LMFDB - Embedded newform 2005.2.a.f.1.11

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			1.11
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)

$f(q)$	$=$	$q-1.26616 q^{2} -0.778484 q^{3} -0.396848 q^{4} -1.00000 q^{5} +0.985683 q^{6} -1.29163 q^{7} +3.03478 q^{8} -2.39396 q^{9} +O(q^{10})$	\(q-1.26616 q^{2} -0.778484 q^{3} -0.396848 q^{4} -1.00000 q^{5} +0.985683 q^{6} -1.29163 q^{7} +3.03478 q^{8} -2.39396 q^{9} +1.26616 q^{10} +2.14181 q^{11} +0.308940 q^{12} +2.88956 q^{13} +1.63540 q^{14} +0.778484 q^{15} -3.04882 q^{16} -3.12092 q^{17} +3.03113 q^{18} -2.18498 q^{19} +0.396848 q^{20} +1.00551 q^{21} -2.71186 q^{22} -0.602053 q^{23} -2.36253 q^{24} +1.00000 q^{25} -3.65864 q^{26} +4.19911 q^{27} +0.512579 q^{28} -6.26167 q^{29} -0.985683 q^{30} -3.95488 q^{31} -2.20929 q^{32} -1.66736 q^{33} +3.95157 q^{34} +1.29163 q^{35} +0.950039 q^{36} -1.82819 q^{37} +2.76652 q^{38} -2.24948 q^{39} -3.03478 q^{40} +7.36685 q^{41} -1.27313 q^{42} -1.60490 q^{43} -0.849972 q^{44} +2.39396 q^{45} +0.762294 q^{46} -7.36387 q^{47} +2.37345 q^{48} -5.33170 q^{49} -1.26616 q^{50} +2.42959 q^{51} -1.14672 q^{52} -10.4219 q^{53} -5.31674 q^{54} -2.14181 q^{55} -3.91980 q^{56} +1.70097 q^{57} +7.92825 q^{58} +8.82113 q^{59} -0.308940 q^{60} +7.81235 q^{61} +5.00750 q^{62} +3.09210 q^{63} +8.89494 q^{64} -2.88956 q^{65} +2.11114 q^{66} -5.92886 q^{67} +1.23853 q^{68} +0.468689 q^{69} -1.63540 q^{70} +7.61083 q^{71} -7.26516 q^{72} +5.10333 q^{73} +2.31477 q^{74} -0.778484 q^{75} +0.867104 q^{76} -2.76641 q^{77} +2.84819 q^{78} -7.09281 q^{79} +3.04882 q^{80} +3.91294 q^{81} -9.32758 q^{82} +3.61233 q^{83} -0.399034 q^{84} +3.12092 q^{85} +2.03206 q^{86} +4.87461 q^{87} +6.49993 q^{88} +14.6912 q^{89} -3.03113 q^{90} -3.73223 q^{91} +0.238924 q^{92} +3.07881 q^{93} +9.32381 q^{94} +2.18498 q^{95} +1.71990 q^{96} +14.4590 q^{97} +6.75077 q^{98} -5.12741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) $ 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.26616	−0.895308	−0.447654	−	0.894207i	$-0.647740\pi$
$2$	−1.26616	−0.895308	−0.447654	+	0.894207i	$0.647740\pi$
$3$	−0.778484	−0.449458	−0.224729	−	0.974421i	$-0.572150\pi$
$3$	−0.778484	−0.449458	−0.224729	+	0.974421i	$0.572150\pi$
$4$	−0.396848	−0.198424
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.985683	0.402403
$7$	−1.29163	−0.488189	−0.244094	−	0.969752i	$-0.578491\pi$
$7$	−1.29163	−0.488189	−0.244094	+	0.969752i	$0.578491\pi$
$8$	3.03478	1.07296
$9$	−2.39396	−0.797988
$10$	1.26616	0.400394
$11$	2.14181	0.645779	0.322890	−	0.946437i	$-0.395346\pi$
$11$	2.14181	0.645779	0.322890	+	0.946437i	$0.395346\pi$
$12$	0.308940	0.0891832
$13$	2.88956	0.801420	0.400710	−	0.916205i	$-0.368763\pi$
$13$	2.88956	0.801420	0.400710	+	0.916205i	$0.368763\pi$
$14$	1.63540	0.437079
$15$	0.778484	0.201004
$16$	−3.04882	−0.762204
$17$	−3.12092	−0.756934	−0.378467	−	0.925615i	$-0.623549\pi$
$17$	−3.12092	−0.756934	−0.378467	+	0.925615i	$0.623549\pi$
$18$	3.03113	0.714444
$19$	−2.18498	−0.501268	−0.250634	−	0.968082i	$-0.580639\pi$
$19$	−2.18498	−0.501268	−0.250634	+	0.968082i	$0.580639\pi$
$20$	0.396848	0.0887378
$21$	1.00551	0.219420
$22$	−2.71186	−0.578171
$23$	−0.602053	−0.125537	−0.0627684	−	0.998028i	$-0.519993\pi$
$23$	−0.602053	−0.125537	−0.0627684	+	0.998028i	$0.519993\pi$
$24$	−2.36253	−0.482250
$25$	1.00000	0.200000
$26$	−3.65864	−0.717518
$27$	4.19911	0.808120
$28$	0.512579	0.0968683
$29$	−6.26167	−1.16276	−0.581381	−	0.813631i	$-0.697487\pi$
$29$	−6.26167	−1.16276	−0.581381	+	0.813631i	$0.697487\pi$
$30$	−0.985683	−0.179960
$31$	−3.95488	−0.710318	−0.355159	−	0.934806i	$-0.615573\pi$
$31$	−3.95488	−0.710318	−0.355159	+	0.934806i	$0.615573\pi$
$32$	−2.20929	−0.390551
$33$	−1.66736	−0.290251
$34$	3.95157	0.677689
$35$	1.29163	0.218325
$36$	0.950039	0.158340
$37$	−1.82819	−0.300553	−0.150276	−	0.988644i	$-0.548016\pi$
$37$	−1.82819	−0.300553	−0.150276	+	0.988644i	$0.548016\pi$
$38$	2.76652	0.448790
$39$	−2.24948	−0.360205
$40$	−3.03478	−0.479842
$41$	7.36685	1.15051	0.575254	−	0.817975i	$-0.304903\pi$
$41$	7.36685	1.15051	0.575254	+	0.817975i	$0.304903\pi$
$42$	−1.27313	−0.196449
$43$	−1.60490	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$43$	−1.60490	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$44$	−0.849972	−0.128138
$45$	2.39396	0.356871
$46$	0.762294	0.112394
$47$	−7.36387	−1.07413	−0.537066	−	0.843540i	$-0.680467\pi$
$47$	−7.36387	−1.07413	−0.537066	+	0.843540i	$0.680467\pi$
$48$	2.37345	0.342579
$49$	−5.33170	−0.761672
$50$	−1.26616	−0.179062
$51$	2.42959	0.340210
$52$	−1.14672	−0.159021
$53$	−10.4219	−1.43155	−0.715776	−	0.698330i	$-0.753927\pi$
$53$	−10.4219	−1.43155	−0.715776	+	0.698330i	$0.753927\pi$
$54$	−5.31674	−0.723516
$55$	−2.14181	−0.288801
$56$	−3.91980	−0.523806
$57$	1.70097	0.225299
$58$	7.92825	1.04103
$59$	8.82113	1.14841	0.574206	−	0.818711i	$-0.305311\pi$
$59$	8.82113	1.14841	0.574206	+	0.818711i	$0.305311\pi$
$60$	−0.308940	−0.0398839
$61$	7.81235	1.00027	0.500134	−	0.865948i	$-0.333284\pi$
$61$	7.81235	1.00027	0.500134	+	0.865948i	$0.333284\pi$
$62$	5.00750	0.635953
$63$	3.09210	0.389568
$64$	8.89494	1.11187
$65$	−2.88956	−0.358406
$66$	2.11114	0.259864
$67$	−5.92886	−0.724325	−0.362163	−	0.932115i	$-0.617961\pi$
$67$	−5.92886	−0.724325	−0.362163	+	0.932115i	$0.617961\pi$
$68$	1.23853	0.150194
$69$	0.468689	0.0564235
$70$	−1.63540	−0.195468
$71$	7.61083	0.903240	0.451620	−	0.892210i	$-0.350846\pi$
$71$	7.61083	0.903240	0.451620	+	0.892210i	$0.350846\pi$
$72$	−7.26516	−0.856207
