LMFDB - Embedded newform 27.5.d.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,5,Mod(8,27)] 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("27.8"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not 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:	$2.79098900326$
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^{4} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-1.28901 + 2.23263i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.5.d.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.86703 + 2.23263i) q^{2} +(1.96929 - 3.41090i) q^{4} +(-13.8760 - 8.01130i) q^{5} +(-36.2418 - 62.7727i) q^{7} -53.8574i q^{8} +71.5451 q^{10} +(-83.2749 + 48.0788i) q^{11} +(-76.9530 + 133.286i) q^{13} +(280.297 + 161.829i) q^{14} +(151.752 + 262.843i) q^{16} -72.7905i q^{17} -190.660 q^{19} +(-54.6515 + 31.5531i) q^{20} +(214.684 - 371.844i) q^{22} +(12.5186 + 7.22762i) q^{23} +(-184.138 - 318.937i) q^{25} -687.231i q^{26} -285.482 q^{28} +(-620.301 + 358.131i) q^{29} +(151.284 - 262.031i) q^{31} +(-427.392 - 246.755i) q^{32} +(162.514 + 281.483i) q^{34} +1161.38i q^{35} +826.277 q^{37} +(737.289 - 425.674i) q^{38} +(-431.468 + 747.325i) q^{40} +(-481.613 - 278.059i) q^{41} +(-446.340 - 773.084i) q^{43} +378.723i q^{44} -64.5464 q^{46} +(3425.50 - 1977.72i) q^{47} +(-1426.44 + 2470.67i) q^{49} +(1424.14 + 822.225i) q^{50} +(303.085 + 524.958i) q^{52} +1966.96i q^{53} +1540.69 q^{55} +(-3380.78 + 1951.89i) q^{56} +(1599.15 - 2769.81i) q^{58} +(-4689.48 - 2707.47i) q^{59} +(856.210 + 1483.00i) q^{61} +1351.04i q^{62} -2652.43 q^{64} +(2135.60 - 1232.99i) q^{65} +(2317.24 - 4013.58i) q^{67} +(-248.281 - 143.345i) q^{68} +(-2592.93 - 4491.08i) q^{70} -6697.12i q^{71} -4823.86 q^{73} +(-3195.24 + 1844.77i) q^{74} +(-375.464 + 650.324i) q^{76} +(6036.07 + 3484.93i) q^{77} +(2864.40 + 4961.28i) q^{79} -4862.94i q^{80} +2483.22 q^{82} +(-2452.78 + 1416.12i) q^{83} +(-583.147 + 1010.04i) q^{85} +(3452.02 + 1993.03i) q^{86} +(2589.40 + 4484.97i) q^{88} +14277.7i q^{89} +11155.7 q^{91} +(49.3054 - 28.4665i) q^{92} +(-8831.02 + 15295.8i) q^{94} +(2645.60 + 1527.44i) q^{95} +(-3582.65 - 6205.34i) q^{97} -12738.9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29}+ \cdots - 28959 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	$-0.855158\pi$
$2$	−3.86703	+	2.23263i	−0.966758	+	0.558158i	−0.0685115	+	0.997650i	$0.521825\pi$
$3$		0			0
$3$		0			0
$4$	1.96929	−	3.41090i	0.123080	−	0.213181i
$5$	−13.8760	−	8.01130i	−0.555039	−	0.320452i	0.196113	−	0.980581i	$-0.437168\pi$
$5$	−13.8760	−	8.01130i	−0.555039	−	0.320452i	−0.751152	+	0.660129i	$0.770501\pi$
$6$		0			0
$7$	−36.2418	−	62.7727i	−0.739630	−	1.28108i	−0.952662	−	0.304031i	$-0.901667\pi$
$7$	−36.2418	−	62.7727i	−0.739630	−	1.28108i	0.213033	−	0.977045i	$-0.431666\pi$
$8$		−	53.8574i		−	0.841523i
$9$		0			0
$10$	71.5451			0.715451
$11$	−83.2749	+	48.0788i	−0.688222	+	0.397345i	−0.802946	−	0.596052i	$-0.796735\pi$
$11$	−83.2749	+	48.0788i	−0.688222	+	0.397345i	0.114723	+	0.993397i	$0.463402\pi$
$12$		0			0
$13$	−76.9530	+	133.286i	−0.455343	+	0.788677i	−0.998708	−	0.0508193i	$-0.983817\pi$
$13$	−76.9530	+	133.286i	−0.455343	+	0.788677i	0.543365	+	0.839497i	$0.317150\pi$
$14$	280.297	+	161.829i	1.43009	+	0.825660i
$15$		0			0
$16$	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	$-0.0401931\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	214.684	−	371.844i	0.443563	−	0.768273i
$23$	12.5186	+	7.22762i	0.0236647	+	0.0136628i	0.511786	−	0.859113i	$-0.328984\pi$
$23$	12.5186	+	7.22762i	0.0236647	+	0.0136628i	−0.488121	+	0.872776i	$0.662318\pi$
$24$		0			0
$25$	−184.138	−	318.937i	−0.294621	−	0.510298i
$26$		−	687.231i		−	1.01661i
$27$		0			0
$28$	−285.482			−0.364135
$29$	−620.301	+	358.131i	−0.737575	+	0.425839i	−0.821187	−	0.570659i	$-0.806688\pi$
$29$	−620.301	+	358.131i	−0.737575	+	0.425839i	0.0836117	+	0.996498i	$0.473354\pi$
$30$		0			0
$31$	151.284	−	262.031i	0.157423	−	0.272665i	−0.776515	−	0.630098i	$-0.783015\pi$
$31$	151.284	−	262.031i	0.157423	−	0.272665i	0.933939	+	0.357433i	$0.116348\pi$
$32$	−427.392	−	246.755i	−0.417375	−	0.240971i
$33$		0			0
$34$	162.514	+	281.483i	0.140583	+	0.243498i
$35$			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	$0.402419\pi$
$38$	737.289	−	425.674i	0.510588	−	0.294788i
$39$		0			0
$40$	−431.468	+	747.325i	−0.269668	+	0.467078i
$41$	−481.613	−	278.059i	−0.286504	−	0.165413i	0.349860	−	0.936802i	$-0.386229\pi$
$41$	−481.613	−	278.059i	−0.286504	−	0.165413i	−0.636364	+	0.771389i	$0.719562\pi$
$42$		0			0
$43$	−446.340	−	773.084i	−0.241395	−	0.418109i	0.719717	−	0.694268i	$-0.244272\pi$
$43$	−446.340	−	773.084i	−0.241395	−	0.418109i	−0.961112	+	0.276159i	$0.910938\pi$
$44$			378.723i			0.195622i
$45$		0			0
$46$	−64.5464			−0.0305040
$47$	3425.50	−	1977.72i	1.55070	−	0.895299i	0.552619	−	0.833434i	$-0.313628\pi$
$47$	3425.50	−	1977.72i	1.55070	−	0.895299i	0.998085	−	0.0618654i	$-0.0197050\pi$
$48$		0			0
$49$	−1426.44	+	2470.67i	−0.594104	+	1.02902i
$50$	1424.14	+	822.225i	0.569654	+	0.328890i
$51$		0			0
$52$	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	$0.886142\pi$
$54$		0			0
$55$	1540.69			0.509320
$56$	−3380.78	+	1951.89i	−1.07805	+	0.622415i
$57$		0			0
$58$	1599.15	−	2769.81i	0.475371	−	0.823367i
$59$	−4689.48	−	2707.47i	−1.34716	−	0.777785i	−0.359316	−	0.933216i	$-0.616990\pi$
$59$	−4689.48	−	2707.47i	−1.34716	−	0.777785i	−0.987847	+	0.155431i	$0.950323\pi$
$60$		0			0
$61$	856.210	+	1483.00i	0.230102	+	0.398549i	0.957838	−	0.287309i	$-0.0927606\pi$
$61$	856.210	+	1483.00i	0.230102	+	0.398549i	−0.727736	+	0.685858i	$0.759427\pi$
$62$			1351.04i			0.351468i
$63$		0			0
$64$	−2652.43			−0.647565
$65$	2135.60	−	1232.99i	0.505467	−	0.291831i
$66$		0			0
$67$	2317.24	−	4013.58i	0.516205	−	0.894093i	−0.483618	−	0.875279i	$-0.660678\pi$
$67$	2317.24	−	4013.58i	0.516205	−	0.894093i	0.999823	−	0.0188141i	$-0.00598907\pi$
$68$	−248.281	−	143.345i	−0.0536941	−	0.0310003i
$69$		0			0
$70$	−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	$-0.231256\pi$
$72$		0			0
$73$	−4823.86			−0.905208			−0.452604	−	0.891712i	$-0.649505\pi$
$73$	−4823.86			−0.905208			−0.452604	+	0.891712i	$0.649505\pi$
