LMFDB - Embedded newform 5290.2.a.z.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:	$1$
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:	$\Z[a_1, a_2, a_3]$
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.93185 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.93185 q^{6} -0.482362 q^{7} +1.00000 q^{8} +0.732051 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.93185 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.93185 q^{6} -0.482362 q^{7} +1.00000 q^{8} +0.732051 q^{9} +1.00000 q^{10} +1.86370 q^{11} -1.93185 q^{12} -2.35311 q^{13} -0.482362 q^{14} -1.93185 q^{15} +1.00000 q^{16} +1.44949 q^{17} +0.732051 q^{18} -3.24969 q^{19} +1.00000 q^{20} +0.931852 q^{21} +1.86370 q^{22} -1.93185 q^{24} +1.00000 q^{25} -2.35311 q^{26} +4.38134 q^{27} -0.482362 q^{28} -6.20977 q^{29} -1.93185 q^{30} -1.16452 q^{31} +1.00000 q^{32} -3.60040 q^{33} +1.44949 q^{34} -0.482362 q^{35} +0.732051 q^{36} +7.19151 q^{37} -3.24969 q^{38} +4.54587 q^{39} +1.00000 q^{40} +1.13165 q^{41} +0.931852 q^{42} -10.7274 q^{43} +1.86370 q^{44} +0.732051 q^{45} -2.17914 q^{47} -1.93185 q^{48} -6.76733 q^{49} +1.00000 q^{50} -2.80020 q^{51} -2.35311 q^{52} -6.49233 q^{53} +4.38134 q^{54} +1.86370 q^{55} -0.482362 q^{56} +6.27792 q^{57} -6.20977 q^{58} -2.29201 q^{59} -1.93185 q^{60} +3.81722 q^{61} -1.16452 q^{62} -0.353113 q^{63} +1.00000 q^{64} -2.35311 q^{65} -3.60040 q^{66} +3.12560 q^{67} +1.44949 q^{68} -0.482362 q^{70} +15.4811 q^{71} +0.732051 q^{72} +0.899975 q^{73} +7.19151 q^{74} -1.93185 q^{75} -3.24969 q^{76} -0.898979 q^{77} +4.54587 q^{78} -7.27500 q^{79} +1.00000 q^{80} -10.6603 q^{81} +1.13165 q^{82} +9.22198 q^{83} +0.931852 q^{84} +1.44949 q^{85} -10.7274 q^{86} +11.9964 q^{87} +1.86370 q^{88} -16.0565 q^{89} +0.732051 q^{90} +1.13505 q^{91} +2.24969 q^{93} -2.17914 q^{94} -3.24969 q^{95} -1.93185 q^{96} -18.1596 q^{97} -6.76733 q^{98} +1.36433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} - 8 q^{11} - 4 q^{13} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 4 q^{18} - 4 q^{19} + 4 q^{20} - 4 q^{21} - 8 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} - 16 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} - 16 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 4 q^{41} - 4 q^{42} - 12 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{47} - 16 q^{49} + 4 q^{50} - 12 q^{51} - 4 q^{52} - 8 q^{55} - 4 q^{56} + 4 q^{57} + 4 q^{58} - 4 q^{59} - 4 q^{61} - 8 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} - 16 q^{66} - 4 q^{68} - 4 q^{70} + 28 q^{71} - 4 q^{72} - 12 q^{73} - 16 q^{74} - 4 q^{76} + 16 q^{77} + 4 q^{78} - 44 q^{79} + 4 q^{80} - 8 q^{81} - 4 q^{82} + 20 q^{83} - 4 q^{84} - 4 q^{85} - 12 q^{86} + 28 q^{87} - 8 q^{88} - 40 q^{89} - 4 q^{90} - 16 q^{91} - 8 q^{94} - 4 q^{95} - 20 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 - 8 * q^11 - 4 * q^13 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 4 * q^18 - 4 * q^19 + 4 * q^20 - 4 * q^21 - 8 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 - 16 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 - 16 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 4 * q^41 - 4 * q^42 - 12 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^47 - 16 * q^49 + 4 * q^50 - 12 * q^51 - 4 * q^52 - 8 * q^55 - 4 * q^56 + 4 * q^57 + 4 * q^58 - 4 * q^59 - 4 * q^61 - 8 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 - 16 * q^66 - 4 * q^68 - 4 * q^70 + 28 * q^71 - 4 * q^72 - 12 * q^73 - 16 * q^74 - 4 * q^76 + 16 * q^77 + 4 * q^78 - 44 * q^79 + 4 * q^80 - 8 * q^81 - 4 * q^82 + 20 * q^83 - 4 * q^84 - 4 * q^85 - 12 * q^86 + 28 * q^87 - 8 * q^88 - 40 * q^89 - 4 * q^90 - 16 * q^91 - 8 * q^94 - 4 * q^95 - 20 * q^97 - 16 * q^98 + 8 * 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
$3$	−1.93185	−1.11536	−0.557678	−	0.830058i	$-0.688307\pi$
$3$	−1.93185	−1.11536	−0.557678	+	0.830058i	$0.688307\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.93185	−0.788675
$7$	−0.482362	−0.182316	−0.0911578	−	0.995836i	$-0.529057\pi$
$7$	−0.482362	−0.182316	−0.0911578	+	0.995836i	$0.529057\pi$
$8$	1.00000	0.353553
$9$	0.732051	0.244017
$10$	1.00000	0.316228
$11$	1.86370	0.561928	0.280964	−	0.959718i	$-0.409346\pi$
$11$	1.86370	0.561928	0.280964	+	0.959718i	$0.409346\pi$
$12$	−1.93185	−0.557678
$13$	−2.35311	−0.652636	−0.326318	−	0.945260i	$-0.605808\pi$
$13$	−2.35311	−0.652636	−0.326318	+	0.945260i	$0.605808\pi$
$14$	−0.482362	−0.128917
$15$	−1.93185	−0.498802
$16$	1.00000	0.250000
$17$	1.44949	0.351553	0.175776	−	0.984430i	$-0.443756\pi$
$17$	1.44949	0.351553	0.175776	+	0.984430i	$0.443756\pi$
$18$	0.732051	0.172546
$19$	−3.24969	−0.745530	−0.372765	−	0.927926i	$-0.621590\pi$
$19$	−3.24969	−0.745530	−0.372765	+	0.927926i	$0.621590\pi$
$20$	1.00000	0.223607
$21$	0.931852	0.203347
$22$	1.86370	0.397343
$23$	0	0
$23$	0	0
$24$	−1.93185	−0.394338
$25$	1.00000	0.200000
$26$	−2.35311	−0.461484
$27$	4.38134	0.843190
$28$	−0.482362	−0.0911578
$29$	−6.20977	−1.15313	−0.576563	−	0.817053i	$-0.695606\pi$
$29$	−6.20977	−1.15313	−0.576563	+	0.817053i	$0.695606\pi$
$30$	−1.93185	−0.352706
$31$	−1.16452	−0.209155	−0.104577	−	0.994517i	$-0.533349\pi$
$31$	−1.16452	−0.209155	−0.104577	+	0.994517i	$0.533349\pi$
$32$	1.00000	0.176777
$33$	−3.60040	−0.626749
$34$	1.44949	0.248585
$35$	−0.482362	−0.0815340
$36$	0.732051	0.122008
$37$	7.19151	1.18228	0.591138	−	0.806570i	$-0.298679\pi$
$37$	7.19151	1.18228	0.591138	+	0.806570i	$0.298679\pi$
$38$	−3.24969	−0.527169
$39$	4.54587	0.727921
$40$	1.00000	0.158114
$41$	1.13165	0.176734	0.0883672	−	0.996088i	$-0.471835\pi$
$41$	1.13165	0.176734	0.0883672	+	0.996088i	$0.471835\pi$
$42$	0.931852	0.143788
$43$	−10.7274	−1.63591	−0.817957	−	0.575279i	$-0.804893\pi$
$43$	−10.7274	−1.63591	−0.817957	+	0.575279i	$0.804893\pi$
$44$	1.86370	0.280964
$45$	0.732051	0.109128
$46$	0	0
$47$	−2.17914	−0.317860	−0.158930	−	0.987290i	$-0.550804\pi$
