LMFDB - Embedded newform 2890.2.a.bi.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2890,2,Mod(1,2890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2890.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2890, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2890 = 2 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2890.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,8,-4,8,-8,-4,-8,8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$23.0767661842$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.32887537664.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 6x^{6} + 28x^{5} + 13x^{4} - 56x^{3} - 12x^{2} + 32x + 2 $ x^8 - 4x^7 - 6x^6 + 28x^5 + 13x^4 - 56x^3 - 12x^2 + 32*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.0614939$ of defining polynomial
Character	$\chi$	$=$	2890.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.47571 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.47571 q^{6} -3.54824 q^{7} +1.00000 q^{8} -0.822287 q^{9} -1.00000 q^{10} +4.70854 q^{11} +1.47571 q^{12} -5.47699 q^{13} -3.54824 q^{14} -1.47571 q^{15} +1.00000 q^{16} -0.822287 q^{18} +1.21304 q^{19} -1.00000 q^{20} -5.23617 q^{21} +4.70854 q^{22} -5.72028 q^{23} +1.47571 q^{24} +1.00000 q^{25} -5.47699 q^{26} -5.64058 q^{27} -3.54824 q^{28} -4.64378 q^{29} -1.47571 q^{30} -7.28334 q^{31} +1.00000 q^{32} +6.94843 q^{33} +3.54824 q^{35} -0.822287 q^{36} -9.29174 q^{37} +1.21304 q^{38} -8.08244 q^{39} -1.00000 q^{40} -0.143094 q^{41} -5.23617 q^{42} -0.830161 q^{43} +4.70854 q^{44} +0.822287 q^{45} -5.72028 q^{46} +5.85635 q^{47} +1.47571 q^{48} +5.59004 q^{49} +1.00000 q^{50} -5.47699 q^{52} +9.25215 q^{53} -5.64058 q^{54} -4.70854 q^{55} -3.54824 q^{56} +1.79009 q^{57} -4.64378 q^{58} +4.71650 q^{59} -1.47571 q^{60} +12.4453 q^{61} -7.28334 q^{62} +2.91768 q^{63} +1.00000 q^{64} +5.47699 q^{65} +6.94843 q^{66} -8.66703 q^{67} -8.44146 q^{69} +3.54824 q^{70} +5.14391 q^{71} -0.822287 q^{72} -16.1322 q^{73} -9.29174 q^{74} +1.47571 q^{75} +1.21304 q^{76} -16.7071 q^{77} -8.08244 q^{78} -10.1159 q^{79} -1.00000 q^{80} -5.85698 q^{81} -0.143094 q^{82} -3.40601 q^{83} -5.23617 q^{84} -0.830161 q^{86} -6.85286 q^{87} +4.70854 q^{88} +2.24175 q^{89} +0.822287 q^{90} +19.4337 q^{91} -5.72028 q^{92} -10.7481 q^{93} +5.85635 q^{94} -1.21304 q^{95} +1.47571 q^{96} +4.35543 q^{97} +5.59004 q^{98} -3.87177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 8 q^{5} - 4 q^{6} - 8 q^{7} + 8 q^{8} + 4 q^{9} - 8 q^{10} - 8 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{18} + 12 q^{19} - 8 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 8 * q^5 - 4 * q^6 - 8 * q^7 + 8 * q^8 + 4 * q^9 - 8 * q^10 - 8 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 8 * q^16 + 4 * q^18 + 12 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^22 - 24 * q^23 - 4 * q^24 + 8 * q^25 - 4 * q^26 - 4 * q^27 - 8 * q^28 - 28 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 8 * q^33 + 8 * q^35 + 4 * q^36 - 24 * q^37 + 12 * q^38 - 12 * q^39 - 8 * q^40 - 16 * q^41 - 8 * q^42 - 8 * q^44 - 4 * q^45 - 24 * q^46 - 12 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 - 4 * q^52 - 12 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^56 - 20 * q^57 - 28 * q^58 - 4 * q^59 + 4 * q^60 - 4 * q^61 - 4 * q^62 - 32 * q^63 + 8 * q^64 + 4 * q^65 - 8 * q^66 - 8 * q^67 - 8 * q^69 + 8 * q^70 - 36 * q^71 + 4 * q^72 - 28 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 - 24 * q^77 - 12 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 8 * q^83 - 8 * q^84 - 28 * q^87 - 8 * q^88 - 12 * q^89 - 4 * q^90 + 8 * q^91 - 24 * q^92 - 12 * q^93 - 12 * q^94 - 12 * q^95 - 4 * q^96 - 28 * q^97 + 8 * q^98 + 8 * q^99

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
$3$	1.47571	0.852000	0.426000	−	0.904723i	$-0.359922\pi$
$3$	1.47571	0.852000	0.426000	+	0.904723i	$0.359922\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.47571	0.602455
$7$	−3.54824	−1.34111	−0.670555	−	0.741860i	$-0.733944\pi$
$7$	−3.54824	−1.34111	−0.670555	+	0.741860i	$0.733944\pi$
$8$	1.00000	0.353553
$9$	−0.822287	−0.274096
$10$	−1.00000	−0.316228
$11$	4.70854	1.41968	0.709839	−	0.704364i	$-0.248768\pi$
$11$	4.70854	1.41968	0.709839	+	0.704364i	$0.248768\pi$
$12$	1.47571	0.426000
$13$	−5.47699	−1.51904	−0.759522	−	0.650481i	$-0.774567\pi$
$13$	−5.47699	−1.51904	−0.759522	+	0.650481i	$0.774567\pi$
$14$	−3.54824	−0.948308
$15$	−1.47571	−0.381026
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−0.822287	−0.193815
$19$	1.21304	0.278290	0.139145	−	0.990272i	$-0.455565\pi$
$19$	1.21304	0.278290	0.139145	+	0.990272i	$0.455565\pi$
$20$	−1.00000	−0.223607
$21$	−5.23617	−1.14263
$22$	4.70854	1.00386
$23$	−5.72028	−1.19276	−0.596381	−	0.802702i	$-0.703395\pi$
$23$	−5.72028	−1.19276	−0.596381	+	0.802702i	$0.703395\pi$
$24$	1.47571	0.301228
$25$	1.00000	0.200000
$26$	−5.47699	−1.07413
$27$	−5.64058	−1.08553
$28$	−3.54824	−0.670555
$29$	−4.64378	−0.862328	−0.431164	−	0.902274i	$-0.641897\pi$
$29$	−4.64378	−0.862328	−0.431164	+	0.902274i	$0.641897\pi$
$30$	−1.47571	−0.269426
$31$	−7.28334	−1.30813	−0.654063	−	0.756440i	$-0.726937\pi$
$31$	−7.28334	−1.30813	−0.654063	+	0.756440i	$0.726937\pi$
$32$	1.00000	0.176777
$33$	6.94843	1.20957
$34$	0	0
$35$	3.54824	0.599763
$36$	−0.822287	−0.137048
$37$	−9.29174	−1.52755	−0.763776	−	0.645481i	$-0.776657\pi$
$37$	−9.29174	−1.52755	−0.763776	+	0.645481i	$0.776657\pi$
$38$	1.21304	0.196781
$39$	−8.08244	−1.29423
$40$	−1.00000	−0.158114
$41$	−0.143094	−0.0223476	−0.0111738	−	0.999938i	$-0.503557\pi$
$41$	−0.143094	−0.0223476	−0.0111738	+	0.999938i	$0.503557\pi$
$42$	−5.23617	−0.807959
$43$	−0.830161	−0.126598	−0.0632992	−	0.997995i	$-0.520162\pi$
$43$	−0.830161	−0.126598	−0.0632992	+	0.997995i	$0.520162\pi$
$44$	4.70854	0.709839
$45$	0.822287	0.122579
$46$	−5.72028	−0.843410
$47$	5.85635	0.854236	0.427118	−	0.904196i	$-0.359529\pi$
