LMFDB - Embedded newform 2001.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.312617.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 $ x^5 - 2x^4 - 5x^3 + 11*x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.70431$ 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)

$f(q)$	$=$	$q+1.51515 q^{2} -1.00000 q^{3} +0.295689 q^{4} -1.86677 q^{5} -1.51515 q^{6} +1.57109 q^{7} -2.58229 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.51515 q^{2} -1.00000 q^{3} +0.295689 q^{4} -1.86677 q^{5} -1.51515 q^{6} +1.57109 q^{7} -2.58229 q^{8} +1.00000 q^{9} -2.82845 q^{10} +0.419828 q^{11} -0.295689 q^{12} +4.28660 q^{13} +2.38043 q^{14} +1.86677 q^{15} -4.50395 q^{16} +1.70431 q^{17} +1.51515 q^{18} -5.83966 q^{19} -0.551985 q^{20} -1.57109 q^{21} +0.636104 q^{22} +1.00000 q^{23} +2.58229 q^{24} -1.51515 q^{25} +6.49486 q^{26} -1.00000 q^{27} +0.464553 q^{28} +1.00000 q^{29} +2.82845 q^{30} -2.45922 q^{31} -1.65959 q^{32} -0.419828 q^{33} +2.58229 q^{34} -2.93286 q^{35} +0.295689 q^{36} -3.07503 q^{37} -8.84797 q^{38} -4.28660 q^{39} +4.82056 q^{40} -9.46667 q^{41} -2.38043 q^{42} -3.20143 q^{43} +0.124139 q^{44} -1.86677 q^{45} +1.51515 q^{46} -10.6476 q^{47} +4.50395 q^{48} -4.53169 q^{49} -2.29569 q^{50} -1.70431 q^{51} +1.26750 q^{52} -5.61260 q^{53} -1.51515 q^{54} -0.783724 q^{55} -4.05700 q^{56} +5.83966 q^{57} +1.51515 q^{58} +2.16824 q^{59} +0.551985 q^{60} +5.23388 q^{61} -3.72610 q^{62} +1.57109 q^{63} +6.49337 q^{64} -8.00212 q^{65} -0.636104 q^{66} -11.3836 q^{67} +0.503947 q^{68} -1.00000 q^{69} -4.44373 q^{70} -9.31691 q^{71} -2.58229 q^{72} +15.9551 q^{73} -4.65914 q^{74} +1.51515 q^{75} -1.72672 q^{76} +0.659586 q^{77} -6.49486 q^{78} +5.67719 q^{79} +8.40785 q^{80} +1.00000 q^{81} -14.3435 q^{82} -3.89987 q^{83} -0.464553 q^{84} -3.18156 q^{85} -4.85066 q^{86} -1.00000 q^{87} -1.08412 q^{88} -6.42772 q^{89} -2.82845 q^{90} +6.73462 q^{91} +0.295689 q^{92} +2.45922 q^{93} -16.1328 q^{94} +10.9013 q^{95} +1.65959 q^{96} +2.73900 q^{97} -6.86621 q^{98} +0.419828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.51515	1.07138	0.535688	−	0.844416i	$-0.320052\pi$
$2$	1.51515	1.07138	0.535688	+	0.844416i	$0.320052\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.295689	0.147845
$5$	−1.86677	−0.834847	−0.417423	−	0.908712i	$-0.637067\pi$
$5$	−1.86677	−0.834847	−0.417423	+	0.908712i	$0.637067\pi$
$6$	−1.51515	−0.618559
$7$	1.57109	0.593814	0.296907	−	0.954906i	$-0.404045\pi$
$7$	1.57109	0.593814	0.296907	+	0.954906i	$0.404045\pi$
$8$	−2.58229	−0.912978
$9$	1.00000	0.333333
$10$	−2.82845	−0.894434
$11$	0.419828	0.126583	0.0632915	−	0.997995i	$-0.479840\pi$
$11$	0.419828	0.126583	0.0632915	+	0.997995i	$0.479840\pi$
$12$	−0.295689	−0.0853582
$13$	4.28660	1.18889	0.594445	−	0.804136i	$-0.297372\pi$
$13$	4.28660	1.18889	0.594445	+	0.804136i	$0.297372\pi$
$14$	2.38043	0.636198
$15$	1.86677	0.481999
$16$	−4.50395	−1.12599
$17$	1.70431	0.413356	0.206678	−	0.978409i	$-0.433735\pi$
$17$	1.70431	0.413356	0.206678	+	0.978409i	$0.433735\pi$
$18$	1.51515	0.357125
$19$	−5.83966	−1.33971	−0.669854	−	0.742492i	$-0.733644\pi$
$19$	−5.83966	−1.33971	−0.669854	+	0.742492i	$0.733644\pi$
$20$	−0.551985	−0.123428
$21$	−1.57109	−0.342839
$22$	0.636104	0.135618
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.58229	0.527108
$25$	−1.51515	−0.303031
$26$	6.49486	1.27375
$27$	−1.00000	−0.192450
$28$	0.464553	0.0877923
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.82845	0.516402
$31$	−2.45922	−0.441689	−0.220845	−	0.975309i	$-0.570881\pi$
$31$	−2.45922	−0.441689	−0.220845	+	0.975309i	$0.570881\pi$
$32$	−1.65959	−0.293376
$33$	−0.419828	−0.0730827
$34$	2.58229	0.442859
$35$	−2.93286	−0.495744
$36$	0.295689	0.0492816
$37$	−3.07503	−0.505532	−0.252766	−	0.967527i	$-0.581340\pi$
$37$	−3.07503	−0.505532	−0.252766	+	0.967527i	$0.581340\pi$
$38$	−8.84797	−1.43533
$39$	−4.28660	−0.686406
$40$	4.82056	0.762197
$41$	−9.46667	−1.47845	−0.739223	−	0.673461i	$-0.764807\pi$
$41$	−9.46667	−1.47845	−0.739223	+	0.673461i	$0.764807\pi$
$42$	−2.38043	−0.367309
$43$	−3.20143	−0.488214	−0.244107	−	0.969748i	$-0.578495\pi$
$43$	−3.20143	−0.488214	−0.244107	+	0.969748i	$0.578495\pi$
$44$	0.124139	0.0187146
$45$	−1.86677	−0.278282
$46$	1.51515	0.223397
$47$	−10.6476	−1.55311	−0.776557	−	0.630047i	$-0.783035\pi$
$47$	−10.6476	−1.55311	−0.776557	+	0.630047i	$0.783035\pi$
$48$	4.50395	0.650089
$49$	−4.53169	−0.647385
$50$	−2.29569	−0.324660
$51$	−1.70431	−0.238651
$52$	1.26750	0.175771
$53$	−5.61260	−0.770950	−0.385475	−	0.922718i	$-0.625962\pi$
$53$	−5.61260	−0.770950	−0.385475	+	0.922718i	$0.625962\pi$
$54$	−1.51515	−0.206186
$55$	−0.783724	−0.105677
$56$	−4.05700	−0.542139
$57$	5.83966	0.773481
$58$	1.51515	0.198949
$59$	2.16824	0.282280	0.141140	−	0.989990i	$-0.454923\pi$
$59$	2.16824	0.282280	0.141140	+	0.989990i	$0.454923\pi$
$60$	0.551985	0.0712610
$61$	5.23388	0.670130	0.335065	−	0.942195i	$-0.391242\pi$
$61$	5.23388	0.670130	0.335065	+	0.942195i	$0.391242\pi$
$62$	−3.72610	−0.473215
$63$	1.57109	0.197938
$64$	6.49337	0.811671
$65$	−8.00212	−0.992541
$66$	−0.636104	−0.0782990
$67$	−11.3836	−1.39073	−0.695365	−	0.718656i	$-0.744757\pi$
$67$	−11.3836	−1.39073	−0.695365	+	0.718656i	$0.744757\pi$
$68$	0.503947	0.0611125
$69$	−1.00000	−0.120386
$70$	−4.44373	−0.531128
$71$	−9.31691	−1.10571	−0.552857	−	0.833276i	$-0.686462\pi$
$71$	−9.31691	−1.10571	−0.552857	+	0.833276i	$0.686462\pi$
$72$	−2.58229	−0.304326
$73$	15.9551	1.86741	0.933704	−	0.358047i	$-0.116557\pi$
$73$	15.9551	1.86741	0.933704	+	0.358047i	$0.116557\pi$
