LMFDB - Embedded newform 164.5.d.f.163.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [164,5,Mod(163,164)] 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("164.163"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(164, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	164.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,6,0,-162,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.9526739458$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.12
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.33380 + 2.21038i) q^{2} +5.00494 q^{3} +(6.22840 - 14.7379i) q^{4} +38.7793 q^{5} +(-16.6855 + 11.0629i) q^{6} -50.6913 q^{7} +(11.8123 + 62.9005i) q^{8} -55.9505 q^{9} +(-129.282 + 85.7171i) q^{10} -167.503 q^{11} +(31.1728 - 73.7626i) q^{12} +87.0973i q^{13} +(168.994 - 112.047i) q^{14} +194.088 q^{15} +(-178.414 - 183.588i) q^{16} +509.403i q^{17} +(186.528 - 123.672i) q^{18} +346.056 q^{19} +(241.533 - 571.527i) q^{20} -253.707 q^{21} +(558.420 - 370.245i) q^{22} +887.511i q^{23} +(59.1200 + 314.813i) q^{24} +878.832 q^{25} +(-192.519 - 290.365i) q^{26} -685.430 q^{27} +(-315.725 + 747.085i) q^{28} +788.499i q^{29} +(-647.050 + 429.009i) q^{30} -511.217i q^{31} +(1000.60 + 217.680i) q^{32} -838.341 q^{33} +(-1125.98 - 1698.24i) q^{34} -1965.77 q^{35} +(-348.482 + 824.596i) q^{36} +880.083 q^{37} +(-1153.68 + 764.918i) q^{38} +435.917i q^{39} +(458.073 + 2439.23i) q^{40} +(652.427 - 1549.23i) q^{41} +(845.808 - 560.790i) q^{42} +966.706i q^{43} +(-1043.27 + 2468.64i) q^{44} -2169.72 q^{45} +(-1961.74 - 2958.78i) q^{46} -1475.89 q^{47} +(-892.953 - 918.846i) q^{48} +168.606 q^{49} +(-2929.85 + 1942.56i) q^{50} +2549.53i q^{51} +(1283.63 + 542.476i) q^{52} +5118.39i q^{53} +(2285.08 - 1515.06i) q^{54} -6495.63 q^{55} +(-598.782 - 3188.51i) q^{56} +1731.99 q^{57} +(-1742.89 - 2628.70i) q^{58} -3552.21i q^{59} +(1208.86 - 2860.46i) q^{60} +6423.69 q^{61} +(1129.99 + 1704.29i) q^{62} +2836.20 q^{63} +(-3816.94 + 1486.00i) q^{64} +3377.57i q^{65} +(2794.86 - 1853.06i) q^{66} -3522.24 q^{67} +(7507.55 + 3172.76i) q^{68} +4441.94i q^{69} +(6553.48 - 4345.11i) q^{70} +1513.35 q^{71} +(-660.906 - 3519.31i) q^{72} -7337.90 q^{73} +(-2934.02 + 1945.32i) q^{74} +4398.51 q^{75} +(2155.38 - 5100.16i) q^{76} +8490.92 q^{77} +(-963.544 - 1453.26i) q^{78} -7740.71 q^{79} +(-6918.77 - 7119.39i) q^{80} +1101.45 q^{81} +(1249.33 + 6606.92i) q^{82} +3440.14i q^{83} +(-1580.19 + 3739.12i) q^{84} +19754.3i q^{85} +(-2136.79 - 3222.80i) q^{86} +3946.39i q^{87} +(-1978.60 - 