LMFDB - Embedded newform 2366.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} -1.00000 q^{10} -2.73205 q^{11} -2.73205 q^{12} -1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} -2.26795 q^{17} -4.46410 q^{18} +5.46410 q^{19} +1.00000 q^{20} -2.73205 q^{21} +2.73205 q^{22} +4.73205 q^{23} +2.73205 q^{24} -4.00000 q^{25} -4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +2.73205 q^{30} -8.73205 q^{31} -1.00000 q^{32} +7.46410 q^{33} +2.26795 q^{34} +1.00000 q^{35} +4.46410 q^{36} -5.19615 q^{37} -5.46410 q^{38} -1.00000 q^{40} -4.46410 q^{41} +2.73205 q^{42} -1.80385 q^{43} -2.73205 q^{44} +4.46410 q^{45} -4.73205 q^{46} +10.9282 q^{47} -2.73205 q^{48} +1.00000 q^{49} +4.00000 q^{50} +6.19615 q^{51} +8.46410 q^{53} +4.00000 q^{54} -2.73205 q^{55} -1.00000 q^{56} -14.9282 q^{57} +3.00000 q^{58} +7.26795 q^{59} -2.73205 q^{60} -8.26795 q^{61} +8.73205 q^{62} +4.46410 q^{63} +1.00000 q^{64} -7.46410 q^{66} +5.66025 q^{67} -2.26795 q^{68} -12.9282 q^{69} -1.00000 q^{70} +13.8564 q^{71} -4.46410 q^{72} -9.39230 q^{73} +5.19615 q^{74} +10.9282 q^{75} +5.46410 q^{76} -2.73205 q^{77} -14.1962 q^{79} +1.00000 q^{80} -2.46410 q^{81} +4.46410 q^{82} +14.1962 q^{83} -2.73205 q^{84} -2.26795 q^{85} +1.80385 q^{86} +8.19615 q^{87} +2.73205 q^{88} +9.46410 q^{89} -4.46410 q^{90} +4.73205 q^{92} +23.8564 q^{93} -10.9282 q^{94} +5.46410 q^{95} +2.73205 q^{96} +1.46410 q^{97} -1.00000 q^{98} -12.1962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 6 q^{23} + 2 q^{24} - 8 q^{25} - 8 q^{27} + 2 q^{28} - 6 q^{29} + 2 q^{30} - 14 q^{31} - 2 q^{32} + 8 q^{33} + 8 q^{34} + 2 q^{35} + 2 q^{36} - 4 q^{38} - 2 q^{40} - 2 q^{41} + 2 q^{42} - 14 q^{43} - 2 q^{44} + 2 q^{45} - 6 q^{46} + 8 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{50} + 2 q^{51} + 10 q^{53} + 8 q^{54} - 2 q^{55} - 2 q^{56} - 16 q^{57} + 6 q^{58} + 18 q^{59} - 2 q^{60} - 20 q^{61} + 14 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{66} - 6 q^{67} - 8 q^{68} - 12 q^{69} - 2 q^{70} - 2 q^{72} + 2 q^{73} + 8 q^{75} + 4 q^{76} - 2 q^{77} - 18 q^{79} + 2 q^{80} + 2 q^{81} + 2 q^{82} + 18 q^{83} - 2 q^{84} - 8 q^{85} + 14 q^{86} + 6 q^{87} + 2 q^{88} + 12 q^{89} - 2 q^{90} + 6 q^{92} + 20 q^{93} - 8 q^{94} + 4 q^{95} + 2 q^{96} - 4 q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 - 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 6 * q^23 + 2 * q^24 - 8 * q^25 - 8 * q^27 + 2 * q^28 - 6 * q^29 + 2 * q^30 - 14 * q^31 - 2 * q^32 + 8 * q^33 + 8 * q^34 + 2 * q^35 + 2 * q^36 - 4 * q^38 - 2 * q^40 - 2 * q^41 + 2 * q^42 - 14 * q^43 - 2 * q^44 + 2 * q^45 - 6 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^49 + 8 * q^50 + 2 * q^51 + 10 * q^53 + 8 * q^54 - 2 * q^55 - 2 * q^56 - 16 * q^57 + 6 * q^58 + 18 * q^59 - 2 * q^60 - 20 * q^61 + 14 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^66 - 6 * q^67 - 8 * q^68 - 12 * q^69 - 2 * q^70 - 2 * q^72 + 2 * q^73 + 8 * q^75 + 4 * q^76 - 2 * q^77 - 18 * q^79 + 2 * q^80 + 2 * q^81 + 2 * q^82 + 18 * q^83 - 2 * q^84 - 8 * q^85 + 14 * q^86 + 6 * q^87 + 2 * q^88 + 12 * q^89 - 2 * q^90 + 6 * q^92 + 20 * q^93 - 8 * q^94 + 4 * q^95 + 2 * q^96 - 4 * q^97 - 2 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	2.73205	1.11536
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	4.46410	1.48803
$10$	−1.00000	−0.316228
$11$	−2.73205	−0.823744	−0.411872	−	0.911242i	$-0.635125\pi$
$11$	−2.73205	−0.823744	−0.411872	+	0.911242i	$0.635125\pi$
$12$	−2.73205	−0.788675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	−2.26795	−0.550058	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−2.26795	−0.550058	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−4.46410	−1.05220
$19$	5.46410	1.25355	0.626775	−	0.779200i	$-0.284374\pi$
$19$	5.46410	1.25355	0.626775	+	0.779200i	$0.284374\pi$
$20$	1.00000	0.223607
$21$	−2.73205	−0.596182
$22$	2.73205	0.582475
$23$	4.73205	0.986701	0.493350	−	0.869831i	$-0.335772\pi$
$23$	4.73205	0.986701	0.493350	+	0.869831i	$0.335772\pi$
$24$	2.73205	0.557678
$25$	−4.00000	−0.800000
$26$	0	0
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	2.73205	0.498802
$31$	−8.73205	−1.56832	−0.784161	−	0.620557i	$-0.786907\pi$
$31$	−8.73205	−1.56832	−0.784161	+	0.620557i	$0.786907\pi$
$32$	−1.00000	−0.176777
$33$	7.46410	1.29933
$34$	2.26795	0.388950
$35$	1.00000	0.169031
$36$	4.46410	0.744017
$37$	−5.19615	−0.854242	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	−5.19615	−0.854242	−0.427121	+	0.904194i	$0.640472\pi$
$38$	−5.46410	−0.886394
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−4.46410	−0.697176	−0.348588	−	0.937276i	$-0.613339\pi$
$41$	−4.46410	−0.697176	−0.348588	+	0.937276i	$0.613339\pi$
$42$	2.73205	0.421565
$43$	−1.80385	−0.275084	−0.137542	−	0.990496i	$-0.543920\pi$
$43$	−1.80385	−0.275084	−0.137542	+	0.990496i	$0.543920\pi$
$44$	−2.73205	−0.411872
$45$	4.46410	0.665469
$46$	−4.73205	−0.697703
$47$	10.9282	1.59404	0.797021	−	0.603951i	$-0.206408\pi$
$47$	10.9282	1.59404	0.797021	+	0.603951i	$0.206408\pi$
$48$	−2.73205	−0.394338
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	6.19615	0.867635
$52$	0	0
$53$	8.46410	1.16263	0.581317	−	0.813677i	$-0.302538\pi$
$53$	8.46410	1.16263	0.581317	+	0.813677i	$0.302538\pi$
$54$	4.00000	0.544331
$55$	−2.73205	−0.368390
$56$	−1.00000	−0.133631
$57$	−14.9282	−1.97729
$58$	3.00000	0.393919
$59$	7.26795	0.946206	0.473103	−	0.881007i	$-0.343134\pi$
$59$	7.26795	0.946206	0.473103	+	0.881007i	$0.343134\pi$
$60$	−2.73205	−0.352706
$61$	−8.26795	−1.05860	−0.529301	−	0.848434i	$-0.677546\pi$
$61$	−8.26795	−1.05860	−0.529301	+	0.848434i	$0.677546\pi$
$62$	8.73205	1.10897
$63$	4.46410	0.562424
$64$	1.00000	0.125000
$65$	0	0
$66$	−7.46410	−0.918767
$67$	5.66025	0.691510	0.345755	−	0.938325i	$-0.387623\pi$