$47$	−2.17914	−0.317860	−0.158930	+	0.987290i	$0.550804\pi$
$48$	−1.93185	−0.278839
$49$	−6.76733	−0.966761
$50$	1.00000	0.141421
$51$	−2.80020	−0.392106
$52$	−2.35311	−0.326318
$53$	−6.49233	−0.891790	−0.445895	−	0.895085i	$-0.647115\pi$
$53$	−6.49233	−0.891790	−0.445895	+	0.895085i	$0.647115\pi$
$54$	4.38134	0.596225
$55$	1.86370	0.251302
$56$	−0.482362	−0.0644583
$57$	6.27792	0.831530
$58$	−6.20977	−0.815383
$59$	−2.29201	−0.298395	−0.149197	−	0.988807i	$-0.547669\pi$
$59$	−2.29201	−0.298395	−0.149197	+	0.988807i	$0.547669\pi$
$60$	−1.93185	−0.249401
$61$	3.81722	0.488744	0.244372	−	0.969682i	$-0.421418\pi$
$61$	3.81722	0.488744	0.244372	+	0.969682i	$0.421418\pi$
$62$	−1.16452	−0.147895
$63$	−0.353113	−0.0444881
$64$	1.00000	0.125000
$65$	−2.35311	−0.291868
$66$	−3.60040	−0.443178
$67$	3.12560	0.381853	0.190926	−	0.981604i	$-0.438851\pi$
$67$	3.12560	0.381853	0.190926	+	0.981604i	$0.438851\pi$
$68$	1.44949	0.175776
$69$	0	0
$70$	−0.482362	−0.0576533
$71$	15.4811	1.83727	0.918635	−	0.395107i	$-0.129292\pi$
$71$	15.4811	1.83727	0.918635	+	0.395107i	$0.129292\pi$
$72$	0.732051	0.0862730
$73$	0.899975	0.105334	0.0526671	−	0.998612i	$-0.483228\pi$
$73$	0.899975	0.105334	0.0526671	+	0.998612i	$0.483228\pi$
$74$	7.19151	0.835996
$75$	−1.93185	−0.223071
$76$	−3.24969	−0.372765
$77$	−0.898979	−0.102448
$78$	4.54587	0.514718
$79$	−7.27500	−0.818501	−0.409251	−	0.912422i	$-0.634210\pi$
$79$	−7.27500	−0.818501	−0.409251	+	0.912422i	$0.634210\pi$
$80$	1.00000	0.111803
$81$	−10.6603	−1.18447
$82$	1.13165	0.124970
$83$	9.22198	1.01224	0.506122	−	0.862462i	$-0.331079\pi$
$83$	9.22198	1.01224	0.506122	+	0.862462i	$0.331079\pi$
$84$	0.931852	0.101673
$85$	1.44949	0.157219
$86$	−10.7274	−1.15677
$87$	11.9964	1.28614
$88$	1.86370	0.198671
$89$	−16.0565	−1.70198	−0.850990	−	0.525181i	$-0.823998\pi$
$89$	−16.0565	−1.70198	−0.850990	+	0.525181i	$0.823998\pi$
$90$	0.732051	0.0771649
$91$	1.13505	0.118986
$92$	0	0
$93$	2.24969	0.233282
$94$	−2.17914	−0.224761
$95$	−3.24969	−0.333411
$96$	−1.93185	−0.197169
$97$	−18.1596	−1.84383	−0.921916	−	0.387391i	$-0.873376\pi$
$97$	−18.1596	−1.84383	−0.921916	+	0.387391i	$0.873376\pi$
$98$	−6.76733	−0.683603
$99$	1.36433	0.137120
$100$	1.00000	0.100000
$101$	2.86976	0.285551	0.142776	−	0.989755i	$-0.454397\pi$
$101$	2.86976	0.285551	0.142776	+	0.989755i	$0.454397\pi$
$102$	−2.80020	−0.277261
$103$	12.7678	1.25805	0.629026	−	0.777384i	$-0.283454\pi$
$103$	12.7678	1.25805	0.629026	+	0.777384i	$0.283454\pi$
$104$	−2.35311	−0.230742
$105$	0.931852	0.0909394
$106$	−6.49233	−0.630591
$107$	−9.29717	−0.898792	−0.449396	−	0.893333i	$-0.648361\pi$
$107$	−9.29717	−0.898792	−0.449396	+	0.893333i	$0.648361\pi$
$108$	4.38134	0.421595
$109$	−1.98638	−0.190261	−0.0951305	−	0.995465i	$-0.530327\pi$
$109$	−1.98638	−0.190261	−0.0951305	+	0.995465i	$0.530327\pi$
$110$	1.86370	0.177697
$111$	−13.8929	−1.31866
$112$	−0.482362	−0.0455789
$113$	−3.08641	−0.290345	−0.145172	−	0.989406i	$-0.546374\pi$
$113$	−3.08641	−0.290345	−0.145172	+	0.989406i	$0.546374\pi$
$114$	6.27792	0.587981
$115$	0	0
$116$	−6.20977	−0.576563
$117$	−1.72260	−0.159254
$118$	−2.29201	−0.210997
$119$	−0.699179	−0.0640936
$120$	−1.93185	−0.176353
$121$	−7.52661	−0.684237
$122$	3.81722	0.345594
$123$	−2.18618	−0.197122
$124$	−1.16452	−0.104577
$125$	1.00000	0.0894427
$126$	−0.353113	−0.0314578
$127$	−12.2456	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$127$	−12.2456	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$128$	1.00000	0.0883883
$129$	20.7238	1.82463
$130$	−2.35311	−0.206382
$131$	10.1051	0.882887	0.441443	−	0.897289i	$-0.354467\pi$
$131$	10.1051	0.882887	0.441443	+	0.897289i	$0.354467\pi$
$132$	−3.60040	−0.313374
$133$	1.56753	0.135922
$134$	3.12560	0.270011
$135$	4.38134	0.377086
$136$	1.44949	0.124293
$137$	−11.9854	−1.02398	−0.511990	−	0.858991i	$-0.671092\pi$
$137$	−11.9854	−1.02398	−0.511990	+	0.858991i	$0.671092\pi$
$138$	0	0
$139$	−14.4482	−1.22548	−0.612742	−	0.790283i	$-0.709934\pi$
$139$	−14.4482	−1.22548	−0.612742	+	0.790283i	$0.709934\pi$
$140$	−0.482362	−0.0407670
$141$	4.20977	0.354526
$142$	15.4811	1.29915
$143$	−4.38551	−0.366734
$144$	0.732051	0.0610042
$145$	−6.20977	−0.515693
$146$	0.899975	0.0744825
$147$	13.0735	1.07828
$148$	7.19151	0.591138
$149$	−7.21028	−0.590689	−0.295345	−	0.955391i	$-0.595435\pi$
$149$	−7.21028	−0.590689	−0.295345	+	0.955391i	$0.595435\pi$
$150$	−1.93185	−0.157735
$151$	15.8888	1.29301	0.646506	−	0.762909i	$-0.276230\pi$
$151$	15.8888	1.29301	0.646506	+	0.762909i	$0.276230\pi$
$152$	−3.24969	−0.263585
$153$	1.06110	0.0857849
$154$	−0.898979	−0.0724418
$155$	−1.16452	−0.0935369
$156$	4.54587	0.363961
$157$	−18.1421	−1.44790	−0.723950	−	0.689852i	$-0.757675\pi$
$157$	−18.1421	−1.44790	−0.723950	+	0.689852i	$0.757675\pi$
$158$	−7.27500	−0.578768
$159$	12.5422	0.994663
$160$	1.00000	0.0790569
$161$	0	0
$162$	−10.6603	−0.837549
$163$	8.54071	0.668960	0.334480	−	0.942403i	$-0.391439\pi$
$163$	8.54071	0.668960	0.334480	+	0.942403i	$0.391439\pi$
$164$	1.13165	0.0883672
$165$	−3.60040	−0.280291
$166$	9.22198	0.715764
$167$	−0.230433	−0.0178314	−0.00891571	−	0.999960i	$-0.502838\pi$
$167$	−0.230433	−0.0178314	−0.00891571	+	0.999960i	$0.502838\pi$
$168$	0.931852	0.0718939
$169$	−7.46286	−0.574066
$170$	1.44949	0.111171
$171$	−2.37894	−0.181922
$172$	−10.7274	−0.817957
$173$	11.6067	0.882442	0.441221	−	0.897398i	$-0.354545\pi$
$173$	11.6067	0.882442	0.441221	+	0.897398i	$0.354545\pi$
$174$	11.9964	0.909441
$175$	−0.482362	−0.0364631
$176$	1.86370	0.140482
$177$	4.42783	0.332816
$178$	−16.0565	−1.20348
$179$	−19.8583	−1.48428	−0.742141	−	0.670244i	$-0.766189\pi$
$179$	−19.8583	−1.48428	−0.742141	+	0.670244i	$0.766189\pi$
$180$	0.732051	0.0545638
$181$	−0.253337	−0.0188304	−0.00941521	−	0.999956i	$-0.502997\pi$
$181$	−0.253337	−0.0188304	−0.00941521	+	0.999956i	$0.502997\pi$
$182$	1.13505	0.0841357
