LMFDB - Embedded newform 5290.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{24})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 1 $ x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.93185$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -1.71744 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -1.71744 q^{7} -1.00000 q^{8} -2.82843 q^{9} -1.00000 q^{10} -0.378937 q^{11} -0.414214 q^{12} -3.03528 q^{13} +1.71744 q^{14} -0.414214 q^{15} +1.00000 q^{16} -0.663902 q^{17} +2.82843 q^{18} -3.53225 q^{19} +1.00000 q^{20} +0.711386 q^{21} +0.378937 q^{22} +0.414214 q^{24} +1.00000 q^{25} +3.03528 q^{26} +2.41421 q^{27} -1.71744 q^{28} -10.0100 q^{29} +0.414214 q^{30} +7.31784 q^{31} -1.00000 q^{32} +0.156961 q^{33} +0.663902 q^{34} -1.71744 q^{35} -2.82843 q^{36} -0.828427 q^{37} +3.53225 q^{38} +1.25725 q^{39} -1.00000 q^{40} +9.19151 q^{41} -0.711386 q^{42} -5.24969 q^{43} -0.378937 q^{44} -2.82843 q^{45} -8.00997 q^{47} -0.414214 q^{48} -4.05040 q^{49} -1.00000 q^{50} +0.274997 q^{51} -3.03528 q^{52} -3.04524 q^{53} -2.41421 q^{54} -0.378937 q^{55} +1.71744 q^{56} +1.46311 q^{57} +10.0100 q^{58} +3.00000 q^{59} -0.414214 q^{60} +4.09978 q^{61} -7.31784 q^{62} +4.85765 q^{63} +1.00000 q^{64} -3.03528 q^{65} -0.156961 q^{66} +2.67800 q^{67} -0.663902 q^{68} +1.71744 q^{70} +2.21201 q^{71} +2.82843 q^{72} +2.25209 q^{73} +0.828427 q^{74} -0.414214 q^{75} -3.53225 q^{76} +0.650802 q^{77} -1.25725 q^{78} -9.63959 q^{79} +1.00000 q^{80} +7.48528 q^{81} -9.19151 q^{82} +2.40060 q^{83} +0.711386 q^{84} -0.663902 q^{85} +5.24969 q^{86} +4.14626 q^{87} +0.378937 q^{88} +9.22146 q^{89} +2.82843 q^{90} +5.21290 q^{91} -3.03115 q^{93} +8.00997 q^{94} -3.53225 q^{95} +0.414214 q^{96} +14.0134 q^{97} +4.05040 q^{98} +1.07180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{10} + 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} - 4 q^{28} - 12 q^{29} - 4 q^{30} + 28 q^{31} - 4 q^{32} + 16 q^{33} - 12 q^{34} - 4 q^{35} + 8 q^{37} + 8 q^{38} - 16 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{42} - 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} + 16 q^{51} - 8 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 4 q^{60} - 28 q^{62} + 4 q^{64} - 8 q^{65} - 16 q^{66} + 12 q^{67} + 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} - 8 q^{74} + 4 q^{75} - 8 q^{76} - 24 q^{77} + 16 q^{78} - 4 q^{79} + 4 q^{80} - 4 q^{81} + 8 q^{82} + 12 q^{83} - 4 q^{84} + 12 q^{85} + 12 q^{86} + 4 q^{87} + 40 q^{89} + 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} + 16 q^{97} - 12 q^{98} + 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^10 + 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 - 4 * q^28 - 12 * q^29 - 4 * q^30 + 28 * q^31 - 4 * q^32 + 16 * q^33 - 12 * q^34 - 4 * q^35 + 8 * q^37 + 8 * q^38 - 16 * q^39 - 4 * q^40 - 8 * q^41 + 4 * q^42 - 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 4 * q^60 - 28 * q^62 + 4 * q^64 - 8 * q^65 - 16 * q^66 + 12 * q^67 + 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 - 8 * q^74 + 4 * q^75 - 8 * q^76 - 24 * q^77 + 16 * q^78 - 4 * q^79 + 4 * q^80 - 4 * q^81 + 8 * q^82 + 12 * q^83 - 4 * q^84 + 12 * q^85 + 12 * q^86 + 4 * q^87 + 40 * q^89 + 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 + 16 * q^97 - 12 * q^98 + 32 * 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
$3$	−0.414214	−0.239146	−0.119573	−	0.992825i	$-0.538153\pi$
$3$	−0.414214	−0.239146	−0.119573	+	0.992825i	$0.538153\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.414214	0.169102
$7$	−1.71744	−0.649131	−0.324565	−	0.945863i	$-0.605218\pi$
$7$	−1.71744	−0.649131	−0.324565	+	0.945863i	$0.605218\pi$
$8$	−1.00000	−0.353553
$9$	−2.82843	−0.942809
$10$	−1.00000	−0.316228
$11$	−0.378937	−0.114254	−0.0571270	−	0.998367i	$-0.518194\pi$
$11$	−0.378937	−0.114254	−0.0571270	+	0.998367i	$0.518194\pi$
$12$	−0.414214	−0.119573
$13$	−3.03528	−0.841834	−0.420917	−	0.907099i	$-0.638292\pi$
$13$	−3.03528	−0.841834	−0.420917	+	0.907099i	$0.638292\pi$
$14$	1.71744	0.459005
$15$	−0.414214	−0.106949
$16$	1.00000	0.250000
$17$	−0.663902	−0.161020	−0.0805100	−	0.996754i	$-0.525655\pi$
$17$	−0.663902	−0.161020	−0.0805100	+	0.996754i	$0.525655\pi$
$18$	2.82843	0.666667
$19$	−3.53225	−0.810354	−0.405177	−	0.914238i	$-0.632790\pi$
$19$	−3.53225	−0.810354	−0.405177	+	0.914238i	$0.632790\pi$
$20$	1.00000	0.223607
$21$	0.711386	0.155237
$22$	0.378937	0.0807897
$23$	0	0
$23$	0	0
$24$	0.414214	0.0845510
$25$	1.00000	0.200000
$26$	3.03528	0.595267
$27$	2.41421	0.464616
$28$	−1.71744	−0.324565
$29$	−10.0100	−1.85880	−0.929402	−	0.369069i	$-0.879677\pi$
$29$	−10.0100	−1.85880	−0.929402	+	0.369069i	$0.879677\pi$
$30$	0.414214	0.0756247
$31$	7.31784	1.31432	0.657161	−	0.753750i	$-0.271757\pi$
$31$	7.31784	1.31432	0.657161	+	0.753750i	$0.271757\pi$
$32$	−1.00000	−0.176777
$33$	0.156961	0.0273234
$34$	0.663902	0.113858
$35$	−1.71744	−0.290300
$36$	−2.82843	−0.471405
$37$	−0.828427	−0.136193	−0.0680963	−	0.997679i	$-0.521693\pi$
$37$	−0.828427	−0.136193	−0.0680963	+	0.997679i	$0.521693\pi$
$38$	3.53225	0.573007
$39$	1.25725	0.201322
$40$	−1.00000	−0.158114
$41$	9.19151	1.43547	0.717736	−	0.696315i	$-0.245178\pi$
$41$	9.19151	1.43547	0.717736	+	0.696315i	$0.245178\pi$
$42$	−0.711386	−0.109769
$43$	−5.24969	−0.800570	−0.400285	−	0.916391i	$-0.631089\pi$
$43$	−5.24969	−0.800570	−0.400285	+	0.916391i	$0.631089\pi$
$44$	−0.378937	−0.0571270
$45$	−2.82843	−0.421637
$46$	0	0
$47$	−8.00997	−1.16837	−0.584187	−	0.811619i	$-0.698587\pi$
$47$	−8.00997	−1.16837	−0.584187	+	0.811619i	$0.698587\pi$
$48$	−0.414214	−0.0597866
$49$	−4.05040	−0.578629
$50$	−1.00000	−0.141421
$51$	0.274997	0.0385073
$52$	−3.03528	−0.420917
$53$	−3.04524	−0.418296	−0.209148	−	0.977884i	$-0.567069\pi$
$53$	−3.04524	−0.418296	−0.209148	+	0.977884i	$0.567069\pi$
