LMFDB - Embedded newform 5290.2.a.v.1.2

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			1.2
Root			$0.517638$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -0.282561 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -0.282561 q^{7} -1.00000 q^{8} -2.82843 q^{9} -1.00000 q^{10} -5.27792 q^{11} -0.414214 q^{12} +1.86370 q^{13} +0.282561 q^{14} -0.414214 q^{15} +1.00000 q^{16} +5.24969 q^{17} +2.82843 q^{18} +0.946464 q^{19} +1.00000 q^{20} +0.117041 q^{21} +5.27792 q^{22} +0.414214 q^{24} +1.00000 q^{25} -1.86370 q^{26} +2.41421 q^{27} -0.282561 q^{28} -1.64689 q^{29} +0.414214 q^{30} +3.85374 q^{31} -1.00000 q^{32} +2.18618 q^{33} -5.24969 q^{34} -0.282561 q^{35} -2.82843 q^{36} -0.828427 q^{37} -0.946464 q^{38} -0.771971 q^{39} -1.00000 q^{40} -7.53465 q^{41} -0.117041 q^{42} +0.663902 q^{43} -5.27792 q^{44} -2.82843 q^{45} +0.353113 q^{47} -0.414214 q^{48} -6.92016 q^{49} -1.00000 q^{50} -2.17449 q^{51} +1.86370 q^{52} +10.2168 q^{53} -2.41421 q^{54} -5.27792 q^{55} +0.282561 q^{56} -0.392038 q^{57} +1.64689 q^{58} +3.00000 q^{59} -0.414214 q^{60} -9.75663 q^{61} -3.85374 q^{62} +0.799203 q^{63} +1.00000 q^{64} +1.86370 q^{65} -2.18618 q^{66} -15.0628 q^{67} +5.24969 q^{68} +0.282561 q^{70} +13.4448 q^{71} +2.82843 q^{72} -15.9089 q^{73} +0.828427 q^{74} -0.414214 q^{75} +0.946464 q^{76} +1.49133 q^{77} +0.771971 q^{78} +4.81116 q^{79} +1.00000 q^{80} +7.48528 q^{81} +7.53465 q^{82} -0.643238 q^{83} +0.117041 q^{84} +5.24969 q^{85} -0.663902 q^{86} +0.682163 q^{87} +5.27792 q^{88} +2.29326 q^{89} +2.82843 q^{90} -0.526610 q^{91} -1.59627 q^{93} -0.353113 q^{94} +0.946464 q^{95} +0.414214 q^{96} -11.6702 q^{97} +6.92016 q^{98} +14.9282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.282561	−0.106798	−0.0533990	−	0.998573i	$-0.517006\pi$
$7$	−0.282561	−0.106798	−0.0533990	+	0.998573i	$0.517006\pi$
$8$	−1.00000	−0.353553
$9$	−2.82843	−0.942809
$10$	−1.00000	−0.316228
$11$	−5.27792	−1.59135	−0.795676	−	0.605723i	$-0.792884\pi$
$11$	−5.27792	−1.59135	−0.795676	+	0.605723i	$0.792884\pi$
$12$	−0.414214	−0.119573
$13$	1.86370	0.516898	0.258449	−	0.966025i	$-0.416789\pi$
$13$	1.86370	0.516898	0.258449	+	0.966025i	$0.416789\pi$
$14$	0.282561	0.0755176
$15$	−0.414214	−0.106949
$16$	1.00000	0.250000
$17$	5.24969	1.27324	0.636618	−	0.771179i	$-0.280333\pi$
$17$	5.24969	1.27324	0.636618	+	0.771179i	$0.280333\pi$
$18$	2.82843	0.666667
$19$	0.946464	0.217134	0.108567	−	0.994089i	$-0.465374\pi$
$19$	0.946464	0.217134	0.108567	+	0.994089i	$0.465374\pi$
$20$	1.00000	0.223607
$21$	0.117041	0.0255404
$22$	5.27792	1.12526
$23$	0	0
$23$	0	0
$24$	0.414214	0.0845510
$25$	1.00000	0.200000
$26$	−1.86370	−0.365502
$27$	2.41421	0.464616
$28$	−0.282561	−0.0533990
$29$	−1.64689	−0.305819	−0.152910	−	0.988240i	$-0.548864\pi$
$29$	−1.64689	−0.305819	−0.152910	+	0.988240i	$0.548864\pi$
$30$	0.414214	0.0756247
$31$	3.85374	0.692151	0.346076	−	0.938207i	$-0.387514\pi$
$31$	3.85374	0.692151	0.346076	+	0.938207i	$0.387514\pi$
$32$	−1.00000	−0.176777
$33$	2.18618	0.380566
$34$	−5.24969	−0.900314
$35$	−0.282561	−0.0477615
$36$	−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	$0.521693\pi$
$38$	−0.946464	−0.153537
$39$	−0.771971	−0.123614
$40$	−1.00000	−0.158114
$41$	−7.53465	−1.17672	−0.588358	−	0.808601i	$-0.700225\pi$
$41$	−7.53465	−1.17672	−0.588358	+	0.808601i	$0.700225\pi$
$42$	−0.117041	−0.0180598
$43$	0.663902	0.101244	0.0506221	−	0.998718i	$-0.483880\pi$
$43$	0.663902	0.101244	0.0506221	+	0.998718i	$0.483880\pi$
$44$	−5.27792	−0.795676
$45$	−2.82843	−0.421637
$46$	0	0
$47$	0.353113	0.0515069	0.0257534	−	0.999668i	$-0.491802\pi$
$47$	0.353113	0.0515069	0.0257534	+	0.999668i	$0.491802\pi$
$48$	−0.414214	−0.0597866
$49$	−6.92016	−0.988594
$50$	−1.00000	−0.141421
$51$	−2.17449	−0.304490
$52$	1.86370	0.258449
$53$	10.2168	1.40339	0.701694	−	0.712479i	$-0.252427\pi$
$53$	10.2168	1.40339	0.701694	+	0.712479i	$0.252427\pi$
$54$	−2.41421	−0.328533
$55$	−5.27792	−0.711674
$56$	0.282561	0.0377588
$57$	−0.392038	−0.0519267
$58$	1.64689	0.216247
$59$	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
$61$	−9.75663	−1.24921	−0.624604	−	0.780941i	$-0.714740\pi$
$61$	−9.75663	−1.24921	−0.624604	+	0.780941i	$0.714740\pi$
$62$	−3.85374	−0.489425
$63$	0.799203	0.100690
$64$	1.00000	0.125000
$65$	1.86370	0.231164
$66$	−2.18618	−0.269101
$67$	−15.0628	−1.84021	−0.920105	−	0.391671i	$-0.871897\pi$
$67$	−15.0628	−1.84021	−0.920105	+	0.391671i	$0.871897\pi$
$68$	5.24969	0.636618
$69$	0	0
$70$	0.282561	0.0337725
$71$	13.4448	1.59561	0.797805	−	0.602916i	$-0.205995\pi$
$71$	13.4448	1.59561	0.797805	+	0.602916i	$0.205995\pi$
$72$	2.82843	0.333333
$73$	−15.9089	−1.86200	−0.931001	−	0.365017i	$-0.881063\pi$
$73$	−15.9089	−1.86200	−0.931001	+	0.365017i	$0.881063\pi$
$74$	0.828427	0.0963027
$75$	−0.414214	−0.0478293
$76$	0.946464	0.108567
$77$	1.49133	0.169953
$78$	0.771971	0.0874085
$79$	4.81116	0.541298	0.270649	−	0.962678i	$-0.412762\pi$
$79$	4.81116	0.541298	0.270649	+	0.962678i	$0.412762\pi$
$80$	1.00000	0.111803
$81$	7.48528	0.831698
$82$	7.53465	0.832063
$83$	−0.643238	−0.0706046	−0.0353023	−	0.999377i	$-0.511239\pi$
$83$	−0.643238	−0.0706046	−0.0353023	+	0.999377i	$0.511239\pi$
$84$	0.117041	0.0127702
$85$	5.24969	0.569409
$86$	−0.663902	−0.0715904
$87$	0.682163	0.0731355
$88$	5.27792	0.562628
$89$	2.29326	0.243085	0.121542	−	0.992586i	$-0.461216\pi$
