LMFDB - Embedded newform 1805.2.a.s.1.4

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			1.4
Root			$-0.256961$ 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)

$f(q)$	$=$	$q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +1.00000 q^{5} +3.78628 q^{6} +3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} +O(q^{10})$	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +1.00000 q^{5} +3.78628 q^{6} +3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} -1.25696 q^{10} -3.35588 q^{11} +1.26529 q^{12} -4.84131 q^{13} -4.68082 q^{14} -3.01225 q^{15} -2.98346 q^{16} -2.67526 q^{17} -7.63436 q^{18} -0.420048 q^{20} -11.2174 q^{21} +4.21821 q^{22} +1.87703 q^{23} -9.16299 q^{24} +1.00000 q^{25} +6.08534 q^{26} -9.25865 q^{27} -1.56423 q^{28} +5.25131 q^{29} +3.78628 q^{30} +3.11891 q^{31} -2.33372 q^{32} +10.1087 q^{33} +3.36269 q^{34} +3.72392 q^{35} -2.55123 q^{36} -0.992927 q^{37} +14.5832 q^{39} +3.04191 q^{40} -0.416383 q^{41} +14.0998 q^{42} -7.21877 q^{43} +1.40963 q^{44} +6.07366 q^{45} -2.35935 q^{46} +2.24086 q^{47} +8.98694 q^{48} +6.86757 q^{49} -1.25696 q^{50} +8.05854 q^{51} +2.03358 q^{52} -0.260252 q^{53} +11.6378 q^{54} -3.35588 q^{55} +11.3278 q^{56} -6.60069 q^{58} +5.18883 q^{59} +1.26529 q^{60} +0.768938 q^{61} -3.92035 q^{62} +22.6178 q^{63} +8.90032 q^{64} -4.84131 q^{65} -12.7063 q^{66} -10.7775 q^{67} +1.12374 q^{68} -5.65409 q^{69} -4.68082 q^{70} -2.00146 q^{71} +18.4755 q^{72} +4.56262 q^{73} +1.24807 q^{74} -3.01225 q^{75} -12.4970 q^{77} -18.3306 q^{78} +12.0521 q^{79} -2.98346 q^{80} +9.66841 q^{81} +0.523377 q^{82} -13.5711 q^{83} +4.71184 q^{84} -2.67526 q^{85} +9.07371 q^{86} -15.8183 q^{87} -10.2083 q^{88} +7.66941 q^{89} -7.63436 q^{90} -18.0286 q^{91} -0.788443 q^{92} -9.39494 q^{93} -2.81668 q^{94} +7.02975 q^{96} +7.22894 q^{97} -8.63226 q^{98} -20.3825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.25696	−0.888806	−0.444403	−	0.895827i	$-0.646584\pi$
$2$	−1.25696	−0.888806	−0.444403	+	0.895827i	$0.646584\pi$
$3$	−3.01225	−1.73912	−0.869562	−	0.493823i	$-0.835599\pi$
$3$	−3.01225	−1.73912	−0.869562	+	0.493823i	$0.835599\pi$
$4$	−0.420048	−0.210024
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.78628	1.54574
$7$	3.72392	1.40751	0.703754	−	0.710443i	$-0.251506\pi$
$7$	3.72392	1.40751	0.703754	+	0.710443i	$0.251506\pi$
$8$	3.04191	1.07548
$9$	6.07366	2.02455
$10$	−1.25696	−0.397486
$11$	−3.35588	−1.01183	−0.505917	−	0.862582i	$-0.668846\pi$
$11$	−3.35588	−1.01183	−0.505917	+	0.862582i	$0.668846\pi$
$12$	1.26529	0.365258
$13$	−4.84131	−1.34274	−0.671369	−	0.741124i	$-0.734293\pi$
$13$	−4.84131	−1.34274	−0.671369	+	0.741124i	$0.734293\pi$
$14$	−4.68082	−1.25100
$15$	−3.01225	−0.777760
$16$	−2.98346	−0.745866
$17$	−2.67526	−0.648845	−0.324422	−	0.945912i	$-0.605170\pi$
$17$	−2.67526	−0.648845	−0.324422	+	0.945912i	$0.605170\pi$
$18$	−7.63436	−1.79944
$19$	0	0
$19$	0	0
$20$	−0.420048	−0.0939257
$21$	−11.2174	−2.44783
$22$	4.21821	0.899325
$23$	1.87703	0.391388	0.195694	−	0.980665i	$-0.437304\pi$
$23$	1.87703	0.391388	0.195694	+	0.980665i	$0.437304\pi$
$24$	−9.16299	−1.87039
$25$	1.00000	0.200000
$26$	6.08534	1.19343
$27$	−9.25865	−1.78183
$28$	−1.56423	−0.295611
$29$	5.25131	0.975143	0.487572	−	0.873083i	$-0.337883\pi$
$29$	5.25131	0.975143	0.487572	+	0.873083i	$0.337883\pi$
$30$	3.78628	0.691278
$31$	3.11891	0.560173	0.280086	−	0.959975i	$-0.409637\pi$
$31$	3.11891	0.560173	0.280086	+	0.959975i	$0.409637\pi$
$32$	−2.33372	−0.412547
$33$	10.1087	1.75971
$34$	3.36269	0.576697
$35$	3.72392	0.629457
$36$	−2.55123	−0.425206
$37$	−0.992927	−0.163236	−0.0816181	−	0.996664i	$-0.526009\pi$
$37$	−0.992927	−0.163236	−0.0816181	+	0.996664i	$0.526009\pi$
$38$	0	0
$39$	14.5832	2.33519
$40$	3.04191	0.480968
$41$	−0.416383	−0.0650281	−0.0325140	−	0.999471i	$-0.510351\pi$
$41$	−0.416383	−0.0650281	−0.0325140	+	0.999471i	$0.510351\pi$
$42$	14.0998	2.17565
$43$	−7.21877	−1.10085	−0.550426	−	0.834884i	$-0.685535\pi$
$43$	−7.21877	−1.10085	−0.550426	+	0.834884i	$0.685535\pi$
$44$	1.40963	0.212510
$45$	6.07366	0.905408
$46$	−2.35935	−0.347868
$47$	2.24086	0.326864	0.163432	−	0.986555i	$-0.447744\pi$
$47$	2.24086	0.326864	0.163432	+	0.986555i	$0.447744\pi$
$48$	8.98694	1.29715
$49$	6.86757	0.981081
$50$	−1.25696	−0.177761
$51$	8.05854	1.12842
$52$	2.03358	0.282007
$53$	−0.260252	−0.0357483	−0.0178742	−	0.999840i	$-0.505690\pi$
$53$	−0.260252	−0.0357483	−0.0178742	+	0.999840i	$0.505690\pi$
$54$	11.6378	1.58370
$55$	−3.35588	−0.452506
$56$	11.3278	1.51374
$57$	0	0
$58$	−6.60069	−0.866713
$59$	5.18883	0.675528	0.337764	−	0.941231i	$-0.390329\pi$
$59$	5.18883	0.675528	0.337764	+	0.941231i	$0.390329\pi$
$60$	1.26529	0.163348
$61$	0.768938	0.0984524	0.0492262	−	0.998788i	$-0.484324\pi$
$61$	0.768938	0.0984524	0.0492262	+	0.998788i	$0.484324\pi$
$62$	−3.92035	−0.497885
$63$	22.6178	2.84958
$64$	8.90032	1.11254
$65$	−4.84131	−0.600490
$66$	−12.7063	−1.56404
$67$	−10.7775	−1.31668	−0.658339	−	0.752722i	$-0.728740\pi$
$67$	−10.7775	−1.31668	−0.658339	+	0.752722i	$0.728740\pi$
$68$	1.12374	0.136273
$69$	−5.65409	−0.680672
$70$	−4.68082	−0.559465
$71$	−2.00146	−0.237529	−0.118765	−	0.992922i	$-0.537893\pi$
$71$	−2.00146	−0.237529	−0.118765	+	0.992922i	$0.537893\pi$
$72$	18.4755	2.17736
$73$	4.56262	0.534015	0.267007	−	0.963694i	$-0.413965\pi$
$73$	4.56262	0.534015	0.267007	+	0.963694i	$0.413965\pi$
$74$	1.24807	0.145085
$75$	−3.01225	−0.347825
$76$	0	0
$77$	−12.4970	−1.42417
$78$	−18.3306	−2.07553
$79$	12.0521	1.35596	0.677981	−	0.735079i	$-0.262855\pi$
