LMFDB - Embedded newform 144.5.q.a.113.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,5,Mod(65,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.65"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,3] 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:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.3
Root			$-1.28901 + 2.23263i$ of defining polynomial
Character	$\chi$	$=$	144.113
Dual form			144.5.q.a.65.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.70335 - 2.29167i) q^{3} +(13.8760 + 8.01130i) q^{5} +(36.2418 + 62.7727i) q^{7} +(70.4965 - 39.8904i) q^{9} +(-83.2749 + 48.0788i) q^{11} +(-76.9530 + 133.286i) q^{13} +(139.127 + 37.9260i) q^{15} +72.7905i q^{17} +190.660 q^{19} +(459.280 + 463.279i) q^{21} +(12.5186 + 7.22762i) q^{23} +(-184.138 - 318.937i) q^{25} +(522.140 - 508.734i) q^{27} +(620.301 - 358.131i) q^{29} +(-151.284 + 262.031i) q^{31} +(-614.590 + 609.285i) q^{33} +1161.38i q^{35} +826.277 q^{37} +(-364.300 + 1336.39i) q^{39} +(481.613 + 278.059i) q^{41} +(446.340 + 773.084i) q^{43} +(1297.78 + 11.2508i) q^{45} +(3425.50 - 1977.72i) q^{47} +(-1426.44 + 2470.67i) q^{49} +(166.812 + 633.521i) q^{51} -1966.96i q^{53} -1540.69 q^{55} +(1659.38 - 436.930i) q^{57} +(-4689.48 - 2707.47i) q^{59} +(856.210 + 1483.00i) q^{61} +(5058.95 + 2979.56i) q^{63} +(-2135.60 + 1232.99i) q^{65} +(-2317.24 + 4013.58i) q^{67} +(125.517 + 34.2160i) q^{69} -6697.12i q^{71} -4823.86 q^{73} +(-2333.51 - 2353.83i) q^{75} +(-6036.07 - 3484.93i) q^{77} +(-2864.40 - 4961.28i) q^{79} +(3378.52 - 5624.26i) q^{81} +(-2452.78 + 1416.12i) q^{83} +(-583.147 + 1010.04i) q^{85} +(4577.98 - 4538.46i) q^{87} -14277.7i q^{89} -11155.7 q^{91} +(-716.187 + 2627.24i) q^{93} +(2645.60 + 1527.44i) q^{95} +(-3582.65 - 6205.34i) q^{97} +(-3952.71 + 6711.25i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 12 q^{5} - 12 q^{7} + 99 q^{9} - 483 q^{11} - 6 q^{13} + 1026 q^{15} + 258 q^{19} + 480 q^{21} + 282 q^{23} - 273 q^{25} - 54 q^{27} - 1056 q^{29} - 1290 q^{31} + 279 q^{33} + 12 q^{37}+ \cdots + 9126 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 12 * q^5 - 12 * q^7 + 99 * q^9 - 483 * q^11 - 6 * q^13 + 1026 * q^15 + 258 * q^19 + 480 * q^21 + 282 * q^23 - 273 * q^25 - 54 * q^27 - 1056 * q^29 - 1290 * q^31 + 279 * q^33 + 12 * q^37 - 1974 * q^39 + 7629 * q^41 + 285 * q^43 - 4212 * q^45 + 9642 * q^47 - 1863 * q^49 - 2457 * q^51 - 2016 * q^55 + 5367 * q^57 - 6225 * q^59 + 3630 * q^61 + 7578 * q^63 - 7158 * q^65 + 5055 * q^67 - 13878 * q^69 - 14622 * q^73 - 21021 * q^75 + 2580 * q^77 - 4764 * q^79 + 18387 * q^81 + 1866 * q^83 + 12366 * q^85 + 21564 * q^87 - 34836 * q^91 + 19254 * q^93 + 13362 * q^95 - 28959 * q^97 + 9126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	8.70335	−	2.29167i	0.967039	−	0.254630i
$3$	8.70335	−	2.29167i	0.967039	−	0.254630i
$4$		0			0
$5$	13.8760	+	8.01130i	0.555039	+	0.320452i	0.751152	−	0.660129i	$-0.229499\pi$
$5$	13.8760	+	8.01130i	0.555039	+	0.320452i	−0.196113	+	0.980581i	$0.562832\pi$
$6$		0			0
$7$	36.2418	+	62.7727i	0.739630	+	1.28108i	0.952662	+	0.304031i	$0.0983326\pi$
$7$	36.2418	+	62.7727i	0.739630	+	1.28108i	−0.213033	+	0.977045i	$0.568334\pi$
$8$		0			0
$9$	70.4965	−	39.8904i	0.870327	−	0.492474i
$10$		0			0
$11$	−83.2749	+	48.0788i	−0.688222	+	0.397345i	−0.802946	−	0.596052i	$-0.796735\pi$
$11$	−83.2749	+	48.0788i	−0.688222	+	0.397345i	0.114723	+	0.993397i	$0.463402\pi$
$12$		0			0
$13$	−76.9530	+	133.286i	−0.455343	+	0.788677i	−0.998708	−	0.0508193i	$-0.983817\pi$
$13$	−76.9530	+	133.286i	−0.455343	+	0.788677i	0.543365	+	0.839497i	$0.317150\pi$
$14$		0			0
$15$	139.127	+	37.9260i	0.618341	+	0.168560i
$16$		0			0
$17$			72.7905i			0.251870i	0.992038	+	0.125935i	$0.0401931\pi$
$17$			72.7905i			0.251870i	−0.992038	+	0.125935i	$0.959807\pi$
$18$		0			0
$19$	190.660			0.528145			0.264072	−	0.964503i	$-0.414934\pi$
$19$	190.660			0.528145			0.264072	+	0.964503i	$0.414934\pi$
$20$		0			0
$21$	459.280	+	463.279i	1.04145	+	1.05052i
$22$		0			0
$23$	12.5186	+	7.22762i	0.0236647	+	0.0136628i	0.511786	−	0.859113i	$-0.328984\pi$
$23$	12.5186	+	7.22762i	0.0236647	+	0.0136628i	−0.488121	+	0.872776i	$0.662318\pi$
$24$		0			0
$25$	−184.138	−	318.937i	−0.294621	−	0.510298i
$26$		0			0
$27$	522.140	−	508.734i	0.716242	−	0.697852i
$28$		0			0
$29$	620.301	−	358.131i	0.737575	−	0.425839i	−0.0836117	−	0.996498i	$-0.526646\pi$
$29$	620.301	−	358.131i	0.737575	−	0.425839i	0.821187	+	0.570659i	$0.193312\pi$
$30$		0			0
$31$	−151.284	+	262.031i	−0.157423	+	0.272665i	−0.933939	−	0.357433i	$-0.883652\pi$
$31$	−151.284	+	262.031i	−0.157423	+	0.272665i	0.776515	+	0.630098i	$0.216985\pi$
$32$		0			0
$33$	−614.590	+	609.285i	−0.564362	+	0.559490i
$34$		0			0
$35$			1161.38i			0.948063i
$36$		0			0
$37$	826.277			0.603562			0.301781	−	0.953377i	$-0.402419\pi$
$37$	826.277			0.603562			0.301781	+	0.953377i	$0.402419\pi$
$38$		0			0
$39$	−364.300	+	1336.39i	−0.239514	+	0.878625i
$40$		0			0
$41$	481.613	+	278.059i	0.286504	+	0.165413i	0.636364	−	0.771389i	$-0.280438\pi$
$41$	481.613	+	278.059i	0.286504	+	0.165413i	−0.349860	+	0.936802i	$0.613771\pi$
$42$		0			0
$43$	446.340	+	773.084i	0.241395	+	0.418109i	0.961112	−	0.276159i	$-0.0890616\pi$
$43$	446.340	+	773.084i	0.241395	+	0.418109i	−0.719717	+	0.694268i	$0.755728\pi$
$44$		0			0
$45$	1297.78	+	11.2508i	0.640880	+	0.00555597i
$46$		0			0
$47$	3425.50	−	1977.72i	1.55070	−	0.895299i	0.552619	−	0.833434i	$-0.313628\pi$
$47$	3425.50	−	1977.72i	1.55070	−	0.895299i	0.998085	−	0.0618654i	$-0.0197050\pi$
$48$		0			0
$49$	−1426.44	+	2470.67i	−0.594104	+	1.02902i
$50$		0			0
$51$	166.812	+	633.521i	0.0641337	+	0.243568i
$52$		0			0
$53$		−	1966.96i		−	0.700234i	−0.936706	−	0.350117i	$-0.886142\pi$
$53$		−	1966.96i		−	0.700234i	0.936706	−	0.350117i	$-0.113858\pi$
$54$		0			0
$55$	−1540.69			−0.509320
$56$		0			0
$57$	1659.38	−	436.930i	0.510736	−	0.134481i
$58$		0			0
$59$	−4689.48	−	2707.47i	−1.34716	−	0.777785i	−0.359316	−	0.933216i	$-0.616990\pi$
$59$	−4689.48	−	2707.47i	−1.34716	−	0.777785i	−0.987847	+	0.155431i	$0.950323\pi$
$60$		0			0
$61$	856.210	+	1483.00i	0.230102	+	0.398549i	0.957838	−	0.287309i	$-0.0927606\pi$
$61$	856.210	+	1483.00i	0.230102	+	0.398549i	−0.727736	+	0.685858i	$0.759427\pi$
$62$		0			0
$63$	5058.95	+	2979.56i	1.27462	+	0.750707i
$64$		0			0
$65$	−2135.60	+	1232.99i	−0.505467	+	0.291831i
$66$		0			0
$67$	−2317.24	+	4013.58i	−0.516205	+	0.894093i	0.483618	+	0.875279i	$0.339322\pi$
$67$	−2317.24	+	4013.58i	−0.516205	+	0.894093i	−0.999823	+	0.0188141i	$0.994011\pi$
$68$		0			0
$69$	125.517	+	34.2160i	0.0263636	+	0.00718672i
$70$		0			0
