LMFDB - Embedded newform 5290.2.a.x.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:	4.4.13888.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 6x + 9 $ x^4 - 2x^3 - 7x^2 + 6*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.53728$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.95150 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.95150 q^{6} +3.36571 q^{7} +1.00000 q^{8} +5.71133 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.95150 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.95150 q^{6} +3.36571 q^{7} +1.00000 q^{8} +5.71133 q^{9} +1.00000 q^{10} -4.95150 q^{11} -2.95150 q^{12} +1.95150 q^{13} +3.36571 q^{14} -2.95150 q^{15} +1.00000 q^{16} -7.71133 q^{17} +5.71133 q^{18} +7.20011 q^{19} +1.00000 q^{20} -9.93388 q^{21} -4.95150 q^{22} -2.95150 q^{24} +1.00000 q^{25} +1.95150 q^{26} -8.00247 q^{27} +3.36571 q^{28} -2.75983 q^{29} -2.95150 q^{30} -7.81081 q^{31} +1.00000 q^{32} +14.6143 q^{33} -7.71133 q^{34} +3.36571 q^{35} +5.71133 q^{36} -6.93388 q^{37} +7.20011 q^{38} -5.75983 q^{39} +1.00000 q^{40} -6.09466 q^{41} -9.93388 q^{42} -5.65685 q^{43} -4.95150 q^{44} +5.71133 q^{45} +3.09948 q^{47} -2.95150 q^{48} +4.32800 q^{49} +1.00000 q^{50} +22.7600 q^{51} +1.95150 q^{52} +0.662824 q^{53} -8.00247 q^{54} -4.95150 q^{55} +3.36571 q^{56} -21.2511 q^{57} -2.75983 q^{58} -12.1825 q^{59} -2.95150 q^{60} -5.63429 q^{61} -7.81081 q^{62} +19.2227 q^{63} +1.00000 q^{64} +1.95150 q^{65} +14.6143 q^{66} +7.93635 q^{67} -7.71133 q^{68} +3.36571 q^{70} +5.95397 q^{71} +5.71133 q^{72} +2.42018 q^{73} -6.93388 q^{74} -2.95150 q^{75} +7.20011 q^{76} -16.6653 q^{77} -5.75983 q^{78} -10.4937 q^{79} +1.00000 q^{80} +6.48528 q^{81} -6.09466 q^{82} +2.75983 q^{83} -9.93388 q^{84} -7.71133 q^{85} -5.65685 q^{86} +8.14563 q^{87} -4.95150 q^{88} +11.2451 q^{89} +5.71133 q^{90} +6.56817 q^{91} +23.0536 q^{93} +3.09948 q^{94} +7.20011 q^{95} -2.95150 q^{96} -3.94553 q^{97} +4.32800 q^{98} -28.2796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 4 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 4 q^{16} - 14 q^{17} + 6 q^{18} - 2 q^{19} + 4 q^{20} - 20 q^{21} - 10 q^{22} - 2 q^{24} + 4 q^{25} - 2 q^{26} - 8 q^{27} - 2 q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} + 4 q^{32} + 22 q^{33} - 14 q^{34} - 2 q^{35} + 6 q^{36} - 8 q^{37} - 2 q^{38} - 16 q^{39} + 4 q^{40} - 2 q^{41} - 20 q^{42} - 10 q^{44} + 6 q^{45} + 8 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{50} + 18 q^{51} - 2 q^{52} - 24 q^{53} - 8 q^{54} - 10 q^{55} - 2 q^{56} - 40 q^{57} - 4 q^{58} - 8 q^{59} - 2 q^{60} - 38 q^{61} - 10 q^{62} + 8 q^{63} + 4 q^{64} - 2 q^{65} + 22 q^{66} - 12 q^{67} - 14 q^{68} - 2 q^{70} - 10 q^{71} + 6 q^{72} - 8 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 16 q^{78} + 20 q^{79} + 4 q^{80} - 8 q^{81} - 2 q^{82} + 4 q^{83} - 20 q^{84} - 14 q^{85} - 4 q^{87} - 10 q^{88} + 4 q^{89} + 6 q^{90} + 22 q^{91} - 12 q^{93} + 8 q^{94} - 2 q^{95} - 2 q^{96} - 10 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 4 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 4 * q^16 - 14 * q^17 + 6 * q^18 - 2 * q^19 + 4 * q^20 - 20 * q^21 - 10 * q^22 - 2 * q^24 + 4 * q^25 - 2 * q^26 - 8 * q^27 - 2 * q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 + 4 * q^32 + 22 * q^33 - 14 * q^34 - 2 * q^35 + 6 * q^36 - 8 * q^37 - 2 * q^38 - 16 * q^39 + 4 * q^40 - 2 * q^41 - 20 * q^42 - 10 * q^44 + 6 * q^45 + 8 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^50 + 18 * q^51 - 2 * q^52 - 24 * q^53 - 8 * q^54 - 10 * q^55 - 2 * q^56 - 40 * q^57 - 4 * q^58 - 8 * q^59 - 2 * q^60 - 38 * q^61 - 10 * q^62 + 8 * q^63 + 4 * q^64 - 2 * q^65 + 22 * q^66 - 12 * q^67 - 14 * q^68 - 2 * q^70 - 10 * q^71 + 6 * q^72 - 8 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 16 * q^78 + 20 * q^79 + 4 * q^80 - 8 * q^81 - 2 * q^82 + 4 * q^83 - 20 * q^84 - 14 * q^85 - 4 * q^87 - 10 * q^88 + 4 * q^89 + 6 * q^90 + 22 * q^91 - 12 * q^93 + 8 * q^94 - 2 * q^95 - 2 * q^96 - 10 * q^97 + 6 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.95150	−1.70405	−0.852023	−	0.523504i	$-0.824625\pi$
$3$	−2.95150	−1.70405	−0.852023	+	0.523504i	$0.824625\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.95150	−1.20494
$7$	3.36571	1.27212	0.636059	−	0.771640i	$-0.280563\pi$
$7$	3.36571	1.27212	0.636059	+	0.771640i	$0.280563\pi$
$8$	1.00000	0.353553
$9$	5.71133	1.90378
$10$	1.00000	0.316228
$11$	−4.95150	−1.49293	−0.746466	−	0.665423i	$-0.768251\pi$
$11$	−4.95150	−1.49293	−0.746466	+	0.665423i	$0.768251\pi$
$12$	−2.95150	−0.852023
$13$	1.95150	0.541248	0.270624	−	0.962685i	$-0.412770\pi$
$13$	1.95150	0.541248	0.270624	+	0.962685i	$0.412770\pi$
$14$	3.36571	0.899524
$15$	−2.95150	−0.762073
$16$	1.00000	0.250000
$17$	−7.71133	−1.87027	−0.935136	−	0.354289i	$-0.884723\pi$
$17$	−7.71133	−1.87027	−0.935136	+	0.354289i	$0.884723\pi$
$18$	5.71133	1.34617
$19$	7.20011	1.65182	0.825909	−	0.563804i	$-0.190663\pi$
$19$	7.20011	1.65182	0.825909	+	0.563804i	$0.190663\pi$
$20$	1.00000	0.223607
$21$	−9.93388	−2.16775
$22$	−4.95150	−1.05566
$23$	0	0
$23$	0	0
$24$	−2.95150	−0.602472
$25$	1.00000	0.200000
$26$	1.95150	0.382720
$27$	−8.00247	−1.54008
$28$	3.36571	0.636059
$29$	−2.75983	−0.512488	−0.256244	−	0.966612i	$-0.582485\pi$
$29$	−2.75983	−0.512488	−0.256244	+	0.966612i	$0.582485\pi$
$30$	−2.95150	−0.538867
$31$	−7.81081	−1.40286	−0.701431	−	0.712737i	$-0.747455\pi$
$31$	−7.81081	−1.40286	−0.701431	+	0.712737i	$0.747455\pi$
$32$	1.00000	0.176777
$33$	14.6143	2.54403
$34$	−7.71133	−1.32248
$35$	3.36571	0.568909
$36$	5.71133	0.951888
$37$	−6.93388	−1.13992	−0.569961	−	0.821672i	$-0.693042\pi$
$37$	−6.93388	−1.13992	−0.569961	+	0.821672i	$0.693042\pi$
$38$	7.20011	1.16801
$39$	−5.75983	−0.922311
$40$	1.00000	0.158114
$41$	−6.09466	−0.951825	−0.475913	−	0.879493i	$-0.657882\pi$
$41$	−6.09466	−0.951825	−0.475913	+	0.879493i	$0.657882\pi$