$67$	5.66025	0.691510	0.345755	+	0.938325i	$0.387623\pi$
$68$	−2.26795	−0.275029
$69$	−12.9282	−1.55637
$70$	−1.00000	−0.119523
$71$	13.8564	1.64445	0.822226	−	0.569160i	$-0.192732\pi$
$71$	13.8564	1.64445	0.822226	+	0.569160i	$0.192732\pi$
$72$	−4.46410	−0.526099
$73$	−9.39230	−1.09929	−0.549643	−	0.835400i	$-0.685236\pi$
$73$	−9.39230	−1.09929	−0.549643	+	0.835400i	$0.685236\pi$
$74$	5.19615	0.604040
$75$	10.9282	1.26188
$76$	5.46410	0.626775
$77$	−2.73205	−0.311346
$78$	0	0
$79$	−14.1962	−1.59719	−0.798596	−	0.601867i	$-0.794424\pi$
$79$	−14.1962	−1.59719	−0.798596	+	0.601867i	$0.794424\pi$
$80$	1.00000	0.111803
$81$	−2.46410	−0.273789
$82$	4.46410	0.492978
$83$	14.1962	1.55823	0.779115	−	0.626881i	$-0.215669\pi$
$83$	14.1962	1.55823	0.779115	+	0.626881i	$0.215669\pi$
$84$	−2.73205	−0.298091
$85$	−2.26795	−0.245994
$86$	1.80385	0.194514
$87$	8.19615	0.878720
$88$	2.73205	0.291238
$89$	9.46410	1.00319	0.501596	−	0.865102i	$-0.332746\pi$
$89$	9.46410	1.00319	0.501596	+	0.865102i	$0.332746\pi$
$90$	−4.46410	−0.470558
$91$	0	0
$92$	4.73205	0.493350
$93$	23.8564	2.47379
$94$	−10.9282	−1.12716
$95$	5.46410	0.560605
$96$	2.73205	0.278839
$97$	1.46410	0.148657	0.0743285	−	0.997234i	$-0.476319\pi$
$97$	1.46410	0.148657	0.0743285	+	0.997234i	$0.476319\pi$
$98$	−1.00000	−0.101015
$99$	−12.1962	−1.22576
$100$	−4.00000	−0.400000
$101$	−9.19615	−0.915051	−0.457526	−	0.889196i	$-0.651264\pi$
$101$	−9.19615	−0.915051	−0.457526	+	0.889196i	$0.651264\pi$
$102$	−6.19615	−0.613511
$103$	12.3923	1.22105	0.610525	−	0.791997i	$-0.290958\pi$
$103$	12.3923	1.22105	0.610525	+	0.791997i	$0.290958\pi$
$104$	0	0
$105$	−2.73205	−0.266621
$106$	−8.46410	−0.822106
$107$	−2.92820	−0.283080	−0.141540	−	0.989933i	$-0.545205\pi$
$107$	−2.92820	−0.283080	−0.141540	+	0.989933i	$0.545205\pi$
$108$	−4.00000	−0.384900
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	2.73205	0.260491
$111$	14.1962	1.34744
$112$	1.00000	0.0944911
$113$	−9.39230	−0.883554	−0.441777	−	0.897125i	$-0.645652\pi$
$113$	−9.39230	−0.883554	−0.441777	+	0.897125i	$0.645652\pi$
$114$	14.9282	1.39815
$115$	4.73205	0.441266
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−7.26795	−0.669069
$119$	−2.26795	−0.207903
$120$	2.73205	0.249401
$121$	−3.53590	−0.321445
$122$	8.26795	0.748545
$123$	12.1962	1.09969
$124$	−8.73205	−0.784161
$125$	−9.00000	−0.804984
$126$	−4.46410	−0.397694
$127$	−17.8564	−1.58450	−0.792250	−	0.610197i	$-0.791090\pi$
$127$	−17.8564	−1.58450	−0.792250	+	0.610197i	$0.791090\pi$
$128$	−1.00000	−0.0883883
$129$	4.92820	0.433904
$130$	0	0
$131$	−18.9282	−1.65376	−0.826882	−	0.562375i	$-0.809888\pi$
$131$	−18.9282	−1.65376	−0.826882	+	0.562375i	$0.809888\pi$
$132$	7.46410	0.649667
$133$	5.46410	0.473798
$134$	−5.66025	−0.488971
$135$	−4.00000	−0.344265
$136$	2.26795	0.194475
$137$	−18.1244	−1.54847	−0.774234	−	0.632899i	$-0.781865\pi$
$137$	−18.1244	−1.54847	−0.774234	+	0.632899i	$0.781865\pi$
$138$	12.9282	1.10052
$139$	−17.6603	−1.49792	−0.748962	−	0.662613i	$-0.769447\pi$
$139$	−17.6603	−1.49792	−0.748962	+	0.662613i	$0.769447\pi$
$140$	1.00000	0.0845154
$141$	−29.8564	−2.51436
$142$	−13.8564	−1.16280
$143$	0	0
$144$	4.46410	0.372008
$145$	−3.00000	−0.249136
$146$	9.39230	0.777313
$147$	−2.73205	−0.225336
$148$	−5.19615	−0.427121
$149$	−6.80385	−0.557393	−0.278696	−	0.960379i	$-0.589902\pi$
$149$	−6.80385	−0.557393	−0.278696	+	0.960379i	$0.589902\pi$
$150$	−10.9282	−0.892284
$151$	−8.39230	−0.682956	−0.341478	−	0.939890i	$-0.610927\pi$
$151$	−8.39230	−0.682956	−0.341478	+	0.939890i	$0.610927\pi$
$152$	−5.46410	−0.443197
$153$	−10.1244	−0.818506
$154$	2.73205	0.220155
$155$	−8.73205	−0.701375
$156$	0	0
$157$	10.2679	0.819472	0.409736	−	0.912204i	$-0.365621\pi$
$157$	10.2679	0.819472	0.409736	+	0.912204i	$0.365621\pi$
$158$	14.1962	1.12939
$159$	−23.1244	−1.83388
$160$	−1.00000	−0.0790569
$161$	4.73205	0.372938
$162$	2.46410	0.193598
$163$	−2.73205	−0.213991	−0.106995	−	0.994260i	$-0.534123\pi$
$163$	−2.73205	−0.213991	−0.106995	+	0.994260i	$0.534123\pi$
$164$	−4.46410	−0.348588
$165$	7.46410	0.581080
$166$	−14.1962	−1.10184
$167$	−8.73205	−0.675706	−0.337853	−	0.941199i	$-0.609701\pi$
$167$	−8.73205	−0.675706	−0.337853	+	0.941199i	$0.609701\pi$
$168$	2.73205	0.210782
$169$	0	0
$170$	2.26795	0.173944
$171$	24.3923	1.86533
$172$	−1.80385	−0.137542
$173$	−7.07180	−0.537659	−0.268829	−	0.963188i	$-0.586637\pi$
$173$	−7.07180	−0.537659	−0.268829	+	0.963188i	$0.586637\pi$
$174$	−8.19615	−0.621349
$175$	−4.00000	−0.302372
$176$	−2.73205	−0.205936
$177$	−19.8564	−1.49250
$178$	−9.46410	−0.709364
$179$	−4.39230	−0.328296	−0.164148	−	0.986436i	$-0.552488\pi$
$179$	−4.39230	−0.328296	−0.164148	+	0.986436i	$0.552488\pi$
$180$	4.46410	0.332734
$181$	7.19615	0.534886	0.267443	−	0.963574i	$-0.413821\pi$
$181$	7.19615	0.534886	0.267443	+	0.963574i	$0.413821\pi$
$182$	0	0
$183$	22.5885	1.66979
$184$	−4.73205	−0.348851
$185$	−5.19615	−0.382029
$186$	−23.8564	−1.74924
$187$	6.19615	0.453108
$188$	10.9282	0.797021
$189$	−4.00000	−0.290957
$190$	−5.46410	−0.396408
$191$	−17.1244	−1.23907	−0.619537	−	0.784967i	$-0.712680\pi$
$191$	−17.1244	−1.23907	−0.619537	+	0.784967i	$0.712680\pi$
$192$	−2.73205	−0.197169
$193$	−12.8038	−0.921641	−0.460821	−	0.887493i	$-0.652445\pi$
$193$	−12.8038	−0.921641	−0.460821	+	0.887493i	$0.652445\pi$
$194$	−1.46410	−0.105116
$195$	0	0
$196$	1.00000	0.0714286
$197$	−20.9282	−1.49107	−0.745536	−	0.666465i	$-0.767807\pi$
$197$	−20.9282	−1.49107	−0.745536	+	0.666465i	$0.767807\pi$
$198$	12.1962	0.866743
$199$	1.46410	0.103787	0.0518937	−	0.998653i	$-0.483474\pi$
$199$	1.46410	0.103787	0.0518937	+	0.998653i	$0.483474\pi$
$200$	4.00000	0.282843
$201$	−15.4641	−1.09075
$202$	9.19615	0.647039
$203$	−3.00000	−0.210559
$204$	6.19615	0.433817
