LMFDB - Embedded newform 5586.2.a.bl.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:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			$-1.73205$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.267949 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.46410 q^{13} -0.267949 q^{15} +1.00000 q^{16} +4.73205 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.267949 q^{20} -1.00000 q^{22} -2.73205 q^{23} -1.00000 q^{24} -4.92820 q^{25} +5.46410 q^{26} -1.00000 q^{27} +1.00000 q^{29} -0.267949 q^{30} -2.46410 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.73205 q^{34} +1.00000 q^{36} +6.19615 q^{37} -1.00000 q^{38} -5.46410 q^{39} +0.267949 q^{40} +5.26795 q^{41} +0.196152 q^{43} -1.00000 q^{44} +0.267949 q^{45} -2.73205 q^{46} +11.4641 q^{47} -1.00000 q^{48} -4.92820 q^{50} -4.73205 q^{51} +5.46410 q^{52} +1.53590 q^{53} -1.00000 q^{54} -0.267949 q^{55} +1.00000 q^{57} +1.00000 q^{58} -1.73205 q^{59} -0.267949 q^{60} +4.53590 q^{61} -2.46410 q^{62} +1.00000 q^{64} +1.46410 q^{65} +1.00000 q^{66} -0.928203 q^{67} +4.73205 q^{68} +2.73205 q^{69} -12.1962 q^{71} +1.00000 q^{72} +6.92820 q^{73} +6.19615 q^{74} +4.92820 q^{75} -1.00000 q^{76} -5.46410 q^{78} -11.3923 q^{79} +0.267949 q^{80} +1.00000 q^{81} +5.26795 q^{82} -3.00000 q^{83} +1.26795 q^{85} +0.196152 q^{86} -1.00000 q^{87} -1.00000 q^{88} +0.339746 q^{89} +0.267949 q^{90} -2.73205 q^{92} +2.46410 q^{93} +11.4641 q^{94} -0.267949 q^{95} -1.00000 q^{96} +5.73205 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 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 + 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{20} - 2 q^{22} - 2 q^{23} - 2 q^{24} + 4 q^{25} + 4 q^{26} - 2 q^{27} + 2 q^{29} - 4 q^{30} + 2 q^{31} + 2 q^{32} + 2 q^{33} + 6 q^{34} + 2 q^{36} + 2 q^{37} - 2 q^{38} - 4 q^{39} + 4 q^{40} + 14 q^{41} - 10 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 16 q^{47} - 2 q^{48} + 4 q^{50} - 6 q^{51} + 4 q^{52} + 10 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{57} + 2 q^{58} - 4 q^{60} + 16 q^{61} + 2 q^{62} + 2 q^{64} - 4 q^{65} + 2 q^{66} + 12 q^{67} + 6 q^{68} + 2 q^{69} - 14 q^{71} + 2 q^{72} + 2 q^{74} - 4 q^{75} - 2 q^{76} - 4 q^{78} - 2 q^{79} + 4 q^{80} + 2 q^{81} + 14 q^{82} - 6 q^{83} + 6 q^{85} - 10 q^{86} - 2 q^{87} - 2 q^{88} + 18 q^{89} + 4 q^{90} - 2 q^{92} - 2 q^{93} + 16 q^{94} - 4 q^{95} - 2 q^{96} + 8 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^15 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^20 - 2 * q^22 - 2 * q^23 - 2 * q^24 + 4 * q^25 + 4 * q^26 - 2 * q^27 + 2 * q^29 - 4 * q^30 + 2 * q^31 + 2 * q^32 + 2 * q^33 + 6 * q^34 + 2 * q^36 + 2 * q^37 - 2 * q^38 - 4 * q^39 + 4 * q^40 + 14 * q^41 - 10 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 16 * q^47 - 2 * q^48 + 4 * q^50 - 6 * q^51 + 4 * q^52 + 10 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^57 + 2 * q^58 - 4 * q^60 + 16 * q^61 + 2 * q^62 + 2 * q^64 - 4 * q^65 + 2 * q^66 + 12 * q^67 + 6 * q^68 + 2 * q^69 - 14 * q^71 + 2 * q^72 + 2 * q^74 - 4 * q^75 - 2 * q^76 - 4 * q^78 - 2 * q^79 + 4 * q^80 + 2 * q^81 + 14 * q^82 - 6 * q^83 + 6 * q^85 - 10 * q^86 - 2 * q^87 - 2 * q^88 + 18 * q^89 + 4 * q^90 - 2 * q^92 - 2 * q^93 + 16 * q^94 - 4 * q^95 - 2 * q^96 + 8 * 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
$5$	0.267949	0.119831	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	0.267949	0.119831	0.0599153	+	0.998203i	$0.480917\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.267949	0.0847330
$11$	−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
$13$	5.46410	1.51547	0.757735	−	0.652563i	$-0.226306\pi$
$13$	5.46410	1.51547	0.757735	+	0.652563i	$0.226306\pi$
$14$	0	0
$15$	−0.267949	−0.0691842
$16$	1.00000	0.250000
$17$	4.73205	1.14769	0.573845	−	0.818964i	$-0.305451\pi$
$17$	4.73205	1.14769	0.573845	+	0.818964i	$0.305451\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.267949	0.0599153
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−2.73205	−0.569672	−0.284836	−	0.958576i	$-0.591939\pi$
$23$	−2.73205	−0.569672	−0.284836	+	0.958576i	$0.591939\pi$
$24$	−1.00000	−0.204124
$25$	−4.92820	−0.985641
$26$	5.46410	1.07160
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	−0.267949	−0.0489206
$31$	−2.46410	−0.442566	−0.221283	−	0.975210i	$-0.571024\pi$
$31$	−2.46410	−0.442566	−0.221283	+	0.975210i	$0.571024\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	4.73205	0.811540
$35$	0	0
$36$	1.00000	0.166667
$37$	6.19615	1.01864	0.509321	−	0.860577i	$-0.329897\pi$
$37$	6.19615	1.01864	0.509321	+	0.860577i	$0.329897\pi$
$38$	−1.00000	−0.162221
$39$	−5.46410	−0.874957
$40$	0.267949	0.0423665
$41$	5.26795	0.822715	0.411358	−	0.911474i	$-0.365055\pi$
$41$	5.26795	0.822715	0.411358	+	0.911474i	$0.365055\pi$
$42$	0	0
$43$	0.196152	0.0299130	0.0149565	−	0.999888i	$-0.495239\pi$
$43$	0.196152	0.0299130	0.0149565	+	0.999888i	$0.495239\pi$
$44$	−1.00000	−0.150756
$45$	0.267949	0.0399435
$46$	−2.73205	−0.402819
$47$	11.4641	1.67221	0.836106	−	0.548569i	$-0.184827\pi$
$47$	11.4641	1.67221	0.836106	+	0.548569i	$0.184827\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.92820	−0.696953
$51$	−4.73205	−0.662620
$52$	5.46410	0.757735
$53$	1.53590	0.210972	0.105486	−	0.994421i	$-0.466360\pi$
$53$	1.53590	0.210972	0.105486	+	0.994421i	$0.466360\pi$
$54$	−1.00000	−0.136083
$55$	−0.267949	−0.0361303
$56$	0	0
$57$	1.00000	0.132453
$58$	1.00000	0.131306
$59$	−1.73205	−0.225494	−0.112747	−	0.993624i	$-0.535965\pi$
$59$	−1.73205	−0.225494	−0.112747	+	0.993624i	$0.535965\pi$
