LMFDB - Embedded newform 2001.2.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.510814$ 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)

$f(q)$	$=$	$q+0.510814 q^{2} +1.00000 q^{3} -1.73907 q^{4} +2.52081 q^{5} +0.510814 q^{6} +1.21289 q^{7} -1.90997 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.510814 q^{2} +1.00000 q^{3} -1.73907 q^{4} +2.52081 q^{5} +0.510814 q^{6} +1.21289 q^{7} -1.90997 q^{8} +1.00000 q^{9} +1.28766 q^{10} -0.502071 q^{11} -1.73907 q^{12} +6.57584 q^{13} +0.619559 q^{14} +2.52081 q^{15} +2.50250 q^{16} -5.32759 q^{17} +0.510814 q^{18} +2.19688 q^{19} -4.38386 q^{20} +1.21289 q^{21} -0.256465 q^{22} -1.00000 q^{23} -1.90997 q^{24} +1.35448 q^{25} +3.35903 q^{26} +1.00000 q^{27} -2.10929 q^{28} -1.00000 q^{29} +1.28766 q^{30} +9.31204 q^{31} +5.09825 q^{32} -0.502071 q^{33} -2.72141 q^{34} +3.05746 q^{35} -1.73907 q^{36} -1.80268 q^{37} +1.12220 q^{38} +6.57584 q^{39} -4.81466 q^{40} +0.987595 q^{41} +0.619559 q^{42} +7.62698 q^{43} +0.873136 q^{44} +2.52081 q^{45} -0.510814 q^{46} -6.90467 q^{47} +2.50250 q^{48} -5.52891 q^{49} +0.691885 q^{50} -5.32759 q^{51} -11.4358 q^{52} +13.2261 q^{53} +0.510814 q^{54} -1.26562 q^{55} -2.31658 q^{56} +2.19688 q^{57} -0.510814 q^{58} -11.6425 q^{59} -4.38386 q^{60} -5.76654 q^{61} +4.75672 q^{62} +1.21289 q^{63} -2.40075 q^{64} +16.5764 q^{65} -0.256465 q^{66} +7.64146 q^{67} +9.26505 q^{68} -1.00000 q^{69} +1.56179 q^{70} +0.291616 q^{71} -1.90997 q^{72} +7.58236 q^{73} -0.920831 q^{74} +1.35448 q^{75} -3.82053 q^{76} -0.608955 q^{77} +3.35903 q^{78} +6.30526 q^{79} +6.30833 q^{80} +1.00000 q^{81} +0.504477 q^{82} -1.76118 q^{83} -2.10929 q^{84} -13.4298 q^{85} +3.89597 q^{86} -1.00000 q^{87} +0.958939 q^{88} +16.6702 q^{89} +1.28766 q^{90} +7.97576 q^{91} +1.73907 q^{92} +9.31204 q^{93} -3.52700 q^{94} +5.53792 q^{95} +5.09825 q^{96} -7.03740 q^{97} -2.82424 q^{98} -0.502071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * 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 $

$2$	0.510814	0.361200	0.180600	−	0.983557i	$-0.442196\pi$
$2$	0.510814	0.361200	0.180600	+	0.983557i	$0.442196\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.73907	−0.869535
$5$	2.52081	1.12734	0.563670	−	0.826000i	$-0.309389\pi$
$5$	2.52081	1.12734	0.563670	+	0.826000i	$0.309389\pi$
$6$	0.510814	0.208539
$7$	1.21289	0.458428	0.229214	−	0.973376i	$-0.426384\pi$
$7$	1.21289	0.458428	0.229214	+	0.973376i	$0.426384\pi$
$8$	−1.90997	−0.675276
$9$	1.00000	0.333333
$10$	1.28766	0.407195
$11$	−0.502071	−0.151380	−0.0756900	−	0.997131i	$-0.524116\pi$
$11$	−0.502071	−0.151380	−0.0756900	+	0.997131i	$0.524116\pi$
$12$	−1.73907	−0.502026
$13$	6.57584	1.82381	0.911906	−	0.410400i	$-0.134611\pi$
$13$	6.57584	1.82381	0.911906	+	0.410400i	$0.134611\pi$
$14$	0.619559	0.165584
$15$	2.52081	0.650870
$16$	2.50250	0.625625
$17$	−5.32759	−1.29213	−0.646066	−	0.763282i	$-0.723587\pi$
$17$	−5.32759	−1.29213	−0.646066	+	0.763282i	$0.723587\pi$
$18$	0.510814	0.120400
$19$	2.19688	0.504000	0.252000	−	0.967727i	$-0.418912\pi$
$19$	2.19688	0.504000	0.252000	+	0.967727i	$0.418912\pi$
$20$	−4.38386	−0.980261
$21$	1.21289	0.264674
$22$	−0.256465	−0.0546784
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.90997	−0.389871
$25$	1.35448	0.270895
$26$	3.35903	0.658760
$27$	1.00000	0.192450
$28$	−2.10929	−0.398619
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.28766	0.235094
$31$	9.31204	1.67249	0.836246	−	0.548355i	$-0.184746\pi$
$31$	9.31204	1.67249	0.836246	+	0.548355i	$0.184746\pi$
$32$	5.09825	0.901251
$33$	−0.502071	−0.0873993
$34$	−2.72141	−0.466717
$35$	3.05746	0.516804
$36$	−1.73907	−0.289845
$37$	−1.80268	−0.296358	−0.148179	−	0.988961i	$-0.547341\pi$
$37$	−1.80268	−0.296358	−0.148179	+	0.988961i	$0.547341\pi$
$38$	1.12220	0.182045
$39$	6.57584	1.05298
$40$	−4.81466	−0.761265
$41$	0.987595	0.154236	0.0771182	−	0.997022i	$-0.475428\pi$
$41$	0.987595	0.154236	0.0771182	+	0.997022i	$0.475428\pi$
$42$	0.619559	0.0956001
$43$	7.62698	1.16310	0.581552	−	0.813509i	$-0.302446\pi$
$43$	7.62698	1.16310	0.581552	+	0.813509i	$0.302446\pi$
$44$	0.873136	0.131630
$45$	2.52081	0.375780
$46$	−0.510814	−0.0753154
$47$	−6.90467	−1.00715	−0.503575	−	0.863952i	$-0.667982\pi$
$47$	−6.90467	−1.00715	−0.503575	+	0.863952i	$0.667982\pi$
$48$	2.50250	0.361205
$49$	−5.52891	−0.789844
$50$	0.691885	0.0978473
$51$	−5.32759	−0.746012
$52$	−11.4358	−1.58587
$53$	13.2261	1.81674	0.908371	−	0.418165i	$-0.137327\pi$
$53$	13.2261	1.81674	0.908371	+	0.418165i	$0.137327\pi$
$54$	0.510814	0.0695129
$55$	−1.26562	−0.170657
$56$	−2.31658	−0.309565
$57$	2.19688	0.290984
$58$	−0.510814	−0.0670731
$59$	−11.6425	−1.51572	−0.757860	−	0.652417i	$-0.773755\pi$
$59$	−11.6425	−1.51572	−0.757860	+	0.652417i	$0.773755\pi$
$60$	−4.38386	−0.565954
$61$	−5.76654	−0.738330	−0.369165	−	0.929364i	$-0.620356\pi$
$61$	−5.76654	−0.738330	−0.369165	+	0.929364i	$0.620356\pi$
$62$	4.75672	0.604104
$63$	1.21289	0.152809
$64$	−2.40075	−0.300094
$65$	16.5764	2.05605
$66$	−0.256465	−0.0315686
$67$	7.64146	0.933553	0.466776	−	0.884375i	$-0.345415\pi$
$67$	7.64146	0.933553	0.466776	+	0.884375i	$0.345415\pi$
$68$	9.26505	1.12355
$69$	−1.00000	−0.120386
$70$	1.56179	0.186670
$71$	0.291616	0.0346085	0.0173042	−	0.999850i	$-0.494492\pi$
$71$	0.291616	0.0346085	0.0173042	+	0.999850i	$0.494492\pi$
$72$	−1.90997	−0.225092
$73$	7.58236	0.887448	0.443724	−	0.896164i	$-0.353657\pi$
$73$	7.58236	0.887448	0.443724	+	0.896164i	$0.353657\pi$
$74$	−0.920831	−0.107044
$75$	1.35448	0.156401
$76$	−3.82053	−0.438245
$77$	−0.608955	−0.0693969
