LMFDB - Embedded newform 1805.2.a.s.1.8

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:	$1$
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			1.8
Root			$1.63278$ 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)

$f(q)$	$=$	$q+0.632780 q^{2} -1.91964 q^{3} -1.59959 q^{4} +1.00000 q^{5} -1.21471 q^{6} +4.08895 q^{7} -2.27775 q^{8} +0.685005 q^{9} +O(q^{10})$	\(q+0.632780 q^{2} -1.91964 q^{3} -1.59959 q^{4} +1.00000 q^{5} -1.21471 q^{6} +4.08895 q^{7} -2.27775 q^{8} +0.685005 q^{9} +0.632780 q^{10} -4.34827 q^{11} +3.07063 q^{12} -1.55185 q^{13} +2.58741 q^{14} -1.91964 q^{15} +1.75786 q^{16} +6.36159 q^{17} +0.433458 q^{18} -1.59959 q^{20} -7.84930 q^{21} -2.75150 q^{22} -3.36213 q^{23} +4.37245 q^{24} +1.00000 q^{25} -0.981980 q^{26} +4.44395 q^{27} -6.54064 q^{28} -5.21282 q^{29} -1.21471 q^{30} -6.56732 q^{31} +5.66784 q^{32} +8.34710 q^{33} +4.02549 q^{34} +4.08895 q^{35} -1.09573 q^{36} -0.180685 q^{37} +2.97899 q^{39} -2.27775 q^{40} -0.0257762 q^{41} -4.96688 q^{42} +4.57243 q^{43} +6.95544 q^{44} +0.685005 q^{45} -2.12749 q^{46} -1.43040 q^{47} -3.37446 q^{48} +9.71953 q^{49} +0.632780 q^{50} -12.2119 q^{51} +2.48232 q^{52} +1.60099 q^{53} +2.81204 q^{54} -4.34827 q^{55} -9.31361 q^{56} -3.29857 q^{58} -9.54619 q^{59} +3.07063 q^{60} -6.09235 q^{61} -4.15567 q^{62} +2.80095 q^{63} +0.0707731 q^{64} -1.55185 q^{65} +5.28188 q^{66} -10.2756 q^{67} -10.1759 q^{68} +6.45408 q^{69} +2.58741 q^{70} +10.8674 q^{71} -1.56027 q^{72} -13.6201 q^{73} -0.114334 q^{74} -1.91964 q^{75} -17.7799 q^{77} +1.88505 q^{78} -17.2698 q^{79} +1.75786 q^{80} -10.5858 q^{81} -0.0163107 q^{82} -5.15663 q^{83} +12.5557 q^{84} +6.36159 q^{85} +2.89335 q^{86} +10.0067 q^{87} +9.90427 q^{88} +0.507821 q^{89} +0.433458 q^{90} -6.34544 q^{91} +5.37803 q^{92} +12.6069 q^{93} -0.905127 q^{94} -10.8802 q^{96} -3.28014 q^{97} +6.15033 q^{98} -2.97859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.632780	0.447443	0.223722	−	0.974653i	$-0.428179\pi$
$2$	0.632780	0.447443	0.223722	+	0.974653i	$0.428179\pi$
$3$	−1.91964	−1.10830	−0.554151	−	0.832416i	$-0.686957\pi$
$3$	−1.91964	−1.10830	−0.554151	+	0.832416i	$0.686957\pi$
$4$	−1.59959	−0.799794
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.21471	−0.495903
$7$	4.08895	1.54548	0.772739	−	0.634724i	$-0.218886\pi$
$7$	4.08895	1.54548	0.772739	+	0.634724i	$0.218886\pi$
$8$	−2.27775	−0.805306
$9$	0.685005	0.228335
$10$	0.632780	0.200103
$11$	−4.34827	−1.31105	−0.655526	−	0.755172i	$-0.727553\pi$
$11$	−4.34827	−1.31105	−0.655526	+	0.755172i	$0.727553\pi$
$12$	3.07063	0.886414
$13$	−1.55185	−0.430406	−0.215203	−	0.976569i	$-0.569041\pi$
$13$	−1.55185	−0.430406	−0.215203	+	0.976569i	$0.569041\pi$
$14$	2.58741	0.691514
$15$	−1.91964	−0.495648
$16$	1.75786	0.439466
$17$	6.36159	1.54291	0.771457	−	0.636282i	$-0.219528\pi$
$17$	6.36159	1.54291	0.771457	+	0.636282i	$0.219528\pi$
$18$	0.433458	0.102167
$19$	0	0
$19$	0	0
$20$	−1.59959	−0.357679
$21$	−7.84930	−1.71286
$22$	−2.75150	−0.586622
$23$	−3.36213	−0.701054	−0.350527	−	0.936553i	$-0.613997\pi$
$23$	−3.36213	−0.701054	−0.350527	+	0.936553i	$0.613997\pi$
$24$	4.37245	0.892523
$25$	1.00000	0.200000
$26$	−0.981980	−0.192582
$27$	4.44395	0.855238
$28$	−6.54064	−1.23607
$29$	−5.21282	−0.967997	−0.483998	−	0.875069i	$-0.660816\pi$
$29$	−5.21282	−0.967997	−0.483998	+	0.875069i	$0.660816\pi$
$30$	−1.21471	−0.221774
$31$	−6.56732	−1.17953	−0.589763	−	0.807577i	$-0.700779\pi$
$31$	−6.56732	−1.17953	−0.589763	+	0.807577i	$0.700779\pi$
$32$	5.66784	1.00194
$33$	8.34710	1.45304
$34$	4.02549	0.690366
$35$	4.08895	0.691159
$36$	−1.09573	−0.182621
$37$	−0.180685	−0.0297045	−0.0148522	−	0.999890i	$-0.504728\pi$
$37$	−0.180685	−0.0297045	−0.0148522	+	0.999890i	$0.504728\pi$
$38$	0	0
$39$	2.97899	0.477020
$40$	−2.27775	−0.360144
$41$	−0.0257762	−0.00402556	−0.00201278	−	0.999998i	$-0.500641\pi$
$41$	−0.0257762	−0.00402556	−0.00201278	+	0.999998i	$0.500641\pi$
$42$	−4.96688	−0.766407
$43$	4.57243	0.697290	0.348645	−	0.937255i	$-0.386642\pi$
$43$	4.57243	0.697290	0.348645	+	0.937255i	$0.386642\pi$
$44$	6.95544	1.04857
$45$	0.685005	0.102115
$46$	−2.12749	−0.313682
$47$	−1.43040	−0.208645	−0.104322	−	0.994544i	$-0.533267\pi$
$47$	−1.43040	−0.208645	−0.104322	+	0.994544i	$0.533267\pi$
$48$	−3.37446	−0.487061
$49$	9.71953	1.38850
$50$	0.632780	0.0894887
$51$	−12.2119	−1.71001
$52$	2.48232	0.344236
$53$	1.60099	0.219914	0.109957	−	0.993936i	$-0.464929\pi$
$53$	1.60099	0.219914	0.109957	+	0.993936i	$0.464929\pi$
$54$	2.81204	0.382671
$55$	−4.34827	−0.586320
$56$	−9.31361	−1.24458
$57$	0	0
$58$	−3.29857	−0.433124
$59$	−9.54619	−1.24281	−0.621404	−	0.783490i	$-0.713437\pi$
$59$	−9.54619	−1.24281	−0.621404	+	0.783490i	$0.713437\pi$
$60$	3.07063	0.396417
$61$	−6.09235	−0.780046	−0.390023	−	0.920805i	$-0.627533\pi$
$61$	−6.09235	−0.780046	−0.390023	+	0.920805i	$0.627533\pi$
$62$	−4.15567	−0.527771
$63$	2.80095	0.352887
$64$	0.0707731	0.00884663
$65$	−1.55185	−0.192483
$66$	5.28188	0.650154
$67$	−10.2756	−1.25537	−0.627684	−	0.778468i	$-0.715997\pi$
$67$	−10.2756	−1.25537	−0.627684	+	0.778468i	$0.715997\pi$
$68$	−10.1759	−1.23401
$69$	6.45408	0.776980
$70$	2.58741	0.309254
$71$	10.8674	1.28972	0.644859	−	0.764301i	$-0.276916\pi$
$71$	10.8674	1.28972	0.644859	+	0.764301i	$0.276916\pi$
$72$	−1.56027	−0.183880
$73$	−13.6201	−1.59412	−0.797058	−	0.603903i	$-0.793611\pi$
$73$	−13.6201	−1.59412	−0.797058	+	0.603903i	$0.793611\pi$
$74$	−0.114334	−0.0132911
$75$	−1.91964	−0.221661
$76$	0	0
$77$	−17.7799	−2.02620
$78$	1.88505	0.213439
