LMFDB - Embedded newform 98.2.c.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,2,Mod(67,98)] 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("98.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$98 = 2 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	98.c (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.2.c.a.79.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{12} +4.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{24} +(2.50000 - 4.33013i) q^{25} +(2.00000 + 3.46410i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-4.00000 + 6.92820i) q^{39} -6.00000 q^{41} +8.00000 q^{43} +(-6.00000 - 10.3923i) q^{47} +2.00000 q^{48} +5.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-2.00000 - 3.46410i) q^{54} -4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(4.00000 + 6.92820i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(5.00000 + 8.66025i) q^{75} -2.00000 q^{76} -8.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(4.00000 + 6.92820i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(6.00000 - 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{96} +10.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} - 2 q^{3} - q^{4} - 4 q^{6} - 2 q^{8} - q^{9} - 2 q^{12} + 8 q^{13} - q^{16} + 6 q^{17} + q^{18} + 2 q^{19} + 2 q^{24} + 5 q^{25} + 4 q^{26} - 8 q^{27} - 12 q^{29} - 4 q^{31} + q^{32}+ \cdots + 20 q^{97}+O(q^{100})$ 2 * q + q^2 - 2 * q^3 - q^4 - 4 * q^6 - 2 * q^8 - q^9 - 2 * q^12 + 8 * q^13 - q^16 + 6 * q^17 + q^18 + 2 * q^19 + 2 * q^24 + 5 * q^25 + 4 * q^26 - 8 * q^27 - 12 * q^29 - 4 * q^31 + q^32 + 12 * q^34 + 2 * q^36 - 2 * q^37 - 2 * q^38 - 8 * q^39 - 12 * q^41 + 16 * q^43 - 12 * q^47 + 4 * q^48 + 10 * q^50 + 12 * q^51 - 4 * q^52 - 6 * q^53 - 4 * q^54 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 8 * q^61 - 8 * q^62 + 2 * q^64 + 4 * q^67 + 6 * q^68 + q^72 + 2 * q^73 + 2 * q^74 + 10 * q^75 - 4 * q^76 - 16 * q^78 - 8 * q^79 + 11 * q^81 - 6 * q^82 + 12 * q^83 + 8 * q^86 + 12 * q^87 - 6 * q^89 - 8 * q^93 + 12 * q^94 + 2 * q^96 + 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	−4.00000	+	6.92820i	−0.640513	+	1.10940i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	5.00000			0.707107
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	5.00000	+	8.66025i	0.577350	+	1.00000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	−8.00000			−0.905822
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$		0			0
$96$	1.00000	+	1.73205i	0.102062	+	0.176777i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−6.00000			−0.552345
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$	6.00000	−	10.3923i	0.541002	−	0.937043i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−8.00000	+	13.8564i	−0.704361	+	1.21999i
$130$		0			0
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	24.0000			2.02116
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	2.00000			0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$	−5.00000	+	8.66025i	−0.408248	+	0.707107i
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	−4.00000	−	6.92820i	−0.320256	−	0.554700i
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$	11.0000			0.864242
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	0.542583	−	0.840002i	$-0.317446\pi$
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	−0.998755	+	0.0498898i	$0.984113\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$		0			0
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$	−16.0000			−1.18275
$184$		0			0
$185$		0			0
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	4.00000	+	6.92820i	0.282138	+	0.488678i
$202$		0			0
$203$		0			0
$204$	−12.0000			−0.840168
$205$		0			0
$206$	2.00000	−	3.46410i	0.139347	−	0.241355i
$207$		0			0
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	4.00000			0.272166
$217$		0			0
$218$	−2.00000			−0.135457
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$	2.00000	+	3.46410i	0.134231	+	0.232495i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	−5.00000			−0.333333
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$	16.0000			1.03931
