LMFDB - Embedded newform 5610.2.a.bq.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			$-2.37228$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.37228 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -2.37228 q^{21} -1.00000 q^{22} -1.62772 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} +2.37228 q^{28} -6.37228 q^{29} +1.00000 q^{30} -9.11684 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +2.37228 q^{35} +1.00000 q^{36} +8.74456 q^{37} -4.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} +10.7446 q^{41} +2.37228 q^{42} -10.3723 q^{43} +1.00000 q^{44} +1.00000 q^{45} +1.62772 q^{46} +10.7446 q^{47} -1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} +1.00000 q^{54} +1.00000 q^{55} -2.37228 q^{56} -4.00000 q^{57} +6.37228 q^{58} +12.7446 q^{59} -1.00000 q^{60} +11.4891 q^{61} +9.11684 q^{62} +2.37228 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +1.62772 q^{69} -2.37228 q^{70} +4.74456 q^{71} -1.00000 q^{72} -6.00000 q^{73} -8.74456 q^{74} -1.00000 q^{75} +4.00000 q^{76} +2.37228 q^{77} -4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} -10.7446 q^{82} -13.4891 q^{83} -2.37228 q^{84} +1.00000 q^{85} +10.3723 q^{86} +6.37228 q^{87} -1.00000 q^{88} -2.74456 q^{89} -1.00000 q^{90} -9.48913 q^{91} -1.62772 q^{92} +9.11684 q^{93} -10.7446 q^{94} +4.00000 q^{95} +1.00000 q^{96} -17.8614 q^{97} +1.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} - 2 q^{22} - 9 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} - 2 q^{27} - q^{28} - 7 q^{29} + 2 q^{30} - q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 8 q^{39} - 2 q^{40} + 10 q^{41} - q^{42} - 15 q^{43} + 2 q^{44} + 2 q^{45} + 9 q^{46} + 10 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 8 q^{52} + 2 q^{54} + 2 q^{55} + q^{56} - 8 q^{57} + 7 q^{58} + 14 q^{59} - 2 q^{60} + q^{62} - q^{63} + 2 q^{64} - 8 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} + 9 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} - 2 q^{75} + 8 q^{76} - q^{77} - 8 q^{78} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 4 q^{83} + q^{84} + 2 q^{85} + 15 q^{86} + 7 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} + 4 q^{91} - 9 q^{92} + q^{93} - 10 q^{94} + 8 q^{95} + 2 q^{96} - 7 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) \) 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 - 8 * 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 - 9 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 - 2 * q^27 - q^28 - 7 * q^29 + 2 * q^30 - q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 8 * q^39 - 2 * q^40 + 10 * q^41 - q^42 - 15 * q^43 + 2 * q^44 + 2 * q^45 + 9 * q^46 + 10 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 8 * q^52 + 2 * q^54 + 2 * q^55 + q^56 - 8 * q^57 + 7 * q^58 + 14 * q^59 - 2 * q^60 + q^62 - q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 + 9 * q^69 + q^70 - 2 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 - 2 * q^75 + 8 * q^76 - q^77 - 8 * q^78 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 4 * q^83 + q^84 + 2 * q^85 + 15 * q^86 + 7 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 + 4 * q^91 - 9 * q^92 + q^93 - 10 * q^94 + 8 * q^95 + 2 * q^96 - 7 * 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
$7$	2.37228	0.896638	0.448319	−	0.893874i	$-0.352023\pi$
$7$	2.37228	0.896638	0.448319	+	0.893874i	$0.352023\pi$
$8$	−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
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.37228	−0.634019
$15$	−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
$21$	−2.37228	−0.517674
$22$	−1.00000	−0.213201
$23$	−1.62772	−0.339403	−0.169701	−	0.985496i	$-0.554280\pi$
$23$	−1.62772	−0.339403	−0.169701	+	0.985496i	$0.554280\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	2.37228	0.448319
$29$	−6.37228	−1.18330	−0.591651	−	0.806194i	$-0.701524\pi$
$29$	−6.37228	−1.18330	−0.591651	+	0.806194i	$0.701524\pi$
$30$	1.00000	0.182574
$31$	−9.11684	−1.63743	−0.818717	−	0.574198i	$-0.805314\pi$
$31$	−9.11684	−1.63743	−0.818717	+	0.574198i	$0.805314\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	2.37228	0.400989
$36$	1.00000	0.166667
$37$	8.74456	1.43760	0.718799	−	0.695218i	$-0.244692\pi$
$37$	8.74456	1.43760	0.718799	+	0.695218i	$0.244692\pi$
$38$	−4.00000	−0.648886
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	10.7446	1.67802	0.839009	−	0.544117i	$-0.183135\pi$
$41$	10.7446	1.67802	0.839009	+	0.544117i	$0.183135\pi$
$42$	2.37228	0.366051
$43$	−10.3723	−1.58176	−0.790879	−	0.611973i	$-0.790376\pi$
$43$	−10.3723	−1.58176	−0.790879	+	0.611973i	$0.790376\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	1.62772	0.239994
$47$	10.7446	1.56726	0.783628	−	0.621231i	$-0.213367\pi$
$47$	10.7446	1.56726	0.783628	+	0.621231i	$0.213367\pi$
$48$	−1.00000	−0.144338
$49$	−1.37228	−0.196040
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−4.00000	−0.554700
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−2.37228	−0.317009
$57$	−4.00000	−0.529813
$58$	6.37228	0.836722
$59$	12.7446	1.65920	0.829600	−	0.558358i	$-0.188568\pi$
$59$	12.7446	1.65920	0.829600	+	0.558358i	$0.188568\pi$
$60$	−1.00000	−0.129099
$61$	11.4891	1.47103	0.735516	−	0.677507i	$-0.236940\pi$
$61$	11.4891	1.47103	0.735516	+	0.677507i	$0.236940\pi$
$62$	9.11684	1.15784
$63$	2.37228	0.298879
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	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
$69$	1.62772	0.195954
$70$	−2.37228	−0.283542
