LMFDB - Embedded newform 2001.2.a.k.1.10

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 $ x^10 - x^9 - 17x^8 + 23x^7 + 69x^6 - 88x^5 - 106x^4 + 101x^3 + 60x^2 - 23x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.19874$ 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)

$f(q)$	$=$	$q+2.74444 q^{2} -1.00000 q^{3} +5.53194 q^{4} +0.0839771 q^{5} -2.74444 q^{6} -2.30146 q^{7} +9.69318 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.74444 q^{2} -1.00000 q^{3} +5.53194 q^{4} +0.0839771 q^{5} -2.74444 q^{6} -2.30146 q^{7} +9.69318 q^{8} +1.00000 q^{9} +0.230470 q^{10} +4.15428 q^{11} -5.53194 q^{12} -0.439258 q^{13} -6.31621 q^{14} -0.0839771 q^{15} +15.5385 q^{16} -0.388355 q^{17} +2.74444 q^{18} +5.29460 q^{19} +0.464556 q^{20} +2.30146 q^{21} +11.4012 q^{22} -1.00000 q^{23} -9.69318 q^{24} -4.99295 q^{25} -1.20552 q^{26} -1.00000 q^{27} -12.7315 q^{28} +1.00000 q^{29} -0.230470 q^{30} +1.44043 q^{31} +23.2580 q^{32} -4.15428 q^{33} -1.06582 q^{34} -0.193270 q^{35} +5.53194 q^{36} +9.04387 q^{37} +14.5307 q^{38} +0.439258 q^{39} +0.814006 q^{40} -0.159033 q^{41} +6.31621 q^{42} -6.03876 q^{43} +22.9812 q^{44} +0.0839771 q^{45} -2.74444 q^{46} -0.396132 q^{47} -15.5385 q^{48} -1.70328 q^{49} -13.7028 q^{50} +0.388355 q^{51} -2.42995 q^{52} +2.43614 q^{53} -2.74444 q^{54} +0.348864 q^{55} -22.3085 q^{56} -5.29460 q^{57} +2.74444 q^{58} -4.08958 q^{59} -0.464556 q^{60} +9.28497 q^{61} +3.95318 q^{62} -2.30146 q^{63} +32.7531 q^{64} -0.0368876 q^{65} -11.4012 q^{66} +4.55339 q^{67} -2.14836 q^{68} +1.00000 q^{69} -0.530417 q^{70} -3.85137 q^{71} +9.69318 q^{72} +0.0113549 q^{73} +24.8203 q^{74} +4.99295 q^{75} +29.2894 q^{76} -9.56090 q^{77} +1.20552 q^{78} +9.57510 q^{79} +1.30488 q^{80} +1.00000 q^{81} -0.436455 q^{82} -5.55983 q^{83} +12.7315 q^{84} -0.0326130 q^{85} -16.5730 q^{86} -1.00000 q^{87} +40.2682 q^{88} -4.02316 q^{89} +0.230470 q^{90} +1.01093 q^{91} -5.53194 q^{92} -1.44043 q^{93} -1.08716 q^{94} +0.444625 q^{95} -23.2580 q^{96} -19.4508 q^{97} -4.67455 q^{98} +4.15428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * 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 $

$2$	2.74444	1.94061	0.970305	−	0.241884i	$-0.0777653\pi$
$2$	2.74444	1.94061	0.970305	+	0.241884i	$0.0777653\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.53194	2.76597
$5$	0.0839771	0.0375557	0.0187779	−	0.999824i	$-0.494022\pi$
$5$	0.0839771	0.0375557	0.0187779	+	0.999824i	$0.494022\pi$
$6$	−2.74444	−1.12041
$7$	−2.30146	−0.869870	−0.434935	−	0.900462i	$-0.643229\pi$
$7$	−2.30146	−0.869870	−0.434935	+	0.900462i	$0.643229\pi$
$8$	9.69318	3.42706
$9$	1.00000	0.333333
$10$	0.230470	0.0728810
$11$	4.15428	1.25256	0.626281	−	0.779597i	$-0.284576\pi$
$11$	4.15428	1.25256	0.626281	+	0.779597i	$0.284576\pi$
$12$	−5.53194	−1.59693
$13$	−0.439258	−0.121828	−0.0609141	−	0.998143i	$-0.519402\pi$
$13$	−0.439258	−0.121828	−0.0609141	+	0.998143i	$0.519402\pi$
$14$	−6.31621	−1.68808
$15$	−0.0839771	−0.0216828
$16$	15.5385	3.88462
$17$	−0.388355	−0.0941900	−0.0470950	−	0.998890i	$-0.514996\pi$
$17$	−0.388355	−0.0941900	−0.0470950	+	0.998890i	$0.514996\pi$
$18$	2.74444	0.646870
$19$	5.29460	1.21466	0.607332	−	0.794448i	$-0.292240\pi$
$19$	5.29460	1.21466	0.607332	+	0.794448i	$0.292240\pi$
$20$	0.464556	0.103878
$21$	2.30146	0.502220
$22$	11.4012	2.43073
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−9.69318	−1.97861
$25$	−4.99295	−0.998590
$26$	−1.20552	−0.236421
$27$	−1.00000	−0.192450
$28$	−12.7315	−2.40603
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.230470	−0.0420779
$31$	1.44043	0.258710	0.129355	−	0.991598i	$-0.458709\pi$
$31$	1.44043	0.258710	0.129355	+	0.991598i	$0.458709\pi$
$32$	23.2580	4.11147
$33$	−4.15428	−0.723167
$34$	−1.06582	−0.182786
$35$	−0.193270	−0.0326686
$36$	5.53194	0.921990
$37$	9.04387	1.48680	0.743402	−	0.668845i	$-0.233211\pi$
$37$	9.04387	1.48680	0.743402	+	0.668845i	$0.233211\pi$
$38$	14.5307	2.35719
$39$	0.439258	0.0703375
$40$	0.814006	0.128706
$41$	−0.159033	−0.0248367	−0.0124184	−	0.999923i	$-0.503953\pi$
$41$	−0.159033	−0.0248367	−0.0124184	+	0.999923i	$0.503953\pi$
$42$	6.31621	0.974613
$43$	−6.03876	−0.920902	−0.460451	−	0.887685i	$-0.652312\pi$
$43$	−6.03876	−0.920902	−0.460451	+	0.887685i	$0.652312\pi$
$44$	22.9812	3.46455
$45$	0.0839771	0.0125186
$46$	−2.74444	−0.404645
$47$	−0.396132	−0.0577817	−0.0288909	−	0.999583i	$-0.509198\pi$
$47$	−0.396132	−0.0577817	−0.0288909	+	0.999583i	$0.509198\pi$
$48$	−15.5385	−2.24278
$49$	−1.70328	−0.243326
$50$	−13.7028	−1.93787
$51$	0.388355	0.0543806
$52$	−2.42995	−0.336973
$53$	2.43614	0.334630	0.167315	−	0.985903i	$-0.446490\pi$
$53$	2.43614	0.334630	0.167315	+	0.985903i	$0.446490\pi$
$54$	−2.74444	−0.373471
$55$	0.348864	0.0470408
$56$	−22.3085	−2.98109
$57$	−5.29460	−0.701286
$58$	2.74444	0.360362
$59$	−4.08958	−0.532418	−0.266209	−	0.963915i	$-0.585771\pi$
$59$	−4.08958	−0.532418	−0.266209	+	0.963915i	$0.585771\pi$
$60$	−0.464556	−0.0599739
$61$	9.28497	1.18882	0.594409	−	0.804163i	$-0.297386\pi$
$61$	9.28497	1.18882	0.594409	+	0.804163i	$0.297386\pi$
$62$	3.95318	0.502054
$63$	−2.30146	−0.289957
$64$	32.7531	4.09414
$65$	−0.0368876	−0.00457534
$66$	−11.4012	−1.40339
$67$	4.55339	0.556285	0.278143	−	0.960540i	$-0.410281\pi$
$67$	4.55339	0.556285	0.278143	+	0.960540i	$0.410281\pi$
$68$	−2.14836	−0.260527
$69$	1.00000	0.120386
$70$	−0.530417	−0.0633970
$71$	−3.85137	−0.457074	−0.228537	−	0.973535i	$-0.573394\pi$
$71$	−3.85137	−0.457074	−0.228537	+	0.973535i	$0.573394\pi$
$72$	9.69318	1.14235
$73$	0.0113549	0.00132899	0.000664497	−	1.00000i	$-0.499788\pi$