$78$	3.35903	0.380335
$79$	6.30526	0.709397	0.354698	−	0.934981i	$-0.384584\pi$
$79$	6.30526	0.709397	0.354698	+	0.934981i	$0.384584\pi$
$80$	6.30833	0.705292
$81$	1.00000	0.111111
$82$	0.504477	0.0557101
$83$	−1.76118	−0.193315	−0.0966575	−	0.995318i	$-0.530815\pi$
$83$	−1.76118	−0.193315	−0.0966575	+	0.995318i	$0.530815\pi$
$84$	−2.10929	−0.230143
$85$	−13.4298	−1.45667
$86$	3.89597	0.420113
$87$	−1.00000	−0.107211
$88$	0.958939	0.102223
$89$	16.6702	1.76704	0.883521	−	0.468392i	$-0.155166\pi$
$89$	16.6702	1.76704	0.883521	+	0.468392i	$0.155166\pi$
$90$	1.28766	0.135732
$91$	7.97576	0.836086
$92$	1.73907	0.181311
$93$	9.31204	0.965613
$94$	−3.52700	−0.363782
$95$	5.53792	0.568179
$96$	5.09825	0.520338
$97$	−7.03740	−0.714540	−0.357270	−	0.934001i	$-0.616292\pi$
$97$	−7.03740	−0.714540	−0.357270	+	0.934001i	$0.616292\pi$
$98$	−2.82424	−0.285291
$99$	−0.502071	−0.0504600
$100$	−2.35553	−0.235553
$101$	12.3857	1.23242	0.616209	−	0.787582i	$-0.288668\pi$
$101$	12.3857	1.23242	0.616209	+	0.787582i	$0.288668\pi$
$102$	−2.72141	−0.269459
$103$	−9.26533	−0.912940	−0.456470	−	0.889739i	$-0.650886\pi$
$103$	−9.26533	−0.912940	−0.456470	+	0.889739i	$0.650886\pi$
$104$	−12.5597	−1.23158
$105$	3.05746	0.298377
$106$	6.75606	0.656207
$107$	1.85332	0.179167	0.0895837	−	0.995979i	$-0.471446\pi$
$107$	1.85332	0.179167	0.0895837	+	0.995979i	$0.471446\pi$
$108$	−1.73907	−0.167342
$109$	8.89625	0.852106	0.426053	−	0.904698i	$-0.359904\pi$
$109$	8.89625	0.852106	0.426053	+	0.904698i	$0.359904\pi$
$110$	−0.646498	−0.0616412
$111$	−1.80268	−0.171102
$112$	3.03525	0.286804
$113$	−4.93101	−0.463871	−0.231935	−	0.972731i	$-0.574506\pi$
$113$	−4.93101	−0.463871	−0.231935	+	0.972731i	$0.574506\pi$
$114$	1.12220	0.105104
$115$	−2.52081	−0.235067
$116$	1.73907	0.161469
$117$	6.57584	0.607937
$118$	−5.94713	−0.547478
$119$	−6.46177	−0.592349
$120$	−4.81466	−0.439517
$121$	−10.7479	−0.977084
$122$	−2.94563	−0.266685
$123$	0.987595	0.0890484
$124$	−16.1943	−1.45429
$125$	−9.18967	−0.821949
$126$	0.619559	0.0551947
$127$	0.0259951	0.00230669	0.00115335	−	0.999999i	$-0.499633\pi$
$127$	0.0259951	0.00230669	0.00115335	+	0.999999i	$0.499633\pi$
$128$	−11.4228	−1.00965
$129$	7.62698	0.671518
$130$	8.46747	0.742647
$131$	10.3177	0.901460	0.450730	−	0.892660i	$-0.351164\pi$
$131$	10.3177	0.901460	0.450730	+	0.892660i	$0.351164\pi$
$132$	0.873136	0.0759967
$133$	2.66457	0.231048
$134$	3.90336	0.337199
$135$	2.52081	0.216957
$136$	10.1755	0.872544
$137$	−1.23202	−0.105258	−0.0526291	−	0.998614i	$-0.516760\pi$
$137$	−1.23202	−0.105258	−0.0526291	+	0.998614i	$0.516760\pi$
$138$	−0.510814	−0.0434833
$139$	8.44793	0.716544	0.358272	−	0.933617i	$-0.383366\pi$
$139$	8.44793	0.716544	0.358272	+	0.933617i	$0.383366\pi$
$140$	−5.31713	−0.449379
$141$	−6.90467	−0.581478
$142$	0.148962	0.0125006
$143$	−3.30154	−0.276088
$144$	2.50250	0.208542
$145$	−2.52081	−0.209342
$146$	3.87317	0.320546
$147$	−5.52891	−0.456016
$148$	3.13498	0.257694
$149$	−9.61316	−0.787541	−0.393770	−	0.919209i	$-0.628830\pi$
$149$	−9.61316	−0.787541	−0.393770	+	0.919209i	$0.628830\pi$
$150$	0.691885	0.0564922
$151$	−2.56226	−0.208514	−0.104257	−	0.994550i	$-0.533246\pi$
$151$	−2.56226	−0.208514	−0.104257	+	0.994550i	$0.533246\pi$
$152$	−4.19598	−0.340339
$153$	−5.32759	−0.430710
$154$	−0.311062	−0.0250661
$155$	23.4739	1.88547
$156$	−11.4358	−0.915601
$157$	−9.73470	−0.776914	−0.388457	−	0.921467i	$-0.626992\pi$
$157$	−9.73470	−0.776914	−0.388457	+	0.921467i	$0.626992\pi$
$158$	3.22081	0.256234
$159$	13.2261	1.04890
$160$	12.8517	1.01602
$161$	−1.21289	−0.0955889
$162$	0.510814	0.0401333
$163$	3.98394	0.312046	0.156023	−	0.987753i	$-0.450133\pi$
$163$	3.98394	0.312046	0.156023	+	0.987753i	$0.450133\pi$
$164$	−1.71750	−0.134114
$165$	−1.26562	−0.0985287
$166$	−0.899636	−0.0698253
$167$	−11.7573	−0.909805	−0.454902	−	0.890541i	$-0.650326\pi$
$167$	−11.7573	−0.909805	−0.454902	+	0.890541i	$0.650326\pi$
$168$	−2.31658	−0.178728
$169$	30.2417	2.32629
$170$	−6.86015	−0.526149
$171$	2.19688	0.168000
$172$	−13.2639	−1.01136
$173$	−21.8207	−1.65900	−0.829498	−	0.558510i	$-0.811373\pi$
$173$	−21.8207	−1.65900	−0.829498	+	0.558510i	$0.811373\pi$
$174$	−0.510814	−0.0387247
$175$	1.64283	0.124186
$176$	−1.25643	−0.0947072
$177$	−11.6425	−0.875101
$178$	8.51538	0.638255
$179$	6.05354	0.452463	0.226231	−	0.974074i	$-0.427359\pi$
$179$	6.05354	0.452463	0.226231	+	0.974074i	$0.427359\pi$
$180$	−4.38386	−0.326754
$181$	−8.79738	−0.653904	−0.326952	−	0.945041i	$-0.606022\pi$
$181$	−8.79738	−0.653904	−0.326952	+	0.945041i	$0.606022\pi$
$182$	4.07413	0.301994
$183$	−5.76654	−0.426275
$184$	1.90997	0.140805
$185$	−4.54420	−0.334096
$186$	4.75672	0.348779
$187$	2.67483	0.195603
$188$	12.0077	0.875752
$189$	1.21289	0.0882245
$190$	2.82885	0.205226
$191$	−8.17121	−0.591248	−0.295624	−	0.955304i	$-0.595528\pi$
$191$	−8.17121	−0.591248	−0.295624	+	0.955304i	$0.595528\pi$
$192$	−2.40075	−0.173259
$193$	−14.0888	−1.01413	−0.507065	−	0.861908i	$-0.669270\pi$
$193$	−14.0888	−1.01413	−0.507065	+	0.861908i	$0.669270\pi$
$194$	−3.59480	−0.258092
$195$	16.5764	1.18706
$196$	9.61515	0.686796
$197$	5.62762	0.400952	0.200476	−	0.979699i	$-0.435751\pi$
$197$	5.62762	0.400952	0.200476	+	0.979699i	$0.435751\pi$
$198$	−0.256465	−0.0182261
$199$	−7.30901	−0.518122	−0.259061	−	0.965861i	$-0.583413\pi$
$199$	−7.30901	−0.518122	−0.259061	+	0.965861i	$0.583413\pi$
$200$	−2.58701	−0.182929
$201$	7.64146	0.538987
$202$	6.32676	0.445149
$203$	−1.21289	−0.0851280
$204$	9.26505	0.648683
$205$	2.48954	0.173877
$206$	−4.73286	−0.329754
