LMFDB - Embedded newform 135.5.h.a.44.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,5,Mod(44,135)] 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("135.44"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	135.h (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:	$13.9549450163$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.11
Character	$\chi$	$=$	135.44
Dual form			135.5.h.a.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.316502 - 0.548197i) q^{2} +(7.79965 - 13.5094i) q^{4} +(18.0085 + 17.3406i) q^{5} +(-73.2178 + 42.2723i) q^{7} -20.0025 q^{8} +(3.80633 - 15.3605i) q^{10} +(-148.474 + 85.7213i) q^{11} +(127.218 + 73.4493i) q^{13} +(46.3471 + 26.7585i) q^{14} +(-118.464 - 205.185i) q^{16} -273.459 q^{17} +229.656 q^{19} +(374.720 - 108.033i) q^{20} +(93.9843 + 54.2618i) q^{22} +(-194.631 + 337.110i) q^{23} +(23.6096 + 624.554i) q^{25} -92.9873i q^{26} +1318.84i q^{28} +(-306.632 + 177.034i) q^{29} +(-310.913 + 538.517i) q^{31} +(-235.008 + 407.045i) q^{32} +(86.5501 + 149.909i) q^{34} +(-2051.57 - 508.379i) q^{35} +730.131i q^{37} +(-72.6865 - 125.897i) q^{38} +(-360.214 - 346.854i) q^{40} +(498.910 + 288.046i) q^{41} +(-783.565 + 452.392i) q^{43} +2674.39i q^{44} +246.404 q^{46} +(-396.417 - 686.614i) q^{47} +(2373.40 - 4110.85i) q^{49} +(334.906 - 210.615i) q^{50} +(1984.51 - 1145.76i) q^{52} +3467.44 q^{53} +(-4160.24 - 1030.91i) q^{55} +(1464.54 - 845.551i) q^{56} +(194.099 + 112.063i) q^{58} +(-2436.74 - 1406.85i) q^{59} +(2660.83 + 4608.69i) q^{61} +393.618 q^{62} -3493.32 q^{64} +(1017.35 + 3528.74i) q^{65} +(147.934 + 85.4097i) q^{67} +(-2132.88 + 3694.26i) q^{68} +(370.633 + 1285.57i) q^{70} -2798.11i q^{71} -5866.22i q^{73} +(400.255 - 231.088i) q^{74} +(1791.24 - 3102.52i) q^{76} +(7247.28 - 12552.7i) q^{77} +(1466.67 + 2540.34i) q^{79} +(1424.68 - 5749.29i) q^{80} -364.668i q^{82} +(-3444.66 - 5966.32i) q^{83} +(-4924.57 - 4741.93i) q^{85} +(495.999 + 286.365i) q^{86} +(2969.84 - 1714.64i) q^{88} +1031.26i q^{89} -12419.5 q^{91} +(3036.10 + 5258.68i) q^{92} +(-250.933 + 434.629i) q^{94} +(4135.75 + 3982.37i) q^{95} +(12170.7 - 7026.75i) q^{97} -3004.74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) $ 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.316502	−	0.548197i	−0.0791254	−	0.137049i	0.823747	−	0.566957i	$-0.191879\pi$
$2$	−0.316502	−	0.548197i	−0.0791254	−	0.137049i	−0.902873	+	0.429908i	$0.858546\pi$
$3$		0			0
$3$		0			0
$4$	7.79965	−	13.5094i	0.487478	−	0.844337i
$5$	18.0085	+	17.3406i	0.720339	+	0.693623i
$5$	18.0085	+	17.3406i	0.720339	+	0.693623i
$6$		0			0
$7$	−73.2178	+	42.2723i	−1.49424	+	0.862701i	−0.999978	−	0.00661118i	$-0.997896\pi$
$7$	−73.2178	+	42.2723i	−1.49424	+	0.862701i	−0.494264	+	0.869312i	$0.664562\pi$
$8$	−20.0025			−0.312538
$9$		0			0
$10$	3.80633	−	15.3605i	0.0380633	−	0.153605i
$11$	−148.474	+	85.7213i	−1.22705	+	0.708440i	−0.966413	−	0.256995i	$-0.917268\pi$
$11$	−148.474	+	85.7213i	−1.22705	+	0.708440i	−0.260642	+	0.965436i	$0.583934\pi$
$12$		0			0
$13$	127.218	+	73.4493i	0.752769	+	0.434611i	0.826693	−	0.562653i	$-0.190219\pi$
$13$	127.218	+	73.4493i	0.752769	+	0.434611i	−0.0739247	+	0.997264i	$0.523552\pi$
$14$	46.3471	+	26.7585i	0.236465	+	0.136523i
$15$		0			0
$16$	−118.464	−	205.185i	−0.462749	−	0.801504i
$17$	−273.459			−0.946224			−0.473112	−	0.881002i	$-0.656869\pi$
$17$	−273.459			−0.946224			−0.473112	+	0.881002i	$0.656869\pi$
$18$		0			0
$19$	229.656			0.636167			0.318083	−	0.948063i	$-0.396961\pi$
$19$	229.656			0.636167			0.318083	+	0.948063i	$0.396961\pi$
$20$	374.720	−	108.033i	0.936801	−	0.270083i
$21$		0			0
$22$	93.9843	+	54.2618i	0.194182	+	0.112111i
$23$	−194.631	+	337.110i	−0.367922	+	0.637259i	−0.989240	−	0.146299i	$-0.953264\pi$
$23$	−194.631	+	337.110i	−0.367922	+	0.637259i	0.621319	+	0.783558i	$0.286597\pi$
$24$		0			0
$25$	23.6096	+	624.554i	0.0377754	+	0.999286i
$26$		−	92.9873i		−	0.137555i
$27$		0			0
$28$			1318.84i			1.68219i
$29$	−306.632	+	177.034i	−0.364604	+	0.210504i	−0.671098	−	0.741368i	$-0.734177\pi$
$29$	−306.632	+	177.034i	−0.364604	+	0.210504i	0.306494	+	0.951872i	$0.400844\pi$
$30$		0			0
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	−0.981214	−	0.192923i	$-0.938203\pi$
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	0.657683	+	0.753295i	$0.271537\pi$
$32$	−235.008	+	407.045i	−0.229500	+	0.397505i
$33$		0			0
$34$	86.5501	+	149.909i	0.0748704	+	0.129679i
$35$	−2051.57	−	508.379i	−1.67475	−	0.415003i
$36$		0			0
$37$			730.131i			0.533332i	0.963789	+	0.266666i	$0.0859220\pi$
$37$			730.131i			0.533332i	−0.963789	+	0.266666i	$0.914078\pi$
$38$	−72.6865	−	125.897i	−0.0503369	−	0.0871861i
$39$		0			0
$40$	−360.214	−	346.854i	−0.225133	−	0.216784i
$41$	498.910	+	288.046i	0.296794	+	0.171354i	0.641002	−	0.767539i	$-0.278519\pi$
$41$	498.910	+	288.046i	0.296794	+	0.171354i	−0.344208	+	0.938893i	$0.611852\pi$
$42$		0			0
$43$	−783.565	+	452.392i	−0.423778	+	0.244668i	−0.696692	−	0.717370i	$-0.745346\pi$
$43$	−783.565	+	452.392i	−0.423778	+	0.244668i	0.272914	+	0.962038i	$0.412012\pi$
$44$			2674.39i			1.38140i
$45$		0			0
$46$	246.404			0.116448
$47$	−396.417	−	686.614i	−0.179455	−	0.310826i	0.762239	−	0.647296i	$-0.224100\pi$
$47$	−396.417	−	686.614i	−0.179455	−	0.310826i	−0.941694	+	0.336470i	$0.890767\pi$
$48$		0			0
$49$	2373.40	−	4110.85i	0.988506	−	1.71214i
$50$	334.906	−	210.615i	0.133962	−	0.0842460i
$51$		0			0
$52$	1984.51	−	1145.76i	0.733917	−	0.423727i
$53$	3467.44			1.23440			0.617202	−	0.786805i	$-0.288266\pi$
$53$	3467.44			1.23440			0.617202	+	0.786805i	$0.288266\pi$
$54$		0			0
$55$	−4160.24	−	1030.91i	−1.37529	−	0.340796i
$56$	1464.54	−	845.551i	0.467008	−	0.269627i
$57$		0			0
$58$	194.099	+	112.063i	0.0576989	+	0.0333125i
$59$	−2436.74	−	1406.85i	−0.700013	−	0.404152i	0.107340	−	0.994222i	$-0.465767\pi$
$59$	−2436.74	−	1406.85i	−0.700013	−	0.404152i	−0.807352	+	0.590070i	$0.799100\pi$
$60$		0			0
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	0.962927	+	0.269762i	$0.0869450\pi$
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	−0.247843	+	0.968800i	$0.579722\pi$
$62$	393.618			0.102398
$63$		0			0
$64$	−3493.32			−0.852860
$65$	1017.35	+	3528.74i	0.240792	+	0.835205i
$66$		0			0
$67$	147.934	+	85.4097i	0.0329548	+	0.0190264i	0.516387	−	0.856355i	$-0.327277\pi$
$67$	147.934	+	85.4097i	0.0329548	+	0.0190264i	−0.483432	+	0.875382i	$0.660610\pi$
$68$	−2132.88	+	3694.26i	−0.461264	+	0.798932i
$69$		0			0
$70$	370.633	+	1285.57i	0.0756393	+	0.262360i
$71$		−	2798.11i		−	0.555071i	−0.960715	−	0.277535i	$-0.910482\pi$
$71$		−	2798.11i		−	0.555071i	0.960715	−	0.277535i	$-0.0895176\pi$
$72$		0			0
$73$		−	5866.22i		−	1.10081i	−0.834898	−	0.550405i	$-0.814473\pi$
$73$		−	5866.22i		−	1.10081i	0.834898	−	0.550405i	$-0.185527\pi$
$74$	400.255	−	231.088i	0.0730927	−	0.0422001i
$75$		0			0
$76$	1791.24	−	3102.52i	0.310117	−	0.537139i
$77$	7247.28	−	12552.7i	1.22234	−	2.11716i
$78$		0			0
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	0.959274	−	0.282477i	$-0.0911560\pi$
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	−0.724269	+	0.689517i	$0.757823\pi$