$42$	−9.93388	−1.53283
$43$	−5.65685	−0.862662	−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685	−0.862662	−0.431331	+	0.902194i	$0.641956\pi$
$44$	−4.95150	−0.746466
$45$	5.71133	0.851394
$46$	0	0
$47$	3.09948	0.452106	0.226053	−	0.974115i	$-0.427418\pi$
$47$	3.09948	0.452106	0.226053	+	0.974115i	$0.427418\pi$
$48$	−2.95150	−0.426012
$49$	4.32800	0.618286
$50$	1.00000	0.141421
$51$	22.7600	3.18703
$52$	1.95150	0.270624
$53$	0.662824	0.0910458	0.0455229	−	0.998963i	$-0.485505\pi$
$53$	0.662824	0.0910458	0.0455229	+	0.998963i	$0.485505\pi$
$54$	−8.00247	−1.08900
$55$	−4.95150	−0.667660
$56$	3.36571	0.449762
$57$	−21.2511	−2.81477
$58$	−2.75983	−0.362384
$59$	−12.1825	−1.58602	−0.793012	−	0.609206i	$-0.791488\pi$
$59$	−12.1825	−1.58602	−0.793012	+	0.609206i	$0.791488\pi$
$60$	−2.95150	−0.381036
$61$	−5.63429	−0.721397	−0.360698	−	0.932682i	$-0.617462\pi$
$61$	−5.63429	−0.721397	−0.360698	+	0.932682i	$0.617462\pi$
$62$	−7.81081	−0.991974
$63$	19.2227	2.42183
$64$	1.00000	0.125000
$65$	1.95150	0.242053
$66$	14.6143	1.79890
$67$	7.93635	0.969579	0.484790	−	0.874631i	$-0.338896\pi$
$67$	7.93635	0.969579	0.484790	+	0.874631i	$0.338896\pi$
$68$	−7.71133	−0.935136
$69$	0	0
$70$	3.36571	0.402279
$71$	5.95397	0.706606	0.353303	−	0.935509i	$-0.385058\pi$
$71$	5.95397	0.706606	0.353303	+	0.935509i	$0.385058\pi$
$72$	5.71133	0.673086
$73$	2.42018	0.283261	0.141630	−	0.989920i	$-0.454766\pi$
$73$	2.42018	0.283261	0.141630	+	0.989920i	$0.454766\pi$
$74$	−6.93388	−0.806047
$75$	−2.95150	−0.340809
$76$	7.20011	0.825909
$77$	−16.6653	−1.89919
$78$	−5.75983	−0.652173
$79$	−10.4937	−1.18064	−0.590318	−	0.807171i	$-0.700998\pi$
$79$	−10.4937	−1.18064	−0.590318	+	0.807171i	$0.700998\pi$
$80$	1.00000	0.111803
$81$	6.48528	0.720587
$82$	−6.09466	−0.673042
$83$	2.75983	0.302931	0.151465	−	0.988463i	$-0.451601\pi$
$83$	2.75983	0.302931	0.151465	+	0.988463i	$0.451601\pi$
$84$	−9.93388	−1.08387
$85$	−7.71133	−0.836411
$86$	−5.65685	−0.609994
$87$	8.14563	0.873303
$88$	−4.95150	−0.527831
$89$	11.2451	1.19198	0.595990	−	0.802992i	$-0.296760\pi$
$89$	11.2451	1.19198	0.595990	+	0.802992i	$0.296760\pi$
$90$	5.71133	0.602027
$91$	6.56817	0.688531
$92$	0	0
$93$	23.0536	2.39054
$94$	3.09948	0.319687
$95$	7.20011	0.738715
$96$	−2.95150	−0.301236
$97$	−3.94553	−0.400608	−0.200304	−	0.979734i	$-0.564193\pi$
$97$	−3.94553	−0.400608	−0.200304	+	0.979734i	$0.564193\pi$
$98$	4.32800	0.437194
$99$	−28.2796	−2.84221
$100$	1.00000	0.100000
$101$	4.03686	0.401682	0.200841	−	0.979624i	$-0.435633\pi$
$101$	4.03686	0.401682	0.200841	+	0.979624i	$0.435633\pi$
$102$	22.7600	2.25357
$103$	−0.183222	−0.0180534	−0.00902670	−	0.999959i	$-0.502873\pi$
$103$	−0.183222	−0.0180534	−0.00902670	+	0.999959i	$0.502873\pi$
$104$	1.95150	0.191360
$105$	−9.93388	−0.969447
$106$	0.662824	0.0643791
$107$	6.52214	0.630519	0.315259	−	0.949006i	$-0.397908\pi$
$107$	6.52214	0.630519	0.315259	+	0.949006i	$0.397908\pi$
$108$	−8.00247	−0.770038
$109$	6.39660	0.612683	0.306341	−	0.951922i	$-0.400895\pi$
$109$	6.39660	0.612683	0.306341	+	0.951922i	$0.400895\pi$
$110$	−4.95150	−0.472107
$111$	20.4653	1.94248
$112$	3.36571	0.318030
$113$	−11.7090	−1.10149	−0.550744	−	0.834674i	$-0.685656\pi$
$113$	−11.7090	−1.10149	−0.550744	+	0.834674i	$0.685656\pi$
$114$	−21.2511	−1.99035
$115$	0	0
$116$	−2.75983	−0.256244
$117$	11.1456	1.03041
$118$	−12.1825	−1.12149
$119$	−25.9541	−2.37921
$120$	−2.95150	−0.269433
$121$	13.5173	1.22885
$122$	−5.63429	−0.510105
$123$	17.9884	1.62195
$124$	−7.81081	−0.701431
$125$	1.00000	0.0894427
$126$	19.2227	1.71249
$127$	−3.28197	−0.291228	−0.145614	−	0.989342i	$-0.546516\pi$
$127$	−3.28197	−0.291228	−0.145614	+	0.989342i	$0.546516\pi$
$128$	1.00000	0.0883883
$129$	16.6962	1.47002
$130$	1.95150	0.171158
$131$	6.33965	0.553898	0.276949	−	0.960885i	$-0.410677\pi$
$131$	6.33965	0.553898	0.276949	+	0.960885i	$0.410677\pi$
$132$	14.6143	1.27201
$133$	24.2335	2.10131
$134$	7.93635	0.685596
$135$	−8.00247	−0.688743
$136$	−7.71133	−0.661241
$137$	−10.7113	−0.915130	−0.457565	−	0.889176i	$-0.651278\pi$
$137$	−10.7113	−0.915130	−0.457565	+	0.889176i	$0.651278\pi$
$138$	0	0
$139$	11.0676	0.938739	0.469370	−	0.883002i	$-0.344481\pi$
$139$	11.0676	0.938739	0.469370	+	0.883002i	$0.344481\pi$
$140$	3.36571	0.284454
$141$	−9.14810	−0.770409
$142$	5.95397	0.499646
$143$	−9.66282	−0.808046
$144$	5.71133	0.475944
$145$	−2.75983	−0.229192
$146$	2.42018	0.200296
$147$	−12.7741	−1.05359
$148$	−6.93388	−0.569961
$149$	−6.81516	−0.558320	−0.279160	−	0.960245i	$-0.590056\pi$
$149$	−6.81516	−0.558320	−0.279160	+	0.960245i	$0.590056\pi$
$150$	−2.95150	−0.240989
$151$	4.23534	0.344667	0.172334	−	0.985039i	$-0.444869\pi$
$151$	4.23534	0.344667	0.172334	+	0.985039i	$0.444869\pi$
$152$	7.20011	0.584006
$153$	−44.0419	−3.56058
$154$	−16.6653	−1.34293
$155$	−7.81081	−0.627379
$156$	−5.75983	−0.461156
$157$	−18.4500	−1.47247	−0.736237	−	0.676724i	$-0.763399\pi$
$157$	−18.4500	−1.47247	−0.736237	+	0.676724i	$0.763399\pi$
$158$	−10.4937	−0.834836
$159$	−1.95632	−0.155146
$160$	1.00000	0.0790569
$161$	0	0
$162$	6.48528	0.509532
$163$	14.9540	1.17129	0.585643	−	0.810569i	$-0.300842\pi$
$163$	14.9540	1.17129	0.585643	+	0.810569i	$0.300842\pi$
$164$	−6.09466	−0.475913
$165$	14.6143	1.13772
$166$	2.75983	0.214204
$167$	4.85684	0.375834	0.187917	−	0.982185i	$-0.439826\pi$
$167$	4.85684	0.375834	0.187917	+	0.982185i	$0.439826\pi$
$168$	−9.93388	−0.766415
$169$	−9.19166	−0.707051
$170$	−7.71133	−0.591432
$171$	41.1222	3.14469
$172$	−5.65685	−0.431331
$173$	−6.22852	−0.473546	−0.236773	−	0.971565i	$-0.576090\pi$
$173$	−6.22852	−0.473546	−0.236773	+	0.971565i	$0.576090\pi$
$174$	8.14563	0.617519
$175$	3.36571	0.254424
$176$	−4.95150	−0.373233
$177$	35.9566	2.70266
$178$	11.2451	0.842857
$179$	12.3883	0.925943	0.462972	−	0.886373i	$-0.346783\pi$
$179$	12.3883	0.925943	0.462972	+	0.886373i	$0.346783\pi$
