LMFDB - Embedded newform 5290.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			1.2
Root			$1.73205$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{6} +2.73205 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{6} +2.73205 q^{7} -1.00000 q^{8} -1.00000 q^{10} -5.46410 q^{11} +1.73205 q^{12} +5.46410 q^{13} -2.73205 q^{14} +1.73205 q^{15} +1.00000 q^{16} -6.46410 q^{17} -3.73205 q^{19} +1.00000 q^{20} +4.73205 q^{21} +5.46410 q^{22} -1.73205 q^{24} +1.00000 q^{25} -5.46410 q^{26} -5.19615 q^{27} +2.73205 q^{28} -4.73205 q^{29} -1.73205 q^{30} -5.26795 q^{31} -1.00000 q^{32} -9.46410 q^{33} +6.46410 q^{34} +2.73205 q^{35} -3.46410 q^{37} +3.73205 q^{38} +9.46410 q^{39} -1.00000 q^{40} +9.46410 q^{41} -4.73205 q^{42} -5.92820 q^{43} -5.46410 q^{44} -13.1244 q^{47} +1.73205 q^{48} +0.464102 q^{49} -1.00000 q^{50} -11.1962 q^{51} +5.46410 q^{52} +4.73205 q^{53} +5.19615 q^{54} -5.46410 q^{55} -2.73205 q^{56} -6.46410 q^{57} +4.73205 q^{58} -7.00000 q^{59} +1.73205 q^{60} +2.92820 q^{61} +5.26795 q^{62} +1.00000 q^{64} +5.46410 q^{65} +9.46410 q^{66} -7.92820 q^{67} -6.46410 q^{68} -2.73205 q^{70} +15.1244 q^{71} -1.73205 q^{73} +3.46410 q^{74} +1.73205 q^{75} -3.73205 q^{76} -14.9282 q^{77} -9.46410 q^{78} -1.26795 q^{79} +1.00000 q^{80} -9.00000 q^{81} -9.46410 q^{82} -17.9282 q^{83} +4.73205 q^{84} -6.46410 q^{85} +5.92820 q^{86} -8.19615 q^{87} +5.46410 q^{88} +4.53590 q^{89} +14.9282 q^{91} -9.12436 q^{93} +13.1244 q^{94} -3.73205 q^{95} -1.73205 q^{96} +14.9282 q^{97} -0.464102 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} - 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 2 q^{16} - 6 q^{17} - 4 q^{19} + 2 q^{20} + 6 q^{21} + 4 q^{22} + 2 q^{25} - 4 q^{26} + 2 q^{28} - 6 q^{29} - 14 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} + 2 q^{35} + 4 q^{38} + 12 q^{39} - 2 q^{40} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} - 2 q^{47} - 6 q^{49} - 2 q^{50} - 12 q^{51} + 4 q^{52} + 6 q^{53} - 4 q^{55} - 2 q^{56} - 6 q^{57} + 6 q^{58} - 14 q^{59} - 8 q^{61} + 14 q^{62} + 2 q^{64} + 4 q^{65} + 12 q^{66} - 2 q^{67} - 6 q^{68} - 2 q^{70} + 6 q^{71} - 4 q^{76} - 16 q^{77} - 12 q^{78} - 6 q^{79} + 2 q^{80} - 18 q^{81} - 12 q^{82} - 22 q^{83} + 6 q^{84} - 6 q^{85} - 2 q^{86} - 6 q^{87} + 4 q^{88} + 16 q^{89} + 16 q^{91} + 6 q^{93} + 2 q^{94} - 4 q^{95} + 16 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 - 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 2 * q^16 - 6 * q^17 - 4 * q^19 + 2 * q^20 + 6 * q^21 + 4 * q^22 + 2 * q^25 - 4 * q^26 + 2 * q^28 - 6 * q^29 - 14 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 + 2 * q^35 + 4 * q^38 + 12 * q^39 - 2 * q^40 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 - 2 * q^47 - 6 * q^49 - 2 * q^50 - 12 * q^51 + 4 * q^52 + 6 * q^53 - 4 * q^55 - 2 * q^56 - 6 * q^57 + 6 * q^58 - 14 * q^59 - 8 * q^61 + 14 * q^62 + 2 * q^64 + 4 * q^65 + 12 * q^66 - 2 * q^67 - 6 * q^68 - 2 * q^70 + 6 * q^71 - 4 * q^76 - 16 * q^77 - 12 * q^78 - 6 * q^79 + 2 * q^80 - 18 * q^81 - 12 * q^82 - 22 * q^83 + 6 * q^84 - 6 * q^85 - 2 * q^86 - 6 * q^87 + 4 * q^88 + 16 * q^89 + 16 * q^91 + 6 * q^93 + 2 * q^94 - 4 * q^95 + 16 * q^97 + 6 * q^98

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
$3$	1.73205	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.73205	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.73205	−0.707107
$7$	2.73205	1.03262	0.516309	−	0.856402i	$-0.327306\pi$
$7$	2.73205	1.03262	0.516309	+	0.856402i	$0.327306\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	−5.46410	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$12$	1.73205	0.500000
$13$	5.46410	1.51547	0.757735	−	0.652563i	$-0.226306\pi$
$13$	5.46410	1.51547	0.757735	+	0.652563i	$0.226306\pi$
$14$	−2.73205	−0.730171
$15$	1.73205	0.447214
$16$	1.00000	0.250000
$17$	−6.46410	−1.56777	−0.783887	−	0.620903i	$-0.786766\pi$
$17$	−6.46410	−1.56777	−0.783887	+	0.620903i	$0.786766\pi$
$18$	0	0
$19$	−3.73205	−0.856191	−0.428096	−	0.903733i	$-0.640815\pi$
$19$	−3.73205	−0.856191	−0.428096	+	0.903733i	$0.640815\pi$
$20$	1.00000	0.223607
$21$	4.73205	1.03262
$22$	5.46410	1.16495
$23$	0	0
$23$	0	0
$24$	−1.73205	−0.353553
$25$	1.00000	0.200000
$26$	−5.46410	−1.07160
$27$	−5.19615	−1.00000
$28$	2.73205	0.516309
$29$	−4.73205	−0.878720	−0.439360	−	0.898311i	$-0.644795\pi$
$29$	−4.73205	−0.878720	−0.439360	+	0.898311i	$0.644795\pi$
$30$	−1.73205	−0.316228
$31$	−5.26795	−0.946152	−0.473076	−	0.881022i	$-0.656856\pi$
$31$	−5.26795	−0.946152	−0.473076	+	0.881022i	$0.656856\pi$
$32$	−1.00000	−0.176777
$33$	−9.46410	−1.64749
$34$	6.46410	1.10858
$35$	2.73205	0.461801
$36$	0	0
$37$	−3.46410	−0.569495	−0.284747	−	0.958603i	$-0.591910\pi$
$37$	−3.46410	−0.569495	−0.284747	+	0.958603i	$0.591910\pi$
$38$	3.73205	0.605419
$39$	9.46410	1.51547
$40$	−1.00000	−0.158114
$41$	9.46410	1.47804	0.739022	−	0.673681i	$-0.235288\pi$
$41$	9.46410	1.47804	0.739022	+	0.673681i	$0.235288\pi$
$42$	−4.73205	−0.730171
$43$	−5.92820	−0.904043	−0.452021	−	0.892007i	$-0.649297\pi$
$43$	−5.92820	−0.904043	−0.452021	+	0.892007i	$0.649297\pi$
$44$	−5.46410	−0.823744
$45$	0	0
$46$	0	0
$47$	−13.1244	−1.91438	−0.957192	−	0.289454i	$-0.906526\pi$
$47$	−13.1244	−1.91438	−0.957192	+	0.289454i	$0.906526\pi$
$48$	1.73205	0.250000
$49$	0.464102	0.0663002
$50$	−1.00000	−0.141421
$51$	−11.1962	−1.56777
$52$	5.46410	0.757735
$53$	4.73205	0.649997	0.324999	−	0.945715i	$-0.394636\pi$
$53$	4.73205	0.649997	0.324999	+	0.945715i	$0.394636\pi$
$54$	5.19615	0.707107
$55$	−5.46410	−0.736779
$56$	−2.73205	−0.365086