$73$	0.0113549	0.00132899	0.000664497		1.00000i	$0.499788\pi$
$74$	24.8203	2.88531
$75$	4.99295	0.576536
$76$	29.2894	3.35972
$77$	−9.56090	−1.08957
$78$	1.20552	0.136498
$79$	9.57510	1.07728	0.538641	−	0.842535i	$-0.318938\pi$
$79$	9.57510	1.07728	0.538641	+	0.842535i	$0.318938\pi$
$80$	1.30488	0.145889
$81$	1.00000	0.111111
$82$	−0.436455	−0.0481984
$83$	−5.55983	−0.610271	−0.305136	−	0.952309i	$-0.598702\pi$
$83$	−5.55983	−0.610271	−0.305136	+	0.952309i	$0.598702\pi$
$84$	12.7315	1.38912
$85$	−0.0326130	−0.00353737
$86$	−16.5730	−1.78711
$87$	−1.00000	−0.107211
$88$	40.2682	4.29260
$89$	−4.02316	−0.426454	−0.213227	−	0.977003i	$-0.568397\pi$
$89$	−4.02316	−0.426454	−0.213227	+	0.977003i	$0.568397\pi$
$90$	0.230470	0.0242937
$91$	1.01093	0.105975
$92$	−5.53194	−0.576744
$93$	−1.44043	−0.149366
$94$	−1.08716	−0.112132
$95$	0.444625	0.0456175
$96$	−23.2580	−2.37376
$97$	−19.4508	−1.97493	−0.987463	−	0.157853i	$-0.949543\pi$
$97$	−19.4508	−1.97493	−0.987463	+	0.157853i	$0.949543\pi$
$98$	−4.67455	−0.472201
$99$	4.15428	0.417521
$100$	−27.6207	−2.76207
$101$	−14.1145	−1.40444	−0.702220	−	0.711960i	$-0.747808\pi$
$101$	−14.1145	−1.40444	−0.702220	+	0.711960i	$0.747808\pi$
$102$	1.06582	0.105532
$103$	−6.05489	−0.596606	−0.298303	−	0.954471i	$-0.596421\pi$
$103$	−6.05489	−0.596606	−0.298303	+	0.954471i	$0.596421\pi$
$104$	−4.25780	−0.417512
$105$	0.193270	0.0188612
$106$	6.68584	0.649386
$107$	−5.56190	−0.537689	−0.268845	−	0.963184i	$-0.586642\pi$
$107$	−5.56190	−0.537689	−0.268845	+	0.963184i	$0.586642\pi$
$108$	−5.53194	−0.532311
$109$	0.180138	0.0172541	0.00862706	−	0.999963i	$-0.497254\pi$
$109$	0.180138	0.0172541	0.00862706	+	0.999963i	$0.497254\pi$
$110$	0.957436	0.0912879
$111$	−9.04387	−0.858406
$112$	−35.7611	−3.37911
$113$	8.51126	0.800672	0.400336	−	0.916368i	$-0.368893\pi$
$113$	8.51126	0.800672	0.400336	+	0.916368i	$0.368893\pi$
$114$	−14.5307	−1.36092
$115$	−0.0839771	−0.00783091
$116$	5.53194	0.513628
$117$	−0.439258	−0.0406094
$118$	−11.2236	−1.03322
$119$	0.893784	0.0819330
$120$	−0.814006	−0.0743082
$121$	6.25802	0.568911
$122$	25.4820	2.30703
$123$	0.159033	0.0143395
$124$	7.96839	0.715583
$125$	−0.839179	−0.0750584
$126$	−6.31621	−0.562693
$127$	−16.5892	−1.47205	−0.736025	−	0.676954i	$-0.763299\pi$
$127$	−16.5892	−1.47205	−0.736025	+	0.676954i	$0.763299\pi$
$128$	43.3730	3.83367
$129$	6.03876	0.531683
$130$	−0.101236	−0.00887896
$131$	−7.62105	−0.665854	−0.332927	−	0.942953i	$-0.608036\pi$
$131$	−7.62105	−0.665854	−0.332927	+	0.942953i	$0.608036\pi$
$132$	−22.9812	−2.00026
$133$	−12.1853	−1.05660
$134$	12.4965	1.07953
$135$	−0.0839771	−0.00722760
$136$	−3.76440	−0.322795
$137$	9.11641	0.778868	0.389434	−	0.921054i	$-0.372671\pi$
$137$	9.11641	0.778868	0.389434	+	0.921054i	$0.372671\pi$
$138$	2.74444	0.233622
$139$	−0.0164781	−0.00139765	−0.000698827	−	1.00000i	$-0.500222\pi$
$139$	−0.0164781	−0.00139765	−0.000698827		1.00000i	$0.500222\pi$
$140$	−1.06916	−0.0903603
$141$	0.396132	0.0333603
$142$	−10.5699	−0.887002
$143$	−1.82480	−0.152597
$144$	15.5385	1.29487
$145$	0.0839771	0.00697392
$146$	0.0311629	0.00257906
$147$	1.70328	0.140484
$148$	50.0301	4.11245
$149$	−15.3748	−1.25955	−0.629775	−	0.776777i	$-0.716853\pi$
$149$	−15.3748	−1.25955	−0.629775	+	0.776777i	$0.716853\pi$
$150$	13.7028	1.11883
$151$	−10.3617	−0.843225	−0.421613	−	0.906776i	$-0.638536\pi$
$151$	−10.3617	−0.843225	−0.421613	+	0.906776i	$0.638536\pi$
$152$	51.3215	4.16272
$153$	−0.388355	−0.0313967
$154$	−26.2393	−2.11442
$155$	0.120963	0.00971602
$156$	2.42995	0.194551
$157$	−0.319033	−0.0254616	−0.0127308	−	0.999919i	$-0.504052\pi$
$157$	−0.319033	−0.0254616	−0.0127308	+	0.999919i	$0.504052\pi$
$158$	26.2783	2.09059
$159$	−2.43614	−0.193199
$160$	1.95314	0.154409
$161$	2.30146	0.181380
$162$	2.74444	0.215623
$163$	18.6190	1.45835	0.729176	−	0.684327i	$-0.239904\pi$
$163$	18.6190	1.45835	0.729176	+	0.684327i	$0.239904\pi$
$164$	−0.879758	−0.0686976
$165$	−0.348864	−0.0271590
$166$	−15.2586	−1.18430
$167$	−20.0675	−1.55287	−0.776435	−	0.630197i	$-0.782974\pi$
$167$	−20.0675	−1.55287	−0.776435	+	0.630197i	$0.782974\pi$
$168$	22.3085	1.72114
$169$	−12.8071	−0.985158
$170$	−0.0895042	−0.00686466
$171$	5.29460	0.404888
$172$	−33.4060	−2.54719
$173$	−14.5928	−1.10947	−0.554736	−	0.832027i	$-0.687181\pi$
$173$	−14.5928	−1.10947	−0.554736	+	0.832027i	$0.687181\pi$
$174$	−2.74444	−0.208055
$175$	11.4911	0.868643
$176$	64.5511	4.86572
$177$	4.08958	0.307392
$178$	−11.0413	−0.827581
$179$	20.7807	1.55322	0.776612	−	0.629979i	$-0.216937\pi$
$179$	20.7807	1.55322	0.776612	+	0.629979i	$0.216937\pi$
$180$	0.464556	0.0346260
$181$	−4.46140	−0.331613	−0.165806	−	0.986158i	$-0.553023\pi$
$181$	−4.46140	−0.331613	−0.165806	+	0.986158i	$0.553023\pi$
$182$	2.77444	0.205655
$183$	−9.28497	−0.686365
$184$	−9.69318	−0.714591
$185$	0.759478	0.0558379
$186$	−3.95318	−0.289861
$187$	−1.61334	−0.117979
$188$	−2.19137	−0.159822
$189$	2.30146	0.167407
$190$	1.22025	0.0885259
$191$	16.4833	1.19269	0.596346	−	0.802727i	$-0.296618\pi$
$191$	16.4833	1.19269	0.596346	+	0.802727i	$0.296618\pi$
$192$	−32.7531	−2.36375
$193$	−6.03329	−0.434286	−0.217143	−	0.976140i	$-0.569674\pi$
$193$	−6.03329	−0.434286	−0.217143	+	0.976140i	$0.569674\pi$
$194$	−53.3814	−3.83256
$195$	0.0368876	0.00264157
$196$	−9.42246	−0.673033
$197$	18.4203	1.31239	0.656197	−	0.754590i	$-0.272164\pi$
$197$	18.4203	1.31239	0.656197	+	0.754590i	$0.272164\pi$
$198$	11.4012	0.810245
$199$	−22.7882	−1.61542	−0.807708	−	0.589583i	$-0.799292\pi$
$199$	−22.7882	−1.61542	−0.807708	+	0.589583i	$0.799292\pi$
$200$	−48.3976	−3.42222
