LMFDB - Embedded newform 5586.2.a.br.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.58579 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.58579 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.58579 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.82843 q^{13} +1.58579 q^{15} +1.00000 q^{16} +4.24264 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.58579 q^{20} -1.00000 q^{22} +3.41421 q^{23} +1.00000 q^{24} -2.48528 q^{25} -2.82843 q^{26} +1.00000 q^{27} +2.17157 q^{29} +1.58579 q^{30} +10.6569 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.24264 q^{34} +1.00000 q^{36} +0.242641 q^{37} -1.00000 q^{38} -2.82843 q^{39} +1.58579 q^{40} +0.585786 q^{41} +6.24264 q^{43} -1.00000 q^{44} +1.58579 q^{45} +3.41421 q^{46} -3.17157 q^{47} +1.00000 q^{48} -2.48528 q^{50} +4.24264 q^{51} -2.82843 q^{52} +1.82843 q^{53} +1.00000 q^{54} -1.58579 q^{55} -1.00000 q^{57} +2.17157 q^{58} -6.07107 q^{59} +1.58579 q^{60} +4.82843 q^{61} +10.6569 q^{62} +1.00000 q^{64} -4.48528 q^{65} -1.00000 q^{66} -2.00000 q^{67} +4.24264 q^{68} +3.41421 q^{69} -7.89949 q^{71} +1.00000 q^{72} +14.8284 q^{73} +0.242641 q^{74} -2.48528 q^{75} -1.00000 q^{76} -2.82843 q^{78} -0.171573 q^{79} +1.58579 q^{80} +1.00000 q^{81} +0.585786 q^{82} +17.1421 q^{83} +6.72792 q^{85} +6.24264 q^{86} +2.17157 q^{87} -1.00000 q^{88} -3.75736 q^{89} +1.58579 q^{90} +3.41421 q^{92} +10.6569 q^{93} -3.17157 q^{94} -1.58579 q^{95} +1.00000 q^{96} +5.58579 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 6 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{15} + 2 q^{16} + 2 q^{18} - 2 q^{19} + 6 q^{20} - 2 q^{22} + 4 q^{23} + 2 q^{24} + 12 q^{25} + 2 q^{27} + 10 q^{29} + 6 q^{30} + 10 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{40} + 4 q^{41} + 4 q^{43} - 2 q^{44} + 6 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 12 q^{50} - 2 q^{53} + 2 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} + 2 q^{59} + 6 q^{60} + 4 q^{61} + 10 q^{62} + 2 q^{64} + 8 q^{65} - 2 q^{66} - 4 q^{67} + 4 q^{69} + 4 q^{71} + 2 q^{72} + 24 q^{73} - 8 q^{74} + 12 q^{75} - 2 q^{76} - 6 q^{79} + 6 q^{80} + 2 q^{81} + 4 q^{82} + 6 q^{83} - 12 q^{85} + 4 q^{86} + 10 q^{87} - 2 q^{88} - 16 q^{89} + 6 q^{90} + 4 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} + 2 q^{96} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 6 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^15 + 2 * q^16 + 2 * q^18 - 2 * q^19 + 6 * q^20 - 2 * q^22 + 4 * q^23 + 2 * q^24 + 12 * q^25 + 2 * q^27 + 10 * q^29 + 6 * q^30 + 10 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^36 - 8 * q^37 - 2 * q^38 + 6 * q^40 + 4 * q^41 + 4 * q^43 - 2 * q^44 + 6 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 12 * q^50 - 2 * q^53 + 2 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 + 2 * q^59 + 6 * q^60 + 4 * q^61 + 10 * q^62 + 2 * q^64 + 8 * q^65 - 2 * q^66 - 4 * q^67 + 4 * q^69 + 4 * q^71 + 2 * q^72 + 24 * q^73 - 8 * q^74 + 12 * q^75 - 2 * q^76 - 6 * q^79 + 6 * q^80 + 2 * q^81 + 4 * q^82 + 6 * q^83 - 12 * q^85 + 4 * q^86 + 10 * q^87 - 2 * q^88 - 16 * q^89 + 6 * q^90 + 4 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 + 2 * q^96 + 14 * q^97 - 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
$5$	1.58579	0.709185	0.354593	−	0.935021i	$-0.384620\pi$
$5$	1.58579	0.709185	0.354593	+	0.935021i	$0.384620\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.58579	0.501470
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	1.00000	0.288675
$13$	−2.82843	−0.784465	−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843	−0.784465	−0.392232	+	0.919866i	$0.628297\pi$
$14$	0	0
$15$	1.58579	0.409448
$16$	1.00000	0.250000
$17$	4.24264	1.02899	0.514496	−	0.857493i	$-0.327979\pi$
$17$	4.24264	1.02899	0.514496	+	0.857493i	$0.327979\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.58579	0.354593
$21$	0	0
$22$	−1.00000	−0.213201
$23$	3.41421	0.711913	0.355956	−	0.934503i	$-0.384155\pi$
$23$	3.41421	0.711913	0.355956	+	0.934503i	$0.384155\pi$
$24$	1.00000	0.204124
$25$	−2.48528	−0.497056
$26$	−2.82843	−0.554700
$27$	1.00000	0.192450
$28$	0	0
$29$	2.17157	0.403251	0.201625	−	0.979463i	$-0.435378\pi$
$29$	2.17157	0.403251	0.201625	+	0.979463i	$0.435378\pi$
$30$	1.58579	0.289524
$31$	10.6569	1.91403	0.957014	−	0.290043i	$-0.0936695\pi$
$31$	10.6569	1.91403	0.957014	+	0.290043i	$0.0936695\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	4.24264	0.727607
$35$	0	0
$36$	1.00000	0.166667
$37$	0.242641	0.0398899	0.0199449	−	0.999801i	$-0.493651\pi$
$37$	0.242641	0.0398899	0.0199449	+	0.999801i	$0.493651\pi$
$38$	−1.00000	−0.162221
$39$	−2.82843	−0.452911
$40$	1.58579	0.250735
$41$	0.585786	0.0914845	0.0457422	−	0.998953i	$-0.485435\pi$
$41$	0.585786	0.0914845	0.0457422	+	0.998953i	$0.485435\pi$
$42$	0	0
$43$	6.24264	0.951994	0.475997	−	0.879447i	$-0.342087\pi$
$43$	6.24264	0.951994	0.475997	+	0.879447i	$0.342087\pi$
$44$	−1.00000	−0.150756
$45$	1.58579	0.236395
$46$	3.41421	0.503398
$47$	−3.17157	−0.462621	−0.231311	−	0.972880i	$-0.574301\pi$
$47$	−3.17157	−0.462621	−0.231311	+	0.972880i	$0.574301\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−2.48528	−0.351472
$51$	4.24264	0.594089
$52$	−2.82843	−0.392232
$53$	1.82843	0.251154	0.125577	−	0.992084i	$-0.459922\pi$
$53$	1.82843	0.251154	0.125577	+	0.992084i	$0.459922\pi$
$54$	1.00000	0.136083
$55$	−1.58579	−0.213827
$56$	0	0
$57$	−1.00000	−0.132453
$58$	2.17157	0.285141
$59$	−6.07107	−0.790386	−0.395193	−	0.918598i	$-0.629322\pi$
$59$	−6.07107	−0.790386	−0.395193	+	0.918598i	$0.629322\pi$
$60$	1.58579	0.204724
