LMFDB - Embedded newform 2005.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.412837 q^{2} +2.39393 q^{3} -1.82957 q^{4} +1.00000 q^{5} +0.988304 q^{6} +0.00790896 q^{7} -1.58099 q^{8} +2.73092 q^{9} +O(q^{10})$	\(q+0.412837 q^{2} +2.39393 q^{3} -1.82957 q^{4} +1.00000 q^{5} +0.988304 q^{6} +0.00790896 q^{7} -1.58099 q^{8} +2.73092 q^{9} +0.412837 q^{10} +5.71395 q^{11} -4.37986 q^{12} -4.38008 q^{13} +0.00326511 q^{14} +2.39393 q^{15} +3.00644 q^{16} +6.42589 q^{17} +1.12742 q^{18} +6.30977 q^{19} -1.82957 q^{20} +0.0189335 q^{21} +2.35893 q^{22} -6.16567 q^{23} -3.78478 q^{24} +1.00000 q^{25} -1.80826 q^{26} -0.644162 q^{27} -0.0144700 q^{28} +1.39637 q^{29} +0.988304 q^{30} -6.59555 q^{31} +4.40314 q^{32} +13.6788 q^{33} +2.65285 q^{34} +0.00790896 q^{35} -4.99640 q^{36} +5.00008 q^{37} +2.60490 q^{38} -10.4856 q^{39} -1.58099 q^{40} -8.98649 q^{41} +0.00781646 q^{42} +4.00468 q^{43} -10.4540 q^{44} +2.73092 q^{45} -2.54542 q^{46} +2.83151 q^{47} +7.19722 q^{48} -6.99994 q^{49} +0.412837 q^{50} +15.3832 q^{51} +8.01365 q^{52} +13.1902 q^{53} -0.265934 q^{54} +5.71395 q^{55} -0.0125040 q^{56} +15.1052 q^{57} +0.576472 q^{58} +8.06728 q^{59} -4.37986 q^{60} +8.61866 q^{61} -2.72289 q^{62} +0.0215987 q^{63} -4.19510 q^{64} -4.38008 q^{65} +5.64712 q^{66} +8.89618 q^{67} -11.7566 q^{68} -14.7602 q^{69} +0.00326511 q^{70} +4.60465 q^{71} -4.31755 q^{72} -3.97470 q^{73} +2.06422 q^{74} +2.39393 q^{75} -11.5441 q^{76} +0.0451914 q^{77} -4.32886 q^{78} +15.4840 q^{79} +3.00644 q^{80} -9.73484 q^{81} -3.70996 q^{82} -5.02715 q^{83} -0.0346401 q^{84} +6.42589 q^{85} +1.65328 q^{86} +3.34281 q^{87} -9.03368 q^{88} +0.897896 q^{89} +1.12742 q^{90} -0.0346419 q^{91} +11.2805 q^{92} -15.7893 q^{93} +1.16895 q^{94} +6.30977 q^{95} +10.5408 q^{96} +16.6065 q^{97} -2.88983 q^{98} +15.6043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * 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 $

$2$	0.412837	0.291920	0.145960	−	0.989291i	$-0.453373\pi$
$2$	0.412837	0.291920	0.145960	+	0.989291i	$0.453373\pi$
$3$	2.39393	1.38214	0.691069	−	0.722789i	$-0.257140\pi$
$3$	2.39393	1.38214	0.691069	+	0.722789i	$0.257140\pi$
$4$	−1.82957	−0.914783
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.988304	0.403474
$7$	0.00790896	0.00298931	0.00149465	−	0.999999i	$-0.499524\pi$
$7$	0.00790896	0.00298931	0.00149465	+	0.999999i	$0.499524\pi$
$8$	−1.58099	−0.558963
$9$	2.73092	0.910306
$10$	0.412837	0.130551
$11$	5.71395	1.72282	0.861411	−	0.507909i	$-0.169581\pi$
$11$	5.71395	1.72282	0.861411	+	0.507909i	$0.169581\pi$
$12$	−4.37986	−1.26436
$13$	−4.38008	−1.21482	−0.607408	−	0.794390i	$-0.707791\pi$
$13$	−4.38008	−1.21482	−0.607408	+	0.794390i	$0.707791\pi$
$14$	0.00326511	0.000872638 0
$15$	2.39393	0.618111
$16$	3.00644	0.751610
$17$	6.42589	1.55851	0.779254	−	0.626708i	$-0.215598\pi$
$17$	6.42589	1.55851	0.779254	+	0.626708i	$0.215598\pi$
$18$	1.12742	0.265736
$19$	6.30977	1.44756	0.723780	−	0.690031i	$-0.242403\pi$
$19$	6.30977	1.44756	0.723780	+	0.690031i	$0.242403\pi$
$20$	−1.82957	−0.409103
$21$	0.0189335	0.00413163
$22$	2.35893	0.502926
$23$	−6.16567	−1.28563	−0.642816	−	0.766021i	$-0.722234\pi$
$23$	−6.16567	−1.28563	−0.642816	+	0.766021i	$0.722234\pi$
$24$	−3.78478	−0.772564
$25$	1.00000	0.200000
$26$	−1.80826	−0.354629
$27$	−0.644162	−0.123969
$28$	−0.0144700	−0.00273457
$29$	1.39637	0.259299	0.129650	−	0.991560i	$-0.458615\pi$
$29$	1.39637	0.259299	0.129650	+	0.991560i	$0.458615\pi$
$30$	0.988304	0.180439
$31$	−6.59555	−1.18460	−0.592298	−	0.805719i	$-0.701779\pi$
$31$	−6.59555	−1.18460	−0.592298	+	0.805719i	$0.701779\pi$
$32$	4.40314	0.778373
$33$	13.6788	2.38118
$34$	2.65285	0.454959
$35$	0.00790896	0.00133686
$36$	−4.99640	−0.832733
$37$	5.00008	0.822008	0.411004	−	0.911634i	$-0.365178\pi$
$37$	5.00008	0.822008	0.411004	+	0.911634i	$0.365178\pi$
$38$	2.60490	0.422571
$39$	−10.4856	−1.67905
$40$	−1.58099	−0.249976
$41$	−8.98649	−1.40345	−0.701727	−	0.712446i	$-0.747587\pi$
$41$	−8.98649	−1.40345	−0.701727	+	0.712446i	$0.747587\pi$
$42$	0.00781646	0.00120611
$43$	4.00468	0.610708	0.305354	−	0.952239i	$-0.401225\pi$
$43$	4.00468	0.610708	0.305354	+	0.952239i	$0.401225\pi$
$44$	−10.4540	−1.57601
$45$	2.73092	0.407101
$46$	−2.54542	−0.375301
$47$	2.83151	0.413018	0.206509	−	0.978445i	$-0.433790\pi$
$47$	2.83151	0.413018	0.206509	+	0.978445i	$0.433790\pi$
$48$	7.19722	1.03883
$49$	−6.99994	−0.999991
$50$	0.412837	0.0583840
$51$	15.3832	2.15407
$52$	8.01365	1.11129
$53$	13.1902	1.81182	0.905908	−	0.423475i	$-0.139190\pi$
$53$	13.1902	1.81182	0.905908	+	0.423475i	$0.139190\pi$
$54$	−0.265934	−0.0361890
$55$	5.71395	0.770469
$56$	−0.0125040	−0.00167091
$57$	15.1052	2.00073
$58$	0.576472	0.0756945
$59$	8.06728	1.05027	0.525136	−	0.851019i	$-0.324015\pi$
$59$	8.06728	1.05027	0.525136	+	0.851019i	$0.324015\pi$
$60$	−4.37986	−0.565437
$61$	8.61866	1.10351	0.551753	−	0.834007i	$-0.313959\pi$
$61$	8.61866	1.10351	0.551753	+	0.834007i	$0.313959\pi$
$62$	−2.72289	−0.345807
$63$	0.0215987	0.00272118
$64$	−4.19510	−0.524388
$65$	−4.38008	−0.543283
$66$	5.64712	0.695113
$67$	8.89618	1.08684	0.543421	−	0.839460i	$-0.317129\pi$
$67$	8.89618	1.08684	0.543421	+	0.839460i	$0.317129\pi$
$68$	−11.7566	−1.42570
$69$	−14.7602	−1.77692
$70$	0.00326511	0.000390255 0
$71$	4.60465	0.546471	0.273236	−	0.961947i	$-0.411906\pi$
$71$	4.60465	0.546471	0.273236	+	0.961947i	$0.411906\pi$
$72$	−4.31755	−0.508828
$73$	−3.97470	−0.465204	−0.232602	−	0.972572i	$-0.574724\pi$
$73$	−3.97470	−0.465204	−0.232602	+	0.972572i	$0.574724\pi$
$74$	2.06422	0.239960
