LMFDB - Embedded newform 722.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 7 $ x^2 - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.64575$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.64575 q^{3} +1.00000 q^{4} -1.64575 q^{5} +2.64575 q^{6} +3.64575 q^{7} +1.00000 q^{8} +4.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.64575 q^{3} +1.00000 q^{4} -1.64575 q^{5} +2.64575 q^{6} +3.64575 q^{7} +1.00000 q^{8} +4.00000 q^{9} -1.64575 q^{10} -4.64575 q^{11} +2.64575 q^{12} +2.00000 q^{13} +3.64575 q^{14} -4.35425 q^{15} +1.00000 q^{16} +4.00000 q^{18} -1.64575 q^{20} +9.64575 q^{21} -4.64575 q^{22} -1.64575 q^{23} +2.64575 q^{24} -2.29150 q^{25} +2.00000 q^{26} +2.64575 q^{27} +3.64575 q^{28} +1.64575 q^{29} -4.35425 q^{30} -5.64575 q^{31} +1.00000 q^{32} -12.2915 q^{33} -6.00000 q^{35} +4.00000 q^{36} +0.354249 q^{37} +5.29150 q^{39} -1.64575 q^{40} -0.291503 q^{41} +9.64575 q^{42} +11.2915 q^{43} -4.64575 q^{44} -6.58301 q^{45} -1.64575 q^{46} +4.35425 q^{47} +2.64575 q^{48} +6.29150 q^{49} -2.29150 q^{50} +2.00000 q^{52} -12.5830 q^{53} +2.64575 q^{54} +7.64575 q^{55} +3.64575 q^{56} +1.64575 q^{58} -7.93725 q^{59} -4.35425 q^{60} +0.937254 q^{61} -5.64575 q^{62} +14.5830 q^{63} +1.00000 q^{64} -3.29150 q^{65} -12.2915 q^{66} +0.645751 q^{67} -4.35425 q^{69} -6.00000 q^{70} -2.70850 q^{71} +4.00000 q^{72} +1.70850 q^{73} +0.354249 q^{74} -6.06275 q^{75} -16.9373 q^{77} +5.29150 q^{78} -4.00000 q^{79} -1.64575 q^{80} -5.00000 q^{81} -0.291503 q^{82} +7.93725 q^{83} +9.64575 q^{84} +11.2915 q^{86} +4.35425 q^{87} -4.64575 q^{88} -6.58301 q^{90} +7.29150 q^{91} -1.64575 q^{92} -14.9373 q^{93} +4.35425 q^{94} +2.64575 q^{96} -3.70850 q^{97} +6.29150 q^{98} -18.5830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 + 8 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{13} + 2 q^{14} - 14 q^{15} + 2 q^{16} + 8 q^{18} + 2 q^{20} + 14 q^{21} - 4 q^{22} + 2 q^{23} + 6 q^{25} + 4 q^{26} + 2 q^{28} - 2 q^{29} - 14 q^{30} - 6 q^{31} + 2 q^{32} - 14 q^{33} - 12 q^{35} + 8 q^{36} + 6 q^{37} + 2 q^{40} + 10 q^{41} + 14 q^{42} + 12 q^{43} - 4 q^{44} + 8 q^{45} + 2 q^{46} + 14 q^{47} + 2 q^{49} + 6 q^{50} + 4 q^{52} - 4 q^{53} + 10 q^{55} + 2 q^{56} - 2 q^{58} - 14 q^{60} - 14 q^{61} - 6 q^{62} + 8 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{66} - 4 q^{67} - 14 q^{69} - 12 q^{70} - 16 q^{71} + 8 q^{72} + 14 q^{73} + 6 q^{74} - 28 q^{75} - 18 q^{77} - 8 q^{79} + 2 q^{80} - 10 q^{81} + 10 q^{82} + 14 q^{84} + 12 q^{86} + 14 q^{87} - 4 q^{88} + 8 q^{90} + 4 q^{91} + 2 q^{92} - 14 q^{93} + 14 q^{94} - 18 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^13 + 2 * q^14 - 14 * q^15 + 2 * q^16 + 8 * q^18 + 2 * q^20 + 14 * q^21 - 4 * q^22 + 2 * q^23 + 6 * q^25 + 4 * q^26 + 2 * q^28 - 2 * q^29 - 14 * q^30 - 6 * q^31 + 2 * q^32 - 14 * q^33 - 12 * q^35 + 8 * q^36 + 6 * q^37 + 2 * q^40 + 10 * q^41 + 14 * q^42 + 12 * q^43 - 4 * q^44 + 8 * q^45 + 2 * q^46 + 14 * q^47 + 2 * q^49 + 6 * q^50 + 4 * q^52 - 4 * q^53 + 10 * q^55 + 2 * q^56 - 2 * q^58 - 14 * q^60 - 14 * q^61 - 6 * q^62 + 8 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^66 - 4 * q^67 - 14 * q^69 - 12 * q^70 - 16 * q^71 + 8 * q^72 + 14 * q^73 + 6 * q^74 - 28 * q^75 - 18 * q^77 - 8 * q^79 + 2 * q^80 - 10 * q^81 + 10 * q^82 + 14 * q^84 + 12 * q^86 + 14 * q^87 - 4 * q^88 + 8 * q^90 + 4 * q^91 + 2 * q^92 - 14 * q^93 + 14 * q^94 - 18 * q^97 + 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.64575	1.52753	0.763763	−	0.645497i	$-0.223350\pi$
$3$	2.64575	1.52753	0.763763	+	0.645497i	$0.223350\pi$
$4$	1.00000	0.500000
$5$	−1.64575	−0.736002	−0.368001	−	0.929825i	$-0.619958\pi$
$5$	−1.64575	−0.736002	−0.368001	+	0.929825i	$0.619958\pi$
$6$	2.64575	1.08012
$7$	3.64575	1.37796	0.688982	−	0.724778i	$-0.258058\pi$
$7$	3.64575	1.37796	0.688982	+	0.724778i	$0.258058\pi$
$8$	1.00000	0.353553
$9$	4.00000	1.33333
$10$	−1.64575	−0.520432
$11$	−4.64575	−1.40075	−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575	−1.40075	−0.700373	+	0.713777i	$0.746983\pi$
$12$	2.64575	0.763763
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	3.64575	0.974368
$15$	−4.35425	−1.12426
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	4.00000	0.942809
$19$	0	0
$19$	0	0
$20$	−1.64575	−0.368001
$21$	9.64575	2.10488
$22$	−4.64575	−0.990478
$23$	−1.64575	−0.343163	−0.171581	−	0.985170i	$-0.554888\pi$
$23$	−1.64575	−0.343163	−0.171581	+	0.985170i	$0.554888\pi$
$24$	2.64575	0.540062
$25$	−2.29150	−0.458301
$26$	2.00000	0.392232
$27$	2.64575	0.509175
$28$	3.64575	0.688982
$29$	1.64575	0.305608	0.152804	−	0.988256i	$-0.451170\pi$
$29$	1.64575	0.305608	0.152804	+	0.988256i	$0.451170\pi$
$30$	−4.35425	−0.794973
$31$	−5.64575	−1.01401	−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575	−1.01401	−0.507003	+	0.861944i	$0.669247\pi$
$32$	1.00000	0.176777
$33$	−12.2915	−2.13968
$34$	0	0
$35$	−6.00000	−1.01419
$36$	4.00000	0.666667
$37$	0.354249	0.0582381	0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249	0.0582381	0.0291191	+	0.999576i	$0.490730\pi$
$38$	0	0
$39$	5.29150	0.847319
$40$	−1.64575	−0.260216
$41$	−0.291503	−0.0455251	−0.0227625	−	0.999741i	$-0.507246\pi$
$41$	−0.291503	−0.0455251	−0.0227625	+	0.999741i	$0.507246\pi$
$42$	9.64575	1.48837
$43$	11.2915	1.72194	0.860969	−	0.508657i	$-0.169858\pi$
$43$	11.2915	1.72194	0.860969	+	0.508657i	$0.169858\pi$
$44$	−4.64575	−0.700373
$45$	−6.58301	−0.981336
$46$	−1.64575	−0.242653
$47$	4.35425	0.635132	0.317566	−	0.948236i	$-0.397134\pi$
$47$	4.35425	0.635132	0.317566	+	0.948236i	$0.397134\pi$
$48$	2.64575	0.381881
$49$	6.29150	0.898786
$50$	−2.29150	−0.324067
$51$	0	0
$52$	2.00000	0.277350
$53$	−12.5830	−1.72841	−0.864204	−	0.503141i	$-0.832178\pi$
$53$	−12.5830	−1.72841	−0.864204	+	0.503141i	$0.832178\pi$
$54$	2.64575	0.360041
$55$	7.64575	1.03095
$56$	3.64575	0.487184
