LMFDB - Embedded newform 1805.2.a.v.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} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
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			$3.22274$ 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)

$f(q)$	$=$	$q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +O(q^{10})$	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} -2.22274 q^{10} +0.0848155 q^{11} +3.04938 q^{12} +5.72097 q^{13} +4.50122 q^{14} +1.03700 q^{15} -1.23419 q^{16} -2.53072 q^{17} +4.27795 q^{18} +2.94057 q^{20} -2.10001 q^{21} -0.188523 q^{22} -0.309088 q^{23} -2.16800 q^{24} +1.00000 q^{25} -12.7162 q^{26} -5.10685 q^{27} -5.95489 q^{28} +2.62414 q^{29} -2.30498 q^{30} +8.07278 q^{31} +6.92456 q^{32} +0.0879538 q^{33} +5.62513 q^{34} -2.02508 q^{35} -5.65951 q^{36} -5.01303 q^{37} +5.93265 q^{39} -2.09064 q^{40} -5.88035 q^{41} +4.66777 q^{42} +0.650519 q^{43} +0.249406 q^{44} -1.92463 q^{45} +0.687021 q^{46} +6.90277 q^{47} -1.27985 q^{48} -2.89906 q^{49} -2.22274 q^{50} -2.62436 q^{51} +16.8229 q^{52} +14.5544 q^{53} +11.3512 q^{54} +0.0848155 q^{55} +4.23372 q^{56} -5.83278 q^{58} +7.47335 q^{59} +3.04938 q^{60} +13.3170 q^{61} -17.9437 q^{62} +3.89752 q^{63} -12.9231 q^{64} +5.72097 q^{65} -0.195498 q^{66} +8.88244 q^{67} -7.44175 q^{68} -0.320524 q^{69} +4.50122 q^{70} -14.3366 q^{71} +4.02371 q^{72} +10.8548 q^{73} +11.1426 q^{74} +1.03700 q^{75} -0.171758 q^{77} -13.1867 q^{78} +0.115898 q^{79} -1.23419 q^{80} +0.478079 q^{81} +13.0705 q^{82} -2.97552 q^{83} -6.17523 q^{84} -2.53072 q^{85} -1.44593 q^{86} +2.72124 q^{87} -0.177319 q^{88} -11.1259 q^{89} +4.27795 q^{90} -11.5854 q^{91} -0.908894 q^{92} +8.37148 q^{93} -15.3431 q^{94} +7.18078 q^{96} -0.225903 q^{97} +6.44385 q^{98} -0.163238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 + 6 * q^8 + 6 * q^9	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 18 q^{12} + 9 q^{13} + 9 q^{15} + 12 q^{16} - 9 q^{17} + 24 q^{18} + 6 q^{20} + 12 q^{21} + 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} + 24 q^{27} - 15 q^{28} + 9 q^{29} + 12 q^{30} + 18 q^{31} + 3 q^{32} - 9 q^{33} - 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} - 9 q^{46} + 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{50} - 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} + 9 q^{65} + 3 q^{66} + 60 q^{67} - 51 q^{68} - 15 q^{69} - 18 q^{71} + 27 q^{73} + 27 q^{74} + 9 q^{75} - 30 q^{77} - 6 q^{78} + 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} - 48 q^{84} - 9 q^{85} - 39 q^{86} + 15 q^{87} + 27 q^{88} - 39 q^{89} + 24 q^{90} + 21 q^{91} - 6 q^{92} + 15 q^{93} + 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 18 * q^12 + 9 * q^13 + 9 * q^15 + 12 * q^16 - 9 * q^17 + 24 * q^18 + 6 * q^20 + 12 * q^21 + 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 + 24 * q^27 - 15 * q^28 + 9 * q^29 + 12 * q^30 + 18 * q^31 + 3 * q^32 - 9 * q^33 - 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 - 9 * q^46 + 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^50 - 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 + 9 * q^65 + 3 * q^66 + 60 * q^67 - 51 * q^68 - 15 * q^69 - 18 * q^71 + 27 * q^73 + 27 * q^74 + 9 * q^75 - 30 * q^77 - 6 * q^78 + 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 - 48 * q^84 - 9 * q^85 - 39 * q^86 + 15 * q^87 + 27 * q^88 - 39 * q^89 + 24 * q^90 + 21 * q^91 - 6 * q^92 + 15 * q^93 + 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * q^98 - 36 * 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 $

$2$	−2.22274	−1.57171	−0.785857	−	0.618408i	$-0.787778\pi$
$2$	−2.22274	−1.57171	−0.785857	+	0.618408i	$0.787778\pi$
$3$	1.03700	0.598713	0.299356	−	0.954141i	$-0.403228\pi$
$3$	1.03700	0.598713	0.299356	+	0.954141i	$0.403228\pi$
$4$	2.94057	1.47029
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.30498	−0.941006
$7$	−2.02508	−0.765408	−0.382704	−	0.923871i	$-0.625007\pi$
$7$	−2.02508	−0.765408	−0.382704	+	0.923871i	$0.625007\pi$
$8$	−2.09064	−0.739154
$9$	−1.92463	−0.641543
$10$	−2.22274	−0.702892
$11$	0.0848155	0.0255728	0.0127864	−	0.999918i	$-0.495930\pi$
$11$	0.0848155	0.0255728	0.0127864	+	0.999918i	$0.495930\pi$
$12$	3.04938	0.880279
$13$	5.72097	1.58671	0.793356	−	0.608758i	$-0.208332\pi$
$13$	5.72097	1.58671	0.793356	+	0.608758i	$0.208332\pi$
$14$	4.50122	1.20300
$15$	1.03700	0.267753
$16$	−1.23419	−0.308546
$17$	−2.53072	−0.613789	−0.306895	−	0.951743i	$-0.599290\pi$
$17$	−2.53072	−0.613789	−0.306895	+	0.951743i	$0.599290\pi$
$18$	4.27795	1.00832
$19$	0	0
$19$	0	0
$20$	2.94057	0.657532
$21$	−2.10001	−0.458260
$22$	−0.188523	−0.0401932
$23$	−0.309088	−0.0644492	−0.0322246	−	0.999481i	$-0.510259\pi$
$23$	−0.309088	−0.0644492	−0.0322246	+	0.999481i	$0.510259\pi$
$24$	−2.16800	−0.442541
$25$	1.00000	0.200000
$26$	−12.7162	−2.49386
$27$	−5.10685	−0.982813
$28$	−5.95489	−1.12537
$29$	2.62414	0.487291	0.243646	−	0.969864i	$-0.421657\pi$
$29$	2.62414	0.487291	0.243646	+	0.969864i	$0.421657\pi$
$30$	−2.30498	−0.420831
$31$	8.07278	1.44991	0.724957	−	0.688795i	$-0.241860\pi$
$31$	8.07278	1.44991	0.724957	+	0.688795i	$0.241860\pi$
$32$	6.92456	1.22410
$33$	0.0879538	0.0153108
$34$	5.62513	0.964701
$35$	−2.02508	−0.342301
$36$	−5.65951	−0.943251
$37$	−5.01303	−0.824136	−0.412068	−	0.911153i	$-0.635193\pi$
$37$	−5.01303	−0.824136	−0.412068	+	0.911153i	$0.635193\pi$
$38$	0	0
$39$	5.93265	0.949985
$40$	−2.09064	−0.330560
$41$	−5.88035	−0.918357	−0.459179	−	0.888344i	$-0.651856\pi$
$41$	−5.88035	−0.918357	−0.459179	+	0.888344i	$0.651856\pi$
$42$	4.66777	0.720253
$43$	0.650519	0.0992032	0.0496016	−	0.998769i	$-0.484205\pi$
$43$	0.650519	0.0992032	0.0496016	+	0.998769i	$0.484205\pi$
$44$	0.249406	0.0375994
$45$	−1.92463	−0.286907
$46$	0.687021	0.101296
$47$	6.90277	1.00687	0.503437	−	0.864032i	$-0.332069\pi$
$47$	6.90277	1.00687	0.503437	+	0.864032i	$0.332069\pi$
$48$	−1.27985	−0.184731
$49$	−2.89906	−0.414151
$50$	−2.22274	−0.314343
