LMFDB - Embedded newform 5610.2.a.bx.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
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			1.2
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.74456 q^{13} +3.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +3.37228 q^{21} +1.00000 q^{22} -3.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.74456 q^{26} +1.00000 q^{27} +3.37228 q^{28} +2.62772 q^{29} +1.00000 q^{30} +4.62772 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +3.37228 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +4.74456 q^{39} +1.00000 q^{40} -12.7446 q^{41} +3.37228 q^{42} +7.37228 q^{43} +1.00000 q^{44} +1.00000 q^{45} -3.37228 q^{46} -13.4891 q^{47} +1.00000 q^{48} +4.37228 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.74456 q^{52} -0.744563 q^{53} +1.00000 q^{54} +1.00000 q^{55} +3.37228 q^{56} +4.00000 q^{57} +2.62772 q^{58} -10.7446 q^{59} +1.00000 q^{60} -2.00000 q^{61} +4.62772 q^{62} +3.37228 q^{63} +1.00000 q^{64} +4.74456 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} -3.37228 q^{69} +3.37228 q^{70} +1.25544 q^{71} +1.00000 q^{72} -6.00000 q^{73} -10.0000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +3.37228 q^{77} +4.74456 q^{78} -13.4891 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.7446 q^{82} -12.0000 q^{83} +3.37228 q^{84} +1.00000 q^{85} +7.37228 q^{86} +2.62772 q^{87} +1.00000 q^{88} +16.7446 q^{89} +1.00000 q^{90} +16.0000 q^{91} -3.37228 q^{92} +4.62772 q^{93} -13.4891 q^{94} +4.00000 q^{95} +1.00000 q^{96} -9.37228 q^{97} +4.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} + 2 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 + 2 * q^22 - q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + q^28 + 11 * q^29 + 2 * q^30 + 15 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 + q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 - 14 * q^41 + q^42 + 9 * q^43 + 2 * q^44 + 2 * q^45 - q^46 - 4 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 + 2 * q^55 + q^56 + 8 * q^57 + 11 * q^58 - 10 * q^59 + 2 * q^60 - 4 * q^61 + 15 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 - q^69 + q^70 + 14 * q^71 + 2 * q^72 - 12 * q^73 - 20 * q^74 + 2 * q^75 + 8 * q^76 + q^77 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 - 14 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 9 * q^86 + 11 * q^87 + 2 * q^88 + 22 * q^89 + 2 * q^90 + 32 * q^91 - q^92 + 15 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 13 * q^97 + 3 * q^98 + 2 * q^99

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	3.37228	1.27460	0.637301	−	0.770615i	$-0.280051\pi$
$7$	3.37228	1.27460	0.637301	+	0.770615i	$0.280051\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	4.74456	1.31590	0.657952	−	0.753059i	$-0.271423\pi$
$13$	4.74456	1.31590	0.657952	+	0.753059i	$0.271423\pi$
$14$	3.37228	0.901280
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	3.37228	0.735892
$22$	1.00000	0.213201
$23$	−3.37228	−0.703169	−0.351585	−	0.936156i	$-0.614357\pi$
$23$	−3.37228	−0.703169	−0.351585	+	0.936156i	$0.614357\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.74456	0.930485
$27$	1.00000	0.192450
$28$	3.37228	0.637301
$29$	2.62772	0.487955	0.243978	−	0.969781i	$-0.421548\pi$
$29$	2.62772	0.487955	0.243978	+	0.969781i	$0.421548\pi$
$30$	1.00000	0.182574
$31$	4.62772	0.831163	0.415581	−	0.909556i	$-0.363578\pi$
$31$	4.62772	0.831163	0.415581	+	0.909556i	$0.363578\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	3.37228	0.570020
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	0.648886
$39$	4.74456	0.759738
$40$	1.00000	0.158114
$41$	−12.7446	−1.99037	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−12.7446	−1.99037	−0.995183	+	0.0980332i	$0.968745\pi$
$42$	3.37228	0.520354
$43$	7.37228	1.12426	0.562131	−	0.827048i	$-0.309982\pi$
$43$	7.37228	1.12426	0.562131	+	0.827048i	$0.309982\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−3.37228	−0.497216
$47$	−13.4891	−1.96759	−0.983796	−	0.179294i	$-0.942619\pi$
$47$	−13.4891	−1.96759	−0.983796	+	0.179294i	$0.942619\pi$
$48$	1.00000	0.144338
$49$	4.37228	0.624612
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	4.74456	0.657952
$53$	−0.744563	−0.102274	−0.0511368	−	0.998692i	$-0.516284\pi$
$53$	−0.744563	−0.102274	−0.0511368	+	0.998692i	$0.516284\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	3.37228	0.450640
$57$	4.00000	0.529813
$58$	2.62772	0.345036
$59$	−10.7446	−1.39882	−0.699411	−	0.714719i	$-0.746554\pi$
$59$	−10.7446	−1.39882	−0.699411	+	0.714719i	$0.746554\pi$
$60$	1.00000	0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	4.62772	0.587721
$63$	3.37228	0.424868
$64$	1.00000	0.125000
$65$	4.74456	0.588491
$66$	1.00000	0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	1.00000	0.121268
$69$	−3.37228	−0.405975
$70$	3.37228	0.403065
$71$	1.25544	0.148993	0.0744965	−	0.997221i	$-0.476265\pi$
$71$	1.25544	0.148993	0.0744965	+	0.997221i	$0.476265\pi$
$72$	1.00000	0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−10.0000	−1.16248
$75$	1.00000	0.115470
$76$	4.00000	0.458831
$77$	3.37228	0.384307
$78$	4.74456	0.537216
$79$	−13.4891	−1.51765	−0.758823	−	0.651297i	$-0.774225\pi$
$79$	−13.4891	−1.51765	−0.758823	+	0.651297i	$0.774225\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−12.7446	−1.40740
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	3.37228	0.367946