$74$	−3195.24	+	1844.77i	−0.583499	+	0.336883i
$75$		0			0
$76$	−375.464	+	650.324i	−0.0650042	+	0.112591i
$77$	6036.07	+	3484.93i	1.01806	+	0.587777i
$78$		0			0
$79$	2864.40	+	4961.28i	0.458964	+	0.794950i	0.998907	−	0.0467524i	$-0.0148872\pi$
$79$	2864.40	+	4961.28i	0.458964	+	0.794950i	−0.539942	+	0.841702i	$0.681554\pi$
$80$		−	4862.94i		−	0.759834i
$81$		0			0
$82$	2483.22			0.369307
$83$	−2452.78	+	1416.12i	−0.356044	+	0.205562i	−0.667344	−	0.744750i	$-0.732569\pi$
$83$	−2452.78	+	1416.12i	−0.356044	+	0.205562i	0.311300	+	0.950312i	$0.399235\pi$
$84$		0			0
$85$	−583.147	+	1010.04i	−0.0807124	+	0.139798i
$86$	3452.02	+	1993.03i	0.466742	+	0.269474i
$87$		0			0
$88$	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	$0.642647\pi$
$90$		0			0
$91$	11155.7			1.34714
$92$	49.3054	−	28.4665i	0.00582531	−	0.00336324i
$93$		0			0
$94$	−8831.02	+	15295.8i	−0.999437	+	1.73107i
$95$	2645.60	+	1527.44i	0.293141	+	0.169245i
$96$		0			0
$97$	−3582.65	−	6205.34i	−0.380769	−	0.659511i	0.610403	−	0.792091i	$-0.291007\pi$
$97$	−3582.65	−	6205.34i	−0.380769	−	0.659511i	−0.991172	+	0.132580i	$0.957674\pi$
$98$		−	12738.9i		−	1.32641i
$99$		0			0
$100$	−1450.48			−0.145048
$101$	1696.72	−	979.600i	0.166328	−	0.0960298i	−0.414525	−	0.910038i	$-0.636052\pi$
$101$	1696.72	−	979.600i	0.166328	−	0.0960298i	0.580853	+	0.814008i	$0.302719\pi$
$102$		0			0
$103$	2577.74	−	4464.77i	0.242976	−	0.420848i	−0.718584	−	0.695440i	$-0.755210\pi$
$103$	2577.74	−	4464.77i	0.242976	−	0.420848i	0.961561	+	0.274592i	$0.0885429\pi$
$104$	7178.47	+	4144.49i	0.663690	+	0.383182i
$105$		0			0
$106$	−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	$-0.130351\pi$
$108$		0			0
$109$	−16161.1			−1.36024			−0.680122	−	0.733099i	$-0.738073\pi$
$109$	−16161.1			−1.36024			−0.680122	+	0.733099i	$0.738073\pi$
$110$	−5957.91	+	3439.80i	−0.492389	+	0.284281i
$111$		0			0
$112$	10999.6	−	19051.8i	0.876879	−	1.51880i
$113$	−18272.5	−	10549.6i	−1.43100	−	0.826189i	−0.433804	−	0.901007i	$-0.642829\pi$
$113$	−18272.5	−	10549.6i	−1.43100	−	0.826189i	−0.997197	+	0.0748185i	$0.976162\pi$
$114$		0			0
$115$	−115.805	−	200.581i	−0.00875654	−	0.0151668i
$116$			2821.05i			0.209650i
$117$		0			0
$118$	24179.1			1.73651
$119$	−4569.26	+	2638.06i	−0.322665	+	0.186291i
$120$		0			0
$121$	−2697.36	+	4671.97i	−0.184233	+	0.319102i
$122$	−6621.98	−	3823.20i	−0.444906	−	0.256867i
$123$		0			0
$124$	−595.842	−	1032.03i	−0.0387514	−	0.0671195i
$125$			15914.9i			1.01855i
$126$		0			0
$127$	−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
$129$		0			0
$130$	−5505.61	+	9536.00i	−0.325776	+	0.564260i
$131$	−2772.53	−	1600.72i	−0.161560	−	0.0932768i	0.417040	−	0.908888i	$-0.363067\pi$
$131$	−2772.53	−	1600.72i	−0.161560	−	0.0932768i	−0.578600	+	0.815611i	$0.696401\pi$
$132$		0			0
$133$	6909.88	+	11968.3i	0.390631	+	0.676594i
$134$			20694.2i			1.15250i
$135$		0			0
$136$	−3920.31			−0.211955
$137$	3353.18	−	1935.96i	0.178655	−	0.103147i	−0.408005	−	0.912980i	$-0.633776\pi$
$137$	3353.18	−	1935.96i	0.178655	−	0.103147i	0.586661	+	0.809833i	$0.300442\pi$
$138$		0			0
$139$	5839.62	−	10114.5i	0.302242	−	0.523499i	−0.674401	−	0.738365i	$-0.735598\pi$
$139$	5839.62	−	10114.5i	0.302242	−	0.523499i	0.976644	+	0.214866i	$0.0689315\pi$
$140$	3961.35	+	2287.08i	0.202109	+	0.116688i
$141$		0			0
$142$	14952.2	+	25898.0i	0.741530	+	1.28437i
$143$		−	14799.2i		−	0.723714i
$144$		0			0
$145$	11476.4			0.545844
$146$	18654.0	−	10769.9i	0.875117	−	0.505249i
$147$		0			0
$148$	1627.18	−	2818.35i	0.0742867	−	0.128668i
$149$	13069.8	+	7545.88i	0.588705	+	0.339889i	0.764585	−	0.644522i	$-0.222944\pi$
$149$	13069.8	+	7545.88i	0.588705	+	0.339889i	−0.175880	+	0.984412i	$0.556277\pi$
$150$		0			0
$151$	−15127.7	−	26201.9i	−0.663465	−	1.14915i	−0.979699	−	0.200474i	$-0.935752\pi$
$151$	−15127.7	−	26201.9i	−0.663465	−	1.14915i	0.316234	−	0.948681i	$-0.397581\pi$
$152$			10268.5i			0.444446i
$153$		0			0
$154$	−31122.2			−1.31229
$155$	−4198.42	+	2423.96i	−0.174752	+	0.100893i
$156$		0			0
$157$	−10311.4	+	17859.8i	−0.418328	+	0.724565i	−0.995771	−	0.0918653i	$-0.970717\pi$
$157$	−10311.4	+	17859.8i	−0.418328	+	0.724565i	0.577443	+	0.816431i	$0.304050\pi$
$158$	−22153.4	−	12790.3i	−0.887415	−	0.512349i
$159$		0			0
$160$	3953.65	+	6847.93i	0.154440	+	0.267497i
$161$		−	1047.77i		−	0.0404216i
$162$		0			0
$163$	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
$165$		0			0
$166$	6323.33	−	10952.3i	0.229472	−	0.397457i
$167$	23773.0	+	13725.3i	0.852414	+	0.492141i	0.861465	−	0.507818i	$-0.169548\pi$
$167$	23773.0	+	13725.3i	0.852414	+	0.492141i	−0.00905084	+	0.999959i	$0.502881\pi$
$168$		0			0
$169$	2436.98	+	4220.97i	0.0853253	+	0.147788i
$170$		−	5207.81i		−	0.180201i
$171$		0			0
$172$	−3515.89			−0.118844
$173$	−8729.26	+	5039.84i	−0.291666	+	0.168393i	−0.638693	−	0.769462i	$-0.720525\pi$
$173$	−8729.26	+	5039.84i	−0.291666	+	0.168393i	0.347027	+	0.937855i	$0.387191\pi$
$174$		0			0
$175$	−13347.0	+	23117.7i	−0.435821	+	0.754864i
$176$	−25274.3	−	14592.1i	−0.815933	−	0.471079i
$177$		0			0
$178$	−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	$-0.00603779\pi$
$180$		0			0
$181$	28359.9			0.865661			0.432831	−	0.901475i	$-0.357515\pi$
$181$	28359.9			0.865661			0.432831	+	0.901475i	$0.357515\pi$
$182$	−43139.3	+	24906.5i	−1.30236	+	0.751917i
$183$		0			0
$184$	389.261	−	674.220i	0.0114976	−	0.0199143i
$185$	−11465.4	−	6619.55i	−0.335001	−	0.193413i
$186$		0			0
$187$	3499.68	+	6061.62i	0.100079	+	0.173343i
$188$		−	15578.8i		−	0.440775i
$189$		0			0
$190$	−13640.8			−0.377862
$191$	8445.34	−	4875.92i	0.231500	−	0.133656i	−0.379764	−	0.925083i	$-0.623995\pi$
$191$	8445.34	−	4875.92i	0.231500	−	0.133656i	0.611264	+	0.791427i	$0.290661\pi$
$192$		0			0
$193$	26701.4	−	46248.2i	0.716836	−	1.24160i	−0.245411	−	0.969419i	$-0.578923\pi$
$193$	26701.4	−	46248.2i	0.716836	−	1.24160i	0.962247	−	0.272177i	$-0.0877436\pi$
$194$	27708.5	+	15997.5i	0.736223	+	0.425058i
$195$		0			0
$196$	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	$-0.344489\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−4374.17	+	7576.28i	−0.107200	+	0.185675i
$203$	44961.7	+	25958.7i	1.09107	+	0.629927i
$204$		0			0
