LMFDB - Embedded newform 63.3.m.c.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,3,Mod(10,63)] 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("63.10"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.71662566547$
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 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.10
Dual form			63.3.m.c.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +(-3.50000 + 6.06218i) q^{7} +7.00000 q^{8} +(4.50000 + 2.59808i) q^{10} +(-5.50000 + 9.52628i) q^{11} -6.92820i q^{13} -7.00000 q^{14} +(-2.50000 - 4.33013i) q^{16} +(-21.0000 - 12.1244i) q^{17} +(-3.00000 + 1.73205i) q^{19} -15.5885i q^{20} -11.0000 q^{22} +(14.0000 + 24.2487i) q^{23} +(1.00000 - 1.73205i) q^{25} +(6.00000 - 3.46410i) q^{26} +(10.5000 + 18.1865i) q^{28} -25.0000 q^{29} +(-28.5000 - 16.4545i) q^{31} +(16.5000 - 28.5788i) q^{32} -24.2487i q^{34} +36.3731i q^{35} +(29.0000 + 50.2295i) q^{37} +(-3.00000 - 1.73205i) q^{38} +(31.5000 - 18.1865i) q^{40} +3.46410i q^{41} +26.0000 q^{43} +(16.5000 + 28.5788i) q^{44} +(-14.0000 + 24.2487i) q^{46} +(66.0000 - 38.1051i) q^{47} +(-24.5000 - 42.4352i) q^{49} +2.00000 q^{50} +(-18.0000 - 10.3923i) q^{52} +(15.5000 - 26.8468i) q^{53} +57.1577i q^{55} +(-24.5000 + 42.4352i) q^{56} +(-12.5000 - 21.6506i) q^{58} +(7.50000 + 4.33013i) q^{59} +(12.0000 - 6.92820i) q^{61} -32.9090i q^{62} +13.0000 q^{64} +(-18.0000 - 31.1769i) q^{65} +(26.0000 - 45.0333i) q^{67} +(-63.0000 + 36.3731i) q^{68} +(-31.5000 + 18.1865i) q^{70} -64.0000 q^{71} +(6.00000 + 3.46410i) q^{73} +(-29.0000 + 50.2295i) q^{74} +10.3923i q^{76} +(-38.5000 - 66.6840i) q^{77} +(-8.50000 - 14.7224i) q^{79} +(-22.5000 - 12.9904i) q^{80} +(-3.00000 + 1.73205i) q^{82} +53.6936i q^{83} -126.000 q^{85} +(13.0000 + 22.5167i) q^{86} +(-38.5000 + 66.6840i) q^{88} +(69.0000 - 39.8372i) q^{89} +(42.0000 + 24.2487i) q^{91} +84.0000 q^{92} +(66.0000 + 38.1051i) q^{94} +(-9.00000 + 15.5885i) q^{95} -91.7987i q^{97} +(24.5000 - 42.4352i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{4} + 9 q^{5} - 7 q^{7} + 14 q^{8} + 9 q^{10} - 11 q^{11} - 14 q^{14} - 5 q^{16} - 42 q^{17} - 6 q^{19} - 22 q^{22} + 28 q^{23} + 2 q^{25} + 12 q^{26} + 21 q^{28} - 50 q^{29} - 57 q^{31}+ \cdots + 49 q^{98}+O(q^{100}) $ 2 * q + q^2 + 3 * q^4 + 9 * q^5 - 7 * q^7 + 14 * q^8 + 9 * q^10 - 11 * q^11 - 14 * q^14 - 5 * q^16 - 42 * q^17 - 6 * q^19 - 22 * q^22 + 28 * q^23 + 2 * q^25 + 12 * q^26 + 21 * q^28 - 50 * q^29 - 57 * q^31 + 33 * q^32 + 58 * q^37 - 6 * q^38 + 63 * q^40 + 52 * q^43 + 33 * q^44 - 28 * q^46 + 132 * q^47 - 49 * q^49 + 4 * q^50 - 36 * q^52 + 31 * q^53 - 49 * q^56 - 25 * q^58 + 15 * q^59 + 24 * q^61 + 26 * q^64 - 36 * q^65 + 52 * q^67 - 126 * q^68 - 63 * q^70 - 128 * q^71 + 12 * q^73 - 58 * q^74 - 77 * q^77 - 17 * q^79 - 45 * q^80 - 6 * q^82 - 252 * q^85 + 26 * q^86 - 77 * q^88 + 138 * q^89 + 84 * q^91 + 168 * q^92 + 132 * q^94 - 18 * q^95 + 49 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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	0.250000	+	0.433013i	0.963525	−	0.267617i	$-0.0862360\pi$
$2$	0.500000	+	0.866025i	0.250000	+	0.433013i	−0.713525	+	0.700629i	$0.752903\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	−	2.59808i	0.375000	−	0.649519i
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.0227998	−	0.999740i	$-0.492742\pi$
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.877200	+	0.480125i	$0.159409\pi$
$6$		0			0
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$8$	7.00000			0.875000
$9$		0			0
$10$	4.50000	+	2.59808i	0.450000	+	0.259808i
$11$	−5.50000	+	9.52628i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$11$	−5.50000	+	9.52628i	−0.500000	+	0.866025i	−1.00000			$\pi$
$12$		0			0
$13$		−	6.92820i		−	0.532939i	−0.963843	−	0.266469i	$-0.914143\pi$
$13$		−	6.92820i		−	0.532939i	0.963843	−	0.266469i	$-0.0858571\pi$
$14$	−7.00000			−0.500000
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$	−21.0000	−	12.1244i	−1.23529	−	0.713197i	−0.267165	−	0.963651i	$-0.586087\pi$
$17$	−21.0000	−	12.1244i	−1.23529	−	0.713197i	−0.968129	+	0.250453i	$0.919420\pi$
$18$		0			0
$19$	−3.00000	+	1.73205i	−0.157895	+	0.0911606i	−0.576865	−	0.816839i	$-0.695724\pi$
$19$	−3.00000	+	1.73205i	−0.157895	+	0.0911606i	0.418971	+	0.908000i	$0.362391\pi$
$20$		−	15.5885i		−	0.779423i
$21$		0			0
$22$	−11.0000			−0.500000
$23$	14.0000	+	24.2487i	0.608696	+	1.05429i	0.991456	+	0.130444i	$0.0416403\pi$
$23$	14.0000	+	24.2487i	0.608696	+	1.05429i	−0.382760	+	0.923848i	$0.625026\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.0400000	−	0.0692820i
$26$	6.00000	−	3.46410i	0.230769	−	0.133235i
$27$		0			0
$28$	10.5000	+	18.1865i	0.375000	+	0.649519i
$29$	−25.0000			−0.862069			−0.431034	−	0.902335i	$-0.641851\pi$
$29$	−25.0000			−0.862069			−0.431034	+	0.902335i	$0.641851\pi$
$30$		0			0
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.0359257	−	0.999354i	$-0.511438\pi$
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.883429	+	0.468565i	$0.844771\pi$
$32$	16.5000	−	28.5788i	0.515625	−	0.893089i
$33$		0			0
$34$		−	24.2487i		−	0.713197i
$35$			36.3731i			1.03923i
$36$		0			0
$37$	29.0000	+	50.2295i	0.783784	+	1.35755i	0.929723	+	0.368260i	$0.120046\pi$
$37$	29.0000	+	50.2295i	0.783784	+	1.35755i	−0.145939	+	0.989294i	$0.546620\pi$
$38$	−3.00000	−	1.73205i	−0.0789474	−	0.0455803i
$39$		0			0
$40$	31.5000	−	18.1865i	0.787500	−	0.454663i
$41$			3.46410i			0.0844903i	0.999107	+	0.0422451i	$0.0134510\pi$
$41$			3.46410i			0.0844903i	−0.999107	+	0.0422451i	$0.986549\pi$
$42$		0			0
$43$	26.0000			0.604651			0.302326	−	0.953205i	$-0.402237\pi$
$43$	26.0000			0.604651			0.302326	+	0.953205i	$0.402237\pi$
$44$	16.5000	+	28.5788i	0.375000	+	0.649519i
$45$		0			0
$46$	−14.0000	+	24.2487i	−0.304348	+	0.527146i
$47$	66.0000	−	38.1051i	1.40426	−	0.810747i	0.409429	−	0.912342i	$-0.365728\pi$
$47$	66.0000	−	38.1051i	1.40426	−	0.810747i	0.994826	+	0.101595i	$0.0323945\pi$
$48$		0			0
$49$	−24.5000	−	42.4352i	−0.500000	−	0.866025i
$50$	2.00000			0.0400000
$51$		0			0
$52$	−18.0000	−	10.3923i	−0.346154	−	0.199852i
$53$	15.5000	−	26.8468i	0.292453	−	0.506543i	−0.681936	−	0.731412i	$-0.738862\pi$
$53$	15.5000	−	26.8468i	0.292453	−	0.506543i	0.974389	+	0.224868i	$0.0721952\pi$
$54$		0			0
$55$			57.1577i			1.03923i
$56$	−24.5000	+	42.4352i	−0.437500	+	0.757772i
$57$		0			0
$58$	−12.5000	−	21.6506i	−0.215517	−	0.373287i
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	0.562211	−	0.826994i	$-0.309951\pi$
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	−0.435092	+	0.900386i	$0.643284\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	0.196721	−	0.113577i	−0.398404	−	0.917210i	$-0.630436\pi$
$61$	12.0000	−	6.92820i	0.196721	−	0.113577i	0.595125	+	0.803633i	$0.297102\pi$
$62$		−	32.9090i		−	0.530790i
$63$		0			0
$64$	13.0000			0.203125
$65$	−18.0000	−	31.1769i	−0.276923	−	0.479645i
$66$		0			0
$67$	26.0000	−	45.0333i	0.388060	−	0.672139i	−0.604129	−	0.796887i	$-0.706479\pi$
$67$	26.0000	−	45.0333i	0.388060	−	0.672139i	0.992189	+	0.124748i	$0.0398121\pi$
$68$	−63.0000	+	36.3731i	−0.926471	+	0.534898i
$69$		0			0
$70$	−31.5000	+	18.1865i	−0.450000	+	0.259808i
$71$	−64.0000			−0.901408			−0.450704	−	0.892673i	$-0.648827\pi$
