LMFDB - Embedded newform 5610.2.a.cg.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:	$4$
Coefficient field:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.655762$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.46569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.46569 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.56998 q^{13} -3.46569 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.73836 q^{19} -1.00000 q^{20} +3.46569 q^{21} +1.00000 q^{22} +6.63408 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.56998 q^{26} -1.00000 q^{27} -3.46569 q^{28} -9.82711 q^{29} +1.00000 q^{30} +3.46569 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +3.46569 q^{35} +1.00000 q^{36} -2.36141 q^{37} -1.73836 q^{38} +4.56998 q^{39} -1.00000 q^{40} -2.83161 q^{41} +3.46569 q^{42} +6.03567 q^{43} +1.00000 q^{44} -1.00000 q^{45} +6.63408 q^{46} -3.47673 q^{47} -1.00000 q^{48} +5.01103 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.56998 q^{52} +2.83161 q^{53} -1.00000 q^{54} -1.00000 q^{55} -3.46569 q^{56} +1.73836 q^{57} -9.82711 q^{58} -14.4081 q^{59} +1.00000 q^{60} -1.63859 q^{61} +3.46569 q^{62} -3.46569 q^{63} +1.00000 q^{64} +4.56998 q^{65} -1.00000 q^{66} +1.73836 q^{67} +1.00000 q^{68} -6.63408 q^{69} +3.46569 q^{70} -2.93139 q^{71} +1.00000 q^{72} +7.13995 q^{73} -2.36141 q^{74} -1.00000 q^{75} -1.73836 q^{76} -3.46569 q^{77} +4.56998 q^{78} +14.0998 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.83161 q^{82} +13.5014 q^{83} +3.46569 q^{84} -1.00000 q^{85} +6.03567 q^{86} +9.82711 q^{87} +1.00000 q^{88} +3.79143 q^{89} -1.00000 q^{90} +15.8381 q^{91} +6.63408 q^{92} -3.46569 q^{93} -3.47673 q^{94} +1.73836 q^{95} -1.00000 q^{96} +6.29731 q^{97} +5.01103 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	−3.46569	−1.30991	−0.654955	−	0.755668i	$-0.727312\pi$
$7$	−3.46569	−1.30991	−0.654955	+	0.755668i	$0.727312\pi$
$8$	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
$13$	−4.56998	−1.26748	−0.633742	−	0.773545i	$-0.718482\pi$
$13$	−4.56998	−1.26748	−0.633742	+	0.773545i	$0.718482\pi$
$14$	−3.46569	−0.926246
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−1.73836	−0.398808	−0.199404	−	0.979917i	$-0.563901\pi$
$19$	−1.73836	−0.398808	−0.199404	+	0.979917i	$0.563901\pi$
$20$	−1.00000	−0.223607
$21$	3.46569	0.756276
$22$	1.00000	0.213201
$23$	6.63408	1.38330	0.691651	−	0.722232i	$-0.256884\pi$
$23$	6.63408	1.38330	0.691651	+	0.722232i	$0.256884\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.56998	−0.896246
$27$	−1.00000	−0.192450
$28$	−3.46569	−0.654955
$29$	−9.82711	−1.82485	−0.912424	−	0.409247i	$-0.865792\pi$
$29$	−9.82711	−1.82485	−0.912424	+	0.409247i	$0.865792\pi$
$30$	1.00000	0.182574
$31$	3.46569	0.622457	0.311228	−	0.950335i	$-0.399260\pi$
$31$	3.46569	0.622457	0.311228	+	0.950335i	$0.399260\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	3.46569	0.585809
$36$	1.00000	0.166667
$37$	−2.36141	−0.388214	−0.194107	−	0.980980i	$-0.562181\pi$
$37$	−2.36141	−0.388214	−0.194107	+	0.980980i	$0.562181\pi$
$38$	−1.73836	−0.282000
$39$	4.56998	0.731782
$40$	−1.00000	−0.158114
$41$	−2.83161	−0.442224	−0.221112	−	0.975248i	$-0.570969\pi$
$41$	−2.83161	−0.442224	−0.221112	+	0.975248i	$0.570969\pi$
$42$	3.46569	0.534768
$43$	6.03567	0.920431	0.460216	−	0.887807i	$-0.347772\pi$
$43$	6.03567	0.920431	0.460216	+	0.887807i	$0.347772\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	6.63408	0.978142
$47$	−3.47673	−0.507133	−0.253566	−	0.967318i	$-0.581604\pi$
$47$	−3.47673	−0.507133	−0.253566	+	0.967318i	$0.581604\pi$
$48$	−1.00000	−0.144338
$49$	5.01103	0.715862
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−4.56998	−0.633742
$53$	2.83161	0.388952	0.194476	−	0.980907i	$-0.437699\pi$
$53$	2.83161	0.388952	0.194476	+	0.980907i	$0.437699\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−3.46569	−0.463123
$57$	1.73836	0.230252
$58$	−9.82711	−1.29036
$59$	−14.4081	−1.87578	−0.937888	−	0.346937i	$-0.887222\pi$
$59$	−14.4081	−1.87578	−0.937888	+	0.346937i	$0.887222\pi$
$60$	1.00000	0.129099
$61$	−1.63859	−0.209800	−0.104900	−	0.994483i	$-0.533452\pi$
$61$	−1.63859	−0.209800	−0.104900	+	0.994483i	$0.533452\pi$
$62$	3.46569	0.440144
$63$	−3.46569	−0.436636
$64$	1.00000	0.125000
$65$	4.56998	0.566836
$66$	−1.00000	−0.123091
$67$	1.73836	0.212375	0.106187	−	0.994346i	$-0.466136\pi$
$67$	1.73836	0.212375	0.106187	+	0.994346i	$0.466136\pi$
$68$	1.00000	0.121268
$69$	−6.63408	−0.798650
$70$	3.46569	0.414230
$71$	−2.93139	−0.347892	−0.173946	−	0.984755i	$-0.555652\pi$
$71$	−2.93139	−0.347892	−0.173946	+	0.984755i	$0.555652\pi$
$72$	1.00000	0.117851
$73$	7.13995	0.835668	0.417834	−	0.908523i	$-0.362789\pi$
$73$	7.13995	0.835668	0.417834	+	0.908523i	$0.362789\pi$
$74$	−2.36141	−0.274508
$75$	−1.00000	−0.115470
$76$	−1.73836	−0.199404
$77$	−3.46569	−0.394952
$78$	4.56998	0.517448
$79$	14.0998	1.58635	0.793174	−	0.608995i	$-0.208427\pi$
$79$	14.0998	1.58635	0.793174	+	0.608995i	$0.208427\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.83161	−0.312699
$83$	13.5014	1.48197	0.740984	−	0.671523i	$-0.234360\pi$
$83$	13.5014	1.48197	0.740984	+	0.671523i	$0.234360\pi$
$84$	3.46569	0.378138
$85$	−1.00000	−0.108465
$86$	6.03567	0.650843
$87$	9.82711	1.05358
$88$	1.00000	0.106600
$89$	3.79143	0.401891	0.200946	−	0.979602i	$-0.435599\pi$
$89$	3.79143	0.401891	0.200946	+	0.979602i	$0.435599\pi$