$205$	−4.46410	−0.311786
$206$	−12.3923	−0.863413
$207$	21.1244	1.46824
$208$	0	0
$209$	−14.9282	−1.03261
$210$	2.73205	0.188529
$211$	−24.7321	−1.70262	−0.851312	−	0.524659i	$-0.824193\pi$
$211$	−24.7321	−1.70262	−0.851312	+	0.524659i	$0.824193\pi$
$212$	8.46410	0.581317
$213$	−37.8564	−2.59388
$214$	2.92820	0.200168
$215$	−1.80385	−0.123021
$216$	4.00000	0.272166
$217$	−8.73205	−0.592770
$218$	−10.0000	−0.677285
$219$	25.6603	1.73396
$220$	−2.73205	−0.184195
$221$	0	0
$222$	−14.1962	−0.952783
$223$	8.39230	0.561990	0.280995	−	0.959709i	$-0.409336\pi$
$223$	8.39230	0.561990	0.280995	+	0.959709i	$0.409336\pi$
$224$	−1.00000	−0.0668153
$225$	−17.8564	−1.19043
$226$	9.39230	0.624767
$227$	4.73205	0.314077	0.157039	−	0.987592i	$-0.449805\pi$
$227$	4.73205	0.314077	0.157039	+	0.987592i	$0.449805\pi$
$228$	−14.9282	−0.988644
$229$	−3.60770	−0.238403	−0.119202	−	0.992870i	$-0.538033\pi$
$229$	−3.60770	−0.238403	−0.119202	+	0.992870i	$0.538033\pi$
$230$	−4.73205	−0.312022
$231$	7.46410	0.491102
$232$	3.00000	0.196960
$233$	16.3923	1.07390	0.536948	−	0.843615i	$-0.319577\pi$
$233$	16.3923	1.07390	0.536948	+	0.843615i	$0.319577\pi$
$234$	0	0
$235$	10.9282	0.712877
$236$	7.26795	0.473103
$237$	38.7846	2.51933
$238$	2.26795	0.147009
$239$	−15.5167	−1.00369	−0.501845	−	0.864958i	$-0.667345\pi$
$239$	−15.5167	−1.00369	−0.501845	+	0.864958i	$0.667345\pi$
$240$	−2.73205	−0.176353
$241$	−5.39230	−0.347349	−0.173674	−	0.984803i	$-0.555564\pi$
$241$	−5.39230	−0.347349	−0.173674	+	0.984803i	$0.555564\pi$
$242$	3.53590	0.227296
$243$	18.7321	1.20166
$244$	−8.26795	−0.529301
$245$	1.00000	0.0638877
$246$	−12.1962	−0.777598
$247$	0	0
$248$	8.73205	0.554486
$249$	−38.7846	−2.45787
$250$	9.00000	0.569210
$251$	9.07180	0.572607	0.286303	−	0.958139i	$-0.407573\pi$
$251$	9.07180	0.572607	0.286303	+	0.958139i	$0.407573\pi$
$252$	4.46410	0.281212
$253$	−12.9282	−0.812789
$254$	17.8564	1.12041
$255$	6.19615	0.388018
$256$	1.00000	0.0625000
$257$	18.6603	1.16399	0.581997	−	0.813191i	$-0.302271\pi$
$257$	18.6603	1.16399	0.581997	+	0.813191i	$0.302271\pi$
$258$	−4.92820	−0.306817
$259$	−5.19615	−0.322873
$260$	0	0
$261$	−13.3923	−0.828963
$262$	18.9282	1.16939
$263$	10.5885	0.652912	0.326456	−	0.945212i	$-0.394145\pi$
$263$	10.5885	0.652912	0.326456	+	0.945212i	$0.394145\pi$
$264$	−7.46410	−0.459384
$265$	8.46410	0.519946
$266$	−5.46410	−0.335026
$267$	−25.8564	−1.58239
$268$	5.66025	0.345755
$269$	12.7846	0.779491	0.389746	−	0.920923i	$-0.372563\pi$
$269$	12.7846	0.779491	0.389746	+	0.920923i	$0.372563\pi$
$270$	4.00000	0.243432
$271$	−17.1244	−1.04023	−0.520115	−	0.854096i	$-0.674111\pi$
$271$	−17.1244	−1.04023	−0.520115	+	0.854096i	$0.674111\pi$
$272$	−2.26795	−0.137515
$273$	0	0
$274$	18.1244	1.09493
$275$	10.9282	0.658995
$276$	−12.9282	−0.778186
$277$	−11.3923	−0.684497	−0.342249	−	0.939609i	$-0.611189\pi$
$277$	−11.3923	−0.684497	−0.342249	+	0.939609i	$0.611189\pi$
$278$	17.6603	1.05919
$279$	−38.9808	−2.33372
$280$	−1.00000	−0.0597614
$281$	0.660254	0.0393875	0.0196937	−	0.999806i	$-0.493731\pi$
$281$	0.660254	0.0393875	0.0196937	+	0.999806i	$0.493731\pi$
$282$	29.8564	1.77792
$283$	20.5885	1.22386	0.611928	−	0.790913i	$-0.290394\pi$
$283$	20.5885	1.22386	0.611928	+	0.790913i	$0.290394\pi$
$284$	13.8564	0.822226
$285$	−14.9282	−0.884270
$286$	0	0
$287$	−4.46410	−0.263508
$288$	−4.46410	−0.263050
$289$	−11.8564	−0.697436
$290$	3.00000	0.176166
$291$	−4.00000	−0.234484
$292$	−9.39230	−0.549643
$293$	3.39230	0.198181	0.0990903	−	0.995078i	$-0.468407\pi$
$293$	3.39230	0.198181	0.0990903	+	0.995078i	$0.468407\pi$
$294$	2.73205	0.159336
$295$	7.26795	0.423156
$296$	5.19615	0.302020
$297$	10.9282	0.634119
$298$	6.80385	0.394136
$299$	0	0
$300$	10.9282	0.630940
$301$	−1.80385	−0.103972
$302$	8.39230	0.482923
$303$	25.1244	1.44336
$304$	5.46410	0.313388
$305$	−8.26795	−0.473421
$306$	10.1244	0.578771
$307$	21.5167	1.22802	0.614010	−	0.789298i	$-0.289555\pi$
$307$	21.5167	1.22802	0.614010	+	0.789298i	$0.289555\pi$
$308$	−2.73205	−0.155673
$309$	−33.8564	−1.92602
$310$	8.73205	0.495947
$311$	0.196152	0.0111228	0.00556139	−	0.999985i	$-0.498230\pi$
$311$	0.196152	0.0111228	0.00556139	+	0.999985i	$0.498230\pi$
$312$	0	0
$313$	−32.0000	−1.80875	−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000	−1.80875	−0.904373	+	0.426742i	$0.859661\pi$
$314$	−10.2679	−0.579454
$315$	4.46410	0.251524
$316$	−14.1962	−0.798596
$317$	31.0526	1.74409	0.872043	−	0.489430i	$-0.162795\pi$
$317$	31.0526	1.74409	0.872043	+	0.489430i	$0.162795\pi$
$318$	23.1244	1.29675
$319$	8.19615	0.458896
$320$	1.00000	0.0559017
$321$	8.00000	0.446516
$322$	−4.73205	−0.263707
$323$	−12.3923	−0.689526
$324$	−2.46410	−0.136895
$325$	0	0
$326$	2.73205	0.151314
$327$	−27.3205	−1.51083
$328$	4.46410	0.246489
$329$	10.9282	0.602491
$330$	−7.46410	−0.410885
$331$	21.6603	1.19056	0.595278	−	0.803520i	$-0.297042\pi$
$331$	21.6603	1.19056	0.595278	+	0.803520i	$0.297042\pi$
$332$	14.1962	0.779115
$333$	−23.1962	−1.27114
$334$	8.73205	0.477797
$335$	5.66025	0.309253
$336$	−2.73205	−0.149046
$337$	−28.3205	−1.54272	−0.771358	−	0.636401i	$-0.780422\pi$
$337$	−28.3205	−1.54272	−0.771358	+	0.636401i	$0.780422\pi$
$338$	0	0
$339$	25.6603	1.39367
$340$	−2.26795	−0.122997
$341$	23.8564	1.29190
$342$	−24.3923	−1.31898
$343$	1.00000	0.0539949
$344$	1.80385	0.0972569
$345$	−12.9282	−0.696031
$346$	7.07180	0.380182
$347$	−22.9808	−1.23367	−0.616836	−	0.787092i	$-0.711586\pi$
$347$	−22.9808	−1.23367	−0.616836	+	0.787092i	$0.711586\pi$
$348$	8.19615	0.439360
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	2.73205	0.145619
$353$	−26.1769	−1.39326	−0.696628	−	0.717432i	$-0.745317\pi$
$353$	−26.1769	−1.39326	−0.696628	+	0.717432i	$0.745317\pi$
$354$	19.8564	1.05536
$355$	13.8564	0.735422
$356$	9.46410	0.501596
