LMFDB - Embedded newform 2001.2.a.o.1.8

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 $ x^20 - 2x^19 - 33x^18 + 64x^17 + 453x^16 - 846x^15 - 3353x^14 + 5985x^13 + 14484x^12 - 24566x^11 - 36791x^10 + 59410x^9 + 52109x^8 - 82362x^7 - 34967x^6 + 60661x^5 + 5201x^4 - 19624x^3 + 2768x^2 + 1408*x - 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.852674$ 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)

$f(q)$	$=$	$q-0.852674 q^{2} +1.00000 q^{3} -1.27295 q^{4} -0.278169 q^{5} -0.852674 q^{6} +2.70488 q^{7} +2.79076 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.852674 q^{2} +1.00000 q^{3} -1.27295 q^{4} -0.278169 q^{5} -0.852674 q^{6} +2.70488 q^{7} +2.79076 q^{8} +1.00000 q^{9} +0.237188 q^{10} +5.07059 q^{11} -1.27295 q^{12} -0.519860 q^{13} -2.30638 q^{14} -0.278169 q^{15} +0.166287 q^{16} +2.19587 q^{17} -0.852674 q^{18} -0.104552 q^{19} +0.354095 q^{20} +2.70488 q^{21} -4.32356 q^{22} +1.00000 q^{23} +2.79076 q^{24} -4.92262 q^{25} +0.443271 q^{26} +1.00000 q^{27} -3.44317 q^{28} +1.00000 q^{29} +0.237188 q^{30} +7.35747 q^{31} -5.72330 q^{32} +5.07059 q^{33} -1.87236 q^{34} -0.752416 q^{35} -1.27295 q^{36} -0.259721 q^{37} +0.0891492 q^{38} -0.519860 q^{39} -0.776303 q^{40} +0.509113 q^{41} -2.30638 q^{42} +4.63055 q^{43} -6.45459 q^{44} -0.278169 q^{45} -0.852674 q^{46} -12.4082 q^{47} +0.166287 q^{48} +0.316385 q^{49} +4.19739 q^{50} +2.19587 q^{51} +0.661754 q^{52} +1.04291 q^{53} -0.852674 q^{54} -1.41048 q^{55} +7.54867 q^{56} -0.104552 q^{57} -0.852674 q^{58} +0.323984 q^{59} +0.354095 q^{60} +8.63178 q^{61} -6.27352 q^{62} +2.70488 q^{63} +4.54754 q^{64} +0.144609 q^{65} -4.32356 q^{66} -3.31184 q^{67} -2.79522 q^{68} +1.00000 q^{69} +0.641565 q^{70} -14.1260 q^{71} +2.79076 q^{72} -0.479599 q^{73} +0.221458 q^{74} -4.92262 q^{75} +0.133090 q^{76} +13.7153 q^{77} +0.443271 q^{78} +9.38238 q^{79} -0.0462559 q^{80} +1.00000 q^{81} -0.434108 q^{82} -6.67576 q^{83} -3.44317 q^{84} -0.610823 q^{85} -3.94835 q^{86} +1.00000 q^{87} +14.1508 q^{88} +5.52034 q^{89} +0.237188 q^{90} -1.40616 q^{91} -1.27295 q^{92} +7.35747 q^{93} +10.5801 q^{94} +0.0290833 q^{95} -5.72330 q^{96} +0.587030 q^{97} -0.269774 q^{98} +5.07059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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 $

$2$	−0.852674	−0.602932	−0.301466	−	0.953477i	$-0.597476\pi$
$2$	−0.852674	−0.602932	−0.301466	+	0.953477i	$0.597476\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.27295	−0.636473
$5$	−0.278169	−0.124401	−0.0622006	−	0.998064i	$-0.519812\pi$
$5$	−0.278169	−0.124401	−0.0622006	+	0.998064i	$0.519812\pi$
$6$	−0.852674	−0.348103
$7$	2.70488	1.02235	0.511175	−	0.859477i	$-0.329211\pi$
$7$	2.70488	1.02235	0.511175	+	0.859477i	$0.329211\pi$
$8$	2.79076	0.986682
$9$	1.00000	0.333333
$10$	0.237188	0.0750054
$11$	5.07059	1.52884	0.764420	−	0.644718i	$-0.223025\pi$
$11$	5.07059	1.52884	0.764420	+	0.644718i	$0.223025\pi$
$12$	−1.27295	−0.367468
$13$	−0.519860	−0.144183	−0.0720916	−	0.997398i	$-0.522967\pi$
$13$	−0.519860	−0.144183	−0.0720916	+	0.997398i	$0.522967\pi$
$14$	−2.30638	−0.616407
$15$	−0.278169	−0.0718230
$16$	0.166287	0.0415717
$17$	2.19587	0.532576	0.266288	−	0.963894i	$-0.414203\pi$
$17$	2.19587	0.532576	0.266288	+	0.963894i	$0.414203\pi$
$18$	−0.852674	−0.200977
$19$	−0.104552	−0.0239860	−0.0119930	−	0.999928i	$-0.503818\pi$
$19$	−0.104552	−0.0239860	−0.0119930	+	0.999928i	$0.503818\pi$
$20$	0.354095	0.0791780
$21$	2.70488	0.590254
$22$	−4.32356	−0.921786
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.79076	0.569661
$25$	−4.92262	−0.984524
$26$	0.443271	0.0869326
$27$	1.00000	0.192450
$28$	−3.44317	−0.650698
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.237188	0.0433044
$31$	7.35747	1.32144	0.660720	−	0.750632i	$-0.270251\pi$
$31$	7.35747	1.32144	0.660720	+	0.750632i	$0.270251\pi$
$32$	−5.72330	−1.01175
$33$	5.07059	0.882676
$34$	−1.87236	−0.321107
$35$	−0.752416	−0.127181
$36$	−1.27295	−0.212158
$37$	−0.259721	−0.0426979	−0.0213490	−	0.999772i	$-0.506796\pi$
$37$	−0.259721	−0.0426979	−0.0213490	+	0.999772i	$0.506796\pi$
$38$	0.0891492	0.0144619
$39$	−0.519860	−0.0832442
$40$	−0.776303	−0.122744
$41$	0.509113	0.0795101	0.0397551	−	0.999209i	$-0.487342\pi$
$41$	0.509113	0.0795101	0.0397551	+	0.999209i	$0.487342\pi$
$42$	−2.30638	−0.355883
$43$	4.63055	0.706152	0.353076	−	0.935595i	$-0.385136\pi$
$43$	4.63055	0.706152	0.353076	+	0.935595i	$0.385136\pi$
$44$	−6.45459	−0.973066
$45$	−0.278169	−0.0414671
$46$	−0.852674	−0.125720
$47$	−12.4082	−1.80992	−0.904959	−	0.425499i	$-0.860098\pi$
$47$	−12.4082	−1.80992	−0.904959	+	0.425499i	$0.860098\pi$
$48$	0.166287	0.0240014
$49$	0.316385	0.0451979
$50$	4.19739	0.593601
$51$	2.19587	0.307483
$52$	0.661754	0.0917687
$53$	1.04291	0.143255	0.0716274	−	0.997431i	$-0.477181\pi$
$53$	1.04291	0.143255	0.0716274	+	0.997431i	$0.477181\pi$
$54$	−0.852674	−0.116034
$55$	−1.41048	−0.190189
$56$	7.54867	1.00873
$57$	−0.104552	−0.0138483
$58$	−0.852674	−0.111962
$59$	0.323984	0.0421792	0.0210896	−	0.999778i	$-0.493286\pi$
$59$	0.323984	0.0421792	0.0210896	+	0.999778i	$0.493286\pi$
$60$	0.354095	0.0457135
$61$	8.63178	1.10519	0.552593	−	0.833451i	$-0.313638\pi$
$61$	8.63178	1.10519	0.552593	+	0.833451i	$0.313638\pi$
$62$	−6.27352	−0.796738
$63$	2.70488	0.340783
$64$	4.54754	0.568442
$65$	0.144609	0.0179366
$66$	−4.32356	−0.532194
$67$	−3.31184	−0.404605	−0.202303	−	0.979323i	$-0.564842\pi$
$67$	−3.31184	−0.404605	−0.202303	+	0.979323i	$0.564842\pi$
$68$	−2.79522	−0.338970
$69$	1.00000	0.120386
$70$	0.641565	0.0766817
$71$	−14.1260	−1.67645	−0.838226	−	0.545323i	$-0.816407\pi$