$207$	−1.00000	−0.0695048
$208$	16.4561	1.14102
$209$	−1.10299	−0.0762955
$210$	1.56179	0.107774
$211$	20.2921	1.39697	0.698484	−	0.715626i	$-0.253858\pi$
$211$	20.2921	1.39697	0.698484	+	0.715626i	$0.253858\pi$
$212$	−23.0011	−1.57972
$213$	0.291616	0.0199812
$214$	0.946702	0.0647152
$215$	19.2262	1.31121
$216$	−1.90997	−0.129957
$217$	11.2945	0.766717
$218$	4.54433	0.307781
$219$	7.58236	0.512368
$220$	2.20101	0.148392
$221$	−35.0334	−2.35660
$222$	−0.920831	−0.0618022
$223$	10.3132	0.690621	0.345311	−	0.938488i	$-0.387774\pi$
$223$	10.3132	0.690621	0.345311	+	0.938488i	$0.387774\pi$
$224$	6.18360	0.413159
$225$	1.35448	0.0902984
$226$	−2.51883	−0.167550
$227$	10.6159	0.704602	0.352301	−	0.935887i	$-0.385399\pi$
$227$	10.6159	0.704602	0.352301	+	0.935887i	$0.385399\pi$
$228$	−3.82053	−0.253021
$229$	12.2748	0.811139	0.405569	−	0.914064i	$-0.367073\pi$
$229$	12.2748	0.811139	0.405569	+	0.914064i	$0.367073\pi$
$230$	−1.28766	−0.0849060
$231$	−0.608955	−0.0400663
$232$	1.90997	0.125396
$233$	1.08278	0.0709356	0.0354678	−	0.999371i	$-0.488708\pi$
$233$	1.08278	0.0709356	0.0354678	+	0.999371i	$0.488708\pi$
$234$	3.35903	0.219587
$235$	−17.4054	−1.13540
$236$	20.2471	1.31797
$237$	6.30526	0.409570
$238$	−3.30076	−0.213956
$239$	−22.4858	−1.45449	−0.727243	−	0.686380i	$-0.759198\pi$
$239$	−22.4858	−1.45449	−0.727243	+	0.686380i	$0.759198\pi$
$240$	6.30833	0.407201
$241$	−14.7491	−0.950073	−0.475036	−	0.879966i	$-0.657565\pi$
$241$	−14.7491	−0.950073	−0.475036	+	0.879966i	$0.657565\pi$
$242$	−5.49019	−0.352923
$243$	1.00000	0.0641500
$244$	10.0284	0.642004
$245$	−13.9373	−0.890422
$246$	0.504477	0.0321643
$247$	14.4464	0.919200
$248$	−17.7857	−1.12939
$249$	−1.76118	−0.111610
$250$	−4.69421	−0.296888
$251$	3.10594	0.196045	0.0980226	−	0.995184i	$-0.468748\pi$
$251$	3.10594	0.196045	0.0980226	+	0.995184i	$0.468748\pi$
$252$	−2.10929	−0.132873
$253$	0.502071	0.0315649
$254$	0.0132786	0.000833176 0
$255$	−13.4298	−0.841009
$256$	−1.03344	−0.0645901
$257$	−23.2603	−1.45094	−0.725470	−	0.688254i	$-0.758377\pi$
$257$	−23.2603	−1.45094	−0.725470	+	0.688254i	$0.758377\pi$
$258$	3.89597	0.242552
$259$	−2.18644	−0.135859
$260$	−28.8276	−1.78781
$261$	−1.00000	−0.0618984
$262$	5.27041	0.325607
$263$	14.4964	0.893884	0.446942	−	0.894563i	$-0.352513\pi$
$263$	14.4964	0.893884	0.446942	+	0.894563i	$0.352513\pi$
$264$	0.958939	0.0590186
$265$	33.3404	2.04809
$266$	1.36110	0.0834544
$267$	16.6702	1.02020
$268$	−13.2890	−0.811757
$269$	−18.7400	−1.14260	−0.571299	−	0.820742i	$-0.693560\pi$
$269$	−18.7400	−1.14260	−0.571299	+	0.820742i	$0.693560\pi$
$270$	1.28766	0.0783647
$271$	−12.6693	−0.769605	−0.384802	−	0.922999i	$-0.625730\pi$
$271$	−12.6693	−0.769605	−0.384802	+	0.922999i	$0.625730\pi$
$272$	−13.3323	−0.808390
$273$	7.97576	0.482715
$274$	−0.629330	−0.0380192
$275$	−0.680043	−0.0410081
$276$	1.73907	0.104680
$277$	−28.8115	−1.73111	−0.865557	−	0.500811i	$-0.833035\pi$
$277$	−28.8115	−1.73111	−0.865557	+	0.500811i	$0.833035\pi$
$278$	4.31532	0.258816
$279$	9.31204	0.557497
$280$	−5.83964	−0.348985
$281$	−25.8074	−1.53954	−0.769770	−	0.638321i	$-0.779629\pi$
$281$	−25.8074	−1.53954	−0.769770	+	0.638321i	$0.779629\pi$
$282$	−3.52700	−0.210030
$283$	−5.95438	−0.353951	−0.176975	−	0.984215i	$-0.556631\pi$
$283$	−5.95438	−0.353951	−0.176975	+	0.984215i	$0.556631\pi$
$284$	−0.507141	−0.0300933
$285$	5.53792	0.328038
$286$	−1.68647	−0.0997231
$287$	1.19784	0.0707063
$288$	5.09825	0.300417
$289$	11.3832	0.669603
$290$	−1.28766	−0.0756142
$291$	−7.03740	−0.412540
$292$	−13.1862	−0.771667
$293$	8.47294	0.494994	0.247497	−	0.968889i	$-0.420392\pi$
$293$	8.47294	0.494994	0.247497	+	0.968889i	$0.420392\pi$
$294$	−2.82424	−0.164713
$295$	−29.3484	−1.70873
$296$	3.44305	0.200123
$297$	−0.502071	−0.0291331
$298$	−4.91053	−0.284460
$299$	−6.57584	−0.380291
$300$	−2.35553	−0.135996
$301$	9.25067	0.533200
$302$	−1.30884	−0.0753151
$303$	12.3857	0.711537
$304$	5.49771	0.315315
$305$	−14.5363	−0.832349
$306$	−2.72141	−0.155572
$307$	16.9797	0.969084	0.484542	−	0.874768i	$-0.338986\pi$
$307$	16.9797	0.969084	0.484542	+	0.874768i	$0.338986\pi$
$308$	1.05901	0.0603430
$309$	−9.26533	−0.527086
$310$	11.9908	0.681030
$311$	7.85324	0.445317	0.222658	−	0.974897i	$-0.428527\pi$
$311$	7.85324	0.445317	0.222658	+	0.974897i	$0.428527\pi$
$312$	−12.5597	−0.711050
$313$	−21.4281	−1.21119	−0.605593	−	0.795775i	$-0.707064\pi$
$313$	−21.4281	−1.21119	−0.605593	+	0.795775i	$0.707064\pi$
$314$	−4.97262	−0.280621
$315$	3.05746	0.172268
$316$	−10.9653	−0.616845
$317$	0.861567	0.0483904	0.0241952	−	0.999707i	$-0.492298\pi$
$317$	0.861567	0.0483904	0.0241952	+	0.999707i	$0.492298\pi$
$318$	6.75606	0.378861
$319$	0.502071	0.0281106
$320$	−6.05183	−0.338307
$321$	1.85332	0.103442
$322$	−0.619559	−0.0345267
$323$	−11.7041	−0.651234
$324$	−1.73907	−0.0966150
$325$	8.90683	0.494062
$326$	2.03505	0.112711
$327$	8.89625	0.491964
$328$	−1.88627	−0.104152
$329$	−8.37458	−0.461706
$330$	−0.646498	−0.0355885
$331$	−13.6652	−0.751105	−0.375552	−	0.926801i	$-0.622547\pi$
$331$	−13.6652	−0.751105	−0.375552	+	0.926801i	$0.622547\pi$
$332$	3.06282	0.168094
$333$	−1.80268	−0.0987860
$334$	−6.00577	−0.328621
$335$	19.2627	1.05243
$336$	3.03525	0.165587
$337$	23.5815	1.28456	0.642282	−	0.766468i	$-0.277988\pi$
$337$	23.5815	1.28456	0.642282	+	0.766468i	$0.277988\pi$
$338$	15.4479	0.840254
$339$	−4.93101	−0.267816
$340$	23.3554	1.26663
$341$	−4.67530	−0.253182
$342$	1.12220	0.0606815
$343$	−15.1961	−0.820515
$344$	−14.5673	−0.785416
$345$	−2.52081	−0.135716
