LMFDB - Embedded newform 2001.2.a.m.1.11

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			1.11
Root			$-1.37642$ 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)

$f(q)$	$=$	$q+1.37642 q^{2} -1.00000 q^{3} -0.105481 q^{4} -1.48313 q^{5} -1.37642 q^{6} +4.92788 q^{7} -2.89802 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.37642 q^{2} -1.00000 q^{3} -0.105481 q^{4} -1.48313 q^{5} -1.37642 q^{6} +4.92788 q^{7} -2.89802 q^{8} +1.00000 q^{9} -2.04140 q^{10} -4.78117 q^{11} +0.105481 q^{12} +0.524666 q^{13} +6.78281 q^{14} +1.48313 q^{15} -3.77791 q^{16} -2.51811 q^{17} +1.37642 q^{18} +6.02409 q^{19} +0.156442 q^{20} -4.92788 q^{21} -6.58088 q^{22} -1.00000 q^{23} +2.89802 q^{24} -2.80033 q^{25} +0.722159 q^{26} -1.00000 q^{27} -0.519799 q^{28} -1.00000 q^{29} +2.04140 q^{30} -4.86009 q^{31} +0.596058 q^{32} +4.78117 q^{33} -3.46596 q^{34} -7.30868 q^{35} -0.105481 q^{36} -1.81490 q^{37} +8.29165 q^{38} -0.524666 q^{39} +4.29813 q^{40} -6.88501 q^{41} -6.78281 q^{42} +5.44082 q^{43} +0.504324 q^{44} -1.48313 q^{45} -1.37642 q^{46} -8.73911 q^{47} +3.77791 q^{48} +17.2840 q^{49} -3.85442 q^{50} +2.51811 q^{51} -0.0553424 q^{52} -7.14027 q^{53} -1.37642 q^{54} +7.09109 q^{55} -14.2811 q^{56} -6.02409 q^{57} -1.37642 q^{58} -8.40962 q^{59} -0.156442 q^{60} -11.8204 q^{61} -6.68951 q^{62} +4.92788 q^{63} +8.37625 q^{64} -0.778147 q^{65} +6.58088 q^{66} +8.80386 q^{67} +0.265613 q^{68} +1.00000 q^{69} -10.0598 q^{70} -11.6325 q^{71} -2.89802 q^{72} -13.0454 q^{73} -2.49805 q^{74} +2.80033 q^{75} -0.635428 q^{76} -23.5611 q^{77} -0.722159 q^{78} -5.81717 q^{79} +5.60313 q^{80} +1.00000 q^{81} -9.47663 q^{82} +7.77527 q^{83} +0.519799 q^{84} +3.73467 q^{85} +7.48882 q^{86} +1.00000 q^{87} +13.8559 q^{88} +14.1010 q^{89} -2.04140 q^{90} +2.58549 q^{91} +0.105481 q^{92} +4.86009 q^{93} -12.0286 q^{94} -8.93450 q^{95} -0.596058 q^{96} -8.12641 q^{97} +23.7900 q^{98} -4.78117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.37642	0.973273	0.486636	−	0.873605i	$-0.338224\pi$
$2$	1.37642	0.973273	0.486636	+	0.873605i	$0.338224\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.105481	−0.0527406
$5$	−1.48313	−0.663275	−0.331638	−	0.943407i	$-0.607601\pi$
$5$	−1.48313	−0.663275	−0.331638	+	0.943407i	$0.607601\pi$
$6$	−1.37642	−0.561919
$7$	4.92788	1.86256	0.931282	−	0.364298i	$-0.118691\pi$
$7$	4.92788	1.86256	0.931282	+	0.364298i	$0.118691\pi$
$8$	−2.89802	−1.02460
$9$	1.00000	0.333333
$10$	−2.04140	−0.645547
$11$	−4.78117	−1.44158	−0.720789	−	0.693154i	$-0.756220\pi$
$11$	−4.78117	−1.44158	−0.720789	+	0.693154i	$0.756220\pi$
$12$	0.105481	0.0304498
$13$	0.524666	0.145516	0.0727581	−	0.997350i	$-0.476820\pi$
$13$	0.524666	0.145516	0.0727581	+	0.997350i	$0.476820\pi$
$14$	6.78281	1.81278
$15$	1.48313	0.382942
$16$	−3.77791	−0.944478
$17$	−2.51811	−0.610730	−0.305365	−	0.952235i	$-0.598779\pi$
$17$	−2.51811	−0.610730	−0.305365	+	0.952235i	$0.598779\pi$
$18$	1.37642	0.324424
$19$	6.02409	1.38202	0.691010	−	0.722845i	$-0.257166\pi$
$19$	6.02409	1.38202	0.691010	+	0.722845i	$0.257166\pi$
$20$	0.156442	0.0349815
$21$	−4.92788	−1.07535
$22$	−6.58088	−1.40305
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.89802	0.591555
$25$	−2.80033	−0.560066
$26$	0.722159	0.141627
$27$	−1.00000	−0.192450
$28$	−0.519799	−0.0982328
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	2.04140	0.372707
$31$	−4.86009	−0.872899	−0.436449	−	0.899729i	$-0.643764\pi$
$31$	−4.86009	−0.872899	−0.436449	+	0.899729i	$0.643764\pi$
$32$	0.596058	0.105369
$33$	4.78117	0.832296
$34$	−3.46596	−0.594407
$35$	−7.30868	−1.23539
$36$	−0.105481	−0.0175802
$37$	−1.81490	−0.298367	−0.149183	−	0.988810i	$-0.547664\pi$
$37$	−1.81490	−0.298367	−0.149183	+	0.988810i	$0.547664\pi$
$38$	8.29165	1.34508
$39$	−0.524666	−0.0840138
$40$	4.29813	0.679594
$41$	−6.88501	−1.07526	−0.537629	−	0.843182i	$-0.680680\pi$
$41$	−6.88501	−1.07526	−0.537629	+	0.843182i	$0.680680\pi$
$42$	−6.78281	−1.04661
$43$	5.44082	0.829717	0.414858	−	0.909886i	$-0.363831\pi$
$43$	5.44082	0.829717	0.414858	+	0.909886i	$0.363831\pi$
$44$	0.504324	0.0760297
$45$	−1.48313	−0.221092
$46$	−1.37642	−0.202941
$47$	−8.73911	−1.27473	−0.637365	−	0.770562i	$-0.719976\pi$
$47$	−8.73911	−1.27473	−0.637365	+	0.770562i	$0.719976\pi$
$48$	3.77791	0.545295
$49$	17.2840	2.46915
$50$	−3.85442	−0.545097
$51$	2.51811	0.352605
$52$	−0.0553424	−0.00767461
$53$	−7.14027	−0.980791	−0.490395	−	0.871500i	$-0.663148\pi$
$53$	−7.14027	−0.980791	−0.490395	+	0.871500i	$0.663148\pi$
$54$	−1.37642	−0.187306
$55$	7.09109	0.956163
$56$	−14.2811	−1.90839
$57$	−6.02409	−0.797910
$58$	−1.37642	−0.180732
$59$	−8.40962	−1.09484	−0.547420	−	0.836858i	$-0.684390\pi$
$59$	−8.40962	−1.09484	−0.547420	+	0.836858i	$0.684390\pi$
$60$	−0.156442	−0.0201966
$61$	−11.8204	−1.51345	−0.756724	−	0.653735i	$-0.773201\pi$
$61$	−11.8204	−1.51345	−0.756724	+	0.653735i	$0.773201\pi$
$62$	−6.68951	−0.849568
$63$	4.92788	0.620855
$64$	8.37625	1.04703
$65$	−0.778147	−0.0965173
$66$	6.58088	0.810050
$67$	8.80386	1.07556	0.537781	−	0.843084i	$-0.319263\pi$
$67$	8.80386	1.07556	0.537781	+	0.843084i	$0.319263\pi$
$68$	0.265613	0.0322103
$69$	1.00000	0.120386
$70$	−10.0598	−1.20237
$71$	−11.6325	−1.38053	−0.690264	−	0.723557i	$-0.742506\pi$
$71$	−11.6325	−1.38053	−0.690264	+	0.723557i	$0.742506\pi$
$72$	−2.89802	−0.341534
$73$	−13.0454	−1.52684	−0.763421	−	0.645901i	$-0.776482\pi$
$73$	−13.0454	−1.52684	−0.763421	+	0.645901i	$0.776482\pi$
$74$	−2.49805	−0.290392
$75$	2.80033	0.323354
$76$	−0.635428	−0.0728886
$77$	−23.5611	−2.68503