$71$	4.74456	0.563076	0.281538	−	0.959550i	$-0.409155\pi$
$71$	4.74456	0.563076	0.281538	+	0.959550i	$0.409155\pi$
$72$	−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	$0.614200\pi$
$74$	−8.74456	−1.01653
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	2.37228	0.270347
$78$	−4.00000	−0.452911
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.7446	−1.18654
$83$	−13.4891	−1.48062	−0.740312	−	0.672264i	$-0.765322\pi$
$83$	−13.4891	−1.48062	−0.740312	+	0.672264i	$0.765322\pi$
$84$	−2.37228	−0.258837
$85$	1.00000	0.108465
$86$	10.3723	1.11847
$87$	6.37228	0.683180
$88$	−1.00000	−0.106600
$89$	−2.74456	−0.290923	−0.145462	−	0.989364i	$-0.546467\pi$
$89$	−2.74456	−0.290923	−0.145462	+	0.989364i	$0.546467\pi$
$90$	−1.00000	−0.105409
$91$	−9.48913	−0.994731
$92$	−1.62772	−0.169701
$93$	9.11684	0.945373
$94$	−10.7446	−1.10822
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−17.8614	−1.81355	−0.906776	−	0.421614i	$-0.861464\pi$
$97$	−17.8614	−1.81355	−0.906776	+	0.421614i	$0.861464\pi$
$98$	1.37228	0.138621
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	1.00000	0.0990148
$103$	18.3723	1.81027	0.905137	−	0.425119i	$-0.139768\pi$
$103$	18.3723	1.81027	0.905137	+	0.425119i	$0.139768\pi$
$104$	4.00000	0.392232
$105$	−2.37228	−0.231511
$106$	0	0
$107$	10.3723	1.00273	0.501363	−	0.865237i	$-0.332832\pi$
$107$	10.3723	1.00273	0.501363	+	0.865237i	$0.332832\pi$
$108$	−1.00000	−0.0962250
$109$	16.2337	1.55491	0.777453	−	0.628941i	$-0.216511\pi$
$109$	16.2337	1.55491	0.777453	+	0.628941i	$0.216511\pi$
$110$	−1.00000	−0.0953463
$111$	−8.74456	−0.829997
$112$	2.37228	0.224160
$113$	7.48913	0.704518	0.352259	−	0.935903i	$-0.385414\pi$
$113$	7.48913	0.704518	0.352259	+	0.935903i	$0.385414\pi$
$114$	4.00000	0.374634
$115$	−1.62772	−0.151786
$116$	−6.37228	−0.591651
$117$	−4.00000	−0.369800
$118$	−12.7446	−1.17323
$119$	2.37228	0.217467
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−11.4891	−1.04018
$123$	−10.7446	−0.968805
$124$	−9.11684	−0.818717
$125$	1.00000	0.0894427
$126$	−2.37228	−0.211340
$127$	−11.4891	−1.01950	−0.509748	−	0.860324i	$-0.670261\pi$
$127$	−11.4891	−1.01950	−0.509748	+	0.860324i	$0.670261\pi$
$128$	−1.00000	−0.0883883
$129$	10.3723	0.913228
$130$	4.00000	0.350823
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	−1.00000	−0.0870388
$133$	9.48913	0.822812
$134$	−4.00000	−0.345547
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	1.11684	0.0954184	0.0477092	−	0.998861i	$-0.484808\pi$
$137$	1.11684	0.0954184	0.0477092	+	0.998861i	$0.484808\pi$
$138$	−1.62772	−0.138561
$139$	1.62772	0.138061	0.0690306	−	0.997615i	$-0.478009\pi$
$139$	1.62772	0.138061	0.0690306	+	0.997615i	$0.478009\pi$
$140$	2.37228	0.200494
$141$	−10.7446	−0.904855
$142$	−4.74456	−0.398155
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	−6.37228	−0.529189
$146$	6.00000	0.496564
$147$	1.37228	0.113184
$148$	8.74456	0.718799
$149$	14.7446	1.20792	0.603961	−	0.797014i	$-0.293588\pi$
$149$	14.7446	1.20792	0.603961	+	0.797014i	$0.293588\pi$
$150$	1.00000	0.0816497
$151$	16.2337	1.32108	0.660539	−	0.750791i	$-0.270328\pi$
$151$	16.2337	1.32108	0.660539	+	0.750791i	$0.270328\pi$
$152$	−4.00000	−0.324443
$153$	1.00000	0.0808452
$154$	−2.37228	−0.191164
$155$	−9.11684	−0.732283
$156$	4.00000	0.320256
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	−3.86141	−0.304321
$162$	−1.00000	−0.0785674
$163$	−7.86141	−0.615753	−0.307876	−	0.951426i	$-0.599618\pi$
$163$	−7.86141	−0.615753	−0.307876	+	0.951426i	$0.599618\pi$
$164$	10.7446	0.839009
$165$	−1.00000	−0.0778499
$166$	13.4891	1.04696
$167$	19.4891	1.50811	0.754057	−	0.656809i	$-0.228094\pi$
$167$	19.4891	1.50811	0.754057	+	0.656809i	$0.228094\pi$
$168$	2.37228	0.183025
$169$	3.00000	0.230769
$170$	−1.00000	−0.0766965
$171$	4.00000	0.305888
$172$	−10.3723	−0.790879
$173$	−14.2337	−1.08217	−0.541084	−	0.840969i	$-0.681986\pi$
$173$	−14.2337	−1.08217	−0.541084	+	0.840969i	$0.681986\pi$
$174$	−6.37228	−0.483081
$175$	2.37228	0.179328
$176$	1.00000	0.0753778
$177$	−12.7446	−0.957940
$178$	2.74456	0.205714
$179$	−0.744563	−0.0556512	−0.0278256	−	0.999613i	$-0.508858\pi$
$179$	−0.744563	−0.0556512	−0.0278256	+	0.999613i	$0.508858\pi$
$180$	1.00000	0.0745356
$181$	−14.3723	−1.06828	−0.534142	−	0.845395i	$-0.679365\pi$
$181$	−14.3723	−1.06828	−0.534142	+	0.845395i	$0.679365\pi$
$182$	9.48913	0.703381
$183$	−11.4891	−0.849301
$184$	1.62772	0.119997
$185$	8.74456	0.642913
$186$	−9.11684	−0.668479
$187$	1.00000	0.0731272
$188$	10.7446	0.783628
$189$	−2.37228	−0.172558
$190$	−4.00000	−0.290191
$191$	7.62772	0.551922	0.275961	−	0.961169i	$-0.411004\pi$
$191$	7.62772	0.551922	0.275961	+	0.961169i	$0.411004\pi$
$192$	−1.00000	−0.0721688
$193$	−3.48913	−0.251153	−0.125576	−	0.992084i	$-0.540078\pi$
$193$	−3.48913	−0.251153	−0.125576	+	0.992084i	$0.540078\pi$
$194$	17.8614	1.28237
$195$	4.00000	0.286446
$196$	−1.37228	−0.0980201
$197$	−13.4891	−0.961060	−0.480530	−	0.876978i	$-0.659556\pi$
$197$	−13.4891	−0.961060	−0.480530	+	0.876978i	$0.659556\pi$
$198$	−1.00000	−0.0710669
$199$	−14.7446	−1.04521	−0.522607	−	0.852574i	$-0.675041\pi$
$199$	−14.7446	−1.04521	−0.522607	+	0.852574i	$0.675041\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	−2.00000	−0.140720
$203$	−15.1168	−1.06099
$204$	−1.00000	−0.0700140
$205$	10.7446	0.750433
$206$	−18.3723	−1.28006
$207$	−1.62772	−0.113134
$208$	−4.00000	−0.277350
$209$	4.00000	0.276686
$210$	2.37228	0.163703
$211$	−9.62772	−0.662799	−0.331400	−	0.943490i	$-0.607521\pi$