$89$	2.29326	0.243085	0.121542	+	0.992586i	$0.461216\pi$
$90$	2.82843	0.298142
$91$	−0.526610	−0.0552037
$92$	0	0
$93$	−1.59627	−0.165525
$94$	−0.353113	−0.0364209
$95$	0.946464	0.0971051
$96$	0.414214	0.0422755
$97$	−11.6702	−1.18493	−0.592466	−	0.805596i	$-0.701845\pi$
$97$	−11.6702	−1.18493	−0.592466	+	0.805596i	$0.701845\pi$
$98$	6.92016	0.699042
$99$	14.9282	1.50034
$100$	1.00000	0.100000
$101$	−10.6357	−1.05829	−0.529145	−	0.848532i	$-0.677487\pi$
$101$	−10.6357	−1.05829	−0.529145	+	0.848532i	$0.677487\pi$
$102$	2.17449	0.215307
$103$	12.2973	1.21169	0.605846	−	0.795582i	$-0.292835\pi$
$103$	12.2973	1.21169	0.605846	+	0.795582i	$0.292835\pi$
$104$	−1.86370	−0.182751
$105$	0.117041	0.0114220
$106$	−10.2168	−0.992345
$107$	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
$109$	6.21201	0.595003	0.297501	−	0.954721i	$-0.403847\pi$
$109$	6.21201	0.595003	0.297501	+	0.954721i	$0.403847\pi$
$110$	5.27792	0.503230
$111$	0.343146	0.0325700
$112$	−0.282561	−0.0266995
$113$	5.12925	0.482519	0.241260	−	0.970461i	$-0.422439\pi$
$113$	5.12925	0.482519	0.241260	+	0.970461i	$0.422439\pi$
$114$	0.392038	0.0367177
$115$	0	0
$116$	−1.64689	−0.152910
$117$	−5.27135	−0.487336
$118$	−3.00000	−0.276172
$119$	−1.48336	−0.135979
$120$	0.414214	0.0378124
$121$	16.8564	1.53240
$122$	9.75663	0.883324
$123$	3.12096	0.281407
$124$	3.85374	0.346076
$125$	1.00000	0.0894427
$126$	−0.799203	−0.0711987
$127$	7.58114	0.672718	0.336359	−	0.941734i	$-0.390805\pi$
$127$	7.58114	0.672718	0.336359	+	0.941734i	$0.390805\pi$
$128$	−1.00000	−0.0883883
$129$	−0.274997	−0.0242122
$130$	−1.86370	−0.163458
$131$	19.8776	1.73671	0.868356	−	0.495941i	$-0.165177\pi$
$131$	19.8776	1.73671	0.868356	+	0.495941i	$0.165177\pi$
$132$	2.18618	0.190283
$133$	−0.267434	−0.0231894
$134$	15.0628	1.30123
$135$	2.41421	0.207782
$136$	−5.24969	−0.450157
$137$	16.6067	1.41881	0.709404	−	0.704802i	$-0.248964\pi$
$137$	16.6067	1.41881	0.709404	+	0.704802i	$0.248964\pi$
$138$	0	0
$139$	16.1623	1.37087	0.685434	−	0.728135i	$-0.259613\pi$
$139$	16.1623	1.37087	0.685434	+	0.728135i	$0.259613\pi$
$140$	−0.282561	−0.0238808
$141$	−0.146264	−0.0123177
$142$	−13.4448	−1.12827
$143$	−9.83647	−0.822567
$144$	−2.82843	−0.235702
$145$	−1.64689	−0.136766
$146$	15.9089	1.31663
$147$	2.86642	0.236419
$148$	−0.828427	−0.0680963
$149$	−4.83839	−0.396377	−0.198188	−	0.980164i	$-0.563506\pi$
$149$	−4.83839	−0.396377	−0.198188	+	0.980164i	$0.563506\pi$
$150$	0.414214	0.0338204
$151$	−3.19151	−0.259721	−0.129861	−	0.991532i	$-0.541453\pi$
$151$	−3.19151	−0.259721	−0.129861	+	0.991532i	$0.541453\pi$
$152$	−0.946464	−0.0767683
$153$	−14.8484	−1.20042
$154$	−1.49133	−0.120175
$155$	3.85374	0.309539
$156$	−0.771971	−0.0618072
$157$	10.4288	0.832311	0.416155	−	0.909293i	$-0.363377\pi$
$157$	10.4288	0.832311	0.416155	+	0.909293i	$0.363377\pi$
$158$	−4.81116	−0.382756
$159$	−4.23194	−0.335615
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−7.48528	−0.588099
$163$	−3.87780	−0.303733	−0.151866	−	0.988401i	$-0.548528\pi$
$163$	−3.87780	−0.303733	−0.151866	+	0.988401i	$0.548528\pi$
$164$	−7.53465	−0.588358
$165$	2.18618	0.170194
$166$	0.643238	0.0499250
$167$	2.76681	0.214102	0.107051	−	0.994254i	$-0.465859\pi$
$167$	2.76681	0.214102	0.107051	+	0.994254i	$0.465859\pi$
$168$	−0.117041	−0.00902988
$169$	−9.52661	−0.732816
$170$	−5.24969	−0.402633
$171$	−2.67700	−0.204716
$172$	0.663902	0.0506221
$173$	19.2015	1.45986	0.729931	−	0.683521i	$-0.239552\pi$
$173$	19.2015	1.45986	0.729931	+	0.683521i	$0.239552\pi$
$174$	−0.682163	−0.0517146
$175$	−0.282561	−0.0213596
$176$	−5.27792	−0.397838
$177$	−1.24264	−0.0934026
$178$	−2.29326	−0.171887
$179$	21.6401	1.61746	0.808729	−	0.588182i	$-0.200156\pi$
$179$	21.6401	1.61746	0.808729	+	0.588182i	$0.200156\pi$
$180$	−2.82843	−0.210819
$181$	16.4288	1.22114	0.610572	−	0.791960i	$-0.290939\pi$
$181$	16.4288	1.22114	0.610572	+	0.791960i	$0.290939\pi$
$182$	0.526610	0.0390349
$183$	4.04133	0.298744
$184$	0	0
$185$	−0.828427	−0.0609072
$186$	1.59627	0.117044
$187$	−27.7074	−2.02617
$188$	0.353113	0.0257534
$189$	−0.682163	−0.0496200
$190$	−0.946464	−0.0686637
$191$	24.6797	1.78576	0.892879	−	0.450296i	$-0.148682\pi$
$191$	24.6797	1.78576	0.892879	+	0.450296i	$0.148682\pi$
$192$	−0.414214	−0.0298933
$193$	−11.1429	−0.802081	−0.401040	−	0.916060i	$-0.631351\pi$
$193$	−11.1429	−0.802081	−0.401040	+	0.916060i	$0.631351\pi$
$194$	11.6702	0.837873
$195$	−0.771971	−0.0552820
$196$	−6.92016	−0.494297
$197$	−10.9262	−0.778460	−0.389230	−	0.921141i	$-0.627259\pi$
$197$	−10.9262	−0.778460	−0.389230	+	0.921141i	$0.627259\pi$
$198$	−14.9282	−1.06090
$199$	21.4600	1.52126	0.760629	−	0.649187i	$-0.224891\pi$
$199$	21.4600	1.52126	0.760629	+	0.649187i	$0.224891\pi$
$200$	−1.00000	−0.0707107
$201$	6.23921	0.440080
$202$	10.6357	0.748323
$203$	0.465346	0.0326609
$204$	−2.17449	−0.152245
$205$	−7.53465	−0.526243
$206$	−12.2973	−0.856796
$207$	0	0
$208$	1.86370	0.129225
$209$	−4.99536	−0.345536
$210$	−0.117041	−0.00807657
$211$	2.88812	0.198826	0.0994132	−	0.995046i	$-0.468303\pi$
$211$	2.88812	0.198826	0.0994132	+	0.995046i	$0.468303\pi$
$212$	10.2168	0.701694
$213$	−5.56904	−0.381584
$214$	−9.07107	−0.620085
$215$	0.663902	0.0452778
$216$	−2.41421	−0.164266
$217$	−1.08892	−0.0739204
$218$	−6.21201	−0.420730
$219$	6.58970	0.445291
$220$	−5.27792	−0.355837
