LMFDB - Embedded newform 2001.2.a.m.1.5

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 $ x^14 - 2x^13 - 18x^12 + 34x^11 + 124x^10 - 216x^9 - 420x^8 + 647x^7 + 750x^6 - 939x^5 - 717x^4 + 604x^3 + 352x^2 - 128*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.35292$ 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)

$f(q)$	$=$	$q-1.35292 q^{2} -1.00000 q^{3} -0.169600 q^{4} -0.738177 q^{5} +1.35292 q^{6} +3.44152 q^{7} +2.93530 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.35292 q^{2} -1.00000 q^{3} -0.169600 q^{4} -0.738177 q^{5} +1.35292 q^{6} +3.44152 q^{7} +2.93530 q^{8} +1.00000 q^{9} +0.998696 q^{10} +1.17333 q^{11} +0.169600 q^{12} -2.89875 q^{13} -4.65611 q^{14} +0.738177 q^{15} -3.63203 q^{16} -3.96681 q^{17} -1.35292 q^{18} -3.02566 q^{19} +0.125195 q^{20} -3.44152 q^{21} -1.58742 q^{22} -1.00000 q^{23} -2.93530 q^{24} -4.45509 q^{25} +3.92179 q^{26} -1.00000 q^{27} -0.583682 q^{28} -1.00000 q^{29} -0.998696 q^{30} +10.3766 q^{31} -0.956741 q^{32} -1.17333 q^{33} +5.36678 q^{34} -2.54045 q^{35} -0.169600 q^{36} +3.14877 q^{37} +4.09349 q^{38} +2.89875 q^{39} -2.16677 q^{40} -7.62266 q^{41} +4.65611 q^{42} +6.17008 q^{43} -0.198997 q^{44} -0.738177 q^{45} +1.35292 q^{46} +11.0057 q^{47} +3.63203 q^{48} +4.84403 q^{49} +6.02740 q^{50} +3.96681 q^{51} +0.491629 q^{52} -12.0907 q^{53} +1.35292 q^{54} -0.866122 q^{55} +10.1019 q^{56} +3.02566 q^{57} +1.35292 q^{58} +1.75699 q^{59} -0.125195 q^{60} +2.90124 q^{61} -14.0387 q^{62} +3.44152 q^{63} +8.55847 q^{64} +2.13979 q^{65} +1.58742 q^{66} +8.65474 q^{67} +0.672772 q^{68} +1.00000 q^{69} +3.43703 q^{70} -8.41446 q^{71} +2.93530 q^{72} +1.23211 q^{73} -4.26004 q^{74} +4.45509 q^{75} +0.513153 q^{76} +4.03802 q^{77} -3.92179 q^{78} -15.7529 q^{79} +2.68108 q^{80} +1.00000 q^{81} +10.3129 q^{82} -9.53737 q^{83} +0.583682 q^{84} +2.92821 q^{85} -8.34764 q^{86} +1.00000 q^{87} +3.44407 q^{88} -10.0938 q^{89} +0.998696 q^{90} -9.97610 q^{91} +0.169600 q^{92} -10.3766 q^{93} -14.8899 q^{94} +2.23347 q^{95} +0.956741 q^{96} -12.9789 q^{97} -6.55360 q^{98} +1.17333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * 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 $

$2$	−1.35292	−0.956661	−0.478330	−	0.878180i	$-0.658758\pi$
$2$	−1.35292	−0.956661	−0.478330	+	0.878180i	$0.658758\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.169600	−0.0848002
$5$	−0.738177	−0.330123	−0.165061	−	0.986283i	$-0.552782\pi$
$5$	−0.738177	−0.330123	−0.165061	+	0.986283i	$0.552782\pi$
$6$	1.35292	0.552328
$7$	3.44152	1.30077	0.650385	−	0.759604i	$-0.274607\pi$
$7$	3.44152	1.30077	0.650385	+	0.759604i	$0.274607\pi$
$8$	2.93530	1.03779
$9$	1.00000	0.333333
$10$	0.998696	0.315816
$11$	1.17333	0.353771	0.176886	−	0.984231i	$-0.443398\pi$
$11$	1.17333	0.353771	0.176886	+	0.984231i	$0.443398\pi$
$12$	0.169600	0.0489594
$13$	−2.89875	−0.803969	−0.401984	−	0.915646i	$-0.631679\pi$
$13$	−2.89875	−0.803969	−0.401984	+	0.915646i	$0.631679\pi$
$14$	−4.65611	−1.24440
$15$	0.738177	0.190596
$16$	−3.63203	−0.908009
$17$	−3.96681	−0.962092	−0.481046	−	0.876695i	$-0.659743\pi$
$17$	−3.96681	−0.962092	−0.481046	+	0.876695i	$0.659743\pi$
$18$	−1.35292	−0.318887
$19$	−3.02566	−0.694134	−0.347067	−	0.937840i	$-0.612822\pi$
$19$	−3.02566	−0.694134	−0.347067	+	0.937840i	$0.612822\pi$
$20$	0.125195	0.0279945
$21$	−3.44152	−0.751000
$22$	−1.58742	−0.338439
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.93530	−0.599166
$25$	−4.45509	−0.891019
$26$	3.92179	0.769126
$27$	−1.00000	−0.192450
$28$	−0.583682	−0.110306
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.998696	−0.182336
$31$	10.3766	1.86369	0.931847	−	0.362852i	$-0.118197\pi$
$31$	10.3766	1.86369	0.931847	+	0.362852i	$0.118197\pi$
$32$	−0.956741	−0.169129
$33$	−1.17333	−0.204250
$34$	5.36678	0.920396
$35$	−2.54045	−0.429414
$36$	−0.169600	−0.0282667
$37$	3.14877	0.517654	0.258827	−	0.965924i	$-0.416664\pi$
$37$	3.14877	0.517654	0.258827	+	0.965924i	$0.416664\pi$
$38$	4.09349	0.664051
$39$	2.89875	0.464172
$40$	−2.16677	−0.342597
$41$	−7.62266	−1.19046	−0.595230	−	0.803556i	$-0.702939\pi$
$41$	−7.62266	−1.19046	−0.595230	+	0.803556i	$0.702939\pi$
$42$	4.65611	0.718453
$43$	6.17008	0.940928	0.470464	−	0.882419i	$-0.344086\pi$
$43$	6.17008	0.940928	0.470464	+	0.882419i	$0.344086\pi$
$44$	−0.198997	−0.0299999
$45$	−0.738177	−0.110041
$46$	1.35292	0.199478
$47$	11.0057	1.60535	0.802673	−	0.596419i	$-0.203410\pi$
$47$	11.0057	1.60535	0.802673	+	0.596419i	$0.203410\pi$
$48$	3.63203	0.524239
$49$	4.84403	0.692005
$50$	6.02740	0.852403
$51$	3.96681	0.555464
$52$	0.491629	0.0681767
$53$	−12.0907	−1.66079	−0.830395	−	0.557176i	$-0.811885\pi$
$53$	−12.0907	−1.66079	−0.830395	+	0.557176i	$0.811885\pi$
$54$	1.35292	0.184109
$55$	−0.866122	−0.116788
$56$	10.1019	1.34992
$57$	3.02566	0.400759
$58$	1.35292	0.177647
$59$	1.75699	0.228741	0.114371	−	0.993438i	$-0.463515\pi$
$59$	1.75699	0.228741	0.114371	+	0.993438i	$0.463515\pi$
$60$	−0.125195	−0.0161626
$61$	2.90124	0.371466	0.185733	−	0.982600i	$-0.440534\pi$
$61$	2.90124	0.371466	0.185733	+	0.982600i	$0.440534\pi$
$62$	−14.0387	−1.78292
$63$	3.44152	0.433590
$64$	8.55847	1.06981
$65$	2.13979	0.265408
$66$	1.58742	0.195398
$67$	8.65474	1.05735	0.528673	−	0.848826i	$-0.322690\pi$
$67$	8.65474	1.05735	0.528673	+	0.848826i	$0.322690\pi$
$68$	0.672772	0.0815856
$69$	1.00000	0.120386
$70$	3.43703	0.410804
$71$	−8.41446	−0.998613	−0.499306	−	0.866425i	$-0.666412\pi$
$71$	−8.41446	−0.998613	−0.499306	+	0.866425i	$0.666412\pi$
$72$	2.93530	0.345929
$73$	1.23211	0.144207	0.0721037	−	0.997397i	$-0.477029\pi$
