LMFDB - Embedded newform 2166.2.a.w.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.90211 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.90211 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.90211 q^{10} +4.06050 q^{11} +1.00000 q^{12} -3.58721 q^{13} -2.61803 q^{14} +3.90211 q^{15} +1.00000 q^{16} -7.39144 q^{17} -1.00000 q^{18} +3.90211 q^{20} +2.61803 q^{21} -4.06050 q^{22} +3.11507 q^{23} -1.00000 q^{24} +10.2265 q^{25} +3.58721 q^{26} +1.00000 q^{27} +2.61803 q^{28} -2.95012 q^{29} -3.90211 q^{30} +5.01905 q^{31} -1.00000 q^{32} +4.06050 q^{33} +7.39144 q^{34} +10.2159 q^{35} +1.00000 q^{36} +5.60845 q^{37} -3.58721 q^{39} -3.90211 q^{40} +10.5065 q^{41} -2.61803 q^{42} -2.33801 q^{43} +4.06050 q^{44} +3.90211 q^{45} -3.11507 q^{46} -9.51243 q^{47} +1.00000 q^{48} -0.145898 q^{49} -10.2265 q^{50} -7.39144 q^{51} -3.58721 q^{52} +2.95012 q^{53} -1.00000 q^{54} +15.8445 q^{55} -2.61803 q^{56} +2.95012 q^{58} +5.75216 q^{59} +3.90211 q^{60} -6.49338 q^{61} -5.01905 q^{62} +2.61803 q^{63} +1.00000 q^{64} -13.9977 q^{65} -4.06050 q^{66} -4.45089 q^{67} -7.39144 q^{68} +3.11507 q^{69} -10.2159 q^{70} +7.49119 q^{71} -1.00000 q^{72} -13.4626 q^{73} -5.60845 q^{74} +10.2265 q^{75} +10.6305 q^{77} +3.58721 q^{78} -1.56712 q^{79} +3.90211 q^{80} +1.00000 q^{81} -10.5065 q^{82} +6.69102 q^{83} +2.61803 q^{84} -28.8422 q^{85} +2.33801 q^{86} -2.95012 q^{87} -4.06050 q^{88} +1.64886 q^{89} -3.90211 q^{90} -9.39144 q^{91} +3.11507 q^{92} +5.01905 q^{93} +9.51243 q^{94} -1.00000 q^{96} +2.93243 q^{97} +0.145898 q^{98} +4.06050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.90211	1.74508	0.872539	−	0.488544i	$-0.162472\pi$
$5$	3.90211	1.74508	0.872539	+	0.488544i	$0.162472\pi$
$6$	−1.00000	−0.408248
$7$	2.61803	0.989524	0.494762	−	0.869029i	$-0.335255\pi$
$7$	2.61803	0.989524	0.494762	+	0.869029i	$0.335255\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.90211	−1.23396
$11$	4.06050	1.22429	0.612143	−	0.790747i	$-0.290308\pi$
$11$	4.06050	1.22429	0.612143	+	0.790747i	$0.290308\pi$
$12$	1.00000	0.288675
$13$	−3.58721	−0.994913	−0.497456	−	0.867489i	$-0.665733\pi$
$13$	−3.58721	−0.994913	−0.497456	+	0.867489i	$0.665733\pi$
$14$	−2.61803	−0.699699
$15$	3.90211	1.00752
$16$	1.00000	0.250000
$17$	−7.39144	−1.79269	−0.896343	−	0.443361i	$-0.853786\pi$
$17$	−7.39144	−1.79269	−0.896343	+	0.443361i	$0.853786\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	3.90211	0.872539
$21$	2.61803	0.571302
$22$	−4.06050	−0.865701
$23$	3.11507	0.649538	0.324769	−	0.945793i	$-0.394714\pi$
$23$	3.11507	0.649538	0.324769	+	0.945793i	$0.394714\pi$
$24$	−1.00000	−0.204124
$25$	10.2265	2.04530
$26$	3.58721	0.703510
$27$	1.00000	0.192450
$28$	2.61803	0.494762
$29$	−2.95012	−0.547824	−0.273912	−	0.961755i	$-0.588318\pi$
$29$	−2.95012	−0.547824	−0.273912	+	0.961755i	$0.588318\pi$
$30$	−3.90211	−0.712425
$31$	5.01905	0.901448	0.450724	−	0.892663i	$-0.351166\pi$
$31$	5.01905	0.901448	0.450724	+	0.892663i	$0.351166\pi$
$32$	−1.00000	−0.176777
$33$	4.06050	0.706842
$34$	7.39144	1.26762
$35$	10.2159	1.72680
$36$	1.00000	0.166667
$37$	5.60845	0.922024	0.461012	−	0.887394i	$-0.347487\pi$
$37$	5.60845	0.922024	0.461012	+	0.887394i	$0.347487\pi$
$38$	0	0
$39$	−3.58721	−0.574413
$40$	−3.90211	−0.616978
$41$	10.5065	1.64084	0.820420	−	0.571761i	$-0.193739\pi$
$41$	10.5065	1.64084	0.820420	+	0.571761i	$0.193739\pi$
$42$	−2.61803	−0.403971
$43$	−2.33801	−0.356543	−0.178272	−	0.983981i	$-0.557051\pi$
$43$	−2.33801	−0.356543	−0.178272	+	0.983981i	$0.557051\pi$
$44$	4.06050	0.612143
$45$	3.90211	0.581693
$46$	−3.11507	−0.459292
$47$	−9.51243	−1.38753	−0.693765	−	0.720201i	$-0.744049\pi$
$47$	−9.51243	−1.38753	−0.693765	+	0.720201i	$0.744049\pi$
$48$	1.00000	0.144338
$49$	−0.145898	−0.0208426
$50$	−10.2265	−1.44624
$51$	−7.39144	−1.03501
$52$	−3.58721	−0.497456
$53$	2.95012	0.405231	0.202615	−	0.979258i	$-0.435056\pi$
$53$	2.95012	0.405231	0.202615	+	0.979258i	$0.435056\pi$
$54$	−1.00000	−0.136083
$55$	15.8445	2.13647
$56$	−2.61803	−0.349850
$57$	0	0
$58$	2.95012	0.387370
$59$	5.75216	0.748867	0.374434	−	0.927254i	$-0.377837\pi$
$59$	5.75216	0.748867	0.374434	+	0.927254i	$0.377837\pi$
$60$	3.90211	0.503761
$61$	−6.49338	−0.831392	−0.415696	−	0.909504i	$-0.636462\pi$
$61$	−6.49338	−0.831392	−0.415696	+	0.909504i	$0.636462\pi$
$62$	−5.01905	−0.637420
$63$	2.61803	0.329841
$64$	1.00000	0.125000
$65$	−13.9977	−1.73620
$66$	−4.06050	−0.499813
$67$	−4.45089	−0.543763	−0.271882	−	0.962331i	$-0.587646\pi$
$67$	−4.45089	−0.543763	−0.271882	+	0.962331i	$0.587646\pi$
$68$	−7.39144	−0.896343
$69$	3.11507	0.375011
$70$	−10.2159	−1.22103
$71$	7.49119	0.889040	0.444520	−	0.895769i	$-0.353374\pi$
$71$	7.49119	0.889040	0.444520	+	0.895769i	$0.353374\pi$
$72$	−1.00000	−0.117851
$73$	−13.4626	−1.57567	−0.787836	−	0.615885i	$-0.788799\pi$
$73$	−13.4626	−1.57567	−0.787836	+	0.615885i	$0.788799\pi$
$74$	−5.60845	−0.651969
$75$	10.2265	1.18085
$76$	0	0
$77$	10.6305	1.21146
$78$	3.58721	0.406171
$79$	−1.56712	−0.176315	−0.0881573	−	0.996107i	$-0.528098\pi$
$79$	−1.56712	−0.176315	−0.0881573	+	0.996107i	$0.528098\pi$
$80$	3.90211	0.436269
$81$	1.00000	0.111111
$82$	−10.5065	−1.16025
$83$	6.69102	0.734435	0.367217	−	0.930135i	$-0.380311\pi$
$83$	6.69102	0.734435	0.367217	+	0.930135i	$0.380311\pi$
$84$	2.61803	0.285651
$85$	−28.8422	−3.12838