$57$	−6.46410	−0.856191
$58$	4.73205	0.621349
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	1.73205	0.223607
$61$	2.92820	0.374918	0.187459	−	0.982272i	$-0.439975\pi$
$61$	2.92820	0.374918	0.187459	+	0.982272i	$0.439975\pi$
$62$	5.26795	0.669030
$63$	0	0
$64$	1.00000	0.125000
$65$	5.46410	0.677738
$66$	9.46410	1.16495
$67$	−7.92820	−0.968584	−0.484292	−	0.874906i	$-0.660923\pi$
$67$	−7.92820	−0.968584	−0.484292	+	0.874906i	$0.660923\pi$
$68$	−6.46410	−0.783887
$69$	0	0
$70$	−2.73205	−0.326543
$71$	15.1244	1.79493	0.897465	−	0.441085i	$-0.145406\pi$
$71$	15.1244	1.79493	0.897465	+	0.441085i	$0.145406\pi$
$72$	0	0
$73$	−1.73205	−0.202721	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−1.73205	−0.202721	−0.101361	+	0.994850i	$0.532320\pi$
$74$	3.46410	0.402694
$75$	1.73205	0.200000
$76$	−3.73205	−0.428096
$77$	−14.9282	−1.70123
$78$	−9.46410	−1.07160
$79$	−1.26795	−0.142655	−0.0713277	−	0.997453i	$-0.522724\pi$
$79$	−1.26795	−0.142655	−0.0713277	+	0.997453i	$0.522724\pi$
$80$	1.00000	0.111803
$81$	−9.00000	−1.00000
$82$	−9.46410	−1.04514
$83$	−17.9282	−1.96788	−0.983938	−	0.178511i	$-0.942872\pi$
$83$	−17.9282	−1.96788	−0.983938	+	0.178511i	$0.942872\pi$
$84$	4.73205	0.516309
$85$	−6.46410	−0.701130
$86$	5.92820	0.639255
$87$	−8.19615	−0.878720
$88$	5.46410	0.582475
$89$	4.53590	0.480804	0.240402	−	0.970673i	$-0.422721\pi$
$89$	4.53590	0.480804	0.240402	+	0.970673i	$0.422721\pi$
$90$	0	0
$91$	14.9282	1.56490
$92$	0	0
$93$	−9.12436	−0.946152
$94$	13.1244	1.35367
$95$	−3.73205	−0.382900
$96$	−1.73205	−0.176777
$97$	14.9282	1.51573	0.757865	−	0.652412i	$-0.226243\pi$
$97$	14.9282	1.51573	0.757865	+	0.652412i	$0.226243\pi$
$98$	−0.464102	−0.0468813
$99$	0	0
$100$	1.00000	0.100000
$101$	−6.92820	−0.689382	−0.344691	−	0.938716i	$-0.612016\pi$
$101$	−6.92820	−0.689382	−0.344691	+	0.938716i	$0.612016\pi$
$102$	11.1962	1.10858
$103$	3.46410	0.341328	0.170664	−	0.985329i	$-0.445409\pi$
$103$	3.46410	0.341328	0.170664	+	0.985329i	$0.445409\pi$
$104$	−5.46410	−0.535799
$105$	4.73205	0.461801
$106$	−4.73205	−0.459617
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	−5.19615	−0.500000
$109$	1.80385	0.172777	0.0863886	−	0.996262i	$-0.472467\pi$
$109$	1.80385	0.172777	0.0863886	+	0.996262i	$0.472467\pi$
$110$	5.46410	0.520982
$111$	−6.00000	−0.569495
$112$	2.73205	0.258155
$113$	−0.464102	−0.0436590	−0.0218295	−	0.999762i	$-0.506949\pi$
$113$	−0.464102	−0.0436590	−0.0218295	+	0.999762i	$0.506949\pi$
$114$	6.46410	0.605419
$115$	0	0
$116$	−4.73205	−0.439360
$117$	0	0
$118$	7.00000	0.644402
$119$	−17.6603	−1.61891
$120$	−1.73205	−0.158114
$121$	18.8564	1.71422
$122$	−2.92820	−0.265107
$123$	16.3923	1.47804
$124$	−5.26795	−0.473076
$125$	1.00000	0.0894427
$126$	0	0
$127$	7.26795	0.644926	0.322463	−	0.946582i	$-0.395489\pi$
$127$	7.26795	0.644926	0.322463	+	0.946582i	$0.395489\pi$
$128$	−1.00000	−0.0883883
$129$	−10.2679	−0.904043
$130$	−5.46410	−0.479233
$131$	0.464102	0.0405487	0.0202744	−	0.999794i	$-0.493546\pi$
$131$	0.464102	0.0405487	0.0202744	+	0.999794i	$0.493546\pi$
$132$	−9.46410	−0.823744
$133$	−10.1962	−0.884119
$134$	7.92820	0.684892
$135$	−5.19615	−0.447214
$136$	6.46410	0.554292
$137$	1.53590	0.131221	0.0656103	−	0.997845i	$-0.479101\pi$
$137$	1.53590	0.131221	0.0656103	+	0.997845i	$0.479101\pi$
$138$	0	0
$139$	5.53590	0.469549	0.234774	−	0.972050i	$-0.424565\pi$
$139$	5.53590	0.469549	0.234774	+	0.972050i	$0.424565\pi$
$140$	2.73205	0.230900
$141$	−22.7321	−1.91438
$142$	−15.1244	−1.26921
$143$	−29.8564	−2.49672
$144$	0	0
$145$	−4.73205	−0.392975
$146$	1.73205	0.143346
$147$	0.803848	0.0663002
$148$	−3.46410	−0.284747
$149$	−22.7321	−1.86228	−0.931141	−	0.364659i	$-0.881186\pi$
$149$	−22.7321	−1.86228	−0.931141	+	0.364659i	$0.881186\pi$
$150$	−1.73205	−0.141421
$151$	−0.535898	−0.0436108	−0.0218054	−	0.999762i	$-0.506941\pi$
$151$	−0.535898	−0.0436108	−0.0218054	+	0.999762i	$0.506941\pi$
$152$	3.73205	0.302709
$153$	0	0
$154$	14.9282	1.20295
$155$	−5.26795	−0.423132
$156$	9.46410	0.757735
$157$	−16.0000	−1.27694	−0.638470	−	0.769647i	$-0.720432\pi$
$157$	−16.0000	−1.27694	−0.638470	+	0.769647i	$0.720432\pi$
$158$	1.26795	0.100873
$159$	8.19615	0.649997
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	9.00000	0.707107
$163$	8.39230	0.657336	0.328668	−	0.944446i	$-0.393400\pi$
$163$	8.39230	0.657336	0.328668	+	0.944446i	$0.393400\pi$
$164$	9.46410	0.739022
$165$	−9.46410	−0.736779
$166$	17.9282	1.39150
$167$	−2.33975	−0.181055	−0.0905275	−	0.995894i	$-0.528855\pi$
$167$	−2.33975	−0.181055	−0.0905275	+	0.995894i	$0.528855\pi$
$168$	−4.73205	−0.365086
$169$	16.8564	1.29665
$170$	6.46410	0.495774
$171$	0	0
$172$	−5.92820	−0.452021
$173$	19.2679	1.46492	0.732458	−	0.680813i	$-0.238373\pi$
$173$	19.2679	1.46492	0.732458	+	0.680813i	$0.238373\pi$
$174$	8.19615	0.621349
$175$	2.73205	0.206524
$176$	−5.46410	−0.411872
$177$	−12.1244	−0.911322
$178$	−4.53590	−0.339980
$179$	−17.9282	−1.34002	−0.670008	−	0.742354i	$-0.733710\pi$
$179$	−17.9282	−1.34002	−0.670008	+	0.742354i	$0.733710\pi$
$180$	0	0
$181$	−3.85641	−0.286644	−0.143322	−	0.989676i	$-0.545779\pi$
$181$	−3.85641	−0.286644	−0.143322	+	0.989676i	$0.545779\pi$
$182$	−14.9282	−1.10655
$183$	5.07180	0.374918
$184$	0	0
$185$	−3.46410	−0.254686
$186$	9.12436	0.669030
$187$	35.3205	2.58289
$188$	−13.1244	−0.957192
$189$	−14.1962	−1.03262
$190$	3.73205	0.270751
$191$	5.66025	0.409562	0.204781	−	0.978808i	$-0.434352\pi$
$191$	5.66025	0.409562	0.204781	+	0.978808i	$0.434352\pi$
$192$	1.73205	0.125000
