LMFDB - Embedded newform 5586.2.a.bf.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(\sqrt{7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 7 $ x^2 - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.64575$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.64575 q^{10} +2.00000 q^{11} +1.00000 q^{12} +5.64575 q^{13} -1.64575 q^{15} +1.00000 q^{16} +7.29150 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.64575 q^{20} -2.00000 q^{22} -3.64575 q^{23} -1.00000 q^{24} -2.29150 q^{25} -5.64575 q^{26} +1.00000 q^{27} +9.29150 q^{29} +1.64575 q^{30} +1.64575 q^{31} -1.00000 q^{32} +2.00000 q^{33} -7.29150 q^{34} +1.00000 q^{36} -3.64575 q^{37} -1.00000 q^{38} +5.64575 q^{39} +1.64575 q^{40} +6.00000 q^{41} -9.29150 q^{43} +2.00000 q^{44} -1.64575 q^{45} +3.64575 q^{46} -1.64575 q^{47} +1.00000 q^{48} +2.29150 q^{50} +7.29150 q^{51} +5.64575 q^{52} +9.29150 q^{53} -1.00000 q^{54} -3.29150 q^{55} +1.00000 q^{57} -9.29150 q^{58} +2.00000 q^{59} -1.64575 q^{60} -9.29150 q^{61} -1.64575 q^{62} +1.00000 q^{64} -9.29150 q^{65} -2.00000 q^{66} +10.0000 q^{67} +7.29150 q^{68} -3.64575 q^{69} +3.29150 q^{71} -1.00000 q^{72} -16.5830 q^{73} +3.64575 q^{74} -2.29150 q^{75} +1.00000 q^{76} -5.64575 q^{78} +14.9373 q^{79} -1.64575 q^{80} +1.00000 q^{81} -6.00000 q^{82} +12.0000 q^{83} -12.0000 q^{85} +9.29150 q^{86} +9.29150 q^{87} -2.00000 q^{88} -8.00000 q^{89} +1.64575 q^{90} -3.64575 q^{92} +1.64575 q^{93} +1.64575 q^{94} -1.64575 q^{95} -1.00000 q^{96} -15.2915 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{22} - 2 q^{23} - 2 q^{24} + 6 q^{25} - 6 q^{26} + 2 q^{27} + 8 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 6 q^{39} - 2 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + 2 q^{45} + 2 q^{46} + 2 q^{47} + 2 q^{48} - 6 q^{50} + 4 q^{51} + 6 q^{52} + 8 q^{53} - 2 q^{54} + 4 q^{55} + 2 q^{57} - 8 q^{58} + 4 q^{59} + 2 q^{60} - 8 q^{61} + 2 q^{62} + 2 q^{64} - 8 q^{65} - 4 q^{66} + 20 q^{67} + 4 q^{68} - 2 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} + 2 q^{74} + 6 q^{75} + 2 q^{76} - 6 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} + 24 q^{83} - 24 q^{85} + 8 q^{86} + 8 q^{87} - 4 q^{88} - 16 q^{89} - 2 q^{90} - 2 q^{92} - 2 q^{93} - 2 q^{94} + 2 q^{95} - 2 q^{96} - 20 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^22 - 2 * q^23 - 2 * q^24 + 6 * q^25 - 6 * q^26 + 2 * q^27 + 8 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 6 * q^39 - 2 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 2 * q^48 - 6 * q^50 + 4 * q^51 + 6 * q^52 + 8 * q^53 - 2 * q^54 + 4 * q^55 + 2 * q^57 - 8 * q^58 + 4 * q^59 + 2 * q^60 - 8 * q^61 + 2 * q^62 + 2 * q^64 - 8 * q^65 - 4 * q^66 + 20 * q^67 + 4 * q^68 - 2 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 + 2 * q^74 + 6 * q^75 + 2 * q^76 - 6 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 + 24 * q^83 - 24 * q^85 + 8 * q^86 + 8 * q^87 - 4 * q^88 - 16 * q^89 - 2 * q^90 - 2 * q^92 - 2 * q^93 - 2 * q^94 + 2 * q^95 - 2 * q^96 - 20 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.64575	−0.736002	−0.368001	−	0.929825i	$-0.619958\pi$
$5$	−1.64575	−0.736002	−0.368001	+	0.929825i	$0.619958\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.64575	0.520432
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	5.64575	1.56585	0.782925	−	0.622116i	$-0.213727\pi$
$13$	5.64575	1.56585	0.782925	+	0.622116i	$0.213727\pi$
$14$	0	0
$15$	−1.64575	−0.424931
$16$	1.00000	0.250000
$17$	7.29150	1.76845	0.884225	−	0.467062i	$-0.154688\pi$
$17$	7.29150	1.76845	0.884225	+	0.467062i	$0.154688\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.64575	−0.368001
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−3.64575	−0.760192	−0.380096	−	0.924947i	$-0.624109\pi$
$23$	−3.64575	−0.760192	−0.380096	+	0.924947i	$0.624109\pi$
$24$	−1.00000	−0.204124
$25$	−2.29150	−0.458301
$26$	−5.64575	−1.10722
$27$	1.00000	0.192450
$28$	0	0
$29$	9.29150	1.72539	0.862694	−	0.505726i	$-0.168775\pi$
$29$	9.29150	1.72539	0.862694	+	0.505726i	$0.168775\pi$
$30$	1.64575	0.300472
$31$	1.64575	0.295586	0.147793	−	0.989018i	$-0.452783\pi$
$31$	1.64575	0.295586	0.147793	+	0.989018i	$0.452783\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	−7.29150	−1.25048
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.64575	−0.599358	−0.299679	−	0.954040i	$-0.596880\pi$
$37$	−3.64575	−0.599358	−0.299679	+	0.954040i	$0.596880\pi$
$38$	−1.00000	−0.162221
$39$	5.64575	0.904044
$40$	1.64575	0.260216
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−9.29150	−1.41694	−0.708470	−	0.705740i	$-0.750614\pi$
$43$	−9.29150	−1.41694	−0.708470	+	0.705740i	$0.750614\pi$
$44$	2.00000	0.301511
$45$	−1.64575	−0.245334
$46$	3.64575	0.537537
$47$	−1.64575	−0.240058	−0.120029	−	0.992770i	$-0.538299\pi$
$47$	−1.64575	−0.240058	−0.120029	+	0.992770i	$0.538299\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	2.29150	0.324067
$51$	7.29150	1.02101
$52$	5.64575	0.782925
$53$	9.29150	1.27629	0.638143	−	0.769918i	$-0.279703\pi$
$53$	9.29150	1.27629	0.638143	+	0.769918i	$0.279703\pi$
$54$	−1.00000	−0.136083
$55$	−3.29150	−0.443826
$56$	0	0
$57$	1.00000	0.132453
$58$	−9.29150	−1.22003
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	−1.64575	−0.212466
$61$	−9.29150	−1.18966	−0.594828	−	0.803853i	$-0.702780\pi$
$61$	−9.29150	−1.18966	−0.594828	+	0.803853i	$0.702780\pi$