$201$	−4.55339	−0.321171
$202$	−38.7362	−2.72547
$203$	−2.30146	−0.161531
$204$	2.14836	0.150415
$205$	−0.0133551	−0.000932760 0
$206$	−16.6173	−1.15778
$207$	−1.00000	−0.0695048
$208$	−6.82539	−0.473255
$209$	21.9952	1.52144
$210$	0.530417	0.0366023
$211$	1.48145	0.101987	0.0509934	−	0.998699i	$-0.483761\pi$
$211$	1.48145	0.101987	0.0509934	+	0.998699i	$0.483761\pi$
$212$	13.4766	0.925576
$213$	3.85137	0.263892
$214$	−15.2643	−1.04345
$215$	−0.507117	−0.0345851
$216$	−9.69318	−0.659538
$217$	−3.31510	−0.225044
$218$	0.494378	0.0334835
$219$	−0.0113549	−0.000767296 0
$220$	1.92990	0.130114
$221$	0.170588	0.0114750
$222$	−24.8203	−1.66583
$223$	−23.0654	−1.54457	−0.772287	−	0.635274i	$-0.780887\pi$
$223$	−23.0654	−1.54457	−0.772287	+	0.635274i	$0.780887\pi$
$224$	−53.5273	−3.57644
$225$	−4.99295	−0.332863
$226$	23.3586	1.55379
$227$	13.2378	0.878621	0.439311	−	0.898335i	$-0.355223\pi$
$227$	13.2378	0.878621	0.439311	+	0.898335i	$0.355223\pi$
$228$	−29.2894	−1.93974
$229$	16.6610	1.10099	0.550496	−	0.834838i	$-0.314439\pi$
$229$	16.6610	1.10099	0.550496	+	0.834838i	$0.314439\pi$
$230$	−0.230470	−0.0151967
$231$	9.56090	0.629061
$232$	9.69318	0.636389
$233$	−13.4436	−0.880717	−0.440359	−	0.897822i	$-0.645149\pi$
$233$	−13.4436	−0.880717	−0.440359	+	0.897822i	$0.645149\pi$
$234$	−1.20552	−0.0788070
$235$	−0.0332660	−0.00217003
$236$	−22.6233	−1.47265
$237$	−9.57510	−0.621970
$238$	2.45293	0.159000
$239$	−7.56856	−0.489570	−0.244785	−	0.969577i	$-0.578717\pi$
$239$	−7.56856	−0.489570	−0.244785	+	0.969577i	$0.578717\pi$
$240$	−1.30488	−0.0842293
$241$	−18.2121	−1.17314	−0.586572	−	0.809897i	$-0.699523\pi$
$241$	−18.2121	−1.17314	−0.586572	+	0.809897i	$0.699523\pi$
$242$	17.1748	1.10403
$243$	−1.00000	−0.0641500
$244$	51.3639	3.28823
$245$	−0.143037	−0.00913829
$246$	0.436455	0.0278274
$247$	−2.32569	−0.147980
$248$	13.9624	0.886613
$249$	5.55983	0.352340
$250$	−2.30307	−0.145659
$251$	19.0091	1.19984	0.599921	−	0.800059i	$-0.295199\pi$
$251$	19.0091	1.19984	0.599921	+	0.800059i	$0.295199\pi$
$252$	−12.7315	−0.802011
$253$	−4.15428	−0.261177
$254$	−45.5279	−2.85668
$255$	0.0326130	0.00204230
$256$	53.5282	3.34551
$257$	−22.6564	−1.41327	−0.706635	−	0.707579i	$-0.749788\pi$
$257$	−22.6564	−1.41327	−0.706635	+	0.707579i	$0.749788\pi$
$258$	16.5730	1.03179
$259$	−20.8141	−1.29333
$260$	−0.204060	−0.0126553
$261$	1.00000	0.0618984
$262$	−20.9155	−1.29216
$263$	−0.221663	−0.0136683	−0.00683416	−	0.999977i	$-0.502175\pi$
$263$	−0.221663	−0.0136683	−0.00683416	+	0.999977i	$0.502175\pi$
$264$	−40.2682	−2.47833
$265$	0.204580	0.0125673
$266$	−33.4418	−2.05045
$267$	4.02316	0.246213
$268$	25.1891	1.53867
$269$	6.77287	0.412949	0.206475	−	0.978452i	$-0.433801\pi$
$269$	6.77287	0.412949	0.206475	+	0.978452i	$0.433801\pi$
$270$	−0.230470	−0.0140260
$271$	31.0475	1.88600	0.943001	−	0.332790i	$-0.107990\pi$
$271$	31.0475	1.88600	0.943001	+	0.332790i	$0.107990\pi$
$272$	−6.03444	−0.365892
$273$	−1.01093	−0.0611845
$274$	25.0194	1.51148
$275$	−20.7421	−1.25080
$276$	5.53194	0.332984
$277$	−15.8947	−0.955018	−0.477509	−	0.878627i	$-0.658460\pi$
$277$	−15.8947	−0.955018	−0.477509	+	0.878627i	$0.658460\pi$
$278$	−0.0452231	−0.00271230
$279$	1.44043	0.0862365
$280$	−1.87340	−0.111957
$281$	4.24811	0.253421	0.126711	−	0.991940i	$-0.459558\pi$
$281$	4.24811	0.253421	0.126711	+	0.991940i	$0.459558\pi$
$282$	1.08716	0.0647393
$283$	25.7398	1.53007	0.765036	−	0.643987i	$-0.222721\pi$
$283$	25.7398	1.53007	0.765036	+	0.643987i	$0.222721\pi$
$284$	−21.3056	−1.26425
$285$	−0.444625	−0.0263373
$286$	−5.00804	−0.296132
$287$	0.366007	0.0216047
$288$	23.2580	1.37049
$289$	−16.8492	−0.991128
$290$	0.230470	0.0135337
$291$	19.4508	1.14022
$292$	0.0628148	0.00367596
$293$	−6.52744	−0.381337	−0.190669	−	0.981654i	$-0.561066\pi$
$293$	−6.52744	−0.381337	−0.190669	+	0.981654i	$0.561066\pi$
$294$	4.67455	0.272626
$295$	−0.343431	−0.0199953
$296$	87.6639	5.09536
$297$	−4.15428	−0.241056
$298$	−42.1951	−2.44430
$299$	0.439258	0.0254029
$300$	27.6207	1.59468
$301$	13.8980	0.801065
$302$	−28.4371	−1.63637
$303$	14.1145	0.810854
$304$	82.2699	4.71850
$305$	0.779725	0.0446469
$306$	−1.06582	−0.0609287
$307$	16.3947	0.935695	0.467847	−	0.883809i	$-0.345030\pi$
$307$	16.3947	0.935695	0.467847	+	0.883809i	$0.345030\pi$
$308$	−52.8903	−3.01371
$309$	6.05489	0.344450
$310$	0.331977	0.0188550
$311$	−6.55243	−0.371554	−0.185777	−	0.982592i	$-0.559480\pi$
$311$	−6.55243	−0.371554	−0.185777	+	0.982592i	$0.559480\pi$
$312$	4.25780	0.241051
$313$	−25.1852	−1.42355	−0.711776	−	0.702406i	$-0.752109\pi$
$313$	−25.1852	−1.42355	−0.711776	+	0.702406i	$0.752109\pi$
$314$	−0.875566	−0.0494111
$315$	−0.193270	−0.0108895
$316$	52.9689	2.97973
$317$	30.9737	1.73965	0.869827	−	0.493357i	$-0.164230\pi$
$317$	30.9737	1.73965	0.869827	+	0.493357i	$0.164230\pi$
$318$	−6.68584	−0.374923
$319$	4.15428	0.232595
$320$	2.75051	0.153758
$321$	5.56190	0.310435
$322$	6.31621	0.351989
$323$	−2.05618	−0.114409
$324$	5.53194	0.307330
$325$	2.19319	0.121656
$326$	51.0986	2.83009
$327$	−0.180138	−0.00996167
$328$	−1.54153	−0.0851169
$329$	0.911681	0.0502626
$330$	−0.957436	−0.0527051
$331$	20.0846	1.10395	0.551973	−	0.833862i	$-0.313875\pi$
$331$	20.0846	1.10395	0.551973	+	0.833862i	$0.313875\pi$
$332$	−30.7567	−1.68799
$333$	9.04387	0.495601
$334$	−55.0740	−3.01352
$335$	0.382381	0.0208917
$336$	35.7611	1.95093
$337$	−11.5444	−0.628864	−0.314432	−	0.949280i	$-0.601814\pi$
$337$	−11.5444	−0.628864	−0.314432	+	0.949280i	$0.601814\pi$
$338$	−35.1482	−1.91181
$339$	−8.51126	−0.462268
$340$	−0.180413	−0.00978426
$341$	5.98396	0.324050
