LMFDB - Embedded newform 201.2.a.e.1.4

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			1.4
Root			$-1.63326$ 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)

$f(q)$	$=$	$q+1.63326 q^{2} +1.00000 q^{3} +0.667538 q^{4} -0.873745 q^{5} +1.63326 q^{6} +4.38246 q^{7} -2.17626 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.63326 q^{2} +1.00000 q^{3} +0.667538 q^{4} -0.873745 q^{5} +1.63326 q^{6} +4.38246 q^{7} -2.17626 q^{8} +1.00000 q^{9} -1.42705 q^{10} -3.80952 q^{11} +0.667538 q^{12} -1.80952 q^{13} +7.15770 q^{14} -0.873745 q^{15} -4.88947 q^{16} +4.43247 q^{17} +1.63326 q^{18} -0.0799522 q^{19} -0.583258 q^{20} +4.38246 q^{21} -6.22193 q^{22} -5.01572 q^{23} -2.17626 q^{24} -4.23657 q^{25} -2.95541 q^{26} +1.00000 q^{27} +2.92546 q^{28} -4.80690 q^{29} -1.42705 q^{30} -0.0919769 q^{31} -3.63326 q^{32} -3.80952 q^{33} +7.23937 q^{34} -3.82916 q^{35} +0.667538 q^{36} +6.77352 q^{37} -0.130583 q^{38} -1.80952 q^{39} +1.90149 q^{40} -0.583258 q^{41} +7.15770 q^{42} +5.35850 q^{43} -2.54300 q^{44} -0.873745 q^{45} -8.19198 q^{46} +0.0799522 q^{47} -4.88947 q^{48} +12.2060 q^{49} -6.91942 q^{50} +4.43247 q^{51} -1.20792 q^{52} +11.3796 q^{53} +1.63326 q^{54} +3.32855 q^{55} -9.53737 q^{56} -0.0799522 q^{57} -7.85092 q^{58} -11.2377 q^{59} -0.583258 q^{60} -11.8410 q^{61} -0.150222 q^{62} +4.38246 q^{63} +3.84488 q^{64} +1.58106 q^{65} -6.22193 q^{66} -1.00000 q^{67} +2.95884 q^{68} -5.01572 q^{69} -6.25401 q^{70} +13.6570 q^{71} -2.17626 q^{72} +12.2706 q^{73} +11.0629 q^{74} -4.23657 q^{75} -0.0533711 q^{76} -16.6951 q^{77} -2.95541 q^{78} +16.4645 q^{79} +4.27215 q^{80} +1.00000 q^{81} -0.952612 q^{82} +1.48007 q^{83} +2.92546 q^{84} -3.87285 q^{85} +8.75182 q^{86} -4.80690 q^{87} +8.29049 q^{88} -6.02005 q^{89} -1.42705 q^{90} -7.93014 q^{91} -3.34819 q^{92} -0.0919769 q^{93} +0.130583 q^{94} +0.0698578 q^{95} -3.63326 q^{96} -3.37305 q^{97} +19.9356 q^{98} -3.80952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.63326	1.15489	0.577445	−	0.816430i	$-0.304050\pi$
$2$	1.63326	1.15489	0.577445	+	0.816430i	$0.304050\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.667538	0.333769
$5$	−0.873745	−0.390751	−0.195375	−	0.980729i	$-0.562593\pi$
$5$	−0.873745	−0.390751	−0.195375	+	0.980729i	$0.562593\pi$
$6$	1.63326	0.666776
$7$	4.38246	1.65642	0.828208	−	0.560421i	$-0.189361\pi$
$7$	4.38246	1.65642	0.828208	+	0.560421i	$0.189361\pi$
$8$	−2.17626	−0.769423
$9$	1.00000	0.333333
$10$	−1.42705	−0.451274
$11$	−3.80952	−1.14861	−0.574306	−	0.818641i	$-0.694728\pi$
$11$	−3.80952	−1.14861	−0.574306	+	0.818641i	$0.694728\pi$
$12$	0.667538	0.192702
$13$	−1.80952	−0.501870	−0.250935	−	0.968004i	$-0.580738\pi$
$13$	−1.80952	−0.501870	−0.250935	+	0.968004i	$0.580738\pi$
$14$	7.15770	1.91298
$15$	−0.873745	−0.225600
$16$	−4.88947	−1.22237
$17$	4.43247	1.07503	0.537515	−	0.843254i	$-0.319363\pi$
$17$	4.43247	1.07503	0.537515	+	0.843254i	$0.319363\pi$
$18$	1.63326	0.384963
$19$	−0.0799522	−0.0183423	−0.00917115	−	0.999958i	$-0.502919\pi$
$19$	−0.0799522	−0.0183423	−0.00917115	+	0.999958i	$0.502919\pi$
$20$	−0.583258	−0.130420
$21$	4.38246	0.956332
$22$	−6.22193	−1.32652
$23$	−5.01572	−1.04585	−0.522925	−	0.852378i	$-0.675159\pi$
$23$	−5.01572	−1.04585	−0.522925	+	0.852378i	$0.675159\pi$
$24$	−2.17626	−0.444227
$25$	−4.23657	−0.847314
$26$	−2.95541	−0.579604
$27$	1.00000	0.192450
$28$	2.92546	0.552860
$29$	−4.80690	−0.892619	−0.446310	−	0.894879i	$-0.647262\pi$
$29$	−4.80690	−0.892619	−0.446310	+	0.894879i	$0.647262\pi$
$30$	−1.42705	−0.260543
$31$	−0.0919769	−0.0165195	−0.00825977	−	0.999966i	$-0.502629\pi$
$31$	−0.0919769	−0.0165195	−0.00825977	+	0.999966i	$0.502629\pi$
$32$	−3.63326	−0.642276
$33$	−3.80952	−0.663152
$34$	7.23937	1.24154
$35$	−3.82916	−0.647246
$36$	0.667538	0.111256
$37$	6.77352	1.11356	0.556780	−	0.830660i	$-0.312037\pi$
$37$	6.77352	1.11356	0.556780	+	0.830660i	$0.312037\pi$
$38$	−0.130583	−0.0211833
$39$	−1.80952	−0.289755
$40$	1.90149	0.300653
$41$	−0.583258	−0.0910896	−0.0455448	−	0.998962i	$-0.514502\pi$
$41$	−0.583258	−0.0910896	−0.0455448	+	0.998962i	$0.514502\pi$
$42$	7.15770	1.10446
$43$	5.35850	0.817163	0.408582	−	0.912722i	$-0.366024\pi$
$43$	5.35850	0.817163	0.408582	+	0.912722i	$0.366024\pi$
$44$	−2.54300	−0.383371
$45$	−0.873745	−0.130250
$46$	−8.19198	−1.20784
$47$	0.0799522	0.0116622	0.00583111	−	0.999983i	$-0.498144\pi$
$47$	0.0799522	0.0116622	0.00583111	+	0.999983i	$0.498144\pi$
$48$	−4.88947	−0.705734
$49$	12.2060	1.74371
$50$	−6.91942	−0.978554
$51$	4.43247	0.620669
$52$	−1.20792	−0.167509
$53$	11.3796	1.56311	0.781556	−	0.623835i	$-0.214426\pi$
$53$	11.3796	1.56311	0.781556	+	0.623835i	$0.214426\pi$
$54$	1.63326	0.222259
$55$	3.32855	0.448821
$56$	−9.53737	−1.27448
$57$	−0.0799522	−0.0105899
$58$	−7.85092	−1.03088
$59$	−11.2377	−1.46302	−0.731509	−	0.681832i	$-0.761184\pi$
$59$	−11.2377	−1.46302	−0.731509	+	0.681832i	$0.761184\pi$
$60$	−0.583258	−0.0752983
$61$	−11.8410	−1.51608	−0.758040	−	0.652208i	$-0.773843\pi$
$61$	−11.8410	−1.51608	−0.758040	+	0.652208i	$0.773843\pi$
$62$	−0.150222	−0.0190782
$63$	4.38246	0.552139
$64$	3.84488	0.480610
$65$	1.58106	0.196106
$66$	−6.22193	−0.765867
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	2.95884	0.358812
$69$	−5.01572	−0.603822
$70$	−6.25401	−0.747497
$71$	13.6570	1.62079	0.810394	−	0.585885i	$-0.199253\pi$
$71$	13.6570	1.62079	0.810394	+	0.585885i	$0.199253\pi$
$72$	−2.17626	−0.256474
$73$	12.2706	1.43617	0.718084	−	0.695956i	$-0.245019\pi$
$73$	12.2706	1.43617	0.718084	+	0.695956i	$0.245019\pi$
$74$	11.0629	1.28604
$75$	−4.23657	−0.489197