$183$	−7.37429	−0.545123
$184$	0	0
$185$	7.19151	0.528730
$186$	2.24969	0.164955
$187$	2.70142	0.197547
$188$	−2.17914	−0.158930
$189$	−2.11339	−0.153727
$190$	−3.24969	−0.235757
$191$	−19.4047	−1.40407	−0.702037	−	0.712141i	$-0.747726\pi$
$191$	−19.4047	−1.40407	−0.702037	+	0.712141i	$0.747726\pi$
$192$	−1.93185	−0.139419
$193$	−4.52280	−0.325558	−0.162779	−	0.986663i	$-0.552046\pi$
$193$	−4.52280	−0.325558	−0.162779	+	0.986663i	$0.552046\pi$
$194$	−18.1596	−1.30379
$195$	4.54587	0.325536
$196$	−6.76733	−0.483380
$197$	23.2945	1.65966	0.829831	−	0.558016i	$-0.188437\pi$
$197$	23.2945	1.65966	0.829831	+	0.558016i	$0.188437\pi$
$198$	1.36433	0.0969584
$199$	11.9964	0.850399	0.425199	−	0.905100i	$-0.360204\pi$
$199$	11.9964	0.850399	0.425199	+	0.905100i	$0.360204\pi$
$200$	1.00000	0.0707107
$201$	−6.03820	−0.425901
$202$	2.86976	0.201915
$203$	2.99536	0.210233
$204$	−2.80020	−0.196053
$205$	1.13165	0.0790380
$206$	12.7678	0.889578
$207$	0	0
$208$	−2.35311	−0.163159
$209$	−6.05646	−0.418934
$210$	0.931852	0.0643039
$211$	−18.3013	−1.25991	−0.629955	−	0.776632i	$-0.716927\pi$
$211$	−18.3013	−1.25991	−0.629955	+	0.776632i	$0.716927\pi$
$212$	−6.49233	−0.445895
$213$	−29.9072	−2.04921
$214$	−9.29717	−0.635542
$215$	−10.7274	−0.731603
$216$	4.38134	0.298113
$217$	0.561722	0.0381322
$218$	−1.98638	−0.134535
$219$	−1.73862	−0.117485
$220$	1.86370	0.125651
$221$	−3.41081	−0.229436
$222$	−13.8929	−0.932432
$223$	18.9747	1.27064	0.635320	−	0.772249i	$-0.280868\pi$
$223$	18.9747	1.27064	0.635320	+	0.772249i	$0.280868\pi$
$224$	−0.482362	−0.0322292
$225$	0.732051	0.0488034
$226$	−3.08641	−0.205305
$227$	8.64956	0.574091	0.287046	−	0.957917i	$-0.407327\pi$
$227$	8.64956	0.574091	0.287046	+	0.957917i	$0.407327\pi$
$228$	6.27792	0.415765
$229$	−12.4373	−0.821879	−0.410939	−	0.911663i	$-0.634799\pi$
$229$	−12.4373	−0.821879	−0.410939	+	0.911663i	$0.634799\pi$
$230$	0	0
$231$	1.73670	0.114266
$232$	−6.20977	−0.407691
$233$	22.0981	1.44769	0.723846	−	0.689962i	$-0.242373\pi$
$233$	22.0981	1.44769	0.723846	+	0.689962i	$0.242373\pi$
$234$	−1.72260	−0.112610
$235$	−2.17914	−0.142151
$236$	−2.29201	−0.149197
$237$	14.0542	0.912919
$238$	−0.699179	−0.0453210
$239$	−0.991956	−0.0641643	−0.0320822	−	0.999485i	$-0.510214\pi$
$239$	−0.991956	−0.0641643	−0.0320822	+	0.999485i	$0.510214\pi$
$240$	−1.93185	−0.124700
$241$	−22.1579	−1.42732	−0.713658	−	0.700494i	$-0.752963\pi$
$241$	−22.1579	−1.42732	−0.713658	+	0.700494i	$0.752963\pi$
$242$	−7.52661	−0.483829
$243$	7.45001	0.477918
$244$	3.81722	0.244372
$245$	−6.76733	−0.432349
$246$	−2.18618	−0.139386
$247$	7.64689	0.486560
$248$	−1.16452	−0.0739474
$249$	−17.8155	−1.12901
$250$	1.00000	0.0632456
$251$	−9.80728	−0.619030	−0.309515	−	0.950895i	$-0.600167\pi$
$251$	−9.80728	−0.619030	−0.309515	+	0.950895i	$0.600167\pi$
$252$	−0.353113	−0.0222441
$253$	0	0
$254$	−12.2456	−0.768355
$255$	−2.80020	−0.175355
$256$	1.00000	0.0625000
$257$	29.5188	1.84133	0.920667	−	0.390349i	$-0.127646\pi$
$257$	29.5188	1.84133	0.920667	+	0.390349i	$0.127646\pi$
$258$	20.7238	1.29020
$259$	−3.46891	−0.215548
$260$	−2.35311	−0.145934
$261$	−4.54587	−0.281382
$262$	10.1051	0.624295
$263$	−24.5485	−1.51373	−0.756864	−	0.653573i	$-0.773269\pi$
$263$	−24.5485	−1.51373	−0.756864	+	0.653573i	$0.773269\pi$
$264$	−3.60040	−0.221589
$265$	−6.49233	−0.398821
$266$	1.56753	0.0961112
$267$	31.0187	1.89831
$268$	3.12560	0.190926
$269$	−10.0757	−0.614327	−0.307164	−	0.951657i	$-0.599380\pi$
$269$	−10.0757	−0.614327	−0.307164	+	0.951657i	$0.599380\pi$
$270$	4.38134	0.266640
$271$	−23.5498	−1.43055	−0.715274	−	0.698844i	$-0.753698\pi$
$271$	−23.5498	−1.43055	−0.715274	+	0.698844i	$0.753698\pi$
$272$	1.44949	0.0878882
$273$	−2.19275	−0.132711
$274$	−11.9854	−0.724064
$275$	1.86370	0.112386
$276$	0	0
$277$	20.9569	1.25918	0.629590	−	0.776927i	$-0.283223\pi$
$277$	20.9569	1.25918	0.629590	+	0.776927i	$0.283223\pi$
$278$	−14.4482	−0.866548
$279$	−0.852491	−0.0510373
$280$	−0.482362	−0.0288266
$281$	−3.70059	−0.220759	−0.110379	−	0.993890i	$-0.535207\pi$
$281$	−3.70059	−0.220759	−0.110379	+	0.993890i	$0.535207\pi$
$282$	4.20977	0.250688
$283$	−16.5532	−0.983984	−0.491992	−	0.870600i	$-0.663731\pi$
$283$	−16.5532	−0.983984	−0.491992	+	0.870600i	$0.663731\pi$
$284$	15.4811	0.918635
$285$	6.27792	0.371872
$286$	−4.38551	−0.259320
$287$	−0.545866	−0.0322215
$288$	0.732051	0.0431365
$289$	−14.8990	−0.876411
$290$	−6.20977	−0.364650
$291$	35.0817	2.05653
$292$	0.899975	0.0526671
$293$	−0.781939	−0.0456814	−0.0228407	−	0.999739i	$-0.507271\pi$
$293$	−0.781939	−0.0456814	−0.0228407	+	0.999739i	$0.507271\pi$
$294$	13.0735	0.762460
$295$	−2.29201	−0.133446
$296$	7.19151	0.417998
$297$	8.16552	0.473812
$298$	−7.21028	−0.417681
$299$	0	0
$300$	−1.93185	−0.111536
$301$	5.17449	0.298253
$302$	15.8888	0.914298
$303$	−5.54394	−0.318491
$304$	−3.24969	−0.186382
$305$	3.81722	0.218573
$306$	1.06110	0.0606591
$307$	−14.6956	−0.838720	−0.419360	−	0.907820i	$-0.637746\pi$
$307$	−14.6956	−0.838720	−0.419360	+	0.907820i	$0.637746\pi$
$308$	−0.898979	−0.0512241
$309$	−24.6656	−1.40318
$310$	−1.16452	−0.0661406
$311$	2.94572	0.167036	0.0835181	−	0.996506i	$-0.473384\pi$
$311$	2.94572	0.167036	0.0835181	+	0.996506i	$0.473384\pi$
$312$	4.54587	0.257359
$313$	4.47606	0.253002	0.126501	−	0.991966i	$-0.459625\pi$
$313$	4.47606	0.253002	0.126501	+	0.991966i	$0.459625\pi$
$314$	−18.1421	−1.02382
$315$	−0.353113	−0.0198957
$316$	−7.27500	−0.409251
$317$	−24.5673	−1.37984	−0.689919	−	0.723887i	$-0.742354\pi$
$317$	−24.5673	−1.37984	−0.689919	+	0.723887i	$0.742354\pi$
$318$	12.5422	0.703333
$319$	−11.5732	−0.647973
$320$	1.00000	0.0559017
$321$	17.9608	1.00247
$322$	0	0
$323$	−4.71039	−0.262093
$324$	−10.6603	−0.592236
$325$	−2.35311	−0.130527
$326$	8.54071	0.473026
$327$	3.83740	0.212209
$328$	1.13165	0.0624851
$329$	1.05113	0.0579508
$330$	−3.60040	−0.198195