$75$	2.39393	0.276428
$76$	−11.5441	−1.32420
$77$	0.0451914	0.00515004
$78$	−4.32886	−0.490147
$79$	15.4840	1.74208	0.871042	−	0.491209i	$-0.163445\pi$
$79$	15.4840	1.74208	0.871042	+	0.491209i	$0.163445\pi$
$80$	3.00644	0.336130
$81$	−9.73484	−1.08165
$82$	−3.70996	−0.409696
$83$	−5.02715	−0.551801	−0.275901	−	0.961186i	$-0.588976\pi$
$83$	−5.02715	−0.551801	−0.275901	+	0.961186i	$0.588976\pi$
$84$	−0.0346401	−0.00377955
$85$	6.42589	0.696986
$86$	1.65328	0.178278
$87$	3.34281	0.358387
$88$	−9.03368	−0.962993
$89$	0.897896	0.0951767	0.0475884	−	0.998867i	$-0.484846\pi$
$89$	0.897896	0.0951767	0.0475884	+	0.998867i	$0.484846\pi$
$90$	1.12742	0.118841
$91$	−0.0346419	−0.00363146
$92$	11.2805	1.17607
$93$	−15.7893	−1.63727
$94$	1.16895	0.120568
$95$	6.30977	0.647368
$96$	10.5408	1.07582
$97$	16.6065	1.68614	0.843069	−	0.537806i	$-0.180747\pi$
$97$	16.6065	1.68614	0.843069	+	0.537806i	$0.180747\pi$
$98$	−2.88983	−0.291917
$99$	15.6043	1.56830
$100$	−1.82957	−0.182957
$101$	−16.5596	−1.64774	−0.823870	−	0.566778i	$-0.808190\pi$
$101$	−16.5596	−1.64774	−0.823870	+	0.566778i	$0.808190\pi$
$102$	6.35074	0.628817
$103$	−6.07525	−0.598612	−0.299306	−	0.954157i	$-0.596755\pi$
$103$	−6.07525	−0.598612	−0.299306	+	0.954157i	$0.596755\pi$
$104$	6.92485	0.679038
$105$	0.0189335	0.00184772
$106$	5.44541	0.528905
$107$	−3.35965	−0.324790	−0.162395	−	0.986726i	$-0.551922\pi$
$107$	−3.35965	−0.324790	−0.162395	+	0.986726i	$0.551922\pi$
$108$	1.17854	0.113405
$109$	−4.61280	−0.441826	−0.220913	−	0.975294i	$-0.570904\pi$
$109$	−4.61280	−0.441826	−0.220913	+	0.975294i	$0.570904\pi$
$110$	2.35893	0.224915
$111$	11.9699	1.13613
$112$	0.0237778	0.00224679
$113$	−8.32571	−0.783217	−0.391608	−	0.920132i	$-0.628081\pi$
$113$	−8.32571	−0.783217	−0.391608	+	0.920132i	$0.628081\pi$
$114$	6.23597	0.584052
$115$	−6.16567	−0.574952
$116$	−2.55475	−0.237202
$117$	−11.9617	−1.10586
$118$	3.33047	0.306595
$119$	0.0508221	0.00465886
$120$	−3.78478	−0.345501
$121$	21.6492	1.96811
$122$	3.55810	0.322135
$123$	−21.5131	−1.93977
$124$	12.0670	1.08365
$125$	1.00000	0.0894427
$126$	0.00891675	0.000794368 0
$127$	5.00207	0.443862	0.221931	−	0.975062i	$-0.428764\pi$
$127$	5.00207	0.443862	0.221931	+	0.975062i	$0.428764\pi$
$128$	−10.5382	−0.931452
$129$	9.58693	0.844083
$130$	−1.80826	−0.158595
$131$	−13.0145	−1.13708	−0.568539	−	0.822656i	$-0.692491\pi$
$131$	−13.0145	−1.13708	−0.568539	+	0.822656i	$0.692491\pi$
$132$	−25.0263	−2.17826
$133$	0.0499037	0.00432720
$134$	3.67267	0.317271
$135$	−0.644162	−0.0554406
$136$	−10.1592	−0.871148
$137$	3.31094	0.282873	0.141436	−	0.989947i	$-0.454828\pi$
$137$	3.31094	0.282873	0.141436	+	0.989947i	$0.454828\pi$
$138$	−6.09356	−0.518718
$139$	−7.20382	−0.611020	−0.305510	−	0.952189i	$-0.598827\pi$
$139$	−7.20382	−0.611020	−0.305510	+	0.952189i	$0.598827\pi$
$140$	−0.0144700	−0.00122293
$141$	6.77845	0.570849
$142$	1.90097	0.159526
$143$	−25.0276	−2.09291
$144$	8.21035	0.684196
$145$	1.39637	0.115962
$146$	−1.64090	−0.135802
$147$	−16.7574	−1.38213
$148$	−9.14798	−0.751959
$149$	0.835737	0.0684663	0.0342331	−	0.999414i	$-0.489101\pi$
$149$	0.835737	0.0684663	0.0342331	+	0.999414i	$0.489101\pi$
$150$	0.988304	0.0806947
$151$	−12.7706	−1.03926	−0.519629	−	0.854392i	$-0.673930\pi$
$151$	−12.7706	−1.03926	−0.519629	+	0.854392i	$0.673930\pi$
$152$	−9.97565	−0.809132
$153$	17.5486	1.41872
$154$	0.0186567	0.00150340
$155$	−6.59555	−0.529767
$156$	19.1842	1.53596
$157$	−5.12696	−0.409176	−0.204588	−	0.978848i	$-0.565585\pi$
$157$	−5.12696	−0.409176	−0.204588	+	0.978848i	$0.565585\pi$
$158$	6.39236	0.508549
$159$	31.5765	2.50418
$160$	4.40314	0.348099
$161$	−0.0487640	−0.00384314
$162$	−4.01890	−0.315755
$163$	0.398543	0.0312163	0.0156081	−	0.999878i	$-0.495032\pi$
$163$	0.398543	0.0312163	0.0156081	+	0.999878i	$0.495032\pi$
$164$	16.4414	1.28386
$165$	13.6788	1.06489
$166$	−2.07539	−0.161082
$167$	−5.11266	−0.395629	−0.197815	−	0.980239i	$-0.563384\pi$
$167$	−5.11266	−0.395629	−0.197815	+	0.980239i	$0.563384\pi$
$168$	−0.0299336	−0.00230943
$169$	6.18514	0.475780
$170$	2.65285	0.203464
$171$	17.2315	1.31772
$172$	−7.32682	−0.558665
$173$	−2.56184	−0.194773	−0.0973866	−	0.995247i	$-0.531048\pi$
$173$	−2.56184	−0.194773	−0.0973866	+	0.995247i	$0.531048\pi$
$174$	1.38004	0.104620
$175$	0.00790896	0.000597861 0
$176$	17.1787	1.29489
$177$	19.3125	1.45162
$178$	0.370685	0.0277840
$179$	−13.7711	−1.02930	−0.514648	−	0.857401i	$-0.672078\pi$
$179$	−13.7711	−1.02930	−0.514648	+	0.857401i	$0.672078\pi$
$180$	−4.99640	−0.372409
$181$	−18.0585	−1.34228	−0.671139	−	0.741332i	$-0.734195\pi$
$181$	−18.0585	−1.34228	−0.671139	+	0.741332i	$0.734195\pi$
$182$	−0.0143015	−0.00106010
$183$	20.6325	1.52520
$184$	9.74784	0.718620
$185$	5.00008	0.367613
$186$	−6.51841	−0.477953
$187$	36.7172	2.68503
$188$	−5.18044	−0.377822
$189$	−0.00509465	−0.000370581 0
$190$	2.60490	0.188980
$191$	2.03723	0.147408	0.0737042	−	0.997280i	$-0.476518\pi$
$191$	2.03723	0.147408	0.0737042	+	0.997280i	$0.476518\pi$
$192$	−10.0428	−0.724777
$193$	12.2412	0.881142	0.440571	−	0.897718i	$-0.354776\pi$
$193$	12.2412	0.881142	0.440571	+	0.897718i	$0.354776\pi$
$194$	6.85579	0.492217
$195$	−10.4856	−0.750892
$196$	12.8068	0.914775
$197$	−13.4152	−0.955797	−0.477898	−	0.878415i	$-0.658601\pi$
$197$	−13.4152	−0.955797	−0.477898	+	0.878415i	$0.658601\pi$
$198$	6.44205	0.457816
$199$	−23.3563	−1.65568	−0.827841	−	0.560964i	$-0.810431\pi$
$199$	−23.3563	−1.65568	−0.827841	+	0.560964i	$0.810431\pi$
$200$	−1.58099	−0.111793
$201$	21.2969	1.50217
$202$	−6.83641	−0.481008
$203$	0.0110438	0.000775124 0