$180$	5.71133	0.425697
$181$	−21.1400	−1.57132	−0.785660	−	0.618658i	$-0.787677\pi$
$181$	−21.1400	−1.57132	−0.785660	+	0.618658i	$0.787677\pi$
$182$	6.56817	0.486865
$183$	16.6296	1.22929
$184$	0	0
$185$	−6.93388	−0.509789
$186$	23.0536	1.69037
$187$	38.1826	2.79219
$188$	3.09948	0.226053
$189$	−26.9340	−1.95916
$190$	7.20011	0.522351
$191$	−21.7623	−1.57467	−0.787333	−	0.616529i	$-0.788538\pi$
$191$	−21.7623	−1.57467	−0.787333	+	0.616529i	$0.788538\pi$
$192$	−2.95150	−0.213006
$193$	2.98105	0.214581	0.107290	−	0.994228i	$-0.465783\pi$
$193$	2.98105	0.214581	0.107290	+	0.994228i	$0.465783\pi$
$194$	−3.94553	−0.283272
$195$	−5.75983	−0.412470
$196$	4.32800	0.309143
$197$	−3.93255	−0.280183	−0.140091	−	0.990139i	$-0.544740\pi$
$197$	−3.93255	−0.280183	−0.140091	+	0.990139i	$0.544740\pi$
$198$	−28.2796	−2.00974
$199$	−22.8369	−1.61886	−0.809431	−	0.587215i	$-0.800225\pi$
$199$	−22.8369	−1.61886	−0.809431	+	0.587215i	$0.800225\pi$
$200$	1.00000	0.0707107
$201$	−23.4241	−1.65221
$202$	4.03686	0.284032
$203$	−9.28879	−0.651945
$204$	22.7600	1.59352
$205$	−6.09466	−0.425669
$206$	−0.183222	−0.0127657
$207$	0	0
$208$	1.95150	0.135312
$209$	−35.6513	−2.46605
$210$	−9.93388	−0.685503
$211$	−17.1044	−1.17752	−0.588759	−	0.808309i	$-0.700383\pi$
$211$	−17.1044	−1.17752	−0.588759	+	0.808309i	$0.700383\pi$
$212$	0.662824	0.0455229
$213$	−17.5731	−1.20409
$214$	6.52214	0.445844
$215$	−5.65685	−0.385794
$216$	−8.00247	−0.544499
$217$	−26.2889	−1.78461
$218$	6.39660	0.433232
$219$	−7.14316	−0.482690
$220$	−4.95150	−0.333830
$221$	−15.0486	−1.01228
$222$	20.4653	1.37354
$223$	13.0074	0.871041	0.435521	−	0.900179i	$-0.356564\pi$
$223$	13.0074	0.871041	0.435521	+	0.900179i	$0.356564\pi$
$224$	3.36571	0.224881
$225$	5.71133	0.380755
$226$	−11.7090	−0.778869
$227$	1.95632	0.129846	0.0649228	−	0.997890i	$-0.479320\pi$
$227$	1.95632	0.129846	0.0649228	+	0.997890i	$0.479320\pi$
$228$	−21.2511	−1.40739
$229$	14.6225	0.966280	0.483140	−	0.875543i	$-0.339496\pi$
$229$	14.6225	0.966280	0.483140	+	0.875543i	$0.339496\pi$
$230$	0	0
$231$	49.1876	3.23630
$232$	−2.75983	−0.181192
$233$	−23.1112	−1.51407	−0.757034	−	0.653375i	$-0.773352\pi$
$233$	−23.1112	−1.51407	−0.757034	+	0.653375i	$0.773352\pi$
$234$	11.1456	0.728613
$235$	3.09948	0.202188
$236$	−12.1825	−0.793012
$237$	30.9722	2.01186
$238$	−25.9541	−1.68235
$239$	−29.8159	−1.92863	−0.964314	−	0.264760i	$-0.914707\pi$
$239$	−29.8159	−1.92863	−0.964314	+	0.264760i	$0.914707\pi$
$240$	−2.95150	−0.190518
$241$	−11.1835	−0.720393	−0.360197	−	0.932876i	$-0.617290\pi$
$241$	−11.1835	−0.720393	−0.360197	+	0.932876i	$0.617290\pi$
$242$	13.5173	0.868926
$243$	4.86614	0.312163
$244$	−5.63429	−0.360698
$245$	4.32800	0.276506
$246$	17.9884	1.14690
$247$	14.0510	0.894042
$248$	−7.81081	−0.495987
$249$	−8.14563	−0.516208
$250$	1.00000	0.0632456
$251$	1.88640	0.119068	0.0595342	−	0.998226i	$-0.481038\pi$
$251$	1.88640	0.119068	0.0595342	+	0.998226i	$0.481038\pi$
$252$	19.2227	1.21091
$253$	0	0
$254$	−3.28197	−0.205929
$255$	22.7600	1.42528
$256$	1.00000	0.0625000
$257$	6.78704	0.423364	0.211682	−	0.977339i	$-0.432106\pi$
$257$	6.78704	0.423364	0.211682	+	0.977339i	$0.432106\pi$
$258$	16.6962	1.03946
$259$	−23.3374	−1.45012
$260$	1.95150	0.121027
$261$	−15.7623	−0.975662
$262$	6.33965	0.391665
$263$	−15.1777	−0.935895	−0.467947	−	0.883756i	$-0.655006\pi$
$263$	−15.1777	−0.935895	−0.467947	+	0.883756i	$0.655006\pi$
$264$	14.6143	0.899449
$265$	0.662824	0.0407169
$266$	24.2335	1.48585
$267$	−33.1899	−2.03119
$268$	7.93635	0.484790
$269$	5.26159	0.320805	0.160402	−	0.987052i	$-0.448721\pi$
$269$	5.26159	0.320805	0.160402	+	0.987052i	$0.448721\pi$
$270$	−8.00247	−0.487015
$271$	−4.84519	−0.294324	−0.147162	−	0.989112i	$-0.547014\pi$
$271$	−4.84519	−0.294324	−0.147162	+	0.989112i	$0.547014\pi$
$272$	−7.71133	−0.467568
$273$	−19.3859	−1.17329
$274$	−10.7113	−0.647095
$275$	−4.95150	−0.298586
$276$	0	0
$277$	10.3833	0.623874	0.311937	−	0.950103i	$-0.399022\pi$
$277$	10.3833	0.623874	0.311937	+	0.950103i	$0.399022\pi$
$278$	11.0676	0.663789
$279$	−44.6101	−2.67074
$280$	3.36571	0.201140
$281$	−20.4202	−1.21817	−0.609083	−	0.793106i	$-0.708462\pi$
$281$	−20.4202	−1.21817	−0.609083	+	0.793106i	$0.708462\pi$
$282$	−9.14810	−0.544762
$283$	25.0478	1.48894	0.744468	−	0.667659i	$-0.232703\pi$
$283$	25.0478	1.48894	0.744468	+	0.667659i	$0.232703\pi$
$284$	5.95397	0.353303
$285$	−21.2511	−1.25881
$286$	−9.66282	−0.571375
$287$	−20.5128	−1.21083
$288$	5.71133	0.336543
$289$	42.4646	2.49792
$290$	−2.75983	−0.162063
$291$	11.6452	0.682654
$292$	2.42018	0.141630
$293$	0.878260	0.0513085	0.0256542	−	0.999671i	$-0.491833\pi$
$293$	0.878260	0.0513085	0.0256542	+	0.999671i	$0.491833\pi$
$294$	−12.7741	−0.744999
$295$	−12.1825	−0.709292
$296$	−6.93388	−0.403023
$297$	39.6242	2.29923
$298$	−6.81516	−0.394792
$299$	0	0
$300$	−2.95150	−0.170405
$301$	−19.0393	−1.09741
$302$	4.23534	0.243717
$303$	−11.9148	−0.684485
$304$	7.20011	0.412954
$305$	−5.63429	−0.322619
$306$	−44.0419	−2.51771
$307$	32.7391	1.86852	0.934260	−	0.356592i	$-0.116061\pi$
$307$	32.7391	1.86852	0.934260	+	0.356592i	$0.116061\pi$
$308$	−16.6653	−0.949593
$309$	0.540779	0.0307638
$310$	−7.81081	−0.443624
$311$	−29.9079	−1.69592	−0.847962	−	0.530057i	$-0.822170\pi$
$311$	−29.9079	−1.69592	−0.847962	+	0.530057i	$0.822170\pi$
$312$	−5.75983	−0.326086
$313$	1.35044	0.0763316	0.0381658	−	0.999271i	$-0.487848\pi$
$313$	1.35044	0.0763316	0.0381658	+	0.999271i	$0.487848\pi$
$314$	−18.4500	−1.04120
$315$	19.2227	1.08307
$316$	−10.4937	−0.590318
$317$	−24.8988	−1.39845	−0.699227	−	0.714900i	$-0.746472\pi$
$317$	−24.8988	−1.39845	−0.699227	+	0.714900i	$0.746472\pi$
$318$	−1.95632	−0.109705
$319$	13.6653	0.765110
$320$	1.00000	0.0559017
$321$	−19.2501	−1.07443
$322$	0	0
$323$	−55.5224	−3.08935
$324$	6.48528	0.360293
$325$	1.95150	0.108250
$326$	14.9540	0.828224