$60$	−0.267949	−0.0345921
$61$	4.53590	0.580762	0.290381	−	0.956911i	$-0.406218\pi$
$61$	4.53590	0.580762	0.290381	+	0.956911i	$0.406218\pi$
$62$	−2.46410	−0.312941
$63$	0	0
$64$	1.00000	0.125000
$65$	1.46410	0.181599
$66$	1.00000	0.123091
$67$	−0.928203	−0.113398	−0.0566990	−	0.998391i	$-0.518058\pi$
$67$	−0.928203	−0.113398	−0.0566990	+	0.998391i	$0.518058\pi$
$68$	4.73205	0.573845
$69$	2.73205	0.328900
$70$	0	0
$71$	−12.1962	−1.44742	−0.723708	−	0.690106i	$-0.757564\pi$
$71$	−12.1962	−1.44742	−0.723708	+	0.690106i	$0.757564\pi$
$72$	1.00000	0.117851
$73$	6.92820	0.810885	0.405442	−	0.914121i	$-0.367117\pi$
$73$	6.92820	0.810885	0.405442	+	0.914121i	$0.367117\pi$
$74$	6.19615	0.720288
$75$	4.92820	0.569060
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−5.46410	−0.618688
$79$	−11.3923	−1.28173	−0.640867	−	0.767652i	$-0.721425\pi$
$79$	−11.3923	−1.28173	−0.640867	+	0.767652i	$0.721425\pi$
$80$	0.267949	0.0299576
$81$	1.00000	0.111111
$82$	5.26795	0.581748
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	0	0
$85$	1.26795	0.137528
$86$	0.196152	0.0211517
$87$	−1.00000	−0.107211
$88$	−1.00000	−0.106600
$89$	0.339746	0.0360130	0.0180065	−	0.999838i	$-0.494268\pi$
$89$	0.339746	0.0360130	0.0180065	+	0.999838i	$0.494268\pi$
$90$	0.267949	0.0282443
$91$	0	0
$92$	−2.73205	−0.284836
$93$	2.46410	0.255515
$94$	11.4641	1.18243
$95$	−0.267949	−0.0274910
$96$	−1.00000	−0.102062
$97$	5.73205	0.582002	0.291001	−	0.956723i	$-0.406012\pi$
$97$	5.73205	0.582002	0.291001	+	0.956723i	$0.406012\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−4.92820	−0.492820
$101$	−4.92820	−0.490375	−0.245187	−	0.969476i	$-0.578849\pi$
$101$	−4.92820	−0.490375	−0.245187	+	0.969476i	$0.578849\pi$
$102$	−4.73205	−0.468543
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	5.46410	0.535799
$105$	0	0
$106$	1.53590	0.149180
$107$	−1.33975	−0.129518	−0.0647591	−	0.997901i	$-0.520628\pi$
$107$	−1.33975	−0.129518	−0.0647591	+	0.997901i	$0.520628\pi$
$108$	−1.00000	−0.0962250
$109$	10.7321	1.02794	0.513972	−	0.857807i	$-0.328174\pi$
$109$	10.7321	1.02794	0.513972	+	0.857807i	$0.328174\pi$
$110$	−0.267949	−0.0255480
$111$	−6.19615	−0.588113
$112$	0	0
$113$	−5.26795	−0.495567	−0.247783	−	0.968815i	$-0.579702\pi$
$113$	−5.26795	−0.495567	−0.247783	+	0.968815i	$0.579702\pi$
$114$	1.00000	0.0936586
$115$	−0.732051	−0.0682641
$116$	1.00000	0.0928477
$117$	5.46410	0.505156
$118$	−1.73205	−0.159448
$119$	0	0
$120$	−0.267949	−0.0244603
$121$	−10.0000	−0.909091
$122$	4.53590	0.410661
$123$	−5.26795	−0.474995
$124$	−2.46410	−0.221283
$125$	−2.66025	−0.237940
$126$	0	0
$127$	3.92820	0.348572	0.174286	−	0.984695i	$-0.444238\pi$
$127$	3.92820	0.348572	0.174286	+	0.984695i	$0.444238\pi$
$128$	1.00000	0.0883883
$129$	−0.196152	−0.0172703
$130$	1.46410	0.128410
$131$	−0.464102	−0.0405487	−0.0202744	−	0.999794i	$-0.506454\pi$
$131$	−0.464102	−0.0405487	−0.0202744	+	0.999794i	$0.506454\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	−0.928203	−0.0801845
$135$	−0.267949	−0.0230614
$136$	4.73205	0.405770
$137$	11.8564	1.01296	0.506481	−	0.862251i	$-0.330946\pi$
$137$	11.8564	1.01296	0.506481	+	0.862251i	$0.330946\pi$
$138$	2.73205	0.232568
$139$	8.19615	0.695189	0.347594	−	0.937645i	$-0.386999\pi$
$139$	8.19615	0.695189	0.347594	+	0.937645i	$0.386999\pi$
$140$	0	0
$141$	−11.4641	−0.965452
$142$	−12.1962	−1.02348
$143$	−5.46410	−0.456931
$144$	1.00000	0.0833333
$145$	0.267949	0.0222520
$146$	6.92820	0.573382
$147$	0	0
$148$	6.19615	0.509321
$149$	1.60770	0.131708	0.0658538	−	0.997829i	$-0.479023\pi$
$149$	1.60770	0.131708	0.0658538	+	0.997829i	$0.479023\pi$
$150$	4.92820	0.402386
$151$	15.3923	1.25261	0.626304	−	0.779579i	$-0.284567\pi$
$151$	15.3923	1.25261	0.626304	+	0.779579i	$0.284567\pi$
$152$	−1.00000	−0.0811107
$153$	4.73205	0.382564
$154$	0	0
$155$	−0.660254	−0.0530329
$156$	−5.46410	−0.437478
$157$	1.46410	0.116848	0.0584240	−	0.998292i	$-0.481392\pi$
$157$	1.46410	0.116848	0.0584240	+	0.998292i	$0.481392\pi$
$158$	−11.3923	−0.906323
$159$	−1.53590	−0.121805
$160$	0.267949	0.0211832
$161$	0	0
$162$	1.00000	0.0785674
$163$	12.3923	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$163$	12.3923	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$164$	5.26795	0.411358
$165$	0.267949	0.0208598
$166$	−3.00000	−0.232845
$167$	20.1962	1.56283	0.781413	−	0.624015i	$-0.214499\pi$
$167$	20.1962	1.56283	0.781413	+	0.624015i	$0.214499\pi$
$168$	0	0
$169$	16.8564	1.29665
$170$	1.26795	0.0972473
$171$	−1.00000	−0.0764719
$172$	0.196152	0.0149565
$173$	−20.7846	−1.58022	−0.790112	−	0.612962i	$-0.789978\pi$
$173$	−20.7846	−1.58022	−0.790112	+	0.612962i	$0.789978\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	1.73205	0.130189
$178$	0.339746	0.0254650
$179$	−9.46410	−0.707380	−0.353690	−	0.935363i	$-0.615073\pi$
$179$	−9.46410	−0.707380	−0.353690	+	0.935363i	$0.615073\pi$
$180$	0.267949	0.0199718
$181$	1.46410	0.108826	0.0544129	−	0.998519i	$-0.482671\pi$
$181$	1.46410	0.108826	0.0544129	+	0.998519i	$0.482671\pi$
$182$	0	0
$183$	−4.53590	−0.335303
$184$	−2.73205	−0.201409
$185$	1.66025	0.122064
$186$	2.46410	0.180677
$187$	−4.73205	−0.346042
$188$	11.4641	0.836106
$189$	0	0
$190$	−0.267949	−0.0194391
$191$	13.4641	0.974228	0.487114	−	0.873338i	$-0.338050\pi$
$191$	13.4641	0.974228	0.487114	+	0.873338i	$0.338050\pi$
$192$	−1.00000	−0.0721688
$193$	27.5885	1.98586	0.992930	−	0.118699i	$-0.0378723\pi$
$193$	27.5885	1.98586	0.992930	+	0.118699i	$0.0378723\pi$
$194$	5.73205	0.411537
$195$	−1.46410	−0.104846
$196$	0	0
