LMFDB - Embedded newform 722.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.17557$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52015 q^{3} +1.00000 q^{4} -2.45965 q^{5} -2.52015 q^{6} -2.79360 q^{7} +1.00000 q^{8} +3.35114 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52015 q^{3} +1.00000 q^{4} -2.45965 q^{5} -2.52015 q^{6} -2.79360 q^{7} +1.00000 q^{8} +3.35114 q^{9} -2.45965 q^{10} -1.67853 q^{11} -2.52015 q^{12} +6.34458 q^{13} -2.79360 q^{14} +6.19868 q^{15} +1.00000 q^{16} +4.96917 q^{17} +3.35114 q^{18} -2.45965 q^{20} +7.04029 q^{21} -1.67853 q^{22} -2.49890 q^{23} -2.52015 q^{24} +1.04988 q^{25} +6.34458 q^{26} -0.884927 q^{27} -2.79360 q^{28} +5.93179 q^{29} +6.19868 q^{30} +7.28408 q^{31} +1.00000 q^{32} +4.23015 q^{33} +4.96917 q^{34} +6.87129 q^{35} +3.35114 q^{36} +0.550972 q^{37} -15.9893 q^{39} -2.45965 q^{40} -2.60741 q^{41} +7.04029 q^{42} +2.87129 q^{43} -1.67853 q^{44} -8.24263 q^{45} -2.49890 q^{46} +0.745593 q^{47} -2.52015 q^{48} +0.804226 q^{49} +1.04988 q^{50} -12.5231 q^{51} +6.34458 q^{52} -1.47027 q^{53} -0.884927 q^{54} +4.12860 q^{55} -2.79360 q^{56} +5.93179 q^{58} -4.96261 q^{59} +6.19868 q^{60} +9.33686 q^{61} +7.28408 q^{62} -9.36176 q^{63} +1.00000 q^{64} -15.6054 q^{65} +4.23015 q^{66} +11.5604 q^{67} +4.96917 q^{68} +6.29761 q^{69} +6.87129 q^{70} -6.99698 q^{71} +3.35114 q^{72} -6.18619 q^{73} +0.550972 q^{74} -2.64584 q^{75} +4.68915 q^{77} -15.9893 q^{78} -5.91158 q^{79} -2.45965 q^{80} -7.82328 q^{81} -2.60741 q^{82} +15.1773 q^{83} +7.04029 q^{84} -12.2224 q^{85} +2.87129 q^{86} -14.9490 q^{87} -1.67853 q^{88} +6.90502 q^{89} -8.24263 q^{90} -17.7242 q^{91} -2.49890 q^{92} -18.3570 q^{93} +0.745593 q^{94} -2.52015 q^{96} +14.3874 q^{97} +0.804226 q^{98} -5.62500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.52015	−1.45501	−0.727504	−	0.686104i	$-0.759320\pi$
$3$	−2.52015	−1.45501	−0.727504	+	0.686104i	$0.759320\pi$
$4$	1.00000	0.500000
$5$	−2.45965	−1.09999	−0.549994	−	0.835168i	$-0.685370\pi$
$5$	−2.45965	−1.09999	−0.549994	+	0.835168i	$0.685370\pi$
$6$	−2.52015	−1.02885
$7$	−2.79360	−1.05588	−0.527942	−	0.849281i	$-0.677036\pi$
$7$	−2.79360	−1.05588	−0.527942	+	0.849281i	$0.677036\pi$
$8$	1.00000	0.353553
$9$	3.35114	1.11705
$10$	−2.45965	−0.777809
$11$	−1.67853	−0.506096	−0.253048	−	0.967454i	$-0.581433\pi$
$11$	−1.67853	−0.506096	−0.253048	+	0.967454i	$0.581433\pi$
$12$	−2.52015	−0.727504
$13$	6.34458	1.75967	0.879834	−	0.475280i	$-0.157653\pi$
$13$	6.34458	1.75967	0.879834	+	0.475280i	$0.157653\pi$
$14$	−2.79360	−0.746622
$15$	6.19868	1.60049
$16$	1.00000	0.250000
$17$	4.96917	1.20520	0.602601	−	0.798043i	$-0.294131\pi$
$17$	4.96917	1.20520	0.602601	+	0.798043i	$0.294131\pi$
$18$	3.35114	0.789872
$19$	0	0
$19$	0	0
$20$	−2.45965	−0.549994
$21$	7.04029	1.53632
$22$	−1.67853	−0.357864
$23$	−2.49890	−0.521057	−0.260529	−	0.965466i	$-0.583897\pi$
$23$	−2.49890	−0.521057	−0.260529	+	0.965466i	$0.583897\pi$
$24$	−2.52015	−0.514423
$25$	1.04988	0.209975
$26$	6.34458	1.24427
$27$	−0.884927	−0.170304
$28$	−2.79360	−0.527942
$29$	5.93179	1.10150	0.550752	−	0.834669i	$-0.314341\pi$
$29$	5.93179	1.10150	0.550752	+	0.834669i	$0.314341\pi$
$30$	6.19868	1.13172
$31$	7.28408	1.30826	0.654130	−	0.756382i	$-0.273035\pi$
$31$	7.28408	1.30826	0.654130	+	0.756382i	$0.273035\pi$
$32$	1.00000	0.176777
$33$	4.23015	0.736374
$34$	4.96917	0.852206
$35$	6.87129	1.16146
$36$	3.35114	0.558524
$37$	0.550972	0.0905792	0.0452896	−	0.998974i	$-0.485579\pi$
$37$	0.550972	0.0905792	0.0452896	+	0.998974i	$0.485579\pi$
$38$	0	0
$39$	−15.9893	−2.56033
$40$	−2.45965	−0.388905
$41$	−2.60741	−0.407209	−0.203605	−	0.979053i	$-0.565266\pi$
$41$	−2.60741	−0.407209	−0.203605	+	0.979053i	$0.565266\pi$
$42$	7.04029	1.08634
$43$	2.87129	0.437867	0.218934	−	0.975740i	$-0.429742\pi$
$43$	2.87129	0.437867	0.218934	+	0.975740i	$0.429742\pi$
$44$	−1.67853	−0.253048
$45$	−8.24263	−1.22874
$46$	−2.49890	−0.368443
$47$	0.745593	0.108756	0.0543780	−	0.998520i	$-0.482682\pi$
$47$	0.745593	0.108756	0.0543780	+	0.998520i	$0.482682\pi$
$48$	−2.52015	−0.363752
$49$	0.804226	0.114889
$50$	1.04988	0.148475
$51$	−12.5231	−1.75358
$52$	6.34458	0.879834
$53$	−1.47027	−0.201957	−0.100979	−	0.994889i	$-0.532197\pi$
$53$	−1.47027	−0.201957	−0.100979	+	0.994889i	$0.532197\pi$
$54$	−0.884927	−0.120423
$55$	4.12860	0.556700
$56$	−2.79360	−0.373311
$57$	0	0
$58$	5.93179	0.778882
$59$	−4.96261	−0.646077	−0.323038	−	0.946386i	$-0.604704\pi$
$59$	−4.96261	−0.646077	−0.323038	+	0.946386i	$0.604704\pi$
$60$	6.19868	0.800246
$61$	9.33686	1.19546	0.597731	−	0.801697i	$-0.296069\pi$
$61$	9.33686	1.19546	0.597731	+	0.801697i	$0.296069\pi$
$62$	7.28408	0.925079
$63$	−9.36176	−1.17947
$64$	1.00000	0.125000
$65$	−15.6054	−1.93562
$66$	4.23015	0.520695
$67$	11.5604	1.41233	0.706166	−	0.708046i	$-0.250423\pi$
$67$	11.5604	1.41233	0.706166	+	0.708046i	$0.250423\pi$
$68$	4.96917	0.602601
$69$	6.29761	0.758143
$70$	6.87129	0.821276
$71$	−6.99698	−0.830389	−0.415195	−	0.909733i	$-0.636286\pi$
$71$	−6.99698	−0.830389	−0.415195	+	0.909733i	$0.636286\pi$
$72$	3.35114	0.394936
$73$	−6.18619	−0.724039	−0.362020	−	0.932171i	$-0.617913\pi$
$73$	−6.18619	−0.724039	−0.362020	+	0.932171i	$0.617913\pi$
$74$	0.550972	0.0640492
$75$	−2.64584	−0.305515
$76$	0	0
$77$	4.68915	0.534379
$78$	−15.9893	−1.81043
$79$	−5.91158	−0.665105	−0.332552	−	0.943085i	$-0.607910\pi$
$79$	−5.91158	−0.665105	−0.332552	+	0.943085i	$0.607910\pi$
$80$	−2.45965	−0.274997
$81$	−7.82328	−0.869253
$82$	−2.60741	−0.287941
$83$	15.1773	1.66593	0.832964	−	0.553328i	$-0.186642\pi$