$221$	9.78386	0.658134
$222$	−0.343146	−0.0230304
$223$	−13.5347	−0.906347	−0.453174	−	0.891422i	$-0.649708\pi$
$223$	−13.5347	−0.906347	−0.453174	+	0.891422i	$0.649708\pi$
$224$	0.282561	0.0188794
$225$	−2.82843	−0.188562
$226$	−5.12925	−0.341193
$227$	7.15648	0.474992	0.237496	−	0.971388i	$-0.423673\pi$
$227$	7.15648	0.474992	0.237496	+	0.971388i	$0.423673\pi$
$228$	−0.392038	−0.0259634
$229$	−0.818459	−0.0540853	−0.0270427	−	0.999634i	$-0.508609\pi$
$229$	−0.818459	−0.0540853	−0.0270427	+	0.999634i	$0.508609\pi$
$230$	0	0
$231$	−0.617731	−0.0406437
$232$	1.64689	0.108123
$233$	−22.0311	−1.44331	−0.721654	−	0.692254i	$-0.756618\pi$
$233$	−22.0311	−1.44331	−0.721654	+	0.692254i	$0.756618\pi$
$234$	5.27135	0.344599
$235$	0.353113	0.0230346
$236$	3.00000	0.195283
$237$	−1.99285	−0.129449
$238$	1.48336	0.0961518
$239$	−27.0892	−1.75226	−0.876129	−	0.482077i	$-0.839882\pi$
$239$	−27.0892	−1.75226	−0.876129	+	0.482077i	$0.839882\pi$
$240$	−0.414214	−0.0267374
$241$	−6.86078	−0.441942	−0.220971	−	0.975280i	$-0.570923\pi$
$241$	−6.86078	−0.441942	−0.220971	+	0.975280i	$0.570923\pi$
$242$	−16.8564	−1.08357
$243$	−10.3431	−0.663513
$244$	−9.75663	−0.624604
$245$	−6.92016	−0.442113
$246$	−3.12096	−0.198985
$247$	1.76393	0.112236
$248$	−3.85374	−0.244712
$249$	0.266438	0.0168848
$250$	−1.00000	−0.0632456
$251$	6.15456	0.388472	0.194236	−	0.980955i	$-0.437777\pi$
$251$	6.15456	0.388472	0.194236	+	0.980955i	$0.437777\pi$
$252$	0.799203	0.0503451
$253$	0	0
$254$	−7.58114	−0.475683
$255$	−2.17449	−0.136172
$256$	1.00000	0.0625000
$257$	−7.41297	−0.462408	−0.231204	−	0.972905i	$-0.574267\pi$
$257$	−7.41297	−0.462408	−0.231204	+	0.972905i	$0.574267\pi$
$258$	0.274997	0.0171206
$259$	0.234081	0.0145451
$260$	1.86370	0.115582
$261$	4.65810	0.288329
$262$	−19.8776	−1.22804
$263$	22.4263	1.38287	0.691434	−	0.722440i	$-0.256979\pi$
$263$	22.4263	1.38287	0.691434	+	0.722440i	$0.256979\pi$
$264$	−2.18618	−0.134550
$265$	10.2168	0.627614
$266$	0.267434	0.0163974
$267$	−0.949898	−0.0581328
$268$	−15.0628	−0.920105
$269$	−4.25120	−0.259200	−0.129600	−	0.991566i	$-0.541369\pi$
$269$	−4.25120	−0.259200	−0.129600	+	0.991566i	$0.541369\pi$
$270$	−2.41421	−0.146924
$271$	13.9859	0.849583	0.424792	−	0.905291i	$-0.360347\pi$
$271$	13.9859	0.849583	0.424792	+	0.905291i	$0.360347\pi$
$272$	5.24969	0.318309
$273$	0.218129	0.0132018
$274$	−16.6067	−1.00325
$275$	−5.27792	−0.318270
$276$	0	0
$277$	18.4023	1.10569	0.552843	−	0.833286i	$-0.313543\pi$
$277$	18.4023	1.10569	0.552843	+	0.833286i	$0.313543\pi$
$278$	−16.1623	−0.969349
$279$	−10.9000	−0.652567
$280$	0.282561	0.0168863
$281$	5.00292	0.298449	0.149225	−	0.988803i	$-0.452322\pi$
$281$	5.00292	0.298449	0.149225	+	0.988803i	$0.452322\pi$
$282$	0.146264	0.00870992
$283$	−18.9114	−1.12416	−0.562082	−	0.827082i	$-0.689999\pi$
$283$	−18.9114	−1.12416	−0.562082	+	0.827082i	$0.689999\pi$
$284$	13.4448	0.797805
$285$	−0.392038	−0.0232223
$286$	9.83647	0.581643
$287$	2.12900	0.125671
$288$	2.82843	0.166667
$289$	10.5592	0.621131
$290$	1.64689	0.0967085
$291$	4.83396	0.283372
$292$	−15.9089	−0.931001
$293$	32.9481	1.92485	0.962425	−	0.271546i	$-0.0875350\pi$
$293$	32.9481	1.92485	0.962425	+	0.271546i	$0.0875350\pi$
$294$	−2.86642	−0.167173
$295$	3.00000	0.174667
$296$	0.828427	0.0481513
$297$	−12.7420	−0.739367
$298$	4.83839	0.280281
$299$	0	0
$300$	−0.414214	−0.0239146
$301$	−0.187593	−0.0108127
$302$	3.19151	0.183651
$303$	4.40544	0.253086
$304$	0.946464	0.0542834
$305$	−9.75663	−0.558663
$306$	14.8484	0.848824
$307$	8.01942	0.457692	0.228846	−	0.973463i	$-0.426505\pi$
$307$	8.01942	0.457692	0.228846	+	0.973463i	$0.426505\pi$
$308$	1.49133	0.0849766
$309$	−5.09372	−0.289772
$310$	−3.85374	−0.218877
$311$	24.6291	1.39659	0.698293	−	0.715812i	$-0.253943\pi$
$311$	24.6291	1.39659	0.698293	+	0.715812i	$0.253943\pi$
$312$	0.771971	0.0437043
$313$	−15.0842	−0.852608	−0.426304	−	0.904580i	$-0.640185\pi$
$313$	−15.0842	−0.852608	−0.426304	+	0.904580i	$0.640185\pi$
$314$	−10.4288	−0.588533
$315$	0.799203	0.0450300
$316$	4.81116	0.270649
$317$	−23.2015	−1.30312	−0.651562	−	0.758595i	$-0.725886\pi$
$317$	−23.2015	−1.30312	−0.651562	+	0.758595i	$0.725886\pi$
$318$	4.23194	0.237316
$319$	8.69213	0.486666
$320$	1.00000	0.0559017
$321$	−3.75736	−0.209715
$322$	0	0
$323$	4.96864	0.276462
$324$	7.48528	0.415849
$325$	1.86370	0.103380
$326$	3.87780	0.214771
$327$	−2.57310	−0.142293
$328$	7.53465	0.416032
$329$	−0.0997761	−0.00550083
$330$	−2.18618	−0.120346
$331$	3.25120	0.178702	0.0893511	−	0.996000i	$-0.471521\pi$
$331$	3.25120	0.178702	0.0893511	+	0.996000i	$0.471521\pi$
$332$	−0.643238	−0.0353023
$333$	2.34315	0.128404
$334$	−2.76681	−0.151393
$335$	−15.0628	−0.822967
$336$	0.117041	0.00638509
$337$	23.5714	1.28402	0.642009	−	0.766697i	$-0.278101\pi$
$337$	23.5714	1.28402	0.642009	+	0.766697i	$0.278101\pi$
$338$	9.52661	0.518179
$339$	−2.12460	−0.115393
$340$	5.24969	0.284704
$341$	−20.3397	−1.10146
$342$	2.67700	0.144756
$343$	3.93330	0.212378
$344$	−0.663902	−0.0357952
$345$	0	0
$346$	−19.2015	−1.03228
$347$	13.0980	0.703138	0.351569	−	0.936162i	$-0.385648\pi$
$347$	13.0980	0.703138	0.351569	+	0.936162i	$0.385648\pi$
$348$	0.682163	0.0365678
$349$	−2.69412	−0.144213	−0.0721065	−	0.997397i	$-0.522972\pi$
$349$	−2.69412	−0.144213	−0.0721065	+	0.997397i	$0.522972\pi$
$350$	0.282561	0.0151035