$205$	4455.24	+	7716.70i	0.106014	+	0.183622i
$206$			23020.6i			0.542477i
$207$		0			0
$208$	−46711.2			−1.07968
$209$	15877.2	−	9166.71i	0.363481	−	0.209856i
$210$		0			0
$211$	−20393.7	+	35322.9i	−0.458069	+	0.793399i	−0.998859	−	0.0477587i	$-0.984792\pi$
$211$	−20393.7	+	35322.9i	−0.458069	+	0.793399i	0.540790	+	0.841158i	$0.318125\pi$
$212$	6709.10	+	3873.50i	0.149277	+	0.0861851i
$213$		0			0
$214$	20355.1	+	35256.0i	0.444473	+	0.769850i
$215$			14303.1i			0.309423i
$216$		0			0
$217$	−21931.2			−0.465740
$218$	62495.4	−	36081.7i	1.31503	−	0.759231i
$219$		0			0
$220$	3034.07	−	5255.16i	0.0626873	−	0.108578i
$221$	9701.99	+	5601.45i	0.198644	+	0.114687i
$222$		0			0
$223$	29959.8	+	51891.9i	0.602461	+	1.04349i	0.992447	+	0.122672i	$0.0391464\pi$
$223$	29959.8	+	51891.9i	0.602461	+	1.04349i	−0.389986	+	0.920821i	$0.627520\pi$
$224$			35771.4i			0.712918i
$225$		0			0
$226$	94213.5			1.84458
$227$	−85572.3	+	49405.2i	−1.66066	+	0.958785i	−0.688265	+	0.725459i	$0.741627\pi$
$227$	−85572.3	+	49405.2i	−1.66066	+	0.958785i	−0.972399	+	0.233325i	$0.925039\pi$
$228$		0			0
$229$	2658.97	−	4605.47i	0.0507040	−	0.0878220i	−0.839559	−	0.543268i	$-0.817187\pi$
$229$	2658.97	−	4605.47i	0.0507040	−	0.0878220i	0.890263	+	0.455446i	$0.150520\pi$
$230$	895.645	+	517.101i	0.0169309	+	0.00977506i
$231$		0			0
$232$	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	$0.945595\pi$
$234$		0			0
$235$	−63376.3			−1.14760
$236$	−18469.8	+	10663.6i	−0.331619	+	0.191460i
$237$		0			0
$238$	11779.6	−	20402.9i	0.207959	−	0.360196i
$239$	−22383.5	−	12923.1i	−0.391861	−	0.226241i	0.291105	−	0.956691i	$-0.405977\pi$
$239$	−22383.5	−	12923.1i	−0.391861	−	0.226241i	−0.682966	+	0.730450i	$0.739310\pi$
$240$		0			0
$241$	−41536.2	−	71942.7i	−0.715142	−	1.23866i	−0.962905	−	0.269841i	$-0.913029\pi$
$241$	−41536.2	−	71942.7i	−0.715142	−	1.23866i	0.247763	−	0.968821i	$-0.420305\pi$
$242$		−	24088.9i		−	0.411325i
$243$		0			0
$244$	6744.49			0.113284
$245$	39586.6	−	22855.3i	0.659502	−	0.380764i
$246$		0			0
$247$	14671.9	−	25412.4i	0.240487	−	0.416536i
$248$	−14112.3	−	8147.76i	−0.229454	−	0.132475i
$249$		0			0
$250$	−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	$-0.127280\pi$
$252$		0			0
$253$	−1389.98			−0.0217154
$254$	79896.3	−	46128.1i	1.23839	−	0.714988i
$255$		0			0
$256$	−22852.6	+	39581.8i	−0.348703	+	0.603971i
$257$	−84096.0	−	48552.9i	−1.27324	−	0.735104i	−0.297641	−	0.954678i	$-0.596200\pi$
$257$	−84096.0	−	48552.9i	−1.27324	−	0.735104i	−0.975596	+	0.219574i	$0.929533\pi$
$258$		0			0
$259$	−29945.8	−	51867.7i	−0.446413	−	0.773209i
$260$		−	9712.41i		−	0.143675i
$261$		0			0
$262$	14295.3			0.208253
$263$	−35921.0	+	20739.0i	−0.519323	+	0.299831i	−0.736658	−	0.676266i	$-0.763597\pi$
$263$	−35921.0	+	20739.0i	−0.519323	+	0.299831i	0.217335	+	0.976097i	$0.430264\pi$
$264$		0			0
$265$	15757.9	−	27293.5i	0.224391	−	0.388657i
$266$	−53441.4	−	30854.4i	−0.755292	−	0.436068i
$267$		0			0
$268$	−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	$0.704980\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	−8644.57	+	14972.8i	−0.115144	+	0.199436i
$275$	30668.2	+	17706.3i	0.405529	+	0.234133i
$276$		0			0
$277$	21192.9	+	36707.2i	0.276205	+	0.478401i	0.970438	−	0.241349i	$-0.0775899\pi$
$277$	21192.9	+	36707.2i	0.276205	+	0.478401i	−0.694234	+	0.719750i	$0.744257\pi$
$278$			52150.9i			0.674795i
$279$		0			0
$280$	62548.8			0.797817
$281$	35902.5	−	20728.3i	0.454687	−	0.262513i	−0.255121	−	0.966909i	$-0.582115\pi$
$281$	35902.5	−	20728.3i	0.454687	−	0.262513i	0.709807	+	0.704396i	$0.248782\pi$
$282$		0			0
$283$	−19194.0	+	33245.0i	−0.239658	+	0.415100i	−0.960616	−	0.277879i	$-0.910369\pi$
$283$	−19194.0	+	33245.0i	−0.239658	+	0.415100i	0.720958	+	0.692979i	$0.243702\pi$
$284$	−22843.2	−	13188.5i	−0.283218	−	0.163516i
$285$		0			0
$286$	33041.2	+	57229.1i	0.403946	+	0.699656i
$287$			40309.6i			0.489378i
$288$		0			0
$289$	78222.5			0.936561
$290$	−44379.5	+	25622.5i	−0.527699	+	0.304667i
$291$		0			0
$292$	−9499.55	+	16453.7i	−0.111413	+	0.192974i
$293$	11239.5	+	6489.12i	0.130922	+	0.0755876i	0.564030	−	0.825754i	$-0.309250\pi$
$293$	11239.5	+	6489.12i	0.130922	+	0.0755876i	−0.433109	+	0.901342i	$0.642583\pi$
$294$		0			0
$295$	43380.7	+	75137.6i	0.498486	+	0.863402i
$296$		−	44501.2i		−	0.507911i
$297$		0			0
$298$	−67388.7			−0.758847
$299$	−1926.69	+	1112.37i	−0.0215511	+	0.0124425i
$300$		0			0
$301$	−32352.4	+	56036.0i	−0.357086	+	0.618492i
$302$	116998.	+	67549.0i	1.28282	+	0.740636i
$303$		0			0
$304$	−28933.2	−	50113.7i	−0.313075	−	0.542262i
$305$		−	27437.4i		−	0.294947i
$306$		0			0
$307$	−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
$309$		0			0
$310$	10823.6	−	18747.1i	0.112629	−	0.195079i
$311$	86432.4	+	49901.7i	0.893626	+	0.515935i	0.875127	−	0.483894i	$-0.160778\pi$
$311$	86432.4	+	49901.7i	0.893626	+	0.515935i	0.0184989	+	0.999829i	$0.494111\pi$
$312$		0			0
$313$	1112.68	+	1927.21i	0.0113574	+	0.0196716i	0.871648	−	0.490132i	$-0.163051\pi$
$313$	1112.68	+	1927.21i	0.0113574	+	0.0196716i	−0.860291	+	0.509804i	$0.829718\pi$
$314$		−	92085.9i		−	0.933972i
$315$		0			0
$316$	22563.3			0.225958
$317$	145552.	−	84034.3i	1.44843	−	0.836254i	0.450046	−	0.893005i	$-0.351408\pi$
$317$	145552.	−	84034.3i	1.44843	−	0.836254i	0.998388	+	0.0567515i	$0.0180743\pi$
$318$		0			0
$319$	34437.0	−	59646.6i	0.338410	−	0.586144i
$320$	36805.0	+	21249.4i	0.359424	+	0.207514i
$321$		0			0
$322$	2339.28	+	4051.76i	0.0225617	+	0.0390779i
$323$			13878.3i			0.133024i
$324$		0			0
$325$	56679.9			0.536615
$326$	−153872.	+	88837.9i	−1.44785	+	0.835917i
$327$		0			0
$328$	−14975.6	+	25938.5i	−0.139199	+	0.241100i
$329$	−248293.	−	143352.i	−2.29389	−	1.32438i
$330$		0			0
$331$	−3379.43	−	5853.34i	−0.0308452	−	0.0534254i	0.850191	−	0.526475i	$-0.176487\pi$
$331$	−3379.43	−	5853.34i	−0.0308452	−	0.0534254i	−0.881036	+	0.473049i	$0.843153\pi$
$332$			11154.9i			0.101202i
$333$		0			0
$334$	−122574.			−1.09877
$335$	−64308.1	+	37128.3i	−0.573028	+	0.330838i
$336$		0			0
$337$	111046.	−	192338.i	0.977787	−	1.69358i	0.307375	−	0.951589i	$-0.400550\pi$
$337$	111046.	−	192338.i	0.977787	−	1.69358i	0.670413	−	0.741988i	$-0.266117\pi$
$338$	−18847.7	−	10881.7i	−0.164978	−	0.0952500i