$73$	5.10333	0.597300	0.298650	−	0.954363i	$-0.403464\pi$
$73$	5.10333	0.597300	0.298650	+	0.954363i	$0.403464\pi$
$74$	2.31477	0.269087
$75$	−0.778484	−0.0898916
$76$	0.867104	0.0994636
$77$	−2.76641	−0.315262
$78$	2.84819	0.322494
$79$	−7.09281	−0.798004	−0.399002	−	0.916950i	$-0.630643\pi$
$79$	−7.09281	−0.798004	−0.399002	+	0.916950i	$0.630643\pi$
$80$	3.04882	0.340868
$81$	3.91294	0.434772
$82$	−9.32758	−1.03006
$83$	3.61233	0.396505	0.198252	−	0.980151i	$-0.436473\pi$
$83$	3.61233	0.396505	0.198252	+	0.980151i	$0.436473\pi$
$84$	−0.399034	−0.0435382
$85$	3.12092	0.338511
$86$	2.03206	0.219122
$87$	4.87461	0.522613
$88$	6.49993	0.692894
$89$	14.6912	1.55727	0.778633	−	0.627479i	$-0.215913\pi$
$89$	14.6912	1.55727	0.778633	+	0.627479i	$0.215913\pi$
$90$	−3.03113	−0.319509
$91$	−3.73223	−0.391244
$92$	0.238924	0.0249095
$93$	3.07881	0.319258
$94$	9.32381	0.961678
$95$	2.18498	0.224174
$96$	1.71990	0.175536
$97$	14.4590	1.46809	0.734046	−	0.679100i	$-0.237630\pi$
$97$	14.4590	1.46809	0.734046	+	0.679100i	$0.237630\pi$
$98$	6.75077	0.681931
$99$	−5.12741	−0.515324
$100$	−0.396848	−0.0396848
$101$	1.48729	0.147991	0.0739954	−	0.997259i	$-0.476425\pi$
$101$	1.48729	0.147991	0.0739954	+	0.997259i	$0.476425\pi$
$102$	−3.07624	−0.304593
$103$	−1.59599	−0.157258	−0.0786290	−	0.996904i	$-0.525054\pi$
$103$	−1.59599	−0.157258	−0.0786290	+	0.996904i	$0.525054\pi$
$104$	8.76920	0.859890
$105$	−1.00551	−0.0981277
$106$	13.1957	1.28168
$107$	−14.5531	−1.40690	−0.703452	−	0.710742i	$-0.748359\pi$
$107$	−14.5531	−1.40690	−0.703452	+	0.710742i	$0.748359\pi$
$108$	−1.66641	−0.160350
$109$	8.73413	0.836578	0.418289	−	0.908314i	$-0.362630\pi$
$109$	8.73413	0.836578	0.418289	+	0.908314i	$0.362630\pi$
$110$	2.71186	0.258566
$111$	1.42322	0.135086
$112$	3.93793	0.372099
$113$	−3.18942	−0.300035	−0.150017	−	0.988683i	$-0.547933\pi$
$113$	−3.18942	−0.300035	−0.150017	+	0.988683i	$0.547933\pi$
$114$	−2.15370	−0.201712
$115$	0.602053	0.0561418
$116$	2.48493	0.230720
$117$	−6.91750	−0.639523
$118$	−11.1689	−1.02818
$119$	4.03106	0.369527
$120$	2.36253	0.215669
$121$	−6.41266	−0.582969
$122$	−9.89165	−0.895548
$123$	−5.73497	−0.517105
$124$	1.56949	0.140944
$125$	−1.00000	−0.0894427
$126$	−3.91509	−0.348784
$127$	0.428247	0.0380008	0.0190004	−	0.999819i	$-0.493952\pi$
$127$	0.428247	0.0380008	0.0190004	+	0.999819i	$0.493952\pi$
$128$	−6.84381	−0.604913
$129$	1.24939	0.110003
$130$	3.65864	0.320884
$131$	12.2965	1.07435	0.537173	−	0.843472i	$-0.319492\pi$
$131$	12.2965	1.07435	0.537173	+	0.843472i	$0.319492\pi$
$132$	0.661689	0.0575927
$133$	2.82217	0.244714
$134$	7.50686	0.648494
$135$	−4.19911	−0.361402
$136$	−9.47132	−0.812159
$137$	5.89564	0.503698	0.251849	−	0.967767i	$-0.418961\pi$
$137$	5.89564	0.503698	0.251849	+	0.967767i	$0.418961\pi$
$138$	−0.593434	−0.0505164
$139$	13.9615	1.18420	0.592099	−	0.805865i	$-0.298299\pi$
$139$	13.9615	1.18420	0.592099	+	0.805865i	$0.298299\pi$
$140$	−0.512579	−0.0433208
$141$	5.73266	0.482777
$142$	−9.63651	−0.808678
$143$	6.18889	0.517541
$144$	7.29875	0.608229
$145$	6.26167	0.520003
$146$	−6.46161	−0.534767
$147$	4.15065	0.342340
$148$	0.725513	0.0596368
$149$	0.399666	0.0327419	0.0163710	−	0.999866i	$-0.494789\pi$
$149$	0.399666	0.0327419	0.0163710	+	0.999866i	$0.494789\pi$
$150$	0.985683	0.0804806
$151$	2.47562	0.201463	0.100732	−	0.994914i	$-0.467882\pi$
$151$	2.47562	0.201463	0.100732	+	0.994914i	$0.467882\pi$
$152$	−6.63094	−0.537840
$153$	7.47137	0.604024
$154$	3.50271	0.282257
$155$	3.95488	0.317664
$156$	0.892700	0.0714732
$157$	−1.13837	−0.0908517	−0.0454258	−	0.998968i	$-0.514464\pi$
$157$	−1.13837	−0.0908517	−0.0454258	+	0.998968i	$0.514464\pi$
$158$	8.98061	0.714459
$159$	8.11325	0.643422
$160$	2.20929	0.174660
$161$	0.777628	0.0612856
$162$	−4.95440	−0.389254
$163$	18.7943	1.47208	0.736042	−	0.676935i	$-0.236692\pi$
$163$	18.7943	1.47208	0.736042	+	0.676935i	$0.236692\pi$
$164$	−2.92352	−0.228288
$165$	1.66736	0.129804
$166$	−4.57377	−0.354994
$167$	21.1926	1.63994	0.819968	−	0.572409i	$-0.193991\pi$
$167$	21.1926	1.63994	0.819968	+	0.572409i	$0.193991\pi$
$168$	3.05151	0.235429
$169$	−4.65043	−0.357726
$170$	−3.95157	−0.303072
$171$	5.23076	0.400006
$172$	0.636902	0.0485633
$173$	−11.1311	−0.846281	−0.423140	−	0.906064i	$-0.639072\pi$
$173$	−11.1311	−0.846281	−0.423140	+	0.906064i	$0.639072\pi$
$174$	−6.17201	−0.467899
$175$	−1.29163	−0.0976377
$176$	−6.52998	−0.492216
$177$	−6.86711	−0.516163
$178$	−18.6014	−1.39423
$179$	14.4538	1.08032	0.540162	−	0.841561i	$-0.318363\pi$
$179$	14.4538	1.08032	0.540162	+	0.841561i	$0.318363\pi$
$180$	−0.950039	−0.0708117
$181$	−2.00937	−0.149355	−0.0746776	−	0.997208i	$-0.523793\pi$
$181$	−2.00937	−0.149355	−0.0746776	+	0.997208i	$0.523793\pi$
$182$	4.72559	0.350284
$183$	−6.08179	−0.449579
$184$	−1.82710	−0.134696
$185$	1.82819	0.134411
$186$	−3.89826	−0.285834
$187$	−6.68441	−0.488813
$188$	2.92234	0.213133
$189$	−5.42368	−0.394515
$190$	−2.76652	−0.200705
$191$	14.2876	1.03381	0.516907	−	0.856042i	$-0.327083\pi$
$191$	14.2876	1.03381	0.516907	+	0.856042i	$0.327083\pi$
$192$	−6.92457	−0.499738
$193$	−7.76635	−0.559034	−0.279517	−	0.960141i	$-0.590174\pi$
$193$	−7.76635	−0.559034	−0.279517	+	0.960141i	$0.590174\pi$
$194$	−18.3074	−1.31439
$195$	2.24948	0.161088
$196$	2.11587	0.151134
$197$	−2.42119	−0.172503	−0.0862515	−	0.996273i	$-0.527489\pi$
$197$	−2.42119	−0.172503	−0.0862515	+	0.996273i	$0.527489\pi$
$198$	6.49210	0.461374
$199$	−7.14994	−0.506846	−0.253423	−	0.967356i	$-0.581556\pi$
$199$	−7.14994	−0.506846	−0.253423	+	0.967356i	$0.581556\pi$