$74$	−4.65914	−0.541614
$75$	1.51515	0.174955
$76$	−1.72672	−0.198069
$77$	0.659586	0.0751667
$78$	−6.49486	−0.735398
$79$	5.67719	0.638734	0.319367	−	0.947631i	$-0.396530\pi$
$79$	5.67719	0.638734	0.319367	+	0.947631i	$0.396530\pi$
$80$	8.40785	0.940026
$81$	1.00000	0.111111
$82$	−14.3435	−1.58397
$83$	−3.89987	−0.428066	−0.214033	−	0.976826i	$-0.568660\pi$
$83$	−3.89987	−0.428066	−0.214033	+	0.976826i	$0.568660\pi$
$84$	−0.464553	−0.0506869
$85$	−3.18156	−0.345089
$86$	−4.85066	−0.523060
$87$	−1.00000	−0.107211
$88$	−1.08412	−0.115567
$89$	−6.42772	−0.681337	−0.340669	−	0.940183i	$-0.610653\pi$
$89$	−6.42772	−0.681337	−0.340669	+	0.940183i	$0.610653\pi$
$90$	−2.82845	−0.298145
$91$	6.73462	0.705980
$92$	0.295689	0.0308277
$93$	2.45922	0.255009
$94$	−16.1328	−1.66397
$95$	10.9013	1.11845
$96$	1.65959	0.169381
$97$	2.73900	0.278103	0.139052	−	0.990285i	$-0.455595\pi$
$97$	2.73900	0.278103	0.139052	+	0.990285i	$0.455595\pi$
$98$	−6.86621	−0.693592
$99$	0.419828	0.0421943
$100$	−0.448015	−0.0448015
$101$	−13.6861	−1.36182	−0.680911	−	0.732366i	$-0.738416\pi$
$101$	−13.6861	−1.36182	−0.680911	+	0.732366i	$0.738416\pi$
$102$	−2.58229	−0.255685
$103$	−11.8950	−1.17205	−0.586023	−	0.810295i	$-0.699307\pi$
$103$	−11.8950	−1.17205	−0.586023	+	0.810295i	$0.699307\pi$
$104$	−11.0693	−1.08543
$105$	2.93286	0.286218
$106$	−8.50395	−0.825976
$107$	−5.99624	−0.579679	−0.289839	−	0.957075i	$-0.593602\pi$
$107$	−5.99624	−0.579679	−0.289839	+	0.957075i	$0.593602\pi$
$108$	−0.295689	−0.0284527
$109$	16.2936	1.56065	0.780323	−	0.625376i	$-0.215055\pi$
$109$	16.2936	1.56065	0.780323	+	0.625376i	$0.215055\pi$
$110$	−1.18746	−0.113220
$111$	3.07503	0.291869
$112$	−7.07608	−0.668627
$113$	−14.6575	−1.37886	−0.689432	−	0.724350i	$-0.742140\pi$
$113$	−14.6575	−1.37886	−0.689432	+	0.724350i	$0.742140\pi$
$114$	8.84797	0.828689
$115$	−1.86677	−0.174078
$116$	0.295689	0.0274541
$117$	4.28660	0.396297
$118$	3.28521	0.302428
$119$	2.67762	0.245457
$120$	−4.82056	−0.440055
$121$	−10.8237	−0.983977
$122$	7.93013	0.717961
$123$	9.46667	0.853581
$124$	−0.727166	−0.0653014
$125$	12.1623	1.08783
$126$	2.38043	0.212066
$127$	−9.57682	−0.849805	−0.424903	−	0.905239i	$-0.639692\pi$
$127$	−9.57682	−0.849805	−0.424903	+	0.905239i	$0.639692\pi$
$128$	13.1576	1.16298
$129$	3.20143	0.281870
$130$	−12.1244	−1.06338
$131$	21.7557	1.90080	0.950402	−	0.311024i	$-0.100672\pi$
$131$	21.7557	1.90080	0.950402	+	0.311024i	$0.100672\pi$
$132$	−0.124139	−0.0108049
$133$	−9.17460	−0.795538
$134$	−17.2479	−1.48999
$135$	1.86677	0.160666
$136$	−4.40103	−0.377385
$137$	8.98693	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$137$	8.98693	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$138$	−1.51515	−0.128978
$139$	4.26843	0.362043	0.181022	−	0.983479i	$-0.442060\pi$
$139$	4.26843	0.362043	0.181022	+	0.983479i	$0.442060\pi$
$140$	−0.867216	−0.0732931
$141$	10.6476	0.896690
$142$	−14.1165	−1.18463
$143$	1.79964	0.150493
$144$	−4.50395	−0.375329
$145$	−1.86677	−0.155027
$146$	24.1745	2.00069
$147$	4.53169	0.373768
$148$	−0.909254	−0.0747402
$149$	−7.58912	−0.621725	−0.310862	−	0.950455i	$-0.600618\pi$
$149$	−7.58912	−0.621725	−0.310862	+	0.950455i	$0.600618\pi$
$150$	2.29569	0.187442
$151$	19.8355	1.61419	0.807096	−	0.590420i	$-0.201038\pi$
$151$	19.8355	1.61419	0.807096	+	0.590420i	$0.201038\pi$
$152$	15.0797	1.22312
$153$	1.70431	0.137785
$154$	0.999373	0.0805318
$155$	4.59081	0.368743
$156$	−1.26750	−0.101481
$157$	13.4006	1.06948	0.534742	−	0.845015i	$-0.320409\pi$
$157$	13.4006	1.06948	0.534742	+	0.845015i	$0.320409\pi$
$158$	8.60182	0.684324
$159$	5.61260	0.445108
$160$	3.09807	0.244924
$161$	1.57109	0.123819
$162$	1.51515	0.119042
$163$	11.2577	0.881768	0.440884	−	0.897564i	$-0.354665\pi$
$163$	11.2577	0.881768	0.440884	+	0.897564i	$0.354665\pi$
$164$	−2.79919	−0.218580
$165$	0.783724	0.0610128
$166$	−5.90890	−0.458619
$167$	−18.4936	−1.43108	−0.715541	−	0.698571i	$-0.753820\pi$
$167$	−18.4936	−1.43108	−0.715541	+	0.698571i	$0.753820\pi$
$168$	4.05700	0.313004
$169$	5.37496	0.413459
$170$	−4.82056	−0.369720
$171$	−5.83966	−0.446570
$172$	−0.946629	−0.0721798
$173$	−5.50544	−0.418571	−0.209285	−	0.977855i	$-0.567114\pi$
$173$	−5.50544	−0.418571	−0.209285	+	0.977855i	$0.567114\pi$
$174$	−1.51515	−0.114863
$175$	−2.38043	−0.179944
$176$	−1.89088	−0.142531
$177$	−2.16824	−0.162975
$178$	−9.73898	−0.729968
$179$	−25.5496	−1.90967	−0.954833	−	0.297142i	$-0.903967\pi$
$179$	−25.5496	−1.90967	−0.954833	+	0.297142i	$0.903967\pi$
$180$	−0.551985	−0.0411426
$181$	−4.71768	−0.350662	−0.175331	−	0.984510i	$-0.556100\pi$
$181$	−4.71768	−0.350662	−0.175331	+	0.984510i	$0.556100\pi$
$182$	10.2040	0.756369
$183$	−5.23388	−0.386900
$184$	−2.58229	−0.190369
$185$	5.74039	0.422042
$186$	3.72610	0.273211
$187$	0.715517	0.0523238
$188$	−3.14838	−0.229620
$189$	−1.57109	−0.114280
$190$	16.5172	1.19828
$191$	22.3806	1.61940	0.809701	−	0.586843i	$-0.199630\pi$
$191$	22.3806	1.61940	0.809701	+	0.586843i	$0.199630\pi$
$192$	−6.49337	−0.468618
$193$	−9.74752	−0.701642	−0.350821	−	0.936443i	$-0.614097\pi$
$193$	−9.74752	−0.701642	−0.350821	+	0.936443i	$0.614097\pi$
$194$	4.15000	0.297953
$195$	8.00212	0.573044
$196$	−1.33997	−0.0957124
$197$	4.95580	0.353086	0.176543	−	0.984293i	$-0.443509\pi$
$197$	4.95580	0.353086	0.176543	+	0.984293i	$0.443509\pi$
$198$	0.636104	0.0452059
$199$	16.4537	1.16638	0.583188	−	0.812337i	$-0.301805\pi$
$199$	16.4537	1.16638	0.583188	+	0.812337i	$0.301805\pi$
$200$	3.91257	0.276660
$201$	11.3836	0.802939
$202$	−20.7366	−1.45902
