	0.364705
$759$	0.206934	0.00751124
$760$	−34.3722	−1.24681
$761$	−40.6429	−1.47330	−0.736652	−	0.676272i	$-0.763594\pi$
$761$	−40.6429	−1.47330	−0.736652	+	0.676272i	$0.763594\pi$
$762$	19.0334	0.689509
$763$	−41.7159	−1.51022
$764$	4.86626	0.176055
$765$	5.68332	0.205481
$766$	8.31204	0.300326
$767$	−0.889262	−0.0321094
$768$	6.15109	0.221958
$769$	−5.13554	−0.185192	−0.0925962	−	0.995704i	$-0.529517\pi$
$769$	−5.13554	−0.185192	−0.0925962	+	0.995704i	$0.529517\pi$
$770$	−1.54534	−0.0556904
$771$	25.4934	0.918121
$772$	2.12927	0.0766339
$773$	0.211642	0.00761222	0.00380611	−	0.999993i	$-0.498788\pi$
$773$	0.211642	0.00761222	0.00380611	+	0.999993i	$0.498788\pi$
$774$	11.2116	0.402992
$775$	−0.811425	−0.0291472
$776$	5.14447	0.184676
$777$	4.15125	0.148925
$778$	25.3119	0.907475
$779$	15.5897	0.558558
$780$	−0.472672	−0.0169244
$781$	−0.281042	−0.0100565
$782$	−2.98157	−0.106621
$783$	−1.00000	−0.0357371
$784$	6.56429	0.234439
$785$	34.4706	1.23031
$786$	−13.1250	−0.468154
$787$	19.8563	0.707799	0.353900	−	0.935283i	$-0.384855\pi$
$787$	19.8563	0.707799	0.353900	+	0.935283i	$0.384855\pi$
$788$	−3.53037	−0.125764
$789$	−5.87654	−0.209210
$790$	−31.0303	−1.10401
$791$	38.8483	1.38129
$792$	−0.616990	−0.0219238
$793$	−6.75562	−0.239899
$794$	−5.24493	−0.186136
$795$	−14.1247	−0.500950
$796$	1.00098	0.0354787
$797$	−6.41446	−0.227212	−0.113606	−	0.993526i	$-0.536240\pi$
$797$	−6.41446	−0.227212	−0.113606	+	0.993526i	$0.536240\pi$
$798$	13.6246	0.482306
$799$	13.3367	0.471819
$800$	−1.93350	−0.0683597
$801$	−3.61318	−0.127665
$802$	10.2462	0.361805
$803$	0.263580	0.00930154
$804$	−2.46140	−0.0868069
$805$	−5.66284	−0.199589
$806$	−0.584749	−0.0205969
$807$	3.61181	0.127142
$808$	−15.9261	−0.560278
$809$	47.7649	1.67932	0.839662	−	0.543109i	$-0.182753\pi$
$809$	47.7649	1.67932	0.839662	+	0.543109i	$0.182753\pi$
$810$	−3.31493	−0.116475
$811$	−12.0735	−0.423959	−0.211979	−	0.977274i	$-0.567991\pi$
$811$	−12.0735	−0.423959	−0.211979	+	0.977274i	$0.567991\pi$
$812$	0.587818	0.0206284
$813$	23.1450	0.811732
$814$	0.502865	0.0176254
$815$	2.82749	0.0990427
$816$	7.70990	0.269900
$817$	38.9901	1.36409
$818$	−32.7540	−1.14522
$819$	1.62345	0.0567281
$820$	2.22961	0.0778615
$821$	2.12441	0.0741424	0.0370712	−	0.999313i	$-0.488197\pi$
$821$	2.12441	0.0741424	0.0370712	+	0.999313i	$0.488197\pi$
$822$	−28.6357	−0.998786
$823$	14.3341	0.499656	0.249828	−	0.968290i	$-0.419626\pi$
$823$	14.3341	0.499656	0.249828	+	0.968290i	$0.419626\pi$
$824$	−23.9639	−0.834821
$825$	0.272892	0.00950089
$826$	3.66594	0.127554
$827$	27.0920	0.942082	0.471041	−	0.882111i	$-0.343878\pi$
$827$	27.0920	0.942082	0.471041	+	0.882111i	$0.343878\pi$
$828$	−0.260930	−0.00906794
$829$	14.1735	0.492268	0.246134	−	0.969236i	$-0.420840\pi$
$829$	14.1735	0.492268	0.246134	+	0.969236i	$0.420840\pi$