$71$	−64.0000			−0.901408			−0.450704	+	0.892673i	$0.648827\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.0821918	+	0.0474534i	0.540533	−	0.841323i	$-0.318223\pi$
$73$	6.00000	+	3.46410i	0.0821918	+	0.0474534i	−0.458341	+	0.888777i	$0.651556\pi$
$74$	−29.0000	+	50.2295i	−0.391892	+	0.678777i
$75$		0			0
$76$			10.3923i			0.136741i
$77$	−38.5000	−	66.6840i	−0.500000	−	0.866025i
$78$		0			0
$79$	−8.50000	−	14.7224i	−0.107595	−	0.186360i	0.807200	−	0.590277i	$-0.200982\pi$
$79$	−8.50000	−	14.7224i	−0.107595	−	0.186360i	−0.914795	+	0.403917i	$0.867648\pi$
$80$	−22.5000	−	12.9904i	−0.281250	−	0.162380i
$81$		0			0
$82$	−3.00000	+	1.73205i	−0.0365854	+	0.0211226i
$83$			53.6936i			0.646911i	0.946243	+	0.323455i	$0.104845\pi$
$83$			53.6936i			0.646911i	−0.946243	+	0.323455i	$0.895155\pi$
$84$		0			0
$85$	−126.000			−1.48235
$86$	13.0000	+	22.5167i	0.151163	+	0.261822i
$87$		0			0
$88$	−38.5000	+	66.6840i	−0.437500	+	0.757772i
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	−0.0594743	−	0.998230i	$-0.518942\pi$
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	0.834755	+	0.550621i	$0.185609\pi$
$90$		0			0
$91$	42.0000	+	24.2487i	0.461538	+	0.266469i
$92$	84.0000			0.913043
$93$		0			0
$94$	66.0000	+	38.1051i	0.702128	+	0.405374i
$95$	−9.00000	+	15.5885i	−0.0947368	+	0.164089i
$96$		0			0
$97$		−	91.7987i		−	0.946378i	−0.880961	−	0.473189i	$-0.843103\pi$
$97$		−	91.7987i		−	0.946378i	0.880961	−	0.473189i	$-0.156897\pi$
$98$	24.5000	−	42.4352i	0.250000	−	0.433013i
$99$		0			0
$100$	−3.00000	−	5.19615i	−0.0300000	−	0.0519615i
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	0.586455	−	0.809982i	$-0.300523\pi$
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	−0.408237	+	0.912876i	$0.633856\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		−	48.4974i		−	0.466321i
$105$		0			0
$106$	31.0000			0.292453
$107$	15.5000	+	26.8468i	0.144860	+	0.250905i	0.929321	−	0.369274i	$-0.120394\pi$
$107$	15.5000	+	26.8468i	0.144860	+	0.250905i	−0.784461	+	0.620178i	$0.787060\pi$
$108$		0			0
$109$	68.0000	−	117.779i	0.623853	−	1.08055i	−0.364908	−	0.931043i	$-0.618900\pi$
$109$	68.0000	−	117.779i	0.623853	−	1.08055i	0.988761	−	0.149502i	$-0.0477670\pi$
$110$	−49.5000	+	28.5788i	−0.450000	+	0.259808i
$111$		0			0
$112$	35.0000			0.312500
$113$	74.0000			0.654867			0.327434	−	0.944874i	$-0.393816\pi$
$113$	74.0000			0.654867			0.327434	+	0.944874i	$0.393816\pi$
$114$		0			0
$115$	126.000	+	72.7461i	1.09565	+	0.632575i
$116$	−37.5000	+	64.9519i	−0.323276	+	0.559930i
$117$		0			0
$118$			8.66025i			0.0733920i
$119$	147.000	−	84.8705i	1.23529	−	0.713197i
$120$		0			0
$121$		0			0
$122$	12.0000	+	6.92820i	0.0983607	+	0.0567886i
$123$		0			0
$124$	−85.5000	+	49.3634i	−0.689516	+	0.398092i
$125$			119.512i			0.956092i
$126$		0			0
$127$	−1.00000			−0.00787402			−0.00393701	−	0.999992i	$-0.501253\pi$
$127$	−1.00000			−0.00787402			−0.00393701	+	0.999992i	$0.501253\pi$
$128$	−59.5000	−	103.057i	−0.464844	−	0.805133i
$129$		0			0
$130$	18.0000	−	31.1769i	0.138462	−	0.239822i
$131$	−157.500	+	90.9327i	−1.20229	+	0.694142i	−0.961064	−	0.276326i	$-0.910883\pi$
$131$	−157.500	+	90.9327i	−1.20229	+	0.694142i	−0.241226	+	0.970469i	$0.577550\pi$
$132$		0			0
$133$		−	24.2487i		−	0.182321i
$134$	52.0000			0.388060
$135$		0			0
$136$	−147.000	−	84.8705i	−1.08088	−	0.624048i
$137$	44.0000	−	76.2102i	0.321168	−	0.556279i	−0.659561	−	0.751651i	$-0.729258\pi$
$137$	44.0000	−	76.2102i	0.321168	−	0.556279i	0.980729	+	0.195372i	$0.0625913\pi$
$138$		0			0
$139$			190.526i			1.37069i	0.728220	+	0.685344i	$0.240348\pi$
$139$			190.526i			1.37069i	−0.728220	+	0.685344i	$0.759652\pi$
$140$	94.5000	+	54.5596i	0.675000	+	0.389711i
$141$		0			0
$142$	−32.0000	−	55.4256i	−0.225352	−	0.390321i
$143$	66.0000	+	38.1051i	0.461538	+	0.266469i
$144$		0			0
$145$	−112.500	+	64.9519i	−0.775862	+	0.447944i
$146$			6.92820i			0.0474534i
$147$		0			0
$148$	174.000			1.17568
$149$	−115.000	−	199.186i	−0.771812	−	1.33682i	−0.936569	−	0.350484i	$-0.886017\pi$
$149$	−115.000	−	199.186i	−0.771812	−	1.33682i	0.164757	−	0.986334i	$-0.447316\pi$
$150$		0			0
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	0.195364	+	0.980731i	$0.437411\pi$
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	−0.947020	+	0.321175i	$0.895922\pi$
$152$	−21.0000	+	12.1244i	−0.138158	+	0.0797655i
$153$		0			0
$154$	38.5000	−	66.6840i	0.250000	−	0.433013i
$155$	−171.000			−1.10323
$156$		0			0
$157$	−42.0000	−	24.2487i	−0.267516	−	0.154450i	0.360242	−	0.932859i	$-0.382694\pi$
$157$	−42.0000	−	24.2487i	−0.267516	−	0.154450i	−0.627758	+	0.778408i	$0.716027\pi$
$158$	8.50000	−	14.7224i	0.0537975	−	0.0931799i
$159$		0			0
$160$		−	171.473i		−	1.07171i
$161$	−196.000			−1.21739
$162$		0			0
$163$	−106.000	−	183.597i	−0.650307	−	1.12636i	−0.983048	−	0.183346i	$-0.941307\pi$
$163$	−106.000	−	183.597i	−0.650307	−	1.12636i	0.332742	−	0.943018i	$-0.392026\pi$
$164$	9.00000	+	5.19615i	0.0548780	+	0.0316839i
$165$		0			0
$166$	−46.5000	+	26.8468i	−0.280120	+	0.161728i
$167$			96.9948i			0.580807i	0.956904	+	0.290404i	$0.0937896\pi$
$167$			96.9948i			0.580807i	−0.956904	+	0.290404i	$0.906210\pi$
$168$		0			0
$169$	121.000			0.715976
$170$	−63.0000	−	109.119i	−0.370588	−	0.641878i
$171$		0			0
$172$	39.0000	−	67.5500i	0.226744	−	0.392732i
$173$	−186.000	+	107.387i	−1.07514	+	0.620735i	−0.929582	−	0.368614i	$-0.879832\pi$
$173$	−186.000	+	107.387i	−1.07514	+	0.620735i	−0.145562	+	0.989349i	$0.546499\pi$
$174$		0			0
$175$	7.00000	+	12.1244i	0.0400000	+	0.0692820i
$176$	55.0000			0.312500
$177$		0			0
$178$	69.0000	+	39.8372i	0.387640	+	0.223804i
$179$	23.0000	−	39.8372i	0.128492	−	0.222554i	−0.794601	−	0.607132i	$-0.792320\pi$
$179$	23.0000	−	39.8372i	0.128492	−	0.222554i	0.923092	+	0.384578i	$0.125653\pi$
$180$		0			0
$181$			31.1769i			0.172248i	0.996284	+	0.0861241i	$0.0274481\pi$
$181$			31.1769i			0.172248i	−0.996284	+	0.0861241i	$0.972552\pi$
$182$			48.4974i			0.266469i
$183$		0			0
$184$	98.0000	+	169.741i	0.532609	+	0.922505i
$185$	261.000	+	150.688i	1.41081	+	0.814532i
$186$		0			0
$187$	231.000	−	133.368i	1.23529	−	0.713197i
$188$		−	228.631i		−	1.21612i
$189$		0			0
$190$	−18.0000			−0.0947368
$191$	104.000	+	180.133i	0.544503	+	0.943106i	0.998638	+	0.0521735i	$0.0166149\pi$
$191$	104.000	+	180.133i	0.544503	+	0.943106i	−0.454135	+	0.890933i	$0.650052\pi$
$192$		0			0
$193$	−119.500	+	206.980i	−0.619171	+	1.07244i	0.370466	+	0.928846i	$0.379198\pi$
$193$	−119.500	+	206.980i	−0.619171	+	1.07244i	−0.989637	+	0.143590i	$0.954135\pi$
$194$	79.5000	−	45.8993i	0.409794	−	0.236595i
$195$		0			0
$196$	−147.000			−0.750000
$197$	26.0000			0.131980			0.0659898	−	0.997820i	$-0.478980\pi$
$197$	26.0000			0.131980			0.0659898	+	0.997820i	$0.478980\pi$
$198$		0			0
$199$	−210.000	−	121.244i	−1.05528	−	0.609264i	−0.131155	−	0.991362i	$-0.541868\pi$
$199$	−210.000	−	121.244i	−1.05528	−	0.609264i	−0.924122	+	0.382098i	$0.875202\pi$
$200$	7.00000	−	12.1244i	0.0350000	−	0.0606218i
$201$		0			0
$202$			20.7846i			0.102894i
$203$	87.5000	−	151.554i	0.431034	−	0.746574i
$204$		0			0
$205$	9.00000	+	15.5885i	0.0439024	+	0.0760413i
$206$		0			0
$207$		0			0
$208$	−30.0000	+	17.3205i	−0.144231	+	0.0832717i