$57$	0	0
$58$	1.64575	0.216098
$59$	−7.93725	−1.03334	−0.516671	−	0.856184i	$-0.672829\pi$
$59$	−7.93725	−1.03334	−0.516671	+	0.856184i	$0.672829\pi$
$60$	−4.35425	−0.562131
$61$	0.937254	0.120003	0.0600015	−	0.998198i	$-0.480889\pi$
$61$	0.937254	0.120003	0.0600015	+	0.998198i	$0.480889\pi$
$62$	−5.64575	−0.717011
$63$	14.5830	1.83729
$64$	1.00000	0.125000
$65$	−3.29150	−0.408261
$66$	−12.2915	−1.51298
$67$	0.645751	0.0788911	0.0394455	−	0.999222i	$-0.487441\pi$
$67$	0.645751	0.0788911	0.0394455	+	0.999222i	$0.487441\pi$
$68$	0	0
$69$	−4.35425	−0.524190
$70$	−6.00000	−0.717137
$71$	−2.70850	−0.321440	−0.160720	−	0.987000i	$-0.551382\pi$
$71$	−2.70850	−0.321440	−0.160720	+	0.987000i	$0.551382\pi$
$72$	4.00000	0.471405
$73$	1.70850	0.199964	0.0999822	−	0.994989i	$-0.468121\pi$
$73$	1.70850	0.199964	0.0999822	+	0.994989i	$0.468121\pi$
$74$	0.354249	0.0411806
$75$	−6.06275	−0.700066
$76$	0	0
$77$	−16.9373	−1.93018
$78$	5.29150	0.599145
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.64575	−0.184001
$81$	−5.00000	−0.555556
$82$	−0.291503	−0.0321911
$83$	7.93725	0.871227	0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725	0.871227	0.435613	+	0.900134i	$0.356531\pi$
$84$	9.64575	1.05244
$85$	0	0
$86$	11.2915	1.21759
$87$	4.35425	0.466824
$88$	−4.64575	−0.495239
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−6.58301	−0.693910
$91$	7.29150	0.764357
$92$	−1.64575	−0.171581
$93$	−14.9373	−1.54892
$94$	4.35425	0.449106
$95$	0	0
$96$	2.64575	0.270031
$97$	−3.70850	−0.376541	−0.188270	−	0.982117i	$-0.560288\pi$
$97$	−3.70850	−0.376541	−0.188270	+	0.982117i	$0.560288\pi$
$98$	6.29150	0.635538
$99$	−18.5830	−1.86766
$100$	−2.29150	−0.229150
$101$	−13.6458	−1.35780	−0.678902	−	0.734229i	$-0.737544\pi$
$101$	−13.6458	−1.35780	−0.678902	+	0.734229i	$0.737544\pi$
$102$	0	0
$103$	−13.2915	−1.30965	−0.654825	−	0.755780i	$-0.727258\pi$
$103$	−13.2915	−1.30965	−0.654825	+	0.755780i	$0.727258\pi$
$104$	2.00000	0.196116
$105$	−15.8745	−1.54919
$106$	−12.5830	−1.22217
$107$	15.2915	1.47829	0.739143	−	0.673549i	$-0.235231\pi$
$107$	15.2915	1.47829	0.739143	+	0.673549i	$0.235231\pi$
$108$	2.64575	0.254588
$109$	14.5830	1.39680	0.698399	−	0.715708i	$-0.253896\pi$
$109$	14.5830	1.39680	0.698399	+	0.715708i	$0.253896\pi$
$110$	7.64575	0.728994
$111$	0.937254	0.0889602
$112$	3.64575	0.344491
$113$	−15.5830	−1.46593	−0.732963	−	0.680269i	$-0.761863\pi$
$113$	−15.5830	−1.46593	−0.732963	+	0.680269i	$0.761863\pi$
$114$	0	0
$115$	2.70850	0.252569
$116$	1.64575	0.152804
$117$	8.00000	0.739600
$118$	−7.93725	−0.730683
$119$	0	0
$120$	−4.35425	−0.397487
$121$	10.5830	0.962091
$122$	0.937254	0.0848550
$123$	−0.771243	−0.0695407
$124$	−5.64575	−0.507003
$125$	12.0000	1.07331
$126$	14.5830	1.29916
$127$	−13.2915	−1.17943	−0.589715	−	0.807611i	$-0.700760\pi$
$127$	−13.2915	−1.17943	−0.589715	+	0.807611i	$0.700760\pi$
$128$	1.00000	0.0883883
$129$	29.8745	2.63030
$130$	−3.29150	−0.288684
$131$	1.93725	0.169259	0.0846293	−	0.996413i	$-0.473029\pi$
$131$	1.93725	0.169259	0.0846293	+	0.996413i	$0.473029\pi$
$132$	−12.2915	−1.06984
$133$	0	0
$134$	0.645751	0.0557844
$135$	−4.35425	−0.374754
$136$	0	0
$137$	15.5830	1.33135	0.665673	−	0.746244i	$-0.268145\pi$
$137$	15.5830	1.33135	0.665673	+	0.746244i	$0.268145\pi$
$138$	−4.35425	−0.370658
$139$	18.6458	1.58151	0.790756	−	0.612131i	$-0.209688\pi$
$139$	18.6458	1.58151	0.790756	+	0.612131i	$0.209688\pi$
$140$	−6.00000	−0.507093
$141$	11.5203	0.970181
$142$	−2.70850	−0.227292
$143$	−9.29150	−0.776994
$144$	4.00000	0.333333
$145$	−2.70850	−0.224928
$146$	1.70850	0.141396
$147$	16.6458	1.37292
$148$	0.354249	0.0291191
$149$	10.9373	0.896015	0.448007	−	0.894030i	$-0.352134\pi$
$149$	10.9373	0.896015	0.448007	+	0.894030i	$0.352134\pi$
$150$	−6.06275	−0.495021
$151$	12.9373	1.05282	0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373	1.05282	0.526409	+	0.850231i	$0.323538\pi$
$152$	0	0
$153$	0	0
$154$	−16.9373	−1.36484
$155$	9.29150	0.746311
$156$	5.29150	0.423659
$157$	−10.5830	−0.844616	−0.422308	−	0.906452i	$-0.638780\pi$
$157$	−10.5830	−0.844616	−0.422308	+	0.906452i	$0.638780\pi$
$158$	−4.00000	−0.318223
$159$	−33.2915	−2.64019
$160$	−1.64575	−0.130108
$161$	−6.00000	−0.472866
$162$	−5.00000	−0.392837
$163$	3.93725	0.308390	0.154195	−	0.988040i	$-0.450722\pi$
$163$	3.93725	0.308390	0.154195	+	0.988040i	$0.450722\pi$
$164$	−0.291503	−0.0227625
$165$	20.2288	1.57481
$166$	7.93725	0.616050
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	9.64575	0.744186
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	11.2915	0.860969
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	4.35425	0.330095
$175$	−8.35425	−0.631522
$176$	−4.64575	−0.350187
$177$	−21.0000	−1.57846
$178$	0	0
$179$	4.06275	0.303664	0.151832	−	0.988406i	$-0.451483\pi$
$179$	4.06275	0.303664	0.151832	+	0.988406i	$0.451483\pi$
$180$	−6.58301	−0.490668
$181$	22.2288	1.65225	0.826125	−	0.563487i	$-0.190540\pi$
$181$	22.2288	1.65225	0.826125	+	0.563487i	$0.190540\pi$
$182$	7.29150	0.540482
$183$	2.47974	0.183308
$184$	−1.64575	−0.121326
$185$	−0.583005	−0.0428634
$186$	−14.9373	−1.09525
$187$	0	0
$188$	4.35425	0.317566
$189$	9.64575	0.701625
$190$	0	0
$191$	6.58301	0.476330	0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301	0.476330	0.238165	+	0.971225i	$0.423454\pi$
$192$	2.64575	0.190941
$193$	14.5830	1.04971	0.524854	−	0.851192i	$-0.324120\pi$
$193$	14.5830	1.04971	0.524854	+	0.851192i	$0.324120\pi$
$194$	−3.70850	−0.266255
$195$	−8.70850	−0.623628
$196$	6.29150	0.449393
$197$	−7.64575	−0.544737	−0.272369	−	0.962193i	$-0.587807\pi$
$197$	−7.64575	−0.544737	−0.272369	+	0.962193i	$0.587807\pi$
$198$	−18.5830	−1.32064
$199$	−19.8745	−1.40887	−0.704433	−	0.709770i	$-0.748799\pi$
$199$	−19.8745	−1.40887	−0.704433	+	0.709770i	$0.748799\pi$
$200$	−2.29150	−0.162034
$201$	1.70850	0.120508
