LMFDB - Embedded newform 1183.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +4.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+1.73205 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +4.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +4.46410 q^{9} +3.00000 q^{10} +1.26795 q^{11} +2.73205 q^{12} +1.73205 q^{14} +4.73205 q^{15} -5.00000 q^{16} -7.73205 q^{17} +7.73205 q^{18} +2.00000 q^{19} +1.73205 q^{20} +2.73205 q^{21} +2.19615 q^{22} +4.73205 q^{23} -4.73205 q^{24} -2.00000 q^{25} +4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +8.19615 q^{30} +4.19615 q^{31} -5.19615 q^{32} +3.46410 q^{33} -13.3923 q^{34} +1.73205 q^{35} +4.46410 q^{36} -7.00000 q^{37} +3.46410 q^{38} -3.00000 q^{40} -5.19615 q^{41} +4.73205 q^{42} -0.196152 q^{43} +1.26795 q^{44} +7.73205 q^{45} +8.19615 q^{46} +12.9282 q^{47} -13.6603 q^{48} +1.00000 q^{49} -3.46410 q^{50} -21.1244 q^{51} -9.92820 q^{53} +6.92820 q^{54} +2.19615 q^{55} -1.73205 q^{56} +5.46410 q^{57} -5.19615 q^{58} +7.26795 q^{59} +4.73205 q^{60} -4.80385 q^{61} +7.26795 q^{62} +4.46410 q^{63} +1.00000 q^{64} +6.00000 q^{66} -6.19615 q^{67} -7.73205 q^{68} +12.9282 q^{69} +3.00000 q^{70} +6.00000 q^{71} -7.73205 q^{72} -3.19615 q^{73} -12.1244 q^{74} -5.46410 q^{75} +2.00000 q^{76} +1.26795 q^{77} +16.1962 q^{79} -8.66025 q^{80} -2.46410 q^{81} -9.00000 q^{82} -2.19615 q^{83} +2.73205 q^{84} -13.3923 q^{85} -0.339746 q^{86} -8.19615 q^{87} -2.19615 q^{88} +12.9282 q^{89} +13.3923 q^{90} +4.73205 q^{92} +11.4641 q^{93} +22.3923 q^{94} +3.46410 q^{95} -14.1962 q^{96} +6.39230 q^{97} +1.73205 q^{98} +5.66025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{15} - 10 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 8 q^{27} + 2 q^{28} - 6 q^{29} + 6 q^{30} - 2 q^{31} - 6 q^{34} + 2 q^{36} - 14 q^{37} - 6 q^{40} + 6 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{45} + 6 q^{46} + 12 q^{47} - 10 q^{48} + 2 q^{49} - 18 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} + 18 q^{59} + 6 q^{60} - 20 q^{61} + 18 q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{66} - 2 q^{67} - 12 q^{68} + 12 q^{69} + 6 q^{70} + 12 q^{71} - 12 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} + 6 q^{77} + 22 q^{79} + 2 q^{81} - 18 q^{82} + 6 q^{83} + 2 q^{84} - 6 q^{85} - 18 q^{86} - 6 q^{87} + 6 q^{88} + 12 q^{89} + 6 q^{90} + 6 q^{92} + 16 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^15 - 10 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 8 * q^27 + 2 * q^28 - 6 * q^29 + 6 * q^30 - 2 * q^31 - 6 * q^34 + 2 * q^36 - 14 * q^37 - 6 * q^40 + 6 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^45 + 6 * q^46 + 12 * q^47 - 10 * q^48 + 2 * q^49 - 18 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 + 18 * q^59 + 6 * q^60 - 20 * q^61 + 18 * q^62 + 2 * q^63 + 2 * q^64 + 12 * q^66 - 2 * q^67 - 12 * q^68 + 12 * q^69 + 6 * q^70 + 12 * q^71 - 12 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 + 6 * q^77 + 22 * q^79 + 2 * q^81 - 18 * q^82 + 6 * q^83 + 2 * q^84 - 6 * q^85 - 18 * q^86 - 6 * q^87 + 6 * q^88 + 12 * q^89 + 6 * q^90 + 6 * q^92 + 16 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 6 * 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 $

$2$	1.73205	1.22474	0.612372	−	0.790569i	$-0.290215\pi$
$2$	1.73205	1.22474	0.612372	+	0.790569i	$0.290215\pi$
$3$	2.73205	1.57735	0.788675	−	0.614810i	$-0.210767\pi$
$3$	2.73205	1.57735	0.788675	+	0.614810i	$0.210767\pi$
$4$	1.00000	0.500000
$5$	1.73205	0.774597	0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205	0.774597	0.387298	+	0.921954i	$0.373408\pi$
$6$	4.73205	1.93185
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.73205	−0.612372
$9$	4.46410	1.48803
$10$	3.00000	0.948683
$11$	1.26795	0.382301	0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795	0.382301	0.191151	+	0.981561i	$0.438778\pi$
$12$	2.73205	0.788675
$13$	0	0
$13$	0	0
$14$	1.73205	0.462910
$15$	4.73205	1.22181
$16$	−5.00000	−1.25000
$17$	−7.73205	−1.87530	−0.937649	−	0.347584i	$-0.887002\pi$
$17$	−7.73205	−1.87530	−0.937649	+	0.347584i	$0.887002\pi$
$18$	7.73205	1.82246
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	1.73205	0.387298
$21$	2.73205	0.596182
$22$	2.19615	0.468221
$23$	4.73205	0.986701	0.493350	−	0.869831i	$-0.335772\pi$
$23$	4.73205	0.986701	0.493350	+	0.869831i	$0.335772\pi$
$24$	−4.73205	−0.965926
$25$	−2.00000	−0.400000
$26$	0	0
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	8.19615	1.49641
$31$	4.19615	0.753651	0.376826	−	0.926284i	$-0.377016\pi$
$31$	4.19615	0.753651	0.376826	+	0.926284i	$0.377016\pi$
$32$	−5.19615	−0.918559
$33$	3.46410	0.603023
$34$	−13.3923	−2.29676
$35$	1.73205	0.292770
$36$	4.46410	0.744017
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	3.46410	0.561951
$39$	0	0
$40$	−3.00000	−0.474342
$41$	−5.19615	−0.811503	−0.405751	−	0.913984i	$-0.632990\pi$
$41$	−5.19615	−0.811503	−0.405751	+	0.913984i	$0.632990\pi$
$42$	4.73205	0.730171
$43$	−0.196152	−0.0299130	−0.0149565	−	0.999888i	$-0.504761\pi$
$43$	−0.196152	−0.0299130	−0.0149565	+	0.999888i	$0.504761\pi$
$44$	1.26795	0.191151
$45$	7.73205	1.15263
$46$	8.19615	1.20846
$47$	12.9282	1.88577	0.942886	−	0.333115i	$-0.108100\pi$
$47$	12.9282	1.88577	0.942886	+	0.333115i	$0.108100\pi$
$48$	−13.6603	−1.97169
$49$	1.00000	0.142857
$50$	−3.46410	−0.489898
$51$	−21.1244	−2.95800
$52$	0	0
$53$	−9.92820	−1.36374	−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820	−1.36374	−0.681872	+	0.731472i	$0.738834\pi$
$54$	6.92820	0.942809
$55$	2.19615	0.296129
$56$	−1.73205	−0.231455
$57$	5.46410	0.723738
$58$	−5.19615	−0.682288
$59$	7.26795	0.946206	0.473103	−	0.881007i	$-0.343134\pi$
$59$	7.26795	0.946206	0.473103	+	0.881007i	$0.343134\pi$
$60$	4.73205	0.610905
