LMFDB - Embedded newform 9.5.d.a.2.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,5,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.930329667755$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.3
Root			$-1.28901 + 2.23263i$ of defining polynomial
Character	$\chi$	$=$	9.2
Dual form			9.5.d.a.5.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.86703 + 2.23263i) q^{2} +(-8.70335 - 2.29167i) q^{3} +(1.96929 + 3.41090i) q^{4} +(13.8760 - 8.01130i) q^{5} +(-28.5397 - 28.2933i) q^{6} +(-36.2418 + 62.7727i) q^{7} -53.8574i q^{8} +(70.4965 + 39.8904i) q^{9} +71.5451 q^{10} +(83.2749 + 48.0788i) q^{11} +(-9.32272 - 34.1992i) q^{12} +(-76.9530 - 133.286i) q^{13} +(-280.297 + 161.829i) q^{14} +(-139.127 + 37.9260i) q^{15} +(151.752 - 262.843i) q^{16} -72.7905i q^{17} +(183.552 + 311.650i) q^{18} -190.660 q^{19} +(54.6515 + 31.5531i) q^{20} +(459.280 - 463.279i) q^{21} +(214.684 + 371.844i) q^{22} +(-12.5186 + 7.22762i) q^{23} +(-123.423 + 468.740i) q^{24} +(-184.138 + 318.937i) q^{25} -687.231i q^{26} +(-522.140 - 508.734i) q^{27} -285.482 q^{28} +(620.301 + 358.131i) q^{29} +(-622.682 - 163.958i) q^{30} +(151.284 + 262.031i) q^{31} +(427.392 - 246.755i) q^{32} +(-614.590 - 609.285i) q^{33} +(162.514 - 281.483i) q^{34} +1161.38i q^{35} +(2.76561 + 319.012i) q^{36} +826.277 q^{37} +(-737.289 - 425.674i) q^{38} +(364.300 + 1336.39i) q^{39} +(-431.468 - 747.325i) q^{40} +(481.613 - 278.059i) q^{41} +(2810.38 - 766.110i) q^{42} +(-446.340 + 773.084i) q^{43} +378.723i q^{44} +(1297.78 - 11.2508i) q^{45} -64.5464 q^{46} +(-3425.50 - 1977.72i) q^{47} +(-1923.10 + 1939.85i) q^{48} +(-1426.44 - 2470.67i) q^{49} +(-1424.14 + 822.225i) q^{50} +(-166.812 + 633.521i) q^{51} +(303.085 - 524.958i) q^{52} +1966.96i q^{53} +(-883.316 - 3133.04i) q^{54} +1540.69 q^{55} +(3380.78 + 1951.89i) q^{56} +(1659.38 + 436.930i) q^{57} +(1599.15 + 2769.81i) q^{58} +(4689.48 - 2707.47i) q^{59} +(-403.342 - 399.861i) q^{60} +(856.210 - 1483.00i) q^{61} +1351.04i q^{62} +(-5058.95 + 2979.56i) q^{63} -2652.43 q^{64} +(-2135.60 - 1232.99i) q^{65} +(-1016.33 - 3728.28i) q^{66} +(2317.24 + 4013.58i) q^{67} +(248.281 - 143.345i) q^{68} +(125.517 - 34.2160i) q^{69} +(-2592.93 + 4491.08i) q^{70} -6697.12i q^{71} +(2148.39 - 3796.76i) q^{72} -4823.86 q^{73} +(3195.24 + 1844.77i) q^{74} +(2333.51 - 2353.83i) q^{75} +(-375.464 - 650.324i) q^{76} +(-6036.07 + 3484.93i) q^{77} +(-1574.90 + 5981.21i) q^{78} +(2864.40 - 4961.28i) q^{79} -4862.94i q^{80} +(3378.52 + 5624.26i) q^{81} +2483.22 q^{82} +(2452.78 + 1416.12i) q^{83} +(2484.65 + 654.230i) q^{84} +(-583.147 - 1010.04i) q^{85} +(-3452.02 + 1993.03i) q^{86} +(-4577.98 - 4538.46i) q^{87} +(2589.40 - 4484.97i) q^{88} +14277.7i q^{89} +(5043.68 + 2853.96i) q^{90} +11155.7 q^{91} +(-49.3054 - 28.4665i) q^{92} +(-716.187 - 2627.24i) q^{93} +(-8831.02 - 15295.8i) q^{94} +(-2645.60 + 1527.44i) q^{95} +(-4285.22 + 1168.15i) q^{96} +(-3582.65 + 6205.34i) q^{97} -12738.9i q^{98} +(3952.71 + 6711.25i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20}+ \cdots - 9126 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	3.86703	+	2.23263i	0.966758	+	0.558158i	0.898246	−	0.439492i	$-0.144842\pi$
$2$	3.86703	+	2.23263i	0.966758	+	0.558158i	0.0685115	+	0.997650i	$0.478175\pi$
$3$	−8.70335	−	2.29167i	−0.967039	−	0.254630i
$3$	−8.70335	−	2.29167i	−0.967039	−	0.254630i
$4$	1.96929	+	3.41090i	0.123080	+	0.213181i
$5$	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	$0.229499\pi$
$6$	−28.5397	−	28.2933i	−0.792768	−	0.785925i
$7$	−36.2418	+	62.7727i	−0.739630	+	1.28108i	0.213033	+	0.977045i	$0.431666\pi$
$7$	−36.2418	+	62.7727i	−0.739630	+	1.28108i	−0.952662	+	0.304031i	$0.901667\pi$
$8$		−	53.8574i		−	0.841523i
$9$	70.4965	+	39.8904i	0.870327	+	0.492474i
$10$	71.5451			0.715451
$11$	83.2749	+	48.0788i	0.688222	+	0.397345i	0.802946	−	0.596052i	$-0.203265\pi$
$11$	83.2749	+	48.0788i	0.688222	+	0.397345i	−0.114723	+	0.993397i	$0.536598\pi$
$12$	−9.32272	−	34.1992i	−0.0647411	−	0.237495i
$13$	−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	$0.983817\pi$
$14$	−280.297	+	161.829i	−1.43009	+	0.825660i
$15$	−139.127	+	37.9260i	−0.618341	+	0.168560i
$16$	151.752	−	262.843i	0.592783	−	1.02673i
$17$		−	72.7905i		−	0.251870i	−0.992038	−	0.125935i	$-0.959807\pi$
$17$		−	72.7905i		−	0.251870i	0.992038	−	0.125935i	$-0.0401931\pi$
$18$	183.552	+	311.650i	0.566518	+	0.961883i
$19$	−190.660			−0.528145			−0.264072	−	0.964503i	$-0.585066\pi$
$19$	−190.660			−0.528145			−0.264072	+	0.964503i	$0.585066\pi$
$20$	54.6515	+	31.5531i	0.136629	+	0.0788827i
$21$	459.280	−	463.279i	1.04145	−	1.05052i
$22$	214.684	+	371.844i	0.443563	+	0.768273i
$23$	−12.5186	+	7.22762i	−0.0236647	+	0.0136628i	−0.511786	−	0.859113i	$-0.671016\pi$
$23$	−12.5186	+	7.22762i	−0.0236647	+	0.0136628i	0.488121	+	0.872776i	$0.337682\pi$
$24$	−123.423	+	468.740i	−0.214277	+	0.813785i
$25$	−184.138	+	318.937i	−0.294621	+	0.510298i
$26$		−	687.231i		−	1.01661i
$27$	−522.140	−	508.734i	−0.716242	−	0.697852i
$28$	−285.482			−0.364135
$29$	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	$0.526646\pi$
$30$	−622.682	−	163.958i	−0.691869	−	0.182175i
$31$	151.284	+	262.031i	0.157423	+	0.272665i	0.933939	−	0.357433i	$-0.116348\pi$
$31$	151.284	+	262.031i	0.157423	+	0.272665i	−0.776515	+	0.630098i	$0.783015\pi$
$32$	427.392	−	246.755i	0.417375	−	0.240971i
$33$	−614.590	−	609.285i	−0.564362	−	0.559490i
$34$	162.514	−	281.483i	0.140583	−	0.243498i
$35$			1161.38i			0.948063i
$36$	2.76561	+	319.012i	0.00213396	+	0.246151i
$37$	826.277			0.603562			0.301781	−	0.953377i	$-0.402419\pi$
$37$	826.277			0.603562			0.301781	+	0.953377i	$0.402419\pi$
$38$	−737.289	−	425.674i	−0.510588	−	0.294788i
$39$	364.300	+	1336.39i	0.239514	+	0.878625i
$40$	−431.468	−	747.325i	−0.269668	−	0.467078i
$41$	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	$0.280438\pi$
$42$	2810.38	−	766.110i	1.59319	−	0.434303i
$43$	−446.340	+	773.084i	−0.241395	+	0.418109i	−0.961112	−	0.276159i	$-0.910938\pi$
$43$	−446.340	+	773.084i	−0.241395	+	0.418109i	0.719717	+	0.694268i	$0.244272\pi$
$44$			378.723i			0.195622i
$45$	1297.78	−	11.2508i	0.640880	−	0.00555597i
$46$	−64.5464			−0.0305040
$47$	−3425.50	−	1977.72i	−1.55070	−	0.895299i	−0.998085	−	0.0618654i	$-0.980295\pi$
$47$	−3425.50	−	1977.72i	−1.55070	−	0.895299i	−0.552619	−	0.833434i	$-0.686372\pi$
$48$	−1923.10	+	1939.85i	−0.834680	+	0.841947i
$49$	−1426.44	−	2470.67i	−0.594104	−	1.02902i
$50$	−1424.14	+	822.225i	−0.569654	+	0.328890i
$51$	−166.812	+	633.521i	−0.0641337	+	0.243568i
$52$	303.085	−	524.958i	0.112088	−	0.194141i
$53$			1966.96i			0.700234i	0.936706	+	0.350117i	$0.113858\pi$
$53$			1966.96i			0.700234i	−0.936706	+	0.350117i	$0.886142\pi$
$54$	−883.316	−	3133.04i	−0.302920	−	1.07443i
$55$	1540.69			0.509320
$56$	3380.78	+	1951.89i	1.07805	+	0.622415i
$57$	1659.38	+	436.930i	0.510736	+	0.134481i
$58$	1599.15	+	2769.81i	0.475371	+	0.823367i
$59$	4689.48	−	2707.47i	1.34716	−	0.777785i	0.359316	−	0.933216i	$-0.383010\pi$
$59$	4689.48	−	2707.47i	1.34716	−	0.777785i	0.987847	+	0.155431i	$0.0496765\pi$
$60$	−403.342	−	399.861i	−0.112039	−	0.111072i
$61$	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	$0.0927606\pi$
$62$			1351.04i			0.351468i
$63$	−5058.95	+	2979.56i	−1.27462	+	0.750707i
$64$	−2652.43			−0.647565
$65$	−2135.60	−	1232.99i	−0.505467	−	0.291831i
$66$	−1016.33	−	3728.28i	−0.233317	−	0.855894i
$67$	2317.24	+	4013.58i	0.516205	+	0.894093i	0.999823	+	0.0188141i	$0.00598907\pi$
$67$	2317.24	+	4013.58i	0.516205	+	0.894093i	−0.483618	+	0.875279i	$0.660678\pi$
$68$	248.281	−	143.345i	0.0536941	−	0.0310003i
$69$	125.517	−	34.2160i	0.0263636	−	0.00718672i
$70$	−2592.93	+	4491.08i	−0.529169	+	0.916547i
$71$		−	6697.12i		−	1.32853i	−0.747497	−	0.664265i	$-0.768744\pi$
$71$		−	6697.12i		−	1.32853i	0.747497	−	0.664265i	$-0.231256\pi$
$72$	2148.39	−	3796.76i	0.414428	−	0.732400i
$73$	−4823.86			−0.905208			−0.452604	−	0.891712i	$-0.649505\pi$