$71$	−14.1260	−1.67645	−0.838226	+	0.545323i	$0.816407\pi$
$72$	2.79076	0.328894
$73$	−0.479599	−0.0561328	−0.0280664	−	0.999606i	$-0.508935\pi$
$73$	−0.479599	−0.0561328	−0.0280664	+	0.999606i	$0.508935\pi$
$74$	0.221458	0.0257439
$75$	−4.92262	−0.568415
$76$	0.133090	0.0152664
$77$	13.7153	1.56301
$78$	0.443271	0.0501906
$79$	9.38238	1.05560	0.527800	−	0.849369i	$-0.323017\pi$
$79$	9.38238	1.05560	0.527800	+	0.849369i	$0.323017\pi$
$80$	−0.0462559	−0.00517156
$81$	1.00000	0.111111
$82$	−0.434108	−0.0479392
$83$	−6.67576	−0.732759	−0.366380	−	0.930465i	$-0.619403\pi$
$83$	−6.67576	−0.732759	−0.366380	+	0.930465i	$0.619403\pi$
$84$	−3.44317	−0.375681
$85$	−0.610823	−0.0662531
$86$	−3.94835	−0.425761
$87$	1.00000	0.107211
$88$	14.1508	1.50848
$89$	5.52034	0.585155	0.292577	−	0.956242i	$-0.405487\pi$
$89$	5.52034	0.585155	0.292577	+	0.956242i	$0.405487\pi$
$90$	0.237188	0.0250018
$91$	−1.40616	−0.147406
$92$	−1.27295	−0.132714
$93$	7.35747	0.762934
$94$	10.5801	1.09126
$95$	0.0290833	0.00298388
$96$	−5.72330	−0.584132
$97$	0.587030	0.0596038	0.0298019	−	0.999556i	$-0.490512\pi$
$97$	0.587030	0.0596038	0.0298019	+	0.999556i	$0.490512\pi$
$98$	−0.269774	−0.0272513
$99$	5.07059	0.509613
$100$	6.26624	0.626624
$101$	12.3741	1.23127	0.615634	−	0.788033i	$-0.288900\pi$
$101$	12.3741	1.23127	0.615634	+	0.788033i	$0.288900\pi$
$102$	−1.87236	−0.185391
$103$	13.6687	1.34681	0.673407	−	0.739272i	$-0.264830\pi$
$103$	13.6687	1.34681	0.673407	+	0.739272i	$0.264830\pi$
$104$	−1.45080	−0.142263
$105$	−0.752416	−0.0734282
$106$	−0.889263	−0.0863728
$107$	−4.99088	−0.482487	−0.241243	−	0.970465i	$-0.577555\pi$
$107$	−4.99088	−0.482487	−0.241243	+	0.970465i	$0.577555\pi$
$108$	−1.27295	−0.122489
$109$	8.14915	0.780547	0.390274	−	0.920699i	$-0.372380\pi$
$109$	8.14915	0.780547	0.390274	+	0.920699i	$0.372380\pi$
$110$	1.20268	0.114671
$111$	−0.259721	−0.0246517
$112$	0.449786	0.0425008
$113$	14.9087	1.40250	0.701248	−	0.712917i	$-0.252627\pi$
$113$	14.9087	1.40250	0.701248	+	0.712917i	$0.252627\pi$
$114$	0.0891492	0.00834959
$115$	−0.278169	−0.0259394
$116$	−1.27295	−0.118190
$117$	−0.519860	−0.0480611
$118$	−0.276253	−0.0254312
$119$	5.93956	0.544479
$120$	−0.776303	−0.0708665
$121$	14.7109	1.33735
$122$	−7.36010	−0.666352
$123$	0.509113	0.0459052
$124$	−9.36566	−0.841062
$125$	2.76017	0.246877
$126$	−2.30638	−0.205469
$127$	−9.41334	−0.835299	−0.417649	−	0.908608i	$-0.637146\pi$
$127$	−9.41334	−0.835299	−0.417649	+	0.908608i	$0.637146\pi$
$128$	7.56904	0.669015
$129$	4.63055	0.407697
$130$	−0.123304	−0.0108145
$131$	2.66337	0.232700	0.116350	−	0.993208i	$-0.462881\pi$
$131$	2.66337	0.232700	0.116350	+	0.993208i	$0.462881\pi$
$132$	−6.45459	−0.561800
$133$	−0.282802	−0.0245220
$134$	2.82392	0.243949
$135$	−0.278169	−0.0239410
$136$	6.12813	0.525483
$137$	−11.4148	−0.975233	−0.487617	−	0.873058i	$-0.662134\pi$
$137$	−11.4148	−0.975233	−0.487617	+	0.873058i	$0.662134\pi$
$138$	−0.852674	−0.0725844
$139$	12.6211	1.07051	0.535254	−	0.844691i	$-0.320216\pi$
$139$	12.6211	1.07051	0.535254	+	0.844691i	$0.320216\pi$
$140$	0.957785	0.0809476
$141$	−12.4082	−1.04496
$142$	12.0449	1.01079
$143$	−2.63600	−0.220433
$144$	0.166287	0.0138572
$145$	−0.278169	−0.0231007
$146$	0.408941	0.0338442
$147$	0.316385	0.0260950
$148$	0.330611	0.0271761
$149$	10.6883	0.875616	0.437808	−	0.899068i	$-0.355755\pi$
$149$	10.6883	0.875616	0.437808	+	0.899068i	$0.355755\pi$
$150$	4.19739	0.342716
$151$	−7.96037	−0.647806	−0.323903	−	0.946090i	$-0.604995\pi$
$151$	−7.96037	−0.647806	−0.323903	+	0.946090i	$0.604995\pi$
$152$	−0.291780	−0.0236665
$153$	2.19587	0.177525
$154$	−11.6947	−0.942387
$155$	−2.04662	−0.164389
$156$	0.661754	0.0529827
$157$	6.59115	0.526031	0.263015	−	0.964792i	$-0.415283\pi$
$157$	6.59115	0.526031	0.263015	+	0.964792i	$0.415283\pi$
$158$	−8.00011	−0.636455
$159$	1.04291	0.0827082
$160$	1.59205	0.125862
$161$	2.70488	0.213175
$162$	−0.852674	−0.0669924
$163$	21.2877	1.66738	0.833691	−	0.552232i	$-0.186224\pi$
$163$	21.2877	1.66738	0.833691	+	0.552232i	$0.186224\pi$
$164$	−0.648074	−0.0506061
$165$	−1.41048	−0.109806
$166$	5.69225	0.441804
$167$	18.6280	1.44148	0.720739	−	0.693207i	$-0.243803\pi$
$167$	18.6280	1.44148	0.720739	+	0.693207i	$0.243803\pi$
$168$	7.54867	0.582392
$169$	−12.7297	−0.979211
$170$	0.520833	0.0399461
$171$	−0.104552	−0.00799533
$172$	−5.89444	−0.449447
$173$	−10.1837	−0.774251	−0.387125	−	0.922027i	$-0.626532\pi$
$173$	−10.1837	−0.774251	−0.387125	+	0.922027i	$0.626532\pi$
$174$	−0.852674	−0.0646411
$175$	−13.3151	−1.00653
$176$	0.843171	0.0635564
$177$	0.323984	0.0243522
$178$	−4.70705	−0.352808
$179$	−5.18551	−0.387583	−0.193792	−	0.981043i	$-0.562079\pi$
$179$	−5.18551	−0.387583	−0.193792	+	0.981043i	$0.562079\pi$
$180$	0.354095	0.0263927
$181$	11.3310	0.842224	0.421112	−	0.907009i	$-0.361640\pi$
$181$	11.3310	0.842224	0.421112	+	0.907009i	$0.361640\pi$
$182$	1.19900	0.0888755
$183$	8.63178	0.638080
$184$	2.79076	0.205737
$185$	0.0722466	0.00531167
$186$	−6.27352	−0.459997
$187$	11.1343	0.814224
$188$	15.7949	1.15196
$189$	2.70488	0.196751
$190$	−0.0247986	−0.00179908
$191$	−15.0350	−1.08789	−0.543947	−	0.839119i	$-0.683071\pi$
$191$	−15.0350	−1.08789	−0.543947	+	0.839119i	$0.683071\pi$
$192$	4.54754	0.328190
$193$	11.4680	0.825487	0.412743	−	0.910847i	$-0.364571\pi$
$193$	11.4680	0.825487	0.412743	+	0.910847i	$0.364571\pi$
$194$	−0.500545	−0.0359370
$195$	0.144609	0.0103557
$196$	−0.402742	−0.0287673
$197$	−25.0347	−1.78365	−0.891826	−	0.452379i	$-0.850575\pi$
$197$	−25.0347	−1.78365	−0.891826	+	0.452379i	$0.850575\pi$
$198$	−4.32356	−0.307262
$199$	−5.75281	−0.407806	−0.203903	−	0.978991i	$-0.565363\pi$