$47$	5.85635	0.854236	0.427118	+	0.904196i	$0.359529\pi$
$48$	1.47571	0.213000
$49$	5.59004	0.798577
$50$	1.00000	0.141421
$51$	0	0
$52$	−5.47699	−0.759522
$53$	9.25215	1.27088	0.635440	−	0.772150i	$-0.280819\pi$
$53$	9.25215	1.27088	0.635440	+	0.772150i	$0.280819\pi$
$54$	−5.64058	−0.767585
$55$	−4.70854	−0.634900
$56$	−3.54824	−0.474154
$57$	1.79009	0.237103
$58$	−4.64378	−0.609758
$59$	4.71650	0.614036	0.307018	−	0.951704i	$-0.400669\pi$
$59$	4.71650	0.614036	0.307018	+	0.951704i	$0.400669\pi$
$60$	−1.47571	−0.190513
$61$	12.4453	1.59346	0.796729	−	0.604336i	$-0.206562\pi$
$61$	12.4453	1.59346	0.796729	+	0.604336i	$0.206562\pi$
$62$	−7.28334	−0.924985
$63$	2.91768	0.367593
$64$	1.00000	0.125000
$65$	5.47699	0.679337
$66$	6.94843	0.855293
$67$	−8.66703	−1.05885	−0.529423	−	0.848358i	$-0.677592\pi$
$67$	−8.66703	−1.05885	−0.529423	+	0.848358i	$0.677592\pi$
$68$	0	0
$69$	−8.44146	−1.01623
$70$	3.54824	0.424096
$71$	5.14391	0.610469	0.305235	−	0.952277i	$-0.401265\pi$
$71$	5.14391	0.610469	0.305235	+	0.952277i	$0.401265\pi$
$72$	−0.822287	−0.0969075
$73$	−16.1322	−1.88813	−0.944064	−	0.329763i	$-0.893031\pi$
$73$	−16.1322	−1.88813	−0.944064	+	0.329763i	$0.893031\pi$
$74$	−9.29174	−1.08014
$75$	1.47571	0.170400
$76$	1.21304	0.139145
$77$	−16.7071	−1.90395
$78$	−8.08244	−0.915156
$79$	−10.1159	−1.13813	−0.569063	−	0.822294i	$-0.692694\pi$
$79$	−10.1159	−1.13813	−0.569063	+	0.822294i	$0.692694\pi$
$80$	−1.00000	−0.111803
$81$	−5.85698	−0.650776
$82$	−0.143094	−0.0158021
$83$	−3.40601	−0.373858	−0.186929	−	0.982373i	$-0.559853\pi$
$83$	−3.40601	−0.373858	−0.186929	+	0.982373i	$0.559853\pi$
$84$	−5.23617	−0.571313
$85$	0	0
$86$	−0.830161	−0.0895186
$87$	−6.85286	−0.734704
$88$	4.70854	0.501932
$89$	2.24175	0.237625	0.118813	−	0.992917i	$-0.462091\pi$
$89$	2.24175	0.237625	0.118813	+	0.992917i	$0.462091\pi$
$90$	0.822287	0.0866767
$91$	19.4337	2.03721
$92$	−5.72028	−0.596381
$93$	−10.7481	−1.11452
$94$	5.85635	0.604036
$95$	−1.21304	−0.124455
$96$	1.47571	0.150614
$97$	4.35543	0.442227	0.221113	−	0.975248i	$-0.429031\pi$
$97$	4.35543	0.442227	0.221113	+	0.975248i	$0.429031\pi$
$98$	5.59004	0.564679
$99$	−3.87177	−0.389128
$100$	1.00000	0.100000
$101$	10.7393	1.06860	0.534301	−	0.845294i	$-0.320575\pi$
$101$	10.7393	1.06860	0.534301	+	0.845294i	$0.320575\pi$
$102$	0	0
$103$	−7.43306	−0.732401	−0.366200	−	0.930536i	$-0.619342\pi$
$103$	−7.43306	−0.732401	−0.366200	+	0.930536i	$0.619342\pi$
$104$	−5.47699	−0.537063
$105$	5.23617	0.510998
$106$	9.25215	0.898648
$107$	−15.7310	−1.52077	−0.760386	−	0.649471i	$-0.774990\pi$
$107$	−15.7310	−1.52077	−0.760386	+	0.649471i	$0.774990\pi$
$108$	−5.64058	−0.542765
$109$	−6.43062	−0.615942	−0.307971	−	0.951396i	$-0.599650\pi$
$109$	−6.43062	−0.615942	−0.307971	+	0.951396i	$0.599650\pi$
$110$	−4.70854	−0.448942
$111$	−13.7119	−1.30147
$112$	−3.54824	−0.335278
$113$	9.64176	0.907020	0.453510	−	0.891251i	$-0.350172\pi$
$113$	9.64176	0.907020	0.453510	+	0.891251i	$0.350172\pi$
$114$	1.79009	0.167657
$115$	5.72028	0.533419
$116$	−4.64378	−0.431164
$117$	4.50366	0.416364
$118$	4.71650	0.434189
$119$	0	0
$120$	−1.47571	−0.134713
$121$	11.1704	1.01549
$122$	12.4453	1.12675
$123$	−0.211165	−0.0190401
$124$	−7.28334	−0.654063
$125$	−1.00000	−0.0894427
$126$	2.91768	0.259927
$127$	−3.20591	−0.284479	−0.142239	−	0.989832i	$-0.545430\pi$
$127$	−3.20591	−0.284479	−0.142239	+	0.989832i	$0.545430\pi$
$128$	1.00000	0.0883883
$129$	−1.22508	−0.107862
$130$	5.47699	0.480364
$131$	−3.57337	−0.312207	−0.156103	−	0.987741i	$-0.549893\pi$
$131$	−3.57337	−0.312207	−0.156103	+	0.987741i	$0.549893\pi$
$132$	6.94843	0.604783
$133$	−4.30416	−0.373218
$134$	−8.66703	−0.748718
$135$	5.64058	0.485464
$136$	0	0
$137$	3.30950	0.282750	0.141375	−	0.989956i	$-0.454848\pi$
$137$	3.30950	0.282750	0.141375	+	0.989956i	$0.454848\pi$
$138$	−8.44146	−0.718585
$139$	−1.79996	−0.152671	−0.0763354	−	0.997082i	$-0.524322\pi$
$139$	−1.79996	−0.152671	−0.0763354	+	0.997082i	$0.524322\pi$
$140$	3.54824	0.299881
$141$	8.64225	0.727809
$142$	5.14391	0.431667
$143$	−25.7886	−2.15656
$144$	−0.822287	−0.0685240
$145$	4.64378	0.385645
$146$	−16.1322	−1.33511
$147$	8.24926	0.680388
$148$	−9.29174	−0.763776
$149$	4.16768	0.341430	0.170715	−	0.985320i	$-0.445392\pi$
$149$	4.16768	0.341430	0.170715	+	0.985320i	$0.445392\pi$
$150$	1.47571	0.120491
$151$	4.59258	0.373739	0.186869	−	0.982385i	$-0.440166\pi$
$151$	4.59258	0.373739	0.186869	+	0.982385i	$0.440166\pi$
$152$	1.21304	0.0983905
$153$	0	0
$154$	−16.7071	−1.34629
$155$	7.28334	0.585012
$156$	−8.08244	−0.647113
$157$	−15.5482	−1.24088	−0.620442	−	0.784253i	$-0.713047\pi$
$157$	−15.5482	−1.24088	−0.620442	+	0.784253i	$0.713047\pi$
$158$	−10.1159	−0.804777
$159$	13.6535	1.08279
$160$	−1.00000	−0.0790569
$161$	20.2970	1.59962
$162$	−5.85698	−0.460168
$163$	10.1378	0.794051	0.397026	−	0.917807i	$-0.370042\pi$
$163$	10.1378	0.794051	0.397026	+	0.917807i	$0.370042\pi$
$164$	−0.143094	−0.0111738
$165$	−6.94843	−0.540935
$166$	−3.40601	−0.264358
$167$	12.4516	0.963531	0.481766	−	0.876300i	$-0.339996\pi$
$167$	12.4516	0.963531	0.481766	+	0.876300i	$0.339996\pi$
$168$	−5.23617	−0.403979
$169$	16.9974	1.30750
$170$	0	0
$171$	−0.997467	−0.0762782
$172$	−0.830161	−0.0632992
$173$	−3.54670	−0.269651	−0.134825	−	0.990869i	$-0.543047\pi$
$173$	−3.54670	−0.269651	−0.134825	+	0.990869i	$0.543047\pi$
$174$	−6.85286	−0.519514
$175$	−3.54824	−0.268222
$176$	4.70854	0.354920
$177$	6.96018	0.523159
$178$	2.24175	0.168027
$179$	−13.1025	−0.979325	−0.489663	−	0.871912i	$-0.662880\pi$
$179$	−13.1025	−0.979325	−0.489663	+	0.871912i	$0.662880\pi$
$180$	0.822287	0.0612897
$181$	−1.82731	−0.135823	−0.0679114	−	0.997691i	$-0.521634\pi$
$181$	−1.82731	−0.135823	−0.0679114	+	0.997691i	$0.521634\pi$
$182$	19.4337	1.44052
$183$	18.3656	1.35763
$184$	−5.72028	−0.421705
