LMFDB - Embedded newform 5610.2.a.bp.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:	$1$
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.37228 q^{13} -3.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.37228 q^{19} -1.00000 q^{20} -3.37228 q^{21} +1.00000 q^{22} +3.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.37228 q^{26} -1.00000 q^{27} +3.37228 q^{28} -2.00000 q^{29} -1.00000 q^{30} +7.37228 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.37228 q^{35} +1.00000 q^{36} -2.62772 q^{37} +3.37228 q^{38} +1.37228 q^{39} +1.00000 q^{40} -6.00000 q^{41} +3.37228 q^{42} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} -3.37228 q^{46} +2.74456 q^{47} -1.00000 q^{48} +4.37228 q^{49} -1.00000 q^{50} +1.00000 q^{51} -1.37228 q^{52} -11.4891 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.37228 q^{56} +3.37228 q^{57} +2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} -4.11684 q^{61} -7.37228 q^{62} +3.37228 q^{63} +1.00000 q^{64} +1.37228 q^{65} -1.00000 q^{66} +0.627719 q^{67} -1.00000 q^{68} -3.37228 q^{69} +3.37228 q^{70} -6.74456 q^{71} -1.00000 q^{72} -12.7446 q^{73} +2.62772 q^{74} -1.00000 q^{75} -3.37228 q^{76} -3.37228 q^{77} -1.37228 q^{78} -6.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -7.37228 q^{83} -3.37228 q^{84} +1.00000 q^{85} -4.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -4.62772 q^{91} +3.37228 q^{92} -7.37228 q^{93} -2.74456 q^{94} +3.37228 q^{95} +1.00000 q^{96} +9.37228 q^{97} -4.37228 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+O(q^{10}) $ 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - q^{21} + 2 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 4 q^{29} - 2 q^{30} + 9 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} - q^{35} + 2 q^{36} - 11 q^{37} + q^{38} - 3 q^{39} + 2 q^{40} - 12 q^{41} + q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} - q^{46} - 6 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} + 2 q^{51} + 3 q^{52} + 2 q^{54} + 2 q^{55} - q^{56} + q^{57} + 4 q^{58} + 8 q^{59} + 2 q^{60} + 9 q^{61} - 9 q^{62} + q^{63} + 2 q^{64} - 3 q^{65} - 2 q^{66} + 7 q^{67} - 2 q^{68} - q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 14 q^{73} + 11 q^{74} - 2 q^{75} - q^{76} - q^{77} + 3 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 9 q^{83} - q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} + 2 q^{88} + 20 q^{89} + 2 q^{90} - 15 q^{91} + q^{92} - 9 q^{93} + 6 q^{94} + q^{95} + 2 q^{96} + 13 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - q^21 + 2 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 4 * q^29 - 2 * q^30 + 9 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - q^35 + 2 * q^36 - 11 * q^37 + q^38 - 3 * q^39 + 2 * q^40 - 12 * q^41 + q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 - q^46 - 6 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 + 2 * q^51 + 3 * q^52 + 2 * q^54 + 2 * q^55 - q^56 + q^57 + 4 * q^58 + 8 * q^59 + 2 * q^60 + 9 * q^61 - 9 * q^62 + q^63 + 2 * q^64 - 3 * q^65 - 2 * q^66 + 7 * q^67 - 2 * q^68 - q^69 + q^70 - 2 * q^71 - 2 * q^72 - 14 * q^73 + 11 * q^74 - 2 * q^75 - q^76 - q^77 + 3 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 9 * q^83 - q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 + 2 * q^88 + 20 * q^89 + 2 * q^90 - 15 * q^91 + q^92 - 9 * q^93 + 6 * q^94 + q^95 + 2 * q^96 + 13 * q^97 - 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−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
$13$	−1.37228	−0.380602	−0.190301	−	0.981726i	$-0.560946\pi$
$13$	−1.37228	−0.380602	−0.190301	+	0.981726i	$0.560946\pi$
$14$	−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
$19$	−3.37228	−0.773654	−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228	−0.773654	−0.386827	+	0.922152i	$0.626429\pi$
$20$	−1.00000	−0.223607
$21$	−3.37228	−0.735892
$22$	1.00000	0.213201
$23$	3.37228	0.703169	0.351585	−	0.936156i	$-0.385643\pi$
$23$	3.37228	0.703169	0.351585	+	0.936156i	$0.385643\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	1.37228	0.269127
$27$	−1.00000	−0.192450
$28$	3.37228	0.637301
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	7.37228	1.32410	0.662050	−	0.749459i	$-0.269686\pi$
$31$	7.37228	1.32410	0.662050	+	0.749459i	$0.269686\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	−3.37228	−0.570020
$36$	1.00000	0.166667
$37$	−2.62772	−0.431994	−0.215997	−	0.976394i	$-0.569300\pi$
$37$	−2.62772	−0.431994	−0.215997	+	0.976394i	$0.569300\pi$
$38$	3.37228	0.547056
$39$	1.37228	0.219741
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	3.37228	0.520354
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−3.37228	−0.497216
$47$	2.74456	0.400336	0.200168	−	0.979762i	$-0.435851\pi$
$47$	2.74456	0.400336	0.200168	+	0.979762i	$0.435851\pi$
$48$	−1.00000	−0.144338
$49$	4.37228	0.624612
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	−1.37228	−0.190301
$53$	−11.4891	−1.57815	−0.789076	−	0.614295i	$-0.789440\pi$
$53$	−11.4891	−1.57815	−0.789076	+	0.614295i	$0.789440\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−3.37228	−0.450640
$57$	3.37228	0.446670
$58$	2.00000	0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	1.00000	0.129099
$61$	−4.11684	−0.527108	−0.263554	−	0.964645i	$-0.584895\pi$
$61$	−4.11684	−0.527108	−0.263554	+	0.964645i	$0.584895\pi$
$62$	−7.37228	−0.936281
$63$	3.37228	0.424868
$64$	1.00000	0.125000
$65$	1.37228	0.170211
$66$	−1.00000	−0.123091
$67$	0.627719	0.0766880	0.0383440	−	0.999265i	$-0.487792\pi$
$67$	0.627719	0.0766880	0.0383440	+	0.999265i	$0.487792\pi$