$73$	−4823.86			−0.905208			−0.452604	+	0.891712i	$0.649505\pi$
$74$	3195.24	+	1844.77i	0.583499	+	0.336883i
$75$	2333.51	−	2353.83i	0.414847	−	0.418459i
$76$	−375.464	−	650.324i	−0.0650042	−	0.112591i
$77$	−6036.07	+	3484.93i	−1.01806	+	0.587777i
$78$	−1574.90	+	5981.21i	−0.258860	+	0.983104i
$79$	2864.40	−	4961.28i	0.458964	−	0.794950i	−0.539942	−	0.841702i	$-0.681554\pi$
$79$	2864.40	−	4961.28i	0.458964	−	0.794950i	0.998907	+	0.0467524i	$0.0148872\pi$
$80$		−	4862.94i		−	0.759834i
$81$	3378.52	+	5624.26i	0.514939	+	0.857227i
$82$	2483.22			0.369307
$83$	2452.78	+	1416.12i	0.356044	+	0.205562i	0.667344	−	0.744750i	$-0.267431\pi$
$83$	2452.78	+	1416.12i	0.356044	+	0.205562i	−0.311300	+	0.950312i	$0.600765\pi$
$84$	2484.65	+	654.230i	0.352133	+	0.0927197i
$85$	−583.147	−	1010.04i	−0.0807124	−	0.139798i
$86$	−3452.02	+	1993.03i	−0.466742	+	0.269474i
$87$	−4577.98	−	4538.46i	−0.604832	−	0.599612i
$88$	2589.40	−	4484.97i	0.334375	−	0.579155i
$89$			14277.7i			1.80251i	0.433290	+	0.901255i	$0.357353\pi$
$89$			14277.7i			1.80251i	−0.433290	+	0.901255i	$0.642647\pi$
$90$	5043.68	+	2853.96i	0.622677	+	0.352341i
$91$	11155.7			1.34714
$92$	−49.3054	−	28.4665i	−0.00582531	−	0.00336324i
$93$	−716.187	−	2627.24i	−0.0828058	−	0.303763i
$94$	−8831.02	−	15295.8i	−0.999437	−	1.73107i
$95$	−2645.60	+	1527.44i	−0.293141	+	0.169245i
$96$	−4285.22	+	1168.15i	−0.464976	+	0.126753i
$97$	−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	$0.291007\pi$
$98$		−	12738.9i		−	1.32641i
$99$	3952.71	+	6711.25i	0.403297	+	0.684752i
$100$	−1450.48			−0.145048
$101$	−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	$0.697281\pi$
$102$	−2059.49	+	2077.42i	−0.197951	+	0.199675i
$103$	2577.74	+	4464.77i	0.242976	+	0.420848i	0.961561	−	0.274592i	$-0.0885429\pi$
$103$	2577.74	+	4464.77i	0.242976	+	0.420848i	−0.718584	+	0.695440i	$0.755210\pi$
$104$	−7178.47	+	4144.49i	−0.663690	+	0.383182i
$105$	2661.49	−	10107.9i	0.241405	−	0.916814i
$106$	−4391.49	+	7606.29i	−0.390841	+	0.676957i
$107$		−	9117.08i		−	0.796321i	−0.917316	−	0.398161i	$-0.869649\pi$
$107$		−	9117.08i		−	0.796321i	0.917316	−	0.398161i	$-0.130351\pi$
$108$	707.000	−	2782.81i	0.0606139	−	0.238581i
$109$	−16161.1			−1.36024			−0.680122	−	0.733099i	$-0.738073\pi$
$109$	−16161.1			−1.36024			−0.680122	+	0.733099i	$0.738073\pi$
$110$	5957.91	+	3439.80i	0.492389	+	0.284281i
$111$	−7191.38	−	1893.55i	−0.583668	−	0.153685i
$112$	10999.6	+	19051.8i	0.876879	+	1.51880i
$113$	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	$0.0238377\pi$
$114$	5441.38	+	5394.41i	0.418696	+	0.415082i
$115$	−115.805	+	200.581i	−0.00875654	+	0.0151668i
$116$			2821.05i			0.209650i
$117$	−108.071	−	12465.9i	−0.00789470	−	0.910652i
$118$	24179.1			1.73651
$119$	4569.26	+	2638.06i	0.322665	+	0.186291i
$120$	2042.60	+	7493.01i	0.141847	+	0.520348i
$121$	−2697.36	−	4671.97i	−0.184233	−	0.319102i
$122$	6621.98	−	3823.20i	0.444906	−	0.256867i
$123$	−4828.87	+	1316.35i	−0.319180	+	0.0870084i
$124$	−595.842	+	1032.03i	−0.0387514	+	0.0671195i
$125$			15914.9i			1.01855i
$126$	−26215.4	+	227.269i	−1.65126	+	0.0143152i
$127$	−20660.9			−1.28098			−0.640489	−	0.767968i	$-0.721268\pi$
$127$	−20660.9			−1.28098			−0.640489	+	0.767968i	$0.721268\pi$
$128$	−17095.3	−	9869.97i	−1.04341	−	0.602415i
$129$	5656.31	−	5705.55i	0.339902	−	0.342861i
$130$	−5505.61	−	9536.00i	−0.325776	−	0.564260i
$131$	2772.53	−	1600.72i	0.161560	−	0.0932768i	−0.417040	−	0.908888i	$-0.636933\pi$
$131$	2772.53	−	1600.72i	0.161560	−	0.0932768i	0.578600	+	0.815611i	$0.303599\pi$
$132$	867.908	−	3296.16i	0.0498111	−	0.189174i
$133$	6909.88	−	11968.3i	0.390631	−	0.676594i
$134$			20694.2i			1.15250i
$135$	−11320.8	−	2876.17i	−0.621170	−	0.157814i
$136$	−3920.31			−0.211955
$137$	−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	$0.699558\pi$
$138$	561.770	+	147.919i	0.0294985	+	0.00776722i
$139$	5839.62	+	10114.5i	0.302242	+	0.523499i	0.976644	−	0.214866i	$-0.0689315\pi$
$139$	5839.62	+	10114.5i	0.302242	+	0.523499i	−0.674401	+	0.738365i	$0.735598\pi$
$140$	−3961.35	+	2287.08i	−0.202109	+	0.116688i
$141$	25281.1	+	25062.9i	1.27162	+	1.26064i
$142$	14952.2	−	25898.0i	0.741530	−	1.28437i
$143$		−	14799.2i		−	0.723714i
$144$	21182.9	−	12476.0i	1.02155	−	0.601661i
$145$	11476.4			0.545844
$146$	−18654.0	−	10769.9i	−0.875117	−	0.505249i
$147$	6752.87	+	24772.1i	0.312503	+	1.14638i
$148$	1627.18	+	2818.35i	0.0742867	+	0.128668i
$149$	−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	$0.443723\pi$
$150$	14279.0	−	3892.46i	0.634623	−	0.172998i
$151$	−15127.7	+	26201.9i	−0.663465	+	1.14915i	0.316234	+	0.948681i	$0.397581\pi$
$151$	−15127.7	+	26201.9i	−0.663465	+	1.14915i	−0.979699	+	0.200474i	$0.935752\pi$
$152$			10268.5i			0.444446i
$153$	2903.64	−	5131.48i	0.124040	−	0.219210i
$154$	−31122.2			−1.31229
$155$	4198.42	+	2423.96i	0.174752	+	0.100893i
$156$	−3840.88	+	3874.32i	−0.157827	+	0.159201i
$157$	−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	$0.970717\pi$
$158$	22153.4	−	12790.3i	0.887415	−	0.512349i
$159$	4507.61	−	17119.1i	0.178300	−	0.677153i
$160$	3953.65	−	6847.93i	0.154440	−	0.267497i
$161$		−	1047.77i		−	0.0404216i
$162$	507.923	+	29292.2i	0.0193539	+	1.11615i
$163$	39790.7			1.49764			0.748818	−	0.662776i	$-0.230622\pi$
$163$	39790.7			1.49764			0.748818	+	0.662776i	$0.230622\pi$
$164$	1896.87	+	1095.16i	0.0705260	+	0.0407182i
$165$	−13409.2	−	3530.76i	−0.492533	−	0.129688i
$166$	6323.33	+	10952.3i	0.229472	+	0.397457i
$167$	−23773.0	+	13725.3i	−0.852414	+	0.492141i	−0.861465	−	0.507818i	$-0.830452\pi$
$167$	−23773.0	+	13725.3i	−0.852414	+	0.492141i	0.00905084	+	0.999959i	$0.497119\pi$
$168$	−24951.0	−	24735.6i	−0.884035	−	0.876404i
$169$	2436.98	−	4220.97i	0.0853253	−	0.147788i
$170$		−	5207.81i		−	0.180201i
$171$	−13440.9	−	7605.51i	−0.459659	−	0.260097i
$172$	−3515.89			−0.118844
$173$	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	$0.612809\pi$
$174$	−7570.47	−	27771.3i	−0.250048	−	0.917271i
$175$	−13347.0	−	23117.7i	−0.435821	−	0.754864i
$176$	25274.3	−	14592.1i	0.815933	−	0.471079i
$177$	−47018.8	+	12817.3i	−1.50081	+	0.409120i
$178$	−31876.8	+	55212.2i	−1.00608	+	1.74259i
$179$		−	1215.45i		−	0.0379343i	−0.999820	−	0.0189672i	$-0.993962\pi$
$179$		−	1215.45i		−	0.0379343i	0.999820	−	0.0189672i	$-0.00603779\pi$
$180$	2594.08	+	4404.45i	0.0800642	+	0.135940i
$181$	28359.9			0.865661			0.432831	−	0.901475i	$-0.357515\pi$
$181$	28359.9			0.865661			0.432831	+	0.901475i	$0.357515\pi$
$182$	43139.3	+	24906.5i	1.30236	+	0.751917i
$183$	−10850.4	+	10944.9i	−0.324000	+	0.326821i
$184$	389.261	+	674.220i	0.0114976	+	0.0199143i
$185$	11465.4	−	6619.55i	0.335001	−	0.193413i
$186$	3096.15	−	11758.6i	0.0894943	−	0.339883i
$187$	3499.68	−	6061.62i	0.100079	−	0.173343i
$188$		−	15578.8i		−	0.440775i
$189$	50858.0	−	14338.7i	1.42376	−	0.401408i
$190$	−13640.8			−0.377862
$191$	−8445.34	−	4875.92i	−0.231500	−	0.133656i	0.379764	−	0.925083i	$-0.376005\pi$
$191$	−8445.34	−	4875.92i	−0.231500	−	0.133656i	−0.611264	+	0.791427i	$0.709339\pi$
$192$	23085.0	+	6078.48i	0.626221	+	0.164889i
$193$	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	$0.578923\pi$
$194$	−27708.5	+	15997.5i	−0.736223	+	0.425058i
$195$	15761.2	+	15625.2i	0.414497	+	0.410919i
$196$	5618.15	−	9730.92i	0.146245	−	0.253304i
$197$		−	68537.7i		−	1.76603i	−0.469349	−	0.883013i	$-0.655511\pi$
$197$		−	68537.7i		−	1.76603i	0.469349	−	0.883013i	$-0.344489\pi$
$198$	301.497	+	34777.6i	0.00769046	+	0.887092i
$199$	−8237.42			−0.208010			−0.104005	−	0.994577i	$-0.533166\pi$
$199$	−8237.42			−0.208010			−0.104005	+	0.994577i	$0.533166\pi$
$200$	17177.1	+	9917.21i	0.429428	+	0.247930i
$201$	−10970.0	−	40242.0i	−0.271527	−	0.996064i
$202$	−4374.17	−	7576.28i	−0.107200	−	0.185675i
$203$	−44961.7	+	25958.7i	−1.09107	+	0.629927i
$204$	−2489.38	+	678.606i	−0.0598178	+	0.0163064i
$205$	4455.24	−	7716.70i	0.106014	−	0.183622i
$206$			23020.6i			0.542477i
$207$	−1170.83	+	10.1503i	−0.0273246	+	0.000236884i
$208$	−46711.2			−1.07968