$204$	−28.1445	−1.97051
$205$	−8.98649	−0.627644
$206$	−2.50809	−0.174747
$207$	−16.8379	−1.17032
$208$	−13.1685	−0.913069
$209$	36.0537	2.49389
$210$	0.00781646	0.000539387 0
$211$	−15.1017	−1.03964	−0.519822	−	0.854274i	$-0.674002\pi$
$211$	−15.1017	−1.03964	−0.519822	+	0.854274i	$0.674002\pi$
$212$	−24.1324	−1.65742
$213$	11.0232	0.755299
$214$	−1.38699	−0.0948126
$215$	4.00468	0.273117
$216$	1.01841	0.0692941
$217$	−0.0521639	−0.00354112
$218$	−1.90433	−0.128978
$219$	−9.51517	−0.642976
$220$	−10.4540	−0.704812
$221$	−28.1460	−1.89330
$222$	4.94160	0.331659
$223$	−11.5267	−0.771884	−0.385942	−	0.922523i	$-0.626123\pi$
$223$	−11.5267	−0.771884	−0.385942	+	0.922523i	$0.626123\pi$
$224$	0.0348243	0.00232680
$225$	2.73092	0.182061
$226$	−3.43716	−0.228637
$227$	−16.6914	−1.10785	−0.553924	−	0.832567i	$-0.686870\pi$
$227$	−16.6914	−1.10785	−0.553924	+	0.832567i	$0.686870\pi$
$228$	−27.6359	−1.83023
$229$	−3.38629	−0.223772	−0.111886	−	0.993721i	$-0.535689\pi$
$229$	−3.38629	−0.223772	−0.111886	+	0.993721i	$0.535689\pi$
$230$	−2.54542	−0.167840
$231$	0.108185	0.00711807
$232$	−2.20764	−0.144939
$233$	9.94335	0.651410	0.325705	−	0.945471i	$-0.394398\pi$
$233$	9.94335	0.651410	0.325705	+	0.945471i	$0.394398\pi$
$234$	−4.93821	−0.322821
$235$	2.83151	0.184707
$236$	−14.7596	−0.960770
$237$	37.0676	2.40780
$238$	0.0209813	0.00136001
$239$	−29.6022	−1.91480	−0.957402	−	0.288757i	$-0.906758\pi$
$239$	−29.6022	−1.91480	−0.957402	+	0.288757i	$0.906758\pi$
$240$	7.19722	0.464579
$241$	−6.04022	−0.389084	−0.194542	−	0.980894i	$-0.562322\pi$
$241$	−6.04022	−0.389084	−0.194542	+	0.980894i	$0.562322\pi$
$242$	8.93761	0.574531
$243$	−21.3721	−1.37102
$244$	−15.7684	−1.00947
$245$	−6.99994	−0.447210
$246$	−8.88139	−0.566257
$247$	−27.6373	−1.75852
$248$	10.4275	0.662145
$249$	−12.0347	−0.762666
$250$	0.412837	0.0261101
$251$	−22.0728	−1.39322	−0.696610	−	0.717450i	$-0.745309\pi$
$251$	−22.0728	−1.39322	−0.696610	+	0.717450i	$0.745309\pi$
$252$	−0.0395163	−0.00248929
$253$	−35.2303	−2.21491
$254$	2.06504	0.129572
$255$	15.3832	0.963331
$256$	4.03966	0.252478
$257$	24.7315	1.54271	0.771355	−	0.636406i	$-0.219580\pi$
$257$	24.7315	1.54271	0.771355	+	0.636406i	$0.219580\pi$
$258$	3.95784	0.246404
$259$	0.0395454	0.00245723
$260$	8.01365	0.496986
$261$	3.81337	0.236042
$262$	−5.37285	−0.331936
$263$	−8.43183	−0.519929	−0.259964	−	0.965618i	$-0.583711\pi$
$263$	−8.43183	−0.519929	−0.259964	+	0.965618i	$0.583711\pi$
$264$	−21.6260	−1.33099
$265$	13.1902	0.810268
$266$	0.0206021	0.00126319
$267$	2.14950	0.131547
$268$	−16.2762	−0.994224
$269$	−22.2579	−1.35709	−0.678543	−	0.734561i	$-0.737388\pi$
$269$	−22.2579	−1.35709	−0.678543	+	0.734561i	$0.737388\pi$
$270$	−0.265934	−0.0161842
$271$	21.7963	1.32403	0.662015	−	0.749491i	$-0.269702\pi$
$271$	21.7963	1.32403	0.662015	+	0.749491i	$0.269702\pi$
$272$	19.3191	1.17139
$273$	−0.0829305	−0.00501918
$274$	1.36688	0.0825762
$275$	5.71395	0.344564
$276$	27.0048	1.62550
$277$	7.17510	0.431110	0.215555	−	0.976492i	$-0.430844\pi$
$277$	7.17510	0.431110	0.215555	+	0.976492i	$0.430844\pi$
$278$	−2.97400	−0.178369
$279$	−18.0119	−1.07834
$280$	−0.0125040	−0.000747254 0
$281$	29.5364	1.76199	0.880997	−	0.473121i	$-0.156873\pi$
$281$	29.5364	1.76199	0.880997	+	0.473121i	$0.156873\pi$
$282$	2.79840	0.166642
$283$	29.7552	1.76877	0.884383	−	0.466762i	$-0.154580\pi$
$283$	29.7552	1.76877	0.884383	+	0.466762i	$0.154580\pi$
$284$	−8.42451	−0.499903
$285$	15.1052	0.894752
$286$	−10.3323	−0.610963
$287$	−0.0710738	−0.00419535
$288$	12.0246	0.708558
$289$	24.2921	1.42895
$290$	0.576472	0.0338516
$291$	39.7549	2.33047
$292$	7.27198	0.425560
$293$	−16.4807	−0.962816	−0.481408	−	0.876497i	$-0.659874\pi$
$293$	−16.4807	−0.962816	−0.481408	+	0.876497i	$0.659874\pi$
$294$	−6.91807	−0.403470
$295$	8.06728	0.469695
$296$	−7.90506	−0.459472
$297$	−3.68071	−0.213576
$298$	0.345023	0.0199867
$299$	27.0062	1.56181
$300$	−4.37986	−0.252871
$301$	0.0316728	0.00182559
$302$	−5.27218	−0.303380
$303$	−39.6426	−2.27741
$304$	18.9699	1.08800
$305$	8.61866	0.493503
$306$	7.24471	0.414152
$307$	−27.3890	−1.56317	−0.781586	−	0.623798i	$-0.785589\pi$
$307$	−27.3890	−1.56317	−0.781586	+	0.623798i	$0.785589\pi$
$308$	−0.0826807	−0.00471117
$309$	−14.5437	−0.827364
$310$	−2.72289	−0.154650
$311$	−3.02010	−0.171254	−0.0856270	−	0.996327i	$-0.527289\pi$
$311$	−3.02010	−0.171254	−0.0856270	+	0.996327i	$0.527289\pi$
$312$	16.5776	0.938524
$313$	−11.3132	−0.639460	−0.319730	−	0.947509i	$-0.603592\pi$
$313$	−11.3132	−0.639460	−0.319730	+	0.947509i	$0.603592\pi$
$314$	−2.11660	−0.119447
$315$	0.0215987	0.00121695
$316$	−28.3290	−1.59363
$317$	17.2736	0.970183	0.485091	−	0.874463i	$-0.338786\pi$
$317$	17.2736	0.970183	0.485091	+	0.874463i	$0.338786\pi$
$318$	13.0359	0.731020
$319$	7.97878	0.446726
$320$	−4.19510	−0.234513
$321$	−8.04279	−0.448905
$322$	−0.0201316	−0.00112189
$323$	40.5459	2.25603
$324$	17.8105	0.989474
$325$	−4.38008	−0.242963
$326$	0.164533	0.00911264
$327$	−11.0427	−0.610664
$328$	14.2075	0.784479
$329$	0.0223943	0.00123464
$330$	5.64712	0.310864
$331$	20.2685	1.11405	0.557027	−	0.830494i	$-0.311942\pi$
$331$	20.2685	1.11405	0.557027	+	0.830494i	$0.311942\pi$
$332$	9.19750	0.504778
$333$	13.6548	0.748279
$334$	−2.11069	−0.115492
$335$	8.89618	0.486050
$336$	0.0569225	0.00310538
$337$	−6.94767	−0.378464	−0.189232	−	0.981932i	$-0.560600\pi$
$337$	−6.94767	−0.378464	−0.189232	+	0.981932i	$0.560600\pi$
$338$	2.55346	0.138890
$339$	−19.9312	−1.08251
$340$	−11.7566	−0.637591
$341$	−37.6866	−2.04085
$342$	7.11378	0.384669