$351$	4.49938	0.240159
$352$	5.27792	0.281314
$353$	3.54727	0.188802	0.0944012	−	0.995534i	$-0.469906\pi$
$353$	3.54727	0.188802	0.0944012	+	0.995534i	$0.469906\pi$
$354$	1.24264	0.0660456
$355$	13.4448	0.713578
$356$	2.29326	0.121542
$357$	0.614427	0.0325189
$358$	−21.6401	−1.14372
$359$	−21.8220	−1.15172	−0.575861	−	0.817548i	$-0.695333\pi$
$359$	−21.8220	−1.15172	−0.575861	+	0.817548i	$0.695333\pi$
$360$	2.82843	0.149071
$361$	−18.1042	−0.952853
$362$	−16.4288	−0.863480
$363$	−6.98215	−0.366468
$364$	−0.526610	−0.0276019
$365$	−15.9089	−0.832712
$366$	−4.04133	−0.211244
$367$	9.98177	0.521044	0.260522	−	0.965468i	$-0.416105\pi$
$367$	9.98177	0.521044	0.260522	+	0.965468i	$0.416105\pi$
$368$	0	0
$369$	21.3112	1.10942
$370$	0.828427	0.0430679
$371$	−2.88687	−0.149879
$372$	−1.59627	−0.0827627
$373$	−13.8537	−0.717319	−0.358660	−	0.933468i	$-0.616766\pi$
$373$	−13.8537	−0.717319	−0.358660	+	0.933468i	$0.616766\pi$
$374$	27.7074	1.43272
$375$	−0.414214	−0.0213899
$376$	−0.353113	−0.0182104
$377$	−3.06931	−0.158077
$378$	0.682163	0.0350867
$379$	27.1798	1.39613	0.698067	−	0.716033i	$-0.254044\pi$
$379$	27.1798	1.39613	0.698067	+	0.716033i	$0.254044\pi$
$380$	0.946464	0.0485526
$381$	−3.14021	−0.160878
$382$	−24.6797	−1.26272
$383$	9.17260	0.468698	0.234349	−	0.972153i	$-0.424704\pi$
$383$	9.17260	0.468698	0.234349	+	0.972153i	$0.424704\pi$
$384$	0.414214	0.0211377
$385$	1.49133	0.0760054
$386$	11.1429	0.567157
$387$	−1.87780	−0.0954539
$388$	−11.6702	−0.592466
$389$	16.0048	0.811476	0.405738	−	0.913989i	$-0.367015\pi$
$389$	16.0048	0.811476	0.405738	+	0.913989i	$0.367015\pi$
$390$	0.771971	0.0390903
$391$	0	0
$392$	6.92016	0.349521
$393$	−8.23357	−0.415328
$394$	10.9262	0.550455
$395$	4.81116	0.242076
$396$	14.9282	0.750170
$397$	28.4776	1.42925	0.714626	−	0.699507i	$-0.246597\pi$
$397$	28.4776	1.42925	0.714626	+	0.699507i	$0.246597\pi$
$398$	−21.4600	−1.07569
$399$	0.110775	0.00554567
$400$	1.00000	0.0500000
$401$	13.9535	0.696807	0.348403	−	0.937345i	$-0.386724\pi$
$401$	13.9535	0.696807	0.348403	+	0.937345i	$0.386724\pi$
$402$	−6.23921	−0.311183
$403$	7.18222	0.357772
$404$	−10.6357	−0.529145
$405$	7.48528	0.371947
$406$	−0.465346	−0.0230947
$407$	4.37237	0.216730
$408$	2.17449	0.107653
$409$	−19.8732	−0.982664	−0.491332	−	0.870972i	$-0.663490\pi$
$409$	−19.8732	−0.982664	−0.491332	+	0.870972i	$0.663490\pi$
$410$	7.53465	0.372110
$411$	−6.87873	−0.339303
$412$	12.2973	0.605846
$413$	−0.847683	−0.0417118
$414$	0	0
$415$	−0.643238	−0.0315753
$416$	−1.86370	−0.0913756
$417$	−6.69464	−0.327838
$418$	4.99536	0.244331
$419$	−22.7512	−1.11147	−0.555735	−	0.831360i	$-0.687563\pi$
$419$	−22.7512	−1.11147	−0.555735	+	0.831360i	$0.687563\pi$
$420$	0.117041	0.00571100
$421$	40.7127	1.98422	0.992109	−	0.125379i	$-0.0400148\pi$
$421$	40.7127	1.98422	0.992109	+	0.125379i	$0.0400148\pi$
$422$	−2.88812	−0.140591
$423$	−0.998756	−0.0485612
$424$	−10.2168	−0.496172
$425$	5.24969	0.254647
$426$	5.56904	0.269821
$427$	2.75684	0.133413
$428$	9.07107	0.438467
$429$	4.07440	0.196714
$430$	−0.663902	−0.0320162
$431$	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
$433$	17.2074	0.826933	0.413467	−	0.910519i	$-0.364318\pi$
$433$	17.2074	0.826933	0.413467	+	0.910519i	$0.364318\pi$
$434$	1.08892	0.0522696
$435$	0.682163	0.0327072
$436$	6.21201	0.297501
$437$	0	0
$438$	−6.58970	−0.314868
$439$	36.9825	1.76508	0.882540	−	0.470238i	$-0.155832\pi$
$439$	36.9825	1.76508	0.882540	+	0.470238i	$0.155832\pi$
$440$	5.27792	0.251615
$441$	19.5732	0.932056
$442$	−9.78386	−0.465371
$443$	−15.0698	−0.715989	−0.357994	−	0.933724i	$-0.616539\pi$
$443$	−15.0698	−0.715989	−0.357994	+	0.933724i	$0.616539\pi$
$444$	0.343146	0.0162850
$445$	2.29326	0.108711
$446$	13.5347	0.640884
$447$	2.00413	0.0947920
$448$	−0.282561	−0.0133498
$449$	−18.4675	−0.871535	−0.435768	−	0.900059i	$-0.643523\pi$
$449$	−18.4675	−0.871535	−0.435768	+	0.900059i	$0.643523\pi$
$450$	2.82843	0.133333
$451$	39.7673	1.87257
$452$	5.12925	0.241260
$453$	1.32197	0.0621114
$454$	−7.15648	−0.335870
$455$	−0.526610	−0.0246879
$456$	0.392038	0.0183589
$457$	28.5891	1.33734	0.668672	−	0.743558i	$-0.266863\pi$
$457$	28.5891	1.33734	0.668672	+	0.743558i	$0.266863\pi$
$458$	0.818459	0.0382441
$459$	12.6739	0.591566
$460$	0	0
$461$	−7.13986	−0.332536	−0.166268	−	0.986081i	$-0.553172\pi$
$461$	−7.13986	−0.332536	−0.166268	+	0.986081i	$0.553172\pi$
$462$	0.617731	0.0287394
$463$	3.77073	0.175241	0.0876203	−	0.996154i	$-0.472074\pi$
$463$	3.77073	0.175241	0.0876203	+	0.996154i	$0.472074\pi$
$464$	−1.64689	−0.0764548
$465$	−1.59627	−0.0740252
$466$	22.0311	1.02057
$467$	−26.5448	−1.22835	−0.614173	−	0.789171i	$-0.710510\pi$
$467$	−26.5448	−1.22835	−0.614173	+	0.789171i	$0.710510\pi$
$468$	−5.27135	−0.243668
$469$	4.25615	0.196531
$470$	−0.353113	−0.0162879
$471$	−4.31976	−0.199044
$472$	−3.00000	−0.138086
$473$	−3.50402	−0.161115
$474$	1.99285	0.0915346
$475$	0.946464	0.0434267
$476$	−1.48336	−0.0679896
$477$	−28.8975	−1.32313
$478$	27.0892	1.23903
$479$	21.1723	0.967385	0.483692	−	0.875238i	$-0.339295\pi$
$479$	21.1723	0.967385	0.483692	+	0.875238i	$0.339295\pi$
$480$	0.414214	0.0189062
$481$	−1.54394	−0.0703977
$482$	6.86078	0.312500
$483$	0	0
$484$	16.8564	0.766200
$485$	−11.6702	−0.529917
$486$	10.3431	0.469175
$487$	−30.3727	−1.37632	−0.688159	−	0.725560i	$-0.741581\pi$