$86$	2.33801	0.252114
$87$	−2.95012	−0.316287
$88$	−4.06050	−0.432850
$89$	1.64886	0.174779	0.0873894	−	0.996174i	$-0.472148\pi$
$89$	1.64886	0.174779	0.0873894	+	0.996174i	$0.472148\pi$
$90$	−3.90211	−0.411319
$91$	−9.39144	−0.984490
$92$	3.11507	0.324769
$93$	5.01905	0.520451
$94$	9.51243	0.981132
$95$	0	0
$96$	−1.00000	−0.102062
$97$	2.93243	0.297743	0.148871	−	0.988857i	$-0.452436\pi$
$97$	2.93243	0.297743	0.148871	+	0.988857i	$0.452436\pi$
$98$	0.145898	0.0147379
$99$	4.06050	0.408095
$100$	10.2265	1.02265
$101$	9.83860	0.978977	0.489489	−	0.872010i	$-0.337183\pi$
$101$	9.83860	0.978977	0.489489	+	0.872010i	$0.337183\pi$
$102$	7.39144	0.731861
$103$	7.76870	0.765473	0.382736	−	0.923858i	$-0.374982\pi$
$103$	7.76870	0.765473	0.382736	+	0.923858i	$0.374982\pi$
$104$	3.58721	0.351755
$105$	10.2159	0.996966
$106$	−2.95012	−0.286541
$107$	−16.3819	−1.58369	−0.791847	−	0.610720i	$-0.790880\pi$
$107$	−16.3819	−1.58369	−0.791847	+	0.610720i	$0.790880\pi$
$108$	1.00000	0.0962250
$109$	−10.8445	−1.03872	−0.519358	−	0.854557i	$-0.673829\pi$
$109$	−10.8445	−1.03872	−0.519358	+	0.854557i	$0.673829\pi$
$110$	−15.8445	−1.51072
$111$	5.60845	0.532331
$112$	2.61803	0.247381
$113$	−4.82328	−0.453736	−0.226868	−	0.973926i	$-0.572849\pi$
$113$	−4.82328	−0.453736	−0.226868	+	0.973926i	$0.572849\pi$
$114$	0	0
$115$	12.1554	1.13349
$116$	−2.95012	−0.273912
$117$	−3.58721	−0.331638
$118$	−5.75216	−0.529529
$119$	−19.3510	−1.77391
$120$	−3.90211	−0.356213
$121$	5.48764	0.498876
$122$	6.49338	0.587883
$123$	10.5065	0.947340
$124$	5.01905	0.450724
$125$	20.3943	1.82413
$126$	−2.61803	−0.233233
$127$	−18.3119	−1.62492	−0.812459	−	0.583019i	$-0.801871\pi$
$127$	−18.3119	−1.62492	−0.812459	+	0.583019i	$0.801871\pi$
$128$	−1.00000	−0.0883883
$129$	−2.33801	−0.205850
$130$	13.9977	1.22768
$131$	16.0919	1.40595	0.702976	−	0.711214i	$-0.251854\pi$
$131$	16.0919	1.40595	0.702976	+	0.711214i	$0.251854\pi$
$132$	4.06050	0.353421
$133$	0	0
$134$	4.45089	0.384499
$135$	3.90211	0.335840
$136$	7.39144	0.633810
$137$	−13.0653	−1.11624	−0.558121	−	0.829760i	$-0.688477\pi$
$137$	−13.0653	−1.11624	−0.558121	+	0.829760i	$0.688477\pi$
$138$	−3.11507	−0.265173
$139$	−5.83860	−0.495223	−0.247612	−	0.968859i	$-0.579646\pi$
$139$	−5.83860	−0.495223	−0.247612	+	0.968859i	$0.579646\pi$
$140$	10.2159	0.863398
$141$	−9.51243	−0.801091
$142$	−7.49119	−0.628646
$143$	−14.5659	−1.21806
$144$	1.00000	0.0833333
$145$	−11.5117	−0.955996
$146$	13.4626	1.11417
$147$	−0.145898	−0.0120335
$148$	5.60845	0.461012
$149$	7.00406	0.573795	0.286897	−	0.957961i	$-0.407376\pi$
$149$	7.00406	0.573795	0.286897	+	0.957961i	$0.407376\pi$
$150$	−10.2265	−0.834989
$151$	−20.5920	−1.67575	−0.837876	−	0.545861i	$-0.816203\pi$
$151$	−20.5920	−1.67575	−0.837876	+	0.545861i	$0.816203\pi$
$152$	0	0
$153$	−7.39144	−0.597562
$154$	−10.6305	−0.856632
$155$	19.5849	1.57310
$156$	−3.58721	−0.287207
$157$	−11.0272	−0.880064	−0.440032	−	0.897982i	$-0.645033\pi$
$157$	−11.0272	−0.880064	−0.440032	+	0.897982i	$0.645033\pi$
$158$	1.56712	0.124673
$159$	2.95012	0.233960
$160$	−3.90211	−0.308489
$161$	8.15537	0.642733
$162$	−1.00000	−0.0785674
$163$	6.50651	0.509629	0.254815	−	0.966990i	$-0.417986\pi$
$163$	6.50651	0.509629	0.254815	+	0.966990i	$0.417986\pi$
$164$	10.5065	0.820420
$165$	15.8445	1.23349
$166$	−6.69102	−0.519324
$167$	11.3783	0.880480	0.440240	−	0.897880i	$-0.354893\pi$
$167$	11.3783	0.880480	0.440240	+	0.897880i	$0.354893\pi$
$168$	−2.61803	−0.201986
$169$	−0.131932	−0.0101486
$170$	28.8422	2.21210
$171$	0	0
$172$	−2.33801	−0.178272
$173$	5.22660	0.397371	0.198685	−	0.980063i	$-0.436333\pi$
$173$	5.22660	0.397371	0.198685	+	0.980063i	$0.436333\pi$
$174$	2.95012	0.223648
$175$	26.7733	2.02387
$176$	4.06050	0.306072
$177$	5.75216	0.432359
$178$	−1.64886	−0.123587
$179$	14.4969	1.08355	0.541776	−	0.840523i	$-0.317752\pi$
$179$	14.4969	1.08355	0.541776	+	0.840523i	$0.317752\pi$
$180$	3.90211	0.290846
$181$	−17.3510	−1.28969	−0.644846	−	0.764313i	$-0.723078\pi$
$181$	−17.3510	−1.28969	−0.644846	+	0.764313i	$0.723078\pi$
$182$	9.39144	0.696139
$183$	−6.49338	−0.480004
$184$	−3.11507	−0.229646
$185$	21.8848	1.60900
$186$	−5.01905	−0.368015
$187$	−30.0129	−2.19476
$188$	−9.51243	−0.693765
$189$	2.61803	0.190434
$190$	0	0
$191$	−8.99177	−0.650622	−0.325311	−	0.945607i	$-0.605469\pi$
$191$	−8.99177	−0.650622	−0.325311	+	0.945607i	$0.605469\pi$
$192$	1.00000	0.0721688
$193$	17.1227	1.23252	0.616261	−	0.787542i	$-0.288647\pi$
$193$	17.1227	1.23252	0.616261	+	0.787542i	$0.288647\pi$
$194$	−2.93243	−0.210536
$195$	−13.9977	−1.00240
$196$	−0.145898	−0.0104213
$197$	−3.81851	−0.272057	−0.136029	−	0.990705i	$-0.543434\pi$
$197$	−3.81851	−0.272057	−0.136029	+	0.990705i	$0.543434\pi$
$198$	−4.06050	−0.288567
$199$	14.1283	1.00153	0.500763	−	0.865584i	$-0.333053\pi$
$199$	14.1283	1.00153	0.500763	+	0.865584i	$0.333053\pi$
$200$	−10.2265	−0.723122
$201$	−4.45089	−0.313942
$202$	−9.83860	−0.692241
$203$	−7.72353	−0.542085
$204$	−7.39144	−0.517504
$205$	40.9976	2.86340
$206$	−7.76870	−0.541271
$207$	3.11507	0.216513
$208$	−3.58721	−0.248728
$209$	0	0
$210$	−10.2159	−0.704962
$211$	−11.4508	−0.788304	−0.394152	−	0.919045i	$-0.628962\pi$
$211$	−11.4508	−0.788304	−0.394152	+	0.919045i	$0.628962\pi$
$212$	2.95012	0.202615
$213$	7.49119	0.513288
$214$	16.3819	1.11984
$215$	−9.12319	−0.622196