$193$	5.73205	0.412602	0.206301	−	0.978489i	$-0.433857\pi$
$193$	5.73205	0.412602	0.206301	+	0.978489i	$0.433857\pi$
$194$	−14.9282	−1.07178
$195$	9.46410	0.677738
$196$	0.464102	0.0331501
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−7.66025	−0.543021	−0.271511	−	0.962435i	$-0.587523\pi$
$199$	−7.66025	−0.543021	−0.271511	+	0.962435i	$0.587523\pi$
$200$	−1.00000	−0.0707107
$201$	−13.7321	−0.968584
$202$	6.92820	0.487467
$203$	−12.9282	−0.907382
$204$	−11.1962	−0.783887
$205$	9.46410	0.661002
$206$	−3.46410	−0.241355
$207$	0	0
$208$	5.46410	0.378867
$209$	20.3923	1.41057
$210$	−4.73205	−0.326543
$211$	20.8564	1.43581	0.717907	−	0.696139i	$-0.245100\pi$
$211$	20.8564	1.43581	0.717907	+	0.696139i	$0.245100\pi$
$212$	4.73205	0.324999
$213$	26.1962	1.79493
$214$	10.0000	0.683586
$215$	−5.92820	−0.404300
$216$	5.19615	0.353553
$217$	−14.3923	−0.977013
$218$	−1.80385	−0.122172
$219$	−3.00000	−0.202721
$220$	−5.46410	−0.368390
$221$	−35.3205	−2.37591
$222$	6.00000	0.402694
$223$	−0.143594	−0.00961573	−0.00480787	−	0.999988i	$-0.501530\pi$
$223$	−0.143594	−0.00961573	−0.00480787	+	0.999988i	$0.501530\pi$
$224$	−2.73205	−0.182543
$225$	0	0
$226$	0.464102	0.0308716
$227$	−6.60770	−0.438568	−0.219284	−	0.975661i	$-0.570372\pi$
$227$	−6.60770	−0.438568	−0.219284	+	0.975661i	$0.570372\pi$
$228$	−6.46410	−0.428096
$229$	26.7321	1.76650	0.883252	−	0.468899i	$-0.155349\pi$
$229$	26.7321	1.76650	0.883252	+	0.468899i	$0.155349\pi$
$230$	0	0
$231$	−25.8564	−1.70123
$232$	4.73205	0.310674
$233$	18.1244	1.18737	0.593683	−	0.804699i	$-0.297673\pi$
$233$	18.1244	1.18737	0.593683	+	0.804699i	$0.297673\pi$
$234$	0	0
$235$	−13.1244	−0.856139
$236$	−7.00000	−0.455661
$237$	−2.19615	−0.142655
$238$	17.6603	1.14474
$239$	−0.392305	−0.0253761	−0.0126880	−	0.999920i	$-0.504039\pi$
$239$	−0.392305	−0.0253761	−0.0126880	+	0.999920i	$0.504039\pi$
$240$	1.73205	0.111803
$241$	2.80385	0.180612	0.0903058	−	0.995914i	$-0.471216\pi$
$241$	2.80385	0.180612	0.0903058	+	0.995914i	$0.471216\pi$
$242$	−18.8564	−1.21214
$243$	0	0
$244$	2.92820	0.187459
$245$	0.464102	0.0296504
$246$	−16.3923	−1.04514
$247$	−20.3923	−1.29753
$248$	5.26795	0.334515
$249$	−31.0526	−1.96788
$250$	−1.00000	−0.0632456
$251$	20.1244	1.27024	0.635119	−	0.772414i	$-0.280951\pi$
$251$	20.1244	1.27024	0.635119	+	0.772414i	$0.280951\pi$
$252$	0	0
$253$	0	0
$254$	−7.26795	−0.456032
$255$	−11.1962	−0.701130
$256$	1.00000	0.0625000
$257$	21.7321	1.35561	0.677804	−	0.735243i	$-0.262932\pi$
$257$	21.7321	1.35561	0.677804	+	0.735243i	$0.262932\pi$
$258$	10.2679	0.639255
$259$	−9.46410	−0.588071
$260$	5.46410	0.338869
$261$	0	0
$262$	−0.464102	−0.0286723
$263$	−8.53590	−0.526346	−0.263173	−	0.964749i	$-0.584769\pi$
$263$	−8.53590	−0.526346	−0.263173	+	0.964749i	$0.584769\pi$
$264$	9.46410	0.582475
$265$	4.73205	0.290688
$266$	10.1962	0.625166
$267$	7.85641	0.480804
$268$	−7.92820	−0.484292
$269$	−28.7846	−1.75503	−0.877514	−	0.479550i	$-0.840800\pi$
$269$	−28.7846	−1.75503	−0.877514	+	0.479550i	$0.840800\pi$
$270$	5.19615	0.316228
$271$	12.9282	0.785332	0.392666	−	0.919681i	$-0.371553\pi$
$271$	12.9282	0.785332	0.392666	+	0.919681i	$0.371553\pi$
$272$	−6.46410	−0.391944
$273$	25.8564	1.56490
$274$	−1.53590	−0.0927870
$275$	−5.46410	−0.329498
$276$	0	0
$277$	−28.4449	−1.70909	−0.854543	−	0.519380i	$-0.826163\pi$
$277$	−28.4449	−1.70909	−0.854543	+	0.519380i	$0.826163\pi$
$278$	−5.53590	−0.332021
$279$	0	0
$280$	−2.73205	−0.163271
$281$	−4.80385	−0.286574	−0.143287	−	0.989681i	$-0.545767\pi$
$281$	−4.80385	−0.286574	−0.143287	+	0.989681i	$0.545767\pi$
$282$	22.7321	1.35367
$283$	−6.60770	−0.392787	−0.196393	−	0.980525i	$-0.562923\pi$
$283$	−6.60770	−0.392787	−0.196393	+	0.980525i	$0.562923\pi$
$284$	15.1244	0.897465
$285$	−6.46410	−0.382900
$286$	29.8564	1.76545
$287$	25.8564	1.52626
$288$	0	0
$289$	24.7846	1.45792
$290$	4.73205	0.277876
$291$	25.8564	1.51573
$292$	−1.73205	−0.101361
$293$	8.92820	0.521591	0.260796	−	0.965394i	$-0.416015\pi$
$293$	8.92820	0.521591	0.260796	+	0.965394i	$0.416015\pi$
$294$	−0.803848	−0.0468813
$295$	−7.00000	−0.407556
$296$	3.46410	0.201347
$297$	28.3923	1.64749
$298$	22.7321	1.31683
$299$	0	0
$300$	1.73205	0.100000
$301$	−16.1962	−0.933531
$302$	0.535898	0.0308375
$303$	−12.0000	−0.689382
$304$	−3.73205	−0.214048
$305$	2.92820	0.167668
$306$	0	0
$307$	−10.1244	−0.577827	−0.288914	−	0.957355i	$-0.593294\pi$
$307$	−10.1244	−0.577827	−0.288914	+	0.957355i	$0.593294\pi$
$308$	−14.9282	−0.850613
$309$	6.00000	0.341328
$310$	5.26795	0.299199
$311$	−7.26795	−0.412128	−0.206064	−	0.978539i	$-0.566065\pi$
$311$	−7.26795	−0.412128	−0.206064	+	0.978539i	$0.566065\pi$
$312$	−9.46410	−0.535799
$313$	23.2487	1.31409	0.657047	−	0.753849i	$-0.271805\pi$
$313$	23.2487	1.31409	0.657047	+	0.753849i	$0.271805\pi$
$314$	16.0000	0.902932
$315$	0	0
$316$	−1.26795	−0.0713277
$317$	−2.87564	−0.161512	−0.0807561	−	0.996734i	$-0.525733\pi$
$317$	−2.87564	−0.161512	−0.0807561	+	0.996734i	$0.525733\pi$
$318$	−8.19615	−0.459617
$319$	25.8564	1.44768
$320$	1.00000	0.0559017
$321$	−17.3205	−0.966736
$322$	0	0
$323$	24.1244	1.34232
$324$	−9.00000	−0.500000
$325$	5.46410	0.303094
$326$	−8.39230	−0.464807
$327$	3.12436	0.172777
$328$	−9.46410	−0.522568
$329$	−35.8564	−1.97683
$330$	9.46410	0.520982
$331$	−8.32051	−0.457336	−0.228668	−	0.973504i	$-0.573437\pi$
$331$	−8.32051	−0.457336	−0.228668	+	0.973504i	$0.573437\pi$
$332$	−17.9282	−0.983938
$333$	0	0
$334$	2.33975	0.128025
$335$	−7.92820	−0.433164
$336$	4.73205	0.258155
$337$	−10.4641	−0.570016	−0.285008	−	0.958525i	$-0.591996\pi$