$200$	3.03478	0.214592
$201$	4.61552	0.325554
$202$	−1.88314	−0.132497
$203$	8.08773	0.567647
$204$	−0.964176	−0.0675058
$205$	−7.36685	−0.514523
$206$	2.02078	0.140794
$207$	1.44129	0.100177
$208$	−8.80974	−0.610846
$209$	−4.67981	−0.323709
$210$	1.27313	0.0878545
$211$	−4.13262	−0.284501	−0.142251	−	0.989831i	$-0.545434\pi$
$211$	−4.13262	−0.284501	−0.142251	+	0.989831i	$0.545434\pi$
$212$	4.13589	0.284054
$213$	−5.92491	−0.405968
$214$	18.4265	1.25961
$215$	1.60490	0.109453
$216$	12.7434	0.867079
$217$	5.10823	0.346769
$218$	−11.0588	−0.748995
$219$	−3.97286	−0.268461
$220$	0.849972	0.0573051
$221$	−9.01809	−0.606622
$222$	−1.80202	−0.120943
$223$	9.00848	0.603253	0.301626	−	0.953426i	$-0.402470\pi$
$223$	9.00848	0.603253	0.301626	+	0.953426i	$0.402470\pi$
$224$	2.85358	0.190663
$225$	−2.39396	−0.159598
$226$	4.03830	0.268624
$227$	3.17279	0.210586	0.105293	−	0.994441i	$-0.466422\pi$
$227$	3.17279	0.210586	0.105293	+	0.994441i	$0.466422\pi$
$228$	−0.675026	−0.0447047
$229$	14.6394	0.967400	0.483700	−	0.875234i	$-0.339293\pi$
$229$	14.6394	0.967400	0.483700	+	0.875234i	$0.339293\pi$
$230$	−0.762294	−0.0502642
$231$	2.15361	0.141697
$232$	−19.0028	−1.24760
$233$	24.4674	1.60291	0.801455	−	0.598055i	$-0.204060\pi$
$233$	24.4674	1.60291	0.801455	+	0.598055i	$0.204060\pi$
$234$	8.75864	0.572570
$235$	7.36387	0.480366
$236$	−3.50064	−0.227873
$237$	5.52164	0.358669
$238$	−5.10395	−0.330840
$239$	25.8654	1.67309	0.836547	−	0.547895i	$-0.184570\pi$
$239$	25.8654	1.67309	0.836547	+	0.547895i	$0.184570\pi$
$240$	−2.37345	−0.153206
$241$	12.3907	0.798155	0.399078	−	0.916917i	$-0.369330\pi$
$241$	12.3907	0.798155	0.399078	+	0.916917i	$0.369330\pi$
$242$	8.11943	0.521937
$243$	−15.6435	−1.00353
$244$	−3.10031	−0.198477
$245$	5.33170	0.340630
$246$	7.26137	0.462968
$247$	−6.31363	−0.401727
$248$	−12.0022	−0.762141
$249$	−2.81214	−0.178212
$250$	1.26616	0.0800788
$251$	1.27071	0.0802064	0.0401032	−	0.999196i	$-0.487231\pi$
$251$	1.27071	0.0802064	0.0401032	+	0.999196i	$0.487231\pi$
$252$	−1.22709	−0.0772997
$253$	−1.28948	−0.0810691
$254$	−0.542228	−0.0340224
$255$	−2.42959	−0.152147
$256$	−9.12455	−0.570284
$257$	7.74420	0.483070	0.241535	−	0.970392i	$-0.422349\pi$
$257$	7.74420	0.483070	0.241535	+	0.970392i	$0.422349\pi$
$258$	−1.58192	−0.0984863
$259$	2.36134	0.146726
$260$	1.14672	0.0711163
$261$	14.9902	0.927870
$262$	−15.5692	−0.961871
$263$	11.2710	0.695003	0.347501	−	0.937679i	$-0.387030\pi$
$263$	11.2710	0.695003	0.347501	+	0.937679i	$0.387030\pi$
$264$	−5.06009	−0.311427
$265$	10.4219	0.640209
$266$	−3.57331	−0.219094
$267$	−11.4369	−0.699926
$268$	2.35285	0.143723
$269$	15.8748	0.967901	0.483951	−	0.875095i	$-0.339201\pi$
$269$	15.8748	0.967901	0.483951	+	0.875095i	$0.339201\pi$
$270$	5.31674	0.323566
$271$	−19.5699	−1.18879	−0.594394	−	0.804174i	$-0.702608\pi$
$271$	−19.5699	−1.18879	−0.594394	+	0.804174i	$0.702608\pi$
$272$	9.51511	0.576938
$273$	2.90548	0.175848
$274$	−7.46480	−0.450965
$275$	2.14181	0.129156
$276$	−0.185998	−0.0111958
$277$	−7.13722	−0.428834	−0.214417	−	0.976742i	$-0.568785\pi$
$277$	−7.13722	−0.428834	−0.214417	+	0.976742i	$0.568785\pi$
$278$	−17.6774	−1.06022
$279$	9.46784	0.566825
$280$	3.91980	0.234253
$281$	17.7397	1.05826	0.529130	−	0.848541i	$-0.322519\pi$
$281$	17.7397	1.05826	0.529130	+	0.848541i	$0.322519\pi$
$282$	−7.25844	−0.432234
$283$	−5.30836	−0.315549	−0.157775	−	0.987475i	$-0.550432\pi$
$283$	−5.30836	−0.315549	−0.157775	+	0.987475i	$0.550432\pi$
$284$	−3.02034	−0.179224
$285$	−1.70097	−0.100757
$286$	−7.83610	−0.463358
$287$	−9.51520	−0.561665
$288$	5.28896	0.311655
$289$	−7.25986	−0.427051
$290$	−7.92825	−0.465563
$291$	−11.2561	−0.659845
$292$	−2.02524	−0.118518
$293$	−15.0597	−0.879795	−0.439898	−	0.898048i	$-0.644985\pi$
$293$	−15.0597	−0.879795	−0.439898	+	0.898048i	$0.644985\pi$
$294$	−5.25537	−0.306499
$295$	−8.82113	−0.513586
$296$	−5.54816	−0.322480
$297$	8.99370	0.521867
$298$	−0.506040	−0.0293141
$299$	−1.73967	−0.100608
$300$	0.308940	0.0178366
$301$	2.07293	0.119482
$302$	−3.13453	−0.180372
$303$	−1.15783	−0.0665157
$304$	6.66160	0.382069
$305$	−7.81235	−0.447334
$306$	−9.45992	−0.540788
$307$	−13.4197	−0.765903	−0.382952	−	0.923768i	$-0.625092\pi$
$307$	−13.4197	−0.765903	−0.382952	+	0.923768i	$0.625092\pi$
$308$	1.09785	0.0625555
$309$	1.24246	0.0706808
$310$	−5.00750	−0.284407
$311$	13.7593	0.780220	0.390110	−	0.920768i	$-0.372437\pi$
$311$	13.7593	0.780220	0.390110	+	0.920768i	$0.372437\pi$
$312$	−6.82668	−0.386485
$313$	−8.20341	−0.463684	−0.231842	−	0.972753i	$-0.574475\pi$
$313$	−8.20341	−0.463684	−0.231842	+	0.972753i	$0.574475\pi$
$314$	1.44135	0.0813402
$315$	−3.09210	−0.174220
$316$	2.81477	0.158343
$317$	2.01282	0.113051	0.0565257	−	0.998401i	$-0.481998\pi$
$317$	2.01282	0.113051	0.0565257	+	0.998401i	$0.481998\pi$
$318$	−10.2726	−0.576061
$319$	−13.4113	−0.750888
$320$	−8.89494	−0.497242
$321$	11.3294	0.632344
$322$	−0.984598	−0.0548695
$323$	6.81914	0.379427
$324$	−1.55284	−0.0862691
$325$	2.88956	0.160284
$326$	−23.7966	−1.31797
$327$	−6.79938	−0.376007
$328$	22.3568	1.23445
$329$	9.51136	0.524379
$330$	−2.11114	−0.116215
$331$	34.4617	1.89419	0.947094	−	0.320958i	$-0.104005\pi$
$331$	34.4617	1.89419	0.947094	+	0.320958i	$0.104005\pi$
$332$	−1.43354	−0.0786760
$333$	4.37662	0.239837
$334$	−26.8332	−1.46825
$335$	5.92886	0.323928
$336$	−3.06561	−0.167243
$337$	4.54233	0.247437	0.123718	−	0.992317i	$-0.460518\pi$
$337$	4.54233	0.247437	0.123718	+	0.992317i	$0.460518\pi$
$338$	5.88818	0.320275
$339$	2.48291	0.134853
