LMFDB - Embedded newform 867.2.e.k.616.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(616,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.616"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-36,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			616.7
Character	$\chi$	$=$	867.616
Dual form			867.2.e.k.829.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.907065i q^{2} +(-0.707107 + 0.707107i) q^{3} +1.17723 q^{4} +(2.25802 - 2.25802i) q^{5} +(-0.641392 - 0.641392i) q^{6} +(2.51896 + 2.51896i) q^{7} +2.88196i q^{8} -1.00000i q^{9} +(2.04818 + 2.04818i) q^{10} +(2.31657 + 2.31657i) q^{11} +(-0.832429 + 0.832429i) q^{12} -5.58411 q^{13} +(-2.28486 + 2.28486i) q^{14} +3.19333i q^{15} -0.259660 q^{16} +0.907065 q^{18} -4.23574i q^{19} +(2.65822 - 2.65822i) q^{20} -3.56234 q^{21} +(-2.10128 + 2.10128i) q^{22} +(3.25360 + 3.25360i) q^{23} +(-2.03785 - 2.03785i) q^{24} -5.19735i q^{25} -5.06515i q^{26} +(0.707107 + 0.707107i) q^{27} +(2.96540 + 2.96540i) q^{28} +(1.47382 - 1.47382i) q^{29} -2.89656 q^{30} +(-0.317397 + 0.317397i) q^{31} +5.52839i q^{32} -3.27613 q^{33} +11.3757 q^{35} -1.17723i q^{36} +(0.525318 - 0.525318i) q^{37} +3.84209 q^{38} +(3.94856 - 3.94856i) q^{39} +(6.50753 + 6.50753i) q^{40} +(-3.17713 - 3.17713i) q^{41} -3.23128i q^{42} -6.10953i q^{43} +(2.72715 + 2.72715i) q^{44} +(-2.25802 - 2.25802i) q^{45} +(-2.95123 + 2.95123i) q^{46} +2.26801 q^{47} +(0.183607 - 0.183607i) q^{48} +5.69028i q^{49} +4.71434 q^{50} -6.57379 q^{52} +7.55680i q^{53} +(-0.641392 + 0.641392i) q^{54} +10.4618 q^{55} +(-7.25952 + 7.25952i) q^{56} +(2.99512 + 2.99512i) q^{57} +(1.33685 + 1.33685i) q^{58} +2.83196i q^{59} +3.75929i q^{60} +(-2.76752 - 2.76752i) q^{61} +(-0.287900 - 0.287900i) q^{62} +(2.51896 - 2.51896i) q^{63} -5.53393 q^{64} +(-12.6091 + 12.6091i) q^{65} -2.97167i q^{66} -14.5019 q^{67} -4.60128 q^{69} +10.3185i q^{70} +(2.57685 - 2.57685i) q^{71} +2.88196 q^{72} +(8.24004 - 8.24004i) q^{73} +(0.476498 + 0.476498i) q^{74} +(3.67508 + 3.67508i) q^{75} -4.98645i q^{76} +11.6707i q^{77} +(3.58160 + 3.58160i) q^{78} +(3.98316 + 3.98316i) q^{79} +(-0.586319 + 0.586319i) q^{80} -1.00000 q^{81} +(2.88187 - 2.88187i) q^{82} -3.92274i q^{83} -4.19370 q^{84} +5.54175 q^{86} +2.08430i q^{87} +(-6.67627 + 6.67627i) q^{88} -14.6181 q^{89} +(2.04818 - 2.04818i) q^{90} +(-14.0661 - 14.0661i) q^{91} +(3.83024 + 3.83024i) q^{92} -0.448868i q^{93} +2.05724i q^{94} +(-9.56440 - 9.56440i) q^{95} +(-3.90916 - 3.90916i) q^{96} +(-0.585758 + 0.585758i) q^{97} -5.16145 q^{98} +(2.31657 - 2.31657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81}+ \cdots + 228 q^{98}+O(q^{100}) $ 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			0.907065i			0.641392i	0.947182	+	0.320696i	$0.103917\pi$
$2$			0.907065i			0.641392i	−0.947182	+	0.320696i	$0.896083\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.17723			0.588616
$5$	2.25802	−	2.25802i	1.00982	−	1.00982i	0.00986808	−	0.999951i	$-0.496859\pi$
$5$	2.25802	−	2.25802i	1.00982	−	1.00982i	0.999951	−	0.00986808i	$-0.00314116\pi$
$6$	−0.641392	−	0.641392i	−0.261847	−	0.261847i
$7$	2.51896	+	2.51896i	0.952076	+	0.952076i	0.998903	−	0.0468272i	$-0.0149110\pi$
$7$	2.51896	+	2.51896i	0.952076	+	0.952076i	−0.0468272	+	0.998903i	$0.514911\pi$
$8$			2.88196i			1.01893i
$9$		−	1.00000i		−	0.333333i
$10$	2.04818	+	2.04818i	0.647690	+	0.647690i
$11$	2.31657	+	2.31657i	0.698473	+	0.698473i	0.964081	−	0.265608i	$-0.0855726\pi$
$11$	2.31657	+	2.31657i	0.698473	+	0.698473i	−0.265608	+	0.964081i	$0.585573\pi$
$12$	−0.832429	+	0.832429i	−0.240302	+	0.240302i
$13$	−5.58411			−1.54875			−0.774377	−	0.632725i	$-0.781936\pi$
$13$	−5.58411			−1.54875			−0.774377	+	0.632725i	$0.781936\pi$
$14$	−2.28486	+	2.28486i	−0.610654	+	0.610654i
$15$			3.19333i			0.824514i
$16$	−0.259660			−0.0649150
$17$		0			0
$17$		0			0
$18$	0.907065			0.213797
$19$		−	4.23574i		−	0.971745i	−0.874030	−	0.485872i	$-0.838502\pi$
$19$		−	4.23574i		−	0.971745i	0.874030	−	0.485872i	$-0.161498\pi$
$20$	2.65822	−	2.65822i	0.594396	−	0.594396i
$21$	−3.56234			−0.777367
$22$	−2.10128	+	2.10128i	−0.447995	+	0.447995i
$23$	3.25360	+	3.25360i	0.678422	+	0.678422i	0.959643	−	0.281221i	$-0.0907393\pi$
$23$	3.25360	+	3.25360i	0.678422	+	0.678422i	−0.281221	+	0.959643i	$0.590739\pi$
$24$	−2.03785	−	2.03785i	−0.415975	−	0.415975i
$25$		−	5.19735i		−	1.03947i
$26$		−	5.06515i		−	0.993358i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.96540	+	2.96540i	0.560407	+	0.560407i
$29$	1.47382	−	1.47382i	0.273682	−	0.273682i	−0.556899	−	0.830580i	$-0.688009\pi$
$29$	1.47382	−	1.47382i	0.273682	−	0.273682i	0.830580	+	0.556899i	$0.188009\pi$
$30$	−2.89656			−0.528837
$31$	−0.317397	+	0.317397i	−0.0570063	+	0.0570063i	−0.735035	−	0.678029i	$-0.762834\pi$
$31$	−0.317397	+	0.317397i	−0.0570063	+	0.0570063i	0.678029	+	0.735035i	$0.262834\pi$
$32$			5.52839i			0.977290i
$33$	−3.27613			−0.570301
$34$		0			0
$35$	11.3757			1.92285
$36$		−	1.17723i		−	0.196205i
$37$	0.525318	−	0.525318i	0.0863618	−	0.0863618i	−0.662606	−	0.748968i	$-0.730550\pi$
$37$	0.525318	−	0.525318i	0.0863618	−	0.0863618i	0.748968	+	0.662606i	$0.230550\pi$
$38$	3.84209			0.623270
$39$	3.94856	−	3.94856i	0.632276	−	0.632276i
$40$	6.50753	+	6.50753i	1.02893	+	1.02893i
$41$	−3.17713	−	3.17713i	−0.496185	−	0.496185i	0.414063	−	0.910248i	$-0.364109\pi$
$41$	−3.17713	−	3.17713i	−0.496185	−	0.496185i	−0.910248	+	0.414063i	$0.864109\pi$
$42$		−	3.23128i		−	0.498597i
$43$		−	6.10953i		−	0.931695i	−0.884865	−	0.465848i	$-0.845750\pi$
$43$		−	6.10953i		−	0.931695i	0.884865	−	0.465848i	$-0.154250\pi$
$44$	2.72715	+	2.72715i	0.411133	+	0.411133i
$45$	−2.25802	−	2.25802i	−0.336606	−	0.336606i
$46$	−2.95123	+	2.95123i	−0.435135	+	0.435135i
$47$	2.26801			0.330824			0.165412	−	0.986225i	$-0.447105\pi$
$47$	2.26801			0.330824			0.165412	+	0.986225i	$0.447105\pi$
$48$	0.183607	−	0.183607i	0.0265014	−	0.0265014i
$49$			5.69028i			0.812897i
$50$	4.71434			0.666708
$51$		0			0
$52$	−6.57379			−0.911621
$53$			7.55680i			1.03801i	0.854772	+	0.519003i	$0.173697\pi$
$53$			7.55680i			1.03801i	−0.854772	+	0.519003i	$0.826303\pi$
$54$	−0.641392	+	0.641392i	−0.0872824	+	0.0872824i
$55$	10.4618			1.41066
$56$	−7.25952	+	7.25952i	−0.970095	+	0.970095i
$57$	2.99512	+	2.99512i	0.396713	+	0.396713i
$58$	1.33685	+	1.33685i	0.175537	+	0.175537i
$59$			2.83196i			0.368690i	0.982862	+	0.184345i	$0.0590163\pi$
$59$			2.83196i			0.368690i	−0.982862	+	0.184345i	$0.940984\pi$
$60$			3.75929i			0.485322i
$61$	−2.76752	−	2.76752i	−0.354344	−	0.354344i	0.507379	−	0.861723i	$-0.330614\pi$
$61$	−2.76752	−	2.76752i	−0.354344	−	0.354344i	−0.861723	+	0.507379i	$0.830614\pi$
$62$	−0.287900	−	0.287900i	−0.0365634	−	0.0365634i
$63$	2.51896	−	2.51896i	0.317359	−	0.317359i
$64$	−5.53393			−0.691741
$65$	−12.6091	+	12.6091i	−1.56396	+	1.56396i
$66$		−	2.97167i		−	0.365787i
$67$	−14.5019			−1.77168			−0.885842	−	0.463986i	$-0.846419\pi$
$67$	−14.5019			−1.77168			−0.885842	+	0.463986i	$0.846419\pi$
$68$		0			0
$69$	−4.60128			−0.553930
$70$			10.3185i			1.23330i
$71$	2.57685	−	2.57685i	0.305816	−	0.305816i	−0.537468	−	0.843284i	$-0.680619\pi$
$71$	2.57685	−	2.57685i	0.305816	−	0.305816i	0.843284	+	0.537468i	$0.180619\pi$
$72$	2.88196			0.339642
$73$	8.24004	−	8.24004i	0.964424	−	0.964424i	−0.0349648	−	0.999389i	$-0.511132\pi$
$73$	8.24004	−	8.24004i	0.964424	−	0.964424i	0.999389	+	0.0349648i	$0.0111319\pi$
$74$	0.476498	+	0.476498i	0.0553918	+	0.0553918i
$75$	3.67508	+	3.67508i	0.424362	+	0.424362i
$76$		−	4.98645i		−	0.571985i
$77$			11.6707i			1.33000i
$78$	3.58160	+	3.58160i	0.405537	+	0.405537i
$79$	3.98316	+	3.98316i	0.448140	+	0.448140i	0.894736	−	0.446596i	$-0.147364\pi$