$327$	−18.8795	−1.04404
$328$	−6.09466	−0.336521
$329$	10.4320	0.575132
$330$	14.6143	0.804492
$331$	10.8890	0.598513	0.299257	−	0.954173i	$-0.403261\pi$
$331$	10.8890	0.598513	0.299257	+	0.954173i	$0.403261\pi$
$332$	2.75983	0.151465
$333$	−39.6016	−2.17016
$334$	4.85684	0.265754
$335$	7.93635	0.433609
$336$	−9.93388	−0.541937
$337$	0.122045	0.00664819	0.00332410	−	0.999994i	$-0.498942\pi$
$337$	0.122045	0.00664819	0.00332410	+	0.999994i	$0.498942\pi$
$338$	−9.19166	−0.499961
$339$	34.5590	1.87699
$340$	−7.71133	−0.418205
$341$	38.6752	2.09438
$342$	41.1222	2.22363
$343$	−8.99318	−0.485586
$344$	−5.65685	−0.304997
$345$	0	0
$346$	−6.22852	−0.334847
$347$	10.0141	0.537586	0.268793	−	0.963198i	$-0.413375\pi$
$347$	10.0141	0.537586	0.268793	+	0.963198i	$0.413375\pi$
$348$	8.14563	0.436652
$349$	−30.7551	−1.64628	−0.823142	−	0.567835i	$-0.807781\pi$
$349$	−30.7551	−1.64628	−0.823142	+	0.567835i	$0.807781\pi$
$350$	3.36571	0.179905
$351$	−15.6168	−0.833563
$352$	−4.95150	−0.263916
$353$	24.3232	1.29459	0.647296	−	0.762239i	$-0.275900\pi$
$353$	24.3232	1.29459	0.647296	+	0.762239i	$0.275900\pi$
$354$	35.9566	1.91107
$355$	5.95397	0.316004
$356$	11.2451	0.595990
$357$	76.6034	4.05428
$358$	12.3883	0.654741
$359$	16.7716	0.885171	0.442586	−	0.896726i	$-0.354061\pi$
$359$	16.7716	0.885171	0.442586	+	0.896726i	$0.354061\pi$
$360$	5.71133	0.301013
$361$	32.8415	1.72850
$362$	−21.1400	−1.11109
$363$	−39.8963	−2.09401
$364$	6.56817	0.344266
$365$	2.42018	0.126678
$366$	16.6296	0.869242
$367$	−2.40021	−0.125290	−0.0626450	−	0.998036i	$-0.519954\pi$
$367$	−2.40021	−0.125290	−0.0626450	+	0.998036i	$0.519954\pi$
$368$	0	0
$369$	−34.8086	−1.81206
$370$	−6.93388	−0.360475
$371$	2.23087	0.115821
$372$	23.0536	1.19527
$373$	−28.6111	−1.48143	−0.740714	−	0.671821i	$-0.765512\pi$
$373$	−28.6111	−1.48143	−0.740714	+	0.671821i	$0.765512\pi$
$374$	38.1826	1.97438
$375$	−2.95150	−0.152415
$376$	3.09948	0.159844
$377$	−5.38580	−0.277383
$378$	−26.9340	−1.38534
$379$	18.3910	0.944684	0.472342	−	0.881415i	$-0.343409\pi$
$379$	18.3910	0.944684	0.472342	+	0.881415i	$0.343409\pi$
$380$	7.20011	0.369358
$381$	9.68672	0.496265
$382$	−21.7623	−1.11346
$383$	−15.3306	−0.783357	−0.391678	−	0.920102i	$-0.628105\pi$
$383$	−15.3306	−0.783357	−0.391678	+	0.920102i	$0.628105\pi$
$384$	−2.95150	−0.150618
$385$	−16.6653	−0.849342
$386$	2.98105	0.151732
$387$	−32.3081	−1.64232
$388$	−3.94553	−0.200304
$389$	−23.8551	−1.20950	−0.604750	−	0.796415i	$-0.706727\pi$
$389$	−23.8551	−1.20950	−0.604750	+	0.796415i	$0.706727\pi$
$390$	−5.75983	−0.291660
$391$	0	0
$392$	4.32800	0.218597
$393$	−18.7114	−0.943868
$394$	−3.93255	−0.198119
$395$	−10.4937	−0.527997
$396$	−28.2796	−1.42110
$397$	5.95585	0.298915	0.149458	−	0.988768i	$-0.452247\pi$
$397$	5.95585	0.298915	0.149458	+	0.988768i	$0.452247\pi$
$398$	−22.8369	−1.14471
$399$	−71.5250	−3.58073
$400$	1.00000	0.0500000
$401$	−21.3411	−1.06572	−0.532861	−	0.846203i	$-0.678883\pi$
$401$	−21.3411	−1.06572	−0.532861	+	0.846203i	$0.678883\pi$
$402$	−23.4241	−1.16829
$403$	−15.2428	−0.759296
$404$	4.03686	0.200841
$405$	6.48528	0.322256
$406$	−9.28879	−0.460995
$407$	34.3331	1.70183
$408$	22.7600	1.12679
$409$	−21.1093	−1.04379	−0.521893	−	0.853011i	$-0.674774\pi$
$409$	−21.1093	−1.04379	−0.521893	+	0.853011i	$0.674774\pi$
$410$	−6.09466	−0.300994
$411$	31.6144	1.55943
$412$	−0.183222	−0.00902670
$413$	−41.0027	−2.01761
$414$	0	0
$415$	2.75983	0.135475
$416$	1.95150	0.0956800
$417$	−32.6659	−1.59966
$418$	−35.6513	−1.74376
$419$	−5.06263	−0.247325	−0.123663	−	0.992324i	$-0.539464\pi$
$419$	−5.06263	−0.247325	−0.123663	+	0.992324i	$0.539464\pi$
$420$	−9.93388	−0.484724
$421$	−12.7849	−0.623096	−0.311548	−	0.950230i	$-0.600848\pi$
$421$	−12.7849	−0.623096	−0.311548	+	0.950230i	$0.600848\pi$
$422$	−17.1044	−0.832630
$423$	17.7022	0.860708
$424$	0.662824	0.0321896
$425$	−7.71133	−0.374054
$426$	−17.5731	−0.851420
$427$	−18.9634	−0.917703
$428$	6.52214	0.315259
$429$	28.5198	1.37695
$430$	−5.65685	−0.272798
$431$	−23.1763	−1.11637	−0.558183	−	0.829718i	$-0.688501\pi$
$431$	−23.1763	−1.11637	−0.558183	+	0.829718i	$0.688501\pi$
$432$	−8.00247	−0.385019
$433$	17.5045	0.841213	0.420607	−	0.907243i	$-0.361817\pi$
$433$	17.5045	0.841213	0.420607	+	0.907243i	$0.361817\pi$
$434$	−26.2889	−1.26191
$435$	8.14563	0.390553
$436$	6.39660	0.306341
$437$	0	0
$438$	−7.14316	−0.341313
$439$	21.0491	1.00462	0.502309	−	0.864688i	$-0.332484\pi$
$439$	21.0491	1.00462	0.502309	+	0.864688i	$0.332484\pi$
$440$	−4.95150	−0.236053
$441$	24.7186	1.17708
$442$	−15.0486	−0.715790
$443$	18.7649	0.891547	0.445774	−	0.895146i	$-0.352929\pi$
$443$	18.7649	0.891547	0.445774	+	0.895146i	$0.352929\pi$
$444$	20.4653	0.971241
$445$	11.2451	0.533069
$446$	13.0074	0.615919
$447$	20.1149	0.951403
$448$	3.36571	0.159015
$449$	1.48763	0.0702058	0.0351029	−	0.999384i	$-0.488824\pi$
$449$	1.48763	0.0702058	0.0351029	+	0.999384i	$0.488824\pi$
$450$	5.71133	0.269235
$451$	30.1777	1.42101
$452$	−11.7090	−0.550744
$453$	−12.5006	−0.587329
$454$	1.95632	0.0918147
$455$	6.56817	0.307920
$456$	−21.2511	−0.995173
$457$	−4.33121	−0.202605	−0.101303	−	0.994856i	$-0.532301\pi$
$457$	−4.33121	−0.202605	−0.101303	+	0.994856i	$0.532301\pi$
$458$	14.6225	0.683263
$459$	61.7097	2.88036
$460$	0	0
$461$	−23.9079	−1.11350	−0.556752	−	0.830679i	$-0.687953\pi$
$461$	−23.9079	−1.11350	−0.556752	+	0.830679i	$0.687953\pi$
$462$	49.1876	2.28841
$463$	5.68177	0.264054	0.132027	−	0.991246i	$-0.457851\pi$
$463$	5.68177	0.264054	0.132027	+	0.991246i	$0.457851\pi$
$464$	−2.75983	−0.128122
$465$	23.0536	1.06908
$466$	−23.1112	−1.07061
$467$	−37.2336	−1.72296	−0.861482	−	0.507787i	$-0.830464\pi$
$467$	−37.2336	−1.72296	−0.861482	+	0.507787i	$0.830464\pi$
$468$	11.1456	0.515207
$469$	26.7114	1.23342
$470$	3.09948	0.142968
$471$	54.4552	2.50916
$472$	−12.1825	−0.560744
$473$	28.0099	1.28790
$474$	30.9722	1.42260