$79$	−17.2698	−1.94300	−0.971500	−	0.237039i	$-0.923823\pi$
$79$	−17.2698	−1.94300	−0.971500	+	0.237039i	$0.923823\pi$
$80$	1.75786	0.196535
$81$	−10.5858	−1.17620
$82$	−0.0163107	−0.00180121
$83$	−5.15663	−0.566013	−0.283007	−	0.959118i	$-0.591332\pi$
$83$	−5.15663	−0.566013	−0.283007	+	0.959118i	$0.591332\pi$
$84$	12.5557	1.36993
$85$	6.36159	0.690012
$86$	2.89335	0.311998
$87$	10.0067	1.07283
$88$	9.90427	1.05580
$89$	0.507821	0.0538289	0.0269145	−	0.999638i	$-0.491432\pi$
$89$	0.507821	0.0538289	0.0269145	+	0.999638i	$0.491432\pi$
$90$	0.433458	0.0456905
$91$	−6.34544	−0.665183
$92$	5.37803	0.560699
$93$	12.6069	1.30727
$94$	−0.905127	−0.0933567
$95$	0	0
$96$	−10.8802	−1.11046
$97$	−3.28014	−0.333047	−0.166524	−	0.986037i	$-0.553254\pi$
$97$	−3.28014	−0.333047	−0.166524	+	0.986037i	$0.553254\pi$
$98$	6.15033	0.621277
$99$	−2.97859	−0.299359
$100$	−1.59959	−0.159959
$101$	−3.49046	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$101$	−3.49046	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$102$	−7.72748	−0.765135
$103$	−8.63143	−0.850480	−0.425240	−	0.905081i	$-0.639810\pi$
$103$	−8.63143	−0.850480	−0.425240	+	0.905081i	$0.639810\pi$
$104$	3.53472	0.346608
$105$	−7.84930	−0.766013
$106$	1.01308	0.0983988
$107$	−6.27464	−0.606592	−0.303296	−	0.952896i	$-0.598087\pi$
$107$	−6.27464	−0.606592	−0.303296	+	0.952896i	$0.598087\pi$
$108$	−7.10849	−0.684015
$109$	−9.86463	−0.944860	−0.472430	−	0.881368i	$-0.656623\pi$
$109$	−9.86463	−0.944860	−0.472430	+	0.881368i	$0.656623\pi$
$110$	−2.75150	−0.262345
$111$	0.346850	0.0329216
$112$	7.18782	0.679185
$113$	5.24756	0.493649	0.246825	−	0.969060i	$-0.420613\pi$
$113$	5.24756	0.493649	0.246825	+	0.969060i	$0.420613\pi$
$114$	0	0
$115$	−3.36213	−0.313521
$116$	8.33837	0.774199
$117$	−1.06302	−0.0982767
$118$	−6.04064	−0.556086
$119$	26.0123	2.38454
$120$	4.37245	0.399148
$121$	7.90744	0.718858
$122$	−3.85512	−0.349026
$123$	0.0494809	0.00446154
$124$	10.5050	0.943378
$125$	1.00000	0.0894427
$126$	1.77239	0.157897
$127$	−5.32853	−0.472831	−0.236416	−	0.971652i	$-0.575973\pi$
$127$	−5.32853	−0.472831	−0.236416	+	0.971652i	$0.575973\pi$
$128$	−11.2909	−0.997984
$129$	−8.77741	−0.772808
$130$	−0.981980	−0.0861254
$131$	−1.71262	−0.149632	−0.0748160	−	0.997197i	$-0.523837\pi$
$131$	−1.71262	−0.149632	−0.0748160	+	0.997197i	$0.523837\pi$
$132$	−13.3519	−1.16214
$133$	0	0
$134$	−6.50222	−0.561706
$135$	4.44395	0.382474
$136$	−14.4901	−1.24252
$137$	5.74575	0.490893	0.245446	−	0.969410i	$-0.421066\pi$
$137$	5.74575	0.490893	0.245446	+	0.969410i	$0.421066\pi$
$138$	4.08401	0.347654
$139$	−17.5854	−1.49158	−0.745789	−	0.666182i	$-0.767927\pi$
$139$	−17.5854	−1.49158	−0.745789	+	0.666182i	$0.767927\pi$
$140$	−6.54064	−0.552785
$141$	2.74584	0.231242
$142$	6.87665	0.577076
$143$	6.74786	0.564284
$144$	1.20414	0.100345
$145$	−5.21282	−0.432901
$146$	−8.61855	−0.713277
$147$	−18.6580	−1.53888
$148$	0.289022	0.0237575
$149$	11.0204	0.902828	0.451414	−	0.892315i	$-0.350920\pi$
$149$	11.0204	0.902828	0.451414	+	0.892315i	$0.350920\pi$
$150$	−1.21471	−0.0991805
$151$	2.37114	0.192960	0.0964802	−	0.995335i	$-0.469242\pi$
$151$	2.37114	0.192960	0.0964802	+	0.995335i	$0.469242\pi$
$152$	0	0
$153$	4.35772	0.352301
$154$	−11.2507	−0.906611
$155$	−6.56732	−0.527500
$156$	−4.76516	−0.381518
$157$	−3.23139	−0.257893	−0.128947	−	0.991652i	$-0.541160\pi$
$157$	−3.23139	−0.257893	−0.128947	+	0.991652i	$0.541160\pi$
$158$	−10.9280	−0.869383
$159$	−3.07333	−0.243731
$160$	5.66784	0.448082
$161$	−13.7476	−1.08346
$162$	−6.69848	−0.526282
$163$	6.58175	0.515522	0.257761	−	0.966209i	$-0.417015\pi$
$163$	6.58175	0.515522	0.257761	+	0.966209i	$0.417015\pi$
$164$	0.0412313	0.00321962
$165$	8.34710	0.649821
$166$	−3.26301	−0.253259
$167$	−15.8526	−1.22671	−0.613355	−	0.789807i	$-0.710181\pi$
$167$	−15.8526	−1.22671	−0.613355	+	0.789807i	$0.710181\pi$
$168$	17.8787	1.37937
$169$	−10.5918	−0.814751
$170$	4.02549	0.308741
$171$	0	0
$172$	−7.31401	−0.557688
$173$	1.90119	0.144545	0.0722723	−	0.997385i	$-0.476975\pi$
$173$	1.90119	0.144545	0.0722723	+	0.997385i	$0.476975\pi$
$174$	6.33206	0.480032
$175$	4.08895	0.309096
$176$	−7.64366	−0.576162
$177$	18.3252	1.37741
$178$	0.321339	0.0240854
$179$	14.2803	1.06736	0.533681	−	0.845686i	$-0.320808\pi$
$179$	14.2803	1.06736	0.533681	+	0.845686i	$0.320808\pi$
$180$	−1.09573	−0.0816706
$181$	−14.3859	−1.06929	−0.534646	−	0.845076i	$-0.679555\pi$
$181$	−14.3859	−1.06929	−0.534646	+	0.845076i	$0.679555\pi$
$182$	−4.01527	−0.297632
$183$	11.6951	0.864527
$184$	7.65810	0.564563
$185$	−0.180685	−0.0132842
$186$	7.97738	0.584930
$187$	−27.6619	−2.02284
$188$	2.28805	0.166873
$189$	18.1711	1.32175
$190$	0	0
$191$	24.1791	1.74954	0.874769	−	0.484540i	$-0.161013\pi$
$191$	24.1791	1.74954	0.874769	+	0.484540i	$0.161013\pi$
$192$	−0.135859	−0.00980475
$193$	5.11380	0.368099	0.184050	−	0.982917i	$-0.441079\pi$
$193$	5.11380	0.368099	0.184050	+	0.982917i	$0.441079\pi$
$194$	−2.07561	−0.149020
$195$	2.97899	0.213330
$196$	−15.5472	−1.11052
$197$	0.0642863	0.00458021	0.00229010	−	0.999997i	$-0.499271\pi$
$197$	0.0642863	0.00458021	0.00229010	+	0.999997i	$0.499271\pi$
$198$	−1.88479	−0.133946
$199$	−6.37999	−0.452265	−0.226133	−	0.974097i	$-0.572608\pi$
$199$	−6.37999	−0.452265	−0.226133	+	0.974097i	$0.572608\pi$
$200$	−2.27775	−0.161061
$201$	19.7255	1.39133
$202$	−2.20870	−0.155403
$203$	−21.3150	−1.49602
$204$	19.5341	1.36766
$205$	−0.0257762	−0.00180029
$206$	−5.46180	−0.380542
$207$	−2.30308	−0.160075
$208$	−2.72794	−0.189149
$209$	0	0
$210$	−4.96688	−0.342748