$346$	−11.1463	−0.599229
$347$	−4.28468	−0.230013	−0.115007	−	0.993365i	$-0.536689\pi$
$347$	−4.28468	−0.230013	−0.115007	+	0.993365i	$0.536689\pi$
$348$	1.73907	0.0932239
$349$	−7.92294	−0.424105	−0.212053	−	0.977258i	$-0.568015\pi$
$349$	−7.92294	−0.424105	−0.212053	+	0.977258i	$0.568015\pi$
$350$	0.839178	0.0448560
$351$	6.57584	0.350993
$352$	−2.55968	−0.136431
$353$	−12.7525	−0.678749	−0.339374	−	0.940651i	$-0.610215\pi$
$353$	−12.7525	−0.678749	−0.339374	+	0.940651i	$0.610215\pi$
$354$	−5.94713	−0.316086
$355$	0.735109	0.0390155
$356$	−28.9907	−1.53650
$357$	−6.46177	−0.341993
$358$	3.09223	0.163430
$359$	−13.4404	−0.709359	−0.354680	−	0.934988i	$-0.615410\pi$
$359$	−13.4404	−0.709359	−0.354680	+	0.934988i	$0.615410\pi$
$360$	−4.81466	−0.253755
$361$	−14.1737	−0.745984
$362$	−4.49382	−0.236190
$363$	−10.7479	−0.564120
$364$	−13.8704	−0.727006
$365$	19.1137	1.00046
$366$	−2.94563	−0.153970
$367$	3.47897	0.181601	0.0908003	−	0.995869i	$-0.471058\pi$
$367$	3.47897	0.181601	0.0908003	+	0.995869i	$0.471058\pi$
$368$	−2.50250	−0.130452
$369$	0.987595	0.0514121
$370$	−2.32124	−0.120676
$371$	16.0417	0.832846
$372$	−16.1943	−0.839634
$373$	25.7726	1.33445	0.667227	−	0.744854i	$-0.267481\pi$
$373$	25.7726	1.33445	0.667227	+	0.744854i	$0.267481\pi$
$374$	1.36634	0.0706517
$375$	−9.18967	−0.474552
$376$	13.1877	0.680104
$377$	−6.57584	−0.338673
$378$	0.619559	0.0318667
$379$	−15.3700	−0.789505	−0.394753	−	0.918787i	$-0.629170\pi$
$379$	−15.3700	−0.789505	−0.394753	+	0.918787i	$0.629170\pi$
$380$	−9.63084	−0.494051
$381$	0.0259951	0.00133177
$382$	−4.17397	−0.213559
$383$	−10.7152	−0.547522	−0.273761	−	0.961798i	$-0.588268\pi$
$383$	−10.7152	−0.547522	−0.273761	+	0.961798i	$0.588268\pi$
$384$	−11.4228	−0.582919
$385$	−1.53506	−0.0782338
$386$	−7.19673	−0.366304
$387$	7.62698	0.387701
$388$	12.2385	0.621317
$389$	−9.32168	−0.472628	−0.236314	−	0.971677i	$-0.575939\pi$
$389$	−9.32168	−0.472628	−0.236314	+	0.971677i	$0.575939\pi$
$390$	8.46747	0.428767
$391$	5.32759	0.269428
$392$	10.5600	0.533362
$393$	10.3177	0.520458
$394$	2.87467	0.144824
$395$	15.8943	0.799731
$396$	0.873136	0.0438767
$397$	5.71651	0.286903	0.143452	−	0.989657i	$-0.454180\pi$
$397$	5.71651	0.286903	0.143452	+	0.989657i	$0.454180\pi$
$398$	−3.73354	−0.187146
$399$	2.66457	0.133395
$400$	3.38958	0.169479
$401$	−16.7193	−0.834923	−0.417462	−	0.908695i	$-0.637080\pi$
$401$	−16.7193	−0.834923	−0.417462	+	0.908695i	$0.637080\pi$
$402$	3.90336	0.194682
$403$	61.2345	3.05031
$404$	−21.5395	−1.07163
$405$	2.52081	0.125260
$406$	−0.619559	−0.0307482
$407$	0.905071	0.0448627
$408$	10.1755	0.503764
$409$	4.89630	0.242106	0.121053	−	0.992646i	$-0.461373\pi$
$409$	4.89630	0.242106	0.121053	+	0.992646i	$0.461373\pi$
$410$	1.27169	0.0628043
$411$	−1.23202	−0.0607708
$412$	16.1131	0.793833
$413$	−14.1210	−0.694849
$414$	−0.510814	−0.0251051
$415$	−4.43961	−0.217932
$416$	33.5253	1.64371
$417$	8.44793	0.413697
$418$	−0.563423	−0.0275579
$419$	−9.53235	−0.465686	−0.232843	−	0.972514i	$-0.574803\pi$
$419$	−9.53235	−0.465686	−0.232843	+	0.972514i	$0.574803\pi$
$420$	−5.31713	−0.259449
$421$	13.9000	0.677446	0.338723	−	0.940886i	$-0.390005\pi$
$421$	13.9000	0.677446	0.338723	+	0.940886i	$0.390005\pi$
$422$	10.3655	0.504584
$423$	−6.90467	−0.335717
$424$	−25.2614	−1.22680
$425$	−7.21610	−0.350032
$426$	0.148962	0.00721721
$427$	−6.99416	−0.338471
$428$	−3.22305	−0.155792
$429$	−3.30154	−0.159400
$430$	9.82099	0.473610
$431$	−34.2413	−1.64935	−0.824673	−	0.565609i	$-0.808641\pi$
$431$	−34.2413	−1.64935	−0.824673	+	0.565609i	$0.808641\pi$
$432$	2.50250	0.120402
$433$	−14.3103	−0.687709	−0.343854	−	0.939023i	$-0.611733\pi$
$433$	−14.3103	−0.687709	−0.343854	+	0.939023i	$0.611733\pi$
$434$	5.76936	0.276938
$435$	−2.52081	−0.120864
$436$	−15.4712	−0.740936
$437$	−2.19688	−0.105091
$438$	3.87317	0.185067
$439$	−24.6983	−1.17879	−0.589393	−	0.807846i	$-0.700633\pi$
$439$	−24.6983	−1.17879	−0.589393	+	0.807846i	$0.700633\pi$
$440$	2.41730	0.115240
$441$	−5.52891	−0.263281
$442$	−17.8955	−0.851204
$443$	−2.83321	−0.134610	−0.0673048	−	0.997732i	$-0.521440\pi$
$443$	−2.83321	−0.134610	−0.0673048	+	0.997732i	$0.521440\pi$
$444$	3.13498	0.148779
$445$	42.0225	1.99206
$446$	5.26811	0.249452
$447$	−9.61316	−0.454687
$448$	−2.91184	−0.137571
$449$	−16.8933	−0.797245	−0.398623	−	0.917115i	$-0.630512\pi$
$449$	−16.8933	−0.797245	−0.398623	+	0.917115i	$0.630512\pi$
$450$	0.691885	0.0326158
$451$	−0.495842	−0.0233483
$452$	8.57537	0.403352
$453$	−2.56226	−0.120385
$454$	5.42275	0.254502
$455$	20.1054	0.942554
$456$	−4.19598	−0.196495
$457$	−26.4008	−1.23498	−0.617490	−	0.786579i	$-0.711850\pi$
$457$	−26.4008	−1.23498	−0.617490	+	0.786579i	$0.711850\pi$
$458$	6.27011	0.292983
$459$	−5.32759	−0.248671
$460$	4.38386	0.204399
$461$	0.0827947	0.00385614	0.00192807	−	0.999998i	$-0.499386\pi$
$461$	0.0827947	0.00385614	0.00192807	+	0.999998i	$0.499386\pi$
$462$	−0.311062	−0.0144719
$463$	6.85070	0.318379	0.159189	−	0.987248i	$-0.449112\pi$
$463$	6.85070	0.318379	0.159189	+	0.987248i	$0.449112\pi$
$464$	−2.50250	−0.116176
$465$	23.4739	1.08857
$466$	0.553101	0.0256219
$467$	28.9311	1.33877	0.669386	−	0.742914i	$-0.266557\pi$
$467$	28.9311	1.33877	0.669386	+	0.742914i	$0.266557\pi$
$468$	−11.4358	−0.528622
$469$	9.26823	0.427967
$470$	−8.89089	−0.410106
$471$	−9.73470	−0.448551
$472$	22.2367	1.02353
$473$	−3.82928	−0.176071
$474$	3.22081	0.147937
$475$	2.97563	0.136531
$476$	11.2375	0.515068
$477$	13.2261	0.605581
$478$	−11.4861	−0.525360
$479$	−10.8301	−0.494841	−0.247421	−	0.968908i	$-0.579583\pi$
