LMFDB - Embedded newform 5610.2.a.bx.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.74456 q^{13} -2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -2.37228 q^{21} +1.00000 q^{22} +2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.74456 q^{26} +1.00000 q^{27} -2.37228 q^{28} +8.37228 q^{29} +1.00000 q^{30} +10.3723 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -2.37228 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} -6.74456 q^{39} +1.00000 q^{40} -1.25544 q^{41} -2.37228 q^{42} +1.62772 q^{43} +1.00000 q^{44} +1.00000 q^{45} +2.37228 q^{46} +9.48913 q^{47} +1.00000 q^{48} -1.37228 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.74456 q^{52} +10.7446 q^{53} +1.00000 q^{54} +1.00000 q^{55} -2.37228 q^{56} +4.00000 q^{57} +8.37228 q^{58} +0.744563 q^{59} +1.00000 q^{60} -2.00000 q^{61} +10.3723 q^{62} -2.37228 q^{63} +1.00000 q^{64} -6.74456 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +2.37228 q^{69} -2.37228 q^{70} +12.7446 q^{71} +1.00000 q^{72} -6.00000 q^{73} -10.0000 q^{74} +1.00000 q^{75} +4.00000 q^{76} -2.37228 q^{77} -6.74456 q^{78} +9.48913 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.25544 q^{82} -12.0000 q^{83} -2.37228 q^{84} +1.00000 q^{85} +1.62772 q^{86} +8.37228 q^{87} +1.00000 q^{88} +5.25544 q^{89} +1.00000 q^{90} +16.0000 q^{91} +2.37228 q^{92} +10.3723 q^{93} +9.48913 q^{94} +4.00000 q^{95} +1.00000 q^{96} -3.62772 q^{97} -1.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} + 2 q^{22} - q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + q^{28} + 11 q^{29} + 2 q^{30} + 15 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{34} + q^{35} + 2 q^{36} - 20 q^{37} + 8 q^{38} - 2 q^{39} + 2 q^{40} - 14 q^{41} + q^{42} + 9 q^{43} + 2 q^{44} + 2 q^{45} - q^{46} - 4 q^{47} + 2 q^{48} + 3 q^{49} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 10 q^{53} + 2 q^{54} + 2 q^{55} + q^{56} + 8 q^{57} + 11 q^{58} - 10 q^{59} + 2 q^{60} - 4 q^{61} + 15 q^{62} + q^{63} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} - q^{69} + q^{70} + 14 q^{71} + 2 q^{72} - 12 q^{73} - 20 q^{74} + 2 q^{75} + 8 q^{76} + q^{77} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 2 q^{81} - 14 q^{82} - 24 q^{83} + q^{84} + 2 q^{85} + 9 q^{86} + 11 q^{87} + 2 q^{88} + 22 q^{89} + 2 q^{90} + 32 q^{91} - q^{92} + 15 q^{93} - 4 q^{94} + 8 q^{95} + 2 q^{96} - 13 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 + 2 * q^22 - q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + q^28 + 11 * q^29 + 2 * q^30 + 15 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 + q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 - 14 * q^41 + q^42 + 9 * q^43 + 2 * q^44 + 2 * q^45 - q^46 - 4 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 + 2 * q^55 + q^56 + 8 * q^57 + 11 * q^58 - 10 * q^59 + 2 * q^60 - 4 * q^61 + 15 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 - q^69 + q^70 + 14 * q^71 + 2 * q^72 - 12 * q^73 - 20 * q^74 + 2 * q^75 + 8 * q^76 + q^77 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 - 14 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 9 * q^86 + 11 * q^87 + 2 * q^88 + 22 * q^89 + 2 * q^90 + 32 * q^91 - q^92 + 15 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 13 * q^97 + 3 * q^98 + 2 * q^99

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	$-0.647977\pi$
$7$	−2.37228	−0.896638	−0.448319	+	0.893874i	$0.647977\pi$
$8$	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
$13$	−6.74456	−1.87061	−0.935303	−	0.353849i	$-0.884873\pi$
$13$	−6.74456	−1.87061	−0.935303	+	0.353849i	$0.884873\pi$
$14$	−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
$23$	2.37228	0.494655	0.247327	−	0.968932i	$-0.420448\pi$
$23$	2.37228	0.494655	0.247327	+	0.968932i	$0.420448\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.74456	−1.32272
$27$	1.00000	0.192450
$28$	−2.37228	−0.448319
$29$	8.37228	1.55469	0.777347	−	0.629072i	$-0.216565\pi$
$29$	8.37228	1.55469	0.777347	+	0.629072i	$0.216565\pi$
$30$	1.00000	0.182574
$31$	10.3723	1.86292	0.931458	−	0.363848i	$-0.118537\pi$
$31$	10.3723	1.86292	0.931458	+	0.363848i	$0.118537\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	−2.37228	−0.400989
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	0.648886
$39$	−6.74456	−1.07999
$40$	1.00000	0.158114
$41$	−1.25544	−0.196066	−0.0980332	−	0.995183i	$-0.531255\pi$
$41$	−1.25544	−0.196066	−0.0980332	+	0.995183i	$0.531255\pi$
$42$	−2.37228	−0.366051
$43$	1.62772	0.248225	0.124112	−	0.992268i	$-0.460392\pi$
$43$	1.62772	0.248225	0.124112	+	0.992268i	$0.460392\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	2.37228	0.349774
$47$	9.48913	1.38413	0.692066	−	0.721835i	$-0.256701\pi$
$47$	9.48913	1.38413	0.692066	+	0.721835i	$0.256701\pi$
$48$	1.00000	0.144338
$49$	−1.37228	−0.196040
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−6.74456	−0.935303
$53$	10.7446	1.47588	0.737940	−	0.674867i	$-0.235799\pi$
$53$	10.7446	1.47588	0.737940	+	0.674867i	$0.235799\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−2.37228	−0.317009
$57$	4.00000	0.529813
$58$	8.37228	1.09933
$59$	0.744563	0.0969338	0.0484669	−	0.998825i	$-0.484566\pi$
$59$	0.744563	0.0969338	0.0484669	+	0.998825i	$0.484566\pi$
$60$	1.00000	0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	10.3723	1.31728
$63$	−2.37228	−0.298879
$64$	1.00000	0.125000
$65$	−6.74456	−0.836560
$66$	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
$69$	2.37228	0.285589
$70$	−2.37228	−0.283542
$71$	12.7446	1.51250	0.756251	−	0.654282i	$-0.227029\pi$