$76$	−0.0533711	−0.00612209
$77$	−16.6951	−1.90258
$78$	−2.95541	−0.334634
$79$	16.4645	1.85240	0.926200	−	0.377034i	$-0.123056\pi$
$79$	16.4645	1.85240	0.926200	+	0.377034i	$0.123056\pi$
$80$	4.27215	0.477641
$81$	1.00000	0.111111
$82$	−0.952612	−0.105198
$83$	1.48007	0.162459	0.0812294	−	0.996695i	$-0.474115\pi$
$83$	1.48007	0.162459	0.0812294	+	0.996695i	$0.474115\pi$
$84$	2.92546	0.319194
$85$	−3.87285	−0.420069
$86$	8.75182	0.943733
$87$	−4.80690	−0.515354
$88$	8.29049	0.883769
$89$	−6.02005	−0.638124	−0.319062	−	0.947734i	$-0.603368\pi$
$89$	−6.02005	−0.638124	−0.319062	+	0.947734i	$0.603368\pi$
$90$	−1.42705	−0.150425
$91$	−7.93014	−0.831305
$92$	−3.34819	−0.349073
$93$	−0.0919769	−0.00953756
$94$	0.130583	0.0134686
$95$	0.0698578	0.00716726
$96$	−3.63326	−0.370818
$97$	−3.37305	−0.342482	−0.171241	−	0.985229i	$-0.554778\pi$
$97$	−3.37305	−0.342482	−0.171241	+	0.985229i	$0.554778\pi$
$98$	19.9356	2.01380
$99$	−3.80952	−0.382871
$100$	−2.82807	−0.282807
$101$	−9.30450	−0.925832	−0.462916	−	0.886402i	$-0.653197\pi$
$101$	−9.30450	−0.925832	−0.462916	+	0.886402i	$0.653197\pi$
$102$	7.23937	0.716804
$103$	14.3460	1.41355	0.706776	−	0.707437i	$-0.250149\pi$
$103$	14.3460	1.41355	0.706776	+	0.707437i	$0.250149\pi$
$104$	3.93797	0.386150
$105$	−3.82916	−0.373687
$106$	18.5859	1.80522
$107$	15.4985	1.49830	0.749150	−	0.662400i	$-0.230462\pi$
$107$	15.4985	1.49830	0.749150	+	0.662400i	$0.230462\pi$
$108$	0.667538	0.0642339
$109$	−15.7570	−1.50925	−0.754624	−	0.656157i	$-0.772181\pi$
$109$	−15.7570	−1.50925	−0.754624	+	0.656157i	$0.772181\pi$
$110$	5.43638	0.518339
$111$	6.77352	0.642915
$112$	−21.4279	−2.02475
$113$	−9.74619	−0.916844	−0.458422	−	0.888735i	$-0.651585\pi$
$113$	−9.74619	−0.916844	−0.458422	+	0.888735i	$0.651585\pi$
$114$	−0.130583	−0.0122302
$115$	4.38246	0.408667
$116$	−3.20879	−0.297929
$117$	−1.80952	−0.167290
$118$	−18.3540	−1.68962
$119$	19.4251	1.78070
$120$	1.90149	0.173582
$121$	3.51242	0.319311
$122$	−19.3394	−1.75090
$123$	−0.583258	−0.0525906
$124$	−0.0613981	−0.00551371
$125$	8.07041	0.721839
$126$	7.15770	0.637659
$127$	−13.2128	−1.17245	−0.586223	−	0.810150i	$-0.699386\pi$
$127$	−13.2128	−1.17245	−0.586223	+	0.810150i	$0.699386\pi$
$128$	13.5462	1.19733
$129$	5.35850	0.471789
$130$	2.58228	0.226481
$131$	−4.72124	−0.412497	−0.206248	−	0.978500i	$-0.566125\pi$
$131$	−4.72124	−0.412497	−0.206248	+	0.978500i	$0.566125\pi$
$132$	−2.54300	−0.221339
$133$	−0.350388	−0.0303825
$134$	−1.63326	−0.141092
$135$	−0.873745	−0.0752000
$136$	−9.64618	−0.827153
$137$	−0.646586	−0.0552416	−0.0276208	−	0.999618i	$-0.508793\pi$
$137$	−0.646586	−0.0552416	−0.0276208	+	0.999618i	$0.508793\pi$
$138$	−8.19198	−0.697348
$139$	−0.700102	−0.0593819	−0.0296909	−	0.999559i	$-0.509452\pi$
$139$	−0.700102	−0.0593819	−0.0296909	+	0.999559i	$0.509452\pi$
$140$	−2.55611	−0.216030
$141$	0.0799522	0.00673319
$142$	22.3054	1.87183
$143$	6.89338	0.576454
$144$	−4.88947	−0.407456
$145$	4.20001	0.348792
$146$	20.0411	1.65862
$147$	12.2060	1.00673
$148$	4.52158	0.371672
$149$	4.88286	0.400019	0.200010	−	0.979794i	$-0.435903\pi$
$149$	4.88286	0.400019	0.200010	+	0.979794i	$0.435903\pi$
$150$	−6.91942	−0.564968
$151$	−9.24946	−0.752711	−0.376355	−	0.926475i	$-0.622823\pi$
$151$	−9.24946	−0.752711	−0.376355	+	0.926475i	$0.622823\pi$
$152$	0.173997	0.0141130
$153$	4.43247	0.358344
$154$	−27.2674	−2.19727
$155$	0.0803644	0.00645502
$156$	−1.20792	−0.0967111
$157$	23.7319	1.89401	0.947007	−	0.321212i	$-0.104090\pi$
$157$	23.7319	1.89401	0.947007	+	0.321212i	$0.104090\pi$
$158$	26.8908	2.13932
$159$	11.3796	0.902464
$160$	3.17454	0.250970
$161$	−21.9812	−1.73236
$162$	1.63326	0.128321
$163$	1.47363	0.115423	0.0577117	−	0.998333i	$-0.481620\pi$
$163$	1.47363	0.115423	0.0577117	+	0.998333i	$0.481620\pi$
$164$	−0.389347	−0.0304029
$165$	3.32855	0.259127
$166$	2.41734	0.187622
$167$	6.99437	0.541241	0.270620	−	0.962686i	$-0.412771\pi$
$167$	6.99437	0.541241	0.270620	+	0.962686i	$0.412771\pi$
$168$	−9.53737	−0.735824
$169$	−9.72565	−0.748127
$170$	−6.32536	−0.485133
$171$	−0.0799522	−0.00611410
$172$	3.57700	0.272744
$173$	−24.3355	−1.85019	−0.925095	−	0.379735i	$-0.876015\pi$
$173$	−24.3355	−1.85019	−0.925095	+	0.379735i	$0.876015\pi$
$174$	−7.85092	−0.595177
$175$	−18.5666	−1.40350
$176$	18.6265	1.40403
$177$	−11.2377	−0.844674
$178$	−9.83231	−0.736963
$179$	15.2652	1.14098	0.570488	−	0.821306i	$-0.306754\pi$
$179$	15.2652	1.14098	0.570488	+	0.821306i	$0.306754\pi$
$180$	−0.583258	−0.0434735
$181$	−15.5350	−1.15471	−0.577355	−	0.816493i	$-0.695915\pi$
$181$	−15.5350	−1.15471	−0.577355	+	0.816493i	$0.695915\pi$
$182$	−12.9520	−0.960065
$183$	−11.8410	−0.875309
$184$	10.9155	0.804702
$185$	−5.91833	−0.435125
$186$	−0.150222	−0.0110148
$187$	−16.8856	−1.23479
$188$	0.0533711	0.00389249
$189$	4.38246	0.318777
$190$	0.114096	0.00827739
$191$	7.74569	0.560458	0.280229	−	0.959933i	$-0.409590\pi$
$191$	7.74569	0.560458	0.280229	+	0.959933i	$0.409590\pi$
$192$	3.84488	0.277480
$193$	−16.9562	−1.22053	−0.610266	−	0.792196i	$-0.708938\pi$
$193$	−16.9562	−1.22053	−0.610266	+	0.792196i	$0.708938\pi$
$194$	−5.50907	−0.395528
$195$	1.58106	0.113222
$196$	8.14796	0.581997
$197$	−0.880274	−0.0627170	−0.0313585	−	0.999508i	$-0.509983\pi$
$197$	−0.880274	−0.0627170	−0.0313585	+	0.999508i	$0.509983\pi$
$198$	−6.22193	−0.442173
$199$	−16.1734	−1.14650	−0.573252	−	0.819379i	$-0.694318\pi$
$199$	−16.1734	−1.14650	−0.573252	+	0.819379i	$0.694318\pi$
$200$	9.21986	0.651943
$201$	−1.00000	−0.0705346
$202$	−15.1967	−1.06923
$203$	−21.0661	−1.47855
$204$	2.95884	0.207160
$205$	0.509619	0.0355933