$68$	−1.00000	−0.121268
$69$	−3.37228	−0.405975
$70$	3.37228	0.403065
$71$	−6.74456	−0.800432	−0.400216	−	0.916421i	$-0.631065\pi$
$71$	−6.74456	−0.800432	−0.400216	+	0.916421i	$0.631065\pi$
$72$	−1.00000	−0.117851
$73$	−12.7446	−1.49164	−0.745819	−	0.666149i	$-0.767942\pi$
$73$	−12.7446	−1.49164	−0.745819	+	0.666149i	$0.767942\pi$
$74$	2.62772	0.305466
$75$	−1.00000	−0.115470
$76$	−3.37228	−0.386827
$77$	−3.37228	−0.384307
$78$	−1.37228	−0.155380
$79$	−6.74456	−0.758823	−0.379411	−	0.925228i	$-0.623873\pi$
$79$	−6.74456	−0.758823	−0.379411	+	0.925228i	$0.623873\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−7.37228	−0.809213	−0.404607	−	0.914491i	$-0.632592\pi$
$83$	−7.37228	−0.809213	−0.404607	+	0.914491i	$0.632592\pi$
$84$	−3.37228	−0.367946
$85$	1.00000	0.108465
$86$	−4.00000	−0.431331
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	−4.62772	−0.485117
$92$	3.37228	0.351585
$93$	−7.37228	−0.764470
$94$	−2.74456	−0.283080
$95$	3.37228	0.345989
$96$	1.00000	0.102062
$97$	9.37228	0.951611	0.475805	−	0.879551i	$-0.342157\pi$
$97$	9.37228	0.951611	0.475805	+	0.879551i	$0.342157\pi$
$98$	−4.37228	−0.441667
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−11.4891	−1.14321	−0.571605	−	0.820529i	$-0.693679\pi$
$101$	−11.4891	−1.14321	−0.571605	+	0.820529i	$0.693679\pi$
$102$	−1.00000	−0.0990148
$103$	10.1168	0.996842	0.498421	−	0.866935i	$-0.333913\pi$
$103$	10.1168	0.996842	0.498421	+	0.866935i	$0.333913\pi$
$104$	1.37228	0.134563
$105$	3.37228	0.329101
$106$	11.4891	1.11592
$107$	−14.7446	−1.42541	−0.712705	−	0.701464i	$-0.752530\pi$
$107$	−14.7446	−1.42541	−0.712705	+	0.701464i	$0.752530\pi$
$108$	−1.00000	−0.0962250
$109$	16.1168	1.54371	0.771857	−	0.635796i	$-0.219328\pi$
$109$	16.1168	1.54371	0.771857	+	0.635796i	$0.219328\pi$
$110$	−1.00000	−0.0953463
$111$	2.62772	0.249412
$112$	3.37228	0.318651
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−3.37228	−0.315843
$115$	−3.37228	−0.314467
$116$	−2.00000	−0.185695
$117$	−1.37228	−0.126867
$118$	−4.00000	−0.368230
$119$	−3.37228	−0.309137
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	4.11684	0.372722
$123$	6.00000	0.541002
$124$	7.37228	0.662050
$125$	−1.00000	−0.0894427
$126$	−3.37228	−0.300427
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−1.37228	−0.120357
$131$	7.37228	0.644119	0.322060	−	0.946719i	$-0.395625\pi$
$131$	7.37228	0.644119	0.322060	+	0.946719i	$0.395625\pi$
$132$	1.00000	0.0870388
$133$	−11.3723	−0.986102
$134$	−0.627719	−0.0542266
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	0.116844	0.00998265	0.00499133	−	0.999988i	$-0.498411\pi$
$137$	0.116844	0.00998265	0.00499133	+	0.999988i	$0.498411\pi$
$138$	3.37228	0.287068
$139$	10.7446	0.911342	0.455671	−	0.890148i	$-0.349399\pi$
$139$	10.7446	0.911342	0.455671	+	0.890148i	$0.349399\pi$
$140$	−3.37228	−0.285010
$141$	−2.74456	−0.231134
$142$	6.74456	0.565991
$143$	1.37228	0.114756
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	12.7446	1.05475
$147$	−4.37228	−0.360620
$148$	−2.62772	−0.215997
$149$	4.11684	0.337265	0.168632	−	0.985679i	$-0.446065\pi$
$149$	4.11684	0.337265	0.168632	+	0.985679i	$0.446065\pi$
$150$	1.00000	0.0816497
$151$	15.3723	1.25098	0.625489	−	0.780233i	$-0.284899\pi$
$151$	15.3723	1.25098	0.625489	+	0.780233i	$0.284899\pi$
$152$	3.37228	0.273528
$153$	−1.00000	−0.0808452
$154$	3.37228	0.271746
$155$	−7.37228	−0.592156
$156$	1.37228	0.109870
$157$	−0.744563	−0.0594226	−0.0297113	−	0.999559i	$-0.509459\pi$
$157$	−0.744563	−0.0594226	−0.0297113	+	0.999559i	$0.509459\pi$
$158$	6.74456	0.536569
$159$	11.4891	0.911147
$160$	1.00000	0.0790569
$161$	11.3723	0.896261
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−6.00000	−0.468521
$165$	−1.00000	−0.0778499
$166$	7.37228	0.572200
$167$	1.48913	0.115232	0.0576160	−	0.998339i	$-0.481650\pi$
$167$	1.48913	0.115232	0.0576160	+	0.998339i	$0.481650\pi$
$168$	3.37228	0.260177
$169$	−11.1168	−0.855142
$170$	−1.00000	−0.0766965
$171$	−3.37228	−0.257885
$172$	4.00000	0.304997
$173$	−22.8614	−1.73812	−0.869060	−	0.494706i	$-0.835276\pi$
$173$	−22.8614	−1.73812	−0.869060	+	0.494706i	$0.835276\pi$
$174$	−2.00000	−0.151620
$175$	3.37228	0.254921
$176$	−1.00000	−0.0753778
$177$	−4.00000	−0.300658
$178$	−10.0000	−0.749532
$179$	−14.1168	−1.05514	−0.527571	−	0.849511i	$-0.676897\pi$
$179$	−14.1168	−1.05514	−0.527571	+	0.849511i	$0.676897\pi$
$180$	−1.00000	−0.0745356
$181$	12.7446	0.947296	0.473648	−	0.880714i	$-0.342937\pi$
$181$	12.7446	0.947296	0.473648	+	0.880714i	$0.342937\pi$
$182$	4.62772	0.343029
$183$	4.11684	0.304326
$184$	−3.37228	−0.248608
$185$	2.62772	0.193194
$186$	7.37228	0.540562
$187$	1.00000	0.0731272
$188$	2.74456	0.200168
$189$	−3.37228	−0.245297
$190$	−3.37228	−0.244651
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	11.2554	0.810184	0.405092	−	0.914276i	$-0.367239\pi$
$193$	11.2554	0.810184	0.405092	+	0.914276i	$0.367239\pi$
$194$	−9.37228	−0.672891
$195$	−1.37228	−0.0982711
$196$	4.37228	0.312306
$197$	25.6060	1.82435	0.912175	−	0.409801i	$-0.134402\pi$
$197$	25.6060	1.82435	0.912175	+	0.409801i	$0.134402\pi$
$198$	1.00000	0.0710669
$199$	−8.62772	−0.611603	−0.305801	−	0.952095i	$-0.598924\pi$
$199$	−8.62772	−0.611603	−0.305801	+	0.952095i	$0.598924\pi$
$200$	−1.00000	−0.0707107
$201$	−0.627719	−0.0442759
$202$	11.4891	0.808372
$203$	−6.74456	−0.473375
$204$	1.00000	0.0700140
$205$	6.00000	0.419058
$206$	−10.1168	−0.704874
$207$	3.37228	0.234390
$208$	−1.37228	−0.0951506
$209$	3.37228	0.233266
$210$	−3.37228	−0.232710
$211$	2.74456	0.188943	0.0944717	−	0.995528i	$-0.469884\pi$