$203$	1.57109	0.110269
$204$	−0.503947	−0.0352833
$205$	17.6721	1.23428
$206$	−18.0227	−1.25570
$207$	1.00000	0.0695048
$208$	−19.3066	−1.33867
$209$	−2.45165	−0.169584
$210$	4.44373	0.306647
$211$	1.02540	0.0705914	0.0352957	−	0.999377i	$-0.488763\pi$
$211$	1.02540	0.0705914	0.0352957	+	0.999377i	$0.488763\pi$
$212$	−1.65959	−0.113981
$213$	9.31691	0.638384
$214$	−9.08523	−0.621054
$215$	5.97635	0.407584
$216$	2.58229	0.175703
$217$	−3.86365	−0.262281
$218$	24.6873	1.67204
$219$	−15.9551	−1.07815
$220$	−0.231739	−0.0156238
$221$	7.30570	0.491435
$222$	4.65914	0.312701
$223$	−17.9525	−1.20219	−0.601096	−	0.799177i	$-0.705269\pi$
$223$	−17.9525	−1.20219	−0.601096	+	0.799177i	$0.705269\pi$
$224$	−2.60735	−0.174211
$225$	−1.51515	−0.101010
$226$	−22.2084	−1.47728
$227$	−18.0150	−1.19570	−0.597849	−	0.801608i	$-0.703978\pi$
$227$	−18.0150	−1.19570	−0.597849	+	0.801608i	$0.703978\pi$
$228$	1.72672	0.114355
$229$	10.0360	0.663200	0.331600	−	0.943420i	$-0.392412\pi$
$229$	10.0360	0.663200	0.331600	+	0.943420i	$0.392412\pi$
$230$	−2.82845	−0.186502
$231$	−0.659586	−0.0433975
$232$	−2.58229	−0.169536
$233$	2.72299	0.178389	0.0891944	−	0.996014i	$-0.471571\pi$
$233$	2.72299	0.178389	0.0891944	+	0.996014i	$0.471571\pi$
$234$	6.49486	0.424582
$235$	19.8767	1.29661
$236$	0.641125	0.0417337
$237$	−5.67719	−0.368773
$238$	4.05700	0.262976
$239$	−21.3708	−1.38236	−0.691180	−	0.722682i	$-0.742909\pi$
$239$	−21.3708	−1.38236	−0.691180	+	0.722682i	$0.742909\pi$
$240$	−8.40785	−0.542725
$241$	9.01276	0.580563	0.290281	−	0.956941i	$-0.406251\pi$
$241$	9.01276	0.580563	0.290281	+	0.956941i	$0.406251\pi$
$242$	−16.3996	−1.05421
$243$	−1.00000	−0.0641500
$244$	1.54760	0.0990752
$245$	8.45965	0.540467
$246$	14.3435	0.914506
$247$	−25.0323	−1.59277
$248$	6.35043	0.403253
$249$	3.89987	0.247144
$250$	18.4278	1.16548
$251$	1.74871	0.110378	0.0551889	−	0.998476i	$-0.482424\pi$
$251$	1.74871	0.110378	0.0551889	+	0.998476i	$0.482424\pi$
$252$	0.464553	0.0292641
$253$	0.419828	0.0263944
$254$	−14.5103	−0.910460
$255$	3.18156	0.199237
$256$	6.94907	0.434317
$257$	7.58239	0.472976	0.236488	−	0.971634i	$-0.424004\pi$
$257$	7.58239	0.472976	0.236488	+	0.971634i	$0.424004\pi$
$258$	4.85066	0.301989
$259$	−4.83114	−0.300192
$260$	−2.36614	−0.146742
$261$	1.00000	0.0618984
$262$	32.9632	2.03647
$263$	19.9211	1.22839	0.614193	−	0.789156i	$-0.289482\pi$
$263$	19.9211	1.22839	0.614193	+	0.789156i	$0.289482\pi$
$264$	1.08412	0.0667229
$265$	10.4775	0.643625
$266$	−13.9009	−0.852320
$267$	6.42772	0.393370
$268$	−3.36602	−0.205612
$269$	17.7510	1.08230	0.541149	−	0.840927i	$-0.317989\pi$
$269$	17.7510	1.08230	0.541149	+	0.840927i	$0.317989\pi$
$270$	2.82845	0.172134
$271$	12.5974	0.765238	0.382619	−	0.923906i	$-0.375022\pi$
$271$	12.5974	0.765238	0.382619	+	0.923906i	$0.375022\pi$
$272$	−7.67612	−0.465433
$273$	−6.73462	−0.407598
$274$	13.6166	0.822608
$275$	−0.636104	−0.0383585
$276$	−0.295689	−0.0177984
$277$	−11.5272	−0.692603	−0.346301	−	0.938123i	$-0.612563\pi$
$277$	−11.5272	−0.692603	−0.346301	+	0.938123i	$0.612563\pi$
$278$	6.46732	0.387884
$279$	−2.45922	−0.147230
$280$	7.57350	0.452603
$281$	−24.7226	−1.47483	−0.737415	−	0.675440i	$-0.763954\pi$
$281$	−24.7226	−1.47483	−0.737415	+	0.675440i	$0.763954\pi$
$282$	16.1328	0.960692
$283$	24.5908	1.46177	0.730885	−	0.682500i	$-0.239107\pi$
$283$	24.5908	1.46177	0.730885	+	0.682500i	$0.239107\pi$
$284$	−2.75491	−0.163474
$285$	−10.9013	−0.645739
$286$	2.72672	0.161235
$287$	−14.8729	−0.877922
$288$	−1.65959	−0.0977920
$289$	−14.0953	−0.829137
$290$	−2.82845	−0.166092
$291$	−2.73900	−0.160563
$292$	4.71776	0.276086
$293$	−9.97847	−0.582949	−0.291474	−	0.956579i	$-0.594146\pi$
$293$	−9.97847	−0.582949	−0.291474	+	0.956579i	$0.594146\pi$
$294$	6.86621	0.400445
$295$	−4.04761	−0.235661
$296$	7.94063	0.461540
$297$	−0.419828	−0.0243609
$298$	−11.4987	−0.666100
$299$	4.28660	0.247901
$300$	0.448015	0.0258661
$301$	−5.02972	−0.289908
$302$	30.0539	1.72941
$303$	13.6861	0.786248
$304$	26.3015	1.50849
$305$	−9.77048	−0.559456
$306$	2.58229	0.147620
$307$	−6.06605	−0.346208	−0.173104	−	0.984904i	$-0.555380\pi$
$307$	−6.06605	−0.346208	−0.173104	+	0.984904i	$0.555380\pi$
$308$	0.195032	0.0111130
$309$	11.8950	0.676681
$310$	6.95578	0.395062
$311$	18.9573	1.07497	0.537484	−	0.843274i	$-0.319375\pi$
$311$	18.9573	1.07497	0.537484	+	0.843274i	$0.319375\pi$
$312$	11.0693	0.626673
$313$	8.41377	0.475574	0.237787	−	0.971317i	$-0.423578\pi$
$313$	8.41377	0.475574	0.237787	+	0.971317i	$0.423578\pi$
$314$	20.3040	1.14582
$315$	−2.93286	−0.165248
$316$	1.67869	0.0944334
$317$	28.7722	1.61601	0.808005	−	0.589176i	$-0.200547\pi$
$317$	28.7722	1.61601	0.808005	+	0.589176i	$0.200547\pi$
$318$	8.50395	0.476878
$319$	0.419828	0.0235059
$320$	−12.1217	−0.677621
$321$	5.99624	0.334678
$322$	2.38043	0.132656
$323$	−9.95259	−0.553777
$324$	0.295689	0.0164272
$325$	−6.49486	−0.360270
$326$	17.0571	0.944705
$327$	−16.2936	−0.901040
$328$	24.4457	1.34979
$329$	−16.7283	−0.922261
$330$	1.18746	0.0653676
$331$	16.5416	0.909206	0.454603	−	0.890694i	$-0.349781\pi$
$331$	16.5416	0.909206	0.454603	+	0.890694i	$0.349781\pi$
$332$	−1.15315	−0.0632873
$333$	−3.07503	−0.168511
$334$	−28.0207	−1.53323
$335$	21.2507	1.16105
$336$	7.07608	0.386032
$337$	−26.7947	−1.45960	−0.729801	−	0.683659i	$-0.760387\pi$
$337$	−26.7947	−1.45960	−0.729801	+	0.683659i	$0.760387\pi$
$338$	8.14389	0.442969
$339$	14.6575	0.796088
$340$	−0.940754	−0.0510196
$341$	−1.03245	−0.0559103
$342$	−8.84797	−0.478444
$343$	−18.1173	−0.978241