$73$	1.23211	0.144207	0.0721037	+	0.997397i	$0.477029\pi$
$74$	−4.26004	−0.495219
$75$	4.45509	0.514430
$76$	0.513153	0.0588627
$77$	4.03802	0.460175
$78$	−3.92179	−0.444055
$79$	−15.7529	−1.77234	−0.886169	−	0.463363i	$-0.846643\pi$
$79$	−15.7529	−1.77234	−0.886169	+	0.463363i	$0.846643\pi$
$80$	2.68108	0.299754
$81$	1.00000	0.111111
$82$	10.3129	1.13887
$83$	−9.53737	−1.04686	−0.523431	−	0.852068i	$-0.675348\pi$
$83$	−9.53737	−1.04686	−0.523431	+	0.852068i	$0.675348\pi$
$84$	0.583682	0.0636850
$85$	2.92821	0.317609
$86$	−8.34764	−0.900149
$87$	1.00000	0.107211
$88$	3.44407	0.367139
$89$	−10.0938	−1.06994	−0.534971	−	0.844871i	$-0.679677\pi$
$89$	−10.0938	−1.06994	−0.534971	+	0.844871i	$0.679677\pi$
$90$	0.998696	0.105272
$91$	−9.97610	−1.04578
$92$	0.169600	0.0176821
$93$	−10.3766	−1.07600
$94$	−14.8899	−1.53577
$95$	2.23347	0.229150
$96$	0.956741	0.0976469
$97$	−12.9789	−1.31780	−0.658902	−	0.752229i	$-0.728979\pi$
$97$	−12.9789	−1.31780	−0.658902	+	0.752229i	$0.728979\pi$
$98$	−6.55360	−0.662014
$99$	1.17333	0.117924
$100$	0.755586	0.0755586
$101$	−6.44364	−0.641166	−0.320583	−	0.947220i	$-0.603879\pi$
$101$	−6.44364	−0.641166	−0.320583	+	0.947220i	$0.603879\pi$
$102$	−5.36678	−0.531391
$103$	4.18324	0.412187	0.206094	−	0.978532i	$-0.433925\pi$
$103$	4.18324	0.412187	0.206094	+	0.978532i	$0.433925\pi$
$104$	−8.50871	−0.834348
$105$	2.54045	0.247922
$106$	16.3578	1.58881
$107$	−5.35867	−0.518042	−0.259021	−	0.965872i	$-0.583400\pi$
$107$	−5.35867	−0.518042	−0.259021	+	0.965872i	$0.583400\pi$
$108$	0.169600	0.0163198
$109$	11.3099	1.08329	0.541647	−	0.840606i	$-0.317801\pi$
$109$	11.3099	1.08329	0.541647	+	0.840606i	$0.317801\pi$
$110$	1.17180	0.111726
$111$	−3.14877	−0.298868
$112$	−12.4997	−1.18111
$113$	−5.42973	−0.510786	−0.255393	−	0.966837i	$-0.582205\pi$
$113$	−5.42973	−0.510786	−0.255393	+	0.966837i	$0.582205\pi$
$114$	−4.09349	−0.383390
$115$	0.738177	0.0688354
$116$	0.169600	0.0157470
$117$	−2.89875	−0.267990
$118$	−2.37708	−0.218828
$119$	−13.6518	−1.25146
$120$	2.16677	0.197798
$121$	−9.62331	−0.874846
$122$	−3.92516	−0.355367
$123$	7.62266	0.687312
$124$	−1.75988	−0.158042
$125$	6.97953	0.624268
$126$	−4.65611	−0.414799
$127$	−9.48395	−0.841564	−0.420782	−	0.907162i	$-0.638244\pi$
$127$	−9.48395	−0.841564	−0.420782	+	0.907162i	$0.638244\pi$
$128$	−9.66546	−0.854314
$129$	−6.17008	−0.543245
$130$	−2.89497	−0.253906
$131$	−0.643336	−0.0562085	−0.0281042	−	0.999605i	$-0.508947\pi$
$131$	−0.643336	−0.0562085	−0.0281042	+	0.999605i	$0.508947\pi$
$132$	0.198997	0.0173204
$133$	−10.4129	−0.902910
$134$	−11.7092	−1.01152
$135$	0.738177	0.0635322
$136$	−11.6438	−0.998446
$137$	−15.3086	−1.30790	−0.653951	−	0.756536i	$-0.726890\pi$
$137$	−15.3086	−1.30790	−0.653951	+	0.756536i	$0.726890\pi$
$138$	−1.35292	−0.115168
$139$	8.30209	0.704174	0.352087	−	0.935967i	$-0.385472\pi$
$139$	8.30209	0.704174	0.352087	+	0.935967i	$0.385472\pi$
$140$	0.430861	0.0364144
$141$	−11.0057	−0.926847
$142$	11.3841	0.955334
$143$	−3.40118	−0.284421
$144$	−3.63203	−0.302670
$145$	0.738177	0.0613023
$146$	−1.66695	−0.137958
$147$	−4.84403	−0.399529
$148$	−0.534032	−0.0438972
$149$	17.6570	1.44652	0.723258	−	0.690578i	$-0.242644\pi$
$149$	17.6570	1.44652	0.723258	+	0.690578i	$0.242644\pi$
$150$	−6.02740	−0.492135
$151$	8.23676	0.670298	0.335149	−	0.942165i	$-0.391213\pi$
$151$	8.23676	0.670298	0.335149	+	0.942165i	$0.391213\pi$
$152$	−8.88123	−0.720363
$153$	−3.96681	−0.320697
$154$	−5.46313	−0.440232
$155$	−7.65977	−0.615248
$156$	−0.491629	−0.0393618
$157$	17.2680	1.37814	0.689068	−	0.724696i	$-0.258020\pi$
$157$	17.2680	1.37814	0.689068	+	0.724696i	$0.258020\pi$
$158$	21.3124	1.69553
$159$	12.0907	0.958857
$160$	0.706244	0.0558335
$161$	−3.44152	−0.271229
$162$	−1.35292	−0.106296
$163$	−21.4179	−1.67758	−0.838791	−	0.544454i	$-0.816737\pi$
$163$	−21.4179	−1.67758	−0.838791	+	0.544454i	$0.816737\pi$
$164$	1.29281	0.100951
$165$	0.866122	0.0674275
$166$	12.9033	1.00149
$167$	1.86970	0.144682	0.0723409	−	0.997380i	$-0.476953\pi$
$167$	1.86970	0.144682	0.0723409	+	0.997380i	$0.476953\pi$
$168$	−10.1019	−0.779378
$169$	−4.59724	−0.353634
$170$	−3.96164	−0.303844
$171$	−3.02566	−0.231378
$172$	−1.04645	−0.0797909
$173$	−8.89523	−0.676292	−0.338146	−	0.941094i	$-0.609800\pi$
$173$	−8.89523	−0.676292	−0.338146	+	0.941094i	$0.609800\pi$
$174$	−1.35292	−0.102565
$175$	−15.3323	−1.15901
$176$	−4.26156	−0.321227
$177$	−1.75699	−0.132064
$178$	13.6561	1.02357
$179$	11.5346	0.862136	0.431068	−	0.902319i	$-0.358137\pi$
$179$	11.5346	0.862136	0.431068	+	0.902319i	$0.358137\pi$
$180$	0.125195	0.00933149
$181$	4.24247	0.315340	0.157670	−	0.987492i	$-0.449602\pi$
$181$	4.24247	0.315340	0.157670	+	0.987492i	$0.449602\pi$
$182$	13.4969	1.00046
$183$	−2.90124	−0.214466
$184$	−2.93530	−0.216393
$185$	−2.32435	−0.170889
$186$	14.0387	1.02937
$187$	−4.65436	−0.340360
$188$	−1.86657	−0.136134
$189$	−3.44152	−0.250333
$190$	−3.02172	−0.219218
$191$	−21.9527	−1.58844	−0.794222	−	0.607628i	$-0.792121\pi$
$191$	−21.9527	−1.58844	−0.794222	+	0.607628i	$0.792121\pi$
$192$	−8.55847	−0.617654
$193$	−16.4290	−1.18258	−0.591292	−	0.806457i	$-0.701382\pi$
$193$	−16.4290	−1.18258	−0.591292	+	0.806457i	$0.701382\pi$
$194$	17.5594	1.26069
$195$	−2.13979	−0.153234
$196$	−0.821550	−0.0586821
$197$	22.2164	1.58285	0.791426	−	0.611266i	$-0.209339\pi$
$197$	22.2164	1.58285	0.791426	+	0.611266i	$0.209339\pi$
$198$	−1.58742	−0.112813
$199$	−16.1955	−1.14807	−0.574033	−	0.818832i	$-0.694622\pi$
$199$	−16.1955	−1.14807	−0.574033	+	0.818832i	$0.694622\pi$