$211$	5.91184	0.406988	0.203494	−	0.979076i	$-0.434770\pi$
$211$	5.91184	0.406988	0.203494	+	0.979076i	$0.434770\pi$
$212$	−2.56093	−0.175886
$213$	−20.8614	−1.42940
$214$	−3.97047	−0.271416
$215$	4.57243	0.311837
$216$	−10.1222	−0.688729
$217$	−26.8535	−1.82293
$218$	−6.24214	−0.422771
$219$	26.1457	1.76676
$220$	6.95544	0.468936
$221$	−9.87224	−0.664079
$222$	0.219480	0.0147305
$223$	29.3146	1.96305	0.981527	−	0.191326i	$-0.0612786\pi$
$223$	29.3146	1.96305	0.981527	+	0.191326i	$0.0612786\pi$
$224$	23.1755	1.54848
$225$	0.685005	0.0456670
$226$	3.32055	0.220880
$227$	−8.00202	−0.531113	−0.265557	−	0.964095i	$-0.585556\pi$
$227$	−8.00202	−0.531113	−0.265557	+	0.964095i	$0.585556\pi$
$228$	0	0
$229$	28.2694	1.86809	0.934047	−	0.357150i	$-0.116251\pi$
$229$	28.2694	1.86809	0.934047	+	0.357150i	$0.116251\pi$
$230$	−2.12749	−0.140283
$231$	34.1309	2.24565
$232$	11.8735	0.779534
$233$	−6.85123	−0.448839	−0.224420	−	0.974493i	$-0.572049\pi$
$233$	−6.85123	−0.448839	−0.224420	+	0.974493i	$0.572049\pi$
$234$	−0.672661	−0.0439732
$235$	−1.43040	−0.0933088
$236$	15.2700	0.993991
$237$	33.1517	2.15343
$238$	16.4600	1.06695
$239$	−13.3935	−0.866352	−0.433176	−	0.901309i	$-0.642607\pi$
$239$	−13.3935	−0.866352	−0.433176	+	0.901309i	$0.642607\pi$
$240$	−3.37446	−0.217820
$241$	25.6541	1.65252	0.826262	−	0.563286i	$-0.190463\pi$
$241$	25.6541	1.65252	0.826262	+	0.563286i	$0.190463\pi$
$242$	5.00367	0.321648
$243$	6.98901	0.448345
$244$	9.74526	0.623876
$245$	9.71953	0.620958
$246$	0.0313106	0.00199629
$247$	0	0
$248$	14.9587	0.949879
$249$	9.89885	0.627314
$250$	0.632780	0.0400205
$251$	−9.12050	−0.575681	−0.287840	−	0.957678i	$-0.592937\pi$
$251$	−9.12050	−0.575681	−0.287840	+	0.957678i	$0.592937\pi$
$252$	−4.48037	−0.282237
$253$	14.6195	0.919118
$254$	−3.37179	−0.211565
$255$	−12.2119	−0.764742
$256$	−7.28620	−0.455388
$257$	24.7466	1.54365	0.771824	−	0.635837i	$-0.219345\pi$
$257$	24.7466	1.54365	0.771824	+	0.635837i	$0.219345\pi$
$258$	−5.55417	−0.345788
$259$	−0.738813	−0.0459076
$260$	2.48232	0.153947
$261$	−3.57081	−0.221028
$262$	−1.08371	−0.0669518
$263$	−14.6315	−0.902220	−0.451110	−	0.892468i	$-0.648972\pi$
$263$	−14.6315	−0.902220	−0.451110	+	0.892468i	$0.648972\pi$
$264$	−19.0126	−1.17014
$265$	1.60099	0.0983483
$266$	0	0
$267$	−0.974832	−0.0596587
$268$	16.4368	1.00404
$269$	−17.2036	−1.04892	−0.524460	−	0.851435i	$-0.675733\pi$
$269$	−17.2036	−1.04892	−0.524460	+	0.851435i	$0.675733\pi$
$270$	2.81204	0.171136
$271$	13.6707	0.830435	0.415217	−	0.909722i	$-0.363706\pi$
$271$	13.6707	0.830435	0.415217	+	0.909722i	$0.363706\pi$
$272$	11.1828	0.678057
$273$	12.1809	0.737224
$274$	3.63580	0.219647
$275$	−4.34827	−0.262210
$276$	−10.3239	−0.621424
$277$	−13.4597	−0.808714	−0.404357	−	0.914601i	$-0.632505\pi$
$277$	−13.4597	−0.808714	−0.404357	+	0.914601i	$0.632505\pi$
$278$	−11.1277	−0.667397
$279$	−4.49865	−0.269327
$280$	−9.31361	−0.556594
$281$	17.4765	1.04256	0.521280	−	0.853386i	$-0.325455\pi$
$281$	17.4765	1.04256	0.521280	+	0.853386i	$0.325455\pi$
$282$	1.73751	0.103467
$283$	−21.0335	−1.25031	−0.625155	−	0.780500i	$-0.714964\pi$
$283$	−21.0335	−1.25031	−0.625155	+	0.780500i	$0.714964\pi$
$284$	−17.3833	−1.03151
$285$	0	0
$286$	4.26991	0.252485
$287$	−0.105398	−0.00622142
$288$	3.88250	0.228778
$289$	23.4699	1.38058
$290$	−3.29857	−0.193699
$291$	6.29667	0.369117
$292$	21.7866	1.27497
$293$	10.7315	0.626939	0.313470	−	0.949598i	$-0.398509\pi$
$293$	10.7315	0.626939	0.313470	+	0.949598i	$0.398509\pi$
$294$	−11.8064	−0.688563
$295$	−9.54619	−0.555801
$296$	0.411556	0.0239212
$297$	−19.3235	−1.12126
$298$	6.97351	0.403965
$299$	5.21753	0.301737
$300$	3.07063	0.177283
$301$	18.6965	1.07765
$302$	1.50041	0.0863388
$303$	6.70042	0.384929
$304$	0	0
$305$	−6.09235	−0.348847
$306$	2.75748	0.157635
$307$	2.70923	0.154624	0.0773119	−	0.997007i	$-0.475366\pi$
$307$	2.70923	0.154624	0.0773119	+	0.997007i	$0.475366\pi$
$308$	28.4405	1.62055
$309$	16.5692	0.942590
$310$	−4.15567	−0.236026
$311$	−7.25704	−0.411509	−0.205755	−	0.978604i	$-0.565965\pi$
$311$	−7.25704	−0.411509	−0.205755	+	0.978604i	$0.565965\pi$
$312$	−6.78539	−0.384147
$313$	−8.67904	−0.490568	−0.245284	−	0.969451i	$-0.578881\pi$
$313$	−8.67904	−0.490568	−0.245284	+	0.969451i	$0.578881\pi$
$314$	−2.04476	−0.115393
$315$	2.80095	0.157816
$316$	27.6245	1.55400
$317$	31.9275	1.79323	0.896613	−	0.442815i	$-0.146020\pi$
$317$	31.9275	1.79323	0.896613	+	0.442815i	$0.146020\pi$
$318$	−1.94474	−0.109056
$319$	22.6668	1.26909
$320$	0.0707731	0.00395633
$321$	12.0450	0.672288
$322$	−8.69922	−0.484788
$323$	0	0
$324$	16.9329	0.940717
$325$	−1.55185	−0.0860811
$326$	4.16480	0.230667
$327$	18.9365	1.04719
$328$	0.0587117	0.00324181
$329$	−5.84882	−0.322456
$330$	5.28188	0.290758
$331$	−24.2999	−1.33564	−0.667822	−	0.744321i	$-0.732773\pi$
$331$	−24.2999	−1.33564	−0.667822	+	0.744321i	$0.732773\pi$
$332$	8.24849	0.452694
$333$	−0.123770	−0.00678257
$334$	−10.0312	−0.548883
$335$	−10.2756	−0.561418
$336$	−13.7980	−0.752742
$337$	−28.3862	−1.54630	−0.773148	−	0.634225i	$-0.781319\pi$
$337$	−28.3862	−1.54630	−0.773148	+	0.634225i	$0.781319\pi$
$338$	−6.70226	−0.364555
$339$	−10.0734	−0.547113
$340$	−10.1759	−0.551868
$341$	28.5565	1.54642
$342$	0	0
$343$	11.1200	0.600424
$344$	−10.4149	−0.561531
$345$	6.45408	0.347476
$346$	1.20303	0.0646755
$347$	−31.1014	−1.66961	−0.834806	−	0.550543i	$-0.814421\pi$
$347$	−31.1014	−1.66961	−0.834806	+	0.550543i	$0.814421\pi$
$348$	−16.0066	−0.858046
$349$	17.4798	0.935671	0.467836	−	0.883816i	$-0.345034\pi$