$343$	−0.110725	−0.00597859
$344$	−6.33134	−0.341363
$345$	−14.7602	−0.794663
$346$	−1.05762	−0.0568581
$347$	7.56936	0.406345	0.203172	−	0.979143i	$-0.434875\pi$
$347$	7.56936	0.406345	0.203172	+	0.979143i	$0.434875\pi$
$348$	−6.11590	−0.327846
$349$	−7.50038	−0.401486	−0.200743	−	0.979644i	$-0.564336\pi$
$349$	−7.50038	−0.401486	−0.200743	+	0.979644i	$0.564336\pi$
$350$	0.00326511	0.000174528 0
$351$	2.82148	0.150600
$352$	25.1593	1.34100
$353$	−13.0904	−0.696731	−0.348366	−	0.937359i	$-0.613263\pi$
$353$	−13.0904	−0.696731	−0.348366	+	0.937359i	$0.613263\pi$
$354$	7.97293	0.423757
$355$	4.60465	0.244389
$356$	−1.64276	−0.0870661
$357$	0.121665	0.00643918
$358$	−5.68520	−0.300472
$359$	23.2609	1.22766	0.613831	−	0.789438i	$-0.289628\pi$
$359$	23.2609	1.22766	0.613831	+	0.789438i	$0.289628\pi$
$360$	−4.31755	−0.227555
$361$	20.8131	1.09543
$362$	−7.45522	−0.391838
$363$	51.8268	2.72020
$364$	0.0633797	0.00332200
$365$	−3.97470	−0.208045
$366$	8.51786	0.445236
$367$	−26.3270	−1.37426	−0.687129	−	0.726535i	$-0.741129\pi$
$367$	−26.3270	−1.37426	−0.687129	+	0.726535i	$0.741129\pi$
$368$	−18.5367	−0.966294
$369$	−24.5414	−1.27757
$370$	2.06422	0.107314
$371$	0.104321	0.00541607
$372$	28.8876	1.49775
$373$	11.3917	0.589841	0.294921	−	0.955522i	$-0.404707\pi$
$373$	11.3917	0.589841	0.294921	+	0.955522i	$0.404707\pi$
$374$	15.1582	0.783814
$375$	2.39393	0.123622
$376$	−4.47658	−0.230862
$377$	−6.11621	−0.315001
$378$	−0.00210326	−0.000108180 0
$379$	−20.0644	−1.03064	−0.515320	−	0.856998i	$-0.672327\pi$
$379$	−20.0644	−1.03064	−0.515320	+	0.856998i	$0.672327\pi$
$380$	−11.5441	−0.592201
$381$	11.9746	0.613479
$382$	0.841042	0.0430315
$383$	−16.6609	−0.851331	−0.425666	−	0.904881i	$-0.639960\pi$
$383$	−16.6609	−0.851331	−0.425666	+	0.904881i	$0.639960\pi$
$384$	−25.2277	−1.28740
$385$	0.0451914	0.00230317
$386$	5.05362	0.257223
$387$	10.9365	0.555931
$388$	−30.3827	−1.54245
$389$	27.7258	1.40575	0.702876	−	0.711313i	$-0.251899\pi$
$389$	27.7258	1.40575	0.702876	+	0.711313i	$0.251899\pi$
$390$	−4.32886	−0.219200
$391$	−39.6199	−2.00367
$392$	11.0668	0.558958
$393$	−31.1558	−1.57160
$394$	−5.53831	−0.279016
$395$	15.4840	0.779083
$396$	−28.5492	−1.43465
$397$	−3.51733	−0.176530	−0.0882649	−	0.996097i	$-0.528132\pi$
$397$	−3.51733	−0.176530	−0.0882649	+	0.996097i	$0.528132\pi$
$398$	−9.64233	−0.483326
$399$	0.119466	0.00598079
$400$	3.00644	0.150322
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	8.79214	0.438512
$403$	28.8891	1.43907
$404$	30.2969	1.50733
$405$	−9.73484	−0.483728
$406$	0.00455930	0.000226274 0
$407$	28.5702	1.41617
$408$	−24.3206	−1.20405
$409$	−20.5602	−1.01664	−0.508319	−	0.861169i	$-0.669733\pi$
$409$	−20.5602	−1.01664	−0.508319	+	0.861169i	$0.669733\pi$
$410$	−3.70996	−0.183222
$411$	7.92617	0.390969
$412$	11.1151	0.547600
$413$	0.0638038	0.00313958
$414$	−6.95133	−0.341639
$415$	−5.02715	−0.246773
$416$	−19.2861	−0.945581
$417$	−17.2455	−0.844514
$418$	14.8843	0.728015
$419$	11.2636	0.550265	0.275132	−	0.961406i	$-0.411278\pi$
$419$	11.2636	0.550265	0.275132	+	0.961406i	$0.411278\pi$
$420$	−0.0346401	−0.00169027
$421$	17.5804	0.856818	0.428409	−	0.903585i	$-0.359074\pi$
$421$	17.5804	0.856818	0.428409	+	0.903585i	$0.359074\pi$
$422$	−6.23455	−0.303493
$423$	7.73263	0.375973
$424$	−20.8535	−1.01274
$425$	6.42589	0.311702
$426$	4.55080	0.220487
$427$	0.0681646	0.00329872
$428$	6.14671	0.297112
$429$	−59.9144	−2.89269
$430$	1.65328	0.0797282
$431$	7.01273	0.337791	0.168896	−	0.985634i	$-0.445980\pi$
$431$	7.01273	0.337791	0.168896	+	0.985634i	$0.445980\pi$
$432$	−1.93664	−0.0931764
$433$	−3.55721	−0.170949	−0.0854743	−	0.996340i	$-0.527241\pi$
$433$	−3.55721	−0.170949	−0.0854743	+	0.996340i	$0.527241\pi$
$434$	−0.0215352	−0.00103372
$435$	3.34281	0.160276
$436$	8.43942	0.404175
$437$	−38.9039	−1.86103
$438$	−3.92821	−0.187697
$439$	25.5812	1.22092	0.610462	−	0.792046i	$-0.290984\pi$
$439$	25.5812	1.22092	0.610462	+	0.792046i	$0.290984\pi$
$440$	−9.03368	−0.430664
$441$	−19.1163	−0.910298
$442$	−11.6197	−0.552692
$443$	29.6420	1.40834	0.704168	−	0.710033i	$-0.251320\pi$
$443$	29.6420	1.40834	0.704168	+	0.710033i	$0.251320\pi$
$444$	−21.8996	−1.03931
$445$	0.897896	0.0425643
$446$	−4.75864	−0.225328
$447$	2.00070	0.0946299
$448$	−0.0331789	−0.00156756
$449$	27.4345	1.29472	0.647358	−	0.762186i	$-0.275874\pi$
$449$	27.4345	1.29472	0.647358	+	0.762186i	$0.275874\pi$
$450$	1.12742	0.0531473
$451$	−51.3484	−2.41790
$452$	15.2324	0.716473
$453$	−30.5720	−1.43640
$454$	−6.89084	−0.323403
$455$	−0.0346419	−0.00162404
$456$	−23.8811	−1.11833
$457$	−7.56071	−0.353675	−0.176838	−	0.984240i	$-0.556587\pi$
$457$	−7.56071	−0.353675	−0.176838	+	0.984240i	$0.556587\pi$
$458$	−1.39799	−0.0653236
$459$	−4.13932	−0.193207
$460$	11.2805	0.525956
$461$	15.8141	0.736536	0.368268	−	0.929720i	$-0.379951\pi$
$461$	15.8141	0.736536	0.368268	+	0.929720i	$0.379951\pi$
$462$	0.0446629	0.00207790
$463$	21.6461	1.00598	0.502990	−	0.864292i	$-0.332233\pi$
$463$	21.6461	1.00598	0.502990	+	0.864292i	$0.332233\pi$
$464$	4.19810	0.194892
$465$	−15.7893	−0.732212
$466$	4.10498	0.190160
$467$	13.8188	0.639460	0.319730	−	0.947509i	$-0.396408\pi$
$467$	13.8188	0.639460	0.319730	+	0.947509i	$0.396408\pi$
$468$	21.8846	1.01162
$469$	0.0703596	0.00324890
$470$	1.16895	0.0539198
$471$	−12.2736	−0.565538
$472$	−12.7543	−0.587063
$473$	22.8825	1.05214
$474$	15.3029	0.702885
$475$	6.30977	0.289512
$476$	−0.0929824	−0.00426184
$477$	36.0214	1.64931
$478$	−12.2209	−0.558969
$479$	−34.1823	−1.56183	−0.780915	−	0.624637i	$-0.785247\pi$