$78$	−0.722159	−0.0817684
$79$	−5.81717	−0.654483	−0.327241	−	0.944941i	$-0.606119\pi$
$79$	−5.81717	−0.654483	−0.327241	+	0.944941i	$0.606119\pi$
$80$	5.60313	0.626449
$81$	1.00000	0.111111
$82$	−9.47663	−1.04652
$83$	7.77527	0.853447	0.426723	−	0.904382i	$-0.359668\pi$
$83$	7.77527	0.853447	0.426723	+	0.904382i	$0.359668\pi$
$84$	0.519799	0.0567147
$85$	3.73467	0.405082
$86$	7.48882	0.807541
$87$	1.00000	0.107211
$88$	13.8559	1.47705
$89$	14.1010	1.49471	0.747353	−	0.664427i	$-0.231324\pi$
$89$	14.1010	1.49471	0.747353	+	0.664427i	$0.231324\pi$
$90$	−2.04140	−0.215182
$91$	2.58549	0.271033
$92$	0.105481	0.0109972
$93$	4.86009	0.503968
$94$	−12.0286	−1.24066
$95$	−8.93450	−0.916660
$96$	−0.596058	−0.0608349
$97$	−8.12641	−0.825112	−0.412556	−	0.910932i	$-0.635364\pi$
$97$	−8.12641	−0.825112	−0.412556	+	0.910932i	$0.635364\pi$
$98$	23.7900	2.40315
$99$	−4.78117	−0.480526
$100$	0.295382	0.0295382
$101$	6.34705	0.631555	0.315778	−	0.948833i	$-0.397735\pi$
$101$	6.34705	0.631555	0.315778	+	0.948833i	$0.397735\pi$
$102$	3.46596	0.343181
$103$	−16.8362	−1.65892	−0.829459	−	0.558568i	$-0.811351\pi$
$103$	−16.8362	−1.65892	−0.829459	+	0.558568i	$0.811351\pi$
$104$	−1.52049	−0.149096
$105$	7.30868	0.713254
$106$	−9.82797	−0.954577
$107$	6.76344	0.653846	0.326923	−	0.945051i	$-0.393988\pi$
$107$	6.76344	0.653846	0.326923	+	0.945051i	$0.393988\pi$
$108$	0.105481	0.0101499
$109$	−15.8184	−1.51512	−0.757562	−	0.652763i	$-0.773610\pi$
$109$	−15.8184	−1.51512	−0.757562	+	0.652763i	$0.773610\pi$
$110$	9.76029	0.930607
$111$	1.81490	0.172262
$112$	−18.6171	−1.75915
$113$	−11.6740	−1.09820	−0.549098	−	0.835758i	$-0.685029\pi$
$113$	−11.6740	−1.09820	−0.549098	+	0.835758i	$0.685029\pi$
$114$	−8.29165	−0.776584
$115$	1.48313	0.138302
$116$	0.105481	0.00979368
$117$	0.524666	0.0485054
$118$	−11.5751	−1.06558
$119$	−12.4089	−1.13752
$120$	−4.29813	−0.392364
$121$	11.8596	1.07815
$122$	−16.2698	−1.47300
$123$	6.88501	0.620800
$124$	0.512649	0.0460372
$125$	11.5689	1.03475
$126$	6.78281	0.604261
$127$	16.1525	1.43330	0.716652	−	0.697431i	$-0.245673\pi$
$127$	16.1525	1.43330	0.716652	+	0.697431i	$0.245673\pi$
$128$	10.3371	0.913677
$129$	−5.44082	−0.479037
$130$	−1.07105	−0.0939376
$131$	−5.52338	−0.482580	−0.241290	−	0.970453i	$-0.577570\pi$
$131$	−5.52338	−0.482580	−0.241290	+	0.970453i	$0.577570\pi$
$132$	−0.504324	−0.0438958
$133$	29.6860	2.57410
$134$	12.1178	1.04682
$135$	1.48313	0.127647
$136$	7.29751	0.625756
$137$	2.67599	0.228625	0.114312	−	0.993445i	$-0.463533\pi$
$137$	2.67599	0.228625	0.114312	+	0.993445i	$0.463533\pi$
$138$	1.37642	0.117168
$139$	20.2927	1.72121	0.860604	−	0.509275i	$-0.170086\pi$
$139$	20.2927	1.72121	0.860604	+	0.509275i	$0.170086\pi$
$140$	0.770928	0.0651553
$141$	8.73911	0.735966
$142$	−16.0112	−1.34363
$143$	−2.50852	−0.209773
$144$	−3.77791	−0.314826
$145$	1.48313	0.123167
$146$	−17.9558	−1.48603
$147$	−17.2840	−1.42556
$148$	0.191437	0.0157360
$149$	10.7950	0.884360	0.442180	−	0.896926i	$-0.354205\pi$
$149$	10.7950	0.884360	0.442180	+	0.896926i	$0.354205\pi$
$150$	3.85442	0.314712
$151$	−13.5193	−1.10019	−0.550094	−	0.835103i	$-0.685408\pi$
$151$	−13.5193	−1.10019	−0.550094	+	0.835103i	$0.685408\pi$
$152$	−17.4579	−1.41602
$153$	−2.51811	−0.203577
$154$	−32.4298	−2.61327
$155$	7.20814	0.578972
$156$	0.0553424	0.00443094
$157$	−6.39919	−0.510711	−0.255355	−	0.966847i	$-0.582192\pi$
$157$	−6.39919	−0.510711	−0.255355	+	0.966847i	$0.582192\pi$
$158$	−8.00684	−0.636990
$159$	7.14027	0.566260
$160$	−0.884030	−0.0698887
$161$	−4.92788	−0.388372
$162$	1.37642	0.108141
$163$	−8.82550	−0.691267	−0.345633	−	0.938370i	$-0.612336\pi$
$163$	−8.82550	−0.691267	−0.345633	+	0.938370i	$0.612336\pi$
$164$	0.726239	0.0567097
$165$	−7.09109	−0.552041
$166$	10.7020	0.830636
$167$	−19.1613	−1.48275	−0.741373	−	0.671093i	$-0.765825\pi$
$167$	−19.1613	−1.48275	−0.741373	+	0.671093i	$0.765825\pi$
$168$	14.2811	1.10181
$169$	−12.7247	−0.978825
$170$	5.14046	0.394255
$171$	6.02409	0.460674
$172$	−0.573904	−0.0437598
$173$	10.0566	0.764587	0.382294	−	0.924041i	$-0.375134\pi$
$173$	10.0566	0.764587	0.382294	+	0.924041i	$0.375134\pi$
$174$	1.37642	0.104346
$175$	−13.7997	−1.04316
$176$	18.0629	1.36154
$177$	8.40962	0.632106
$178$	19.4089	1.45476
$179$	8.03079	0.600249	0.300125	−	0.953900i	$-0.402972\pi$
$179$	8.03079	0.600249	0.300125	+	0.953900i	$0.402972\pi$
$180$	0.156442	0.0116605
$181$	−13.1680	−0.978768	−0.489384	−	0.872068i	$-0.662778\pi$
$181$	−13.1680	−0.978768	−0.489384	+	0.872068i	$0.662778\pi$
$182$	3.55871	0.263789
$183$	11.8204	0.873789
$184$	2.89802	0.213645
$185$	2.69172	0.197899
$186$	6.68951	0.490499
$187$	12.0395	0.880416
$188$	0.921811	0.0672300
$189$	−4.92788	−0.358451
$190$	−12.2976	−0.892160
$191$	13.9071	1.00628	0.503142	−	0.864204i	$-0.332177\pi$
$191$	13.9071	1.00628	0.503142	+	0.864204i	$0.332177\pi$
$192$	−8.37625	−0.604503
$193$	−12.5196	−0.901181	−0.450591	−	0.892731i	$-0.648787\pi$
$193$	−12.5196	−0.901181	−0.450591	+	0.892731i	$0.648787\pi$
$194$	−11.1853	−0.803058
$195$	0.778147	0.0557243
$196$	−1.82314	−0.130224
$197$	11.2711	0.803031	0.401516	−	0.915852i	$-0.368484\pi$
$197$	11.2711	0.803031	0.401516	+	0.915852i	$0.368484\pi$
$198$	−6.58088	−0.467683
$199$	−3.41641	−0.242183	−0.121091	−	0.992641i	$-0.538639\pi$
$199$	−3.41641	−0.242183	−0.121091	+	0.992641i	$0.538639\pi$
$200$	8.11540	0.573846
$201$	−8.80386	−0.620977
$202$	8.73618	0.614675
$203$	−4.92788	−0.345870
$204$	−0.265613	−0.0185966
$205$	10.2114	0.713192
$206$	−23.1736	−1.61458
$207$	−1.00000	−0.0695048