$342$	14.5307	0.785730
$343$	20.0303	1.08153
$344$	−58.5348	−3.15598
$345$	0.0839771	0.00452118
$346$	−40.0491	−2.15305
$347$	26.3029	1.41202	0.706008	−	0.708204i	$-0.250494\pi$
$347$	26.3029	1.41202	0.706008	+	0.708204i	$0.250494\pi$
$348$	−5.53194	−0.296543
$349$	−1.41214	−0.0755899	−0.0377949	−	0.999286i	$-0.512033\pi$
$349$	−1.41214	−0.0755899	−0.0377949	+	0.999286i	$0.512033\pi$
$350$	31.5365	1.68570
$351$	0.439258	0.0234458
$352$	96.6201	5.14987
$353$	−14.2825	−0.760182	−0.380091	−	0.924949i	$-0.624107\pi$
$353$	−14.2825	−0.760182	−0.380091	+	0.924949i	$0.624107\pi$
$354$	11.2236	0.596527
$355$	−0.323427	−0.0171657
$356$	−22.2559	−1.17956
$357$	−0.893784	−0.0473041
$358$	57.0314	3.01420
$359$	12.7403	0.672408	0.336204	−	0.941789i	$-0.390857\pi$
$359$	12.7403	0.672408	0.336204	+	0.941789i	$0.390857\pi$
$360$	0.814006	0.0429019
$361$	9.03274	0.475407
$362$	−12.2440	−0.643532
$363$	−6.25802	−0.328461
$364$	5.59242	0.293123
$365$	0.000953555 0	4.99113e−5 0
$366$	−25.4820	−1.33197
$367$	19.7406	1.03045	0.515224	−	0.857055i	$-0.327709\pi$
$367$	19.7406	1.03045	0.515224	+	0.857055i	$0.327709\pi$
$368$	−15.5385	−0.809998
$369$	−0.159033	−0.00827890
$370$	2.08434	0.108360
$371$	−5.60668	−0.291085
$372$	−7.96839	−0.413142
$373$	−12.0840	−0.625685	−0.312843	−	0.949805i	$-0.601281\pi$
$373$	−12.0840	−0.625685	−0.312843	+	0.949805i	$0.601281\pi$
$374$	−4.42770	−0.228951
$375$	0.839179	0.0433350
$376$	−3.83978	−0.198021
$377$	−0.439258	−0.0226229
$378$	6.31621	0.324871
$379$	9.89440	0.508241	0.254121	−	0.967173i	$-0.418214\pi$
$379$	9.89440	0.508241	0.254121	+	0.967173i	$0.418214\pi$
$380$	2.45964	0.126177
$381$	16.5892	0.849888
$382$	45.2375	2.31455
$383$	14.5063	0.741238	0.370619	−	0.928785i	$-0.379146\pi$
$383$	14.5063	0.741238	0.370619	+	0.928785i	$0.379146\pi$
$384$	−43.3730	−2.21337
$385$	−0.802897	−0.0409194
$386$	−16.5580	−0.842780
$387$	−6.03876	−0.306967
$388$	−107.600	−5.46258
$389$	−32.8023	−1.66314	−0.831571	−	0.555418i	$-0.812558\pi$
$389$	−32.8023	−1.66314	−0.831571	+	0.555418i	$0.812558\pi$
$390$	0.101236	0.00512627
$391$	0.388355	0.0196400
$392$	−16.5102	−0.833893
$393$	7.62105	0.384431
$394$	50.5534	2.54685
$395$	0.804089	0.0404581
$396$	22.9812	1.15485
$397$	−27.4361	−1.37698	−0.688489	−	0.725247i	$-0.741726\pi$
$397$	−27.4361	−1.37698	−0.688489	+	0.725247i	$0.741726\pi$
$398$	−62.5409	−3.13489
$399$	12.1853	0.610028
$400$	−77.5827	−3.87914
$401$	−2.77335	−0.138495	−0.0692473	−	0.997600i	$-0.522060\pi$
$401$	−2.77335	−0.138495	−0.0692473	+	0.997600i	$0.522060\pi$
$402$	−12.4965	−0.623269
$403$	−0.632721	−0.0315181
$404$	−78.0803	−3.88464
$405$	0.0839771	0.00417286
$406$	−6.31621	−0.313468
$407$	37.5707	1.86231
$408$	3.76440	0.186366
$409$	−3.98777	−0.197183	−0.0985914	−	0.995128i	$-0.531434\pi$
$409$	−3.98777	−0.197183	−0.0985914	+	0.995128i	$0.531434\pi$
$410$	−0.0366522	−0.00181012
$411$	−9.11641	−0.449679
$412$	−33.4953	−1.65019
$413$	9.41200	0.463134
$414$	−2.74444	−0.134882
$415$	−0.466899	−0.0229192
$416$	−10.2162	−0.500892
$417$	0.0164781	0.000806936 0
$418$	60.3645	2.95252
$419$	26.5230	1.29573	0.647867	−	0.761753i	$-0.275661\pi$
$419$	26.5230	1.29573	0.647867	+	0.761753i	$0.275661\pi$
$420$	1.06916	0.0521695
$421$	34.1443	1.66409	0.832046	−	0.554706i	$-0.187169\pi$
$421$	34.1443	1.66409	0.832046	+	0.554706i	$0.187169\pi$
$422$	4.06573	0.197917
$423$	−0.396132	−0.0192606
$424$	23.6140	1.14680
$425$	1.93904	0.0940571
$426$	10.5699	0.512111
$427$	−21.3690	−1.03412
$428$	−30.7681	−1.48723
$429$	1.82480	0.0881021
$430$	−1.39175	−0.0671162
$431$	32.0693	1.54472	0.772362	−	0.635183i	$-0.219075\pi$
$431$	32.0693	1.54472	0.772362	+	0.635183i	$0.219075\pi$
$432$	−15.5385	−0.747595
$433$	−18.9769	−0.911971	−0.455985	−	0.889987i	$-0.650713\pi$
$433$	−18.9769	−0.911971	−0.455985	+	0.889987i	$0.650713\pi$
$434$	−9.09809	−0.436722
$435$	−0.0839771	−0.00402639
$436$	0.996514	0.0477244
$437$	−5.29460	−0.253275
$438$	−0.0311629	−0.00148902
$439$	32.8955	1.57002	0.785008	−	0.619485i	$-0.212659\pi$
$439$	32.8955	1.57002	0.785008	+	0.619485i	$0.212659\pi$
$440$	3.38160	0.161212
$441$	−1.70328	−0.0811087
$442$	0.468168	0.0222685
$443$	34.0029	1.61553	0.807763	−	0.589507i	$-0.200678\pi$
$443$	34.0029	1.61553	0.807763	+	0.589507i	$0.200678\pi$
$444$	−50.0301	−2.37432
$445$	−0.337853	−0.0160158
$446$	−63.3015	−2.99741
$447$	15.3748	0.727202
$448$	−75.3800	−3.56137
$449$	−13.9903	−0.660244	−0.330122	−	0.943938i	$-0.607090\pi$
$449$	−13.9903	−0.660244	−0.330122	+	0.943938i	$0.607090\pi$
$450$	−13.7028	−0.645958
$451$	−0.660665	−0.0311095
$452$	47.0838	2.21463
$453$	10.3617	0.486836
$454$	36.3302	1.70506
$455$	0.0848953	0.00397995
$456$	−51.3215	−2.40335
$457$	−26.2419	−1.22755	−0.613773	−	0.789483i	$-0.710349\pi$
$457$	−26.2419	−1.22755	−0.613773	+	0.789483i	$0.710349\pi$
$458$	45.7251	2.13660
$459$	0.388355	0.0181269
$460$	−0.464556	−0.0216600
$461$	4.16446	0.193958	0.0969792	−	0.995286i	$-0.469082\pi$
$461$	4.16446	0.193958	0.0969792	+	0.995286i	$0.469082\pi$
$462$	26.2393	1.22076
$463$	−24.8490	−1.15483	−0.577415	−	0.816451i	$-0.695939\pi$
$463$	−24.8490	−1.15483	−0.577415	+	0.816451i	$0.695939\pi$
$464$	15.5385	0.721355
$465$	−0.120963	−0.00560955
$466$	−36.8950	−1.70913
$467$	−2.92425	−0.135318	−0.0676590	−	0.997709i	$-0.521553\pi$
$467$	−2.92425	−0.135318	−0.0676590	+	0.997709i	$0.521553\pi$
$468$	−2.42995	−0.112324
$469$	−10.4794	−0.483896
$470$	−0.0912964	−0.00421119
$471$	0.319033	0.0147003
$472$	−39.6410	−1.82463
$473$	−25.0867	−1.15349
$474$	−26.2783	−1.20700
$475$	−26.4356	−1.21295
$476$	4.94436	0.226624
$477$	2.43614	0.111543