$357$	6.19615	0.327935
$358$	4.39230	0.232141
$359$	−4.39230	−0.231817	−0.115908	−	0.993260i	$-0.536978\pi$
$359$	−4.39230	−0.231817	−0.115908	+	0.993260i	$0.536978\pi$
$360$	−4.46410	−0.235279
$361$	10.8564	0.571390
$362$	−7.19615	−0.378221
$363$	9.66025	0.507032
$364$	0	0
$365$	−9.39230	−0.491616
$366$	−22.5885	−1.18072
$367$	−31.9090	−1.66563	−0.832817	−	0.553548i	$-0.813274\pi$
$367$	−31.9090	−1.66563	−0.832817	+	0.553548i	$0.813274\pi$
$368$	4.73205	0.246675
$369$	−19.9282	−1.03742
$370$	5.19615	0.270135
$371$	8.46410	0.439434
$372$	23.8564	1.23690
$373$	−25.5359	−1.32220	−0.661099	−	0.750298i	$-0.729910\pi$
$373$	−25.5359	−1.32220	−0.661099	+	0.750298i	$0.729910\pi$
$374$	−6.19615	−0.320395
$375$	24.5885	1.26974
$376$	−10.9282	−0.563579
$377$	0	0
$378$	4.00000	0.205738
$379$	−11.8038	−0.606323	−0.303161	−	0.952939i	$-0.598042\pi$
$379$	−11.8038	−0.606323	−0.303161	+	0.952939i	$0.598042\pi$
$380$	5.46410	0.280302
$381$	48.7846	2.49931
$382$	17.1244	0.876158
$383$	1.41154	0.0721265	0.0360632	−	0.999350i	$-0.488518\pi$
$383$	1.41154	0.0721265	0.0360632	+	0.999350i	$0.488518\pi$
$384$	2.73205	0.139419
$385$	−2.73205	−0.139238
$386$	12.8038	0.651699
$387$	−8.05256	−0.409335
$388$	1.46410	0.0743285
$389$	−10.3205	−0.523271	−0.261635	−	0.965167i	$-0.584262\pi$
$389$	−10.3205	−0.523271	−0.261635	+	0.965167i	$0.584262\pi$
$390$	0	0
$391$	−10.7321	−0.542743
$392$	−1.00000	−0.0505076
$393$	51.7128	2.60857
$394$	20.9282	1.05435
$395$	−14.1962	−0.714286
$396$	−12.1962	−0.612880
$397$	22.5359	1.13104	0.565522	−	0.824733i	$-0.308675\pi$
$397$	22.5359	1.13104	0.565522	+	0.824733i	$0.308675\pi$
$398$	−1.46410	−0.0733888
$399$	−14.9282	−0.747345
$400$	−4.00000	−0.200000
$401$	5.05256	0.252313	0.126156	−	0.992010i	$-0.459736\pi$
$401$	5.05256	0.252313	0.126156	+	0.992010i	$0.459736\pi$
$402$	15.4641	0.771279
$403$	0	0
$404$	−9.19615	−0.457526
$405$	−2.46410	−0.122442
$406$	3.00000	0.148888
$407$	14.1962	0.703677
$408$	−6.19615	−0.306755
$409$	−8.32051	−0.411423	−0.205711	−	0.978613i	$-0.565951\pi$
$409$	−8.32051	−0.411423	−0.205711	+	0.978613i	$0.565951\pi$
$410$	4.46410	0.220466
$411$	49.5167	2.44248
$412$	12.3923	0.610525
$413$	7.26795	0.357632
$414$	−21.1244	−1.03821
$415$	14.1962	0.696862
$416$	0	0
$417$	48.2487	2.36275
$418$	14.9282	0.730162
$419$	−19.1244	−0.934286	−0.467143	−	0.884182i	$-0.654717\pi$
$419$	−19.1244	−0.934286	−0.467143	+	0.884182i	$0.654717\pi$
$420$	−2.73205	−0.133310
$421$	10.1244	0.493431	0.246715	−	0.969088i	$-0.420649\pi$
$421$	10.1244	0.493431	0.246715	+	0.969088i	$0.420649\pi$
$422$	24.7321	1.20394
$423$	48.7846	2.37199
$424$	−8.46410	−0.411053
$425$	9.07180	0.440047
$426$	37.8564	1.83415
$427$	−8.26795	−0.400114
$428$	−2.92820	−0.141540
$429$	0	0
$430$	1.80385	0.0869893
$431$	−33.4641	−1.61191	−0.805955	−	0.591977i	$-0.798347\pi$
$431$	−33.4641	−1.61191	−0.805955	+	0.591977i	$0.798347\pi$
$432$	−4.00000	−0.192450
$433$	18.2679	0.877902	0.438951	−	0.898511i	$-0.355350\pi$
$433$	18.2679	0.877902	0.438951	+	0.898511i	$0.355350\pi$
$434$	8.73205	0.419152
$435$	8.19615	0.392975
$436$	10.0000	0.478913
$437$	25.8564	1.23688
$438$	−25.6603	−1.22609
$439$	−22.7321	−1.08494	−0.542471	−	0.840075i	$-0.682511\pi$
$439$	−22.7321	−1.08494	−0.542471	+	0.840075i	$0.682511\pi$
$440$	2.73205	0.130245
$441$	4.46410	0.212576
$442$	0	0
$443$	0.679492	0.0322836	0.0161418	−	0.999870i	$-0.494862\pi$
$443$	0.679492	0.0322836	0.0161418	+	0.999870i	$0.494862\pi$
$444$	14.1962	0.673720
$445$	9.46410	0.448641
$446$	−8.39230	−0.397387
$447$	18.5885	0.879204
$448$	1.00000	0.0472456
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	17.8564	0.841759
$451$	12.1962	0.574294
$452$	−9.39230	−0.441777
$453$	22.9282	1.07726
$454$	−4.73205	−0.222086
$455$	0	0
$456$	14.9282	0.699077
$457$	17.7321	0.829470	0.414735	−	0.909942i	$-0.363874\pi$
$457$	17.7321	0.829470	0.414735	+	0.909942i	$0.363874\pi$
$458$	3.60770	0.168577
$459$	9.07180	0.423435
$460$	4.73205	0.220633
$461$	−26.3205	−1.22587	−0.612934	−	0.790134i	$-0.710011\pi$
$461$	−26.3205	−1.22587	−0.612934	+	0.790134i	$0.710011\pi$
$462$	−7.46410	−0.347261
$463$	−42.0526	−1.95435	−0.977174	−	0.212440i	$-0.931859\pi$
$463$	−42.0526	−1.95435	−0.977174	+	0.212440i	$0.931859\pi$
$464$	−3.00000	−0.139272
$465$	23.8564	1.10631
$466$	−16.3923	−0.759359
$467$	−21.2679	−0.984163	−0.492082	−	0.870549i	$-0.663764\pi$
$467$	−21.2679	−0.984163	−0.492082	+	0.870549i	$0.663764\pi$
$468$	0	0
$469$	5.66025	0.261366
$470$	−10.9282	−0.504080
$471$	−28.0526	−1.29259
$472$	−7.26795	−0.334534
$473$	4.92820	0.226599
$474$	−38.7846	−1.78144
$475$	−21.8564	−1.00284
$476$	−2.26795	−0.103951
$477$	37.7846	1.73004
$478$	15.5167	0.709716
$479$	21.8038	0.996243	0.498122	−	0.867107i	$-0.334023\pi$
$479$	21.8038	0.996243	0.498122	+	0.867107i	$0.334023\pi$
$480$	2.73205	0.124700
$481$	0	0
$482$	5.39230	0.245613
$483$	−12.9282	−0.588254
$484$	−3.53590	−0.160723
$485$	1.46410	0.0664814
$486$	−18.7321	−0.849703
$487$	−3.32051	−0.150467	−0.0752333	−	0.997166i	$-0.523970\pi$
$487$	−3.32051	−0.150467	−0.0752333	+	0.997166i	$0.523970\pi$
$488$	8.26795	0.374272
$489$	7.46410	0.337538
$490$	−1.00000	−0.0451754
$491$	27.7128	1.25066	0.625331	−	0.780360i	$-0.284964\pi$
$491$	27.7128	1.25066	0.625331	+	0.780360i	$0.284964\pi$
$492$	12.1962	0.549845
$493$	6.80385	0.306430
$494$	0	0
$495$	−12.1962	−0.548176
$496$	−8.73205	−0.392081
$497$	13.8564	0.621545
$498$	38.7846	1.73798
$499$	−14.7321	−0.659497	−0.329749	−	0.944069i	$-0.606964\pi$
$499$	−14.7321	−0.659497	−0.329749	+	0.944069i	$0.606964\pi$
$500$	−9.00000	−0.402492
$501$	23.8564	1.06583
$502$	−9.07180	−0.404894
$503$	17.2679	0.769940	0.384970	−	0.922929i	$-0.374212\pi$
$503$	17.2679	0.769940	0.384970	+	0.922929i	$0.374212\pi$
$504$	−4.46410	−0.198847