$197$	16.7846	1.19585	0.597927	−	0.801551i	$-0.295991\pi$
$197$	16.7846	1.19585	0.597927	+	0.801551i	$0.295991\pi$
$198$	−1.00000	−0.0710669
$199$	12.3923	0.878467	0.439234	−	0.898373i	$-0.355250\pi$
$199$	12.3923	0.878467	0.439234	+	0.898373i	$0.355250\pi$
$200$	−4.92820	−0.348477
$201$	0.928203	0.0654704
$202$	−4.92820	−0.346747
$203$	0	0
$204$	−4.73205	−0.331310
$205$	1.41154	0.0985864
$206$	6.00000	0.418040
$207$	−2.73205	−0.189891
$208$	5.46410	0.378867
$209$	1.00000	0.0691714
$210$	0	0
$211$	−7.26795	−0.500346	−0.250173	−	0.968201i	$-0.580488\pi$
$211$	−7.26795	−0.500346	−0.250173	+	0.968201i	$0.580488\pi$
$212$	1.53590	0.105486
$213$	12.1962	0.835667
$214$	−1.33975	−0.0915831
$215$	0.0525589	0.00358449
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	10.7321	0.726866
$219$	−6.92820	−0.468165
$220$	−0.267949	−0.0180651
$221$	25.8564	1.73929
$222$	−6.19615	−0.415859
$223$	10.3205	0.691112	0.345556	−	0.938398i	$-0.387690\pi$
$223$	10.3205	0.691112	0.345556	+	0.938398i	$0.387690\pi$
$224$	0	0
$225$	−4.92820	−0.328547
$226$	−5.26795	−0.350419
$227$	18.6603	1.23852	0.619262	−	0.785184i	$-0.287432\pi$
$227$	18.6603	1.23852	0.619262	+	0.785184i	$0.287432\pi$
$228$	1.00000	0.0662266
$229$	−27.3205	−1.80539	−0.902695	−	0.430281i	$-0.858414\pi$
$229$	−27.3205	−1.80539	−0.902695	+	0.430281i	$0.858414\pi$
$230$	−0.732051	−0.0482700
$231$	0	0
$232$	1.00000	0.0656532
$233$	2.53590	0.166132	0.0830661	−	0.996544i	$-0.473529\pi$
$233$	2.53590	0.166132	0.0830661	+	0.996544i	$0.473529\pi$
$234$	5.46410	0.357199
$235$	3.07180	0.200382
$236$	−1.73205	−0.112747
$237$	11.3923	0.740010
$238$	0	0
$239$	−18.9282	−1.22436	−0.612182	−	0.790717i	$-0.709708\pi$
$239$	−18.9282	−1.22436	−0.612182	+	0.790717i	$0.709708\pi$
$240$	−0.267949	−0.0172960
$241$	23.9808	1.54474	0.772368	−	0.635175i	$-0.219072\pi$
$241$	23.9808	1.54474	0.772368	+	0.635175i	$0.219072\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	4.53590	0.290381
$245$	0	0
$246$	−5.26795	−0.335872
$247$	−5.46410	−0.347672
$248$	−2.46410	−0.156471
$249$	3.00000	0.190117
$250$	−2.66025	−0.168249
$251$	−2.85641	−0.180295	−0.0901474	−	0.995928i	$-0.528734\pi$
$251$	−2.85641	−0.180295	−0.0901474	+	0.995928i	$0.528734\pi$
$252$	0	0
$253$	2.73205	0.171763
$254$	3.92820	0.246477
$255$	−1.26795	−0.0794021
$256$	1.00000	0.0625000
$257$	−4.92820	−0.307413	−0.153706	−	0.988117i	$-0.549121\pi$
$257$	−4.92820	−0.307413	−0.153706	+	0.988117i	$0.549121\pi$
$258$	−0.196152	−0.0122119
$259$	0	0
$260$	1.46410	0.0907997
$261$	1.00000	0.0618984
$262$	−0.464102	−0.0286723
$263$	16.0526	0.989843	0.494922	−	0.868938i	$-0.335197\pi$
$263$	16.0526	0.989843	0.494922	+	0.868938i	$0.335197\pi$
$264$	1.00000	0.0615457
$265$	0.411543	0.0252809
$266$	0	0
$267$	−0.339746	−0.0207921
$268$	−0.928203	−0.0566990
$269$	20.3205	1.23896	0.619482	−	0.785011i	$-0.287343\pi$
$269$	20.3205	1.23896	0.619482	+	0.785011i	$0.287343\pi$
$270$	−0.267949	−0.0163069
$271$	23.0526	1.40034	0.700172	−	0.713975i	$-0.253107\pi$
$271$	23.0526	1.40034	0.700172	+	0.713975i	$0.253107\pi$
$272$	4.73205	0.286923
$273$	0	0
$274$	11.8564	0.716272
$275$	4.92820	0.297182
$276$	2.73205	0.164450
$277$	19.8038	1.18990	0.594949	−	0.803763i	$-0.297172\pi$
$277$	19.8038	1.18990	0.594949	+	0.803763i	$0.297172\pi$
$278$	8.19615	0.491573
$279$	−2.46410	−0.147522
$280$	0	0
$281$	−27.8564	−1.66177	−0.830887	−	0.556441i	$-0.812166\pi$
$281$	−27.8564	−1.66177	−0.830887	+	0.556441i	$0.812166\pi$
$282$	−11.4641	−0.682677
$283$	−26.4449	−1.57198	−0.785992	−	0.618237i	$-0.787847\pi$
$283$	−26.4449	−1.57198	−0.785992	+	0.618237i	$0.787847\pi$
$284$	−12.1962	−0.723708
$285$	0.267949	0.0158719
$286$	−5.46410	−0.323099
$287$	0	0
$288$	1.00000	0.0589256
$289$	5.39230	0.317194
$290$	0.267949	0.0157345
$291$	−5.73205	−0.336019
$292$	6.92820	0.405442
$293$	30.4641	1.77973	0.889866	−	0.456222i	$-0.150798\pi$
$293$	30.4641	1.77973	0.889866	+	0.456222i	$0.150798\pi$
$294$	0	0
$295$	−0.464102	−0.0270210
$296$	6.19615	0.360144
$297$	1.00000	0.0580259
$298$	1.60770	0.0931313
$299$	−14.9282	−0.863320
$300$	4.92820	0.284530
$301$	0	0
$302$	15.3923	0.885728
$303$	4.92820	0.283118
$304$	−1.00000	−0.0573539
$305$	1.21539	0.0695930
$306$	4.73205	0.270513
$307$	−24.5885	−1.40334	−0.701669	−	0.712503i	$-0.747561\pi$
$307$	−24.5885	−1.40334	−0.701669	+	0.712503i	$0.747561\pi$
$308$	0	0
$309$	−6.00000	−0.341328
$310$	−0.660254	−0.0374999
$311$	−35.1244	−1.99172	−0.995860	−	0.0909031i	$-0.971025\pi$
$311$	−35.1244	−1.99172	−0.995860	+	0.0909031i	$0.971025\pi$
$312$	−5.46410	−0.309344
$313$	31.7846	1.79657	0.898286	−	0.439411i	$-0.144813\pi$
$313$	31.7846	1.79657	0.898286	+	0.439411i	$0.144813\pi$
$314$	1.46410	0.0826240
$315$	0	0
$316$	−11.3923	−0.640867
$317$	−25.3923	−1.42617	−0.713087	−	0.701076i	$-0.752704\pi$
$317$	−25.3923	−1.42617	−0.713087	+	0.701076i	$0.752704\pi$
$318$	−1.53590	−0.0861289
$319$	−1.00000	−0.0559893
$320$	0.267949	0.0149788
$321$	1.33975	0.0747773
$322$	0	0
$323$	−4.73205	−0.263298
$324$	1.00000	0.0555556
$325$	−26.9282	−1.49371
$326$	12.3923	0.686346
$327$	−10.7321	−0.593484
$328$	5.26795	0.290874
$329$	0	0
$330$	0.267949	0.0147501
$331$	15.5167	0.852873	0.426436	−	0.904518i	$-0.359769\pi$
$331$	15.5167	0.852873	0.426436	+	0.904518i	$0.359769\pi$
$332$	−3.00000	−0.164646
$333$	6.19615	0.339547
$334$	20.1962	1.10508
$335$	−0.248711	−0.0135886
$336$	0	0
$337$	−27.9808	−1.52421	−0.762105	−	0.647454i	$-0.775834\pi$
$337$	−27.9808	−1.52421	−0.762105	+	0.647454i	$0.775834\pi$
$338$	16.8564	0.916868
$339$	5.26795	0.286116
$340$	1.26795	0.0687642
$341$	2.46410	0.133439