$202$	−13.6458	−0.960112
$203$	6.00000	0.421117
$204$	0	0
$205$	0.479741	0.0335066
$206$	−13.2915	−0.926063
$207$	−6.58301	−0.457550
$208$	2.00000	0.138675
$209$	0	0
$210$	−15.8745	−1.09545
$211$	−13.2915	−0.915025	−0.457512	−	0.889203i	$-0.651259\pi$
$211$	−13.2915	−0.915025	−0.457512	+	0.889203i	$0.651259\pi$
$212$	−12.5830	−0.864204
$213$	−7.16601	−0.491007
$214$	15.2915	1.04531
$215$	−18.5830	−1.26735
$216$	2.64575	0.180021
$217$	−20.5830	−1.39727
$218$	14.5830	0.987686
$219$	4.52026	0.305451
$220$	7.64575	0.515476
$221$	0	0
$222$	0.937254	0.0629044
$223$	−18.8118	−1.25973	−0.629864	−	0.776705i	$-0.716890\pi$
$223$	−18.8118	−1.25973	−0.629864	+	0.776705i	$0.716890\pi$
$224$	3.64575	0.243592
$225$	−9.16601	−0.611067
$226$	−15.5830	−1.03657
$227$	−7.35425	−0.488119	−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425	−0.488119	−0.244059	+	0.969760i	$0.578479\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	2.70850	0.178593
$231$	−44.8118	−2.94840
$232$	1.64575	0.108049
$233$	18.8745	1.23651	0.618255	−	0.785978i	$-0.287840\pi$
$233$	18.8745	1.23651	0.618255	+	0.785978i	$0.287840\pi$
$234$	8.00000	0.522976
$235$	−7.16601	−0.467459
$236$	−7.93725	−0.516671
$237$	−10.5830	−0.687440
$238$	0	0
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	−4.35425	−0.281066
$241$	−7.58301	−0.488464	−0.244232	−	0.969717i	$-0.578536\pi$
$241$	−7.58301	−0.488464	−0.244232	+	0.969717i	$0.578536\pi$
$242$	10.5830	0.680301
$243$	−21.1660	−1.35780
$244$	0.937254	0.0600015
$245$	−10.3542	−0.661509
$246$	−0.771243	−0.0491727
$247$	0	0
$248$	−5.64575	−0.358506
$249$	21.0000	1.33082
$250$	12.0000	0.758947
$251$	29.2288	1.84490	0.922451	−	0.386113i	$-0.126183\pi$
$251$	29.2288	1.84490	0.922451	+	0.386113i	$0.126183\pi$
$252$	14.5830	0.918643
$253$	7.64575	0.480684
$254$	−13.2915	−0.833983
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.2915	0.766723	0.383361	−	0.923598i	$-0.374766\pi$
$257$	12.2915	0.766723	0.383361	+	0.923598i	$0.374766\pi$
$258$	29.8745	1.85991
$259$	1.29150	0.0802501
$260$	−3.29150	−0.204130
$261$	6.58301	0.407478
$262$	1.93725	0.119684
$263$	−10.9373	−0.674420	−0.337210	−	0.941429i	$-0.609483\pi$
$263$	−10.9373	−0.674420	−0.337210	+	0.941429i	$0.609483\pi$
$264$	−12.2915	−0.756490
$265$	20.7085	1.27211
$266$	0	0
$267$	0	0
$268$	0.645751	0.0394455
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	−4.35425	−0.264991
$271$	12.3542	0.750467	0.375234	−	0.926930i	$-0.377562\pi$
$271$	12.3542	0.750467	0.375234	+	0.926930i	$0.377562\pi$
$272$	0	0
$273$	19.2915	1.16757
$274$	15.5830	0.941404
$275$	10.6458	0.641963
$276$	−4.35425	−0.262095
$277$	−27.5203	−1.65353	−0.826766	−	0.562546i	$-0.809822\pi$
$277$	−27.5203	−1.65353	−0.826766	+	0.562546i	$0.809822\pi$
$278$	18.6458	1.11830
$279$	−22.5830	−1.35201
$280$	−6.00000	−0.358569
$281$	25.4575	1.51867	0.759334	−	0.650701i	$-0.225525\pi$
$281$	25.4575	1.51867	0.759334	+	0.650701i	$0.225525\pi$
$282$	11.5203	0.686021
$283$	30.6458	1.82170	0.910850	−	0.412737i	$-0.135427\pi$
$283$	30.6458	1.82170	0.910850	+	0.412737i	$0.135427\pi$
$284$	−2.70850	−0.160720
$285$	0	0
$286$	−9.29150	−0.549418
$287$	−1.06275	−0.0627319
$288$	4.00000	0.235702
$289$	−17.0000	−1.00000
$290$	−2.70850	−0.159048
$291$	−9.81176	−0.575176
$292$	1.70850	0.0999822
$293$	28.9373	1.69053	0.845266	−	0.534345i	$-0.179442\pi$
$293$	28.9373	1.69053	0.845266	+	0.534345i	$0.179442\pi$
$294$	16.6458	0.970800
$295$	13.0627	0.760542
$296$	0.354249	0.0205903
$297$	−12.2915	−0.713225
$298$	10.9373	0.633578
$299$	−3.29150	−0.190353
$300$	−6.06275	−0.350033
$301$	41.1660	2.37277
$302$	12.9373	0.744455
$303$	−36.1033	−2.07408
$304$	0	0
$305$	−1.54249	−0.0883225
$306$	0	0
$307$	0.645751	0.0368550	0.0184275	−	0.999830i	$-0.494134\pi$
$307$	0.645751	0.0368550	0.0184275	+	0.999830i	$0.494134\pi$
$308$	−16.9373	−0.965090
$309$	−35.1660	−2.00052
$310$	9.29150	0.527722
$311$	13.6458	0.773780	0.386890	−	0.922126i	$-0.373549\pi$
$311$	13.6458	0.773780	0.386890	+	0.922126i	$0.373549\pi$
$312$	5.29150	0.299572
$313$	8.87451	0.501617	0.250808	−	0.968037i	$-0.419304\pi$
$313$	8.87451	0.501617	0.250808	+	0.968037i	$0.419304\pi$
$314$	−10.5830	−0.597234
$315$	−24.0000	−1.35225
$316$	−4.00000	−0.225018
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−33.2915	−1.86689
$319$	−7.64575	−0.428080
$320$	−1.64575	−0.0920003
$321$	40.4575	2.25812
$322$	−6.00000	−0.334367
$323$	0	0
$324$	−5.00000	−0.277778
$325$	−4.58301	−0.254219
$326$	3.93725	0.218064
$327$	38.5830	2.13365
$328$	−0.291503	−0.0160955
$329$	15.8745	0.875190
$330$	20.2288	1.11356
$331$	19.8118	1.08895	0.544476	−	0.838776i	$-0.316728\pi$
$331$	19.8118	1.08895	0.544476	+	0.838776i	$0.316728\pi$
$332$	7.93725	0.435613
$333$	1.41699	0.0776508
$334$	−12.0000	−0.656611
$335$	−1.06275	−0.0580640
$336$	9.64575	0.526219
$337$	−9.70850	−0.528856	−0.264428	−	0.964405i	$-0.585183\pi$
$337$	−9.70850	−0.528856	−0.264428	+	0.964405i	$0.585183\pi$
$338$	−9.00000	−0.489535
$339$	−41.2288	−2.23924
$340$	0	0
$341$	26.2288	1.42037
$342$	0	0
$343$	−2.58301	−0.139469
$344$	11.2915	0.608797
$345$	7.16601	0.385805
$346$	−6.00000	−0.322562
$347$	−23.2288	−1.24698	−0.623492	−	0.781829i	$-0.714287\pi$
$347$	−23.2288	−1.24698	−0.623492	+	0.781829i	$0.714287\pi$
$348$	4.35425	0.233412
$349$	21.1660	1.13299	0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660	1.13299	0.566495	+	0.824065i	$0.308299\pi$
$350$	−8.35425	−0.446553
$351$	5.29150	0.282440
$352$	−4.64575	−0.247619
$353$	12.8745	0.685241	0.342620	−	0.939474i	$-0.388686\pi$
$353$	12.8745	0.685241	0.342620	+	0.939474i	$0.388686\pi$
$354$	−21.0000	−1.11614
$355$	4.45751	0.236580
$356$	0	0
$357$	0	0
$358$	4.06275	0.214723
$359$	−4.93725	−0.260578	−0.130289	−	0.991476i	$-0.541591\pi$
$359$	−4.93725	−0.260578	−0.130289	+	0.991476i	$0.541591\pi$
$360$	−6.58301	−0.346955
$361$	0	0
$362$	22.2288	1.16832