$79$	12.0521	1.35596	0.677981	+	0.735079i	$0.262855\pi$
$80$	−2.98346	−0.333561
$81$	9.66841	1.07427
$82$	0.523377	0.0577973
$83$	−13.5711	−1.48962	−0.744809	−	0.667278i	$-0.767459\pi$
$83$	−13.5711	−1.48962	−0.744809	+	0.667278i	$0.767459\pi$
$84$	4.71184	0.514104
$85$	−2.67526	−0.290172
$86$	9.07371	0.978443
$87$	−15.8183	−1.69590
$88$	−10.2083	−1.08820
$89$	7.66941	0.812956	0.406478	−	0.913661i	$-0.366757\pi$
$89$	7.66941	0.812956	0.406478	+	0.913661i	$0.366757\pi$
$90$	−7.63436	−0.804732
$91$	−18.0286	−1.88991
$92$	−0.788443	−0.0822009
$93$	−9.39494	−0.974210
$94$	−2.81668	−0.290518
$95$	0	0
$96$	7.02975	0.717471
$97$	7.22894	0.733988	0.366994	−	0.930223i	$-0.380387\pi$
$97$	7.22894	0.733988	0.366994	+	0.930223i	$0.380387\pi$
$98$	−8.63226	−0.871990
$99$	−20.3825	−2.04852
$100$	−0.420048	−0.0420048
$101$	4.49184	0.446955	0.223477	−	0.974709i	$-0.428259\pi$
$101$	4.49184	0.446955	0.223477	+	0.974709i	$0.428259\pi$
$102$	−10.1293	−1.00295
$103$	−10.7445	−1.05869	−0.529345	−	0.848407i	$-0.677562\pi$
$103$	−10.7445	−1.05869	−0.529345	+	0.848407i	$0.677562\pi$
$104$	−14.7268	−1.44408
$105$	−11.2174	−1.09470
$106$	0.327127	0.0317733
$107$	−1.37863	−0.133277	−0.0666386	−	0.997777i	$-0.521227\pi$
$107$	−1.37863	−0.133277	−0.0666386	+	0.997777i	$0.521227\pi$
$108$	3.88908	0.374227
$109$	−9.49878	−0.909818	−0.454909	−	0.890538i	$-0.650328\pi$
$109$	−9.49878	−0.909818	−0.454909	+	0.890538i	$0.650328\pi$
$110$	4.21821	0.402190
$111$	2.99095	0.283888
$112$	−11.1102	−1.04981
$113$	17.0436	1.60333	0.801666	−	0.597772i	$-0.203947\pi$
$113$	17.0436	1.60333	0.801666	+	0.597772i	$0.203947\pi$
$114$	0	0
$115$	1.87703	0.175034
$116$	−2.20580	−0.204804
$117$	−29.4045	−2.71844
$118$	−6.52216	−0.600413
$119$	−9.96243	−0.913255
$120$	−9.16299	−0.836463
$121$	0.261910	0.0238100
$122$	−0.966525	−0.0875051
$123$	1.25425	0.113092
$124$	−1.31009	−0.117650
$125$	1.00000	0.0894427
$126$	−28.4297	−2.53272
$127$	−19.8598	−1.76227	−0.881137	−	0.472860i	$-0.843221\pi$
$127$	−19.8598	−1.76227	−0.881137	+	0.472860i	$0.843221\pi$
$128$	−6.51992	−0.576285
$129$	21.7447	1.91452
$130$	6.08534	0.533719
$131$	5.42317	0.473824	0.236912	−	0.971531i	$-0.423865\pi$
$131$	5.42317	0.473824	0.236912	+	0.971531i	$0.423865\pi$
$132$	−4.24616	−0.369581
$133$	0	0
$134$	13.5469	1.17027
$135$	−9.25865	−0.796858
$136$	−8.13788	−0.697817
$137$	−18.5615	−1.58581	−0.792906	−	0.609344i	$-0.791433\pi$
$137$	−18.5615	−1.58581	−0.792906	+	0.609344i	$0.791433\pi$
$138$	7.10697	0.604985
$139$	−10.5127	−0.891675	−0.445838	−	0.895114i	$-0.647094\pi$
$139$	−10.5127	−0.891675	−0.445838	+	0.895114i	$0.647094\pi$
$140$	−1.56423	−0.132201
$141$	−6.75005	−0.568457
$142$	2.51575	0.211117
$143$	16.2468	1.35863
$144$	−18.1205	−1.51005
$145$	5.25131	0.436097
$146$	−5.73504	−0.474635
$147$	−20.6868	−1.70622
$148$	0.417077	0.0342835
$149$	15.1409	1.24039	0.620196	−	0.784447i	$-0.287053\pi$
$149$	15.1409	1.24039	0.620196	+	0.784447i	$0.287053\pi$
$150$	3.78628	0.309149
$151$	−11.3432	−0.923095	−0.461548	−	0.887115i	$-0.652706\pi$
$151$	−11.3432	−0.923095	−0.461548	+	0.887115i	$0.652706\pi$
$152$	0	0
$153$	−16.2486	−1.31362
$154$	15.7083	1.26581
$155$	3.11891	0.250517
$156$	−6.12567	−0.490446
$157$	−4.21528	−0.336416	−0.168208	−	0.985752i	$-0.553798\pi$
$157$	−4.21528	−0.336416	−0.168208	+	0.985752i	$0.553798\pi$
$158$	−15.1490	−1.20519
$159$	0.783944	0.0621708
$160$	−2.33372	−0.184497
$161$	6.98990	0.550882
$162$	−12.1528	−0.954815
$163$	−13.9056	−1.08917	−0.544585	−	0.838706i	$-0.683313\pi$
$163$	−13.9056	−1.08917	−0.544585	+	0.838706i	$0.683313\pi$
$164$	0.174901	0.0136575
$165$	10.1087	0.786965
$166$	17.0583	1.32398
$167$	−17.6222	−1.36365	−0.681824	−	0.731516i	$-0.738813\pi$
$167$	−17.6222	−1.36365	−0.681824	+	0.731516i	$0.738813\pi$
$168$	−34.1222	−2.63259
$169$	10.4383	0.802943
$170$	3.36269	0.257907
$171$	0	0
$172$	3.03223	0.231206
$173$	13.3182	1.01256	0.506282	−	0.862368i	$-0.331019\pi$
$173$	13.3182	1.01256	0.506282	+	0.862368i	$0.331019\pi$
$174$	19.8829	1.50732
$175$	3.72392	0.281502
$176$	10.0121	0.754693
$177$	−15.6301	−1.17483
$178$	−9.64015	−0.722560
$179$	−14.6264	−1.09323	−0.546616	−	0.837383i	$-0.684084\pi$
$179$	−14.6264	−1.09323	−0.546616	+	0.837383i	$0.684084\pi$
$180$	−2.55123	−0.190158
$181$	8.78476	0.652966	0.326483	−	0.945203i	$-0.394136\pi$
$181$	8.78476	0.652966	0.326483	+	0.945203i	$0.394136\pi$
$182$	22.6613	1.67977
$183$	−2.31623	−0.171221
$184$	5.70975	0.420928
$185$	−0.992927	−0.0730014
$186$	11.8091	0.865883
$187$	8.97783	0.656524
$188$	−0.941271	−0.0686493
$189$	−34.4785	−2.50794
$190$	0	0
$191$	−9.70737	−0.702401	−0.351200	−	0.936300i	$-0.614226\pi$
$191$	−9.70737	−0.702401	−0.351200	+	0.936300i	$0.614226\pi$
$192$	−26.8100	−1.93485
$193$	20.2546	1.45796	0.728981	−	0.684534i	$-0.239994\pi$
$193$	20.2546	1.45796	0.728981	+	0.684534i	$0.239994\pi$
$194$	−9.08650	−0.652373
$195$	14.5832	1.04433
$196$	−2.88471	−0.206051
$197$	−9.26182	−0.659877	−0.329939	−	0.944002i	$-0.607028\pi$
$197$	−9.26182	−0.659877	−0.329939	+	0.944002i	$0.607028\pi$
$198$	25.6200	1.82073
$199$	18.1521	1.28676	0.643382	−	0.765545i	$-0.277531\pi$
$199$	18.1521	1.28676	0.643382	+	0.765545i	$0.277531\pi$
$200$	3.04191	0.215095
$201$	32.4644	2.28987
$202$	−5.64607	−0.397256
$203$	19.5554	1.37252
$204$	−3.38498	−0.236996
$205$	−0.416383	−0.0290814
$206$	13.5055	0.940970
$207$	11.4004	0.792386
$208$	14.4439	1.00150
$209$	0	0
$210$	14.0998	0.972980
$211$	−17.3820	−1.19662	−0.598311	−	0.801264i	$-0.704161\pi$