$79$	3.98316	+	3.98316i	0.448140	+	0.448140i	−0.446596	+	0.894736i	$0.647364\pi$
$80$	−0.586319	+	0.586319i	−0.0655524	+	0.0655524i
$81$	−1.00000			−0.111111
$82$	2.88187	−	2.88187i	0.318249	−	0.318249i
$83$		−	3.92274i		−	0.430577i	−0.976551	−	0.215288i	$-0.930931\pi$
$83$		−	3.92274i		−	0.430577i	0.976551	−	0.215288i	$-0.0690691\pi$
$84$	−4.19370			−0.457571
$85$		0			0
$86$	5.54175			0.597582
$87$			2.08430i			0.223460i
$88$	−6.67627	+	6.67627i	−0.711693	+	0.711693i
$89$	−14.6181			−1.54951			−0.774757	−	0.632259i	$-0.782128\pi$
$89$	−14.6181			−1.54951			−0.774757	+	0.632259i	$0.782128\pi$
$90$	2.04818	−	2.04818i	0.215897	−	0.215897i
$91$	−14.0661	−	14.0661i	−1.47453	−	1.47453i
$92$	3.83024	+	3.83024i	0.399330	+	0.399330i
$93$		−	0.448868i		−	0.0465454i
$94$			2.05724i			0.212188i
$95$	−9.56440	−	9.56440i	−0.981287	−	0.981287i
$96$	−3.90916	−	3.90916i	−0.398977	−	0.398977i
$97$	−0.585758	+	0.585758i	−0.0594747	+	0.0594747i	−0.736219	−	0.676744i	$-0.763390\pi$
$97$	−0.585758	+	0.585758i	−0.0594747	+	0.0594747i	0.676744	+	0.736219i	$0.263390\pi$
$98$	−5.16145			−0.521386
$99$	2.31657	−	2.31657i	0.232824	−	0.232824i
$100$		−	6.11849i		−	0.611849i
$101$	4.92944			0.490497			0.245249	−	0.969460i	$-0.421130\pi$
$101$	4.92944			0.490497			0.245249	+	0.969460i	$0.421130\pi$
$102$		0			0
$103$	11.4347			1.12669			0.563347	−	0.826221i	$-0.309514\pi$
$103$	11.4347			1.12669			0.563347	+	0.826221i	$0.309514\pi$
$104$		−	16.0932i		−	1.57807i
$105$	−8.04386	+	8.04386i	−0.785000	+	0.785000i
$106$	−6.85452			−0.665769
$107$	−12.4398	+	12.4398i	−1.20260	+	1.20260i	−0.229226	+	0.973373i	$0.573619\pi$
$107$	−12.4398	+	12.4398i	−1.20260	+	1.20260i	−0.973373	+	0.229226i	$0.926381\pi$
$108$	0.832429	+	0.832429i	0.0801005	+	0.0801005i
$109$	−10.0066	−	10.0066i	−0.958458	−	0.958458i	0.0407126	−	0.999171i	$-0.487037\pi$
$109$	−10.0066	−	10.0066i	−0.958458	−	0.958458i	−0.999171	+	0.0407126i	$0.987037\pi$
$110$			9.48951i			0.904789i
$111$			0.742912i			0.0705141i
$112$	−0.654072	−	0.654072i	−0.0618040	−	0.0618040i
$113$	14.4260	+	14.4260i	1.35709	+	1.35709i	0.877486	+	0.479603i	$0.159219\pi$
$113$	14.4260	+	14.4260i	1.35709	+	1.35709i	0.479603	+	0.877486i	$0.340781\pi$
$114$	−2.71677	+	2.71677i	−0.254449	+	0.254449i
$115$	14.6934			1.37017
$116$	1.73503	−	1.73503i	0.161093	−	0.161093i
$117$			5.58411i			0.516251i
$118$	−2.56877			−0.236475
$119$		0			0
$120$	−9.20304			−0.840119
$121$		−	0.266966i		−	0.0242696i
$122$	2.51032	−	2.51032i	0.227274	−	0.227274i
$123$	4.49315			0.405133
$124$	−0.373650	+	0.373650i	−0.0335548	+	0.0335548i
$125$	−0.445626	−	0.445626i	−0.0398580	−	0.0398580i
$126$	2.28486	+	2.28486i	0.203551	+	0.203551i
$127$		−	2.93340i		−	0.260297i	−0.991495	−	0.130148i	$-0.958455\pi$
$127$		−	2.93340i		−	0.260297i	0.991495	−	0.130148i	$-0.0415454\pi$
$128$			6.03714i			0.533613i
$129$	4.32009	+	4.32009i	0.380363	+	0.380363i
$130$	−11.4372	−	11.4372i	−1.00311	−	1.00311i
$131$	4.67872	−	4.67872i	0.408782	−	0.408782i	−0.472532	−	0.881314i	$-0.656660\pi$
$131$	4.67872	−	4.67872i	0.408782	−	0.408782i	0.881314	+	0.472532i	$0.156660\pi$
$132$	−3.85677			−0.335688
$133$	10.6696	−	10.6696i	0.925175	−	0.925175i
$134$		−	13.1541i		−	1.13634i
$135$	3.19333			0.274838
$136$		0			0
$137$	−10.4851			−0.895804			−0.447902	−	0.894083i	$-0.647829\pi$
$137$	−10.4851			−0.895804			−0.447902	+	0.894083i	$0.647829\pi$
$138$		−	4.17367i		−	0.355286i
$139$	−3.73775	+	3.73775i	−0.317032	+	0.317032i	−0.847626	−	0.530594i	$-0.821969\pi$
$139$	−3.73775	+	3.73775i	−0.317032	+	0.317032i	0.530594	+	0.847626i	$0.321969\pi$
$140$	13.3919			1.13182
$141$	−1.60373	+	1.60373i	−0.135058	+	0.135058i
$142$	2.33737	+	2.33737i	0.196148	+	0.196148i
$143$	−12.9360	−	12.9360i	−1.08176	−	1.08176i
$144$			0.259660i			0.0216383i
$145$		−	6.65585i		−	0.552738i
$146$	7.47426	+	7.47426i	0.618574	+	0.618574i
$147$	−4.02363	−	4.02363i	−0.331864	−	0.331864i
$148$	0.618422	−	0.618422i	0.0508340	−	0.0508340i
$149$	22.4592			1.83993			0.919965	−	0.392000i	$-0.128217\pi$
$149$	22.4592			1.83993			0.919965	+	0.392000i	$0.128217\pi$
$150$	−3.33354	+	3.33354i	−0.272182	+	0.272182i
$151$		−	9.52717i		−	0.775310i	−0.921804	−	0.387655i	$-0.873285\pi$
$151$		−	9.52717i		−	0.775310i	0.921804	−	0.387655i	$-0.126715\pi$
$152$	12.2072			0.990136
$153$		0			0
$154$	−10.5861			−0.853051
$155$			1.43338i			0.115132i
$156$	4.64837	−	4.64837i	0.372168	−	0.372168i
$157$	−14.1185			−1.12678			−0.563390	−	0.826191i	$-0.690503\pi$
$157$	−14.1185			−1.12678			−0.563390	+	0.826191i	$0.690503\pi$
$158$	−3.61298	+	3.61298i	−0.287434	+	0.287434i
$159$	−5.34347	−	5.34347i	−0.423765	−	0.423765i
$160$	12.4832	+	12.4832i	0.986886	+	0.986886i
$161$			16.3913i			1.29182i
$162$		−	0.907065i		−	0.0712658i
$163$	2.49885	+	2.49885i	0.195725	+	0.195725i	0.798164	−	0.602440i	$-0.205805\pi$
$163$	2.49885	+	2.49885i	0.195725	+	0.195725i	−0.602440	+	0.798164i	$0.705805\pi$
$164$	−3.74022	−	3.74022i	−0.292062	−	0.292062i
$165$	−7.39759	+	7.39759i	−0.575901	+	0.575901i
$166$	3.55818			0.276169
$167$	11.4461	−	11.4461i	0.885722	−	0.885722i	−0.108387	−	0.994109i	$-0.534568\pi$
$167$	11.4461	−	11.4461i	0.885722	−	0.885722i	0.994109	+	0.108387i	$0.0345684\pi$
$168$		−	10.2665i		−	0.792079i
$169$	18.1823			1.39864
$170$		0			0
$171$	−4.23574			−0.323915
$172$		−	7.19234i		−	0.548411i
$173$	12.9528	−	12.9528i	0.984782	−	0.984782i	−0.0151035	−	0.999886i	$-0.504808\pi$
$173$	12.9528	−	12.9528i	0.984782	−	0.984782i	0.999886	+	0.0151035i	$0.00480777\pi$
$174$	−1.89059			−0.143326
$175$	13.0919	−	13.0919i	0.989655	−	0.989655i
$176$	−0.601522	−	0.601522i	−0.0453414	−	0.0453414i
$177$	−2.00250	−	2.00250i	−0.150517	−	0.150517i
$178$		−	13.2596i		−	0.993846i
$179$		−	20.7057i		−	1.54762i	−0.633419	−	0.773809i	$-0.718349\pi$
$179$		−	20.7057i		−	1.54762i	0.633419	−	0.773809i	$-0.281651\pi$
$180$	−2.65822	−	2.65822i	−0.198132	−	0.198132i
$181$	−13.1875	−	13.1875i	−0.980223	−	0.980223i	0.0195857	−	0.999808i	$-0.493765\pi$
$181$	−13.1875	−	13.1875i	−0.980223	−	0.980223i	−0.999808	+	0.0195857i	$0.993765\pi$
$182$	12.7589	−	12.7589i	0.945753	−	0.945753i
$183$	3.91386			0.289321
$184$	−9.37674	+	9.37674i	−0.691262	+	0.691262i
$185$		−	2.37236i		−	0.174420i
$186$	0.407152			0.0298539
$187$		0			0
$188$	2.66998			0.194728
$189$			3.56234i			0.259122i
$190$	8.67554	−	8.67554i	0.629390	−	0.629390i
$191$	−2.19374			−0.158734			−0.0793669	−	0.996845i	$-0.525290\pi$
$191$	−2.19374			−0.158734			−0.0793669	+	0.996845i	$0.525290\pi$
$192$	3.91308	−	3.91308i	0.282402	−	0.282402i
$193$	−2.34198	−	2.34198i	−0.168579	−	0.168579i	0.617775	−	0.786355i	$-0.288034\pi$
$193$	−2.34198	−	2.34198i	−0.168579	−	0.168579i	−0.786355	+	0.617775i	$0.788034\pi$
$194$	−0.531321	−	0.531321i	−0.0381466	−	0.0381466i
$195$		−	17.8319i		−	1.27697i
$196$			6.69878i			0.478484i
$197$	−12.7408	−	12.7408i	−0.907745	−	0.907745i	0.0883452	−	0.996090i	$-0.471842\pi$
$197$	−12.7408	−	12.7408i	−0.907745	−	0.907745i	−0.996090	+	0.0883452i	$0.971842\pi$
$198$	2.10128	+	2.10128i	0.149332	+	0.149332i
$199$	−2.81539	+	2.81539i	−0.199577	+	0.199577i	−0.799819	−	0.600241i	$-0.795071\pi$
$199$	−2.81539	+	2.81539i	−0.199577	+	0.199577i	0.600241	+	0.799819i	$0.295071\pi$
$200$	14.9785			1.05914
$201$	10.2544	−	10.2544i	0.723287	−	0.723287i
$202$			4.47132i			0.314601i
$203$	7.42498			0.521131
$204$		0			0
$205$	−14.3481			−1.00211
$206$			10.3720i			0.722652i
$207$	3.25360	−	3.25360i	0.226141	−	0.226141i
$208$	1.44997			0.100537
$209$	9.81240	−	9.81240i	0.678738	−	0.678738i
$210$	−7.29630	−	7.29630i	−0.503493	−	0.503493i
$211$	−0.142055	−	0.142055i	−0.00977948	−	0.00977948i	0.702200	−	0.711980i	$-0.252201\pi$
$211$	−0.142055	−	0.142055i	−0.00977948	−	0.00977948i	−0.711980	+	0.702200i	$0.752201\pi$