$71$		−	6697.12i		−	1.32853i	−0.747497	−	0.664265i	$-0.768744\pi$
$71$		−	6697.12i		−	1.32853i	0.747497	−	0.664265i	$-0.231256\pi$
$72$		0			0
$73$	−4823.86			−0.905208			−0.452604	−	0.891712i	$-0.649505\pi$
$73$	−4823.86			−0.905208			−0.452604	+	0.891712i	$0.649505\pi$
$74$		0			0
$75$	−2333.51	−	2353.83i	−0.414847	−	0.418459i
$76$		0			0
$77$	−6036.07	−	3484.93i	−1.01806	−	0.587777i
$78$		0			0
$79$	−2864.40	−	4961.28i	−0.458964	−	0.794950i	0.539942	−	0.841702i	$-0.318446\pi$
$79$	−2864.40	−	4961.28i	−0.458964	−	0.794950i	−0.998907	+	0.0467524i	$0.985113\pi$
$80$		0			0
$81$	3378.52	−	5624.26i	0.514939	−	0.857227i
$82$		0			0
$83$	−2452.78	+	1416.12i	−0.356044	+	0.205562i	−0.667344	−	0.744750i	$-0.732569\pi$
$83$	−2452.78	+	1416.12i	−0.356044	+	0.205562i	0.311300	+	0.950312i	$0.399235\pi$
$84$		0			0
$85$	−583.147	+	1010.04i	−0.0807124	+	0.139798i
$86$		0			0
$87$	4577.98	−	4538.46i	0.604832	−	0.599612i
$88$		0			0
$89$		−	14277.7i		−	1.80251i	−0.433290	−	0.901255i	$-0.642647\pi$
$89$		−	14277.7i		−	1.80251i	0.433290	−	0.901255i	$-0.357353\pi$
$90$		0			0
$91$	−11155.7			−1.34714
$92$		0			0
$93$	−716.187	+	2627.24i	−0.0828058	+	0.303763i
$94$		0			0
$95$	2645.60	+	1527.44i	0.293141	+	0.169245i
$96$		0			0
$97$	−3582.65	−	6205.34i	−0.380769	−	0.659511i	0.610403	−	0.792091i	$-0.291007\pi$
$97$	−3582.65	−	6205.34i	−0.380769	−	0.659511i	−0.991172	+	0.132580i	$0.957674\pi$
$98$		0			0
$99$	−3952.71	+	6711.25i	−0.403297	+	0.684752i
$100$		0			0
$101$	−1696.72	+	979.600i	−0.166328	+	0.0960298i	−0.580853	−	0.814008i	$-0.697281\pi$
$101$	−1696.72	+	979.600i	−0.166328	+	0.0960298i	0.414525	+	0.910038i	$0.363948\pi$
$102$		0			0
$103$	−2577.74	+	4464.77i	−0.242976	+	0.420848i	−0.961561	−	0.274592i	$-0.911457\pi$
$103$	−2577.74	+	4464.77i	−0.242976	+	0.420848i	0.718584	+	0.695440i	$0.244790\pi$
$104$		0			0
$105$	2661.49	+	10107.9i	0.241405	+	0.916814i
$106$		0			0
$107$		−	9117.08i		−	0.796321i	−0.917316	−	0.398161i	$-0.869649\pi$
$107$		−	9117.08i		−	0.796321i	0.917316	−	0.398161i	$-0.130351\pi$
$108$		0			0
$109$	−16161.1			−1.36024			−0.680122	−	0.733099i	$-0.738073\pi$
$109$	−16161.1			−1.36024			−0.680122	+	0.733099i	$0.738073\pi$
$110$		0			0
$111$	7191.38	−	1893.55i	0.583668	−	0.153685i
$112$		0			0
$113$	18272.5	+	10549.6i	1.43100	+	0.826189i	0.997197	−	0.0748185i	$-0.0238377\pi$
$113$	18272.5	+	10549.6i	1.43100	+	0.826189i	0.433804	+	0.901007i	$0.357171\pi$
$114$		0			0
$115$	115.805	+	200.581i	0.00875654	+	0.0151668i
$116$		0			0
$117$	−108.071	+	12465.9i	−0.00789470	+	0.910652i
$118$		0			0
$119$	−4569.26	+	2638.06i	−0.322665	+	0.186291i
$120$		0			0
$121$	−2697.36	+	4671.97i	−0.184233	+	0.319102i
$122$		0			0
$123$	4828.87	+	1316.35i	0.319180	+	0.0870084i
$124$		0			0
$125$		−	15914.9i		−	1.01855i
$126$		0			0
$127$	20660.9			1.28098			0.640489	−	0.767968i	$-0.278732\pi$
$127$	20660.9			1.28098			0.640489	+	0.767968i	$0.278732\pi$
$128$		0			0
$129$	5656.31	+	5705.55i	0.339902	+	0.342861i
$130$		0			0
$131$	−2772.53	−	1600.72i	−0.161560	−	0.0932768i	0.417040	−	0.908888i	$-0.363067\pi$
$131$	−2772.53	−	1600.72i	−0.161560	−	0.0932768i	−0.578600	+	0.815611i	$0.696401\pi$
$132$		0			0
$133$	6909.88	+	11968.3i	0.390631	+	0.676594i
$134$		0			0
$135$	11320.8	−	2876.17i	0.621170	−	0.157814i
$136$		0			0
$137$	−3353.18	+	1935.96i	−0.178655	+	0.103147i	−0.586661	−	0.809833i	$-0.699558\pi$
$137$	−3353.18	+	1935.96i	−0.178655	+	0.103147i	0.408005	+	0.912980i	$0.366224\pi$
$138$		0			0
$139$	−5839.62	+	10114.5i	−0.302242	+	0.523499i	−0.976644	−	0.214866i	$-0.931068\pi$
$139$	−5839.62	+	10114.5i	−0.302242	+	0.523499i	0.674401	+	0.738365i	$0.264402\pi$
$140$		0			0
$141$	25281.1	−	25062.9i	1.27162	−	1.26064i
$142$		0			0
$143$		−	14799.2i		−	0.723714i
$144$		0			0
$145$	11476.4			0.545844
$146$		0			0
$147$	−6752.87	+	24772.1i	−0.312503	+	1.14638i
$148$		0			0
$149$	−13069.8	−	7545.88i	−0.588705	−	0.339889i	0.175880	−	0.984412i	$-0.443723\pi$
$149$	−13069.8	−	7545.88i	−0.588705	−	0.339889i	−0.764585	+	0.644522i	$0.777056\pi$
$150$		0			0
$151$	15127.7	+	26201.9i	0.663465	+	1.14915i	0.979699	+	0.200474i	$0.0642481\pi$
$151$	15127.7	+	26201.9i	0.663465	+	1.14915i	−0.316234	+	0.948681i	$0.602419\pi$
$152$		0			0
$153$	2903.64	+	5131.48i	0.124040	+	0.219210i
$154$		0			0
$155$	−4198.42	+	2423.96i	−0.174752	+	0.100893i
$156$		0			0
$157$	−10311.4	+	17859.8i	−0.418328	+	0.724565i	−0.995771	−	0.0918653i	$-0.970717\pi$
$157$	−10311.4	+	17859.8i	−0.418328	+	0.724565i	0.577443	+	0.816431i	$0.304050\pi$
$158$		0			0
$159$	−4507.61	−	17119.1i	−0.178300	−	0.677153i
$160$		0			0
$161$			1047.77i			0.0404216i
$162$		0			0
$163$	−39790.7			−1.49764			−0.748818	−	0.662776i	$-0.769378\pi$
$163$	−39790.7			−1.49764			−0.748818	+	0.662776i	$0.769378\pi$
$164$		0			0
$165$	−13409.2	+	3530.76i	−0.492533	+	0.129688i
$166$		0			0
$167$	23773.0	+	13725.3i	0.852414	+	0.492141i	0.861465	−	0.507818i	$-0.169548\pi$
$167$	23773.0	+	13725.3i	0.852414	+	0.492141i	−0.00905084	+	0.999959i	$0.502881\pi$
$168$		0			0
$169$	2436.98	+	4220.97i	0.0853253	+	0.147788i
$170$		0			0
$171$	13440.9	−	7605.51i	0.459659	−	0.260097i
$172$		0			0
$173$	8729.26	−	5039.84i	0.291666	−	0.168393i	−0.347027	−	0.937855i	$-0.612809\pi$
$173$	8729.26	−	5039.84i	0.291666	−	0.168393i	0.638693	+	0.769462i	$0.279475\pi$
$174$		0			0
$175$	13347.0	−	23117.7i	0.435821	−	0.754864i
$176$		0			0
$177$	−47018.8	−	12817.3i	−1.50081	−	0.409120i
$178$		0			0
$179$		−	1215.45i		−	0.0379343i	−0.999820	−	0.0189672i	$-0.993962\pi$
$179$		−	1215.45i		−	0.0379343i	0.999820	−	0.0189672i	$-0.00603779\pi$
$180$		0			0
$181$	28359.9			0.865661			0.432831	−	0.901475i	$-0.357515\pi$
$181$	28359.9			0.865661			0.432831	+	0.901475i	$0.357515\pi$
$182$		0			0
$183$	10850.4	+	10944.9i	0.324000	+	0.326821i
$184$		0			0
$185$	11465.4	+	6619.55i	0.335001	+	0.193413i
$186$		0			0
$187$	−3499.68	−	6061.62i	−0.100079	−	0.173343i
$188$		0			0
$189$	50858.0	+	14338.7i	1.42376	+	0.401408i
$190$		0			0
$191$	8445.34	−	4875.92i	0.231500	−	0.133656i	−0.379764	−	0.925083i	$-0.623995\pi$
$191$	8445.34	−	4875.92i	0.231500	−	0.133656i	0.611264	+	0.791427i	$0.290661\pi$
$192$		0			0
$193$	26701.4	−	46248.2i	0.716836	−	1.24160i	−0.245411	−	0.969419i	$-0.578923\pi$
$193$	26701.4	−	46248.2i	0.716836	−	1.24160i	0.962247	−	0.272177i	$-0.0877436\pi$
$194$		0			0
$195$	−15761.2	+	15625.2i	−0.414497	+	0.410919i
$196$		0			0
$197$			68537.7i			1.76603i	0.469349	+	0.883013i	$0.344489\pi$
$197$			68537.7i			1.76603i	−0.469349	+	0.883013i	$0.655511\pi$
$198$		0			0
$199$	8237.42			0.208010			0.104005	−	0.994577i	$-0.466834\pi$
$199$	8237.42			0.208010			0.104005	+	0.994577i	$0.466834\pi$