$211$	−17.3820	−1.19662	−0.598311	+	0.801264i	$0.704161\pi$
$212$	0.109318	0.00750802
$213$	6.02889	0.413093
$214$	1.73288	0.118458
$215$	−7.21877	−0.492316
$216$	−28.1640	−1.91631
$217$	11.6146	0.788448
$218$	11.9396	0.808651
$219$	−13.7438	−0.928718
$220$	1.40963	0.0950373
$221$	12.9517	0.871228
$222$	−3.75950	−0.252321
$223$	8.72670	0.584383	0.292191	−	0.956360i	$-0.405616\pi$
$223$	8.72670	0.584383	0.292191	+	0.956360i	$0.405616\pi$
$224$	−8.69057	−0.580663
$225$	6.07366	0.404911
$226$	−21.4232	−1.42505
$227$	20.1154	1.33510	0.667552	−	0.744563i	$-0.267342\pi$
$227$	20.1154	1.33510	0.667552	+	0.744563i	$0.267342\pi$
$228$	0	0
$229$	−20.8410	−1.37721	−0.688607	−	0.725135i	$-0.741778\pi$
$229$	−20.8410	−1.37721	−0.688607	+	0.725135i	$0.741778\pi$
$230$	−2.35935	−0.155571
$231$	37.6442	2.47680
$232$	15.9740	1.04874
$233$	0.544051	0.0356420	0.0178210	−	0.999841i	$-0.494327\pi$
$233$	0.544051	0.0356420	0.0178210	+	0.999841i	$0.494327\pi$
$234$	36.9603	2.41617
$235$	2.24086	0.146178
$236$	−2.17956	−0.141877
$237$	−36.3038	−2.35819
$238$	12.5224	0.811706
$239$	−22.2235	−1.43752	−0.718758	−	0.695260i	$-0.755289\pi$
$239$	−22.2235	−1.43752	−0.718758	+	0.695260i	$0.755289\pi$
$240$	8.98694	0.580105
$241$	−21.7336	−1.39998	−0.699991	−	0.714152i	$-0.746813\pi$
$241$	−21.7336	−1.39998	−0.699991	+	0.714152i	$0.746813\pi$
$242$	−0.329211	−0.0211625
$243$	−1.34772	−0.0864565
$244$	−0.322991	−0.0206774
$245$	6.86757	0.438753
$246$	−1.57654	−0.100517
$247$	0	0
$248$	9.48743	0.602452
$249$	40.8795	2.59063
$250$	−1.25696	−0.0794972
$251$	17.8239	1.12504	0.562518	−	0.826785i	$-0.309833\pi$
$251$	17.8239	1.12504	0.562518	+	0.826785i	$0.309833\pi$
$252$	−9.50058	−0.598481
$253$	−6.29908	−0.396020
$254$	24.9630	1.56632
$255$	8.05854	0.504646
$256$	−9.60535	−0.600334
$257$	−15.7239	−0.980829	−0.490414	−	0.871489i	$-0.663155\pi$
$257$	−15.7239	−0.980829	−0.490414	+	0.871489i	$0.663155\pi$
$258$	−27.3323	−1.70163
$259$	−3.69758	−0.229756
$260$	2.03358	0.126118
$261$	31.8947	1.97423
$262$	−6.81671	−0.421138
$263$	−30.4504	−1.87765	−0.938826	−	0.344391i	$-0.888085\pi$
$263$	−30.4504	−1.87765	−0.938826	+	0.344391i	$0.888085\pi$
$264$	30.7499	1.89252
$265$	−0.260252	−0.0159871
$266$	0	0
$267$	−23.1022	−1.41383
$268$	4.52706	0.276534
$269$	−2.61192	−0.159251	−0.0796257	−	0.996825i	$-0.525373\pi$
$269$	−2.61192	−0.159251	−0.0796257	+	0.996825i	$0.525373\pi$
$270$	11.6378	0.708252
$271$	−9.60823	−0.583658	−0.291829	−	0.956470i	$-0.594264\pi$
$271$	−9.60823	−0.583658	−0.291829	+	0.956470i	$0.594264\pi$
$272$	7.98152	0.483951
$273$	54.3068	3.28680
$274$	23.3310	1.40948
$275$	−3.35588	−0.202367
$276$	2.37499	0.142958
$277$	20.0672	1.20572	0.602860	−	0.797847i	$-0.294028\pi$
$277$	20.0672	1.20572	0.602860	+	0.797847i	$0.294028\pi$
$278$	13.2140	0.792526
$279$	18.9432	1.13410
$280$	11.3278	0.676966
$281$	−26.5556	−1.58417	−0.792086	−	0.610409i	$-0.791005\pi$
$281$	−26.5556	−1.58417	−0.792086	+	0.610409i	$0.791005\pi$
$282$	8.48455	0.505247
$283$	−16.7788	−0.997397	−0.498699	−	0.866776i	$-0.666189\pi$
$283$	−16.7788	−0.997397	−0.498699	+	0.866776i	$0.666189\pi$
$284$	0.840709	0.0498869
$285$	0	0
$286$	−20.4216	−1.20756
$287$	−1.55058	−0.0915276
$288$	−14.1742	−0.835224
$289$	−9.84301	−0.579000
$290$	−6.60069	−0.387606
$291$	−21.7754	−1.27650
$292$	−1.91652	−0.112156
$293$	−13.3788	−0.781597	−0.390799	−	0.920476i	$-0.627801\pi$
$293$	−13.3788	−0.781597	−0.390799	+	0.920476i	$0.627801\pi$
$294$	26.0026	1.51650
$295$	5.18883	0.302105
$296$	−3.02039	−0.175557
$297$	31.0709	1.80292
$298$	−19.0315	−1.10247
$299$	−9.08728	−0.525531
$300$	1.26529	0.0730517
$301$	−26.8821	−1.54946
$302$	14.2579	0.820452
$303$	−13.5305	−0.777310
$304$	0	0
$305$	0.768938	0.0440293
$306$	20.4239	1.16755
$307$	−27.9723	−1.59646	−0.798232	−	0.602350i	$-0.794231\pi$
$307$	−27.9723	−1.59646	−0.798232	+	0.602350i	$0.794231\pi$
$308$	5.24935	0.299109
$309$	32.3653	1.84119
$310$	−3.92035	−0.222661
$311$	24.8350	1.40826	0.704132	−	0.710069i	$-0.251336\pi$
$311$	24.8350	1.40826	0.704132	+	0.710069i	$0.251336\pi$
$312$	44.3609	2.51144
$313$	−22.2726	−1.25892	−0.629462	−	0.777031i	$-0.716725\pi$
$313$	−22.2726	−1.25892	−0.629462	+	0.777031i	$0.716725\pi$
$314$	5.29845	0.299009
$315$	22.6178	1.27437
$316$	−5.06245	−0.284785
$317$	14.0757	0.790568	0.395284	−	0.918559i	$-0.370646\pi$
$317$	14.0757	0.790568	0.395284	+	0.918559i	$0.370646\pi$
$318$	−0.985388	−0.0552578
$319$	−17.6227	−0.986684
$320$	8.90032	0.497543
$321$	4.15278	0.231786
$322$	−8.78604	−0.489627
$323$	0	0
$324$	−4.06120	−0.225622
$325$	−4.84131	−0.268547
$326$	17.4788	0.968061
$327$	28.6127	1.58229
$328$	−1.26660	−0.0699362
$329$	8.34479	0.460063
$330$	−12.7063	−0.699459
$331$	5.28549	0.290517	0.145258	−	0.989394i	$-0.453599\pi$
$331$	5.28549	0.290517	0.145258	+	0.989394i	$0.453599\pi$
$332$	5.70050	0.312856
$333$	−6.03070	−0.330481
$334$	22.1505	1.21202
$335$	−10.7775	−0.588836
$336$	33.4666	1.82575
$337$	−23.8881	−1.30127	−0.650633	−	0.759392i	$-0.725496\pi$
$337$	−23.8881	−1.30127	−0.650633	+	0.759392i	$0.725496\pi$
$338$	−13.1205	−0.713660
$339$	−51.3398	−2.78839
$340$	1.12374	0.0609432
$341$	−10.4667	−0.566802
$342$	0	0
$343$	−0.493173	−0.0266288
$344$	−21.9588	−1.18394
$345$	−5.65409	−0.304406
$346$	−16.7405	−0.899973
$347$	−8.76704	−0.470639	−0.235320	−	0.971918i	$-0.575614\pi$
$347$	−8.76704	−0.470639	−0.235320	+	0.971918i	$0.575614\pi$
$348$	6.64444	0.356179
$349$	2.04011	0.109205	0.0546023	−	0.998508i	$-0.482611\pi$
$349$	2.04011	0.109205	0.0546023	+	0.998508i	$0.482611\pi$