$340$	−1.23853	−0.0671687
$341$	−8.47060	−0.458709
$342$	−6.62296	−0.358129
$343$	15.9279	0.860028
$344$	−4.87053	−0.262602
$345$	−0.468689	−0.0252334
$346$	14.0937	0.757682
$347$	−7.09728	−0.381002	−0.190501	−	0.981687i	$-0.561011\pi$
$347$	−7.09728	−0.381002	−0.190501	+	0.981687i	$0.561011\pi$
$348$	−1.93448	−0.103699
$349$	−15.4192	−0.825368	−0.412684	−	0.910874i	$-0.635409\pi$
$349$	−15.4192	−0.825368	−0.412684	+	0.910874i	$0.635409\pi$
$350$	1.63540	0.0874158
$351$	12.1336	0.647644
$352$	−4.73188	−0.252210
$353$	−30.0527	−1.59954	−0.799772	−	0.600304i	$-0.795046\pi$
$353$	−30.0527	−1.59954	−0.799772	+	0.600304i	$0.795046\pi$
$354$	8.69483	0.462125
$355$	−7.61083	−0.403941
$356$	−5.83018	−0.308999
$357$	−3.13812	−0.166087
$358$	−18.3007	−0.967223
$359$	−1.65445	−0.0873187	−0.0436594	−	0.999046i	$-0.513902\pi$
$359$	−1.65445	−0.0873187	−0.0436594	+	0.999046i	$0.513902\pi$
$360$	7.26516	0.382908
$361$	−14.2259	−0.748730
$362$	2.54418	0.133719
$363$	4.99215	0.262020
$364$	1.48113	0.0776322
$365$	−5.10333	−0.267120
$366$	7.70049	0.402511
$367$	−16.8234	−0.878174	−0.439087	−	0.898445i	$-0.644698\pi$
$367$	−16.8234	−0.878174	−0.439087	+	0.898445i	$0.644698\pi$
$368$	1.83555	0.0956847
$369$	−17.6360	−0.918091
$370$	−2.31477	−0.120339
$371$	13.4611	0.698867
$372$	−1.22182	−0.0633484
$373$	−22.1420	−1.14647	−0.573234	−	0.819392i	$-0.694311\pi$
$373$	−22.1420	−1.14647	−0.573234	+	0.819392i	$0.694311\pi$
$374$	8.46351	0.437638
$375$	0.778484	0.0402007
$376$	−22.3478	−1.15250
$377$	−18.0935	−0.931861
$378$	6.86723	0.353212
$379$	−10.2118	−0.524543	−0.262272	−	0.964994i	$-0.584472\pi$
$379$	−10.2118	−0.524543	−0.262272	+	0.964994i	$0.584472\pi$
$380$	−0.867104	−0.0444815
$381$	−0.333384	−0.0170798
$382$	−18.0903	−0.925582
$383$	18.0232	0.920942	0.460471	−	0.887675i	$-0.347681\pi$
$383$	18.0232	0.920942	0.460471	+	0.887675i	$0.347681\pi$
$384$	5.32779	0.271883
$385$	2.76641	0.140990
$386$	9.83341	0.500507
$387$	3.84208	0.195304
$388$	−5.73803	−0.291304
$389$	25.8509	1.31069	0.655346	−	0.755329i	$-0.272523\pi$
$389$	25.8509	1.31069	0.655346	+	0.755329i	$0.272523\pi$
$390$	−2.84819	−0.144224
$391$	1.87896	0.0950231
$392$	−16.1806	−0.817242
$393$	−9.57260	−0.482874
$394$	3.06561	0.154443
$395$	7.09281	0.356878
$396$	2.03480	0.102253
$397$	−12.7469	−0.639750	−0.319875	−	0.947460i	$-0.603641\pi$
$397$	−12.7469	−0.639750	−0.319875	+	0.947460i	$0.603641\pi$
$398$	9.05295	0.453783
$399$	−2.19702	−0.109988
$400$	−3.04882	−0.152441
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−5.84397	−0.291471
$403$	−11.4279	−0.569263
$404$	−0.590227	−0.0293649
$405$	−3.91294	−0.194436
$406$	−10.2403	−0.508219
$407$	−3.91563	−0.194091
$408$	7.37327	0.365031
$409$	18.3197	0.905849	0.452925	−	0.891549i	$-0.350381\pi$
$409$	18.3197	0.905849	0.452925	+	0.891549i	$0.350381\pi$
$410$	9.32758	0.460656
$411$	−4.58966	−0.226391
$412$	0.633367	0.0312037
$413$	−11.3936	−0.560642
$414$	−1.82490	−0.0896891
$415$	−3.61233	−0.177322
$416$	−6.38388	−0.312995
$417$	−10.8688	−0.532247
$418$	5.92537	0.289819
$419$	15.8836	0.775963	0.387981	−	0.921667i	$-0.373172\pi$
$419$	15.8836	0.775963	0.387981	+	0.921667i	$0.373172\pi$
$420$	0.399034	0.0194709
$421$	−6.15057	−0.299760	−0.149880	−	0.988704i	$-0.547889\pi$
$421$	−6.15057	−0.299760	−0.149880	+	0.988704i	$0.547889\pi$
$422$	5.23254	0.254716
$423$	17.6288	0.857143
$424$	−31.6281	−1.53599
$425$	−3.12092	−0.151387
$426$	7.50187	0.363467
$427$	−10.0906	−0.488320
$428$	5.77538	0.279163
$429$	−4.81795	−0.232613
$430$	−2.03206	−0.0979945
$431$	18.4869	0.890483	0.445242	−	0.895411i	$-0.353118\pi$
$431$	18.4869	0.890483	0.445242	+	0.895411i	$0.353118\pi$
$432$	−12.8023	−0.615952
$433$	−6.57791	−0.316114	−0.158057	−	0.987430i	$-0.550523\pi$
$433$	−6.57791	−0.316114	−0.158057	+	0.987430i	$0.550523\pi$
$434$	−6.46781	−0.310465
$435$	−4.87461	−0.233719
$436$	−3.46612	−0.165997
$437$	1.31547	0.0629277
$438$	5.03026	0.240355
$439$	−19.0072	−0.907163	−0.453581	−	0.891215i	$-0.649854\pi$
$439$	−19.0072	−0.907163	−0.453581	+	0.891215i	$0.649854\pi$
$440$	−6.49993	−0.309872
$441$	12.7639	0.607805
$442$	11.4183	0.543114
$443$	−4.88321	−0.232008	−0.116004	−	0.993249i	$-0.537009\pi$
$443$	−4.88321	−0.232008	−0.116004	+	0.993249i	$0.537009\pi$
$444$	−0.564800	−0.0268042
$445$	−14.6912	−0.696431
$446$	−11.4062	−0.540097
$447$	−0.311134	−0.0147161
$448$	−11.4889	−0.542801
$449$	36.6287	1.72861	0.864307	−	0.502965i	$-0.167758\pi$
$449$	36.6287	1.72861	0.864307	+	0.502965i	$0.167758\pi$
$450$	3.03113	0.142889
$451$	15.7784	0.742974
$452$	1.26571	0.0595341
$453$	−1.92723	−0.0905493
$454$	−4.01725	−0.188539
$455$	3.73223	0.174970
$456$	5.16208	0.241737
$457$	5.44832	0.254861	0.127431	−	0.991847i	$-0.459327\pi$
$457$	5.44832	0.254861	0.127431	+	0.991847i	$0.459327\pi$
$458$	−18.5358	−0.866121
$459$	−13.1051	−0.611694
$460$	−0.238924	−0.0111399
$461$	13.3310	0.620887	0.310444	−	0.950592i	$-0.399522\pi$
$461$	13.3310	0.620887	0.310444	+	0.950592i	$0.399522\pi$
$462$	−2.72681	−0.126862
$463$	13.9790	0.649660	0.324830	−	0.945772i	$-0.394693\pi$
$463$	13.9790	0.649660	0.324830	+	0.945772i	$0.394693\pi$
$464$	19.0907	0.886262
$465$	−3.07881	−0.142776
$466$	−30.9795	−1.43510
$467$	3.38392	0.156589	0.0782946	−	0.996930i	$-0.475053\pi$
$467$	3.38392	0.156589	0.0782946	+	0.996930i	$0.475053\pi$
$468$	2.74520	0.126897
$469$	7.65786	0.353607
$470$	−9.32381	−0.430076
$471$	0.886201	0.0408340
$472$	26.7702	1.23220
$473$	−3.43739	−0.158052
$474$	−6.99126	−0.321119
$475$	−2.18498	−0.100254
$476$	−1.59972	−0.0733229
$477$	24.9495	1.14236