$478$	−20.7714	−0.950064
$479$	6.71092	0.306630	0.153315	−	0.988177i	$-0.451005\pi$
$479$	6.71092	0.306630	0.153315	+	0.988177i	$0.451005\pi$
$480$	−1.95314	−0.0891481
$481$	−3.97259	−0.181134
$482$	−49.9820	−2.27662
$483$	−2.30146	−0.104720
$484$	34.6190	1.57359
$485$	−1.63342	−0.0741697
$486$	−2.74444	−0.124490
$487$	15.1508	0.686550	0.343275	−	0.939235i	$-0.388464\pi$
$487$	15.1508	0.686550	0.343275	+	0.939235i	$0.388464\pi$
$488$	90.0009	4.07415
$489$	−18.6190	−0.841980
$490$	−0.392556	−0.0177339
$491$	−14.6498	−0.661136	−0.330568	−	0.943782i	$-0.607240\pi$
$491$	−14.6498	−0.661136	−0.330568	+	0.943782i	$0.607240\pi$
$492$	0.879758	0.0396626
$493$	−0.388355	−0.0174906
$494$	−6.38271	−0.287172
$495$	0.348864	0.0156803
$496$	22.3821	1.00499
$497$	8.86378	0.397595
$498$	15.2586	0.683755
$499$	−12.3563	−0.553143	−0.276572	−	0.960993i	$-0.589198\pi$
$499$	−12.3563	−0.553143	−0.276572	+	0.960993i	$0.589198\pi$
$500$	−4.64229	−0.207609
$501$	20.0675	0.896550
$502$	52.1692	2.32843
$503$	−15.4559	−0.689144	−0.344572	−	0.938760i	$-0.611976\pi$
$503$	−15.4559	−0.689144	−0.344572	+	0.938760i	$0.611976\pi$
$504$	−22.3085	−0.993698
$505$	−1.18529	−0.0527448
$506$	−11.4012	−0.506843
$507$	12.8071	0.568781
$508$	−91.7702	−4.07164
$509$	38.3172	1.69838	0.849190	−	0.528087i	$-0.177091\pi$
$509$	38.3172	1.69838	0.849190	+	0.528087i	$0.177091\pi$
$510$	0.0895042	0.00396331
$511$	−0.0261329	−0.00115605
$512$	60.1588	2.65867
$513$	−5.29460	−0.233762
$514$	−62.1792	−2.74261
$515$	−0.508472	−0.0224059
$516$	33.4060	1.47062
$517$	−1.64564	−0.0723752
$518$	−57.1230	−2.50984
$519$	14.5928	0.640553
$520$	−0.357558	−0.0156800
$521$	33.0818	1.44934	0.724670	−	0.689096i	$-0.241992\pi$
$521$	33.0818	1.44934	0.724670	+	0.689096i	$0.241992\pi$
$522$	2.74444	0.120121
$523$	−33.4006	−1.46051	−0.730253	−	0.683176i	$-0.760598\pi$
$523$	−33.4006	−1.46051	−0.730253	+	0.683176i	$0.760598\pi$
$524$	−42.1592	−1.84173
$525$	−11.4911	−0.501511
$526$	−0.608340	−0.0265249
$527$	−0.559400	−0.0243679
$528$	−64.5511	−2.80923
$529$	1.00000	0.0434783
$530$	0.561458	0.0243882
$531$	−4.08958	−0.177473
$532$	−67.4083	−2.92252
$533$	0.0698563	0.00302581
$534$	11.0413	0.477804
$535$	−0.467072	−0.0201933
$536$	44.1369	1.90642
$537$	−20.7807	−0.896754
$538$	18.5877	0.801374
$539$	−7.07591	−0.304781
$540$	−0.464556	−0.0199913
$541$	−10.7021	−0.460117	−0.230059	−	0.973177i	$-0.573892\pi$
$541$	−10.7021	−0.460117	−0.230059	+	0.973177i	$0.573892\pi$
$542$	85.2080	3.66000
$543$	4.46140	0.191457
$544$	−9.03236	−0.387259
$545$	0.0151275	0.000647991 0
$546$	−2.77444	−0.118735
$547$	−35.8489	−1.53279	−0.766395	−	0.642370i	$-0.777951\pi$
$547$	−35.8489	−1.53279	−0.766395	+	0.642370i	$0.777951\pi$
$548$	50.4314	2.15432
$549$	9.28497	0.396273
$550$	−56.9254	−2.42731
$551$	5.29460	0.225557
$552$	9.69318	0.412569
$553$	−22.0367	−0.937096
$554$	−43.6219	−1.85332
$555$	−0.759478	−0.0322380
$556$	−0.0911559	−0.00386587
$557$	−25.0458	−1.06123	−0.530613	−	0.847614i	$-0.678038\pi$
$557$	−25.0458	−1.06123	−0.530613	+	0.847614i	$0.678038\pi$
$558$	3.95318	0.167351
$559$	2.65257	0.112192
$560$	−3.00312	−0.126905
$561$	1.61334	0.0681151
$562$	11.6587	0.491792
$563$	−20.8013	−0.876668	−0.438334	−	0.898812i	$-0.644431\pi$
$563$	−20.8013	−0.876668	−0.438334	+	0.898812i	$0.644431\pi$
$564$	2.19137	0.0922735
$565$	0.714751	0.0300698
$566$	70.6413	2.96927
$567$	−2.30146	−0.0966522
$568$	−37.3321	−1.56642
$569$	21.0178	0.881111	0.440556	−	0.897725i	$-0.354781\pi$
$569$	21.0178	0.881111	0.440556	+	0.897725i	$0.354781\pi$
$570$	−1.22025	−0.0511104
$571$	−8.08678	−0.338421	−0.169211	−	0.985580i	$-0.554122\pi$
$571$	−8.08678	−0.338421	−0.169211	+	0.985580i	$0.554122\pi$
$572$	−10.0947	−0.422079
$573$	−16.4833	−0.688602
$574$	1.00448	0.0419263
$575$	4.99295	0.208220
$576$	32.7531	1.36471
$577$	−5.09269	−0.212012	−0.106006	−	0.994366i	$-0.533806\pi$
$577$	−5.09269	−0.212012	−0.106006	+	0.994366i	$0.533806\pi$
$578$	−46.2415	−1.92339
$579$	6.03329	0.250735
$580$	0.464556	0.0192896
$581$	12.7957	0.530856
$582$	53.3814	2.21273
$583$	10.1204	0.419145
$584$	0.110065	0.00455454
$585$	−0.0368876	−0.00152511
$586$	−17.9142	−0.740027
$587$	−21.0953	−0.870696	−0.435348	−	0.900262i	$-0.643375\pi$
$587$	−21.0953	−0.870696	−0.435348	+	0.900262i	$0.643375\pi$
$588$	9.42246	0.388576
$589$	7.62651	0.314245
$590$	−0.942525	−0.0388031
$591$	−18.4203	−0.757711
$592$	140.528	5.77566
$593$	16.2516	0.667372	0.333686	−	0.942684i	$-0.391707\pi$
$593$	16.2516	0.667372	0.333686	+	0.942684i	$0.391707\pi$
$594$	−11.4012	−0.467795
$595$	0.0750574	0.00307705
$596$	−85.0523	−3.48388
$597$	22.7882	0.932661
$598$	1.20552	0.0492972
$599$	−22.2935	−0.910889	−0.455445	−	0.890264i	$-0.650520\pi$
$599$	−22.2935	−0.910889	−0.455445	+	0.890264i	$0.650520\pi$
$600$	48.3976	1.97582
$601$	33.0543	1.34831	0.674156	−	0.738589i	$-0.264508\pi$
$601$	33.0543	1.34831	0.674156	+	0.738589i	$0.264508\pi$
$602$	38.1421	1.55455
$603$	4.55339	0.185428
$604$	−57.3204	−2.33234
$605$	0.525531	0.0213659
$606$	38.7362	1.57355
$607$	15.8841	0.644716	0.322358	−	0.946618i	$-0.395525\pi$
$607$	15.8841	0.644716	0.322358	+	0.946618i	$0.395525\pi$
$608$	123.142	4.99405
$609$	2.30146	0.0932599
$610$	2.13991	0.0866423
$611$	0.174004	0.00703944
$612$	−2.14836	−0.0868422
$613$	−13.7622	−0.555851	−0.277925	−	0.960603i	$-0.589647\pi$
$613$	−13.7622	−0.555851	−0.277925	+	0.960603i	$0.589647\pi$
$614$	44.9942	1.81582
$615$	0.0133551	0.000538529 0
$616$	−92.6756	−3.73401
$617$	19.1332	0.770274	0.385137	−	0.922859i	$-0.374154\pi$
$617$	19.1332	0.770274	0.385137	+	0.922859i	$0.374154\pi$
$618$	16.6173	0.668444