$209$		−	38.1051i		−	0.182321i
$210$		0			0
$211$	−52.0000			−0.246445			−0.123223	−	0.992379i	$-0.539323\pi$
$211$	−52.0000			−0.246445			−0.123223	+	0.992379i	$0.539323\pi$
$212$	−46.5000	−	80.5404i	−0.219340	−	0.379907i
$213$		0			0
$214$	−15.5000	+	26.8468i	−0.0724299	+	0.125452i
$215$	117.000	−	67.5500i	0.544186	−	0.314186i
$216$		0			0
$217$	199.500	−	115.181i	0.919355	−	0.530790i
$218$	136.000			0.623853
$219$		0			0
$220$	148.500	+	85.7365i	0.675000	+	0.389711i
$221$	−84.0000	+	145.492i	−0.380090	+	0.658336i
$222$		0			0
$223$			22.5167i			0.100972i	0.998725	+	0.0504858i	$0.0160770\pi$
$223$			22.5167i			0.100972i	−0.998725	+	0.0504858i	$0.983923\pi$
$224$	115.500	+	200.052i	0.515625	+	0.893089i
$225$		0			0
$226$	37.0000	+	64.0859i	0.163717	+	0.283566i
$227$	−58.5000	−	33.7750i	−0.257709	−	0.148789i	0.365580	−	0.930780i	$-0.380871\pi$
$227$	−58.5000	−	33.7750i	−0.257709	−	0.148789i	−0.623289	+	0.781991i	$0.714204\pi$
$228$		0			0
$229$	−27.0000	+	15.5885i	−0.117904	+	0.0680719i	−0.557792	−	0.829981i	$-0.688351\pi$
$229$	−27.0000	+	15.5885i	−0.117904	+	0.0680719i	0.439888	+	0.898053i	$0.355018\pi$
$230$			145.492i			0.632575i
$231$		0			0
$232$	−175.000			−0.754310
$233$	131.000	+	226.899i	0.562232	+	0.973814i	0.997301	+	0.0734171i	$0.0233904\pi$
$233$	131.000	+	226.899i	0.562232	+	0.973814i	−0.435070	+	0.900397i	$0.643276\pi$
$234$		0			0
$235$	198.000	−	342.946i	0.842553	−	1.45934i
$236$	22.5000	−	12.9904i	0.0953390	−	0.0550440i
$237$		0			0
$238$	147.000	+	84.8705i	0.617647	+	0.356599i
$239$	−160.000			−0.669456			−0.334728	−	0.942315i	$-0.608644\pi$
$239$	−160.000			−0.669456			−0.334728	+	0.942315i	$0.608644\pi$
$240$		0			0
$241$	409.500	+	236.425i	1.69917	+	0.981016i	0.946548	+	0.322564i	$0.104545\pi$
$241$	409.500	+	236.425i	1.69917	+	0.981016i	0.752622	+	0.658452i	$0.228789\pi$
$242$		0			0
$243$		0			0
$244$		−	41.5692i		−	0.170366i
$245$	−220.500	−	127.306i	−0.900000	−	0.519615i
$246$		0			0
$247$	12.0000	+	20.7846i	0.0485830	+	0.0841482i
$248$	−199.500	−	115.181i	−0.804435	−	0.464441i
$249$		0			0
$250$	−103.500	+	59.7558i	−0.414000	+	0.239023i
$251$		−	67.5500i		−	0.269123i	−0.990905	−	0.134562i	$-0.957037\pi$
$251$		−	67.5500i		−	0.269123i	0.990905	−	0.134562i	$-0.0429626\pi$
$252$		0			0
$253$	−308.000			−1.21739
$254$	−0.500000	−	0.866025i	−0.00196850	−	0.00340955i
$255$		0			0
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	351.000	−	202.650i	1.36576	−	0.788521i	0.375376	−	0.926873i	$-0.377514\pi$
$257$	351.000	−	202.650i	1.36576	−	0.788521i	0.990383	+	0.138352i	$0.0441804\pi$
$258$		0			0
$259$	−406.000			−1.56757
$260$	−108.000			−0.415385
$261$		0			0
$262$	−157.500	−	90.9327i	−0.601145	−	0.347071i
$263$	53.0000	−	91.7987i	0.201521	−	0.349044i	−0.747498	−	0.664264i	$-0.768745\pi$
$263$	53.0000	−	91.7987i	0.201521	−	0.349044i	0.949019	+	0.315220i	$0.102078\pi$
$264$		0			0
$265$		−	161.081i		−	0.607852i
$266$	21.0000	−	12.1244i	0.0789474	−	0.0455803i
$267$		0			0
$268$	−78.0000	−	135.100i	−0.291045	−	0.504104i
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.405275	−	0.914195i	$-0.632824\pi$
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.994353	+	0.106119i	$0.966158\pi$
$270$		0			0
$271$	109.500	−	63.2199i	0.404059	−	0.233284i	−0.284175	−	0.958772i	$-0.591720\pi$
$271$	109.500	−	63.2199i	0.404059	−	0.233284i	0.688234	+	0.725489i	$0.258386\pi$
$272$			121.244i			0.445748i
$273$		0			0
$274$	88.0000			0.321168
$275$	11.0000	+	19.0526i	0.0400000	+	0.0692820i
$276$		0			0
$277$	−118.000	+	204.382i	−0.425993	+	0.737841i	−0.996513	−	0.0834427i	$-0.973408\pi$
$277$	−118.000	+	204.382i	−0.425993	+	0.737841i	0.570520	+	0.821284i	$0.306742\pi$
$278$	−165.000	+	95.2628i	−0.593525	+	0.342672i
$279$		0			0
$280$			254.611i			0.909327i
$281$	116.000			0.412811			0.206406	−	0.978466i	$-0.433823\pi$
$281$	116.000			0.412811			0.206406	+	0.978466i	$0.433823\pi$
$282$		0			0
$283$	−321.000	−	185.329i	−1.13428	−	0.654874i	−0.189269	−	0.981925i	$-0.560612\pi$
$283$	−321.000	−	185.329i	−1.13428	−	0.654874i	−0.945007	+	0.327051i	$0.893945\pi$
$284$	−96.0000	+	166.277i	−0.338028	+	0.585482i
$285$		0			0
$286$			76.2102i			0.266469i
$287$	−21.0000	−	12.1244i	−0.0731707	−	0.0422451i
$288$		0			0
$289$	149.500	+	258.942i	0.517301	+	0.895992i
$290$	−112.500	−	64.9519i	−0.387931	−	0.223972i
$291$		0			0
$292$	18.0000	−	10.3923i	0.0616438	−	0.0355901i
$293$			19.0526i			0.0650258i	0.999471	+	0.0325129i	$0.0103510\pi$
$293$			19.0526i			0.0650258i	−0.999471	+	0.0325129i	$0.989649\pi$
$294$		0			0
$295$	45.0000			0.152542
$296$	203.000	+	351.606i	0.685811	+	1.18786i
$297$		0			0
$298$	115.000	−	199.186i	0.385906	−	0.668409i
$299$	168.000	−	96.9948i	0.561873	−	0.324397i
$300$		0			0
$301$	−91.0000	+	157.617i	−0.302326	+	0.523643i
$302$	−227.000			−0.751656
$303$		0			0
$304$	15.0000	+	8.66025i	0.0493421	+	0.0284877i
$305$	36.0000	−	62.3538i	0.118033	−	0.204439i
$306$		0			0
$307$			457.261i			1.48945i	0.667371	+	0.744725i	$0.267420\pi$
$307$			457.261i			1.48945i	−0.667371	+	0.744725i	$0.732580\pi$
$308$	−231.000			−0.750000
$309$		0			0
$310$	−85.5000	−	148.090i	−0.275806	−	0.477711i
$311$	−285.000	−	164.545i	−0.916399	−	0.529083i	−0.0339143	−	0.999425i	$-0.510797\pi$
$311$	−285.000	−	164.545i	−0.916399	−	0.529083i	−0.882484	+	0.470342i	$0.844131\pi$
$312$		0			0
$313$	475.500	−	274.530i	1.51917	−	0.877093i	0.519424	−	0.854517i	$-0.326146\pi$
$313$	475.500	−	274.530i	1.51917	−	0.877093i	0.999745	−	0.0225763i	$-0.00718687\pi$
$314$		−	48.4974i		−	0.154450i
$315$		0			0
$316$	−51.0000			−0.161392
$317$	93.5000	+	161.947i	0.294953	+	0.510873i	0.974974	−	0.222319i	$-0.0713628\pi$
$317$	93.5000	+	161.947i	0.294953	+	0.510873i	−0.680021	+	0.733192i	$0.738029\pi$
$318$		0			0
$319$	137.500	−	238.157i	0.431034	−	0.746574i
$320$	58.5000	−	33.7750i	0.182812	−	0.105547i
$321$		0			0
$322$	−98.0000	−	169.741i	−0.304348	−	0.527146i
$323$	84.0000			0.260062
$324$		0			0
$325$	−12.0000	−	6.92820i	−0.0369231	−	0.0213175i
$326$	106.000	−	183.597i	0.325153	−	0.563182i
$327$		0			0
$328$			24.2487i			0.0739290i
$329$			533.472i			1.62149i
$330$		0			0
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	0.877857	−	0.478923i	$-0.158973\pi$
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	−0.853688	+	0.520785i	$0.825639\pi$
$332$	139.500	+	80.5404i	0.420181	+	0.242591i
$333$		0			0
$334$	−84.0000	+	48.4974i	−0.251497	+	0.145202i
$335$		−	270.200i		−	0.806567i
$336$		0			0
$337$	83.0000			0.246291			0.123145	−	0.992389i	$-0.460702\pi$
$337$	83.0000			0.246291			0.123145	+	0.992389i	$0.460702\pi$
$338$	60.5000	+	104.789i	0.178994	+	0.310027i
$339$		0			0
$340$	−189.000	+	327.358i	−0.555882	+	0.962816i
$341$	313.500	−	180.999i	0.919355	−	0.530790i
$342$		0			0
$343$	343.000			1.00000
$344$	182.000			0.529070
$345$		0			0
$346$	−186.000	−	107.387i	−0.537572	−	0.310367i
$347$	179.000	−	310.037i	0.515850	−	0.893479i	−0.483981	−	0.875079i	$-0.660809\pi$
$347$	179.000	−	310.037i	0.515850	−	0.893479i	0.999831	−	0.0183999i	$-0.00585720\pi$
$348$		0			0
$349$		−	678.964i		−	1.94546i	−0.231950	−	0.972728i	$-0.574511\pi$
$349$		−	678.964i		−	1.94546i	0.231950	−	0.972728i	$-0.425489\pi$
$350$	−7.00000	+	12.1244i	−0.0200000	+	0.0346410i