$71$	12.7446	1.51250	0.756251	+	0.654282i	$0.227029\pi$
$72$	1.00000	0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−10.0000	−1.16248
$75$	1.00000	0.115470
$76$	4.00000	0.458831
$77$	−2.37228	−0.270347
$78$	−6.74456	−0.763671
$79$	9.48913	1.06761	0.533805	−	0.845608i	$-0.320762\pi$
$79$	9.48913	1.06761	0.533805	+	0.845608i	$0.320762\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.25544	−0.138640
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−2.37228	−0.258837
$85$	1.00000	0.108465
$86$	1.62772	0.175521
$87$	8.37228	0.897603
$88$	1.00000	0.106600
$89$	5.25544	0.557075	0.278538	−	0.960425i	$-0.410150\pi$
$89$	5.25544	0.557075	0.278538	+	0.960425i	$0.410150\pi$
$90$	1.00000	0.105409
$91$	16.0000	1.67726
$92$	2.37228	0.247327
$93$	10.3723	1.07556
$94$	9.48913	0.978729
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−3.62772	−0.368339	−0.184170	−	0.982894i	$-0.558960\pi$
$97$	−3.62772	−0.368339	−0.184170	+	0.982894i	$0.558960\pi$
$98$	−1.37228	−0.138621
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	2.37228	0.233748	0.116874	−	0.993147i	$-0.462713\pi$
$103$	2.37228	0.233748	0.116874	+	0.993147i	$0.462713\pi$
$104$	−6.74456	−0.661359
$105$	−2.37228	−0.231511
$106$	10.7446	1.04360
$107$	−3.11684	−0.301317	−0.150658	−	0.988586i	$-0.548139\pi$
$107$	−3.11684	−0.301317	−0.150658	+	0.988586i	$0.548139\pi$
$108$	1.00000	0.0962250
$109$	2.74456	0.262881	0.131441	−	0.991324i	$-0.458040\pi$
$109$	2.74456	0.262881	0.131441	+	0.991324i	$0.458040\pi$
$110$	1.00000	0.0953463
$111$	−10.0000	−0.949158
$112$	−2.37228	−0.224160
$113$	11.4891	1.08081	0.540403	−	0.841406i	$-0.318272\pi$
$113$	11.4891	1.08081	0.540403	+	0.841406i	$0.318272\pi$
$114$	4.00000	0.374634
$115$	2.37228	0.221216
$116$	8.37228	0.777347
$117$	−6.74456	−0.623535
$118$	0.744563	0.0685425
$119$	−2.37228	−0.217467
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−1.25544	−0.113199
$124$	10.3723	0.931458
$125$	1.00000	0.0894427
$126$	−2.37228	−0.211340
$127$	−14.2337	−1.26304	−0.631518	−	0.775361i	$-0.717568\pi$
$127$	−14.2337	−1.26304	−0.631518	+	0.775361i	$0.717568\pi$
$128$	1.00000	0.0883883
$129$	1.62772	0.143313
$130$	−6.74456	−0.591537
$131$	13.4891	1.17855	0.589275	−	0.807932i	$-0.299413\pi$
$131$	13.4891	1.17855	0.589275	+	0.807932i	$0.299413\pi$
$132$	1.00000	0.0870388
$133$	−9.48913	−0.822812
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	13.8614	1.18426	0.592130	−	0.805842i	$-0.298287\pi$
$137$	13.8614	1.18426	0.592130	+	0.805842i	$0.298287\pi$
$138$	2.37228	0.201942
$139$	−3.11684	−0.264367	−0.132184	−	0.991225i	$-0.542199\pi$
$139$	−3.11684	−0.264367	−0.132184	+	0.991225i	$0.542199\pi$
$140$	−2.37228	−0.200494
$141$	9.48913	0.799129
$142$	12.7446	1.06950
$143$	−6.74456	−0.564009
$144$	1.00000	0.0833333
$145$	8.37228	0.695280
$146$	−6.00000	−0.496564
$147$	−1.37228	−0.113184
$148$	−10.0000	−0.821995
$149$	10.7446	0.880229	0.440114	−	0.897942i	$-0.354938\pi$
$149$	10.7446	0.880229	0.440114	+	0.897942i	$0.354938\pi$
$150$	1.00000	0.0816497
$151$	−1.48913	−0.121183	−0.0605916	−	0.998163i	$-0.519299\pi$
$151$	−1.48913	−0.121183	−0.0605916	+	0.998163i	$0.519299\pi$
$152$	4.00000	0.324443
$153$	1.00000	0.0808452
$154$	−2.37228	−0.191164
$155$	10.3723	0.833122
$156$	−6.74456	−0.539997
$157$	−11.4891	−0.916932	−0.458466	−	0.888712i	$-0.651601\pi$
$157$	−11.4891	−0.916932	−0.458466	+	0.888712i	$0.651601\pi$
$158$	9.48913	0.754914
$159$	10.7446	0.852099
$160$	1.00000	0.0790569
$161$	−5.62772	−0.443526
$162$	1.00000	0.0785674
$163$	−1.62772	−0.127493	−0.0637464	−	0.997966i	$-0.520305\pi$
$163$	−1.62772	−0.127493	−0.0637464	+	0.997966i	$0.520305\pi$
$164$	−1.25544	−0.0980332
$165$	1.00000	0.0778499
$166$	−12.0000	−0.931381
$167$	22.2337	1.72049	0.860247	−	0.509877i	$-0.170309\pi$
$167$	22.2337	1.72049	0.860247	+	0.509877i	$0.170309\pi$
$168$	−2.37228	−0.183025
$169$	32.4891	2.49916
$170$	1.00000	0.0766965
$171$	4.00000	0.305888
$172$	1.62772	0.124112
$173$	−11.4891	−0.873502	−0.436751	−	0.899582i	$-0.643871\pi$
$173$	−11.4891	−0.873502	−0.436751	+	0.899582i	$0.643871\pi$
$174$	8.37228	0.634701
$175$	−2.37228	−0.179328
$176$	1.00000	0.0753778
$177$	0.744563	0.0559648
$178$	5.25544	0.393912
$179$	−7.25544	−0.542297	−0.271148	−	0.962538i	$-0.587403\pi$
$179$	−7.25544	−0.542297	−0.271148	+	0.962538i	$0.587403\pi$
$180$	1.00000	0.0745356
$181$	−20.3723	−1.51426	−0.757130	−	0.653264i	$-0.773399\pi$
$181$	−20.3723	−1.51426	−0.757130	+	0.653264i	$0.773399\pi$
$182$	16.0000	1.18600
$183$	−2.00000	−0.147844
$184$	2.37228	0.174887
$185$	−10.0000	−0.735215
$186$	10.3723	0.760533
$187$	1.00000	0.0731272
$188$	9.48913	0.692066
$189$	−2.37228	−0.172558
$190$	4.00000	0.290191
$191$	−10.3723	−0.750512	−0.375256	−	0.926921i	$-0.622445\pi$
$191$	−10.3723	−0.750512	−0.375256	+	0.926921i	$0.622445\pi$
$192$	1.00000	0.0721688
$193$	−23.4891	−1.69078	−0.845392	−	0.534146i	$-0.820633\pi$
$193$	−23.4891	−1.69078	−0.845392	+	0.534146i	$0.820633\pi$
$194$	−3.62772	−0.260455
$195$	−6.74456	−0.482988
$196$	−1.37228	−0.0980201
$197$	−8.23369	−0.586626	−0.293313	−	0.956016i	$-0.594758\pi$
$197$	−8.23369	−0.586626	−0.293313	+	0.956016i	$0.594758\pi$
$198$	1.00000	0.0710669
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	1.00000	0.0707107
$201$	4.00000	0.282138
$202$	6.00000	0.422159
$203$	−19.8614	−1.39400
$204$	1.00000	0.0700140
$205$	−1.25544	−0.0876835
$206$	2.37228	0.165285
$207$	2.37228	0.164885
$208$	−6.74456	−0.467651
$209$	4.00000	0.276686
$210$	−2.37228	−0.163703
$211$	3.11684	0.214572	0.107286	−	0.994228i	$-0.465784\pi$