$479$	−10.8301	−0.494841	−0.247421	+	0.968908i	$0.579583\pi$
$480$	12.8517	0.586597
$481$	−11.8541	−0.540501
$482$	−7.53404	−0.343166
$483$	−1.21289	−0.0551883
$484$	18.6914	0.849609
$485$	−17.7399	−0.805529
$486$	0.510814	0.0231710
$487$	−25.0320	−1.13431	−0.567154	−	0.823612i	$-0.691956\pi$
$487$	−25.0320	−1.13431	−0.567154	+	0.823612i	$0.691956\pi$
$488$	11.0139	0.498576
$489$	3.98394	0.180160
$490$	−7.11937	−0.321620
$491$	20.1985	0.911543	0.455772	−	0.890097i	$-0.349363\pi$
$491$	20.1985	0.911543	0.455772	+	0.890097i	$0.349363\pi$
$492$	−1.71750	−0.0774307
$493$	5.32759	0.239943
$494$	7.37940	0.332015
$495$	−1.26562	−0.0568856
$496$	23.3034	1.04635
$497$	0.353698	0.0158655
$498$	−0.899636	−0.0403137
$499$	38.6070	1.72829	0.864143	−	0.503247i	$-0.167861\pi$
$499$	38.6070	1.72829	0.864143	+	0.503247i	$0.167861\pi$
$500$	15.9815	0.714713
$501$	−11.7573	−0.525276
$502$	1.58656	0.0708115
$503$	18.7133	0.834385	0.417193	−	0.908818i	$-0.363014\pi$
$503$	18.7133	0.834385	0.417193	+	0.908818i	$0.363014\pi$
$504$	−2.31658	−0.103188
$505$	31.2219	1.38935
$506$	0.256465	0.0114012
$507$	30.2417	1.34308
$508$	−0.0452073	−0.00200575
$509$	1.89925	0.0841826	0.0420913	−	0.999114i	$-0.486598\pi$
$509$	1.89925	0.0841826	0.0420913	+	0.999114i	$0.486598\pi$
$510$	−6.86015	−0.303772
$511$	9.19654	0.406831
$512$	22.3178	0.986315
$513$	2.19688	0.0969948
$514$	−11.8817	−0.524079
$515$	−23.3561	−1.02919
$516$	−13.2639	−0.583909
$517$	3.46663	0.152462
$518$	−1.11686	−0.0490722
$519$	−21.8207	−0.957822
$520$	−31.6605	−1.38840
$521$	6.18015	0.270757	0.135379	−	0.990794i	$-0.456775\pi$
$521$	6.18015	0.270757	0.135379	+	0.990794i	$0.456775\pi$
$522$	−0.510814	−0.0223577
$523$	−27.8680	−1.21858	−0.609291	−	0.792947i	$-0.708546\pi$
$523$	−27.8680	−1.21858	−0.609291	+	0.792947i	$0.708546\pi$
$524$	−17.9432	−0.783851
$525$	1.64283	0.0716988
$526$	7.40494	0.322871
$527$	−49.6107	−2.16108
$528$	−1.25643	−0.0546792
$529$	1.00000	0.0434783
$530$	17.0307	0.739768
$531$	−11.6425	−0.505240
$532$	−4.63388	−0.200904
$533$	6.49427	0.281298
$534$	8.51538	0.368497
$535$	4.67187	0.201983
$536$	−14.5949	−0.630405
$537$	6.05354	0.261230
$538$	−9.57264	−0.412706
$539$	2.77590	0.119567
$540$	−4.38386	−0.188651
$541$	−14.8798	−0.639733	−0.319866	−	0.947463i	$-0.603638\pi$
$541$	−14.8798	−0.639733	−0.319866	+	0.947463i	$0.603638\pi$
$542$	−6.47165	−0.277981
$543$	−8.79738	−0.377532
$544$	−27.1614	−1.16453
$545$	22.4257	0.960614
$546$	4.07413	0.174356
$547$	−26.2488	−1.12232	−0.561159	−	0.827708i	$-0.689644\pi$
$547$	−26.2488	−1.12232	−0.561159	+	0.827708i	$0.689644\pi$
$548$	2.14256	0.0915256
$549$	−5.76654	−0.246110
$550$	−0.347375	−0.0148121
$551$	−2.19688	−0.0935904
$552$	1.90997	0.0812936
$553$	7.64756	0.325207
$554$	−14.7173	−0.625278
$555$	−4.54420	−0.192891
$556$	−14.6915	−0.623060
$557$	28.2623	1.19751	0.598756	−	0.800931i	$-0.295662\pi$
$557$	28.2623	1.19751	0.598756	+	0.800931i	$0.295662\pi$
$558$	4.75672	0.201368
$559$	50.1539	2.12128
$560$	7.65129	0.323326
$561$	2.67483	0.112931
$562$	−13.1828	−0.556082
$563$	10.4549	0.440623	0.220311	−	0.975430i	$-0.429293\pi$
$563$	10.4549	0.440623	0.220311	+	0.975430i	$0.429293\pi$
$564$	12.0077	0.505615
$565$	−12.4301	−0.522940
$566$	−3.04158	−0.127847
$567$	1.21289	0.0509365
$568$	−0.556978	−0.0233703
$569$	−21.3535	−0.895185	−0.447593	−	0.894238i	$-0.647719\pi$
$569$	−21.3535	−0.895185	−0.447593	+	0.894238i	$0.647719\pi$
$570$	2.82885	0.118487
$571$	−21.1597	−0.885508	−0.442754	−	0.896643i	$-0.645998\pi$
$571$	−21.1597	−0.885508	−0.442754	+	0.896643i	$0.645998\pi$
$572$	5.74160	0.240069
$573$	−8.17121	−0.341357
$574$	0.611873	0.0255391
$575$	−1.35448	−0.0564856
$576$	−2.40075	−0.100031
$577$	14.3012	0.595368	0.297684	−	0.954664i	$-0.403786\pi$
$577$	14.3012	0.595368	0.297684	+	0.954664i	$0.403786\pi$
$578$	5.81472	0.241860
$579$	−14.0888	−0.585509
$580$	4.38386	0.182030
$581$	−2.13612	−0.0886210
$582$	−3.59480	−0.149009
$583$	−6.64043	−0.275018
$584$	−14.4821	−0.599272
$585$	16.5764	0.685352
$586$	4.32809	0.178792
$587$	25.4131	1.04891	0.524455	−	0.851438i	$-0.324269\pi$
$587$	25.4131	1.04891	0.524455	+	0.851438i	$0.324269\pi$
$588$	9.61515	0.396522
$589$	20.4575	0.842935
$590$	−14.9916	−0.617193
$591$	5.62762	0.231490
$592$	−4.51120	−0.185409
$593$	11.0315	0.453008	0.226504	−	0.974010i	$-0.427270\pi$
$593$	11.0315	0.453008	0.226504	+	0.974010i	$0.427270\pi$
$594$	−0.256465	−0.0105229
$595$	−16.2889	−0.667779
$596$	16.7180	0.684794
$597$	−7.30901	−0.299138
$598$	−3.35903	−0.137361
$599$	−48.1605	−1.96779	−0.983893	−	0.178761i	$-0.942791\pi$
$599$	−48.1605	−1.96779	−0.983893	+	0.178761i	$0.942791\pi$
$600$	−2.58701	−0.105614
$601$	−27.1335	−1.10680	−0.553400	−	0.832915i	$-0.686670\pi$
$601$	−27.1335	−1.10680	−0.553400	+	0.832915i	$0.686670\pi$
$602$	4.72537	0.192592
$603$	7.64146	0.311184
$604$	4.45594	0.181310
$605$	−27.0935	−1.10151
$606$	6.32676	0.257007
$607$	−20.5726	−0.835015	−0.417507	−	0.908674i	$-0.637096\pi$
$607$	−20.5726	−0.835015	−0.417507	+	0.908674i	$0.637096\pi$
$608$	11.2003	0.454230
$609$	−1.21289	−0.0491487
$610$	−7.42537	−0.300644
$611$	−45.4040	−1.83685
$612$	9.26505	0.374518
$613$	19.5402	0.789221	0.394611	−	0.918848i	$-0.370880\pi$
$613$	19.5402	0.789221	0.394611	+	0.918848i	$0.370880\pi$
$614$	8.67348	0.350033
$615$	2.48954	0.100388
$616$	1.16308	0.0468620
$617$	4.95291	0.199396	0.0996982	−	0.995018i	$-0.468212\pi$
$617$	4.95291	0.199396	0.0996982	+	0.995018i	$0.468212\pi$
$618$	−4.73286	−0.190383
$619$	40.8807	1.64313	0.821567	−	0.570111i	$-0.193100\pi$