$61$	4.82843	0.618217	0.309108	−	0.951027i	$-0.399969\pi$
$61$	4.82843	0.618217	0.309108	+	0.951027i	$0.399969\pi$
$62$	10.6569	1.35342
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.48528	−0.556331
$66$	−1.00000	−0.123091
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	4.24264	0.514496
$69$	3.41421	0.411023
$70$	0	0
$71$	−7.89949	−0.937498	−0.468749	−	0.883332i	$-0.655295\pi$
$71$	−7.89949	−0.937498	−0.468749	+	0.883332i	$0.655295\pi$
$72$	1.00000	0.117851
$73$	14.8284	1.73554	0.867768	−	0.496969i	$-0.165554\pi$
$73$	14.8284	1.73554	0.867768	+	0.496969i	$0.165554\pi$
$74$	0.242641	0.0282064
$75$	−2.48528	−0.286976
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−2.82843	−0.320256
$79$	−0.171573	−0.0193035	−0.00965173	−	0.999953i	$-0.503072\pi$
$79$	−0.171573	−0.0193035	−0.00965173	+	0.999953i	$0.503072\pi$
$80$	1.58579	0.177296
$81$	1.00000	0.111111
$82$	0.585786	0.0646893
$83$	17.1421	1.88159	0.940797	−	0.338971i	$-0.110079\pi$
$83$	17.1421	1.88159	0.940797	+	0.338971i	$0.110079\pi$
$84$	0	0
$85$	6.72792	0.729746
$86$	6.24264	0.673161
$87$	2.17157	0.232817
$88$	−1.00000	−0.106600
$89$	−3.75736	−0.398279	−0.199140	−	0.979971i	$-0.563815\pi$
$89$	−3.75736	−0.398279	−0.199140	+	0.979971i	$0.563815\pi$
$90$	1.58579	0.167157
$91$	0	0
$92$	3.41421	0.355956
$93$	10.6569	1.10506
$94$	−3.17157	−0.327123
$95$	−1.58579	−0.162698
$96$	1.00000	0.102062
$97$	5.58579	0.567151	0.283575	−	0.958950i	$-0.408479\pi$
$97$	5.58579	0.567151	0.283575	+	0.958950i	$0.408479\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−2.48528	−0.248528
$101$	−14.9706	−1.48963	−0.744813	−	0.667273i	$-0.767461\pi$
$101$	−14.9706	−1.48963	−0.744813	+	0.667273i	$0.767461\pi$
$102$	4.24264	0.420084
$103$	18.4853	1.82141	0.910704	−	0.413059i	$-0.135540\pi$
$103$	18.4853	1.82141	0.910704	+	0.413059i	$0.135540\pi$
$104$	−2.82843	−0.277350
$105$	0	0
$106$	1.82843	0.177593
$107$	11.7279	1.13378	0.566891	−	0.823793i	$-0.308146\pi$
$107$	11.7279	1.13378	0.566891	+	0.823793i	$0.308146\pi$
$108$	1.00000	0.0962250
$109$	1.75736	0.168324	0.0841622	−	0.996452i	$-0.473179\pi$
$109$	1.75736	0.168324	0.0841622	+	0.996452i	$0.473179\pi$
$110$	−1.58579	−0.151199
$111$	0.242641	0.0230304
$112$	0	0
$113$	10.2426	0.963547	0.481773	−	0.876296i	$-0.339993\pi$
$113$	10.2426	0.963547	0.481773	+	0.876296i	$0.339993\pi$
$114$	−1.00000	−0.0936586
$115$	5.41421	0.504878
$116$	2.17157	0.201625
$117$	−2.82843	−0.261488
$118$	−6.07107	−0.558887
$119$	0	0
$120$	1.58579	0.144762
$121$	−10.0000	−0.909091
$122$	4.82843	0.437145
$123$	0.585786	0.0528186
$124$	10.6569	0.957014
$125$	−11.8701	−1.06169
$126$	0	0
$127$	−5.82843	−0.517189	−0.258595	−	0.965986i	$-0.583259\pi$
$127$	−5.82843	−0.517189	−0.258595	+	0.965986i	$0.583259\pi$
$128$	1.00000	0.0883883
$129$	6.24264	0.549634
$130$	−4.48528	−0.393385
$131$	−4.31371	−0.376890	−0.188445	−	0.982084i	$-0.560345\pi$
$131$	−4.31371	−0.376890	−0.188445	+	0.982084i	$0.560345\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−2.00000	−0.172774
$135$	1.58579	0.136483
$136$	4.24264	0.363803
$137$	−0.343146	−0.0293169	−0.0146585	−	0.999893i	$-0.504666\pi$
$137$	−0.343146	−0.0293169	−0.0146585	+	0.999893i	$0.504666\pi$
$138$	3.41421	0.290637
$139$	−7.89949	−0.670026	−0.335013	−	0.942213i	$-0.608741\pi$
$139$	−7.89949	−0.670026	−0.335013	+	0.942213i	$0.608741\pi$
$140$	0	0
$141$	−3.17157	−0.267095
$142$	−7.89949	−0.662911
$143$	2.82843	0.236525
$144$	1.00000	0.0833333
$145$	3.44365	0.285980
$146$	14.8284	1.22721
$147$	0	0
$148$	0.242641	0.0199449
$149$	−18.4853	−1.51437	−0.757187	−	0.653199i	$-0.773427\pi$
$149$	−18.4853	−1.51437	−0.757187	+	0.653199i	$0.773427\pi$
$150$	−2.48528	−0.202922
$151$	−11.3431	−0.923092	−0.461546	−	0.887116i	$-0.652705\pi$
$151$	−11.3431	−0.923092	−0.461546	+	0.887116i	$0.652705\pi$
$152$	−1.00000	−0.0811107
$153$	4.24264	0.342997
$154$	0	0
$155$	16.8995	1.35740
$156$	−2.82843	−0.226455
$157$	4.48528	0.357964	0.178982	−	0.983852i	$-0.442720\pi$
$157$	4.48528	0.357964	0.178982	+	0.983852i	$0.442720\pi$
$158$	−0.171573	−0.0136496
$159$	1.82843	0.145004
$160$	1.58579	0.125367
$161$	0	0
$162$	1.00000	0.0785674
$163$	−10.8284	−0.848148	−0.424074	−	0.905628i	$-0.639400\pi$
$163$	−10.8284	−0.848148	−0.424074	+	0.905628i	$0.639400\pi$
$164$	0.585786	0.0457422
$165$	−1.58579	−0.123453
$166$	17.1421	1.33049
$167$	6.72792	0.520622	0.260311	−	0.965525i	$-0.416175\pi$
$167$	6.72792	0.520622	0.260311	+	0.965525i	$0.416175\pi$
$168$	0	0
$169$	−5.00000	−0.384615
$170$	6.72792	0.516008
$171$	−1.00000	−0.0764719
$172$	6.24264	0.475997
$173$	15.7990	1.20117	0.600587	−	0.799559i	$-0.294933\pi$
$173$	15.7990	1.20117	0.600587	+	0.799559i	$0.294933\pi$
$174$	2.17157	0.164627
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−6.07107	−0.456329
$178$	−3.75736	−0.281626
$179$	−7.51472	−0.561676	−0.280838	−	0.959755i	$-0.590612\pi$
$179$	−7.51472	−0.561676	−0.280838	+	0.959755i	$0.590612\pi$
$180$	1.58579	0.118198
$181$	20.4853	1.52266	0.761329	−	0.648365i	$-0.224547\pi$
$181$	20.4853	1.52266	0.761329	+	0.648365i	$0.224547\pi$
$182$	0	0
$183$	4.82843	0.356928
$184$	3.41421	0.251699
$185$	0.384776	0.0282893
$186$	10.6569	0.781398
$187$	−4.24264	−0.310253
$188$	−3.17157	−0.231311
$189$	0	0
$190$	−1.58579	−0.115045
$191$	−18.1421	−1.31272	−0.656359	−	0.754448i	$-0.727904\pi$
$191$	−18.1421	−1.31272	−0.656359	+	0.754448i	$0.727904\pi$
$192$	1.00000	0.0721688
$193$	−23.7279	−1.70797	−0.853987	−	0.520295i	$-0.825822\pi$
$193$	−23.7279	−1.70797	−0.853987	+	0.520295i	$0.825822\pi$
$194$	5.58579	0.401036
$195$	−4.48528	−0.321198
$196$	0	0
