LMFDB - Embedded newform 1210.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1210,2,Mod(1,1210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1210, 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("1210.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1210 = 2 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1210.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:	$9.66189864457$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + x + 11 $ x^4 - x^3 - 8*x^2 + x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.26498$ of defining polynomial
Character	$\chi$	$=$	1210.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.264977 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.264977 q^{6} -4.31175 q^{7} -1.00000 q^{8} -2.92979 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.264977 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.264977 q^{6} -4.31175 q^{7} -1.00000 q^{8} -2.92979 q^{9} -1.00000 q^{10} -0.264977 q^{12} +1.21054 q^{13} +4.31175 q^{14} -0.264977 q^{15} +1.00000 q^{16} -7.16586 q^{17} +2.92979 q^{18} +2.71925 q^{19} +1.00000 q^{20} +1.14252 q^{21} +7.01787 q^{23} +0.264977 q^{24} +1.00000 q^{25} -1.21054 q^{26} +1.57126 q^{27} -4.31175 q^{28} +10.5657 q^{29} +0.264977 q^{30} +3.62142 q^{31} -1.00000 q^{32} +7.16586 q^{34} -4.31175 q^{35} -2.92979 q^{36} +2.11908 q^{37} -2.71925 q^{38} -0.320766 q^{39} -1.00000 q^{40} +2.75289 q^{41} -1.14252 q^{42} +6.59251 q^{43} -2.92979 q^{45} -7.01787 q^{46} +5.74050 q^{47} -0.264977 q^{48} +11.5912 q^{49} -1.00000 q^{50} +1.89879 q^{51} +1.21054 q^{52} -5.87535 q^{53} -1.57126 q^{54} +4.31175 q^{56} -0.720538 q^{57} -10.5657 q^{58} -5.89750 q^{59} -0.264977 q^{60} -6.14461 q^{61} -3.62142 q^{62} +12.6325 q^{63} +1.00000 q^{64} +1.21054 q^{65} -1.63381 q^{67} -7.16586 q^{68} -1.85957 q^{69} +4.31175 q^{70} +7.43849 q^{71} +2.92979 q^{72} -7.39217 q^{73} -2.11908 q^{74} -0.264977 q^{75} +2.71925 q^{76} +0.320766 q^{78} +7.00209 q^{79} +1.00000 q^{80} +8.37301 q^{81} -2.75289 q^{82} -1.59460 q^{83} +1.14252 q^{84} -7.16586 q^{85} -6.59251 q^{86} -2.79967 q^{87} +1.24711 q^{89} +2.92979 q^{90} -5.21955 q^{91} +7.01787 q^{92} -0.959592 q^{93} -5.74050 q^{94} +2.71925 q^{95} +0.264977 q^{96} -6.91327 q^{97} -11.5912 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9	$ 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9} - 4 q^{10} + 3 q^{12} - 7 q^{13} + 3 q^{14} + 3 q^{15} + 4 q^{16} - q^{17} - 7 q^{18} + 4 q^{19} + 4 q^{20} + 16 q^{21} + 13 q^{23} - 3 q^{24} + 4 q^{25} + 7 q^{26} + 12 q^{27} - 3 q^{28} + 4 q^{29} - 3 q^{30} + 12 q^{31} - 4 q^{32} + q^{34} - 3 q^{35} + 7 q^{36} - 9 q^{37} - 4 q^{38} + 6 q^{39} - 4 q^{40} - 16 q^{42} + 19 q^{43} + 7 q^{45} - 13 q^{46} + 3 q^{47} + 3 q^{48} + 11 q^{49} - 4 q^{50} + 10 q^{51} - 7 q^{52} + 3 q^{53} - 12 q^{54} + 3 q^{56} - 24 q^{57} - 4 q^{58} + 2 q^{59} + 3 q^{60} - 10 q^{61} - 12 q^{62} + 29 q^{63} + 4 q^{64} - 7 q^{65} - 13 q^{67} - q^{68} + 30 q^{69} + 3 q^{70} + 16 q^{71} - 7 q^{72} - q^{73} + 9 q^{74} + 3 q^{75} + 4 q^{76} - 6 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} + 27 q^{83} + 16 q^{84} - q^{85} - 19 q^{86} + 10 q^{87} + 16 q^{89} - 7 q^{90} - 16 q^{91} + 13 q^{92} - 4 q^{93} - 3 q^{94} + 4 q^{95} - 3 q^{96} - 13 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9 - 4 * q^10 + 3 * q^12 - 7 * q^13 + 3 * q^14 + 3 * q^15 + 4 * q^16 - q^17 - 7 * q^18 + 4 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^23 - 3 * q^24 + 4 * q^25 + 7 * q^26 + 12 * q^27 - 3 * q^28 + 4 * q^29 - 3 * q^30 + 12 * q^31 - 4 * q^32 + q^34 - 3 * q^35 + 7 * q^36 - 9 * q^37 - 4 * q^38 + 6 * q^39 - 4 * q^40 - 16 * q^42 + 19 * q^43 + 7 * q^45 - 13 * q^46 + 3 * q^47 + 3 * q^48 + 11 * q^49 - 4 * q^50 + 10 * q^51 - 7 * q^52 + 3 * q^53 - 12 * q^54 + 3 * q^56 - 24 * q^57 - 4 * q^58 + 2 * q^59 + 3 * q^60 - 10 * q^61 - 12 * q^62 + 29 * q^63 + 4 * q^64 - 7 * q^65 - 13 * q^67 - q^68 + 30 * q^69 + 3 * q^70 + 16 * q^71 - 7 * q^72 - q^73 + 9 * q^74 + 3 * q^75 + 4 * q^76 - 6 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 + 27 * q^83 + 16 * q^84 - q^85 - 19 * q^86 + 10 * q^87 + 16 * q^89 - 7 * q^90 - 16 * q^91 + 13 * q^92 - 4 * q^93 - 3 * q^94 + 4 * q^95 - 3 * q^96 - 13 * q^97 - 11 * q^98

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
$3$	−0.264977	−0.152985	−0.0764923	−	0.997070i	$-0.524372\pi$
$3$	−0.264977	−0.152985	−0.0764923	+	0.997070i	$0.524372\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.264977	0.108176
$7$	−4.31175	−1.62969	−0.814845	−	0.579679i	$-0.803178\pi$
$7$	−4.31175	−1.62969	−0.814845	+	0.579679i	$0.803178\pi$
$8$	−1.00000	−0.353553
$9$	−2.92979	−0.976596
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−0.264977	−0.0764923
$13$	1.21054	0.335744	0.167872	−	0.985809i	$-0.446311\pi$
$13$	1.21054	0.335744	0.167872	+	0.985809i	$0.446311\pi$
$14$	4.31175	1.15236
$15$	−0.264977	−0.0684168
$16$	1.00000	0.250000
$17$	−7.16586	−1.73798	−0.868988	−	0.494834i	$-0.835229\pi$
$17$	−7.16586	−1.73798	−0.868988	+	0.494834i	$0.835229\pi$
$18$	2.92979	0.690557
$19$	2.71925	0.623838	0.311919	−	0.950109i	$-0.399028\pi$
$19$	2.71925	0.623838	0.311919	+	0.950109i	$0.399028\pi$
$20$	1.00000	0.223607
$21$	1.14252	0.249317
$22$	0	0
$23$	7.01787	1.46333	0.731663	−	0.681666i	$-0.238744\pi$
$23$	7.01787	1.46333	0.731663	+	0.681666i	$0.238744\pi$
$24$	0.264977	0.0540882
$25$	1.00000	0.200000
$26$	−1.21054	−0.237407
$27$	1.57126	0.302389
$28$	−4.31175	−0.814845
$29$	10.5657	1.96200	0.980999	−	0.194010i	$-0.0621495\pi$
$29$	10.5657	1.96200	0.980999	+	0.194010i	$0.0621495\pi$
$30$	0.264977	0.0483780
$31$	3.62142	0.650426	0.325213	−	0.945641i	$-0.394564\pi$
$31$	3.62142	0.650426	0.325213	+	0.945641i	$0.394564\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.16586	1.22893
$35$	−4.31175	−0.728819
$36$	−2.92979	−0.488298
$37$	2.11908	0.348374	0.174187	−	0.984713i	$-0.444270\pi$
$37$	2.11908	0.348374	0.174187	+	0.984713i	$0.444270\pi$
$38$	−2.71925	−0.441120
$39$	−0.320766	−0.0513636
$40$	−1.00000	−0.158114