$80$	1424.68	−	5749.29i	0.222606	−	0.898327i
$81$		0			0
$82$		−	364.668i		−	0.0542338i
$83$	−3444.66	−	5966.32i	−0.500023	−	0.866065i	−1.00000		2.64929e-5i	$-0.999992\pi$
$83$	−3444.66	−	5966.32i	−0.500023	−	0.866065i	0.499977	−	0.866039i	$-0.333342\pi$
$84$		0			0
$85$	−4924.57	−	4741.93i	−0.681602	−	0.656323i
$86$	495.999	+	286.365i	0.0670632	+	0.0387189i
$87$		0			0
$88$	2969.84	−	1714.64i	0.383502	−	0.221415i
$89$			1031.26i			0.130193i	0.997879	+	0.0650966i	$0.0207356\pi$
$89$			1031.26i			0.130193i	−0.997879	+	0.0650966i	$0.979264\pi$
$90$		0			0
$91$	−12419.5			−1.49976
$92$	3036.10	+	5258.68i	0.358708	+	0.621300i
$93$		0			0
$94$	−250.933	+	434.629i	−0.0283990	+	0.0491884i
$95$	4135.75	+	3982.37i	0.458255	+	0.441259i
$96$		0			0
$97$	12170.7	−	7026.75i	1.29352	−	0.746811i	0.314240	−	0.949344i	$-0.398250\pi$
$97$	12170.7	−	7026.75i	1.29352	−	0.746811i	0.979276	+	0.202532i	$0.0649171\pi$
$98$	−3004.74			−0.312864
$99$		0			0
$100$	8621.49	+	4552.35i	0.862149	+	0.455235i
$101$	−11797.3	+	6811.17i	−1.15648	+	0.667696i	−0.950459	−	0.310851i	$-0.899386\pi$
$101$	−11797.3	+	6811.17i	−1.15648	+	0.667696i	−0.206025	+	0.978547i	$0.566053\pi$
$102$		0			0
$103$	−14156.3	−	8173.15i	−1.33437	−	0.770397i	−0.348402	−	0.937345i	$-0.613276\pi$
$103$	−14156.3	−	8173.15i	−1.33437	−	0.770397i	−0.985966	+	0.166948i	$0.946609\pi$
$104$	−2544.67	−	1469.17i	−0.235269	−	0.135833i
$105$		0			0
$106$	−1097.45	−	1900.84i	−0.0976727	−	0.169174i
$107$	15293.8			1.33582			0.667909	−	0.744243i	$-0.267190\pi$
$107$	15293.8			1.33582			0.667909	+	0.744243i	$0.267190\pi$
$108$		0			0
$109$	−3110.73			−0.261824			−0.130912	−	0.991394i	$-0.541791\pi$
$109$	−3110.73			−0.261824			−0.130912	+	0.991394i	$0.541791\pi$
$110$	751.581	+	2606.91i	0.0621142	+	0.215447i
$111$		0			0
$112$	17347.3	+	10015.5i	1.38292	+	0.798427i
$113$	−4020.47	+	6963.67i	−0.314862	+	0.545357i	−0.979408	−	0.201890i	$-0.935292\pi$
$113$	−4020.47	+	6963.67i	−0.314862	+	0.545357i	0.664546	+	0.747247i	$0.268625\pi$
$114$		0			0
$115$	−9350.68	+	2695.83i	−0.707046	+	0.203844i
$116$			5523.22i			0.410465i
$117$		0			0
$118$			1781.09i			0.127915i
$119$	20022.1	−	11559.7i	1.41389	−	0.816308i
$120$		0			0
$121$	7375.77	−	12775.2i	0.503775	−	0.872564i
$122$	1684.31	−	2917.31i	0.113163	−	0.196003i
$123$		0			0
$124$	4850.02	+	8400.49i	0.315428	+	0.546338i
$125$	−10404.9	+	11656.7i	−0.665916	+	0.746026i
$126$		0			0
$127$			8105.72i			0.502555i	0.967915	+	0.251278i	$0.0808507\pi$
$127$			8105.72i			0.502555i	−0.967915	+	0.251278i	$0.919149\pi$
$128$	4865.76	+	8427.74i	0.296982	+	0.514389i
$129$		0			0
$130$	1612.45	−	1674.56i	0.0954113	−	0.0990863i
$131$	5088.68	+	2937.95i	0.296526	+	0.171199i	0.640881	−	0.767640i	$-0.278569\pi$
$131$	5088.68	+	2937.95i	0.296526	+	0.171199i	−0.344355	+	0.938839i	$0.611902\pi$
$132$		0			0
$133$	−16814.9	+	9708.10i	−0.950587	+	0.548821i
$134$		−	108.129i		−	0.00602190i
$135$		0			0
$136$	5469.85			0.295731
$137$	−17524.8	−	30353.8i	−0.933710	−	1.61723i	−0.776918	−	0.629601i	$-0.783218\pi$
$137$	−17524.8	−	30353.8i	−0.933710	−	1.61723i	−0.156792	−	0.987632i	$-0.550115\pi$
$138$		0			0
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	−0.978407	−	0.206686i	$-0.933732\pi$
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	0.668199	+	0.743982i	$0.267065\pi$
$140$	−22869.4	+	23750.3i	−1.16681	+	1.21175i
$141$		0			0
$142$	−1533.92	+	885.606i	−0.0760720	+	0.0439202i
$143$	−25184.7			−1.23158
$144$		0			0
$145$	−8591.84	−	2129.06i	−0.408649	−	0.101263i
$146$	−3215.84	+	1856.67i	−0.150865	+	0.0871021i
$147$		0			0
$148$	9863.63	+	5694.77i	0.450312	+	0.259988i
$149$	−11303.5	−	6526.09i	−0.509145	−	0.293955i	0.223337	−	0.974741i	$-0.428305\pi$
$149$	−11303.5	−	6526.09i	−0.509145	−	0.293955i	−0.732482	+	0.680786i	$0.761638\pi$
$150$		0			0
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	0.986850	+	0.161639i	$0.0516781\pi$
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	−0.353441	+	0.935457i	$0.614989\pi$
$152$	−4593.69			−0.198826
$153$		0			0
$154$	−9175.10			−0.386874
$155$	−14937.2	+	4306.46i	−0.621738	+	0.179249i
$156$		0			0
$157$	18003.8	+	10394.5i	0.730405	+	0.421700i	0.818570	−	0.574406i	$-0.194767\pi$
$157$	18003.8	+	10394.5i	0.730405	+	0.421700i	−0.0881652	+	0.996106i	$0.528100\pi$
$158$	928.404	−	1608.04i	0.0371897	−	0.0644145i
$159$		0			0
$160$	−11290.5	+	3255.09i	−0.441036	+	0.127152i
$161$		−	32910.0i		−	1.26963i
$162$		0			0
$163$			24195.2i			0.910654i	0.890324	+	0.455327i	$0.150478\pi$
$163$			24195.2i			0.910654i	−0.890324	+	0.455327i	$0.849522\pi$
$164$	7782.66	−	4493.32i	0.289361	−	0.167063i
$165$		0			0
$166$	−2180.48	+	3776.70i	−0.0791290	+	0.137055i
$167$	5184.25	−	8979.38i	0.185889	−	0.321969i	−0.757987	−	0.652270i	$-0.773817\pi$
$167$	5184.25	−	8979.38i	0.185889	−	0.321969i	0.943876	+	0.330301i	$0.107150\pi$
$168$		0			0
$169$	−3490.90	−	6046.42i	−0.122226	−	0.211702i
$170$	−1040.88	+	4200.46i	−0.0360165	+	0.145345i
$171$		0			0
$172$			14114.0i			0.477082i
$173$	19114.0	+	33106.4i	0.638644	+	1.10616i	0.985731	+	0.168331i	$0.0538376\pi$
$173$	19114.0	+	33106.4i	0.638644	+	1.10616i	−0.347087	+	0.937833i	$0.612829\pi$
$174$		0			0
$175$	−28130.0	−	44730.5i	−0.918531	−	1.46059i
$176$	35177.5	+	20309.7i	1.13564	+	0.655660i
$177$		0			0
$178$	565.334	−	326.396i	0.0178429	−	0.0103016i
$179$			29062.0i			0.907025i	0.891250	+	0.453512i	$0.149829\pi$
$179$			29062.0i			0.907025i	−0.891250	+	0.453512i	$0.850171\pi$
$180$		0			0
$181$	23849.6			0.727988			0.363994	−	0.931401i	$-0.381413\pi$
$181$	23849.6			0.727988			0.363994	+	0.931401i	$0.381413\pi$
$182$	3930.79	+	6808.33i	0.118669	+	0.205541i
$183$		0			0
$184$	3893.09	−	6743.03i	0.114990	−	0.199168i
$185$	−12660.9	+	13148.5i	−0.369931	+	0.384179i
$186$		0			0
$187$	40601.4	−	23441.2i	1.16107	−	0.670343i
$188$	−12367.7			−0.349923
$189$		0			0
$190$	874.148	−	3527.63i	0.0242146	−	0.0977183i
$191$	4976.77	−	2873.34i	0.136421	−	0.0787626i	−0.430236	−	0.902716i	$-0.641570\pi$
$191$	4976.77	−	2873.34i	0.136421	−	0.0787626i	0.566657	+	0.823954i	$0.308236\pi$
$192$		0			0
$193$	5427.21	+	3133.40i	0.145701	+	0.0841204i	0.571078	−	0.820896i	$-0.306525\pi$
$193$	5427.21	+	3133.40i	0.145701	+	0.0841204i	−0.425377	+	0.905016i	$0.639859\pi$
$194$	−7704.08	−	4447.95i	−0.204700	−	0.118183i
$195$		0			0
$196$	−37023.4	−	64126.5i	−0.963750	−	1.66926i
$197$	55114.0			1.42013			0.710067	−	0.704134i	$-0.248665\pi$
$197$	55114.0			1.42013			0.710067	+	0.704134i	$0.248665\pi$
$198$		0			0
$199$	10375.3			0.261995			0.130998	−	0.991383i	$-0.458182\pi$
$199$	10375.3			0.261995			0.130998	+	0.991383i	$0.458182\pi$
$200$	−472.250	−	12492.6i	−0.0118063	−	0.312315i
$201$		0			0
$202$	7467.72	+	4311.49i	0.183014	+	0.105663i
$203$	14967.3	−	25924.1i	0.363204	−	0.629088i
$204$		0			0
$205$	3989.73	+	13838.7i	0.0949371	+	0.329296i
$206$			10347.3i			0.243832i
$207$		0			0
$208$		−	34804.3i		−	0.804463i
$209$	−34097.9	+	19686.4i	−0.780611	+	0.450686i
$210$		0			0
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	0.413560	+	0.910477i	$0.364285\pi$