$349$	17.4798	0.935671	0.467836	+	0.883816i	$0.345034\pi$
$350$	2.58741	0.138303
$351$	−6.89634	−0.368099
$352$	−24.6453	−1.31360
$353$	−8.82541	−0.469729	−0.234865	−	0.972028i	$-0.575465\pi$
$353$	−8.82541	−0.469729	−0.234865	+	0.972028i	$0.575465\pi$
$354$	11.5958	0.616312
$355$	10.8674	0.576780
$356$	−0.812305	−0.0430521
$357$	−49.9341	−2.64279
$358$	9.03631	0.477584
$359$	19.9218	1.05143	0.525715	−	0.850661i	$-0.323798\pi$
$359$	19.9218	1.05143	0.525715	+	0.850661i	$0.323798\pi$
$360$	−1.56027	−0.0822334
$361$	0	0
$362$	−9.10309	−0.478448
$363$	−15.1794	−0.796713
$364$	10.1501	0.532009
$365$	−13.6201	−0.712910
$366$	7.40043	0.386827
$367$	8.45640	0.441420	0.220710	−	0.975339i	$-0.429163\pi$
$367$	8.45640	0.441420	0.220710	+	0.975339i	$0.429163\pi$
$368$	−5.91017	−0.308089
$369$	−0.0176568	−0.000919177 0
$370$	−0.114334	−0.00594395
$371$	6.54639	0.339872
$372$	−20.1658	−1.04555
$373$	7.13789	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$373$	7.13789	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$374$	−17.5039	−0.905106
$375$	−1.91964	−0.0991296
$376$	3.25808	0.168023
$377$	8.08952	0.416631
$378$	11.4983	0.591409
$379$	−6.11358	−0.314033	−0.157017	−	0.987596i	$-0.550188\pi$
$379$	−6.11358	−0.314033	−0.157017	+	0.987596i	$0.550188\pi$
$380$	0	0
$381$	10.2289	0.524040
$382$	15.3001	0.782819
$383$	−0.523794	−0.0267646	−0.0133823	−	0.999910i	$-0.504260\pi$
$383$	−0.523794	−0.0267646	−0.0133823	+	0.999910i	$0.504260\pi$
$384$	21.6744	1.10607
$385$	−17.7799	−0.906146
$386$	3.23591	0.164704
$387$	3.13214	0.159216
$388$	5.24687	0.266369
$389$	−2.49637	−0.126571	−0.0632855	−	0.997995i	$-0.520158\pi$
$389$	−2.49637	−0.126571	−0.0632855	+	0.997995i	$0.520158\pi$
$390$	1.88505	0.0954530
$391$	−21.3885	−1.08166
$392$	−22.1386	−1.11817
$393$	3.28760	0.165838
$394$	0.0406791	0.00204938
$395$	−17.2698	−0.868936
$396$	4.76451	0.239426
$397$	−2.88775	−0.144932	−0.0724659	−	0.997371i	$-0.523087\pi$
$397$	−2.88775	−0.144932	−0.0724659	+	0.997371i	$0.523087\pi$
$398$	−4.03713	−0.202363
$399$	0	0
$400$	1.75786	0.0878931
$401$	17.2440	0.861123	0.430561	−	0.902561i	$-0.358316\pi$
$401$	17.2440	0.861123	0.430561	+	0.902561i	$0.358316\pi$
$402$	12.4819	0.622540
$403$	10.1915	0.507674
$404$	5.58331	0.277780
$405$	−10.5858	−0.526012
$406$	−13.4877	−0.669383
$407$	0.785668	0.0389441
$408$	27.8158	1.37709
$409$	26.1103	1.29107	0.645536	−	0.763729i	$-0.276634\pi$
$409$	26.1103	1.29107	0.645536	+	0.763729i	$0.276634\pi$
$410$	−0.0163107	−0.000805526 0
$411$	−11.0298	−0.544058
$412$	13.8067	0.680209
$413$	−39.0339	−1.92073
$414$	−1.45734	−0.0716245
$415$	−5.15663	−0.253129
$416$	−8.79564	−0.431242
$417$	33.7577	1.65312
$418$	0	0
$419$	−0.112702	−0.00550586	−0.00275293	−	0.999996i	$-0.500876\pi$
$419$	−0.112702	−0.00550586	−0.00275293	+	0.999996i	$0.500876\pi$
$420$	12.5557	0.612653
$421$	−20.2190	−0.985412	−0.492706	−	0.870196i	$-0.663992\pi$
$421$	−20.2190	−0.985412	−0.492706	+	0.870196i	$0.663992\pi$
$422$	3.74090	0.182104
$423$	−0.979828	−0.0476409
$424$	−3.64666	−0.177098
$425$	6.36159	0.308583
$426$	−13.2007	−0.639575
$427$	−24.9113	−1.20554
$428$	10.0368	0.485149
$429$	−12.9534	−0.625398
$430$	2.89335	0.139530
$431$	40.5463	1.95305	0.976524	−	0.215409i	$-0.0691083\pi$
$431$	40.5463	1.95305	0.976524	+	0.215409i	$0.0691083\pi$
$432$	7.81185	0.375848
$433$	22.7734	1.09442	0.547211	−	0.836995i	$-0.315690\pi$
$433$	22.7734	1.09442	0.547211	+	0.836995i	$0.315690\pi$
$434$	−16.9923	−0.815658
$435$	10.0067	0.479786
$436$	15.7794	0.755694
$437$	0	0
$438$	16.5445	0.790526
$439$	32.6724	1.55937	0.779684	−	0.626173i	$-0.215380\pi$
$439$	32.6724	1.55937	0.779684	+	0.626173i	$0.215380\pi$
$440$	9.90427	0.472167
$441$	6.65792	0.317044
$442$	−6.24696	−0.297138
$443$	−13.8752	−0.659232	−0.329616	−	0.944115i	$-0.606919\pi$
$443$	−13.8752	−0.659232	−0.329616	+	0.944115i	$0.606919\pi$
$444$	−0.554818	−0.0263305
$445$	0.507821	0.0240730
$446$	18.5497	0.878355
$447$	−21.1552	−1.00061
$448$	0.289388	0.0136723
$449$	6.00750	0.283511	0.141756	−	0.989902i	$-0.454725\pi$
$449$	6.00750	0.283511	0.141756	+	0.989902i	$0.454725\pi$
$450$	0.433458	0.0204334
$451$	0.112082	0.00527772
$452$	−8.39394	−0.394818
$453$	−4.55172	−0.213858
$454$	−5.06352	−0.237643
$455$	−6.34544	−0.297479
$456$	0	0
$457$	−23.9751	−1.12151	−0.560754	−	0.827982i	$-0.689489\pi$
$457$	−23.9751	−1.12151	−0.560754	+	0.827982i	$0.689489\pi$
$458$	17.8883	0.835866
$459$	28.2706	1.31956
$460$	5.37803	0.250752
$461$	−36.0859	−1.68069	−0.840343	−	0.542055i	$-0.817647\pi$
$461$	−36.0859	−1.68069	−0.840343	+	0.542055i	$0.817647\pi$
$462$	21.5973	1.00480
$463$	7.04282	0.327308	0.163654	−	0.986518i	$-0.447672\pi$
$463$	7.04282	0.327308	0.163654	+	0.986518i	$0.447672\pi$
$464$	−9.16343	−0.425401
$465$	12.6069	0.584630
$466$	−4.33533	−0.200830
$467$	39.7301	1.83849	0.919244	−	0.393688i	$-0.128801\pi$
$467$	39.7301	1.83849	0.919244	+	0.393688i	$0.128801\pi$
$468$	1.70040	0.0786011
$469$	−42.0166	−1.94014
$470$	−0.905127	−0.0417504
$471$	6.20310	0.285824
$472$	21.7438	1.00084
$473$	−19.8822	−0.914183
$474$	20.9777	0.963539
$475$	0	0
$476$	−41.6089	−1.90714
$477$	1.09669	0.0502140
$478$	−8.47513	−0.387644
$479$	−36.3033	−1.65874	−0.829371	−	0.558698i	$-0.811301\pi$
$479$	−36.3033	−1.65874	−0.829371	+	0.558698i	$0.811301\pi$
$480$	−10.8802	−0.496611
$481$	0.280396	0.0127850
$482$	16.2334	0.739411
$483$	26.3904	1.20081
$484$	−12.6487	−0.574939
$485$	−3.28014	−0.148943
$486$	4.42251	0.200609
$487$	2.53504	0.114874	0.0574368	−	0.998349i	$-0.481707\pi$
$487$	2.53504	0.114874	0.0574368	+	0.998349i	$0.481707\pi$