$200$		0			0
$201$	−10970.0	+	40242.0i	−0.271527	+	0.996064i
$202$		0			0
$203$	44961.7	+	25958.7i	1.09107	+	0.629927i
$204$		0			0
$205$	4455.24	+	7716.70i	0.106014	+	0.183622i
$206$		0			0
$207$	1170.83	+	10.1503i	0.0273246	+	0.000236884i
$208$		0			0
$209$	−15877.2	+	9166.71i	−0.363481	+	0.209856i
$210$		0			0
$211$	20393.7	−	35322.9i	0.458069	−	0.793399i	−0.540790	−	0.841158i	$-0.681875\pi$
$211$	20393.7	−	35322.9i	0.458069	−	0.793399i	0.998859	+	0.0477587i	$0.0152079\pi$
$212$		0			0
$213$	−15347.6	−	58287.4i	−0.338284	−	1.28474i
$214$		0			0
$215$			14303.1i			0.309423i
$216$		0			0
$217$	−21931.2			−0.465740
$218$		0			0
$219$	−41983.7	+	11054.7i	−0.875371	+	0.230493i
$220$		0			0
$221$	−9701.99	−	5601.45i	−0.198644	−	0.114687i
$222$		0			0
$223$	−29959.8	−	51891.9i	−0.602461	−	1.04349i	−0.992447	−	0.122672i	$-0.960854\pi$
$223$	−29959.8	−	51891.9i	−0.602461	−	1.04349i	0.389986	−	0.920821i	$-0.372480\pi$
$224$		0			0
$225$	−25703.6	−	15138.6i	−0.507725	−	0.299034i
$226$		0			0
$227$	−85572.3	+	49405.2i	−1.66066	+	0.958785i	−0.688265	+	0.725459i	$0.741627\pi$
$227$	−85572.3	+	49405.2i	−1.66066	+	0.958785i	−0.972399	+	0.233325i	$0.925039\pi$
$228$		0			0
$229$	2658.97	−	4605.47i	0.0507040	−	0.0878220i	−0.839559	−	0.543268i	$-0.817187\pi$
$229$	2658.97	−	4605.47i	0.0507040	−	0.0878220i	0.890263	+	0.455446i	$0.150520\pi$
$230$		0			0
$231$	−60520.3	−	16497.9i	−1.13417	−	0.309175i
$232$		0			0
$233$		−	18467.8i		−	0.340176i	−0.985429	−	0.170088i	$-0.945595\pi$
$233$		−	18467.8i		−	0.340176i	0.985429	−	0.170088i	$-0.0544052\pi$
$234$		0			0
$235$	63376.3			1.14760
$236$		0			0
$237$	−36299.5	−	36615.5i	−0.646254	−	0.651881i
$238$		0			0
$239$	−22383.5	−	12923.1i	−0.391861	−	0.226241i	0.291105	−	0.956691i	$-0.405977\pi$
$239$	−22383.5	−	12923.1i	−0.391861	−	0.226241i	−0.682966	+	0.730450i	$0.739310\pi$
$240$		0			0
$241$	−41536.2	−	71942.7i	−0.715142	−	1.23866i	−0.962905	−	0.269841i	$-0.913029\pi$
$241$	−41536.2	−	71942.7i	−0.715142	−	1.23866i	0.247763	−	0.968821i	$-0.420305\pi$
$242$		0			0
$243$	16515.5	−	56692.4i	0.279691	−	0.960090i
$244$		0			0
$245$	−39586.6	+	22855.3i	−0.659502	+	0.380764i
$246$		0			0
$247$	−14671.9	+	25412.4i	−0.240487	+	0.416536i
$248$		0			0
$249$	−18102.2	+	17945.9i	−0.291966	+	0.289446i
$250$		0			0
$251$		−	49051.6i		−	0.778585i	−0.921114	−	0.389292i	$-0.872720\pi$
$251$		−	49051.6i		−	0.778585i	0.921114	−	0.389292i	$-0.127280\pi$
$252$		0			0
$253$	−1389.98			−0.0217154
$254$		0			0
$255$	−2760.65	+	10127.1i	−0.0424553	+	0.155742i
$256$		0			0
$257$	84096.0	+	48552.9i	1.27324	+	0.735104i	0.975596	−	0.219574i	$-0.0704668\pi$
$257$	84096.0	+	48552.9i	1.27324	+	0.735104i	0.297641	+	0.954678i	$0.403800\pi$
$258$		0			0
$259$	29945.8	+	51867.7i	0.446413	+	0.773209i
$260$		0			0
$261$	29443.1	−	49991.0i	0.432217	−	0.733856i
$262$		0			0
$263$	−35921.0	+	20739.0i	−0.519323	+	0.299831i	−0.736658	−	0.676266i	$-0.763597\pi$
$263$	−35921.0	+	20739.0i	−0.519323	+	0.299831i	0.217335	+	0.976097i	$0.430264\pi$
$264$		0			0
$265$	15757.9	−	27293.5i	0.224391	−	0.388657i
$266$		0			0
$267$	−32719.7	−	124264.i	−0.458973	−	1.74310i
$268$		0			0
$269$		−	115737.i		−	1.59944i	−0.600370	−	0.799722i	$-0.704980\pi$
$269$		−	115737.i		−	1.59944i	0.600370	−	0.799722i	$-0.295020\pi$
$270$		0			0
$271$	5077.71			0.0691400			0.0345700	−	0.999402i	$-0.488994\pi$
$271$	5077.71			0.0691400			0.0345700	+	0.999402i	$0.488994\pi$
$272$		0			0
$273$	−97091.7	+	25565.1i	−1.30274	+	0.343022i
$274$		0			0
$275$	30668.2	+	17706.3i	0.405529	+	0.234133i
$276$		0			0
$277$	21192.9	+	36707.2i	0.276205	+	0.478401i	0.970438	−	0.241349i	$-0.0775899\pi$
$277$	21192.9	+	36707.2i	0.276205	+	0.478401i	−0.694234	+	0.719750i	$0.744257\pi$
$278$		0			0
$279$	−212.459	+	24507.1i	−0.00272939	+	0.314835i
$280$		0			0
$281$	−35902.5	+	20728.3i	−0.454687	+	0.262513i	−0.709807	−	0.704396i	$-0.751218\pi$
$281$	−35902.5	+	20728.3i	−0.454687	+	0.262513i	0.255121	+	0.966909i	$0.417885\pi$
$282$		0			0
$283$	19194.0	−	33245.0i	0.239658	−	0.415100i	−0.720958	−	0.692979i	$-0.756298\pi$
$283$	19194.0	−	33245.0i	0.239658	−	0.415100i	0.960616	+	0.277879i	$0.0896313\pi$
$284$		0			0
$285$	26525.9	+	7230.98i	0.326574	+	0.0890241i
$286$		0			0
$287$			40309.6i			0.489378i
$288$		0			0
$289$	78222.5			0.936561
$290$		0			0
$291$	−45401.7	−	45797.0i	−0.536149	−	0.540818i
$292$		0			0
$293$	−11239.5	−	6489.12i	−0.130922	−	0.0755876i	0.433109	−	0.901342i	$-0.357417\pi$
$293$	−11239.5	−	6489.12i	−0.130922	−	0.0755876i	−0.564030	+	0.825754i	$0.690750\pi$
$294$		0			0
$295$	−43380.7	−	75137.6i	−0.498486	−	0.863402i
$296$		0			0
$297$	−19021.8	+	67468.7i	−0.215645	+	0.764873i
$298$		0			0
$299$	−1926.69	+	1112.37i	−0.0215511	+	0.0124425i
$300$		0			0
$301$	−32352.4	+	56036.0i	−0.357086	+	0.618492i
$302$		0			0
$303$	−12522.2	+	12414.1i	−0.136394	+	0.135217i
$304$		0			0
$305$			27437.4i			0.294947i
$306$		0			0
$307$	126105.			1.33799			0.668997	−	0.743265i	$-0.266724\pi$
$307$	126105.			1.33799			0.668997	+	0.743265i	$0.266724\pi$
$308$		0			0
$309$	−12203.2	+	44765.8i	−0.127807	+	0.468845i
$310$		0			0
$311$	86432.4	+	49901.7i	0.893626	+	0.515935i	0.875127	−	0.483894i	$-0.160778\pi$
$311$	86432.4	+	49901.7i	0.893626	+	0.515935i	0.0184989	+	0.999829i	$0.494111\pi$
$312$		0			0
$313$	1112.68	+	1927.21i	0.0113574	+	0.0196716i	0.871648	−	0.490132i	$-0.163051\pi$
$313$	1112.68	+	1927.21i	0.0113574	+	0.0196716i	−0.860291	+	0.509804i	$0.829718\pi$
$314$		0			0
$315$	46327.8	+	81873.1i	0.466896	+	0.825125i
$316$		0			0
$317$	−145552.	+	84034.3i	−1.44843	+	0.836254i	−0.998388	−	0.0567515i	$-0.981926\pi$
$317$	−145552.	+	84034.3i	−1.44843	+	0.836254i	−0.450046	+	0.893005i	$0.648592\pi$
$318$		0			0
$319$	−34437.0	+	59646.6i	−0.338410	+	0.586144i
$320$		0			0
$321$	−20893.3	−	79349.1i	−0.202767	−	0.770073i
$322$		0			0
$323$			13878.3i			0.133024i
$324$		0			0
$325$	56679.9			0.536615
$326$		0			0
$327$	−140655.	+	37035.8i	−1.31541	+	0.346359i
$328$		0			0
$329$	248293.	+	143352.i	2.29389	+	1.32438i
$330$		0			0
$331$	3379.43	+	5853.34i	0.0308452	+	0.0534254i	0.881036	−	0.473049i	$-0.156847\pi$
$331$	3379.43	+	5853.34i	0.0308452	+	0.0534254i	−0.850191	+	0.526475i	$0.823513\pi$
$332$		0			0
$333$	58249.6	−	32960.5i	0.525297	−	0.297239i
$334$		0			0
$335$	−64308.1	+	37128.3i	−0.573028	+	0.330838i
$336$		0			0
$337$	111046.	−	192338.i	0.977787	−	1.69358i	0.307375	−	0.951589i	$-0.400550\pi$
$337$	111046.	−	192338.i	0.977787	−	1.69358i	0.670413	−	0.741988i	$-0.266117\pi$
$338$		0			0
$339$	183208.	+	49942.5i	1.59421	+	0.434581i
$340$		0			0
$341$		−	29094.2i		−	0.250206i
$342$		0			0
$343$	−32754.4			−0.278408