$85$	1.00000	0.108465
$86$	7.37228	0.794974
$87$	2.62772	0.281721
$88$	1.00000	0.106600
$89$	16.7446	1.77492	0.887460	−	0.460885i	$-0.152468\pi$
$89$	16.7446	1.77492	0.887460	+	0.460885i	$0.152468\pi$
$90$	1.00000	0.105409
$91$	16.0000	1.67726
$92$	−3.37228	−0.351585
$93$	4.62772	0.479872
$94$	−13.4891	−1.39130
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−9.37228	−0.951611	−0.475805	−	0.879551i	$-0.657843\pi$
$97$	−9.37228	−0.951611	−0.475805	+	0.879551i	$0.657843\pi$
$98$	4.37228	0.441667
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	−3.37228	−0.332281	−0.166140	−	0.986102i	$-0.553130\pi$
$103$	−3.37228	−0.332281	−0.166140	+	0.986102i	$0.553130\pi$
$104$	4.74456	0.465243
$105$	3.37228	0.329101
$106$	−0.744563	−0.0723183
$107$	14.1168	1.36473	0.682363	−	0.731013i	$-0.260952\pi$
$107$	14.1168	1.36473	0.682363	+	0.731013i	$0.260952\pi$
$108$	1.00000	0.0962250
$109$	−8.74456	−0.837577	−0.418789	−	0.908084i	$-0.637545\pi$
$109$	−8.74456	−0.837577	−0.418789	+	0.908084i	$0.637545\pi$
$110$	1.00000	0.0953463
$111$	−10.0000	−0.949158
$112$	3.37228	0.318651
$113$	−11.4891	−1.08081	−0.540403	−	0.841406i	$-0.681728\pi$
$113$	−11.4891	−1.08081	−0.540403	+	0.841406i	$0.681728\pi$
$114$	4.00000	0.374634
$115$	−3.37228	−0.314467
$116$	2.62772	0.243978
$117$	4.74456	0.438635
$118$	−10.7446	−0.989117
$119$	3.37228	0.309137
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−12.7446	−1.14914
$124$	4.62772	0.415581
$125$	1.00000	0.0894427
$126$	3.37228	0.300427
$127$	20.2337	1.79545	0.897725	−	0.440557i	$-0.145219\pi$
$127$	20.2337	1.79545	0.897725	+	0.440557i	$0.145219\pi$
$128$	1.00000	0.0883883
$129$	7.37228	0.649093
$130$	4.74456	0.416126
$131$	−9.48913	−0.829069	−0.414534	−	0.910034i	$-0.636056\pi$
$131$	−9.48913	−0.829069	−0.414534	+	0.910034i	$0.636056\pi$
$132$	1.00000	0.0870388
$133$	13.4891	1.16966
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	−14.8614	−1.26970	−0.634848	−	0.772637i	$-0.718937\pi$
$137$	−14.8614	−1.26970	−0.634848	+	0.772637i	$0.718937\pi$
$138$	−3.37228	−0.287068
$139$	14.1168	1.19738	0.598688	−	0.800983i	$-0.295689\pi$
$139$	14.1168	1.19738	0.598688	+	0.800983i	$0.295689\pi$
$140$	3.37228	0.285010
$141$	−13.4891	−1.13599
$142$	1.25544	0.105354
$143$	4.74456	0.396760
$144$	1.00000	0.0833333
$145$	2.62772	0.218220
$146$	−6.00000	−0.496564
$147$	4.37228	0.360620
$148$	−10.0000	−0.821995
$149$	−0.744563	−0.0609969	−0.0304985	−	0.999535i	$-0.509709\pi$
$149$	−0.744563	−0.0609969	−0.0304985	+	0.999535i	$0.509709\pi$
$150$	1.00000	0.0816497
$151$	21.4891	1.74876	0.874380	−	0.485242i	$-0.161268\pi$
$151$	21.4891	1.74876	0.874380	+	0.485242i	$0.161268\pi$
$152$	4.00000	0.324443
$153$	1.00000	0.0808452
$154$	3.37228	0.271746
$155$	4.62772	0.371707
$156$	4.74456	0.379869
$157$	11.4891	0.916932	0.458466	−	0.888712i	$-0.348399\pi$
$157$	11.4891	0.916932	0.458466	+	0.888712i	$0.348399\pi$
$158$	−13.4891	−1.07314
$159$	−0.744563	−0.0590477
$160$	1.00000	0.0790569
$161$	−11.3723	−0.896261
$162$	1.00000	0.0785674
$163$	−7.37228	−0.577442	−0.288721	−	0.957413i	$-0.593230\pi$
$163$	−7.37228	−0.577442	−0.288721	+	0.957413i	$0.593230\pi$
$164$	−12.7446	−0.995183
$165$	1.00000	0.0778499
$166$	−12.0000	−0.931381
$167$	−12.2337	−0.946671	−0.473336	−	0.880882i	$-0.656950\pi$
$167$	−12.2337	−0.946671	−0.473336	+	0.880882i	$0.656950\pi$
$168$	3.37228	0.260177
$169$	9.51087	0.731606
$170$	1.00000	0.0766965
$171$	4.00000	0.305888
$172$	7.37228	0.562131
$173$	11.4891	0.873502	0.436751	−	0.899582i	$-0.356129\pi$
$173$	11.4891	0.873502	0.436751	+	0.899582i	$0.356129\pi$
$174$	2.62772	0.199207
$175$	3.37228	0.254921
$176$	1.00000	0.0753778
$177$	−10.7446	−0.807611
$178$	16.7446	1.25506
$179$	−18.7446	−1.40103	−0.700517	−	0.713636i	$-0.747047\pi$
$179$	−18.7446	−1.40103	−0.700517	+	0.713636i	$0.747047\pi$
$180$	1.00000	0.0745356
$181$	−14.6277	−1.08727	−0.543635	−	0.839322i	$-0.682952\pi$
$181$	−14.6277	−1.08727	−0.543635	+	0.839322i	$0.682952\pi$
$182$	16.0000	1.18600
$183$	−2.00000	−0.147844
$184$	−3.37228	−0.248608
$185$	−10.0000	−0.735215
$186$	4.62772	0.339321
$187$	1.00000	0.0731272
$188$	−13.4891	−0.983796
$189$	3.37228	0.245297
$190$	4.00000	0.290191
$191$	−4.62772	−0.334850	−0.167425	−	0.985885i	$-0.553545\pi$
$191$	−4.62772	−0.334850	−0.167425	+	0.985885i	$0.553545\pi$
$192$	1.00000	0.0721688
$193$	−0.510875	−0.0367736	−0.0183868	−	0.999831i	$-0.505853\pi$
$193$	−0.510875	−0.0367736	−0.0183868	+	0.999831i	$0.505853\pi$
$194$	−9.37228	−0.672891
$195$	4.74456	0.339765
$196$	4.37228	0.312306
$197$	26.2337	1.86907	0.934536	−	0.355867i	$-0.115815\pi$
$197$	26.2337	1.86907	0.934536	+	0.355867i	$0.115815\pi$
$198$	1.00000	0.0710669
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	1.00000	0.0707107
$201$	4.00000	0.282138
$202$	6.00000	0.422159
$203$	8.86141	0.621949
$204$	1.00000	0.0700140
$205$	−12.7446	−0.890119
$206$	−3.37228	−0.234958
$207$	−3.37228	−0.234390
$208$	4.74456	0.328976
$209$	4.00000	0.276686
$210$	3.37228	0.232710
$211$	−14.1168	−0.971844	−0.485922	−	0.874002i	$-0.661516\pi$
$211$	−14.1168	−0.971844	−0.485922	+	0.874002i	$0.661516\pi$
$212$	−0.744563	−0.0511368
$213$	1.25544	0.0860212
$214$	14.1168	0.965008
$215$	7.37228	0.502785
$216$	1.00000	0.0680414
$217$	15.6060	1.05940
$218$	−8.74456	−0.592257
$219$	−6.00000	−0.405442
$220$	1.00000	0.0674200
$221$	4.74456	0.319154