$339$		0			0
$340$	2296.77	+	3978.11i	0.0198682	+	0.0344128i
$341$			29094.2i			0.250206i
$342$		0			0
$343$	32754.4			0.278408
$344$	−41636.3	+	24038.7i	−0.351848	+	0.203140i
$345$		0			0
$346$	22504.2	−	38978.4i	0.187980	−	0.325591i
$347$	140770.	+	81273.8i	1.16910	+	0.674981i	0.953468	−	0.301494i	$-0.0974853\pi$
$347$	140770.	+	81273.8i	1.16910	+	0.674981i	0.215633	+	0.976475i	$0.430819\pi$
$348$		0			0
$349$	36348.5	+	62957.4i	0.298425	+	0.516887i	0.975776	−	0.218773i	$-0.0702054\pi$
$349$	36348.5	+	62957.4i	0.298425	+	0.516887i	−0.677351	+	0.735660i	$0.736872\pi$
$350$		−	119196.i		−	0.973027i
$351$		0			0
$352$	47454.7			0.382995
$353$	−111396.	+	64314.6i	−0.893966	+	0.516131i	−0.875238	−	0.483693i	$-0.839295\pi$
$353$	−111396.	+	64314.6i	−0.893966	+	0.516131i	−0.0187281	+	0.999825i	$0.505962\pi$
$354$		0			0
$355$	−53652.7	+	92929.2i	−0.425730	+	0.737387i
$356$	48699.8	+	28116.8i	0.384261	+	0.221853i
$357$		0			0
$358$	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	$-0.120550\pi$
$360$		0			0
$361$	−93969.7			−0.721063
$362$	−109669.	+	63317.3i	−0.836885	+	0.483176i
$363$		0			0
$364$	21968.7	−	38050.9i	0.165807	−	0.287185i
$365$	66935.7	+	38645.4i	0.502426	+	0.290076i
$366$		0			0
$367$	−52073.0	−	90193.1i	−0.386616	−	0.669639i	0.605376	−	0.795940i	$-0.293023\pi$
$367$	−52073.0	−	90193.1i	−0.386616	−	0.669639i	−0.991992	+	0.126301i	$0.959690\pi$
$368$			4387.23i			0.0323963i
$369$		0			0
$370$	59116.1			0.431820
$371$	123471.	−	71286.2i	0.897053	−	0.517914i
$372$		0			0
$373$	−122915.	+	212896.i	−0.883463	+	1.53020i	−0.0359975	+	0.999352i	$0.511461\pi$
$373$	−122915.	+	212896.i	−0.883463	+	1.53020i	−0.847465	+	0.530851i	$0.821872\pi$
$374$	−27066.7	−	15627.0i	−0.193505	−	0.111720i
$375$		0			0
$376$	−106515.	−	184489.i	−0.753415	−	1.30495i
$377$		−	110237.i		−	0.775612i
$378$		0			0
$379$	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
$381$		0			0
$382$	−21772.3	+	37710.7i	−0.149203	+	0.258427i
$383$	−117206.	−	67668.8i	−0.799008	−	0.461308i	0.0441160	−	0.999026i	$-0.485953\pi$
$383$	−117206.	−	67668.8i	−0.799008	−	0.461308i	−0.843124	+	0.537719i	$0.819286\pi$
$384$		0			0
$385$	−55837.6	−	96713.6i	−0.376708	−	0.652478i
$386$			238458.i			1.60043i
$387$		0			0
$388$	−28221.1			−0.187461
$389$	175090.	−	101088.i	1.15708	−	0.668039i	0.206475	−	0.978452i	$-0.433801\pi$
$389$	175090.	−	101088.i	1.15708	−	0.668039i	0.950602	+	0.310413i	$0.100467\pi$
$390$		0			0
$391$	526.102	−	911.236i	0.00344125	−	0.00596043i
$392$	133064.	+	76824.6i	0.865942	+	0.499952i
$393$		0			0
$394$	153019.	+	265037.i	0.985721	+	1.70732i
$395$		−	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	$0.394702\pi$
$398$	31854.4	−	18391.1i	0.201096	−	0.116103i
$399$		0			0
$400$	55886.8	−	96798.8i	0.349292	−	0.604992i
$401$	78026.4	+	45048.6i	0.485236	+	0.280151i	0.722596	−	0.691271i	$-0.242949\pi$
$401$	78026.4	+	45048.6i	0.485236	+	0.280151i	−0.237360	+	0.971422i	$0.576282\pi$
$402$		0			0
$403$	23283.5	+	40328.2i	0.143363	+	0.248313i
$404$		−	7716.45i		−	0.0472775i
$405$		0			0
$406$	−231824.			−1.40639
$407$	−68808.1	+	39726.4i	−0.415385	+	0.239823i
$408$		0			0
$409$	−74861.0	+	129663.i	−0.447517	+	0.775122i	−0.998224	−	0.0595770i	$-0.981025\pi$
$409$	−74861.0	+	129663.i	−0.447517	+	0.775122i	0.550707	+	0.834699i	$0.314358\pi$
$410$	−34457.1	−	19893.8i	−0.204980	−	0.118345i
$411$		0			0
$412$	−10152.6	−	17584.8i	−0.0598113	−	0.103596i
$413$			392495.i			2.30109i
$414$		0			0
$415$	45379.7			0.263491
$416$	65778.1	−	37977.0i	0.380097	−	0.219449i
$417$		0			0
$418$	−40931.8	+	70895.9i	−0.234265	+	0.405759i
$419$	−109423.	−	63175.3i	−0.623276	−	0.359848i	0.154868	−	0.987935i	$-0.450505\pi$
$419$	−109423.	−	63175.3i	−0.623276	−	0.359848i	−0.778143	+	0.628087i	$0.783838\pi$
$420$		0			0
$421$	107645.	+	186446.i	0.607335	+	1.05194i	0.991678	+	0.128745i	$0.0410949\pi$
$421$	107645.	+	186446.i	0.607335	+	1.05194i	−0.384342	+	0.923191i	$0.625572\pi$
$422$		−	182126.i		−	1.02270i
$423$		0			0
$424$	105935.			0.589263
$425$	−23215.6	+	13403.5i	−0.128529	+	0.0742063i
$426$		0			0
$427$	62061.3	−	107493.i	0.340381	−	0.589557i
$428$	−31097.5	−	17954.1i	−0.169761	−	0.0980115i
$429$		0			0
$430$	−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	$0.893523\pi$
$432$		0			0
$433$	−152419.			−0.812951			−0.406475	−	0.913662i	$-0.633242\pi$
$433$	−152419.			−0.812951			−0.406475	+	0.913662i	$0.633242\pi$
$434$	84808.7	−	48964.3i	0.450258	−	0.259956i
$435$		0			0
$436$	−31825.8	+	55123.8i	−0.167419	+	0.289979i
$437$	−2386.80	−	1378.02i	−0.0124984	−	0.00721593i
$438$		0			0
$439$	−115564.	−	200162.i	−0.599643	−	1.03861i	−0.992874	−	0.119173i	$-0.961976\pi$
$439$	−115564.	−	200162.i	−0.599643	−	1.03861i	0.393230	−	0.919440i	$-0.371358\pi$
$440$		−	82977.9i		−	0.428605i
$441$		0			0
$442$	−50023.9			−0.256055
$443$	17481.4	−	10092.9i	0.0890774	−	0.0514289i	−0.454800	−	0.890594i	$-0.650289\pi$
$443$	17481.4	−	10092.9i	0.0890774	−	0.0514289i	0.543877	+	0.839165i	$0.316956\pi$
$444$		0			0
$445$	114383.	−	198117.i	0.577618	−	1.00046i
$446$	−231711.	−	133778.i	−1.16487	−	0.672537i
$447$		0			0
$448$	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	$0.925944\pi$
$450$		0			0
$451$	53475.0			0.262905
$452$	−71967.4	+	41550.4i	−0.352256	+	0.203375i
$453$		0			0
$454$	220607.	−	382103.i	1.07031	−	1.85383i
$455$	−154796.	−	89371.5i	−0.747716	−	0.431694i
$456$		0			0
$457$	−110443.	−	191293.i	−0.528819	−	0.915941i	−0.999435	−	0.0336033i	$-0.989302\pi$
$457$	−110443.	−	191293.i	−0.528819	−	0.915941i	0.470616	−	0.882338i	$-0.344032\pi$
$458$			23746.0i			0.113203i
$459$		0			0
$460$	−912.215			−0.00431103
$461$	−91967.2	+	53097.3i	−0.432744	+	0.249845i	−0.700515	−	0.713638i	$-0.747046\pi$
$461$	−91967.2	+	53097.3i	−0.432744	+	0.249845i	0.267771	+	0.963483i	$0.413713\pi$
$462$		0			0
$463$	34090.0	−	59045.5i	0.159025	−	0.275439i	−0.775493	−	0.631357i	$-0.782498\pi$
$463$	34090.0	−	59045.5i	0.159025	−	0.275439i	0.934517	+	0.355918i	$0.115832\pi$
$464$	−188264.	−	108694.i	−0.874444	−	0.504860i
$465$		0			0
$466$	−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	$-0.171968\pi$
$468$		0			0
$469$	−335925.			−1.52720
$470$	245078.	−	141496.i	1.10945	−	0.640543i