$62$	−1.64575	−0.209011
$63$	0	0
$64$	1.00000	0.125000
$65$	−9.29150	−1.15247
$66$	−2.00000	−0.246183
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	7.29150	0.884225
$69$	−3.64575	−0.438897
$70$	0	0
$71$	3.29150	0.390629	0.195315	−	0.980741i	$-0.437427\pi$
$71$	3.29150	0.390629	0.195315	+	0.980741i	$0.437427\pi$
$72$	−1.00000	−0.117851
$73$	−16.5830	−1.94089	−0.970447	−	0.241314i	$-0.922421\pi$
$73$	−16.5830	−1.94089	−0.970447	+	0.241314i	$0.922421\pi$
$74$	3.64575	0.423810
$75$	−2.29150	−0.264600
$76$	1.00000	0.114708
$77$	0	0
$78$	−5.64575	−0.639255
$79$	14.9373	1.68057	0.840286	−	0.542143i	$-0.182387\pi$
$79$	14.9373	1.68057	0.840286	+	0.542143i	$0.182387\pi$
$80$	−1.64575	−0.184001
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	−12.0000	−1.30158
$86$	9.29150	1.00193
$87$	9.29150	0.996154
$88$	−2.00000	−0.213201
$89$	−8.00000	−0.847998	−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000	−0.847998	−0.423999	+	0.905663i	$0.639374\pi$
$90$	1.64575	0.173477
$91$	0	0
$92$	−3.64575	−0.380096
$93$	1.64575	0.170656
$94$	1.64575	0.169746
$95$	−1.64575	−0.168851
$96$	−1.00000	−0.102062
$97$	−15.2915	−1.55262	−0.776308	−	0.630353i	$-0.782910\pi$
$97$	−15.2915	−1.55262	−0.776308	+	0.630353i	$0.782910\pi$
$98$	0	0
$99$	2.00000	0.201008
$100$	−2.29150	−0.229150
$101$	−16.2288	−1.61482	−0.807411	−	0.589990i	$-0.799132\pi$
$101$	−16.2288	−1.61482	−0.807411	+	0.589990i	$0.799132\pi$
$102$	−7.29150	−0.721966
$103$	−8.93725	−0.880614	−0.440307	−	0.897847i	$-0.645130\pi$
$103$	−8.93725	−0.880614	−0.440307	+	0.897847i	$0.645130\pi$
$104$	−5.64575	−0.553611
$105$	0	0
$106$	−9.29150	−0.902471
$107$	18.5830	1.79649	0.898243	−	0.439498i	$-0.144844\pi$
$107$	18.5830	1.79649	0.898243	+	0.439498i	$0.144844\pi$
$108$	1.00000	0.0962250
$109$	12.3542	1.18332	0.591661	−	0.806187i	$-0.298472\pi$
$109$	12.3542	1.18332	0.591661	+	0.806187i	$0.298472\pi$
$110$	3.29150	0.313832
$111$	−3.64575	−0.346039
$112$	0	0
$113$	−15.2915	−1.43850	−0.719252	−	0.694750i	$-0.755515\pi$
$113$	−15.2915	−1.43850	−0.719252	+	0.694750i	$0.755515\pi$
$114$	−1.00000	−0.0936586
$115$	6.00000	0.559503
$116$	9.29150	0.862694
$117$	5.64575	0.521950
$118$	−2.00000	−0.184115
$119$	0	0
$120$	1.64575	0.150236
$121$	−7.00000	−0.636364
$122$	9.29150	0.841213
$123$	6.00000	0.541002
$124$	1.64575	0.147793
$125$	12.0000	1.07331
$126$	0	0
$127$	−14.9373	−1.32547	−0.662733	−	0.748855i	$-0.730604\pi$
$127$	−14.9373	−1.32547	−0.662733	+	0.748855i	$0.730604\pi$
$128$	−1.00000	−0.0883883
$129$	−9.29150	−0.818071
$130$	9.29150	0.814919
$131$	−2.58301	−0.225678	−0.112839	−	0.993613i	$-0.535994\pi$
$131$	−2.58301	−0.225678	−0.112839	+	0.993613i	$0.535994\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−10.0000	−0.863868
$135$	−1.64575	−0.141644
$136$	−7.29150	−0.625241
$137$	9.29150	0.793827	0.396913	−	0.917856i	$-0.370081\pi$
$137$	9.29150	0.793827	0.396913	+	0.917856i	$0.370081\pi$
$138$	3.64575	0.310347
$139$	−6.00000	−0.508913	−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000	−0.508913	−0.254457	+	0.967084i	$0.581897\pi$
$140$	0	0
$141$	−1.64575	−0.138597
$142$	−3.29150	−0.276217
$143$	11.2915	0.944243
$144$	1.00000	0.0833333
$145$	−15.2915	−1.26989
$146$	16.5830	1.37242
$147$	0	0
$148$	−3.64575	−0.299679
$149$	−10.2288	−0.837972	−0.418986	−	0.907993i	$-0.637614\pi$
$149$	−10.2288	−0.837972	−0.418986	+	0.907993i	$0.637614\pi$
$150$	2.29150	0.187100
$151$	5.06275	0.412000	0.206000	−	0.978552i	$-0.433955\pi$
$151$	5.06275	0.412000	0.206000	+	0.978552i	$0.433955\pi$
$152$	−1.00000	−0.0811107
$153$	7.29150	0.589483
$154$	0	0
$155$	−2.70850	−0.217552
$156$	5.64575	0.452022
$157$	6.70850	0.535396	0.267698	−	0.963503i	$-0.413737\pi$
$157$	6.70850	0.535396	0.267698	+	0.963503i	$0.413737\pi$
$158$	−14.9373	−1.18834
$159$	9.29150	0.736864
$160$	1.64575	0.130108
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	14.5830	1.14223	0.571115	−	0.820870i	$-0.306511\pi$
$163$	14.5830	1.14223	0.571115	+	0.820870i	$0.306511\pi$
$164$	6.00000	0.468521
$165$	−3.29150	−0.256243
$166$	−12.0000	−0.931381
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	0	0
$169$	18.8745	1.45189
$170$	12.0000	0.920358
$171$	1.00000	0.0764719
$172$	−9.29150	−0.708470
$173$	12.5830	0.956668	0.478334	−	0.878178i	$-0.341241\pi$
$173$	12.5830	0.956668	0.478334	+	0.878178i	$0.341241\pi$
$174$	−9.29150	−0.704387
$175$	0	0
$176$	2.00000	0.150756
$177$	2.00000	0.150329
$178$	8.00000	0.599625
$179$	15.8745	1.18652	0.593258	−	0.805012i	$-0.297841\pi$
$179$	15.8745	1.18652	0.593258	+	0.805012i	$0.297841\pi$
$180$	−1.64575	−0.122667
$181$	4.22876	0.314321	0.157160	−	0.987573i	$-0.449766\pi$
$181$	4.22876	0.314321	0.157160	+	0.987573i	$0.449766\pi$
$182$	0	0
$183$	−9.29150	−0.686848
$184$	3.64575	0.268768
$185$	6.00000	0.441129
$186$	−1.64575	−0.120672
$187$	14.5830	1.06641
$188$	−1.64575	−0.120029
$189$	0	0
$190$	1.64575	0.119395
$191$	−13.5203	−0.978292	−0.489146	−	0.872202i	$-0.662691\pi$
$191$	−13.5203	−0.978292	−0.489146	+	0.872202i	$0.662691\pi$
$192$	1.00000	0.0721688
$193$	−5.29150	−0.380891	−0.190445	−	0.981698i	$-0.560993\pi$
$193$	−5.29150	−0.380891	−0.190445	+	0.981698i	$0.560993\pi$
$194$	15.2915	1.09787
$195$	−9.29150	−0.665378
$196$	0	0
$197$	−8.35425	−0.595216	−0.297608	−	0.954688i	$-0.596189\pi$
$197$	−8.35425	−0.595216	−0.297608	+	0.954688i	$0.596189\pi$