$830$	44.6321	1.54920
$831$	−15.9558	−0.553502
$832$	−6.30825	−0.218699
$833$	−4.35225	−0.150796
$834$	−12.7127	−0.440206
$835$	18.0472	0.624550
$836$	−0.247630	−0.00856446
$837$	0.615304	0.0212680
$838$	−3.34067	−0.115402
$839$	−41.6889	−1.43926	−0.719631	−	0.694357i	$-0.755689\pi$
$839$	−41.6889	−1.43926	−0.719631	+	0.694357i	$0.755689\pi$
$840$	16.8842	0.582559
$841$	1.00000	0.0344828
$842$	0.641694	0.0221142
$843$	3.25850	0.112229
$844$	4.71347	0.162244
$845$	−31.3728	−1.07926
$846$	−7.77895	−0.267446
$847$	24.6841	0.848156
$848$	−19.1613	−0.658001
$849$	−7.75465	−0.266139
$850$	−3.93192	−0.134864
$851$	1.84272	0.0631678
$852$	0.354374	0.0121407
$853$	24.0066	0.821970	0.410985	−	0.911642i	$-0.365185\pi$
$853$	24.0066	0.821970	0.410985	+	0.911642i	$0.365185\pi$
$854$	27.8498	0.953000
$855$	−11.5282	−0.394256
$856$	−10.4737	−0.357983
$857$	28.3597	0.968749	0.484374	−	0.874861i	$-0.339047\pi$
$857$	28.3597	0.968749	0.484374	+	0.874861i	$0.339047\pi$
$858$	0.196658	0.00671381
$859$	−12.0011	−0.409474	−0.204737	−	0.978817i	$-0.565634\pi$
$859$	−12.0011	−0.409474	−0.204737	+	0.978817i	$0.565634\pi$
$860$	5.57631	0.190151
$861$	−7.65790	−0.260980
$862$	−22.5665	−0.768620
$863$	31.8630	1.08463	0.542314	−	0.840176i	$-0.317548\pi$
$863$	31.8630	1.08463	0.542314	+	0.840176i	$0.317548\pi$
$864$	1.46618	0.0498804
$865$	8.52957	0.290014
$866$	33.7478	1.14680
$867$	11.8882	0.403744
$868$	−0.361686	−0.0122764
$869$	−1.93707	−0.0657105
$870$	3.31493	0.112386
$871$	6.79798	0.230341
$872$	55.2113	1.86969
$873$	1.72542	0.0583967
$874$	6.04791	0.204573
$875$	20.8464	0.704736
$876$	−0.332356	−0.0112293
$877$	5.74793	0.194094	0.0970469	−	0.995280i	$-0.469060\pi$
$877$	5.74793	0.194094	0.0970469	+	0.995280i	$0.469060\pi$
$878$	9.99519	0.337321
$879$	−23.5594	−0.794640
$880$	1.77382	0.0597955
$881$	−11.9952	−0.404128	−0.202064	−	0.979372i	$-0.564765\pi$
$881$	−11.9952	−0.404128	−0.202064	+	0.979372i	$0.564765\pi$
$882$	2.53855	0.0854773
$883$	30.2919	1.01940	0.509701	−	0.860352i	$-0.329756\pi$
$883$	30.2919	1.01940	0.509701	+	0.860352i	$0.329756\pi$
$884$	0.425140	0.0142990
$885$	−3.10187	−0.104268
$886$	−11.0736	−0.372023
$887$	−28.8927	−0.970123	−0.485062	−	0.874480i	$-0.661203\pi$
$887$	−28.8927	−0.970123	−0.485062	+	0.874480i	$0.661203\pi$
$888$	−5.49422	−0.184374
$889$	−32.5145	−1.09050
$890$	11.9774	0.401484
$891$	−0.206934	−0.00693256
$892$	−1.51861	−0.0508468
$893$	−27.0526	−0.905280
$894$	5.02747	0.168144
$895$	−31.1114	−1.03994
$896$	19.3995	0.648093
$897$	0.720644	0.0240616
$898$	−40.5262	−1.35238
$899$	−0.615304	−0.0205215
$900$	−0.344098	−0.0114699
$901$	12.7043	0.423241
$902$	−0.927645	−0.0308872
$903$	−19.1526	−0.637358
$904$	−51.4161	−1.71007
$905$	−54.1266	−1.79923
$906$	−31.8444	−1.05796
$907$	40.3737	1.34059	0.670293	−	0.742097i	$-0.266168\pi$