$61$	−4.80385	−0.615070	−0.307535	−	0.951537i	$-0.599504\pi$
$61$	−4.80385	−0.615070	−0.307535	+	0.951537i	$0.599504\pi$
$62$	7.26795	0.923030
$63$	4.46410	0.562424
$64$	1.00000	0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	−6.19615	−0.756980	−0.378490	−	0.925605i	$-0.623557\pi$
$67$	−6.19615	−0.756980	−0.378490	+	0.925605i	$0.623557\pi$
$68$	−7.73205	−0.937649
$69$	12.9282	1.55637
$70$	3.00000	0.358569
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−7.73205	−0.911231
$73$	−3.19615	−0.374081	−0.187041	−	0.982352i	$-0.559890\pi$
$73$	−3.19615	−0.374081	−0.187041	+	0.982352i	$0.559890\pi$
$74$	−12.1244	−1.40943
$75$	−5.46410	−0.630940
$76$	2.00000	0.229416
$77$	1.26795	0.144496
$78$	0	0
$79$	16.1962	1.82221	0.911105	−	0.412175i	$-0.135231\pi$
$79$	16.1962	1.82221	0.911105	+	0.412175i	$0.135231\pi$
$80$	−8.66025	−0.968246
$81$	−2.46410	−0.273789
$82$	−9.00000	−0.993884
$83$	−2.19615	−0.241059	−0.120530	−	0.992710i	$-0.538459\pi$
$83$	−2.19615	−0.241059	−0.120530	+	0.992710i	$0.538459\pi$
$84$	2.73205	0.298091
$85$	−13.3923	−1.45260
$86$	−0.339746	−0.0366357
$87$	−8.19615	−0.878720
$88$	−2.19615	−0.234111
$89$	12.9282	1.37039	0.685193	−	0.728361i	$-0.259718\pi$
$89$	12.9282	1.37039	0.685193	+	0.728361i	$0.259718\pi$
$90$	13.3923	1.41167
$91$	0	0
$92$	4.73205	0.493350
$93$	11.4641	1.18877
$94$	22.3923	2.30959
$95$	3.46410	0.355409
$96$	−14.1962	−1.44889
$97$	6.39230	0.649040	0.324520	−	0.945879i	$-0.394797\pi$
$97$	6.39230	0.649040	0.324520	+	0.945879i	$0.394797\pi$
$98$	1.73205	0.174964
$99$	5.66025	0.568877
$100$	−2.00000	−0.200000
$101$	−7.73205	−0.769368	−0.384684	−	0.923048i	$-0.625690\pi$
$101$	−7.73205	−0.769368	−0.384684	+	0.923048i	$0.625690\pi$
$102$	−36.5885	−3.62280
$103$	−14.3923	−1.41812	−0.709058	−	0.705150i	$-0.750880\pi$
$103$	−14.3923	−1.41812	−0.709058	+	0.705150i	$0.750880\pi$
$104$	0	0
$105$	4.73205	0.461801
$106$	−17.1962	−1.67024
$107$	−7.85641	−0.759507	−0.379754	−	0.925088i	$-0.623991\pi$
$107$	−7.85641	−0.759507	−0.379754	+	0.925088i	$0.623991\pi$
$108$	4.00000	0.384900
$109$	−8.39230	−0.803837	−0.401919	−	0.915675i	$-0.631656\pi$
$109$	−8.39230	−0.803837	−0.401919	+	0.915675i	$0.631656\pi$
$110$	3.80385	0.362683
$111$	−19.1244	−1.81520
$112$	−5.00000	−0.472456
$113$	13.3923	1.25984	0.629921	−	0.776659i	$-0.283087\pi$
$113$	13.3923	1.25984	0.629921	+	0.776659i	$0.283087\pi$
$114$	9.46410	0.886394
$115$	8.19615	0.764295
$116$	−3.00000	−0.278543
$117$	0	0
$118$	12.5885	1.15886
$119$	−7.73205	−0.708796
$120$	−8.19615	−0.748203
$121$	−9.39230	−0.853846
$122$	−8.32051	−0.753303
$123$	−14.1962	−1.28002
$124$	4.19615	0.376826
$125$	−12.1244	−1.08444
$126$	7.73205	0.688826
$127$	18.3923	1.63205	0.816027	−	0.578014i	$-0.196172\pi$
$127$	18.3923	1.63205	0.816027	+	0.578014i	$0.196172\pi$
$128$	12.1244	1.07165
$129$	−0.535898	−0.0471832
$130$	0	0
$131$	−3.46410	−0.302660	−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410	−0.302660	−0.151330	+	0.988483i	$0.548356\pi$
$132$	3.46410	0.301511
$133$	2.00000	0.173422
$134$	−10.7321	−0.927108
$135$	6.92820	0.596285
$136$	13.3923	1.14838
$137$	8.07180	0.689620	0.344810	−	0.938672i	$-0.387943\pi$
$137$	8.07180	0.689620	0.344810	+	0.938672i	$0.387943\pi$
$138$	22.3923	1.90616
$139$	−10.5885	−0.898101	−0.449051	−	0.893506i	$-0.648238\pi$
$139$	−10.5885	−0.898101	−0.449051	+	0.893506i	$0.648238\pi$
$140$	1.73205	0.146385
$141$	35.3205	2.97452
$142$	10.3923	0.872103
$143$	0	0
$144$	−22.3205	−1.86004
$145$	−5.19615	−0.431517
$146$	−5.53590	−0.458154
$147$	2.73205	0.225336
$148$	−7.00000	−0.575396
$149$	−6.46410	−0.529560	−0.264780	−	0.964309i	$-0.585299\pi$
$149$	−6.46410	−0.529560	−0.264780	+	0.964309i	$0.585299\pi$
$150$	−9.46410	−0.772741
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−3.46410	−0.280976
$153$	−34.5167	−2.79051
$154$	2.19615	0.176971
$155$	7.26795	0.583776
$156$	0	0
$157$	1.19615	0.0954634	0.0477317	−	0.998860i	$-0.484801\pi$
$157$	1.19615	0.0954634	0.0477317	+	0.998860i	$0.484801\pi$
$158$	28.0526	2.23174
$159$	−27.1244	−2.15110
$160$	−9.00000	−0.711512
$161$	4.73205	0.372938
$162$	−4.26795	−0.335322
$163$	16.1962	1.26858	0.634290	−	0.773095i	$-0.281292\pi$
$163$	16.1962	1.26858	0.634290	+	0.773095i	$0.281292\pi$
$164$	−5.19615	−0.405751
$165$	6.00000	0.467099
$166$	−3.80385	−0.295236
$167$	−6.58846	−0.509830	−0.254915	−	0.966963i	$-0.582048\pi$
$167$	−6.58846	−0.509830	−0.254915	+	0.966963i	$0.582048\pi$
$168$	−4.73205	−0.365086
$169$	0	0
$170$	−23.1962	−1.77906
$171$	8.92820	0.682757
$172$	−0.196152	−0.0149565
$173$	8.53590	0.648972	0.324486	−	0.945890i	$-0.394809\pi$
$173$	8.53590	0.648972	0.324486	+	0.945890i	$0.394809\pi$
$174$	−14.1962	−1.07621
$175$	−2.00000	−0.151186
$176$	−6.33975	−0.477876
$177$	19.8564	1.49250
$178$	22.3923	1.67837
$179$	−6.92820	−0.517838	−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820	−0.517838	−0.258919	+	0.965899i	$0.583366\pi$
$180$	7.73205	0.576313
$181$	5.58846	0.415387	0.207693	−	0.978194i	$-0.433404\pi$
$181$	5.58846	0.415387	0.207693	+	0.978194i	$0.433404\pi$
$182$	0	0
$183$	−13.1244	−0.970180
$184$	−8.19615	−0.604228
$185$	−12.1244	−0.891400
$186$	19.8564	1.45594
$187$	−9.80385	−0.716928
$188$	12.9282	0.942886
$189$	4.00000	0.290957
$190$	6.00000	0.435286
$191$	4.73205	0.342399	0.171200	−	0.985236i	$-0.445236\pi$
$191$	4.73205	0.342399	0.171200	+	0.985236i	$0.445236\pi$
$192$	2.73205	0.197169
$193$	5.00000	0.359908	0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000	0.359908	0.179954	+	0.983675i	$0.442405\pi$
$194$	11.0718	0.794909
$195$	0	0
$196$	1.00000	0.0714286
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	9.80385	0.696729
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	3.46410	0.244949
$201$	−16.9282	−1.19402
$202$	−13.3923	−0.942279