$199$	−5.75281	−0.407806	−0.203903	+	0.978991i	$0.565363\pi$
$200$	−13.7378	−0.971412
$201$	−3.31184	−0.233599
$202$	−10.5511	−0.742370
$203$	2.70488	0.189845
$204$	−2.79522	−0.195705
$205$	−0.141620	−0.00989115
$206$	−11.6549	−0.812037
$207$	1.00000	0.0695048
$208$	−0.0864458	−0.00599393
$209$	−0.530143	−0.0366707
$210$	0.641565	0.0442722
$211$	3.52515	0.242682	0.121341	−	0.992611i	$-0.461281\pi$
$211$	3.52515	0.242682	0.121341	+	0.992611i	$0.461281\pi$
$212$	−1.32757	−0.0911778
$213$	−14.1260	−0.967900
$214$	4.25560	0.290907
$215$	−1.28808	−0.0878461
$216$	2.79076	0.189887
$217$	19.9011	1.35097
$218$	−6.94857	−0.470617
$219$	−0.479599	−0.0324083
$220$	1.79547	0.121051
$221$	−1.14154	−0.0767885
$222$	0.221458	0.0148633
$223$	−22.4725	−1.50487	−0.752436	−	0.658665i	$-0.771121\pi$
$223$	−22.4725	−1.50487	−0.752436	+	0.658665i	$0.771121\pi$
$224$	−15.4809	−1.03436
$225$	−4.92262	−0.328175
$226$	−12.7123	−0.845609
$227$	−13.5150	−0.897023	−0.448511	−	0.893777i	$-0.648046\pi$
$227$	−13.5150	−0.897023	−0.448511	+	0.893777i	$0.648046\pi$
$228$	0.133090	0.00881408
$229$	−6.11059	−0.403799	−0.201900	−	0.979406i	$-0.564711\pi$
$229$	−6.11059	−0.403799	−0.201900	+	0.979406i	$0.564711\pi$
$230$	0.237188	0.0156397
$231$	13.7153	0.902403
$232$	2.79076	0.183222
$233$	−17.3863	−1.13902	−0.569509	−	0.821985i	$-0.692867\pi$
$233$	−17.3863	−1.13902	−0.569509	+	0.821985i	$0.692867\pi$
$234$	0.443271	0.0289775
$235$	3.45157	0.225156
$236$	−0.412415	−0.0268459
$237$	9.38238	0.609451
$238$	−5.06451	−0.328283
$239$	1.65727	0.107200	0.0535998	−	0.998562i	$-0.482930\pi$
$239$	1.65727	0.107200	0.0535998	+	0.998562i	$0.482930\pi$
$240$	−0.0462559	−0.00298580
$241$	19.8147	1.27637	0.638187	−	0.769881i	$-0.279685\pi$
$241$	19.8147	1.27637	0.638187	+	0.769881i	$0.279685\pi$
$242$	−12.5436	−0.806332
$243$	1.00000	0.0641500
$244$	−10.9878	−0.703422
$245$	−0.0880088	−0.00562267
$246$	−0.434108	−0.0276777
$247$	0.0543526	0.00345837
$248$	20.5329	1.30384
$249$	−6.67576	−0.423059
$250$	−2.35353	−0.148850
$251$	−9.99777	−0.631054	−0.315527	−	0.948917i	$-0.602181\pi$
$251$	−9.99777	−0.631054	−0.315527	+	0.948917i	$0.602181\pi$
$252$	−3.44317	−0.216899
$253$	5.07059	0.318785
$254$	8.02651	0.503628
$255$	−0.610823	−0.0382512
$256$	−15.5490	−0.971813
$257$	−2.47265	−0.154239	−0.0771197	−	0.997022i	$-0.524572\pi$
$257$	−2.47265	−0.154239	−0.0771197	+	0.997022i	$0.524572\pi$
$258$	−3.94835	−0.245813
$259$	−0.702516	−0.0436522
$260$	−0.184080	−0.0114161
$261$	1.00000	0.0618984
$262$	−2.27099	−0.140302
$263$	23.9486	1.47673	0.738367	−	0.674399i	$-0.235597\pi$
$263$	23.9486	1.47673	0.738367	+	0.674399i	$0.235597\pi$
$264$	14.1508	0.870921
$265$	−0.290106	−0.0178211
$266$	0.241138	0.0147851
$267$	5.52034	0.337839
$268$	4.21579	0.257521
$269$	−17.5956	−1.07282	−0.536412	−	0.843956i	$-0.680221\pi$
$269$	−17.5956	−1.07282	−0.536412	+	0.843956i	$0.680221\pi$
$270$	0.237188	0.0144348
$271$	12.5307	0.761183	0.380591	−	0.924743i	$-0.375720\pi$
$271$	12.5307	0.761183	0.380591	+	0.924743i	$0.375720\pi$
$272$	0.365143	0.0221401
$273$	−1.40616	−0.0851046
$274$	9.73312	0.587999
$275$	−24.9606	−1.50518
$276$	−1.27295	−0.0766224
$277$	7.17339	0.431007	0.215504	−	0.976503i	$-0.430861\pi$
$277$	7.17339	0.431007	0.215504	+	0.976503i	$0.430861\pi$
$278$	−10.7617	−0.645443
$279$	7.35747	0.440480
$280$	−2.09981	−0.125488
$281$	−3.53636	−0.210961	−0.105481	−	0.994421i	$-0.533638\pi$
$281$	−3.53636	−0.210961	−0.105481	+	0.994421i	$0.533638\pi$
$282$	10.5801	0.630037
$283$	−2.19773	−0.130642	−0.0653208	−	0.997864i	$-0.520807\pi$
$283$	−2.19773	−0.130642	−0.0653208	+	0.997864i	$0.520807\pi$
$284$	17.9817	1.06702
$285$	0.0290833	0.00172275
$286$	2.24765	0.132906
$287$	1.37709	0.0812871
$288$	−5.72330	−0.337249
$289$	−12.1782	−0.716363
$290$	0.237188	0.0139282
$291$	0.587030	0.0344123
$292$	0.610504	0.0357270
$293$	−3.48709	−0.203718	−0.101859	−	0.994799i	$-0.532479\pi$
$293$	−3.48709	−0.203718	−0.101859	+	0.994799i	$0.532479\pi$
$294$	−0.269774	−0.0157335
$295$	−0.0901226	−0.00524714
$296$	−0.724819	−0.0421293
$297$	5.07059	0.294225
$298$	−9.11360	−0.527937
$299$	−0.519860	−0.0300643
$300$	6.26624	0.361781
$301$	12.5251	0.721934
$302$	6.78761	0.390583
$303$	12.3741	0.710872
$304$	−0.0173857	−0.000997137 0
$305$	−2.40110	−0.137487
$306$	−1.87236	−0.107036
$307$	−10.3415	−0.590222	−0.295111	−	0.955463i	$-0.595357\pi$
$307$	−10.3415	−0.590222	−0.295111	+	0.955463i	$0.595357\pi$
$308$	−17.4589	−0.994813
$309$	13.6687	0.777584
$310$	1.74510	0.0991152
$311$	−3.44449	−0.195319	−0.0976595	−	0.995220i	$-0.531136\pi$
$311$	−3.44449	−0.195319	−0.0976595	+	0.995220i	$0.531136\pi$
$312$	−1.45080	−0.0821355
$313$	9.39424	0.530994	0.265497	−	0.964112i	$-0.414464\pi$
$313$	9.39424	0.530994	0.265497	+	0.964112i	$0.414464\pi$
$314$	−5.62010	−0.317161
$315$	−0.752416	−0.0423938
$316$	−11.9433	−0.671861
$317$	20.4150	1.14662	0.573310	−	0.819338i	$-0.305659\pi$
$317$	20.4150	1.14662	0.573310	+	0.819338i	$0.305659\pi$
$318$	−0.889263	−0.0498674
$319$	5.07059	0.283898
$320$	−1.26499	−0.0707149
$321$	−4.99088	−0.278564
$322$	−2.30638	−0.128530
$323$	−0.229583	−0.0127744
$324$	−1.27295	−0.0707193
$325$	2.55907	0.141952
$326$	−18.1515	−1.00532
$327$	8.14915	0.450649
$328$	1.42081	0.0784512
$329$	−33.5626	−1.85037
$330$	1.20268	0.0662055
$331$	−1.63941	−0.0901101	−0.0450551	−	0.998985i	$-0.514346\pi$
$331$	−1.63941	−0.0901101	−0.0450551	+	0.998985i	$0.514346\pi$
$332$	8.49788	0.466382
$333$	−0.259721	−0.0142326
$334$	−15.8836	−0.869113
$335$	0.921252	0.0503334
$336$	0.449786	0.0245378
$337$	25.4684	1.38735	0.693677	−	0.720286i	$-0.255990\pi$
$337$	25.4684	1.38735	0.693677	+	0.720286i	$0.255990\pi$