$471$		0			0
$472$	−145817.	+	252563.i	−0.654524	+	1.13367i
$473$	74337.9	+	42919.0i	0.332267	+	0.191835i
$474$		0			0
$475$	35107.8	+	60808.5i	0.155603	+	0.269511i
$476$			20780.4i			0.0917149i
$477$		0			0
$478$	115410.			0.505113
$479$	94542.7	−	54584.3i	0.412057	−	0.237901i	−0.279616	−	0.960112i	$-0.590207\pi$
$479$	94542.7	−	54584.3i	0.412057	−	0.237901i	0.691673	+	0.722211i	$0.256874\pi$
$480$		0			0
$481$	−63584.5	+	110132.i	−0.274828	+	0.476016i
$482$	321243.	+	185470.i	1.38274	+	0.798324i
$483$		0			0
$484$	10623.8	+	18400.9i	0.0453510	+	0.0785503i
$485$			114807.i			0.488073i
$486$		0			0
$487$	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
$489$		0			0
$490$	−102055.	+	176765.i	−0.425052	+	0.736212i
$491$	64472.7	+	37223.3i	0.267432	+	0.154402i	0.627720	−	0.778439i	$-0.283988\pi$
$491$	64472.7	+	37223.3i	0.267432	+	0.154402i	−0.360288	+	0.932841i	$0.617322\pi$
$492$		0			0
$493$	26068.5	+	45152.0i	0.107256	+	0.185773i
$494$			131028.i			0.536919i
$495$		0			0
$496$	91830.8			0.373271
$497$	−420397.	+	242716.i	−1.70195	+	0.982621i
$498$		0			0
$499$	55603.4	−	96308.0i	0.223306	−	0.386777i	−0.732504	−	0.680763i	$-0.761648\pi$
$499$	55603.4	−	96308.0i	0.223306	−	0.386777i	0.955810	+	0.293985i	$0.0949817\pi$
$500$	54284.1	+	31340.9i	0.217136	+	0.125364i
$501$		0			0
$502$	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	$-0.0735581\pi$
$504$		0			0
$505$	−31391.5			−0.123092
$506$	5375.10	−	3103.31i	0.0209935	−	0.0121206i
$507$		0			0
$508$	−40687.2	+	70472.3i	−0.157663	+	0.273081i
$509$	170299.	+	98322.1i	0.657319	+	0.379503i	0.791255	−	0.611487i	$-0.209428\pi$
$509$	170299.	+	98322.1i	0.657319	+	0.379503i	−0.133936	+	0.990990i	$0.542762\pi$
$510$		0			0
$511$	174825.	+	302807.i	0.669519	+	1.15964i
$512$			111753.i			0.426305i
$513$		0			0
$514$	433603.			1.64122
$515$	−71537.3	+	41302.1i	−0.269723	+	0.155725i
$516$		0			0
$517$	−190172.	+	329388.i	−0.711486	+	1.23233i
$518$	231603.	+	133716.i	0.863146	+	0.498337i
$519$		0			0
$520$	−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	$-0.185879\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	92605.2	−	160397.i	0.334706	−	0.579728i
$527$	−19073.4	−	11012.0i	−0.0686763	−	0.0396503i
$528$		0			0
$529$	−139816.	−	242168.i	−0.499627	−	0.865379i
$530$			140726.i			0.500983i
$531$		0			0
$532$	54430.1			0.192316
$533$	74123.1	−	42795.0i	0.260915	−	0.150639i
$534$		0			0
$535$	−73039.7	+	126508.i	−0.255183	+	0.441989i
$536$	−216161.	−	124801.i	−0.752400	−	0.434398i
$537$		0			0
$538$	−258399.	−	447560.i	−0.892742	−	1.54628i
$539$		−	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	$0.534280\pi$
$542$	19635.7	−	11336.7i	0.0668416	−	0.0385910i
$543$		0			0
$544$	−17961.4	+	31110.1i	−0.0606936	+	0.105124i
$545$	224251.	+	129471.i	0.754989	+	0.435893i
$546$		0			0
$547$	7403.57	+	12823.4i	0.0247438	+	0.0428575i	0.878132	−	0.478418i	$-0.158790\pi$
$547$	7403.57	+	12823.4i	0.0247438	+	0.0428575i	−0.853388	+	0.521276i	$0.825456\pi$
$548$		−	15249.8i		−	0.0507813i
$549$		0			0
$550$	−158126.			−0.522732
$551$	118267.	−	68281.3i	0.389547	−	0.224905i
$552$		0			0
$553$	207622.	−	359612.i	0.678927	−	1.17594i
$554$	−163907.	−	94631.9i	−0.534046	−	0.308332i
$555$		0			0
$556$	−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	$-0.134465\pi$
$558$		0			0
$559$	137389.			0.439671
$560$	−305260.	+	176242.i	−0.973405	+	0.561996i
$561$		0			0
$562$	−92557.4	+	160314.i	−0.293048	+	0.507574i
$563$	−80806.7	−	46653.8i	−0.254936	−	0.147187i	0.367087	−	0.930187i	$-0.380355\pi$
$563$	−80806.7	−	46653.8i	−0.254936	−	0.147187i	−0.622022	+	0.783000i	$0.713689\pi$
$564$		0			0
$565$	169032.	+	292772.i	0.529508	+	0.917134i
$566$		−	171412.i		−	0.535068i
$567$		0			0
$568$	−360690.			−1.11799
$569$	136853.	−	79012.1i	0.422698	−	0.244045i	−0.273533	−	0.961863i	$-0.588192\pi$
$569$	136853.	−	79012.1i	0.422698	−	0.244045i	0.696231	+	0.717818i	$0.254859\pi$
$570$		0			0
$571$	219188.	−	379644.i	0.672270	−	1.16441i	−0.304988	−	0.952356i	$-0.598653\pi$
$571$	219188.	−	379644.i	0.672270	−	1.16441i	0.977259	−	0.212050i	$-0.0680141\pi$
$572$	−50478.7	−	29143.9i	−0.154282	−	0.0890749i
$573$		0			0
$574$	−89996.4	−	155878.i	−0.273150	−	0.473110i
$575$		−	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	$0.395461\pi$
$578$	−302489.	+	174642.i	−0.905428	+	0.522749i
$579$		0			0
$580$	22600.3	−	39144.8i	0.0671827	−	0.116364i
$581$	177787.	+	102645.i	0.526681	+	0.304079i
$582$		0			0
$583$	−94568.9	−	163798.i	−0.278235	−	0.481917i
$584$			259801.i			0.761753i
$585$		0			0
$586$	−57951.3			−0.168759
$587$	−568470.	+	328206.i	−1.64980	+	0.952512i	−0.672649	+	0.739962i	$0.734843\pi$
$587$	−568470.	+	328206.i	−1.64980	+	0.952512i	−0.977150	+	0.212550i	$0.931823\pi$
$588$		0			0
$589$	−28843.8	+	49959.0i	−0.0831423	+	0.144007i
$590$	−335509.	−	193706.i	−0.963830	−	0.556467i
$591$		0			0
$592$	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	$0.946170\pi$
$594$		0			0
$595$	84537.3			0.238789
$596$	51476.5	−	29720.0i	0.144916	−	0.0836673i
$597$		0			0
$598$	4967.04	−	8603.17i	0.0138898	−	0.0240578i
$599$	306693.	+	177069.i	0.854772	+	0.493503i	0.862258	−	0.506469i	$-0.169050\pi$
$599$	306693.	+	177069.i	0.854772	+	0.493503i	−0.00748620	+	0.999972i	$0.502383\pi$
$600$		0			0
$601$	297820.	+	515839.i	0.824526	+	1.42812i	0.902281	+	0.431148i	$0.141891\pi$
$601$	297820.	+	515839.i	0.824526	+	1.42812i	−0.0777554	+	0.996972i	$0.524775\pi$
$602$		−	288924.i		−	0.797242i
$603$		0			0
$604$	−119163.			−0.326638
$605$	74857.1	−	43218.8i	0.204514	−	0.118076i
$606$		0			0
$607$	−4860.81	+	8419.17i	−0.0131926	+	0.0228503i	−0.872546	−	0.488531i	$-0.837533\pi$
$607$	−4860.81	+	8419.17i	−0.0131926	+	0.0228503i	0.859354	+	0.511382i	$0.170866\pi$
$608$	81486.6	+	47046.3i	0.220434	+	0.127268i
$609$		0			0
$610$	61257.7	+	106101.i	0.164627	+	0.285142i
$611$			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	$0.416694\pi$
$614$	487650.	−	281545.i	1.29352	−	0.746811i
$615$		0			0
$616$	187689.	−	325087.i	0.494627	−	0.856720i
$617$	−422308.	−	243819.i	−1.10932	−	0.640469i	−0.170670	−	0.985328i	$-0.554593\pi$
$617$	−422308.	−	243819.i	−1.10932	−	0.640469i	−0.938654	+	0.344860i	$0.887927\pi$