$203$	−3.00000	−0.210559
$204$	−21.1244	−1.47900
$205$	−9.00000	−0.628587
$206$	−24.9282	−1.73683
$207$	21.1244	1.46824
$208$	0	0
$209$	2.53590	0.175412
$210$	8.19615	0.565588
$211$	−1.80385	−0.124182	−0.0620910	−	0.998070i	$-0.519777\pi$
$211$	−1.80385	−0.124182	−0.0620910	+	0.998070i	$0.519777\pi$
$212$	−9.92820	−0.681872
$213$	16.3923	1.12318
$214$	−13.6077	−0.930203
$215$	−0.339746	−0.0231705
$216$	−6.92820	−0.471405
$217$	4.19615	0.284853
$218$	−14.5359	−0.984495
$219$	−8.73205	−0.590057
$220$	2.19615	0.148065
$221$	0	0
$222$	−33.1244	−2.22316
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	−5.19615	−0.347183
$225$	−8.92820	−0.595214
$226$	23.1962	1.54299
$227$	5.66025	0.375684	0.187842	−	0.982199i	$-0.439851\pi$
$227$	5.66025	0.375684	0.187842	+	0.982199i	$0.439851\pi$
$228$	5.46410	0.361869
$229$	−14.3923	−0.951070	−0.475535	−	0.879697i	$-0.657746\pi$
$229$	−14.3923	−0.951070	−0.475535	+	0.879697i	$0.657746\pi$
$230$	14.1962	0.936067
$231$	3.46410	0.227921
$232$	5.19615	0.341144
$233$	−1.85641	−0.121617	−0.0608086	−	0.998149i	$-0.519368\pi$
$233$	−1.85641	−0.121617	−0.0608086	+	0.998149i	$0.519368\pi$
$234$	0	0
$235$	22.3923	1.46071
$236$	7.26795	0.473103
$237$	44.2487	2.87426
$238$	−13.3923	−0.868094
$239$	−15.8038	−1.02227	−0.511133	−	0.859502i	$-0.670774\pi$
$239$	−15.8038	−1.02227	−0.511133	+	0.859502i	$0.670774\pi$
$240$	−23.6603	−1.52726
$241$	−21.1962	−1.36536	−0.682682	−	0.730716i	$-0.739187\pi$
$241$	−21.1962	−1.36536	−0.682682	+	0.730716i	$0.739187\pi$
$242$	−16.2679	−1.04574
$243$	−18.7321	−1.20166
$244$	−4.80385	−0.307535
$245$	1.73205	0.110657
$246$	−24.5885	−1.56770
$247$	0	0
$248$	−7.26795	−0.461515
$249$	−6.00000	−0.380235
$250$	−21.0000	−1.32816
$251$	−1.60770	−0.101477	−0.0507384	−	0.998712i	$-0.516157\pi$
$251$	−1.60770	−0.101477	−0.0507384	+	0.998712i	$0.516157\pi$
$252$	4.46410	0.281212
$253$	6.00000	0.377217
$254$	31.8564	1.99885
$255$	−36.5885	−2.29126
$256$	19.0000	1.18750
$257$	6.12436	0.382027	0.191013	−	0.981587i	$-0.438823\pi$
$257$	6.12436	0.382027	0.191013	+	0.981587i	$0.438823\pi$
$258$	−0.928203	−0.0577874
$259$	−7.00000	−0.434959
$260$	0	0
$261$	−13.3923	−0.828963
$262$	−6.00000	−0.370681
$263$	1.26795	0.0781851	0.0390925	−	0.999236i	$-0.487553\pi$
$263$	1.26795	0.0781851	0.0390925	+	0.999236i	$0.487553\pi$
$264$	−6.00000	−0.369274
$265$	−17.1962	−1.05635
$266$	3.46410	0.212398
$267$	35.3205	2.16158
$268$	−6.19615	−0.378490
$269$	5.07180	0.309233	0.154616	−	0.987975i	$-0.450586\pi$
$269$	5.07180	0.309233	0.154616	+	0.987975i	$0.450586\pi$
$270$	12.0000	0.730297
$271$	5.80385	0.352559	0.176279	−	0.984340i	$-0.443594\pi$
$271$	5.80385	0.352559	0.176279	+	0.984340i	$0.443594\pi$
$272$	38.6603	2.34412
$273$	0	0
$274$	13.9808	0.844609
$275$	−2.53590	−0.152920
$276$	12.9282	0.778186
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	−18.3397	−1.09994
$279$	18.7321	1.12146
$280$	−3.00000	−0.179284
$281$	13.3923	0.798918	0.399459	−	0.916751i	$-0.369198\pi$
$281$	13.3923	0.798918	0.399459	+	0.916751i	$0.369198\pi$
$282$	61.1769	3.64303
$283$	10.1962	0.606098	0.303049	−	0.952975i	$-0.401995\pi$
$283$	10.1962	0.606098	0.303049	+	0.952975i	$0.401995\pi$
$284$	6.00000	0.356034
$285$	9.46410	0.560605
$286$	0	0
$287$	−5.19615	−0.306719
$288$	−23.1962	−1.36685
$289$	42.7846	2.51674
$290$	−9.00000	−0.528498
$291$	17.4641	1.02376
$292$	−3.19615	−0.187041
$293$	−0.803848	−0.0469613	−0.0234806	−	0.999724i	$-0.507475\pi$
$293$	−0.803848	−0.0469613	−0.0234806	+	0.999724i	$0.507475\pi$
$294$	4.73205	0.275979
$295$	12.5885	0.732928
$296$	12.1244	0.704714
$297$	5.07180	0.294295
$298$	−11.1962	−0.648576
$299$	0	0
$300$	−5.46410	−0.315470
$301$	−0.196152	−0.0113060
$302$	3.46410	0.199337
$303$	−21.1244	−1.21356
$304$	−10.0000	−0.573539
$305$	−8.32051	−0.476431
$306$	−59.7846	−3.41766
$307$	−4.58846	−0.261877	−0.130939	−	0.991390i	$-0.541799\pi$
$307$	−4.58846	−0.261877	−0.130939	+	0.991390i	$0.541799\pi$
$308$	1.26795	0.0722481
$309$	−39.3205	−2.23687
$310$	12.5885	0.714976
$311$	1.26795	0.0718988	0.0359494	−	0.999354i	$-0.488554\pi$
$311$	1.26795	0.0718988	0.0359494	+	0.999354i	$0.488554\pi$
$312$	0	0
$313$	28.7846	1.62700	0.813501	−	0.581563i	$-0.197559\pi$
$313$	28.7846	1.62700	0.813501	+	0.581563i	$0.197559\pi$
$314$	2.07180	0.116918
$315$	7.73205	0.435652
$316$	16.1962	0.911105
$317$	−6.46410	−0.363060	−0.181530	−	0.983385i	$-0.558105\pi$
$317$	−6.46410	−0.363060	−0.181530	+	0.983385i	$0.558105\pi$
$318$	−46.9808	−2.63455
$319$	−3.80385	−0.212975
$320$	1.73205	0.0968246
$321$	−21.4641	−1.19801
$322$	8.19615	0.456754
$323$	−15.4641	−0.860446
$324$	−2.46410	−0.136895
$325$	0	0
$326$	28.0526	1.55369
$327$	−22.9282	−1.26793
$328$	9.00000	0.496942
$329$	12.9282	0.712755
$330$	10.3923	0.572078
$331$	24.9808	1.37307	0.686533	−	0.727098i	$-0.259132\pi$
$331$	24.9808	1.37307	0.686533	+	0.727098i	$0.259132\pi$
$332$	−2.19615	−0.120530
$333$	−31.2487	−1.71242
$334$	−11.4115	−0.624412
$335$	−10.7321	−0.586355
$336$	−13.6603	−0.745228
$337$	11.0000	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$338$	0	0
$339$	36.5885	1.98721
$340$	−13.3923	−0.726300
$341$	5.32051	0.288122
$342$	15.4641	0.836203
$343$	1.00000	0.0539949
$344$	0.339746	0.0183179
$345$	22.3923	1.20556
$346$	14.7846	0.794826
$347$	7.26795	0.390164	0.195082	−	0.980787i	$-0.437503\pi$
$347$	7.26795	0.390164	0.195082	+	0.980787i	$0.437503\pi$
$348$	−8.19615	−0.439360
$349$	−24.7846	−1.32669	−0.663345	−	0.748314i	$-0.730864\pi$
$349$	−24.7846	−1.32669	−0.663345	+	0.748314i	$0.730864\pi$
$350$	−3.46410	−0.185164
$351$	0	0
$352$	−6.58846	−0.351166
$353$	20.6603	1.09963	0.549817	−	0.835285i	$-0.314697\pi$
$353$	20.6603	1.09963	0.549817	+	0.835285i	$0.314697\pi$
$354$	34.3923	1.82793
$355$	10.3923	0.551566