$479$	−34.1823	−1.56183	−0.780915	+	0.624637i	$0.785247\pi$
$480$	10.5408	0.481121
$481$	−21.9008	−0.998589
$482$	−2.49362	−0.113581
$483$	−0.116738	−0.00531176
$484$	−39.6087	−1.80040
$485$	16.6065	0.754063
$486$	−8.82318	−0.400228
$487$	16.3846	0.742455	0.371228	−	0.928542i	$-0.378937\pi$
$487$	16.3846	0.742455	0.371228	+	0.928542i	$0.378937\pi$
$488$	−13.6260	−0.616819
$489$	0.954084	0.0431452
$490$	−2.88983	−0.130549
$491$	11.2505	0.507726	0.253863	−	0.967240i	$-0.418299\pi$
$491$	11.2505	0.507726	0.253863	+	0.967240i	$0.418299\pi$
$492$	39.3596	1.77447
$493$	8.97291	0.404120
$494$	−11.4097	−0.513347
$495$	15.6043	0.701363
$496$	−19.8291	−0.890354
$497$	0.0364180	0.00163357
$498$	−4.96835	−0.222637
$499$	−42.6718	−1.91025	−0.955126	−	0.296200i	$-0.904281\pi$
$499$	−42.6718	−1.91025	−0.955126	+	0.296200i	$0.904281\pi$
$500$	−1.82957	−0.0818207
$501$	−12.2394	−0.546815
$502$	−9.11245	−0.406709
$503$	−19.0778	−0.850635	−0.425317	−	0.905044i	$-0.639838\pi$
$503$	−19.0778	−0.850635	−0.425317	+	0.905044i	$0.639838\pi$
$504$	−0.0341473	−0.00152104
$505$	−16.5596	−0.736892
$506$	−14.5444	−0.646577
$507$	14.8068	0.657594
$508$	−9.15161	−0.406037
$509$	−29.7049	−1.31665	−0.658324	−	0.752735i	$-0.728734\pi$
$509$	−29.7049	−1.31665	−0.658324	+	0.752735i	$0.728734\pi$
$510$	6.35074	0.281215
$511$	−0.0314358	−0.00139064
$512$	22.7441	1.00516
$513$	−4.06451	−0.179453
$514$	10.2101	0.450347
$515$	−6.07525	−0.267707
$516$	−17.5399	−0.772152
$517$	16.1791	0.711557
$518$	0.0163258	0.000717315 0
$519$	−6.13288	−0.269203
$520$	6.92485	0.303675
$521$	24.6158	1.07844	0.539218	−	0.842166i	$-0.318720\pi$
$521$	24.6158	1.07844	0.539218	+	0.842166i	$0.318720\pi$
$522$	1.57430	0.0689052
$523$	26.7779	1.17092	0.585458	−	0.810703i	$-0.300915\pi$
$523$	26.7779	1.17092	0.585458	+	0.810703i	$0.300915\pi$
$524$	23.8108	1.04018
$525$	0.0189335	0.000826327 0
$526$	−3.48097	−0.151778
$527$	−42.3823	−1.84620
$528$	41.1246	1.78972
$529$	15.0155	0.652847
$530$	5.44541	0.236533
$531$	22.0311	0.956068
$532$	−0.0913021	−0.00395845
$533$	39.3616	1.70494
$534$	0.887394	0.0384013
$535$	−3.35965	−0.145250
$536$	−14.0647	−0.607504
$537$	−32.9670	−1.42263
$538$	−9.18887	−0.396160
$539$	−39.9973	−1.72281
$540$	1.17854	0.0507161
$541$	−16.6641	−0.716445	−0.358222	−	0.933636i	$-0.616617\pi$
$541$	−16.6641	−0.716445	−0.358222	+	0.933636i	$0.616617\pi$
$542$	8.99831	0.386510
$543$	−43.2309	−1.85521
$544$	28.2941	1.21310
$545$	−4.61280	−0.197591
$546$	−0.0342368	−0.00146520
$547$	−10.4837	−0.448252	−0.224126	−	0.974560i	$-0.571953\pi$
$547$	−10.4837	−0.448252	−0.224126	+	0.974560i	$0.571953\pi$
$548$	−6.05758	−0.258767
$549$	23.5369	1.00453
$550$	2.35893	0.100585
$551$	8.81075	0.375351
$552$	23.3357	0.993233
$553$	0.122462	0.00520762
$554$	2.96215	0.125850
$555$	11.9699	0.508092
$556$	13.1799	0.558951
$557$	−19.5332	−0.827648	−0.413824	−	0.910357i	$-0.635807\pi$
$557$	−19.5332	−0.827648	−0.413824	+	0.910357i	$0.635807\pi$
$558$	−7.43598	−0.314790
$559$	−17.5408	−0.741898
$560$	0.0237778	0.00100480
$561$	87.8986	3.71108
$562$	12.1937	0.514361
$563$	0.00408139	0.000172010 0	8.60051e−5	−	1.00000i	$-0.499973\pi$
$563$	0.00408139	0.000172010 0	8.60051e−5		1.00000i	$0.499973\pi$
$564$	−12.4016	−0.522202
$565$	−8.32571	−0.350265
$566$	12.2841	0.516338
$567$	−0.0769924	−0.00323338
$568$	−7.27989	−0.305457
$569$	−39.6277	−1.66128	−0.830639	−	0.556811i	$-0.812025\pi$
$569$	−39.6277	−1.66128	−0.830639	+	0.556811i	$0.812025\pi$
$570$	6.23597	0.261196
$571$	28.0812	1.17516	0.587580	−	0.809166i	$-0.300081\pi$
$571$	28.0812	1.17516	0.587580	+	0.809166i	$0.300081\pi$
$572$	45.7896	1.91456
$573$	4.87698	0.203739
$574$	−0.0293419	−0.00122471
$575$	−6.16567	−0.257126
$576$	−11.4565	−0.477354
$577$	−2.24677	−0.0935342	−0.0467671	−	0.998906i	$-0.514892\pi$
$577$	−2.24677	−0.0935342	−0.0467671	+	0.998906i	$0.514892\pi$
$578$	10.0287	0.417138
$579$	29.3046	1.21786
$580$	−2.55475	−0.106080
$581$	−0.0397595	−0.00164950
$582$	16.4123	0.680312
$583$	75.3682	3.12143
$584$	6.28395	0.260032
$585$	−11.9617	−0.494554
$586$	−6.80386	−0.281065
$587$	−7.64786	−0.315661	−0.157831	−	0.987466i	$-0.550450\pi$
$587$	−7.64786	−0.315661	−0.157831	+	0.987466i	$0.550450\pi$
$588$	30.6587	1.26435
$589$	−41.6164	−1.71477
$590$	3.33047	0.137113
$591$	−32.1152	−1.32104
$592$	15.0324	0.617830
$593$	16.7769	0.688945	0.344473	−	0.938796i	$-0.388058\pi$
$593$	16.7769	0.688945	0.344473	+	0.938796i	$0.388058\pi$
$594$	−1.51953	−0.0623472
$595$	0.0508221	0.00208350
$596$	−1.52904	−0.0626318
$597$	−55.9133	−2.28838
$598$	11.1491	0.455922
$599$	−31.0382	−1.26819	−0.634093	−	0.773257i	$-0.718626\pi$
$599$	−31.0382	−1.26819	−0.634093	+	0.773257i	$0.718626\pi$
$600$	−3.78478	−0.154513
$601$	−37.0374	−1.51079	−0.755394	−	0.655271i	$-0.772554\pi$
$601$	−37.0374	−1.51079	−0.755394	+	0.655271i	$0.772554\pi$
$602$	0.0130757	0.000532927 0
$603$	24.2948	0.989359
$604$	23.3647	0.950696
$605$	21.6492	0.880167
$606$	−16.3659	−0.664820
$607$	18.7886	0.762606	0.381303	−	0.924450i	$-0.375475\pi$
$607$	18.7886	0.762606	0.381303	+	0.924450i	$0.375475\pi$
$608$	27.7828	1.12674
$609$	0.0264382	0.00107133
$610$	3.55810	0.144063
$611$	−12.4023	−0.501742
$612$	−32.1063	−1.29782
$613$	−31.1524	−1.25823	−0.629116	−	0.777311i	$-0.716583\pi$
$613$	−31.1524	−1.25823	−0.629116	+	0.777311i	$0.716583\pi$
$614$	−11.3072	−0.456321
$615$	−21.5131	−0.867491
$616$	−0.0714470	−0.00287868
$617$	26.8055	1.07915	0.539575	−	0.841938i	$-0.318585\pi$
$617$	26.8055	1.07915	0.539575	+	0.841938i	$0.318585\pi$
$618$	−6.00419	−0.241524
$619$	−34.0817	−1.36986	−0.684929	−	0.728610i	$-0.740167\pi$
