LMFDB - Embedded newform 7935.2.a.bm.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.27924$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.27924 q^{2} +1.00000 q^{3} -0.363534 q^{4} +1.00000 q^{5} +1.27924 q^{6} -2.12712 q^{7} -3.02354 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.27924 q^{2} +1.00000 q^{3} -0.363534 q^{4} +1.00000 q^{5} +1.27924 q^{6} -2.12712 q^{7} -3.02354 q^{8} +1.00000 q^{9} +1.27924 q^{10} +4.20264 q^{11} -0.363534 q^{12} -0.372214 q^{13} -2.72110 q^{14} +1.00000 q^{15} -3.14078 q^{16} -2.93237 q^{17} +1.27924 q^{18} -3.42876 q^{19} -0.363534 q^{20} -2.12712 q^{21} +5.37620 q^{22} -3.02354 q^{24} +1.00000 q^{25} -0.476153 q^{26} +1.00000 q^{27} +0.773279 q^{28} +5.53718 q^{29} +1.27924 q^{30} -6.77268 q^{31} +2.02926 q^{32} +4.20264 q^{33} -3.75121 q^{34} -2.12712 q^{35} -0.363534 q^{36} -3.81859 q^{37} -4.38622 q^{38} -0.372214 q^{39} -3.02354 q^{40} -6.57321 q^{41} -2.72110 q^{42} +0.320137 q^{43} -1.52780 q^{44} +1.00000 q^{45} +5.48104 q^{47} -3.14078 q^{48} -2.47538 q^{49} +1.27924 q^{50} -2.93237 q^{51} +0.135312 q^{52} -4.21815 q^{53} +1.27924 q^{54} +4.20264 q^{55} +6.43141 q^{56} -3.42876 q^{57} +7.08341 q^{58} +9.18864 q^{59} -0.363534 q^{60} -5.44249 q^{61} -8.66391 q^{62} -2.12712 q^{63} +8.87746 q^{64} -0.372214 q^{65} +5.37620 q^{66} +5.77183 q^{67} +1.06601 q^{68} -2.72110 q^{70} -8.88214 q^{71} -3.02354 q^{72} -7.35312 q^{73} -4.88491 q^{74} +1.00000 q^{75} +1.24647 q^{76} -8.93949 q^{77} -0.476153 q^{78} -15.5670 q^{79} -3.14078 q^{80} +1.00000 q^{81} -8.40874 q^{82} -3.05792 q^{83} +0.773279 q^{84} -2.93237 q^{85} +0.409534 q^{86} +5.53718 q^{87} -12.7068 q^{88} -3.04581 q^{89} +1.27924 q^{90} +0.791742 q^{91} -6.77268 q^{93} +7.01159 q^{94} -3.42876 q^{95} +2.02926 q^{96} -14.0191 q^{97} -3.16662 q^{98} +4.20264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * 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 $

$2$	1.27924	0.904562	0.452281	−	0.891875i	$-0.350610\pi$
$2$	1.27924	0.904562	0.452281	+	0.891875i	$0.350610\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.363534	−0.181767
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.27924	0.522249
$7$	−2.12712	−0.803974	−0.401987	−	0.915645i	$-0.631680\pi$
$7$	−2.12712	−0.803974	−0.401987	+	0.915645i	$0.631680\pi$
$8$	−3.02354	−1.06898
$9$	1.00000	0.333333
$10$	1.27924	0.404533
$11$	4.20264	1.26714	0.633571	−	0.773684i	$-0.281588\pi$
$11$	4.20264	1.26714	0.633571	+	0.773684i	$0.281588\pi$
$12$	−0.363534	−0.104943
$13$	−0.372214	−0.103234	−0.0516168	−	0.998667i	$-0.516437\pi$
$13$	−0.372214	−0.103234	−0.0516168	+	0.998667i	$0.516437\pi$
$14$	−2.72110	−0.727245
$15$	1.00000	0.258199
$16$	−3.14078	−0.785194
$17$	−2.93237	−0.711203	−0.355602	−	0.934638i	$-0.615724\pi$
$17$	−2.93237	−0.711203	−0.355602	+	0.934638i	$0.615724\pi$
$18$	1.27924	0.301521
$19$	−3.42876	−0.786611	−0.393305	−	0.919408i	$-0.628669\pi$
$19$	−3.42876	−0.786611	−0.393305	+	0.919408i	$0.628669\pi$
$20$	−0.363534	−0.0812887
$21$	−2.12712	−0.464175
$22$	5.37620	1.14621
$23$	0	0
$23$	0	0
$24$	−3.02354	−0.617177
$25$	1.00000	0.200000
$26$	−0.476153	−0.0933813
$27$	1.00000	0.192450
$28$	0.773279	0.146136
$29$	5.53718	1.02823	0.514114	−	0.857722i	$-0.328121\pi$
$29$	5.53718	1.02823	0.514114	+	0.857722i	$0.328121\pi$
$30$	1.27924	0.233557
$31$	−6.77268	−1.21641	−0.608205	−	0.793780i	$-0.708110\pi$
$31$	−6.77268	−1.21641	−0.608205	+	0.793780i	$0.708110\pi$
$32$	2.02926	0.358725
$33$	4.20264	0.731585
$34$	−3.75121	−0.643328
$35$	−2.12712	−0.359548
$36$	−0.363534	−0.0605890
$37$	−3.81859	−0.627772	−0.313886	−	0.949461i	$-0.601631\pi$
$37$	−3.81859	−0.627772	−0.313886	+	0.949461i	$0.601631\pi$
$38$	−4.38622	−0.711539
$39$	−0.372214	−0.0596020
$40$	−3.02354	−0.478063
$41$	−6.57321	−1.02656	−0.513281	−	0.858220i	$-0.671570\pi$
$41$	−6.57321	−1.02656	−0.513281	+	0.858220i	$0.671570\pi$
$42$	−2.72110	−0.419875
$43$	0.320137	0.0488205	0.0244102	−	0.999702i	$-0.492229\pi$
$43$	0.320137	0.0488205	0.0244102	+	0.999702i	$0.492229\pi$
$44$	−1.52780	−0.230325
$45$	1.00000	0.149071
$46$	0	0
$47$	5.48104	0.799492	0.399746	−	0.916626i	$-0.369098\pi$
$47$	5.48104	0.799492	0.399746	+	0.916626i	$0.369098\pi$
$48$	−3.14078	−0.453332
$49$	−2.47538	−0.353626
$50$	1.27924	0.180912
$51$	−2.93237	−0.410613
$52$	0.135312	0.0187645
$53$	−4.21815	−0.579408	−0.289704	−	0.957116i	$-0.593557\pi$
$53$	−4.21815	−0.579408	−0.289704	+	0.957116i	$0.593557\pi$
$54$	1.27924	0.174083
$55$	4.20264	0.566683
$56$	6.43141	0.859434
$57$	−3.42876	−0.454150
$58$	7.08341	0.930097
$59$	9.18864	1.19626	0.598130	−	0.801399i	$-0.295911\pi$
$59$	9.18864	1.19626	0.598130	+	0.801399i	$0.295911\pi$
$60$	−0.363534	−0.0469320
$61$	−5.44249	−0.696840	−0.348420	−	0.937339i	$-0.613282\pi$
$61$	−5.44249	−0.696840	−0.348420	+	0.937339i	$0.613282\pi$
$62$	−8.66391	−1.10032
$63$	−2.12712	−0.267991
$64$	8.87746	1.10968
$65$	−0.372214	−0.0461675
$66$	5.37620	0.661764
$67$	5.77183	0.705141	0.352570	−	0.935785i	$-0.385308\pi$
$67$	5.77183	0.705141	0.352570	+	0.935785i	$0.385308\pi$
$68$	1.06601	0.129273
$69$	0	0
$70$	−2.72110	−0.325234
$71$	−8.88214	−1.05412	−0.527058	−	0.849829i	$-0.676705\pi$
$71$	−8.88214	−1.05412	−0.527058	+	0.849829i	$0.676705\pi$
$72$	−3.02354	−0.356327
$73$	−7.35312	−0.860617	−0.430309	−	0.902682i	$-0.641595\pi$
$73$	−7.35312	−0.860617	−0.430309	+	0.902682i	$0.641595\pi$
$74$	−4.88491	−0.567859
$75$	1.00000	0.115470
$76$	1.24647	0.142980
$77$	−8.93949	−1.01875