$209$	−15877.2	−	9166.71i	−0.363481	−	0.209856i
$210$	32859.2	−	33145.3i	0.745107	−	0.751595i
$211$	−20393.7	−	35322.9i	−0.458069	−	0.793399i	0.540790	−	0.841158i	$-0.318125\pi$
$211$	−20393.7	−	35322.9i	−0.458069	−	0.793399i	−0.998859	+	0.0477587i	$0.984792\pi$
$212$	−6709.10	+	3873.50i	−0.149277	+	0.0861851i
$213$	−15347.6	+	58287.4i	−0.338284	+	1.28474i
$214$	20355.1	−	35256.0i	0.444473	−	0.769850i
$215$			14303.1i			0.309423i
$216$	−27399.1	+	28121.1i	−0.587259	+	0.602734i
$217$	−21931.2			−0.465740
$218$	−62495.4	−	36081.7i	−1.31503	−	0.759231i
$219$	41983.7	+	11054.7i	0.875371	+	0.230493i
$220$	3034.07	+	5255.16i	0.0626873	+	0.108578i
$221$	−9701.99	+	5601.45i	−0.198644	+	0.114687i
$222$	−23581.7	−	23378.1i	−0.478485	−	0.474355i
$223$	29959.8	−	51891.9i	0.602461	−	1.04349i	−0.389986	−	0.920821i	$-0.627520\pi$
$223$	29959.8	−	51891.9i	0.602461	−	1.04349i	0.992447	−	0.122672i	$-0.0391464\pi$
$224$			35771.4i			0.712918i
$225$	−25703.6	+	15138.6i	−0.507725	+	0.299034i
$226$	94213.5			1.84458
$227$	85572.3	+	49405.2i	1.66066	+	0.958785i	0.972399	+	0.233325i	$0.0749607\pi$
$227$	85572.3	+	49405.2i	1.66066	+	0.958785i	0.688265	+	0.725459i	$0.258373\pi$
$228$	1777.47	+	6520.43i	0.0341927	+	0.125432i
$229$	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	$0.817187\pi$
$230$	−895.645	+	517.101i	−0.0169309	+	0.00977506i
$231$	60520.3	−	16497.9i	1.13417	−	0.309175i
$232$	19288.0	−	33407.8i	0.358353	−	0.620686i
$233$			18467.8i			0.340176i	0.985429	+	0.170088i	$0.0544052\pi$
$233$			18467.8i			0.340176i	−0.985429	+	0.170088i	$0.945595\pi$
$234$	27413.9	−	48447.4i	0.500655	−	0.884786i
$235$	−63376.3			−1.14760
$236$	18469.8	+	10663.6i	0.331619	+	0.191460i
$237$	−36299.5	+	36615.5i	−0.646254	+	0.651881i
$238$	11779.6	+	20402.9i	0.207959	+	0.360196i
$239$	22383.5	−	12923.1i	0.391861	−	0.226241i	−0.291105	−	0.956691i	$-0.594023\pi$
$239$	22383.5	−	12923.1i	0.391861	−	0.226241i	0.682966	+	0.730450i	$0.260690\pi$
$240$	−11144.2	+	42323.8i	−0.193476	+	0.734789i
$241$	−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	$0.913029\pi$
$242$		−	24088.9i		−	0.411325i
$243$	−16515.5	−	56692.4i	−0.279691	−	0.960090i
$244$	6744.49			0.113284
$245$	−39586.6	−	22855.3i	−0.659502	−	0.380764i
$246$	−21612.3	−	5690.71i	−0.357134	−	0.0940365i
$247$	14671.9	+	25412.4i	0.240487	+	0.416536i
$248$	14112.3	−	8147.76i	0.229454	−	0.132475i
$249$	−18102.2	−	17945.9i	−0.291966	−	0.289446i
$250$	−35532.0	+	61543.3i	−0.568513	+	0.984693i
$251$		−	49051.6i		−	0.778585i	−0.921114	−	0.389292i	$-0.872720\pi$
$251$		−	49051.6i		−	0.778585i	0.921114	−	0.389292i	$-0.127280\pi$
$252$	−20125.5	−	11388.0i	−0.316917	−	0.179327i
$253$	−1389.98			−0.0217154
$254$	−79896.3	−	46128.1i	−1.23839	−	0.714988i
$255$	2760.65	+	10127.1i	0.0424553	+	0.155742i
$256$	−22852.6	−	39581.8i	−0.348703	−	0.603971i
$257$	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	$0.0704668\pi$
$258$	34611.5	−	9435.11i	0.519973	−	0.141745i
$259$	−29945.8	+	51867.7i	−0.446413	+	0.773209i
$260$		−	9712.41i		−	0.143675i
$261$	29443.1	+	49991.0i	0.432217	+	0.733856i
$262$	14295.3			0.208253
$263$	35921.0	+	20739.0i	0.519323	+	0.299831i	0.736658	−	0.676266i	$-0.236403\pi$
$263$	35921.0	+	20739.0i	0.519323	+	0.299831i	−0.217335	+	0.976097i	$0.569736\pi$
$264$	−32814.5	+	33100.2i	−0.470824	+	0.474923i
$265$	15757.9	+	27293.5i	0.224391	+	0.388657i
$266$	53441.4	−	30854.4i	0.755292	−	0.436068i
$267$	32719.7	−	124264.i	0.458973	−	1.74310i
$268$	−9126.63	+	15807.8i	−0.127069	+	0.220091i
$269$			115737.i			1.59944i	0.600370	+	0.799722i	$0.295020\pi$
$269$			115737.i			1.59944i	−0.600370	+	0.799722i	$0.704980\pi$
$270$	−37356.6	−	36397.5i	−0.512436	−	0.499279i
$271$	−5077.71			−0.0691400			−0.0345700	−	0.999402i	$-0.511006\pi$
$271$	−5077.71			−0.0691400			−0.0345700	+	0.999402i	$0.511006\pi$
$272$	−19132.5	−	11046.1i	−0.258603	−	0.149304i
$273$	−97091.7	−	25565.1i	−1.30274	−	0.343022i
$274$	−8644.57	−	14972.8i	−0.115144	−	0.199436i
$275$	−30668.2	+	17706.3i	−0.405529	+	0.234133i
$276$	363.886	+	360.745i	0.00477692	+	0.00473568i
$277$	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	$0.0775899\pi$
$278$			52150.9i			0.674795i
$279$	212.459	+	24507.1i	0.00272939	+	0.314835i
$280$	62548.8			0.797817
$281$	−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	$0.751218\pi$
$282$	41806.6	+	153362.i	0.525711	+	1.92850i
$283$	−19194.0	−	33245.0i	−0.239658	−	0.415100i	0.720958	−	0.692979i	$-0.243702\pi$
$283$	−19194.0	−	33245.0i	−0.239658	−	0.415100i	−0.960616	+	0.277879i	$0.910369\pi$
$284$	22843.2	−	13188.5i	0.283218	−	0.163516i
$285$	26525.9	−	7230.98i	0.326574	−	0.0890241i
$286$	33041.2	−	57229.1i	0.403946	−	0.699656i
$287$			40309.6i			0.489378i
$288$	39972.8	−	346.535i	0.481925	−	0.00417794i
$289$	78222.5			0.936561
$290$	44379.5	+	25622.5i	0.527699	+	0.304667i
$291$	45401.7	−	45797.0i	0.536149	−	0.540818i
$292$	−9499.55	−	16453.7i	−0.111413	−	0.192974i
$293$	−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	$0.357417\pi$
$294$	−29193.3	+	110871.i	−0.337745	+	1.28269i
$295$	43380.7	−	75137.6i	0.498486	−	0.863402i
$296$		−	44501.2i		−	0.507911i
$297$	−19021.8	−	67468.7i	−0.215645	−	0.764873i
$298$	−67388.7			−0.758847
$299$	1926.69	+	1112.37i	0.0215511	+	0.0124425i
$300$	12624.0	+	3324.02i	0.140267	+	0.0369336i
$301$	−32352.4	−	56036.0i	−0.357086	−	0.618492i
$302$	−116998.	+	67549.0i	−1.28282	+	0.740636i
$303$	12522.2	+	12414.1i	0.136394	+	0.135217i
$304$	−28933.2	+	50113.7i	−0.313075	+	0.542262i
$305$		−	27437.4i		−	0.294947i
$306$	22685.2	−	13360.8i	0.242270	−	0.142689i
$307$	−126105.			−1.33799			−0.668997	−	0.743265i	$-0.733276\pi$
$307$	−126105.			−1.33799			−0.668997	+	0.743265i	$0.733276\pi$
$308$	−23773.5	−	13725.6i	−0.250606	−	0.144688i
$309$	−12203.2	−	44765.8i	−0.127807	−	0.468845i
$310$	10823.6	+	18747.1i	0.112629	+	0.195079i
$311$	−86432.4	+	49901.7i	−0.893626	+	0.515935i	−0.875127	−	0.483894i	$-0.839222\pi$
$311$	−86432.4	+	49901.7i	−0.893626	+	0.515935i	−0.0184989	+	0.999829i	$0.505889\pi$
$312$	71974.5	−	19620.3i	0.739383	−	0.201556i
$313$	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	$0.163051\pi$
$314$		−	92085.9i		−	0.933972i
$315$	−46327.8	+	81873.1i	−0.466896	+	0.825125i
$316$	22563.3			0.225958
$317$	−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	$0.981926\pi$
$318$	55651.8	−	56136.3i	0.550332	−	0.555124i
$319$	34437.0	+	59646.6i	0.338410	+	0.586144i
$320$	−36805.0	+	21249.4i	−0.359424	+	0.207514i
$321$	−20893.3	+	79349.1i	−0.202767	+	0.770073i
$322$	2339.28	−	4051.76i	0.0225617	−	0.0390779i
$323$			13878.3i			0.133024i
$324$	−12530.6	+	22599.6i	−0.119366	+	0.215283i
$325$	56679.9			0.536615
$326$	153872.	+	88837.9i	1.44785	+	0.835917i
$327$	140655.	+	37035.8i	1.31541	+	0.346359i
$328$	−14975.6	−	25938.5i	−0.139199	−	0.241100i
$329$	248293.	−	143352.i	2.29389	−	1.32438i
$330$	−43970.9	−	43591.4i	−0.403773	−	0.400288i
$331$	−3379.43	+	5853.34i	−0.0308452	+	0.0534254i	−0.881036	−	0.473049i	$-0.843153\pi$
$331$	−3379.43	+	5853.34i	−0.0308452	+	0.0534254i	0.850191	+	0.526475i	$0.176487\pi$
$332$			11154.9i			0.101202i
$333$	58249.6	+	32960.5i	0.525297	+	0.297239i
$334$	−122574.			−1.09877
$335$	64308.1	+	37128.3i	0.573028	+	0.330838i
$336$	−52072.7	−	191022.i	−0.461245	−	1.69202i
$337$	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	$0.400550\pi$
$338$	18847.7	−	10881.7i	0.164978	−	0.0952500i
$339$	−183208.	+	49942.5i	−1.59421	+	0.434581i
$340$	2296.77	−	3978.11i	0.0198682	−	0.0344128i
$341$			29094.2i			0.250206i
$342$	−34996.0	−	59419.3i	−0.299203	−	0.508013i
$343$	32754.4			0.278408
$344$	41636.3	+	24038.7i	0.351848	+	0.203140i
$345$	1467.56	−	1480.34i	0.0123298	−	0.0124372i
$346$	22504.2	+	38978.4i	0.187980	+	0.325591i
$347$	−140770.	+	81273.8i	−1.16910	+	0.674981i	−0.953468	−	0.301494i	$-0.902515\pi$
$347$	−140770.	+	81273.8i	−1.16910	+	0.674981i	−0.215633	+	0.976475i	$0.569181\pi$
$348$	6464.91	−	24552.6i	0.0533831	−	0.202739i
$349$	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	$0.0702054\pi$