$619$	40.8807	1.64313	0.821567	+	0.570111i	$0.193100\pi$
$620$	−40.8227	−1.63948
$621$	−1.00000	−0.0401286
$622$	4.01154	0.160848
$623$	20.2191	0.810062
$624$	16.4561	0.658770
$625$	−29.9378	−1.19751
$626$	−10.9457	−0.437480
$627$	−1.10299	−0.0440492
$628$	16.9293	0.675554
$629$	9.60392	0.382933
$630$	1.56179	0.0622232
$631$	0.835217	0.0332494	0.0166247	−	0.999862i	$-0.494708\pi$
$631$	0.835217	0.0332494	0.0166247	+	0.999862i	$0.494708\pi$
$632$	−12.0428	−0.479038
$633$	20.2921	0.806539
$634$	0.440100	0.0174786
$635$	0.0655286	0.00260042
$636$	−23.0011	−0.912052
$637$	−36.3572	−1.44053
$638$	0.256465	0.0101535
$639$	0.291616	0.0115362
$640$	−28.7948	−1.13821
$641$	27.4004	1.08225	0.541126	−	0.840942i	$-0.317998\pi$
$641$	27.4004	1.08225	0.541126	+	0.840942i	$0.317998\pi$
$642$	0.946702	0.0373633
$643$	41.9630	1.65486	0.827430	−	0.561569i	$-0.189802\pi$
$643$	41.9630	1.65486	0.827430	+	0.561569i	$0.189802\pi$
$644$	2.10929	0.0831179
$645$	19.2262	0.757029
$646$	−5.97862	−0.235226
$647$	−16.1202	−0.633750	−0.316875	−	0.948467i	$-0.602633\pi$
$647$	−16.1202	−0.633750	−0.316875	+	0.948467i	$0.602633\pi$
$648$	−1.90997	−0.0750306
$649$	5.84534	0.229450
$650$	4.54973	0.178455
$651$	11.2945	0.442664
$652$	−6.92834	−0.271335
$653$	−8.66870	−0.339232	−0.169616	−	0.985510i	$-0.554253\pi$
$653$	−8.66870	−0.339232	−0.169616	+	0.985510i	$0.554253\pi$
$654$	4.54433	0.177697
$655$	26.0089	1.01625
$656$	2.47146	0.0964942
$657$	7.58236	0.295816
$658$	−4.27785	−0.166768
$659$	15.8552	0.617631	0.308815	−	0.951122i	$-0.400067\pi$
$659$	15.8552	0.617631	0.308815	+	0.951122i	$0.400067\pi$
$660$	2.20101	0.0856741
$661$	41.2840	1.60576	0.802881	−	0.596140i	$-0.203300\pi$
$661$	41.2840	1.60576	0.802881	+	0.596140i	$0.203300\pi$
$662$	−6.98035	−0.271299
$663$	−35.0334	−1.36059
$664$	3.36380	0.130541
$665$	6.71688	0.260469
$666$	−0.920831	−0.0356815
$667$	1.00000	0.0387202
$668$	20.4467	0.791107
$669$	10.3132	0.398730
$670$	9.83963	0.380138
$671$	2.89521	0.111768
$672$	6.18360	0.238537
$673$	−12.8807	−0.496515	−0.248258	−	0.968694i	$-0.579858\pi$
$673$	−12.8807	−0.496515	−0.248258	+	0.968694i	$0.579858\pi$
$674$	12.0457	0.463984
$675$	1.35448	0.0521338
$676$	−52.5925	−2.02279
$677$	4.01480	0.154301	0.0771506	−	0.997019i	$-0.475418\pi$
$677$	4.01480	0.154301	0.0771506	+	0.997019i	$0.475418\pi$
$678$	−2.51883	−0.0967350
$679$	−8.53557	−0.327565
$680$	25.6506	0.983654
$681$	10.6159	0.406802
$682$	−2.38821	−0.0914492
$683$	12.8052	0.489979	0.244990	−	0.969526i	$-0.421215\pi$
$683$	12.8052	0.489979	0.244990	+	0.969526i	$0.421215\pi$
$684$	−3.82053	−0.146082
$685$	−3.10567	−0.118662
$686$	−7.76240	−0.296370
$687$	12.2748	0.468311
$688$	19.0865	0.727667
$689$	86.9726	3.31339
$690$	−1.28766	−0.0490205
$691$	−50.1919	−1.90939	−0.954694	−	0.297589i	$-0.903818\pi$
$691$	−50.1919	−1.90939	−0.954694	+	0.297589i	$0.903818\pi$
$692$	37.9477	1.44255
$693$	−0.608955	−0.0231323
$694$	−2.18867	−0.0830808
$695$	21.2956	0.807789
$696$	1.90997	0.0723971
$697$	−5.26150	−0.199294
$698$	−4.04715	−0.153187
$699$	1.08278	0.0409547
$700$	−2.85699	−0.107984
$701$	−47.5567	−1.79619	−0.898095	−	0.439802i	$-0.855049\pi$
$701$	−47.5567	−1.79619	−0.898095	+	0.439802i	$0.855049\pi$
$702$	3.35903	0.126778
$703$	−3.96027	−0.149364
$704$	1.20535	0.0454282
$705$	−17.4054	−0.655523
$706$	−6.51417	−0.245164
$707$	15.0224	0.564975
$708$	20.2471	0.760931
$709$	27.2576	1.02368	0.511841	−	0.859080i	$-0.328964\pi$
$709$	27.2576	1.02368	0.511841	+	0.859080i	$0.328964\pi$
$710$	0.375504	0.0140924
$711$	6.30526	0.236466
$712$	−31.8396	−1.19324
$713$	−9.31204	−0.348739
$714$	−3.30076	−0.123528
$715$	−8.32255	−0.311246
$716$	−10.5275	−0.393432
$717$	−22.4858	−0.839747
$718$	−6.86556	−0.256220
$719$	30.0570	1.12094	0.560468	−	0.828176i	$-0.310621\pi$
$719$	30.0570	1.12094	0.560468	+	0.828176i	$0.310621\pi$
$720$	6.30833	0.235097
$721$	−11.2378	−0.418517
$722$	−7.24012	−0.269449
$723$	−14.7491	−0.548525
$724$	15.2993	0.568593
$725$	−1.35448	−0.0503040
$726$	−5.49019	−0.203760
$727$	−30.8267	−1.14330	−0.571650	−	0.820497i	$-0.693697\pi$
$727$	−30.8267	−1.14330	−0.571650	+	0.820497i	$0.693697\pi$
$728$	−15.2334	−0.564589
$729$	1.00000	0.0370370
$730$	9.76352	0.361364
$731$	−40.6335	−1.50288
$732$	10.0284	0.370661
$733$	−44.0671	−1.62765	−0.813827	−	0.581107i	$-0.802620\pi$
$733$	−44.0671	−1.62765	−0.813827	+	0.581107i	$0.802620\pi$
$734$	1.77710	0.0655941
$735$	−13.9373	−0.514085
$736$	−5.09825	−0.187924
$737$	−3.83655	−0.141321
$738$	0.504477	0.0185700
$739$	−3.94561	−0.145142	−0.0725708	−	0.997363i	$-0.523120\pi$
$739$	−3.94561	−0.145142	−0.0725708	+	0.997363i	$0.523120\pi$
$740$	7.90268	0.290508
$741$	14.4464	0.530701
$742$	8.19434	0.300824
$743$	41.0117	1.50457	0.752287	−	0.658836i	$-0.228951\pi$
$743$	41.0117	1.50457	0.752287	+	0.658836i	$0.228951\pi$
$744$	−17.7857	−0.652055
$745$	−24.2329	−0.887826
$746$	13.1650	0.482005
$747$	−1.76118	−0.0644383
$748$	−4.65171	−0.170083
$749$	2.24787	0.0821354
$750$	−4.69421	−0.171408
$751$	40.2066	1.46716	0.733581	−	0.679602i	$-0.237848\pi$
$751$	40.2066	1.46716	0.733581	+	0.679602i	$0.237848\pi$
$752$	−17.2789	−0.630098
$753$	3.10594	0.113187
$754$	−3.35903	−0.122329
$755$	−6.45896	−0.235066
$756$	−2.10929	−0.0767143
$757$	−26.5726	−0.965796	−0.482898	−	0.875677i	$-0.660416\pi$
$757$	−26.5726	−0.965796	−0.482898	+	0.875677i	$0.660416\pi$
$758$	−7.85122	−0.285169
$759$	0.502071	0.0182240
$760$	−10.5773	−0.383677
$761$	−32.4080	−1.17479	−0.587395	−	0.809301i	$-0.699846\pi$
$761$	−32.4080	−1.17479	−0.587395	+	0.809301i	$0.699846\pi$
$762$	0.0132786	0.000481035 0