$54$	−2.41421	−0.328533
$55$	−0.378937	−0.0510959
$56$	1.71744	0.229502
$57$	1.46311	0.193793
$58$	10.0100	1.31437
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	−0.414214	−0.0534747
$61$	4.09978	0.524923	0.262461	−	0.964943i	$-0.415466\pi$
$61$	4.09978	0.524923	0.262461	+	0.964943i	$0.415466\pi$
$62$	−7.31784	−0.929366
$63$	4.85765	0.612006
$64$	1.00000	0.125000
$65$	−3.03528	−0.376480
$66$	−0.156961	−0.0193206
$67$	2.67800	0.327170	0.163585	−	0.986529i	$-0.447694\pi$
$67$	2.67800	0.327170	0.163585	+	0.986529i	$0.447694\pi$
$68$	−0.663902	−0.0805100
$69$	0	0
$70$	1.71744	0.205273
$71$	2.21201	0.262517	0.131259	−	0.991348i	$-0.458098\pi$
$71$	2.21201	0.262517	0.131259	+	0.991348i	$0.458098\pi$
$72$	2.82843	0.333333
$73$	2.25209	0.263588	0.131794	−	0.991277i	$-0.457926\pi$
$73$	2.25209	0.263588	0.131794	+	0.991277i	$0.457926\pi$
$74$	0.828427	0.0963027
$75$	−0.414214	−0.0478293
$76$	−3.53225	−0.405177
$77$	0.650802	0.0741657
$78$	−1.25725	−0.142356
$79$	−9.63959	−1.08454	−0.542269	−	0.840205i	$-0.682435\pi$
$79$	−9.63959	−1.08454	−0.542269	+	0.840205i	$0.682435\pi$
$80$	1.00000	0.111803
$81$	7.48528	0.831698
$82$	−9.19151	−1.01503
$83$	2.40060	0.263500	0.131750	−	0.991283i	$-0.457940\pi$
$83$	2.40060	0.263500	0.131750	+	0.991283i	$0.457940\pi$
$84$	0.711386	0.0776186
$85$	−0.663902	−0.0720103
$86$	5.24969	0.566089
$87$	4.14626	0.444526
$88$	0.378937	0.0403949
$89$	9.22146	0.977473	0.488736	−	0.872431i	$-0.337458\pi$
$89$	9.22146	0.977473	0.488736	+	0.872431i	$0.337458\pi$
$90$	2.82843	0.298142
$91$	5.21290	0.546461
$92$	0	0
$93$	−3.03115	−0.314315
$94$	8.00997	0.826165
$95$	−3.53225	−0.362401
$96$	0.414214	0.0422755
$97$	14.0134	1.42284	0.711421	−	0.702766i	$-0.248052\pi$
$97$	14.0134	1.42284	0.711421	+	0.702766i	$0.248052\pi$
$98$	4.05040	0.409153
$99$	1.07180	0.107720
$100$	1.00000	0.100000
$101$	−3.70747	−0.368907	−0.184454	−	0.982841i	$-0.559052\pi$
$101$	−3.70747	−0.368907	−0.184454	+	0.982841i	$0.559052\pi$
$102$	−0.274997	−0.0272288
$103$	−19.1258	−1.88452	−0.942259	−	0.334886i	$-0.891302\pi$
$103$	−19.1258	−1.88452	−0.942259	+	0.334886i	$0.891302\pi$
$104$	3.03528	0.297633
$105$	0.711386	0.0694242
$106$	3.04524	0.295780
$107$	9.07107	0.876933	0.438467	−	0.898747i	$-0.355522\pi$
$107$	9.07107	0.876933	0.438467	+	0.898747i	$0.355522\pi$
$108$	2.41421	0.232308
$109$	17.4448	1.67091	0.835457	−	0.549556i	$-0.185203\pi$
$109$	17.4448	1.67091	0.835457	+	0.549556i	$0.185203\pi$
$110$	0.378937	0.0361303
$111$	0.343146	0.0325700
$112$	−1.71744	−0.162283
$113$	15.9418	1.49968	0.749840	−	0.661619i	$-0.230130\pi$
$113$	15.9418	1.49968	0.749840	+	0.661619i	$0.230130\pi$
$114$	−1.46311	−0.137032
$115$	0	0
$116$	−10.0100	−0.929402
$117$	8.58506	0.793689
$118$	−3.00000	−0.276172
$119$	1.14021	0.104523
$120$	0.414214	0.0378124
$121$	−10.8564	−0.986946
$122$	−4.09978	−0.371176
$123$	−3.80725	−0.343288
$124$	7.31784	0.657161
$125$	1.00000	0.0894427
$126$	−4.85765	−0.432754
$127$	1.24728	0.110679	0.0553393	−	0.998468i	$-0.482376\pi$
$127$	1.24728	0.110679	0.0553393	+	0.998468i	$0.482376\pi$
$128$	−1.00000	−0.0883883
$129$	2.17449	0.191453
$130$	3.03528	0.266211
$131$	−0.907023	−0.0792470	−0.0396235	−	0.999215i	$-0.512616\pi$
$131$	−0.907023	−0.0792470	−0.0396235	+	0.999215i	$0.512616\pi$
$132$	0.156961	0.0136617
$133$	6.06642	0.526026
$134$	−2.67800	−0.231344
$135$	2.41421	0.207782
$136$	0.663902	0.0569292
$137$	−5.19250	−0.443626	−0.221813	−	0.975089i	$-0.571197\pi$
$137$	−5.19250	−0.443626	−0.221813	+	0.975089i	$0.571197\pi$
$138$	0	0
$139$	3.49457	0.296406	0.148203	−	0.988957i	$-0.452651\pi$
$139$	3.49457	0.296406	0.148203	+	0.988957i	$0.452651\pi$
$140$	−1.71744	−0.145150
$141$	3.31784	0.279412
$142$	−2.21201	−0.185628
$143$	1.15018	0.0961829
$144$	−2.82843	−0.235702
$145$	−10.0100	−0.831283
$146$	−2.25209	−0.186385
$147$	1.67773	0.138377
$148$	−0.828427	−0.0680963
$149$	3.52469	0.288754	0.144377	−	0.989523i	$-0.453882\pi$
$149$	3.52469	0.288754	0.144377	+	0.989523i	$0.453882\pi$
$150$	0.414214	0.0338204
$151$	13.5347	1.10143	0.550717	−	0.834692i	$-0.314354\pi$
$151$	13.5347	1.10143	0.550717	+	0.834692i	$0.314354\pi$
$152$	3.53225	0.286503
$153$	1.87780	0.151811
$154$	−0.650802	−0.0524431
$155$	7.31784	0.587783
$156$	1.25725	0.100661
$157$	8.39960	0.670361	0.335181	−	0.942154i	$-0.391203\pi$
$157$	8.39960	0.670361	0.335181	+	0.942154i	$0.391203\pi$
$158$	9.63959	0.766885
$159$	1.26138	0.100034
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−7.48528	−0.588099
$163$	12.8484	1.00636	0.503181	−	0.864181i	$-0.332163\pi$
$163$	12.8484	1.00636	0.503181	+	0.864181i	$0.332163\pi$
$164$	9.19151	0.717736
$165$	0.156961	0.0122194
$166$	−2.40060	−0.186322
$167$	−15.3942	−1.19124	−0.595621	−	0.803266i	$-0.703094\pi$
$167$	−15.3942	−1.19124	−0.595621	+	0.803266i	$0.703094\pi$
$168$	−0.711386	−0.0548847
$169$	−3.78710	−0.291315
$170$	0.663902	0.0509190
$171$	9.99071	0.764009
$172$	−5.24969	−0.400285
$173$	−5.88777	−0.447639	−0.223819	−	0.974631i	$-0.571853\pi$
$173$	−5.88777	−0.447639	−0.223819	+	0.974631i	$0.571853\pi$
$174$	−4.14626	−0.314327
$175$	−1.71744	−0.129826
$176$	−0.378937	−0.0285635
$177$	−1.24264	−0.0934026
$178$	−9.22146	−0.691178
$179$	16.9873	1.26969	0.634846	−	0.772639i	$-0.281064\pi$
$179$	16.9873	1.26969	0.634846	+	0.772639i	$0.281064\pi$
$180$	−2.82843	−0.210819
$181$	14.3996	1.07031	0.535157	−	0.844753i	$-0.320252\pi$
$181$	14.3996	1.07031	0.535157	+	0.844753i	$0.320252\pi$
$182$	−5.21290	−0.386406
$183$	−1.69818	−0.125533
$184$	0	0
$185$	−0.828427	−0.0609072
$186$	3.03115	0.222255
$187$	0.251577	0.0183972
$188$	−8.00997	−0.584187
$189$	−4.14626	−0.301596
$190$	3.53225	0.256256
$191$	−19.1650	−1.38673	−0.693364	−	0.720588i	$-0.743872\pi$
$191$	−19.1650	−1.38673	−0.693364	+	0.720588i	$0.743872\pi$