$350$		−	119196.i		−	0.973027i
$351$	−27627.2	+	108743.i	−0.224245	+	0.882646i
$352$	47454.7			0.382995
$353$	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	$0.494038\pi$
$354$	−210439.	−	55410.5i	−1.67927	−	0.442166i
$355$	−53652.7	−	92929.2i	−0.425730	−	0.737387i
$356$	−48699.8	+	28116.8i	−0.384261	+	0.221853i
$357$	−33722.3	−	33431.2i	−0.264594	−	0.262310i
$358$	2713.66	−	4700.19i	0.0211733	−	0.0366733i
$359$		−	95302.8i		−	0.739463i	−0.929139	−	0.369732i	$-0.879450\pi$
$359$		−	95302.8i		−	0.739463i	0.929139	−	0.369732i	$-0.120550\pi$
$360$	−605.942	−	69895.2i	−0.00467548	−	0.539315i
$361$	−93969.7			−0.721063
$362$	109669.	+	63317.3i	0.836885	+	0.483176i
$363$	12769.5	+	46843.2i	0.0969081	+	0.355495i
$364$	21968.7	+	38050.9i	0.165807	+	0.287185i
$365$	−66935.7	+	38645.4i	−0.502426	+	0.290076i
$366$	−66394.9	+	18099.3i	−0.495647	+	0.135114i
$367$	−52073.0	+	90193.1i	−0.386616	+	0.669639i	−0.991992	−	0.126301i	$-0.959690\pi$
$367$	−52073.0	+	90193.1i	−0.386616	+	0.669639i	0.605376	+	0.795940i	$0.293023\pi$
$368$			4387.23i			0.0323963i
$369$	45043.9	−	390.499i	0.330814	−	0.00286792i
$370$	59116.1			0.431820
$371$	−123471.	−	71286.2i	−0.897053	−	0.517914i
$372$	7550.89	−	7616.63i	0.0545648	−	0.0550399i
$373$	−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	$-0.511461\pi$
$374$	27066.7	−	15627.0i	0.193505	−	0.111720i
$375$	36471.6	−	138513.i	0.259354	−	0.984979i
$376$	−106515.	+	184489.i	−0.753415	+	1.30495i
$377$		−	110237.i		−	0.775612i
$378$	228682.	+	58098.9i	1.60048	+	0.406616i
$379$	200830.			1.39814			0.699070	−	0.715053i	$-0.253597\pi$
$379$	200830.			1.39814			0.699070	+	0.715053i	$0.253597\pi$
$380$	−10419.9	−	6015.92i	−0.0721598	−	0.0416615i
$381$	179819.	+	47347.9i	1.23875	+	0.326175i
$382$	−21772.3	−	37710.7i	−0.149203	−	0.258427i
$383$	117206.	−	67668.8i	0.799008	−	0.461308i	−0.0441160	−	0.999026i	$-0.514047\pi$
$383$	117206.	−	67668.8i	0.799008	−	0.461308i	0.843124	+	0.537719i	$0.180714\pi$
$384$	126168.	+	125078.i	0.855628	+	0.848243i
$385$	−55837.6	+	96713.6i	−0.376708	+	0.652478i
$386$			238458.i			1.60043i
$387$	−62304.0	+	36695.0i	−0.416001	+	0.245011i
$388$	−28221.1			−0.187461
$389$	−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	$0.899533\pi$
$390$	26063.9	+	95612.1i	0.171360	+	0.628614i
$391$	526.102	+	911.236i	0.00344125	+	0.00596043i
$392$	−133064.	+	76824.6i	−0.865942	+	0.499952i
$393$	−27798.7	+	7577.92i	−0.179986	+	0.0490642i
$394$	153019.	−	265037.i	0.985721	−	1.70732i
$395$		−	91790.2i		−	0.588304i
$396$	−15107.4	+	26698.7i	−0.0963385	+	0.170255i
$397$	102384.			0.649608			0.324804	−	0.945781i	$-0.394702\pi$
$397$	102384.			0.649608			0.324804	+	0.945781i	$0.394702\pi$
$398$	−31854.4	−	18391.1i	−0.201096	−	0.116103i
$399$	−87566.4	+	88328.8i	−0.550037	+	0.554826i
$400$	55886.8	+	96798.8i	0.349292	+	0.604992i
$401$	−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	$0.423718\pi$
$402$	47424.3	−	180109.i	0.293460	−	1.11451i
$403$	23283.5	−	40328.2i	0.143363	−	0.248313i
$404$		−	7716.45i		−	0.0472775i
$405$	91937.9	+	50975.9i	0.560512	+	0.310781i
$406$	−231824.			−1.40639
$407$	68808.1	+	39726.4i	0.415385	+	0.239823i
$408$	34119.8	+	8984.05i	0.204968	+	0.0539700i
$409$	−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	$0.981025\pi$
$410$	34457.1	−	19893.8i	0.204980	−	0.118345i
$411$	24747.3	+	24533.7i	0.146502	+	0.145238i
$412$	−10152.6	+	17584.8i	−0.0598113	+	0.103596i
$413$			392495.i			2.30109i
$414$	−4550.30	−	2574.78i	−0.0265485	−	0.0150224i
$415$	45379.7			0.263491
$416$	−65778.1	−	37977.0i	−0.380097	−	0.219449i
$417$	−27645.1	−	101413.i	−0.158981	−	0.583203i
$418$	−40931.8	−	70895.9i	−0.234265	−	0.405759i
$419$	109423.	−	63175.3i	0.623276	−	0.359848i	−0.154868	−	0.987935i	$-0.549495\pi$
$419$	109423.	−	63175.3i	0.623276	−	0.359848i	0.778143	+	0.628087i	$0.216162\pi$
$420$	39718.2	−	10827.2i	0.225160	−	0.0613787i
$421$	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	$-0.0410949\pi$
$422$		−	182126.i		−	1.02270i
$423$	−162594.	−	276067.i	−0.908709	−	1.54288i
$424$	105935.			0.589263
$425$	23215.6	+	13403.5i	0.128529	+	0.0742063i
$426$	−189484.	+	191134.i	−1.04413	+	1.05322i
$427$	62061.3	+	107493.i	0.340381	+	0.589557i
$428$	31097.5	−	17954.1i	0.169761	−	0.0980115i
$429$	−33914.9	+	128803.i	−0.184279	+	0.699859i
$430$	−31933.5	+	55310.4i	−0.172707	+	0.299137i
$431$			121972.i			0.656607i	0.944572	+	0.328304i	$0.106477\pi$
$431$			121972.i			0.656607i	−0.944572	+	0.328304i	$0.893523\pi$
$432$	−212953.	+	60039.2i	−1.14108	+	0.321712i
$433$	−152419.			−0.812951			−0.406475	−	0.913662i	$-0.633242\pi$
$433$	−152419.			−0.812951			−0.406475	+	0.913662i	$0.633242\pi$
$434$	−84808.7	−	48964.3i	−0.450258	−	0.259956i
$435$	−99882.9	−	26300.0i	−0.527853	−	0.138988i
$436$	−31825.8	−	55123.8i	−0.167419	−	0.289979i
$437$	2386.80	−	1378.02i	0.0124984	−	0.00721593i
$438$	137671.	+	136483.i	0.717621	+	0.711426i
$439$	−115564.	+	200162.i	−0.599643	+	1.03861i	0.393230	+	0.919440i	$0.371358\pi$
$439$	−115564.	+	200162.i	−0.599643	+	1.03861i	−0.992874	+	0.119173i	$0.961976\pi$
$440$		−	82977.9i		−	0.428605i
$441$	−2003.26	−	231075.i	−0.0103005	−	1.18816i
$442$	−50023.9			−0.256055
$443$	−17481.4	−	10092.9i	−0.0890774	−	0.0514289i	0.454800	−	0.890594i	$-0.349711\pi$
$443$	−17481.4	−	10092.9i	−0.0890774	−	0.0514289i	−0.543877	+	0.839165i	$0.683044\pi$
$444$	−7703.15	−	28258.0i	−0.0390753	−	0.143343i
$445$	114383.	+	198117.i	0.577618	+	1.00046i
$446$	231711.	−	133778.i	1.16487	−	0.672537i
$447$	131044.	−	35722.7i	0.655847	−	0.178784i
$448$	96128.9	−	166500.i	0.478958	−	0.829580i
$449$			92962.8i			0.461123i	0.973058	+	0.230561i	$0.0740562\pi$
$449$			92962.8i			0.461123i	−0.973058	+	0.230561i	$0.925944\pi$
$450$	−133195.	+	1154.71i	−0.657755	+	0.00570227i
$451$	53475.0			0.262905
$452$	71967.4	+	41550.4i	0.352256	+	0.203375i
$453$	191707.	−	193376.i	0.934205	−	0.942339i
$454$	220607.	+	382103.i	1.07031	+	1.85383i
$455$	154796.	−	89371.5i	0.747716	−	0.431694i
$456$	23531.9	−	89370.1i	0.113169	−	0.429796i
$457$	−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	$0.989302\pi$
$458$			23746.0i			0.113203i
$459$	−37031.0	+	38006.9i	−0.175768	+	0.180400i
$460$	−912.215			−0.00431103
$461$	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	$0.586287\pi$
$462$	270868.	+	71321.8i	1.26903	+	0.334148i
$463$	34090.0	+	59045.5i	0.159025	+	0.275439i	0.934517	−	0.355918i	$-0.115832\pi$
$463$	34090.0	+	59045.5i	0.159025	+	0.275439i	−0.775493	+	0.631357i	$0.782498\pi$
$464$	188264.	−	108694.i	0.874444	−	0.504860i
$465$	−30985.4	−	30718.0i	−0.143302	−	0.142065i
$466$	−41231.8	+	71415.6i	−0.189872	+	0.328868i
$467$		−	224350.i		−	1.02871i	−0.857578	−	0.514353i	$-0.828032\pi$
$467$		−	224350.i		−	1.02871i	0.857578	−	0.514353i	$-0.171968\pi$
$468$	42307.2	−	24917.6i	0.193162	−	0.113766i
$469$	−335925.			−1.52720
$470$	−245078.	−	141496.i	−1.10945	−	0.640543i
$471$	48814.7	+	179070.i	0.220043	+	0.807202i
$472$	−145817.	−	252563.i	−0.654524	−	1.13367i
$473$	−74337.9	+	42919.0i	−0.332267	+	0.191835i
$474$	−222120.	+	60550.0i	−0.988624	+	0.269499i
$475$	35107.8	−	60808.5i	0.155603	−	0.269511i
$476$			20780.4i			0.0917149i
$477$	−78462.7	+	138664.i	−0.344847	+	0.609433i
$478$	115410.			0.505113
$479$	−94542.7	−	54584.3i	−0.412057	−	0.237901i	0.279616	−	0.960112i	$-0.409793\pi$
$479$	−94542.7	−	54584.3i	−0.412057	−	0.237901i	−0.691673	+	0.722211i	$0.743126\pi$
$480$	−50103.2	+	50539.4i	−0.217462	+	0.219355i
$481$	−63584.5	−	110132.i	−0.274828	−	0.476016i
$482$	−321243.	+	185470.i	−1.38274	+	0.798324i
$483$	−2401.14	+	9119.10i	−0.0102926	+	0.0390893i
$484$	10623.8	−	18400.9i	0.0453510	−	0.0785503i
$485$			114807.i			0.488073i
$486$	62707.3	−	256104.i	0.265489	−	1.08429i
$487$	106309.			0.448240			0.224120	−	0.974562i	$-0.428049\pi$
$487$	106309.			0.448240			0.224120	+	0.974562i	$0.428049\pi$
$488$	−79870.6	−	46113.3i	−0.335388	−	0.193636i
$489$	−346312.	−	91187.0i	−1.44827	−	0.381343i