$331$	19.0465	1.04689	0.523445	−	0.852060i	$-0.324647\pi$
$331$	19.0465	1.04689	0.523445	+	0.852060i	$0.324647\pi$
$332$	9.22198	0.506122
$333$	5.26455	0.288496
$334$	−0.230433	−0.0126087
$335$	3.12560	0.170770
$336$	0.931852	0.0508367
$337$	−27.8442	−1.51677	−0.758386	−	0.651806i	$-0.774012\pi$
$337$	−27.8442	−1.51677	−0.758386	+	0.651806i	$0.774012\pi$
$338$	−7.46286	−0.405926
$339$	5.96248	0.323838
$340$	1.44949	0.0786096
$341$	−2.17033	−0.117530
$342$	−2.37894	−0.128638
$343$	6.64083	0.358571
$344$	−10.7274	−0.578383
$345$	0	0
$346$	11.6067	0.623981
$347$	0.0522921	0.00280719	0.00140359	−	0.999999i	$-0.499553\pi$
$347$	0.0522921	0.00280719	0.00140359	+	0.999999i	$0.499553\pi$
$348$	11.9964	0.643072
$349$	−25.0119	−1.33886	−0.669428	−	0.742877i	$-0.733461\pi$
$349$	−25.0119	−1.33886	−0.669428	+	0.742877i	$0.733461\pi$
$350$	−0.482362	−0.0257833
$351$	−10.3098	−0.550296
$352$	1.86370	0.0993357
$353$	−9.80625	−0.521934	−0.260967	−	0.965348i	$-0.584041\pi$
$353$	−9.80625	−0.521934	−0.260967	+	0.965348i	$0.584041\pi$
$354$	4.42783	0.235336
$355$	15.4811	0.821652
$356$	−16.0565	−0.850990
$357$	1.35071	0.0714871
$358$	−19.8583	−1.04955
$359$	0.444433	0.0234563	0.0117281	−	0.999931i	$-0.496267\pi$
$359$	0.444433	0.0234563	0.0117281	+	0.999931i	$0.496267\pi$
$360$	0.732051	0.0385825
$361$	−8.43952	−0.444185
$362$	−0.253337	−0.0133151
$363$	14.5403	0.763168
$364$	1.13505	0.0594929
$365$	0.899975	0.0471069
$366$	−7.37429	−0.385460
$367$	−31.0165	−1.61905	−0.809523	−	0.587088i	$-0.800274\pi$
$367$	−31.0165	−1.61905	−0.809523	+	0.587088i	$0.800274\pi$
$368$	0	0
$369$	0.828427	0.0431262
$370$	7.19151	0.373869
$371$	3.13165	0.162587
$372$	2.24969	0.116641
$373$	−12.9645	−0.671275	−0.335638	−	0.941991i	$-0.608952\pi$
$373$	−12.9645	−0.671275	−0.335638	+	0.941991i	$0.608952\pi$
$374$	2.70142	0.139687
$375$	−1.93185	−0.0997604
$376$	−2.17914	−0.112380
$377$	14.6123	0.752571
$378$	−2.11339	−0.108701
$379$	−6.94057	−0.356513	−0.178257	−	0.983984i	$-0.557046\pi$
$379$	−6.94057	−0.356513	−0.178257	+	0.983984i	$0.557046\pi$
$380$	−3.24969	−0.166706
$381$	23.6566	1.21196
$382$	−19.4047	−0.992830
$383$	−11.2793	−0.576347	−0.288173	−	0.957578i	$-0.593048\pi$
$383$	−11.2793	−0.576347	−0.288173	+	0.957578i	$0.593048\pi$
$384$	−1.93185	−0.0985844
$385$	−0.898979	−0.0458162
$386$	−4.52280	−0.230204
$387$	−7.85301	−0.399191
$388$	−18.1596	−0.921916
$389$	−11.9118	−0.603954	−0.301977	−	0.953315i	$-0.597647\pi$
$389$	−11.9118	−0.603954	−0.301977	+	0.953315i	$0.597647\pi$
$390$	4.54587	0.230189
$391$	0	0
$392$	−6.76733	−0.341802
$393$	−19.5216	−0.984732
$394$	23.2945	1.17356
$395$	−7.27500	−0.366045
$396$	1.36433	0.0685599
$397$	13.1659	0.660779	0.330390	−	0.943845i	$-0.392820\pi$
$397$	13.1659	0.660779	0.330390	+	0.943845i	$0.392820\pi$
$398$	11.9964	0.601323
$399$	−3.02823	−0.151601
$400$	1.00000	0.0500000
$401$	−27.4743	−1.37200	−0.686001	−	0.727600i	$-0.740636\pi$
$401$	−27.4743	−1.37200	−0.686001	+	0.727600i	$0.740636\pi$
$402$	−6.03820	−0.301158
$403$	2.74026	0.136502
$404$	2.86976	0.142776
$405$	−10.6603	−0.529712
$406$	2.99536	0.148657
$407$	13.4028	0.664354
$408$	−2.80020	−0.138631
$409$	−39.4687	−1.95160	−0.975801	−	0.218662i	$-0.929831\pi$
$409$	−39.4687	−1.95160	−0.975801	+	0.218662i	$0.929831\pi$
$410$	1.13165	0.0558883
$411$	23.1540	1.14210
$412$	12.7678	0.629026
$413$	1.10558	0.0544020
$414$	0	0
$415$	9.22198	0.452689
$416$	−2.35311	−0.115371
$417$	27.9119	1.36685
$418$	−6.05646	−0.296231
$419$	25.4558	1.24360	0.621799	−	0.783177i	$-0.286402\pi$
$419$	25.4558	1.24360	0.621799	+	0.783177i	$0.286402\pi$
$420$	0.931852	0.0454697
$421$	−21.7086	−1.05801	−0.529007	−	0.848617i	$-0.677435\pi$
$421$	−21.7086	−1.05801	−0.529007	+	0.848617i	$0.677435\pi$
$422$	−18.3013	−0.890891
$423$	−1.59524	−0.0775632
$424$	−6.49233	−0.315295
$425$	1.44949	0.0703106
$426$	−29.9072	−1.44901
$427$	−1.84128	−0.0891057
$428$	−9.29717	−0.449396
$429$	8.47215	0.409039
$430$	−10.7274	−0.517321
$431$	−16.8817	−0.813164	−0.406582	−	0.913614i	$-0.633279\pi$
$431$	−16.8817	−0.813164	−0.406582	+	0.913614i	$0.633279\pi$
$432$	4.38134	0.210797
$433$	18.8416	0.905468	0.452734	−	0.891646i	$-0.350449\pi$
$433$	18.8416	0.905468	0.452734	+	0.891646i	$0.350449\pi$
$434$	0.561722	0.0269635
$435$	11.9964	0.575181
$436$	−1.98638	−0.0951305
$437$	0	0
$438$	−1.73862	−0.0830744
$439$	12.2730	0.585759	0.292880	−	0.956149i	$-0.405386\pi$
$439$	12.2730	0.585759	0.292880	+	0.956149i	$0.405386\pi$
$440$	1.86370	0.0888486
$441$	−4.95403	−0.235906
$442$	−3.41081	−0.162236
$443$	−24.5943	−1.16851	−0.584254	−	0.811571i	$-0.698613\pi$
$443$	−24.5943	−1.16851	−0.584254	+	0.811571i	$0.698613\pi$
$444$	−13.8929	−0.659329
$445$	−16.0565	−0.761149
$446$	18.9747	0.898478
$447$	13.9292	0.658829
$448$	−0.482362	−0.0227895
$449$	28.8637	1.36216	0.681080	−	0.732209i	$-0.261511\pi$
$449$	28.8637	1.36216	0.681080	+	0.732209i	$0.261511\pi$
$450$	0.732051	0.0345092
$451$	2.10906	0.0993120
$452$	−3.08641	−0.145172
$453$	−30.6948	−1.44217
$454$	8.64956	0.405944
$455$	1.13505	0.0532121
$456$	6.27792	0.293990
$457$	15.3780	0.719355	0.359677	−	0.933077i	$-0.382887\pi$
$457$	15.3780	0.719355	0.359677	+	0.933077i	$0.382887\pi$
$458$	−12.4373	−0.581156
$459$	6.35071	0.296426
$460$	0	0
$461$	42.7513	1.99112	0.995562	−	0.0941050i	$-0.0299989\pi$
$461$	42.7513	1.99112	0.995562	+	0.0941050i	$0.0299989\pi$
$462$	1.73670	0.0807984
$463$	13.4616	0.625614	0.312807	−	0.949817i	$-0.398731\pi$
$463$	13.4616	0.625614	0.312807	+	0.949817i	$0.398731\pi$
$464$	−6.20977	−0.288281
$465$	2.24969	0.104327
$466$	22.0981	1.02367
$467$	14.0720	0.651173	0.325586	−	0.945512i	$-0.394438\pi$
$467$	14.0720	0.651173	0.325586	+	0.945512i	$0.394438\pi$
$468$	−1.72260	−0.0796271
$469$	−1.50767	−0.0696178
$470$	−2.17914	−0.100516
$471$	35.0479	1.61492
$472$	−2.29201	−0.105498
$473$	−19.9927	−0.919265
$474$	14.0542	0.645532
$475$	−3.24969	−0.149106
$476$	−0.699179	−0.0320468