$198$	−2.00000	−0.142134
$199$	13.8745	0.983538	0.491769	−	0.870726i	$-0.336350\pi$
$199$	13.8745	0.983538	0.491769	+	0.870726i	$0.336350\pi$
$200$	2.29150	0.162034
$201$	10.0000	0.705346
$202$	16.2288	1.14185
$203$	0	0
$204$	7.29150	0.510507
$205$	−9.87451	−0.689666
$206$	8.93725	0.622688
$207$	−3.64575	−0.253397
$208$	5.64575	0.391462
$209$	2.00000	0.138343
$210$	0	0
$211$	23.8745	1.64359	0.821794	−	0.569784i	$-0.192973\pi$
$211$	23.8745	1.64359	0.821794	+	0.569784i	$0.192973\pi$
$212$	9.29150	0.638143
$213$	3.29150	0.225530
$214$	−18.5830	−1.27031
$215$	15.2915	1.04287
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.3542	−0.836735
$219$	−16.5830	−1.12058
$220$	−3.29150	−0.221913
$221$	41.1660	2.76913
$222$	3.64575	0.244687
$223$	11.5203	0.771454	0.385727	−	0.922613i	$-0.373951\pi$
$223$	11.5203	0.771454	0.385727	+	0.922613i	$0.373951\pi$
$224$	0	0
$225$	−2.29150	−0.152767
$226$	15.2915	1.01718
$227$	−25.1660	−1.67033	−0.835163	−	0.550002i	$-0.814627\pi$
$227$	−25.1660	−1.67033	−0.835163	+	0.550002i	$0.814627\pi$
$228$	1.00000	0.0662266
$229$	16.5830	1.09584	0.547918	−	0.836532i	$-0.315421\pi$
$229$	16.5830	1.09584	0.547918	+	0.836532i	$0.315421\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	−9.29150	−0.610017
$233$	16.5830	1.08639	0.543194	−	0.839607i	$-0.317215\pi$
$233$	16.5830	1.08639	0.543194	+	0.839607i	$0.317215\pi$
$234$	−5.64575	−0.369074
$235$	2.70850	0.176683
$236$	2.00000	0.130189
$237$	14.9373	0.970279
$238$	0	0
$239$	10.9373	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$239$	10.9373	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$240$	−1.64575	−0.106233
$241$	−3.29150	−0.212024	−0.106012	−	0.994365i	$-0.533808\pi$
$241$	−3.29150	−0.212024	−0.106012	+	0.994365i	$0.533808\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−9.29150	−0.594828
$245$	0	0
$246$	−6.00000	−0.382546
$247$	5.64575	0.359231
$248$	−1.64575	−0.104505
$249$	12.0000	0.760469
$250$	−12.0000	−0.758947
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	−7.29150	−0.458413
$254$	14.9373	0.937247
$255$	−12.0000	−0.751469
$256$	1.00000	0.0625000
$257$	6.58301	0.410637	0.205318	−	0.978695i	$-0.434177\pi$
$257$	6.58301	0.410637	0.205318	+	0.978695i	$0.434177\pi$
$258$	9.29150	0.578464
$259$	0	0
$260$	−9.29150	−0.576235
$261$	9.29150	0.575130
$262$	2.58301	0.159579
$263$	16.3542	1.00845	0.504223	−	0.863573i	$-0.331779\pi$
$263$	16.3542	1.00845	0.504223	+	0.863573i	$0.331779\pi$
$264$	−2.00000	−0.123091
$265$	−15.2915	−0.939350
$266$	0	0
$267$	−8.00000	−0.489592
$268$	10.0000	0.610847
$269$	9.29150	0.566513	0.283256	−	0.959044i	$-0.408585\pi$
$269$	9.29150	0.566513	0.283256	+	0.959044i	$0.408585\pi$
$270$	1.64575	0.100157
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	7.29150	0.442112
$273$	0	0
$274$	−9.29150	−0.561320
$275$	−4.58301	−0.276366
$276$	−3.64575	−0.219448
$277$	−4.58301	−0.275366	−0.137683	−	0.990476i	$-0.543966\pi$
$277$	−4.58301	−0.275366	−0.137683	+	0.990476i	$0.543966\pi$
$278$	6.00000	0.359856
$279$	1.64575	0.0985286
$280$	0	0
$281$	−24.4575	−1.45901	−0.729506	−	0.683974i	$-0.760250\pi$
$281$	−24.4575	−1.45901	−0.729506	+	0.683974i	$0.760250\pi$
$282$	1.64575	0.0980031
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	3.29150	0.195315
$285$	−1.64575	−0.0974859
$286$	−11.2915	−0.667681
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	36.1660	2.12741
$290$	15.2915	0.897948
$291$	−15.2915	−0.896404
$292$	−16.5830	−0.970447
$293$	3.87451	0.226351	0.113176	−	0.993575i	$-0.463898\pi$
$293$	3.87451	0.226351	0.113176	+	0.993575i	$0.463898\pi$
$294$	0	0
$295$	−3.29150	−0.191639
$296$	3.64575	0.211905
$297$	2.00000	0.116052
$298$	10.2288	0.592536
$299$	−20.5830	−1.19035
$300$	−2.29150	−0.132300
$301$	0	0
$302$	−5.06275	−0.291328
$303$	−16.2288	−0.932318
$304$	1.00000	0.0573539
$305$	15.2915	0.875589
$306$	−7.29150	−0.416827
$307$	−15.2915	−0.872732	−0.436366	−	0.899769i	$-0.643735\pi$
$307$	−15.2915	−0.872732	−0.436366	+	0.899769i	$0.643735\pi$
$308$	0	0
$309$	−8.93725	−0.508423
$310$	2.70850	0.153832
$311$	23.5203	1.33371	0.666856	−	0.745187i	$-0.267640\pi$
$311$	23.5203	1.33371	0.666856	+	0.745187i	$0.267640\pi$
$312$	−5.64575	−0.319628
$313$	23.1660	1.30942	0.654710	−	0.755880i	$-0.272791\pi$
$313$	23.1660	1.30942	0.654710	+	0.755880i	$0.272791\pi$
$314$	−6.70850	−0.378582
$315$	0	0
$316$	14.9373	0.840286
$317$	3.87451	0.217614	0.108807	−	0.994063i	$-0.465297\pi$
$317$	3.87451	0.217614	0.108807	+	0.994063i	$0.465297\pi$
$318$	−9.29150	−0.521042
$319$	18.5830	1.04045
$320$	−1.64575	−0.0920003
$321$	18.5830	1.03720
$322$	0	0
$323$	7.29150	0.405710
$324$	1.00000	0.0555556
$325$	−12.9373	−0.717630
$326$	−14.5830	−0.807678
$327$	12.3542	0.683192
$328$	−6.00000	−0.331295
$329$	0	0
$330$	3.29150	0.181191
$331$	33.7490	1.85501	0.927507	−	0.373806i	$-0.121947\pi$
$331$	33.7490	1.85501	0.927507	+	0.373806i	$0.121947\pi$
$332$	12.0000	0.658586
$333$	−3.64575	−0.199786
$334$	−4.00000	−0.218870
$335$	−16.4575	−0.899170
$336$	0	0
$337$	31.1660	1.69772	0.848860	−	0.528617i	$-0.177289\pi$
$337$	31.1660	1.69772	0.848860	+	0.528617i	$0.177289\pi$
$338$	−18.8745	−1.02664
$339$	−15.2915	−0.830520
$340$	−12.0000	−0.650791
$341$	3.29150	0.178245
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	9.29150	0.500964
$345$	6.00000	0.323029
$346$	−12.5830	−0.676467