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−5.50000	+	9.52628i	−0.353553	+	0.612372i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	12.0000			0.765092
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$		0			0
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	−16.0000			−0.996116
$259$		0			0
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	−9.00000	+	15.5885i	−0.556022	+	0.963058i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.0000			0.734388
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	4.00000			0.239474
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	0.328291	+	0.944577i	$0.393527\pi$
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	−0.982173	+	0.187980i	$0.939806\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−10.0000	+	17.3205i	−0.586210	+	1.01535i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		0			0
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$	−10.0000			−0.577350
$301$		0			0
$302$	−8.00000			−0.460348
$303$		0			0
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$		0			0
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$	4.00000	−	6.92820i	0.226455	−	0.392232i
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	8.00000			0.450035
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$	6.00000	−	10.3923i	0.336463	−	0.582772i
$319$		0			0
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	12.0000			0.667698
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	10.0000	−	17.3205i	0.554700	−	0.960769i
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	−2.00000	−	3.46410i	−0.110600	−	0.191565i
$328$	6.00000			0.331295
$329$		0			0
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$		0			0
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$		0			0
$342$	2.00000			0.108148
$343$		0			0
$344$	−8.00000			−0.431331
$345$		0			0
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$	−16.0000			−0.854017
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	6.00000	−	10.3923i	0.318896	−	0.552345i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−10.0000	−	17.3205i	−0.525588	−	0.910346i
$363$	−22.0000			−1.15470
$364$		0			0
$365$		0			0
$366$	−8.00000	−	13.8564i	−0.418167	−	0.724286i
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$	8.00000			0.414781
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		0			0
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	16.0000	−	27.7128i	0.819705	−	1.41977i
$382$	12.0000	−	20.7846i	0.613973	−	1.06343i
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−36.0000			−1.81596
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$		0			0
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	−5.00000			−0.250000
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$	−4.00000	+	6.92820i	−0.199502	+	0.345547i
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−6.00000	−	10.3923i	−0.297044	−	0.514496i
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		0			0
$411$	−18.0000	−	31.1769i	−0.887875	−	1.53784i
$412$	4.00000			0.197066
$413$		0			0
$414$		0			0
$415$		0			0
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	14.0000	−	24.2487i	0.685583	−	1.18746i
$418$		0			0
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$		0			0
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$		0			0
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$		0			0
$438$	−2.00000	+	3.46410i	−0.0955637	+	0.165521i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$	24.0000			1.14156
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$		0			0
$446$	−4.00000	−	6.92820i	−0.189405	−	0.328060i
$447$	−36.0000			−1.70274
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	−2.50000	−	4.33013i	−0.117851	−	0.204124i
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−8.00000	−	13.8564i	−0.375873	−	0.651031i
$454$	18.0000			0.844782
$455$		0			0
$456$	4.00000			0.187317
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$	−12.0000	+	20.7846i	−0.560112	+	0.970143i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	0.788228	−	0.615383i	$-0.210999\pi$