$363$	28.0000	1.46962
$364$	7.29150	0.382179
$365$	−2.81176	−0.147174
$366$	2.47974	0.129618
$367$	16.2288	0.847134	0.423567	−	0.905865i	$-0.360778\pi$
$367$	16.2288	0.847134	0.423567	+	0.905865i	$0.360778\pi$
$368$	−1.64575	−0.0857907
$369$	−1.16601	−0.0607001
$370$	−0.583005	−0.0303090
$371$	−45.8745	−2.38169
$372$	−14.9373	−0.774461
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	31.7490	1.63951
$376$	4.35425	0.224553
$377$	3.29150	0.169521
$378$	9.64575	0.496124
$379$	10.7085	0.550059	0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085	0.550059	0.275029	+	0.961436i	$0.411312\pi$
$380$	0	0
$381$	−35.1660	−1.80161
$382$	6.58301	0.336816
$383$	5.52026	0.282072	0.141036	−	0.990004i	$-0.454957\pi$
$383$	5.52026	0.282072	0.141036	+	0.990004i	$0.454957\pi$
$384$	2.64575	0.135015
$385$	27.8745	1.42062
$386$	14.5830	0.742255
$387$	45.1660	2.29592
$388$	−3.70850	−0.188270
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	−8.70850	−0.440972
$391$	0	0
$392$	6.29150	0.317769
$393$	5.12549	0.258547
$394$	−7.64575	−0.385187
$395$	6.58301	0.331227
$396$	−18.5830	−0.933831
$397$	21.0627	1.05711	0.528554	−	0.848899i	$-0.322734\pi$
$397$	21.0627	1.05711	0.528554	+	0.848899i	$0.322734\pi$
$398$	−19.8745	−0.996219
$399$	0	0
$400$	−2.29150	−0.114575
$401$	27.5830	1.37743	0.688715	−	0.725032i	$-0.258175\pi$
$401$	27.5830	1.37743	0.688715	+	0.725032i	$0.258175\pi$
$402$	1.70850	0.0852121
$403$	−11.2915	−0.562470
$404$	−13.6458	−0.678902
$405$	8.22876	0.408890
$406$	6.00000	0.297775
$407$	−1.64575	−0.0815769
$408$	0	0
$409$	−7.58301	−0.374955	−0.187478	−	0.982269i	$-0.560031\pi$
$409$	−7.58301	−0.374955	−0.187478	+	0.982269i	$0.560031\pi$
$410$	0.479741	0.0236927
$411$	41.2288	2.03366
$412$	−13.2915	−0.654825
$413$	−28.9373	−1.42391
$414$	−6.58301	−0.323537
$415$	−13.0627	−0.641225
$416$	2.00000	0.0980581
$417$	49.3320	2.41580
$418$	0	0
$419$	−31.7490	−1.55104	−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490	−1.55104	−0.775520	+	0.631322i	$0.782512\pi$
$420$	−15.8745	−0.774597
$421$	−24.8118	−1.20925	−0.604626	−	0.796510i	$-0.706677\pi$
$421$	−24.8118	−1.20925	−0.604626	+	0.796510i	$0.706677\pi$
$422$	−13.2915	−0.647020
$423$	17.4170	0.846843
$424$	−12.5830	−0.611085
$425$	0	0
$426$	−7.16601	−0.347194
$427$	3.41699	0.165360
$428$	15.2915	0.739143
$429$	−24.5830	−1.18688
$430$	−18.5830	−0.896152
$431$	27.8745	1.34267	0.671334	−	0.741155i	$-0.265722\pi$
$431$	27.8745	1.34267	0.671334	+	0.741155i	$0.265722\pi$
$432$	2.64575	0.127294
$433$	17.8745	0.858994	0.429497	−	0.903068i	$-0.358691\pi$
$433$	17.8745	0.858994	0.429497	+	0.903068i	$0.358691\pi$
$434$	−20.5830	−0.988016
$435$	−7.16601	−0.343584
$436$	14.5830	0.698399
$437$	0	0
$438$	4.52026	0.215986
$439$	10.8118	0.516017	0.258009	−	0.966143i	$-0.416934\pi$
$439$	10.8118	0.516017	0.258009	+	0.966143i	$0.416934\pi$
$440$	7.64575	0.364497
$441$	25.1660	1.19838
$442$	0	0
$443$	10.6458	0.505795	0.252897	−	0.967493i	$-0.418616\pi$
$443$	10.6458	0.505795	0.252897	+	0.967493i	$0.418616\pi$
$444$	0.937254	0.0444801
$445$	0	0
$446$	−18.8118	−0.890763
$447$	28.9373	1.36869
$448$	3.64575	0.172246
$449$	−24.2915	−1.14639	−0.573193	−	0.819420i	$-0.694296\pi$
$449$	−24.2915	−1.14639	−0.573193	+	0.819420i	$0.694296\pi$
$450$	−9.16601	−0.432090
$451$	1.35425	0.0637691
$452$	−15.5830	−0.732963
$453$	34.2288	1.60821
$454$	−7.35425	−0.345152
$455$	−12.0000	−0.562569
$456$	0	0
$457$	32.8745	1.53780	0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745	1.53780	0.768902	+	0.639366i	$0.220803\pi$
$458$	20.0000	0.934539
$459$	0	0
$460$	2.70850	0.126284
$461$	19.1660	0.892650	0.446325	−	0.894871i	$-0.352733\pi$
$461$	19.1660	0.892650	0.446325	+	0.894871i	$0.352733\pi$
$462$	−44.8118	−2.08483
$463$	−38.4575	−1.78727	−0.893636	−	0.448792i	$-0.851854\pi$
$463$	−38.4575	−1.78727	−0.893636	+	0.448792i	$0.851854\pi$
$464$	1.64575	0.0764021
$465$	24.5830	1.14001
$466$	18.8745	0.874345
$467$	−19.3542	−0.895608	−0.447804	−	0.894132i	$-0.647794\pi$
$467$	−19.3542	−0.895608	−0.447804	+	0.894132i	$0.647794\pi$
$468$	8.00000	0.369800
$469$	2.35425	0.108709
$470$	−7.16601	−0.330543
$471$	−28.0000	−1.29017
$472$	−7.93725	−0.365342
$473$	−52.4575	−2.41200
$474$	−10.5830	−0.486094
$475$	0	0
$476$	0	0
$477$	−50.3320	−2.30454
$478$	−12.0000	−0.548867
$479$	6.58301	0.300785	0.150393	−	0.988626i	$-0.451946\pi$
$479$	6.58301	0.300785	0.150393	+	0.988626i	$0.451946\pi$
$480$	−4.35425	−0.198743
$481$	0.708497	0.0323047
$482$	−7.58301	−0.345396
$483$	−15.8745	−0.722315
$484$	10.5830	0.481046
$485$	6.10326	0.277135
$486$	−21.1660	−0.960110
$487$	4.22876	0.191623	0.0958116	−	0.995399i	$-0.469455\pi$
$487$	4.22876	0.191623	0.0958116	+	0.995399i	$0.469455\pi$
$488$	0.937254	0.0424275
$489$	10.4170	0.471073
$490$	−10.3542	−0.467757
$491$	39.2915	1.77320	0.886600	−	0.462536i	$-0.153061\pi$
$491$	39.2915	1.77320	0.886600	+	0.462536i	$0.153061\pi$
$492$	−0.771243	−0.0347703
$493$	0	0
$494$	0	0
$495$	30.5830	1.37460
$496$	−5.64575	−0.253502
$497$	−9.87451	−0.442932
$498$	21.0000	0.941033
$499$	−4.77124	−0.213590	−0.106795	−	0.994281i	$-0.534059\pi$
$499$	−4.77124	−0.213590	−0.106795	+	0.994281i	$0.534059\pi$
$500$	12.0000	0.536656
$501$	−31.7490	−1.41844
$502$	29.2288	1.30454
$503$	−40.9373	−1.82530	−0.912651	−	0.408740i	$-0.865968\pi$
$503$	−40.9373	−1.82530	−0.912651	+	0.408740i	$0.865968\pi$
$504$	14.5830	0.649579
$505$	22.4575	0.999346
$506$	7.64575	0.339895
$507$	−23.8118	−1.05752
$508$	−13.2915	−0.589715
$509$	−31.7490	−1.40725	−0.703625	−	0.710571i	$-0.748437\pi$
$509$	−31.7490	−1.40725	−0.703625	+	0.710571i	$0.748437\pi$
$510$	0	0
$511$	6.22876	0.275544
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.2915	0.542155
$515$	21.8745	0.963906
$516$	29.8745	1.31515
$517$	−20.2288	−0.889660
$518$	1.29150	0.0567454
$519$	−15.8745	−0.696814
$520$	−3.29150	−0.144342