$192$	−0.414214	−0.0298933
$193$	−24.9993	−1.79949	−0.899743	−	0.436419i	$-0.856246\pi$
$193$	−24.9993	−1.79949	−0.899743	+	0.436419i	$0.856246\pi$
$194$	−14.0134	−1.00610
$195$	1.25725	0.0900337
$196$	−4.05040	−0.289315
$197$	−7.21592	−0.514113	−0.257057	−	0.966396i	$-0.582753\pi$
$197$	−7.21592	−0.514113	−0.257057	+	0.966396i	$0.582753\pi$
$198$	−1.07180	−0.0761693
$199$	17.9959	1.27569	0.637847	−	0.770163i	$-0.279825\pi$
$199$	17.9959	1.27569	0.637847	+	0.770163i	$0.279825\pi$
$200$	−1.00000	−0.0707107
$201$	−1.10926	−0.0782414
$202$	3.70747	0.260857
$203$	17.1915	1.20661
$204$	0.274997	0.0192537
$205$	9.19151	0.641963
$206$	19.1258	1.33256
$207$	0	0
$208$	−3.03528	−0.210459
$209$	1.33850	0.0925861
$210$	−0.711386	−0.0490903
$211$	18.4256	1.26847	0.634235	−	0.773140i	$-0.281315\pi$
$211$	18.4256	1.26847	0.634235	+	0.773140i	$0.281315\pi$
$212$	−3.04524	−0.209148
$213$	−0.916244	−0.0627800
$214$	−9.07107	−0.620085
$215$	−5.24969	−0.358026
$216$	−2.41421	−0.164266
$217$	−12.5679	−0.853167
$218$	−17.4448	−1.18151
$219$	−0.932847	−0.0630360
$220$	−0.378937	−0.0255480
$221$	2.01513	0.135552
$222$	−0.343146	−0.0230304
$223$	3.19151	0.213719	0.106860	−	0.994274i	$-0.465920\pi$
$223$	3.19151	0.213719	0.106860	+	0.994274i	$0.465920\pi$
$224$	1.71744	0.114751
$225$	−2.82843	−0.188562
$226$	−15.9418	−1.06043
$227$	24.0567	1.59670	0.798350	−	0.602193i	$-0.205706\pi$
$227$	24.0567	1.59670	0.798350	+	0.602193i	$0.205706\pi$
$228$	1.46311	0.0968966
$229$	−9.18154	−0.606733	−0.303367	−	0.952874i	$-0.598111\pi$
$229$	−9.18154	−0.606733	−0.303367	+	0.952874i	$0.598111\pi$
$230$	0	0
$231$	−0.269571	−0.0177365
$232$	10.0100	0.657187
$233$	−20.5963	−1.34931	−0.674653	−	0.738135i	$-0.735707\pi$
$233$	−20.5963	−1.34931	−0.674653	+	0.738135i	$0.735707\pi$
$234$	−8.58506	−0.561223
$235$	−8.00997	−0.522513
$236$	3.00000	0.195283
$237$	3.99285	0.259363
$238$	−1.14021	−0.0739090
$239$	23.0892	1.49352	0.746759	−	0.665094i	$-0.231609\pi$
$239$	23.0892	1.49352	0.746759	+	0.665094i	$0.231609\pi$
$240$	−0.414214	−0.0267374
$241$	−4.41129	−0.284156	−0.142078	−	0.989855i	$-0.545378\pi$
$241$	−4.41129	−0.284156	−0.142078	+	0.989855i	$0.545378\pi$
$242$	10.8564	0.697876
$243$	−10.3431	−0.663513
$244$	4.09978	0.262461
$245$	−4.05040	−0.258771
$246$	3.80725	0.242741
$247$	10.7214	0.682183
$248$	−7.31784	−0.464683
$249$	−0.994360	−0.0630150
$250$	−1.00000	−0.0632456
$251$	20.4312	1.28961	0.644804	−	0.764348i	$-0.276939\pi$
$251$	20.4312	1.28961	0.644804	+	0.764348i	$0.276939\pi$
$252$	4.85765	0.306003
$253$	0	0
$254$	−1.24728	−0.0782616
$255$	0.274997	0.0172210
$256$	1.00000	0.0625000
$257$	16.2414	1.01311	0.506555	−	0.862208i	$-0.330919\pi$
$257$	16.2414	1.01311	0.506555	+	0.862208i	$0.330919\pi$
$258$	−2.17449	−0.135378
$259$	1.42277	0.0884068
$260$	−3.03528	−0.188240
$261$	28.3125	1.75250
$262$	0.907023	0.0560361
$263$	−26.9116	−1.65944	−0.829721	−	0.558179i	$-0.811500\pi$
$263$	−26.9116	−1.65944	−0.829721	+	0.558179i	$0.811500\pi$
$264$	−0.156961	−0.00966028
$265$	−3.04524	−0.187068
$266$	−6.06642	−0.371956
$267$	−3.81965	−0.233759
$268$	2.67800	0.163585
$269$	−3.06251	−0.186724	−0.0933622	−	0.995632i	$-0.529761\pi$
$269$	−3.06251	−0.186724	−0.0933622	+	0.995632i	$0.529761\pi$
$270$	−2.41421	−0.146924
$271$	25.8131	1.56803	0.784017	−	0.620740i	$-0.213168\pi$
$271$	25.8131	1.56803	0.784017	+	0.620740i	$0.213168\pi$
$272$	−0.663902	−0.0402550
$273$	−2.15925	−0.130684
$274$	5.19250	0.313691
$275$	−0.378937	−0.0228508
$276$	0	0
$277$	−10.7454	−0.645630	−0.322815	−	0.946462i	$-0.604629\pi$
$277$	−10.7454	−0.645630	−0.322815	+	0.946462i	$0.604629\pi$
$278$	−3.49457	−0.209590
$279$	−20.6980	−1.23916
$280$	1.71744	0.102637
$281$	2.55343	0.152325	0.0761624	−	0.997095i	$-0.475733\pi$
$281$	2.55343	0.152325	0.0761624	+	0.997095i	$0.475733\pi$
$282$	−3.31784	−0.197574
$283$	11.4971	0.683434	0.341717	−	0.939803i	$-0.388992\pi$
$283$	11.4971	0.683434	0.341717	+	0.939803i	$0.388992\pi$
$284$	2.21201	0.131259
$285$	1.46311	0.0866669
$286$	−1.15018	−0.0680115
$287$	−15.7859	−0.931810
$288$	2.82843	0.166667
$289$	−16.5592	−0.974073
$290$	10.0100	0.587806
$291$	−5.80453	−0.340267
$292$	2.25209	0.131794
$293$	2.36557	0.138198	0.0690990	−	0.997610i	$-0.477988\pi$
$293$	2.36557	0.138198	0.0690990	+	0.997610i	$0.477988\pi$
$294$	−1.67773	−0.0978473
$295$	3.00000	0.174667
$296$	0.828427	0.0481513
$297$	−0.914836	−0.0530842
$298$	−3.52469	−0.204180
$299$	0	0
$300$	−0.414214	−0.0239146
$301$	9.01602	0.519675
$302$	−13.5347	−0.778832
$303$	1.53568	0.0882228
$304$	−3.53225	−0.202588
$305$	4.09978	0.234752
$306$	−1.87780	−0.107347
$307$	−18.5047	−1.05612	−0.528060	−	0.849207i	$-0.677080\pi$
$307$	−18.5047	−1.05612	−0.528060	+	0.849207i	$0.677080\pi$
$308$	0.650802	0.0370829
$309$	7.92215	0.450675
$310$	−7.31784	−0.415625
$311$	−26.1438	−1.48248	−0.741239	−	0.671241i	$-0.765761\pi$
$311$	−26.1438	−1.48248	−0.741239	+	0.671241i	$0.765761\pi$
$312$	−1.25725	−0.0711779
$313$	−8.33005	−0.470842	−0.235421	−	0.971893i	$-0.575647\pi$
$313$	−8.33005	−0.470842	−0.235421	+	0.971893i	$0.575647\pi$
$314$	−8.39960	−0.474017
$315$	4.85765	0.273698
$316$	−9.63959	−0.542269
$317$	1.88777	0.106028	0.0530138	−	0.998594i	$-0.483117\pi$
$317$	1.88777	0.106028	0.0530138	+	0.998594i	$0.483117\pi$
$318$	−1.26138	−0.0707348
$319$	3.79315	0.212376
$320$	1.00000	0.0559017
$321$	−3.75736	−0.209715
$322$	0	0
$323$	2.34507	0.130483
$324$	7.48528	0.415849
$325$	−3.03528	−0.168367
$326$	−12.8484	−0.711605
$327$	−7.22589	−0.399593
$328$	−9.19151	−0.507516
$329$	13.7566	0.758428
$330$	−0.156961	−0.00864042
$331$	2.06251	0.113366	0.0566829	−	0.998392i	$-0.481948\pi$
$331$	2.06251	0.113366	0.0566829	+	0.998392i	$0.481948\pi$
$332$	2.40060	0.131750
$333$	2.34315	0.128404
$334$	15.3942	0.842335
$335$	2.67800	0.146315