$197$	1.17157	0.0834711	0.0417356	−	0.999129i	$-0.486711\pi$
$197$	1.17157	0.0834711	0.0417356	+	0.999129i	$0.486711\pi$
$198$	−1.00000	−0.0710669
$199$	−8.48528	−0.601506	−0.300753	−	0.953702i	$-0.597238\pi$
$199$	−8.48528	−0.601506	−0.300753	+	0.953702i	$0.597238\pi$
$200$	−2.48528	−0.175736
$201$	−2.00000	−0.141069
$202$	−14.9706	−1.05333
$203$	0	0
$204$	4.24264	0.297044
$205$	0.928932	0.0648794
$206$	18.4853	1.28793
$207$	3.41421	0.237304
$208$	−2.82843	−0.196116
$209$	1.00000	0.0691714
$210$	0	0
$211$	−15.0711	−1.03754	−0.518768	−	0.854915i	$-0.673609\pi$
$211$	−15.0711	−1.03754	−0.518768	+	0.854915i	$0.673609\pi$
$212$	1.82843	0.125577
$213$	−7.89949	−0.541264
$214$	11.7279	0.801704
$215$	9.89949	0.675140
$216$	1.00000	0.0680414
$217$	0	0
$218$	1.75736	0.119023
$219$	14.8284	1.00201
$220$	−1.58579	−0.106914
$221$	−12.0000	−0.807207
$222$	0.242641	0.0162850
$223$	−23.4853	−1.57269	−0.786345	−	0.617787i	$-0.788029\pi$
$223$	−23.4853	−1.57269	−0.786345	+	0.617787i	$0.788029\pi$
$224$	0	0
$225$	−2.48528	−0.165685
$226$	10.2426	0.681330
$227$	−1.10051	−0.0730431	−0.0365215	−	0.999333i	$-0.511628\pi$
$227$	−1.10051	−0.0730431	−0.0365215	+	0.999333i	$0.511628\pi$
$228$	−1.00000	−0.0662266
$229$	19.7990	1.30835	0.654177	−	0.756341i	$-0.273015\pi$
$229$	19.7990	1.30835	0.654177	+	0.756341i	$0.273015\pi$
$230$	5.41421	0.357003
$231$	0	0
$232$	2.17157	0.142571
$233$	−5.17157	−0.338801	−0.169401	−	0.985547i	$-0.554183\pi$
$233$	−5.17157	−0.338801	−0.169401	+	0.985547i	$0.554183\pi$
$234$	−2.82843	−0.184900
$235$	−5.02944	−0.328084
$236$	−6.07107	−0.395193
$237$	−0.171573	−0.0111449
$238$	0	0
$239$	28.2843	1.82956	0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843	1.82956	0.914779	+	0.403955i	$0.132365\pi$
$240$	1.58579	0.102362
$241$	−0.556349	−0.0358376	−0.0179188	−	0.999839i	$-0.505704\pi$
$241$	−0.556349	−0.0358376	−0.0179188	+	0.999839i	$0.505704\pi$
$242$	−10.0000	−0.642824
$243$	1.00000	0.0641500
$244$	4.82843	0.309108
$245$	0	0
$246$	0.585786	0.0373484
$247$	2.82843	0.179969
$248$	10.6569	0.676711
$249$	17.1421	1.08634
$250$	−11.8701	−0.750728
$251$	21.0000	1.32551	0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000	1.32551	0.662754	+	0.748837i	$0.269387\pi$
$252$	0	0
$253$	−3.41421	−0.214650
$254$	−5.82843	−0.365708
$255$	6.72792	0.421319
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	6.24264	0.388650
$259$	0	0
$260$	−4.48528	−0.278165
$261$	2.17157	0.134417
$262$	−4.31371	−0.266502
$263$	−11.5563	−0.712595	−0.356298	−	0.934373i	$-0.615961\pi$
$263$	−11.5563	−0.712595	−0.356298	+	0.934373i	$0.615961\pi$
$264$	−1.00000	−0.0615457
$265$	2.89949	0.178115
$266$	0	0
$267$	−3.75736	−0.229947
$268$	−2.00000	−0.122169
$269$	−1.00000	−0.0609711	−0.0304855	−	0.999535i	$-0.509705\pi$
$269$	−1.00000	−0.0609711	−0.0304855	+	0.999535i	$0.509705\pi$
$270$	1.58579	0.0965079
$271$	−8.89949	−0.540606	−0.270303	−	0.962775i	$-0.587124\pi$
$271$	−8.89949	−0.540606	−0.270303	+	0.962775i	$0.587124\pi$
$272$	4.24264	0.257248
$273$	0	0
$274$	−0.343146	−0.0207302
$275$	2.48528	0.149868
$276$	3.41421	0.205512
$277$	−13.7574	−0.826600	−0.413300	−	0.910595i	$-0.635624\pi$
$277$	−13.7574	−0.826600	−0.413300	+	0.910595i	$0.635624\pi$
$278$	−7.89949	−0.473780
$279$	10.6569	0.638009
$280$	0	0
$281$	−1.31371	−0.0783693	−0.0391846	−	0.999232i	$-0.512476\pi$
$281$	−1.31371	−0.0783693	−0.0391846	+	0.999232i	$0.512476\pi$
$282$	−3.17157	−0.188864
$283$	−21.5563	−1.28139	−0.640696	−	0.767795i	$-0.721354\pi$
$283$	−21.5563	−1.28139	−0.640696	+	0.767795i	$0.721354\pi$
$284$	−7.89949	−0.468749
$285$	−1.58579	−0.0939339
$286$	2.82843	0.167248
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	3.44365	0.202218
$291$	5.58579	0.327445
$292$	14.8284	0.867768
$293$	23.0000	1.34367	0.671837	−	0.740699i	$-0.265505\pi$
$293$	23.0000	1.34367	0.671837	+	0.740699i	$0.265505\pi$
$294$	0	0
$295$	−9.62742	−0.560530
$296$	0.242641	0.0141032
$297$	−1.00000	−0.0580259
$298$	−18.4853	−1.07082
$299$	−9.65685	−0.558470
$300$	−2.48528	−0.143488
$301$	0	0
$302$	−11.3431	−0.652725
$303$	−14.9706	−0.860036
$304$	−1.00000	−0.0573539
$305$	7.65685	0.438430
$306$	4.24264	0.242536
$307$	−7.41421	−0.423152	−0.211576	−	0.977362i	$-0.567860\pi$
$307$	−7.41421	−0.423152	−0.211576	+	0.977362i	$0.567860\pi$
$308$	0	0
$309$	18.4853	1.05159
$310$	16.8995	0.959827
$311$	−22.2426	−1.26126	−0.630632	−	0.776082i	$-0.717204\pi$
$311$	−22.2426	−1.26126	−0.630632	+	0.776082i	$0.717204\pi$
$312$	−2.82843	−0.160128
$313$	3.82843	0.216395	0.108198	−	0.994129i	$-0.465492\pi$
$313$	3.82843	0.216395	0.108198	+	0.994129i	$0.465492\pi$
$314$	4.48528	0.253119
$315$	0	0
$316$	−0.171573	−0.00965173
$317$	−9.48528	−0.532746	−0.266373	−	0.963870i	$-0.585825\pi$
$317$	−9.48528	−0.532746	−0.266373	+	0.963870i	$0.585825\pi$
$318$	1.82843	0.102533
$319$	−2.17157	−0.121585
$320$	1.58579	0.0886482
$321$	11.7279	0.654589
$322$	0	0
$323$	−4.24264	−0.236067
$324$	1.00000	0.0555556
$325$	7.02944	0.389923
$326$	−10.8284	−0.599731
$327$	1.75736	0.0971822
$328$	0.585786	0.0323446
$329$	0	0
$330$	−1.58579	−0.0872947
$331$	−4.38478	−0.241009	−0.120505	−	0.992713i	$-0.538451\pi$
$331$	−4.38478	−0.241009	−0.120505	+	0.992713i	$0.538451\pi$
$332$	17.1421	0.940797
$333$	0.242641	0.0132966
$334$	6.72792	0.368136
$335$	−3.17157	−0.173282
$336$	0	0
$337$	2.07107	0.112818	0.0564091	−	0.998408i	$-0.482035\pi$
$337$	2.07107	0.112818	0.0564091	+	0.998408i	$0.482035\pi$
$338$	−5.00000	−0.271964
$339$	10.2426	0.556304
$340$	6.72792	0.364873
$341$	−10.6569	−0.577101
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	6.24264	0.336581