$211$	3.11684	0.214572	0.107286	+	0.994228i	$0.465784\pi$
$212$	10.7446	0.737940
$213$	12.7446	0.873243
$214$	−3.11684	−0.213063
$215$	1.62772	0.111009
$216$	1.00000	0.0680414
$217$	−24.6060	−1.67036
$218$	2.74456	0.185885
$219$	−6.00000	−0.405442
$220$	1.00000	0.0674200
$221$	−6.74456	−0.453688
$222$	−10.0000	−0.671156
$223$	−5.62772	−0.376860	−0.188430	−	0.982087i	$-0.560340\pi$
$223$	−5.62772	−0.376860	−0.188430	+	0.982087i	$0.560340\pi$
$224$	−2.37228	−0.158505
$225$	1.00000	0.0666667
$226$	11.4891	0.764245
$227$	−11.1168	−0.737851	−0.368925	−	0.929459i	$-0.620274\pi$
$227$	−11.1168	−0.737851	−0.368925	+	0.929459i	$0.620274\pi$
$228$	4.00000	0.264906
$229$	−14.7446	−0.974348	−0.487174	−	0.873305i	$-0.661972\pi$
$229$	−14.7446	−0.974348	−0.487174	+	0.873305i	$0.661972\pi$
$230$	2.37228	0.156424
$231$	−2.37228	−0.156085
$232$	8.37228	0.549667
$233$	13.8614	0.908091	0.454045	−	0.890979i	$-0.349980\pi$
$233$	13.8614	0.908091	0.454045	+	0.890979i	$0.349980\pi$
$234$	−6.74456	−0.440906
$235$	9.48913	0.619002
$236$	0.744563	0.0484669
$237$	9.48913	0.616385
$238$	−2.37228	−0.153772
$239$	−14.2337	−0.920701	−0.460350	−	0.887737i	$-0.652276\pi$
$239$	−14.2337	−0.920701	−0.460350	+	0.887737i	$0.652276\pi$
$240$	1.00000	0.0645497
$241$	−3.62772	−0.233682	−0.116841	−	0.993151i	$-0.537277\pi$
$241$	−3.62772	−0.233682	−0.116841	+	0.993151i	$0.537277\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	−1.37228	−0.0876718
$246$	−1.25544	−0.0800438
$247$	−26.9783	−1.71658
$248$	10.3723	0.658641
$249$	−12.0000	−0.760469
$250$	1.00000	0.0632456
$251$	−29.4891	−1.86134	−0.930669	−	0.365863i	$-0.880774\pi$
$251$	−29.4891	−1.86134	−0.930669	+	0.365863i	$0.880774\pi$
$252$	−2.37228	−0.149440
$253$	2.37228	0.149144
$254$	−14.2337	−0.893101
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	7.62772	0.475804	0.237902	−	0.971289i	$-0.423540\pi$
$257$	7.62772	0.475804	0.237902	+	0.971289i	$0.423540\pi$
$258$	1.62772	0.101337
$259$	23.7228	1.47406
$260$	−6.74456	−0.418280
$261$	8.37228	0.518231
$262$	13.4891	0.833361
$263$	−27.8614	−1.71801	−0.859004	−	0.511969i	$-0.828916\pi$
$263$	−27.8614	−1.71801	−0.859004	+	0.511969i	$0.828916\pi$
$264$	1.00000	0.0615457
$265$	10.7446	0.660033
$266$	−9.48913	−0.581816
$267$	5.25544	0.321628
$268$	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
$271$	15.1168	0.918283	0.459141	−	0.888363i	$-0.348157\pi$
$271$	15.1168	0.918283	0.459141	+	0.888363i	$0.348157\pi$
$272$	1.00000	0.0606339
$273$	16.0000	0.968364
$274$	13.8614	0.837398
$275$	1.00000	0.0603023
$276$	2.37228	0.142795
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−3.11684	−0.186936
$279$	10.3723	0.620972
$280$	−2.37228	−0.141771
$281$	−9.86141	−0.588282	−0.294141	−	0.955762i	$-0.595034\pi$
$281$	−9.86141	−0.588282	−0.294141	+	0.955762i	$0.595034\pi$
$282$	9.48913	0.565069
$283$	7.25544	0.431291	0.215645	−	0.976472i	$-0.430814\pi$
$283$	7.25544	0.431291	0.215645	+	0.976472i	$0.430814\pi$
$284$	12.7446	0.756251
$285$	4.00000	0.236940
$286$	−6.74456	−0.398814
$287$	2.97825	0.175801
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	8.37228	0.491637
$291$	−3.62772	−0.212661
$292$	−6.00000	−0.351123
$293$	2.13859	0.124938	0.0624690	−	0.998047i	$-0.480103\pi$
$293$	2.13859	0.124938	0.0624690	+	0.998047i	$0.480103\pi$
$294$	−1.37228	−0.0800331
$295$	0.744563	0.0433501
$296$	−10.0000	−0.581238
$297$	1.00000	0.0580259
$298$	10.7446	0.622416
$299$	−16.0000	−0.925304
$300$	1.00000	0.0577350
$301$	−3.86141	−0.222568
$302$	−1.48913	−0.0856895
$303$	6.00000	0.344691
$304$	4.00000	0.229416
$305$	−2.00000	−0.114520
$306$	1.00000	0.0571662
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−2.37228	−0.135173
$309$	2.37228	0.134954
$310$	10.3723	0.589106
$311$	17.4891	0.991717	0.495859	−	0.868403i	$-0.334853\pi$
$311$	17.4891	0.991717	0.495859	+	0.868403i	$0.334853\pi$
$312$	−6.74456	−0.381836
$313$	−9.86141	−0.557400	−0.278700	−	0.960378i	$-0.589903\pi$
$313$	−9.86141	−0.557400	−0.278700	+	0.960378i	$0.589903\pi$
$314$	−11.4891	−0.648369
$315$	−2.37228	−0.133663
$316$	9.48913	0.533805
$317$	−17.1168	−0.961378	−0.480689	−	0.876891i	$-0.659613\pi$
$317$	−17.1168	−0.961378	−0.480689	+	0.876891i	$0.659613\pi$
$318$	10.7446	0.602525
$319$	8.37228	0.468758
$320$	1.00000	0.0559017
$321$	−3.11684	−0.173965
$322$	−5.62772	−0.313621
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−6.74456	−0.374121
$326$	−1.62772	−0.0901510
$327$	2.74456	0.151775
$328$	−1.25544	−0.0693199
$329$	−22.5109	−1.24106
$330$	1.00000	0.0550482
$331$	−33.3505	−1.83311	−0.916556	−	0.399907i	$-0.869042\pi$
$331$	−33.3505	−1.83311	−0.916556	+	0.399907i	$0.869042\pi$
$332$	−12.0000	−0.658586
$333$	−10.0000	−0.547997
$334$	22.2337	1.21657
$335$	4.00000	0.218543
$336$	−2.37228	−0.129419
$337$	20.9783	1.14276	0.571379	−	0.820686i	$-0.306409\pi$
$337$	20.9783	1.14276	0.571379	+	0.820686i	$0.306409\pi$
$338$	32.4891	1.76718
$339$	11.4891	0.624004
$340$	1.00000	0.0542326
$341$	10.3723	0.561691
$342$	4.00000	0.216295
$343$	19.8614	1.07242
$344$	1.62772	0.0877607
$345$	2.37228	0.127719
$346$	−11.4891	−0.617659
$347$	−22.9783	−1.23354	−0.616769	−	0.787145i	$-0.711559\pi$
$347$	−22.9783	−1.23354	−0.616769	+	0.787145i	$0.711559\pi$
$348$	8.37228	0.448801
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−2.37228	−0.126804
$351$	−6.74456	−0.359998
$352$	1.00000	0.0533002
$353$	5.86141	0.311971	0.155986	−	0.987759i	$-0.450145\pi$
$353$	5.86141	0.311971	0.155986	+	0.987759i	$0.450145\pi$
$354$	0.744563	0.0395731
$355$	12.7446	0.676411
$356$	5.25544	0.278538
$357$	−2.37228	−0.125554