$51$	−2.62436	−0.367484
$52$	16.8229	2.33292
$53$	14.5544	1.99920	0.999601	−	0.0282415i	$-0.00899075\pi$
$53$	14.5544	1.99920	0.999601	+	0.0282415i	$0.00899075\pi$
$54$	11.3512	1.54470
$55$	0.0848155	0.0114365
$56$	4.23372	0.565754
$57$	0	0
$58$	−5.83278	−0.765882
$59$	7.47335	0.972947	0.486474	−	0.873695i	$-0.338283\pi$
$59$	7.47335	0.972947	0.486474	+	0.873695i	$0.338283\pi$
$60$	3.04938	0.393673
$61$	13.3170	1.70507	0.852534	−	0.522672i	$-0.175065\pi$
$61$	13.3170	1.70507	0.852534	+	0.522672i	$0.175065\pi$
$62$	−17.9437	−2.27885
$63$	3.89752	0.491042
$64$	−12.9231	−1.61539
$65$	5.72097	0.709599
$66$	−0.195498	−0.0240642
$67$	8.88244	1.08516	0.542582	−	0.840003i	$-0.317447\pi$
$67$	8.88244	1.08516	0.542582	+	0.840003i	$0.317447\pi$
$68$	−7.44175	−0.902445
$69$	−0.320524	−0.0385866
$70$	4.50122	0.537999
$71$	−14.3366	−1.70144	−0.850719	−	0.525620i	$-0.823833\pi$
$71$	−14.3366	−1.70144	−0.850719	+	0.525620i	$0.823833\pi$
$72$	4.02371	0.474199
$73$	10.8548	1.27046	0.635229	−	0.772324i	$-0.280906\pi$
$73$	10.8548	1.27046	0.635229	+	0.772324i	$0.280906\pi$
$74$	11.1426	1.29531
$75$	1.03700	0.119743
$76$	0	0
$77$	−0.171758	−0.0195737
$78$	−13.1867	−1.49310
$79$	0.115898	0.0130395	0.00651976	−	0.999979i	$-0.497925\pi$
$79$	0.115898	0.0130395	0.00651976	+	0.999979i	$0.497925\pi$
$80$	−1.23419	−0.137986
$81$	0.478079	0.0531198
$82$	13.0705	1.44339
$83$	−2.97552	−0.326606	−0.163303	−	0.986576i	$-0.552215\pi$
$83$	−2.97552	−0.326606	−0.163303	+	0.986576i	$0.552215\pi$
$84$	−6.17523	−0.673772
$85$	−2.53072	−0.274495
$86$	−1.44593	−0.155919
$87$	2.72124	0.291747
$88$	−0.177319	−0.0189023
$89$	−11.1259	−1.17934	−0.589670	−	0.807644i	$-0.700742\pi$
$89$	−11.1259	−1.17934	−0.589670	+	0.807644i	$0.700742\pi$
$90$	4.27795	0.450935
$91$	−11.5854	−1.21448
$92$	−0.908894	−0.0947587
$93$	8.37148	0.868082
$94$	−15.3431	−1.58252
$95$	0	0
$96$	7.18078	0.732885
$97$	−0.225903	−0.0229370	−0.0114685	−	0.999934i	$-0.503651\pi$
$97$	−0.225903	−0.0229370	−0.0114685	+	0.999934i	$0.503651\pi$
$98$	6.44385	0.650927
$99$	−0.163238	−0.0164061
$100$	2.94057	0.294057
$101$	−12.6014	−1.25388	−0.626942	−	0.779066i	$-0.715694\pi$
$101$	−12.6014	−1.25388	−0.626942	+	0.779066i	$0.715694\pi$
$102$	5.83326	0.577579
$103$	17.7230	1.74630	0.873152	−	0.487448i	$-0.162072\pi$
$103$	17.7230	1.74630	0.873152	+	0.487448i	$0.162072\pi$
$104$	−11.9605	−1.17282
$105$	−2.10001	−0.204940
$106$	−32.3507	−3.14217
$107$	5.09612	0.492661	0.246330	−	0.969186i	$-0.420775\pi$
$107$	5.09612	0.492661	0.246330	+	0.969186i	$0.420775\pi$
$108$	−15.0170	−1.44502
$109$	−6.13513	−0.587639	−0.293819	−	0.955861i	$-0.594926\pi$
$109$	−6.13513	−0.587639	−0.293819	+	0.955861i	$0.594926\pi$
$110$	−0.188523	−0.0179749
$111$	−5.19851	−0.493421
$112$	2.49932	0.236164
$113$	11.4316	1.07539	0.537697	−	0.843138i	$-0.319294\pi$
$113$	11.4316	1.07539	0.537697	+	0.843138i	$0.319294\pi$
$114$	0	0
$115$	−0.309088	−0.0288226
$116$	7.71648	0.716457
$117$	−11.0107	−1.01794
$118$	−16.6113	−1.52919
$119$	5.12490	0.469799
$120$	−2.16800	−0.197910
$121$	−10.9928	−0.999346
$122$	−29.6002	−2.67988
$123$	−6.09794	−0.549832
$124$	23.7386	2.13179
$125$	1.00000	0.0894427
$126$	−8.66318	−0.771777
$127$	−1.43978	−0.127760	−0.0638799	−	0.997958i	$-0.520347\pi$
$127$	−1.43978	−0.127760	−0.0638799	+	0.997958i	$0.520347\pi$
$128$	14.8756	1.31483
$129$	0.674589	0.0593942
$130$	−12.7162	−1.11529
$131$	−1.00345	−0.0876720	−0.0438360	−	0.999039i	$-0.513958\pi$
$131$	−1.00345	−0.0876720	−0.0438360	+	0.999039i	$0.513958\pi$
$132$	0.258634	0.0225112
$133$	0	0
$134$	−19.7434	−1.70557
$135$	−5.10685	−0.439527
$136$	5.29083	0.453685
$137$	−10.4468	−0.892530	−0.446265	−	0.894901i	$-0.647246\pi$
$137$	−10.4468	−0.892530	−0.446265	+	0.894901i	$0.647246\pi$
$138$	0.712442	0.0606471
$139$	10.6846	0.906256	0.453128	−	0.891445i	$-0.350308\pi$
$139$	10.6846	0.906256	0.453128	+	0.891445i	$0.350308\pi$
$140$	−5.95489	−0.503280
$141$	7.15819	0.602828
$142$	31.8665	2.67417
$143$	0.485227	0.0405767
$144$	2.37535	0.197946
$145$	2.62414	0.217923
$146$	−24.1274	−1.99680
$147$	−3.00632	−0.247957
$148$	−14.7412	−1.21172
$149$	−5.04462	−0.413271	−0.206636	−	0.978418i	$-0.566251\pi$
$149$	−5.04462	−0.413271	−0.206636	+	0.978418i	$0.566251\pi$
$150$	−2.30498	−0.188201
$151$	20.8114	1.69360	0.846802	−	0.531909i	$-0.178525\pi$
$151$	20.8114	1.69360	0.846802	+	0.531909i	$0.178525\pi$
$152$	0	0
$153$	4.87069	0.393772
$154$	0.381774	0.0307642
$155$	8.07278	0.648421
$156$	17.4454	1.39675
$157$	23.6158	1.88475	0.942374	−	0.334561i	$-0.108588\pi$
$157$	23.6158	1.88475	0.942374	+	0.334561i	$0.108588\pi$
$158$	−0.257611	−0.0204944
$159$	15.0929	1.19695
$160$	6.92456	0.547435
$161$	0.625927	0.0493299
$162$	−1.06264	−0.0834892
$163$	−0.213533	−0.0167252	−0.00836258	−	0.999965i	$-0.502662\pi$
$163$	−0.213533	−0.0167252	−0.00836258	+	0.999965i	$0.502662\pi$
$164$	−17.2916	−1.35025
$165$	0.0879538	0.00684719
$166$	6.61382	0.513332
$167$	19.7249	1.52636	0.763178	−	0.646188i	$-0.223638\pi$
$167$	19.7249	1.52636	0.763178	+	0.646188i	$0.223638\pi$
$168$	4.39037	0.338724
$169$	19.7295	1.51765
$170$	5.62513	0.431428
$171$	0	0
$172$	1.91290	0.145857
$173$	12.5749	0.956051	0.478026	−	0.878346i	$-0.341353\pi$
$173$	12.5749	0.956051	0.478026	+	0.878346i	$0.341353\pi$
$174$	−6.04861	−0.458544
$175$	−2.02508	−0.153082
$176$	−0.104678	−0.00789041
$177$	7.74987	0.582516
$178$	24.7299	1.85358
$179$	−10.8183	−0.808596	−0.404298	−	0.914627i	$-0.632484\pi$
$179$	−10.8183	−0.808596	−0.404298	+	0.914627i	$0.632484\pi$
$180$	−5.65951	−0.421835
$181$	−5.41191	−0.402264	−0.201132	−	0.979564i	$-0.564462\pi$
$181$	−5.41191	−0.402264	−0.201132	+	0.979564i	$0.564462\pi$
$182$	25.7514	1.90882
$183$	13.8098	1.02085
$184$	0.646192	0.0476379
$185$	−5.01303	−0.368565
$186$	−18.6076	−1.36438
$187$	−0.214644	−0.0156963
$188$	20.2981	1.48039
$189$	10.3418	0.752253
$190$	0	0
$191$	4.87144	0.352485	0.176243	−	0.984347i	$-0.443606\pi$
$191$	4.87144	0.352485	0.176243	+	0.984347i	$0.443606\pi$