$90$	−1.00000	−0.105409
$91$	15.8381	1.66029
$92$	6.63408	0.691651
$93$	−3.46569	−0.359376
$94$	−3.47673	−0.358597
$95$	1.73836	0.178352
$96$	−1.00000	−0.102062
$97$	6.29731	0.639395	0.319697	−	0.947520i	$-0.396419\pi$
$97$	6.29731	0.639395	0.319697	+	0.947520i	$0.396419\pi$
$98$	5.01103	0.506191
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	4.62305	0.460010	0.230005	−	0.973189i	$-0.426126\pi$
$101$	4.62305	0.460010	0.230005	+	0.973189i	$0.426126\pi$
$102$	−1.00000	−0.0990148
$103$	17.1510	1.68994	0.844968	−	0.534816i	$-0.179619\pi$
$103$	17.1510	1.68994	0.844968	+	0.534816i	$0.179619\pi$
$104$	−4.56998	−0.448123
$105$	−3.46569	−0.338217
$106$	2.83161	0.275031
$107$	−0.895717	−0.0865923	−0.0432961	−	0.999062i	$-0.513786\pi$
$107$	−0.895717	−0.0865923	−0.0432961	+	0.999062i	$0.513786\pi$
$108$	−1.00000	−0.0962250
$109$	8.04670	0.770734	0.385367	−	0.922763i	$-0.374075\pi$
$109$	8.04670	0.770734	0.385367	+	0.922763i	$0.374075\pi$
$110$	−1.00000	−0.0953463
$111$	2.36141	0.224135
$112$	−3.46569	−0.327477
$113$	8.62305	0.811188	0.405594	−	0.914053i	$-0.367065\pi$
$113$	8.62305	0.811188	0.405594	+	0.914053i	$0.367065\pi$
$114$	1.73836	0.162813
$115$	−6.63408	−0.618631
$116$	−9.82711	−0.912424
$117$	−4.56998	−0.422494
$118$	−14.4081	−1.32637
$119$	−3.46569	−0.317700
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−1.63859	−0.148351
$123$	2.83161	0.255318
$124$	3.46569	0.311228
$125$	−1.00000	−0.0894427
$126$	−3.46569	−0.308749
$127$	3.45466	0.306552	0.153276	−	0.988183i	$-0.451018\pi$
$127$	3.45466	0.306552	0.153276	+	0.988183i	$0.451018\pi$
$128$	1.00000	0.0883883
$129$	−6.03567	−0.531411
$130$	4.56998	0.400813
$131$	−13.5014	−1.17962	−0.589810	−	0.807542i	$-0.700797\pi$
$131$	−13.5014	−1.17962	−0.589810	+	0.807542i	$0.700797\pi$
$132$	−1.00000	−0.0870388
$133$	6.02464	0.522402
$134$	1.73836	0.150172
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	10.5343	0.900007	0.450003	−	0.893027i	$-0.351423\pi$
$137$	10.5343	0.900007	0.450003	+	0.893027i	$0.351423\pi$
$138$	−6.63408	−0.564730
$139$	−11.3038	−0.958779	−0.479389	−	0.877602i	$-0.659142\pi$
$139$	−11.3038	−0.958779	−0.479389	+	0.877602i	$0.659142\pi$
$140$	3.46569	0.292905
$141$	3.47673	0.292793
$142$	−2.93139	−0.245997
$143$	−4.56998	−0.382161
$144$	1.00000	0.0833333
$145$	9.82711	0.816097
$146$	7.13995	0.590907
$147$	−5.01103	−0.413303
$148$	−2.36141	−0.194107
$149$	17.0065	1.39323	0.696614	−	0.717446i	$-0.254689\pi$
$149$	17.0065	1.39323	0.696614	+	0.717446i	$0.254689\pi$
$150$	−1.00000	−0.0816497
$151$	4.36141	0.354927	0.177463	−	0.984127i	$-0.443211\pi$
$151$	4.36141	0.354927	0.177463	+	0.984127i	$0.443211\pi$
$152$	−1.73836	−0.141000
$153$	1.00000	0.0808452
$154$	−3.46569	−0.279274
$155$	−3.46569	−0.278371
$156$	4.56998	0.365891
$157$	16.0998	1.28490	0.642451	−	0.766327i	$-0.277918\pi$
$157$	16.0998	1.28490	0.642451	+	0.766327i	$0.277918\pi$
$158$	14.0998	1.12172
$159$	−2.83161	−0.224561
$160$	−1.00000	−0.0790569
$161$	−22.9917	−1.81200
$162$	1.00000	0.0785674
$163$	−12.2442	−0.959043	−0.479521	−	0.877530i	$-0.659190\pi$
$163$	−12.2442	−0.959043	−0.479521	+	0.877530i	$0.659190\pi$
$164$	−2.83161	−0.221112
$165$	1.00000	0.0778499
$166$	13.5014	1.04791
$167$	16.0713	1.24364	0.621819	−	0.783161i	$-0.286394\pi$
$167$	16.0713	1.24364	0.621819	+	0.783161i	$0.286394\pi$
$168$	3.46569	0.267384
$169$	7.88468	0.606514
$170$	−1.00000	−0.0766965
$171$	−1.73836	−0.132936
$172$	6.03567	0.460216
$173$	2.88468	0.219318	0.109659	−	0.993969i	$-0.465024\pi$
$173$	2.88468	0.219318	0.109659	+	0.993969i	$0.465024\pi$
$174$	9.82711	0.744991
$175$	−3.46569	−0.261982
$176$	1.00000	0.0753778
$177$	14.4081	1.08298
$178$	3.79143	0.284180
$179$	−6.56998	−0.491063	−0.245532	−	0.969389i	$-0.578962\pi$
$179$	−6.56998	−0.491063	−0.245532	+	0.969389i	$0.578962\pi$
$180$	−1.00000	−0.0745356
$181$	0.558943	0.0415459	0.0207729	−	0.999784i	$-0.493387\pi$
$181$	0.558943	0.0415459	0.0207729	+	0.999784i	$0.493387\pi$
$182$	15.8381	1.17400
$183$	1.63859	0.121128
$184$	6.63408	0.489071
$185$	2.36141	0.173614
$186$	−3.46569	−0.254117
$187$	1.00000	0.0731272
$188$	−3.47673	−0.253566
$189$	3.46569	0.252092
$190$	1.73836	0.126114
$191$	26.6524	1.92850	0.964248	−	0.265001i	$-0.0853722\pi$
$191$	26.6524	1.92850	0.964248	+	0.265001i	$0.0853722\pi$
$192$	−1.00000	−0.0721688
$193$	−3.13995	−0.226019	−0.113009	−	0.993594i	$-0.536049\pi$
$193$	−3.13995	−0.226019	−0.113009	+	0.993594i	$0.536049\pi$
$194$	6.29731	0.452120
$195$	−4.56998	−0.327263
$196$	5.01103	0.357931
$197$	9.09325	0.647867	0.323934	−	0.946080i	$-0.394995\pi$
$197$	9.09325	0.647867	0.323934	+	0.946080i	$0.394995\pi$
$198$	1.00000	0.0710669
$199$	−8.36141	−0.592725	−0.296362	−	0.955076i	$-0.595774\pi$
$199$	−8.36141	−0.592725	−0.296362	+	0.955076i	$0.595774\pi$
$200$	1.00000	0.0707107
$201$	−1.73836	−0.122615
$202$	4.62305	0.325276
$203$	34.0577	2.39038
$204$	−1.00000	−0.0700140
$205$	2.83161	0.197768
$206$	17.1510	1.19497
$207$	6.63408	0.461101
$208$	−4.56998	−0.316871
$209$	−1.73836	−0.120245
$210$	−3.46569	−0.239156
$211$	−15.8492	−1.09110	−0.545551	−	0.838078i	$-0.683680\pi$
$211$	−15.8492	−1.09110	−0.545551	+	0.838078i	$0.683680\pi$
$212$	2.83161	0.194476
$213$	2.93139	0.200855
$214$	−0.895717	−0.0612300
$215$	−6.03567	−0.411629
$216$	−1.00000	−0.0680414
$217$	−12.0110	−0.815362
$218$	8.04670	0.544992
$219$	−7.13995	−0.482473
$220$	−1.00000	−0.0674200
$221$	−4.56998	−0.307410