$356$	12.9282	0.685193
$357$	−21.1244	−1.11802
$358$	−12.0000	−0.634220
$359$	18.9282	0.998992	0.499496	−	0.866316i	$-0.333518\pi$
$359$	18.9282	0.998992	0.499496	+	0.866316i	$0.333518\pi$
$360$	−13.3923	−0.705836
$361$	−15.0000	−0.789474
$362$	9.67949	0.508743
$363$	−25.6603	−1.34681
$364$	0	0
$365$	−5.53590	−0.289762
$366$	−22.7321	−1.18822
$367$	4.19615	0.219037	0.109519	−	0.993985i	$-0.465069\pi$
$367$	4.19615	0.219037	0.109519	+	0.993985i	$0.465069\pi$
$368$	−23.6603	−1.23338
$369$	−23.1962	−1.20754
$370$	−21.0000	−1.09174
$371$	−9.92820	−0.515447
$372$	11.4641	0.594386
$373$	−11.3923	−0.589871	−0.294936	−	0.955517i	$-0.595298\pi$
$373$	−11.3923	−0.589871	−0.294936	+	0.955517i	$0.595298\pi$
$374$	−16.9808	−0.878054
$375$	−33.1244	−1.71053
$376$	−22.3923	−1.15479
$377$	0	0
$378$	6.92820	0.356348
$379$	26.5885	1.36576	0.682879	−	0.730532i	$-0.260728\pi$
$379$	26.5885	1.36576	0.682879	+	0.730532i	$0.260728\pi$
$380$	3.46410	0.177705
$381$	50.2487	2.57432
$382$	8.19615	0.419352
$383$	−11.6603	−0.595811	−0.297906	−	0.954595i	$-0.596288\pi$
$383$	−11.6603	−0.595811	−0.297906	+	0.954595i	$0.596288\pi$
$384$	33.1244	1.69037
$385$	2.19615	0.111926
$386$	8.66025	0.440795
$387$	−0.875644	−0.0445115
$388$	6.39230	0.324520
$389$	−23.5359	−1.19332	−0.596659	−	0.802495i	$-0.703505\pi$
$389$	−23.5359	−1.19332	−0.596659	+	0.802495i	$0.703505\pi$
$390$	0	0
$391$	−36.5885	−1.85036
$392$	−1.73205	−0.0874818
$393$	−9.46410	−0.477401
$394$	20.7846	1.04711
$395$	28.0526	1.41148
$396$	5.66025	0.284438
$397$	−18.7846	−0.942773	−0.471386	−	0.881927i	$-0.656246\pi$
$397$	−18.7846	−0.942773	−0.471386	+	0.881927i	$0.656246\pi$
$398$	3.46410	0.173640
$399$	5.46410	0.273547
$400$	10.0000	0.500000
$401$	−10.8564	−0.542143	−0.271072	−	0.962559i	$-0.587378\pi$
$401$	−10.8564	−0.542143	−0.271072	+	0.962559i	$0.587378\pi$
$402$	−29.3205	−1.46237
$403$	0	0
$404$	−7.73205	−0.384684
$405$	−4.26795	−0.212076
$406$	−5.19615	−0.257881
$407$	−8.87564	−0.439949
$408$	36.5885	1.81140
$409$	−16.8038	−0.830897	−0.415448	−	0.909617i	$-0.636375\pi$
$409$	−16.8038	−0.830897	−0.415448	+	0.909617i	$0.636375\pi$
$410$	−15.5885	−0.769859
$411$	22.0526	1.08777
$412$	−14.3923	−0.709058
$413$	7.26795	0.357632
$414$	36.5885	1.79822
$415$	−3.80385	−0.186724
$416$	0	0
$417$	−28.9282	−1.41662
$418$	4.39230	0.214835
$419$	−32.1962	−1.57288	−0.786442	−	0.617664i	$-0.788079\pi$
$419$	−32.1962	−1.57288	−0.786442	+	0.617664i	$0.788079\pi$
$420$	4.73205	0.230900
$421$	−32.1769	−1.56821	−0.784103	−	0.620630i	$-0.786877\pi$
$421$	−32.1769	−1.56821	−0.784103	+	0.620630i	$0.786877\pi$
$422$	−3.12436	−0.152091
$423$	57.7128	2.80609
$424$	17.1962	0.835119
$425$	15.4641	0.750119
$426$	28.3923	1.37561
$427$	−4.80385	−0.232474
$428$	−7.85641	−0.379754
$429$	0	0
$430$	−0.588457	−0.0283779
$431$	0.679492	0.0327300	0.0163650	−	0.999866i	$-0.494791\pi$
$431$	0.679492	0.0327300	0.0163650	+	0.999866i	$0.494791\pi$
$432$	−20.0000	−0.962250
$433$	−13.5885	−0.653020	−0.326510	−	0.945194i	$-0.605873\pi$
$433$	−13.5885	−0.653020	−0.326510	+	0.945194i	$0.605873\pi$
$434$	7.26795	0.348873
$435$	−14.1962	−0.680653
$436$	−8.39230	−0.401919
$437$	9.46410	0.452729
$438$	−15.1244	−0.722670
$439$	14.5885	0.696269	0.348135	−	0.937445i	$-0.386815\pi$
$439$	14.5885	0.696269	0.348135	+	0.937445i	$0.386815\pi$
$440$	−3.80385	−0.181341
$441$	4.46410	0.212576
$442$	0	0
$443$	23.3205	1.10799	0.553995	−	0.832520i	$-0.313103\pi$
$443$	23.3205	1.10799	0.553995	+	0.832520i	$0.313103\pi$
$444$	−19.1244	−0.907602
$445$	22.3923	1.06150
$446$	−17.3205	−0.820150
$447$	−17.6603	−0.835301
$448$	1.00000	0.0472456
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	−15.4641	−0.728985
$451$	−6.58846	−0.310238
$452$	13.3923	0.629921
$453$	5.46410	0.256726
$454$	9.80385	0.460117
$455$	0	0
$456$	−9.46410	−0.443197
$457$	11.0000	0.514558	0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000	0.514558	0.257279	+	0.966337i	$0.417174\pi$
$458$	−24.9282	−1.16482
$459$	−30.9282	−1.44360
$460$	8.19615	0.382148
$461$	−15.5885	−0.726027	−0.363013	−	0.931784i	$-0.618252\pi$
$461$	−15.5885	−0.726027	−0.363013	+	0.931784i	$0.618252\pi$
$462$	6.00000	0.279145
$463$	−4.58846	−0.213244	−0.106622	−	0.994300i	$-0.534003\pi$
$463$	−4.58846	−0.213244	−0.106622	+	0.994300i	$0.534003\pi$
$464$	15.0000	0.696358
$465$	19.8564	0.920819
$466$	−3.21539	−0.148950
$467$	25.5167	1.18077	0.590385	−	0.807122i	$-0.298976\pi$
$467$	25.5167	1.18077	0.590385	+	0.807122i	$0.298976\pi$
$468$	0	0
$469$	−6.19615	−0.286112
$470$	38.7846	1.78900
$471$	3.26795	0.150579
$472$	−12.5885	−0.579431
$473$	−0.248711	−0.0114358
$474$	76.6410	3.52024
$475$	−4.00000	−0.183533
$476$	−7.73205	−0.354398
$477$	−44.3205	−2.02930
$478$	−27.3731	−1.25201
$479$	1.26795	0.0579341	0.0289670	−	0.999580i	$-0.490778\pi$
$479$	1.26795	0.0579341	0.0289670	+	0.999580i	$0.490778\pi$
$480$	−24.5885	−1.12230
$481$	0	0
$482$	−36.7128	−1.67222
$483$	12.9282	0.588254
$484$	−9.39230	−0.426923
$485$	11.0718	0.502744
$486$	−32.4449	−1.47173
$487$	40.7846	1.84813	0.924064	−	0.382239i	$-0.124847\pi$
$487$	40.7846	1.84813	0.924064	+	0.382239i	$0.124847\pi$
$488$	8.32051	0.376652
$489$	44.2487	2.00100
$490$	3.00000	0.135526
$491$	7.60770	0.343330	0.171665	−	0.985155i	$-0.445085\pi$
$491$	7.60770	0.343330	0.171665	+	0.985155i	$0.445085\pi$
$492$	−14.1962	−0.640012
$493$	23.1962	1.04470
$494$	0	0
$495$	9.80385	0.440650
$496$	−20.9808	−0.942064
$497$	6.00000	0.269137
$498$	−10.3923	−0.465690
$499$	−38.9808	−1.74502	−0.872509	−	0.488598i	$-0.837509\pi$
$499$	−38.9808	−1.74502	−0.872509	+	0.488598i	$0.837509\pi$
$500$	−12.1244	−0.542218
$501$	−18.0000	−0.804181
$502$	−2.78461	−0.124283
$503$	−18.5885	−0.828818	−0.414409	−	0.910091i	$-0.636012\pi$