$619$	18.0073	0.723776	0.361888	−	0.932222i	$-0.382132\pi$
$619$	18.0073	0.723776	0.361888	+	0.932222i	$0.382132\pi$
$620$	0.669162	0.0268742
$621$	1.00000	0.0401286
$622$	−17.9827	−0.721042
$623$	9.25914	0.370959
$624$	6.82539	0.273234
$625$	24.8943	0.995771
$626$	−69.1193	−2.76256
$627$	−21.9952	−0.878404
$628$	−1.76487	−0.0704260
$629$	−3.51223	−0.140042
$630$	−0.530417	−0.0211323
$631$	19.2913	0.767973	0.383987	−	0.923339i	$-0.374551\pi$
$631$	19.2913	0.767973	0.383987	+	0.923339i	$0.374551\pi$
$632$	92.8132	3.69191
$633$	−1.48145	−0.0588822
$634$	85.0053	3.37599
$635$	−1.39311	−0.0552839
$636$	−13.4766	−0.534382
$637$	0.748180	0.0296440
$638$	11.4012	0.451376
$639$	−3.85137	−0.152358
$640$	3.64234	0.143976
$641$	−20.8851	−0.824913	−0.412457	−	0.910977i	$-0.635329\pi$
$641$	−20.8851	−0.824913	−0.412457	+	0.910977i	$0.635329\pi$
$642$	15.2643	0.602433
$643$	34.3708	1.35545	0.677725	−	0.735315i	$-0.262966\pi$
$643$	34.3708	1.35545	0.677725	+	0.735315i	$0.262966\pi$
$644$	12.7315	0.501693
$645$	0.507117	0.0199677
$646$	−5.64307	−0.222024
$647$	−2.96720	−0.116653	−0.0583263	−	0.998298i	$-0.518576\pi$
$647$	−2.96720	−0.116653	−0.0583263	+	0.998298i	$0.518576\pi$
$648$	9.69318	0.380784
$649$	−16.9892	−0.666886
$650$	6.01907	0.236088
$651$	3.31510	0.129929
$652$	102.999	4.03375
$653$	47.8737	1.87344	0.936722	−	0.350074i	$-0.113844\pi$
$653$	47.8737	1.87344	0.936722	+	0.350074i	$0.113844\pi$
$654$	−0.494378	−0.0193317
$655$	−0.639994	−0.0250066
$656$	−2.47112	−0.0964811
$657$	0.0113549	0.000442998 0
$658$	2.50205	0.0975401
$659$	−7.75068	−0.301923	−0.150962	−	0.988540i	$-0.548237\pi$
$659$	−7.75068	−0.301923	−0.150962	+	0.988540i	$0.548237\pi$
$660$	−1.92990	−0.0751211
$661$	−31.9075	−1.24106	−0.620529	−	0.784183i	$-0.713082\pi$
$661$	−31.9075	−1.24106	−0.620529	+	0.784183i	$0.713082\pi$
$662$	55.1208	2.14233
$663$	−0.170588	−0.00662509
$664$	−53.8925	−2.09143
$665$	−1.02329	−0.0396813
$666$	24.8203	0.961769
$667$	−1.00000	−0.0387202
$668$	−111.012	−4.29519
$669$	23.0654	0.891760
$670$	1.04942	0.0405426
$671$	38.5723	1.48907
$672$	53.5273	2.06486
$673$	−41.8507	−1.61323	−0.806613	−	0.591081i	$-0.798702\pi$
$673$	−41.8507	−1.61323	−0.806613	+	0.591081i	$0.798702\pi$
$674$	−31.6829	−1.22038
$675$	4.99295	0.192179
$676$	−70.8478	−2.72492
$677$	45.1097	1.73371	0.866854	−	0.498563i	$-0.166139\pi$
$677$	45.1097	1.73371	0.866854	+	0.498563i	$0.166139\pi$
$678$	−23.3586	−0.897083
$679$	44.7651	1.71793
$680$	−0.316123	−0.0121228
$681$	−13.2378	−0.507272
$682$	16.4226	0.628854
$683$	−3.91287	−0.149722	−0.0748609	−	0.997194i	$-0.523851\pi$
$683$	−3.91287	−0.149722	−0.0748609	+	0.997194i	$0.523851\pi$
$684$	29.2894	1.11991
$685$	0.765570	0.0292509
$686$	54.9718	2.09883
$687$	−16.6610	−0.635658
$688$	−93.8330	−3.57735
$689$	−1.07009	−0.0407673
$690$	0.230470	0.00877384
$691$	12.2317	0.465317	0.232659	−	0.972558i	$-0.425258\pi$
$691$	12.2317	0.465317	0.232659	+	0.972558i	$0.425258\pi$
$692$	−80.7265	−3.06876
$693$	−9.56090	−0.363189
$694$	72.1868	2.74017
$695$	−0.00138378	−5.24899e−5 0
$696$	−9.69318	−0.367419
$697$	0.0617611	0.00233937
$698$	−3.87552	−0.146691
$699$	13.4436	0.508482
$700$	63.5679	2.40264
$701$	21.6681	0.818391	0.409195	−	0.912447i	$-0.365809\pi$
$701$	21.6681	0.818391	0.409195	+	0.912447i	$0.365809\pi$
$702$	1.20552	0.0454992
$703$	47.8836	1.80597
$704$	136.066	5.12817
$705$	0.0332660	0.00125287
$706$	−39.1975	−1.47522
$707$	32.4838	1.22168
$708$	22.6233	0.850236
$709$	−6.77011	−0.254257	−0.127128	−	0.991886i	$-0.540576\pi$
$709$	−6.77011	−0.254257	−0.127128	+	0.991886i	$0.540576\pi$
$710$	−0.887625	−0.0333120
$711$	9.57510	0.359094
$712$	−38.9972	−1.46148
$713$	−1.44043	−0.0539447
$714$	−2.45293	−0.0917988
$715$	−0.153241	−0.00573090
$716$	114.958	4.29617
$717$	7.56856	0.282653
$718$	34.9650	1.30488
$719$	36.9817	1.37919	0.689593	−	0.724197i	$-0.257789\pi$
$719$	36.9817	1.37919	0.689593	+	0.724197i	$0.257789\pi$
$720$	1.30488	0.0486298
$721$	13.9351	0.518969
$722$	24.7898	0.922580
$723$	18.2121	0.677315
$724$	−24.6802	−0.917231
$725$	−4.99295	−0.185433
$726$	−17.1748	−0.637415
$727$	−11.5276	−0.427536	−0.213768	−	0.976884i	$-0.568574\pi$
$727$	−11.5276	−0.427536	−0.213768	+	0.976884i	$0.568574\pi$
$728$	9.79917	0.363181
$729$	1.00000	0.0370370
$730$	0.00261697	9.68585e−5 0
$731$	2.34518	0.0867397
$732$	−51.3639	−1.89846
$733$	−34.5558	−1.27635	−0.638174	−	0.769892i	$-0.720310\pi$
$733$	−34.5558	−1.27635	−0.638174	+	0.769892i	$0.720310\pi$
$734$	54.1767	1.99970
$735$	0.143037	0.00527599
$736$	−23.2580	−0.857300
$737$	18.9160	0.696782
$738$	−0.436455	−0.0160661
$739$	−11.0597	−0.406838	−0.203419	−	0.979092i	$-0.565205\pi$
$739$	−11.0597	−0.406838	−0.203419	+	0.979092i	$0.565205\pi$
$740$	4.20139	0.154446
$741$	2.32569	0.0854364
$742$	−15.3872	−0.564882
$743$	37.7977	1.38666	0.693331	−	0.720619i	$-0.256142\pi$
$743$	37.7977	1.38666	0.693331	+	0.720619i	$0.256142\pi$
$744$	−13.9624	−0.511886
$745$	−1.29113	−0.0473033
$746$	−33.1638	−1.21421
$747$	−5.55983	−0.203424
$748$	−8.92487	−0.326326
$749$	12.8005	0.467720
$750$	2.30307	0.0840964
$751$	−34.4216	−1.25606	−0.628032	−	0.778188i	$-0.716139\pi$
$751$	−34.4216	−1.25606	−0.628032	+	0.778188i	$0.716139\pi$
$752$	−6.15527	−0.224460
$753$	−19.0091	−0.692729
$754$	−1.20552	−0.0439023
$755$	−0.870148	−0.0316679
$756$	12.7315	0.463041
$757$	−31.9962	−1.16292	−0.581461	−	0.813574i	$-0.697519\pi$
$757$	−31.9962	−1.16292	−0.581461	+	0.813574i	$0.697519\pi$
$758$	27.1546	0.986298
$759$	4.15428	0.150791
$760$	4.30983	0.156334
$761$	−14.0910	−0.510800	−0.255400	−	0.966836i	$-0.582207\pi$