$521$	−11.7085	−0.512959	−0.256479	−	0.966550i	$-0.582563\pi$
$521$	−11.7085	−0.512959	−0.256479	+	0.966550i	$0.582563\pi$
$522$	6.58301	0.288130
$523$	−1.87451	−0.0819665	−0.0409833	−	0.999160i	$-0.513049\pi$
$523$	−1.87451	−0.0819665	−0.0409833	+	0.999160i	$0.513049\pi$
$524$	1.93725	0.0846293
$525$	−22.1033	−0.964666
$526$	−10.9373	−0.476887
$527$	0	0
$528$	−12.2915	−0.534919
$529$	−20.2915	−0.882239
$530$	20.7085	0.899520
$531$	−31.7490	−1.37779
$532$	0	0
$533$	−0.583005	−0.0252528
$534$	0	0
$535$	−25.1660	−1.08802
$536$	0.645751	0.0278922
$537$	10.7490	0.463854
$538$	0	0
$539$	−29.2288	−1.25897
$540$	−4.35425	−0.187377
$541$	8.00000	0.343947	0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000	0.343947	0.171973	+	0.985102i	$0.444986\pi$
$542$	12.3542	0.530660
$543$	58.8118	2.52385
$544$	0	0
$545$	−24.0000	−1.02805
$546$	19.2915	0.825600
$547$	11.2915	0.482790	0.241395	−	0.970427i	$-0.422395\pi$
$547$	11.2915	0.482790	0.241395	+	0.970427i	$0.422395\pi$
$548$	15.5830	0.665673
$549$	3.74902	0.160004
$550$	10.6458	0.453936
$551$	0	0
$552$	−4.35425	−0.185329
$553$	−14.5830	−0.620132
$554$	−27.5203	−1.16922
$555$	−1.54249	−0.0654749
$556$	18.6458	0.790756
$557$	−5.41699	−0.229525	−0.114763	−	0.993393i	$-0.536611\pi$
$557$	−5.41699	−0.229525	−0.114763	+	0.993393i	$0.536611\pi$
$558$	−22.5830	−0.956015
$559$	22.5830	0.955159
$560$	−6.00000	−0.253546
$561$	0	0
$562$	25.4575	1.07386
$563$	10.0627	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$563$	10.0627	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$564$	11.5203	0.485090
$565$	25.6458	1.07892
$566$	30.6458	1.28814
$567$	−18.2288	−0.765536
$568$	−2.70850	−0.113646
$569$	6.58301	0.275974	0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301	0.275974	0.137987	+	0.990434i	$0.455937\pi$
$570$	0	0
$571$	7.81176	0.326912	0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176	0.326912	0.163456	+	0.986551i	$0.447736\pi$
$572$	−9.29150	−0.388497
$573$	17.4170	0.727605
$574$	−1.06275	−0.0443582
$575$	3.77124	0.157272
$576$	4.00000	0.166667
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	−17.0000	−0.707107
$579$	38.5830	1.60345
$580$	−2.70850	−0.112464
$581$	28.9373	1.20052
$582$	−9.81176	−0.406711
$583$	58.4575	2.42106
$584$	1.70850	0.0706981
$585$	−13.1660	−0.544348
$586$	28.9373	1.19539
$587$	−14.1255	−0.583021	−0.291511	−	0.956568i	$-0.594158\pi$
$587$	−14.1255	−0.583021	−0.291511	+	0.956568i	$0.594158\pi$
$588$	16.6458	0.686459
$589$	0	0
$590$	13.0627	0.537785
$591$	−20.2288	−0.832100
$592$	0.354249	0.0145595
$593$	29.7085	1.21998	0.609991	−	0.792408i	$-0.291173\pi$
$593$	29.7085	1.21998	0.609991	+	0.792408i	$0.291173\pi$
$594$	−12.2915	−0.504326
$595$	0	0
$596$	10.9373	0.448007
$597$	−52.5830	−2.15208
$598$	−3.29150	−0.134600
$599$	−16.9373	−0.692037	−0.346019	−	0.938228i	$-0.612467\pi$
$599$	−16.9373	−0.692037	−0.346019	+	0.938228i	$0.612467\pi$
$600$	−6.06275	−0.247511
$601$	10.4170	0.424918	0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170	0.424918	0.212459	+	0.977170i	$0.431853\pi$
$602$	41.1660	1.67780
$603$	2.58301	0.105188
$604$	12.9373	0.526409
$605$	−17.4170	−0.708102
$606$	−36.1033	−1.46659
$607$	6.93725	0.281574	0.140787	−	0.990040i	$-0.455037\pi$
$607$	6.93725	0.281574	0.140787	+	0.990040i	$0.455037\pi$
$608$	0	0
$609$	15.8745	0.643268
$610$	−1.54249	−0.0624535
$611$	8.70850	0.352308
$612$	0	0
$613$	7.41699	0.299570	0.149785	−	0.988719i	$-0.452142\pi$
$613$	7.41699	0.299570	0.149785	+	0.988719i	$0.452142\pi$
$614$	0.645751	0.0260604
$615$	1.26927	0.0511821
$616$	−16.9373	−0.682421
$617$	−30.8745	−1.24296	−0.621480	−	0.783430i	$-0.713468\pi$
$617$	−30.8745	−1.24296	−0.621480	+	0.783430i	$0.713468\pi$
$618$	−35.1660	−1.41458
$619$	−8.45751	−0.339936	−0.169968	−	0.985450i	$-0.554366\pi$
$619$	−8.45751	−0.339936	−0.169968	+	0.985450i	$0.554366\pi$
$620$	9.29150	0.373156
$621$	−4.35425	−0.174730
$622$	13.6458	0.547145
$623$	0	0
$624$	5.29150	0.211830
$625$	−8.29150	−0.331660
$626$	8.87451	0.354697
$627$	0	0
$628$	−10.5830	−0.422308
$629$	0	0
$630$	−24.0000	−0.956183
$631$	−24.8118	−0.987741	−0.493870	−	0.869536i	$-0.664418\pi$
$631$	−24.8118	−0.987741	−0.493870	+	0.869536i	$0.664418\pi$
$632$	−4.00000	−0.159111
$633$	−35.1660	−1.39772
$634$	−6.00000	−0.238290
$635$	21.8745	0.868063
$636$	−33.2915	−1.32009
$637$	12.5830	0.498557
$638$	−7.64575	−0.302698
$639$	−10.8340	−0.428586
$640$	−1.64575	−0.0650540
$641$	12.8745	0.508512	0.254256	−	0.967137i	$-0.418169\pi$
$641$	12.8745	0.508512	0.254256	+	0.967137i	$0.418169\pi$
$642$	40.4575	1.59673
$643$	−6.52026	−0.257134	−0.128567	−	0.991701i	$-0.541038\pi$
$643$	−6.52026	−0.257134	−0.128567	+	0.991701i	$0.541038\pi$
$644$	−6.00000	−0.236433
$645$	−49.1660	−1.93591
$646$	0	0
$647$	−22.4575	−0.882896	−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575	−0.882896	−0.441448	+	0.897287i	$0.645535\pi$
$648$	−5.00000	−0.196419
$649$	36.8745	1.44745
$650$	−4.58301	−0.179760
$651$	−54.4575	−2.13436
$652$	3.93725	0.154195
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	38.5830	1.50871
$655$	−3.18824	−0.124575
$656$	−0.291503	−0.0113813
$657$	6.83399	0.266619
$658$	15.8745	0.618853
$659$	−18.5830	−0.723891	−0.361946	−	0.932199i	$-0.617887\pi$
$659$	−18.5830	−0.723891	−0.361946	+	0.932199i	$0.617887\pi$
$660$	20.2288	0.787403
$661$	16.2288	0.631225	0.315613	−	0.948888i	$-0.397790\pi$
$661$	16.2288	0.631225	0.315613	+	0.948888i	$0.397790\pi$
$662$	19.8118	0.770006
$663$	0	0
$664$	7.93725	0.308025
$665$	0	0
$666$	1.41699	0.0549074
$667$	−2.70850	−0.104873
$668$	−12.0000	−0.464294
$669$	−49.7712	−1.92427
$670$	−1.06275	−0.0410575
$671$	−4.35425	−0.168094
$672$	9.64575	0.372093
$673$	−13.8745	−0.534823	−0.267411	−	0.963582i	$-0.586168\pi$
$673$	−13.8745	−0.534823	−0.267411	+	0.963582i	$0.586168\pi$
$674$	−9.70850	−0.373957
$675$	−6.06275	−0.233355
$676$	−9.00000	−0.346154