$185$	9.29174	0.683142
$186$	−10.7481	−0.788087
$187$	0	0
$188$	5.85635	0.427118
$189$	20.0142	1.45582
$190$	−1.21304	−0.0880031
$191$	−16.8319	−1.21791	−0.608955	−	0.793205i	$-0.708411\pi$
$191$	−16.8319	−1.21791	−0.608955	+	0.793205i	$0.708411\pi$
$192$	1.47571	0.106500
$193$	−5.82873	−0.419561	−0.209781	−	0.977749i	$-0.567275\pi$
$193$	−5.82873	−0.419561	−0.209781	+	0.977749i	$0.567275\pi$
$194$	4.35543	0.312702
$195$	8.08244	0.578795
$196$	5.59004	0.399288
$197$	3.52144	0.250892	0.125446	−	0.992100i	$-0.459964\pi$
$197$	3.52144	0.250892	0.125446	+	0.992100i	$0.459964\pi$
$198$	−3.87177	−0.275155
$199$	−16.8001	−1.19092	−0.595462	−	0.803383i	$-0.703031\pi$
$199$	−16.8001	−1.19092	−0.595462	+	0.803383i	$0.703031\pi$
$200$	1.00000	0.0707107
$201$	−12.7900	−0.902137
$202$	10.7393	0.755616
$203$	16.4773	1.15648
$204$	0	0
$205$	0.143094	0.00999414
$206$	−7.43306	−0.517886
$207$	4.70372	0.326931
$208$	−5.47699	−0.379761
$209$	5.71165	0.395083
$210$	5.23617	0.361330
$211$	22.8199	1.57099	0.785493	−	0.618870i	$-0.212409\pi$
$211$	22.8199	1.57099	0.785493	+	0.618870i	$0.212409\pi$
$212$	9.25215	0.635440
$213$	7.59090	0.520120
$214$	−15.7310	−1.07535
$215$	0.830161	0.0566165
$216$	−5.64058	−0.383793
$217$	25.8431	1.75434
$218$	−6.43062	−0.435537
$219$	−23.8064	−1.60868
$220$	−4.70854	−0.317450
$221$	0	0
$222$	−13.7119	−0.920281
$223$	−9.06859	−0.607278	−0.303639	−	0.952787i	$-0.598202\pi$
$223$	−9.06859	−0.607278	−0.303639	+	0.952787i	$0.598202\pi$
$224$	−3.54824	−0.237077
$225$	−0.822287	−0.0548192
$226$	9.64176	0.641360
$227$	15.7478	1.04522	0.522610	−	0.852572i	$-0.324958\pi$
$227$	15.7478	1.04522	0.522610	+	0.852572i	$0.324958\pi$
$228$	1.79009	0.118552
$229$	−20.1188	−1.32949	−0.664745	−	0.747070i	$-0.731460\pi$
$229$	−20.1188	−1.32949	−0.664745	+	0.747070i	$0.731460\pi$
$230$	5.72028	0.377184
$231$	−24.6547	−1.62216
$232$	−4.64378	−0.304879
$233$	−19.2748	−1.26273	−0.631366	−	0.775485i	$-0.717505\pi$
$233$	−19.2748	−1.26273	−0.631366	+	0.775485i	$0.717505\pi$
$234$	4.50366	0.294414
$235$	−5.85635	−0.382026
$236$	4.71650	0.307018
$237$	−14.9281	−0.969684
$238$	0	0
$239$	14.2040	0.918778	0.459389	−	0.888235i	$-0.348068\pi$
$239$	14.2040	0.918778	0.459389	+	0.888235i	$0.348068\pi$
$240$	−1.47571	−0.0952565
$241$	−4.57455	−0.294673	−0.147336	−	0.989086i	$-0.547070\pi$
$241$	−4.57455	−0.294673	−0.147336	+	0.989086i	$0.547070\pi$
$242$	11.1704	0.718058
$243$	8.27854	0.531069
$244$	12.4453	0.796729
$245$	−5.59004	−0.357134
$246$	−0.211165	−0.0134634
$247$	−6.64381	−0.422735
$248$	−7.28334	−0.462492
$249$	−5.02628	−0.318527
$250$	−1.00000	−0.0632456
$251$	9.00712	0.568524	0.284262	−	0.958747i	$-0.408251\pi$
$251$	9.00712	0.568524	0.284262	+	0.958747i	$0.408251\pi$
$252$	2.91768	0.183796
$253$	−26.9342	−1.69334
$254$	−3.20591	−0.201157
$255$	0	0
$256$	1.00000	0.0625000
$257$	28.6580	1.78764	0.893819	−	0.448429i	$-0.148016\pi$
$257$	28.6580	1.78764	0.893819	+	0.448429i	$0.148016\pi$
$258$	−1.22508	−0.0762698
$259$	32.9693	2.04862
$260$	5.47699	0.339669
$261$	3.81852	0.236361
$262$	−3.57337	−0.220763
$263$	6.04573	0.372796	0.186398	−	0.982474i	$-0.440319\pi$
$263$	6.04573	0.372796	0.186398	+	0.982474i	$0.440319\pi$
$264$	6.94843	0.427646
$265$	−9.25215	−0.568355
$266$	−4.30416	−0.263905
$267$	3.30817	0.202457
$268$	−8.66703	−0.529423
$269$	16.8933	1.03000	0.515000	−	0.857190i	$-0.327792\pi$
$269$	16.8933	1.03000	0.515000	+	0.857190i	$0.327792\pi$
$270$	5.64058	0.343275
$271$	22.9305	1.39293	0.696463	−	0.717593i	$-0.254756\pi$
$271$	22.9305	1.39293	0.696463	+	0.717593i	$0.254756\pi$
$272$	0	0
$273$	28.6785	1.73570
$274$	3.30950	0.199934
$275$	4.70854	0.283936
$276$	−8.44146	−0.508116
$277$	−20.0018	−1.20179	−0.600895	−	0.799328i	$-0.705189\pi$
$277$	−20.0018	−1.20179	−0.600895	+	0.799328i	$0.705189\pi$
$278$	−1.79996	−0.107955
$279$	5.98900	0.358552
$280$	3.54824	0.212048
$281$	23.2826	1.38892	0.694462	−	0.719529i	$-0.255642\pi$
$281$	23.2826	1.38892	0.694462	+	0.719529i	$0.255642\pi$
$282$	8.64225	0.514639
$283$	25.1508	1.49506	0.747528	−	0.664230i	$-0.231240\pi$
$283$	25.1508	1.49506	0.747528	+	0.664230i	$0.231240\pi$
$284$	5.14391	0.305235
$285$	−1.79009	−0.106036
$286$	−25.7886	−1.52491
$287$	0.507734	0.0299706
$288$	−0.822287	−0.0484538
$289$	0	0
$290$	4.64378	0.272692
$291$	6.42734	0.376777
$292$	−16.1322	−0.944064
$293$	25.5251	1.49119	0.745595	−	0.666399i	$-0.232165\pi$
$293$	25.5251	1.49119	0.745595	+	0.666399i	$0.232165\pi$
$294$	8.24926	0.481107
$295$	−4.71650	−0.274605
$296$	−9.29174	−0.540071
$297$	−26.5589	−1.54110
$298$	4.16768	0.241427
$299$	31.3299	1.81186
$300$	1.47571	0.0852000
$301$	2.94561	0.169782
$302$	4.59258	0.264273
$303$	15.8481	0.910449
$304$	1.21304	0.0695726
$305$	−12.4453	−0.712616
$306$	0	0
$307$	−14.2382	−0.812616	−0.406308	−	0.913736i	$-0.633184\pi$
$307$	−14.2382	−0.812616	−0.406308	+	0.913736i	$0.633184\pi$
$308$	−16.7071	−0.951973
$309$	−10.9690	−0.624006
$310$	7.28334	0.413666
$311$	12.1514	0.689040	0.344520	−	0.938779i	$-0.388042\pi$
$311$	12.1514	0.689040	0.344520	+	0.938779i	$0.388042\pi$
$312$	−8.08244	−0.457578
$313$	21.7897	1.23162	0.615812	−	0.787893i	$-0.288828\pi$
$313$	21.7897	1.23162	0.615812	+	0.787893i	$0.288828\pi$
$314$	−15.5482	−0.877437
$315$	−2.91768	−0.164392
$316$	−10.1159	−0.569063
$317$	−10.2517	−0.575791	−0.287895	−	0.957662i	$-0.592956\pi$
$317$	−10.2517	−0.575791	−0.287895	+	0.957662i	$0.592956\pi$
$318$	13.6535	0.765648
$319$	−21.8654	−1.22423
$320$	−1.00000	−0.0559017
$321$	−23.2143	−1.29570
$322$	20.2970	1.13111
$323$	0	0
$324$	−5.85698	−0.325388
$325$	−5.47699	−0.303809
$326$	10.1378	0.561479
$327$	−9.48972	−0.524783
$328$	−0.143094	−0.00790106
$329$	−20.7797	−1.14562
$330$	−6.94843	−0.382499
$331$	0.296190	0.0162801	0.00814003	−	0.999967i	$-0.497409\pi$
$331$	0.296190	0.0162801	0.00814003	+	0.999967i	$0.497409\pi$
$332$	−3.40601	−0.186929
$333$	7.64048	0.418696