$618$		0			0
$619$	−8628.23	−	14944.5i	−0.0225185	−	0.0390033i	0.854547	−	0.519375i	$-0.173835\pi$
$619$	−8628.23	−	14944.5i	−0.0225185	−	0.0390033i	−0.877065	+	0.480372i	$0.840502\pi$
$620$			19093.9i			0.0496719i
$621$		0			0
$622$	−445649.			−1.15189
$623$	896249.	−	517449.i	2.30915	−	1.33319i
$624$		0			0
$625$	12412.5	−	21499.1i	0.0317760	−	0.0550376i
$626$	−8605.50	−	4968.39i	−0.0219598	−	0.0126785i
$627$		0			0
$628$	40612.1	+	70342.1i	0.102976	+	0.178360i
$629$		−	60145.1i		−	0.152019i
$630$		0			0
$631$	−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
$633$		0			0
$634$	−375235.	+	649927.i	−0.933523	+	1.61691i
$635$	286690.	+	165521.i	0.710993	+	0.410492i
$636$		0			0
$637$	−219538.	−	380251.i	−0.541042	−	0.937113i
$638$			307540.i			0.755546i
$639$		0			0
$640$	−316285.			−0.772181
$641$	27979.5	−	16154.0i	0.0680964	−	0.0393155i	−0.465565	−	0.885014i	$-0.654149\pi$
$641$	27979.5	−	16154.0i	0.0680964	−	0.0393155i	0.533662	+	0.845698i	$0.320816\pi$
$642$		0			0
$643$	−138524.	+	239931.i	−0.335045	+	0.580315i	−0.983494	−	0.180943i	$-0.942085\pi$
$643$	−138524.	+	239931.i	−0.335045	+	0.580315i	0.648448	+	0.761259i	$0.275418\pi$
$644$	−3573.84	−	2063.36i	−0.00861714	−	0.00497511i
$645$		0			0
$646$	−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	$0.952123\pi$
$648$		0			0
$649$	520687.			1.23620
$650$	−219183.	+	126545.i	−0.518776	+	0.299516i
$651$		0			0
$652$	78359.2	−	135722.i	0.184330	−	0.319268i
$653$	−245936.	−	141991.i	−0.576760	−	0.332992i	0.183085	−	0.983097i	$-0.441392\pi$
$653$	−245936.	−	141991.i	−0.576760	−	0.332992i	−0.759845	+	0.650105i	$0.774725\pi$
$654$		0			0
$655$	25647.8	+	44423.2i	0.0597815	+	0.103545i
$656$		−	168785.i		−	0.392216i
$657$		0			0
$658$	1.28021e6			2.95685
$659$	−311139.	+	179636.i	−0.716446	+	0.413640i	−0.813443	−	0.581644i	$-0.802410\pi$
$659$	−311139.	+	179636.i	−0.716446	+	0.413640i	0.0969973	+	0.995285i	$0.469076\pi$
$660$		0			0
$661$	−98902.1	+	171303.i	−0.226362	+	0.392070i	−0.956727	−	0.290987i	$-0.906016\pi$
$661$	−98902.1	+	171303.i	−0.226362	+	0.392070i	0.730366	+	0.683057i	$0.239350\pi$
$662$	26136.7	+	15090.0i	0.0596396	+	0.0344330i
$663$		0			0
$664$	76268.4	+	132101.i	0.172985	+	0.299619i
$665$		−	221429.i		−	0.500715i
$666$		0			0
$667$	−10353.7			−0.0232726
$668$	93631.5	−	54058.2i	0.209831	−	0.121146i
$669$		0			0
$670$	165788.	−	287152.i	0.369320	−	0.639680i
$671$	−142602.	−	82331.1i	−0.316723	−	0.182860i
$672$		0			0
$673$	−119036.	−	206176.i	−0.262814	−	0.455207i	0.704175	−	0.710027i	$-0.251317\pi$
$673$	−119036.	−	206176.i	−0.262814	−	0.455207i	−0.966989	+	0.254820i	$0.917984\pi$
$674$			991702.i			2.18304i
$675$		0			0
$676$	19196.4			0.0420075
$677$	−216636.	+	125075.i	−0.472666	+	0.272894i	−0.717355	−	0.696708i	$-0.754647\pi$
$677$	−216636.	+	125075.i	−0.472666	+	0.272894i	0.244689	+	0.969602i	$0.421314\pi$
$678$		0			0
$679$	−259684.	+	449786.i	−0.563256	+	0.975588i
$680$	54398.2	+	31406.8i	0.117643	+	0.0679213i
$681$		0			0
$682$	−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	$-0.0925132\pi$
$684$		0			0
$685$	−62038.2			−0.132214
$686$	−126662.	+	73128.5i	−0.269153	+	0.155396i
$687$		0			0
$688$	135466.	−	234635.i	0.286190	−	0.495696i
$689$	−262169.	−	151363.i	−0.552259	−	0.318847i
$690$		0			0
$691$	−168343.	−	291579.i	−0.352565	−	0.610660i	0.634133	−	0.773224i	$-0.281357\pi$
$691$	−168343.	−	291579.i	−0.352565	−	0.610660i	−0.986698	+	0.162564i	$0.948024\pi$
$692$			39699.5i			0.0829036i
$693$		0			0
$694$	−725817.			−1.50698
$695$	−162061.	+	93565.9i	−0.335513	+	0.193708i
$696$		0			0
$697$	−20240.1	+	35056.9i	−0.0416627	+	0.0721618i
$698$	−281121.	−	162305.i	−0.577009	−	0.333137i
$699$		0			0
$700$	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	$-0.223944\pi$
$702$		0			0
$703$	−157538.			−0.318768
$704$	220881.	−	127525.i	0.445669	−	0.257307i
$705$		0			0
$706$	287182.	−	497413.i	0.576165	−	0.997948i
$707$	−122984.	−	71005.0i	−0.246043	−	0.142053i
$708$		0			0
$709$	−215513.	−	373280.i	−0.428728	−	0.742578i	0.568033	−	0.823006i	$-0.307705\pi$
$709$	−215513.	−	373280.i	−0.428728	−	0.742578i	−0.996760	+	0.0804279i	$0.974371\pi$
$710$		−	479147.i		−	0.950499i
$711$		0			0
$712$	768959.			1.51685
$713$	3787.73	−	2186.84i	0.00745074	−	0.00430169i
$714$		0			0
$715$	−118561.	+	205354.i	−0.231916	+	0.401690i
$716$	−4145.79	−	2393.57i	−0.00808689	−	0.00466897i
$717$		0			0
$718$	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	$0.719168\pi$
$720$		0			0
$721$	−373688.			−0.718850
$722$	363384.	−	209800.i	0.697093	−	0.402467i
$723$		0			0
$724$	55848.8	−	96732.9i	0.106546	−	0.184543i
$725$	228442.	+	131891.i	0.434610	+	0.250922i
$726$		0			0
$727$	−158557.	−	274628.i	−0.299996	−	0.519609i	0.676139	−	0.736775i	$-0.263652\pi$
$727$	−158557.	−	274628.i	−0.299996	−	0.519609i	−0.976135	+	0.217166i	$0.930319\pi$
$728$		−	600816.i		−	1.13365i
$729$		0			0
$730$	−345123.			−0.647632
$731$	−56273.2	+	32489.3i	−0.105309	+	0.0608004i
$732$		0			0
$733$	488922.	−	846837.i	0.909979	−	1.57613i	0.0958883	−	0.995392i	$-0.469431\pi$
$733$	488922.	−	846837.i	0.909979	−	1.57613i	0.814091	−	0.580738i	$-0.197236\pi$
$734$	402736.	+	232520.i	0.747529	+	0.431586i
$735$		0			0
$736$	−3566.90	−	6178.05i	−0.00658469	−	0.0114050i
$737$			445641.i			0.820446i
$738$		0			0
$739$	−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
$741$		0			0
$742$	−318312.	+	551332.i	−0.578155	+	1.00139i
$743$	−899450.	−	519298.i	−1.62929	−	0.940673i	−0.984304	−	0.176482i	$-0.943528\pi$
$743$	−899450.	−	519298.i	−1.62929	−	0.940673i	−0.644990	−	0.764191i	$-0.723139\pi$
$744$		0			0
$745$	−120905.	−	209413.i	−0.217836	−	0.377304i
$746$		−	1.09770e6i		−	1.97245i
$747$		0			0
$748$	27567.5			0.0492713
$749$	−572304.	+	330420.i	−1.02015	+	0.588983i
$750$		0			0
$751$	−159783.	+	276752.i	−0.283302	+	0.490694i	−0.972196	−	0.234168i	$-0.924763\pi$
$751$	−159783.	+	276752.i	−0.283302	+	0.490694i	0.688894	+	0.724862i	$0.258097\pi$
$752$	1.03966e6	+	600246.i	1.83846	+	1.06144i
$753$		0			0
$754$	246118.	+	426290.i	0.432914	+	0.749829i
$755$			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	$0.356203\pi$
$758$	−776617.	+	448380.i	−1.35166	+	0.780383i
$759$		0			0