$222$	−10.0000	−0.671156
$223$	−11.3723	−0.761544	−0.380772	−	0.924669i	$-0.624342\pi$
$223$	−11.3723	−0.761544	−0.380772	+	0.924669i	$0.624342\pi$
$224$	3.37228	0.225320
$225$	1.00000	0.0666667
$226$	−11.4891	−0.764245
$227$	6.11684	0.405989	0.202995	−	0.979180i	$-0.434933\pi$
$227$	6.11684	0.405989	0.202995	+	0.979180i	$0.434933\pi$
$228$	4.00000	0.264906
$229$	−3.25544	−0.215125	−0.107563	−	0.994198i	$-0.534305\pi$
$229$	−3.25544	−0.215125	−0.107563	+	0.994198i	$0.534305\pi$
$230$	−3.37228	−0.222362
$231$	3.37228	0.221880
$232$	2.62772	0.172518
$233$	−14.8614	−0.973603	−0.486802	−	0.873513i	$-0.661837\pi$
$233$	−14.8614	−0.973603	−0.486802	+	0.873513i	$0.661837\pi$
$234$	4.74456	0.310162
$235$	−13.4891	−0.879934
$236$	−10.7446	−0.699411
$237$	−13.4891	−0.876213
$238$	3.37228	0.218593
$239$	20.2337	1.30881	0.654404	−	0.756145i	$-0.272919\pi$
$239$	20.2337	1.30881	0.654404	+	0.756145i	$0.272919\pi$
$240$	1.00000	0.0645497
$241$	−9.37228	−0.603722	−0.301861	−	0.953352i	$-0.597608\pi$
$241$	−9.37228	−0.603722	−0.301861	+	0.953352i	$0.597608\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	4.37228	0.279335
$246$	−12.7446	−0.812564
$247$	18.9783	1.20756
$248$	4.62772	0.293860
$249$	−12.0000	−0.760469
$250$	1.00000	0.0632456
$251$	−6.51087	−0.410963	−0.205481	−	0.978661i	$-0.565876\pi$
$251$	−6.51087	−0.410963	−0.205481	+	0.978661i	$0.565876\pi$
$252$	3.37228	0.212434
$253$	−3.37228	−0.212014
$254$	20.2337	1.26957
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	13.3723	0.834140	0.417070	−	0.908874i	$-0.363057\pi$
$257$	13.3723	0.834140	0.417070	+	0.908874i	$0.363057\pi$
$258$	7.37228	0.458978
$259$	−33.7228	−2.09543
$260$	4.74456	0.294245
$261$	2.62772	0.162652
$262$	−9.48913	−0.586240
$263$	0.861407	0.0531166	0.0265583	−	0.999647i	$-0.491545\pi$
$263$	0.861407	0.0531166	0.0265583	+	0.999647i	$0.491545\pi$
$264$	1.00000	0.0615457
$265$	−0.744563	−0.0457381
$266$	13.4891	0.827071
$267$	16.7446	1.02475
$268$	4.00000	0.244339
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	1.00000	0.0608581
$271$	−2.11684	−0.128589	−0.0642946	−	0.997931i	$-0.520480\pi$
$271$	−2.11684	−0.128589	−0.0642946	+	0.997931i	$0.520480\pi$
$272$	1.00000	0.0606339
$273$	16.0000	0.968364
$274$	−14.8614	−0.897810
$275$	1.00000	0.0603023
$276$	−3.37228	−0.202987
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	14.1168	0.846672
$279$	4.62772	0.277054
$280$	3.37228	0.201532
$281$	18.8614	1.12518	0.562589	−	0.826737i	$-0.309806\pi$
$281$	18.8614	1.12518	0.562589	+	0.826737i	$0.309806\pi$
$282$	−13.4891	−0.803266
$283$	18.7446	1.11425	0.557124	−	0.830429i	$-0.311905\pi$
$283$	18.7446	1.11425	0.557124	+	0.830429i	$0.311905\pi$
$284$	1.25544	0.0744965
$285$	4.00000	0.236940
$286$	4.74456	0.280552
$287$	−42.9783	−2.53693
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	2.62772	0.154305
$291$	−9.37228	−0.549413
$292$	−6.00000	−0.351123
$293$	30.8614	1.80294	0.901471	−	0.432839i	$-0.142488\pi$
$293$	30.8614	1.80294	0.901471	+	0.432839i	$0.142488\pi$
$294$	4.37228	0.254997
$295$	−10.7446	−0.625573
$296$	−10.0000	−0.581238
$297$	1.00000	0.0580259
$298$	−0.744563	−0.0431314
$299$	−16.0000	−0.925304
$300$	1.00000	0.0577350
$301$	24.8614	1.43299
$302$	21.4891	1.23656
$303$	6.00000	0.344691
$304$	4.00000	0.229416
$305$	−2.00000	−0.114520
$306$	1.00000	0.0571662
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	3.37228	0.192154
$309$	−3.37228	−0.191842
$310$	4.62772	0.262837
$311$	−5.48913	−0.311260	−0.155630	−	0.987815i	$-0.549741\pi$
$311$	−5.48913	−0.311260	−0.155630	+	0.987815i	$0.549741\pi$
$312$	4.74456	0.268608
$313$	18.8614	1.06611	0.533055	−	0.846081i	$-0.321044\pi$
$313$	18.8614	1.06611	0.533055	+	0.846081i	$0.321044\pi$
$314$	11.4891	0.648369
$315$	3.37228	0.190007
$316$	−13.4891	−0.758823
$317$	0.116844	0.00656261	0.00328131	−	0.999995i	$-0.498956\pi$
$317$	0.116844	0.00656261	0.00328131	+	0.999995i	$0.498956\pi$
$318$	−0.744563	−0.0417530
$319$	2.62772	0.147124
$320$	1.00000	0.0559017
$321$	14.1168	0.787925
$322$	−11.3723	−0.633752
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	4.74456	0.263181
$326$	−7.37228	−0.408313
$327$	−8.74456	−0.483575
$328$	−12.7446	−0.703701
$329$	−45.4891	−2.50790
$330$	1.00000	0.0550482
$331$	18.3505	1.00864	0.504318	−	0.863518i	$-0.331744\pi$
$331$	18.3505	1.00864	0.504318	+	0.863518i	$0.331744\pi$
$332$	−12.0000	−0.658586
$333$	−10.0000	−0.547997
$334$	−12.2337	−0.669398
$335$	4.00000	0.218543
$336$	3.37228	0.183973
$337$	−24.9783	−1.36065	−0.680326	−	0.732910i	$-0.738162\pi$
$337$	−24.9783	−1.36065	−0.680326	+	0.732910i	$0.738162\pi$
$338$	9.51087	0.517323
$339$	−11.4891	−0.624004
$340$	1.00000	0.0542326
$341$	4.62772	0.250605
$342$	4.00000	0.216295
$343$	−8.86141	−0.478471
$344$	7.37228	0.397487
$345$	−3.37228	−0.181558
$346$	11.4891	0.617659
$347$	22.9783	1.23354	0.616769	−	0.787145i	$-0.288441\pi$
$347$	22.9783	1.23354	0.616769	+	0.787145i	$0.288441\pi$
$348$	2.62772	0.140861
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	3.37228	0.180256
$351$	4.74456	0.253246
$352$	1.00000	0.0533002
$353$	−22.8614	−1.21679	−0.608395	−	0.793634i	$-0.708186\pi$
$353$	−22.8614	−1.21679	−0.608395	+	0.793634i	$0.708186\pi$
$354$	−10.7446	−0.571067
$355$	1.25544	0.0666317
$356$	16.7446	0.887460
$357$	3.37228	0.178480
$358$	−18.7446	−0.990681
$359$	−28.2337	−1.49012	−0.745059	−	0.666999i	$-0.767578\pi$