$78$	−0.476153	−0.0539137
$79$	−15.5670	−1.75143	−0.875714	−	0.482830i	$-0.839609\pi$
$79$	−15.5670	−1.75143	−0.875714	+	0.482830i	$0.839609\pi$
$80$	−3.14078	−0.351149
$81$	1.00000	0.111111
$82$	−8.40874	−0.928590
$83$	−3.05792	−0.335651	−0.167825	−	0.985817i	$-0.553674\pi$
$83$	−3.05792	−0.335651	−0.167825	+	0.985817i	$0.553674\pi$
$84$	0.773279	0.0843716
$85$	−2.93237	−0.318060
$86$	0.409534	0.0441612
$87$	5.53718	0.593648
$88$	−12.7068	−1.35455
$89$	−3.04581	−0.322855	−0.161428	−	0.986885i	$-0.551610\pi$
$89$	−3.04581	−0.322855	−0.161428	+	0.986885i	$0.551610\pi$
$90$	1.27924	0.134844
$91$	0.791742	0.0829971
$92$	0	0
$93$	−6.77268	−0.702294
$94$	7.01159	0.723190
$95$	−3.42876	−0.351783
$96$	2.02926	0.207110
$97$	−14.0191	−1.42343	−0.711714	−	0.702470i	$-0.752081\pi$
$97$	−14.0191	−1.42343	−0.711714	+	0.702470i	$0.752081\pi$
$98$	−3.16662	−0.319877
$99$	4.20264	0.422381
$100$	−0.363534	−0.0363534
$101$	17.2679	1.71822	0.859111	−	0.511790i	$-0.171017\pi$
$101$	17.2679	1.71822	0.859111	+	0.511790i	$0.171017\pi$
$102$	−3.75121	−0.371425
$103$	−2.36277	−0.232811	−0.116405	−	0.993202i	$-0.537137\pi$
$103$	−2.36277	−0.232811	−0.116405	+	0.993202i	$0.537137\pi$
$104$	1.12540	0.110355
$105$	−2.12712	−0.207585
$106$	−5.39605	−0.524111
$107$	−18.3372	−1.77272	−0.886361	−	0.462995i	$-0.846775\pi$
$107$	−18.3372	−1.77272	−0.886361	+	0.462995i	$0.846775\pi$
$108$	−0.363534	−0.0349811
$109$	−4.54103	−0.434952	−0.217476	−	0.976066i	$-0.569782\pi$
$109$	−4.54103	−0.434952	−0.217476	+	0.976066i	$0.569782\pi$
$110$	5.37620	0.512600
$111$	−3.81859	−0.362444
$112$	6.68079	0.631275
$113$	4.42509	0.416278	0.208139	−	0.978099i	$-0.433259\pi$
$113$	4.42509	0.416278	0.208139	+	0.978099i	$0.433259\pi$
$114$	−4.38622	−0.410807
$115$	0	0
$116$	−2.01295	−0.186898
$117$	−0.372214	−0.0344112
$118$	11.7545	1.08209
$119$	6.23748	0.571789
$120$	−3.02354	−0.276010
$121$	6.66215	0.605650
$122$	−6.96228	−0.630335
$123$	−6.57321	−0.592686
$124$	2.46210	0.221103
$125$	1.00000	0.0894427
$126$	−2.72110	−0.242415
$127$	−7.19577	−0.638521	−0.319261	−	0.947667i	$-0.603435\pi$
$127$	−7.19577	−0.638521	−0.319261	+	0.947667i	$0.603435\pi$
$128$	7.29793	0.645052
$129$	0.320137	0.0281865
$130$	−0.476153	−0.0417614
$131$	20.4094	1.78317	0.891587	−	0.452849i	$-0.149592\pi$
$131$	20.4094	1.78317	0.891587	+	0.452849i	$0.149592\pi$
$132$	−1.52780	−0.132978
$133$	7.29336	0.632415
$134$	7.38358	0.637844
$135$	1.00000	0.0860663
$136$	8.86612	0.760263
$137$	−1.18658	−0.101376	−0.0506882	−	0.998715i	$-0.516141\pi$
$137$	−1.18658	−0.101376	−0.0506882	+	0.998715i	$0.516141\pi$
$138$	0	0
$139$	−23.2141	−1.96899	−0.984495	−	0.175411i	$-0.943875\pi$
$139$	−23.2141	−1.96899	−0.984495	+	0.175411i	$0.943875\pi$
$140$	0.773279	0.0653540
$141$	5.48104	0.461587
$142$	−11.3624	−0.953513
$143$	−1.56428	−0.130812
$144$	−3.14078	−0.261731
$145$	5.53718	0.459838
$146$	−9.40643	−0.778482
$147$	−2.47538	−0.204166
$148$	1.38819	0.114108
$149$	−11.7479	−0.962423	−0.481212	−	0.876604i	$-0.659803\pi$
$149$	−11.7479	−0.962423	−0.481212	+	0.876604i	$0.659803\pi$
$150$	1.27924	0.104450
$151$	−2.97189	−0.241849	−0.120925	−	0.992662i	$-0.538586\pi$
$151$	−2.97189	−0.241849	−0.120925	+	0.992662i	$0.538586\pi$
$152$	10.3670	0.840873
$153$	−2.93237	−0.237068
$154$	−11.4358	−0.921522
$155$	−6.77268	−0.543995
$156$	0.135312	0.0108337
$157$	12.2840	0.980371	0.490185	−	0.871618i	$-0.336929\pi$
$157$	12.2840	0.980371	0.490185	+	0.871618i	$0.336929\pi$
$158$	−19.9140	−1.58428
$159$	−4.21815	−0.334521
$160$	2.02926	0.160427
$161$	0	0
$162$	1.27924	0.100507
$163$	0.344269	0.0269653	0.0134826	−	0.999909i	$-0.495708\pi$
$163$	0.344269	0.0269653	0.0134826	+	0.999909i	$0.495708\pi$
$164$	2.38958	0.186595
$165$	4.20264	0.327175
$166$	−3.91183	−0.303617
$167$	−1.96630	−0.152157	−0.0760785	−	0.997102i	$-0.524240\pi$
$167$	−1.96630	−0.152157	−0.0760785	+	0.997102i	$0.524240\pi$
$168$	6.43141	0.496194
$169$	−12.8615	−0.989343
$170$	−3.75121	−0.287705
$171$	−3.42876	−0.262204
$172$	−0.116381	−0.00887395
$173$	20.0420	1.52377	0.761883	−	0.647714i	$-0.224275\pi$
$173$	20.0420	1.52377	0.761883	+	0.647714i	$0.224275\pi$
$174$	7.08341	0.536992
$175$	−2.12712	−0.160795
$176$	−13.1995	−0.994952
$177$	9.18864	0.690661
$178$	−3.89634	−0.292043
$179$	−19.7723	−1.47785	−0.738926	−	0.673786i	$-0.764667\pi$
$179$	−19.7723	−1.47785	−0.738926	+	0.673786i	$0.764667\pi$
$180$	−0.363534	−0.0270962
$181$	−5.45298	−0.405317	−0.202658	−	0.979249i	$-0.564958\pi$
$181$	−5.45298	−0.405317	−0.202658	+	0.979249i	$0.564958\pi$
$182$	1.01283	0.0750761
$183$	−5.44249	−0.402321
$184$	0	0
$185$	−3.81859	−0.280748
$186$	−8.66391	−0.635269
$187$	−12.3237	−0.901196
$188$	−1.99254	−0.145321
$189$	−2.12712	−0.154725
$190$	−4.38622	−0.318210
$191$	−20.9501	−1.51589	−0.757946	−	0.652317i	$-0.773797\pi$
$191$	−20.9501	−1.51589	−0.757946	+	0.652317i	$0.773797\pi$
$192$	8.87746	0.640676
$193$	14.2945	1.02894	0.514471	−	0.857508i	$-0.327988\pi$
$193$	14.2945	1.02894	0.514471	+	0.857508i	$0.327988\pi$
$194$	−17.9339	−1.28758
$195$	−0.372214	−0.0266548
$196$	0.899885	0.0642775
$197$	0.0764917	0.00544981	0.00272490	−	0.999996i	$-0.499133\pi$
$197$	0.0764917	0.00544981	0.00272490	+	0.999996i	$0.499133\pi$
$198$	5.37620	0.382070
$199$	−11.5413	−0.818139	−0.409070	−	0.912503i	$-0.634147\pi$
$199$	−11.5413	−0.818139	−0.409070	+	0.912503i	$0.634147\pi$
$200$	−3.02354	−0.213796
$201$	5.77183	0.407113
$202$	22.0899	1.55424
$203$	−11.7782	−0.826669
$204$	1.06601	0.0746359