$208$	−1.98214	−0.137437
$209$	−28.8022	−1.99229
$210$	10.0598	0.694191
$211$	6.89502	0.474673	0.237336	−	0.971428i	$-0.423726\pi$
$211$	6.89502	0.474673	0.237336	+	0.971428i	$0.423726\pi$
$212$	0.753164	0.0517275
$213$	11.6325	0.797049
$214$	9.30930	0.636371
$215$	−8.06943	−0.550331
$216$	2.89802	0.197185
$217$	−23.9500	−1.62583
$218$	−21.7726	−1.47463
$219$	13.0454	0.881523
$220$	−0.747977	−0.0504286
$221$	−1.32116	−0.0888712
$222$	2.49805	0.167658
$223$	−4.85054	−0.324816	−0.162408	−	0.986724i	$-0.551926\pi$
$223$	−4.85054	−0.324816	−0.162408	+	0.986724i	$0.551926\pi$
$224$	2.93730	0.196257
$225$	−2.80033	−0.186689
$226$	−16.0682	−1.06884
$227$	18.5953	1.23422	0.617108	−	0.786879i	$-0.288304\pi$
$227$	18.5953	1.23422	0.617108	+	0.786879i	$0.288304\pi$
$228$	0.635428	0.0420823
$229$	17.0684	1.12791	0.563955	−	0.825805i	$-0.309279\pi$
$229$	17.0684	1.12791	0.563955	+	0.825805i	$0.309279\pi$
$230$	2.04140	0.134606
$231$	23.5611	1.55020
$232$	2.89802	0.190264
$233$	−9.38867	−0.615073	−0.307536	−	0.951536i	$-0.599505\pi$
$233$	−9.38867	−0.615073	−0.307536	+	0.951536i	$0.599505\pi$
$234$	0.722159	0.0472090
$235$	12.9612	0.845496
$236$	0.887057	0.0577425
$237$	5.81717	0.377866
$238$	−17.0798	−1.10712
$239$	14.9793	0.968929	0.484465	−	0.874811i	$-0.339014\pi$
$239$	14.9793	0.968929	0.484465	+	0.874811i	$0.339014\pi$
$240$	−5.60313	−0.361680
$241$	10.6067	0.683239	0.341619	−	0.939838i	$-0.389025\pi$
$241$	10.6067	0.683239	0.341619	+	0.939838i	$0.389025\pi$
$242$	16.3238	1.04933
$243$	−1.00000	−0.0641500
$244$	1.24683	0.0798201
$245$	−25.6344	−1.63772
$246$	9.47663	0.604208
$247$	3.16064	0.201106
$248$	14.0846	0.894375
$249$	−7.77527	−0.492738
$250$	15.9236	1.00710
$251$	29.5202	1.86330	0.931650	−	0.363357i	$-0.118369\pi$
$251$	29.5202	1.86330	0.931650	+	0.363357i	$0.118369\pi$
$252$	−0.519799	−0.0327443
$253$	4.78117	0.300590
$254$	22.2326	1.39500
$255$	−3.73467	−0.233874
$256$	−2.52438	−0.157774
$257$	23.5471	1.46883	0.734414	−	0.678701i	$-0.237457\pi$
$257$	23.5471	1.46883	0.734414	+	0.678701i	$0.237457\pi$
$258$	−7.48882	−0.466234
$259$	−8.94359	−0.555728
$260$	0.0820799	0.00509038
$261$	−1.00000	−0.0618984
$262$	−7.60246	−0.469682
$263$	−4.17470	−0.257423	−0.128711	−	0.991682i	$-0.541084\pi$
$263$	−4.17470	−0.257423	−0.128711	+	0.991682i	$0.541084\pi$
$264$	−13.8559	−0.852773
$265$	10.5899	0.650534
$266$	40.8603	2.50530
$267$	−14.1010	−0.862969
$268$	−0.928642	−0.0567258
$269$	−23.3314	−1.42254	−0.711271	−	0.702918i	$-0.751880\pi$
$269$	−23.3314	−1.42254	−0.711271	+	0.702918i	$0.751880\pi$
$270$	2.04140	0.124236
$271$	30.5545	1.85605	0.928027	−	0.372513i	$-0.121504\pi$
$271$	30.5545	1.85605	0.928027	+	0.372513i	$0.121504\pi$
$272$	9.51318	0.576821
$273$	−2.58549	−0.156481
$274$	3.68327	0.222514
$275$	13.3889	0.807379
$276$	−0.105481	−0.00634922
$277$	4.64255	0.278944	0.139472	−	0.990226i	$-0.455459\pi$
$277$	4.64255	0.278944	0.139472	+	0.990226i	$0.455459\pi$
$278$	27.9312	1.67520
$279$	−4.86009	−0.290966
$280$	21.1807	1.26579
$281$	23.1599	1.38160	0.690802	−	0.723044i	$-0.257258\pi$
$281$	23.1599	1.38160	0.690802	+	0.723044i	$0.257258\pi$
$282$	12.0286	0.716295
$283$	6.01659	0.357649	0.178825	−	0.983881i	$-0.442770\pi$
$283$	6.01659	0.357649	0.178825	+	0.983881i	$0.442770\pi$
$284$	1.22701	0.0728099
$285$	8.93450	0.529234
$286$	−3.45277	−0.204166
$287$	−33.9285	−2.00274
$288$	0.596058	0.0351231
$289$	−10.6591	−0.627008
$290$	2.04140	0.119875
$291$	8.12641	0.476378
$292$	1.37604	0.0805266
$293$	19.9569	1.16589	0.582947	−	0.812510i	$-0.301899\pi$
$293$	19.9569	1.16589	0.582947	+	0.812510i	$0.301899\pi$
$294$	−23.7900	−1.38746
$295$	12.4725	0.726180
$296$	5.25960	0.305708
$297$	4.78117	0.277432
$298$	14.8584	0.860723
$299$	−0.524666	−0.0303422
$300$	−0.295382	−0.0170539
$301$	26.8117	1.54540
$302$	−18.6082	−1.07078
$303$	−6.34705	−0.364629
$304$	−22.7585	−1.30529
$305$	17.5312	1.00383
$306$	−3.46596	−0.198136
$307$	−30.5457	−1.74334	−0.871668	−	0.490097i	$-0.836961\pi$
$307$	−30.5457	−1.74334	−0.871668	+	0.490097i	$0.836961\pi$
$308$	2.48525	0.141610
$309$	16.8362	0.957777
$310$	9.92140	0.563497
$311$	−20.4913	−1.16196	−0.580979	−	0.813919i	$-0.697330\pi$
$311$	−20.4913	−1.16196	−0.580979	+	0.813919i	$0.697330\pi$
$312$	1.52049	0.0860809
$313$	26.7843	1.51394	0.756969	−	0.653451i	$-0.226679\pi$
$313$	26.7843	1.51394	0.756969	+	0.653451i	$0.226679\pi$
$314$	−8.80794	−0.497061
$315$	−7.30868	−0.411798
$316$	0.613602	0.0345178
$317$	29.1115	1.63506	0.817532	−	0.575883i	$-0.195342\pi$
$317$	29.1115	1.63506	0.817532	+	0.575883i	$0.195342\pi$
$318$	9.82797	0.551125
$319$	4.78117	0.267694
$320$	−12.4230	−0.694469
$321$	−6.76344	−0.377498
$322$	−6.78281	−0.377991
$323$	−15.1693	−0.844042
$324$	−0.105481	−0.00586007
$325$	−1.46924	−0.0814987
$326$	−12.1476	−0.672791
$327$	15.8184	0.874758
$328$	19.9529	1.10171
$329$	−43.0653	−2.37427
$330$	−9.76029	−0.537286
$331$	−22.7491	−1.25040	−0.625201	−	0.780464i	$-0.714983\pi$
$331$	−22.7491	−1.25040	−0.625201	+	0.780464i	$0.714983\pi$
$332$	−0.820145	−0.0450113
$333$	−1.81490	−0.0994556
$334$	−26.3739	−1.44312
$335$	−13.0573	−0.713394
$336$	18.6171	1.01565
$337$	−21.1999	−1.15483	−0.577416	−	0.816450i	$-0.695939\pi$
$337$	−21.1999	−1.15483	−0.577416	+	0.816450i	$0.695939\pi$
$338$	−17.5145	−0.952664
$339$	11.6740	0.634044
$340$	−0.393938	−0.0213643
$341$	23.2370	1.25835
$342$	8.29165	0.448361
$343$	50.6785	2.73638
$344$	−15.7676	−0.850131
$345$	−1.48313	−0.0798489
$346$	13.8420	0.744152
$347$	−7.79477	−0.418445	−0.209223	−	0.977868i	$-0.567093\pi$
