LMFDB - Embedded newform 1805.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.62224$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62224 q^{2} +0.928776 q^{3} +4.87613 q^{4} -1.00000 q^{5} -2.43547 q^{6} -3.83157 q^{7} -7.54188 q^{8} -2.13737 q^{9} +O(q^{10})$	\(q-2.62224 q^{2} +0.928776 q^{3} +4.87613 q^{4} -1.00000 q^{5} -2.43547 q^{6} -3.83157 q^{7} -7.54188 q^{8} -2.13737 q^{9} +2.62224 q^{10} -3.26723 q^{11} +4.52883 q^{12} +0.364142 q^{13} +10.0473 q^{14} -0.928776 q^{15} +10.0243 q^{16} -0.684217 q^{17} +5.60470 q^{18} -4.87613 q^{20} -3.55868 q^{21} +8.56746 q^{22} -9.36807 q^{23} -7.00472 q^{24} +1.00000 q^{25} -0.954866 q^{26} -4.77147 q^{27} -18.6832 q^{28} -1.53985 q^{29} +2.43547 q^{30} +2.44889 q^{31} -11.2024 q^{32} -3.03453 q^{33} +1.79418 q^{34} +3.83157 q^{35} -10.4221 q^{36} -0.163399 q^{37} +0.338206 q^{39} +7.54188 q^{40} +7.37370 q^{41} +9.33169 q^{42} +2.58788 q^{43} -15.9314 q^{44} +2.13737 q^{45} +24.5653 q^{46} +8.79680 q^{47} +9.31037 q^{48} +7.68097 q^{49} -2.62224 q^{50} -0.635485 q^{51} +1.77560 q^{52} -11.1190 q^{53} +12.5119 q^{54} +3.26723 q^{55} +28.8973 q^{56} +4.03786 q^{58} +7.78980 q^{59} -4.52883 q^{60} +2.41893 q^{61} -6.42156 q^{62} +8.18951 q^{63} +9.32678 q^{64} -0.364142 q^{65} +7.95725 q^{66} +9.55736 q^{67} -3.33633 q^{68} -8.70084 q^{69} -10.0473 q^{70} +5.12085 q^{71} +16.1198 q^{72} -7.88413 q^{73} +0.428471 q^{74} +0.928776 q^{75} +12.5186 q^{77} -0.886857 q^{78} +9.32066 q^{79} -10.0243 q^{80} +1.98050 q^{81} -19.3356 q^{82} +0.729119 q^{83} -17.3525 q^{84} +0.684217 q^{85} -6.78603 q^{86} -1.43018 q^{87} +24.6411 q^{88} -12.6405 q^{89} -5.60470 q^{90} -1.39524 q^{91} -45.6799 q^{92} +2.27447 q^{93} -23.0673 q^{94} -10.4046 q^{96} +7.54714 q^{97} -20.1413 q^{98} +6.98330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.62224	−1.85420	−0.927101	−	0.374812i	$-0.877707\pi$
$2$	−2.62224	−1.85420	−0.927101	+	0.374812i	$0.877707\pi$
$3$	0.928776	0.536229	0.268115	−	0.963387i	$-0.413599\pi$
$3$	0.928776	0.536229	0.268115	+	0.963387i	$0.413599\pi$
$4$	4.87613	2.43806
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.43547	−0.994277
$7$	−3.83157	−1.44820	−0.724100	−	0.689695i	$-0.757744\pi$
$7$	−3.83157	−1.44820	−0.724100	+	0.689695i	$0.757744\pi$
$8$	−7.54188	−2.66646
$9$	−2.13737	−0.712458
$10$	2.62224	0.829224
$11$	−3.26723	−0.985108	−0.492554	−	0.870282i	$-0.663937\pi$
$11$	−3.26723	−0.985108	−0.492554	+	0.870282i	$0.663937\pi$
$12$	4.52883	1.30736
$13$	0.364142	0.100995	0.0504974	−	0.998724i	$-0.483919\pi$
$13$	0.364142	0.100995	0.0504974	+	0.998724i	$0.483919\pi$
$14$	10.0473	2.68525
$15$	−0.928776	−0.239809
$16$	10.0243	2.50609
$17$	−0.684217	−0.165947	−0.0829735	−	0.996552i	$-0.526442\pi$
$17$	−0.684217	−0.165947	−0.0829735	+	0.996552i	$0.526442\pi$
$18$	5.60470	1.32104
$19$	0	0
$19$	0	0
$20$	−4.87613	−1.09033
$21$	−3.55868	−0.776567
$22$	8.56746	1.82659
$23$	−9.36807	−1.95338	−0.976688	−	0.214662i	$-0.931135\pi$
$23$	−9.36807	−1.95338	−0.976688	+	0.214662i	$0.931135\pi$
$24$	−7.00472	−1.42983
$25$	1.00000	0.200000
$26$	−0.954866	−0.187265
$27$	−4.77147	−0.918270
$28$	−18.6832	−3.53080
$29$	−1.53985	−0.285944	−0.142972	−	0.989727i	$-0.545666\pi$
$29$	−1.53985	−0.285944	−0.142972	+	0.989727i	$0.545666\pi$
$30$	2.43547	0.444654
$31$	2.44889	0.439833	0.219916	−	0.975519i	$-0.429422\pi$
$31$	2.44889	0.439833	0.219916	+	0.975519i	$0.429422\pi$
$32$	−11.2024	−1.98033
$33$	−3.03453	−0.528244
$34$	1.79418	0.307699
$35$	3.83157	0.647654
$36$	−10.4221	−1.73702
$37$	−0.163399	−0.0268627	−0.0134313	−	0.999910i	$-0.504275\pi$
$37$	−0.163399	−0.0268627	−0.0134313	+	0.999910i	$0.504275\pi$
$38$	0	0
$39$	0.338206	0.0541564
$40$	7.54188	1.19248
$41$	7.37370	1.15158	0.575789	−	0.817598i	$-0.304695\pi$
$41$	7.37370	1.15158	0.575789	+	0.817598i	$0.304695\pi$
$42$	9.33169	1.43991
$43$	2.58788	0.394648	0.197324	−	0.980338i	$-0.436775\pi$
$43$	2.58788	0.394648	0.197324	+	0.980338i	$0.436775\pi$
$44$	−15.9314	−2.40175
$45$	2.13737	0.318621
$46$	24.5653	3.62195
$47$	8.79680	1.28315	0.641573	−	0.767062i	$-0.278282\pi$
$47$	8.79680	1.28315	0.641573	+	0.767062i	$0.278282\pi$
$48$	9.31037	1.34384
$49$	7.68097	1.09728
$50$	−2.62224	−0.370840
$51$	−0.635485	−0.0889857
$52$	1.77560	0.246232
$53$	−11.1190	−1.52731	−0.763654	−	0.645626i	$-0.776597\pi$
$53$	−11.1190	−1.52731	−0.763654	+	0.645626i	$0.776597\pi$
$54$	12.5119	1.70266
$55$	3.26723	0.440554
$56$	28.8973	3.86156
$57$	0	0
$58$	4.03786	0.530197
$59$	7.78980	1.01415	0.507073	−	0.861903i	$-0.330727\pi$
$59$	7.78980	1.01415	0.507073	+	0.861903i	$0.330727\pi$
$60$	−4.52883	−0.584669
$61$	2.41893	0.309712	0.154856	−	0.987937i	$-0.450509\pi$
$61$	2.41893	0.309712	0.154856	+	0.987937i	$0.450509\pi$
$62$	−6.42156	−0.815539
$63$	8.18951	1.03178
$64$	9.32678	1.16585
$65$	−0.364142	−0.0451663
$66$	7.95725	0.979470
$67$	9.55736	1.16762	0.583808	−	0.811891i	$-0.301562\pi$
$67$	9.55736	1.16762	0.583808	+	0.811891i	$0.301562\pi$
$68$	−3.33633	−0.404589
$69$	−8.70084	−1.04746
$70$	−10.0473	−1.20088
$71$	5.12085	0.607734	0.303867	−	0.952715i	$-0.401722\pi$
$71$	5.12085	0.607734	0.303867	+	0.952715i	$0.401722\pi$
$72$	16.1198	1.89974
$73$	−7.88413	−0.922768	−0.461384	−	0.887201i	$-0.652647\pi$
$73$	−7.88413	−0.922768	−0.461384	+	0.887201i	$0.652647\pi$
$74$	0.428471	0.0498088
$75$	0.928776	0.107246
$76$	0	0
$77$	12.5186	1.42663
$78$	−0.886857	−0.100417
$79$	9.32066	1.04866	0.524328	−	0.851516i	$-0.324316\pi$
$79$	9.32066	1.04866	0.524328	+	0.851516i	$0.324316\pi$