$344$		0			0
$345$	1467.56	+	1480.34i	0.0123298	+	0.0124372i
$346$		0			0
$347$	140770.	+	81273.8i	1.16910	+	0.674981i	0.953468	−	0.301494i	$-0.0974853\pi$
$347$	140770.	+	81273.8i	1.16910	+	0.674981i	0.215633	+	0.976475i	$0.430819\pi$
$348$		0			0
$349$	36348.5	+	62957.4i	0.298425	+	0.516887i	0.975776	−	0.218773i	$-0.0702054\pi$
$349$	36348.5	+	62957.4i	0.298425	+	0.516887i	−0.677351	+	0.735660i	$0.736872\pi$
$350$		0			0
$351$	27627.2	+	108743.i	0.224245	+	0.882646i
$352$		0			0
$353$	111396.	−	64314.6i	0.893966	−	0.516131i	0.0187281	−	0.999825i	$-0.494038\pi$
$353$	111396.	−	64314.6i	0.893966	−	0.516131i	0.875238	+	0.483693i	$0.160705\pi$
$354$		0			0
$355$	53652.7	−	92929.2i	0.425730	−	0.737387i
$356$		0			0
$357$	−33722.3	+	33431.2i	−0.264594	+	0.262310i
$358$		0			0
$359$		−	95302.8i		−	0.739463i	−0.929139	−	0.369732i	$-0.879450\pi$
$359$		−	95302.8i		−	0.739463i	0.929139	−	0.369732i	$-0.120550\pi$
$360$		0			0
$361$	−93969.7			−0.721063
$362$		0			0
$363$	−12769.5	+	46843.2i	−0.0969081	+	0.355495i
$364$		0			0
$365$	−66935.7	−	38645.4i	−0.502426	−	0.290076i
$366$		0			0
$367$	52073.0	+	90193.1i	0.386616	+	0.669639i	0.991992	−	0.126301i	$-0.0403104\pi$
$367$	52073.0	+	90193.1i	0.386616	+	0.669639i	−0.605376	+	0.795940i	$0.706977\pi$
$368$		0			0
$369$	45043.9	+	390.499i	0.330814	+	0.00286792i
$370$		0			0
$371$	123471.	−	71286.2i	0.897053	−	0.517914i
$372$		0			0
$373$	−122915.	+	212896.i	−0.883463	+	1.53020i	−0.0359975	+	0.999352i	$0.511461\pi$
$373$	−122915.	+	212896.i	−0.883463	+	1.53020i	−0.847465	+	0.530851i	$0.821872\pi$
$374$		0			0
$375$	−36471.6	−	138513.i	−0.259354	−	0.984979i
$376$		0			0
$377$			110237.i			0.775612i
$378$		0			0
$379$	−200830.			−1.39814			−0.699070	−	0.715053i	$-0.746403\pi$
$379$	−200830.			−1.39814			−0.699070	+	0.715053i	$0.746403\pi$
$380$		0			0
$381$	179819.	−	47347.9i	1.23875	−	0.326175i
$382$		0			0
$383$	−117206.	−	67668.8i	−0.799008	−	0.461308i	0.0441160	−	0.999026i	$-0.485953\pi$
$383$	−117206.	−	67668.8i	−0.799008	−	0.461308i	−0.843124	+	0.537719i	$0.819286\pi$
$384$		0			0
$385$	−55837.6	−	96713.6i	−0.376708	−	0.652478i
$386$		0			0
$387$	62304.0	+	36695.0i	0.416001	+	0.245011i
$388$		0			0
$389$	−175090.	+	101088.i	−1.15708	+	0.668039i	−0.950602	−	0.310413i	$-0.899533\pi$
$389$	−175090.	+	101088.i	−1.15708	+	0.668039i	−0.206475	+	0.978452i	$0.566199\pi$
$390$		0			0
$391$	−526.102	+	911.236i	−0.00344125	+	0.00596043i
$392$		0			0
$393$	−27798.7	−	7577.92i	−0.179986	−	0.0490642i
$394$		0			0
$395$		−	91790.2i		−	0.588304i
$396$		0			0
$397$	102384.			0.649608			0.324804	−	0.945781i	$-0.394702\pi$
$397$	102384.			0.649608			0.324804	+	0.945781i	$0.394702\pi$
$398$		0			0
$399$	87566.4	+	88328.8i	0.550037	+	0.554826i
$400$		0			0
$401$	−78026.4	−	45048.6i	−0.485236	−	0.280151i	0.237360	−	0.971422i	$-0.423718\pi$
$401$	−78026.4	−	45048.6i	−0.485236	−	0.280151i	−0.722596	+	0.691271i	$0.757051\pi$
$402$		0			0
$403$	−23283.5	−	40328.2i	−0.143363	−	0.248313i
$404$		0			0
$405$	91937.9	−	50975.9i	0.560512	−	0.310781i
$406$		0			0
$407$	−68808.1	+	39726.4i	−0.415385	+	0.239823i
$408$		0			0
$409$	−74861.0	+	129663.i	−0.447517	+	0.775122i	−0.998224	−	0.0595770i	$-0.981025\pi$
$409$	−74861.0	+	129663.i	−0.447517	+	0.775122i	0.550707	+	0.834699i	$0.314358\pi$
$410$		0			0
$411$	−24747.3	+	24533.7i	−0.146502	+	0.145238i
$412$		0			0
$413$		−	392495.i		−	2.30109i
$414$		0			0
$415$	−45379.7			−0.263491
$416$		0			0
$417$	−27645.1	+	101413.i	−0.158981	+	0.583203i
$418$		0			0
$419$	−109423.	−	63175.3i	−0.623276	−	0.359848i	0.154868	−	0.987935i	$-0.450505\pi$
$419$	−109423.	−	63175.3i	−0.623276	−	0.359848i	−0.778143	+	0.628087i	$0.783838\pi$
$420$		0			0
$421$	107645.	+	186446.i	0.607335	+	1.05194i	0.991678	+	0.128745i	$0.0410949\pi$
$421$	107645.	+	186446.i	0.607335	+	1.05194i	−0.384342	+	0.923191i	$0.625572\pi$
$422$		0			0
$423$	162594.	−	276067.i	0.908709	−	1.54288i
$424$		0			0
$425$	23215.6	−	13403.5i	0.128529	−	0.0742063i
$426$		0			0
$427$	−62061.3	+	107493.i	−0.340381	+	0.589557i
$428$		0			0
$429$	−33914.9	−	128803.i	−0.184279	−	0.699859i
$430$		0			0
$431$			121972.i			0.656607i	0.944572	+	0.328304i	$0.106477\pi$
$431$			121972.i			0.656607i	−0.944572	+	0.328304i	$0.893523\pi$
$432$		0			0
$433$	−152419.			−0.812951			−0.406475	−	0.913662i	$-0.633242\pi$
$433$	−152419.			−0.812951			−0.406475	+	0.913662i	$0.633242\pi$
$434$		0			0
$435$	99882.9	−	26300.0i	0.527853	−	0.138988i
$436$		0			0
$437$	2386.80	+	1378.02i	0.0124984	+	0.00721593i
$438$		0			0
$439$	115564.	+	200162.i	0.599643	+	1.03861i	0.992874	+	0.119173i	$0.0380242\pi$
$439$	115564.	+	200162.i	0.599643	+	1.03861i	−0.393230	+	0.919440i	$0.628642\pi$
$440$		0			0
$441$	−2003.26	+	231075.i	−0.0103005	+	1.18816i
$442$		0			0
$443$	17481.4	−	10092.9i	0.0890774	−	0.0514289i	−0.454800	−	0.890594i	$-0.650289\pi$
$443$	17481.4	−	10092.9i	0.0890774	−	0.0514289i	0.543877	+	0.839165i	$0.316956\pi$
$444$		0			0
$445$	114383.	−	198117.i	0.577618	−	1.00046i
$446$		0			0
$447$	−131044.	−	35722.7i	−0.655847	−	0.178784i
$448$		0			0
$449$		−	92962.8i		−	0.461123i	−0.973058	−	0.230561i	$-0.925944\pi$
$449$		−	92962.8i		−	0.461123i	0.973058	−	0.230561i	$-0.0740562\pi$
$450$		0			0
$451$	−53475.0			−0.262905
$452$		0			0
$453$	191707.	+	193376.i	0.934205	+	0.942339i
$454$		0			0
$455$	−154796.	−	89371.5i	−0.747716	−	0.431694i
$456$		0			0
$457$	−110443.	−	191293.i	−0.528819	−	0.915941i	−0.999435	−	0.0336033i	$-0.989302\pi$
$457$	−110443.	−	191293.i	−0.528819	−	0.915941i	0.470616	−	0.882338i	$-0.344032\pi$
$458$		0			0
$459$	37031.0	+	38006.9i	0.175768	+	0.180400i
$460$		0			0
$461$	91967.2	−	53097.3i	0.432744	−	0.249845i	−0.267771	−	0.963483i	$-0.586287\pi$
$461$	91967.2	−	53097.3i	0.432744	−	0.249845i	0.700515	+	0.713638i	$0.252954\pi$
$462$		0			0
$463$	−34090.0	+	59045.5i	−0.159025	+	0.275439i	−0.934517	−	0.355918i	$-0.884168\pi$
$463$	−34090.0	+	59045.5i	−0.159025	+	0.275439i	0.775493	+	0.631357i	$0.217502\pi$
$464$		0			0
$465$	−30985.4	+	30718.0i	−0.143302	+	0.142065i
$466$		0			0
$467$		−	224350.i		−	1.02871i	−0.857578	−	0.514353i	$-0.828032\pi$
$467$		−	224350.i		−	1.02871i	0.857578	−	0.514353i	$-0.171968\pi$
$468$		0			0
$469$	−335925.			−1.52720
$470$		0			0
$471$	−48814.7	+	179070.i	−0.220043	+	0.807202i
$472$		0			0
$473$	−74337.9	−	42919.0i	−0.332267	−	0.191835i
$474$		0			0
$475$	−35107.8	−	60808.5i	−0.155603	−	0.269511i
$476$		0			0
$477$	−78462.7	−	138664.i	−0.344847	−	0.609433i
$478$		0			0
$479$	94542.7	−	54584.3i	0.412057	−	0.237901i	−0.279616	−	0.960112i	$-0.590207\pi$
$479$	94542.7	−	54584.3i	0.412057	−	0.237901i	0.691673	+	0.722211i	$0.256874\pi$