$358$	−7.25544	−0.383462
$359$	6.23369	0.329001	0.164501	−	0.986377i	$-0.447399\pi$
$359$	6.23369	0.329001	0.164501	+	0.986377i	$0.447399\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	−20.3723	−1.07074
$363$	1.00000	0.0524864
$364$	16.0000	0.838628
$365$	−6.00000	−0.314054
$366$	−2.00000	−0.104542
$367$	−11.2554	−0.587529	−0.293765	−	0.955878i	$-0.594908\pi$
$367$	−11.2554	−0.587529	−0.293765	+	0.955878i	$0.594908\pi$
$368$	2.37228	0.123664
$369$	−1.25544	−0.0653555
$370$	−10.0000	−0.519875
$371$	−25.4891	−1.32333
$372$	10.3723	0.537778
$373$	−0.510875	−0.0264521	−0.0132260	−	0.999913i	$-0.504210\pi$
$373$	−0.510875	−0.0264521	−0.0132260	+	0.999913i	$0.504210\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	9.48913	0.489364
$377$	−56.4674	−2.90822
$378$	−2.37228	−0.122017
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	4.00000	0.205196
$381$	−14.2337	−0.729214
$382$	−10.3723	−0.530692
$383$	25.4891	1.30243	0.651217	−	0.758892i	$-0.274259\pi$
$383$	25.4891	1.30243	0.651217	+	0.758892i	$0.274259\pi$
$384$	1.00000	0.0510310
$385$	−2.37228	−0.120903
$386$	−23.4891	−1.19556
$387$	1.62772	0.0827416
$388$	−3.62772	−0.184170
$389$	34.4674	1.74757	0.873783	−	0.486317i	$-0.161660\pi$
$389$	34.4674	1.74757	0.873783	+	0.486317i	$0.161660\pi$
$390$	−6.74456	−0.341524
$391$	2.37228	0.119971
$392$	−1.37228	−0.0693107
$393$	13.4891	0.680436
$394$	−8.23369	−0.414807
$395$	9.48913	0.477450
$396$	1.00000	0.0502519
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	−9.48913	−0.475050
$400$	1.00000	0.0500000
$401$	−3.62772	−0.181160	−0.0905798	−	0.995889i	$-0.528872\pi$
$401$	−3.62772	−0.181160	−0.0905798	+	0.995889i	$0.528872\pi$
$402$	4.00000	0.199502
$403$	−69.9565	−3.48478
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−19.8614	−0.985705
$407$	−10.0000	−0.495682
$408$	1.00000	0.0495074
$409$	−4.23369	−0.209342	−0.104671	−	0.994507i	$-0.533379\pi$
$409$	−4.23369	−0.209342	−0.104671	+	0.994507i	$0.533379\pi$
$410$	−1.25544	−0.0620016
$411$	13.8614	0.683733
$412$	2.37228	0.116874
$413$	−1.76631	−0.0869145
$414$	2.37228	0.116591
$415$	−12.0000	−0.589057
$416$	−6.74456	−0.330679
$417$	−3.11684	−0.152633
$418$	4.00000	0.195646
$419$	30.3723	1.48378	0.741892	−	0.670520i	$-0.233929\pi$
$419$	30.3723	1.48378	0.741892	+	0.670520i	$0.233929\pi$
$420$	−2.37228	−0.115755
$421$	−5.25544	−0.256134	−0.128067	−	0.991765i	$-0.540877\pi$
$421$	−5.25544	−0.256134	−0.128067	+	0.991765i	$0.540877\pi$
$422$	3.11684	0.151726
$423$	9.48913	0.461377
$424$	10.7446	0.521802
$425$	1.00000	0.0485071
$426$	12.7446	0.617476
$427$	4.74456	0.229605
$428$	−3.11684	−0.150658
$429$	−6.74456	−0.325631
$430$	1.62772	0.0784956
$431$	−15.1168	−0.728153	−0.364076	−	0.931369i	$-0.618615\pi$
$431$	−15.1168	−0.728153	−0.364076	+	0.931369i	$0.618615\pi$
$432$	1.00000	0.0481125
$433$	38.7446	1.86194	0.930972	−	0.365089i	$-0.118962\pi$
$433$	38.7446	1.86194	0.930972	+	0.365089i	$0.118962\pi$
$434$	−24.6060	−1.18112
$435$	8.37228	0.401420
$436$	2.74456	0.131441
$437$	9.48913	0.453926
$438$	−6.00000	−0.286691
$439$	6.23369	0.297518	0.148759	−	0.988874i	$-0.452472\pi$
$439$	6.23369	0.297518	0.148759	+	0.988874i	$0.452472\pi$
$440$	1.00000	0.0476731
$441$	−1.37228	−0.0653467
$442$	−6.74456	−0.320806
$443$	−4.88316	−0.232006	−0.116003	−	0.993249i	$-0.537008\pi$
$443$	−4.88316	−0.232006	−0.116003	+	0.993249i	$0.537008\pi$
$444$	−10.0000	−0.474579
$445$	5.25544	0.249132
$446$	−5.62772	−0.266480
$447$	10.7446	0.508200
$448$	−2.37228	−0.112080
$449$	23.6277	1.11506	0.557530	−	0.830156i	$-0.311749\pi$
$449$	23.6277	1.11506	0.557530	+	0.830156i	$0.311749\pi$
$450$	1.00000	0.0471405
$451$	−1.25544	−0.0591162
$452$	11.4891	0.540403
$453$	−1.48913	−0.0699652
$454$	−11.1168	−0.521739
$455$	16.0000	0.750092
$456$	4.00000	0.187317
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−14.7446	−0.688968
$459$	1.00000	0.0466760
$460$	2.37228	0.110608
$461$	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
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	8.37228	0.388673
$465$	10.3723	0.481003
$466$	13.8614	0.642117
$467$	−14.9783	−0.693111	−0.346555	−	0.938030i	$-0.612649\pi$
$467$	−14.9783	−0.693111	−0.346555	+	0.938030i	$0.612649\pi$
$468$	−6.74456	−0.311768
$469$	−9.48913	−0.438167
$470$	9.48913	0.437701
$471$	−11.4891	−0.529391
$472$	0.744563	0.0342713
$473$	1.62772	0.0748426
$474$	9.48913	0.435850
$475$	4.00000	0.183533
$476$	−2.37228	−0.108733
$477$	10.7446	0.491960
$478$	−14.2337	−0.651034
$479$	−38.8397	−1.77463	−0.887315	−	0.461165i	$-0.847432\pi$
$479$	−38.8397	−1.77463	−0.887315	+	0.461165i	$0.847432\pi$
$480$	1.00000	0.0456435
$481$	67.4456	3.07526
$482$	−3.62772	−0.165238
$483$	−5.62772	−0.256070
$484$	1.00000	0.0454545
$485$	−3.62772	−0.164726
$486$	1.00000	0.0453609
$487$	12.7446	0.577511	0.288756	−	0.957403i	$-0.406758\pi$
$487$	12.7446	0.577511	0.288756	+	0.957403i	$0.406758\pi$
$488$	−2.00000	−0.0905357
$489$	−1.62772	−0.0736080
$490$	−1.37228	−0.0619934
$491$	−29.4891	−1.33083	−0.665413	−	0.746476i	$-0.731744\pi$
$491$	−29.4891	−1.33083	−0.665413	+	0.746476i	$0.731744\pi$
$492$	−1.25544	−0.0565995
$493$	8.37228	0.377069
$494$	−26.9783	−1.21381
$495$	1.00000	0.0449467
$496$	10.3723	0.465729
$497$	−30.2337	−1.35617
$498$	−12.0000	−0.537733
$499$	−21.4891	−0.961985	−0.480993	−	0.876725i	$-0.659724\pi$
$499$	−21.4891	−0.961985	−0.480993	+	0.876725i	$0.659724\pi$
$500$	1.00000	0.0447214
$501$	22.2337	0.993328
$502$	−29.4891	−1.31616
$503$	−42.9783	−1.91631	−0.958153	−	0.286257i	$-0.907589\pi$
$503$	−42.9783	−1.91631	−0.958153	+	0.286257i	$0.907589\pi$