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	9.29150	0.498077
$349$	−13.2915	−0.711478	−0.355739	−	0.934585i	$-0.615771\pi$
$349$	−13.2915	−0.711478	−0.355739	+	0.934585i	$0.615771\pi$
$350$	0	0
$351$	5.64575	0.301348
$352$	−2.00000	−0.106600
$353$	12.0000	0.638696	0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000	0.638696	0.319348	+	0.947638i	$0.396536\pi$
$354$	−2.00000	−0.106299
$355$	−5.41699	−0.287504
$356$	−8.00000	−0.423999
$357$	0	0
$358$	−15.8745	−0.838994
$359$	19.6458	1.03686	0.518432	−	0.855119i	$-0.326516\pi$
$359$	19.6458	1.03686	0.518432	+	0.855119i	$0.326516\pi$
$360$	1.64575	0.0867387
$361$	1.00000	0.0526316
$362$	−4.22876	−0.222259
$363$	−7.00000	−0.367405
$364$	0	0
$365$	27.2915	1.42850
$366$	9.29150	0.485675
$367$	6.58301	0.343630	0.171815	−	0.985129i	$-0.445037\pi$
$367$	6.58301	0.343630	0.171815	+	0.985129i	$0.445037\pi$
$368$	−3.64575	−0.190048
$369$	6.00000	0.312348
$370$	−6.00000	−0.311925
$371$	0	0
$372$	1.64575	0.0853282
$373$	−9.06275	−0.469251	−0.234626	−	0.972086i	$-0.575386\pi$
$373$	−9.06275	−0.469251	−0.234626	+	0.972086i	$0.575386\pi$
$374$	−14.5830	−0.754069
$375$	12.0000	0.619677
$376$	1.64575	0.0848731
$377$	52.4575	2.70170
$378$	0	0
$379$	−37.7490	−1.93904	−0.969518	−	0.245019i	$-0.921206\pi$
$379$	−37.7490	−1.93904	−0.969518	+	0.245019i	$0.921206\pi$
$380$	−1.64575	−0.0844253
$381$	−14.9373	−0.765259
$382$	13.5203	0.691757
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	5.29150	0.269330
$387$	−9.29150	−0.472314
$388$	−15.2915	−0.776308
$389$	−35.3948	−1.79459	−0.897293	−	0.441436i	$-0.854469\pi$
$389$	−35.3948	−1.79459	−0.897293	+	0.441436i	$0.854469\pi$
$390$	9.29150	0.470494
$391$	−26.5830	−1.34436
$392$	0	0
$393$	−2.58301	−0.130295
$394$	8.35425	0.420881
$395$	−24.5830	−1.23691
$396$	2.00000	0.100504
$397$	−24.5830	−1.23379	−0.616893	−	0.787047i	$-0.711609\pi$
$397$	−24.5830	−1.23379	−0.616893	+	0.787047i	$0.711609\pi$
$398$	−13.8745	−0.695466
$399$	0	0
$400$	−2.29150	−0.114575
$401$	−21.8745	−1.09236	−0.546180	−	0.837668i	$-0.683919\pi$
$401$	−21.8745	−1.09236	−0.546180	+	0.837668i	$0.683919\pi$
$402$	−10.0000	−0.498755
$403$	9.29150	0.462843
$404$	−16.2288	−0.807411
$405$	−1.64575	−0.0817780
$406$	0	0
$407$	−7.29150	−0.361426
$408$	−7.29150	−0.360983
$409$	−4.70850	−0.232820	−0.116410	−	0.993201i	$-0.537139\pi$
$409$	−4.70850	−0.232820	−0.116410	+	0.993201i	$0.537139\pi$
$410$	9.87451	0.487667
$411$	9.29150	0.458316
$412$	−8.93725	−0.440307
$413$	0	0
$414$	3.64575	0.179179
$415$	−19.7490	−0.969441
$416$	−5.64575	−0.276806
$417$	−6.00000	−0.293821
$418$	−2.00000	−0.0978232
$419$	27.2915	1.33328	0.666639	−	0.745381i	$-0.267732\pi$
$419$	27.2915	1.33328	0.666639	+	0.745381i	$0.267732\pi$
$420$	0	0
$421$	13.5203	0.658937	0.329469	−	0.944167i	$-0.393130\pi$
$421$	13.5203	0.658937	0.329469	+	0.944167i	$0.393130\pi$
$422$	−23.8745	−1.16219
$423$	−1.64575	−0.0800192
$424$	−9.29150	−0.451235
$425$	−16.7085	−0.810481
$426$	−3.29150	−0.159474
$427$	0	0
$428$	18.5830	0.898243
$429$	11.2915	0.545159
$430$	−15.2915	−0.737422
$431$	−5.87451	−0.282965	−0.141483	−	0.989941i	$-0.545187\pi$
$431$	−5.87451	−0.282965	−0.141483	+	0.989941i	$0.545187\pi$
$432$	1.00000	0.0481125
$433$	−8.70850	−0.418504	−0.209252	−	0.977862i	$-0.567103\pi$
$433$	−8.70850	−0.418504	−0.209252	+	0.977862i	$0.567103\pi$
$434$	0	0
$435$	−15.2915	−0.733171
$436$	12.3542	0.591661
$437$	−3.64575	−0.174400
$438$	16.5830	0.792367
$439$	−36.2288	−1.72910	−0.864552	−	0.502543i	$-0.832398\pi$
$439$	−36.2288	−1.72910	−0.864552	+	0.502543i	$0.832398\pi$
$440$	3.29150	0.156916
$441$	0	0
$442$	−41.1660	−1.95807
$443$	30.0000	1.42534	0.712672	−	0.701498i	$-0.247485\pi$
$443$	30.0000	1.42534	0.712672	+	0.701498i	$0.247485\pi$
$444$	−3.64575	−0.173020
$445$	13.1660	0.624129
$446$	−11.5203	−0.545500
$447$	−10.2288	−0.483804
$448$	0	0
$449$	−23.1660	−1.09327	−0.546636	−	0.837370i	$-0.684092\pi$
$449$	−23.1660	−1.09327	−0.546636	+	0.837370i	$0.684092\pi$
$450$	2.29150	0.108022
$451$	12.0000	0.565058
$452$	−15.2915	−0.719252
$453$	5.06275	0.237869
$454$	25.1660	1.18110
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	−16.5830	−0.774873
$459$	7.29150	0.340338
$460$	6.00000	0.279751
$461$	16.9373	0.788847	0.394423	−	0.918929i	$-0.370944\pi$
$461$	16.9373	0.788847	0.394423	+	0.918929i	$0.370944\pi$
$462$	0	0
$463$	27.7490	1.28961	0.644803	−	0.764349i	$-0.276939\pi$
$463$	27.7490	1.28961	0.644803	+	0.764349i	$0.276939\pi$
$464$	9.29150	0.431347
$465$	−2.70850	−0.125604
$466$	−16.5830	−0.768193
$467$	16.0000	0.740392	0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000	0.740392	0.370196	+	0.928954i	$0.379291\pi$
$468$	5.64575	0.260975
$469$	0	0
$470$	−2.70850	−0.124934
$471$	6.70850	0.309111
$472$	−2.00000	−0.0920575
$473$	−18.5830	−0.854447
$474$	−14.9373	−0.686091
$475$	−2.29150	−0.105141
$476$	0	0
$477$	9.29150	0.425429
$478$	−10.9373	−0.500258
$479$	26.8118	1.22506	0.612530	−	0.790447i	$-0.290152\pi$
$479$	26.8118	1.22506	0.612530	+	0.790447i	$0.290152\pi$
$480$	1.64575	0.0751179
$481$	−20.5830	−0.938504
$482$	3.29150	0.149924
$483$	0	0
$484$	−7.00000	−0.318182
$485$	25.1660	1.14273
$486$	−1.00000	−0.0453609
$487$	17.5203	0.793919	0.396959	−	0.917836i	$-0.370065\pi$
$487$	17.5203	0.793919	0.396959	+	0.917836i	$0.370065\pi$
$488$	9.29150	0.420607
$489$	14.5830	0.659466
$490$	0	0