$212$			8.89611i			0.610988i
$213$			3.64422i			0.249698i
$214$	−11.2837	−	11.2837i	−0.771338	−	0.771338i
$215$	−13.7955	−	13.7955i	−0.940844	−	0.940844i
$216$	−2.03785	+	2.03785i	−0.138658	+	0.138658i
$217$	−1.59902			−0.108549
$218$	9.07664	−	9.07664i	0.614748	−	0.614748i
$219$			11.6532i			0.787449i
$220$	12.3159			0.830340
$221$		0			0
$222$	−0.673870			−0.0452272
$223$		−	11.5997i		−	0.776770i	−0.921497	−	0.388385i	$-0.873033\pi$
$223$		−	11.5997i		−	0.776770i	0.921497	−	0.388385i	$-0.126967\pi$
$224$	−13.9258	+	13.9258i	−0.930454	+	0.930454i
$225$	−5.19735			−0.346490
$226$	−13.0854	+	13.0854i	−0.870426	+	0.870426i
$227$	−6.72737	−	6.72737i	−0.446511	−	0.446511i	0.447682	−	0.894193i	$-0.352250\pi$
$227$	−6.72737	−	6.72737i	−0.446511	−	0.446511i	−0.894193	+	0.447682i	$0.852250\pi$
$228$	3.52595	+	3.52595i	0.233512	+	0.233512i
$229$			16.7700i			1.10819i	0.832452	+	0.554097i	$0.186936\pi$
$229$			16.7700i			1.10819i	−0.832452	+	0.554097i	$0.813064\pi$
$230$			13.3279i			0.878815i
$231$	−8.25243	−	8.25243i	−0.542970	−	0.542970i
$232$	4.24749	+	4.24749i	0.278861	+	0.278861i
$233$	−6.68122	+	6.68122i	−0.437701	+	0.437701i	−0.891238	−	0.453537i	$-0.850162\pi$
$233$	−6.68122	+	6.68122i	−0.437701	+	0.437701i	0.453537	+	0.891238i	$0.350162\pi$
$234$	−5.06515			−0.331119
$235$	5.12123	−	5.12123i	0.334072	−	0.334072i
$236$			3.33387i			0.217017i
$237$	−5.63303			−0.365905
$238$		0			0
$239$	6.42079			0.415326			0.207663	−	0.978200i	$-0.433414\pi$
$239$	6.42079			0.415326			0.207663	+	0.978200i	$0.433414\pi$
$240$		−	0.829180i		−	0.0535233i
$241$	−10.9482	+	10.9482i	−0.705237	+	0.705237i	−0.965530	−	0.260293i	$-0.916181\pi$
$241$	−10.9482	+	10.9482i	−0.705237	+	0.705237i	0.260293	+	0.965530i	$0.416181\pi$
$242$	0.242155			0.0155663
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−3.25801	−	3.25801i	−0.208573	−	0.208573i
$245$	12.8488	+	12.8488i	0.820879	+	0.820879i
$246$			4.07558i			0.259849i
$247$			23.6528i			1.50499i
$248$	−0.914726	−	0.914726i	−0.0580851	−	0.0580851i
$249$	2.77380	+	2.77380i	0.175782	+	0.175782i
$250$	0.404212	−	0.404212i	0.0255646	−	0.0255646i
$251$	−25.7024			−1.62232			−0.811162	−	0.584821i	$-0.801165\pi$
$251$	−25.7024			−1.62232			−0.811162	+	0.584821i	$0.801165\pi$
$252$	2.96540	−	2.96540i	0.186802	−	0.186802i
$253$			15.0744i			0.947720i
$254$	2.66078			0.166952
$255$		0			0
$256$	−16.5439			−1.03400
$257$			2.50466i			0.156236i	0.996944	+	0.0781182i	$0.0248911\pi$
$257$			2.50466i			0.156236i	−0.996944	+	0.0781182i	$0.975109\pi$
$258$	−3.91861	+	3.91861i	−0.243962	+	0.243962i
$259$	2.64651			0.164446
$260$	−14.8438	+	14.8438i	−0.920573	+	0.920573i
$261$	−1.47382	−	1.47382i	−0.0912272	−	0.0912272i
$262$	4.24390	+	4.24390i	0.262189	+	0.262189i
$263$		−	6.09867i		−	0.376060i	−0.982163	−	0.188030i	$-0.939790\pi$
$263$		−	6.09867i		−	0.376060i	0.982163	−	0.188030i	$-0.0602102\pi$
$264$		−	9.44167i		−	0.581095i
$265$	17.0635	+	17.0635i	1.04820	+	1.04820i
$266$	9.67806	+	9.67806i	0.593400	+	0.593400i
$267$	10.3365	−	10.3365i	0.632586	−	0.632586i
$268$	−17.0721			−1.04284
$269$	2.90940	−	2.90940i	0.177389	−	0.177389i	−0.612828	−	0.790217i	$-0.709968\pi$
$269$	2.90940	−	2.90940i	0.177389	−	0.177389i	0.790217	+	0.612828i	$0.209968\pi$
$270$			2.89656i			0.176279i
$271$	−11.8548			−0.720128			−0.360064	−	0.932928i	$-0.617245\pi$
$271$	−11.8548			−0.720128			−0.360064	+	0.932928i	$0.617245\pi$
$272$		0			0
$273$	19.8925			1.20395
$274$		−	9.51068i		−	0.574561i
$275$	12.0401	−	12.0401i	0.726043	−	0.726043i
$276$	−5.41678			−0.326052
$277$	−11.5086	+	11.5086i	−0.691486	+	0.691486i	−0.962559	−	0.271073i	$-0.912621\pi$
$277$	−11.5086	+	11.5086i	−0.691486	+	0.691486i	0.271073	+	0.962559i	$0.412621\pi$
$278$	−3.39038	−	3.39038i	−0.203342	−	0.203342i
$279$	0.317397	+	0.317397i	0.0190021	+	0.0190021i
$280$			32.7844i			1.95924i
$281$		−	15.2506i		−	0.909774i	−0.890549	−	0.454887i	$-0.849680\pi$
$281$		−	15.2506i		−	0.909774i	0.890549	−	0.454887i	$-0.150320\pi$
$282$	−1.45469	−	1.45469i	−0.0866253	−	0.0866253i
$283$	−14.7723	−	14.7723i	−0.878119	−	0.878119i	0.115221	−	0.993340i	$-0.463242\pi$
$283$	−14.7723	−	14.7723i	−0.878119	−	0.878119i	−0.993340	+	0.115221i	$0.963242\pi$
$284$	3.03355	−	3.03355i	0.180008	−	0.180008i
$285$	13.5261			0.801217
$286$	11.7338	−	11.7338i	0.693835	−	0.693835i
$287$		−	16.0061i		−	0.944811i
$288$	5.52839			0.325763
$289$		0			0
$290$	6.03729			0.354522
$291$		−	0.828387i		−	0.0485609i
$292$	9.70044	−	9.70044i	0.567675	−	0.567675i
$293$	−22.4544			−1.31180			−0.655900	−	0.754848i	$-0.727711\pi$
$293$	−22.4544			−1.31180			−0.655900	+	0.754848i	$0.727711\pi$
$294$	3.64970	−	3.64970i	0.212855	−	0.212855i
$295$	6.39463	+	6.39463i	0.372310	+	0.372310i
$296$	1.51395	+	1.51395i	0.0879963	+	0.0879963i
$297$			3.27613i			0.190100i
$298$			20.3720i			1.18012i
$299$	−18.1685	−	18.1685i	−1.05071	−	1.05071i
$300$	4.32643	+	4.32643i	0.249786	+	0.249786i
$301$	15.3896	−	15.3896i	0.887044	−	0.887044i
$302$	8.64177			0.497278
$303$	−3.48564	+	3.48564i	−0.200245	+	0.200245i
$304$			1.09985i			0.0630808i
$305$	−12.4982			−0.715647
$306$		0			0
$307$	−0.733467			−0.0418611			−0.0209306	−	0.999781i	$-0.506663\pi$
$307$	−0.733467			−0.0418611			−0.0209306	+	0.999781i	$0.506663\pi$
$308$			13.7391i			0.782859i
$309$	−8.08554	+	8.08554i	−0.459971	+	0.459971i
$310$	−1.30017			−0.0738448
$311$	17.1258	−	17.1258i	0.971114	−	0.971114i	−0.0284806	−	0.999594i	$-0.509067\pi$
$311$	17.1258	−	17.1258i	0.971114	−	0.971114i	0.999594	+	0.0284806i	$0.00906688\pi$
$312$	11.3796	+	11.3796i	0.644242	+	0.644242i
$313$	−2.70711	−	2.70711i	−0.153015	−	0.153015i	0.626448	−	0.779463i	$-0.284508\pi$
$313$	−2.70711	−	2.70711i	−0.153015	−	0.153015i	−0.779463	+	0.626448i	$0.784508\pi$
$314$		−	12.8064i		−	0.722708i
$315$		−	11.3757i		−	0.640950i
$316$	4.68910	+	4.68910i	0.263782	+	0.263782i
$317$	2.46980	+	2.46980i	0.138718	+	0.138718i	0.773056	−	0.634338i	$-0.218727\pi$
$317$	2.46980	+	2.46980i	0.138718	+	0.138718i	−0.634338	+	0.773056i	$0.718727\pi$
$318$	4.84688	−	4.84688i	0.271799	−	0.271799i
$319$	6.82843			0.382319
$320$	−12.4957	+	12.4957i	−0.698534	+	0.698534i
$321$		−	17.5925i		−	0.981918i
$322$	−14.8680			−0.828563
$323$		0			0
$324$	−1.17723			−0.0654018
$325$			29.0226i			1.60988i
$326$	−2.26662	+	2.26662i	−0.125536	+	0.125536i
$327$	14.1515			0.782578
$328$	9.15637	−	9.15637i	0.505576	−	0.505576i
$329$	5.71303	+	5.71303i	0.314969	+	0.314969i
$330$	−6.71009	−	6.71009i	−0.369379	−	0.369379i
$331$		−	5.00357i		−	0.275021i	−0.990500	−	0.137511i	$-0.956090\pi$
$331$		−	5.00357i		−	0.275021i	0.990500	−	0.137511i	$-0.0439101\pi$
$332$		−	4.61798i		−	0.253444i
$333$	−0.525318	−	0.525318i	−0.0287873	−	0.0287873i
$334$	10.3823	+	10.3823i	0.568095	+	0.568095i
$335$	−32.7456	+	32.7456i	−1.78908	+	1.78908i
$336$	0.924998			0.0504628
$337$	−19.1226	+	19.1226i	−1.04167	+	1.04167i	−0.0425789	+	0.999093i	$0.513557\pi$
$337$	−19.1226	+	19.1226i	−1.04167	+	1.04167i	−0.999093	+	0.0425789i	$0.986443\pi$
$338$			16.4925i			0.897075i
$339$	−20.4015			−1.10806
$340$		0			0
$341$	−1.47055			−0.0796347
$342$		−	3.84209i		−	0.207757i
$343$	3.29913	−	3.29913i	0.178136	−	0.178136i
$344$	17.6074			0.949328
$345$	−10.3898	+	10.3898i	−0.559369	+	0.559369i
$346$	11.7490	+	11.7490i	0.631632	+	0.631632i
$347$	3.04979	+	3.04979i	0.163721	+	0.163721i	0.784213	−	0.620492i	$-0.213067\pi$
$347$	3.04979	+	3.04979i	0.163721	+	0.163721i	−0.620492	+	0.784213i	$0.713067\pi$
$348$			2.45370i			0.131532i
$349$		−	29.1251i		−	1.55903i	−0.626382	−	0.779516i	$-0.715465\pi$
$349$		−	29.1251i		−	1.55903i	0.626382	−	0.779516i	$-0.284535\pi$
$350$	11.8752	+	11.8752i	0.634757	+	0.634757i
