LMFDB - Embedded newform 201.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1025428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 8x^{3} + 13x - 2 $ x^5 - 8x^3 + 13x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.44016$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44016 q^{2} +1.00000 q^{3} +3.95438 q^{4} +1.05143 q^{5} -2.44016 q^{6} +1.76320 q^{7} -4.76901 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.44016 q^{2} +1.00000 q^{3} +3.95438 q^{4} +1.05143 q^{5} -2.44016 q^{6} +1.76320 q^{7} -4.76901 q^{8} +1.00000 q^{9} -2.56565 q^{10} -2.32885 q^{11} +3.95438 q^{12} -0.328851 q^{13} -4.30249 q^{14} +1.05143 q^{15} +3.72839 q^{16} +2.48079 q^{17} -2.44016 q^{18} +7.05724 q^{19} +4.15775 q^{20} +1.76320 q^{21} +5.68277 q^{22} +1.67696 q^{23} -4.76901 q^{24} -3.89450 q^{25} +0.802450 q^{26} +1.00000 q^{27} +6.97237 q^{28} +6.53430 q^{29} -2.56565 q^{30} +5.34312 q^{31} +0.440161 q^{32} -2.32885 q^{33} -6.05352 q^{34} +1.85388 q^{35} +3.95438 q^{36} -7.37191 q^{37} -17.2208 q^{38} -0.328851 q^{39} -5.01427 q^{40} +4.15775 q^{41} -4.30249 q^{42} -8.22344 q^{43} -9.20917 q^{44} +1.05143 q^{45} -4.09205 q^{46} -7.05724 q^{47} +3.72839 q^{48} -3.89112 q^{49} +9.50321 q^{50} +2.48079 q^{51} -1.30040 q^{52} -11.9853 q^{53} -2.44016 q^{54} -2.44862 q^{55} -8.40873 q^{56} +7.05724 q^{57} -15.9447 q^{58} +7.35973 q^{59} +4.15775 q^{60} +3.02507 q^{61} -13.0381 q^{62} +1.76320 q^{63} -8.53084 q^{64} -0.345763 q^{65} +5.68277 q^{66} -1.00000 q^{67} +9.80998 q^{68} +1.67696 q^{69} -4.52376 q^{70} +9.66117 q^{71} -4.76901 q^{72} +8.40373 q^{73} +17.9886 q^{74} -3.89450 q^{75} +27.9070 q^{76} -4.10623 q^{77} +0.802450 q^{78} -14.5497 q^{79} +3.92013 q^{80} +1.00000 q^{81} -10.1456 q^{82} +1.22053 q^{83} +6.97237 q^{84} +2.60836 q^{85} +20.0665 q^{86} +6.53430 q^{87} +11.1063 q^{88} -14.4924 q^{89} -2.56565 q^{90} -0.579831 q^{91} +6.63134 q^{92} +5.34312 q^{93} +17.2208 q^{94} +7.42017 q^{95} +0.440161 q^{96} -8.91223 q^{97} +9.49497 q^{98} -2.32885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^3 + 6 * q^4 - 3 * q^5 + 7 * q^7 + 5 * q^9	$ 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9} - 3 q^{10} + 6 q^{12} + 10 q^{13} - 9 q^{14} - 3 q^{15} - 5 q^{17} + 5 q^{19} - 7 q^{20} + 7 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{25} - 4 q^{26} + 5 q^{27} - 3 q^{28} + 3 q^{29} - 3 q^{30} + 9 q^{31} - 10 q^{32} - 18 q^{34} - 7 q^{35} + 6 q^{36} + 8 q^{37} - 6 q^{38} + 10 q^{39} - 19 q^{40} - 7 q^{41} - 9 q^{42} + q^{43} - 10 q^{44} - 3 q^{45} - 7 q^{46} - 5 q^{47} + 8 q^{49} - 17 q^{50} - 5 q^{51} + 2 q^{52} - 15 q^{53} - 16 q^{55} - 19 q^{56} + 5 q^{57} - 4 q^{58} - 6 q^{59} - 7 q^{60} + 6 q^{61} - 13 q^{62} + 7 q^{63} - 16 q^{64} - 22 q^{65} - 4 q^{66} - 5 q^{67} - 4 q^{68} - 2 q^{69} + 19 q^{70} + 22 q^{71} + 51 q^{74} + 2 q^{75} + 24 q^{76} - 10 q^{77} - 4 q^{78} + 28 q^{79} + 31 q^{80} + 5 q^{81} - 25 q^{82} + 9 q^{83} - 3 q^{84} - 6 q^{85} + 45 q^{86} + 3 q^{87} + 36 q^{88} - 11 q^{89} - 3 q^{90} + 4 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} + 44 q^{95} - 10 q^{96} - 14 q^{97} + 33 q^{98}+O(q^{100}) $ 5 * q + 5 * q^3 + 6 * q^4 - 3 * q^5 + 7 * q^7 + 5 * q^9 - 3 * q^10 + 6 * q^12 + 10 * q^13 - 9 * q^14 - 3 * q^15 - 5 * q^17 + 5 * q^19 - 7 * q^20 + 7 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^25 - 4 * q^26 + 5 * q^27 - 3 * q^28 + 3 * q^29 - 3 * q^30 + 9 * q^31 - 10 * q^32 - 18 * q^34 - 7 * q^35 + 6 * q^36 + 8 * q^37 - 6 * q^38 + 10 * q^39 - 19 * q^40 - 7 * q^41 - 9 * q^42 + q^43 - 10 * q^44 - 3 * q^45 - 7 * q^46 - 5 * q^47 + 8 * q^49 - 17 * q^50 - 5 * q^51 + 2 * q^52 - 15 * q^53 - 16 * q^55 - 19 * q^56 + 5 * q^57 - 4 * q^58 - 6 * q^59 - 7 * q^60 + 6 * q^61 - 13 * q^62 + 7 * q^63 - 16 * q^64 - 22 * q^65 - 4 * q^66 - 5 * q^67 - 4 * q^68 - 2 * q^69 + 19 * q^70 + 22 * q^71 + 51 * q^74 + 2 * q^75 + 24 * q^76 - 10 * q^77 - 4 * q^78 + 28 * q^79 + 31 * q^80 + 5 * q^81 - 25 * q^82 + 9 * q^83 - 3 * q^84 - 6 * q^85 + 45 * q^86 + 3 * q^87 + 36 * q^88 - 11 * q^89 - 3 * q^90 + 4 * q^91 + 9 * q^92 + 9 * q^93 + 6 * q^94 + 44 * q^95 - 10 * q^96 - 14 * q^97 + 33 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.44016	−1.72545	−0.862727	−	0.505670i	$-0.831245\pi$
$2$	−2.44016	−1.72545	−0.862727	+	0.505670i	$0.831245\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.95438	1.97719
$5$	1.05143	0.470212	0.235106	−	0.971970i	$-0.424456\pi$
$5$	1.05143	0.470212	0.235106	+	0.971970i	$0.424456\pi$
$6$	−2.44016	−0.996191
$7$	1.76320	0.666427	0.333214	−	0.942851i	$-0.391867\pi$
$7$	1.76320	0.666427	0.333214	+	0.942851i	$0.391867\pi$
$8$	−4.76901	−1.68610
$9$	1.00000	0.333333
$10$	−2.56565	−0.811330
$11$	−2.32885	−0.702175	−0.351088	−	0.936343i	$-0.614188\pi$
$11$	−2.32885	−0.702175	−0.351088	+	0.936343i	$0.614188\pi$
$12$	3.95438	1.14153
$13$	−0.328851	−0.0912069	−0.0456035	−	0.998960i	$-0.514521\pi$
$13$	−0.328851	−0.0912069	−0.0456035	+	0.998960i	$0.514521\pi$
$14$	−4.30249	−1.14989
$15$	1.05143	0.271477
$16$	3.72839	0.932097
$17$	2.48079	0.601679	0.300839	−	0.953675i	$-0.402733\pi$
$17$	2.48079	0.601679	0.300839	+	0.953675i	$0.402733\pi$
$18$	−2.44016	−0.575151
$19$	7.05724	1.61904	0.809521	−	0.587091i	$-0.199727\pi$
$19$	7.05724	1.61904	0.809521	+	0.587091i	$0.199727\pi$
$20$	4.15775	0.929700
$21$	1.76320	0.384762
$22$	5.68277	1.21157
$23$	1.67696	0.349670	0.174835	−	0.984598i	$-0.444061\pi$
$23$	1.67696	0.349670	0.174835	+	0.984598i	$0.444061\pi$
$24$	−4.76901	−0.973470
$25$	−3.89450	−0.778900
$26$	0.802450	0.157373
$27$	1.00000	0.192450
$28$	6.97237	1.31765
$29$	6.53430	1.21339	0.606695	−	0.794935i	$-0.292495\pi$
$29$	6.53430	1.21339	0.606695	+	0.794935i	$0.292495\pi$
$30$	−2.56565	−0.468422
$31$	5.34312	0.959652	0.479826	−	0.877364i	$-0.340700\pi$
$31$	5.34312	0.959652	0.479826	+	0.877364i	$0.340700\pi$
$32$	0.440161	0.0778102
$33$	−2.32885	−0.405401
$34$	−6.05352	−1.03817
$35$	1.85388	0.313362
$36$	3.95438	0.659064
$37$	−7.37191	−1.21193	−0.605967	−	0.795490i	$-0.707214\pi$
$37$	−7.37191	−1.21193	−0.605967	+	0.795490i	$0.707214\pi$
$38$	−17.2208	−2.79358