$907$	40.3737	1.34059	0.670293	+	0.742097i	$0.266168\pi$
$908$	4.00484	0.132905
$909$	−5.34150	−0.177166
$910$	−5.38163	−0.178399
$911$	−8.30349	−0.275107	−0.137553	−	0.990494i	$-0.543924\pi$
$911$	−8.30349	−0.275107	−0.137553	+	0.990494i	$0.543924\pi$
$912$	−15.6390	−0.517858
$913$	2.78616	0.0922085
$914$	−1.75331	−0.0579944
$915$	−23.5646	−0.779021
$916$	4.12733	0.136371
$917$	22.4213	0.740416
$918$	2.98157	0.0984066
$919$	−39.2171	−1.29365	−0.646827	−	0.762637i	$-0.723904\pi$
$919$	−39.2171	−1.29365	−0.646827	+	0.762637i	$0.723904\pi$
$920$	7.49481	0.247097
$921$	−11.0124	−0.362870
$922$	9.67695	0.318693
$923$	−0.978722	−0.0322150
$924$	0.121640	0.00400165
$925$	2.43007	0.0799002
$926$	3.54418	0.116469
$927$	−8.03732	−0.263980
$928$	−1.46618	−0.0481296
$929$	40.1694	1.31792	0.658958	−	0.752180i	$-0.270998\pi$
$929$	40.1694	1.31792	0.658958	+	0.752180i	$0.270998\pi$
$930$	−2.03969	−0.0668840
$931$	8.82822	0.289333
$932$	−2.81971	−0.0923627
$933$	4.46225	0.146087
$934$	−9.02883	−0.295432
$935$	−1.17608	−0.0384618
$936$	−2.14866	−0.0702310
$937$	−26.5512	−0.867390	−0.433695	−	0.901060i	$-0.642791\pi$
$937$	−26.5512	−0.867390	−0.433695	+	0.901060i	$0.642791\pi$
$938$	−28.0244	−0.915029
$939$	−11.9157	−0.388855
$940$	−3.86902	−0.126194
$941$	−17.2684	−0.562934	−0.281467	−	0.959571i	$-0.590821\pi$
$941$	−17.2684	−0.562934	−0.281467	+	0.959571i	$0.590821\pi$
$942$	18.0839	0.589205
$943$	−3.39931	−0.110697
$944$	−4.20794	−0.136957
$945$	5.66284	0.184212
$946$	−2.32006	−0.0754317
$947$	44.4634	1.44487	0.722434	−	0.691440i	$-0.243023\pi$
$947$	44.4634	1.44487	0.722434	+	0.691440i	$0.243023\pi$
$948$	2.44250	0.0793289
$949$	0.917912	0.0297967
$950$	7.97560	0.258763
$951$	2.70900	0.0878454
$952$	−15.1863	−0.492190
$953$	−22.6887	−0.734958	−0.367479	−	0.930032i	$-0.619779\pi$
$953$	−22.6887	−0.734958	−0.367479	+	0.930032i	$0.619779\pi$
$954$	−7.41006	−0.239909
$955$	−46.8799	−1.51700
$956$	3.25804	0.105373
$957$	0.206934	0.00668924
$958$	−19.9793	−0.645502
$959$	48.9180	1.57964
$960$	−22.0041	−0.710178
$961$	−30.6214	−0.987787
$962$	1.75122	0.0564615
$963$	−3.51280	−0.113198
$964$	1.02862	0.0331297
$965$	−20.5126	−0.660325
$966$	−2.97083	−0.0955848
$967$	4.31252	0.138681	0.0693406	−	0.997593i	$-0.477910\pi$
$967$	4.31252	0.138681	0.0693406	+	0.997593i	$0.477910\pi$
$968$	−32.6696	−1.05004
$969$	10.3689	0.333098
$970$	−5.71964	−0.183647
$971$	46.8188	1.50249	0.751243	−	0.660025i	$-0.229454\pi$
$971$	46.8188	1.50249	0.751243	+	0.660025i	$0.229454\pi$
$972$	0.260930	0.00836933
$973$	21.7170	0.696214
$974$	3.04105	0.0974414
$975$	0.950341	0.0304353
$976$	−31.9673	−1.02325
$977$	51.8522	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$977$	51.8522	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$978$	1.48335	0.0474324
$979$	0.747691	0.0238963
$980$	1.26260	0.0403322
$981$	18.5175	0.591219
