LMFDB - Embedded newform 7935.2.a.bl.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:	$0$
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	$-0.368320\pi$
$7$	2.12712	0.803974	0.401987	+	0.915645i	$0.368320\pi$
$8$	−3.02354	−1.06898
$9$	1.00000	0.333333
$10$	−1.27924	−0.404533
$11$	−4.20264	−1.26714	−0.633571	−	0.773684i	$-0.718412\pi$
$11$	−4.20264	−1.26714	−0.633571	+	0.773684i	$0.718412\pi$
$12$	−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	$-0.384276\pi$
$17$	2.93237	0.711203	0.355602	+	0.934638i	$0.384276\pi$
$18$	1.27924	0.301521
$19$	3.42876	0.786611	0.393305	−	0.919408i	$-0.371331\pi$
$19$	3.42876	0.786611	0.393305	+	0.919408i	$0.371331\pi$
$20$	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	$-0.398369\pi$
$37$	3.81859	0.627772	0.313886	+	0.949461i	$0.398369\pi$
$38$	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	$-0.507771\pi$
$43$	−0.320137	−0.0488205	−0.0244102	+	0.999702i	$0.507771\pi$
$44$	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	$-0.406443\pi$
$53$	4.21815	0.579408	0.289704	+	0.957116i	$0.406443\pi$
$54$	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	$-0.386718\pi$
$61$	5.44249	0.696840	0.348420	+	0.937339i	$0.386718\pi$
$62$	−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	$-0.614692\pi$
$67$	−5.77183	−0.705141	−0.352570	+	0.935785i	$0.614692\pi$
$68$	−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	$-0.160391\pi$
$79$	15.5670	1.75143	0.875714	+	0.482830i	$0.160391\pi$
$80$	3.14078	0.351149
$81$	1.00000	0.111111
$82$	−8.40874	−0.928590
$83$	3.05792	0.335651	0.167825	−	0.985817i	$-0.446326\pi$
$83$	3.05792	0.335651	0.167825	+	0.985817i	$0.446326\pi$
$84$	−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	$-0.448390\pi$
$89$	3.04581	0.322855	0.161428	+	0.986885i	$0.448390\pi$
$90$	−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	$-0.247919\pi$
$97$	14.0191	1.42343	0.711714	+	0.702470i	$0.247919\pi$
$98$	−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	$-0.462863\pi$
$103$	2.36277	0.232811	0.116405	+	0.993202i	$0.462863\pi$
$104$	1.12540	0.110355
$105$	−2.12712	−0.207585
$106$	5.39605	0.524111
$107$	18.3372	1.77272	0.886361	−	0.462995i	$-0.153225\pi$
$107$	18.3372	1.77272	0.886361	+	0.462995i	$0.153225\pi$
$108$	−0.363534	−0.0349811
$109$	4.54103	0.434952	0.217476	−	0.976066i	$-0.430218\pi$
$109$	4.54103	0.434952	0.217476	+	0.976066i	$0.430218\pi$
$110$	5.37620	0.512600
$111$	3.81859	0.362444
$112$	−6.68079	−0.631275
$113$	−4.42509	−0.416278	−0.208139	−	0.978099i	$-0.566741\pi$
$113$	−4.42509	−0.416278	−0.208139	+	0.978099i	$0.566741\pi$
$114$	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	$-0.483859\pi$
$137$	1.18658	0.101376	0.0506882	+	0.998715i	$0.483859\pi$
$138$	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	$-0.340197\pi$
$149$	11.7479	0.962423	0.481212	+	0.876604i	$0.340197\pi$
$150$	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	$-0.663071\pi$
$157$	−12.2840	−0.980371	−0.490185	+	0.871618i	$0.663071\pi$
$158$	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	$-0.435042\pi$
$181$	5.45298	0.405317	0.202658	+	0.979249i	$0.435042\pi$
$182$	−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	$-0.226203\pi$
$191$	20.9501	1.51589	0.757946	+	0.652317i	$0.226203\pi$
$192$	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	$-0.365853\pi$
$199$	11.5413	0.818139	0.409070	+	0.912503i	$0.365853\pi$
$200$	−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	$-0.0606100\pi$
$227$	29.5884	1.96385	0.981926	+	0.189263i	$0.0606100\pi$
$228$	−1.24647	−0.0825495
$229$	22.7779	1.50521	0.752603	−	0.658474i	$-0.228798\pi$
$229$	22.7779	1.50521	0.752603	+	0.658474i	$0.228798\pi$
$230$	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	$-0.479930\pi$
$241$	1.95635	0.126020	0.0630099	+	0.998013i	$0.479930\pi$
$242$	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	$-0.635341\pi$
$251$	−13.0702	−0.824982	−0.412491	+	0.910962i	$0.635341\pi$
$252$	−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	$-0.748208\pi$
$263$	−22.8052	−1.40623	−0.703115	+	0.711076i	$0.748208\pi$
$264$	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	$-0.636685\pi$