$39$	−0.328851	−0.0526583
$40$	−5.01427	−0.792825
$41$	4.15775	0.649331	0.324665	−	0.945829i	$-0.394748\pi$
$41$	4.15775	0.649331	0.324665	+	0.945829i	$0.394748\pi$
$42$	−4.30249	−0.663889
$43$	−8.22344	−1.25406	−0.627031	−	0.778994i	$-0.715730\pi$
$43$	−8.22344	−1.25406	−0.627031	+	0.778994i	$0.715730\pi$
$44$	−9.20917	−1.38834
$45$	1.05143	0.156737
$46$	−4.09205	−0.603340
$47$	−7.05724	−1.02940	−0.514702	−	0.857369i	$-0.672097\pi$
$47$	−7.05724	−1.02940	−0.514702	+	0.857369i	$0.672097\pi$
$48$	3.72839	0.538146
$49$	−3.89112	−0.555875
$50$	9.50321	1.34396
$51$	2.48079	0.347379
$52$	−1.30040	−0.180334
$53$	−11.9853	−1.64630	−0.823151	−	0.567822i	$-0.807786\pi$
$53$	−11.9853	−1.64630	−0.823151	+	0.567822i	$0.807786\pi$
$54$	−2.44016	−0.332064
$55$	−2.44862	−0.330171
$56$	−8.40873	−1.12366
$57$	7.05724	0.934754
$58$	−15.9447	−2.09365
$59$	7.35973	0.958155	0.479078	−	0.877773i	$-0.340971\pi$
$59$	7.35973	0.958155	0.479078	+	0.877773i	$0.340971\pi$
$60$	4.15775	0.536763
$61$	3.02507	0.387320	0.193660	−	0.981069i	$-0.437964\pi$
$61$	3.02507	0.387320	0.193660	+	0.981069i	$0.437964\pi$
$62$	−13.0381	−1.65584
$63$	1.76320	0.222142
$64$	−8.53084	−1.06635
$65$	−0.345763	−0.0428866
$66$	5.68277	0.699501
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	9.80998	1.18963
$69$	1.67696	0.201882
$70$	−4.52376	−0.540692
$71$	9.66117	1.14657	0.573285	−	0.819356i	$-0.305669\pi$
$71$	9.66117	1.14657	0.573285	+	0.819356i	$0.305669\pi$
$72$	−4.76901	−0.562033
$73$	8.40373	0.983583	0.491791	−	0.870713i	$-0.336342\pi$
$73$	8.40373	0.983583	0.491791	+	0.870713i	$0.336342\pi$
$74$	17.9886	2.09114
$75$	−3.89450	−0.449698
$76$	27.9070	3.20116
$77$	−4.10623	−0.467949
$78$	0.802450	0.0908595
$79$	−14.5497	−1.63697	−0.818486	−	0.574526i	$-0.805186\pi$
$79$	−14.5497	−1.63697	−0.818486	+	0.574526i	$0.805186\pi$
$80$	3.92013	0.438283
$81$	1.00000	0.111111
$82$	−10.1456	−1.12039
$83$	1.22053	0.133971	0.0669853	−	0.997754i	$-0.478662\pi$
$83$	1.22053	0.133971	0.0669853	+	0.997754i	$0.478662\pi$
$84$	6.97237	0.760748
$85$	2.60836	0.282917
$86$	20.0665	2.16383
$87$	6.53430	0.700551
$88$	11.1063	1.18394
$89$	−14.4924	−1.53619	−0.768096	−	0.640335i	$-0.778796\pi$
$89$	−14.4924	−1.53619	−0.768096	+	0.640335i	$0.778796\pi$
$90$	−2.56565	−0.270443
$91$	−0.579831	−0.0607828
$92$	6.63134	0.691365
$93$	5.34312	0.554056
$94$	17.2208	1.77619
$95$	7.42017	0.761293
$96$	0.440161	0.0449237
$97$	−8.91223	−0.904900	−0.452450	−	0.891790i	$-0.649450\pi$
$97$	−8.91223	−0.904900	−0.452450	+	0.891790i	$0.649450\pi$
$98$	9.49497	0.959136
$99$	−2.32885	−0.234058
$100$	−15.4004	−1.54004
$101$	−0.123144	−0.0122533	−0.00612664	−	0.999981i	$-0.501950\pi$
$101$	−0.123144	−0.0122533	−0.00612664	+	0.999981i	$0.501950\pi$
$102$	−6.05352	−0.599387
$103$	7.18064	0.707529	0.353765	−	0.935334i	$-0.384901\pi$
$103$	7.18064	0.707529	0.353765	+	0.935334i	$0.384901\pi$
$104$	1.56830	0.153784
$105$	1.85388	0.180920
$106$	29.2460	2.84062
$107$	−19.0405	−1.84071	−0.920357	−	0.391079i	$-0.872102\pi$
$107$	−19.0405	−1.84071	−0.920357	+	0.391079i	$0.872102\pi$
$108$	3.95438	0.380511
$109$	−13.0963	−1.25440	−0.627201	−	0.778858i	$-0.715799\pi$
$109$	−13.0963	−1.25440	−0.627201	+	0.778858i	$0.715799\pi$
$110$	5.97502	0.569696
$111$	−7.37191	−0.699711
$112$	6.57389	0.621175
$113$	−13.2661	−1.24797	−0.623983	−	0.781438i	$-0.714487\pi$
$113$	−13.2661	−1.24797	−0.623983	+	0.781438i	$0.714487\pi$
$114$	−17.2208	−1.61288
$115$	1.76320	0.164419
$116$	25.8391	2.39910
$117$	−0.328851	−0.0304023
$118$	−17.9589	−1.65325
$119$	4.37412	0.400975
$120$	−5.01427	−0.457738
$121$	−5.57645	−0.506950
$122$	−7.38165	−0.668304
$123$	4.15775	0.374891
$124$	21.1287	1.89742
$125$	−9.35192	−0.836461
$126$	−4.30249	−0.383297
$127$	20.9033	1.85487	0.927434	−	0.373986i	$-0.122009\pi$
$127$	20.9033	1.85487	0.927434	+	0.373986i	$0.122009\pi$
$128$	19.9363	1.76214
$129$	−8.22344	−0.724033
$130$	0.843717	0.0739989
$131$	−0.280890	−0.0245414	−0.0122707	−	0.999925i	$-0.503906\pi$
$131$	−0.280890	−0.0245414	−0.0122707	+	0.999925i	$0.503906\pi$
$132$	−9.20917	−0.801556
$133$	12.4433	1.07897
$134$	2.44016	0.210798
$135$	1.05143	0.0904924
$136$	−11.8309	−1.01449
$137$	9.09496	0.777035	0.388518	−	0.921441i	$-0.372987\pi$
$137$	9.09496	0.777035	0.388518	+	0.921441i	$0.372987\pi$
$138$	−4.09205	−0.348339
$139$	−6.04271	−0.512536	−0.256268	−	0.966606i	$-0.582493\pi$
$139$	−6.04271	−0.512536	−0.256268	+	0.966606i	$0.582493\pi$
$140$	7.33094	0.619578
$141$	−7.05724	−0.594327
$142$	−23.5748	−1.97835
$143$	0.765845	0.0640432
$144$	3.72839	0.310699
$145$	6.87034	0.570551
$146$	−20.5065	−1.69713
$147$	−3.89112	−0.320934
$148$	−29.1514	−2.39623
$149$	−8.52737	−0.698589	−0.349295	−	0.937013i	$-0.613579\pi$
$149$	−8.52737	−0.698589	−0.349295	+	0.937013i	$0.613579\pi$
$150$	9.50321	0.775934
$151$	18.5309	1.50803	0.754013	−	0.656860i	$-0.228116\pi$
$151$	18.5309	1.50803	0.754013	+	0.656860i	$0.228116\pi$
$152$	−33.6561	−2.72987
$153$	2.48079	0.200560
$154$	10.0199	0.807424
$155$	5.61790	0.451240
$156$	−1.30040	−0.104116
$157$	−5.33255	−0.425584	−0.212792	−	0.977098i	$-0.568256\pi$
$157$	−5.33255	−0.425584	−0.212792	+	0.977098i	$0.568256\pi$
$158$	35.5037	2.82452
$159$	−11.9853	−0.950493
$160$	0.462797	0.0365873
$161$	2.95682	0.233030
$162$	−2.44016	−0.191717
$163$	−7.32919	−0.574067	−0.287033	−	0.957921i	$-0.592669\pi$
$163$	−7.32919	−0.574067	−0.287033	+	0.957921i	$0.592669\pi$
$164$	16.4413	1.28385
$165$	−2.44862	−0.190625
$166$	−2.97829	−0.231160
$167$	−0.800447	−0.0619405	−0.0309702	−	0.999520i	$-0.509860\pi$
$167$	−0.800447	−0.0619405	−0.0309702	+	0.999520i	$0.509860\pi$
$168$	−8.40873	−0.648747
$169$	−12.8919	−0.991681
$170$	−6.36483	−0.488160
$171$	7.05724	0.539680
$172$	−32.5186	−2.47952
$173$	−9.88742	−0.751727	−0.375863	−	0.926675i	$-0.622654\pi$
$173$	−9.88742	−0.751727	−0.375863	+	0.926675i	$0.622654\pi$
$174$	−15.9447	−1.20877
$175$	−6.86679	−0.519080
$176$	−8.68286	−0.654495
$177$	7.35973	0.553191
$178$	35.3638	2.65063
$179$	14.4886	1.08293	0.541464	−	0.840724i	$-0.317870\pi$
$179$	14.4886	1.08293	0.541464	+	0.840724i	$0.317870\pi$