$338$	10.8543	0.590397
$339$	14.9087	0.809731
$340$	0.777545	0.0421683
$341$	37.3067	2.02027
$342$	0.0891492	0.00482064
$343$	−18.0784	−0.976141
$344$	12.9227	0.696747
$345$	−0.278169	−0.0149761
$346$	8.68336	0.466820
$347$	−30.8489	−1.65606	−0.828029	−	0.560686i	$-0.810538\pi$
$347$	−30.8489	−1.65606	−0.828029	+	0.560686i	$0.810538\pi$
$348$	−1.27295	−0.0682371
$349$	7.05975	0.377900	0.188950	−	0.981987i	$-0.439492\pi$
$349$	7.05975	0.377900	0.188950	+	0.981987i	$0.439492\pi$
$350$	11.3535	0.606867
$351$	−0.519860	−0.0277481
$352$	−29.0205	−1.54680
$353$	16.3887	0.872282	0.436141	−	0.899878i	$-0.356345\pi$
$353$	16.3887	0.872282	0.436141	+	0.899878i	$0.356345\pi$
$354$	−0.276253	−0.0146827
$355$	3.92943	0.208553
$356$	−7.02710	−0.372435
$357$	5.93956	0.314355
$358$	4.42155	0.233686
$359$	24.2910	1.28203	0.641014	−	0.767529i	$-0.278514\pi$
$359$	24.2910	1.28203	0.641014	+	0.767529i	$0.278514\pi$
$360$	−0.776303	−0.0409148
$361$	−18.9891	−0.999425
$362$	−9.66162	−0.507803
$363$	14.7109	0.772121
$364$	1.78997	0.0938197
$365$	0.133410	0.00698298
$366$	−7.36010	−0.384719
$367$	20.9932	1.09583	0.547917	−	0.836532i	$-0.315421\pi$
$367$	20.9932	1.09583	0.547917	+	0.836532i	$0.315421\pi$
$368$	0.166287	0.00866829
$369$	0.509113	0.0265034
$370$	−0.0616028	−0.00320258
$371$	2.82095	0.146456
$372$	−9.36566	−0.485587
$373$	8.86668	0.459099	0.229550	−	0.973297i	$-0.426275\pi$
$373$	8.86668	0.459099	0.229550	+	0.973297i	$0.426275\pi$
$374$	−9.49396	−0.490921
$375$	2.76017	0.142535
$376$	−34.6282	−1.78581
$377$	−0.519860	−0.0267741
$378$	−2.30638	−0.118628
$379$	−18.0116	−0.925195	−0.462597	−	0.886568i	$-0.653082\pi$
$379$	−18.0116	−0.925195	−0.462597	+	0.886568i	$0.653082\pi$
$380$	−0.0370215	−0.00189916
$381$	−9.41334	−0.482260
$382$	12.8200	0.655926
$383$	23.2088	1.18591	0.592957	−	0.805234i	$-0.297961\pi$
$383$	23.2088	1.18591	0.592957	+	0.805234i	$0.297961\pi$
$384$	7.56904	0.386256
$385$	−3.81519	−0.194440
$386$	−9.77849	−0.497712
$387$	4.63055	0.235384
$388$	−0.747258	−0.0379363
$389$	−12.7471	−0.646306	−0.323153	−	0.946347i	$-0.604743\pi$
$389$	−12.7471	−0.646306	−0.323153	+	0.946347i	$0.604743\pi$
$390$	−0.123304	−0.00624376
$391$	2.19587	0.111050
$392$	0.882955	0.0445960
$393$	2.66337	0.134349
$394$	21.3465	1.07542
$395$	−2.60989	−0.131318
$396$	−6.45459	−0.324355
$397$	0.267573	0.0134291	0.00671456	−	0.999977i	$-0.497863\pi$
$397$	0.267573	0.0134291	0.00671456	+	0.999977i	$0.497863\pi$
$398$	4.90528	0.245879
$399$	−0.282802	−0.0141578
$400$	−0.818566	−0.0409283
$401$	−25.0956	−1.25321	−0.626607	−	0.779335i	$-0.715557\pi$
$401$	−25.0956	−1.25321	−0.626607	+	0.779335i	$0.715557\pi$
$402$	2.82392	0.140844
$403$	−3.82485	−0.190529
$404$	−15.7515	−0.783669
$405$	−0.278169	−0.0138224
$406$	−2.30638	−0.114464
$407$	−1.31694	−0.0652783
$408$	6.12813	0.303388
$409$	−24.7033	−1.22150	−0.610750	−	0.791823i	$-0.709132\pi$
$409$	−24.7033	−1.22150	−0.610750	+	0.791823i	$0.709132\pi$
$410$	0.120755	0.00596369
$411$	−11.4148	−0.563051
$412$	−17.3995	−0.857211
$413$	0.876339	0.0431218
$414$	−0.852674	−0.0419067
$415$	1.85699	0.0911561
$416$	2.97532	0.145877
$417$	12.6211	0.618058
$418$	0.452039	0.0221099
$419$	−14.0991	−0.688786	−0.344393	−	0.938826i	$-0.611915\pi$
$419$	−14.0991	−0.688786	−0.344393	+	0.938826i	$0.611915\pi$
$420$	0.957785	0.0467351
$421$	18.9132	0.921772	0.460886	−	0.887459i	$-0.347532\pi$
$421$	18.9132	0.921772	0.460886	+	0.887459i	$0.347532\pi$
$422$	−3.00581	−0.146320
$423$	−12.4082	−0.603306
$424$	2.91051	0.141347
$425$	−10.8094	−0.524334
$426$	12.0449	0.583578
$427$	23.3480	1.12989
$428$	6.35313	0.307090
$429$	−2.63600	−0.127267
$430$	1.09831	0.0529652
$431$	−7.03206	−0.338722	−0.169361	−	0.985554i	$-0.554170\pi$
$431$	−7.03206	−0.338722	−0.169361	+	0.985554i	$0.554170\pi$
$432$	0.166287	0.00800047
$433$	−20.4589	−0.983192	−0.491596	−	0.870823i	$-0.663586\pi$
$433$	−20.4589	−0.983192	−0.491596	+	0.870823i	$0.663586\pi$
$434$	−16.9691	−0.814545
$435$	−0.278169	−0.0133372
$436$	−10.3734	−0.496798
$437$	−0.104552	−0.00500142
$438$	0.408941	0.0195400
$439$	−28.6535	−1.36756	−0.683778	−	0.729690i	$-0.739664\pi$
$439$	−28.6535	−1.36756	−0.683778	+	0.729690i	$0.739664\pi$
$440$	−3.93632	−0.187656
$441$	0.316385	0.0150660
$442$	0.973364	0.0462982
$443$	−37.4338	−1.77854	−0.889268	−	0.457387i	$-0.848786\pi$
$443$	−37.4338	−1.77854	−0.889268	+	0.457387i	$0.848786\pi$
$444$	0.330611	0.0156901
$445$	−1.53559	−0.0727939
$446$	19.1617	0.907335
$447$	10.6883	0.505537
$448$	12.3006	0.581147
$449$	4.16541	0.196578	0.0982889	−	0.995158i	$-0.468663\pi$
$449$	4.16541	0.196578	0.0982889	+	0.995158i	$0.468663\pi$
$450$	4.19739	0.197867
$451$	2.58150	0.121558
$452$	−18.9780	−0.892651
$453$	−7.96037	−0.374011
$454$	11.5239	0.540843
$455$	0.391151	0.0183374
$456$	−0.291780	−0.0136639
$457$	15.6569	0.732399	0.366200	−	0.930536i	$-0.380659\pi$
$457$	15.6569	0.732399	0.366200	+	0.930536i	$0.380659\pi$
$458$	5.21035	0.243463
$459$	2.19587	0.102494
$460$	0.354095	0.0165098
$461$	−22.6379	−1.05435	−0.527177	−	0.849756i	$-0.676749\pi$
$461$	−22.6379	−1.05435	−0.527177	+	0.849756i	$0.676749\pi$
$462$	−11.6947	−0.544088
$463$	−4.04786	−0.188120	−0.0940599	−	0.995567i	$-0.529985\pi$
$463$	−4.04786	−0.188120	−0.0940599	+	0.995567i	$0.529985\pi$
$464$	0.166287	0.00771966
$465$	−2.04662	−0.0949099
$466$	14.8249	0.686750
$467$	−2.50969	−0.116135	−0.0580673	−	0.998313i	$-0.518494\pi$
$467$	−2.50969	−0.116135	−0.0580673	+	0.998313i	$0.518494\pi$
$468$	0.661754	0.0305896
$469$	−8.95813	−0.413648
$470$	−2.94307	−0.135754
$471$	6.59115	0.303704
$472$	0.904162	0.0416174
$473$	23.4796	1.07959
$474$	−8.00011	−0.367457
$475$	0.514672	0.0236148