$200$	−13.0770	−0.924687
$201$	−8.65474	−0.610459
$202$	8.71775	0.613379
$203$	−3.44152	−0.241547
$204$	−0.672772	−0.0471035
$205$	5.62687	0.392998
$206$	−5.65960	−0.394323
$207$	−1.00000	−0.0695048
$208$	10.5284	0.730011
$209$	−3.55009	−0.245565
$210$	−3.43703	−0.237178
$211$	19.9907	1.37621	0.688107	−	0.725609i	$-0.258442\pi$
$211$	19.9907	1.37621	0.688107	+	0.725609i	$0.258442\pi$
$212$	2.05059	0.140835
$213$	8.41446	0.576549
$214$	7.24987	0.495591
$215$	−4.55461	−0.310622
$216$	−2.93530	−0.199722
$217$	35.7113	2.42424
$218$	−15.3014	−1.03634
$219$	−1.23211	−0.0832582
$220$	0.146895	0.00990364
$221$	11.4988	0.773492
$222$	4.26004	0.285915
$223$	8.34982	0.559145	0.279573	−	0.960125i	$-0.409807\pi$
$223$	8.34982	0.559145	0.279573	+	0.960125i	$0.409807\pi$
$224$	−3.29264	−0.219999
$225$	−4.45509	−0.297006
$226$	7.34600	0.488649
$227$	−7.28325	−0.483406	−0.241703	−	0.970350i	$-0.577706\pi$
$227$	−7.28325	−0.483406	−0.241703	+	0.970350i	$0.577706\pi$
$228$	−0.513153	−0.0339844
$229$	−16.3948	−1.08340	−0.541700	−	0.840572i	$-0.682219\pi$
$229$	−16.3948	−1.08340	−0.541700	+	0.840572i	$0.682219\pi$
$230$	−0.998696	−0.0658521
$231$	−4.03802	−0.265682
$232$	−2.93530	−0.192712
$233$	17.6144	1.15396	0.576980	−	0.816758i	$-0.304231\pi$
$233$	17.6144	1.15396	0.576980	+	0.816758i	$0.304231\pi$
$234$	3.92179	0.256375
$235$	−8.12416	−0.529962
$236$	−0.297987	−0.0193973
$237$	15.7529	1.02326
$238$	18.4699	1.19722
$239$	−20.3195	−1.31436	−0.657178	−	0.753735i	$-0.728250\pi$
$239$	−20.3195	−1.31436	−0.657178	+	0.753735i	$0.728250\pi$
$240$	−2.68108	−0.173063
$241$	2.51402	0.161942	0.0809712	−	0.996716i	$-0.474198\pi$
$241$	2.51402	0.161942	0.0809712	+	0.996716i	$0.474198\pi$
$242$	13.0196	0.836931
$243$	−1.00000	−0.0641500
$244$	−0.492052	−0.0315004
$245$	−3.57575	−0.228447
$246$	−10.3129	−0.657524
$247$	8.77064	0.558062
$248$	30.4585	1.93411
$249$	9.53737	0.604407
$250$	−9.44277	−0.597213
$251$	−4.97478	−0.314005	−0.157003	−	0.987598i	$-0.550183\pi$
$251$	−4.97478	−0.314005	−0.157003	+	0.987598i	$0.550183\pi$
$252$	−0.583682	−0.0367685
$253$	−1.17333	−0.0737664
$254$	12.8310	0.805092
$255$	−2.92821	−0.183371
$256$	−4.04031	−0.252519
$257$	−14.1760	−0.884275	−0.442137	−	0.896947i	$-0.645780\pi$
$257$	−14.1760	−0.884275	−0.442137	+	0.896947i	$0.645780\pi$
$258$	8.34764	0.519701
$259$	10.8365	0.673349
$260$	−0.362909	−0.0225067
$261$	−1.00000	−0.0618984
$262$	0.870383	0.0537725
$263$	−18.3150	−1.12935	−0.564675	−	0.825313i	$-0.690998\pi$
$263$	−18.3150	−1.12935	−0.564675	+	0.825313i	$0.690998\pi$
$264$	−3.44407	−0.211968
$265$	8.92510	0.548264
$266$	14.0878	0.863778
$267$	10.0938	0.617731
$268$	−1.46785	−0.0896631
$269$	−12.3846	−0.755103	−0.377551	−	0.925989i	$-0.623234\pi$
$269$	−12.3846	−0.755103	−0.377551	+	0.925989i	$0.623234\pi$
$270$	−0.998696	−0.0607787
$271$	0.0474151	0.00288026	0.00144013	−	0.999999i	$-0.499542\pi$
$271$	0.0474151	0.00288026	0.00144013	+	0.999999i	$0.499542\pi$
$272$	14.4076	0.873588
$273$	9.97610	0.603781
$274$	20.7114	1.25122
$275$	−5.22728	−0.315217
$276$	−0.169600	−0.0102087
$277$	15.5455	0.934039	0.467020	−	0.884247i	$-0.345328\pi$
$277$	15.5455	0.934039	0.467020	+	0.884247i	$0.345328\pi$
$278$	−11.2321	−0.673655
$279$	10.3766	0.621231
$280$	−7.45698	−0.445640
$281$	−24.5204	−1.46277	−0.731383	−	0.681967i	$-0.761125\pi$
$281$	−24.5204	−1.46277	−0.731383	+	0.681967i	$0.761125\pi$
$282$	14.8899	0.886678
$283$	24.5260	1.45792	0.728961	−	0.684556i	$-0.240004\pi$
$283$	24.5260	1.45792	0.728961	+	0.684556i	$0.240004\pi$
$284$	1.42710	0.0846826
$285$	−2.23347	−0.132300
$286$	4.60153	0.272094
$287$	−26.2335	−1.54851
$288$	−0.956741	−0.0563765
$289$	−1.26444	−0.0743786
$290$	−0.998696	−0.0586455
$291$	12.9789	0.760834
$292$	−0.208966	−0.0122288
$293$	−28.1398	−1.64394	−0.821972	−	0.569528i	$-0.807126\pi$
$293$	−28.1398	−1.64394	−0.821972	+	0.569528i	$0.807126\pi$
$294$	6.55360	0.382214
$295$	−1.29697	−0.0755127
$296$	9.24258	0.537214
$297$	−1.17333	−0.0680833
$298$	−23.8885	−1.38383
$299$	2.89875	0.167639
$300$	−0.755586	−0.0436238
$301$	21.2344	1.22393
$302$	−11.1437	−0.641247
$303$	6.44364	0.370178
$304$	10.9893	0.630280
$305$	−2.14163	−0.122629
$306$	5.36678	0.306799
$307$	−20.2600	−1.15630	−0.578149	−	0.815931i	$-0.696225\pi$
$307$	−20.2600	−1.15630	−0.578149	+	0.815931i	$0.696225\pi$
$308$	−0.684850	−0.0390229
$309$	−4.18324	−0.237976
$310$	10.3631	0.588583
$311$	19.5818	1.11038	0.555191	−	0.831723i	$-0.312645\pi$
$311$	19.5818	1.11038	0.555191	+	0.831723i	$0.312645\pi$
$312$	8.50871	0.481711
$313$	−32.6842	−1.84742	−0.923710	−	0.383092i	$-0.874859\pi$
$313$	−32.6842	−1.84742	−0.923710	+	0.383092i	$0.874859\pi$
$314$	−23.3623	−1.31841
$315$	−2.54045	−0.143138
$316$	2.67169	0.150295
$317$	−13.2909	−0.746493	−0.373247	−	0.927732i	$-0.621755\pi$
$317$	−13.2909	−0.746493	−0.373247	+	0.927732i	$0.621755\pi$
$318$	−16.3578	−0.917301
$319$	−1.17333	−0.0656936
$320$	−6.31766	−0.353168
$321$	5.35867	0.299092
$322$	4.65611	0.259475
$323$	12.0022	0.667821
$324$	−0.169600	−0.00942224
$325$	12.9142	0.716352
$326$	28.9768	1.60488
$327$	−11.3099	−0.625440
$328$	−22.3748	−1.23544
$329$	37.8763	2.08819
$330$	−1.17180	−0.0645053
$331$	−24.6966	−1.35745	−0.678724	−	0.734394i	$-0.737467\pi$
$331$	−24.6966	−1.35745	−0.678724	+	0.734394i	$0.737467\pi$
$332$	1.61754	0.0887742
$333$	3.14877	0.172551
$334$	−2.52956	−0.138411
$335$	−6.38873	−0.349054
$336$	12.4997	0.681915
$337$	−28.3431	−1.54395	−0.771974	−	0.635654i	$-0.780731\pi$
$337$	−28.3431	−1.54395	−0.771974	+	0.635654i	$0.780731\pi$
$338$	6.21971	0.338308