$211$	−9.62772	−0.662799	−0.331400	+	0.943490i	$0.607521\pi$
$212$	0	0
$213$	−4.74456	−0.325092
$214$	−10.3723	−0.709035
$215$	−10.3723	−0.707384
$216$	1.00000	0.0680414
$217$	−21.6277	−1.46819
$218$	−16.2337	−1.09948
$219$	6.00000	0.405442
$220$	1.00000	0.0674200
$221$	−4.00000	−0.269069
$222$	8.74456	0.586897
$223$	−3.11684	−0.208719	−0.104360	−	0.994540i	$-0.533279\pi$
$223$	−3.11684	−0.208719	−0.104360	+	0.994540i	$0.533279\pi$
$224$	−2.37228	−0.158505
$225$	1.00000	0.0666667
$226$	−7.48913	−0.498169
$227$	23.8614	1.58374	0.791869	−	0.610692i	$-0.209108\pi$
$227$	23.8614	1.58374	0.791869	+	0.610692i	$0.209108\pi$
$228$	−4.00000	−0.264906
$229$	−1.25544	−0.0829616	−0.0414808	−	0.999139i	$-0.513208\pi$
$229$	−1.25544	−0.0829616	−0.0414808	+	0.999139i	$0.513208\pi$
$230$	1.62772	0.107329
$231$	−2.37228	−0.156085
$232$	6.37228	0.418361
$233$	−1.11684	−0.0731669	−0.0365834	−	0.999331i	$-0.511647\pi$
$233$	−1.11684	−0.0731669	−0.0365834	+	0.999331i	$0.511647\pi$
$234$	4.00000	0.261488
$235$	10.7446	0.700898
$236$	12.7446	0.829600
$237$	0	0
$238$	−2.37228	−0.153772
$239$	−30.2337	−1.95565	−0.977827	−	0.209413i	$-0.932845\pi$
$239$	−30.2337	−1.95565	−0.977827	+	0.209413i	$0.932845\pi$
$240$	−1.00000	−0.0645497
$241$	22.6060	1.45618	0.728089	−	0.685482i	$-0.240409\pi$
$241$	22.6060	1.45618	0.728089	+	0.685482i	$0.240409\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	11.4891	0.735516
$245$	−1.37228	−0.0876718
$246$	10.7446	0.685048
$247$	−16.0000	−1.01806
$248$	9.11684	0.578920
$249$	13.4891	0.854839
$250$	−1.00000	−0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	2.37228	0.149440
$253$	−1.62772	−0.102334
$254$	11.4891	0.720892
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−9.11684	−0.568693	−0.284347	−	0.958722i	$-0.591777\pi$
$257$	−9.11684	−0.568693	−0.284347	+	0.958722i	$0.591777\pi$
$258$	−10.3723	−0.645750
$259$	20.7446	1.28900
$260$	−4.00000	−0.248069
$261$	−6.37228	−0.394434
$262$	−8.00000	−0.494242
$263$	−19.1168	−1.17880	−0.589398	−	0.807843i	$-0.700635\pi$
$263$	−19.1168	−1.17880	−0.589398	+	0.807843i	$0.700635\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	−9.48913	−0.581816
$267$	2.74456	0.167965
$268$	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
$271$	−7.62772	−0.463351	−0.231675	−	0.972793i	$-0.574421\pi$
$271$	−7.62772	−0.463351	−0.231675	+	0.972793i	$0.574421\pi$
$272$	1.00000	0.0606339
$273$	9.48913	0.574308
$274$	−1.11684	−0.0674710
$275$	1.00000	0.0603023
$276$	1.62772	0.0979772
$277$	15.4891	0.930651	0.465326	−	0.885140i	$-0.345937\pi$
$277$	15.4891	0.930651	0.465326	+	0.885140i	$0.345937\pi$
$278$	−1.62772	−0.0976241
$279$	−9.11684	−0.545811
$280$	−2.37228	−0.141771
$281$	13.8614	0.826902	0.413451	−	0.910526i	$-0.364323\pi$
$281$	13.8614	0.826902	0.413451	+	0.910526i	$0.364323\pi$
$282$	10.7446	0.639829
$283$	−24.7446	−1.47091	−0.735456	−	0.677573i	$-0.763032\pi$
$283$	−24.7446	−1.47091	−0.735456	+	0.677573i	$0.763032\pi$
$284$	4.74456	0.281538
$285$	−4.00000	−0.236940
$286$	4.00000	0.236525
$287$	25.4891	1.50458
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.37228	0.374193
$291$	17.8614	1.04705
$292$	−6.00000	−0.351123
$293$	2.88316	0.168436	0.0842179	−	0.996447i	$-0.473161\pi$
$293$	2.88316	0.168436	0.0842179	+	0.996447i	$0.473161\pi$
$294$	−1.37228	−0.0800331
$295$	12.7446	0.742017
$296$	−8.74456	−0.508267
$297$	−1.00000	−0.0580259
$298$	−14.7446	−0.854130
$299$	6.51087	0.376534
$300$	−1.00000	−0.0577350
$301$	−24.6060	−1.41826
$302$	−16.2337	−0.934144
$303$	−2.00000	−0.114897
$304$	4.00000	0.229416
$305$	11.4891	0.657865
$306$	−1.00000	−0.0571662
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	2.37228	0.135173
$309$	−18.3723	−1.04516
$310$	9.11684	0.517802
$311$	10.5109	0.596017	0.298009	−	0.954563i	$-0.403678\pi$
$311$	10.5109	0.596017	0.298009	+	0.954563i	$0.403678\pi$
$312$	−4.00000	−0.226455
$313$	4.37228	0.247136	0.123568	−	0.992336i	$-0.460566\pi$
$313$	4.37228	0.247136	0.123568	+	0.992336i	$0.460566\pi$
$314$	−10.0000	−0.564333
$315$	2.37228	0.133663
$316$	0	0
$317$	−1.11684	−0.0627282	−0.0313641	−	0.999508i	$-0.509985\pi$
$317$	−1.11684	−0.0627282	−0.0313641	+	0.999508i	$0.509985\pi$
$318$	0	0
$319$	−6.37228	−0.356779
$320$	1.00000	0.0559017
$321$	−10.3723	−0.578924
$322$	3.86141	0.215188
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	7.86141	0.435403
$327$	−16.2337	−0.897725
$328$	−10.7446	−0.593269
$329$	25.4891	1.40526
$330$	1.00000	0.0550482
$331$	27.1168	1.49048	0.745238	−	0.666798i	$-0.232336\pi$
$331$	27.1168	1.49048	0.745238	+	0.666798i	$0.232336\pi$
$332$	−13.4891	−0.740312
$333$	8.74456	0.479199
$334$	−19.4891	−1.06640
$335$	4.00000	0.218543
$336$	−2.37228	−0.129419
$337$	−11.4891	−0.625853	−0.312926	−	0.949777i	$-0.601309\pi$
$337$	−11.4891	−0.625853	−0.312926	+	0.949777i	$0.601309\pi$
$338$	−3.00000	−0.163178
$339$	−7.48913	−0.406753
$340$	1.00000	0.0542326
$341$	−9.11684	−0.493705
$342$	−4.00000	−0.216295
$343$	−19.8614	−1.07242
$344$	10.3723	0.559236
$345$	1.62772	0.0876334
$346$	14.2337	0.765208
$347$	17.4891	0.938865	0.469433	−	0.882968i	$-0.344458\pi$
$347$	17.4891	0.938865	0.469433	+	0.882968i	$0.344458\pi$
$348$	6.37228	0.341590
$349$	−30.2337	−1.61837	−0.809186	−	0.587552i	$-0.800092\pi$
$349$	−30.2337	−1.61837	−0.809186	+	0.587552i	$0.800092\pi$
$350$	−2.37228	−0.126804
$351$	4.00000	0.213504
$352$	−1.00000	−0.0533002
$353$	19.6277	1.04468	0.522339	−	0.852738i	$-0.325060\pi$
$353$	19.6277	1.04468	0.522339	+	0.852738i	$0.325060\pi$