$205$	−6.57321	−0.459093
$206$	−3.02256	−0.210592
$207$	0	0
$208$	1.16904	0.0810584
$209$	−14.4098	−0.996748
$210$	−2.72110	−0.187774
$211$	11.3887	0.784031	0.392016	−	0.919959i	$-0.371778\pi$
$211$	11.3887	0.784031	0.392016	+	0.919959i	$0.371778\pi$
$212$	1.53344	0.105317
$213$	−8.88214	−0.608594
$214$	−23.4577	−1.60354
$215$	0.320137	0.0218332
$216$	−3.02354	−0.205726
$217$	14.4063	0.977961
$218$	−5.80908	−0.393441
$219$	−7.35312	−0.496878
$220$	−1.52780	−0.103004
$221$	1.09147	0.0734201
$222$	−4.88491	−0.327854
$223$	3.11999	0.208930	0.104465	−	0.994529i	$-0.466687\pi$
$223$	3.11999	0.208930	0.104465	+	0.994529i	$0.466687\pi$
$224$	−4.31646	−0.288406
$225$	1.00000	0.0666667
$226$	5.66077	0.376549
$227$	−29.5884	−1.96385	−0.981926	−	0.189263i	$-0.939390\pi$
$227$	−29.5884	−1.96385	−0.981926	+	0.189263i	$0.939390\pi$
$228$	1.24647	0.0825495
$229$	−22.7779	−1.50521	−0.752603	−	0.658474i	$-0.771202\pi$
$229$	−22.7779	−1.50521	−0.752603	+	0.658474i	$0.771202\pi$
$230$	0	0
$231$	−8.93949	−0.588175
$232$	−16.7419	−1.09916
$233$	26.1911	1.71584	0.857920	−	0.513784i	$-0.171757\pi$
$233$	26.1911	1.71584	0.857920	+	0.513784i	$0.171757\pi$
$234$	−0.476153	−0.0311271
$235$	5.48104	0.357544
$236$	−3.34038	−0.217440
$237$	−15.5670	−1.01119
$238$	7.97926	0.517219
$239$	29.3337	1.89744	0.948718	−	0.316122i	$-0.102381\pi$
$239$	29.3337	1.89744	0.948718	+	0.316122i	$0.102381\pi$
$240$	−3.14078	−0.202736
$241$	−1.95635	−0.126020	−0.0630099	−	0.998013i	$-0.520070\pi$
$241$	−1.95635	−0.126020	−0.0630099	+	0.998013i	$0.520070\pi$
$242$	8.52251	0.547848
$243$	1.00000	0.0641500
$244$	1.97853	0.126662
$245$	−2.47538	−0.158146
$246$	−8.40874	−0.536122
$247$	1.27623	0.0812047
$248$	20.4775	1.30032
$249$	−3.05792	−0.193788
$250$	1.27924	0.0809065
$251$	13.0702	0.824982	0.412491	−	0.910962i	$-0.364659\pi$
$251$	13.0702	0.824982	0.412491	+	0.910962i	$0.364659\pi$
$252$	0.773279	0.0487120
$253$	0	0
$254$	−9.20515	−0.577582
$255$	−2.93237	−0.183632
$256$	−8.41909	−0.526193
$257$	11.1770	0.697200	0.348600	−	0.937272i	$-0.386657\pi$
$257$	11.1770	0.697200	0.348600	+	0.937272i	$0.386657\pi$
$258$	0.409534	0.0254965
$259$	8.12258	0.504712
$260$	0.135312	0.00839172
$261$	5.53718	0.342743
$262$	26.1086	1.61299
$263$	22.8052	1.40623	0.703115	−	0.711076i	$-0.251792\pi$
$263$	22.8052	1.40623	0.703115	+	0.711076i	$0.251792\pi$
$264$	−12.7068	−0.782051
$265$	−4.21815	−0.259119
$266$	9.32999	0.572058
$267$	−3.04581	−0.186401
$268$	−2.09825	−0.128171
$269$	6.91948	0.421888	0.210944	−	0.977498i	$-0.432346\pi$
$269$	6.91948	0.421888	0.210944	+	0.977498i	$0.432346\pi$
$270$	1.27924	0.0778523
$271$	−1.99678	−0.121296	−0.0606480	−	0.998159i	$-0.519317\pi$
$271$	−1.99678	−0.121296	−0.0606480	+	0.998159i	$0.519317\pi$
$272$	9.20990	0.558432
$273$	0.791742	0.0479184
$274$	−1.51793	−0.0917013
$275$	4.20264	0.253428
$276$	0	0
$277$	−14.3870	−0.864430	−0.432215	−	0.901771i	$-0.642268\pi$
$277$	−14.3870	−0.864430	−0.432215	+	0.901771i	$0.642268\pi$
$278$	−29.6964	−1.78107
$279$	−6.77268	−0.405470
$280$	6.43141	0.384350
$281$	13.9580	0.832667	0.416334	−	0.909212i	$-0.363315\pi$
$281$	13.9580	0.832667	0.416334	+	0.909212i	$0.363315\pi$
$282$	7.01159	0.417534
$283$	20.3377	1.20895	0.604476	−	0.796623i	$-0.293382\pi$
$283$	20.3377	1.20895	0.604476	+	0.796623i	$0.293382\pi$
$284$	3.22896	0.191603
$285$	−3.42876	−0.203102
$286$	−2.00110	−0.118327
$287$	13.9820	0.825330
$288$	2.02926	0.119575
$289$	−8.40123	−0.494190
$290$	7.08341	0.415952
$291$	−14.0191	−0.821816
$292$	2.67311	0.156432
$293$	−5.30776	−0.310083	−0.155041	−	0.987908i	$-0.549551\pi$
$293$	−5.30776	−0.310083	−0.155041	+	0.987908i	$0.549551\pi$
$294$	−3.16662	−0.184681
$295$	9.18864	0.534984
$296$	11.5456	0.671077
$297$	4.20264	0.243862
$298$	−15.0284	−0.870572
$299$	0	0
$300$	−0.363534	−0.0209886
$301$	−0.680969	−0.0392504
$302$	−3.80178	−0.218768
$303$	17.2679	0.992016
$304$	10.7690	0.617642
$305$	−5.44249	−0.311636
$306$	−3.75121	−0.214443
$307$	−26.0861	−1.48881	−0.744406	−	0.667727i	$-0.767267\pi$
$307$	−26.0861	−1.48881	−0.744406	+	0.667727i	$0.767267\pi$
$308$	3.24981	0.185175
$309$	−2.36277	−0.134413
$310$	−8.66391	−0.492077
$311$	−5.39851	−0.306121	−0.153061	−	0.988217i	$-0.548913\pi$
$311$	−5.39851	−0.306121	−0.153061	+	0.988217i	$0.548913\pi$
$312$	1.12540	0.0637134
$313$	−25.1315	−1.42052	−0.710258	−	0.703942i	$-0.751422\pi$
$313$	−25.1315	−1.42052	−0.710258	+	0.703942i	$0.751422\pi$
$314$	15.7142	0.886806
$315$	−2.12712	−0.119849
$316$	5.65915	0.318352
$317$	13.6791	0.768297	0.384149	−	0.923271i	$-0.374495\pi$
$317$	13.6791	0.768297	0.384149	+	0.923271i	$0.374495\pi$
$318$	−5.39605	−0.302595
$319$	23.2707	1.30291
$320$	8.87746	0.496265
$321$	−18.3372	−1.02348
$322$	0	0
$323$	10.0544	0.559440
$324$	−0.363534	−0.0201963
$325$	−0.372214	−0.0206467
$326$	0.440405	0.0243918
$327$	−4.54103	−0.251119
$328$	19.8743	1.09738
$329$	−11.6588	−0.642771
$330$	5.37620	0.295950
$331$	10.4563	0.574731	0.287366	−	0.957821i	$-0.407221\pi$
$331$	10.4563	0.574731	0.287366	+	0.957821i	$0.407221\pi$
$332$	1.11166	0.0610102
$333$	−3.81859	−0.209257
$334$	−2.51538	−0.137635
$335$	5.77183	0.315349
$336$	6.68079	0.364467
$337$	−18.5498	−1.01047	−0.505235	−	0.862982i	$-0.668594\pi$
$337$	−18.5498	−1.01047	−0.505235	+	0.862982i	$0.668594\pi$
$338$	−16.4529	−0.894922
$339$	4.42509	0.240338
$340$	1.06601	0.0578128
$341$	−28.4631	−1.54136
$342$	−4.38622	−0.237180
$343$	20.1552	1.08828
$344$	−0.967947	−0.0521882