$487$	−30.3727	−1.37632	−0.688159	+	0.725560i	$0.741581\pi$
$488$	9.75663	0.441662
$489$	1.60624	0.0726366
$490$	6.92016	0.312621
$491$	28.0706	1.26681	0.633403	−	0.773822i	$-0.281658\pi$
$491$	28.0706	1.26681	0.633403	+	0.773822i	$0.281658\pi$
$492$	3.12096	0.140704
$493$	−8.64564	−0.389380
$494$	−1.76393	−0.0793628
$495$	14.9282	0.670973
$496$	3.85374	0.173038
$497$	−3.79899	−0.170408
$498$	−0.266438	−0.0119394
$499$	1.52719	0.0683666	0.0341833	−	0.999416i	$-0.489117\pi$
$499$	1.52719	0.0683666	0.0341833	+	0.999416i	$0.489117\pi$
$500$	1.00000	0.0447214
$501$	−1.14605	−0.0512018
$502$	−6.15456	−0.274691
$503$	30.1177	1.34288	0.671441	−	0.741058i	$-0.265676\pi$
$503$	30.1177	1.34288	0.671441	+	0.741058i	$0.265676\pi$
$504$	−0.799203	−0.0355993
$505$	−10.6357	−0.473281
$506$	0	0
$507$	3.94605	0.175250
$508$	7.58114	0.336359
$509$	27.4988	1.21886	0.609432	−	0.792839i	$-0.291398\pi$
$509$	27.4988	1.21886	0.609432	+	0.792839i	$0.291398\pi$
$510$	2.17449	0.0962881
$511$	4.49525	0.198858
$512$	−1.00000	−0.0441942
$513$	2.28497	0.100884
$514$	7.41297	0.326972
$515$	12.2973	0.541885
$516$	−0.274997	−0.0121061
$517$	−1.86370	−0.0819656
$518$	−0.234081	−0.0102849
$519$	−7.95351	−0.349120
$520$	−1.86370	−0.0817288
$521$	41.2097	1.80543	0.902715	−	0.430240i	$-0.141571\pi$
$521$	41.2097	1.80543	0.902715	+	0.430240i	$0.141571\pi$
$522$	−4.65810	−0.203879
$523$	−2.30390	−0.100743	−0.0503714	−	0.998731i	$-0.516040\pi$
$523$	−2.30390	−0.100743	−0.0503714	+	0.998731i	$0.516040\pi$
$524$	19.8776	0.868356
$525$	0.117041	0.00510807
$526$	−22.4263	−0.977835
$527$	20.2309	0.881272
$528$	2.18618	0.0951415
$529$	0	0
$530$	−10.2168	−0.443790
$531$	−8.48528	−0.368230
$532$	−0.267434	−0.0115947
$533$	−14.0424	−0.608242
$534$	0.949898	0.0411061
$535$	9.07107	0.392176
$536$	15.0628	0.650613
$537$	−8.96363	−0.386809
$538$	4.25120	0.183282
$539$	36.5240	1.57320
$540$	2.41421	0.103891
$541$	25.1430	1.08098	0.540492	−	0.841349i	$-0.318238\pi$
$541$	25.1430	1.08098	0.540492	+	0.841349i	$0.318238\pi$
$542$	−13.9859	−0.600746
$543$	−6.80504	−0.292032
$544$	−5.24969	−0.225079
$545$	6.21201	0.266093
$546$	−0.218129	−0.00933506
$547$	−43.1127	−1.84337	−0.921683	−	0.387944i	$-0.873185\pi$
$547$	−43.1127	−1.84337	−0.921683	+	0.387944i	$0.873185\pi$
$548$	16.6067	0.709404
$549$	27.5959	1.17777
$550$	5.27792	0.225051
$551$	−1.55872	−0.0664036
$552$	0	0
$553$	−1.35945	−0.0578096
$554$	−18.4023	−0.781838
$555$	0.343146	0.0145657
$556$	16.1623	0.685434
$557$	24.3814	1.03307	0.516536	−	0.856265i	$-0.327221\pi$
$557$	24.3814	1.03307	0.516536	+	0.856265i	$0.327221\pi$
$558$	10.9000	0.461434
$559$	1.23732	0.0523329
$560$	−0.282561	−0.0119404
$561$	11.4768	0.484550
$562$	−5.00292	−0.211035
$563$	42.5108	1.79162	0.895808	−	0.444441i	$-0.146598\pi$
$563$	42.5108	1.79162	0.895808	+	0.444441i	$0.146598\pi$
$564$	−0.146264	−0.00615884
$565$	5.12925	0.215789
$566$	18.9114	0.794903
$567$	−2.11505	−0.0888237
$568$	−13.4448	−0.564133
$569$	−29.2954	−1.22813	−0.614065	−	0.789256i	$-0.710467\pi$
$569$	−29.2954	−1.22813	−0.614065	+	0.789256i	$0.710467\pi$
$570$	0.392038	0.0164207
$571$	−35.8550	−1.50049	−0.750243	−	0.661162i	$-0.770064\pi$
$571$	−35.8550	−1.50049	−0.750243	+	0.661162i	$0.770064\pi$
$572$	−9.83647	−0.411284
$573$	−10.2227	−0.427058
$574$	−2.12900	−0.0888627
$575$	0	0
$576$	−2.82843	−0.117851
$577$	14.7477	0.613955	0.306977	−	0.951717i	$-0.400682\pi$
$577$	14.7477	0.613955	0.306977	+	0.951717i	$0.400682\pi$
$578$	−10.5592	−0.439206
$579$	4.61553	0.191815
$580$	−1.64689	−0.0683832
$581$	0.181754	0.00754043
$582$	−4.83396	−0.200374
$583$	−53.9235	−2.23328
$584$	15.9089	0.658317
$585$	−5.27135	−0.217943
$586$	−32.9481	−1.36108
$587$	−44.8649	−1.85177	−0.925887	−	0.377801i	$-0.876680\pi$
$587$	−44.8649	−1.85177	−0.925887	+	0.377801i	$0.876680\pi$
$588$	2.86642	0.118209
$589$	3.64742	0.150289
$590$	−3.00000	−0.123508
$591$	4.52579	0.186166
$592$	−0.828427	−0.0340481
$593$	−8.71603	−0.357924	−0.178962	−	0.983856i	$-0.557274\pi$
$593$	−8.71603	−0.357924	−0.178962	+	0.983856i	$0.557274\pi$
$594$	12.7420	0.522811
$595$	−1.48336	−0.0608117
$596$	−4.83839	−0.198188
$597$	−8.88901	−0.363803
$598$	0	0
$599$	−22.1390	−0.904574	−0.452287	−	0.891873i	$-0.649392\pi$
$599$	−22.1390	−0.904574	−0.452287	+	0.891873i	$0.649392\pi$
$600$	0.414214	0.0169102
$601$	40.3898	1.64753	0.823767	−	0.566928i	$-0.191868\pi$
$601$	40.3898	1.64753	0.823767	+	0.566928i	$0.191868\pi$
$602$	0.187593	0.00764572
$603$	42.6040	1.73497
$604$	−3.19151	−0.129861
$605$	16.8564	0.685310
$606$	−4.40544	−0.178959
$607$	−17.8158	−0.723119	−0.361560	−	0.932349i	$-0.617756\pi$
$607$	−17.8158	−0.723119	−0.361560	+	0.932349i	$0.617756\pi$
$608$	−0.946464	−0.0383842
$609$	−0.192753	−0.00781073
$610$	9.75663	0.395034
$611$	0.658099	0.0266238
$612$	−14.8484	−0.600209
$613$	−15.3499	−0.619976	−0.309988	−	0.950741i	$-0.600325\pi$
$613$	−15.3499	−0.619976	−0.309988	+	0.950741i	$0.600325\pi$
$614$	−8.01942	−0.323637
$615$	3.12096	0.125849
$616$	−1.49133	−0.0600876
$617$	20.2454	0.815049	0.407524	−	0.913194i	$-0.366392\pi$
$617$	20.2454	0.815049	0.407524	+	0.913194i	$0.366392\pi$
$618$	5.09372	0.204900
$619$	10.0426	0.403646	0.201823	−	0.979422i	$-0.435313\pi$
$619$	10.0426	0.403646	0.201823	+	0.979422i	$0.435313\pi$
$620$	3.85374	0.154770
$621$	0	0
$622$	−24.6291	−0.987535
$623$	−0.647985	−0.0259610
$624$	−0.771971	−0.0309036