$339$	5.42973	0.294902
$340$	−0.496625	−0.0269333
$341$	12.1751	0.659321
$342$	4.09349	0.221350
$343$	−7.41979	−0.400631
$344$	18.1110	0.976482
$345$	−0.738177	−0.0397421
$346$	12.0346	0.646982
$347$	−7.12832	−0.382668	−0.191334	−	0.981525i	$-0.561281\pi$
$347$	−7.12832	−0.382668	−0.191334	+	0.981525i	$0.561281\pi$
$348$	−0.169600	−0.00909153
$349$	−20.1149	−1.07673	−0.538364	−	0.842713i	$-0.680957\pi$
$349$	−20.1149	−1.07673	−0.538364	+	0.842713i	$0.680957\pi$
$350$	20.7434	1.10878
$351$	2.89875	0.154724
$352$	−1.12257	−0.0598331
$353$	−5.22872	−0.278297	−0.139148	−	0.990272i	$-0.544437\pi$
$353$	−5.22872	−0.278297	−0.139148	+	0.990272i	$0.544437\pi$
$354$	2.37708	0.126340
$355$	6.21136	0.329665
$356$	1.71191	0.0907312
$357$	13.6518	0.722532
$358$	−15.6054	−0.824772
$359$	−6.09563	−0.321715	−0.160857	−	0.986978i	$-0.551426\pi$
$359$	−6.09563	−0.321715	−0.160857	+	0.986978i	$0.551426\pi$
$360$	−2.16677	−0.114199
$361$	−9.84537	−0.518178
$362$	−5.73973	−0.301674
$363$	9.62331	0.505093
$364$	1.69195	0.0886823
$365$	−0.909514	−0.0476061
$366$	3.92516	0.205171
$367$	24.0718	1.25654	0.628268	−	0.777997i	$-0.283764\pi$
$367$	24.0718	1.25654	0.628268	+	0.777997i	$0.283764\pi$
$368$	3.63203	0.189333
$369$	−7.62266	−0.396820
$370$	3.14466	0.163483
$371$	−41.6104	−2.16031
$372$	1.75988	0.0912453
$373$	8.81626	0.456488	0.228244	−	0.973604i	$-0.426702\pi$
$373$	8.81626	0.456488	0.228244	+	0.973604i	$0.426702\pi$
$374$	6.29699	0.325609
$375$	−6.97953	−0.360422
$376$	32.3051	1.66601
$377$	2.89875	0.149293
$378$	4.65611	0.239484
$379$	16.9793	0.872169	0.436085	−	0.899906i	$-0.356365\pi$
$379$	16.9793	0.872169	0.436085	+	0.899906i	$0.356365\pi$
$380$	−0.378798	−0.0194319
$381$	9.48395	0.485877
$382$	29.7003	1.51960
$383$	20.0054	1.02223	0.511114	−	0.859513i	$-0.329233\pi$
$383$	20.0054	1.02223	0.511114	+	0.859513i	$0.329233\pi$
$384$	9.66546	0.493238
$385$	−2.98077	−0.151914
$386$	22.2271	1.13133
$387$	6.17008	0.313643
$388$	2.20122	0.111750
$389$	2.36742	0.120033	0.0600164	−	0.998197i	$-0.480885\pi$
$389$	2.36742	0.120033	0.0600164	+	0.998197i	$0.480885\pi$
$390$	2.89497	0.146593
$391$	3.96681	0.200610
$392$	14.2187	0.718153
$393$	0.643336	0.0324520
$394$	−30.0570	−1.51425
$395$	11.6284	0.585089
$396$	−0.198997	−0.00999995
$397$	−22.4601	−1.12724	−0.563619	−	0.826035i	$-0.690591\pi$
$397$	−22.4601	−1.12724	−0.563619	+	0.826035i	$0.690591\pi$
$398$	21.9112	1.09831
$399$	10.4129	0.521295
$400$	16.1811	0.809053
$401$	−38.1990	−1.90757	−0.953783	−	0.300498i	$-0.902847\pi$
$401$	−38.1990	−1.90757	−0.953783	+	0.300498i	$0.902847\pi$
$402$	11.7092	0.584002
$403$	−30.0792	−1.49835
$404$	1.09284	0.0543710
$405$	−0.738177	−0.0366803
$406$	4.65611	0.231079
$407$	3.69453	0.183131
$408$	11.6438	0.576453
$409$	−26.4483	−1.30778	−0.653892	−	0.756588i	$-0.726865\pi$
$409$	−26.4483	−1.30778	−0.653892	+	0.756588i	$0.726865\pi$
$410$	−7.61272	−0.375965
$411$	15.3086	0.755118
$412$	−0.709480	−0.0349536
$413$	6.04672	0.297540
$414$	1.35292	0.0664925
$415$	7.04027	0.345593
$416$	2.77335	0.135975
$417$	−8.30209	−0.406555
$418$	4.80299	0.234922
$419$	−18.1958	−0.888925	−0.444462	−	0.895798i	$-0.646605\pi$
$419$	−18.1958	−0.888925	−0.444462	+	0.895798i	$0.646605\pi$
$420$	−0.430861	−0.0210239
$421$	17.3568	0.845920	0.422960	−	0.906148i	$-0.360991\pi$
$421$	17.3568	0.845920	0.422960	+	0.906148i	$0.360991\pi$
$422$	−27.0458	−1.31657
$423$	11.0057	0.535116
$424$	−35.4899	−1.72354
$425$	17.6725	0.857242
$426$	−11.3841	−0.551562
$427$	9.98468	0.483192
$428$	0.908833	0.0439301
$429$	3.40118	0.164211
$430$	6.16204	0.297160
$431$	6.91304	0.332990	0.166495	−	0.986042i	$-0.446755\pi$
$431$	6.91304	0.332990	0.166495	+	0.986042i	$0.446755\pi$
$432$	3.63203	0.174746
$433$	14.4908	0.696383	0.348192	−	0.937423i	$-0.386796\pi$
$433$	14.4908	0.696383	0.348192	+	0.937423i	$0.386796\pi$
$434$	−48.3146	−2.31917
$435$	−0.738177	−0.0353929
$436$	−1.91817	−0.0918635
$437$	3.02566	0.144737
$438$	1.66695	0.0796498
$439$	−23.0948	−1.10225	−0.551127	−	0.834421i	$-0.685802\pi$
$439$	−23.0948	−1.10225	−0.551127	+	0.834421i	$0.685802\pi$
$440$	−2.54233	−0.121201
$441$	4.84403	0.230668
$442$	−15.5570	−0.739970
$443$	3.39253	0.161184	0.0805920	−	0.996747i	$-0.474319\pi$
$443$	3.39253	0.161184	0.0805920	+	0.996747i	$0.474319\pi$
$444$	0.534032	0.0253440
$445$	7.45102	0.353212
$446$	−11.2967	−0.534912
$447$	−17.6570	−0.835147
$448$	29.4541	1.39158
$449$	−8.19587	−0.386787	−0.193394	−	0.981121i	$-0.561949\pi$
$449$	−8.19587	−0.386787	−0.193394	+	0.981121i	$0.561949\pi$
$450$	6.02740	0.284134
$451$	−8.94386	−0.421150
$452$	0.920884	0.0433147
$453$	−8.23676	−0.386997
$454$	9.85367	0.462456
$455$	7.36413	0.345236
$456$	8.88123	0.415902
$457$	39.5184	1.84859	0.924297	−	0.381674i	$-0.124652\pi$
$457$	39.5184	1.84859	0.924297	+	0.381674i	$0.124652\pi$
$458$	22.1809	1.03645
$459$	3.96681	0.185155
$460$	−0.125195	−0.00583725
$461$	25.3442	1.18040	0.590200	−	0.807257i	$-0.299049\pi$
$461$	25.3442	1.18040	0.590200	+	0.807257i	$0.299049\pi$
$462$	5.46313	0.254168
$463$	18.3101	0.850943	0.425471	−	0.904972i	$-0.360108\pi$
$463$	18.3101	0.850943	0.425471	+	0.904972i	$0.360108\pi$
$464$	3.63203	0.168613
$465$	7.65977	0.355213
$466$	−23.8310	−1.10395
$467$	−4.56418	−0.211205	−0.105603	−	0.994408i	$-0.533677\pi$
$467$	−4.56418	−0.211205	−0.105603	+	0.994408i	$0.533677\pi$
$468$	0.491629	0.0227256
$469$	29.7854	1.37536
$470$	10.9914	0.506993
$471$	−17.2680	−0.795668
$472$	5.15731	0.237384
$473$	7.23952	0.332873
$474$	−21.3124	−0.978912
$475$	13.4796	0.618487
$476$	2.31536	0.106124
$477$	−12.0907	−0.553596