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	−0.927052	+	0.374934i	$0.877665\pi$
$468$	4.00000			0.184900
$469$		0			0
$470$		0			0
$471$	−4.00000	−	6.92820i	−0.184310	−	0.319235i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$		0			0
$474$	8.00000	+	13.8564i	0.367452	+	0.636446i
$475$	10.0000			0.458831
$476$		0			0
$477$	6.00000			0.274721
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−11.0000			−0.500000
$485$		0			0
$486$	−5.00000	+	8.66025i	−0.226805	+	0.392837i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	−32.0000			−1.44709
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$	−4.00000	+	6.92820i	−0.179969	+	0.311715i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$	−12.0000			−0.537733
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$		0			0
$501$	−12.0000	+	20.7846i	−0.536120	+	0.928588i
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.00000	+	5.19615i	−0.133235	+	0.230769i
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	0.921023	+	0.389509i	$0.127355\pi$
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	−0.123187	+	0.992384i	$0.539311\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−4.00000	−	6.92820i	−0.176604	−	0.305888i
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$		0			0
$516$	−8.00000	−	13.8564i	−0.352180	−	0.609994i
$517$		0			0
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	0.887061	−	0.461653i	$-0.152744\pi$
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	−0.843334	+	0.537390i	$0.819410\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$		0			0
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	6.00000			0.260378
$532$		0			0
$533$	−24.0000			−1.03956
$534$	6.00000	+	10.3923i	0.259645	+	0.449719i
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	12.0000	+	20.7846i	0.517838	+	0.896922i
$538$	−12.0000			−0.517357
$539$		0			0
$540$		0			0
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	20.0000	−	34.6410i	0.858282	−	1.48659i
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$		0			0
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	10.0000			0.424859
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	−0.922557	−	0.385860i	$-0.873905\pi$
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	0.795443	+	0.606028i	$0.207238\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	32.0000			1.35346
$560$		0			0
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	15.0000	−	25.9808i	0.632175	−	1.09496i	−0.354932	−	0.934892i	$-0.615496\pi$
$563$	15.0000	−	25.9808i	0.632175	−	1.09496i	0.987106	−	0.160066i	$-0.0511708\pi$
$564$	−12.0000	+	20.7846i	−0.505291	+	0.875190i
$565$		0			0
$566$	−22.0000			−0.924729
$567$		0			0
$568$		0			0
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$		0			0
$573$	48.0000			2.00523
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	−14.0000	−	24.2487i	−0.581820	−	1.00774i
$580$		0			0
$581$		0			0
$582$	−20.0000			−0.829027
$583$		0			0
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$	20.0000	+	34.6410i	0.818546	+	1.41776i
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−5.00000	−	8.66025i	−0.204124	−	0.353553i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$		0			0
$606$		0			0
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	0.983262	+	0.182199i	$0.0583216\pi$
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	−0.333842	+	0.942629i	$0.608345\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$		0			0
$611$	−24.0000	−	41.5692i	−0.970936	−	1.68171i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	−0.477143	−	0.878826i	$-0.658328\pi$
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	0.999657	−	0.0261952i	$-0.00833914\pi$
$620$		0			0
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$	8.00000			0.320256
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$		0			0
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$		0			0
$636$	12.0000			0.475831
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	12.0000	+	20.7846i	0.473602	+	0.820303i
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$	−5.50000	+	9.52628i	−0.216060	+	0.374228i