$80$	−10.0243	−1.12076
$81$	1.98050	0.220055
$82$	−19.3356	−2.13526
$83$	0.729119	0.0800312	0.0400156	−	0.999199i	$-0.487259\pi$
$83$	0.729119	0.0800312	0.0400156	+	0.999199i	$0.487259\pi$
$84$	−17.3525	−1.89332
$85$	0.684217	0.0742138
$86$	−6.78603	−0.731757
$87$	−1.43018	−0.153331
$88$	24.6411	2.62675
$89$	−12.6405	−1.33989	−0.669945	−	0.742410i	$-0.733683\pi$
$89$	−12.6405	−1.33989	−0.669945	+	0.742410i	$0.733683\pi$
$90$	−5.60470	−0.590788
$91$	−1.39524	−0.146261
$92$	−45.6799	−4.76246
$93$	2.27447	0.235851
$94$	−23.0673	−2.37921
$95$	0	0
$96$	−10.4046	−1.06191
$97$	7.54714	0.766296	0.383148	−	0.923687i	$-0.374840\pi$
$97$	7.54714	0.766296	0.383148	+	0.923687i	$0.374840\pi$
$98$	−20.1413	−2.03458
$99$	6.98330	0.701848
$100$	4.87613	0.487613
$101$	4.05864	0.403849	0.201925	−	0.979401i	$-0.435280\pi$
$101$	4.05864	0.403849	0.201925	+	0.979401i	$0.435280\pi$
$102$	1.66639	0.164997
$103$	−13.7780	−1.35759	−0.678794	−	0.734329i	$-0.737497\pi$
$103$	−13.7780	−1.35759	−0.678794	+	0.734329i	$0.737497\pi$
$104$	−2.74632	−0.269298
$105$	3.55868	0.347291
$106$	29.1566	2.83194
$107$	−6.52460	−0.630757	−0.315379	−	0.948966i	$-0.602131\pi$
$107$	−6.52460	−0.630757	−0.315379	+	0.948966i	$0.602131\pi$
$108$	−23.2663	−2.23880
$109$	9.00874	0.862881	0.431440	−	0.902141i	$-0.358006\pi$
$109$	9.00874	0.862881	0.431440	+	0.902141i	$0.358006\pi$
$110$	−8.56746	−0.816875
$111$	−0.151761	−0.0144045
$112$	−38.4090	−3.62931
$113$	−13.1464	−1.23670	−0.618352	−	0.785901i	$-0.712200\pi$
$113$	−13.1464	−1.23670	−0.618352	+	0.785901i	$0.712200\pi$
$114$	0	0
$115$	9.36807	0.873577
$116$	−7.50852	−0.697148
$117$	−0.778308	−0.0719546
$118$	−20.4267	−1.88043
$119$	2.62163	0.240324
$120$	7.00472	0.639440
$121$	−0.325189	−0.0295627
$122$	−6.34300	−0.574269
$123$	6.84851	0.617510
$124$	11.9411	1.07234
$125$	−1.00000	−0.0894427
$126$	−21.4748	−1.91313
$127$	8.77090	0.778292	0.389146	−	0.921176i	$-0.372770\pi$
$127$	8.77090	0.778292	0.389146	+	0.921176i	$0.372770\pi$
$128$	−2.05212	−0.181383
$129$	2.40356	0.211622
$130$	0.954866	0.0837473
$131$	10.3928	0.908020	0.454010	−	0.890996i	$-0.349993\pi$
$131$	10.3928	0.908020	0.454010	+	0.890996i	$0.349993\pi$
$132$	−14.7967	−1.28789
$133$	0	0
$134$	−25.0616	−2.16500
$135$	4.77147	0.410663
$136$	5.16029	0.442491
$137$	3.56528	0.304602	0.152301	−	0.988334i	$-0.451332\pi$
$137$	3.56528	0.304602	0.152301	+	0.988334i	$0.451332\pi$
$138$	22.8157	1.94220
$139$	8.67144	0.735502	0.367751	−	0.929924i	$-0.380128\pi$
$139$	8.67144	0.735502	0.367751	+	0.929924i	$0.380128\pi$
$140$	18.6832	1.57902
$141$	8.17026	0.688060
$142$	−13.4281	−1.12686
$143$	−1.18974	−0.0994908
$144$	−21.4258	−1.78548
$145$	1.53985	0.127878
$146$	20.6741	1.71100
$147$	7.13390	0.588394
$148$	−0.796755	−0.0654928
$149$	−16.9633	−1.38969	−0.694844	−	0.719161i	$-0.744526\pi$
$149$	−16.9633	−1.38969	−0.694844	+	0.719161i	$0.744526\pi$
$150$	−2.43547	−0.198855
$151$	11.0821	0.901849	0.450925	−	0.892562i	$-0.351094\pi$
$151$	11.0821	0.901849	0.450925	+	0.892562i	$0.351094\pi$
$152$	0	0
$153$	1.46243	0.118230
$154$	−32.8269	−2.64526
$155$	−2.44889	−0.196699
$156$	1.64914	0.132037
$157$	−0.932456	−0.0744181	−0.0372091	−	0.999308i	$-0.511847\pi$
$157$	−0.932456	−0.0744181	−0.0372091	+	0.999308i	$0.511847\pi$
$158$	−24.4410	−1.94442
$159$	−10.3270	−0.818987
$160$	11.2024	0.885631
$161$	35.8944	2.82888
$162$	−5.19333	−0.408026
$163$	8.07308	0.632332	0.316166	−	0.948704i	$-0.397604\pi$
$163$	8.07308	0.632332	0.316166	+	0.948704i	$0.397604\pi$
$164$	35.9551	2.80762
$165$	3.03453	0.236238
$166$	−1.91192	−0.148394
$167$	13.6495	1.05623	0.528114	−	0.849174i	$-0.322899\pi$
$167$	13.6495	1.05623	0.528114	+	0.849174i	$0.322899\pi$
$168$	26.8391	2.07068
$169$	−12.8674	−0.989800
$170$	−1.79418	−0.137607
$171$	0	0
$172$	12.6188	0.962176
$173$	−8.37417	−0.636677	−0.318338	−	0.947977i	$-0.603125\pi$
$173$	−8.37417	−0.636677	−0.318338	+	0.947977i	$0.603125\pi$
$174$	3.75027	0.284307
$175$	−3.83157	−0.289640
$176$	−32.7519	−2.46877
$177$	7.23498	0.543815
$178$	33.1464	2.48443
$179$	5.70454	0.426378	0.213189	−	0.977011i	$-0.431615\pi$
$179$	5.70454	0.426378	0.213189	+	0.977011i	$0.431615\pi$
$180$	10.4221	0.776818
$181$	−14.8415	−1.10316	−0.551579	−	0.834123i	$-0.685974\pi$
$181$	−14.8415	−1.10316	−0.551579	+	0.834123i	$0.685974\pi$
$182$	3.65864	0.271197
$183$	2.24664	0.166077
$184$	70.6528	5.20860
$185$	0.163399	0.0120133
$186$	−5.96419	−0.437316
$187$	2.23550	0.163476
$188$	42.8943	3.12839
$189$	18.2822	1.32984
$190$	0	0
$191$	−19.7204	−1.42692	−0.713460	−	0.700695i	$-0.752873\pi$
$191$	−19.7204	−1.42692	−0.713460	+	0.700695i	$0.752873\pi$
$192$	8.66249	0.625161
$193$	4.13045	0.297316	0.148658	−	0.988889i	$-0.452505\pi$
$193$	4.13045	0.297316	0.148658	+	0.988889i	$0.452505\pi$
$194$	−19.7904	−1.42087
$195$	−0.338206	−0.0242195
$196$	37.4534	2.67524
$197$	0.166616	0.0118709	0.00593544	−	0.999982i	$-0.498111\pi$
$197$	0.166616	0.0118709	0.00593544	+	0.999982i	$0.498111\pi$
$198$	−18.3119	−1.30137
$199$	−5.18639	−0.367653	−0.183827	−	0.982959i	$-0.558848\pi$
$199$	−5.18639	−0.367653	−0.183827	+	0.982959i	$0.558848\pi$
$200$	−7.54188	−0.533292
$201$	8.87664	0.626110
$202$	−10.6427	−0.748818
$203$	5.90006	0.414103
$204$	−3.09870	−0.216953
$205$	−7.37370	−0.515001
$206$	36.1292	2.51724
$207$	20.0231	1.39170
$208$	3.65029	0.253102
$209$	0	0
$210$	−9.33169	−0.643948
$211$	4.91656	0.338470	0.169235	−	0.985576i	$-0.445870\pi$
$211$	4.91656	0.338470	0.169235	+	0.985576i	$0.445870\pi$