$491$	13.2915	0.599837	0.299919	−	0.953965i	$-0.403040\pi$
$491$	13.2915	0.599837	0.299919	+	0.953965i	$0.403040\pi$
$492$	6.00000	0.270501
$493$	67.7490	3.05126
$494$	−5.64575	−0.254014
$495$	−3.29150	−0.147942
$496$	1.64575	0.0738964
$497$	0	0
$498$	−12.0000	−0.537733
$499$	13.2915	0.595009	0.297505	−	0.954720i	$-0.403846\pi$
$499$	13.2915	0.595009	0.297505	+	0.954720i	$0.403846\pi$
$500$	12.0000	0.536656
$501$	4.00000	0.178707
$502$	4.00000	0.178529
$503$	1.64575	0.0733804	0.0366902	−	0.999327i	$-0.488319\pi$
$503$	1.64575	0.0733804	0.0366902	+	0.999327i	$0.488319\pi$
$504$	0	0
$505$	26.7085	1.18851
$506$	7.29150	0.324147
$507$	18.8745	0.838246
$508$	−14.9373	−0.662733
$509$	−33.2915	−1.47562	−0.737810	−	0.675008i	$-0.764140\pi$
$509$	−33.2915	−1.47562	−0.737810	+	0.675008i	$0.764140\pi$
$510$	12.0000	0.531369
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−6.58301	−0.290364
$515$	14.7085	0.648134
$516$	−9.29150	−0.409036
$517$	−3.29150	−0.144760
$518$	0	0
$519$	12.5830	0.552333
$520$	9.29150	0.407459
$521$	−20.0000	−0.876216	−0.438108	−	0.898922i	$-0.644351\pi$
$521$	−20.0000	−0.876216	−0.438108	+	0.898922i	$0.644351\pi$
$522$	−9.29150	−0.406678
$523$	−16.4575	−0.719637	−0.359818	−	0.933022i	$-0.617161\pi$
$523$	−16.4575	−0.719637	−0.359818	+	0.933022i	$0.617161\pi$
$524$	−2.58301	−0.112839
$525$	0	0
$526$	−16.3542	−0.713079
$527$	12.0000	0.522728
$528$	2.00000	0.0870388
$529$	−9.70850	−0.422109
$530$	15.2915	0.664220
$531$	2.00000	0.0867926
$532$	0	0
$533$	33.8745	1.46727
$534$	8.00000	0.346194
$535$	−30.5830	−1.32222
$536$	−10.0000	−0.431934
$537$	15.8745	0.685036
$538$	−9.29150	−0.400585
$539$	0	0
$540$	−1.64575	−0.0708219
$541$	7.41699	0.318882	0.159441	−	0.987207i	$-0.449031\pi$
$541$	7.41699	0.318882	0.159441	+	0.987207i	$0.449031\pi$
$542$	4.00000	0.171815
$543$	4.22876	0.181473
$544$	−7.29150	−0.312621
$545$	−20.3320	−0.870928
$546$	0	0
$547$	24.5830	1.05109	0.525547	−	0.850765i	$-0.323861\pi$
$547$	24.5830	1.05109	0.525547	+	0.850765i	$0.323861\pi$
$548$	9.29150	0.396913
$549$	−9.29150	−0.396552
$550$	4.58301	0.195420
$551$	9.29150	0.395831
$552$	3.64575	0.155173
$553$	0	0
$554$	4.58301	0.194713
$555$	6.00000	0.254686
$556$	−6.00000	−0.254457
$557$	20.3542	0.862437	0.431219	−	0.902247i	$-0.358084\pi$
$557$	20.3542	0.862437	0.431219	+	0.902247i	$0.358084\pi$
$558$	−1.64575	−0.0696702
$559$	−52.4575	−2.21872
$560$	0	0
$561$	14.5830	0.615695
$562$	24.4575	1.03168
$563$	−28.5830	−1.20463	−0.602315	−	0.798258i	$-0.705755\pi$
$563$	−28.5830	−1.20463	−0.602315	+	0.798258i	$0.705755\pi$
$564$	−1.64575	−0.0692986
$565$	25.1660	1.05874
$566$	26.0000	1.09286
$567$	0	0
$568$	−3.29150	−0.138108
$569$	−8.58301	−0.359818	−0.179909	−	0.983683i	$-0.557580\pi$
$569$	−8.58301	−0.359818	−0.179909	+	0.983683i	$0.557580\pi$
$570$	1.64575	0.0689329
$571$	34.7085	1.45251	0.726253	−	0.687428i	$-0.241260\pi$
$571$	34.7085	1.45251	0.726253	+	0.687428i	$0.241260\pi$
$572$	11.2915	0.472121
$573$	−13.5203	−0.564817
$574$	0	0
$575$	8.35425	0.348396
$576$	1.00000	0.0416667
$577$	−8.00000	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$578$	−36.1660	−1.50431
$579$	−5.29150	−0.219907
$580$	−15.2915	−0.634945
$581$	0	0
$582$	15.2915	0.633853
$583$	18.5830	0.769629
$584$	16.5830	0.686210
$585$	−9.29150	−0.384156
$586$	−3.87451	−0.160054
$587$	−1.87451	−0.0773692	−0.0386846	−	0.999251i	$-0.512317\pi$
$587$	−1.87451	−0.0773692	−0.0386846	+	0.999251i	$0.512317\pi$
$588$	0	0
$589$	1.64575	0.0678120
$590$	3.29150	0.135509
$591$	−8.35425	−0.343648
$592$	−3.64575	−0.149839
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	−10.2288	−0.418986
$597$	13.8745	0.567846
$598$	20.5830	0.841702
$599$	33.8745	1.38407	0.692037	−	0.721862i	$-0.256713\pi$
$599$	33.8745	1.38407	0.692037	+	0.721862i	$0.256713\pi$
$600$	2.29150	0.0935502
$601$	1.16601	0.0475626	0.0237813	−	0.999717i	$-0.492429\pi$
$601$	1.16601	0.0475626	0.0237813	+	0.999717i	$0.492429\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	5.06275	0.206000
$605$	11.5203	0.468365
$606$	16.2288	0.659248
$607$	16.9373	0.687462	0.343731	−	0.939068i	$-0.388309\pi$
$607$	16.9373	0.687462	0.343731	+	0.939068i	$0.388309\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−15.2915	−0.619135
$611$	−9.29150	−0.375894
$612$	7.29150	0.294742
$613$	−0.125492	−0.00506858	−0.00253429	−	0.999997i	$-0.500807\pi$
$613$	−0.125492	−0.00506858	−0.00253429	+	0.999997i	$0.500807\pi$
$614$	15.2915	0.617115
$615$	−9.87451	−0.398179
$616$	0	0
$617$	−28.5830	−1.15071	−0.575354	−	0.817904i	$-0.695136\pi$
$617$	−28.5830	−1.15071	−0.575354	+	0.817904i	$0.695136\pi$
$618$	8.93725	0.359509
$619$	−1.16601	−0.0468659	−0.0234330	−	0.999725i	$-0.507460\pi$
$619$	−1.16601	−0.0468659	−0.0234330	+	0.999725i	$0.507460\pi$
$620$	−2.70850	−0.108776
$621$	−3.64575	−0.146299
$622$	−23.5203	−0.943076
$623$	0	0
$624$	5.64575	0.226011
$625$	−8.29150	−0.331660
$626$	−23.1660	−0.925900
$627$	2.00000	0.0798723
$628$	6.70850	0.267698
$629$	−26.5830	−1.05993
$630$	0	0
$631$	−27.0405	−1.07647	−0.538233	−	0.842796i	$-0.680908\pi$
$631$	−27.0405	−1.07647	−0.538233	+	0.842796i	$0.680908\pi$
$632$	−14.9373	−0.594172
$633$	23.8745	0.948926
$634$	−3.87451	−0.153876
$635$	24.5830	0.975547
$636$	9.29150	0.368432
$637$	0	0
$638$	−18.5830	−0.735708
$639$	3.29150	0.130210
$640$	1.64575	0.0650540
$641$	−33.7490	−1.33301	−0.666503	−	0.745502i	$-0.732210\pi$