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	−0.995276	+	0.0970851i	$0.969048\pi$
$212$	27044.8	−	46843.0i	0.601745	−	1.04225i
$213$		0			0
$214$	−4840.50	−	8384.00i	−0.105697	−	0.183073i
$215$	−21955.5	−	5440.59i	−0.474971	−	0.117698i
$216$		0			0
$217$		−	52572.1i		−	1.11644i
$218$	984.552	+	1705.29i	0.0207169	+	0.0358828i
$219$		0			0
$220$	−46375.3	+	48161.6i	−0.958168	+	0.995074i
$221$	−34788.9	−	20085.4i	−0.712288	−	0.411240i
$222$		0			0
$223$	−22259.2	+	12851.4i	−0.447611	+	0.258428i	−0.706821	−	0.707393i	$-0.749871\pi$
$223$	−22259.2	+	12851.4i	−0.447611	+	0.258428i	0.259210	+	0.965821i	$0.416538\pi$
$224$		−	39737.3i		−	0.791958i
$225$		0			0
$226$	5089.94			0.0996543
$227$	−17114.5	−	29643.2i	−0.332133	−	0.575272i	0.650797	−	0.759252i	$-0.274435\pi$
$227$	−17114.5	−	29643.2i	−0.332133	−	0.575272i	−0.982930	+	0.183980i	$0.941102\pi$
$228$		0			0
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	−0.889924	−	0.456109i	$-0.849243\pi$
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	0.839964	+	0.542643i	$0.182576\pi$
$230$	4437.35	+	4272.78i	0.0838819	+	0.0807708i
$231$		0			0
$232$	6133.39	−	3541.12i	0.113953	−	0.0657907i
$233$	44606.8			0.821654			0.410827	−	0.911713i	$-0.365240\pi$
$233$	44606.8			0.821654			0.410827	+	0.911713i	$0.365240\pi$
$234$		0			0
$235$	4767.42	−	19239.0i	0.0863272	−	0.348374i
$236$	−38011.5	+	21946.0i	−0.682482	+	0.394031i
$237$		0			0
$238$	−12674.0	−	7317.35i	−0.223749	−	0.129181i
$239$	31245.6	+	18039.7i	0.547008	+	0.315815i	0.747914	−	0.663795i	$-0.231055\pi$
$239$	31245.6	+	18039.7i	0.547008	+	0.315815i	−0.200907	+	0.979610i	$0.564389\pi$
$240$		0			0
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	0.681511	−	0.731808i	$-0.261323\pi$
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	−0.974520	+	0.224301i	$0.927990\pi$
$242$	−9337.78			−0.159446
$243$		0			0
$244$	83014.2			1.39435
$245$	114026.	−	32874.0i	1.89964	−	0.547672i
$246$		0			0
$247$	29216.4	+	16868.1i	0.478886	+	0.276485i
$248$	6219.02	−	10771.7i	0.101116	−	0.175138i
$249$		0			0
$250$	9683.32	+	2014.61i	0.154933	+	0.0322337i
$251$		−	60480.3i		−	0.959990i	−0.877271	−	0.479995i	$-0.840639\pi$
$251$		−	60480.3i		−	0.959990i	0.877271	−	0.479995i	$-0.159361\pi$
$252$		0			0
$253$		−	66735.9i		−	1.04260i
$254$	4443.53	−	2565.47i	0.0688748	−	0.0397649i
$255$		0			0
$256$	−24866.5	+	43070.0i	−0.379432	+	0.657196i
$257$	−7619.79	+	13197.9i	−0.115366	+	0.199819i	−0.917926	−	0.396752i	$-0.870137\pi$
$257$	−7619.79	+	13197.9i	−0.115366	+	0.199819i	0.802560	+	0.596571i	$0.203471\pi$
$258$		0			0
$259$	−30864.3	−	53458.6i	−0.460106	−	0.796926i
$260$	55606.1	+	13779.2i	0.822575	+	0.203834i
$261$		0			0
$262$		−	3719.46i		−	0.0541848i
$263$	−3230.92	−	5596.12i	−0.0467106	−	0.0809051i	0.841725	−	0.539907i	$-0.181541\pi$
$263$	−3230.92	−	5596.12i	−0.0467106	−	0.0809051i	−0.888435	+	0.459002i	$0.848207\pi$
$264$		0			0
$265$	62443.3	+	60127.4i	0.889189	+	0.856210i
$266$	10643.9	+	6145.26i	0.150431	+	0.0868514i
$267$		0			0
$268$	2307.67	−	1332.33i	0.0321295	−	0.0185500i
$269$			77325.2i			1.06860i	0.845294	+	0.534301i	$0.179425\pi$
$269$			77325.2i			1.06860i	−0.845294	+	0.534301i	$0.820575\pi$
$270$		0			0
$271$	−5856.99			−0.0797510			−0.0398755	−	0.999205i	$-0.512696\pi$
$271$	−5856.99			−0.0797510			−0.0398755	+	0.999205i	$0.512696\pi$
$272$	32394.9	+	56109.7i	0.437864	+	0.758403i
$273$		0			0
$274$	−11093.3	+	19214.1i	−0.147760	+	0.255928i
$275$	−57043.0	−	90705.9i	−0.754287	−	1.19942i
$276$		0			0
$277$	−45287.4	+	26146.7i	−0.590225	+	0.340767i	−0.765187	−	0.643809i	$-0.777353\pi$
$277$	−45287.4	+	26146.7i	−0.590225	+	0.340767i	0.174961	+	0.984575i	$0.444020\pi$
$278$	7587.84			0.0981813
$279$		0			0
$280$	41036.4	+	10168.8i	0.523423	+	0.129704i
$281$	−9078.13	+	5241.26i	−0.114970	+	0.0663779i	−0.556382	−	0.830927i	$-0.687811\pi$
$281$	−9078.13	+	5241.26i	−0.114970	+	0.0663779i	0.441412	+	0.897304i	$0.354478\pi$
$282$		0			0
$283$	4813.64	+	2779.16i	0.0601036	+	0.0347009i	0.529751	−	0.848153i	$-0.322285\pi$
$283$	4813.64	+	2779.16i	0.0601036	+	0.0347009i	−0.469647	+	0.882854i	$0.655619\pi$
$284$	−37800.8	−	21824.3i	−0.468667	−	0.270585i
$285$		0			0
$286$	7970.99	+	13806.2i	0.0974496	+	0.168788i
$287$	−48705.5			−0.591309
$288$		0			0
$289$	−8741.28			−0.104660
$290$	1552.19	+	5383.87i	0.0184564	+	0.0640175i
$291$		0			0
$292$	−79249.1	−	45754.5i	−0.929455	−	0.536621i
$293$	−75376.9	+	130557.i	−0.878017	+	1.52077i	−0.0245037	+	0.999700i	$0.507801\pi$
$293$	−75376.9	+	130557.i	−0.878017	+	1.52077i	−0.853514	+	0.521071i	$0.825533\pi$
$294$		0			0
$295$	−19486.4	−	67589.8i	−0.223917	−	0.776671i
$296$		−	14604.4i		−	0.166687i
$297$		0			0
$298$			8262.07i			0.0930371i
$299$	−49521.0	+	28591.0i	−0.553920	+	0.319806i
$300$		0			0
$301$	38247.3	−	66246.3i	0.422151	−	0.731187i
$302$	9142.05	−	15834.5i	0.100237	−	0.173616i
$303$		0			0
$304$	−27205.9	−	47122.0i	−0.294385	−	0.509890i
$305$	−31999.9	+	129136.i	−0.343992	+	1.38818i
$306$		0			0
$307$			140225.i			1.48781i	0.668284	+	0.743906i	$0.267029\pi$
$307$			140225.i			1.48781i	−0.668284	+	0.743906i	$0.732971\pi$
$308$	−113053.	−	195813.i	−1.19173	−	2.06414i
$309$		0			0
$310$	7088.45	+	6825.55i	0.0737612	+	0.0710255i
$311$	165187.	+	95370.9i	1.70787	+	0.986041i	0.937187	+	0.348827i	$0.113420\pi$
$311$	165187.	+	95370.9i	1.70787	+	0.986041i	0.770687	+	0.637214i	$0.219913\pi$
$312$		0			0
$313$	29158.8	−	16834.8i	0.297633	−	0.171838i	−0.343746	−	0.939063i	$-0.611696\pi$
$313$	29158.8	−	16834.8i	0.297633	−	0.171838i	0.641379	+	0.767224i	$0.278363\pi$
$314$		−	13159.5i		−	0.133469i
$315$		0			0
$316$	45757.9			0.458239
$317$	39248.1	+	67979.6i	0.390571	+	0.676488i	0.992525	−	0.122042i	$-0.0389444\pi$
$317$	39248.1	+	67979.6i	0.390571	+	0.676488i	−0.601954	+	0.798531i	$0.705611\pi$
$318$		0			0
$319$	30351.2	−	52569.8i	0.298259	−	0.516600i
$320$	−62909.3	−	60576.1i	−0.614348	−	0.591563i
$321$		0			0
$322$	−18041.1	+	10416.1i	−0.174001	+	0.100460i
$323$	−62801.5			−0.601956
$324$		0			0
$325$	−42869.5	+	81188.6i	−0.405865	+	0.768649i
$326$	13263.7	−	7657.81i	0.124804	−	0.0720559i
$327$		0			0
$328$	−9979.44	−	5761.63i	−0.0927595	−	0.0535547i
$329$	58049.6	+	33515.0i	0.536300	+	0.309633i
$330$		0			0
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	0.927677	+	0.373384i	$0.121803\pi$
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	−0.140478	+	0.990084i	$0.544864\pi$
$332$	−107469.			−0.975001
$333$		0			0
$334$	−6563.29			−0.0588340
$335$	1183.01	+	4103.36i	0.0105414	+	0.0365637i
$336$		0			0
$337$	−27972.6	−	16150.0i	−0.246305	−	0.142204i	0.371766	−	0.928326i	$-0.378752\pi$
$337$	−27972.6	−	16150.0i	−0.246305	−	0.142204i	−0.618071	+	0.786122i	$0.712086\pi$
$338$	−2209.75	+	3827.40i	−0.0193424	+	0.0335020i
$339$		0			0
$340$	−102471.	+	29542.6i	−0.886424	+	0.255559i
$341$		−	106607.i		−	0.916808i
$342$		0			0
$343$			198325.i			1.68574i
$344$	15673.2	−	9048.94i	0.132447	−	0.0764682i
$345$		0			0
$346$	12099.2	−	20956.4i	0.101066	−	0.175051i
$347$	−116127.	+	201138.i	−0.964440	+	1.67046i	−0.253329	+	0.967380i	$0.581526\pi$
$347$	−116127.	+	201138.i	−0.964440	+	1.67046i	−0.711111	+	0.703080i	$0.751808\pi$