$192$	−13.4013	−0.967155
$193$	−1.38414	−0.0996323	−0.0498162	−	0.998758i	$-0.515864\pi$
$193$	−1.38414	−0.0996323	−0.0498162	+	0.998758i	$0.515864\pi$
$194$	0.502123	0.0360503
$195$	5.93265	0.424846
$196$	−8.52488	−0.608920
$197$	6.40750	0.456515	0.228258	−	0.973601i	$-0.426697\pi$
$197$	6.40750	0.456515	0.228258	+	0.973601i	$0.426697\pi$
$198$	0.362836	0.0257857
$199$	15.6405	1.10873	0.554363	−	0.832275i	$-0.312962\pi$
$199$	15.6405	1.10873	0.554363	+	0.832275i	$0.312962\pi$
$200$	−2.09064	−0.147831
$201$	9.21111	0.649701
$202$	28.0096	1.97075
$203$	−5.31410	−0.372976
$204$	−7.71711	−0.540306
$205$	−5.88035	−0.410702
$206$	−39.3937	−2.74469
$207$	0.594879	0.0413469
$208$	−7.06074	−0.489574
$209$	0	0
$210$	4.66777	0.322107
$211$	7.68384	0.528978	0.264489	−	0.964389i	$-0.414797\pi$
$211$	7.68384	0.528978	0.264489	+	0.964389i	$0.414797\pi$
$212$	42.7983	2.93940
$213$	−14.8670	−1.01867
$214$	−11.3274	−0.774322
$215$	0.650519	0.0443650
$216$	10.6766	0.726450
$217$	−16.3480	−1.10977
$218$	13.6368	0.923600
$219$	11.2564	0.760640
$220$	0.249406	0.0168149
$221$	−14.4782	−0.973906
$222$	11.5549	0.775517
$223$	2.47996	0.166070	0.0830351	−	0.996547i	$-0.473539\pi$
$223$	2.47996	0.166070	0.0830351	+	0.996547i	$0.473539\pi$
$224$	−14.0228	−0.936936
$225$	−1.92463	−0.128309
$226$	−25.4095	−1.69021
$227$	−0.453554	−0.0301034	−0.0150517	−	0.999887i	$-0.504791\pi$
$227$	−0.453554	−0.0301034	−0.0150517	+	0.999887i	$0.504791\pi$
$228$	0	0
$229$	0.993282	0.0656379	0.0328190	−	0.999461i	$-0.489552\pi$
$229$	0.993282	0.0656379	0.0328190	+	0.999461i	$0.489552\pi$
$230$	0.687021	0.0453008
$231$	−0.178113	−0.0117190
$232$	−5.48615	−0.360183
$233$	−4.26321	−0.279292	−0.139646	−	0.990201i	$-0.544597\pi$
$233$	−4.26321	−0.279292	−0.139646	+	0.990201i	$0.544597\pi$
$234$	24.4740	1.59992
$235$	6.90277	0.450287
$236$	21.9759	1.43051
$237$	0.120186	0.00780693
$238$	−11.3913	−0.738390
$239$	24.4583	1.58207	0.791037	−	0.611768i	$-0.209541\pi$
$239$	24.4583	1.58207	0.791037	+	0.611768i	$0.209541\pi$
$240$	−1.27985	−0.0826141
$241$	4.39485	0.283097	0.141548	−	0.989931i	$-0.454792\pi$
$241$	4.39485	0.283097	0.141548	+	0.989931i	$0.454792\pi$
$242$	24.4341	1.57069
$243$	15.8163	1.01462
$244$	39.1596	2.50694
$245$	−2.89906	−0.185214
$246$	13.5541	0.864179
$247$	0	0
$248$	−16.8773	−1.07171
$249$	−3.08562	−0.195543
$250$	−2.22274	−0.140578
$251$	−0.387468	−0.0244568	−0.0122284	−	0.999925i	$-0.503893\pi$
$251$	−0.387468	−0.0244568	−0.0122284	+	0.999925i	$0.503893\pi$
$252$	11.4609	0.721972
$253$	−0.0262154	−0.00164815
$254$	3.20025	0.200802
$255$	−2.62436	−0.164344
$256$	−7.21836	−0.451148
$257$	−2.85296	−0.177963	−0.0889814	−	0.996033i	$-0.528361\pi$
$257$	−2.85296	−0.177963	−0.0889814	+	0.996033i	$0.528361\pi$
$258$	−1.49944	−0.0933508
$259$	10.1518	0.630800
$260$	16.8229	1.04331
$261$	−5.05050	−0.312618
$262$	2.23041	0.137795
$263$	−10.8075	−0.666417	−0.333209	−	0.942853i	$-0.608131\pi$
$263$	−10.8075	−0.666417	−0.333209	+	0.942853i	$0.608131\pi$
$264$	−0.183880	−0.0113170
$265$	14.5544	0.894070
$266$	0	0
$267$	−11.5375	−0.706086
$268$	26.1195	1.59550
$269$	2.77764	0.169356	0.0846780	−	0.996408i	$-0.473014\pi$
$269$	2.77764	0.169356	0.0846780	+	0.996408i	$0.473014\pi$
$270$	11.3512	0.690811
$271$	14.8624	0.902828	0.451414	−	0.892315i	$-0.350920\pi$
$271$	14.8624	0.902828	0.451414	+	0.892315i	$0.350920\pi$
$272$	3.12338	0.189382
$273$	−12.0141	−0.727126
$274$	23.2205	1.40280
$275$	0.0848155	0.00511457
$276$	−0.942524	−0.0567333
$277$	18.0876	1.08678	0.543389	−	0.839481i	$-0.317141\pi$
$277$	18.0876	1.08678	0.543389	+	0.839481i	$0.317141\pi$
$278$	−23.7491	−1.42438
$279$	−15.5371	−0.930181
$280$	4.23372	0.253013
$281$	−3.88426	−0.231716	−0.115858	−	0.993266i	$-0.536962\pi$
$281$	−3.88426	−0.231716	−0.115858	+	0.993266i	$0.536962\pi$
$282$	−15.9108	−0.947473
$283$	−22.2860	−1.32477	−0.662383	−	0.749165i	$-0.730455\pi$
$283$	−22.2860	−1.32477	−0.662383	+	0.749165i	$0.730455\pi$
$284$	−42.1577	−2.50160
$285$	0	0
$286$	−1.07853	−0.0637750
$287$	11.9082	0.702918
$288$	−13.3272	−0.785313
$289$	−10.5955	−0.623263
$290$	−5.83278	−0.342513
$291$	−0.234262	−0.0137327
$292$	31.9193	1.86794
$293$	−24.4514	−1.42846	−0.714232	−	0.699909i	$-0.753224\pi$
$293$	−24.4514	−1.42846	−0.714232	+	0.699909i	$0.753224\pi$
$294$	6.68228	0.389718
$295$	7.47335	0.435115
$296$	10.4804	0.609164
$297$	−0.433140	−0.0251333
$298$	11.2129	0.649544
$299$	−1.76828	−0.102262
$300$	3.04938	0.176056
$301$	−1.31735	−0.0759309
$302$	−46.2582	−2.66186
$303$	−13.0676	−0.750717
$304$	0	0
$305$	13.3170	0.762529
$306$	−10.8263	−0.618897
$307$	6.42519	0.366705	0.183353	−	0.983047i	$-0.441305\pi$
$307$	6.42519	0.366705	0.183353	+	0.983047i	$0.441305\pi$
$308$	−0.505067	−0.0287789
$309$	18.3788	1.04553
$310$	−17.9437	−1.01913
$311$	−17.5640	−0.995963	−0.497982	−	0.867188i	$-0.665925\pi$
$311$	−17.5640	−0.995963	−0.497982	+	0.867188i	$0.665925\pi$
$312$	−12.4031	−0.702185
$313$	−3.64359	−0.205948	−0.102974	−	0.994684i	$-0.532836\pi$
$313$	−3.64359	−0.205948	−0.102974	+	0.994684i	$0.532836\pi$
$314$	−52.4918	−2.96228
$315$	3.89752	0.219601
$316$	0.340806	0.0191718
$317$	4.49901	0.252689	0.126345	−	0.991986i	$-0.459675\pi$
$317$	4.49901	0.252689	0.126345	+	0.991986i	$0.459675\pi$
$318$	−33.5477	−1.88126
$319$	0.222568	0.0124614
$320$	−12.9231	−0.722424
$321$	5.28469	0.294962
$322$	−1.39127	−0.0775325
$323$	0	0
$324$	1.40582	0.0781013
$325$	5.72097	0.317342
$326$	0.474627	0.0262872
$327$	−6.36214	−0.351827
$328$	12.2937	0.678807
$329$	−13.9787	−0.770669
$330$	−0.195498	−0.0107618
$331$	34.1003	1.87432	0.937161	−	0.348898i	$-0.113444\pi$
$331$	34.1003	1.87432	0.937161	+	0.348898i	$0.113444\pi$
$332$	−8.74974	−0.480204
$333$	9.64821	0.528719
$334$	−43.8433	−2.39900
$335$	8.88244	0.485300
$336$	2.59180	0.141394
$337$	−0.968932	−0.0527811	−0.0263905	−	0.999652i	$-0.508401\pi$
$337$	−0.968932	−0.0527811	−0.0263905	+	0.999652i	$0.508401\pi$