$351$		0			0
$352$	181.500	+	314.367i	0.515625	+	0.893089i
$353$	558.000	+	322.161i	1.58074	+	0.912639i	0.994752	+	0.102317i	$0.0326255\pi$
$353$	558.000	+	322.161i	1.58074	+	0.912639i	0.585985	+	0.810322i	$0.300708\pi$
$354$		0			0
$355$	−288.000	+	166.277i	−0.811268	+	0.468386i
$356$		−	239.023i		−	0.671413i
$357$		0			0
$358$	46.0000			0.128492
$359$	−142.000	−	245.951i	−0.395543	−	0.685101i	0.597627	−	0.801774i	$-0.296110\pi$
$359$	−142.000	−	245.951i	−0.395543	−	0.685101i	−0.993170	+	0.116673i	$0.962777\pi$
$360$		0			0
$361$	−174.500	+	302.243i	−0.483380	+	0.837238i
$362$	−27.0000	+	15.5885i	−0.0745856	+	0.0430620i
$363$		0			0
$364$	126.000	−	72.7461i	0.346154	−	0.199852i
$365$	36.0000			0.0986301
$366$		0			0
$367$	238.500	+	137.698i	0.649864	+	0.375199i	0.788404	−	0.615158i	$-0.210908\pi$
$367$	238.500	+	137.698i	0.649864	+	0.375199i	−0.138540	+	0.990357i	$0.544241\pi$
$368$	70.0000	−	121.244i	0.190217	−	0.329466i
$369$		0			0
$370$			301.377i			0.814532i
$371$	108.500	+	187.928i	0.292453	+	0.506543i
$372$		0			0
$373$	−25.0000	−	43.3013i	−0.0670241	−	0.116089i	0.830566	−	0.556920i	$-0.188017\pi$
$373$	−25.0000	−	43.3013i	−0.0670241	−	0.116089i	−0.897590	+	0.440831i	$0.854684\pi$
$374$	231.000	+	133.368i	0.617647	+	0.356599i
$375$		0			0
$376$	462.000	−	266.736i	1.22872	−	0.709404i
$377$			173.205i			0.459430i
$378$		0			0
$379$	458.000			1.20844			0.604222	−	0.796816i	$-0.293484\pi$
$379$	458.000			1.20844			0.604222	+	0.796816i	$0.293484\pi$
$380$	27.0000	+	46.7654i	0.0710526	+	0.123067i
$381$		0			0
$382$	−104.000	+	180.133i	−0.272251	+	0.471553i
$383$	−351.000	+	202.650i	−0.916449	+	0.529112i	−0.882501	−	0.470311i	$-0.844142\pi$
$383$	−351.000	+	202.650i	−0.916449	+	0.529112i	−0.0339486	+	0.999424i	$0.510808\pi$
$384$		0			0
$385$	−346.500	−	200.052i	−0.900000	−	0.519615i
$386$	−239.000			−0.619171
$387$		0			0
$388$	−238.500	−	137.698i	−0.614691	−	0.354892i
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.0660793	+	0.997814i	$0.521049\pi$
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.831093	+	0.556134i	$0.812284\pi$
$390$		0			0
$391$		−	678.964i		−	1.73648i
$392$	−171.500	−	297.047i	−0.437500	−	0.757772i
$393$		0			0
$394$	13.0000	+	22.5167i	0.0329949	+	0.0571489i
$395$	−76.5000	−	44.1673i	−0.193671	−	0.111816i
$396$		0			0
$397$	−498.000	+	287.520i	−1.25441	+	0.724233i	−0.971982	−	0.235056i	$-0.924473\pi$
$397$	−498.000	+	287.520i	−1.25441	+	0.724233i	−0.282426	+	0.959289i	$0.591139\pi$
$398$		−	242.487i		−	0.609264i
$399$		0			0
$400$	−10.0000			−0.0250000
$401$	−142.000	−	245.951i	−0.354115	−	0.613345i	0.632851	−	0.774273i	$-0.281884\pi$
$401$	−142.000	−	245.951i	−0.354115	−	0.613345i	−0.986966	+	0.160929i	$0.948551\pi$
$402$		0			0
$403$	−114.000	+	197.454i	−0.282878	+	0.489960i
$404$	54.0000	−	31.1769i	0.133663	−	0.0771706i
$405$		0			0
$406$	175.000			0.431034
$407$	−638.000			−1.56757
$408$		0			0
$409$	−181.500	−	104.789i	−0.443765	−	0.256208i	0.261428	−	0.965223i	$-0.415807\pi$
$409$	−181.500	−	104.789i	−0.443765	−	0.256208i	−0.705193	+	0.709015i	$0.749140\pi$
$410$	−9.00000	+	15.5885i	−0.0219512	+	0.0380206i
$411$		0			0
$412$		0			0
$413$	−52.5000	+	30.3109i	−0.127119	+	0.0733920i
$414$		0			0
$415$	139.500	+	241.621i	0.336145	+	0.582219i
$416$	−198.000	−	114.315i	−0.475962	−	0.274797i
$417$		0			0
$418$	33.0000	−	19.0526i	0.0789474	−	0.0455803i
$419$		−	131.636i		−	0.314167i	−0.987585	−	0.157083i	$-0.949791\pi$
$419$		−	131.636i		−	0.314167i	0.987585	−	0.157083i	$-0.0502091\pi$
$420$		0			0
$421$	−28.0000			−0.0665083			−0.0332542	−	0.999447i	$-0.510587\pi$
$421$	−28.0000			−0.0665083			−0.0332542	+	0.999447i	$0.510587\pi$
$422$	−26.0000	−	45.0333i	−0.0616114	−	0.106714i
$423$		0			0
$424$	108.500	−	187.928i	0.255896	−	0.443225i
$425$	−42.0000	+	24.2487i	−0.0988235	+	0.0570558i
$426$		0			0
$427$			96.9948i			0.227154i
$428$	93.0000			0.217290
$429$		0			0
$430$	117.000	+	67.5500i	0.272093	+	0.157093i
$431$	59.0000	−	102.191i	0.136891	−	0.237102i	−0.789427	−	0.613844i	$-0.789622\pi$
$431$	59.0000	−	102.191i	0.136891	−	0.237102i	0.926318	+	0.376742i	$0.122956\pi$
$432$		0			0
$433$			561.184i			1.29604i	0.761624	+	0.648019i	$0.224402\pi$
$433$			561.184i			1.29604i	−0.761624	+	0.648019i	$0.775598\pi$
$434$	199.500	+	115.181i	0.459677	+	0.265395i
$435$		0			0
$436$	−204.000	−	353.338i	−0.467890	−	0.810409i
$437$	−84.0000	−	48.4974i	−0.192220	−	0.110978i
$438$		0			0
$439$	−640.500	+	369.793i	−1.45900	+	0.842353i	−0.998962	−	0.0455478i	$-0.985497\pi$
$439$	−640.500	+	369.793i	−1.45900	+	0.842353i	−0.460036	+	0.887900i	$0.652163\pi$
$440$			400.104i			0.909327i
$441$		0			0
$442$	−168.000			−0.380090
$443$	−77.5000	−	134.234i	−0.174944	−	0.303011i	0.765198	−	0.643795i	$-0.222641\pi$
$443$	−77.5000	−	134.234i	−0.174944	−	0.303011i	−0.940142	+	0.340784i	$0.889308\pi$
$444$		0			0
$445$	207.000	−	358.535i	0.465169	−	0.805696i
$446$	−19.5000	+	11.2583i	−0.0437220	+	0.0252429i
$447$		0			0
$448$	−45.5000	+	78.8083i	−0.101562	+	0.175911i
$449$	368.000			0.819599			0.409800	−	0.912176i	$-0.365599\pi$
$449$	368.000			0.819599			0.409800	+	0.912176i	$0.365599\pi$
$450$		0			0
$451$	−33.0000	−	19.0526i	−0.0731707	−	0.0422451i
$452$	111.000	−	192.258i	0.245575	−	0.425349i
$453$		0			0
$454$		−	67.5500i		−	0.148789i
$455$	252.000			0.553846
$456$		0			0
$457$	−170.500	−	295.315i	−0.373085	−	0.646203i	0.616953	−	0.787000i	$-0.288367\pi$
$457$	−170.500	−	295.315i	−0.373085	−	0.646203i	−0.990038	+	0.140797i	$0.955033\pi$
$458$	−27.0000	−	15.5885i	−0.0589520	−	0.0340359i
$459$		0			0
$460$	378.000	−	218.238i	0.821739	−	0.474431i
$461$		−	55.4256i		−	0.120229i	−0.998191	−	0.0601146i	$-0.980853\pi$
$461$		−	55.4256i		−	0.120229i	0.998191	−	0.0601146i	$-0.0191466\pi$
$462$		0			0
$463$	−178.000			−0.384449			−0.192225	−	0.981351i	$-0.561570\pi$
$463$	−178.000			−0.384449			−0.192225	+	0.981351i	$0.561570\pi$
$464$	62.5000	+	108.253i	0.134698	+	0.233304i
$465$		0			0
$466$	−131.000	+	226.899i	−0.281116	+	0.486907i
$467$	−570.000	+	329.090i	−1.22056	+	0.704689i	−0.965037	−	0.262115i	$-0.915580\pi$
$467$	−570.000	+	329.090i	−1.22056	+	0.704689i	−0.255520	+	0.966804i	$0.582247\pi$
$468$		0			0
$469$	182.000	+	315.233i	0.388060	+	0.672139i
$470$	396.000			0.842553
$471$		0			0
$472$	52.5000	+	30.3109i	0.111229	+	0.0642180i
$473$	−143.000	+	247.683i	−0.302326	+	0.523643i
$474$		0			0
$475$			6.92820i			0.0145857i
$476$		−	509.223i		−	1.06980i
$477$		0			0
$478$	−80.0000	−	138.564i	−0.167364	−	0.289883i
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.0368199	−	0.999322i	$-0.511723\pi$
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.883848	+	0.467774i	$0.845056\pi$
$480$		0			0
$481$	348.000	−	200.918i	0.723493	−	0.417709i
$482$			472.850i			0.981016i
$483$		0			0
$484$		0			0
$485$	−238.500	−	413.094i	−0.491753	−	0.851740i
$486$		0			0
$487$	420.500	−	728.327i	0.863450	−	1.49554i	−0.00512864	−	0.999987i	$-0.501633\pi$
$487$	420.500	−	728.327i	0.863450	−	1.49554i	0.868578	−	0.495552i	$-0.165034\pi$
$488$	84.0000	−	48.4974i	0.172131	−	0.0993800i
$489$		0			0
$490$		−	254.611i		−	0.519615i
$491$	959.000			1.95316			0.976578	−	0.215162i	$-0.0690279\pi$
$491$	959.000			1.95316			0.976578	+	0.215162i	$0.0690279\pi$