$41$	2.75289	0.429929	0.214965	−	0.976622i	$-0.431036\pi$
$41$	2.75289	0.429929	0.214965	+	0.976622i	$0.431036\pi$
$42$	−1.14252	−0.176294
$43$	6.59251	1.00535	0.502674	−	0.864476i	$-0.332350\pi$
$43$	6.59251	1.00535	0.502674	+	0.864476i	$0.332350\pi$
$44$	0	0
$45$	−2.92979	−0.436747
$46$	−7.01787	−1.03473
$47$	5.74050	0.837337	0.418669	−	0.908139i	$-0.362497\pi$
$47$	5.74050	0.837337	0.418669	+	0.908139i	$0.362497\pi$
$48$	−0.264977	−0.0382462
$49$	11.5912	1.65589
$50$	−1.00000	−0.141421
$51$	1.89879	0.265883
$52$	1.21054	0.167872
$53$	−5.87535	−0.807042	−0.403521	−	0.914970i	$-0.632214\pi$
$53$	−5.87535	−0.807042	−0.403521	+	0.914970i	$0.632214\pi$
$54$	−1.57126	−0.213821
$55$	0	0
$56$	4.31175	0.576182
$57$	−0.720538	−0.0954376
$58$	−10.5657	−1.38734
$59$	−5.89750	−0.767789	−0.383894	−	0.923377i	$-0.625417\pi$
$59$	−5.89750	−0.767789	−0.383894	+	0.923377i	$0.625417\pi$
$60$	−0.264977	−0.0342084
$61$	−6.14461	−0.786736	−0.393368	−	0.919381i	$-0.628690\pi$
$61$	−6.14461	−0.786736	−0.393368	+	0.919381i	$0.628690\pi$
$62$	−3.62142	−0.459920
$63$	12.6325	1.59155
$64$	1.00000	0.125000
$65$	1.21054	0.150149
$66$	0	0
$67$	−1.63381	−0.199602	−0.0998009	−	0.995007i	$-0.531821\pi$
$67$	−1.63381	−0.199602	−0.0998009	+	0.995007i	$0.531821\pi$
$68$	−7.16586	−0.868988
$69$	−1.85957	−0.223866
$70$	4.31175	0.515353
$71$	7.43849	0.882787	0.441393	−	0.897314i	$-0.354484\pi$
$71$	7.43849	0.882787	0.441393	+	0.897314i	$0.354484\pi$
$72$	2.92979	0.345279
$73$	−7.39217	−0.865188	−0.432594	−	0.901589i	$-0.642402\pi$
$73$	−7.39217	−0.865188	−0.432594	+	0.901589i	$0.642402\pi$
$74$	−2.11908	−0.246338
$75$	−0.264977	−0.0305969
$76$	2.71925	0.311919
$77$	0	0
$78$	0.320766	0.0363196
$79$	7.00209	0.787797	0.393898	−	0.919154i	$-0.371126\pi$
$79$	7.00209	0.787797	0.393898	+	0.919154i	$0.371126\pi$
$80$	1.00000	0.111803
$81$	8.37301	0.930335
$82$	−2.75289	−0.304006
$83$	−1.59460	−0.175030	−0.0875149	−	0.996163i	$-0.527893\pi$
$83$	−1.59460	−0.175030	−0.0875149	+	0.996163i	$0.527893\pi$
$84$	1.14252	0.124659
$85$	−7.16586	−0.777246
$86$	−6.59251	−0.710888
$87$	−2.79967	−0.300156
$88$	0	0
$89$	1.24711	0.132193	0.0660967	−	0.997813i	$-0.478945\pi$
$89$	1.24711	0.132193	0.0660967	+	0.997813i	$0.478945\pi$
$90$	2.92979	0.308827
$91$	−5.21955	−0.547158
$92$	7.01787	0.731663
$93$	−0.959592	−0.0995051
$94$	−5.74050	−0.592087
$95$	2.71925	0.278989
$96$	0.264977	0.0270441
$97$	−6.91327	−0.701936	−0.350968	−	0.936387i	$-0.614147\pi$
$97$	−6.91327	−0.701936	−0.350968	+	0.936387i	$0.614147\pi$
$98$	−11.5912	−1.17089
$99$	0	0
$100$	1.00000	0.100000
$101$	3.23607	0.322001	0.161000	−	0.986954i	$-0.448528\pi$
$101$	3.23607	0.322001	0.161000	+	0.986954i	$0.448528\pi$
$102$	−1.89879	−0.188008
$103$	5.77623	0.569149	0.284574	−	0.958654i	$-0.408148\pi$
$103$	5.77623	0.569149	0.284574	+	0.958654i	$0.408148\pi$
$104$	−1.21054	−0.118703
$105$	1.14252	0.111498
$106$	5.87535	0.570665
$107$	0.171425	0.0165723	0.00828615	−	0.999966i	$-0.497362\pi$
$107$	0.171425	0.0165723	0.00828615	+	0.999966i	$0.497362\pi$
$108$	1.57126	0.151194
$109$	−2.32753	−0.222937	−0.111468	−	0.993768i	$-0.535555\pi$
$109$	−2.32753	−0.222937	−0.111468	+	0.993768i	$0.535555\pi$
$110$	0	0
$111$	−0.561508	−0.0532959
$112$	−4.31175	−0.407422
$113$	4.30837	0.405297	0.202649	−	0.979251i	$-0.435045\pi$
$113$	4.30837	0.405297	0.202649	+	0.979251i	$0.435045\pi$
$114$	0.720538	0.0674846
$115$	7.01787	0.654419
$116$	10.5657	0.980999
$117$	−3.54663	−0.327886
$118$	5.89750	0.542909
$119$	30.8974	2.83236
$120$	0.264977	0.0241890
$121$	0	0
$122$	6.14461	0.556307
$123$	−0.729453	−0.0657725
$124$	3.62142	0.325213
$125$	1.00000	0.0894427
$126$	−12.6325	−1.12539
$127$	10.8361	0.961552	0.480776	−	0.876844i	$-0.340355\pi$
$127$	10.8361	0.961552	0.480776	+	0.876844i	$0.340355\pi$
$128$	−1.00000	−0.0883883
$129$	−1.74686	−0.153803
$130$	−1.21054	−0.106171
$131$	5.78518	0.505454	0.252727	−	0.967538i	$-0.418673\pi$
$131$	5.78518	0.505454	0.252727	+	0.967538i	$0.418673\pi$
$132$	0	0
$133$	−11.7247	−1.01666
$134$	1.63381	0.141140
$135$	1.57126	0.135232
$136$	7.16586	0.614467
$137$	8.65033	0.739047	0.369524	−	0.929221i	$-0.379521\pi$
$137$	8.65033	0.739047	0.369524	+	0.929221i	$0.379521\pi$
$138$	1.85957	0.158297
$139$	12.7482	1.08128	0.540642	−	0.841253i	$-0.318181\pi$
$139$	12.7482	1.08128	0.540642	+	0.841253i	$0.318181\pi$
$140$	−4.31175	−0.364410
$141$	−1.52110	−0.128100
$142$	−7.43849	−0.624224
$143$	0	0
$144$	−2.92979	−0.244149
$145$	10.5657	0.877433
$146$	7.39217	0.611781
$147$	−3.07141	−0.253325
$148$	2.11908	0.174187
$149$	6.61256	0.541722	0.270861	−	0.962618i	$-0.412692\pi$
$149$	6.61256	0.541722	0.270861	+	0.962618i	$0.412692\pi$
$150$	0.264977	0.0216353
$151$	20.8974	1.70061	0.850303	−	0.526293i	$-0.176419\pi$
$151$	20.8974	1.70061	0.850303	+	0.526293i	$0.176419\pi$
$152$	−2.71925	−0.220560
$153$	20.9944	1.69730
$154$	0	0
$155$	3.62142	0.290879
$156$	−0.320766	−0.0256818
$157$	−20.2291	−1.61446	−0.807231	−	0.590236i	$-0.799035\pi$
$157$	−20.2291	−1.61446	−0.807231	+	0.590236i	$0.799035\pi$
$158$	−7.00209	−0.557056
$159$	1.55683	0.123465
$160$	−1.00000	−0.0790569
$161$	−30.2593	−2.38477
$162$	−8.37301	−0.657846
$163$	−8.08116	−0.632965	−0.316483	−	0.948598i	$-0.602502\pi$
$163$	−8.08116	−0.632965	−0.316483	+	0.948598i	$0.602502\pi$
$164$	2.75289	0.214965
$165$	0	0
$166$	1.59460	0.123765
$167$	17.2725	1.33659	0.668295	−	0.743897i	$-0.267025\pi$
$167$	17.2725	1.33659	0.668295	+	0.743897i	$0.267025\pi$
$168$	−1.14252	−0.0881470
$169$	−11.5346	−0.887276
$170$	7.16586	0.549596
$171$	−7.96681	−0.609237
$172$	6.59251	0.502674
$173$	14.3738	1.09282	0.546408	−	0.837519i	$-0.315995\pi$
$173$	14.3738	1.09282	0.546408	+	0.837519i	$0.315995\pi$
$174$	2.79967	0.212242
$175$	−4.31175	−0.325938
$176$	0	0
$177$	1.56270	0.117460
$178$	−1.24711	−0.0934749
$179$	18.8541	1.40922	0.704611	−	0.709594i	$-0.251122\pi$
$179$	18.8541	1.40922	0.704611	+	0.709594i	$0.251122\pi$
$180$	−2.92979	−0.218373
$181$	−13.1024	−0.973894	−0.486947	−	0.873431i	$-0.661890\pi$
$181$	−13.1024	−0.973894	−0.486947	+	0.873431i	$0.661890\pi$