$475$	7.20011	0.330364
$476$	−25.9541	−1.18960
$477$	3.78560	0.173331
$478$	−29.8159	−1.36375
$479$	−22.1341	−1.01133	−0.505666	−	0.862729i	$-0.668753\pi$
$479$	−22.1341	−1.01133	−0.505666	+	0.862729i	$0.668753\pi$
$480$	−2.95150	−0.134717
$481$	−13.5314	−0.616980
$482$	−11.1835	−0.509395
$483$	0	0
$484$	13.5173	0.614423
$485$	−3.94553	−0.179157
$486$	4.86614	0.220732
$487$	2.81033	0.127348	0.0636742	−	0.997971i	$-0.479718\pi$
$487$	2.81033	0.127348	0.0636742	+	0.997971i	$0.479718\pi$
$488$	−5.63429	−0.255052
$489$	−44.1366	−1.99592
$490$	4.32800	0.195519
$491$	14.9423	0.674337	0.337169	−	0.941444i	$-0.390531\pi$
$491$	14.9423	0.674337	0.337169	+	0.941444i	$0.390531\pi$
$492$	17.9884	0.810977
$493$	21.2820	0.958492
$494$	14.0510	0.632183
$495$	−28.2796	−1.27107
$496$	−7.81081	−0.350716
$497$	20.0393	0.898887
$498$	−8.14563	−0.365015
$499$	18.9036	0.846241	0.423120	−	0.906073i	$-0.360935\pi$
$499$	18.9036	0.846241	0.423120	+	0.906073i	$0.360935\pi$
$500$	1.00000	0.0447214
$501$	−14.3349	−0.640438
$502$	1.88640	0.0841940
$503$	6.84049	0.305002	0.152501	−	0.988303i	$-0.451267\pi$
$503$	6.84049	0.305002	0.152501	+	0.988303i	$0.451267\pi$
$504$	19.2227	0.856246
$505$	4.03686	0.179638
$506$	0	0
$507$	27.1292	1.20485
$508$	−3.28197	−0.145614
$509$	−41.3588	−1.83320	−0.916599	−	0.399808i	$-0.869077\pi$
$509$	−41.3588	−1.83320	−0.916599	+	0.399808i	$0.869077\pi$
$510$	22.7600	1.00783
$511$	8.14563	0.360342
$512$	1.00000	0.0441942
$513$	−57.6186	−2.54393
$514$	6.78704	0.299363
$515$	−0.183222	−0.00807373
$516$	16.6962	0.735008
$517$	−15.3471	−0.674963
$518$	−23.3374	−1.02539
$519$	18.3834	0.806944
$520$	1.95150	0.0855788
$521$	0.761711	0.0333711	0.0166856	−	0.999861i	$-0.494689\pi$
$521$	0.761711	0.0333711	0.0166856	+	0.999861i	$0.494689\pi$
$522$	−15.7623	−0.689897
$523$	10.3380	0.452051	0.226025	−	0.974121i	$-0.427427\pi$
$523$	10.3380	0.452051	0.226025	+	0.974121i	$0.427427\pi$
$524$	6.33965	0.276949
$525$	−9.93388	−0.433550
$526$	−15.1777	−0.661778
$527$	60.2317	2.62373
$528$	14.6143	0.636007
$529$	0	0
$530$	0.662824	0.0287912
$531$	−69.5782	−3.01944
$532$	24.2335	1.05065
$533$	−11.8937	−0.515173
$534$	−33.1899	−1.43627
$535$	6.52214	0.281977
$536$	7.93635	0.342798
$537$	−36.5639	−1.57785
$538$	5.26159	0.226843
$539$	−21.4301	−0.923059
$540$	−8.00247	−0.344372
$541$	−7.35365	−0.316158	−0.158079	−	0.987426i	$-0.550530\pi$
$541$	−7.35365	−0.316158	−0.158079	+	0.987426i	$0.550530\pi$
$542$	−4.84519	−0.208119
$543$	62.3945	2.67760
$544$	−7.71133	−0.330620
$545$	6.39660	0.274000
$546$	−19.3859	−0.829641
$547$	2.10866	0.0901597	0.0450798	−	0.998983i	$-0.485646\pi$
$547$	2.10866	0.0901597	0.0450798	+	0.998983i	$0.485646\pi$
$548$	−10.7113	−0.457565
$549$	−32.1793	−1.37338
$550$	−4.95150	−0.211132
$551$	−19.8711	−0.846537
$552$	0	0
$553$	−35.3188	−1.50191
$554$	10.3833	0.441145
$555$	20.4653	0.868704
$556$	11.0676	0.469370
$557$	27.9283	1.18336	0.591680	−	0.806173i	$-0.298465\pi$
$557$	27.9283	1.18336	0.591680	+	0.806173i	$0.298465\pi$
$558$	−44.6101	−1.88850
$559$	−11.0393	−0.466914
$560$	3.36571	0.142227
$561$	−112.696	−4.75802
$562$	−20.4202	−0.861373
$563$	15.8214	0.666793	0.333397	−	0.942787i	$-0.391805\pi$
$563$	15.8214	0.666793	0.333397	+	0.942787i	$0.391805\pi$
$564$	−9.14810	−0.385205
$565$	−11.7090	−0.492600
$566$	25.0478	1.05284
$567$	21.8276	0.916672
$568$	5.95397	0.249823
$569$	1.73039	0.0725419	0.0362710	−	0.999342i	$-0.488452\pi$
$569$	1.73039	0.0725419	0.0362710	+	0.999342i	$0.488452\pi$
$570$	−21.2511	−0.890110
$571$	9.61886	0.402537	0.201268	−	0.979536i	$-0.435494\pi$
$571$	9.61886	0.402537	0.201268	+	0.979536i	$0.435494\pi$
$572$	−9.66282	−0.404023
$573$	64.2314	2.68330
$574$	−20.5128	−0.856189
$575$	0	0
$576$	5.71133	0.237972
$577$	41.0181	1.70761	0.853804	−	0.520595i	$-0.174290\pi$
$577$	41.0181	1.70761	0.853804	+	0.520595i	$0.174290\pi$
$578$	42.4646	1.76629
$579$	−8.79857	−0.365656
$580$	−2.75983	−0.114596
$581$	9.28879	0.385364
$582$	11.6452	0.482709
$583$	−3.28197	−0.135925
$584$	2.42018	0.100148
$585$	11.1456	0.460815
$586$	0.878260	0.0362806
$587$	31.2378	1.28932	0.644661	−	0.764468i	$-0.276998\pi$
$587$	31.2378	1.28932	0.644661	+	0.764468i	$0.276998\pi$
$588$	−12.7741	−0.526794
$589$	−56.2386	−2.31727
$590$	−12.1825	−0.501545
$591$	11.6069	0.477444
$592$	−6.93388	−0.284981
$593$	−19.1432	−0.786115	−0.393058	−	0.919514i	$-0.628583\pi$
$593$	−19.1432	−0.786115	−0.393058	+	0.919514i	$0.628583\pi$
$594$	39.6242	1.62580
$595$	−25.9541	−1.06401
$596$	−6.81516	−0.279160
$597$	67.4029	2.75862
$598$	0	0
$599$	33.1544	1.35465	0.677325	−	0.735684i	$-0.263139\pi$
$599$	33.1544	1.35465	0.677325	+	0.735684i	$0.263139\pi$
$600$	−2.95150	−0.120494
$601$	42.9105	1.75036	0.875179	−	0.483800i	$-0.160744\pi$
$601$	42.9105	1.75036	0.875179	+	0.483800i	$0.160744\pi$
$602$	−19.0393	−0.775985
$603$	45.3271	1.84586
$604$	4.23534	0.172334
$605$	13.5173	0.549557
$606$	−11.9148	−0.484004
$607$	−33.8682	−1.37467	−0.687333	−	0.726342i	$-0.741219\pi$
$607$	−33.8682	−1.37467	−0.687333	+	0.726342i	$0.741219\pi$
$608$	7.20011	0.292003
$609$	27.4158	1.11095
$610$	−5.63429	−0.228126
$611$	6.04862	0.244701
$612$	−44.0419	−1.78029
$613$	16.5458	0.668280	0.334140	−	0.942523i	$-0.391554\pi$
$613$	16.5458	0.668280	0.334140	+	0.942523i	$0.391554\pi$
$614$	32.7391	1.32124
$615$	17.9884	0.725360
$616$	−16.6653	−0.671464
$617$	−10.8759	−0.437848	−0.218924	−	0.975742i	$-0.570255\pi$
$617$	−10.8759	−0.437848	−0.218924	+	0.975742i	$0.570255\pi$
$618$	0.540779	0.0217533
$619$	−35.5531	−1.42900	−0.714501	−	0.699635i	$-0.753346\pi$
$619$	−35.5531	−1.42900	−0.714501	+	0.699635i	$0.753346\pi$
$620$	−7.81081	−0.313690
$621$	0	0
$622$	−29.9079	−1.19920
$623$	37.8478	1.51634
$624$	−5.75983	−0.230578
$625$	1.00000	0.0400000
$626$	1.35044	0.0539746
$627$	105.225	4.20227
$628$	−18.4500	−0.736237
$629$	53.4694	2.13196
$630$	19.2227	0.765849