$337$	−10.4641	−0.570016	−0.285008	+	0.958525i	$0.591996\pi$
$338$	−16.8564	−0.916868
$339$	−0.803848	−0.0436590
$340$	−6.46410	−0.350565
$341$	28.7846	1.55877
$342$	0	0
$343$	−17.8564	−0.964155
$344$	5.92820	0.319627
$345$	0	0
$346$	−19.2679	−1.03585
$347$	16.6603	0.894369	0.447185	−	0.894442i	$-0.352427\pi$
$347$	16.6603	0.894369	0.447185	+	0.894442i	$0.352427\pi$
$348$	−8.19615	−0.439360
$349$	28.3923	1.51981	0.759903	−	0.650037i	$-0.225247\pi$
$349$	28.3923	1.51981	0.759903	+	0.650037i	$0.225247\pi$
$350$	−2.73205	−0.146034
$351$	−28.3923	−1.51547
$352$	5.46410	0.291238
$353$	26.6603	1.41898	0.709491	−	0.704714i	$-0.248925\pi$
$353$	26.6603	1.41898	0.709491	+	0.704714i	$0.248925\pi$
$354$	12.1244	0.644402
$355$	15.1244	0.802717
$356$	4.53590	0.240402
$357$	−30.5885	−1.61891
$358$	17.9282	0.947535
$359$	−2.87564	−0.151771	−0.0758854	−	0.997117i	$-0.524178\pi$
$359$	−2.87564	−0.151771	−0.0758854	+	0.997117i	$0.524178\pi$
$360$	0	0
$361$	−5.07180	−0.266937
$362$	3.85641	0.202688
$363$	32.6603	1.71422
$364$	14.9282	0.782450
$365$	−1.73205	−0.0906597
$366$	−5.07180	−0.265107
$367$	2.58846	0.135116	0.0675582	−	0.997715i	$-0.478479\pi$
$367$	2.58846	0.135116	0.0675582	+	0.997715i	$0.478479\pi$
$368$	0	0
$369$	0	0
$370$	3.46410	0.180090
$371$	12.9282	0.671199
$372$	−9.12436	−0.473076
$373$	−2.33975	−0.121147	−0.0605737	−	0.998164i	$-0.519293\pi$
$373$	−2.33975	−0.121147	−0.0605737	+	0.998164i	$0.519293\pi$
$374$	−35.3205	−1.82638
$375$	1.73205	0.0894427
$376$	13.1244	0.676837
$377$	−25.8564	−1.33167
$378$	14.1962	0.730171
$379$	−20.2679	−1.04109	−0.520547	−	0.853833i	$-0.674272\pi$
$379$	−20.2679	−1.04109	−0.520547	+	0.853833i	$0.674272\pi$
$380$	−3.73205	−0.191450
$381$	12.5885	0.644926
$382$	−5.66025	−0.289604
$383$	−29.3205	−1.49821	−0.749104	−	0.662452i	$-0.769516\pi$
$383$	−29.3205	−1.49821	−0.749104	+	0.662452i	$0.769516\pi$
$384$	−1.73205	−0.0883883
$385$	−14.9282	−0.760812
$386$	−5.73205	−0.291754
$387$	0	0
$388$	14.9282	0.757865
$389$	−23.4641	−1.18968	−0.594839	−	0.803845i	$-0.702784\pi$
$389$	−23.4641	−1.18968	−0.594839	+	0.803845i	$0.702784\pi$
$390$	−9.46410	−0.479233
$391$	0	0
$392$	−0.464102	−0.0234407
$393$	0.803848	0.0405487
$394$	−10.0000	−0.503793
$395$	−1.26795	−0.0637974
$396$	0	0
$397$	−0.875644	−0.0439473	−0.0219737	−	0.999759i	$-0.506995\pi$
$397$	−0.875644	−0.0439473	−0.0219737	+	0.999759i	$0.506995\pi$
$398$	7.66025	0.383974
$399$	−17.6603	−0.884119
$400$	1.00000	0.0500000
$401$	21.9808	1.09767	0.548833	−	0.835932i	$-0.315072\pi$
$401$	21.9808	1.09767	0.548833	+	0.835932i	$0.315072\pi$
$402$	13.7321	0.684892
$403$	−28.7846	−1.43386
$404$	−6.92820	−0.344691
$405$	−9.00000	−0.447214
$406$	12.9282	0.641616
$407$	18.9282	0.938236
$408$	11.1962	0.554292
$409$	−23.3923	−1.15668	−0.578338	−	0.815798i	$-0.696298\pi$
$409$	−23.3923	−1.15668	−0.578338	+	0.815798i	$0.696298\pi$
$410$	−9.46410	−0.467399
$411$	2.66025	0.131221
$412$	3.46410	0.170664
$413$	−19.1244	−0.941048
$414$	0	0
$415$	−17.9282	−0.880061
$416$	−5.46410	−0.267900
$417$	9.58846	0.469549
$418$	−20.3923	−0.997420
$419$	−2.41154	−0.117812	−0.0589058	−	0.998264i	$-0.518761\pi$
$419$	−2.41154	−0.117812	−0.0589058	+	0.998264i	$0.518761\pi$
$420$	4.73205	0.230900
$421$	−12.1962	−0.594404	−0.297202	−	0.954815i	$-0.596053\pi$
$421$	−12.1962	−0.594404	−0.297202	+	0.954815i	$0.596053\pi$
$422$	−20.8564	−1.01527
$423$	0	0
$424$	−4.73205	−0.229809
$425$	−6.46410	−0.313555
$426$	−26.1962	−1.26921
$427$	8.00000	0.387147
$428$	−10.0000	−0.483368
$429$	−51.7128	−2.49672
$430$	5.92820	0.285883
$431$	2.92820	0.141047	0.0705233	−	0.997510i	$-0.477533\pi$
$431$	2.92820	0.141047	0.0705233	+	0.997510i	$0.477533\pi$
$432$	−5.19615	−0.250000
$433$	−4.92820	−0.236834	−0.118417	−	0.992964i	$-0.537782\pi$
$433$	−4.92820	−0.236834	−0.118417	+	0.992964i	$0.537782\pi$
$434$	14.3923	0.690853
$435$	−8.19615	−0.392975
$436$	1.80385	0.0863886
$437$	0	0
$438$	3.00000	0.143346
$439$	−32.9808	−1.57409	−0.787043	−	0.616898i	$-0.788389\pi$
$439$	−32.9808	−1.57409	−0.787043	+	0.616898i	$0.788389\pi$
$440$	5.46410	0.260491
$441$	0	0
$442$	35.3205	1.68003
$443$	24.1244	1.14618	0.573091	−	0.819491i	$-0.305744\pi$
$443$	24.1244	1.14618	0.573091	+	0.819491i	$0.305744\pi$
$444$	−6.00000	−0.284747
$445$	4.53590	0.215022
$446$	0.143594	0.00679935
$447$	−39.3731	−1.86228
$448$	2.73205	0.129077
$449$	1.92820	0.0909975	0.0454988	−	0.998964i	$-0.485512\pi$
$449$	1.92820	0.0909975	0.0454988	+	0.998964i	$0.485512\pi$
$450$	0	0
$451$	−51.7128	−2.43506
$452$	−0.464102	−0.0218295
$453$	−0.928203	−0.0436108
$454$	6.60770	0.310114
$455$	14.9282	0.699845
$456$	6.46410	0.302709
$457$	33.1769	1.55195	0.775975	−	0.630763i	$-0.217258\pi$
$457$	33.1769	1.55195	0.775975	+	0.630763i	$0.217258\pi$
$458$	−26.7321	−1.24911
$459$	33.5885	1.56777
$460$	0	0
$461$	−17.6077	−0.820072	−0.410036	−	0.912069i	$-0.634484\pi$
$461$	−17.6077	−0.820072	−0.410036	+	0.912069i	$0.634484\pi$
$462$	25.8564	1.20295
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	−4.73205	−0.219680
$465$	−9.12436	−0.423132
$466$	−18.1244	−0.839595
$467$	33.3205	1.54189	0.770945	−	0.636902i	$-0.219784\pi$
$467$	33.3205	1.54189	0.770945	+	0.636902i	$0.219784\pi$
$468$	0	0
$469$	−21.6603	−1.00018
$470$	13.1244	0.605381
$471$	−27.7128	−1.27694
$472$	7.00000	0.322201
$473$	32.3923	1.48940
$474$	2.19615	0.100873
$475$	−3.73205	−0.171238
$476$	−17.6603	−0.809456
$477$	0	0
$478$	0.392305	0.0179436
$479$	29.6603	1.35521	0.677606	−	0.735425i	$-0.263018\pi$
$479$	29.6603	1.35521	0.677606	+	0.735425i	$0.263018\pi$