$345$	5.41421	0.291491
$346$	15.7990	0.849359
$347$	−34.0000	−1.82522	−0.912608	−	0.408836i	$-0.865935\pi$
$347$	−34.0000	−1.82522	−0.912608	+	0.408836i	$0.865935\pi$
$348$	2.17157	0.116409
$349$	7.75736	0.415242	0.207621	−	0.978209i	$-0.433428\pi$
$349$	7.75736	0.415242	0.207621	+	0.978209i	$0.433428\pi$
$350$	0	0
$351$	−2.82843	−0.150970
$352$	−1.00000	−0.0533002
$353$	−14.1005	−0.750494	−0.375247	−	0.926925i	$-0.622442\pi$
$353$	−14.1005	−0.750494	−0.375247	+	0.926925i	$0.622442\pi$
$354$	−6.07107	−0.322674
$355$	−12.5269	−0.664859
$356$	−3.75736	−0.199140
$357$	0	0
$358$	−7.51472	−0.397165
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	1.58579	0.0835783
$361$	1.00000	0.0526316
$362$	20.4853	1.07668
$363$	−10.0000	−0.524864
$364$	0	0
$365$	23.5147	1.23082
$366$	4.82843	0.252386
$367$	−5.24264	−0.273664	−0.136832	−	0.990594i	$-0.543692\pi$
$367$	−5.24264	−0.273664	−0.136832	+	0.990594i	$0.543692\pi$
$368$	3.41421	0.177978
$369$	0.585786	0.0304948
$370$	0.384776	0.0200036
$371$	0	0
$372$	10.6569	0.552532
$373$	0.485281	0.0251269	0.0125635	−	0.999921i	$-0.496001\pi$
$373$	0.485281	0.0251269	0.0125635	+	0.999921i	$0.496001\pi$
$374$	−4.24264	−0.219382
$375$	−11.8701	−0.612967
$376$	−3.17157	−0.163561
$377$	−6.14214	−0.316336
$378$	0	0
$379$	3.31371	0.170214	0.0851069	−	0.996372i	$-0.472877\pi$
$379$	3.31371	0.170214	0.0851069	+	0.996372i	$0.472877\pi$
$380$	−1.58579	−0.0813491
$381$	−5.82843	−0.298599
$382$	−18.1421	−0.928232
$383$	−15.6569	−0.800028	−0.400014	−	0.916509i	$-0.630995\pi$
$383$	−15.6569	−0.800028	−0.400014	+	0.916509i	$0.630995\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−23.7279	−1.20772
$387$	6.24264	0.317331
$388$	5.58579	0.283575
$389$	23.1716	1.17485	0.587423	−	0.809280i	$-0.300143\pi$
$389$	23.1716	1.17485	0.587423	+	0.809280i	$0.300143\pi$
$390$	−4.48528	−0.227121
$391$	14.4853	0.732552
$392$	0	0
$393$	−4.31371	−0.217598
$394$	1.17157	0.0590230
$395$	−0.272078	−0.0136897
$396$	−1.00000	−0.0502519
$397$	10.8284	0.543463	0.271732	−	0.962373i	$-0.412404\pi$
$397$	10.8284	0.543463	0.271732	+	0.962373i	$0.412404\pi$
$398$	−8.48528	−0.425329
$399$	0	0
$400$	−2.48528	−0.124264
$401$	14.1421	0.706225	0.353112	−	0.935581i	$-0.385123\pi$
$401$	14.1421	0.706225	0.353112	+	0.935581i	$0.385123\pi$
$402$	−2.00000	−0.0997509
$403$	−30.1421	−1.50149
$404$	−14.9706	−0.744813
$405$	1.58579	0.0787984
$406$	0	0
$407$	−0.242641	−0.0120273
$408$	4.24264	0.210042
$409$	−30.8995	−1.52788	−0.763941	−	0.645286i	$-0.776738\pi$
$409$	−30.8995	−1.52788	−0.763941	+	0.645286i	$0.776738\pi$
$410$	0.928932	0.0458767
$411$	−0.343146	−0.0169261
$412$	18.4853	0.910704
$413$	0	0
$414$	3.41421	0.167799
$415$	27.1838	1.33440
$416$	−2.82843	−0.138675
$417$	−7.89949	−0.386840
$418$	1.00000	0.0489116
$419$	30.9706	1.51301	0.756505	−	0.653987i	$-0.226905\pi$
$419$	30.9706	1.51301	0.756505	+	0.653987i	$0.226905\pi$
$420$	0	0
$421$	15.1716	0.739417	0.369709	−	0.929148i	$-0.379458\pi$
$421$	15.1716	0.739417	0.369709	+	0.929148i	$0.379458\pi$
$422$	−15.0711	−0.733648
$423$	−3.17157	−0.154207
$424$	1.82843	0.0887963
$425$	−10.5442	−0.511467
$426$	−7.89949	−0.382732
$427$	0	0
$428$	11.7279	0.566891
$429$	2.82843	0.136558
$430$	9.89949	0.477396
$431$	−14.1005	−0.679197	−0.339599	−	0.940570i	$-0.610291\pi$
$431$	−14.1005	−0.679197	−0.339599	+	0.940570i	$0.610291\pi$
$432$	1.00000	0.0481125
$433$	30.8284	1.48152	0.740760	−	0.671770i	$-0.234466\pi$
$433$	30.8284	1.48152	0.740760	+	0.671770i	$0.234466\pi$
$434$	0	0
$435$	3.44365	0.165110
$436$	1.75736	0.0841622
$437$	−3.41421	−0.163324
$438$	14.8284	0.708530
$439$	−22.4558	−1.07176	−0.535879	−	0.844294i	$-0.680020\pi$
$439$	−22.4558	−1.07176	−0.535879	+	0.844294i	$0.680020\pi$
$440$	−1.58579	−0.0755994
$441$	0	0
$442$	−12.0000	−0.570782
$443$	−14.6569	−0.696368	−0.348184	−	0.937426i	$-0.613202\pi$
$443$	−14.6569	−0.696368	−0.348184	+	0.937426i	$0.613202\pi$
$444$	0.242641	0.0115152
$445$	−5.95837	−0.282454
$446$	−23.4853	−1.11206
$447$	−18.4853	−0.874324
$448$	0	0
$449$	14.2426	0.672152	0.336076	−	0.941835i	$-0.390900\pi$
$449$	14.2426	0.672152	0.336076	+	0.941835i	$0.390900\pi$
$450$	−2.48528	−0.117157
$451$	−0.585786	−0.0275836
$452$	10.2426	0.481773
$453$	−11.3431	−0.532947
$454$	−1.10051	−0.0516493
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	36.1127	1.68928	0.844640	−	0.535334i	$-0.179814\pi$
$457$	36.1127	1.68928	0.844640	+	0.535334i	$0.179814\pi$
$458$	19.7990	0.925146
$459$	4.24264	0.198030
$460$	5.41421	0.252439
$461$	17.3137	0.806380	0.403190	−	0.915116i	$-0.367901\pi$
$461$	17.3137	0.806380	0.403190	+	0.915116i	$0.367901\pi$
$462$	0	0
$463$	1.65685	0.0770005	0.0385003	−	0.999259i	$-0.487742\pi$
$463$	1.65685	0.0770005	0.0385003	+	0.999259i	$0.487742\pi$
$464$	2.17157	0.100813
$465$	16.8995	0.783695
$466$	−5.17157	−0.239568
$467$	15.1716	0.702057	0.351028	−	0.936365i	$-0.385832\pi$
$467$	15.1716	0.702057	0.351028	+	0.936365i	$0.385832\pi$
$468$	−2.82843	−0.130744
$469$	0	0
$470$	−5.02944	−0.231991
$471$	4.48528	0.206671
$472$	−6.07107	−0.279444
$473$	−6.24264	−0.287037
$474$	−0.171573	−0.00788060
$475$	2.48528	0.114033
$476$	0	0
$477$	1.82843	0.0837179
$478$	28.2843	1.29369
$479$	−1.31371	−0.0600249	−0.0300124	−	0.999550i	$-0.509555\pi$
$479$	−1.31371	−0.0600249	−0.0300124	+	0.999550i	$0.509555\pi$
$480$	1.58579	0.0723809
$481$	−0.686292	−0.0312922
$482$	−0.556349	−0.0253410
$483$	0	0
$484$	−10.0000	−0.454545
$485$	8.85786	0.402215
$486$	1.00000	0.0453609
$487$	−38.7990	−1.75815	−0.879075	−	0.476683i	$-0.841839\pi$
$487$	−38.7990	−1.75815	−0.879075	+	0.476683i	$0.841839\pi$