10536.0i) q^{88} -5342.23i q^{89} +(7233.41 - 4795.92i) q^{90} -4415.07i q^{91} +(13080.1 + 5527.77i) q^{92} -2558.61i q^{93} +(4920.30 - 3262.28i) q^{94} +13419.8 q^{95} +(5007.93 + 1089.47i) q^{96} -11673.9i q^{97} +(-562.099 + 372.685i) q^{98} +9371.86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) $ 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.33380	+	2.21038i	−0.833449	+	0.552596i
$2$	−3.33380	+	2.21038i	−0.833449	+	0.552596i
$3$	5.00494			0.556105			0.278052	−	0.960566i	$-0.410311\pi$
$3$	5.00494			0.556105			0.278052	+	0.960566i	$0.410311\pi$
$4$	6.22840	−	14.7379i	0.389275	−	0.921122i
$5$	38.7793			1.55117			0.775586	−	0.631242i	$-0.217455\pi$
$5$	38.7793			1.55117			0.775586	+	0.631242i	$0.217455\pi$
$6$	−16.6855	+	11.0629i	−0.463485	+	0.307301i
$7$	−50.6913			−1.03452			−0.517258	−	0.855830i	$-0.673047\pi$
$7$	−50.6913			−1.03452			−0.517258	+	0.855830i	$0.673047\pi$
$8$	11.8123	+	62.9005i	0.184568	+	0.982820i
$9$	−55.9505			−0.690747
$10$	−129.282	+	85.7171i	−1.29282	+	0.857171i
$11$	−167.503			−1.38432			−0.692160	−	0.721744i	$-0.743341\pi$
$11$	−167.503			−1.38432			−0.692160	+	0.721744i	$0.743341\pi$
$12$	31.1728	−	73.7626i	0.216478	−	0.512240i
$13$			87.0973i			0.515368i	0.966229	+	0.257684i	$0.0829594\pi$
$13$			87.0973i			0.515368i	−0.966229	+	0.257684i	$0.917041\pi$
$14$	168.994	−	112.047i	0.862216	−	0.571670i
$15$	194.088			0.862614
$16$	−178.414	−	183.588i	−0.696930	−	0.717139i
$17$			509.403i			1.76264i	0.472521	+	0.881319i	$0.343344\pi$
$17$			509.403i			1.76264i	−0.472521	+	0.881319i	$0.656656\pi$
$18$	186.528	−	123.672i	0.575703	−	0.381704i
$19$	346.056			0.958605			0.479302	−	0.877650i	$-0.340890\pi$
$19$	346.056			0.958605			0.479302	+	0.877650i	$0.340890\pi$
$20$	241.533	−	571.527i	0.603832	−	1.42882i
$21$	−253.707			−0.575299
$22$	558.420	−	370.245i	1.15376	−	0.764970i
$23$			887.511i			1.67771i	0.544351	+	0.838857i	$0.316776\pi$
$23$			887.511i			1.67771i	−0.544351	+	0.838857i	$0.683224\pi$
$24$	59.1200	+	314.813i	0.102639	+	0.546551i
$25$	878.832			1.40613
$26$	−192.519	−	290.365i	−0.284791	−	0.429533i
$27$	−685.430			−0.940233
$28$	−315.725	+	747.085i	−0.402711	+	0.952915i
$29$			788.499i			0.937573i	0.883311	+	0.468787i	$0.155309\pi$
$29$			788.499i			0.937573i	−0.883311	+	0.468787i	$0.844691\pi$
$30$	−647.050	+	429.009i	−0.718945	+	0.476677i
$31$		−	511.217i		−	0.531964i	−0.963978	−	0.265982i	$-0.914304\pi$
$31$		−	511.217i		−	0.531964i	0.963978	−	0.265982i	$-0.0856961\pi$
$32$	1000.60	+	217.680i	0.977144	+	0.212578i
$33$	−838.341			−0.769827