$180$	4.15775	0.309900
$181$	14.4579	1.07465	0.537325	−	0.843375i	$-0.319435\pi$
$181$	14.4579	1.07465	0.537325	+	0.843375i	$0.319435\pi$
$182$	1.41488	0.104878
$183$	3.02507	0.223620
$184$	−7.99744	−0.589579
$185$	−7.75102	−0.569867
$186$	−13.0381	−0.955997
$187$	−5.77738	−0.422484
$188$	−27.9070	−2.03533
$189$	1.76320	0.128254
$190$	−18.1064	−1.31358
$191$	−5.21673	−0.377469	−0.188735	−	0.982028i	$-0.560439\pi$
$191$	−5.21673	−0.377469	−0.188735	+	0.982028i	$0.560439\pi$
$192$	−8.53084	−0.615660
$193$	0.689225	0.0496115	0.0248057	−	0.999692i	$-0.492103\pi$
$193$	0.689225	0.0496115	0.0248057	+	0.999692i	$0.492103\pi$
$194$	21.7473	1.56136
$195$	−0.345763	−0.0247606
$196$	−15.3870	−1.09907
$197$	−11.3060	−0.805516	−0.402758	−	0.915306i	$-0.631948\pi$
$197$	−11.3060	−0.805516	−0.402758	+	0.915306i	$0.631948\pi$
$198$	5.68277	0.403857
$199$	1.97945	0.140320	0.0701599	−	0.997536i	$-0.477649\pi$
$199$	1.97945	0.140320	0.0701599	+	0.997536i	$0.477649\pi$
$200$	18.5729	1.31330
$201$	−1.00000	−0.0705346
$202$	0.300491	0.0211425
$203$	11.5213	0.808636
$204$	9.80998	0.686836
$205$	4.37157	0.305323
$206$	−17.5219	−1.22081
$207$	1.67696	0.116557
$208$	−1.22608	−0.0850137
$209$	−16.4353	−1.13685
$210$	−4.52376	−0.312169
$211$	22.0761	1.51978	0.759892	−	0.650049i	$-0.225252\pi$
$211$	22.0761	1.51978	0.759892	+	0.650049i	$0.225252\pi$
$212$	−47.3943	−3.25506
$213$	9.66117	0.661972
$214$	46.4619	3.17607
$215$	−8.64635	−0.589676
$216$	−4.76901	−0.324490
$217$	9.42099	0.639538
$218$	31.9572	2.16441
$219$	8.40373	0.567872
$220$	−9.68277	−0.652812
$221$	−0.815809	−0.0548773
$222$	17.9886	1.20732
$223$	19.7928	1.32542	0.662712	−	0.748874i	$-0.269405\pi$
$223$	19.7928	1.32542	0.662712	+	0.748874i	$0.269405\pi$
$224$	0.776092	0.0518548
$225$	−3.89450	−0.259633
$226$	32.3713	2.15331
$227$	10.8978	0.723309	0.361655	−	0.932312i	$-0.382212\pi$
$227$	10.8978	0.723309	0.361655	+	0.932312i	$0.382212\pi$
$228$	27.9070	1.84819
$229$	16.2802	1.07583	0.537913	−	0.843000i	$-0.319213\pi$
$229$	16.2802	1.07583	0.537913	+	0.843000i	$0.319213\pi$
$230$	−4.30249	−0.283698
$231$	−4.10623	−0.270170
$232$	−31.1622	−2.04590
$233$	−8.10423	−0.530926	−0.265463	−	0.964121i	$-0.585525\pi$
$233$	−8.10423	−0.530926	−0.265463	+	0.964121i	$0.585525\pi$
$234$	0.802450	0.0524578
$235$	−7.42017	−0.484038
$236$	29.1032	1.89446
$237$	−14.5497	−0.945107
$238$	−10.6736	−0.691864
$239$	6.55485	0.423998	0.211999	−	0.977270i	$-0.432003\pi$
$239$	6.55485	0.423998	0.211999	+	0.977270i	$0.432003\pi$
$240$	3.92013	0.253043
$241$	3.79955	0.244750	0.122375	−	0.992484i	$-0.460949\pi$
$241$	3.79955	0.244750	0.122375	+	0.992484i	$0.460949\pi$
$242$	13.6074	0.874719
$243$	1.00000	0.0641500
$244$	11.9623	0.765807
$245$	−4.09123	−0.261379
$246$	−10.1456	−0.646858
$247$	−2.32078	−0.147668
$248$	−25.4814	−1.61807
$249$	1.22053	0.0773479
$250$	22.8202	1.44328
$251$	−10.0074	−0.631664	−0.315832	−	0.948815i	$-0.602284\pi$
$251$	−10.0074	−0.631664	−0.315832	+	0.948815i	$0.602284\pi$
$252$	6.97237	0.439218
$253$	−3.90539	−0.245530
$254$	−51.0074	−3.20049
$255$	2.60836	0.163342
$256$	−31.5861	−1.97413
$257$	29.4279	1.83566	0.917831	−	0.396972i	$-0.129939\pi$
$257$	29.4279	1.83566	0.917831	+	0.396972i	$0.129939\pi$
$258$	20.0665	1.24929
$259$	−12.9982	−0.807666
$260$	−1.36728	−0.0847951
$261$	6.53430	0.404463
$262$	0.685416	0.0423451
$263$	−5.62145	−0.346633	−0.173317	−	0.984866i	$-0.555448\pi$
$263$	−5.62145	−0.346633	−0.173317	+	0.984866i	$0.555448\pi$
$264$	11.1063	0.683547
$265$	−12.6016	−0.774112
$266$	−30.3637	−1.86172
$267$	−14.4924	−0.886921
$268$	−3.95438	−0.241552
$269$	−7.66117	−0.467110	−0.233555	−	0.972344i	$-0.575036\pi$
$269$	−7.66117	−0.467110	−0.233555	+	0.972344i	$0.575036\pi$
$270$	−2.56565	−0.156141
$271$	−18.2459	−1.10836	−0.554179	−	0.832398i	$-0.686968\pi$
$271$	−18.2459	−1.10836	−0.554179	+	0.832398i	$0.686968\pi$
$272$	9.24933	0.560823
$273$	−0.579831	−0.0350929
$274$	−22.1932	−1.34074
$275$	9.06971	0.546924
$276$	6.63134	0.399160
$277$	22.1496	1.33084	0.665421	−	0.746468i	$-0.268252\pi$
$277$	22.1496	1.33084	0.665421	+	0.746468i	$0.268252\pi$
$278$	14.7452	0.884358
$279$	5.34312	0.319884
$280$	−8.84116	−0.528360
$281$	−18.5004	−1.10364	−0.551821	−	0.833963i	$-0.686067\pi$
$281$	−18.5004	−1.10364	−0.551821	+	0.833963i	$0.686067\pi$
$282$	17.2208	1.02548
$283$	−20.3227	−1.20806	−0.604029	−	0.796962i	$-0.706439\pi$
$283$	−20.3227	−1.20806	−0.604029	+	0.796962i	$0.706439\pi$
$284$	38.2040	2.26699
$285$	7.42017	0.439533
$286$	−1.86879	−0.110504
$287$	7.33094	0.432732
$288$	0.440161	0.0259367
$289$	−10.8457	−0.637982
$290$	−16.7647	−0.984459
$291$	−8.91223	−0.522444
$292$	33.2316	1.94473
$293$	28.8692	1.68656	0.843279	−	0.537476i	$-0.180622\pi$
$293$	28.8692	1.68656	0.843279	+	0.537476i	$0.180622\pi$
$294$	9.49497	0.553758
$295$	7.73822	0.450537
$296$	35.1567	2.04344
$297$	−2.32885	−0.135134
$298$	20.8082	1.20538
$299$	−0.551470	−0.0318923
$300$	−15.4004	−0.889140
$301$	−14.4996	−0.835742
$302$	−45.2184	−2.60203
$303$	−0.123144	−0.00707443
$304$	26.3121	1.50910
$305$	3.18064	0.182123
$306$	−6.05352	−0.346056
$307$	5.34611	0.305118	0.152559	−	0.988294i	$-0.451249\pi$
$307$	5.34611	0.305118	0.152559	+	0.988294i	$0.451249\pi$
$308$	−16.2376	−0.925224
$309$	7.18064	0.408492
$310$	−13.7086	−0.778595
$311$	22.0610	1.25096	0.625481	−	0.780239i	$-0.284903\pi$
$311$	22.0610	1.25096	0.625481	+	0.780239i	$0.284903\pi$
$312$	1.56830	0.0887872
$313$	−24.8090	−1.40229	−0.701143	−	0.713021i	$-0.747326\pi$
$313$	−24.8090	−1.40229	−0.701143	+	0.713021i	$0.747326\pi$
$314$	13.0123	0.734326
$315$	1.85388	0.104454
$316$	−57.5352	−3.23661
$317$	−8.94546	−0.502427	−0.251214	−	0.967932i	$-0.580830\pi$
$317$	−8.94546	−0.502427	−0.251214	+	0.967932i	$0.580830\pi$
$318$	29.2460	1.64003
$319$	−15.2174	−0.852012
$320$	−8.96955	−0.501413
$321$	−19.0405	−1.06274
$322$	−7.21511	−0.402082
$323$	17.5075	0.974143
$324$	3.95438	0.219688
$325$	1.28071	0.0710411
$326$	17.8844	0.990526
$327$	−13.0963	−0.724229
$328$	−19.8283	−1.09484
$329$	−12.4433	−0.686023
$330$	5.97502	0.328914