$763$	10.7901	0.390630
$764$	14.2103	0.514111
$765$	−13.4298	−0.485557
$766$	−5.47348	−0.197765
$767$	−76.5590	−2.76439
$768$	−1.03344	−0.0372911
$769$	−16.4485	−0.593149	−0.296575	−	0.955010i	$-0.595844\pi$
$769$	−16.4485	−0.593149	−0.296575	+	0.955010i	$0.595844\pi$
$770$	−0.784129	−0.0282580
$771$	−23.2603	−0.837700
$772$	24.5013	0.881822
$773$	−33.8571	−1.21775	−0.608877	−	0.793265i	$-0.708380\pi$
$773$	−33.8571	−1.21775	−0.608877	+	0.793265i	$0.708380\pi$
$774$	3.89597	0.140038
$775$	12.6129	0.453070
$776$	13.4412	0.482511
$777$	−2.18644	−0.0784382
$778$	−4.76164	−0.170713
$779$	2.16963	0.0777351
$780$	−28.8276	−1.03219
$781$	−0.146412	−0.00523903
$782$	2.72141	0.0973173
$783$	−1.00000	−0.0357371
$784$	−13.8361	−0.494146
$785$	−24.5393	−0.875846
$786$	5.27041	0.187989
$787$	36.1190	1.28750	0.643751	−	0.765235i	$-0.277377\pi$
$787$	36.1190	1.28750	0.643751	+	0.765235i	$0.277377\pi$
$788$	−9.78683	−0.348641
$789$	14.4964	0.516084
$790$	8.11905	0.288863
$791$	−5.98076	−0.212651
$792$	0.958939	0.0340744
$793$	−37.9199	−1.34657
$794$	2.92007	0.103629
$795$	33.3404	1.18246
$796$	12.7109	0.450525
$797$	24.0715	0.852656	0.426328	−	0.904569i	$-0.359807\pi$
$797$	24.0715	0.852656	0.426328	+	0.904569i	$0.359807\pi$
$798$	1.36110	0.0481824
$799$	36.7853	1.30137
$800$	6.90546	0.244145
$801$	16.6702	0.589014
$802$	−8.54046	−0.301574
$803$	−3.80688	−0.134342
$804$	−13.2890	−0.468668
$805$	−3.05746	−0.107761
$806$	31.2794	1.10177
$807$	−18.7400	−0.659679
$808$	−23.6562	−0.832222
$809$	19.3808	0.681393	0.340696	−	0.940173i	$-0.389337\pi$
$809$	19.3808	0.681393	0.340696	+	0.940173i	$0.389337\pi$
$810$	1.28766	0.0452439
$811$	53.5687	1.88105	0.940525	−	0.339723i	$-0.110333\pi$
$811$	53.5687	1.88105	0.940525	+	0.339723i	$0.110333\pi$
$812$	2.10929	0.0740217
$813$	−12.6693	−0.444332
$814$	0.462322	0.0162044
$815$	10.0427	0.351782
$816$	−13.3323	−0.466724
$817$	16.7556	0.586204
$818$	2.50109	0.0874487
$819$	7.97576	0.278695
$820$	−4.32948	−0.151192
$821$	24.7395	0.863416	0.431708	−	0.902013i	$-0.357911\pi$
$821$	24.7395	0.863416	0.431708	+	0.902013i	$0.357911\pi$
$822$	−0.629330	−0.0219504
$823$	−0.0903977	−0.00315106	−0.00157553	−	0.999999i	$-0.500502\pi$
$823$	−0.0903977	−0.00315106	−0.00157553	+	0.999999i	$0.500502\pi$
$824$	17.6965	0.616486
$825$	−0.680043	−0.0236761
$826$	−7.21320	−0.250979
$827$	10.1907	0.354364	0.177182	−	0.984178i	$-0.443302\pi$
$827$	10.1907	0.354364	0.177182	+	0.984178i	$0.443302\pi$
$828$	1.73907	0.0604368
$829$	−16.6333	−0.577698	−0.288849	−	0.957375i	$-0.593273\pi$
$829$	−16.6333	−0.577698	−0.288849	+	0.957375i	$0.593273\pi$
$830$	−2.26781	−0.0787169
$831$	−28.8115	−0.999459
$832$	−15.7869	−0.547314
$833$	29.4558	1.02058
$834$	4.31532	0.149427
$835$	−29.6378	−1.02566
$836$	1.91818	0.0663416
$837$	9.31204	0.321871
$838$	−4.86925	−0.168206
$839$	36.8517	1.27226	0.636131	−	0.771581i	$-0.280534\pi$
$839$	36.8517	1.27226	0.636131	+	0.771581i	$0.280534\pi$
$840$	−5.83964	−0.201487
$841$	1.00000	0.0344828
$842$	7.10033	0.244693
$843$	−25.8074	−0.888854
$844$	−35.2894	−1.21471
$845$	76.2336	2.62252
$846$	−3.52700	−0.121261
$847$	−13.0360	−0.447923
$848$	33.0983	1.13660
$849$	−5.95438	−0.204354
$850$	−3.68608	−0.126432
$851$	1.80268	0.0617949
$852$	−0.507141	−0.0173744
$853$	30.6934	1.05092	0.525461	−	0.850818i	$-0.323893\pi$
$853$	30.6934	1.05092	0.525461	+	0.850818i	$0.323893\pi$
$854$	−3.57271	−0.122256
$855$	5.53792	0.189393
$856$	−3.53978	−0.120987
$857$	−38.6243	−1.31938	−0.659690	−	0.751538i	$-0.729312\pi$
$857$	−38.6243	−1.31938	−0.659690	+	0.751538i	$0.729312\pi$
$858$	−1.68647	−0.0575752
$859$	49.7993	1.69913	0.849564	−	0.527485i	$-0.176865\pi$
$859$	49.7993	1.69913	0.849564	+	0.527485i	$0.176865\pi$
$860$	−33.4356	−1.14015
$861$	1.19784	0.0408223
$862$	−17.4909	−0.595744
$863$	50.3080	1.71250	0.856252	−	0.516559i	$-0.172787\pi$
$863$	50.3080	1.71250	0.856252	+	0.516559i	$0.172787\pi$
$864$	5.09825	0.173446
$865$	−55.0058	−1.87025
$866$	−7.30989	−0.248400
$867$	11.3832	0.386595
$868$	−19.6418	−0.666687
$869$	−3.16568	−0.107388
$870$	−1.28766	−0.0436559
$871$	50.2490	1.70262
$872$	−16.9916	−0.575407
$873$	−7.03740	−0.238180
$874$	−1.12220	−0.0379589
$875$	−11.1460	−0.376805
$876$	−13.1862	−0.445522
$877$	−26.6720	−0.900650	−0.450325	−	0.892865i	$-0.648692\pi$
$877$	−26.6720	−0.900650	−0.450325	+	0.892865i	$0.648692\pi$
$878$	−12.6162	−0.425777
$879$	8.47294	0.285785
$880$	−3.16723	−0.106767
$881$	−18.4999	−0.623277	−0.311638	−	0.950201i	$-0.600878\pi$
$881$	−18.4999	−0.623277	−0.311638	+	0.950201i	$0.600878\pi$
$882$	−2.82424	−0.0950971
$883$	43.6866	1.47017	0.735085	−	0.677975i	$-0.237142\pi$
$883$	43.6866	1.47017	0.735085	+	0.677975i	$0.237142\pi$
$884$	60.9255	2.04915
$885$	−29.3484	−0.986537
$886$	−1.44724	−0.0486210
$887$	5.09759	0.171160	0.0855802	−	0.996331i	$-0.472726\pi$
$887$	5.09759	0.171160	0.0855802	+	0.996331i	$0.472726\pi$
$888$	3.44305	0.115541
$889$	0.0315291	0.00105745
$890$	21.4657	0.719530
$891$	−0.502071	−0.0168200
$892$	−17.9353	−0.600519
$893$	−15.1688	−0.507603
$894$	−4.91053	−0.164233
$895$	15.2598	0.510080
$896$	−13.8546	−0.462850
$897$	−6.57584	−0.219561
$898$	−8.62934	−0.287965
$899$	−9.31204	−0.310574
$900$	−2.35553	−0.0785176
$901$	−70.4632	−2.34747
$902$	−0.253283	−0.00843340
$903$	9.25067	0.307843
$904$	9.41808	0.313241
$905$	−22.1765	−0.737173
$906$	−1.30884	−0.0434832
$907$	1.46127	0.0485207	0.0242604	−	0.999706i	$-0.492277\pi$
$907$	1.46127	0.0485207	0.0242604	+	0.999706i	$0.492277\pi$
$908$	−18.4618	−0.612676
$909$	12.3857	0.410806
$910$	10.2701	0.340450