$34$	−1125.98	−	1698.24i	−0.974027	−	1.46907i
$35$	−1965.77			−1.60471
$36$	−348.482	+	824.596i	−0.268891	+	0.636262i
$37$	880.083			0.642866			0.321433	−	0.946932i	$-0.395836\pi$
$37$	880.083			0.642866			0.321433	+	0.946932i	$0.395836\pi$
$38$	−1153.68	+	764.918i	−0.798948	+	0.529721i
$39$			435.917i			0.286599i
$40$	458.073	+	2439.23i	0.286296	+	1.52452i
$41$	652.427	−	1549.23i	0.388118	−	0.921610i
$41$	652.427	−	1549.23i	0.388118	−	0.921610i
$42$	845.808	−	560.790i	0.479483	−	0.317908i
$43$			966.706i			0.522826i	0.965227	+	0.261413i	$0.0841885\pi$
$43$			966.706i			0.522826i	−0.965227	+	0.261413i	$0.915811\pi$
$44$	−1043.27	+	2468.64i	−0.538881	+	1.27513i
$45$	−2169.72			−1.07147
$46$	−1961.74	−	2958.78i	−0.927099	−	1.39829i
$47$	−1475.89			−0.668124			−0.334062	−	0.942551i	$-0.608420\pi$
$47$	−1475.89			−0.668124			−0.334062	+	0.942551i	$0.608420\pi$
$48$	−892.953	−	918.846i	−0.387566	−	0.398805i
$49$	168.606			0.0702233
$50$	−2929.85	+	1942.56i	−1.17194	+	0.777023i
$51$			2549.53i			0.980212i
$52$	1283.63	+	542.476i	0.474717	+	0.200620i
$53$			5118.39i			1.82214i	0.412253	+	0.911069i	$0.364742\pi$
$53$			5118.39i			1.82214i	−0.412253	+	0.911069i	$0.635258\pi$
$54$	2285.08	−	1515.06i	0.783636	−	0.519569i
$55$	−6495.63			−2.14732
$56$	−598.782	−	3188.51i	−0.190938	−	1.01674i
$57$	1731.99			0.533085
$58$	−1742.89	−	2628.70i	−0.518099	−	0.781420i
$59$		−	3552.21i		−	1.02046i	−0.860039	−	0.510228i	$-0.829561\pi$
$59$		−	3552.21i		−	1.02046i	0.860039	−	0.510228i	$-0.170439\pi$
$60$	1208.86	−	2860.46i	0.335794	−	0.794572i
$61$	6423.69			1.72633			0.863167	−	0.504919i	$-0.168478\pi$
$61$	6423.69			1.72633			0.863167	+	0.504919i	$0.168478\pi$
$62$	1129.99	+	1704.29i	0.293961	+	0.443365i
$63$	2836.20			0.714589
$64$	−3816.94	+	1486.00i	−0.931870	+	0.362793i
$65$			3377.57i			0.799425i
$66$	2794.86	−	1853.06i	0.641611	−	0.425403i
$67$	−3522.24			−0.784638			−0.392319	−	0.919829i	$-0.628327\pi$
$67$	−3522.24			−0.784638			−0.392319	+	0.919829i	$0.628327\pi$
$68$	7507.55	+	3172.76i	1.62360	+	0.686151i
$69$			4441.94i			0.932985i
$70$	6553.48	−	4345.11i	1.33745	−	0.886757i
$71$	1513.35			0.300209			0.150104	−	0.988670i	$-0.452039\pi$
$71$	1513.35			0.300209			0.150104	+	0.988670i	$0.452039\pi$
$72$	−660.906	−	3519.31i	−0.127490	−	0.678880i
$73$	−7337.90			−1.37698			−0.688488	−	0.725248i	$-0.741725\pi$
$73$	−7337.90			−1.37698			−0.688488	+	0.725248i	$0.741725\pi$
$74$	−2934.02	+	1945.32i	−0.535796	+	0.355245i
$75$	4398.51			0.781957
$76$	2155.38	−	5100.16i	0.373161	−	0.882992i
$77$	8490.92			1.43210