$83$	15.1773	1.66593	0.832964	+	0.553328i	$0.186642\pi$
$84$	7.04029	0.768159
$85$	−12.2224	−1.32571
$86$	2.87129	0.309619
$87$	−14.9490	−1.60270
$88$	−1.67853	−0.178932
$89$	6.90502	0.731930	0.365965	−	0.930629i	$-0.380739\pi$
$89$	6.90502	0.731930	0.365965	+	0.930629i	$0.380739\pi$
$90$	−8.24263	−0.868850
$91$	−17.7242	−1.85800
$92$	−2.49890	−0.260529
$93$	−18.3570	−1.90353
$94$	0.745593	0.0769021
$95$	0	0
$96$	−2.52015	−0.257211
$97$	14.3874	1.46082	0.730408	−	0.683011i	$-0.239330\pi$
$97$	14.3874	1.46082	0.730408	+	0.683011i	$0.239330\pi$
$98$	0.804226	0.0812391
$99$	−5.62500	−0.565333
$100$	1.04988	0.104988
$101$	11.2829	1.12269	0.561347	−	0.827581i	$-0.310283\pi$
$101$	11.2829	1.12269	0.561347	+	0.827581i	$0.310283\pi$
$102$	−12.5231	−1.23997
$103$	14.8280	1.46104	0.730522	−	0.682889i	$-0.239277\pi$
$103$	14.8280	1.46104	0.730522	+	0.682889i	$0.239277\pi$
$104$	6.34458	0.622137
$105$	−17.3167	−1.68993
$106$	−1.47027	−0.142805
$107$	−2.82849	−0.273440	−0.136720	−	0.990610i	$-0.543656\pi$
$107$	−2.82849	−0.273440	−0.136720	+	0.990610i	$0.543656\pi$
$108$	−0.884927	−0.0851521
$109$	1.72539	0.165262	0.0826312	−	0.996580i	$-0.473668\pi$
$109$	1.72539	0.165262	0.0826312	+	0.996580i	$0.473668\pi$
$110$	4.12860	0.393646
$111$	−1.38853	−0.131793
$112$	−2.79360	−0.263971
$113$	−0.427785	−0.0402426	−0.0201213	−	0.999798i	$-0.506405\pi$
$113$	−0.427785	−0.0402426	−0.0201213	+	0.999798i	$0.506405\pi$
$114$	0	0
$115$	6.14643	0.573157
$116$	5.93179	0.550752
$117$	21.2616	1.96563
$118$	−4.96261	−0.456845
$119$	−13.8819	−1.27255
$120$	6.19868	0.565859
$121$	−8.18253	−0.743867
$122$	9.33686	0.845320
$123$	6.57106	0.592493
$124$	7.28408	0.654130
$125$	9.71592	0.869018
$126$	−9.36176	−0.834012
$127$	−1.13632	−0.100832	−0.0504159	−	0.998728i	$-0.516055\pi$
$127$	−1.13632	−0.100832	−0.0504159	+	0.998728i	$0.516055\pi$
$128$	1.00000	0.0883883
$129$	−7.23607	−0.637100
$130$	−15.6054	−1.36869
$131$	−17.8415	−1.55882	−0.779410	−	0.626515i	$-0.784481\pi$
$131$	−17.8415	−1.55882	−0.779410	+	0.626515i	$0.784481\pi$
$132$	4.23015	0.368187
$133$	0	0
$134$	11.5604	0.998670
$135$	2.17661	0.187333
$136$	4.96917	0.426103
$137$	−15.9156	−1.35976	−0.679882	−	0.733321i	$-0.737969\pi$
$137$	−15.9156	−1.35976	−0.679882	+	0.733321i	$0.737969\pi$
$138$	6.29761	0.536088
$139$	10.1202	0.858382	0.429191	−	0.903214i	$-0.358799\pi$
$139$	10.1202	0.858382	0.429191	+	0.903214i	$0.358799\pi$
$140$	6.87129	0.580730
$141$	−1.87901	−0.158241
$142$	−6.99698	−0.587174
$143$	−10.6496	−0.890562
$144$	3.35114	0.279262
$145$	−14.5901	−1.21164
$146$	−6.18619	−0.511973
$147$	−2.02677	−0.167165
$148$	0.550972	0.0452896
$149$	9.39851	0.769956	0.384978	−	0.922926i	$-0.374209\pi$
$149$	9.39851	0.769956	0.384978	+	0.922926i	$0.374209\pi$
$150$	−2.64584	−0.216032
$151$	−10.2632	−0.835210	−0.417605	−	0.908629i	$-0.637130\pi$
$151$	−10.2632	−0.835210	−0.417605	+	0.908629i	$0.637130\pi$
$152$	0	0
$153$	16.6524	1.34627
$154$	4.68915	0.377863
$155$	−17.9163	−1.43907
$156$	−15.9893	−1.28017
$157$	2.97387	0.237341	0.118671	−	0.992934i	$-0.462137\pi$
$157$	2.97387	0.237341	0.118671	+	0.992934i	$0.462137\pi$
$158$	−5.91158	−0.470300
$159$	3.70530	0.293849
$160$	−2.45965	−0.194452
$161$	6.98095	0.550176
$162$	−7.82328	−0.614655
$163$	5.59191	0.437992	0.218996	−	0.975726i	$-0.429722\pi$
$163$	5.59191	0.437992	0.218996	+	0.975726i	$0.429722\pi$
$164$	−2.60741	−0.203605
$165$	−10.4047	−0.810003
$166$	15.1773	1.17799
$167$	−7.08361	−0.548146	−0.274073	−	0.961709i	$-0.588371\pi$
$167$	−7.08361	−0.548146	−0.274073	+	0.961709i	$0.588371\pi$
$168$	7.04029	0.543170
$169$	27.2537	2.09643
$170$	−12.2224	−0.937418
$171$	0	0
$172$	2.87129	0.218934
$173$	−23.0208	−1.75024	−0.875120	−	0.483907i	$-0.839217\pi$
$173$	−23.0208	−1.75024	−0.875120	+	0.483907i	$0.839217\pi$
$174$	−14.9490	−1.13328
$175$	−2.93294	−0.221709
$176$	−1.67853	−0.126524
$177$	12.5065	0.940047
$178$	6.90502	0.517553
$179$	8.21471	0.613996	0.306998	−	0.951710i	$-0.400675\pi$
$179$	8.21471	0.613996	0.306998	+	0.951710i	$0.400675\pi$
$180$	−8.24263	−0.614370
$181$	−12.9999	−0.966274	−0.483137	−	0.875545i	$-0.660503\pi$
$181$	−12.9999	−0.966274	−0.483137	+	0.875545i	$0.660503\pi$
$182$	−17.7242	−1.31381
$183$	−23.5303	−1.73941
$184$	−2.49890	−0.184222
$185$	−1.35520	−0.0996361
$186$	−18.3570	−1.34600
$187$	−8.34092	−0.609948
$188$	0.745593	0.0543780
$189$	2.47214	0.179821
$190$	0	0
$191$	6.57479	0.475735	0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479	0.475735	0.237868	+	0.971298i	$0.423552\pi$
$192$	−2.52015	−0.181876
$193$	26.8826	1.93505	0.967527	−	0.252769i	$-0.0813412\pi$
$193$	26.8826	1.93505	0.967527	+	0.252769i	$0.0813412\pi$
$194$	14.3874	1.03295
$195$	39.3280	2.81634
$196$	0.804226	0.0574447
$197$	−9.84940	−0.701741	−0.350870	−	0.936424i	$-0.614114\pi$
$197$	−9.84940	−0.701741	−0.350870	+	0.936424i	$0.614114\pi$
$198$	−5.62500	−0.399751
$199$	−20.4661	−1.45080	−0.725402	−	0.688326i	$-0.758346\pi$
$199$	−20.4661	−1.45080	−0.725402	+	0.688326i	$0.758346\pi$
$200$	1.04988	0.0742374
$201$	−29.1340	−2.05495
$202$	11.2829	0.793864
$203$	−16.5711	−1.16306
$204$	−12.5231	−0.876789
$205$	6.41332	0.447926
$206$	14.8280	1.03311
$207$	−8.37418	−0.582046
$208$	6.34458	0.439917
$209$	0	0
$210$	−17.3167	−1.19496
$211$	8.11630	0.558749	0.279374	−	0.960182i	$-0.409873\pi$
$211$	8.11630	0.558749	0.279374	+	0.960182i	$0.409873\pi$
$212$	−1.47027	−0.100979
$213$	17.6334	1.20822
$214$	−2.82849	−0.193351
$215$	−7.06236	−0.481649
$216$	−0.884927	−0.0602117
$217$	−20.3488	−1.38137
$218$	1.72539	0.116858