$354$	12.7446	0.677366
$355$	4.74456	0.251815
$356$	−2.74456	−0.145462
$357$	−2.37228	−0.125554
$358$	0.744563	0.0393514
$359$	24.7446	1.30597	0.652984	−	0.757372i	$-0.273517\pi$
$359$	24.7446	1.30597	0.652984	+	0.757372i	$0.273517\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	14.3723	0.755390
$363$	−1.00000	−0.0524864
$364$	−9.48913	−0.497365
$365$	−6.00000	−0.314054
$366$	11.4891	0.600546
$367$	0.510875	0.0266674	0.0133337	−	0.999911i	$-0.495756\pi$
$367$	0.510875	0.0266674	0.0133337	+	0.999911i	$0.495756\pi$
$368$	−1.62772	−0.0848507
$369$	10.7446	0.559340
$370$	−8.74456	−0.454608
$371$	0	0
$372$	9.11684	0.472686
$373$	35.7228	1.84966	0.924829	−	0.380384i	$-0.124208\pi$
$373$	35.7228	1.84966	0.924829	+	0.380384i	$0.124208\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	−10.7446	−0.554109
$377$	25.4891	1.31276
$378$	2.37228	0.122017
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	4.00000	0.205196
$381$	11.4891	0.588606
$382$	−7.62772	−0.390268
$383$	−2.74456	−0.140241	−0.0701203	−	0.997539i	$-0.522338\pi$
$383$	−2.74456	−0.140241	−0.0701203	+	0.997539i	$0.522338\pi$
$384$	1.00000	0.0510310
$385$	2.37228	0.120903
$386$	3.48913	0.177592
$387$	−10.3723	−0.527253
$388$	−17.8614	−0.906776
$389$	20.7446	1.05179	0.525896	−	0.850549i	$-0.323730\pi$
$389$	20.7446	1.05179	0.525896	+	0.850549i	$0.323730\pi$
$390$	−4.00000	−0.202548
$391$	−1.62772	−0.0823173
$392$	1.37228	0.0693107
$393$	−8.00000	−0.403547
$394$	13.4891	0.679572
$395$	0	0
$396$	1.00000	0.0502519
$397$	22.2337	1.11588	0.557938	−	0.829882i	$-0.311593\pi$
$397$	22.2337	1.11588	0.557938	+	0.829882i	$0.311593\pi$
$398$	14.7446	0.739078
$399$	−9.48913	−0.475050
$400$	1.00000	0.0500000
$401$	29.8614	1.49121	0.745604	−	0.666390i	$-0.232161\pi$
$401$	29.8614	1.49121	0.745604	+	0.666390i	$0.232161\pi$
$402$	4.00000	0.199502
$403$	36.4674	1.81657
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	15.1168	0.750236
$407$	8.74456	0.433452
$408$	1.00000	0.0495074
$409$	12.2337	0.604917	0.302458	−	0.953163i	$-0.402193\pi$
$409$	12.2337	0.604917	0.302458	+	0.953163i	$0.402193\pi$
$410$	−10.7446	−0.530636
$411$	−1.11684	−0.0550899
$412$	18.3723	0.905137
$413$	30.2337	1.48770
$414$	1.62772	0.0799980
$415$	−13.4891	−0.662155
$416$	4.00000	0.196116
$417$	−1.62772	−0.0797097
$418$	−4.00000	−0.195646
$419$	38.3723	1.87461	0.937304	−	0.348512i	$-0.113313\pi$
$419$	38.3723	1.87461	0.937304	+	0.348512i	$0.113313\pi$
$420$	−2.37228	−0.115755
$421$	−25.2554	−1.23087	−0.615437	−	0.788186i	$-0.711021\pi$
$421$	−25.2554	−1.23087	−0.615437	+	0.788186i	$0.711021\pi$
$422$	9.62772	0.468670
$423$	10.7446	0.522419
$424$	0	0
$425$	1.00000	0.0485071
$426$	4.74456	0.229875
$427$	27.2554	1.31898
$428$	10.3723	0.501363
$429$	4.00000	0.193122
$430$	10.3723	0.500196
$431$	−17.8614	−0.860354	−0.430177	−	0.902745i	$-0.641549\pi$
$431$	−17.8614	−0.860354	−0.430177	+	0.902745i	$0.641549\pi$
$432$	−1.00000	−0.0481125
$433$	18.7446	0.900806	0.450403	−	0.892825i	$-0.351280\pi$
$433$	18.7446	0.900806	0.450403	+	0.892825i	$0.351280\pi$
$434$	21.6277	1.03816
$435$	6.37228	0.305528
$436$	16.2337	0.777453
$437$	−6.51087	−0.311457
$438$	−6.00000	−0.286691
$439$	32.7446	1.56281	0.781406	−	0.624023i	$-0.214503\pi$
$439$	32.7446	1.56281	0.781406	+	0.624023i	$0.214503\pi$
$440$	−1.00000	−0.0476731
$441$	−1.37228	−0.0653467
$442$	4.00000	0.190261
$443$	10.3723	0.492802	0.246401	−	0.969168i	$-0.420752\pi$
$443$	10.3723	0.492802	0.246401	+	0.969168i	$0.420752\pi$
$444$	−8.74456	−0.414999
$445$	−2.74456	−0.130105
$446$	3.11684	0.147587
$447$	−14.7446	−0.697394
$448$	2.37228	0.112080
$449$	−1.86141	−0.0878452	−0.0439226	−	0.999035i	$-0.513985\pi$
$449$	−1.86141	−0.0878452	−0.0439226	+	0.999035i	$0.513985\pi$
$450$	−1.00000	−0.0471405
$451$	10.7446	0.505942
$452$	7.48913	0.352259
$453$	−16.2337	−0.762725
$454$	−23.8614	−1.11987
$455$	−9.48913	−0.444857
$456$	4.00000	0.187317
$457$	−16.9783	−0.794209	−0.397105	−	0.917773i	$-0.629985\pi$
$457$	−16.9783	−0.794209	−0.397105	+	0.917773i	$0.629985\pi$
$458$	1.25544	0.0586627
$459$	−1.00000	−0.0466760
$460$	−1.62772	−0.0758928
$461$	23.4891	1.09400	0.546999	−	0.837133i	$-0.315770\pi$
$461$	23.4891	1.09400	0.546999	+	0.837133i	$0.315770\pi$
$462$	2.37228	0.110369
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−6.37228	−0.295826
$465$	9.11684	0.422784
$466$	1.11684	0.0517368
$467$	30.9783	1.43350	0.716751	−	0.697329i	$-0.245628\pi$
$467$	30.9783	1.43350	0.716751	+	0.697329i	$0.245628\pi$
$468$	−4.00000	−0.184900
$469$	9.48913	0.438167
$470$	−10.7446	−0.495610
$471$	−10.0000	−0.460776
$472$	−12.7446	−0.586616
$473$	−10.3723	−0.476918
$474$	0	0
$475$	4.00000	0.183533
$476$	2.37228	0.108733
$477$	0	0
$478$	30.2337	1.38286
$479$	−33.1168	−1.51315	−0.756574	−	0.653909i	$-0.773128\pi$
$479$	−33.1168	−1.51315	−0.756574	+	0.653909i	$0.773128\pi$
$480$	1.00000	0.0456435
$481$	−34.9783	−1.59487
$482$	−22.6060	−1.02967
$483$	3.86141	0.175700
$484$	1.00000	0.0454545
$485$	−17.8614	−0.811045
$486$	1.00000	0.0453609
$487$	7.48913	0.339365	0.169682	−	0.985499i	$-0.445726\pi$
$487$	7.48913	0.339365	0.169682	+	0.985499i	$0.445726\pi$
$488$	−11.4891	−0.520088
$489$	7.86141	0.355505
$490$	1.37228	0.0619934
$491$	18.5109	0.835384	0.417692	−	0.908589i	$-0.362839\pi$
$491$	18.5109	0.835384	0.417692	+	0.908589i	$0.362839\pi$
$492$	−10.7446	−0.484402
$493$	−6.37228	−0.286993
$494$	16.0000	0.719874
$495$	1.00000	0.0449467
$496$	−9.11684	−0.409358
$497$	11.2554	0.504875