$338$	−43.8535	−2.38532
$339$	11.8546	0.643852
$340$	−7.44175	−0.403586
$341$	0.684697	0.0370784
$342$	0	0
$343$	20.0464	1.08240
$344$	−1.36000	−0.0733264
$345$	−0.320524	−0.0172564
$346$	−27.9507	−1.50264
$347$	−23.5064	−1.26189	−0.630945	−	0.775827i	$-0.717333\pi$
$347$	−23.5064	−1.26189	−0.630945	+	0.775827i	$0.717333\pi$
$348$	8.00200	0.428952
$349$	19.4375	1.04047	0.520234	−	0.854024i	$-0.325845\pi$
$349$	19.4375	1.04047	0.520234	+	0.854024i	$0.325845\pi$
$350$	4.50122	0.240600
$351$	−29.2161	−1.55944
$352$	0.587310	0.0313037
$353$	−11.9646	−0.636814	−0.318407	−	0.947954i	$-0.603148\pi$
$353$	−11.9646	−0.636814	−0.318407	+	0.947954i	$0.603148\pi$
$354$	−17.2259	−0.915549
$355$	−14.3366	−0.760906
$356$	−32.7164	−1.73397
$357$	5.31453	0.281275
$358$	24.0462	1.27088
$359$	17.1901	0.907256	0.453628	−	0.891191i	$-0.350129\pi$
$359$	17.1901	0.907256	0.453628	+	0.891191i	$0.350129\pi$
$360$	4.02371	0.212068
$361$	0	0
$362$	12.0293	0.632244
$363$	−11.3996	−0.598321
$364$	−34.0677	−1.78563
$365$	10.8548	0.568166
$366$	−30.6955	−1.60448
$367$	−17.6232	−0.919924	−0.459962	−	0.887938i	$-0.652137\pi$
$367$	−17.6232	−0.919924	−0.459962	+	0.887938i	$0.652137\pi$
$368$	0.381471	0.0198856
$369$	11.3175	0.589165
$370$	11.1426	0.579279
$371$	−29.4738	−1.53021
$372$	24.6169	1.27633
$373$	−2.65476	−0.137458	−0.0687292	−	0.997635i	$-0.521894\pi$
$373$	−2.65476	−0.137458	−0.0687292	+	0.997635i	$0.521894\pi$
$374$	0.477098	0.0246701
$375$	1.03700	0.0535505
$376$	−14.4312	−0.744234
$377$	15.0126	0.773190
$378$	−22.9871	−1.18233
$379$	−18.9795	−0.974909	−0.487455	−	0.873148i	$-0.662075\pi$
$379$	−18.9795	−0.974909	−0.487455	+	0.873148i	$0.662075\pi$
$380$	0	0
$381$	−1.49305	−0.0764914
$382$	−10.8279	−0.554006
$383$	−11.9285	−0.609519	−0.304759	−	0.952429i	$-0.598576\pi$
$383$	−11.9285	−0.609519	−0.304759	+	0.952429i	$0.598576\pi$
$384$	15.4260	0.787206
$385$	−0.171758	−0.00875360
$386$	3.07657	0.156594
$387$	−1.25201	−0.0636431
$388$	−0.664283	−0.0337239
$389$	−9.76564	−0.495138	−0.247569	−	0.968870i	$-0.579632\pi$
$389$	−9.76564	−0.495138	−0.247569	+	0.968870i	$0.579632\pi$
$390$	−13.1867	−0.667737
$391$	0.782213	0.0395582
$392$	6.06089	0.306121
$393$	−1.04058	−0.0524903
$394$	−14.2422	−0.717512
$395$	0.115898	0.00583145
$396$	−0.480014	−0.0241216
$397$	28.8426	1.44757	0.723784	−	0.690026i	$-0.242401\pi$
$397$	28.8426	1.44757	0.723784	+	0.690026i	$0.242401\pi$
$398$	−34.7648	−1.74260
$399$	0	0
$400$	−1.23419	−0.0617093
$401$	6.27130	0.313174	0.156587	−	0.987664i	$-0.449951\pi$
$401$	6.27130	0.313174	0.156587	+	0.987664i	$0.449951\pi$
$402$	−20.4739	−1.02114
$403$	46.1841	2.30059
$404$	−37.0552	−1.84357
$405$	0.478079	0.0237559
$406$	11.8118	0.586212
$407$	−0.425182	−0.0210755
$408$	5.48660	0.271627
$409$	11.2239	0.554988	0.277494	−	0.960727i	$-0.410496\pi$
$409$	11.2239	0.554988	0.277494	+	0.960727i	$0.410496\pi$
$410$	13.0705	0.645506
$411$	−10.8333	−0.534369
$412$	52.1159	2.56756
$413$	−15.1341	−0.744701
$414$	−1.32226	−0.0649855
$415$	−2.97552	−0.146063
$416$	39.6152	1.94229
$417$	11.0800	0.542588
$418$	0	0
$419$	−26.0754	−1.27387	−0.636934	−	0.770918i	$-0.719798\pi$
$419$	−26.0754	−1.27387	−0.636934	+	0.770918i	$0.719798\pi$
$420$	−6.17523	−0.301320
$421$	−25.2605	−1.23112	−0.615562	−	0.788089i	$-0.711071\pi$
$421$	−25.2605	−1.23112	−0.615562	+	0.788089i	$0.711071\pi$
$422$	−17.0792	−0.831401
$423$	−13.2853	−0.645952
$424$	−30.4281	−1.47772
$425$	−2.53072	−0.122758
$426$	33.0456	1.60106
$427$	−26.9680	−1.30507
$428$	14.9855	0.724352
$429$	0.503181	0.0242938
$430$	−1.44593	−0.0697291
$431$	38.1890	1.83950	0.919749	−	0.392508i	$-0.128392\pi$
$431$	38.1890	1.83950	0.919749	+	0.392508i	$0.128392\pi$
$432$	6.30280	0.303243
$433$	2.62102	0.125958	0.0629792	−	0.998015i	$-0.479940\pi$
$433$	2.62102	0.125958	0.0629792	+	0.998015i	$0.479940\pi$
$434$	36.3374	1.74425
$435$	2.72124	0.130473
$436$	−18.0408	−0.863997
$437$	0	0
$438$	−25.0201	−1.19551
$439$	6.71666	0.320569	0.160284	−	0.987071i	$-0.448759\pi$
$439$	6.71666	0.320569	0.160284	+	0.987071i	$0.448759\pi$
$440$	−0.177319	−0.00845335
$441$	5.57960	0.265695
$442$	32.1812	1.53070
$443$	−26.0060	−1.23558	−0.617791	−	0.786342i	$-0.711972\pi$
$443$	−26.0060	−1.23558	−0.617791	+	0.786342i	$0.711972\pi$
$444$	−15.2866	−0.725470
$445$	−11.1259	−0.527417
$446$	−5.51230	−0.261015
$447$	−5.23127	−0.247431
$448$	26.1703	1.23643
$449$	−27.5720	−1.30120	−0.650602	−	0.759419i	$-0.725483\pi$
$449$	−27.5720	−1.30120	−0.650602	+	0.759419i	$0.725483\pi$
$450$	4.27795	0.201664
$451$	−0.498745	−0.0234850
$452$	33.6154	1.58114
$453$	21.5814	1.01398
$454$	1.00813	0.0473139
$455$	−11.5854	−0.543133
$456$	0	0
$457$	2.22524	0.104092	0.0520462	−	0.998645i	$-0.483426\pi$
$457$	2.22524	0.104092	0.0520462	+	0.998645i	$0.483426\pi$
$458$	−2.20781	−0.103164
$459$	12.9240	0.603240
$460$	−0.908894	−0.0423774
$461$	20.4553	0.952698	0.476349	−	0.879256i	$-0.341960\pi$
$461$	20.4553	0.952698	0.476349	+	0.879256i	$0.341960\pi$
$462$	0.395900	0.0184189
$463$	−32.4300	−1.50715	−0.753575	−	0.657362i	$-0.771672\pi$
$463$	−32.4300	−1.50715	−0.753575	+	0.657362i	$0.771672\pi$
$464$	−3.23868	−0.150352
$465$	8.37148	0.388218
$466$	9.47601	0.438968
$467$	−6.92098	−0.320265	−0.160132	−	0.987096i	$-0.551192\pi$
$467$	−6.92098	−0.320265	−0.160132	+	0.987096i	$0.551192\pi$
$468$	−32.3779	−1.49667
$469$	−17.9876	−0.830592
$470$	−15.3431	−0.707723
$471$	24.4896	1.12842
$472$	−15.6241	−0.719158
$473$	0.0551741	0.00253691
$474$	−0.267143	−0.0122703
$475$	0	0
$476$	15.0701	0.690739
$477$	−28.0118	−1.28257
$478$	−54.3644	−2.48657
$479$	−20.0438	−0.915825	−0.457913	−	0.888997i	$-0.651403\pi$
$479$	−20.0438	−0.915825	−0.457913	+	0.888997i	$0.651403\pi$
$480$	7.18078	0.327756
$481$	−28.6794	−1.30767
$482$	−9.76860	−0.444947
$483$	0.649087	0.0295345
$484$	−32.3251	−1.46932
$485$	−0.225903	−0.0102577
$486$	−35.1555	−1.59469
$487$	7.12927	0.323058	0.161529	−	0.986868i	$-0.448357\pi$
$487$	7.12927	0.323058	0.161529	+	0.986868i	$0.448357\pi$