$219$	15.5901	1.05348
$220$	4.12860	0.278350
$221$	31.5273	2.12076
$222$	−1.38853	−0.0931921
$223$	10.7540	0.720143	0.360071	−	0.932925i	$-0.382752\pi$
$223$	10.7540	0.720143	0.360071	+	0.932925i	$0.382752\pi$
$224$	−2.79360	−0.186656
$225$	3.51828	0.234552
$226$	−0.427785	−0.0284558
$227$	27.0936	1.79827	0.899133	−	0.437676i	$-0.144198\pi$
$227$	27.0936	1.79827	0.899133	+	0.437676i	$0.144198\pi$
$228$	0	0
$229$	9.46557	0.625503	0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557	0.625503	0.312751	+	0.949835i	$0.398749\pi$
$230$	6.14643	0.405283
$231$	−11.8174	−0.777525
$232$	5.93179	0.389441
$233$	22.8621	1.49775	0.748873	−	0.662713i	$-0.230595\pi$
$233$	22.8621	1.49775	0.748873	+	0.662713i	$0.230595\pi$
$234$	21.2616	1.38991
$235$	−1.83390	−0.119630
$236$	−4.96261	−0.323038
$237$	14.8981	0.967733
$238$	−13.8819	−0.899831
$239$	8.66611	0.560564	0.280282	−	0.959918i	$-0.409572\pi$
$239$	8.66611	0.560564	0.280282	+	0.959918i	$0.409572\pi$
$240$	6.19868	0.400123
$241$	5.65826	0.364480	0.182240	−	0.983254i	$-0.441665\pi$
$241$	5.65826	0.364480	0.182240	+	0.983254i	$0.441665\pi$
$242$	−8.18253	−0.525993
$243$	22.3706	1.43507
$244$	9.33686	0.597731
$245$	−1.97811	−0.126377
$246$	6.57106	0.418956
$247$	0	0
$248$	7.28408	0.462539
$249$	−38.2491	−2.42394
$250$	9.71592	0.614489
$251$	−13.5552	−0.855599	−0.427799	−	0.903874i	$-0.640711\pi$
$251$	−13.5552	−0.855599	−0.427799	+	0.903874i	$0.640711\pi$
$252$	−9.36176	−0.589736
$253$	4.19449	0.263705
$254$	−1.13632	−0.0712988
$255$	30.8023	1.92892
$256$	1.00000	0.0625000
$257$	10.0393	0.626231	0.313116	−	0.949715i	$-0.398627\pi$
$257$	10.0393	0.626231	0.313116	+	0.949715i	$0.398627\pi$
$258$	−7.23607	−0.450498
$259$	−1.53920	−0.0956411
$260$	−15.6054	−0.967808
$261$	19.8782	1.23043
$262$	−17.8415	−1.10225
$263$	−18.8262	−1.16087	−0.580436	−	0.814306i	$-0.697118\pi$
$263$	−18.8262	−1.16087	−0.580436	+	0.814306i	$0.697118\pi$
$264$	4.23015	0.260347
$265$	3.61635	0.222151
$266$	0	0
$267$	−17.4017	−1.06496
$268$	11.5604	0.706166
$269$	−16.3827	−0.998870	−0.499435	−	0.866351i	$-0.666459\pi$
$269$	−16.3827	−0.998870	−0.499435	+	0.866351i	$0.666459\pi$
$270$	2.17661	0.132464
$271$	−2.76684	−0.168073	−0.0840367	−	0.996463i	$-0.526781\pi$
$271$	−2.76684	−0.168073	−0.0840367	+	0.996463i	$0.526781\pi$
$272$	4.96917	0.301300
$273$	44.6677	2.70341
$274$	−15.9156	−0.961499
$275$	−1.76225	−0.106268
$276$	6.29761	0.379071
$277$	24.5321	1.47399	0.736996	−	0.675897i	$-0.236244\pi$
$277$	24.5321	1.47399	0.736996	+	0.675897i	$0.236244\pi$
$278$	10.1202	0.606967
$279$	24.4100	1.46139
$280$	6.87129	0.410638
$281$	10.1704	0.606713	0.303356	−	0.952877i	$-0.401893\pi$
$281$	10.1704	0.606713	0.303356	+	0.952877i	$0.401893\pi$
$282$	−1.87901	−0.111893
$283$	27.6678	1.64468	0.822340	−	0.568997i	$-0.192668\pi$
$283$	27.6678	1.64468	0.822340	+	0.568997i	$0.192668\pi$
$284$	−6.99698	−0.415195
$285$	0	0
$286$	−10.6496	−0.629722
$287$	7.28408	0.429966
$288$	3.35114	0.197468
$289$	7.69270	0.452512
$290$	−14.5901	−0.856761
$291$	−36.2583	−2.12550
$292$	−6.18619	−0.362020
$293$	23.8386	1.39267	0.696333	−	0.717719i	$-0.254814\pi$
$293$	23.8386	1.39267	0.696333	+	0.717719i	$0.254814\pi$
$294$	−2.02677	−0.118204
$295$	12.2063	0.710677
$296$	0.550972	0.0320246
$297$	1.48538	0.0861904
$298$	9.39851	0.544441
$299$	−15.8545	−0.916889
$300$	−2.64584	−0.152758
$301$	−8.02124	−0.462337
$302$	−10.2632	−0.590583
$303$	−28.4346	−1.63353
$304$	0	0
$305$	−22.9654	−1.31500
$306$	16.6524	0.951955
$307$	25.9884	1.48324	0.741619	−	0.670821i	$-0.234058\pi$
$307$	25.9884	1.48324	0.741619	+	0.670821i	$0.234058\pi$
$308$	4.68915	0.267189
$309$	−37.3687	−2.12583
$310$	−17.9163	−1.01758
$311$	−23.1043	−1.31013	−0.655063	−	0.755574i	$-0.727358\pi$
$311$	−23.1043	−1.31013	−0.655063	+	0.755574i	$0.727358\pi$
$312$	−15.9893	−0.905214
$313$	12.2647	0.693242	0.346621	−	0.938005i	$-0.387329\pi$
$313$	12.2647	0.693242	0.346621	+	0.938005i	$0.387329\pi$
$314$	2.97387	0.167825
$315$	23.0267	1.29741
$316$	−5.91158	−0.332552
$317$	−0.272305	−0.0152942	−0.00764708	−	0.999971i	$-0.502434\pi$
$317$	−0.272305	−0.0152942	−0.00764708	+	0.999971i	$0.502434\pi$
$318$	3.70530	0.207783
$319$	−9.95669	−0.557468
$320$	−2.45965	−0.137499
$321$	7.12820	0.397857
$322$	6.98095	0.389033
$323$	0	0
$324$	−7.82328	−0.434626
$325$	6.66102	0.369487
$326$	5.59191	0.309707
$327$	−4.34824	−0.240458
$328$	−2.60741	−0.143970
$329$	−2.08289	−0.114834
$330$	−10.4047	−0.572759
$331$	−19.9930	−1.09891	−0.549457	−	0.835522i	$-0.685165\pi$
$331$	−19.9930	−1.09891	−0.549457	+	0.835522i	$0.685165\pi$
$332$	15.1773	0.832964
$333$	1.84638	0.101181
$334$	−7.08361	−0.387598
$335$	−28.4346	−1.55355
$336$	7.04029	0.384080
$337$	−17.2824	−0.941433	−0.470717	−	0.882284i	$-0.656005\pi$
$337$	−17.2824	−0.941433	−0.470717	+	0.882284i	$0.656005\pi$
$338$	27.2537	1.48240
$339$	1.07808	0.0585533
$340$	−12.2224	−0.662854
$341$	−12.2266	−0.662105
$342$	0	0
$343$	17.3085	0.934573
$344$	2.87129	0.154809
$345$	−15.4899	−0.833948
$346$	−23.0208	−1.23761
$347$	−18.5456	−0.995579	−0.497789	−	0.867298i	$-0.665855\pi$
$347$	−18.5456	−0.995579	−0.497789	+	0.867298i	$0.665855\pi$
$348$	−14.9490	−0.801349
$349$	−20.1210	−1.07705	−0.538527	−	0.842609i	$-0.681019\pi$
$349$	−20.1210	−1.07705	−0.538527	+	0.842609i	$0.681019\pi$
$350$	−2.93294	−0.156772
$351$	−5.61449	−0.299679
$352$	−1.67853	−0.0894660
$353$	24.0557	1.28035	0.640177	−	0.768227i	$-0.278861\pi$
$353$	24.0557	1.28035	0.640177	+	0.768227i	$0.278861\pi$
$354$	12.5065	0.664713
$355$	17.2101	0.913419
$356$	6.90502	0.365965