$488$	4.82843	0.218573
$489$	−10.8284	−0.489678
$490$	0	0
$491$	−9.14214	−0.412579	−0.206289	−	0.978491i	$-0.566139\pi$
$491$	−9.14214	−0.412579	−0.206289	+	0.978491i	$0.566139\pi$
$492$	0.585786	0.0264093
$493$	9.21320	0.414942
$494$	2.82843	0.127257
$495$	−1.58579	−0.0712758
$496$	10.6569	0.478507
$497$	0	0
$498$	17.1421	0.768157
$499$	9.31371	0.416939	0.208469	−	0.978029i	$-0.433152\pi$
$499$	9.31371	0.416939	0.208469	+	0.978029i	$0.433152\pi$
$500$	−11.8701	−0.530845
$501$	6.72792	0.300581
$502$	21.0000	0.937276
$503$	−9.75736	−0.435059	−0.217530	−	0.976054i	$-0.569800\pi$
$503$	−9.75736	−0.435059	−0.217530	+	0.976054i	$0.569800\pi$
$504$	0	0
$505$	−23.7401	−1.05642
$506$	−3.41421	−0.151780
$507$	−5.00000	−0.222058
$508$	−5.82843	−0.258595
$509$	14.3137	0.634444	0.317222	−	0.948351i	$-0.397250\pi$
$509$	14.3137	0.634444	0.317222	+	0.948351i	$0.397250\pi$
$510$	6.72792	0.297917
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−6.00000	−0.264649
$515$	29.3137	1.29172
$516$	6.24264	0.274817
$517$	3.17157	0.139486
$518$	0	0
$519$	15.7990	0.693499
$520$	−4.48528	−0.196693
$521$	−35.9411	−1.57461	−0.787305	−	0.616564i	$-0.788524\pi$
$521$	−35.9411	−1.57461	−0.787305	+	0.616564i	$0.788524\pi$
$522$	2.17157	0.0950472
$523$	−4.10051	−0.179303	−0.0896513	−	0.995973i	$-0.528575\pi$
$523$	−4.10051	−0.179303	−0.0896513	+	0.995973i	$0.528575\pi$
$524$	−4.31371	−0.188445
$525$	0	0
$526$	−11.5563	−0.503881
$527$	45.2132	1.96952
$528$	−1.00000	−0.0435194
$529$	−11.3431	−0.493180
$530$	2.89949	0.125946
$531$	−6.07107	−0.263462
$532$	0	0
$533$	−1.65685	−0.0717663
$534$	−3.75736	−0.162597
$535$	18.5980	0.804061
$536$	−2.00000	−0.0863868
$537$	−7.51472	−0.324284
$538$	−1.00000	−0.0431131
$539$	0	0
$540$	1.58579	0.0682414
$541$	−30.3848	−1.30634	−0.653172	−	0.757210i	$-0.726562\pi$
$541$	−30.3848	−1.30634	−0.653172	+	0.757210i	$0.726562\pi$
$542$	−8.89949	−0.382266
$543$	20.4853	0.879108
$544$	4.24264	0.181902
$545$	2.78680	0.119373
$546$	0	0
$547$	10.7279	0.458693	0.229346	−	0.973345i	$-0.426341\pi$
$547$	10.7279	0.458693	0.229346	+	0.973345i	$0.426341\pi$
$548$	−0.343146	−0.0146585
$549$	4.82843	0.206072
$550$	2.48528	0.105973
$551$	−2.17157	−0.0925121
$552$	3.41421	0.145319
$553$	0	0
$554$	−13.7574	−0.584494
$555$	0.384776	0.0163328
$556$	−7.89949	−0.335013
$557$	24.4142	1.03446	0.517232	−	0.855845i	$-0.326963\pi$
$557$	24.4142	1.03446	0.517232	+	0.855845i	$0.326963\pi$
$558$	10.6569	0.451141
$559$	−17.6569	−0.746805
$560$	0	0
$561$	−4.24264	−0.179124
$562$	−1.31371	−0.0554154
$563$	34.8995	1.47084	0.735419	−	0.677612i	$-0.236985\pi$
$563$	34.8995	1.47084	0.735419	+	0.677612i	$0.236985\pi$
$564$	−3.17157	−0.133547
$565$	16.2426	0.683333
$566$	−21.5563	−0.906081
$567$	0	0
$568$	−7.89949	−0.331455
$569$	−22.6274	−0.948591	−0.474295	−	0.880366i	$-0.657297\pi$
$569$	−22.6274	−0.948591	−0.474295	+	0.880366i	$0.657297\pi$
$570$	−1.58579	−0.0664213
$571$	34.5269	1.44491	0.722453	−	0.691420i	$-0.243015\pi$
$571$	34.5269	1.44491	0.722453	+	0.691420i	$0.243015\pi$
$572$	2.82843	0.118262
$573$	−18.1421	−0.757899
$574$	0	0
$575$	−8.48528	−0.353861
$576$	1.00000	0.0416667
$577$	−15.4853	−0.644661	−0.322330	−	0.946627i	$-0.604466\pi$
$577$	−15.4853	−0.644661	−0.322330	+	0.946627i	$0.604466\pi$
$578$	1.00000	0.0415945
$579$	−23.7279	−0.986099
$580$	3.44365	0.142990
$581$	0	0
$582$	5.58579	0.231538
$583$	−1.82843	−0.0757257
$584$	14.8284	0.613605
$585$	−4.48528	−0.185444
$586$	23.0000	0.950121
$587$	−23.6274	−0.975208	−0.487604	−	0.873065i	$-0.662129\pi$
$587$	−23.6274	−0.975208	−0.487604	+	0.873065i	$0.662129\pi$
$588$	0	0
$589$	−10.6569	−0.439108
$590$	−9.62742	−0.396354
$591$	1.17157	0.0481921
$592$	0.242641	0.00997247
$593$	−28.7696	−1.18142	−0.590712	−	0.806883i	$-0.701153\pi$
$593$	−28.7696	−1.18142	−0.590712	+	0.806883i	$0.701153\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−18.4853	−0.757187
$597$	−8.48528	−0.347279
$598$	−9.65685	−0.394898
$599$	38.2426	1.56255	0.781276	−	0.624186i	$-0.214569\pi$
$599$	38.2426	1.56255	0.781276	+	0.624186i	$0.214569\pi$
$600$	−2.48528	−0.101461
$601$	29.5858	1.20683	0.603415	−	0.797428i	$-0.293806\pi$
$601$	29.5858	1.20683	0.603415	+	0.797428i	$0.293806\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	−11.3431	−0.461546
$605$	−15.8579	−0.644714
$606$	−14.9706	−0.608138
$607$	16.7990	0.681850	0.340925	−	0.940091i	$-0.389260\pi$
$607$	16.7990	0.681850	0.340925	+	0.940091i	$0.389260\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	7.65685	0.310017
$611$	8.97056	0.362910
$612$	4.24264	0.171499
$613$	−25.3553	−1.02409	−0.512046	−	0.858958i	$-0.671112\pi$
$613$	−25.3553	−1.02409	−0.512046	+	0.858958i	$0.671112\pi$
$614$	−7.41421	−0.299213
$615$	0.928932	0.0374582
$616$	0	0
$617$	30.5269	1.22897	0.614484	−	0.788930i	$-0.289364\pi$
$617$	30.5269	1.22897	0.614484	+	0.788930i	$0.289364\pi$
$618$	18.4853	0.743587
$619$	5.79899	0.233081	0.116541	−	0.993186i	$-0.462820\pi$
$619$	5.79899	0.233081	0.116541	+	0.993186i	$0.462820\pi$
$620$	16.8995	0.678700
$621$	3.41421	0.137008
$622$	−22.2426	−0.891849
$623$	0	0
$624$	−2.82843	−0.113228
$625$	−6.39697	−0.255879
$626$	3.82843	0.153015
$627$	1.00000	0.0399362
$628$	4.48528	0.178982
$629$	1.02944	0.0410464
$630$	0	0
$631$	−6.55635	−0.261004	−0.130502	−	0.991448i	$-0.541659\pi$
$631$	−6.55635	−0.261004	−0.130502	+	0.991448i	$0.541659\pi$
$632$	−0.171573	−0.00682480
$633$	−15.0711	−0.599021
$634$	−9.48528	−0.376709
$635$	−9.24264	−0.366783
$636$	1.82843	0.0725019
$637$	0	0
$638$	−2.17157	−0.0859734
$639$	−7.89949	−0.312499
$640$	1.58579	0.0626837