$498$	−13.4891	−0.604462
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	1.00000	0.0447214
$501$	−19.4891	−0.870710
$502$	−12.0000	−0.535586
$503$	33.7228	1.50363	0.751813	−	0.659376i	$-0.229180\pi$
$503$	33.7228	1.50363	0.751813	+	0.659376i	$0.229180\pi$
$504$	−2.37228	−0.105670
$505$	2.00000	0.0889988
$506$	1.62772	0.0723609
$507$	−3.00000	−0.133235
$508$	−11.4891	−0.509748
$509$	20.7446	0.919487	0.459743	−	0.888052i	$-0.347941\pi$
$509$	20.7446	0.919487	0.459743	+	0.888052i	$0.347941\pi$
$510$	1.00000	0.0442807
$511$	−14.2337	−0.629661
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	9.11684	0.402127
$515$	18.3723	0.809579
$516$	10.3723	0.456614
$517$	10.7446	0.472545
$518$	−20.7446	−0.911464
$519$	14.2337	0.624790
$520$	4.00000	0.175412
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	6.37228	0.278907
$523$	3.11684	0.136290	0.0681450	−	0.997675i	$-0.478292\pi$
$523$	3.11684	0.136290	0.0681450	+	0.997675i	$0.478292\pi$
$524$	8.00000	0.349482
$525$	−2.37228	−0.103535
$526$	19.1168	0.833534
$527$	−9.11684	−0.397136
$528$	−1.00000	−0.0435194
$529$	−20.3505	−0.884806
$530$	0	0
$531$	12.7446	0.553067
$532$	9.48913	0.411406
$533$	−42.9783	−1.86159
$534$	−2.74456	−0.118769
$535$	10.3723	0.448433
$536$	−4.00000	−0.172774
$537$	0.744563	0.0321302
$538$	−14.0000	−0.603583
$539$	−1.37228	−0.0591083
$540$	−1.00000	−0.0430331
$541$	−32.2337	−1.38583	−0.692917	−	0.721017i	$-0.743675\pi$
$541$	−32.2337	−1.38583	−0.692917	+	0.721017i	$0.743675\pi$
$542$	7.62772	0.327639
$543$	14.3723	0.616774
$544$	−1.00000	−0.0428746
$545$	16.2337	0.695375
$546$	−9.48913	−0.406097
$547$	16.7446	0.715946	0.357973	−	0.933732i	$-0.383468\pi$
$547$	16.7446	0.715946	0.357973	+	0.933732i	$0.383468\pi$
$548$	1.11684	0.0477092
$549$	11.4891	0.490344
$550$	−1.00000	−0.0426401
$551$	−25.4891	−1.08587
$552$	−1.62772	−0.0692803
$553$	0	0
$554$	−15.4891	−0.658070
$555$	−8.74456	−0.371186
$556$	1.62772	0.0690306
$557$	−29.8614	−1.26527	−0.632634	−	0.774451i	$-0.718026\pi$
$557$	−29.8614	−1.26527	−0.632634	+	0.774451i	$0.718026\pi$
$558$	9.11684	0.385947
$559$	41.4891	1.75480
$560$	2.37228	0.100247
$561$	−1.00000	−0.0422200
$562$	−13.8614	−0.584708
$563$	10.5109	0.442981	0.221490	−	0.975163i	$-0.428908\pi$
$563$	10.5109	0.442981	0.221490	+	0.975163i	$0.428908\pi$
$564$	−10.7446	−0.452428
$565$	7.48913	0.315070
$566$	24.7446	1.04009
$567$	2.37228	0.0996265
$568$	−4.74456	−0.199077
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	4.00000	0.167542
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	−4.00000	−0.167248
$573$	−7.62772	−0.318653
$574$	−25.4891	−1.06390
$575$	−1.62772	−0.0678806
$576$	1.00000	0.0416667
$577$	−30.4674	−1.26837	−0.634187	−	0.773180i	$-0.718665\pi$
$577$	−30.4674	−1.26837	−0.634187	+	0.773180i	$0.718665\pi$
$578$	−1.00000	−0.0415945
$579$	3.48913	0.145003
$580$	−6.37228	−0.264595
$581$	−32.0000	−1.32758
$582$	−17.8614	−0.740379
$583$	0	0
$584$	6.00000	0.248282
$585$	−4.00000	−0.165380
$586$	−2.88316	−0.119102
$587$	−29.3505	−1.21143	−0.605713	−	0.795683i	$-0.707112\pi$
$587$	−29.3505	−1.21143	−0.605713	+	0.795683i	$0.707112\pi$
$588$	1.37228	0.0565919
$589$	−36.4674	−1.50261
$590$	−12.7446	−0.524685
$591$	13.4891	0.554868
$592$	8.74456	0.359399
$593$	−4.97825	−0.204432	−0.102216	−	0.994762i	$-0.532593\pi$
$593$	−4.97825	−0.204432	−0.102216	+	0.994762i	$0.532593\pi$
$594$	1.00000	0.0410305
$595$	2.37228	0.0972541
$596$	14.7446	0.603961
$597$	14.7446	0.603455
$598$	−6.51087	−0.266249
$599$	26.8832	1.09842	0.549208	−	0.835686i	$-0.314929\pi$
$599$	26.8832	1.09842	0.549208	+	0.835686i	$0.314929\pi$
$600$	1.00000	0.0408248
$601$	−8.97825	−0.366230	−0.183115	−	0.983091i	$-0.558618\pi$
$601$	−8.97825	−0.366230	−0.183115	+	0.983091i	$0.558618\pi$
$602$	24.6060	1.00286
$603$	4.00000	0.162893
$604$	16.2337	0.660539
$605$	1.00000	0.0406558
$606$	2.00000	0.0812444
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−4.00000	−0.162221
$609$	15.1168	0.612565
$610$	−11.4891	−0.465181
$611$	−42.9783	−1.73871
$612$	1.00000	0.0404226
$613$	−16.7446	−0.676307	−0.338153	−	0.941091i	$-0.609802\pi$
$613$	−16.7446	−0.676307	−0.338153	+	0.941091i	$0.609802\pi$
$614$	12.0000	0.484281
$615$	−10.7446	−0.433263
$616$	−2.37228	−0.0955819
$617$	−42.4674	−1.70967	−0.854836	−	0.518898i	$-0.826342\pi$
$617$	−42.4674	−1.70967	−0.854836	+	0.518898i	$0.826342\pi$
$618$	18.3723	0.739042
$619$	18.2337	0.732874	0.366437	−	0.930443i	$-0.380578\pi$
$619$	18.2337	0.732874	0.366437	+	0.930443i	$0.380578\pi$
$620$	−9.11684	−0.366141
$621$	1.62772	0.0653181
$622$	−10.5109	−0.421448
$623$	−6.51087	−0.260853
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	−4.37228	−0.174752
$627$	−4.00000	−0.159745
$628$	10.0000	0.399043
$629$	8.74456	0.348669
$630$	−2.37228	−0.0945140
$631$	34.2337	1.36282	0.681411	−	0.731901i	$-0.261367\pi$
$631$	34.2337	1.36282	0.681411	+	0.731901i	$0.261367\pi$
$632$	0	0
$633$	9.62772	0.382667
$634$	1.11684	0.0443555
$635$	−11.4891	−0.455932
$636$	0	0
$637$	5.48913	0.217487
$638$	6.37228	0.252281
$639$	4.74456	0.187692
$640$	−1.00000	−0.0395285
$641$	−18.8832	−0.745840	−0.372920	−	0.927864i	$-0.621643\pi$
$641$	−18.8832	−0.745840	−0.372920	+	0.927864i	$0.621643\pi$
$642$	10.3723	0.409361
$643$	10.3723	0.409043	0.204521	−	0.978862i	$-0.434436\pi$
$643$	10.3723	0.409043	0.204521	+	0.978862i	$0.434436\pi$
$644$	−3.86141	−0.152161
$645$	10.3723	0.408408
$646$	−4.00000	−0.157378
$647$	−32.9783	−1.29651	−0.648254	−	0.761424i	$-0.724501\pi$