$504$	−2.37228	−0.105670
$505$	6.00000	0.266996
$506$	2.37228	0.105461
$507$	32.4891	1.44289
$508$	−14.2337	−0.631518
$509$	−11.4891	−0.509247	−0.254623	−	0.967040i	$-0.581951\pi$
$509$	−11.4891	−0.509247	−0.254623	+	0.967040i	$0.581951\pi$
$510$	1.00000	0.0442807
$511$	14.2337	0.629661
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	7.62772	0.336444
$515$	2.37228	0.104535
$516$	1.62772	0.0716563
$517$	9.48913	0.417331
$518$	23.7228	1.04232
$519$	−11.4891	−0.504317
$520$	−6.74456	−0.295769
$521$	−24.9783	−1.09432	−0.547159	−	0.837029i	$-0.684291\pi$
$521$	−24.9783	−1.09432	−0.547159	+	0.837029i	$0.684291\pi$
$522$	8.37228	0.366445
$523$	−30.3723	−1.32809	−0.664044	−	0.747694i	$-0.731161\pi$
$523$	−30.3723	−1.32809	−0.664044	+	0.747694i	$0.731161\pi$
$524$	13.4891	0.589275
$525$	−2.37228	−0.103535
$526$	−27.8614	−1.21482
$527$	10.3723	0.451824
$528$	1.00000	0.0435194
$529$	−17.3723	−0.755317
$530$	10.7446	0.466714
$531$	0.744563	0.0323113
$532$	−9.48913	−0.411406
$533$	8.46738	0.366763
$534$	5.25544	0.227425
$535$	−3.11684	−0.134753
$536$	4.00000	0.172774
$537$	−7.25544	−0.313095
$538$	14.0000	0.603583
$539$	−1.37228	−0.0591083
$540$	1.00000	0.0430331
$541$	28.2337	1.21386	0.606931	−	0.794755i	$-0.292401\pi$
$541$	28.2337	1.21386	0.606931	+	0.794755i	$0.292401\pi$
$542$	15.1168	0.649324
$543$	−20.3723	−0.874258
$544$	1.00000	0.0428746
$545$	2.74456	0.117564
$546$	16.0000	0.684737
$547$	−26.2337	−1.12167	−0.560836	−	0.827927i	$-0.689520\pi$
$547$	−26.2337	−1.12167	−0.560836	+	0.827927i	$0.689520\pi$
$548$	13.8614	0.592130
$549$	−2.00000	−0.0853579
$550$	1.00000	0.0426401
$551$	33.4891	1.42668
$552$	2.37228	0.100971
$553$	−22.5109	−0.957260
$554$	22.0000	0.934690
$555$	−10.0000	−0.424476
$556$	−3.11684	−0.132184
$557$	27.3505	1.15888	0.579440	−	0.815015i	$-0.303271\pi$
$557$	27.3505	1.15888	0.579440	+	0.815015i	$0.303271\pi$
$558$	10.3723	0.439094
$559$	−10.9783	−0.464331
$560$	−2.37228	−0.100247
$561$	1.00000	0.0422200
$562$	−9.86141	−0.415978
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	9.48913	0.399564
$565$	11.4891	0.483351
$566$	7.25544	0.304969
$567$	−2.37228	−0.0996265
$568$	12.7446	0.534750
$569$	−24.9783	−1.04714	−0.523571	−	0.851982i	$-0.675401\pi$
$569$	−24.9783	−1.04714	−0.523571	+	0.851982i	$0.675401\pi$
$570$	4.00000	0.167542
$571$	−22.9783	−0.961610	−0.480805	−	0.876828i	$-0.659655\pi$
$571$	−22.9783	−0.961610	−0.480805	+	0.876828i	$0.659655\pi$
$572$	−6.74456	−0.282004
$573$	−10.3723	−0.433308
$574$	2.97825	0.124310
$575$	2.37228	0.0989310
$576$	1.00000	0.0416667
$577$	24.5109	1.02040	0.510201	−	0.860055i	$-0.329571\pi$
$577$	24.5109	1.02040	0.510201	+	0.860055i	$0.329571\pi$
$578$	1.00000	0.0415945
$579$	−23.4891	−0.976175
$580$	8.37228	0.347640
$581$	28.4674	1.18103
$582$	−3.62772	−0.150374
$583$	10.7446	0.444994
$584$	−6.00000	−0.248282
$585$	−6.74456	−0.278853
$586$	2.13859	0.0883445
$587$	−38.0951	−1.57235	−0.786176	−	0.618002i	$-0.787942\pi$
$587$	−38.0951	−1.57235	−0.786176	+	0.618002i	$0.787942\pi$
$588$	−1.37228	−0.0565919
$589$	41.4891	1.70953
$590$	0.744563	0.0306532
$591$	−8.23369	−0.338689
$592$	−10.0000	−0.410997
$593$	−23.4891	−0.964583	−0.482291	−	0.876011i	$-0.660195\pi$
$593$	−23.4891	−0.964583	−0.482291	+	0.876011i	$0.660195\pi$
$594$	1.00000	0.0410305
$595$	−2.37228	−0.0972541
$596$	10.7446	0.440114
$597$	−8.00000	−0.327418
$598$	−16.0000	−0.654289
$599$	21.3505	0.872359	0.436180	−	0.899860i	$-0.356331\pi$
$599$	21.3505	0.872359	0.436180	+	0.899860i	$0.356331\pi$
$600$	1.00000	0.0408248
$601$	−31.4891	−1.28447	−0.642234	−	0.766509i	$-0.721992\pi$
$601$	−31.4891	−1.28447	−0.642234	+	0.766509i	$0.721992\pi$
$602$	−3.86141	−0.157379
$603$	4.00000	0.162893
$604$	−1.48913	−0.0605916
$605$	1.00000	0.0406558
$606$	6.00000	0.243733
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	4.00000	0.162221
$609$	−19.8614	−0.804825
$610$	−2.00000	−0.0809776
$611$	−64.0000	−2.58916
$612$	1.00000	0.0404226
$613$	43.9565	1.77539	0.887693	−	0.460435i	$-0.152307\pi$
$613$	43.9565	1.77539	0.887693	+	0.460435i	$0.152307\pi$
$614$	4.00000	0.161427
$615$	−1.25544	−0.0506241
$616$	−2.37228	−0.0955819
$617$	35.4891	1.42874	0.714369	−	0.699769i	$-0.246714\pi$
$617$	35.4891	1.42874	0.714369	+	0.699769i	$0.246714\pi$
$618$	2.37228	0.0954271
$619$	−18.2337	−0.732874	−0.366437	−	0.930443i	$-0.619422\pi$
$619$	−18.2337	−0.732874	−0.366437	+	0.930443i	$0.619422\pi$
$620$	10.3723	0.416561
$621$	2.37228	0.0951964
$622$	17.4891	0.701250
$623$	−12.4674	−0.499495
$624$	−6.74456	−0.269999
$625$	1.00000	0.0400000
$626$	−9.86141	−0.394141
$627$	4.00000	0.159745
$628$	−11.4891	−0.458466
$629$	−10.0000	−0.398726
$630$	−2.37228	−0.0945140
$631$	22.2337	0.885109	0.442555	−	0.896742i	$-0.354072\pi$
$631$	22.2337	0.885109	0.442555	+	0.896742i	$0.354072\pi$
$632$	9.48913	0.377457
$633$	3.11684	0.123883
$634$	−17.1168	−0.679797
$635$	−14.2337	−0.564847
$636$	10.7446	0.426050
$637$	9.25544	0.366714
$638$	8.37228	0.331462
$639$	12.7446	0.504167
$640$	1.00000	0.0395285
$641$	−49.8614	−1.96941	−0.984704	−	0.174238i	$-0.944254\pi$
$641$	−49.8614	−1.96941	−0.984704	+	0.174238i	$0.944254\pi$
$642$	−3.11684	−0.123012
$643$	−41.3505	−1.63071	−0.815353	−	0.578964i	$-0.803457\pi$
$643$	−41.3505	−1.63071	−0.815353	+	0.578964i	$0.803457\pi$
$644$	−5.62772	−0.221763
$645$	1.62772	0.0640914
$646$	4.00000	0.157378
$647$	31.7228	1.24715	0.623576	−	0.781763i	$-0.285679\pi$
$647$	31.7228	1.24715	0.623576	+	0.781763i	$0.285679\pi$
$648$	1.00000	0.0392837
$649$	0.744563	0.0292266