$488$	−27.8411	−1.26031
$489$	−0.221434	−0.0100136
$490$	6.44385	0.291103
$491$	16.5051	0.744865	0.372433	−	0.928059i	$-0.378524\pi$
$491$	16.5051	0.744865	0.372433	+	0.928059i	$0.378524\pi$
$492$	−17.9314	−0.808410
$493$	−6.64096	−0.299094
$494$	0	0
$495$	−0.163238	−0.00733702
$496$	−9.96330	−0.447366
$497$	29.0327	1.30229
$498$	6.85854	0.307338
$499$	−30.3605	−1.35912	−0.679562	−	0.733618i	$-0.737830\pi$
$499$	−30.3605	−1.35912	−0.679562	+	0.733618i	$0.737830\pi$
$500$	2.94057	0.131506
$501$	20.4547	0.913850
$502$	0.861241	0.0384390
$503$	−5.76940	−0.257245	−0.128622	−	0.991694i	$-0.541056\pi$
$503$	−5.76940	−0.257245	−0.128622	+	0.991694i	$0.541056\pi$
$504$	−8.14833	−0.362956
$505$	−12.6014	−0.560754
$506$	0.0582700	0.00259042
$507$	20.4595	0.908639
$508$	−4.23377	−0.187843
$509$	−38.8654	−1.72268	−0.861340	−	0.508029i	$-0.830374\pi$
$509$	−38.8654	−1.72268	−0.861340	+	0.508029i	$0.830374\pi$
$510$	5.83326	0.258301
$511$	−21.9818	−0.972418
$512$	−13.7067	−0.605755
$513$	0	0
$514$	6.34139	0.279707
$515$	17.7230	0.780971
$516$	1.98368	0.0873265
$517$	0.585462	0.0257486
$518$	−22.5647	−0.991438
$519$	13.0402	0.572400
$520$	−11.9605	−0.524503
$521$	−36.5105	−1.59956	−0.799778	−	0.600296i	$-0.795049\pi$
$521$	−36.5105	−1.59956	−0.799778	+	0.600296i	$0.795049\pi$
$522$	11.2259	0.491346
$523$	27.8101	1.21605	0.608025	−	0.793918i	$-0.291962\pi$
$523$	27.8101	1.21605	0.608025	+	0.793918i	$0.291962\pi$
$524$	−2.95072	−0.128903
$525$	−2.10001	−0.0916519
$526$	24.0222	1.04742
$527$	−20.4299	−0.889941
$528$	−0.108551	−0.00472409
$529$	−22.9045	−0.995846
$530$	−32.3507	−1.40522
$531$	−14.3834	−0.624187
$532$	0	0
$533$	−33.6413	−1.45717
$534$	25.6449	1.10977
$535$	5.09612	0.220325
$536$	−18.5700	−0.802103
$537$	−11.2186	−0.484117
$538$	−6.17398	−0.266179
$539$	−0.245885	−0.0105910
$540$	−15.0170	−0.646231
$541$	−24.2484	−1.04252	−0.521261	−	0.853398i	$-0.674538\pi$
$541$	−24.2484	−1.04252	−0.521261	+	0.853398i	$0.674538\pi$
$542$	−33.0353	−1.41899
$543$	−5.61216	−0.240841
$544$	−17.5241	−0.751340
$545$	−6.13513	−0.262800
$546$	26.7042	1.14283
$547$	−0.591692	−0.0252989	−0.0126495	−	0.999920i	$-0.504027\pi$
$547$	−0.591692	−0.0252989	−0.0126495	+	0.999920i	$0.504027\pi$
$548$	−30.7195	−1.31227
$549$	−25.6303	−1.09387
$550$	−0.188523	−0.00803864
$551$	0	0
$552$	0.670102	0.0285214
$553$	−0.234702	−0.00998056
$554$	−40.2040	−1.70810
$555$	−5.19851	−0.220665
$556$	31.4188	1.33246
$557$	−24.7130	−1.04712	−0.523561	−	0.851988i	$-0.675397\pi$
$557$	−24.7130	−1.04712	−0.523561	+	0.851988i	$0.675397\pi$
$558$	34.5349	1.46198
$559$	3.72160	0.157407
$560$	2.49932	0.105616
$561$	−0.222586	−0.00939760
$562$	8.63370	0.364191
$563$	11.9955	0.505550	0.252775	−	0.967525i	$-0.418657\pi$
$563$	11.9955	0.505550	0.252775	+	0.967525i	$0.418657\pi$
$564$	21.0492	0.886329
$565$	11.4316	0.480931
$566$	49.5360	2.08215
$567$	−0.968147	−0.0406583
$568$	29.9727	1.25763
$569$	33.9446	1.42303	0.711517	−	0.702669i	$-0.248009\pi$
$569$	33.9446	1.42303	0.711517	+	0.702669i	$0.248009\pi$
$570$	0	0
$571$	−3.81177	−0.159518	−0.0797588	−	0.996814i	$-0.525415\pi$
$571$	−3.81177	−0.159518	−0.0797588	+	0.996814i	$0.525415\pi$
$572$	1.42684	0.0596594
$573$	5.05169	0.211038
$574$	−26.4688	−1.10479
$575$	−0.309088	−0.0128898
$576$	24.8722	1.03634
$577$	1.65440	0.0688734	0.0344367	−	0.999407i	$-0.489036\pi$
$577$	1.65440	0.0688734	0.0344367	+	0.999407i	$0.489036\pi$
$578$	23.5510	0.979591
$579$	−1.43535	−0.0596512
$580$	7.71648	0.320409
$581$	6.02567	0.249987
$582$	0.520702	0.0215838
$583$	1.23444	0.0511253
$584$	−22.6935	−0.939064
$585$	−11.0107	−0.455238
$586$	54.3490	2.24514
$587$	−29.4152	−1.21409	−0.607047	−	0.794666i	$-0.707646\pi$
$587$	−29.4152	−1.21409	−0.607047	+	0.794666i	$0.707646\pi$
$588$	−8.84031	−0.364568
$589$	0	0
$590$	−16.6113	−0.683877
$591$	6.64458	0.273322
$592$	6.18700	0.254284
$593$	46.8254	1.92289	0.961445	−	0.274998i	$-0.0886770\pi$
$593$	46.8254	1.92289	0.961445	+	0.274998i	$0.0886770\pi$
$594$	0.962757	0.0395024
$595$	5.12490	0.210101
$596$	−14.8340	−0.607626
$597$	16.2192	0.663808
$598$	3.93043	0.160727
$599$	12.1717	0.497321	0.248660	−	0.968591i	$-0.420010\pi$
$599$	12.1717	0.497321	0.248660	+	0.968591i	$0.420010\pi$
$600$	−2.16800	−0.0885082
$601$	10.0391	0.409504	0.204752	−	0.978814i	$-0.434361\pi$
$601$	10.0391	0.409504	0.204752	+	0.978814i	$0.434361\pi$
$602$	2.92813	0.119342
$603$	−17.0954	−0.696179
$604$	61.1972	2.49008
$605$	−10.9928	−0.446921
$606$	29.0460	1.17991
$607$	20.5318	0.833358	0.416679	−	0.909054i	$-0.363194\pi$
$607$	20.5318	0.833358	0.416679	+	0.909054i	$0.363194\pi$
$608$	0	0
$609$	−5.51072	−0.223306
$610$	−29.6002	−1.19848
$611$	39.4906	1.59762
$612$	14.3226	0.578957
$613$	−36.4730	−1.47313	−0.736565	−	0.676367i	$-0.763553\pi$
$613$	−36.4730	−1.47313	−0.736565	+	0.676367i	$0.763553\pi$
$614$	−14.2815	−0.576356
$615$	−6.09794	−0.245893
$616$	0.359085	0.0144679
$617$	21.4068	0.861805	0.430903	−	0.902398i	$-0.358195\pi$
$617$	21.4068	0.861805	0.430903	+	0.902398i	$0.358195\pi$
$618$	−40.8513	−1.64328
$619$	−15.3752	−0.617981	−0.308991	−	0.951065i	$-0.599991\pi$
$619$	−15.3752	−0.617981	−0.308991	+	0.951065i	$0.599991\pi$
$620$	23.7386	0.953364
$621$	1.57846	0.0633415
$622$	39.0402	1.56537
$623$	22.5308	0.902676
$624$	−7.32200	−0.293114
$625$	1.00000	0.0400000
$626$	8.09876	0.323691
$627$	0	0
$628$	69.4440	2.77112
$629$	12.6866	0.505846
$630$	−8.66318	−0.345149
$631$	−29.7129	−1.18285	−0.591426	−	0.806359i	$-0.701435\pi$
$631$	−29.7129	−1.18285	−0.591426	+	0.806359i	$0.701435\pi$
$632$	−0.242301	−0.00963822
$633$	7.96816	0.316706
$634$	−10.0001	−0.397156
$635$	−1.43978	−0.0571359
$636$	44.3819	1.75986
$637$	−16.5854	−0.657138
$638$	−0.494711	−0.0195858
$639$	27.5926	1.09155
$640$	14.8756	0.588010
$641$	19.1099	0.754795	0.377398	−	0.926051i	$-0.376819\pi$
$641$	19.1099	0.754795	0.377398	+	0.926051i	$0.376819\pi$
$642$	−11.7465	−0.463597