$488$	13.8769	0.628176
$489$	−12.6346	−0.571355
$490$	6.15033	0.277843
$491$	−36.3143	−1.63884	−0.819420	−	0.573193i	$-0.805704\pi$
$491$	−36.3143	−1.63884	−0.819420	+	0.573193i	$0.805704\pi$
$492$	−0.0791491	−0.00356832
$493$	−33.1619	−1.49354
$494$	0	0
$495$	−2.97859	−0.133877
$496$	−11.5444	−0.518361
$497$	44.4361	1.99323
$498$	6.26380	0.280688
$499$	−17.9194	−0.802181	−0.401091	−	0.916038i	$-0.631369\pi$
$499$	−17.9194	−0.802181	−0.401091	+	0.916038i	$0.631369\pi$
$500$	−1.59959	−0.0715358
$501$	30.4312	1.35957
$502$	−5.77128	−0.257585
$503$	−20.5074	−0.914382	−0.457191	−	0.889369i	$-0.651144\pi$
$503$	−20.5074	−0.914382	−0.457191	+	0.889369i	$0.651144\pi$
$504$	−6.37987	−0.284182
$505$	−3.49046	−0.155324
$506$	9.25091	0.411253
$507$	20.3323	0.902991
$508$	8.52347	0.378168
$509$	15.4014	0.682654	0.341327	−	0.939945i	$-0.389124\pi$
$509$	15.4014	0.682654	0.341327	+	0.939945i	$0.389124\pi$
$510$	−7.72748	−0.342179
$511$	−55.6921	−2.46367
$512$	17.9712	0.794223
$513$	0	0
$514$	15.6591	0.690695
$515$	−8.63143	−0.380346
$516$	14.0402	0.618087
$517$	6.21975	0.273544
$518$	−0.467507	−0.0205411
$519$	−3.64959	−0.160199
$520$	3.53472	0.155008
$521$	2.35999	0.103393	0.0516965	−	0.998663i	$-0.483537\pi$
$521$	2.35999	0.103393	0.0516965	+	0.998663i	$0.483537\pi$
$522$	−2.25954	−0.0988973
$523$	−19.0470	−0.832869	−0.416434	−	0.909166i	$-0.636720\pi$
$523$	−19.0470	−0.832869	−0.416434	+	0.909166i	$0.636720\pi$
$524$	2.73948	0.119675
$525$	−7.84930	−0.342572
$526$	−9.25855	−0.403692
$527$	−41.7786	−1.81991
$528$	14.6730	0.638562
$529$	−11.6960	−0.508524
$530$	1.01308	0.0440053
$531$	−6.53919	−0.283777
$532$	0	0
$533$	0.0400008	0.00173263
$534$	−0.616854	−0.0266939
$535$	−6.27464	−0.271276
$536$	23.4053	1.01096
$537$	−27.4130	−1.18296
$538$	−10.8861	−0.469332
$539$	−42.2631	−1.82040
$540$	−7.10849	−0.305901
$541$	−5.00100	−0.215010	−0.107505	−	0.994205i	$-0.534286\pi$
$541$	−5.00100	−0.215010	−0.107505	+	0.994205i	$0.534286\pi$
$542$	8.65054	0.371573
$543$	27.6156	1.18510
$544$	36.0565	1.54591
$545$	−9.86463	−0.422554
$546$	7.70786	0.329866
$547$	2.45583	0.105004	0.0525018	−	0.998621i	$-0.483280\pi$
$547$	2.45583	0.105004	0.0525018	+	0.998621i	$0.483280\pi$
$548$	−9.19084	−0.392613
$549$	−4.17329	−0.178112
$550$	−2.75150	−0.117324
$551$	0	0
$552$	−14.7008	−0.625706
$553$	−70.6152	−3.00287
$554$	−8.51703	−0.361854
$555$	0.346850	0.0147230
$556$	28.1295	1.19296
$557$	−4.66392	−0.197617	−0.0988083	−	0.995106i	$-0.531503\pi$
$557$	−4.66392	−0.197617	−0.0988083	+	0.995106i	$0.531503\pi$
$558$	−2.84666	−0.120509
$559$	−7.09573	−0.300117
$560$	7.18782	0.303741
$561$	53.1008	2.24192
$562$	11.0588	0.466487
$563$	−34.6330	−1.45961	−0.729803	−	0.683658i	$-0.760388\pi$
$563$	−34.6330	−1.45961	−0.729803	+	0.683658i	$0.760388\pi$
$564$	−4.39222	−0.184946
$565$	5.24756	0.220767
$566$	−13.3096	−0.559443
$567$	−43.2848	−1.81779
$568$	−24.7531	−1.03862
$569$	20.6116	0.864081	0.432041	−	0.901854i	$-0.357794\pi$
$569$	20.6116	0.864081	0.432041	+	0.901854i	$0.357794\pi$
$570$	0	0
$571$	11.1132	0.465071	0.232536	−	0.972588i	$-0.425298\pi$
$571$	11.1132	0.465071	0.232536	+	0.972588i	$0.425298\pi$
$572$	−10.7938	−0.451312
$573$	−46.4151	−1.93902
$574$	−0.0666935	−0.00278373
$575$	−3.36213	−0.140211
$576$	0.0484799	0.00202000
$577$	−28.7054	−1.19502	−0.597510	−	0.801861i	$-0.703843\pi$
$577$	−28.7054	−1.19502	−0.597510	+	0.801861i	$0.703843\pi$
$578$	14.8513	0.617732
$579$	−9.81664	−0.407965
$580$	8.33837	0.346232
$581$	−21.0852	−0.874762
$582$	3.98441	0.165159
$583$	−6.96156	−0.288318
$584$	31.0232	1.28375
$585$	−1.06302	−0.0439507
$586$	6.79067	0.280520
$587$	1.79240	0.0739804	0.0369902	−	0.999316i	$-0.488223\pi$
$587$	1.79240	0.0739804	0.0369902	+	0.999316i	$0.488223\pi$
$588$	29.8451	1.23079
$589$	0	0
$590$	−6.04064	−0.248689
$591$	−0.123406	−0.00507626
$592$	−0.317620	−0.0130541
$593$	1.68134	0.0690444	0.0345222	−	0.999404i	$-0.489009\pi$
$593$	1.68134	0.0690444	0.0345222	+	0.999404i	$0.489009\pi$
$594$	−12.2275	−0.501701
$595$	26.0123	1.06640
$596$	−17.6281	−0.722077
$597$	12.2473	0.501247
$598$	3.30155	0.135010
$599$	2.16158	0.0883196	0.0441598	−	0.999024i	$-0.485939\pi$
$599$	2.16158	0.0883196	0.0441598	+	0.999024i	$0.485939\pi$
$600$	4.37245	0.178505
$601$	−4.43204	−0.180787	−0.0903934	−	0.995906i	$-0.528812\pi$
$601$	−4.43204	−0.180787	−0.0903934	+	0.995906i	$0.528812\pi$
$602$	11.8308	0.482186
$603$	−7.03886	−0.286644
$604$	−3.79284	−0.154329
$605$	7.90744	0.321483
$606$	4.23990	0.172234
$607$	−29.9817	−1.21692	−0.608460	−	0.793585i	$-0.708212\pi$
$607$	−29.9817	−1.21692	−0.608460	+	0.793585i	$0.708212\pi$
$608$	0	0
$609$	40.9170	1.65804
$610$	−3.85512	−0.156089
$611$	2.21976	0.0898019
$612$	−6.97057	−0.281768
$613$	19.8364	0.801185	0.400593	−	0.916256i	$-0.368804\pi$
$613$	19.8364	0.801185	0.400593	+	0.916256i	$0.368804\pi$
$614$	1.71435	0.0691854
$615$	0.0494809	0.00199526
$616$	40.4981	1.63171
$617$	21.0185	0.846172	0.423086	−	0.906089i	$-0.360947\pi$
$617$	21.0185	0.846172	0.423086	+	0.906089i	$0.360947\pi$
$618$	10.4847	0.421755
$619$	20.2632	0.814446	0.407223	−	0.913329i	$-0.366497\pi$
$619$	20.2632	0.814446	0.407223	+	0.913329i	$0.366497\pi$
$620$	10.5050	0.421891
$621$	−14.9412	−0.599568
$622$	−4.59212	−0.184127
$623$	2.07645	0.0831914
$624$	5.23665	0.209634
$625$	1.00000	0.0400000
$626$	−5.49193	−0.219501
$627$	0	0
$628$	5.16890	0.206261
$629$	−1.14945	−0.0458314
$630$	1.77239	0.0706136
$631$	40.1978	1.60025	0.800125	−	0.599834i	$-0.204767\pi$
$631$	40.1978	1.60025	0.800125	+	0.599834i	$0.204767\pi$