$631$	40.7413	1.62189	0.810943	−	0.585125i	$-0.198955\pi$
$631$	40.7413	1.62189	0.810943	+	0.585125i	$0.198955\pi$
$632$	−10.4937	−0.417418
$633$	50.4836	2.00654
$634$	−24.8988	−0.988856
$635$	−3.28197	−0.130241
$636$	−1.95632	−0.0775732
$637$	8.44607	0.334646
$638$	13.6653	0.541014
$639$	34.0051	1.34522
$640$	1.00000	0.0395285
$641$	18.8871	0.745996	0.372998	−	0.927832i	$-0.378330\pi$
$641$	18.8871	0.745996	0.372998	+	0.927832i	$0.378330\pi$
$642$	−19.2501	−0.759739
$643$	6.22925	0.245658	0.122829	−	0.992428i	$-0.460803\pi$
$643$	6.22925	0.245658	0.122829	+	0.992428i	$0.460803\pi$
$644$	0	0
$645$	16.6962	0.657412
$646$	−55.5224	−2.18450
$647$	28.3436	1.11430	0.557150	−	0.830412i	$-0.311895\pi$
$647$	28.3436	1.11430	0.557150	+	0.830412i	$0.311895\pi$
$648$	6.48528	0.254766
$649$	60.3215	2.36783
$650$	1.95150	0.0765440
$651$	77.5916	3.04106
$652$	14.9540	0.585643
$653$	22.7182	0.889030	0.444515	−	0.895771i	$-0.353376\pi$
$653$	22.7182	0.889030	0.444515	+	0.895771i	$0.353376\pi$
$654$	−18.8795	−0.738248
$655$	6.33965	0.247711
$656$	−6.09466	−0.237956
$657$	13.8225	0.539265
$658$	10.4320	0.406680
$659$	29.6499	1.15499	0.577497	−	0.816393i	$-0.304029\pi$
$659$	29.6499	1.15499	0.577497	+	0.816393i	$0.304029\pi$
$660$	14.6143	0.568862
$661$	38.6054	1.50158	0.750789	−	0.660543i	$-0.229674\pi$
$661$	38.6054	1.50158	0.750789	+	0.660543i	$0.229674\pi$
$662$	10.8890	0.423213
$663$	44.4160	1.72497
$664$	2.75983	0.107102
$665$	24.2335	0.939733
$666$	−39.6016	−1.53453
$667$	0	0
$668$	4.85684	0.187917
$669$	−38.3913	−1.48429
$670$	7.93635	0.306608
$671$	27.8982	1.07700
$672$	−9.93388	−0.383208
$673$	−22.2495	−0.857654	−0.428827	−	0.903387i	$-0.641073\pi$
$673$	−22.2495	−0.857654	−0.428827	+	0.903387i	$0.641073\pi$
$674$	0.122045	0.00470098
$675$	−8.00247	−0.308015
$676$	−9.19166	−0.353526
$677$	−22.3728	−0.859858	−0.429929	−	0.902863i	$-0.641461\pi$
$677$	−22.3728	−0.859858	−0.429929	+	0.902863i	$0.641461\pi$
$678$	34.5590	1.32723
$679$	−13.2795	−0.509620
$680$	−7.71133	−0.295716
$681$	−5.77407	−0.221263
$682$	38.6752	1.48095
$683$	−38.3816	−1.46863	−0.734315	−	0.678809i	$-0.762496\pi$
$683$	−38.3816	−1.46863	−0.734315	+	0.678809i	$0.762496\pi$
$684$	41.1222	1.57235
$685$	−10.7113	−0.409259
$686$	−8.99318	−0.343361
$687$	−43.1582	−1.64659
$688$	−5.65685	−0.215666
$689$	1.29350	0.0492783
$690$	0	0
$691$	−0.937374	−0.0356594	−0.0178297	−	0.999841i	$-0.505676\pi$
$691$	−0.937374	−0.0356594	−0.0178297	+	0.999841i	$0.505676\pi$
$692$	−6.22852	−0.236773
$693$	−95.1810	−3.61563
$694$	10.0141	0.380131
$695$	11.0676	0.419817
$696$	8.14563	0.308759
$697$	46.9979	1.78017
$698$	−30.7551	−1.16410
$699$	68.2128	2.58004
$700$	3.36571	0.127212
$701$	−22.6028	−0.853696	−0.426848	−	0.904323i	$-0.640376\pi$
$701$	−22.6028	−0.853696	−0.426848	+	0.904323i	$0.640376\pi$
$702$	−15.6168	−0.589418
$703$	−49.9247	−1.88294
$704$	−4.95150	−0.186617
$705$	−9.14810	−0.344538
$706$	24.3232	0.915415
$707$	13.5869	0.510987
$708$	35.9566	1.35133
$709$	−40.5746	−1.52381	−0.761905	−	0.647689i	$-0.775736\pi$
$709$	−40.5746	−1.52381	−0.761905	+	0.647689i	$0.775736\pi$
$710$	5.95397	0.223448
$711$	−59.9331	−2.24767
$712$	11.2451	0.421428
$713$	0	0
$714$	76.6034	2.86681
$715$	−9.66282	−0.361369
$716$	12.3883	0.462972
$717$	88.0014	3.28647
$718$	16.7716	0.625911
$719$	47.0823	1.75587	0.877937	−	0.478777i	$-0.158920\pi$
$719$	47.0823	1.75587	0.877937	+	0.478777i	$0.158920\pi$
$720$	5.71133	0.212849
$721$	−0.616672	−0.0229661
$722$	32.8415	1.22223
$723$	33.0081	1.22758
$724$	−21.1400	−0.785660
$725$	−2.75983	−0.102498
$726$	−39.8963	−1.48069
$727$	41.1305	1.52545	0.762723	−	0.646726i	$-0.223862\pi$
$727$	41.1305	1.52545	0.762723	+	0.646726i	$0.223862\pi$
$728$	6.56817	0.243432
$729$	−33.8182	−1.25253
$730$	2.42018	0.0895750
$731$	43.6219	1.61341
$732$	16.6296	0.614647
$733$	10.4807	0.387115	0.193558	−	0.981089i	$-0.437997\pi$
$733$	10.4807	0.387115	0.193558	+	0.981089i	$0.437997\pi$
$734$	−2.40021	−0.0885934
$735$	−12.7741	−0.471179
$736$	0	0
$737$	−39.2968	−1.44752
$738$	−34.8086	−1.28132
$739$	−5.80965	−0.213711	−0.106856	−	0.994275i	$-0.534078\pi$
$739$	−5.80965	−0.213711	−0.106856	+	0.994275i	$0.534078\pi$
$740$	−6.93388	−0.254894
$741$	−41.4714	−1.52349
$742$	2.23087	0.0818979
$743$	23.8440	0.874751	0.437376	−	0.899279i	$-0.355908\pi$
$743$	23.8440	0.874751	0.437376	+	0.899279i	$0.355908\pi$
$744$	23.0536	0.845185
$745$	−6.81516	−0.249688
$746$	−28.6111	−1.04753
$747$	15.7623	0.576713
$748$	38.1826	1.39609
$749$	21.9516	0.802095
$750$	−2.95150	−0.107773
$751$	−48.2694	−1.76138	−0.880688	−	0.473697i	$-0.842919\pi$
$751$	−48.2694	−1.76138	−0.880688	+	0.473697i	$0.842919\pi$
$752$	3.09948	0.113026
$753$	−5.56769	−0.202898
$754$	−5.38580	−0.196139
$755$	4.23534	0.154140
$756$	−26.9340	−0.979580
$757$	−12.2381	−0.444801	−0.222401	−	0.974955i	$-0.571389\pi$
$757$	−12.2381	−0.444801	−0.222401	+	0.974955i	$0.571389\pi$
$758$	18.3910	0.667992
$759$	0	0
$760$	7.20011	0.261175
$761$	38.4165	1.39260	0.696299	−	0.717752i	$-0.254829\pi$
$761$	38.4165	1.39260	0.696299	+	0.717752i	$0.254829\pi$
$762$	9.68672	0.350913
$763$	21.5291	0.779405
$764$	−21.7623	−0.787333
$765$	−44.0419	−1.59234
$766$	−15.3306	−0.553917
$767$	−23.7741	−0.858432
$768$	−2.95150	−0.106503
$769$	−27.2890	−0.984065	−0.492033	−	0.870577i	$-0.663746\pi$
$769$	−27.2890	−0.984065	−0.492033	+	0.870577i	$0.663746\pi$
$770$	−16.6653	−0.600576
$771$	−20.0319	−0.721432
$772$	2.98105	0.107290
$773$	−1.69226	−0.0608664	−0.0304332	−	0.999537i	$-0.509689\pi$
$773$	−1.69226	−0.0608664	−0.0304332	+	0.999537i	$0.509689\pi$
$774$	−32.3081	−1.16129
$775$	−7.81081	−0.280573
$776$	−3.94553	−0.141636
$777$	68.8803	2.47107
$778$	−23.8551	−0.855246
$779$	−43.8822	−1.57224
$780$	−5.75983	−0.206235
$781$	−29.4810	−1.05491
$782$	0	0
$783$	22.0855	0.789271
$784$	4.32800	0.154571
$785$	−18.4500	−0.658510
$786$	−18.7114	−0.667415