$216$	−1.00000	−0.0680414
$217$	13.1400	0.892004
$218$	10.8445	0.734484
$219$	−13.4626	−0.909715
$220$	15.8445	1.06824
$221$	26.5146	1.78357
$222$	−5.60845	−0.376415
$223$	−11.2319	−0.752144	−0.376072	−	0.926591i	$-0.622725\pi$
$223$	−11.2319	−0.752144	−0.376072	+	0.926591i	$0.622725\pi$
$224$	−2.61803	−0.174925
$225$	10.2265	0.681766
$226$	4.82328	0.320840
$227$	−15.3878	−1.02132	−0.510661	−	0.859782i	$-0.670599\pi$
$227$	−15.3878	−1.02132	−0.510661	+	0.859782i	$0.670599\pi$
$228$	0	0
$229$	12.6750	0.837588	0.418794	−	0.908081i	$-0.362453\pi$
$229$	12.6750	0.837588	0.418794	+	0.908081i	$0.362453\pi$
$230$	−12.1554	−0.801501
$231$	10.6305	0.699437
$232$	2.95012	0.193685
$233$	16.2147	1.06226	0.531131	−	0.847290i	$-0.321767\pi$
$233$	16.2147	1.06226	0.531131	+	0.847290i	$0.321767\pi$
$234$	3.58721	0.234503
$235$	−37.1186	−2.42135
$236$	5.75216	0.374434
$237$	−1.56712	−0.101795
$238$	19.3510	1.25434
$239$	−5.06154	−0.327404	−0.163702	−	0.986510i	$-0.552343\pi$
$239$	−5.06154	−0.327404	−0.163702	+	0.986510i	$0.552343\pi$
$240$	3.90211	0.251880
$241$	15.6902	1.01069	0.505347	−	0.862916i	$-0.331364\pi$
$241$	15.6902	1.01069	0.505347	+	0.862916i	$0.331364\pi$
$242$	−5.48764	−0.352759
$243$	1.00000	0.0641500
$244$	−6.49338	−0.415696
$245$	−0.569311	−0.0363719
$246$	−10.5065	−0.669870
$247$	0	0
$248$	−5.01905	−0.318710
$249$	6.69102	0.424026
$250$	−20.3943	−1.28985
$251$	−21.1945	−1.33779	−0.668893	−	0.743359i	$-0.733231\pi$
$251$	−21.1945	−1.33779	−0.668893	+	0.743359i	$0.733231\pi$
$252$	2.61803	0.164921
$253$	12.6487	0.795220
$254$	18.3119	1.14899
$255$	−28.8422	−1.80617
$256$	1.00000	0.0625000
$257$	18.7367	1.16876	0.584380	−	0.811480i	$-0.301338\pi$
$257$	18.7367	1.16876	0.584380	+	0.811480i	$0.301338\pi$
$258$	2.33801	0.145558
$259$	14.6831	0.912365
$260$	−13.9977	−0.868100
$261$	−2.95012	−0.182608
$262$	−16.0919	−0.994158
$263$	0.676024	0.0416854	0.0208427	−	0.999783i	$-0.493365\pi$
$263$	0.676024	0.0416854	0.0208427	+	0.999783i	$0.493365\pi$
$264$	−4.06050	−0.249906
$265$	11.5117	0.707159
$266$	0	0
$267$	1.64886	0.100909
$268$	−4.45089	−0.271882
$269$	−12.5622	−0.765930	−0.382965	−	0.923763i	$-0.625097\pi$
$269$	−12.5622	−0.765930	−0.382965	+	0.923763i	$0.625097\pi$
$270$	−3.90211	−0.237475
$271$	−8.59887	−0.522344	−0.261172	−	0.965292i	$-0.584109\pi$
$271$	−8.59887	−0.522344	−0.261172	+	0.965292i	$0.584109\pi$
$272$	−7.39144	−0.448172
$273$	−9.39144	−0.568396
$274$	13.0653	0.789302
$275$	41.5246	2.50403
$276$	3.11507	0.187505
$277$	15.9940	0.960984	0.480492	−	0.876999i	$-0.340458\pi$
$277$	15.9940	0.960984	0.480492	+	0.876999i	$0.340458\pi$
$278$	5.83860	0.350176
$279$	5.01905	0.300483
$280$	−10.2159	−0.610515
$281$	9.70447	0.578920	0.289460	−	0.957190i	$-0.406524\pi$
$281$	9.70447	0.578920	0.289460	+	0.957190i	$0.406524\pi$
$282$	9.51243	0.566457
$283$	17.6143	1.04706	0.523530	−	0.852008i	$-0.324615\pi$
$283$	17.6143	1.04706	0.523530	+	0.852008i	$0.324615\pi$
$284$	7.49119	0.444520
$285$	0	0
$286$	14.5659	0.861297
$287$	27.5064	1.62365
$288$	−1.00000	−0.0589256
$289$	37.6333	2.21372
$290$	11.5117	0.675991
$291$	2.93243	0.171902
$292$	−13.4626	−0.787836
$293$	7.16495	0.418581	0.209290	−	0.977854i	$-0.432885\pi$
$293$	7.16495	0.418581	0.209290	+	0.977854i	$0.432885\pi$
$294$	0.145898	0.00850895
$295$	22.4456	1.30683
$296$	−5.60845	−0.325985
$297$	4.06050	0.235614
$298$	−7.00406	−0.405734
$299$	−11.1744	−0.646233
$300$	10.2265	0.590426
$301$	−6.12099	−0.352808
$302$	20.5920	1.18494
$303$	9.83860	0.565213
$304$	0	0
$305$	−25.3379	−1.45084
$306$	7.39144	0.422540
$307$	−28.5278	−1.62816	−0.814082	−	0.580749i	$-0.802760\pi$
$307$	−28.5278	−1.62816	−0.814082	+	0.580749i	$0.802760\pi$
$308$	10.6305	0.605730
$309$	7.76870	0.441946
$310$	−19.5849	−1.11235
$311$	23.1896	1.31496	0.657482	−	0.753471i	$-0.271622\pi$
$311$	23.1896	1.31496	0.657482	+	0.753471i	$0.271622\pi$
$312$	3.58721	0.203086
$313$	−24.9975	−1.41294	−0.706471	−	0.707742i	$-0.749714\pi$
$313$	−24.9975	−1.41294	−0.706471	+	0.707742i	$0.749714\pi$
$314$	11.0272	0.622299
$315$	10.2159	0.575599
$316$	−1.56712	−0.0881573
$317$	7.67157	0.430878	0.215439	−	0.976517i	$-0.430882\pi$
$317$	7.67157	0.430878	0.215439	+	0.976517i	$0.430882\pi$
$318$	−2.95012	−0.165435
$319$	−11.9790	−0.670694
$320$	3.90211	0.218135
$321$	−16.3819	−0.914346
$322$	−8.15537	−0.454481
$323$	0	0
$324$	1.00000	0.0555556
$325$	−36.6845	−2.03489
$326$	−6.50651	−0.360362
$327$	−10.8445	−0.599703
$328$	−10.5065	−0.580125
$329$	−24.9039	−1.37299
$330$	−15.8445	−0.872212
$331$	−20.0806	−1.10373	−0.551864	−	0.833934i	$-0.686083\pi$
$331$	−20.0806	−1.10373	−0.551864	+	0.833934i	$0.686083\pi$
$332$	6.69102	0.367217
$333$	5.60845	0.307341
$334$	−11.3783	−0.622593
$335$	−17.3679	−0.948909
$336$	2.61803	0.142825
$337$	13.8386	0.753836	0.376918	−	0.926247i	$-0.376984\pi$
$337$	13.8386	0.753836	0.376918	+	0.926247i	$0.376984\pi$
$338$	0.131932	0.00717614
$339$	−4.82328	−0.261964
$340$	−28.8422	−1.56419
$341$	20.3798	1.10363
$342$	0	0
$343$	−18.7082	−1.01015
$344$	2.33801	0.126057
$345$	12.1554	0.654423
$346$	−5.22660	−0.280984
$347$	−17.0758	−0.916678	−0.458339	−	0.888777i	$-0.651555\pi$
$347$	−17.0758	−0.916678	−0.458339	+	0.888777i	$0.651555\pi$
$348$	−2.95012	−0.158143
$349$	2.01313	0.107760	0.0538802	−	0.998547i	$-0.482841\pi$
$349$	2.01313	0.107760	0.0538802	+	0.998547i	$0.482841\pi$