$357$	34.9845	1.85157
$358$	8.21471	0.434161
$359$	−10.8535	−0.572824	−0.286412	−	0.958107i	$-0.592463\pi$
$359$	−10.8535	−0.572824	−0.286412	+	0.958107i	$0.592463\pi$
$360$	−8.24263	−0.434425
$361$	0	0
$362$	−12.9999	−0.683259
$363$	20.6212	1.08233
$364$	−17.7242	−0.929002
$365$	15.2159	0.796435
$366$	−23.5303	−1.22995
$367$	−32.6121	−1.70234	−0.851168	−	0.524893i	$-0.824105\pi$
$367$	−32.6121	−1.70234	−0.851168	+	0.524893i	$0.824105\pi$
$368$	−2.49890	−0.130264
$369$	−8.73781	−0.454872
$370$	−1.35520	−0.0704534
$371$	4.10736	0.213243
$372$	−18.3570	−0.951764
$373$	−5.30198	−0.274526	−0.137263	−	0.990535i	$-0.543831\pi$
$373$	−5.30198	−0.274526	−0.137263	+	0.990535i	$0.543831\pi$
$374$	−8.34092	−0.431299
$375$	−24.4855	−1.26443
$376$	0.745593	0.0384510
$377$	37.6347	1.93828
$378$	2.47214	0.127153
$379$	24.6656	1.26699	0.633494	−	0.773748i	$-0.281620\pi$
$379$	24.6656	1.26699	0.633494	+	0.773748i	$0.281620\pi$
$380$	0	0
$381$	2.86368	0.146711
$382$	6.57479	0.336396
$383$	3.64416	0.186208	0.0931039	−	0.995656i	$-0.470321\pi$
$383$	3.64416	0.186208	0.0931039	+	0.995656i	$0.470321\pi$
$384$	−2.52015	−0.128606
$385$	−11.5337	−0.587810
$386$	26.8826	1.36829
$387$	9.62209	0.489118
$388$	14.3874	0.730408
$389$	2.79353	0.141638	0.0708189	−	0.997489i	$-0.477439\pi$
$389$	2.79353	0.141638	0.0708189	+	0.997489i	$0.477439\pi$
$390$	39.3280	1.99145
$391$	−12.4175	−0.627979
$392$	0.804226	0.0406196
$393$	44.9632	2.26809
$394$	−9.84940	−0.496206
$395$	14.5404	0.731608
$396$	−5.62500	−0.282667
$397$	−39.5101	−1.98296	−0.991478	−	0.130273i	$-0.958415\pi$
$397$	−39.5101	−1.98296	−0.991478	+	0.130273i	$0.958415\pi$
$398$	−20.4661	−1.02587
$399$	0	0
$400$	1.04988	0.0524938
$401$	−18.6215	−0.929912	−0.464956	−	0.885334i	$-0.653930\pi$
$401$	−18.6215	−0.929912	−0.464956	+	0.885334i	$0.653930\pi$
$402$	−29.1340	−1.45307
$403$	46.2144	2.30210
$404$	11.2829	0.561347
$405$	19.2425	0.956168
$406$	−16.5711	−0.822408
$407$	−0.924824	−0.0458418
$408$	−12.5231	−0.619983
$409$	−17.1433	−0.847681	−0.423840	−	0.905737i	$-0.639318\pi$
$409$	−17.1433	−0.847681	−0.423840	+	0.905737i	$0.639318\pi$
$410$	6.41332	0.316731
$411$	40.1098	1.97847
$412$	14.8280	0.730522
$413$	13.8636	0.682182
$414$	−8.37418	−0.411568
$415$	−37.3309	−1.83250
$416$	6.34458	0.311068
$417$	−25.5043	−1.24895
$418$	0	0
$419$	−18.5042	−0.903989	−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042	−0.903989	−0.451995	+	0.892021i	$0.649287\pi$
$420$	−17.3167	−0.844966
$421$	−16.1996	−0.789520	−0.394760	−	0.918784i	$-0.629172\pi$
$421$	−16.1996	−0.789520	−0.394760	+	0.918784i	$0.629172\pi$
$422$	8.11630	0.395095
$423$	2.49859	0.121486
$424$	−1.47027	−0.0714027
$425$	5.21702	0.253062
$426$	17.6334	0.854342
$427$	−26.0835	−1.26227
$428$	−2.82849	−0.136720
$429$	26.8385	1.29577
$430$	−7.06236	−0.340577
$431$	12.6997	0.611721	0.305861	−	0.952076i	$-0.401056\pi$
$431$	12.6997	0.611721	0.305861	+	0.952076i	$0.401056\pi$
$432$	−0.884927	−0.0425761
$433$	14.2350	0.684092	0.342046	−	0.939683i	$-0.388880\pi$
$433$	14.2350	0.684092	0.342046	+	0.939683i	$0.388880\pi$
$434$	−20.3488	−0.976775
$435$	36.7692	1.76295
$436$	1.72539	0.0826312
$437$	0	0
$438$	15.5901	0.744924
$439$	28.1900	1.34544	0.672718	−	0.739899i	$-0.265127\pi$
$439$	28.1900	1.34544	0.672718	+	0.739899i	$0.265127\pi$
$440$	4.12860	0.196823
$441$	2.69507	0.128337
$442$	31.5273	1.49960
$443$	−32.9944	−1.56761	−0.783805	−	0.621007i	$-0.786724\pi$
$443$	−32.9944	−1.56761	−0.783805	+	0.621007i	$0.786724\pi$
$444$	−1.38853	−0.0658967
$445$	−16.9839	−0.805115
$446$	10.7540	0.509218
$447$	−23.6856	−1.12029
$448$	−2.79360	−0.131985
$449$	−17.1975	−0.811601	−0.405801	−	0.913962i	$-0.633007\pi$
$449$	−17.1975	−0.811601	−0.405801	+	0.913962i	$0.633007\pi$
$450$	3.51828	0.165853
$451$	4.37662	0.206087
$452$	−0.427785	−0.0201213
$453$	25.8649	1.21524
$454$	27.0936	1.27157
$455$	43.5954	2.04378
$456$	0	0
$457$	−31.1517	−1.45722	−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517	−1.45722	−0.728608	+	0.684931i	$0.759832\pi$
$458$	9.46557	0.442297
$459$	−4.39736	−0.205251
$460$	6.14643	0.286579
$461$	15.5410	0.723816	0.361908	−	0.932214i	$-0.382125\pi$
$461$	15.5410	0.723816	0.361908	+	0.932214i	$0.382125\pi$
$462$	−11.8174	−0.549793
$463$	20.6648	0.960374	0.480187	−	0.877166i	$-0.340569\pi$
$463$	20.6648	0.960374	0.480187	+	0.877166i	$0.340569\pi$
$464$	5.93179	0.275376
$465$	45.1517	2.09386
$466$	22.8621	1.05907
$467$	−28.4830	−1.31803	−0.659017	−	0.752128i	$-0.729028\pi$
$467$	−28.4830	−1.31803	−0.659017	+	0.752128i	$0.729028\pi$
$468$	21.2616	0.982816
$469$	−32.2953	−1.49126
$470$	−1.83390	−0.0845914
$471$	−7.49460	−0.345333
$472$	−4.96261	−0.228423
$473$	−4.81955	−0.221603
$474$	14.8981	0.684290
$475$	0	0
$476$	−13.8819	−0.636276
$477$	−4.92709	−0.225596
$478$	8.66611	0.396379
$479$	−10.4726	−0.478507	−0.239254	−	0.970957i	$-0.576903\pi$
$479$	−10.4726	−0.478507	−0.239254	+	0.970957i	$0.576903\pi$
$480$	6.19868	0.282930
$481$	3.49568	0.159389
$482$	5.65826	0.257727
$483$	−17.5930	−0.800510
$484$	−8.18253	−0.371933
$485$	−35.3879	−1.60688
$486$	22.3706	1.01475
$487$	2.29894	0.104175	0.0520875	−	0.998643i	$-0.483413\pi$
$487$	2.29894	0.104175	0.0520875	+	0.998643i	$0.483413\pi$
$488$	9.33686	0.422660
$489$	−14.0924	−0.637282
$490$	−1.97811	−0.0893621
$491$	12.1612	0.548826	0.274413	−	0.961612i	$-0.411516\pi$
$491$	12.1612	0.548826	0.274413	+	0.961612i	$0.411516\pi$
$492$	6.57106	0.296246
$493$	29.4761	1.32754
$494$	0	0
$495$	13.8355	0.621860
$496$	7.28408	0.327065
$497$	19.5468	0.876794
$498$	−38.2491	−1.71398