$787$	−19.3673	−0.690369	−0.345184	−	0.938535i	$-0.612184\pi$
$787$	−19.3673	−0.690369	−0.345184	+	0.938535i	$0.612184\pi$
$788$	−3.93255	−0.140091
$789$	44.7968	1.59481
$790$	−10.4937	−0.373350
$791$	−39.4090	−1.40122
$792$	−28.2796	−1.00487
$793$	−10.9953	−0.390454
$794$	5.95585	0.211365
$795$	−1.95632	−0.0693836
$796$	−22.8369	−0.809431
$797$	28.3833	1.00539	0.502695	−	0.864464i	$-0.332342\pi$
$797$	28.3833	1.00539	0.502695	+	0.864464i	$0.332342\pi$
$798$	−71.5250	−2.53196
$799$	−23.9011	−0.845561
$800$	1.00000	0.0353553
$801$	64.2245	2.26926
$802$	−21.3411	−0.753580
$803$	−11.9835	−0.422889
$804$	−23.4241	−0.826104
$805$	0	0
$806$	−15.2428	−0.536903
$807$	−15.5296	−0.546666
$808$	4.03686	0.142016
$809$	−35.5223	−1.24890	−0.624448	−	0.781066i	$-0.714676\pi$
$809$	−35.5223	−1.24890	−0.624448	+	0.781066i	$0.714676\pi$
$810$	6.48528	0.227870
$811$	8.79481	0.308827	0.154414	−	0.988006i	$-0.450651\pi$
$811$	8.79481	0.308827	0.154414	+	0.988006i	$0.450651\pi$
$812$	−9.28879	−0.325973
$813$	14.3006	0.501543
$814$	34.3331	1.20337
$815$	14.9540	0.523815
$816$	22.7600	0.796758
$817$	−40.7299	−1.42496
$818$	−21.1093	−0.738068
$819$	37.5130	1.31081
$820$	−6.09466	−0.212835
$821$	26.6328	0.929491	0.464745	−	0.885444i	$-0.346146\pi$
$821$	26.6328	0.929491	0.464745	+	0.885444i	$0.346146\pi$
$822$	31.6144	1.10268
$823$	4.49023	0.156519	0.0782597	−	0.996933i	$-0.475064\pi$
$823$	4.49023	0.156519	0.0782597	+	0.996933i	$0.475064\pi$
$824$	−0.183222	−0.00638284
$825$	14.6143	0.508805
$826$	−41.0027	−1.42667
$827$	29.5578	1.02783	0.513913	−	0.857843i	$-0.328196\pi$
$827$	29.5578	1.02783	0.513913	+	0.857843i	$0.328196\pi$
$828$	0	0
$829$	−31.9176	−1.10854	−0.554272	−	0.832336i	$-0.687003\pi$
$829$	−31.9176	−1.10854	−0.554272	+	0.832336i	$0.687003\pi$
$830$	2.75983	0.0957952
$831$	−30.6463	−1.06311
$832$	1.95150	0.0676559
$833$	−33.3746	−1.15636
$834$	−32.6659	−1.13113
$835$	4.85684	0.168078
$836$	−35.6513	−1.23303
$837$	62.5058	2.16052
$838$	−5.06263	−0.174886
$839$	−24.2476	−0.837120	−0.418560	−	0.908189i	$-0.637465\pi$
$839$	−24.2476	−0.837120	−0.418560	+	0.908189i	$0.637465\pi$
$840$	−9.93388	−0.342751
$841$	−21.3833	−0.737356
$842$	−12.7849	−0.440596
$843$	60.2701	2.07581
$844$	−17.1044	−0.588759
$845$	−9.19166	−0.316203
$846$	17.7022	0.608612
$847$	45.4953	1.56324
$848$	0.662824	0.0227615
$849$	−73.9284	−2.53722
$850$	−7.71133	−0.264496
$851$	0	0
$852$	−17.5731	−0.602045
$853$	17.7292	0.607037	0.303519	−	0.952825i	$-0.401839\pi$
$853$	17.7292	0.607037	0.303519	+	0.952825i	$0.401839\pi$
$854$	−18.9634	−0.648914
$855$	41.1222	1.40635
$856$	6.52214	0.222922
$857$	39.9613	1.36505	0.682525	−	0.730862i	$-0.260882\pi$
$857$	39.9613	1.36505	0.682525	+	0.730862i	$0.260882\pi$
$858$	28.5198	0.973649
$859$	−43.5887	−1.48723	−0.743613	−	0.668610i	$-0.766890\pi$
$859$	−43.5887	−1.48723	−0.743613	+	0.668610i	$0.766890\pi$
$860$	−5.65685	−0.192897
$861$	60.5436	2.06332
$862$	−23.1763	−0.789390
$863$	0.862625	0.0293641	0.0146821	−	0.999892i	$-0.495326\pi$
$863$	0.862625	0.0293641	0.0146821	+	0.999892i	$0.495326\pi$
$864$	−8.00247	−0.272250
$865$	−6.22852	−0.211776
$866$	17.5045	0.594828
$867$	−125.334	−4.25657
$868$	−26.2889	−0.892304
$869$	51.9596	1.76261
$870$	8.14563	0.276163
$871$	15.4878	0.524783
$872$	6.39660	0.216616
$873$	−22.5342	−0.762667
$874$	0	0
$875$	3.36571	0.113782
$876$	−7.14316	−0.241345
$877$	40.7420	1.37576	0.687881	−	0.725824i	$-0.258541\pi$
$877$	40.7420	1.37576	0.687881	+	0.725824i	$0.258541\pi$
$878$	21.0491	0.710373
$879$	−2.59218	−0.0874321
$880$	−4.95150	−0.166915
$881$	−4.59194	−0.154706	−0.0773532	−	0.997004i	$-0.524647\pi$
$881$	−4.59194	−0.154706	−0.0773532	+	0.997004i	$0.524647\pi$
$882$	24.7186	0.832319
$883$	−28.5473	−0.960695	−0.480347	−	0.877078i	$-0.659489\pi$
$883$	−28.5473	−0.960695	−0.480347	+	0.877078i	$0.659489\pi$
$884$	−15.0486	−0.506140
$885$	35.9566	1.20867
$886$	18.7649	0.630419
$887$	41.0783	1.37927	0.689637	−	0.724155i	$-0.257770\pi$
$887$	41.0783	1.37927	0.689637	+	0.724155i	$0.257770\pi$
$888$	20.4653	0.686771
$889$	−11.0462	−0.370476
$890$	11.2451	0.376937
$891$	−32.1118	−1.07579
$892$	13.0074	0.435521
$893$	22.3166	0.746796
$894$	20.1149	0.672743
$895$	12.3883	0.414094
$896$	3.36571	0.112440
$897$	0	0
$898$	1.48763	0.0496430
$899$	21.5565	0.718950
$900$	5.71133	0.190378
$901$	−5.11125	−0.170280
$902$	30.1777	1.00481
$903$	56.1945	1.87004
$904$	−11.7090	−0.389435
$905$	−21.1400	−0.702716
$906$	−12.5006	−0.415305
$907$	0.330168	0.0109631	0.00548153	−	0.999985i	$-0.498255\pi$
$907$	0.330168	0.0109631	0.00548153	+	0.999985i	$0.498255\pi$
$908$	1.95632	0.0649228
$909$	23.0558	0.764713
$910$	6.56817	0.217733
$911$	−42.5708	−1.41043	−0.705216	−	0.708992i	$-0.749150\pi$
$911$	−42.5708	−1.41043	−0.705216	+	0.708992i	$0.749150\pi$
$912$	−21.2511	−0.703694
$913$	−13.6653	−0.452255
$914$	−4.33121	−0.143264
$915$	16.6296	0.549757
$916$	14.6225	0.483140
$917$	21.3374	0.704624
$918$	61.7097	2.03672
$919$	13.0573	0.430719	0.215359	−	0.976535i	$-0.430908\pi$
$919$	13.0573	0.430719	0.215359	+	0.976535i	$0.430908\pi$
$920$	0	0
$921$	−96.6294	−3.18405
$922$	−23.9079	−0.787366
$923$	11.6191	0.382449
$924$	49.1876	1.61815
$925$	−6.93388	−0.227984
$926$	5.68177	0.186715
$927$	−1.04644	−0.0343696
$928$	−2.75983	−0.0905959
$929$	3.53802	0.116079	0.0580393	−	0.998314i	$-0.481515\pi$
$929$	3.53802	0.116079	0.0580393	+	0.998314i	$0.481515\pi$
$930$	23.0536	0.755956
$931$	31.1621	1.02130
$932$	−23.1112	−0.757034
$933$	88.2732	2.88993
$934$	−37.2336	−1.21832
$935$	38.1826	1.24870
$936$	11.1456	0.364306
$937$	−41.1284	−1.34361	−0.671804	−	0.740729i	$-0.734480\pi$
$937$	−41.1284	−1.34361	−0.671804	+	0.740729i	$0.734480\pi$
$938$	26.7114	0.872160
$939$	−3.98583	−0.130073
$940$	3.09948	0.101094
$941$	20.5245	0.669079	0.334540	−	0.942382i	$-0.391419\pi$
$941$	20.5245	0.669079	0.334540	+	0.942382i	$0.391419\pi$
$942$	54.4552	1.77425