$350$	−4.68082	−0.250200
$351$	44.8240	2.39253
$352$	7.83167	0.417429
$353$	9.06450	0.482455	0.241227	−	0.970469i	$-0.422450\pi$
$353$	9.06450	0.482455	0.241227	+	0.970469i	$0.422450\pi$
$354$	19.6464	1.04419
$355$	−2.00146	−0.106226
$356$	−3.22152	−0.170740
$357$	30.0094	1.58826
$358$	18.3849	0.971671
$359$	−23.6209	−1.24667	−0.623333	−	0.781956i	$-0.714222\pi$
$359$	−23.6209	−1.24667	−0.623333	+	0.781956i	$0.714222\pi$
$360$	18.4755	0.973746
$361$	0	0
$362$	−11.0421	−0.580360
$363$	−0.788939	−0.0414086
$364$	7.57290	0.396928
$365$	4.56262	0.238819
$366$	2.91142	0.152182
$367$	10.4211	0.543977	0.271988	−	0.962301i	$-0.412319\pi$
$367$	10.4211	0.543977	0.271988	+	0.962301i	$0.412319\pi$
$368$	−5.60005	−0.291923
$369$	−2.52897	−0.131653
$370$	1.24807	0.0648841
$371$	−0.969157	−0.0503161
$372$	3.94633	0.204608
$373$	−9.20454	−0.476593	−0.238297	−	0.971192i	$-0.576589\pi$
$373$	−9.20454	−0.476593	−0.238297	+	0.971192i	$0.576589\pi$
$374$	−11.2848	−0.583522
$375$	−3.01225	−0.155552
$376$	6.81650	0.351534
$377$	−25.4232	−1.30936
$378$	43.3381	2.22907
$379$	−12.6143	−0.647954	−0.323977	−	0.946065i	$-0.605020\pi$
$379$	−12.6143	−0.647954	−0.323977	+	0.946065i	$0.605020\pi$
$380$	0	0
$381$	59.8228	3.06482
$382$	12.2018	0.624298
$383$	−0.529736	−0.0270682	−0.0135341	−	0.999908i	$-0.504308\pi$
$383$	−0.529736	−0.0270682	−0.0135341	+	0.999908i	$0.504308\pi$
$384$	19.6396	1.00223
$385$	−12.4970	−0.636907
$386$	−25.4593	−1.29584
$387$	−43.8444	−2.22873
$388$	−3.03651	−0.154155
$389$	30.3866	1.54066	0.770331	−	0.637644i	$-0.220091\pi$
$389$	30.3866	1.54066	0.770331	+	0.637644i	$0.220091\pi$
$390$	−18.3306	−0.928204
$391$	−5.02153	−0.253950
$392$	20.8905	1.05513
$393$	−16.3359	−0.824040
$394$	11.6417	0.586503
$395$	12.0521	0.606405
$396$	8.56163	0.430238
$397$	−12.1258	−0.608577	−0.304288	−	0.952580i	$-0.598419\pi$
$397$	−12.1258	−0.608577	−0.304288	+	0.952580i	$0.598419\pi$
$398$	−22.8164	−1.14368
$399$	0	0
$400$	−2.98346	−0.149173
$401$	11.5906	0.578806	0.289403	−	0.957207i	$-0.406543\pi$
$401$	11.5906	0.578806	0.289403	+	0.957207i	$0.406543\pi$
$402$	−40.8066	−2.03525
$403$	−15.0996	−0.752164
$404$	−1.88679	−0.0938713
$405$	9.66841	0.480427
$406$	−24.5804	−1.21991
$407$	3.33214	0.165168
$408$	24.5133	1.21359
$409$	−4.83657	−0.239153	−0.119577	−	0.992825i	$-0.538154\pi$
$409$	−4.83657	−0.239153	−0.119577	+	0.992825i	$0.538154\pi$
$410$	0.523377	0.0258477
$411$	55.9118	2.75793
$412$	4.51323	0.222351
$413$	19.3228	0.950812
$414$	−14.3299	−0.704277
$415$	−13.5711	−0.666177
$416$	11.2982	0.553942
$417$	31.6669	1.55073
$418$	0	0
$419$	12.4329	0.607385	0.303693	−	0.952770i	$-0.401780\pi$
$419$	12.4329	0.607385	0.303693	+	0.952770i	$0.401780\pi$
$420$	4.71184	0.229914
$421$	−27.6160	−1.34592	−0.672961	−	0.739678i	$-0.734978\pi$
$421$	−27.6160	−1.34592	−0.672961	+	0.739678i	$0.734978\pi$
$422$	21.8484	1.06357
$423$	13.6103	0.661753
$424$	−0.791662	−0.0384465
$425$	−2.67526	−0.129769
$426$	−7.57809	−0.367159
$427$	2.86346	0.138573
$428$	0.579091	0.0279914
$429$	−48.9396	−2.36282
$430$	9.07371	0.437573
$431$	−7.09165	−0.341593	−0.170796	−	0.985306i	$-0.554634\pi$
$431$	−7.09165	−0.341593	−0.170796	+	0.985306i	$0.554634\pi$
$432$	27.6228	1.32900
$433$	6.58386	0.316400	0.158200	−	0.987407i	$-0.449431\pi$
$433$	6.58386	0.316400	0.158200	+	0.987407i	$0.449431\pi$
$434$	−14.5991	−0.700777
$435$	−15.8183	−0.758428
$436$	3.98995	0.191084
$437$	0	0
$438$	17.2754	0.825450
$439$	−4.42825	−0.211349	−0.105674	−	0.994401i	$-0.533700\pi$
$439$	−4.42825	−0.211349	−0.105674	+	0.994401i	$0.533700\pi$
$440$	−10.2083	−0.486660
$441$	41.7113	1.98625
$442$	−16.2798	−0.774352
$443$	−2.77214	−0.131708	−0.0658541	−	0.997829i	$-0.520977\pi$
$443$	−2.77214	−0.131708	−0.0658541	+	0.997829i	$0.520977\pi$
$444$	−1.25634	−0.0596234
$445$	7.66941	0.363565
$446$	−10.9691	−0.519403
$447$	−45.6083	−2.15720
$448$	33.1441	1.56591
$449$	−26.3569	−1.24386	−0.621930	−	0.783073i	$-0.713651\pi$
$449$	−26.3569	−1.24386	−0.621930	+	0.783073i	$0.713651\pi$
$450$	−7.63436	−0.359887
$451$	1.39733	0.0657977
$452$	−7.15916	−0.336739
$453$	34.1685	1.60538
$454$	−25.2842	−1.18665
$455$	−18.0286	−0.845195
$456$	0	0
$457$	33.5784	1.57073	0.785366	−	0.619032i	$-0.212475\pi$
$457$	33.5784	1.57073	0.785366	+	0.619032i	$0.212475\pi$
$458$	26.1964	1.22408
$459$	24.7693	1.15613
$460$	−0.788443	−0.0367614
$461$	30.4525	1.41831	0.709156	−	0.705051i	$-0.249076\pi$
$461$	30.4525	1.41831	0.709156	+	0.705051i	$0.249076\pi$
$462$	−47.3172	−2.20140
$463$	−28.5762	−1.32805	−0.664025	−	0.747710i	$-0.731153\pi$
$463$	−28.5762	−1.32805	−0.664025	+	0.747710i	$0.731153\pi$
$464$	−15.6671	−0.727326
$465$	−9.39494	−0.435680
$466$	−0.683851	−0.0316788
$467$	−11.2173	−0.519073	−0.259536	−	0.965733i	$-0.583570\pi$
$467$	−11.2173	−0.519073	−0.259536	+	0.965733i	$0.583570\pi$
$468$	12.3513	0.570939
$469$	−40.1344	−1.85323
$470$	−2.81668	−0.129924
$471$	12.6975	0.585070
$472$	15.7839	0.726515
$473$	24.2253	1.11388
$474$	45.6325	2.09597
$475$	0	0
$476$	4.18470	0.191806
$477$	−1.58068	−0.0723745
$478$	27.9340	1.27767
$479$	−17.3905	−0.794594	−0.397297	−	0.917690i	$-0.630052\pi$
$479$	−17.3905	−0.794594	−0.397297	+	0.917690i	$0.630052\pi$
$480$	7.02975	0.320863
$481$	4.80706	0.219183
$482$	27.3182	1.24431
$483$	−21.0554	−0.958052
$484$	−0.110015	−0.00500068
$485$	7.22894	0.328249
$486$	1.69404	0.0768430
$487$	−15.3473	−0.695451	−0.347726	−	0.937596i	$-0.613046\pi$
$487$	−15.3473	−0.695451	−0.347726	+	0.937596i	$0.613046\pi$
$488$	2.33904	0.105883