$359$	−28.2337	−1.49012	−0.745059	+	0.666999i	$0.767578\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	−14.6277	−0.768816
$363$	1.00000	0.0524864
$364$	16.0000	0.838628
$365$	−6.00000	−0.314054
$366$	−2.00000	−0.104542
$367$	−22.7446	−1.18726	−0.593628	−	0.804739i	$-0.702305\pi$
$367$	−22.7446	−1.18726	−0.593628	+	0.804739i	$0.702305\pi$
$368$	−3.37228	−0.175792
$369$	−12.7446	−0.663455
$370$	−10.0000	−0.519875
$371$	−2.51087	−0.130358
$372$	4.62772	0.239936
$373$	−23.4891	−1.21622	−0.608110	−	0.793852i	$-0.708072\pi$
$373$	−23.4891	−1.21622	−0.608110	+	0.793852i	$0.708072\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−13.4891	−0.695649
$377$	12.4674	0.642103
$378$	3.37228	0.173451
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	4.00000	0.205196
$381$	20.2337	1.03660
$382$	−4.62772	−0.236775
$383$	2.51087	0.128300	0.0641499	−	0.997940i	$-0.479566\pi$
$383$	2.51087	0.128300	0.0641499	+	0.997940i	$0.479566\pi$
$384$	1.00000	0.0510310
$385$	3.37228	0.171867
$386$	−0.510875	−0.0260028
$387$	7.37228	0.374754
$388$	−9.37228	−0.475805
$389$	−34.4674	−1.74757	−0.873783	−	0.486317i	$-0.838340\pi$
$389$	−34.4674	−1.74757	−0.873783	+	0.486317i	$0.838340\pi$
$390$	4.74456	0.240250
$391$	−3.37228	−0.170544
$392$	4.37228	0.220834
$393$	−9.48913	−0.478663
$394$	26.2337	1.32163
$395$	−13.4891	−0.678712
$396$	1.00000	0.0502519
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	13.4891	0.675301
$400$	1.00000	0.0500000
$401$	−9.37228	−0.468029	−0.234015	−	0.972233i	$-0.575186\pi$
$401$	−9.37228	−0.468029	−0.234015	+	0.972233i	$0.575186\pi$
$402$	4.00000	0.199502
$403$	21.9565	1.09373
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	8.86141	0.439784
$407$	−10.0000	−0.495682
$408$	1.00000	0.0495074
$409$	30.2337	1.49496	0.747480	−	0.664285i	$-0.231264\pi$
$409$	30.2337	1.49496	0.747480	+	0.664285i	$0.231264\pi$
$410$	−12.7446	−0.629409
$411$	−14.8614	−0.733059
$412$	−3.37228	−0.166140
$413$	−36.2337	−1.78294
$414$	−3.37228	−0.165739
$415$	−12.0000	−0.589057
$416$	4.74456	0.232621
$417$	14.1168	0.691305
$418$	4.00000	0.195646
$419$	24.6277	1.20314	0.601571	−	0.798819i	$-0.294542\pi$
$419$	24.6277	1.20314	0.601571	+	0.798819i	$0.294542\pi$
$420$	3.37228	0.164550
$421$	−16.7446	−0.816080	−0.408040	−	0.912964i	$-0.633788\pi$
$421$	−16.7446	−0.816080	−0.408040	+	0.912964i	$0.633788\pi$
$422$	−14.1168	−0.687197
$423$	−13.4891	−0.655864
$424$	−0.744563	−0.0361592
$425$	1.00000	0.0485071
$426$	1.25544	0.0608261
$427$	−6.74456	−0.326392
$428$	14.1168	0.682363
$429$	4.74456	0.229070
$430$	7.37228	0.355523
$431$	2.11684	0.101965	0.0509824	−	0.998700i	$-0.483765\pi$
$431$	2.11684	0.101965	0.0509824	+	0.998700i	$0.483765\pi$
$432$	1.00000	0.0481125
$433$	27.2554	1.30981	0.654906	−	0.755710i	$-0.272708\pi$
$433$	27.2554	1.30981	0.654906	+	0.755710i	$0.272708\pi$
$434$	15.6060	0.749110
$435$	2.62772	0.125989
$436$	−8.74456	−0.418789
$437$	−13.4891	−0.645272
$438$	−6.00000	−0.286691
$439$	−28.2337	−1.34752	−0.673760	−	0.738950i	$-0.735322\pi$
$439$	−28.2337	−1.34752	−0.673760	+	0.738950i	$0.735322\pi$
$440$	1.00000	0.0476731
$441$	4.37228	0.208204
$442$	4.74456	0.225676
$443$	−22.1168	−1.05080	−0.525401	−	0.850854i	$-0.676085\pi$
$443$	−22.1168	−1.05080	−0.525401	+	0.850854i	$0.676085\pi$
$444$	−10.0000	−0.474579
$445$	16.7446	0.793768
$446$	−11.3723	−0.538493
$447$	−0.744563	−0.0352166
$448$	3.37228	0.159325
$449$	29.3723	1.38616	0.693082	−	0.720859i	$-0.256252\pi$
$449$	29.3723	1.38616	0.693082	+	0.720859i	$0.256252\pi$
$450$	1.00000	0.0471405
$451$	−12.7446	−0.600118
$452$	−11.4891	−0.540403
$453$	21.4891	1.00965
$454$	6.11684	0.287078
$455$	16.0000	0.750092
$456$	4.00000	0.187317
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−3.25544	−0.152117
$459$	1.00000	0.0466760
$460$	−3.37228	−0.157233
$461$	0.510875	0.0237938	0.0118969	−	0.999929i	$-0.496213\pi$
$461$	0.510875	0.0237938	0.0118969	+	0.999929i	$0.496213\pi$
$462$	3.37228	0.156893
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	2.62772	0.121989
$465$	4.62772	0.214605
$466$	−14.8614	−0.688441
$467$	30.9783	1.43350	0.716751	−	0.697329i	$-0.245628\pi$
$467$	30.9783	1.43350	0.716751	+	0.697329i	$0.245628\pi$
$468$	4.74456	0.219317
$469$	13.4891	0.622870
$470$	−13.4891	−0.622207
$471$	11.4891	0.529391
$472$	−10.7446	−0.494559
$473$	7.37228	0.338978
$474$	−13.4891	−0.619576
$475$	4.00000	0.183533
$476$	3.37228	0.154568
$477$	−0.744563	−0.0340912
$478$	20.2337	0.925467
$479$	35.8397	1.63756	0.818778	−	0.574110i	$-0.194652\pi$
$479$	35.8397	1.63756	0.818778	+	0.574110i	$0.194652\pi$
$480$	1.00000	0.0456435
$481$	−47.4456	−2.16333
$482$	−9.37228	−0.426896
$483$	−11.3723	−0.517457
$484$	1.00000	0.0454545
$485$	−9.37228	−0.425573
$486$	1.00000	0.0453609
$487$	1.25544	0.0568893	0.0284446	−	0.999595i	$-0.490945\pi$
$487$	1.25544	0.0568893	0.0284446	+	0.999595i	$0.490945\pi$
$488$	−2.00000	−0.0905357
$489$	−7.37228	−0.333386
$490$	4.37228	0.197520
$491$	−6.51087	−0.293832	−0.146916	−	0.989149i	$-0.546935\pi$
$491$	−6.51087	−0.293832	−0.146916	+	0.989149i	$0.546935\pi$
$492$	−12.7446	−0.574569
$493$	2.62772	0.118346
$494$	18.9783	0.853872
$495$	1.00000	0.0449467
$496$	4.62772	0.207791
$497$	4.23369	0.189907
$498$	−12.0000	−0.537733
$499$	1.48913	0.0666624	0.0333312	−	0.999444i	$-0.489388\pi$
$499$	1.48913	0.0666624	0.0333312	+	0.999444i	$0.489388\pi$
$500$	1.00000	0.0447214