$632$	39.3362	1.56471
$633$	−11.3486	−0.451066
$634$	20.2031	0.802367
$635$	−5.32853	−0.211456
$636$	4.91606	0.194935
$637$	−15.0832	−0.597620
$638$	14.3431	0.567848
$639$	7.44420	0.294488
$640$	−11.2909	−0.446312
$641$	−3.49097	−0.137885	−0.0689425	−	0.997621i	$-0.521963\pi$
$641$	−3.49097	−0.137885	−0.0689425	+	0.997621i	$0.521963\pi$
$642$	7.62185	0.300811
$643$	36.1897	1.42718	0.713590	−	0.700563i	$-0.247068\pi$
$643$	36.1897	1.42718	0.713590	+	0.700563i	$0.247068\pi$
$644$	21.9905	0.866548
$645$	−8.77741	−0.345610
$646$	0	0
$647$	−21.1005	−0.829545	−0.414772	−	0.909925i	$-0.636139\pi$
$647$	−21.1005	−0.829545	−0.414772	+	0.909925i	$0.636139\pi$
$648$	24.1118	0.947199
$649$	41.5094	1.62939
$650$	−0.981980	−0.0385164
$651$	51.5489	2.02036
$652$	−10.5281	−0.412312
$653$	−16.7605	−0.655888	−0.327944	−	0.944697i	$-0.606356\pi$
$653$	−16.7605	−0.655888	−0.327944	+	0.944697i	$0.606356\pi$
$654$	11.9826	0.468559
$655$	−1.71262	−0.0669174
$656$	−0.0453110	−0.00176910
$657$	−9.32986	−0.363992
$658$	−3.70102	−0.144281
$659$	−37.0525	−1.44336	−0.721679	−	0.692227i	$-0.756629\pi$
$659$	−37.0525	−1.44336	−0.721679	+	0.692227i	$0.756629\pi$
$660$	−13.3519	−0.519723
$661$	−21.6904	−0.843658	−0.421829	−	0.906676i	$-0.638612\pi$
$661$	−21.6904	−0.843658	−0.421829	+	0.906676i	$0.638612\pi$
$662$	−15.3765	−0.597625
$663$	18.9511	0.736000
$664$	11.7455	0.455814
$665$	0	0
$666$	−0.0783194	−0.00303482
$667$	17.5262	0.678618
$668$	25.3576	0.981116
$669$	−56.2735	−2.17566
$670$	−6.50222	−0.251203
$671$	26.4912	1.02268
$672$	−44.4886	−1.71618
$673$	5.39580	0.207993	0.103996	−	0.994578i	$-0.466837\pi$
$673$	5.39580	0.207993	0.103996	+	0.994578i	$0.466837\pi$
$674$	−17.9623	−0.691880
$675$	4.44395	0.171048
$676$	16.9425	0.651633
$677$	30.9221	1.18843	0.594217	−	0.804305i	$-0.297462\pi$
$677$	30.9221	1.18843	0.594217	+	0.804305i	$0.297462\pi$
$678$	−6.37426	−0.244802
$679$	−13.4123	−0.514718
$680$	−14.4901	−0.555671
$681$	15.3610	0.588634
$682$	18.0700	0.691935
$683$	21.3136	0.815542	0.407771	−	0.913084i	$-0.366306\pi$
$683$	21.3136	0.815542	0.407771	+	0.913084i	$0.366306\pi$
$684$	0	0
$685$	5.74575	0.219534
$686$	7.03652	0.268656
$687$	−54.2670	−2.07041
$688$	8.03771	0.306435
$689$	−2.48450	−0.0946520
$690$	4.08401	0.155476
$691$	−7.63194	−0.290333	−0.145166	−	0.989407i	$-0.546372\pi$
$691$	−7.63194	−0.290333	−0.145166	+	0.989407i	$0.546372\pi$
$692$	−3.04112	−0.115606
$693$	−12.1793	−0.462653
$694$	−19.6804	−0.747057
$695$	−17.5854	−0.667054
$696$	−22.7928	−0.863959
$697$	−0.163978	−0.00621110
$698$	11.0609	0.418660
$699$	13.1519	0.497450
$700$	−6.54064	−0.247213
$701$	15.9184	0.601229	0.300615	−	0.953746i	$-0.402808\pi$
$701$	15.9184	0.601229	0.300615	+	0.953746i	$0.402808\pi$
$702$	−4.36387	−0.164704
$703$	0	0
$704$	−0.307740	−0.0115984
$705$	2.74584	0.103414
$706$	−5.58455	−0.210177
$707$	−14.2723	−0.536767
$708$	−29.3128	−1.10164
$709$	−39.7317	−1.49215	−0.746077	−	0.665860i	$-0.768065\pi$
$709$	−39.7317	−1.49215	−0.746077	+	0.665860i	$0.768065\pi$
$710$	6.87665	0.258076
$711$	−11.8299	−0.443655
$712$	−1.15669	−0.0433487
$713$	22.0802	0.826911
$714$	−31.5973	−1.18250
$715$	6.74786	0.252356
$716$	−22.8427	−0.853670
$717$	25.7106	0.960180
$718$	12.6061	0.470456
$719$	−8.16160	−0.304376	−0.152188	−	0.988352i	$-0.548632\pi$
$719$	−8.16160	−0.304376	−0.152188	+	0.988352i	$0.548632\pi$
$720$	1.20414	0.0448758
$721$	−35.2935	−1.31440
$722$	0	0
$723$	−49.2465	−1.83150
$724$	23.0114	0.855214
$725$	−5.21282	−0.193599
$726$	−9.60524	−0.356484
$727$	−1.56996	−0.0582265	−0.0291132	−	0.999576i	$-0.509268\pi$
$727$	−1.56996	−0.0582265	−0.0291132	+	0.999576i	$0.509268\pi$
$728$	14.4533	0.535676
$729$	18.3410	0.679296
$730$	−8.61855	−0.318987
$731$	29.0880	1.07586
$732$	−18.7074	−0.691444
$733$	4.41462	0.163058	0.0815288	−	0.996671i	$-0.474020\pi$
$733$	4.41462	0.163058	0.0815288	+	0.996671i	$0.474020\pi$
$734$	5.35104	0.197511
$735$	−18.6580	−0.688209
$736$	−19.0560	−0.702415
$737$	44.6812	1.64585
$738$	−0.0111729	−0.000411280 0
$739$	−10.1671	−0.374004	−0.187002	−	0.982360i	$-0.559877\pi$
$739$	−10.1671	−0.374004	−0.187002	+	0.982360i	$0.559877\pi$
$740$	0.289022	0.0106247
$741$	0	0
$742$	4.14243	0.152073
$743$	−7.04452	−0.258438	−0.129219	−	0.991616i	$-0.541247\pi$
$743$	−7.04452	−0.258438	−0.129219	+	0.991616i	$0.541247\pi$
$744$	−28.7153	−1.05275
$745$	11.0204	0.403757
$746$	4.51672	0.165369
$747$	−3.53232	−0.129241
$748$	44.2477	1.61786
$749$	−25.6567	−0.937475
$750$	−1.21471	−0.0443549
$751$	−25.7844	−0.940885	−0.470443	−	0.882431i	$-0.655906\pi$
$751$	−25.7844	−0.940885	−0.470443	+	0.882431i	$0.655906\pi$
$752$	−2.51444	−0.0916922
$753$	17.5080	0.638029
$754$	5.11889	0.186419
$755$	2.37114	0.0862945
$756$	−29.0663	−1.05713
$757$	19.2560	0.699872	0.349936	−	0.936774i	$-0.386203\pi$
$757$	19.2560	0.699872	0.349936	+	0.936774i	$0.386203\pi$
$758$	−3.86855	−0.140512
$759$	−28.0641	−1.01866
$760$	0	0
$761$	30.9500	1.12194	0.560969	−	0.827837i	$-0.310429\pi$
$761$	30.9500	1.12194	0.560969	+	0.827837i	$0.310429\pi$
$762$	6.47262	0.234478
$763$	−40.3360	−1.46026
$764$	−38.6766	−1.39927
$765$	4.35772	0.157554
$766$	−0.331447	−0.0119757
$767$	14.8143	0.534912
$768$	13.9869	0.504708
$769$	−29.7228	−1.07183	−0.535916	−	0.844271i	$-0.680034\pi$
$769$	−29.7228	−1.07183	−0.535916	+	0.844271i	$0.680034\pi$
$770$	−11.2507	−0.405449
$771$	−47.5044	−1.71083
$772$	−8.17998	−0.294404
$773$	12.3647	0.444728	0.222364	−	0.974964i	$-0.428623\pi$
$773$	12.3647	0.444728	0.222364	+	0.974964i	$0.428623\pi$
$774$	1.98196	0.0712400
$775$	−6.56732	−0.235905