$505$	−9.19615	−0.409223
$506$	12.9282	0.574729
$507$	0	0
$508$	−17.8564	−0.792250
$509$	6.60770	0.292881	0.146440	−	0.989219i	$-0.453218\pi$
$509$	6.60770	0.292881	0.146440	+	0.989219i	$0.453218\pi$
$510$	−6.19615	−0.274370
$511$	−9.39230	−0.415491
$512$	−1.00000	−0.0441942
$513$	−21.8564	−0.964984
$514$	−18.6603	−0.823069
$515$	12.3923	0.546070
$516$	4.92820	0.216952
$517$	−29.8564	−1.31308
$518$	5.19615	0.228306
$519$	19.3205	0.848076
$520$	0	0
$521$	−28.3731	−1.24305	−0.621523	−	0.783396i	$-0.713486\pi$
$521$	−28.3731	−1.24305	−0.621523	+	0.783396i	$0.713486\pi$
$522$	13.3923	0.586165
$523$	14.5359	0.635610	0.317805	−	0.948156i	$-0.397054\pi$
$523$	14.5359	0.635610	0.317805	+	0.948156i	$0.397054\pi$
$524$	−18.9282	−0.826882
$525$	10.9282	0.476946
$526$	−10.5885	−0.461679
$527$	19.8038	0.862669
$528$	7.46410	0.324833
$529$	−0.607695	−0.0264215
$530$	−8.46410	−0.367657
$531$	32.4449	1.40799
$532$	5.46410	0.236899
$533$	0	0
$534$	25.8564	1.11892
$535$	−2.92820	−0.126597
$536$	−5.66025	−0.244486
$537$	12.0000	0.517838
$538$	−12.7846	−0.551184
$539$	−2.73205	−0.117678
$540$	−4.00000	−0.172133
$541$	11.7321	0.504400	0.252200	−	0.967675i	$-0.418846\pi$
$541$	11.7321	0.504400	0.252200	+	0.967675i	$0.418846\pi$
$542$	17.1244	0.735554
$543$	−19.6603	−0.843702
$544$	2.26795	0.0972375
$545$	10.0000	0.428353
$546$	0	0
$547$	28.4449	1.21621	0.608107	−	0.793855i	$-0.291929\pi$
$547$	28.4449	1.21621	0.608107	+	0.793855i	$0.291929\pi$
$548$	−18.1244	−0.774234
$549$	−36.9090	−1.57524
$550$	−10.9282	−0.465980
$551$	−16.3923	−0.698336
$552$	12.9282	0.550261
$553$	−14.1962	−0.603682
$554$	11.3923	0.484013
$555$	14.1962	0.602593
$556$	−17.6603	−0.748962
$557$	1.87564	0.0794736	0.0397368	−	0.999210i	$-0.487348\pi$
$557$	1.87564	0.0794736	0.0397368	+	0.999210i	$0.487348\pi$
$558$	38.9808	1.65019
$559$	0	0
$560$	1.00000	0.0422577
$561$	−16.9282	−0.714709
$562$	−0.660254	−0.0278511
$563$	30.4449	1.28310	0.641549	−	0.767082i	$-0.278292\pi$
$563$	30.4449	1.28310	0.641549	+	0.767082i	$0.278292\pi$
$564$	−29.8564	−1.25718
$565$	−9.39230	−0.395137
$566$	−20.5885	−0.865397
$567$	−2.46410	−0.103483
$568$	−13.8564	−0.581402
$569$	23.3205	0.977647	0.488823	−	0.872383i	$-0.337426\pi$
$569$	23.3205	0.977647	0.488823	+	0.872383i	$0.337426\pi$
$570$	14.9282	0.625274
$571$	1.46410	0.0612707	0.0306354	−	0.999531i	$-0.490247\pi$
$571$	1.46410	0.0612707	0.0306354	+	0.999531i	$0.490247\pi$
$572$	0	0
$573$	46.7846	1.95446
$574$	4.46410	0.186328
$575$	−18.9282	−0.789361
$576$	4.46410	0.186004
$577$	28.1769	1.17302	0.586510	−	0.809942i	$-0.300501\pi$
$577$	28.1769	1.17302	0.586510	+	0.809942i	$0.300501\pi$
$578$	11.8564	0.493161
$579$	34.9808	1.45375
$580$	−3.00000	−0.124568
$581$	14.1962	0.588956
$582$	4.00000	0.165805
$583$	−23.1244	−0.957713
$584$	9.39230	0.388656
$585$	0	0
$586$	−3.39230	−0.140135
$587$	−12.7846	−0.527677	−0.263839	−	0.964567i	$-0.584989\pi$
$587$	−12.7846	−0.527677	−0.263839	+	0.964567i	$0.584989\pi$
$588$	−2.73205	−0.112668
$589$	−47.7128	−1.96597
$590$	−7.26795	−0.299217
$591$	57.1769	2.35194
$592$	−5.19615	−0.213561
$593$	−30.8564	−1.26712	−0.633560	−	0.773693i	$-0.718407\pi$
$593$	−30.8564	−1.26712	−0.633560	+	0.773693i	$0.718407\pi$
$594$	−10.9282	−0.448390
$595$	−2.26795	−0.0929769
$596$	−6.80385	−0.278696
$597$	−4.00000	−0.163709
$598$	0	0
$599$	17.0718	0.697535	0.348767	−	0.937209i	$-0.386600\pi$
$599$	17.0718	0.697535	0.348767	+	0.937209i	$0.386600\pi$
$600$	−10.9282	−0.446142
$601$	15.0526	0.614007	0.307003	−	0.951708i	$-0.400674\pi$
$601$	15.0526	0.614007	0.307003	+	0.951708i	$0.400674\pi$
$602$	1.80385	0.0735193
$603$	25.2679	1.02899
$604$	−8.39230	−0.341478
$605$	−3.53590	−0.143755
$606$	−25.1244	−1.02061
$607$	17.8564	0.724769	0.362385	−	0.932029i	$-0.381963\pi$
$607$	17.8564	0.724769	0.362385	+	0.932029i	$0.381963\pi$
$608$	−5.46410	−0.221599
$609$	8.19615	0.332125
$610$	8.26795	0.334759
$611$	0	0
$612$	−10.1244	−0.409253
$613$	35.9808	1.45325	0.726625	−	0.687035i	$-0.241088\pi$
$613$	35.9808	1.45325	0.726625	+	0.687035i	$0.241088\pi$
$614$	−21.5167	−0.868342
$615$	12.1962	0.491796
$616$	2.73205	0.110077
$617$	−22.8038	−0.918048	−0.459024	−	0.888424i	$-0.651801\pi$
$617$	−22.8038	−0.918048	−0.459024	+	0.888424i	$0.651801\pi$
$618$	33.8564	1.36190
$619$	−4.05256	−0.162886	−0.0814430	−	0.996678i	$-0.525953\pi$
$619$	−4.05256	−0.162886	−0.0814430	+	0.996678i	$0.525953\pi$
$620$	−8.73205	−0.350688
$621$	−18.9282	−0.759563
$622$	−0.196152	−0.00786500
$623$	9.46410	0.379171
$624$	0	0
$625$	11.0000	0.440000
$626$	32.0000	1.27898
$627$	40.7846	1.62878
$628$	10.2679	0.409736
$629$	11.7846	0.469883
$630$	−4.46410	−0.177854
$631$	−17.4641	−0.695235	−0.347617	−	0.937636i	$-0.613009\pi$
$631$	−17.4641	−0.695235	−0.347617	+	0.937636i	$0.613009\pi$
$632$	14.1962	0.564693
$633$	67.5692	2.68564
$634$	−31.0526	−1.23325
$635$	−17.8564	−0.708610
$636$	−23.1244	−0.916940
$637$	0	0
$638$	−8.19615	−0.324489
$639$	61.8564	2.44700
$640$	−1.00000	−0.0395285
$641$	37.5359	1.48258	0.741289	−	0.671186i	$-0.234215\pi$
$641$	37.5359	1.48258	0.741289	+	0.671186i	$0.234215\pi$
$642$	−8.00000	−0.315735
$643$	−19.7128	−0.777397	−0.388699	−	0.921365i	$-0.627075\pi$
$643$	−19.7128	−0.777397	−0.388699	+	0.921365i	$0.627075\pi$
$644$	4.73205	0.186469
$645$	4.92820	0.194048
$646$	12.3923	0.487569
$647$	13.8564	0.544752	0.272376	−	0.962191i	$-0.412191\pi$
$647$	13.8564	0.544752	0.272376	+	0.962191i	$0.412191\pi$
$648$	2.46410	0.0967991
$649$	−19.8564	−0.779432
$650$	0	0
$651$	23.8564	0.935006
$652$	−2.73205	−0.106995
$653$	−8.39230	−0.328416	−0.164208	−	0.986426i	$-0.552507\pi$
$653$	−8.39230	−0.328416	−0.164208	+	0.986426i	$0.552507\pi$
$654$	27.3205	1.06832
$655$	−18.9282	−0.739586
$656$	−4.46410	−0.174294
$657$	−41.9282	−1.63578
$658$	−10.9282	−0.426026