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	0.196152	0.0105758
$345$	0.732051	0.0394123
$346$	−20.7846	−1.11739
$347$	−6.39230	−0.343157	−0.171578	−	0.985170i	$-0.554887\pi$
$347$	−6.39230	−0.343157	−0.171578	+	0.985170i	$0.554887\pi$
$348$	−1.00000	−0.0536056
$349$	−15.2679	−0.817275	−0.408637	−	0.912697i	$-0.633996\pi$
$349$	−15.2679	−0.817275	−0.408637	+	0.912697i	$0.633996\pi$
$350$	0	0
$351$	−5.46410	−0.291652
$352$	−1.00000	−0.0533002
$353$	−14.1962	−0.755585	−0.377792	−	0.925890i	$-0.623317\pi$
$353$	−14.1962	−0.755585	−0.377792	+	0.925890i	$0.623317\pi$
$354$	1.73205	0.0920575
$355$	−3.26795	−0.173445
$356$	0.339746	0.0180065
$357$	0	0
$358$	−9.46410	−0.500193
$359$	−0.928203	−0.0489887	−0.0244943	−	0.999700i	$-0.507798\pi$
$359$	−0.928203	−0.0489887	−0.0244943	+	0.999700i	$0.507798\pi$
$360$	0.267949	0.0141222
$361$	1.00000	0.0526316
$362$	1.46410	0.0769515
$363$	10.0000	0.524864
$364$	0	0
$365$	1.85641	0.0971688
$366$	−4.53590	−0.237095
$367$	−24.5167	−1.27976	−0.639880	−	0.768475i	$-0.721016\pi$
$367$	−24.5167	−1.27976	−0.639880	+	0.768475i	$0.721016\pi$
$368$	−2.73205	−0.142418
$369$	5.26795	0.274238
$370$	1.66025	0.0863125
$371$	0	0
$372$	2.46410	0.127758
$373$	−15.3205	−0.793266	−0.396633	−	0.917977i	$-0.629821\pi$
$373$	−15.3205	−0.793266	−0.396633	+	0.917977i	$0.629821\pi$
$374$	−4.73205	−0.244689
$375$	2.66025	0.137375
$376$	11.4641	0.591216
$377$	5.46410	0.281416
$378$	0	0
$379$	10.1436	0.521041	0.260521	−	0.965468i	$-0.416106\pi$
$379$	10.1436	0.521041	0.260521	+	0.965468i	$0.416106\pi$
$380$	−0.267949	−0.0137455
$381$	−3.92820	−0.201248
$382$	13.4641	0.688883
$383$	6.78461	0.346677	0.173339	−	0.984862i	$-0.444544\pi$
$383$	6.78461	0.346677	0.173339	+	0.984862i	$0.444544\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	27.5885	1.40422
$387$	0.196152	0.00997099
$388$	5.73205	0.291001
$389$	17.3205	0.878185	0.439092	−	0.898442i	$-0.355300\pi$
$389$	17.3205	0.878185	0.439092	+	0.898442i	$0.355300\pi$
$390$	−1.46410	−0.0741377
$391$	−12.9282	−0.653807
$392$	0	0
$393$	0.464102	0.0234108
$394$	16.7846	0.845596
$395$	−3.05256	−0.153591
$396$	−1.00000	−0.0502519
$397$	19.3205	0.969669	0.484834	−	0.874606i	$-0.338880\pi$
$397$	19.3205	0.969669	0.484834	+	0.874606i	$0.338880\pi$
$398$	12.3923	0.621170
$399$	0	0
$400$	−4.92820	−0.246410
$401$	−0.392305	−0.0195908	−0.00979538	−	0.999952i	$-0.503118\pi$
$401$	−0.392305	−0.0195908	−0.00979538	+	0.999952i	$0.503118\pi$
$402$	0.928203	0.0462946
$403$	−13.4641	−0.670695
$404$	−4.92820	−0.245187
$405$	0.267949	0.0133145
$406$	0	0
$407$	−6.19615	−0.307132
$408$	−4.73205	−0.234271
$409$	−10.6603	−0.527116	−0.263558	−	0.964644i	$-0.584896\pi$
$409$	−10.6603	−0.527116	−0.263558	+	0.964644i	$0.584896\pi$
$410$	1.41154	0.0697111
$411$	−11.8564	−0.584833
$412$	6.00000	0.295599
$413$	0	0
$414$	−2.73205	−0.134273
$415$	−0.803848	−0.0394593
$416$	5.46410	0.267900
$417$	−8.19615	−0.401367
$418$	1.00000	0.0489116
$419$	31.1769	1.52309	0.761546	−	0.648111i	$-0.224441\pi$
$419$	31.1769	1.52309	0.761546	+	0.648111i	$0.224441\pi$
$420$	0	0
$421$	−16.2487	−0.791914	−0.395957	−	0.918269i	$-0.629587\pi$
$421$	−16.2487	−0.791914	−0.395957	+	0.918269i	$0.629587\pi$
$422$	−7.26795	−0.353798
$423$	11.4641	0.557404
$424$	1.53590	0.0745898
$425$	−23.3205	−1.13121
$426$	12.1962	0.590906
$427$	0	0
$428$	−1.33975	−0.0647591
$429$	5.46410	0.263809
$430$	0.0525589	0.00253461
$431$	−20.4449	−0.984794	−0.492397	−	0.870371i	$-0.663879\pi$
$431$	−20.4449	−0.984794	−0.492397	+	0.870371i	$0.663879\pi$
$432$	−1.00000	−0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	−0.267949	−0.0128472
$436$	10.7321	0.513972
$437$	2.73205	0.130692
$438$	−6.92820	−0.331042
$439$	2.46410	0.117605	0.0588026	−	0.998270i	$-0.481272\pi$
$439$	2.46410	0.117605	0.0588026	+	0.998270i	$0.481272\pi$
$440$	−0.267949	−0.0127740
$441$	0	0
$442$	25.8564	1.22986
$443$	7.00000	0.332580	0.166290	−	0.986077i	$-0.446821\pi$
$443$	7.00000	0.332580	0.166290	+	0.986077i	$0.446821\pi$
$444$	−6.19615	−0.294056
$445$	0.0910347	0.00431546
$446$	10.3205	0.488690
$447$	−1.60770	−0.0760414
$448$	0	0
$449$	−23.1244	−1.09131	−0.545653	−	0.838011i	$-0.683718\pi$
$449$	−23.1244	−1.09131	−0.545653	+	0.838011i	$0.683718\pi$
$450$	−4.92820	−0.232318
$451$	−5.26795	−0.248058
$452$	−5.26795	−0.247783
$453$	−15.3923	−0.723194
$454$	18.6603	0.875769
$455$	0	0
$456$	1.00000	0.0468293
$457$	23.9282	1.11931	0.559657	−	0.828724i	$-0.310933\pi$
$457$	23.9282	1.11931	0.559657	+	0.828724i	$0.310933\pi$
$458$	−27.3205	−1.27660
$459$	−4.73205	−0.220873
$460$	−0.732051	−0.0341320
$461$	39.8564	1.85630	0.928149	−	0.372209i	$-0.121400\pi$
$461$	39.8564	1.85630	0.928149	+	0.372209i	$0.121400\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	1.00000	0.0464238
$465$	0.660254	0.0306185
$466$	2.53590	0.117473
$467$	16.9282	0.783344	0.391672	−	0.920105i	$-0.371897\pi$
$467$	16.9282	0.783344	0.391672	+	0.920105i	$0.371897\pi$
$468$	5.46410	0.252578
$469$	0	0
$470$	3.07180	0.141691
$471$	−1.46410	−0.0674622
$472$	−1.73205	−0.0797241
$473$	−0.196152	−0.00901910
$474$	11.3923	0.523266
$475$	4.92820	0.226121
$476$	0	0
$477$	1.53590	0.0703240
$478$	−18.9282	−0.865756
$479$	23.8564	1.09003	0.545014	−	0.838427i	$-0.316525\pi$
$479$	23.8564	1.09003	0.545014	+	0.838427i	$0.316525\pi$
$480$	−0.267949	−0.0122302
$481$	33.8564	1.54372
$482$	23.9808	1.09229
$483$	0	0
$484$	−10.0000	−0.454545
$485$	1.53590	0.0697416
$486$	−1.00000	−0.0453609
$487$	38.8564	1.76075	0.880376	−	0.474277i	$-0.157290\pi$
$487$	38.8564	1.76075	0.880376	+	0.474277i	$0.157290\pi$