$182$	5.21955	0.386899
$183$	1.62818	0.120359
$184$	−7.01787	−0.517364
$185$	2.11908	0.155798
$186$	0.959592	0.0703607
$187$	0	0
$188$	5.74050	0.418669
$189$	−6.77488	−0.492800
$190$	−2.71925	−0.197275
$191$	−11.2718	−0.815599	−0.407799	−	0.913072i	$-0.633704\pi$
$191$	−11.2718	−0.815599	−0.407799	+	0.913072i	$0.633704\pi$
$192$	−0.264977	−0.0191231
$193$	6.94427	0.499860	0.249930	−	0.968264i	$-0.419592\pi$
$193$	6.94427	0.499860	0.249930	+	0.968264i	$0.419592\pi$
$194$	6.91327	0.496344
$195$	−0.320766	−0.0229705
$196$	11.5912	0.827944
$197$	−13.4389	−0.957485	−0.478743	−	0.877955i	$-0.658907\pi$
$197$	−13.4389	−0.957485	−0.478743	+	0.877955i	$0.658907\pi$
$198$	0	0
$199$	−19.4427	−1.37825	−0.689127	−	0.724640i	$-0.742006\pi$
$199$	−19.4427	−1.37825	−0.689127	+	0.724640i	$0.742006\pi$
$200$	−1.00000	−0.0707107
$201$	0.432922	0.0305360
$202$	−3.23607	−0.227689
$203$	−45.5566	−3.19745
$204$	1.89879	0.132942
$205$	2.75289	0.192270
$206$	−5.77623	−0.402449
$207$	−20.5609	−1.42908
$208$	1.21054	0.0839359
$209$	0	0
$210$	−1.14252	−0.0788411
$211$	−2.35853	−0.162368	−0.0811839	−	0.996699i	$-0.525870\pi$
$211$	−2.35853	−0.162368	−0.0811839	+	0.996699i	$0.525870\pi$
$212$	−5.87535	−0.403521
$213$	−1.97103	−0.135053
$214$	−0.171425	−0.0117184
$215$	6.59251	0.449605
$216$	−1.57126	−0.106911
$217$	−15.6147	−1.05999
$218$	2.32753	0.157640
$219$	1.95876	0.132361
$220$	0	0
$221$	−8.67456	−0.583514
$222$	0.561508	0.0376859
$223$	−14.5968	−0.977473	−0.488737	−	0.872431i	$-0.662542\pi$
$223$	−14.5968	−0.977473	−0.488737	+	0.872431i	$0.662542\pi$
$224$	4.31175	0.288091
$225$	−2.92979	−0.195319
$226$	−4.30837	−0.286589
$227$	2.98970	0.198433	0.0992165	−	0.995066i	$-0.468366\pi$
$227$	2.98970	0.198433	0.0992165	+	0.995066i	$0.468366\pi$
$228$	−0.720538	−0.0477188
$229$	1.57892	0.104338	0.0521689	−	0.998638i	$-0.483387\pi$
$229$	1.57892	0.104338	0.0521689	+	0.998638i	$0.483387\pi$
$230$	−7.01787	−0.462744
$231$	0	0
$232$	−10.5657	−0.693671
$233$	0.505719	0.0331308	0.0165654	−	0.999863i	$-0.494727\pi$
$233$	0.505719	0.0331308	0.0165654	+	0.999863i	$0.494727\pi$
$234$	3.54663	0.231850
$235$	5.74050	0.374469
$236$	−5.89750	−0.383894
$237$	−1.85539	−0.120521
$238$	−30.8974	−2.00278
$239$	−16.7418	−1.08294	−0.541470	−	0.840720i	$-0.682132\pi$
$239$	−16.7418	−1.08294	−0.541470	+	0.840720i	$0.682132\pi$
$240$	−0.264977	−0.0171042
$241$	−15.2947	−0.985217	−0.492609	−	0.870251i	$-0.663957\pi$
$241$	−15.2947	−0.985217	−0.492609	+	0.870251i	$0.663957\pi$
$242$	0	0
$243$	−6.93243	−0.444716
$244$	−6.14461	−0.393368
$245$	11.5912	0.740536
$246$	0.729453	0.0465082
$247$	3.29176	0.209450
$248$	−3.62142	−0.229960
$249$	0.422532	0.0267769
$250$	−1.00000	−0.0632456
$251$	−0.427390	−0.0269766	−0.0134883	−	0.999909i	$-0.504294\pi$
$251$	−0.427390	−0.0269766	−0.0134883	+	0.999909i	$0.504294\pi$
$252$	12.6325	0.795774
$253$	0	0
$254$	−10.8361	−0.679920
$255$	1.89879	0.118907
$256$	1.00000	0.0625000
$257$	17.8753	1.11503	0.557514	−	0.830168i	$-0.311755\pi$
$257$	17.8753	1.11503	0.557514	+	0.830168i	$0.311755\pi$
$258$	1.74686	0.108755
$259$	−9.13695	−0.567742
$260$	1.21054	0.0750746
$261$	−30.9552	−1.91608
$262$	−5.78518	−0.357410
$263$	14.4977	0.893964	0.446982	−	0.894543i	$-0.352499\pi$
$263$	14.4977	0.893964	0.446982	+	0.894543i	$0.352499\pi$
$264$	0	0
$265$	−5.87535	−0.360920
$266$	11.7247	0.718889
$267$	−0.330456	−0.0202236
$268$	−1.63381	−0.0998009
$269$	27.9378	1.70340	0.851699	−	0.524031i	$-0.175573\pi$
$269$	27.9378	1.70340	0.851699	+	0.524031i	$0.175573\pi$
$270$	−1.57126	−0.0956237
$271$	10.3895	0.631119	0.315559	−	0.948906i	$-0.397808\pi$
$271$	10.3895	0.631119	0.315559	+	0.948906i	$0.397808\pi$
$272$	−7.16586	−0.434494
$273$	1.38306	0.0837067
$274$	−8.65033	−0.522585
$275$	0	0
$276$	−1.85957	−0.111933
$277$	−0.628338	−0.0377532	−0.0188766	−	0.999822i	$-0.506009\pi$
$277$	−0.628338	−0.0377532	−0.0188766	+	0.999822i	$0.506009\pi$
$278$	−12.7482	−0.764584
$279$	−10.6100	−0.635203
$280$	4.31175	0.257677
$281$	30.1066	1.79601	0.898006	−	0.439983i	$-0.145016\pi$
$281$	30.1066	1.79601	0.898006	+	0.439983i	$0.145016\pi$
$282$	1.52110	0.0905802
$283$	−16.1045	−0.957313	−0.478656	−	0.878002i	$-0.658876\pi$
$283$	−16.1045	−0.957313	−0.478656	+	0.878002i	$0.658876\pi$
$284$	7.43849	0.441393
$285$	−0.720538	−0.0426810
$286$	0	0
$287$	−11.8698	−0.700651
$288$	2.92979	0.172639
$289$	34.3495	2.02056
$290$	−10.5657	−0.620439
$291$	1.83186	0.107385
$292$	−7.39217	−0.432594
$293$	−3.98004	−0.232517	−0.116258	−	0.993219i	$-0.537090\pi$
$293$	−3.98004	−0.232517	−0.116258	+	0.993219i	$0.537090\pi$
$294$	3.07141	0.179128
$295$	−5.89750	−0.343365
$296$	−2.11908	−0.123169
$297$	0	0
$298$	−6.61256	−0.383055
$299$	8.49541	0.491303
$300$	−0.264977	−0.0152985
$301$	−28.4253	−1.63840
$302$	−20.8974	−1.20251
$303$	−0.857484	−0.0492612
$304$	2.71925	0.155959
$305$	−6.14461	−0.351839
$306$	−20.9944	−1.20017
$307$	17.6055	1.00480	0.502401	−	0.864635i	$-0.332450\pi$
$307$	17.6055	1.00480	0.502401	+	0.864635i	$0.332450\pi$
$308$	0	0
$309$	−1.53057	−0.0870710
$310$	−3.62142	−0.205683
$311$	−22.6345	−1.28348	−0.641741	−	0.766921i	$-0.721788\pi$
$311$	−22.6345	−1.28348	−0.641741	+	0.766921i	$0.721788\pi$
$312$	0.320766	0.0181598
$313$	−12.6096	−0.712739	−0.356369	−	0.934345i	$-0.615986\pi$
$313$	−12.6096	−0.712739	−0.356369	+	0.934345i	$0.615986\pi$
$314$	20.2291	1.14160
$315$	12.6325	0.711762
$316$	7.00209	0.393898
$317$	26.2679	1.47535	0.737675	−	0.675156i	$-0.235924\pi$
$317$	26.2679	1.47535	0.737675	+	0.675156i	$0.235924\pi$
$318$	−1.55683	−0.0873029
$319$	0	0
$320$	1.00000	0.0559017
$321$	−0.0454237	−0.00253531
$322$	30.2593	1.68629
$323$	−19.4857	−1.08421
$324$	8.37301	0.465167
$325$	1.21054	0.0671487
$326$	8.08116	0.447574
$327$	0.616742	0.0341059
$328$	−2.75289	−0.152003
$329$	−24.7516	−1.36460
$330$	0	0
$331$	12.7406	0.700284	0.350142	−	0.936697i	$-0.386133\pi$
$331$	12.7406	0.700284	0.350142	+	0.936697i	$0.386133\pi$
$332$	−1.59460	−0.0875149
$333$	−6.20845	−0.340221
$334$	−17.2725	−0.945111