$499$	15.1348	0.677528	0.338764	−	0.940871i	$-0.389991\pi$
$499$	15.1348	0.677528	0.338764	+	0.940871i	$0.389991\pi$
$500$	9.71592	0.434509
$501$	17.8517	0.797556
$502$	−13.5552	−0.605000
$503$	−0.573683	−0.0255793	−0.0127896	−	0.999918i	$-0.504071\pi$
$503$	−0.573683	−0.0255793	−0.0127896	+	0.999918i	$0.504071\pi$
$504$	−9.36176	−0.417006
$505$	−27.7520	−1.23495
$506$	4.19449	0.186468
$507$	−68.6832	−3.05033
$508$	−1.13632	−0.0504159
$509$	−26.2163	−1.16202	−0.581008	−	0.813898i	$-0.697341\pi$
$509$	−26.2163	−1.16202	−0.581008	+	0.813898i	$0.697341\pi$
$510$	30.8023	1.36395
$511$	17.2818	0.764501
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.0393	0.442813
$515$	−36.4716	−1.60713
$516$	−7.23607	−0.318550
$517$	−1.25150	−0.0550410
$518$	−1.53920	−0.0676285
$519$	58.0158	2.54661
$520$	−15.6054	−0.684344
$521$	−12.9637	−0.567948	−0.283974	−	0.958832i	$-0.591653\pi$
$521$	−12.9637	−0.567948	−0.283974	+	0.958832i	$0.591653\pi$
$522$	19.8782	0.870047
$523$	17.7793	0.777432	0.388716	−	0.921358i	$-0.372919\pi$
$523$	17.7793	0.777432	0.388716	+	0.921358i	$0.372919\pi$
$524$	−17.8415	−0.779410
$525$	7.39144	0.322589
$526$	−18.8262	−0.820861
$527$	36.1959	1.57672
$528$	4.23015	0.184093
$529$	−16.7555	−0.728499
$530$	3.61635	0.157084
$531$	−16.6304	−0.721698
$532$	0	0
$533$	−16.5429	−0.716554
$534$	−17.4017	−0.753043
$535$	6.95709	0.300781
$536$	11.5604	0.499335
$537$	−20.7023	−0.893369
$538$	−16.3827	−0.706307
$539$	−1.34992	−0.0581451
$540$	2.17661	0.0936664
$541$	−5.34418	−0.229764	−0.114882	−	0.993379i	$-0.536649\pi$
$541$	−5.34418	−0.229764	−0.114882	+	0.993379i	$0.536649\pi$
$542$	−2.76684	−0.118846
$543$	32.7616	1.40594
$544$	4.96917	0.213052
$545$	−4.24385	−0.181787
$546$	44.6677	1.91160
$547$	5.10112	0.218108	0.109054	−	0.994036i	$-0.465218\pi$
$547$	5.10112	0.218108	0.109054	+	0.994036i	$0.465218\pi$
$548$	−15.9156	−0.679882
$549$	31.2891	1.33539
$550$	−1.76225	−0.0751426
$551$	0	0
$552$	6.29761	0.268044
$553$	16.5146	0.702273
$554$	24.5321	1.04227
$555$	3.41530	0.144971
$556$	10.1202	0.429191
$557$	−10.7235	−0.454370	−0.227185	−	0.973852i	$-0.572952\pi$
$557$	−10.7235	−0.454370	−0.227185	+	0.973852i	$0.572952\pi$
$558$	24.4100	1.03336
$559$	18.2171	0.770502
$560$	6.87129	0.290365
$561$	21.0203	0.887479
$562$	10.1704	0.429011
$563$	9.76285	0.411455	0.205728	−	0.978609i	$-0.434044\pi$
$563$	9.76285	0.411455	0.205728	+	0.978609i	$0.434044\pi$
$564$	−1.87901	−0.0791204
$565$	1.05220	0.0442664
$566$	27.6678	1.16296
$567$	21.8551	0.917830
$568$	−6.99698	−0.293587
$569$	−8.84194	−0.370674	−0.185337	−	0.982675i	$-0.559338\pi$
$569$	−8.84194	−0.370674	−0.185337	+	0.982675i	$0.559338\pi$
$570$	0	0
$571$	22.8411	0.955871	0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411	0.955871	0.477935	+	0.878395i	$0.341385\pi$
$572$	−10.6496	−0.445281
$573$	−16.5694	−0.692198
$574$	7.28408	0.304032
$575$	−2.62354	−0.109409
$576$	3.35114	0.139631
$577$	−14.0176	−0.583560	−0.291780	−	0.956486i	$-0.594247\pi$
$577$	−14.0176	−0.583560	−0.291780	+	0.956486i	$0.594247\pi$
$578$	7.69270	0.319974
$579$	−67.7482	−2.81552
$580$	−14.5901	−0.605821
$581$	−42.3994	−1.75903
$582$	−36.2583	−1.50296
$583$	2.46790	0.102210
$584$	−6.18619	−0.255986
$585$	−52.2960	−2.16217
$586$	23.8386	0.984763
$587$	21.0356	0.868232	0.434116	−	0.900857i	$-0.357061\pi$
$587$	21.0356	0.868232	0.434116	+	0.900857i	$0.357061\pi$
$588$	−2.02677	−0.0835825
$589$	0	0
$590$	12.2063	0.502525
$591$	24.8219	1.02104
$592$	0.550972	0.0226448
$593$	−34.9193	−1.43396	−0.716981	−	0.697093i	$-0.754477\pi$
$593$	−34.9193	−1.43396	−0.716981	+	0.697093i	$0.754477\pi$
$594$	1.48538	0.0609458
$595$	34.1446	1.39979
$596$	9.39851	0.384978
$597$	51.5776	2.11093
$598$	−15.8545	−0.648338
$599$	21.5106	0.878901	0.439450	−	0.898267i	$-0.355173\pi$
$599$	21.5106	0.878901	0.439450	+	0.898267i	$0.355173\pi$
$600$	−2.64584	−0.108016
$601$	−14.3417	−0.585012	−0.292506	−	0.956264i	$-0.594489\pi$
$601$	−14.3417	−0.585012	−0.292506	+	0.956264i	$0.594489\pi$
$602$	−8.02124	−0.326921
$603$	38.7407	1.57764
$604$	−10.2632	−0.417605
$605$	20.1262	0.818245
$606$	−28.4346	−1.15508
$607$	−10.3488	−0.420046	−0.210023	−	0.977696i	$-0.567354\pi$
$607$	−10.3488	−0.420046	−0.210023	+	0.977696i	$0.567354\pi$
$608$	0	0
$609$	41.7615	1.69226
$610$	−22.9654	−0.929842
$611$	4.73047	0.191375
$612$	16.6524	0.673134
$613$	19.5674	0.790320	0.395160	−	0.918612i	$-0.370689\pi$
$613$	19.5674	0.790320	0.395160	+	0.918612i	$0.370689\pi$
$614$	25.9884	1.04881
$615$	−16.1625	−0.651735
$616$	4.68915	0.188931
$617$	−5.92522	−0.238540	−0.119270	−	0.992862i	$-0.538055\pi$
$617$	−5.92522	−0.238540	−0.119270	+	0.992862i	$0.538055\pi$
$618$	−37.3687	−1.50319
$619$	8.03958	0.323138	0.161569	−	0.986861i	$-0.448345\pi$
$619$	8.03958	0.323138	0.161569	+	0.986861i	$0.448345\pi$
$620$	−17.9163	−0.719535
$621$	2.21135	0.0887383
$622$	−23.1043	−0.926400
$623$	−19.2899	−0.772833
$624$	−15.9893	−0.640083
$625$	−29.1471	−1.16589
$626$	12.2647	0.490196
$627$	0	0
$628$	2.97387	0.118671
$629$	2.73788	0.109166
$630$	23.0267	0.917404
$631$	−12.9006	−0.513567	−0.256783	−	0.966469i	$-0.582663\pi$
$631$	−12.9006	−0.513567	−0.256783	+	0.966469i	$0.582663\pi$
$632$	−5.91158	−0.235150
$633$	−20.4543	−0.812984
$634$	−0.272305	−0.0108146
$635$	2.79494	0.110914
$636$	3.70530	0.146925
$637$	5.10247	0.202167
$638$	−9.95669	−0.394189
$639$	−23.4479	−0.927584
$640$	−2.45965	−0.0972262
$641$	−28.8639	−1.14006	−0.570028	−	0.821625i	$-0.693068\pi$
$641$	−28.8639	−1.14006	−0.570028	+	0.821625i	$0.693068\pi$
$642$	7.12820	0.281328
$643$	26.3394	1.03873	0.519363	−	0.854554i	$-0.326169\pi$