$350$	−26.7733	−1.43109
$351$	−3.58721	−0.191471
$352$	−4.06050	−0.216425
$353$	−28.1187	−1.49661	−0.748303	−	0.663357i	$-0.769131\pi$
$353$	−28.1187	−1.49661	−0.748303	+	0.663357i	$0.769131\pi$
$354$	−5.75216	−0.305724
$355$	29.2315	1.55144
$356$	1.64886	0.0873894
$357$	−19.3510	−1.02417
$358$	−14.4969	−0.766186
$359$	−17.5680	−0.927206	−0.463603	−	0.886043i	$-0.653444\pi$
$359$	−17.5680	−0.927206	−0.463603	+	0.886043i	$0.653444\pi$
$360$	−3.90211	−0.205659
$361$	0	0
$362$	17.3510	0.911950
$363$	5.48764	0.288026
$364$	−9.39144	−0.492245
$365$	−52.5324	−2.74967
$366$	6.49338	0.339414
$367$	21.4208	1.11816	0.559078	−	0.829115i	$-0.311155\pi$
$367$	21.4208	1.11816	0.559078	+	0.829115i	$0.311155\pi$
$368$	3.11507	0.162384
$369$	10.5065	0.546947
$370$	−21.8848	−1.13774
$371$	7.72353	0.400985
$372$	5.01905	0.260226
$373$	10.9480	0.566866	0.283433	−	0.958992i	$-0.408527\pi$
$373$	10.9480	0.566866	0.283433	+	0.958992i	$0.408527\pi$
$374$	30.0129	1.55193
$375$	20.3943	1.05316
$376$	9.51243	0.490566
$377$	10.5827	0.545037
$378$	−2.61803	−0.134657
$379$	−25.6415	−1.31712	−0.658559	−	0.752529i	$-0.728834\pi$
$379$	−25.6415	−1.31712	−0.658559	+	0.752529i	$0.728834\pi$
$380$	0	0
$381$	−18.3119	−0.938146
$382$	8.99177	0.460059
$383$	−20.1068	−1.02741	−0.513706	−	0.857966i	$-0.671728\pi$
$383$	−20.1068	−1.02741	−0.513706	+	0.857966i	$0.671728\pi$
$384$	−1.00000	−0.0510310
$385$	41.4815	2.11409
$386$	−17.1227	−0.871525
$387$	−2.33801	−0.118848
$388$	2.93243	0.148871
$389$	−8.06874	−0.409102	−0.204551	−	0.978856i	$-0.565573\pi$
$389$	−8.06874	−0.409102	−0.204551	+	0.978856i	$0.565573\pi$
$390$	13.9977	0.708801
$391$	−23.0249	−1.16442
$392$	0.145898	0.00736896
$393$	16.0919	0.811727
$394$	3.81851	0.192374
$395$	−6.11507	−0.307683
$396$	4.06050	0.204048
$397$	13.1421	0.659584	0.329792	−	0.944054i	$-0.393021\pi$
$397$	13.1421	0.659584	0.329792	+	0.944054i	$0.393021\pi$
$398$	−14.1283	−0.708186
$399$	0	0
$400$	10.2265	0.511324
$401$	20.9905	1.04821	0.524107	−	0.851652i	$-0.324399\pi$
$401$	20.9905	1.04821	0.524107	+	0.851652i	$0.324399\pi$
$402$	4.45089	0.221990
$403$	−18.0044	−0.896862
$404$	9.83860	0.489489
$405$	3.90211	0.193898
$406$	7.72353	0.383312
$407$	22.7731	1.12882
$408$	7.39144	0.365931
$409$	−4.59628	−0.227271	−0.113636	−	0.993522i	$-0.536250\pi$
$409$	−4.59628	−0.227271	−0.113636	+	0.993522i	$0.536250\pi$
$410$	−40.9976	−2.02473
$411$	−13.0653	−0.644462
$412$	7.76870	0.382736
$413$	15.0593	0.741022
$414$	−3.11507	−0.153097
$415$	26.1091	1.28165
$416$	3.58721	0.175877
$417$	−5.83860	−0.285917
$418$	0	0
$419$	7.04424	0.344134	0.172067	−	0.985085i	$-0.444956\pi$
$419$	7.04424	0.344134	0.172067	+	0.985085i	$0.444956\pi$
$420$	10.2159	0.498483
$421$	−20.2397	−0.986422	−0.493211	−	0.869910i	$-0.664177\pi$
$421$	−20.2397	−0.986422	−0.493211	+	0.869910i	$0.664177\pi$
$422$	11.4508	0.557415
$423$	−9.51243	−0.462510
$424$	−2.95012	−0.143271
$425$	−75.5884	−3.66658
$426$	−7.49119	−0.362949
$427$	−16.9999	−0.822682
$428$	−16.3819	−0.791847
$429$	−14.5659	−0.703246
$430$	9.12319	0.439959
$431$	11.9477	0.575503	0.287751	−	0.957705i	$-0.407092\pi$
$431$	11.9477	0.575503	0.287751	+	0.957705i	$0.407092\pi$
$432$	1.00000	0.0481125
$433$	−32.6322	−1.56820	−0.784101	−	0.620634i	$-0.786875\pi$
$433$	−32.6322	−1.56820	−0.784101	+	0.620634i	$0.786875\pi$
$434$	−13.1400	−0.630742
$435$	−11.5117	−0.551945
$436$	−10.8445	−0.519358
$437$	0	0
$438$	13.4626	0.643266
$439$	−34.5778	−1.65031	−0.825155	−	0.564907i	$-0.808912\pi$
$439$	−34.5778	−1.65031	−0.825155	+	0.564907i	$0.808912\pi$
$440$	−15.8445	−0.755358
$441$	−0.145898	−0.00694753
$442$	−26.5146	−1.26117
$443$	29.7846	1.41511	0.707555	−	0.706658i	$-0.249798\pi$
$443$	29.7846	1.41511	0.707555	+	0.706658i	$0.249798\pi$
$444$	5.60845	0.266165
$445$	6.43403	0.305002
$446$	11.2319	0.531846
$447$	7.00406	0.331281
$448$	2.61803	0.123690
$449$	2.95239	0.139332	0.0696659	−	0.997570i	$-0.477807\pi$
$449$	2.95239	0.139332	0.0696659	+	0.997570i	$0.477807\pi$
$450$	−10.2265	−0.482081
$451$	42.6616	2.00886
$452$	−4.82328	−0.226868
$453$	−20.5920	−0.967496
$454$	15.3878	0.722184
$455$	−36.6464	−1.71801
$456$	0	0
$457$	15.6466	0.731915	0.365957	−	0.930632i	$-0.380742\pi$
$457$	15.6466	0.731915	0.365957	+	0.930632i	$0.380742\pi$
$458$	−12.6750	−0.592264
$459$	−7.39144	−0.345003
$460$	12.1554	0.566747
$461$	1.74444	0.0812467	0.0406234	−	0.999175i	$-0.487066\pi$
$461$	1.74444	0.0812467	0.0406234	+	0.999175i	$0.487066\pi$
$462$	−10.6305	−0.494577
$463$	−28.6429	−1.33115	−0.665574	−	0.746332i	$-0.731813\pi$
$463$	−28.6429	−1.33115	−0.665574	+	0.746332i	$0.731813\pi$
$464$	−2.95012	−0.136956
$465$	19.5849	0.908228
$466$	−16.2147	−0.751132
$467$	−2.64480	−0.122387	−0.0611934	−	0.998126i	$-0.519491\pi$
$467$	−2.64480	−0.122387	−0.0611934	+	0.998126i	$0.519491\pi$
$468$	−3.58721	−0.165819
$469$	−11.6526	−0.538067
$470$	37.1186	1.71215
$471$	−11.0272	−0.508105
$472$	−5.75216	−0.264765
$473$	−9.49349	−0.436511
$474$	1.56712	0.0719801
$475$	0	0
$476$	−19.3510	−0.886953
$477$	2.95012	0.135077
$478$	5.06154	0.231509
$479$	30.9359	1.41350	0.706749	−	0.707464i	$-0.250161\pi$
$479$	30.9359	1.41350	0.706749	+	0.707464i	$0.250161\pi$
$480$	−3.90211	−0.178106
$481$	−20.1187	−0.917333
$482$	−15.6902	−0.714669
$483$	8.15537	0.371082
$484$	5.48764	0.249438
$485$	11.4427	0.519585
$486$	−1.00000	−0.0453609