$222$	2.36141	0.158488
$223$	13.6743	0.915696	0.457848	−	0.889030i	$-0.348620\pi$
$223$	13.6743	0.915696	0.457848	+	0.889030i	$0.348620\pi$
$224$	−3.46569	−0.231561
$225$	1.00000	0.0666667
$226$	8.62305	0.573597
$227$	−21.0953	−1.40014	−0.700071	−	0.714073i	$-0.746848\pi$
$227$	−21.0953	−1.40014	−0.700071	+	0.714073i	$0.746848\pi$
$228$	1.73836	0.115126
$229$	27.5727	1.82206	0.911028	−	0.412345i	$-0.135290\pi$
$229$	27.5727	1.82206	0.911028	+	0.412345i	$0.135290\pi$
$230$	−6.63408	−0.437438
$231$	3.46569	0.228026
$232$	−9.82711	−0.645181
$233$	9.62756	0.630722	0.315361	−	0.948972i	$-0.397874\pi$
$233$	9.62756	0.630722	0.315361	+	0.948972i	$0.397874\pi$
$234$	−4.56998	−0.298749
$235$	3.47673	0.226797
$236$	−14.4081	−0.937888
$237$	−14.0998	−0.915879
$238$	−3.46569	−0.224648
$239$	9.68529	0.626489	0.313245	−	0.949672i	$-0.398584\pi$
$239$	9.68529	0.626489	0.313245	+	0.949672i	$0.398584\pi$
$240$	1.00000	0.0645497
$241$	−25.2287	−1.62512	−0.812562	−	0.582875i	$-0.801928\pi$
$241$	−25.2287	−1.62512	−0.812562	+	0.582875i	$0.801928\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.63859	−0.104900
$245$	−5.01103	−0.320143
$246$	2.83161	0.180537
$247$	7.94428	0.505483
$248$	3.46569	0.220072
$249$	−13.5014	−0.855614
$250$	−1.00000	−0.0632456
$251$	−18.0246	−1.13770	−0.568852	−	0.822440i	$-0.692612\pi$
$251$	−18.0246	−1.13770	−0.568852	+	0.822440i	$0.692612\pi$
$252$	−3.46569	−0.218318
$253$	6.63408	0.417081
$254$	3.45466	0.216765
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	16.5810	1.03429	0.517147	−	0.855896i	$-0.326994\pi$
$257$	16.5810	1.03429	0.517147	+	0.855896i	$0.326994\pi$
$258$	−6.03567	−0.375764
$259$	8.18393	0.508525
$260$	4.56998	0.283418
$261$	−9.82711	−0.608283
$262$	−13.5014	−0.834117
$263$	−8.18852	−0.504926	−0.252463	−	0.967607i	$-0.581241\pi$
$263$	−8.18852	−0.504926	−0.252463	+	0.967607i	$0.581241\pi$
$264$	−1.00000	−0.0615457
$265$	−2.83161	−0.173945
$266$	6.02464	0.369394
$267$	−3.79143	−0.232032
$268$	1.73836	0.106187
$269$	9.83814	0.599842	0.299921	−	0.953964i	$-0.403040\pi$
$269$	9.83814	0.599842	0.299921	+	0.953964i	$0.403040\pi$
$270$	1.00000	0.0608581
$271$	−18.0357	−1.09559	−0.547794	−	0.836613i	$-0.684532\pi$
$271$	−18.0357	−1.09559	−0.547794	+	0.836613i	$0.684532\pi$
$272$	1.00000	0.0606339
$273$	−15.8381	−0.958568
$274$	10.5343	0.636401
$275$	1.00000	0.0603023
$276$	−6.63408	−0.399325
$277$	−13.0596	−0.784675	−0.392338	−	0.919821i	$-0.628333\pi$
$277$	−13.0596	−0.784675	−0.392338	+	0.919821i	$0.628333\pi$
$278$	−11.3038	−0.677959
$279$	3.46569	0.207486
$280$	3.46569	0.207115
$281$	18.2442	1.08836	0.544180	−	0.838969i	$-0.316841\pi$
$281$	18.2442	1.08836	0.544180	+	0.838969i	$0.316841\pi$
$282$	3.47673	0.207036
$283$	−17.7346	−1.05421	−0.527105	−	0.849800i	$-0.676723\pi$
$283$	−17.7346	−1.05421	−0.527105	+	0.849800i	$0.676723\pi$
$284$	−2.93139	−0.173946
$285$	−1.73836	−0.102972
$286$	−4.56998	−0.270228
$287$	9.81350	0.579273
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	9.82711	0.577067
$291$	−6.29731	−0.369155
$292$	7.13995	0.417834
$293$	29.4320	1.71944	0.859719	−	0.510767i	$-0.170639\pi$
$293$	29.4320	1.71944	0.859719	+	0.510767i	$0.170639\pi$
$294$	−5.01103	−0.292249
$295$	14.4081	0.838873
$296$	−2.36141	−0.137254
$297$	−1.00000	−0.0580259
$298$	17.0065	0.985162
$299$	−30.3176	−1.75331
$300$	−1.00000	−0.0577350
$301$	−20.9178	−1.20568
$302$	4.36141	0.250971
$303$	−4.62305	−0.265587
$304$	−1.73836	−0.0997020
$305$	1.63859	0.0938253
$306$	1.00000	0.0571662
$307$	16.1996	0.924557	0.462279	−	0.886735i	$-0.347032\pi$
$307$	16.1996	0.924557	0.462279	+	0.886735i	$0.347032\pi$
$308$	−3.46569	−0.197476
$309$	−17.1510	−0.975686
$310$	−3.46569	−0.196838
$311$	−7.47673	−0.423966	−0.211983	−	0.977273i	$-0.567992\pi$
$311$	−7.47673	−0.423966	−0.211983	+	0.977273i	$0.567992\pi$
$312$	4.56998	0.258724
$313$	22.3194	1.26157	0.630783	−	0.775959i	$-0.282734\pi$
$313$	22.3194	1.26157	0.630783	+	0.775959i	$0.282734\pi$
$314$	16.0998	0.908563
$315$	3.46569	0.195270
$316$	14.0998	0.793174
$317$	16.2352	0.911861	0.455930	−	0.890015i	$-0.349307\pi$
$317$	16.2352	0.911861	0.455930	+	0.890015i	$0.349307\pi$
$318$	−2.83161	−0.158789
$319$	−9.82711	−0.550212
$320$	−1.00000	−0.0559017
$321$	0.895717	0.0499941
$322$	−22.9917	−1.28128
$323$	−1.73836	−0.0967251
$324$	1.00000	0.0555556
$325$	−4.56998	−0.253497
$326$	−12.2442	−0.678145
$327$	−8.04670	−0.444984
$328$	−2.83161	−0.156350
$329$	12.0493	0.664298
$330$	1.00000	0.0550482
$331$	−6.16388	−0.338797	−0.169399	−	0.985548i	$-0.554183\pi$
$331$	−6.16388	−0.338797	−0.169399	+	0.985548i	$0.554183\pi$
$332$	13.5014	0.740984
$333$	−2.36141	−0.129405
$334$	16.0713	0.879385
$335$	−1.73836	−0.0949770
$336$	3.46569	0.189069
$337$	−13.2772	−0.723254	−0.361627	−	0.932323i	$-0.617779\pi$
$337$	−13.2772	−0.723254	−0.361627	+	0.932323i	$0.617779\pi$
$338$	7.88468	0.428870
$339$	−8.62305	−0.468340
$340$	−1.00000	−0.0542326
$341$	3.46569	0.187678
$342$	−1.73836	−0.0939999
$343$	6.89315	0.372195
$344$	6.03567	0.325422
$345$	6.63408	0.357167
$346$	2.88468	0.155082
$347$	15.4767	0.830834	0.415417	−	0.909631i	$-0.363636\pi$
$347$	15.4767	0.830834	0.415417	+	0.909631i	$0.363636\pi$
$348$	9.82711	0.526788
$349$	−22.4858	−1.20364	−0.601819	−	0.798632i	$-0.705557\pi$
$349$	−22.4858	−1.20364	−0.601819	+	0.798632i	$0.705557\pi$
$350$	−3.46569	−0.185249
$351$	4.56998	0.243927
$352$	1.00000	0.0533002