$351$	−3.94856	−	3.94856i	−0.210759	−	0.210759i
$352$	−12.8069	+	12.8069i	−0.682611	+	0.682611i
$353$	11.5730			0.615971			0.307985	−	0.951391i	$-0.400345\pi$
$353$	11.5730			0.615971			0.307985	+	0.951391i	$0.400345\pi$
$354$	1.81640	−	1.81640i	0.0965404	−	0.0965404i
$355$		−	11.6372i		−	0.617638i
$356$	−17.2089			−0.912069
$357$		0			0
$358$	18.7814			0.992630
$359$		−	26.1470i		−	1.37998i	−0.723817	−	0.689992i	$-0.757614\pi$
$359$		−	26.1470i		−	1.37998i	0.723817	−	0.689992i	$-0.242386\pi$
$360$	6.50753	−	6.50753i	0.342977	−	0.342977i
$361$	1.05852			0.0557118
$362$	11.9620	−	11.9620i	0.628707	−	0.628707i
$363$	0.188773	+	0.188773i	0.00990802	+	0.00990802i
$364$	−16.5591	−	16.5591i	−0.867933	−	0.867933i
$365$		−	37.2124i		−	1.94779i
$366$			3.55013i			0.185568i
$367$	15.4451	+	15.4451i	0.806228	+	0.806228i	0.984061	−	0.177833i	$-0.0569087\pi$
$367$	15.4451	+	15.4451i	0.806228	+	0.806228i	−0.177833	+	0.984061i	$0.556909\pi$
$368$	−0.844830	−	0.844830i	−0.0440398	−	0.0440398i
$369$	−3.17713	+	3.17713i	−0.165395	+	0.165395i
$370$	2.15189			0.111871
$371$	−19.0353	+	19.0353i	−0.988261	+	0.988261i
$372$		−	0.528421i		−	0.0273974i
$373$	31.0065			1.60545			0.802727	−	0.596347i	$-0.203382\pi$
$373$	31.0065			1.60545			0.802727	+	0.596347i	$0.203382\pi$
$374$		0			0
$375$	0.630210			0.0325439
$376$			6.53632i			0.337085i
$377$	−8.22998	+	8.22998i	−0.423866	+	0.423866i
$378$	−3.23128			−0.166199
$379$	−8.32166	+	8.32166i	−0.427455	+	0.427455i	−0.887761	−	0.460305i	$-0.847740\pi$
$379$	−8.32166	+	8.32166i	−0.427455	+	0.427455i	0.460305	+	0.887761i	$0.347740\pi$
$380$	−11.2595	−	11.2595i	−0.577601	−	0.577601i
$381$	2.07422	+	2.07422i	0.106266	+	0.106266i
$382$		−	1.98987i		−	0.101811i
$383$			20.0262i			1.02329i	0.859197	+	0.511645i	$0.170964\pi$
$383$			20.0262i			1.02329i	−0.859197	+	0.511645i	$0.829036\pi$
$384$	−4.26890	−	4.26890i	−0.217846	−	0.217846i
$385$	26.3527	+	26.3527i	1.34306	+	1.34306i
$386$	2.12432	−	2.12432i	0.108125	−	0.108125i
$387$	−6.10953			−0.310565
$388$	−0.689573	+	0.689573i	−0.0350078	+	0.0350078i
$389$			12.7561i			0.646758i	0.946270	+	0.323379i	$0.104819\pi$
$389$			12.7561i			0.646758i	−0.946270	+	0.323379i	$0.895181\pi$
$390$	16.1747			0.819038
$391$		0			0
$392$	−16.3991			−0.828282
$393$			6.61671i			0.333769i
$394$	11.5567	−	11.5567i	0.582220	−	0.582220i
$395$	17.9881			0.905081
$396$	2.72715	−	2.72715i	0.137044	−	0.137044i
$397$	19.3140	+	19.3140i	0.969342	+	0.969342i	0.999544	−	0.0302019i	$-0.00961503\pi$
$397$	19.3140	+	19.3140i	0.969342	+	0.969342i	−0.0302019	+	0.999544i	$0.509615\pi$
$398$	−2.55374	−	2.55374i	−0.128007	−	0.128007i
$399$			15.0891i			0.755402i
$400$			1.34954i			0.0674772i
$401$	22.1745	+	22.1745i	1.10734	+	1.10734i	0.993499	+	0.113840i	$0.0363153\pi$
$401$	22.1745	+	22.1745i	1.10734	+	1.10734i	0.113840	+	0.993499i	$0.463685\pi$
$402$	9.30138	+	9.30138i	0.463911	+	0.463911i
$403$	1.77238	−	1.77238i	0.0882886	−	0.0882886i
$404$	5.80309			0.288715
$405$	−2.25802	+	2.25802i	−0.112202	+	0.112202i
$406$			6.73494i			0.334250i
$407$	2.43388			0.120643
$408$		0			0
$409$	17.1030			0.845688			0.422844	−	0.906202i	$-0.361032\pi$
$409$	17.1030			0.845688			0.422844	+	0.906202i	$0.361032\pi$
$410$		−	13.0147i		−	0.642748i
$411$	7.41409	−	7.41409i	0.365710	−	0.365710i
$412$	13.4613			0.663190
$413$	−7.13358	+	7.13358i	−0.351021	+	0.351021i
$414$	2.95123	+	2.95123i	0.145045	+	0.145045i
$415$	−8.85765	−	8.85765i	−0.434805	−	0.434805i
$416$		−	30.8711i		−	1.51358i
$417$		−	5.28597i		−	0.258855i
$418$	8.90049	+	8.90049i	0.435337	+	0.435337i
$419$	−10.7783	−	10.7783i	−0.526554	−	0.526554i	0.392989	−	0.919543i	$-0.371441\pi$
$419$	−10.7783	−	10.7783i	−0.526554	−	0.526554i	−0.919543	+	0.392989i	$0.871441\pi$
$420$	−9.46949	+	9.46949i	−0.462064	+	0.462064i
$421$	−6.96252			−0.339332			−0.169666	−	0.985502i	$-0.554269\pi$
$421$	−6.96252			−0.339332			−0.169666	+	0.985502i	$0.554269\pi$
$422$	0.128853	−	0.128853i	0.00627248	−	0.00627248i
$423$		−	2.26801i		−	0.110275i
$424$	−21.7784			−1.05765
$425$		0			0
$426$	−3.30555			−0.160154
$427$		−	13.9425i		−	0.674725i
$428$	−14.6445	+	14.6445i	−0.707869	+	0.707869i
$429$	18.2943			0.883256
$430$	12.5134	−	12.5134i	0.603450	−	0.603450i
$431$	15.1805	+	15.1805i	0.731218	+	0.731218i	0.970861	−	0.239643i	$-0.0770305\pi$
$431$	15.1805	+	15.1805i	0.731218	+	0.731218i	−0.239643	+	0.970861i	$0.577031\pi$
$432$	−0.183607	−	0.183607i	−0.00883381	−	0.00883381i
$433$		−	33.1954i		−	1.59527i	−0.603140	−	0.797635i	$-0.706084\pi$
$433$		−	33.1954i		−	1.59527i	0.603140	−	0.797635i	$-0.293916\pi$
$434$		−	1.45042i		−	0.0696222i
$435$	4.70640	+	4.70640i	0.225654	+	0.225654i
$436$	−11.7801	−	11.7801i	−0.564164	−	0.564164i
$437$	13.7814	−	13.7814i	0.659253	−	0.659253i
$438$	−10.5702			−0.505063
$439$	−25.2580	+	25.2580i	−1.20550	+	1.20550i	−0.233032	+	0.972469i	$0.574865\pi$
$439$	−25.2580	+	25.2580i	−1.20550	+	1.20550i	−0.972469	+	0.233032i	$0.925135\pi$
$440$			30.1504i			1.43736i
$441$	5.69028			0.270966
$442$		0			0
$443$	13.8366			0.657398			0.328699	−	0.944435i	$-0.393390\pi$
$443$	13.8366			0.657398			0.328699	+	0.944435i	$0.393390\pi$
$444$			0.874580i			0.0415057i
$445$	−33.0080	+	33.0080i	−1.56473	+	1.56473i
$446$	10.5216			0.498214
$447$	−15.8811	+	15.8811i	−0.751148	+	0.751148i
$448$	−13.9397	−	13.9397i	−0.658590	−	0.658590i
$449$	3.30552	+	3.30552i	0.155997	+	0.155997i	0.780790	−	0.624793i	$-0.214817\pi$
$449$	3.30552	+	3.30552i	0.155997	+	0.155997i	−0.624793	+	0.780790i	$0.714817\pi$
$450$		−	4.71434i		−	0.222236i
$451$		−	14.7201i		−	0.693144i
$452$	16.9828	+	16.9828i	0.798804	+	0.798804i
$453$	6.73673	+	6.73673i	0.316519	+	0.316519i
$454$	6.10217	−	6.10217i	0.286389	−	0.286389i
$455$	−63.5233			−2.97802
$456$	−8.63181	+	8.63181i	−0.404221	+	0.404221i
$457$		−	5.17186i		−	0.241930i	−0.992657	−	0.120965i	$-0.961401\pi$
$457$		−	5.17186i		−	0.241930i	0.992657	−	0.120965i	$-0.0385988\pi$
$458$	−15.2115			−0.710787
$459$		0			0
$460$	17.2976			0.806503
$461$			22.6450i			1.05468i	0.849654	+	0.527341i	$0.176811\pi$
$461$			22.6450i			1.05468i	−0.849654	+	0.527341i	$0.823189\pi$
$462$	7.48549	−	7.48549i	0.348257	−	0.348257i
$463$	−38.8961			−1.80766			−0.903828	−	0.427897i	$-0.859255\pi$
$463$	−38.8961			−1.80766			−0.903828	+	0.427897i	$0.859255\pi$
$464$	−0.382692	+	0.382692i	−0.0177660	+	0.0177660i
$465$	−1.01355	−	1.01355i	−0.0470025	−	0.0470025i
$466$	−6.06030	−	6.06030i	−0.280738	−	0.280738i
$467$			16.7116i			0.773322i	0.922222	+	0.386661i	$0.126372\pi$
$467$			16.7116i			0.773322i	−0.922222	+	0.386661i	$0.873628\pi$
$468$			6.57379i			0.303874i
$469$	−36.5296	−	36.5296i	−1.68678	−	1.68678i
$470$	4.64529	+	4.64529i	0.214271	+	0.214271i
$471$	9.98330	−	9.98330i	0.460006	−	0.460006i
$472$	−8.16159			−0.375667
$473$	14.1532	−	14.1532i	0.650764	−	0.650764i
$474$		−	5.10953i		−	0.234688i
$475$	−22.0146			−1.01010
$476$		0			0
$477$	7.55680			0.346002
$478$			5.82408i			0.266387i
$479$	−7.42681	+	7.42681i	−0.339340	+	0.339340i	−0.856119	−	0.516779i	$-0.827131\pi$
$479$	−7.42681	+	7.42681i	−0.339340	+	0.339340i	0.516779	+	0.856119i	$0.327131\pi$
$480$	−17.6540			−0.805789
$481$	−2.93344	+	2.93344i	−0.133753	+	0.133753i
$482$	−9.93075	−	9.93075i	−0.452333	−	0.452333i
$483$	−11.5904	−	11.5904i	−0.527383	−	0.527383i
$484$		−	0.314280i		−	0.0142855i
$485$			2.64531i			0.120117i
$486$	0.641392	+	0.641392i	0.0290941	+	0.0290941i
$487$	17.1442	+	17.1442i	0.776879	+	0.776879i	0.979299	−	0.202420i	$-0.0648805\pi$
$487$	17.1442	+	17.1442i	0.776879	+	0.776879i	−0.202420	+	0.979299i	$0.564881\pi$
$488$	7.97587	−	7.97587i	0.361050	−	0.361050i
$489$	−3.53391			−0.159809
$490$	−11.6547	+	11.6547i	−0.526505	+	0.526505i
$491$		−	14.7261i		−	0.664580i	−0.943177	−	0.332290i	$-0.892179\pi$