$477$	−4.75272	−0.217612
$478$	−0.991956	−0.0453710
$479$	−7.20231	−0.329082	−0.164541	−	0.986370i	$-0.552614\pi$
$479$	−7.20231	−0.329082	−0.164541	+	0.986370i	$0.552614\pi$
$480$	−1.93185	−0.0881766
$481$	−16.9224	−0.771597
$482$	−22.1579	−1.00927
$483$	0	0
$484$	−7.52661	−0.342119
$485$	−18.1596	−0.824586
$486$	7.45001	0.337939
$487$	35.8090	1.62266	0.811329	−	0.584589i	$-0.198744\pi$
$487$	35.8090	1.62266	0.811329	+	0.584589i	$0.198744\pi$
$488$	3.81722	0.172797
$489$	−16.4994	−0.746128
$490$	−6.76733	−0.305717
$491$	−10.1951	−0.460099	−0.230050	−	0.973179i	$-0.573889\pi$
$491$	−10.1951	−0.460099	−0.230050	+	0.973179i	$0.573889\pi$
$492$	−2.18618	−0.0985608
$493$	−9.00100	−0.405384
$494$	7.64689	0.344050
$495$	1.36433	0.0613219
$496$	−1.16452	−0.0522887
$497$	−7.46750	−0.334963
$498$	−17.8155	−0.798331
$499$	28.7160	1.28550	0.642752	−	0.766074i	$-0.277793\pi$
$499$	28.7160	1.28550	0.642752	+	0.766074i	$0.277793\pi$
$500$	1.00000	0.0447214
$501$	0.445162	0.0198884
$502$	−9.80728	−0.437720
$503$	27.7614	1.23782	0.618911	−	0.785461i	$-0.287574\pi$
$503$	27.7614	1.23782	0.618911	+	0.785461i	$0.287574\pi$
$504$	−0.353113	−0.0157289
$505$	2.86976	0.127702
$506$	0	0
$507$	14.4171	0.640287
$508$	−12.2456	−0.543309
$509$	31.5292	1.39751	0.698755	−	0.715361i	$-0.253738\pi$
$509$	31.5292	1.39751	0.698755	+	0.715361i	$0.253738\pi$
$510$	−2.80020	−0.123995
$511$	−0.434114	−0.0192041
$512$	1.00000	0.0441942
$513$	−14.2380	−0.628623
$514$	29.5188	1.30202
$515$	12.7678	0.562618
$516$	20.7238	0.912313
$517$	−4.06126	−0.178614
$518$	−3.46891	−0.152415
$519$	−22.4225	−0.984237
$520$	−2.35311	−0.103191
$521$	23.6554	1.03636	0.518181	−	0.855271i	$-0.326609\pi$
$521$	23.6554	1.03636	0.518181	+	0.855271i	$0.326609\pi$
$522$	−4.54587	−0.198967
$523$	22.9881	1.00520	0.502599	−	0.864520i	$-0.332377\pi$
$523$	22.9881	1.00520	0.502599	+	0.864520i	$0.332377\pi$
$524$	10.1051	0.441443
$525$	0.931852	0.0406693
$526$	−24.5485	−1.07037
$527$	−1.68797	−0.0735290
$528$	−3.60040	−0.156687
$529$	0	0
$530$	−6.49233	−0.282009
$531$	−1.67787	−0.0728134
$532$	1.56753	0.0679609
$533$	−2.66291	−0.115343
$534$	31.0187	1.34231
$535$	−9.29717	−0.401952
$536$	3.12560	0.135005
$537$	38.3633	1.65550
$538$	−10.0757	−0.434395
$539$	−12.6123	−0.543250
$540$	4.38134	0.188543
$541$	−15.7840	−0.678606	−0.339303	−	0.940677i	$-0.610191\pi$
$541$	−15.7840	−0.678606	−0.339303	+	0.940677i	$0.610191\pi$
$542$	−23.5498	−1.01155
$543$	0.489410	0.0210026
$544$	1.44949	0.0621464
$545$	−1.98638	−0.0850873
$546$	−2.19275	−0.0938411
$547$	15.3616	0.656815	0.328407	−	0.944536i	$-0.393488\pi$
$547$	15.3616	0.656815	0.328407	+	0.944536i	$0.393488\pi$
$548$	−11.9854	−0.511990
$549$	2.79440	0.119262
$550$	1.86370	0.0794686
$551$	20.1798	0.859689
$552$	0	0
$553$	3.50918	0.149226
$554$	20.9569	0.890375
$555$	−13.8929	−0.589722
$556$	−14.4482	−0.612742
$557$	14.4757	0.613357	0.306678	−	0.951813i	$-0.400782\pi$
$557$	14.4757	0.613357	0.306678	+	0.951813i	$0.400782\pi$
$558$	−0.852491	−0.0360888
$559$	25.2428	1.06766
$560$	−0.482362	−0.0203835
$561$	−5.21874	−0.220335
$562$	−3.70059	−0.156100
$563$	27.7967	1.17149	0.585746	−	0.810495i	$-0.300802\pi$
$563$	27.7967	1.17149	0.585746	+	0.810495i	$0.300802\pi$
$564$	4.20977	0.177263
$565$	−3.08641	−0.129846
$566$	−16.5532	−0.695782
$567$	5.14210	0.215948
$568$	15.4811	0.649573
$569$	−10.7330	−0.449953	−0.224976	−	0.974364i	$-0.572230\pi$
$569$	−10.7330	−0.449953	−0.224976	+	0.974364i	$0.572230\pi$
$570$	6.27792	0.262953
$571$	30.6284	1.28176	0.640880	−	0.767641i	$-0.278570\pi$
$571$	30.6284	1.28176	0.640880	+	0.767641i	$0.278570\pi$
$572$	−4.38551	−0.183367
$573$	37.4870	1.56604
$574$	−0.545866	−0.0227840
$575$	0	0
$576$	0.732051	0.0305021
$577$	−4.21192	−0.175345	−0.0876723	−	0.996149i	$-0.527943\pi$
$577$	−4.21192	−0.175345	−0.0876723	+	0.996149i	$0.527943\pi$
$578$	−14.8990	−0.619716
$579$	8.73737	0.363113
$580$	−6.20977	−0.257847
$581$	−4.44833	−0.184548
$582$	35.0817	1.45418
$583$	−12.0998	−0.501122
$584$	0.899975	0.0372412
$585$	−1.72260	−0.0712207
$586$	−0.781939	−0.0323016
$587$	28.9281	1.19399	0.596996	−	0.802244i	$-0.296361\pi$
$587$	28.9281	1.19399	0.596996	+	0.802244i	$0.296361\pi$
$588$	13.0735	0.539141
$589$	3.78434	0.155931
$590$	−2.29201	−0.0943607
$591$	−45.0014	−1.85111
$592$	7.19151	0.295569
$593$	−22.4006	−0.919882	−0.459941	−	0.887949i	$-0.652129\pi$
$593$	−22.4006	−0.919882	−0.459941	+	0.887949i	$0.652129\pi$
$594$	8.16552	0.335035
$595$	−0.699179	−0.0286635
$596$	−7.21028	−0.295345
$597$	−23.1752	−0.948497
$598$	0	0
$599$	−34.0640	−1.39182	−0.695909	−	0.718130i	$-0.744999\pi$
$599$	−34.0640	−1.39182	−0.695909	+	0.718130i	$0.744999\pi$
$600$	−1.93185	−0.0788675
$601$	−18.4425	−0.752287	−0.376144	−	0.926561i	$-0.622750\pi$
$601$	−18.4425	−0.752287	−0.376144	+	0.926561i	$0.622750\pi$
$602$	5.17449	0.210897
$603$	2.28810	0.0931786
$604$	15.8888	0.646506
$605$	−7.52661	−0.306000
$606$	−5.54394	−0.225207
$607$	27.2078	1.10433	0.552165	−	0.833735i	$-0.313802\pi$
$607$	27.2078	1.10433	0.552165	+	0.833735i	$0.313802\pi$
$608$	−3.24969	−0.131792
$609$	−5.78658	−0.234484
$610$	3.81722	0.154555
$611$	5.12776	0.207447
$612$	1.06110	0.0428924
$613$	21.2329	0.857590	0.428795	−	0.903402i	$-0.358938\pi$
$613$	21.2329	0.857590	0.428795	+	0.903402i	$0.358938\pi$
$614$	−14.6956	−0.593065
$615$	−2.18618	−0.0881555
$616$	−0.898979	−0.0362209
$617$	−19.5279	−0.786163	−0.393081	−	0.919504i	$-0.628591\pi$
$617$	−19.5279	−0.786163	−0.393081	+	0.919504i	$0.628591\pi$
$618$	−24.6656	−0.992195
$619$	35.0527	1.40889	0.704444	−	0.709760i	$-0.251196\pi$
$619$	35.0527	1.40889	0.704444	+	0.709760i	$0.251196\pi$
$620$	−1.16452	−0.0467684
$621$	0	0
$622$	2.94572	0.118112
$623$	7.74502	0.310298
$624$	4.54587	0.181980
$625$	1.00000	0.0400000
$626$	4.47606	0.178899
$627$	11.7002	0.467260
$628$	−18.1421	−0.723950
$629$	10.4240	0.415633
$630$	−0.353113	−0.0140684