$344$	8.26703	0.445729
$345$	1.86677	0.100504
$346$	−8.34158	−0.448446
$347$	−23.6775	−1.27107	−0.635536	−	0.772071i	$-0.719221\pi$
$347$	−23.6775	−1.27107	−0.635536	+	0.772071i	$0.719221\pi$
$348$	−0.295689	−0.0158506
$349$	16.9950	0.909719	0.454859	−	0.890563i	$-0.349690\pi$
$349$	16.9950	0.909719	0.454859	+	0.890563i	$0.349690\pi$
$350$	−3.60672	−0.192787
$351$	−4.28660	−0.228802
$352$	−0.696741	−0.0371364
$353$	3.65595	0.194587	0.0972933	−	0.995256i	$-0.468982\pi$
$353$	3.65595	0.194587	0.0972933	+	0.995256i	$0.468982\pi$
$354$	−3.28521	−0.174607
$355$	17.3926	0.923102
$356$	−1.90061	−0.100732
$357$	−2.67762	−0.141715
$358$	−38.7116	−2.04597
$359$	35.3447	1.86542	0.932712	−	0.360623i	$-0.117436\pi$
$359$	35.3447	1.86542	0.932712	+	0.360623i	$0.117436\pi$
$360$	4.82056	0.254066
$361$	15.1016	0.794820
$362$	−7.14800	−0.375691
$363$	10.8237	0.568099
$364$	1.99135	0.104375
$365$	−29.7846	−1.55900
$366$	−7.93013	−0.414515
$367$	−30.7514	−1.60521	−0.802605	−	0.596510i	$-0.796553\pi$
$367$	−30.7514	−1.60521	−0.802605	+	0.596510i	$0.796553\pi$
$368$	−4.50395	−0.234784
$369$	−9.46667	−0.492815
$370$	8.69757	0.452165
$371$	−8.81787	−0.457801
$372$	0.727166	0.0377018
$373$	34.6601	1.79463	0.897317	−	0.441386i	$-0.145513\pi$
$373$	34.6601	1.79463	0.897317	+	0.441386i	$0.145513\pi$
$374$	1.08412	0.0560584
$375$	−12.1623	−0.628060
$376$	27.4952	1.41796
$377$	4.28660	0.220771
$378$	−2.38043	−0.122436
$379$	−3.56470	−0.183106	−0.0915532	−	0.995800i	$-0.529183\pi$
$379$	−3.56470	−0.183106	−0.0915532	+	0.995800i	$0.529183\pi$
$380$	3.22340	0.165357
$381$	9.57682	0.490635
$382$	33.9100	1.73499
$383$	−15.6249	−0.798394	−0.399197	−	0.916865i	$-0.630711\pi$
$383$	−15.6249	−0.798394	−0.399197	+	0.916865i	$0.630711\pi$
$384$	−13.1576	−0.671447
$385$	−1.23130	−0.0627527
$386$	−14.7690	−0.751722
$387$	−3.20143	−0.162738
$388$	0.809893	0.0411161
$389$	−36.6916	−1.86034	−0.930170	−	0.367130i	$-0.880341\pi$
$389$	−36.6916	−1.86034	−0.930170	+	0.367130i	$0.880341\pi$
$390$	12.1244	0.613945
$391$	1.70431	0.0861907
$392$	11.7022	0.591048
$393$	−21.7557	−1.09743
$394$	7.50880	0.378288
$395$	−10.5980	−0.533245
$396$	0.124139	0.00623820
$397$	−7.20129	−0.361422	−0.180711	−	0.983536i	$-0.557840\pi$
$397$	−7.20129	−0.361422	−0.180711	+	0.983536i	$0.557840\pi$
$398$	24.9299	1.24963
$399$	9.17460	0.459304
$400$	6.82417	0.341208
$401$	−10.0148	−0.500117	−0.250059	−	0.968231i	$-0.580450\pi$
$401$	−10.0148	−0.500117	−0.250059	+	0.968231i	$0.580450\pi$
$402$	17.2479	0.860249
$403$	−10.5417	−0.525120
$404$	−4.04684	−0.201338
$405$	−1.86677	−0.0927608
$406$	2.38043	0.118139
$407$	−1.29098	−0.0639917
$408$	4.40103	0.217883
$409$	−23.3666	−1.15540	−0.577702	−	0.816248i	$-0.696050\pi$
$409$	−23.3666	−1.15540	−0.577702	+	0.816248i	$0.696050\pi$
$410$	26.7760	1.32237
$411$	−8.98693	−0.443293
$412$	−3.51721	−0.173281
$413$	3.40648	0.167622
$414$	1.51515	0.0744657
$415$	7.28017	0.357370
$416$	−7.11398	−0.348792
$417$	−4.26843	−0.209026
$418$	−3.71463	−0.181688
$419$	−16.3504	−0.798769	−0.399385	−	0.916783i	$-0.630776\pi$
$419$	−16.3504	−0.798769	−0.399385	+	0.916783i	$0.630776\pi$
$420$	0.867216	0.0423158
$421$	16.1831	0.788714	0.394357	−	0.918957i	$-0.370967\pi$
$421$	16.1831	0.788714	0.394357	+	0.918957i	$0.370967\pi$
$422$	1.55364	0.0756299
$423$	−10.6476	−0.517704
$424$	14.4934	0.703860
$425$	−2.58229	−0.125260
$426$	14.1165	0.683949
$427$	8.22287	0.397933
$428$	−1.77303	−0.0857024
$429$	−1.79964	−0.0868872
$430$	9.05509	0.436675
$431$	−41.4045	−1.99439	−0.997193	−	0.0748703i	$-0.976146\pi$
$431$	−41.4045	−1.99439	−0.997193	+	0.0748703i	$0.976146\pi$
$432$	4.50395	0.216696
$433$	35.6014	1.71090	0.855448	−	0.517888i	$-0.173282\pi$
$433$	35.6014	1.71090	0.855448	+	0.517888i	$0.173282\pi$
$434$	−5.85402	−0.281002
$435$	1.86677	0.0895050
$436$	4.81785	0.230733
$437$	−5.83966	−0.279349
$438$	−24.1745	−1.15510
$439$	−25.2390	−1.20459	−0.602296	−	0.798273i	$-0.705747\pi$
$439$	−25.2390	−1.20459	−0.602296	+	0.798273i	$0.705747\pi$
$440$	2.02380	0.0964811
$441$	−4.53169	−0.215795
$442$	11.0693	0.526511
$443$	12.3832	0.588343	0.294171	−	0.955753i	$-0.404956\pi$
$443$	12.3832	0.588343	0.294171	+	0.955753i	$0.404956\pi$
$444$	0.909254	0.0431513
$445$	11.9991	0.568812
$446$	−27.2009	−1.28800
$447$	7.58912	0.358953
$448$	10.2016	0.481982
$449$	−29.7182	−1.40249	−0.701244	−	0.712921i	$-0.747372\pi$
$449$	−29.7182	−1.40249	−0.701244	+	0.712921i	$0.747372\pi$
$450$	−2.29569	−0.108220
$451$	−3.97437	−0.187146
$452$	−4.33407	−0.203858
$453$	−19.8355	−0.931955
$454$	−27.2955	−1.28104
$455$	−12.5720	−0.589385
$456$	−15.0797	−0.706171
$457$	8.75434	0.409511	0.204755	−	0.978813i	$-0.434360\pi$
$457$	8.75434	0.409511	0.204755	+	0.978813i	$0.434360\pi$
$458$	15.2061	0.710536
$459$	−1.70431	−0.0795504
$460$	−0.551985	−0.0257364
$461$	15.2003	0.707950	0.353975	−	0.935255i	$-0.384830\pi$
$461$	15.2003	0.707950	0.353975	+	0.935255i	$0.384830\pi$
$462$	−0.999373	−0.0464950
$463$	31.0270	1.44195	0.720974	−	0.692962i	$-0.243695\pi$
$463$	31.0270	1.44195	0.720974	+	0.692962i	$0.243695\pi$
$464$	−4.50395	−0.209090
$465$	−4.59081	−0.212894
$466$	4.12574	0.191121
$467$	−8.09486	−0.374585	−0.187293	−	0.982304i	$-0.559971\pi$
$467$	−8.09486	−0.374585	−0.187293	+	0.982304i	$0.559971\pi$
$468$	1.26750	0.0585903
$469$	−17.8846	−0.825836
$470$	30.1162	1.38916
$471$	−13.4006	−0.617467
$472$	−5.59902	−0.257716
$473$	−1.34405	−0.0617995
$474$	−8.60182	−0.395095
$475$	8.84797	0.405973
$476$	0.791743	0.0362895
$477$	−5.61260	−0.256983
$478$	−32.3800	−1.48103