$491$		−	14.7261i		−	0.664580i	0.943177	−	0.332290i	$-0.107821\pi$
$492$	5.28948			0.238468
$493$		0			0
$494$	−21.4547			−0.965291
$495$		−	10.4618i		−	0.470221i
$496$	0.0824154	−	0.0824154i	0.00370056	−	0.00370056i
$497$	12.9820			0.582320
$498$	−2.51602	+	2.51602i	−0.112745	+	0.112745i
$499$	−10.1530	−	10.1530i	−0.454511	−	0.454511i	0.442338	−	0.896849i	$-0.354149\pi$
$499$	−10.1530	−	10.1530i	−0.454511	−	0.454511i	−0.896849	+	0.442338i	$0.854149\pi$
$500$	−0.524605	−	0.524605i	−0.0234611	−	0.0234611i
$501$			16.1872i			0.723189i
$502$		−	23.3138i		−	1.04055i
$503$	11.7358	+	11.7358i	0.523275	+	0.523275i	0.918559	−	0.395284i	$-0.129354\pi$
$503$	11.7358	+	11.7358i	0.523275	+	0.523275i	−0.395284	+	0.918559i	$0.629354\pi$
$504$	7.25952	+	7.25952i	0.323365	+	0.323365i
$505$	11.1308	−	11.1308i	0.495314	−	0.495314i
$506$	−13.6735			−0.607860
$507$	−12.8568	+	12.8568i	−0.570992	+	0.570992i
$508$		−	3.45329i		−	0.153215i
$509$	−33.1048			−1.46734			−0.733672	−	0.679503i	$-0.762195\pi$
$509$	−33.1048			−1.46734			−0.733672	+	0.679503i	$0.762195\pi$
$510$		0			0
$511$	41.5126			1.83641
$512$		−	2.93216i		−	0.129584i
$513$	2.99512	−	2.99512i	0.132238	−	0.132238i
$514$	−2.27189			−0.100209
$515$	25.8198	−	25.8198i	1.13776	−	1.13776i
$516$	5.08575	+	5.08575i	0.223888	+	0.223888i
$517$	5.25402	+	5.25402i	0.231072	+	0.231072i
$518$			2.40056i			0.105474i
$519$			18.3180i			0.804072i
$520$	−36.3388	−	36.3388i	−1.59356	−	1.59356i
$521$	17.1502	+	17.1502i	0.751365	+	0.751365i	0.974734	−	0.223369i	$-0.0717056\pi$
$521$	17.1502	+	17.1502i	0.751365	+	0.751365i	−0.223369	+	0.974734i	$0.571706\pi$
$522$	1.33685	−	1.33685i	0.0585124	−	0.0585124i
$523$	2.14935			0.0939843			0.0469922	−	0.998895i	$-0.485036\pi$
$523$	2.14935			0.0939843			0.0469922	+	0.998895i	$0.485036\pi$
$524$	5.50794	−	5.50794i	0.240615	−	0.240615i
$525$			18.5147i			0.808050i
$526$	5.53189			0.241202
$527$		0			0
$528$	0.850680			0.0370211
$529$		−	1.82818i		−	0.0794862i
$530$	−15.4777	+	15.4777i	−0.672307	+	0.672307i
$531$	2.83196			0.122897
$532$	12.5606	−	12.5606i	0.544573	−	0.544573i
$533$	17.7415	+	17.7415i	0.768468	+	0.768468i
$534$	9.37592	+	9.37592i	0.405736	+	0.405736i
$535$			56.1787i			2.42882i
$536$		−	41.7938i		−	1.80522i
$537$	14.6411	+	14.6411i	0.631812	+	0.631812i
$538$	2.63901	+	2.63901i	0.113776	+	0.113776i
$539$	−13.1820	+	13.1820i	−0.567787	+	0.567787i
$540$	3.75929			0.161774
$541$	2.86223	−	2.86223i	0.123057	−	0.123057i	−0.642896	−	0.765953i	$-0.722267\pi$
$541$	2.86223	−	2.86223i	0.123057	−	0.123057i	0.765953	+	0.642896i	$0.222267\pi$
$542$		−	10.7531i		−	0.461884i
$543$	18.6500			0.800348
$544$		0			0
$545$	−45.1903			−1.93574
$546$			18.0438i			0.772204i
$547$	26.9431	−	26.9431i	1.15201	−	1.15201i	0.165855	−	0.986150i	$-0.446961\pi$
$547$	26.9431	−	26.9431i	1.15201	−	1.15201i	0.986150	−	0.165855i	$-0.0530385\pi$
$548$	−12.3434			−0.527284
$549$	−2.76752	+	2.76752i	−0.118115	+	0.118115i
$550$	10.9211	+	10.9211i	0.465678	+	0.465678i
$551$	−6.24272	−	6.24272i	−0.265949	−	0.265949i
$552$		−	13.2607i		−	0.564413i
$553$			20.0668i			0.853327i
$554$	−10.4391	−	10.4391i	−0.443513	−	0.443513i
$555$	1.67751	+	1.67751i	0.0712065	+	0.0712065i
$556$	−4.40020	+	4.40020i	−0.186610	+	0.186610i
$557$	−47.0274			−1.99262			−0.996308	−	0.0858461i	$-0.972641\pi$
$557$	−47.0274			−1.99262			−0.996308	+	0.0858461i	$0.972641\pi$
$558$	−0.287900	+	0.287900i	−0.0121878	+	0.0121878i
$559$			34.1163i			1.44297i
$560$	−2.95382			−0.124822
$561$		0			0
$562$	13.8333			0.583522
$563$			28.7543i			1.21185i	0.795521	+	0.605925i	$0.207197\pi$
$563$			28.7543i			1.21185i	−0.795521	+	0.605925i	$0.792803\pi$
$564$	−1.88796	+	1.88796i	−0.0794975	+	0.0794975i
$565$	65.1488			2.74083
$566$	13.3994	−	13.3994i	0.563219	−	0.563219i
$567$	−2.51896	−	2.51896i	−0.105786	−	0.105786i
$568$	7.42638	+	7.42638i	0.311604	+	0.311604i
$569$			1.04600i			0.0438505i	0.999760	+	0.0219252i	$0.00697958\pi$
$569$			1.04600i			0.0438505i	−0.999760	+	0.0219252i	$0.993020\pi$
$570$			12.2691i			0.513895i
$571$	18.5638	+	18.5638i	0.776869	+	0.776869i	0.979297	−	0.202428i	$-0.0648832\pi$
$571$	18.5638	+	18.5638i	0.776869	+	0.776869i	−0.202428	+	0.979297i	$0.564883\pi$
$572$	−15.2287	−	15.2287i	−0.636743	−	0.636743i
$573$	1.55121	−	1.55121i	0.0648028	−	0.0648028i
$574$	14.5186			0.605995
$575$	16.9101	−	16.9101i	0.705200	−	0.705200i
$576$			5.53393i			0.230580i
$577$	38.7607			1.61363			0.806814	−	0.590806i	$-0.201190\pi$
$577$	38.7607			1.61363			0.806814	+	0.590806i	$0.201190\pi$
$578$		0			0
$579$	3.31205			0.137644
$580$		−	7.83548i		−	0.325351i
$581$	9.88121	−	9.88121i	0.409942	−	0.409942i
$582$	0.751401			0.0311466
$583$	−17.5059	+	17.5059i	−0.725020	+	0.725020i
$584$	23.7474	+	23.7474i	0.982676	+	0.982676i
$585$	12.6091	+	12.6091i	0.521320	+	0.521320i
$586$		−	20.3676i		−	0.841378i
$587$			41.5716i			1.71584i	0.513781	+	0.857921i	$0.328244\pi$
$587$			41.5716i			1.71584i	−0.513781	+	0.857921i	$0.671756\pi$
$588$	−4.73675	−	4.73675i	−0.195340	−	0.195340i
$589$	1.34441	+	1.34441i	0.0553955	+	0.0553955i
$590$	−5.80035	+	5.80035i	−0.238797	+	0.238797i
$591$	18.0182			0.741170
$592$	−0.136404	+	0.136404i	−0.00560618	+	0.00560618i
$593$		−	13.7886i		−	0.566230i	−0.959086	−	0.283115i	$-0.908632\pi$
$593$		−	13.7886i		−	0.566230i	0.959086	−	0.283115i	$-0.0913678\pi$
$594$	−2.97167			−0.121929
$595$		0			0
$596$	26.4397			1.08301
$597$		−	3.98156i		−	0.162954i
$598$	16.4800	−	16.4800i	0.673917	−	0.673917i
$599$	−0.372690			−0.0152277			−0.00761386	−	0.999971i	$-0.502424\pi$
$599$	−0.372690			−0.0152277			−0.00761386	+	0.999971i	$0.502424\pi$
$600$	−10.5914	+	10.5914i	−0.432393	+	0.432393i
$601$	−16.2864	−	16.2864i	−0.664337	−	0.664337i	0.292062	−	0.956399i	$-0.405659\pi$
$601$	−16.2864	−	16.2864i	−0.664337	−	0.664337i	−0.956399	+	0.292062i	$0.905659\pi$
$602$	13.9594	+	13.9594i	0.568943	+	0.568943i
$603$			14.5019i			0.590562i
$604$		−	11.2157i		−	0.456360i
$605$	−0.602815	−	0.602815i	−0.0245079	−	0.0245079i
$606$	−3.16170	−	3.16170i	−0.128435	−	0.128435i
$607$	−11.3879	+	11.3879i	−0.462222	+	0.462222i	−0.899383	−	0.437161i	$-0.855984\pi$
$607$	−11.3879	+	11.3879i	−0.462222	+	0.462222i	0.437161	+	0.899383i	$0.355984\pi$
$608$	23.4168			0.949677
$609$	−5.25025	+	5.25025i	−0.212751	+	0.212751i
$610$		−	11.3367i		−	0.459011i
$611$	−12.6648			−0.512365
$612$		0			0
$613$	−14.9606			−0.604251			−0.302126	−	0.953268i	$-0.597696\pi$
$613$	−14.9606			−0.604251			−0.302126	+	0.953268i	$0.597696\pi$
$614$		−	0.665302i		−	0.0268494i
$615$	10.1456	−	10.1456i	0.409112	−	0.409112i
$616$	−33.6345			−1.35517
$617$	−3.36259	+	3.36259i	−0.135373	+	0.135373i	−0.771546	−	0.636173i	$-0.780516\pi$
$617$	−3.36259	+	3.36259i	−0.135373	+	0.135373i	0.636173	+	0.771546i	$0.280516\pi$
$618$	−7.33412	−	7.33412i	−0.295021	−	0.295021i
$619$	30.4760	+	30.4760i	1.22493	+	1.22493i	0.965857	+	0.259076i	$0.0834179\pi$
$619$	30.4760	+	30.4760i	1.22493	+	1.22493i	0.259076	+	0.965857i	$0.416582\pi$
$620$			1.68742i			0.0677686i
$621$			4.60128i			0.184643i
$622$	15.5342	+	15.5342i	0.622865	+	0.622865i
$623$	−36.8223	−	36.8223i	−1.47525	−	1.47525i
$624$	−1.02528	+	1.02528i	−0.0410442	+	0.0410442i
$625$	23.9743			0.958972
$626$	2.45553	−	2.45553i	0.0981426	−	0.0981426i
$627$			13.8768i			0.554187i
$628$	−16.6208			−0.663241
$629$		0			0
$630$	10.3185			0.411100
$631$			11.3212i			0.450690i	0.974279	+	0.225345i	$0.0723510\pi$
$631$			11.3212i			0.450690i	−0.974279	+	0.225345i	$0.927649\pi$
$632$	−11.4793	+	11.4793i	−0.456622	+	0.456622i
$633$	0.200896			0.00798491
$634$	−2.24027	+	2.24027i	−0.0889726	+	0.0889726i
$635$	−6.62368	−	6.62368i	−0.262853	−	0.262853i