$206$	23.4307	1.63250
$207$	−5.01572	−0.348617
$208$	8.84758	0.613469
$209$	0.304579	0.0210682
$210$	−6.25401	−0.431568
$211$	−3.69956	−0.254688	−0.127344	−	0.991859i	$-0.540645\pi$
$211$	−3.69956	−0.254688	−0.127344	+	0.991859i	$0.540645\pi$
$212$	7.59634	0.521719
$213$	13.6570	0.935763
$214$	25.3132	1.73037
$215$	−4.68196	−0.319307
$216$	−2.17626	−0.148076
$217$	−0.403086	−0.0273632
$218$	−25.7353	−1.74301
$219$	12.2706	0.829172
$220$	2.22193	0.149803
$221$	−8.02062	−0.539525
$222$	11.0629	0.742495
$223$	11.2280	0.751881	0.375940	−	0.926644i	$-0.377320\pi$
$223$	11.2280	0.751881	0.375940	+	0.926644i	$0.377320\pi$
$224$	−15.9226	−1.06388
$225$	−4.23657	−0.282438
$226$	−15.9181	−1.05885
$227$	−12.8851	−0.855217	−0.427608	−	0.903964i	$-0.640644\pi$
$227$	−12.8851	−0.855217	−0.427608	+	0.903964i	$0.640644\pi$
$228$	−0.0533711	−0.00353459
$229$	−12.2486	−0.809414	−0.404707	−	0.914447i	$-0.632626\pi$
$229$	−12.2486	−0.809414	−0.404707	+	0.914447i	$0.632626\pi$
$230$	7.15770	0.471965
$231$	−16.6951	−1.09845
$232$	10.4611	0.686802
$233$	−16.6561	−1.09118	−0.545589	−	0.838053i	$-0.683694\pi$
$233$	−16.6561	−1.09118	−0.545589	+	0.838053i	$0.683694\pi$
$234$	−2.95541	−0.193201
$235$	−0.0698578	−0.00455702
$236$	−7.50156	−0.488310
$237$	16.4645	1.06948
$238$	31.7263	2.05651
$239$	13.3665	0.864609	0.432304	−	0.901728i	$-0.357701\pi$
$239$	13.3665	0.864609	0.432304	+	0.901728i	$0.357701\pi$
$240$	4.27215	0.275766
$241$	−8.58777	−0.553187	−0.276593	−	0.960987i	$-0.589206\pi$
$241$	−8.58777	−0.553187	−0.276593	+	0.960987i	$0.589206\pi$
$242$	5.73669	0.368769
$243$	1.00000	0.0641500
$244$	−7.90429	−0.506021
$245$	−10.6649	−0.681357
$246$	−0.952612	−0.0607363
$247$	0.144675	0.00920544
$248$	0.200165	0.0127105
$249$	1.48007	0.0937957
$250$	13.1811	0.833644
$251$	−22.3188	−1.40875	−0.704376	−	0.709827i	$-0.748773\pi$
$251$	−22.3188	−1.40875	−0.704376	+	0.709827i	$0.748773\pi$
$252$	2.92546	0.184287
$253$	19.1075	1.20128
$254$	−21.5799	−1.35404
$255$	−3.87285	−0.242527
$256$	14.4347	0.902170
$257$	−5.43172	−0.338822	−0.169411	−	0.985546i	$-0.554186\pi$
$257$	−5.43172	−0.338822	−0.169411	+	0.985546i	$0.554186\pi$
$258$	8.75182	0.544864
$259$	29.6847	1.84452
$260$	1.05542	0.0654541
$261$	−4.80690	−0.297540
$262$	−7.71101	−0.476388
$263$	14.2862	0.880927	0.440464	−	0.897770i	$-0.354814\pi$
$263$	14.2862	0.880927	0.440464	+	0.897770i	$0.354814\pi$
$264$	8.29049	0.510244
$265$	−9.94290	−0.610787
$266$	−0.572274	−0.0350884
$267$	−6.02005	−0.368421
$268$	−0.667538	−0.0407764
$269$	−11.6570	−0.710740	−0.355370	−	0.934726i	$-0.615645\pi$
$269$	−11.6570	−0.710740	−0.355370	+	0.934726i	$0.615645\pi$
$270$	−1.42705	−0.0868477
$271$	13.7104	0.832846	0.416423	−	0.909171i	$-0.363283\pi$
$271$	13.7104	0.832846	0.416423	+	0.909171i	$0.363283\pi$
$272$	−21.6724	−1.31408
$273$	−7.93014	−0.479954
$274$	−1.05604	−0.0637979
$275$	16.1393	0.973235
$276$	−3.34819	−0.201537
$277$	8.82889	0.530476	0.265238	−	0.964183i	$-0.414549\pi$
$277$	8.82889	0.530476	0.265238	+	0.964183i	$0.414549\pi$
$278$	−1.14345	−0.0685795
$279$	−0.0919769	−0.00550651
$280$	8.33323	0.498006
$281$	21.9564	1.30981	0.654903	−	0.755713i	$-0.272709\pi$
$281$	21.9564	1.30981	0.654903	+	0.755713i	$0.272709\pi$
$282$	0.130583	0.00777609
$283$	−18.0309	−1.07182	−0.535912	−	0.844274i	$-0.680032\pi$
$283$	−18.0309	−1.07182	−0.535912	+	0.844274i	$0.680032\pi$
$284$	9.11657	0.540969
$285$	0.0698578	0.00413802
$286$	11.2587	0.665740
$287$	−2.55611	−0.150882
$288$	−3.63326	−0.214092
$289$	2.64675	0.155691
$290$	6.85970	0.402816
$291$	−3.37305	−0.197732
$292$	8.19111	0.479349
$293$	−3.55308	−0.207573	−0.103787	−	0.994600i	$-0.533096\pi$
$293$	−3.55308	−0.207573	−0.103787	+	0.994600i	$0.533096\pi$
$294$	19.9356	1.16267
$295$	9.81885	0.571675
$296$	−14.7409	−0.856799
$297$	−3.80952	−0.221051
$298$	7.97498	0.461978
$299$	9.07604	0.524881
$300$	−2.82807	−0.163279
$301$	23.4834	1.35356
$302$	−15.1068	−0.869297
$303$	−9.30450	−0.534529
$304$	0.390924	0.0224210
$305$	10.3460	0.592409
$306$	7.23937	0.413847
$307$	−6.86420	−0.391761	−0.195880	−	0.980628i	$-0.562756\pi$
$307$	−6.86420	−0.391761	−0.195880	+	0.980628i	$0.562756\pi$
$308$	−11.1446	−0.635022
$309$	14.3460	0.816115
$310$	0.131256	0.00745483
$311$	21.0795	1.19531	0.597653	−	0.801755i	$-0.296100\pi$
$311$	21.0795	1.19531	0.597653	+	0.801755i	$0.296100\pi$
$312$	3.93797	0.222944
$313$	27.1988	1.53737	0.768684	−	0.639628i	$-0.220912\pi$
$313$	27.1988	1.53737	0.768684	+	0.639628i	$0.220912\pi$
$314$	38.7604	2.18738
$315$	−3.82916	−0.215749
$316$	10.9907	0.618273
$317$	22.9183	1.28722	0.643610	−	0.765354i	$-0.277436\pi$
$317$	22.9183	1.28722	0.643610	+	0.765354i	$0.277436\pi$
$318$	18.5859	1.04225
$319$	18.3120	1.02527
$320$	−3.35945	−0.187799
$321$	15.4985	0.865044
$322$	−35.9011	−2.00069
$323$	−0.354385	−0.0197185
$324$	0.667538	0.0370854
$325$	7.66614	0.425241
$326$	2.40682	0.133301
$327$	−15.7570	−0.871365
$328$	1.26932	0.0700864
$329$	0.350388	0.0193175
$330$	5.43638	0.299263
$331$	−16.7358	−0.919885	−0.459943	−	0.887949i	$-0.652130\pi$
$331$	−16.7358	−0.919885	−0.459943	+	0.887949i	$0.652130\pi$
$332$	0.988003	0.0542237
$333$	6.77352	0.371187
$334$	11.4236	0.625073
$335$	0.873745	0.0477378
$336$	−21.4279	−1.16899
$337$	−29.8690	−1.62707	−0.813534	−	0.581518i	$-0.802459\pi$
$337$	−29.8690	−1.62707	−0.813534	+	0.581518i	$0.802459\pi$
$338$	−15.8845	−0.864004
$339$	−9.74619	−0.529340
$340$	−2.58527	−0.140206
$341$	0.350388	0.0189746
$342$	−0.130583	−0.00706110
$343$	22.8151	1.23190
$344$	−11.6615	−0.628744
$345$	4.38246	0.235944
$346$	−39.7461	−2.13677
$347$	−7.53508	−0.404504	−0.202252	−	0.979333i	$-0.564826\pi$