$345$	0	0
$346$	25.6386	1.37834
$347$	−28.3461	−1.52170	−0.760848	−	0.648930i	$-0.775217\pi$
$347$	−28.3461	−1.52170	−0.760848	+	0.648930i	$0.775217\pi$
$348$	−2.01295	−0.107906
$349$	−31.2361	−1.67203	−0.836015	−	0.548706i	$-0.815121\pi$
$349$	−31.2361	−1.67203	−0.836015	+	0.548706i	$0.815121\pi$
$350$	−2.72110	−0.145449
$351$	−0.372214	−0.0198673
$352$	8.52822	0.454556
$353$	−9.16021	−0.487549	−0.243774	−	0.969832i	$-0.578386\pi$
$353$	−9.16021	−0.487549	−0.243774	+	0.969832i	$0.578386\pi$
$354$	11.7545	0.624746
$355$	−8.88214	−0.471415
$356$	1.10726	0.0586845
$357$	6.23748	0.330122
$358$	−25.2936	−1.33681
$359$	−20.5225	−1.08314	−0.541568	−	0.840657i	$-0.682169\pi$
$359$	−20.5225	−1.08314	−0.541568	+	0.840657i	$0.682169\pi$
$360$	−3.02354	−0.159354
$361$	−7.24362	−0.381243
$362$	−6.97570	−0.366634
$363$	6.66215	0.349672
$364$	−0.287825	−0.0150861
$365$	−7.35312	−0.384880
$366$	−6.96228	−0.363924
$367$	15.7476	0.822016	0.411008	−	0.911632i	$-0.365177\pi$
$367$	15.7476	0.822016	0.411008	+	0.911632i	$0.365177\pi$
$368$	0	0
$369$	−6.57321	−0.342188
$370$	−4.88491	−0.253954
$371$	8.97250	0.465829
$372$	2.46210	0.127654
$373$	31.1327	1.61199	0.805995	−	0.591923i	$-0.201631\pi$
$373$	31.1327	1.61199	0.805995	+	0.591923i	$0.201631\pi$
$374$	−15.7650	−0.815188
$375$	1.00000	0.0516398
$376$	−16.5721	−0.854642
$377$	−2.06102	−0.106148
$378$	−2.72110	−0.139958
$379$	−17.1718	−0.882054	−0.441027	−	0.897494i	$-0.645386\pi$
$379$	−17.1718	−0.882054	−0.441027	+	0.897494i	$0.645386\pi$
$380$	1.24647	0.0639425
$381$	−7.19577	−0.368651
$382$	−26.8002	−1.37122
$383$	25.3693	1.29631	0.648156	−	0.761507i	$-0.275540\pi$
$383$	25.3693	1.29631	0.648156	+	0.761507i	$0.275540\pi$
$384$	7.29793	0.372421
$385$	−8.93949	−0.455599
$386$	18.2862	0.930743
$387$	0.320137	0.0162735
$388$	5.09643	0.258732
$389$	17.5876	0.891726	0.445863	−	0.895101i	$-0.352897\pi$
$389$	17.5876	0.891726	0.445863	+	0.895101i	$0.352897\pi$
$390$	−0.476153	−0.0241109
$391$	0	0
$392$	7.48441	0.378020
$393$	20.4094	1.02952
$394$	0.0978516	0.00492969
$395$	−15.5670	−0.783262
$396$	−1.52780	−0.0767749
$397$	−17.6345	−0.885050	−0.442525	−	0.896756i	$-0.645917\pi$
$397$	−17.6345	−0.885050	−0.442525	+	0.896756i	$0.645917\pi$
$398$	−14.7641	−0.740058
$399$	7.29336	0.365125
$400$	−3.14078	−0.157039
$401$	1.88961	0.0943627	0.0471813	−	0.998886i	$-0.484976\pi$
$401$	1.88961	0.0943627	0.0471813	+	0.998886i	$0.484976\pi$
$402$	7.38358	0.368259
$403$	2.52089	0.125574
$404$	−6.27747	−0.312316
$405$	1.00000	0.0496904
$406$	−15.0672	−0.747774
$407$	−16.0481	−0.795477
$408$	8.86612	0.438938
$409$	−29.9786	−1.48235	−0.741173	−	0.671314i	$-0.765730\pi$
$409$	−29.9786	−1.48235	−0.741173	+	0.671314i	$0.765730\pi$
$410$	−8.40874	−0.415278
$411$	−1.18658	−0.0585297
$412$	0.858948	0.0423173
$413$	−19.5453	−0.961761
$414$	0	0
$415$	−3.05792	−0.150108
$416$	−0.755318	−0.0370325
$417$	−23.2141	−1.13680
$418$	−18.4337	−0.901621
$419$	−4.72561	−0.230861	−0.115430	−	0.993316i	$-0.536825\pi$
$419$	−4.72561	−0.230861	−0.115430	+	0.993316i	$0.536825\pi$
$420$	0.773279	0.0377321
$421$	−30.5889	−1.49081	−0.745406	−	0.666610i	$-0.767745\pi$
$421$	−30.5889	−1.49081	−0.745406	+	0.666610i	$0.767745\pi$
$422$	14.5689	0.709205
$423$	5.48104	0.266497
$424$	12.7537	0.619377
$425$	−2.93237	−0.142241
$426$	−11.3624	−0.550511
$427$	11.5768	0.560241
$428$	6.66619	0.322222
$429$	−1.56428	−0.0755242
$430$	0.409534	0.0197495
$431$	−9.26596	−0.446326	−0.223163	−	0.974781i	$-0.571638\pi$
$431$	−9.26596	−0.446326	−0.223163	+	0.974781i	$0.571638\pi$
$432$	−3.14078	−0.151111
$433$	−20.3252	−0.976768	−0.488384	−	0.872629i	$-0.662413\pi$
$433$	−20.3252	−0.976768	−0.488384	+	0.872629i	$0.662413\pi$
$434$	18.4291	0.884627
$435$	5.53718	0.265487
$436$	1.65082	0.0790598
$437$	0	0
$438$	−9.40643	−0.449457
$439$	27.4489	1.31007	0.655033	−	0.755600i	$-0.272655\pi$
$439$	27.4489	1.31007	0.655033	+	0.755600i	$0.272655\pi$
$440$	−12.7068	−0.605774
$441$	−2.47538	−0.117875
$442$	1.39625	0.0664130
$443$	−9.72870	−0.462225	−0.231112	−	0.972927i	$-0.574236\pi$
$443$	−9.72870	−0.462225	−0.231112	+	0.972927i	$0.574236\pi$
$444$	1.38819	0.0658804
$445$	−3.04581	−0.144385
$446$	3.99124	0.188990
$447$	−11.7479	−0.555655
$448$	−18.8834	−0.892156
$449$	18.0533	0.851989	0.425995	−	0.904726i	$-0.359924\pi$
$449$	18.0533	0.851989	0.425995	+	0.904726i	$0.359924\pi$
$450$	1.27924	0.0603042
$451$	−27.6248	−1.30080
$452$	−1.60867	−0.0756655
$453$	−2.97189	−0.139632
$454$	−37.8508	−1.77643
$455$	0.791742	0.0371175
$456$	10.3670	0.485478
$457$	36.4936	1.70710	0.853549	−	0.521013i	$-0.174446\pi$
$457$	36.4936	1.70710	0.853549	+	0.521013i	$0.174446\pi$
$458$	−29.1385	−1.36155
$459$	−2.93237	−0.136871
$460$	0	0
$461$	−18.7519	−0.873365	−0.436682	−	0.899616i	$-0.643847\pi$
$461$	−18.7519	−0.873365	−0.436682	+	0.899616i	$0.643847\pi$
$462$	−11.4358	−0.532041
$463$	−0.585188	−0.0271960	−0.0135980	−	0.999908i	$-0.504329\pi$
$463$	−0.585188	−0.0271960	−0.0135980	+	0.999908i	$0.504329\pi$
$464$	−17.3910	−0.807359
$465$	−6.77268	−0.314076
$466$	33.5049	1.55208
$467$	28.5756	1.32232	0.661160	−	0.750245i	$-0.270064\pi$
$467$	28.5756	1.32232	0.661160	+	0.750245i	$0.270064\pi$
$468$	0.135312	0.00625482
$469$	−12.2773	−0.566915
$470$	7.01159	0.323421
$471$	12.2840	0.566017
$472$	−27.7822	−1.27878
$473$	1.34542	0.0618625
$474$	−19.9140	−0.914682
$475$	−3.42876	−0.157322
$476$	−2.26754	−0.103932
$477$	−4.21815	−0.193136
$478$	37.5249	1.71635