$643$	16.2284	0.639984	0.319992	−	0.947420i	$-0.396320\pi$
$643$	16.2284	0.639984	0.319992	+	0.947420i	$0.396320\pi$
$644$	1.84058	0.0725291
$645$	0.674589	0.0265619
$646$	0	0
$647$	26.6353	1.04714	0.523571	−	0.851982i	$-0.324600\pi$
$647$	26.6353	1.04714	0.523571	+	0.851982i	$0.324600\pi$
$648$	−0.999492	−0.0392637
$649$	0.633856	0.0248810
$650$	−12.7162	−0.498771
$651$	−16.9529	−0.664437
$652$	−0.627908	−0.0245908
$653$	−40.8476	−1.59849	−0.799245	−	0.601005i	$-0.794767\pi$
$653$	−40.8476	−1.59849	−0.799245	+	0.601005i	$0.794767\pi$
$654$	14.1414	0.552972
$655$	−1.00345	−0.0392081
$656$	7.25745	0.283356
$657$	−20.8914	−0.815053
$658$	31.0709	1.21127
$659$	−18.3460	−0.714658	−0.357329	−	0.933979i	$-0.616312\pi$
$659$	−18.3460	−0.714658	−0.357329	+	0.933979i	$0.616312\pi$
$660$	0.258634	0.0100673
$661$	−24.3103	−0.945560	−0.472780	−	0.881181i	$-0.656749\pi$
$661$	−24.3103	−0.945560	−0.472780	+	0.881181i	$0.656749\pi$
$662$	−75.7961	−2.94590
$663$	−15.0139	−0.583090
$664$	6.22076	0.241412
$665$	0	0
$666$	−21.4455	−0.830995
$667$	−0.811090	−0.0314055
$668$	58.0024	2.24418
$669$	2.57172	0.0994283
$670$	−19.7434	−0.762752
$671$	1.12949	0.0436034
$672$	−14.5416	−0.560956
$673$	−31.5695	−1.21691	−0.608457	−	0.793587i	$-0.708211\pi$
$673$	−31.5695	−1.21691	−0.608457	+	0.793587i	$0.708211\pi$
$674$	2.15368	0.0829568
$675$	−5.10685	−0.196563
$676$	58.0160	2.23138
$677$	−12.4254	−0.477545	−0.238773	−	0.971076i	$-0.576745\pi$
$677$	−12.4254	−0.477545	−0.238773	+	0.971076i	$0.576745\pi$
$678$	−26.3496	−1.01195
$679$	0.457471	0.0175561
$680$	5.29083	0.202894
$681$	−0.470336	−0.0180233
$682$	−1.52190	−0.0582766
$683$	9.71494	0.371732	0.185866	−	0.982575i	$-0.440491\pi$
$683$	9.71494	0.371732	0.185866	+	0.982575i	$0.440491\pi$
$684$	0	0
$685$	−10.4468	−0.399152
$686$	−44.5579	−1.70123
$687$	1.03003	0.0392983
$688$	−0.802861	−0.0306088
$689$	83.2653	3.17216
$690$	0.712442	0.0271222
$691$	38.5888	1.46799	0.733994	−	0.679156i	$-0.237654\pi$
$691$	38.5888	1.46799	0.733994	+	0.679156i	$0.237654\pi$
$692$	36.9774	1.40567
$693$	0.330570	0.0125573
$694$	52.2486	1.98333
$695$	10.6846	0.405290
$696$	−5.68914	−0.215646
$697$	14.8815	0.563678
$698$	−43.2046	−1.63532
$699$	−4.42096	−0.167216
$700$	−5.95489	−0.225074
$701$	−18.2907	−0.690832	−0.345416	−	0.938450i	$-0.612262\pi$
$701$	−18.2907	−0.690832	−0.345416	+	0.938450i	$0.612262\pi$
$702$	64.9398	2.45099
$703$	0	0
$704$	−1.09608	−0.0413101
$705$	7.15819	0.269593
$706$	26.5943	1.00089
$707$	25.5188	0.959733
$708$	22.7890	0.856465
$709$	−10.9453	−0.411060	−0.205530	−	0.978651i	$-0.565892\pi$
$709$	−10.9453	−0.411060	−0.205530	+	0.978651i	$0.565892\pi$
$710$	31.8665	1.19593
$711$	−0.223060	−0.00836541
$712$	23.2602	0.871714
$713$	−2.49519	−0.0934458
$714$	−11.8128	−0.442084
$715$	0.485227	0.0181465
$716$	−31.8119	−1.18887
$717$	25.3633	0.947209
$718$	−38.2090	−1.42595
$719$	−7.98877	−0.297931	−0.148965	−	0.988842i	$-0.547594\pi$
$719$	−7.98877	−0.297931	−0.148965	+	0.988842i	$0.547594\pi$
$720$	2.37535	0.0885240
$721$	−35.8906	−1.33663
$722$	0	0
$723$	4.55746	0.169494
$724$	−15.9141	−0.591443
$725$	2.62414	0.0974582
$726$	25.3382	0.940390
$727$	−13.5437	−0.502309	−0.251154	−	0.967947i	$-0.580810\pi$
$727$	−13.5437	−0.502309	−0.251154	+	0.967947i	$0.580810\pi$
$728$	24.2210	0.897689
$729$	14.9673	0.554344
$730$	−24.1274	−0.892995
$731$	−1.64628	−0.0608898
$732$	40.6085	1.50094
$733$	12.2354	0.451925	0.225962	−	0.974136i	$-0.427447\pi$
$733$	12.2354	0.451925	0.225962	+	0.974136i	$0.427447\pi$
$734$	39.1718	1.44586
$735$	−3.00632	−0.110890
$736$	−2.14030	−0.0788923
$737$	0.753369	0.0277507
$738$	−25.1558	−0.926000
$739$	−5.42922	−0.199717	−0.0998586	−	0.995002i	$-0.531839\pi$
$739$	−5.42922	−0.199717	−0.0998586	+	0.995002i	$0.531839\pi$
$740$	−14.7412	−0.541896
$741$	0	0
$742$	65.5126	2.40505
$743$	−3.77234	−0.138394	−0.0691968	−	0.997603i	$-0.522044\pi$
$743$	−3.77234	−0.138394	−0.0691968	+	0.997603i	$0.522044\pi$
$744$	−17.5018	−0.641646
$745$	−5.04462	−0.184820
$746$	5.90084	0.216045
$747$	5.72678	0.209532
$748$	−0.631176	−0.0230781
$749$	−10.3201	−0.377086
$750$	−2.30498	−0.0841661
$751$	−6.28316	−0.229276	−0.114638	−	0.993407i	$-0.536571\pi$
$751$	−6.28316	−0.229276	−0.114638	+	0.993407i	$0.536571\pi$
$752$	−8.51931	−0.310667
$753$	−0.401805	−0.0146426
$754$	−33.3692	−1.21523
$755$	20.8114	0.757403
$756$	30.4107	1.10603
$757$	−50.8221	−1.84716	−0.923580	−	0.383406i	$-0.874751\pi$
$757$	−50.8221	−1.84716	−0.923580	+	0.383406i	$0.874751\pi$
$758$	42.1864	1.53228
$759$	−0.0271854	−0.000986768 0
$760$	0	0
$761$	−10.2538	−0.371701	−0.185850	−	0.982578i	$-0.559504\pi$
$761$	−10.2538	−0.371701	−0.185850	+	0.982578i	$0.559504\pi$
$762$	3.31867	0.120223
$763$	12.4241	0.449783
$764$	14.3248	0.518254
$765$	4.87069	0.176100
$766$	26.5140	0.957989
$767$	42.7548	1.54379
$768$	−7.48545	−0.270108
$769$	−1.50423	−0.0542440	−0.0271220	−	0.999632i	$-0.508634\pi$
$769$	−1.50423	−0.0542440	−0.0271220	+	0.999632i	$0.508634\pi$
$770$	0.381774	0.0137582
$771$	−2.95852	−0.106549
$772$	−4.07015	−0.146488
$773$	37.3223	1.34239	0.671195	−	0.741281i	$-0.265781\pi$
$773$	37.3223	1.34239	0.671195	+	0.741281i	$0.265781\pi$
$774$	2.78288	0.100029
$775$	8.07278	0.289983
$776$	0.472282	0.0169539
$777$	10.5274	0.377668
$778$	21.7065	0.778215
$779$	0	0
$780$	17.4454	0.624645
$781$	−1.21596	−0.0435106
$782$	−1.73866	−0.0621742
$783$	−13.4011	−0.478916
$784$	3.57797	0.127785
$785$	23.6158	0.842885
$786$	2.31294	0.0824998
$787$	32.9294	1.17381	0.586903	−	0.809657i	$-0.300347\pi$
$787$	32.9294	1.17381	0.586903	+	0.809657i	$0.300347\pi$
$788$	18.8417	0.671208
$789$	−11.2074	−0.398993
$790$	−0.257611	−0.00916538
$791$	−23.1499	−0.823115
$792$	0.341273	0.0121266
$793$	76.1862	2.70545
$794$	−64.1096	−2.27516
$795$	15.0929	0.535292
$796$	45.9920	1.63014
$797$	−18.1078	−0.641410	−0.320705	−	0.947179i	$-0.603920\pi$
$797$	−18.1078	−0.641410	−0.320705	+	0.947179i	$0.603920\pi$
$798$	0	0
$799$	−17.4690	−0.618008
$800$	6.92456	0.244820