$347$	−7.53508	−0.404504	−0.202252	+	0.979333i	$0.564826\pi$
$348$	−3.20879	−0.172009
$349$	18.4790	0.989160	0.494580	−	0.869132i	$-0.335322\pi$
$349$	18.4790	0.989160	0.494580	+	0.869132i	$0.335322\pi$
$350$	−30.3241	−1.62089
$351$	−1.80952	−0.0965849
$352$	13.8410	0.737726
$353$	−18.6854	−0.994523	−0.497261	−	0.867601i	$-0.665661\pi$
$353$	−18.6854	−0.994523	−0.497261	+	0.867601i	$0.665661\pi$
$354$	−18.3540	−0.975505
$355$	−11.9327	−0.633324
$356$	−4.01861	−0.212986
$357$	19.4251	1.02809
$358$	24.9321	1.31770
$359$	31.8492	1.68094	0.840468	−	0.541860i	$-0.182280\pi$
$359$	31.8492	1.68094	0.840468	+	0.541860i	$0.182280\pi$
$360$	1.90149	0.100218
$361$	−18.9936	−0.999664
$362$	−25.3727	−1.33356
$363$	3.51242	0.184354
$364$	−5.29367	−0.277464
$365$	−10.7214	−0.561184
$366$	−19.3394	−1.01089
$367$	−27.9464	−1.45879	−0.729395	−	0.684093i	$-0.760198\pi$
$367$	−27.9464	−1.45879	−0.729395	+	0.684093i	$0.760198\pi$
$368$	24.5242	1.27841
$369$	−0.583258	−0.0303632
$370$	−9.66618	−0.502521
$371$	49.8708	2.58916
$372$	−0.0613981	−0.00318334
$373$	25.8331	1.33759	0.668794	−	0.743447i	$-0.266811\pi$
$373$	25.8331	1.33759	0.668794	+	0.743447i	$0.266811\pi$
$374$	−27.5785	−1.42605
$375$	8.07041	0.416754
$376$	−0.173997	−0.00897318
$377$	8.69817	0.447979
$378$	7.15770	0.368153
$379$	10.8983	0.559809	0.279904	−	0.960028i	$-0.409697\pi$
$379$	10.8983	0.559809	0.279904	+	0.960028i	$0.409697\pi$
$380$	0.0466328	0.00239221
$381$	−13.2128	−0.676912
$382$	12.6507	0.647267
$383$	−0.264476	−0.0135141	−0.00675704	−	0.999977i	$-0.502151\pi$
$383$	−0.264476	−0.0135141	−0.00675704	+	0.999977i	$0.502151\pi$
$384$	13.5462	0.691277
$385$	14.5872	0.743434
$386$	−27.6938	−1.40958
$387$	5.35850	0.272388
$388$	−2.25164	−0.114310
$389$	23.9245	1.21302	0.606510	−	0.795076i	$-0.292569\pi$
$389$	23.9245	1.21302	0.606510	+	0.795076i	$0.292569\pi$
$390$	2.58228	0.130759
$391$	−22.2320	−1.12432
$392$	−26.5634	−1.34165
$393$	−4.72124	−0.238155
$394$	−1.43772	−0.0724311
$395$	−14.3858	−0.723826
$396$	−2.54300	−0.127790
$397$	38.6911	1.94185	0.970925	−	0.239385i	$-0.0769459\pi$
$397$	38.6911	1.94185	0.970925	+	0.239385i	$0.0769459\pi$
$398$	−26.4154	−1.32408
$399$	−0.350388	−0.0175413
$400$	20.7146	1.03573
$401$	16.2862	0.813296	0.406648	−	0.913585i	$-0.366698\pi$
$401$	16.2862	0.813296	0.406648	+	0.913585i	$0.366698\pi$
$402$	−1.63326	−0.0814596
$403$	0.166434	0.00829066
$404$	−6.21110	−0.309014
$405$	−0.873745	−0.0434167
$406$	−34.4064	−1.70756
$407$	−25.8039	−1.27905
$408$	−9.64618	−0.477557
$409$	−22.7439	−1.12461	−0.562306	−	0.826929i	$-0.690086\pi$
$409$	−22.7439	−1.12461	−0.562306	+	0.826929i	$0.690086\pi$
$410$	0.832340	0.0411063
$411$	−0.646586	−0.0318938
$412$	9.57649	0.471800
$413$	−49.2486	−2.42337
$414$	−8.19198	−0.402614
$415$	−1.29320	−0.0634809
$416$	6.57444	0.322339
$417$	−0.700102	−0.0342841
$418$	0.497457	0.0243314
$419$	−10.8632	−0.530703	−0.265351	−	0.964152i	$-0.585488\pi$
$419$	−10.8632	−0.530703	−0.265351	+	0.964152i	$0.585488\pi$
$420$	−2.55611	−0.124725
$421$	−34.4414	−1.67857	−0.839285	−	0.543692i	$-0.817026\pi$
$421$	−34.4414	−1.67857	−0.839285	+	0.543692i	$0.817026\pi$
$422$	−6.04234	−0.294136
$423$	0.0799522	0.00388741
$424$	−24.7650	−1.20270
$425$	−18.7785	−0.910889
$426$	22.3054	1.08070
$427$	−51.8926	−2.51126
$428$	10.3459	0.500086
$429$	6.89338	0.332816
$430$	−7.64686	−0.368764
$431$	28.8886	1.39151	0.695757	−	0.718278i	$-0.255069\pi$
$431$	28.8886	1.39151	0.695757	+	0.718278i	$0.255069\pi$
$432$	−4.88947	−0.235245
$433$	−37.2010	−1.78776	−0.893882	−	0.448302i	$-0.852029\pi$
$433$	−37.2010	−1.78776	−0.893882	+	0.448302i	$0.852029\pi$
$434$	−0.658343	−0.0316015
$435$	4.20001	0.201375
$436$	−10.5184	−0.503740
$437$	0.401018	0.0191833
$438$	20.0411	0.957602
$439$	36.1962	1.72755	0.863776	−	0.503877i	$-0.168093\pi$
$439$	36.1962	1.72755	0.863776	+	0.503877i	$0.168093\pi$
$440$	−7.24377	−0.345333
$441$	12.2060	0.581238
$442$	−13.0998	−0.623092
$443$	4.04994	0.192419	0.0962093	−	0.995361i	$-0.469328\pi$
$443$	4.04994	0.192419	0.0962093	+	0.995361i	$0.469328\pi$
$444$	4.52158	0.214585
$445$	5.25999	0.249347
$446$	18.3382	0.868339
$447$	4.88286	0.230951
$448$	16.8500	0.796090
$449$	−9.52520	−0.449522	−0.224761	−	0.974414i	$-0.572160\pi$
$449$	−9.52520	−0.449522	−0.224761	+	0.974414i	$0.572160\pi$
$450$	−6.91942	−0.326185
$451$	2.22193	0.104627
$452$	−6.50595	−0.306014
$453$	−9.24946	−0.434578
$454$	−21.0448	−0.987681
$455$	6.92892	0.324833
$456$	0.173997	0.00814813
$457$	−9.19086	−0.429931	−0.214965	−	0.976622i	$-0.568964\pi$
$457$	−9.19086	−0.429931	−0.214965	+	0.976622i	$0.568964\pi$
$458$	−20.0052	−0.934783
$459$	4.43247	0.206890
$460$	2.92546	0.136400
$461$	11.6977	0.544815	0.272408	−	0.962182i	$-0.412180\pi$
$461$	11.6977	0.544815	0.272408	+	0.962182i	$0.412180\pi$
$462$	−27.2674	−1.26859
$463$	−5.28907	−0.245804	−0.122902	−	0.992419i	$-0.539220\pi$
$463$	−5.28907	−0.245804	−0.122902	+	0.992419i	$0.539220\pi$
$464$	23.5032	1.09111
$465$	0.0803644	0.00372681
$466$	−27.2038	−1.26019
$467$	34.5447	1.59854	0.799270	−	0.600972i	$-0.205220\pi$
$467$	34.5447	1.59854	0.799270	+	0.600972i	$0.205220\pi$
$468$	−1.20792	−0.0558362
$469$	−4.38246	−0.202363
$470$	−0.114096	−0.00526286
$471$	23.7319	1.09351
$472$	24.4560	1.12568
$473$	−20.4133	−0.938604
$474$	26.8908	1.23513
$475$	0.338723	0.0155417
$476$	12.9670	0.594342
$477$	11.3796	0.521038
$478$	21.8310	0.998527
$479$	−2.70859	−0.123758	−0.0618792	−	0.998084i	$-0.519709\pi$
$479$	−2.70859	−0.123758	−0.0618792	+	0.998084i	$0.519709\pi$
$480$	3.17454	0.144897
$481$	−12.2568	−0.558862