$479$	7.40578	0.338379	0.169189	−	0.985584i	$-0.445885\pi$
$479$	7.40578	0.338379	0.169189	+	0.985584i	$0.445885\pi$
$480$	2.02926	0.0926224
$481$	1.42133	0.0648072
$482$	−2.50265	−0.113993
$483$	0	0
$484$	−2.42192	−0.110087
$485$	−14.0191	−0.636576
$486$	1.27924	0.0580277
$487$	33.1992	1.50440	0.752199	−	0.658936i	$-0.228993\pi$
$487$	33.1992	1.50440	0.752199	+	0.658936i	$0.228993\pi$
$488$	16.4556	0.744909
$489$	0.344269	0.0155684
$490$	−3.16662	−0.143053
$491$	1.87184	0.0844749	0.0422374	−	0.999108i	$-0.486551\pi$
$491$	1.87184	0.0844749	0.0422374	+	0.999108i	$0.486551\pi$
$492$	2.38958	0.107731
$493$	−16.2370	−0.731279
$494$	1.63261	0.0734547
$495$	4.20264	0.188894
$496$	21.2715	0.955117
$497$	18.8933	0.847481
$498$	−3.91183	−0.175293
$499$	−37.4895	−1.67826	−0.839130	−	0.543932i	$-0.816935\pi$
$499$	−37.4895	−1.67826	−0.839130	+	0.543932i	$0.816935\pi$
$500$	−0.363534	−0.0162577
$501$	−1.96630	−0.0878479
$502$	16.7199	0.746247
$503$	36.4208	1.62392	0.811962	−	0.583710i	$-0.198400\pi$
$503$	36.4208	1.62392	0.811962	+	0.583710i	$0.198400\pi$
$504$	6.43141	0.286478
$505$	17.2679	0.768412
$506$	0	0
$507$	−12.8615	−0.571197
$508$	2.61591	0.116062
$509$	32.8880	1.45774	0.728868	−	0.684654i	$-0.240047\pi$
$509$	32.8880	1.45774	0.728868	+	0.684654i	$0.240047\pi$
$510$	−3.75121	−0.166106
$511$	15.6409	0.691914
$512$	−25.3659	−1.12103
$513$	−3.42876	−0.151383
$514$	14.2981	0.630661
$515$	−2.36277	−0.104116
$516$	−0.116381	−0.00512338
$517$	23.0348	1.01307
$518$	10.3908	0.456544
$519$	20.0420	0.879747
$520$	1.12540	0.0493522
$521$	−0.940584	−0.0412077	−0.0206039	−	0.999788i	$-0.506559\pi$
$521$	−0.940584	−0.0412077	−0.0206039	+	0.999788i	$0.506559\pi$
$522$	7.08341	0.310032
$523$	−18.7666	−0.820604	−0.410302	−	0.911950i	$-0.634577\pi$
$523$	−18.7666	−0.820604	−0.410302	+	0.911950i	$0.634577\pi$
$524$	−7.41950	−0.324122
$525$	−2.12712	−0.0928349
$526$	29.1734	1.27202
$527$	19.8600	0.865114
$528$	−13.1995	−0.574436
$529$	0	0
$530$	−5.39605	−0.234389
$531$	9.18864	0.398753
$532$	−2.65138	−0.114952
$533$	2.44664	0.105976
$534$	−3.89634	−0.168611
$535$	−18.3372	−0.792785
$536$	−17.4513	−0.753783
$537$	−19.7723	−0.853239
$538$	8.85170	0.381624
$539$	−10.4031	−0.448094
$540$	−0.363534	−0.0156440
$541$	10.3441	0.444726	0.222363	−	0.974964i	$-0.428623\pi$
$541$	10.3441	0.444726	0.222363	+	0.974964i	$0.428623\pi$
$542$	−2.55437	−0.109720
$543$	−5.45298	−0.234010
$544$	−5.95052	−0.255126
$545$	−4.54103	−0.194516
$546$	1.01283	0.0433452
$547$	0.575897	0.0246236	0.0123118	−	0.999924i	$-0.496081\pi$
$547$	0.575897	0.0246236	0.0123118	+	0.999924i	$0.496081\pi$
$548$	0.431362	0.0184269
$549$	−5.44249	−0.232280
$550$	5.37620	0.229242
$551$	−18.9856	−0.808816
$552$	0	0
$553$	33.1129	1.40810
$554$	−18.4045	−0.781931
$555$	−3.81859	−0.162090
$556$	8.43910	0.357897
$557$	4.76591	0.201938	0.100969	−	0.994890i	$-0.467806\pi$
$557$	4.76591	0.201938	0.100969	+	0.994890i	$0.467806\pi$
$558$	−8.66391	−0.366773
$559$	−0.119160	−0.00503992
$560$	6.68079	0.282315
$561$	−12.3237	−0.520306
$562$	17.8558	0.753200
$563$	10.3016	0.434159	0.217080	−	0.976154i	$-0.430347\pi$
$563$	10.3016	0.434159	0.217080	+	0.976154i	$0.430347\pi$
$564$	−1.99254	−0.0839013
$565$	4.42509	0.186165
$566$	26.0169	1.09357
$567$	−2.12712	−0.0893304
$568$	26.8555	1.12683
$569$	4.33529	0.181745	0.0908724	−	0.995863i	$-0.471034\pi$
$569$	4.33529	0.181745	0.0908724	+	0.995863i	$0.471034\pi$
$570$	−4.38622	−0.183718
$571$	35.6108	1.49027	0.745133	−	0.666916i	$-0.232386\pi$
$571$	35.6108	1.49027	0.745133	+	0.666916i	$0.232386\pi$
$572$	0.568669	0.0237772
$573$	−20.9501	−0.875201
$574$	17.8864	0.746562
$575$	0	0
$576$	8.87746	0.369894
$577$	37.8478	1.57563	0.787813	−	0.615915i	$-0.211213\pi$
$577$	37.8478	1.57563	0.787813	+	0.615915i	$0.211213\pi$
$578$	−10.7472	−0.447026
$579$	14.2945	0.594060
$580$	−2.01295	−0.0835833
$581$	6.50456	0.269854
$582$	−17.9339	−0.743384
$583$	−17.7274	−0.734192
$584$	22.2324	0.919984
$585$	−0.372214	−0.0153892
$586$	−6.78993	−0.280489
$587$	−4.40526	−0.181825	−0.0909123	−	0.995859i	$-0.528978\pi$
$587$	−4.40526	−0.181825	−0.0909123	+	0.995859i	$0.528978\pi$
$588$	0.899885	0.0371106
$589$	23.2219	0.956841
$590$	11.7545	0.483926
$591$	0.0764917	0.00314645
$592$	11.9933	0.492923
$593$	9.84893	0.404447	0.202224	−	0.979339i	$-0.435183\pi$
$593$	9.84893	0.404447	0.202224	+	0.979339i	$0.435183\pi$
$594$	5.37620	0.220588
$595$	6.23748	0.255712
$596$	4.27075	0.174937
$597$	−11.5413	−0.472353
$598$	0	0
$599$	18.8072	0.768443	0.384222	−	0.923241i	$-0.374470\pi$
$599$	18.8072	0.768443	0.384222	+	0.923241i	$0.374470\pi$
$600$	−3.02354	−0.123435
$601$	1.21223	0.0494478	0.0247239	−	0.999694i	$-0.492129\pi$
$601$	1.21223	0.0494478	0.0247239	+	0.999694i	$0.492129\pi$
$602$	−0.871126	−0.0355044
$603$	5.77183	0.235047
$604$	1.08038	0.0439602
$605$	6.66215	0.270855
$606$	22.0899	0.897340
$607$	−31.4450	−1.27631	−0.638157	−	0.769906i	$-0.720303\pi$
$607$	−31.4450	−1.27631	−0.638157	+	0.769906i	$0.720303\pi$
$608$	−6.95783	−0.282177
$609$	−11.7782	−0.477277
$610$	−6.96228	−0.281894
$611$	−2.04012	−0.0825345
$612$	1.06601	0.0430911
$613$	−0.477169	−0.0192727	−0.00963633	−	0.999954i	$-0.503067\pi$
$613$	−0.477169	−0.0192727	−0.00963633	+	0.999954i	$0.503067\pi$
$614$	−33.3705	−1.34672
$615$	−6.57321	−0.265057
$616$	27.0289	1.08902
$617$	−27.1717	−1.09389	−0.546945	−	0.837169i	$-0.684209\pi$
$617$	−27.1717	−1.09389	−0.546945	+	0.837169i	$0.684209\pi$
$618$	−3.02256	−0.121585