$641$	−33.7490	−1.33301	−0.666503	+	0.745502i	$0.732210\pi$
$642$	−18.5830	−0.733413
$643$	−8.58301	−0.338481	−0.169240	−	0.985575i	$-0.554131\pi$
$643$	−8.58301	−0.338481	−0.169240	+	0.985575i	$0.554131\pi$
$644$	0	0
$645$	15.2915	0.602102
$646$	−7.29150	−0.286880
$647$	26.8118	1.05408	0.527040	−	0.849841i	$-0.323302\pi$
$647$	26.8118	1.05408	0.527040	+	0.849841i	$0.323302\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	12.9373	0.507441
$651$	0	0
$652$	14.5830	0.571115
$653$	−31.6458	−1.23839	−0.619197	−	0.785236i	$-0.712542\pi$
$653$	−31.6458	−1.23839	−0.619197	+	0.785236i	$0.712542\pi$
$654$	−12.3542	−0.483089
$655$	4.25098	0.166100
$656$	6.00000	0.234261
$657$	−16.5830	−0.646965
$658$	0	0
$659$	14.7085	0.572962	0.286481	−	0.958086i	$-0.407515\pi$
$659$	14.7085	0.572962	0.286481	+	0.958086i	$0.407515\pi$
$660$	−3.29150	−0.128122
$661$	48.9373	1.90344	0.951719	−	0.306970i	$-0.0993150\pi$
$661$	48.9373	1.90344	0.951719	+	0.306970i	$0.0993150\pi$
$662$	−33.7490	−1.31169
$663$	41.1660	1.59876
$664$	−12.0000	−0.465690
$665$	0	0
$666$	3.64575	0.141270
$667$	−33.8745	−1.31163
$668$	4.00000	0.154765
$669$	11.5203	0.445399
$670$	16.4575	0.635809
$671$	−18.5830	−0.717389
$672$	0	0
$673$	6.70850	0.258594	0.129297	−	0.991606i	$-0.458728\pi$
$673$	6.70850	0.258594	0.129297	+	0.991606i	$0.458728\pi$
$674$	−31.1660	−1.20047
$675$	−2.29150	−0.0882000
$676$	18.8745	0.725943
$677$	15.8745	0.610107	0.305053	−	0.952335i	$-0.401326\pi$
$677$	15.8745	0.610107	0.305053	+	0.952335i	$0.401326\pi$
$678$	15.2915	0.587267
$679$	0	0
$680$	12.0000	0.460179
$681$	−25.1660	−0.964364
$682$	−3.29150	−0.126038
$683$	2.70850	0.103638	0.0518189	−	0.998656i	$-0.483498\pi$
$683$	2.70850	0.103638	0.0518189	+	0.998656i	$0.483498\pi$
$684$	1.00000	0.0382360
$685$	−15.2915	−0.584258
$686$	0	0
$687$	16.5830	0.632681
$688$	−9.29150	−0.354235
$689$	52.4575	1.99847
$690$	−6.00000	−0.228416
$691$	−34.5830	−1.31560	−0.657800	−	0.753193i	$-0.728513\pi$
$691$	−34.5830	−1.31560	−0.657800	+	0.753193i	$0.728513\pi$
$692$	12.5830	0.478334
$693$	0	0
$694$	18.0000	0.683271
$695$	9.87451	0.374561
$696$	−9.29150	−0.352193
$697$	43.7490	1.65711
$698$	13.2915	0.503091
$699$	16.5830	0.627227
$700$	0	0
$701$	9.77124	0.369055	0.184527	−	0.982827i	$-0.440925\pi$
$701$	9.77124	0.369055	0.184527	+	0.982827i	$0.440925\pi$
$702$	−5.64575	−0.213085
$703$	−3.64575	−0.137502
$704$	2.00000	0.0753778
$705$	2.70850	0.102008
$706$	−12.0000	−0.451626
$707$	0	0
$708$	2.00000	0.0751646
$709$	−11.8745	−0.445957	−0.222978	−	0.974823i	$-0.571578\pi$
$709$	−11.8745	−0.445957	−0.222978	+	0.974823i	$0.571578\pi$
$710$	5.41699	0.203296
$711$	14.9373	0.560191
$712$	8.00000	0.299813
$713$	−6.00000	−0.224702
$714$	0	0
$715$	−18.5830	−0.694965
$716$	15.8745	0.593258
$717$	10.9373	0.408459
$718$	−19.6458	−0.733173
$719$	−50.8118	−1.89496	−0.947479	−	0.319817i	$-0.896379\pi$
$719$	−50.8118	−1.89496	−0.947479	+	0.319817i	$0.896379\pi$
$720$	−1.64575	−0.0613335
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−3.29150	−0.122412
$724$	4.22876	0.157160
$725$	−21.2915	−0.790747
$726$	7.00000	0.259794
$727$	−49.8745	−1.84974	−0.924872	−	0.380280i	$-0.875828\pi$
$727$	−49.8745	−1.84974	−0.924872	+	0.380280i	$0.875828\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−27.2915	−1.01010
$731$	−67.7490	−2.50579
$732$	−9.29150	−0.343424
$733$	0.125492	0.00463516	0.00231758	−	0.999997i	$-0.499262\pi$
$733$	0.125492	0.00463516	0.00231758	+	0.999997i	$0.499262\pi$
$734$	−6.58301	−0.242983
$735$	0	0
$736$	3.64575	0.134384
$737$	20.0000	0.736709
$738$	−6.00000	−0.220863
$739$	−34.5830	−1.27216	−0.636078	−	0.771625i	$-0.719444\pi$
$739$	−34.5830	−1.27216	−0.636078	+	0.771625i	$0.719444\pi$
$740$	6.00000	0.220564
$741$	5.64575	0.207402
$742$	0	0
$743$	21.4170	0.785713	0.392857	−	0.919600i	$-0.371487\pi$
$743$	21.4170	0.785713	0.392857	+	0.919600i	$0.371487\pi$
$744$	−1.64575	−0.0603362
$745$	16.8340	0.616750
$746$	9.06275	0.331811
$747$	12.0000	0.439057
$748$	14.5830	0.533207
$749$	0	0
$750$	−12.0000	−0.438178
$751$	6.22876	0.227291	0.113645	−	0.993521i	$-0.463747\pi$
$751$	6.22876	0.227291	0.113645	+	0.993521i	$0.463747\pi$
$752$	−1.64575	−0.0600144
$753$	−4.00000	−0.145768
$754$	−52.4575	−1.91039
$755$	−8.33202	−0.303233
$756$	0	0
$757$	34.4575	1.25238	0.626190	−	0.779671i	$-0.284614\pi$
$757$	34.4575	1.25238	0.626190	+	0.779671i	$0.284614\pi$
$758$	37.7490	1.37111
$759$	−7.29150	−0.264665
$760$	1.64575	0.0596977
$761$	36.7085	1.33068	0.665341	−	0.746540i	$-0.268286\pi$
$761$	36.7085	1.33068	0.665341	+	0.746540i	$0.268286\pi$
$762$	14.9373	0.541120
$763$	0	0
$764$	−13.5203	−0.489146
$765$	−12.0000	−0.433861
$766$	−12.0000	−0.433578
$767$	11.2915	0.407713
$768$	1.00000	0.0360844
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	6.58301	0.237081
$772$	−5.29150	−0.190445
$773$	−42.4575	−1.52709	−0.763545	−	0.645754i	$-0.776543\pi$
$773$	−42.4575	−1.52709	−0.763545	+	0.645754i	$0.776543\pi$
$774$	9.29150	0.333976
$775$	−3.77124	−0.135467
$776$	15.2915	0.548933
$777$	0	0
$778$	35.3948	1.26896
$779$	6.00000	0.214972
$780$	−9.29150	−0.332689
$781$	6.58301	0.235558
$782$	26.5830	0.950606
$783$	9.29150	0.332051
$784$	0	0
$785$	−11.0405	−0.394053
$786$	2.58301	0.0921327
$787$	−34.5830	−1.23275	−0.616376	−	0.787452i	$-0.711400\pi$
$787$	−34.5830	−1.23275	−0.616376	+	0.787452i	$0.711400\pi$