$347$	−7.79477	−0.418445	−0.209223	+	0.977868i	$0.567093\pi$
$348$	−0.105481	−0.00565439
$349$	17.0834	0.914451	0.457226	−	0.889351i	$-0.348843\pi$
$349$	17.0834	0.914451	0.457226	+	0.889351i	$0.348843\pi$
$350$	−18.9941	−1.01528
$351$	−0.524666	−0.0280046
$352$	−2.84986	−0.151898
$353$	13.2100	0.703099	0.351550	−	0.936169i	$-0.385655\pi$
$353$	13.2100	0.703099	0.351550	+	0.936169i	$0.385655\pi$
$354$	11.5751	0.615211
$355$	17.2526	0.915670
$356$	−1.48739	−0.0788317
$357$	12.4089	0.656750
$358$	11.0537	0.584206
$359$	9.87969	0.521430	0.260715	−	0.965416i	$-0.416042\pi$
$359$	9.87969	0.521430	0.260715	+	0.965416i	$0.416042\pi$
$360$	4.29813	0.226531
$361$	17.2896	0.909981
$362$	−18.1246	−0.952608
$363$	−11.8596	−0.622469
$364$	−0.272721	−0.0142945
$365$	19.3479	1.01272
$366$	16.2698	0.850435
$367$	17.8042	0.929372	0.464686	−	0.885475i	$-0.346167\pi$
$367$	17.8042	0.929372	0.464686	+	0.885475i	$0.346167\pi$
$368$	3.77791	0.196937
$369$	−6.88501	−0.358419
$370$	3.70493	0.192610
$371$	−35.1864	−1.82679
$372$	−0.512649	−0.0265796
$373$	−12.5979	−0.652297	−0.326148	−	0.945319i	$-0.605751\pi$
$373$	−12.5979	−0.652297	−0.326148	+	0.945319i	$0.605751\pi$
$374$	16.5714	0.856884
$375$	−11.5689	−0.597415
$376$	25.3261	1.30609
$377$	−0.524666	−0.0270217
$378$	−6.78281	−0.348870
$379$	−18.5593	−0.953328	−0.476664	−	0.879086i	$-0.658154\pi$
$379$	−18.5593	−0.953328	−0.476664	+	0.879086i	$0.658154\pi$
$380$	0.942421	0.0483452
$381$	−16.1525	−0.827519
$382$	19.1420	0.979388
$383$	6.16130	0.314828	0.157414	−	0.987533i	$-0.449684\pi$
$383$	6.16130	0.314828	0.157414	+	0.987533i	$0.449684\pi$
$384$	−10.3371	−0.527512
$385$	34.9441	1.78092
$386$	−17.2322	−0.877095
$387$	5.44082	0.276572
$388$	0.857183	0.0435169
$389$	−17.4876	−0.886656	−0.443328	−	0.896359i	$-0.646202\pi$
$389$	−17.4876	−0.886656	−0.443328	+	0.896359i	$0.646202\pi$
$390$	1.07105	0.0542349
$391$	2.51811	0.127346
$392$	−50.0894	−2.52990
$393$	5.52338	0.278618
$394$	15.5137	0.781568
$395$	8.62761	0.434102
$396$	0.504324	0.0253432
$397$	−16.6427	−0.835272	−0.417636	−	0.908614i	$-0.637141\pi$
$397$	−16.6427	−0.835272	−0.417636	+	0.908614i	$0.637141\pi$
$398$	−4.70239	−0.235710
$399$	−29.6860	−1.48616
$400$	10.5794	0.528970
$401$	14.6527	0.731722	0.365861	−	0.930669i	$-0.380774\pi$
$401$	14.6527	0.731722	0.365861	+	0.930669i	$0.380774\pi$
$402$	−12.1178	−0.604379
$403$	−2.54993	−0.127021
$404$	−0.669495	−0.0333086
$405$	−1.48313	−0.0736972
$406$	−6.78281	−0.336625
$407$	8.67733	0.430119
$408$	−7.29751	−0.361281
$409$	−23.9553	−1.18451	−0.592257	−	0.805749i	$-0.701763\pi$
$409$	−23.9553	−1.18451	−0.592257	+	0.805749i	$0.701763\pi$
$410$	14.0551	0.694130
$411$	−2.67599	−0.131997
$412$	1.77590	0.0874923
$413$	−41.4416	−2.03921
$414$	−1.37642	−0.0676471
$415$	−11.5317	−0.566070
$416$	0.312732	0.0153329
$417$	−20.2927	−0.993740
$418$	−39.6438	−1.93904
$419$	−15.4521	−0.754886	−0.377443	−	0.926033i	$-0.623197\pi$
$419$	−15.4521	−0.754886	−0.377443	+	0.926033i	$0.623197\pi$
$420$	−0.770928	−0.0376175
$421$	4.79223	0.233559	0.116780	−	0.993158i	$-0.462743\pi$
$421$	4.79223	0.233559	0.116780	+	0.993158i	$0.462743\pi$
$422$	9.49041	0.461986
$423$	−8.73911	−0.424910
$424$	20.6926	1.00492
$425$	7.05153	0.342049
$426$	16.0112	0.775746
$427$	−58.2496	−2.81889
$428$	−0.713416	−0.0344842
$429$	2.50852	0.121113
$430$	−11.1069	−0.535622
$431$	−24.6103	−1.18544	−0.592719	−	0.805410i	$-0.701945\pi$
$431$	−24.6103	−1.18544	−0.592719	+	0.805410i	$0.701945\pi$
$432$	3.77791	0.181765
$433$	−12.2569	−0.589031	−0.294516	−	0.955647i	$-0.595158\pi$
$433$	−12.2569	−0.589031	−0.294516	+	0.955647i	$0.595158\pi$
$434$	−32.9651	−1.58238
$435$	−1.48313	−0.0711106
$436$	1.66854	0.0799086
$437$	−6.02409	−0.288171
$438$	17.9558	0.857962
$439$	18.0437	0.861177	0.430588	−	0.902548i	$-0.358306\pi$
$439$	18.0437	0.861177	0.430588	+	0.902548i	$0.358306\pi$
$440$	−20.5501	−0.979688
$441$	17.2840	0.823049
$442$	−1.81847	−0.0864959
$443$	−0.405869	−0.0192834	−0.00964171	−	0.999954i	$-0.503069\pi$
$443$	−0.405869	−0.0192834	−0.00964171	+	0.999954i	$0.503069\pi$
$444$	−0.191437	−0.00908521
$445$	−20.9136	−0.991401
$446$	−6.67636	−0.316135
$447$	−10.7950	−0.510586
$448$	41.2772	1.95016
$449$	1.01695	0.0479929	0.0239965	−	0.999712i	$-0.492361\pi$
$449$	1.01695	0.0479929	0.0239965	+	0.999712i	$0.492361\pi$
$450$	−3.85442	−0.181699
$451$	32.9184	1.55007
$452$	1.23139	0.0579195
$453$	13.5193	0.635194
$454$	25.5949	1.20123
$455$	−3.83462	−0.179770
$456$	17.4579	0.817541
$457$	−22.1164	−1.03456	−0.517281	−	0.855815i	$-0.673056\pi$
$457$	−22.1164	−1.03456	−0.517281	+	0.855815i	$0.673056\pi$
$458$	23.4932	1.09776
$459$	2.51811	0.117535
$460$	−0.156442	−0.00729415
$461$	41.1018	1.91430	0.957150	−	0.289593i	$-0.0935201\pi$
$461$	41.1018	1.91430	0.957150	+	0.289593i	$0.0935201\pi$
$462$	32.4298	1.50877
$463$	−14.1273	−0.656551	−0.328276	−	0.944582i	$-0.606467\pi$
$463$	−14.1273	−0.656551	−0.328276	+	0.944582i	$0.606467\pi$
$464$	3.77791	0.175385
$465$	−7.20814	−0.334270
$466$	−12.9227	−0.598633
$467$	−26.8320	−1.24164	−0.620819	−	0.783954i	$-0.713200\pi$
$467$	−26.8320	−1.24164	−0.620819	+	0.783954i	$0.713200\pi$
$468$	−0.0553424	−0.00255820
$469$	43.3844	2.00331
$470$	17.8400	0.822898
$471$	6.39919	0.294859
$472$	24.3712	1.12178
$473$	−26.0135	−1.19610
$474$	8.00684	0.367766
$475$	−16.8694	−0.774023
$476$	1.30891	0.0599937
$477$	−7.14027	−0.326930
$478$	20.6177	0.943032
$479$	−14.9429	−0.682759	−0.341379	−	0.939926i	$-0.610894\pi$
$479$	−14.9429	−0.682759	−0.341379	+	0.939926i	$0.610894\pi$
$480$	0.884030	0.0403503