$649$		0			0
$650$	20.0000			0.784465
$651$		0			0
$652$	−16.0000			−0.626608
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$		0			0
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	0.155235	+	0.987878i	$0.450387\pi$
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	−0.933144	+	0.359502i	$0.882947\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	24.0000	+	41.5692i	0.932083	+	1.61441i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−2.00000			−0.0774984
$667$		0			0
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	−10.0000	+	17.3205i	−0.384900	+	0.666667i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$	−12.0000			−0.460857
$679$		0			0
$680$		0			0
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$		0			0
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$		0			0
$686$		0			0
$687$	8.00000			0.305219
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−23.0000	−	39.8372i	−0.874961	−	1.51548i	−0.856804	−	0.515642i	$-0.827553\pi$
$691$	−23.0000	−	39.8372i	−0.874961	−	1.51548i	−0.0181572	−	0.999835i	$-0.505780\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	24.0000			0.911028
$695$		0			0
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$	−12.0000			−0.453882
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−8.00000	−	13.8564i	−0.301941	−	0.522976i
$703$	2.00000	−	3.46410i	0.0754314	−	0.130651i
$704$		0			0
$705$		0			0
$706$	18.0000			0.677439
$707$		0			0
$708$	12.0000			0.450988
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	0.868250	+	0.496126i	$0.165245\pi$
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	−0.00446726	+	0.999990i	$0.501422\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	−24.0000	+	41.5692i	−0.896296	+	1.55243i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	0.955947	−	0.293538i	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$		0			0
$721$		0			0
$722$	15.0000			0.558242
$723$	−10.0000	−	17.3205i	−0.371904	−	0.644157i
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$	−15.0000	+	25.9808i	−0.557086	+	0.964901i
$726$	−11.0000	−	19.0526i	−0.408248	−	0.707107i
$727$	−44.0000			−1.63187			−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000			−1.63187			−0.815935	+	0.578144i	$0.803777\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	8.00000	−	13.8564i	0.295689	−	0.512148i
$733$	−20.0000	−	34.6410i	−0.738717	−	1.27950i	−0.953073	−	0.302740i	$-0.902099\pi$
$733$	−20.0000	−	34.6410i	−0.738717	−	1.27950i	0.214356	−	0.976756i	$-0.431235\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	−16.0000			−0.587775
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$		0			0
$746$	7.00000	−	12.1244i	0.256288	−	0.443904i
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−6.00000	+	10.3923i	−0.218797	+	0.378968i
$753$	−18.0000	+	31.1769i	−0.655956	+	1.13615i
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$		0			0
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	32.0000			1.15924
$763$		0			0
$764$	24.0000			0.868290
$765$		0			0
$766$	−18.0000	+	31.1769i	−0.650366	+	1.12647i
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$	4.00000	−	6.92820i	0.143777	−	0.249029i
$775$	10.0000	+	17.3205i	0.359211	+	0.622171i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	−18.0000			−0.645331
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$		0			0
$786$	−18.0000	−	31.1769i	−0.642039	−	1.11204i
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	16.0000	+	27.7128i	0.568177	+	0.984111i
$794$	−10.0000	+	17.3205i	−0.354887	+	0.614682i
$795$		0			0
$796$	10.0000	+	17.3205i	0.354441	+	0.613909i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$	−72.0000			−2.54718
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	−8.00000			−0.282138
$805$		0			0
$806$	−16.0000			−0.563576
$807$	−12.0000	−	20.7846i	−0.422420	−	0.731653i
$808$		0			0
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$		0			0
$815$		0			0
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	14.0000			0.489499
$819$		0			0
$820$		0			0
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	28.0000	−	48.4974i	0.972480	−	1.68439i	0.284469	−	0.958685i	$-0.408183\pi$