$348$		0			0
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	0.974598	+	0.223963i	$0.0718994\pi$
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	−0.293342	+	0.956008i	$0.594767\pi$
$350$	−15617.9	+	29578.0i	−0.127493	+	0.241453i
$351$		0			0
$352$		−	80580.6i		−	0.650347i
$353$	64590.4	+	111874.i	0.518345	+	0.897800i	0.999773	+	0.0213140i	$0.00678497\pi$
$353$	64590.4	+	111874.i	0.518345	+	0.897800i	−0.481428	+	0.876486i	$0.659882\pi$
$354$		0			0
$355$	48520.8	−	50389.7i	0.385010	−	0.399839i
$356$	13931.7	+	8043.48i	0.109927	+	0.0634664i
$357$		0			0
$358$	15931.7	−	9198.16i	0.124307	−	0.0717687i
$359$		−	205368.i		−	1.59347i	−0.604331	−	0.796734i	$-0.706559\pi$
$359$		−	205368.i		−	1.59347i	0.604331	−	0.796734i	$-0.293441\pi$
$360$		0			0
$361$	−77579.1			−0.595292
$362$	−7548.44	−	13074.3i	−0.0576023	−	0.0997702i
$363$		0			0
$364$	−96867.8	+	167780.i	−0.731100	+	1.26630i
$365$	101724.	−	105642.i	0.763547	−	0.792956i
$366$		0			0
$367$	−89820.1	+	51857.7i	−0.666870	+	0.385018i	−0.794890	−	0.606754i	$-0.792471\pi$
$367$	−89820.1	+	51857.7i	−0.666870	+	0.385018i	0.128019	+	0.991772i	$0.459138\pi$
$368$	92226.6			0.681021
$369$		0			0
$370$	11215.2	+	2779.12i	0.0819224	+	0.0203004i
$371$	−253879.	+	146577.i	−1.84450	+	1.06492i
$372$		0			0
$373$	156191.	+	90176.7i	1.12263	+	0.648152i	0.942071	−	0.335412i	$-0.108876\pi$
$373$	156191.	+	90176.7i	1.12263	+	0.648152i	0.180560	+	0.983564i	$0.442209\pi$
$374$	−25700.8	−	14838.4i	−0.183740	−	0.106082i
$375$		0			0
$376$	7929.31	+	13734.0i	0.0560867	+	0.0971450i
$377$	−52012.1			−0.365950
$378$		0			0
$379$	−145168.			−1.01063			−0.505317	−	0.862934i	$-0.668624\pi$
$379$	−145168.			−1.01063			−0.505317	+	0.862934i	$0.668624\pi$
$380$	86056.8	−	24810.5i	0.595961	−	0.171818i
$381$		0			0
$382$	−3150.31	−	1818.83i	−0.0215887	−	0.0124642i
$383$	56718.9	−	98240.0i	0.386661	−	0.669716i	−0.605337	−	0.795969i	$-0.706962\pi$
$383$	56718.9	−	98240.0i	0.386661	−	0.669716i	0.991998	+	0.126253i	$0.0402951\pi$
$384$		0			0
$385$	348182.	−	100382.i	2.34901	−	0.677228i
$386$		−	3966.91i		−	0.0266242i
$387$		0			0
$388$		−	219225.i		−	1.45622i
$389$	229341.	−	132410.i	1.51559	−	0.875026i	0.515757	−	0.856735i	$-0.327511\pi$
$389$	229341.	−	132410.i	1.51559	−	0.875026i	0.999833	−	0.0182911i	$-0.00582258\pi$
$390$		0			0
$391$	53223.5	−	92185.7i	0.348137	−	0.602990i
$392$	−47473.9	+	82227.2i	−0.308946	+	0.535110i
$393$		0			0
$394$	−17443.7	−	30213.3i	−0.112369	−	0.194628i
$395$	−17638.5	+	71180.4i	−0.113049	+	0.456212i
$396$		0			0
$397$		−	82700.5i		−	0.524719i	−0.964970	−	0.262360i	$-0.915499\pi$
$397$		−	82700.5i		−	0.524719i	0.964970	−	0.262360i	$-0.0845007\pi$
$398$	−3283.79	−	5687.70i	−0.0207305	−	0.0359063i
$399$		0			0
$400$	125352.	−	78831.3i	0.783452	−	0.492695i
$401$	−20868.1	−	12048.2i	−0.129776	−	0.0749261i	0.433707	−	0.901054i	$-0.357205\pi$
$401$	−20868.1	−	12048.2i	−0.129776	−	0.0749261i	−0.563482	+	0.826128i	$0.690539\pi$
$402$		0			0
$403$	−79107.4	+	45672.7i	−0.487087	+	0.281220i
$404$			212499.i			1.30195i
$405$		0			0
$406$	−18948.7			−0.114955
$407$	−62587.7	−	108405.i	−0.377834	−	0.654427i
$408$		0			0
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	−0.501985	−	0.864876i	$-0.667397\pi$
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	0.999997	+	0.00229409i	$0.000730232\pi$
$410$	6323.55	−	6567.11i	0.0376178	−	0.0390667i
$411$		0			0
$412$	−220829.	+	127495.i	−1.30095	+	0.751104i
$413$	237884.			1.39465
$414$		0			0
$415$	41426.4	−	167177.i	0.240537	−	0.970687i
$416$	−59794.3	+	34522.3i	−0.345520	+	0.199486i
$417$		0			0
$418$	21584.1	+	12461.6i	0.123532	+	0.0713214i
$419$	−93529.3	−	53999.2i	−0.532745	−	0.307581i	0.209388	−	0.977833i	$-0.432853\pi$
$419$	−93529.3	−	53999.2i	−0.532745	−	0.307581i	−0.742134	+	0.670252i	$0.766186\pi$
$420$		0			0
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	−0.956788	−	0.290785i	$-0.906084\pi$
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	0.226567	−	0.973996i	$-0.427250\pi$
$422$	32787.8			0.184114
$423$		0			0
$424$	−69357.3			−0.385799
$425$	−6456.26	−	170790.i	−0.0357440	−	0.945549i
$426$		0			0
$427$	−389640.	−	224959.i	−2.13702	−	1.23381i
$428$	119286.	−	206610.i	0.651182	−	1.12788i
$429$		0			0
$430$	3966.45	+	13757.9i	0.0214519	+	0.0744073i
$431$			81054.9i			0.436340i	0.975911	+	0.218170i	$0.0700087\pi$
$431$			81054.9i			0.436340i	−0.975911	+	0.218170i	$0.929991\pi$
$432$		0			0
$433$			173783.i			0.926897i	0.886124	+	0.463448i	$0.153388\pi$
$433$			173783.i			0.926897i	−0.886124	+	0.463448i	$0.846612\pi$
$434$	−28819.8	+	16639.1i	−0.153007	+	0.0883388i
$435$		0			0
$436$	−24262.6	+	42024.1i	−0.127634	+	0.221068i
$437$	−44698.1	+	77419.4i	−0.234060	+	0.405403i
$438$		0			0
$439$	129440.	+	224196.i	0.671642	+	1.16332i	0.977438	+	0.211221i	$0.0677441\pi$
$439$	129440.	+	224196.i	0.671642	+	1.16332i	−0.305796	+	0.952097i	$0.598923\pi$
$440$	83215.0	+	20620.7i	0.429829	+	0.106512i
$441$		0			0
$442$			25428.2i			0.130158i
$443$	96232.4	+	166679.i	0.490358	+	0.849326i	0.999938	−	0.0110976i	$-0.00353254\pi$
$443$	96232.4	+	166679.i	0.490358	+	0.849326i	−0.509580	+	0.860423i	$0.670199\pi$
$444$		0			0
$445$	−17882.6	+	18571.4i	−0.0903050	+	0.0937832i
$446$	14090.2	+	8134.96i	0.0708347	+	0.0408964i
$447$		0			0
$448$	255773.	−	147671.i	1.27438	−	0.735763i
$449$		−	56772.8i		−	0.281610i	−0.990037	−	0.140805i	$-0.955031\pi$
$449$		−	56772.8i		−	0.281610i	0.990037	−	0.140805i	$-0.0449690\pi$
$450$		0			0
$451$	−98766.7			−0.485576
$452$	62716.6	+	108628.i	0.306977	+	0.531700i
$453$		0			0
$454$	−10833.5	+	18764.2i	−0.0525604	+	0.0910372i
$455$	−223656.	−	215361.i	−1.08033	−	1.04027i
$456$		0			0
$457$	271096.	−	156518.i	1.29805	−	0.749429i	0.317983	−	0.948096i	$-0.396995\pi$
$457$	271096.	−	156518.i	1.29805	−	0.749429i	0.980067	+	0.198667i	$0.0636612\pi$
$458$	3316.91			0.0158126
$459$		0			0
$460$	−36513.0	+	147349.i	−0.172557	+	0.696354i
$461$	−53494.0	+	30884.8i	−0.251712	+	0.145326i	−0.620548	−	0.784169i	$-0.713090\pi$
$461$	−53494.0	+	30884.8i	−0.251712	+	0.145326i	0.368836	+	0.929494i	$0.379756\pi$
$462$		0			0
$463$	−146977.	−	84857.4i	−0.685628	−	0.395847i	0.116344	−	0.993209i	$-0.462882\pi$
$463$	−146977.	−	84857.4i	−0.685628	−	0.395847i	−0.801972	+	0.597362i	$0.796216\pi$
$464$	72649.5	+	41944.2i	0.337440	+	0.194821i
$465$		0			0
$466$	−14118.1	−	24453.3i	−0.0650137	−	0.112607i
$467$	−76633.3			−0.351386			−0.175693	−	0.984445i	$-0.556217\pi$
$467$	−76633.3			−0.351386			−0.175693	+	0.984445i	$0.556217\pi$
$468$		0			0
$469$	−14441.9			−0.0656565
$470$	−12055.6	+	3475.68i	−0.0545751	+	0.0157342i
$471$		0			0
$472$	48740.9	+	28140.5i	0.218781	+	0.126313i
$473$	77559.2	−	134336.i	0.346666	−	0.600443i
$474$		0			0
$475$	5422.09	+	143433.i	0.0240314	+	0.635712i
$476$		−	360648.i		−	1.59173i
$477$		0			0
$478$		−	22838.3i		−	0.0999559i
$479$	30431.7	−	17569.8i	0.132634	−	0.0765763i	−0.432215	−	0.901771i	$-0.642268\pi$
$479$	30431.7	−	17569.8i	0.132634	−	0.0765763i	0.564849	+	0.825194i	$0.308934\pi$
$480$		0			0
$481$	−53627.6	+	92885.7i	−0.231792	+	0.401475i