$487$	1.36331	0.0617776	0.0308888	−	0.999523i	$-0.490166\pi$
$487$	1.36331	0.0617776	0.0308888	+	0.999523i	$0.490166\pi$
$488$	6.49338	0.293941
$489$	6.50651	0.294234
$490$	0.569311	0.0257188
$491$	−10.7173	−0.483664	−0.241832	−	0.970318i	$-0.577748\pi$
$491$	−10.7173	−0.483664	−0.241832	+	0.970318i	$0.577748\pi$
$492$	10.5065	0.473670
$493$	21.8057	0.982077
$494$	0	0
$495$	15.8445	0.712158
$496$	5.01905	0.225362
$497$	19.6122	0.879727
$498$	−6.69102	−0.299832
$499$	−1.49119	−0.0667547	−0.0333773	−	0.999443i	$-0.510626\pi$
$499$	−1.49119	−0.0667547	−0.0333773	+	0.999443i	$0.510626\pi$
$500$	20.3943	0.912063
$501$	11.3783	0.508345
$502$	21.1945	0.945957
$503$	−44.6083	−1.98899	−0.994494	−	0.104796i	$-0.966581\pi$
$503$	−44.6083	−1.98899	−0.994494	+	0.104796i	$0.966581\pi$
$504$	−2.61803	−0.116617
$505$	38.3913	1.70839
$506$	−12.6487	−0.562305
$507$	−0.131932	−0.00585929
$508$	−18.3119	−0.812459
$509$	−29.5563	−1.31006	−0.655029	−	0.755603i	$-0.727344\pi$
$509$	−29.5563	−1.31006	−0.655029	+	0.755603i	$0.727344\pi$
$510$	28.8422	1.27715
$511$	−35.2454	−1.55917
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−18.7367	−0.826438
$515$	30.3144	1.33581
$516$	−2.33801	−0.102925
$517$	−38.6252	−1.69873
$518$	−14.6831	−0.645139
$519$	5.22660	0.229422
$520$	13.9977	0.613840
$521$	34.9574	1.53151	0.765756	−	0.643131i	$-0.222365\pi$
$521$	34.9574	1.53151	0.765756	+	0.643131i	$0.222365\pi$
$522$	2.95012	0.129123
$523$	−4.98468	−0.217965	−0.108982	−	0.994044i	$-0.534759\pi$
$523$	−4.98468	−0.217965	−0.108982	+	0.994044i	$0.534759\pi$
$524$	16.0919	0.702976
$525$	26.7733	1.16848
$526$	−0.676024	−0.0294760
$527$	−37.0980	−1.61601
$528$	4.06050	0.176710
$529$	−13.2963	−0.578101
$530$	−11.5117	−0.500037
$531$	5.75216	0.249622
$532$	0	0
$533$	−37.6890	−1.63249
$534$	−1.64886	−0.0713531
$535$	−63.9238	−2.76367
$536$	4.45089	0.192249
$537$	14.4969	0.625589
$538$	12.5622	0.541595
$539$	−0.592419	−0.0255173
$540$	3.90211	0.167920
$541$	1.12692	0.0484499	0.0242250	−	0.999707i	$-0.492288\pi$
$541$	1.12692	0.0484499	0.0242250	+	0.999707i	$0.492288\pi$
$542$	8.59887	0.369353
$543$	−17.3510	−0.744604
$544$	7.39144	0.316905
$545$	−42.3165	−1.81264
$546$	9.39144	0.401916
$547$	39.4435	1.68648	0.843240	−	0.537537i	$-0.180645\pi$
$547$	39.4435	1.68648	0.843240	+	0.537537i	$0.180645\pi$
$548$	−13.0653	−0.558121
$549$	−6.49338	−0.277131
$550$	−41.5246	−1.77062
$551$	0	0
$552$	−3.11507	−0.132586
$553$	−4.10277	−0.174467
$554$	−15.9940	−0.679518
$555$	21.8848	0.928959
$556$	−5.83860	−0.247612
$557$	7.70913	0.326646	0.163323	−	0.986573i	$-0.447779\pi$
$557$	7.70913	0.326646	0.163323	+	0.986573i	$0.447779\pi$
$558$	−5.01905	−0.212473
$559$	8.38694	0.354730
$560$	10.2159	0.431699
$561$	−30.0129	−1.26715
$562$	−9.70447	−0.409359
$563$	35.5099	1.49657	0.748283	−	0.663380i	$-0.230879\pi$
$563$	35.5099	1.49657	0.748283	+	0.663380i	$0.230879\pi$
$564$	−9.51243	−0.400546
$565$	−18.8210	−0.791804
$566$	−17.6143	−0.740383
$567$	2.61803	0.109947
$568$	−7.49119	−0.314323
$569$	−2.74269	−0.114979	−0.0574897	−	0.998346i	$-0.518310\pi$
$569$	−2.74269	−0.114979	−0.0574897	+	0.998346i	$0.518310\pi$
$570$	0	0
$571$	4.18845	0.175281	0.0876407	−	0.996152i	$-0.472067\pi$
$571$	4.18845	0.175281	0.0876407	+	0.996152i	$0.472067\pi$
$572$	−14.5659	−0.609029
$573$	−8.99177	−0.375637
$574$	−27.5064	−1.14809
$575$	31.8563	1.32850
$576$	1.00000	0.0416667
$577$	18.3270	0.762961	0.381481	−	0.924377i	$-0.375414\pi$
$577$	18.3270	0.762961	0.381481	+	0.924377i	$0.375414\pi$
$578$	−37.6333	−1.56534
$579$	17.1227	0.711597
$580$	−11.5117	−0.477998
$581$	17.5173	0.726741
$582$	−2.93243	−0.121553
$583$	11.9790	0.496118
$584$	13.4626	0.557084
$585$	−13.9977	−0.578733
$586$	−7.16495	−0.295981
$587$	−38.7843	−1.60080	−0.800400	−	0.599467i	$-0.795379\pi$
$587$	−38.7843	−1.60080	−0.800400	+	0.599467i	$0.795379\pi$
$588$	−0.145898	−0.00601673
$589$	0	0
$590$	−22.4456	−0.924070
$591$	−3.81851	−0.157072
$592$	5.60845	0.230506
$593$	45.3687	1.86307	0.931534	−	0.363654i	$-0.118471\pi$
$593$	45.3687	1.86307	0.931534	+	0.363654i	$0.118471\pi$
$594$	−4.06050	−0.166604
$595$	−75.5099	−3.09560
$596$	7.00406	0.286897
$597$	14.1283	0.578232
$598$	11.1744	0.456956
$599$	−3.53390	−0.144391	−0.0721956	−	0.997390i	$-0.523001\pi$
$599$	−3.53390	−0.144391	−0.0721956	+	0.997390i	$0.523001\pi$
$600$	−10.2265	−0.417495
$601$	32.0977	1.30929	0.654645	−	0.755936i	$-0.272818\pi$
$601$	32.0977	1.30929	0.654645	+	0.755936i	$0.272818\pi$
$602$	6.12099	0.249473
$603$	−4.45089	−0.181254
$604$	−20.5920	−0.837876
$605$	21.4134	0.870578
$606$	−9.83860	−0.399666
$607$	−33.0018	−1.33950	−0.669750	−	0.742587i	$-0.733599\pi$
$607$	−33.0018	−1.33950	−0.669750	+	0.742587i	$0.733599\pi$
$608$	0	0
$609$	−7.72353	−0.312973
$610$	25.3379	1.02590
$611$	34.1231	1.38047
$612$	−7.39144	−0.298781
$613$	12.3582	0.499144	0.249572	−	0.968356i	$-0.419710\pi$
$613$	12.3582	0.499144	0.249572	+	0.968356i	$0.419710\pi$
$614$	28.5278	1.15129
$615$	40.9976	1.65318
$616$	−10.6305	−0.428316
$617$	−5.52054	−0.222249	−0.111124	−	0.993807i	$-0.535445\pi$
$617$	−5.52054	−0.222249	−0.111124	+	0.993807i	$0.535445\pi$
$618$	−7.76870	−0.312503
$619$	−39.9843	−1.60711	−0.803553	−	0.595233i	$-0.797060\pi$
$619$	−39.9843	−1.60711	−0.803553	+	0.595233i	$0.797060\pi$
$620$	19.5849	0.786549
$621$	3.11507	0.125004
$622$	−23.1896	−0.929819
$623$	4.31677	0.172948
