LMFDB - Embedded newform 144.5.q.a.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(65,144)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			65.3
Root			$-1.28901 - 2.23263i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.5.q.a.113.3

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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			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	−0.196113	−	0.980581i	$-0.562832\pi$
$5$	13.8760	−	8.01130i	0.555039	−	0.320452i	0.751152	+	0.660129i	$0.229499\pi$
$6$		0			0
$7$	36.2418	−	62.7727i	0.739630	−	1.28108i	−0.213033	−	0.977045i	$-0.568334\pi$
$7$	36.2418	−	62.7727i	0.739630	−	1.28108i	0.952662	−	0.304031i	$-0.0983326\pi$
$8$		0			0
$9$	70.4965	+	39.8904i	0.870327	+	0.492474i
$10$		0			0
$11$	−83.2749	−	48.0788i	−0.688222	−	0.397345i	0.114723	−	0.993397i	$-0.463402\pi$
$11$	−83.2749	−	48.0788i	−0.688222	−	0.397345i	−0.802946	+	0.596052i	$0.796735\pi$
$12$		0			0
$13$	−76.9530	−	133.286i	−0.455343	−	0.788677i	0.543365	−	0.839497i	$-0.317150\pi$
$13$	−76.9530	−	133.286i	−0.455343	−	0.788677i	−0.998708	+	0.0508193i	$0.983817\pi$
$14$		0			0
$15$	139.127	−	37.9260i	0.618341	−	0.168560i
$16$		0			0
$17$		−	72.7905i		−	0.251870i	−0.992038	−	0.125935i	$-0.959807\pi$
$17$		−	72.7905i		−	0.251870i	0.992038	−	0.125935i	$-0.0401931\pi$
$18$		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	−0.488121	−	0.872776i	$-0.662318\pi$
$23$	12.5186	−	7.22762i	0.0236647	−	0.0136628i	0.511786	+	0.859113i	$0.328984\pi$
$24$		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	0.821187	−	0.570659i	$-0.193312\pi$
$29$	620.301	+	358.131i	0.737575	+	0.425839i	−0.0836117	+	0.996498i	$0.526646\pi$
$30$		0			0
$31$	−151.284	−	262.031i	−0.157423	−	0.272665i	0.776515	−	0.630098i	$-0.216985\pi$
$31$	−151.284	−	262.031i	−0.157423	−	0.272665i	−0.933939	+	0.357433i	$0.883652\pi$
$32$		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	−0.349860	−	0.936802i	$-0.613771\pi$
$41$	481.613	−	278.059i	0.286504	−	0.165413i	0.636364	+	0.771389i	$0.280438\pi$
$42$		0			0
$43$	446.340	−	773.084i	0.241395	−	0.418109i	−0.719717	−	0.694268i	$-0.755728\pi$
$43$	446.340	−	773.084i	0.241395	−	0.418109i	0.961112	+	0.276159i	$0.0890616\pi$
$44$		0			0
$45$	1297.78	−	11.2508i	0.640880	−	0.00555597i
$46$		0			0
$47$	3425.50	+	1977.72i	1.55070	+	0.895299i	0.998085	+	0.0618654i	$0.0197050\pi$
$47$	3425.50	+	1977.72i	1.55070	+	0.895299i	0.552619	+	0.833434i	$0.313628\pi$
$48$		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	$0.113858\pi$
$53$			1966.96i			0.700234i	−0.936706	+	0.350117i	$0.886142\pi$
$54$		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	−0.987847	−	0.155431i	$-0.950323\pi$
$59$	−4689.48	+	2707.47i	−1.34716	+	0.777785i	−0.359316	+	0.933216i	$0.616990\pi$
$60$		0			0
$61$	856.210	−	1483.00i	0.230102	−	0.398549i	−0.727736	−	0.685858i	$-0.759427\pi$
$61$	856.210	−	1483.00i	0.230102	−	0.398549i	0.957838	+	0.287309i	$0.0927606\pi$
$62$		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	−0.999823	−	0.0188141i	$-0.994011\pi$
$67$	−2317.24	−	4013.58i	−0.516205	−	0.894093i	0.483618	−	0.875279i	$-0.339322\pi$
$68$		0			0
$69$	125.517	−	34.2160i	0.0263636	−	0.00718672i
$70$		0			0
$71$			6697.12i			1.32853i	0.747497	+	0.664265i	$0.231256\pi$
$71$			6697.12i			1.32853i	−0.747497	+	0.664265i	$0.768744\pi$