$641$	−18.5858	−0.734094	−0.367047	−	0.930202i	$-0.619631\pi$
$641$	−18.5858	−0.734094	−0.367047	+	0.930202i	$0.619631\pi$
$642$	11.7279	0.462864
$643$	−42.2426	−1.66589	−0.832944	−	0.553358i	$-0.813346\pi$
$643$	−42.2426	−1.66589	−0.832944	+	0.553358i	$0.813346\pi$
$644$	0	0
$645$	9.89949	0.389792
$646$	−4.24264	−0.166924
$647$	−43.3553	−1.70447	−0.852237	−	0.523156i	$-0.824755\pi$
$647$	−43.3553	−1.70447	−0.852237	+	0.523156i	$0.824755\pi$
$648$	1.00000	0.0392837
$649$	6.07107	0.238310
$650$	7.02944	0.275717
$651$	0	0
$652$	−10.8284	−0.424074
$653$	−26.2132	−1.02580	−0.512901	−	0.858448i	$-0.671429\pi$
$653$	−26.2132	−1.02580	−0.512901	+	0.858448i	$0.671429\pi$
$654$	1.75736	0.0687182
$655$	−6.84062	−0.267285
$656$	0.585786	0.0228711
$657$	14.8284	0.578512
$658$	0	0
$659$	2.97056	0.115717	0.0578583	−	0.998325i	$-0.481573\pi$
$659$	2.97056	0.115717	0.0578583	+	0.998325i	$0.481573\pi$
$660$	−1.58579	−0.0617267
$661$	−32.3848	−1.25962	−0.629811	−	0.776748i	$-0.716868\pi$
$661$	−32.3848	−1.25962	−0.629811	+	0.776748i	$0.716868\pi$
$662$	−4.38478	−0.170419
$663$	−12.0000	−0.466041
$664$	17.1421	0.665244
$665$	0	0
$666$	0.242641	0.00940214
$667$	7.41421	0.287079
$668$	6.72792	0.260311
$669$	−23.4853	−0.907993
$670$	−3.17157	−0.122529
$671$	−4.82843	−0.186399
$672$	0	0
$673$	−2.27208	−0.0875822	−0.0437911	−	0.999041i	$-0.513944\pi$
$673$	−2.27208	−0.0875822	−0.0437911	+	0.999041i	$0.513944\pi$
$674$	2.07107	0.0797746
$675$	−2.48528	−0.0956585
$676$	−5.00000	−0.192308
$677$	22.3137	0.857585	0.428793	−	0.903403i	$-0.358939\pi$
$677$	22.3137	0.857585	0.428793	+	0.903403i	$0.358939\pi$
$678$	10.2426	0.393366
$679$	0	0
$680$	6.72792	0.258004
$681$	−1.10051	−0.0421714
$682$	−10.6569	−0.408072
$683$	31.2426	1.19547	0.597733	−	0.801695i	$-0.296068\pi$
$683$	31.2426	1.19547	0.597733	+	0.801695i	$0.296068\pi$
$684$	−1.00000	−0.0382360
$685$	−0.544156	−0.0207911
$686$	0	0
$687$	19.7990	0.755379
$688$	6.24264	0.237998
$689$	−5.17157	−0.197021
$690$	5.41421	0.206116
$691$	−20.4437	−0.777713	−0.388857	−	0.921298i	$-0.627130\pi$
$691$	−20.4437	−0.777713	−0.388857	+	0.921298i	$0.627130\pi$
$692$	15.7990	0.600587
$693$	0	0
$694$	−34.0000	−1.29062
$695$	−12.5269	−0.475173
$696$	2.17157	0.0823133
$697$	2.48528	0.0941367
$698$	7.75736	0.293620
$699$	−5.17157	−0.195607
$700$	0	0
$701$	41.0416	1.55012	0.775060	−	0.631887i	$-0.217719\pi$
$701$	41.0416	1.55012	0.775060	+	0.631887i	$0.217719\pi$
$702$	−2.82843	−0.106752
$703$	−0.242641	−0.00915137
$704$	−1.00000	−0.0376889
$705$	−5.02944	−0.189420
$706$	−14.1005	−0.530680
$707$	0	0
$708$	−6.07107	−0.228165
$709$	−50.3848	−1.89224	−0.946120	−	0.323816i	$-0.895034\pi$
$709$	−50.3848	−1.89224	−0.946120	+	0.323816i	$0.895034\pi$
$710$	−12.5269	−0.470127
$711$	−0.171573	−0.00643449
$712$	−3.75736	−0.140813
$713$	36.3848	1.36262
$714$	0	0
$715$	4.48528	0.167740
$716$	−7.51472	−0.280838
$717$	28.2843	1.05630
$718$	10.0000	0.373197
$719$	−8.82843	−0.329245	−0.164622	−	0.986357i	$-0.552641\pi$
$719$	−8.82843	−0.329245	−0.164622	+	0.986357i	$0.552641\pi$
$720$	1.58579	0.0590988
$721$	0	0
$722$	1.00000	0.0372161
$723$	−0.556349	−0.0206908
$724$	20.4853	0.761329
$725$	−5.39697	−0.200438
$726$	−10.0000	−0.371135
$727$	−43.7279	−1.62178	−0.810889	−	0.585199i	$-0.801016\pi$
$727$	−43.7279	−1.62178	−0.810889	+	0.585199i	$0.801016\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	23.5147	0.870319
$731$	26.4853	0.979594
$732$	4.82843	0.178464
$733$	−34.1838	−1.26261	−0.631303	−	0.775536i	$-0.717480\pi$
$733$	−34.1838	−1.26261	−0.631303	+	0.775536i	$0.717480\pi$
$734$	−5.24264	−0.193509
$735$	0	0
$736$	3.41421	0.125850
$737$	2.00000	0.0736709
$738$	0.585786	0.0215631
$739$	33.5563	1.23439	0.617195	−	0.786810i	$-0.288269\pi$
$739$	33.5563	1.23439	0.617195	+	0.786810i	$0.288269\pi$
$740$	0.384776	0.0141447
$741$	2.82843	0.103905
$742$	0	0
$743$	−48.9117	−1.79440	−0.897198	−	0.441629i	$-0.854401\pi$
$743$	−48.9117	−1.79440	−0.897198	+	0.441629i	$0.854401\pi$
$744$	10.6569	0.390699
$745$	−29.3137	−1.07397
$746$	0.485281	0.0177674
$747$	17.1421	0.627198
$748$	−4.24264	−0.155126
$749$	0	0
$750$	−11.8701	−0.433433
$751$	−16.1127	−0.587961	−0.293980	−	0.955811i	$-0.594980\pi$
$751$	−16.1127	−0.587961	−0.293980	+	0.955811i	$0.594980\pi$
$752$	−3.17157	−0.115655
$753$	21.0000	0.765283
$754$	−6.14214	−0.223683
$755$	−17.9878	−0.654643
$756$	0	0
$757$	1.21320	0.0440946	0.0220473	−	0.999757i	$-0.492982\pi$
$757$	1.21320	0.0440946	0.0220473	+	0.999757i	$0.492982\pi$
$758$	3.31371	0.120359
$759$	−3.41421	−0.123928
$760$	−1.58579	−0.0575225
$761$	−6.14214	−0.222652	−0.111326	−	0.993784i	$-0.535510\pi$
$761$	−6.14214	−0.222652	−0.111326	+	0.993784i	$0.535510\pi$
$762$	−5.82843	−0.211142
$763$	0	0
$764$	−18.1421	−0.656359
$765$	6.72792	0.243249
$766$	−15.6569	−0.565705
$767$	17.1716	0.620030
$768$	1.00000	0.0360844
$769$	−33.3431	−1.20238	−0.601192	−	0.799104i	$-0.705307\pi$
$769$	−33.3431	−1.20238	−0.601192	+	0.799104i	$0.705307\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	−23.7279	−0.853987
$773$	34.6274	1.24546	0.622731	−	0.782436i	$-0.286023\pi$
$773$	34.6274	1.24546	0.622731	+	0.782436i	$0.286023\pi$
$774$	6.24264	0.224387
$775$	−26.4853	−0.951379
$776$	5.58579	0.200518
$777$	0	0
$778$	23.1716	0.830741
$779$	−0.585786	−0.0209880
$780$	−4.48528	−0.160599
$781$	7.89949	0.282666
$782$	14.4853	0.517993
$783$	2.17157	0.0776057
$784$	0	0
$785$	7.11270	0.253863
$786$	−4.31371	−0.153865
$787$	−18.6863	−0.666094	−0.333047	−	0.942910i	$-0.608077\pi$
$787$	−18.6863	−0.666094	−0.333047	+	0.942910i	$0.608077\pi$
$788$	1.17157	0.0417356