$488$	4.53590	0.205330
$489$	−12.3923	−0.560399
$490$	0	0
$491$	−43.0000	−1.94056	−0.970281	−	0.241979i	$-0.922203\pi$
$491$	−43.0000	−1.94056	−0.970281	+	0.241979i	$0.922203\pi$
$492$	−5.26795	−0.237497
$493$	4.73205	0.213121
$494$	−5.46410	−0.245842
$495$	−0.267949	−0.0120434
$496$	−2.46410	−0.110641
$497$	0	0
$498$	3.00000	0.134433
$499$	−7.07180	−0.316577	−0.158289	−	0.987393i	$-0.550598\pi$
$499$	−7.07180	−0.316577	−0.158289	+	0.987393i	$0.550598\pi$
$500$	−2.66025	−0.118970
$501$	−20.1962	−0.902298
$502$	−2.85641	−0.127488
$503$	−41.6603	−1.85754	−0.928769	−	0.370658i	$-0.879132\pi$
$503$	−41.6603	−1.85754	−0.928769	+	0.370658i	$0.879132\pi$
$504$	0	0
$505$	−1.32051	−0.0587618
$506$	2.73205	0.121454
$507$	−16.8564	−0.748619
$508$	3.92820	0.174286
$509$	−0.464102	−0.0205709	−0.0102855	−	0.999947i	$-0.503274\pi$
$509$	−0.464102	−0.0205709	−0.0102855	+	0.999947i	$0.503274\pi$
$510$	−1.26795	−0.0561457
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−4.92820	−0.217374
$515$	1.60770	0.0708435
$516$	−0.196152	−0.00863513
$517$	−11.4641	−0.504191
$518$	0	0
$519$	20.7846	0.912343
$520$	1.46410	0.0642051
$521$	−23.8564	−1.04517	−0.522584	−	0.852588i	$-0.675032\pi$
$521$	−23.8564	−1.04517	−0.522584	+	0.852588i	$0.675032\pi$
$522$	1.00000	0.0437688
$523$	−9.66025	−0.422413	−0.211207	−	0.977441i	$-0.567739\pi$
$523$	−9.66025	−0.422413	−0.211207	+	0.977441i	$0.567739\pi$
$524$	−0.464102	−0.0202744
$525$	0	0
$526$	16.0526	0.699925
$527$	−11.6603	−0.507929
$528$	1.00000	0.0435194
$529$	−15.5359	−0.675474
$530$	0.411543	0.0178763
$531$	−1.73205	−0.0751646
$532$	0	0
$533$	28.7846	1.24680
$534$	−0.339746	−0.0147022
$535$	−0.358984	−0.0155202
$536$	−0.928203	−0.0400923
$537$	9.46410	0.408406
$538$	20.3205	0.876079
$539$	0	0
$540$	−0.267949	−0.0115307
$541$	16.4449	0.707020	0.353510	−	0.935431i	$-0.384988\pi$
$541$	16.4449	0.707020	0.353510	+	0.935431i	$0.384988\pi$
$542$	23.0526	0.990192
$543$	−1.46410	−0.0628306
$544$	4.73205	0.202885
$545$	2.87564	0.123179
$546$	0	0
$547$	44.9808	1.92324	0.961619	−	0.274387i	$-0.0884750\pi$
$547$	44.9808	1.92324	0.961619	+	0.274387i	$0.0884750\pi$
$548$	11.8564	0.506481
$549$	4.53590	0.193587
$550$	4.92820	0.210139
$551$	−1.00000	−0.0426014
$552$	2.73205	0.116284
$553$	0	0
$554$	19.8038	0.841385
$555$	−1.66025	−0.0704739
$556$	8.19615	0.347594
$557$	−0.267949	−0.0113534	−0.00567669	−	0.999984i	$-0.501807\pi$
$557$	−0.267949	−0.0113534	−0.00567669	+	0.999984i	$0.501807\pi$
$558$	−2.46410	−0.104314
$559$	1.07180	0.0453322
$560$	0	0
$561$	4.73205	0.199787
$562$	−27.8564	−1.17505
$563$	−11.8756	−0.500499	−0.250249	−	0.968181i	$-0.580513\pi$
$563$	−11.8756	−0.500499	−0.250249	+	0.968181i	$0.580513\pi$
$564$	−11.4641	−0.482726
$565$	−1.41154	−0.0593840
$566$	−26.4449	−1.11156
$567$	0	0
$568$	−12.1962	−0.511739
$569$	−42.6410	−1.78760	−0.893802	−	0.448461i	$-0.851972\pi$
$569$	−42.6410	−1.78760	−0.893802	+	0.448461i	$0.851972\pi$
$570$	0.267949	0.0112232
$571$	18.0526	0.755476	0.377738	−	0.925913i	$-0.376702\pi$
$571$	18.0526	0.755476	0.377738	+	0.925913i	$0.376702\pi$
$572$	−5.46410	−0.228466
$573$	−13.4641	−0.562471
$574$	0	0
$575$	13.4641	0.561492
$576$	1.00000	0.0416667
$577$	−20.6077	−0.857910	−0.428955	−	0.903326i	$-0.641118\pi$
$577$	−20.6077	−0.857910	−0.428955	+	0.903326i	$0.641118\pi$
$578$	5.39230	0.224290
$579$	−27.5885	−1.14654
$580$	0.267949	0.0111260
$581$	0	0
$582$	−5.73205	−0.237601
$583$	−1.53590	−0.0636104
$584$	6.92820	0.286691
$585$	1.46410	0.0605332
$586$	30.4641	1.25846
$587$	−1.14359	−0.0472012	−0.0236006	−	0.999721i	$-0.507513\pi$
$587$	−1.14359	−0.0472012	−0.0236006	+	0.999721i	$0.507513\pi$
$588$	0	0
$589$	2.46410	0.101532
$590$	−0.464102	−0.0191068
$591$	−16.7846	−0.690427
$592$	6.19615	0.254660
$593$	−22.5359	−0.925438	−0.462719	−	0.886505i	$-0.653126\pi$
$593$	−22.5359	−0.925438	−0.462719	+	0.886505i	$0.653126\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	1.60770	0.0658538
$597$	−12.3923	−0.507183
$598$	−14.9282	−0.610460
$599$	35.9090	1.46720	0.733600	−	0.679581i	$-0.237838\pi$
$599$	35.9090	1.46720	0.733600	+	0.679581i	$0.237838\pi$
$600$	4.92820	0.201193
$601$	−21.9808	−0.896614	−0.448307	−	0.893880i	$-0.647973\pi$
$601$	−21.9808	−0.896614	−0.448307	+	0.893880i	$0.647973\pi$
$602$	0	0
$603$	−0.928203	−0.0377994
$604$	15.3923	0.626304
$605$	−2.67949	−0.108937
$606$	4.92820	0.200195
$607$	−14.1769	−0.575423	−0.287712	−	0.957717i	$-0.592894\pi$
$607$	−14.1769	−0.575423	−0.287712	+	0.957717i	$0.592894\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	1.21539	0.0492097
$611$	62.6410	2.53418
$612$	4.73205	0.191282
$613$	19.8038	0.799870	0.399935	−	0.916544i	$-0.369033\pi$
$613$	19.8038	0.799870	0.399935	+	0.916544i	$0.369033\pi$
$614$	−24.5885	−0.992309
$615$	−1.41154	−0.0569189
$616$	0	0
$617$	−12.5885	−0.506792	−0.253396	−	0.967363i	$-0.581548\pi$
$617$	−12.5885	−0.506792	−0.253396	+	0.967363i	$0.581548\pi$
$618$	−6.00000	−0.241355
$619$	31.4641	1.26465	0.632325	−	0.774704i	$-0.282101\pi$
$619$	31.4641	1.26465	0.632325	+	0.774704i	$0.282101\pi$
$620$	−0.660254	−0.0265164
$621$	2.73205	0.109633
$622$	−35.1244	−1.40836
$623$	0	0
$624$	−5.46410	−0.218739
$625$	23.9282	0.957128
$626$	31.7846	1.27037
$627$	−1.00000	−0.0399362
$628$	1.46410	0.0584240
$629$	29.3205	1.16909
$630$	0	0
$631$	−17.9808	−0.715803	−0.357901	−	0.933759i	$-0.616508\pi$
$631$	−17.9808	−0.715803	−0.357901	+	0.933759i	$0.616508\pi$
$632$	−11.3923	−0.453162
$633$	7.26795	0.288875
$634$	−25.3923	−1.00846
$635$	1.05256	0.0417695
$636$	−1.53590	−0.0609023