$72$		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	−0.998907	−	0.0467524i	$-0.985113\pi$
$79$	−2864.40	+	4961.28i	−0.458964	+	0.794950i	0.539942	+	0.841702i	$0.318446\pi$
$80$		0			0
$81$	3378.52	+	5624.26i	0.514939	+	0.857227i
$82$		0			0
$83$	−2452.78	−	1416.12i	−0.356044	−	0.205562i	0.311300	−	0.950312i	$-0.399235\pi$
$83$	−2452.78	−	1416.12i	−0.356044	−	0.205562i	−0.667344	+	0.744750i	$0.732569\pi$
$84$		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	$0.357353\pi$
$89$			14277.7i			1.80251i	−0.433290	+	0.901255i	$0.642647\pi$
$90$		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	−0.991172	−	0.132580i	$-0.957674\pi$
$97$	−3582.65	+	6205.34i	−0.380769	+	0.659511i	0.610403	+	0.792091i	$0.291007\pi$
$98$		0			0
$99$	−3952.71	−	6711.25i	−0.403297	−	0.684752i
$100$		0			0
$101$	−1696.72	−	979.600i	−0.166328	−	0.0960298i	0.414525	−	0.910038i	$-0.363948\pi$
$101$	−1696.72	−	979.600i	−0.166328	−	0.0960298i	−0.580853	+	0.814008i	$0.697281\pi$
$102$		0			0
$103$	−2577.74	−	4464.77i	−0.242976	−	0.420848i	0.718584	−	0.695440i	$-0.244790\pi$
$103$	−2577.74	−	4464.77i	−0.242976	−	0.420848i	−0.961561	+	0.274592i	$0.911457\pi$
$104$		0			0
$105$	2661.49	−	10107.9i	0.241405	−	0.916814i
$106$		0			0
$107$			9117.08i			0.796321i	0.917316	+	0.398161i	$0.130351\pi$
$107$			9117.08i			0.796321i	−0.917316	+	0.398161i	$0.869649\pi$
$108$		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	0.433804	−	0.901007i	$-0.357171\pi$
$113$	18272.5	−	10549.6i	1.43100	−	0.826189i	0.997197	+	0.0748185i	$0.0238377\pi$
$114$		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	−0.578600	−	0.815611i	$-0.696401\pi$
$131$	−2772.53	+	1600.72i	−0.161560	+	0.0932768i	0.417040	+	0.908888i	$0.363067\pi$
$132$		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	0.408005	−	0.912980i	$-0.366224\pi$
$137$	−3353.18	−	1935.96i	−0.178655	−	0.103147i	−0.586661	+	0.809833i	$0.699558\pi$
$138$		0			0
$139$	−5839.62	−	10114.5i	−0.302242	−	0.523499i	0.674401	−	0.738365i	$-0.264402\pi$
$139$	−5839.62	−	10114.5i	−0.302242	−	0.523499i	−0.976644	+	0.214866i	$0.931068\pi$
$140$		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	−0.764585	−	0.644522i	$-0.777056\pi$
$149$	−13069.8	+	7545.88i	−0.588705	+	0.339889i	0.175880	+	0.984412i	$0.443723\pi$
$150$		0			0
$151$	15127.7	−	26201.9i	0.663465	−	1.14915i	−0.316234	−	0.948681i	$-0.602419\pi$
$151$	15127.7	−	26201.9i	0.663465	−	1.14915i	0.979699	−	0.200474i	$-0.0642481\pi$
$152$		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	0.577443	−	0.816431i	$-0.304050\pi$
$157$	−10311.4	−	17859.8i	−0.418328	−	0.724565i	−0.995771	+	0.0918653i	$0.970717\pi$
$158$		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	−0.00905084	−	0.999959i	$-0.502881\pi$
$167$	23773.0	−	13725.3i	0.852414	−	0.492141i	0.861465	+	0.507818i	$0.169548\pi$
$168$		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	0.638693	−	0.769462i	$-0.279475\pi$
$173$	8729.26	+	5039.84i	0.291666	+	0.168393i	−0.347027	+	0.937855i	$0.612809\pi$
$174$		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	$0.00603779\pi$
$179$			1215.45i			0.0379343i	−0.999820	+	0.0189672i	$0.993962\pi$
$180$		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	0.611264	−	0.791427i	$-0.290661\pi$
$191$	8445.34	+	4875.92i	0.231500	+	0.133656i	−0.379764	+	0.925083i	$0.623995\pi$