$211$	2.74456	0.188943	0.0944717	+	0.995528i	$0.469884\pi$
$212$	−11.4891	−0.789076
$213$	6.74456	0.462130
$214$	14.7446	1.00792
$215$	−4.00000	−0.272798
$216$	1.00000	0.0680414
$217$	24.8614	1.68770
$218$	−16.1168	−1.09157
$219$	12.7446	0.861198
$220$	1.00000	0.0674200
$221$	1.37228	0.0923096
$222$	−2.62772	−0.176361
$223$	8.86141	0.593404	0.296702	−	0.954970i	$-0.404113\pi$
$223$	8.86141	0.593404	0.296702	+	0.954970i	$0.404113\pi$
$224$	−3.37228	−0.225320
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−1.25544	−0.0833263	−0.0416632	−	0.999132i	$-0.513266\pi$
$227$	−1.25544	−0.0833263	−0.0416632	+	0.999132i	$0.513266\pi$
$228$	3.37228	0.223335
$229$	−12.1168	−0.800704	−0.400352	−	0.916362i	$-0.631112\pi$
$229$	−12.1168	−0.800704	−0.400352	+	0.916362i	$0.631112\pi$
$230$	3.37228	0.222362
$231$	3.37228	0.221880
$232$	2.00000	0.131306
$233$	−23.4891	−1.53882	−0.769412	−	0.638753i	$-0.779451\pi$
$233$	−23.4891	−1.53882	−0.769412	+	0.638753i	$0.779451\pi$
$234$	1.37228	0.0897088
$235$	−2.74456	−0.179036
$236$	4.00000	0.260378
$237$	6.74456	0.438106
$238$	3.37228	0.218593
$239$	1.25544	0.0812075	0.0406037	−	0.999175i	$-0.487072\pi$
$239$	1.25544	0.0812075	0.0406037	+	0.999175i	$0.487072\pi$
$240$	1.00000	0.0645497
$241$	17.6060	1.13410	0.567050	−	0.823683i	$-0.308085\pi$
$241$	17.6060	1.13410	0.567050	+	0.823683i	$0.308085\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−4.11684	−0.263554
$245$	−4.37228	−0.279335
$246$	−6.00000	−0.382546
$247$	4.62772	0.294455
$248$	−7.37228	−0.468140
$249$	7.37228	0.467199
$250$	1.00000	0.0632456
$251$	−16.6277	−1.04953	−0.524766	−	0.851246i	$-0.675847\pi$
$251$	−16.6277	−1.04953	−0.524766	+	0.851246i	$0.675847\pi$
$252$	3.37228	0.212434
$253$	−3.37228	−0.212014
$254$	8.00000	0.501965
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−23.4891	−1.46521	−0.732606	−	0.680653i	$-0.761696\pi$
$257$	−23.4891	−1.46521	−0.732606	+	0.680653i	$0.761696\pi$
$258$	4.00000	0.249029
$259$	−8.86141	−0.550621
$260$	1.37228	0.0851053
$261$	−2.00000	−0.123797
$262$	−7.37228	−0.455461
$263$	−19.3723	−1.19455	−0.597273	−	0.802038i	$-0.703749\pi$
$263$	−19.3723	−1.19455	−0.597273	+	0.802038i	$0.703749\pi$
$264$	−1.00000	−0.0615457
$265$	11.4891	0.705771
$266$	11.3723	0.697279
$267$	−10.0000	−0.611990
$268$	0.627719	0.0383440
$269$	13.3723	0.815322	0.407661	−	0.913133i	$-0.366344\pi$
$269$	13.3723	0.815322	0.407661	+	0.913133i	$0.366344\pi$
$270$	−1.00000	−0.0608581
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−1.00000	−0.0606339
$273$	4.62772	0.280082
$274$	−0.116844	−0.00705880
$275$	−1.00000	−0.0603023
$276$	−3.37228	−0.202987
$277$	−30.2337	−1.81657	−0.908283	−	0.418356i	$-0.862606\pi$
$277$	−30.2337	−1.81657	−0.908283	+	0.418356i	$0.862606\pi$
$278$	−10.7446	−0.644416
$279$	7.37228	0.441367
$280$	3.37228	0.201532
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	2.74456	0.163436
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	−6.74456	−0.400216
$285$	−3.37228	−0.199757
$286$	−1.37228	−0.0811447
$287$	−20.2337	−1.19436
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	−9.37228	−0.549413
$292$	−12.7446	−0.745819
$293$	−15.2554	−0.891232	−0.445616	−	0.895224i	$-0.647015\pi$
$293$	−15.2554	−0.891232	−0.445616	+	0.895224i	$0.647015\pi$
$294$	4.37228	0.254997
$295$	−4.00000	−0.232889
$296$	2.62772	0.152733
$297$	1.00000	0.0580259
$298$	−4.11684	−0.238482
$299$	−4.62772	−0.267628
$300$	−1.00000	−0.0577350
$301$	13.4891	0.777500
$302$	−15.3723	−0.884575
$303$	11.4891	0.660033
$304$	−3.37228	−0.193414
$305$	4.11684	0.235730
$306$	1.00000	0.0571662
$307$	1.48913	0.0849889	0.0424944	−	0.999097i	$-0.486470\pi$
$307$	1.48913	0.0849889	0.0424944	+	0.999097i	$0.486470\pi$
$308$	−3.37228	−0.192154
$309$	−10.1168	−0.575527
$310$	7.37228	0.418717
$311$	4.23369	0.240070	0.120035	−	0.992770i	$-0.461699\pi$
$311$	4.23369	0.240070	0.120035	+	0.992770i	$0.461699\pi$
$312$	−1.37228	−0.0776901
$313$	8.11684	0.458791	0.229396	−	0.973333i	$-0.426325\pi$
$313$	8.11684	0.458791	0.229396	+	0.973333i	$0.426325\pi$
$314$	0.744563	0.0420181
$315$	−3.37228	−0.190007
$316$	−6.74456	−0.379411
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	−11.4891	−0.644278
$319$	2.00000	0.111979
$320$	−1.00000	−0.0559017
$321$	14.7446	0.822961
$322$	−11.3723	−0.633752
$323$	3.37228	0.187639
$324$	1.00000	0.0555556
$325$	−1.37228	−0.0761205
$326$	4.00000	0.221540
$327$	−16.1168	−0.891264
$328$	6.00000	0.331295
$329$	9.25544	0.510269
$330$	1.00000	0.0550482
$331$	−1.48913	−0.0818497	−0.0409249	−	0.999162i	$-0.513030\pi$
$331$	−1.48913	−0.0818497	−0.0409249	+	0.999162i	$0.513030\pi$
$332$	−7.37228	−0.404607
$333$	−2.62772	−0.143998
$334$	−1.48913	−0.0814813
$335$	−0.627719	−0.0342959
$336$	−3.37228	−0.183973
$337$	−34.2337	−1.86483	−0.932414	−	0.361392i	$-0.882302\pi$
$337$	−34.2337	−1.86483	−0.932414	+	0.361392i	$0.882302\pi$
$338$	11.1168	0.604677
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	−7.37228	−0.399231
$342$	3.37228	0.182352
$343$	−8.86141	−0.478471
$344$	−4.00000	−0.215666
$345$	3.37228	0.181558
$346$	22.8614	1.22904
$347$	25.7228	1.38087	0.690436	−	0.723393i	$-0.257418\pi$
$347$	25.7228	1.38087	0.690436	+	0.723393i	$0.257418\pi$
$348$	2.00000	0.107211
$349$	−28.9783	−1.55117	−0.775585	−	0.631243i	$-0.782545\pi$
$349$	−28.9783	−1.55117	−0.775585	+	0.631243i	$0.782545\pi$
$350$	−3.37228	−0.180256
$351$	1.37228	0.0732470
$352$	1.00000	0.0533002
$353$	−17.6060	−0.937071	−0.468536	−	0.883445i	$-0.655218\pi$
$353$	−17.6060	−0.937071	−0.468536	+	0.883445i	$0.655218\pi$
$354$	4.00000	0.212598