$482$	−14.0261	−0.638870
$483$	−21.9812	−1.00018
$484$	2.34467	0.106576
$485$	2.94719	0.133825
$486$	1.63326	0.0740862
$487$	8.33126	0.377526	0.188763	−	0.982023i	$-0.439552\pi$
$487$	8.33126	0.377526	0.188763	+	0.982023i	$0.439552\pi$
$488$	25.7690	1.16651
$489$	1.47363	0.0666397
$490$	−17.4186	−0.786892
$491$	7.25828	0.327561	0.163781	−	0.986497i	$-0.447631\pi$
$491$	7.25828	0.327561	0.163781	+	0.986497i	$0.447631\pi$
$492$	−0.389347	−0.0175531
$493$	−21.3064	−0.959594
$494$	0.236292	0.0106313
$495$	3.32855	0.149607
$496$	0.449718	0.0201929
$497$	59.8514	2.68470
$498$	2.41734	0.108324
$499$	12.4977	0.559475	0.279738	−	0.960076i	$-0.409753\pi$
$499$	12.4977	0.559475	0.279738	+	0.960076i	$0.409753\pi$
$500$	5.38730	0.240928
$501$	6.99437	0.312485
$502$	−36.4525	−1.62695
$503$	13.2554	0.591030	0.295515	−	0.955338i	$-0.404509\pi$
$503$	13.2554	0.591030	0.295515	+	0.955338i	$0.404509\pi$
$504$	−9.53737	−0.424828
$505$	8.12976	0.361769
$506$	31.2075	1.38734
$507$	−9.72565	−0.431931
$508$	−8.82004	−0.391326
$509$	32.9171	1.45903	0.729513	−	0.683967i	$-0.239747\pi$
$509$	32.9171	1.45903	0.729513	+	0.683967i	$0.239747\pi$
$510$	−6.32536	−0.280092
$511$	53.7756	2.37889
$512$	−3.51677	−0.155421
$513$	−0.0799522	−0.00352998
$514$	−8.87142	−0.391301
$515$	−12.5347	−0.552346
$516$	3.57700	0.157469
$517$	−0.304579	−0.0133954
$518$	48.4829	2.13022
$519$	−24.3355	−1.06821
$520$	−3.44078	−0.150888
$521$	33.3315	1.46028	0.730141	−	0.683297i	$-0.239455\pi$
$521$	33.3315	1.46028	0.730141	+	0.683297i	$0.239455\pi$
$522$	−7.85092	−0.343626
$523$	−24.7505	−1.08226	−0.541131	−	0.840938i	$-0.682004\pi$
$523$	−24.7505	−1.08226	−0.541131	+	0.840938i	$0.682004\pi$
$524$	−3.15161	−0.137679
$525$	−18.5666	−0.810313
$526$	23.3331	1.01737
$527$	−0.407685	−0.0177590
$528$	18.6265	0.810615
$529$	2.15749	0.0938038
$530$	−16.2393	−0.705392
$531$	−11.2377	−0.487673
$532$	−0.233897	−0.0101407
$533$	1.05542	0.0457151
$534$	−9.83231	−0.425486
$535$	−13.5418	−0.585462
$536$	2.17626	0.0940000
$537$	15.2652	0.658743
$538$	−19.0389	−0.820826
$539$	−46.4989	−2.00285
$540$	−0.583258	−0.0250994
$541$	21.3014	0.915819	0.457909	−	0.888999i	$-0.348598\pi$
$541$	21.3014	0.915819	0.457909	+	0.888999i	$0.348598\pi$
$542$	22.3926	0.961845
$543$	−15.5350	−0.666672
$544$	−16.1043	−0.690466
$545$	13.7676	0.589740
$546$	−12.9520	−0.554294
$547$	27.1177	1.15947	0.579734	−	0.814806i	$-0.303156\pi$
$547$	27.1177	1.15947	0.579734	+	0.814806i	$0.303156\pi$
$548$	−0.431621	−0.0184379
$549$	−11.8410	−0.505360
$550$	26.3596	1.12398
$551$	0.384322	0.0163727
$552$	10.9155	0.464595
$553$	72.1550	3.06834
$554$	14.4199	0.612641
$555$	−5.91833	−0.251219
$556$	−0.467345	−0.0198198
$557$	−44.4249	−1.88234	−0.941172	−	0.337927i	$-0.890274\pi$
$557$	−44.4249	−1.88234	−0.941172	+	0.337927i	$0.890274\pi$
$558$	−0.150222	−0.00635941
$559$	−9.69629	−0.410109
$560$	18.7225	0.791172
$561$	−16.8856	−0.712909
$562$	35.8604	1.51268
$563$	−17.1520	−0.722870	−0.361435	−	0.932397i	$-0.617713\pi$
$563$	−17.1520	−0.722870	−0.361435	+	0.932397i	$0.617713\pi$
$564$	0.0533711	0.00224733
$565$	8.51568	0.358258
$566$	−29.4491	−1.23784
$567$	4.38246	0.184046
$568$	−29.7212	−1.24707
$569$	−10.9685	−0.459823	−0.229912	−	0.973211i	$-0.573844\pi$
$569$	−10.9685	−0.459823	−0.229912	+	0.973211i	$0.573844\pi$
$570$	0.114096	0.00477896
$571$	−1.31105	−0.0548659	−0.0274329	−	0.999624i	$-0.508733\pi$
$571$	−1.31105	−0.0548659	−0.0274329	+	0.999624i	$0.508733\pi$
$572$	4.60160	0.192402
$573$	7.74569	0.323581
$574$	−4.17479	−0.174252
$575$	21.2495	0.886164
$576$	3.84488	0.160203
$577$	−9.37049	−0.390099	−0.195049	−	0.980793i	$-0.562487\pi$
$577$	−9.37049	−0.390099	−0.195049	+	0.980793i	$0.562487\pi$
$578$	4.32284	0.179806
$579$	−16.9562	−0.704675
$580$	2.80366	0.116416
$581$	6.48636	0.269099
$582$	−5.50907	−0.228358
$583$	−43.3509	−1.79541
$584$	−26.7040	−1.10502
$585$	1.58106	0.0653686
$586$	−5.80310	−0.239724
$587$	−36.9358	−1.52450	−0.762252	−	0.647280i	$-0.775906\pi$
$587$	−36.9358	−1.52450	−0.762252	+	0.647280i	$0.775906\pi$
$588$	8.14796	0.336016
$589$	0.00735376	0.000303006 0
$590$	16.0367	0.660222
$591$	−0.880274	−0.0362097
$592$	−33.1189	−1.36118
$593$	−15.3964	−0.632254	−0.316127	−	0.948717i	$-0.602383\pi$
$593$	−15.3964	−0.632254	−0.316127	+	0.948717i	$0.602383\pi$
$594$	−6.22193	−0.255289
$595$	−16.9726	−0.695809
$596$	3.25949	0.133514
$597$	−16.1734	−0.661934
$598$	14.8235	0.606179
$599$	12.9187	0.527845	0.263923	−	0.964544i	$-0.414984\pi$
$599$	12.9187	0.527845	0.263923	+	0.964544i	$0.414984\pi$
$600$	9.21986	0.376399
$601$	9.80552	0.399975	0.199988	−	0.979798i	$-0.435910\pi$
$601$	9.80552	0.399975	0.199988	+	0.979798i	$0.435910\pi$
$602$	38.3545	1.56321
$603$	−1.00000	−0.0407231
$604$	−6.17437	−0.251231
$605$	−3.06896	−0.124771
$606$	−15.1967	−0.617322
$607$	−15.7049	−0.637444	−0.318722	−	0.947848i	$-0.603254\pi$
$607$	−15.7049	−0.637444	−0.318722	+	0.947848i	$0.603254\pi$
$608$	0.290487	0.0117808
$609$	−21.0661	−0.853641
$610$	16.8977	0.684167
$611$	−0.144675	−0.00585292
$612$	2.95884	0.119604
$613$	−14.9071	−0.602092	−0.301046	−	0.953610i	$-0.597336\pi$
$613$	−14.9071	−0.602092	−0.301046	+	0.953610i	$0.597336\pi$
$614$	−11.2110	−0.452440
$615$	0.509619	0.0205498
$616$	36.3328	1.46389
$617$	4.39705	0.177018	0.0885092	−	0.996075i	$-0.471790\pi$
$617$	4.39705	0.177018	0.0885092	+	0.996075i	$0.471790\pi$
$618$	23.4307	0.942522
$619$	18.3945	0.739336	0.369668	−	0.929164i	$-0.379471\pi$
$619$	18.3945	0.739336	0.369668	+	0.929164i	$0.379471\pi$
$620$	0.0536463	0.00215449
$621$	−5.01572	−0.201274
$622$	34.4282	1.38045
$623$	−26.3827	−1.05700