$192$		0			0
$193$	26701.4	+	46248.2i	0.716836	+	1.24160i	0.962247	+	0.272177i	$0.0877436\pi$
$193$	26701.4	+	46248.2i	0.716836	+	1.24160i	−0.245411	+	0.969419i	$0.578923\pi$
$194$		0			0
$195$	−15761.2	−	15625.2i	−0.414497	−	0.410919i
$196$		0			0
$197$		−	68537.7i		−	1.76603i	−0.469349	−	0.883013i	$-0.655511\pi$
$197$		−	68537.7i		−	1.76603i	0.469349	−	0.883013i	$-0.344489\pi$
$198$		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	0.998859	−	0.0477587i	$-0.0152079\pi$
$211$	20393.7	+	35322.9i	0.458069	+	0.793399i	−0.540790	+	0.841158i	$0.681875\pi$
$212$		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	0.389986	+	0.920821i	$0.372480\pi$
$223$	−29959.8	+	51891.9i	−0.602461	+	1.04349i	−0.992447	+	0.122672i	$0.960854\pi$
$224$		0			0
$225$	−25703.6	+	15138.6i	−0.507725	+	0.299034i
$226$		0			0
$227$	−85572.3	−	49405.2i	−1.66066	−	0.958785i	−0.972399	−	0.233325i	$-0.925039\pi$
$227$	−85572.3	−	49405.2i	−1.66066	−	0.958785i	−0.688265	−	0.725459i	$-0.741627\pi$
$228$		0			0
$229$	2658.97	+	4605.47i	0.0507040	+	0.0878220i	0.890263	−	0.455446i	$-0.150520\pi$
$229$	2658.97	+	4605.47i	0.0507040	+	0.0878220i	−0.839559	+	0.543268i	$0.817187\pi$
$230$		0			0
$231$	−60520.3	+	16497.9i	−1.13417	+	0.309175i
$232$		0			0
$233$			18467.8i			0.340176i	0.985429	+	0.170088i	$0.0544052\pi$
$233$			18467.8i			0.340176i	−0.985429	+	0.170088i	$0.945595\pi$
$234$		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	−0.682966	−	0.730450i	$-0.739310\pi$
$239$	−22383.5	+	12923.1i	−0.391861	+	0.226241i	0.291105	+	0.956691i	$0.405977\pi$
$240$		0			0
$241$	−41536.2	+	71942.7i	−0.715142	+	1.23866i	0.247763	+	0.968821i	$0.420305\pi$
$241$	−41536.2	+	71942.7i	−0.715142	+	1.23866i	−0.962905	+	0.269841i	$0.913029\pi$
$242$		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	$0.127280\pi$
$251$			49051.6i			0.778585i	−0.921114	+	0.389292i	$0.872720\pi$
$252$		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	0.297641	−	0.954678i	$-0.403800\pi$
$257$	84096.0	−	48552.9i	1.27324	−	0.735104i	0.975596	+	0.219574i	$0.0704668\pi$
$258$		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	0.217335	−	0.976097i	$-0.430264\pi$
$263$	−35921.0	−	20739.0i	−0.519323	−	0.299831i	−0.736658	+	0.676266i	$0.763597\pi$
$264$		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	$0.295020\pi$
$269$			115737.i			1.59944i	−0.600370	+	0.799722i	$0.704980\pi$
$270$		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	−0.694234	−	0.719750i	$-0.744257\pi$
$277$	21192.9	−	36707.2i	0.276205	−	0.478401i	0.970438	+	0.241349i	$0.0775899\pi$
$278$		0			0
$279$	−212.459	−	24507.1i	−0.00272939	−	0.314835i
$280$		0			0
$281$	−35902.5	−	20728.3i	−0.454687	−	0.262513i	0.255121	−	0.966909i	$-0.417885\pi$
$281$	−35902.5	−	20728.3i	−0.454687	−	0.262513i	−0.709807	+	0.704396i	$0.751218\pi$
$282$		0			0
$283$	19194.0	+	33245.0i	0.239658	+	0.415100i	0.960616	−	0.277879i	$-0.0896313\pi$
$283$	19194.0	+	33245.0i	0.239658	+	0.415100i	−0.720958	+	0.692979i	$0.756298\pi$
$284$		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	−0.564030	−	0.825754i	$-0.690750\pi$
$293$	−11239.5	+	6489.12i	−0.130922	+	0.0755876i	0.433109	+	0.901342i	$0.357417\pi$
$294$		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	0.0184989	−	0.999829i	$-0.494111\pi$