$625$	1.00000	0.0400000
$626$	15.0842	0.602885
$627$	2.06914	0.0826337
$628$	10.4288	0.416155
$629$	−4.34898	−0.173405
$630$	−0.799203	−0.0318410
$631$	−24.4305	−0.972561	−0.486281	−	0.873803i	$-0.661647\pi$
$631$	−24.4305	−0.972561	−0.486281	+	0.873803i	$0.661647\pi$
$632$	−4.81116	−0.191378
$633$	−1.19630	−0.0475486
$634$	23.2015	0.921448
$635$	7.58114	0.300848
$636$	−4.23194	−0.167807
$637$	−12.8971	−0.511003
$638$	−8.69213	−0.344125
$639$	−38.0278	−1.50436
$640$	−1.00000	−0.0395285
$641$	19.3395	0.763864	0.381932	−	0.924190i	$-0.375259\pi$
$641$	19.3395	0.763864	0.381932	+	0.924190i	$0.375259\pi$
$642$	3.75736	0.148291
$643$	−35.7466	−1.40971	−0.704854	−	0.709352i	$-0.748988\pi$
$643$	−35.7466	−1.40971	−0.704854	+	0.709352i	$0.748988\pi$
$644$	0	0
$645$	−0.274997	−0.0108280
$646$	−4.96864	−0.195488
$647$	−31.8753	−1.25315	−0.626574	−	0.779362i	$-0.715543\pi$
$647$	−31.8753	−1.25315	−0.626574	+	0.779362i	$0.715543\pi$
$648$	−7.48528	−0.294050
$649$	−15.8338	−0.621529
$650$	−1.86370	−0.0731005
$651$	0.451044	0.0176778
$652$	−3.87780	−0.151866
$653$	−31.3226	−1.22575	−0.612875	−	0.790180i	$-0.709987\pi$
$653$	−31.3226	−1.22575	−0.612875	+	0.790180i	$0.709987\pi$
$654$	2.57310	0.100616
$655$	19.8776	0.776682
$656$	−7.53465	−0.294179
$657$	44.9973	1.75551
$658$	0.0997761	0.00388968
$659$	14.1631	0.551717	0.275858	−	0.961198i	$-0.411038\pi$
$659$	14.1631	0.551717	0.275858	+	0.961198i	$0.411038\pi$
$660$	2.18618	0.0850971
$661$	34.3365	1.33554	0.667768	−	0.744369i	$-0.267250\pi$
$661$	34.3365	1.33554	0.667768	+	0.744369i	$0.267250\pi$
$662$	−3.25120	−0.126361
$663$	−4.05261	−0.157390
$664$	0.643238	0.0249625
$665$	−0.267434	−0.0103706
$666$	−2.34315	−0.0907951
$667$	0	0
$668$	2.76681	0.107051
$669$	5.60624	0.216750
$670$	15.0628	0.581926
$671$	51.4947	1.98793
$672$	−0.117041	−0.00451494
$673$	−22.5656	−0.869841	−0.434921	−	0.900469i	$-0.643224\pi$
$673$	−22.5656	−0.869841	−0.434921	+	0.900469i	$0.643224\pi$
$674$	−23.5714	−0.907938
$675$	2.41421	0.0929231
$676$	−9.52661	−0.366408
$677$	2.61539	0.100518	0.0502588	−	0.998736i	$-0.483995\pi$
$677$	2.61539	0.100518	0.0502588	+	0.998736i	$0.483995\pi$
$678$	2.12460	0.0815949
$679$	3.29755	0.126548
$680$	−5.24969	−0.201316
$681$	−2.96431	−0.113593
$682$	20.3397	0.778847
$683$	3.99911	0.153022	0.0765108	−	0.997069i	$-0.475622\pi$
$683$	3.99911	0.153022	0.0765108	+	0.997069i	$0.475622\pi$
$684$	−2.67700	−0.102358
$685$	16.6067	0.634510
$686$	−3.93330	−0.150174
$687$	0.339017	0.0129343
$688$	0.663902	0.0253110
$689$	19.0411	0.725409
$690$	0	0
$691$	−30.3616	−1.15501	−0.577505	−	0.816387i	$-0.695974\pi$
$691$	−30.3616	−1.15501	−0.577505	+	0.816387i	$0.695974\pi$
$692$	19.2015	0.729931
$693$	−4.21813	−0.160233
$694$	−13.0980	−0.497194
$695$	16.1623	0.613070
$696$	−0.682163	−0.0258573
$697$	−39.5546	−1.49824
$698$	2.69412	0.101974
$699$	9.12560	0.345162
$700$	−0.282561	−0.0106798
$701$	−31.0073	−1.17113	−0.585564	−	0.810626i	$-0.699127\pi$
$701$	−31.0073	−1.17113	−0.585564	+	0.810626i	$0.699127\pi$
$702$	−4.49938	−0.169818
$703$	−0.784076	−0.0295720
$704$	−5.27792	−0.198919
$705$	−0.146264	−0.00550863
$706$	−3.54727	−0.133503
$707$	3.00523	0.113023
$708$	−1.24264	−0.0467013
$709$	−28.9157	−1.08595	−0.542977	−	0.839748i	$-0.682703\pi$
$709$	−28.9157	−1.08595	−0.542977	+	0.839748i	$0.682703\pi$
$710$	−13.4448	−0.504576
$711$	−13.6080	−0.510341
$712$	−2.29326	−0.0859435
$713$	0	0
$714$	−0.614427	−0.0229943
$715$	−9.83647	−0.367863
$716$	21.6401	0.808729
$717$	11.2207	0.419046
$718$	21.8220	0.814391
$719$	−2.06340	−0.0769519	−0.0384759	−	0.999260i	$-0.512250\pi$
$719$	−2.06340	−0.0769519	−0.0384759	+	0.999260i	$0.512250\pi$
$720$	−2.82843	−0.105409
$721$	−3.47475	−0.129406
$722$	18.1042	0.673769
$723$	2.84183	0.105689
$724$	16.4288	0.610572
$725$	−1.64689	−0.0611638
$726$	6.98215	0.259132
$727$	7.61304	0.282352	0.141176	−	0.989985i	$-0.454912\pi$
$727$	7.61304	0.282352	0.141176	+	0.989985i	$0.454912\pi$
$728$	0.526610	0.0195175
$729$	−18.1716	−0.673021
$730$	15.9089	0.588817
$731$	3.48528	0.128908
$732$	4.04133	0.149372
$733$	−0.545866	−0.0201620	−0.0100810	−	0.999949i	$-0.503209\pi$
$733$	−0.545866	−0.0201620	−0.0100810	+	0.999949i	$0.503209\pi$
$734$	−9.98177	−0.368434
$735$	2.86642	0.105730
$736$	0	0
$737$	79.5001	2.92842
$738$	−21.3112	−0.784477
$739$	−1.49333	−0.0549329	−0.0274664	−	0.999623i	$-0.508744\pi$
$739$	−1.49333	−0.0549329	−0.0274664	+	0.999623i	$0.508744\pi$
$740$	−0.828427	−0.0304536
$741$	−0.730643	−0.0268408
$742$	2.88687	0.105981
$743$	−42.4290	−1.55657	−0.778285	−	0.627912i	$-0.783910\pi$
$743$	−42.4290	−1.55657	−0.778285	+	0.627912i	$0.783910\pi$
$744$	1.59627	0.0585221
$745$	−4.83839	−0.177265
$746$	13.8537	0.507221
$747$	1.81935	0.0665666
$748$	−27.7074	−1.01308
$749$	−2.56313	−0.0936548
$750$	0.414214	0.0151249
$751$	−32.0575	−1.16979	−0.584897	−	0.811107i	$-0.698865\pi$
$751$	−32.0575	−1.16979	−0.584897	+	0.811107i	$0.698865\pi$
$752$	0.353113	0.0128767
$753$	−2.54930	−0.0929017
$754$	3.06931	0.111778
$755$	−3.19151	−0.116151
$756$	−0.682163	−0.0248100
$757$	−24.4763	−0.889608	−0.444804	−	0.895628i	$-0.646727\pi$
$757$	−24.4763	−0.889608	−0.444804	+	0.895628i	$0.646727\pi$
$758$	−27.1798	−0.987215
$759$	0	0
$760$	−0.946464	−0.0343318
$761$	−19.3184	−0.700290	−0.350145	−	0.936696i	$-0.613868\pi$
$761$	−19.3184	−0.700290	−0.350145	+	0.936696i	$0.613868\pi$