$78$	−963.544	−	1453.26i	−0.158374	−	0.238866i
$79$	−7740.71			−1.24030			−0.620150	−	0.784483i	$-0.712928\pi$
$79$	−7740.71			−1.24030			−0.620150	+	0.784483i	$0.712928\pi$
$80$	−6918.77	−	7119.39i	−1.08106	−	1.11241i
$81$	1101.45			0.167879
$82$	1249.33	+	6606.92i	0.185801	+	0.982587i
$83$			3440.14i			0.499367i	0.968327	+	0.249684i	$0.0803266\pi$
$83$			3440.14i			0.499367i	−0.968327	+	0.249684i	$0.919673\pi$
$84$	−1580.19	+	3739.12i	−0.223950	+	0.529921i
$85$			19754.3i			2.73415i
$86$	−2136.79	−	3222.80i	−0.288912	−	0.435749i
$87$			3946.39i			0.521389i
$88$	−1978.60	−	10536.0i	−0.255500	−	1.36054i
$89$		−	5342.23i		−	0.674439i	−0.941426	−	0.337219i	$-0.890514\pi$
$89$		−	5342.23i		−	0.674439i	0.941426	−	0.337219i	$-0.109486\pi$
$90$	7233.41	−	4795.92i	0.893013	−	0.592089i
$91$		−	4415.07i		−	0.533157i
$92$	13080.1	+	5527.77i	1.54538	+	0.653092i
$93$		−	2558.61i		−	0.295828i
$94$	4920.30	−	3262.28i	0.556847	−	0.369203i
$95$	13419.8			1.48696
$96$	5007.93	+	1089.47i	0.543395	+	0.118216i
$97$		−	11673.9i		−	1.24072i	−0.784317	−	0.620360i	$-0.786986\pi$
$97$		−	11673.9i		−	1.24072i	0.784317	−	0.620360i	$-0.213014\pi$
$98$	−562.099	+	372.685i	−0.0585276	+	0.0388051i
$99$	9371.86			0.956215
$100$	5473.72	−	12952.2i	0.547372	−	1.29522i
$101$		−	6091.71i		−	0.597168i	−0.954383	−	0.298584i	$-0.903486\pi$
$101$		−	6091.71i		−	0.597168i	0.954383	−	0.298584i	$-0.0965142\pi$
$102$	−5635.45	−	8499.62i	−0.541661	−	0.816957i
$103$		−	10382.3i		−	0.978632i	−0.872107	−	0.489316i	$-0.837246\pi$
$103$		−	10382.3i		−	0.978632i	0.872107	−	0.489316i	$-0.162754\pi$
$104$	−5478.46	+	1028.82i	−0.506514	+	0.0951203i
$105$	−9838.58			−0.892388
$106$	−11313.6	−	17063.7i	−1.00691	−	1.51866i
$107$		−	7278.87i		−	0.635765i	−0.948130	−	0.317882i	$-0.897028\pi$
$107$		−	7278.87i		−	0.635765i	0.948130	−	0.317882i	$-0.102972\pi$
$108$	−4269.13	+	10101.8i	−0.366009	+	0.866069i
$109$		−	4093.19i		−	0.344516i	−0.985052	−	0.172258i	$-0.944894\pi$
$109$		−	4093.19i		−	0.344516i	0.985052	−	0.172258i	$-0.0551062\pi$
$110$	21655.1	−	14357.8i	1.78968	−	1.18660i
$111$	4404.77			0.357501
$112$	9044.04	+	9306.29i	0.720985	+	0.741892i
$113$	−5981.01			−0.468401			−0.234200	−	0.972188i	$-0.575247\pi$
$113$	−5981.01			−0.468401			−0.234200	+	0.972188i	$0.575247\pi$
$114$	−5774.11	+	3828.37i	−0.444299	+	0.294581i
$115$			34417.0i			2.60242i
$116$	11620.9	+	4911.09i	0.863619	+	0.364974i
$117$		−	4873.14i		−	0.355989i
$118$	7851.75	+	11842.3i	0.563900	+	0.850498i
$119$		−	25822.3i		−	1.82348i
$120$	2292.63	+	12208.2i	0.159211	+	0.847794i