$311$	86432.4	−	49901.7i	0.893626	−	0.515935i	0.875127	+	0.483894i	$0.160778\pi$
$312$		0			0
$313$	1112.68	−	1927.21i	0.0113574	−	0.0196716i	−0.860291	−	0.509804i	$-0.829718\pi$
$313$	1112.68	−	1927.21i	0.0113574	−	0.0196716i	0.871648	+	0.490132i	$0.163051\pi$
$314$		0			0
$315$	46327.8	−	81873.1i	0.466896	−	0.825125i
$316$		0			0
$317$	−145552.	−	84034.3i	−1.44843	−	0.836254i	−0.450046	−	0.893005i	$-0.648592\pi$
$317$	−145552.	−	84034.3i	−1.44843	−	0.836254i	−0.998388	+	0.0567515i	$0.981926\pi$
$318$		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	−0.850191	−	0.526475i	$-0.823513\pi$
$331$	3379.43	−	5853.34i	0.0308452	−	0.0534254i	0.881036	+	0.473049i	$0.156847\pi$
$332$		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	0.670413	+	0.741988i	$0.266117\pi$
$337$	111046.	+	192338.i	0.977787	+	1.69358i	0.307375	+	0.951589i	$0.400550\pi$
$338$		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	0.215633	−	0.976475i	$-0.430819\pi$
$347$	140770.	−	81273.8i	1.16910	−	0.674981i	0.953468	+	0.301494i	$0.0974853\pi$
$348$		0			0
$349$	36348.5	−	62957.4i	0.298425	−	0.516887i	−0.677351	−	0.735660i	$-0.736872\pi$
$349$	36348.5	−	62957.4i	0.298425	−	0.516887i	0.975776	+	0.218773i	$0.0702054\pi$
$350$		0			0
$351$	27627.2	−	108743.i	0.224245	−	0.882646i
$352$		0			0
$353$	111396.	+	64314.6i	0.893966	+	0.516131i	0.875238	−	0.483693i	$-0.160705\pi$
$353$	111396.	+	64314.6i	0.893966	+	0.516131i	0.0187281	+	0.999825i	$0.494038\pi$
$354$		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	$0.120550\pi$
$359$			95302.8i			0.739463i	−0.929139	+	0.369732i	$0.879450\pi$
$360$		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	−0.605376	−	0.795940i	$-0.706977\pi$
$367$	52073.0	−	90193.1i	0.386616	−	0.669639i	0.991992	+	0.126301i	$0.0403104\pi$
$368$		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	−0.847465	−	0.530851i	$-0.821872\pi$
$373$	−122915.	−	212896.i	−0.883463	−	1.53020i	−0.0359975	−	0.999352i	$-0.511461\pi$
$374$		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	−0.843124	−	0.537719i	$-0.819286\pi$
$383$	−117206.	+	67668.8i	−0.799008	+	0.461308i	0.0441160	+	0.999026i	$0.485953\pi$
$384$		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	−0.206475	−	0.978452i	$-0.566199\pi$
$389$	−175090.	−	101088.i	−1.15708	−	0.668039i	−0.950602	+	0.310413i	$0.899533\pi$
$390$		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	−0.722596	−	0.691271i	$-0.757051\pi$
$401$	−78026.4	+	45048.6i	−0.485236	+	0.280151i	0.237360	+	0.971422i	$0.423718\pi$
$402$		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	0.550707	−	0.834699i	$-0.314358\pi$
$409$	−74861.0	−	129663.i	−0.447517	−	0.775122i	−0.998224	+	0.0595770i	$0.981025\pi$
$410$		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	−0.778143	−	0.628087i	$-0.783838\pi$
$419$	−109423.	+	63175.3i	−0.623276	+	0.359848i	0.154868	+	0.987935i	$0.450505\pi$
$420$		0			0
$421$	107645.	−	186446.i	0.607335	−	1.05194i	−0.384342	−	0.923191i	$-0.625572\pi$
$421$	107645.	−	186446.i	0.607335	−	1.05194i	0.991678	−	0.128745i	$-0.0410949\pi$
$422$		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	$-0.893523\pi$
$431$		−	121972.i		−	0.656607i	0.944572	−	0.328304i	$-0.106477\pi$
$432$		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	−0.393230	−	0.919440i	$-0.628642\pi$
$439$	115564.	−	200162.i	0.599643	−	1.03861i	0.992874	−	0.119173i	$-0.0380242\pi$