$492$		0			0
$493$	525.000	+	303.109i	1.06491	+	0.614825i
$494$	−12.0000	+	20.7846i	−0.0242915	+	0.0420741i
$495$		0			0
$496$			164.545i			0.331744i
$497$	224.000	−	387.979i	0.450704	−	0.780643i
$498$		0			0
$499$	59.0000	+	102.191i	0.118236	+	0.204792i	0.919069	−	0.394097i	$-0.128943\pi$
$499$	59.0000	+	102.191i	0.118236	+	0.204792i	−0.800832	+	0.598889i	$0.795609\pi$
$500$	310.500	+	179.267i	0.621000	+	0.358535i
$501$		0			0
$502$	58.5000	−	33.7750i	0.116534	−	0.0672809i
$503$			363.731i			0.723123i	0.932348	+	0.361561i	$0.117756\pi$
$503$			363.731i			0.723123i	−0.932348	+	0.361561i	$0.882244\pi$
$504$		0			0
$505$	108.000			0.213861
$506$	−154.000	−	266.736i	−0.304348	−	0.527146i
$507$		0			0
$508$	−1.50000	+	2.59808i	−0.00295276	+	0.00511432i
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	−0.826226	−	0.563339i	$-0.809517\pi$
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	0.0747526	+	0.997202i	$0.476183\pi$
$510$		0			0
$511$	−42.0000	+	24.2487i	−0.0821918	+	0.0474534i
$512$	−305.000			−0.595703
$513$		0			0
$514$	351.000	+	202.650i	0.682879	+	0.394261i
$515$		0			0
$516$		0			0
$517$			838.313i			1.62149i
$518$	−203.000	−	351.606i	−0.391892	−	0.678777i
$519$		0			0
$520$	−126.000	−	218.238i	−0.242308	−	0.419689i
$521$	843.000	+	486.706i	1.61804	+	0.934177i	0.987426	+	0.158082i	$0.0505311\pi$
$521$	843.000	+	486.706i	1.61804	+	0.934177i	0.630616	+	0.776095i	$0.282802\pi$
$522$		0			0
$523$	−408.000	+	235.559i	−0.780115	+	0.450399i	−0.836471	−	0.548011i	$-0.815385\pi$
$523$	−408.000	+	235.559i	−0.780115	+	0.450399i	0.0563562	+	0.998411i	$0.482052\pi$
$524$			545.596i			1.04121i
$525$		0			0
$526$	106.000			0.201521
$527$	399.000	+	691.088i	0.757116	+	1.31136i
$528$		0			0
$529$	−127.500	+	220.836i	−0.241021	+	0.417460i
$530$	139.500	−	80.5404i	0.263208	−	0.151963i
$531$		0			0
$532$	−63.0000	−	36.3731i	−0.118421	−	0.0683704i
$533$	24.0000			0.0450281
$534$		0			0
$535$	139.500	+	80.5404i	0.260748	+	0.150543i
$536$	182.000	−	315.233i	0.339552	−	0.588122i
$537$		0			0
$538$		−	434.745i		−	0.808076i
$539$	539.000			1.00000
$540$		0			0
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	−0.950234	−	0.311538i	$-0.899156\pi$
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	0.205317	−	0.978696i	$-0.434178\pi$
$542$	109.500	+	63.2199i	0.202030	+	0.116642i
$543$		0			0
$544$	−693.000	+	400.104i	−1.27390	+	0.735485i
$545$		−	706.677i		−	1.29665i
$546$		0			0
$547$	−154.000			−0.281536			−0.140768	−	0.990043i	$-0.544957\pi$
$547$	−154.000			−0.281536			−0.140768	+	0.990043i	$0.544957\pi$
$548$	−132.000	−	228.631i	−0.240876	−	0.417209i
$549$		0			0
$550$	−11.0000	+	19.0526i	−0.0200000	+	0.0346410i
$551$	75.0000	−	43.3013i	0.136116	−	0.0785867i
$552$		0			0
$553$	119.000			0.215190
$554$	−236.000			−0.425993
$555$		0			0
$556$	495.000	+	285.788i	0.890288	+	0.514008i
$557$	−425.500	+	736.988i	−0.763914	+	1.32314i	0.176905	+	0.984228i	$0.443391\pi$
$557$	−425.500	+	736.988i	−0.763914	+	1.32314i	−0.940819	+	0.338910i	$0.889942\pi$
$558$		0			0
$559$		−	180.133i		−	0.322242i
$560$	157.500	−	90.9327i	0.281250	−	0.162380i
$561$		0			0
$562$	58.0000	+	100.459i	0.103203	+	0.178753i
$563$	−370.500	−	213.908i	−0.658082	−	0.379944i	0.133464	−	0.991054i	$-0.457390\pi$
$563$	−370.500	−	213.908i	−0.658082	−	0.379944i	−0.791546	+	0.611110i	$0.790723\pi$
$564$		0			0
$565$	333.000	−	192.258i	0.589381	−	0.340279i
$566$		−	370.659i		−	0.654874i
$567$		0			0
$568$	−448.000			−0.788732
$569$	−409.000	−	708.409i	−0.718805	−	1.24501i	−0.961474	−	0.274897i	$-0.911356\pi$
$569$	−409.000	−	708.409i	−0.718805	−	1.24501i	0.242669	−	0.970109i	$-0.421977\pi$
$570$		0			0
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	−0.963162	−	0.268923i	$-0.913332\pi$
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	0.714475	+	0.699661i	$0.246666\pi$
$572$	198.000	−	114.315i	0.346154	−	0.199852i
$573$		0			0
$574$		−	24.2487i		−	0.0422451i
$575$	56.0000			0.0973913
$576$		0			0
$577$	−655.500	−	378.453i	−1.13605	−	0.655898i	−0.190599	−	0.981668i	$-0.561043\pi$
$577$	−655.500	−	378.453i	−1.13605	−	0.655898i	−0.945449	+	0.325770i	$0.894377\pi$
$578$	−149.500	+	258.942i	−0.258651	+	0.447996i
$579$		0			0
$580$			389.711i			0.671916i
$581$	−325.500	−	187.928i	−0.560241	−	0.323455i
$582$		0			0
$583$	170.500	+	295.315i	0.292453	+	0.506543i
$584$	42.0000	+	24.2487i	0.0719178	+	0.0415218i
$585$		0			0
$586$	−16.5000	+	9.52628i	−0.0281570	+	0.0162564i
$587$			947.432i			1.61402i	0.590535	+	0.807012i	$0.298917\pi$
$587$			947.432i			1.61402i	−0.590535	+	0.807012i	$0.701083\pi$
$588$		0			0
$589$	114.000			0.193548
$590$	22.5000	+	38.9711i	0.0381356	+	0.0660528i
$591$		0			0
$592$	145.000	−	251.147i	0.244932	−	0.424235i
$593$	−354.000	+	204.382i	−0.596965	+	0.344658i	−0.767847	−	0.640634i	$-0.778672\pi$
$593$	−354.000	+	204.382i	−0.596965	+	0.344658i	0.170882	+	0.985292i	$0.445338\pi$
$594$		0			0
$595$	441.000	−	763.834i	0.741176	−	1.28376i
$596$	−690.000			−1.15772
$597$		0			0
$598$	168.000	+	96.9948i	0.280936	+	0.162199i
$599$	278.000	−	481.510i	0.464107	−	0.803857i	−0.535054	−	0.844818i	$-0.679709\pi$
$599$	278.000	−	481.510i	0.464107	−	0.803857i	0.999161	+	0.0409613i	$0.0130420\pi$
$600$		0			0
$601$		−	580.237i		−	0.965453i	−0.875771	−	0.482726i	$-0.839647\pi$
$601$		−	580.237i		−	0.965453i	0.875771	−	0.482726i	$-0.160353\pi$
$602$	−182.000			−0.302326
$603$		0			0
$604$	340.500	+	589.763i	0.563742	+	0.976429i
$605$		0			0
$606$		0			0
$607$	571.500	−	329.956i	0.941516	−	0.543584i	0.0510805	−	0.998695i	$-0.483733\pi$
$607$	571.500	−	329.956i	0.941516	−	0.543584i	0.890435	+	0.455110i	$0.150400\pi$
$608$			114.315i			0.188019i
$609$		0			0
$610$	72.0000			0.118033
$611$	−264.000	−	457.261i	−0.432079	−	0.748382i
$612$		0			0
$613$	−160.000	+	277.128i	−0.261011	+	0.452085i	−0.966511	−	0.256625i	$-0.917389\pi$
$613$	−160.000	+	277.128i	−0.261011	+	0.452085i	0.705500	+	0.708710i	$0.250723\pi$
$614$	−396.000	+	228.631i	−0.644951	+	0.372363i
$615$		0			0
$616$	−269.500	−	466.788i	−0.437500	−	0.757772i
$617$	−652.000			−1.05673			−0.528363	−	0.849019i	$-0.677194\pi$
$617$	−652.000			−1.05673			−0.528363	+	0.849019i	$0.677194\pi$
$618$		0			0
$619$	−558.000	−	322.161i	−0.901454	−	0.520455i	−0.0237823	−	0.999717i	$-0.507571\pi$
$619$	−558.000	−	322.161i	−0.901454	−	0.520455i	−0.877672	+	0.479262i	$0.840904\pi$
$620$	−256.500	+	444.271i	−0.413710	+	0.716566i
$621$		0			0
$622$		−	329.090i		−	0.529083i
$623$			557.720i			0.895217i
$624$		0			0
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$	475.500	+	274.530i	0.759585	+	0.438546i
$627$		0			0
$628$	−126.000	+	72.7461i	−0.200637	+	0.115838i
$629$		−	1406.43i		−	2.23597i
$630$		0			0
$631$	−97.0000			−0.153724			−0.0768621	−	0.997042i	$-0.524490\pi$
$631$	−97.0000			−0.153724			−0.0768621	+	0.997042i	$0.524490\pi$
$632$	−59.5000	−	103.057i	−0.0941456	−	0.163065i
$633$		0			0
$634$	−93.5000	+	161.947i	−0.147476	+	0.255437i
$635$	−4.50000	+	2.59808i	−0.00708661	+	0.00409146i
$636$		0			0
$637$	−294.000	+	169.741i	−0.461538	+	0.266469i
$638$	275.000			0.431034
$639$		0			0
$640$	−535.500	−	309.171i	−0.836719	−	0.483080i
$641$	350.000	−	606.218i	0.546022	−	0.945738i	−0.452520	−	0.891754i	$-0.649475\pi$