$490$	−102055.	−	176765.i	−0.425052	−	0.736212i
$491$	−64472.7	+	37223.3i	−0.267432	+	0.154402i	−0.627720	−	0.778439i	$-0.716012\pi$
$491$	−64472.7	+	37223.3i	−0.267432	+	0.154402i	0.360288	+	0.932841i	$0.382678\pi$
$492$	−13999.4	−	13878.5i	−0.0578333	−	0.0573341i
$493$	26068.5	−	45152.0i	0.107256	−	0.185773i
$494$			131028.i			0.536919i
$495$	108614.	+	61458.9i	0.443275	+	0.250827i
$496$	91830.8			0.373271
$497$	420397.	+	242716.i	1.70195	+	0.982621i
$498$	−29935.0	−	109813.i	−0.120704	−	0.442787i
$499$	55603.4	+	96308.0i	0.223306	+	0.386777i	0.955810	−	0.293985i	$-0.0949817\pi$
$499$	55603.4	+	96308.0i	0.223306	+	0.386777i	−0.732504	+	0.680763i	$0.761648\pi$
$500$	−54284.1	+	31340.9i	−0.217136	+	0.125364i
$501$	238358.	−	64976.6i	0.949631	−	0.258870i
$502$	109514.	−	189684.i	0.434573	−	0.752703i
$503$		−	115897.i		−	0.458077i	−0.973417	−	0.229038i	$-0.926442\pi$
$503$		−	115897.i		−	0.458077i	0.973417	−	0.229038i	$-0.0735581\pi$
$504$	160471.	+	272462.i	0.631737	+	1.07262i
$505$	−31391.5			−0.123092
$506$	−5375.10	−	3103.31i	−0.0209935	−	0.0121206i
$507$	−30882.9	+	31151.8i	−0.120144	+	0.121190i
$508$	−40687.2	−	70472.3i	−0.157663	−	0.273081i
$509$	−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	$0.457238\pi$
$510$	−11934.6	+	45325.4i	−0.0458845	+	0.174261i
$511$	174825.	−	302807.i	0.669519	−	1.15964i
$512$			111753.i			0.426305i
$513$	99551.4	+	96995.4i	0.378279	+	0.368567i
$514$	433603.			1.64122
$515$	71537.3	+	41302.1i	0.269723	+	0.155725i
$516$	30600.0	+	8057.24i	0.114927	+	0.0302613i
$517$	−190172.	−	329388.i	−0.711486	−	1.23233i
$518$	−231603.	+	133716.i	−0.863146	+	0.498337i
$519$	−64424.2	−	63868.1i	−0.239174	−	0.237110i
$520$	−66405.5	+	115018.i	−0.245583	+	0.425362i
$521$		−	299306.i		−	1.10266i	−0.834289	−	0.551328i	$-0.814121\pi$
$521$		−	299306.i		−	1.10266i	0.834289	−	0.551328i	$-0.185879\pi$
$522$	2245.80	+	259052.i	0.00824195	+	0.950707i
$523$	−162892.			−0.595520			−0.297760	−	0.954641i	$-0.596240\pi$
$523$	−162892.			−0.595520			−0.297760	+	0.954641i	$0.596240\pi$
$524$	10919.8	+	6304.56i	0.0397698	+	0.0229611i
$525$	63185.6	+	231788.i	0.229245	+	0.840955i
$526$	92605.2	+	160397.i	0.334706	+	0.579728i
$527$	19073.4	−	11012.0i	0.0686763	−	0.0396503i
$528$	−253412.	+	69080.1i	−0.908989	+	0.247791i
$529$	−139816.	+	242168.i	−0.499627	+	0.865379i
$530$			140726.i			0.500983i
$531$	438594.	−	3802.29i	1.55551	−	0.0134852i
$532$	54430.1			0.192316
$533$	−74123.1	−	42795.0i	−0.260915	−	0.150639i
$534$	403963.	−	407480.i	1.41664	−	1.42897i
$535$	−73039.7	−	126508.i	−0.255183	−	0.441989i
$536$	216161.	−	124801.i	0.752400	−	0.434398i
$537$	−2785.41	+	10578.5i	−0.00965920	+	0.0366839i
$538$	−258399.	+	447560.i	−0.892742	+	1.54628i
$539$		−	274327.i		−	0.944257i
$540$	−12483.6	−	44278.2i	−0.0428108	−	0.151846i
$541$	−62918.7			−0.214974			−0.107487	−	0.994207i	$-0.534280\pi$
$541$	−62918.7			−0.214974			−0.107487	+	0.994207i	$0.534280\pi$
$542$	−19635.7	−	11336.7i	−0.0668416	−	0.0385910i
$543$	−246826.	−	64991.5i	−0.837128	−	0.220423i
$544$	−17961.4	−	31110.1i	−0.0606936	−	0.105124i
$545$	−224251.	+	129471.i	−0.754989	+	0.435893i
$546$	−318379.	−	315631.i	−1.06797	−	1.05875i
$547$	7403.57	−	12823.4i	0.0247438	−	0.0428575i	−0.853388	−	0.521276i	$-0.825456\pi$
$547$	7403.57	−	12823.4i	0.0247438	−	0.0428575i	0.878132	+	0.478418i	$0.158790\pi$
$548$		−	15249.8i		−	0.0507813i
$549$	119517.	−	70391.8i	0.396539	−	0.233549i
$550$	−158126.			−0.522732
$551$	−118267.	−	68281.3i	−0.389547	−	0.224905i
$552$	−1842.79	−	6760.03i	−0.00604779	−	0.0221856i
$553$	207622.	+	359612.i	0.678927	+	1.17594i
$554$	163907.	−	94631.9i	0.534046	−	0.308332i
$555$	−114957.	+	31337.4i	−0.373207	+	0.101736i
$556$	−22999.8	+	39836.8i	−0.0744002	+	0.128865i
$557$		−	254392.i		−	0.819962i	−0.912094	−	0.409981i	$-0.865535\pi$
$557$		−	254392.i		−	0.819962i	0.912094	−	0.409981i	$-0.134465\pi$
$558$	−53893.7	+	95243.9i	−0.173089	+	0.305893i
$559$	137389.			0.439671
$560$	305260.	+	176242.i	0.973405	+	0.561996i
$561$	−44350.2	+	44736.3i	−0.140919	+	0.142146i
$562$	−92557.4	−	160314.i	−0.293048	−	0.507574i
$563$	80806.7	−	46653.8i	0.254936	−	0.147187i	−0.367087	−	0.930187i	$-0.619645\pi$
$563$	80806.7	−	46653.8i	0.254936	−	0.147187i	0.622022	+	0.783000i	$0.286311\pi$
$564$	−35701.3	+	135587.i	−0.112234	+	0.426246i
$565$	169032.	−	292772.i	0.529508	−	0.917134i
$566$		−	171412.i		−	0.535068i
$567$	−475494.	+	8245.01i	−1.47904	+	0.0256463i
$568$	−360690.			−1.11799
$569$	−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	$0.745141\pi$
$570$	118721.	+	31260.2i	0.365407	+	0.0962149i
$571$	219188.	+	379644.i	0.672270	+	1.16441i	0.977259	+	0.212050i	$0.0680141\pi$
$571$	219188.	+	379644.i	0.672270	+	1.16441i	−0.304988	+	0.952356i	$0.598653\pi$
$572$	50478.7	−	29143.9i	0.154282	−	0.0890749i
$573$	62328.8	+	61790.8i	0.189836	+	0.188198i
$574$	−89996.4	+	155878.i	−0.273150	+	0.473110i
$575$		−	5323.52i		−	0.0161014i
$576$	−186987.	−	105806.i	−0.563594	−	0.318909i
$577$	214770.			0.645094			0.322547	−	0.946554i	$-0.395461\pi$
$577$	214770.			0.645094			0.322547	+	0.946554i	$0.395461\pi$
$578$	302489.	+	174642.i	0.905428	+	0.522749i
$579$	−126406.	−	463705.i	−0.377061	−	1.38320i
$580$	22600.3	+	39144.8i	0.0671827	+	0.116364i
$581$	−177787.	+	102645.i	−0.526681	+	0.304079i
$582$	277817.	−	75733.1i	0.820188	−	0.223584i
$583$	−94568.9	+	163798.i	−0.278235	+	0.481917i
$584$			259801.i			0.761753i
$585$	−101368.	−	172111.i	−0.296202	−	0.502918i
$586$	−57951.3			−0.168759
$587$	568470.	+	328206.i	1.64980	+	0.952512i	0.977150	+	0.212550i	$0.0681767\pi$
$587$	568470.	+	328206.i	1.64980	+	0.952512i	0.672649	+	0.739962i	$0.265157\pi$
$588$	−71196.7	+	71816.6i	−0.205923	+	0.207716i
$589$	−28843.8	−	49959.0i	−0.0831423	−	0.144007i
$590$	335509.	−	193706.i	0.963830	−	0.556467i
$591$	−157066.	+	596507.i	−0.449683	+	1.70781i
$592$	125390.	−	217181.i	0.357781	−	0.619696i
$593$			118369.i			0.336612i	0.985735	+	0.168306i	$0.0538296\pi$
$593$			118369.i			0.336612i	−0.985735	+	0.168306i	$0.946170\pi$
$594$	77074.6	−	303372.i	0.218443	−	0.859811i
$595$	84537.3			0.238789
$596$	−51476.5	−	29720.0i	−0.144916	−	0.0836673i
$597$	71693.1	+	18877.4i	0.201154	+	0.0529656i
$598$	4967.04	+	8603.17i	0.0138898	+	0.0240578i
$599$	−306693.	+	177069.i	−0.854772	+	0.493503i	−0.862258	−	0.506469i	$-0.830950\pi$
$599$	−306693.	+	177069.i	−0.854772	+	0.493503i	0.00748620	+	0.999972i	$0.497617\pi$
$600$	−126771.	−	125677.i	−0.352143	−	0.349103i
$601$	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	$-0.141891\pi$
$602$		−	288924.i		−	0.797242i
$603$	3254.27	+	375379.i	0.00894992	+	1.03237i
$604$	−119163.			−0.326638
$605$	−74857.1	−	43218.8i	−0.204514	−	0.118076i
$606$	20707.6	+	75963.2i	0.0563877	+	0.206851i
$607$	−4860.81	−	8419.17i	−0.0131926	−	0.0228503i	0.859354	−	0.511382i	$-0.170866\pi$
$607$	−4860.81	−	8419.17i	−0.0131926	−	0.0228503i	−0.872546	+	0.488531i	$0.837533\pi$
$608$	−81486.6	+	47046.3i	−0.220434	+	0.127268i
$609$	450806.	−	122890.i	1.21550	−	0.331346i
$610$	61257.7	−	106101.i	0.164627	−	0.285142i
$611$			608765.i			1.63067i
$612$	23221.1	−	201.310i	0.0619982	−	0.000537480i
$613$	194450.			0.517473			0.258736	−	0.965948i	$-0.416694\pi$
$613$	194450.			0.517473			0.258736	+	0.965948i	$0.416694\pi$
$614$	−487650.	−	281545.i	−1.29352	−	0.746811i
$615$	−56459.6	+	56951.2i	−0.149275	+	0.150575i
$616$	187689.	+	325087.i	0.494627	+	0.856720i
$617$	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	$0.112073\pi$
$618$	52755.5	−	200356.i	0.138131	−	0.524596i
$619$	−8628.23	+	14944.5i	−0.0225185	+	0.0390033i	−0.877065	−	0.480372i	$-0.840502\pi$
$619$	−8628.23	+	14944.5i	−0.0225185	+	0.0390033i	0.854547	+	0.519375i	$0.173835\pi$
$620$			19093.9i			0.0496719i
$621$	10213.4	+	2594.81i	0.0264842	+	0.00672857i
$622$	−445649.			−1.15189
$623$	−896249.	−	517449.i	−2.30915	−	1.33319i
$624$	406544.	+	107047.i	1.04409	+	0.274918i
$625$	12412.5	+	21499.1i	0.0317760	+	0.0550376i
$626$	8605.50	−	4968.39i	0.0219598	−	0.0126785i