$677$	−11.4170	−0.438791	−0.219395	−	0.975636i	$-0.570408\pi$
$677$	−11.4170	−0.438791	−0.219395	+	0.975636i	$0.570408\pi$
$678$	−41.2288	−1.58338
$679$	−13.5203	−0.518860
$680$	0	0
$681$	−19.4575	−0.745614
$682$	26.2288	1.00435
$683$	−5.41699	−0.207276	−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699	−0.207276	−0.103638	+	0.994615i	$0.533048\pi$
$684$	0	0
$685$	−25.6458	−0.979874
$686$	−2.58301	−0.0986196
$687$	52.9150	2.01883
$688$	11.2915	0.430485
$689$	−25.1660	−0.958749
$690$	7.16601	0.272805
$691$	2.58301	0.0982622	0.0491311	−	0.998792i	$-0.484355\pi$
$691$	2.58301	0.0982622	0.0491311	+	0.998792i	$0.484355\pi$
$692$	−6.00000	−0.228086
$693$	−67.7490	−2.57357
$694$	−23.2288	−0.881752
$695$	−30.6863	−1.16400
$696$	4.35425	0.165047
$697$	0	0
$698$	21.1660	0.801145
$699$	49.9373	1.88880
$700$	−8.35425	−0.315761
$701$	10.3542	0.391075	0.195537	−	0.980696i	$-0.437355\pi$
$701$	10.3542	0.391075	0.195537	+	0.980696i	$0.437355\pi$
$702$	5.29150	0.199715
$703$	0	0
$704$	−4.64575	−0.175093
$705$	−18.9595	−0.714055
$706$	12.8745	0.484538
$707$	−49.7490	−1.87100
$708$	−21.0000	−0.789228
$709$	3.64575	0.136919	0.0684595	−	0.997654i	$-0.478192\pi$
$709$	3.64575	0.136919	0.0684595	+	0.997654i	$0.478192\pi$
$710$	4.45751	0.167287
$711$	−16.0000	−0.600047
$712$	0	0
$713$	9.29150	0.347970
$714$	0	0
$715$	15.2915	0.571870
$716$	4.06275	0.151832
$717$	−31.7490	−1.18569
$718$	−4.93725	−0.184257
$719$	2.70850	0.101010	0.0505050	−	0.998724i	$-0.483917\pi$
$719$	2.70850	0.101010	0.0505050	+	0.998724i	$0.483917\pi$
$720$	−6.58301	−0.245334
$721$	−48.4575	−1.80465
$722$	0	0
$723$	−20.0627	−0.746142
$724$	22.2288	0.826125
$725$	−3.77124	−0.140060
$726$	28.0000	1.03918
$727$	1.41699	0.0525534	0.0262767	−	0.999655i	$-0.491635\pi$
$727$	1.41699	0.0525534	0.0262767	+	0.999655i	$0.491635\pi$
$728$	7.29150	0.270241
$729$	−41.0000	−1.51852
$730$	−2.81176	−0.104068
$731$	0	0
$732$	2.47974	0.0916539
$733$	−16.1033	−0.594788	−0.297394	−	0.954755i	$-0.596117\pi$
$733$	−16.1033	−0.594788	−0.297394	+	0.954755i	$0.596117\pi$
$734$	16.2288	0.599014
$735$	−27.3948	−1.01047
$736$	−1.64575	−0.0606632
$737$	−3.00000	−0.110506
$738$	−1.16601	−0.0429214
$739$	−33.8118	−1.24379	−0.621893	−	0.783102i	$-0.713636\pi$
$739$	−33.8118	−1.24379	−0.621893	+	0.783102i	$0.713636\pi$
$740$	−0.583005	−0.0214317
$741$	0	0
$742$	−45.8745	−1.68411
$743$	−47.5203	−1.74335	−0.871675	−	0.490085i	$-0.836966\pi$
$743$	−47.5203	−1.74335	−0.871675	+	0.490085i	$0.836966\pi$
$744$	−14.9373	−0.547626
$745$	−18.0000	−0.659469
$746$	−4.00000	−0.146450
$747$	31.7490	1.16164
$748$	0	0
$749$	55.7490	2.03702
$750$	31.7490	1.15931
$751$	−7.87451	−0.287345	−0.143672	−	0.989625i	$-0.545891\pi$
$751$	−7.87451	−0.287345	−0.143672	+	0.989625i	$0.545891\pi$
$752$	4.35425	0.158783
$753$	77.3320	2.81814
$754$	3.29150	0.119869
$755$	−21.2915	−0.774877
$756$	9.64575	0.350813
$757$	−4.58301	−0.166572	−0.0832861	−	0.996526i	$-0.526542\pi$
$757$	−4.58301	−0.166572	−0.0832861	+	0.996526i	$0.526542\pi$
$758$	10.7085	0.388950
$759$	20.2288	0.734257
$760$	0	0
$761$	42.8745	1.55420	0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745	1.55420	0.777100	+	0.629377i	$0.216690\pi$
$762$	−35.1660	−1.27393
$763$	53.1660	1.92474
$764$	6.58301	0.238165
$765$	0	0
$766$	5.52026	0.199455
$767$	−15.8745	−0.573195
$768$	2.64575	0.0954703
$769$	35.2915	1.27264	0.636322	−	0.771424i	$-0.280455\pi$
$769$	35.2915	1.27264	0.636322	+	0.771424i	$0.280455\pi$
$770$	27.8745	1.00453
$771$	32.5203	1.17119
$772$	14.5830	0.524854
$773$	−4.93725	−0.177581	−0.0887903	−	0.996050i	$-0.528300\pi$
$773$	−4.93725	−0.177581	−0.0887903	+	0.996050i	$0.528300\pi$
$774$	45.1660	1.62346
$775$	12.9373	0.464720
$776$	−3.70850	−0.133127
$777$	3.41699	0.122584
$778$	12.0000	0.430221
$779$	0	0
$780$	−8.70850	−0.311814
$781$	12.5830	0.450255
$782$	0	0
$783$	4.35425	0.155608
$784$	6.29150	0.224697
$785$	17.4170	0.621639
$786$	5.12549	0.182820
$787$	−42.5203	−1.51568	−0.757842	−	0.652438i	$-0.773746\pi$
$787$	−42.5203	−1.51568	−0.757842	+	0.652438i	$0.773746\pi$
$788$	−7.64575	−0.272369
$789$	−28.9373	−1.03019
$790$	6.58301	0.234213
$791$	−56.8118	−2.01999
$792$	−18.5830	−0.660318
$793$	1.87451	0.0665657
$794$	21.0627	0.747489
$795$	54.7895	1.94318
$796$	−19.8745	−0.704433
$797$	−44.8118	−1.58731	−0.793657	−	0.608365i	$-0.791826\pi$
$797$	−44.8118	−1.58731	−0.793657	+	0.608365i	$0.791826\pi$
$798$	0	0
$799$	0	0
$800$	−2.29150	−0.0810169
$801$	0	0
$802$	27.5830	0.973990
$803$	−7.93725	−0.280100
$804$	1.70850	0.0602541
$805$	9.87451	0.348031
$806$	−11.2915	−0.397726
$807$	0	0
$808$	−13.6458	−0.480056
$809$	−9.00000	−0.316423	−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000	−0.316423	−0.158212	+	0.987405i	$0.550573\pi$
$810$	8.22876	0.289129
$811$	−31.2915	−1.09879	−0.549397	−	0.835562i	$-0.685142\pi$
$811$	−31.2915	−1.09879	−0.549397	+	0.835562i	$0.685142\pi$
$812$	6.00000	0.210559
$813$	32.6863	1.14636
$814$	−1.64575	−0.0576836
$815$	−6.47974	−0.226975
$816$	0	0
$817$	0	0
$818$	−7.58301	−0.265134
$819$	29.1660	1.01914
$820$	0.479741	0.0167533
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	41.2288	1.43802
$823$	−31.8745	−1.11108	−0.555538	−	0.831491i	$-0.687488\pi$
$823$	−31.8745	−1.11108	−0.555538	+	0.831491i	$0.687488\pi$
$824$	−13.2915	−0.463031
$825$	28.1660	0.980615
$826$	−28.9373	−1.00686
$827$	−52.6458	−1.83067	−0.915336	−	0.402691i	$-0.868075\pi$
$827$	−52.6458	−1.83067	−0.915336	+	0.402691i	$0.868075\pi$
$828$	−6.58301	−0.228775
$829$	−17.1660	−0.596200	−0.298100	−	0.954535i	$-0.596353\pi$
$829$	−17.1660	−0.596200	−0.298100	+	0.954535i	$0.596353\pi$
$830$	−13.0627	−0.453415
$831$	−72.8118	−2.52581
$832$	2.00000	0.0693375
$833$	0	0
$834$	49.3320	1.70823
$835$	19.7490	0.683443
$836$	0	0
$837$	−14.9373	−0.516307
$838$	−31.7490	−1.09675
$839$	−41.5203	−1.43344	−0.716719	−	0.697362i	$-0.754357\pi$