$643$	26.3394	1.03873	0.519363	+	0.854554i	$0.326169\pi$
$644$	6.98095	0.275088
$645$	17.7982	0.700803
$646$	0	0
$647$	−3.04601	−0.119751	−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601	−0.119751	−0.0598756	+	0.998206i	$0.519070\pi$
$648$	−7.82328	−0.307327
$649$	8.32990	0.326977
$650$	6.66102	0.261267
$651$	51.2821	2.00990
$652$	5.59191	0.218996
$653$	−15.1973	−0.594717	−0.297359	−	0.954766i	$-0.596106\pi$
$653$	−15.1973	−0.594717	−0.297359	+	0.954766i	$0.596106\pi$
$654$	−4.34824	−0.170030
$655$	43.8838	1.71468
$656$	−2.60741	−0.101802
$657$	−20.7308	−0.808786
$658$	−2.08289	−0.0811996
$659$	17.8741	0.696275	0.348138	−	0.937443i	$-0.386814\pi$
$659$	17.8741	0.696275	0.348138	+	0.937443i	$0.386814\pi$
$660$	−10.4047	−0.405001
$661$	37.8525	1.47229	0.736146	−	0.676823i	$-0.236644\pi$
$661$	37.8525	1.47229	0.736146	+	0.676823i	$0.236644\pi$
$662$	−19.9930	−0.777050
$663$	−79.4535	−3.08572
$664$	15.1773	0.588994
$665$	0	0
$666$	1.84638	0.0715460
$667$	−14.8230	−0.573947
$668$	−7.08361	−0.274073
$669$	−27.1017	−1.04781
$670$	−28.4346	−1.09853
$671$	−15.6722	−0.605019
$672$	7.04029	0.271585
$673$	−8.28461	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$673$	−8.28461	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$674$	−17.2824	−0.665694
$675$	−0.929063	−0.0357597
$676$	27.2537	1.04822
$677$	−18.3233	−0.704223	−0.352111	−	0.935958i	$-0.614536\pi$
$677$	−18.3233	−0.704223	−0.352111	+	0.935958i	$0.614536\pi$
$678$	1.07808	0.0414034
$679$	−40.1926	−1.54245
$680$	−12.2224	−0.468709
$681$	−68.2799	−2.61649
$682$	−12.2266	−0.468179
$683$	−49.2217	−1.88342	−0.941709	−	0.336429i	$-0.890781\pi$
$683$	−49.2217	−1.88342	−0.941709	+	0.336429i	$0.890781\pi$
$684$	0	0
$685$	39.1469	1.49573
$686$	17.3085	0.660843
$687$	−23.8546	−0.910111
$688$	2.87129	0.109467
$689$	−9.32825	−0.355378
$690$	−15.4899	−0.589690
$691$	16.6779	0.634458	0.317229	−	0.948349i	$-0.397248\pi$
$691$	16.6779	0.634458	0.317229	+	0.948349i	$0.397248\pi$
$692$	−23.0208	−0.875120
$693$	15.7140	0.596926
$694$	−18.5456	−0.703981
$695$	−24.8921	−0.944210
$696$	−14.9490	−0.566639
$697$	−12.9567	−0.490770
$698$	−20.1210	−0.761592
$699$	−57.6159	−2.17923
$700$	−2.93294	−0.110855
$701$	−30.9066	−1.16733	−0.583663	−	0.811996i	$-0.698381\pi$
$701$	−30.9066	−1.16733	−0.583663	+	0.811996i	$0.698381\pi$
$702$	−5.61449	−0.211905
$703$	0	0
$704$	−1.67853	−0.0632620
$705$	4.62169	0.174063
$706$	24.0557	0.905348
$707$	−31.5200	−1.18543
$708$	12.5065	0.470023
$709$	40.1056	1.50620	0.753098	−	0.657908i	$-0.228558\pi$
$709$	40.1056	1.50620	0.753098	+	0.657908i	$0.228558\pi$
$710$	17.2101	0.645884
$711$	−19.8105	−0.742953
$712$	6.90502	0.258776
$713$	−18.2022	−0.681678
$714$	34.9845	1.30926
$715$	26.1942	0.979608
$716$	8.21471	0.306998
$717$	−21.8399	−0.815625
$718$	−10.8535	−0.405048
$719$	−45.6529	−1.70256	−0.851282	−	0.524708i	$-0.824175\pi$
$719$	−45.6529	−1.70256	−0.851282	+	0.524708i	$0.824175\pi$
$720$	−8.24263	−0.307185
$721$	−41.4235	−1.54269
$722$	0	0
$723$	−14.2596	−0.530322
$724$	−12.9999	−0.483137
$725$	6.22764	0.231289
$726$	20.6212	0.765324
$727$	−15.1811	−0.563034	−0.281517	−	0.959556i	$-0.590838\pi$
$727$	−15.1811	−0.563034	−0.281517	+	0.959556i	$0.590838\pi$
$728$	−17.7242	−0.656904
$729$	−32.9073	−1.21879
$730$	15.2159	0.563164
$731$	14.2679	0.527719
$732$	−23.5303	−0.869703
$733$	−26.9986	−0.997217	−0.498608	−	0.866827i	$-0.666155\pi$
$733$	−26.9986	−0.997217	−0.498608	+	0.866827i	$0.666155\pi$
$734$	−32.6121	−1.20373
$735$	4.98514	0.183880
$736$	−2.49890	−0.0921108
$737$	−19.4046	−0.714776
$738$	−8.73781	−0.321643
$739$	−5.20782	−0.191573	−0.0957864	−	0.995402i	$-0.530537\pi$
$739$	−5.20782	−0.191573	−0.0957864	+	0.995402i	$0.530537\pi$
$740$	−1.35520	−0.0498181
$741$	0	0
$742$	4.10736	0.150786
$743$	22.1079	0.811059	0.405529	−	0.914082i	$-0.367087\pi$
$743$	22.1079	0.811059	0.405529	+	0.914082i	$0.367087\pi$
$744$	−18.3570	−0.672998
$745$	−23.1170	−0.846943
$746$	−5.30198	−0.194119
$747$	50.8613	1.86092
$748$	−8.34092	−0.304974
$749$	7.90167	0.288721
$750$	−24.4855	−0.894086
$751$	−12.4960	−0.455984	−0.227992	−	0.973663i	$-0.573216\pi$
$751$	−12.4960	−0.455984	−0.227992	+	0.973663i	$0.573216\pi$
$752$	0.745593	0.0271890
$753$	34.1612	1.24490
$754$	37.6347	1.37057
$755$	25.2440	0.918722
$756$	2.47214	0.0899107
$757$	−30.9988	−1.12667	−0.563336	−	0.826228i	$-0.690482\pi$
$757$	−30.9988	−1.12667	−0.563336	+	0.826228i	$0.690482\pi$
$758$	24.6656	0.895895
$759$	−10.5707	−0.383693
$760$	0	0
$761$	1.96398	0.0711941	0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398	0.0711941	0.0355971	+	0.999366i	$0.488667\pi$
$762$	2.86368	0.103740
$763$	−4.82006	−0.174498
$764$	6.57479	0.237868
$765$	−40.9591	−1.48088
$766$	3.64416	0.131669
$767$	−31.4857	−1.13688
$768$	−2.52015	−0.0909380
$769$	−22.3322	−0.805318	−0.402659	−	0.915350i	$-0.631914\pi$
$769$	−22.3322	−0.805318	−0.402659	+	0.915350i	$0.631914\pi$
$770$	−11.5337	−0.415645
$771$	−25.3004	−0.911172
$772$	26.8826	0.967527
$773$	27.3553	0.983901	0.491951	−	0.870623i	$-0.336284\pi$
$773$	27.3553	0.983901	0.491951	+	0.870623i	$0.336284\pi$
$774$	9.62209	0.345859
$775$	7.64738	0.274702
$776$	14.3874	0.516477
$777$	3.87901	0.139159
$778$	2.79353	0.100153
$779$	0	0
$780$	39.3280	1.40817
$781$	11.7447	0.420257
$782$	−12.4175	−0.444049
$783$	−5.24920	−0.187591
$784$	0.804226	0.0287224
$785$	−7.31469	−0.261072
$786$	44.9632	1.60378
$787$	7.78962	0.277670	0.138835	−	0.990316i	$-0.455664\pi$
$787$	7.78962	0.277670	0.138835	+	0.990316i	$0.455664\pi$
$788$	−9.84940	−0.350870