$355$	6.74456	0.357964
$356$	10.0000	0.529999
$357$	3.37228	0.178480
$358$	14.1168	0.746098
$359$	20.2337	1.06789	0.533947	−	0.845518i	$-0.320708\pi$
$359$	20.2337	1.06789	0.533947	+	0.845518i	$0.320708\pi$
$360$	1.00000	0.0527046
$361$	−7.62772	−0.401459
$362$	−12.7446	−0.669839
$363$	−1.00000	−0.0524864
$364$	−4.62772	−0.242558
$365$	12.7446	0.667081
$366$	−4.11684	−0.215191
$367$	2.51087	0.131067	0.0655333	−	0.997850i	$-0.479125\pi$
$367$	2.51087	0.131067	0.0655333	+	0.997850i	$0.479125\pi$
$368$	3.37228	0.175792
$369$	−6.00000	−0.312348
$370$	−2.62772	−0.136609
$371$	−38.7446	−2.01152
$372$	−7.37228	−0.382235
$373$	−19.4891	−1.00911	−0.504554	−	0.863380i	$-0.668343\pi$
$373$	−19.4891	−1.00911	−0.504554	+	0.863380i	$0.668343\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−2.74456	−0.141540
$377$	2.74456	0.141352
$378$	3.37228	0.173451
$379$	−18.1168	−0.930600	−0.465300	−	0.885153i	$-0.654054\pi$
$379$	−18.1168	−0.930600	−0.465300	+	0.885153i	$0.654054\pi$
$380$	3.37228	0.172994
$381$	8.00000	0.409852
$382$	0	0
$383$	−32.2337	−1.64706	−0.823532	−	0.567269i	$-0.808000\pi$
$383$	−32.2337	−1.64706	−0.823532	+	0.567269i	$0.808000\pi$
$384$	1.00000	0.0510310
$385$	3.37228	0.171867
$386$	−11.2554	−0.572887
$387$	4.00000	0.203331
$388$	9.37228	0.475805
$389$	−6.23369	−0.316061	−0.158030	−	0.987434i	$-0.550514\pi$
$389$	−6.23369	−0.316061	−0.158030	+	0.987434i	$0.550514\pi$
$390$	1.37228	0.0694882
$391$	−3.37228	−0.170544
$392$	−4.37228	−0.220834
$393$	−7.37228	−0.371882
$394$	−25.6060	−1.29001
$395$	6.74456	0.339356
$396$	−1.00000	−0.0502519
$397$	−11.4891	−0.576623	−0.288311	−	0.957537i	$-0.593094\pi$
$397$	−11.4891	−0.576623	−0.288311	+	0.957537i	$0.593094\pi$
$398$	8.62772	0.432468
$399$	11.3723	0.569326
$400$	1.00000	0.0500000
$401$	−18.8614	−0.941894	−0.470947	−	0.882162i	$-0.656088\pi$
$401$	−18.8614	−0.941894	−0.470947	+	0.882162i	$0.656088\pi$
$402$	0.627719	0.0313078
$403$	−10.1168	−0.503956
$404$	−11.4891	−0.571605
$405$	−1.00000	−0.0496904
$406$	6.74456	0.334727
$407$	2.62772	0.130251
$408$	−1.00000	−0.0495074
$409$	28.9783	1.43288	0.716441	−	0.697648i	$-0.245770\pi$
$409$	28.9783	1.43288	0.716441	+	0.697648i	$0.245770\pi$
$410$	−6.00000	−0.296319
$411$	−0.116844	−0.00576349
$412$	10.1168	0.498421
$413$	13.4891	0.663756
$414$	−3.37228	−0.165739
$415$	7.37228	0.361891
$416$	1.37228	0.0672816
$417$	−10.7446	−0.526163
$418$	−3.37228	−0.164944
$419$	9.48913	0.463574	0.231787	−	0.972767i	$-0.425543\pi$
$419$	9.48913	0.463574	0.231787	+	0.972767i	$0.425543\pi$
$420$	3.37228	0.164550
$421$	−39.0951	−1.90538	−0.952689	−	0.303946i	$-0.901696\pi$
$421$	−39.0951	−1.90538	−0.952689	+	0.303946i	$0.901696\pi$
$422$	−2.74456	−0.133603
$423$	2.74456	0.133445
$424$	11.4891	0.557961
$425$	−1.00000	−0.0485071
$426$	−6.74456	−0.326775
$427$	−13.8832	−0.671853
$428$	−14.7446	−0.712705
$429$	−1.37228	−0.0662544
$430$	4.00000	0.192897
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	−1.00000	−0.0481125
$433$	10.0000	0.480569	0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000	0.480569	0.240285	+	0.970702i	$0.422759\pi$
$434$	−24.8614	−1.19339
$435$	−2.00000	−0.0958927
$436$	16.1168	0.771857
$437$	−11.3723	−0.544010
$438$	−12.7446	−0.608959
$439$	17.2554	0.823557	0.411779	−	0.911284i	$-0.364908\pi$
$439$	17.2554	0.823557	0.411779	+	0.911284i	$0.364908\pi$
$440$	−1.00000	−0.0476731
$441$	4.37228	0.208204
$442$	−1.37228	−0.0652728
$443$	12.2337	0.581240	0.290620	−	0.956839i	$-0.406138\pi$
$443$	12.2337	0.581240	0.290620	+	0.956839i	$0.406138\pi$
$444$	2.62772	0.124706
$445$	−10.0000	−0.474045
$446$	−8.86141	−0.419600
$447$	−4.11684	−0.194720
$448$	3.37228	0.159325
$449$	33.8397	1.59699	0.798496	−	0.602000i	$-0.205629\pi$
$449$	33.8397	1.59699	0.798496	+	0.602000i	$0.205629\pi$
$450$	−1.00000	−0.0471405
$451$	6.00000	0.282529
$452$	−2.00000	−0.0940721
$453$	−15.3723	−0.722253
$454$	1.25544	0.0589206
$455$	4.62772	0.216951
$456$	−3.37228	−0.157922
$457$	1.37228	0.0641926	0.0320963	−	0.999485i	$-0.489782\pi$
$457$	1.37228	0.0641926	0.0320963	+	0.999485i	$0.489782\pi$
$458$	12.1168	0.566183
$459$	1.00000	0.0466760
$460$	−3.37228	−0.157233
$461$	−11.4891	−0.535102	−0.267551	−	0.963544i	$-0.586214\pi$
$461$	−11.4891	−0.535102	−0.267551	+	0.963544i	$0.586214\pi$
$462$	−3.37228	−0.156893
$463$	−20.6277	−0.958651	−0.479326	−	0.877637i	$-0.659119\pi$
$463$	−20.6277	−0.958651	−0.479326	+	0.877637i	$0.659119\pi$
$464$	−2.00000	−0.0928477
$465$	7.37228	0.341881
$466$	23.4891	1.08811
$467$	34.9783	1.61860	0.809300	−	0.587395i	$-0.199847\pi$
$467$	34.9783	1.61860	0.809300	+	0.587395i	$0.199847\pi$
$468$	−1.37228	−0.0634337
$469$	2.11684	0.0977468
$470$	2.74456	0.126597
$471$	0.744563	0.0343076
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	−6.74456	−0.309788
$475$	−3.37228	−0.154731
$476$	−3.37228	−0.154568
$477$	−11.4891	−0.526051
$478$	−1.25544	−0.0574224
$479$	15.6060	0.713055	0.356527	−	0.934285i	$-0.383961\pi$
$479$	15.6060	0.713055	0.356527	+	0.934285i	$0.383961\pi$
$480$	−1.00000	−0.0456435
$481$	3.60597	0.164418
$482$	−17.6060	−0.801930
$483$	−11.3723	−0.517457
$484$	1.00000	0.0454545
$485$	−9.37228	−0.425573
$486$	1.00000	0.0453609
$487$	−29.4891	−1.33628	−0.668140	−	0.744036i	$-0.732909\pi$
$487$	−29.4891	−1.33628	−0.668140	+	0.744036i	$0.732909\pi$
$488$	4.11684	0.186361
$489$	4.00000	0.180886
$490$	4.37228	0.197520
$491$	−26.7446	−1.20697	−0.603483	−	0.797376i	$-0.706221\pi$
$491$	−26.7446	−1.20697	−0.603483	+	0.797376i	$0.706221\pi$
$492$	6.00000	0.270501
$493$	2.00000	0.0900755
$494$	−4.62772	−0.208211
$495$	1.00000	0.0449467