$650$	−6.74456	−0.264544
$651$	−24.6060	−0.964384
$652$	−1.62772	−0.0637464
$653$	−1.11684	−0.0437055	−0.0218527	−	0.999761i	$-0.506956\pi$
$653$	−1.11684	−0.0437055	−0.0218527	+	0.999761i	$0.506956\pi$
$654$	2.74456	0.107321
$655$	13.4891	0.527064
$656$	−1.25544	−0.0490166
$657$	−6.00000	−0.234082
$658$	−22.5109	−0.877565
$659$	25.6277	0.998314	0.499157	−	0.866512i	$-0.333643\pi$
$659$	25.6277	0.998314	0.499157	+	0.866512i	$0.333643\pi$
$660$	1.00000	0.0389249
$661$	−40.2337	−1.56491	−0.782455	−	0.622708i	$-0.786033\pi$
$661$	−40.2337	−1.56491	−0.782455	+	0.622708i	$0.786033\pi$
$662$	−33.3505	−1.29621
$663$	−6.74456	−0.261937
$664$	−12.0000	−0.465690
$665$	−9.48913	−0.367972
$666$	−10.0000	−0.387492
$667$	19.8614	0.769037
$668$	22.2337	0.860247
$669$	−5.62772	−0.217580
$670$	4.00000	0.154533
$671$	−2.00000	−0.0772091
$672$	−2.37228	−0.0915127
$673$	16.2337	0.625763	0.312881	−	0.949792i	$-0.398706\pi$
$673$	16.2337	0.625763	0.312881	+	0.949792i	$0.398706\pi$
$674$	20.9783	0.808052
$675$	1.00000	0.0384900
$676$	32.4891	1.24958
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	11.4891	0.441237
$679$	8.60597	0.330267
$680$	1.00000	0.0383482
$681$	−11.1168	−0.425998
$682$	10.3723	0.397175
$683$	−29.4891	−1.12837	−0.564185	−	0.825648i	$-0.690810\pi$
$683$	−29.4891	−1.12837	−0.564185	+	0.825648i	$0.690810\pi$
$684$	4.00000	0.152944
$685$	13.8614	0.529617
$686$	19.8614	0.758312
$687$	−14.7446	−0.562540
$688$	1.62772	0.0620562
$689$	−72.4674	−2.76079
$690$	2.37228	0.0903112
$691$	1.02175	0.0388692	0.0194346	−	0.999811i	$-0.493813\pi$
$691$	1.02175	0.0388692	0.0194346	+	0.999811i	$0.493813\pi$
$692$	−11.4891	−0.436751
$693$	−2.37228	−0.0901155
$694$	−22.9783	−0.872242
$695$	−3.11684	−0.118229
$696$	8.37228	0.317351
$697$	−1.25544	−0.0475531
$698$	−2.00000	−0.0757011
$699$	13.8614	0.524287
$700$	−2.37228	−0.0896638
$701$	−11.4891	−0.433938	−0.216969	−	0.976178i	$-0.569617\pi$
$701$	−11.4891	−0.433938	−0.216969	+	0.976178i	$0.569617\pi$
$702$	−6.74456	−0.254557
$703$	−40.0000	−1.50863
$704$	1.00000	0.0376889
$705$	9.48913	0.357381
$706$	5.86141	0.220597
$707$	−14.2337	−0.535313
$708$	0.744563	0.0279824
$709$	−38.4674	−1.44467	−0.722336	−	0.691542i	$-0.756932\pi$
$709$	−38.4674	−1.44467	−0.722336	+	0.691542i	$0.756932\pi$
$710$	12.7446	0.478295
$711$	9.48913	0.355870
$712$	5.25544	0.196956
$713$	24.6060	0.921501
$714$	−2.37228	−0.0887804
$715$	−6.74456	−0.252232
$716$	−7.25544	−0.271148
$717$	−14.2337	−0.531567
$718$	6.23369	0.232639
$719$	7.72281	0.288012	0.144006	−	0.989577i	$-0.454001\pi$
$719$	7.72281	0.288012	0.144006	+	0.989577i	$0.454001\pi$
$720$	1.00000	0.0372678
$721$	−5.62772	−0.209587
$722$	−3.00000	−0.111648
$723$	−3.62772	−0.134916
$724$	−20.3723	−0.757130
$725$	8.37228	0.310939
$726$	1.00000	0.0371135
$727$	37.3505	1.38525	0.692627	−	0.721296i	$-0.256453\pi$
$727$	37.3505	1.38525	0.692627	+	0.721296i	$0.256453\pi$
$728$	16.0000	0.592999
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	1.62772	0.0602034
$732$	−2.00000	−0.0739221
$733$	−32.2337	−1.19058	−0.595289	−	0.803512i	$-0.702963\pi$
$733$	−32.2337	−1.19058	−0.595289	+	0.803512i	$0.702963\pi$
$734$	−11.2554	−0.415446
$735$	−1.37228	−0.0506174
$736$	2.37228	0.0874434
$737$	4.00000	0.147342
$738$	−1.25544	−0.0462133
$739$	−0.744563	−0.0273892	−0.0136946	−	0.999906i	$-0.504359\pi$
$739$	−0.744563	−0.0273892	−0.0136946	+	0.999906i	$0.504359\pi$
$740$	−10.0000	−0.367607
$741$	−26.9783	−0.991071
$742$	−25.4891	−0.935735
$743$	−17.4891	−0.641614	−0.320807	−	0.947145i	$-0.603954\pi$
$743$	−17.4891	−0.641614	−0.320807	+	0.947145i	$0.603954\pi$
$744$	10.3723	0.380266
$745$	10.7446	0.393650
$746$	−0.510875	−0.0187045
$747$	−12.0000	−0.439057
$748$	1.00000	0.0365636
$749$	7.39403	0.270172
$750$	1.00000	0.0365148
$751$	−26.3723	−0.962338	−0.481169	−	0.876628i	$-0.659788\pi$
$751$	−26.3723	−0.962338	−0.481169	+	0.876628i	$0.659788\pi$
$752$	9.48913	0.346033
$753$	−29.4891	−1.07464
$754$	−56.4674	−2.05642
$755$	−1.48913	−0.0541948
$756$	−2.37228	−0.0862790
$757$	37.1168	1.34903	0.674517	−	0.738259i	$-0.264352\pi$
$757$	37.1168	1.34903	0.674517	+	0.738259i	$0.264352\pi$
$758$	28.0000	1.01701
$759$	2.37228	0.0861084
$760$	4.00000	0.145095
$761$	7.35053	0.266457	0.133228	−	0.991085i	$-0.457466\pi$
$761$	7.35053	0.266457	0.133228	+	0.991085i	$0.457466\pi$
$762$	−14.2337	−0.515632
$763$	−6.51087	−0.235709
$764$	−10.3723	−0.375256
$765$	1.00000	0.0361551
$766$	25.4891	0.920960
$767$	−5.02175	−0.181325
$768$	1.00000	0.0360844
$769$	−7.48913	−0.270065	−0.135032	−	0.990841i	$-0.543114\pi$
$769$	−7.48913	−0.270065	−0.135032	+	0.990841i	$0.543114\pi$
$770$	−2.37228	−0.0854911
$771$	7.62772	0.274706
$772$	−23.4891	−0.845392
$773$	26.7446	0.961935	0.480968	−	0.876738i	$-0.340285\pi$
$773$	26.7446	0.961935	0.480968	+	0.876738i	$0.340285\pi$
$774$	1.62772	0.0585071
$775$	10.3723	0.372583
$776$	−3.62772	−0.130228
$777$	23.7228	0.851051
$778$	34.4674	1.23572
$779$	−5.02175	−0.179923
$780$	−6.74456	−0.241494
$781$	12.7446	0.456036
$782$	2.37228	0.0848326
$783$	8.37228	0.299201
$784$	−1.37228	−0.0490100
$785$	−11.4891	−0.410064
$786$	13.4891	0.481141
$787$	−2.51087	−0.0895030	−0.0447515	−	0.998998i	$-0.514250\pi$
$787$	−2.51087	−0.0895030	−0.0447515	+	0.998998i	$0.514250\pi$
$788$	−8.23369	−0.293313
$789$	−27.8614	−0.991892
$790$	9.48913	0.337608
$791$	−27.2554	−0.969092
$792$	1.00000	0.0355335
$793$	13.4891	0.479013
$794$	−2.00000	−0.0709773
$795$	10.7446	0.381070
$796$	−8.00000	−0.283552
$797$	50.7446	1.79746	0.898732	−	0.438498i	$-0.144489\pi$