$480$		0			0
$481$	−63584.5	+	110132.i	−0.274828	+	0.476016i
$482$		0			0
$483$	2401.14	+	9119.10i	0.0102926	+	0.0390893i
$484$		0			0
$485$		−	114807.i		−	0.488073i
$486$		0			0
$487$	−106309.			−0.448240			−0.224120	−	0.974562i	$-0.571951\pi$
$487$	−106309.			−0.448240			−0.224120	+	0.974562i	$0.571951\pi$
$488$		0			0
$489$	−346312.	+	91187.0i	−1.44827	+	0.381343i
$490$		0			0
$491$	64472.7	+	37223.3i	0.267432	+	0.154402i	0.627720	−	0.778439i	$-0.283988\pi$
$491$	64472.7	+	37223.3i	0.267432	+	0.154402i	−0.360288	+	0.932841i	$0.617322\pi$
$492$		0			0
$493$	26068.5	+	45152.0i	0.107256	+	0.185773i
$494$		0			0
$495$	−108614.	+	61458.9i	−0.443275	+	0.250827i
$496$		0			0
$497$	420397.	−	242716.i	1.70195	−	0.982621i
$498$		0			0
$499$	−55603.4	+	96308.0i	−0.223306	+	0.386777i	−0.955810	−	0.293985i	$-0.905018\pi$
$499$	−55603.4	+	96308.0i	−0.223306	+	0.386777i	0.732504	+	0.680763i	$0.238352\pi$
$500$		0			0
$501$	238358.	+	64976.6i	0.949631	+	0.258870i
$502$		0			0
$503$		−	115897.i		−	0.458077i	−0.973417	−	0.229038i	$-0.926442\pi$
$503$		−	115897.i		−	0.458077i	0.973417	−	0.229038i	$-0.0735581\pi$
$504$		0			0
$505$	−31391.5			−0.123092
$506$		0			0
$507$	30882.9	+	31151.8i	0.120144	+	0.121190i
$508$		0			0
$509$	−170299.	−	98322.1i	−0.657319	−	0.379503i	0.133936	−	0.990990i	$-0.457238\pi$
$509$	−170299.	−	98322.1i	−0.657319	−	0.379503i	−0.791255	+	0.611487i	$0.790572\pi$
$510$		0			0
$511$	−174825.	−	302807.i	−0.669519	−	1.15964i
$512$		0			0
$513$	99551.4	−	96995.4i	0.378279	−	0.368567i
$514$		0			0
$515$	−71537.3	+	41302.1i	−0.269723	+	0.155725i
$516$		0			0
$517$	−190172.	+	329388.i	−0.711486	+	1.23233i
$518$		0			0
$519$	64424.2	−	63868.1i	0.239174	−	0.237110i
$520$		0			0
$521$			299306.i			1.10266i	0.834289	+	0.551328i	$0.185879\pi$
$521$			299306.i			1.10266i	−0.834289	+	0.551328i	$0.814121\pi$
$522$		0			0
$523$	162892.			0.595520			0.297760	−	0.954641i	$-0.403760\pi$
$523$	162892.			0.595520			0.297760	+	0.954641i	$0.403760\pi$
$524$		0			0
$525$	63185.6	−	231788.i	0.229245	−	0.840955i
$526$		0			0
$527$	−19073.4	−	11012.0i	−0.0686763	−	0.0396503i
$528$		0			0
$529$	−139816.	−	242168.i	−0.499627	−	0.865379i
$530$		0			0
$531$	−438594.	−	3802.29i	−1.55551	−	0.0134852i
$532$		0			0
$533$	−74123.1	+	42795.0i	−0.260915	+	0.150639i
$534$		0			0
$535$	73039.7	−	126508.i	0.255183	−	0.441989i
$536$		0			0
$537$	−2785.41	−	10578.5i	−0.00965920	−	0.0366839i
$538$		0			0
$539$		−	274327.i		−	0.944257i
$540$		0			0
$541$	−62918.7			−0.214974			−0.107487	−	0.994207i	$-0.534280\pi$
$541$	−62918.7			−0.214974			−0.107487	+	0.994207i	$0.534280\pi$
$542$		0			0
$543$	246826.	−	64991.5i	0.837128	−	0.220423i
$544$		0			0
$545$	−224251.	−	129471.i	−0.754989	−	0.435893i
$546$		0			0
$547$	−7403.57	−	12823.4i	−0.0247438	−	0.0428575i	0.853388	−	0.521276i	$-0.174544\pi$
$547$	−7403.57	−	12823.4i	−0.0247438	−	0.0428575i	−0.878132	+	0.478418i	$0.841210\pi$
$548$		0			0
$549$	119517.	+	70391.8i	0.396539	+	0.233549i
$550$		0			0
$551$	118267.	−	68281.3i	0.389547	−	0.224905i
$552$		0			0
$553$	207622.	−	359612.i	0.678927	−	1.17594i
$554$		0			0
$555$	114957.	+	31337.4i	0.373207	+	0.101736i
$556$		0			0
$557$			254392.i			0.819962i	0.912094	+	0.409981i	$0.134465\pi$
$557$			254392.i			0.819962i	−0.912094	+	0.409981i	$0.865535\pi$
$558$		0			0
$559$	−137389.			−0.439671
$560$		0			0
$561$	−44350.2	−	44736.3i	−0.140919	−	0.142146i
$562$		0			0
$563$	−80806.7	−	46653.8i	−0.254936	−	0.147187i	0.367087	−	0.930187i	$-0.380355\pi$
$563$	−80806.7	−	46653.8i	−0.254936	−	0.147187i	−0.622022	+	0.783000i	$0.713689\pi$
$564$		0			0
$565$	169032.	+	292772.i	0.529508	+	0.917134i
$566$		0			0
$567$	475494.	+	8245.01i	1.47904	+	0.0256463i
$568$		0			0
$569$	−136853.	+	79012.1i	−0.422698	+	0.244045i	−0.696231	−	0.717818i	$-0.745141\pi$
$569$	−136853.	+	79012.1i	−0.422698	+	0.244045i	0.273533	+	0.961863i	$0.411808\pi$
$570$		0			0
$571$	−219188.	+	379644.i	−0.672270	+	1.16441i	0.304988	+	0.952356i	$0.401347\pi$
$571$	−219188.	+	379644.i	−0.672270	+	1.16441i	−0.977259	+	0.212050i	$0.931986\pi$
$572$		0			0
$573$	62328.8	−	61790.8i	0.189836	−	0.188198i
$574$		0			0
$575$		−	5323.52i		−	0.0161014i
$576$		0			0
$577$	214770.			0.645094			0.322547	−	0.946554i	$-0.395461\pi$
$577$	214770.			0.645094			0.322547	+	0.946554i	$0.395461\pi$
$578$		0			0
$579$	126406.	−	463705.i	0.377061	−	1.38320i
$580$		0			0
$581$	−177787.	−	102645.i	−0.526681	−	0.304079i
$582$		0			0
$583$	94568.9	+	163798.i	0.278235	+	0.481917i
$584$		0			0
$585$	−101368.	+	172111.i	−0.296202	+	0.502918i
$586$		0			0
$587$	−568470.	+	328206.i	−1.64980	+	0.952512i	−0.672649	+	0.739962i	$0.734843\pi$
$587$	−568470.	+	328206.i	−1.64980	+	0.952512i	−0.977150	+	0.212550i	$0.931823\pi$
$588$		0			0
$589$	−28843.8	+	49959.0i	−0.0831423	+	0.144007i
$590$		0			0
$591$	157066.	+	596507.i	0.449683	+	1.70781i
$592$		0			0
$593$		−	118369.i		−	0.336612i	−0.985735	−	0.168306i	$-0.946170\pi$
$593$		−	118369.i		−	0.336612i	0.985735	−	0.168306i	$-0.0538296\pi$
$594$		0			0
$595$	−84537.3			−0.238789
$596$		0			0
$597$	71693.1	−	18877.4i	0.201154	−	0.0529656i
$598$		0			0
$599$	306693.	+	177069.i	0.854772	+	0.493503i	0.862258	−	0.506469i	$-0.169050\pi$
$599$	306693.	+	177069.i	0.854772	+	0.493503i	−0.00748620	+	0.999972i	$0.502383\pi$
$600$		0			0
$601$	297820.	+	515839.i	0.824526	+	1.42812i	0.902281	+	0.431148i	$0.141891\pi$
$601$	297820.	+	515839.i	0.824526	+	1.42812i	−0.0777554	+	0.996972i	$0.524775\pi$
$602$		0			0
$603$	−3254.27	+	375379.i	−0.00894992	+	1.03237i
$604$		0			0
$605$	−74857.1	+	43218.8i	−0.204514	+	0.118076i
$606$		0			0
$607$	4860.81	−	8419.17i	0.0131926	−	0.0228503i	−0.859354	−	0.511382i	$-0.829134\pi$
$607$	4860.81	−	8419.17i	0.0131926	−	0.0228503i	0.872546	+	0.488531i	$0.162467\pi$
$608$		0			0
$609$	450806.	+	122890.i	1.21550	+	0.331346i
$610$		0			0
$611$			608765.i			1.63067i
$612$		0			0
$613$	194450.			0.517473			0.258736	−	0.965948i	$-0.416694\pi$
$613$	194450.			0.517473			0.258736	+	0.965948i	$0.416694\pi$
$614$		0			0
$615$	56459.6	+	56951.2i	0.149275	+	0.150575i
$616$		0			0
$617$	422308.	+	243819.i	1.10932	+	0.640469i	0.938654	−	0.344860i	$-0.112073\pi$
$617$	422308.	+	243819.i	1.10932	+	0.640469i	0.170670	+	0.985328i	$0.445407\pi$
$618$		0			0
$619$	8628.23	+	14944.5i	0.0225185	+	0.0390033i	0.877065	−	0.480372i	$-0.159498\pi$
$619$	8628.23	+	14944.5i	0.0225185	+	0.0390033i	−0.854547	+	0.519375i	$0.826165\pi$
$620$		0			0
$621$	10213.4	−	2594.81i	0.0264842	−	0.00672857i
$622$		0			0
$623$	896249.	−	517449.i	2.30915	−	1.33319i
$624$		0			0
$625$	12412.5	−	21499.1i	0.0317760	−	0.0550376i
$626$		0			0