$481$	−0.952214	−0.0434172
$482$	14.5992	0.664978
$483$	4.92788	0.224226
$484$	−1.25097	−0.0568622
$485$	12.0525	0.547276
$486$	−1.37642	−0.0624355
$487$	7.07224	0.320474	0.160237	−	0.987079i	$-0.448774\pi$
$487$	7.07224	0.320474	0.160237	+	0.987079i	$0.448774\pi$
$488$	34.2557	1.55068
$489$	8.82550	0.399103
$490$	−35.2836	−1.59395
$491$	−23.1087	−1.04288	−0.521440	−	0.853288i	$-0.674605\pi$
$491$	−23.1087	−1.04288	−0.521440	+	0.853288i	$0.674605\pi$
$492$	−0.726239	−0.0327414
$493$	2.51811	0.113410
$494$	4.35035	0.195731
$495$	7.09109	0.318721
$496$	18.3610	0.824433
$497$	−57.3238	−2.57132
$498$	−10.7020	−0.479568
$499$	34.2464	1.53308	0.766541	−	0.642196i	$-0.221976\pi$
$499$	34.2464	1.53308	0.766541	+	0.642196i	$0.221976\pi$
$500$	−1.22030	−0.0545735
$501$	19.1613	0.856064
$502$	40.6321	1.81350
$503$	−30.4574	−1.35803	−0.679015	−	0.734124i	$-0.737593\pi$
$503$	−30.4574	−1.35803	−0.679015	+	0.734124i	$0.737593\pi$
$504$	−14.2811	−0.636130
$505$	−9.41349	−0.418895
$506$	6.58088	0.292556
$507$	12.7247	0.565125
$508$	−1.70379	−0.0755933
$509$	−23.0616	−1.02219	−0.511095	−	0.859524i	$-0.670760\pi$
$509$	−23.0616	−1.02219	−0.511095	+	0.859524i	$0.670760\pi$
$510$	−5.14046	−0.227623
$511$	−64.2860	−2.84384
$512$	−24.1488	−1.06723
$513$	−6.02409	−0.265970
$514$	32.4106	1.42957
$515$	24.9702	1.10032
$516$	0.573904	0.0252647
$517$	41.7832	1.83762
$518$	−12.3101	−0.540874
$519$	−10.0566	−0.441435
$520$	2.25508	0.0988919
$521$	7.60212	0.333055	0.166527	−	0.986037i	$-0.446745\pi$
$521$	7.60212	0.333055	0.166527	+	0.986037i	$0.446745\pi$
$522$	−1.37642	−0.0602441
$523$	−9.05401	−0.395904	−0.197952	−	0.980212i	$-0.563429\pi$
$523$	−9.05401	−0.395904	−0.197952	+	0.980212i	$0.563429\pi$
$524$	0.582613	0.0254515
$525$	13.7997	0.602268
$526$	−5.74612	−0.250543
$527$	12.2382	0.533106
$528$	−18.0629	−0.786085
$529$	1.00000	0.0434783
$530$	14.5761	0.633147
$531$	−8.40962	−0.364946
$532$	−3.13132	−0.135760
$533$	−3.61233	−0.156467
$534$	−19.4089	−0.839904
$535$	−10.0310	−0.433680
$536$	−25.5137	−1.10203
$537$	−8.03079	−0.346554
$538$	−32.1137	−1.38452
$539$	−82.6380	−3.55947
$540$	−0.156442	−0.00673220
$541$	20.6458	0.887632	0.443816	−	0.896118i	$-0.353624\pi$
$541$	20.6458	0.887632	0.443816	+	0.896118i	$0.353624\pi$
$542$	42.0557	1.80645
$543$	13.1680	0.565092
$544$	−1.50094	−0.0643522
$545$	23.4607	1.00494
$546$	−3.55871	−0.152299
$547$	−7.07622	−0.302557	−0.151279	−	0.988491i	$-0.548339\pi$
$547$	−7.07622	−0.302557	−0.151279	+	0.988491i	$0.548339\pi$
$548$	−0.282266	−0.0120578
$549$	−11.8204	−0.504482
$550$	18.4286	0.785800
$551$	−6.02409	−0.256635
$552$	−2.89802	−0.123348
$553$	−28.6663	−1.21902
$554$	6.39008	0.271488
$555$	−2.69172	−0.114257
$556$	−2.14050	−0.0907775
$557$	10.9839	0.465404	0.232702	−	0.972548i	$-0.425243\pi$
$557$	10.9839	0.465404	0.232702	+	0.972548i	$0.425243\pi$
$558$	−6.68951	−0.283189
$559$	2.85461	0.120737
$560$	27.6116	1.16680
$561$	−12.0395	−0.508308
$562$	31.8776	1.34468
$563$	4.36253	0.183859	0.0919293	−	0.995766i	$-0.470697\pi$
$563$	4.36253	0.183859	0.0919293	+	0.995766i	$0.470697\pi$
$564$	−0.921811	−0.0388153
$565$	17.3140	0.728406
$566$	8.28133	0.348090
$567$	4.92788	0.206952
$568$	33.7113	1.41449
$569$	12.5393	0.525676	0.262838	−	0.964840i	$-0.415341\pi$
$569$	12.5393	0.525676	0.262838	+	0.964840i	$0.415341\pi$
$570$	12.2976	0.515089
$571$	−26.7780	−1.12062	−0.560312	−	0.828282i	$-0.689319\pi$
$571$	−26.7780	−1.12062	−0.560312	+	0.828282i	$0.689319\pi$
$572$	0.264602	0.0110636
$573$	−13.9071	−0.580978
$574$	−46.6997	−1.94921
$575$	2.80033	0.116782
$576$	8.37625	0.349010
$577$	−30.5483	−1.27174	−0.635871	−	0.771795i	$-0.719359\pi$
$577$	−30.5483	−1.27174	−0.635871	+	0.771795i	$0.719359\pi$
$578$	−14.6714	−0.610250
$579$	12.5196	0.520297
$580$	−0.156442	−0.00649591
$581$	38.3156	1.58960
$582$	11.1853	0.463646
$583$	34.1389	1.41389
$584$	37.8056	1.56441
$585$	−0.778147	−0.0321724
$586$	27.4690	1.13473
$587$	17.8790	0.737945	0.368973	−	0.929440i	$-0.379710\pi$
$587$	17.8790	0.737945	0.368973	+	0.929440i	$0.379710\pi$
$588$	1.82314	0.0751850
$589$	−29.2776	−1.20636
$590$	17.1674	0.706771
$591$	−11.2711	−0.463630
$592$	6.85651	0.281801
$593$	−24.1803	−0.992966	−0.496483	−	0.868047i	$-0.665375\pi$
$593$	−24.1803	−0.992966	−0.496483	+	0.868047i	$0.665375\pi$
$594$	6.58088	0.270017
$595$	18.4040	0.754492
$596$	−1.13867	−0.0466417
$597$	3.41641	0.139824
$598$	−0.722159	−0.0295313
$599$	−33.7750	−1.38001	−0.690004	−	0.723805i	$-0.742391\pi$
$599$	−33.7750	−1.38001	−0.690004	+	0.723805i	$0.742391\pi$
$600$	−8.11540	−0.331310
$601$	47.8919	1.95355	0.976776	−	0.214263i	$-0.0687350\pi$
$601$	47.8919	1.95355	0.976776	+	0.214263i	$0.0687350\pi$
$602$	36.9040	1.50410
$603$	8.80386	0.358521
$604$	1.42604	0.0580246
$605$	−17.5893	−0.715108
$606$	−8.73618	−0.354883
$607$	1.35443	0.0549746	0.0274873	−	0.999622i	$-0.491249\pi$
$607$	1.35443	0.0549746	0.0274873	+	0.999622i	$0.491249\pi$
$608$	3.59071	0.145622
$609$	4.92788	0.199688
$610$	24.1302	0.977002
$611$	−4.58511	−0.185494
$612$	0.265613	0.0107368
$613$	−22.4155	−0.905353	−0.452677	−	0.891675i	$-0.649531\pi$
$613$	−22.4155	−0.905353	−0.452677	+	0.891675i	$0.649531\pi$
$614$	−42.0436	−1.69674
$615$	−10.2114	−0.411761
$616$	68.2804	2.75109
$617$	−3.75650	−0.151231	−0.0756155	−	0.997137i	$-0.524092\pi$
$617$	−3.75650	−0.151231	−0.0756155	+	0.997137i	$0.524092\pi$
$618$	23.1736	0.932178
$619$	−4.17326	−0.167738	−0.0838688	−	0.996477i	$-0.526728\pi$
$619$	−4.17326	−0.167738	−0.0838688	+	0.996477i	$0.526728\pi$
$620$	−0.760324	−0.0305353