$336$	0.711386	0.0388093
$337$	6.67120	0.363403	0.181702	−	0.983354i	$-0.441839\pi$
$337$	6.67120	0.363403	0.181702	+	0.983354i	$0.441839\pi$
$338$	3.78710	0.205991
$339$	−6.60332	−0.358643
$340$	−0.663902	−0.0360052
$341$	−2.77300	−0.150166
$342$	−9.99071	−0.540236
$343$	18.9784	1.02474
$344$	5.24969	0.283044
$345$	0	0
$346$	5.88777	0.316528
$347$	−34.2107	−1.83653	−0.918264	−	0.395969i	$-0.870409\pi$
$347$	−34.2107	−1.83653	−0.918264	+	0.395969i	$0.870409\pi$
$348$	4.14626	0.222263
$349$	12.3510	0.661133	0.330566	−	0.943783i	$-0.392760\pi$
$349$	12.3510	0.661133	0.330566	+	0.943783i	$0.392760\pi$
$350$	1.71744	0.0918010
$351$	−7.32780	−0.391129
$352$	0.378937	0.0201974
$353$	−5.06199	−0.269423	−0.134711	−	0.990885i	$-0.543011\pi$
$353$	−5.06199	−0.269423	−0.134711	+	0.990885i	$0.543011\pi$
$354$	1.24264	0.0660456
$355$	2.21201	0.117401
$356$	9.22146	0.488736
$357$	−0.472291	−0.0249963
$358$	−16.9873	−0.897807
$359$	17.9642	0.948112	0.474056	−	0.880495i	$-0.342789\pi$
$359$	17.9642	0.948112	0.474056	+	0.880495i	$0.342789\pi$
$360$	2.82843	0.149071
$361$	−6.52321	−0.343327
$362$	−14.3996	−0.756826
$363$	4.49687	0.236025
$364$	5.21290	0.273230
$365$	2.25209	0.117880
$366$	1.69818	0.0887654
$367$	25.2731	1.31924	0.659621	−	0.751598i	$-0.270717\pi$
$367$	25.2731	1.31924	0.659621	+	0.751598i	$0.270717\pi$
$368$	0	0
$369$	−25.9975	−1.35338
$370$	0.828427	0.0430679
$371$	5.23002	0.271529
$372$	−3.03115	−0.157158
$373$	−17.3178	−0.896684	−0.448342	−	0.893862i	$-0.647985\pi$
$373$	−17.3178	−0.896684	−0.448342	+	0.893862i	$0.647985\pi$
$374$	−0.251577	−0.0130088
$375$	−0.414214	−0.0213899
$376$	8.00997	0.413083
$377$	30.3830	1.56480
$378$	4.14626	0.213261
$379$	10.0334	0.515381	0.257690	−	0.966228i	$-0.417039\pi$
$379$	10.0334	0.515381	0.257690	+	0.966228i	$0.417039\pi$
$380$	−3.53225	−0.181201
$381$	−0.516642	−0.0264684
$382$	19.1650	0.980564
$383$	28.7685	1.47000	0.735001	−	0.678066i	$-0.237181\pi$
$383$	28.7685	1.47000	0.735001	+	0.678066i	$0.237181\pi$
$384$	0.414214	0.0211377
$385$	0.650802	0.0331679
$386$	24.9993	1.27243
$387$	14.8484	0.754785
$388$	14.0134	0.711421
$389$	−8.49009	−0.430465	−0.215232	−	0.976563i	$-0.569051\pi$
$389$	−8.49009	−0.430465	−0.215232	+	0.976563i	$0.569051\pi$
$390$	−1.25725	−0.0636635
$391$	0	0
$392$	4.05040	0.204576
$393$	0.375701	0.0189516
$394$	7.21592	0.363533
$395$	−9.63959	−0.485020
$396$	1.07180	0.0538598
$397$	−34.9629	−1.75474	−0.877369	−	0.479816i	$-0.840703\pi$
$397$	−34.9629	−1.75474	−0.877369	+	0.479816i	$0.840703\pi$
$398$	−17.9959	−0.902052
$399$	−2.51279	−0.125797
$400$	1.00000	0.0500000
$401$	28.2302	1.40975	0.704875	−	0.709332i	$-0.251003\pi$
$401$	28.2302	1.40975	0.704875	+	0.709332i	$0.251003\pi$
$402$	1.10926	0.0553250
$403$	−22.2117	−1.10644
$404$	−3.70747	−0.184454
$405$	7.48528	0.371947
$406$	−17.1915	−0.853200
$407$	0.313922	0.0155605
$408$	−0.274997	−0.0136144
$409$	3.18686	0.157580	0.0787901	−	0.996891i	$-0.474894\pi$
$409$	3.18686	0.157580	0.0787901	+	0.996891i	$0.474894\pi$
$410$	−9.19151	−0.453936
$411$	2.15081	0.106091
$412$	−19.1258	−0.942259
$413$	−5.15232	−0.253529
$414$	0	0
$415$	2.40060	0.117841
$416$	3.03528	0.148817
$417$	−1.44750	−0.0708843
$418$	−1.33850	−0.0654683
$419$	35.9644	1.75698	0.878489	−	0.477763i	$-0.158552\pi$
$419$	35.9644	1.75698	0.878489	+	0.477763i	$0.158552\pi$
$420$	0.711386	0.0347121
$421$	−1.94319	−0.0947054	−0.0473527	−	0.998878i	$-0.515078\pi$
$421$	−1.94319	−0.0947054	−0.0473527	+	0.998878i	$0.515078\pi$
$422$	−18.4256	−0.896944
$423$	22.6556	1.10155
$424$	3.04524	0.147890
$425$	−0.663902	−0.0322040
$426$	0.916244	0.0443922
$427$	−7.04112	−0.340743
$428$	9.07107	0.438467
$429$	−0.476420	−0.0230018
$430$	5.24969	0.253162
$431$	24.2843	1.16973	0.584866	−	0.811130i	$-0.301147\pi$
$431$	24.2843	1.16973	0.584866	+	0.811130i	$0.301147\pi$
$432$	2.41421	0.116154
$433$	22.1063	1.06236	0.531182	−	0.847258i	$-0.321748\pi$
$433$	22.1063	1.06236	0.531182	+	0.847258i	$0.321748\pi$
$434$	12.5679	0.603280
$435$	4.14626	0.198798
$436$	17.4448	0.835457
$437$	0	0
$438$	0.932847	0.0445732
$439$	18.4733	0.881684	0.440842	−	0.897585i	$-0.354680\pi$
$439$	18.4733	0.881684	0.440842	+	0.897585i	$0.354680\pi$
$440$	0.378937	0.0180651
$441$	11.4563	0.545537
$442$	−2.01513	−0.0958498
$443$	8.58454	0.407864	0.203932	−	0.978985i	$-0.434628\pi$
$443$	8.58454	0.407864	0.203932	+	0.978985i	$0.434628\pi$
$444$	0.343146	0.0162850
$445$	9.22146	0.437139
$446$	−3.19151	−0.151122
$447$	−1.45997	−0.0690543
$448$	−1.71744	−0.0811414
$449$	5.78121	0.272832	0.136416	−	0.990652i	$-0.456442\pi$
$449$	5.78121	0.272832	0.136416	+	0.990652i	$0.456442\pi$
$450$	2.82843	0.133333
$451$	−3.48301	−0.164008
$452$	15.9418	0.749840
$453$	−5.60624	−0.263404
$454$	−24.0567	−1.12904
$455$	5.21290	0.244385
$456$	−1.46311	−0.0685162
$457$	−23.6186	−1.10483	−0.552415	−	0.833569i	$-0.686294\pi$
$457$	−23.6186	−1.10483	−0.552415	+	0.833569i	$0.686294\pi$
$458$	9.18154	0.429025
$459$	−1.60280	−0.0748124
$460$	0	0
$461$	36.1104	1.68183	0.840915	−	0.541167i	$-0.182017\pi$
$461$	36.1104	1.68183	0.840915	+	0.541167i	$0.182017\pi$
$462$	0.269571	0.0125416
$463$	−21.9129	−1.01838	−0.509189	−	0.860655i	$-0.670054\pi$
$463$	−21.9129	−1.01838	−0.509189	+	0.860655i	$0.670054\pi$
$464$	−10.0100	−0.464701
$465$	−3.03115	−0.140566
$466$	20.5963	0.954104
$467$	29.3732	1.35923	0.679615	−	0.733569i	$-0.262147\pi$
$467$	29.3732	1.35923	0.679615	+	0.733569i	$0.262147\pi$
$468$	8.58506	0.396844
$469$	−4.59930	−0.212376
$470$	8.00997	0.369472
$471$	−3.47923	−0.160314
$472$	−3.00000	−0.138086
$473$	1.98930	0.0914683
$474$	−3.99285	−0.183398
$475$	−3.53225	−0.162071
$476$	1.14021	0.0522615
$477$	8.61325	0.394374
$478$	−23.0892	−1.05608
$479$	0.141456	0.00646331	0.00323165	−	0.999995i	$-0.498971\pi$