$496$	7.37228	0.331025
$497$	−22.7446	−1.02023
$498$	−7.37228	−0.330360
$499$	10.5109	0.470531	0.235266	−	0.971931i	$-0.424404\pi$
$499$	10.5109	0.470531	0.235266	+	0.971931i	$0.424404\pi$
$500$	−1.00000	−0.0447214
$501$	−1.48913	−0.0665292
$502$	16.6277	0.742131
$503$	1.48913	0.0663968	0.0331984	−	0.999449i	$-0.489431\pi$
$503$	1.48913	0.0663968	0.0331984	+	0.999449i	$0.489431\pi$
$504$	−3.37228	−0.150213
$505$	11.4891	0.511259
$506$	3.37228	0.149916
$507$	11.1168	0.493716
$508$	−8.00000	−0.354943
$509$	−12.5109	−0.554535	−0.277267	−	0.960793i	$-0.589429\pi$
$509$	−12.5109	−0.554535	−0.277267	+	0.960793i	$0.589429\pi$
$510$	1.00000	0.0442807
$511$	−42.9783	−1.90125
$512$	−1.00000	−0.0441942
$513$	3.37228	0.148890
$514$	23.4891	1.03606
$515$	−10.1168	−0.445801
$516$	−4.00000	−0.176090
$517$	−2.74456	−0.120706
$518$	8.86141	0.389348
$519$	22.8614	1.00350
$520$	−1.37228	−0.0601785
$521$	−26.8614	−1.17682	−0.588410	−	0.808563i	$-0.700246\pi$
$521$	−26.8614	−1.17682	−0.588410	+	0.808563i	$0.700246\pi$
$522$	2.00000	0.0875376
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	7.37228	0.322060
$525$	−3.37228	−0.147178
$526$	19.3723	0.844672
$527$	−7.37228	−0.321142
$528$	1.00000	0.0435194
$529$	−11.6277	−0.505553
$530$	−11.4891	−0.499056
$531$	4.00000	0.173585
$532$	−11.3723	−0.493051
$533$	8.23369	0.356641
$534$	10.0000	0.432742
$535$	14.7446	0.637463
$536$	−0.627719	−0.0271133
$537$	14.1168	0.609187
$538$	−13.3723	−0.576520
$539$	−4.37228	−0.188327
$540$	1.00000	0.0430331
$541$	11.4891	0.493956	0.246978	−	0.969021i	$-0.420562\pi$
$541$	11.4891	0.493956	0.246978	+	0.969021i	$0.420562\pi$
$542$	20.0000	0.859074
$543$	−12.7446	−0.546922
$544$	1.00000	0.0428746
$545$	−16.1168	−0.690370
$546$	−4.62772	−0.198048
$547$	−31.3723	−1.34138	−0.670691	−	0.741737i	$-0.734002\pi$
$547$	−31.3723	−1.34138	−0.670691	+	0.741737i	$0.734002\pi$
$548$	0.116844	0.00499133
$549$	−4.11684	−0.175703
$550$	1.00000	0.0426401
$551$	6.74456	0.287328
$552$	3.37228	0.143534
$553$	−22.7446	−0.967197
$554$	30.2337	1.28451
$555$	−2.62772	−0.111540
$556$	10.7446	0.455671
$557$	−9.76631	−0.413812	−0.206906	−	0.978361i	$-0.566339\pi$
$557$	−9.76631	−0.413812	−0.206906	+	0.978361i	$0.566339\pi$
$558$	−7.37228	−0.312094
$559$	−5.48913	−0.232165
$560$	−3.37228	−0.142505
$561$	−1.00000	−0.0422200
$562$	−14.0000	−0.590554
$563$	−22.1168	−0.932114	−0.466057	−	0.884755i	$-0.654326\pi$
$563$	−22.1168	−0.932114	−0.466057	+	0.884755i	$0.654326\pi$
$564$	−2.74456	−0.115567
$565$	2.00000	0.0841406
$566$	28.0000	1.17693
$567$	3.37228	0.141623
$568$	6.74456	0.282996
$569$	41.8397	1.75401	0.877005	−	0.480482i	$-0.159538\pi$
$569$	41.8397	1.75401	0.877005	+	0.480482i	$0.159538\pi$
$570$	3.37228	0.141249
$571$	26.7446	1.11923	0.559613	−	0.828754i	$-0.310950\pi$
$571$	26.7446	1.11923	0.559613	+	0.828754i	$0.310950\pi$
$572$	1.37228	0.0573780
$573$	0	0
$574$	20.2337	0.844538
$575$	3.37228	0.140634
$576$	1.00000	0.0416667
$577$	4.51087	0.187790	0.0938951	−	0.995582i	$-0.470068\pi$
$577$	4.51087	0.187790	0.0938951	+	0.995582i	$0.470068\pi$
$578$	−1.00000	−0.0415945
$579$	−11.2554	−0.467760
$580$	2.00000	0.0830455
$581$	−24.8614	−1.03142
$582$	9.37228	0.388494
$583$	11.4891	0.475831
$584$	12.7446	0.527374
$585$	1.37228	0.0567368
$586$	15.2554	0.630196
$587$	1.25544	0.0518174	0.0259087	−	0.999664i	$-0.491752\pi$
$587$	1.25544	0.0518174	0.0259087	+	0.999664i	$0.491752\pi$
$588$	−4.37228	−0.180310
$589$	−24.8614	−1.02440
$590$	4.00000	0.164677
$591$	−25.6060	−1.05329
$592$	−2.62772	−0.107999
$593$	16.5109	0.678020	0.339010	−	0.940783i	$-0.389908\pi$
$593$	16.5109	0.678020	0.339010	+	0.940783i	$0.389908\pi$
$594$	−1.00000	−0.0410305
$595$	3.37228	0.138250
$596$	4.11684	0.168632
$597$	8.62772	0.353109
$598$	4.62772	0.189241
$599$	−35.8397	−1.46437	−0.732184	−	0.681107i	$-0.761499\pi$
$599$	−35.8397	−1.46437	−0.732184	+	0.681107i	$0.761499\pi$
$600$	1.00000	0.0408248
$601$	−1.37228	−0.0559765	−0.0279883	−	0.999608i	$-0.508910\pi$
$601$	−1.37228	−0.0559765	−0.0279883	+	0.999608i	$0.508910\pi$
$602$	−13.4891	−0.549776
$603$	0.627719	0.0255627
$604$	15.3723	0.625489
$605$	−1.00000	−0.0406558
$606$	−11.4891	−0.466714
$607$	−23.6060	−0.958137	−0.479068	−	0.877778i	$-0.659025\pi$
$607$	−23.6060	−0.958137	−0.479068	+	0.877778i	$0.659025\pi$
$608$	3.37228	0.136764
$609$	6.74456	0.273303
$610$	−4.11684	−0.166686
$611$	−3.76631	−0.152369
$612$	−1.00000	−0.0404226
$613$	−3.02175	−0.122047	−0.0610237	−	0.998136i	$-0.519437\pi$
$613$	−3.02175	−0.122047	−0.0610237	+	0.998136i	$0.519437\pi$
$614$	−1.48913	−0.0600962
$615$	−6.00000	−0.241943
$616$	3.37228	0.135873
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	10.1168	0.406959
$619$	10.1168	0.406630	0.203315	−	0.979113i	$-0.434828\pi$
$619$	10.1168	0.406630	0.203315	+	0.979113i	$0.434828\pi$
$620$	−7.37228	−0.296078
$621$	−3.37228	−0.135325
$622$	−4.23369	−0.169755
$623$	33.7228	1.35108
$624$	1.37228	0.0549352
$625$	1.00000	0.0400000
$626$	−8.11684	−0.324414
$627$	−3.37228	−0.134676
$628$	−0.744563	−0.0297113
$629$	2.62772	0.104774
$630$	3.37228	0.134355
$631$	−20.2337	−0.805490	−0.402745	−	0.915312i	$-0.631944\pi$
$631$	−20.2337	−0.805490	−0.402745	+	0.915312i	$0.631944\pi$
$632$	6.74456	0.268284
$633$	−2.74456	−0.109087
$634$	−2.00000	−0.0794301
$635$	8.00000	0.317470
$636$	11.4891	0.455573
$637$	−6.00000	−0.237729
$638$	−2.00000	−0.0791808
$639$	−6.74456	−0.266811
$640$	1.00000	0.0395285
$641$	0.978251	0.0386386	0.0193193	−	0.999813i	$-0.493850\pi$
$641$	0.978251	0.0386386	0.0193193	+	0.999813i	$0.493850\pi$
$642$	−14.7446	−0.581921