$121$	13416.1			0.916340
$122$	−21415.3	+	14198.8i	−1.43881	+	0.953965i
$123$	3265.36	−	7753.79i	0.215835	−	0.512512i
$124$	−7534.29	−	3184.06i	−0.490003	−	0.207080i
$125$	9843.44			0.629980
$126$	−9455.33	+	6269.10i	−0.595574	+	0.394879i
$127$		−	8185.66i		−	0.507512i	−0.967268	−	0.253756i	$-0.918334\pi$
$127$		−	8185.66i		−	0.507512i	0.967268	−	0.253756i	$-0.0816660\pi$
$128$	9440.26	−	13390.9i	0.576188	−	0.817317i
$129$			4838.31i			0.290746i
$130$	−7465.73	−	11260.1i	−0.441759	−	0.666280i
$131$			15034.8i			0.876100i	0.898951	+	0.438050i	$0.144331\pi$
$131$			15034.8i			0.876100i	−0.898951	+	0.438050i	$0.855669\pi$
$132$	−5221.52	+	12355.4i	−0.299674	+	0.709104i
$133$	−17542.0			−0.991692
$134$	11742.4	−	7785.50i	0.653955	−	0.433588i
$135$	−26580.5			−1.45846
$136$	−32041.7	+	6017.23i	−1.73236	+	0.325326i
$137$			11240.6i			0.598893i	0.954113	+	0.299446i	$0.0968020\pi$
$137$			11240.6i			0.598893i	−0.954113	+	0.299446i	$0.903198\pi$
$138$	−9818.40	−	14808.5i	−0.515564	−	0.777596i
$139$			36382.1i			1.88304i	0.336964	+	0.941518i	$0.390600\pi$
$139$			36382.1i			1.88304i	−0.336964	+	0.941518i	$0.609400\pi$
$140$	−12243.6	+	28971.4i	−0.624674	+	1.47813i
$141$	−7386.73			−0.371547
$142$	−5045.21	+	3345.09i	−0.250209	+	0.165894i
$143$		−	14589.0i		−	0.713434i
$144$	9982.37	+	10271.8i	0.481403	+	0.495362i
$145$			30577.4i			1.45434i
$146$	24463.1	−	16219.6i	1.14764	−	0.760911i
$147$	843.865			0.0390515
$148$	5481.51	−	12970.6i	0.250251	−	0.592157i
$149$		−	10985.0i		−	0.494798i	−0.968914	−	0.247399i	$-0.920424\pi$
$149$		−	10985.0i		−	0.494798i	0.968914	−	0.247399i	$-0.0795759\pi$
$150$	−14663.7	+	9722.39i	−0.651721	+	0.432106i
$151$	−18669.0			−0.818780			−0.409390	−	0.912359i	$-0.634258\pi$
$151$	−18669.0			−0.818780			−0.409390	+	0.912359i	$0.634258\pi$
$152$	4087.73	+	21767.1i	0.176927	+	0.942136i
$153$		−	28501.3i		−	1.21754i
$154$	−28307.0	+	18768.2i	−1.19358	+	0.791373i
$155$		−	19824.6i		−	0.825167i
$156$	6424.52	+	2715.06i	0.263993	+	0.111566i
$157$			43640.6i			1.77048i	0.465135	+	0.885240i	$0.346006\pi$
$157$			43640.6i			1.77048i	−0.465135	+	0.885240i	$0.653994\pi$
$158$	25805.9	−	17109.9i	1.03373	−	0.685385i
$159$			25617.2i			1.01330i
$160$	38802.4	+	8441.46i	1.51572	+	0.329745i
$161$		−	44989.1i		−	1.73562i
$162$	−3672.03	+	2434.64i	−0.139919	+	0.0927694i
$163$			23765.1i			0.894467i	0.894417	+	0.447233i	$0.147591\pi$
$163$			23765.1i			0.894467i	−0.894417	+	0.447233i	$0.852409\pi$
$164$	−18768.8	−	19264.6i	−0.697830	−	0.716264i
$165$	−32510.3			−1.19413