$647$	−32.9783	−1.29651	−0.648254	+	0.761424i	$0.724501\pi$
$648$	−1.00000	−0.0392837
$649$	12.7446	0.500268
$650$	4.00000	0.156893
$651$	21.6277	0.847657
$652$	−7.86141	−0.307876
$653$	28.3723	1.11029	0.555147	−	0.831753i	$-0.312662\pi$
$653$	28.3723	1.11029	0.555147	+	0.831753i	$0.312662\pi$
$654$	16.2337	0.634787
$655$	8.00000	0.312586
$656$	10.7446	0.419505
$657$	−6.00000	−0.234082
$658$	−25.4891	−0.993670
$659$	14.3723	0.559865	0.279932	−	0.960020i	$-0.409688\pi$
$659$	14.3723	0.559865	0.279932	+	0.960020i	$0.409688\pi$
$660$	−1.00000	−0.0389249
$661$	17.2554	0.671159	0.335579	−	0.942012i	$-0.391068\pi$
$661$	17.2554	0.671159	0.335579	+	0.942012i	$0.391068\pi$
$662$	−27.1168	−1.05393
$663$	4.00000	0.155347
$664$	13.4891	0.523480
$665$	9.48913	0.367972
$666$	−8.74456	−0.338845
$667$	10.3723	0.401616
$668$	19.4891	0.754057
$669$	3.11684	0.120504
$670$	−4.00000	−0.154533
$671$	11.4891	0.443533
$672$	2.37228	0.0915127
$673$	−24.2337	−0.934140	−0.467070	−	0.884220i	$-0.654690\pi$
$673$	−24.2337	−0.934140	−0.467070	+	0.884220i	$0.654690\pi$
$674$	11.4891	0.442545
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	−23.2554	−0.893779	−0.446890	−	0.894589i	$-0.647468\pi$
$677$	−23.2554	−0.893779	−0.446890	+	0.894589i	$0.647468\pi$
$678$	7.48913	0.287618
$679$	−42.3723	−1.62610
$680$	−1.00000	−0.0383482
$681$	−23.8614	−0.914371
$682$	9.11684	0.349102
$683$	46.9783	1.79757	0.898786	−	0.438387i	$-0.144450\pi$
$683$	46.9783	1.79757	0.898786	+	0.438387i	$0.144450\pi$
$684$	4.00000	0.152944
$685$	1.11684	0.0426724
$686$	19.8614	0.758312
$687$	1.25544	0.0478979
$688$	−10.3723	−0.395440
$689$	0	0
$690$	−1.62772	−0.0619662
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−14.2337	−0.541084
$693$	2.37228	0.0901155
$694$	−17.4891	−0.663878
$695$	1.62772	0.0617429
$696$	−6.37228	−0.241541
$697$	10.7446	0.406979
$698$	30.2337	1.14436
$699$	1.11684	0.0422429
$700$	2.37228	0.0896638
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−4.00000	−0.150970
$703$	34.9783	1.31923
$704$	1.00000	0.0376889
$705$	−10.7446	−0.404664
$706$	−19.6277	−0.738699
$707$	4.74456	0.178438
$708$	−12.7446	−0.478970
$709$	−11.2554	−0.422707	−0.211353	−	0.977410i	$-0.567787\pi$
$709$	−11.2554	−0.422707	−0.211353	+	0.977410i	$0.567787\pi$
$710$	−4.74456	−0.178060
$711$	0	0
$712$	2.74456	0.102857
$713$	14.8397	0.555750
$714$	2.37228	0.0887804
$715$	−4.00000	−0.149592
$716$	−0.744563	−0.0278256
$717$	30.2337	1.12910
$718$	−24.7446	−0.923459
$719$	−22.2337	−0.829177	−0.414588	−	0.910009i	$-0.636074\pi$
$719$	−22.2337	−0.829177	−0.414588	+	0.910009i	$0.636074\pi$
$720$	1.00000	0.0372678
$721$	43.5842	1.62316
$722$	3.00000	0.111648
$723$	−22.6060	−0.840725
$724$	−14.3723	−0.534142
$725$	−6.37228	−0.236661
$726$	1.00000	0.0371135
$727$	−11.1168	−0.412301	−0.206150	−	0.978520i	$-0.566094\pi$
$727$	−11.1168	−0.412301	−0.206150	+	0.978520i	$0.566094\pi$
$728$	9.48913	0.351690
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	−10.3723	−0.383633
$732$	−11.4891	−0.424650
$733$	−13.4891	−0.498232	−0.249116	−	0.968474i	$-0.580140\pi$
$733$	−13.4891	−0.498232	−0.249116	+	0.968474i	$0.580140\pi$
$734$	−0.510875	−0.0188567
$735$	1.37228	0.0506174
$736$	1.62772	0.0599985
$737$	4.00000	0.147342
$738$	−10.7446	−0.395513
$739$	1.76631	0.0649748	0.0324874	−	0.999472i	$-0.489657\pi$
$739$	1.76631	0.0649748	0.0324874	+	0.999472i	$0.489657\pi$
$740$	8.74456	0.321457
$741$	16.0000	0.587775
$742$	0	0
$743$	35.2119	1.29180	0.645900	−	0.763422i	$-0.276482\pi$
$743$	35.2119	1.29180	0.645900	+	0.763422i	$0.276482\pi$
$744$	−9.11684	−0.334240
$745$	14.7446	0.540199
$746$	−35.7228	−1.30791
$747$	−13.4891	−0.493541
$748$	1.00000	0.0365636
$749$	24.6060	0.899083
$750$	1.00000	0.0365148
$751$	17.1168	0.624603	0.312301	−	0.949983i	$-0.398900\pi$
$751$	17.1168	0.624603	0.312301	+	0.949983i	$0.398900\pi$
$752$	10.7446	0.391814
$753$	−12.0000	−0.437304
$754$	−25.4891	−0.928259
$755$	16.2337	0.590804
$756$	−2.37228	−0.0862790
$757$	−20.3723	−0.740443	−0.370222	−	0.928943i	$-0.620718\pi$
$757$	−20.3723	−0.740443	−0.370222	+	0.928943i	$0.620718\pi$
$758$	0	0
$759$	1.62772	0.0590824
$760$	−4.00000	−0.145095
$761$	24.0951	0.873446	0.436723	−	0.899596i	$-0.356139\pi$
$761$	24.0951	0.873446	0.436723	+	0.899596i	$0.356139\pi$
$762$	−11.4891	−0.416207
$763$	38.5109	1.39419
$764$	7.62772	0.275961
$765$	1.00000	0.0361551
$766$	2.74456	0.0991651
$767$	−50.9783	−1.84072
$768$	−1.00000	−0.0360844
$769$	−20.9783	−0.756495	−0.378248	−	0.925704i	$-0.623473\pi$
$769$	−20.9783	−0.756495	−0.378248	+	0.925704i	$0.623473\pi$
$770$	−2.37228	−0.0854911
$771$	9.11684	0.328335
$772$	−3.48913	−0.125576
$773$	−10.5109	−0.378050	−0.189025	−	0.981972i	$-0.560533\pi$
$773$	−10.5109	−0.378050	−0.189025	+	0.981972i	$0.560533\pi$
$774$	10.3723	0.372824
$775$	−9.11684	−0.327487
$776$	17.8614	0.641187
$777$	−20.7446	−0.744207
$778$	−20.7446	−0.743729
$779$	42.9783	1.53986
$780$	4.00000	0.143223
$781$	4.74456	0.169774
$782$	1.62772	0.0582071
$783$	6.37228	0.227727
$784$	−1.37228	−0.0490100
$785$	10.0000	0.356915
$786$	8.00000	0.285351
$787$	13.4891	0.480835	0.240418	−	0.970670i	$-0.422716\pi$
$787$	13.4891	0.480835	0.240418	+	0.970670i	$0.422716\pi$
$788$	−13.4891	−0.480530
$789$	19.1168	0.680578
$790$	0	0
$791$	17.7663	0.631697
$792$	−1.00000	−0.0355335
$793$	−45.9565	−1.63196
$794$	−22.2337	−0.789044
$795$	0	0
$796$	−14.7446	−0.522607
$797$	17.4891	0.619497	0.309748	−	0.950819i	$-0.399755\pi$
$797$	17.4891	0.619497	0.309748	+	0.950819i	$0.399755\pi$