$760$	82263.8	−	142485.i	0.142424	−	0.246685i
$761$	783645.	+	452437.i	1.35316	+	0.781249i	0.988691	−	0.149966i	$-0.0479165\pi$
$761$	783645.	+	452437.i	1.35316	+	0.781249i	0.364471	+	0.931215i	$0.381250\pi$
$762$		0			0
$763$	585707.	+	1.01447e6i	1.00608	+	1.74258i
$764$		−	38408.3i		−	0.0658019i
$765$		0			0
$766$	604318.			1.02993
$767$	721738.	−	416696.i	1.22684	−	0.708318i
$768$		0			0
$769$	−71688.6	+	124168.i	−0.121227	+	0.209970i	−0.920252	−	0.391327i	$-0.872016\pi$
$769$	−71688.6	+	124168.i	−0.121227	+	0.209970i	0.799025	+	0.601298i	$0.205349\pi$
$770$	431852.	+	249330.i	0.728372	+	0.420526i
$771$		0			0
$772$	−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	$-0.202518\pi$
$774$		0			0
$775$	−111428.			−0.185521
$776$	−334204.	+	192953.i	−0.554993	+	0.320426i
$777$		0			0
$778$	−451386.	+	781823.i	−0.745742	+	1.29166i
$779$	91824.5	+	53014.9i	0.151316	+	0.0873621i
$780$		0			0
$781$	321990.	+	557702.i	0.527885	+	0.914324i
$782$			4698.37i			0.00768305i
$783$		0			0
$784$	−865865.			−1.40870
$785$	286161.	−	165215.i	0.464377	−	0.268108i
$786$		0			0
$787$	300855.	−	521097.i	0.485745	−	0.841335i	−0.514121	−	0.857718i	$-0.671882\pi$
$787$	300855.	−	521097.i	0.485745	−	0.841335i	0.999866	+	0.0163827i	$0.00521501\pi$
$788$	−233775.	−	134970.i	−0.376484	−	0.217363i
$789$		0			0
$790$	204934.	+	354956.i	0.328367	+	0.568748i
$791$			1.52935e6i			2.44429i
$792$		0			0
$793$	−263552.			−0.419102
$794$	−395923.	+	228586.i	−0.628014	+	0.362584i
$795$		0			0
$796$	−16221.8	+	28097.0i	−0.0256020	+	0.0443439i
$797$	372227.	+	214905.i	0.585991	+	0.338322i	0.763511	−	0.645795i	$-0.223474\pi$
$797$	372227.	+	214905.i	0.585991	+	0.338322i	−0.177519	+	0.984117i	$0.556807\pi$
$798$		0			0
$799$	−143959.	−	249344.i	−0.225499	−	0.390576i
$800$			181748.i			0.283981i
$801$		0			0
$802$	−402308.			−0.625474
$803$	401706.	−	231925.i	0.622984	−	0.359680i
$804$		0			0
$805$	−8393.99	+	14538.8i	−0.0129532	+	0.0224356i
$806$	−180076.	−	103967.i	−0.277195	−	0.160039i
$807$		0			0
$808$	−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	$-0.159734\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	177389.	−	307246.i	0.267718	−	0.463701i
$815$	−552135.	−	318775.i	−0.831246	−	0.479920i
$816$		0			0
$817$	85099.3	+	147396.i	0.127492	+	0.220822i
$818$		−	668548.i		−	0.999140i
$819$		0			0
$820$	35094.5			0.0521929
$821$	−38728.3	+	22359.8i	−0.0574569	+	0.0331727i	−0.528453	−	0.848962i	$-0.677228\pi$
$821$	−38728.3	+	22359.8i	−0.0574569	+	0.0331727i	0.470996	+	0.882135i	$0.343894\pi$
$822$		0			0
$823$	146289.	−	253380.i	0.215979	−	0.374087i	−0.737596	−	0.675242i	$-0.764039\pi$
$823$	146289.	−	253380.i	0.215979	−	0.374087i	0.953575	+	0.301155i	$0.0973723\pi$
$824$	−240461.	−	138830.i	−0.354153	−	0.204470i
$825$		0			0
$826$	−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	$-0.200715\pi$
$828$		0			0
$829$	204904.			0.298154			0.149077	−	0.988826i	$-0.452370\pi$
$829$	204904.			0.298154			0.149077	+	0.988826i	$0.452370\pi$
$830$	−175485.	+	101316.i	−0.254732	+	0.147069i
$831$		0			0
$832$	204112.	−	353533.i	0.294864	−	0.510720i
$833$	179842.	+	103832.i	0.259179	+	0.149637i
$834$		0			0
$835$	−219915.	−	380905.i	−0.315415	−	0.546315i
$836$		−	72207.5i		−	0.103317i
$837$		0			0
$838$	564189.			0.803409
$839$	−667796.	+	385552.i	−0.948681	+	0.547721i	−0.892671	−	0.450709i	$-0.851171\pi$
$839$	−667796.	+	385552.i	−0.948681	+	0.547721i	−0.0560100	+	0.998430i	$0.517838\pi$
$840$		0			0
$841$	−97125.1	+	168226.i	−0.137322	+	0.237848i
$842$	−832531.	−	480662.i	−1.17429	−	0.677978i
$843$		0			0
$844$	80322.0	+	139122.i	0.112759	+	0.195304i
$845$		−	78093.4i		−	0.109371i
$846$		0			0
$847$	391030.			0.545058
$848$	−517001.	+	298491.i	−0.718951	+	0.415087i
$849$		0			0
$850$	59850.2	−	103664.i	0.0828376	−	0.143479i
$851$	10343.8	+	5972.02i	0.0142831	+	0.00824635i
$852$		0			0
$853$	−541184.	−	937358.i	−0.743784	−	1.28827i	−0.950761	−	0.309925i	$-0.899696\pi$
$853$	−541184.	−	937358.i	−0.743784	−	1.28827i	0.206977	−	0.978346i	$-0.433637\pi$
$854$			554240.i			0.759945i
$855$		0			0
$856$	−491023.			−0.670122
$857$	461890.	−	266672.i	0.628893	−	0.363092i	−0.151430	−	0.988468i	$-0.548388\pi$
$857$	461890.	−	266672.i	0.628893	−	0.363092i	0.780323	+	0.625376i	$0.215055\pi$
$858$		0			0
$859$	−565525.	+	979517.i	−0.766417	+	1.32747i	0.173077	+	0.984908i	$0.444629\pi$
$859$	−565525.	+	979517.i	−0.766417	+	1.32747i	−0.939494	+	0.342565i	$0.888704\pi$
$860$	48786.4	+	28166.8i	0.0659632	+	0.0380839i
$861$		0			0
$862$	−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	$0.976467\pi$
$864$		0			0
$865$	161503.			0.215848
$866$	589410.	−	340296.i	0.785926	−	0.453755i
$867$		0			0
$868$	−43188.8	+	74805.3i	−0.0573234	+	0.0992871i
$869$	−477065.	−	275433.i	−0.631739	−	0.364735i
$870$		0			0
$871$	356638.	+	617715.i	0.470101	+	0.814238i
$872$			870394.i			1.14468i
$873$		0			0
$874$	12306.4			0.0161105
$875$	999020.	−	576784.i	1.30484	−	0.753351i
$876$		0			0
$877$	204377.	−	353991.i	0.265725	−	0.460249i	−0.702028	−	0.712149i	$-0.747722\pi$
$877$	204377.	−	353991.i	0.265725	−	0.460249i	0.967753	+	0.251900i	$0.0810554\pi$
$878$	893778.	+	516023.i	1.15942	+	0.669391i
$879$		0			0
$880$	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	$-0.0485416\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	−45067.3	+	78058.8i	−0.0574109	+	0.0994385i
$887$	−322071.	−	185948.i	−0.409359	−	0.236344i	0.281155	−	0.959662i	$-0.409282\pi$
$887$	−322071.	−	185948.i	−0.409359	−	0.236344i	−0.690514	+	0.723319i	$0.742616\pi$
$888$		0			0
$889$	748789.	+	1.29694e6i	0.947449	+	1.64103i
$890$			1.02150e6i			1.28961i
$891$		0			0
$892$	235997.			0.296604
$893$	−653108.	+	377072.i	−0.818996	+	0.472848i
$894$		0			0
$895$	−9737.36	+	16865.6i	−0.0121561	+	0.0210550i
$896$	−1.23913e6	−	715412.i	−1.54348	−	0.891128i
$897$		0			0
$898$	−207552.	−	359490.i	−0.257379	−	0.445794i
$899$			216718.i			0.268148i
$900$		0			0
$901$	143176.			0.176368
$902$	−206790.	+	119390.i	−0.254165	+	0.146742i
$903$		0			0
$904$	−568175.	+	984108.i	−0.695257	+	1.20422i
$905$	−393522.	−	227200.i	−0.480476	−	0.277403i
$906$		0			0
$907$	71965.4	+	124648.i	0.0874801	+	0.151520i	0.906445	−	0.422323i	$-0.138785\pi$