$943$	0	0
$944$	−12.1825	−0.396506
$945$	−26.9340	−0.876163
$946$	28.0099	0.910680
$947$	−43.0463	−1.39882	−0.699408	−	0.714723i	$-0.746553\pi$
$947$	−43.0463	−1.39882	−0.699408	+	0.714723i	$0.746553\pi$
$948$	30.9722	1.00593
$949$	4.72298	0.153314
$950$	7.20011	0.233602
$951$	73.4886	2.38303
$952$	−25.9541	−0.841177
$953$	−14.0160	−0.454023	−0.227011	−	0.973892i	$-0.572895\pi$
$953$	−14.0160	−0.454023	−0.227011	+	0.973892i	$0.572895\pi$
$954$	3.78560	0.122563
$955$	−21.7623	−0.704212
$956$	−29.8159	−0.964314
$957$	−40.3331	−1.30378
$958$	−22.1341	−0.715120
$959$	−36.0512	−1.16415
$960$	−2.95150	−0.0952591
$961$	30.0087	0.968024
$962$	−13.5314	−0.436271
$963$	37.2501	1.20037
$964$	−11.1835	−0.360197
$965$	2.98105	0.0959635
$966$	0	0
$967$	33.3567	1.07268	0.536340	−	0.844002i	$-0.319807\pi$
$967$	33.3567	1.07268	0.536340	+	0.844002i	$0.319807\pi$
$968$	13.5173	0.434463
$969$	163.874	5.26439
$970$	−3.94553	−0.126683
$971$	23.9122	0.767378	0.383689	−	0.923462i	$-0.374653\pi$
$971$	23.9122	0.767378	0.383689	+	0.923462i	$0.374653\pi$
$972$	4.86614	0.156081
$973$	37.2502	1.19419
$974$	2.81033	0.0900489
$975$	−5.75983	−0.184462
$976$	−5.63429	−0.180349
$977$	35.2986	1.12930	0.564651	−	0.825330i	$-0.309011\pi$
$977$	35.2986	1.12930	0.564651	+	0.825330i	$0.309011\pi$
$978$	−44.1366	−1.41133
$979$	−55.6801	−1.77954
$980$	4.32800	0.138253
$981$	36.5331	1.16641
$982$	14.9423	0.476829
$983$	3.36697	0.107390	0.0536949	−	0.998557i	$-0.482900\pi$
$983$	3.36697	0.107390	0.0536949	+	0.998557i	$0.482900\pi$
$984$	17.9884	0.573448
$985$	−3.93255	−0.125301
$986$	21.2820	0.677756
$987$	−30.7899	−0.980052
$988$	14.0510	0.447021
$989$	0	0
$990$	−28.2796	−0.898785
$991$	4.70227	0.149373	0.0746863	−	0.997207i	$-0.476204\pi$
$991$	4.70227	0.149373	0.0746863	+	0.997207i	$0.476204\pi$
$992$	−7.81081	−0.247993
$993$	−32.1388	−1.01989
$994$	20.0393	0.635609
$995$	−22.8369	−0.723977
$996$	−8.14563	−0.258104
$997$	33.8441	1.07185	0.535927	−	0.844264i	$-0.319962\pi$
$997$	33.8441	1.07185	0.535927	+	0.844264i	$0.319962\pi$
$998$	18.9036	0.598383
$999$	55.4882	1.75557

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.95150 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.95150 q^{6} +3.36571 q^{7} +1.00000 q^{8} +5.71133 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.95150 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.95150 q^{6} +3.36571 q^{7} +1.00000 q^{8} +5.71133 q^{9} +1.00000 q^{10} -4.95150 q^{11} -2.95150 q^{12} +1.95150 q^{13} +3.36571 q^{14} -2.95150 q^{15} +1.00000 q^{16} -7.71133 q^{17} +5.71133 q^{18} +7.20011 q^{19} +1.00000 q^{20} -9.93388 q^{21} -4.95150 q^{22} -2.95150 q^{24} +1.00000 q^{25} +1.95150 q^{26} -8.00247 q^{27} +3.36571 q^{28} -2.75983 q^{29} -2.95150 q^{30} -7.81081 q^{31} +1.00000 q^{32} +14.6143 q^{33} -7.71133 q^{34} +3.36571 q^{35} +5.71133 q^{36} -6.93388 q^{37} +7.20011 q^{38} -5.75983 q^{39} +1.00000 q^{40} -6.09466 q^{41} -9.93388 q^{42} -5.65685 q^{43} -4.95150 q^{44} +5.71133 q^{45} +3.09948 q^{47} -2.95150 q^{48} +4.32800 q^{49} +1.00000 q^{50} +22.7600 q^{51} +1.95150 q^{52} +0.662824 q^{53} -8.00247 q^{54} -4.95150 q^{55} +3.36571 q^{56} -21.2511 q^{57} -2.75983 q^{58} -12.1825 q^{59} -2.95150 q^{60} -5.63429 q^{61} -7.81081 q^{62} +19.2227 q^{63} +1.00000 q^{64} +1.95150 q^{65} +14.6143 q^{66} +7.93635 q^{67} -7.71133 q^{68} +3.36571 q^{70} +5.95397 q^{71} +5.71133 q^{72} +2.42018 q^{73} -6.93388 q^{74} -2.95150 q^{75} +7.20011 q^{76} -16.6653 q^{77} -5.75983 q^{78} -10.4937 q^{79} +1.00000 q^{80} +6.48528 q^{81} -6.09466 q^{82} +2.75983 q^{83} -9.93388 q^{84} -7.71133 q^{85} -5.65685 q^{86} +8.14563 q^{87} -4.95150 q^{88} +11.2451 q^{89} +5.71133 q^{90} +6.56817 q^{91} +23.0536 q^{93} +3.09948 q^{94} +7.20011 q^{95} -2.95150 q^{96} -3.94553 q^{97} +4.32800 q^{98} -28.2796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 4 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 4 q^{16} - 14 q^{17} + 6 q^{18} - 2 q^{19} + 4 q^{20} - 20 q^{21} - 10 q^{22} - 2 q^{24} + 4 q^{25} - 2 q^{26} - 8 q^{27} - 2 q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} + 4 q^{32} + 22 q^{33} - 14 q^{34} - 2 q^{35} + 6 q^{36} - 8 q^{37} - 2 q^{38} - 16 q^{39} + 4 q^{40} - 2 q^{41} - 20 q^{42} - 10 q^{44} + 6 q^{45} + 8 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{50} + 18 q^{51} - 2 q^{52} - 24 q^{53} - 8 q^{54} - 10 q^{55} - 2 q^{56} - 40 q^{57} - 4 q^{58} - 8 q^{59} - 2 q^{60} - 38 q^{61} - 10 q^{62} + 8 q^{63} + 4 q^{64} - 2 q^{65} + 22 q^{66} - 12 q^{67} - 14 q^{68} - 2 q^{70} - 10 q^{71} + 6 q^{72} - 8 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 16 q^{78} + 20 q^{79} + 4 q^{80} - 8 q^{81} - 2 q^{82} + 4 q^{83} - 20 q^{84} - 14 q^{85} - 4 q^{87} - 10 q^{88} + 4 q^{89} + 6 q^{90} + 22 q^{91} - 12 q^{93} + 8 q^{94} - 2 q^{95} - 2 q^{96} - 10 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 4 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 4 * q^16 - 14 * q^17 + 6 * q^18 - 2 * q^19 + 4 * q^20 - 20 * q^21 - 10 * q^22 - 2 * q^24 + 4 * q^25 - 2 * q^26 - 8 * q^27 - 2 * q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 + 4 * q^32 + 22 * q^33 - 14 * q^34 - 2 * q^35 + 6 * q^36 - 8 * q^37 - 2 * q^38 - 16 * q^39 + 4 * q^40 - 2 * q^41 - 20 * q^42 - 10 * q^44 + 6 * q^45 + 8 * q^47 - 2 * q^48 + 6 * q^49 + 4 * q^50 + 18 * q^51 - 2 * q^52 - 24 * q^53 - 8 * q^54 - 10 * q^55 - 2 * q^56 - 40 * q^57 - 4 * q^58 - 8 * q^59 - 2 * q^60 - 38 * q^61 - 10 * q^62 + 8 * q^63 + 4 * q^64 - 2 * q^65 + 22 * q^66 - 12 * q^67 - 14 * q^68 - 2 * q^70 - 10 * q^71 + 6 * q^72 - 8 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 16 * q^78 + 20 * q^79 + 4 * q^80 - 8 * q^81 - 2 * q^82 + 4 * q^83 - 20 * q^84 - 14 * q^85 - 4 * q^87 - 10 * q^88 + 4 * q^89 + 6 * q^90 + 22 * q^91 - 12 * q^93 + 8 * q^94 - 2 * q^95 - 2 * q^96 - 10 * q^97 + 6 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more