$624$	8.84758	0.354187
$625$	14.1314	0.565255
$626$	44.4228	1.77549
$627$	0.304579	0.0121637
$628$	15.8420	0.632163
$629$	30.0234	1.19711
$630$	−6.25401	−0.249166
$631$	−38.8360	−1.54604	−0.773019	−	0.634383i	$-0.781254\pi$
$631$	−38.8360	−1.54604	−0.773019	+	0.634383i	$0.781254\pi$
$632$	−35.8309	−1.42528
$633$	−3.69956	−0.147044
$634$	37.4315	1.48660
$635$	11.5446	0.458134
$636$	7.59634	0.301214
$637$	−22.0869	−0.875117
$638$	29.9082	1.18408
$639$	13.6570	0.540263
$640$	−11.8359	−0.467856
$641$	23.4343	0.925598	0.462799	−	0.886463i	$-0.346845\pi$
$641$	23.4343	0.925598	0.462799	+	0.886463i	$0.346845\pi$
$642$	25.3132	0.999030
$643$	−27.0304	−1.06597	−0.532987	−	0.846123i	$-0.678931\pi$
$643$	−27.0304	−1.06597	−0.532987	+	0.846123i	$0.678931\pi$
$644$	−14.6733	−0.578209
$645$	−4.68196	−0.184352
$646$	−0.578803	−0.0227727
$647$	−5.81082	−0.228447	−0.114223	−	0.993455i	$-0.536438\pi$
$647$	−5.81082	−0.228447	−0.114223	+	0.993455i	$0.536438\pi$
$648$	−2.17626	−0.0854914
$649$	42.8100	1.68044
$650$	12.5208	0.491106
$651$	−0.403086	−0.0157982
$652$	0.983702	0.0385247
$653$	−2.88614	−0.112944	−0.0564718	−	0.998404i	$-0.517985\pi$
$653$	−2.88614	−0.112944	−0.0564718	+	0.998404i	$0.517985\pi$
$654$	−25.7353	−1.00633
$655$	4.12516	0.161183
$656$	2.85182	0.111345
$657$	12.2706	0.478723
$658$	0.572274	0.0223096
$659$	−21.2604	−0.828188	−0.414094	−	0.910234i	$-0.635901\pi$
$659$	−21.2604	−0.828188	−0.414094	+	0.910234i	$0.635901\pi$
$660$	2.22193	0.0864885
$661$	−20.5421	−0.798994	−0.399497	−	0.916735i	$-0.630815\pi$
$661$	−20.5421	−0.798994	−0.399497	+	0.916735i	$0.630815\pi$
$662$	−27.3340	−1.06237
$663$	−8.02062	−0.311495
$664$	−3.22101	−0.125000
$665$	0.306149	0.0118720
$666$	11.0629	0.428680
$667$	24.1101	0.933547
$668$	4.66901	0.180649
$669$	11.2280	0.434099
$670$	1.42705	0.0551319
$671$	45.1084	1.74139
$672$	−15.9226	−0.614229
$673$	16.0245	0.617699	0.308849	−	0.951111i	$-0.400056\pi$
$673$	16.0245	0.617699	0.308849	+	0.951111i	$0.400056\pi$
$674$	−48.7838	−1.87908
$675$	−4.23657	−0.163066
$676$	−6.49224	−0.249702
$677$	7.49003	0.287865	0.143933	−	0.989587i	$-0.454025\pi$
$677$	7.49003	0.287865	0.143933	+	0.989587i	$0.454025\pi$
$678$	−15.9181	−0.611329
$679$	−14.7823	−0.567292
$680$	8.42831	0.323211
$681$	−12.8851	−0.493760
$682$	0.572274	0.0219135
$683$	−6.01975	−0.230339	−0.115170	−	0.993346i	$-0.536741\pi$
$683$	−6.01975	−0.230339	−0.115170	+	0.993346i	$0.536741\pi$
$684$	−0.0533711	−0.00204070
$685$	0.564952	0.0215857
$686$	37.2629	1.42271
$687$	−12.2486	−0.467315
$688$	−26.2002	−0.998873
$689$	−20.5916	−0.784479
$690$	7.15770	0.272489
$691$	25.0646	0.953502	0.476751	−	0.879039i	$-0.341814\pi$
$691$	25.0646	0.953502	0.476751	+	0.879039i	$0.341814\pi$
$692$	−16.2448	−0.617536
$693$	−16.6951	−0.634193
$694$	−12.3067	−0.467158
$695$	0.611711	0.0232035
$696$	10.4611	0.396525
$697$	−2.58527	−0.0979241
$698$	30.1811	1.14237
$699$	−16.6561	−0.629992
$700$	−12.3939	−0.468446
$701$	−27.6240	−1.04334	−0.521672	−	0.853146i	$-0.674691\pi$
$701$	−27.6240	−1.04334	−0.521672	+	0.853146i	$0.674691\pi$
$702$	−2.95541	−0.111545
$703$	−0.541558	−0.0204253
$704$	−14.6471	−0.552035
$705$	−0.0698578	−0.00263100
$706$	−30.5181	−1.14856
$707$	−40.7766	−1.53356
$708$	−7.50156	−0.281926
$709$	21.5304	0.808590	0.404295	−	0.914629i	$-0.367517\pi$
$709$	21.5304	0.808590	0.404295	+	0.914629i	$0.367517\pi$
$710$	−19.4893	−0.731419
$711$	16.4645	0.617466
$712$	13.1012	0.490987
$713$	0.461331	0.0172770
$714$	31.7263	1.18733
$715$	−6.02306	−0.225250
$716$	10.1901	0.380822
$717$	13.3665	0.499182
$718$	52.0180	1.94130
$719$	−51.9617	−1.93785	−0.968923	−	0.247363i	$-0.920436\pi$
$719$	−51.9617	−1.93785	−0.968923	+	0.247363i	$0.920436\pi$
$720$	4.27215	0.159214
$721$	62.8708	2.34143
$722$	−31.0215	−1.15450
$723$	−8.58777	−0.319383
$724$	−10.3702	−0.385406
$725$	20.3648	0.756329
$726$	5.73669	0.212909
$727$	−23.3554	−0.866205	−0.433103	−	0.901345i	$-0.642581\pi$
$727$	−23.3554	−0.866205	−0.433103	+	0.901345i	$0.642581\pi$
$728$	17.2580	0.639625
$729$	1.00000	0.0370370
$730$	−17.5108	−0.648105
$731$	23.7514	0.878476
$732$	−7.90429	−0.292151
$733$	1.17517	0.0434059	0.0217030	−	0.999764i	$-0.493091\pi$
$733$	1.17517	0.0434059	0.0217030	+	0.999764i	$0.493091\pi$
$734$	−45.6437	−1.68474
$735$	−10.6649	−0.393382
$736$	18.2234	0.671724
$737$	3.80952	0.140325
$738$	−0.952612	−0.0350661
$739$	−17.2847	−0.635828	−0.317914	−	0.948119i	$-0.602982\pi$
$739$	−17.2847	−0.635828	−0.317914	+	0.948119i	$0.602982\pi$
$740$	−3.95071	−0.145231
$741$	0.144675	0.00531476
$742$	81.4520	2.99020
$743$	−34.3919	−1.26172	−0.630858	−	0.775898i	$-0.717297\pi$
$743$	−34.3919	−1.26172	−0.630858	+	0.775898i	$0.717297\pi$
$744$	0.200165	0.00733842
$745$	−4.26637	−0.156308
$746$	42.1922	1.54477
$747$	1.48007	0.0541529
$748$	−11.2717	−0.412136
$749$	67.9218	2.48181
$750$	13.1811	0.481305
$751$	30.0576	1.09682	0.548409	−	0.836210i	$-0.315234\pi$
$751$	30.0576	1.09682	0.548409	+	0.836210i	$0.315234\pi$
$752$	−0.390924	−0.0142555
$753$	−22.3188	−0.813344
$754$	14.2064	0.517366
$755$	8.08167	0.294122
$756$	2.92546	0.106398
$757$	−8.60899	−0.312899	−0.156450	−	0.987686i	$-0.550005\pi$
$757$	−8.60899	−0.312899	−0.156450	+	0.987686i	$0.550005\pi$
$758$	17.7998	0.646517
$759$	19.1075	0.693558
$760$	−0.152029	−0.00551466
$761$	10.7555	0.389888	0.194944	−	0.980814i	$-0.437547\pi$
$761$	10.7555	0.389888	0.194944	+	0.980814i	$0.437547\pi$
$762$	−21.5799	−0.781758
$763$	−69.0545	−2.49994
$764$	5.17054	0.187064
$765$	−3.87285	−0.140023
$766$	−0.431958	−0.0156073
$767$	20.3347	0.734244
$768$	14.4347	0.520868