$659$	−32.7846	−1.27711	−0.638554	−	0.769577i	$-0.720467\pi$
$659$	−32.7846	−1.27711	−0.638554	+	0.769577i	$0.720467\pi$
$660$	7.46410	0.290540
$661$	−11.9282	−0.463953	−0.231977	−	0.972721i	$-0.574519\pi$
$661$	−11.9282	−0.463953	−0.231977	+	0.972721i	$0.574519\pi$
$662$	−21.6603	−0.841850
$663$	0	0
$664$	−14.1962	−0.550918
$665$	5.46410	0.211889
$666$	23.1962	0.898833
$667$	−14.1962	−0.549677
$668$	−8.73205	−0.337853
$669$	−22.9282	−0.886456
$670$	−5.66025	−0.218675
$671$	22.5885	0.872018
$672$	2.73205	0.105391
$673$	−19.7846	−0.762641	−0.381320	−	0.924443i	$-0.624531\pi$
$673$	−19.7846	−0.762641	−0.381320	+	0.924443i	$0.624531\pi$
$674$	28.3205	1.09087
$675$	16.0000	0.615840
$676$	0	0
$677$	0.143594	0.00551875	0.00275937	−	0.999996i	$-0.499122\pi$
$677$	0.143594	0.00551875	0.00275937	+	0.999996i	$0.499122\pi$
$678$	−25.6603	−0.985476
$679$	1.46410	0.0561871
$680$	2.26795	0.0869719
$681$	−12.9282	−0.495410
$682$	−23.8564	−0.913509
$683$	−13.4641	−0.515190	−0.257595	−	0.966253i	$-0.582930\pi$
$683$	−13.4641	−0.515190	−0.257595	+	0.966253i	$0.582930\pi$
$684$	24.3923	0.932663
$685$	−18.1244	−0.692496
$686$	−1.00000	−0.0381802
$687$	9.85641	0.376045
$688$	−1.80385	−0.0687710
$689$	0	0
$690$	12.9282	0.492168
$691$	21.8564	0.831457	0.415728	−	0.909489i	$-0.363527\pi$
$691$	21.8564	0.831457	0.415728	+	0.909489i	$0.363527\pi$
$692$	−7.07180	−0.268829
$693$	−12.1962	−0.463294
$694$	22.9808	0.872338
$695$	−17.6603	−0.669892
$696$	−8.19615	−0.310674
$697$	10.1244	0.383487
$698$	2.00000	0.0757011
$699$	−44.7846	−1.69391
$700$	−4.00000	−0.151186
$701$	21.4641	0.810688	0.405344	−	0.914164i	$-0.367152\pi$
$701$	21.4641	0.810688	0.405344	+	0.914164i	$0.367152\pi$
$702$	0	0
$703$	−28.3923	−1.07084
$704$	−2.73205	−0.102968
$705$	−29.8564	−1.12446
$706$	26.1769	0.985181
$707$	−9.19615	−0.345857
$708$	−19.8564	−0.746249
$709$	−38.5167	−1.44652	−0.723262	−	0.690574i	$-0.757358\pi$
$709$	−38.5167	−1.44652	−0.723262	+	0.690574i	$0.757358\pi$
$710$	−13.8564	−0.520022
$711$	−63.3731	−2.37668
$712$	−9.46410	−0.354682
$713$	−41.3205	−1.54747
$714$	−6.19615	−0.231885
$715$	0	0
$716$	−4.39230	−0.164148
$717$	42.3923	1.58317
$718$	4.39230	0.163919
$719$	4.19615	0.156490	0.0782450	−	0.996934i	$-0.475068\pi$
$719$	4.19615	0.156490	0.0782450	+	0.996934i	$0.475068\pi$
$720$	4.46410	0.166367
$721$	12.3923	0.461514
$722$	−10.8564	−0.404034
$723$	14.7321	0.547891
$724$	7.19615	0.267443
$725$	12.0000	0.445669
$726$	−9.66025	−0.358526
$727$	26.1436	0.969612	0.484806	−	0.874622i	$-0.338890\pi$
$727$	26.1436	0.969612	0.484806	+	0.874622i	$0.338890\pi$
$728$	0	0
$729$	−43.7846	−1.62165
$730$	9.39230	0.347625
$731$	4.09103	0.151312
$732$	22.5885	0.834893
$733$	−4.46410	−0.164885	−0.0824427	−	0.996596i	$-0.526272\pi$
$733$	−4.46410	−0.164885	−0.0824427	+	0.996596i	$0.526272\pi$
$734$	31.9090	1.17778
$735$	−2.73205	−0.100773
$736$	−4.73205	−0.174426
$737$	−15.4641	−0.569628
$738$	19.9282	0.733567
$739$	13.4641	0.495285	0.247642	−	0.968851i	$-0.420344\pi$
$739$	13.4641	0.495285	0.247642	+	0.968851i	$0.420344\pi$
$740$	−5.19615	−0.191014
$741$	0	0
$742$	−8.46410	−0.310727
$743$	18.9282	0.694408	0.347204	−	0.937790i	$-0.387131\pi$
$743$	18.9282	0.694408	0.347204	+	0.937790i	$0.387131\pi$
$744$	−23.8564	−0.874618
$745$	−6.80385	−0.249274
$746$	25.5359	0.934936
$747$	63.3731	2.31870
$748$	6.19615	0.226554
$749$	−2.92820	−0.106994
$750$	−24.5885	−0.897844
$751$	−52.4449	−1.91374	−0.956870	−	0.290516i	$-0.906173\pi$
$751$	−52.4449	−1.91374	−0.956870	+	0.290516i	$0.906173\pi$
$752$	10.9282	0.398511
$753$	−24.7846	−0.903201
$754$	0	0
$755$	−8.39230	−0.305427
$756$	−4.00000	−0.145479
$757$	−23.6077	−0.858036	−0.429018	−	0.903296i	$-0.641140\pi$
$757$	−23.6077	−0.858036	−0.429018	+	0.903296i	$0.641140\pi$
$758$	11.8038	0.428735
$759$	35.3205	1.28205
$760$	−5.46410	−0.198204
$761$	30.2487	1.09651	0.548257	−	0.836310i	$-0.315291\pi$
$761$	30.2487	1.09651	0.548257	+	0.836310i	$0.315291\pi$
$762$	−48.7846	−1.76728
$763$	10.0000	0.362024
$764$	−17.1244	−0.619537
$765$	−10.1244	−0.366047
$766$	−1.41154	−0.0510011
$767$	0	0
$768$	−2.73205	−0.0985844
$769$	20.3923	0.735365	0.367683	−	0.929951i	$-0.380151\pi$
$769$	20.3923	0.735365	0.367683	+	0.929951i	$0.380151\pi$
$770$	2.73205	0.0984563
$771$	−50.9808	−1.83603
$772$	−12.8038	−0.460821
$773$	−2.24871	−0.0808805	−0.0404403	−	0.999182i	$-0.512876\pi$
$773$	−2.24871	−0.0808805	−0.0404403	+	0.999182i	$0.512876\pi$
$774$	8.05256	0.289443
$775$	34.9282	1.25466
$776$	−1.46410	−0.0525582
$777$	14.1962	0.509284
$778$	10.3205	0.370008
$779$	−24.3923	−0.873945
$780$	0	0
$781$	−37.8564	−1.35461
$782$	10.7321	0.383777
$783$	12.0000	0.428845
$784$	1.00000	0.0357143
$785$	10.2679	0.366479
$786$	−51.7128	−1.84453
$787$	−6.98076	−0.248837	−0.124419	−	0.992230i	$-0.539707\pi$
$787$	−6.98076	−0.248837	−0.124419	+	0.992230i	$0.539707\pi$
$788$	−20.9282	−0.745536
$789$	−28.9282	−1.02987
$790$	14.1962	0.505076
$791$	−9.39230	−0.333952
$792$	12.1962	0.433371
$793$	0	0
$794$	−22.5359	−0.799769
$795$	−23.1244	−0.820136
$796$	1.46410	0.0518937
$797$	4.92820	0.174566	0.0872830	−	0.996184i	$-0.472182\pi$
$797$	4.92820	0.174566	0.0872830	+	0.996184i	$0.472182\pi$
$798$	14.9282	0.528453
$799$	−24.7846	−0.876816
$800$	4.00000	0.141421
$801$	42.2487	1.49278
$802$	−5.05256	−0.178412
$803$	25.6603	0.905531
$804$	−15.4641	−0.545377
$805$	4.73205	0.166783
$806$	0	0
$807$	−34.9282	−1.22953
$808$	9.19615	0.323520
$809$	41.2487	1.45023	0.725114	−	0.688629i	$-0.241787\pi$
$809$	41.2487	1.45023	0.725114	+	0.688629i	$0.241787\pi$
$810$	2.46410	0.0865797
$811$	45.1244	1.58453	0.792265	−	0.610177i	$-0.208902\pi$
$811$	45.1244	1.58453	0.792265	+	0.610177i	$0.208902\pi$
$812$	−3.00000	−0.105279
$813$	46.7846	1.64081
$814$	−14.1962	−0.497575