$476$	−7.56074	−0.346546
$477$	1.04291	0.0477516
$478$	−1.41311	−0.0646341
$479$	15.3017	0.699154	0.349577	−	0.936908i	$-0.386325\pi$
$479$	15.3017	0.699154	0.349577	+	0.936908i	$0.386325\pi$
$480$	1.59205	0.0726667
$481$	0.135019	0.00615632
$482$	−16.8954	−0.769566
$483$	2.70488	0.123076
$484$	−18.7262	−0.851189
$485$	−0.163294	−0.00741479
$486$	−0.852674	−0.0386781
$487$	−12.4632	−0.564760	−0.282380	−	0.959303i	$-0.591124\pi$
$487$	−12.4632	−0.564760	−0.282380	+	0.959303i	$0.591124\pi$
$488$	24.0892	1.09047
$489$	21.2877	0.962663
$490$	0.0750428	0.00339009
$491$	6.93040	0.312764	0.156382	−	0.987697i	$-0.450017\pi$
$491$	6.93040	0.312764	0.156382	+	0.987697i	$0.450017\pi$
$492$	−0.648074	−0.0292174
$493$	2.19587	0.0988969
$494$	−0.0463451	−0.00208516
$495$	−1.41048	−0.0633965
$496$	1.22345	0.0549345
$497$	−38.2093	−1.71392
$498$	5.69225	0.255076
$499$	27.5543	1.23350	0.616749	−	0.787160i	$-0.288449\pi$
$499$	27.5543	1.23350	0.616749	+	0.787160i	$0.288449\pi$
$500$	−3.51355	−0.157131
$501$	18.6280	0.832238
$502$	8.52484	0.380482
$503$	−7.21927	−0.321891	−0.160946	−	0.986963i	$-0.551454\pi$
$503$	−7.21927	−0.321891	−0.160946	+	0.986963i	$0.551454\pi$
$504$	7.54867	0.336244
$505$	−3.44209	−0.153171
$506$	−4.32356	−0.192206
$507$	−12.7297	−0.565348
$508$	11.9827	0.531645
$509$	−30.1844	−1.33790	−0.668950	−	0.743308i	$-0.733256\pi$
$509$	−30.1844	−1.33790	−0.668950	+	0.743308i	$0.733256\pi$
$510$	0.520833	0.0230629
$511$	−1.29726	−0.0573873
$512$	−1.87984	−0.0830780
$513$	−0.104552	−0.00461610
$514$	2.10836	0.0929958
$515$	−3.80221	−0.167545
$516$	−5.89444	−0.259488
$517$	−62.9167	−2.76707
$518$	0.599017	0.0263193
$519$	−10.1837	−0.447014
$520$	0.403569	0.0176977
$521$	−10.4106	−0.456096	−0.228048	−	0.973650i	$-0.573234\pi$
$521$	−10.4106	−0.456096	−0.228048	+	0.973650i	$0.573234\pi$
$522$	−0.852674	−0.0373205
$523$	−30.7711	−1.34552	−0.672762	−	0.739859i	$-0.734892\pi$
$523$	−30.7711	−1.34552	−0.672762	+	0.739859i	$0.734892\pi$
$524$	−3.39033	−0.148107
$525$	−13.3151	−0.581119
$526$	−20.4203	−0.890369
$527$	16.1560	0.703767
$528$	0.843171	0.0366943
$529$	1.00000	0.0434783
$530$	0.247366	0.0107449
$531$	0.323984	0.0140597
$532$	0.359992	0.0156076
$533$	−0.264667	−0.0114640
$534$	−4.70705	−0.203694
$535$	1.38831	0.0600219
$536$	−9.24254	−0.399217
$537$	−5.18551	−0.223771
$538$	15.0033	0.646840
$539$	1.60426	0.0691004
$540$	0.354095	0.0152378
$541$	24.0739	1.03502	0.517509	−	0.855678i	$-0.326860\pi$
$541$	24.0739	1.03502	0.517509	+	0.855678i	$0.326860\pi$
$542$	−10.6846	−0.458941
$543$	11.3310	0.486258
$544$	−12.5676	−0.538832
$545$	−2.26685	−0.0971010
$546$	1.19900	0.0513123
$547$	−2.60380	−0.111330	−0.0556652	−	0.998449i	$-0.517728\pi$
$547$	−2.60380	−0.111330	−0.0556652	+	0.998449i	$0.517728\pi$
$548$	14.5304	0.620710
$549$	8.63178	0.368396
$550$	21.2833	0.907521
$551$	−0.104552	−0.00445408
$552$	2.79076	0.118783
$553$	25.3782	1.07919
$554$	−6.11656	−0.259868
$555$	0.0722466	0.00306670
$556$	−16.0660	−0.681349
$557$	16.5729	0.702215	0.351108	−	0.936335i	$-0.385805\pi$
$557$	16.5729	0.702215	0.351108	+	0.936335i	$0.385805\pi$
$558$	−6.27352	−0.265579
$559$	−2.40724	−0.101815
$560$	−0.125117	−0.00528714
$561$	11.1343	0.470092
$562$	3.01536	0.127195
$563$	−4.71445	−0.198690	−0.0993452	−	0.995053i	$-0.531675\pi$
$563$	−4.71445	−0.198690	−0.0993452	+	0.995053i	$0.531675\pi$
$564$	15.7949	0.665087
$565$	−4.14716	−0.174472
$566$	1.87395	0.0787680
$567$	2.70488	0.113594
$568$	−39.4223	−1.65412
$569$	2.24239	0.0940058	0.0470029	−	0.998895i	$-0.485033\pi$
$569$	2.24239	0.0940058	0.0470029	+	0.998895i	$0.485033\pi$
$570$	−0.0247986	−0.00103870
$571$	38.4824	1.61044	0.805220	−	0.592977i	$-0.202047\pi$
$571$	38.4824	1.61044	0.805220	+	0.592977i	$0.202047\pi$
$572$	3.35548	0.140300
$573$	−15.0350	−0.628096
$574$	−1.17421	−0.0490106
$575$	−4.92262	−0.205288
$576$	4.54754	0.189481
$577$	−31.8247	−1.32488	−0.662439	−	0.749116i	$-0.730479\pi$
$577$	−31.8247	−1.32488	−0.662439	+	0.749116i	$0.730479\pi$
$578$	10.3840	0.431918
$579$	11.4680	0.476595
$580$	0.354095	0.0147030
$581$	−18.0571	−0.749136
$582$	−0.500545	−0.0207483
$583$	5.28817	0.219014
$584$	−1.33844	−0.0553852
$585$	0.144609	0.00597885
$586$	2.97335	0.122828
$587$	−35.1398	−1.45038	−0.725188	−	0.688551i	$-0.758247\pi$
$587$	−35.1398	−1.45038	−0.725188	+	0.688551i	$0.758247\pi$
$588$	−0.402742	−0.0166088
$589$	−0.769241	−0.0316960
$590$	0.0768452	0.00316367
$591$	−25.0347	−1.02979
$592$	−0.0431882	−0.00177502
$593$	13.1988	0.542009	0.271004	−	0.962578i	$-0.412644\pi$
$593$	13.1988	0.542009	0.271004	+	0.962578i	$0.412644\pi$
$594$	−4.32356	−0.177398
$595$	−1.65220	−0.0677338
$596$	−13.6056	−0.557306
$597$	−5.75281	−0.235447
$598$	0.443271	0.0181267
$599$	−42.6629	−1.74316	−0.871579	−	0.490254i	$-0.836904\pi$
$599$	−42.6629	−1.74316	−0.871579	+	0.490254i	$0.836904\pi$
$600$	−13.7378	−0.560845
$601$	−4.17667	−0.170370	−0.0851850	−	0.996365i	$-0.527148\pi$
$601$	−4.17667	−0.170370	−0.0851850	+	0.996365i	$0.527148\pi$
$602$	−10.6798	−0.435277
$603$	−3.31184	−0.134868
$604$	10.1331	0.412311
$605$	−4.09212	−0.166368
$606$	−10.5511	−0.428608
$607$	−19.0944	−0.775017	−0.387508	−	0.921866i	$-0.626664\pi$
$607$	−19.0944	−0.775017	−0.387508	+	0.921866i	$0.626664\pi$
$608$	0.598385	0.0242677
$609$	2.70488	0.109607
$610$	2.04736	0.0828950
$611$	6.45051	0.260960
$612$	−2.79522	−0.112990
$613$	18.3726	0.742062	0.371031	−	0.928620i	$-0.379004\pi$
$613$	18.3726	0.742062	0.371031	+	0.928620i	$0.379004\pi$
$614$	8.81795	0.355864
$615$	−0.141620	−0.00571066
$616$	38.2762	1.54219
$617$	−36.9471	−1.48743	−0.743716	−	0.668495i	$-0.766939\pi$
$617$	−36.9471	−1.48743	−0.743716	+	0.668495i	$0.766939\pi$