$482$	−10772.6	+	18658.7i	−0.0463689	+	0.0803133i
$483$		0			0
$484$	−115057.	−	199285.i	−0.491159	−	0.850713i
$485$	341023.	+	84505.6i	1.44977	+	0.359254i
$486$		0			0
$487$		−	290883.i		−	1.22648i	−0.789896	−	0.613240i	$-0.789866\pi$
$487$		−	290883.i		−	1.22648i	0.789896	−	0.613240i	$-0.210134\pi$
$488$	−53223.1	−	92185.1i	−0.223491	−	0.387098i
$489$		0			0
$490$	−54110.8	−	52103.9i	−0.225368	−	0.217009i
$491$	384175.	+	221803.i	1.59355	+	0.920037i	0.992691	+	0.120682i	$0.0385082\pi$
$491$	384175.	+	221803.i	1.59355	+	0.920037i	0.600860	+	0.799355i	$0.294825\pi$
$492$		0			0
$493$	83851.2	−	48411.5i	0.344997	−	0.199184i
$494$		−	21355.1i		−	0.0875080i
$495$		0			0
$496$	147327.			0.598853
$497$	118283.	+	204872.i	0.478860	+	0.829410i
$498$		0			0
$499$	144661.	−	250561.i	0.580967	−	1.00626i	−0.414398	−	0.910096i	$-0.636008\pi$
$499$	144661.	−	250561.i	0.580967	−	1.00626i	0.995365	−	0.0961687i	$-0.0306588\pi$
$500$	76319.5	+	231482.i	0.305278	+	0.925930i
$501$		0			0
$502$	−33155.1	+	19142.1i	−0.131566	+	0.0759596i
$503$	−349897.			−1.38294			−0.691472	−	0.722403i	$-0.743037\pi$
$503$	−349897.			−1.38294			−0.691472	+	0.722403i	$0.743037\pi$
$504$		0			0
$505$	−330561.	−	81913.0i	−1.29619	−	0.321196i
$506$	−36584.4	+	21122.0i	−0.142888	+	0.0824963i
$507$		0			0
$508$	109503.	+	63221.8i	0.424326	+	0.244985i
$509$	−406475.	−	234679.i	−1.56891	−	0.905812i	−0.996296	−	0.0859889i	$-0.972595\pi$
$509$	−406475.	−	234679.i	−1.56891	−	0.905812i	−0.572617	−	0.819823i	$-0.694072\pi$
$510$		0			0
$511$	247979.	+	429512.i	0.949670	+	1.64488i
$512$	187185.			0.714056
$513$		0			0
$514$	9646.70			0.0365134
$515$	−113206.	−	392664.i	−0.426831	−	1.48049i
$516$		0			0
$517$	117715.	+	67962.7i	0.440403	+	0.254267i
$518$	−19537.2	+	33839.5i	−0.0728121	+	0.126114i
$519$		0			0
$520$	−20349.4	−	70583.5i	−0.0752568	−	0.261034i
$521$		−	430054.i		−	1.58434i	−0.610302	−	0.792169i	$-0.708952\pi$
$521$		−	430054.i		−	1.58434i	0.610302	−	0.792169i	$-0.291048\pi$
$522$		0			0
$523$		−	21279.4i		−	0.0777959i	−0.999243	−	0.0388980i	$-0.987615\pi$
$523$		−	21279.4i		−	0.0777959i	0.999243	−	0.0388980i	$-0.0123847\pi$
$524$	79379.9	−	45830.0i	0.289100	−	0.166912i
$525$		0			0
$526$	−2045.18	+	3542.36i	−0.00739198	+	0.0128033i
$527$	85021.9	−	147262.i	0.306132	−	0.530237i
$528$		0			0
$529$	64158.3	+	111125.i	0.229267	+	0.397102i
$530$	13198.2	−	53261.6i	0.0469855	−	0.189611i
$531$		0			0
$532$			302879.i			1.07015i
$533$	42313.6	+	73289.2i	0.148945	+	0.257980i
$534$		0			0
$535$	275417.	+	265203.i	0.962241	+	0.926553i
$536$	−2959.04	−	1708.40i	−0.0102996	−	0.00594649i
$537$		0			0
$538$	42389.4	−	24473.5i	0.146451	−	0.0845536i
$539$			813804.i			2.80119i
$540$		0			0
$541$	−127926.			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$541$	−127926.			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$542$	1853.75	+	3210.78i	0.00631033	+	0.0109298i
$543$		0			0
$544$	64264.9	−	111310.i	0.217158	−	0.376129i
$545$	−56019.5	−	53941.9i	−0.188602	−	0.181607i
$546$		0			0
$547$	−437484.	+	252582.i	−1.46214	+	0.844165i	−0.999110	−	0.0421802i	$-0.986570\pi$
$547$	−437484.	+	252582.i	−1.46214	+	0.844165i	−0.463026	+	0.886345i	$0.653236\pi$
$548$	−546750.			−1.82065
$549$		0			0
$550$	−31670.5	+	59979.3i	−0.104696	+	0.198279i
$551$	−70419.9	+	40657.0i	−0.231949	+	0.133916i
$552$		0			0
$553$	−214772.	−	123999.i	−0.702308	−	0.405478i
$554$	28667.1	+	16550.9i	0.0934036	+	0.0539266i
$555$		0			0
$556$	93494.9	+	161938.i	0.302439	+	0.523840i
$557$	−277756.			−0.895268			−0.447634	−	0.894217i	$-0.647733\pi$
$557$	−277756.			−0.895268			−0.447634	+	0.894217i	$0.647733\pi$
$558$		0			0
$559$	−132911.			−0.425342
$560$	138724.	+	481175.i	0.442361	+	1.53436i
$561$		0			0
$562$	5746.49	+	3317.74i	0.0181941	+	0.0105043i
$563$	−80007.5	+	138577.i	−0.252414	+	0.437194i	−0.964190	−	0.265213i	$-0.914558\pi$
$563$	−80007.5	+	138577.i	−0.252414	+	0.437194i	0.711776	+	0.702407i	$0.247891\pi$
$564$		0			0
$565$	−193156.	+	55687.6i	−0.605079	+	0.174446i
$566$		−	3518.43i		−	0.0109829i
$567$		0			0
$568$			55969.1i			0.173481i
$569$	−152572.	+	88087.7i	−0.471250	+	0.272076i	−0.716763	−	0.697317i	$-0.754377\pi$
$569$	−152572.	+	88087.7i	−0.471250	+	0.272076i	0.245513	+	0.969393i	$0.421044\pi$
$570$		0			0
$571$	227502.	−	394045.i	0.697770	−	1.20857i	−0.271467	−	0.962448i	$-0.587509\pi$
$571$	227502.	−	394045.i	0.697770	−	1.20857i	0.969238	−	0.246126i	$-0.0791577\pi$
$572$	−196432.	+	340230.i	−0.600371	+	1.03987i
$573$		0			0
$574$	15415.4	+	26700.2i	0.0467876	+	0.0810384i
$575$	−215139.	−	113598.i	−0.650703	−	0.343586i
$576$		0			0
$577$			356530.i			1.07089i	0.844571	+	0.535444i	$0.179856\pi$
$577$			356530.i			1.07089i	−0.844571	+	0.535444i	$0.820144\pi$
$578$	2766.63	+	4791.94i	0.00828124	+	0.0143435i
$579$		0			0
$580$	−95775.7	+	99464.7i	−0.284708	+	0.295674i
$581$	504421.	+	291228.i	1.49431	+	0.862740i
$582$		0			0
$583$	−514823.	+	297233.i	−1.51468	+	0.874501i
$584$			117339.i			0.344046i
$585$		0			0
$586$	95427.6			0.277894
$587$	−253068.	−	438326.i	−0.734447	−	1.27210i	−0.954965	−	0.296717i	$-0.904108\pi$
$587$	−253068.	−	438326.i	−0.734447	−	1.27210i	0.220518	−	0.975383i	$-0.429225\pi$
$588$		0			0
$589$	−71403.0	+	123674.i	−0.205819	+	0.356489i
$590$	−30885.0	+	32074.6i	−0.0887246	+	0.0921420i
$591$		0			0
$592$	149812.	−	86494.0i	0.427467	−	0.246798i
$593$	412533.			1.17314			0.586570	−	0.809899i	$-0.300478\pi$
$593$	412533.			1.17314			0.586570	+	0.809899i	$0.300478\pi$
$594$		0			0
$595$	561019.	+	139021.i	1.58469	+	0.392686i
$596$	−176327.	+	101802.i	−0.496394	+	0.286593i
$597$		0			0
$598$	31347.0	+	18098.2i	0.0876583	+	0.0506095i
$599$	43173.5	+	24926.2i	0.120327	+	0.0694708i	0.558956	−	0.829198i	$-0.311202\pi$
$599$	43173.5	+	24926.2i	0.120327	+	0.0694708i	−0.438628	+	0.898668i	$0.644536\pi$
$600$		0			0
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.863367	−	0.504577i	$-0.831648\pi$
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.00529310	−	0.999986i	$-0.501685\pi$
$602$	−48421.3			−0.133611
$603$		0			0
$604$	450581.			1.23509
$605$	354356.	−	102162.i	0.968119	−	0.279112i
$606$		0			0
$607$	281368.	+	162448.i	0.763654	+	0.440896i	0.830606	−	0.556860i	$-0.187994\pi$
$607$	281368.	+	162448.i	0.763654	+	0.440896i	−0.0669521	+	0.997756i	$0.521327\pi$
$608$	−53970.9	+	93480.4i	−0.146000	+	0.252879i
$609$		0			0
$610$	80919.8	−	23329.4i	0.217468	−	0.0626967i
$611$		−	116466.i		−	0.311973i
$612$		0			0
$613$		−	53253.9i		−	0.141720i	−0.997486	−	0.0708599i	$-0.977426\pi$
$613$		−	53253.9i		−	0.141720i	0.997486	−	0.0708599i	$-0.0225743\pi$
$614$	76870.8	−	44381.4i	0.203903	−	0.117724i
$615$		0			0
$616$	−144963.	+	251084.i	−0.382030	+	0.661695i
$617$	186658.	−	323301.i	0.490316	−	0.849252i	−0.509622	−	0.860398i	$-0.670215\pi$
$617$	186658.	−	323301.i	0.490316	−	0.849252i	0.999938	+	0.0111464i	$0.00354807\pi$
$618$		0			0
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	−0.981851	−	0.189652i	$-0.939264\pi$
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	0.326683	−	0.945134i	$-0.394069\pi$
$620$	−58327.7	+	235382.i	−0.151737	+	0.612336i
$621$		0			0