$479$	27.1982	1.24272	0.621358	−	0.783527i	$-0.286581\pi$
$479$	27.1982	1.24272	0.621358	+	0.783527i	$0.286581\pi$
$480$	−3.09807	−0.141407
$481$	−13.1814	−0.601022
$482$	13.6557	0.622001
$483$	−1.57109	−0.0714868
$484$	−3.20047	−0.145476
$485$	−5.11309	−0.232174
$486$	−1.51515	−0.0687287
$487$	−19.1963	−0.869867	−0.434933	−	0.900463i	$-0.643228\pi$
$487$	−19.1963	−0.869867	−0.434933	+	0.900463i	$0.643228\pi$
$488$	−13.5154	−0.611814
$489$	−11.2577	−0.509089
$490$	12.8177	0.579043
$491$	0.858089	0.0387250	0.0193625	−	0.999813i	$-0.493836\pi$
$491$	0.858089	0.0387250	0.0193625	+	0.999813i	$0.493836\pi$
$492$	2.79919	0.126197
$493$	1.70431	0.0767583
$494$	−37.9277	−1.70645
$495$	−0.783724	−0.0352258
$496$	11.0762	0.497336
$497$	−14.6377	−0.656589
$498$	5.90890	0.264784
$499$	3.20783	0.143602	0.0718012	−	0.997419i	$-0.477125\pi$
$499$	3.20783	0.143602	0.0718012	+	0.997419i	$0.477125\pi$
$500$	3.59627	0.160830
$501$	18.4936	0.826235
$502$	2.64957	0.118256
$503$	21.1458	0.942845	0.471422	−	0.881908i	$-0.343741\pi$
$503$	21.1458	0.942845	0.471422	+	0.881908i	$0.343741\pi$
$504$	−4.05700	−0.180713
$505$	25.5489	1.13691
$506$	0.636104	0.0282783
$507$	−5.37496	−0.238710
$508$	−2.83176	−0.125639
$509$	27.8425	1.23410	0.617049	−	0.786925i	$-0.288328\pi$
$509$	27.8425	1.23410	0.617049	+	0.786925i	$0.288328\pi$
$510$	4.82056	0.213458
$511$	25.0669	1.10889
$512$	−15.7863	−0.697664
$513$	5.83966	0.257827
$514$	11.4885	0.506735
$515$	22.2052	0.978478
$516$	0.946629	0.0416730
$517$	−4.47016	−0.196598
$518$	−7.31991	−0.321618
$519$	5.50544	0.241662
$520$	20.6638	0.906168
$521$	−2.90463	−0.127254	−0.0636272	−	0.997974i	$-0.520267\pi$
$521$	−2.90463	−0.127254	−0.0636272	+	0.997974i	$0.520267\pi$
$522$	1.51515	0.0663165
$523$	−26.8931	−1.17595	−0.587976	−	0.808878i	$-0.700075\pi$
$523$	−26.8931	−1.17595	−0.587976	+	0.808878i	$0.700075\pi$
$524$	6.43293	0.281024
$525$	2.38043	0.103891
$526$	30.1835	1.31606
$527$	−4.19128	−0.182575
$528$	1.89088	0.0822901
$529$	1.00000	0.0434783
$530$	15.8749	0.689564
$531$	2.16824	0.0940935
$532$	−2.71283	−0.117616
$533$	−40.5799	−1.75771
$534$	9.73898	0.421447
$535$	11.1936	0.483943
$536$	29.3958	1.26971
$537$	25.5496	1.10255
$538$	26.8955	1.15955
$539$	−1.90253	−0.0819478
$540$	0.551985	0.0237537
$541$	9.96123	0.428267	0.214133	−	0.976804i	$-0.431307\pi$
$541$	9.96123	0.428267	0.214133	+	0.976804i	$0.431307\pi$
$542$	19.0870	0.819857
$543$	4.71768	0.202455
$544$	−2.82845	−0.121269
$545$	−30.4165	−1.30290
$546$	−10.2040	−0.436690
$547$	−5.73452	−0.245190	−0.122595	−	0.992457i	$-0.539122\pi$
$547$	−5.73452	−0.245190	−0.122595	+	0.992457i	$0.539122\pi$
$548$	2.65734	0.113516
$549$	5.23388	0.223377
$550$	−0.963795	−0.0410963
$551$	−5.83966	−0.248778
$552$	2.58229	0.109910
$553$	8.91935	0.379289
$554$	−17.4655	−0.742038
$555$	−5.74039	−0.243666
$556$	1.26213	0.0535262
$557$	−13.4606	−0.570343	−0.285172	−	0.958476i	$-0.592051\pi$
$557$	−13.4606	−0.570343	−0.285172	+	0.958476i	$0.592051\pi$
$558$	−3.72610	−0.157738
$559$	−13.7233	−0.580432
$560$	13.2095	0.558201
$561$	−0.715517	−0.0302092
$562$	−37.4586	−1.58010
$563$	6.69738	0.282261	0.141131	−	0.989991i	$-0.454926\pi$
$563$	6.69738	0.282261	0.141131	+	0.989991i	$0.454926\pi$
$564$	3.14838	0.132571
$565$	27.3623	1.15114
$566$	37.2588	1.56610
$567$	1.57109	0.0659794
$568$	24.0590	1.00949
$569$	3.62488	0.151963	0.0759814	−	0.997109i	$-0.475791\pi$
$569$	3.62488	0.151963	0.0759814	+	0.997109i	$0.475791\pi$
$570$	−16.5172	−0.691828
$571$	3.49750	0.146366	0.0731830	−	0.997319i	$-0.476684\pi$
$571$	3.49750	0.146366	0.0731830	+	0.997319i	$0.476684\pi$
$572$	0.532133	0.0222496
$573$	−22.3806	−0.934962
$574$	−22.5348	−0.940584
$575$	−1.51515	−0.0631863
$576$	6.49337	0.270557
$577$	11.2173	0.466983	0.233491	−	0.972359i	$-0.424985\pi$
$577$	11.2173	0.466983	0.233491	+	0.972359i	$0.424985\pi$
$578$	−21.3566	−0.888317
$579$	9.74752	0.405093
$580$	−0.551985	−0.0229199
$581$	−6.12702	−0.254192
$582$	−4.15000	−0.172023
$583$	−2.35633	−0.0975891
$584$	−41.2008	−1.70490
$585$	−8.00212	−0.330847
$586$	−15.1189	−0.624557
$587$	37.1499	1.53334	0.766670	−	0.642042i	$-0.221912\pi$
$587$	37.1499	1.53334	0.766670	+	0.642042i	$0.221912\pi$
$588$	1.33997	0.0552596
$589$	14.3610	0.591735
$590$	−6.13275	−0.252481
$591$	−4.95580	−0.203854
$592$	13.8498	0.569222
$593$	13.5478	0.556341	0.278170	−	0.960532i	$-0.410272\pi$
$593$	13.5478	0.556341	0.278170	+	0.960532i	$0.410272\pi$
$594$	−0.636104	−0.0260997
$595$	−4.99851	−0.204919
$596$	−2.24402	−0.0919187
$597$	−16.4537	−0.673407
$598$	6.49486	0.265595
$599$	−32.8797	−1.34343	−0.671715	−	0.740810i	$-0.734442\pi$
$599$	−32.8797	−1.34343	−0.671715	+	0.740810i	$0.734442\pi$
$600$	−3.91257	−0.159730
$601$	−18.3935	−0.750287	−0.375144	−	0.926967i	$-0.622407\pi$
$601$	−18.3935	−0.750287	−0.375144	+	0.926967i	$0.622407\pi$
$602$	−7.62080	−0.310601
$603$	−11.3836	−0.463577
$604$	5.86516	0.238650
$605$	20.2055	0.821470
$606$	20.7366	0.842367
$607$	−17.4333	−0.707596	−0.353798	−	0.935322i	$-0.615110\pi$
$607$	−17.4333	−0.707596	−0.353798	+	0.935322i	$0.615110\pi$
$608$	9.69141	0.393039
$609$	−1.57109	−0.0636636
$610$	−14.8038	−0.599387
$611$	−45.6421	−1.84648
$612$	0.503947	0.0203708
$613$	31.0897	1.25570	0.627851	−	0.778334i	$-0.283935\pi$
$613$	31.0897	1.25570	0.627851	+	0.778334i	$0.283935\pi$
$614$	−9.19099	−0.370918
$615$	−17.6721	−0.712610
$616$	−1.70324	−0.0686256
$617$	8.08626	0.325541	0.162770	−	0.986664i	$-0.447957\pi$
$617$	8.08626	0.325541	0.162770	+	0.986664i	$0.447957\pi$
$618$	18.0227	0.724979
$619$	−35.7851	−1.43833	−0.719163	−	0.694841i	$-0.755475\pi$