$503$	−18.5885	−0.828818	−0.414409	+	0.910091i	$0.636012\pi$
$504$	−7.73205	−0.344413
$505$	−13.3923	−0.595950
$506$	10.3923	0.461994
$507$	0	0
$508$	18.3923	0.816027
$509$	13.7321	0.608662	0.304331	−	0.952566i	$-0.401567\pi$
$509$	13.7321	0.608662	0.304331	+	0.952566i	$0.401567\pi$
$510$	−63.3731	−2.80621
$511$	−3.19615	−0.141389
$512$	8.66025	0.382733
$513$	8.00000	0.353209
$514$	10.6077	0.467885
$515$	−24.9282	−1.09847
$516$	−0.535898	−0.0235916
$517$	16.3923	0.720933
$518$	−12.1244	−0.532714
$519$	23.3205	1.02366
$520$	0	0
$521$	−24.1244	−1.05691	−0.528454	−	0.848962i	$-0.677228\pi$
$521$	−24.1244	−1.05691	−0.528454	+	0.848962i	$0.677228\pi$
$522$	−23.1962	−1.01527
$523$	−29.1769	−1.27582	−0.637909	−	0.770112i	$-0.720200\pi$
$523$	−29.1769	−1.27582	−0.637909	+	0.770112i	$0.720200\pi$
$524$	−3.46410	−0.151330
$525$	−5.46410	−0.238473
$526$	2.19615	0.0957568
$527$	−32.4449	−1.41332
$528$	−17.3205	−0.753778
$529$	−0.607695	−0.0264215
$530$	−29.7846	−1.29376
$531$	32.4449	1.40799
$532$	2.00000	0.0867110
$533$	0	0
$534$	61.1769	2.64738
$535$	−13.6077	−0.588312
$536$	10.7321	0.463554
$537$	−18.9282	−0.816812
$538$	8.78461	0.378731
$539$	1.26795	0.0546144
$540$	6.92820	0.298142
$541$	−14.6077	−0.628034	−0.314017	−	0.949417i	$-0.601675\pi$
$541$	−14.6077	−0.628034	−0.314017	+	0.949417i	$0.601675\pi$
$542$	10.0526	0.431794
$543$	15.2679	0.655210
$544$	40.1769	1.72257
$545$	−14.5359	−0.622649
$546$	0	0
$547$	17.8038	0.761238	0.380619	−	0.924732i	$-0.375711\pi$
$547$	17.8038	0.761238	0.380619	+	0.924732i	$0.375711\pi$
$548$	8.07180	0.344810
$549$	−21.4449	−0.915244
$550$	−4.39230	−0.187289
$551$	−6.00000	−0.255609
$552$	−22.3923	−0.953080
$553$	16.1962	0.688730
$554$	29.4449	1.25099
$555$	−33.1244	−1.40605
$556$	−10.5885	−0.449051
$557$	43.6410	1.84913	0.924565	−	0.381025i	$-0.124429\pi$
$557$	43.6410	1.84913	0.924565	+	0.381025i	$0.124429\pi$
$558$	32.4449	1.37350
$559$	0	0
$560$	−8.66025	−0.365963
$561$	−26.7846	−1.13085
$562$	23.1962	0.978471
$563$	28.0526	1.18227	0.591137	−	0.806571i	$-0.298679\pi$
$563$	28.0526	1.18227	0.591137	+	0.806571i	$0.298679\pi$
$564$	35.3205	1.48726
$565$	23.1962	0.975869
$566$	17.6603	0.742316
$567$	−2.46410	−0.103483
$568$	−10.3923	−0.436051
$569$	42.9282	1.79964	0.899822	−	0.436257i	$-0.143696\pi$
$569$	42.9282	1.79964	0.899822	+	0.436257i	$0.143696\pi$
$570$	16.3923	0.686598
$571$	16.7846	0.702414	0.351207	−	0.936298i	$-0.385771\pi$
$571$	16.7846	0.702414	0.351207	+	0.936298i	$0.385771\pi$
$572$	0	0
$573$	12.9282	0.540083
$574$	−9.00000	−0.375653
$575$	−9.46410	−0.394680
$576$	4.46410	0.186004
$577$	43.1962	1.79828	0.899140	−	0.437662i	$-0.144193\pi$
$577$	43.1962	1.79828	0.899140	+	0.437662i	$0.144193\pi$
$578$	74.1051	3.08237
$579$	13.6603	0.567701
$580$	−5.19615	−0.215758
$581$	−2.19615	−0.0911118
$582$	30.2487	1.25385
$583$	−12.5885	−0.521361
$584$	5.53590	0.229077
$585$	0	0
$586$	−1.39230	−0.0575156
$587$	16.3923	0.676583	0.338291	−	0.941041i	$-0.390151\pi$
$587$	16.3923	0.676583	0.338291	+	0.941041i	$0.390151\pi$
$588$	2.73205	0.112668
$589$	8.39230	0.345799
$590$	21.8038	0.897650
$591$	32.7846	1.34858
$592$	35.0000	1.43849
$593$	−17.4449	−0.716375	−0.358187	−	0.933650i	$-0.616605\pi$
$593$	−17.4449	−0.716375	−0.358187	+	0.933650i	$0.616605\pi$
$594$	8.78461	0.360437
$595$	−13.3923	−0.549031
$596$	−6.46410	−0.264780
$597$	5.46410	0.223631
$598$	0	0
$599$	43.8564	1.79192	0.895962	−	0.444131i	$-0.146487\pi$
$599$	43.8564	1.79192	0.895962	+	0.444131i	$0.146487\pi$
$600$	9.46410	0.386370
$601$	−29.9808	−1.22294	−0.611470	−	0.791267i	$-0.709422\pi$
$601$	−29.9808	−1.22294	−0.611470	+	0.791267i	$0.709422\pi$
$602$	−0.339746	−0.0138470
$603$	−27.6603	−1.12641
$604$	2.00000	0.0813788
$605$	−16.2679	−0.661386
$606$	−36.5885	−1.48630
$607$	−14.3923	−0.584166	−0.292083	−	0.956393i	$-0.594348\pi$
$607$	−14.3923	−0.584166	−0.292083	+	0.956393i	$0.594348\pi$
$608$	−10.3923	−0.421464
$609$	−8.19615	−0.332125
$610$	−14.4115	−0.583506
$611$	0	0
$612$	−34.5167	−1.39525
$613$	3.39230	0.137014	0.0685070	−	0.997651i	$-0.478176\pi$
$613$	3.39230	0.137014	0.0685070	+	0.997651i	$0.478176\pi$
$614$	−7.94744	−0.320733
$615$	−24.5885	−0.991502
$616$	−2.19615	−0.0884855
$617$	49.3923	1.98846	0.994230	−	0.107272i	$-0.0342117\pi$
$617$	49.3923	1.98846	0.994230	+	0.107272i	$0.0342117\pi$
$618$	−68.1051	−2.73959
$619$	35.3731	1.42176	0.710882	−	0.703311i	$-0.248296\pi$
$619$	35.3731	1.42176	0.710882	+	0.703311i	$0.248296\pi$
$620$	7.26795	0.291888
$621$	18.9282	0.759563
$622$	2.19615	0.0880577
$623$	12.9282	0.517958
$624$	0	0
$625$	−11.0000	−0.440000
$626$	49.8564	1.99266
$627$	6.92820	0.276686
$628$	1.19615	0.0477317
$629$	54.1244	2.15808
$630$	13.3923	0.533562
$631$	−12.7846	−0.508947	−0.254474	−	0.967080i	$-0.581902\pi$
$631$	−12.7846	−0.508947	−0.254474	+	0.967080i	$0.581902\pi$
$632$	−28.0526	−1.11587
$633$	−4.92820	−0.195878
$634$	−11.1962	−0.444656
$635$	31.8564	1.26418
$636$	−27.1244	−1.07555
$637$	0	0
$638$	−6.58846	−0.260840
$639$	26.7846	1.05958
$640$	21.0000	0.830098
$641$	28.8564	1.13976	0.569880	−	0.821728i	$-0.306990\pi$
$641$	28.8564	1.13976	0.569880	+	0.821728i	$0.306990\pi$
$642$	−37.1769	−1.46726
$643$	−0.784610	−0.0309420	−0.0154710	−	0.999880i	$-0.504925\pi$
$643$	−0.784610	−0.0309420	−0.0154710	+	0.999880i	$0.504925\pi$
$644$	4.73205	0.186469
$645$	−0.928203	−0.0365480
$646$	−26.7846	−1.05383
$647$	45.0333	1.77044	0.885221	−	0.465170i	$-0.154007\pi$
$647$	45.0333	1.77044	0.885221	+	0.465170i	$0.154007\pi$
$648$	4.26795	0.167661
$649$	9.21539	0.361736
$650$	0	0
$651$	11.4641	0.449314
$652$	16.1962	0.634290
$653$	−37.8564	−1.48144	−0.740718	−	0.671816i	$-0.765514\pi$
$653$	−37.8564	−1.48144	−0.740718	+	0.671816i	$0.765514\pi$
$654$	−39.7128	−1.55289
$655$	−6.00000	−0.234439