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	11.3723	0.448131
$645$	4.00000	0.157500
$646$	−3.37228	−0.132681
$647$	16.2337	0.638212	0.319106	−	0.947719i	$-0.396617\pi$
$647$	16.2337	0.638212	0.319106	+	0.947719i	$0.396617\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	1.37228	0.0538253
$651$	−24.8614	−0.974395
$652$	−4.00000	−0.156652
$653$	−2.23369	−0.0874110	−0.0437055	−	0.999044i	$-0.513916\pi$
$653$	−2.23369	−0.0874110	−0.0437055	+	0.999044i	$0.513916\pi$
$654$	16.1168	0.630218
$655$	−7.37228	−0.288059
$656$	−6.00000	−0.234261
$657$	−12.7446	−0.497213
$658$	−9.25544	−0.360815
$659$	−8.23369	−0.320739	−0.160369	−	0.987057i	$-0.551269\pi$
$659$	−8.23369	−0.320739	−0.160369	+	0.987057i	$0.551269\pi$
$660$	−1.00000	−0.0389249
$661$	5.60597	0.218047	0.109023	−	0.994039i	$-0.465228\pi$
$661$	5.60597	0.218047	0.109023	+	0.994039i	$0.465228\pi$
$662$	1.48913	0.0578765
$663$	−1.37228	−0.0532950
$664$	7.37228	0.286100
$665$	11.3723	0.440998
$666$	2.62772	0.101822
$667$	−6.74456	−0.261151
$668$	1.48913	0.0576160
$669$	−8.86141	−0.342602
$670$	0.627719	0.0242509
$671$	4.11684	0.158929
$672$	3.37228	0.130089
$673$	−4.74456	−0.182889	−0.0914447	−	0.995810i	$-0.529148\pi$
$673$	−4.74456	−0.182889	−0.0914447	+	0.995810i	$0.529148\pi$
$674$	34.2337	1.31863
$675$	−1.00000	−0.0384900
$676$	−11.1168	−0.427571
$677$	−11.4891	−0.441563	−0.220781	−	0.975323i	$-0.570861\pi$
$677$	−11.4891	−0.441563	−0.220781	+	0.975323i	$0.570861\pi$
$678$	−2.00000	−0.0768095
$679$	31.6060	1.21293
$680$	−1.00000	−0.0383482
$681$	1.25544	0.0481085
$682$	7.37228	0.282299
$683$	−16.6277	−0.636242	−0.318121	−	0.948050i	$-0.603052\pi$
$683$	−16.6277	−0.636242	−0.318121	+	0.948050i	$0.603052\pi$
$684$	−3.37228	−0.128942
$685$	−0.116844	−0.00446438
$686$	8.86141	0.338330
$687$	12.1168	0.462286
$688$	4.00000	0.152499
$689$	15.7663	0.600649
$690$	−3.37228	−0.128381
$691$	−30.3505	−1.15459	−0.577294	−	0.816536i	$-0.695891\pi$
$691$	−30.3505	−1.15459	−0.577294	+	0.816536i	$0.695891\pi$
$692$	−22.8614	−0.869060
$693$	−3.37228	−0.128102
$694$	−25.7228	−0.976425
$695$	−10.7446	−0.407564
$696$	−2.00000	−0.0758098
$697$	6.00000	0.227266
$698$	28.9783	1.09684
$699$	23.4891	0.888440
$700$	3.37228	0.127460
$701$	15.4891	0.585016	0.292508	−	0.956263i	$-0.405510\pi$
$701$	15.4891	0.585016	0.292508	+	0.956263i	$0.405510\pi$
$702$	−1.37228	−0.0517934
$703$	8.86141	0.334214
$704$	−1.00000	−0.0376889
$705$	2.74456	0.103366
$706$	17.6060	0.662609
$707$	−38.7446	−1.45714
$708$	−4.00000	−0.150329
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−6.74456	−0.253119
$711$	−6.74456	−0.252941
$712$	−10.0000	−0.374766
$713$	24.8614	0.931067
$714$	−3.37228	−0.126204
$715$	−1.37228	−0.0513204
$716$	−14.1168	−0.527571
$717$	−1.25544	−0.0468852
$718$	−20.2337	−0.755115
$719$	−6.74456	−0.251530	−0.125765	−	0.992060i	$-0.540138\pi$
$719$	−6.74456	−0.251530	−0.125765	+	0.992060i	$0.540138\pi$
$720$	−1.00000	−0.0372678
$721$	34.1168	1.27058
$722$	7.62772	0.283874
$723$	−17.6060	−0.654773
$724$	12.7446	0.473648
$725$	−2.00000	−0.0742781
$726$	1.00000	0.0371135
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	4.62772	0.171515
$729$	1.00000	0.0370370
$730$	−12.7446	−0.471697
$731$	−4.00000	−0.147945
$732$	4.11684	0.152163
$733$	51.3288	1.89587	0.947936	−	0.318461i	$-0.103166\pi$
$733$	51.3288	1.89587	0.947936	+	0.318461i	$0.103166\pi$
$734$	−2.51087	−0.0926781
$735$	4.37228	0.161274
$736$	−3.37228	−0.124304
$737$	−0.627719	−0.0231223
$738$	6.00000	0.220863
$739$	22.3505	0.822178	0.411089	−	0.911595i	$-0.365149\pi$
$739$	22.3505	0.822178	0.411089	+	0.911595i	$0.365149\pi$
$740$	2.62772	0.0965969
$741$	−4.62772	−0.170003
$742$	38.7446	1.42236
$743$	−41.4891	−1.52209	−0.761044	−	0.648700i	$-0.775313\pi$
$743$	−41.4891	−1.52209	−0.761044	+	0.648700i	$0.775313\pi$
$744$	7.37228	0.270281
$745$	−4.11684	−0.150829
$746$	19.4891	0.713548
$747$	−7.37228	−0.269738
$748$	1.00000	0.0365636
$749$	−49.7228	−1.81683
$750$	−1.00000	−0.0365148
$751$	9.48913	0.346263	0.173132	−	0.984899i	$-0.444611\pi$
$751$	9.48913	0.346263	0.173132	+	0.984899i	$0.444611\pi$
$752$	2.74456	0.100084
$753$	16.6277	0.605948
$754$	−2.74456	−0.0999511
$755$	−15.3723	−0.559455
$756$	−3.37228	−0.122649
$757$	32.9783	1.19861	0.599307	−	0.800519i	$-0.295443\pi$
$757$	32.9783	1.19861	0.599307	+	0.800519i	$0.295443\pi$
$758$	18.1168	0.658033
$759$	3.37228	0.122406
$760$	−3.37228	−0.122326
$761$	3.88316	0.140764	0.0703821	−	0.997520i	$-0.477578\pi$
$761$	3.88316	0.140764	0.0703821	+	0.997520i	$0.477578\pi$
$762$	−8.00000	−0.289809
$763$	54.3505	1.96762
$764$	0	0
$765$	1.00000	0.0361551
$766$	32.2337	1.16465
$767$	−5.48913	−0.198201
$768$	−1.00000	−0.0360844
$769$	25.2119	0.909166	0.454583	−	0.890704i	$-0.349788\pi$
$769$	25.2119	0.909166	0.454583	+	0.890704i	$0.349788\pi$
$770$	−3.37228	−0.121529
$771$	23.4891	0.845940
$772$	11.2554	0.405092
$773$	−45.6060	−1.64033	−0.820166	−	0.572125i	$-0.806119\pi$
$773$	−45.6060	−1.64033	−0.820166	+	0.572125i	$0.806119\pi$
$774$	−4.00000	−0.143777
$775$	7.37228	0.264820
$776$	−9.37228	−0.336445
$777$	8.86141	0.317901
$778$	6.23369	0.223489
$779$	20.2337	0.724947
$780$	−1.37228	−0.0491356
$781$	6.74456	0.241339
$782$	3.37228	0.120593
$783$	2.00000	0.0714742
$784$	4.37228	0.156153
$785$	0.744563	0.0265746
$786$	7.37228	0.262961
$787$	−14.1168	−0.503211	−0.251606	−	0.967830i	$-0.580959\pi$
$787$	−14.1168	−0.503211	−0.251606	+	0.967830i	$0.580959\pi$
$788$	25.6060	0.912175
$789$	19.3723	0.689671
$790$	−6.74456	−0.239961
$791$	−6.74456	−0.239809
$792$	1.00000	0.0355335