$480$	−1.73205	−0.0790569
$481$	−18.9282	−0.863052
$482$	−2.80385	−0.127712
$483$	0	0
$484$	18.8564	0.857109
$485$	14.9282	0.677855
$486$	0	0
$487$	−21.8564	−0.990408	−0.495204	−	0.868777i	$-0.664907\pi$
$487$	−21.8564	−0.990408	−0.495204	+	0.868777i	$0.664907\pi$
$488$	−2.92820	−0.132554
$489$	14.5359	0.657336
$490$	−0.464102	−0.0209660
$491$	0.535898	0.0241848	0.0120924	−	0.999927i	$-0.496151\pi$
$491$	0.535898	0.0241848	0.0120924	+	0.999927i	$0.496151\pi$
$492$	16.3923	0.739022
$493$	30.5885	1.37763
$494$	20.3923	0.917493
$495$	0	0
$496$	−5.26795	−0.236538
$497$	41.3205	1.85348
$498$	31.0526	1.39150
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	1.00000	0.0447214
$501$	−4.05256	−0.181055
$502$	−20.1244	−0.898194
$503$	−25.4641	−1.13539	−0.567694	−	0.823240i	$-0.692164\pi$
$503$	−25.4641	−1.13539	−0.567694	+	0.823240i	$0.692164\pi$
$504$	0	0
$505$	−6.92820	−0.308301
$506$	0	0
$507$	29.1962	1.29665
$508$	7.26795	0.322463
$509$	7.26795	0.322146	0.161073	−	0.986942i	$-0.448505\pi$
$509$	7.26795	0.322146	0.161073	+	0.986942i	$0.448505\pi$
$510$	11.1962	0.495774
$511$	−4.73205	−0.209334
$512$	−1.00000	−0.0441942
$513$	19.3923	0.856191
$514$	−21.7321	−0.958560
$515$	3.46410	0.152647
$516$	−10.2679	−0.452021
$517$	71.7128	3.15393
$518$	9.46410	0.415829
$519$	33.3731	1.46492
$520$	−5.46410	−0.239617
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	0	0
$523$	26.3923	1.15405	0.577027	−	0.816725i	$-0.304213\pi$
$523$	26.3923	1.15405	0.577027	+	0.816725i	$0.304213\pi$
$524$	0.464102	0.0202744
$525$	4.73205	0.206524
$526$	8.53590	0.372183
$527$	34.0526	1.48335
$528$	−9.46410	−0.411872
$529$	0	0
$530$	−4.73205	−0.205547
$531$	0	0
$532$	−10.1962	−0.442059
$533$	51.7128	2.23993
$534$	−7.85641	−0.339980
$535$	−10.0000	−0.432338
$536$	7.92820	0.342446
$537$	−31.0526	−1.34002
$538$	28.7846	1.24099
$539$	−2.53590	−0.109229
$540$	−5.19615	−0.223607
$541$	−36.0526	−1.55002	−0.775010	−	0.631949i	$-0.782255\pi$
$541$	−36.0526	−1.55002	−0.775010	+	0.631949i	$0.782255\pi$
$542$	−12.9282	−0.555314
$543$	−6.67949	−0.286644
$544$	6.46410	0.277146
$545$	1.80385	0.0772683
$546$	−25.8564	−1.10655
$547$	−1.60770	−0.0687401	−0.0343700	−	0.999409i	$-0.510942\pi$
$547$	−1.60770	−0.0687401	−0.0343700	+	0.999409i	$0.510942\pi$
$548$	1.53590	0.0656103
$549$	0	0
$550$	5.46410	0.232990
$551$	17.6603	0.752352
$552$	0	0
$553$	−3.46410	−0.147309
$554$	28.4449	1.20851
$555$	−6.00000	−0.254686
$556$	5.53590	0.234774
$557$	7.51666	0.318491	0.159246	−	0.987239i	$-0.449094\pi$
$557$	7.51666	0.318491	0.159246	+	0.987239i	$0.449094\pi$
$558$	0	0
$559$	−32.3923	−1.37005
$560$	2.73205	0.115450
$561$	61.1769	2.58289
$562$	4.80385	0.202638
$563$	−14.0718	−0.593056	−0.296528	−	0.955024i	$-0.595829\pi$
$563$	−14.0718	−0.593056	−0.296528	+	0.955024i	$0.595829\pi$
$564$	−22.7321	−0.957192
$565$	−0.464102	−0.0195249
$566$	6.60770	0.277742
$567$	−24.5885	−1.03262
$568$	−15.1244	−0.634604
$569$	−19.5885	−0.821191	−0.410595	−	0.911818i	$-0.634679\pi$
$569$	−19.5885	−0.821191	−0.410595	+	0.911818i	$0.634679\pi$
$570$	6.46410	0.270751
$571$	6.51666	0.272714	0.136357	−	0.990660i	$-0.456461\pi$
$571$	6.51666	0.272714	0.136357	+	0.990660i	$0.456461\pi$
$572$	−29.8564	−1.24836
$573$	9.80385	0.409562
$574$	−25.8564	−1.07923
$575$	0	0
$576$	0	0
$577$	−43.4449	−1.80863	−0.904317	−	0.426862i	$-0.859619\pi$
$577$	−43.4449	−1.80863	−0.904317	+	0.426862i	$0.859619\pi$
$578$	−24.7846	−1.03090
$579$	9.92820	0.412602
$580$	−4.73205	−0.196488
$581$	−48.9808	−2.03206
$582$	−25.8564	−1.07178
$583$	−25.8564	−1.07086
$584$	1.73205	0.0716728
$585$	0	0
$586$	−8.92820	−0.368821
$587$	−24.6603	−1.01784	−0.508919	−	0.860815i	$-0.669955\pi$
$587$	−24.6603	−1.01784	−0.508919	+	0.860815i	$0.669955\pi$
$588$	0.803848	0.0331501
$589$	19.6603	0.810087
$590$	7.00000	0.288185
$591$	17.3205	0.712470
$592$	−3.46410	−0.142374
$593$	−29.7321	−1.22095	−0.610474	−	0.792036i	$-0.709021\pi$
$593$	−29.7321	−1.22095	−0.610474	+	0.792036i	$0.709021\pi$
$594$	−28.3923	−1.16495
$595$	−17.6603	−0.724000
$596$	−22.7321	−0.931141
$597$	−13.2679	−0.543021
$598$	0	0
$599$	37.5167	1.53289	0.766445	−	0.642310i	$-0.222024\pi$
$599$	37.5167	1.53289	0.766445	+	0.642310i	$0.222024\pi$
$600$	−1.73205	−0.0707107
$601$	3.32051	0.135446	0.0677232	−	0.997704i	$-0.478427\pi$
$601$	3.32051	0.135446	0.0677232	+	0.997704i	$0.478427\pi$
$602$	16.1962	0.660106
$603$	0	0
$604$	−0.535898	−0.0218054
$605$	18.8564	0.766622
$606$	12.0000	0.487467
$607$	4.73205	0.192068	0.0960340	−	0.995378i	$-0.469384\pi$
$607$	4.73205	0.192068	0.0960340	+	0.995378i	$0.469384\pi$
$608$	3.73205	0.151355
$609$	−22.3923	−0.907382
$610$	−2.92820	−0.118559
$611$	−71.7128	−2.90119
$612$	0	0
$613$	22.5885	0.912339	0.456170	−	0.889893i	$-0.349221\pi$
$613$	22.5885	0.912339	0.456170	+	0.889893i	$0.349221\pi$
$614$	10.1244	0.408586
$615$	16.3923	0.661002
$616$	14.9282	0.601474
$617$	−42.3205	−1.70376	−0.851880	−	0.523737i	$-0.824537\pi$
$617$	−42.3205	−1.70376	−0.851880	+	0.523737i	$0.824537\pi$
$618$	−6.00000	−0.241355
$619$	26.6410	1.07079	0.535396	−	0.844601i	$-0.320162\pi$
$619$	26.6410	1.07079	0.535396	+	0.844601i	$0.320162\pi$
$620$	−5.26795	−0.211566
$621$	0	0
$622$	7.26795	0.291418
$623$	12.3923	0.496487
$624$	9.46410	0.378867
$625$	1.00000	0.0400000
$626$	−23.2487	−0.929205
$627$	35.3205	1.41057
$628$	−16.0000	−0.638470
$629$	22.3923	0.892840
$630$	0	0
$631$	−15.2679	−0.607807	−0.303904	−	0.952703i	$-0.598290\pi$
$631$	−15.2679	−0.607807	−0.303904	+	0.952703i	$0.598290\pi$
$632$	1.26795	0.0504363
$633$	36.1244	1.43581
$634$	2.87564	0.114206