$335$	−1.63381	−0.0892646
$336$	1.14252	0.0623294
$337$	−19.0570	−1.03810	−0.519050	−	0.854744i	$-0.673714\pi$
$337$	−19.0570	−1.03810	−0.519050	+	0.854744i	$0.673714\pi$
$338$	11.5346	0.627399
$339$	−1.14162	−0.0620043
$340$	−7.16586	−0.388623
$341$	0	0
$342$	7.96681	0.430796
$343$	−19.7962	−1.06889
$344$	−6.59251	−0.355444
$345$	−1.85957	−0.100116
$346$	−14.3738	−0.772738
$347$	18.8230	1.01047	0.505236	−	0.862981i	$-0.331405\pi$
$347$	18.8230	1.01047	0.505236	+	0.862981i	$0.331405\pi$
$348$	−2.79967	−0.150078
$349$	−27.2182	−1.45695	−0.728477	−	0.685070i	$-0.759772\pi$
$349$	−27.2182	−1.45695	−0.728477	+	0.685070i	$0.759772\pi$
$350$	4.31175	0.230473
$351$	1.90207	0.101525
$352$	0	0
$353$	25.6380	1.36457	0.682286	−	0.731085i	$-0.260986\pi$
$353$	25.6380	1.36457	0.682286	+	0.731085i	$0.260986\pi$
$354$	−1.56270	−0.0830567
$355$	7.43849	0.394794
$356$	1.24711	0.0660967
$357$	−8.18710	−0.433307
$358$	−18.8541	−0.996470
$359$	9.67665	0.510714	0.255357	−	0.966847i	$-0.417807\pi$
$359$	9.67665	0.510714	0.255357	+	0.966847i	$0.417807\pi$
$360$	2.92979	0.154413
$361$	−11.6057	−0.610826
$362$	13.1024	0.688647
$363$	0	0
$364$	−5.21955	−0.273579
$365$	−7.39217	−0.386924
$366$	−1.62818	−0.0851063
$367$	−20.7035	−1.08072	−0.540358	−	0.841435i	$-0.681711\pi$
$367$	−20.7035	−1.08072	−0.540358	+	0.841435i	$0.681711\pi$
$368$	7.01787	0.365832
$369$	−8.06538	−0.419867
$370$	−2.11908	−0.110166
$371$	25.3331	1.31523
$372$	−0.959592	−0.0497526
$373$	−16.1463	−0.836021	−0.418011	−	0.908442i	$-0.637273\pi$
$373$	−16.1463	−0.836021	−0.418011	+	0.908442i	$0.637273\pi$
$374$	0	0
$375$	−0.264977	−0.0136834
$376$	−5.74050	−0.296043
$377$	12.7902	0.658729
$378$	6.77488	0.348462
$379$	−0.229700	−0.0117989	−0.00589944	−	0.999983i	$-0.501878\pi$
$379$	−0.229700	−0.0117989	−0.00589944	+	0.999983i	$0.501878\pi$
$380$	2.71925	0.139494
$381$	−2.87133	−0.147103
$382$	11.2718	0.576716
$383$	13.0220	0.665396	0.332698	−	0.943034i	$-0.392041\pi$
$383$	13.0220	0.665396	0.332698	+	0.943034i	$0.392041\pi$
$384$	0.264977	0.0135221
$385$	0	0
$386$	−6.94427	−0.353454
$387$	−19.3146	−0.981818
$388$	−6.91327	−0.350968
$389$	29.6256	1.50208	0.751039	−	0.660258i	$-0.229553\pi$
$389$	29.6256	1.50208	0.751039	+	0.660258i	$0.229553\pi$
$390$	0.320766	0.0162426
$391$	−50.2890	−2.54322
$392$	−11.5912	−0.585445
$393$	−1.53294	−0.0773266
$394$	13.4389	0.677044
$395$	7.00209	0.352313
$396$	0	0
$397$	2.18665	0.109745	0.0548724	−	0.998493i	$-0.482525\pi$
$397$	2.18665	0.109745	0.0548724	+	0.998493i	$0.482525\pi$
$398$	19.4427	0.974573
$399$	3.10678	0.155534
$400$	1.00000	0.0500000
$401$	−13.0944	−0.653901	−0.326950	−	0.945042i	$-0.606021\pi$
$401$	−13.0944	−0.653901	−0.326950	+	0.945042i	$0.606021\pi$
$402$	−0.432922	−0.0215922
$403$	4.38387	0.218376
$404$	3.23607	0.161000
$405$	8.37301	0.416058
$406$	45.5566	2.26094
$407$	0	0
$408$	−1.89879	−0.0940040
$409$	30.4287	1.50460	0.752301	−	0.658819i	$-0.228944\pi$
$409$	30.4287	1.50460	0.752301	+	0.658819i	$0.228944\pi$
$410$	−2.75289	−0.135956
$411$	−2.29214	−0.113063
$412$	5.77623	0.284574
$413$	25.4285	1.25126
$414$	20.5609	1.01051
$415$	−1.59460	−0.0782757
$416$	−1.21054	−0.0593516
$417$	−3.37797	−0.165420
$418$	0	0
$419$	26.7473	1.30669	0.653346	−	0.757059i	$-0.273365\pi$
$419$	26.7473	1.30669	0.653346	+	0.757059i	$0.273365\pi$
$420$	1.14252	0.0557491
$421$	−30.3427	−1.47881	−0.739405	−	0.673261i	$-0.764893\pi$
$421$	−30.3427	−1.47881	−0.739405	+	0.673261i	$0.764893\pi$
$422$	2.35853	0.114811
$423$	−16.8184	−0.817740
$424$	5.87535	0.285332
$425$	−7.16586	−0.347595
$426$	1.97103	0.0954967
$427$	26.4940	1.28214
$428$	0.171425	0.00828615
$429$	0	0
$430$	−6.59251	−0.317919
$431$	−11.8280	−0.569736	−0.284868	−	0.958567i	$-0.591950\pi$
$431$	−11.8280	−0.569736	−0.284868	+	0.958567i	$0.591950\pi$
$432$	1.57126	0.0755972
$433$	32.5932	1.56633	0.783165	−	0.621814i	$-0.213604\pi$
$433$	32.5932	1.56633	0.783165	+	0.621814i	$0.213604\pi$
$434$	15.6147	0.749527
$435$	−2.79967	−0.134234
$436$	−2.32753	−0.111468
$437$	19.0833	0.912878
$438$	−1.95876	−0.0935930
$439$	5.09564	0.243202	0.121601	−	0.992579i	$-0.461197\pi$
$439$	5.09564	0.243202	0.121601	+	0.992579i	$0.461197\pi$
$440$	0	0
$441$	−33.9598	−1.61713
$442$	8.67456	0.412607
$443$	24.6793	1.17255	0.586274	−	0.810113i	$-0.300594\pi$
$443$	24.6793	1.17255	0.586274	+	0.810113i	$0.300594\pi$
$444$	−0.561508	−0.0266480
$445$	1.24711	0.0591187
$446$	14.5968	0.691178
$447$	−1.75218	−0.0828752
$448$	−4.31175	−0.203711
$449$	−18.9683	−0.895172	−0.447586	−	0.894241i	$-0.647716\pi$
$449$	−18.9683	−0.895172	−0.447586	+	0.894241i	$0.647716\pi$
$450$	2.92979	0.138111
$451$	0	0
$452$	4.30837	0.202649
$453$	−5.53733	−0.260167
$454$	−2.98970	−0.140313
$455$	−5.21955	−0.244696
$456$	0.720538	0.0337423
$457$	−28.5141	−1.33383	−0.666916	−	0.745133i	$-0.732386\pi$
$457$	−28.5141	−1.33383	−0.666916	+	0.745133i	$0.732386\pi$
$458$	−1.57892	−0.0737780
$459$	−11.2594	−0.525544
$460$	7.01787	0.327210
$461$	−35.3117	−1.64463	−0.822315	−	0.569032i	$-0.807318\pi$
$461$	−35.3117	−1.64463	−0.822315	+	0.569032i	$0.807318\pi$
$462$	0	0
$463$	3.89605	0.181065	0.0905323	−	0.995894i	$-0.471143\pi$
$463$	3.89605	0.181065	0.0905323	+	0.995894i	$0.471143\pi$
$464$	10.5657	0.490500
$465$	−0.959592	−0.0445000
$466$	−0.505719	−0.0234270
$467$	−11.8528	−0.548483	−0.274241	−	0.961661i	$-0.588427\pi$
$467$	−11.8528	−0.548483	−0.274241	+	0.961661i	$0.588427\pi$
$468$	−3.54663	−0.163943
$469$	7.04459	0.325289
$470$	−5.74050	−0.264789
$471$	5.36026	0.246988
$472$	5.89750	0.271454
$473$	0	0
$474$	1.85539	0.0852211
$475$	2.71925	0.124768
$476$	30.8974	1.41618
$477$	17.2135	0.788153
$478$	16.7418	0.765754
$479$	10.4253	0.476342	0.238171	−	0.971223i	$-0.423452\pi$
$479$	10.4253	0.476342	0.238171	+	0.971223i	$0.423452\pi$
$480$	0.264977	0.0120945
$481$	2.56523	0.116965
$482$	15.2947	0.696654
$483$	8.01803	0.364833
$484$	0	0
$485$	−6.91327	−0.313916
$486$	6.93243	0.314461
$487$	−24.6014	−1.11480	−0.557398	−	0.830245i	$-0.688200\pi$
$487$	−24.6014	−1.11480	−0.557398	+	0.830245i	$0.688200\pi$