$789$	−11.5563	−0.411417
$790$	−0.272078	−0.00968010
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−13.6569	−0.484969
$794$	10.8284	0.384286
$795$	2.89949	0.102834
$796$	−8.48528	−0.300753
$797$	9.00000	0.318796	0.159398	−	0.987214i	$-0.449045\pi$
$797$	9.00000	0.318796	0.159398	+	0.987214i	$0.449045\pi$
$798$	0	0
$799$	−13.4558	−0.476034
$800$	−2.48528	−0.0878680
$801$	−3.75736	−0.132760
$802$	14.1421	0.499376
$803$	−14.8284	−0.523284
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	−30.1421	−1.06171
$807$	−1.00000	−0.0352017
$808$	−14.9706	−0.526663
$809$	−50.8701	−1.78850	−0.894248	−	0.447572i	$-0.852289\pi$
$809$	−50.8701	−1.78850	−0.894248	+	0.447572i	$0.852289\pi$
$810$	1.58579	0.0557189
$811$	−3.55635	−0.124880	−0.0624402	−	0.998049i	$-0.519888\pi$
$811$	−3.55635	−0.124880	−0.0624402	+	0.998049i	$0.519888\pi$
$812$	0	0
$813$	−8.89949	−0.312119
$814$	−0.242641	−0.00850455
$815$	−17.1716	−0.601494
$816$	4.24264	0.148522
$817$	−6.24264	−0.218402
$818$	−30.8995	−1.08038
$819$	0	0
$820$	0.928932	0.0324397
$821$	31.1838	1.08832	0.544160	−	0.838981i	$-0.316848\pi$
$821$	31.1838	1.08832	0.544160	+	0.838981i	$0.316848\pi$
$822$	−0.343146	−0.0119686
$823$	24.2843	0.846496	0.423248	−	0.906014i	$-0.360890\pi$
$823$	24.2843	0.846496	0.423248	+	0.906014i	$0.360890\pi$
$824$	18.4853	0.643965
$825$	2.48528	0.0865264
$826$	0	0
$827$	27.7279	0.964194	0.482097	−	0.876118i	$-0.339875\pi$
$827$	27.7279	0.964194	0.482097	+	0.876118i	$0.339875\pi$
$828$	3.41421	0.118652
$829$	48.9706	1.70082	0.850409	−	0.526122i	$-0.176355\pi$
$829$	48.9706	1.70082	0.850409	+	0.526122i	$0.176355\pi$
$830$	27.1838	0.943562
$831$	−13.7574	−0.477238
$832$	−2.82843	−0.0980581
$833$	0	0
$834$	−7.89949	−0.273537
$835$	10.6690	0.369218
$836$	1.00000	0.0345857
$837$	10.6569	0.368355
$838$	30.9706	1.06986
$839$	−53.2132	−1.83712	−0.918562	−	0.395277i	$-0.870649\pi$
$839$	−53.2132	−1.83712	−0.918562	+	0.395277i	$0.870649\pi$
$840$	0	0
$841$	−24.2843	−0.837389
$842$	15.1716	0.522847
$843$	−1.31371	−0.0452465
$844$	−15.0711	−0.518768
$845$	−7.92893	−0.272764
$846$	−3.17157	−0.109041
$847$	0	0
$848$	1.82843	0.0627884
$849$	−21.5563	−0.739812
$850$	−10.5442	−0.361662
$851$	0.828427	0.0283981
$852$	−7.89949	−0.270632
$853$	−57.4975	−1.96868	−0.984338	−	0.176291i	$-0.943590\pi$
$853$	−57.4975	−1.96868	−0.984338	+	0.176291i	$0.943590\pi$
$854$	0	0
$855$	−1.58579	−0.0542328
$856$	11.7279	0.400852
$857$	18.6863	0.638312	0.319156	−	0.947702i	$-0.396601\pi$
$857$	18.6863	0.638312	0.319156	+	0.947702i	$0.396601\pi$
$858$	2.82843	0.0965609
$859$	48.4264	1.65229	0.826144	−	0.563459i	$-0.190530\pi$
$859$	48.4264	1.65229	0.826144	+	0.563459i	$0.190530\pi$
$860$	9.89949	0.337570
$861$	0	0
$862$	−14.1005	−0.480265
$863$	38.2426	1.30179	0.650897	−	0.759166i	$-0.274393\pi$
$863$	38.2426	1.30179	0.650897	+	0.759166i	$0.274393\pi$
$864$	1.00000	0.0340207
$865$	25.0538	0.851856
$866$	30.8284	1.04759
$867$	1.00000	0.0339618
$868$	0	0
$869$	0.171573	0.00582021
$870$	3.44365	0.116751
$871$	5.65685	0.191675
$872$	1.75736	0.0595117
$873$	5.58579	0.189050
$874$	−3.41421	−0.115487
$875$	0	0
$876$	14.8284	0.501006
$877$	40.7279	1.37528	0.687642	−	0.726050i	$-0.258646\pi$
$877$	40.7279	1.37528	0.687642	+	0.726050i	$0.258646\pi$
$878$	−22.4558	−0.757848
$879$	23.0000	0.775771
$880$	−1.58579	−0.0534568
$881$	23.9411	0.806597	0.403299	−	0.915068i	$-0.367864\pi$
$881$	23.9411	0.806597	0.403299	+	0.915068i	$0.367864\pi$
$882$	0	0
$883$	46.8701	1.57730	0.788652	−	0.614840i	$-0.210780\pi$
$883$	46.8701	1.57730	0.788652	+	0.614840i	$0.210780\pi$
$884$	−12.0000	−0.403604
$885$	−9.62742	−0.323622
$886$	−14.6569	−0.492407
$887$	51.0711	1.71480	0.857399	−	0.514652i	$-0.172079\pi$
$887$	51.0711	1.71480	0.857399	+	0.514652i	$0.172079\pi$
$888$	0.242641	0.00814249
$889$	0	0
$890$	−5.95837	−0.199725
$891$	−1.00000	−0.0335013
$892$	−23.4853	−0.786345
$893$	3.17157	0.106133
$894$	−18.4853	−0.618240
$895$	−11.9167	−0.398333
$896$	0	0
$897$	−9.65685	−0.322433
$898$	14.2426	0.475283
$899$	23.1421	0.771833
$900$	−2.48528	−0.0828427
$901$	7.75736	0.258435
$902$	−0.585786	−0.0195046
$903$	0	0
$904$	10.2426	0.340665
$905$	32.4853	1.07985
$906$	−11.3431	−0.376851
$907$	16.1005	0.534608	0.267304	−	0.963612i	$-0.413867\pi$
$907$	16.1005	0.534608	0.267304	+	0.963612i	$0.413867\pi$
$908$	−1.10051	−0.0365215
$909$	−14.9706	−0.496542
$910$	0	0
$911$	−28.8284	−0.955128	−0.477564	−	0.878597i	$-0.658480\pi$
$911$	−28.8284	−0.955128	−0.477564	+	0.878597i	$0.658480\pi$
$912$	−1.00000	−0.0331133
$913$	−17.1421	−0.567322
$914$	36.1127	1.19450
$915$	7.65685	0.253128
$916$	19.7990	0.654177
$917$	0	0
$918$	4.24264	0.140028
$919$	−40.3431	−1.33080	−0.665399	−	0.746488i	$-0.731738\pi$
$919$	−40.3431	−1.33080	−0.665399	+	0.746488i	$0.731738\pi$
$920$	5.41421	0.178501
$921$	−7.41421	−0.244307
$922$	17.3137	0.570197
$923$	22.3431	0.735434
$924$	0	0
$925$	−0.603030	−0.0198275
$926$	1.65685	0.0544476
$927$	18.4853	0.607136
$928$	2.17157	0.0712854
$929$	2.92893	0.0960951	0.0480476	−	0.998845i	$-0.484700\pi$
$929$	2.92893	0.0960951	0.0480476	+	0.998845i	$0.484700\pi$
$930$	16.8995	0.554156
$931$	0	0
$932$	−5.17157	−0.169401
$933$	−22.2426	−0.728191
$934$	15.1716	0.496429
$935$	−6.72792	−0.220027
$936$	−2.82843	−0.0924500
$937$	−0.857864	−0.0280252	−0.0140126	−	0.999902i	$-0.504460\pi$
$937$	−0.857864	−0.0280252	−0.0140126	+	0.999902i	$0.504460\pi$
$938$	0	0
$939$	3.82843	0.124936
$940$	−5.02944	−0.164042
$941$	26.3137	0.857802	0.428901	−	0.903351i	$-0.358901\pi$
$941$	26.3137	0.857802	0.428901	+	0.903351i	$0.358901\pi$
$942$	4.48528	0.146138