$331$	9.83832	0.540763	0.270381	−	0.962753i	$-0.412850\pi$
$331$	9.83832	0.540763	0.270381	+	0.962753i	$0.412850\pi$
$332$	4.82644	0.264886
$333$	−7.37191	−0.403978
$334$	1.95322	0.106875
$335$	−1.05143	−0.0574456
$336$	6.57389	0.358635
$337$	8.99142	0.489794	0.244897	−	0.969549i	$-0.421246\pi$
$337$	8.99142	0.489794	0.244897	+	0.969549i	$0.421246\pi$
$338$	31.4582	1.71110
$339$	−13.2661	−0.720514
$340$	10.3145	0.559381
$341$	−12.4433	−0.673844
$342$	−17.2208	−0.931194
$343$	−19.2032	−1.03688
$344$	39.2177	2.11448
$345$	1.76320	0.0949275
$346$	24.1269	1.29707
$347$	−16.7791	−0.900750	−0.450375	−	0.892840i	$-0.648710\pi$
$347$	−16.7791	−0.900750	−0.450375	+	0.892840i	$0.648710\pi$
$348$	25.8391	1.38512
$349$	6.58594	0.352537	0.176269	−	0.984342i	$-0.443597\pi$
$349$	6.58594	0.352537	0.176269	+	0.984342i	$0.443597\pi$
$350$	16.7561	0.895649
$351$	−0.328851	−0.0175528
$352$	−1.02507	−0.0546364
$353$	−33.2588	−1.77019	−0.885093	−	0.465414i	$-0.845905\pi$
$353$	−33.2588	−1.77019	−0.885093	+	0.465414i	$0.845905\pi$
$354$	−17.9589	−0.954506
$355$	10.1580	0.539131
$356$	−57.3086	−3.03735
$357$	4.37412	0.231503
$358$	−35.3545	−1.86854
$359$	34.6385	1.82815	0.914076	−	0.405543i	$-0.132918\pi$
$359$	34.6385	1.82815	0.914076	+	0.405543i	$0.132918\pi$
$360$	−5.01427	−0.264275
$361$	30.8046	1.62130
$362$	−35.2797	−1.85426
$363$	−5.57645	−0.292688
$364$	−2.29287	−0.120179
$365$	8.83591	0.462493
$366$	−7.38165	−0.385845
$367$	35.4702	1.85153	0.925765	−	0.378099i	$-0.123422\pi$
$367$	35.4702	1.85153	0.925765	+	0.378099i	$0.123422\pi$
$368$	6.25236	0.325927
$369$	4.15775	0.216444
$370$	18.9137	0.983279
$371$	−21.1324	−1.09714
$372$	21.1287	1.09547
$373$	5.98647	0.309967	0.154984	−	0.987917i	$-0.450467\pi$
$373$	5.98647	0.309967	0.154984	+	0.987917i	$0.450467\pi$
$374$	14.0977	0.728977
$375$	−9.35192	−0.482931
$376$	33.6561	1.73568
$377$	−2.14881	−0.110669
$378$	−4.30249	−0.221296
$379$	9.79918	0.503350	0.251675	−	0.967812i	$-0.419019\pi$
$379$	9.79918	0.503350	0.251675	+	0.967812i	$0.419019\pi$
$380$	29.3422	1.50522
$381$	20.9033	1.07091
$382$	12.7297	0.651306
$383$	33.4201	1.70769	0.853843	−	0.520531i	$-0.174266\pi$
$383$	33.4201	1.70769	0.853843	+	0.520531i	$0.174266\pi$
$384$	19.9363	1.01737
$385$	−4.31740	−0.220035
$386$	−1.68182	−0.0856023
$387$	−8.22344	−0.418021
$388$	−35.2424	−1.78916
$389$	−24.9171	−1.26335	−0.631674	−	0.775235i	$-0.717632\pi$
$389$	−24.9171	−1.26335	−0.631674	+	0.775235i	$0.717632\pi$
$390$	0.843717	0.0427233
$391$	4.16018	0.210389
$392$	18.5568	0.937261
$393$	−0.280890	−0.0141690
$394$	27.5884	1.38988
$395$	−15.2980	−0.769725
$396$	−9.20917	−0.462778
$397$	31.1704	1.56440	0.782199	−	0.623029i	$-0.214098\pi$
$397$	31.1704	1.56440	0.782199	+	0.623029i	$0.214098\pi$
$398$	−4.83018	−0.242115
$399$	12.4433	0.622946
$400$	−14.5202	−0.726010
$401$	−3.62145	−0.180847	−0.0904233	−	0.995903i	$-0.528822\pi$
$401$	−3.62145	−0.180847	−0.0904233	+	0.995903i	$0.528822\pi$
$402$	2.44016	0.121704
$403$	−1.75709	−0.0875269
$404$	−0.486958	−0.0242271
$405$	1.05143	0.0522458
$406$	−28.1138	−1.39526
$407$	17.1681	0.850990
$408$	−11.8309	−0.585717
$409$	−2.93997	−0.145372	−0.0726860	−	0.997355i	$-0.523157\pi$
$409$	−2.93997	−0.145372	−0.0726860	+	0.997355i	$0.523157\pi$
$410$	−10.6673	−0.526821
$411$	9.09496	0.448621
$412$	28.3950	1.39892
$413$	12.9767	0.638541
$414$	−4.09205	−0.201113
$415$	1.28330	0.0629946
$416$	−0.144747	−0.00709682
$417$	−6.04271	−0.295913
$418$	40.1047	1.96158
$419$	−1.65536	−0.0808695	−0.0404347	−	0.999182i	$-0.512874\pi$
$419$	−1.65536	−0.0808695	−0.0404347	+	0.999182i	$0.512874\pi$
$420$	7.33094	0.357713
$421$	−10.1195	−0.493196	−0.246598	−	0.969118i	$-0.579313\pi$
$421$	−10.1195	−0.493196	−0.246598	+	0.969118i	$0.579313\pi$
$422$	−53.8693	−2.62232
$423$	−7.05724	−0.343135
$424$	57.1579	2.77583
$425$	−9.66142	−0.468648
$426$	−23.5748	−1.14220
$427$	5.33380	0.258121
$428$	−75.2935	−3.63945
$429$	0.765845	0.0369754
$430$	21.0985	1.01746
$431$	15.7147	0.756949	0.378475	−	0.925612i	$-0.376449\pi$
$431$	15.7147	0.756949	0.378475	+	0.925612i	$0.376449\pi$
$432$	3.72839	0.179382
$433$	−3.17239	−0.152456	−0.0762278	−	0.997090i	$-0.524288\pi$
$433$	−3.17239	−0.152456	−0.0762278	+	0.997090i	$0.524288\pi$
$434$	−22.9887	−1.10349
$435$	6.87034	0.329408
$436$	−51.7880	−2.48019
$437$	11.8347	0.566131
$438$	−20.5065	−0.979837
$439$	−25.6721	−1.22526	−0.612631	−	0.790369i	$-0.709889\pi$
$439$	−25.6721	−1.22526	−0.612631	+	0.790369i	$0.709889\pi$
$440$	11.6775	0.556702
$441$	−3.89112	−0.185292
$442$	1.99071	0.0946882
$443$	−34.5195	−1.64007	−0.820035	−	0.572314i	$-0.806046\pi$
$443$	−34.5195	−1.64007	−0.820035	+	0.572314i	$0.806046\pi$
$444$	−29.1514	−1.38346
$445$	−15.2377	−0.722337
$446$	−48.2976	−2.28696
$447$	−8.52737	−0.403331
$448$	−15.0416	−0.710648
$449$	36.3501	1.71547	0.857734	−	0.514094i	$-0.171872\pi$
$449$	36.3501	1.71547	0.857734	+	0.514094i	$0.171872\pi$
$450$	9.50321	0.447986
$451$	−9.68277	−0.455944
$452$	−52.4591	−2.46747
$453$	18.5309	0.870659
$454$	−26.5923	−1.24804
$455$	−0.609649	−0.0285808
$456$	−33.6561	−1.57609
$457$	10.3502	0.484162	0.242081	−	0.970256i	$-0.422170\pi$
$457$	10.3502	0.484162	0.242081	+	0.970256i	$0.422170\pi$
$458$	−39.7263	−1.85629
$459$	2.48079	0.115793
$460$	6.97237	0.325089
$461$	8.96939	0.417746	0.208873	−	0.977943i	$-0.433020\pi$
$461$	8.96939	0.417746	0.208873	+	0.977943i	$0.433020\pi$
$462$	10.0199	0.466166
$463$	−6.12702	−0.284747	−0.142373	−	0.989813i	$-0.545473\pi$
$463$	−6.12702	−0.284747	−0.142373	+	0.989813i	$0.545473\pi$
$464$	24.3624	1.13100
$465$	5.61790	0.260524
$466$	19.7756	0.916088
$467$	−17.0699	−0.789902	−0.394951	−	0.918702i	$-0.629238\pi$
$467$	−17.0699	−0.789902	−0.394951	+	0.918702i	$0.629238\pi$
$468$	−1.30040	−0.0601112
$469$	−1.76320	−0.0814170
$470$	18.1064	0.835186
$471$	−5.33255	−0.245711
$472$	−35.0986	−1.61555
$473$	19.1512	0.880572
$474$	35.5037	1.63074
$475$	−27.4844	−1.26107
$476$	17.2970	0.792805
$477$	−11.9853	−0.548768
$478$	−15.9949	−0.731589
$479$	26.9937	1.23337	0.616686	−	0.787209i	$-0.288475\pi$