$789$	47.4447	1.68908
$790$	14.5404	0.517325
$791$	1.19506	0.0424915
$792$	−5.62500	−0.199876
$793$	59.2384	2.10362
$794$	−39.5101	−1.40216
$795$	−9.11374	−0.323231
$796$	−20.4661	−0.725402
$797$	−6.09655	−0.215951	−0.107975	−	0.994154i	$-0.534437\pi$
$797$	−6.09655	−0.215951	−0.107975	+	0.994154i	$0.534437\pi$
$798$	0	0
$799$	3.70498	0.131073
$800$	1.04988	0.0371187
$801$	23.1397	0.817601
$802$	−18.6215	−0.657547
$803$	10.3837	0.366433
$804$	−29.1340	−1.02748
$805$	−17.1707	−0.605187
$806$	46.2144	1.62783
$807$	41.2868	1.45336
$808$	11.2829	0.396932
$809$	56.8455	1.99858	0.999291	−	0.0376413i	$-0.0119844\pi$
$809$	56.8455	1.99858	0.999291	+	0.0376413i	$0.0119844\pi$
$810$	19.2425	0.676113
$811$	−20.9209	−0.734631	−0.367316	−	0.930096i	$-0.619723\pi$
$811$	−20.9209	−0.734631	−0.367316	+	0.930096i	$0.619723\pi$
$812$	−16.5711	−0.581530
$813$	6.97283	0.244548
$814$	−0.924824	−0.0324151
$815$	−13.7541	−0.481786
$816$	−12.5231	−0.438394
$817$	0	0
$818$	−17.1433	−0.599401
$819$	−59.3964	−2.07548
$820$	6.41332	0.223963
$821$	16.2582	0.567416	0.283708	−	0.958911i	$-0.408435\pi$
$821$	16.2582	0.567416	0.283708	+	0.958911i	$0.408435\pi$
$822$	40.1098	1.39899
$823$	−17.5328	−0.611157	−0.305578	−	0.952167i	$-0.598850\pi$
$823$	−17.5328	−0.611157	−0.305578	+	0.952167i	$0.598850\pi$
$824$	14.8280	0.516557
$825$	4.44113	0.154620
$826$	13.8636	0.482375
$827$	−17.0254	−0.592030	−0.296015	−	0.955183i	$-0.595658\pi$
$827$	−17.0254	−0.592030	−0.296015	+	0.955183i	$0.595658\pi$
$828$	−8.37418	−0.291023
$829$	−5.76207	−0.200125	−0.100062	−	0.994981i	$-0.531904\pi$
$829$	−5.76207	−0.200125	−0.100062	+	0.994981i	$0.531904\pi$
$830$	−37.3309	−1.29577
$831$	−61.8246	−2.14467
$832$	6.34458	0.219959
$833$	3.99634	0.138465
$834$	−25.5043	−0.883142
$835$	17.4232	0.602954
$836$	0	0
$837$	−6.44588	−0.222802
$838$	−18.5042	−0.639217
$839$	8.89954	0.307246	0.153623	−	0.988130i	$-0.450906\pi$
$839$	8.89954	0.307246	0.153623	+	0.988130i	$0.450906\pi$
$840$	−17.3167	−0.597481
$841$	6.18608	0.213313
$842$	−16.1996	−0.558275
$843$	−25.6308	−0.882772
$844$	8.11630	0.279374
$845$	−67.0344	−2.30605
$846$	2.49859	0.0859032
$847$	22.8588	0.785436
$848$	−1.47027	−0.0504893
$849$	−69.7269	−2.39302
$850$	5.21702	0.178942
$851$	−1.37683	−0.0471970
$852$	17.6334	0.604111
$853$	2.78915	0.0954987	0.0477493	−	0.998859i	$-0.484795\pi$
$853$	2.78915	0.0954987	0.0477493	+	0.998859i	$0.484795\pi$
$854$	−26.0835	−0.892559
$855$	0	0
$856$	−2.82849	−0.0966757
$857$	16.3945	0.560025	0.280012	−	0.959996i	$-0.409661\pi$
$857$	16.3945	0.560025	0.280012	+	0.959996i	$0.409661\pi$
$858$	26.8385	0.916251
$859$	9.52505	0.324990	0.162495	−	0.986709i	$-0.448046\pi$
$859$	9.52505	0.324990	0.162495	+	0.986709i	$0.448046\pi$
$860$	−7.06236	−0.240825
$861$	−18.3570	−0.625603
$862$	12.6997	0.432552
$863$	−50.6764	−1.72505	−0.862523	−	0.506018i	$-0.831117\pi$
$863$	−50.6764	−1.72505	−0.862523	+	0.506018i	$0.831117\pi$
$864$	−0.884927	−0.0301058
$865$	56.6231	1.92524
$866$	14.2350	0.483726
$867$	−19.3867	−0.658408
$868$	−20.3488	−0.690684
$869$	9.92278	0.336607
$870$	36.7692	1.24659
$871$	73.3461	2.48524
$872$	1.72539	0.0584291
$873$	48.2141	1.63180
$874$	0	0
$875$	−27.1424	−0.917582
$876$	15.5901	0.526741
$877$	19.2578	0.650291	0.325146	−	0.945664i	$-0.394587\pi$
$877$	19.2578	0.650291	0.325146	+	0.945664i	$0.394587\pi$
$878$	28.1900	0.951367
$879$	−60.0768	−2.02634
$880$	4.12860	0.139175
$881$	19.1076	0.643750	0.321875	−	0.946782i	$-0.395687\pi$
$881$	19.1076	0.643750	0.321875	+	0.946782i	$0.395687\pi$
$882$	2.69507	0.0907479
$883$	49.9980	1.68257	0.841283	−	0.540595i	$-0.181801\pi$
$883$	49.9980	1.68257	0.841283	+	0.540595i	$0.181801\pi$
$884$	31.5273	1.06038
$885$	−30.7616	−1.03404
$886$	−32.9944	−1.10847
$887$	39.6195	1.33029	0.665146	−	0.746713i	$-0.268369\pi$
$887$	39.6195	1.33029	0.665146	+	0.746713i	$0.268369\pi$
$888$	−1.38853	−0.0465960
$889$	3.17442	0.106467
$890$	−16.9839	−0.569302
$891$	13.1316	0.439926
$892$	10.7540	0.360071
$893$	0	0
$894$	−23.6856	−0.792166
$895$	−20.2053	−0.675389
$896$	−2.79360	−0.0933278
$897$	39.9556	1.33408
$898$	−17.1975	−0.573889
$899$	43.2076	1.44105
$900$	3.51828	0.117276
$901$	−7.30603	−0.243399
$902$	4.37662	0.145726
$903$	20.2147	0.672703
$904$	−0.427785	−0.0142279
$905$	31.9752	1.06289
$906$	25.8649	0.859302
$907$	55.2545	1.83470	0.917348	−	0.398087i	$-0.130326\pi$
$907$	55.2545	1.83470	0.917348	+	0.398087i	$0.130326\pi$
$908$	27.0936	0.899133
$909$	37.8107	1.25410
$910$	43.5954	1.44517
$911$	27.7087	0.918031	0.459015	−	0.888428i	$-0.348202\pi$
$911$	27.7087	0.918031	0.459015	+	0.888428i	$0.348202\pi$
$912$	0	0
$913$	−25.4756	−0.843120
$914$	−31.1517	−1.03041
$915$	57.8762	1.91333
$916$	9.46557	0.312751
$917$	49.8421	1.64593
$918$	−4.39736	−0.145134
$919$	27.2500	0.898894	0.449447	−	0.893307i	$-0.351621\pi$
$919$	27.2500	0.898894	0.449447	+	0.893307i	$0.351621\pi$
$920$	6.14643	0.202642
$921$	−65.4947	−2.15812
$922$	15.5410	0.511815
$923$	−44.3929	−1.46121
$924$	−11.8174	−0.388762
$925$	0.578452	0.0190194
$926$	20.6648	0.679087
$927$	49.6906	1.63205
$928$	5.93179	0.194720
$929$	44.4410	1.45806	0.729031	−	0.684481i	$-0.239971\pi$
$929$	44.4410	1.45806	0.729031	+	0.684481i	$0.239971\pi$
$930$	45.1517	1.48058
$931$	0	0
$932$	22.8621	0.748873
$933$	58.2263	1.90624
$934$	−28.4830	−0.931991
$935$	20.5157	0.670936
$936$	21.2616	0.694956
$937$	−18.2097	−0.594885	−0.297442	−	0.954740i	$-0.596134\pi$
$937$	−18.2097	−0.594885	−0.297442	+	0.954740i	$0.596134\pi$
$938$	−32.2953	−1.05448
$939$	−30.9088	−1.00867
$940$	−1.83390	−0.0598152