$479$	0.141456	0.00646331	0.00323165	+	0.999995i	$0.498971\pi$
$480$	0.414214	0.0189062
$481$	2.51451	0.114652
$482$	4.41129	0.200929
$483$	0	0
$484$	−10.8564	−0.493473
$485$	14.0134	0.636314
$486$	10.3431	0.469175
$487$	35.3433	1.60156	0.800778	−	0.598961i	$-0.204420\pi$
$487$	35.3433	1.60156	0.800778	+	0.598961i	$0.204420\pi$
$488$	−4.09978	−0.185588
$489$	−5.32197	−0.240668
$490$	4.05040	0.182979
$491$	18.2726	0.824631	0.412315	−	0.911041i	$-0.364720\pi$
$491$	18.2726	0.824631	0.412315	+	0.911041i	$0.364720\pi$
$492$	−3.80725	−0.171644
$493$	6.64564	0.299305
$494$	−10.7214	−0.482377
$495$	1.07180	0.0481737
$496$	7.31784	0.328581
$497$	−3.79899	−0.170408
$498$	0.994360	0.0445583
$499$	−7.18405	−0.321602	−0.160801	−	0.986987i	$-0.551408\pi$
$499$	−7.18405	−0.321602	−0.160801	+	0.986987i	$0.551408\pi$
$500$	1.00000	0.0447214
$501$	6.37650	0.284881
$502$	−20.4312	−0.911890
$503$	9.68127	0.431666	0.215833	−	0.976430i	$-0.430753\pi$
$503$	9.68127	0.431666	0.215833	+	0.976430i	$0.430753\pi$
$504$	−4.85765	−0.216377
$505$	−3.70747	−0.164980
$506$	0	0
$507$	1.56867	0.0696670
$508$	1.24728	0.0553393
$509$	−29.0135	−1.28600	−0.643001	−	0.765865i	$-0.722311\pi$
$509$	−29.0135	−1.28600	−0.643001	+	0.765865i	$0.722311\pi$
$510$	−0.274997	−0.0121771
$511$	−3.86783	−0.171103
$512$	−1.00000	−0.0441942
$513$	−8.52761	−0.376503
$514$	−16.2414	−0.716377
$515$	−19.1258	−0.842782
$516$	2.17449	0.0957267
$517$	3.03528	0.133491
$518$	−1.42277	−0.0625131
$519$	2.43879	0.107051
$520$	3.03528	0.133106
$521$	−25.6950	−1.12572	−0.562858	−	0.826553i	$-0.690298\pi$
$521$	−25.6950	−1.12572	−0.562858	+	0.826553i	$0.690298\pi$
$522$	−28.3125	−1.23920
$523$	20.1618	0.881613	0.440806	−	0.897602i	$-0.354693\pi$
$523$	20.1618	0.881613	0.440806	+	0.897602i	$0.354693\pi$
$524$	−0.907023	−0.0396235
$525$	0.711386	0.0310475
$526$	26.9116	1.17340
$527$	−4.85833	−0.211632
$528$	0.156961	0.00683085
$529$	0	0
$530$	3.04524	0.132277
$531$	−8.48528	−0.368230
$532$	6.06642	0.263013
$533$	−27.8988	−1.20843
$534$	3.81965	0.165293
$535$	9.07107	0.392176
$536$	−2.67800	−0.115672
$537$	−7.03637	−0.303642
$538$	3.06251	0.132034
$539$	1.53485	0.0661106
$540$	2.41421	0.103891
$541$	8.17068	0.351285	0.175642	−	0.984454i	$-0.443800\pi$
$541$	8.17068	0.351285	0.175642	+	0.984454i	$0.443800\pi$
$542$	−25.8131	−1.10877
$543$	−5.96451	−0.255962
$544$	0.663902	0.0284646
$545$	17.4448	0.747255
$546$	2.15925	0.0924076
$547$	−43.1127	−1.84337	−0.921683	−	0.387944i	$-0.873185\pi$
$547$	−43.1127	−1.84337	−0.921683	+	0.387944i	$0.873185\pi$
$548$	−5.19250	−0.221813
$549$	−11.5959	−0.494902
$550$	0.378937	0.0161579
$551$	35.3577	1.50629
$552$	0	0
$553$	16.5554	0.704008
$554$	10.7454	0.456529
$555$	0.343146	0.0145657
$556$	3.49457	0.148203
$557$	41.7019	1.76697	0.883483	−	0.468464i	$-0.155192\pi$
$557$	41.7019	1.76697	0.883483	+	0.468464i	$0.155192\pi$
$558$	20.6980	0.876215
$559$	15.9343	0.673947
$560$	−1.71744	−0.0725750
$561$	−0.104207	−0.00439961
$562$	−2.55343	−0.107710
$563$	39.8151	1.67801	0.839003	−	0.544126i	$-0.183139\pi$
$563$	39.8151	1.67801	0.839003	+	0.544126i	$0.183139\pi$
$564$	3.31784	0.139706
$565$	15.9418	0.670677
$566$	−11.4971	−0.483261
$567$	−12.8555	−0.539881
$568$	−2.21201	−0.0928138
$569$	−19.9178	−0.834996	−0.417498	−	0.908678i	$-0.637093\pi$
$569$	−19.9178	−0.834996	−0.417498	+	0.908678i	$0.637093\pi$
$570$	−1.46311	−0.0612828
$571$	−39.9856	−1.67334	−0.836672	−	0.547704i	$-0.815502\pi$
$571$	−39.9856	−1.67334	−0.836672	+	0.547704i	$0.815502\pi$
$572$	1.15018	0.0480914
$573$	7.93838	0.331631
$574$	15.7859	0.658889
$575$	0	0
$576$	−2.82843	−0.117851
$577$	28.8503	1.20105	0.600527	−	0.799605i	$-0.294958\pi$
$577$	28.8503	1.20105	0.600527	+	0.799605i	$0.294958\pi$
$578$	16.5592	0.688773
$579$	10.3550	0.430341
$580$	−10.0100	−0.415641
$581$	−4.12288	−0.171046
$582$	5.80453	0.240605
$583$	1.15396	0.0477920
$584$	−2.25209	−0.0931923
$585$	8.58506	0.354948
$586$	−2.36557	−0.0977208
$587$	18.9238	0.781068	0.390534	−	0.920588i	$-0.372290\pi$
$587$	18.9238	0.781068	0.390534	+	0.920588i	$0.372290\pi$
$588$	1.67773	0.0691885
$589$	−25.8484	−1.06507
$590$	−3.00000	−0.123508
$591$	2.98893	0.122948
$592$	−0.828427	−0.0340481
$593$	−14.4555	−0.593618	−0.296809	−	0.954937i	$-0.595922\pi$
$593$	−14.4555	−0.593618	−0.296809	+	0.954937i	$0.595922\pi$
$594$	0.914836	0.0375362
$595$	1.14021	0.0467441
$596$	3.52469	0.144377
$597$	−7.45413	−0.305077
$598$	0	0
$599$	4.13897	0.169114	0.0845568	−	0.996419i	$-0.473053\pi$
$599$	4.13897	0.169114	0.0845568	+	0.996419i	$0.473053\pi$
$600$	0.414214	0.0169102
$601$	−27.7035	−1.13005	−0.565025	−	0.825074i	$-0.691134\pi$
$601$	−27.7035	−1.13005	−0.565025	+	0.825074i	$0.691134\pi$
$602$	−9.01602	−0.367466
$603$	−7.57452	−0.308458
$604$	13.5347	0.550717
$605$	−10.8564	−0.441376
$606$	−1.53568	−0.0623829
$607$	25.1883	1.02236	0.511182	−	0.859473i	$-0.329208\pi$
$607$	25.1883	1.02236	0.511182	+	0.859473i	$0.329208\pi$
$608$	3.53225	0.143252
$609$	−7.12096	−0.288556
$610$	−4.09978	−0.165995
$611$	24.3125	0.983577
$612$	1.87780	0.0759056
$613$	6.52145	0.263399	0.131699	−	0.991290i	$-0.457957\pi$
$613$	6.52145	0.263399	0.131699	+	0.991290i	$0.457957\pi$
$614$	18.5047	0.746789
$615$	−3.80725	−0.153523
$616$	−0.650802	−0.0262216
$617$	48.6247	1.95756	0.978778	−	0.204925i	$-0.0656952\pi$
$617$	48.6247	1.95756	0.978778	+	0.204925i	$0.0656952\pi$
$618$	−7.92215	−0.318676
$619$	−19.6994	−0.791788	−0.395894	−	0.918296i	$-0.629565\pi$
$619$	−19.6994	−0.791788	−0.395894	+	0.918296i	$0.629565\pi$
$620$	7.31784	0.293891
$621$	0	0
$622$	26.1438	1.04827
$623$	−15.8373	−0.634508
$624$	1.25725	0.0503304
$625$	1.00000	0.0400000
$626$	8.33005	0.332936
$627$	−0.554425	−0.0221416
$628$	8.39960	0.335181
$629$	0.549995	0.0219297
$630$	−4.85765	−0.193533
$631$	28.3716	1.12946	0.564728	−	0.825277i	$-0.308981\pi$