$166$	−7604.04	−	11468.7i	−0.275949	−	0.416197i
$167$	33492.2			1.20091			0.600455	−	0.799659i	$-0.294986\pi$
$167$	33492.2			1.20091			0.600455	+	0.799659i	$0.294986\pi$
$168$	−2996.87	−	15958.3i	−0.106182	−	0.565416i
$169$	20975.1			0.734395
$170$	−43664.5	−	65856.7i	−1.51088	−	2.27878i
$171$	−19362.0			−0.662154
$172$	14247.3	+	6021.03i	0.481587	+	0.203523i
$173$	−428.561			−0.0143192			−0.00715962	−	0.999974i	$-0.502279\pi$
$173$	−428.561			−0.0143192			−0.00715962	+	0.999974i	$0.502279\pi$
$174$	−8723.05	−	13156.5i	−0.288118	−	0.434551i
$175$	−44549.1			−1.45467
$176$	29884.8	+	30751.4i	0.964774	+	0.992749i
$177$		−	17778.6i		−	0.567481i
$178$	11808.4	+	17809.9i	0.372692	+	0.562111i
$179$	3930.10			0.122658			0.0613292	−	0.998118i	$-0.480466\pi$
$179$	3930.10			0.122658			0.0613292	+	0.998118i	$0.480466\pi$
$180$	−13513.9	+	31977.2i	−0.417095	+	0.986952i
$181$		−	15195.0i		−	0.463813i	−0.972738	−	0.231907i	$-0.925504\pi$
$181$		−	15195.0i		−	0.463813i	0.972738	−	0.231907i	$-0.0744964\pi$
$182$	9759.01	+	14719.0i	0.294621	+	0.444359i
$183$	32150.2			0.960022
$184$	−55824.9	+	10483.6i	−1.64889	+	0.309652i
$185$	34129.0			0.997195
$186$	5655.52	+	8529.90i	0.163473	+	0.246557i
$187$		−	85326.3i		−	2.44005i
$188$	−9192.41	+	21751.5i	−0.260084	+	0.615424i
$189$	34745.3			0.972686
$190$	−44738.9	+	29663.0i	−1.23931	+	0.821689i
$191$	35493.8			0.972940			0.486470	−	0.873697i	$-0.338284\pi$
$191$	35493.8			0.972940			0.486470	+	0.873697i	$0.338284\pi$
$192$	−19103.6	+	7437.36i	−0.518217	+	0.201751i
$193$		−	7354.72i		−	0.197447i	−0.995115	−	0.0987237i	$-0.968524\pi$
$193$		−	7354.72i		−	0.197447i	0.995115	−	0.0987237i	$-0.0314760\pi$
$194$	25803.9	+	38918.5i	0.685617	+	1.03408i
$195$			16904.5i			0.444564i
$196$	1050.15	−	2484.91i	0.0273362	−	0.0646842i
$197$	1913.10			0.0492952			0.0246476	−	0.999696i	$-0.492154\pi$
$197$	1913.10			0.0492952			0.0246476	+	0.999696i	$0.492154\pi$
$198$	−31243.9	+	20715.4i	−0.796956	+	0.528401i
$199$	−43549.9			−1.09972			−0.549858	−	0.835258i	$-0.685318\pi$
$199$	−43549.9			−1.09972			−0.549858	+	0.835258i	$0.685318\pi$
$200$	10381.1	+	55279.0i	0.259526	+	1.38197i
$201$	−17628.6			−0.436341
$202$	13465.0	+	20308.5i	0.329993	+	0.497709i
$203$		−	39970.0i		−	0.969935i
$204$	37574.9	+	15879.5i	0.902894	+	0.381572i
$205$	25300.7	−	60077.9i	0.602038	−	1.42957i
$206$	22948.9	+	34612.5i	0.540788	+	0.815640i
$207$		−	49656.7i		−	1.15888i
$208$	15990.0	−	15539.4i	0.369591	−	0.359176i
$209$	−57965.3			−1.32702
$210$	32799.8	−	21747.0i	0.743760	−	0.493130i