$624$	−3.58721	−0.143603
$625$	28.4486	1.13794
$626$	24.9975	0.999102
$627$	0	0
$628$	−11.0272	−0.440032
$629$	−41.4545	−1.65290
$630$	−10.2159	−0.407010
$631$	27.3628	1.08930	0.544648	−	0.838665i	$-0.316663\pi$
$631$	27.3628	1.08930	0.544648	+	0.838665i	$0.316663\pi$
$632$	1.56712	0.0623366
$633$	−11.4508	−0.455128
$634$	−7.67157	−0.304677
$635$	−71.4551	−2.83561
$636$	2.95012	0.116980
$637$	0.523367	0.0207365
$638$	11.9790	0.474252
$639$	7.49119	0.296347
$640$	−3.90211	−0.154245
$641$	−6.36054	−0.251226	−0.125613	−	0.992079i	$-0.540090\pi$
$641$	−6.36054	−0.251226	−0.125613	+	0.992079i	$0.540090\pi$
$642$	16.3819	0.646540
$643$	−1.15548	−0.0455677	−0.0227838	−	0.999740i	$-0.507253\pi$
$643$	−1.15548	−0.0455677	−0.0227838	+	0.999740i	$0.507253\pi$
$644$	8.15537	0.321366
$645$	−9.12319	−0.359225
$646$	0	0
$647$	−1.81026	−0.0711687	−0.0355843	−	0.999367i	$-0.511329\pi$
$647$	−1.81026	−0.0711687	−0.0355843	+	0.999367i	$0.511329\pi$
$648$	−1.00000	−0.0392837
$649$	23.3566	0.916828
$650$	36.6845	1.43889
$651$	13.1400	0.514999
$652$	6.50651	0.254815
$653$	10.1285	0.396360	0.198180	−	0.980166i	$-0.436497\pi$
$653$	10.1285	0.396360	0.198180	+	0.980166i	$0.436497\pi$
$654$	10.8445	0.424054
$655$	62.7922	2.45350
$656$	10.5065	0.410210
$657$	−13.4626	−0.525224
$658$	24.9039	0.970854
$659$	9.41056	0.366583	0.183292	−	0.983059i	$-0.441325\pi$
$659$	9.41056	0.366583	0.183292	+	0.983059i	$0.441325\pi$
$660$	15.8445	0.616747
$661$	−43.1611	−1.67877	−0.839385	−	0.543537i	$-0.817085\pi$
$661$	−43.1611	−1.67877	−0.839385	+	0.543537i	$0.817085\pi$
$662$	20.0806	0.780454
$663$	26.5146	1.02974
$664$	−6.69102	−0.259662
$665$	0	0
$666$	−5.60845	−0.217323
$667$	−9.18985	−0.355832
$668$	11.3783	0.440240
$669$	−11.2319	−0.434250
$670$	17.3679	0.670980
$671$	−26.3663	−1.01786
$672$	−2.61803	−0.100993
$673$	25.6466	0.988602	0.494301	−	0.869291i	$-0.335424\pi$
$673$	25.6466	0.988602	0.494301	+	0.869291i	$0.335424\pi$
$674$	−13.8386	−0.533043
$675$	10.2265	0.393618
$676$	−0.131932	−0.00507430
$677$	1.60260	0.0615929	0.0307965	−	0.999526i	$-0.490196\pi$
$677$	1.60260	0.0615929	0.0307965	+	0.999526i	$0.490196\pi$
$678$	4.82328	0.185237
$679$	7.67720	0.294624
$680$	28.8422	1.10605
$681$	−15.3878	−0.589661
$682$	−20.3798	−0.780385
$683$	−14.0357	−0.537062	−0.268531	−	0.963271i	$-0.586538\pi$
$683$	−14.0357	−0.537062	−0.268531	+	0.963271i	$0.586538\pi$
$684$	0	0
$685$	−50.9821	−1.94793
$686$	18.7082	0.714283
$687$	12.6750	0.483582
$688$	−2.33801	−0.0891359
$689$	−10.5827	−0.403169
$690$	−12.1554	−0.462747
$691$	−8.97363	−0.341373	−0.170686	−	0.985325i	$-0.554599\pi$
$691$	−8.97363	−0.341373	−0.170686	+	0.985325i	$0.554599\pi$
$692$	5.22660	0.198685
$693$	10.6305	0.403820
$694$	17.0758	0.648189
$695$	−22.7829	−0.864204
$696$	2.95012	0.111824
$697$	−77.6582	−2.94151
$698$	−2.01313	−0.0761981
$699$	16.2147	0.613297
$700$	26.7733	1.01194
$701$	−39.0756	−1.47586	−0.737932	−	0.674875i	$-0.764198\pi$
$701$	−39.0756	−1.47586	−0.737932	+	0.674875i	$0.764198\pi$
$702$	3.58721	0.135390
$703$	0	0
$704$	4.06050	0.153036
$705$	−37.1186	−1.39797
$706$	28.1187	1.05826
$707$	25.7578	0.968721
$708$	5.75216	0.216179
$709$	47.4377	1.78156	0.890779	−	0.454436i	$-0.150159\pi$
$709$	47.4377	1.78156	0.890779	+	0.454436i	$0.150159\pi$
$710$	−29.2315	−1.09704
$711$	−1.56712	−0.0587715
$712$	−1.64886	−0.0617936
$713$	15.6347	0.585524
$714$	19.3510	0.724194
$715$	−56.8376	−2.12561
$716$	14.4969	0.541776
$717$	−5.06154	−0.189027
$718$	17.5680	0.655634
$719$	−6.07349	−0.226503	−0.113252	−	0.993566i	$-0.536127\pi$
$719$	−6.07349	−0.226503	−0.113252	+	0.993566i	$0.536127\pi$
$720$	3.90211	0.145423
$721$	20.3387	0.757454
$722$	0	0
$723$	15.6902	0.583525
$724$	−17.3510	−0.644846
$725$	−30.1694	−1.12046
$726$	−5.48764	−0.203665
$727$	33.2148	1.23187	0.615934	−	0.787798i	$-0.288779\pi$
$727$	33.2148	1.23187	0.615934	+	0.787798i	$0.288779\pi$
$728$	9.39144	0.348070
$729$	1.00000	0.0370370
$730$	52.5324	1.94431
$731$	17.2813	0.639171
$732$	−6.49338	−0.240002
$733$	−3.72967	−0.137759	−0.0688793	−	0.997625i	$-0.521942\pi$
$733$	−3.72967	−0.137759	−0.0688793	+	0.997625i	$0.521942\pi$
$734$	−21.4208	−0.790656
$735$	−0.569311	−0.0209993
$736$	−3.11507	−0.114823
$737$	−18.0728	−0.665722
$738$	−10.5065	−0.386750
$739$	2.52337	0.0928235	0.0464118	−	0.998922i	$-0.485221\pi$
$739$	2.52337	0.0928235	0.0464118	+	0.998922i	$0.485221\pi$
$740$	21.8848	0.804502
$741$	0	0
$742$	−7.72353	−0.283540
$743$	23.7403	0.870946	0.435473	−	0.900202i	$-0.356581\pi$
$743$	23.7403	0.870946	0.435473	+	0.900202i	$0.356581\pi$
$744$	−5.01905	−0.184007
$745$	27.3306	1.00132
$746$	−10.9480	−0.400835
$747$	6.69102	0.244812
$748$	−30.0129	−1.09738
$749$	−42.8882	−1.56710
$750$	−20.3943	−0.744696
$751$	−35.9804	−1.31294	−0.656472	−	0.754351i	$-0.727952\pi$
$751$	−35.9804	−1.31294	−0.656472	+	0.754351i	$0.727952\pi$
$752$	−9.51243	−0.346883
$753$	−21.1945	−0.772371
$754$	−10.5827	−0.385400
$755$	−80.3522	−2.92432
$756$	2.61803	0.0952170
$757$	27.2398	0.990047	0.495024	−	0.868880i	$-0.335159\pi$
$757$	27.2398	0.990047	0.495024	+	0.868880i	$0.335159\pi$
$758$	25.6415	0.931343
$759$	12.6487	0.459120
$760$	0	0
$761$	−19.0592	−0.690897	−0.345448	−	0.938438i	$-0.612273\pi$
$761$	−19.0592	−0.690897	−0.345448	+	0.938438i	$0.612273\pi$
$762$	18.3119	0.663370
$763$	−28.3913	−1.02783
$764$	−8.99177	−0.325311