$353$	11.2571	0.599157	0.299578	−	0.954072i	$-0.403154\pi$
$353$	11.2571	0.599157	0.299578	+	0.954072i	$0.403154\pi$
$354$	14.4081	0.765783
$355$	2.93139	0.155582
$356$	3.79143	0.200946
$357$	3.46569	0.183424
$358$	−6.56998	−0.347234
$359$	−3.60494	−0.190261	−0.0951307	−	0.995465i	$-0.530327\pi$
$359$	−3.60494	−0.190261	−0.0951307	+	0.995465i	$0.530327\pi$
$360$	−1.00000	−0.0527046
$361$	−15.9781	−0.840952
$362$	0.558943	0.0293774
$363$	−1.00000	−0.0524864
$364$	15.8381	0.830144
$365$	−7.13995	−0.373722
$366$	1.63859	0.0856504
$367$	−6.07771	−0.317254	−0.158627	−	0.987339i	$-0.550707\pi$
$367$	−6.07771	−0.317254	−0.158627	+	0.987339i	$0.550707\pi$
$368$	6.63408	0.345825
$369$	−2.83161	−0.147408
$370$	2.36141	0.122764
$371$	−9.81350	−0.509492
$372$	−3.46569	−0.179688
$373$	−0.953455	−0.0493680	−0.0246840	−	0.999695i	$-0.507858\pi$
$373$	−0.953455	−0.0493680	−0.0246840	+	0.999695i	$0.507858\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−3.47673	−0.179299
$377$	44.9096	2.31296
$378$	3.46569	0.178256
$379$	8.25527	0.424045	0.212022	−	0.977265i	$-0.431995\pi$
$379$	8.25527	0.424045	0.212022	+	0.977265i	$0.431995\pi$
$380$	1.73836	0.0891762
$381$	−3.45466	−0.176988
$382$	26.6524	1.36365
$383$	−33.3395	−1.70357	−0.851785	−	0.523892i	$-0.824479\pi$
$383$	−33.3395	−1.70357	−0.851785	+	0.523892i	$0.824479\pi$
$384$	−1.00000	−0.0510310
$385$	3.46569	0.176628
$386$	−3.13995	−0.159819
$387$	6.03567	0.306810
$388$	6.29731	0.319697
$389$	26.0934	1.32299	0.661494	−	0.749950i	$-0.269923\pi$
$389$	26.0934	1.32299	0.661494	+	0.749950i	$0.269923\pi$
$390$	−4.56998	−0.231410
$391$	6.63408	0.335500
$392$	5.01103	0.253095
$393$	13.5014	0.681054
$394$	9.09325	0.458111
$395$	−14.0998	−0.709437
$396$	1.00000	0.0502519
$397$	−2.19955	−0.110392	−0.0551961	−	0.998476i	$-0.517578\pi$
$397$	−2.19955	−0.110392	−0.0551961	+	0.998476i	$0.517578\pi$
$398$	−8.36141	−0.419120
$399$	−6.02464	−0.301609
$400$	1.00000	0.0500000
$401$	−6.21058	−0.310142	−0.155071	−	0.987903i	$-0.549561\pi$
$401$	−6.21058	−0.310142	−0.155071	+	0.987903i	$0.549561\pi$
$402$	−1.73836	−0.0867017
$403$	−15.8381	−0.788954
$404$	4.62305	0.230005
$405$	−1.00000	−0.0496904
$406$	34.0577	1.69026
$407$	−2.36141	−0.117051
$408$	−1.00000	−0.0495074
$409$	−16.4081	−0.811329	−0.405665	−	0.914022i	$-0.632960\pi$
$409$	−16.4081	−0.811329	−0.405665	+	0.914022i	$0.632960\pi$
$410$	2.83161	0.139843
$411$	−10.5343	−0.519619
$412$	17.1510	0.844968
$413$	49.9341	2.45710
$414$	6.63408	0.326047
$415$	−13.5014	−0.662756
$416$	−4.56998	−0.224062
$417$	11.3038	0.553551
$418$	−1.73836	−0.0850262
$419$	−1.83612	−0.0897003	−0.0448502	−	0.998994i	$-0.514281\pi$
$419$	−1.83612	−0.0897003	−0.0448502	+	0.998994i	$0.514281\pi$
$420$	−3.46569	−0.169109
$421$	25.9095	1.26275	0.631375	−	0.775477i	$-0.282491\pi$
$421$	25.9095	1.26275	0.631375	+	0.775477i	$0.282491\pi$
$422$	−15.8492	−0.771526
$423$	−3.47673	−0.169044
$424$	2.83161	0.137515
$425$	1.00000	0.0485071
$426$	2.93139	0.142026
$427$	5.67885	0.274819
$428$	−0.895717	−0.0432961
$429$	4.56998	0.220641
$430$	−6.03567	−0.291066
$431$	29.2754	1.41015	0.705073	−	0.709135i	$-0.250914\pi$
$431$	29.2754	1.41015	0.705073	+	0.709135i	$0.250914\pi$
$432$	−1.00000	−0.0481125
$433$	2.12821	0.102275	0.0511376	−	0.998692i	$-0.483715\pi$
$433$	2.12821	0.102275	0.0511376	+	0.998692i	$0.483715\pi$
$434$	−12.0110	−0.576548
$435$	−9.82711	−0.471174
$436$	8.04670	0.385367
$437$	−11.5324	−0.551672
$438$	−7.13995	−0.341160
$439$	−15.0622	−0.718882	−0.359441	−	0.933168i	$-0.617033\pi$
$439$	−15.0622	−0.718882	−0.359441	+	0.933168i	$0.617033\pi$
$440$	−1.00000	−0.0476731
$441$	5.01103	0.238621
$442$	−4.56998	−0.217372
$443$	−6.47222	−0.307504	−0.153752	−	0.988109i	$-0.549136\pi$
$443$	−6.47222	−0.307504	−0.153752	+	0.988109i	$0.549136\pi$
$444$	2.36141	0.112068
$445$	−3.79143	−0.179731
$446$	13.6743	0.647495
$447$	−17.0065	−0.804381
$448$	−3.46569	−0.163739
$449$	16.2909	0.768817	0.384408	−	0.923163i	$-0.374405\pi$
$449$	16.2909	0.768817	0.384408	+	0.923163i	$0.374405\pi$
$450$	1.00000	0.0471405
$451$	−2.83161	−0.133335
$452$	8.62305	0.405594
$453$	−4.36141	−0.204917
$454$	−21.0953	−0.990050
$455$	−15.8381	−0.742503
$456$	1.73836	0.0814063
$457$	0.0246365	0.00115245	0.000576223	−	1.00000i	$-0.499817\pi$
$457$	0.0246365	0.00115245	0.000576223		1.00000i	$0.499817\pi$
$458$	27.5727	1.28839
$459$	−1.00000	−0.0466760
$460$	−6.63408	−0.309316
$461$	9.29660	0.432986	0.216493	−	0.976284i	$-0.430538\pi$
$461$	9.29660	0.432986	0.216493	+	0.976284i	$0.430538\pi$
$462$	3.46569	0.161239
$463$	18.5479	0.861994	0.430997	−	0.902353i	$-0.358162\pi$
$463$	18.5479	0.861994	0.430997	+	0.902353i	$0.358162\pi$
$464$	−9.82711	−0.456212
$465$	3.46569	0.160718
$466$	9.62756	0.445988
$467$	−25.1025	−1.16161	−0.580803	−	0.814044i	$-0.697261\pi$
$467$	−25.1025	−1.16161	−0.580803	+	0.814044i	$0.697261\pi$
$468$	−4.56998	−0.211247
$469$	−6.02464	−0.278192
$470$	3.47673	0.160369
$471$	−16.0998	−0.741838
$472$	−14.4081	−0.663187
$473$	6.03567	0.277520
$474$	−14.0998	−0.647624
$475$	−1.73836	−0.0797616
$476$	−3.46569	−0.158850
$477$	2.83161	0.129651
$478$	9.68529	0.442995
$479$	−18.7275	−0.855681	−0.427840	−	0.903854i	$-0.640725\pi$
$479$	−18.7275	−0.855681	−0.427840	+	0.903854i	$0.640725\pi$
$480$	1.00000	0.0456435
$481$	10.7916	0.492054
$482$	−25.2287	−1.14914
$483$	22.9917	1.04616
$484$	1.00000	0.0454545
$485$	−6.29731	−0.285946
$486$	−1.00000	−0.0453609