$440$		0			0
$441$	−2003.26	−	231075.i	−0.0103005	−	1.18816i
$442$		0			0
$443$	17481.4	+	10092.9i	0.0890774	+	0.0514289i	0.543877	−	0.839165i	$-0.316956\pi$
$443$	17481.4	+	10092.9i	0.0890774	+	0.0514289i	−0.454800	+	0.890594i	$0.650289\pi$
$444$		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	$0.0740562\pi$
$449$			92962.8i			0.461123i	−0.973058	+	0.230561i	$0.925944\pi$
$450$		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	0.470616	+	0.882338i	$0.344032\pi$
$457$	−110443.	+	191293.i	−0.528819	+	0.915941i	−0.999435	+	0.0336033i	$0.989302\pi$
$458$		0			0
$459$	37031.0	−	38006.9i	0.175768	−	0.180400i
$460$		0			0
$461$	91967.2	+	53097.3i	0.432744	+	0.249845i	0.700515	−	0.713638i	$-0.252954\pi$
$461$	91967.2	+	53097.3i	0.432744	+	0.249845i	−0.267771	+	0.963483i	$0.586287\pi$
$462$		0			0
$463$	−34090.0	−	59045.5i	−0.159025	−	0.275439i	0.775493	−	0.631357i	$-0.217502\pi$
$463$	−34090.0	−	59045.5i	−0.159025	−	0.275439i	−0.934517	+	0.355918i	$0.884168\pi$
$464$		0			0
$465$	−30985.4	−	30718.0i	−0.143302	−	0.142065i
$466$		0			0
$467$			224350.i			1.02871i	0.857578	+	0.514353i	$0.171968\pi$
$467$			224350.i			1.02871i	−0.857578	+	0.514353i	$0.828032\pi$
$468$		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	0.691673	−	0.722211i	$-0.256874\pi$
$479$	94542.7	+	54584.3i	0.412057	+	0.237901i	−0.279616	+	0.960112i	$0.590207\pi$
$480$		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	−0.360288	−	0.932841i	$-0.617322\pi$
$491$	64472.7	−	37223.3i	0.267432	−	0.154402i	0.627720	+	0.778439i	$0.283988\pi$
$492$		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	0.732504	−	0.680763i	$-0.238352\pi$
$499$	−55603.4	−	96308.0i	−0.223306	−	0.386777i	−0.955810	+	0.293985i	$0.905018\pi$
$500$		0			0
$501$	238358.	−	64976.6i	0.949631	−	0.258870i
$502$		0			0
$503$			115897.i			0.458077i	0.973417	+	0.229038i	$0.0735581\pi$
$503$			115897.i			0.458077i	−0.973417	+	0.229038i	$0.926442\pi$
$504$		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	−0.791255	−	0.611487i	$-0.790572\pi$
$509$	−170299.	+	98322.1i	−0.657319	+	0.379503i	0.133936	+	0.990990i	$0.457238\pi$
$510$		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	$-0.814121\pi$
$521$		−	299306.i		−	1.10266i	0.834289	−	0.551328i	$-0.185879\pi$
$522$		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	−0.878132	−	0.478418i	$-0.841210\pi$
$547$	−7403.57	+	12823.4i	−0.0247438	+	0.0428575i	0.853388	+	0.521276i	$0.174544\pi$
$548$		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	$-0.865535\pi$
$557$		−	254392.i		−	0.819962i	0.912094	−	0.409981i	$-0.134465\pi$
$558$		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	−0.622022	−	0.783000i	$-0.713689\pi$
$563$	−80806.7	+	46653.8i	−0.254936	+	0.147187i	0.367087	+	0.930187i	$0.380355\pi$
$564$		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	0.273533	−	0.961863i	$-0.411808\pi$
$569$	−136853.	−	79012.1i	−0.422698	−	0.244045i	−0.696231	+	0.717818i	$0.745141\pi$
$570$		0			0
$571$	−219188.	−	379644.i	−0.672270	−	1.16441i	−0.977259	−	0.212050i	$-0.931986\pi$
$571$	−219188.	−	379644.i	−0.672270	−	1.16441i	0.304988	−	0.952356i	$-0.401347\pi$
$572$		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	−0.977150	−	0.212550i	$-0.931823\pi$
$587$	−568470.	−	328206.i	−1.64980	−	0.952512i	−0.672649	−	0.739962i	$-0.734843\pi$