$627$	117178.	+	116166.i	0.298065	+	0.295492i
$628$	40612.1	−	70342.1i	0.102976	−	0.178360i
$629$		−	60145.1i		−	0.152019i
$630$	−361943.	+	213173.i	−0.911926	+	0.537095i
$631$	−429836.			−1.07955			−0.539777	−	0.841808i	$-0.681491\pi$
$631$	−429836.			−1.07955			−0.539777	+	0.841808i	$0.681491\pi$
$632$	−267202.	−	154269.i	−0.668968	−	0.386229i
$633$	96545.0	+	354163.i	0.240948	+	0.883886i
$634$	−375235.	−	649927.i	−0.933523	−	1.61691i
$635$	−286690.	+	165521.i	−0.710993	+	0.410492i
$636$	67268.4	−	18337.4i	0.166302	−	0.0453339i
$637$	−219538.	+	380251.i	−0.541042	+	0.937113i
$638$			307540.i			0.755546i
$639$	267151.	−	472124.i	0.654266	−	1.15626i
$640$	−316285.			−0.772181
$641$	−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	$0.679184\pi$
$642$	−257952.	+	260198.i	−0.625849	+	0.631298i
$643$	−138524.	−	239931.i	−0.335045	−	0.580315i	0.648448	−	0.761259i	$-0.275418\pi$
$643$	−138524.	−	239931.i	−0.335045	−	0.580315i	−0.983494	+	0.180943i	$0.942085\pi$
$644$	3573.84	−	2063.36i	0.00861714	−	0.00497511i
$645$	32777.9	−	124485.i	0.0787882	−	0.299224i
$646$	−30985.0	+	53667.7i	−0.0742484	+	0.128602i
$647$			125452.i			0.299689i	0.988710	+	0.149844i	$0.0478773\pi$
$647$			125452.i			0.299689i	−0.988710	+	0.149844i	$0.952123\pi$
$648$	302908.	−	181958.i	0.721376	−	0.433333i
$649$	520687.			1.23620
$650$	219183.	+	126545.i	0.518776	+	0.299516i
$651$	190875.	+	50259.1i	0.450388	+	0.118591i
$652$	78359.2	+	135722.i	0.184330	+	0.319268i
$653$	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	$0.225275\pi$
$654$	461231.	+	457250.i	1.07836	+	1.06905i
$655$	25647.8	−	44423.2i	0.0597815	−	0.103545i
$656$		−	168785.i		−	0.392216i
$657$	−340065.	−	192425.i	−0.787828	−	0.445791i
$658$	1.28021e6			2.95685
$659$	311139.	+	179636.i	0.716446	+	0.413640i	0.813443	−	0.581644i	$-0.197590\pi$
$659$	311139.	+	179636.i	0.716446	+	0.413640i	−0.0969973	+	0.995285i	$0.530924\pi$
$660$	−14363.5	−	52690.5i	−0.0329740	−	0.120961i
$661$	−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	$0.906016\pi$
$662$	−26136.7	+	15090.0i	−0.0596396	+	0.0344330i
$663$	97276.5	−	26517.6i	0.221300	−	0.0603264i
$664$	76268.4	−	132101.i	0.172985	−	0.299619i
$665$		−	221429.i		−	0.500715i
$666$	151665.	+	257509.i	0.341929	+	0.580556i
$667$	−10353.7			−0.0232726
$668$	−93631.5	−	54058.2i	−0.209831	−	0.121146i
$669$	−379669.	+	382975.i	−0.848307	+	0.855693i
$670$	165788.	+	287152.i	0.369320	+	0.639680i
$671$	142602.	−	82331.1i	0.316723	−	0.182860i
$672$	81976.2	−	311331.i	0.181530	−	0.689420i
$673$	−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	$0.251317\pi$
$674$			991702.i			2.18304i
$675$	258400.	−	72852.2i	0.567133	−	0.159895i
$676$	19196.4			0.0420075
$677$	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	$0.578686\pi$
$678$	−819973.	−	215906.i	−1.78378	−	0.469684i
$679$	−259684.	−	449786.i	−0.563256	−	0.975588i
$680$	−54398.2	+	31406.8i	−0.117643	+	0.0679213i
$681$	−631545.	−	626094.i	−1.36179	−	1.35004i
$682$	−64956.6	+	112508.i	−0.139654	+	0.241888i
$683$		−	267358.i		−	0.573129i	−0.958061	−	0.286564i	$-0.907487\pi$
$683$		−	267358.i		−	0.573129i	0.958061	−	0.286564i	$-0.0925132\pi$
$684$	−527.292	−	60823.0i	−0.00112704	−	0.130004i
$685$	−62038.2			−0.132214
$686$	126662.	+	73128.5i	0.269153	+	0.155396i
$687$	−12587.7	−	46176.5i	−0.0266707	−	0.0978380i
$688$	135466.	+	234635.i	0.286190	+	0.495696i
$689$	262169.	−	151363.i	0.552259	−	0.318847i
$690$	8980.13	−	2447.99i	0.0188619	−	0.00514175i
$691$	−168343.	+	291579.i	−0.352565	+	0.610660i	−0.986698	−	0.162564i	$-0.948024\pi$
$691$	−168343.	+	291579.i	−0.352565	+	0.610660i	0.634133	+	0.773224i	$0.281357\pi$
$692$			39699.5i			0.0829036i
$693$	−564537.	+	4894.13i	−1.17551	+	0.0101908i
$694$	−725817.			−1.50698
$695$	162061.	+	93565.9i	0.335513	+	0.193708i
$696$	−244430.	+	246558.i	−0.504587	+	0.508980i
$697$	−20240.1	−	35056.9i	−0.0416627	−	0.0721618i
$698$	281121.	−	162305.i	0.577009	−	0.333137i
$699$	42322.1	−	160732.i	0.0866189	−	0.328963i
$700$	52568.2	−	91050.7i	0.107282	−	0.185818i
$701$		−	635795.i		−	1.29384i	−0.762557	−	0.646921i	$-0.776056\pi$
$701$		−	635795.i		−	1.29384i	0.762557	−	0.646921i	$-0.223944\pi$
$702$	−349618.	+	358831.i	−0.709446	+	0.728141i
$703$	−157538.			−0.318768
$704$	−220881.	−	127525.i	−0.445669	−	0.257307i
$705$	551586.	+	145237.i	1.10978	+	0.292214i
$706$	287182.	+	497413.i	0.576165	+	0.997948i
$707$	122984.	−	71005.0i	0.246043	−	0.142053i
$708$	−136312.	−	135135.i	−0.271937	−	0.269589i
$709$	−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	$0.307705\pi$
$710$		−	479147.i		−	0.950499i
$711$	399837.	−	235491.i	0.790941	−	0.465839i
$712$	768959.			1.51685
$713$	−3787.73	−	2186.84i	−0.00745074	−	0.00430169i
$714$	−55765.6	−	204569.i	−0.109388	−	0.401276i
$715$	−118561.	−	205354.i	−0.231916	−	0.401690i
$716$	4145.79	−	2393.57i	0.00808689	−	0.00466897i
$717$	−224427.	+	61178.9i	−0.436553	+	0.119004i
$718$	212776.	−	368539.i	0.412737	−	0.714882i
$719$			798370.i			1.54435i	0.635409	+	0.772176i	$0.280832\pi$
$719$			798370.i			1.54435i	−0.635409	+	0.772176i	$0.719168\pi$
$720$	193984.	−	342820.i	0.374198	−	0.661304i
$721$	−373688.			−0.718850
$722$	−363384.	−	209800.i	−0.697093	−	0.402467i
$723$	526372.	−	530956.i	1.00697	−	1.01574i
$724$	55848.8	+	96732.9i	0.106546	+	0.184543i
$725$	−228442.	+	131891.i	−0.434610	+	0.250922i
$726$	−55203.7	+	209654.i	−0.104736	+	0.397768i
$727$	−158557.	+	274628.i	−0.299996	+	0.519609i	−0.976135	−	0.217166i	$-0.930319\pi$
$727$	−158557.	+	274628.i	−0.299996	+	0.519609i	0.676139	+	0.736775i	$0.263652\pi$
$728$		−	600816.i		−	1.13365i
$729$	13819.7	+	531261.i	0.0260043	+	0.999662i
$730$	−345123.			−0.647632
$731$	56273.2	+	32489.3i	0.105309	+	0.0608004i
$732$	−58699.6	−	15456.1i	−0.109550	−	0.0288455i
$733$	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	$0.469431\pi$
$734$	−402736.	+	232520.i	−0.747529	+	0.431586i
$735$	292159.	+	289637.i	0.540810	+	0.536142i
$736$	−3566.90	+	6178.05i	−0.00658469	+	0.0114050i
$737$			445641.i			0.820446i
$738$	175058.	+	99056.5i	0.321418	+	0.181874i
$739$	−392565.			−0.718825			−0.359412	−	0.933179i	$-0.617023\pi$
$739$	−392565.			−0.718825			−0.359412	+	0.933179i	$0.617023\pi$
$740$	45157.3	+	26071.6i	0.0824640	+	0.0476106i
$741$	−69457.6	−	254796.i	−0.126498	−	0.464041i
$742$	−318312.	−	551332.i	−0.578155	−	1.00139i
$743$	899450.	−	519298.i	1.62929	−	0.940673i	0.644990	−	0.764191i	$-0.276861\pi$
$743$	899450.	−	519298.i	1.62929	−	0.940673i	0.984304	−	0.176482i	$-0.0564719\pi$
$744$	−141497.	+	38572.0i	−0.255623	+	0.0696829i
$745$	−120905.	+	209413.i	−0.217836	+	0.377304i
$746$		−	1.09770e6i		−	1.97245i
$747$	116423.	+	197674.i	0.208641	+	0.354248i
$748$	27567.5			0.0492713
$749$	572304.	+	330420.i	1.02015	+	0.588983i
$750$	450284.	−	454205.i	0.800506	−	0.807476i
$751$	−159783.	−	276752.i	−0.283302	−	0.490694i	0.688894	−	0.724862i	$-0.258097\pi$
$751$	−159783.	−	276752.i	−0.283302	−	0.490694i	−0.972196	+	0.234168i	$0.924763\pi$
$752$	−1.03966e6	+	600246.i	−1.83846	+	1.06144i
$753$	−112410.	+	426913.i	−0.198251	+	0.752921i
$754$	246118.	−	426290.i	0.432914	−	0.749829i
$755$			484769.i			0.850435i
$756$	149062.	+	145235.i	0.260809	+	0.254113i
$757$	500321.			0.873085			0.436543	−	0.899684i	$-0.356203\pi$
$757$	500321.			0.873085			0.436543	+	0.899684i	$0.356203\pi$
$758$	776617.	+	448380.i	1.35166	+	0.780383i
$759$	12097.5	+	3185.37i	0.0209996	+	0.00552939i
$760$	82263.8	+	142485.i	0.142424	+	0.246685i
$761$	−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	$0.618750\pi$
$762$	589655.	+	584565.i	1.01552	+	1.00675i
$763$	585707.	−	1.01447e6i	1.00608	−	1.74258i
$764$		−	38408.3i		−	0.0658019i
$765$	−818.955	−	94466.2i	−0.00139938	−	0.161419i
$766$	604318.			1.02993
$767$	−721738.	−	416696.i	−1.22684	−	0.708318i
$768$	108186.	+	396865.i	0.183420	+	0.672853i
$769$	−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	$0.872016\pi$
$770$	−431852.	+	249330.i	−0.728372	+	0.420526i
$771$	−843184.	+	229852.i	−1.41845	+	0.386670i