$801$	21.4132	0.756597
$802$	−13.9395	−0.492220
$803$	0.920655	0.0324892
$804$	27.0859	0.955246
$805$	0.625927	0.0220610
$806$	−102.655	−3.61588
$807$	2.88042	0.101396
$808$	26.3450	0.926814
$809$	−7.85536	−0.276180	−0.138090	−	0.990420i	$-0.544096\pi$
$809$	−7.85536	−0.276180	−0.138090	+	0.990420i	$0.544096\pi$
$810$	−1.06264	−0.0373375
$811$	−19.5323	−0.685873	−0.342936	−	0.939359i	$-0.611422\pi$
$811$	−19.5323	−0.685873	−0.342936	+	0.939359i	$0.611422\pi$
$812$	−15.6265	−0.548382
$813$	15.4124	0.540535
$814$	0.945069	0.0331247
$815$	−0.213533	−0.00747972
$816$	3.23895	0.113386
$817$	0	0
$818$	−24.9479	−0.872282
$819$	22.2976	0.779142
$820$	−17.2916	−0.603849
$821$	−18.2498	−0.636922	−0.318461	−	0.947936i	$-0.603166\pi$
$821$	−18.2498	−0.636922	−0.318461	+	0.947936i	$0.603166\pi$
$822$	24.0797	0.839876
$823$	16.5637	0.577373	0.288687	−	0.957424i	$-0.406781\pi$
$823$	16.5637	0.577373	0.288687	+	0.957424i	$0.406781\pi$
$824$	−37.0526	−1.29079
$825$	0.0879538	0.00306216
$826$	33.6392	1.17046
$827$	16.7592	0.582774	0.291387	−	0.956605i	$-0.405883\pi$
$827$	16.7592	0.582774	0.291387	+	0.956605i	$0.405883\pi$
$828$	1.74928	0.0607918
$829$	−9.99830	−0.347255	−0.173628	−	0.984811i	$-0.555549\pi$
$829$	−9.99830	−0.347255	−0.173628	+	0.984811i	$0.555549\pi$
$830$	6.61382	0.229569
$831$	18.7569	0.650668
$832$	−73.9328	−2.56316
$833$	7.33669	0.254201
$834$	−24.6278	−0.852793
$835$	19.7249	0.682607
$836$	0	0
$837$	−41.2264	−1.42499
$838$	57.9589	2.00216
$839$	45.5490	1.57253	0.786263	−	0.617892i	$-0.212013\pi$
$839$	45.5490	1.57253	0.786263	+	0.617892i	$0.212013\pi$
$840$	4.39037	0.151482
$841$	−22.1139	−0.762547
$842$	56.1476	1.93497
$843$	−4.02798	−0.138731
$844$	22.5949	0.777748
$845$	19.7295	0.678715
$846$	29.5297	1.01525
$847$	22.2613	0.764907
$848$	−17.9628	−0.616847
$849$	−23.1106	−0.793155
$850$	5.62513	0.192940
$851$	1.54946	0.0531149
$852$	−43.7176	−1.49774
$853$	25.5008	0.873129	0.436565	−	0.899673i	$-0.356195\pi$
$853$	25.5008	0.873129	0.436565	+	0.899673i	$0.356195\pi$
$854$	59.9428	2.05120
$855$	0	0
$856$	−10.6542	−0.364152
$857$	−7.24518	−0.247491	−0.123745	−	0.992314i	$-0.539491\pi$
$857$	−7.24518	−0.247491	−0.123745	+	0.992314i	$0.539491\pi$
$858$	−1.11844	−0.0381829
$859$	−30.1074	−1.02725	−0.513625	−	0.858015i	$-0.671698\pi$
$859$	−30.1074	−1.02725	−0.513625	+	0.858015i	$0.671698\pi$
$860$	1.91290	0.0652292
$861$	12.3488	0.420846
$862$	−84.8841	−2.89116
$863$	7.47961	0.254609	0.127305	−	0.991864i	$-0.459367\pi$
$863$	7.47961	0.254609	0.127305	+	0.991864i	$0.459367\pi$
$864$	−35.3627	−1.20306
$865$	12.5749	0.427559
$866$	−5.82585	−0.197971
$867$	−10.9875	−0.373156
$868$	−48.0725	−1.63169
$869$	0.00982994	0.000333458 0
$870$	−6.04861	−0.205067
$871$	50.8162	1.72184
$872$	12.8264	0.434356
$873$	0.434779	0.0147150
$874$	0	0
$875$	−2.02508	−0.0684602
$876$	33.1004	1.11836
$877$	−24.6798	−0.833377	−0.416689	−	0.909049i	$-0.636809\pi$
$877$	−24.6798	−0.833377	−0.416689	+	0.909049i	$0.636809\pi$
$878$	−14.9294	−0.503843
$879$	−25.3561	−0.855240
$880$	−0.104678	−0.00352870
$881$	7.30247	0.246026	0.123013	−	0.992405i	$-0.460744\pi$
$881$	7.30247	0.246026	0.123013	+	0.992405i	$0.460744\pi$
$882$	−12.4020	−0.417597
$883$	−43.8146	−1.47448	−0.737239	−	0.675632i	$-0.763871\pi$
$883$	−43.8146	−1.47448	−0.737239	+	0.675632i	$0.763871\pi$
$884$	−42.5741	−1.43192
$885$	7.74987	0.260509
$886$	57.8046	1.94198
$887$	−49.3920	−1.65842	−0.829211	−	0.558936i	$-0.811210\pi$
$887$	−49.3920	−1.65842	−0.829211	+	0.558936i	$0.811210\pi$
$888$	10.8682	0.364714
$889$	2.91567	0.0977883
$890$	24.7299	0.828948
$891$	0.0405485	0.00135843
$892$	7.29249	0.244170
$893$	0	0
$894$	11.6278	0.388890
$895$	−10.8183	−0.361615
$896$	−30.1243	−1.00638
$897$	−1.83371	−0.0612258
$898$	61.2854	2.04512
$899$	21.1841	0.706530
$900$	−5.65951	−0.188650
$901$	−36.8331	−1.22709
$902$	1.10858	0.0369117
$903$	−1.36610	−0.0454608
$904$	−23.8994	−0.794882
$905$	−5.41191	−0.179898
$906$	−47.9698	−1.59369
$907$	−10.6373	−0.353206	−0.176603	−	0.984282i	$-0.556511\pi$
$907$	−10.6373	−0.353206	−0.176603	+	0.984282i	$0.556511\pi$
$908$	−1.33371	−0.0442606
$909$	24.2530	0.804420
$910$	25.7514	0.853649
$911$	−40.5583	−1.34376	−0.671878	−	0.740662i	$-0.734512\pi$
$911$	−40.5583	−1.34376	−0.671878	+	0.740662i	$0.734512\pi$
$912$	0	0
$913$	−0.252371	−0.00835225
$914$	−4.94613	−0.163603
$915$	13.8098	0.456536
$916$	2.92082	0.0965065
$917$	2.03207	0.0671048
$918$	−28.7267	−0.948121
$919$	38.3456	1.26491	0.632453	−	0.774599i	$-0.282048\pi$
$919$	38.3456	1.26491	0.632453	+	0.774599i	$0.282048\pi$
$920$	0.646192	0.0213043
$921$	6.66294	0.219551
$922$	−45.4668	−1.49737
$923$	−82.0191	−2.69969
$924$	−0.523755	−0.0172303
$925$	−5.01303	−0.164827
$926$	72.0835	2.36881
$927$	−34.1103	−1.12033
$928$	18.1710	0.596493
$929$	43.6424	1.43186	0.715931	−	0.698171i	$-0.246003\pi$
$929$	43.6424	1.43186	0.715931	+	0.698171i	$0.246003\pi$
$930$	−18.6076	−0.610168
$931$	0	0
$932$	−12.5363	−0.410639
$933$	−18.2139	−0.596296
$934$	15.3835	0.503365
$935$	−0.214644	−0.00701961
$936$	23.0195	0.752417
$937$	−35.9137	−1.17325	−0.586624	−	0.809859i	$-0.699543\pi$
$937$	−35.9137	−1.17325	−0.586624	+	0.809859i	$0.699543\pi$
$938$	39.9819	1.30545
$939$	−3.77841	−0.123304
$940$	20.2981	0.662051
$941$	30.9209	1.00799	0.503997	−	0.863706i	$-0.331862\pi$
$941$	30.9209	1.00799	0.503997	+	0.863706i	$0.331862\pi$
$942$	−54.4341	−1.77356
$943$	1.81754	0.0591874
$944$	−9.22350	−0.300199
$945$	10.3418	0.336418
$946$	−0.122638	−0.00398729
$947$	11.1663	0.362856	0.181428	−	0.983404i	$-0.441928\pi$
$947$	11.1663	0.362856	0.181428	+	0.983404i	$0.441928\pi$
$948$	0.353416	0.0114784
$949$	62.1000	2.01585
$950$	0	0
$951$	4.66548	0.151288
$952$	−10.7143	−0.347254
$953$	−7.40383	−0.239834	−0.119917	−	0.992784i	$-0.538263\pi$
$953$	−7.40383	−0.239834	−0.119917	+	0.992784i	$0.538263\pi$
$954$	62.2630	2.01584
$955$	4.87144	0.157636
$956$	71.9213	2.32610
$957$	0.230803	0.00746081