$334$	12.4516	0.681320
$335$	8.66703	0.473531
$336$	−5.23617	−0.285657
$337$	14.0520	0.765463	0.382732	−	0.923860i	$-0.374983\pi$
$337$	14.0520	0.765463	0.382732	+	0.923860i	$0.374983\pi$
$338$	16.9974	0.924539
$339$	14.2284	0.772782
$340$	0	0
$341$	−34.2939	−1.85712
$342$	−0.997467	−0.0539368
$343$	5.00289	0.270130
$344$	−0.830161	−0.0447593
$345$	8.44146	0.454473
$346$	−3.54670	−0.190672
$347$	11.1494	0.598532	0.299266	−	0.954170i	$-0.403258\pi$
$347$	11.1494	0.598532	0.299266	+	0.954170i	$0.403258\pi$
$348$	−6.85286	−0.367352
$349$	−2.51265	−0.134499	−0.0672494	−	0.997736i	$-0.521422\pi$
$349$	−2.51265	−0.134499	−0.0672494	+	0.997736i	$0.521422\pi$
$350$	−3.54824	−0.189662
$351$	30.8934	1.64897
$352$	4.70854	0.250966
$353$	10.0823	0.536629	0.268314	−	0.963331i	$-0.413533\pi$
$353$	10.0823	0.536629	0.268314	+	0.963331i	$0.413533\pi$
$354$	6.96018	0.369929
$355$	−5.14391	−0.273010
$356$	2.24175	0.118813
$357$	0	0
$358$	−13.1025	−0.692487
$359$	−24.6679	−1.30192	−0.650962	−	0.759110i	$-0.725634\pi$
$359$	−24.6679	−1.30192	−0.650962	+	0.759110i	$0.725634\pi$
$360$	0.822287	0.0433384
$361$	−17.5285	−0.922555
$362$	−1.82731	−0.0960413
$363$	16.4842	0.865196
$364$	19.4337	1.01860
$365$	16.1322	0.844396
$366$	18.3656	0.959987
$367$	29.7736	1.55417	0.777085	−	0.629396i	$-0.216698\pi$
$367$	29.7736	1.55417	0.777085	+	0.629396i	$0.216698\pi$
$368$	−5.72028	−0.298190
$369$	0.117665	0.00612538
$370$	9.29174	0.483054
$371$	−32.8289	−1.70439
$372$	−10.7481	−0.557262
$373$	−20.8039	−1.07718	−0.538592	−	0.842567i	$-0.681044\pi$
$373$	−20.8039	−1.07718	−0.538592	+	0.842567i	$0.681044\pi$
$374$	0	0
$375$	−1.47571	−0.0762052
$376$	5.85635	0.302018
$377$	25.4339	1.30992
$378$	20.0142	1.02942
$379$	−10.4448	−0.536514	−0.268257	−	0.963347i	$-0.586448\pi$
$379$	−10.4448	−0.536514	−0.268257	+	0.963347i	$0.586448\pi$
$380$	−1.21304	−0.0622276
$381$	−4.73099	−0.242376
$382$	−16.8319	−0.861193
$383$	−20.1518	−1.02971	−0.514854	−	0.857278i	$-0.672154\pi$
$383$	−20.1518	−1.02971	−0.514854	+	0.857278i	$0.672154\pi$
$384$	1.47571	0.0753069
$385$	16.7071	0.851471
$386$	−5.82873	−0.296674
$387$	0.682631	0.0347001
$388$	4.35543	0.221113
$389$	19.6657	0.997092	0.498546	−	0.866863i	$-0.333867\pi$
$389$	19.6657	0.997092	0.498546	+	0.866863i	$0.333867\pi$
$390$	8.08244	0.409270
$391$	0	0
$392$	5.59004	0.282340
$393$	−5.27324	−0.266000
$394$	3.52144	0.177408
$395$	10.1159	0.508986
$396$	−3.87177	−0.194564
$397$	−23.9479	−1.20191	−0.600955	−	0.799283i	$-0.705213\pi$
$397$	−23.9479	−1.20191	−0.600955	+	0.799283i	$0.705213\pi$
$398$	−16.8001	−0.842111
$399$	−6.35168	−0.317982
$400$	1.00000	0.0500000
$401$	−23.0408	−1.15060	−0.575302	−	0.817941i	$-0.695115\pi$
$401$	−23.0408	−1.15060	−0.575302	+	0.817941i	$0.695115\pi$
$402$	−12.7900	−0.637907
$403$	39.8908	1.98710
$404$	10.7393	0.534301
$405$	5.85698	0.291036
$406$	16.4773	0.817753
$407$	−43.7505	−2.16863
$408$	0	0
$409$	12.7488	0.630389	0.315195	−	0.949027i	$-0.397930\pi$
$409$	12.7488	0.630389	0.315195	+	0.949027i	$0.397930\pi$
$410$	0.143094	0.00706692
$411$	4.88385	0.240903
$412$	−7.43306	−0.366200
$413$	−16.7353	−0.823491
$414$	4.70372	0.231175
$415$	3.40601	0.167195
$416$	−5.47699	−0.268532
$417$	−2.65622	−0.130076
$418$	5.71165	0.279366
$419$	−27.3719	−1.33720	−0.668602	−	0.743621i	$-0.733107\pi$
$419$	−27.3719	−1.33720	−0.668602	+	0.743621i	$0.733107\pi$
$420$	5.23617	0.255499
$421$	−33.6813	−1.64153	−0.820764	−	0.571268i	$-0.806452\pi$
$421$	−33.6813	−1.64153	−0.820764	+	0.571268i	$0.806452\pi$
$422$	22.8199	1.11086
$423$	−4.81560	−0.234142
$424$	9.25215	0.449324
$425$	0	0
$426$	7.59090	0.367780
$427$	−44.1590	−2.13700
$428$	−15.7310	−0.760386
$429$	−38.0565	−1.83739
$430$	0.830161	0.0400339
$431$	−18.1802	−0.875709	−0.437854	−	0.899046i	$-0.644261\pi$
$431$	−18.1802	−0.875709	−0.437854	+	0.899046i	$0.644261\pi$
$432$	−5.64058	−0.271382
$433$	8.10392	0.389450	0.194725	−	0.980858i	$-0.437619\pi$
$433$	8.10392	0.389450	0.194725	+	0.980858i	$0.437619\pi$
$434$	25.8431	1.24051
$435$	6.85286	0.328570
$436$	−6.43062	−0.307971
$437$	−6.93893	−0.331934
$438$	−23.8064	−1.13751
$439$	−23.9774	−1.14438	−0.572188	−	0.820122i	$-0.693905\pi$
$439$	−23.9774	−1.14438	−0.572188	+	0.820122i	$0.693905\pi$
$440$	−4.70854	−0.224471
$441$	−4.59662	−0.218887
$442$	0	0
$443$	0.244075	0.0115964	0.00579819	−	0.999983i	$-0.498154\pi$
$443$	0.244075	0.0115964	0.00579819	+	0.999983i	$0.498154\pi$
$444$	−13.7119	−0.650737
$445$	−2.24175	−0.106269
$446$	−9.06859	−0.429410
$447$	6.15028	0.290898
$448$	−3.54824	−0.167639
$449$	0.0824322	0.00389021	0.00194511	−	0.999998i	$-0.499381\pi$
$449$	0.0824322	0.00389021	0.00194511	+	0.999998i	$0.499381\pi$
$450$	−0.822287	−0.0387630
$451$	−0.673765	−0.0317264
$452$	9.64176	0.453510
$453$	6.77731	0.318426
$454$	15.7478	0.739082
$455$	−19.4337	−0.911066
$456$	1.79009	0.0838287
$457$	−24.3896	−1.14090	−0.570449	−	0.821333i	$-0.693231\pi$
$457$	−24.3896	−1.14090	−0.570449	+	0.821333i	$0.693231\pi$
$458$	−20.1188	−0.940092
$459$	0	0
$460$	5.72028	0.266710
$461$	29.1100	1.35579	0.677894	−	0.735159i	$-0.262893\pi$
$461$	29.1100	1.35579	0.677894	+	0.735159i	$0.262893\pi$
$462$	−24.6547	−1.14704
$463$	27.9762	1.30016	0.650081	−	0.759865i	$-0.274735\pi$
$463$	27.9762	1.30016	0.650081	+	0.759865i	$0.274735\pi$
$464$	−4.64378	−0.215582
$465$	10.7481	0.498430
$466$	−19.2748	−0.892886
$467$	−31.2786	−1.44740	−0.723701	−	0.690113i	$-0.757561\pi$
$467$	−31.2786	−1.44740	−0.723701	+	0.690113i	$0.757561\pi$
$468$	4.50366	0.208182
$469$	30.7528	1.42003
$470$	−5.85635	−0.270133
$471$	−22.9446	−1.05723
$472$	4.71650	0.217095
$473$	−3.90885	−0.179729
$474$	−14.9281	−0.685670
$475$	1.21304	0.0556581
$476$	0	0
$477$	−7.60792	−0.348343
$478$	14.2040	0.649674
$479$	−12.0756	−0.551747	−0.275873	−	0.961194i	$-0.588967\pi$
$479$	−12.0756	−0.551747	−0.275873	+	0.961194i	$0.588967\pi$