$478$	27.4907	1.25739
$479$	15.6660	0.715797	0.357898	−	0.933761i	$-0.383493\pi$
$479$	15.6660	0.715797	0.357898	+	0.933761i	$0.383493\pi$
$480$	−0.706244	−0.0322355
$481$	−9.12749	−0.416178
$482$	−3.40128	−0.154924
$483$	3.44152	0.156594
$484$	1.63212	0.0741871
$485$	9.58070	0.435037
$486$	1.35292	0.0613698
$487$	13.9794	0.633468	0.316734	−	0.948514i	$-0.397414\pi$
$487$	13.9794	0.633468	0.316734	+	0.948514i	$0.397414\pi$
$488$	8.51603	0.385502
$489$	21.4179	0.968552
$490$	4.83772	0.218546
$491$	−41.1904	−1.85890	−0.929449	−	0.368951i	$-0.879717\pi$
$491$	−41.1904	−1.85890	−0.929449	+	0.368951i	$0.879717\pi$
$492$	−1.29281	−0.0582842
$493$	3.96681	0.178656
$494$	−11.8660	−0.533876
$495$	−0.866122	−0.0389293
$496$	−37.6882	−1.69225
$497$	−28.9585	−1.29897
$498$	−12.9033	−0.578212
$499$	−41.4979	−1.85770	−0.928851	−	0.370454i	$-0.879202\pi$
$499$	−41.4979	−1.85770	−0.928851	+	0.370454i	$0.879202\pi$
$500$	−1.18373	−0.0529381
$501$	−1.86970	−0.0835320
$502$	6.73050	0.300397
$503$	16.9864	0.757384	0.378692	−	0.925523i	$-0.376374\pi$
$503$	16.9864	0.757384	0.378692	+	0.925523i	$0.376374\pi$
$504$	10.1019	0.449974
$505$	4.75655	0.211664
$506$	1.58742	0.0705694
$507$	4.59724	0.204171
$508$	1.60848	0.0713648
$509$	27.3370	1.21169	0.605846	−	0.795582i	$-0.292835\pi$
$509$	27.3370	1.21169	0.605846	+	0.795582i	$0.292835\pi$
$510$	3.96164	0.175424
$511$	4.24032	0.187581
$512$	24.7972	1.09589
$513$	3.02566	0.133586
$514$	19.1790	0.845951
$515$	−3.08797	−0.136072
$516$	1.04645	0.0460673
$517$	12.9133	0.567925
$518$	−14.6610	−0.644167
$519$	8.89523	0.390457
$520$	6.28093	0.275437
$521$	−11.3336	−0.496535	−0.248268	−	0.968691i	$-0.579861\pi$
$521$	−11.3336	−0.496535	−0.248268	+	0.968691i	$0.579861\pi$
$522$	1.35292	0.0592158
$523$	−3.81341	−0.166749	−0.0833743	−	0.996518i	$-0.526570\pi$
$523$	−3.81341	−0.166749	−0.0833743	+	0.996518i	$0.526570\pi$
$524$	0.109110	0.00476649
$525$	15.3323	0.669156
$526$	24.7787	1.08040
$527$	−41.1620	−1.79304
$528$	4.26156	0.185461
$529$	1.00000	0.0434783
$530$	−12.0750	−0.524503
$531$	1.75699	0.0762470
$532$	1.76603	0.0765669
$533$	22.0962	0.957092
$534$	−13.6561	−0.590959
$535$	3.95565	0.171018
$536$	25.4043	1.09730
$537$	−11.5346	−0.497755
$538$	16.7554	0.722377
$539$	5.68363	0.244811
$540$	−0.125195	−0.00538754
$541$	−12.8352	−0.551827	−0.275913	−	0.961183i	$-0.588980\pi$
$541$	−12.8352	−0.551827	−0.275913	+	0.961183i	$0.588980\pi$
$542$	−0.0641489	−0.00275543
$543$	−4.24247	−0.182062
$544$	3.79521	0.162718
$545$	−8.34872	−0.357620
$546$	−13.4969	−0.577614
$547$	25.7312	1.10019	0.550094	−	0.835103i	$-0.314592\pi$
$547$	25.7312	1.10019	0.550094	+	0.835103i	$0.314592\pi$
$548$	2.59635	0.110910
$549$	2.90124	0.123822
$550$	7.07210	0.301556
$551$	3.02566	0.128898
$552$	2.93530	0.124935
$553$	−54.2138	−2.30540
$554$	−21.0319	−0.893559
$555$	2.32435	0.0986631
$556$	−1.40804	−0.0597141
$557$	34.7825	1.47378	0.736890	−	0.676012i	$-0.236293\pi$
$557$	34.7825	1.47378	0.736890	+	0.676012i	$0.236293\pi$
$558$	−14.0387	−0.594307
$559$	−17.8855	−0.756477
$560$	9.22700	0.389912
$561$	4.65436	0.196507
$562$	33.1742	1.39937
$563$	16.3561	0.689326	0.344663	−	0.938727i	$-0.387993\pi$
$563$	16.3561	0.689326	0.344663	+	0.938727i	$0.387993\pi$
$564$	1.86657	0.0785968
$565$	4.00810	0.168622
$566$	−33.1818	−1.39474
$567$	3.44152	0.144530
$568$	−24.6990	−1.03635
$569$	10.5054	0.440407	0.220204	−	0.975454i	$-0.429328\pi$
$569$	10.5054	0.440407	0.220204	+	0.975454i	$0.429328\pi$
$570$	3.02172	0.126566
$571$	−21.7569	−0.910498	−0.455249	−	0.890364i	$-0.650450\pi$
$571$	−21.7569	−0.910498	−0.455249	+	0.890364i	$0.650450\pi$
$572$	0.576841	0.0241190
$573$	21.9527	0.917088
$574$	35.4919	1.48140
$575$	4.45509	0.185790
$576$	8.55847	0.356603
$577$	31.5980	1.31544	0.657721	−	0.753262i	$-0.271521\pi$
$577$	31.5980	1.31544	0.657721	+	0.753262i	$0.271521\pi$
$578$	1.71068	0.0711551
$579$	16.4290	0.682765
$580$	−0.125195	−0.00519844
$581$	−32.8230	−1.36173
$582$	−17.5594	−0.727860
$583$	−14.1864	−0.587539
$584$	3.61661	0.149656
$585$	2.13979	0.0884695
$586$	38.0710	1.57270
$587$	38.0454	1.57030	0.785151	−	0.619304i	$-0.212585\pi$
$587$	38.0454	1.57030	0.785151	+	0.619304i	$0.212585\pi$
$588$	0.821550	0.0338801
$589$	−31.3961	−1.29365
$590$	1.75470	0.0722400
$591$	−22.2164	−0.913860
$592$	−11.4364	−0.470034
$593$	18.4978	0.759612	0.379806	−	0.925066i	$-0.375991\pi$
$593$	18.4978	0.759612	0.379806	+	0.925066i	$0.375991\pi$
$594$	1.58742	0.0651326
$595$	10.0775	0.413136
$596$	−2.99463	−0.122665
$597$	16.1955	0.662836
$598$	−3.92179	−0.160374
$599$	−0.949485	−0.0387949	−0.0193975	−	0.999812i	$-0.506175\pi$
$599$	−0.949485	−0.0387949	−0.0193975	+	0.999812i	$0.506175\pi$
$600$	13.0770	0.533868
$601$	30.9918	1.26418	0.632091	−	0.774894i	$-0.282197\pi$
$601$	30.9918	1.26418	0.632091	+	0.774894i	$0.282197\pi$
$602$	−28.7285	−1.17089
$603$	8.65474	0.352448
$604$	−1.39696	−0.0568414
$605$	7.10370	0.288807
$606$	−8.71775	−0.354134
$607$	−23.3743	−0.948734	−0.474367	−	0.880327i	$-0.657323\pi$
$607$	−23.3743	−0.948734	−0.474367	+	0.880327i	$0.657323\pi$
$608$	2.89477	0.117399
$609$	3.44152	0.139457
$610$	2.89746	0.117315
$611$	−31.9028	−1.29065
$612$	0.672772	0.0271952
$613$	−7.83570	−0.316481	−0.158241	−	0.987401i	$-0.550582\pi$
$613$	−7.83570	−0.316481	−0.158241	+	0.987401i	$0.550582\pi$
$614$	27.4102	1.10618
$615$	−5.62687	−0.226897
$616$	11.8528	0.477563
$617$	1.46753	0.0590806	0.0295403	−	0.999564i	$-0.490596\pi$
$617$	1.46753	0.0590806	0.0295403	+	0.999564i	$0.490596\pi$
$618$	5.65960	0.227663
$619$	27.2490	1.09523	0.547614	−	0.836731i	$-0.315536\pi$