$815$	−2.73205	−0.0956996
$816$	6.19615	0.216909
$817$	−9.85641	−0.344832
$818$	8.32051	0.290920
$819$	0	0
$820$	−4.46410	−0.155893
$821$	17.0718	0.595810	0.297905	−	0.954596i	$-0.403712\pi$
$821$	17.0718	0.595810	0.297905	+	0.954596i	$0.403712\pi$
$822$	−49.5167	−1.72709
$823$	−46.2487	−1.61213	−0.806064	−	0.591828i	$-0.798407\pi$
$823$	−46.2487	−1.61213	−0.806064	+	0.591828i	$0.798407\pi$
$824$	−12.3923	−0.431706
$825$	−29.8564	−1.03947
$826$	−7.26795	−0.252884
$827$	38.4449	1.33686	0.668429	−	0.743776i	$-0.266967\pi$
$827$	38.4449	1.33686	0.668429	+	0.743776i	$0.266967\pi$
$828$	21.1244	0.734122
$829$	−37.5885	−1.30550	−0.652751	−	0.757573i	$-0.726385\pi$
$829$	−37.5885	−1.30550	−0.652751	+	0.757573i	$0.726385\pi$
$830$	−14.1962	−0.492756
$831$	31.1244	1.07969
$832$	0	0
$833$	−2.26795	−0.0785798
$834$	−48.2487	−1.67072
$835$	−8.73205	−0.302185
$836$	−14.9282	−0.516303
$837$	34.9282	1.20730
$838$	19.1244	0.660640
$839$	23.7128	0.818657	0.409329	−	0.912387i	$-0.365763\pi$
$839$	23.7128	0.818657	0.409329	+	0.912387i	$0.365763\pi$
$840$	2.73205	0.0942647
$841$	−20.0000	−0.689655
$842$	−10.1244	−0.348908
$843$	−1.80385	−0.0621278
$844$	−24.7321	−0.851312
$845$	0	0
$846$	−48.7846	−1.67725
$847$	−3.53590	−0.121495
$848$	8.46410	0.290658
$849$	−56.2487	−1.93045
$850$	−9.07180	−0.311160
$851$	−24.5885	−0.842881
$852$	−37.8564	−1.29694
$853$	−19.0000	−0.650548	−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000	−0.650548	−0.325274	+	0.945620i	$0.605456\pi$
$854$	8.26795	0.282923
$855$	24.3923	0.834199
$856$	2.92820	0.100084
$857$	−39.0526	−1.33401	−0.667005	−	0.745053i	$-0.732424\pi$
$857$	−39.0526	−1.33401	−0.667005	+	0.745053i	$0.732424\pi$
$858$	0	0
$859$	46.8372	1.59806	0.799032	−	0.601289i	$-0.205346\pi$
$859$	46.8372	1.59806	0.799032	+	0.601289i	$0.205346\pi$
$860$	−1.80385	−0.0615107
$861$	12.1962	0.415644
$862$	33.4641	1.13979
$863$	−14.4449	−0.491709	−0.245854	−	0.969307i	$-0.579069\pi$
$863$	−14.4449	−0.491709	−0.245854	+	0.969307i	$0.579069\pi$
$864$	4.00000	0.136083
$865$	−7.07180	−0.240448
$866$	−18.2679	−0.620770
$867$	32.3923	1.10010
$868$	−8.73205	−0.296385
$869$	38.7846	1.31568
$870$	−8.19615	−0.277876
$871$	0	0
$872$	−10.0000	−0.338643
$873$	6.53590	0.221207
$874$	−25.8564	−0.874606
$875$	−9.00000	−0.304256
$876$	25.6603	0.866980
$877$	26.1244	0.882157	0.441078	−	0.897469i	$-0.354596\pi$
$877$	26.1244	0.882157	0.441078	+	0.897469i	$0.354596\pi$
$878$	22.7321	0.767170
$879$	−9.26795	−0.312600
$880$	−2.73205	−0.0920974
$881$	38.3731	1.29282	0.646411	−	0.762990i	$-0.276269\pi$
$881$	38.3731	1.29282	0.646411	+	0.762990i	$0.276269\pi$
$882$	−4.46410	−0.150314
$883$	21.5167	0.724093	0.362047	−	0.932160i	$-0.382078\pi$
$883$	21.5167	0.724093	0.362047	+	0.932160i	$0.382078\pi$
$884$	0	0
$885$	−19.8564	−0.667466
$886$	−0.679492	−0.0228280
$887$	−10.9282	−0.366933	−0.183467	−	0.983026i	$-0.558732\pi$
$887$	−10.9282	−0.366933	−0.183467	+	0.983026i	$0.558732\pi$
$888$	−14.1962	−0.476392
$889$	−17.8564	−0.598885
$890$	−9.46410	−0.317237
$891$	6.73205	0.225532
$892$	8.39230	0.280995
$893$	59.7128	1.99821
$894$	−18.5885	−0.621691
$895$	−4.39230	−0.146819
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	26.1962	0.873691
$900$	−17.8564	−0.595214
$901$	−19.1962	−0.639517
$902$	−12.1962	−0.406087
$903$	4.92820	0.164000
$904$	9.39230	0.312383
$905$	7.19615	0.239208
$906$	−22.9282	−0.761739
$907$	16.0526	0.533016	0.266508	−	0.963833i	$-0.414130\pi$
$907$	16.0526	0.533016	0.266508	+	0.963833i	$0.414130\pi$
$908$	4.73205	0.157039
$909$	−41.0526	−1.36163
$910$	0	0
$911$	36.1051	1.19622	0.598108	−	0.801416i	$-0.295919\pi$
$911$	36.1051	1.19622	0.598108	+	0.801416i	$0.295919\pi$
$912$	−14.9282	−0.494322
$913$	−38.7846	−1.28358
$914$	−17.7321	−0.586524
$915$	22.5885	0.746751
$916$	−3.60770	−0.119202
$917$	−18.9282	−0.625064
$918$	−9.07180	−0.299414
$919$	−40.7846	−1.34536	−0.672680	−	0.739933i	$-0.734857\pi$
$919$	−40.7846	−1.34536	−0.672680	+	0.739933i	$0.734857\pi$
$920$	−4.73205	−0.156011
$921$	−58.7846	−1.93702
$922$	26.3205	0.866820
$923$	0	0
$924$	7.46410	0.245551
$925$	20.7846	0.683394
$926$	42.0526	1.38193
$927$	55.3205	1.81696
$928$	3.00000	0.0984798
$929$	21.1051	0.692436	0.346218	−	0.938154i	$-0.387466\pi$
$929$	21.1051	0.692436	0.346218	+	0.938154i	$0.387466\pi$
$930$	−23.8564	−0.782282
$931$	5.46410	0.179079
$932$	16.3923	0.536948
$933$	−0.535898	−0.0175445
$934$	21.2679	0.695909
$935$	6.19615	0.202636
$936$	0	0
$937$	24.4115	0.797490	0.398745	−	0.917062i	$-0.369446\pi$
$937$	24.4115	0.797490	0.398745	+	0.917062i	$0.369446\pi$
$938$	−5.66025	−0.184814
$939$	87.4256	2.85303
$940$	10.9282	0.356439
$941$	−23.3205	−0.760227	−0.380113	−	0.924940i	$-0.624115\pi$
$941$	−23.3205	−0.760227	−0.380113	+	0.924940i	$0.624115\pi$
$942$	28.0526	0.914002
$943$	−21.1244	−0.687904
$944$	7.26795	0.236552
$945$	−4.00000	−0.130120
$946$	−4.92820	−0.160230
$947$	28.8756	0.938332	0.469166	−	0.883110i	$-0.344555\pi$
$947$	28.8756	0.938332	0.469166	+	0.883110i	$0.344555\pi$
$948$	38.7846	1.25967
$949$	0	0
$950$	21.8564	0.709115
$951$	−84.8372	−2.75103
$952$	2.26795	0.0735047
$953$	−25.1769	−0.815560	−0.407780	−	0.913080i	$-0.633697\pi$
$953$	−25.1769	−0.815560	−0.407780	+	0.913080i	$0.633697\pi$
$954$	−37.7846	−1.22332
$955$	−17.1244	−0.554131
$956$	−15.5167	−0.501845
$957$	−22.3923	−0.723840
$958$	−21.8038	−0.704450
$959$	−18.1244	−0.585266
$960$	−2.73205	−0.0881766
$961$	45.2487	1.45964
$962$	0	0
$963$	−13.0718	−0.421233
$964$	−5.39230	−0.173674
$965$	−12.8038	−0.412170
$966$	12.9282	0.415958
$967$	31.5167	1.01351	0.506754	−	0.862091i	$-0.330845\pi$
$967$	31.5167	1.01351	0.506754	+	0.862091i	$0.330845\pi$
$968$	3.53590	0.113648
$969$	33.8564	1.08762
$970$	−1.46410	−0.0470095
$971$	0.392305	0.0125897	0.00629483	−	0.999980i	$-0.497996\pi$