$488$	6.14461	0.278153
$489$	2.14132	0.0968339
$490$	−11.5912	−0.523638
$491$	−23.1522	−1.04484	−0.522421	−	0.852687i	$-0.674971\pi$
$491$	−23.1522	−1.04484	−0.522421	+	0.852687i	$0.674971\pi$
$492$	−0.729453	−0.0328863
$493$	−75.7122	−3.40991
$494$	−3.29176	−0.148103
$495$	0	0
$496$	3.62142	0.162606
$497$	−32.0729	−1.43867
$498$	−0.422532	−0.0189341
$499$	22.6703	1.01486	0.507431	−	0.861693i	$-0.330595\pi$
$499$	22.6703	1.01486	0.507431	+	0.861693i	$0.330595\pi$
$500$	1.00000	0.0447214
$501$	−4.57683	−0.204478
$502$	0.427390	0.0190753
$503$	21.6606	0.965798	0.482899	−	0.875676i	$-0.339584\pi$
$503$	21.6606	0.965798	0.482899	+	0.875676i	$0.339584\pi$
$504$	−12.6325	−0.562697
$505$	3.23607	0.144003
$506$	0	0
$507$	3.05640	0.135740
$508$	10.8361	0.480776
$509$	−15.4002	−0.682601	−0.341300	−	0.939954i	$-0.610867\pi$
$509$	−15.4002	−0.682601	−0.341300	+	0.939954i	$0.610867\pi$
$510$	−1.89879	−0.0840797
$511$	31.8732	1.40999
$512$	−1.00000	−0.0441942
$513$	4.27264	0.188642
$514$	−17.8753	−0.788444
$515$	5.77623	0.254531
$516$	−1.74686	−0.0769014
$517$	0	0
$518$	9.13695	0.401454
$519$	−3.80872	−0.167184
$520$	−1.21054	−0.0530857
$521$	28.8167	1.26248	0.631241	−	0.775587i	$-0.282546\pi$
$521$	28.8167	1.26248	0.631241	+	0.775587i	$0.282546\pi$
$522$	30.9552	1.35487
$523$	35.8829	1.56905	0.784525	−	0.620097i	$-0.212907\pi$
$523$	35.8829	1.56905	0.784525	+	0.620097i	$0.212907\pi$
$524$	5.78518	0.252727
$525$	1.14252	0.0498635
$526$	−14.4977	−0.632128
$527$	−25.9505	−1.13042
$528$	0	0
$529$	26.2505	1.14132
$530$	5.87535	0.255209
$531$	17.2784	0.749819
$532$	−11.7247	−0.508331
$533$	3.33249	0.144346
$534$	0.330456	0.0143002
$535$	0.171425	0.00741136
$536$	1.63381	0.0705699
$537$	−4.99591	−0.215589
$538$	−27.9378	−1.20448
$539$	0	0
$540$	1.57126	0.0676162
$541$	7.04877	0.303050	0.151525	−	0.988453i	$-0.451582\pi$
$541$	7.04877	0.303050	0.151525	+	0.988453i	$0.451582\pi$
$542$	−10.3895	−0.446268
$543$	3.47184	0.148991
$544$	7.16586	0.307234
$545$	−2.32753	−0.0997004
$546$	−1.38306	−0.0591896
$547$	15.1617	0.648266	0.324133	−	0.946011i	$-0.394927\pi$
$547$	15.1617	0.648266	0.324133	+	0.946011i	$0.394927\pi$
$548$	8.65033	0.369524
$549$	18.0024	0.768323
$550$	0	0
$551$	28.7307	1.22397
$552$	1.85957	0.0791487
$553$	−30.1913	−1.28386
$554$	0.628338	0.0266955
$555$	−0.561508	−0.0238347
$556$	12.7482	0.540642
$557$	−11.5313	−0.488597	−0.244299	−	0.969700i	$-0.578558\pi$
$557$	−11.5313	−0.488597	−0.244299	+	0.969700i	$0.578558\pi$
$558$	10.6100	0.449156
$559$	7.98050	0.337539
$560$	−4.31175	−0.182205
$561$	0	0
$562$	−30.1066	−1.26997
$563$	−34.1220	−1.43807	−0.719035	−	0.694974i	$-0.755416\pi$
$563$	−34.1220	−1.43807	−0.719035	+	0.694974i	$0.755416\pi$
$564$	−1.52110	−0.0640499
$565$	4.30837	0.181255
$566$	16.1045	0.676922
$567$	−36.1024	−1.51616
$568$	−7.43849	−0.312112
$569$	−7.98130	−0.334593	−0.167297	−	0.985907i	$-0.553504\pi$
$569$	−7.98130	−0.334593	−0.167297	+	0.985907i	$0.553504\pi$
$570$	0.720538	0.0301800
$571$	−3.62605	−0.151746	−0.0758728	−	0.997118i	$-0.524174\pi$
$571$	−3.62605	−0.151746	−0.0758728	+	0.997118i	$0.524174\pi$
$572$	0	0
$573$	2.98677	0.124774
$574$	11.8698	0.495435
$575$	7.01787	0.292665
$576$	−2.92979	−0.122074
$577$	−3.66008	−0.152371	−0.0761855	−	0.997094i	$-0.524274\pi$
$577$	−3.66008	−0.152371	−0.0761855	+	0.997094i	$0.524274\pi$
$578$	−34.3495	−1.42875
$579$	−1.84007	−0.0764708
$580$	10.5657	0.438716
$581$	6.87551	0.285244
$582$	−1.83186	−0.0759330
$583$	0	0
$584$	7.39217	0.305890
$585$	−3.54663	−0.146635
$586$	3.98004	0.164414
$587$	−17.8293	−0.735893	−0.367946	−	0.929847i	$-0.619939\pi$
$587$	−17.8293	−0.735893	−0.367946	+	0.929847i	$0.619939\pi$
$588$	−3.07141	−0.126663
$589$	9.84752	0.405760
$590$	5.89750	0.242796
$591$	3.56101	0.146481
$592$	2.11908	0.0870936
$593$	23.0006	0.944523	0.472262	−	0.881458i	$-0.343438\pi$
$593$	23.0006	0.944523	0.472262	+	0.881458i	$0.343438\pi$
$594$	0	0
$595$	30.8974	1.26667
$596$	6.61256	0.270861
$597$	5.15186	0.210852
$598$	−8.49541	−0.347403
$599$	3.34076	0.136500	0.0682499	−	0.997668i	$-0.478258\pi$
$599$	3.34076	0.136500	0.0682499	+	0.997668i	$0.478258\pi$
$600$	0.264977	0.0108176
$601$	34.9318	1.42490	0.712450	−	0.701723i	$-0.247586\pi$
$601$	34.9318	1.42490	0.712450	+	0.701723i	$0.247586\pi$
$602$	28.4253	1.15853
$603$	4.78672	0.194930
$604$	20.8974	0.850303
$605$	0	0
$606$	0.857484	0.0348329
$607$	12.6084	0.511758	0.255879	−	0.966709i	$-0.417635\pi$
$607$	12.6084	0.511758	0.255879	+	0.966709i	$0.417635\pi$
$608$	−2.71925	−0.110280
$609$	12.0715	0.489161
$610$	6.14461	0.248788
$611$	6.94910	0.281131
$612$	20.9944	0.848650
$613$	8.56298	0.345856	0.172928	−	0.984934i	$-0.444677\pi$
$613$	8.56298	0.345856	0.172928	+	0.984934i	$0.444677\pi$
$614$	−17.6055	−0.710502
$615$	−0.729453	−0.0294144
$616$	0	0
$617$	1.77165	0.0713241	0.0356620	−	0.999364i	$-0.488646\pi$
$617$	1.77165	0.0713241	0.0356620	+	0.999364i	$0.488646\pi$
$618$	1.53057	0.0615685
$619$	−19.3699	−0.778543	−0.389272	−	0.921123i	$-0.627273\pi$
$619$	−19.3699	−0.778543	−0.389272	+	0.921123i	$0.627273\pi$
$620$	3.62142	0.145440
$621$	11.0269	0.442493
$622$	22.6345	0.907559
$623$	−5.37723	−0.215434
$624$	−0.320766	−0.0128409
$625$	1.00000	0.0400000
$626$	12.6096	0.503982
$627$	0	0
$628$	−20.2291	−0.807231
$629$	−15.1850	−0.605466
$630$	−12.6325	−0.503292
$631$	27.4069	1.09105	0.545527	−	0.838094i	$-0.316330\pi$
$631$	27.4069	1.09105	0.545527	+	0.838094i	$0.316330\pi$
$632$	−7.00209	−0.278528
$633$	0.624956	0.0248398
$634$	−26.2679	−1.04323
$635$	10.8361	0.430019
$636$	1.55683	0.0617325
$637$	14.0316	0.555954
$638$	0	0
$639$	−21.7932	−0.862126
$640$	−1.00000	−0.0395285
$641$	−23.8678	−0.942719	−0.471360	−	0.881941i	$-0.656237\pi$
$641$	−23.8678	−0.942719	−0.471360	+	0.881941i	$0.656237\pi$
$642$	0.0454237	0.00179273
$643$	12.4836	0.492306	0.246153	−	0.969231i	$-0.420833\pi$
$643$	12.4836	0.492306	0.246153	+	0.969231i	$0.420833\pi$
$644$	−30.2593	−1.19238
$645$	−1.74686	−0.0687827
$646$	19.4857	0.766656