$619$	−34.0817	−1.36986	−0.684929	+	0.728610i	$0.740167\pi$
$620$	12.0670	0.484622
$621$	3.97169	0.159378
$622$	−1.24681	−0.0499924
$623$	0.00710142	0.000284512 0
$624$	−31.5244	−1.26199
$625$	1.00000	0.0400000
$626$	−4.67051	−0.186671
$627$	86.3101	3.44690
$628$	9.38011	0.374307
$629$	32.1300	1.28111
$630$	0.00891675	0.000355252 0
$631$	23.1479	0.921502	0.460751	−	0.887530i	$-0.347580\pi$
$631$	23.1479	0.921502	0.460751	+	0.887530i	$0.347580\pi$
$632$	−24.4800	−0.973760
$633$	−36.1525	−1.43693
$634$	7.13119	0.283216
$635$	5.00207	0.198501
$636$	−57.7713	−2.29078
$637$	30.6603	1.21481
$638$	3.29394	0.130408
$639$	12.5749	0.497456
$640$	−10.5382	−0.416558
$641$	−19.6884	−0.777647	−0.388823	−	0.921312i	$-0.627118\pi$
$641$	−19.6884	−0.777647	−0.388823	+	0.921312i	$0.627118\pi$
$642$	−3.32036	−0.131044
$643$	16.5572	0.652954	0.326477	−	0.945205i	$-0.394138\pi$
$643$	16.5572	0.652954	0.326477	+	0.945205i	$0.394138\pi$
$644$	0.0892170	0.00351564
$645$	9.58693	0.377485
$646$	16.7388	0.658581
$647$	40.7473	1.60194	0.800970	−	0.598704i	$-0.204317\pi$
$647$	40.7473	1.60194	0.800970	+	0.598704i	$0.204317\pi$
$648$	15.3906	0.604602
$649$	46.0961	1.80943
$650$	−1.80826	−0.0709258
$651$	−0.124877	−0.00489432
$652$	−0.729160	−0.0285561
$653$	−17.7751	−0.695593	−0.347797	−	0.937570i	$-0.613070\pi$
$653$	−17.7751	−0.695593	−0.347797	+	0.937570i	$0.613070\pi$
$654$	−4.55885	−0.178265
$655$	−13.0145	−0.508517
$656$	−27.0174	−1.05485
$657$	−10.8546	−0.423478
$658$	0.00924520	0.000360415 0
$659$	−11.7311	−0.456978	−0.228489	−	0.973546i	$-0.573379\pi$
$659$	−11.7311	−0.456978	−0.228489	+	0.973546i	$0.573379\pi$
$660$	−25.0263	−0.974147
$661$	22.7384	0.884420	0.442210	−	0.896912i	$-0.354195\pi$
$661$	22.7384	0.884420	0.442210	+	0.896912i	$0.354195\pi$
$662$	8.36757	0.325215
$663$	−67.3796	−2.61680
$664$	7.94785	0.308437
$665$	0.0499037	0.00193518
$666$	5.63721	0.218438
$667$	−8.60954	−0.333363
$668$	9.35394	0.361915
$669$	−27.5941	−1.06685
$670$	3.67267	0.141888
$671$	49.2466	1.90114
$672$	0.0833670	0.00321595
$673$	−40.3717	−1.55621	−0.778107	−	0.628132i	$-0.783820\pi$
$673$	−40.3717	−1.55621	−0.778107	+	0.628132i	$0.783820\pi$
$674$	−2.86825	−0.110481
$675$	−0.644162	−0.0247938
$676$	−11.3161	−0.435235
$677$	23.2274	0.892701	0.446351	−	0.894858i	$-0.352723\pi$
$677$	23.2274	0.892701	0.446351	+	0.894858i	$0.352723\pi$
$678$	−8.22834	−0.316007
$679$	0.131340	0.00504038
$680$	−10.1592	−0.389589
$681$	−39.9582	−1.53120
$682$	−15.5584	−0.595763
$683$	33.4828	1.28118	0.640592	−	0.767881i	$-0.278689\pi$
$683$	33.4828	1.28118	0.640592	+	0.767881i	$0.278689\pi$
$684$	−31.5261	−1.20543
$685$	3.31094	0.126505
$686$	−0.0457114	−0.00174527
$687$	−8.10655	−0.309284
$688$	12.0398	0.459014
$689$	−57.7743	−2.20102
$690$	−6.09356	−0.231978
$691$	−12.2816	−0.467214	−0.233607	−	0.972331i	$-0.575053\pi$
$691$	−12.2816	−0.467214	−0.233607	+	0.972331i	$0.575053\pi$
$692$	4.68706	0.178175
$693$	0.123414	0.00468811
$694$	3.12491	0.118620
$695$	−7.20382	−0.273257
$696$	−5.28494	−0.200325
$697$	−57.7462	−2.18729
$698$	−3.09643	−0.117202
$699$	23.8037	0.900339
$700$	−0.0144700	−0.000546913 0
$701$	−18.5654	−0.701207	−0.350603	−	0.936524i	$-0.614023\pi$
$701$	−18.5654	−0.701207	−0.350603	+	0.936524i	$0.614023\pi$
$702$	1.16481	0.0439630
$703$	31.5493	1.18991
$704$	−23.9706	−0.903427
$705$	6.77845	0.255291
$706$	−5.40420	−0.203390
$707$	−0.130969	−0.00492560
$708$	−35.3336	−1.32792
$709$	−29.9252	−1.12387	−0.561933	−	0.827183i	$-0.689942\pi$
$709$	−29.9252	−1.12387	−0.561933	+	0.827183i	$0.689942\pi$
$710$	1.90097	0.0713421
$711$	42.2855	1.58583
$712$	−1.41956	−0.0532003
$713$	40.6660	1.52295
$714$	0.0502277	0.00187973
$715$	−25.0276	−0.935979
$716$	25.1950	0.941583
$717$	−70.8656	−2.64652
$718$	9.60295	0.358379
$719$	−27.0298	−1.00804	−0.504020	−	0.863692i	$-0.668146\pi$
$719$	−27.0298	−1.00804	−0.504020	+	0.863692i	$0.668146\pi$
$720$	8.21035	0.305982
$721$	−0.0480489	−0.00178943
$722$	8.59243	0.319777
$723$	−14.4599	−0.537769
$724$	33.0392	1.22789
$725$	1.39637	0.0518598
$726$	21.3960	0.794082
$727$	−5.31019	−0.196944	−0.0984720	−	0.995140i	$-0.531395\pi$
$727$	−5.31019	−0.196944	−0.0984720	+	0.995140i	$0.531395\pi$
$728$	0.0547684	0.00202985
$729$	−21.9588	−0.813289
$730$	−1.64090	−0.0607326
$731$	25.7336	0.951793
$732$	−37.7485	−1.39523
$733$	49.1610	1.81580	0.907902	−	0.419183i	$-0.137683\pi$
$733$	49.1610	1.81580	0.907902	+	0.419183i	$0.137683\pi$
$734$	−10.8688	−0.401173
$735$	−16.7574	−0.618106
$736$	−27.1483	−1.00070
$737$	50.8324	1.87243
$738$	−10.1316	−0.372949
$739$	38.8591	1.42945	0.714727	−	0.699404i	$-0.246551\pi$
$739$	38.8591	1.42945	0.714727	+	0.699404i	$0.246551\pi$
$740$	−9.14798	−0.336286
$741$	−66.1619	−2.43052
$742$	0.0430675	0.00158106
$743$	−11.5346	−0.423164	−0.211582	−	0.977360i	$-0.567861\pi$
$743$	−11.5346	−0.423164	−0.211582	+	0.977360i	$0.567861\pi$
$744$	24.9627	0.915176
$745$	0.835737	0.0306191
$746$	4.70293	0.172186
$747$	−13.7287	−0.502308
$748$	−67.1766	−2.45622
$749$	−0.0265714	−0.000970896 0
$750$	0.988304	0.0360878
$751$	7.12427	0.259968	0.129984	−	0.991516i	$-0.458507\pi$
$751$	7.12427	0.259968	0.129984	+	0.991516i	$0.458507\pi$
$752$	8.51277	0.310429
$753$	−52.8407	−1.92562
$754$	−2.52500	−0.0919550
$755$	−12.7706	−0.464771
$756$	0.00932100	0.000339001 0
$757$	−24.1945	−0.879363	−0.439681	−	0.898154i	$-0.644909\pi$
$757$	−24.1945	−0.879363	−0.439681	+	0.898154i	$0.644909\pi$
$758$	−8.28333	−0.300864
$759$	−84.3391	−3.06132
$760$	−9.97565	−0.361855
$761$	51.4030	1.86336	0.931679	−	0.363283i	$-0.118344\pi$