$798$	9.48913	0.335911
$799$	10.7446	0.380115
$800$	−1.00000	−0.0353553
$801$	−2.74456	−0.0969744
$802$	−29.8614	−1.05444
$803$	−6.00000	−0.211735
$804$	−4.00000	−0.141069
$805$	−3.86141	−0.136097
$806$	−36.4674	−1.28451
$807$	−14.0000	−0.492823
$808$	−2.00000	−0.0703598
$809$	−4.97825	−0.175026	−0.0875130	−	0.996163i	$-0.527892\pi$
$809$	−4.97825	−0.175026	−0.0875130	+	0.996163i	$0.527892\pi$
$810$	−1.00000	−0.0351364
$811$	13.4891	0.473667	0.236834	−	0.971550i	$-0.423890\pi$
$811$	13.4891	0.473667	0.236834	+	0.971550i	$0.423890\pi$
$812$	−15.1168	−0.530497
$813$	7.62772	0.267516
$814$	−8.74456	−0.306497
$815$	−7.86141	−0.275373
$816$	−1.00000	−0.0350070
$817$	−41.4891	−1.45152
$818$	−12.2337	−0.427741
$819$	−9.48913	−0.331577
$820$	10.7446	0.375216
$821$	−21.6277	−0.754813	−0.377406	−	0.926048i	$-0.623184\pi$
$821$	−21.6277	−0.754813	−0.377406	+	0.926048i	$0.623184\pi$
$822$	1.11684	0.0389544
$823$	10.0000	0.348578	0.174289	−	0.984695i	$-0.444237\pi$
$823$	10.0000	0.348578	0.174289	+	0.984695i	$0.444237\pi$
$824$	−18.3723	−0.640029
$825$	−1.00000	−0.0348155
$826$	−30.2337	−1.05196
$827$	−50.8397	−1.76787	−0.883934	−	0.467612i	$-0.845115\pi$
$827$	−50.8397	−1.76787	−0.883934	+	0.467612i	$0.845115\pi$
$828$	−1.62772	−0.0565671
$829$	−20.9783	−0.728605	−0.364302	−	0.931281i	$-0.618693\pi$
$829$	−20.9783	−0.728605	−0.364302	+	0.931281i	$0.618693\pi$
$830$	13.4891	0.468214
$831$	−15.4891	−0.537312
$832$	−4.00000	−0.138675
$833$	−1.37228	−0.0475467
$834$	1.62772	0.0563633
$835$	19.4891	0.674449
$836$	4.00000	0.138343
$837$	9.11684	0.315124
$838$	−38.3723	−1.32555
$839$	43.7228	1.50948	0.754740	−	0.656025i	$-0.227763\pi$
$839$	43.7228	1.50948	0.754740	+	0.656025i	$0.227763\pi$
$840$	2.37228	0.0818515
$841$	11.6060	0.400206
$842$	25.2554	0.870360
$843$	−13.8614	−0.477412
$844$	−9.62772	−0.331400
$845$	3.00000	0.103203
$846$	−10.7446	−0.369406
$847$	2.37228	0.0815126
$848$	0	0
$849$	24.7446	0.849231
$850$	−1.00000	−0.0342997
$851$	−14.2337	−0.487925
$852$	−4.74456	−0.162546
$853$	13.1168	0.449112	0.224556	−	0.974461i	$-0.427907\pi$
$853$	13.1168	0.449112	0.224556	+	0.974461i	$0.427907\pi$
$854$	−27.2554	−0.932662
$855$	4.00000	0.136797
$856$	−10.3723	−0.354517
$857$	−9.86141	−0.336859	−0.168430	−	0.985714i	$-0.553870\pi$
$857$	−9.86141	−0.336859	−0.168430	+	0.985714i	$0.553870\pi$
$858$	−4.00000	−0.136558
$859$	34.8397	1.18871	0.594357	−	0.804201i	$-0.297407\pi$
$859$	34.8397	1.18871	0.594357	+	0.804201i	$0.297407\pi$
$860$	−10.3723	−0.353692
$861$	−25.4891	−0.868667
$862$	17.8614	0.608362
$863$	−37.7228	−1.28410	−0.642050	−	0.766663i	$-0.721916\pi$
$863$	−37.7228	−1.28410	−0.642050	+	0.766663i	$0.721916\pi$
$864$	1.00000	0.0340207
$865$	−14.2337	−0.483960
$866$	−18.7446	−0.636966
$867$	−1.00000	−0.0339618
$868$	−21.6277	−0.734093
$869$	0	0
$870$	−6.37228	−0.216041
$871$	−16.0000	−0.542139
$872$	−16.2337	−0.549742
$873$	−17.8614	−0.604517
$874$	6.51087	0.220234
$875$	2.37228	0.0801977
$876$	6.00000	0.202721
$877$	−24.3723	−0.822993	−0.411497	−	0.911411i	$-0.634994\pi$
$877$	−24.3723	−0.822993	−0.411497	+	0.911411i	$0.634994\pi$
$878$	−32.7446	−1.10508
$879$	−2.88316	−0.0972464
$880$	1.00000	0.0337100
$881$	−29.1168	−0.980971	−0.490486	−	0.871449i	$-0.663181\pi$
$881$	−29.1168	−0.980971	−0.490486	+	0.871449i	$0.663181\pi$
$882$	1.37228	0.0462071
$883$	−21.4891	−0.723167	−0.361583	−	0.932340i	$-0.617764\pi$
$883$	−21.4891	−0.723167	−0.361583	+	0.932340i	$0.617764\pi$
$884$	−4.00000	−0.134535
$885$	−12.7446	−0.428404
$886$	−10.3723	−0.348464
$887$	45.7228	1.53522	0.767611	−	0.640916i	$-0.221445\pi$
$887$	45.7228	1.53522	0.767611	+	0.640916i	$0.221445\pi$
$888$	8.74456	0.293448
$889$	−27.2554	−0.914118
$890$	2.74456	0.0919979
$891$	1.00000	0.0335013
$892$	−3.11684	−0.104360
$893$	42.9783	1.43821
$894$	14.7446	0.493132
$895$	−0.744563	−0.0248880
$896$	−2.37228	−0.0792524
$897$	−6.51087	−0.217392
$898$	1.86141	0.0621159
$899$	58.0951	1.93758
$900$	1.00000	0.0333333
$901$	0	0
$902$	−10.7446	−0.357755
$903$	24.6060	0.818835
$904$	−7.48913	−0.249085
$905$	−14.3723	−0.477751
$906$	16.2337	0.539328
$907$	47.8614	1.58921	0.794606	−	0.607125i	$-0.207677\pi$
$907$	47.8614	1.58921	0.794606	+	0.607125i	$0.207677\pi$
$908$	23.8614	0.791869
$909$	2.00000	0.0663358
$910$	9.48913	0.314561
$911$	28.4674	0.943166	0.471583	−	0.881822i	$-0.343683\pi$
$911$	28.4674	0.943166	0.471583	+	0.881822i	$0.343683\pi$
$912$	−4.00000	−0.132453
$913$	−13.4891	−0.446425
$914$	16.9783	0.561591
$915$	−11.4891	−0.379819
$916$	−1.25544	−0.0414808
$917$	18.9783	0.626717
$918$	1.00000	0.0330049
$919$	45.1168	1.48827	0.744134	−	0.668031i	$-0.232863\pi$
$919$	45.1168	1.48827	0.744134	+	0.668031i	$0.232863\pi$
$920$	1.62772	0.0536643
$921$	12.0000	0.395413
$922$	−23.4891	−0.773573
$923$	−18.9783	−0.624677
$924$	−2.37228	−0.0780423
$925$	8.74456	0.287519
$926$	−8.00000	−0.262896
$927$	18.3723	0.603425
$928$	6.37228	0.209180
$929$	19.6277	0.643965	0.321982	−	0.946746i	$-0.395651\pi$
$929$	19.6277	0.643965	0.321982	+	0.946746i	$0.395651\pi$
$930$	−9.11684	−0.298953
$931$	−5.48913	−0.179899
$932$	−1.11684	−0.0365834
$933$	−10.5109	−0.344111
$934$	−30.9783	−1.01364
$935$	1.00000	0.0327035
$936$	4.00000	0.130744
$937$	34.4674	1.12600	0.563000	−	0.826457i	$-0.309647\pi$
$937$	34.4674	1.12600	0.563000	+	0.826457i	$0.309647\pi$
$938$	−9.48913	−0.309831
$939$	−4.37228	−0.142684
$940$	10.7446	0.350449
$941$	−3.25544	−0.106124	−0.0530621	−	0.998591i	$-0.516898\pi$