$829$	28.0000	−	48.4974i	0.972480	−	1.68439i	0.688012	−	0.725700i	$-0.258484\pi$
$830$		0			0
$831$	10.0000	+	17.3205i	0.346896	+	0.600842i
$832$	4.00000			0.138675
$833$		0			0
$834$	28.0000			0.969561
$835$		0			0
$836$		0			0
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$	−3.00000	−	5.19615i	−0.103633	−	0.179498i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$		0			0
$846$	−12.0000			−0.412568
$847$		0			0
$848$	6.00000			0.206041
$849$	−22.0000	−	38.1051i	−0.755038	−	1.30776i
$850$	15.0000	−	25.9808i	0.514496	−	0.891133i
$851$		0			0
$852$		0			0
$853$	−44.0000			−1.50653			−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000			−1.50653			−0.753266	+	0.657716i	$0.771523\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$		0			0
$861$		0			0
$862$	−24.0000			−0.817443
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	0.994720	−	0.102624i	$-0.0327240\pi$
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	−0.586235	+	0.810141i	$0.699391\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	17.0000	+	29.4449i	0.577684	+	1.00058i
$867$	38.0000			1.29055
$868$		0			0
$869$		0			0
$870$		0			0
$871$	8.00000	−	13.8564i	0.271070	−	0.469506i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	−5.00000	−	8.66025i	−0.169224	−	0.293105i
$874$		0			0
$875$		0			0
$876$	−4.00000			−0.135147
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$	24.0000	−	41.5692i	0.809500	−	1.40209i
$880$		0			0
$881$	54.0000			1.81931			0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000			1.81931			0.909653	+	0.415369i	$0.136347\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$	−4.00000			−0.134231
$889$		0			0
$890$		0			0
$891$		0			0
$892$	4.00000	−	6.92820i	0.133930	−	0.231973i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$	−18.0000	−	31.1769i	−0.602010	−	1.04271i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	9.00000	+	15.5885i	0.300334	+	0.520194i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	2.50000	−	4.33013i	0.0833333	−	0.144338i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$	−6.00000			−0.199557
$905$		0			0
$906$	8.00000	−	13.8564i	0.265782	−	0.460348i
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$		0			0
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$		0			0
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	4.00000			0.132164
$917$		0			0
$918$	−24.0000			−0.792118
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.793742	−	0.608254i	$-0.791870\pi$
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.129893	−	0.991528i	$-0.541463\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$	−6.00000	−	10.3923i	−0.197599	−	0.342252i
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−24.0000	−	41.5692i	−0.785725	−	1.36092i
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$		0			0
$936$	2.00000	+	3.46410i	0.0653720	+	0.113228i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$		0			0
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$	4.00000	−	6.92820i	0.130327	−	0.225733i
$943$		0			0
$944$	6.00000			0.195283
$945$		0			0
$946$		0			0
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	0.602494	−	0.798123i	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$	−8.00000	+	13.8564i	−0.259828	+	0.450035i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	5.00000	+	8.66025i	0.162221	+	0.280976i
$951$	12.0000			0.389127
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$	3.00000	+	5.19615i	0.0971286	+	0.168232i
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−36.0000			−1.16311
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$		0			0
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$	−12.0000	+	20.7846i	−0.385496	+	0.667698i
$970$		0			0
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	16.0000			0.512673
$975$	20.0000	+	34.6410i	0.640513	+	1.10940i
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$	−16.0000	−	27.7128i	−0.511624	−	0.886158i
$979$		0			0
$980$		0			0
$981$	2.00000			0.0638551
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$	−6.00000	+	10.3923i	−0.191273	+	0.331295i