$588$		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	$0.0538296\pi$
$593$			118369.i			0.336612i	−0.985735	+	0.168306i	$0.946170\pi$
$594$		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	−0.00748620	−	0.999972i	$-0.502383\pi$
$599$	306693.	−	177069.i	0.854772	−	0.493503i	0.862258	+	0.506469i	$0.169050\pi$
$600$		0			0
$601$	297820.	−	515839.i	0.824526	−	1.42812i	−0.0777554	−	0.996972i	$-0.524775\pi$
$601$	297820.	−	515839.i	0.824526	−	1.42812i	0.902281	−	0.431148i	$-0.141891\pi$
$602$		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	0.872546	−	0.488531i	$-0.162467\pi$
$607$	4860.81	+	8419.17i	0.0131926	+	0.0228503i	−0.859354	+	0.511382i	$0.829134\pi$
$608$		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	0.170670	−	0.985328i	$-0.445407\pi$
$617$	422308.	−	243819.i	1.10932	−	0.640469i	0.938654	+	0.344860i	$0.112073\pi$
$618$		0			0
$619$	8628.23	−	14944.5i	0.0225185	−	0.0390033i	−0.854547	−	0.519375i	$-0.826165\pi$
$619$	8628.23	−	14944.5i	0.0225185	−	0.0390033i	0.877065	+	0.480372i	$0.159498\pi$
$620$		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	0.465565	−	0.885014i	$-0.345851\pi$
$641$	−27979.5	−	16154.0i	−0.0680964	−	0.0393155i	−0.533662	+	0.845698i	$0.679184\pi$
$642$		0			0
$643$	138524.	+	239931.i	0.335045	+	0.580315i	0.983494	−	0.180943i	$-0.0579150\pi$
$643$	138524.	+	239931.i	0.335045	+	0.580315i	−0.648448	+	0.761259i	$0.724582\pi$
$644$		0			0
$645$	32777.9	−	124485.i	0.0787882	−	0.299224i
$646$		0			0
$647$		−	125452.i		−	0.299689i	−0.988710	−	0.149844i	$-0.952123\pi$
$647$		−	125452.i		−	0.299689i	0.988710	−	0.149844i	$-0.0478773\pi$
$648$		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	−0.183085	−	0.983097i	$-0.558608\pi$
$653$	245936.	−	141991.i	0.576760	−	0.332992i	0.759845	+	0.650105i	$0.225275\pi$
$654$		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	0.0969973	−	0.995285i	$-0.469076\pi$
$659$	−311139.	−	179636.i	−0.716446	−	0.413640i	−0.813443	+	0.581644i	$0.802410\pi$
$660$		0			0
$661$	−98902.1	−	171303.i	−0.226362	−	0.392070i	0.730366	−	0.683057i	$-0.239350\pi$
$661$	−98902.1	−	171303.i	−0.226362	−	0.392070i	−0.956727	+	0.290987i	$0.906016\pi$
$662$		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	−0.966989	−	0.254820i	$-0.917984\pi$
$673$	−119036.	+	206176.i	−0.262814	+	0.455207i	0.704175	+	0.710027i	$0.251317\pi$
$674$		0			0
$675$	−258400.	+	72852.2i	−0.567133	+	0.159895i
$676$		0			0
$677$	216636.	+	125075.i	0.472666	+	0.272894i	0.717355	−	0.696708i	$-0.245353\pi$
$677$	216636.	+	125075.i	0.472666	+	0.272894i	−0.244689	+	0.969602i	$0.578686\pi$
$678$		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	$0.0925132\pi$
$683$			267358.i			0.573129i	−0.958061	+	0.286564i	$0.907487\pi$
$684$		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	−0.634133	−	0.773224i	$-0.718643\pi$
$691$	168343.	−	291579.i	0.352565	−	0.610660i	0.986698	+	0.162564i	$0.0519763\pi$
$692$		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	$-0.776056\pi$
$701$		−	635795.i		−	1.29384i	0.762557	−	0.646921i	$-0.223944\pi$
$702$		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	−0.996760	−	0.0804279i	$-0.974371\pi$
$709$	−215513.	+	373280.i	−0.428728	+	0.742578i	0.568033	+	0.823006i	$0.307705\pi$
$710$		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	$-0.719168\pi$