$212$	−54.2175	−3.72367
$213$	4.75613	0.325884
$214$	17.1091	1.16955
$215$	−2.58788	−0.176492
$216$	35.9859	2.44853
$217$	−9.38309	−0.636966
$218$	−23.6230	−1.59995
$219$	−7.32259	−0.494815
$220$	15.9314	1.07410
$221$	−0.249152	−0.0167598
$222$	0.397954	0.0267089
$223$	8.76182	0.586735	0.293367	−	0.956000i	$-0.405224\pi$
$223$	8.76182	0.586735	0.293367	+	0.956000i	$0.405224\pi$
$224$	42.9230	2.86791
$225$	−2.13737	−0.142492
$226$	34.4728	2.29310
$227$	5.53943	0.367665	0.183833	−	0.982958i	$-0.441150\pi$
$227$	5.53943	0.367665	0.183833	+	0.982958i	$0.441150\pi$
$228$	0	0
$229$	26.8762	1.77603	0.888014	−	0.459816i	$-0.152085\pi$
$229$	26.8762	1.77603	0.888014	+	0.459816i	$0.152085\pi$
$230$	−24.5653	−1.61979
$231$	11.6270	0.765002
$232$	11.6134	0.762457
$233$	2.55264	0.167229	0.0836146	−	0.996498i	$-0.473354\pi$
$233$	2.55264	0.167229	0.0836146	+	0.996498i	$0.473354\pi$
$234$	2.04091	0.133418
$235$	−8.79680	−0.573840
$236$	37.9841	2.47255
$237$	8.65681	0.562320
$238$	−6.87453	−0.445610
$239$	−25.5326	−1.65157	−0.825784	−	0.563986i	$-0.809267\pi$
$239$	−25.5326	−1.65157	−0.825784	+	0.563986i	$0.809267\pi$
$240$	−9.31037	−0.600982
$241$	0.991881	0.0638927	0.0319463	−	0.999490i	$-0.489829\pi$
$241$	0.991881	0.0638927	0.0319463	+	0.999490i	$0.489829\pi$
$242$	0.852723	0.0548151
$243$	16.1539	1.03627
$244$	11.7950	0.755097
$245$	−7.68097	−0.490719
$246$	−17.9584	−1.14499
$247$	0	0
$248$	−18.4692	−1.17280
$249$	0.677188	0.0429151
$250$	2.62224	0.165845
$251$	−14.5366	−0.917542	−0.458771	−	0.888555i	$-0.651710\pi$
$251$	−14.5366	−0.917542	−0.458771	+	0.888555i	$0.651710\pi$
$252$	39.9331	2.51555
$253$	30.6077	1.92429
$254$	−22.9994	−1.44311
$255$	0.635485	0.0397956
$256$	−13.2724	−0.829526
$257$	17.1678	1.07090	0.535448	−	0.844568i	$-0.320143\pi$
$257$	17.1678	1.07090	0.535448	+	0.844568i	$0.320143\pi$
$258$	−6.30270	−0.392389
$259$	0.626076	0.0389025
$260$	−1.77560	−0.110118
$261$	3.29124	0.203723
$262$	−27.2523	−1.68365
$263$	1.25408	0.0773297	0.0386648	−	0.999252i	$-0.487690\pi$
$263$	1.25408	0.0773297	0.0386648	+	0.999252i	$0.487690\pi$
$264$	22.8860	1.40854
$265$	11.1190	0.683033
$266$	0	0
$267$	−11.7402	−0.718489
$268$	46.6029	2.84672
$269$	13.6745	0.833750	0.416875	−	0.908964i	$-0.363125\pi$
$269$	13.6745	0.833750	0.416875	+	0.908964i	$0.363125\pi$
$270$	−12.5119	−0.761452
$271$	13.4394	0.816384	0.408192	−	0.912896i	$-0.366159\pi$
$271$	13.4394	0.816384	0.408192	+	0.912896i	$0.366159\pi$
$272$	−6.85883	−0.415878
$273$	−1.29586	−0.0784292
$274$	−9.34900	−0.564794
$275$	−3.26723	−0.197022
$276$	−42.4264	−2.55377
$277$	−12.0342	−0.723067	−0.361533	−	0.932359i	$-0.617747\pi$
$277$	−12.0342	−0.723067	−0.361533	+	0.932359i	$0.617747\pi$
$278$	−22.7386	−1.36377
$279$	−5.23419	−0.313363
$280$	−28.8973	−1.72694
$281$	14.3211	0.854324	0.427162	−	0.904175i	$-0.359513\pi$
$281$	14.3211	0.854324	0.427162	+	0.904175i	$0.359513\pi$
$282$	−21.4244	−1.27580
$283$	5.31010	0.315653	0.157826	−	0.987467i	$-0.449551\pi$
$283$	5.31010	0.315653	0.157826	+	0.987467i	$0.449551\pi$
$284$	24.9699	1.48169
$285$	0	0
$286$	3.11977	0.184476
$287$	−28.2529	−1.66771
$288$	23.9438	1.41090
$289$	−16.5318	−0.972462
$290$	−4.03786	−0.237111
$291$	7.00961	0.410910
$292$	−38.4440	−2.24977
$293$	0.884916	0.0516973	0.0258487	−	0.999666i	$-0.491771\pi$
$293$	0.884916	0.0516973	0.0258487	+	0.999666i	$0.491771\pi$
$294$	−18.7068	−1.09100
$295$	−7.78980	−0.453540
$296$	1.23234	0.0716281
$297$	15.5895	0.904595
$298$	44.4818	2.57676
$299$	−3.41131	−0.197281
$300$	4.52883	0.261472
$301$	−9.91565	−0.571529
$302$	−29.0599	−1.67221
$303$	3.76956	0.216556
$304$	0	0
$305$	−2.41893	−0.138507
$306$	−3.83483	−0.219223
$307$	24.8492	1.41822	0.709110	−	0.705098i	$-0.249097\pi$
$307$	24.8492	1.41822	0.709110	+	0.705098i	$0.249097\pi$
$308$	61.0425	3.47822
$309$	−12.7967	−0.727978
$310$	6.42156	0.364720
$311$	18.5001	1.04904	0.524521	−	0.851398i	$-0.324244\pi$
$311$	18.5001	1.04904	0.524521	+	0.851398i	$0.324244\pi$
$312$	−2.55071	−0.144406
$313$	33.2114	1.87722	0.938610	−	0.344980i	$-0.112114\pi$
$313$	33.2114	1.87722	0.938610	+	0.344980i	$0.112114\pi$
$314$	2.44512	0.137986
$315$	−8.18951	−0.461427
$316$	45.4487	2.55669
$317$	−6.60973	−0.371240	−0.185620	−	0.982622i	$-0.559429\pi$
$317$	−6.60973	−0.371240	−0.185620	+	0.982622i	$0.559429\pi$
$318$	27.0799	1.51857
$319$	5.03106	0.281685
$320$	−9.32678	−0.521383
$321$	−6.05989	−0.338230
$322$	−94.1237	−5.24531
$323$	0	0
$324$	9.65715	0.536508
$325$	0.364142	0.0201990
$326$	−21.1695	−1.17247
$327$	8.36710	0.462702
$328$	−55.6115	−3.07063
$329$	−33.7056	−1.85825
$330$	−7.95725	−0.438032
$331$	−16.5015	−0.907005	−0.453502	−	0.891255i	$-0.649826\pi$
$331$	−16.5015	−0.907005	−0.453502	+	0.891255i	$0.649826\pi$
$332$	3.55528	0.195121
$333$	0.349245	0.0191385
$334$	−35.7921	−1.95846
$335$	−9.55736	−0.522174
$336$	−35.6734	−1.94614
$337$	5.95271	0.324265	0.162132	−	0.986769i	$-0.448163\pi$
$337$	5.95271	0.324265	0.162132	+	0.986769i	$0.448163\pi$
$338$	33.7414	1.83529
$339$	−12.2100	−0.663157
$340$	3.33633	0.180938
$341$	−8.00108	−0.433283
$342$	0	0
$343$	−2.60918	−0.140882
$344$	−19.5175	−1.05231
$345$	8.70084	0.468437
$346$	21.9591	1.18053
$347$	21.6126	1.16022	0.580112	−	0.814537i	$-0.303009\pi$
$347$	21.6126	1.16022	0.580112	+	0.814537i	$0.303009\pi$
$348$	−6.97373	−0.373831
$349$	−2.42190	−0.129642	−0.0648208	−	0.997897i	$-0.520648\pi$
$349$	−2.42190	−0.129642	−0.0648208	+	0.997897i	$0.520648\pi$
$350$	10.0473	0.537051
$351$	−1.73749	−0.0927405