$622$		−	120740.i		−	0.312084i
$623$	−43593.8	−	75506.7i	−0.112318	−	0.194540i
$624$		0			0
$625$	−389510.	+	29491.0i	−0.997146	+	0.0754969i
$626$	−18457.6	−	10656.5i	−0.0471006	−	0.0271935i
$627$		0			0
$628$	280846.	−	162147.i	0.712113	−	0.411139i
$629$		−	199661.i		−	0.504651i
$630$		0			0
$631$	−379130.			−0.952202			−0.476101	−	0.879391i	$-0.657950\pi$
$631$	−379130.			−0.952202			−0.476101	+	0.879391i	$0.657950\pi$
$632$	−29336.9	−	50813.0i	−0.0734481	−	0.127216i
$633$		0			0
$634$	24844.1	−	43031.3i	0.0618081	−	0.107055i
$635$	−140558.	+	145972.i	−0.348584	+	0.362010i
$636$		0			0
$637$	603879.	−	348649.i	1.48823	−	0.859231i
$638$	−38424.8			−0.0943996
$639$		0			0
$640$	−58517.0	+	236146.i	−0.142864	+	0.576528i
$641$	−325664.	+	188022.i	−0.792599	+	0.457607i	−0.840877	−	0.541227i	$-0.817960\pi$
$641$	−325664.	+	188022.i	−0.792599	+	0.457607i	0.0482776	+	0.998834i	$0.484627\pi$
$642$		0			0
$643$	−140867.	−	81329.8i	−0.340713	−	0.196711i	0.319874	−	0.947460i	$-0.396359\pi$
$643$	−140867.	−	81329.8i	−0.340713	−	0.196711i	−0.660587	+	0.750749i	$0.729693\pi$
$644$	−444594.	−	256686.i	−1.07199	−	0.618915i
$645$		0			0
$646$	19876.8	+	34427.6i	0.0476300	+	0.0824976i
$647$	344019.			0.821814			0.410907	−	0.911677i	$-0.365212\pi$
$647$	344019.			0.821814			0.410907	+	0.911677i	$0.365212\pi$
$648$		0			0
$649$	482389.			1.14527
$650$	58075.6	−	2195.39i	0.137457	−	0.00519620i
$651$		0			0
$652$	326862.	+	188714.i	0.768899	+	0.443924i
$653$	−263282.	+	456018.i	−0.617440	+	1.06944i	0.372511	+	0.928028i	$0.378497\pi$
$653$	−263282.	+	456018.i	−0.617440	+	1.06944i	−0.989951	+	0.141410i	$0.954836\pi$
$654$		0			0
$655$	40693.6	+	141149.i	0.0948513	+	0.328998i
$656$		−	136492.i		−	0.317175i
$657$		0			0
$658$		−	42430.1i		−	0.0979992i
$659$	417516.	−	241053.i	0.961396	−	0.555062i	0.0647933	−	0.997899i	$-0.479361\pi$
$659$	417516.	−	241053.i	0.961396	−	0.555062i	0.896602	+	0.442837i	$0.146028\pi$
$660$		0			0
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	−0.996480	−	0.0838268i	$-0.973286\pi$
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	0.570836	+	0.821064i	$0.306619\pi$
$662$	54594.2	−	94559.9i	0.124575	−	0.215770i
$663$		0			0
$664$	68901.6	+	119341.i	0.156276	+	0.270679i
$665$	−471155.	−	116752.i	−1.06542	−	0.264011i
$666$		0			0
$667$		−	137825.i		−	0.309796i
$668$	−80870.7	−	140072.i	−0.181233	−	0.313905i
$669$		0			0
$670$	1875.02	−	1947.24i	0.00417693	−	0.00433781i
$671$	−790126.	−	456179.i	−1.75489	−	1.01319i
$672$		0			0
$673$	−243512.	+	140592.i	−0.537638	+	0.310406i	−0.744121	−	0.668045i	$-0.767132\pi$
$673$	−243512.	+	140592.i	−0.537638	+	0.310406i	0.206483	+	0.978450i	$0.433798\pi$
$674$			20446.0i			0.0450078i
$675$		0			0
$676$	−108911.			−0.238330
$677$	134768.	+	233424.i	0.294041	+	0.509295i	0.974761	−	0.223249i	$-0.0716663\pi$
$677$	134768.	+	233424.i	0.294041	+	0.509295i	−0.680720	+	0.732544i	$0.738333\pi$
$678$		0			0
$679$	−594074.	+	1.02897e6i	−1.28855	+	2.23183i
$680$	98503.6	+	94850.3i	0.213027	+	0.205126i
$681$		0			0
$682$	−58441.8	+	33741.4i	−0.125648	+	0.0725428i
$683$	425001.			0.911063			0.455531	−	0.890220i	$-0.349449\pi$
$683$	425001.			0.911063			0.455531	+	0.890220i	$0.349449\pi$
$684$		0			0
$685$	210758.	−	850516.i	0.449162	−	1.81260i
$686$	108721.	−	62770.3i	0.231029	−	0.133385i
$687$		0			0
$688$	185648.	+	107184.i	0.392205	+	0.226440i
$689$	441121.	+	254681.i	0.929221	+	0.536486i
$690$		0			0
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	0.568028	−	0.823009i	$-0.307706\pi$
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	−0.996761	+	0.0804226i	$0.974373\pi$
$692$	596329.			1.24530
$693$		0			0
$694$	147018.			0.305247
$695$	−287948.	+	83016.4i	−0.596135	+	0.171868i
$696$		0			0
$697$	−136431.	−	78768.7i	−0.280834	−	0.162139i
$698$	52525.1	−	90976.2i	0.107809	−	0.186731i
$699$		0			0
$700$	−823686.	+	31137.3i	−1.68099	+	0.0635455i
$701$			590764.i			1.20220i	0.799172	+	0.601102i	$0.205272\pi$
$701$			590764.i			1.20220i	−0.799172	+	0.601102i	$0.794728\pi$
$702$		0			0
$703$			167679.i			0.339288i
$704$	518665.	−	299451.i	1.04651	−	0.604201i
$705$		0			0
$706$	40885.9	−	70816.5i	0.0820285	−	0.142077i
$707$	575848.	−	997398.i	1.15204	−	1.99540i
$708$		0			0
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	0.686912	−	0.726741i	$-0.258966\pi$
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	−0.972832	+	0.231513i	$0.925632\pi$
$710$	−42980.4	−	10650.5i	−0.0852616	−	0.0211278i
$711$		0			0
$712$		−	20627.7i		−	0.0406904i
$713$	−121026.	−	209624.i	−0.238068	−	0.412346i
$714$		0			0
$715$	−453537.	−	436716.i	−0.887158	−	0.854255i
$716$	392610.	+	226673.i	0.765835	+	0.442155i
$717$		0			0
$718$	−112582.	+	64999.2i	−0.218383	+	0.126084i
$719$		−	645625.i		−	1.24889i	−0.781070	−	0.624443i	$-0.785326\pi$
$719$		−	645625.i		−	1.24889i	0.781070	−	0.624443i	$-0.214674\pi$
$720$		0			0
$721$	1.38199e6			2.65849
$722$	24553.9	+	42528.6i	0.0471027	+	0.0815843i
$723$		0			0
$724$	186019.	−	322194.i	0.354878	−	0.614668i
$725$	−117807.	−	187329.i	−0.224127	−	0.356392i
$726$		0			0
$727$	462909.	−	267261.i	0.875844	−	0.505669i	0.00655839	−	0.999978i	$-0.497912\pi$
$727$	462909.	−	267261.i	0.875844	−	0.505669i	0.869286	+	0.494310i	$0.164579\pi$
$728$	248420.			0.468732
$729$		0			0
$730$	−90108.0	−	22328.8i	−0.169090	−	0.0419005i
$731$	214273.	−	123710.i	0.400989	−	0.231511i
$732$		0			0
$733$	163651.	+	94483.8i	0.304586	+	0.175853i	0.644501	−	0.764603i	$-0.277065\pi$
$733$	163651.	+	94483.8i	0.304586	+	0.175853i	−0.339915	+	0.940456i	$0.610398\pi$
$734$	56856.4	+	32826.1i	0.105533	+	0.0609294i
$735$		0			0
$736$	−91479.3	−	158447.i	−0.168876	−	0.292501i
$737$	−29285.7			−0.0539164
$738$		0			0
$739$	−683135.			−1.25089			−0.625443	−	0.780270i	$-0.715082\pi$
$739$	−683135.			−1.25089			−0.625443	+	0.780270i	$0.715082\pi$
$740$	78878.3	+	273595.i	0.144044	+	0.499625i
$741$		0			0
$742$	160706.	+	92783.6i	0.291893	+	0.168525i
$743$	−150819.	+	261226.i	−0.273198	+	0.473193i	−0.969679	−	0.244382i	$-0.921415\pi$
$743$	−150819.	+	261226.i	−0.273198	+	0.473193i	0.696481	+	0.717576i	$0.254748\pi$
$744$		0			0
$745$	−90393.0	−	313534.i	−0.162863	−	0.564901i
$746$		−	114164.i		−	0.205141i
$747$		0			0
$748$		−	731334.i		−	1.30711i
$749$	−1.11978e6	+	646504.i	−1.99603	+	1.15241i
$750$		0			0
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	−0.949784	−	0.312906i	$-0.898697\pi$
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	0.745877	+	0.666084i	$0.232031\pi$
$752$	−93922.0	+	162678.i	−0.166085	+	0.287669i
$753$		0			0
$754$	16461.9	+	28512.9i	0.0289559	+	0.0501532i
$755$	−173688.	+	700918.i	−0.304702	+	1.22963i
$756$		0			0
$757$		−	897739.i		−	1.56660i	−0.621644	−	0.783300i	$-0.713535\pi$
$757$		−	897739.i		−	1.56660i	0.621644	−	0.783300i	$-0.286465\pi$
$758$	45946.1	+	79580.9i	0.0799668	+	0.138507i
$759$		0			0
$760$	−82725.3	−	79657.1i	−0.143222	−	0.137911i
$761$	343014.	+	198039.i	0.592301	+	0.341965i	0.766007	−	0.642833i	$-0.222241\pi$
$761$	343014.	+	198039.i	0.592301	+	0.341965i	−0.173706	+	0.984798i	$0.555574\pi$
$762$		0			0
$763$	227761.	−	131498.i	0.391229	−	0.225876i