$480$	−1.47571	−0.0673565
$481$	50.8908	2.32042
$482$	−4.57455	−0.208365
$483$	29.9524	1.36288
$484$	11.1704	0.507744
$485$	−4.35543	−0.197770
$486$	8.27854	0.375522
$487$	−5.01555	−0.227276	−0.113638	−	0.993522i	$-0.536250\pi$
$487$	−5.01555	−0.227276	−0.113638	+	0.993522i	$0.536250\pi$
$488$	12.4453	0.563373
$489$	14.9604	0.676532
$490$	−5.59004	−0.252532
$491$	26.4441	1.19341	0.596703	−	0.802462i	$-0.296477\pi$
$491$	26.4441	1.19341	0.596703	+	0.802462i	$0.296477\pi$
$492$	−0.211165	−0.00952007
$493$	0	0
$494$	−6.64381	−0.298919
$495$	3.87177	0.174023
$496$	−7.28334	−0.327031
$497$	−18.2518	−0.818707
$498$	−5.02628	−0.225233
$499$	−29.9384	−1.34023	−0.670113	−	0.742259i	$-0.733754\pi$
$499$	−29.9384	−1.34023	−0.670113	+	0.742259i	$0.733754\pi$
$500$	−1.00000	−0.0447214
$501$	18.3749	0.820929
$502$	9.00712	0.402007
$503$	34.1010	1.52049	0.760244	−	0.649638i	$-0.225080\pi$
$503$	34.1010	1.52049	0.760244	+	0.649638i	$0.225080\pi$
$504$	2.91768	0.129964
$505$	−10.7393	−0.477893
$506$	−26.9342	−1.19737
$507$	25.0833	1.11399
$508$	−3.20591	−0.142239
$509$	−28.0939	−1.24524	−0.622620	−	0.782525i	$-0.713932\pi$
$509$	−28.0939	−1.24524	−0.622620	+	0.782525i	$0.713932\pi$
$510$	0	0
$511$	57.2409	2.53219
$512$	1.00000	0.0441942
$513$	−6.84224	−0.302092
$514$	28.6580	1.26405
$515$	7.43306	0.327540
$516$	−1.22508	−0.0539309
$517$	27.5749	1.21274
$518$	32.9693	1.44859
$519$	−5.23389	−0.229742
$520$	5.47699	0.240182
$521$	−19.0734	−0.835620	−0.417810	−	0.908534i	$-0.637202\pi$
$521$	−19.0734	−0.835620	−0.417810	+	0.908534i	$0.637202\pi$
$522$	3.81852	0.167132
$523$	−6.69653	−0.292819	−0.146409	−	0.989224i	$-0.546772\pi$
$523$	−6.69653	−0.292819	−0.146409	+	0.989224i	$0.546772\pi$
$524$	−3.57337	−0.156103
$525$	−5.23617	−0.228525
$526$	6.04573	0.263606
$527$	0	0
$528$	6.94843	0.302392
$529$	9.72163	0.422679
$530$	−9.25215	−0.401888
$531$	−3.87832	−0.168305
$532$	−4.30416	−0.186609
$533$	0.783726	0.0339470
$534$	3.30817	0.143159
$535$	15.7310	0.680110
$536$	−8.66703	−0.374359
$537$	−19.3354	−0.834385
$538$	16.8933	0.728320
$539$	26.3209	1.13372
$540$	5.64058	0.242732
$541$	6.84763	0.294403	0.147201	−	0.989107i	$-0.452973\pi$
$541$	6.84763	0.294403	0.147201	+	0.989107i	$0.452973\pi$
$542$	22.9305	0.984947
$543$	−2.69657	−0.115721
$544$	0	0
$545$	6.43062	0.275458
$546$	28.6785	1.22733
$547$	−3.53078	−0.150965	−0.0754827	−	0.997147i	$-0.524050\pi$
$547$	−3.53078	−0.150965	−0.0754827	+	0.997147i	$0.524050\pi$
$548$	3.30950	0.141375
$549$	−10.2336	−0.436760
$550$	4.70854	0.200773
$551$	−5.63309	−0.239978
$552$	−8.44146	−0.359293
$553$	35.8937	1.52635
$554$	−20.0018	−0.849794
$555$	13.7119	0.582037
$556$	−1.79996	−0.0763354
$557$	−45.7591	−1.93888	−0.969438	−	0.245338i	$-0.921101\pi$
$557$	−45.7591	−1.93888	−0.969438	+	0.245338i	$0.921101\pi$
$558$	5.98900	0.253534
$559$	4.54679	0.192309
$560$	3.54824	0.149941
$561$	0	0
$562$	23.2826	0.982118
$563$	−9.97870	−0.420552	−0.210276	−	0.977642i	$-0.567436\pi$
$563$	−9.97870	−0.420552	−0.210276	+	0.977642i	$0.567436\pi$
$564$	8.64225	0.363905
$565$	−9.64176	−0.405632
$566$	25.1508	1.05716
$567$	20.7820	0.872762
$568$	5.14391	0.215834
$569$	13.5202	0.566795	0.283397	−	0.959003i	$-0.408538\pi$
$569$	13.5202	0.566795	0.283397	+	0.959003i	$0.408538\pi$
$570$	−1.79009	−0.0749787
$571$	16.9714	0.710233	0.355116	−	0.934822i	$-0.384441\pi$
$571$	16.9714	0.710233	0.355116	+	0.934822i	$0.384441\pi$
$572$	−25.7886	−1.07828
$573$	−24.8389	−1.03766
$574$	0.507734	0.0211924
$575$	−5.72028	−0.238552
$576$	−0.822287	−0.0342620
$577$	9.67374	0.402723	0.201361	−	0.979517i	$-0.435463\pi$
$577$	9.67374	0.402723	0.201361	+	0.979517i	$0.435463\pi$
$578$	0	0
$579$	−8.60150	−0.357466
$580$	4.64378	0.192822
$581$	12.0854	0.501385
$582$	6.42734	0.266422
$583$	43.5641	1.80424
$584$	−16.1322	−0.667554
$585$	−4.50366	−0.186204
$586$	25.5251	1.05443
$587$	4.59186	0.189526	0.0947632	−	0.995500i	$-0.469791\pi$
$587$	4.59186	0.189526	0.0947632	+	0.995500i	$0.469791\pi$
$588$	8.24926	0.340194
$589$	−8.83497	−0.364039
$590$	−4.71650	−0.194175
$591$	5.19661	0.213760
$592$	−9.29174	−0.381888
$593$	0.778841	0.0319832	0.0159916	−	0.999872i	$-0.494910\pi$
$593$	0.778841	0.0319832	0.0159916	+	0.999872i	$0.494910\pi$
$594$	−26.5589	−1.08972
$595$	0	0
$596$	4.16768	0.170715
$597$	−24.7920	−1.01467
$598$	31.3299	1.28118
$599$	−10.4846	−0.428391	−0.214196	−	0.976791i	$-0.568713\pi$
$599$	−10.4846	−0.428391	−0.214196	+	0.976791i	$0.568713\pi$
$600$	1.47571	0.0602455
$601$	−15.3435	−0.625875	−0.312937	−	0.949774i	$-0.601313\pi$
$601$	−15.3435	−0.625875	−0.312937	+	0.949774i	$0.601313\pi$
$602$	2.94561	0.120054
$603$	7.12679	0.290225
$604$	4.59258	0.186869
$605$	−11.1704	−0.454140
$606$	15.8481	0.643785
$607$	21.6225	0.877631	0.438815	−	0.898577i	$-0.355398\pi$
$607$	21.6225	0.877631	0.438815	+	0.898577i	$0.355398\pi$
$608$	1.21304	0.0491952
$609$	24.3156	0.985319
$610$	−12.4453	−0.503896
$611$	−32.0752	−1.29762
$612$	0	0
$613$	−18.6071	−0.751535	−0.375768	−	0.926714i	$-0.622621\pi$
$613$	−18.6071	−0.751535	−0.375768	+	0.926714i	$0.622621\pi$
$614$	−14.2382	−0.574606
$615$	0.211165	0.00851501
$616$	−16.7071	−0.673147
$617$	−5.70409	−0.229638	−0.114819	−	0.993386i	$-0.536629\pi$
$617$	−5.70409	−0.229638	−0.114819	+	0.993386i	$0.536629\pi$
$618$	−10.9690	−0.441239
$619$	−29.2325	−1.17495	−0.587477	−	0.809241i	$-0.699879\pi$
$619$	−29.2325	−1.17495	−0.587477	+	0.809241i	$0.699879\pi$
$620$	7.28334	0.292506
$621$	32.2657	1.29478
$622$	12.1514	0.487225
$623$	−7.95429	−0.318682
$624$	−8.08244	−0.323557
$625$	1.00000	0.0400000
$626$	21.7897	0.870890
$627$	8.42872	0.336611
$628$	−15.5482	−0.620442
$629$	0	0
$630$	−2.91768	−0.116243
$631$	43.7803	1.74287	0.871433	−	0.490514i	$-0.163191\pi$
$631$	43.7803	1.74287	0.871433	+	0.490514i	$0.163191\pi$
$632$	−10.1159	−0.402389
$633$	33.6755	1.33848
$634$	−10.2517	−0.407146
$635$	3.20591	0.127223