$479$	26.9937	1.23337	0.616686	+	0.787209i	$0.288475\pi$
$480$	0.462797	0.0211237
$481$	2.42426	0.110537
$482$	−9.27151	−0.422306
$483$	2.95682	0.134540
$484$	−22.0514	−1.00234
$485$	−9.37056	−0.425495
$486$	−2.44016	−0.110688
$487$	−2.83823	−0.128613	−0.0643063	−	0.997930i	$-0.520483\pi$
$487$	−2.83823	−0.128613	−0.0643063	+	0.997930i	$0.520483\pi$
$488$	−14.4266	−0.653061
$489$	−7.32919	−0.331438
$490$	9.98326	0.450998
$491$	−18.5439	−0.836875	−0.418438	−	0.908245i	$-0.637422\pi$
$491$	−18.5439	−0.836875	−0.418438	+	0.908245i	$0.637422\pi$
$492$	16.4413	0.741232
$493$	16.2102	0.730071
$494$	5.66308	0.254794
$495$	−2.44862	−0.110057
$496$	19.9212	0.894489
$497$	17.0346	0.764105
$498$	−2.97829	−0.133460
$499$	−22.7898	−1.02021	−0.510105	−	0.860112i	$-0.670394\pi$
$499$	−22.7898	−1.02021	−0.510105	+	0.860112i	$0.670394\pi$
$500$	−36.9811	−1.65384
$501$	−0.800447	−0.0357614
$502$	24.4198	1.08991
$503$	13.5031	0.602072	0.301036	−	0.953613i	$-0.402668\pi$
$503$	13.5031	0.602072	0.301036	+	0.953613i	$0.402668\pi$
$504$	−8.40873	−0.374554
$505$	−0.129477	−0.00576164
$506$	9.52978	0.423650
$507$	−12.8919	−0.572547
$508$	82.6597	3.66743
$509$	−29.0238	−1.28646	−0.643228	−	0.765675i	$-0.722405\pi$
$509$	−29.0238	−1.28646	−0.643228	+	0.765675i	$0.722405\pi$
$510$	−6.36483	−0.281839
$511$	14.8175	0.655486
$512$	37.2025	1.64414
$513$	7.05724	0.311585
$514$	−71.8088	−3.16735
$515$	7.54992	0.332689
$516$	−32.5186	−1.43155
$517$	16.4353	0.722822
$518$	31.7176	1.39359
$519$	−9.88742	−0.434010
$520$	1.64895	0.0723111
$521$	16.3932	0.718199	0.359099	−	0.933299i	$-0.383084\pi$
$521$	16.3932	0.718199	0.359099	+	0.933299i	$0.383084\pi$
$522$	−15.9447	−0.697883
$523$	14.8620	0.649872	0.324936	−	0.945736i	$-0.394657\pi$
$523$	14.8620	0.649872	0.324936	+	0.945736i	$0.394657\pi$
$524$	−1.11075	−0.0485231
$525$	−6.86679	−0.299691
$526$	13.7172	0.598100
$527$	13.2551	0.577403
$528$	−8.68286	−0.377873
$529$	−20.1878	−0.877731
$530$	30.7500	1.33569
$531$	7.35973	0.319385
$532$	49.2057	2.13334
$533$	−1.36728	−0.0592235
$534$	35.3638	1.53034
$535$	−20.0197	−0.865527
$536$	4.76901	0.205990
$537$	14.4886	0.625229
$538$	18.6945	0.805976
$539$	9.06185	0.390321
$540$	4.15775	0.178921
$541$	10.3782	0.446193	0.223097	−	0.974796i	$-0.428383\pi$
$541$	10.3782	0.446193	0.223097	+	0.974796i	$0.428383\pi$
$542$	44.5228	1.91242
$543$	14.4579	0.620449
$544$	1.09194	0.0468167
$545$	−13.7698	−0.589835
$546$	1.41488	0.0605513
$547$	−25.6356	−1.09610	−0.548049	−	0.836446i	$-0.684629\pi$
$547$	−25.6356	−1.09610	−0.548049	+	0.836446i	$0.684629\pi$
$548$	35.9650	1.53635
$549$	3.02507	0.129107
$550$	−22.1316	−0.943693
$551$	46.1141	1.96453
$552$	−7.99744	−0.340394
$553$	−25.6541	−1.09092
$554$	−54.0487	−2.29631
$555$	−7.75102	−0.329013
$556$	−23.8952	−1.01338
$557$	−24.0294	−1.01816	−0.509079	−	0.860720i	$-0.670014\pi$
$557$	−24.0294	−1.01816	−0.509079	+	0.860720i	$0.670014\pi$
$558$	−13.0381	−0.551945
$559$	2.70429	0.114379
$560$	6.91197	0.292084
$561$	−5.77738	−0.243921
$562$	45.1439	1.90428
$563$	−5.45546	−0.229920	−0.114960	−	0.993370i	$-0.536674\pi$
$563$	−5.45546	−0.229920	−0.114960	+	0.993370i	$0.536674\pi$
$564$	−27.9070	−1.17510
$565$	−13.9483	−0.586809
$566$	49.5906	2.08445
$567$	1.76320	0.0740475
$568$	−46.0742	−1.93323
$569$	18.4381	0.772963	0.386482	−	0.922297i	$-0.373690\pi$
$569$	18.4381	0.772963	0.386482	+	0.922297i	$0.373690\pi$
$570$	−18.1064	−0.758394
$571$	−26.8110	−1.12200	−0.561002	−	0.827815i	$-0.689584\pi$
$571$	−26.8110	−1.12200	−0.561002	+	0.827815i	$0.689584\pi$
$572$	3.02845	0.126626
$573$	−5.21673	−0.217932
$574$	−17.8887	−0.746659
$575$	−6.53092	−0.272358
$576$	−8.53084	−0.355452
$577$	24.8397	1.03409	0.517046	−	0.855958i	$-0.327032\pi$
$577$	24.8397	1.03409	0.517046	+	0.855958i	$0.327032\pi$
$578$	26.4653	1.10081
$579$	0.689225	0.0286432
$580$	27.1680	1.12809
$581$	2.15204	0.0892816
$582$	21.7473	0.901454
$583$	27.9119	1.15599
$584$	−40.0775	−1.65842
$585$	−0.345763	−0.0142955
$586$	−70.4456	−2.91008
$587$	3.87461	0.159922	0.0799610	−	0.996798i	$-0.474520\pi$
$587$	3.87461	0.159922	0.0799610	+	0.996798i	$0.474520\pi$
$588$	−15.3870	−0.634549
$589$	37.7077	1.55372
$590$	−18.8825	−0.777380
$591$	−11.3060	−0.465065
$592$	−27.4853	−1.12964
$593$	47.5525	1.95275	0.976374	−	0.216089i	$-0.0693300\pi$
$593$	47.5525	1.95275	0.976374	+	0.216089i	$0.0693300\pi$
$594$	5.68277	0.233167
$595$	4.59907	0.188544
$596$	−33.7205	−1.38125
$597$	1.97945	0.0810136
$598$	1.34568	0.0550288
$599$	2.82516	0.115433	0.0577165	−	0.998333i	$-0.481618\pi$
$599$	2.82516	0.115433	0.0577165	+	0.998333i	$0.481618\pi$
$600$	18.5729	0.758236
$601$	13.3930	0.546313	0.273156	−	0.961970i	$-0.411932\pi$
$601$	13.3930	0.546313	0.273156	+	0.961970i	$0.411932\pi$
$602$	35.3813	1.44203
$603$	−1.00000	−0.0407231
$604$	73.2784	2.98166
$605$	−5.86323	−0.238374
$606$	0.300491	0.0122066
$607$	−33.6344	−1.36518	−0.682590	−	0.730801i	$-0.739147\pi$
$607$	−33.6344	−1.36518	−0.682590	+	0.730801i	$0.739147\pi$
$608$	3.10632	0.125978
$609$	11.5213	0.466866
$610$	−7.76127	−0.314245
$611$	2.32078	0.0938887
$612$	9.80998	0.396545
$613$	−6.69069	−0.270235	−0.135117	−	0.990830i	$-0.543141\pi$
$613$	−6.69069	−0.270235	−0.135117	+	0.990830i	$0.543141\pi$
$614$	−13.0454	−0.526468
$615$	4.37157	0.176279
$616$	19.5827	0.789008
$617$	43.2293	1.74035	0.870173	−	0.492746i	$-0.164007\pi$
$617$	43.2293	1.74035	0.870173	+	0.492746i	$0.164007\pi$
$618$	−17.5219	−0.704835
$619$	−4.85310	−0.195063	−0.0975313	−	0.995232i	$-0.531095\pi$
$619$	−4.85310	−0.195063	−0.0975313	+	0.995232i	$0.531095\pi$
$620$	22.2153	0.892189
$621$	1.67696	0.0672941
$622$	−53.8323	−2.15848
$623$	−25.5530	−1.02376
$624$	−1.22608	−0.0490827
$625$	9.63965	0.385586
$626$	60.5378	2.41958
$627$	−16.4353	−0.656361
$628$	−21.0870	−0.841461
$629$	−18.2881	−0.729195
$630$	−4.52376	−0.180231
$631$	−15.3867	−0.612534	−0.306267	−	0.951946i	$-0.599080\pi$
$631$	−15.3867	−0.612534	−0.306267	+	0.951946i	$0.599080\pi$
$632$	69.3878	2.76010
$633$	22.0761	0.877448
$634$	21.8284	0.866915
$635$	21.9783	0.872182
$636$	−47.3943	−1.87931
$637$	1.27960	0.0506996