$631$	28.3716	1.12946	0.564728	+	0.825277i	$0.308981\pi$
$632$	9.63959	0.383442
$633$	−7.63213	−0.303350
$634$	−1.88777	−0.0749728
$635$	1.24728	0.0494970
$636$	1.26138	0.0500170
$637$	12.2941	0.487110
$638$	−3.79315	−0.150172
$639$	−6.25651	−0.247504
$640$	−1.00000	−0.0395285
$641$	7.93258	0.313318	0.156659	−	0.987653i	$-0.449928\pi$
$641$	7.93258	0.313318	0.156659	+	0.987653i	$0.449928\pi$
$642$	3.75736	0.148291
$643$	4.63391	0.182744	0.0913719	−	0.995817i	$-0.470875\pi$
$643$	4.63391	0.182744	0.0913719	+	0.995817i	$0.470875\pi$
$644$	0	0
$645$	2.17449	0.0856206
$646$	−2.34507	−0.0922655
$647$	32.1596	1.26432	0.632162	−	0.774836i	$-0.282168\pi$
$647$	32.1596	1.26432	0.632162	+	0.774836i	$0.282168\pi$
$648$	−7.48528	−0.294050
$649$	−1.13681	−0.0446238
$650$	3.03528	0.119053
$651$	5.20581	0.204032
$652$	12.8484	0.503181
$653$	−3.36365	−0.131630	−0.0658148	−	0.997832i	$-0.520965\pi$
$653$	−3.36365	−0.131630	−0.0658148	+	0.997832i	$0.520965\pi$
$654$	7.22589	0.282555
$655$	−0.907023	−0.0354403
$656$	9.19151	0.358868
$657$	−6.36988	−0.248513
$658$	−13.7566	−0.536289
$659$	27.2511	1.06155	0.530776	−	0.847512i	$-0.321901\pi$
$659$	27.2511	1.06155	0.530776	+	0.847512i	$0.321901\pi$
$660$	0.156961	0.00610970
$661$	−9.50810	−0.369822	−0.184911	−	0.982755i	$-0.559200\pi$
$661$	−9.50810	−0.369822	−0.184911	+	0.982755i	$0.559200\pi$
$662$	−2.06251	−0.0801617
$663$	−0.834693	−0.0324168
$664$	−2.40060	−0.0931612
$665$	6.06642	0.235246
$666$	−2.34315	−0.0907951
$667$	0	0
$668$	−15.3942	−0.595621
$669$	−1.32197	−0.0511102
$670$	−2.67800	−0.103460
$671$	−1.55356	−0.0599745
$672$	−0.711386	−0.0274423
$673$	−35.2334	−1.35815	−0.679073	−	0.734071i	$-0.737618\pi$
$673$	−35.2334	−1.35815	−0.679073	+	0.734071i	$0.737618\pi$
$674$	−6.67120	−0.256965
$675$	2.41421	0.0929231
$676$	−3.78710	−0.145658
$677$	−28.2134	−1.08433	−0.542164	−	0.840273i	$-0.682395\pi$
$677$	−28.2134	−1.08433	−0.542164	+	0.840273i	$0.682395\pi$
$678$	6.60332	0.253599
$679$	−24.0671	−0.923611
$680$	0.663902	0.0254595
$681$	−9.96462	−0.381845
$682$	2.77300	0.106184
$683$	20.9715	0.802450	0.401225	−	0.915979i	$-0.368584\pi$
$683$	20.9715	0.802450	0.401225	+	0.915979i	$0.368584\pi$
$684$	9.99071	0.382004
$685$	−5.19250	−0.198395
$686$	−18.9784	−0.724598
$687$	3.80312	0.145098
$688$	−5.24969	−0.200143
$689$	9.24316	0.352136
$690$	0	0
$691$	14.0774	0.535528	0.267764	−	0.963485i	$-0.413715\pi$
$691$	14.0774	0.535528	0.267764	+	0.963485i	$0.413715\pi$
$692$	−5.88777	−0.223819
$693$	−1.84075	−0.0699241
$694$	34.2107	1.29862
$695$	3.49457	0.132557
$696$	−4.14626	−0.157164
$697$	−6.10226	−0.231140
$698$	−12.3510	−0.467491
$699$	8.53125	0.322682
$700$	−1.71744	−0.0649131
$701$	28.7230	1.08485	0.542426	−	0.840103i	$-0.317506\pi$
$701$	28.7230	1.08485	0.542426	+	0.840103i	$0.317506\pi$
$702$	7.32780	0.276570
$703$	2.92621	0.110364
$704$	−0.378937	−0.0142817
$705$	3.31784	0.124957
$706$	5.06199	0.190511
$707$	6.36736	0.239469
$708$	−1.24264	−0.0467013
$709$	23.8863	0.897069	0.448535	−	0.893765i	$-0.351946\pi$
$709$	23.8863	0.897069	0.448535	+	0.893765i	$0.351946\pi$
$710$	−2.21201	−0.0830152
$711$	27.2649	1.02251
$712$	−9.22146	−0.345589
$713$	0	0
$714$	0.472291	0.0176751
$715$	1.15018	0.0430143
$716$	16.9873	0.634846
$717$	−9.56388	−0.357170
$718$	−17.9642	−0.670416
$719$	13.7203	0.511679	0.255840	−	0.966719i	$-0.417648\pi$
$719$	13.7203	0.511679	0.255840	+	0.966719i	$0.417648\pi$
$720$	−2.82843	−0.105409
$721$	32.8473	1.22330
$722$	6.52321	0.242769
$723$	1.82722	0.0679550
$724$	14.3996	0.535157
$725$	−10.0100	−0.371761
$726$	−4.49687	−0.166895
$727$	−33.9562	−1.25937	−0.629683	−	0.776853i	$-0.716815\pi$
$727$	−33.9562	−1.25937	−0.629683	+	0.776853i	$0.716815\pi$
$728$	−5.21290	−0.193203
$729$	−18.1716	−0.673021
$730$	−2.25209	−0.0833537
$731$	3.48528	0.128908
$732$	−1.69818	−0.0627666
$733$	0.889012	0.0328364	0.0164182	−	0.999865i	$-0.494774\pi$
$733$	0.889012	0.0328364	0.0164182	+	0.999865i	$0.494774\pi$
$734$	−25.2731	−0.932846
$735$	1.67773	0.0618841
$736$	0	0
$737$	−1.01479	−0.0373804
$738$	25.9975	0.956982
$739$	9.49333	0.349218	0.174609	−	0.984638i	$-0.444134\pi$
$739$	9.49333	0.349218	0.174609	+	0.984638i	$0.444134\pi$
$740$	−0.828427	−0.0304536
$741$	−4.44093	−0.163142
$742$	−5.23002	−0.192000
$743$	38.0859	1.39723	0.698617	−	0.715495i	$-0.253799\pi$
$743$	38.0859	1.39723	0.698617	+	0.715495i	$0.253799\pi$
$744$	3.03115	0.111127
$745$	3.52469	0.129135
$746$	17.3178	0.634051
$747$	−6.78991	−0.248430
$748$	0.251577	0.00919858
$749$	−15.5790	−0.569244
$750$	0.414214	0.0151249
$751$	−53.6826	−1.95891	−0.979453	−	0.201670i	$-0.935363\pi$
$751$	−53.6826	−1.95891	−0.979453	+	0.201670i	$0.935363\pi$
$752$	−8.00997	−0.292093
$753$	−8.46289	−0.308405
$754$	−30.3830	−1.10648
$755$	13.5347	0.492576
$756$	−4.14626	−0.150798
$757$	−52.4353	−1.90579	−0.952897	−	0.303293i	$-0.901914\pi$
$757$	−52.4353	−1.90579	−0.952897	+	0.303293i	$0.901914\pi$
$758$	−10.0334	−0.364429
$759$	0	0
$760$	3.53225	0.128128
$761$	−25.6522	−0.929892	−0.464946	−	0.885339i	$-0.653926\pi$
$761$	−25.6522	−0.929892	−0.464946	+	0.885339i	$0.653926\pi$
$762$	0.516642	0.0187160
$763$	−29.9605	−1.08464
$764$	−19.1650	−0.693364
$765$	1.87780	0.0678920
$766$	−28.7685	−1.03945
$767$	−9.10583	−0.328792
$768$	−0.414214	−0.0149466
$769$	0.0780809	0.00281567	0.00140783	−	0.999999i	$-0.499552\pi$
$769$	0.0780809	0.00281567	0.00140783	+	0.999999i	$0.499552\pi$
$770$	−0.650802	−0.0234533
$771$	−6.72741	−0.242282
$772$	−24.9993	−0.899743
$773$	48.1528	1.73194	0.865968	−	0.500100i	$-0.166703\pi$
$773$	48.1528	1.73194	0.865968	+	0.500100i	$0.166703\pi$
$774$	−14.8484	−0.533713
$775$	7.31784	0.262864
$776$	−14.0134	−0.503051
$777$	−0.589332	−0.0211422
$778$	8.49009	0.304384
$779$	−32.4667	−1.16324
$780$	1.25725	0.0450169