$839$	−41.5203	−1.43344	−0.716719	+	0.697362i	$0.754357\pi$
$840$	−15.8745	−0.547723
$841$	−26.2915	−0.906604
$842$	−24.8118	−0.855070
$843$	67.3542	2.31980
$844$	−13.2915	−0.457512
$845$	14.8118	0.509540
$846$	17.4170	0.598809
$847$	38.5830	1.32573
$848$	−12.5830	−0.432102
$849$	81.0810	2.78269
$850$	0	0
$851$	−0.583005	−0.0199852
$852$	−7.16601	−0.245503
$853$	8.58301	0.293877	0.146938	−	0.989146i	$-0.453058\pi$
$853$	8.58301	0.293877	0.146938	+	0.989146i	$0.453058\pi$
$854$	3.41699	0.116927
$855$	0	0
$856$	15.2915	0.522653
$857$	21.0000	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$858$	−24.5830	−0.839250
$859$	13.2288	0.451359	0.225680	−	0.974202i	$-0.427540\pi$
$859$	13.2288	0.451359	0.225680	+	0.974202i	$0.427540\pi$
$860$	−18.5830	−0.633675
$861$	−2.81176	−0.0958246
$862$	27.8745	0.949410
$863$	−31.0627	−1.05739	−0.528694	−	0.848812i	$-0.677318\pi$
$863$	−31.0627	−1.05739	−0.528694	+	0.848812i	$0.677318\pi$
$864$	2.64575	0.0900103
$865$	9.87451	0.335743
$866$	17.8745	0.607401
$867$	−44.9778	−1.52753
$868$	−20.5830	−0.698633
$869$	18.5830	0.630385
$870$	−7.16601	−0.242951
$871$	1.29150	0.0437609
$872$	14.5830	0.493843
$873$	−14.8340	−0.502054
$874$	0	0
$875$	43.7490	1.47899
$876$	4.52026	0.152725
$877$	−41.6458	−1.40628	−0.703139	−	0.711053i	$-0.748219\pi$
$877$	−41.6458	−1.40628	−0.703139	+	0.711053i	$0.748219\pi$
$878$	10.8118	0.364879
$879$	76.5608	2.58233
$880$	7.64575	0.257738
$881$	−36.8745	−1.24233	−0.621167	−	0.783678i	$-0.713341\pi$
$881$	−36.8745	−1.24233	−0.621167	+	0.783678i	$0.713341\pi$
$882$	25.1660	0.847384
$883$	−28.3948	−0.955560	−0.477780	−	0.878480i	$-0.658558\pi$
$883$	−28.3948	−0.955560	−0.477780	+	0.878480i	$0.658558\pi$
$884$	0	0
$885$	34.5608	1.16175
$886$	10.6458	0.357651
$887$	−17.4170	−0.584805	−0.292403	−	0.956295i	$-0.594455\pi$
$887$	−17.4170	−0.584805	−0.292403	+	0.956295i	$0.594455\pi$
$888$	0.937254	0.0314522
$889$	−48.4575	−1.62521
$890$	0	0
$891$	23.2288	0.778193
$892$	−18.8118	−0.629864
$893$	0	0
$894$	28.9373	0.967807
$895$	−6.68627	−0.223497
$896$	3.64575	0.121796
$897$	−8.70850	−0.290768
$898$	−24.2915	−0.810618
$899$	−9.29150	−0.309889
$900$	−9.16601	−0.305534
$901$	0	0
$902$	1.35425	0.0450915
$903$	108.915	3.62447
$904$	−15.5830	−0.518283
$905$	−36.5830	−1.21606
$906$	34.2288	1.13717
$907$	39.9373	1.32609	0.663047	−	0.748577i	$-0.269263\pi$
$907$	39.9373	1.32609	0.663047	+	0.748577i	$0.269263\pi$
$908$	−7.35425	−0.244059
$909$	−54.5830	−1.81040
$910$	−12.0000	−0.397796
$911$	16.9373	0.561156	0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373	0.561156	0.280578	+	0.959831i	$0.409474\pi$
$912$	0	0
$913$	−36.8745	−1.22037
$914$	32.8745	1.08739
$915$	−4.08104	−0.134915
$916$	20.0000	0.660819
$917$	7.06275	0.233232
$918$	0	0
$919$	−19.8745	−0.655600	−0.327800	−	0.944747i	$-0.606307\pi$
$919$	−19.8745	−0.655600	−0.327800	+	0.944747i	$0.606307\pi$
$920$	2.70850	0.0892965
$921$	1.70850	0.0562969
$922$	19.1660	0.631199
$923$	−5.41699	−0.178303
$924$	−44.8118	−1.47420
$925$	−0.811762	−0.0266906
$926$	−38.4575	−1.26379
$927$	−53.1660	−1.74620
$928$	1.64575	0.0540244
$929$	−9.58301	−0.314408	−0.157204	−	0.987566i	$-0.550248\pi$
$929$	−9.58301	−0.314408	−0.157204	+	0.987566i	$0.550248\pi$
$930$	24.5830	0.806108
$931$	0	0
$932$	18.8745	0.618255
$933$	36.1033	1.18197
$934$	−19.3542	−0.633290
$935$	0	0
$936$	8.00000	0.261488
$937$	7.12549	0.232780	0.116390	−	0.993204i	$-0.462868\pi$
$937$	7.12549	0.232780	0.116390	+	0.993204i	$0.462868\pi$
$938$	2.35425	0.0768689
$939$	23.4797	0.766232
$940$	−7.16601	−0.233729
$941$	16.8340	0.548772	0.274386	−	0.961620i	$-0.411525\pi$
$941$	16.8340	0.548772	0.274386	+	0.961620i	$0.411525\pi$
$942$	−28.0000	−0.912289
$943$	0.479741	0.0156225
$944$	−7.93725	−0.258336
$945$	−15.8745	−0.516398
$946$	−52.4575	−1.70554
$947$	−7.74902	−0.251809	−0.125905	−	0.992042i	$-0.540183\pi$
$947$	−7.74902	−0.251809	−0.125905	+	0.992042i	$0.540183\pi$
$948$	−10.5830	−0.343720
$949$	3.41699	0.110920
$950$	0	0
$951$	−15.8745	−0.514766
$952$	0	0
$953$	−13.4575	−0.435932	−0.217966	−	0.975956i	$-0.569942\pi$
$953$	−13.4575	−0.435932	−0.217966	+	0.975956i	$0.569942\pi$
$954$	−50.3320	−1.62956
$955$	−10.8340	−0.350580
$956$	−12.0000	−0.388108
$957$	−20.2288	−0.653903
$958$	6.58301	0.212687
$959$	56.8118	1.83455
$960$	−4.35425	−0.140533
$961$	0.874508	0.0282099
$962$	0.708497	0.0228429
$963$	61.1660	1.97105
$964$	−7.58301	−0.244232
$965$	−24.0000	−0.772587
$966$	−15.8745	−0.510754
$967$	−13.2915	−0.427426	−0.213713	−	0.976897i	$-0.568556\pi$
$967$	−13.2915	−0.427426	−0.213713	+	0.976897i	$0.568556\pi$
$968$	10.5830	0.340151
$969$	0	0
$970$	6.10326	0.195964
$971$	−54.3948	−1.74561	−0.872806	−	0.488068i	$-0.837702\pi$
$971$	−54.3948	−1.74561	−0.872806	+	0.488068i	$0.837702\pi$
$972$	−21.1660	−0.678900
$973$	67.9778	2.17927
$974$	4.22876	0.135498
$975$	−12.1255	−0.388327
$976$	0.937254	0.0300008
$977$	−7.45751	−0.238587	−0.119293	−	0.992859i	$-0.538063\pi$
$977$	−7.45751	−0.238587	−0.119293	+	0.992859i	$0.538063\pi$
$978$	10.4170	0.333099
$979$	0	0
$980$	−10.3542	−0.330754
$981$	58.3320	1.86240
$982$	39.2915	1.25384
$983$	31.7490	1.01264	0.506318	−	0.862347i	$-0.331006\pi$
$983$	31.7490	1.01264	0.506318	+	0.862347i	$0.331006\pi$
$984$	−0.771243	−0.0245863
$985$	12.5830	0.400928
$986$	0	0
$987$	42.0000	1.33687
$988$	0	0
$989$	−18.5830	−0.590905
$990$	30.5830	0.971992
$991$	−2.83399	−0.0900246	−0.0450123	−	0.998986i	$-0.514333\pi$
$991$	−2.83399	−0.0900246	−0.0450123	+	0.998986i	$0.514333\pi$
$992$	−5.64575	−0.179253
$993$	52.4170	1.66340
$994$	−9.87451	−0.313200
$995$	32.7085	1.03693
$996$	21.0000	0.665410
$997$	16.2288	0.513970	0.256985	−	0.966415i	$-0.417271\pi$
$997$	16.2288	0.513970	0.256985	+	0.966415i	$0.417271\pi$
$998$	−4.77124	−0.151031
$999$	0.937254	0.0296534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.j.1.2		2