$635$	7.26795	0.288420
$636$	8.19615	0.324999
$637$	2.53590	0.100476
$638$	−25.8564	−1.02366
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−41.4449	−1.63697	−0.818487	−	0.574525i	$-0.805187\pi$
$641$	−41.4449	−1.63697	−0.818487	+	0.574525i	$0.805187\pi$
$642$	17.3205	0.683586
$643$	5.32051	0.209820	0.104910	−	0.994482i	$-0.466544\pi$
$643$	5.32051	0.209820	0.104910	+	0.994482i	$0.466544\pi$
$644$	0	0
$645$	−10.2679	−0.404300
$646$	−24.1244	−0.949160
$647$	13.0718	0.513905	0.256953	−	0.966424i	$-0.417282\pi$
$647$	13.0718	0.513905	0.256953	+	0.966424i	$0.417282\pi$
$648$	9.00000	0.353553
$649$	38.2487	1.50139
$650$	−5.46410	−0.214320
$651$	−24.9282	−0.977013
$652$	8.39230	0.328668
$653$	−35.2679	−1.38014	−0.690071	−	0.723742i	$-0.742421\pi$
$653$	−35.2679	−1.38014	−0.690071	+	0.723742i	$0.742421\pi$
$654$	−3.12436	−0.122172
$655$	0.464102	0.0181340
$656$	9.46410	0.369511
$657$	0	0
$658$	35.8564	1.39783
$659$	19.5885	0.763058	0.381529	−	0.924357i	$-0.375398\pi$
$659$	19.5885	0.763058	0.381529	+	0.924357i	$0.375398\pi$
$660$	−9.46410	−0.368390
$661$	27.8038	1.08144	0.540722	−	0.841201i	$-0.318151\pi$
$661$	27.8038	1.08144	0.540722	+	0.841201i	$0.318151\pi$
$662$	8.32051	0.323386
$663$	−61.1769	−2.37591
$664$	17.9282	0.695749
$665$	−10.1962	−0.395390
$666$	0	0
$667$	0	0
$668$	−2.33975	−0.0905275
$669$	−0.248711	−0.00961573
$670$	7.92820	0.306293
$671$	−16.0000	−0.617673
$672$	−4.73205	−0.182543
$673$	−38.9090	−1.49983	−0.749915	−	0.661534i	$-0.769906\pi$
$673$	−38.9090	−1.49983	−0.749915	+	0.661534i	$0.769906\pi$
$674$	10.4641	0.403062
$675$	−5.19615	−0.200000
$676$	16.8564	0.648323
$677$	−22.4449	−0.862626	−0.431313	−	0.902202i	$-0.641950\pi$
$677$	−22.4449	−0.862626	−0.431313	+	0.902202i	$0.641950\pi$
$678$	0.803848	0.0308716
$679$	40.7846	1.56517
$680$	6.46410	0.247887
$681$	−11.4449	−0.438568
$682$	−28.7846	−1.10222
$683$	−14.2679	−0.545948	−0.272974	−	0.962021i	$-0.588007\pi$
$683$	−14.2679	−0.545948	−0.272974	+	0.962021i	$0.588007\pi$
$684$	0	0
$685$	1.53590	0.0586837
$686$	17.8564	0.681761
$687$	46.3013	1.76650
$688$	−5.92820	−0.226011
$689$	25.8564	0.985051
$690$	0	0
$691$	−39.4641	−1.50129	−0.750643	−	0.660708i	$-0.770256\pi$
$691$	−39.4641	−1.50129	−0.750643	+	0.660708i	$0.770256\pi$
$692$	19.2679	0.732458
$693$	0	0
$694$	−16.6603	−0.632415
$695$	5.53590	0.209989
$696$	8.19615	0.310674
$697$	−61.1769	−2.31724
$698$	−28.3923	−1.07466
$699$	31.3923	1.18737
$700$	2.73205	0.103262
$701$	−39.1244	−1.47771	−0.738853	−	0.673866i	$-0.764632\pi$
$701$	−39.1244	−1.47771	−0.738853	+	0.673866i	$0.764632\pi$
$702$	28.3923	1.07160
$703$	12.9282	0.487596
$704$	−5.46410	−0.205936
$705$	−22.7321	−0.856139
$706$	−26.6603	−1.00337
$707$	−18.9282	−0.711868
$708$	−12.1244	−0.455661
$709$	17.1244	0.643119	0.321559	−	0.946889i	$-0.395793\pi$
$709$	17.1244	0.643119	0.321559	+	0.946889i	$0.395793\pi$
$710$	−15.1244	−0.567607
$711$	0	0
$712$	−4.53590	−0.169990
$713$	0	0
$714$	30.5885	1.14474
$715$	−29.8564	−1.11657
$716$	−17.9282	−0.670008
$717$	−0.679492	−0.0253761
$718$	2.87564	0.107318
$719$	35.6603	1.32990	0.664952	−	0.746887i	$-0.268452\pi$
$719$	35.6603	1.32990	0.664952	+	0.746887i	$0.268452\pi$
$720$	0	0
$721$	9.46410	0.352462
$722$	5.07180	0.188753
$723$	4.85641	0.180612
$724$	−3.85641	−0.143322
$725$	−4.73205	−0.175744
$726$	−32.6603	−1.21214
$727$	−43.3205	−1.60667	−0.803334	−	0.595528i	$-0.796943\pi$
$727$	−43.3205	−1.60667	−0.803334	+	0.595528i	$0.796943\pi$
$728$	−14.9282	−0.553276
$729$	27.0000	1.00000
$730$	1.73205	0.0641061
$731$	38.3205	1.41734
$732$	5.07180	0.187459
$733$	−39.3731	−1.45428	−0.727139	−	0.686491i	$-0.759150\pi$
$733$	−39.3731	−1.45428	−0.727139	+	0.686491i	$0.759150\pi$
$734$	−2.58846	−0.0955417
$735$	0.803848	0.0296504
$736$	0	0
$737$	43.3205	1.59573
$738$	0	0
$739$	−16.6410	−0.612150	−0.306075	−	0.952007i	$-0.599016\pi$
$739$	−16.6410	−0.612150	−0.306075	+	0.952007i	$0.599016\pi$
$740$	−3.46410	−0.127343
$741$	−35.3205	−1.29753
$742$	−12.9282	−0.474609
$743$	−18.5885	−0.681944	−0.340972	−	0.940073i	$-0.610756\pi$
$743$	−18.5885	−0.681944	−0.340972	+	0.940073i	$0.610756\pi$
$744$	9.12436	0.334515
$745$	−22.7321	−0.832838
$746$	2.33975	0.0856642
$747$	0	0
$748$	35.3205	1.29145
$749$	−27.3205	−0.998270
$750$	−1.73205	−0.0632456
$751$	48.7846	1.78018	0.890088	−	0.455789i	$-0.150643\pi$
$751$	48.7846	1.78018	0.890088	+	0.455789i	$0.150643\pi$
$752$	−13.1244	−0.478596
$753$	34.8564	1.27024
$754$	25.8564	0.941635
$755$	−0.535898	−0.0195033
$756$	−14.1962	−0.516309
$757$	−38.3013	−1.39208	−0.696042	−	0.718001i	$-0.745057\pi$
$757$	−38.3013	−1.39208	−0.696042	+	0.718001i	$0.745057\pi$
$758$	20.2679	0.736165
$759$	0	0
$760$	3.73205	0.135376
$761$	−54.3205	−1.96912	−0.984558	−	0.175056i	$-0.943989\pi$
$761$	−54.3205	−1.96912	−0.984558	+	0.175056i	$0.943989\pi$
$762$	−12.5885	−0.456032
$763$	4.92820	0.178413
$764$	5.66025	0.204781
$765$	0	0
$766$	29.3205	1.05939
$767$	−38.2487	−1.38108
$768$	1.73205	0.0625000
$769$	−13.3205	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$769$	−13.3205	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$770$	14.9282	0.537975
$771$	37.6410	1.35561
$772$	5.73205	0.206301
$773$	−12.7846	−0.459830	−0.229915	−	0.973211i	$-0.573845\pi$
$773$	−12.7846	−0.459830	−0.229915	+	0.973211i	$0.573845\pi$
$774$	0	0
$775$	−5.26795	−0.189230
$776$	−14.9282	−0.535891
$777$	−16.3923	−0.588071
$778$	23.4641	0.841229
$779$	−35.3205	−1.26549
$780$	9.46410	0.338869
$781$	−82.6410	−2.95713
$782$	0	0
$783$	24.5885	0.878720
$784$	0.464102	0.0165751