$769$	−43.6034	−1.57238	−0.786190	−	0.617985i	$-0.787949\pi$
$769$	−43.6034	−1.57238	−0.786190	+	0.617985i	$0.787949\pi$
$770$	23.8247	0.858584
$771$	−5.43172	−0.195619
$772$	−11.3189	−0.407376
$773$	8.09927	0.291311	0.145655	−	0.989335i	$-0.453471\pi$
$773$	8.09927	0.291311	0.145655	+	0.989335i	$0.453471\pi$
$774$	8.75182	0.314578
$775$	0.389667	0.0139972
$776$	7.34063	0.263513
$777$	29.6847	1.06493
$778$	39.0749	1.40090
$779$	0.0466328	0.00167079
$780$	1.05542	0.0377899
$781$	−52.0266	−1.86166
$782$	−36.3107	−1.29847
$783$	−4.80690	−0.171785
$784$	−59.6808	−2.13146
$785$	−20.7357	−0.740087
$786$	−7.71101	−0.275043
$787$	10.3069	0.367403	0.183701	−	0.982982i	$-0.441192\pi$
$787$	10.3069	0.367403	0.183701	+	0.982982i	$0.441192\pi$
$788$	−0.587617	−0.0209330
$789$	14.2862	0.508604
$790$	−23.4957	−0.835939
$791$	−42.7123	−1.51868
$792$	8.29049	0.294590
$793$	21.4264	0.760875
$794$	63.1926	2.24262
$795$	−9.94290	−0.352638
$796$	−10.7964	−0.382667
$797$	−33.5492	−1.18837	−0.594186	−	0.804327i	$-0.702526\pi$
$797$	−33.5492	−1.18837	−0.594186	+	0.804327i	$0.702526\pi$
$798$	−0.572274	−0.0202583
$799$	0.354385	0.0125373
$800$	15.3926	0.544209
$801$	−6.02005	−0.212708
$802$	26.5997	0.939267
$803$	−46.7452	−1.64960
$804$	−0.667538	−0.0235422
$805$	19.2060	0.676922
$806$	0.271830	0.00957479
$807$	−11.6570	−0.410346
$808$	20.2490	0.712356
$809$	−17.6127	−0.619228	−0.309614	−	0.950862i	$-0.600200\pi$
$809$	−17.6127	−0.619228	−0.309614	+	0.950862i	$0.600200\pi$
$810$	−1.42705	−0.0501415
$811$	30.4108	1.06787	0.533934	−	0.845526i	$-0.320713\pi$
$811$	30.4108	1.06787	0.533934	+	0.845526i	$0.320713\pi$
$812$	−14.0624	−0.493494
$813$	13.7104	0.480844
$814$	−42.1444	−1.47716
$815$	−1.28757	−0.0451018
$816$	−21.6724	−0.758686
$817$	−0.428424	−0.0149886
$818$	−37.1467	−1.29880
$819$	−7.93014	−0.277102
$820$	0.340190	0.0118799
$821$	−38.5581	−1.34569	−0.672843	−	0.739785i	$-0.734927\pi$
$821$	−38.5581	−1.34569	−0.672843	+	0.739785i	$0.734927\pi$
$822$	−1.05604	−0.0368338
$823$	21.1724	0.738022	0.369011	−	0.929425i	$-0.379696\pi$
$823$	21.1724	0.738022	0.369011	+	0.929425i	$0.379696\pi$
$824$	−31.2205	−1.08762
$825$	16.1393	0.561898
$826$	−80.4358	−2.79872
$827$	52.4871	1.82516	0.912578	−	0.408904i	$-0.134089\pi$
$827$	52.4871	1.82516	0.912578	+	0.408904i	$0.134089\pi$
$828$	−3.34819	−0.116358
$829$	6.55325	0.227604	0.113802	−	0.993503i	$-0.463697\pi$
$829$	6.55325	0.227604	0.113802	+	0.993503i	$0.463697\pi$
$830$	−2.11214	−0.0733134
$831$	8.82889	0.306271
$832$	−6.95738	−0.241204
$833$	54.1026	1.87455
$834$	−1.14345	−0.0395944
$835$	−6.11130	−0.211490
$836$	0.203318	0.00703191
$837$	−0.0919769	−0.00317919
$838$	−17.7425	−0.612903
$839$	20.5983	0.711132	0.355566	−	0.934651i	$-0.384288\pi$
$839$	20.5983	0.711132	0.355566	+	0.934651i	$0.384288\pi$
$840$	8.33323	0.287524
$841$	−5.89368	−0.203230
$842$	−56.2517	−1.93856
$843$	21.9564	0.756217
$844$	−2.46959	−0.0850069
$845$	8.49774	0.292331
$846$	0.130583	0.00448953
$847$	15.3930	0.528911
$848$	−55.6404	−1.91070
$849$	−18.0309	−0.618818
$850$	−30.6701	−1.05198
$851$	−33.9741	−1.16462
$852$	9.11657	0.312329
$853$	−15.7239	−0.538376	−0.269188	−	0.963088i	$-0.586755\pi$
$853$	−15.7239	−0.538376	−0.269188	+	0.963088i	$0.586755\pi$
$854$	−84.7541	−2.90023
$855$	0.0698578	0.00238909
$856$	−33.7288	−1.15283
$857$	38.3368	1.30956	0.654781	−	0.755819i	$-0.272761\pi$
$857$	38.3368	1.30956	0.654781	+	0.755819i	$0.272761\pi$
$858$	11.2587	0.384365
$859$	−12.6597	−0.431942	−0.215971	−	0.976400i	$-0.569292\pi$
$859$	−12.6597	−0.431942	−0.215971	+	0.976400i	$0.569292\pi$
$860$	−3.12539	−0.106575
$861$	−2.55611	−0.0871119
$862$	47.1825	1.60704
$863$	6.48961	0.220909	0.110454	−	0.993881i	$-0.464769\pi$
$863$	6.48961	0.220909	0.110454	+	0.993881i	$0.464769\pi$
$864$	−3.63326	−0.123606
$865$	21.2630	0.722963
$866$	−60.7588	−2.06467
$867$	2.64675	0.0898885
$868$	−0.269075	−0.00913300
$869$	−62.7217	−2.12769
$870$	6.85970	0.232566
$871$	1.80952	0.0613131
$872$	34.2913	1.16125
$873$	−3.37305	−0.114161
$874$	0.654967	0.0221546
$875$	35.3683	1.19567
$876$	8.19111	0.276752
$877$	48.6475	1.64271	0.821354	−	0.570418i	$-0.193219\pi$
$877$	48.6475	1.64271	0.821354	+	0.570418i	$0.193219\pi$
$878$	59.1178	1.99513
$879$	−3.55308	−0.119842
$880$	−16.2748	−0.548624
$881$	12.3757	0.416947	0.208473	−	0.978028i	$-0.433151\pi$
$881$	12.3757	0.416947	0.208473	+	0.978028i	$0.433151\pi$
$882$	19.9356	0.671265
$883$	10.0463	0.338086	0.169043	−	0.985609i	$-0.445932\pi$
$883$	10.0463	0.338086	0.169043	+	0.985609i	$0.445932\pi$
$884$	−5.35407	−0.180077
$885$	9.81885	0.330057
$886$	6.61461	0.222222
$887$	37.8737	1.27167	0.635837	−	0.771823i	$-0.280655\pi$
$887$	37.8737	1.27167	0.635837	+	0.771823i	$0.280655\pi$
$888$	−14.7409	−0.494673
$889$	−57.9046	−1.94206
$890$	8.59093	0.287969
$891$	−3.80952	−0.127624
$892$	7.49510	0.250954
$893$	−0.00639235	−0.000213912 0
$894$	7.97498	0.266723
$895$	−13.3379	−0.445837
$896$	59.3658	1.98327
$897$	9.07604	0.303040
$898$	−15.5571	−0.519148
$899$	0.442124	0.0147457
$900$	−2.82807	−0.0942690
$901$	50.4398	1.68039
$902$	3.62899	0.120832
$903$	23.4834	0.781479
$904$	21.2102	0.705441
$905$	13.5737	0.451203
$906$	−15.1068	−0.501889
$907$	−19.1181	−0.634805	−0.317403	−	0.948291i	$-0.602811\pi$
$907$	−19.1181	−0.634805	−0.317403	+	0.948291i	$0.602811\pi$
$908$	−8.60132	−0.285445
$909$	−9.30450	−0.308611
$910$	11.3167	0.375146
$911$	−39.9514	−1.32365	−0.661825	−	0.749658i	$-0.730218\pi$
$911$	−39.9514	−1.32365	−0.661825	+	0.749658i	$0.730218\pi$
$912$	0.390924	0.0129448
$913$	−5.63835	−0.186602
$914$	−15.0111	−0.496522
$915$	10.3460	0.342028
$916$	−8.17644	−0.270157