$982$	39.7286	1.26779
$983$	2.68187	0.0855382	0.0427691	−	0.999085i	$-0.486382\pi$
$983$	2.68187	0.0855382	0.0427691	+	0.999085i	$0.486382\pi$
$984$	10.1353	0.323101
$985$	34.0104	1.08366
$986$	−2.98157	−0.0949527
$987$	13.2887	0.422983
$988$	−0.862365	−0.0274355
$989$	−8.50175	−0.270340
$990$	0.685972	0.0218016
$991$	11.1114	0.352966	0.176483	−	0.984304i	$-0.443528\pi$
$991$	11.1114	0.352966	0.176483	+	0.984304i	$0.443528\pi$
$992$	0.902145	0.0286431
$993$	10.9224	0.346612
$994$	4.03474	0.127974
$995$	−9.64308	−0.305706
$996$	−3.51316	−0.111319
$997$	35.6328	1.12850	0.564251	−	0.825603i	$-0.309165\pi$
$997$	35.6328	1.12850	0.564251	+	0.825603i	$0.309165\pi$
$998$	−18.6274	−0.589639
$999$	−1.84272	−0.0583012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.h.1.3	✓	5
3.2	odd	2		6003.2.a.h.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.h.1.3	✓	5	1.1	even	1	trivial
6003.2.a.h.1.3		5	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31874 q^{2} -1.00000 q^{3} -0.260930 q^{4} +2.51371 q^{5} +1.31874 q^{6} -2.25278 q^{7} +2.98157 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.31874 q^{2} -1.00000 q^{3} -0.260930 q^{4} +2.51371 q^{5} +1.31874 q^{6} -2.25278 q^{7} +2.98157 q^{8} +1.00000 q^{9} -3.31493 q^{10} -0.206934 q^{11} +0.260930 q^{12} -0.720644 q^{13} +2.97083 q^{14} -2.51371 q^{15} -3.41006 q^{16} +2.26093 q^{17} -1.31874 q^{18} -4.58613 q^{19} -0.655902 q^{20} +2.25278 q^{21} +0.272892 q^{22} +1.00000 q^{23} -2.98157 q^{24} +1.31874 q^{25} +0.950341 q^{26} -1.00000 q^{27} +0.587818 q^{28} +1.00000 q^{29} +3.31493 q^{30} -0.615304 q^{31} -1.46618 q^{32} +0.206934 q^{33} -2.98157 q^{34} -5.66284 q^{35} -0.260930 q^{36} +1.84272 q^{37} +6.04791 q^{38} +0.720644 q^{39} +7.49481 q^{40} -3.39931 q^{41} -2.97083 q^{42} -8.50175 q^{43} +0.0539954 q^{44} +2.51371 q^{45} -1.31874 q^{46} +5.89878 q^{47} +3.41006 q^{48} -1.92498 q^{49} -1.73907 q^{50} -2.26093 q^{51} +0.188038 q^{52} +5.61905 q^{53} +1.31874 q^{54} -0.520173 q^{55} -6.71683 q^{56} +4.58613 q^{57} -1.31874 q^{58} +1.23398 q^{59} +0.655902 q^{60} +9.37442 q^{61} +0.811425 q^{62} -2.25278 q^{63} +8.75362 q^{64} -1.81149 q^{65} -0.272892 q^{66} -9.43319 q^{67} -0.589944 q^{68} -1.00000 q^{69} +7.46780 q^{70} +1.35812 q^{71} +2.98157 q^{72} -1.27374 q^{73} -2.43007 q^{74} -1.31874 q^{75} +1.19666 q^{76} +0.466178 q^{77} -0.950341 q^{78} +9.36077 q^{79} -8.57189 q^{80} +1.00000 q^{81} +4.48280 q^{82} -13.4640 q^{83} -0.587818 q^{84} +5.68332 q^{85} +11.2116 q^{86} -1.00000 q^{87} -0.616990 q^{88} -3.61318 q^{89} -3.31493 q^{90} +1.62345 q^{91} -0.260930 q^{92} +0.615304 q^{93} -7.77895 q^{94} -11.5282 q^{95} +1.46618 q^{96} +1.72542 q^{97} +2.53855 q^{98} -0.206934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * q^99

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