$785$	−16.0000	−0.571064
$786$	−0.803848	−0.0286723
$787$	8.46410	0.301713	0.150856	−	0.988556i	$-0.451797\pi$
$787$	8.46410	0.301713	0.150856	+	0.988556i	$0.451797\pi$
$788$	10.0000	0.356235
$789$	−14.7846	−0.526346
$790$	1.26795	0.0451116
$791$	−1.26795	−0.0450831
$792$	0	0
$793$	16.0000	0.568177
$794$	0.875644	0.0310755
$795$	8.19615	0.290688
$796$	−7.66025	−0.271511
$797$	15.5167	0.549628	0.274814	−	0.961497i	$-0.411384\pi$
$797$	15.5167	0.549628	0.274814	+	0.961497i	$0.411384\pi$
$798$	17.6603	0.625166
$799$	84.8372	3.00132
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−21.9808	−0.776168
$803$	9.46410	0.333981
$804$	−13.7321	−0.484292
$805$	0	0
$806$	28.7846	1.01389
$807$	−49.8564	−1.75503
$808$	6.92820	0.243733
$809$	−2.21539	−0.0778890	−0.0389445	−	0.999241i	$-0.512400\pi$
$809$	−2.21539	−0.0778890	−0.0389445	+	0.999241i	$0.512400\pi$
$810$	9.00000	0.316228
$811$	40.7128	1.42962	0.714810	−	0.699319i	$-0.246513\pi$
$811$	40.7128	1.42962	0.714810	+	0.699319i	$0.246513\pi$
$812$	−12.9282	−0.453691
$813$	22.3923	0.785332
$814$	−18.9282	−0.663433
$815$	8.39230	0.293970
$816$	−11.1962	−0.391944
$817$	22.1244	0.774033
$818$	23.3923	0.817893
$819$	0	0
$820$	9.46410	0.330501
$821$	−16.3923	−0.572095	−0.286048	−	0.958215i	$-0.592342\pi$
$821$	−16.3923	−0.572095	−0.286048	+	0.958215i	$0.592342\pi$
$822$	−2.66025	−0.0927870
$823$	23.8038	0.829750	0.414875	−	0.909878i	$-0.363825\pi$
$823$	23.8038	0.829750	0.414875	+	0.909878i	$0.363825\pi$
$824$	−3.46410	−0.120678
$825$	−9.46410	−0.329498
$826$	19.1244	0.665421
$827$	7.39230	0.257056	0.128528	−	0.991706i	$-0.458975\pi$
$827$	7.39230	0.257056	0.128528	+	0.991706i	$0.458975\pi$
$828$	0	0
$829$	−31.1769	−1.08282	−0.541409	−	0.840759i	$-0.682109\pi$
$829$	−31.1769	−1.08282	−0.541409	+	0.840759i	$0.682109\pi$
$830$	17.9282	0.622297
$831$	−49.2679	−1.70909
$832$	5.46410	0.189434
$833$	−3.00000	−0.103944
$834$	−9.58846	−0.332021
$835$	−2.33975	−0.0809702
$836$	20.3923	0.705283
$837$	27.3731	0.946152
$838$	2.41154	0.0833054
$839$	24.2487	0.837158	0.418579	−	0.908180i	$-0.362528\pi$
$839$	24.2487	0.837158	0.418579	+	0.908180i	$0.362528\pi$
$840$	−4.73205	−0.163271
$841$	−6.60770	−0.227852
$842$	12.1962	0.420307
$843$	−8.32051	−0.286574
$844$	20.8564	0.717907
$845$	16.8564	0.579878
$846$	0	0
$847$	51.5167	1.77013
$848$	4.73205	0.162499
$849$	−11.4449	−0.392787
$850$	6.46410	0.221717
$851$	0	0
$852$	26.1962	0.897465
$853$	44.9282	1.53831	0.769156	−	0.639061i	$-0.220677\pi$
$853$	44.9282	1.53831	0.769156	+	0.639061i	$0.220677\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	10.0000	0.341793
$857$	23.8756	0.815576	0.407788	−	0.913077i	$-0.366300\pi$
$857$	23.8756	0.815576	0.407788	+	0.913077i	$0.366300\pi$
$858$	51.7128	1.76545
$859$	−32.3205	−1.10276	−0.551381	−	0.834254i	$-0.685899\pi$
$859$	−32.3205	−1.10276	−0.551381	+	0.834254i	$0.685899\pi$
$860$	−5.92820	−0.202150
$861$	44.7846	1.52626
$862$	−2.92820	−0.0997350
$863$	11.8038	0.401808	0.200904	−	0.979611i	$-0.435612\pi$
$863$	11.8038	0.401808	0.200904	+	0.979611i	$0.435612\pi$
$864$	5.19615	0.176777
$865$	19.2679	0.655130
$866$	4.92820	0.167467
$867$	42.9282	1.45792
$868$	−14.3923	−0.488507
$869$	6.92820	0.235023
$870$	8.19615	0.277876
$871$	−43.3205	−1.46786
$872$	−1.80385	−0.0610860
$873$	0	0
$874$	0	0
$875$	2.73205	0.0923602
$876$	−3.00000	−0.101361
$877$	−4.78461	−0.161565	−0.0807824	−	0.996732i	$-0.525742\pi$
$877$	−4.78461	−0.161565	−0.0807824	+	0.996732i	$0.525742\pi$
$878$	32.9808	1.11305
$879$	15.4641	0.521591
$880$	−5.46410	−0.184195
$881$	2.28719	0.0770573	0.0385286	−	0.999257i	$-0.487733\pi$
$881$	2.28719	0.0770573	0.0385286	+	0.999257i	$0.487733\pi$
$882$	0	0
$883$	−50.5167	−1.70002	−0.850010	−	0.526766i	$-0.823405\pi$
$883$	−50.5167	−1.70002	−0.850010	+	0.526766i	$0.823405\pi$
$884$	−35.3205	−1.18796
$885$	−12.1244	−0.407556
$886$	−24.1244	−0.810474
$887$	−25.5167	−0.856766	−0.428383	−	0.903597i	$-0.640917\pi$
$887$	−25.5167	−0.856766	−0.428383	+	0.903597i	$0.640917\pi$
$888$	6.00000	0.201347
$889$	19.8564	0.665962
$890$	−4.53590	−0.152044
$891$	49.1769	1.64749
$892$	−0.143594	−0.00480787
$893$	48.9808	1.63908
$894$	39.3731	1.31683
$895$	−17.9282	−0.599274
$896$	−2.73205	−0.0912714
$897$	0	0
$898$	−1.92820	−0.0643450
$899$	24.9282	0.831402
$900$	0	0
$901$	−30.5885	−1.01905
$902$	51.7128	1.72185
$903$	−28.0526	−0.933531
$904$	0.464102	0.0154358
$905$	−3.85641	−0.128191
$906$	0.928203	0.0308375
$907$	−12.7128	−0.422122	−0.211061	−	0.977473i	$-0.567692\pi$
$907$	−12.7128	−0.422122	−0.211061	+	0.977473i	$0.567692\pi$
$908$	−6.60770	−0.219284
$909$	0	0
$910$	−14.9282	−0.494865
$911$	−2.78461	−0.0922582	−0.0461291	−	0.998935i	$-0.514689\pi$
$911$	−2.78461	−0.0922582	−0.0461291	+	0.998935i	$0.514689\pi$
$912$	−6.46410	−0.214048
$913$	97.9615	3.24205
$914$	−33.1769	−1.09739
$915$	5.07180	0.167668
$916$	26.7321	0.883252
$917$	1.26795	0.0418714
$918$	−33.5885	−1.10858
$919$	10.5885	0.349281	0.174640	−	0.984632i	$-0.444124\pi$
$919$	10.5885	0.349281	0.174640	+	0.984632i	$0.444124\pi$
$920$	0	0
$921$	−17.5359	−0.577827
$922$	17.6077	0.579879
$923$	82.6410	2.72016
$924$	−25.8564	−0.850613
$925$	−3.46410	−0.113899
$926$	−6.00000	−0.197172
$927$	0	0
$928$	4.73205	0.155337
$929$	26.7846	0.878775	0.439387	−	0.898298i	$-0.355196\pi$
$929$	26.7846	0.878775	0.439387	+	0.898298i	$0.355196\pi$
$930$	9.12436	0.299199
$931$	−1.73205	−0.0567657
$932$	18.1244	0.593683
$933$	−12.5885	−0.412128
$934$	−33.3205	−1.09028
$935$	35.3205	1.15510
$936$	0	0
$937$	−27.1051	−0.885486	−0.442743	−	0.896649i	$-0.645995\pi$