$971$	0.392305	0.0125897	0.00629483	+	0.999980i	$0.497996\pi$
$972$	18.7321	0.600831
$973$	−17.6603	−0.566162
$974$	3.32051	0.106396
$975$	0	0
$976$	−8.26795	−0.264651
$977$	0.124356	0.00397849	0.00198924	−	0.999998i	$-0.499367\pi$
$977$	0.124356	0.00397849	0.00198924	+	0.999998i	$0.499367\pi$
$978$	−7.46410	−0.238676
$979$	−25.8564	−0.826374
$980$	1.00000	0.0319438
$981$	44.6410	1.42528
$982$	−27.7128	−0.884351
$983$	−32.1051	−1.02399	−0.511997	−	0.858987i	$-0.671094\pi$
$983$	−32.1051	−1.02399	−0.511997	+	0.858987i	$0.671094\pi$
$984$	−12.1962	−0.388799
$985$	−20.9282	−0.666828
$986$	−6.80385	−0.216679
$987$	−29.8564	−0.950340
$988$	0	0
$989$	−8.53590	−0.271426
$990$	12.1962	0.387619
$991$	27.3731	0.869534	0.434767	−	0.900543i	$-0.356831\pi$
$991$	27.3731	0.869534	0.434767	+	0.900543i	$0.356831\pi$
$992$	8.73205	0.277243
$993$	−59.1769	−1.87792
$994$	−13.8564	−0.439499
$995$	1.46410	0.0464151
$996$	−38.7846	−1.22894
$997$	29.9808	0.949500	0.474750	−	0.880121i	$-0.342538\pi$
$997$	29.9808	0.949500	0.474750	+	0.880121i	$0.342538\pi$
$998$	14.7321	0.466335
$999$	20.7846	0.657596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.q.1.1		2
13.2	odd	12		182.2.m.a.43.1	✓	4
13.5	odd	4		2366.2.d.k.337.3		4
13.7	odd	12		182.2.m.a.127.1	yes	4
13.8	odd	4		2366.2.d.k.337.1		4
13.12	even	2		2366.2.a.s.1.1		2
39.2	even	12		1638.2.bj.c.1135.2		4
39.20	even	12		1638.2.bj.c.127.2		4
52.7	even	12		1456.2.cc.b.673.1		4
52.15	even	12		1456.2.cc.b.225.1		4
91.2	odd	12		1274.2.o.b.459.2		4
91.20	even	12		1274.2.m.a.491.1		4
91.33	even	12		1274.2.v.b.361.2		4
91.41	even	12		1274.2.m.a.589.1		4
91.46	odd	12		1274.2.o.b.569.1		4
91.54	even	12		1274.2.o.a.459.2		4
91.59	even	12		1274.2.o.a.569.1		4
91.67	odd	12		1274.2.v.a.667.2		4
91.72	odd	12		1274.2.v.a.361.2		4
91.80	even	12		1274.2.v.b.667.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.a.43.1	✓	4	13.2	odd	12
182.2.m.a.127.1	yes	4	13.7	odd	12
1274.2.m.a.491.1		4	91.20	even	12
1274.2.m.a.589.1		4	91.41	even	12
1274.2.o.a.459.2		4	91.54	even	12
1274.2.o.a.569.1		4	91.59	even	12
1274.2.o.b.459.2		4	91.2	odd	12
1274.2.o.b.569.1		4	91.46	odd	12
1274.2.v.a.361.2		4	91.72	odd	12
1274.2.v.a.667.2		4	91.67	odd	12
1274.2.v.b.361.2		4	91.33	even	12
1274.2.v.b.667.2		4	91.80	even	12
1456.2.cc.b.225.1		4	52.15	even	12
1456.2.cc.b.673.1		4	52.7	even	12
1638.2.bj.c.127.2		4	39.20	even	12
1638.2.bj.c.1135.2		4	39.2	even	12
2366.2.a.q.1.1		2	1.1	even	1	trivial
2366.2.a.s.1.1		2	13.12	even	2
2366.2.d.k.337.1		4	13.8	odd	4
2366.2.d.k.337.3		4	13.5	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.46410 q^{9} -1.00000 q^{10} -2.73205 q^{11} -2.73205 q^{12} -1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} -2.26795 q^{17} -4.46410 q^{18} +5.46410 q^{19} +1.00000 q^{20} -2.73205 q^{21} +2.73205 q^{22} +4.73205 q^{23} +2.73205 q^{24} -4.00000 q^{25} -4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +2.73205 q^{30} -8.73205 q^{31} -1.00000 q^{32} +7.46410 q^{33} +2.26795 q^{34} +1.00000 q^{35} +4.46410 q^{36} -5.19615 q^{37} -5.46410 q^{38} -1.00000 q^{40} -4.46410 q^{41} +2.73205 q^{42} -1.80385 q^{43} -2.73205 q^{44} +4.46410 q^{45} -4.73205 q^{46} +10.9282 q^{47} -2.73205 q^{48} +1.00000 q^{49} +4.00000 q^{50} +6.19615 q^{51} +8.46410 q^{53} +4.00000 q^{54} -2.73205 q^{55} -1.00000 q^{56} -14.9282 q^{57} +3.00000 q^{58} +7.26795 q^{59} -2.73205 q^{60} -8.26795 q^{61} +8.73205 q^{62} +4.46410 q^{63} +1.00000 q^{64} -7.46410 q^{66} +5.66025 q^{67} -2.26795 q^{68} -12.9282 q^{69} -1.00000 q^{70} +13.8564 q^{71} -4.46410 q^{72} -9.39230 q^{73} +5.19615 q^{74} +10.9282 q^{75} +5.46410 q^{76} -2.73205 q^{77} -14.1962 q^{79} +1.00000 q^{80} -2.46410 q^{81} +4.46410 q^{82} +14.1962 q^{83} -2.73205 q^{84} -2.26795 q^{85} +1.80385 q^{86} +8.19615 q^{87} +2.73205 q^{88} +9.46410 q^{89} -4.46410 q^{90} +4.73205 q^{92} +23.8564 q^{93} -10.9282 q^{94} +5.46410 q^{95} +2.73205 q^{96} +1.46410 q^{97} -1.00000 q^{98} -12.1962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 6 q^{23} + 2 q^{24} - 8 q^{25} - 8 q^{27} + 2 q^{28} - 6 q^{29} + 2 q^{30} - 14 q^{31} - 2 q^{32} + 8 q^{33} + 8 q^{34} + 2 q^{35} + 2 q^{36} - 4 q^{38} - 2 q^{40} - 2 q^{41} + 2 q^{42} - 14 q^{43} - 2 q^{44} + 2 q^{45} - 6 q^{46} + 8 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{50} + 2 q^{51} + 10 q^{53} + 8 q^{54} - 2 q^{55} - 2 q^{56} - 16 q^{57} + 6 q^{58} + 18 q^{59} - 2 q^{60} - 20 q^{61} + 14 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{66} - 6 q^{67} - 8 q^{68} - 12 q^{69} - 2 q^{70} - 2 q^{72} + 2 q^{73} + 8 q^{75} + 4 q^{76} - 2 q^{77} - 18 q^{79} + 2 q^{80} + 2 q^{81} + 2 q^{82} + 18 q^{83} - 2 q^{84} - 8 q^{85} + 14 q^{86} + 6 q^{87} + 2 q^{88} + 12 q^{89} - 2 q^{90} + 6 q^{92} + 20 q^{93} - 8 q^{94} + 4 q^{95} + 2 q^{96} - 4 q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 - 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 6 * q^23 + 2 * q^24 - 8 * q^25 - 8 * q^27 + 2 * q^28 - 6 * q^29 + 2 * q^30 - 14 * q^31 - 2 * q^32 + 8 * q^33 + 8 * q^34 + 2 * q^35 + 2 * q^36 - 4 * q^38 - 2 * q^40 - 2 * q^41 + 2 * q^42 - 14 * q^43 - 2 * q^44 + 2 * q^45 - 6 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^49 + 8 * q^50 + 2 * q^51 + 10 * q^53 + 8 * q^54 - 2 * q^55 - 2 * q^56 - 16 * q^57 + 6 * q^58 + 18 * q^59 - 2 * q^60 - 20 * q^61 + 14 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^66 - 6 * q^67 - 8 * q^68 - 12 * q^69 - 2 * q^70 - 2 * q^72 + 2 * q^73 + 8 * q^75 + 4 * q^76 - 2 * q^77 - 18 * q^79 + 2 * q^80 + 2 * q^81 + 2 * q^82 + 18 * q^83 - 2 * q^84 - 8 * q^85 + 14 * q^86 + 6 * q^87 + 2 * q^88 + 12 * q^89 - 2 * q^90 + 6 * q^92 + 20 * q^93 - 8 * q^94 + 4 * q^95 + 2 * q^96 - 4 * q^97 - 2 * q^98 - 14 * q^99

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