$781$	−0.838213	−0.0299936
$782$	0	0
$783$	−24.1662	−0.863630
$784$	−4.05040	−0.144657
$785$	8.39960	0.299795
$786$	−0.375701	−0.0134008
$787$	26.9189	0.959557	0.479778	−	0.877390i	$-0.340717\pi$
$787$	26.9189	0.959557	0.479778	+	0.877390i	$0.340717\pi$
$788$	−7.21592	−0.257057
$789$	11.1472	0.396849
$790$	9.63959	0.342961
$791$	−27.3791	−0.973489
$792$	−1.07180	−0.0380846
$793$	−12.4440	−0.441898
$794$	34.9629	1.24079
$795$	1.26138	0.0447366
$796$	17.9959	0.637847
$797$	−34.1111	−1.20828	−0.604139	−	0.796879i	$-0.706483\pi$
$797$	−34.1111	−1.20828	−0.604139	+	0.796879i	$0.706483\pi$
$798$	2.51279	0.0889520
$799$	5.31784	0.188132
$800$	−1.00000	−0.0353553
$801$	−26.0822	−0.921570
$802$	−28.2302	−0.996844
$803$	−0.853402	−0.0301159
$804$	−1.10926	−0.0391207
$805$	0	0
$806$	22.2117	0.782372
$807$	1.26853	0.0446545
$808$	3.70747	0.130428
$809$	6.50883	0.228838	0.114419	−	0.993433i	$-0.463499\pi$
$809$	6.50883	0.228838	0.114419	+	0.993433i	$0.463499\pi$
$810$	−7.48528	−0.263006
$811$	35.0570	1.23102	0.615509	−	0.788130i	$-0.288951\pi$
$811$	35.0570	1.23102	0.615509	+	0.788130i	$0.288951\pi$
$812$	17.1915	0.603304
$813$	−10.6921	−0.374989
$814$	−0.313922	−0.0110030
$815$	12.8484	0.450059
$816$	0.274997	0.00962683
$817$	18.5432	0.648745
$818$	−3.18686	−0.111426
$819$	−14.7443	−0.515208
$820$	9.19151	0.320981
$821$	−10.5840	−0.369385	−0.184693	−	0.982796i	$-0.559129\pi$
$821$	−10.5840	−0.369385	−0.184693	+	0.982796i	$0.559129\pi$
$822$	−2.15081	−0.0750180
$823$	−52.5097	−1.83037	−0.915186	−	0.403032i	$-0.867956\pi$
$823$	−52.5097	−1.83037	−0.915186	+	0.403032i	$0.867956\pi$
$824$	19.1258	0.666278
$825$	0.156961	0.00546468
$826$	5.15232	0.179272
$827$	−35.5363	−1.23572	−0.617859	−	0.786289i	$-0.712000\pi$
$827$	−35.5363	−1.23572	−0.617859	+	0.786289i	$0.712000\pi$
$828$	0	0
$829$	24.8625	0.863509	0.431754	−	0.901991i	$-0.357895\pi$
$829$	24.8625	0.863509	0.431754	+	0.901991i	$0.357895\pi$
$830$	−2.40060	−0.0833260
$831$	4.45090	0.154400
$832$	−3.03528	−0.105229
$833$	2.68907	0.0931709
$834$	1.44750	0.0501228
$835$	−15.3942	−0.532739
$836$	1.33850	0.0462930
$837$	17.6668	0.610655
$838$	−35.9644	−1.24237
$839$	17.2275	0.594760	0.297380	−	0.954759i	$-0.403887\pi$
$839$	17.2275	0.594760	0.297380	+	0.954759i	$0.403887\pi$
$840$	−0.711386	−0.0245452
$841$	71.1995	2.45515
$842$	1.94319	0.0669668
$843$	−1.05767	−0.0364279
$844$	18.4256	0.634235
$845$	−3.78710	−0.130280
$846$	−22.6556	−0.778916
$847$	18.6452	0.640657
$848$	−3.04524	−0.104574
$849$	−4.76227	−0.163441
$850$	0.663902	0.0227717
$851$	0	0
$852$	−0.916244	−0.0313900
$853$	−40.0048	−1.36974	−0.684869	−	0.728666i	$-0.740141\pi$
$853$	−40.0048	−1.36974	−0.684869	+	0.728666i	$0.740141\pi$
$854$	7.04112	0.240942
$855$	9.99071	0.341675
$856$	−9.07107	−0.310043
$857$	25.8480	0.882951	0.441476	−	0.897273i	$-0.354455\pi$
$857$	25.8480	0.882951	0.441476	+	0.897273i	$0.354455\pi$
$858$	0.476420	0.0162647
$859$	−11.9765	−0.408631	−0.204316	−	0.978905i	$-0.565497\pi$
$859$	−11.9765	−0.408631	−0.204316	+	0.978905i	$0.565497\pi$
$860$	−5.24969	−0.179013
$861$	6.53871	0.222839
$862$	−24.2843	−0.827126
$863$	13.5801	0.462272	0.231136	−	0.972921i	$-0.425756\pi$
$863$	13.5801	0.462272	0.231136	+	0.972921i	$0.425756\pi$
$864$	−2.41421	−0.0821332
$865$	−5.88777	−0.200190
$866$	−22.1063	−0.751204
$867$	6.85906	0.232946
$868$	−12.5679	−0.426584
$869$	3.65280	0.123913
$870$	−4.14626	−0.140572
$871$	−8.12847	−0.275423
$872$	−17.4448	−0.590757
$873$	−39.6358	−1.34147
$874$	0	0
$875$	−1.71744	−0.0580600
$876$	−0.932847	−0.0315180
$877$	−25.1540	−0.849389	−0.424694	−	0.905337i	$-0.639618\pi$
$877$	−25.1540	−0.849389	−0.424694	+	0.905337i	$0.639618\pi$
$878$	−18.4733	−0.623444
$879$	−0.979851	−0.0330496
$880$	−0.378937	−0.0127740
$881$	−36.3652	−1.22517	−0.612587	−	0.790403i	$-0.709871\pi$
$881$	−36.3652	−1.22517	−0.612587	+	0.790403i	$0.709871\pi$
$882$	−11.4563	−0.385753
$883$	−24.6857	−0.830741	−0.415370	−	0.909652i	$-0.636348\pi$
$883$	−24.6857	−0.830741	−0.415370	+	0.909652i	$0.636348\pi$
$884$	2.01513	0.0677761
$885$	−1.24264	−0.0417709
$886$	−8.58454	−0.288403
$887$	−24.5088	−0.822927	−0.411463	−	0.911426i	$-0.634982\pi$
$887$	−24.5088	−0.822927	−0.411463	+	0.911426i	$0.634982\pi$
$888$	−0.343146	−0.0115152
$889$	−2.14214	−0.0718449
$890$	−9.22146	−0.309104
$891$	−2.83645	−0.0950247
$892$	3.19151	0.106860
$893$	28.2932	0.946796
$894$	1.45997	0.0488288
$895$	16.9873	0.567823
$896$	1.71744	0.0573756
$897$	0	0
$898$	−5.78121	−0.192921
$899$	−73.2513	−2.44307
$900$	−2.82843	−0.0942809
$901$	2.02174	0.0673541
$902$	3.48301	0.115971
$903$	−3.73456	−0.124278
$904$	−15.9418	−0.530217
$905$	14.3996	0.478659
$906$	5.60624	0.186255
$907$	−20.8567	−0.692534	−0.346267	−	0.938136i	$-0.612551\pi$
$907$	−20.8567	−0.692534	−0.346267	+	0.938136i	$0.612551\pi$
$908$	24.0567	0.798350
$909$	10.4863	0.347809
$910$	−5.21290	−0.172806
$911$	11.4374	0.378937	0.189468	−	0.981887i	$-0.439324\pi$
$911$	11.4374	0.378937	0.189468	+	0.981887i	$0.439324\pi$
$912$	1.46311	0.0484483
$913$	−0.909676	−0.0301059
$914$	23.6186	0.781233
$915$	−1.69818	−0.0561402
$916$	−9.18154	−0.303367
$917$	1.55776	0.0514417
$918$	1.60280	0.0529004
$919$	−20.3073	−0.669876	−0.334938	−	0.942240i	$-0.608715\pi$
$919$	−20.3073	−0.669876	−0.334938	+	0.942240i	$0.608715\pi$
$920$	0	0
$921$	7.66490	0.252567
$922$	−36.1104	−1.18923
$923$	−6.71406	−0.220996
$924$	−0.269571	−0.00886823
$925$	−0.828427	−0.0272385
$926$	21.9129	0.720101
$927$	54.0958	1.77674
$928$	10.0100	0.328593
$929$	−22.6652	−0.743622	−0.371811	−	0.928308i	$-0.621263\pi$
$929$	−22.6652	−0.743622	−0.371811	+	0.928308i	$0.621263\pi$
$930$	3.03115	0.0993952
$931$	14.3070	0.468894
$932$	−20.5963	−0.674653
$933$	10.8291	0.354529
$934$	−29.3732	−0.961121
$935$	0.251577	0.00822746