$352$	36.6010	1.95084
$353$	7.65155	0.407251	0.203625	−	0.979049i	$-0.434728\pi$
$353$	7.65155	0.407251	0.203625	+	0.979049i	$0.434728\pi$
$354$	−18.9718	−1.00834
$355$	−5.12085	−0.271787
$356$	−61.6367	−3.26674
$357$	2.43491	0.128869
$358$	−14.9587	−0.790590
$359$	6.81080	0.359460	0.179730	−	0.983716i	$-0.442478\pi$
$359$	6.81080	0.359460	0.179730	+	0.983716i	$0.442478\pi$
$360$	−16.1198	−0.849589
$361$	0	0
$362$	38.9178	2.04548
$363$	−0.302028	−0.0158524
$364$	−6.80335	−0.356593
$365$	7.88413	0.412674
$366$	−5.89123	−0.307940
$367$	−13.7610	−0.718320	−0.359160	−	0.933276i	$-0.616937\pi$
$367$	−13.7610	−0.718320	−0.359160	+	0.933276i	$0.616937\pi$
$368$	−93.9087	−4.89533
$369$	−15.7604	−0.820451
$370$	−0.428471	−0.0222752
$371$	42.6032	2.21185
$372$	11.0906	0.575020
$373$	−30.3103	−1.56941	−0.784705	−	0.619869i	$-0.787186\pi$
$373$	−30.3103	−1.56941	−0.784705	+	0.619869i	$0.787186\pi$
$374$	−5.86200	−0.303117
$375$	−0.928776	−0.0479618
$376$	−66.3444	−3.42145
$377$	−0.560725	−0.0288788
$378$	−47.9404	−2.46579
$379$	3.43860	0.176629	0.0883144	−	0.996093i	$-0.471852\pi$
$379$	3.43860	0.176629	0.0883144	+	0.996093i	$0.471852\pi$
$380$	0	0
$381$	8.14620	0.417343
$382$	51.7117	2.64580
$383$	−18.3320	−0.936723	−0.468362	−	0.883537i	$-0.655156\pi$
$383$	−18.3320	−0.936723	−0.468362	+	0.883537i	$0.655156\pi$
$384$	−1.90596	−0.0972631
$385$	−12.5186	−0.638009
$386$	−10.8310	−0.551284
$387$	−5.53127	−0.281170
$388$	36.8008	1.86828
$389$	4.16543	0.211196	0.105598	−	0.994409i	$-0.466324\pi$
$389$	4.16543	0.211196	0.105598	+	0.994409i	$0.466324\pi$
$390$	0.886857	0.0449078
$391$	6.40979	0.324157
$392$	−57.9289	−2.92585
$393$	9.65256	0.486907
$394$	−0.436906	−0.0220110
$395$	−9.32066	−0.468973
$396$	34.0515	1.71115
$397$	−19.9018	−0.998844	−0.499422	−	0.866359i	$-0.666454\pi$
$397$	−19.9018	−0.998844	−0.499422	+	0.866359i	$0.666454\pi$
$398$	13.5999	0.681703
$399$	0	0
$400$	10.0243	0.501217
$401$	9.47897	0.473357	0.236679	−	0.971588i	$-0.423941\pi$
$401$	9.47897	0.473357	0.236679	+	0.971588i	$0.423941\pi$
$402$	−23.2767	−1.16093
$403$	0.891742	0.0444208
$404$	19.7904	0.984610
$405$	−1.98050	−0.0984116
$406$	−15.4714	−0.767831
$407$	0.533863	0.0264626
$408$	4.79275	0.237276
$409$	23.2733	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$409$	23.2733	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$410$	19.3356	0.954916
$411$	3.31134	0.163336
$412$	−67.1833	−3.30988
$413$	−29.8472	−1.46869
$414$	−52.5052	−2.58049
$415$	−0.729119	−0.0357910
$416$	−4.07928	−0.200003
$417$	8.05382	0.394397
$418$	0	0
$419$	3.05296	0.149147	0.0745735	−	0.997216i	$-0.476240\pi$
$419$	3.05296	0.149147	0.0745735	+	0.997216i	$0.476240\pi$
$420$	17.3525	0.846718
$421$	−28.0405	−1.36661	−0.683306	−	0.730132i	$-0.739458\pi$
$421$	−28.0405	−1.36661	−0.683306	+	0.730132i	$0.739458\pi$
$422$	−12.8924	−0.627592
$423$	−18.8021	−0.914187
$424$	83.8579	4.07250
$425$	−0.684217	−0.0331894
$426$	−12.4717	−0.604255
$427$	−9.26831	−0.448525
$428$	−31.8148	−1.53783
$429$	−1.10500	−0.0533499
$430$	6.78603	0.327252
$431$	−30.2151	−1.45541	−0.727706	−	0.685889i	$-0.759414\pi$
$431$	−30.2151	−1.45541	−0.727706	+	0.685889i	$0.759414\pi$
$432$	−47.8309	−2.30126
$433$	−15.0375	−0.722657	−0.361329	−	0.932439i	$-0.617677\pi$
$433$	−15.0375	−0.722657	−0.361329	+	0.932439i	$0.617677\pi$
$434$	24.6047	1.18106
$435$	1.43018	0.0685718
$436$	43.9277	2.10376
$437$	0	0
$438$	19.2016	0.917487
$439$	38.6365	1.84402	0.922009	−	0.387168i	$-0.126547\pi$
$439$	38.6365	1.84402	0.922009	+	0.387168i	$0.126547\pi$
$440$	−24.6411	−1.17472
$441$	−16.4171	−0.781767
$442$	0.653336	0.0310760
$443$	4.38795	0.208478	0.104239	−	0.994552i	$-0.466759\pi$
$443$	4.38795	0.208478	0.104239	+	0.994552i	$0.466759\pi$
$444$	−0.740007	−0.0351192
$445$	12.6405	0.599217
$446$	−22.9756	−1.08792
$447$	−15.7551	−0.745191
$448$	−35.7362	−1.68838
$449$	24.7932	1.17006	0.585032	−	0.811010i	$-0.301082\pi$
$449$	24.7932	1.17006	0.585032	+	0.811010i	$0.301082\pi$
$450$	5.60470	0.264208
$451$	−24.0916	−1.13443
$452$	−64.1033	−3.01516
$453$	10.2928	0.483598
$454$	−14.5257	−0.681725
$455$	1.39524	0.0654097
$456$	0	0
$457$	−21.1249	−0.988182	−0.494091	−	0.869410i	$-0.664499\pi$
$457$	−21.1249	−0.988182	−0.494091	+	0.869410i	$0.664499\pi$
$458$	−70.4757	−3.29311
$459$	3.26472	0.152384
$460$	45.6799	2.12983
$461$	−11.1595	−0.519749	−0.259875	−	0.965642i	$-0.583681\pi$
$461$	−11.1595	−0.519749	−0.259875	+	0.965642i	$0.583681\pi$
$462$	−30.4888	−1.41847
$463$	−4.04445	−0.187962	−0.0939808	−	0.995574i	$-0.529959\pi$
$463$	−4.04445	−0.187962	−0.0939808	+	0.995574i	$0.529959\pi$
$464$	−15.4360	−0.716600
$465$	−2.27447	−0.105476
$466$	−6.69363	−0.310077
$467$	21.1217	0.977394	0.488697	−	0.872453i	$-0.337472\pi$
$467$	21.1217	0.977394	0.488697	+	0.872453i	$0.337472\pi$
$468$	−3.79513	−0.175430
$469$	−36.6197	−1.69094
$470$	23.0673	1.06401
$471$	−0.866043	−0.0399052
$472$	−58.7498	−2.70418
$473$	−8.45520	−0.388771
$474$	−22.7002	−1.04265
$475$	0	0
$476$	12.7834	0.585926
$477$	23.7654	1.08814
$478$	66.9526	3.06234
$479$	34.2076	1.56298	0.781492	−	0.623915i	$-0.214459\pi$
$479$	34.2076	1.56298	0.781492	+	0.623915i	$0.214459\pi$
$480$	10.4046	0.474901
$481$	−0.0595005	−0.00271299
$482$	−2.60095	−0.118470
$483$	33.3379	1.51693
$484$	−1.58566	−0.0720756
$485$	−7.54714	−0.342698
$486$	−42.3592	−1.92145
$487$	−1.77681	−0.0805148	−0.0402574	−	0.999189i	$-0.512818\pi$
$487$	−1.77681	−0.0805148	−0.0402574	+	0.999189i	$0.512818\pi$
$488$	−18.2433	−0.825834
$489$	7.49808	0.339075