$797$	50.7446	1.79746	0.898732	+	0.438498i	$0.144489\pi$
$798$	−9.48913	−0.335911
$799$	9.48913	0.335701
$800$	1.00000	0.0353553
$801$	5.25544	0.185692
$802$	−3.62772	−0.128099
$803$	−6.00000	−0.211735
$804$	4.00000	0.141069
$805$	−5.62772	−0.198351
$806$	−69.9565	−2.46411
$807$	14.0000	0.492823
$808$	6.00000	0.211079
$809$	−3.02175	−0.106239	−0.0531195	−	0.998588i	$-0.516916\pi$
$809$	−3.02175	−0.106239	−0.0531195	+	0.998588i	$0.516916\pi$
$810$	1.00000	0.0351364
$811$	21.4891	0.754585	0.377293	−	0.926094i	$-0.376855\pi$
$811$	21.4891	0.754585	0.377293	+	0.926094i	$0.376855\pi$
$812$	−19.8614	−0.696999
$813$	15.1168	0.530171
$814$	−10.0000	−0.350500
$815$	−1.62772	−0.0570165
$816$	1.00000	0.0350070
$817$	6.51087	0.227787
$818$	−4.23369	−0.148027
$819$	16.0000	0.559085
$820$	−1.25544	−0.0438418
$821$	11.6277	0.405810	0.202905	−	0.979198i	$-0.434962\pi$
$821$	11.6277	0.405810	0.202905	+	0.979198i	$0.434962\pi$
$822$	13.8614	0.483472
$823$	28.7446	1.00197	0.500986	−	0.865455i	$-0.332971\pi$
$823$	28.7446	1.00197	0.500986	+	0.865455i	$0.332971\pi$
$824$	2.37228	0.0826423
$825$	1.00000	0.0348155
$826$	−1.76631	−0.0614579
$827$	11.1168	0.386571	0.193285	−	0.981143i	$-0.438086\pi$
$827$	11.1168	0.386571	0.193285	+	0.981143i	$0.438086\pi$
$828$	2.37228	0.0824425
$829$	−20.9783	−0.728605	−0.364302	−	0.931281i	$-0.618693\pi$
$829$	−20.9783	−0.728605	−0.364302	+	0.931281i	$0.618693\pi$
$830$	−12.0000	−0.416526
$831$	22.0000	0.763172
$832$	−6.74456	−0.233826
$833$	−1.37228	−0.0475467
$834$	−3.11684	−0.107927
$835$	22.2337	0.769428
$836$	4.00000	0.138343
$837$	10.3723	0.358518
$838$	30.3723	1.04919
$839$	3.25544	0.112390	0.0561951	−	0.998420i	$-0.482103\pi$
$839$	3.25544	0.112390	0.0561951	+	0.998420i	$0.482103\pi$
$840$	−2.37228	−0.0818515
$841$	41.0951	1.41707
$842$	−5.25544	−0.181114
$843$	−9.86141	−0.339645
$844$	3.11684	0.107286
$845$	32.4891	1.11766
$846$	9.48913	0.326243
$847$	−2.37228	−0.0815126
$848$	10.7446	0.368970
$849$	7.25544	0.249006
$850$	1.00000	0.0342997
$851$	−23.7228	−0.813208
$852$	12.7446	0.436622
$853$	−6.13859	−0.210181	−0.105091	−	0.994463i	$-0.533513\pi$
$853$	−6.13859	−0.210181	−0.105091	+	0.994463i	$0.533513\pi$
$854$	4.74456	0.162356
$855$	4.00000	0.136797
$856$	−3.11684	−0.106532
$857$	50.6060	1.72867	0.864333	−	0.502919i	$-0.167741\pi$
$857$	50.6060	1.72867	0.864333	+	0.502919i	$0.167741\pi$
$858$	−6.74456	−0.230256
$859$	−9.62772	−0.328494	−0.164247	−	0.986419i	$-0.552519\pi$
$859$	−9.62772	−0.328494	−0.164247	+	0.986419i	$0.552519\pi$
$860$	1.62772	0.0555047
$861$	2.97825	0.101499
$862$	−15.1168	−0.514882
$863$	34.9783	1.19067	0.595337	−	0.803476i	$-0.297019\pi$
$863$	34.9783	1.19067	0.595337	+	0.803476i	$0.297019\pi$
$864$	1.00000	0.0340207
$865$	−11.4891	−0.390642
$866$	38.7446	1.31659
$867$	1.00000	0.0339618
$868$	−24.6060	−0.835181
$869$	9.48913	0.321897
$870$	8.37228	0.283847
$871$	−26.9783	−0.914123
$872$	2.74456	0.0929426
$873$	−3.62772	−0.122780
$874$	9.48913	0.320974
$875$	−2.37228	−0.0801977
$876$	−6.00000	−0.202721
$877$	−14.1386	−0.477426	−0.238713	−	0.971090i	$-0.576726\pi$
$877$	−14.1386	−0.477426	−0.238713	+	0.971090i	$0.576726\pi$
$878$	6.23369	0.210377
$879$	2.13859	0.0721330
$880$	1.00000	0.0337100
$881$	−22.6060	−0.761614	−0.380807	−	0.924654i	$-0.624354\pi$
$881$	−22.6060	−0.761614	−0.380807	+	0.924654i	$0.624354\pi$
$882$	−1.37228	−0.0462071
$883$	57.9565	1.95039	0.975196	−	0.221344i	$-0.0710444\pi$
$883$	57.9565	1.95039	0.975196	+	0.221344i	$0.0710444\pi$
$884$	−6.74456	−0.226844
$885$	0.744563	0.0250282
$886$	−4.88316	−0.164053
$887$	55.4456	1.86168	0.930841	−	0.365425i	$-0.119076\pi$
$887$	55.4456	1.86168	0.930841	+	0.365425i	$0.119076\pi$
$888$	−10.0000	−0.335578
$889$	33.7663	1.13249
$890$	5.25544	0.176163
$891$	1.00000	0.0335013
$892$	−5.62772	−0.188430
$893$	37.9565	1.27017
$894$	10.7446	0.359352
$895$	−7.25544	−0.242523
$896$	−2.37228	−0.0792524
$897$	−16.0000	−0.534224
$898$	23.6277	0.788467
$899$	86.8397	2.89626
$900$	1.00000	0.0333333
$901$	10.7446	0.357953
$902$	−1.25544	−0.0418015
$903$	−3.86141	−0.128500
$904$	11.4891	0.382123
$905$	−20.3723	−0.677198
$906$	−1.48913	−0.0494729
$907$	55.5842	1.84564	0.922822	−	0.385227i	$-0.125877\pi$
$907$	55.5842	1.84564	0.922822	+	0.385227i	$0.125877\pi$
$908$	−11.1168	−0.368925
$909$	6.00000	0.199007
$910$	16.0000	0.530395
$911$	−50.9783	−1.68898	−0.844492	−	0.535568i	$-0.820098\pi$
$911$	−50.9783	−1.68898	−0.844492	+	0.535568i	$0.820098\pi$
$912$	4.00000	0.132453
$913$	−12.0000	−0.397142
$914$	10.0000	0.330771
$915$	−2.00000	−0.0661180
$916$	−14.7446	−0.487174
$917$	−32.0000	−1.05673
$918$	1.00000	0.0330049
$919$	43.8614	1.44685	0.723427	−	0.690401i	$-0.242566\pi$
$919$	43.8614	1.44685	0.723427	+	0.690401i	$0.242566\pi$
$920$	2.37228	0.0782118
$921$	4.00000	0.131804
$922$	23.4891	0.773573
$923$	−85.9565	−2.82929
$924$	−2.37228	−0.0780423
$925$	−10.0000	−0.328798
$926$	16.0000	0.525793
$927$	2.37228	0.0779159
$928$	8.37228	0.274834
$929$	−8.37228	−0.274686	−0.137343	−	0.990524i	$-0.543856\pi$
$929$	−8.37228	−0.274686	−0.137343	+	0.990524i	$0.543856\pi$
$930$	10.3723	0.340121
$931$	−5.48913	−0.179899
$932$	13.8614	0.454045
$933$	17.4891	0.572568
$934$	−14.9783	−0.490103
$935$	1.00000	0.0327035
$936$	−6.74456	−0.220453
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	−9.48913	−0.309831
$939$	−9.86141	−0.321815
$940$	9.48913	0.309501
$941$	−2.00000	−0.0651981	−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000	−0.0651981	−0.0325991	+	0.999469i	$0.510378\pi$
$942$	−11.4891	−0.374336
$943$	−2.97825	−0.0969852