$911$	−2.61553	−0.0866562	−0.0433281	−	0.999061i	$-0.513796\pi$
$911$	−2.61553	−0.0866562	−0.0433281	+	0.999061i	$0.513796\pi$
$912$	5.49771	0.182047
$913$	0.884238	0.0292640
$914$	−13.4859	−0.446074
$915$	−14.5363	−0.480557
$916$	−21.3467	−0.705313
$917$	12.5142	0.413255
$918$	−2.72141	−0.0898198
$919$	−8.94338	−0.295015	−0.147508	−	0.989061i	$-0.547125\pi$
$919$	−8.94338	−0.295015	−0.147508	+	0.989061i	$0.547125\pi$
$920$	4.81466	0.158735
$921$	16.9797	0.559501
$922$	0.0422927	0.00139284
$923$	1.91762	0.0631194
$924$	1.05901	0.0348390
$925$	−2.44168	−0.0802820
$926$	3.49943	0.114998
$927$	−9.26533	−0.304313
$928$	−5.09825	−0.167358
$929$	2.35870	0.0773866	0.0386933	−	0.999251i	$-0.487680\pi$
$929$	2.35870	0.0773866	0.0386933	+	0.999251i	$0.487680\pi$
$930$	11.9908	0.393193
$931$	−12.1464	−0.398081
$932$	−1.88304	−0.0616809
$933$	7.85324	0.257104
$934$	14.7784	0.483564
$935$	6.74273	0.220511
$936$	−12.5597	−0.410525
$937$	−2.96754	−0.0969453	−0.0484726	−	0.998825i	$-0.515435\pi$
$937$	−2.96754	−0.0969453	−0.0484726	+	0.998825i	$0.515435\pi$
$938$	4.73434	0.154582
$939$	−21.4281	−0.699278
$940$	30.2691	0.987270
$941$	9.55520	0.311490	0.155745	−	0.987797i	$-0.450222\pi$
$941$	9.55520	0.311490	0.155745	+	0.987797i	$0.450222\pi$
$942$	−4.97262	−0.162017
$943$	−0.987595	−0.0321605
$944$	−29.1353	−0.948273
$945$	3.05746	0.0994591
$946$	−1.95605	−0.0635967
$947$	−32.3691	−1.05185	−0.525927	−	0.850529i	$-0.676282\pi$
$947$	−32.3691	−1.05185	−0.525927	+	0.850529i	$0.676282\pi$
$948$	−10.9653	−0.356136
$949$	49.8604	1.61854
$950$	1.51999	0.0493150
$951$	0.861567	0.0279382
$952$	12.3418	0.399999
$953$	−3.76001	−0.121799	−0.0608993	−	0.998144i	$-0.519397\pi$
$953$	−3.76001	−0.121799	−0.0608993	+	0.998144i	$0.519397\pi$
$954$	6.75606	0.218736
$955$	−20.5981	−0.666538
$956$	39.1044	1.26473
$957$	0.502071	0.0162296
$958$	−5.53218	−0.178737
$959$	−1.49430	−0.0482533
$960$	−6.05183	−0.195322
$961$	55.7141	1.79723
$962$	−6.05524	−0.195229
$963$	1.85332	0.0597224
$964$	25.6497	0.826121
$965$	−35.5151	−1.14327
$966$	−0.619559	−0.0199340
$967$	57.6853	1.85504	0.927518	−	0.373779i	$-0.121938\pi$
$967$	57.6853	1.85504	0.927518	+	0.373779i	$0.121938\pi$
$968$	20.5282	0.659801
$969$	−11.7041	−0.375990
$970$	−9.06180	−0.290957
$971$	42.5620	1.36588	0.682940	−	0.730475i	$-0.260701\pi$
$971$	42.5620	1.36588	0.682940	+	0.730475i	$0.260701\pi$
$972$	−1.73907	−0.0557807
$973$	10.2464	0.328484
$974$	−12.7867	−0.409712
$975$	8.90683	0.285247
$976$	−14.4308	−0.461918
$977$	−25.8972	−0.828524	−0.414262	−	0.910158i	$-0.635960\pi$
$977$	−25.8972	−0.828524	−0.414262	+	0.910158i	$0.635960\pi$
$978$	2.03505	0.0650737
$979$	−8.36964	−0.267495
$980$	24.2380	0.774253
$981$	8.89625	0.284035
$982$	10.3176	0.329249
$983$	36.3230	1.15852	0.579262	−	0.815142i	$-0.303341\pi$
$983$	36.3230	1.15852	0.579262	+	0.815142i	$0.303341\pi$
$984$	−1.88627	−0.0601322
$985$	14.1862	0.452009
$986$	2.72141	0.0866673
$987$	−8.37458	−0.266566
$988$	−25.1232	−0.799277
$989$	−7.62698	−0.242524
$990$	−0.646498	−0.0205471
$991$	−45.8075	−1.45512	−0.727562	−	0.686042i	$-0.759347\pi$
$991$	−45.8075	−1.45512	−0.727562	+	0.686042i	$0.759347\pi$
$992$	47.4751	1.50734
$993$	−13.6652	−0.433651
$994$	0.180674	0.00573062
$995$	−18.4246	−0.584099
$996$	3.06282	0.0970491
$997$	49.2764	1.56060	0.780300	−	0.625405i	$-0.215066\pi$
$997$	49.2764	1.56060	0.780300	+	0.625405i	$0.215066\pi$
$998$	19.7210	0.624256
$999$	−1.80268	−0.0570341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.10	✓	16
3.2	odd	2		6003.2.a.r.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.10	✓	16	1.1	even	1	trivial
6003.2.a.r.1.7		16	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)

\(f(q)\)	\(=\)	\(q+0.510814 q^{2} +1.00000 q^{3} -1.73907 q^{4} +2.52081 q^{5} +0.510814 q^{6} +1.21289 q^{7} -1.90997 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.510814 q^{2} +1.00000 q^{3} -1.73907 q^{4} +2.52081 q^{5} +0.510814 q^{6} +1.21289 q^{7} -1.90997 q^{8} +1.00000 q^{9} +1.28766 q^{10} -0.502071 q^{11} -1.73907 q^{12} +6.57584 q^{13} +0.619559 q^{14} +2.52081 q^{15} +2.50250 q^{16} -5.32759 q^{17} +0.510814 q^{18} +2.19688 q^{19} -4.38386 q^{20} +1.21289 q^{21} -0.256465 q^{22} -1.00000 q^{23} -1.90997 q^{24} +1.35448 q^{25} +3.35903 q^{26} +1.00000 q^{27} -2.10929 q^{28} -1.00000 q^{29} +1.28766 q^{30} +9.31204 q^{31} +5.09825 q^{32} -0.502071 q^{33} -2.72141 q^{34} +3.05746 q^{35} -1.73907 q^{36} -1.80268 q^{37} +1.12220 q^{38} +6.57584 q^{39} -4.81466 q^{40} +0.987595 q^{41} +0.619559 q^{42} +7.62698 q^{43} +0.873136 q^{44} +2.52081 q^{45} -0.510814 q^{46} -6.90467 q^{47} +2.50250 q^{48} -5.52891 q^{49} +0.691885 q^{50} -5.32759 q^{51} -11.4358 q^{52} +13.2261 q^{53} +0.510814 q^{54} -1.26562 q^{55} -2.31658 q^{56} +2.19688 q^{57} -0.510814 q^{58} -11.6425 q^{59} -4.38386 q^{60} -5.76654 q^{61} +4.75672 q^{62} +1.21289 q^{63} -2.40075 q^{64} +16.5764 q^{65} -0.256465 q^{66} +7.64146 q^{67} +9.26505 q^{68} -1.00000 q^{69} +1.56179 q^{70} +0.291616 q^{71} -1.90997 q^{72} +7.58236 q^{73} -0.920831 q^{74} +1.35448 q^{75} -3.82053 q^{76} -0.608955 q^{77} +3.35903 q^{78} +6.30526 q^{79} +6.30833 q^{80} +1.00000 q^{81} +0.504477 q^{82} -1.76118 q^{83} -2.10929 q^{84} -13.4298 q^{85} +3.89597 q^{86} -1.00000 q^{87} +0.958939 q^{88} +16.6702 q^{89} +1.28766 q^{90} +7.97576 q^{91} +1.73907 q^{92} +9.31204 q^{93} -3.52700 q^{94} +5.53792 q^{95} +5.09825 q^{96} -7.03740 q^{97} -2.82424 q^{98} -0.502071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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