$788$	−8.35425	−0.297608
$789$	16.3542	0.582227
$790$	24.5830	0.874624
$791$	0	0
$792$	−2.00000	−0.0710669
$793$	−52.4575	−1.86282
$794$	24.5830	0.872418
$795$	−15.2915	−0.542334
$796$	13.8745	0.491769
$797$	37.7490	1.33714	0.668569	−	0.743650i	$-0.266907\pi$
$797$	37.7490	1.33714	0.668569	+	0.743650i	$0.266907\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	2.29150	0.0810169
$801$	−8.00000	−0.282666
$802$	21.8745	0.772416
$803$	−33.1660	−1.17040
$804$	10.0000	0.352673
$805$	0	0
$806$	−9.29150	−0.327279
$807$	9.29150	0.327076
$808$	16.2288	0.570926
$809$	3.87451	0.136220	0.0681102	−	0.997678i	$-0.478303\pi$
$809$	3.87451	0.136220	0.0681102	+	0.997678i	$0.478303\pi$
$810$	1.64575	0.0578258
$811$	29.8745	1.04904	0.524518	−	0.851399i	$-0.324246\pi$
$811$	29.8745	1.04904	0.524518	+	0.851399i	$0.324246\pi$
$812$	0	0
$813$	−4.00000	−0.140286
$814$	7.29150	0.255567
$815$	−24.0000	−0.840683
$816$	7.29150	0.255254
$817$	−9.29150	−0.325069
$818$	4.70850	0.164629
$819$	0	0
$820$	−9.87451	−0.344833
$821$	−14.4797	−0.505346	−0.252673	−	0.967552i	$-0.581310\pi$
$821$	−14.4797	−0.505346	−0.252673	+	0.967552i	$0.581310\pi$
$822$	−9.29150	−0.324078
$823$	−1.16601	−0.0406446	−0.0203223	−	0.999793i	$-0.506469\pi$
$823$	−1.16601	−0.0406446	−0.0203223	+	0.999793i	$0.506469\pi$
$824$	8.93725	0.311344
$825$	−4.58301	−0.159560
$826$	0	0
$827$	−15.8745	−0.552011	−0.276005	−	0.961156i	$-0.589011\pi$
$827$	−15.8745	−0.552011	−0.276005	+	0.961156i	$0.589011\pi$
$828$	−3.64575	−0.126699
$829$	30.8118	1.07014	0.535068	−	0.844809i	$-0.320286\pi$
$829$	30.8118	1.07014	0.535068	+	0.844809i	$0.320286\pi$
$830$	19.7490	0.685498
$831$	−4.58301	−0.158983
$832$	5.64575	0.195731
$833$	0	0
$834$	6.00000	0.207763
$835$	−6.58301	−0.227814
$836$	2.00000	0.0691714
$837$	1.64575	0.0568855
$838$	−27.2915	−0.942769
$839$	34.3320	1.18527	0.592636	−	0.805470i	$-0.298087\pi$
$839$	34.3320	1.18527	0.592636	+	0.805470i	$0.298087\pi$
$840$	0	0
$841$	57.3320	1.97697
$842$	−13.5203	−0.465939
$843$	−24.4575	−0.842361
$844$	23.8745	0.821794
$845$	−31.0627	−1.06859
$846$	1.64575	0.0565821
$847$	0	0
$848$	9.29150	0.319072
$849$	−26.0000	−0.892318
$850$	16.7085	0.573097
$851$	13.2915	0.455627
$852$	3.29150	0.112765
$853$	14.4575	0.495016	0.247508	−	0.968886i	$-0.420388\pi$
$853$	14.4575	0.495016	0.247508	+	0.968886i	$0.420388\pi$
$854$	0	0
$855$	−1.64575	−0.0562835
$856$	−18.5830	−0.635154
$857$	−21.4170	−0.731591	−0.365795	−	0.930695i	$-0.619203\pi$
$857$	−21.4170	−0.731591	−0.365795	+	0.930695i	$0.619203\pi$
$858$	−11.2915	−0.385486
$859$	−26.5830	−0.907000	−0.453500	−	0.891256i	$-0.649825\pi$
$859$	−26.5830	−0.907000	−0.453500	+	0.891256i	$0.649825\pi$
$860$	15.2915	0.521436
$861$	0	0
$862$	5.87451	0.200087
$863$	46.3320	1.57716	0.788580	−	0.614932i	$-0.210817\pi$
$863$	46.3320	1.57716	0.788580	+	0.614932i	$0.210817\pi$
$864$	−1.00000	−0.0340207
$865$	−20.7085	−0.704110
$866$	8.70850	0.295927
$867$	36.1660	1.22826
$868$	0	0
$869$	29.8745	1.01342
$870$	15.2915	0.518430
$871$	56.4575	1.91299
$872$	−12.3542	−0.418368
$873$	−15.2915	−0.517539
$874$	3.64575	0.123319
$875$	0	0
$876$	−16.5830	−0.560288
$877$	−18.2288	−0.615541	−0.307771	−	0.951461i	$-0.599583\pi$
$877$	−18.2288	−0.615541	−0.307771	+	0.951461i	$0.599583\pi$
$878$	36.2288	1.22266
$879$	3.87451	0.130684
$880$	−3.29150	−0.110957
$881$	49.1660	1.65644	0.828222	−	0.560399i	$-0.189352\pi$
$881$	49.1660	1.65644	0.828222	+	0.560399i	$0.189352\pi$
$882$	0	0
$883$	7.87451	0.264998	0.132499	−	0.991183i	$-0.457700\pi$
$883$	7.87451	0.264998	0.132499	+	0.991183i	$0.457700\pi$
$884$	41.1660	1.38456
$885$	−3.29150	−0.110643
$886$	−30.0000	−1.00787
$887$	−21.8745	−0.734474	−0.367237	−	0.930127i	$-0.619696\pi$
$887$	−21.8745	−0.734474	−0.367237	+	0.930127i	$0.619696\pi$
$888$	3.64575	0.122343
$889$	0	0
$890$	−13.1660	−0.441326
$891$	2.00000	0.0670025
$892$	11.5203	0.385727
$893$	−1.64575	−0.0550730
$894$	10.2288	0.342101
$895$	−26.1255	−0.873279
$896$	0	0
$897$	−20.5830	−0.687247
$898$	23.1660	0.773060
$899$	15.2915	0.510000
$900$	−2.29150	−0.0763834
$901$	67.7490	2.25705
$902$	−12.0000	−0.399556
$903$	0	0
$904$	15.2915	0.508588
$905$	−6.95948	−0.231341
$906$	−5.06275	−0.168198
$907$	−19.1660	−0.636397	−0.318198	−	0.948024i	$-0.603078\pi$
$907$	−19.1660	−0.636397	−0.318198	+	0.948024i	$0.603078\pi$
$908$	−25.1660	−0.835163
$909$	−16.2288	−0.538274
$910$	0	0
$911$	23.2915	0.771682	0.385841	−	0.922565i	$-0.373911\pi$
$911$	23.2915	0.771682	0.385841	+	0.922565i	$0.373911\pi$
$912$	1.00000	0.0331133
$913$	24.0000	0.794284
$914$	22.0000	0.727695
$915$	15.2915	0.505521
$916$	16.5830	0.547918
$917$	0	0
$918$	−7.29150	−0.240655
$919$	−2.58301	−0.0852055	−0.0426027	−	0.999092i	$-0.513565\pi$
$919$	−2.58301	−0.0852055	−0.0426027	+	0.999092i	$0.513565\pi$
$920$	−6.00000	−0.197814
$921$	−15.2915	−0.503872
$922$	−16.9373	−0.557799
$923$	18.5830	0.611667
$924$	0	0
$925$	8.35425	0.274686
$926$	−27.7490	−0.911889
$927$	−8.93725	−0.293538
$928$	−9.29150	−0.305009
$929$	−19.2915	−0.632934	−0.316467	−	0.948604i	$-0.602497\pi$
$929$	−19.2915	−0.632934	−0.316467	+	0.948604i	$0.602497\pi$
$930$	2.70850	0.0888151
$931$	0	0
$932$	16.5830	0.543194
$933$	23.5203	0.770019
$934$	−16.0000	−0.523536
$935$	−24.0000	−0.784884
$936$	−5.64575	−0.184537
$937$	35.1660	1.14882	0.574412	−	0.818567i	$-0.305231\pi$