$621$	1.00000	0.0401286
$622$	−28.2046	−1.13090
$623$	69.4882	2.78399
$624$	1.98214	0.0793492
$625$	−3.15649	−0.126260
$626$	36.8663	1.47347
$627$	28.8022	1.15025
$628$	0.674994	0.0269352
$629$	4.57010	0.182222
$630$	−10.0598	−0.400791
$631$	−33.2279	−1.32278	−0.661390	−	0.750042i	$-0.730033\pi$
$631$	−33.2279	−1.32278	−0.661390	+	0.750042i	$0.730033\pi$
$632$	16.8582	0.670585
$633$	−6.89502	−0.274052
$634$	40.0695	1.59136
$635$	−23.9563	−0.950675
$636$	−0.753164	−0.0298649
$637$	9.06835	0.359301
$638$	6.58088	0.260540
$639$	−11.6325	−0.460176
$640$	−15.3312	−0.606019
$641$	12.6802	0.500838	0.250419	−	0.968138i	$-0.419432\pi$
$641$	12.6802	0.500838	0.250419	+	0.968138i	$0.419432\pi$
$642$	−9.30930	−0.367409
$643$	−9.73223	−0.383802	−0.191901	−	0.981414i	$-0.561465\pi$
$643$	−9.73223	−0.383802	−0.191901	+	0.981414i	$0.561465\pi$
$644$	0.519799	0.0204829
$645$	8.06943	0.317733
$646$	−20.8792	−0.821483
$647$	0.0196233	0.000771470 0	0.000385735	−	1.00000i	$-0.499877\pi$
$647$	0.0196233	0.000771470 0	0.000385735		1.00000i	$0.499877\pi$
$648$	−2.89802	−0.113845
$649$	40.2079	1.57830
$650$	−2.02228	−0.0793205
$651$	23.9500	0.938674
$652$	0.930924	0.0364578
$653$	−26.8683	−1.05144	−0.525719	−	0.850658i	$-0.676204\pi$
$653$	−26.8683	−1.05144	−0.525719	+	0.850658i	$0.676204\pi$
$654$	21.7726	0.851377
$655$	8.19188	0.320083
$656$	26.0110	1.01556
$657$	−13.0454	−0.508948
$658$	−59.2757	−2.31081
$659$	−29.6280	−1.15414	−0.577071	−	0.816694i	$-0.695804\pi$
$659$	−29.6280	−1.15414	−0.577071	+	0.816694i	$0.695804\pi$
$660$	0.747977	0.0291150
$661$	12.3242	0.479356	0.239678	−	0.970852i	$-0.422958\pi$
$661$	12.3242	0.479356	0.239678	+	0.970852i	$0.422958\pi$
$662$	−31.3121	−1.21698
$663$	1.32116	0.0513098
$664$	−22.5329	−0.874445
$665$	−44.0281	−1.70734
$666$	−2.49805	−0.0967974
$667$	1.00000	0.0387202
$668$	2.02116	0.0782010
$669$	4.85054	0.187533
$670$	−17.9722	−0.694327
$671$	56.5154	2.18175
$672$	−2.93730	−0.113309
$673$	−5.47404	−0.211009	−0.105504	−	0.994419i	$-0.533646\pi$
$673$	−5.47404	−0.211009	−0.105504	+	0.994419i	$0.533646\pi$
$674$	−29.1798	−1.12397
$675$	2.80033	0.107785
$676$	1.34222	0.0516238
$677$	−41.7308	−1.60385	−0.801923	−	0.597427i	$-0.796190\pi$
$677$	−41.7308	−1.60385	−0.801923	+	0.597427i	$0.796190\pi$
$678$	16.0682	0.617097
$679$	−40.0460	−1.53682
$680$	−10.8231	−0.415049
$681$	−18.5953	−0.712575
$682$	31.9837	1.22472
$683$	−1.83472	−0.0702037	−0.0351019	−	0.999384i	$-0.511176\pi$
$683$	−1.83472	−0.0702037	−0.0351019	+	0.999384i	$0.511176\pi$
$684$	−0.635428	−0.0242962
$685$	−3.96883	−0.151641
$686$	69.7547	2.66324
$687$	−17.0684	−0.651199
$688$	−20.5549	−0.783649
$689$	−3.74626	−0.142721
$690$	−2.04140	−0.0777148
$691$	33.0805	1.25844	0.629220	−	0.777227i	$-0.283374\pi$
$691$	33.0805	1.25844	0.629220	+	0.777227i	$0.283374\pi$
$692$	−1.06078	−0.0403248
$693$	−23.5611	−0.895011
$694$	−10.7288	−0.407261
$695$	−30.0967	−1.14163
$696$	−2.89802	−0.109849
$697$	17.3372	0.656693
$698$	23.5138	0.890010
$699$	9.38867	0.355112
$700$	1.45561	0.0550169
$701$	16.2570	0.614020	0.307010	−	0.951706i	$-0.400672\pi$
$701$	16.2570	0.614020	0.307010	+	0.951706i	$0.400672\pi$
$702$	−0.722159	−0.0272561
$703$	−10.9331	−0.412349
$704$	−40.0483	−1.50938
$705$	−12.9612	−0.488148
$706$	18.1825	0.684307
$707$	31.2775	1.17631
$708$	−0.887057	−0.0333376
$709$	0.0198177	0.000744270 0	0.000372135	−	1.00000i	$-0.499882\pi$
$709$	0.0198177	0.000744270 0	0.000372135		1.00000i	$0.499882\pi$
$710$	23.7467	0.891197
$711$	−5.81717	−0.218161
$712$	−40.8650	−1.53148
$713$	4.86009	0.182012
$714$	17.0798	0.639197
$715$	3.72046	0.139137
$716$	−0.847097	−0.0316575
$717$	−14.9793	−0.559412
$718$	13.5986	0.507493
$719$	−26.1632	−0.975723	−0.487862	−	0.872921i	$-0.662223\pi$
$719$	−26.1632	−0.975723	−0.487862	+	0.872921i	$0.662223\pi$
$720$	5.60313	0.208816
$721$	−82.9667	−3.08984
$722$	23.7977	0.885660
$723$	−10.6067	−0.394468
$724$	1.38897	0.0516208
$725$	2.80033	0.104002
$726$	−16.3238	−0.605832
$727$	−17.3000	−0.641623	−0.320811	−	0.947143i	$-0.603956\pi$
$727$	−17.3000	−0.641623	−0.320811	+	0.947143i	$0.603956\pi$
$728$	−7.49280	−0.277702
$729$	1.00000	0.0370370
$730$	26.6308	0.985649
$731$	−13.7006	−0.506733
$732$	−1.24683	−0.0460842
$733$	−33.2459	−1.22797	−0.613983	−	0.789319i	$-0.710434\pi$
$733$	−33.2459	−1.22797	−0.613983	+	0.789319i	$0.710434\pi$
$734$	24.5060	0.904533
$735$	25.6344	0.945540
$736$	−0.596058	−0.0219710
$737$	−42.0928	−1.55051
$738$	−9.47663	−0.348840
$739$	22.0846	0.812394	0.406197	−	0.913786i	$-0.366855\pi$
$739$	22.0846	0.812394	0.406197	+	0.913786i	$0.366855\pi$
$740$	−0.283926	−0.0104373
$741$	−3.16064	−0.116109
$742$	−48.4311	−1.77796
$743$	−21.7767	−0.798909	−0.399455	−	0.916753i	$-0.630800\pi$
$743$	−21.7767	−0.798909	−0.399455	+	0.916753i	$0.630800\pi$
$744$	−14.0846	−0.516368
$745$	−16.0104	−0.586574
$746$	−17.3400	−0.634862
$747$	7.77527	0.284482
$748$	−1.26994	−0.0464336
$749$	33.3294	1.21783
$750$	−15.9236	−0.581448
$751$	−17.9180	−0.653836	−0.326918	−	0.945053i	$-0.606010\pi$
$751$	−17.9180	−0.653836	−0.326918	+	0.945053i	$0.606010\pi$
$752$	33.0156	1.20395
$753$	−29.5202	−1.07578
$754$	−0.722159	−0.0262995
$755$	20.0509	0.729728
$756$	0.519799	0.0189049
$757$	−8.33584	−0.302971	−0.151486	−	0.988459i	$-0.548406\pi$
$757$	−8.33584	−0.302971	−0.151486	+	0.988459i	$0.548406\pi$
$758$	−25.5453	−0.927848
$759$	−4.78117	−0.173546
$760$	25.8923	0.939213
$761$	30.3649	1.10073	0.550363	−	0.834925i	$-0.314489\pi$
$761$	30.3649	1.10073	0.550363	+	0.834925i	$0.314489\pi$
$762$	−22.2326	−0.805401