$762$	3.14021	0.113758
$763$	−1.75527	−0.0635451
$764$	24.6797	0.892879
$765$	−14.8484	−0.536844
$766$	−9.17260	−0.331420
$767$	5.59111	0.201883
$768$	−0.414214	−0.0149466
$769$	−30.5045	−1.10002	−0.550010	−	0.835158i	$-0.685376\pi$
$769$	−30.5045	−1.10002	−0.550010	+	0.835158i	$0.685376\pi$
$770$	−1.49133	−0.0537439
$771$	3.07055	0.110583
$772$	−11.1429	−0.401040
$773$	18.7589	0.674711	0.337355	−	0.941377i	$-0.390468\pi$
$773$	18.7589	0.674711	0.337355	+	0.941377i	$0.390468\pi$
$774$	1.87780	0.0674961
$775$	3.85374	0.138430
$776$	11.6702	0.418937
$777$	−0.0969596	−0.00347841
$778$	−16.0048	−0.573800
$779$	−7.13128	−0.255504
$780$	−0.771971	−0.0276410
$781$	−70.9608	−2.53918
$782$	0	0
$783$	−3.97594	−0.142088
$784$	−6.92016	−0.247149
$785$	10.4288	0.372221
$786$	8.23357	0.293682
$787$	25.0638	0.893428	0.446714	−	0.894677i	$-0.352594\pi$
$787$	25.0638	0.893428	0.446714	+	0.894677i	$0.352594\pi$
$788$	−10.9262	−0.389230
$789$	−9.28929	−0.330708
$790$	−4.81116	−0.171173
$791$	−1.44933	−0.0515321
$792$	−14.9282	−0.530451
$793$	−18.1835	−0.645714
$794$	−28.4776	−1.01063
$795$	−4.23194	−0.150092
$796$	21.4600	0.760629
$797$	30.1700	1.06868	0.534338	−	0.845271i	$-0.320561\pi$
$797$	30.1700	1.06868	0.534338	+	0.845271i	$0.320561\pi$
$798$	−0.110775	−0.00392138
$799$	1.85374	0.0655805
$800$	−1.00000	−0.0353553
$801$	−6.48631	−0.229183
$802$	−13.9535	−0.492717
$803$	83.9661	2.96310
$804$	6.23921	0.220040
$805$	0	0
$806$	−7.18222	−0.252983
$807$	1.76090	0.0619868
$808$	10.6357	0.374162
$809$	−23.4794	−0.825491	−0.412746	−	0.910846i	$-0.635430\pi$
$809$	−23.4794	−0.825491	−0.412746	+	0.910846i	$0.635430\pi$
$810$	−7.48528	−0.263006
$811$	−0.772718	−0.0271338	−0.0135669	−	0.999908i	$-0.504319\pi$
$811$	−0.772718	−0.0271338	−0.0135669	+	0.999908i	$0.504319\pi$
$812$	0.465346	0.0163304
$813$	−5.79315	−0.203175
$814$	−4.37237	−0.153251
$815$	−3.87780	−0.135833
$816$	−2.17449	−0.0761225
$817$	0.628359	0.0219835
$818$	19.8732	0.694849
$819$	1.48948	0.0520466
$820$	−7.53465	−0.263122
$821$	22.8683	0.798109	0.399055	−	0.916927i	$-0.369338\pi$
$821$	22.8683	0.798109	0.399055	+	0.916927i	$0.369338\pi$
$822$	6.87873	0.239923
$823$	29.3381	1.02266	0.511331	−	0.859384i	$-0.329153\pi$
$823$	29.3381	1.02266	0.511331	+	0.859384i	$0.329153\pi$
$824$	−12.2973	−0.428398
$825$	2.18618	0.0761132
$826$	0.847683	0.0294947
$827$	42.1809	1.46678	0.733388	−	0.679811i	$-0.237938\pi$
$827$	42.1809	1.46678	0.733388	+	0.679811i	$0.237938\pi$
$828$	0	0
$829$	−3.69089	−0.128190	−0.0640949	−	0.997944i	$-0.520416\pi$
$829$	−3.69089	−0.128190	−0.0640949	+	0.997944i	$0.520416\pi$
$830$	0.643238	0.0223271
$831$	−7.62247	−0.264421
$832$	1.86370	0.0646123
$833$	−36.3287	−1.25871
$834$	6.69464	0.231816
$835$	2.76681	0.0957495
$836$	−4.99536	−0.172768
$837$	9.30374	0.321584
$838$	22.7512	0.785928
$839$	−38.1981	−1.31874	−0.659372	−	0.751817i	$-0.729178\pi$
$839$	−38.1981	−1.31874	−0.659372	+	0.751817i	$0.729178\pi$
$840$	−0.117041	−0.00403829
$841$	−26.2878	−0.906475
$842$	−40.7127	−1.40305
$843$	−2.07228	−0.0713730
$844$	2.88812	0.0994132
$845$	−9.52661	−0.327725
$846$	0.998756	0.0343379
$847$	−4.76296	−0.163657
$848$	10.2168	0.350847
$849$	7.83334	0.268839
$850$	−5.24969	−0.180063
$851$	0	0
$852$	−5.56904	−0.190792
$853$	−15.5099	−0.531049	−0.265525	−	0.964104i	$-0.585545\pi$
$853$	−15.5099	−0.531049	−0.265525	+	0.964104i	$0.585545\pi$
$854$	−2.75684	−0.0943373
$855$	−2.67700	−0.0915516
$856$	−9.07107	−0.310043
$857$	−31.5049	−1.07619	−0.538093	−	0.842886i	$-0.680855\pi$
$857$	−31.5049	−1.07619	−0.538093	+	0.842886i	$0.680855\pi$
$858$	−4.07440	−0.139098
$859$	−41.9647	−1.43182	−0.715908	−	0.698195i	$-0.753987\pi$
$859$	−41.9647	−1.43182	−0.715908	+	0.698195i	$0.753987\pi$
$860$	0.663902	0.0226389
$861$	−0.881861	−0.0300537
$862$	−24.2843	−0.827126
$863$	−12.3497	−0.420387	−0.210194	−	0.977660i	$-0.567409\pi$
$863$	−12.3497	−0.420387	−0.210194	+	0.977660i	$0.567409\pi$
$864$	−2.41421	−0.0821332
$865$	19.2015	0.652870
$866$	−17.2074	−0.584730
$867$	−4.37378	−0.148541
$868$	−1.08892	−0.0369602
$869$	−25.3929	−0.861396
$870$	−0.682163	−0.0231275
$871$	−28.0725	−0.951202
$872$	−6.21201	−0.210365
$873$	33.0084	1.11716
$874$	0	0
$875$	−0.282561	−0.00955231
$876$	6.58970	0.222645
$877$	29.9235	1.01045	0.505223	−	0.862989i	$-0.331410\pi$
$877$	29.9235	1.01045	0.505223	+	0.862989i	$0.331410\pi$
$878$	−36.9825	−1.24810
$879$	−13.6476	−0.460321
$880$	−5.27792	−0.177919
$881$	8.56618	0.288602	0.144301	−	0.989534i	$-0.453907\pi$
$881$	8.56618	0.288602	0.144301	+	0.989534i	$0.453907\pi$
$882$	−19.5732	−0.659063
$883$	19.9994	0.673035	0.336517	−	0.941677i	$-0.390751\pi$
$883$	19.9994	0.673035	0.336517	+	0.941677i	$0.390751\pi$
$884$	9.78386	0.329067
$885$	−1.24264	−0.0417709
$886$	15.0698	0.506281
$887$	53.1363	1.78414	0.892071	−	0.451896i	$-0.149252\pi$
$887$	53.1363	1.78414	0.892071	+	0.451896i	$0.149252\pi$
$888$	−0.343146	−0.0115152
$889$	−2.14214	−0.0718449
$890$	−2.29326	−0.0768702
$891$	−39.5067	−1.32352
$892$	−13.5347	−0.453174
$893$	0.334209	0.0111839
$894$	−2.00413	−0.0670281
$895$	21.6401	0.723349
$896$	0.282561	0.00943970
$897$	0	0
$898$	18.4675	0.616269
$899$	−6.34667	−0.211673
$900$	−2.82843	−0.0942809
$901$	53.6351	1.78684
$902$	−39.7673	−1.32411
$903$	0.0777036	0.00258581
$904$	−5.12925	−0.170596
$905$	16.4288	0.546113
$906$	−1.32197	−0.0439194