$917$	−20.6907	−0.683266
$918$	7.23937	0.238935
$919$	11.4882	0.378961	0.189481	−	0.981884i	$-0.439320\pi$
$919$	11.4882	0.378961	0.189481	+	0.981884i	$0.439320\pi$
$920$	−9.53737	−0.314438
$921$	−6.86420	−0.226183
$922$	19.1054	0.629201
$923$	−24.7126	−0.813425
$924$	−11.1446	−0.366630
$925$	−28.6965	−0.943535
$926$	−8.63843	−0.283876
$927$	14.3460	0.471184
$928$	17.4647	0.573308
$929$	−39.3368	−1.29060	−0.645299	−	0.763930i	$-0.723267\pi$
$929$	−39.3368	−1.29060	−0.645299	+	0.763930i	$0.723267\pi$
$930$	0.131256	0.00430405
$931$	−0.975896	−0.0319837
$932$	−11.1186	−0.364201
$933$	21.0795	0.690111
$934$	56.4205	1.84614
$935$	14.7537	0.482497
$936$	3.93797	0.128717
$937$	24.5490	0.801982	0.400991	−	0.916082i	$-0.368666\pi$
$937$	24.5490	0.801982	0.400991	+	0.916082i	$0.368666\pi$
$938$	−7.15770	−0.233707
$939$	27.1988	0.887600
$940$	−0.0466328	−0.00152099
$941$	−38.4244	−1.25260	−0.626300	−	0.779582i	$-0.715431\pi$
$941$	−38.4244	−1.25260	−0.626300	+	0.779582i	$0.715431\pi$
$942$	38.7604	1.26288
$943$	2.92546	0.0952661
$944$	54.9462	1.78835
$945$	−3.82916	−0.124562
$946$	−33.3402	−1.08398
$947$	17.8672	0.580606	0.290303	−	0.956935i	$-0.406244\pi$
$947$	17.8672	0.580606	0.290303	+	0.956935i	$0.406244\pi$
$948$	10.9907	0.356960
$949$	−22.2039	−0.720770
$950$	0.553223	0.0179489
$951$	22.9183	0.743177
$952$	−42.2741	−1.37011
$953$	−20.3652	−0.659694	−0.329847	−	0.944034i	$-0.606997\pi$
$953$	−20.3652	−0.659694	−0.329847	+	0.944034i	$0.606997\pi$
$954$	18.5859	0.601741
$955$	−6.76776	−0.219000
$956$	8.92266	0.288580
$957$	18.3120	0.591942
$958$	−4.42382	−0.142927
$959$	−2.83364	−0.0915031
$960$	−3.35945	−0.108426
$961$	−30.9915	−0.999727
$962$	−20.0186	−0.645424
$963$	15.4985	0.499434
$964$	−5.73266	−0.184637
$965$	14.8154	0.476924
$966$	−35.9011	−1.15510
$967$	23.4919	0.755448	0.377724	−	0.925918i	$-0.376707\pi$
$967$	23.4919	0.755448	0.377724	+	0.925918i	$0.376707\pi$
$968$	−7.64392	−0.245685
$969$	−0.354385	−0.0113845
$970$	4.81352	0.154553
$971$	35.4717	1.13834	0.569171	−	0.822219i	$-0.307264\pi$
$971$	35.4717	1.13834	0.569171	+	0.822219i	$0.307264\pi$
$972$	0.667538	0.0214113
$973$	−3.06817	−0.0983611
$974$	13.6071	0.436000
$975$	7.66614	0.245513
$976$	57.8960	1.85321
$977$	62.3118	1.99353	0.996766	−	0.0803557i	$-0.0256056\pi$
$977$	62.3118	1.99353	0.996766	+	0.0803557i	$0.0256056\pi$
$978$	2.40682	0.0769615
$979$	22.9335	0.732957
$980$	−7.11924	−0.227416
$981$	−15.7570	−0.503083
$982$	11.8547	0.378297
$983$	40.8266	1.30217	0.651083	−	0.759007i	$-0.274315\pi$
$983$	40.8266	1.30217	0.651083	+	0.759007i	$0.274315\pi$
$984$	1.26932	0.0404644
$985$	0.769135	0.0245067
$986$	−34.7989	−1.10822
$987$	0.350388	0.0111530
$988$	0.0965759	0.00307249
$989$	−26.8767	−0.854631
$990$	5.43638	0.172780
$991$	−62.0733	−1.97182	−0.985912	−	0.167265i	$-0.946507\pi$
$991$	−62.0733	−1.97182	−0.985912	+	0.167265i	$0.946507\pi$
$992$	0.334176	0.0106101
$993$	−16.7358	−0.531096
$994$	97.7528	3.10053
$995$	14.1315	0.447997
$996$	0.988003	0.0313061
$997$	−7.72837	−0.244760	−0.122380	−	0.992483i	$-0.539053\pi$
$997$	−7.72837	−0.244760	−0.122380	+	0.992483i	$0.539053\pi$
$998$	20.4120	0.646132
$999$	6.77352	0.214305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.a.e.1.4	✓	5
3.2	odd	2		603.2.a.k.1.2		5
4.3	odd	2		3216.2.a.y.1.3		5
5.4	even	2		5025.2.a.x.1.2		5
7.6	odd	2		9849.2.a.bb.1.4		5
12.11	even	2		9648.2.a.cd.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.e.1.4	✓	5	1.1	even	1	trivial
603.2.a.k.1.2		5	3.2	odd	2
3216.2.a.y.1.3		5	4.3	odd	2
5025.2.a.x.1.2		5	5.4	even	2
9648.2.a.cd.1.3		5	12.11	even	2
9849.2.a.bb.1.4		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)

\(f(q)\)	\(=\)	\(q+1.63326 q^{2} +1.00000 q^{3} +0.667538 q^{4} -0.873745 q^{5} +1.63326 q^{6} +4.38246 q^{7} -2.17626 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.63326 q^{2} +1.00000 q^{3} +0.667538 q^{4} -0.873745 q^{5} +1.63326 q^{6} +4.38246 q^{7} -2.17626 q^{8} +1.00000 q^{9} -1.42705 q^{10} -3.80952 q^{11} +0.667538 q^{12} -1.80952 q^{13} +7.15770 q^{14} -0.873745 q^{15} -4.88947 q^{16} +4.43247 q^{17} +1.63326 q^{18} -0.0799522 q^{19} -0.583258 q^{20} +4.38246 q^{21} -6.22193 q^{22} -5.01572 q^{23} -2.17626 q^{24} -4.23657 q^{25} -2.95541 q^{26} +1.00000 q^{27} +2.92546 q^{28} -4.80690 q^{29} -1.42705 q^{30} -0.0919769 q^{31} -3.63326 q^{32} -3.80952 q^{33} +7.23937 q^{34} -3.82916 q^{35} +0.667538 q^{36} +6.77352 q^{37} -0.130583 q^{38} -1.80952 q^{39} +1.90149 q^{40} -0.583258 q^{41} +7.15770 q^{42} +5.35850 q^{43} -2.54300 q^{44} -0.873745 q^{45} -8.19198 q^{46} +0.0799522 q^{47} -4.88947 q^{48} +12.2060 q^{49} -6.91942 q^{50} +4.43247 q^{51} -1.20792 q^{52} +11.3796 q^{53} +1.63326 q^{54} +3.32855 q^{55} -9.53737 q^{56} -0.0799522 q^{57} -7.85092 q^{58} -11.2377 q^{59} -0.583258 q^{60} -11.8410 q^{61} -0.150222 q^{62} +4.38246 q^{63} +3.84488 q^{64} +1.58106 q^{65} -6.22193 q^{66} -1.00000 q^{67} +2.95884 q^{68} -5.01572 q^{69} -6.25401 q^{70} +13.6570 q^{71} -2.17626 q^{72} +12.2706 q^{73} +11.0629 q^{74} -4.23657 q^{75} -0.0533711 q^{76} -16.6951 q^{77} -2.95541 q^{78} +16.4645 q^{79} +4.27215 q^{80} +1.00000 q^{81} -0.952612 q^{82} +1.48007 q^{83} +2.92546 q^{84} -3.87285 q^{85} +8.75182 q^{86} -4.80690 q^{87} +8.29049 q^{88} -6.02005 q^{89} -1.42705 q^{90} -7.93014 q^{91} -3.34819 q^{92} -0.0919769 q^{93} +0.130583 q^{94} +0.0698578 q^{95} -3.63326 q^{96} -3.37305 q^{97} +19.9356 q^{98} -3.80952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9}+O(q^{10}) \) 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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