$490$	20.1413	0.909892
$491$	−20.6693	−0.932794	−0.466397	−	0.884575i	$-0.654448\pi$
$491$	−20.6693	−0.932794	−0.466397	+	0.884575i	$0.654448\pi$
$492$	33.3942	1.50553
$493$	1.05359	0.0474515
$494$	0	0
$495$	−6.98330	−0.313876
$496$	24.5485	1.10226
$497$	−19.6209	−0.880119
$498$	−1.77575	−0.0795732
$499$	−42.6379	−1.90874	−0.954368	−	0.298632i	$-0.903470\pi$
$499$	−42.6379	−1.90874	−0.954368	+	0.298632i	$0.903470\pi$
$500$	−4.87613	−0.218067
$501$	12.6773	0.566380
$502$	38.1184	1.70131
$503$	24.4713	1.09112	0.545561	−	0.838071i	$-0.316317\pi$
$503$	24.4713	1.09112	0.545561	+	0.838071i	$0.316317\pi$
$504$	−61.7643	−2.75120
$505$	−4.05864	−0.180607
$506$	−80.2605	−3.56802
$507$	−11.9509	−0.530760
$508$	42.7680	1.89752
$509$	−33.7570	−1.49625	−0.748127	−	0.663555i	$-0.769047\pi$
$509$	−33.7570	−1.49625	−0.748127	+	0.663555i	$0.769047\pi$
$510$	−1.66639	−0.0737890
$511$	30.2086	1.33635
$512$	38.9076	1.71949
$513$	0	0
$514$	−45.0179	−1.98566
$515$	13.7780	0.607132
$516$	11.7201	0.515947
$517$	−28.7412	−1.26404
$518$	−1.64172	−0.0721330
$519$	−7.77773	−0.341405
$520$	2.74632	0.120434
$521$	1.48699	0.0651461	0.0325731	−	0.999469i	$-0.489630\pi$
$521$	1.48699	0.0651461	0.0325731	+	0.999469i	$0.489630\pi$
$522$	−8.63042	−0.377743
$523$	−6.31385	−0.276085	−0.138043	−	0.990426i	$-0.544081\pi$
$523$	−6.31385	−0.276085	−0.138043	+	0.990426i	$0.544081\pi$
$524$	50.6764	2.21381
$525$	−3.55868	−0.155313
$526$	−3.28849	−0.143385
$527$	−1.67557	−0.0729890
$528$	−30.4192	−1.32382
$529$	64.7607	2.81568
$530$	−29.1566	−1.26648
$531$	−16.6497	−0.722537
$532$	0	0
$533$	2.68507	0.116303
$534$	30.7856	1.33222
$535$	6.52460	0.282083
$536$	−72.0804	−3.11340
$537$	5.29825	0.228636
$538$	−35.8578	−1.54594
$539$	−25.0955	−1.08094
$540$	23.2663	1.00122
$541$	−29.9146	−1.28613	−0.643064	−	0.765812i	$-0.722337\pi$
$541$	−29.9146	−1.28613	−0.643064	+	0.765812i	$0.722337\pi$
$542$	−35.2412	−1.51374
$543$	−13.7844	−0.591545
$544$	7.66491	0.328630
$545$	−9.00874	−0.385892
$546$	3.39806	0.145424
$547$	29.9956	1.28252	0.641260	−	0.767323i	$-0.278412\pi$
$547$	29.9956	1.28252	0.641260	+	0.767323i	$0.278412\pi$
$548$	17.3847	0.742639
$549$	−5.17016	−0.220657
$550$	8.56746	0.365318
$551$	0	0
$552$	65.6207	2.79300
$553$	−35.7128	−1.51866
$554$	31.5566	1.34071
$555$	0.151761	0.00644191
$556$	42.2830	1.79320
$557$	27.1347	1.14973	0.574866	−	0.818248i	$-0.305054\pi$
$557$	27.1347	1.14973	0.574866	+	0.818248i	$0.305054\pi$
$558$	13.7253	0.581037
$559$	0.942355	0.0398574
$560$	38.4090	1.62308
$561$	2.07628	0.0876605
$562$	−37.5533	−1.58409
$563$	39.7602	1.67569	0.837847	−	0.545906i	$-0.183814\pi$
$563$	39.7602	1.67569	0.837847	+	0.545906i	$0.183814\pi$
$564$	39.8392	1.67753
$565$	13.1464	0.553071
$566$	−13.9243	−0.585284
$567$	−7.58842	−0.318684
$568$	−38.6209	−1.62050
$569$	6.66486	0.279405	0.139703	−	0.990194i	$-0.455385\pi$
$569$	6.66486	0.279405	0.139703	+	0.990194i	$0.455385\pi$
$570$	0	0
$571$	−27.6502	−1.15713	−0.578563	−	0.815638i	$-0.696386\pi$
$571$	−27.6502	−1.15713	−0.578563	+	0.815638i	$0.696386\pi$
$572$	−5.80131	−0.242565
$573$	−18.3159	−0.765157
$574$	74.0857	3.09228
$575$	−9.36807	−0.390675
$576$	−19.9348	−0.830617
$577$	30.0267	1.25003	0.625015	−	0.780613i	$-0.285093\pi$
$577$	30.0267	1.25003	0.625015	+	0.780613i	$0.285093\pi$
$578$	43.3504	1.80314
$579$	3.83626	0.159430
$580$	7.50852	0.311774
$581$	−2.79367	−0.115901
$582$	−18.3808	−0.761911
$583$	36.3283	1.50456
$584$	59.4612	2.46052
$585$	0.778308	0.0321791
$586$	−2.32046	−0.0958573
$587$	−13.2734	−0.547850	−0.273925	−	0.961751i	$-0.588322\pi$
$587$	−13.2734	−0.547850	−0.273925	+	0.961751i	$0.588322\pi$
$588$	34.7858	1.43454
$589$	0	0
$590$	20.4267	0.840954
$591$	0.154749	0.00636551
$592$	−1.63797	−0.0673202
$593$	12.4741	0.512249	0.256124	−	0.966644i	$-0.417554\pi$
$593$	12.4741	0.512249	0.256124	+	0.966644i	$0.417554\pi$
$594$	−40.8794	−1.67730
$595$	−2.62163	−0.107476
$596$	−82.7152	−3.38815
$597$	−4.81699	−0.197146
$598$	8.94525	0.365799
$599$	33.1549	1.35467	0.677337	−	0.735673i	$-0.263134\pi$
$599$	33.1549	1.35467	0.677337	+	0.735673i	$0.263134\pi$
$600$	−7.00472	−0.285966
$601$	24.9506	1.01776	0.508879	−	0.860838i	$-0.330060\pi$
$601$	24.9506	1.01776	0.508879	+	0.860838i	$0.330060\pi$
$602$	26.0012	1.05973
$603$	−20.4277	−0.831878
$604$	54.0378	2.19876
$605$	0.325189	0.0132208
$606$	−9.88469	−0.401538
$607$	3.04625	0.123644	0.0618218	−	0.998087i	$-0.480309\pi$
$607$	3.04625	0.123644	0.0618218	+	0.998087i	$0.480309\pi$
$608$	0	0
$609$	5.47984	0.222054
$610$	6.34300	0.256821
$611$	3.20328	0.129591
$612$	7.13099	0.288253
$613$	22.0833	0.891935	0.445968	−	0.895049i	$-0.352860\pi$
$613$	22.0833	0.891935	0.445968	+	0.895049i	$0.352860\pi$
$614$	−65.1605	−2.62967
$615$	−6.84851	−0.276159
$616$	−94.4142	−3.80405
$617$	−44.8219	−1.80446	−0.902231	−	0.431252i	$-0.858072\pi$
$617$	−44.8219	−1.80446	−0.902231	+	0.431252i	$0.858072\pi$
$618$	33.5559	1.34982
$619$	7.28645	0.292867	0.146434	−	0.989220i	$-0.453221\pi$
$619$	7.28645	0.292867	0.146434	+	0.989220i	$0.453221\pi$
$620$	−11.9411	−0.479565
$621$	44.6995	1.79373
$622$	−48.5115	−1.94513
$623$	48.4330	1.94043
$624$	3.39030	0.135721
$625$	1.00000	0.0400000
$626$	−87.0882	−3.48074
$627$	0	0
$628$	−4.54677	−0.181436
$629$	0.111801	0.00445778
$630$	21.4748	0.855578
$631$	−40.2130	−1.60086	−0.800428	−	0.599429i	$-0.795394\pi$
$631$	−40.2130	−1.60086	−0.800428	+	0.599429i	$0.795394\pi$
$632$	−70.2953	−2.79620
$633$	4.56639	0.181498
$634$	17.3323	0.688353