$489$	41.8872	1.89420
$490$	−8.63226	−0.389966
$491$	8.35401	0.377011	0.188506	−	0.982072i	$-0.439636\pi$
$491$	8.35401	0.377011	0.188506	+	0.982072i	$0.439636\pi$
$492$	−0.526846	−0.0237520
$493$	−14.0486	−0.632717
$494$	0	0
$495$	−20.3825	−0.916124
$496$	−9.30515	−0.417813
$497$	−7.45326	−0.334324
$498$	−51.3839	−2.30257
$499$	0.270833	0.0121241	0.00606207	−	0.999982i	$-0.498070\pi$
$499$	0.270833	0.0121241	0.00606207	+	0.999982i	$0.498070\pi$
$500$	−0.420048	−0.0187851
$501$	53.0826	2.37156
$502$	−22.4040	−0.999939
$503$	41.5995	1.85483	0.927415	−	0.374034i	$-0.122026\pi$
$503$	41.5995	1.85483	0.927415	+	0.374034i	$0.122026\pi$
$504$	68.8013	3.06466
$505$	4.49184	0.199884
$506$	7.91770	0.351985
$507$	−31.4427	−1.39642
$508$	8.34209	0.370120
$509$	−1.62776	−0.0721493	−0.0360747	−	0.999349i	$-0.511485\pi$
$509$	−1.62776	−0.0721493	−0.0360747	+	0.999349i	$0.511485\pi$
$510$	−10.1293	−0.448532
$511$	16.9908	0.751630
$512$	25.1134	1.10987
$513$	0	0
$514$	19.7643	0.871766
$515$	−10.7445	−0.473461
$516$	−9.13385	−0.402095
$517$	−7.52006	−0.330732
$518$	4.64771	0.204209
$519$	−40.1178	−1.76098
$520$	−14.7268	−0.645813
$521$	9.14124	0.400485	0.200243	−	0.979746i	$-0.435827\pi$
$521$	9.14124	0.400485	0.200243	+	0.979746i	$0.435827\pi$
$522$	−40.0904	−1.75471
$523$	−37.2995	−1.63099	−0.815497	−	0.578762i	$-0.803536\pi$
$523$	−37.2995	−1.63099	−0.815497	+	0.578762i	$0.803536\pi$
$524$	−2.27799	−0.0995146
$525$	−11.2174	−0.489567
$526$	38.2750	1.66887
$527$	−8.34388	−0.363465
$528$	−30.1591	−1.31251
$529$	−19.4768	−0.846816
$530$	0.327127	0.0142095
$531$	31.5152	1.36764
$532$	0	0
$533$	2.01584	0.0873156
$534$	29.0386	1.25662
$535$	−1.37863	−0.0596034
$536$	−32.7841	−1.41606
$537$	44.0585	1.90127
$538$	3.28308	0.141544
$539$	−23.0467	−0.992692
$540$	3.88908	0.167359
$541$	−36.2441	−1.55826	−0.779128	−	0.626864i	$-0.784338\pi$
$541$	−36.2441	−1.55826	−0.779128	+	0.626864i	$0.784338\pi$
$542$	12.0772	0.518759
$543$	−26.4619	−1.13559
$544$	6.24329	0.267679
$545$	−9.49878	−0.406883
$546$	−68.2615	−2.92132
$547$	15.1033	0.645772	0.322886	−	0.946438i	$-0.395347\pi$
$547$	15.1033	0.645772	0.322886	+	0.946438i	$0.395347\pi$
$548$	7.79671	0.333059
$549$	4.67027	0.199322
$550$	4.21821	0.179865
$551$	0	0
$552$	−17.1992	−0.732047
$553$	44.8809	1.90853
$554$	−25.2236	−1.07165
$555$	2.99095	0.126959
$556$	4.41584	0.187273
$557$	−9.36275	−0.396712	−0.198356	−	0.980130i	$-0.563560\pi$
$557$	−9.36275	−0.396712	−0.198356	+	0.980130i	$0.563560\pi$
$558$	−23.8109	−1.00799
$559$	34.9483	1.47815
$560$	−11.1102	−0.469490
$561$	−27.0435	−1.14178
$562$	33.3793	1.40802
$563$	14.4454	0.608802	0.304401	−	0.952544i	$-0.401544\pi$
$563$	14.4454	0.608802	0.304401	+	0.952544i	$0.401544\pi$
$564$	2.83535	0.119390
$565$	17.0436	0.717032
$566$	21.0903	0.886492
$567$	36.0044	1.51204
$568$	−6.08825	−0.255457
$569$	37.8642	1.58735	0.793675	−	0.608342i	$-0.208165\pi$
$569$	37.8642	1.58735	0.793675	+	0.608342i	$0.208165\pi$
$570$	0	0
$571$	−18.5203	−0.775048	−0.387524	−	0.921860i	$-0.626670\pi$
$571$	−18.5203	−0.775048	−0.387524	+	0.921860i	$0.626670\pi$
$572$	−6.82446	−0.285345
$573$	29.2411	1.22156
$574$	1.94901	0.0813502
$575$	1.87703	0.0782775
$576$	54.0575	2.25240
$577$	−9.08095	−0.378045	−0.189022	−	0.981973i	$-0.560532\pi$
$577$	−9.08095	−0.378045	−0.189022	+	0.981973i	$0.560532\pi$
$578$	12.3723	0.514619
$579$	−61.0121	−2.53558
$580$	−2.20580	−0.0915910
$581$	−50.5375	−2.09665
$582$	27.3708	1.13456
$583$	0.873373	0.0361714
$584$	13.8791	0.574320
$585$	−29.4045	−1.21573
$586$	16.8166	0.694688
$587$	−23.0373	−0.950852	−0.475426	−	0.879756i	$-0.657706\pi$
$587$	−23.0373	−0.950852	−0.475426	+	0.879756i	$0.657706\pi$
$588$	8.68948	0.358348
$589$	0	0
$590$	−6.52216	−0.268513
$591$	27.8989	1.14761
$592$	2.96236	0.121752
$593$	40.2431	1.65259	0.826294	−	0.563239i	$-0.190445\pi$
$593$	40.2431	1.65259	0.826294	+	0.563239i	$0.190445\pi$
$594$	−39.0549	−1.60244
$595$	−9.96243	−0.408420
$596$	−6.35992	−0.260512
$597$	−54.6786	−2.23784
$598$	11.4224	0.467095
$599$	37.7691	1.54320	0.771602	−	0.636106i	$-0.219456\pi$
$599$	37.7691	1.54320	0.771602	+	0.636106i	$0.219456\pi$
$600$	−9.16299	−0.374078
$601$	−43.8389	−1.78823	−0.894113	−	0.447841i	$-0.852193\pi$
$601$	−43.8389	−1.78823	−0.894113	+	0.447841i	$0.852193\pi$
$602$	33.7898	1.37717
$603$	−65.4587	−2.66568
$604$	4.76469	0.193872
$605$	0.261910	0.0106482
$606$	17.0074	0.690877
$607$	7.80810	0.316921	0.158461	−	0.987365i	$-0.449347\pi$
$607$	7.80810	0.316921	0.158461	+	0.987365i	$0.449347\pi$
$608$	0	0
$609$	−58.9059	−2.38699
$610$	−0.966525	−0.0391335
$611$	−10.8487	−0.438892
$612$	6.82520	0.275892
$613$	−38.8957	−1.57098	−0.785491	−	0.618873i	$-0.787590\pi$
$613$	−38.8957	−1.57098	−0.785491	+	0.618873i	$0.787590\pi$
$614$	35.1601	1.41895
$615$	1.25425	0.0505762
$616$	−38.0147	−1.53166
$617$	12.4615	0.501681	0.250841	−	0.968028i	$-0.419293\pi$
$617$	12.4615	0.501681	0.250841	+	0.968028i	$0.419293\pi$
$618$	−40.6819	−1.63646
$619$	−2.75741	−0.110830	−0.0554148	−	0.998463i	$-0.517648\pi$
$619$	−2.75741	−0.110830	−0.0554148	+	0.998463i	$0.517648\pi$
$620$	−1.31009	−0.0526146
$621$	−17.3788	−0.697386
$622$	−31.2167	−1.25167
$623$	28.5602	1.14424
$624$	−43.5085	−1.74174
$625$	1.00000	0.0400000
$626$	27.9958	1.11894
$627$	0	0
$628$	1.77062	0.0706555
$629$	2.65633	0.105915
$630$	−28.4297	−1.13267
$631$	−39.9220	−1.58927	−0.794636	−	0.607087i	$-0.792338\pi$
$631$	−39.9220	−1.58927	−0.794636	+	0.607087i	$0.792338\pi$
$632$	36.6612	1.45831
$633$	52.3588	2.08108