$641$	350.000	−	606.218i	0.546022	−	0.945738i	0.998542	−	0.0539833i	$-0.0171918\pi$
$642$		0			0
$643$			325.626i			0.506416i	0.967412	+	0.253208i	$0.0814857\pi$
$643$			325.626i			0.506416i	−0.967412	+	0.253208i	$0.918514\pi$
$644$	−294.000	+	509.223i	−0.456522	+	0.790719i
$645$		0			0
$646$	42.0000	+	72.7461i	0.0650155	+	0.112610i
$647$	312.000	+	180.133i	0.482226	+	0.278413i	0.721344	−	0.692577i	$-0.243525\pi$
$647$	312.000	+	180.133i	0.482226	+	0.278413i	−0.239118	+	0.970991i	$0.576858\pi$
$648$		0			0
$649$	−82.5000	+	47.6314i	−0.127119	+	0.0733920i
$650$		−	13.8564i		−	0.0213175i
$651$		0			0
$652$	−636.000			−0.975460
$653$	186.500	+	323.027i	0.285605	+	0.494682i	0.972756	−	0.231833i	$-0.0744722\pi$
$653$	186.500	+	323.027i	0.285605	+	0.494682i	−0.687151	+	0.726515i	$0.741139\pi$
$654$		0			0
$655$	−472.500	+	818.394i	−0.721374	+	1.24946i
$656$	15.0000	−	8.66025i	0.0228659	−	0.0132016i
$657$		0			0
$658$	−462.000	+	266.736i	−0.702128	+	0.405374i
$659$	818.000			1.24127			0.620637	−	0.784098i	$-0.286874\pi$
$659$	818.000			1.24127			0.620637	+	0.784098i	$0.286874\pi$
$660$		0			0
$661$	327.000	+	188.794i	0.494705	+	0.285618i	0.726524	−	0.687141i	$-0.241134\pi$
$661$	327.000	+	188.794i	0.494705	+	0.285618i	−0.231819	+	0.972759i	$0.574468\pi$
$662$	−8.00000	+	13.8564i	−0.0120846	+	0.0209311i
$663$		0			0
$664$			375.855i			0.566047i
$665$	−63.0000	−	109.119i	−0.0947368	−	0.164089i
$666$		0			0
$667$	−350.000	−	606.218i	−0.524738	−	0.908872i
$668$	252.000	+	145.492i	0.377246	+	0.217803i
$669$		0			0
$670$	234.000	−	135.100i	0.349254	−	0.201642i
$671$			152.420i			0.227154i
$672$		0			0
$673$	1205.00			1.79049			0.895245	−	0.445574i	$-0.147000\pi$
$673$	1205.00			1.79049			0.895245	+	0.445574i	$0.147000\pi$
$674$	41.5000	+	71.8801i	0.0615727	+	0.106647i
$675$		0			0
$676$	181.500	−	314.367i	0.268491	−	0.465040i
$677$	466.500	−	269.334i	0.689069	−	0.397834i	−0.114194	−	0.993458i	$-0.536429\pi$
$677$	466.500	−	269.334i	0.689069	−	0.397834i	0.803263	+	0.595624i	$0.203095\pi$
$678$		0			0
$679$	556.500	+	321.295i	0.819588	+	0.473189i
$680$	−882.000			−1.29706
$681$		0			0
$682$	313.500	+	180.999i	0.459677	+	0.265395i
$683$	474.500	−	821.858i	0.694729	−	1.20331i	−0.275543	−	0.961289i	$-0.588858\pi$
$683$	474.500	−	821.858i	0.694729	−	1.20331i	0.970272	−	0.242017i	$-0.0778091\pi$
$684$		0			0
$685$		−	457.261i		−	0.667535i
$686$	171.500	+	297.047i	0.250000	+	0.433013i
$687$		0			0
$688$	−65.0000	−	112.583i	−0.0944767	−	0.163639i
$689$	−186.000	−	107.387i	−0.269956	−	0.155859i
$690$		0			0
$691$	−267.000	+	154.153i	−0.386397	+	0.223086i	−0.680598	−	0.732657i	$-0.738280\pi$
$691$	−267.000	+	154.153i	−0.386397	+	0.223086i	0.294201	+	0.955744i	$0.404946\pi$
$692$			644.323i			0.931102i
$693$		0			0
$694$	358.000			0.515850
$695$	495.000	+	857.365i	0.712230	+	1.23362i
$696$		0			0
$697$	42.0000	−	72.7461i	0.0602582	−	0.104370i
$698$	588.000	−	339.482i	0.842407	−	0.486364i
$699$		0			0
$700$	42.0000			0.0600000
$701$	413.000			0.589158			0.294579	−	0.955627i	$-0.404821\pi$
$701$	413.000			0.589158			0.294579	+	0.955627i	$0.404821\pi$
$702$		0			0
$703$	−174.000	−	100.459i	−0.247511	−	0.142900i
$704$	−71.5000	+	123.842i	−0.101562	+	0.175911i
$705$		0			0
$706$			644.323i			0.912639i
$707$	−126.000	+	72.7461i	−0.178218	+	0.102894i
$708$		0			0
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	−0.988023	−	0.154306i	$-0.950686\pi$
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	0.360379	−	0.932806i	$-0.382648\pi$
$710$	−288.000	−	166.277i	−0.405634	−	0.234193i
$711$		0			0
$712$	483.000	−	278.860i	0.678371	−	0.391658i
$713$		−	921.451i		−	1.29236i
$714$		0			0
$715$	396.000			0.553846
$716$	−69.0000	−	119.512i	−0.0963687	−	0.166916i
$717$		0			0
$718$	142.000	−	245.951i	0.197772	−	0.342550i
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	−0.845316	−	0.534267i	$-0.820588\pi$
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	0.0400307	+	0.999198i	$0.487254\pi$
$720$		0			0
$721$		0			0
$722$	−349.000			−0.483380
$723$		0			0
$724$	81.0000	+	46.7654i	0.111878	+	0.0645931i
$725$	−25.0000	+	43.3013i	−0.0344828	+	0.0597259i
$726$		0			0
$727$			417.424i			0.574174i	0.957905	+	0.287087i	$0.0926868\pi$
$727$			417.424i			0.574174i	−0.957905	+	0.287087i	$0.907313\pi$
$728$	294.000	+	169.741i	0.403846	+	0.233161i
$729$		0			0
$730$	18.0000	+	31.1769i	0.0246575	+	0.0427081i
$731$	−546.000	−	315.233i	−0.746922	−	0.431236i
$732$		0			0
$733$	171.000	−	98.7269i	0.233288	−	0.134689i	−0.378800	−	0.925479i	$-0.623663\pi$
$733$	171.000	−	98.7269i	0.233288	−	0.134689i	0.612088	+	0.790790i	$0.290330\pi$
$734$			275.396i			0.375199i
$735$		0			0
$736$	924.000			1.25543
$737$	286.000	+	495.367i	0.388060	+	0.672139i
$738$		0			0
$739$	155.000	−	268.468i	0.209743	−	0.363285i	−0.741891	−	0.670521i	$-0.766071\pi$
$739$	155.000	−	268.468i	0.209743	−	0.363285i	0.951633	+	0.307236i	$0.0994040\pi$
$740$	783.000	−	452.065i	1.05811	−	0.610899i
$741$		0			0
$742$	−108.500	+	187.928i	−0.146226	+	0.253272i
$743$	812.000			1.09287			0.546433	−	0.837503i	$-0.315985\pi$
$743$	812.000			1.09287			0.546433	+	0.837503i	$0.315985\pi$
$744$		0			0
$745$	−1035.00	−	597.558i	−1.38926	−	0.802091i
$746$	25.0000	−	43.3013i	0.0335121	−	0.0580446i
$747$		0			0
$748$		−	800.207i		−	1.06980i
$749$	−217.000			−0.289720
$750$		0			0
$751$	537.500	+	930.977i	0.715712	+	1.23965i	0.962684	+	0.270628i	$0.0872312\pi$
$751$	537.500	+	930.977i	0.715712	+	1.23965i	−0.246972	+	0.969023i	$0.579435\pi$
$752$	−330.000	−	190.526i	−0.438830	−	0.253358i
$753$		0			0
$754$	−150.000	+	86.6025i	−0.198939	+	0.114857i
$755$			1179.53i			1.56229i
$756$		0			0
$757$	−484.000			−0.639366			−0.319683	−	0.947525i	$-0.603576\pi$
$757$	−484.000			−0.639366			−0.319683	+	0.947525i	$0.603576\pi$
$758$	229.000	+	396.640i	0.302111	+	0.523271i
$759$		0			0
$760$	−63.0000	+	109.119i	−0.0828947	+	0.143578i
$761$	−144.000	+	83.1384i	−0.189225	+	0.109249i	−0.591620	−	0.806217i	$-0.701511\pi$
$761$	−144.000	+	83.1384i	−0.189225	+	0.109249i	0.402395	+	0.915466i	$0.368178\pi$
$762$		0			0
$763$	476.000	+	824.456i	0.623853	+	1.08055i
$764$	624.000			0.816754
$765$		0			0
$766$	−351.000	−	202.650i	−0.458225	−	0.264556i
$767$	30.0000	−	51.9615i	0.0391134	−	0.0677464i
$768$		0			0
$769$		−	594.093i		−	0.772553i	−0.922383	−	0.386277i	$-0.873761\pi$
$769$		−	594.093i		−	0.772553i	0.922383	−	0.386277i	$-0.126239\pi$
$770$		−	400.104i		−	0.519615i
$771$		0			0
$772$	358.500	+	620.940i	0.464378	+	0.804327i
$773$	−894.000	−	516.151i	−1.15653	−	0.667725i	−0.206062	−	0.978539i	$-0.566065\pi$
$773$	−894.000	−	516.151i	−1.15653	−	0.667725i	−0.950471	+	0.310814i	$0.899398\pi$
$774$		0			0
$775$	−57.0000	+	32.9090i	−0.0735484	+	0.0424632i
$776$		−	642.591i		−	0.828081i
$777$		0			0
$778$	−698.000			−0.897172
$779$	−6.00000	−	10.3923i	−0.00770218	−	0.0133406i
$780$		0			0
$781$	352.000	−	609.682i	0.450704	−	0.780643i
$782$	588.000	−	339.482i	0.751918	−	0.434120i
$783$		0			0
$784$	−122.500	+	212.176i	−0.156250	+	0.270633i
$785$	−252.000			−0.321019
$786$		0			0
$787$	354.000	+	204.382i	0.449809	+	0.259698i	0.707750	−	0.706463i	$-0.249710\pi$
$787$	354.000	+	204.382i	0.449809	+	0.259698i	−0.257940	+	0.966161i	$0.583044\pi$