$772$	−105165.	+	182152.i	−0.176457	+	0.305632i
$773$		−	710063.i		−	1.18833i	−0.804342	−	0.594166i	$-0.797482\pi$
$773$		−	710063.i		−	1.18833i	0.804342	−	0.594166i	$-0.202518\pi$
$774$	−322858.	+	2798.95i	−0.538927	+	0.00467211i
$775$	−111428.			−0.185521
$776$	334204.	+	192953.i	0.554993	+	0.320426i
$777$	379492.	−	382796.i	0.628580	−	0.634053i
$778$	−451386.	−	781823.i	−0.745742	−	1.29166i
$779$	−91824.5	+	53014.9i	−0.151316	+	0.0873621i
$780$	−22257.6	+	84530.5i	−0.0365839	+	0.138939i
$781$	321990.	−	557702.i	0.527885	−	0.914324i
$782$			4698.37i			0.00768305i
$783$	−141691.	−	502563.i	−0.231109	−	0.819723i
$784$	−865865.			−1.40870
$785$	−286161.	−	165215.i	−0.464377	−	0.268108i
$786$	−124417.	−	32760.1i	−0.201388	−	0.0530274i
$787$	300855.	+	521097.i	0.485745	+	0.841335i	0.999866	−	0.0163827i	$-0.00521501\pi$
$787$	300855.	+	521097.i	0.485745	+	0.841335i	−0.514121	+	0.857718i	$0.671882\pi$
$788$	233775.	−	134970.i	0.376484	−	0.217363i
$789$	−265106.	−	262818.i	−0.425859	−	0.422183i
$790$	204934.	−	354956.i	0.328367	−	0.568748i
$791$			1.52935e6i			2.44429i
$792$	361451.	−	212883.i	0.576234	−	0.339383i
$793$	−263552.			−0.419102
$794$	395923.	+	228586.i	0.628014	+	0.362584i
$795$	−74598.8	−	273656.i	−0.118031	−	0.432983i
$796$	−16221.8	−	28097.0i	−0.0256020	−	0.0443439i
$797$	−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	$0.443193\pi$
$798$	−535828.	+	146067.i	−0.841432	+	0.229375i
$799$	−143959.	+	249344.i	−0.225499	+	0.390576i
$800$			181748.i			0.283981i
$801$	−569542.	+	1.00653e6i	−0.887688	+	1.56877i
$802$	−402308.			−0.625474
$803$	−401706.	−	231925.i	−0.622984	−	0.359680i
$804$	115658.	−	116665.i	0.178923	−	0.180480i
$805$	−8393.99	−	14538.8i	−0.0129532	−	0.0224356i
$806$	180076.	−	103967.i	0.277195	−	0.160039i
$807$	265232.	−	1.00730e6i	0.407266	−	1.54672i
$808$	−52758.7	+	91380.8i	−0.0808112	+	0.139969i
$809$		−	629639.i		−	0.962042i	−0.876709	−	0.481021i	$-0.840266\pi$
$809$		−	629639.i		−	0.962042i	0.876709	−	0.481021i	$-0.159734\pi$
$810$	241716.	+	402389.i	0.368414	+	0.613304i
$811$	577760.			0.878428			0.439214	−	0.898383i	$-0.355257\pi$
$811$	577760.			0.878428			0.439214	+	0.898383i	$0.355257\pi$
$812$	−177085.	−	102240.i	−0.268577	−	0.155063i
$813$	44193.1	+	11636.4i	0.0668610	+	0.0176051i
$814$	177389.	+	307246.i	0.267718	+	0.463701i
$815$	552135.	−	318775.i	0.831246	−	0.479920i
$816$	141202.	+	139984.i	0.212062	+	0.210231i
$817$	85099.3	−	147396.i	0.127492	−	0.220822i
$818$		−	668548.i		−	0.999140i
$819$	786436.	+	445004.i	1.17245	+	0.663431i
$820$	35094.5			0.0521929
$821$	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	$0.656106\pi$
$822$	40923.9	+	150124.i	0.0605667	+	0.222181i
$823$	146289.	+	253380.i	0.215979	+	0.374087i	0.953575	−	0.301155i	$-0.0973723\pi$
$823$	146289.	+	253380.i	0.215979	+	0.374087i	−0.737596	+	0.675242i	$0.764039\pi$
$824$	240461.	−	138830.i	0.354153	−	0.204470i
$825$	307493.	−	83822.6i	0.451780	−	0.123155i
$826$	−876296.	+	1.51779e6i	−1.28437	+	2.22460i
$827$		−	806491.i		−	1.17920i	−0.807694	−	0.589601i	$-0.799285\pi$
$827$		−	806491.i		−	1.17920i	0.807694	−	0.589601i	$-0.200715\pi$
$828$	−2340.32	−	3973.60i	−0.00341362	−	0.00579593i
$829$	204904.			0.298154			0.149077	−	0.988826i	$-0.452370\pi$
$829$	204904.			0.298154			0.149077	+	0.988826i	$0.452370\pi$
$830$	175485.	+	101316.i	0.254732	+	0.147069i
$831$	−268570.	+	270908.i	−0.388916	+	0.392302i
$832$	204112.	+	353533.i	0.294864	+	0.510720i
$833$	−179842.	+	103832.i	−0.259179	+	0.149637i
$834$	119513.	−	453887.i	0.171823	−	0.652553i
$835$	−219915.	+	380905.i	−0.315415	+	0.546315i
$836$		−	72207.5i		−	0.103317i
$837$	54313.0	−	213780.i	0.0775269	−	0.305152i
$838$	564189.			0.803409
$839$	667796.	+	385552.i	0.948681	+	0.547721i	0.892671	−	0.450709i	$-0.148829\pi$
$839$	667796.	+	385552.i	0.948681	+	0.547721i	0.0560100	+	0.998430i	$0.482162\pi$
$840$	−544384.	−	143341.i	−0.771520	−	0.203148i
$841$	−97125.1	−	168226.i	−0.137322	−	0.237848i
$842$	832531.	−	480662.i	1.17429	−	0.677978i
$843$	264970.	+	262682.i	0.372856	+	0.369637i
$844$	80322.0	−	139122.i	0.112759	−	0.195304i
$845$		−	78093.4i		−	0.109371i
$846$	−12402.0	−	1.43057e6i	−0.0173281	−	1.99880i
$847$	391030.			0.545058
$848$	517001.	+	298491.i	0.718951	+	0.415087i
$849$	90865.5	+	333329.i	0.126062	+	0.462442i
$850$	59850.2	+	103664.i	0.0828376	+	0.143479i
$851$	−10343.8	+	5972.02i	−0.0142831	+	0.00824635i
$852$	−229036.	+	62435.4i	−0.315519	+	0.0860106i
$853$	−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	$0.899696\pi$
$854$			554240.i			0.759945i
$855$	−247435.	+	2145.09i	−0.338477	+	0.00293436i
$856$	−491023.			−0.670122
$857$	−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	$0.784945\pi$
$858$	−418719.	+	422365.i	−0.568785	+	0.573737i
$859$	−565525.	−	979517.i	−0.766417	−	1.32747i	−0.939494	−	0.342565i	$-0.888704\pi$
$859$	−565525.	−	979517.i	−0.766417	−	1.32747i	0.173077	−	0.984908i	$-0.444629\pi$
$860$	−48786.4	+	28166.8i	−0.0659632	+	0.0380839i
$861$	92376.1	−	350828.i	0.124610	−	0.473247i
$862$	−272319.	+	471670.i	−0.366490	+	0.634780i
$863$			110025.i			0.147730i	0.997268	+	0.0738649i	$0.0235334\pi$
$863$			110025.i			0.147730i	−0.997268	+	0.0738649i	$0.976467\pi$
$864$	−348691.	−	88588.3i	−0.467104	−	0.118672i
$865$	161503.			0.215848
$866$	−589410.	−	340296.i	−0.785926	−	0.453755i
$867$	−680798.	−	179260.i	−0.905691	−	0.238476i
$868$	−43188.8	−	74805.3i	−0.0573234	−	0.0992871i
$869$	477065.	−	275433.i	0.631739	−	0.364735i
$870$	−327532.	−	324705.i	−0.432728	−	0.428993i
$871$	356638.	−	617715.i	0.470101	−	0.814238i
$872$			870394.i			1.14468i
$873$	−500098.	+	294541.i	−0.656185	+	0.386472i
$874$	12306.4			0.0161105
$875$	−999020.	−	576784.i	−1.30484	−	0.753351i
$876$	44971.5	+	164972.i	0.0586042	+	0.214982i
$877$	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	$0.747722\pi$
$878$	−893778.	+	516023.i	−1.15942	+	0.669391i
$879$	112692.	−	30719.9i	0.145853	−	0.0397596i
$880$	233804.	−	404960.i	0.301916	−	0.522935i
$881$		−	235809.i		−	0.303815i	−0.988395	−	0.151907i	$-0.951458\pi$
$881$		−	235809.i		−	0.303815i	0.988395	−	0.151907i	$-0.0485416\pi$
$882$	508159.	−	898047.i	0.653224	−	1.15442i
$883$	−273719.			−0.351061			−0.175531	−	0.984474i	$-0.556164\pi$
$883$	−273719.			−0.351061			−0.175531	+	0.984474i	$0.556164\pi$
$884$	−38212.0	−	22061.7i	−0.0488985	−	0.0282315i
$885$	−549748.	+	554534.i	−0.701903	+	0.708014i
$886$	−45067.3	−	78058.8i	−0.0574109	−	0.0994385i
$887$	322071.	−	185948.i	0.409359	−	0.236344i	−0.281155	−	0.959662i	$-0.590718\pi$
$887$	322071.	−	185948.i	0.409359	−	0.236344i	0.690514	+	0.723319i	$0.257384\pi$
$888$	−101982.	+	387309.i	−0.129329	+	0.491170i
$889$	748789.	−	1.29694e6i	0.947449	−	1.64103i
$890$			1.02150e6i			1.28961i
$891$	10937.9	+	630795.i	0.0137778	+	0.794571i
$892$	235997.			0.296604
$893$	653108.	+	377072.i	0.818996	+	0.472848i
$894$	586507.	+	154432.i	0.733835	+	0.193225i
$895$	−9737.36	−	16865.6i	−0.0121561	−	0.0210550i
$896$	1.23913e6	−	715412.i	1.54348	−	0.891128i
$897$	−14219.4	−	14096.7i	−0.0176725	−	0.0175199i
$898$	−207552.	+	359490.i	−0.257379	+	0.445794i
$899$			216718.i			0.268148i
$900$	−102254.	−	57860.3i	−0.126239	−	0.0714324i
$901$	143176.			0.176368
$902$	206790.	+	119390.i	0.254165	+	0.146742i
$903$	153158.	+	561842.i	0.187830	+	0.689030i
$904$	−568175.	−	984108.i	−0.695257	−	1.20422i
$905$	393522.	−	227200.i	0.480476	−	0.277403i
$906$	1.17308e6	−	319781.i	1.42912	−	0.389580i
$907$	71965.4	−	124648.i	0.0874801	−	0.151520i	−0.818965	−	0.573843i	$-0.805452\pi$
$907$	71965.4	−	124648.i	0.0874801	−	0.151520i	0.906445	+	0.422323i	$0.138785\pi$
$908$			389172.i			0.472030i
$909$	−80536.0	−	136741.i	−0.0974680	−	0.165490i
$910$	798134.			0.963814
$911$	−772201.	−	445830.i	−0.930451	−	0.537196i	−0.0434969	−	0.999054i	$-0.513850\pi$
$911$	−772201.	−	445830.i	−0.930451	−	0.537196i	−0.886954	+	0.461857i	$0.847183\pi$
$912$	366659.	−	369852.i	0.440832	−	0.444670i
$913$	136170.	+	235854.i	0.163358	+	0.282944i