$937$	−27.1051	−0.885486	−0.442743	+	0.896649i	$0.645995\pi$
$938$	21.6603	0.707232
$939$	40.2679	1.31409
$940$	−13.1244	−0.428069
$941$	47.3731	1.54432	0.772159	−	0.635429i	$-0.219177\pi$
$941$	47.3731	1.54432	0.772159	+	0.635429i	$0.219177\pi$
$942$	27.7128	0.902932
$943$	0	0
$944$	−7.00000	−0.227831
$945$	−14.1962	−0.461801
$946$	−32.3923	−1.05316
$947$	24.5167	0.796684	0.398342	−	0.917237i	$-0.369586\pi$
$947$	24.5167	0.796684	0.398342	+	0.917237i	$0.369586\pi$
$948$	−2.19615	−0.0713277
$949$	−9.46410	−0.307218
$950$	3.73205	0.121084
$951$	−4.98076	−0.161512
$952$	17.6603	0.572372
$953$	−2.14359	−0.0694378	−0.0347189	−	0.999397i	$-0.511054\pi$
$953$	−2.14359	−0.0694378	−0.0347189	+	0.999397i	$0.511054\pi$
$954$	0	0
$955$	5.66025	0.183162
$956$	−0.392305	−0.0126880
$957$	44.7846	1.44768
$958$	−29.6603	−0.958279
$959$	4.19615	0.135501
$960$	1.73205	0.0559017
$961$	−3.24871	−0.104797
$962$	18.9282	0.610270
$963$	0	0
$964$	2.80385	0.0903058
$965$	5.73205	0.184521
$966$	0	0
$967$	30.3923	0.977351	0.488675	−	0.872466i	$-0.337480\pi$
$967$	30.3923	0.977351	0.488675	+	0.872466i	$0.337480\pi$
$968$	−18.8564	−0.606068
$969$	41.7846	1.34232
$970$	−14.9282	−0.479316
$971$	−36.3731	−1.16727	−0.583634	−	0.812017i	$-0.698370\pi$
$971$	−36.3731	−1.16727	−0.583634	+	0.812017i	$0.698370\pi$
$972$	0	0
$973$	15.1244	0.484865
$974$	21.8564	0.700324
$975$	9.46410	0.303094
$976$	2.92820	0.0937295
$977$	−35.6077	−1.13919	−0.569596	−	0.821925i	$-0.692900\pi$
$977$	−35.6077	−1.13919	−0.569596	+	0.821925i	$0.692900\pi$
$978$	−14.5359	−0.464807
$979$	−24.7846	−0.792120
$980$	0.464102	0.0148252
$981$	0	0
$982$	−0.535898	−0.0171012
$983$	−10.0000	−0.318950	−0.159475	−	0.987202i	$-0.550980\pi$
$983$	−10.0000	−0.318950	−0.159475	+	0.987202i	$0.550980\pi$
$984$	−16.3923	−0.522568
$985$	10.0000	0.318626
$986$	−30.5885	−0.974135
$987$	−62.1051	−1.97683
$988$	−20.3923	−0.648766
$989$	0	0
$990$	0	0
$991$	−23.1769	−0.736239	−0.368119	−	0.929778i	$-0.619998\pi$
$991$	−23.1769	−0.736239	−0.368119	+	0.929778i	$0.619998\pi$
$992$	5.26795	0.167258
$993$	−14.4115	−0.457336
$994$	−41.3205	−1.31061
$995$	−7.66025	−0.242846
$996$	−31.0526	−0.983938
$997$	51.5692	1.63321	0.816607	−	0.577194i	$-0.195853\pi$
$997$	51.5692	1.63321	0.816607	+	0.577194i	$0.195853\pi$
$998$	−5.00000	−0.158272
$999$	18.0000	0.569495

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.f.1.2	✓	2	23.22	odd	2
5290.2.a.g.1.2	yes	2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{6} +2.73205 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{6} +2.73205 q^{7} -1.00000 q^{8} -1.00000 q^{10} -5.46410 q^{11} +1.73205 q^{12} +5.46410 q^{13} -2.73205 q^{14} +1.73205 q^{15} +1.00000 q^{16} -6.46410 q^{17} -3.73205 q^{19} +1.00000 q^{20} +4.73205 q^{21} +5.46410 q^{22} -1.73205 q^{24} +1.00000 q^{25} -5.46410 q^{26} -5.19615 q^{27} +2.73205 q^{28} -4.73205 q^{29} -1.73205 q^{30} -5.26795 q^{31} -1.00000 q^{32} -9.46410 q^{33} +6.46410 q^{34} +2.73205 q^{35} -3.46410 q^{37} +3.73205 q^{38} +9.46410 q^{39} -1.00000 q^{40} +9.46410 q^{41} -4.73205 q^{42} -5.92820 q^{43} -5.46410 q^{44} -13.1244 q^{47} +1.73205 q^{48} +0.464102 q^{49} -1.00000 q^{50} -11.1962 q^{51} +5.46410 q^{52} +4.73205 q^{53} +5.19615 q^{54} -5.46410 q^{55} -2.73205 q^{56} -6.46410 q^{57} +4.73205 q^{58} -7.00000 q^{59} +1.73205 q^{60} +2.92820 q^{61} +5.26795 q^{62} +1.00000 q^{64} +5.46410 q^{65} +9.46410 q^{66} -7.92820 q^{67} -6.46410 q^{68} -2.73205 q^{70} +15.1244 q^{71} -1.73205 q^{73} +3.46410 q^{74} +1.73205 q^{75} -3.73205 q^{76} -14.9282 q^{77} -9.46410 q^{78} -1.26795 q^{79} +1.00000 q^{80} -9.00000 q^{81} -9.46410 q^{82} -17.9282 q^{83} +4.73205 q^{84} -6.46410 q^{85} +5.92820 q^{86} -8.19615 q^{87} +5.46410 q^{88} +4.53590 q^{89} +14.9282 q^{91} -9.12436 q^{93} +13.1244 q^{94} -3.73205 q^{95} -1.73205 q^{96} +14.9282 q^{97} -0.464102 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} - 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 2 q^{16} - 6 q^{17} - 4 q^{19} + 2 q^{20} + 6 q^{21} + 4 q^{22} + 2 q^{25} - 4 q^{26} + 2 q^{28} - 6 q^{29} - 14 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} + 2 q^{35} + 4 q^{38} + 12 q^{39} - 2 q^{40} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} - 2 q^{47} - 6 q^{49} - 2 q^{50} - 12 q^{51} + 4 q^{52} + 6 q^{53} - 4 q^{55} - 2 q^{56} - 6 q^{57} + 6 q^{58} - 14 q^{59} - 8 q^{61} + 14 q^{62} + 2 q^{64} + 4 q^{65} + 12 q^{66} - 2 q^{67} - 6 q^{68} - 2 q^{70} + 6 q^{71} - 4 q^{76} - 16 q^{77} - 12 q^{78} - 6 q^{79} + 2 q^{80} - 18 q^{81} - 12 q^{82} - 22 q^{83} + 6 q^{84} - 6 q^{85} - 2 q^{86} - 6 q^{87} + 4 q^{88} + 16 q^{89} + 16 q^{91} + 6 q^{93} + 2 q^{94} - 4 q^{95} + 16 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 - 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 2 * q^16 - 6 * q^17 - 4 * q^19 + 2 * q^20 + 6 * q^21 + 4 * q^22 + 2 * q^25 - 4 * q^26 + 2 * q^28 - 6 * q^29 - 14 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 + 2 * q^35 + 4 * q^38 + 12 * q^39 - 2 * q^40 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 - 2 * q^47 - 6 * q^49 - 2 * q^50 - 12 * q^51 + 4 * q^52 + 6 * q^53 - 4 * q^55 - 2 * q^56 - 6 * q^57 + 6 * q^58 - 14 * q^59 - 8 * q^61 + 14 * q^62 + 2 * q^64 + 4 * q^65 + 12 * q^66 - 2 * q^67 - 6 * q^68 - 2 * q^70 + 6 * q^71 - 4 * q^76 - 16 * q^77 - 12 * q^78 - 6 * q^79 + 2 * q^80 - 18 * q^81 - 12 * q^82 - 22 * q^83 + 6 * q^84 - 6 * q^85 - 2 * q^86 - 6 * q^87 + 4 * q^88 + 16 * q^89 + 16 * q^91 + 6 * q^93 + 2 * q^94 - 4 * q^95 + 16 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more