$635$	−8.77090	−0.348063
$636$	−50.3559	−1.99674
$637$	2.79696	0.110820
$638$	−13.1926	−0.522301
$639$	−10.9452	−0.432985
$640$	2.05212	0.0811171
$641$	25.4740	1.00616	0.503080	−	0.864240i	$-0.332200\pi$
$641$	25.4740	1.00616	0.503080	+	0.864240i	$0.332200\pi$
$642$	15.8905	0.627147
$643$	−42.2982	−1.66808	−0.834040	−	0.551705i	$-0.813978\pi$
$643$	−42.2982	−1.66808	−0.834040	+	0.551705i	$0.813978\pi$
$644$	175.026	6.89698
$645$	−2.40356	−0.0946401
$646$	0	0
$647$	1.66919	0.0656226	0.0328113	−	0.999462i	$-0.489554\pi$
$647$	1.66919	0.0656226	0.0328113	+	0.999462i	$0.489554\pi$
$648$	−14.9367	−0.586768
$649$	−25.4511	−0.999043
$650$	−0.954866	−0.0374529
$651$	−8.71479	−0.341560
$652$	39.3653	1.54167
$653$	5.79382	0.226730	0.113365	−	0.993553i	$-0.463837\pi$
$653$	5.79382	0.226730	0.113365	+	0.993553i	$0.463837\pi$
$654$	−21.9405	−0.857942
$655$	−10.3928	−0.406079
$656$	73.9165	2.88595
$657$	16.8513	0.657434
$658$	88.3841	3.44557
$659$	−22.2378	−0.866261	−0.433131	−	0.901331i	$-0.642591\pi$
$659$	−22.2378	−0.866261	−0.433131	+	0.901331i	$0.642591\pi$
$660$	14.7967	0.575962
$661$	9.28274	0.361057	0.180528	−	0.983570i	$-0.442219\pi$
$661$	9.28274	0.361057	0.180528	+	0.983570i	$0.442219\pi$
$662$	43.2708	1.68177
$663$	−0.231407	−0.00898709
$664$	−5.49893	−0.213400
$665$	0	0
$666$	−0.915804	−0.0354867
$667$	14.4255	0.558556
$668$	66.5565	2.57515
$669$	8.13777	0.314624
$670$	25.0616	0.968216
$671$	−7.90320	−0.305100
$672$	39.8659	1.53786
$673$	−30.8569	−1.18945	−0.594723	−	0.803930i	$-0.702738\pi$
$673$	−30.8569	−1.18945	−0.594723	+	0.803930i	$0.702738\pi$
$674$	−15.6094	−0.601252
$675$	−4.77147	−0.183654
$676$	−62.7431	−2.41319
$677$	40.7289	1.56534	0.782669	−	0.622439i	$-0.213858\pi$
$677$	40.7289	1.56534	0.782669	+	0.622439i	$0.213858\pi$
$678$	32.0176	1.22963
$679$	−28.9174	−1.10975
$680$	−5.16029	−0.197888
$681$	5.14489	0.197153
$682$	20.9807	0.803394
$683$	−16.1788	−0.619066	−0.309533	−	0.950889i	$-0.600173\pi$
$683$	−16.1788	−0.619066	−0.309533	+	0.950889i	$0.600173\pi$
$684$	0	0
$685$	−3.56528	−0.136222
$686$	6.84187	0.261224
$687$	24.9620	0.952358
$688$	25.9418	0.989022
$689$	−4.04888	−0.154250
$690$	−22.8157	−0.868577
$691$	14.6606	0.557717	0.278859	−	0.960332i	$-0.410044\pi$
$691$	14.6606	0.557717	0.278859	+	0.960332i	$0.410044\pi$
$692$	−40.8335	−1.55226
$693$	−26.7570	−1.01642
$694$	−56.6733	−2.15129
$695$	−8.67144	−0.328926
$696$	10.7862	0.408851
$697$	−5.04521	−0.191101
$698$	6.35081	0.240382
$699$	2.37083	0.0896732
$700$	−18.6832	−0.706160
$701$	−14.5737	−0.550442	−0.275221	−	0.961381i	$-0.588751\pi$
$701$	−14.5737	−0.550442	−0.275221	+	0.961381i	$0.588751\pi$
$702$	4.55612	0.171960
$703$	0	0
$704$	−30.4728	−1.14848
$705$	−8.17026	−0.307710
$706$	−20.0642	−0.755125
$707$	−15.5510	−0.584854
$708$	35.2787	1.32585
$709$	−11.8520	−0.445109	−0.222555	−	0.974920i	$-0.571440\pi$
$709$	−11.8520	−0.445109	−0.222555	+	0.974920i	$0.571440\pi$
$710$	13.4281	0.503947
$711$	−19.9218	−0.747124
$712$	95.3332	3.57276
$713$	−22.9413	−0.859159
$714$	−6.38490	−0.238949
$715$	1.18974	0.0444936
$716$	27.8161	1.03954
$717$	−23.7141	−0.885619
$718$	−17.8595	−0.666512
$719$	17.0626	0.636328	0.318164	−	0.948036i	$-0.396934\pi$
$719$	17.0626	0.636328	0.318164	+	0.948036i	$0.396934\pi$
$720$	21.4258	0.798492
$721$	52.7915	1.96606
$722$	0	0
$723$	0.921235	0.0342611
$724$	−72.3689	−2.68957
$725$	−1.53985	−0.0571887
$726$	0.791989	0.0293935
$727$	−13.2398	−0.491038	−0.245519	−	0.969392i	$-0.578958\pi$
$727$	−13.2398	−0.491038	−0.245519	+	0.969392i	$0.578958\pi$
$728$	10.5227	0.389998
$729$	9.06182	0.335623
$730$	−20.6741	−0.765181
$731$	−1.77067	−0.0654907
$732$	10.9549	0.404905
$733$	−53.5193	−1.97678	−0.988391	−	0.151933i	$-0.951450\pi$
$733$	−53.5193	−1.97678	−0.988391	+	0.151933i	$0.951450\pi$
$734$	36.0847	1.33191
$735$	−7.13390	−0.263138
$736$	104.945	3.86833
$737$	−31.2261	−1.15023
$738$	41.3274	1.52128
$739$	−42.2016	−1.55241	−0.776205	−	0.630481i	$-0.782858\pi$
$739$	−42.2016	−1.55241	−0.776205	+	0.630481i	$0.782858\pi$
$740$	0.796755	0.0292893
$741$	0	0
$742$	−111.716	−4.10121
$743$	18.0827	0.663388	0.331694	−	0.943387i	$-0.392380\pi$
$743$	18.0827	0.663388	0.331694	+	0.943387i	$0.392380\pi$
$744$	−17.1538	−0.628887
$745$	16.9633	0.621487
$746$	79.4809	2.91000
$747$	−1.55840	−0.0570189
$748$	10.9006	0.398564
$749$	24.9995	0.913462
$750$	2.43547	0.0889308
$751$	−2.96303	−0.108123	−0.0540613	−	0.998538i	$-0.517217\pi$
$751$	−2.96303	−0.108123	−0.0540613	+	0.998538i	$0.517217\pi$
$752$	88.1822	3.21567
$753$	−13.5012	−0.492013
$754$	1.47035	0.0535472
$755$	−11.0821	−0.403319
$756$	89.1465	3.24223
$757$	4.77329	0.173488	0.0867440	−	0.996231i	$-0.472354\pi$
$757$	4.77329	0.173488	0.0867440	+	0.996231i	$0.472354\pi$
$758$	−9.01681	−0.327505
$759$	28.4277	1.03186
$760$	0	0
$761$	31.1552	1.12938	0.564688	−	0.825305i	$-0.308997\pi$
$761$	31.1552	1.12938	0.564688	+	0.825305i	$0.308997\pi$
$762$	−21.3613	−0.773837
$763$	−34.5177	−1.24962
$764$	−96.1593	−3.47892
$765$	−1.46243	−0.0528742
$766$	48.0709	1.73687
$767$	2.83659	0.102423
$768$	−12.3271	−0.444816
$769$	−48.3873	−1.74489	−0.872445	−	0.488712i	$-0.837467\pi$
$769$	−48.3873	−1.74489	−0.872445	+	0.488712i	$0.837467\pi$
$770$	32.8269	1.18300
$771$	15.9450	0.574245
$772$	20.1406	0.724876
$773$	46.8758	1.68600	0.843002	−	0.537910i	$-0.180786\pi$
$773$	46.8758	1.68600	0.843002	+	0.537910i	$0.180786\pi$
$774$	14.5043	0.521346
$775$	2.44889	0.0879666
$776$	−56.9197	−2.04330
$777$	0.581485	0.0208606