$619$	27.2490	1.09523	0.547614	+	0.836731i	$0.315536\pi$
$620$	1.29910	0.0521731
$621$	1.00000	0.0401286
$622$	−26.4927	−1.06226
$623$	−34.7380	−1.39175
$624$	−10.5284	−0.421472
$625$	17.1233	0.684934
$626$	44.2192	1.76735
$627$	3.55009	0.141777
$628$	−2.92866	−0.116866
$629$	−12.4906	−0.498031
$630$	3.43703	0.136935
$631$	−5.06096	−0.201474	−0.100737	−	0.994913i	$-0.532120\pi$
$631$	−5.06096	−0.201474	−0.100737	+	0.994913i	$0.532120\pi$
$632$	−46.2394	−1.83931
$633$	−19.9907	−0.794558
$634$	17.9816	0.714141
$635$	7.00083	0.277820
$636$	−2.05059	−0.0813113
$637$	−14.0416	−0.556350
$638$	1.58742	0.0628465
$639$	−8.41446	−0.332871
$640$	7.13482	0.282029
$641$	10.4401	0.412358	0.206179	−	0.978514i	$-0.433897\pi$
$641$	10.4401	0.412358	0.206179	+	0.978514i	$0.433897\pi$
$642$	−7.24987	−0.286129
$643$	12.1008	0.477209	0.238605	−	0.971117i	$-0.423310\pi$
$643$	12.1008	0.477209	0.238605	+	0.971117i	$0.423310\pi$
$644$	0.583682	0.0230003
$645$	4.55461	0.179338
$646$	−16.2381	−0.638878
$647$	34.6932	1.36393	0.681966	−	0.731384i	$-0.261125\pi$
$647$	34.6932	1.36393	0.681966	+	0.731384i	$0.261125\pi$
$648$	2.93530	0.115310
$649$	2.06153	0.0809220
$650$	−17.4719	−0.685305
$651$	−35.7113	−1.39963
$652$	3.63249	0.142259
$653$	10.2303	0.400342	0.200171	−	0.979761i	$-0.435850\pi$
$653$	10.2303	0.400342	0.200171	+	0.979761i	$0.435850\pi$
$654$	15.3014	0.598334
$655$	0.474896	0.0185557
$656$	27.6858	1.08095
$657$	1.23211	0.0480691
$658$	−51.2437	−1.99769
$659$	−13.9869	−0.544853	−0.272427	−	0.962177i	$-0.587826\pi$
$659$	−13.9869	−0.544853	−0.272427	+	0.962177i	$0.587826\pi$
$660$	−0.146895	−0.00571787
$661$	35.3316	1.37424	0.687120	−	0.726544i	$-0.258875\pi$
$661$	35.3316	1.37424	0.687120	+	0.726544i	$0.258875\pi$
$662$	33.4126	1.29862
$663$	−11.4988	−0.446576
$664$	−27.9951	−1.08642
$665$	7.68654	0.298071
$666$	−4.26004	−0.165073
$667$	1.00000	0.0387202
$668$	−0.317102	−0.0122690
$669$	−8.34982	−0.322823
$670$	8.64346	0.333926
$671$	3.40411	0.131414
$672$	3.29264	0.127016
$673$	35.8417	1.38160	0.690799	−	0.723047i	$-0.257259\pi$
$673$	35.8417	1.38160	0.690799	+	0.723047i	$0.257259\pi$
$674$	38.3461	1.47703
$675$	4.45509	0.171477
$676$	0.779694	0.0299882
$677$	18.3954	0.706992	0.353496	−	0.935436i	$-0.384993\pi$
$677$	18.3954	0.706992	0.353496	+	0.935436i	$0.384993\pi$
$678$	−7.34600	−0.282122
$679$	−44.6670	−1.71416
$680$	8.59517	0.329610
$681$	7.28325	0.279095
$682$	−16.4720	−0.630746
$683$	14.3777	0.550146	0.275073	−	0.961423i	$-0.411298\pi$
$683$	14.3777	0.550146	0.275073	+	0.961423i	$0.411298\pi$
$684$	0.513153	0.0196209
$685$	11.3005	0.431769
$686$	10.0384	0.383268
$687$	16.3948	0.625501
$688$	−22.4099	−0.854371
$689$	35.0480	1.33522
$690$	0.998696	0.0380197
$691$	−35.0831	−1.33462	−0.667311	−	0.744779i	$-0.732555\pi$
$691$	−35.0831	−1.33462	−0.667311	+	0.744779i	$0.732555\pi$
$692$	1.50864	0.0573497
$693$	4.03802	0.153392
$694$	9.64406	0.366084
$695$	−6.12841	−0.232464
$696$	2.93530	0.111262
$697$	30.2376	1.14533
$698$	27.2139	1.03006
$699$	−17.6144	−0.666239
$700$	2.60036	0.0982844
$701$	−30.9498	−1.16896	−0.584480	−	0.811408i	$-0.698701\pi$
$701$	−30.9498	−1.16896	−0.584480	+	0.811408i	$0.698701\pi$
$702$	−3.92179	−0.148018
$703$	−9.52710	−0.359322
$704$	10.0419	0.378467
$705$	8.12416	0.305973
$706$	7.07406	0.266236
$707$	−22.1759	−0.834010
$708$	0.297987	0.0111990
$709$	−11.5484	−0.433708	−0.216854	−	0.976204i	$-0.569580\pi$
$709$	−11.5484	−0.433708	−0.216854	+	0.976204i	$0.569580\pi$
$710$	−8.40349	−0.315377
$711$	−15.7529	−0.590779
$712$	−29.6284	−1.11037
$713$	−10.3766	−0.388607
$714$	−18.4699	−0.691218
$715$	2.51067	0.0938939
$716$	−1.95627	−0.0731093
$717$	20.3195	0.758844
$718$	8.24691	0.307772
$719$	21.9392	0.818192	0.409096	−	0.912491i	$-0.365844\pi$
$719$	21.9392	0.818192	0.409096	+	0.912491i	$0.365844\pi$
$720$	2.68108	0.0999181
$721$	14.3967	0.536161
$722$	13.3200	0.495720
$723$	−2.51402	−0.0934975
$724$	−0.719524	−0.0267409
$725$	4.45509	0.165458
$726$	−13.0196	−0.483202
$727$	−0.989895	−0.0367132	−0.0183566	−	0.999832i	$-0.505843\pi$
$727$	−0.989895	−0.0367132	−0.0183566	+	0.999832i	$0.505843\pi$
$728$	−29.2829	−1.08529
$729$	1.00000	0.0370370
$730$	1.23050	0.0455429
$731$	−24.4755	−0.905260
$732$	0.492052	0.0181868
$733$	−17.2010	−0.635334	−0.317667	−	0.948202i	$-0.602899\pi$
$733$	−17.2010	−0.635334	−0.317667	+	0.948202i	$0.602899\pi$
$734$	−32.5672	−1.20208
$735$	3.57575	0.131894
$736$	0.956741	0.0352659
$737$	10.1548	0.374058
$738$	10.3129	0.379622
$739$	−50.3396	−1.85177	−0.925885	−	0.377804i	$-0.876679\pi$
$739$	−50.3396	−1.85177	−0.925885	+	0.377804i	$0.876679\pi$
$740$	0.394210	0.0144915
$741$	−8.77064	−0.322198
$742$	56.2957	2.06668
$743$	19.7654	0.725123	0.362562	−	0.931960i	$-0.381902\pi$
$743$	19.7654	0.725123	0.362562	+	0.931960i	$0.381902\pi$
$744$	−30.4585	−1.11666
$745$	−13.0340	−0.477528
$746$	−11.9277	−0.436705
$747$	−9.53737	−0.348954
$748$	0.789381	0.0288626
$749$	−18.4420	−0.673854
$750$	9.44277	0.344801
$751$	5.73724	0.209355	0.104677	−	0.994506i	$-0.466619\pi$
$751$	5.73724	0.209355	0.104677	+	0.994506i	$0.466619\pi$
$752$	−39.9731	−1.45767
$753$	4.97478	0.181291
$754$	−3.92179	−0.142823
$755$	−6.08018	−0.221281
$756$	0.583682	0.0212283
$757$	−16.1728	−0.587811	−0.293905	−	0.955834i	$-0.594955\pi$
$757$	−16.1728	−0.587811	−0.293905	+	0.955834i	$0.594955\pi$
$758$	−22.9717	−0.834370
$759$	1.17333	0.0425890
$760$	6.55592	0.237808
$761$	47.5884	1.72508	0.862538	−	0.505992i	$-0.168873\pi$
$761$	47.5884	1.72508	0.862538	+	0.505992i	$0.168873\pi$
$762$	−12.8310	−0.464820