$631$	−1.73621	−0.0691176	−0.0345588	−	0.999403i	$-0.511003\pi$
$631$	−1.73621	−0.0691176	−0.0345588	+	0.999403i	$0.511003\pi$
$632$	−7.27500	−0.289384
$633$	35.3553	1.40525
$634$	−24.5673	−0.975693
$635$	−12.2456	−0.485950
$636$	12.5422	0.497331
$637$	15.9243	0.630943
$638$	−11.5732	−0.458186
$639$	11.3330	0.448325
$640$	1.00000	0.0395285
$641$	41.0844	1.62273	0.811367	−	0.584537i	$-0.198724\pi$
$641$	41.0844	1.62273	0.811367	+	0.584537i	$0.198724\pi$
$642$	17.9608	0.708855
$643$	−10.4108	−0.410563	−0.205282	−	0.978703i	$-0.565811\pi$
$643$	−10.4108	−0.410563	−0.205282	+	0.978703i	$0.565811\pi$
$644$	0	0
$645$	20.7238	0.815997
$646$	−4.71039	−0.185328
$647$	−27.7359	−1.09041	−0.545206	−	0.838302i	$-0.683548\pi$
$647$	−27.7359	−1.09041	−0.545206	+	0.838302i	$0.683548\pi$
$648$	−10.6603	−0.418774
$649$	−4.27163	−0.167676
$650$	−2.35311	−0.0922967
$651$	−1.08516	−0.0425309
$652$	8.54071	0.334480
$653$	−36.4373	−1.42590	−0.712951	−	0.701214i	$-0.752642\pi$
$653$	−36.4373	−1.42590	−0.712951	+	0.701214i	$0.752642\pi$
$654$	3.83740	0.150054
$655$	10.1051	0.394839
$656$	1.13165	0.0441836
$657$	0.658828	0.0257033
$658$	1.05113	0.0409774
$659$	19.9645	0.777706	0.388853	−	0.921300i	$-0.372871\pi$
$659$	19.9645	0.777706	0.388853	+	0.921300i	$0.372871\pi$
$660$	−3.60040	−0.140145
$661$	9.27183	0.360632	0.180316	−	0.983609i	$-0.442288\pi$
$661$	9.27183	0.360632	0.180316	+	0.983609i	$0.442288\pi$
$662$	19.0465	0.740263
$663$	6.58919	0.255903
$664$	9.22198	0.357882
$665$	1.56753	0.0607861
$666$	5.26455	0.203997
$667$	0	0
$668$	−0.230433	−0.00891571
$669$	−36.6563	−1.41721
$670$	3.12560	0.120752
$671$	7.11416	0.274639
$672$	0.931852	0.0359470
$673$	−7.83674	−0.302084	−0.151042	−	0.988527i	$-0.548263\pi$
$673$	−7.83674	−0.302084	−0.151042	+	0.988527i	$0.548263\pi$
$674$	−27.8442	−1.07252
$675$	4.38134	0.168638
$676$	−7.46286	−0.287033
$677$	22.5347	0.866078	0.433039	−	0.901375i	$-0.357441\pi$
$677$	22.5347	0.866078	0.433039	+	0.901375i	$0.357441\pi$
$678$	5.96248	0.228988
$679$	8.75951	0.336159
$680$	1.44949	0.0555854
$681$	−16.7097	−0.640316
$682$	−2.17033	−0.0831062
$683$	−0.0654278	−0.00250353	−0.00125176	−	0.999999i	$-0.500398\pi$
$683$	−0.0654278	−0.00250353	−0.00125176	+	0.999999i	$0.500398\pi$
$684$	−2.37894	−0.0909609
$685$	−11.9854	−0.457938
$686$	6.64083	0.253548
$687$	24.0270	0.916687
$688$	−10.7274	−0.408979
$689$	15.2772	0.582015
$690$	0	0
$691$	−19.8837	−0.756411	−0.378206	−	0.925722i	$-0.623459\pi$
$691$	−19.8837	−0.756411	−0.378206	+	0.925722i	$0.623459\pi$
$692$	11.6067	0.441221
$693$	−0.658099	−0.0249991
$694$	0.0522921	0.00198498
$695$	−14.4482	−0.548053
$696$	11.9964	0.454721
$697$	1.64032	0.0621315
$698$	−25.0119	−0.946714
$699$	−42.6902	−1.61469
$700$	−0.482362	−0.0182316
$701$	−10.6974	−0.404036	−0.202018	−	0.979382i	$-0.564750\pi$
$701$	−10.6974	−0.404036	−0.202018	+	0.979382i	$0.564750\pi$
$702$	−10.3098	−0.389118
$703$	−23.3702	−0.881422
$704$	1.86370	0.0702410
$705$	4.20977	0.158549
$706$	−9.80625	−0.369063
$707$	−1.38426	−0.0520605
$708$	4.42783	0.166408
$709$	−15.6908	−0.589279	−0.294639	−	0.955609i	$-0.595200\pi$
$709$	−15.6908	−0.589279	−0.294639	+	0.955609i	$0.595200\pi$
$710$	15.4811	0.580996
$711$	−5.32567	−0.199728
$712$	−16.0565	−0.601741
$713$	0	0
$714$	1.35071	0.0505490
$715$	−4.38551	−0.164009
$716$	−19.8583	−0.742141
$717$	1.91631	0.0715660
$718$	0.444433	0.0165861
$719$	2.12092	0.0790970	0.0395485	−	0.999218i	$-0.487408\pi$
$719$	2.12092	0.0790970	0.0395485	+	0.999218i	$0.487408\pi$
$720$	0.732051	0.0272819
$721$	−6.15872	−0.229363
$722$	−8.43952	−0.314086
$723$	42.8058	1.59196
$724$	−0.253337	−0.00941521
$725$	−6.20977	−0.230625
$726$	14.5403	0.539641
$727$	31.5818	1.17130	0.585652	−	0.810562i	$-0.300838\pi$
$727$	31.5818	1.17130	0.585652	+	0.810562i	$0.300838\pi$
$728$	1.13505	0.0420678
$729$	17.5885	0.651424
$730$	0.899975	0.0333096
$731$	−15.5493	−0.575110
$732$	−7.37429	−0.272562
$733$	2.08689	0.0770810	0.0385405	−	0.999257i	$-0.487729\pi$
$733$	2.08689	0.0770810	0.0385405	+	0.999257i	$0.487729\pi$
$734$	−31.0165	−1.14484
$735$	13.0735	0.482222
$736$	0	0
$737$	5.82519	0.214574
$738$	0.828427	0.0304948
$739$	−32.3456	−1.18985	−0.594926	−	0.803781i	$-0.702819\pi$
$739$	−32.3456	−1.18985	−0.594926	+	0.803781i	$0.702819\pi$
$740$	7.19151	0.264365
$741$	−14.7727	−0.542687
$742$	3.13165	0.114967
$743$	−23.0550	−0.845805	−0.422902	−	0.906175i	$-0.638989\pi$
$743$	−23.0550	−0.845805	−0.422902	+	0.906175i	$0.638989\pi$
$744$	2.24969	0.0824776
$745$	−7.21028	−0.264164
$746$	−12.9645	−0.474663
$747$	6.75096	0.247005
$748$	2.70142	0.0987737
$749$	4.48460	0.163864
$750$	−1.93185	−0.0705412
$751$	47.7777	1.74343	0.871717	−	0.490009i	$-0.163007\pi$
$751$	47.7777	1.74343	0.871717	+	0.490009i	$0.163007\pi$
$752$	−2.17914	−0.0794649
$753$	18.9462	0.690438
$754$	14.6123	0.532148
$755$	15.8888	0.578253
$756$	−2.11339	−0.0768633
$757$	4.76079	0.173034	0.0865170	−	0.996250i	$-0.472426\pi$
$757$	4.76079	0.173034	0.0865170	+	0.996250i	$0.472426\pi$
$758$	−6.94057	−0.252093
$759$	0	0
$760$	−3.24969	−0.117879
$761$	2.88331	0.104520	0.0522600	−	0.998634i	$-0.483358\pi$
$761$	2.88331	0.104520	0.0522600	+	0.998634i	$0.483358\pi$
$762$	23.6566	0.856988
$763$	0.958156	0.0346876
$764$	−19.4047	−0.702037
$765$	1.06110	0.0383642
$766$	−11.2793	−0.407539
$767$	5.39337	0.194743
$768$	−1.93185	−0.0697097
$769$	42.2185	1.52244	0.761220	−	0.648494i	$-0.224601\pi$
$769$	42.2185	1.52244	0.761220	+	0.648494i	$0.224601\pi$
$770$	−0.898979	−0.0323970
$771$	−57.0260	−2.05374
$772$	−4.52280	−0.162779
$773$	−3.05617	−0.109923	−0.0549614	−	0.998488i	$-0.517504\pi$
$773$	−3.05617	−0.109923	−0.0549614	+	0.998488i	$0.517504\pi$
$774$	−7.85301	−0.282270
$775$	−1.16452	−0.0418310
$776$	−18.1596	−0.651893
$777$	6.70142	0.240412
$778$	−11.9118	−0.427060
$779$	−3.67752	−0.131761
$780$	4.54587	0.162768
$781$	28.8522	1.03241
$782$	0	0
$783$	−27.2071	−0.972303