$618$	−11.6549	−0.468830
$619$	−35.4201	−1.42365	−0.711827	−	0.702355i	$-0.752132\pi$
$619$	−35.4201	−1.42365	−0.711827	+	0.702355i	$0.752132\pi$
$620$	2.60524	0.104629
$621$	1.00000	0.0401286
$622$	2.93703	0.117764
$623$	14.9319	0.598233
$624$	−0.0864458	−0.00346060
$625$	23.8453	0.953813
$626$	−8.01023	−0.320153
$627$	−0.530143	−0.0211719
$628$	−8.39018	−0.334805
$629$	−0.570314	−0.0227399
$630$	0.641565	0.0255606
$631$	−29.4582	−1.17271	−0.586355	−	0.810054i	$-0.699438\pi$
$631$	−29.4582	−1.17271	−0.586355	+	0.810054i	$0.699438\pi$
$632$	26.1839	1.04154
$633$	3.52515	0.140112
$634$	−17.4073	−0.691334
$635$	2.61850	0.103912
$636$	−1.32757	−0.0526416
$637$	−0.164476	−0.00651678
$638$	−4.32356	−0.171171
$639$	−14.1260	−0.558817
$640$	−2.10547	−0.0832262
$641$	14.9498	0.590481	0.295241	−	0.955423i	$-0.404600\pi$
$641$	14.9498	0.590481	0.295241	+	0.955423i	$0.404600\pi$
$642$	4.25560	0.167955
$643$	25.7271	1.01458	0.507289	−	0.861776i	$-0.330648\pi$
$643$	25.7271	1.01458	0.507289	+	0.861776i	$0.330648\pi$
$644$	−3.44317	−0.135680
$645$	−1.28808	−0.0507180
$646$	0.195760	0.00770206
$647$	25.3141	0.995201	0.497600	−	0.867406i	$-0.334215\pi$
$647$	25.3141	0.995201	0.497600	+	0.867406i	$0.334215\pi$
$648$	2.79076	0.109631
$649$	1.64279	0.0644852
$650$	−2.18206	−0.0855873
$651$	19.9011	0.779985
$652$	−27.0981	−1.06124
$653$	17.9366	0.701914	0.350957	−	0.936391i	$-0.385856\pi$
$653$	17.9366	0.701914	0.350957	+	0.936391i	$0.385856\pi$
$654$	−6.94857	−0.271711
$655$	−0.740869	−0.0289481
$656$	0.0846587	0.00330537
$657$	−0.479599	−0.0187109
$658$	28.6180	1.11565
$659$	0.907905	0.0353670	0.0176835	−	0.999844i	$-0.494371\pi$
$659$	0.907905	0.0353670	0.0176835	+	0.999844i	$0.494371\pi$
$660$	1.79547	0.0698886
$661$	−21.1348	−0.822048	−0.411024	−	0.911624i	$-0.634829\pi$
$661$	−21.1348	−0.822048	−0.411024	+	0.911624i	$0.634829\pi$
$662$	1.39788	0.0543303
$663$	−1.14154	−0.0443339
$664$	−18.6304	−0.723000
$665$	0.0786669	0.00305057
$666$	0.221458	0.00858131
$667$	1.00000	0.0387202
$668$	−23.7125	−0.917462
$669$	−22.4725	−0.868838
$670$	−0.785528	−0.0303476
$671$	43.7682	1.68965
$672$	−15.4809	−0.597187
$673$	−9.47393	−0.365193	−0.182597	−	0.983188i	$-0.558450\pi$
$673$	−9.47393	−0.365193	−0.182597	+	0.983188i	$0.558450\pi$
$674$	−21.7163	−0.836480
$675$	−4.92262	−0.189472
$676$	16.2043	0.623242
$677$	−44.9991	−1.72945	−0.864727	−	0.502242i	$-0.832509\pi$
$677$	−44.9991	−1.72945	−0.864727	+	0.502242i	$0.832509\pi$
$678$	−12.7123	−0.488213
$679$	1.58785	0.0609359
$680$	−1.70466	−0.0653707
$681$	−13.5150	−0.517896
$682$	−31.8105	−1.21809
$683$	−15.2628	−0.584016	−0.292008	−	0.956416i	$-0.594323\pi$
$683$	−15.2628	−0.584016	−0.292008	+	0.956416i	$0.594323\pi$
$684$	0.133090	0.00508881
$685$	3.17525	0.121320
$686$	15.4150	0.588546
$687$	−6.11059	−0.233134
$688$	0.769998	0.0293559
$689$	−0.542167	−0.0206549
$690$	0.237188	0.00902959
$691$	35.3108	1.34329	0.671644	−	0.740874i	$-0.265589\pi$
$691$	35.3108	1.34329	0.671644	+	0.740874i	$0.265589\pi$
$692$	12.9633	0.492790
$693$	13.7153	0.521003
$694$	26.3041	0.998489
$695$	−3.51080	−0.133172
$696$	2.79076	0.105783
$697$	1.11794	0.0423452
$698$	−6.01967	−0.227848
$699$	−17.3863	−0.657612
$700$	16.9494	0.640628
$701$	20.2694	0.765565	0.382782	−	0.923839i	$-0.374966\pi$
$701$	20.2694	0.765565	0.382782	+	0.923839i	$0.374966\pi$
$702$	0.443271	0.0167302
$703$	0.0271545	0.00102415
$704$	23.0587	0.869058
$705$	3.45157	0.129994
$706$	−13.9742	−0.525926
$707$	33.4704	1.25879
$708$	−0.412415	−0.0154995
$709$	−14.0026	−0.525879	−0.262939	−	0.964812i	$-0.584692\pi$
$709$	−14.0026	−0.525879	−0.262939	+	0.964812i	$0.584692\pi$
$710$	−3.35053	−0.125743
$711$	9.38238	0.351867
$712$	15.4059	0.577362
$713$	7.35747	0.275539
$714$	−5.06451	−0.189535
$715$	0.733253	0.0274221
$716$	6.60087	0.246686
$717$	1.65727	0.0618917
$718$	−20.7123	−0.772975
$719$	29.9013	1.11513	0.557566	−	0.830133i	$-0.311735\pi$
$719$	29.9013	1.11513	0.557566	+	0.830133i	$0.311735\pi$
$720$	−0.0462559	−0.00172385
$721$	36.9721	1.37691
$722$	16.1915	0.602585
$723$	19.8147	0.736915
$724$	−14.4237	−0.536053
$725$	−4.92262	−0.182822
$726$	−12.5436	−0.465536
$727$	17.5958	0.652593	0.326297	−	0.945267i	$-0.394199\pi$
$727$	17.5958	0.652593	0.326297	+	0.945267i	$0.394199\pi$
$728$	−3.92425	−0.145442
$729$	1.00000	0.0370370
$730$	−0.113755	−0.00421026
$731$	10.1681	0.376080
$732$	−10.9878	−0.406121
$733$	−26.8913	−0.993254	−0.496627	−	0.867964i	$-0.665428\pi$
$733$	−26.8913	−0.993254	−0.496627	+	0.867964i	$0.665428\pi$
$734$	−17.9003	−0.660714
$735$	−0.0880088	−0.00324625
$736$	−5.72330	−0.210964
$737$	−16.7930	−0.618577
$738$	−0.434108	−0.0159797
$739$	−25.8478	−0.950828	−0.475414	−	0.879762i	$-0.657702\pi$
$739$	−25.8478	−0.950828	−0.475414	+	0.879762i	$0.657702\pi$
$740$	−0.0919660	−0.00338074
$741$	0.0543526	0.00199669
$742$	−2.40535	−0.0883032
$743$	40.1155	1.47170	0.735848	−	0.677147i	$-0.236784\pi$
$743$	40.1155	1.47170	0.735848	+	0.677147i	$0.236784\pi$
$744$	20.5329	0.752773
$745$	−2.97315	−0.108928
$746$	−7.56039	−0.276805
$747$	−6.67576	−0.244253
$748$	−14.1734	−0.518232
$749$	−13.4997	−0.493270
$750$	−2.35353	−0.0859386
$751$	17.9390	0.654603	0.327302	−	0.944920i	$-0.393861\pi$
$751$	17.9390	0.654603	0.327302	+	0.944920i	$0.393861\pi$
$752$	−2.06331	−0.0752413
$753$	−9.99777	−0.364339
$754$	0.443271	0.0161430
$755$	2.21433	0.0805878
$756$	−3.44317	−0.125227
$757$	−39.6003	−1.43930	−0.719648	−	0.694339i	$-0.755697\pi$
$757$	−39.6003	−1.43930	−0.719648	+	0.694339i	$0.755697\pi$
$758$	15.3580	0.557829
$759$	5.07059	0.184051
$760$	0.0811644	0.00294414
$761$	4.42374	0.160361	0.0801803	−	0.996780i	$-0.474450\pi$