$501$	−12.2337	−0.546561
$502$	−6.51087	−0.290595
$503$	2.97825	0.132794	0.0663968	−	0.997793i	$-0.478850\pi$
$503$	2.97825	0.132794	0.0663968	+	0.997793i	$0.478850\pi$
$504$	3.37228	0.150213
$505$	6.00000	0.266996
$506$	−3.37228	−0.149916
$507$	9.51087	0.422393
$508$	20.2337	0.897725
$509$	11.4891	0.509247	0.254623	−	0.967040i	$-0.418049\pi$
$509$	11.4891	0.509247	0.254623	+	0.967040i	$0.418049\pi$
$510$	1.00000	0.0442807
$511$	−20.2337	−0.895086
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	13.3723	0.589826
$515$	−3.37228	−0.148600
$516$	7.37228	0.324547
$517$	−13.4891	−0.593251
$518$	−33.7228	−1.48170
$519$	11.4891	0.504317
$520$	4.74456	0.208063
$521$	20.9783	0.919074	0.459537	−	0.888159i	$-0.348015\pi$
$521$	20.9783	0.919074	0.459537	+	0.888159i	$0.348015\pi$
$522$	2.62772	0.115012
$523$	−24.6277	−1.07689	−0.538447	−	0.842659i	$-0.680989\pi$
$523$	−24.6277	−1.07689	−0.538447	+	0.842659i	$0.680989\pi$
$524$	−9.48913	−0.414534
$525$	3.37228	0.147178
$526$	0.861407	0.0375591
$527$	4.62772	0.201587
$528$	1.00000	0.0435194
$529$	−11.6277	−0.505553
$530$	−0.744563	−0.0323417
$531$	−10.7446	−0.466274
$532$	13.4891	0.584828
$533$	−60.4674	−2.61913
$534$	16.7446	0.724608
$535$	14.1168	0.610324
$536$	4.00000	0.172774
$537$	−18.7446	−0.808888
$538$	14.0000	0.603583
$539$	4.37228	0.188327
$540$	1.00000	0.0430331
$541$	−6.23369	−0.268007	−0.134004	−	0.990981i	$-0.542783\pi$
$541$	−6.23369	−0.268007	−0.134004	+	0.990981i	$0.542783\pi$
$542$	−2.11684	−0.0909262
$543$	−14.6277	−0.627735
$544$	1.00000	0.0428746
$545$	−8.74456	−0.374576
$546$	16.0000	0.684737
$547$	8.23369	0.352047	0.176024	−	0.984386i	$-0.443677\pi$
$547$	8.23369	0.352047	0.176024	+	0.984386i	$0.443677\pi$
$548$	−14.8614	−0.634848
$549$	−2.00000	−0.0853579
$550$	1.00000	0.0426401
$551$	10.5109	0.447778
$552$	−3.37228	−0.143534
$553$	−45.4891	−1.93439
$554$	22.0000	0.934690
$555$	−10.0000	−0.424476
$556$	14.1168	0.598688
$557$	−24.3505	−1.03177	−0.515883	−	0.856659i	$-0.672536\pi$
$557$	−24.3505	−1.03177	−0.515883	+	0.856659i	$0.672536\pi$
$558$	4.62772	0.195907
$559$	34.9783	1.47942
$560$	3.37228	0.142505
$561$	1.00000	0.0422200
$562$	18.8614	0.795620
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−13.4891	−0.567995
$565$	−11.4891	−0.483351
$566$	18.7446	0.787893
$567$	3.37228	0.141623
$568$	1.25544	0.0526770
$569$	20.9783	0.879454	0.439727	−	0.898131i	$-0.355075\pi$
$569$	20.9783	0.879454	0.439727	+	0.898131i	$0.355075\pi$
$570$	4.00000	0.167542
$571$	22.9783	0.961610	0.480805	−	0.876828i	$-0.340345\pi$
$571$	22.9783	0.961610	0.480805	+	0.876828i	$0.340345\pi$
$572$	4.74456	0.198380
$573$	−4.62772	−0.193326
$574$	−42.9783	−1.79388
$575$	−3.37228	−0.140634
$576$	1.00000	0.0416667
$577$	47.4891	1.97700	0.988499	−	0.151227i	$-0.0483224\pi$
$577$	47.4891	1.97700	0.988499	+	0.151227i	$0.0483224\pi$
$578$	1.00000	0.0415945
$579$	−0.510875	−0.0212312
$580$	2.62772	0.109110
$581$	−40.4674	−1.67887
$582$	−9.37228	−0.388494
$583$	−0.744563	−0.0308366
$584$	−6.00000	−0.248282
$585$	4.74456	0.196164
$586$	30.8614	1.27487
$587$	25.0951	1.03579	0.517893	−	0.855446i	$-0.326717\pi$
$587$	25.0951	1.03579	0.517893	+	0.855446i	$0.326717\pi$
$588$	4.37228	0.180310
$589$	18.5109	0.762727
$590$	−10.7446	−0.442347
$591$	26.2337	1.07911
$592$	−10.0000	−0.410997
$593$	−0.510875	−0.0209791	−0.0104896	−	0.999945i	$-0.503339\pi$
$593$	−0.510875	−0.0209791	−0.0104896	+	0.999945i	$0.503339\pi$
$594$	1.00000	0.0410305
$595$	3.37228	0.138250
$596$	−0.744563	−0.0304985
$597$	−8.00000	−0.327418
$598$	−16.0000	−0.654289
$599$	−30.3505	−1.24009	−0.620045	−	0.784567i	$-0.712885\pi$
$599$	−30.3505	−1.24009	−0.620045	+	0.784567i	$0.712885\pi$
$600$	1.00000	0.0408248
$601$	−8.51087	−0.347166	−0.173583	−	0.984819i	$-0.555534\pi$
$601$	−8.51087	−0.347166	−0.173583	+	0.984819i	$0.555534\pi$
$602$	24.8614	1.01328
$603$	4.00000	0.162893
$604$	21.4891	0.874380
$605$	1.00000	0.0406558
$606$	6.00000	0.243733
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	4.00000	0.162221
$609$	8.86141	0.359082
$610$	−2.00000	−0.0809776
$611$	−64.0000	−2.58916
$612$	1.00000	0.0404226
$613$	−47.9565	−1.93694	−0.968472	−	0.249121i	$-0.919858\pi$
$613$	−47.9565	−1.93694	−0.968472	+	0.249121i	$0.919858\pi$
$614$	4.00000	0.161427
$615$	−12.7446	−0.513910
$616$	3.37228	0.135873
$617$	12.5109	0.503669	0.251834	−	0.967770i	$-0.418966\pi$
$617$	12.5109	0.503669	0.251834	+	0.967770i	$0.418966\pi$
$618$	−3.37228	−0.135653
$619$	16.2337	0.652487	0.326244	−	0.945286i	$-0.394217\pi$
$619$	16.2337	0.652487	0.326244	+	0.945286i	$0.394217\pi$
$620$	4.62772	0.185854
$621$	−3.37228	−0.135325
$622$	−5.48913	−0.220094
$623$	56.4674	2.26232
$624$	4.74456	0.189935
$625$	1.00000	0.0400000
$626$	18.8614	0.753853
$627$	4.00000	0.159745
$628$	11.4891	0.458466
$629$	−10.0000	−0.398726
$630$	3.37228	0.134355
$631$	−12.2337	−0.487015	−0.243508	−	0.969899i	$-0.578298\pi$
$631$	−12.2337	−0.487015	−0.243508	+	0.969899i	$0.578298\pi$
$632$	−13.4891	−0.536569
$633$	−14.1168	−0.561094
$634$	0.116844	0.00464047
$635$	20.2337	0.802949
$636$	−0.744563	−0.0295238
$637$	20.7446	0.821929
$638$	2.62772	0.104032
$639$	1.25544	0.0496643
$640$	1.00000	0.0395285
$641$	−21.1386	−0.834924	−0.417462	−	0.908694i	$-0.637080\pi$
$641$	−21.1386	−0.834924	−0.417462	+	0.908694i	$0.637080\pi$
$642$	14.1168	0.557147
$643$	10.3505	0.408185	0.204093	−	0.978952i	$-0.434576\pi$