$793$	5.64947	0.200618
$794$	11.4891	0.407734
$795$	−11.4891	−0.407477
$796$	−8.62772	−0.305801
$797$	22.6277	0.801515	0.400757	−	0.916184i	$-0.368747\pi$
$797$	22.6277	0.801515	0.400757	+	0.916184i	$0.368747\pi$
$798$	−11.3723	−0.402574
$799$	−2.74456	−0.0970956
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	18.8614	0.666019
$803$	12.7446	0.449746
$804$	−0.627719	−0.0221379
$805$	−11.3723	−0.400820
$806$	10.1168	0.356351
$807$	−13.3723	−0.470727
$808$	11.4891	0.404186
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	1.00000	0.0351364
$811$	−29.2554	−1.02730	−0.513649	−	0.858001i	$-0.671707\pi$
$811$	−29.2554	−1.02730	−0.513649	+	0.858001i	$0.671707\pi$
$812$	−6.74456	−0.236688
$813$	20.0000	0.701431
$814$	−2.62772	−0.0921015
$815$	4.00000	0.140114
$816$	1.00000	0.0350070
$817$	−13.4891	−0.471925
$818$	−28.9783	−1.01320
$819$	−4.62772	−0.161706
$820$	6.00000	0.209529
$821$	−44.9783	−1.56975	−0.784876	−	0.619653i	$-0.787273\pi$
$821$	−44.9783	−1.56975	−0.784876	+	0.619653i	$0.787273\pi$
$822$	0.116844	0.00407540
$823$	−6.74456	−0.235101	−0.117550	−	0.993067i	$-0.537504\pi$
$823$	−6.74456	−0.235101	−0.117550	+	0.993067i	$0.537504\pi$
$824$	−10.1168	−0.352437
$825$	1.00000	0.0348155
$826$	−13.4891	−0.469347
$827$	−36.2337	−1.25997	−0.629984	−	0.776608i	$-0.716939\pi$
$827$	−36.2337	−1.25997	−0.629984	+	0.776608i	$0.716939\pi$
$828$	3.37228	0.117195
$829$	22.8614	0.794009	0.397005	−	0.917817i	$-0.370050\pi$
$829$	22.8614	0.794009	0.397005	+	0.917817i	$0.370050\pi$
$830$	−7.37228	−0.255896
$831$	30.2337	1.04880
$832$	−1.37228	−0.0475753
$833$	−4.37228	−0.151491
$834$	10.7446	0.372054
$835$	−1.48913	−0.0515333
$836$	3.37228	0.116633
$837$	−7.37228	−0.254823
$838$	−9.48913	−0.327796
$839$	−8.00000	−0.276191	−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000	−0.276191	−0.138095	+	0.990419i	$0.544098\pi$
$840$	−3.37228	−0.116355
$841$	−25.0000	−0.862069
$842$	39.0951	1.34731
$843$	−14.0000	−0.482186
$844$	2.74456	0.0944717
$845$	11.1168	0.382431
$846$	−2.74456	−0.0943600
$847$	3.37228	0.115873
$848$	−11.4891	−0.394538
$849$	28.0000	0.960958
$850$	1.00000	0.0342997
$851$	−8.86141	−0.303765
$852$	6.74456	0.231065
$853$	−5.76631	−0.197435	−0.0987174	−	0.995116i	$-0.531474\pi$
$853$	−5.76631	−0.197435	−0.0987174	+	0.995116i	$0.531474\pi$
$854$	13.8832	0.475072
$855$	3.37228	0.115330
$856$	14.7446	0.503959
$857$	26.6277	0.909586	0.454793	−	0.890597i	$-0.349713\pi$
$857$	26.6277	0.909586	0.454793	+	0.890597i	$0.349713\pi$
$858$	1.37228	0.0468489
$859$	25.4891	0.869678	0.434839	−	0.900508i	$-0.356805\pi$
$859$	25.4891	0.869678	0.434839	+	0.900508i	$0.356805\pi$
$860$	−4.00000	−0.136399
$861$	20.2337	0.689562
$862$	8.00000	0.272481
$863$	−17.4891	−0.595337	−0.297668	−	0.954669i	$-0.596209\pi$
$863$	−17.4891	−0.595337	−0.297668	+	0.954669i	$0.596209\pi$
$864$	1.00000	0.0340207
$865$	22.8614	0.777311
$866$	−10.0000	−0.339814
$867$	−1.00000	−0.0339618
$868$	24.8614	0.843851
$869$	6.74456	0.228794
$870$	2.00000	0.0678064
$871$	−0.861407	−0.0291876
$872$	−16.1168	−0.545785
$873$	9.37228	0.317204
$874$	11.3723	0.384673
$875$	−3.37228	−0.114004
$876$	12.7446	0.430599
$877$	−46.2337	−1.56120	−0.780600	−	0.625030i	$-0.785087\pi$
$877$	−46.2337	−1.56120	−0.780600	+	0.625030i	$0.785087\pi$
$878$	−17.2554	−0.582343
$879$	15.2554	0.514553
$880$	1.00000	0.0337100
$881$	46.4674	1.56553	0.782763	−	0.622320i	$-0.213810\pi$
$881$	46.4674	1.56553	0.782763	+	0.622320i	$0.213810\pi$
$882$	−4.37228	−0.147222
$883$	52.0000	1.74994	0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000	1.74994	0.874970	+	0.484178i	$0.160881\pi$
$884$	1.37228	0.0461548
$885$	4.00000	0.134459
$886$	−12.2337	−0.410999
$887$	17.4891	0.587227	0.293614	−	0.955924i	$-0.405142\pi$
$887$	17.4891	0.587227	0.293614	+	0.955924i	$0.405142\pi$
$888$	−2.62772	−0.0881805
$889$	−26.9783	−0.904821
$890$	10.0000	0.335201
$891$	−1.00000	−0.0335013
$892$	8.86141	0.296702
$893$	−9.25544	−0.309721
$894$	4.11684	0.137688
$895$	14.1168	0.471874
$896$	−3.37228	−0.112660
$897$	4.62772	0.154515
$898$	−33.8397	−1.12924
$899$	−14.7446	−0.491759
$900$	1.00000	0.0333333
$901$	11.4891	0.382758
$902$	−6.00000	−0.199778
$903$	−13.4891	−0.448890
$904$	2.00000	0.0665190
$905$	−12.7446	−0.423644
$906$	15.3723	0.510710
$907$	25.4891	0.846353	0.423176	−	0.906047i	$-0.360915\pi$
$907$	25.4891	0.846353	0.423176	+	0.906047i	$0.360915\pi$
$908$	−1.25544	−0.0416632
$909$	−11.4891	−0.381070
$910$	−4.62772	−0.153407
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	3.37228	0.111667
$913$	7.37228	0.243987
$914$	−1.37228	−0.0453910
$915$	−4.11684	−0.136099
$916$	−12.1168	−0.400352
$917$	24.8614	0.820996
$918$	−1.00000	−0.0330049
$919$	−6.11684	−0.201776	−0.100888	−	0.994898i	$-0.532168\pi$
$919$	−6.11684	−0.201776	−0.100888	+	0.994898i	$0.532168\pi$
$920$	3.37228	0.111181
$921$	−1.48913	−0.0490683
$922$	11.4891	0.378374
$923$	9.25544	0.304646
$924$	3.37228	0.110940
$925$	−2.62772	−0.0863989
$926$	20.6277	0.677869
$927$	10.1168	0.332281
$928$	2.00000	0.0656532
$929$	−1.60597	−0.0526901	−0.0263451	−	0.999653i	$-0.508387\pi$
$929$	−1.60597	−0.0526901	−0.0263451	+	0.999653i	$0.508387\pi$
$930$	−7.37228	−0.241747
$931$	−14.7446	−0.483234
$932$	−23.4891	−0.769412
$933$	−4.23369	−0.138605
$934$	−34.9783	−1.14452
$935$	−1.00000	−0.0327035
$936$	1.37228	0.0448544
$937$	−60.5842	−1.97920	−0.989600	−	0.143846i	$-0.954053\pi$
$937$	−60.5842	−1.97920	−0.989600	+	0.143846i	$0.954053\pi$
$938$	−2.11684	−0.0691174
$939$	−8.11684	−0.264883
$940$	−2.74456	−0.0895178
$941$	−43.7228	−1.42532	−0.712661	−	0.701508i	$-0.752510\pi$