$784$	−6.76733	−0.241690
$785$	−18.1421	−0.647521
$786$	−19.5216	−0.696311
$787$	20.8053	0.741627	0.370814	−	0.928707i	$-0.379079\pi$
$787$	20.8053	0.741627	0.370814	+	0.928707i	$0.379079\pi$
$788$	23.2945	0.829831
$789$	47.4241	1.68834
$790$	−7.27500	−0.258833
$791$	1.48877	0.0529344
$792$	1.36433	0.0484792
$793$	−8.98234	−0.318972
$794$	13.1659	0.467241
$795$	12.5422	0.444827
$796$	11.9964	0.425199
$797$	−43.2388	−1.53160	−0.765798	−	0.643081i	$-0.777656\pi$
$797$	−43.2388	−1.53160	−0.765798	+	0.643081i	$0.777656\pi$
$798$	−3.02823	−0.107198
$799$	−3.15864	−0.111745
$800$	1.00000	0.0353553
$801$	−11.7541	−0.415312
$802$	−27.4743	−0.970153
$803$	1.67729	0.0591902
$804$	−6.03820	−0.212951
$805$	0	0
$806$	2.74026	0.0965215
$807$	19.4648	0.685193
$808$	2.86976	0.100958
$809$	49.3933	1.73658	0.868289	−	0.496059i	$-0.165220\pi$
$809$	49.3933	1.73658	0.868289	+	0.496059i	$0.165220\pi$
$810$	−10.6603	−0.374563
$811$	47.5619	1.67012	0.835061	−	0.550157i	$-0.185432\pi$
$811$	47.5619	1.67012	0.835061	+	0.550157i	$0.185432\pi$
$812$	2.99536	0.105116
$813$	45.4947	1.59557
$814$	13.4028	0.469769
$815$	8.54071	0.299168
$816$	−2.80020	−0.0980266
$817$	34.8607	1.21962
$818$	−39.4687	−1.37999
$819$	0.830916	0.0290346
$820$	1.13165	0.0395190
$821$	−46.8009	−1.63336	−0.816682	−	0.577089i	$-0.804189\pi$
$821$	−46.8009	−1.63336	−0.816682	+	0.577089i	$0.804189\pi$
$822$	23.1540	0.807588
$823$	42.3752	1.47711	0.738554	−	0.674194i	$-0.235509\pi$
$823$	42.3752	1.47711	0.738554	+	0.674194i	$0.235509\pi$
$824$	12.7678	0.444789
$825$	−3.60040	−0.125350
$826$	1.10558	0.0384680
$827$	−1.83324	−0.0637478	−0.0318739	−	0.999492i	$-0.510148\pi$
$827$	−1.83324	−0.0637478	−0.0318739	+	0.999492i	$0.510148\pi$
$828$	0	0
$829$	−2.17446	−0.0755220	−0.0377610	−	0.999287i	$-0.512023\pi$
$829$	−2.17446	−0.0755220	−0.0377610	+	0.999287i	$0.512023\pi$
$830$	9.22198	0.320099
$831$	−40.4857	−1.40443
$832$	−2.35311	−0.0815795
$833$	−9.80917	−0.339868
$834$	27.9119	0.966509
$835$	−0.230433	−0.00797446
$836$	−6.05646	−0.209467
$837$	−5.10218	−0.176357
$838$	25.4558	0.879356
$839$	26.6394	0.919693	0.459847	−	0.887998i	$-0.347904\pi$
$839$	26.6394	0.919693	0.459847	+	0.887998i	$0.347904\pi$
$840$	0.931852	0.0321519
$841$	9.56123	0.329697
$842$	−21.7086	−0.748129
$843$	7.14898	0.246224
$844$	−18.3013	−0.629955
$845$	−7.46286	−0.256730
$846$	−1.59524	−0.0548454
$847$	3.63055	0.124747
$848$	−6.49233	−0.222948
$849$	31.9783	1.09749
$850$	1.44949	0.0497171
$851$	0	0
$852$	−29.9072	−1.02460
$853$	−3.56121	−0.121933	−0.0609667	−	0.998140i	$-0.519418\pi$
$853$	−3.56121	−0.121933	−0.0609667	+	0.998140i	$0.519418\pi$
$854$	−1.84128	−0.0630073
$855$	−2.37894	−0.0813579
$856$	−9.29717	−0.317771
$857$	14.7193	0.502803	0.251401	−	0.967883i	$-0.419109\pi$
$857$	14.7193	0.502803	0.251401	+	0.967883i	$0.419109\pi$
$858$	8.47215	0.289234
$859$	−12.2469	−0.417859	−0.208930	−	0.977931i	$-0.566998\pi$
$859$	−12.2469	−0.417859	−0.208930	+	0.977931i	$0.566998\pi$
$860$	−10.7274	−0.365802
$861$	1.05453	0.0359384
$862$	−16.8817	−0.574993
$863$	34.2484	1.16583	0.582914	−	0.812534i	$-0.301912\pi$
$863$	34.2484	1.16583	0.582914	+	0.812534i	$0.301912\pi$
$864$	4.38134	0.149056
$865$	11.6067	0.394640
$866$	18.8416	0.640262
$867$	28.7826	0.977509
$868$	0.561722	0.0190661
$869$	−13.5584	−0.459938
$870$	11.9964	0.406714
$871$	−7.35489	−0.249211
$872$	−1.98638	−0.0672674
$873$	−13.2938	−0.449926
$874$	0	0
$875$	−0.482362	−0.0163068
$876$	−1.73862	−0.0587425
$877$	3.84178	0.129728	0.0648638	−	0.997894i	$-0.479339\pi$
$877$	3.84178	0.129728	0.0648638	+	0.997894i	$0.479339\pi$
$878$	12.2730	0.414194
$879$	1.51059	0.0509509
$880$	1.86370	0.0628254
$881$	−0.915892	−0.0308572	−0.0154286	−	0.999881i	$-0.504911\pi$
$881$	−0.915892	−0.0308572	−0.0154286	+	0.999881i	$0.504911\pi$
$882$	−4.95403	−0.166811
$883$	−10.1012	−0.339933	−0.169967	−	0.985450i	$-0.554366\pi$
$883$	−10.1012	−0.339933	−0.169967	+	0.985450i	$0.554366\pi$
$884$	−3.41081	−0.114718
$885$	4.42783	0.148840
$886$	−24.5943	−0.826260
$887$	8.63897	0.290068	0.145034	−	0.989427i	$-0.453671\pi$
$887$	8.63897	0.290068	0.145034	+	0.989427i	$0.453671\pi$
$888$	−13.8929	−0.466216
$889$	5.90679	0.198107
$890$	−16.0565	−0.538214
$891$	−19.8676	−0.665588
$892$	18.9747	0.635320
$893$	7.08152	0.236974
$894$	13.9292	0.465862
$895$	−19.8583	−0.663791
$896$	−0.482362	−0.0161146
$897$	0	0
$898$	28.8637	0.963193
$899$	7.23143	0.241182
$900$	0.732051	0.0244017
$901$	−9.41057	−0.313511
$902$	2.10906	0.0702242
$903$	−9.99635	−0.332658
$904$	−3.08641	−0.102652
$905$	−0.253337	−0.00842122
$906$	−30.6948	−1.01977
$907$	34.6355	1.15005	0.575026	−	0.818135i	$-0.304992\pi$
$907$	34.6355	1.15005	0.575026	+	0.818135i	$0.304992\pi$
$908$	8.64956	0.287046
$909$	2.10081	0.0696794
$910$	1.13505	0.0376266
$911$	−26.4952	−0.877827	−0.438913	−	0.898529i	$-0.644637\pi$
$911$	−26.4952	−0.877827	−0.438913	+	0.898529i	$0.644637\pi$
$912$	6.27792	0.207883
$913$	17.1870	0.568808
$914$	15.3780	0.508661
$915$	−7.37429	−0.243787
$916$	−12.4373	−0.410939
$917$	−4.87432	−0.160964
$918$	6.35071	0.209605
$919$	−21.6386	−0.713792	−0.356896	−	0.934144i	$-0.616165\pi$
$919$	−21.6386	−0.713792	−0.356896	+	0.934144i	$0.616165\pi$
$920$	0	0
$921$	28.3897	0.935471
$922$	42.7513	1.40794
$923$	−36.4288	−1.19907
$924$	1.73670	0.0571331
$925$	7.19151	0.236455
$926$	13.4616	0.442376
$927$	9.34671	0.306986
$928$	−6.20977	−0.203846
$929$	−10.5135	−0.344936	−0.172468	−	0.985015i	$-0.555174\pi$
$929$	−10.5135	−0.344936	−0.172468	+	0.985015i	$0.555174\pi$
$930$	2.24969	0.0737702
$931$	21.9917	0.720749
$932$	22.0981	0.723846
$933$	−5.69069	−0.186305
$934$	14.0720	0.460449
$935$	2.70142	0.0883458
$936$	−1.72260	−0.0563049
$937$	50.6395	1.65432	0.827161	−	0.561965i	$-0.189955\pi$
$937$	50.6395	1.65432	0.827161	+	0.561965i	$0.189955\pi$
$938$	−1.50767	−0.0492272
$939$	−8.64709	−0.282187
$940$	−2.17914	−0.0710756