$643$	10.3505	0.408185	0.204093	+	0.978952i	$0.434576\pi$
$644$	−11.3723	−0.448131
$645$	7.37228	0.290283
$646$	4.00000	0.157378
$647$	−25.7228	−1.01127	−0.505634	−	0.862748i	$-0.668741\pi$
$647$	−25.7228	−1.01127	−0.505634	+	0.862748i	$0.668741\pi$
$648$	1.00000	0.0392837
$649$	−10.7446	−0.421761
$650$	4.74456	0.186097
$651$	15.6060	0.611646
$652$	−7.37228	−0.288721
$653$	16.1168	0.630701	0.315350	−	0.948975i	$-0.397878\pi$
$653$	16.1168	0.630701	0.315350	+	0.948975i	$0.397878\pi$
$654$	−8.74456	−0.341939
$655$	−9.48913	−0.370771
$656$	−12.7446	−0.497592
$657$	−6.00000	−0.234082
$658$	−45.4891	−1.77335
$659$	31.3723	1.22209	0.611045	−	0.791596i	$-0.290749\pi$
$659$	31.3723	1.22209	0.611045	+	0.791596i	$0.290749\pi$
$660$	1.00000	0.0389249
$661$	−5.76631	−0.224284	−0.112142	−	0.993692i	$-0.535771\pi$
$661$	−5.76631	−0.224284	−0.112142	+	0.993692i	$0.535771\pi$
$662$	18.3505	0.713214
$663$	4.74456	0.184264
$664$	−12.0000	−0.465690
$665$	13.4891	0.523086
$666$	−10.0000	−0.387492
$667$	−8.86141	−0.343115
$668$	−12.2337	−0.473336
$669$	−11.3723	−0.439678
$670$	4.00000	0.154533
$671$	−2.00000	−0.0772091
$672$	3.37228	0.130089
$673$	−18.2337	−0.702857	−0.351429	−	0.936215i	$-0.614304\pi$
$673$	−18.2337	−0.702857	−0.351429	+	0.936215i	$0.614304\pi$
$674$	−24.9783	−0.962126
$675$	1.00000	0.0384900
$676$	9.51087	0.365803
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	−11.4891	−0.441237
$679$	−31.6060	−1.21293
$680$	1.00000	0.0383482
$681$	6.11684	0.234398
$682$	4.62772	0.177205
$683$	−6.51087	−0.249132	−0.124566	−	0.992211i	$-0.539754\pi$
$683$	−6.51087	−0.249132	−0.124566	+	0.992211i	$0.539754\pi$
$684$	4.00000	0.152944
$685$	−14.8614	−0.567825
$686$	−8.86141	−0.338330
$687$	−3.25544	−0.124203
$688$	7.37228	0.281066
$689$	−3.53262	−0.134582
$690$	−3.37228	−0.128381
$691$	46.9783	1.78714	0.893568	−	0.448927i	$-0.148194\pi$
$691$	46.9783	1.78714	0.893568	+	0.448927i	$0.148194\pi$
$692$	11.4891	0.436751
$693$	3.37228	0.128102
$694$	22.9783	0.872242
$695$	14.1168	0.535482
$696$	2.62772	0.0996034
$697$	−12.7446	−0.482735
$698$	−2.00000	−0.0757011
$699$	−14.8614	−0.562110
$700$	3.37228	0.127460
$701$	11.4891	0.433938	0.216969	−	0.976178i	$-0.430383\pi$
$701$	11.4891	0.433938	0.216969	+	0.976178i	$0.430383\pi$
$702$	4.74456	0.179072
$703$	−40.0000	−1.50863
$704$	1.00000	0.0376889
$705$	−13.4891	−0.508030
$706$	−22.8614	−0.860400
$707$	20.2337	0.760966
$708$	−10.7446	−0.403805
$709$	30.4674	1.14423	0.572113	−	0.820175i	$-0.306124\pi$
$709$	30.4674	1.14423	0.572113	+	0.820175i	$0.306124\pi$
$710$	1.25544	0.0471157
$711$	−13.4891	−0.505882
$712$	16.7446	0.627529
$713$	−15.6060	−0.584448
$714$	3.37228	0.126204
$715$	4.74456	0.177437
$716$	−18.7446	−0.700517
$717$	20.2337	0.755641
$718$	−28.2337	−1.05367
$719$	−49.7228	−1.85435	−0.927174	−	0.374631i	$-0.877769\pi$
$719$	−49.7228	−1.85435	−0.927174	+	0.374631i	$0.877769\pi$
$720$	1.00000	0.0372678
$721$	−11.3723	−0.423526
$722$	−3.00000	−0.111648
$723$	−9.37228	−0.348559
$724$	−14.6277	−0.543635
$725$	2.62772	0.0975910
$726$	1.00000	0.0371135
$727$	−14.3505	−0.532232	−0.266116	−	0.963941i	$-0.585740\pi$
$727$	−14.3505	−0.532232	−0.266116	+	0.963941i	$0.585740\pi$
$728$	16.0000	0.592999
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	7.37228	0.272674
$732$	−2.00000	−0.0739221
$733$	2.23369	0.0825031	0.0412516	−	0.999149i	$-0.486865\pi$
$733$	2.23369	0.0825031	0.0412516	+	0.999149i	$0.486865\pi$
$734$	−22.7446	−0.839517
$735$	4.37228	0.161274
$736$	−3.37228	−0.124304
$737$	4.00000	0.147342
$738$	−12.7446	−0.469134
$739$	10.7446	0.395245	0.197623	−	0.980278i	$-0.436678\pi$
$739$	10.7446	0.395245	0.197623	+	0.980278i	$0.436678\pi$
$740$	−10.0000	−0.367607
$741$	18.9783	0.697183
$742$	−2.51087	−0.0921771
$743$	5.48913	0.201376	0.100688	−	0.994918i	$-0.467896\pi$
$743$	5.48913	0.201376	0.100688	+	0.994918i	$0.467896\pi$
$744$	4.62772	0.169660
$745$	−0.744563	−0.0272787
$746$	−23.4891	−0.859998
$747$	−12.0000	−0.439057
$748$	1.00000	0.0365636
$749$	47.6060	1.73948
$750$	1.00000	0.0365148
$751$	−20.6277	−0.752716	−0.376358	−	0.926474i	$-0.622824\pi$
$751$	−20.6277	−0.752716	−0.376358	+	0.926474i	$0.622824\pi$
$752$	−13.4891	−0.491898
$753$	−6.51087	−0.237269
$754$	12.4674	0.454035
$755$	21.4891	0.782069
$756$	3.37228	0.122649
$757$	19.8832	0.722666	0.361333	−	0.932437i	$-0.382322\pi$
$757$	19.8832	0.722666	0.361333	+	0.932437i	$0.382322\pi$
$758$	28.0000	1.01701
$759$	−3.37228	−0.122406
$760$	4.00000	0.145095
$761$	−44.3505	−1.60771	−0.803853	−	0.594828i	$-0.797220\pi$
$761$	−44.3505	−1.60771	−0.803853	+	0.594828i	$0.797220\pi$
$762$	20.2337	0.732989
$763$	−29.4891	−1.06758
$764$	−4.62772	−0.167425
$765$	1.00000	0.0361551
$766$	2.51087	0.0907216
$767$	−50.9783	−1.84072
$768$	1.00000	0.0360844
$769$	15.4891	0.558552	0.279276	−	0.960211i	$-0.409906\pi$
$769$	15.4891	0.558552	0.279276	+	0.960211i	$0.409906\pi$
$770$	3.37228	0.121529
$771$	13.3723	0.481591
$772$	−0.510875	−0.0183868
$773$	15.2554	0.548700	0.274350	−	0.961630i	$-0.411537\pi$
$773$	15.2554	0.548700	0.274350	+	0.961630i	$0.411537\pi$
$774$	7.37228	0.264991
$775$	4.62772	0.166233
$776$	−9.37228	−0.336445
$777$	−33.7228	−1.20980
$778$	−34.4674	−1.23572
$779$	−50.9783	−1.82649
$780$	4.74456	0.169883
$781$	1.25544	0.0449231
$782$	−3.37228	−0.120593
$783$	2.62772	0.0939070
$784$	4.37228	0.156153