$636$	−6.29050	−	6.29050i	−0.249435	−	0.249435i
$637$		−	31.7751i		−	1.25898i
$638$			6.19384i			0.245216i
$639$	−2.57685	−	2.57685i	−0.101939	−	0.101939i
$640$	13.6320	+	13.6320i	0.538852	+	0.538852i
$641$	−11.2263	+	11.2263i	−0.443414	+	0.443414i	−0.893158	−	0.449744i	$-0.851515\pi$
$641$	−11.2263	+	11.2263i	−0.443414	+	0.443414i	0.449744	+	0.893158i	$0.351515\pi$
$642$	15.9576			0.629795
$643$	18.1975	−	18.1975i	0.717640	−	0.717640i	−0.250481	−	0.968121i	$-0.580589\pi$
$643$	18.1975	−	18.1975i	0.717640	−	0.717640i	0.968121	+	0.250481i	$0.0805889\pi$
$644$			19.2964i			0.760386i
$645$	19.5097			0.768196
$646$		0			0
$647$	−26.9015			−1.05761			−0.528804	−	0.848744i	$-0.677359\pi$
$647$	−26.9015			−1.05761			−0.528804	+	0.848744i	$0.677359\pi$
$648$		−	2.88196i		−	0.113214i
$649$	−6.56044	+	6.56044i	−0.257520	+	0.257520i
$650$	−26.3254			−1.03257
$651$	1.13068	−	1.13068i	0.0443148	−	0.0443148i
$652$	2.94172	+	2.94172i	0.115207	+	0.115207i
$653$	14.6088	+	14.6088i	0.571685	+	0.571685i	0.932599	−	0.360914i	$-0.117535\pi$
$653$	14.6088	+	14.6088i	0.571685	+	0.571685i	−0.360914	+	0.932599i	$0.617535\pi$
$654$			12.8363i			0.501939i
$655$		−	21.1293i		−	0.825591i
$656$	0.824975	+	0.824975i	0.0322099	+	0.0322099i
$657$	−8.24004	−	8.24004i	−0.321475	−	0.321475i
$658$	−5.18209	+	5.18209i	−0.202019	+	0.202019i
$659$	25.5651			0.995875			0.497937	−	0.867213i	$-0.334091\pi$
$659$	25.5651			0.995875			0.497937	+	0.867213i	$0.334091\pi$
$660$	−8.70868	+	8.70868i	−0.338985	+	0.338985i
$661$			27.9387i			1.08669i	0.839510	+	0.543345i	$0.182842\pi$
$661$			27.9387i			1.08669i	−0.839510	+	0.543345i	$0.817158\pi$
$662$	4.53857			0.176396
$663$		0			0
$664$	11.3052			0.438726
$665$		−	48.1846i		−	1.86852i
$666$	0.476498	−	0.476498i	0.0184639	−	0.0184639i
$667$	9.59045			0.371344
$668$	13.4747	−	13.4747i	0.521350	−	0.521350i
$669$	8.20219	+	8.20219i	0.317115	+	0.317115i
$670$	−29.7024	−	29.7024i	−1.14750	−	1.14750i
$671$		−	12.8223i		−	0.495000i
$672$		−	19.6940i		−	0.759713i
$673$	1.82876	+	1.82876i	0.0704934	+	0.0704934i	0.741474	−	0.670981i	$-0.234127\pi$
$673$	1.82876	+	1.82876i	0.0704934	+	0.0704934i	−0.670981	+	0.741474i	$0.734127\pi$
$674$	−17.3454	−	17.3454i	−0.668120	−	0.668120i
$675$	3.67508	−	3.67508i	0.141454	−	0.141454i
$676$	21.4048			0.823261
$677$	−0.627088	+	0.627088i	−0.0241010	+	0.0241010i	−0.719055	−	0.694954i	$-0.755425\pi$
$677$	−0.627088	+	0.627088i	−0.0241010	+	0.0241010i	0.694954	+	0.719055i	$0.255425\pi$
$678$		−	18.5055i		−	0.710700i
$679$	−2.95100			−0.113249
$680$		0			0
$681$	9.51394			0.364575
$682$		−	1.33388i		−	0.0510771i
$683$	19.0444	−	19.0444i	0.728712	−	0.728712i	−0.241651	−	0.970363i	$-0.577689\pi$
$683$	19.0444	−	19.0444i	0.728712	−	0.728712i	0.970363	+	0.241651i	$0.0776890\pi$
$684$	−4.98645			−0.190662
$685$	−23.6756	+	23.6756i	−0.904600	+	0.904600i
$686$	2.99253	+	2.99253i	0.114255	+	0.114255i
$687$	−11.8582	−	11.8582i	−0.452418	−	0.452418i
$688$			1.58640i			0.0604810i
$689$		−	42.1980i		−	1.60762i
$690$	−9.42424	−	9.42424i	−0.358775	−	0.358775i
$691$	7.34201	+	7.34201i	0.279303	+	0.279303i	0.832831	−	0.553528i	$-0.186719\pi$
$691$	7.34201	+	7.34201i	0.279303	+	0.279303i	−0.553528	+	0.832831i	$0.686719\pi$
$692$	15.2484	−	15.2484i	0.579659	−	0.579659i
$693$	11.6707			0.443333
$694$	−2.76636	+	2.76636i	−0.105009	+	0.105009i
$695$			16.8798i			0.640289i
$696$	−6.00686			−0.227689
$697$		0			0
$698$	26.4184			0.999951
$699$		−	9.44867i		−	0.357381i
$700$	15.4122	−	15.4122i	0.582527	−	0.582527i
$701$	−49.5351			−1.87091			−0.935457	−	0.353440i	$-0.885012\pi$
$701$	−49.5351			−1.87091			−0.935457	+	0.353440i	$0.885012\pi$
$702$	3.58160	−	3.58160i	0.135179	−	0.135179i
$703$	−2.22511	−	2.22511i	−0.0839217	−	0.0839217i
$704$	−12.8198	−	12.8198i	−0.483163	−	0.483163i
$705$			7.24251i			0.272769i
$706$			10.4975i			0.395079i
$707$	12.4170	+	12.4170i	0.466991	+	0.466991i
$708$	−2.35740	−	2.35740i	−0.0885967	−	0.0885967i
$709$	−25.7053	+	25.7053i	−0.965381	+	0.965381i	−0.999421	−	0.0340391i	$-0.989163\pi$
$709$	−25.7053	+	25.7053i	−0.965381	+	0.965381i	0.0340391	+	0.999421i	$0.489163\pi$
$710$	10.5557			0.396148
$711$	3.98316	−	3.98316i	0.149380	−	0.149380i
$712$		−	42.1287i		−	1.57884i
$713$	−2.06537			−0.0773486
$714$		0			0
$715$	−58.4197			−2.18477
$716$		−	24.3754i		−	0.910953i
$717$	−4.54018	+	4.54018i	−0.169556	+	0.169556i
$718$	23.7170			0.885112
$719$	12.7637	−	12.7637i	0.476007	−	0.476007i	−0.427845	−	0.903852i	$-0.640727\pi$
$719$	12.7637	−	12.7637i	0.476007	−	0.476007i	0.903852	+	0.427845i	$0.140727\pi$
$720$	0.586319	+	0.586319i	0.0218508	+	0.0218508i
$721$	28.8035	+	28.8035i	1.07270	+	1.07270i
$722$			0.960151i			0.0357331i
$723$		−	15.4831i		−	0.575823i
$724$	−15.5248	−	15.5248i	−0.576975	−	0.576975i
$725$	−7.65997	−	7.65997i	−0.284484	−	0.284484i
$726$	−0.171230	+	0.171230i	−0.00635493	+	0.00635493i
$727$	−25.6114			−0.949873			−0.474936	−	0.880020i	$-0.657529\pi$
$727$	−25.6114			−0.949873			−0.474936	+	0.880020i	$0.657529\pi$
$728$	40.5380	−	40.5380i	1.50244	−	1.50244i
$729$			1.00000i			0.0370370i
$730$	33.7541			1.24930
$731$		0			0
$732$	4.60752			0.170299
$733$			31.6733i			1.16988i	0.811076	+	0.584941i	$0.198882\pi$
$733$			31.6733i			1.16988i	−0.811076	+	0.584941i	$0.801118\pi$
$734$	−14.0097	+	14.0097i	−0.517108	+	0.517108i
$735$	−18.1709			−0.670245
$736$	−17.9872	+	17.9872i	−0.663015	+	0.663015i
$737$	−33.5946	−	33.5946i	−1.23747	−	1.23747i
$738$	−2.88187	−	2.88187i	−0.106083	−	0.106083i
$739$			31.3462i			1.15309i	0.817066	+	0.576543i	$0.195599\pi$
$739$			31.3462i			1.15309i	−0.817066	+	0.576543i	$0.804401\pi$
$740$		−	2.79282i		−	0.102666i
$741$	−16.7251	−	16.7251i	−0.614411	−	0.614411i
$742$	−17.2662	−	17.2662i	−0.633863	−	0.633863i
$743$	2.26275	−	2.26275i	0.0830121	−	0.0830121i	−0.664381	−	0.747394i	$-0.731305\pi$
$743$	2.26275	−	2.26275i	0.0830121	−	0.0830121i	0.747394	+	0.664381i	$0.231305\pi$
$744$	1.29362			0.0474263
$745$	50.7134	−	50.7134i	1.85800	−	1.85800i
$746$			28.1249i			1.02973i
$747$	−3.92274			−0.143526
$748$		0			0
$749$	−62.6705			−2.28993
$750$			0.571642i			0.0208734i
$751$	19.5114	−	19.5114i	0.711981	−	0.711981i	−0.254969	−	0.966949i	$-0.582065\pi$
$751$	19.5114	−	19.5114i	0.711981	−	0.711981i	0.966949	+	0.254969i	$0.0820651\pi$
$752$	−0.588913			−0.0214754
$753$	18.1744	−	18.1744i	0.662311	−	0.662311i
$754$	−7.46513	−	7.46513i	−0.271864	−	0.271864i
$755$	−21.5126	−	21.5126i	−0.782923	−	0.782923i
$756$			4.19370i			0.152524i
$757$			10.1597i			0.369259i	0.982808	+	0.184629i	$0.0591085\pi$
$757$			10.1597i			0.369259i	−0.982808	+	0.184629i	$0.940892\pi$
$758$	−7.54829	−	7.54829i	−0.274166	−	0.274166i
$759$	−10.6592	−	10.6592i	−0.386905	−	0.386905i
$760$	27.5642	−	27.5642i	0.999859	−	0.999859i
$761$	−8.12911			−0.294680			−0.147340	−	0.989086i	$-0.547071\pi$
$761$	−8.12911			−0.294680			−0.147340	+	0.989086i	$0.547071\pi$
$762$	−1.88146	+	1.88146i	−0.0681580	+	0.0681580i
$763$		−	50.4124i		−	1.82505i
$764$	−2.58255			−0.0934333
$765$		0			0
$766$	−18.1650			−0.656330
$767$		−	15.8140i		−	0.571009i
$768$	11.6983	−	11.6983i	0.422127	−	0.422127i
$769$	−16.6656			−0.600978			−0.300489	−	0.953785i	$-0.597150\pi$
$769$	−16.6656			−0.600978			−0.300489	+	0.953785i	$0.597150\pi$
$770$	−23.9036	+	23.9036i	−0.861428	+	0.861428i
$771$	−1.77106	−	1.77106i	−0.0637832	−	0.0637832i
$772$	−2.75705	−	2.75705i	−0.0992284	−	0.0992284i
$773$		−	42.9077i		−	1.54328i	−0.636058	−	0.771641i	$-0.719436\pi$
$773$		−	42.9077i		−	1.54328i	0.636058	−	0.771641i	$-0.280564\pi$
$774$		−	5.54175i		−	0.199194i
$775$	1.64963	+	1.64963i	0.0592563	+	0.0592563i
$776$	−1.68813	−	1.68813i	−0.0606003	−	0.0606003i
$777$	−1.87136	+	1.87136i	−0.0671348	+	0.0671348i
$778$	−11.5706			−0.414826