$634$	−17.6926	−0.702661
$635$	−19.8598	−0.788113
$636$	−0.329295	−0.0130574
$637$	−33.2480	−1.31733
$638$	22.1511	0.876970
$639$	−12.1562	−0.480891
$640$	−6.51992	−0.257722
$641$	5.01268	0.197989	0.0989945	−	0.995088i	$-0.468437\pi$
$641$	5.01268	0.197989	0.0989945	+	0.995088i	$0.468437\pi$
$642$	−5.21989	−0.206012
$643$	49.9753	1.97083	0.985417	−	0.170157i	$-0.0544275\pi$
$643$	49.9753	1.97083	0.985417	+	0.170157i	$0.0544275\pi$
$644$	−2.93610	−0.115698
$645$	21.7447	0.856199
$646$	0	0
$647$	32.7681	1.28825	0.644123	−	0.764922i	$-0.277223\pi$
$647$	32.7681	1.28825	0.644123	+	0.764922i	$0.277223\pi$
$648$	29.4104	1.15535
$649$	−17.4131	−0.683523
$650$	6.08534	0.238686
$651$	−34.9860	−1.37121
$652$	5.84102	0.228752
$653$	15.7996	0.618284	0.309142	−	0.951016i	$-0.399958\pi$
$653$	15.7996	0.618284	0.309142	+	0.951016i	$0.399958\pi$
$654$	−35.9651	−1.40635
$655$	5.42317	0.211901
$656$	1.24226	0.0485022
$657$	27.7118	1.08114
$658$	−10.4891	−0.408907
$659$	13.5485	0.527773	0.263887	−	0.964554i	$-0.414996\pi$
$659$	13.5485	0.527773	0.263887	+	0.964554i	$0.414996\pi$
$660$	−4.24616	−0.165282
$661$	−3.65778	−0.142271	−0.0711355	−	0.997467i	$-0.522662\pi$
$661$	−3.65778	−0.142271	−0.0711355	+	0.997467i	$0.522662\pi$
$662$	−6.64365	−0.258213
$663$	−39.0139	−1.51517
$664$	−41.2819	−1.60205
$665$	0	0
$666$	7.58036	0.293733
$667$	9.85686	0.381659
$668$	7.40219	0.286399
$669$	−26.2870	−1.01631
$670$	13.5469	0.523361
$671$	−2.58046	−0.0996176
$672$	26.1782	1.00985
$673$	26.9303	1.03809	0.519043	−	0.854748i	$-0.326288\pi$
$673$	26.9303	1.03809	0.519043	+	0.854748i	$0.326288\pi$
$674$	30.0264	1.15657
$675$	−9.25865	−0.356366
$676$	−4.38457	−0.168637
$677$	−20.6933	−0.795308	−0.397654	−	0.917535i	$-0.630176\pi$
$677$	−20.6933	−0.795308	−0.397654	+	0.917535i	$0.630176\pi$
$678$	64.5321	2.47834
$679$	26.9200	1.03309
$680$	−8.13788	−0.312073
$681$	−60.5926	−2.32191
$682$	13.1562	0.503777
$683$	−26.9573	−1.03149	−0.515745	−	0.856742i	$-0.672485\pi$
$683$	−26.9573	−1.03149	−0.515745	+	0.856742i	$0.672485\pi$
$684$	0	0
$685$	−18.5615	−0.709197
$686$	0.619899	0.0236679
$687$	62.7785	2.39515
$688$	21.5369	0.821087
$689$	1.25996	0.0480006
$690$	7.10697	0.270558
$691$	8.70043	0.330980	0.165490	−	0.986211i	$-0.447079\pi$
$691$	8.70043	0.330980	0.165490	+	0.986211i	$0.447079\pi$
$692$	−5.59429	−0.212663
$693$	−75.9027	−2.88330
$694$	11.0198	0.418307
$695$	−10.5127	−0.398769
$696$	−48.1177	−1.82390
$697$	1.11393	0.0421931
$698$	−2.56434	−0.0970616
$699$	−1.63882	−0.0619858
$700$	−1.56423	−0.0591222
$701$	−0.403070	−0.0152237	−0.00761187	−	0.999971i	$-0.502423\pi$
$701$	−0.403070	−0.0152237	−0.00761187	+	0.999971i	$0.502423\pi$
$702$	−56.3420	−2.12649
$703$	0	0
$704$	−29.8684	−1.12571
$705$	−6.75005	−0.254221
$706$	−11.3937	−0.428808
$707$	16.7272	0.629092
$708$	6.56538	0.246742
$709$	40.0543	1.50427	0.752135	−	0.659010i	$-0.229024\pi$
$709$	40.0543	1.50427	0.752135	+	0.659010i	$0.229024\pi$
$710$	2.51575	0.0944146
$711$	73.2002	2.74522
$712$	23.3296	0.874315
$713$	5.85428	0.219245
$714$	−37.7206	−1.41166
$715$	16.2468	0.607597
$716$	6.14382	0.229605
$717$	66.9427	2.50002
$718$	29.6906	1.10804
$719$	18.0756	0.674108	0.337054	−	0.941485i	$-0.390570\pi$
$719$	18.0756	0.674108	0.337054	+	0.941485i	$0.390570\pi$
$720$	−18.1205	−0.675313
$721$	−40.0118	−1.49012
$722$	0	0
$723$	65.4670	2.43474
$724$	−3.69002	−0.137139
$725$	5.25131	0.195029
$726$	0.991666	0.0368042
$727$	26.3614	0.977689	0.488844	−	0.872371i	$-0.337419\pi$
$727$	26.3614	0.977689	0.488844	+	0.872371i	$0.337419\pi$
$728$	−54.8414	−2.03256
$729$	−24.9455	−0.923909
$730$	−5.73504	−0.212263
$731$	19.3120	0.714282
$732$	0.972931	0.0359606
$733$	−3.30919	−0.122228	−0.0611139	−	0.998131i	$-0.519465\pi$
$733$	−3.30919	−0.122228	−0.0611139	+	0.998131i	$0.519465\pi$
$734$	−13.0989	−0.483490
$735$	−20.6868	−0.763046
$736$	−4.38046	−0.161466
$737$	36.1678	1.33226
$738$	3.17882	0.117014
$739$	17.6943	0.650894	0.325447	−	0.945560i	$-0.394485\pi$
$739$	17.6943	0.650894	0.325447	+	0.945560i	$0.394485\pi$
$740$	0.417077	0.0153321
$741$	0	0
$742$	1.21819	0.0447212
$743$	−37.2532	−1.36669	−0.683343	−	0.730097i	$-0.739475\pi$
$743$	−37.2532	−1.36669	−0.683343	+	0.730097i	$0.739475\pi$
$744$	−28.5785	−1.04774
$745$	15.1409	0.554720
$746$	11.5698	0.423599
$747$	−82.4261	−3.01581
$748$	−3.77112	−0.137886
$749$	−5.13391	−0.187589
$750$	3.78628	0.138256
$751$	13.5647	0.494982	0.247491	−	0.968890i	$-0.420394\pi$
$751$	13.5647	0.494982	0.247491	+	0.968890i	$0.420394\pi$
$752$	−6.68553	−0.243796
$753$	−53.6902	−1.95658
$754$	31.9560	1.16377
$755$	−11.3432	−0.412821
$756$	14.4826	0.526728
$757$	12.5370	0.455665	0.227833	−	0.973700i	$-0.426836\pi$
$757$	12.5370	0.455665	0.227833	+	0.973700i	$0.426836\pi$
$758$	15.8557	0.575905
$759$	18.9744	0.688728
$760$	0	0
$761$	−27.2282	−0.987022	−0.493511	−	0.869740i	$-0.664287\pi$
$761$	−27.2282	−0.987022	−0.493511	+	0.869740i	$0.664287\pi$
$762$	−75.1950	−2.72403
$763$	−35.3727	−1.28058
$764$	4.07757	0.147521
$765$	−16.2486	−0.587470
$766$	0.665858	0.0240584
$767$	−25.1207	−0.907056
$768$	28.9337	1.04406
$769$	−0.920184	−0.0331827	−0.0165913	−	0.999862i	$-0.505281\pi$
$769$	−0.920184	−0.0331827	−0.0165913	+	0.999862i	$0.505281\pi$
$770$	15.7083	0.566086
$771$	47.3643	1.70578
$772$	−8.50793	−0.306207
$773$	1.82987	0.0658157	0.0329079	−	0.999458i	$-0.489523\pi$
$773$	1.82987	0.0658157	0.0329079	+	0.999458i	$0.489523\pi$
$774$	55.1107	1.98091
$775$	3.11891	0.112035
$776$	21.9898	0.789387
$777$	11.1380	0.399575