$487$	−20.2022	−0.915449	−0.457724	−	0.889094i	$-0.651335\pi$
$487$	−20.2022	−0.915449	−0.457724	+	0.889094i	$0.651335\pi$
$488$	−1.63859	−0.0741754
$489$	12.2442	0.553703
$490$	−5.01103	−0.226375
$491$	−8.23700	−0.371731	−0.185865	−	0.982575i	$-0.559509\pi$
$491$	−8.23700	−0.371731	−0.185865	+	0.982575i	$0.559509\pi$
$492$	2.83161	0.127659
$493$	−9.82711	−0.442591
$494$	7.94428	0.357430
$495$	−1.00000	−0.0449467
$496$	3.46569	0.155614
$497$	10.1593	0.455707
$498$	−13.5014	−0.605011
$499$	−8.41713	−0.376802	−0.188401	−	0.982092i	$-0.560331\pi$
$499$	−8.41713	−0.376802	−0.188401	+	0.982092i	$0.560331\pi$
$500$	−1.00000	−0.0447214
$501$	−16.0713	−0.718015
$502$	−18.0246	−0.804479
$503$	−7.32645	−0.326670	−0.163335	−	0.986571i	$-0.552225\pi$
$503$	−7.32645	−0.326670	−0.163335	+	0.986571i	$0.552225\pi$
$504$	−3.46569	−0.154374
$505$	−4.62305	−0.205723
$506$	6.63408	0.294921
$507$	−7.88468	−0.350171
$508$	3.45466	0.153276
$509$	42.8162	1.89780	0.948898	−	0.315583i	$-0.102200\pi$
$509$	42.8162	1.89780	0.948898	+	0.315583i	$0.102200\pi$
$510$	1.00000	0.0442807
$511$	−24.7449	−1.09465
$512$	1.00000	0.0441942
$513$	1.73836	0.0767506
$514$	16.5810	0.731357
$515$	−17.1510	−0.755763
$516$	−6.03567	−0.265706
$517$	−3.47673	−0.152906
$518$	8.18393	0.359581
$519$	−2.88468	−0.126624
$520$	4.56998	0.200407
$521$	−5.22146	−0.228756	−0.114378	−	0.993437i	$-0.536488\pi$
$521$	−5.22146	−0.228756	−0.114378	+	0.993437i	$0.536488\pi$
$522$	−9.82711	−0.430121
$523$	−8.91778	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$523$	−8.91778	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$524$	−13.5014	−0.589810
$525$	3.46569	0.151255
$526$	−8.18852	−0.357036
$527$	3.46569	0.150968
$528$	−1.00000	−0.0435194
$529$	21.0110	0.913523
$530$	−2.83161	−0.122997
$531$	−14.4081	−0.625259
$532$	6.02464	0.261201
$533$	12.9404	0.560511
$534$	−3.79143	−0.164071
$535$	0.895717	0.0387252
$536$	1.73836	0.0750859
$537$	6.56998	0.283515
$538$	9.83814	0.424152
$539$	5.01103	0.215840
$540$	1.00000	0.0430331
$541$	5.45466	0.234514	0.117257	−	0.993102i	$-0.462590\pi$
$541$	5.45466	0.234514	0.117257	+	0.993102i	$0.462590\pi$
$542$	−18.0357	−0.774698
$543$	−0.558943	−0.0239865
$544$	1.00000	0.0428746
$545$	−8.04670	−0.344683
$546$	−15.8381	−0.677810
$547$	−34.7695	−1.48664	−0.743319	−	0.668937i	$-0.766749\pi$
$547$	−34.7695	−1.48664	−0.743319	+	0.668937i	$0.766749\pi$
$548$	10.5343	0.450003
$549$	−1.63859	−0.0699333
$550$	1.00000	0.0426401
$551$	17.0831	0.727764
$552$	−6.63408	−0.282365
$553$	−48.8655	−2.07797
$554$	−13.0596	−0.554849
$555$	−2.36141	−0.100236
$556$	−11.3038	−0.479389
$557$	−19.9295	−0.844441	−0.422221	−	0.906493i	$-0.638749\pi$
$557$	−19.9295	−0.844441	−0.422221	+	0.906493i	$0.638749\pi$
$558$	3.46569	0.146715
$559$	−27.5829	−1.16663
$560$	3.46569	0.146452
$561$	−1.00000	−0.0422200
$562$	18.2442	0.769587
$563$	41.5948	1.75301	0.876505	−	0.481392i	$-0.159869\pi$
$563$	41.5948	1.75301	0.876505	+	0.481392i	$0.159869\pi$
$564$	3.47673	0.146397
$565$	−8.62305	−0.362774
$566$	−17.7346	−0.745439
$567$	−3.46569	−0.145545
$568$	−2.93139	−0.122998
$569$	22.3614	0.937439	0.468720	−	0.883347i	$-0.344715\pi$
$569$	22.3614	0.937439	0.468720	+	0.883347i	$0.344715\pi$
$570$	−1.73836	−0.0728120
$571$	22.4302	0.938674	0.469337	−	0.883019i	$-0.344493\pi$
$571$	22.4302	0.938674	0.469337	+	0.883019i	$0.344493\pi$
$572$	−4.56998	−0.191080
$573$	−26.6524	−1.11342
$574$	9.81350	0.409608
$575$	6.63408	0.276660
$576$	1.00000	0.0416667
$577$	−4.33677	−0.180542	−0.0902711	−	0.995917i	$-0.528773\pi$
$577$	−4.33677	−0.180542	−0.0902711	+	0.995917i	$0.528773\pi$
$578$	1.00000	0.0415945
$579$	3.13995	0.130492
$580$	9.82711	0.408048
$581$	−46.7916	−1.94124
$582$	−6.29731	−0.261032
$583$	2.83161	0.117273
$584$	7.13995	0.295453
$585$	4.56998	0.188945
$586$	29.4320	1.21583
$587$	4.55258	0.187905	0.0939524	−	0.995577i	$-0.470050\pi$
$587$	4.55258	0.187905	0.0939524	+	0.995577i	$0.470050\pi$
$588$	−5.01103	−0.206652
$589$	−6.02464	−0.248241
$590$	14.4081	0.593173
$591$	−9.09325	−0.374046
$592$	−2.36141	−0.0970534
$593$	−34.8162	−1.42973	−0.714866	−	0.699262i	$-0.753512\pi$
$593$	−34.8162	−1.42973	−0.714866	+	0.699262i	$0.753512\pi$
$594$	−1.00000	−0.0410305
$595$	3.46569	0.142080
$596$	17.0065	0.696614
$597$	8.36141	0.342210
$598$	−30.3176	−1.23978
$599$	−20.6277	−0.842826	−0.421413	−	0.906869i	$-0.638466\pi$
$599$	−20.6277	−0.842826	−0.421413	+	0.906869i	$0.638466\pi$
$600$	−1.00000	−0.0408248
$601$	2.59841	0.105991	0.0529957	−	0.998595i	$-0.483123\pi$
$601$	2.59841	0.105991	0.0529957	+	0.998595i	$0.483123\pi$
$602$	−20.9178	−0.852545
$603$	1.73836	0.0707916
$604$	4.36141	0.177463
$605$	−1.00000	−0.0406558
$606$	−4.62305	−0.187798
$607$	22.2683	0.903843	0.451922	−	0.892058i	$-0.350739\pi$
$607$	22.2683	0.903843	0.451922	+	0.892058i	$0.350739\pi$
$608$	−1.73836	−0.0705000
$609$	−34.0577	−1.38009
$610$	1.63859	0.0663445
$611$	15.8886	0.642782
$612$	1.00000	0.0404226
$613$	−5.32645	−0.215133	−0.107567	−	0.994198i	$-0.534306\pi$
$613$	−5.32645	−0.215133	−0.107567	+	0.994198i	$0.534306\pi$
$614$	16.1996	0.653761
$615$	−2.83161	−0.114182
$616$	−3.46569	−0.139637
$617$	−13.2397	−0.533011	−0.266506	−	0.963833i	$-0.585869\pi$
$617$	−13.2397	−0.533011	−0.266506	+	0.963833i	$0.585869\pi$
$618$	−17.1510	−0.689914
$619$	−39.9095	−1.60410	−0.802049	−	0.597259i	$-0.796257\pi$
$619$	−39.9095	−1.60410	−0.802049	+	0.597259i	$0.796257\pi$