$281$	−13.9580	−0.832667	−0.416334	+	0.909212i	$0.636685\pi$
$282$	7.01159	0.417534
$283$	−20.3377	−1.20895	−0.604476	−	0.796623i	$-0.706618\pi$
$283$	−20.3377	−1.20895	−0.604476	+	0.796623i	$0.706618\pi$
$284$	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	$-0.450449\pi$
$293$	5.30776	0.310083	0.155041	+	0.987908i	$0.450449\pi$
$294$	−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	$-0.248578\pi$
$313$	25.1315	1.42052	0.710258	+	0.703942i	$0.248578\pi$
$314$	−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	$-0.331406\pi$
$337$	18.5498	1.01047	0.505235	+	0.862982i	$0.331406\pi$
$338$	−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	$-0.317831\pi$
$359$	20.5225	1.08314	0.541568	+	0.840657i	$0.317831\pi$
$360$	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	$-0.634823\pi$
$367$	−15.7476	−0.822016	−0.411008	+	0.911632i	$0.634823\pi$
$368$	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	$-0.798369\pi$
$373$	−31.1327	−1.61199	−0.805995	+	0.591923i	$0.798369\pi$
$374$	−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	$-0.354614\pi$
$379$	17.1718	0.882054	0.441027	+	0.897494i	$0.354614\pi$
$380$	1.24647	0.0639425
$381$	−7.19577	−0.368651
$382$	26.8002	1.37122
$383$	−25.3693	−1.29631	−0.648156	−	0.761507i	$-0.724460\pi$
$383$	−25.3693	−1.29631	−0.648156	+	0.761507i	$0.724460\pi$
$384$	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	$-0.647103\pi$
$389$	−17.5876	−0.891726	−0.445863	+	0.895101i	$0.647103\pi$
$390$	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	$-0.515024\pi$
$401$	−1.88961	−0.0943627	−0.0471813	+	0.998886i	$0.515024\pi$
$402$	−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	$-0.463175\pi$
$419$	4.72561	0.230861	0.115430	+	0.993316i	$0.463175\pi$
$420$	0.773279	0.0377321
$421$	30.5889	1.49081	0.745406	−	0.666610i	$-0.232255\pi$
$421$	30.5889	1.49081	0.745406	+	0.666610i	$0.232255\pi$
$422$	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	$-0.428362\pi$
$431$	9.26596	0.446326	0.223163	+	0.974781i	$0.428362\pi$
$432$	−3.14078	−0.151111
$433$	20.3252	0.976768	0.488384	−	0.872629i	$-0.337587\pi$
$433$	20.3252	0.976768	0.488384	+	0.872629i	$0.337587\pi$
$434$	−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	$-0.825554\pi$
$457$	−36.4936	−1.70710	−0.853549	+	0.521013i	$0.825554\pi$
$458$	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	$-0.729936\pi$
$467$	−28.5756	−1.32232	−0.661160	+	0.750245i	$0.729936\pi$
$468$	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	$-0.554115\pi$
$479$	−7.40578	−0.338379	−0.169189	+	0.985584i	$0.554115\pi$
$480$	−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	$-0.801600\pi$
$503$	−36.4208	−1.62392	−0.811962	+	0.583710i	$0.801600\pi$
$504$	−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	$-0.493441\pi$
$521$	0.940584	0.0412077	0.0206039	+	0.999788i	$0.493441\pi$
$522$	7.08341	0.310032
$523$	18.7666	0.820604	0.410302	−	0.911950i	$-0.365423\pi$
$523$	18.7666	0.820604	0.410302	+	0.911950i	$0.365423\pi$
$524$	−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	$-0.532194\pi$
$557$	−4.76591	−0.201938	−0.100969	+	0.994890i	$0.532194\pi$
$558$	−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	$-0.569653\pi$
$563$	−10.3016	−0.434159	−0.217080	+	0.976154i	$0.569653\pi$
$564$	−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	$-0.528966\pi$
$569$	−4.33529	−0.181745	−0.0908724	+	0.995863i	$0.528966\pi$
$570$	−4.38622	−0.183718
$571$	−35.6108	−1.49027	−0.745133	−	0.666916i	$-0.767614\pi$
$571$	−35.6108	−1.49027	−0.745133	+	0.666916i	$0.767614\pi$
$572$	−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	$-0.496933\pi$
$613$	0.477169	0.0192727	0.00963633	+	0.999954i	$0.496933\pi$
$614$	−33.3705	−1.34672
$615$	6.57321	0.265057
$616$	27.0289	1.08902
$617$	27.1717	1.09389	0.546945	−	0.837169i	$-0.315791\pi$
$617$	27.1717	1.09389	0.546945	+	0.837169i	$0.315791\pi$
$618$	3.02256	0.121585
$619$	−35.8843	−1.44231	−0.721157	−	0.692772i	$-0.756389\pi$
$619$	−35.8843	−1.44231	−0.721157	+	0.692772i	$0.756389\pi$
$620$	−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	$-0.293976\pi$
$631$	30.2939	1.20598	0.602990	+	0.797749i	$0.293976\pi$