$637$	0	0
$638$	−1.00000	−0.0395904
$639$	−12.1962	−0.482472
$640$	0.267949	0.0105916
$641$	34.9808	1.38166	0.690829	−	0.723019i	$-0.257246\pi$
$641$	34.9808	1.38166	0.690829	+	0.723019i	$0.257246\pi$
$642$	1.33975	0.0528756
$643$	−23.8038	−0.938732	−0.469366	−	0.883004i	$-0.655518\pi$
$643$	−23.8038	−0.938732	−0.469366	+	0.883004i	$0.655518\pi$
$644$	0	0
$645$	−0.0525589	−0.00206950
$646$	−4.73205	−0.186180
$647$	−46.5885	−1.83158	−0.915791	−	0.401656i	$-0.868435\pi$
$647$	−46.5885	−1.83158	−0.915791	+	0.401656i	$0.868435\pi$
$648$	1.00000	0.0392837
$649$	1.73205	0.0679889
$650$	−26.9282	−1.05621
$651$	0	0
$652$	12.3923	0.485320
$653$	−42.1244	−1.64845	−0.824227	−	0.566260i	$-0.808390\pi$
$653$	−42.1244	−1.64845	−0.824227	+	0.566260i	$0.808390\pi$
$654$	−10.7321	−0.419656
$655$	−0.124356	−0.00485898
$656$	5.26795	0.205679
$657$	6.92820	0.270295
$658$	0	0
$659$	−19.4641	−0.758214	−0.379107	−	0.925353i	$-0.623769\pi$
$659$	−19.4641	−0.758214	−0.379107	+	0.925353i	$0.623769\pi$
$660$	0.267949	0.0104299
$661$	23.5167	0.914692	0.457346	−	0.889289i	$-0.348800\pi$
$661$	23.5167	0.914692	0.457346	+	0.889289i	$0.348800\pi$
$662$	15.5167	0.603072
$663$	−25.8564	−1.00418
$664$	−3.00000	−0.116423
$665$	0	0
$666$	6.19615	0.240096
$667$	−2.73205	−0.105785
$668$	20.1962	0.781413
$669$	−10.3205	−0.399014
$670$	−0.248711	−0.00960856
$671$	−4.53590	−0.175106
$672$	0	0
$673$	27.9808	1.07858	0.539290	−	0.842120i	$-0.318693\pi$
$673$	27.9808	1.07858	0.539290	+	0.842120i	$0.318693\pi$
$674$	−27.9808	−1.07778
$675$	4.92820	0.189687
$676$	16.8564	0.648323
$677$	−21.6410	−0.831732	−0.415866	−	0.909426i	$-0.636521\pi$
$677$	−21.6410	−0.831732	−0.415866	+	0.909426i	$0.636521\pi$
$678$	5.26795	0.202314
$679$	0	0
$680$	1.26795	0.0486236
$681$	−18.6603	−0.715062
$682$	2.46410	0.0943553
$683$	−38.8038	−1.48479	−0.742394	−	0.669964i	$-0.766310\pi$
$683$	−38.8038	−1.48479	−0.742394	+	0.669964i	$0.766310\pi$
$684$	−1.00000	−0.0382360
$685$	3.17691	0.121384
$686$	0	0
$687$	27.3205	1.04234
$688$	0.196152	0.00747824
$689$	8.39230	0.319721
$690$	0.732051	0.0278687
$691$	18.5885	0.707138	0.353569	−	0.935408i	$-0.384968\pi$
$691$	18.5885	0.707138	0.353569	+	0.935408i	$0.384968\pi$
$692$	−20.7846	−0.790112
$693$	0	0
$694$	−6.39230	−0.242649
$695$	2.19615	0.0833048
$696$	−1.00000	−0.0379049
$697$	24.9282	0.944223
$698$	−15.2679	−0.577900
$699$	−2.53590	−0.0959165
$700$	0	0
$701$	−4.12436	−0.155775	−0.0778874	−	0.996962i	$-0.524817\pi$
$701$	−4.12436	−0.155775	−0.0778874	+	0.996962i	$0.524817\pi$
$702$	−5.46410	−0.206229
$703$	−6.19615	−0.233692
$704$	−1.00000	−0.0376889
$705$	−3.07180	−0.115691
$706$	−14.1962	−0.534279
$707$	0	0
$708$	1.73205	0.0650945
$709$	−21.1244	−0.793342	−0.396671	−	0.917961i	$-0.629835\pi$
$709$	−21.1244	−0.793342	−0.396671	+	0.917961i	$0.629835\pi$
$710$	−3.26795	−0.122644
$711$	−11.3923	−0.427245
$712$	0.339746	0.0127325
$713$	6.73205	0.252117
$714$	0	0
$715$	−1.46410	−0.0547543
$716$	−9.46410	−0.353690
$717$	18.9282	0.706887
$718$	−0.928203	−0.0346402
$719$	−40.5359	−1.51173	−0.755867	−	0.654725i	$-0.772784\pi$
$719$	−40.5359	−1.51173	−0.755867	+	0.654725i	$0.772784\pi$
$720$	0.267949	0.00998588
$721$	0	0
$722$	1.00000	0.0372161
$723$	−23.9808	−0.891854
$724$	1.46410	0.0544129
$725$	−4.92820	−0.183029
$726$	10.0000	0.371135
$727$	−0.267949	−0.00993769	−0.00496884	−	0.999988i	$-0.501582\pi$
$727$	−0.267949	−0.00993769	−0.00496884	+	0.999988i	$0.501582\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.85641	0.0687087
$731$	0.928203	0.0343308
$732$	−4.53590	−0.167652
$733$	−17.9090	−0.661483	−0.330741	−	0.943721i	$-0.607299\pi$
$733$	−17.9090	−0.661483	−0.330741	+	0.943721i	$0.607299\pi$
$734$	−24.5167	−0.904926
$735$	0	0
$736$	−2.73205	−0.100705
$737$	0.928203	0.0341908
$738$	5.26795	0.193916
$739$	−30.4449	−1.11993	−0.559966	−	0.828515i	$-0.689186\pi$
$739$	−30.4449	−1.11993	−0.559966	+	0.828515i	$0.689186\pi$
$740$	1.66025	0.0610322
$741$	5.46410	0.200729
$742$	0	0
$743$	−1.21539	−0.0445883	−0.0222942	−	0.999751i	$-0.507097\pi$
$743$	−1.21539	−0.0445883	−0.0222942	+	0.999751i	$0.507097\pi$
$744$	2.46410	0.0903383
$745$	0.430781	0.0157826
$746$	−15.3205	−0.560924
$747$	−3.00000	−0.109764
$748$	−4.73205	−0.173021
$749$	0	0
$750$	2.66025	0.0971387
$751$	6.60770	0.241118	0.120559	−	0.992706i	$-0.461531\pi$
$751$	6.60770	0.241118	0.120559	+	0.992706i	$0.461531\pi$
$752$	11.4641	0.418053
$753$	2.85641	0.104093
$754$	5.46410	0.198991
$755$	4.12436	0.150101
$756$	0	0
$757$	−17.1244	−0.622395	−0.311198	−	0.950345i	$-0.600730\pi$
$757$	−17.1244	−0.622395	−0.311198	+	0.950345i	$0.600730\pi$
$758$	10.1436	0.368432
$759$	−2.73205	−0.0991672
$760$	−0.267949	−0.00971954
$761$	−12.6795	−0.459631	−0.229816	−	0.973234i	$-0.573812\pi$
$761$	−12.6795	−0.459631	−0.229816	+	0.973234i	$0.573812\pi$
$762$	−3.92820	−0.142304
$763$	0	0
$764$	13.4641	0.487114
$765$	1.26795	0.0458428
$766$	6.78461	0.245138
$767$	−9.46410	−0.341729
$768$	−1.00000	−0.0360844
$769$	−12.6077	−0.454645	−0.227323	−	0.973820i	$-0.572997\pi$
$769$	−12.6077	−0.454645	−0.227323	+	0.973820i	$0.572997\pi$
$770$	0	0
$771$	4.92820	0.177485
$772$	27.5885	0.992930
$773$	−35.3205	−1.27039	−0.635195	−	0.772352i	$-0.719080\pi$
$773$	−35.3205	−1.27039	−0.635195	+	0.772352i	$0.719080\pi$
$774$	0.196152	0.00705055
$775$	12.1436	0.436211
$776$	5.73205	0.205769
$777$	0	0
$778$	17.3205	0.620970
$779$	−5.26795	−0.188744
$780$	−1.46410	−0.0524232
$781$	12.1962	0.436413
$782$	−12.9282	−0.462312
$783$	−1.00000	−0.0357371
$784$	0	0
$785$	0.392305	0.0140020