$914$	−854175.	+	493158.i	−1.02248	+	0.590329i
$915$	−62877.5	+	238798.i	−0.0751023	+	0.285225i
$916$	−10472.5	+	18139.0i	−0.0124813	+	0.0216183i
$917$			232053.i			0.275961i
$918$	−228055.	+	64297.0i	−0.270617	+	0.0762967i
$919$	−582156.			−0.689300			−0.344650	−	0.938731i	$-0.612002\pi$
$919$	−582156.			−0.689300			−0.344650	+	0.938731i	$0.612002\pi$
$920$	10802.8	+	6236.98i	0.0127632	+	0.00736883i
$921$	1.09753e6	+	288990.i	1.29389	+	0.340693i
$922$	237093.	+	410658.i	0.278906	+	0.483079i
$923$	−892636.	+	515364.i	−1.04778	+	0.604937i
$924$	175454.	+	173940.i	0.205504	+	0.203730i
$925$	−152149.	+	263530.i	−0.177822	+	0.307997i
$926$			304441.i			0.355043i
$927$	3620.10	+	417578.i	0.00421271	+	0.485935i
$928$	353482.			0.410460
$929$	−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	$0.814136\pi$
$930$	−51239.7	−	187966.i	−0.0592435	−	0.217327i
$931$	271966.	+	471059.i	0.313773	+	0.543470i
$932$	−62991.9	+	36368.4i	−0.0725192	+	0.0418690i
$933$	866609.	−	236238.i	0.995543	−	0.271385i
$934$	500890.	−	867567.i	0.574181	−	0.994510i
$935$		−	112148.i		−	0.128283i
$936$	−671382.	+	5820.41i	−0.766334	+	0.00664357i
$937$	−1.46097e6			−1.66403			−0.832015	−	0.554753i	$-0.812813\pi$
$937$	−1.46097e6			−1.66403			−0.832015	+	0.554753i	$0.812813\pi$
$938$	−1.29903e6	−	749996.i	−1.47643	−	0.852420i
$939$	−14100.5	+	14223.3i	−0.0159921	+	0.0161313i
$940$	−124806.	−	216170.i	−0.141247	−	0.244647i
$941$	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	$0.302849\pi$
$942$	−211030.	+	801456.i	−0.237817	+	0.903187i
$943$	−4019.42	+	6961.83i	−0.00452001	+	0.00782889i
$944$		−	1.64346e6i		−	1.84423i
$945$	590833.	−	606402.i	0.661608	−	0.679042i
$946$	−383289.			−0.428296
$947$	514322.	+	296944.i	0.573503	+	0.331112i	0.758547	−	0.651618i	$-0.225910\pi$
$947$	514322.	+	296944.i	0.573503	+	0.331112i	−0.185044	+	0.982730i	$0.559243\pi$
$948$	−196376.	−	51707.5i	−0.218510	−	0.0575356i
$949$	371210.	+	642955.i	0.412180	+	0.713917i
$950$	271526.	−	156766.i	0.300860	−	0.173702i
$951$	1.07421e6	+	1.06494e6i	1.18776	+	1.17750i
$952$	142079.	−	246089.i	0.156768	−	0.271530i
$953$			1.25477e6i			1.38159i	0.723050	+	0.690796i	$0.242740\pi$
$953$			1.25477e6i			1.38159i	−0.723050	+	0.690796i	$0.757260\pi$
$954$	−613002.	+	361038.i	−0.673543	+	0.396695i
$955$	−156250.			−0.171322
$956$	88159.0	+	50898.6i	0.0964608	+	0.0556917i
$957$	−163027.	−	598043.i	−0.178006	−	0.652993i
$958$	−243733.	−	422158.i	−0.265573	−	0.459985i
$959$	243051.	−	140326.i	0.264278	−	0.152581i
$960$	369024.	−	100596.i	0.400416	−	0.109154i
$961$	415987.	−	720510.i	0.450436	−	0.780178i
$962$		−	567843.i		−	0.613590i
$963$	363684.	−	642722.i	0.392167	−	0.693060i
$964$	−327186.			−0.352080
$965$	741017.	+	427826.i	0.795744	+	0.459423i
$966$	−29644.9	+	29903.0i	−0.0317684	+	0.0320450i
$967$	528928.	+	916130.i	0.565645	+	0.979725i	0.996989	+	0.0775381i	$0.0247059\pi$
$967$	528928.	+	916130.i	0.565645	+	0.979725i	−0.431345	+	0.902187i	$0.641961\pi$
$968$	−251620.	+	145273.i	−0.268531	+	0.155037i
$969$	31804.4	−	120787.i	0.0338719	−	0.128639i
$970$	−256321.	+	443962.i	−0.272422	+	0.471848i
$971$		−	775745.i		−	0.822774i	−0.911461	−	0.411387i	$-0.865044\pi$
$971$		−	775745.i		−	0.822774i	0.911461	−	0.411387i	$-0.134956\pi$
$972$	160848.	−	167976.i	0.170249	−	0.177793i
$973$	−846555.			−0.894189
$974$	411099.	+	237348.i	0.433339	+	0.250189i
$975$	−493305.	−	129892.i	−0.518927	−	0.136638i
$976$	−259864.	−	450098.i	−0.272801	−	0.472506i
$977$	−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	$0.417084\pi$
$978$	−1.13561e6	−	1.12581e6i	−1.18728	−	1.17703i
$979$	−686453.	+	1.18897e6i	−0.716218	+	1.24053i
$980$		−	180035.i		−	0.187458i
$981$	−1.13930e6	−	644671.i	−1.18386	−	0.669885i
$982$	−332424.			−0.344722
$983$	260643.	+	150482.i	0.269736	+	0.155732i	0.628768	−	0.777593i	$-0.283560\pi$
$983$	260643.	+	150482.i	0.269736	+	0.155732i	−0.359032	+	0.933325i	$0.616893\pi$
$984$	70895.3	+	260070.i	0.0732196	+	0.268597i
$985$	−549076.	−	951028.i	−0.565927	−	0.980214i
$986$	201616.	−	116403.i	0.207382	−	0.119732i
$987$	−2.48950e6	+	678638.i	−2.55551	+	0.696633i
$988$	−57786.2	+	100089.i	−0.0591985	+	0.102535i
$989$		−	12903.9i		−	0.0131925i
$990$	282797.	+	480157.i	0.288539	+	0.489907i
$991$	1.70094e6			1.73197			0.865987	−	0.500067i	$-0.166691\pi$
$991$	1.70094e6			1.73197			0.865987	+	0.500067i	$0.166691\pi$
$992$	129315.	+	74660.0i	0.131409	+	0.0758691i
$993$	42826.3	−	43199.1i	0.0434322	−	0.0438103i
$994$	1.08379e6	+	1.87718e6i	1.09691	+	1.89991i
$995$	−114302.	+	65992.4i	−0.115454	+	0.0666573i
$996$	25563.4	−	97085.3i	0.0257692	−	0.0978667i
$997$	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	$0.0647276\pi$
$998$			496568.i			0.498560i
$999$	−431432.	−	420355.i	−0.432297	−	0.421197i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.3	✓	6	1.1	even	1	trivial
9.5.d.a.5.3	yes	6	9.5	odd	6	inner
27.5.d.a.8.1		6	3.2	odd	2
27.5.d.a.17.1		6	9.4	even	3
81.5.b.a.80.2		6	9.7	even	3
81.5.b.a.80.5		6	9.2	odd	6
144.5.q.a.65.3		6	4.3	odd	2
144.5.q.a.113.3		6	36.23	even	6
432.5.q.a.17.1		6	36.31	odd	6
432.5.q.a.305.1		6	12.11	even	2
1296.5.e.c.161.2		6	36.11	even	6
1296.5.e.c.161.5		6	36.7	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.86703 + 2.23263i) q^{2} +(-8.70335 - 2.29167i) q^{3} +(1.96929 + 3.41090i) q^{4} +(13.8760 - 8.01130i) q^{5} +(-28.5397 - 28.2933i) q^{6} +(-36.2418 + 62.7727i) q^{7} -53.8574i q^{8} +(70.4965 + 39.8904i) q^{9} +71.5451 q^{10} +(83.2749 + 48.0788i) q^{11} +(-9.32272 - 34.1992i) q^{12} +(-76.9530 - 133.286i) q^{13} +(-280.297 + 161.829i) q^{14} +(-139.127 + 37.9260i) q^{15} +(151.752 - 262.843i) q^{16} -72.7905i q^{17} +(183.552 + 311.650i) q^{18} -190.660 q^{19} +(54.6515 + 31.5531i) q^{20} +(459.280 - 463.279i) q^{21} +(214.684 + 371.844i) q^{22} +(-12.5186 + 7.22762i) q^{23} +(-123.423 + 468.740i) q^{24} +(-184.138 + 318.937i) q^{25} -687.231i q^{26} +(-522.140 - 508.734i) q^{27} -285.482 q^{28} +(620.301 + 358.131i) q^{29} +(-622.682 - 163.958i) q^{30} +(151.284 + 262.031i) q^{31} +(427.392 - 246.755i) q^{32} +(-614.590 - 609.285i) q^{33} +(162.514 - 281.483i) q^{34} +1161.38i q^{35} +(2.76561 + 319.012i) q^{36} +826.277 q^{37} +(-737.289 - 425.674i) q^{38} +(364.300 + 1336.39i) q^{39} +(-431.468 - 747.325i) q^{40} +(481.613 - 278.059i) q^{41} +(2810.38 - 766.110i) q^{42} +(-446.340 + 773.084i) q^{43} +378.723i q^{44} +(1297.78 - 11.2508i) q^{45} -64.5464 q^{46} +(-3425.50 - 1977.72i) q^{47} +(-1923.10 + 1939.85i) q^{48} +(-1426.44 - 2470.67i) q^{49} +(-1424.14 + 822.225i) q^{50} +(-166.812 + 633.521i) q^{51} +(303.085 - 524.958i) q^{52} +1966.96i q^{53} +(-883.316 - 3133.04i) q^{54} +1540.69 q^{55} +(3380.78 + 1951.89i) q^{56} +(1659.38 + 436.930i) q^{57} +(1599.15 + 2769.81i) q^{58} +(4689.48 - 2707.47i) q^{59} +(-403.342 - 399.861i) q^{60} +(856.210 - 1483.00i) q^{61} +1351.04i q^{62} +(-5058.95 + 2979.56i) q^{63} -2652.43 q^{64} +(-2135.60 - 1232.99i) q^{65} +(-1016.33 - 3728.28i) q^{66} +(2317.24 + 4013.58i) q^{67} +(248.281 - 143.345i) q^{68} +(125.517 - 34.2160i) q^{69} +(-2592.93 + 4491.08i) q^{70} -6697.12i q^{71} +(2148.39 - 3796.76i) q^{72} -4823.86 q^{73} +(3195.24 + 1844.77i) q^{74} +(2333.51 - 2353.83i) q^{75} +(-375.464 - 650.324i) q^{76} +(-6036.07 + 3484.93i) q^{77} +(-1574.90 + 5981.21i) q^{78} +(2864.40 - 4961.28i) q^{79} -4862.94i q^{80} +(3378.52 + 5624.26i) q^{81} +2483.22 q^{82} +(2452.78 + 1416.12i) q^{83} +(2484.65 + 654.230i) q^{84} +(-583.147 - 1010.04i) q^{85} +(-3452.02 + 1993.03i) q^{86} +(-4577.98 - 4538.46i) q^{87} +(2589.40 - 4484.97i) q^{88} +14277.7i q^{89} +(5043.68 + 2853.96i) q^{90} +11155.7 q^{91} +(-49.3054 - 28.4665i) q^{92} +(-716.187 - 2627.24i) q^{93} +(-8831.02 - 15295.8i) q^{94} +(-2645.60 + 1527.44i) q^{95} +(-4285.22 + 1168.15i) q^{96} +(-3582.65 + 6205.34i) q^{97} -12738.9i q^{98} +(3952.71 + 6711.25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20}+ \cdots - 9126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more