$656$	25.9808	1.01438
$657$	−14.2679	−0.556646
$658$	22.3923	0.872943
$659$	28.3923	1.10601	0.553004	−	0.833179i	$-0.313482\pi$
$659$	28.3923	1.10601	0.553004	+	0.833179i	$0.313482\pi$
$660$	6.00000	0.233550
$661$	−33.1962	−1.29118	−0.645590	−	0.763684i	$-0.723389\pi$
$661$	−33.1962	−1.29118	−0.645590	+	0.763684i	$0.723389\pi$
$662$	43.2679	1.68166
$663$	0	0
$664$	3.80385	0.147618
$665$	3.46410	0.134332
$666$	−54.1244	−2.09728
$667$	−14.1962	−0.549677
$668$	−6.58846	−0.254915
$669$	−27.3205	−1.05627
$670$	−18.5885	−0.718135
$671$	−6.09103	−0.235142
$672$	−14.1962	−0.547628
$673$	−44.1769	−1.70289	−0.851447	−	0.524440i	$-0.824275\pi$
$673$	−44.1769	−1.70289	−0.851447	+	0.524440i	$0.824275\pi$
$674$	19.0526	0.733877
$675$	−8.00000	−0.307920
$676$	0	0
$677$	−23.0718	−0.886721	−0.443361	−	0.896343i	$-0.646214\pi$
$677$	−23.0718	−0.886721	−0.443361	+	0.896343i	$0.646214\pi$
$678$	63.3731	2.43383
$679$	6.39230	0.245314
$680$	23.1962	0.889532
$681$	15.4641	0.592586
$682$	9.21539	0.352876
$683$	15.4641	0.591717	0.295859	−	0.955232i	$-0.404394\pi$
$683$	15.4641	0.591717	0.295859	+	0.955232i	$0.404394\pi$
$684$	8.92820	0.341378
$685$	13.9808	0.534177
$686$	1.73205	0.0661300
$687$	−39.3205	−1.50017
$688$	0.980762	0.0373912
$689$	0	0
$690$	38.7846	1.47650
$691$	0.392305	0.0149240	0.00746199	−	0.999972i	$-0.497625\pi$
$691$	0.392305	0.0149240	0.00746199	+	0.999972i	$0.497625\pi$
$692$	8.53590	0.324486
$693$	5.66025	0.215015
$694$	12.5885	0.477851
$695$	−18.3397	−0.695666
$696$	14.1962	0.538104
$697$	40.1769	1.52181
$698$	−42.9282	−1.62486
$699$	−5.07180	−0.191833
$700$	−2.00000	−0.0755929
$701$	20.7846	0.785024	0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846	0.785024	0.392512	+	0.919747i	$0.371606\pi$
$702$	0	0
$703$	−14.0000	−0.528020
$704$	1.26795	0.0477876
$705$	61.1769	2.30406
$706$	35.7846	1.34677
$707$	−7.73205	−0.290794
$708$	19.8564	0.746249
$709$	30.1769	1.13332	0.566659	−	0.823952i	$-0.308236\pi$
$709$	30.1769	1.13332	0.566659	+	0.823952i	$0.308236\pi$
$710$	18.0000	0.675528
$711$	72.3013	2.71151
$712$	−22.3923	−0.839187
$713$	19.8564	0.743628
$714$	−36.5885	−1.36929
$715$	0	0
$716$	−6.92820	−0.258919
$717$	−43.1769	−1.61247
$718$	32.7846	1.22351
$719$	−7.26795	−0.271049	−0.135524	−	0.990774i	$-0.543272\pi$
$719$	−7.26795	−0.271049	−0.135524	+	0.990774i	$0.543272\pi$
$720$	−38.6603	−1.44078
$721$	−14.3923	−0.535997
$722$	−25.9808	−0.966904
$723$	−57.9090	−2.15366
$724$	5.58846	0.207693
$725$	6.00000	0.222834
$726$	−44.4449	−1.64950
$727$	−41.1769	−1.52717	−0.763584	−	0.645709i	$-0.776562\pi$
$727$	−41.1769	−1.52717	−0.763584	+	0.645709i	$0.776562\pi$
$728$	0	0
$729$	−43.7846	−1.62165
$730$	−9.58846	−0.354885
$731$	1.51666	0.0560957
$732$	−13.1244	−0.485090
$733$	23.5885	0.871260	0.435630	−	0.900126i	$-0.356526\pi$
$733$	23.5885	0.871260	0.435630	+	0.900126i	$0.356526\pi$
$734$	7.26795	0.268265
$735$	4.73205	0.174544
$736$	−24.5885	−0.906343
$737$	−7.85641	−0.289394
$738$	−40.1769	−1.47893
$739$	40.7846	1.50029	0.750143	−	0.661276i	$-0.229985\pi$
$739$	40.7846	1.50029	0.750143	+	0.661276i	$0.229985\pi$
$740$	−12.1244	−0.445700
$741$	0	0
$742$	−17.1962	−0.631291
$743$	−7.60770	−0.279099	−0.139550	−	0.990215i	$-0.544565\pi$
$743$	−7.60770	−0.279099	−0.139550	+	0.990215i	$0.544565\pi$
$744$	−19.8564	−0.727971
$745$	−11.1962	−0.410195
$746$	−19.7321	−0.722442
$747$	−9.80385	−0.358704
$748$	−9.80385	−0.358464
$749$	−7.85641	−0.287067
$750$	−57.3731	−2.09497
$751$	35.8038	1.30650	0.653250	−	0.757142i	$-0.273405\pi$
$751$	35.8038	1.30650	0.653250	+	0.757142i	$0.273405\pi$
$752$	−64.6410	−2.35722
$753$	−4.39230	−0.160064
$754$	0	0
$755$	3.46410	0.126072
$756$	4.00000	0.145479
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	46.0526	1.67270
$759$	16.3923	0.595003
$760$	−6.00000	−0.217643
$761$	41.3205	1.49787	0.748934	−	0.662645i	$-0.230566\pi$
$761$	41.3205	1.49787	0.748934	+	0.662645i	$0.230566\pi$
$762$	87.0333	3.15288
$763$	−8.39230	−0.303822
$764$	4.73205	0.171200
$765$	−59.7846	−2.16152
$766$	−20.1962	−0.729717
$767$	0	0
$768$	51.9090	1.87310
$769$	15.1769	0.547294	0.273647	−	0.961830i	$-0.411770\pi$
$769$	15.1769	0.547294	0.273647	+	0.961830i	$0.411770\pi$
$770$	3.80385	0.137081
$771$	16.7321	0.602590
$772$	5.00000	0.179954
$773$	−12.9282	−0.464995	−0.232498	−	0.972597i	$-0.574690\pi$
$773$	−12.9282	−0.464995	−0.232498	+	0.972597i	$0.574690\pi$
$774$	−1.51666	−0.0545152
$775$	−8.39230	−0.301460
$776$	−11.0718	−0.397454
$777$	−19.1244	−0.686082
$778$	−40.7654	−1.46151
$779$	−10.3923	−0.372343
$780$	0	0
$781$	7.60770	0.272225
$782$	−63.3731	−2.26622
$783$	−12.0000	−0.428845
$784$	−5.00000	−0.178571
$785$	2.07180	0.0739456
$786$	−16.3923	−0.584694
$787$	12.9808	0.462714	0.231357	−	0.972869i	$-0.425683\pi$
$787$	12.9808	0.462714	0.231357	+	0.972869i	$0.425683\pi$
$788$	12.0000	0.427482
$789$	3.46410	0.123325
$790$	48.5885	1.72870
$791$	13.3923	0.476176
$792$	−9.80385	−0.348365
$793$	0	0
$794$	−32.5359	−1.15466
$795$	−46.9808	−1.66624
$796$	2.00000	0.0708881
$797$	−34.3923	−1.21824	−0.609119	−	0.793079i	$-0.708477\pi$
$797$	−34.3923	−1.21824	−0.609119	+	0.793079i	$0.708477\pi$
$798$	9.46410	0.335026
$799$	−99.9615	−3.53638
$800$	10.3923	0.367423
$801$	57.7128	2.03918
$802$	−18.8038	−0.663987
$803$	−4.05256	−0.143012
$804$	−16.9282	−0.597012
$805$	8.19615	0.288876
$806$	0	0
$807$	13.8564	0.487769
$808$	13.3923	0.471140
$809$	2.07180	0.0728405	0.0364202	−	0.999337i	$-0.488405\pi$
$809$	2.07180	0.0728405	0.0364202	+	0.999337i	$0.488405\pi$
$810$	−7.39230	−0.259739
$811$	−16.5885	−0.582500	−0.291250	−	0.956647i	$-0.594071\pi$
$811$	−16.5885	−0.582500	−0.291250	+	0.956647i	$0.594071\pi$
$812$	−3.00000	−0.105279
$813$	15.8564	0.556108
$814$	−15.3731	−0.538826
$815$	28.0526	0.982638