$627$	−117178.	+	116166.i	−0.298065	+	0.295492i
$628$		0			0
$629$			60145.1i			0.152019i
$630$		0			0
$631$	429836.			1.07955			0.539777	−	0.841808i	$-0.318509\pi$
$631$	429836.			1.07955			0.539777	+	0.841808i	$0.318509\pi$
$632$		0			0
$633$	96545.0	−	354163.i	0.240948	−	0.883886i
$634$		0			0
$635$	286690.	+	165521.i	0.710993	+	0.410492i
$636$		0			0
$637$	−219538.	−	380251.i	−0.541042	−	0.937113i
$638$		0			0
$639$	−267151.	−	472124.i	−0.654266	−	1.15626i
$640$		0			0
$641$	−27979.5	+	16154.0i	−0.0680964	+	0.0393155i	−0.533662	−	0.845698i	$-0.679184\pi$
$641$	−27979.5	+	16154.0i	−0.0680964	+	0.0393155i	0.465565	+	0.885014i	$0.345851\pi$
$642$		0			0
$643$	138524.	−	239931.i	0.335045	−	0.580315i	−0.648448	−	0.761259i	$-0.724582\pi$
$643$	138524.	−	239931.i	0.335045	−	0.580315i	0.983494	+	0.180943i	$0.0579150\pi$
$644$		0			0
$645$	32777.9	+	124485.i	0.0787882	+	0.299224i
$646$		0			0
$647$			125452.i			0.299689i	0.988710	+	0.149844i	$0.0478773\pi$
$647$			125452.i			0.299689i	−0.988710	+	0.149844i	$0.952123\pi$
$648$		0			0
$649$	520687.			1.23620
$650$		0			0
$651$	−190875.	+	50259.1i	−0.450388	+	0.118591i
$652$		0			0
$653$	245936.	+	141991.i	0.576760	+	0.332992i	0.759845	−	0.650105i	$-0.225275\pi$
$653$	245936.	+	141991.i	0.576760	+	0.332992i	−0.183085	+	0.983097i	$0.558608\pi$
$654$		0			0
$655$	−25647.8	−	44423.2i	−0.0597815	−	0.103545i
$656$		0			0
$657$	−340065.	+	192425.i	−0.787828	+	0.445791i
$658$		0			0
$659$	−311139.	+	179636.i	−0.716446	+	0.413640i	−0.813443	−	0.581644i	$-0.802410\pi$
$659$	−311139.	+	179636.i	−0.716446	+	0.413640i	0.0969973	+	0.995285i	$0.469076\pi$
$660$		0			0
$661$	−98902.1	+	171303.i	−0.226362	+	0.392070i	−0.956727	−	0.290987i	$-0.906016\pi$
$661$	−98902.1	+	171303.i	−0.226362	+	0.392070i	0.730366	+	0.683057i	$0.239350\pi$
$662$		0			0
$663$	−97276.5	−	26517.6i	−0.221300	−	0.0603264i
$664$		0			0
$665$			221429.i			0.500715i
$666$		0			0
$667$	10353.7			0.0232726
$668$		0			0
$669$	−379669.	−	382975.i	−0.848307	−	0.855693i
$670$		0			0
$671$	−142602.	−	82331.1i	−0.316723	−	0.182860i
$672$		0			0
$673$	−119036.	−	206176.i	−0.262814	−	0.455207i	0.704175	−	0.710027i	$-0.251317\pi$
$673$	−119036.	−	206176.i	−0.262814	−	0.455207i	−0.966989	+	0.254820i	$0.917984\pi$
$674$		0			0
$675$	−258400.	−	72852.2i	−0.567133	−	0.159895i
$676$		0			0
$677$	216636.	−	125075.i	0.472666	−	0.272894i	−0.244689	−	0.969602i	$-0.578686\pi$
$677$	216636.	−	125075.i	0.472666	−	0.272894i	0.717355	+	0.696708i	$0.245353\pi$
$678$		0			0
$679$	259684.	−	449786.i	0.563256	−	0.975588i
$680$		0			0
$681$	−631545.	+	626094.i	−1.36179	+	1.35004i
$682$		0			0
$683$		−	267358.i		−	0.573129i	−0.958061	−	0.286564i	$-0.907487\pi$
$683$		−	267358.i		−	0.573129i	0.958061	−	0.286564i	$-0.0925132\pi$
$684$		0			0
$685$	−62038.2			−0.132214
$686$		0			0
$687$	12587.7	−	46176.5i	0.0266707	−	0.0978380i
$688$		0			0
$689$	262169.	+	151363.i	0.552259	+	0.318847i
$690$		0			0
$691$	168343.	+	291579.i	0.352565	+	0.610660i	0.986698	−	0.162564i	$-0.0519763\pi$
$691$	168343.	+	291579.i	0.352565	+	0.610660i	−0.634133	+	0.773224i	$0.718643\pi$
$692$		0			0
$693$	−564537.	−	4894.13i	−1.17551	−	0.0101908i
$694$		0			0
$695$	−162061.	+	93565.9i	−0.335513	+	0.193708i
$696$		0			0
$697$	−20240.1	+	35056.9i	−0.0416627	+	0.0721618i
$698$		0			0
$699$	−42322.1	−	160732.i	−0.0866189	−	0.328963i
$700$		0			0
$701$			635795.i			1.29384i	0.762557	+	0.646921i	$0.223944\pi$
$701$			635795.i			1.29384i	−0.762557	+	0.646921i	$0.776056\pi$
$702$		0			0
$703$	157538.			0.318768
$704$		0			0
$705$	551586.	−	145237.i	1.10978	−	0.292214i
$706$		0			0
$707$	−122984.	−	71005.0i	−0.246043	−	0.142053i
$708$		0			0
$709$	−215513.	−	373280.i	−0.428728	−	0.742578i	0.568033	−	0.823006i	$-0.307705\pi$
$709$	−215513.	−	373280.i	−0.428728	−	0.742578i	−0.996760	+	0.0804279i	$0.974371\pi$
$710$		0			0
$711$	−399837.	−	235491.i	−0.790941	−	0.465839i
$712$		0			0
$713$	−3787.73	+	2186.84i	−0.00745074	+	0.00430169i
$714$		0			0
$715$	118561.	−	205354.i	0.231916	−	0.401690i
$716$		0			0
$717$	−224427.	−	61178.9i	−0.436553	−	0.119004i
$718$		0			0
$719$			798370.i			1.54435i	0.635409	+	0.772176i	$0.280832\pi$
$719$			798370.i			1.54435i	−0.635409	+	0.772176i	$0.719168\pi$
$720$		0			0
$721$	−373688.			−0.718850
$722$		0			0
$723$	−526372.	−	530956.i	−1.00697	−	1.01574i
$724$		0			0
$725$	−228442.	−	131891.i	−0.434610	−	0.250922i
$726$		0			0
$727$	158557.	+	274628.i	0.299996	+	0.519609i	0.976135	−	0.217166i	$-0.0696812\pi$
$727$	158557.	+	274628.i	0.299996	+	0.519609i	−0.676139	+	0.736775i	$0.736348\pi$
$728$		0			0
$729$	13819.7	−	531261.i	0.0260043	−	0.999662i
$730$		0			0
$731$	−56273.2	+	32489.3i	−0.105309	+	0.0608004i
$732$		0			0
$733$	488922.	−	846837.i	0.909979	−	1.57613i	0.0958883	−	0.995392i	$-0.469431\pi$
$733$	488922.	−	846837.i	0.909979	−	1.57613i	0.814091	−	0.580738i	$-0.197236\pi$
$734$		0			0
$735$	−292159.	+	289637.i	−0.540810	+	0.536142i
$736$		0			0
$737$		−	445641.i		−	0.820446i
$738$		0			0
$739$	392565.			0.718825			0.359412	−	0.933179i	$-0.382977\pi$
$739$	392565.			0.718825			0.359412	+	0.933179i	$0.382977\pi$
$740$		0			0
$741$	−69457.6	+	254796.i	−0.126498	+	0.464041i
$742$		0			0
$743$	−899450.	−	519298.i	−1.62929	−	0.940673i	−0.984304	−	0.176482i	$-0.943528\pi$
$743$	−899450.	−	519298.i	−1.62929	−	0.940673i	−0.644990	−	0.764191i	$-0.723139\pi$
$744$		0			0
$745$	−120905.	−	209413.i	−0.217836	−	0.377304i
$746$		0			0
$747$	−116423.	+	197674.i	−0.208641	+	0.354248i
$748$		0			0
$749$	572304.	−	330420.i	1.02015	−	0.588983i
$750$		0			0
$751$	159783.	−	276752.i	0.283302	−	0.490694i	−0.688894	−	0.724862i	$-0.741903\pi$
$751$	159783.	−	276752.i	0.283302	−	0.490694i	0.972196	+	0.234168i	$0.0752367\pi$
$752$		0			0
$753$	−112410.	−	426913.i	−0.198251	−	0.752921i
$754$		0			0
$755$			484769.i			0.850435i
$756$		0			0
$757$	500321.			0.873085			0.436543	−	0.899684i	$-0.356203\pi$
$757$	500321.			0.873085			0.436543	+	0.899684i	$0.356203\pi$
$758$		0			0
$759$	−12097.5	+	3185.37i	−0.0209996	+	0.00552939i
$760$		0			0
$761$	−783645.	−	452437.i	−1.35316	−	0.781249i	−0.364471	−	0.931215i	$-0.618750\pi$
$761$	−783645.	−	452437.i	−1.35316	−	0.781249i	−0.988691	+	0.149966i	$0.952083\pi$
$762$		0			0
$763$	−585707.	−	1.01447e6i	−1.00608	−	1.74258i
$764$		0			0
$765$	−818.955	+	94466.2i	−0.00139938	+	0.161419i
$766$		0			0
$767$	721738.	−	416696.i	1.22684	−	0.708318i
$768$		0			0
$769$	−71688.6	+	124168.i	−0.121227	+	0.209970i	−0.920252	−	0.391327i	$-0.872016\pi$
$769$	−71688.6	+	124168.i	−0.121227	+	0.209970i	0.799025	+	0.601298i	$0.205349\pi$
$770$		0			0
$771$	843184.	+	229852.i	1.41845	+	0.386670i