$620$	−3.46569	−0.139186
$621$	−6.63408	−0.266217
$622$	−7.47673	−0.299789
$623$	−13.1400	−0.526441
$624$	4.56998	0.182945
$625$	1.00000	0.0400000
$626$	22.3194	0.892062
$627$	1.73836	0.0694236
$628$	16.0998	0.642451
$629$	−2.36141	−0.0941556
$630$	3.46569	0.138077
$631$	22.4574	0.894015	0.447007	−	0.894530i	$-0.352490\pi$
$631$	22.4574	0.894015	0.447007	+	0.894530i	$0.352490\pi$
$632$	14.0998	0.560859
$633$	15.8492	0.629948
$634$	16.2352	0.644783
$635$	−3.45466	−0.137094
$636$	−2.83161	−0.112281
$637$	−22.9003	−0.907343
$638$	−9.82711	−0.389059
$639$	−2.93139	−0.115964
$640$	−1.00000	−0.0395285
$641$	−0.954005	−0.0376809	−0.0188405	−	0.999823i	$-0.505997\pi$
$641$	−0.954005	−0.0376809	−0.0188405	+	0.999823i	$0.505997\pi$
$642$	0.895717	0.0353511
$643$	25.8894	1.02098	0.510490	−	0.859884i	$-0.329464\pi$
$643$	25.8894	1.02098	0.510490	+	0.859884i	$0.329464\pi$
$644$	−22.9917	−0.906000
$645$	6.03567	0.237654
$646$	−1.73836	−0.0683950
$647$	−11.6049	−0.456237	−0.228119	−	0.973633i	$-0.573257\pi$
$647$	−11.6049	−0.456237	−0.228119	+	0.973633i	$0.573257\pi$
$648$	1.00000	0.0392837
$649$	−14.4081	−0.565568
$650$	−4.56998	−0.179249
$651$	12.0110	0.470750
$652$	−12.2442	−0.479521
$653$	−20.4749	−0.801243	−0.400622	−	0.916244i	$-0.631206\pi$
$653$	−20.4749	−0.801243	−0.400622	+	0.916244i	$0.631206\pi$
$654$	−8.04670	−0.314651
$655$	13.5014	0.527542
$656$	−2.83161	−0.110556
$657$	7.13995	0.278556
$658$	12.0493	0.469730
$659$	10.5436	0.410719	0.205359	−	0.978687i	$-0.434164\pi$
$659$	10.5436	0.410719	0.205359	+	0.978687i	$0.434164\pi$
$660$	1.00000	0.0389249
$661$	20.5131	0.797867	0.398934	−	0.916980i	$-0.369380\pi$
$661$	20.5131	0.797867	0.398934	+	0.916980i	$0.369380\pi$
$662$	−6.16388	−0.239566
$663$	4.56998	0.177483
$664$	13.5014	0.523955
$665$	−6.02464	−0.233625
$666$	−2.36141	−0.0915028
$667$	−65.1938	−2.52431
$668$	16.0713	0.621819
$669$	−13.6743	−0.528677
$670$	−1.73836	−0.0671589
$671$	−1.63859	−0.0632570
$672$	3.46569	0.133692
$673$	−25.3485	−0.977114	−0.488557	−	0.872532i	$-0.662476\pi$
$673$	−25.3485	−0.977114	−0.488557	+	0.872532i	$0.662476\pi$
$674$	−13.2772	−0.511418
$675$	−1.00000	−0.0384900
$676$	7.88468	0.303257
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	−8.62305	−0.331166
$679$	−21.8245	−0.837549
$680$	−1.00000	−0.0383482
$681$	21.0953	0.808372
$682$	3.46569	0.132708
$683$	29.2838	1.12051	0.560256	−	0.828319i	$-0.310703\pi$
$683$	29.2838	1.12051	0.560256	+	0.828319i	$0.310703\pi$
$684$	−1.73836	−0.0664680
$685$	−10.5343	−0.402495
$686$	6.89315	0.263182
$687$	−27.5727	−1.05196
$688$	6.03567	0.230108
$689$	−12.9404	−0.492990
$690$	6.63408	0.252555
$691$	21.1776	0.805635	0.402818	−	0.915280i	$-0.368031\pi$
$691$	21.1776	0.805635	0.402818	+	0.915280i	$0.368031\pi$
$692$	2.88468	0.109659
$693$	−3.46569	−0.131651
$694$	15.4767	0.587489
$695$	11.3038	0.428779
$696$	9.82711	0.372495
$697$	−2.83161	−0.107255
$698$	−22.4858	−0.851101
$699$	−9.62756	−0.364148
$700$	−3.46569	−0.130991
$701$	−3.63337	−0.137231	−0.0686153	−	0.997643i	$-0.521858\pi$
$701$	−3.63337	−0.137231	−0.0686153	+	0.997643i	$0.521858\pi$
$702$	4.56998	0.172483
$703$	4.10499	0.154823
$704$	1.00000	0.0376889
$705$	−3.47673	−0.130941
$706$	11.2571	0.423668
$707$	−16.0221	−0.602572
$708$	14.4081	0.541490
$709$	15.2461	0.572579	0.286290	−	0.958143i	$-0.407578\pi$
$709$	15.2461	0.572579	0.286290	+	0.958143i	$0.407578\pi$
$710$	2.93139	0.110013
$711$	14.0998	0.528783
$712$	3.79143	0.142090
$713$	22.9917	0.861046
$714$	3.46569	0.129700
$715$	4.56998	0.170907
$716$	−6.56998	−0.245532
$717$	−9.68529	−0.361704
$718$	−3.60494	−0.134535
$719$	36.9937	1.37963	0.689816	−	0.723984i	$-0.257691\pi$
$719$	36.9937	1.37963	0.689816	+	0.723984i	$0.257691\pi$
$720$	−1.00000	−0.0372678
$721$	−59.4401	−2.21366
$722$	−15.9781	−0.594643
$723$	25.2287	0.938265
$724$	0.558943	0.0207729
$725$	−9.82711	−0.364970
$726$	−1.00000	−0.0371135
$727$	−19.8271	−0.735347	−0.367673	−	0.929955i	$-0.619846\pi$
$727$	−19.8271	−0.735347	−0.367673	+	0.929955i	$0.619846\pi$
$728$	15.8381	0.587000
$729$	1.00000	0.0370370
$730$	−7.13995	−0.264262
$731$	6.03567	0.223237
$732$	1.63859	0.0605640
$733$	13.8161	0.510308	0.255154	−	0.966900i	$-0.417874\pi$
$733$	13.8161	0.510308	0.255154	+	0.966900i	$0.417874\pi$
$734$	−6.07771	−0.224332
$735$	5.01103	0.184835
$736$	6.63408	0.244535
$737$	1.73836	0.0640335
$738$	−2.83161	−0.104233
$739$	−26.3330	−0.968674	−0.484337	−	0.874881i	$-0.660939\pi$
$739$	−26.3330	−0.968674	−0.484337	+	0.874881i	$0.660939\pi$
$740$	2.36141	0.0868072
$741$	−7.94428	−0.291840
$742$	−9.81350	−0.360265
$743$	−1.24610	−0.0457148	−0.0228574	−	0.999739i	$-0.507276\pi$
$743$	−1.24610	−0.0457148	−0.0228574	+	0.999739i	$0.507276\pi$
$744$	−3.46569	−0.127059
$745$	−17.0065	−0.623071
$746$	−0.953455	−0.0349085
$747$	13.5014	0.493989
$748$	1.00000	0.0365636
$749$	3.10428	0.113428
$750$	1.00000	0.0365148
$751$	35.6809	1.30201	0.651007	−	0.759072i	$-0.274347\pi$
$751$	35.6809	1.30201	0.651007	+	0.759072i	$0.274347\pi$
$752$	−3.47673	−0.126783
$753$	18.0246	0.656854
$754$	44.9096	1.63551
$755$	−4.36141	−0.158728
$756$	3.46569	0.126046
$757$	−19.2754	−0.700576	−0.350288	−	0.936642i	$-0.613916\pi$
$757$	−19.2754	−0.700576	−0.350288	+	0.936642i	$0.613916\pi$
$758$	8.25527	0.299845
$759$	−6.63408	−0.240802
$760$	1.73836	0.0630571
$761$	18.6770	0.677040	0.338520	−	0.940959i	$-0.390074\pi$