$785$	11.4891	0.410064
$786$	−9.48913	−0.338466
$787$	−25.4891	−0.908589	−0.454295	−	0.890852i	$-0.650109\pi$
$787$	−25.4891	−0.908589	−0.454295	+	0.890852i	$0.650109\pi$
$788$	26.2337	0.934536
$789$	0.861407	0.0306669
$790$	−13.4891	−0.479922
$791$	−38.7446	−1.37760
$792$	1.00000	0.0355335
$793$	−9.48913	−0.336969
$794$	−2.00000	−0.0709773
$795$	−0.744563	−0.0264069
$796$	−8.00000	−0.283552
$797$	39.2554	1.39050	0.695249	−	0.718769i	$-0.255294\pi$
$797$	39.2554	1.39050	0.695249	+	0.718769i	$0.255294\pi$
$798$	13.4891	0.477510
$799$	−13.4891	−0.477211
$800$	1.00000	0.0353553
$801$	16.7446	0.591640
$802$	−9.37228	−0.330947
$803$	−6.00000	−0.211735
$804$	4.00000	0.141069
$805$	−11.3723	−0.400820
$806$	21.9565	0.773385
$807$	14.0000	0.492823
$808$	6.00000	0.211079
$809$	−48.9783	−1.72198	−0.860992	−	0.508619i	$-0.830156\pi$
$809$	−48.9783	−1.72198	−0.860992	+	0.508619i	$0.830156\pi$
$810$	1.00000	0.0351364
$811$	−1.48913	−0.0522903	−0.0261451	−	0.999658i	$-0.508323\pi$
$811$	−1.48913	−0.0522903	−0.0261451	+	0.999658i	$0.508323\pi$
$812$	8.86141	0.310974
$813$	−2.11684	−0.0742410
$814$	−10.0000	−0.350500
$815$	−7.37228	−0.258240
$816$	1.00000	0.0350070
$817$	29.4891	1.03169
$818$	30.2337	1.05710
$819$	16.0000	0.559085
$820$	−12.7446	−0.445059
$821$	17.3723	0.606297	0.303148	−	0.952943i	$-0.401962\pi$
$821$	17.3723	0.606297	0.303148	+	0.952943i	$0.401962\pi$
$822$	−14.8614	−0.518351
$823$	17.2554	0.601487	0.300743	−	0.953705i	$-0.402765\pi$
$823$	17.2554	0.601487	0.300743	+	0.953705i	$0.402765\pi$
$824$	−3.37228	−0.117479
$825$	1.00000	0.0348155
$826$	−36.2337	−1.26073
$827$	−6.11684	−0.212704	−0.106352	−	0.994329i	$-0.533917\pi$
$827$	−6.11684	−0.212704	−0.106352	+	0.994329i	$0.533917\pi$
$828$	−3.37228	−0.117195
$829$	24.9783	0.867531	0.433765	−	0.901026i	$-0.357185\pi$
$829$	24.9783	0.867531	0.433765	+	0.901026i	$0.357185\pi$
$830$	−12.0000	−0.416526
$831$	22.0000	0.763172
$832$	4.74456	0.164488
$833$	4.37228	0.151491
$834$	14.1168	0.488826
$835$	−12.2337	−0.423364
$836$	4.00000	0.138343
$837$	4.62772	0.159957
$838$	24.6277	0.850750
$839$	14.7446	0.509039	0.254519	−	0.967068i	$-0.418083\pi$
$839$	14.7446	0.509039	0.254519	+	0.967068i	$0.418083\pi$
$840$	3.37228	0.116355
$841$	−22.0951	−0.761900
$842$	−16.7446	−0.577056
$843$	18.8614	0.649621
$844$	−14.1168	−0.485922
$845$	9.51087	0.327184
$846$	−13.4891	−0.463766
$847$	3.37228	0.115873
$848$	−0.744563	−0.0255684
$849$	18.7446	0.643312
$850$	1.00000	0.0342997
$851$	33.7228	1.15600
$852$	1.25544	0.0430106
$853$	−34.8614	−1.19363	−0.596816	−	0.802378i	$-0.703568\pi$
$853$	−34.8614	−1.19363	−0.596816	+	0.802378i	$0.703568\pi$
$854$	−6.74456	−0.230794
$855$	4.00000	0.136797
$856$	14.1168	0.482504
$857$	10.3940	0.355053	0.177527	−	0.984116i	$-0.443190\pi$
$857$	10.3940	0.355053	0.177527	+	0.984116i	$0.443190\pi$
$858$	4.74456	0.161977
$859$	−15.3723	−0.524495	−0.262248	−	0.965001i	$-0.584464\pi$
$859$	−15.3723	−0.524495	−0.262248	+	0.965001i	$0.584464\pi$
$860$	7.37228	0.251393
$861$	−42.9783	−1.46469
$862$	2.11684	0.0721000
$863$	−10.9783	−0.373704	−0.186852	−	0.982388i	$-0.559828\pi$
$863$	−10.9783	−0.373704	−0.186852	+	0.982388i	$0.559828\pi$
$864$	1.00000	0.0340207
$865$	11.4891	0.390642
$866$	27.2554	0.926177
$867$	1.00000	0.0339618
$868$	15.6060	0.529701
$869$	−13.4891	−0.457587
$870$	2.62772	0.0890880
$871$	18.9783	0.643053
$872$	−8.74456	−0.296128
$873$	−9.37228	−0.317204
$874$	−13.4891	−0.456276
$875$	3.37228	0.114004
$876$	−6.00000	−0.202721
$877$	−42.8614	−1.44733	−0.723663	−	0.690153i	$-0.757543\pi$
$877$	−42.8614	−1.44733	−0.723663	+	0.690153i	$0.757543\pi$
$878$	−28.2337	−0.952841
$879$	30.8614	1.04093
$880$	1.00000	0.0337100
$881$	17.6060	0.593160	0.296580	−	0.955008i	$-0.404154\pi$
$881$	17.6060	0.593160	0.296580	+	0.955008i	$0.404154\pi$
$882$	4.37228	0.147222
$883$	−33.9565	−1.14273	−0.571364	−	0.820697i	$-0.693585\pi$
$883$	−33.9565	−1.14273	−0.571364	+	0.820697i	$0.693585\pi$
$884$	4.74456	0.159577
$885$	−10.7446	−0.361175
$886$	−22.1168	−0.743030
$887$	−59.4456	−1.99599	−0.997994	−	0.0633023i	$-0.979837\pi$
$887$	−59.4456	−1.99599	−0.997994	+	0.0633023i	$0.979837\pi$
$888$	−10.0000	−0.335578
$889$	68.2337	2.28848
$890$	16.7446	0.561279
$891$	1.00000	0.0335013
$892$	−11.3723	−0.380772
$893$	−53.9565	−1.80559
$894$	−0.744563	−0.0249019
$895$	−18.7446	−0.626562
$896$	3.37228	0.112660
$897$	−16.0000	−0.534224
$898$	29.3723	0.980166
$899$	12.1603	0.405570
$900$	1.00000	0.0333333
$901$	−0.744563	−0.0248050
$902$	−12.7446	−0.424348
$903$	24.8614	0.827336
$904$	−11.4891	−0.382123
$905$	−14.6277	−0.486242
$906$	21.4891	0.713928
$907$	−30.5842	−1.01553	−0.507766	−	0.861495i	$-0.669529\pi$
$907$	−30.5842	−1.01553	−0.507766	+	0.861495i	$0.669529\pi$
$908$	6.11684	0.202995
$909$	6.00000	0.199007
$910$	16.0000	0.530395
$911$	−5.02175	−0.166378	−0.0831890	−	0.996534i	$-0.526511\pi$
$911$	−5.02175	−0.166378	−0.0831890	+	0.996534i	$0.526511\pi$
$912$	4.00000	0.132453
$913$	−12.0000	−0.397142
$914$	10.0000	0.330771
$915$	−2.00000	−0.0661180
$916$	−3.25544	−0.107563
$917$	−32.0000	−1.05673
$918$	1.00000	0.0330049
$919$	15.1386	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$919$	15.1386	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$920$	−3.37228	−0.111181
$921$	4.00000	0.131804
$922$	0.510875	0.0168248
$923$	5.95650	0.196061
$924$	3.37228	0.110940
$925$	−10.0000	−0.328798