$636$	13.6535	0.541395
$637$	−30.6166	−1.21307
$638$	−21.8654	−0.865661
$639$	−4.22977	−0.167327
$640$	−1.00000	−0.0395285
$641$	−43.6164	−1.72274	−0.861372	−	0.507975i	$-0.830394\pi$
$641$	−43.6164	−1.72274	−0.861372	+	0.507975i	$0.830394\pi$
$642$	−23.2143	−0.916197
$643$	5.54619	0.218720	0.109360	−	0.994002i	$-0.465120\pi$
$643$	5.54619	0.218720	0.109360	+	0.994002i	$0.465120\pi$
$644$	20.2970	0.799812
$645$	1.22508	0.0482373
$646$	0	0
$647$	−25.3893	−0.998155	−0.499078	−	0.866557i	$-0.666328\pi$
$647$	−25.3893	−0.998155	−0.499078	+	0.866557i	$0.666328\pi$
$648$	−5.85698	−0.230084
$649$	22.2079	0.871734
$650$	−5.47699	−0.214825
$651$	38.1368	1.49470
$652$	10.1378	0.397026
$653$	−39.3163	−1.53857	−0.769283	−	0.638908i	$-0.779387\pi$
$653$	−39.3163	−1.53857	−0.769283	+	0.638908i	$0.779387\pi$
$654$	−9.48972	−0.371077
$655$	3.57337	0.139623
$656$	−0.143094	−0.00558689
$657$	13.2653	0.517528
$658$	−20.7797	−0.810079
$659$	−39.5179	−1.53940	−0.769698	−	0.638408i	$-0.779593\pi$
$659$	−39.5179	−1.53940	−0.769698	+	0.638408i	$0.779593\pi$
$660$	−6.94843	−0.270467
$661$	3.13936	0.122107	0.0610535	−	0.998134i	$-0.480554\pi$
$661$	3.13936	0.122107	0.0610535	+	0.998134i	$0.480554\pi$
$662$	0.296190	0.0115117
$663$	0	0
$664$	−3.40601	−0.132179
$665$	4.30416	0.166908
$666$	7.64048	0.296062
$667$	26.5637	1.02855
$668$	12.4516	0.481766
$669$	−13.3826	−0.517401
$670$	8.66703	0.334837
$671$	58.5993	2.26220
$672$	−5.23617	−0.201990
$673$	−23.2880	−0.897688	−0.448844	−	0.893610i	$-0.648164\pi$
$673$	−23.2880	−0.897688	−0.448844	+	0.893610i	$0.648164\pi$
$674$	14.0520	0.541264
$675$	−5.64058	−0.217106
$676$	16.9974	0.653748
$677$	41.2769	1.58640	0.793200	−	0.608961i	$-0.208413\pi$
$677$	41.2769	1.58640	0.793200	+	0.608961i	$0.208413\pi$
$678$	14.2284	0.546439
$679$	−15.4541	−0.593075
$680$	0	0
$681$	23.2392	0.890528
$682$	−34.2939	−1.31318
$683$	6.25229	0.239237	0.119619	−	0.992820i	$-0.461833\pi$
$683$	6.25229	0.239237	0.119619	+	0.992820i	$0.461833\pi$
$684$	−0.997467	−0.0381391
$685$	−3.30950	−0.126449
$686$	5.00289	0.191011
$687$	−29.6895	−1.13273
$688$	−0.830161	−0.0316496
$689$	−50.6739	−1.93052
$690$	8.44146	0.321361
$691$	32.1462	1.22290	0.611449	−	0.791284i	$-0.290587\pi$
$691$	32.1462	1.22290	0.611449	+	0.791284i	$0.290587\pi$
$692$	−3.54670	−0.134825
$693$	13.7380	0.521864
$694$	11.1494	0.423226
$695$	1.79996	0.0682765
$696$	−6.85286	−0.259757
$697$	0	0
$698$	−2.51265	−0.0951051
$699$	−28.4439	−1.07585
$700$	−3.54824	−0.134111
$701$	−12.7609	−0.481972	−0.240986	−	0.970529i	$-0.577471\pi$
$701$	−12.7609	−0.481972	−0.240986	+	0.970529i	$0.577471\pi$
$702$	30.8934	1.16600
$703$	−11.2712	−0.425103
$704$	4.70854	0.177460
$705$	−8.64225	−0.325486
$706$	10.0823	0.379454
$707$	−38.1057	−1.43311
$708$	6.96018	0.261580
$709$	33.5197	1.25886	0.629429	−	0.777058i	$-0.283289\pi$
$709$	33.5197	1.25886	0.629429	+	0.777058i	$0.283289\pi$
$710$	−5.14391	−0.193047
$711$	8.31817	0.311956
$712$	2.24175	0.0840133
$713$	41.6627	1.56028
$714$	0	0
$715$	25.7886	0.964441
$716$	−13.1025	−0.489663
$717$	20.9609	0.782799
$718$	−24.6679	−0.920599
$719$	28.6679	1.06913	0.534567	−	0.845126i	$-0.320475\pi$
$719$	28.6679	1.06913	0.534567	+	0.845126i	$0.320475\pi$
$720$	0.822287	0.0306448
$721$	26.3743	0.982231
$722$	−17.5285	−0.652345
$723$	−6.75070	−0.251061
$724$	−1.82731	−0.0679114
$725$	−4.64378	−0.172466
$726$	16.4842	0.611786
$727$	−21.0302	−0.779966	−0.389983	−	0.920822i	$-0.627519\pi$
$727$	−21.0302	−0.779966	−0.389983	+	0.920822i	$0.627519\pi$
$728$	19.4337	0.720261
$729$	29.7877	1.10325
$730$	16.1322	0.597078
$731$	0	0
$732$	18.3656	0.678813
$733$	−9.02619	−0.333390	−0.166695	−	0.986009i	$-0.553310\pi$
$733$	−9.02619	−0.333390	−0.166695	+	0.986009i	$0.553310\pi$
$734$	29.7736	1.09896
$735$	−8.24926	−0.304279
$736$	−5.72028	−0.210852
$737$	−40.8091	−1.50322
$738$	0.117665	0.00433130
$739$	−14.4038	−0.529852	−0.264926	−	0.964269i	$-0.585347\pi$
$739$	−14.4038	−0.529852	−0.264926	+	0.964269i	$0.585347\pi$
$740$	9.29174	0.341571
$741$	−9.80432	−0.360171
$742$	−32.8289	−1.20519
$743$	33.1127	1.21479	0.607393	−	0.794401i	$-0.292215\pi$
$743$	33.1127	1.21479	0.607393	+	0.794401i	$0.292215\pi$
$744$	−10.7481	−0.394043
$745$	−4.16768	−0.152692
$746$	−20.8039	−0.761684
$747$	2.80072	0.102473
$748$	0	0
$749$	55.8174	2.03952
$750$	−1.47571	−0.0538852
$751$	−6.41038	−0.233918	−0.116959	−	0.993137i	$-0.537315\pi$
$751$	−6.41038	−0.233918	−0.116959	+	0.993137i	$0.537315\pi$
$752$	5.85635	0.213559
$753$	13.2919	0.484383
$754$	25.4339	0.926250
$755$	−4.59258	−0.167141
$756$	20.0142	0.727908
$757$	49.0252	1.78185	0.890925	−	0.454150i	$-0.150057\pi$
$757$	49.0252	1.78185	0.890925	+	0.454150i	$0.150057\pi$
$758$	−10.4448	−0.379373
$759$	−39.7470	−1.44272
$760$	−1.21304	−0.0440016
$761$	−42.6819	−1.54722	−0.773610	−	0.633662i	$-0.781551\pi$
$761$	−42.6819	−1.54722	−0.773610	+	0.633662i	$0.781551\pi$
$762$	−4.73099	−0.171386
$763$	22.8174	0.826046
$764$	−16.8319	−0.608955
$765$	0	0
$766$	−20.1518	−0.728113
$767$	−25.8323	−0.932749
$768$	1.47571	0.0532500
$769$	14.6429	0.528035	0.264018	−	0.964518i	$-0.414952\pi$
$769$	14.6429	0.528035	0.264018	+	0.964518i	$0.414952\pi$
$770$	16.7071	0.602081
$771$	42.2908	1.52307
$772$	−5.82873	−0.209781
$773$	−14.8507	−0.534142	−0.267071	−	0.963677i	$-0.586056\pi$
$773$	−14.8507	−0.534142	−0.267071	+	0.963677i	$0.586056\pi$
$774$	0.682631	0.0245367
$775$	−7.28334	−0.261625
$776$	4.35543	0.156351
$777$	48.6531	1.74542
$778$	19.6657	0.705051
$779$	−0.173579	−0.00621911
$780$	8.08244	0.289398
$781$	24.2203	0.866670
$782$	0	0
$783$	26.1936	0.936083
$784$	5.59004	0.199644
$785$	15.5482	0.554940
$786$	−5.27324	−0.188090
$787$	−21.4953	−0.766224	−0.383112	−	0.923702i	$-0.625148\pi$
$787$	−21.4953	−0.766224	−0.383112	+	0.923702i	$0.625148\pi$
$788$	3.52144	0.125446
$789$	8.92173	0.317622
$790$	10.1159	0.359907