$632$	−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	$-0.301945\pi$
$641$	29.5122	1.16566	0.582832	+	0.812593i	$0.301945\pi$
$642$	23.4577	0.925803
$643$	11.8341	0.466692	0.233346	−	0.972394i	$-0.425033\pi$
$643$	11.8341	0.466692	0.233346	+	0.972394i	$0.425033\pi$
$644$	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	$-0.550739\pi$
$659$	−8.14940	−0.317455	−0.158728	+	0.987322i	$0.550739\pi$
$660$	−1.52780	−0.0594696
$661$	46.0751	1.79211	0.896057	−	0.443938i	$-0.146419\pi$
$661$	46.0751	1.79211	0.896057	+	0.443938i	$0.146419\pi$
$662$	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	$-0.437618\pi$
$677$	10.1332	0.389450	0.194725	+	0.980858i	$0.437618\pi$
$678$	−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	$-0.729901\pi$
$701$	−35.0059	−1.32216	−0.661078	+	0.750318i	$0.729901\pi$
$702$	−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	$-0.597429\pi$
$709$	−16.0469	−0.602653	−0.301327	+	0.953521i	$0.597429\pi$
$710$	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	$-0.317476\pi$
$727$	29.2551	1.08501	0.542505	+	0.840052i	$0.317476\pi$
$728$	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	$-0.779542\pi$
$733$	−41.6720	−1.53919	−0.769594	+	0.638533i	$0.779542\pi$
$734$	−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	$-0.637313\pi$
$743$	−22.7946	−0.836254	−0.418127	+	0.908388i	$0.637313\pi$
$744$	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	$-0.815240\pi$
$751$	−45.8322	−1.67244	−0.836220	+	0.548394i	$0.815240\pi$
$752$	−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	$-0.778336\pi$
$757$	−42.2153	−1.53434	−0.767171	+	0.641442i	$0.778336\pi$
$758$	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	$-0.278690\pi$
$769$	35.5281	1.28118	0.640589	+	0.767884i	$0.278690\pi$
$770$	11.4358	0.412117
$771$	11.1770	0.402529
$772$	−5.19655	−0.187028
$773$	−3.56006	−0.128047	−0.0640233	−	0.997948i	$-0.520393\pi$
$773$	−3.56006	−0.128047	−0.0640233	+	0.997948i	$0.520393\pi$
$774$	−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	$-0.348236\pi$
$787$	25.7488	0.917845	0.458922	+	0.888476i	$0.348236\pi$
$788$	−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	$-0.739004\pi$
$797$	−38.5221	−1.36452	−0.682262	+	0.731108i	$0.739004\pi$
$798$	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	$-0.392546\pi$
$827$	19.0491	0.662401	0.331200	+	0.943560i	$0.392546\pi$
$828$	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	$-0.558140\pi$
$839$	−10.5225	−0.363278	−0.181639	+	0.983365i	$0.558140\pi$
$840$	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	$-0.573348\pi$
$881$	−13.5584	−0.456794	−0.228397	+	0.973568i	$0.573348\pi$
$882$	−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	$-0.592040\pi$
$907$	−17.1748	−0.570281	−0.285141	+	0.958486i	$0.592040\pi$
$908$	−10.7564	−0.356964
$909$	17.2679	0.572741
$910$	1.01283	0.0335751
$911$	15.6732	0.519276	0.259638	−	0.965706i	$-0.416397\pi$
$911$	15.6732	0.519276	0.259638	+	0.965706i	$0.416397\pi$
$912$	−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	$-0.646821\pi$
$919$	−26.9845	−0.890137	−0.445069	+	0.895496i	$0.646821\pi$
$920$	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	$-0.320165\pi$
$937$	32.7771	1.07078	0.535390	+	0.844605i	$0.320165\pi$
$938$	−15.7057	−0.512810
$939$	25.1315	0.820135
$940$	1.99254	0.0649896
$941$	21.6772	0.706655	0.353328	−	0.935500i	$-0.385050\pi$
$941$	21.6772	0.706655	0.353328	+	0.935500i	$0.385050\pi$
$942$	−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	$-0.486034\pi$
$953$	2.70808	0.0877234	0.0438617	+	0.999038i	$0.486034\pi$
$954$	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	$-0.322215\pi$
$971$	33.0267	1.05988	0.529938	+	0.848036i	$0.322215\pi$
$972$	−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	$-0.845036\pi$
$977$	−55.2511	−1.76764	−0.883819	+	0.467829i	$0.845036\pi$
$978$	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	$-0.940942\pi$
$983$	−61.6295	−1.96568	−0.982838	+	0.184473i	$0.940942\pi$
$984$	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.bl.1.9	✓	12
23.22	odd	2		7935.2.a.bm.1.9	yes	12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more