$765$	−28.8422	−1.04279
$766$	20.1068	0.726490
$767$	−20.6342	−0.745058
$768$	1.00000	0.0360844
$769$	2.38906	0.0861517	0.0430759	−	0.999072i	$-0.486284\pi$
$769$	2.38906	0.0861517	0.0430759	+	0.999072i	$0.486284\pi$
$770$	−41.4815	−1.49489
$771$	18.7367	0.674784
$772$	17.1227	0.616261
$773$	9.92888	0.357117	0.178559	−	0.983929i	$-0.442857\pi$
$773$	9.92888	0.357117	0.178559	+	0.983929i	$0.442857\pi$
$774$	2.33801	0.0840381
$775$	51.3273	1.84373
$776$	−2.93243	−0.105268
$777$	14.6831	0.526754
$778$	8.06874	0.289278
$779$	0	0
$780$	−13.9977	−0.501198
$781$	30.4179	1.08844
$782$	23.0249	0.823367
$783$	−2.95012	−0.105429
$784$	−0.145898	−0.00521064
$785$	−43.0292	−1.53578
$786$	−16.0919	−0.573977
$787$	−16.6942	−0.595083	−0.297541	−	0.954709i	$-0.596167\pi$
$787$	−16.6942	−0.595083	−0.297541	+	0.954709i	$0.596167\pi$
$788$	−3.81851	−0.136029
$789$	0.676024	0.0240671
$790$	6.11507	0.217565
$791$	−12.6275	−0.448982
$792$	−4.06050	−0.144283
$793$	23.2931	0.827163
$794$	−13.1421	−0.466397
$795$	11.5117	0.408279
$796$	14.1283	0.500763
$797$	−40.6596	−1.44024	−0.720118	−	0.693852i	$-0.755912\pi$
$797$	−40.6596	−1.44024	−0.720118	+	0.693852i	$0.755912\pi$
$798$	0	0
$799$	70.3105	2.48741
$800$	−10.2265	−0.361561
$801$	1.64886	0.0582596
$802$	−20.9905	−0.741200
$803$	−54.6647	−1.92907
$804$	−4.45089	−0.156971
$805$	31.8232	1.12162
$806$	18.0044	0.634177
$807$	−12.5622	−0.442210
$808$	−9.83860	−0.346121
$809$	17.5974	0.618692	0.309346	−	0.950950i	$-0.399890\pi$
$809$	17.5974	0.618692	0.309346	+	0.950950i	$0.399890\pi$
$810$	−3.90211	−0.137106
$811$	15.6607	0.549922	0.274961	−	0.961455i	$-0.411335\pi$
$811$	15.6607	0.549922	0.274961	+	0.961455i	$0.411335\pi$
$812$	−7.72353	−0.271043
$813$	−8.59887	−0.301576
$814$	−22.7731	−0.798197
$815$	25.3891	0.889342
$816$	−7.39144	−0.258752
$817$	0	0
$818$	4.59628	0.160705
$819$	−9.39144	−0.328163
$820$	40.9976	1.43170
$821$	−25.9393	−0.905287	−0.452644	−	0.891692i	$-0.649519\pi$
$821$	−25.9393	−0.905287	−0.452644	+	0.891692i	$0.649519\pi$
$822$	13.0653	0.455704
$823$	19.7806	0.689509	0.344754	−	0.938693i	$-0.387962\pi$
$823$	19.7806	0.689509	0.344754	+	0.938693i	$0.387962\pi$
$824$	−7.76870	−0.270636
$825$	41.5246	1.44570
$826$	−15.0593	−0.523982
$827$	23.2683	0.809119	0.404559	−	0.914512i	$-0.367425\pi$
$827$	23.2683	0.809119	0.404559	+	0.914512i	$0.367425\pi$
$828$	3.11507	0.108256
$829$	−33.9142	−1.17789	−0.588944	−	0.808174i	$-0.700456\pi$
$829$	−33.9142	−1.17789	−0.588944	+	0.808174i	$0.700456\pi$
$830$	−26.1091	−0.906260
$831$	15.9940	0.554825
$832$	−3.58721	−0.124364
$833$	1.07840	0.0373642
$834$	5.83860	0.202174
$835$	44.3994	1.53651
$836$	0	0
$837$	5.01905	0.173484
$838$	−7.04424	−0.243339
$839$	−29.9933	−1.03548	−0.517742	−	0.855537i	$-0.673227\pi$
$839$	−29.9933	−1.03548	−0.517742	+	0.855537i	$0.673227\pi$
$840$	−10.2159	−0.352481
$841$	−20.2968	−0.699889
$842$	20.2397	0.697506
$843$	9.70447	0.334240
$844$	−11.4508	−0.394152
$845$	−0.514812	−0.0177101
$846$	9.51243	0.327044
$847$	14.3668	0.493650
$848$	2.95012	0.101308
$849$	17.6143	0.604520
$850$	75.5884	2.59266
$851$	17.4707	0.598889
$852$	7.49119	0.256644
$853$	14.3703	0.492030	0.246015	−	0.969266i	$-0.420879\pi$
$853$	14.3703	0.492030	0.246015	+	0.969266i	$0.420879\pi$
$854$	16.9999	0.581724
$855$	0	0
$856$	16.3819	0.559920
$857$	−47.2918	−1.61546	−0.807729	−	0.589554i	$-0.799304\pi$
$857$	−47.2918	−1.61546	−0.807729	+	0.589554i	$0.799304\pi$
$858$	14.5659	0.497270
$859$	−14.1920	−0.484226	−0.242113	−	0.970248i	$-0.577841\pi$
$859$	−14.1920	−0.484226	−0.242113	+	0.970248i	$0.577841\pi$
$860$	−9.12319	−0.311098
$861$	27.5064	0.937415
$862$	−11.9477	−0.406942
$863$	−21.9917	−0.748605	−0.374302	−	0.927307i	$-0.622118\pi$
$863$	−21.9917	−0.748605	−0.374302	+	0.927307i	$0.622118\pi$
$864$	−1.00000	−0.0340207
$865$	20.3948	0.693443
$866$	32.6322	1.10889
$867$	37.6333	1.27809
$868$	13.1400	0.446002
$869$	−6.36328	−0.215859
$870$	11.5117	0.390284
$871$	15.9663	0.540997
$872$	10.8445	0.367242
$873$	2.93243	0.0992477
$874$	0	0
$875$	53.3931	1.80502
$876$	−13.4626	−0.454858
$877$	24.0900	0.813461	0.406731	−	0.913548i	$-0.366669\pi$
$877$	24.0900	0.813461	0.406731	+	0.913548i	$0.366669\pi$
$878$	34.5778	1.16695
$879$	7.16495	0.241668
$880$	15.8445	0.534119
$881$	19.5381	0.658254	0.329127	−	0.944286i	$-0.393246\pi$
$881$	19.5381	0.658254	0.329127	+	0.944286i	$0.393246\pi$
$882$	0.145898	0.00491264
$883$	14.6238	0.492129	0.246065	−	0.969253i	$-0.420862\pi$
$883$	14.6238	0.492129	0.246065	+	0.969253i	$0.420862\pi$
$884$	26.5146	0.891783
$885$	22.4456	0.754500
$886$	−29.7846	−1.00063
$887$	−10.5395	−0.353880	−0.176940	−	0.984222i	$-0.556620\pi$
$887$	−10.5395	−0.353880	−0.176940	+	0.984222i	$0.556620\pi$
$888$	−5.60845	−0.188207
$889$	−47.9411	−1.60789
$890$	−6.43403	−0.215669
$891$	4.06050	0.136032
$892$	−11.2319	−0.376072
$893$	0	0
$894$	−7.00406	−0.234251
$895$	56.5686	1.89088
$896$	−2.61803	−0.0874624
$897$	−11.1744	−0.373103
$898$	−2.95239	−0.0985224
$899$	−14.8068	−0.493835
$900$	10.2265	0.340883
$901$	−21.8057	−0.726452
$902$	−42.6616	−1.42048
$903$	−6.12099	−0.203694
$904$	4.82328	0.160420
$905$	−67.7057	−2.25061
$906$	20.5920	0.684123
$907$	2.96782	0.0985448	0.0492724	−	0.998785i	$-0.484310\pi$
$907$	2.96782	0.0985448	0.0492724	+	0.998785i	$0.484310\pi$
$908$	−15.3878	−0.510661
$909$	9.83860	0.326326
$910$	36.6464	1.21482