$941$	−43.7228	−1.42532	−0.712661	+	0.701508i	$0.752510\pi$
$942$	−0.744563	−0.0242592
$943$	−20.2337	−0.658900
$944$	4.00000	0.130189
$945$	3.37228	0.109700
$946$	4.00000	0.130051
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	6.74456	0.219053
$949$	17.4891	0.567721
$950$	3.37228	0.109411
$951$	−2.00000	−0.0648544
$952$	3.37228	0.109296
$953$	−30.2337	−0.979365	−0.489683	−	0.871901i	$-0.662887\pi$
$953$	−30.2337	−0.979365	−0.489683	+	0.871901i	$0.662887\pi$
$954$	11.4891	0.371974
$955$	0	0
$956$	1.25544	0.0406037
$957$	−2.00000	−0.0646508
$958$	−15.6060	−0.504206
$959$	0.394031	0.0127239
$960$	1.00000	0.0322749
$961$	23.3505	0.753243
$962$	−3.60597	−0.116261
$963$	−14.7446	−0.475137
$964$	17.6060	0.567050
$965$	−11.2554	−0.362325
$966$	11.3723	0.365897
$967$	19.7663	0.635642	0.317821	−	0.948151i	$-0.397049\pi$
$967$	19.7663	0.635642	0.317821	+	0.948151i	$0.397049\pi$
$968$	−1.00000	−0.0321412
$969$	−3.37228	−0.108333
$970$	9.37228	0.300926
$971$	3.60597	0.115721	0.0578605	−	0.998325i	$-0.481572\pi$
$971$	3.60597	0.115721	0.0578605	+	0.998325i	$0.481572\pi$
$972$	−1.00000	−0.0320750
$973$	36.2337	1.16160
$974$	29.4891	0.944893
$975$	1.37228	0.0439482
$976$	−4.11684	−0.131777
$977$	22.8614	0.731401	0.365701	−	0.930733i	$-0.380829\pi$
$977$	22.8614	0.731401	0.365701	+	0.930733i	$0.380829\pi$
$978$	−4.00000	−0.127906
$979$	−10.0000	−0.319601
$980$	−4.37228	−0.139667
$981$	16.1168	0.514571
$982$	26.7446	0.853453
$983$	53.4891	1.70604	0.853019	−	0.521880i	$-0.174769\pi$
$983$	53.4891	1.70604	0.853019	+	0.521880i	$0.174769\pi$
$984$	−6.00000	−0.191273
$985$	−25.6060	−0.815874
$986$	−2.00000	−0.0636930
$987$	−9.25544	−0.294604
$988$	4.62772	0.147227
$989$	13.4891	0.428929
$990$	−1.00000	−0.0317821
$991$	−36.8614	−1.17094	−0.585471	−	0.810694i	$-0.699090\pi$
$991$	−36.8614	−1.17094	−0.585471	+	0.810694i	$0.699090\pi$
$992$	−7.37228	−0.234070
$993$	1.48913	0.0472560
$994$	22.7446	0.721414
$995$	8.62772	0.273517
$996$	7.37228	0.233600
$997$	−36.9783	−1.17111	−0.585556	−	0.810632i	$-0.699124\pi$
$997$	−36.9783	−1.17111	−0.585556	+	0.810632i	$0.699124\pi$
$998$	−10.5109	−0.332716
$999$	2.62772	0.0831373

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bp.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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.37228 q^{13} -3.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.37228 q^{19} -1.00000 q^{20} -3.37228 q^{21} +1.00000 q^{22} +3.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.37228 q^{26} -1.00000 q^{27} +3.37228 q^{28} -2.00000 q^{29} -1.00000 q^{30} +7.37228 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.37228 q^{35} +1.00000 q^{36} -2.62772 q^{37} +3.37228 q^{38} +1.37228 q^{39} +1.00000 q^{40} -6.00000 q^{41} +3.37228 q^{42} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} -3.37228 q^{46} +2.74456 q^{47} -1.00000 q^{48} +4.37228 q^{49} -1.00000 q^{50} +1.00000 q^{51} -1.37228 q^{52} -11.4891 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.37228 q^{56} +3.37228 q^{57} +2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} -4.11684 q^{61} -7.37228 q^{62} +3.37228 q^{63} +1.00000 q^{64} +1.37228 q^{65} -1.00000 q^{66} +0.627719 q^{67} -1.00000 q^{68} -3.37228 q^{69} +3.37228 q^{70} -6.74456 q^{71} -1.00000 q^{72} -12.7446 q^{73} +2.62772 q^{74} -1.00000 q^{75} -3.37228 q^{76} -3.37228 q^{77} -1.37228 q^{78} -6.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -7.37228 q^{83} -3.37228 q^{84} +1.00000 q^{85} -4.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -4.62772 q^{91} +3.37228 q^{92} -7.37228 q^{93} -2.74456 q^{94} +3.37228 q^{95} +1.00000 q^{96} +9.37228 q^{97} -4.37228 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - q^{21} + 2 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 4 q^{29} - 2 q^{30} + 9 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} - q^{35} + 2 q^{36} - 11 q^{37} + q^{38} - 3 q^{39} + 2 q^{40} - 12 q^{41} + q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} - q^{46} - 6 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} + 2 q^{51} + 3 q^{52} + 2 q^{54} + 2 q^{55} - q^{56} + q^{57} + 4 q^{58} + 8 q^{59} + 2 q^{60} + 9 q^{61} - 9 q^{62} + q^{63} + 2 q^{64} - 3 q^{65} - 2 q^{66} + 7 q^{67} - 2 q^{68} - q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 14 q^{73} + 11 q^{74} - 2 q^{75} - q^{76} - q^{77} + 3 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 9 q^{83} - q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} + 2 q^{88} + 20 q^{89} + 2 q^{90} - 15 q^{91} + q^{92} - 9 q^{93} + 6 q^{94} + q^{95} + 2 q^{96} + 13 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - q^21 + 2 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 4 * q^29 - 2 * q^30 + 9 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - q^35 + 2 * q^36 - 11 * q^37 + q^38 - 3 * q^39 + 2 * q^40 - 12 * q^41 + q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 - q^46 - 6 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 + 2 * q^51 + 3 * q^52 + 2 * q^54 + 2 * q^55 - q^56 + q^57 + 4 * q^58 + 8 * q^59 + 2 * q^60 + 9 * q^61 - 9 * q^62 + q^63 + 2 * q^64 - 3 * q^65 - 2 * q^66 + 7 * q^67 - 2 * q^68 - q^69 + q^70 - 2 * q^71 - 2 * q^72 - 14 * q^73 + 11 * q^74 - 2 * q^75 - q^76 - q^77 + 3 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 9 * q^83 - q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 + 2 * q^88 + 20 * q^89 + 2 * q^90 - 15 * q^91 + q^92 - 9 * q^93 + 6 * q^94 + 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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