$619$	35.8843	1.44231	0.721157	−	0.692772i	$-0.243611\pi$
$619$	35.8843	1.44231	0.721157	+	0.692772i	$0.243611\pi$
$620$	2.46210	0.0988803
$621$	0	0
$622$	−6.90601	−0.276906
$623$	6.47879	0.259567
$624$	1.16904	0.0467991
$625$	1.00000	0.0400000
$626$	−32.1493	−1.28494
$627$	−14.4098	−0.575473
$628$	−4.46565	−0.178199
$629$	11.1975	0.446474
$630$	−2.72110	−0.108411
$631$	−30.2939	−1.20598	−0.602990	−	0.797749i	$-0.706024\pi$
$631$	−30.2939	−1.20598	−0.602990	+	0.797749i	$0.706024\pi$
$632$	47.0675	1.87224
$633$	11.3887	0.452661
$634$	17.4990	0.694973
$635$	−7.19577	−0.285555
$636$	1.53344	0.0608049
$637$	0.921372	0.0365061
$638$	29.7690	1.17856
$639$	−8.88214	−0.351372
$640$	7.29793	0.288476
$641$	−29.5122	−1.16566	−0.582832	−	0.812593i	$-0.698055\pi$
$641$	−29.5122	−1.16566	−0.582832	+	0.812593i	$0.698055\pi$
$642$	−23.4577	−0.925803
$643$	−11.8341	−0.466692	−0.233346	−	0.972394i	$-0.574967\pi$
$643$	−11.8341	−0.466692	−0.233346	+	0.972394i	$0.574967\pi$
$644$	0	0
$645$	0.320137	0.0126054
$646$	12.8620	0.506048
$647$	−9.06046	−0.356204	−0.178102	−	0.984012i	$-0.556996\pi$
$647$	−9.06046	−0.356204	−0.178102	+	0.984012i	$0.556996\pi$
$648$	−3.02354	−0.118776
$649$	38.6165	1.51583
$650$	−0.476153	−0.0186763
$651$	14.4063	0.564626
$652$	−0.125154	−0.00490139
$653$	26.9548	1.05482	0.527412	−	0.849610i	$-0.323162\pi$
$653$	26.9548	1.05482	0.527412	+	0.849610i	$0.323162\pi$
$654$	−5.80908	−0.227153
$655$	20.4094	0.797460
$656$	20.6450	0.806051
$657$	−7.35312	−0.286872
$658$	−14.9145	−0.581426
$659$	8.14940	0.317455	0.158728	−	0.987322i	$-0.449261\pi$
$659$	8.14940	0.317455	0.158728	+	0.987322i	$0.449261\pi$
$660$	−1.52780	−0.0594696
$661$	−46.0751	−1.79211	−0.896057	−	0.443938i	$-0.853581\pi$
$661$	−46.0751	−1.79211	−0.896057	+	0.443938i	$0.853581\pi$
$662$	13.3762	0.519880
$663$	1.09147	0.0423891
$664$	9.24575	0.358805
$665$	7.29336	0.282824
$666$	−4.88491	−0.189286
$667$	0	0
$668$	0.714817	0.0276571
$669$	3.11999	0.120626
$670$	7.38358	0.285252
$671$	−22.8728	−0.882995
$672$	−4.31646	−0.166511
$673$	24.4404	0.942109	0.471054	−	0.882104i	$-0.343874\pi$
$673$	24.4404	0.942109	0.471054	+	0.882104i	$0.343874\pi$
$674$	−23.7297	−0.914032
$675$	1.00000	0.0384900
$676$	4.67558	0.179830
$677$	−10.1332	−0.389450	−0.194725	−	0.980858i	$-0.562382\pi$
$677$	−10.1332	−0.389450	−0.194725	+	0.980858i	$0.562382\pi$
$678$	5.66077	0.217401
$679$	29.8203	1.14440
$680$	8.86612	0.340000
$681$	−29.5884	−1.13383
$682$	−36.4113	−1.39426
$683$	34.7201	1.32853	0.664264	−	0.747498i	$-0.268745\pi$
$683$	34.7201	1.32853	0.664264	+	0.747498i	$0.268745\pi$
$684$	1.24647	0.0476600
$685$	−1.18658	−0.0453369
$686$	25.7835	0.984417
$687$	−22.7779	−0.869031
$688$	−1.00548	−0.0383335
$689$	1.57006	0.0598144
$690$	0	0
$691$	35.2278	1.34013	0.670065	−	0.742302i	$-0.266266\pi$
$691$	35.2278	1.34013	0.670065	+	0.742302i	$0.266266\pi$
$692$	−7.28595	−0.276970
$693$	−8.93949	−0.339583
$694$	−36.2615	−1.37647
$695$	−23.2141	−0.880559
$696$	−16.7419	−0.634599
$697$	19.2751	0.730095
$698$	−39.9586	−1.51246
$699$	26.1911	0.990640
$700$	0.773279	0.0292272
$701$	35.0059	1.32216	0.661078	−	0.750318i	$-0.270099\pi$
$701$	35.0059	1.32216	0.661078	+	0.750318i	$0.270099\pi$
$702$	−0.476153	−0.0179712
$703$	13.0930	0.493812
$704$	37.3087	1.40613
$705$	5.48104	0.206428
$706$	−11.7181	−0.441018
$707$	−36.7308	−1.38141
$708$	−3.34038	−0.125539
$709$	16.0469	0.602653	0.301327	−	0.953521i	$-0.402571\pi$
$709$	16.0469	0.602653	0.301327	+	0.953521i	$0.402571\pi$
$710$	−11.3624	−0.426424
$711$	−15.5670	−0.583809
$712$	9.20913	0.345127
$713$	0	0
$714$	7.97926	0.298616
$715$	−1.56428	−0.0585008
$716$	7.18791	0.268625
$717$	29.3337	1.09549
$718$	−26.2533	−0.979764
$719$	−33.6268	−1.25407	−0.627033	−	0.778992i	$-0.715731\pi$
$719$	−33.6268	−1.25407	−0.627033	+	0.778992i	$0.715731\pi$
$720$	−3.14078	−0.117050
$721$	5.02589	0.187174
$722$	−9.26636	−0.344858
$723$	−1.95635	−0.0727576
$724$	1.98234	0.0736732
$725$	5.53718	0.205646
$726$	8.52251	0.316300
$727$	−29.2551	−1.08501	−0.542505	−	0.840052i	$-0.682524\pi$
$727$	−29.2551	−1.08501	−0.542505	+	0.840052i	$0.682524\pi$
$728$	−2.39386	−0.0887224
$729$	1.00000	0.0370370
$730$	−9.40643	−0.348148
$731$	−0.938760	−0.0347213
$732$	1.97853	0.0731286
$733$	41.6720	1.53919	0.769594	−	0.638533i	$-0.220458\pi$
$733$	41.6720	1.53919	0.769594	+	0.638533i	$0.220458\pi$
$734$	20.1450	0.743564
$735$	−2.47538	−0.0913058
$736$	0	0
$737$	24.2569	0.893514
$738$	−8.40874	−0.309530
$739$	41.2229	1.51641	0.758204	−	0.652017i	$-0.226077\pi$
$739$	41.2229	1.51641	0.758204	+	0.652017i	$0.226077\pi$
$740$	1.38819	0.0510308
$741$	1.27623	0.0468836
$742$	11.4780	0.421371
$743$	22.7946	0.836254	0.418127	−	0.908388i	$-0.362687\pi$
$743$	22.7946	0.836254	0.418127	+	0.908388i	$0.362687\pi$
$744$	20.4775	0.750740
$745$	−11.7479	−0.430409
$746$	39.8263	1.45815
$747$	−3.05792	−0.111884
$748$	4.48007	0.163808
$749$	39.0053	1.42522
$750$	1.27924	0.0467114
$751$	45.8322	1.67244	0.836220	−	0.548394i	$-0.184760\pi$
$751$	45.8322	1.67244	0.836220	+	0.548394i	$0.184760\pi$
$752$	−17.2147	−0.627756
$753$	13.0702	0.476303
$754$	−2.63654	−0.0960173
$755$	−2.97189	−0.108158
$756$	0.773279	0.0281239
$757$	42.2153	1.53434	0.767171	−	0.641442i	$-0.221664\pi$
$757$	42.2153	1.53434	0.767171	+	0.641442i	$0.221664\pi$
$758$	−21.9669	−0.797873
$759$	0	0
$760$	10.3670	0.376050
$761$	−20.1664	−0.731032	−0.365516	−	0.930805i	$-0.619107\pi$
$761$	−20.1664	−0.731032	−0.365516	+	0.930805i	$0.619107\pi$