$941$	−40.2680	−1.31270	−0.656350	−	0.754457i	$-0.727901\pi$
$941$	−40.2680	−1.31270	−0.656350	+	0.754457i	$0.727901\pi$
$942$	−7.49460	−0.244187
$943$	6.51567	0.212180
$944$	−4.96261	−0.161519
$945$	−6.08059	−0.197802
$946$	−4.81955	−0.156697
$947$	6.36561	0.206854	0.103427	−	0.994637i	$-0.467019\pi$
$947$	6.36561	0.206854	0.103427	+	0.994637i	$0.467019\pi$
$948$	14.8981	0.483866
$949$	−39.2488	−1.27407
$950$	0	0
$951$	0.686248	0.0222531
$952$	−13.8819	−0.449915
$953$	−32.6944	−1.05907	−0.529537	−	0.848287i	$-0.677634\pi$
$953$	−32.6944	−1.05907	−0.529537	+	0.848287i	$0.677634\pi$
$954$	−4.92709	−0.159520
$955$	−16.1717	−0.523303
$956$	8.66611	0.280282
$957$	25.0923	0.811119
$958$	−10.4726	−0.338356
$959$	44.4620	1.43575
$960$	6.19868	0.200061
$961$	22.0578	0.711542
$962$	3.49568	0.112705
$963$	−9.47866	−0.305445
$964$	5.65826	0.182240
$965$	−66.1218	−2.12854
$966$	−17.5930	−0.566046
$967$	8.55936	0.275250	0.137625	−	0.990484i	$-0.456053\pi$
$967$	8.55936	0.275250	0.137625	+	0.990484i	$0.456053\pi$
$968$	−8.18253	−0.262997
$969$	0	0
$970$	−35.3879	−1.13624
$971$	−41.8789	−1.34396	−0.671978	−	0.740571i	$-0.734555\pi$
$971$	−41.8789	−1.34396	−0.671978	+	0.740571i	$0.734555\pi$
$972$	22.3706	0.717537
$973$	−28.2718	−0.906351
$974$	2.29894	0.0736628
$975$	−16.7867	−0.537606
$976$	9.33686	0.298866
$977$	−6.18021	−0.197722	−0.0988612	−	0.995101i	$-0.531520\pi$
$977$	−6.18021	−0.197722	−0.0988612	+	0.995101i	$0.531520\pi$
$978$	−14.0924	−0.450626
$979$	−11.5903	−0.370427
$980$	−1.97811	−0.0631885
$981$	5.78203	0.184606
$982$	12.1612	0.388079
$983$	33.5742	1.07085	0.535425	−	0.844583i	$-0.320152\pi$
$983$	33.5742	1.07085	0.535425	+	0.844583i	$0.320152\pi$
$984$	6.57106	0.209478
$985$	24.2261	0.771907
$986$	29.4761	0.938710
$987$	5.24920	0.167084
$988$	0	0
$989$	−7.17507	−0.228154
$990$	13.8355	0.439722
$991$	−46.1746	−1.46679	−0.733393	−	0.679805i	$-0.762064\pi$
$991$	−46.1746	−1.46679	−0.733393	+	0.679805i	$0.762064\pi$
$992$	7.28408	0.231270
$993$	50.3853	1.59893
$994$	19.5468	0.619987
$995$	50.3394	1.59587
$996$	−38.2491	−1.21197
$997$	−0.819130	−0.0259421	−0.0129711	−	0.999916i	$-0.504129\pi$
$997$	−0.819130	−0.0259421	−0.0129711	+	0.999916i	$0.504129\pi$
$998$	15.1348	0.479085
$999$	−0.487570	−0.0154260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.n.1.1	yes	4
3.2	odd	2		6498.2.a.bx.1.4		4
4.3	odd	2		5776.2.a.bt.1.4		4
19.2	odd	18		722.2.e.s.99.4		24
19.3	odd	18		722.2.e.s.389.4		24
19.4	even	9		722.2.e.r.415.4		24
19.5	even	9		722.2.e.r.595.4		24
19.6	even	9		722.2.e.r.245.1		24
19.7	even	3		722.2.c.m.429.4		8
19.8	odd	6		722.2.c.n.653.1		8
19.9	even	9		722.2.e.r.423.1		24
19.10	odd	18		722.2.e.s.423.4		24
19.11	even	3		722.2.c.m.653.4		8
19.12	odd	6		722.2.c.n.429.1		8
19.13	odd	18		722.2.e.s.245.4		24
19.14	odd	18		722.2.e.s.595.1		24
19.15	odd	18		722.2.e.s.415.1		24
19.16	even	9		722.2.e.r.389.1		24
19.17	even	9		722.2.e.r.99.1		24
19.18	odd	2		722.2.a.m.1.4	✓	4
57.56	even	2		6498.2.a.ca.1.4		4
76.75	even	2		5776.2.a.bv.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.4	✓	4	19.18	odd	2
722.2.a.n.1.1	yes	4	1.1	even	1	trivial
722.2.c.m.429.4		8	19.7	even	3
722.2.c.m.653.4		8	19.11	even	3
722.2.c.n.429.1		8	19.12	odd	6
722.2.c.n.653.1		8	19.8	odd	6
722.2.e.r.99.1		24	19.17	even	9
722.2.e.r.245.1		24	19.6	even	9
722.2.e.r.389.1		24	19.16	even	9
722.2.e.r.415.4		24	19.4	even	9
722.2.e.r.423.1		24	19.9	even	9
722.2.e.r.595.4		24	19.5	even	9
722.2.e.s.99.4		24	19.2	odd	18
722.2.e.s.245.4		24	19.13	odd	18
722.2.e.s.389.4		24	19.3	odd	18
722.2.e.s.415.1		24	19.15	odd	18
722.2.e.s.423.4		24	19.10	odd	18
722.2.e.s.595.1		24	19.14	odd	18
5776.2.a.bt.1.4		4	4.3	odd	2
5776.2.a.bv.1.1		4	76.75	even	2
6498.2.a.bx.1.4		4	3.2	odd	2
6498.2.a.ca.1.4		4	57.56	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52015 q^{3} +1.00000 q^{4} -2.45965 q^{5} -2.52015 q^{6} -2.79360 q^{7} +1.00000 q^{8} +3.35114 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52015 q^{3} +1.00000 q^{4} -2.45965 q^{5} -2.52015 q^{6} -2.79360 q^{7} +1.00000 q^{8} +3.35114 q^{9} -2.45965 q^{10} -1.67853 q^{11} -2.52015 q^{12} +6.34458 q^{13} -2.79360 q^{14} +6.19868 q^{15} +1.00000 q^{16} +4.96917 q^{17} +3.35114 q^{18} -2.45965 q^{20} +7.04029 q^{21} -1.67853 q^{22} -2.49890 q^{23} -2.52015 q^{24} +1.04988 q^{25} +6.34458 q^{26} -0.884927 q^{27} -2.79360 q^{28} +5.93179 q^{29} +6.19868 q^{30} +7.28408 q^{31} +1.00000 q^{32} +4.23015 q^{33} +4.96917 q^{34} +6.87129 q^{35} +3.35114 q^{36} +0.550972 q^{37} -15.9893 q^{39} -2.45965 q^{40} -2.60741 q^{41} +7.04029 q^{42} +2.87129 q^{43} -1.67853 q^{44} -8.24263 q^{45} -2.49890 q^{46} +0.745593 q^{47} -2.52015 q^{48} +0.804226 q^{49} +1.04988 q^{50} -12.5231 q^{51} +6.34458 q^{52} -1.47027 q^{53} -0.884927 q^{54} +4.12860 q^{55} -2.79360 q^{56} +5.93179 q^{58} -4.96261 q^{59} +6.19868 q^{60} +9.33686 q^{61} +7.28408 q^{62} -9.36176 q^{63} +1.00000 q^{64} -15.6054 q^{65} +4.23015 q^{66} +11.5604 q^{67} +4.96917 q^{68} +6.29761 q^{69} +6.87129 q^{70} -6.99698 q^{71} +3.35114 q^{72} -6.18619 q^{73} +0.550972 q^{74} -2.64584 q^{75} +4.68915 q^{77} -15.9893 q^{78} -5.91158 q^{79} -2.45965 q^{80} -7.82328 q^{81} -2.60741 q^{82} +15.1773 q^{83} +7.04029 q^{84} -12.2224 q^{85} +2.87129 q^{86} -14.9490 q^{87} -1.67853 q^{88} +6.90502 q^{89} -8.24263 q^{90} -17.7242 q^{91} -2.49890 q^{92} -18.3570 q^{93} +0.745593 q^{94} -2.52015 q^{96} +14.3874 q^{97} +0.804226 q^{98} -5.62500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * q^99

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