$778$	−38.1948	−1.36935
$779$	0	0
$780$	−6.12567	−0.219334
$781$	6.71664	0.240340
$782$	6.31187	0.225712
$783$	−48.6200	−1.73754
$784$	−20.4891	−0.731754
$785$	−4.21528	−0.150450
$786$	20.5337	0.732411
$787$	2.90489	0.103548	0.0517740	−	0.998659i	$-0.483512\pi$
$787$	2.90489	0.103548	0.0517740	+	0.998659i	$0.483512\pi$
$788$	3.89041	0.138590
$789$	91.7243	3.26547
$790$	−15.1490	−0.538976
$791$	63.4692	2.25670
$792$	−62.0016	−2.20313
$793$	−3.72266	−0.132196
$794$	15.2417	0.540907
$795$	0.783944	0.0278036
$796$	−7.62474	−0.270252
$797$	−19.9042	−0.705044	−0.352522	−	0.935804i	$-0.614676\pi$
$797$	−19.9042	−0.705044	−0.352522	+	0.935804i	$0.614676\pi$
$798$	0	0
$799$	−5.99488	−0.212084
$800$	−2.33372	−0.0825094
$801$	46.5814	1.64587
$802$	−14.5689	−0.514447
$803$	−15.3116	−0.540335
$804$	−13.6366	−0.480927
$805$	6.98990	0.246362
$806$	18.9796	0.668528
$807$	7.86775	0.276958
$808$	13.6638	0.480689
$809$	44.4186	1.56168	0.780838	−	0.624734i	$-0.214792\pi$
$809$	44.4186	1.56168	0.780838	+	0.624734i	$0.214792\pi$
$810$	−12.1528	−0.427006
$811$	−34.0494	−1.19564	−0.597819	−	0.801631i	$-0.703966\pi$
$811$	−34.0494	−1.19564	−0.597819	+	0.801631i	$0.703966\pi$
$812$	−8.21423	−0.288263
$813$	28.9424	1.01505
$814$	−4.18837	−0.146802
$815$	−13.9056	−0.487092
$816$	−24.0424	−0.841651
$817$	0	0
$818$	6.07938	0.212561
$819$	−109.500	−3.82623
$820$	0.174901	0.00610781
$821$	−26.8065	−0.935553	−0.467776	−	0.883847i	$-0.654945\pi$
$821$	−26.8065	−0.935553	−0.467776	+	0.883847i	$0.654945\pi$
$822$	−70.2790	−2.45126
$823$	11.0407	0.384853	0.192426	−	0.981311i	$-0.438364\pi$
$823$	11.0407	0.384853	0.192426	+	0.981311i	$0.438364\pi$
$824$	−32.6839	−1.13860
$825$	10.1087	0.351941
$826$	−24.2880	−0.845087
$827$	−11.8987	−0.413757	−0.206878	−	0.978367i	$-0.566330\pi$
$827$	−11.8987	−0.413757	−0.206878	+	0.978367i	$0.566330\pi$
$828$	−4.78874	−0.166420
$829$	−11.2194	−0.389665	−0.194832	−	0.980837i	$-0.562416\pi$
$829$	−11.2194	−0.389665	−0.194832	+	0.980837i	$0.562416\pi$
$830$	17.0583	0.592102
$831$	−60.4474	−2.09690
$832$	−43.0892	−1.49385
$833$	−18.3725	−0.636569
$834$	−39.8040	−1.37830
$835$	−17.6222	−0.609842
$836$	0	0
$837$	−28.8769	−0.998132
$838$	−15.6276	−0.539848
$839$	35.8294	1.23697	0.618484	−	0.785797i	$-0.287747\pi$
$839$	35.8294	1.23697	0.618484	+	0.785797i	$0.287747\pi$
$840$	−34.1222	−1.17733
$841$	−1.42378	−0.0490959
$842$	34.7123	1.19626
$843$	79.9921	2.75507
$844$	7.30126	0.251320
$845$	10.4383	0.359087
$846$	−17.1076	−0.588170
$847$	0.975332	0.0335128
$848$	0.776452	0.0266635
$849$	50.5420	1.73460
$850$	3.36269	0.115339
$851$	−1.86375	−0.0638886
$852$	−2.53243	−0.0867595
$853$	13.0632	0.447276	0.223638	−	0.974672i	$-0.428207\pi$
$853$	13.0632	0.447276	0.223638	+	0.974672i	$0.428207\pi$
$854$	−3.59926	−0.123164
$855$	0	0
$856$	−4.19366	−0.143337
$857$	24.1902	0.826323	0.413161	−	0.910658i	$-0.364425\pi$
$857$	24.1902	0.826323	0.413161	+	0.910658i	$0.364425\pi$
$858$	61.5151	2.10009
$859$	54.1525	1.84766	0.923830	−	0.382804i	$-0.125041\pi$
$859$	54.1525	1.84766	0.923830	+	0.382804i	$0.125041\pi$
$860$	3.03223	0.103398
$861$	4.67072	0.159178
$862$	8.91393	0.303610
$863$	−49.6852	−1.69131	−0.845653	−	0.533733i	$-0.820789\pi$
$863$	−49.6852	−1.69131	−0.845653	+	0.533733i	$0.820789\pi$
$864$	21.6071	0.735088
$865$	13.3182	0.452833
$866$	−8.27566	−0.281218
$867$	29.6496	1.00695
$868$	−4.87868	−0.165593
$869$	−40.4452	−1.37201
$870$	19.8829	0.674095
$871$	52.1770	1.76795
$872$	−28.8944	−0.978488
$873$	43.9062	1.48600
$874$	0	0
$875$	3.72392	0.125891
$876$	5.77305	0.195053
$877$	8.27138	0.279305	0.139652	−	0.990201i	$-0.455402\pi$
$877$	8.27138	0.279305	0.139652	+	0.990201i	$0.455402\pi$
$878$	5.56614	0.187848
$879$	40.3003	1.35929
$880$	10.0121	0.337509
$881$	−24.5193	−0.826075	−0.413037	−	0.910714i	$-0.635532\pi$
$881$	−24.5193	−0.826075	−0.413037	+	0.910714i	$0.635532\pi$
$882$	−52.4295	−1.76539
$883$	49.1833	1.65515	0.827575	−	0.561355i	$-0.189720\pi$
$883$	49.1833	1.65515	0.827575	+	0.561355i	$0.189720\pi$
$884$	−5.44036	−0.182979
$885$	−15.6301	−0.525399
$886$	3.48447	0.117063
$887$	−21.6466	−0.726821	−0.363411	−	0.931629i	$-0.618388\pi$
$887$	−21.6466	−0.726821	−0.363411	+	0.931629i	$0.618388\pi$
$888$	9.09818	0.305315
$889$	−73.9564	−2.48042
$890$	−9.64015	−0.323139
$891$	−32.4460	−1.08698
$892$	−3.66564	−0.122735
$893$	0	0
$894$	57.3278	1.91733
$895$	−14.6264	−0.488908
$896$	−24.2796	−0.811126
$897$	27.3732	0.913964
$898$	33.1296	1.10555
$899$	16.3783	0.546248
$900$	−2.55123	−0.0850411
$901$	0.696240	0.0231951
$902$	−1.75639	−0.0584813
$903$	80.9757	2.69470
$904$	51.8452	1.72435
$905$	8.78476	0.292015
$906$	−42.9485	−1.42687
$907$	−13.4933	−0.448039	−0.224020	−	0.974585i	$-0.571918\pi$
$907$	−13.4933	−0.448039	−0.224020	+	0.974585i	$0.571918\pi$
$908$	−8.44943	−0.280404
$909$	27.2819	0.904884
$910$	22.6613	0.751214
$911$	−16.2069	−0.536958	−0.268479	−	0.963286i	$-0.586521\pi$
$911$	−16.2069	−0.536958	−0.268479	+	0.963286i	$0.586521\pi$
$912$	0	0
$913$	45.5428	1.50725
$914$	−42.2068	−1.39608
$915$	−2.31623	−0.0765724
$916$	8.75424	0.289248
$917$	20.1954	0.666912
$918$	−31.1340	−1.02758
$919$	19.7373	0.651075	0.325537	−	0.945529i	$-0.394455\pi$
$919$	19.7373	0.651075	0.325537	+	0.945529i	$0.394455\pi$
$920$	5.70975	0.188245
$921$	84.2596	2.77645
$922$	−38.2776	−1.26060
$923$	9.68967	0.318939
$924$	−15.8124	−0.520189
$925$	−0.992927	−0.0326472
$926$	35.9192	1.18038
$927$	−65.2587	−2.14338
$928$	−12.2551	−0.402292
$929$	6.48784	0.212859	0.106430	−	0.994320i	$-0.466058\pi$