$764$		−	89644.1i		−	0.153580i
$765$		0			0
$766$	−71806.5			−0.122379
$767$	−206665.	−	357954.i	−0.351298	−	0.608467i
$768$		0			0
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	−0.935852	−	0.352392i	$-0.885368\pi$
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	0.773107	+	0.634276i	$0.218702\pi$
$770$	−165229.	−	159101.i	−0.278680	−	0.268344i
$771$		0			0
$772$	84660.7	−	48878.9i	0.142052	−	0.0820138i
$773$	542226.			0.907447			0.453723	−	0.891143i	$-0.350095\pi$
$773$	542226.			0.907447			0.453723	+	0.891143i	$0.350095\pi$
$774$		0			0
$775$	−343673.	−	181468.i	−0.572193	−	0.302131i
$776$	−243444.	+	140552.i	−0.404273	+	0.233407i
$777$		0			0
$778$	−145173.	−	83815.8i	−0.239843	−	0.138474i
$779$	114578.	+	66151.5i	0.188810	+	0.109010i
$780$		0			0
$781$	239858.	+	415446.i	0.393234	+	0.681102i
$782$	−67381.2			−0.110186
$783$		0			0
$784$	−1.12465e6			−1.82972
$785$	143974.	+	499384.i	0.233639	+	0.810392i
$786$		0			0
$787$	852809.	+	492370.i	1.37690	+	0.794954i	0.991785	−	0.127915i	$-0.0408285\pi$
$787$	852809.	+	492370.i	1.37690	+	0.794954i	0.385115	+	0.922869i	$0.374162\pi$
$788$	429870.	−	744557.i	0.692285	−	1.19907i
$789$		0			0
$790$	44603.5	−	12859.3i	0.0714685	−	0.0206046i
$791$		−	679819.i		−	1.08653i
$792$		0			0
$793$			781744.i			1.24313i
$794$	−45336.2	+	26174.8i	−0.0719124	+	0.0415186i
$795$		0			0
$796$	80923.6	−	140164.i	0.127717	−	0.221213i
$797$	455717.	−	789324.i	0.717428	−	1.24262i	−0.244588	−	0.969627i	$-0.578653\pi$
$797$	455717.	−	789324.i	0.717428	−	1.24262i	0.962016	−	0.272994i	$-0.0880140\pi$
$798$		0			0
$799$	108404.	+	187761.i	0.169805	+	0.294111i
$800$	−259770.	−	137165.i	−0.405891	−	0.214320i
$801$		0			0
$802$			15253.1i			0.0237142i
$803$	502860.	+	870979.i	0.779859	+	1.35075i
$804$		0			0
$805$	570678.	−	592658.i	0.880641	−	0.914561i
$806$	50075.2	+	28910.9i	0.0770819	+	0.0445033i
$807$		0			0
$808$	235975.	−	136240.i	0.361446	−	0.208681i
$809$		−	485562.i		−	0.741904i	−0.928652	−	0.370952i	$-0.879031\pi$
$809$		−	485562.i		−	0.741904i	0.928652	−	0.370952i	$-0.120969\pi$
$810$		0			0
$811$	157252.			0.239087			0.119543	−	0.992829i	$-0.461857\pi$
$811$	157252.			0.239087			0.119543	+	0.992829i	$0.461857\pi$
$812$	−233479.	−	404398.i	−0.354109	−	0.613334i
$813$		0			0
$814$	−39618.2	+	68620.8i	−0.0597924	+	0.103564i
$815$	−419558.	+	435718.i	−0.631650	+	0.655979i
$816$		0			0
$817$	−179951.	+	103895.i	−0.269593	+	0.155650i
$818$	−105468.			−0.157622
$819$		0			0
$820$	218070.	+	54037.9i	0.324316	+	0.0803657i
$821$	492419.	−	284298.i	0.730548	−	0.421782i	−0.0880747	−	0.996114i	$-0.528071\pi$
$821$	492419.	−	284298.i	0.730548	−	0.421782i	0.818623	+	0.574332i	$0.194738\pi$
$822$		0			0
$823$	−621801.	−	358997.i	−0.918019	−	0.530018i	−0.0350164	−	0.999387i	$-0.511148\pi$
$823$	−621801.	−	358997.i	−0.918019	−	0.530018i	−0.883002	+	0.469368i	$0.844482\pi$
$824$	283161.	+	163483.i	0.417041	+	0.240779i
$825$		0			0
$826$	−75290.7	−	130407.i	−0.110352	−	0.191136i
$827$	39891.9			0.0583275			0.0291638	−	0.999575i	$-0.490716\pi$
$827$	39891.9			0.0583275			0.0291638	+	0.999575i	$0.490716\pi$
$828$		0			0
$829$	1.05219e6			1.53103			0.765515	−	0.643418i	$-0.222484\pi$
$829$	1.05219e6			1.53103			0.765515	+	0.643418i	$0.222484\pi$
$830$	−104757.	+	30201.8i	−0.152064	+	0.0438407i
$831$		0			0
$832$	−444412.	−	256582.i	−0.642007	−	0.370663i
$833$	−649028.	+	1.12415e6i	−0.935348	+	1.62007i
$834$		0			0
$835$	249068.	−	71807.1i	0.357227	−	0.102990i
$836$			614189.i			0.878799i
$837$		0			0
$838$			68363.3i			0.0973498i
$839$	849479.	−	490447.i	1.20678	−	0.696736i	0.244727	−	0.969592i	$-0.421302\pi$
$839$	849479.	−	490447.i	1.20678	−	0.696736i	0.962055	+	0.272856i	$0.0879684\pi$
$840$		0			0
$841$	−290958.	+	503955.i	−0.411376	+	0.712524i
$842$	−81926.5	+	141901.i	−0.115558	+	0.200153i
$843$		0			0
$844$	404000.	+	699749.i	0.567148	+	0.982329i
$845$	41982.5	−	169421.i	0.0587970	−	0.237276i
$846$		0			0
$847$			1.24717e6i			1.73843i
$848$	−410766.	−	711467.i	−0.571219	−	0.989380i
$849$		0			0
$850$	−91583.0	+	57594.5i	−0.126758	+	0.0797156i
$851$	−246135.	−	142106.i	−0.339870	−	0.196224i
$852$		0			0
$853$	−608193.	+	351140.i	−0.835879	+	0.482595i	−0.855861	−	0.517205i	$-0.826972\pi$
$853$	−608193.	+	351140.i	−0.835879	+	0.482595i	0.0199823	+	0.999800i	$0.493639\pi$
$854$			284799.i			0.390502i
$855$		0			0
$856$	−305913.			−0.417494
$857$	258863.	+	448364.i	0.352459	+	0.610476i	0.986680	−	0.162676i	$-0.0520124\pi$
$857$	258863.	+	448364.i	0.352459	+	0.610476i	−0.634221	+	0.773152i	$0.718679\pi$
$858$		0			0
$859$	324805.	−	562579.i	0.440186	−	0.762425i	−0.557517	−	0.830166i	$-0.688246\pi$
$859$	324805.	−	562579.i	0.440186	−	0.762425i	0.997703	+	0.0677408i	$0.0215791\pi$
$860$	−244745.	+	254171.i	−0.330915	+	0.343661i
$861$		0			0
$862$	44434.0	−	25654.0i	0.0598000	−	0.0345255i
$863$	−1.39346e6			−1.87100			−0.935499	−	0.353329i	$-0.885050\pi$
$863$	−1.39346e6			−1.87100			−0.935499	+	0.353329i	$0.885050\pi$
$864$		0			0
$865$	−229870.	+	927642.i	−0.307220	+	1.23979i
$866$	95267.2	−	55002.6i	0.127030	−	0.0733410i
$867$		0			0
$868$	−710217.	−	410044.i	−0.942652	−	0.544240i
$869$	−435522.	−	251449.i	−0.576728	−	0.332974i
$870$		0			0
$871$	12546.6	+	21731.3i	0.0165382	+	0.0286450i
$872$	62222.3			0.0818301
$873$		0			0
$874$	56588.1			0.0740802
$875$	269073.	−	1.29332e6i	0.351443	−	1.68923i
$876$		0			0
$877$	642695.	+	371060.i	0.835614	+	0.482442i	0.855771	−	0.517355i	$-0.173083\pi$
$877$	642695.	+	371060.i	0.835614	+	0.482442i	−0.0201572	+	0.999797i	$0.506417\pi$
$878$	81935.6	−	141917.i	0.106288	−	0.184096i
$879$		0			0
$880$	281310.	+	975744.i	0.363262	+	1.26000i
$881$			737962.i			0.950784i	0.879774	+	0.475392i	$0.157694\pi$
$881$			737962.i			0.950784i	−0.879774	+	0.475392i	$0.842306\pi$
$882$		0			0
$883$			143168.i			0.183622i	0.995776	+	0.0918109i	$0.0292655\pi$
$883$			143168.i			0.183622i	−0.995776	+	0.0918109i	$0.970734\pi$
$884$	−542682.	+	313318.i	−0.694450	+	0.400941i
$885$		0			0
$886$	60915.4	−	105509.i	0.0775996	−	0.134406i
$887$	−504758.	+	874267.i	−0.641559	+	1.11121i	0.343526	+	0.939143i	$0.388379\pi$
$887$	−504758.	+	874267.i	−0.641559	+	1.11121i	−0.985085	+	0.172069i	$0.944955\pi$
$888$		0			0
$889$	−342648.	−	593483.i	−0.433555	−	0.750939i
$890$	15840.7	+	3925.32i	0.0199983	+	0.00495559i
$891$		0			0
$892$			400945.i			0.503912i
$893$	−91039.6	−	157685.i	−0.114164	−	0.197737i
$894$		0			0
$895$	−503951.	+	523362.i	−0.629133	+	0.653365i
$896$	−712521.	−	411374.i	−0.887527	−	0.512414i
$897$		0			0
$898$	−31122.7	+	17968.7i	−0.0385944	+	0.0222825i
$899$		−	220169.i		−	0.272418i
$900$		0			0
$901$	−948202.			−1.16802
$902$	31259.8	+	54143.6i	0.0384214	+	0.0665478i
$903$		0			0
$904$	80419.4	−	139290.i	0.0984065	−	0.170445i
$905$	429495.	+	413566.i	0.524398	+	0.504949i
$906$		0			0
$907$	415123.	−	239672.i	0.504618	−	0.291341i	−0.226001	−	0.974127i	$-0.572565\pi$
$907$	415123.	−	239672.i	0.504618	−	0.291341i	0.730618	+	0.682786i	$0.239232\pi$
$908$	−533949.			−0.647631
$909$		0			0
$910$	−47272.8	+	190770.i	−0.0570858	+	0.230370i