$772$		0			0
$773$			710063.i			1.18833i	0.804342	+	0.594166i	$0.202518\pi$
$773$			710063.i			1.18833i	−0.804342	+	0.594166i	$0.797482\pi$
$774$		0			0
$775$	111428.			0.185521
$776$		0			0
$777$	379492.	+	382796.i	0.628580	+	0.634053i
$778$		0			0
$779$	91824.5	+	53014.9i	0.151316	+	0.0873621i
$780$		0			0
$781$	321990.	+	557702.i	0.527885	+	0.914324i
$782$		0			0
$783$	141691.	−	502563.i	0.231109	−	0.819723i
$784$		0			0
$785$	−286161.	+	165215.i	−0.464377	+	0.268108i
$786$		0			0
$787$	−300855.	+	521097.i	−0.485745	+	0.841335i	−0.999866	−	0.0163827i	$-0.994785\pi$
$787$	−300855.	+	521097.i	−0.485745	+	0.841335i	0.514121	+	0.857718i	$0.328118\pi$
$788$		0			0
$789$	−265106.	+	262818.i	−0.425859	+	0.422183i
$790$		0			0
$791$			1.52935e6i			2.44429i
$792$		0			0
$793$	−263552.			−0.419102
$794$		0			0
$795$	74598.8	−	273656.i	0.118031	−	0.432983i
$796$		0			0
$797$	−372227.	−	214905.i	−0.585991	−	0.338322i	0.177519	−	0.984117i	$-0.443193\pi$
$797$	−372227.	−	214905.i	−0.585991	−	0.338322i	−0.763511	+	0.645795i	$0.776526\pi$
$798$		0			0
$799$	143959.	+	249344.i	0.225499	+	0.390576i
$800$		0			0
$801$	−569542.	−	1.00653e6i	−0.887688	−	1.56877i
$802$		0			0
$803$	401706.	−	231925.i	0.622984	−	0.359680i
$804$		0			0
$805$	−8393.99	+	14538.8i	−0.0129532	+	0.0224356i
$806$		0			0
$807$	−265232.	−	1.00730e6i	−0.407266	−	1.54672i
$808$		0			0
$809$			629639.i			0.962042i	0.876709	+	0.481021i	$0.159734\pi$
$809$			629639.i			0.962042i	−0.876709	+	0.481021i	$0.840266\pi$
$810$		0			0
$811$	−577760.			−0.878428			−0.439214	−	0.898383i	$-0.644743\pi$
$811$	−577760.			−0.878428			−0.439214	+	0.898383i	$0.644743\pi$
$812$		0			0
$813$	44193.1	−	11636.4i	0.0668610	−	0.0176051i
$814$		0			0
$815$	−552135.	−	318775.i	−0.831246	−	0.479920i
$816$		0			0
$817$	85099.3	+	147396.i	0.127492	+	0.220822i
$818$		0			0
$819$	−786436.	+	445004.i	−1.17245	+	0.663431i
$820$		0			0
$821$	38728.3	−	22359.8i	0.0574569	−	0.0331727i	−0.470996	−	0.882135i	$-0.656106\pi$
$821$	38728.3	−	22359.8i	0.0574569	−	0.0331727i	0.528453	+	0.848962i	$0.322772\pi$
$822$		0			0
$823$	−146289.	+	253380.i	−0.215979	+	0.374087i	−0.953575	−	0.301155i	$-0.902628\pi$
$823$	−146289.	+	253380.i	−0.215979	+	0.374087i	0.737596	+	0.675242i	$0.235961\pi$
$824$		0			0
$825$	307493.	+	83822.6i	0.451780	+	0.123155i
$826$		0			0
$827$		−	806491.i		−	1.17920i	−0.807694	−	0.589601i	$-0.799285\pi$
$827$		−	806491.i		−	1.17920i	0.807694	−	0.589601i	$-0.200715\pi$
$828$		0			0
$829$	204904.			0.298154			0.149077	−	0.988826i	$-0.452370\pi$
$829$	204904.			0.298154			0.149077	+	0.988826i	$0.452370\pi$
$830$		0			0
$831$	268570.	+	270908.i	0.388916	+	0.392302i
$832$		0			0
$833$	−179842.	−	103832.i	−0.259179	−	0.149637i
$834$		0			0
$835$	219915.	+	380905.i	0.315415	+	0.546315i
$836$		0			0
$837$	54313.0	+	213780.i	0.0775269	+	0.305152i
$838$		0			0
$839$	−667796.	+	385552.i	−0.948681	+	0.547721i	−0.892671	−	0.450709i	$-0.851171\pi$
$839$	−667796.	+	385552.i	−0.948681	+	0.547721i	−0.0560100	+	0.998430i	$0.517838\pi$
$840$		0			0
$841$	−97125.1	+	168226.i	−0.137322	+	0.237848i
$842$		0			0
$843$	−264970.	+	262682.i	−0.372856	+	0.369637i
$844$		0			0
$845$			78093.4i			0.109371i
$846$		0			0
$847$	−391030.			−0.545058
$848$		0			0
$849$	90865.5	−	333329.i	0.126062	−	0.462442i
$850$		0			0
$851$	10343.8	+	5972.02i	0.0142831	+	0.00824635i
$852$		0			0
$853$	−541184.	−	937358.i	−0.743784	−	1.28827i	−0.950761	−	0.309925i	$-0.899696\pi$
$853$	−541184.	−	937358.i	−0.743784	−	1.28827i	0.206977	−	0.978346i	$-0.433637\pi$
$854$		0			0
$855$	247435.	+	2145.09i	0.338477	+	0.00293436i
$856$		0			0
$857$	−461890.	+	266672.i	−0.628893	+	0.363092i	−0.780323	−	0.625376i	$-0.784945\pi$
$857$	−461890.	+	266672.i	−0.628893	+	0.363092i	0.151430	+	0.988468i	$0.451612\pi$
$858$		0			0
$859$	565525.	−	979517.i	0.766417	−	1.32747i	−0.173077	−	0.984908i	$-0.555371\pi$
$859$	565525.	−	979517.i	0.766417	−	1.32747i	0.939494	−	0.342565i	$-0.111296\pi$
$860$		0			0
$861$	92376.1	+	350828.i	0.124610	+	0.473247i
$862$		0			0
$863$			110025.i			0.147730i	0.997268	+	0.0738649i	$0.0235334\pi$
$863$			110025.i			0.147730i	−0.997268	+	0.0738649i	$0.976467\pi$
$864$		0			0
$865$	161503.			0.215848
$866$		0			0
$867$	680798.	−	179260.i	0.905691	−	0.238476i
$868$		0			0
$869$	477065.	+	275433.i	0.631739	+	0.364735i
$870$		0			0
$871$	−356638.	−	617715.i	−0.470101	−	0.814238i
$872$		0			0
$873$	−500098.	−	294541.i	−0.656185	−	0.386472i
$874$		0			0
$875$	999020.	−	576784.i	1.30484	−	0.753351i
$876$		0			0
$877$	204377.	−	353991.i	0.265725	−	0.460249i	−0.702028	−	0.712149i	$-0.747722\pi$
$877$	204377.	−	353991.i	0.265725	−	0.460249i	0.967753	+	0.251900i	$0.0810554\pi$
$878$		0			0
$879$	−112692.	−	30719.9i	−0.145853	−	0.0397596i
$880$		0			0
$881$			235809.i			0.303815i	0.988395	+	0.151907i	$0.0485416\pi$
$881$			235809.i			0.303815i	−0.988395	+	0.151907i	$0.951458\pi$
$882$		0			0
$883$	273719.			0.351061			0.175531	−	0.984474i	$-0.443836\pi$
$883$	273719.			0.351061			0.175531	+	0.984474i	$0.443836\pi$
$884$		0			0
$885$	−549748.	−	554534.i	−0.701903	−	0.708014i
$886$		0			0
$887$	−322071.	−	185948.i	−0.409359	−	0.236344i	0.281155	−	0.959662i	$-0.409282\pi$
$887$	−322071.	−	185948.i	−0.409359	−	0.236344i	−0.690514	+	0.723319i	$0.742616\pi$
$888$		0			0
$889$	748789.	+	1.29694e6i	0.947449	+	1.64103i
$890$		0			0
$891$	−10937.9	+	630795.i	−0.0137778	+	0.794571i
$892$		0			0
$893$	653108.	−	377072.i	0.818996	−	0.472848i
$894$		0			0
$895$	9737.36	−	16865.6i	0.0121561	−	0.0210550i
$896$		0			0
$897$	−14219.4	+	14096.7i	−0.0176725	+	0.0175199i
$898$		0			0
$899$			216718.i			0.268148i
$900$		0			0
$901$	143176.			0.176368
$902$		0			0
$903$	−153158.	+	561842.i	−0.187830	+	0.689030i
$904$		0			0
$905$	393522.	+	227200.i	0.480476	+	0.277403i
$906$		0			0
$907$	−71965.4	−	124648.i	−0.0874801	−	0.151520i	0.818965	−	0.573843i	$-0.194548\pi$
$907$	−71965.4	−	124648.i	−0.0874801	−	0.151520i	−0.906445	+	0.422323i	$0.861215\pi$
$908$		0			0
$909$	−80536.0	+	136741.i	−0.0974680	+	0.165490i
$910$		0			0
$911$	772201.	−	445830.i	0.930451	−	0.537196i	0.0434969	−	0.999054i	$-0.486150\pi$
$911$	772201.	−	445830.i	0.930451	−	0.537196i	0.886954	+	0.461857i	$0.152817\pi$
$912$		0			0
$913$	136170.	−	235854.i	0.163358	−	0.282944i
$914$		0			0
$915$	62877.5	+	238798.i	0.0751023	+	0.285225i
$916$		0			0
$917$		−	232053.i		−	0.275961i
$918$		0			0
$919$	582156.			0.689300			0.344650	−	0.938731i	$-0.387998\pi$
$919$	582156.			0.689300			0.344650	+	0.938731i	$0.387998\pi$
$920$		0			0
$921$	1.09753e6	−	288990.i	1.29389	−	0.340693i
$922$		0			0
$923$	892636.	+	515364.i	1.04778	+	0.604937i