$761$	51.4030	1.86336	0.931679	+	0.363283i	$0.118344\pi$
$762$	4.94357	0.179087
$763$	−0.0364824	−0.00132075
$764$	−3.72724	−0.134847
$765$	17.5486	0.634471
$766$	−6.87823	−0.248520
$767$	−35.3354	−1.27589
$768$	9.67067	0.348960
$769$	35.4070	1.27681	0.638404	−	0.769701i	$-0.279595\pi$
$769$	35.4070	1.27681	0.638404	+	0.769701i	$0.279595\pi$
$770$	0.0186567	0.000672340 0
$771$	59.2056	2.13224
$772$	−22.3961	−0.806053
$773$	31.9166	1.14796	0.573980	−	0.818869i	$-0.305399\pi$
$773$	31.9166	1.14796	0.573980	+	0.818869i	$0.305399\pi$
$774$	4.51497	0.162287
$775$	−6.59555	−0.236919
$776$	−26.2547	−0.942488
$777$	0.0946692	0.00339624
$778$	11.4462	0.410367
$779$	−56.7026	−2.03158
$780$	19.1842	0.686903
$781$	26.3107	0.941473
$782$	−16.3566	−0.584910
$783$	−0.899487	−0.0321451
$784$	−21.0449	−0.751604
$785$	−5.12696	−0.182989
$786$	−12.8622	−0.458781
$787$	−5.83031	−0.207828	−0.103914	−	0.994586i	$-0.533137\pi$
$787$	−5.83031	−0.207828	−0.103914	+	0.994586i	$0.533137\pi$
$788$	24.5441	0.874347
$789$	−20.1852	−0.718614
$790$	6.39236	0.227430
$791$	−0.0658477	−0.00234128
$792$	−24.6702	−0.876619
$793$	−37.7505	−1.34056
$794$	−1.45208	−0.0515325
$795$	31.5765	1.11990
$796$	42.7318	1.51459
$797$	8.23564	0.291721	0.145861	−	0.989305i	$-0.453405\pi$
$797$	8.23564	0.291721	0.145861	+	0.989305i	$0.453405\pi$
$798$	0.0493200	0.00174591
$799$	18.1950	0.643692
$800$	4.40314	0.155675
$801$	2.45208	0.0866400
$802$	−0.412837	−0.0145778
$803$	−22.7112	−0.801463
$804$	−38.9640	−1.37416
$805$	−0.0487640	−0.00171871
$806$	11.9265	0.420092
$807$	−53.2839	−1.87568
$808$	26.1805	0.921026
$809$	4.38440	0.154147	0.0770736	−	0.997025i	$-0.475442\pi$
$809$	4.38440	0.154147	0.0770736	+	0.997025i	$0.475442\pi$
$810$	−4.01890	−0.141210
$811$	−2.15785	−0.0757723	−0.0378861	−	0.999282i	$-0.512062\pi$
$811$	−2.15785	−0.0757723	−0.0378861	+	0.999282i	$0.512062\pi$
$812$	−0.0202054	−0.000709070 0
$813$	52.1788	1.82999
$814$	11.7948	0.413409
$815$	0.398543	0.0139603
$816$	46.2486	1.61902
$817$	25.2686	0.884036
$818$	−8.48803	−0.296777
$819$	−0.0946043	−0.00330574
$820$	16.4414	0.574158
$821$	2.17198	0.0758027	0.0379013	−	0.999281i	$-0.487933\pi$
$821$	2.17198	0.0758027	0.0379013	+	0.999281i	$0.487933\pi$
$822$	3.27222	0.114132
$823$	27.2411	0.949566	0.474783	−	0.880103i	$-0.342527\pi$
$823$	27.2411	0.949566	0.474783	+	0.880103i	$0.342527\pi$
$824$	9.60488	0.334602
$825$	13.6788	0.476235
$826$	0.0263406	0.000916506 0
$827$	−0.455606	−0.0158430	−0.00792148	−	0.999969i	$-0.502522\pi$
$827$	−0.455606	−0.0158430	−0.00792148	+	0.999969i	$0.502522\pi$
$828$	30.8061	1.07059
$829$	−43.7453	−1.51934	−0.759669	−	0.650310i	$-0.774639\pi$
$829$	−43.7453	−1.51934	−0.759669	+	0.650310i	$0.774639\pi$
$830$	−2.07539	−0.0720379
$831$	17.1767	0.595854
$832$	18.3749	0.637035
$833$	−44.9808	−1.55849
$834$	−7.11957	−0.246530
$835$	−5.11266	−0.176931
$836$	−65.9626	−2.28136
$837$	4.24860	0.146853
$838$	4.65005	0.160633
$839$	−12.6218	−0.435754	−0.217877	−	0.975976i	$-0.569913\pi$
$839$	−12.6218	−0.435754	−0.217877	+	0.975976i	$0.569913\pi$
$840$	−0.0299336	−0.00103281
$841$	−27.0502	−0.932764
$842$	7.25786	0.250122
$843$	70.7082	2.43532
$844$	27.6296	0.951049
$845$	6.18514	0.212775
$846$	3.19232	0.109754
$847$	0.171223	0.00588329
$848$	39.6556	1.36178
$849$	71.2321	2.44468
$850$	2.65285	0.0909919
$851$	−30.8288	−1.05680
$852$	−20.1677	−0.690935
$853$	−42.9880	−1.47188	−0.735941	−	0.677045i	$-0.763260\pi$
$853$	−42.9880	−1.47188	−0.735941	+	0.677045i	$0.763260\pi$
$854$	0.0281409	0.000962961 0
$855$	17.2315	0.589303
$856$	5.31157	0.181546
$857$	−29.2869	−1.00042	−0.500210	−	0.865904i	$-0.666744\pi$
$857$	−29.2869	−1.00042	−0.500210	+	0.865904i	$0.666744\pi$
$858$	−24.7349	−0.844435
$859$	9.67451	0.330090	0.165045	−	0.986286i	$-0.447223\pi$
$859$	9.67451	0.330090	0.165045	+	0.986286i	$0.447223\pi$
$860$	−7.32682	−0.249843
$861$	−0.170146	−0.00579856
$862$	2.89511	0.0986080
$863$	−12.2184	−0.415919	−0.207960	−	0.978137i	$-0.566682\pi$
$863$	−12.2184	−0.415919	−0.207960	+	0.978137i	$0.566682\pi$
$864$	−2.83634	−0.0964942
$865$	−2.56184	−0.0871052
$866$	−1.46855	−0.0499033
$867$	58.1537	1.97500
$868$	0.0954373	0.00323935
$869$	88.4747	3.00130
$870$	1.38004	0.0467876
$871$	−38.9660	−1.32031
$872$	7.29277	0.246964
$873$	45.3511	1.53490
$874$	−16.0610	−0.543271
$875$	0.00790896	0.000267372 0
$876$	17.4086	0.588183
$877$	−12.9767	−0.438192	−0.219096	−	0.975703i	$-0.570311\pi$
$877$	−12.9767	−0.438192	−0.219096	+	0.975703i	$0.570311\pi$
$878$	10.5609	0.356412
$879$	−39.4538	−1.33074
$880$	17.1787	0.579093
$881$	−37.1816	−1.25268	−0.626339	−	0.779551i	$-0.715448\pi$
$881$	−37.1816	−1.25268	−0.626339	+	0.779551i	$0.715448\pi$
$882$	−7.89190	−0.265734
$883$	−19.9927	−0.672808	−0.336404	−	0.941718i	$-0.609211\pi$
$883$	−19.9927	−0.672808	−0.336404	+	0.941718i	$0.609211\pi$
$884$	51.4949	1.73196
$885$	19.3125	0.649184
$886$	12.2373	0.411121
$887$	−11.7749	−0.395362	−0.197681	−	0.980266i	$-0.563341\pi$
$887$	−11.7749	−0.395362	−0.197681	+	0.980266i	$0.563341\pi$
$888$	−18.9242	−0.635054
$889$	0.0395612	0.00132684
$890$	0.370685	0.0124254
$891$	−55.6244	−1.86349
$892$	21.0888	0.706106
$893$	17.8662	0.597869
$894$	0.825963	0.0276243
$895$	−13.7711	−0.460315
$896$	−0.0833460	−0.00278440
$897$	64.6510	2.15863
$898$	11.3260	0.377953
$899$	−9.20981	−0.307164
$900$	−4.99640	−0.166547
$901$	84.7589	2.82373
$902$	−21.1985	−0.705833
$903$	0.0758227	0.00252322
$904$	13.1628	0.437789
$905$	−18.0585	−0.600285
$906$	−12.6213	−0.419313
$907$	−44.8281	−1.48849	−0.744246	−	0.667905i	$-0.767191\pi$