$761$	18.6770	0.677040	0.338520	+	0.940959i	$0.390074\pi$
$762$	−3.45466	−0.125149
$763$	−27.8874	−1.00959
$764$	26.6524	0.964248
$765$	−1.00000	−0.0361551
$766$	−33.3395	−1.20461
$767$	65.8447	2.37752
$768$	−1.00000	−0.0360844
$769$	−39.9562	−1.44086	−0.720428	−	0.693529i	$-0.756055\pi$
$769$	−39.9562	−1.44086	−0.720428	+	0.693529i	$0.756055\pi$
$770$	3.46569	0.124895
$771$	−16.5810	−0.597150
$772$	−3.13995	−0.113009
$773$	19.2864	0.693685	0.346842	−	0.937923i	$-0.387254\pi$
$773$	19.2864	0.693685	0.346842	+	0.937923i	$0.387254\pi$
$774$	6.03567	0.216948
$775$	3.46569	0.124491
$776$	6.29731	0.226060
$777$	−8.18393	−0.293597
$778$	26.0934	0.935494
$779$	4.92237	0.176362
$780$	−4.56998	−0.163631
$781$	−2.93139	−0.104893
$782$	6.63408	0.237234
$783$	9.82711	0.351192
$784$	5.01103	0.178965
$785$	−16.0998	−0.574626
$786$	13.5014	0.481578
$787$	−36.4107	−1.29790	−0.648950	−	0.760831i	$-0.724792\pi$
$787$	−36.4107	−1.29790	−0.648950	+	0.760831i	$0.724792\pi$
$788$	9.09325	0.323934
$789$	8.18852	0.291519
$790$	−14.0998	−0.501647
$791$	−29.8848	−1.06258
$792$	1.00000	0.0355335
$793$	7.48831	0.265918
$794$	−2.19955	−0.0780591
$795$	2.83161	0.100427
$796$	−8.36141	−0.296362
$797$	−29.6232	−1.04931	−0.524654	−	0.851316i	$-0.675805\pi$
$797$	−29.6232	−1.04931	−0.524654	+	0.851316i	$0.675805\pi$
$798$	−6.02464	−0.213270
$799$	−3.47673	−0.122998
$800$	1.00000	0.0353553
$801$	3.79143	0.133964
$802$	−6.21058	−0.219303
$803$	7.13995	0.251963
$804$	−1.73836	−0.0613074
$805$	22.9917	0.810351
$806$	−15.8381	−0.557875
$807$	−9.83814	−0.346319
$808$	4.62305	0.162638
$809$	−20.4055	−0.717418	−0.358709	−	0.933449i	$-0.616783\pi$
$809$	−20.4055	−0.717418	−0.358709	+	0.933449i	$0.616783\pi$
$810$	−1.00000	−0.0351364
$811$	16.0934	0.565116	0.282558	−	0.959250i	$-0.408817\pi$
$811$	16.0934	0.565116	0.282558	+	0.959250i	$0.408817\pi$
$812$	34.0577	1.19519
$813$	18.0357	0.632539
$814$	−2.36141	−0.0827674
$815$	12.2442	0.428897
$816$	−1.00000	−0.0350070
$817$	−10.4922	−0.367075
$818$	−16.4081	−0.573696
$819$	15.8381	0.553429
$820$	2.83161	0.0988842
$821$	−29.3259	−1.02348	−0.511740	−	0.859140i	$-0.670999\pi$
$821$	−29.3259	−1.02348	−0.511740	+	0.859140i	$0.670999\pi$
$822$	−10.5343	−0.367426
$823$	51.6168	1.79925	0.899624	−	0.436666i	$-0.143841\pi$
$823$	51.6168	1.79925	0.899624	+	0.436666i	$0.143841\pi$
$824$	17.1510	0.597483
$825$	−1.00000	−0.0348155
$826$	49.9341	1.73743
$827$	−9.85819	−0.342803	−0.171401	−	0.985201i	$-0.554829\pi$
$827$	−9.85819	−0.342803	−0.171401	+	0.985201i	$0.554829\pi$
$828$	6.63408	0.230550
$829$	−12.2242	−0.424564	−0.212282	−	0.977208i	$-0.568089\pi$
$829$	−12.2242	−0.424564	−0.212282	+	0.977208i	$0.568089\pi$
$830$	−13.5014	−0.468639
$831$	13.0596	0.453032
$832$	−4.56998	−0.158435
$833$	5.01103	0.173622
$834$	11.3038	0.391420
$835$	−16.0713	−0.556172
$836$	−1.73836	−0.0601226
$837$	−3.46569	−0.119792
$838$	−1.83612	−0.0634277
$839$	−12.9625	−0.447514	−0.223757	−	0.974645i	$-0.571832\pi$
$839$	−12.9625	−0.447514	−0.223757	+	0.974645i	$0.571832\pi$
$840$	−3.46569	−0.119578
$841$	67.5720	2.33007
$842$	25.9095	0.892900
$843$	−18.2442	−0.628365
$844$	−15.8492	−0.545551
$845$	−7.88468	−0.271241
$846$	−3.47673	−0.119532
$847$	−3.46569	−0.119083
$848$	2.83161	0.0972380
$849$	17.7346	0.608649
$850$	1.00000	0.0342997
$851$	−15.6658	−0.537017
$852$	2.93139	0.100428
$853$	53.0294	1.81569	0.907846	−	0.419304i	$-0.137726\pi$
$853$	53.0294	1.81569	0.907846	+	0.419304i	$0.137726\pi$
$854$	5.67885	0.194326
$855$	1.73836	0.0594508
$856$	−0.895717	−0.0306150
$857$	−27.2223	−0.929897	−0.464948	−	0.885338i	$-0.653927\pi$
$857$	−27.2223	−0.929897	−0.464948	+	0.885338i	$0.653927\pi$
$858$	4.56998	0.156016
$859$	25.8894	0.883336	0.441668	−	0.897179i	$-0.354387\pi$
$859$	25.8894	0.883336	0.441668	+	0.897179i	$0.354387\pi$
$860$	−6.03567	−0.205815
$861$	−9.81350	−0.334443
$862$	29.2754	0.997124
$863$	−6.95345	−0.236698	−0.118349	−	0.992972i	$-0.537760\pi$
$863$	−6.95345	−0.236698	−0.118349	+	0.992972i	$0.537760\pi$
$864$	−1.00000	−0.0340207
$865$	−2.88468	−0.0980822
$866$	2.12821	0.0723195
$867$	−1.00000	−0.0339618
$868$	−12.0110	−0.407681
$869$	14.0998	0.478302
$870$	−9.82711	−0.333170
$871$	−7.94428	−0.269182
$872$	8.04670	0.272496
$873$	6.29731	0.213132
$874$	−11.5324	−0.390091
$875$	3.46569	0.117162
$876$	−7.13995	−0.241237
$877$	17.3038	0.584309	0.292154	−	0.956371i	$-0.405628\pi$
$877$	17.3038	0.584309	0.292154	+	0.956371i	$0.405628\pi$
$878$	−15.0622	−0.508326
$879$	−29.4320	−0.992718
$880$	−1.00000	−0.0337100
$881$	−9.08222	−0.305988	−0.152994	−	0.988227i	$-0.548891\pi$
$881$	−9.08222	−0.305988	−0.152994	+	0.988227i	$0.548891\pi$
$882$	5.01103	0.168730
$883$	16.4858	0.554792	0.277396	−	0.960756i	$-0.410529\pi$
$883$	16.4858	0.554792	0.277396	+	0.960756i	$0.410529\pi$
$884$	−4.56998	−0.153705
$885$	−14.4081	−0.484323
$886$	−6.47222	−0.217438
$887$	−32.1996	−1.08116	−0.540578	−	0.841294i	$-0.681794\pi$
$887$	−32.1996	−1.08116	−0.540578	+	0.841294i	$0.681794\pi$
$888$	2.36141	0.0792438
$889$	−11.9728	−0.401555
$890$	−3.79143	−0.127089
$891$	1.00000	0.0335013
$892$	13.6743	0.457848
$893$	6.04382	0.202249
$894$	−17.0065	−0.568783
$895$	6.56998	0.219610
$896$	−3.46569	−0.115781
$897$	30.3176	1.01228
$898$	16.2909	0.543636
$899$	−34.0577	−1.13589
$900$	1.00000	0.0333333
$901$	2.83161	0.0943347
$902$	−2.83161	−0.0942824
$903$	20.9178	0.696100
$904$	8.62305	0.286798
$905$	−0.558943	−0.0185799