$776$	7.47133	0.268205
$777$	1.41825	0.0508796
$778$	−1.57965	−0.0566333
$779$	0	0
$780$	−4.76516	−0.170620
$781$	−47.2542	−1.69089
$782$	−13.5342	−0.483984
$783$	−23.1655	−0.827868
$784$	17.0856	0.610200
$785$	−3.23139	−0.115333
$786$	2.08033	0.0742029
$787$	−43.8706	−1.56382	−0.781909	−	0.623393i	$-0.785754\pi$
$787$	−43.8706	−1.56382	−0.781909	+	0.623393i	$0.785754\pi$
$788$	−0.102832	−0.00366322
$789$	28.0872	0.999932
$790$	−10.9280	−0.388800
$791$	21.4570	0.762924
$792$	6.78447	0.241076
$793$	9.45442	0.335736
$794$	−1.82731	−0.0648488
$795$	−3.07333	−0.109000
$796$	10.2054	0.361719
$797$	5.08657	0.180176	0.0900879	−	0.995934i	$-0.471285\pi$
$797$	5.08657	0.180176	0.0900879	+	0.995934i	$0.471285\pi$
$798$	0	0
$799$	−9.09960	−0.321921
$800$	5.66784	0.200388
$801$	0.347860	0.0122910
$802$	10.9116	0.385304
$803$	59.2240	2.08997
$804$	−31.5527	−1.11278
$805$	−13.7476	−0.484539
$806$	6.44898	0.227156
$807$	33.0246	1.16252
$808$	7.95040	0.279694
$809$	30.2128	1.06222	0.531112	−	0.847301i	$-0.321774\pi$
$809$	30.2128	1.06222	0.531112	+	0.847301i	$0.321774\pi$
$810$	−6.69848	−0.235360
$811$	−3.65799	−0.128449	−0.0642247	−	0.997935i	$-0.520457\pi$
$811$	−3.65799	−0.128449	−0.0642247	+	0.997935i	$0.520457\pi$
$812$	34.0952	1.19651
$813$	−26.2427	−0.920373
$814$	0.497156	0.0174253
$815$	6.58175	0.230549
$816$	−21.4669	−0.751493
$817$	0	0
$818$	16.5221	0.577682
$819$	−4.34666	−0.151884
$820$	0.0412313	0.00143986
$821$	−19.4309	−0.678142	−0.339071	−	0.940761i	$-0.610113\pi$
$821$	−19.4309	−0.678142	−0.339071	+	0.940761i	$0.610113\pi$
$822$	−6.97941	−0.243435
$823$	−5.24032	−0.182666	−0.0913331	−	0.995820i	$-0.529113\pi$
$823$	−5.24032	−0.182666	−0.0913331	+	0.995820i	$0.529113\pi$
$824$	19.6602	0.684897
$825$	8.34710	0.290609
$826$	−24.6999	−0.859419
$827$	−57.1792	−1.98832	−0.994158	−	0.107939i	$-0.965575\pi$
$827$	−57.1792	−1.98832	−0.994158	+	0.107939i	$0.965575\pi$
$828$	3.68398	0.128027
$829$	14.6857	0.510056	0.255028	−	0.966934i	$-0.417915\pi$
$829$	14.6857	0.510056	0.255028	+	0.966934i	$0.417915\pi$
$830$	−3.26301	−0.113261
$831$	25.8377	0.896300
$832$	−0.109829	−0.00380764
$833$	61.8317	2.14234
$834$	21.3612	0.739678
$835$	−15.8526	−0.548602
$836$	0	0
$837$	−29.1848	−1.00878
$838$	−0.0713156	−0.00246356
$839$	−20.9038	−0.721678	−0.360839	−	0.932628i	$-0.617510\pi$
$839$	−20.9038	−0.721678	−0.360839	+	0.932628i	$0.617510\pi$
$840$	17.8787	0.616875
$841$	−1.82648	−0.0629820
$842$	−12.7942	−0.440916
$843$	−33.5485	−1.15547
$844$	−9.45652	−0.325507
$845$	−10.5918	−0.364368
$846$	−0.620016	−0.0213166
$847$	32.3331	1.11098
$848$	2.81433	0.0966444
$849$	40.3766	1.38572
$850$	4.02549	0.138073
$851$	0.607488	0.0208244
$852$	33.3696	1.14322
$853$	21.5030	0.736250	0.368125	−	0.929776i	$-0.380000\pi$
$853$	21.5030	0.736250	0.368125	+	0.929776i	$0.380000\pi$
$854$	−15.7634	−0.539413
$855$	0	0
$856$	14.2920	0.488492
$857$	50.8041	1.73543	0.867717	−	0.497058i	$-0.165586\pi$
$857$	50.8041	1.73543	0.867717	+	0.497058i	$0.165586\pi$
$858$	−8.19668	−0.279830
$859$	−7.20203	−0.245730	−0.122865	−	0.992423i	$-0.539208\pi$
$859$	−7.20203	−0.245730	−0.122865	+	0.992423i	$0.539208\pi$
$860$	−7.31401	−0.249406
$861$	0.202325	0.00689522
$862$	25.6569	0.873878
$863$	−18.0469	−0.614323	−0.307161	−	0.951657i	$-0.599379\pi$
$863$	−18.0469	−0.614323	−0.307161	+	0.951657i	$0.599379\pi$
$864$	25.1876	0.856899
$865$	1.90119	0.0646423
$866$	14.4106	0.489692
$867$	−45.0536	−1.53010
$868$	42.9545	1.45797
$869$	75.0936	2.54738
$870$	6.33206	0.214677
$871$	15.9462	0.540318
$872$	22.4692	0.760902
$873$	−2.24691	−0.0760464
$874$	0	0
$875$	4.08895	0.138232
$876$	−41.8224	−1.41305
$877$	23.7394	0.801623	0.400812	−	0.916160i	$-0.368728\pi$
$877$	23.7394	0.801623	0.400812	+	0.916160i	$0.368728\pi$
$878$	20.6745	0.697729
$879$	−20.6005	−0.694839
$880$	−7.64366	−0.257668
$881$	33.4076	1.12553	0.562765	−	0.826617i	$-0.309738\pi$
$881$	33.4076	1.12553	0.562765	+	0.826617i	$0.309738\pi$
$882$	4.21300	0.141859
$883$	42.4811	1.42960	0.714801	−	0.699328i	$-0.246517\pi$
$883$	42.4811	1.42960	0.714801	+	0.699328i	$0.246517\pi$
$884$	15.7915	0.531126
$885$	18.3252	0.615995
$886$	−8.77997	−0.294969
$887$	9.38621	0.315158	0.157579	−	0.987506i	$-0.449631\pi$
$887$	9.38621	0.315158	0.157579	+	0.987506i	$0.449631\pi$
$888$	−0.790038	−0.0265119
$889$	−21.7881	−0.730750
$890$	0.321339	0.0107713
$891$	46.0298	1.54206
$892$	−46.8914	−1.57004
$893$	0	0
$894$	−13.3866	−0.447715
$895$	14.2803	0.477339
$896$	−46.1679	−1.54236
$897$	−10.0158	−0.334416
$898$	3.80143	0.126855
$899$	34.2343	1.14178
$900$	−1.09573	−0.0365242
$901$	10.1849	0.339308
$902$	0.0709232	0.00236148
$903$	−35.8904	−1.19436
$904$	−11.9526	−0.397539
$905$	−14.3859	−0.478202
$906$	−2.88024	−0.0956896
$907$	7.74264	0.257090	0.128545	−	0.991704i	$-0.458969\pi$
$907$	7.74264	0.257090	0.128545	+	0.991704i	$0.458969\pi$
$908$	12.8000	0.424781
$909$	−2.39099	−0.0793040
$910$	−4.01527	−0.133105
$911$	31.8865	1.05645	0.528223	−	0.849106i	$-0.322858\pi$
$911$	31.8865	1.05645	0.528223	+	0.849106i	$0.322858\pi$
$912$	0	0
$913$	22.4224	0.742073
$914$	−15.1710	−0.501812
$915$	11.6951	0.386628
$916$	−45.2194	−1.49409
$917$	−7.00280	−0.231253
$918$	17.8891	0.590428
$919$	−19.3685	−0.638909	−0.319455	−	0.947602i	$-0.603500\pi$
$919$	−19.3685	−0.638909	−0.319455	+	0.947602i	$0.603500\pi$
$920$	7.65810	0.252480
$921$	−5.20073	−0.171370
$922$	−22.8344	−0.752012
$923$	−16.8645	−0.555102
$924$	−54.5954	−1.79606
$925$	−0.180685	−0.00594090
$926$	4.45656	0.146452
$927$	−5.91257	−0.194194
$928$	−29.5454	−0.969877