$907$	−21.8713	−0.726223	−0.363112	−	0.931746i	$-0.618286\pi$
$907$	−21.8713	−0.726223	−0.363112	+	0.931746i	$0.618286\pi$
$908$	7.15648	0.237496
$909$	30.0822	0.997765
$910$	0.526610	0.0174570
$911$	55.8763	1.85127	0.925633	−	0.378423i	$-0.123533\pi$
$911$	55.8763	1.85127	0.925633	+	0.378423i	$0.123533\pi$
$912$	−0.392038	−0.0129817
$913$	3.39496	0.112357
$914$	−28.5891	−0.945645
$915$	4.04133	0.133602
$916$	−0.818459	−0.0270427
$917$	−5.61663	−0.185478
$918$	−12.6739	−0.418300
$919$	19.4789	0.642549	0.321274	−	0.946986i	$-0.395889\pi$
$919$	19.4789	0.642549	0.321274	+	0.946986i	$0.395889\pi$
$920$	0	0
$921$	−3.32175	−0.109455
$922$	7.13986	0.235139
$923$	25.0572	0.824768
$924$	−0.617731	−0.0203218
$925$	−0.828427	−0.0272385
$926$	−3.77073	−0.123914
$927$	−34.7821	−1.14239
$928$	1.64689	0.0540617
$929$	49.9789	1.63976	0.819878	−	0.572539i	$-0.194041\pi$
$929$	49.9789	1.63976	0.819878	+	0.572539i	$0.194041\pi$
$930$	1.59627	0.0523437
$931$	−6.54968	−0.214657
$932$	−22.0311	−0.721654
$933$	−10.2017	−0.333988
$934$	26.5448	0.868572
$935$	−27.7074	−0.906130
$936$	5.27135	0.172299
$937$	−26.2127	−0.856330	−0.428165	−	0.903701i	$-0.640840\pi$
$937$	−26.2127	−0.856330	−0.428165	+	0.903701i	$0.640840\pi$
$938$	−4.25615	−0.138968
$939$	6.24807	0.203898
$940$	0.353113	0.0115173
$941$	23.1300	0.754015	0.377008	−	0.926210i	$-0.376953\pi$
$941$	23.1300	0.754015	0.377008	+	0.926210i	$0.376953\pi$
$942$	4.31976	0.140745
$943$	0	0
$944$	3.00000	0.0976417
$945$	−0.682163	−0.0221908
$946$	3.50402	0.113926
$947$	−31.2797	−1.01645	−0.508227	−	0.861223i	$-0.669699\pi$
$947$	−31.2797	−1.01645	−0.508227	+	0.861223i	$0.669699\pi$
$948$	−1.99285	−0.0647247
$949$	−29.6496	−0.962465
$950$	−0.946464	−0.0307073
$951$	9.61037	0.311637
$952$	1.48336	0.0480759
$953$	−46.1117	−1.49370	−0.746852	−	0.664990i	$-0.768436\pi$
$953$	−46.1117	−1.49370	−0.746852	+	0.664990i	$0.768436\pi$
$954$	28.8975	0.935592
$955$	24.6797	0.798615
$956$	−27.0892	−0.876129
$957$	−3.60040	−0.116384
$958$	−21.1723	−0.684044
$959$	−4.69241	−0.151526
$960$	−0.414214	−0.0133687
$961$	−16.1487	−0.520927
$962$	1.54394	0.0497787
$963$	−25.6569	−0.826781
$964$	−6.86078	−0.220971
$965$	−11.1429	−0.358702
$966$	0	0
$967$	−17.5750	−0.565175	−0.282587	−	0.959242i	$-0.591193\pi$
$967$	−17.5750	−0.565175	−0.282587	+	0.959242i	$0.591193\pi$
$968$	−16.8564	−0.541785
$969$	−2.05808	−0.0661150
$970$	11.6702	0.374708
$971$	−21.9107	−0.703148	−0.351574	−	0.936160i	$-0.614353\pi$
$971$	−21.9107	−0.703148	−0.351574	+	0.936160i	$0.614353\pi$
$972$	−10.3431	−0.331757
$973$	−4.56683	−0.146406
$974$	30.3727	0.973204
$975$	−0.771971	−0.0247229
$976$	−9.75663	−0.312302
$977$	24.4929	0.783597	0.391798	−	0.920051i	$-0.371853\pi$
$977$	24.4929	0.783597	0.391798	+	0.920051i	$0.371853\pi$
$978$	−1.60624	−0.0513618
$979$	−12.1036	−0.386833
$980$	−6.92016	−0.221056
$981$	−17.5702	−0.560974
$982$	−28.0706	−0.895767
$983$	11.9177	0.380115	0.190057	−	0.981773i	$-0.439133\pi$
$983$	11.9177	0.380115	0.190057	+	0.981773i	$0.439133\pi$
$984$	−3.12096	−0.0994924
$985$	−10.9262	−0.348138
$986$	8.64564	0.275333
$987$	0.0413286	0.00131550
$988$	1.76393	0.0561180
$989$	0	0
$990$	−14.9282	−0.474449
$991$	53.9572	1.71401	0.857004	−	0.515310i	$-0.172323\pi$
$991$	53.9572	1.71401	0.857004	+	0.515310i	$0.172323\pi$
$992$	−3.85374	−0.122356
$993$	−1.34669	−0.0427360
$994$	3.79899	0.120497
$995$	21.4600	0.680327
$996$	0.266438	0.00844241
$997$	−9.63795	−0.305237	−0.152618	−	0.988285i	$-0.548771\pi$
$997$	−9.63795	−0.305237	−0.152618	+	0.988285i	$0.548771\pi$
$998$	−1.52719	−0.0483425
$999$	−2.00000	−0.0632772

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -0.282561 q^{7} -1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -0.282561 q^{7} -1.00000 q^{8} -2.82843 q^{9} -1.00000 q^{10} -5.27792 q^{11} -0.414214 q^{12} +1.86370 q^{13} +0.282561 q^{14} -0.414214 q^{15} +1.00000 q^{16} +5.24969 q^{17} +2.82843 q^{18} +0.946464 q^{19} +1.00000 q^{20} +0.117041 q^{21} +5.27792 q^{22} +0.414214 q^{24} +1.00000 q^{25} -1.86370 q^{26} +2.41421 q^{27} -0.282561 q^{28} -1.64689 q^{29} +0.414214 q^{30} +3.85374 q^{31} -1.00000 q^{32} +2.18618 q^{33} -5.24969 q^{34} -0.282561 q^{35} -2.82843 q^{36} -0.828427 q^{37} -0.946464 q^{38} -0.771971 q^{39} -1.00000 q^{40} -7.53465 q^{41} -0.117041 q^{42} +0.663902 q^{43} -5.27792 q^{44} -2.82843 q^{45} +0.353113 q^{47} -0.414214 q^{48} -6.92016 q^{49} -1.00000 q^{50} -2.17449 q^{51} +1.86370 q^{52} +10.2168 q^{53} -2.41421 q^{54} -5.27792 q^{55} +0.282561 q^{56} -0.392038 q^{57} +1.64689 q^{58} +3.00000 q^{59} -0.414214 q^{60} -9.75663 q^{61} -3.85374 q^{62} +0.799203 q^{63} +1.00000 q^{64} +1.86370 q^{65} -2.18618 q^{66} -15.0628 q^{67} +5.24969 q^{68} +0.282561 q^{70} +13.4448 q^{71} +2.82843 q^{72} -15.9089 q^{73} +0.828427 q^{74} -0.414214 q^{75} +0.946464 q^{76} +1.49133 q^{77} +0.771971 q^{78} +4.81116 q^{79} +1.00000 q^{80} +7.48528 q^{81} +7.53465 q^{82} -0.643238 q^{83} +0.117041 q^{84} +5.24969 q^{85} -0.663902 q^{86} +0.682163 q^{87} +5.27792 q^{88} +2.29326 q^{89} +2.82843 q^{90} -0.526610 q^{91} -1.59627 q^{93} -0.353113 q^{94} +0.946464 q^{95} +0.414214 q^{96} -11.6702 q^{97} +6.92016 q^{98} +14.9282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 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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