$478$	−32.7497	−1.49793
$479$	7.39619	0.337941	0.168970	−	0.985621i	$-0.445956\pi$
$479$	7.39619	0.337941	0.168970	+	0.985621i	$0.445956\pi$
$480$	−1.71990	−0.0785022
$481$	−5.28267	−0.240869
$482$	−15.6886	−0.714595
$483$	−0.605371	−0.0275453
$484$	2.54485	0.115675
$485$	−14.4590	−0.656550
$486$	19.8071	0.898470
$487$	−15.4296	−0.699181	−0.349590	−	0.936903i	$-0.613679\pi$
$487$	−15.4296	−0.699181	−0.349590	+	0.936903i	$0.613679\pi$
$488$	23.7088	1.07325
$489$	−14.6311	−0.661640
$490$	−6.75077	−0.304969
$491$	−10.7172	−0.483660	−0.241830	−	0.970319i	$-0.577748\pi$
$491$	−10.7172	−0.483660	−0.241830	+	0.970319i	$0.577748\pi$
$492$	2.27591	0.102606
$493$	19.5422	0.880134
$494$	7.99404	0.359669
$495$	5.12741	0.230460
$496$	12.0577	0.541407
$497$	−9.83035	−0.440951
$498$	3.56061	0.159555
$499$	2.30329	0.103110	0.0515548	−	0.998670i	$-0.483582\pi$
$499$	2.30329	0.103110	0.0515548	+	0.998670i	$0.483582\pi$
$500$	0.396848	0.0177476
$501$	−16.4981	−0.737082
$502$	−1.60892	−0.0718094
$503$	28.5053	1.27099	0.635493	−	0.772106i	$-0.280797\pi$
$503$	28.5053	1.27099	0.635493	+	0.772106i	$0.280797\pi$
$504$	9.38387	0.417991
$505$	−1.48729	−0.0661835
$506$	1.63269	0.0725818
$507$	3.62029	0.160783
$508$	−0.169949	−0.00754027
$509$	−34.2220	−1.51687	−0.758433	−	0.651752i	$-0.774034\pi$
$509$	−34.2220	−1.51687	−0.758433	+	0.651752i	$0.774034\pi$
$510$	3.07624	0.136218
$511$	−6.59159	−0.291595
$512$	25.2407	1.11549
$513$	−9.17497	−0.405085
$514$	−9.80537	−0.432497
$515$	1.59599	0.0703279
$516$	−0.495818	−0.0218272
$517$	−15.7720	−0.693652
$518$	−2.98982	−0.131365
$519$	8.66537	0.380368
$520$	−8.76920	−0.384555
$521$	−32.1337	−1.40780	−0.703902	−	0.710298i	$-0.748560\pi$
$521$	−32.1337	−1.40780	−0.703902	+	0.710298i	$0.748560\pi$
$522$	−18.9799	−0.830729
$523$	−22.3673	−0.978053	−0.489027	−	0.872269i	$-0.662648\pi$
$523$	−22.3673	−0.978053	−0.489027	+	0.872269i	$0.662648\pi$
$524$	−4.87982	−0.213176
$525$	1.00551	0.0438840
$526$	−14.2709	−0.622241
$527$	12.3429	0.537664
$528$	5.08348	0.221230
$529$	−22.6375	−0.984241
$530$	−13.1957	−0.573184
$531$	−21.1174	−0.916419
$532$	−1.11997	−0.0485570
$533$	21.2870	0.922040
$534$	14.4809	0.626649
$535$	14.5531	0.629187
$536$	−17.9928	−0.777171
$537$	−11.2520	−0.485561
$538$	−20.0999	−0.866570
$539$	−11.4195	−0.491872
$540$	1.66641	0.0717108
$541$	−17.2645	−0.742261	−0.371130	−	0.928581i	$-0.621030\pi$
$541$	−17.2645	−0.742261	−0.371130	+	0.928581i	$0.621030\pi$
$542$	24.7786	1.06433
$543$	1.56426	0.0671289
$544$	6.89502	0.295621
$545$	−8.73413	−0.374129
$546$	−3.67880	−0.157438
$547$	11.4529	0.489693	0.244846	−	0.969562i	$-0.421262\pi$
$547$	11.4529	0.489693	0.244846	+	0.969562i	$0.421262\pi$
$548$	−2.33967	−0.0999458
$549$	−18.7025	−0.798202
$550$	−2.71186	−0.115634
$551$	13.6816	0.582856
$552$	1.42237	0.0605401
$553$	9.16126	0.389576
$554$	9.03684	0.383939
$555$	−1.42322	−0.0604122
$556$	−5.54059	−0.234973
$557$	−16.7084	−0.707958	−0.353979	−	0.935253i	$-0.615172\pi$
$557$	−16.7084	−0.707958	−0.353979	+	0.935253i	$0.615172\pi$
$558$	−11.9878	−0.507483
$559$	−4.63747	−0.196144
$560$	−3.93793	−0.166408
$561$	5.20371	0.219701
$562$	−22.4612	−0.947468
$563$	33.0053	1.39101	0.695503	−	0.718523i	$-0.255181\pi$
$563$	33.0053	1.39101	0.695503	+	0.718523i	$0.255181\pi$
$564$	−2.27499	−0.0957944
$565$	3.18942	0.134180
$566$	6.72121	0.282514
$567$	−5.05406	−0.212251
$568$	23.0972	0.969139
$569$	26.8014	1.12357	0.561786	−	0.827282i	$-0.310114\pi$
$569$	26.8014	1.12357	0.561786	+	0.827282i	$0.310114\pi$
$570$	2.15370	0.0902084
$571$	10.1324	0.424029	0.212015	−	0.977266i	$-0.431998\pi$
$571$	10.1324	0.424029	0.212015	+	0.977266i	$0.431998\pi$
$572$	−2.45605	−0.102692
$573$	−11.1227	−0.464656
$574$	12.0477	0.502863
$575$	−0.602053	−0.0251074
$576$	−21.2942	−0.887256
$577$	−12.7030	−0.528832	−0.264416	−	0.964409i	$-0.585179\pi$
$577$	−12.7030	−0.528832	−0.264416	+	0.964409i	$0.585179\pi$
$578$	9.19212	0.382342
$579$	6.04598	0.251262
$580$	−2.48493	−0.103181
$581$	−4.66578	−0.193569
$582$	14.2520	0.590765
$583$	−22.3216	−0.924466
$584$	15.4875	0.640878
$585$	6.91750	0.286004
$586$	19.0679	0.787688
$587$	−9.44524	−0.389847	−0.194923	−	0.980818i	$-0.562446\pi$
$587$	−9.44524	−0.389847	−0.194923	+	0.980818i	$0.562446\pi$
$588$	−1.64717	−0.0679283
$589$	8.64133	0.356060
$590$	11.1689	0.459817
$591$	1.88486	0.0775328
$592$	5.57382	0.229082
$593$	−17.9509	−0.737157	−0.368579	−	0.929597i	$-0.620155\pi$
$593$	−17.9509	−0.737157	−0.368579	+	0.929597i	$0.620155\pi$
$594$	−11.3874	−0.467232
$595$	−4.03106	−0.165257
$596$	−0.158607	−0.00649678
$597$	5.56612	0.227806
$598$	2.20270	0.0900749
$599$	−3.00456	−0.122763	−0.0613816	−	0.998114i	$-0.519551\pi$
$599$	−3.00456	−0.122763	−0.0613816	+	0.998114i	$0.519551\pi$
$600$	−2.36253	−0.0964499
$601$	−30.5663	−1.24682	−0.623412	−	0.781893i	$-0.714254\pi$
$601$	−30.5663	−1.24682	−0.623412	+	0.781893i	$0.714254\pi$
$602$	−2.62466	−0.106973
$603$	14.1935	0.578002
$604$	−0.982445	−0.0399751
$605$	6.41266	0.260712
$606$	1.46600	0.0595520
$607$	14.1656	0.574965	0.287482	−	0.957786i	$-0.407182\pi$
$607$	14.1656	0.574965	0.287482	+	0.957786i	$0.407182\pi$
$608$	4.82725	0.195771
$609$	−6.29617	−0.255134
$610$	9.89165	0.400501
$611$	−21.2784	−0.860830
$612$	−2.96499	−0.119853
$613$	14.3406	0.579213	0.289607	−	0.957146i	$-0.406476\pi$
$613$	14.3406	0.579213	0.289607	+	0.957146i	$0.406476\pi$
$614$	16.9915	0.685719
$615$	5.73497	0.231256
$616$	−8.39547	−0.338263
$617$	−2.60034	−0.104686	−0.0523428	−	0.998629i	$-0.516669\pi$
$617$	−2.60034	−0.104686	−0.0523428	+	0.998629i	$0.516669\pi$