$985$		0			0
$986$	−36.0000			−1.14647
$987$		0			0
$988$	−8.00000			−0.254514
$989$		0			0
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	16.0000			0.507745
$994$		0			0
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	4.00000	−	6.92820i	0.126681	−	0.219418i	−0.795708	−	0.605681i	$-0.792901\pi$
$997$	4.00000	−	6.92820i	0.126681	−	0.219418i	0.922389	+	0.386263i	$0.126234\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.c.a.67.1		2
3.2	odd	2		882.2.g.d.361.1		2
4.3	odd	2		784.2.i.i.753.1		2
7.2	even	3	inner	98.2.c.a.79.1		2
7.3	odd	6		14.2.a.a.1.1	✓	1
7.4	even	3		98.2.a.a.1.1		1
7.5	odd	6		98.2.c.b.79.1		2
7.6	odd	2		98.2.c.b.67.1		2
21.2	odd	6		882.2.g.d.667.1		2
21.5	even	6		882.2.g.c.667.1		2
21.11	odd	6		882.2.a.i.1.1		1
21.17	even	6		126.2.a.b.1.1		1
21.20	even	2		882.2.g.c.361.1		2
28.3	even	6		112.2.a.c.1.1		1
28.11	odd	6		784.2.a.b.1.1		1
28.19	even	6		784.2.i.c.177.1		2
28.23	odd	6		784.2.i.i.177.1		2
28.27	even	2		784.2.i.c.753.1		2
35.3	even	12		350.2.c.d.99.2		2
35.4	even	6		2450.2.a.t.1.1		1
35.17	even	12		350.2.c.d.99.1		2
35.18	odd	12		2450.2.c.c.99.2		2
35.24	odd	6		350.2.a.f.1.1		1
35.32	odd	12		2450.2.c.c.99.1		2
56.3	even	6		448.2.a.a.1.1		1
56.11	odd	6		3136.2.a.z.1.1		1
56.45	odd	6		448.2.a.g.1.1		1
56.53	even	6		3136.2.a.e.1.1		1
63.31	odd	6		1134.2.f.l.379.1		2
63.38	even	6		1134.2.f.f.757.1		2
63.52	odd	6		1134.2.f.l.757.1		2
63.59	even	6		1134.2.f.f.379.1		2
77.10	even	6		1694.2.a.e.1.1		1
84.11	even	6		7056.2.a.bd.1.1		1
84.59	odd	6		1008.2.a.h.1.1		1
91.31	even	12		2366.2.d.b.337.2		2
91.38	odd	6		2366.2.a.j.1.1		1
91.73	even	12		2366.2.d.b.337.1		2
105.17	odd	12		3150.2.g.j.2899.2		2
105.38	odd	12		3150.2.g.j.2899.1		2
105.59	even	6		3150.2.a.i.1.1		1
112.3	even	12		1792.2.b.g.897.2		2
112.45	odd	12		1792.2.b.c.897.1		2
112.59	even	12		1792.2.b.g.897.1		2
112.101	odd	12		1792.2.b.c.897.2		2
119.101	odd	6		4046.2.a.f.1.1		1
133.94	even	6		5054.2.a.c.1.1		1
140.3	odd	12		2800.2.g.h.449.2		2
140.59	even	6		2800.2.a.g.1.1		1
140.87	odd	12		2800.2.g.h.449.1		2
161.45	even	6		7406.2.a.a.1.1		1
168.59	odd	6		4032.2.a.r.1.1		1
168.101	even	6		4032.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.2.a.a.1.1	✓	1	7.3	odd	6
98.2.a.a.1.1		1	7.4	even	3
98.2.c.a.67.1		2	1.1	even	1	trivial
98.2.c.a.79.1		2	7.2	even	3	inner
98.2.c.b.67.1		2	7.6	odd	2
98.2.c.b.79.1		2	7.5	odd	6
112.2.a.c.1.1		1	28.3	even	6
126.2.a.b.1.1		1	21.17	even	6
350.2.a.f.1.1		1	35.24	odd	6
350.2.c.d.99.1		2	35.17	even	12
350.2.c.d.99.2		2	35.3	even	12
448.2.a.a.1.1		1	56.3	even	6
448.2.a.g.1.1		1	56.45	odd	6
784.2.a.b.1.1		1	28.11	odd	6
784.2.i.c.177.1		2	28.19	even	6
784.2.i.c.753.1		2	28.27	even	2
784.2.i.i.177.1		2	28.23	odd	6
784.2.i.i.753.1		2	4.3	odd	2
882.2.a.i.1.1		1	21.11	odd	6
882.2.g.c.361.1		2	21.20	even	2
882.2.g.c.667.1		2	21.5	even	6
882.2.g.d.361.1		2	3.2	odd	2
882.2.g.d.667.1		2	21.2	odd	6
1008.2.a.h.1.1		1	84.59	odd	6
1134.2.f.f.379.1		2	63.59	even	6
1134.2.f.f.757.1		2	63.38	even	6
1134.2.f.l.379.1		2	63.31	odd	6
1134.2.f.l.757.1		2	63.52	odd	6
1694.2.a.e.1.1		1	77.10	even	6
1792.2.b.c.897.1		2	112.45	odd	12
1792.2.b.c.897.2		2	112.101	odd	12
1792.2.b.g.897.1		2	112.59	even	12
1792.2.b.g.897.2		2	112.3	even	12
2366.2.a.j.1.1		1	91.38	odd	6
2366.2.d.b.337.1		2	91.73	even	12
2366.2.d.b.337.2		2	91.31	even	12
2450.2.a.t.1.1		1	35.4	even	6
2450.2.c.c.99.1		2	35.32	odd	12
2450.2.c.c.99.2		2	35.18	odd	12
2800.2.a.g.1.1		1	140.59	even	6
2800.2.g.h.449.1		2	140.87	odd	12
2800.2.g.h.449.2		2	140.3	odd	12
3136.2.a.e.1.1		1	56.53	even	6
3136.2.a.z.1.1		1	56.11	odd	6
3150.2.a.i.1.1		1	105.59	even	6
3150.2.g.j.2899.1		2	105.38	odd	12
3150.2.g.j.2899.2		2	105.17	odd	12
4032.2.a.r.1.1		1	168.59	odd	6
4032.2.a.w.1.1		1	168.101	even	6
4046.2.a.f.1.1		1	119.101	odd	6
5054.2.a.c.1.1		1	133.94	even	6
7056.2.a.bd.1.1		1	84.11	even	6
7406.2.a.a.1.1		1	161.45	even	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	98.2.c.a.67.1

Level	$98$
Weight	$2$
Character	98.67
Analytic conductor	$0.783$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$