$762$	−9.20515	−0.333467
$763$	9.65929	0.349690
$764$	7.61606	0.275539
$765$	−2.93237	−0.106020
$766$	32.4536	1.17260
$767$	−3.42014	−0.123494
$768$	−8.41909	−0.303798
$769$	−35.5281	−1.28118	−0.640589	−	0.767884i	$-0.721310\pi$
$769$	−35.5281	−1.28118	−0.640589	+	0.767884i	$0.721310\pi$
$770$	−11.4358	−0.412117
$771$	11.1770	0.402529
$772$	−5.19655	−0.187028
$773$	3.56006	0.128047	0.0640233	−	0.997948i	$-0.479607\pi$
$773$	3.56006	0.128047	0.0640233	+	0.997948i	$0.479607\pi$
$774$	0.409534	0.0147204
$775$	−6.77268	−0.243282
$776$	42.3874	1.52162
$777$	8.12258	0.291396
$778$	22.4988	0.806622
$779$	22.5379	0.807505
$780$	0.135312	0.00484496
$781$	−37.3284	−1.33571
$782$	0	0
$783$	5.53718	0.197883
$784$	7.77462	0.277665
$785$	12.2840	0.438435
$786$	26.1086	0.931261
$787$	−25.7488	−0.917845	−0.458922	−	0.888476i	$-0.651764\pi$
$787$	−25.7488	−0.917845	−0.458922	+	0.888476i	$0.651764\pi$
$788$	−0.0278073	−0.000990595 0
$789$	22.8052	0.811887
$790$	−19.9140	−0.708510
$791$	−9.41268	−0.334676
$792$	−12.7068	−0.451517
$793$	2.02577	0.0719373
$794$	−22.5588	−0.800583
$795$	−4.21815	−0.149602
$796$	4.19565	0.148711
$797$	38.5221	1.36452	0.682262	−	0.731108i	$-0.260996\pi$
$797$	38.5221	1.36452	0.682262	+	0.731108i	$0.260996\pi$
$798$	9.32999	0.330278
$799$	−16.0724	−0.568601
$800$	2.02926	0.0717450
$801$	−3.04581	−0.107618
$802$	2.41727	0.0853569
$803$	−30.9025	−1.09052
$804$	−2.09825	−0.0739997
$805$	0	0
$806$	3.22483	0.113590
$807$	6.91948	0.243577
$808$	−52.2102	−1.83675
$809$	−27.9320	−0.982037	−0.491019	−	0.871149i	$-0.663375\pi$
$809$	−27.9320	−0.982037	−0.491019	+	0.871149i	$0.663375\pi$
$810$	1.27924	0.0449481
$811$	27.4764	0.964829	0.482414	−	0.875943i	$-0.339760\pi$
$811$	27.4764	0.964829	0.482414	+	0.875943i	$0.339760\pi$
$812$	4.28178	0.150261
$813$	−1.99678	−0.0700302
$814$	−20.5295	−0.719558
$815$	0.344269	0.0120592
$816$	9.20990	0.322411
$817$	−1.09767	−0.0384027
$818$	−38.3499	−1.34087
$819$	0.791742	0.0276657
$820$	2.38958	0.0834479
$821$	17.7217	0.618490	0.309245	−	0.950982i	$-0.399924\pi$
$821$	17.7217	0.618490	0.309245	+	0.950982i	$0.399924\pi$
$822$	−1.51793	−0.0529438
$823$	−2.24622	−0.0782982	−0.0391491	−	0.999233i	$-0.512465\pi$
$823$	−2.24622	−0.0782982	−0.0391491	+	0.999233i	$0.512465\pi$
$824$	7.14393	0.248871
$825$	4.20264	0.146317
$826$	−25.0032	−0.869973
$827$	−19.0491	−0.662401	−0.331200	−	0.943560i	$-0.607454\pi$
$827$	−19.0491	−0.662401	−0.331200	+	0.943560i	$0.607454\pi$
$828$	0	0
$829$	−30.8723	−1.07224	−0.536120	−	0.844142i	$-0.680111\pi$
$829$	−30.8723	−1.07224	−0.536120	+	0.844142i	$0.680111\pi$
$830$	−3.91183	−0.135782
$831$	−14.3870	−0.499079
$832$	−3.30432	−0.114557
$833$	7.25872	0.251500
$834$	−29.6964	−1.02830
$835$	−1.96630	−0.0680467
$836$	5.23846	0.181176
$837$	−6.77268	−0.234098
$838$	−6.04521	−0.208828
$839$	10.5225	0.363278	0.181639	−	0.983365i	$-0.441860\pi$
$839$	10.5225	0.363278	0.181639	+	0.983365i	$0.441860\pi$
$840$	6.43141	0.221905
$841$	1.66036	0.0572538
$842$	−39.1307	−1.34853
$843$	13.9580	0.480741
$844$	−4.14018	−0.142511
$845$	−12.8615	−0.442448
$846$	7.01159	0.241063
$847$	−14.1712	−0.486926
$848$	13.2483	0.454948
$849$	20.3377	0.697989
$850$	−3.75121	−0.128666
$851$	0	0
$852$	3.22896	0.110622
$853$	−37.0326	−1.26797	−0.633987	−	0.773344i	$-0.718583\pi$
$853$	−37.0326	−1.26797	−0.633987	+	0.773344i	$0.718583\pi$
$854$	14.8096	0.506773
$855$	−3.42876	−0.117261
$856$	55.4431	1.89501
$857$	−1.51604	−0.0517870	−0.0258935	−	0.999665i	$-0.508243\pi$
$857$	−1.51604	−0.0517870	−0.0258935	+	0.999665i	$0.508243\pi$
$858$	−2.00110	−0.0683163
$859$	28.8212	0.983367	0.491684	−	0.870774i	$-0.336382\pi$
$859$	28.8212	0.983367	0.491684	+	0.870774i	$0.336382\pi$
$860$	−0.116381	−0.00396855
$861$	13.9820	0.476504
$862$	−11.8534	−0.403729
$863$	−4.71058	−0.160350	−0.0801749	−	0.996781i	$-0.525548\pi$
$863$	−4.71058	−0.160350	−0.0801749	+	0.996781i	$0.525548\pi$
$864$	2.02926	0.0690367
$865$	20.0420	0.681449
$866$	−26.0009	−0.883547
$867$	−8.40123	−0.285321
$868$	−5.23717	−0.177761
$869$	−65.4226	−2.21931
$870$	7.08341	0.240150
$871$	−2.14836	−0.0727942
$872$	13.7300	0.464955
$873$	−14.0191	−0.474476
$874$	0	0
$875$	−2.12712	−0.0719096
$876$	2.67311	0.0903159
$877$	11.0109	0.371813	0.185906	−	0.982567i	$-0.440478\pi$
$877$	11.0109	0.371813	0.185906	+	0.982567i	$0.440478\pi$
$878$	35.1139	1.18504
$879$	−5.30776	−0.179026
$880$	−13.1995	−0.444956
$881$	13.5584	0.456794	0.228397	−	0.973568i	$-0.426652\pi$
$881$	13.5584	0.456794	0.228397	+	0.973568i	$0.426652\pi$
$882$	−3.16662	−0.106626
$883$	−29.9726	−1.00866	−0.504329	−	0.863511i	$-0.668260\pi$
$883$	−29.9726	−1.00866	−0.504329	+	0.863511i	$0.668260\pi$
$884$	−0.396786	−0.0133453
$885$	9.18864	0.308873
$886$	−12.4454	−0.418111
$887$	41.4447	1.39158	0.695788	−	0.718247i	$-0.255055\pi$
$887$	41.4447	1.39158	0.695788	+	0.718247i	$0.255055\pi$
$888$	11.5456	0.387447
$889$	15.3062	0.513355
$890$	−3.89634	−0.130606
$891$	4.20264	0.140794
$892$	−1.13422	−0.0379766
$893$	−18.7932	−0.628889
$894$	−15.0284	−0.502625
$895$	−19.7723	−0.660916
$896$	−15.5235	−0.518605
$897$	0	0
$898$	23.0946	0.770677
$899$	−37.5015	−1.25075
$900$	−0.363534	−0.0121178
$901$	12.3692	0.412077
$902$	−35.3389	−1.17666
$903$	−0.680969	−0.0226612
$904$	−13.3794	−0.444993
$905$	−5.45298	−0.181263
$906$	−3.80178	−0.126306
$907$	17.1748	0.570281	0.285141	−	0.958486i	$-0.407960\pi$
$907$	17.1748	0.570281	0.285141	+	0.958486i	$0.407960\pi$
$908$	10.7564	0.356964