$763$	−77.9510	−2.82202
$764$	−1.46694	−0.0530720
$765$	3.73467	0.135027
$766$	8.48051	0.306413
$767$	−4.41224	−0.159317
$768$	2.52438	0.0910908
$769$	13.4279	0.484222	0.242111	−	0.970249i	$-0.422160\pi$
$769$	13.4279	0.484222	0.242111	+	0.970249i	$0.422160\pi$
$770$	48.0976	1.73332
$771$	−23.5471	−0.848029
$772$	1.32058	0.0475288
$773$	−38.3206	−1.37830	−0.689149	−	0.724620i	$-0.742015\pi$
$773$	−38.3206	−1.37830	−0.689149	+	0.724620i	$0.742015\pi$
$774$	7.48882	0.269180
$775$	13.6099	0.488881
$776$	23.5505	0.845412
$777$	8.94359	0.320850
$778$	−24.0702	−0.862958
$779$	−41.4759	−1.48603
$780$	−0.0820799	−0.00293893
$781$	55.6172	1.99014
$782$	3.46596	0.123942
$783$	1.00000	0.0357371
$784$	−65.2975	−2.33205
$785$	9.49081	0.338742
$786$	7.60246	0.271171
$787$	39.6436	1.41314	0.706570	−	0.707643i	$-0.250241\pi$
$787$	39.6436	1.41314	0.706570	+	0.707643i	$0.250241\pi$
$788$	−1.18889	−0.0423523
$789$	4.17470	0.148623
$790$	11.8752	0.422499
$791$	−57.5280	−2.04546
$792$	13.8559	0.492349
$793$	−6.20177	−0.220231
$794$	−22.9072	−0.812947
$795$	−10.5899	−0.375586
$796$	0.360367	0.0127729
$797$	40.1420	1.42190	0.710951	−	0.703242i	$-0.248265\pi$
$797$	40.1420	1.42190	0.710951	+	0.703242i	$0.248265\pi$
$798$	−40.8603	−1.44644
$799$	22.0060	0.778516
$800$	−1.66916	−0.0590137
$801$	14.1010	0.498235
$802$	20.1682	0.712165
$803$	62.3721	2.20106
$804$	0.928642	0.0327507
$805$	7.30868	0.257597
$806$	−3.50976	−0.123626
$807$	23.3314	0.821305
$808$	−18.3939	−0.647094
$809$	0.173541	0.00610138	0.00305069	−	0.999995i	$-0.499029\pi$
$809$	0.173541	0.00610138	0.00305069	+	0.999995i	$0.499029\pi$
$810$	−2.04140	−0.0717275
$811$	−0.873050	−0.0306569	−0.0153285	−	0.999883i	$-0.504879\pi$
$811$	−0.873050	−0.0306569	−0.0153285	+	0.999883i	$0.504879\pi$
$812$	0.519799	0.0182414
$813$	−30.5545	−1.07159
$814$	11.9436	0.418623
$815$	13.0893	0.458500
$816$	−9.51318	−0.333028
$817$	32.7760	1.14669
$818$	−32.9724	−1.15285
$819$	2.58549	0.0903445
$820$	−1.07711	−0.0376142
$821$	−5.99107	−0.209090	−0.104545	−	0.994520i	$-0.533339\pi$
$821$	−5.99107	−0.209090	−0.104545	+	0.994520i	$0.533339\pi$
$822$	−3.68327	−0.128469
$823$	18.7788	0.654589	0.327294	−	0.944922i	$-0.393863\pi$
$823$	18.7788	0.654589	0.327294	+	0.944922i	$0.393863\pi$
$824$	48.7915	1.69973
$825$	−13.3889	−0.466141
$826$	−57.0409	−1.98471
$827$	−53.3963	−1.85677	−0.928387	−	0.371616i	$-0.878804\pi$
$827$	−53.3963	−1.85677	−0.928387	+	0.371616i	$0.878804\pi$
$828$	0.105481	0.00366572
$829$	−31.4472	−1.09221	−0.546103	−	0.837718i	$-0.683889\pi$
$829$	−31.4472	−1.09221	−0.546103	+	0.837718i	$0.683889\pi$
$830$	−15.8724	−0.550940
$831$	−4.64255	−0.161048
$832$	4.39473	0.152360
$833$	−43.5230	−1.50798
$834$	−27.9312	−0.967180
$835$	28.4187	0.983469
$836$	3.03809	0.105075
$837$	4.86009	0.167989
$838$	−21.2685	−0.734710
$839$	43.6126	1.50568	0.752838	−	0.658206i	$-0.228684\pi$
$839$	43.6126	1.50568	0.752838	+	0.658206i	$0.228684\pi$
$840$	−21.1807	−0.730803
$841$	1.00000	0.0344828
$842$	6.59610	0.227317
$843$	−23.1599	−0.797669
$844$	−0.727295	−0.0250345
$845$	18.8724	0.649230
$846$	−12.0286	−0.413553
$847$	58.4428	2.00812
$848$	26.9753	0.926335
$849$	−6.01659	−0.206489
$850$	9.70583	0.332907
$851$	1.81490	0.0622138
$852$	−1.22701	−0.0420368
$853$	24.3777	0.834678	0.417339	−	0.908751i	$-0.362963\pi$
$853$	24.3777	0.834678	0.417339	+	0.908751i	$0.362963\pi$
$854$	−80.1756	−2.74355
$855$	−8.93450	−0.305553
$856$	−19.6006	−0.669933
$857$	42.7652	1.46083	0.730416	−	0.683003i	$-0.239326\pi$
$857$	42.7652	1.46083	0.730416	+	0.683003i	$0.239326\pi$
$858$	3.45277	0.117875
$859$	3.97878	0.135754	0.0678771	−	0.997694i	$-0.478377\pi$
$859$	3.97878	0.135754	0.0678771	+	0.997694i	$0.478377\pi$
$860$	0.851173	0.0290248
$861$	33.9285	1.15628
$862$	−33.8740	−1.15375
$863$	−31.5448	−1.07380	−0.536899	−	0.843646i	$-0.680405\pi$
$863$	−31.5448	−1.07380	−0.536899	+	0.843646i	$0.680405\pi$
$864$	−0.596058	−0.0202783
$865$	−14.9152	−0.507132
$866$	−16.8706	−0.573288
$867$	10.6591	0.362003
$868$	2.52627	0.0857473
$869$	27.8129	0.943488
$870$	−2.04140	−0.0692099
$871$	4.61909	0.156512
$872$	45.8419	1.55240
$873$	−8.12641	−0.275037
$874$	−8.29165	−0.280469
$875$	57.0101	1.92729
$876$	−1.37604	−0.0464921
$877$	−30.3834	−1.02598	−0.512988	−	0.858396i	$-0.671461\pi$
$877$	−30.3834	−1.02598	−0.512988	+	0.858396i	$0.671461\pi$
$878$	24.8356	0.838160
$879$	−19.9569	−0.673130
$880$	−26.7895	−0.903075
$881$	−6.35686	−0.214168	−0.107084	−	0.994250i	$-0.534151\pi$
$881$	−6.35686	−0.214168	−0.107084	+	0.994250i	$0.534151\pi$
$882$	23.7900	0.801051
$883$	4.78642	0.161076	0.0805380	−	0.996752i	$-0.474336\pi$
$883$	4.78642	0.161076	0.0805380	+	0.996752i	$0.474336\pi$
$884$	0.139358	0.00468712
$885$	−12.4725	−0.419260
$886$	−0.558645	−0.0187680
$887$	−17.9828	−0.603804	−0.301902	−	0.953339i	$-0.597622\pi$
$887$	−17.9828	−0.603804	−0.301902	+	0.953339i	$0.597622\pi$
$888$	−5.25960	−0.176500
$889$	79.5977	2.66962
$890$	−28.7858	−0.964904
$891$	−4.78117	−0.160175
$892$	0.511641	0.0171310
$893$	−52.6452	−1.76170
$894$	−14.8584	−0.496939
$895$	−11.9107	−0.398130
$896$	50.9399	1.70178
$897$	0.524666	0.0175181
$898$	1.39975	0.0467102
$899$	4.86009	0.162093
$900$	0.295382	0.00984608
$901$	17.9799	0.598999
$902$	45.3094	1.50864
$903$	−26.8117	−0.892238
$904$	33.8314	1.12522
$905$	19.5298	0.649192
$906$	18.6082	0.618217
$907$	6.79373	0.225582	0.112791	−	0.993619i	$-0.464021\pi$
$907$	6.79373	0.225582	0.112791	+	0.993619i	$0.464021\pi$
$908$	−1.96146	−0.0650933
$909$	6.34705	0.210518
$910$	−5.27803	−0.174965