$929$	24.3742	0.799692	0.399846	−	0.916582i	$-0.369064\pi$
$929$	24.3742	0.799692	0.399846	+	0.916582i	$0.369064\pi$
$930$	7.97738	0.261589
$931$	0	0
$932$	10.9592	0.358979
$933$	13.9309	0.456077
$934$	25.1404	0.822619
$935$	−27.6619	−0.904642
$936$	2.42130	0.0791428
$937$	18.6817	0.610305	0.305153	−	0.952303i	$-0.401293\pi$
$937$	18.6817	0.610305	0.305153	+	0.952303i	$0.401293\pi$
$938$	−26.5873	−0.868105
$939$	16.6606	0.543698
$940$	2.28805	0.0746278
$941$	23.4123	0.763218	0.381609	−	0.924324i	$-0.375370\pi$
$941$	23.4123	0.763218	0.381609	+	0.924324i	$0.375370\pi$
$942$	3.92520	0.127890
$943$	0.0866630	0.00282214
$944$	−16.7809	−0.546171
$945$	18.1711	0.591106
$946$	−12.5810	−0.409045
$947$	39.6979	1.29001	0.645004	−	0.764180i	$-0.276856\pi$
$947$	39.6979	1.29001	0.645004	+	0.764180i	$0.276856\pi$
$948$	−53.0290	−1.72230
$949$	21.1364	0.686117
$950$	0	0
$951$	−61.2892	−1.98744
$952$	−59.2494	−1.92028
$953$	49.8966	1.61631	0.808155	−	0.588969i	$-0.200466\pi$
$953$	49.8966	1.61631	0.808155	+	0.588969i	$0.200466\pi$
$954$	0.693964	0.0224679
$955$	24.1791	0.782417
$956$	21.4241	0.692904
$957$	−43.5119	−1.40654
$958$	−22.9720	−0.742193
$959$	23.4941	0.758664
$960$	−0.135859	−0.00438482
$961$	12.1297	0.391280
$962$	0.177429	0.00572055
$963$	−4.29816	−0.138506
$964$	−41.0360	−1.32168
$965$	5.11380	0.164619
$966$	16.6993	0.537292
$967$	−53.8482	−1.73164	−0.865821	−	0.500354i	$-0.833203\pi$
$967$	−53.8482	−1.73164	−0.865821	+	0.500354i	$0.833203\pi$
$968$	−18.0112	−0.578901
$969$	0	0
$970$	−2.07561	−0.0666437
$971$	23.9740	0.769363	0.384682	−	0.923049i	$-0.374311\pi$
$971$	23.9740	0.769363	0.384682	+	0.923049i	$0.374311\pi$
$972$	−11.1795	−0.358584
$973$	−71.9060	−2.30520
$974$	1.60412	0.0513995
$975$	2.97899	0.0954040
$976$	−10.7095	−0.342803
$977$	52.6466	1.68431	0.842157	−	0.539232i	$-0.181286\pi$
$977$	52.6466	1.68431	0.842157	+	0.539232i	$0.181286\pi$
$978$	−7.99491	−0.255649
$979$	−2.20814	−0.0705725
$980$	−15.5472	−0.496639
$981$	−6.75732	−0.215745
$982$	−22.9790	−0.733288
$983$	41.0293	1.30863	0.654316	−	0.756221i	$-0.272957\pi$
$983$	41.0293	1.30863	0.654316	+	0.756221i	$0.272957\pi$
$984$	−0.112705	−0.00359291
$985$	0.0642863	0.00204833
$986$	−20.9842	−0.668272
$987$	11.2276	0.357379
$988$	0	0
$989$	−15.3731	−0.488837
$990$	−1.88479	−0.0599026
$991$	−28.4463	−0.903628	−0.451814	−	0.892112i	$-0.649223\pi$
$991$	−28.4463	−0.903628	−0.451814	+	0.892112i	$0.649223\pi$
$992$	−37.2225	−1.18182
$993$	46.6470	1.48030
$994$	28.1183	0.891858
$995$	−6.37999	−0.202259
$996$	−15.8341	−0.501722
$997$	−35.1869	−1.11438	−0.557190	−	0.830385i	$-0.688120\pi$
$997$	−35.1869	−1.11438	−0.557190	+	0.830385i	$0.688120\pi$
$998$	−11.3390	−0.358931
$999$	−0.802956	−0.0254044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.8		9
5.4	even	2		9025.2.a.cf.1.2		9
19.14	odd	18		95.2.k.a.6.1	✓	18
19.15	odd	18		95.2.k.a.16.1	yes	18
19.18	odd	2		1805.2.a.v.1.2		9
57.14	even	18		855.2.bs.c.766.3		18
57.53	even	18		855.2.bs.c.586.3		18
95.14	odd	18		475.2.l.c.101.3		18
95.33	even	36		475.2.u.b.424.4		36
95.34	odd	18		475.2.l.c.301.3		18
95.52	even	36		475.2.u.b.424.3		36
95.53	even	36		475.2.u.b.149.3		36
95.72	even	36		475.2.u.b.149.4		36
95.94	odd	2		9025.2.a.cc.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.1	✓	18	19.14	odd	18
95.2.k.a.16.1	yes	18	19.15	odd	18
475.2.l.c.101.3		18	95.14	odd	18
475.2.l.c.301.3		18	95.34	odd	18
475.2.u.b.149.3		36	95.53	even	36
475.2.u.b.149.4		36	95.72	even	36
475.2.u.b.424.3		36	95.52	even	36
475.2.u.b.424.4		36	95.33	even	36
855.2.bs.c.586.3		18	57.53	even	18
855.2.bs.c.766.3		18	57.14	even	18
1805.2.a.s.1.8		9	1.1	even	1	trivial
1805.2.a.v.1.2		9	19.18	odd	2
9025.2.a.cc.1.8		9	95.94	odd	2
9025.2.a.cf.1.2		9	5.4	even	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)

\(f(q)\)	\(=\)	\(q+0.632780 q^{2} -1.91964 q^{3} -1.59959 q^{4} +1.00000 q^{5} -1.21471 q^{6} +4.08895 q^{7} -2.27775 q^{8} +0.685005 q^{9} +O(q^{10})\)	\(q+0.632780 q^{2} -1.91964 q^{3} -1.59959 q^{4} +1.00000 q^{5} -1.21471 q^{6} +4.08895 q^{7} -2.27775 q^{8} +0.685005 q^{9} +0.632780 q^{10} -4.34827 q^{11} +3.07063 q^{12} -1.55185 q^{13} +2.58741 q^{14} -1.91964 q^{15} +1.75786 q^{16} +6.36159 q^{17} +0.433458 q^{18} -1.59959 q^{20} -7.84930 q^{21} -2.75150 q^{22} -3.36213 q^{23} +4.37245 q^{24} +1.00000 q^{25} -0.981980 q^{26} +4.44395 q^{27} -6.54064 q^{28} -5.21282 q^{29} -1.21471 q^{30} -6.56732 q^{31} +5.66784 q^{32} +8.34710 q^{33} +4.02549 q^{34} +4.08895 q^{35} -1.09573 q^{36} -0.180685 q^{37} +2.97899 q^{39} -2.27775 q^{40} -0.0257762 q^{41} -4.96688 q^{42} +4.57243 q^{43} +6.95544 q^{44} +0.685005 q^{45} -2.12749 q^{46} -1.43040 q^{47} -3.37446 q^{48} +9.71953 q^{49} +0.632780 q^{50} -12.2119 q^{51} +2.48232 q^{52} +1.60099 q^{53} +2.81204 q^{54} -4.34827 q^{55} -9.31361 q^{56} -3.29857 q^{58} -9.54619 q^{59} +3.07063 q^{60} -6.09235 q^{61} -4.15567 q^{62} +2.80095 q^{63} +0.0707731 q^{64} -1.55185 q^{65} +5.28188 q^{66} -10.2756 q^{67} -10.1759 q^{68} +6.45408 q^{69} +2.58741 q^{70} +10.8674 q^{71} -1.56027 q^{72} -13.6201 q^{73} -0.114334 q^{74} -1.91964 q^{75} -17.7799 q^{77} +1.88505 q^{78} -17.2698 q^{79} +1.75786 q^{80} -10.5858 q^{81} -0.0163107 q^{82} -5.15663 q^{83} +12.5557 q^{84} +6.36159 q^{85} +2.89335 q^{86} +10.0067 q^{87} +9.90427 q^{88} +0.507821 q^{89} +0.433458 q^{90} -6.34544 q^{91} +5.37803 q^{92} +12.6069 q^{93} -0.905127 q^{94} -10.8802 q^{96} -3.28014 q^{97} +6.15033 q^{98} -2.97859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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