$618$	−1.57314	−0.0632811
$619$	−30.1999	−1.21384	−0.606919	−	0.794764i	$-0.707595\pi$
$619$	−30.1999	−1.21384	−0.606919	+	0.794764i	$0.707595\pi$
$620$	−1.56949	−0.0630321
$621$	−2.52809	−0.101449
$622$	−17.4215	−0.698537
$623$	−18.9756	−0.760240
$624$	6.85824	0.274549
$625$	1.00000	0.0400000
$626$	10.3868	0.415140
$627$	3.64315	0.145494
$628$	0.451759	0.0180271
$629$	5.70563	0.227499
$630$	3.91509	0.155981
$631$	−8.88455	−0.353688	−0.176844	−	0.984239i	$-0.556589\pi$
$631$	−8.88455	−0.353688	−0.176844	+	0.984239i	$0.556589\pi$
$632$	−21.5252	−0.856225
$633$	3.21718	0.127871
$634$	−2.54855	−0.101216
$635$	−0.428247	−0.0169945
$636$	−3.21972	−0.127670
$637$	−15.4063	−0.610419
$638$	16.9808	0.672276
$639$	−18.2201	−0.720774
$640$	6.84381	0.270525
$641$	−0.322973	−0.0127567	−0.00637833	−	0.999980i	$-0.502030\pi$
$641$	−0.322973	−0.0127567	−0.00637833	+	0.999980i	$0.502030\pi$
$642$	−14.3448	−0.566143
$643$	29.6686	1.17002	0.585008	−	0.811028i	$-0.301091\pi$
$643$	29.6686	1.17002	0.585008	+	0.811028i	$0.301091\pi$
$644$	−0.308600	−0.0121605
$645$	−1.24939	−0.0491947
$646$	−8.63410	−0.339704
$647$	−22.4772	−0.883668	−0.441834	−	0.897097i	$-0.645672\pi$
$647$	−22.4772	−0.883668	−0.441834	+	0.897097i	$0.645672\pi$
$648$	11.8749	0.466492
$649$	18.8932	0.741621
$650$	−3.65864	−0.143504
$651$	−3.97667	−0.155858
$652$	−7.45848	−0.292097
$653$	28.6483	1.12109	0.560547	−	0.828123i	$-0.310591\pi$
$653$	28.6483	1.12109	0.560547	+	0.828123i	$0.310591\pi$
$654$	8.60908	0.336642
$655$	−12.2965	−0.480462
$656$	−22.4602	−0.876922
$657$	−12.2172	−0.476638
$658$	−12.0429	−0.469480
$659$	−36.8880	−1.43695	−0.718476	−	0.695552i	$-0.755160\pi$
$659$	−36.8880	−1.43695	−0.718476	+	0.695552i	$0.755160\pi$
$660$	−0.661689	−0.0257562
$661$	27.0346	1.05153	0.525763	−	0.850631i	$-0.323780\pi$
$661$	27.0346	1.05153	0.525763	+	0.850631i	$0.323780\pi$
$662$	−43.6339	−1.69588
$663$	7.02044	0.272651
$664$	10.9626	0.425433
$665$	−2.82217	−0.109439
$666$	−5.54148	−0.214728
$667$	3.76986	0.145969
$668$	−8.41025	−0.325402
$669$	−7.01296	−0.271137
$670$	−7.50686	−0.290015
$671$	16.7325	0.645953
$672$	−2.22146	−0.0856948
$673$	5.25672	0.202632	0.101316	−	0.994854i	$-0.467695\pi$
$673$	5.25672	0.202632	0.101316	+	0.994854i	$0.467695\pi$
$674$	−5.75131	−0.221532
$675$	4.19911	0.161624
$676$	1.84551	0.0709813
$677$	−43.7235	−1.68043	−0.840215	−	0.542254i	$-0.817571\pi$
$677$	−43.7235	−1.68043	−0.840215	+	0.542254i	$0.817571\pi$
$678$	−3.14375	−0.120735
$679$	−18.6756	−0.716705
$680$	9.47132	0.363208
$681$	−2.46997	−0.0946494
$682$	10.7251	0.410685
$683$	18.2458	0.698158	0.349079	−	0.937093i	$-0.386495\pi$
$683$	18.2458	0.698158	0.349079	+	0.937093i	$0.386495\pi$
$684$	−2.07581	−0.0793707
$685$	−5.89564	−0.225261
$686$	−20.1673	−0.769990
$687$	−11.3966	−0.434806
$688$	4.89305	0.186546
$689$	−30.1146	−1.14727
$690$	0.593434	0.0225916
$691$	21.6212	0.822510	0.411255	−	0.911520i	$-0.365091\pi$
$691$	21.6212	0.822510	0.411255	+	0.911520i	$0.365091\pi$
$692$	4.41735	0.167922
$693$	6.62269	0.251575
$694$	8.98627	0.341114
$695$	−13.9615	−0.529590
$696$	14.7934	0.560742
$697$	−22.9913	−0.870859
$698$	19.5231	0.738959
$699$	−19.0474	−0.720441
$700$	0.512579	0.0193737
$701$	6.50809	0.245807	0.122904	−	0.992419i	$-0.460779\pi$
$701$	6.50809	0.245807	0.122904	+	0.992419i	$0.460779\pi$
$702$	−15.3630	−0.579840
$703$	3.99456	0.150658
$704$	19.0513	0.718021
$705$	−5.73266	−0.215904
$706$	38.0514	1.43208
$707$	−1.92102	−0.0722474
$708$	2.72520	0.102419
$709$	22.9150	0.860589	0.430295	−	0.902688i	$-0.358410\pi$
$709$	22.9150	0.860589	0.430295	+	0.902688i	$0.358410\pi$
$710$	9.63651	0.361652
$711$	16.9799	0.636797
$712$	44.5847	1.67088
$713$	2.38105	0.0891710
$714$	3.97335	0.148699
$715$	−6.18889	−0.231451
$716$	−5.73594	−0.214362
$717$	−20.1358	−0.751986
$718$	2.09480	0.0781772
$719$	34.9688	1.30412	0.652058	−	0.758169i	$-0.273906\pi$
$719$	34.9688	1.30412	0.652058	+	0.758169i	$0.273906\pi$
$720$	−7.29875	−0.272008
$721$	2.06143	0.0767715
$722$	18.0122	0.670344
$723$	−9.64596	−0.358737
$724$	0.797414	0.0296356
$725$	−6.26167	−0.232552
$726$	−6.32085	−0.234589
$727$	−7.66421	−0.284250	−0.142125	−	0.989849i	$-0.545393\pi$
$727$	−7.66421	−0.284250	−0.142125	+	0.989849i	$0.545393\pi$
$728$	−11.3265	−0.419789
$729$	0.439386	0.0162735
$730$	6.46161	0.239155
$731$	5.00877	0.185256
$732$	2.41354	0.0892071
$733$	−5.20294	−0.192175	−0.0960875	−	0.995373i	$-0.530633\pi$
$733$	−5.20294	−0.192175	−0.0960875	+	0.995373i	$0.530633\pi$
$734$	21.3010	0.786236
$735$	−4.15065	−0.153099
$736$	1.33011	0.0490285
$737$	−12.6985	−0.467754
$738$	22.3299	0.821974
$739$	8.09463	0.297766	0.148883	−	0.988855i	$-0.452432\pi$
$739$	8.09463	0.297766	0.148883	+	0.988855i	$0.452432\pi$
$740$	−0.725513	−0.0266704
$741$	4.91506	0.180559
$742$	−17.0439	−0.625701
$743$	19.1212	0.701487	0.350744	−	0.936472i	$-0.385929\pi$
$743$	19.1212	0.701487	0.350744	+	0.936472i	$0.385929\pi$
$744$	9.34353	0.342550
$745$	−0.399666	−0.0146426
$746$	28.0352	1.02644
$747$	−8.64778	−0.316406
$748$	2.65269	0.0969921
$749$	18.7972	0.686835
$750$	−0.985683	−0.0359920
$751$	24.0530	0.877708	0.438854	−	0.898558i	$-0.355385\pi$
$751$	24.0530	0.877708	0.438854	+	0.898558i	$0.355385\pi$
$752$	22.4511	0.818707
$753$	−0.989226	−0.0360494
$754$	22.9092	0.834302
$755$	−2.47562	−0.0900971
$756$	2.15238	0.0782812
$757$	37.2311	1.35319	0.676594	−	0.736356i	$-0.263455\pi$
$757$	37.2311	1.35319	0.676594	+	0.736356i	$0.263455\pi$
$758$	12.9297	0.469628
$759$	1.00384	0.0364372
$760$	6.63094	0.240529