$816$	105.622	3.69750
$817$	−0.392305	−0.0137250
$818$	−29.1051	−1.01764
$819$	0	0
$820$	−9.00000	−0.314294
$821$	4.14359	0.144612	0.0723062	−	0.997382i	$-0.476964\pi$
$821$	4.14359	0.144612	0.0723062	+	0.997382i	$0.476964\pi$
$822$	38.1962	1.33224
$823$	−41.1769	−1.43534	−0.717669	−	0.696385i	$-0.754791\pi$
$823$	−41.1769	−1.43534	−0.717669	+	0.696385i	$0.754791\pi$
$824$	24.9282	0.868415
$825$	−6.92820	−0.241209
$826$	12.5885	0.438008
$827$	−16.9808	−0.590479	−0.295239	−	0.955423i	$-0.595399\pi$
$827$	−16.9808	−0.590479	−0.295239	+	0.955423i	$0.595399\pi$
$828$	21.1244	0.734122
$829$	−0.411543	−0.0142935	−0.00714673	−	0.999974i	$-0.502275\pi$
$829$	−0.411543	−0.0142935	−0.00714673	+	0.999974i	$0.502275\pi$
$830$	−6.58846	−0.228689
$831$	46.4449	1.61115
$832$	0	0
$833$	−7.73205	−0.267900
$834$	−50.1051	−1.73500
$835$	−11.4115	−0.394913
$836$	2.53590	0.0877059
$837$	16.7846	0.580161
$838$	−55.7654	−1.92638
$839$	−18.0000	−0.621429	−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000	−0.621429	−0.310715	+	0.950503i	$0.600568\pi$
$840$	−8.19615	−0.282794
$841$	−20.0000	−0.689655
$842$	−55.7321	−1.92065
$843$	36.5885	1.26017
$844$	−1.80385	−0.0620910
$845$	0	0
$846$	99.9615	3.43675
$847$	−9.39230	−0.322723
$848$	49.6410	1.70468
$849$	27.8564	0.956029
$850$	26.7846	0.918705
$851$	−33.1244	−1.13549
$852$	16.3923	0.561591
$853$	5.58846	0.191345	0.0956726	−	0.995413i	$-0.469500\pi$
$853$	5.58846	0.191345	0.0956726	+	0.995413i	$0.469500\pi$
$854$	−8.32051	−0.284722
$855$	15.4641	0.528861
$856$	13.6077	0.465101
$857$	−30.1244	−1.02903	−0.514514	−	0.857482i	$-0.672028\pi$
$857$	−30.1244	−1.02903	−0.514514	+	0.857482i	$0.672028\pi$
$858$	0	0
$859$	−7.80385	−0.266264	−0.133132	−	0.991098i	$-0.542503\pi$
$859$	−7.80385	−0.266264	−0.133132	+	0.991098i	$0.542503\pi$
$860$	−0.339746	−0.0115852
$861$	−14.1962	−0.483804
$862$	1.17691	0.0400859
$863$	7.51666	0.255870	0.127935	−	0.991783i	$-0.459165\pi$
$863$	7.51666	0.255870	0.127935	+	0.991783i	$0.459165\pi$
$864$	−20.7846	−0.707107
$865$	14.7846	0.502692
$866$	−23.5359	−0.799782
$867$	116.890	3.96978
$868$	4.19615	0.142427
$869$	20.5359	0.696633
$870$	−24.5885	−0.833627
$871$	0	0
$872$	14.5359	0.492248
$873$	28.5359	0.965794
$874$	16.3923	0.554478
$875$	−12.1244	−0.409878
$876$	−8.73205	−0.295029
$877$	19.7846	0.668079	0.334039	−	0.942559i	$-0.391588\pi$
$877$	19.7846	0.668079	0.334039	+	0.942559i	$0.391588\pi$
$878$	25.2679	0.852752
$879$	−2.19615	−0.0740744
$880$	−10.9808	−0.370161
$881$	−8.41154	−0.283392	−0.141696	−	0.989910i	$-0.545256\pi$
$881$	−8.41154	−0.283392	−0.141696	+	0.989910i	$0.545256\pi$
$882$	7.73205	0.260352
$883$	−47.7654	−1.60743	−0.803716	−	0.595013i	$-0.797147\pi$
$883$	−47.7654	−1.60743	−0.803716	+	0.595013i	$0.797147\pi$
$884$	0	0
$885$	34.3923	1.15608
$886$	40.3923	1.35701
$887$	11.3205	0.380105	0.190053	−	0.981774i	$-0.439134\pi$
$887$	11.3205	0.380105	0.190053	+	0.981774i	$0.439134\pi$
$888$	33.1244	1.11158
$889$	18.3923	0.616858
$890$	38.7846	1.30006
$891$	−3.12436	−0.104670
$892$	−10.0000	−0.334825
$893$	25.8564	0.865252
$894$	−30.5885	−1.02303
$895$	−12.0000	−0.401116
$896$	12.1244	0.405046
$897$	0	0
$898$	−20.7846	−0.693591
$899$	−12.5885	−0.419849
$900$	−8.92820	−0.297607
$901$	76.7654	2.55743
$902$	−11.4115	−0.379963
$903$	−0.535898	−0.0178336
$904$	−23.1962	−0.771493
$905$	9.67949	0.321757
$906$	9.46410	0.314424
$907$	−16.5885	−0.550811	−0.275405	−	0.961328i	$-0.588812\pi$
$907$	−16.5885	−0.550811	−0.275405	+	0.961328i	$0.588812\pi$
$908$	5.66025	0.187842
$909$	−34.5167	−1.14485
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	−27.3205	−0.904672
$913$	−2.78461	−0.0921571
$914$	19.0526	0.630203
$915$	−22.7321	−0.751498
$916$	−14.3923	−0.475535
$917$	−3.46410	−0.114395
$918$	−53.5692	−1.76805
$919$	−39.5692	−1.30527	−0.652634	−	0.757673i	$-0.726336\pi$
$919$	−39.5692	−1.30527	−0.652634	+	0.757673i	$0.726336\pi$
$920$	−14.1962	−0.468033
$921$	−12.5359	−0.413072
$922$	−27.0000	−0.889198
$923$	0	0
$924$	3.46410	0.113961
$925$	14.0000	0.460317
$926$	−7.94744	−0.261169
$927$	−64.2487	−2.11020
$928$	15.5885	0.511716
$929$	52.5167	1.72302	0.861508	−	0.507744i	$-0.169520\pi$
$929$	52.5167	1.72302	0.861508	+	0.507744i	$0.169520\pi$
$930$	34.3923	1.12777
$931$	2.00000	0.0655474
$932$	−1.85641	−0.0608086
$933$	3.46410	0.113410
$934$	44.1962	1.44614
$935$	−16.9808	−0.555330
$936$	0	0
$937$	−51.1962	−1.67251	−0.836253	−	0.548344i	$-0.815258\pi$
$937$	−51.1962	−1.67251	−0.836253	+	0.548344i	$0.815258\pi$
$938$	−10.7321	−0.350414
$939$	78.6410	2.56635
$940$	22.3923	0.730356
$941$	−28.1436	−0.917455	−0.458727	−	0.888577i	$-0.651695\pi$
$941$	−28.1436	−0.917455	−0.458727	+	0.888577i	$0.651695\pi$
$942$	5.66025	0.184421
$943$	−24.5885	−0.800710
$944$	−36.3397	−1.18276
$945$	6.92820	0.225374
$946$	−0.430781	−0.0140059
$947$	−7.26795	−0.236177	−0.118088	−	0.993003i	$-0.537677\pi$
$947$	−7.26795	−0.236177	−0.118088	+	0.993003i	$0.537677\pi$
$948$	44.2487	1.43713
$949$	0	0
$950$	−6.92820	−0.224781
$951$	−17.6603	−0.572673
$952$	13.3923	0.434047
$953$	−25.1769	−0.815560	−0.407780	−	0.913080i	$-0.633697\pi$
$953$	−25.1769	−0.815560	−0.407780	+	0.913080i	$0.633697\pi$
$954$	−76.7654	−2.48537
$955$	8.19615	0.265221
$956$	−15.8038	−0.511133
$957$	−10.3923	−0.335936
$958$	2.19615	0.0709545
$959$	8.07180	0.260652
$960$	4.73205	0.152726
$961$	−13.3923	−0.432010
$962$	0	0
$963$	−35.0718	−1.13017
$964$	−21.1962	−0.682682
$965$	8.66025	0.278783
$966$	22.3923	0.720461
$967$	54.9808	1.76806	0.884031	−	0.467428i	$-0.154819\pi$
$967$	54.9808	1.76806	0.884031	+	0.467428i	$0.154819\pi$
$968$	16.2679	0.522872
$969$	−42.2487	−1.35722
$970$	19.1769	0.615734
$971$	−52.6410	−1.68933	−0.844665	−	0.535295i	$-0.820201\pi$
$971$	−52.6410	−1.68933	−0.844665	+	0.535295i	$0.820201\pi$