$941$	−3.25544	−0.106124	−0.0530621	+	0.998591i	$0.516898\pi$
$942$	10.0000	0.325818
$943$	−17.4891	−0.569524
$944$	12.7446	0.414800
$945$	−2.37228	−0.0771703
$946$	10.3723	0.337232
$947$	−23.2554	−0.755700	−0.377850	−	0.925867i	$-0.623337\pi$
$947$	−23.2554	−0.755700	−0.377850	+	0.925867i	$0.623337\pi$
$948$	0	0
$949$	24.0000	0.779073
$950$	−4.00000	−0.129777
$951$	1.11684	0.0362161
$952$	−2.37228	−0.0768861
$953$	−52.9783	−1.71613	−0.858067	−	0.513538i	$-0.828335\pi$
$953$	−52.9783	−1.71613	−0.858067	+	0.513538i	$0.828335\pi$
$954$	0	0
$955$	7.62772	0.246827
$956$	−30.2337	−0.977827
$957$	6.37228	0.205987
$958$	33.1168	1.06996
$959$	2.64947	0.0855558
$960$	−1.00000	−0.0322749
$961$	52.1168	1.68119
$962$	34.9783	1.12774
$963$	10.3723	0.334242
$964$	22.6060	0.728089
$965$	−3.48913	−0.112319
$966$	−3.86141	−0.124239
$967$	−42.4674	−1.36566	−0.682829	−	0.730578i	$-0.739251\pi$
$967$	−42.4674	−1.36566	−0.682829	+	0.730578i	$0.739251\pi$
$968$	−1.00000	−0.0321412
$969$	−4.00000	−0.128499
$970$	17.8614	0.573495
$971$	−20.4674	−0.656829	−0.328415	−	0.944534i	$-0.606514\pi$
$971$	−20.4674	−0.656829	−0.328415	+	0.944534i	$0.606514\pi$
$972$	−1.00000	−0.0320750
$973$	3.86141	0.123791
$974$	−7.48913	−0.239967
$975$	4.00000	0.128103
$976$	11.4891	0.367758
$977$	11.4891	0.367570	0.183785	−	0.982966i	$-0.441165\pi$
$977$	11.4891	0.367570	0.183785	+	0.982966i	$0.441165\pi$
$978$	−7.86141	−0.251380
$979$	−2.74456	−0.0877166
$980$	−1.37228	−0.0438359
$981$	16.2337	0.518302
$982$	−18.5109	−0.590706
$983$	−23.1168	−0.737313	−0.368656	−	0.929566i	$-0.620182\pi$
$983$	−23.1168	−0.737313	−0.368656	+	0.929566i	$0.620182\pi$
$984$	10.7446	0.342524
$985$	−13.4891	−0.429799
$986$	6.37228	0.202935
$987$	−25.4891	−0.811328
$988$	−16.0000	−0.509028
$989$	16.8832	0.536853
$990$	−1.00000	−0.0317821
$991$	7.62772	0.242302	0.121151	−	0.992634i	$-0.461341\pi$
$991$	7.62772	0.242302	0.121151	+	0.992634i	$0.461341\pi$
$992$	9.11684	0.289460
$993$	−27.1168	−0.860527
$994$	−11.2554	−0.357001
$995$	−14.7446	−0.467434
$996$	13.4891	0.427419
$997$	6.88316	0.217992	0.108996	−	0.994042i	$-0.465236\pi$
$997$	6.88316	0.217992	0.108996	+	0.994042i	$0.465236\pi$
$998$	−36.0000	−1.13956
$999$	−8.74456	−0.276666

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bq.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.37228 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -2.37228 q^{21} -1.00000 q^{22} -1.62772 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} +2.37228 q^{28} -6.37228 q^{29} +1.00000 q^{30} -9.11684 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +2.37228 q^{35} +1.00000 q^{36} +8.74456 q^{37} -4.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} +10.7446 q^{41} +2.37228 q^{42} -10.3723 q^{43} +1.00000 q^{44} +1.00000 q^{45} +1.62772 q^{46} +10.7446 q^{47} -1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} +1.00000 q^{54} +1.00000 q^{55} -2.37228 q^{56} -4.00000 q^{57} +6.37228 q^{58} +12.7446 q^{59} -1.00000 q^{60} +11.4891 q^{61} +9.11684 q^{62} +2.37228 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +1.62772 q^{69} -2.37228 q^{70} +4.74456 q^{71} -1.00000 q^{72} -6.00000 q^{73} -8.74456 q^{74} -1.00000 q^{75} +4.00000 q^{76} +2.37228 q^{77} -4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} -10.7446 q^{82} -13.4891 q^{83} -2.37228 q^{84} +1.00000 q^{85} +10.3723 q^{86} +6.37228 q^{87} -1.00000 q^{88} -2.74456 q^{89} -1.00000 q^{90} -9.48913 q^{91} -1.62772 q^{92} +9.11684 q^{93} -10.7446 q^{94} +4.00000 q^{95} +1.00000 q^{96} -17.8614 q^{97} +1.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} - 2 q^{22} - 9 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} - 2 q^{27} - q^{28} - 7 q^{29} + 2 q^{30} - q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 8 q^{39} - 2 q^{40} + 10 q^{41} - q^{42} - 15 q^{43} + 2 q^{44} + 2 q^{45} + 9 q^{46} + 10 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 8 q^{52} + 2 q^{54} + 2 q^{55} + q^{56} - 8 q^{57} + 7 q^{58} + 14 q^{59} - 2 q^{60} + q^{62} - q^{63} + 2 q^{64} - 8 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} + 9 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} - 2 q^{75} + 8 q^{76} - q^{77} - 8 q^{78} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 4 q^{83} + q^{84} + 2 q^{85} + 15 q^{86} + 7 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} + 4 q^{91} - 9 q^{92} + q^{93} - 10 q^{94} + 8 q^{95} + 2 q^{96} - 7 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) \) 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 - 8 * 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 - 9 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 - 2 * q^27 - q^28 - 7 * q^29 + 2 * q^30 - q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 8 * q^39 - 2 * q^40 + 10 * q^41 - q^42 - 15 * q^43 + 2 * q^44 + 2 * q^45 + 9 * q^46 + 10 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 8 * q^52 + 2 * q^54 + 2 * q^55 + q^56 - 8 * q^57 + 7 * q^58 + 14 * q^59 - 2 * q^60 + q^62 - q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 + 9 * q^69 + q^70 - 2 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 - 2 * q^75 + 8 * q^76 - q^77 - 8 * q^78 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 4 * q^83 + q^84 + 2 * q^85 + 15 * q^86 + 7 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 + 4 * q^91 - 9 * q^92 + q^93 - 10 * q^94 + 8 * q^95 + 2 * q^96 - 7 * q^97 - 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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