$761$	−12.4060	−0.449719	−0.224859	−	0.974391i	$-0.572192\pi$
$761$	−12.4060	−0.449719	−0.224859	+	0.974391i	$0.572192\pi$
$762$	0.422116	0.0152916
$763$	−11.2812	−0.408408
$764$	−5.67000	−0.205133
$765$	−7.47137	−0.270128
$766$	−22.8202	−0.824526
$767$	25.4892	0.920361
$768$	7.10332	0.256319
$769$	−13.8476	−0.499358	−0.249679	−	0.968329i	$-0.580325\pi$
$769$	−13.8476	−0.499358	−0.249679	+	0.968329i	$0.580325\pi$
$770$	−3.50271	−0.126229
$771$	−6.02874	−0.217120
$772$	3.08206	0.110926
$773$	16.7023	0.600741	0.300370	−	0.953823i	$-0.402890\pi$
$773$	16.7023	0.600741	0.300370	+	0.953823i	$0.402890\pi$
$774$	−4.86467	−0.174857
$775$	−3.95488	−0.142064
$776$	43.8800	1.57520
$777$	−1.83826	−0.0659473
$778$	−32.7313	−1.17347
$779$	−16.0964	−0.576713
$780$	−0.892700	−0.0319638
$781$	16.3009	0.583294
$782$	−2.37906	−0.0850749
$783$	−26.2934	−0.939651
$784$	16.2554	0.580549
$785$	1.13837	0.0406301
$786$	12.1204	0.432321
$787$	47.4569	1.69165	0.845827	−	0.533457i	$-0.179107\pi$
$787$	47.4569	1.69165	0.845827	+	0.533457i	$0.179107\pi$
$788$	0.960846	0.0342287
$789$	−8.77433	−0.312375
$790$	−8.98061	−0.319516
$791$	4.11953	0.146474
$792$	−15.5606	−0.552921
$793$	22.5743	0.801635
$794$	16.1396	0.572773
$795$	−8.11325	−0.287747
$796$	2.83744	0.100570
$797$	39.4260	1.39654	0.698270	−	0.715835i	$-0.253954\pi$
$797$	39.4260	1.39654	0.698270	+	0.715835i	$0.253954\pi$
$798$	2.78177	0.0984735
$799$	22.9821	0.813047
$800$	−2.20929	−0.0781102
$801$	−35.1702	−1.24268
$802$	−1.26616	−0.0447095
$803$	10.9304	0.385724
$804$	−1.83166	−0.0645976
$805$	−0.777628	−0.0274078
$806$	14.4695	0.509666
$807$	−12.3582	−0.435031
$808$	4.51360	0.158788
$809$	−12.8036	−0.450152	−0.225076	−	0.974341i	$-0.572263\pi$
$809$	−12.8036	−0.450152	−0.225076	+	0.974341i	$0.572263\pi$
$810$	4.95440	0.174080
$811$	−5.90083	−0.207206	−0.103603	−	0.994619i	$-0.533037\pi$
$811$	−5.90083	−0.207206	−0.103603	+	0.994619i	$0.533037\pi$
$812$	−3.20960	−0.112635
$813$	15.2349	0.534310
$814$	4.95780	0.173771
$815$	−18.7943	−0.658336
$816$	−7.40736	−0.259310
$817$	3.50668	0.122683
$818$	−23.1956	−0.811014
$819$	8.93482	0.312208
$820$	2.92352	0.102094
$821$	49.5724	1.73009	0.865044	−	0.501697i	$-0.167291\pi$
$821$	49.5724	1.73009	0.865044	+	0.501697i	$0.167291\pi$
$822$	5.81123	0.202690
$823$	−22.1365	−0.771631	−0.385816	−	0.922576i	$-0.626080\pi$
$823$	−22.1365	−0.771631	−0.385816	+	0.922576i	$0.626080\pi$
$824$	−4.84350	−0.168731
$825$	−1.66736	−0.0580501
$826$	14.4261	0.501947
$827$	46.1068	1.60329	0.801645	−	0.597801i	$-0.203959\pi$
$827$	46.1068	1.60329	0.801645	+	0.597801i	$0.203959\pi$
$828$	−0.571974	−0.0198775
$829$	−28.3620	−0.985053	−0.492527	−	0.870297i	$-0.663927\pi$
$829$	−28.3620	−0.985053	−0.492527	+	0.870297i	$0.663927\pi$
$830$	4.57377	0.158758
$831$	5.55622	0.192743
$832$	25.7025	0.891073
$833$	16.6398	0.576536
$834$	13.7616	0.476525
$835$	−21.1926	−0.733402
$836$	1.85717	0.0642316
$837$	−16.6070	−0.574022
$838$	−20.1111	−0.694726
$839$	−9.35324	−0.322910	−0.161455	−	0.986880i	$-0.551619\pi$
$839$	−9.35324	−0.322910	−0.161455	+	0.986880i	$0.551619\pi$
$840$	−3.05151	−0.105287
$841$	10.2085	0.352016
$842$	7.78758	0.268378
$843$	−13.8100	−0.475643
$844$	1.64002	0.0564518
$845$	4.65043	0.159980
$846$	−22.3209	−0.767407
$847$	8.28275	0.284599
$848$	31.7743	1.09113
$849$	4.13247	0.141826
$850$	3.95157	0.135538
$851$	1.10067	0.0377304
$852$	2.35129	0.0805538
$853$	−32.1489	−1.10076	−0.550379	−	0.834915i	$-0.685517\pi$
$853$	−32.1489	−1.10076	−0.550379	+	0.834915i	$0.685517\pi$
$854$	12.7763	0.437196
$855$	−5.23076	−0.178888
$856$	−44.1656	−1.50955
$857$	19.6666	0.671798	0.335899	−	0.941898i	$-0.390960\pi$
$857$	19.6666	0.671798	0.335899	+	0.941898i	$0.390960\pi$
$858$	6.10028	0.208260
$859$	−19.2575	−0.657058	−0.328529	−	0.944494i	$-0.606553\pi$
$859$	−19.2575	−0.657058	−0.328529	+	0.944494i	$0.606553\pi$
$860$	−0.636902	−0.0217182
$861$	7.40743	0.252445
$862$	−23.4073	−0.797256
$863$	14.4789	0.492867	0.246433	−	0.969160i	$-0.420741\pi$
$863$	14.4789	0.492867	0.246433	+	0.969160i	$0.420741\pi$
$864$	−9.27706	−0.315612
$865$	11.1311	0.378468
$866$	8.32866	0.283019
$867$	5.65168	0.191941
$868$	−2.02719	−0.0688072
$869$	−15.1914	−0.515334
$870$	6.17201	0.209251
$871$	−17.1318	−0.580489
$872$	26.5062	0.897614
$873$	−34.6144	−1.17152
$874$	−1.66560	−0.0563396
$875$	1.29163	0.0436649
$876$	1.57662	0.0532691
$877$	−3.50415	−0.118327	−0.0591633	−	0.998248i	$-0.518843\pi$
$877$	−3.50415	−0.118327	−0.0591633	+	0.998248i	$0.518843\pi$
$878$	24.0661	0.812190
$879$	11.7237	0.395431
$880$	6.52998	0.220126
$881$	−58.8288	−1.98199	−0.990997	−	0.133885i	$-0.957255\pi$
$881$	−58.8288	−1.98199	−0.990997	+	0.133885i	$0.957255\pi$
$882$	−16.1611	−0.544172
$883$	55.1700	1.85662	0.928308	−	0.371811i	$-0.121263\pi$
$883$	55.1700	1.85662	0.928308	+	0.371811i	$0.121263\pi$
$884$	3.57881	0.120368
$885$	6.86711	0.230835
$886$	6.18291	0.207719
$887$	25.6433	0.861018	0.430509	−	0.902586i	$-0.358334\pi$
$887$	25.6433	0.861018	0.430509	+	0.902586i	$0.358334\pi$
$888$	4.31916	0.144941
$889$	−0.553135	−0.0185516
$890$	18.6014	0.623520
$891$	8.38078	0.280767
$892$	−3.57500	−0.119700
$893$	16.0899	0.538428
$894$	0.393944	0.0131755
$895$	−14.4538	−0.483136
$896$	8.83963	0.295311
$897$	1.35431	0.0452190
$898$	−46.3776	−1.54764
$899$	24.7641	0.825930
$900$	0.950039	0.0316680
$901$	32.5258	1.08359
$902$	−19.9779	−0.665191
$903$	−1.61375	−0.0537021
$904$	−9.67919	−0.321925
$905$	2.00937	0.0667937
$906$	2.44018	0.0810695