$936$	−8.58506	−0.280611
$937$	8.25428	0.269656	0.134828	−	0.990869i	$-0.456952\pi$
$937$	8.25428	0.269656	0.134828	+	0.990869i	$0.456952\pi$
$938$	4.59930	0.150172
$939$	3.45042	0.112600
$940$	−8.00997	−0.261256
$941$	37.5807	1.22510	0.612548	−	0.790433i	$-0.290145\pi$
$941$	37.5807	1.22510	0.612548	+	0.790433i	$0.290145\pi$
$942$	3.47923	0.113359
$943$	0	0
$944$	3.00000	0.0976417
$945$	−4.14626	−0.134878
$946$	−1.98930	−0.0646778
$947$	−12.1761	−0.395672	−0.197836	−	0.980235i	$-0.563391\pi$
$947$	−12.1761	−0.395672	−0.197836	+	0.980235i	$0.563391\pi$
$948$	3.99285	0.129682
$949$	−6.83572	−0.221897
$950$	3.53225	0.114601
$951$	−0.781939	−0.0253561
$952$	−1.14021	−0.0369545
$953$	21.1411	0.684828	0.342414	−	0.939549i	$-0.388755\pi$
$953$	21.1411	0.684828	0.342414	+	0.939549i	$0.388755\pi$
$954$	−8.61325	−0.278864
$955$	−19.1650	−0.620163
$956$	23.0892	0.746759
$957$	−1.57117	−0.0507889
$958$	−0.141456	−0.00457025
$959$	8.91781	0.287971
$960$	−0.414214	−0.0133687
$961$	22.5507	0.727443
$962$	−2.51451	−0.0810709
$963$	−25.6569	−0.826781
$964$	−4.41129	−0.142078
$965$	−24.9993	−0.804755
$966$	0	0
$967$	−24.8514	−0.799167	−0.399583	−	0.916697i	$-0.630845\pi$
$967$	−24.8514	−0.799167	−0.399583	+	0.916697i	$0.630845\pi$
$968$	10.8564	0.348938
$969$	−0.971360	−0.0312046
$970$	−14.0134	−0.449942
$971$	35.1239	1.12718	0.563590	−	0.826055i	$-0.309420\pi$
$971$	35.1239	1.12718	0.563590	+	0.826055i	$0.309420\pi$
$972$	−10.3431	−0.331757
$973$	−6.00171	−0.192406
$974$	−35.3433	−1.13247
$975$	1.25725	0.0402643
$976$	4.09978	0.131231
$977$	53.0462	1.69710	0.848550	−	0.529116i	$-0.177476\pi$
$977$	53.0462	1.69710	0.848550	+	0.529116i	$0.177476\pi$
$978$	5.32197	0.170178
$979$	−3.49436	−0.111680
$980$	−4.05040	−0.129385
$981$	−49.3415	−1.57535
$982$	−18.2726	−0.583102
$983$	−38.2608	−1.22033	−0.610165	−	0.792274i	$-0.708897\pi$
$983$	−38.2608	−1.22033	−0.610165	+	0.792274i	$0.708897\pi$
$984$	3.80725	0.121371
$985$	−7.21592	−0.229918
$986$	−6.64564	−0.211640
$987$	−5.69818	−0.181375
$988$	10.7214	0.341092
$989$	0	0
$990$	−1.07180	−0.0340639
$991$	31.9839	1.01600	0.508001	−	0.861356i	$-0.330385\pi$
$991$	31.9839	1.01600	0.508001	+	0.861356i	$0.330385\pi$
$992$	−7.31784	−0.232342
$993$	−0.854319	−0.0271110
$994$	3.79899	0.120497
$995$	17.9959	0.570507
$996$	−0.994360	−0.0315075
$997$	−45.9600	−1.45557	−0.727784	−	0.685806i	$-0.759450\pi$
$997$	−45.9600	−1.45557	−0.727784	+	0.685806i	$0.759450\pi$
$998$	7.18405	0.227407
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.v.1.1	yes	4
23.22	odd	2		5290.2.a.u.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.u.1.2	✓	4	23.22	odd	2
5290.2.a.v.1.1	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -1.71744 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -1.71744 q^{7} -1.00000 q^{8} -2.82843 q^{9} -1.00000 q^{10} -0.378937 q^{11} -0.414214 q^{12} -3.03528 q^{13} +1.71744 q^{14} -0.414214 q^{15} +1.00000 q^{16} -0.663902 q^{17} +2.82843 q^{18} -3.53225 q^{19} +1.00000 q^{20} +0.711386 q^{21} +0.378937 q^{22} +0.414214 q^{24} +1.00000 q^{25} +3.03528 q^{26} +2.41421 q^{27} -1.71744 q^{28} -10.0100 q^{29} +0.414214 q^{30} +7.31784 q^{31} -1.00000 q^{32} +0.156961 q^{33} +0.663902 q^{34} -1.71744 q^{35} -2.82843 q^{36} -0.828427 q^{37} +3.53225 q^{38} +1.25725 q^{39} -1.00000 q^{40} +9.19151 q^{41} -0.711386 q^{42} -5.24969 q^{43} -0.378937 q^{44} -2.82843 q^{45} -8.00997 q^{47} -0.414214 q^{48} -4.05040 q^{49} -1.00000 q^{50} +0.274997 q^{51} -3.03528 q^{52} -3.04524 q^{53} -2.41421 q^{54} -0.378937 q^{55} +1.71744 q^{56} +1.46311 q^{57} +10.0100 q^{58} +3.00000 q^{59} -0.414214 q^{60} +4.09978 q^{61} -7.31784 q^{62} +4.85765 q^{63} +1.00000 q^{64} -3.03528 q^{65} -0.156961 q^{66} +2.67800 q^{67} -0.663902 q^{68} +1.71744 q^{70} +2.21201 q^{71} +2.82843 q^{72} +2.25209 q^{73} +0.828427 q^{74} -0.414214 q^{75} -3.53225 q^{76} +0.650802 q^{77} -1.25725 q^{78} -9.63959 q^{79} +1.00000 q^{80} +7.48528 q^{81} -9.19151 q^{82} +2.40060 q^{83} +0.711386 q^{84} -0.663902 q^{85} +5.24969 q^{86} +4.14626 q^{87} +0.378937 q^{88} +9.22146 q^{89} +2.82843 q^{90} +5.21290 q^{91} -3.03115 q^{93} +8.00997 q^{94} -3.53225 q^{95} +0.414214 q^{96} +14.0134 q^{97} +4.05040 q^{98} +1.07180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{10} + 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} - 4 q^{28} - 12 q^{29} - 4 q^{30} + 28 q^{31} - 4 q^{32} + 16 q^{33} - 12 q^{34} - 4 q^{35} + 8 q^{37} + 8 q^{38} - 16 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{42} - 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} + 16 q^{51} - 8 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 4 q^{60} - 28 q^{62} + 4 q^{64} - 8 q^{65} - 16 q^{66} + 12 q^{67} + 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} - 8 q^{74} + 4 q^{75} - 8 q^{76} - 24 q^{77} + 16 q^{78} - 4 q^{79} + 4 q^{80} - 4 q^{81} + 8 q^{82} + 12 q^{83} - 4 q^{84} + 12 q^{85} + 12 q^{86} + 4 q^{87} + 40 q^{89} + 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} + 16 q^{97} - 12 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^10 + 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 - 4 * q^28 - 12 * q^29 - 4 * q^30 + 28 * q^31 - 4 * q^32 + 16 * q^33 - 12 * q^34 - 4 * q^35 + 8 * q^37 + 8 * q^38 - 16 * q^39 - 4 * q^40 - 8 * q^41 + 4 * q^42 - 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 4 * q^60 - 28 * q^62 + 4 * q^64 - 8 * q^65 - 16 * q^66 + 12 * q^67 + 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 - 8 * q^74 + 4 * q^75 - 8 * q^76 - 24 * q^77 + 16 * q^78 - 4 * q^79 + 4 * q^80 - 4 * q^81 + 8 * q^82 + 12 * q^83 - 4 * q^84 + 12 * q^85 + 12 * q^86 + 4 * q^87 + 40 * q^89 + 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 + 16 * q^97 - 12 * q^98 + 32 * q^99

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