$943$	2.00000	0.0651290
$944$	−6.07107	−0.197596
$945$	0	0
$946$	−6.24264	−0.202966
$947$	−31.6569	−1.02871	−0.514355	−	0.857578i	$-0.671969\pi$
$947$	−31.6569	−1.02871	−0.514355	+	0.857578i	$0.671969\pi$
$948$	−0.171573	−0.00557243
$949$	−41.9411	−1.36147
$950$	2.48528	0.0806332
$951$	−9.48528	−0.307581
$952$	0	0
$953$	39.1716	1.26889	0.634446	−	0.772967i	$-0.281228\pi$
$953$	39.1716	1.26889	0.634446	+	0.772967i	$0.281228\pi$
$954$	1.82843	0.0591975
$955$	−28.7696	−0.930961
$956$	28.2843	0.914779
$957$	−2.17157	−0.0701970
$958$	−1.31371	−0.0424440
$959$	0	0
$960$	1.58579	0.0511810
$961$	82.5685	2.66350
$962$	−0.686292	−0.0221269
$963$	11.7279	0.377927
$964$	−0.556349	−0.0179188
$965$	−37.6274	−1.21127
$966$	0	0
$967$	−30.5563	−0.982626	−0.491313	−	0.870983i	$-0.663483\pi$
$967$	−30.5563	−0.982626	−0.491313	+	0.870983i	$0.663483\pi$
$968$	−10.0000	−0.321412
$969$	−4.24264	−0.136293
$970$	8.85786	0.284409
$971$	−37.0416	−1.18872	−0.594361	−	0.804198i	$-0.702595\pi$
$971$	−37.0416	−1.18872	−0.594361	+	0.804198i	$0.702595\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−38.7990	−1.24320
$975$	7.02944	0.225122
$976$	4.82843	0.154554
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	−10.8284	−0.346255
$979$	3.75736	0.120086
$980$	0	0
$981$	1.75736	0.0561082
$982$	−9.14214	−0.291737
$983$	−48.9706	−1.56192	−0.780959	−	0.624582i	$-0.785269\pi$
$983$	−48.9706	−1.56192	−0.780959	+	0.624582i	$0.785269\pi$
$984$	0.585786	0.0186742
$985$	1.85786	0.0591965
$986$	9.21320	0.293408
$987$	0	0
$988$	2.82843	0.0899843
$989$	21.3137	0.677737
$990$	−1.58579	−0.0503996
$991$	−11.6274	−0.369357	−0.184679	−	0.982799i	$-0.559124\pi$
$991$	−11.6274	−0.369357	−0.184679	+	0.982799i	$0.559124\pi$
$992$	10.6569	0.338355
$993$	−4.38478	−0.139147
$994$	0	0
$995$	−13.4558	−0.426579
$996$	17.1421	0.543169
$997$	−3.17157	−0.100445	−0.0502224	−	0.998738i	$-0.515993\pi$
$997$	−3.17157	−0.100445	−0.0502224	+	0.998738i	$0.515993\pi$
$998$	9.31371	0.294820
$999$	0.242641	0.00767681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.br.1.1		2
7.3	odd	6		798.2.j.h.457.1	✓	4
7.5	odd	6		798.2.j.h.571.1	yes	4
7.6	odd	2		5586.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.h.457.1	✓	4	7.3	odd	6
798.2.j.h.571.1	yes	4	7.5	odd	6
5586.2.a.bg.1.2		2	7.6	odd	2
5586.2.a.br.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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.58579 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.58579 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.58579 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.82843 q^{13} +1.58579 q^{15} +1.00000 q^{16} +4.24264 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.58579 q^{20} -1.00000 q^{22} +3.41421 q^{23} +1.00000 q^{24} -2.48528 q^{25} -2.82843 q^{26} +1.00000 q^{27} +2.17157 q^{29} +1.58579 q^{30} +10.6569 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.24264 q^{34} +1.00000 q^{36} +0.242641 q^{37} -1.00000 q^{38} -2.82843 q^{39} +1.58579 q^{40} +0.585786 q^{41} +6.24264 q^{43} -1.00000 q^{44} +1.58579 q^{45} +3.41421 q^{46} -3.17157 q^{47} +1.00000 q^{48} -2.48528 q^{50} +4.24264 q^{51} -2.82843 q^{52} +1.82843 q^{53} +1.00000 q^{54} -1.58579 q^{55} -1.00000 q^{57} +2.17157 q^{58} -6.07107 q^{59} +1.58579 q^{60} +4.82843 q^{61} +10.6569 q^{62} +1.00000 q^{64} -4.48528 q^{65} -1.00000 q^{66} -2.00000 q^{67} +4.24264 q^{68} +3.41421 q^{69} -7.89949 q^{71} +1.00000 q^{72} +14.8284 q^{73} +0.242641 q^{74} -2.48528 q^{75} -1.00000 q^{76} -2.82843 q^{78} -0.171573 q^{79} +1.58579 q^{80} +1.00000 q^{81} +0.585786 q^{82} +17.1421 q^{83} +6.72792 q^{85} +6.24264 q^{86} +2.17157 q^{87} -1.00000 q^{88} -3.75736 q^{89} +1.58579 q^{90} +3.41421 q^{92} +10.6569 q^{93} -3.17157 q^{94} -1.58579 q^{95} +1.00000 q^{96} +5.58579 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 6 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{15} + 2 q^{16} + 2 q^{18} - 2 q^{19} + 6 q^{20} - 2 q^{22} + 4 q^{23} + 2 q^{24} + 12 q^{25} + 2 q^{27} + 10 q^{29} + 6 q^{30} + 10 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{40} + 4 q^{41} + 4 q^{43} - 2 q^{44} + 6 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 12 q^{50} - 2 q^{53} + 2 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} + 2 q^{59} + 6 q^{60} + 4 q^{61} + 10 q^{62} + 2 q^{64} + 8 q^{65} - 2 q^{66} - 4 q^{67} + 4 q^{69} + 4 q^{71} + 2 q^{72} + 24 q^{73} - 8 q^{74} + 12 q^{75} - 2 q^{76} - 6 q^{79} + 6 q^{80} + 2 q^{81} + 4 q^{82} + 6 q^{83} - 12 q^{85} + 4 q^{86} + 10 q^{87} - 2 q^{88} - 16 q^{89} + 6 q^{90} + 4 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} + 2 q^{96} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 6 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^15 + 2 * q^16 + 2 * q^18 - 2 * q^19 + 6 * q^20 - 2 * q^22 + 4 * q^23 + 2 * q^24 + 12 * q^25 + 2 * q^27 + 10 * q^29 + 6 * q^30 + 10 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^36 - 8 * q^37 - 2 * q^38 + 6 * q^40 + 4 * q^41 + 4 * q^43 - 2 * q^44 + 6 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 12 * q^50 - 2 * q^53 + 2 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 + 2 * q^59 + 6 * q^60 + 4 * q^61 + 10 * q^62 + 2 * q^64 + 8 * q^65 - 2 * q^66 - 4 * q^67 + 4 * q^69 + 4 * q^71 + 2 * q^72 + 24 * q^73 - 8 * q^74 + 12 * q^75 - 2 * q^76 - 6 * q^79 + 6 * q^80 + 2 * q^81 + 4 * q^82 + 6 * q^83 - 12 * q^85 + 4 * q^86 + 10 * q^87 - 2 * q^88 - 16 * q^89 + 6 * q^90 + 4 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 + 2 * q^96 + 14 * q^97 - 2 * q^99

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