$647$	7.05573	0.277389	0.138695	−	0.990335i	$-0.455709\pi$
$647$	7.05573	0.277389	0.138695	+	0.990335i	$0.455709\pi$
$648$	−8.37301	−0.328923
$649$	0	0
$650$	−1.21054	−0.0474813
$651$	4.13753	0.162162
$652$	−8.08116	−0.316483
$653$	2.67641	0.104736	0.0523679	−	0.998628i	$-0.483323\pi$
$653$	2.67641	0.104736	0.0523679	+	0.998628i	$0.483323\pi$
$654$	−0.616742	−0.0241165
$655$	5.78518	0.226046
$656$	2.75289	0.107482
$657$	21.6575	0.844939
$658$	24.7516	0.964918
$659$	−36.5069	−1.42211	−0.711053	−	0.703138i	$-0.751781\pi$
$659$	−36.5069	−1.42211	−0.711053	+	0.703138i	$0.751781\pi$
$660$	0	0
$661$	40.3521	1.56952	0.784758	−	0.619802i	$-0.212787\pi$
$661$	40.3521	1.56952	0.784758	+	0.619802i	$0.212787\pi$
$662$	−12.7406	−0.495176
$663$	2.29856	0.0892687
$664$	1.59460	0.0618824
$665$	−11.7247	−0.454665
$666$	6.20845	0.240573
$667$	74.1486	2.87104
$668$	17.2725	0.668295
$669$	3.86781	0.149538
$670$	1.63381	0.0631196
$671$	0	0
$672$	−1.14252	−0.0440735
$673$	12.7584	0.491801	0.245901	−	0.969295i	$-0.420916\pi$
$673$	12.7584	0.491801	0.245901	+	0.969295i	$0.420916\pi$
$674$	19.0570	0.734048
$675$	1.57126	0.0604777
$676$	−11.5346	−0.443638
$677$	−12.4816	−0.479707	−0.239854	−	0.970809i	$-0.577099\pi$
$677$	−12.4816	−0.479707	−0.239854	+	0.970809i	$0.577099\pi$
$678$	1.14162	0.0438436
$679$	29.8083	1.14394
$680$	7.16586	0.274798
$681$	−0.792201	−0.0303572
$682$	0	0
$683$	5.10260	0.195246	0.0976228	−	0.995223i	$-0.468876\pi$
$683$	5.10260	0.195246	0.0976228	+	0.995223i	$0.468876\pi$
$684$	−7.96681	−0.304619
$685$	8.65033	0.330512
$686$	19.7962	0.755822
$687$	−0.418377	−0.0159621
$688$	6.59251	0.251337
$689$	−7.11235	−0.270959
$690$	1.85957	0.0707928
$691$	11.9208	0.453488	0.226744	−	0.973954i	$-0.427192\pi$
$691$	11.9208	0.453488	0.226744	+	0.973954i	$0.427192\pi$
$692$	14.3738	0.546408
$693$	0	0
$694$	−18.8230	−0.714511
$695$	12.7482	0.483565
$696$	2.79967	0.106121
$697$	−19.7268	−0.747206
$698$	27.2182	1.03022
$699$	−0.134004	−0.00506850
$700$	−4.31175	−0.162969
$701$	−11.3612	−0.429106	−0.214553	−	0.976712i	$-0.568829\pi$
$701$	−11.3612	−0.429106	−0.214553	+	0.976712i	$0.568829\pi$
$702$	−1.90207	−0.0717891
$703$	5.76230	0.217329
$704$	0	0
$705$	−1.52110	−0.0572879
$706$	−25.6380	−0.964899
$707$	−13.9531	−0.524761
$708$	1.56270	0.0587299
$709$	12.1608	0.456710	0.228355	−	0.973578i	$-0.426665\pi$
$709$	12.1608	0.456710	0.228355	+	0.973578i	$0.426665\pi$
$710$	−7.43849	−0.279162
$711$	−20.5146	−0.769359
$712$	−1.24711	−0.0467374
$713$	25.4146	0.951785
$714$	8.18710	0.306395
$715$	0	0
$716$	18.8541	0.704611
$717$	4.43621	0.165673
$718$	−9.67665	−0.361129
$719$	−34.5681	−1.28917	−0.644586	−	0.764532i	$-0.722970\pi$
$719$	−34.5681	−1.28917	−0.644586	+	0.764532i	$0.722970\pi$
$720$	−2.92979	−0.109187
$721$	−24.9057	−0.927536
$722$	11.6057	0.431919
$723$	4.05274	0.150723
$724$	−13.1024	−0.486947
$725$	10.5657	0.392400
$726$	0	0
$727$	46.4273	1.72189	0.860947	−	0.508695i	$-0.169872\pi$
$727$	46.4273	1.72189	0.860947	+	0.508695i	$0.169872\pi$
$728$	5.21955	0.193450
$729$	−23.2821	−0.862300
$730$	7.39217	0.273597
$731$	−47.2409	−1.74727
$732$	1.62818	0.0601793
$733$	14.6167	0.539882	0.269941	−	0.962877i	$-0.412996\pi$
$733$	14.6167	0.539882	0.269941	+	0.962877i	$0.412996\pi$
$734$	20.7035	0.764181
$735$	−3.07141	−0.113291
$736$	−7.01787	−0.258682
$737$	0	0
$738$	8.06538	0.296891
$739$	−41.5285	−1.52765	−0.763825	−	0.645424i	$-0.776681\pi$
$739$	−41.5285	−1.52765	−0.763825	+	0.645424i	$0.776681\pi$
$740$	2.11908	0.0778989
$741$	−0.872241	−0.0320426
$742$	−25.3331	−0.930006
$743$	−40.0156	−1.46803	−0.734015	−	0.679134i	$-0.762356\pi$
$743$	−40.0156	−1.46803	−0.734015	+	0.679134i	$0.762356\pi$
$744$	0.959592	0.0351804
$745$	6.61256	0.242266
$746$	16.1463	0.591156
$747$	4.67183	0.170933
$748$	0	0
$749$	−0.739143	−0.0270077
$750$	0.264977	0.00967560
$751$	14.2407	0.519652	0.259826	−	0.965655i	$-0.416335\pi$
$751$	14.2407	0.519652	0.259826	+	0.965655i	$0.416335\pi$
$752$	5.74050	0.209334
$753$	0.113249	0.00412701
$754$	−12.7902	−0.465792
$755$	20.8974	0.760534
$756$	−6.77488	−0.246400
$757$	−29.8025	−1.08319	−0.541595	−	0.840640i	$-0.682179\pi$
$757$	−29.8025	−1.08319	−0.541595	+	0.840640i	$0.682179\pi$
$758$	0.229700	0.00834306
$759$	0	0
$760$	−2.71925	−0.0986374
$761$	−13.2689	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$761$	−13.2689	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$762$	2.87133	0.104017
$763$	10.0357	0.363318
$764$	−11.2718	−0.407799
$765$	20.9944	0.759055
$766$	−13.0220	−0.470506
$767$	−7.13916	−0.257780
$768$	−0.264977	−0.00956154
$769$	−46.3160	−1.67020	−0.835099	−	0.550099i	$-0.814590\pi$
$769$	−46.3160	−1.67020	−0.835099	+	0.550099i	$0.814590\pi$
$770$	0	0
$771$	−4.73653	−0.170582
$772$	6.94427	0.249930
$773$	51.1487	1.83969	0.919846	−	0.392279i	$-0.128313\pi$
$773$	51.1487	1.83969	0.919846	+	0.392279i	$0.128313\pi$
$774$	19.3146	0.694250
$775$	3.62142	0.130085
$776$	6.91327	0.248172
$777$	2.42108	0.0868558
$778$	−29.6256	−1.06213
$779$	7.48579	0.268206
$780$	−0.320766	−0.0114853
$781$	0	0
$782$	50.2890	1.79833
$783$	16.6014	0.593286
$784$	11.5912	0.413972
$785$	−20.2291	−0.722009
$786$	1.53294	0.0546782
$787$	34.7006	1.23694	0.618471	−	0.785807i	$-0.287752\pi$
$787$	34.7006	1.23694	0.618471	+	0.785807i	$0.287752\pi$
$788$	−13.4389	−0.478743
$789$	−3.84155	−0.136763
$790$	−7.00209	−0.249123
$791$	−18.5766	−0.660509
$792$	0	0
$793$	−7.43830	−0.264142
$794$	−2.18665	−0.0776012
$795$	1.55683	0.0552152
$796$	−19.4427	−0.689127
$797$	44.6751	1.58247	0.791237	−	0.611510i	$-0.209438\pi$
$797$	44.6751	1.58247	0.791237	+	0.611510i	$0.209438\pi$
$798$	−3.10678	−0.109979
$799$	−41.1356	−1.45527
$800$	−1.00000	−0.0353553
$801$	−3.65377	−0.129100
$802$	13.0944	0.462378
$803$	0	0
$804$	0.432922	0.0152680
$805$	−30.2593	−1.06650
$806$	−4.38387	−0.154415
$807$	−7.40288	−0.260594
$808$	−3.23607	−0.113844
$809$	−13.1002	−0.460579	−0.230290	−	0.973122i	$-0.573967\pi$
$809$	−13.1002	−0.460579	−0.230290	+	0.973122i	$0.573967\pi$
$810$	−8.37301	−0.294198