$937$	35.1660	1.14882	0.574412	+	0.818567i	$0.305231\pi$
$938$	0	0
$939$	23.1660	0.755994
$940$	2.70850	0.0883414
$941$	8.12549	0.264883	0.132442	−	0.991191i	$-0.457718\pi$
$941$	8.12549	0.264883	0.132442	+	0.991191i	$0.457718\pi$
$942$	−6.70850	−0.218575
$943$	−21.8745	−0.712332
$944$	2.00000	0.0650945
$945$	0	0
$946$	18.5830	0.604186
$947$	−46.4575	−1.50967	−0.754833	−	0.655917i	$-0.772282\pi$
$947$	−46.4575	−1.50967	−0.754833	+	0.655917i	$0.772282\pi$
$948$	14.9373	0.485139
$949$	−93.6235	−3.03915
$950$	2.29150	0.0743462
$951$	3.87451	0.125640
$952$	0	0
$953$	21.8745	0.708585	0.354292	−	0.935135i	$-0.384722\pi$
$953$	21.8745	0.708585	0.354292	+	0.935135i	$0.384722\pi$
$954$	−9.29150	−0.300824
$955$	22.2510	0.720025
$956$	10.9373	0.353736
$957$	18.5830	0.600703
$958$	−26.8118	−0.866249
$959$	0	0
$960$	−1.64575	−0.0531164
$961$	−28.2915	−0.912629
$962$	20.5830	0.663623
$963$	18.5830	0.598829
$964$	−3.29150	−0.106012
$965$	8.70850	0.280336
$966$	0	0
$967$	−17.8745	−0.574805	−0.287403	−	0.957810i	$-0.592792\pi$
$967$	−17.8745	−0.574805	−0.287403	+	0.957810i	$0.592792\pi$
$968$	7.00000	0.224989
$969$	7.29150	0.234237
$970$	−25.1660	−0.808032
$971$	1.16601	0.0374191	0.0187095	−	0.999825i	$-0.494044\pi$
$971$	1.16601	0.0374191	0.0187095	+	0.999825i	$0.494044\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−17.5203	−0.561385
$975$	−12.9373	−0.414324
$976$	−9.29150	−0.297414
$977$	−3.54249	−0.113334	−0.0566671	−	0.998393i	$-0.518047\pi$
$977$	−3.54249	−0.113334	−0.0566671	+	0.998393i	$0.518047\pi$
$978$	−14.5830	−0.466313
$979$	−16.0000	−0.511362
$980$	0	0
$981$	12.3542	0.394441
$982$	−13.2915	−0.424149
$983$	−32.7085	−1.04324	−0.521620	−	0.853178i	$-0.674672\pi$
$983$	−32.7085	−1.04324	−0.521620	+	0.853178i	$0.674672\pi$
$984$	−6.00000	−0.191273
$985$	13.7490	0.438080
$986$	−67.7490	−2.15757
$987$	0	0
$988$	5.64575	0.179615
$989$	33.8745	1.07715
$990$	3.29150	0.104611
$991$	−2.93725	−0.0933049	−0.0466525	−	0.998911i	$-0.514855\pi$
$991$	−2.93725	−0.0933049	−0.0466525	+	0.998911i	$0.514855\pi$
$992$	−1.64575	−0.0522527
$993$	33.7490	1.07099
$994$	0	0
$995$	−22.8340	−0.723886
$996$	12.0000	0.380235
$997$	4.12549	0.130656	0.0653278	−	0.997864i	$-0.479191\pi$
$997$	4.12549	0.130656	0.0653278	+	0.997864i	$0.479191\pi$
$998$	−13.2915	−0.420735
$999$	−3.64575	−0.115346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bf.1.1	yes	2
7.6	odd	2		5586.2.a.bc.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.bc.1.2	✓	2	7.6	odd	2
5586.2.a.bf.1.1	yes	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.64575 q^{10} +2.00000 q^{11} +1.00000 q^{12} +5.64575 q^{13} -1.64575 q^{15} +1.00000 q^{16} +7.29150 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.64575 q^{20} -2.00000 q^{22} -3.64575 q^{23} -1.00000 q^{24} -2.29150 q^{25} -5.64575 q^{26} +1.00000 q^{27} +9.29150 q^{29} +1.64575 q^{30} +1.64575 q^{31} -1.00000 q^{32} +2.00000 q^{33} -7.29150 q^{34} +1.00000 q^{36} -3.64575 q^{37} -1.00000 q^{38} +5.64575 q^{39} +1.64575 q^{40} +6.00000 q^{41} -9.29150 q^{43} +2.00000 q^{44} -1.64575 q^{45} +3.64575 q^{46} -1.64575 q^{47} +1.00000 q^{48} +2.29150 q^{50} +7.29150 q^{51} +5.64575 q^{52} +9.29150 q^{53} -1.00000 q^{54} -3.29150 q^{55} +1.00000 q^{57} -9.29150 q^{58} +2.00000 q^{59} -1.64575 q^{60} -9.29150 q^{61} -1.64575 q^{62} +1.00000 q^{64} -9.29150 q^{65} -2.00000 q^{66} +10.0000 q^{67} +7.29150 q^{68} -3.64575 q^{69} +3.29150 q^{71} -1.00000 q^{72} -16.5830 q^{73} +3.64575 q^{74} -2.29150 q^{75} +1.00000 q^{76} -5.64575 q^{78} +14.9373 q^{79} -1.64575 q^{80} +1.00000 q^{81} -6.00000 q^{82} +12.0000 q^{83} -12.0000 q^{85} +9.29150 q^{86} +9.29150 q^{87} -2.00000 q^{88} -8.00000 q^{89} +1.64575 q^{90} -3.64575 q^{92} +1.64575 q^{93} +1.64575 q^{94} -1.64575 q^{95} -1.00000 q^{96} -15.2915 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{22} - 2 q^{23} - 2 q^{24} + 6 q^{25} - 6 q^{26} + 2 q^{27} + 8 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 6 q^{39} - 2 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + 2 q^{45} + 2 q^{46} + 2 q^{47} + 2 q^{48} - 6 q^{50} + 4 q^{51} + 6 q^{52} + 8 q^{53} - 2 q^{54} + 4 q^{55} + 2 q^{57} - 8 q^{58} + 4 q^{59} + 2 q^{60} - 8 q^{61} + 2 q^{62} + 2 q^{64} - 8 q^{65} - 4 q^{66} + 20 q^{67} + 4 q^{68} - 2 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} + 2 q^{74} + 6 q^{75} + 2 q^{76} - 6 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} + 24 q^{83} - 24 q^{85} + 8 q^{86} + 8 q^{87} - 4 q^{88} - 16 q^{89} - 2 q^{90} - 2 q^{92} - 2 q^{93} - 2 q^{94} + 2 q^{95} - 2 q^{96} - 20 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^22 - 2 * q^23 - 2 * q^24 + 6 * q^25 - 6 * q^26 + 2 * q^27 + 8 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 6 * q^39 - 2 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 2 * q^48 - 6 * q^50 + 4 * q^51 + 6 * q^52 + 8 * q^53 - 2 * q^54 + 4 * q^55 + 2 * q^57 - 8 * q^58 + 4 * q^59 + 2 * q^60 - 8 * q^61 + 2 * q^62 + 2 * q^64 - 8 * q^65 - 4 * q^66 + 20 * q^67 + 4 * q^68 - 2 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 + 2 * q^74 + 6 * q^75 + 2 * q^76 - 6 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 + 24 * q^83 - 24 * q^85 + 8 * q^86 + 8 * q^87 - 4 * q^88 - 16 * q^89 - 2 * q^90 - 2 * q^92 - 2 * q^93 - 2 * q^94 + 2 * q^95 - 2 * q^96 - 20 * q^97 + 4 * q^99

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