$911$	−16.0402	−0.531435	−0.265717	−	0.964051i	$-0.585609\pi$
$911$	−16.0402	−0.531435	−0.265717	+	0.964051i	$0.585609\pi$
$912$	0	0
$913$	27.1689	0.899158
$914$	−15.6466	−0.517542
$915$	−25.3379	−0.837645
$916$	12.6750	0.418794
$917$	42.1290	1.39122
$918$	7.39144	0.243954
$919$	42.0666	1.38765	0.693825	−	0.720144i	$-0.255924\pi$
$919$	42.0666	1.38765	0.693825	+	0.720144i	$0.255924\pi$
$920$	−12.1554	−0.400751
$921$	−28.5278	−0.940021
$922$	−1.74444	−0.0574501
$923$	−26.8725	−0.884518
$924$	10.6305	0.349718
$925$	57.3548	1.88581
$926$	28.6429	0.941264
$927$	7.76870	0.255158
$928$	2.95012	0.0968426
$929$	24.4355	0.801701	0.400851	−	0.916143i	$-0.368715\pi$
$929$	24.4355	0.801701	0.400851	+	0.916143i	$0.368715\pi$
$930$	−19.5849	−0.642214
$931$	0	0
$932$	16.2147	0.531131
$933$	23.1896	0.759194
$934$	2.64480	0.0865406
$935$	−117.114	−3.83003
$936$	3.58721	0.117252
$937$	−40.8774	−1.33541	−0.667704	−	0.744427i	$-0.732723\pi$
$937$	−40.8774	−1.33541	−0.667704	+	0.744427i	$0.732723\pi$
$938$	11.6526	0.380471
$939$	−24.9975	−0.815763
$940$	−37.1186	−1.21067
$941$	24.9003	0.811727	0.405864	−	0.913934i	$-0.366971\pi$
$941$	24.9003	0.811727	0.405864	+	0.913934i	$0.366971\pi$
$942$	11.0272	0.359284
$943$	32.7285	1.06579
$944$	5.75216	0.187217
$945$	10.2159	0.332322
$946$	9.49349	0.308660
$947$	−8.67917	−0.282035	−0.141018	−	0.990007i	$-0.545037\pi$
$947$	−8.67917	−0.282035	−0.141018	+	0.990007i	$0.545037\pi$
$948$	−1.56712	−0.0508976
$949$	48.2930	1.56766
$950$	0	0
$951$	7.67157	0.248768
$952$	19.3510	0.627170
$953$	26.2814	0.851337	0.425669	−	0.904879i	$-0.360039\pi$
$953$	26.2814	0.851337	0.425669	+	0.904879i	$0.360039\pi$
$954$	−2.95012	−0.0955138
$955$	−35.0869	−1.13539
$956$	−5.06154	−0.163702
$957$	−11.9790	−0.387225
$958$	−30.9359	−0.999495
$959$	−34.2053	−1.10455
$960$	3.90211	0.125940
$961$	−5.80913	−0.187391
$962$	20.1187	0.648653
$963$	−16.3819	−0.527898
$964$	15.6902	0.505347
$965$	66.8149	2.15085
$966$	−8.15537	−0.262395
$967$	−22.4390	−0.721590	−0.360795	−	0.932645i	$-0.617495\pi$
$967$	−22.4390	−0.721590	−0.360795	+	0.932645i	$0.617495\pi$
$968$	−5.48764	−0.176379
$969$	0	0
$970$	−11.4427	−0.367402
$971$	−2.51700	−0.0807743	−0.0403871	−	0.999184i	$-0.512859\pi$
$971$	−2.51700	−0.0807743	−0.0403871	+	0.999184i	$0.512859\pi$
$972$	1.00000	0.0320750
$973$	−15.2856	−0.490035
$974$	−1.36331	−0.0436833
$975$	−36.6845	−1.17485
$976$	−6.49338	−0.207848
$977$	23.6369	0.756212	0.378106	−	0.925762i	$-0.376575\pi$
$977$	23.6369	0.756212	0.378106	+	0.925762i	$0.376575\pi$
$978$	−6.50651	−0.208055
$979$	6.69519	0.213979
$980$	−0.569311	−0.0181860
$981$	−10.8445	−0.346239
$982$	10.7173	0.342002
$983$	11.2242	0.357997	0.178999	−	0.983849i	$-0.442714\pi$
$983$	11.2242	0.357997	0.178999	+	0.983849i	$0.442714\pi$
$984$	−10.5065	−0.334935
$985$	−14.9002	−0.474761
$986$	−21.8057	−0.694433
$987$	−24.9039	−0.792699
$988$	0	0
$989$	−7.28308	−0.231588
$990$	−15.8445	−0.503572
$991$	45.9723	1.46036	0.730179	−	0.683256i	$-0.239437\pi$
$991$	45.9723	1.46036	0.730179	+	0.683256i	$0.239437\pi$
$992$	−5.01905	−0.159355
$993$	−20.0806	−0.637238
$994$	−19.6122	−0.622061
$995$	55.1301	1.74774
$996$	6.69102	0.212013
$997$	20.1291	0.637495	0.318748	−	0.947840i	$-0.396738\pi$
$997$	20.1291	0.637495	0.318748	+	0.947840i	$0.396738\pi$
$998$	1.49119	0.0472027
$999$	5.60845	0.177444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.w.1.4	✓	4
3.2	odd	2		6498.2.a.by.1.1		4
19.18	odd	2		2166.2.a.x.1.4	yes	4
57.56	even	2		6498.2.a.bv.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.w.1.4	✓	4	1.1	even	1	trivial
2166.2.a.x.1.4	yes	4	19.18	odd	2
6498.2.a.bv.1.1		4	57.56	even	2
6498.2.a.by.1.1		4	3.2	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.90211 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.90211 q^{5} -1.00000 q^{6} +2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.90211 q^{10} +4.06050 q^{11} +1.00000 q^{12} -3.58721 q^{13} -2.61803 q^{14} +3.90211 q^{15} +1.00000 q^{16} -7.39144 q^{17} -1.00000 q^{18} +3.90211 q^{20} +2.61803 q^{21} -4.06050 q^{22} +3.11507 q^{23} -1.00000 q^{24} +10.2265 q^{25} +3.58721 q^{26} +1.00000 q^{27} +2.61803 q^{28} -2.95012 q^{29} -3.90211 q^{30} +5.01905 q^{31} -1.00000 q^{32} +4.06050 q^{33} +7.39144 q^{34} +10.2159 q^{35} +1.00000 q^{36} +5.60845 q^{37} -3.58721 q^{39} -3.90211 q^{40} +10.5065 q^{41} -2.61803 q^{42} -2.33801 q^{43} +4.06050 q^{44} +3.90211 q^{45} -3.11507 q^{46} -9.51243 q^{47} +1.00000 q^{48} -0.145898 q^{49} -10.2265 q^{50} -7.39144 q^{51} -3.58721 q^{52} +2.95012 q^{53} -1.00000 q^{54} +15.8445 q^{55} -2.61803 q^{56} +2.95012 q^{58} +5.75216 q^{59} +3.90211 q^{60} -6.49338 q^{61} -5.01905 q^{62} +2.61803 q^{63} +1.00000 q^{64} -13.9977 q^{65} -4.06050 q^{66} -4.45089 q^{67} -7.39144 q^{68} +3.11507 q^{69} -10.2159 q^{70} +7.49119 q^{71} -1.00000 q^{72} -13.4626 q^{73} -5.60845 q^{74} +10.2265 q^{75} +10.6305 q^{77} +3.58721 q^{78} -1.56712 q^{79} +3.90211 q^{80} +1.00000 q^{81} -10.5065 q^{82} +6.69102 q^{83} +2.61803 q^{84} -28.8422 q^{85} +2.33801 q^{86} -2.95012 q^{87} -4.06050 q^{88} +1.64886 q^{89} -3.90211 q^{90} -9.39144 q^{91} +3.11507 q^{92} +5.01905 q^{93} +9.51243 q^{94} -1.00000 q^{96} +2.93243 q^{97} +0.145898 q^{98} +4.06050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * q^99

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