$811$	−7.83230	−0.275029	−0.137515	−	0.990500i	$-0.543911\pi$
$811$	−7.83230	−0.275029	−0.137515	+	0.990500i	$0.543911\pi$
$812$	−45.5566	−1.59872
$813$	−2.75299	−0.0965515
$814$	0	0
$815$	−8.08116	−0.283071
$816$	1.89879	0.0664709
$817$	17.9266	0.627174
$818$	−30.4287	−1.06391
$819$	15.2922	0.534352
$820$	2.75289	0.0961351
$821$	−24.0332	−0.838763	−0.419381	−	0.907810i	$-0.637753\pi$
$821$	−24.0332	−0.838763	−0.419381	+	0.907810i	$0.637753\pi$
$822$	2.29214	0.0799475
$823$	12.0722	0.420811	0.210405	−	0.977614i	$-0.432522\pi$
$823$	12.0722	0.420811	0.210405	+	0.977614i	$0.432522\pi$
$824$	−5.77623	−0.201224
$825$	0	0
$826$	−25.4285	−0.884772
$827$	35.2406	1.22544	0.612718	−	0.790302i	$-0.290076\pi$
$827$	35.2406	1.22544	0.612718	+	0.790302i	$0.290076\pi$
$828$	−20.5609	−0.714539
$829$	24.2834	0.843396	0.421698	−	0.906736i	$-0.361434\pi$
$829$	24.2834	0.843396	0.421698	+	0.906736i	$0.361434\pi$
$830$	1.59460	0.0553493
$831$	0.166495	0.00577566
$832$	1.21054	0.0419680
$833$	−83.0610	−2.87789
$834$	3.37797	0.116970
$835$	17.2725	0.597741
$836$	0	0
$837$	5.69018	0.196681
$838$	−26.7473	−0.923971
$839$	15.2308	0.525825	0.262912	−	0.964820i	$-0.415317\pi$
$839$	15.2308	0.525825	0.262912	+	0.964820i	$0.415317\pi$
$840$	−1.14252	−0.0394205
$841$	82.6338	2.84944
$842$	30.3427	1.04568
$843$	−7.97757	−0.274762
$844$	−2.35853	−0.0811839
$845$	−11.5346	−0.396802
$846$	16.8184	0.578229
$847$	0	0
$848$	−5.87535	−0.201760
$849$	4.26732	0.146454
$850$	7.16586	0.245787
$851$	14.8714	0.509786
$852$	−1.97103	−0.0675264
$853$	−6.90641	−0.236471	−0.118235	−	0.992986i	$-0.537724\pi$
$853$	−6.90641	−0.236471	−0.118235	+	0.992986i	$0.537724\pi$
$854$	−26.4940	−0.906607
$855$	−7.96681	−0.272459
$856$	−0.171425	−0.00585919
$857$	−1.68576	−0.0575845	−0.0287922	−	0.999585i	$-0.509166\pi$
$857$	−1.68576	−0.0575845	−0.0287922	+	0.999585i	$0.509166\pi$
$858$	0	0
$859$	−52.7330	−1.79923	−0.899613	−	0.436688i	$-0.856151\pi$
$859$	−52.7330	−1.79923	−0.899613	+	0.436688i	$0.856151\pi$
$860$	6.59251	0.224803
$861$	3.14522	0.107189
$862$	11.8280	0.402864
$863$	29.4939	1.00398	0.501992	−	0.864872i	$-0.332601\pi$
$863$	29.4939	1.00398	0.501992	+	0.864872i	$0.332601\pi$
$864$	−1.57126	−0.0534553
$865$	14.3738	0.488722
$866$	−32.5932	−1.10756
$867$	−9.10183	−0.309114
$868$	−15.6147	−0.529996
$869$	0	0
$870$	2.79967	0.0949176
$871$	−1.97779	−0.0670150
$872$	2.32753	0.0788201
$873$	20.2544	0.685508
$874$	−19.0833	−0.645503
$875$	−4.31175	−0.145764
$876$	1.95876	0.0661803
$877$	−28.0229	−0.946268	−0.473134	−	0.880991i	$-0.656877\pi$
$877$	−28.0229	−0.946268	−0.473134	+	0.880991i	$0.656877\pi$
$878$	−5.09564	−0.171970
$879$	1.05462	0.0355715
$880$	0	0
$881$	−28.1345	−0.947875	−0.473937	−	0.880559i	$-0.657168\pi$
$881$	−28.1345	−0.947875	−0.473937	+	0.880559i	$0.657168\pi$
$882$	33.9598	1.14349
$883$	40.5235	1.36373	0.681863	−	0.731480i	$-0.261170\pi$
$883$	40.5235	1.36373	0.681863	+	0.731480i	$0.261170\pi$
$884$	−8.67456	−0.291757
$885$	1.56270	0.0525296
$886$	−24.6793	−0.829117
$887$	14.2539	0.478600	0.239300	−	0.970946i	$-0.423082\pi$
$887$	14.2539	0.478600	0.239300	+	0.970946i	$0.423082\pi$
$888$	0.561508	0.0188430
$889$	−46.7227	−1.56703
$890$	−1.24711	−0.0418032
$891$	0	0
$892$	−14.5968	−0.488737
$893$	15.6098	0.522363
$894$	1.75218	0.0586016
$895$	18.8541	0.630223
$896$	4.31175	0.144046
$897$	−2.25109	−0.0751617
$898$	18.9683	0.632982
$899$	38.2628	1.27613
$900$	−2.92979	−0.0976596
$901$	42.1019	1.40262
$902$	0	0
$903$	7.53204	0.250651
$904$	−4.30837	−0.143294
$905$	−13.1024	−0.435539
$906$	5.53733	0.183966
$907$	−43.3624	−1.43983	−0.719913	−	0.694064i	$-0.755818\pi$
$907$	−43.3624	−1.43983	−0.719913	+	0.694064i	$0.755818\pi$
$908$	2.98970	0.0992165
$909$	−9.48099	−0.314465
$910$	5.21955	0.173027
$911$	23.7345	0.786358	0.393179	−	0.919462i	$-0.371375\pi$
$911$	23.7345	0.786358	0.393179	+	0.919462i	$0.371375\pi$
$912$	−0.720538	−0.0238594
$913$	0	0
$914$	28.5141	0.943162
$915$	1.62818	0.0538260
$916$	1.57892	0.0521689
$917$	−24.9443	−0.823732
$918$	11.2594	0.371616
$919$	−14.0578	−0.463725	−0.231862	−	0.972749i	$-0.574482\pi$
$919$	−14.0578	−0.463725	−0.231862	+	0.972749i	$0.574482\pi$
$920$	−7.01787	−0.231372
$921$	−4.66507	−0.153719
$922$	35.3117	1.16293
$923$	9.00460	0.296390
$924$	0	0
$925$	2.11908	0.0696749
$926$	−3.89605	−0.128032
$927$	−16.9231	−0.555828
$928$	−10.5657	−0.346836
$929$	−55.8244	−1.83154	−0.915770	−	0.401702i	$-0.868419\pi$
$929$	−55.8244	−1.83154	−0.915770	+	0.401702i	$0.868419\pi$
$930$	0.959592	0.0314663
$931$	31.5194	1.03301
$932$	0.505719	0.0165654
$933$	5.99761	0.196353
$934$	11.8528	0.387836
$935$	0	0
$936$	3.54663	0.115925
$937$	−12.4265	−0.405957	−0.202978	−	0.979183i	$-0.565062\pi$
$937$	−12.4265	−0.405957	−0.202978	+	0.979183i	$0.565062\pi$
$938$	−7.04459	−0.230014
$939$	3.34127	0.109038
$940$	5.74050	0.187234
$941$	−14.5945	−0.475768	−0.237884	−	0.971294i	$-0.576454\pi$
$941$	−14.5945	−0.475768	−0.237884	+	0.971294i	$0.576454\pi$
$942$	−5.36026	−0.174647
$943$	19.3194	0.629127
$944$	−5.89750	−0.191947
$945$	−6.77488	−0.220387
$946$	0	0
$947$	38.1184	1.23868	0.619340	−	0.785123i	$-0.287400\pi$
$947$	38.1184	1.23868	0.619340	+	0.785123i	$0.287400\pi$
$948$	−1.85539	−0.0602604
$949$	−8.94853	−0.290481
$950$	−2.71925	−0.0882240
$951$	−6.96038	−0.225706
$952$	−30.8974	−1.00139
$953$	0.471582	0.0152760	0.00763802	−	0.999971i	$-0.497569\pi$
$953$	0.471582	0.0152760	0.00763802	+	0.999971i	$0.497569\pi$
$954$	−17.2135	−0.557309
$955$	−11.2718	−0.364747
$956$	−16.7418	−0.541470
$957$	0	0
$958$	−10.4253	−0.336825
$959$	−37.2981	−1.20442
$960$	−0.264977	−0.00855210
$961$	−17.8853	−0.576947
$962$	−2.56523	−0.0827064
$963$	−0.502239	−0.0161844
$964$	−15.2947	−0.492609
$965$	6.94427	0.223544
$966$	−8.01803	−0.257976
$967$	−29.1678	−0.937975	−0.468987	−	0.883205i	$-0.655381\pi$
$967$	−29.1678	−0.937975	−0.468987	+	0.883205i	$0.655381\pi$
$968$	0	0
$969$	5.16327	0.165868
$970$	6.91327	0.221972
$971$	−15.8258	−0.507873	−0.253937	−	0.967221i	$-0.581725\pi$
$971$	−15.8258	−0.507873	−0.253937	+	0.967221i	$0.581725\pi$