$791$	−34.2113	−1.21641
$792$	−3.87177	−0.137578
$793$	−68.1629	−2.42053
$794$	−23.9479	−0.849879
$795$	−13.6535	−0.484238
$796$	−16.8001	−0.595462
$797$	−21.0624	−0.746068	−0.373034	−	0.927818i	$-0.621683\pi$
$797$	−21.0624	−0.746068	−0.373034	+	0.927818i	$0.621683\pi$
$798$	−6.35168	−0.224847
$799$	0	0
$800$	1.00000	0.0353553
$801$	−1.84337	−0.0651321
$802$	−23.0408	−0.813599
$803$	−75.9590	−2.68053
$804$	−12.7900	−0.451069
$805$	−20.2970	−0.715374
$806$	39.8908	1.40509
$807$	24.9295	0.877560
$808$	10.7393	0.377808
$809$	−18.2576	−0.641904	−0.320952	−	0.947095i	$-0.604003\pi$
$809$	−18.2576	−0.641904	−0.320952	+	0.947095i	$0.604003\pi$
$810$	5.85698	0.205793
$811$	−14.5457	−0.510767	−0.255384	−	0.966840i	$-0.582202\pi$
$811$	−14.5457	−0.510767	−0.255384	+	0.966840i	$0.582202\pi$
$812$	16.4773	0.578239
$813$	33.8386	1.18677
$814$	−43.7505	−1.53346
$815$	−10.1378	−0.355111
$816$	0	0
$817$	−1.00702	−0.0352311
$818$	12.7488	0.445752
$819$	−15.9801	−0.558390
$820$	0.143094	0.00499707
$821$	−40.8248	−1.42480	−0.712399	−	0.701775i	$-0.752391\pi$
$821$	−40.8248	−1.42480	−0.712399	+	0.701775i	$0.752391\pi$
$822$	4.88385	0.170344
$823$	−1.82250	−0.0635283	−0.0317641	−	0.999495i	$-0.510113\pi$
$823$	−1.82250	−0.0635283	−0.0317641	+	0.999495i	$0.510113\pi$
$824$	−7.43306	−0.258943
$825$	6.94843	0.241913
$826$	−16.7353	−0.582296
$827$	−46.4355	−1.61472	−0.807360	−	0.590059i	$-0.799104\pi$
$827$	−46.4355	−1.61472	−0.807360	+	0.590059i	$0.799104\pi$
$828$	4.70372	0.163465
$829$	34.9749	1.21473	0.607364	−	0.794424i	$-0.292227\pi$
$829$	34.9749	1.21473	0.607364	+	0.794424i	$0.292227\pi$
$830$	3.40601	0.118224
$831$	−29.5168	−1.02393
$832$	−5.47699	−0.189881
$833$	0	0
$834$	−2.65622	−0.0919773
$835$	−12.4516	−0.430904
$836$	5.71165	0.197541
$837$	41.0822	1.42001
$838$	−27.3719	−0.945545
$839$	42.9558	1.48300	0.741500	−	0.670953i	$-0.234115\pi$
$839$	42.9558	1.48300	0.741500	+	0.670953i	$0.234115\pi$
$840$	5.23617	0.180665
$841$	−7.43531	−0.256390
$842$	−33.6813	−1.16074
$843$	34.3583	1.18336
$844$	22.8199	0.785493
$845$	−16.9974	−0.584730
$846$	−4.81560	−0.165564
$847$	−39.6352	−1.36188
$848$	9.25215	0.317720
$849$	37.1152	1.27379
$850$	0	0
$851$	53.1513	1.82200
$852$	7.59090	0.260060
$853$	−9.29809	−0.318360	−0.159180	−	0.987250i	$-0.550885\pi$
$853$	−9.29809	−0.318360	−0.159180	+	0.987250i	$0.550885\pi$
$854$	−44.1590	−1.51109
$855$	0.997467	0.0341127
$856$	−15.7310	−0.537674
$857$	30.9726	1.05801	0.529003	−	0.848620i	$-0.322566\pi$
$857$	30.9726	1.05801	0.529003	+	0.848620i	$0.322566\pi$
$858$	−38.0565	−1.29923
$859$	18.5274	0.632145	0.316073	−	0.948735i	$-0.397636\pi$
$859$	18.5274	0.632145	0.316073	+	0.948735i	$0.397636\pi$
$860$	0.830161	0.0283083
$861$	0.749266	0.0255349
$862$	−18.1802	−0.619219
$863$	18.5377	0.631030	0.315515	−	0.948921i	$-0.397823\pi$
$863$	18.5377	0.631030	0.315515	+	0.948921i	$0.397823\pi$
$864$	−5.64058	−0.191896
$865$	3.54670	0.120591
$866$	8.10392	0.275382
$867$	0	0
$868$	25.8431	0.877170
$869$	−47.6311	−1.61577
$870$	6.85286	0.232334
$871$	47.4693	1.60843
$872$	−6.43062	−0.217768
$873$	−3.58141	−0.121212
$874$	−6.93893	−0.234713
$875$	3.54824	0.119953
$876$	−23.8064	−0.804342
$877$	42.8547	1.44710	0.723550	−	0.690272i	$-0.242509\pi$
$877$	42.8547	1.44710	0.723550	+	0.690272i	$0.242509\pi$
$878$	−23.9774	−0.809197
$879$	37.6675	1.27049
$880$	−4.70854	−0.158725
$881$	−40.8762	−1.37715	−0.688576	−	0.725164i	$-0.741764\pi$
$881$	−40.8762	−1.37715	−0.688576	+	0.725164i	$0.741764\pi$
$882$	−4.59662	−0.154776
$883$	−52.3174	−1.76062	−0.880310	−	0.474398i	$-0.842666\pi$
$883$	−52.3174	−1.76062	−0.880310	+	0.474398i	$0.842666\pi$
$884$	0	0
$885$	−6.96018	−0.233964
$886$	0.244075	0.00819987
$887$	−15.1110	−0.507377	−0.253689	−	0.967286i	$-0.581644\pi$
$887$	−15.1110	−0.507377	−0.253689	+	0.967286i	$0.581644\pi$
$888$	−13.7119	−0.460141
$889$	11.3754	0.381518
$890$	−2.24175	−0.0751437
$891$	−27.5778	−0.923892
$892$	−9.06859	−0.303639
$893$	7.10398	0.237726
$894$	6.15028	0.205696
$895$	13.1025	0.437967
$896$	−3.54824	−0.118539
$897$	46.2338	1.54370
$898$	0.0824322	0.00275080
$899$	33.8222	1.12803
$900$	−0.822287	−0.0274096
$901$	0	0
$902$	−0.673765	−0.0224339
$903$	4.34687	0.144655
$904$	9.64176	0.320680
$905$	1.82731	0.0607418
$906$	6.77731	0.225161
$907$	−25.0639	−0.832234	−0.416117	−	0.909311i	$-0.636609\pi$
$907$	−25.0639	−0.832234	−0.416117	+	0.909311i	$0.636609\pi$
$908$	15.7478	0.522610
$909$	−8.83080	−0.292899
$910$	−19.4337	−0.644221
$911$	−2.88456	−0.0955698	−0.0477849	−	0.998858i	$-0.515216\pi$
$911$	−2.88456	−0.0955698	−0.0477849	+	0.998858i	$0.515216\pi$
$912$	1.79009	0.0592758
$913$	−16.0373	−0.530759
$914$	−24.3896	−0.806737
$915$	−18.3656	−0.607149
$916$	−20.1188	−0.664745
$917$	12.6792	0.418703
$918$	0	0
$919$	−48.0746	−1.58584	−0.792918	−	0.609328i	$-0.791439\pi$
$919$	−48.0746	−1.58584	−0.792918	+	0.609328i	$0.791439\pi$
$920$	5.72028	0.188592
$921$	−21.0114	−0.692349
$922$	29.1100	0.958687
$923$	−28.1731	−0.927330
$924$	−24.6547	−0.811081
$925$	−9.29174	−0.305510
$926$	27.9762	0.919354
$927$	6.11211	0.200748
$928$	−4.64378	−0.152440
$929$	−27.4311	−0.899985	−0.449992	−	0.893032i	$-0.648573\pi$
$929$	−27.4311	−0.899985	−0.449992	+	0.893032i	$0.648573\pi$
$930$	10.7481	0.352443
$931$	6.78094	0.222236
$932$	−19.2748	−0.631366
$933$	17.9318	0.587062
$934$	−31.2786	−1.02347
$935$	0	0
$936$	4.50366	0.147207
$937$	−14.6741	−0.479382	−0.239691	−	0.970849i	$-0.577046\pi$
$937$	−14.6741	−0.479382	−0.239691	+	0.970849i	$0.577046\pi$
$938$	30.7528	1.00411
$939$	32.1552	1.04934
$940$	−5.85635	−0.191013
$941$	24.7215	0.805897	0.402949	−	0.915223i	$-0.367985\pi$
$941$	24.7215	0.805897	0.402949	+	0.915223i	$0.367985\pi$
$942$	−22.9446	−0.747577
$943$	0.818540	0.0266553
$944$	4.71650	0.153509
$945$	−20.0142	−0.651060
$946$	−3.90885	−0.127088
$947$	−6.51543	−0.211723	−0.105861	−	0.994381i	$-0.533760\pi$