$779$	−13.4575	+	13.4575i	−0.482165	+	0.482165i
$780$		−	20.9923i		−	0.751645i
$781$	11.9389			0.427209
$782$		0			0
$783$	2.08430			0.0744867
$784$		−	1.47754i		−	0.0527692i
$785$	−31.8800	+	31.8800i	−1.13784	+	1.13784i
$786$	−6.00179			−0.214077
$787$	−7.52696	+	7.52696i	−0.268307	+	0.268307i	−0.828418	−	0.560111i	$-0.810759\pi$
$787$	−7.52696	+	7.52696i	−0.268307	+	0.268307i	0.560111	+	0.828418i	$0.310759\pi$
$788$	−14.9989	−	14.9989i	−0.534313	−	0.534313i
$789$	4.31241	+	4.31241i	0.153526	+	0.153526i
$790$			16.3164i			0.580512i
$791$			72.6772i			2.58410i
$792$	6.67627	+	6.67627i	0.237231	+	0.237231i
$793$	15.4541	+	15.4541i	0.548792	+	0.548792i
$794$	−17.5191	+	17.5191i	−0.621728	+	0.621728i
$795$	−24.1314			−0.855851
$796$	−3.31436	+	3.31436i	−0.117474	+	0.117474i
$797$		−	29.6872i		−	1.05157i	−0.850617	−	0.525787i	$-0.823771\pi$
$797$		−	29.6872i		−	1.05157i	0.850617	−	0.525787i	$-0.176229\pi$
$798$	−13.6868			−0.484509
$799$		0			0
$800$	28.7330			1.01586
$801$			14.6181i			0.516505i
$802$	−20.1137	+	20.1137i	−0.710239	+	0.710239i
$803$	38.1773			1.34725
$804$	12.0718	−	12.0718i	0.425738	−	0.425738i
$805$	37.0121	+	37.0121i	1.30450	+	1.30450i
$806$	1.60767	+	1.60767i	0.0566276	+	0.0566276i
$807$			4.11451i			0.144838i
$808$			14.2064i			0.499780i
$809$	−16.1439	−	16.1439i	−0.567590	−	0.567590i	0.363862	−	0.931453i	$-0.381458\pi$
$809$	−16.1439	−	16.1439i	−0.567590	−	0.567590i	−0.931453	+	0.363862i	$0.881458\pi$
$810$	−2.04818	−	2.04818i	−0.0719656	−	0.0719656i
$811$	26.3402	−	26.3402i	0.924928	−	0.924928i	−0.0724446	−	0.997372i	$-0.523080\pi$
$811$	26.3402	−	26.3402i	0.924928	−	0.924928i	0.997372	+	0.0724446i	$0.0230800\pi$
$812$	8.74093			0.306746
$813$	8.38261	−	8.38261i	0.293991	−	0.293991i
$814$			2.20769i			0.0773794i
$815$	11.2849			0.395294
$816$		0			0
$817$	−25.8784			−0.905370
$818$			15.5135i			0.542418i
$819$	−14.0661	+	14.0661i	−0.491510	+	0.491510i
$820$	−16.8910			−0.589861
$821$	−2.32827	+	2.32827i	−0.0812571	+	0.0812571i	−0.746567	−	0.665310i	$-0.768299\pi$
$821$	−2.32827	+	2.32827i	−0.0812571	+	0.0812571i	0.665310	+	0.746567i	$0.268299\pi$
$822$	6.72507	+	6.72507i	0.234564	+	0.234564i
$823$	−9.04297	−	9.04297i	−0.315218	−	0.315218i	0.531709	−	0.846927i	$-0.321550\pi$
$823$	−9.04297	−	9.04297i	−0.315218	−	0.315218i	−0.846927	+	0.531709i	$0.821550\pi$
$824$			32.9543i			1.14802i
$825$			17.0272i			0.592811i
$826$	−6.47062	−	6.47062i	−0.225142	−	0.225142i
$827$	25.8039	+	25.8039i	0.897290	+	0.897290i	0.995196	−	0.0979056i	$-0.0312143\pi$
$827$	25.8039	+	25.8039i	0.897290	+	0.897290i	−0.0979056	+	0.995196i	$0.531214\pi$
$828$	3.83024	−	3.83024i	0.133110	−	0.133110i
$829$	0.425058			0.0147629			0.00738144	−	0.999973i	$-0.497650\pi$
$829$	0.425058			0.0147629			0.00738144	+	0.999973i	$0.497650\pi$
$830$	8.03446	−	8.03446i	0.278880	−	0.278880i
$831$		−	16.2756i		−	0.564596i
$832$	30.9021			1.07134
$833$		0			0
$834$	4.79472			0.166028
$835$		−	51.6909i		−	1.78884i
$836$	11.5515	−	11.5515i	0.399516	−	0.399516i
$837$	−0.448868			−0.0155151
$838$	9.77661	−	9.77661i	0.337728	−	0.337728i
$839$	−22.4020	−	22.4020i	−0.773403	−	0.773403i	0.205296	−	0.978700i	$-0.434184\pi$
$839$	−22.4020	−	22.4020i	−0.773403	−	0.773403i	−0.978700	+	0.205296i	$0.934184\pi$
$840$	−23.1821	−	23.1821i	−0.799857	−	0.799857i
$841$			24.6557i			0.850197i
$842$		−	6.31546i		−	0.217645i
$843$	10.7838	+	10.7838i	0.371414	+	0.371414i
$844$	−0.167232	−	0.167232i	−0.00575636	−	0.00575636i
$845$	41.0561	−	41.0561i	1.41237	−	1.41237i
$846$	2.05724			0.0707293
$847$	0.672475	−	0.672475i	0.0231065	−	0.0231065i
$848$		−	1.96220i		−	0.0673822i
$849$	20.8911			0.716981
$850$		0			0
$851$	3.41835			0.117180
$852$			4.29009i			0.146976i
$853$	10.8857	−	10.8857i	0.372719	−	0.372719i	−0.495748	−	0.868467i	$-0.665106\pi$
$853$	10.8857	−	10.8857i	0.372719	−	0.372719i	0.868467	+	0.495748i	$0.165106\pi$
$854$	12.6468			0.432763
$855$	−9.56440	+	9.56440i	−0.327096	+	0.327096i
$856$	−35.8509	−	35.8509i	−1.22536	−	1.22536i
$857$	28.8158	+	28.8158i	0.984330	+	0.984330i	0.999879	−	0.0155486i	$-0.00494948\pi$
$857$	28.8158	+	28.8158i	0.984330	+	0.984330i	−0.0155486	+	0.999879i	$0.504949\pi$
$858$			16.5941i			0.566514i
$859$			46.4431i			1.58462i	0.610119	+	0.792310i	$0.291122\pi$
$859$			46.4431i			1.58462i	−0.610119	+	0.792310i	$0.708878\pi$
$860$	−16.2405	−	16.2405i	−0.553796	−	0.553796i
$861$	11.3180	+	11.3180i	0.385718	+	0.385718i
$862$	−13.7697	+	13.7697i	−0.468997	+	0.468997i
$863$	47.2341			1.60787			0.803934	−	0.594719i	$-0.202737\pi$
$863$	47.2341			1.60787			0.803934	+	0.594719i	$0.202737\pi$
$864$	−3.90916	+	3.90916i	−0.132992	+	0.132992i
$865$		−	58.4954i		−	1.98890i
$866$	30.1104			1.02319
$867$		0			0
$868$	−1.88242			−0.0638934
$869$			18.4546i			0.626028i
$870$	−4.26901	+	4.26901i	−0.144733	+	0.144733i
$871$	80.9800			2.74390
$872$	28.8386	−	28.8386i	0.976598	−	0.976598i
$873$	0.585758	+	0.585758i	0.0198249	+	0.0198249i
$874$	12.5006	+	12.5006i	0.422840	+	0.422840i
$875$		−	2.24502i		−	0.0758957i
$876$			13.7185i			0.463505i
$877$	−0.223756	−	0.223756i	−0.00755569	−	0.00755569i	0.703319	−	0.710875i	$-0.251701\pi$
$877$	−0.223756	−	0.223756i	−0.00755569	−	0.00755569i	−0.710875	+	0.703319i	$0.751701\pi$
$878$	−22.9107	−	22.9107i	−0.773199	−	0.773199i
$879$	15.8777	−	15.8777i	0.535540	−	0.535540i
$880$	−2.71650			−0.0915733
$881$	−25.5518	+	25.5518i	−0.860861	+	0.860861i	−0.991438	−	0.130577i	$-0.958317\pi$
$881$	−25.5518	+	25.5518i	−0.860861	+	0.860861i	0.130577	+	0.991438i	$0.458317\pi$
$882$			5.16145i			0.173795i
$883$	0.156899			0.00528008			0.00264004	−	0.999997i	$-0.499160\pi$
$883$	0.156899			0.00528008			0.00264004	+	0.999997i	$0.499160\pi$
$884$		0			0
$885$	−9.04338			−0.303990
$886$			12.5507i			0.421650i
$887$	−21.2889	+	21.2889i	−0.714811	+	0.714811i	−0.967538	−	0.252726i	$-0.918673\pi$
$887$	−21.2889	+	21.2889i	−0.714811	+	0.714811i	0.252726	+	0.967538i	$0.418673\pi$
$888$	−2.14104			−0.0718487
$889$	7.38909	−	7.38909i	0.247822	−	0.247822i
$890$	−29.9404	−	29.9404i	−1.00360	−	1.00360i
$891$	−2.31657	−	2.31657i	−0.0776082	−	0.0776082i
$892$		−	13.6555i		−	0.457219i
$893$		−	9.60671i		−	0.321476i
$894$	−14.4052	−	14.4052i	−0.481781	−	0.481781i
$895$	−46.7540	−	46.7540i	−1.56281	−	1.56281i
$896$	−15.2073	+	15.2073i	−0.508040	+	0.508040i
$897$	25.6941			0.857900
$898$	−2.99832	+	2.99832i	−0.100055	+	0.100055i
$899$			0.935574i			0.0312031i
$900$	−6.11849			−0.203950
$901$		0			0
$902$	13.3521			0.444577
$903$			21.7642i			0.724269i
$904$	−41.5753	+	41.5753i	−1.38277	+	1.38277i
$905$	−59.5556			−1.97970
$906$	−6.11065	+	6.11065i	−0.203013	+	0.203013i
$907$	−27.2070	−	27.2070i	−0.903393	−	0.903393i	0.0923354	−	0.995728i	$-0.470567\pi$
$907$	−27.2070	−	27.2070i	−0.903393	−	0.903393i	−0.995728	+	0.0923354i	$0.970567\pi$
$908$	−7.91968	−	7.91968i	−0.262824	−	0.262824i
$909$		−	4.92944i		−	0.163499i
$910$		−	57.6198i		−	1.91008i
$911$	−1.32358	−	1.32358i	−0.0438521	−	0.0438521i	0.684841	−	0.728693i	$-0.259872\pi$
$911$	−1.32358	−	1.32358i	−0.0438521	−	0.0438521i	−0.728693	+	0.684841i	$0.759872\pi$
$912$	−0.777713	−	0.777713i	−0.0257526	−	0.0257526i
$913$	9.08732	−	9.08732i	0.300746	−	0.300746i
$914$	4.69122			0.155172
$915$	8.83759	−	8.83759i	0.292162	−	0.292162i
$916$			19.7422i			0.652301i
$917$	23.5710			0.778382
$918$		0			0
$919$	6.41003			0.211447			0.105724	−	0.994396i	$-0.466284\pi$
$919$	6.41003			0.211447			0.105724	+	0.994396i	$0.466284\pi$
$920$			42.3458i			1.39610i
$921$	0.518639	−	0.518639i	0.0170897	−	0.0170897i
$922$	−20.5405			−0.676464
$923$	−14.3894	+	14.3894i	−0.473634	+	0.473634i
$924$	−9.71503	−	9.71503i	−0.319601	−	0.319601i
$925$	−2.73026	−	2.73026i	−0.0897706	−	0.0897706i