$786$	0.464102	0.0165540
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	16.7846	0.597927
$789$	−16.0526	−0.571486
$790$	−3.05256	−0.108605
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	24.7846	0.880127
$794$	19.3205	0.685659
$795$	−0.411543	−0.0145959
$796$	12.3923	0.439234
$797$	2.32051	0.0821966	0.0410983	−	0.999155i	$-0.486914\pi$
$797$	2.32051	0.0821966	0.0410983	+	0.999155i	$0.486914\pi$
$798$	0	0
$799$	54.2487	1.91918
$800$	−4.92820	−0.174238
$801$	0.339746	0.0120043
$802$	−0.392305	−0.0138528
$803$	−6.92820	−0.244491
$804$	0.928203	0.0327352
$805$	0	0
$806$	−13.4641	−0.474253
$807$	−20.3205	−0.715316
$808$	−4.92820	−0.173374
$809$	−40.0526	−1.40817	−0.704086	−	0.710114i	$-0.748643\pi$
$809$	−40.0526	−1.40817	−0.704086	+	0.710114i	$0.748643\pi$
$810$	0.267949	0.00941477
$811$	−22.9808	−0.806964	−0.403482	−	0.914988i	$-0.632200\pi$
$811$	−22.9808	−0.806964	−0.403482	+	0.914988i	$0.632200\pi$
$812$	0	0
$813$	−23.0526	−0.808489
$814$	−6.19615	−0.217175
$815$	3.32051	0.116312
$816$	−4.73205	−0.165655
$817$	−0.196152	−0.00686250
$818$	−10.6603	−0.372727
$819$	0	0
$820$	1.41154	0.0492932
$821$	−7.73205	−0.269850	−0.134925	−	0.990856i	$-0.543079\pi$
$821$	−7.73205	−0.269850	−0.134925	+	0.990856i	$0.543079\pi$
$822$	−11.8564	−0.413540
$823$	−33.0718	−1.15281	−0.576405	−	0.817164i	$-0.695545\pi$
$823$	−33.0718	−1.15281	−0.576405	+	0.817164i	$0.695545\pi$
$824$	6.00000	0.209020
$825$	−4.92820	−0.171578
$826$	0	0
$827$	33.9808	1.18163	0.590813	−	0.806808i	$-0.298807\pi$
$827$	33.9808	1.18163	0.590813	+	0.806808i	$0.298807\pi$
$828$	−2.73205	−0.0949453
$829$	−10.1436	−0.352302	−0.176151	−	0.984363i	$-0.556365\pi$
$829$	−10.1436	−0.352302	−0.176151	+	0.984363i	$0.556365\pi$
$830$	−0.803848	−0.0279020
$831$	−19.8038	−0.686988
$832$	5.46410	0.189434
$833$	0	0
$834$	−8.19615	−0.283810
$835$	5.41154	0.187274
$836$	1.00000	0.0345857
$837$	2.46410	0.0851718
$838$	31.1769	1.07699
$839$	−24.4449	−0.843930	−0.421965	−	0.906612i	$-0.638660\pi$
$839$	−24.4449	−0.843930	−0.421965	+	0.906612i	$0.638660\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−16.2487	−0.559968
$843$	27.8564	0.959426
$844$	−7.26795	−0.250173
$845$	4.51666	0.155378
$846$	11.4641	0.394144
$847$	0	0
$848$	1.53590	0.0527430
$849$	26.4449	0.907585
$850$	−23.3205	−0.799887
$851$	−16.9282	−0.580291
$852$	12.1962	0.417833
$853$	40.7321	1.39464	0.697319	−	0.716761i	$-0.254376\pi$
$853$	40.7321	1.39464	0.697319	+	0.716761i	$0.254376\pi$
$854$	0	0
$855$	−0.267949	−0.00916367
$856$	−1.33975	−0.0457916
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	5.46410	0.186541
$859$	−15.1769	−0.517830	−0.258915	−	0.965900i	$-0.583365\pi$
$859$	−15.1769	−0.517830	−0.258915	+	0.965900i	$0.583365\pi$
$860$	0.0525589	0.00179224
$861$	0	0
$862$	−20.4449	−0.696355
$863$	15.1244	0.514839	0.257420	−	0.966300i	$-0.417128\pi$
$863$	15.1244	0.514839	0.257420	+	0.966300i	$0.417128\pi$
$864$	−1.00000	−0.0340207
$865$	−5.56922	−0.189359
$866$	−16.0000	−0.543702
$867$	−5.39230	−0.183132
$868$	0	0
$869$	11.3923	0.386457
$870$	−0.267949	−0.00908433
$871$	−5.07180	−0.171851
$872$	10.7321	0.363433
$873$	5.73205	0.194001
$874$	2.73205	0.0924130
$875$	0	0
$876$	−6.92820	−0.234082
$877$	6.87564	0.232174	0.116087	−	0.993239i	$-0.462965\pi$
$877$	6.87564	0.232174	0.116087	+	0.993239i	$0.462965\pi$
$878$	2.46410	0.0831594
$879$	−30.4641	−1.02753
$880$	−0.267949	−0.00903257
$881$	−9.21539	−0.310474	−0.155237	−	0.987877i	$-0.549614\pi$
$881$	−9.21539	−0.310474	−0.155237	+	0.987877i	$0.549614\pi$
$882$	0	0
$883$	42.1962	1.42001	0.710007	−	0.704195i	$-0.248692\pi$
$883$	42.1962	1.42001	0.710007	+	0.704195i	$0.248692\pi$
$884$	25.8564	0.869645
$885$	0.464102	0.0156006
$886$	7.00000	0.235170
$887$	26.9808	0.905925	0.452963	−	0.891529i	$-0.350367\pi$
$887$	26.9808	0.905925	0.452963	+	0.891529i	$0.350367\pi$
$888$	−6.19615	−0.207929
$889$	0	0
$890$	0.0910347	0.00305149
$891$	−1.00000	−0.0335013
$892$	10.3205	0.345556
$893$	−11.4641	−0.383632
$894$	−1.60770	−0.0537694
$895$	−2.53590	−0.0847657
$896$	0	0
$897$	14.9282	0.498438
$898$	−23.1244	−0.771670
$899$	−2.46410	−0.0821824
$900$	−4.92820	−0.164273
$901$	7.26795	0.242130
$902$	−5.26795	−0.175404
$903$	0	0
$904$	−5.26795	−0.175209
$905$	0.392305	0.0130407
$906$	−15.3923	−0.511375
$907$	−31.8038	−1.05603	−0.528015	−	0.849235i	$-0.677063\pi$
$907$	−31.8038	−1.05603	−0.528015	+	0.849235i	$0.677063\pi$
$908$	18.6603	0.619262
$909$	−4.92820	−0.163458
$910$	0	0
$911$	−8.53590	−0.282807	−0.141403	−	0.989952i	$-0.545161\pi$
$911$	−8.53590	−0.282807	−0.141403	+	0.989952i	$0.545161\pi$
$912$	1.00000	0.0331133
$913$	3.00000	0.0992855
$914$	23.9282	0.791475
$915$	−1.21539	−0.0401796
$916$	−27.3205	−0.902695
$917$	0	0
$918$	−4.73205	−0.156181
$919$	−47.1769	−1.55622	−0.778111	−	0.628126i	$-0.783822\pi$
$919$	−47.1769	−1.55622	−0.778111	+	0.628126i	$0.783822\pi$
$920$	−0.732051	−0.0241350
$921$	24.5885	0.810217
$922$	39.8564	1.31260
$923$	−66.6410	−2.19352
$924$	0	0
$925$	−30.5359	−1.00401
$926$	4.00000	0.131448
$927$	6.00000	0.197066
$928$	1.00000	0.0328266
$929$	−0.196152	−0.00643555	−0.00321778	−	0.999995i	$-0.501024\pi$
$929$	−0.196152	−0.00643555	−0.00321778	+	0.999995i	$0.501024\pi$
$930$	0.660254	0.0216506
$931$	0	0
$932$	2.53590	0.0830661
$933$	35.1244	1.14992
$934$	16.9282	0.553908
$935$	−1.26795	−0.0414664
$936$	5.46410	0.178600
$937$	27.3923	0.894868	0.447434	−	0.894317i	$-0.352338\pi$
$937$	27.3923	0.894868	0.447434	+	0.894317i	$0.352338\pi$
$938$	0	0
$939$	−31.7846	−1.03725
$940$	3.07180	0.100191
$941$	−19.7846	−0.644960	−0.322480	−	0.946576i	$-0.604516\pi$