$907$	71965.4	+	124648.i	0.0874801	+	0.151520i	−0.818965	+	0.573843i	$0.805452\pi$
$908$			389172.i			0.472030i
$909$		0			0
$910$	798134.			0.963814
$911$	772201.	−	445830.i	0.930451	−	0.537196i	0.0434969	−	0.999054i	$-0.486150\pi$
$911$	772201.	−	445830.i	0.930451	−	0.537196i	0.886954	+	0.461857i	$0.152817\pi$
$912$		0			0
$913$	136170.	−	235854.i	0.163358	−	0.282944i
$914$	854175.	+	493158.i	1.02248	+	0.590329i
$915$		0			0
$916$	−10472.5	−	18139.0i	−0.0124813	−	0.0216183i
$917$			232053.i			0.275961i
$918$		0			0
$919$	−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
$921$		0			0
$922$	237093.	−	410658.i	0.278906	−	0.483079i
$923$	892636.	+	515364.i	1.04778	+	0.604937i
$924$		0			0
$925$	−152149.	−	263530.i	−0.177822	−	0.307997i
$926$			304441.i			0.355043i
$927$		0			0
$928$	353482.			0.410460
$929$	668027.	−	385685.i	0.774038	−	0.446891i	−0.0602751	−	0.998182i	$-0.519198\pi$
$929$	668027.	−	385685.i	0.774038	−	0.446891i	0.834313	+	0.551291i	$0.185864\pi$
$930$		0			0
$931$	271966.	−	471059.i	0.313773	−	0.543470i
$932$	62991.9	+	36368.4i	0.0725192	+	0.0418690i
$933$		0			0
$934$	500890.	+	867567.i	0.574181	+	0.994510i
$935$		−	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	$0.812813\pi$
$938$	1.29903e6	−	749996.i	1.47643	−	0.852420i
$939$		0			0
$940$	−124806.	+	216170.i	−0.141247	+	0.244647i
$941$	−146658.	−	84673.2i	−0.165626	−	0.0956240i	0.414896	−	0.909869i	$-0.363818\pi$
$941$	−146658.	−	84673.2i	−0.165626	−	0.0956240i	−0.580522	+	0.814245i	$0.697151\pi$
$942$		0			0
$943$	−4019.42	−	6961.83i	−0.00452001	−	0.00782889i
$944$		−	1.64346e6i		−	1.84423i
$945$		0			0
$946$	−383289.			−0.428296
$947$	−514322.	+	296944.i	−0.573503	+	0.331112i	−0.758547	−	0.651618i	$-0.774090\pi$
$947$	−514322.	+	296944.i	−0.573503	+	0.331112i	0.185044	+	0.982730i	$0.440757\pi$
$948$		0			0
$949$	371210.	−	642955.i	0.412180	−	0.713917i
$950$	−271526.	−	156766.i	−0.300860	−	0.173702i
$951$		0			0
$952$	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	$0.757260\pi$
$954$		0			0
$955$	−156250.			−0.171322
$956$	−88159.0	+	50898.6i	−0.0964608	+	0.0556917i
$957$		0			0
$958$	−243733.	+	422158.i	−0.265573	+	0.459985i
$959$	−243051.	−	140326.i	−0.264278	−	0.152581i
$960$		0			0
$961$	415987.	+	720510.i	0.450436	+	0.780178i
$962$		−	567843.i		−	0.613590i
$963$		0			0
$964$	−327186.			−0.352080
$965$	−741017.	+	427826.i	−0.795744	+	0.459423i
$966$		0			0
$967$	528928.	−	916130.i	0.565645	−	0.979725i	−0.431345	−	0.902187i	$-0.641961\pi$
$967$	528928.	−	916130.i	0.565645	−	0.979725i	0.996989	−	0.0775381i	$-0.0247059\pi$
$968$	251620.	+	145273.i	0.268531	+	0.155037i
$969$		0			0
$970$	−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	$-0.134956\pi$
$972$		0			0
$973$	−846555.			−0.894189
$974$	−411099.	+	237348.i	−0.433339	+	0.250189i
$975$		0			0
$976$	−259864.	+	450098.i	−0.272801	+	0.472506i
$977$	429995.	+	248258.i	0.450479	+	0.260084i	0.708032	−	0.706180i	$-0.249583\pi$
$977$	429995.	+	248258.i	0.450479	+	0.260084i	−0.257554	+	0.966264i	$0.582916\pi$
$978$		0			0
$979$	−686453.	−	1.18897e6i	−0.716218	−	1.24053i
$980$		−	180035.i		−	0.187458i
$981$		0			0
$982$	−332424.			−0.344722
$983$	−260643.	+	150482.i	−0.269736	+	0.155732i	−0.628768	−	0.777593i	$-0.716440\pi$
$983$	−260643.	+	150482.i	−0.269736	+	0.155732i	0.359032	+	0.933325i	$0.383107\pi$
$984$		0			0
$985$	−549076.	+	951028.i	−0.565927	+	0.980214i
$986$	−201616.	−	116403.i	−0.207382	−	0.119732i
$987$		0			0
$988$	−57786.2	−	100089.i	−0.0591985	−	0.102535i
$989$		−	12903.9i		−	0.0131925i
$990$		0			0
$991$	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
$993$		0			0
$994$	1.08379e6	−	1.87718e6i	1.09691	−	1.89991i
$995$	114302.	+	65992.4i	0.115454	+	0.0666573i
$996$		0			0
$997$	312919.	+	541991.i	0.314805	+	0.545258i	0.979396	−	0.201949i	$-0.0647276\pi$
$997$	312919.	+	541991.i	0.314805	+	0.545258i	−0.664591	+	0.747207i	$0.731394\pi$
$998$			496568.i			0.498560i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.3	✓	6	9.7	even	3
9.5.d.a.5.3	yes	6	3.2	odd	2
27.5.d.a.8.1		6	9.2	odd	6	inner
27.5.d.a.17.1		6	1.1	even	1	trivial
81.5.b.a.80.2		6	9.4	even	3
81.5.b.a.80.5		6	9.5	odd	6
144.5.q.a.65.3		6	36.7	odd	6
144.5.q.a.113.3		6	12.11	even	2
432.5.q.a.17.1		6	4.3	odd	2
432.5.q.a.305.1		6	36.11	even	6
1296.5.e.c.161.2		6	36.23	even	6
1296.5.e.c.161.5		6	36.31	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.86703 + 2.23263i) q^{2} +(1.96929 - 3.41090i) q^{4} +(-13.8760 - 8.01130i) q^{5} +(-36.2418 - 62.7727i) q^{7} -53.8574i q^{8} +71.5451 q^{10} +(-83.2749 + 48.0788i) q^{11} +(-76.9530 + 133.286i) q^{13} +(280.297 + 161.829i) q^{14} +(151.752 + 262.843i) q^{16} -72.7905i q^{17} -190.660 q^{19} +(-54.6515 + 31.5531i) q^{20} +(214.684 - 371.844i) q^{22} +(12.5186 + 7.22762i) q^{23} +(-184.138 - 318.937i) q^{25} -687.231i q^{26} -285.482 q^{28} +(-620.301 + 358.131i) q^{29} +(151.284 - 262.031i) q^{31} +(-427.392 - 246.755i) q^{32} +(162.514 + 281.483i) q^{34} +1161.38i q^{35} +826.277 q^{37} +(737.289 - 425.674i) q^{38} +(-431.468 + 747.325i) q^{40} +(-481.613 - 278.059i) q^{41} +(-446.340 - 773.084i) q^{43} +378.723i q^{44} -64.5464 q^{46} +(3425.50 - 1977.72i) q^{47} +(-1426.44 + 2470.67i) q^{49} +(1424.14 + 822.225i) q^{50} +(303.085 + 524.958i) q^{52} +1966.96i q^{53} +1540.69 q^{55} +(-3380.78 + 1951.89i) q^{56} +(1599.15 - 2769.81i) q^{58} +(-4689.48 - 2707.47i) q^{59} +(856.210 + 1483.00i) q^{61} +1351.04i q^{62} -2652.43 q^{64} +(2135.60 - 1232.99i) q^{65} +(2317.24 - 4013.58i) q^{67} +(-248.281 - 143.345i) q^{68} +(-2592.93 - 4491.08i) q^{70} -6697.12i q^{71} -4823.86 q^{73} +(-3195.24 + 1844.77i) q^{74} +(-375.464 + 650.324i) q^{76} +(6036.07 + 3484.93i) q^{77} +(2864.40 + 4961.28i) q^{79} -4862.94i q^{80} +2483.22 q^{82} +(-2452.78 + 1416.12i) q^{83} +(-583.147 + 1010.04i) q^{85} +(3452.02 + 1993.03i) q^{86} +(2589.40 + 4484.97i) q^{88} +14277.7i q^{89} +11155.7 q^{91} +(49.3054 - 28.4665i) q^{92} +(-8831.02 + 15295.8i) q^{94} +(2645.60 + 1527.44i) q^{95} +(-3582.65 - 6205.34i) q^{97} -12738.9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29}+ \cdots - 28959 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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