$638$	37.1329	1.47011
$639$	9.66117	0.382190
$640$	20.9616	0.828578
$641$	19.2286	0.759484	0.379742	−	0.925092i	$-0.376013\pi$
$641$	19.2286	0.759484	0.379742	+	0.925092i	$0.376013\pi$
$642$	46.4619	1.83370
$643$	−37.4409	−1.47652	−0.738262	−	0.674514i	$-0.764353\pi$
$643$	−37.4409	−1.47652	−0.738262	+	0.674514i	$0.764353\pi$
$644$	11.6924	0.460745
$645$	−8.64635	−0.340450
$646$	−42.7211	−1.68084
$647$	3.04007	0.119517	0.0597587	−	0.998213i	$-0.480967\pi$
$647$	3.04007	0.119517	0.0597587	+	0.998213i	$0.480967\pi$
$648$	−4.76901	−0.187344
$649$	−17.1397	−0.672793
$650$	−3.12514	−0.122578
$651$	9.42099	0.369238
$652$	−28.9825	−1.13504
$653$	14.8037	0.579315	0.289657	−	0.957130i	$-0.406459\pi$
$653$	14.8037	0.579315	0.289657	+	0.957130i	$0.406459\pi$
$654$	31.9572	1.24962
$655$	−0.295335	−0.0115397
$656$	15.5017	0.605239
$657$	8.40373	0.327861
$658$	30.3637	1.18370
$659$	−13.4374	−0.523448	−0.261724	−	0.965143i	$-0.584291\pi$
$659$	−13.4374	−0.523448	−0.261724	+	0.965143i	$0.584291\pi$
$660$	−9.68277	−0.376901
$661$	11.0442	0.429571	0.214786	−	0.976661i	$-0.431095\pi$
$661$	11.0442	0.429571	0.214786	+	0.976661i	$0.431095\pi$
$662$	−24.0071	−0.933062
$663$	−0.815809	−0.0316834
$664$	−5.82072	−0.225888
$665$	13.0832	0.507347
$666$	17.9886	0.697046
$667$	10.9578	0.424286
$668$	−3.16528	−0.122468
$669$	19.7928	0.765234
$670$	2.56565	0.0991197
$671$	−7.04494	−0.271967
$672$	0.776092	0.0299384
$673$	−31.4819	−1.21354	−0.606770	−	0.794878i	$-0.707535\pi$
$673$	−31.4819	−1.21354	−0.606770	+	0.794878i	$0.707535\pi$
$674$	−21.9405	−0.845117
$675$	−3.89450	−0.149899
$676$	−50.9794	−1.96074
$677$	30.1903	1.16031	0.580155	−	0.814506i	$-0.302992\pi$
$677$	30.1903	1.16031	0.580155	+	0.814506i	$0.302992\pi$
$678$	32.3713	1.24321
$679$	−15.7141	−0.603050
$680$	−12.4393	−0.477026
$681$	10.8978	0.417603
$682$	30.3637	1.16269
$683$	−27.9554	−1.06968	−0.534841	−	0.844953i	$-0.679628\pi$
$683$	−27.9554	−1.06968	−0.534841	+	0.844953i	$0.679628\pi$
$684$	27.9070	1.06705
$685$	9.56269	0.365371
$686$	46.8590	1.78908
$687$	16.2802	0.621128
$688$	−30.6602	−1.16891
$689$	3.94137	0.150154
$690$	−4.30249	−0.163793
$691$	−30.0981	−1.14499	−0.572493	−	0.819910i	$-0.694024\pi$
$691$	−30.0981	−1.14499	−0.572493	+	0.819910i	$0.694024\pi$
$692$	−39.0987	−1.48631
$693$	−4.10623	−0.155983
$694$	40.9437	1.55420
$695$	−6.35347	−0.241001
$696$	−31.1622	−1.18120
$697$	10.3145	0.390689
$698$	−16.0708	−0.608287
$699$	−8.10423	−0.306530
$700$	−27.1539	−1.02632
$701$	5.73835	0.216735	0.108367	−	0.994111i	$-0.465438\pi$
$701$	5.73835	0.216735	0.108367	+	0.994111i	$0.465438\pi$
$702$	0.802450	0.0302865
$703$	−52.0253	−1.96217
$704$	19.8670	0.748768
$705$	−7.42017	−0.279460
$706$	81.1568	3.05437
$707$	−0.217127	−0.00816591
$708$	29.1032	1.09377
$709$	−43.8608	−1.64723	−0.823614	−	0.567150i	$-0.808046\pi$
$709$	−43.8608	−1.64723	−0.823614	+	0.567150i	$0.808046\pi$
$710$	−24.7872	−0.930246
$711$	−14.5497	−0.545658
$712$	69.1145	2.59017
$713$	8.96020	0.335562
$714$	−10.6736	−0.399448
$715$	0.805230	0.0301139
$716$	57.2935	2.14116
$717$	6.55485	0.244795
$718$	−84.5236	−3.15439
$719$	−46.1147	−1.71979	−0.859894	−	0.510473i	$-0.829470\pi$
$719$	−46.1147	−1.71979	−0.859894	+	0.510473i	$0.829470\pi$
$720$	3.92013	0.146094
$721$	12.6609	0.471517
$722$	−75.1682	−2.79747
$723$	3.79955	0.141307
$724$	57.1722	2.12479
$725$	−25.4478	−0.945109
$726$	13.6074	0.505019
$727$	46.4582	1.72304	0.861520	−	0.507724i	$-0.169513\pi$
$727$	46.4582	1.72304	0.861520	+	0.507724i	$0.169513\pi$
$728$	2.76522	0.102486
$729$	1.00000	0.0370370
$730$	−21.5610	−0.798010
$731$	−20.4006	−0.754543
$732$	11.9623	0.442139
$733$	22.0232	0.813447	0.406724	−	0.913551i	$-0.366671\pi$
$733$	22.0232	0.813447	0.406724	+	0.913551i	$0.366671\pi$
$734$	−86.5530	−3.19473
$735$	−4.09123	−0.150907
$736$	0.738132	0.0272079
$737$	2.32885	0.0857843
$738$	−10.1456	−0.373464
$739$	30.7388	1.13075	0.565373	−	0.824835i	$-0.308732\pi$
$739$	30.7388	1.13075	0.565373	+	0.824835i	$0.308732\pi$
$740$	−30.6505	−1.12674
$741$	−2.32078	−0.0852560
$742$	51.5665	1.89307
$743$	15.3701	0.563876	0.281938	−	0.959433i	$-0.409023\pi$
$743$	15.3701	0.563876	0.281938	+	0.959433i	$0.409023\pi$
$744$	−25.4814	−0.934193
$745$	−8.96591	−0.328485
$746$	−14.6079	−0.534835
$747$	1.22053	0.0446569
$748$	−22.8460	−0.835332
$749$	−33.5722	−1.22670
$750$	22.8202	0.833275
$751$	15.7252	0.573822	0.286911	−	0.957957i	$-0.407372\pi$
$751$	15.7252	0.573822	0.286911	+	0.957957i	$0.407372\pi$
$752$	−26.3121	−0.959504
$753$	−10.0074	−0.364692
$754$	5.24345	0.190955
$755$	19.4839	0.709092
$756$	6.97237	0.253583
$757$	9.75371	0.354505	0.177252	−	0.984165i	$-0.443279\pi$
$757$	9.75371	0.354505	0.177252	+	0.984165i	$0.443279\pi$
$758$	−23.9116	−0.868507
$759$	−3.90539	−0.141757
$760$	−35.3869	−1.28362
$761$	−33.1200	−1.20060	−0.600300	−	0.799775i	$-0.704952\pi$
$761$	−33.1200	−1.20060	−0.600300	+	0.799775i	$0.704952\pi$
$762$	−51.0074	−1.84780
$763$	−23.0915	−0.835967
$764$	−20.6290	−0.746329
$765$	2.60836	0.0943056
$766$	−81.5504	−2.94653
$767$	−2.42026	−0.0873904
$768$	−31.5861	−1.13976
$769$	23.8090	0.858576	0.429288	−	0.903168i	$-0.358765\pi$
$769$	23.8090	0.858576	0.429288	+	0.903168i	$0.358765\pi$
$770$	10.5352	0.379661
$771$	29.4279	1.05982
$772$	2.72546	0.0980914
$773$	1.12749	0.0405531	0.0202765	−	0.999794i	$-0.493545\pi$
$773$	1.12749	0.0405531	0.0202765	+	0.999794i	$0.493545\pi$
$774$	20.0665	0.721276
$775$	−20.8088	−0.747474
$776$	42.5025	1.52575
$777$	−12.9982	−0.466306
$778$	60.8017	2.17985
$779$	29.3422	1.05129
$780$	−1.36728	−0.0489565
$781$	−22.4994	−0.805093
$782$	−10.1515	−0.363017
$783$	6.53430	0.233517
$784$	−14.5076	−0.518129
$785$	−5.60679	−0.200115
$786$	0.685416	0.0244480
$787$	−41.1539	−1.46698	−0.733489	−	0.679701i	$-0.762109\pi$
$787$	−41.1539	−1.46698	−0.733489	+	0.679701i	$0.762109\pi$
$788$	−44.7081	−1.59266
$789$	−5.62145	−0.200129
$790$	37.3295	1.32813
$791$	−23.3907	−0.831679
$792$	11.1063	0.394646
$793$	−0.994797	−0.0353263
$794$	−76.0608	−2.69930
$795$	−12.6016	−0.446934
$796$	7.82752	0.277439