$788$	39.0000	−	67.5500i	0.0494924	−	0.0857233i
$789$		0			0
$790$		−	88.3346i		−	0.111816i
$791$	−259.000	+	448.601i	−0.327434	+	0.567132i
$792$		0			0
$793$	−48.0000	−	83.1384i	−0.0605296	−	0.104840i
$794$	−498.000	−	287.520i	−0.627204	−	0.362116i
$795$		0			0
$796$	−630.000	+	363.731i	−0.791457	+	0.456948i
$797$		−	625.270i		−	0.784530i	−0.919852	−	0.392265i	$-0.871692\pi$
$797$		−	625.270i		−	0.784530i	0.919852	−	0.392265i	$-0.128308\pi$
$798$		0			0
$799$	−1848.00			−2.31289
$800$	−33.0000	−	57.1577i	−0.0412500	−	0.0714471i
$801$		0			0
$802$	142.000	−	245.951i	0.177057	−	0.306672i
$803$	−66.0000	+	38.1051i	−0.0821918	+	0.0474534i
$804$		0			0
$805$	−882.000	+	509.223i	−1.09565	+	0.632575i
$806$	−228.000			−0.282878
$807$		0			0
$808$	126.000	+	72.7461i	0.155941	+	0.0900323i
$809$	−376.000	+	651.251i	−0.464771	+	0.805008i	−0.999191	−	0.0402116i	$-0.987197\pi$
$809$	−376.000	+	651.251i	−0.464771	+	0.805008i	0.534420	+	0.845219i	$0.320530\pi$
$810$		0			0
$811$		−	270.200i		−	0.333169i	−0.986027	−	0.166584i	$-0.946726\pi$
$811$		−	270.200i		−	0.333169i	0.986027	−	0.166584i	$-0.0532738\pi$
$812$	−262.500	−	454.663i	−0.323276	−	0.559930i
$813$		0			0
$814$	−319.000	−	552.524i	−0.391892	−	0.678777i
$815$	−954.000	−	550.792i	−1.17055	−	0.675819i
$816$		0			0
$817$	−78.0000	+	45.0333i	−0.0954712	+	0.0551203i
$818$		−	209.578i		−	0.256208i
$819$		0			0
$820$	54.0000			0.0658537
$821$	441.500	+	764.700i	0.537759	+	0.931426i	0.999024	+	0.0441635i	$0.0140622\pi$
$821$	441.500	+	764.700i	0.537759	+	0.931426i	−0.461265	+	0.887262i	$0.652604\pi$
$822$		0			0
$823$	245.000	−	424.352i	0.297691	−	0.515617i	−0.677916	−	0.735139i	$-0.737117\pi$
$823$	245.000	−	424.352i	0.297691	−	0.515617i	0.975607	+	0.219523i	$0.0704500\pi$
$824$		0			0
$825$		0			0
$826$	−52.5000	−	30.3109i	−0.0635593	−	0.0366960i
$827$	−1279.00			−1.54655			−0.773277	−	0.634068i	$-0.781384\pi$
$827$	−1279.00			−1.54655			−0.773277	+	0.634068i	$0.781384\pi$
$828$		0			0
$829$	1311.00	+	756.906i	1.58142	+	0.913035i	0.994652	+	0.103283i	$0.0329346\pi$
$829$	1311.00	+	756.906i	1.58142	+	0.913035i	0.586771	+	0.809753i	$0.300399\pi$
$830$	−139.500	+	241.621i	−0.168072	+	0.291110i
$831$		0			0
$832$		−	90.0666i		−	0.108253i
$833$			1188.19i			1.42639i
$834$		0			0
$835$	252.000	+	436.477i	0.301796	+	0.522727i
$836$	−99.0000	−	57.1577i	−0.118421	−	0.0683704i
$837$		0			0
$838$	114.000	−	65.8179i	0.136038	−	0.0785417i
$839$		−	523.079i		−	0.623456i	−0.950171	−	0.311728i	$-0.899092\pi$
$839$		−	523.079i		−	0.623456i	0.950171	−	0.311728i	$-0.100908\pi$
$840$		0			0
$841$	−216.000			−0.256837
$842$	−14.0000	−	24.2487i	−0.0166271	−	0.0287989i
$843$		0			0
$844$	−78.0000	+	135.100i	−0.0924171	+	0.160071i
$845$	544.500	−	314.367i	0.644379	−	0.372032i
$846$		0			0
$847$		0			0
$848$	−155.000			−0.182783
$849$		0			0
$850$	−42.0000	−	24.2487i	−0.0494118	−	0.0285279i
$851$	−812.000	+	1406.43i	−0.954172	+	1.65267i
$852$		0			0
$853$		−	387.979i		−	0.454841i	−0.973797	−	0.227421i	$-0.926971\pi$
$853$		−	387.979i		−	0.454841i	0.973797	−	0.227421i	$-0.0730292\pi$
$854$	−84.0000	+	48.4974i	−0.0983607	+	0.0567886i
$855$		0			0
$856$	108.500	+	187.928i	0.126752	+	0.219541i
$857$	720.000	+	415.692i	0.840140	+	0.485055i	0.857312	−	0.514797i	$-0.172133\pi$
$857$	720.000	+	415.692i	0.840140	+	0.485055i	−0.0171718	+	0.999853i	$0.505466\pi$
$858$		0			0
$859$	981.000	−	566.381i	1.14203	−	0.659349i	0.195094	−	0.980785i	$-0.437499\pi$
$859$	981.000	−	566.381i	1.14203	−	0.659349i	0.946931	+	0.321436i	$0.104165\pi$
$860$		−	405.300i		−	0.471279i
$861$		0			0
$862$	118.000			0.136891
$863$	11.0000	+	19.0526i	0.0127462	+	0.0220771i	0.872328	−	0.488921i	$-0.162609\pi$
$863$	11.0000	+	19.0526i	0.0127462	+	0.0220771i	−0.859582	+	0.510998i	$0.829276\pi$
$864$		0			0
$865$	−558.000	+	966.484i	−0.645087	+	1.11732i
$866$	−486.000	+	280.592i	−0.561201	+	0.324010i
$867$		0			0
$868$		−	691.088i		−	0.796185i
$869$	187.000			0.215190
$870$		0			0
$871$	−312.000	−	180.133i	−0.358209	−	0.206812i
$872$	476.000	−	824.456i	0.545872	−	0.945477i
$873$		0			0
$874$		−	96.9948i		−	0.110978i
$875$	−724.500	−	418.290i	−0.828000	−	0.478046i
$876$		0			0
$877$	20.0000	+	34.6410i	0.0228050	+	0.0394994i	0.877203	−	0.480120i	$-0.159407\pi$
$877$	20.0000	+	34.6410i	0.0228050	+	0.0394994i	−0.854398	+	0.519620i	$0.826074\pi$
$878$	−640.500	−	369.793i	−0.729499	−	0.421176i
$879$		0			0
$880$	247.500	−	142.894i	0.281250	−	0.162380i
$881$			20.7846i			0.0235921i	0.999930	+	0.0117960i	$0.00375488\pi$
$881$			20.7846i			0.0235921i	−0.999930	+	0.0117960i	$0.996245\pi$
$882$		0			0
$883$	386.000			0.437146			0.218573	−	0.975821i	$-0.429860\pi$
$883$	386.000			0.437146			0.218573	+	0.975821i	$0.429860\pi$
$884$	252.000	+	436.477i	0.285068	+	0.493752i
$885$		0			0
$886$	77.5000	−	134.234i	0.0874718	−	0.151506i
$887$	1494.00	−	862.561i	1.68433	−	0.972448i	0.725604	−	0.688112i	$-0.241560\pi$
$887$	1494.00	−	862.561i	1.68433	−	0.972448i	0.958725	−	0.284336i	$-0.0917731\pi$
$888$		0			0
$889$	3.50000	−	6.06218i	0.00393701	−	0.00681910i
$890$	414.000			0.465169
$891$		0			0
$892$	58.5000	+	33.7750i	0.0655830	+	0.0378643i
$893$	−132.000	+	228.631i	−0.147816	+	0.256025i
$894$		0			0
$895$		−	239.023i		−	0.267065i
$896$	833.000			0.929688
$897$		0			0
$898$	184.000	+	318.697i	0.204900	+	0.354897i
$899$	712.500	+	411.362i	0.792547	+	0.457577i
$900$		0			0
$901$	−651.000	+	375.855i	−0.722531	+	0.417153i
$902$		−	38.1051i		−	0.0422451i
$903$		0			0
$904$	518.000			0.573009
$905$	81.0000	+	140.296i	0.0895028	+	0.155023i
$906$		0			0
$907$	296.000	−	512.687i	0.326351	−	0.565256i	−0.655434	−	0.755252i	$-0.727514\pi$
$907$	296.000	−	512.687i	0.326351	−	0.565256i	0.981785	+	0.189996i	$0.0608477\pi$
$908$	−175.500	+	101.325i	−0.193282	+	0.111591i
$909$		0			0
$910$	126.000	+	218.238i	0.138462	+	0.239822i
$911$	416.000			0.456641			0.228321	−	0.973586i	$-0.426677\pi$
$911$	416.000			0.456641			0.228321	+	0.973586i	$0.426677\pi$
$912$		0			0
$913$	−511.500	−	295.315i	−0.560241	−	0.323455i
$914$	170.500	−	295.315i	0.186543	−	0.323101i
$915$		0			0
$916$			93.5307i			0.102108i
$917$		−	1273.06i		−	1.38828i
$918$		0			0
$919$	−25.0000	−	43.3013i	−0.0272035	−	0.0471178i	0.852103	−	0.523374i	$-0.175327\pi$
$919$	−25.0000	−	43.3013i	−0.0272035	−	0.0471178i	−0.879307	+	0.476256i	$0.841994\pi$
$920$	882.000	+	509.223i	0.958696	+	0.553503i
$921$		0			0
$922$	48.0000	−	27.7128i	0.0520607	−	0.0300573i
$923$			443.405i			0.480395i
$924$		0			0
$925$	116.000			0.125405
$926$	−89.0000	−	154.153i	−0.0961123	−	0.166471i
$927$		0			0
$928$	−412.500	+	714.471i	−0.444504	+	0.769904i
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	−0.679681	−	0.733508i	$-0.737882\pi$
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	0.295396	+	0.955375i	$0.404548\pi$
$930$		0			0
$931$	147.000	+	84.8705i	0.157895	+	0.0911606i
$932$	786.000			0.843348
$933$		0			0
$934$	−570.000	−	329.090i	−0.610278	−	0.352344i
$935$	693.000	−	1200.31i	0.741176	−	1.28376i
$936$		0			0
$937$			1605.61i			1.71357i	0.515677	+	0.856783i	$0.327540\pi$
$937$			1605.61i			1.71357i	−0.515677	+	0.856783i	$0.672460\pi$
$938$	−182.000	+	315.233i	−0.194030	+	0.336070i
$939$		0			0
$940$	−594.000	−	1028.84i	−0.631915	−	1.09451i