$619$	−35.7851	−1.43833	−0.719163	+	0.694841i	$0.755475\pi$
$620$	1.35745	0.0545167
$621$	−1.00000	−0.0401286
$622$	28.7231	1.15169
$623$	−10.0985	−0.404588
$624$	19.3066	0.772884
$625$	−15.1285	−0.605142
$626$	12.7481	0.509518
$627$	2.45165	0.0979095
$628$	3.96242	0.158118
$629$	−5.24081	−0.208965
$630$	−4.44373	−0.177043
$631$	26.5209	1.05578	0.527889	−	0.849313i	$-0.322984\pi$
$631$	26.5209	1.05578	0.527889	+	0.849313i	$0.322984\pi$
$632$	−14.6602	−0.583150
$633$	−1.02540	−0.0407560
$634$	43.5943	1.73135
$635$	17.8778	0.709457
$636$	1.65959	0.0658068
$637$	−19.4256	−0.769669
$638$	0.636104	0.0251836
$639$	−9.31691	−0.368571
$640$	−24.5623	−0.970910
$641$	−2.63203	−0.103959	−0.0519794	−	0.998648i	$-0.516553\pi$
$641$	−2.63203	−0.103959	−0.0519794	+	0.998648i	$0.516553\pi$
$642$	9.08523	0.358565
$643$	28.6353	1.12926	0.564632	−	0.825342i	$-0.309018\pi$
$643$	28.6353	1.12926	0.564632	+	0.825342i	$0.309018\pi$
$644$	0.464553	0.0183060
$645$	−5.97635	−0.235319
$646$	−15.0797	−0.593303
$647$	2.36067	0.0928074	0.0464037	−	0.998923i	$-0.485224\pi$
$647$	2.36067	0.0928074	0.0464037	+	0.998923i	$0.485224\pi$
$648$	−2.58229	−0.101442
$649$	0.910287	0.0357319
$650$	−9.84071	−0.385984
$651$	3.86365	0.151428
$652$	3.32877	0.130365
$653$	15.1326	0.592185	0.296093	−	0.955159i	$-0.404316\pi$
$653$	15.1326	0.592185	0.296093	+	0.955159i	$0.404316\pi$
$654$	−24.6873	−0.965352
$655$	−40.6130	−1.58688
$656$	42.6374	1.66471
$657$	15.9551	0.622469
$658$	−25.3459	−0.988088
$659$	26.9174	1.04855	0.524277	−	0.851548i	$-0.324336\pi$
$659$	26.9174	1.04855	0.524277	+	0.851548i	$0.324336\pi$
$660$	0.231739	0.00902042
$661$	13.3764	0.520280	0.260140	−	0.965571i	$-0.416231\pi$
$661$	13.3764	0.520280	0.260140	+	0.965571i	$0.416231\pi$
$662$	25.0630	0.974101
$663$	−7.30570	−0.283730
$664$	10.0706	0.390815
$665$	17.1269	0.664153
$666$	−4.65914	−0.180538
$667$	1.00000	0.0387202
$668$	−5.46838	−0.211578
$669$	17.9525	0.694086
$670$	32.1980	1.24392
$671$	2.19733	0.0848270
$672$	2.60735	0.100581
$673$	3.96220	0.152731	0.0763657	−	0.997080i	$-0.475668\pi$
$673$	3.96220	0.152731	0.0763657	+	0.997080i	$0.475668\pi$
$674$	−40.5981	−1.56378
$675$	1.51515	0.0583183
$676$	1.58932	0.0611276
$677$	11.3080	0.434602	0.217301	−	0.976105i	$-0.430275\pi$
$677$	11.3080	0.434602	0.217301	+	0.976105i	$0.430275\pi$
$678$	22.2084	0.852908
$679$	4.30320	0.165142
$680$	8.21573	0.315059
$681$	18.0150	0.690337
$682$	−1.56432	−0.0599009
$683$	−33.1445	−1.26824	−0.634120	−	0.773235i	$-0.718637\pi$
$683$	−33.1445	−1.26824	−0.634120	+	0.773235i	$0.718637\pi$
$684$	−1.72672	−0.0660229
$685$	−16.7766	−0.641000
$686$	−27.4504	−1.04806
$687$	−10.0360	−0.382899
$688$	14.4191	0.549722
$689$	−24.0590	−0.916574
$690$	2.82845	0.107677
$691$	−19.5760	−0.744705	−0.372353	−	0.928091i	$-0.621449\pi$
$691$	−19.5760	−0.744705	−0.372353	+	0.928091i	$0.621449\pi$
$692$	−1.62790	−0.0618835
$693$	0.659586	0.0250556
$694$	−35.8750	−1.36180
$695$	−7.96819	−0.302251
$696$	2.58229	0.0978815
$697$	−16.1342	−0.611125
$698$	25.7500	0.974650
$699$	−2.72299	−0.102993
$700$	−0.703869	−0.0266038
$701$	−49.5887	−1.87294	−0.936470	−	0.350747i	$-0.885928\pi$
$701$	−49.5887	−1.87294	−0.936470	+	0.350747i	$0.885928\pi$
$702$	−6.49486	−0.245133
$703$	17.9571	0.677266
$704$	2.72610	0.102744
$705$	−19.8767	−0.748599
$706$	5.53932	0.208475
$707$	−21.5021	−0.808669
$708$	−0.641125	−0.0240949
$709$	−11.6586	−0.437847	−0.218923	−	0.975742i	$-0.570255\pi$
$709$	−11.6586	−0.437847	−0.218923	+	0.975742i	$0.570255\pi$
$710$	26.3524	0.988988
$711$	5.67719	0.212911
$712$	16.5983	0.622046
$713$	−2.45922	−0.0920986
$714$	−4.05700	−0.151829
$715$	−3.35951	−0.125639
$716$	−7.55474	−0.282334
$717$	21.3708	0.798106
$718$	53.5527	1.99857
$719$	−48.6812	−1.81550	−0.907751	−	0.419510i	$-0.862202\pi$
$719$	−48.6812	−1.81550	−0.907751	+	0.419510i	$0.862202\pi$
$720$	8.40785	0.313342
$721$	−18.6880	−0.695977
$722$	22.8812	0.851551
$723$	−9.01276	−0.335188
$724$	−1.39497	−0.0518435
$725$	−1.51515	−0.0562714
$726$	16.3996	0.608647
$727$	−17.4324	−0.646531	−0.323265	−	0.946308i	$-0.604781\pi$
$727$	−17.4324	−0.646531	−0.323265	+	0.946308i	$0.604781\pi$
$728$	−17.3907	−0.644544
$729$	1.00000	0.0370370
$730$	−45.1283	−1.67027
$731$	−5.45624	−0.201806
$732$	−1.54760	−0.0572011
$733$	52.2101	1.92843	0.964213	−	0.265129i	$-0.0854146\pi$
$733$	52.2101	1.92843	0.964213	+	0.265129i	$0.0854146\pi$
$734$	−46.5931	−1.71978
$735$	−8.45965	−0.312039
$736$	−1.65959	−0.0611731
$737$	−4.77916	−0.176043
$738$	−14.3435	−0.527990
$739$	−50.6242	−1.86224	−0.931120	−	0.364713i	$-0.881167\pi$
$739$	−50.6242	−1.86224	−0.931120	+	0.364713i	$0.881167\pi$
$740$	1.69737	0.0623966
$741$	25.0323	0.919584
$742$	−13.3604	−0.490477
$743$	−13.3966	−0.491475	−0.245738	−	0.969336i	$-0.579030\pi$
$743$	−13.3966	−0.491475	−0.245738	+	0.969336i	$0.579030\pi$
$744$	−6.35043	−0.232818
$745$	14.1672	0.519045
$746$	52.5154	1.92273
$747$	−3.89987	−0.142689
$748$	0.211571	0.00773580
$749$	−9.42061	−0.344222
$750$	−18.4278	−0.672887
$751$	25.0172	0.912892	0.456446	−	0.889751i	$-0.349122\pi$
$751$	25.0172	0.912892	0.456446	+	0.889751i	$0.349122\pi$
$752$	47.9563	1.74879
$753$	−1.74871	−0.0637266
$754$	6.49486	0.236529
$755$	−37.0285	−1.34760
$756$	−0.464553	−0.0168956
$757$	12.6825	0.460954	0.230477	−	0.973078i	$-0.425971\pi$
$757$	12.6825	0.460954	0.230477	+	0.973078i	$0.425971\pi$
$758$	−5.40107	−0.196176
$759$	−0.419828	−0.0152388
$760$	−28.1504	−1.02112
$761$	5.60837	0.203303	0.101652	−	0.994820i	$-0.467587\pi$