$797$	−23.2375	−0.823116	−0.411558	−	0.911384i	$-0.635015\pi$
$797$	−23.2375	−0.823116	−0.411558	+	0.911384i	$0.635015\pi$
$798$	−30.3637	−1.07486
$799$	−17.5075	−0.619371
$800$	−1.71421	−0.0606064
$801$	−14.4924	−0.512064
$802$	8.83692	0.312042
$803$	−19.5710	−0.690647
$804$	−3.95438	−0.139460
$805$	3.10888	0.109574
$806$	4.28758	0.151024
$807$	−7.66117	−0.269686
$808$	0.587275	0.0206602
$809$	26.0514	0.915919	0.457960	−	0.888973i	$-0.348580\pi$
$809$	26.0514	0.915919	0.457960	+	0.888973i	$0.348580\pi$
$810$	−2.56565	−0.0901478
$811$	12.6643	0.444705	0.222352	−	0.974966i	$-0.428626\pi$
$811$	12.6643	0.444705	0.222352	+	0.974966i	$0.428626\pi$
$812$	45.5596	1.59883
$813$	−18.2459	−0.639910
$814$	−41.8929	−1.46834
$815$	−7.70611	−0.269933
$816$	9.24933	0.323791
$817$	−58.0348	−2.03038
$818$	7.17399	0.250833
$819$	−0.579831	−0.0202609
$820$	17.2869	0.603683
$821$	40.9192	1.42809	0.714044	−	0.700100i	$-0.246861\pi$
$821$	40.9192	1.42809	0.714044	+	0.700100i	$0.246861\pi$
$822$	−22.1932	−0.774076
$823$	26.8153	0.934724	0.467362	−	0.884066i	$-0.345204\pi$
$823$	26.8153	0.934724	0.467362	+	0.884066i	$0.345204\pi$
$824$	−34.2446	−1.19297
$825$	9.06971	0.315767
$826$	−31.6652	−1.10177
$827$	−2.98614	−0.103838	−0.0519192	−	0.998651i	$-0.516534\pi$
$827$	−2.98614	−0.103838	−0.0519192	+	0.998651i	$0.516534\pi$
$828$	6.63134	0.230455
$829$	22.7160	0.788961	0.394480	−	0.918904i	$-0.370925\pi$
$829$	22.7160	0.788961	0.394480	+	0.918904i	$0.370925\pi$
$830$	−3.13145	−0.108694
$831$	22.1496	0.768362
$832$	2.80538	0.0972589
$833$	−9.65304	−0.334458
$834$	14.7452	0.510584
$835$	−0.841612	−0.0291252
$836$	−64.9913	−2.24777
$837$	5.34312	0.184685
$838$	4.03934	0.139537
$839$	−29.0312	−1.00227	−0.501134	−	0.865370i	$-0.667084\pi$
$839$	−29.0312	−1.00227	−0.501134	+	0.865370i	$0.667084\pi$
$840$	−8.84116	−0.305049
$841$	13.6971	0.472314
$842$	24.6933	0.850987
$843$	−18.5004	−0.637187
$844$	87.2975	3.00490
$845$	−13.5548	−0.466301
$846$	17.2208	0.592063
$847$	−9.83240	−0.337845
$848$	−44.6857	−1.53451
$849$	−20.3227	−0.697473
$850$	23.5754	0.808631
$851$	−12.3624	−0.423777
$852$	38.2040	1.30885
$853$	20.1108	0.688582	0.344291	−	0.938863i	$-0.388119\pi$
$853$	20.1108	0.688582	0.344291	+	0.938863i	$0.388119\pi$
$854$	−13.0153	−0.445376
$855$	7.42017	0.253764
$856$	90.8044	3.10363
$857$	20.3262	0.694328	0.347164	−	0.937804i	$-0.387145\pi$
$857$	20.3262	0.694328	0.347164	+	0.937804i	$0.387145\pi$
$858$	−1.86879	−0.0637993
$859$	−40.8547	−1.39395	−0.696973	−	0.717097i	$-0.745470\pi$
$859$	−40.8547	−1.39395	−0.696973	+	0.717097i	$0.745470\pi$
$860$	−34.1910	−1.16590
$861$	7.33094	0.249838
$862$	−38.3463	−1.30608
$863$	32.0207	1.09000	0.544999	−	0.838437i	$-0.316530\pi$
$863$	32.0207	1.09000	0.544999	+	0.838437i	$0.316530\pi$
$864$	0.440161	0.0149746
$865$	−10.3959	−0.353471
$866$	7.74115	0.263055
$867$	−10.8457	−0.368339
$868$	37.2542	1.26449
$869$	33.8842	1.14944
$870$	−16.7647	−0.568378
$871$	0.328851	0.0111427
$872$	62.4566	2.11505
$873$	−8.91223	−0.301633
$874$	−28.8786	−0.976833
$875$	−16.4893	−0.557440
$876$	33.2316	1.12279
$877$	−53.8198	−1.81737	−0.908683	−	0.417487i	$-0.862911\pi$
$877$	−53.8198	−1.81737	−0.908683	+	0.417487i	$0.862911\pi$
$878$	62.6441	2.11414
$879$	28.8692	0.973735
$880$	−9.12939	−0.307752
$881$	27.7754	0.935777	0.467888	−	0.883788i	$-0.345015\pi$
$881$	27.7754	0.935777	0.467888	+	0.883788i	$0.345015\pi$
$882$	9.49497	0.319712
$883$	24.6492	0.829513	0.414756	−	0.909933i	$-0.363867\pi$
$883$	24.6492	0.829513	0.414756	+	0.909933i	$0.363867\pi$
$884$	−3.22602	−0.108503
$885$	7.73822	0.260117
$886$	84.2330	2.82986
$887$	−6.84340	−0.229779	−0.114889	−	0.993378i	$-0.536651\pi$
$887$	−6.84340	−0.229779	−0.114889	+	0.993378i	$0.536651\pi$
$888$	35.1567	1.17978
$889$	36.8567	1.23614
$890$	37.1825	1.24636
$891$	−2.32885	−0.0780194
$892$	78.2684	2.62062
$893$	−49.8046	−1.66665
$894$	20.8082	0.695929
$895$	15.2337	0.509207
$896$	35.1517	1.17434
$897$	−0.551470	−0.0184131
$898$	−88.7001	−2.95996
$899$	34.9135	1.16443
$900$	−15.4004	−0.513345
$901$	−29.7329	−0.990546
$902$	23.6275	0.786710
$903$	−14.4996	−0.482516
$904$	63.2660	2.10420
$905$	15.2015	0.505314
$906$	−45.2184	−1.50228
$907$	1.90000	0.0630885	0.0315442	−	0.999502i	$-0.489957\pi$
$907$	1.90000	0.0630885	0.0315442	+	0.999502i	$0.489957\pi$
$908$	43.0939	1.43012
$909$	−0.123144	−0.00408442
$910$	1.48764	0.0493149
$911$	33.6896	1.11619	0.558094	−	0.829778i	$-0.311533\pi$
$911$	33.6896	1.11619	0.558094	+	0.829778i	$0.311533\pi$
$912$	26.3121	0.871281
$913$	−2.84243	−0.0940708
$914$	−25.2561	−0.835399
$915$	3.18064	0.105149
$916$	64.3782	2.12711
$917$	−0.495265	−0.0163551
$918$	−6.05352	−0.199796
$919$	44.1369	1.45594	0.727971	−	0.685608i	$-0.240464\pi$
$919$	44.1369	1.45594	0.727971	+	0.685608i	$0.240464\pi$
$920$	−8.40873	−0.277227
$921$	5.34611	0.176160
$922$	−21.8867	−0.720801
$923$	−3.17709	−0.104575
$924$	−16.2376	−0.534178
$925$	28.7099	0.943976
$926$	14.9509	0.491317
$927$	7.18064	0.235843
$928$	2.87614	0.0944140
$929$	−42.1195	−1.38190	−0.690948	−	0.722905i	$-0.742807\pi$
$929$	−42.1195	−1.38190	−0.690948	+	0.722905i	$0.742807\pi$
$930$	−13.7086	−0.449522
$931$	−27.4606	−0.899984
$932$	−32.0472	−1.04974
$933$	22.0610	0.722243
$934$	41.6533	1.36294
$935$	−6.07449	−0.198657
$936$	1.56830	0.0512613
$937$	27.0838	0.884788	0.442394	−	0.896821i	$-0.354129\pi$
$937$	27.0838	0.884788	0.442394	+	0.896821i	$0.354129\pi$
$938$	4.30249	0.140481
$939$	−24.8090	−0.809610
$940$	−29.3422	−0.957037
$941$	−56.0364	−1.82673	−0.913367	−	0.407137i	$-0.866527\pi$
$941$	−56.0364	−1.82673	−0.913367	+	0.407137i	$0.866527\pi$
$942$	13.0123	0.423963
$943$	6.97237	0.227052
$944$	27.4399	0.893093
$945$	1.85388	0.0603066
$946$	−46.7319	−1.51939
$947$	−21.0098	−0.682727	−0.341363	−	0.939931i	$-0.610889\pi$
$947$	−21.0098	−0.682727	−0.341363	+	0.939931i	$0.610889\pi$
$948$	−57.5352	−1.86866
$949$	−2.76358	−0.0897095
$950$	67.0664	2.17592
$951$	−8.94546	−0.290076
$952$	−20.8602	−0.676084
$953$	3.67723	0.119117	0.0595585	−	0.998225i	$-0.481031\pi$
$953$	3.67723	0.119117	0.0595585	+	0.998225i	$0.481031\pi$