$761$	4.42374	0.160361	0.0801803	+	0.996780i	$0.474450\pi$
$762$	8.02651	0.290770
$763$	22.0425	0.797992
$764$	19.1388	0.692416
$765$	−0.610823	−0.0220844
$766$	−19.7895	−0.715025
$767$	−0.168426	−0.00608153
$768$	−15.5490	−0.561076
$769$	−22.4905	−0.811029	−0.405514	−	0.914089i	$-0.632908\pi$
$769$	−22.4905	−0.811029	−0.405514	+	0.914089i	$0.632908\pi$
$770$	3.25311	0.117234
$771$	−2.47265	−0.0890502
$772$	−14.5982	−0.525400
$773$	−24.2864	−0.873521	−0.436760	−	0.899578i	$-0.643874\pi$
$773$	−24.2864	−0.873521	−0.436760	+	0.899578i	$0.643874\pi$
$774$	−3.94835	−0.141920
$775$	−36.2180	−1.30099
$776$	1.63826	0.0588100
$777$	−0.702516	−0.0252026
$778$	10.8692	0.389678
$779$	−0.0532290	−0.00190713
$780$	−0.184080	−0.00659111
$781$	−71.6273	−2.56303
$782$	−1.87236	−0.0669554
$783$	1.00000	0.0357371
$784$	0.0526107	0.00187895
$785$	−1.83346	−0.0654388
$786$	−2.27099	−0.0810035
$787$	−33.4845	−1.19359	−0.596797	−	0.802393i	$-0.703560\pi$
$787$	−33.4845	−1.19359	−0.596797	+	0.802393i	$0.703560\pi$
$788$	31.8679	1.13525
$789$	23.9486	0.852592
$790$	2.22539	0.0791757
$791$	40.3264	1.43384
$792$	14.1508	0.502826
$793$	−4.48732	−0.159349
$794$	−0.228153	−0.00809684
$795$	−0.290106	−0.0102890
$796$	7.32303	0.259558
$797$	31.4213	1.11300	0.556500	−	0.830847i	$-0.312144\pi$
$797$	31.4213	1.11300	0.556500	+	0.830847i	$0.312144\pi$
$798$	0.241138	0.00853619
$799$	−27.2467	−0.963919
$800$	28.1737	0.996089
$801$	5.52034	0.195052
$802$	21.3984	0.755603
$803$	−2.43185	−0.0858180
$804$	4.21579	0.148680
$805$	−0.752416	−0.0265192
$806$	3.26135	0.114876
$807$	−17.5956	−0.619395
$808$	34.5331	1.21487
$809$	33.6559	1.18328	0.591639	−	0.806203i	$-0.298481\pi$
$809$	33.6559	1.18328	0.591639	+	0.806203i	$0.298481\pi$
$810$	0.237188	0.00833393
$811$	−2.12467	−0.0746072	−0.0373036	−	0.999304i	$-0.511877\pi$
$811$	−2.12467	−0.0746072	−0.0373036	+	0.999304i	$0.511877\pi$
$812$	−3.44317	−0.120832
$813$	12.5307	0.439469
$814$	1.12292	0.0393584
$815$	−5.92159	−0.207424
$816$	0.365143	0.0127826
$817$	−0.484135	−0.0169377
$818$	21.0639	0.736481
$819$	−1.40616	−0.0491352
$820$	0.180274	0.00629545
$821$	−33.4063	−1.16589	−0.582944	−	0.812512i	$-0.698099\pi$
$821$	−33.4063	−1.16589	−0.582944	+	0.812512i	$0.698099\pi$
$822$	9.73312	0.339481
$823$	21.5526	0.751276	0.375638	−	0.926766i	$-0.377424\pi$
$823$	21.5526	0.751276	0.375638	+	0.926766i	$0.377424\pi$
$824$	38.1459	1.32888
$825$	−24.9606	−0.869016
$826$	−0.747232	−0.0259995
$827$	37.6143	1.30798	0.653988	−	0.756505i	$-0.273095\pi$
$827$	37.6143	1.30798	0.653988	+	0.756505i	$0.273095\pi$
$828$	−1.27295	−0.0442380
$829$	27.0749	0.940349	0.470174	−	0.882574i	$-0.344191\pi$
$829$	27.0749	0.940349	0.470174	+	0.882574i	$0.344191\pi$
$830$	−1.58341	−0.0549609
$831$	7.17339	0.248842
$832$	−2.36408	−0.0819598
$833$	0.694740	0.0240713
$834$	−10.7617	−0.372647
$835$	−5.18174	−0.179322
$836$	0.674843	0.0233399
$837$	7.35747	0.254311
$838$	12.0219	0.415291
$839$	36.0003	1.24287	0.621434	−	0.783467i	$-0.286551\pi$
$839$	36.0003	1.24287	0.621434	+	0.783467i	$0.286551\pi$
$840$	−2.09981	−0.0724503
$841$	1.00000	0.0344828
$842$	−16.1268	−0.555765
$843$	−3.53636	−0.121799
$844$	−4.48733	−0.154460
$845$	3.54103	0.121815
$846$	10.5801	0.363752
$847$	39.7912	1.36724
$848$	0.173422	0.00595534
$849$	−2.19773	−0.0754260
$850$	9.21692	0.316138
$851$	−0.259721	−0.00890313
$852$	17.9817	0.616043
$853$	−8.31131	−0.284574	−0.142287	−	0.989825i	$-0.545446\pi$
$853$	−8.31131	−0.284574	−0.142287	+	0.989825i	$0.545446\pi$
$854$	−19.9082	−0.681245
$855$	0.0290833	0.000994628 0
$856$	−13.9283	−0.476061
$857$	13.7510	0.469726	0.234863	−	0.972029i	$-0.424536\pi$
$857$	13.7510	0.469726	0.234863	+	0.972029i	$0.424536\pi$
$858$	2.24765	0.0767334
$859$	−28.3847	−0.968474	−0.484237	−	0.874937i	$-0.660903\pi$
$859$	−28.3847	−0.968474	−0.484237	+	0.874937i	$0.660903\pi$
$860$	1.63965	0.0559117
$861$	1.37709	0.0469311
$862$	5.99606	0.204226
$863$	13.2385	0.450643	0.225322	−	0.974284i	$-0.427657\pi$
$863$	13.2385	0.450643	0.225322	+	0.974284i	$0.427657\pi$
$864$	−5.72330	−0.194711
$865$	2.83279	0.0963177
$866$	17.4448	0.592798
$867$	−12.1782	−0.413592
$868$	−25.3330	−0.859859
$869$	47.5742	1.61384
$870$	0.237188	0.00804142
$871$	1.72169	0.0583373
$872$	22.7423	0.770152
$873$	0.587030	0.0198679
$874$	0.0891492	0.00301552
$875$	7.46593	0.252395
$876$	0.610504	0.0206270
$877$	51.8672	1.75143	0.875715	−	0.482829i	$-0.160391\pi$
$877$	51.8672	1.75143	0.875715	+	0.482829i	$0.160391\pi$
$878$	24.4321	0.824543
$879$	−3.48709	−0.117617
$880$	−0.234545	−0.00790649
$881$	53.8584	1.81454	0.907268	−	0.420553i	$-0.138164\pi$
$881$	53.8584	1.81454	0.907268	+	0.420553i	$0.138164\pi$
$882$	−0.269774	−0.00908375
$883$	7.91168	0.266249	0.133125	−	0.991099i	$-0.457499\pi$
$883$	7.91168	0.266249	0.133125	+	0.991099i	$0.457499\pi$
$884$	1.45312	0.0488738
$885$	−0.0901226	−0.00302944
$886$	31.9189	1.07234
$887$	23.3214	0.783054	0.391527	−	0.920167i	$-0.371947\pi$
$887$	23.3214	0.783054	0.391527	+	0.920167i	$0.371947\pi$
$888$	−0.724819	−0.0243233
$889$	−25.4620	−0.853967
$890$	1.30936	0.0438898
$891$	5.07059	0.169871
$892$	28.6063	0.957811
$893$	1.29730	0.0434126
$894$	−9.11360	−0.304804
$895$	1.44245	0.0482158
$896$	20.4733	0.683967
$897$	−0.519860	−0.0173576
$898$	−3.55174	−0.118523
$899$	7.35747	0.245385
$900$	6.26624	0.208875
$901$	2.29009	0.0762941
$902$	−2.20118	−0.0732913
$903$	12.5251	0.416809
$904$	41.6067	1.38382
$905$	−3.15193	−0.104774
$906$	6.78761	0.225503
$907$	−23.9008	−0.793612	−0.396806	−	0.917902i	$-0.629881\pi$
$907$	−23.9008	−0.793612	−0.396806	+	0.917902i	$0.629881\pi$
$908$	17.2039	0.570931
$909$	12.3741	0.410422