$941$	1150.50	+	664.241i	1.22264	+	0.705889i	0.965479	−	0.260481i	$-0.0838811\pi$
$941$	1150.50	+	664.241i	1.22264	+	0.705889i	0.257156	+	0.966370i	$0.417214\pi$
$942$		0			0
$943$	−84.0000	+	48.4974i	−0.0890774	+	0.0514289i
$944$		−	43.3013i		−	0.0458700i
$945$		0			0
$946$	−286.000			−0.302326
$947$	−685.000	−	1186.45i	−0.723337	−	1.25286i	−0.959655	−	0.281180i	$-0.909274\pi$
$947$	−685.000	−	1186.45i	−0.723337	−	1.25286i	0.236318	−	0.971676i	$-0.424059\pi$
$948$		0			0
$949$	24.0000	−	41.5692i	0.0252898	−	0.0438032i
$950$	−6.00000	+	3.46410i	−0.00631579	+	0.00364642i
$951$		0			0
$952$	1029.00	−	594.093i	1.08088	−	0.624048i
$953$	−1150.00			−1.20672			−0.603358	−	0.797471i	$-0.706171\pi$
$953$	−1150.00			−1.20672			−0.603358	+	0.797471i	$0.706171\pi$
$954$		0			0
$955$	936.000	+	540.400i	0.980105	+	0.565864i
$956$	−240.000	+	415.692i	−0.251046	+	0.434824i
$957$		0			0
$958$		−	509.223i		−	0.531548i
$959$	308.000	+	533.472i	0.321168	+	0.556279i
$960$		0			0
$961$	61.0000	+	105.655i	0.0634755	+	0.109943i
$962$	348.000	+	200.918i	0.361746	+	0.208854i
$963$		0			0
$964$	1228.50	−	709.275i	1.27438	−	0.735762i
$965$			1241.88i			1.28692i
$966$		0			0
$967$	5.00000			0.00517063			0.00258532	−	0.999997i	$-0.499177\pi$
$967$	5.00000			0.00517063			0.00258532	+	0.999997i	$0.499177\pi$
$968$		0			0
$969$		0			0
$970$	238.500	−	413.094i	0.245876	−	0.425870i
$971$	−385.500	+	222.569i	−0.397013	+	0.229216i	−0.685195	−	0.728360i	$-0.740283\pi$
$971$	−385.500	+	222.569i	−0.397013	+	0.229216i	0.288181	+	0.957576i	$0.406949\pi$
$972$		0			0
$973$	−1155.00	−	666.840i	−1.18705	−	0.685344i
$974$	841.000			0.863450
$975$		0			0
$976$	−60.0000	−	34.6410i	−0.0614754	−	0.0354928i
$977$	479.000	−	829.652i	0.490276	−	0.849184i	−0.509661	−	0.860375i	$-0.670229\pi$
$977$	479.000	−	829.652i	0.490276	−	0.849184i	0.999937	+	0.0111917i	$0.00356252\pi$
$978$		0			0
$979$			876.418i			0.895217i
$980$	−661.500	+	381.917i	−0.675000	+	0.389711i
$981$		0			0
$982$	479.500	+	830.518i	0.488289	+	0.845742i
$983$	−243.000	−	140.296i	−0.247202	−	0.142722i	0.371280	−	0.928521i	$-0.378919\pi$
$983$	−243.000	−	140.296i	−0.247202	−	0.142722i	−0.618483	+	0.785798i	$0.712252\pi$
$984$		0			0
$985$	117.000	−	67.5500i	0.118782	−	0.0685787i
$986$			606.218i			0.614825i
$987$		0			0
$988$	72.0000			0.0728745
$989$	364.000	+	630.466i	0.368049	+	0.637479i
$990$		0			0
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	−0.999232	−	0.0391732i	$-0.987528\pi$
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	0.533541	+	0.845774i	$0.320861\pi$
$992$	−940.500	+	542.998i	−0.948085	+	0.547377i
$993$		0			0
$994$	448.000			0.450704
$995$	−1260.00			−1.26633
$996$		0			0
$997$	18.0000	+	10.3923i	0.0180542	+	0.0104236i	0.509000	−	0.860767i	$-0.330015\pi$
$997$	18.0000	+	10.3923i	0.0180542	+	0.0104236i	−0.490946	+	0.871190i	$0.663349\pi$
$998$	−59.0000	+	102.191i	−0.0591182	+	0.102396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.m.c.10.1		2
3.2	odd	2		21.3.f.b.10.1	✓	2
4.3	odd	2		1008.3.cg.g.577.1		2
7.2	even	3		441.3.m.e.19.1		2
7.3	odd	6		441.3.d.b.244.1		2
7.4	even	3		441.3.d.b.244.2		2
7.5	odd	6	inner	63.3.m.c.19.1		2
7.6	odd	2		441.3.m.e.325.1		2
12.11	even	2		336.3.bh.a.241.1		2
15.2	even	4		525.3.s.c.199.2		4
15.8	even	4		525.3.s.c.199.1		4
15.14	odd	2		525.3.o.g.451.1		2
21.2	odd	6		147.3.f.c.19.1		2
21.5	even	6		21.3.f.b.19.1	yes	2
21.11	odd	6		147.3.d.b.97.1		2
21.17	even	6		147.3.d.b.97.2		2
21.20	even	2		147.3.f.c.31.1		2
28.19	even	6		1008.3.cg.g.145.1		2
84.11	even	6		2352.3.f.d.97.2		2
84.47	odd	6		336.3.bh.a.145.1		2
84.59	odd	6		2352.3.f.d.97.1		2
105.47	odd	12		525.3.s.c.124.1		4
105.68	odd	12		525.3.s.c.124.2		4
105.89	even	6		525.3.o.g.376.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.b.10.1	✓	2	3.2	odd	2
21.3.f.b.19.1	yes	2	21.5	even	6
63.3.m.c.10.1		2	1.1	even	1	trivial
63.3.m.c.19.1		2	7.5	odd	6	inner
147.3.d.b.97.1		2	21.11	odd	6
147.3.d.b.97.2		2	21.17	even	6
147.3.f.c.19.1		2	21.2	odd	6
147.3.f.c.31.1		2	21.20	even	2
336.3.bh.a.145.1		2	84.47	odd	6
336.3.bh.a.241.1		2	12.11	even	2
441.3.d.b.244.1		2	7.3	odd	6
441.3.d.b.244.2		2	7.4	even	3
441.3.m.e.19.1		2	7.2	even	3
441.3.m.e.325.1		2	7.6	odd	2
525.3.o.g.376.1		2	105.89	even	6
525.3.o.g.451.1		2	15.14	odd	2
525.3.s.c.124.1		4	105.47	odd	12
525.3.s.c.124.2		4	105.68	odd	12
525.3.s.c.199.1		4	15.8	even	4
525.3.s.c.199.2		4	15.2	even	4
1008.3.cg.g.145.1		2	28.19	even	6
1008.3.cg.g.577.1		2	4.3	odd	2
2352.3.f.d.97.1		2	84.59	odd	6
2352.3.f.d.97.2		2	84.11	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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +(-3.50000 + 6.06218i) q^{7} +7.00000 q^{8} +(4.50000 + 2.59808i) q^{10} +(-5.50000 + 9.52628i) q^{11} -6.92820i q^{13} -7.00000 q^{14} +(-2.50000 - 4.33013i) q^{16} +(-21.0000 - 12.1244i) q^{17} +(-3.00000 + 1.73205i) q^{19} -15.5885i q^{20} -11.0000 q^{22} +(14.0000 + 24.2487i) q^{23} +(1.00000 - 1.73205i) q^{25} +(6.00000 - 3.46410i) q^{26} +(10.5000 + 18.1865i) q^{28} -25.0000 q^{29} +(-28.5000 - 16.4545i) q^{31} +(16.5000 - 28.5788i) q^{32} -24.2487i q^{34} +36.3731i q^{35} +(29.0000 + 50.2295i) q^{37} +(-3.00000 - 1.73205i) q^{38} +(31.5000 - 18.1865i) q^{40} +3.46410i q^{41} +26.0000 q^{43} +(16.5000 + 28.5788i) q^{44} +(-14.0000 + 24.2487i) q^{46} +(66.0000 - 38.1051i) q^{47} +(-24.5000 - 42.4352i) q^{49} +2.00000 q^{50} +(-18.0000 - 10.3923i) q^{52} +(15.5000 - 26.8468i) q^{53} +57.1577i q^{55} +(-24.5000 + 42.4352i) q^{56} +(-12.5000 - 21.6506i) q^{58} +(7.50000 + 4.33013i) q^{59} +(12.0000 - 6.92820i) q^{61} -32.9090i q^{62} +13.0000 q^{64} +(-18.0000 - 31.1769i) q^{65} +(26.0000 - 45.0333i) q^{67} +(-63.0000 + 36.3731i) q^{68} +(-31.5000 + 18.1865i) q^{70} -64.0000 q^{71} +(6.00000 + 3.46410i) q^{73} +(-29.0000 + 50.2295i) q^{74} +10.3923i q^{76} +(-38.5000 - 66.6840i) q^{77} +(-8.50000 - 14.7224i) q^{79} +(-22.5000 - 12.9904i) q^{80} +(-3.00000 + 1.73205i) q^{82} +53.6936i q^{83} -126.000 q^{85} +(13.0000 + 22.5167i) q^{86} +(-38.5000 + 66.6840i) q^{88} +(69.0000 - 39.8372i) q^{89} +(42.0000 + 24.2487i) q^{91} +84.0000 q^{92} +(66.0000 + 38.1051i) q^{94} +(-9.00000 + 15.5885i) q^{95} -91.7987i q^{97} +(24.5000 - 42.4352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{4} + 9 q^{5} - 7 q^{7} + 14 q^{8} + 9 q^{10} - 11 q^{11} - 14 q^{14} - 5 q^{16} - 42 q^{17} - 6 q^{19} - 22 q^{22} + 28 q^{23} + 2 q^{25} + 12 q^{26} + 21 q^{28} - 50 q^{29} - 57 q^{31}+ \cdots + 49 q^{98}+O(q^{100}) \) 2 * q + q^2 + 3 * q^4 + 9 * q^5 - 7 * q^7 + 14 * q^8 + 9 * q^10 - 11 * q^11 - 14 * q^14 - 5 * q^16 - 42 * q^17 - 6 * q^19 - 22 * q^22 + 28 * q^23 + 2 * q^25 + 12 * q^26 + 21 * q^28 - 50 * q^29 - 57 * q^31 + 33 * q^32 + 58 * q^37 - 6 * q^38 + 63 * q^40 + 52 * q^43 + 33 * q^44 - 28 * q^46 + 132 * q^47 - 49 * q^49 + 4 * q^50 - 36 * q^52 + 31 * q^53 - 49 * q^56 - 25 * q^58 + 15 * q^59 + 24 * q^61 + 26 * q^64 - 36 * q^65 + 52 * q^67 - 126 * q^68 - 63 * q^70 - 128 * q^71 + 12 * q^73 - 58 * q^74 - 77 * q^77 - 17 * q^79 - 45 * q^80 - 6 * q^82 - 252 * q^85 + 26 * q^86 - 77 * q^88 + 138 * q^89 + 84 * q^91 + 168 * q^92 + 132 * q^94 - 18 * q^95 + 49 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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