$954$	29.2460	0.946873
$955$	−5.48501	−0.177491
$956$	25.9204	0.838325
$957$	−15.2174	−0.491909
$958$	−65.8689	−2.12813
$959$	16.0362	0.517837
$960$	−8.96955	−0.289491
$961$	−2.45109	−0.0790673
$962$	−5.91559	−0.190726
$963$	−19.0405	−0.613572
$964$	15.0249	0.483919
$965$	0.724669	0.0233279
$966$	−7.21511	−0.232142
$967$	14.0493	0.451796	0.225898	−	0.974151i	$-0.427468\pi$
$967$	14.0493	0.451796	0.225898	+	0.974151i	$0.427468\pi$
$968$	26.5942	0.854769
$969$	17.5075	0.562422
$970$	22.8657	0.734173
$971$	4.65378	0.149347	0.0746735	−	0.997208i	$-0.476209\pi$
$971$	4.65378	0.149347	0.0746735	+	0.997208i	$0.476209\pi$
$972$	3.95438	0.126837
$973$	−10.6545	−0.341568
$974$	6.92575	0.221915
$975$	1.28071	0.0410156
$976$	11.2786	0.361020
$977$	−6.45099	−0.206385	−0.103193	−	0.994661i	$-0.532906\pi$
$977$	−6.45099	−0.206385	−0.103193	+	0.994661i	$0.532906\pi$
$978$	17.8844	0.571880
$979$	33.7507	1.07868
$980$	−16.1783	−0.516797
$981$	−13.0963	−0.418134
$982$	45.2501	1.44399
$983$	−38.3023	−1.22165	−0.610827	−	0.791764i	$-0.709163\pi$
$983$	−38.3023	−1.22165	−0.610827	+	0.791764i	$0.709163\pi$
$984$	−19.8283	−0.632104
$985$	−11.8874	−0.378764
$986$	−39.5555	−1.25970
$987$	−12.4433	−0.396075
$988$	−9.17726	−0.291968
$989$	−13.7904	−0.438509
$990$	5.97502	0.189899
$991$	14.8426	0.471492	0.235746	−	0.971815i	$-0.424247\pi$
$991$	14.8426	0.471492	0.235746	+	0.971815i	$0.424247\pi$
$992$	2.35183	0.0746707
$993$	9.83832	0.312210
$994$	−41.5671	−1.31843
$995$	2.08125	0.0659801
$996$	4.82644	0.152932
$997$	−5.50224	−0.174258	−0.0871288	−	0.996197i	$-0.527769\pi$
$997$	−5.50224	−0.174258	−0.0871288	+	0.996197i	$0.527769\pi$
$998$	55.6107	1.76033
$999$	−7.37191	−0.233237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.a.e.1.1	✓	5
3.2	odd	2		603.2.a.k.1.5		5
4.3	odd	2		3216.2.a.y.1.4		5
5.4	even	2		5025.2.a.x.1.5		5
7.6	odd	2		9849.2.a.bb.1.1		5
12.11	even	2		9648.2.a.cd.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.e.1.1	✓	5	1.1	even	1	trivial
603.2.a.k.1.5		5	3.2	odd	2
3216.2.a.y.1.4		5	4.3	odd	2
5025.2.a.x.1.5		5	5.4	even	2
9648.2.a.cd.1.2		5	12.11	even	2
9849.2.a.bb.1.1		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44016 q^{2} +1.00000 q^{3} +3.95438 q^{4} +1.05143 q^{5} -2.44016 q^{6} +1.76320 q^{7} -4.76901 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.44016 q^{2} +1.00000 q^{3} +3.95438 q^{4} +1.05143 q^{5} -2.44016 q^{6} +1.76320 q^{7} -4.76901 q^{8} +1.00000 q^{9} -2.56565 q^{10} -2.32885 q^{11} +3.95438 q^{12} -0.328851 q^{13} -4.30249 q^{14} +1.05143 q^{15} +3.72839 q^{16} +2.48079 q^{17} -2.44016 q^{18} +7.05724 q^{19} +4.15775 q^{20} +1.76320 q^{21} +5.68277 q^{22} +1.67696 q^{23} -4.76901 q^{24} -3.89450 q^{25} +0.802450 q^{26} +1.00000 q^{27} +6.97237 q^{28} +6.53430 q^{29} -2.56565 q^{30} +5.34312 q^{31} +0.440161 q^{32} -2.32885 q^{33} -6.05352 q^{34} +1.85388 q^{35} +3.95438 q^{36} -7.37191 q^{37} -17.2208 q^{38} -0.328851 q^{39} -5.01427 q^{40} +4.15775 q^{41} -4.30249 q^{42} -8.22344 q^{43} -9.20917 q^{44} +1.05143 q^{45} -4.09205 q^{46} -7.05724 q^{47} +3.72839 q^{48} -3.89112 q^{49} +9.50321 q^{50} +2.48079 q^{51} -1.30040 q^{52} -11.9853 q^{53} -2.44016 q^{54} -2.44862 q^{55} -8.40873 q^{56} +7.05724 q^{57} -15.9447 q^{58} +7.35973 q^{59} +4.15775 q^{60} +3.02507 q^{61} -13.0381 q^{62} +1.76320 q^{63} -8.53084 q^{64} -0.345763 q^{65} +5.68277 q^{66} -1.00000 q^{67} +9.80998 q^{68} +1.67696 q^{69} -4.52376 q^{70} +9.66117 q^{71} -4.76901 q^{72} +8.40373 q^{73} +17.9886 q^{74} -3.89450 q^{75} +27.9070 q^{76} -4.10623 q^{77} +0.802450 q^{78} -14.5497 q^{79} +3.92013 q^{80} +1.00000 q^{81} -10.1456 q^{82} +1.22053 q^{83} +6.97237 q^{84} +2.60836 q^{85} +20.0665 q^{86} +6.53430 q^{87} +11.1063 q^{88} -14.4924 q^{89} -2.56565 q^{90} -0.579831 q^{91} +6.63134 q^{92} +5.34312 q^{93} +17.2208 q^{94} +7.42017 q^{95} +0.440161 q^{96} -8.91223 q^{97} +9.49497 q^{98} -2.32885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^3 + 6 * q^4 - 3 * q^5 + 7 * q^7 + 5 * q^9	\( 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9} - 3 q^{10} + 6 q^{12} + 10 q^{13} - 9 q^{14} - 3 q^{15} - 5 q^{17} + 5 q^{19} - 7 q^{20} + 7 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{25} - 4 q^{26} + 5 q^{27} - 3 q^{28} + 3 q^{29} - 3 q^{30} + 9 q^{31} - 10 q^{32} - 18 q^{34} - 7 q^{35} + 6 q^{36} + 8 q^{37} - 6 q^{38} + 10 q^{39} - 19 q^{40} - 7 q^{41} - 9 q^{42} + q^{43} - 10 q^{44} - 3 q^{45} - 7 q^{46} - 5 q^{47} + 8 q^{49} - 17 q^{50} - 5 q^{51} + 2 q^{52} - 15 q^{53} - 16 q^{55} - 19 q^{56} + 5 q^{57} - 4 q^{58} - 6 q^{59} - 7 q^{60} + 6 q^{61} - 13 q^{62} + 7 q^{63} - 16 q^{64} - 22 q^{65} - 4 q^{66} - 5 q^{67} - 4 q^{68} - 2 q^{69} + 19 q^{70} + 22 q^{71} + 51 q^{74} + 2 q^{75} + 24 q^{76} - 10 q^{77} - 4 q^{78} + 28 q^{79} + 31 q^{80} + 5 q^{81} - 25 q^{82} + 9 q^{83} - 3 q^{84} - 6 q^{85} + 45 q^{86} + 3 q^{87} + 36 q^{88} - 11 q^{89} - 3 q^{90} + 4 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} + 44 q^{95} - 10 q^{96} - 14 q^{97} + 33 q^{98}+O(q^{100}) \) 5 * q + 5 * q^3 + 6 * q^4 - 3 * q^5 + 7 * q^7 + 5 * q^9 - 3 * q^10 + 6 * q^12 + 10 * q^13 - 9 * q^14 - 3 * q^15 - 5 * q^17 + 5 * q^19 - 7 * q^20 + 7 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^25 - 4 * q^26 + 5 * q^27 - 3 * q^28 + 3 * q^29 - 3 * q^30 + 9 * q^31 - 10 * q^32 - 18 * q^34 - 7 * q^35 + 6 * q^36 + 8 * q^37 - 6 * q^38 + 10 * q^39 - 19 * q^40 - 7 * q^41 - 9 * q^42 + q^43 - 10 * q^44 - 3 * q^45 - 7 * q^46 - 5 * q^47 + 8 * q^49 - 17 * q^50 - 5 * q^51 + 2 * q^52 - 15 * q^53 - 16 * q^55 - 19 * q^56 + 5 * q^57 - 4 * q^58 - 6 * q^59 - 7 * q^60 + 6 * q^61 - 13 * q^62 + 7 * q^63 - 16 * q^64 - 22 * q^65 - 4 * q^66 - 5 * q^67 - 4 * q^68 - 2 * q^69 + 19 * q^70 + 22 * q^71 + 51 * q^74 + 2 * q^75 + 24 * q^76 - 10 * q^77 - 4 * q^78 + 28 * q^79 + 31 * q^80 + 5 * q^81 - 25 * q^82 + 9 * q^83 - 3 * q^84 - 6 * q^85 + 45 * q^86 + 3 * q^87 + 36 * q^88 - 11 * q^89 - 3 * q^90 + 4 * q^91 + 9 * q^92 + 9 * q^93 + 6 * q^94 + 44 * q^95 - 10 * q^96 - 14 * q^97 + 33 * q^98

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