$761$	−14.0910	−0.510800	−0.255400	+	0.966836i	$0.582207\pi$
$762$	45.5279	1.64930
$763$	−0.414581	−0.0150088
$764$	91.1848	3.29895
$765$	−0.0326130	−0.00117912
$766$	39.8117	1.43845
$767$	1.79638	0.0648635
$768$	−53.5282	−1.93153
$769$	41.1134	1.48259	0.741294	−	0.671181i	$-0.234213\pi$
$769$	41.1134	1.48259	0.741294	+	0.671181i	$0.234213\pi$
$770$	−2.20350	−0.0794086
$771$	22.6564	0.815951
$772$	−33.3758	−1.20122
$773$	−21.0358	−0.756604	−0.378302	−	0.925682i	$-0.623492\pi$
$773$	−21.0358	−0.756604	−0.378302	+	0.925682i	$0.623492\pi$
$774$	−16.5730	−0.595704
$775$	−7.19201	−0.258345
$776$	−188.540	−6.76818
$777$	20.8141	0.746702
$778$	−90.0239	−3.22751
$779$	−0.842013	−0.0301682
$780$	0.204060	0.00730651
$781$	−15.9997	−0.572513
$782$	1.06582	0.0381135
$783$	−1.00000	−0.0357371
$784$	−26.4664	−0.945229
$785$	−0.0267915	−0.000956229 0
$786$	20.9155	0.746031
$787$	25.6134	0.913019	0.456510	−	0.889719i	$-0.349099\pi$
$787$	25.6134	0.913019	0.456510	+	0.889719i	$0.349099\pi$
$788$	101.900	3.63004
$789$	0.221663	0.00789141
$790$	2.20677	0.0785134
$791$	−19.5883	−0.696481
$792$	40.2682	1.43087
$793$	−4.07849	−0.144832
$794$	−75.2967	−2.67218
$795$	−0.204580	−0.00725571
$796$	−126.063	−4.46819
$797$	32.8527	1.16370	0.581851	−	0.813296i	$-0.302329\pi$
$797$	32.8527	1.16370	0.581851	+	0.813296i	$0.302329\pi$
$798$	33.4418	1.18383
$799$	0.153840	0.00544246
$800$	−116.126	−4.10567
$801$	−4.02316	−0.142151
$802$	−7.61130	−0.268764
$803$	0.0471716	0.00166465
$804$	−25.1891	−0.888350
$805$	0.193270	0.00681187
$806$	−1.73646	−0.0611644
$807$	−6.77287	−0.238416
$808$	−136.814	−4.81310
$809$	9.76643	0.343369	0.171685	−	0.985152i	$-0.445079\pi$
$809$	9.76643	0.343369	0.171685	+	0.985152i	$0.445079\pi$
$810$	0.230470	0.00809789
$811$	35.6839	1.25303	0.626516	−	0.779408i	$-0.284480\pi$
$811$	35.6839	1.25303	0.626516	+	0.779408i	$0.284480\pi$
$812$	−12.7315	−0.446789
$813$	−31.0475	−1.08888
$814$	103.111	3.61402
$815$	1.56357	0.0547694
$816$	6.03444	0.211248
$817$	−31.9728	−1.11859
$818$	−10.9442	−0.382655
$819$	1.01093	0.0353249
$820$	−0.0738796	−0.00257999
$821$	−49.2275	−1.71805	−0.859026	−	0.511931i	$-0.828930\pi$
$821$	−49.2275	−1.71805	−0.859026	+	0.511931i	$0.828930\pi$
$822$	−25.0194	−0.872653
$823$	30.5680	1.06553	0.532766	−	0.846263i	$-0.321153\pi$
$823$	30.5680	1.06553	0.532766	+	0.846263i	$0.321153\pi$
$824$	−58.6911	−2.04460
$825$	20.7421	0.722147
$826$	25.8307	0.898763
$827$	26.6441	0.926505	0.463253	−	0.886226i	$-0.346682\pi$
$827$	26.6441	0.926505	0.463253	+	0.886226i	$0.346682\pi$
$828$	−5.53194	−0.192248
$829$	15.9172	0.552828	0.276414	−	0.961039i	$-0.410854\pi$
$829$	15.9172	0.552828	0.276414	+	0.961039i	$0.410854\pi$
$830$	−1.28137	−0.0444772
$831$	15.8947	0.551380
$832$	−14.3871	−0.498782
$833$	0.661479	0.0229189
$834$	0.0452231	0.00156595
$835$	−1.68521	−0.0583191
$836$	121.676	4.20826
$837$	−1.44043	−0.0497887
$838$	72.7908	2.51452
$839$	17.3019	0.597328	0.298664	−	0.954358i	$-0.403459\pi$
$839$	17.3019	0.597328	0.298664	+	0.954358i	$0.403459\pi$
$840$	1.87340	0.0646385
$841$	1.00000	0.0344828
$842$	93.7070	3.22936
$843$	−4.24811	−0.146313
$844$	8.19526	0.282093
$845$	−1.07550	−0.0369983
$846$	−1.08716	−0.0373773
$847$	−14.4026	−0.494879
$848$	37.8539	1.29991
$849$	−25.7398	−0.883388
$850$	5.32157	0.182528
$851$	−9.04387	−0.310020
$852$	21.3056	0.729916
$853$	49.6636	1.70045	0.850224	−	0.526421i	$-0.176466\pi$
$853$	49.6636	1.70045	0.850224	+	0.526421i	$0.176466\pi$
$854$	−58.6458	−2.00682
$855$	0.444625	0.0152058
$856$	−53.9125	−1.84269
$857$	48.7452	1.66511	0.832553	−	0.553946i	$-0.186879\pi$
$857$	48.7452	1.66511	0.832553	+	0.553946i	$0.186879\pi$
$858$	5.00804	0.170972
$859$	−27.2365	−0.929298	−0.464649	−	0.885495i	$-0.653820\pi$
$859$	−27.2365	−0.929298	−0.464649	+	0.885495i	$0.653820\pi$
$860$	−2.80534	−0.0956614
$861$	−0.366007	−0.0124735
$862$	88.0122	2.99771
$863$	5.96572	0.203076	0.101538	−	0.994832i	$-0.467624\pi$
$863$	5.96572	0.203076	0.101538	+	0.994832i	$0.467624\pi$
$864$	−23.2580	−0.791252
$865$	−1.22546	−0.0416670
$866$	−52.0809	−1.76978
$867$	16.8492	0.572228
$868$	−18.3389	−0.622464
$869$	39.7776	1.34936
$870$	−0.230470	−0.00781366
$871$	−2.00011	−0.0677712
$872$	1.74611	0.0591309
$873$	−19.4508	−0.658308
$874$	−14.5307	−0.491508
$875$	1.93134	0.0652911
$876$	−0.0628148	−0.00212232
$877$	38.5251	1.30090	0.650450	−	0.759549i	$-0.274580\pi$
$877$	38.5251	1.30090	0.650450	+	0.759549i	$0.274580\pi$
$878$	90.2797	3.04679
$879$	6.52744	0.220165
$880$	5.42081	0.182736
$881$	−1.78900	−0.0602730	−0.0301365	−	0.999546i	$-0.509594\pi$
$881$	−1.78900	−0.0602730	−0.0301365	+	0.999546i	$0.509594\pi$
$882$	−4.67455	−0.157400
$883$	−44.6128	−1.50134	−0.750669	−	0.660678i	$-0.770269\pi$
$883$	−44.6128	−1.50134	−0.750669	+	0.660678i	$0.770269\pi$
$884$	0.943682	0.0317395
$885$	0.343431	0.0115443
$886$	93.3189	3.13511
$887$	14.6813	0.492950	0.246475	−	0.969149i	$-0.420728\pi$
$887$	14.6813	0.492950	0.246475	+	0.969149i	$0.420728\pi$
$888$	−87.6639	−2.94181
$889$	38.1793	1.28049
$890$	−0.927217	−0.0310804
$891$	4.15428	0.139174
$892$	−127.596	−4.27224
$893$	−2.09736	−0.0701853
$894$	42.1951	1.41122
$895$	1.74510	0.0583324
$896$	−99.8212	−3.33479
$897$	−0.439258	−0.0146664
$898$	−38.3956	−1.28128
$899$	1.44043	0.0480412
$900$	−27.6207	−0.920689
$901$	−0.946089	−0.0315188
$902$	−1.81316	−0.0603715
$903$	−13.8980	−0.462495
$904$	82.5012	2.74395
$905$	−0.374655	−0.0124540
$906$	28.4371	0.944760
$907$	−29.0029	−0.963027	−0.481513	−	0.876439i	$-0.659913\pi$
$907$	−29.0029	−0.963027	−0.481513	+	0.876439i	$0.659913\pi$
$908$	73.2305	2.43024
$909$	−14.1145	−0.468147