$929$	6.48784	0.212859	0.106430	+	0.994320i	$0.466058\pi$
$930$	11.8091	0.387235
$931$	0	0
$932$	−0.228528	−0.00748568
$933$	−74.8094	−2.44915
$934$	14.0997	0.461355
$935$	8.97783	0.293606
$936$	−89.4457	−2.92362
$937$	−7.40129	−0.241790	−0.120895	−	0.992665i	$-0.538576\pi$
$937$	−7.40129	−0.241790	−0.120895	+	0.992665i	$0.538576\pi$
$938$	50.4474	1.64717
$939$	67.0908	2.18943
$940$	−0.941271	−0.0307009
$941$	−53.1005	−1.73103	−0.865513	−	0.500887i	$-0.833007\pi$
$941$	−53.1005	−1.73103	−0.865513	+	0.500887i	$0.833007\pi$
$942$	−15.9603	−0.520013
$943$	−0.781563	−0.0254512
$944$	−15.4807	−0.503853
$945$	−34.4785	−1.12158
$946$	−30.4503	−0.990023
$947$	15.2771	0.496438	0.248219	−	0.968704i	$-0.420155\pi$
$947$	15.2771	0.496438	0.248219	+	0.968704i	$0.420155\pi$
$948$	15.2494	0.495277
$949$	−22.0891	−0.717041
$950$	0	0
$951$	−42.3994	−1.37490
$952$	−30.3048	−0.982184
$953$	16.9121	0.547836	0.273918	−	0.961753i	$-0.411680\pi$
$953$	16.9121	0.547836	0.273918	+	0.961753i	$0.411680\pi$
$954$	1.98686	0.0643269
$955$	−9.70737	−0.314123
$956$	9.33494	0.301913
$957$	53.0841	1.71597
$958$	21.8592	0.706240
$959$	−69.1214	−2.23205
$960$	−26.8100	−0.865289
$961$	−21.2724	−0.686207
$962$	−6.04229	−0.194811
$963$	−8.37334	−0.269827
$964$	9.12915	0.294030
$965$	20.2546	0.652020
$966$	26.4658	0.851522
$967$	14.5256	0.467110	0.233555	−	0.972344i	$-0.424964\pi$
$967$	14.5256	0.467110	0.233555	+	0.972344i	$0.424964\pi$
$968$	0.796706	0.0256071
$969$	0	0
$970$	−9.08650	−0.291750
$971$	−30.6047	−0.982151	−0.491076	−	0.871117i	$-0.663396\pi$
$971$	−30.6047	−0.982151	−0.491076	+	0.871117i	$0.663396\pi$
$972$	0.566109	0.0181580
$973$	−39.1484	−1.25504
$974$	19.2909	0.618121
$975$	14.5832	0.467037
$976$	−2.29410	−0.0734323
$977$	44.0014	1.40773	0.703865	−	0.710333i	$-0.251456\pi$
$977$	44.0014	1.40773	0.703865	+	0.710333i	$0.251456\pi$
$978$	−52.6505	−1.68358
$979$	−25.7376	−0.822577
$980$	−2.88471	−0.0921487
$981$	−57.6924	−1.84198
$982$	−10.5007	−0.335090
$983$	−35.3620	−1.12787	−0.563936	−	0.825819i	$-0.690714\pi$
$983$	−35.3620	−1.12787	−0.563936	+	0.825819i	$0.690714\pi$
$984$	3.81531	0.121628
$985$	−9.26182	−0.295106
$986$	17.6585	0.562362
$987$	−25.1366	−0.800108
$988$	0	0
$989$	−13.5498	−0.430860
$990$	25.6200	0.814256
$991$	−32.1513	−1.02132	−0.510660	−	0.859783i	$-0.670599\pi$
$991$	−32.1513	−1.02132	−0.510660	+	0.859783i	$0.670599\pi$
$992$	−7.27865	−0.231097
$993$	−15.9212	−0.505245
$994$	9.36846	0.297150
$995$	18.1521	0.575459
$996$	−17.1714	−0.544095
$997$	−8.31350	−0.263291	−0.131646	−	0.991297i	$-0.542026\pi$
$997$	−8.31350	−0.263291	−0.131646	+	0.991297i	$0.542026\pi$
$998$	−0.340427	−0.0107760
$999$	9.19316	0.290859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.4		9
5.4	even	2		9025.2.a.cf.1.6		9
19.2	odd	18		95.2.k.a.61.2	✓	18
19.10	odd	18		95.2.k.a.81.2	yes	18
19.18	odd	2		1805.2.a.v.1.6		9
57.2	even	18		855.2.bs.c.631.2		18
57.29	even	18		855.2.bs.c.271.2		18
95.2	even	36		475.2.u.b.99.5		36
95.29	odd	18		475.2.l.c.176.2		18
95.48	even	36		475.2.u.b.24.5		36
95.59	odd	18		475.2.l.c.251.2		18
95.67	even	36		475.2.u.b.24.2		36
95.78	even	36		475.2.u.b.99.2		36
95.94	odd	2		9025.2.a.cc.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.2	✓	18	19.2	odd	18
95.2.k.a.81.2	yes	18	19.10	odd	18
475.2.l.c.176.2		18	95.29	odd	18
475.2.l.c.251.2		18	95.59	odd	18
475.2.u.b.24.2		36	95.67	even	36
475.2.u.b.24.5		36	95.48	even	36
475.2.u.b.99.2		36	95.78	even	36
475.2.u.b.99.5		36	95.2	even	36
855.2.bs.c.271.2		18	57.29	even	18
855.2.bs.c.631.2		18	57.2	even	18
1805.2.a.s.1.4		9	1.1	even	1	trivial
1805.2.a.v.1.6		9	19.18	odd	2
9025.2.a.cc.1.4		9	95.94	odd	2
9025.2.a.cf.1.6		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)

\(f(q)\)	\(=\)	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +1.00000 q^{5} +3.78628 q^{6} +3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} +O(q^{10})\)	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +1.00000 q^{5} +3.78628 q^{6} +3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} -1.25696 q^{10} -3.35588 q^{11} +1.26529 q^{12} -4.84131 q^{13} -4.68082 q^{14} -3.01225 q^{15} -2.98346 q^{16} -2.67526 q^{17} -7.63436 q^{18} -0.420048 q^{20} -11.2174 q^{21} +4.21821 q^{22} +1.87703 q^{23} -9.16299 q^{24} +1.00000 q^{25} +6.08534 q^{26} -9.25865 q^{27} -1.56423 q^{28} +5.25131 q^{29} +3.78628 q^{30} +3.11891 q^{31} -2.33372 q^{32} +10.1087 q^{33} +3.36269 q^{34} +3.72392 q^{35} -2.55123 q^{36} -0.992927 q^{37} +14.5832 q^{39} +3.04191 q^{40} -0.416383 q^{41} +14.0998 q^{42} -7.21877 q^{43} +1.40963 q^{44} +6.07366 q^{45} -2.35935 q^{46} +2.24086 q^{47} +8.98694 q^{48} +6.86757 q^{49} -1.25696 q^{50} +8.05854 q^{51} +2.03358 q^{52} -0.260252 q^{53} +11.6378 q^{54} -3.35588 q^{55} +11.3278 q^{56} -6.60069 q^{58} +5.18883 q^{59} +1.26529 q^{60} +0.768938 q^{61} -3.92035 q^{62} +22.6178 q^{63} +8.90032 q^{64} -4.84131 q^{65} -12.7063 q^{66} -10.7775 q^{67} +1.12374 q^{68} -5.65409 q^{69} -4.68082 q^{70} -2.00146 q^{71} +18.4755 q^{72} +4.56262 q^{73} +1.24807 q^{74} -3.01225 q^{75} -12.4970 q^{77} -18.3306 q^{78} +12.0521 q^{79} -2.98346 q^{80} +9.66841 q^{81} +0.523377 q^{82} -13.5711 q^{83} +4.71184 q^{84} -2.67526 q^{85} +9.07371 q^{86} -15.8183 q^{87} -10.2083 q^{88} +7.66941 q^{89} -7.63436 q^{90} -18.0286 q^{91} -0.788443 q^{92} -9.39494 q^{93} -2.81668 q^{94} +7.02975 q^{96} +7.22894 q^{97} -8.63226 q^{98} -20.3825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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