$778$	−10.9227	−0.391599
$779$	0	0
$780$	−1.64914	−0.0590486
$781$	−16.7310	−0.598683
$782$	−16.8080	−0.601053
$783$	7.34737	0.262573
$784$	76.9967	2.74988
$785$	0.932456	0.0332808
$786$	−25.3113	−0.902824
$787$	50.6962	1.80713	0.903563	−	0.428456i	$-0.140942\pi$
$787$	50.6962	1.80713	0.903563	+	0.428456i	$0.140942\pi$
$788$	0.812439	0.0289419
$789$	1.16476	0.0414664
$790$	24.4410	0.869571
$791$	50.3712	1.79099
$792$	−52.6672	−1.87145
$793$	0.880833	0.0312793
$794$	52.1873	1.85206
$795$	10.3270	0.366262
$796$	−25.2895	−0.896361
$797$	11.3007	0.400291	0.200146	−	0.979766i	$-0.435858\pi$
$797$	11.3007	0.400291	0.200146	+	0.979766i	$0.435858\pi$
$798$	0	0
$799$	−6.01892	−0.212934
$800$	−11.2024	−0.396066
$801$	27.0175	0.954616
$802$	−24.8561	−0.877699
$803$	25.7593	0.909026
$804$	43.2836	1.52650
$805$	−35.8944	−1.26511
$806$	−2.33836	−0.0823652
$807$	12.7006	0.447081
$808$	−30.6097	−1.07685
$809$	−5.96745	−0.209804	−0.104902	−	0.994483i	$-0.533453\pi$
$809$	−5.96745	−0.209804	−0.104902	+	0.994483i	$0.533453\pi$
$810$	5.19333	0.182475
$811$	23.5332	0.826362	0.413181	−	0.910649i	$-0.364418\pi$
$811$	23.5332	0.826362	0.413181	+	0.910649i	$0.364418\pi$
$812$	28.7695	1.00961
$813$	12.4822	0.437769
$814$	−1.39992	−0.0490670
$815$	−8.07308	−0.282788
$816$	−6.37032	−0.223006
$817$	0	0
$818$	−61.0282	−2.13380
$819$	2.98215	0.104205
$820$	−35.9551	−1.25561
$821$	30.0014	1.04706	0.523528	−	0.852009i	$-0.324616\pi$
$821$	30.0014	1.04706	0.523528	+	0.852009i	$0.324616\pi$
$822$	−8.68312	−0.302859
$823$	8.41454	0.293313	0.146656	−	0.989188i	$-0.453149\pi$
$823$	8.41454	0.293313	0.146656	+	0.989188i	$0.453149\pi$
$824$	103.912	3.61995
$825$	−3.03453	−0.105649
$826$	78.2665	2.72324
$827$	−27.7002	−0.963230	−0.481615	−	0.876383i	$-0.659950\pi$
$827$	−27.7002	−0.963230	−0.481615	+	0.876383i	$0.659950\pi$
$828$	97.6350	3.39305
$829$	−48.2559	−1.67600	−0.837998	−	0.545674i	$-0.816274\pi$
$829$	−48.2559	−1.67600	−0.837998	+	0.545674i	$0.816274\pi$
$830$	1.91192	0.0663638
$831$	−11.1771	−0.387729
$832$	3.39627	0.117745
$833$	−5.25545	−0.182091
$834$	−21.1190	−0.731292
$835$	−13.6495	−0.472359
$836$	0	0
$837$	−11.6848	−0.403885
$838$	−8.00559	−0.276549
$839$	19.4513	0.671534	0.335767	−	0.941945i	$-0.391005\pi$
$839$	19.4513	0.671534	0.335767	+	0.941945i	$0.391005\pi$
$840$	−26.8391	−0.926037
$841$	−26.6289	−0.918236
$842$	73.5289	2.53397
$843$	13.3011	0.458113
$844$	23.9738	0.825211
$845$	12.8674	0.442652
$846$	49.3034	1.69509
$847$	1.24599	0.0428126
$848$	−111.460	−3.82757
$849$	4.93190	0.169262
$850$	1.79418	0.0615399
$851$	1.53073	0.0524729
$852$	23.1915	0.794527
$853$	36.1307	1.23709	0.618547	−	0.785748i	$-0.287722\pi$
$853$	36.1307	1.23709	0.618547	+	0.785748i	$0.287722\pi$
$854$	24.3037	0.831655
$855$	0	0
$856$	49.2078	1.68189
$857$	−46.8598	−1.60070	−0.800350	−	0.599533i	$-0.795353\pi$
$857$	−46.8598	−1.60070	−0.800350	+	0.599533i	$0.795353\pi$
$858$	2.89757	0.0989214
$859$	14.0323	0.478776	0.239388	−	0.970924i	$-0.423053\pi$
$859$	14.0323	0.478776	0.239388	+	0.970924i	$0.423053\pi$
$860$	−12.6188	−0.430298
$861$	−26.2406	−0.894277
$862$	79.2313	2.69863
$863$	40.6050	1.38221	0.691105	−	0.722755i	$-0.257124\pi$
$863$	40.6050	1.38221	0.691105	+	0.722755i	$0.257124\pi$
$864$	53.4522	1.81848
$865$	8.37417	0.284730
$866$	39.4319	1.33995
$867$	−15.3544	−0.521462
$868$	−45.7531	−1.55296
$869$	−30.4528	−1.03304
$870$	−3.75027	−0.127146
$871$	3.48023	0.117923
$872$	−67.9428	−2.30083
$873$	−16.1311	−0.545954
$874$	0	0
$875$	3.83157	0.129531
$876$	−35.7059	−1.20639
$877$	−26.8085	−0.905257	−0.452629	−	0.891699i	$-0.649514\pi$
$877$	−26.8085	−0.905257	−0.452629	+	0.891699i	$0.649514\pi$
$878$	−101.314	−3.41918
$879$	0.821889	0.0277216
$880$	32.7519	1.10407
$881$	50.2819	1.69404	0.847021	−	0.531560i	$-0.178394\pi$
$881$	50.2819	1.69404	0.847021	+	0.531560i	$0.178394\pi$
$882$	43.0495	1.44955
$883$	11.0827	0.372964	0.186482	−	0.982458i	$-0.440291\pi$
$883$	11.0827	0.372964	0.186482	+	0.982458i	$0.440291\pi$
$884$	−1.21490	−0.0408614
$885$	−7.23498	−0.243201
$886$	−11.5063	−0.386560
$887$	−9.91366	−0.332868	−0.166434	−	0.986053i	$-0.553225\pi$
$887$	−9.91366	−0.332868	−0.166434	+	0.986053i	$0.553225\pi$
$888$	1.14457	0.0384091
$889$	−33.6064	−1.12712
$890$	−33.1464	−1.11107
$891$	−6.47074	−0.216778
$892$	42.7237	1.43050
$893$	0	0
$894$	41.3136	1.38173
$895$	−5.70454	−0.190682
$896$	7.86285	0.262679
$897$	−3.16834	−0.105788
$898$	−65.0137	−2.16953
$899$	−3.77093	−0.125767
$900$	−10.4221	−0.347404
$901$	7.60779	0.253452
$902$	63.1738	2.10346
$903$	−9.20942	−0.306470
$904$	99.1482	3.29762
$905$	14.8415	0.493347
$906$	−26.9902	−0.896688
$907$	−18.2308	−0.605343	−0.302671	−	0.953095i	$-0.597878\pi$
$907$	−18.2308	−0.605343	−0.302671	+	0.953095i	$0.597878\pi$
$908$	27.0110	0.896391
$909$	−8.67483	−0.287726
$910$	−3.65864	−0.121283
$911$	−21.7792	−0.721576	−0.360788	−	0.932648i	$-0.617492\pi$
$911$	−21.7792	−0.721576	−0.360788	+	0.932648i	$0.617492\pi$
$912$	0	0
$913$	−2.38220	−0.0788394
$914$	55.3945	1.83229
$915$	−2.24664	−0.0742717
$916$	131.052	4.33007
$917$	−39.8207	−1.31499
$918$	−8.56088	−0.282551
$919$	−26.2299	−0.865246	−0.432623	−	0.901575i	$-0.642412\pi$
$919$	−26.2299	−0.865246	−0.432623	+	0.901575i	$0.642412\pi$
$920$	−70.6528	−2.32936
$921$	23.0794	0.760491
$922$	29.2628	0.963720
$923$	1.86472	0.0613779
$924$	56.6948	1.86512
$925$	−0.163399	−0.00537253
$926$	10.6055	0.348519
$927$	29.4488	0.967225
$928$	17.2501	0.566263
$929$	−10.4394	−0.342505	−0.171253	−	0.985227i	$-0.554781\pi$