$910$	0.232990	0.00772354
$911$	−32.3586	−1.07209	−0.536044	−	0.844190i	$-0.680082\pi$
$911$	−32.3586	−1.07209	−0.536044	+	0.844190i	$0.680082\pi$
$912$	−82.2699	−2.72423
$913$	−23.0971	−0.764402
$914$	−72.0193	−2.38219
$915$	−0.779725	−0.0257769
$916$	92.1678	3.04531
$917$	17.5395	0.579207
$918$	1.06582	0.0351772
$919$	51.9475	1.71359	0.856795	−	0.515656i	$-0.172452\pi$
$919$	51.9475	1.71359	0.856795	+	0.515656i	$0.172452\pi$
$920$	−0.814006	−0.0268370
$921$	−16.3947	−0.540224
$922$	11.4291	0.376398
$923$	1.69174	0.0556844
$924$	52.8903	1.73996
$925$	−45.1556	−1.48471
$926$	−68.1965	−2.24108
$927$	−6.05489	−0.198869
$928$	23.2580	0.763480
$929$	13.1004	0.429809	0.214904	−	0.976635i	$-0.431056\pi$
$929$	13.1004	0.429809	0.214904	+	0.976635i	$0.431056\pi$
$930$	−0.331977	−0.0108859
$931$	−9.01820	−0.295559
$932$	−74.3690	−2.43604
$933$	6.55243	0.214517
$934$	−8.02541	−0.262599
$935$	−0.135483	−0.00443078
$936$	−4.25780	−0.139171
$937$	13.1382	0.429205	0.214602	−	0.976701i	$-0.431154\pi$
$937$	13.1382	0.429205	0.214602	+	0.976701i	$0.431154\pi$
$938$	−28.7602	−0.939053
$939$	25.1852	0.821889
$940$	−0.184025	−0.00600224
$941$	34.5161	1.12519	0.562596	−	0.826732i	$-0.309803\pi$
$941$	34.5161	1.12519	0.562596	+	0.826732i	$0.309803\pi$
$942$	0.875566	0.0285275
$943$	0.159033	0.00517881
$944$	−63.5458	−2.06824
$945$	0.193270	0.00628707
$946$	−68.8488	−2.23847
$947$	1.49916	0.0487161	0.0243581	−	0.999703i	$-0.492246\pi$
$947$	1.49916	0.0487161	0.0243581	+	0.999703i	$0.492246\pi$
$948$	−52.9689	−1.72035
$949$	−0.00498774	−0.000161909 0
$950$	−72.5510	−2.35386
$951$	−30.9737	−1.00439
$952$	8.66361	0.280789
$953$	−34.1120	−1.10499	−0.552497	−	0.833515i	$-0.686325\pi$
$953$	−34.1120	−1.10499	−0.552497	+	0.833515i	$0.686325\pi$
$954$	6.68584	0.216462
$955$	1.38422	0.0447924
$956$	−41.8688	−1.35413
$957$	−4.15428	−0.134289
$958$	18.4177	0.595049
$959$	−20.9811	−0.677514
$960$	−2.75051	−0.0887724
$961$	−28.9252	−0.933069
$962$	−10.9025	−0.351511
$963$	−5.56190	−0.179230
$964$	−100.748	−3.24488
$965$	−0.506658	−0.0163099
$966$	−6.31621	−0.203221
$967$	5.38589	0.173199	0.0865993	−	0.996243i	$-0.472400\pi$
$967$	5.38589	0.173199	0.0865993	+	0.996243i	$0.472400\pi$
$968$	60.6602	1.94969
$969$	2.05618	0.0660541
$970$	−4.48281	−0.143935
$971$	−28.2316	−0.905994	−0.452997	−	0.891512i	$-0.649645\pi$
$971$	−28.2316	−0.905994	−0.452997	+	0.891512i	$0.649645\pi$
$972$	−5.53194	−0.177437
$973$	0.0379237	0.00121578
$974$	41.5805	1.33233
$975$	−2.19319	−0.0702383
$976$	144.274	4.61810
$977$	44.7588	1.43196	0.715981	−	0.698120i	$-0.245980\pi$
$977$	44.7588	1.43196	0.715981	+	0.698120i	$0.245980\pi$
$978$	−51.0986	−1.63395
$979$	−16.7133	−0.534160
$980$	−0.791271	−0.0252762
$981$	0.180138	0.00575137
$982$	−40.2054	−1.28301
$983$	23.6003	0.752732	0.376366	−	0.926471i	$-0.377173\pi$
$983$	23.6003	0.752732	0.376366	+	0.926471i	$0.377173\pi$
$984$	1.54153	0.0491422
$985$	1.54689	0.0492879
$986$	−1.06582	−0.0339425
$987$	−0.911681	−0.0290191
$988$	−12.8656	−0.409309
$989$	6.03876	0.192021
$990$	0.957436	0.0304293
$991$	−51.8865	−1.64823	−0.824114	−	0.566423i	$-0.808327\pi$
$991$	−51.8865	−1.64823	−0.824114	+	0.566423i	$0.808327\pi$
$992$	33.5016	1.06368
$993$	−20.0846	−0.637364
$994$	24.3261	0.771577
$995$	−1.91369	−0.0606681
$996$	30.7567	0.974562
$997$	−14.0976	−0.446476	−0.223238	−	0.974764i	$-0.571663\pi$
$997$	−14.0976	−0.446476	−0.223238	+	0.974764i	$0.571663\pi$
$998$	−33.9111	−1.07344
$999$	−9.04387	−0.286135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.10	✓	10
3.2	odd	2		6003.2.a.k.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.10	✓	10	1.1	even	1	trivial
6003.2.a.k.1.1		10	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)

\(f(q)\)	\(=\)	\(q+2.74444 q^{2} -1.00000 q^{3} +5.53194 q^{4} +0.0839771 q^{5} -2.74444 q^{6} -2.30146 q^{7} +9.69318 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.74444 q^{2} -1.00000 q^{3} +5.53194 q^{4} +0.0839771 q^{5} -2.74444 q^{6} -2.30146 q^{7} +9.69318 q^{8} +1.00000 q^{9} +0.230470 q^{10} +4.15428 q^{11} -5.53194 q^{12} -0.439258 q^{13} -6.31621 q^{14} -0.0839771 q^{15} +15.5385 q^{16} -0.388355 q^{17} +2.74444 q^{18} +5.29460 q^{19} +0.464556 q^{20} +2.30146 q^{21} +11.4012 q^{22} -1.00000 q^{23} -9.69318 q^{24} -4.99295 q^{25} -1.20552 q^{26} -1.00000 q^{27} -12.7315 q^{28} +1.00000 q^{29} -0.230470 q^{30} +1.44043 q^{31} +23.2580 q^{32} -4.15428 q^{33} -1.06582 q^{34} -0.193270 q^{35} +5.53194 q^{36} +9.04387 q^{37} +14.5307 q^{38} +0.439258 q^{39} +0.814006 q^{40} -0.159033 q^{41} +6.31621 q^{42} -6.03876 q^{43} +22.9812 q^{44} +0.0839771 q^{45} -2.74444 q^{46} -0.396132 q^{47} -15.5385 q^{48} -1.70328 q^{49} -13.7028 q^{50} +0.388355 q^{51} -2.42995 q^{52} +2.43614 q^{53} -2.74444 q^{54} +0.348864 q^{55} -22.3085 q^{56} -5.29460 q^{57} +2.74444 q^{58} -4.08958 q^{59} -0.464556 q^{60} +9.28497 q^{61} +3.95318 q^{62} -2.30146 q^{63} +32.7531 q^{64} -0.0368876 q^{65} -11.4012 q^{66} +4.55339 q^{67} -2.14836 q^{68} +1.00000 q^{69} -0.530417 q^{70} -3.85137 q^{71} +9.69318 q^{72} +0.0113549 q^{73} +24.8203 q^{74} +4.99295 q^{75} +29.2894 q^{76} -9.56090 q^{77} +1.20552 q^{78} +9.57510 q^{79} +1.30488 q^{80} +1.00000 q^{81} -0.436455 q^{82} -5.55983 q^{83} +12.7315 q^{84} -0.0326130 q^{85} -16.5730 q^{86} -1.00000 q^{87} +40.2682 q^{88} -4.02316 q^{89} +0.230470 q^{90} +1.01093 q^{91} -5.53194 q^{92} -1.44043 q^{93} -1.08716 q^{94} +0.444625 q^{95} -23.2580 q^{96} -19.4508 q^{97} -4.67455 q^{98} +4.15428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * q^99

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