$941$	−2.38901	−0.0778794	−0.0389397	−	0.999242i	$-0.512398\pi$
$941$	−2.38901	−0.0778794	−0.0389397	+	0.999242i	$0.512398\pi$
$942$	35.0479	1.14192
$943$	0	0
$944$	−2.29201	−0.0745987
$945$	−2.11339	−0.0687487
$946$	−19.9927	−0.650019
$947$	48.0218	1.56050	0.780250	−	0.625468i	$-0.215092\pi$
$947$	48.0218	1.56050	0.780250	+	0.625468i	$0.215092\pi$
$948$	14.0542	0.456460
$949$	−2.11774	−0.0687449
$950$	−3.24969	−0.105434
$951$	47.4604	1.53901
$952$	−0.699179	−0.0226605
$953$	−5.47480	−0.177346	−0.0886731	−	0.996061i	$-0.528263\pi$
$953$	−5.47480	−0.177346	−0.0886731	+	0.996061i	$0.528263\pi$
$954$	−4.75272	−0.153875
$955$	−19.4047	−0.627921
$956$	−0.991956	−0.0320822
$957$	22.3576	0.722720
$958$	−7.20231	−0.232696
$959$	5.78129	0.186688
$960$	−1.93185	−0.0623502
$961$	−29.6439	−0.956254
$962$	−16.9224	−0.545601
$963$	−6.80600	−0.219320
$964$	−22.1579	−0.713658
$965$	−4.52280	−0.145594
$966$	0	0
$967$	−44.8614	−1.44264	−0.721322	−	0.692600i	$-0.756465\pi$
$967$	−44.8614	−1.44264	−0.721322	+	0.692600i	$0.756465\pi$
$968$	−7.52661	−0.241914
$969$	9.09978	0.292327
$970$	−18.1596	−0.583071
$971$	−17.4293	−0.559333	−0.279667	−	0.960097i	$-0.590224\pi$
$971$	−17.4293	−0.559333	−0.279667	+	0.960097i	$0.590224\pi$
$972$	7.45001	0.238959
$973$	6.96928	0.223425
$974$	35.8090	1.14739
$975$	4.54587	0.145584
$976$	3.81722	0.122186
$977$	−34.5621	−1.10574	−0.552869	−	0.833268i	$-0.686467\pi$
$977$	−34.5621	−1.10574	−0.552869	+	0.833268i	$0.686467\pi$
$978$	−16.4994	−0.527592
$979$	−29.9245	−0.956390
$980$	−6.76733	−0.216174
$981$	−1.45413	−0.0464269
$982$	−10.1951	−0.325339
$983$	−11.6881	−0.372792	−0.186396	−	0.982475i	$-0.559681\pi$
$983$	−11.6881	−0.372792	−0.186396	+	0.982475i	$0.559681\pi$
$984$	−2.18618	−0.0696930
$985$	23.2945	0.742223
$986$	−9.00100	−0.286650
$987$	−2.03063	−0.0646357
$988$	7.64689	0.243280
$989$	0	0
$990$	1.36433	0.0433611
$991$	45.6785	1.45103	0.725513	−	0.688209i	$-0.241603\pi$
$991$	45.6785	1.45103	0.725513	+	0.688209i	$0.241603\pi$
$992$	−1.16452	−0.0369737
$993$	−36.7950	−1.16765
$994$	−7.46750	−0.236855
$995$	11.9964	0.380310
$996$	−17.8155	−0.564505
$997$	38.3782	1.21545	0.607725	−	0.794148i	$-0.292082\pi$
$997$	38.3782	1.21545	0.607725	+	0.794148i	$0.292082\pi$
$998$	28.7160	0.908988
$999$	31.5085	0.996883

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.93185 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.93185 q^{6} -0.482362 q^{7} +1.00000 q^{8} +0.732051 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.93185 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.93185 q^{6} -0.482362 q^{7} +1.00000 q^{8} +0.732051 q^{9} +1.00000 q^{10} +1.86370 q^{11} -1.93185 q^{12} -2.35311 q^{13} -0.482362 q^{14} -1.93185 q^{15} +1.00000 q^{16} +1.44949 q^{17} +0.732051 q^{18} -3.24969 q^{19} +1.00000 q^{20} +0.931852 q^{21} +1.86370 q^{22} -1.93185 q^{24} +1.00000 q^{25} -2.35311 q^{26} +4.38134 q^{27} -0.482362 q^{28} -6.20977 q^{29} -1.93185 q^{30} -1.16452 q^{31} +1.00000 q^{32} -3.60040 q^{33} +1.44949 q^{34} -0.482362 q^{35} +0.732051 q^{36} +7.19151 q^{37} -3.24969 q^{38} +4.54587 q^{39} +1.00000 q^{40} +1.13165 q^{41} +0.931852 q^{42} -10.7274 q^{43} +1.86370 q^{44} +0.732051 q^{45} -2.17914 q^{47} -1.93185 q^{48} -6.76733 q^{49} +1.00000 q^{50} -2.80020 q^{51} -2.35311 q^{52} -6.49233 q^{53} +4.38134 q^{54} +1.86370 q^{55} -0.482362 q^{56} +6.27792 q^{57} -6.20977 q^{58} -2.29201 q^{59} -1.93185 q^{60} +3.81722 q^{61} -1.16452 q^{62} -0.353113 q^{63} +1.00000 q^{64} -2.35311 q^{65} -3.60040 q^{66} +3.12560 q^{67} +1.44949 q^{68} -0.482362 q^{70} +15.4811 q^{71} +0.732051 q^{72} +0.899975 q^{73} +7.19151 q^{74} -1.93185 q^{75} -3.24969 q^{76} -0.898979 q^{77} +4.54587 q^{78} -7.27500 q^{79} +1.00000 q^{80} -10.6603 q^{81} +1.13165 q^{82} +9.22198 q^{83} +0.931852 q^{84} +1.44949 q^{85} -10.7274 q^{86} +11.9964 q^{87} +1.86370 q^{88} -16.0565 q^{89} +0.732051 q^{90} +1.13505 q^{91} +2.24969 q^{93} -2.17914 q^{94} -3.24969 q^{95} -1.93185 q^{96} -18.1596 q^{97} -6.76733 q^{98} +1.36433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} - 8 q^{11} - 4 q^{13} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 4 q^{18} - 4 q^{19} + 4 q^{20} - 4 q^{21} - 8 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} - 16 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} - 16 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 4 q^{41} - 4 q^{42} - 12 q^{43} - 8 q^{44} - 4 q^{45} - 8 q^{47} - 16 q^{49} + 4 q^{50} - 12 q^{51} - 4 q^{52} - 8 q^{55} - 4 q^{56} + 4 q^{57} + 4 q^{58} - 4 q^{59} - 4 q^{61} - 8 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} - 16 q^{66} - 4 q^{68} - 4 q^{70} + 28 q^{71} - 4 q^{72} - 12 q^{73} - 16 q^{74} - 4 q^{76} + 16 q^{77} + 4 q^{78} - 44 q^{79} + 4 q^{80} - 8 q^{81} - 4 q^{82} + 20 q^{83} - 4 q^{84} - 4 q^{85} - 12 q^{86} + 28 q^{87} - 8 q^{88} - 40 q^{89} - 4 q^{90} - 16 q^{91} - 8 q^{94} - 4 q^{95} - 20 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 - 8 * q^11 - 4 * q^13 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 4 * q^18 - 4 * q^19 + 4 * q^20 - 4 * q^21 - 8 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 - 16 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 - 16 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 4 * q^41 - 4 * q^42 - 12 * q^43 - 8 * q^44 - 4 * q^45 - 8 * q^47 - 16 * q^49 + 4 * q^50 - 12 * q^51 - 4 * q^52 - 8 * q^55 - 4 * q^56 + 4 * q^57 + 4 * q^58 - 4 * q^59 - 4 * q^61 - 8 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 - 16 * q^66 - 4 * q^68 - 4 * q^70 + 28 * q^71 - 4 * q^72 - 12 * q^73 - 16 * q^74 - 4 * q^76 + 16 * q^77 + 4 * q^78 - 44 * q^79 + 4 * q^80 - 8 * q^81 - 4 * q^82 + 20 * q^83 - 4 * q^84 - 4 * q^85 - 12 * q^86 + 28 * q^87 - 8 * q^88 - 40 * q^89 - 4 * q^90 - 16 * q^91 - 8 * q^94 - 4 * q^95 - 20 * q^97 - 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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