$907$	14.4265	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$907$	14.4265	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$908$	−1.25912	−0.0417852
$909$	−3.56052	−0.118095
$910$	−4.72559	−0.156652
$911$	37.9505	1.25736	0.628678	−	0.777666i	$-0.283596\pi$
$911$	37.9505	1.25736	0.628678	+	0.777666i	$0.283596\pi$
$912$	−5.18595	−0.171724
$913$	7.73691	0.256054
$914$	−6.89842	−0.228179
$915$	6.08179	0.201058
$916$	−5.80962	−0.191955
$917$	−15.8824	−0.524484
$918$	16.5931	0.547654
$919$	−23.7158	−0.782312	−0.391156	−	0.920324i	$-0.627925\pi$
$919$	−23.7158	−0.782312	−0.391156	+	0.920324i	$0.627925\pi$
$920$	1.82710	0.0602378
$921$	10.4470	0.344241
$922$	−16.8791	−0.555885
$923$	21.9920	0.723875
$924$	−0.854655	−0.0281161
$925$	−1.82819	−0.0601105
$926$	−17.6996	−0.581645
$927$	3.82075	0.125490
$928$	13.8338	0.454118
$929$	57.3011	1.87999	0.939994	−	0.341192i	$-0.110831\pi$
$929$	57.3011	1.87999	0.939994	+	0.341192i	$0.110831\pi$
$930$	3.89826	0.127829
$931$	11.6497	0.381802
$932$	−9.70981	−0.318056
$933$	−10.7114	−0.350676
$934$	−4.28457	−0.140196
$935$	6.68441	0.218604
$936$	−20.9931	−0.686182
$937$	14.8503	0.485138	0.242569	−	0.970134i	$-0.422010\pi$
$937$	14.8503	0.485138	0.242569	+	0.970134i	$0.422010\pi$
$938$	−9.69605	−0.316587
$939$	6.38623	0.208407
$940$	−2.92234	−0.0953161
$941$	42.7664	1.39414	0.697072	−	0.717001i	$-0.254486\pi$
$941$	42.7664	1.39414	0.697072	+	0.717001i	$0.254486\pi$
$942$	−1.12207	−0.0365590
$943$	−4.43523	−0.144431
$944$	−26.8940	−0.875325
$945$	5.42368	0.176432
$946$	4.35228	0.141505
$947$	−13.3949	−0.435275	−0.217638	−	0.976030i	$-0.569835\pi$
$947$	−13.3949	−0.435275	−0.217638	+	0.976030i	$0.569835\pi$
$948$	−2.19125	−0.0711685
$949$	14.7464	0.478688
$950$	2.76652	0.0897579
$951$	−1.56695	−0.0508118
$952$	12.2334	0.396487
$953$	−57.1433	−1.85105	−0.925526	−	0.378684i	$-0.876377\pi$
$953$	−57.1433	−1.85105	−0.925526	+	0.378684i	$0.876377\pi$
$954$	−31.5900	−1.02276
$955$	−14.2876	−0.462336
$956$	−10.2646	−0.331982
$957$	10.4405	0.337493
$958$	−9.36474	−0.302561
$959$	−7.61495	−0.245900
$960$	6.92457	0.223489
$961$	−15.3589	−0.495449
$962$	6.68868	0.215652
$963$	34.8397	1.12269
$964$	−4.91722	−0.158373
$965$	7.76635	0.250008
$966$	0.766494	0.0246615
$967$	14.0562	0.452017	0.226009	−	0.974125i	$-0.427432\pi$
$967$	14.0562	0.452017	0.226009	+	0.974125i	$0.427432\pi$
$968$	−19.4610	−0.625501
$969$	−5.30859	−0.170537
$970$	18.3074	0.587815
$971$	15.5244	0.498202	0.249101	−	0.968477i	$-0.419865\pi$
$971$	15.5244	0.498202	0.249101	+	0.968477i	$0.419865\pi$
$972$	6.20809	0.199125
$973$	−18.0330	−0.578112
$974$	19.5363	0.625982
$975$	−2.24948	−0.0720409
$976$	−23.8184	−0.762409
$977$	9.40921	0.301027	0.150514	−	0.988608i	$-0.451907\pi$
$977$	9.40921	0.301027	0.150514	+	0.988608i	$0.451907\pi$
$978$	18.5252	0.592372
$979$	31.4658	1.00565
$980$	−2.11587	−0.0675891
$981$	−20.9092	−0.667579
$982$	13.5696	0.433024
$983$	49.4812	1.57821	0.789103	−	0.614261i	$-0.210546\pi$
$983$	49.4812	1.57821	0.789103	+	0.614261i	$0.210546\pi$
$984$	−17.4044	−0.554832
$985$	2.42119	0.0771457
$986$	−24.7434	−0.787991
$987$	−7.40445	−0.235686
$988$	2.50555	0.0797122
$989$	0.966237	0.0307246
$990$	−6.49210	−0.206333
$991$	15.4438	0.490588	0.245294	−	0.969449i	$-0.421116\pi$
$991$	15.4438	0.490588	0.245294	+	0.969449i	$0.421116\pi$
$992$	8.73748	0.277415
$993$	−26.8279	−0.851358
$994$	12.4468	0.394787
$995$	7.14994	0.226668
$996$	1.11599	0.0353615
$997$	−17.0770	−0.540834	−0.270417	−	0.962743i	$-0.587162\pi$
$997$	−17.0770	−0.540834	−0.270417	+	0.962743i	$0.587162\pi$
$998$	−2.91633	−0.0923148
$999$	−7.67678	−0.242883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.f.1.11	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.f.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-1.26616 q^{2} -0.778484 q^{3} -0.396848 q^{4} -1.00000 q^{5} +0.985683 q^{6} -1.29163 q^{7} +3.03478 q^{8} -2.39396 q^{9} +O(q^{10})\)	\(q-1.26616 q^{2} -0.778484 q^{3} -0.396848 q^{4} -1.00000 q^{5} +0.985683 q^{6} -1.29163 q^{7} +3.03478 q^{8} -2.39396 q^{9} +1.26616 q^{10} +2.14181 q^{11} +0.308940 q^{12} +2.88956 q^{13} +1.63540 q^{14} +0.778484 q^{15} -3.04882 q^{16} -3.12092 q^{17} +3.03113 q^{18} -2.18498 q^{19} +0.396848 q^{20} +1.00551 q^{21} -2.71186 q^{22} -0.602053 q^{23} -2.36253 q^{24} +1.00000 q^{25} -3.65864 q^{26} +4.19911 q^{27} +0.512579 q^{28} -6.26167 q^{29} -0.985683 q^{30} -3.95488 q^{31} -2.20929 q^{32} -1.66736 q^{33} +3.95157 q^{34} +1.29163 q^{35} +0.950039 q^{36} -1.82819 q^{37} +2.76652 q^{38} -2.24948 q^{39} -3.03478 q^{40} +7.36685 q^{41} -1.27313 q^{42} -1.60490 q^{43} -0.849972 q^{44} +2.39396 q^{45} +0.762294 q^{46} -7.36387 q^{47} +2.37345 q^{48} -5.33170 q^{49} -1.26616 q^{50} +2.42959 q^{51} -1.14672 q^{52} -10.4219 q^{53} -5.31674 q^{54} -2.14181 q^{55} -3.91980 q^{56} +1.70097 q^{57} +7.92825 q^{58} +8.82113 q^{59} -0.308940 q^{60} +7.81235 q^{61} +5.00750 q^{62} +3.09210 q^{63} +8.89494 q^{64} -2.88956 q^{65} +2.11114 q^{66} -5.92886 q^{67} +1.23853 q^{68} +0.468689 q^{69} -1.63540 q^{70} +7.61083 q^{71} -7.26516 q^{72} +5.10333 q^{73} +2.31477 q^{74} -0.778484 q^{75} +0.867104 q^{76} -2.76641 q^{77} +2.84819 q^{78} -7.09281 q^{79} +3.04882 q^{80} +3.91294 q^{81} -9.32758 q^{82} +3.61233 q^{83} -0.399034 q^{84} +3.12092 q^{85} +2.03206 q^{86} +4.87461 q^{87} +6.49993 q^{88} +14.6912 q^{89} -3.03113 q^{90} -3.73223 q^{91} +0.238924 q^{92} +3.07881 q^{93} +9.32381 q^{94} +2.18498 q^{95} +1.71990 q^{96} +14.4590 q^{97} +6.75077 q^{98} -5.12741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

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