$761$	5.60837	0.203303	0.101652	+	0.994820i	$0.467587\pi$
$762$	14.5103	0.525654
$763$	25.5987	0.926734
$764$	6.61770	0.239420
$765$	−3.18156	−0.115030
$766$	−23.6741	−0.855379
$767$	9.29437	0.335600
$768$	−6.94907	−0.250753
$769$	31.9204	1.15108	0.575539	−	0.817774i	$-0.304792\pi$
$769$	31.9204	1.15108	0.575539	+	0.817774i	$0.304792\pi$
$770$	−1.86560	−0.0672317
$771$	−7.58239	−0.273073
$772$	−2.88224	−0.103734
$773$	28.6849	1.03173	0.515863	−	0.856671i	$-0.327472\pi$
$773$	28.6849	1.03173	0.515863	+	0.856671i	$0.327472\pi$
$774$	−4.85066	−0.174353
$775$	3.72610	0.133845
$776$	−7.07290	−0.253902
$777$	4.83114	0.173316
$778$	−55.5934	−1.99312
$779$	55.2821	1.98069
$780$	2.36614	0.0847215
$781$	−3.91150	−0.139964
$782$	2.58229	0.0923426
$783$	−1.00000	−0.0357371
$784$	20.4105	0.728946
$785$	−25.0159	−0.892856
$786$	−32.9632	−1.17576
$787$	15.9337	0.567974	0.283987	−	0.958828i	$-0.408343\pi$
$787$	15.9337	0.567974	0.283987	+	0.958828i	$0.408343\pi$
$788$	1.46538	0.0522019
$789$	−19.9211	−0.709209
$790$	−16.0577	−0.571306
$791$	−23.0282	−0.818789
$792$	−1.08412	−0.0385225
$793$	22.4356	0.796711
$794$	−10.9111	−0.387219
$795$	−10.4775	−0.371597
$796$	4.86520	0.172442
$797$	−23.8512	−0.844852	−0.422426	−	0.906398i	$-0.638821\pi$
$797$	−23.8512	−0.844852	−0.422426	+	0.906398i	$0.638821\pi$
$798$	13.9009	0.492087
$799$	−18.1468	−0.641989
$800$	2.51453	0.0889019
$801$	−6.42772	−0.227112
$802$	−15.1740	−0.535813
$803$	6.69841	0.236382
$804$	3.36602	0.118710
$805$	−2.93286	−0.103370
$806$	−15.9723	−0.562600
$807$	−17.7510	−0.624865
$808$	35.3416	1.24331
$809$	−35.2057	−1.23777	−0.618883	−	0.785483i	$-0.712415\pi$
$809$	−35.2057	−1.23777	−0.618883	+	0.785483i	$0.712415\pi$
$810$	−2.82845	−0.0993816
$811$	36.1669	1.26999	0.634995	−	0.772516i	$-0.281002\pi$
$811$	36.1669	1.26999	0.634995	+	0.772516i	$0.281002\pi$
$812$	0.464553	0.0163026
$813$	−12.5974	−0.441810
$814$	−1.95604	−0.0685591
$815$	−21.0155	−0.736141
$816$	7.67612	0.268718
$817$	18.6953	0.654065
$818$	−35.4040	−1.23787
$819$	6.73462	0.235327
$820$	5.22546	0.182481
$821$	34.7595	1.21312	0.606558	−	0.795040i	$-0.292550\pi$
$821$	34.7595	1.21312	0.606558	+	0.795040i	$0.292550\pi$
$822$	−13.6166	−0.474933
$823$	−42.7161	−1.48899	−0.744495	−	0.667629i	$-0.767309\pi$
$823$	−42.7161	−1.48899	−0.744495	+	0.667629i	$0.767309\pi$
$824$	30.7163	1.07005
$825$	0.636104	0.0221463
$826$	5.16135	0.179586
$827$	−41.8359	−1.45478	−0.727389	−	0.686225i	$-0.759266\pi$
$827$	−41.8359	−1.45478	−0.727389	+	0.686225i	$0.759266\pi$
$828$	0.295689	0.0102759
$829$	−16.5895	−0.576178	−0.288089	−	0.957604i	$-0.593020\pi$
$829$	−16.5895	−0.576178	−0.288089	+	0.957604i	$0.593020\pi$
$830$	11.0306	0.382877
$831$	11.5272	0.399874
$832$	27.8345	0.964987
$833$	−7.72341	−0.267600
$834$	−6.46732	−0.223945
$835$	34.5235	1.19473
$836$	−0.724927	−0.0250721
$837$	2.45922	0.0850031
$838$	−24.7734	−0.855782
$839$	−25.7568	−0.889224	−0.444612	−	0.895723i	$-0.646658\pi$
$839$	−25.7568	−0.889224	−0.444612	+	0.895723i	$0.646658\pi$
$840$	−7.57350	−0.261311
$841$	1.00000	0.0344828
$842$	24.5198	0.845008
$843$	24.7226	0.851493
$844$	0.303200	0.0104366
$845$	−10.0338	−0.345175
$846$	−16.1328	−0.554656
$847$	−17.0050	−0.584300
$848$	25.2788	0.868079
$849$	−24.5908	−0.843954
$850$	−3.91257	−0.134200
$851$	−3.07503	−0.105411
$852$	2.75491	0.0943817
$853$	17.6313	0.603686	0.301843	−	0.953358i	$-0.402398\pi$
$853$	17.6313	0.603686	0.301843	+	0.953358i	$0.402398\pi$
$854$	12.4589	0.426335
$855$	10.9013	0.372817
$856$	15.4841	0.529234
$857$	−16.0474	−0.548168	−0.274084	−	0.961706i	$-0.588375\pi$
$857$	−16.0474	−0.548168	−0.274084	+	0.961706i	$0.588375\pi$
$858$	−2.72672	−0.0930888
$859$	−7.16630	−0.244511	−0.122256	−	0.992499i	$-0.539013\pi$
$859$	−7.16630	−0.244511	−0.122256	+	0.992499i	$0.539013\pi$
$860$	1.76714	0.0602591
$861$	14.8729	0.506869
$862$	−62.7342	−2.13674
$863$	20.1130	0.684655	0.342327	−	0.939581i	$-0.388785\pi$
$863$	20.1130	0.684655	0.342327	+	0.939581i	$0.388785\pi$
$864$	1.65959	0.0564602
$865$	10.2774	0.349443
$866$	53.9416	1.83301
$867$	14.0953	0.478702
$868$	−1.14244	−0.0387769
$869$	2.38344	0.0808528
$870$	2.82845	0.0958934
$871$	−48.7971	−1.65343
$872$	−42.0749	−1.42484
$873$	2.73900	0.0927011
$874$	−8.84797	−0.299287
$875$	19.1080	0.645970
$876$	−4.71776	−0.159398
$877$	−29.4766	−0.995354	−0.497677	−	0.867363i	$-0.665813\pi$
$877$	−29.4766	−0.995354	−0.497677	+	0.867363i	$0.665813\pi$
$878$	−38.2409	−1.29057
$879$	9.97847	0.336566
$880$	3.52985	0.118991
$881$	43.0652	1.45090	0.725452	−	0.688273i	$-0.241631\pi$
$881$	43.0652	1.45090	0.725452	+	0.688273i	$0.241631\pi$
$882$	−6.86621	−0.231197
$883$	−47.2446	−1.58991	−0.794954	−	0.606669i	$-0.792505\pi$
$883$	−47.2446	−1.58991	−0.794954	+	0.606669i	$0.792505\pi$
$884$	2.16022	0.0726560
$885$	4.04761	0.136059
$886$	18.7624	0.630336
$887$	14.8000	0.496934	0.248467	−	0.968640i	$-0.420073\pi$
$887$	14.8000	0.496934	0.248467	+	0.968640i	$0.420073\pi$
$888$	−7.94063	−0.266470
$889$	−15.0460	−0.504626
$890$	18.1805	0.609411
$891$	0.419828	0.0140648
$892$	−5.30838	−0.177738
$893$	62.1784	2.08072
$894$	11.4987	0.384573
$895$	47.6953	1.59428
$896$	20.6717	0.690594
$897$	−4.28660	−0.143125
$898$	−45.0276	−1.50259
$899$	−2.45922	−0.0820196
$900$	−0.448015	−0.0149338
$901$	−9.56561	−0.318677
$902$	−6.02179	−0.200504
$903$	5.02972	0.167379
$904$	37.8500	1.25887
$905$	8.80684	0.292749
$906$	−30.0539	−0.998473
$907$	54.9862	1.82579	0.912893	−	0.408198i	$-0.133843\pi$
$907$	54.9862	1.82579	0.912893	+	0.408198i	$0.133843\pi$
$908$	−5.32685	−0.176778
$909$	−13.6861	−0.453941