$909$	17.2679	0.572741
$910$	1.01283	0.0335751
$911$	−15.6732	−0.519276	−0.259638	−	0.965706i	$-0.583603\pi$
$911$	−15.6732	−0.519276	−0.259638	+	0.965706i	$0.583603\pi$
$912$	10.7690	0.356596
$913$	−12.8513	−0.425317
$914$	46.6842	1.54418
$915$	−5.44249	−0.179923
$916$	8.28054	0.273597
$917$	−43.4131	−1.43363
$918$	−3.75121	−0.123808
$919$	26.9845	0.890137	0.445069	−	0.895496i	$-0.353179\pi$
$919$	26.9845	0.890137	0.445069	+	0.895496i	$0.353179\pi$
$920$	0	0
$921$	−26.0861	−0.859566
$922$	−23.9883	−0.790013
$923$	3.30606	0.108820
$924$	3.24981	0.106911
$925$	−3.81859	−0.125554
$926$	−0.748599	−0.0246005
$927$	−2.36277	−0.0776037
$928$	11.2364	0.368851
$929$	−17.9200	−0.587935	−0.293967	−	0.955815i	$-0.594976\pi$
$929$	−17.9200	−0.587935	−0.293967	+	0.955815i	$0.594976\pi$
$930$	−8.66391	−0.284101
$931$	8.48748	0.278166
$932$	−9.52137	−0.311883
$933$	−5.39851	−0.176739
$934$	36.5552	1.19612
$935$	−12.3237	−0.403027
$936$	1.12540	0.0367850
$937$	−32.7771	−1.07078	−0.535390	−	0.844605i	$-0.679835\pi$
$937$	−32.7771	−1.07078	−0.535390	+	0.844605i	$0.679835\pi$
$938$	−15.7057	−0.512810
$939$	−25.1315	−0.820135
$940$	−1.99254	−0.0649896
$941$	−21.6772	−0.706655	−0.353328	−	0.935500i	$-0.614950\pi$
$941$	−21.6772	−0.706655	−0.353328	+	0.935500i	$0.614950\pi$
$942$	15.7142	0.511998
$943$	0	0
$944$	−28.8595	−0.939296
$945$	−2.12712	−0.0691951
$946$	1.72112	0.0559585
$947$	40.4802	1.31543	0.657715	−	0.753267i	$-0.271523\pi$
$947$	40.4802	1.31543	0.657715	+	0.753267i	$0.271523\pi$
$948$	5.65915	0.183800
$949$	2.73693	0.0888446
$950$	−4.38622	−0.142308
$951$	13.6791	0.443577
$952$	−18.8593	−0.611232
$953$	−2.70808	−0.0877234	−0.0438617	−	0.999038i	$-0.513966\pi$
$953$	−2.70808	−0.0877234	−0.0438617	+	0.999038i	$0.513966\pi$
$954$	−5.39605	−0.174704
$955$	−20.9501	−0.677928
$956$	−10.6638	−0.344891
$957$	23.2707	0.752236
$958$	9.47380	0.306085
$959$	2.52399	0.0815040
$960$	8.87746	0.286519
$961$	14.8692	0.479651
$962$	1.81823	0.0586222
$963$	−18.3372	−0.590907
$964$	0.711201	0.0229062
$965$	14.2945	0.460157
$966$	0	0
$967$	24.5955	0.790939	0.395470	−	0.918479i	$-0.370582\pi$
$967$	24.5955	0.790939	0.395470	+	0.918479i	$0.370582\pi$
$968$	−20.1432	−0.647428
$969$	10.0544	0.322993
$970$	−17.9339	−0.575823
$971$	−33.0267	−1.05988	−0.529938	−	0.848036i	$-0.677785\pi$
$971$	−33.0267	−1.05988	−0.529938	+	0.848036i	$0.677785\pi$
$972$	−0.363534	−0.0116604
$973$	49.3790	1.58302
$974$	42.4699	1.36082
$975$	−0.372214	−0.0119204
$976$	17.0936	0.547154
$977$	55.2511	1.76764	0.883819	−	0.467829i	$-0.154964\pi$
$977$	55.2511	1.76764	0.883819	+	0.467829i	$0.154964\pi$
$978$	0.440405	0.0140826
$979$	−12.8004	−0.409104
$980$	0.899885	0.0287458
$981$	−4.54103	−0.144984
$982$	2.39454	0.0764128
$983$	61.6295	1.96568	0.982838	−	0.184473i	$-0.0590579\pi$
$983$	61.6295	1.96568	0.982838	+	0.184473i	$0.0590579\pi$
$984$	19.8743	0.633571
$985$	0.0764917	0.00243723
$986$	−20.7711	−0.661488
$987$	−11.6588	−0.371104
$988$	−0.463954	−0.0147603
$989$	0	0
$990$	5.37620	0.170867
$991$	34.5356	1.09706	0.548530	−	0.836131i	$-0.315188\pi$
$991$	34.5356	1.09706	0.548530	+	0.836131i	$0.315188\pi$
$992$	−13.7435	−0.436357
$993$	10.4563	0.331821
$994$	24.1692	0.766600
$995$	−11.5413	−0.365883
$996$	1.11166	0.0352243
$997$	−42.2748	−1.33886	−0.669429	−	0.742876i	$-0.733461\pi$
$997$	−42.2748	−1.33886	−0.669429	+	0.742876i	$0.733461\pi$
$998$	−47.9582	−1.51809
$999$	−3.81859	−0.120815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bm.1.9	yes	12
23.22	odd	2		7935.2.a.bl.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.9	✓	12	23.22	odd	2
7935.2.a.bm.1.9	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+1.27924 q^{2} +1.00000 q^{3} -0.363534 q^{4} +1.00000 q^{5} +1.27924 q^{6} -2.12712 q^{7} -3.02354 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.27924 q^{2} +1.00000 q^{3} -0.363534 q^{4} +1.00000 q^{5} +1.27924 q^{6} -2.12712 q^{7} -3.02354 q^{8} +1.00000 q^{9} +1.27924 q^{10} +4.20264 q^{11} -0.363534 q^{12} -0.372214 q^{13} -2.72110 q^{14} +1.00000 q^{15} -3.14078 q^{16} -2.93237 q^{17} +1.27924 q^{18} -3.42876 q^{19} -0.363534 q^{20} -2.12712 q^{21} +5.37620 q^{22} -3.02354 q^{24} +1.00000 q^{25} -0.476153 q^{26} +1.00000 q^{27} +0.773279 q^{28} +5.53718 q^{29} +1.27924 q^{30} -6.77268 q^{31} +2.02926 q^{32} +4.20264 q^{33} -3.75121 q^{34} -2.12712 q^{35} -0.363534 q^{36} -3.81859 q^{37} -4.38622 q^{38} -0.372214 q^{39} -3.02354 q^{40} -6.57321 q^{41} -2.72110 q^{42} +0.320137 q^{43} -1.52780 q^{44} +1.00000 q^{45} +5.48104 q^{47} -3.14078 q^{48} -2.47538 q^{49} +1.27924 q^{50} -2.93237 q^{51} +0.135312 q^{52} -4.21815 q^{53} +1.27924 q^{54} +4.20264 q^{55} +6.43141 q^{56} -3.42876 q^{57} +7.08341 q^{58} +9.18864 q^{59} -0.363534 q^{60} -5.44249 q^{61} -8.66391 q^{62} -2.12712 q^{63} +8.87746 q^{64} -0.372214 q^{65} +5.37620 q^{66} +5.77183 q^{67} +1.06601 q^{68} -2.72110 q^{70} -8.88214 q^{71} -3.02354 q^{72} -7.35312 q^{73} -4.88491 q^{74} +1.00000 q^{75} +1.24647 q^{76} -8.93949 q^{77} -0.476153 q^{78} -15.5670 q^{79} -3.14078 q^{80} +1.00000 q^{81} -8.40874 q^{82} -3.05792 q^{83} +0.773279 q^{84} -2.93237 q^{85} +0.409534 q^{86} +5.53718 q^{87} -12.7068 q^{88} -3.04581 q^{89} +1.27924 q^{90} +0.791742 q^{91} -6.77268 q^{93} +7.01159 q^{94} -3.42876 q^{95} +2.02926 q^{96} -14.0191 q^{97} -3.16662 q^{98} +4.20264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * q^99

Introduction

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