$763$	38.9233	1.40912
$764$	3.72319	0.134700
$765$	2.92821	0.105870
$766$	−27.0657	−0.977925
$767$	−5.09309	−0.183901
$768$	4.04031	0.145792
$769$	−26.6504	−0.961038	−0.480519	−	0.876984i	$-0.659552\pi$
$769$	−26.6504	−0.961038	−0.480519	+	0.876984i	$0.659552\pi$
$770$	4.03276	0.145330
$771$	14.1760	0.510536
$772$	2.78636	0.100283
$773$	−12.8708	−0.462932	−0.231466	−	0.972843i	$-0.574352\pi$
$773$	−12.8708	−0.462932	−0.231466	+	0.972843i	$0.574352\pi$
$774$	−8.34764	−0.300050
$775$	−46.2288	−1.66059
$776$	−38.0969	−1.36760
$777$	−10.8365	−0.388758
$778$	−3.20293	−0.114831
$779$	23.0636	0.826338
$780$	0.362909	0.0129942
$781$	−9.87291	−0.353280
$782$	−5.36678	−0.191916
$783$	1.00000	0.0357371
$784$	−17.5937	−0.628346
$785$	−12.7468	−0.454954
$786$	−0.870383	−0.0310455
$787$	45.1481	1.60936	0.804678	−	0.593712i	$-0.202338\pi$
$787$	45.1481	1.60936	0.804678	+	0.593712i	$0.202338\pi$
$788$	−3.76791	−0.134226
$789$	18.3150	0.652031
$790$	−15.7323	−0.559732
$791$	−18.6865	−0.664415
$792$	3.44407	0.122380
$793$	−8.40999	−0.298647
$794$	30.3867	1.07838
$795$	−8.92510	−0.316541
$796$	2.74676	0.0973562
$797$	53.6633	1.90085	0.950427	−	0.310949i	$-0.100647\pi$
$797$	53.6633	1.90085	0.950427	+	0.310949i	$0.100647\pi$
$798$	−14.0878	−0.498703
$799$	−43.6575	−1.54449
$800$	4.26237	0.150698
$801$	−10.0938	−0.356647
$802$	51.6802	1.82489
$803$	1.44566	0.0510164
$804$	1.46785	0.0517670
$805$	2.54045	0.0895390
$806$	40.6948	1.43341
$807$	12.3846	0.435959
$808$	−18.9140	−0.665393
$809$	−1.77290	−0.0623319	−0.0311660	−	0.999514i	$-0.509922\pi$
$809$	−1.77290	−0.0623319	−0.0311660	+	0.999514i	$0.509922\pi$
$810$	0.998696	0.0350906
$811$	−1.70116	−0.0597359	−0.0298680	−	0.999554i	$-0.509509\pi$
$811$	−1.70116	−0.0597359	−0.0298680	+	0.999554i	$0.509509\pi$
$812$	0.583682	0.0204832
$813$	−0.0474151	−0.00166292
$814$	−4.99841	−0.175194
$815$	15.8102	0.553808
$816$	−14.4076	−0.504366
$817$	−18.6686	−0.653131
$818$	35.7825	1.25111
$819$	−9.97610	−0.348593
$820$	−0.954319	−0.0333263
$821$	−43.2876	−1.51075	−0.755374	−	0.655294i	$-0.772545\pi$
$821$	−43.2876	−1.51075	−0.755374	+	0.655294i	$0.772545\pi$
$822$	−20.7114	−0.722392
$823$	−40.8222	−1.42297	−0.711485	−	0.702701i	$-0.751977\pi$
$823$	−40.8222	−1.42297	−0.711485	+	0.702701i	$0.751977\pi$
$824$	12.2791	0.427762
$825$	5.22728	0.181990
$826$	−8.18075	−0.284645
$827$	40.1223	1.39519	0.697595	−	0.716493i	$-0.254254\pi$
$827$	40.1223	1.39519	0.697595	+	0.716493i	$0.254254\pi$
$828$	0.169600	0.00589402
$829$	−14.4375	−0.501437	−0.250718	−	0.968060i	$-0.580667\pi$
$829$	−14.4375	−0.501437	−0.250718	+	0.968060i	$0.580667\pi$
$830$	−9.52494	−0.330616
$831$	−15.5455	−0.539268
$832$	−24.8089	−0.860093
$833$	−19.2153	−0.665772
$834$	11.2321	0.388935
$835$	−1.38017	−0.0477627
$836$	0.602096	0.0208239
$837$	−10.3766	−0.358668
$838$	24.6176	0.850399
$839$	−50.2263	−1.73401	−0.867003	−	0.498303i	$-0.833957\pi$
$839$	−50.2263	−1.73401	−0.867003	+	0.498303i	$0.833957\pi$
$840$	7.45698	0.257290
$841$	1.00000	0.0344828
$842$	−23.4824	−0.809258
$843$	24.5204	0.844528
$844$	−3.39042	−0.116703
$845$	3.39358	0.116743
$846$	−14.8899	−0.511924
$847$	−33.1188	−1.13797
$848$	43.9139	1.50801
$849$	−24.5260	−0.841731
$850$	−23.9095	−0.820090
$851$	−3.14877	−0.107938
$852$	−1.42710	−0.0488915
$853$	−29.4488	−1.00831	−0.504154	−	0.863614i	$-0.668196\pi$
$853$	−29.4488	−1.00831	−0.504154	+	0.863614i	$0.668196\pi$
$854$	−13.5085	−0.462251
$855$	2.23347	0.0763832
$856$	−15.7293	−0.537617
$857$	3.87360	0.132320	0.0661598	−	0.997809i	$-0.478925\pi$
$857$	3.87360	0.132320	0.0661598	+	0.997809i	$0.478925\pi$
$858$	−4.60153	−0.157094
$859$	24.7385	0.844068	0.422034	−	0.906580i	$-0.361316\pi$
$859$	24.7385	0.844068	0.422034	+	0.906580i	$0.361316\pi$
$860$	0.772464	0.0263408
$861$	26.2335	0.894035
$862$	−9.35281	−0.318558
$863$	−14.4203	−0.490873	−0.245437	−	0.969413i	$-0.578931\pi$
$863$	−14.4203	−0.490873	−0.245437	+	0.969413i	$0.578931\pi$
$864$	0.956741	0.0325490
$865$	6.56626	0.223259
$866$	−19.6049	−0.666202
$867$	1.26444	0.0429425
$868$	−6.05664	−0.205576
$869$	−18.4833	−0.627002
$870$	0.998696	0.0338590
$871$	−25.0879	−0.850073
$872$	33.1980	1.12423
$873$	−12.9789	−0.439268
$874$	−4.09349	−0.138464
$875$	24.0202	0.812030
$876$	0.208966	0.00706031
$877$	24.0202	0.811103	0.405552	−	0.914072i	$-0.367079\pi$
$877$	24.0202	0.811103	0.405552	+	0.914072i	$0.367079\pi$
$878$	31.2455	1.05448
$879$	28.1398	0.949132
$880$	3.14579	0.106044
$881$	37.0159	1.24710	0.623549	−	0.781785i	$-0.285690\pi$
$881$	37.0159	1.24710	0.623549	+	0.781785i	$0.285690\pi$
$882$	−6.55360	−0.220671
$883$	−23.0023	−0.774089	−0.387045	−	0.922061i	$-0.626504\pi$
$883$	−23.0023	−0.774089	−0.387045	+	0.922061i	$0.626504\pi$
$884$	−1.95020	−0.0655923
$885$	1.29697	0.0435973
$886$	−4.58983	−0.154198
$887$	41.1958	1.38322	0.691610	−	0.722271i	$-0.256902\pi$
$887$	41.1958	1.38322	0.691610	+	0.722271i	$0.256902\pi$
$888$	−9.24258	−0.310161
$889$	−32.6392	−1.09468
$890$	−10.0806	−0.337904
$891$	1.17333	0.0393079
$892$	−1.41613	−0.0474156
$893$	−33.2995	−1.11433
$894$	23.8885	0.798952
$895$	−8.51457	−0.284611
$896$	−33.2638	−1.11127
$897$	−2.89875	−0.0967865
$898$	11.0884	0.370024
$899$	−10.3766	−0.346079
$900$	0.755586	0.0251862
$901$	47.9616	1.59783
$902$	12.1004	0.402898
$903$	−21.2344	−0.706638
$904$	−15.9379	−0.530086
$905$	−3.13169	−0.104101
$906$	11.1437	0.370224
$907$	−19.8581	−0.659379	−0.329689	−	0.944089i	$-0.606944\pi$
$907$	−19.8581	−0.659379	−0.329689	+	0.944089i	$0.606944\pi$
$908$	1.23524	0.0409929
$909$	−6.44364	−0.213722
$910$	−9.96309	−0.330273