$719$		−	798370.i		−	1.54435i	0.635409	−	0.772176i	$-0.280832\pi$
$720$		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	−0.676139	−	0.736775i	$-0.736348\pi$
$727$	158557.	−	274628.i	0.299996	−	0.519609i	0.976135	+	0.217166i	$0.0696812\pi$
$728$		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	0.814091	+	0.580738i	$0.197236\pi$
$733$	488922.	+	846837.i	0.909979	+	1.57613i	0.0958883	+	0.995392i	$0.469431\pi$
$734$		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	−0.644990	+	0.764191i	$0.723139\pi$
$743$	−899450.	+	519298.i	−1.62929	+	0.940673i	−0.984304	+	0.176482i	$0.943528\pi$
$744$		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	0.972196	−	0.234168i	$-0.0752367\pi$
$751$	159783.	+	276752.i	0.283302	+	0.490694i	−0.688894	+	0.724862i	$0.741903\pi$
$752$		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	−0.988691	−	0.149966i	$-0.952083\pi$
$761$	−783645.	+	452437.i	−1.35316	+	0.781249i	−0.364471	+	0.931215i	$0.618750\pi$
$762$		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	0.799025	−	0.601298i	$-0.205349\pi$
$769$	−71688.6	−	124168.i	−0.121227	−	0.209970i	−0.920252	+	0.391327i	$0.872016\pi$
$770$		0			0
$771$	843184.	−	229852.i	1.41845	−	0.386670i
$772$		0			0
$773$		−	710063.i		−	1.18833i	−0.804342	−	0.594166i	$-0.797482\pi$
$773$		−	710063.i		−	1.18833i	0.804342	−	0.594166i	$-0.202518\pi$
$774$		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	0.514121	−	0.857718i	$-0.328118\pi$
$787$	−300855.	−	521097.i	−0.485745	−	0.841335i	−0.999866	+	0.0163827i	$0.994785\pi$
$788$		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	−0.763511	−	0.645795i	$-0.776526\pi$
$797$	−372227.	+	214905.i	−0.585991	+	0.338322i	0.177519	+	0.984117i	$0.443193\pi$
$798$		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	$-0.840266\pi$
$809$		−	629639.i		−	0.962042i	0.876709	−	0.481021i	$-0.159734\pi$
$810$		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	0.528453	−	0.848962i	$-0.322772\pi$
$821$	38728.3	+	22359.8i	0.0574569	+	0.0331727i	−0.470996	+	0.882135i	$0.656106\pi$
$822$		0			0
$823$	−146289.	−	253380.i	−0.215979	−	0.374087i	0.737596	−	0.675242i	$-0.235961\pi$
$823$	−146289.	−	253380.i	−0.215979	−	0.374087i	−0.953575	+	0.301155i	$0.902628\pi$
$824$		0			0
$825$	307493.	−	83822.6i	0.451780	−	0.123155i
$826$		0			0
$827$			806491.i			1.17920i	0.807694	+	0.589601i	$0.200715\pi$
$827$			806491.i			1.17920i	−0.807694	+	0.589601i	$0.799285\pi$
$828$		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	−0.0560100	−	0.998430i	$-0.517838\pi$
$839$	−667796.	−	385552.i	−0.948681	−	0.547721i	−0.892671	+	0.450709i	$0.851171\pi$
$840$		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	0.206977	+	0.978346i	$0.433637\pi$
$853$	−541184.	+	937358.i	−0.743784	+	1.28827i	−0.950761	+	0.309925i	$0.899696\pi$
$854$		0			0
$855$	247435.	−	2145.09i	0.338477	−	0.00293436i
$856$		0			0
$857$	−461890.	−	266672.i	−0.628893	−	0.363092i	0.151430	−	0.988468i	$-0.451612\pi$
$857$	−461890.	−	266672.i	−0.628893	−	0.363092i	−0.780323	+	0.625376i	$0.784945\pi$
$858$		0			0
$859$	565525.	+	979517.i	0.766417	+	1.32747i	0.939494	+	0.342565i	$0.111296\pi$
$859$	565525.	+	979517.i	0.766417	+	1.32747i	−0.173077	+	0.984908i	$0.555371\pi$
$860$		0			0
$861$	92376.1	−	350828.i	0.124610	−	0.473247i
$862$		0			0