$926$	16.0000	0.525793
$927$	−3.37228	−0.110760
$928$	2.62772	0.0862591
$929$	−2.62772	−0.0862127	−0.0431063	−	0.999070i	$-0.513725\pi$
$929$	−2.62772	−0.0862127	−0.0431063	+	0.999070i	$0.513725\pi$
$930$	4.62772	0.151749
$931$	17.4891	0.573183
$932$	−14.8614	−0.486802
$933$	−5.48913	−0.179706
$934$	30.9783	1.01364
$935$	1.00000	0.0327035
$936$	4.74456	0.155081
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	13.4891	0.440436
$939$	18.8614	0.615519
$940$	−13.4891	−0.439967
$941$	−2.00000	−0.0651981	−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000	−0.0651981	−0.0325991	+	0.999469i	$0.510378\pi$
$942$	11.4891	0.374336
$943$	42.9783	1.39956
$944$	−10.7446	−0.349706
$945$	3.37228	0.109700
$946$	7.37228	0.239694
$947$	29.2554	0.950674	0.475337	−	0.879804i	$-0.342326\pi$
$947$	29.2554	0.950674	0.475337	+	0.879804i	$0.342326\pi$
$948$	−13.4891	−0.438106
$949$	−28.4674	−0.924090
$950$	4.00000	0.129777
$951$	0.116844	0.00378893
$952$	3.37228	0.109296
$953$	−24.5109	−0.793985	−0.396993	−	0.917822i	$-0.629946\pi$
$953$	−24.5109	−0.793985	−0.396993	+	0.917822i	$0.629946\pi$
$954$	−0.744563	−0.0241061
$955$	−4.62772	−0.149749
$956$	20.2337	0.654404
$957$	2.62772	0.0849421
$958$	35.8397	1.15793
$959$	−50.1168	−1.61836
$960$	1.00000	0.0322749
$961$	−9.58422	−0.309168
$962$	−47.4456	−1.52971
$963$	14.1168	0.454909
$964$	−9.37228	−0.301861
$965$	−0.510875	−0.0164456
$966$	−11.3723	−0.365897
$967$	−30.7446	−0.988678	−0.494339	−	0.869269i	$-0.664590\pi$
$967$	−30.7446	−0.988678	−0.494339	+	0.869269i	$0.664590\pi$
$968$	1.00000	0.0321412
$969$	4.00000	0.128499
$970$	−9.37228	−0.300926
$971$	−44.4674	−1.42703	−0.713513	−	0.700642i	$-0.752897\pi$
$971$	−44.4674	−1.42703	−0.713513	+	0.700642i	$0.752897\pi$
$972$	1.00000	0.0320750
$973$	47.6060	1.52618
$974$	1.25544	0.0402268
$975$	4.74456	0.151948
$976$	−2.00000	−0.0640184
$977$	−14.0000	−0.447900	−0.223950	−	0.974601i	$-0.571895\pi$
$977$	−14.0000	−0.447900	−0.223950	+	0.974601i	$0.571895\pi$
$978$	−7.37228	−0.235740
$979$	16.7446	0.535159
$980$	4.37228	0.139667
$981$	−8.74456	−0.279192
$982$	−6.51087	−0.207770
$983$	−8.39403	−0.267728	−0.133864	−	0.991000i	$-0.542739\pi$
$983$	−8.39403	−0.267728	−0.133864	+	0.991000i	$0.542739\pi$
$984$	−12.7446	−0.406282
$985$	26.2337	0.835875
$986$	2.62772	0.0836836
$987$	−45.4891	−1.44793
$988$	18.9783	0.603779
$989$	−24.8614	−0.790547
$990$	1.00000	0.0317821
$991$	35.8397	1.13848	0.569242	−	0.822170i	$-0.307237\pi$
$991$	35.8397	1.13848	0.569242	+	0.822170i	$0.307237\pi$
$992$	4.62772	0.146930
$993$	18.3505	0.582337
$994$	4.23369	0.134284
$995$	−8.00000	−0.253617
$996$	−12.0000	−0.380235
$997$	−28.1168	−0.890469	−0.445235	−	0.895414i	$-0.646880\pi$
$997$	−28.1168	−0.890469	−0.445235	+	0.895414i	$0.646880\pi$
$998$	1.48913	0.0471374
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bx.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bx.1.2	✓	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.74456 q^{13} +3.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +3.37228 q^{21} +1.00000 q^{22} -3.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.74456 q^{26} +1.00000 q^{27} +3.37228 q^{28} +2.62772 q^{29} +1.00000 q^{30} +4.62772 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +3.37228 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +4.74456 q^{39} +1.00000 q^{40} -12.7446 q^{41} +3.37228 q^{42} +7.37228 q^{43} +1.00000 q^{44} +1.00000 q^{45} -3.37228 q^{46} -13.4891 q^{47} +1.00000 q^{48} +4.37228 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.74456 q^{52} -0.744563 q^{53} +1.00000 q^{54} +1.00000 q^{55} +3.37228 q^{56} +4.00000 q^{57} +2.62772 q^{58} -10.7446 q^{59} +1.00000 q^{60} -2.00000 q^{61} +4.62772 q^{62} +3.37228 q^{63} +1.00000 q^{64} +4.74456 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} -3.37228 q^{69} +3.37228 q^{70} +1.25544 q^{71} +1.00000 q^{72} -6.00000 q^{73} -10.0000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +3.37228 q^{77} +4.74456 q^{78} -13.4891 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.7446 q^{82} -12.0000 q^{83} +3.37228 q^{84} +1.00000 q^{85} +7.37228 q^{86} +2.62772 q^{87} +1.00000 q^{88} +16.7446 q^{89} +1.00000 q^{90} +16.0000 q^{91} -3.37228 q^{92} +4.62772 q^{93} -13.4891 q^{94} +4.00000 q^{95} +1.00000 q^{96} -9.37228 q^{97} +4.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} + 2 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 + 2 * q^22 - q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + q^28 + 11 * q^29 + 2 * q^30 + 15 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 + q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 - 14 * q^41 + q^42 + 9 * q^43 + 2 * q^44 + 2 * q^45 - q^46 - 4 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 + 2 * q^55 + q^56 + 8 * q^57 + 11 * q^58 - 10 * q^59 + 2 * q^60 - 4 * q^61 + 15 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 - q^69 + q^70 + 14 * q^71 + 2 * q^72 - 12 * q^73 - 20 * q^74 + 2 * q^75 + 8 * q^76 + q^77 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 - 14 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 9 * q^86 + 11 * q^87 + 2 * q^88 + 22 * q^89 + 2 * q^90 + 32 * q^91 - q^92 + 15 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 13 * q^97 + 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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