$929$	−10.4394	−0.342505	−0.171253	+	0.985227i	$0.554781\pi$
$930$	5.96419	0.195574
$931$	0	0
$932$	12.4470	0.407715
$933$	17.1824	0.562527
$934$	−55.3860	−1.81229
$935$	−2.23550	−0.0731086
$936$	5.86991	0.191864
$937$	21.2197	0.693217	0.346609	−	0.938010i	$-0.387333\pi$
$937$	21.2197	0.693217	0.346609	+	0.938010i	$0.387333\pi$
$938$	96.0256	3.13535
$939$	30.8460	1.00662
$940$	−42.8943	−1.39906
$941$	−50.4839	−1.64573	−0.822864	−	0.568239i	$-0.807625\pi$
$941$	−50.4839	−1.64573	−0.822864	+	0.568239i	$0.807625\pi$
$942$	2.27097	0.0739922
$943$	−69.0773	−2.24947
$944$	78.0877	2.54154
$945$	−18.2822	−0.594722
$946$	22.1715	0.720859
$947$	11.9831	0.389399	0.194699	−	0.980863i	$-0.437627\pi$
$947$	11.9831	0.389399	0.194699	+	0.980863i	$0.437627\pi$
$948$	42.2117	1.37097
$949$	−2.87094	−0.0931948
$950$	0	0
$951$	−6.13896	−0.199069
$952$	−19.7720	−0.640815
$953$	−34.1984	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$953$	−34.1984	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$954$	−62.3185	−2.01764
$955$	19.7204	0.638138
$956$	−124.500	−4.02663
$957$	4.67273	0.151048
$958$	−89.7004	−2.89809
$959$	−13.6606	−0.441124
$960$	−8.66249	−0.279581
$961$	−25.0030	−0.806547
$962$	0.156024	0.00503043
$963$	13.9455	0.449388
$964$	4.83654	0.155774
$965$	−4.13045	−0.132964
$966$	−87.4199	−2.81269
$967$	−12.2077	−0.392574	−0.196287	−	0.980546i	$-0.562888\pi$
$967$	−12.2077	−0.392574	−0.196287	+	0.980546i	$0.562888\pi$
$968$	2.45254	0.0788276
$969$	0	0
$970$	19.7904	0.635431
$971$	14.7902	0.474642	0.237321	−	0.971431i	$-0.423731\pi$
$971$	14.7902	0.474642	0.237321	+	0.971431i	$0.423731\pi$
$972$	78.7682	2.52649
$973$	−33.2253	−1.06515
$974$	4.65921	0.149291
$975$	0.338206	0.0108313
$976$	24.2482	0.776165
$977$	−13.4956	−0.431764	−0.215882	−	0.976419i	$-0.569263\pi$
$977$	−13.4956	−0.431764	−0.215882	+	0.976419i	$0.569263\pi$
$978$	−19.6617	−0.628713
$979$	41.2995	1.31994
$980$	−37.4534	−1.19640
$981$	−19.2551	−0.614766
$982$	54.1999	1.72959
$983$	−47.9982	−1.53090	−0.765452	−	0.643493i	$-0.777485\pi$
$983$	−47.9982	−1.53090	−0.765452	+	0.643493i	$0.777485\pi$
$984$	−51.6507	−1.64656
$985$	−0.166616	−0.00530882
$986$	−2.76277	−0.0879846
$987$	−31.3050	−0.996448
$988$	0	0
$989$	−24.2434	−0.770896
$990$	18.3119	0.581989
$991$	−53.9230	−1.71292	−0.856461	−	0.516212i	$-0.827342\pi$
$991$	−53.9230	−1.71292	−0.856461	+	0.516212i	$0.827342\pi$
$992$	−27.4335	−0.871015
$993$	−15.3262	−0.486362
$994$	51.4507	1.63192
$995$	5.18639	0.164419
$996$	3.30205	0.104630
$997$	33.5959	1.06399	0.531996	−	0.846747i	$-0.321442\pi$
$997$	33.5959	1.06399	0.531996	+	0.846747i	$0.321442\pi$
$998$	111.807	3.53918
$999$	0.779654	0.0246672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.u.1.1		9
5.4	even	2		9025.2.a.cd.1.9		9
19.3	odd	18		95.2.k.b.66.3	yes	18
19.13	odd	18		95.2.k.b.36.3	✓	18
19.18	odd	2		1805.2.a.t.1.9		9
57.32	even	18		855.2.bs.b.226.1		18
57.41	even	18		855.2.bs.b.541.1		18
95.3	even	36		475.2.u.c.199.6		36
95.13	even	36		475.2.u.c.74.1		36
95.22	even	36		475.2.u.c.199.1		36
95.32	even	36		475.2.u.c.74.6		36
95.79	odd	18		475.2.l.b.351.1		18
95.89	odd	18		475.2.l.b.226.1		18
95.94	odd	2		9025.2.a.ce.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.3	✓	18	19.13	odd	18
95.2.k.b.66.3	yes	18	19.3	odd	18
475.2.l.b.226.1		18	95.89	odd	18
475.2.l.b.351.1		18	95.79	odd	18
475.2.u.c.74.1		36	95.13	even	36
475.2.u.c.74.6		36	95.32	even	36
475.2.u.c.199.1		36	95.22	even	36
475.2.u.c.199.6		36	95.3	even	36
855.2.bs.b.226.1		18	57.32	even	18
855.2.bs.b.541.1		18	57.41	even	18
1805.2.a.t.1.9		9	19.18	odd	2
1805.2.a.u.1.1		9	1.1	even	1	trivial
9025.2.a.cd.1.9		9	5.4	even	2
9025.2.a.ce.1.1		9	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62224 q^{2} +0.928776 q^{3} +4.87613 q^{4} -1.00000 q^{5} -2.43547 q^{6} -3.83157 q^{7} -7.54188 q^{8} -2.13737 q^{9} +O(q^{10})\)	\(q-2.62224 q^{2} +0.928776 q^{3} +4.87613 q^{4} -1.00000 q^{5} -2.43547 q^{6} -3.83157 q^{7} -7.54188 q^{8} -2.13737 q^{9} +2.62224 q^{10} -3.26723 q^{11} +4.52883 q^{12} +0.364142 q^{13} +10.0473 q^{14} -0.928776 q^{15} +10.0243 q^{16} -0.684217 q^{17} +5.60470 q^{18} -4.87613 q^{20} -3.55868 q^{21} +8.56746 q^{22} -9.36807 q^{23} -7.00472 q^{24} +1.00000 q^{25} -0.954866 q^{26} -4.77147 q^{27} -18.6832 q^{28} -1.53985 q^{29} +2.43547 q^{30} +2.44889 q^{31} -11.2024 q^{32} -3.03453 q^{33} +1.79418 q^{34} +3.83157 q^{35} -10.4221 q^{36} -0.163399 q^{37} +0.338206 q^{39} +7.54188 q^{40} +7.37370 q^{41} +9.33169 q^{42} +2.58788 q^{43} -15.9314 q^{44} +2.13737 q^{45} +24.5653 q^{46} +8.79680 q^{47} +9.31037 q^{48} +7.68097 q^{49} -2.62224 q^{50} -0.635485 q^{51} +1.77560 q^{52} -11.1190 q^{53} +12.5119 q^{54} +3.26723 q^{55} +28.8973 q^{56} +4.03786 q^{58} +7.78980 q^{59} -4.52883 q^{60} +2.41893 q^{61} -6.42156 q^{62} +8.18951 q^{63} +9.32678 q^{64} -0.364142 q^{65} +7.95725 q^{66} +9.55736 q^{67} -3.33633 q^{68} -8.70084 q^{69} -10.0473 q^{70} +5.12085 q^{71} +16.1198 q^{72} -7.88413 q^{73} +0.428471 q^{74} +0.928776 q^{75} +12.5186 q^{77} -0.886857 q^{78} +9.32066 q^{79} -10.0243 q^{80} +1.98050 q^{81} -19.3356 q^{82} +0.729119 q^{83} -17.3525 q^{84} +0.684217 q^{85} -6.78603 q^{86} -1.43018 q^{87} +24.6411 q^{88} -12.6405 q^{89} -5.60470 q^{90} -1.39524 q^{91} -45.6799 q^{92} +2.27447 q^{93} -23.0673 q^{94} -10.4046 q^{96} +7.54714 q^{97} -20.1413 q^{98} +6.98330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * q^99

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