$926$		−	35.2813i		−	1.15942i
$927$		−	11.4347i		−	0.375564i
$928$	8.14785	+	8.14785i	0.267466	+	0.267466i
$929$	−4.06041	−	4.06041i	−0.133218	−	0.133218i	0.637354	−	0.770571i	$-0.280029\pi$
$929$	−4.06041	−	4.06041i	−0.133218	−	0.133218i	−0.770571	+	0.637354i	$0.780029\pi$
$930$	0.919360	−	0.919360i	0.0301470	−	0.0301470i
$931$	24.1025			0.789928
$932$	−7.86534	+	7.86534i	−0.257638	+	0.257638i
$933$			24.2195i			0.792911i
$934$	−15.1585			−0.496003
$935$		0			0
$936$	−16.0932			−0.526022
$937$		−	35.7264i		−	1.16713i	−0.812066	−	0.583566i	$-0.801657\pi$
$937$		−	35.7264i		−	1.16713i	0.812066	−	0.583566i	$-0.198343\pi$
$938$	33.1347	−	33.1347i	1.08189	−	1.08189i
$939$	3.82843			0.124936
$940$	6.02888	−	6.02888i	0.196640	−	0.196640i
$941$	7.75479	+	7.75479i	0.252799	+	0.252799i	0.822117	−	0.569318i	$-0.192793\pi$
$941$	7.75479	+	7.75479i	0.252799	+	0.252799i	−0.569318	+	0.822117i	$0.692793\pi$
$942$	9.05550	+	9.05550i	0.295044	+	0.295044i
$943$		−	20.6742i		−	0.673246i
$944$		−	0.735347i		−	0.0239335i
$945$	8.04386	+	8.04386i	0.261667	+	0.261667i
$946$	12.8379	+	12.8379i	0.417395	+	0.417395i
$947$	−28.0836	+	28.0836i	−0.912594	+	0.912594i	−0.996476	−	0.0838820i	$-0.973268\pi$
$947$	−28.0836	+	28.0836i	−0.912594	+	0.912594i	0.0838820	+	0.996476i	$0.473268\pi$
$948$	−6.63139			−0.215377
$949$	−46.0133	+	46.0133i	−1.49365	+	1.49365i
$950$		−	19.9687i		−	0.647870i
$951$	−3.49283			−0.113263
$952$		0			0
$953$	−5.33601			−0.172850			−0.0864252	−	0.996258i	$-0.527544\pi$
$953$	−5.33601			−0.172850			−0.0864252	+	0.996258i	$0.527544\pi$
$954$			6.85452i			0.221923i
$955$	−4.95353	+	4.95353i	−0.160292	+	0.160292i
$956$	7.55876			0.244468
$957$	−4.82843	+	4.82843i	−0.156081	+	0.156081i
$958$	−6.73661	−	6.73661i	−0.217650	−	0.217650i
$959$	−26.4115	−	26.4115i	−0.852873	−	0.852873i
$960$		−	17.6717i		−	0.570350i
$961$			30.7985i			0.993501i
$962$	−2.66082	−	2.66082i	−0.0857882	−	0.0857882i
$963$	12.4398	+	12.4398i	0.400866	+	0.400866i
$964$	−12.8886	+	12.8886i	−0.415114	+	0.415114i
$965$	−10.5765			−0.340469
$966$	10.5133	−	10.5133i	0.338259	−	0.338259i
$967$			49.3477i			1.58692i	0.608625	+	0.793458i	$0.291721\pi$
$967$			49.3477i			1.58692i	−0.608625	+	0.793458i	$0.708279\pi$
$968$	0.769384			0.0247289
$969$		0			0
$970$	−2.39947			−0.0770424
$971$		−	15.7566i		−	0.505654i	−0.967512	−	0.252827i	$-0.918640\pi$
$971$		−	15.7566i		−	0.505654i	0.967512	−	0.252827i	$-0.0813603\pi$
$972$	0.832429	−	0.832429i	0.0267002	−	0.0267002i
$973$	−18.8304			−0.603676
$974$	−15.5509	+	15.5509i	−0.498284	+	0.498284i
$975$	−20.5221	−	20.5221i	−0.657232	−	0.657232i
$976$	0.718613	+	0.718613i	0.0230023	+	0.0230023i
$977$			37.9092i			1.21282i	0.795151	+	0.606411i	$0.207391\pi$
$977$			37.9092i			1.21282i	−0.795151	+	0.606411i	$0.792609\pi$
$978$		−	3.20548i		−	0.102500i
$979$	−33.8639	−	33.8639i	−1.08229	−	1.08229i
$980$	15.1260	+	15.1260i	0.483183	+	0.483183i
$981$	−10.0066	+	10.0066i	−0.319486	+	0.319486i
$982$	13.3575			0.426257
$983$	0.764937	−	0.764937i	0.0243977	−	0.0243977i	−0.694803	−	0.719200i	$-0.744508\pi$
$983$	0.764937	−	0.764937i	0.0243977	−	0.0243977i	0.719200	+	0.694803i	$0.244508\pi$
$984$			12.9491i			0.412801i
$985$	−57.5381			−1.83332
$986$		0			0
$987$	−8.07944			−0.257171
$988$			27.8449i			0.885863i
$989$	19.8780	−	19.8780i	0.632083	−	0.632083i
$990$	9.48951			0.301596
$991$	−6.81790	+	6.81790i	−0.216578	+	0.216578i	−0.807055	−	0.590477i	$-0.798940\pi$
$991$	−6.81790	+	6.81790i	−0.216578	+	0.216578i	0.590477	+	0.807055i	$0.298940\pi$
$992$	−1.75470	−	1.75470i	−0.0557116	−	0.0557116i
$993$	3.53806	+	3.53806i	0.112277	+	0.112277i
$994$			11.7755i			0.373496i
$995$			12.7144i			0.403074i
$996$	3.26540	+	3.26540i	0.103468	+	0.103468i
$997$	−4.84046	−	4.84046i	−0.153299	−	0.153299i	0.626291	−	0.779590i	$-0.284572\pi$
$997$	−4.84046	−	4.84046i	−0.153299	−	0.153299i	−0.779590	+	0.626291i	$0.784572\pi$
$998$	9.20944	−	9.20944i	0.291520	−	0.291520i
$999$	0.742912			0.0235047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.k.616.7		24
17.2	even	8		867.2.d.g.577.6		12
17.3	odd	16		867.2.h.m.733.7		48
17.4	even	4	inner	867.2.e.k.829.6		24
17.5	odd	16		867.2.h.m.712.5		48
17.6	odd	16		867.2.h.m.688.5		48
17.7	odd	16		867.2.h.m.757.8		48
17.8	even	8		867.2.a.p.1.4	yes	6
17.9	even	8		867.2.a.o.1.4	✓	6
17.10	odd	16		867.2.h.m.757.7		48
17.11	odd	16		867.2.h.m.688.6		48
17.12	odd	16		867.2.h.m.712.6		48
17.13	even	4	inner	867.2.e.k.829.5		24
17.14	odd	16		867.2.h.m.733.8		48
17.15	even	8		867.2.d.g.577.5		12
17.16	even	2	inner	867.2.e.k.616.8		24
51.8	odd	8		2601.2.a.bi.1.3		6
51.26	odd	8		2601.2.a.bh.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.4	✓	6	17.9	even	8
867.2.a.p.1.4	yes	6	17.8	even	8
867.2.d.g.577.5		12	17.15	even	8
867.2.d.g.577.6		12	17.2	even	8
867.2.e.k.616.7		24	1.1	even	1	trivial
867.2.e.k.616.8		24	17.16	even	2	inner
867.2.e.k.829.5		24	17.13	even	4	inner
867.2.e.k.829.6		24	17.4	even	4	inner
867.2.h.m.688.5		48	17.6	odd	16
867.2.h.m.688.6		48	17.11	odd	16
867.2.h.m.712.5		48	17.5	odd	16
867.2.h.m.712.6		48	17.12	odd	16
867.2.h.m.733.7		48	17.3	odd	16
867.2.h.m.733.8		48	17.14	odd	16
867.2.h.m.757.7		48	17.10	odd	16
867.2.h.m.757.8		48	17.7	odd	16
2601.2.a.bh.1.3		6	51.26	odd	8
2601.2.a.bi.1.3		6	51.8	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.907065i q^{2} +(-0.707107 + 0.707107i) q^{3} +1.17723 q^{4} +(2.25802 - 2.25802i) q^{5} +(-0.641392 - 0.641392i) q^{6} +(2.51896 + 2.51896i) q^{7} +2.88196i q^{8} -1.00000i q^{9} +(2.04818 + 2.04818i) q^{10} +(2.31657 + 2.31657i) q^{11} +(-0.832429 + 0.832429i) q^{12} -5.58411 q^{13} +(-2.28486 + 2.28486i) q^{14} +3.19333i q^{15} -0.259660 q^{16} +0.907065 q^{18} -4.23574i q^{19} +(2.65822 - 2.65822i) q^{20} -3.56234 q^{21} +(-2.10128 + 2.10128i) q^{22} +(3.25360 + 3.25360i) q^{23} +(-2.03785 - 2.03785i) q^{24} -5.19735i q^{25} -5.06515i q^{26} +(0.707107 + 0.707107i) q^{27} +(2.96540 + 2.96540i) q^{28} +(1.47382 - 1.47382i) q^{29} -2.89656 q^{30} +(-0.317397 + 0.317397i) q^{31} +5.52839i q^{32} -3.27613 q^{33} +11.3757 q^{35} -1.17723i q^{36} +(0.525318 - 0.525318i) q^{37} +3.84209 q^{38} +(3.94856 - 3.94856i) q^{39} +(6.50753 + 6.50753i) q^{40} +(-3.17713 - 3.17713i) q^{41} -3.23128i q^{42} -6.10953i q^{43} +(2.72715 + 2.72715i) q^{44} +(-2.25802 - 2.25802i) q^{45} +(-2.95123 + 2.95123i) q^{46} +2.26801 q^{47} +(0.183607 - 0.183607i) q^{48} +5.69028i q^{49} +4.71434 q^{50} -6.57379 q^{52} +7.55680i q^{53} +(-0.641392 + 0.641392i) q^{54} +10.4618 q^{55} +(-7.25952 + 7.25952i) q^{56} +(2.99512 + 2.99512i) q^{57} +(1.33685 + 1.33685i) q^{58} +2.83196i q^{59} +3.75929i q^{60} +(-2.76752 - 2.76752i) q^{61} +(-0.287900 - 0.287900i) q^{62} +(2.51896 - 2.51896i) q^{63} -5.53393 q^{64} +(-12.6091 + 12.6091i) q^{65} -2.97167i q^{66} -14.5019 q^{67} -4.60128 q^{69} +10.3185i q^{70} +(2.57685 - 2.57685i) q^{71} +2.88196 q^{72} +(8.24004 - 8.24004i) q^{73} +(0.476498 + 0.476498i) q^{74} +(3.67508 + 3.67508i) q^{75} -4.98645i q^{76} +11.6707i q^{77} +(3.58160 + 3.58160i) q^{78} +(3.98316 + 3.98316i) q^{79} +(-0.586319 + 0.586319i) q^{80} -1.00000 q^{81} +(2.88187 - 2.88187i) q^{82} -3.92274i q^{83} -4.19370 q^{84} +5.54175 q^{86} +2.08430i q^{87} +(-6.67627 + 6.67627i) q^{88} -14.6181 q^{89} +(2.04818 - 2.04818i) q^{90} +(-14.0661 - 14.0661i) q^{91} +(3.83024 + 3.83024i) q^{92} -0.448868i q^{93} +2.05724i q^{94} +(-9.56440 - 9.56440i) q^{95} +(-3.90916 - 3.90916i) q^{96} +(-0.585758 + 0.585758i) q^{97} -5.16145 q^{98} +(2.31657 - 2.31657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81}+ \cdots + 228 q^{98}+O(q^{100}) \) 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

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