$906$	−4.36141	−0.144898
$907$	8.44379	0.280371	0.140186	−	0.990125i	$-0.455230\pi$
$907$	8.44379	0.280371	0.140186	+	0.990125i	$0.455230\pi$
$908$	−21.0953	−0.700071
$909$	4.62305	0.153337
$910$	−15.8381	−0.525029
$911$	38.6790	1.28149	0.640746	−	0.767753i	$-0.278625\pi$
$911$	38.6790	1.28149	0.640746	+	0.767753i	$0.278625\pi$
$912$	1.73836	0.0575630
$913$	13.5014	0.446830
$914$	0.0246365	0.000814903 0
$915$	−1.63859	−0.0541701
$916$	27.5727	0.911028
$917$	46.7916	1.54519
$918$	−1.00000	−0.0330049
$919$	25.9800	0.857000	0.428500	−	0.903542i	$-0.359042\pi$
$919$	25.9800	0.857000	0.428500	+	0.903542i	$0.359042\pi$
$920$	−6.63408	−0.218719
$921$	−16.1996	−0.533793
$922$	9.29660	0.306167
$923$	13.3964	0.440947
$924$	3.46569	0.114013
$925$	−2.36141	−0.0776427
$926$	18.5479	0.609522
$927$	17.1510	0.563312
$928$	−9.82711	−0.322591
$929$	8.76494	0.287568	0.143784	−	0.989609i	$-0.454073\pi$
$929$	8.76494	0.287568	0.143784	+	0.989609i	$0.454073\pi$
$930$	3.46569	0.113645
$931$	−8.71100	−0.285491
$932$	9.62756	0.315361
$933$	7.47673	0.244777
$934$	−25.1025	−0.821379
$935$	−1.00000	−0.0327035
$936$	−4.56998	−0.149374
$937$	0.0246365	0.000804839 0	0.000402420	−	1.00000i	$-0.499872\pi$
$937$	0.0246365	0.000804839 0	0.000402420		1.00000i	$0.499872\pi$
$938$	−6.02464	−0.196711
$939$	−22.3194	−0.728365
$940$	3.47673	0.113398
$941$	38.7101	1.26191	0.630956	−	0.775818i	$-0.282663\pi$
$941$	38.7101	1.26191	0.630956	+	0.775818i	$0.282663\pi$
$942$	−16.0998	−0.524559
$943$	−18.7851	−0.611729
$944$	−14.4081	−0.468944
$945$	−3.46569	−0.112739
$946$	6.03567	0.196237
$947$	−19.6542	−0.638676	−0.319338	−	0.947641i	$-0.603461\pi$
$947$	−19.6542	−0.638676	−0.319338	+	0.947641i	$0.603461\pi$
$948$	−14.0998	−0.457939
$949$	−32.6294	−1.05920
$950$	−1.73836	−0.0564000
$951$	−16.2352	−0.526463
$952$	−3.46569	−0.112324
$953$	−16.1685	−0.523748	−0.261874	−	0.965102i	$-0.584340\pi$
$953$	−16.1685	−0.523748	−0.261874	+	0.965102i	$0.584340\pi$
$954$	2.83161	0.0916768
$955$	−26.6524	−0.862450
$956$	9.68529	0.313245
$957$	9.82711	0.317665
$958$	−18.7275	−0.605058
$959$	−36.5087	−1.17893
$960$	1.00000	0.0322749
$961$	−18.9890	−0.612547
$962$	10.7916	0.347935
$963$	−0.895717	−0.0288641
$964$	−25.2287	−0.812562
$965$	3.13995	0.101079
$966$	22.9917	0.739746
$967$	−11.6049	−0.373190	−0.186595	−	0.982437i	$-0.559745\pi$
$967$	−11.6049	−0.373190	−0.186595	+	0.982437i	$0.559745\pi$
$968$	1.00000	0.0321412
$969$	1.73836	0.0558443
$970$	−6.29731	−0.202194
$971$	−54.1180	−1.73673	−0.868365	−	0.495925i	$-0.834829\pi$
$971$	−54.1180	−1.73673	−0.868365	+	0.495925i	$0.834829\pi$
$972$	−1.00000	−0.0320750
$973$	39.1756	1.25591
$974$	−20.2022	−0.647320
$975$	4.56998	0.146356
$976$	−1.63859	−0.0524499
$977$	0.130779	0.00418399	0.00209199	−	0.999998i	$-0.499334\pi$
$977$	0.130779	0.00418399	0.00209199	+	0.999998i	$0.499334\pi$
$978$	12.2442	0.391527
$979$	3.79143	0.121175
$980$	−5.01103	−0.160072
$981$	8.04670	0.256911
$982$	−8.23700	−0.262853
$983$	33.9048	1.08140	0.540698	−	0.841217i	$-0.318160\pi$
$983$	33.9048	1.08140	0.540698	+	0.841217i	$0.318160\pi$
$984$	2.83161	0.0902685
$985$	−9.09325	−0.289735
$986$	−9.82711	−0.312959
$987$	−12.0493	−0.383533
$988$	7.94428	0.252741
$989$	40.0411	1.27323
$990$	−1.00000	−0.0317821
$991$	23.6432	0.751050	0.375525	−	0.926812i	$-0.377462\pi$
$991$	23.6432	0.751050	0.375525	+	0.926812i	$0.377462\pi$
$992$	3.46569	0.110036
$993$	6.16388	0.195605
$994$	10.1593	0.322233
$995$	8.36141	0.265075
$996$	−13.5014	−0.427807
$997$	−57.3531	−1.81639	−0.908196	−	0.418546i	$-0.862540\pi$
$997$	−57.3531	−1.81639	−0.908196	+	0.418546i	$0.862540\pi$
$998$	−8.41713	−0.266440
$999$	2.36141	0.0747117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cg.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cg.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.46569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.46569 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.56998 q^{13} -3.46569 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.73836 q^{19} -1.00000 q^{20} +3.46569 q^{21} +1.00000 q^{22} +6.63408 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.56998 q^{26} -1.00000 q^{27} -3.46569 q^{28} -9.82711 q^{29} +1.00000 q^{30} +3.46569 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +3.46569 q^{35} +1.00000 q^{36} -2.36141 q^{37} -1.73836 q^{38} +4.56998 q^{39} -1.00000 q^{40} -2.83161 q^{41} +3.46569 q^{42} +6.03567 q^{43} +1.00000 q^{44} -1.00000 q^{45} +6.63408 q^{46} -3.47673 q^{47} -1.00000 q^{48} +5.01103 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.56998 q^{52} +2.83161 q^{53} -1.00000 q^{54} -1.00000 q^{55} -3.46569 q^{56} +1.73836 q^{57} -9.82711 q^{58} -14.4081 q^{59} +1.00000 q^{60} -1.63859 q^{61} +3.46569 q^{62} -3.46569 q^{63} +1.00000 q^{64} +4.56998 q^{65} -1.00000 q^{66} +1.73836 q^{67} +1.00000 q^{68} -6.63408 q^{69} +3.46569 q^{70} -2.93139 q^{71} +1.00000 q^{72} +7.13995 q^{73} -2.36141 q^{74} -1.00000 q^{75} -1.73836 q^{76} -3.46569 q^{77} +4.56998 q^{78} +14.0998 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.83161 q^{82} +13.5014 q^{83} +3.46569 q^{84} -1.00000 q^{85} +6.03567 q^{86} +9.82711 q^{87} +1.00000 q^{88} +3.79143 q^{89} -1.00000 q^{90} +15.8381 q^{91} +6.63408 q^{92} -3.46569 q^{93} -3.47673 q^{94} +1.73836 q^{95} -1.00000 q^{96} +6.29731 q^{97} +5.01103 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more