$947$	−6.51543	−0.211723	−0.105861	+	0.994381i	$0.533760\pi$
$948$	−14.9281	−0.484842
$949$	88.3558	2.86815
$950$	1.21304	0.0393562
$951$	−15.1285	−0.490574
$952$	0	0
$953$	13.6944	0.443607	0.221803	−	0.975091i	$-0.428806\pi$
$953$	13.6944	0.443607	0.221803	+	0.975091i	$0.428806\pi$
$954$	−7.60792	−0.246316
$955$	16.8319	0.544666
$956$	14.2040	0.459389
$957$	−32.2670	−1.04304
$958$	−12.0756	−0.390144
$959$	−11.7429	−0.379198
$960$	−1.47571	−0.0476283
$961$	22.0470	0.711193
$962$	50.8908	1.64078
$963$	12.9354	0.416837
$964$	−4.57455	−0.147336
$965$	5.82873	0.187633
$966$	29.9524	0.963702
$967$	−16.3167	−0.524709	−0.262355	−	0.964972i	$-0.584499\pi$
$967$	−16.3167	−0.524709	−0.262355	+	0.964972i	$0.584499\pi$
$968$	11.1704	0.359029
$969$	0	0
$970$	−4.35543	−0.139844
$971$	−26.8893	−0.862919	−0.431460	−	0.902132i	$-0.642001\pi$
$971$	−26.8893	−0.862919	−0.431460	+	0.902132i	$0.642001\pi$
$972$	8.27854	0.265534
$973$	6.38671	0.204748
$974$	−5.01555	−0.160709
$975$	−8.08244	−0.258845
$976$	12.4453	0.398365
$977$	20.0002	0.639862	0.319931	−	0.947441i	$-0.396340\pi$
$977$	20.0002	0.639862	0.319931	+	0.947441i	$0.396340\pi$
$978$	14.9604	0.478380
$979$	10.5554	0.337352
$980$	−5.59004	−0.178567
$981$	5.28782	0.168827
$982$	26.4441	0.843865
$983$	28.8356	0.919713	0.459856	−	0.887993i	$-0.347901\pi$
$983$	28.8356	0.919713	0.459856	+	0.887993i	$0.347901\pi$
$984$	−0.211165	−0.00673170
$985$	−3.52144	−0.112202
$986$	0	0
$987$	−30.6648	−0.976072
$988$	−6.64381	−0.211368
$989$	4.74876	0.151002
$990$	3.87177	0.123053
$991$	26.8968	0.854404	0.427202	−	0.904156i	$-0.359499\pi$
$991$	26.8968	0.854404	0.427202	+	0.904156i	$0.359499\pi$
$992$	−7.28334	−0.231246
$993$	0.437089	0.0138706
$994$	−18.2518	−0.578913
$995$	16.8001	0.532598
$996$	−5.02628	−0.159264
$997$	−30.4622	−0.964747	−0.482373	−	0.875966i	$-0.660225\pi$
$997$	−30.4622	−0.964747	−0.482373	+	0.875966i	$0.660225\pi$
$998$	−29.9384	−0.947683
$999$	52.4108	1.65820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2890.2.a.bi.1.7		8
17.3	odd	16		170.2.k.b.111.3	✓	16
17.4	even	4		2890.2.b.r.2311.5		16
17.6	odd	16		170.2.k.b.121.3	yes	16
17.13	even	4		2890.2.b.r.2311.12		16
17.16	even	2		2890.2.a.bj.1.2		8
85.3	even	16		850.2.o.g.349.2		16
85.23	even	16		850.2.o.j.699.3		16
85.37	even	16		850.2.o.j.349.3		16
85.54	odd	16		850.2.l.e.451.2		16
85.57	even	16		850.2.o.g.699.2		16
85.74	odd	16		850.2.l.e.801.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.3	✓	16	17.3	odd	16
170.2.k.b.121.3	yes	16	17.6	odd	16
850.2.l.e.451.2		16	85.54	odd	16
850.2.l.e.801.2		16	85.74	odd	16
850.2.o.g.349.2		16	85.3	even	16
850.2.o.g.699.2		16	85.57	even	16
850.2.o.j.349.3		16	85.37	even	16
850.2.o.j.699.3		16	85.23	even	16
2890.2.a.bi.1.7		8	1.1	even	1	trivial
2890.2.a.bj.1.2		8	17.16	even	2
2890.2.b.r.2311.5		16	17.4	even	4
2890.2.b.r.2311.12		16	17.13	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2890.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.47571 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.47571 q^{6} -3.54824 q^{7} +1.00000 q^{8} -0.822287 q^{9} -1.00000 q^{10} +4.70854 q^{11} +1.47571 q^{12} -5.47699 q^{13} -3.54824 q^{14} -1.47571 q^{15} +1.00000 q^{16} -0.822287 q^{18} +1.21304 q^{19} -1.00000 q^{20} -5.23617 q^{21} +4.70854 q^{22} -5.72028 q^{23} +1.47571 q^{24} +1.00000 q^{25} -5.47699 q^{26} -5.64058 q^{27} -3.54824 q^{28} -4.64378 q^{29} -1.47571 q^{30} -7.28334 q^{31} +1.00000 q^{32} +6.94843 q^{33} +3.54824 q^{35} -0.822287 q^{36} -9.29174 q^{37} +1.21304 q^{38} -8.08244 q^{39} -1.00000 q^{40} -0.143094 q^{41} -5.23617 q^{42} -0.830161 q^{43} +4.70854 q^{44} +0.822287 q^{45} -5.72028 q^{46} +5.85635 q^{47} +1.47571 q^{48} +5.59004 q^{49} +1.00000 q^{50} -5.47699 q^{52} +9.25215 q^{53} -5.64058 q^{54} -4.70854 q^{55} -3.54824 q^{56} +1.79009 q^{57} -4.64378 q^{58} +4.71650 q^{59} -1.47571 q^{60} +12.4453 q^{61} -7.28334 q^{62} +2.91768 q^{63} +1.00000 q^{64} +5.47699 q^{65} +6.94843 q^{66} -8.66703 q^{67} -8.44146 q^{69} +3.54824 q^{70} +5.14391 q^{71} -0.822287 q^{72} -16.1322 q^{73} -9.29174 q^{74} +1.47571 q^{75} +1.21304 q^{76} -16.7071 q^{77} -8.08244 q^{78} -10.1159 q^{79} -1.00000 q^{80} -5.85698 q^{81} -0.143094 q^{82} -3.40601 q^{83} -5.23617 q^{84} -0.830161 q^{86} -6.85286 q^{87} +4.70854 q^{88} +2.24175 q^{89} +0.822287 q^{90} +19.4337 q^{91} -5.72028 q^{92} -10.7481 q^{93} +5.85635 q^{94} -1.21304 q^{95} +1.47571 q^{96} +4.35543 q^{97} +5.59004 q^{98} -3.87177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 8 q^{5} - 4 q^{6} - 8 q^{7} + 8 q^{8} + 4 q^{9} - 8 q^{10} - 8 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{18} + 12 q^{19} - 8 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 8 * q^5 - 4 * q^6 - 8 * q^7 + 8 * q^8 + 4 * q^9 - 8 * q^10 - 8 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 8 * q^16 + 4 * q^18 + 12 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^22 - 24 * q^23 - 4 * q^24 + 8 * q^25 - 4 * q^26 - 4 * q^27 - 8 * q^28 - 28 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 8 * q^33 + 8 * q^35 + 4 * q^36 - 24 * q^37 + 12 * q^38 - 12 * q^39 - 8 * q^40 - 16 * q^41 - 8 * q^42 - 8 * q^44 - 4 * q^45 - 24 * q^46 - 12 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 - 4 * q^52 - 12 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^56 - 20 * q^57 - 28 * q^58 - 4 * q^59 + 4 * q^60 - 4 * q^61 - 4 * q^62 - 32 * q^63 + 8 * q^64 + 4 * q^65 - 8 * q^66 - 8 * q^67 - 8 * q^69 + 8 * q^70 - 36 * q^71 + 4 * q^72 - 28 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 - 24 * q^77 - 12 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 8 * q^83 - 8 * q^84 - 28 * q^87 - 8 * q^88 - 12 * q^89 - 4 * q^90 + 8 * q^91 - 24 * q^92 - 12 * q^93 - 12 * q^94 - 12 * q^95 - 4 * q^96 - 28 * q^97 + 8 * q^98 + 8 * q^99

Introduction

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