3.2	odd	2		6498.2.a.ba.1.2		2
4.3	odd	2		5776.2.a.ba.1.1		2
19.2	odd	18		722.2.e.o.99.1		12
19.3	odd	18		722.2.e.o.389.1		12
19.4	even	9		722.2.e.n.415.1		12
19.5	even	9		722.2.e.n.595.1		12
19.6	even	9		722.2.e.n.245.2		12
19.7	even	3		38.2.c.b.11.1	yes	4
19.8	odd	6		722.2.c.j.653.2		4
19.9	even	9		722.2.e.n.423.2		12
19.10	odd	18		722.2.e.o.423.1		12
19.11	even	3		38.2.c.b.7.1	✓	4
19.12	odd	6		722.2.c.j.429.2		4
19.13	odd	18		722.2.e.o.245.1		12
19.14	odd	18		722.2.e.o.595.2		12
19.15	odd	18		722.2.e.o.415.2		12
19.16	even	9		722.2.e.n.389.2		12
19.17	even	9		722.2.e.n.99.2		12
19.18	odd	2		722.2.a.g.1.1		2
57.11	odd	6		342.2.g.f.235.1		4
57.26	odd	6		342.2.g.f.163.1		4
57.56	even	2		6498.2.a.bg.1.2		2
76.7	odd	6		304.2.i.e.49.2		4
76.11	odd	6		304.2.i.e.273.2		4
76.75	even	2		5776.2.a.z.1.2		2
95.7	odd	12		950.2.j.g.49.2		8
95.49	even	6		950.2.e.k.501.2		4
95.64	even	6		950.2.e.k.201.2		4
95.68	odd	12		950.2.j.g.349.2		8
95.83	odd	12		950.2.j.g.49.3		8
95.87	odd	12		950.2.j.g.349.3		8
152.11	odd	6		1216.2.i.k.577.1		4
152.45	even	6		1216.2.i.l.961.2		4
152.83	odd	6		1216.2.i.k.961.1		4
152.125	even	6		1216.2.i.l.577.2		4
228.11	even	6		2736.2.s.v.577.1		4
228.83	even	6		2736.2.s.v.1873.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	19.11	even	3
38.2.c.b.11.1	yes	4	19.7	even	3
304.2.i.e.49.2		4	76.7	odd	6
304.2.i.e.273.2		4	76.11	odd	6
342.2.g.f.163.1		4	57.26	odd	6
342.2.g.f.235.1		4	57.11	odd	6
722.2.a.g.1.1		2	19.18	odd	2
722.2.a.j.1.2		2	1.1	even	1	trivial
722.2.c.j.429.2		4	19.12	odd	6
722.2.c.j.653.2		4	19.8	odd	6
722.2.e.n.99.2		12	19.17	even	9
722.2.e.n.245.2		12	19.6	even	9
722.2.e.n.389.2		12	19.16	even	9
722.2.e.n.415.1		12	19.4	even	9
722.2.e.n.423.2		12	19.9	even	9
722.2.e.n.595.1		12	19.5	even	9
722.2.e.o.99.1		12	19.2	odd	18
722.2.e.o.245.1		12	19.13	odd	18
722.2.e.o.389.1		12	19.3	odd	18
722.2.e.o.415.2		12	19.15	odd	18
722.2.e.o.423.1		12	19.10	odd	18
722.2.e.o.595.2		12	19.14	odd	18
950.2.e.k.201.2		4	95.64	even	6
950.2.e.k.501.2		4	95.49	even	6
950.2.j.g.49.2		8	95.7	odd	12
950.2.j.g.49.3		8	95.83	odd	12
950.2.j.g.349.2		8	95.68	odd	12
950.2.j.g.349.3		8	95.87	odd	12
1216.2.i.k.577.1		4	152.11	odd	6
1216.2.i.k.961.1		4	152.83	odd	6
1216.2.i.l.577.2		4	152.125	even	6
1216.2.i.l.961.2		4	152.45	even	6
2736.2.s.v.577.1		4	228.11	even	6
2736.2.s.v.1873.1		4	228.83	even	6
5776.2.a.z.1.2		2	76.75	even	2
5776.2.a.ba.1.1		2	4.3	odd	2
6498.2.a.ba.1.2		2	3.2	odd	2
6498.2.a.bg.1.2		2	57.56	even	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.64575 q^{3} +1.00000 q^{4} -1.64575 q^{5} +2.64575 q^{6} +3.64575 q^{7} +1.00000 q^{8} +4.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.64575 q^{3} +1.00000 q^{4} -1.64575 q^{5} +2.64575 q^{6} +3.64575 q^{7} +1.00000 q^{8} +4.00000 q^{9} -1.64575 q^{10} -4.64575 q^{11} +2.64575 q^{12} +2.00000 q^{13} +3.64575 q^{14} -4.35425 q^{15} +1.00000 q^{16} +4.00000 q^{18} -1.64575 q^{20} +9.64575 q^{21} -4.64575 q^{22} -1.64575 q^{23} +2.64575 q^{24} -2.29150 q^{25} +2.00000 q^{26} +2.64575 q^{27} +3.64575 q^{28} +1.64575 q^{29} -4.35425 q^{30} -5.64575 q^{31} +1.00000 q^{32} -12.2915 q^{33} -6.00000 q^{35} +4.00000 q^{36} +0.354249 q^{37} +5.29150 q^{39} -1.64575 q^{40} -0.291503 q^{41} +9.64575 q^{42} +11.2915 q^{43} -4.64575 q^{44} -6.58301 q^{45} -1.64575 q^{46} +4.35425 q^{47} +2.64575 q^{48} +6.29150 q^{49} -2.29150 q^{50} +2.00000 q^{52} -12.5830 q^{53} +2.64575 q^{54} +7.64575 q^{55} +3.64575 q^{56} +1.64575 q^{58} -7.93725 q^{59} -4.35425 q^{60} +0.937254 q^{61} -5.64575 q^{62} +14.5830 q^{63} +1.00000 q^{64} -3.29150 q^{65} -12.2915 q^{66} +0.645751 q^{67} -4.35425 q^{69} -6.00000 q^{70} -2.70850 q^{71} +4.00000 q^{72} +1.70850 q^{73} +0.354249 q^{74} -6.06275 q^{75} -16.9373 q^{77} +5.29150 q^{78} -4.00000 q^{79} -1.64575 q^{80} -5.00000 q^{81} -0.291503 q^{82} +7.93725 q^{83} +9.64575 q^{84} +11.2915 q^{86} +4.35425 q^{87} -4.64575 q^{88} -6.58301 q^{90} +7.29150 q^{91} -1.64575 q^{92} -14.9373 q^{93} +4.35425 q^{94} +2.64575 q^{96} -3.70850 q^{97} +6.29150 q^{98} -18.5830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 + 8 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 4 q^{13} + 2 q^{14} - 14 q^{15} + 2 q^{16} + 8 q^{18} + 2 q^{20} + 14 q^{21} - 4 q^{22} + 2 q^{23} + 6 q^{25} + 4 q^{26} + 2 q^{28} - 2 q^{29} - 14 q^{30} - 6 q^{31} + 2 q^{32} - 14 q^{33} - 12 q^{35} + 8 q^{36} + 6 q^{37} + 2 q^{40} + 10 q^{41} + 14 q^{42} + 12 q^{43} - 4 q^{44} + 8 q^{45} + 2 q^{46} + 14 q^{47} + 2 q^{49} + 6 q^{50} + 4 q^{52} - 4 q^{53} + 10 q^{55} + 2 q^{56} - 2 q^{58} - 14 q^{60} - 14 q^{61} - 6 q^{62} + 8 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{66} - 4 q^{67} - 14 q^{69} - 12 q^{70} - 16 q^{71} + 8 q^{72} + 14 q^{73} + 6 q^{74} - 28 q^{75} - 18 q^{77} - 8 q^{79} + 2 q^{80} - 10 q^{81} + 10 q^{82} + 14 q^{84} + 12 q^{86} + 14 q^{87} - 4 q^{88} + 8 q^{90} + 4 q^{91} + 2 q^{92} - 14 q^{93} + 14 q^{94} - 18 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 4 * q^13 + 2 * q^14 - 14 * q^15 + 2 * q^16 + 8 * q^18 + 2 * q^20 + 14 * q^21 - 4 * q^22 + 2 * q^23 + 6 * q^25 + 4 * q^26 + 2 * q^28 - 2 * q^29 - 14 * q^30 - 6 * q^31 + 2 * q^32 - 14 * q^33 - 12 * q^35 + 8 * q^36 + 6 * q^37 + 2 * q^40 + 10 * q^41 + 14 * q^42 + 12 * q^43 - 4 * q^44 + 8 * q^45 + 2 * q^46 + 14 * q^47 + 2 * q^49 + 6 * q^50 + 4 * q^52 - 4 * q^53 + 10 * q^55 + 2 * q^56 - 2 * q^58 - 14 * q^60 - 14 * q^61 - 6 * q^62 + 8 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^66 - 4 * q^67 - 14 * q^69 - 12 * q^70 - 16 * q^71 + 8 * q^72 + 14 * q^73 + 6 * q^74 - 28 * q^75 - 18 * q^77 - 8 * q^79 + 2 * q^80 - 10 * q^81 + 10 * q^82 + 14 * q^84 + 12 * q^86 + 14 * q^87 - 4 * q^88 + 8 * q^90 + 4 * q^91 + 2 * q^92 - 14 * q^93 + 14 * q^94 - 18 * q^97 + 2 * q^98 - 16 * q^99

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