$910$	−0.333524	−0.0110562
$911$	−29.0376	−0.962058	−0.481029	−	0.876705i	$-0.659737\pi$
$911$	−29.0376	−0.962058	−0.481029	+	0.876705i	$0.659737\pi$
$912$	−0.0173857	−0.000575697 0
$913$	−33.8500	−1.12027
$914$	−13.3502	−0.441587
$915$	−2.40110	−0.0793779
$916$	7.77846	0.257008
$917$	7.20411	0.237901
$918$	−1.87236	−0.0617971
$919$	43.7999	1.44483	0.722413	−	0.691462i	$-0.243033\pi$
$919$	43.7999	1.44483	0.722413	+	0.691462i	$0.243033\pi$
$920$	−0.776303	−0.0255940
$921$	−10.3415	−0.340765
$922$	19.3028	0.635703
$923$	7.34356	0.241716
$924$	−17.4589	−0.574356
$925$	1.27851	0.0420372
$926$	3.45150	0.113423
$927$	13.6687	0.448938
$928$	−5.72330	−0.187877
$929$	−26.4998	−0.869431	−0.434715	−	0.900568i	$-0.643151\pi$
$929$	−26.4998	−0.869431	−0.434715	+	0.900568i	$0.643151\pi$
$930$	1.74510	0.0572242
$931$	−0.0330789	−0.00108412
$932$	22.1319	0.724954
$933$	−3.44449	−0.112768
$934$	2.13995	0.0700213
$935$	−3.09723	−0.101290
$936$	−1.45080	−0.0474210
$937$	−20.4056	−0.666621	−0.333310	−	0.942817i	$-0.608166\pi$
$937$	−20.4056	−0.666621	−0.333310	+	0.942817i	$0.608166\pi$
$938$	7.63837	0.249402
$939$	9.39424	0.306569
$940$	−4.39367	−0.143306
$941$	−50.4396	−1.64428	−0.822142	−	0.569282i	$-0.807221\pi$
$941$	−50.4396	−1.64428	−0.822142	+	0.569282i	$0.807221\pi$
$942$	−5.62010	−0.183113
$943$	0.509113	0.0165790
$944$	0.0538743	0.00175346
$945$	−0.752416	−0.0244761
$946$	−20.0205	−0.650921
$947$	33.4712	1.08767	0.543833	−	0.839193i	$-0.316972\pi$
$947$	33.4712	1.08767	0.543833	+	0.839193i	$0.316972\pi$
$948$	−11.9433	−0.387899
$949$	0.249324	0.00809340
$950$	−0.438848	−0.0142381
$951$	20.4150	0.662002
$952$	16.5759	0.537227
$953$	−17.1268	−0.554790	−0.277395	−	0.960756i	$-0.589471\pi$
$953$	−17.1268	−0.554790	−0.277395	+	0.960756i	$0.589471\pi$
$954$	−0.889263	−0.0287909
$955$	4.18228	0.135335
$956$	−2.10961	−0.0682297
$957$	5.07059	0.163909
$958$	−13.0474	−0.421542
$959$	−30.8757	−0.997029
$960$	−1.26499	−0.0408273
$961$	23.1323	0.746204
$962$	−0.115127	−0.00371184
$963$	−4.99088	−0.160829
$964$	−25.2230	−0.812378
$965$	−3.19006	−0.102692
$966$	−2.30638	−0.0742067
$967$	50.4031	1.62085	0.810427	−	0.585839i	$-0.199235\pi$
$967$	50.4031	1.62085	0.810427	+	0.585839i	$0.199235\pi$
$968$	41.0545	1.31954
$969$	−0.229583	−0.00737528
$970$	0.139236	0.00447061
$971$	24.2480	0.778156	0.389078	−	0.921205i	$-0.372794\pi$
$971$	24.2480	0.778156	0.389078	+	0.921205i	$0.372794\pi$
$972$	−1.27295	−0.0408298
$973$	34.1386	1.09443
$974$	10.6270	0.340512
$975$	2.55907	0.0819559
$976$	1.43535	0.0459445
$977$	−17.1751	−0.549480	−0.274740	−	0.961519i	$-0.588592\pi$
$977$	−17.1751	−0.549480	−0.274740	+	0.961519i	$0.588592\pi$
$978$	−18.1515	−0.580420
$979$	27.9914	0.894608
$980$	0.112030	0.00357868
$981$	8.14915	0.260182
$982$	−5.90937	−0.188576
$983$	−34.0769	−1.08689	−0.543443	−	0.839446i	$-0.682879\pi$
$983$	−34.0769	−1.08689	−0.543443	+	0.839446i	$0.682879\pi$
$984$	1.42081	0.0452938
$985$	6.96390	0.221888
$986$	−1.87236	−0.0596281
$987$	−33.5626	−1.06831
$988$	−0.0691880	−0.00220116
$989$	4.63055	0.147243
$990$	1.20268	0.0382238
$991$	−52.6162	−1.67141	−0.835705	−	0.549179i	$-0.814940\pi$
$991$	−52.6162	−1.67141	−0.835705	+	0.549179i	$0.814940\pi$
$992$	−42.1090	−1.33696
$993$	−1.63941	−0.0520251
$994$	32.5801	1.03338
$995$	1.60026	0.0507316
$996$	8.49788	0.269266
$997$	−15.7721	−0.499506	−0.249753	−	0.968310i	$-0.580349\pi$
$997$	−15.7721	−0.499506	−0.249753	+	0.968310i	$0.580349\pi$
$998$	−23.4948	−0.743715
$999$	−0.259721	−0.00821722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.8	✓	20
3.2	odd	2		6003.2.a.s.1.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.8	✓	20	1.1	even	1	trivial
6003.2.a.s.1.13		20	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)

\(f(q)\)	\(=\)	\(q-0.852674 q^{2} +1.00000 q^{3} -1.27295 q^{4} -0.278169 q^{5} -0.852674 q^{6} +2.70488 q^{7} +2.79076 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.852674 q^{2} +1.00000 q^{3} -1.27295 q^{4} -0.278169 q^{5} -0.852674 q^{6} +2.70488 q^{7} +2.79076 q^{8} +1.00000 q^{9} +0.237188 q^{10} +5.07059 q^{11} -1.27295 q^{12} -0.519860 q^{13} -2.30638 q^{14} -0.278169 q^{15} +0.166287 q^{16} +2.19587 q^{17} -0.852674 q^{18} -0.104552 q^{19} +0.354095 q^{20} +2.70488 q^{21} -4.32356 q^{22} +1.00000 q^{23} +2.79076 q^{24} -4.92262 q^{25} +0.443271 q^{26} +1.00000 q^{27} -3.44317 q^{28} +1.00000 q^{29} +0.237188 q^{30} +7.35747 q^{31} -5.72330 q^{32} +5.07059 q^{33} -1.87236 q^{34} -0.752416 q^{35} -1.27295 q^{36} -0.259721 q^{37} +0.0891492 q^{38} -0.519860 q^{39} -0.776303 q^{40} +0.509113 q^{41} -2.30638 q^{42} +4.63055 q^{43} -6.45459 q^{44} -0.278169 q^{45} -0.852674 q^{46} -12.4082 q^{47} +0.166287 q^{48} +0.316385 q^{49} +4.19739 q^{50} +2.19587 q^{51} +0.661754 q^{52} +1.04291 q^{53} -0.852674 q^{54} -1.41048 q^{55} +7.54867 q^{56} -0.104552 q^{57} -0.852674 q^{58} +0.323984 q^{59} +0.354095 q^{60} +8.63178 q^{61} -6.27352 q^{62} +2.70488 q^{63} +4.54754 q^{64} +0.144609 q^{65} -4.32356 q^{66} -3.31184 q^{67} -2.79522 q^{68} +1.00000 q^{69} +0.641565 q^{70} -14.1260 q^{71} +2.79076 q^{72} -0.479599 q^{73} +0.221458 q^{74} -4.92262 q^{75} +0.133090 q^{76} +13.7153 q^{77} +0.443271 q^{78} +9.38238 q^{79} -0.0462559 q^{80} +1.00000 q^{81} -0.434108 q^{82} -6.67576 q^{83} -3.44317 q^{84} -0.610823 q^{85} -3.94835 q^{86} +1.00000 q^{87} +14.1508 q^{88} +5.52034 q^{89} +0.237188 q^{90} -1.40616 q^{91} -1.27295 q^{92} +7.35747 q^{93} +10.5801 q^{94} +0.0290833 q^{95} -5.72330 q^{96} +0.587030 q^{97} -0.269774 q^{98} +5.07059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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