$958$	44.5522	1.43942
$959$	21.1556	0.683149
$960$	−13.4013	−0.432525
$961$	34.1697	1.10225
$962$	63.7468	2.05528
$963$	−9.80814	−0.316063
$964$	12.9234	0.416233
$965$	−1.38414	−0.0445569
$966$	−1.44275	−0.0464197
$967$	−17.5783	−0.565279	−0.282640	−	0.959226i	$-0.591210\pi$
$967$	−17.5783	−0.565279	−0.282640	+	0.959226i	$0.591210\pi$
$968$	22.9820	0.738671
$969$	0	0
$970$	0.502123	0.0161222
$971$	−5.31430	−0.170544	−0.0852721	−	0.996358i	$-0.527176\pi$
$971$	−5.31430	−0.170544	−0.0852721	+	0.996358i	$0.527176\pi$
$972$	46.5090	1.49178
$973$	−21.6372	−0.693656
$974$	−15.8465	−0.507755
$975$	5.93265	0.189997
$976$	−16.4357	−0.526093
$977$	13.6507	0.436723	0.218362	−	0.975868i	$-0.429929\pi$
$977$	13.6507	0.436723	0.218362	+	0.975868i	$0.429929\pi$
$978$	0.492189	0.0157385
$979$	−0.943646	−0.0301591
$980$	−8.52488	−0.272317
$981$	11.8078	0.376995
$982$	−36.6866	−1.17072
$983$	28.7597	0.917291	0.458646	−	0.888619i	$-0.348335\pi$
$983$	28.7597	0.917291	0.458646	+	0.888619i	$0.348335\pi$
$984$	12.7486	0.406411
$985$	6.40750	0.204160
$986$	14.7611	0.470090
$987$	−14.4959	−0.461409
$988$	0	0
$989$	−0.201067	−0.00639357
$990$	0.362836	0.0115317
$991$	−56.4946	−1.79461	−0.897306	−	0.441410i	$-0.854479\pi$
$991$	−56.4946	−1.79461	−0.897306	+	0.441410i	$0.854479\pi$
$992$	55.9004	1.77484
$993$	35.3621	1.12218
$994$	−64.5321	−2.04683
$995$	15.6405	0.495837
$996$	−9.07349	−0.287505
$997$	−14.1163	−0.447066	−0.223533	−	0.974696i	$-0.571759\pi$
$997$	−14.1163	−0.447066	−0.223533	+	0.974696i	$0.571759\pi$
$998$	67.4835	2.13615
$999$	25.6007	0.809972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.v.1.1		9
5.4	even	2		9025.2.a.cc.1.9		9
19.6	even	9		95.2.k.a.36.1	✓	18
19.16	even	9		95.2.k.a.66.1	yes	18
19.18	odd	2		1805.2.a.s.1.9		9
57.35	odd	18		855.2.bs.c.541.3		18
57.44	odd	18		855.2.bs.c.226.3		18
95.44	even	18		475.2.l.c.226.3		18
95.54	even	18		475.2.l.c.351.3		18
95.63	odd	36		475.2.u.b.74.6		36
95.73	odd	36		475.2.u.b.199.1		36
95.82	odd	36		475.2.u.b.74.1		36
95.92	odd	36		475.2.u.b.199.6		36
95.94	odd	2		9025.2.a.cf.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.1	✓	18	19.6	even	9
95.2.k.a.66.1	yes	18	19.16	even	9
475.2.l.c.226.3		18	95.44	even	18
475.2.l.c.351.3		18	95.54	even	18
475.2.u.b.74.1		36	95.82	odd	36
475.2.u.b.74.6		36	95.63	odd	36
475.2.u.b.199.1		36	95.73	odd	36
475.2.u.b.199.6		36	95.92	odd	36
855.2.bs.c.226.3		18	57.44	odd	18
855.2.bs.c.541.3		18	57.35	odd	18
1805.2.a.s.1.9		9	19.18	odd	2
1805.2.a.v.1.1		9	1.1	even	1	trivial
9025.2.a.cc.1.9		9	5.4	even	2
9025.2.a.cf.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)

\(f(q)\)	\(=\)	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} +O(q^{10})\)	\(q-2.22274 q^{2} +1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} -2.09064 q^{8} -1.92463 q^{9} -2.22274 q^{10} +0.0848155 q^{11} +3.04938 q^{12} +5.72097 q^{13} +4.50122 q^{14} +1.03700 q^{15} -1.23419 q^{16} -2.53072 q^{17} +4.27795 q^{18} +2.94057 q^{20} -2.10001 q^{21} -0.188523 q^{22} -0.309088 q^{23} -2.16800 q^{24} +1.00000 q^{25} -12.7162 q^{26} -5.10685 q^{27} -5.95489 q^{28} +2.62414 q^{29} -2.30498 q^{30} +8.07278 q^{31} +6.92456 q^{32} +0.0879538 q^{33} +5.62513 q^{34} -2.02508 q^{35} -5.65951 q^{36} -5.01303 q^{37} +5.93265 q^{39} -2.09064 q^{40} -5.88035 q^{41} +4.66777 q^{42} +0.650519 q^{43} +0.249406 q^{44} -1.92463 q^{45} +0.687021 q^{46} +6.90277 q^{47} -1.27985 q^{48} -2.89906 q^{49} -2.22274 q^{50} -2.62436 q^{51} +16.8229 q^{52} +14.5544 q^{53} +11.3512 q^{54} +0.0848155 q^{55} +4.23372 q^{56} -5.83278 q^{58} +7.47335 q^{59} +3.04938 q^{60} +13.3170 q^{61} -17.9437 q^{62} +3.89752 q^{63} -12.9231 q^{64} +5.72097 q^{65} -0.195498 q^{66} +8.88244 q^{67} -7.44175 q^{68} -0.320524 q^{69} +4.50122 q^{70} -14.3366 q^{71} +4.02371 q^{72} +10.8548 q^{73} +11.1426 q^{74} +1.03700 q^{75} -0.171758 q^{77} -13.1867 q^{78} +0.115898 q^{79} -1.23419 q^{80} +0.478079 q^{81} +13.0705 q^{82} -2.97552 q^{83} -6.17523 q^{84} -2.53072 q^{85} -1.44593 q^{86} +2.72124 q^{87} -0.177319 q^{88} -11.1259 q^{89} +4.27795 q^{90} -11.5854 q^{91} -0.908894 q^{92} +8.37148 q^{93} -15.3431 q^{94} +7.18078 q^{96} -0.225903 q^{97} +6.44385 q^{98} -0.163238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 + 6 * q^8 + 6 * q^9	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 18 q^{12} + 9 q^{13} + 9 q^{15} + 12 q^{16} - 9 q^{17} + 24 q^{18} + 6 q^{20} + 12 q^{21} + 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} + 24 q^{27} - 15 q^{28} + 9 q^{29} + 12 q^{30} + 18 q^{31} + 3 q^{32} - 9 q^{33} - 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} - 9 q^{46} + 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{50} - 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} + 9 q^{65} + 3 q^{66} + 60 q^{67} - 51 q^{68} - 15 q^{69} - 18 q^{71} + 27 q^{73} + 27 q^{74} + 9 q^{75} - 30 q^{77} - 6 q^{78} + 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} - 48 q^{84} - 9 q^{85} - 39 q^{86} + 15 q^{87} + 27 q^{88} - 39 q^{89} + 24 q^{90} + 21 q^{91} - 6 q^{92} + 15 q^{93} + 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 18 * q^12 + 9 * q^13 + 9 * q^15 + 12 * q^16 - 9 * q^17 + 24 * q^18 + 6 * q^20 + 12 * q^21 + 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 + 24 * q^27 - 15 * q^28 + 9 * q^29 + 12 * q^30 + 18 * q^31 + 3 * q^32 - 9 * q^33 - 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 - 9 * q^46 + 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^50 - 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 + 9 * q^65 + 3 * q^66 + 60 * q^67 - 51 * q^68 - 15 * q^69 - 18 * q^71 + 27 * q^73 + 27 * q^74 + 9 * q^75 - 30 * q^77 - 6 * q^78 + 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 - 48 * q^84 - 9 * q^85 - 39 * q^86 + 15 * q^87 + 27 * q^88 - 39 * q^89 + 24 * q^90 + 21 * q^91 - 6 * q^92 + 15 * q^93 + 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * q^98 - 36 * q^99

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