$972$	−18.7321	−0.600831
$973$	−10.5885	−0.339450
$974$	70.6410	2.26348
$975$	0	0
$976$	24.0192	0.768837
$977$	31.6410	1.01229	0.506143	−	0.862450i	$-0.331071\pi$
$977$	31.6410	1.01229	0.506143	+	0.862450i	$0.331071\pi$
$978$	76.6410	2.45071
$979$	16.3923	0.523900
$980$	1.73205	0.0553283
$981$	−37.4641	−1.19614
$982$	13.1769	0.420492
$983$	−17.3205	−0.552438	−0.276219	−	0.961095i	$-0.589082\pi$
$983$	−17.3205	−0.552438	−0.276219	+	0.961095i	$0.589082\pi$
$984$	24.5885	0.783851
$985$	20.7846	0.662253
$986$	40.1769	1.27949
$987$	35.3205	1.12426
$988$	0	0
$989$	−0.928203	−0.0295151
$990$	16.9808	0.539684
$991$	18.9808	0.602944	0.301472	−	0.953475i	$-0.402522\pi$
$991$	18.9808	0.602944	0.301472	+	0.953475i	$0.402522\pi$
$992$	−21.8038	−0.692273
$993$	68.2487	2.16581
$994$	10.3923	0.329624
$995$	3.46410	0.109819
$996$	−6.00000	−0.190117
$997$	−4.80385	−0.152139	−0.0760697	−	0.997103i	$-0.524237\pi$
$997$	−4.80385	−0.152139	−0.0760697	+	0.997103i	$0.524237\pi$
$998$	−67.5167	−2.13720
$999$	−28.0000	−0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.f.1.2		2
7.6	odd	2		8281.2.a.r.1.2		2
13.3	even	3		91.2.f.b.22.1	✓	4
13.5	odd	4		1183.2.c.e.337.2		4
13.8	odd	4		1183.2.c.e.337.4		4
13.9	even	3		91.2.f.b.29.1	yes	4
13.12	even	2		1183.2.a.e.1.1		2
39.29	odd	6		819.2.o.b.568.2		4
39.35	odd	6		819.2.o.b.757.2		4
52.3	odd	6		1456.2.s.o.113.2		4
52.35	odd	6		1456.2.s.o.1121.2		4
91.3	odd	6		637.2.g.d.373.1		4
91.9	even	3		637.2.g.e.263.1		4
91.16	even	3		637.2.h.d.165.2		4
91.48	odd	6		637.2.f.d.393.1		4
91.55	odd	6		637.2.f.d.295.1		4
91.61	odd	6		637.2.g.d.263.1		4
91.68	odd	6		637.2.h.e.165.2		4
91.74	even	3		637.2.h.d.471.2		4
91.81	even	3		637.2.g.e.373.1		4
91.87	odd	6		637.2.h.e.471.2		4
91.90	odd	2		8281.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.1	✓	4	13.3	even	3
91.2.f.b.29.1	yes	4	13.9	even	3
637.2.f.d.295.1		4	91.55	odd	6
637.2.f.d.393.1		4	91.48	odd	6
637.2.g.d.263.1		4	91.61	odd	6
637.2.g.d.373.1		4	91.3	odd	6
637.2.g.e.263.1		4	91.9	even	3
637.2.g.e.373.1		4	91.81	even	3
637.2.h.d.165.2		4	91.16	even	3
637.2.h.d.471.2		4	91.74	even	3
637.2.h.e.165.2		4	91.68	odd	6
637.2.h.e.471.2		4	91.87	odd	6
819.2.o.b.568.2		4	39.29	odd	6
819.2.o.b.757.2		4	39.35	odd	6
1183.2.a.e.1.1		2	13.12	even	2
1183.2.a.f.1.2		2	1.1	even	1	trivial
1183.2.c.e.337.2		4	13.5	odd	4
1183.2.c.e.337.4		4	13.8	odd	4
1456.2.s.o.113.2		4	52.3	odd	6
1456.2.s.o.1121.2		4	52.35	odd	6
8281.2.a.r.1.2		2	7.6	odd	2
8281.2.a.t.1.1		2	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73205 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +4.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+1.73205 q^{2} +2.73205 q^{3} +1.00000 q^{4} +1.73205 q^{5} +4.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +4.46410 q^{9} +3.00000 q^{10} +1.26795 q^{11} +2.73205 q^{12} +1.73205 q^{14} +4.73205 q^{15} -5.00000 q^{16} -7.73205 q^{17} +7.73205 q^{18} +2.00000 q^{19} +1.73205 q^{20} +2.73205 q^{21} +2.19615 q^{22} +4.73205 q^{23} -4.73205 q^{24} -2.00000 q^{25} +4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +8.19615 q^{30} +4.19615 q^{31} -5.19615 q^{32} +3.46410 q^{33} -13.3923 q^{34} +1.73205 q^{35} +4.46410 q^{36} -7.00000 q^{37} +3.46410 q^{38} -3.00000 q^{40} -5.19615 q^{41} +4.73205 q^{42} -0.196152 q^{43} +1.26795 q^{44} +7.73205 q^{45} +8.19615 q^{46} +12.9282 q^{47} -13.6603 q^{48} +1.00000 q^{49} -3.46410 q^{50} -21.1244 q^{51} -9.92820 q^{53} +6.92820 q^{54} +2.19615 q^{55} -1.73205 q^{56} +5.46410 q^{57} -5.19615 q^{58} +7.26795 q^{59} +4.73205 q^{60} -4.80385 q^{61} +7.26795 q^{62} +4.46410 q^{63} +1.00000 q^{64} +6.00000 q^{66} -6.19615 q^{67} -7.73205 q^{68} +12.9282 q^{69} +3.00000 q^{70} +6.00000 q^{71} -7.73205 q^{72} -3.19615 q^{73} -12.1244 q^{74} -5.46410 q^{75} +2.00000 q^{76} +1.26795 q^{77} +16.1962 q^{79} -8.66025 q^{80} -2.46410 q^{81} -9.00000 q^{82} -2.19615 q^{83} +2.73205 q^{84} -13.3923 q^{85} -0.339746 q^{86} -8.19615 q^{87} -2.19615 q^{88} +12.9282 q^{89} +13.3923 q^{90} +4.73205 q^{92} +11.4641 q^{93} +22.3923 q^{94} +3.46410 q^{95} -14.1962 q^{96} +6.39230 q^{97} +1.73205 q^{98} +5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{15} - 10 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 8 q^{27} + 2 q^{28} - 6 q^{29} + 6 q^{30} - 2 q^{31} - 6 q^{34} + 2 q^{36} - 14 q^{37} - 6 q^{40} + 6 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{45} + 6 q^{46} + 12 q^{47} - 10 q^{48} + 2 q^{49} - 18 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} + 18 q^{59} + 6 q^{60} - 20 q^{61} + 18 q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{66} - 2 q^{67} - 12 q^{68} + 12 q^{69} + 6 q^{70} + 12 q^{71} - 12 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} + 6 q^{77} + 22 q^{79} + 2 q^{81} - 18 q^{82} + 6 q^{83} + 2 q^{84} - 6 q^{85} - 18 q^{86} - 6 q^{87} + 6 q^{88} + 12 q^{89} + 6 q^{90} + 6 q^{92} + 16 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^15 - 10 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 8 * q^27 + 2 * q^28 - 6 * q^29 + 6 * q^30 - 2 * q^31 - 6 * q^34 + 2 * q^36 - 14 * q^37 - 6 * q^40 + 6 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^45 + 6 * q^46 + 12 * q^47 - 10 * q^48 + 2 * q^49 - 18 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 + 18 * q^59 + 6 * q^60 - 20 * q^61 + 18 * q^62 + 2 * q^63 + 2 * q^64 + 12 * q^66 - 2 * q^67 - 12 * q^68 + 12 * q^69 + 6 * q^70 + 12 * q^71 - 12 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 + 6 * q^77 + 22 * q^79 + 2 * q^81 - 18 * q^82 + 6 * q^83 + 2 * q^84 - 6 * q^85 - 18 * q^86 - 6 * q^87 + 6 * q^88 + 12 * q^89 + 6 * q^90 + 6 * q^92 + 16 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 6 * q^99

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