$911$	0.186985	0.00619509	0.00309755	−	0.999995i	$-0.499014\pi$
$911$	0.186985	0.00619509	0.00309755	+	0.999995i	$0.499014\pi$
$912$	−10.9893	−0.363892
$913$	−11.1904	−0.370350
$914$	−53.4654	−1.76848
$915$	2.14163	0.0708002
$916$	2.78057	0.0918725
$917$	−2.21405	−0.0731144
$918$	−5.36678	−0.177130
$919$	10.2250	0.337293	0.168646	−	0.985677i	$-0.446060\pi$
$919$	10.2250	0.337293	0.168646	+	0.985677i	$0.446060\pi$
$920$	2.16677	0.0714364
$921$	20.2600	0.667589
$922$	−34.2888	−1.12924
$923$	24.3914	0.802854
$924$	0.684850	0.0225299
$925$	−14.0281	−0.461240
$926$	−24.7722	−0.814064
$927$	4.18324	0.137396
$928$	0.956741	0.0314065
$929$	−5.47909	−0.179763	−0.0898815	−	0.995952i	$-0.528649\pi$
$929$	−5.47909	−0.179763	−0.0898815	+	0.995952i	$0.528649\pi$
$930$	−10.3631	−0.339819
$931$	−14.6564	−0.480344
$932$	−2.98741	−0.0978560
$933$	−19.5818	−0.641080
$934$	6.17498	0.202052
$935$	3.43574	0.112361
$936$	−8.50871	−0.278116
$937$	−12.6673	−0.413822	−0.206911	−	0.978360i	$-0.566341\pi$
$937$	−12.6673	−0.413822	−0.206911	+	0.978360i	$0.566341\pi$
$938$	−40.2974	−1.31576
$939$	32.6842	1.06661
$940$	1.37786	0.0449408
$941$	−29.4280	−0.959325	−0.479663	−	0.877453i	$-0.659241\pi$
$941$	−29.4280	−0.959325	−0.479663	+	0.877453i	$0.659241\pi$
$942$	23.3623	0.761184
$943$	7.62266	0.248228
$944$	−6.38146	−0.207699
$945$	2.54045	0.0826408
$946$	−9.79451	−0.318447
$947$	−26.1468	−0.849656	−0.424828	−	0.905274i	$-0.639665\pi$
$947$	−26.1468	−0.849656	−0.424828	+	0.905274i	$0.639665\pi$
$948$	−2.67169	−0.0867726
$949$	−3.57158	−0.115938
$950$	−18.2369	−0.591682
$951$	13.2909	0.430988
$952$	−40.0722	−1.29875
$953$	8.31667	0.269403	0.134702	−	0.990886i	$-0.456992\pi$
$953$	8.31667	0.269403	0.134702	+	0.990886i	$0.456992\pi$
$954$	16.3578	0.529604
$955$	16.2050	0.524381
$956$	3.44619	0.111458
$957$	1.17333	0.0379282
$958$	−21.1949	−0.684775
$959$	−52.6848	−1.70128
$960$	6.31766	0.203902
$961$	76.6739	2.47335
$962$	12.3488	0.398141
$963$	−5.35867	−0.172681
$964$	−0.426379	−0.0137327
$965$	12.1275	0.390398
$966$	−4.65611	−0.149808
$967$	−53.2301	−1.71176	−0.855882	−	0.517171i	$-0.826985\pi$
$967$	−53.2301	−1.71176	−0.855882	+	0.517171i	$0.826985\pi$
$968$	−28.2473	−0.907903
$969$	−12.0022	−0.385567
$970$	−12.9619	−0.416183
$971$	−59.8856	−1.92182	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−59.8856	−1.92182	−0.960910	+	0.276861i	$0.910706\pi$
$972$	0.169600	0.00543993
$973$	28.5718	0.915969
$974$	−18.9131	−0.606014
$975$	−12.9142	−0.413586
$976$	−10.5374	−0.337295
$977$	−22.6380	−0.724253	−0.362126	−	0.932129i	$-0.617949\pi$
$977$	−22.6380	−0.724253	−0.362126	+	0.932129i	$0.617949\pi$
$978$	−28.9768	−0.926576
$979$	−11.8433	−0.378514
$980$	0.606449	0.0193723
$981$	11.3099	0.361098
$982$	55.7275	1.77833
$983$	−6.36352	−0.202965	−0.101482	−	0.994837i	$-0.532359\pi$
$983$	−6.36352	−0.202965	−0.101482	+	0.994837i	$0.532359\pi$
$984$	22.3748	0.713282
$985$	−16.3996	−0.522535
$986$	−5.36678	−0.170913
$987$	−37.8763	−1.20562
$988$	−1.48750	−0.0473238
$989$	−6.17008	−0.196197
$990$	1.17180	0.0372421
$991$	−7.24797	−0.230239	−0.115120	−	0.993352i	$-0.536725\pi$
$991$	−7.24797	−0.230239	−0.115120	+	0.993352i	$0.536725\pi$
$992$	−9.92772	−0.315205
$993$	24.6966	0.783722
$994$	39.1786	1.24267
$995$	11.9551	0.379003
$996$	−1.61754	−0.0512538
$997$	32.7559	1.03739	0.518694	−	0.854960i	$-0.326418\pi$
$997$	32.7559	1.03739	0.518694	+	0.854960i	$0.326418\pi$
$998$	56.1435	1.77719
$999$	−3.14877	−0.0996226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.5	✓	14
3.2	odd	2		6003.2.a.p.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.5	✓	14	1.1	even	1	trivial
6003.2.a.p.1.10		14	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)

\(f(q)\)	\(=\)	\(q-1.35292 q^{2} -1.00000 q^{3} -0.169600 q^{4} -0.738177 q^{5} +1.35292 q^{6} +3.44152 q^{7} +2.93530 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.35292 q^{2} -1.00000 q^{3} -0.169600 q^{4} -0.738177 q^{5} +1.35292 q^{6} +3.44152 q^{7} +2.93530 q^{8} +1.00000 q^{9} +0.998696 q^{10} +1.17333 q^{11} +0.169600 q^{12} -2.89875 q^{13} -4.65611 q^{14} +0.738177 q^{15} -3.63203 q^{16} -3.96681 q^{17} -1.35292 q^{18} -3.02566 q^{19} +0.125195 q^{20} -3.44152 q^{21} -1.58742 q^{22} -1.00000 q^{23} -2.93530 q^{24} -4.45509 q^{25} +3.92179 q^{26} -1.00000 q^{27} -0.583682 q^{28} -1.00000 q^{29} -0.998696 q^{30} +10.3766 q^{31} -0.956741 q^{32} -1.17333 q^{33} +5.36678 q^{34} -2.54045 q^{35} -0.169600 q^{36} +3.14877 q^{37} +4.09349 q^{38} +2.89875 q^{39} -2.16677 q^{40} -7.62266 q^{41} +4.65611 q^{42} +6.17008 q^{43} -0.198997 q^{44} -0.738177 q^{45} +1.35292 q^{46} +11.0057 q^{47} +3.63203 q^{48} +4.84403 q^{49} +6.02740 q^{50} +3.96681 q^{51} +0.491629 q^{52} -12.0907 q^{53} +1.35292 q^{54} -0.866122 q^{55} +10.1019 q^{56} +3.02566 q^{57} +1.35292 q^{58} +1.75699 q^{59} -0.125195 q^{60} +2.90124 q^{61} -14.0387 q^{62} +3.44152 q^{63} +8.55847 q^{64} +2.13979 q^{65} +1.58742 q^{66} +8.65474 q^{67} +0.672772 q^{68} +1.00000 q^{69} +3.43703 q^{70} -8.41446 q^{71} +2.93530 q^{72} +1.23211 q^{73} -4.26004 q^{74} +4.45509 q^{75} +0.513153 q^{76} +4.03802 q^{77} -3.92179 q^{78} -15.7529 q^{79} +2.68108 q^{80} +1.00000 q^{81} +10.3129 q^{82} -9.53737 q^{83} +0.583682 q^{84} +2.92821 q^{85} -8.34764 q^{86} +1.00000 q^{87} +3.44407 q^{88} -10.0938 q^{89} +0.998696 q^{90} -9.97610 q^{91} +0.169600 q^{92} -10.3766 q^{93} -14.8899 q^{94} +2.23347 q^{95} +0.956741 q^{96} -12.9789 q^{97} -6.55360 q^{98} +1.17333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

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