$911$	−755164.	+	435994.i	−0.909923	+	0.525344i	−0.880406	−	0.474220i	$-0.842730\pi$
$911$	−755164.	+	435994.i	−0.909923	+	0.525344i	−0.0295167	+	0.999564i	$0.509397\pi$
$912$		0			0
$913$	1.02288e6	+	590561.i	1.22711	+	0.708473i
$914$	−171605.	−	99076.1i	−0.205417	−	0.118598i
$915$		0			0
$916$	40869.8	+	70788.6i	0.0487093	+	0.0843670i
$917$	−496776.			−0.590775
$918$		0			0
$919$	411896.			0.487705			0.243852	−	0.969812i	$-0.421589\pi$
$919$	411896.			0.487705			0.243852	+	0.969812i	$0.421589\pi$
$920$	187037.	−	53923.3i	0.220979	−	0.0637089i
$921$		0			0
$922$	33861.9	+	19550.2i	0.0398336	+	0.0229979i
$923$	205519.	−	355970.i	0.241240	−	0.417840i
$924$		0			0
$925$	−456006.	+	17238.1i	−0.532951	+	0.0201468i
$926$			107430.i			0.125286i
$927$		0			0
$928$		−	166417.i		−	0.193243i
$929$	−756603.	+	436825.i	−0.876671	+	0.506146i	−0.869559	−	0.493828i	$-0.835597\pi$
$929$	−756603.	+	436825.i	−0.876671	+	0.506146i	−0.00711192	+	0.999975i	$0.502264\pi$
$930$		0			0
$931$	545066.	−	944083.i	0.628854	−	1.08921i
$932$	347918.	−	602611.i	0.400539	−	0.693753i
$933$		0			0
$934$	24254.6	+	42010.1i	0.0278035	+	0.0481571i
$935$	1.13765e6	+	281911.i	1.30133	+	0.322469i
$936$		0			0
$937$		−	271368.i		−	0.309086i	−0.987986	−	0.154543i	$-0.950609\pi$
$937$		−	271368.i		−	0.309086i	0.987986	−	0.154543i	$-0.0493906\pi$
$938$	4570.88	+	7916.99i	0.00519510	+	0.00899817i
$939$		0			0
$940$	−222723.	−	214462.i	−0.252063	−	0.242714i
$941$	−554563.	−	320177.i	−0.626284	−	0.361585i	0.153027	−	0.988222i	$-0.451098\pi$
$941$	−554563.	−	320177.i	−0.626284	−	0.361585i	−0.779312	+	0.626636i	$0.784431\pi$
$942$		0			0
$943$	−194207.	+	112125.i	−0.218394	+	0.126090i
$944$			666644.i			0.748084i
$945$		0			0
$946$	−98190.4			−0.109720
$947$	257159.	+	445412.i	0.286749	+	0.496663i	0.973032	−	0.230671i	$-0.0740922\pi$
$947$	257159.	+	445412.i	0.286749	+	0.496663i	−0.686283	+	0.727335i	$0.740759\pi$
$948$		0			0
$949$	430870.	−	746288.i	0.478425	−	0.828656i
$950$	76913.2	−	48369.0i	0.0852224	−	0.0535945i
$951$		0			0
$952$	−400491.	+	231223.i	−0.441894	+	0.255128i
$953$	−926631.			−1.02028			−0.510142	−	0.860090i	$-0.670407\pi$
$953$	−926631.			−1.02028			−0.510142	+	0.860090i	$0.670407\pi$
$954$		0			0
$955$	139449.	+	34555.5i	0.152901	+	0.0378888i
$956$	487410.	−	281406.i	0.533309	−	0.307906i
$957$		0			0
$958$	−19263.4	−	11121.7i	−0.0209895	−	0.0121183i
$959$	2.56626e6	+	1.48163e6i	2.79038	+	1.61102i
$960$		0			0
$961$	268427.	+	464929.i	0.290656	+	0.503431i
$962$	67892.9			0.0733625
$963$		0			0
$964$	−530946.			−0.571343
$965$	43400.8	+	150539.i	0.0466061	+	0.161657i
$966$		0			0
$967$	−236777.	−	136703.i	−0.253213	−	0.146193i	0.368022	−	0.929817i	$-0.380035\pi$
$967$	−236777.	−	136703.i	−0.253213	−	0.146193i	−0.621235	+	0.783625i	$0.713369\pi$
$968$	−147534.	+	255536.i	−0.157449	+	0.272710i
$969$		0			0
$970$	−61608.7	−	213694.i	−0.0654784	−	0.227117i
$971$			952676.i			1.01043i	0.862993	+	0.505215i	$0.168587\pi$
$971$			952676.i			1.01043i	−0.862993	+	0.505215i	$0.831413\pi$
$972$		0			0
$973$		−	1.01344e6i		−	1.07047i
$974$	−159461.	+	92065.0i	−0.168088	+	0.0970457i
$975$		0			0
$976$	630423.	−	1.09192e6i	0.661808	−	1.14629i
$977$	−551504.	+	955232.i	−0.577776	+	1.00074i	0.417958	+	0.908466i	$0.362746\pi$
$977$	−551504.	+	955232.i	−0.577776	+	1.00074i	−0.995734	+	0.0922705i	$0.970588\pi$
$978$		0			0
$979$	−88401.0	−	153115.i	−0.0922341	−	0.159754i
$980$	445254.	−	1.79683e6i	0.463613	−	1.87091i
$981$		0			0
$982$		−	280805.i		−	0.291193i
$983$	572312.	+	991274.i	0.592278	+	1.02586i	0.993925	+	0.110062i	$0.0351048\pi$
$983$	572312.	+	991274.i	0.592278	+	1.02586i	−0.401646	+	0.915795i	$0.631562\pi$
$984$		0			0
$985$	992518.	+	955708.i	1.02298	+	0.985037i
$986$	−53078.1	−	30644.6i	−0.0545961	−	0.0315211i
$987$		0			0
$988$	455755.	−	263130.i	0.466893	−	0.269561i
$989$		−	352197.i		−	0.360075i
$990$		0			0
$991$	−320938.			−0.326794			−0.163397	−	0.986560i	$-0.552245\pi$
$991$	−320938.			−0.326794			−0.163397	+	0.986560i	$0.552245\pi$
$992$	−146134.	−	253111.i	−0.148500	−	0.257210i
$993$		0			0
$994$	74873.3	−	129684.i	0.0757800	−	0.131255i
$995$	186843.	+	179913.i	0.188725	+	0.181726i
$996$		0			0
$997$	−863459.	+	498518.i	−0.868663	+	0.501523i	−0.866904	−	0.498475i	$-0.833893\pi$
$997$	−863459.	+	498518.i	−0.868663	+	0.501523i	−0.00175952	+	0.999998i	$0.500560\pi$
$998$	−183142.			−0.183877
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.h.a.44.11		44
3.2	odd	2		45.5.h.a.14.12	yes	44
5.4	even	2	inner	135.5.h.a.44.12		44
9.2	odd	6	inner	135.5.h.a.89.12		44
9.4	even	3		405.5.d.a.404.23		44
9.5	odd	6		405.5.d.a.404.21		44
9.7	even	3		45.5.h.a.29.11	yes	44
15.14	odd	2		45.5.h.a.14.11	✓	44
45.4	even	6		405.5.d.a.404.22		44
45.14	odd	6		405.5.d.a.404.24		44
45.29	odd	6	inner	135.5.h.a.89.11		44
45.34	even	6		45.5.h.a.29.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.11	✓	44	15.14	odd	2
45.5.h.a.14.12	yes	44	3.2	odd	2
45.5.h.a.29.11	yes	44	9.7	even	3
45.5.h.a.29.12	yes	44	45.34	even	6
135.5.h.a.44.11		44	1.1	even	1	trivial
135.5.h.a.44.12		44	5.4	even	2	inner
135.5.h.a.89.11		44	45.29	odd	6	inner
135.5.h.a.89.12		44	9.2	odd	6	inner
405.5.d.a.404.21		44	9.5	odd	6
405.5.d.a.404.22		44	45.4	even	6
405.5.d.a.404.23		44	9.4	even	3
405.5.d.a.404.24		44	45.14	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.316502 - 0.548197i) q^{2} +(7.79965 - 13.5094i) q^{4} +(18.0085 + 17.3406i) q^{5} +(-73.2178 + 42.2723i) q^{7} -20.0025 q^{8} +(3.80633 - 15.3605i) q^{10} +(-148.474 + 85.7213i) q^{11} +(127.218 + 73.4493i) q^{13} +(46.3471 + 26.7585i) q^{14} +(-118.464 - 205.185i) q^{16} -273.459 q^{17} +229.656 q^{19} +(374.720 - 108.033i) q^{20} +(93.9843 + 54.2618i) q^{22} +(-194.631 + 337.110i) q^{23} +(23.6096 + 624.554i) q^{25} -92.9873i q^{26} +1318.84i q^{28} +(-306.632 + 177.034i) q^{29} +(-310.913 + 538.517i) q^{31} +(-235.008 + 407.045i) q^{32} +(86.5501 + 149.909i) q^{34} +(-2051.57 - 508.379i) q^{35} +730.131i q^{37} +(-72.6865 - 125.897i) q^{38} +(-360.214 - 346.854i) q^{40} +(498.910 + 288.046i) q^{41} +(-783.565 + 452.392i) q^{43} +2674.39i q^{44} +246.404 q^{46} +(-396.417 - 686.614i) q^{47} +(2373.40 - 4110.85i) q^{49} +(334.906 - 210.615i) q^{50} +(1984.51 - 1145.76i) q^{52} +3467.44 q^{53} +(-4160.24 - 1030.91i) q^{55} +(1464.54 - 845.551i) q^{56} +(194.099 + 112.063i) q^{58} +(-2436.74 - 1406.85i) q^{59} +(2660.83 + 4608.69i) q^{61} +393.618 q^{62} -3493.32 q^{64} +(1017.35 + 3528.74i) q^{65} +(147.934 + 85.4097i) q^{67} +(-2132.88 + 3694.26i) q^{68} +(370.633 + 1285.57i) q^{70} -2798.11i q^{71} -5866.22i q^{73} +(400.255 - 231.088i) q^{74} +(1791.24 - 3102.52i) q^{76} +(7247.28 - 12552.7i) q^{77} +(1466.67 + 2540.34i) q^{79} +(1424.68 - 5749.29i) q^{80} -364.668i q^{82} +(-3444.66 - 5966.32i) q^{83} +(-4924.57 - 4741.93i) q^{85} +(495.999 + 286.365i) q^{86} +(2969.84 - 1714.64i) q^{88} +1031.26i q^{89} -12419.5 q^{91} +(3036.10 + 5258.68i) q^{92} +(-250.933 + 434.629i) q^{94} +(4135.75 + 3982.37i) q^{95} +(12170.7 - 7026.75i) q^{97} -3004.74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Introduction

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