$863$		−	110025.i		−	0.147730i	−0.997268	−	0.0738649i	$-0.976467\pi$
$863$		−	110025.i		−	0.147730i	0.997268	−	0.0738649i	$-0.0235334\pi$
$864$		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	0.967753	−	0.251900i	$-0.0810554\pi$
$877$	204377.	+	353991.i	0.265725	+	0.460249i	−0.702028	+	0.712149i	$0.747722\pi$
$878$		0			0
$879$	−112692.	+	30719.9i	−0.145853	+	0.0397596i
$880$		0			0
$881$		−	235809.i		−	0.303815i	−0.988395	−	0.151907i	$-0.951458\pi$
$881$		−	235809.i		−	0.303815i	0.988395	−	0.151907i	$-0.0485416\pi$
$882$		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	−0.690514	−	0.723319i	$-0.742616\pi$
$887$	−322071.	+	185948.i	−0.409359	+	0.236344i	0.281155	+	0.959662i	$0.409282\pi$
$888$		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	−0.906445	−	0.422323i	$-0.861215\pi$
$907$	−71965.4	+	124648.i	−0.0874801	+	0.151520i	0.818965	+	0.573843i	$0.194548\pi$
$908$		0			0
$909$	−80536.0	−	136741.i	−0.0974680	−	0.165490i
$910$		0			0
$911$	772201.	+	445830.i	0.930451	+	0.537196i	0.886954	−	0.461857i	$-0.152817\pi$
$911$	772201.	+	445830.i	0.930451	+	0.537196i	0.0434969	+	0.999054i	$0.486150\pi$
$912$		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	0.0602751	−	0.998182i	$-0.480802\pi$
$929$	−668027.	−	385685.i	−0.774038	−	0.446891i	−0.834313	+	0.551291i	$0.814136\pi$
$930$		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	−0.414896	−	0.909869i	$-0.636182\pi$
$941$	146658.	−	84673.2i	0.165626	−	0.0956240i	0.580522	+	0.814245i	$0.302849\pi$
$942$		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	0.185044	−	0.982730i	$-0.440757\pi$
$947$	−514322.	−	296944.i	−0.573503	−	0.331112i	−0.758547	+	0.651618i	$0.774090\pi$
$948$		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	$0.242740\pi$
$953$			1.25477e6i			1.38159i	−0.723050	+	0.690796i	$0.757260\pi$
$954$		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	−0.996989	−	0.0775381i	$-0.975294\pi$
$967$	−528928.	−	916130.i	−0.565645	−	0.979725i	0.431345	−	0.902187i	$-0.358039\pi$
$968$		0			0
$969$	31804.4	−	120787.i	0.0338719	−	0.128639i
$970$		0			0
$971$			775745.i			0.822774i	0.911461	+	0.411387i	$0.134956\pi$
$971$			775745.i			0.822774i	−0.911461	+	0.411387i	$0.865044\pi$
$972$		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	−0.708032	−	0.706180i	$-0.750417\pi$
$977$	−429995.	+	248258.i	−0.450479	+	0.260084i	0.257554	+	0.966264i	$0.417084\pi$
$978$		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	0.359032	−	0.933325i	$-0.383107\pi$
$983$	−260643.	−	150482.i	−0.269736	−	0.155732i	−0.628768	+	0.777593i	$0.716440\pi$
$984$		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	−0.664591	−	0.747207i	$-0.731394\pi$
$997$	312919.	−	541991.i	0.314805	−	0.545258i	0.979396	+	0.201949i	$0.0647276\pi$
$998$		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.65.3		6
3.2	odd	2		432.5.q.a.305.1		6
4.3	odd	2		9.5.d.a.2.3	✓	6
9.2	odd	6		1296.5.e.c.161.2		6
9.4	even	3		432.5.q.a.17.1		6
9.5	odd	6	inner	144.5.q.a.113.3		6
9.7	even	3		1296.5.e.c.161.5		6
12.11	even	2		27.5.d.a.8.1		6
36.7	odd	6		81.5.b.a.80.2		6
36.11	even	6		81.5.b.a.80.5		6
36.23	even	6		9.5.d.a.5.3	yes	6
36.31	odd	6		27.5.d.a.17.1		6

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

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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