$972$	−6.93243	−0.222358
$973$	−54.9669	−1.76216
$974$	24.6014	0.788280
$975$	−0.320766	−0.0102727
$976$	−6.14461	−0.196684
$977$	41.8441	1.33871	0.669355	−	0.742943i	$-0.266571\pi$
$977$	41.8441	1.33871	0.669355	+	0.742943i	$0.266571\pi$
$978$	−2.14132	−0.0684719
$979$	0	0
$980$	11.5912	0.370268
$981$	6.81917	0.217719
$982$	23.1522	0.738815
$983$	5.09868	0.162623	0.0813113	−	0.996689i	$-0.474089\pi$
$983$	5.09868	0.162623	0.0813113	+	0.996689i	$0.474089\pi$
$984$	0.729453	0.0232541
$985$	−13.4389	−0.428201
$986$	75.7122	2.41117
$987$	6.55861	0.208763
$988$	3.29176	0.104725
$989$	46.2653	1.47115
$990$	0	0
$991$	−14.8133	−0.470560	−0.235280	−	0.971928i	$-0.575601\pi$
$991$	−14.8133	−0.470560	−0.235280	+	0.971928i	$0.575601\pi$
$992$	−3.62142	−0.114980
$993$	−3.37596	−0.107133
$994$	32.0729	1.01729
$995$	−19.4427	−0.616374
$996$	0.422532	0.0133884
$997$	−58.0780	−1.83935	−0.919675	−	0.392681i	$-0.871548\pi$
$997$	−58.0780	−1.83935	−0.919675	+	0.392681i	$0.871548\pi$
$998$	−22.6703	−0.717615
$999$	3.32962	0.105345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.a.u.1.2		4
4.3	odd	2		9680.2.a.cj.1.3		4
5.4	even	2		6050.2.a.dh.1.3		4
11.3	even	5		110.2.g.c.31.2	✓	8
11.4	even	5		110.2.g.c.71.2	yes	8
11.10	odd	2		1210.2.a.v.1.2		4
33.14	odd	10		990.2.n.j.361.2		8
33.26	odd	10		990.2.n.j.181.2		8
44.3	odd	10		880.2.bo.g.801.1		8
44.15	odd	10		880.2.bo.g.401.1		8
44.43	even	2		9680.2.a.ci.1.3		4
55.3	odd	20		550.2.ba.f.449.4		16
55.4	even	10		550.2.h.l.401.1		8
55.14	even	10		550.2.h.l.251.1		8
55.37	odd	20		550.2.ba.f.49.4		16
55.47	odd	20		550.2.ba.f.449.1		16
55.48	odd	20		550.2.ba.f.49.1		16
55.54	odd	2		6050.2.a.cy.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.2	✓	8	11.3	even	5
110.2.g.c.71.2	yes	8	11.4	even	5
550.2.h.l.251.1		8	55.14	even	10
550.2.h.l.401.1		8	55.4	even	10
550.2.ba.f.49.1		16	55.48	odd	20
550.2.ba.f.49.4		16	55.37	odd	20
550.2.ba.f.449.1		16	55.47	odd	20
550.2.ba.f.449.4		16	55.3	odd	20
880.2.bo.g.401.1		8	44.15	odd	10
880.2.bo.g.801.1		8	44.3	odd	10
990.2.n.j.181.2		8	33.26	odd	10
990.2.n.j.361.2		8	33.14	odd	10
1210.2.a.u.1.2		4	1.1	even	1	trivial
1210.2.a.v.1.2		4	11.10	odd	2
6050.2.a.cy.1.3		4	55.54	odd	2
6050.2.a.dh.1.3		4	5.4	even	2
9680.2.a.ci.1.3		4	44.43	even	2
9680.2.a.cj.1.3		4	4.3	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:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.264977 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.264977 q^{6} -4.31175 q^{7} -1.00000 q^{8} -2.92979 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.264977 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.264977 q^{6} -4.31175 q^{7} -1.00000 q^{8} -2.92979 q^{9} -1.00000 q^{10} -0.264977 q^{12} +1.21054 q^{13} +4.31175 q^{14} -0.264977 q^{15} +1.00000 q^{16} -7.16586 q^{17} +2.92979 q^{18} +2.71925 q^{19} +1.00000 q^{20} +1.14252 q^{21} +7.01787 q^{23} +0.264977 q^{24} +1.00000 q^{25} -1.21054 q^{26} +1.57126 q^{27} -4.31175 q^{28} +10.5657 q^{29} +0.264977 q^{30} +3.62142 q^{31} -1.00000 q^{32} +7.16586 q^{34} -4.31175 q^{35} -2.92979 q^{36} +2.11908 q^{37} -2.71925 q^{38} -0.320766 q^{39} -1.00000 q^{40} +2.75289 q^{41} -1.14252 q^{42} +6.59251 q^{43} -2.92979 q^{45} -7.01787 q^{46} +5.74050 q^{47} -0.264977 q^{48} +11.5912 q^{49} -1.00000 q^{50} +1.89879 q^{51} +1.21054 q^{52} -5.87535 q^{53} -1.57126 q^{54} +4.31175 q^{56} -0.720538 q^{57} -10.5657 q^{58} -5.89750 q^{59} -0.264977 q^{60} -6.14461 q^{61} -3.62142 q^{62} +12.6325 q^{63} +1.00000 q^{64} +1.21054 q^{65} -1.63381 q^{67} -7.16586 q^{68} -1.85957 q^{69} +4.31175 q^{70} +7.43849 q^{71} +2.92979 q^{72} -7.39217 q^{73} -2.11908 q^{74} -0.264977 q^{75} +2.71925 q^{76} +0.320766 q^{78} +7.00209 q^{79} +1.00000 q^{80} +8.37301 q^{81} -2.75289 q^{82} -1.59460 q^{83} +1.14252 q^{84} -7.16586 q^{85} -6.59251 q^{86} -2.79967 q^{87} +1.24711 q^{89} +2.92979 q^{90} -5.21955 q^{91} +7.01787 q^{92} -0.959592 q^{93} -5.74050 q^{94} +2.71925 q^{95} +0.264977 q^{96} -6.91327 q^{97} -11.5912 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9	\( 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9} - 4 q^{10} + 3 q^{12} - 7 q^{13} + 3 q^{14} + 3 q^{15} + 4 q^{16} - q^{17} - 7 q^{18} + 4 q^{19} + 4 q^{20} + 16 q^{21} + 13 q^{23} - 3 q^{24} + 4 q^{25} + 7 q^{26} + 12 q^{27} - 3 q^{28} + 4 q^{29} - 3 q^{30} + 12 q^{31} - 4 q^{32} + q^{34} - 3 q^{35} + 7 q^{36} - 9 q^{37} - 4 q^{38} + 6 q^{39} - 4 q^{40} - 16 q^{42} + 19 q^{43} + 7 q^{45} - 13 q^{46} + 3 q^{47} + 3 q^{48} + 11 q^{49} - 4 q^{50} + 10 q^{51} - 7 q^{52} + 3 q^{53} - 12 q^{54} + 3 q^{56} - 24 q^{57} - 4 q^{58} + 2 q^{59} + 3 q^{60} - 10 q^{61} - 12 q^{62} + 29 q^{63} + 4 q^{64} - 7 q^{65} - 13 q^{67} - q^{68} + 30 q^{69} + 3 q^{70} + 16 q^{71} - 7 q^{72} - q^{73} + 9 q^{74} + 3 q^{75} + 4 q^{76} - 6 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} + 27 q^{83} + 16 q^{84} - q^{85} - 19 q^{86} + 10 q^{87} + 16 q^{89} - 7 q^{90} - 16 q^{91} + 13 q^{92} - 4 q^{93} - 3 q^{94} + 4 q^{95} - 3 q^{96} - 13 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9 - 4 * q^10 + 3 * q^12 - 7 * q^13 + 3 * q^14 + 3 * q^15 + 4 * q^16 - q^17 - 7 * q^18 + 4 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^23 - 3 * q^24 + 4 * q^25 + 7 * q^26 + 12 * q^27 - 3 * q^28 + 4 * q^29 - 3 * q^30 + 12 * q^31 - 4 * q^32 + q^34 - 3 * q^35 + 7 * q^36 - 9 * q^37 - 4 * q^38 + 6 * q^39 - 4 * q^40 - 16 * q^42 + 19 * q^43 + 7 * q^45 - 13 * q^46 + 3 * q^47 + 3 * q^48 + 11 * q^49 - 4 * q^50 + 10 * q^51 - 7 * q^52 + 3 * q^53 - 12 * q^54 + 3 * q^56 - 24 * q^57 - 4 * q^58 + 2 * q^59 + 3 * q^60 - 10 * q^61 - 12 * q^62 + 29 * q^63 + 4 * q^64 - 7 * q^65 - 13 * q^67 - q^68 + 30 * q^69 + 3 * q^70 + 16 * q^71 - 7 * q^72 - q^73 + 9 * q^74 + 3 * q^75 + 4 * q^76 - 6 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 + 27 * q^83 + 16 * q^84 - q^85 - 19 * q^86 + 10 * q^87 + 16 * q^89 - 7 * q^90 - 16 * q^91 + 13 * q^92 - 4 * q^93 - 3 * q^94 + 4 * q^95 - 3 * q^96 - 13 * q^97 - 11 * q^98

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