$911$	−30.4854	−1.01003	−0.505013	−	0.863112i	$-0.668512\pi$
$911$	−30.4854	−1.01003	−0.505013	+	0.863112i	$0.668512\pi$
$912$	22.7585	0.753608
$913$	−37.1749	−1.23031
$914$	−30.4414	−1.00691
$915$	−17.5312	−0.579563
$916$	−1.80039	−0.0594867
$917$	−27.2186	−0.898836
$918$	3.46596	0.114394
$919$	31.7293	1.04665	0.523326	−	0.852132i	$-0.324691\pi$
$919$	31.7293	1.04665	0.523326	+	0.852132i	$0.324691\pi$
$920$	−4.29813	−0.141705
$921$	30.5457	1.00652
$922$	56.5731	1.86314
$923$	−6.10320	−0.200889
$924$	−2.48525	−0.0817587
$925$	5.08231	0.167105
$926$	−19.4450	−0.639003
$927$	−16.8362	−0.552973
$928$	−0.596058	−0.0195666
$929$	20.9650	0.687838	0.343919	−	0.938999i	$-0.388245\pi$
$929$	20.9650	0.687838	0.343919	+	0.938999i	$0.388245\pi$
$930$	−9.92140	−0.325335
$931$	104.121	3.41241
$932$	0.990329	0.0324393
$933$	20.4913	0.670856
$934$	−36.9320	−1.20845
$935$	−17.8561	−0.583958
$936$	−1.52049	−0.0496988
$937$	12.3540	0.403588	0.201794	−	0.979428i	$-0.435323\pi$
$937$	12.3540	0.403588	0.201794	+	0.979428i	$0.435323\pi$
$938$	59.7149	1.94976
$939$	−26.7843	−0.874072
$940$	−1.36716	−0.0445920
$941$	4.48801	0.146305	0.0731524	−	0.997321i	$-0.476694\pi$
$941$	4.48801	0.146305	0.0731524	+	0.997321i	$0.476694\pi$
$942$	8.80794	0.286978
$943$	6.88501	0.224207
$944$	31.7708	1.03405
$945$	7.30868	0.237751
$946$	−35.8054	−1.16413
$947$	24.5673	0.798330	0.399165	−	0.916879i	$-0.369300\pi$
$947$	24.5673	0.798330	0.399165	+	0.916879i	$0.369300\pi$
$948$	−0.613602	−0.0199289
$949$	−6.84445	−0.222180
$950$	−23.2194	−0.753335
$951$	−29.1115	−0.944005
$952$	35.9613	1.16551
$953$	−17.9457	−0.581319	−0.290660	−	0.956826i	$-0.593875\pi$
$953$	−17.9457	−0.581319	−0.290660	+	0.956826i	$0.593875\pi$
$954$	−9.82797	−0.318192
$955$	−20.6260	−0.667443
$956$	−1.58003	−0.0511019
$957$	−4.78117	−0.154553
$958$	−20.5676	−0.664511
$959$	13.1869	0.425829
$960$	12.4230	0.400952
$961$	−7.37948	−0.238048
$962$	−1.31064	−0.0422568
$963$	6.76344	0.217949
$964$	−1.11881	−0.0360344
$965$	18.5682	0.597731
$966$	6.78281	0.218233
$967$	47.2541	1.51959	0.759794	−	0.650164i	$-0.225300\pi$
$967$	47.2541	1.51959	0.759794	+	0.650164i	$0.225300\pi$
$968$	−34.3694	−1.10467
$969$	15.1693	0.487308
$970$	16.5892	0.532649
$971$	11.7649	0.377553	0.188776	−	0.982020i	$-0.439548\pi$
$971$	11.7649	0.377553	0.188776	+	0.982020i	$0.439548\pi$
$972$	0.105481	0.00338331
$973$	100.000	3.20586
$974$	9.73433	0.311908
$975$	1.46924	0.0470533
$976$	44.6564	1.42942
$977$	−4.23462	−0.135478	−0.0677388	−	0.997703i	$-0.521578\pi$
$977$	−4.23462	−0.135478	−0.0677388	+	0.997703i	$0.521578\pi$
$978$	12.1476	0.388436
$979$	−67.4195	−2.15474
$980$	2.70395	0.0863745
$981$	−15.8184	−0.505042
$982$	−31.8071	−1.01501
$983$	19.8985	0.634664	0.317332	−	0.948315i	$-0.397213\pi$
$983$	19.8985	0.634664	0.317332	+	0.948315i	$0.397213\pi$
$984$	−19.9529	−0.636074
$985$	−16.7165	−0.532631
$986$	3.46596	0.110379
$987$	43.0653	1.37078
$988$	−0.333388	−0.0106065
$989$	−5.44082	−0.173008
$990$	9.76029	0.310202
$991$	−39.7115	−1.26148	−0.630739	−	0.775995i	$-0.717248\pi$
$991$	−39.7115	−1.26148	−0.630739	+	0.775995i	$0.717248\pi$
$992$	−2.89690	−0.0919766
$993$	22.7491	0.721920
$994$	−78.9014	−2.50260
$995$	5.06697	0.160634
$996$	0.820145	0.0259873
$997$	28.2172	0.893647	0.446824	−	0.894622i	$-0.352555\pi$
$997$	28.2172	0.893647	0.446824	+	0.894622i	$0.352555\pi$
$998$	47.1373	1.49211
$999$	1.81490	0.0574207

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.11	✓	14
3.2	odd	2		6003.2.a.p.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.11	✓	14	1.1	even	1	trivial
6003.2.a.p.1.4		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)

\(f(q)\)	\(=\)	\(q+1.37642 q^{2} -1.00000 q^{3} -0.105481 q^{4} -1.48313 q^{5} -1.37642 q^{6} +4.92788 q^{7} -2.89802 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.37642 q^{2} -1.00000 q^{3} -0.105481 q^{4} -1.48313 q^{5} -1.37642 q^{6} +4.92788 q^{7} -2.89802 q^{8} +1.00000 q^{9} -2.04140 q^{10} -4.78117 q^{11} +0.105481 q^{12} +0.524666 q^{13} +6.78281 q^{14} +1.48313 q^{15} -3.77791 q^{16} -2.51811 q^{17} +1.37642 q^{18} +6.02409 q^{19} +0.156442 q^{20} -4.92788 q^{21} -6.58088 q^{22} -1.00000 q^{23} +2.89802 q^{24} -2.80033 q^{25} +0.722159 q^{26} -1.00000 q^{27} -0.519799 q^{28} -1.00000 q^{29} +2.04140 q^{30} -4.86009 q^{31} +0.596058 q^{32} +4.78117 q^{33} -3.46596 q^{34} -7.30868 q^{35} -0.105481 q^{36} -1.81490 q^{37} +8.29165 q^{38} -0.524666 q^{39} +4.29813 q^{40} -6.88501 q^{41} -6.78281 q^{42} +5.44082 q^{43} +0.504324 q^{44} -1.48313 q^{45} -1.37642 q^{46} -8.73911 q^{47} +3.77791 q^{48} +17.2840 q^{49} -3.85442 q^{50} +2.51811 q^{51} -0.0553424 q^{52} -7.14027 q^{53} -1.37642 q^{54} +7.09109 q^{55} -14.2811 q^{56} -6.02409 q^{57} -1.37642 q^{58} -8.40962 q^{59} -0.156442 q^{60} -11.8204 q^{61} -6.68951 q^{62} +4.92788 q^{63} +8.37625 q^{64} -0.778147 q^{65} +6.58088 q^{66} +8.80386 q^{67} +0.265613 q^{68} +1.00000 q^{69} -10.0598 q^{70} -11.6325 q^{71} -2.89802 q^{72} -13.0454 q^{73} -2.49805 q^{74} +2.80033 q^{75} -0.635428 q^{76} -23.5611 q^{77} -0.722159 q^{78} -5.81717 q^{79} +5.60313 q^{80} +1.00000 q^{81} -9.47663 q^{82} +7.77527 q^{83} +0.519799 q^{84} +3.73467 q^{85} +7.48882 q^{86} +1.00000 q^{87} +13.8559 q^{88} +14.1010 q^{89} -2.04140 q^{90} +2.58549 q^{91} +0.105481 q^{92} +4.86009 q^{93} -12.0286 q^{94} -8.93450 q^{95} -0.596058 q^{96} -8.12641 q^{97} +23.7900 q^{98} -4.78117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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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