$910$	−19.0485	−0.631452
$911$	8.95163	0.296581	0.148290	−	0.988944i	$-0.452623\pi$
$911$	8.95163	0.296581	0.148290	+	0.988944i	$0.452623\pi$
$912$	−26.3015	−0.870930
$913$	−1.63727	−0.0541859
$914$	13.2642	0.438740
$915$	9.77048	0.323002
$916$	2.96755	0.0980506
$917$	34.1800	1.12872
$918$	−2.58229	−0.0852283
$919$	−34.6629	−1.14342	−0.571711	−	0.820455i	$-0.693720\pi$
$919$	−34.6629	−1.14342	−0.571711	+	0.820455i	$0.693720\pi$
$920$	4.82056	0.158929
$921$	6.06605	0.199883
$922$	23.0308	0.758480
$923$	−39.9379	−1.31457
$924$	−0.195032	−0.00641610
$925$	4.65914	0.153192
$926$	47.0107	1.54487
$927$	−11.8950	−0.390682
$928$	−1.65959	−0.0544786
$929$	−27.1346	−0.890257	−0.445129	−	0.895467i	$-0.646842\pi$
$929$	−27.1346	−0.890257	−0.445129	+	0.895467i	$0.646842\pi$
$930$	−6.95578	−0.228089
$931$	26.4635	0.867307
$932$	0.805158	0.0263738
$933$	−18.9573	−0.620633
$934$	−12.2650	−0.401322
$935$	−1.33571	−0.0436824
$936$	−11.0693	−0.361810
$937$	50.2854	1.64275	0.821377	−	0.570386i	$-0.193206\pi$
$937$	50.2854	1.64275	0.821377	+	0.570386i	$0.193206\pi$
$938$	−27.0980	−0.884780
$939$	−8.41377	−0.274573
$940$	5.87732	0.191697
$941$	40.0745	1.30639	0.653195	−	0.757189i	$-0.273428\pi$
$941$	40.0745	1.30639	0.653195	+	0.757189i	$0.273428\pi$
$942$	−20.3040	−0.661539
$943$	−9.46667	−0.308277
$944$	−9.76562	−0.317844
$945$	2.93286	0.0954060
$946$	−2.03644	−0.0662105
$947$	31.4413	1.02170	0.510852	−	0.859669i	$-0.329330\pi$
$947$	31.4413	1.02170	0.510852	+	0.859669i	$0.329330\pi$
$948$	−1.67869	−0.0545212
$949$	68.3933	2.22014
$950$	13.4060	0.434949
$951$	−28.7722	−0.933004
$952$	−6.91439	−0.224097
$953$	−20.1304	−0.652088	−0.326044	−	0.945355i	$-0.605716\pi$
$953$	−20.1304	−0.652088	−0.326044	+	0.945355i	$0.605716\pi$
$954$	−8.50395	−0.275325
$955$	−41.7795	−1.35195
$956$	−6.31911	−0.204375
$957$	−0.419828	−0.0135711
$958$	41.2094	1.33141
$959$	14.1192	0.455934
$960$	12.1217	0.391225
$961$	−24.9522	−0.804911
$962$	−19.9719	−0.643920
$963$	−5.99624	−0.193226
$964$	2.66498	0.0858331
$965$	18.1964	0.585763
$966$	−2.38043	−0.0765892
$967$	14.9479	0.480691	0.240345	−	0.970687i	$-0.422739\pi$
$967$	14.9479	0.480691	0.240345	+	0.970687i	$0.422739\pi$
$968$	27.9501	0.898349
$969$	9.95259	0.319723
$970$	−7.74712	−0.248745
$971$	6.25401	0.200701	0.100350	−	0.994952i	$-0.468004\pi$
$971$	6.25401	0.200701	0.100350	+	0.994952i	$0.468004\pi$
$972$	−0.295689	−0.00948424
$973$	6.70606	0.214987
$974$	−29.0853	−0.931953
$975$	6.49486	0.208002
$976$	−23.5731	−0.754557
$977$	45.0757	1.44210	0.721050	−	0.692883i	$-0.243660\pi$
$977$	45.0757	1.44210	0.721050	+	0.692883i	$0.243660\pi$
$978$	−17.0571	−0.545425
$979$	−2.69854	−0.0862456
$980$	2.50143	0.0799052
$981$	16.2936	0.520216
$982$	1.30014	0.0414890
$983$	−30.1896	−0.962899	−0.481449	−	0.876474i	$-0.659889\pi$
$983$	−30.1896	−0.962899	−0.481449	+	0.876474i	$0.659889\pi$
$984$	−24.4457	−0.779301
$985$	−9.25136	−0.294773
$986$	2.58229	0.0822369
$987$	16.7283	0.532468
$988$	−7.40178	−0.235482
$989$	−3.20143	−0.101800
$990$	−1.18746	−0.0377400
$991$	−10.0771	−0.320109	−0.160054	−	0.987108i	$-0.551167\pi$
$991$	−10.0771	−0.320109	−0.160054	+	0.987108i	$0.551167\pi$
$992$	4.08129	0.129581
$993$	−16.5416	−0.524931
$994$	−22.1783	−0.703453
$995$	−30.7154	−0.973745
$996$	1.15315	0.0365389
$997$	25.1052	0.795089	0.397544	−	0.917583i	$-0.369862\pi$
$997$	25.1052	0.795089	0.397544	+	0.917583i	$0.369862\pi$
$998$	4.86036	0.153852
$999$	3.07503	0.0972897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.h.1.4	✓	5
3.2	odd	2		6003.2.a.h.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.h.1.4	✓	5	1.1	even	1	trivial
6003.2.a.h.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.51515 q^{2} -1.00000 q^{3} +0.295689 q^{4} -1.86677 q^{5} -1.51515 q^{6} +1.57109 q^{7} -2.58229 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.51515 q^{2} -1.00000 q^{3} +0.295689 q^{4} -1.86677 q^{5} -1.51515 q^{6} +1.57109 q^{7} -2.58229 q^{8} +1.00000 q^{9} -2.82845 q^{10} +0.419828 q^{11} -0.295689 q^{12} +4.28660 q^{13} +2.38043 q^{14} +1.86677 q^{15} -4.50395 q^{16} +1.70431 q^{17} +1.51515 q^{18} -5.83966 q^{19} -0.551985 q^{20} -1.57109 q^{21} +0.636104 q^{22} +1.00000 q^{23} +2.58229 q^{24} -1.51515 q^{25} +6.49486 q^{26} -1.00000 q^{27} +0.464553 q^{28} +1.00000 q^{29} +2.82845 q^{30} -2.45922 q^{31} -1.65959 q^{32} -0.419828 q^{33} +2.58229 q^{34} -2.93286 q^{35} +0.295689 q^{36} -3.07503 q^{37} -8.84797 q^{38} -4.28660 q^{39} +4.82056 q^{40} -9.46667 q^{41} -2.38043 q^{42} -3.20143 q^{43} +0.124139 q^{44} -1.86677 q^{45} +1.51515 q^{46} -10.6476 q^{47} +4.50395 q^{48} -4.53169 q^{49} -2.29569 q^{50} -1.70431 q^{51} +1.26750 q^{52} -5.61260 q^{53} -1.51515 q^{54} -0.783724 q^{55} -4.05700 q^{56} +5.83966 q^{57} +1.51515 q^{58} +2.16824 q^{59} +0.551985 q^{60} +5.23388 q^{61} -3.72610 q^{62} +1.57109 q^{63} +6.49337 q^{64} -8.00212 q^{65} -0.636104 q^{66} -11.3836 q^{67} +0.503947 q^{68} -1.00000 q^{69} -4.44373 q^{70} -9.31691 q^{71} -2.58229 q^{72} +15.9551 q^{73} -4.65914 q^{74} +1.51515 q^{75} -1.72672 q^{76} +0.659586 q^{77} -6.49486 q^{78} +5.67719 q^{79} +8.40785 q^{80} +1.00000 q^{81} -14.3435 q^{82} -3.89987 q^{83} -0.464553 q^{84} -3.18156 q^{85} -4.85066 q^{86} -1.00000 q^{87} -1.08412 q^{88} -6.42772 q^{89} -2.82845 q^{90} +6.73462 q^{91} +0.295689 q^{92} +2.45922 q^{93} -16.1328 q^{94} +10.9013 q^{95} +1.65959 q^{96} +2.73900 q^{97} -6.86621 q^{98} +0.419828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * q^99

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