$907$	−44.8281	−1.48849	−0.744246	+	0.667905i	$0.767191\pi$
$908$	30.5381	1.01344
$909$	−45.2229	−1.49995
$910$	−0.0143015	−0.000474089 0
$911$	53.7104	1.77950	0.889752	−	0.456445i	$-0.150877\pi$
$911$	53.7104	1.77950	0.889752	+	0.456445i	$0.150877\pi$
$912$	45.4128	1.50377
$913$	−28.7249	−0.950655
$914$	−3.12134	−0.103245
$915$	20.6325	0.682090
$916$	6.19544	0.204703
$917$	−0.102931	−0.00339908
$918$	−1.70886	−0.0564009
$919$	7.73063	0.255010	0.127505	−	0.991838i	$-0.459303\pi$
$919$	7.73063	0.255010	0.127505	+	0.991838i	$0.459303\pi$
$920$	9.74784	0.321377
$921$	−65.5674	−2.16052
$922$	6.52865	0.215009
$923$	−20.1688	−0.663863
$924$	−0.197932	−0.00651149
$925$	5.00008	0.164402
$926$	8.93632	0.293666
$927$	−16.5910	−0.544920
$928$	6.14841	0.201831
$929$	29.2681	0.960256	0.480128	−	0.877198i	$-0.340590\pi$
$929$	29.2681	0.960256	0.480128	+	0.877198i	$0.340590\pi$
$930$	−6.51841	−0.213747
$931$	−44.1680	−1.44755
$932$	−18.1920	−0.595899
$933$	−7.22991	−0.236697
$934$	5.70493	0.186671
$935$	36.7172	1.20078
$936$	18.9112	0.618132
$937$	56.5156	1.84628	0.923142	−	0.384460i	$-0.125612\pi$
$937$	56.5156	1.84628	0.923142	+	0.384460i	$0.125612\pi$
$938$	0.0290470	0.000948419 0
$939$	−27.0831	−0.883822
$940$	−5.18044	−0.168967
$941$	1.85825	0.0605772	0.0302886	−	0.999541i	$-0.490357\pi$
$941$	1.85825	0.0605772	0.0302886	+	0.999541i	$0.490357\pi$
$942$	−5.06700	−0.165092
$943$	55.4077	1.80432
$944$	24.2538	0.789395
$945$	−0.00509465	−0.000165729 0
$946$	9.44676	0.307141
$947$	−34.4619	−1.11986	−0.559930	−	0.828540i	$-0.689172\pi$
$947$	−34.4619	−1.11986	−0.559930	+	0.828540i	$0.689172\pi$
$948$	−67.8176	−2.20261
$949$	17.4095	0.565137
$950$	2.60490	0.0845143
$951$	41.3519	1.34093
$952$	−0.0803491	−0.00260413
$953$	1.55842	0.0504821	0.0252411	−	0.999681i	$-0.491965\pi$
$953$	1.55842	0.0504821	0.0252411	+	0.999681i	$0.491965\pi$
$954$	14.8710	0.481465
$955$	2.03723	0.0659231
$956$	54.1591	1.75163
$957$	19.1007	0.617437
$958$	−14.1117	−0.455929
$959$	0.0261861	0.000845593 0
$960$	−10.0428	−0.324130
$961$	12.5013	0.403267
$962$	−9.04145	−0.291508
$963$	−9.17494	−0.295658
$964$	11.0510	0.355928
$965$	12.2412	0.394059
$966$	−0.0481937	−0.00155061
$967$	−19.2415	−0.618765	−0.309382	−	0.950938i	$-0.600122\pi$
$967$	−19.2415	−0.618765	−0.309382	+	0.950938i	$0.600122\pi$
$968$	−34.2272	−1.10010
$969$	97.0641	3.11815
$970$	6.85579	0.220126
$971$	26.3550	0.845772	0.422886	−	0.906183i	$-0.361017\pi$
$971$	26.3550	0.845772	0.422886	+	0.906183i	$0.361017\pi$
$972$	39.1016	1.25418
$973$	−0.0569747	−0.00182653
$974$	6.76415	0.216737
$975$	−10.4856	−0.335809
$976$	25.9115	0.829407
$977$	21.9691	0.702852	0.351426	−	0.936216i	$-0.385697\pi$
$977$	21.9691	0.702852	0.351426	+	0.936216i	$0.385697\pi$
$978$	0.393881	0.0125949
$979$	5.13053	0.163973
$980$	12.8068	0.409100
$981$	−12.5972	−0.402197
$982$	4.64461	0.148215
$983$	23.3768	0.745605	0.372802	−	0.927911i	$-0.378397\pi$
$983$	23.3768	0.745605	0.372802	+	0.927911i	$0.378397\pi$
$984$	34.0119	1.08426
$985$	−13.4152	−0.427445
$986$	3.70435	0.117971
$987$	0.0536105	0.00170644
$988$	50.5643	1.60866
$989$	−24.6915	−0.785145
$990$	6.44205	0.204742
$991$	22.3120	0.708766	0.354383	−	0.935100i	$-0.384691\pi$
$991$	22.3120	0.708766	0.354383	+	0.935100i	$0.384691\pi$
$992$	−29.0411	−0.922057
$993$	48.5213	1.53978
$994$	0.0150347	0.000476872 0
$995$	−23.3563	−0.740443
$996$	22.0182	0.697673
$997$	−55.0560	−1.74364	−0.871820	−	0.489826i	$-0.837060\pi$
$997$	−55.0560	−1.74364	−0.871820	+	0.489826i	$0.837060\pi$
$998$	−17.6165	−0.557640
$999$	−3.22086	−0.101904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.19	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.19	✓	37	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q+0.412837 q^{2} +2.39393 q^{3} -1.82957 q^{4} +1.00000 q^{5} +0.988304 q^{6} +0.00790896 q^{7} -1.58099 q^{8} +2.73092 q^{9} +O(q^{10})\)	\(q+0.412837 q^{2} +2.39393 q^{3} -1.82957 q^{4} +1.00000 q^{5} +0.988304 q^{6} +0.00790896 q^{7} -1.58099 q^{8} +2.73092 q^{9} +0.412837 q^{10} +5.71395 q^{11} -4.37986 q^{12} -4.38008 q^{13} +0.00326511 q^{14} +2.39393 q^{15} +3.00644 q^{16} +6.42589 q^{17} +1.12742 q^{18} +6.30977 q^{19} -1.82957 q^{20} +0.0189335 q^{21} +2.35893 q^{22} -6.16567 q^{23} -3.78478 q^{24} +1.00000 q^{25} -1.80826 q^{26} -0.644162 q^{27} -0.0144700 q^{28} +1.39637 q^{29} +0.988304 q^{30} -6.59555 q^{31} +4.40314 q^{32} +13.6788 q^{33} +2.65285 q^{34} +0.00790896 q^{35} -4.99640 q^{36} +5.00008 q^{37} +2.60490 q^{38} -10.4856 q^{39} -1.58099 q^{40} -8.98649 q^{41} +0.00781646 q^{42} +4.00468 q^{43} -10.4540 q^{44} +2.73092 q^{45} -2.54542 q^{46} +2.83151 q^{47} +7.19722 q^{48} -6.99994 q^{49} +0.412837 q^{50} +15.3832 q^{51} +8.01365 q^{52} +13.1902 q^{53} -0.265934 q^{54} +5.71395 q^{55} -0.0125040 q^{56} +15.1052 q^{57} +0.576472 q^{58} +8.06728 q^{59} -4.37986 q^{60} +8.61866 q^{61} -2.72289 q^{62} +0.0215987 q^{63} -4.19510 q^{64} -4.38008 q^{65} +5.64712 q^{66} +8.89618 q^{67} -11.7566 q^{68} -14.7602 q^{69} +0.00326511 q^{70} +4.60465 q^{71} -4.31755 q^{72} -3.97470 q^{73} +2.06422 q^{74} +2.39393 q^{75} -11.5441 q^{76} +0.0451914 q^{77} -4.32886 q^{78} +15.4840 q^{79} +3.00644 q^{80} -9.73484 q^{81} -3.70996 q^{82} -5.02715 q^{83} -0.0346401 q^{84} +6.42589 q^{85} +1.65328 q^{86} +3.34281 q^{87} -9.03368 q^{88} +0.897896 q^{89} +1.12742 q^{90} -0.0346419 q^{91} +11.2805 q^{92} -15.7893 q^{93} +1.16895 q^{94} +6.30977 q^{95} +10.5408 q^{96} +16.6065 q^{97} -2.88983 q^{98} +15.6043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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