$944$	0.744563	0.0242335
$945$	−2.37228	−0.0771703
$946$	1.62772	0.0529217
$947$	40.7446	1.32402	0.662010	−	0.749495i	$-0.269704\pi$
$947$	40.7446	1.32402	0.662010	+	0.749495i	$0.269704\pi$
$948$	9.48913	0.308192
$949$	40.4674	1.31363
$950$	4.00000	0.129777
$951$	−17.1168	−0.555052
$952$	−2.37228	−0.0768861
$953$	−47.4891	−1.53832	−0.769162	−	0.639054i	$-0.779326\pi$
$953$	−47.4891	−1.53832	−0.769162	+	0.639054i	$0.779326\pi$
$954$	10.7446	0.347868
$955$	−10.3723	−0.335639
$956$	−14.2337	−0.460350
$957$	8.37228	0.270637
$958$	−38.8397	−1.25485
$959$	−32.8832	−1.06185
$960$	1.00000	0.0322749
$961$	76.5842	2.47046
$962$	67.4456	2.17453
$963$	−3.11684	−0.100439
$964$	−3.62772	−0.116841
$965$	−23.4891	−0.756142
$966$	−5.62772	−0.181069
$967$	−19.2554	−0.619213	−0.309607	−	0.950865i	$-0.600197\pi$
$967$	−19.2554	−0.619213	−0.309607	+	0.950865i	$0.600197\pi$
$968$	1.00000	0.0321412
$969$	4.00000	0.128499
$970$	−3.62772	−0.116479
$971$	24.4674	0.785195	0.392598	−	0.919710i	$-0.371576\pi$
$971$	24.4674	0.785195	0.392598	+	0.919710i	$0.371576\pi$
$972$	1.00000	0.0320750
$973$	7.39403	0.237042
$974$	12.7446	0.408362
$975$	−6.74456	−0.215999
$976$	−2.00000	−0.0640184
$977$	−14.0000	−0.447900	−0.223950	−	0.974601i	$-0.571895\pi$
$977$	−14.0000	−0.447900	−0.223950	+	0.974601i	$0.571895\pi$
$978$	−1.62772	−0.0520487
$979$	5.25544	0.167965
$980$	−1.37228	−0.0438359
$981$	2.74456	0.0876271
$982$	−29.4891	−0.941036
$983$	−48.6060	−1.55029	−0.775145	−	0.631784i	$-0.782323\pi$
$983$	−48.6060	−1.55029	−0.775145	+	0.631784i	$0.782323\pi$
$984$	−1.25544	−0.0400219
$985$	−8.23369	−0.262347
$986$	8.37228	0.266628
$987$	−22.5109	−0.716529
$988$	−26.9783	−0.858292
$989$	3.86141	0.122786
$990$	1.00000	0.0317821
$991$	−38.8397	−1.23378	−0.616891	−	0.787048i	$-0.711608\pi$
$991$	−38.8397	−1.23378	−0.616891	+	0.787048i	$0.711608\pi$
$992$	10.3723	0.329320
$993$	−33.3505	−1.05835
$994$	−30.2337	−0.958954
$995$	−8.00000	−0.253617
$996$	−12.0000	−0.380235
$997$	−10.8832	−0.344673	−0.172337	−	0.985038i	$-0.555132\pi$
$997$	−10.8832	−0.344673	−0.172337	+	0.985038i	$0.555132\pi$
$998$	−21.4891	−0.680226
$999$	−10.0000	−0.316386

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bx.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.74456 q^{13} -2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -2.37228 q^{21} +1.00000 q^{22} +2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.74456 q^{26} +1.00000 q^{27} -2.37228 q^{28} +8.37228 q^{29} +1.00000 q^{30} +10.3723 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -2.37228 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} -6.74456 q^{39} +1.00000 q^{40} -1.25544 q^{41} -2.37228 q^{42} +1.62772 q^{43} +1.00000 q^{44} +1.00000 q^{45} +2.37228 q^{46} +9.48913 q^{47} +1.00000 q^{48} -1.37228 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.74456 q^{52} +10.7446 q^{53} +1.00000 q^{54} +1.00000 q^{55} -2.37228 q^{56} +4.00000 q^{57} +8.37228 q^{58} +0.744563 q^{59} +1.00000 q^{60} -2.00000 q^{61} +10.3723 q^{62} -2.37228 q^{63} +1.00000 q^{64} -6.74456 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +2.37228 q^{69} -2.37228 q^{70} +12.7446 q^{71} +1.00000 q^{72} -6.00000 q^{73} -10.0000 q^{74} +1.00000 q^{75} +4.00000 q^{76} -2.37228 q^{77} -6.74456 q^{78} +9.48913 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.25544 q^{82} -12.0000 q^{83} -2.37228 q^{84} +1.00000 q^{85} +1.62772 q^{86} +8.37228 q^{87} +1.00000 q^{88} +5.25544 q^{89} +1.00000 q^{90} +16.0000 q^{91} +2.37228 q^{92} +10.3723 q^{93} +9.48913 q^{94} +4.00000 q^{95} +1.00000 q^{96} -3.62772 q^{97} -1.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} + 2 q^{22} - q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + q^{28} + 11 q^{29} + 2 q^{30} + 15 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{34} + q^{35} + 2 q^{36} - 20 q^{37} + 8 q^{38} - 2 q^{39} + 2 q^{40} - 14 q^{41} + q^{42} + 9 q^{43} + 2 q^{44} + 2 q^{45} - q^{46} - 4 q^{47} + 2 q^{48} + 3 q^{49} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 10 q^{53} + 2 q^{54} + 2 q^{55} + q^{56} + 8 q^{57} + 11 q^{58} - 10 q^{59} + 2 q^{60} - 4 q^{61} + 15 q^{62} + q^{63} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} - q^{69} + q^{70} + 14 q^{71} + 2 q^{72} - 12 q^{73} - 20 q^{74} + 2 q^{75} + 8 q^{76} + q^{77} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 2 q^{81} - 14 q^{82} - 24 q^{83} + q^{84} + 2 q^{85} + 9 q^{86} + 11 q^{87} + 2 q^{88} + 22 q^{89} + 2 q^{90} + 32 q^{91} - q^{92} + 15 q^{93} - 4 q^{94} + 8 q^{95} + 2 q^{96} - 13 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 + 2 * q^22 - q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + q^28 + 11 * q^29 + 2 * q^30 + 15 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 + q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 - 14 * q^41 + q^42 + 9 * q^43 + 2 * q^44 + 2 * q^45 - q^46 - 4 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 10 * q^53 + 2 * q^54 + 2 * q^55 + q^56 + 8 * q^57 + 11 * q^58 - 10 * q^59 + 2 * q^60 - 4 * q^61 + 15 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 - q^69 + q^70 + 14 * q^71 + 2 * q^72 - 12 * q^73 - 20 * q^74 + 2 * q^75 + 8 * q^76 + q^77 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 - 14 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 9 * q^86 + 11 * q^87 + 2 * q^88 + 22 * q^89 + 2 * q^90 + 32 * q^91 - q^92 + 15 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 13 * q^97 + 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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