$924$		0			0
$925$	−152149.	−	263530.i	−0.177822	−	0.307997i
$926$		0			0
$927$	−3620.10	+	417578.i	−0.00421271	+	0.485935i
$928$		0			0
$929$	−668027.	+	385685.i	−0.774038	+	0.446891i	−0.834313	−	0.551291i	$-0.814136\pi$
$929$	−668027.	+	385685.i	−0.774038	+	0.446891i	0.0602751	+	0.998182i	$0.480802\pi$
$930$		0			0
$931$	−271966.	+	471059.i	−0.313773	+	0.543470i
$932$		0			0
$933$	866609.	+	236238.i	0.995543	+	0.271385i
$934$		0			0
$935$		−	112148.i		−	0.128283i
$936$		0			0
$937$	−1.46097e6			−1.66403			−0.832015	−	0.554753i	$-0.812813\pi$
$937$	−1.46097e6			−1.66403			−0.832015	+	0.554753i	$0.812813\pi$
$938$		0			0
$939$	14100.5	+	14223.3i	0.0159921	+	0.0161313i
$940$		0			0
$941$	146658.	+	84673.2i	0.165626	+	0.0956240i	0.580522	−	0.814245i	$-0.302849\pi$
$941$	146658.	+	84673.2i	0.165626	+	0.0956240i	−0.414896	+	0.909869i	$0.636182\pi$
$942$		0			0
$943$	4019.42	+	6961.83i	0.00452001	+	0.00782889i
$944$		0			0
$945$	590833.	+	606402.i	0.661608	+	0.679042i
$946$		0			0
$947$	−514322.	+	296944.i	−0.573503	+	0.331112i	−0.758547	−	0.651618i	$-0.774090\pi$
$947$	−514322.	+	296944.i	−0.573503	+	0.331112i	0.185044	+	0.982730i	$0.440757\pi$
$948$		0			0
$949$	371210.	−	642955.i	0.412180	−	0.713917i
$950$		0			0
$951$	−1.07421e6	+	1.06494e6i	−1.18776	+	1.17750i
$952$		0			0
$953$		−	1.25477e6i		−	1.38159i	−0.723050	−	0.690796i	$-0.757260\pi$
$953$		−	1.25477e6i		−	1.38159i	0.723050	−	0.690796i	$-0.242740\pi$
$954$		0			0
$955$	156250.			0.171322
$956$		0			0
$957$	−163027.	+	598043.i	−0.178006	+	0.652993i
$958$		0			0
$959$	−243051.	−	140326.i	−0.264278	−	0.152581i
$960$		0			0
$961$	415987.	+	720510.i	0.450436	+	0.780178i
$962$		0			0
$963$	−363684.	−	642722.i	−0.392167	−	0.693060i
$964$		0			0
$965$	741017.	−	427826.i	0.795744	−	0.459423i
$966$		0			0
$967$	−528928.	+	916130.i	−0.565645	+	0.979725i	0.431345	+	0.902187i	$0.358039\pi$
$967$	−528928.	+	916130.i	−0.565645	+	0.979725i	−0.996989	+	0.0775381i	$0.975294\pi$
$968$		0			0
$969$	31804.4	+	120787.i	0.0338719	+	0.128639i
$970$		0			0
$971$		−	775745.i		−	0.822774i	−0.911461	−	0.411387i	$-0.865044\pi$
$971$		−	775745.i		−	0.822774i	0.911461	−	0.411387i	$-0.134956\pi$
$972$		0			0
$973$	−846555.			−0.894189
$974$		0			0
$975$	493305.	−	129892.i	0.518927	−	0.136638i
$976$		0			0
$977$	−429995.	−	248258.i	−0.450479	−	0.260084i	0.257554	−	0.966264i	$-0.417084\pi$
$977$	−429995.	−	248258.i	−0.450479	−	0.260084i	−0.708032	+	0.706180i	$0.750417\pi$
$978$		0			0
$979$	686453.	+	1.18897e6i	0.716218	+	1.24053i
$980$		0			0
$981$	−1.13930e6	+	644671.i	−1.18386	+	0.669885i
$982$		0			0
$983$	−260643.	+	150482.i	−0.269736	+	0.155732i	−0.628768	−	0.777593i	$-0.716440\pi$
$983$	−260643.	+	150482.i	−0.269736	+	0.155732i	0.359032	+	0.933325i	$0.383107\pi$
$984$		0			0
$985$	−549076.	+	951028.i	−0.565927	+	0.980214i
$986$		0			0
$987$	2.48950e6	+	678638.i	2.55551	+	0.696633i
$988$		0			0
$989$			12903.9i			0.0131925i
$990$		0			0
$991$	−1.70094e6			−1.73197			−0.865987	−	0.500067i	$-0.833309\pi$
$991$	−1.70094e6			−1.73197			−0.865987	+	0.500067i	$0.833309\pi$
$992$		0			0
$993$	42826.3	+	43199.1i	0.0434322	+	0.0438103i
$994$		0			0
$995$	114302.	+	65992.4i	0.115454	+	0.0666573i
$996$		0			0
$997$	312919.	+	541991.i	0.314805	+	0.545258i	0.979396	−	0.201949i	$-0.0647276\pi$
$997$	312919.	+	541991.i	0.314805	+	0.545258i	−0.664591	+	0.747207i	$0.731394\pi$
$998$		0			0
$999$	431432.	−	420355.i	0.432297	−	0.421197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.q.a.113.3		6
3.2	odd	2		432.5.q.a.17.1		6
4.3	odd	2		9.5.d.a.5.3	yes	6
9.2	odd	6	inner	144.5.q.a.65.3		6
9.4	even	3		1296.5.e.c.161.2		6
9.5	odd	6		1296.5.e.c.161.5		6
9.7	even	3		432.5.q.a.305.1		6
12.11	even	2		27.5.d.a.17.1		6
36.7	odd	6		27.5.d.a.8.1		6
36.11	even	6		9.5.d.a.2.3	✓	6
36.23	even	6		81.5.b.a.80.2		6
36.31	odd	6		81.5.b.a.80.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.3	✓	6	36.11	even	6
9.5.d.a.5.3	yes	6	4.3	odd	2
27.5.d.a.8.1		6	36.7	odd	6
27.5.d.a.17.1		6	12.11	even	2
81.5.b.a.80.2		6	36.23	even	6
81.5.b.a.80.5		6	36.31	odd	6
144.5.q.a.65.3		6	9.2	odd	6	inner
144.5.q.a.113.3		6	1.1	even	1	trivial
432.5.q.a.17.1		6	3.2	odd	2
432.5.q.a.305.1		6	9.7	even	3
1296.5.e.c.161.2		6	9.4	even	3
1296.5.e.c.161.5		6	9.5	odd	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.70335 - 2.29167i) q^{3} +(13.8760 + 8.01130i) q^{5} +(36.2418 + 62.7727i) q^{7} +(70.4965 - 39.8904i) q^{9} +(-83.2749 + 48.0788i) q^{11} +(-76.9530 + 133.286i) q^{13} +(139.127 + 37.9260i) q^{15} +72.7905i q^{17} +190.660 q^{19} +(459.280 + 463.279i) q^{21} +(12.5186 + 7.22762i) q^{23} +(-184.138 - 318.937i) q^{25} +(522.140 - 508.734i) q^{27} +(620.301 - 358.131i) q^{29} +(-151.284 + 262.031i) q^{31} +(-614.590 + 609.285i) q^{33} +1161.38i q^{35} +826.277 q^{37} +(-364.300 + 1336.39i) q^{39} +(481.613 + 278.059i) q^{41} +(446.340 + 773.084i) q^{43} +(1297.78 + 11.2508i) q^{45} +(3425.50 - 1977.72i) q^{47} +(-1426.44 + 2470.67i) q^{49} +(166.812 + 633.521i) q^{51} -1966.96i q^{53} -1540.69 q^{55} +(1659.38 - 436.930i) q^{57} +(-4689.48 - 2707.47i) q^{59} +(856.210 + 1483.00i) q^{61} +(5058.95 + 2979.56i) q^{63} +(-2135.60 + 1232.99i) q^{65} +(-2317.24 + 4013.58i) q^{67} +(125.517 + 34.2160i) q^{69} -6697.12i q^{71} -4823.86 q^{73} +(-2333.51 - 2353.83i) q^{75} +(-6036.07 - 3484.93i) q^{77} +(-2864.40 - 4961.28i) q^{79} +(3378.52 - 5624.26i) q^{81} +(-2452.78 + 1416.12i) q^{83} +(-583.147 + 1010.04i) q^{85} +(4577.98 - 4538.46i) q^{87} -14277.7i q^{89} -11155.7 q^{91} +(-716.187 + 2627.24i) q^{93} +(2645.60 + 1527.44i) q^{95} +(-3582.65 - 6205.34i) q^{97} +(-3952.71 + 6711.25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 12 q^{5} - 12 q^{7} + 99 q^{9} - 483 q^{11} - 6 q^{13} + 1026 q^{15} + 258 q^{19} + 480 q^{21} + 282 q^{23} - 273 q^{25} - 54 q^{27} - 1056 q^{29} - 1290 q^{31} + 279 q^{33} + 12 q^{37}+ \cdots + 9126 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 12 * q^5 - 12 * q^7 + 99 * q^9 - 483 * q^11 - 6 * q^13 + 1026 * q^15 + 258 * q^19 + 480 * q^21 + 282 * q^23 - 273 * q^25 - 54 * q^27 - 1056 * q^29 - 1290 * q^31 + 279 * q^33 + 12 * q^37 - 1974 * q^39 + 7629 * q^41 + 285 * q^43 - 4212 * q^45 + 9642 * q^47 - 1863 * q^49 - 2457 * q^51 - 2016 * q^55 + 5367 * q^57 - 6225 * q^59 + 3630 * q^61 + 7578 * q^63 - 7158 * q^65 + 5055 * q^67 - 13878 * q^69 - 14622 * q^73 - 21021 * q^75 + 2580 * q^77 - 4764 * q^79 + 18387 * q^81 + 1866 * q^83 + 12366 * q^85 + 21564 * q^87 - 34836 * q^91 + 19254 * q^93 + 13362 * q^95 - 28959 * q^97 + 9126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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