$941$	−19.7846	−0.644960	−0.322480	+	0.946576i	$0.604516\pi$
$942$	−1.46410	−0.0477030
$943$	−14.3923	−0.468678
$944$	−1.73205	−0.0563735
$945$	0	0
$946$	−0.196152	−0.00637747
$947$	1.60770	0.0522431	0.0261215	−	0.999659i	$-0.491684\pi$
$947$	1.60770	0.0522431	0.0261215	+	0.999659i	$0.491684\pi$
$948$	11.3923	0.370005
$949$	37.8564	1.22887
$950$	4.92820	0.159892
$951$	25.3923	0.823402
$952$	0	0
$953$	−52.2487	−1.69250	−0.846251	−	0.532785i	$-0.821146\pi$
$953$	−52.2487	−1.69250	−0.846251	+	0.532785i	$0.821146\pi$
$954$	1.53590	0.0497265
$955$	3.60770	0.116742
$956$	−18.9282	−0.612182
$957$	1.00000	0.0323254
$958$	23.8564	0.770766
$959$	0	0
$960$	−0.267949	−0.00864802
$961$	−24.9282	−0.804136
$962$	33.8564	1.09157
$963$	−1.33975	−0.0431727
$964$	23.9808	0.772368
$965$	7.39230	0.237967
$966$	0	0
$967$	−9.58846	−0.308344	−0.154172	−	0.988044i	$-0.549271\pi$
$967$	−9.58846	−0.308344	−0.154172	+	0.988044i	$0.549271\pi$
$968$	−10.0000	−0.321412
$969$	4.73205	0.152015
$970$	1.53590	0.0493147
$971$	7.19615	0.230936	0.115468	−	0.993311i	$-0.463163\pi$
$971$	7.19615	0.230936	0.115468	+	0.993311i	$0.463163\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	38.8564	1.24504
$975$	26.9282	0.862393
$976$	4.53590	0.145191
$977$	0.143594	0.00459396	0.00229698	−	0.999997i	$-0.499269\pi$
$977$	0.143594	0.00459396	0.00229698	+	0.999997i	$0.499269\pi$
$978$	−12.3923	−0.396262
$979$	−0.339746	−0.0108583
$980$	0	0
$981$	10.7321	0.342648
$982$	−43.0000	−1.37219
$983$	51.7128	1.64938	0.824691	−	0.565583i	$-0.191349\pi$
$983$	51.7128	1.64938	0.824691	+	0.565583i	$0.191349\pi$
$984$	−5.26795	−0.167936
$985$	4.49742	0.143300
$986$	4.73205	0.150699
$987$	0	0
$988$	−5.46410	−0.173836
$989$	−0.535898	−0.0170406
$990$	−0.267949	−0.00851598
$991$	58.0333	1.84349	0.921745	−	0.387797i	$-0.126764\pi$
$991$	58.0333	1.84349	0.921745	+	0.387797i	$0.126764\pi$
$992$	−2.46410	−0.0782353
$993$	−15.5167	−0.492406
$994$	0	0
$995$	3.32051	0.105267
$996$	3.00000	0.0950586
$997$	−61.3205	−1.94204	−0.971020	−	0.238998i	$-0.923181\pi$
$997$	−61.3205	−1.94204	−0.971020	+	0.238998i	$0.923181\pi$
$998$	−7.07180	−0.223854
$999$	−6.19615	−0.196038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bl.1.1		2
7.2	even	3		798.2.j.g.571.2	yes	4
7.4	even	3		798.2.j.g.457.2	✓	4
7.6	odd	2		5586.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.g.457.2	✓	4	7.4	even	3
798.2.j.g.571.2	yes	4	7.2	even	3
5586.2.a.bl.1.1		2	1.1	even	1	trivial
5586.2.a.bm.1.2		2	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.267949 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.46410 q^{13} -0.267949 q^{15} +1.00000 q^{16} +4.73205 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.267949 q^{20} -1.00000 q^{22} -2.73205 q^{23} -1.00000 q^{24} -4.92820 q^{25} +5.46410 q^{26} -1.00000 q^{27} +1.00000 q^{29} -0.267949 q^{30} -2.46410 q^{31} +1.00000 q^{32} +1.00000 q^{33} +4.73205 q^{34} +1.00000 q^{36} +6.19615 q^{37} -1.00000 q^{38} -5.46410 q^{39} +0.267949 q^{40} +5.26795 q^{41} +0.196152 q^{43} -1.00000 q^{44} +0.267949 q^{45} -2.73205 q^{46} +11.4641 q^{47} -1.00000 q^{48} -4.92820 q^{50} -4.73205 q^{51} +5.46410 q^{52} +1.53590 q^{53} -1.00000 q^{54} -0.267949 q^{55} +1.00000 q^{57} +1.00000 q^{58} -1.73205 q^{59} -0.267949 q^{60} +4.53590 q^{61} -2.46410 q^{62} +1.00000 q^{64} +1.46410 q^{65} +1.00000 q^{66} -0.928203 q^{67} +4.73205 q^{68} +2.73205 q^{69} -12.1962 q^{71} +1.00000 q^{72} +6.92820 q^{73} +6.19615 q^{74} +4.92820 q^{75} -1.00000 q^{76} -5.46410 q^{78} -11.3923 q^{79} +0.267949 q^{80} +1.00000 q^{81} +5.26795 q^{82} -3.00000 q^{83} +1.26795 q^{85} +0.196152 q^{86} -1.00000 q^{87} -1.00000 q^{88} +0.339746 q^{89} +0.267949 q^{90} -2.73205 q^{92} +2.46410 q^{93} +11.4641 q^{94} -0.267949 q^{95} -1.00000 q^{96} +5.73205 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{20} - 2 q^{22} - 2 q^{23} - 2 q^{24} + 4 q^{25} + 4 q^{26} - 2 q^{27} + 2 q^{29} - 4 q^{30} + 2 q^{31} + 2 q^{32} + 2 q^{33} + 6 q^{34} + 2 q^{36} + 2 q^{37} - 2 q^{38} - 4 q^{39} + 4 q^{40} + 14 q^{41} - 10 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 16 q^{47} - 2 q^{48} + 4 q^{50} - 6 q^{51} + 4 q^{52} + 10 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{57} + 2 q^{58} - 4 q^{60} + 16 q^{61} + 2 q^{62} + 2 q^{64} - 4 q^{65} + 2 q^{66} + 12 q^{67} + 6 q^{68} + 2 q^{69} - 14 q^{71} + 2 q^{72} + 2 q^{74} - 4 q^{75} - 2 q^{76} - 4 q^{78} - 2 q^{79} + 4 q^{80} + 2 q^{81} + 14 q^{82} - 6 q^{83} + 6 q^{85} - 10 q^{86} - 2 q^{87} - 2 q^{88} + 18 q^{89} + 4 q^{90} - 2 q^{92} - 2 q^{93} + 16 q^{94} - 4 q^{95} - 2 q^{96} + 8 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^15 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^20 - 2 * q^22 - 2 * q^23 - 2 * q^24 + 4 * q^25 + 4 * q^26 - 2 * q^27 + 2 * q^29 - 4 * q^30 + 2 * q^31 + 2 * q^32 + 2 * q^33 + 6 * q^34 + 2 * q^36 + 2 * q^37 - 2 * q^38 - 4 * q^39 + 4 * q^40 + 14 * q^41 - 10 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 16 * q^47 - 2 * q^48 + 4 * q^50 - 6 * q^51 + 4 * q^52 + 10 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^57 + 2 * q^58 - 4 * q^60 + 16 * q^61 + 2 * q^62 + 2 * q^64 - 4 * q^65 + 2 * q^66 + 12 * q^67 + 6 * q^68 + 2 * q^69 - 14 * q^71 + 2 * q^72 + 2 * q^74 - 4 * q^75 - 2 * q^76 - 4 * q^78 - 2 * q^79 + 4 * q^80 + 2 * q^81 + 14 * q^82 - 6 * q^83 + 6 * q^85 - 10 * q^86 - 2 * q^87 - 2 * q^88 + 18 * q^89 + 4 * q^90 - 2 * q^92 - 2 * q^93 + 16 * q^94 - 4 * q^95 - 2 * q^96 + 8 * q^97 - 2 * q^99

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