$211$	67812.3			1.52315			0.761577	−	0.648075i	$-0.224426\pi$
$211$	67812.3			1.52315			0.761577	+	0.648075i	$0.224426\pi$
$212$	75434.5	+	31879.4i	1.67841	+	0.709313i
$213$	7574.25			0.166948
$214$	16089.1	+	24266.3i	0.351321	+	0.529878i
$215$			37488.2i			0.810993i
$216$	−8096.52	−	43113.9i	−0.173537	−	0.924080i
$217$			25914.3i			0.550325i
$218$	9047.53	+	13645.9i	0.190378	+	0.287136i
$219$	−36725.8			−0.765743
$220$	−40457.4	+	95732.3i	−0.835896	+	1.97794i
$221$	−44367.6			−0.908408
$222$	−14684.6	+	9736.23i	−0.297959	+	0.197554i
$223$			23135.1i			0.465224i	0.972570	+	0.232612i	$0.0747272\pi$
$223$			23135.1i			0.465224i	−0.972570	+	0.232612i	$0.925273\pi$
$224$	−50721.5	−	11034.5i	−1.01087	−	0.219915i
$225$	−49171.1			−0.971282
$226$	19939.5	−	13220.3i	0.390388	−	0.258837i
$227$	83756.8			1.62543			0.812715	−	0.582662i	$-0.197989\pi$
$227$	83756.8			1.62543			0.812715	+	0.582662i	$0.197989\pi$
$228$	10787.5	−	25526.0i	0.207517	−	0.491036i
$229$		−	56551.7i		−	1.07839i	−0.842182	−	0.539194i	$-0.818729\pi$
$229$		−	56551.7i		−	1.07839i	0.842182	−	0.539194i	$-0.181271\pi$
$230$	−76074.9	−	114739.i	−1.43809	−	2.16899i
$231$	42496.6			0.796398
$232$	−49597.0	+	9314.01i	−0.921466	+	0.173046i
$233$			22216.7i			0.409229i	0.978843	+	0.204615i	$0.0655942\pi$
$233$			22216.7i			0.409229i	−0.978843	+	0.204615i	$0.934406\pi$
$234$	10771.5	+	16246.1i	0.196718	+	0.296699i
$235$	−57233.8			−1.03637
$236$	−52352.2	−	22124.6i	−0.939964	−	0.397238i
$237$	−38741.8			−0.689737
$238$	57077.2	+	86086.2i	1.00765	+	1.51978i
$239$	20085.7			0.351634			0.175817	−	0.984423i	$-0.443743\pi$
$239$	20085.7			0.351634			0.175817	+	0.984423i	$0.443743\pi$
$240$	−34628.1	−	35632.2i	−0.601182	−	0.618614i
$241$	60909.8			1.04870			0.524352	−	0.851502i	$-0.324308\pi$
$241$	60909.8			1.04870			0.524352	+	0.851502i	$0.324308\pi$
$242$	−44726.6	+	29654.8i	−0.763722	+	0.506366i
$243$	61032.5			1.03359
$244$	40009.3	−	94671.9i	0.672018	−	1.59016i
$245$	6538.43			0.108928
$246$	6252.81	+	33067.3i	0.103325	+	0.546422i
$247$			30140.6i			0.494035i
$248$	32155.8	−	6038.66i	0.522825	−	0.0981833i
$249$			17217.7i			0.277701i
$250$	−32816.0	+	21757.8i	−0.525056	+	0.348125i
$251$		−	21076.2i		−	0.334537i	−0.985911	−	0.167268i	$-0.946505\pi$
$251$		−	21076.2i		−	0.334537i	0.985911	−	0.167268i	$-0.0534947\pi$
$252$	17665.0	−	41799.8i	0.278172	−	0.658224i
$253$		−	148660.i		−	2.32249i
$254$	18093.5	+	27289.3i	0.280449	+	0.422985i
$255$			98869.0i			1.52048i
$256$	−1872.79	+	65509.2i	−0.0285765	+	0.999592i
$257$		−	50287.9i		−	0.761373i	−0.924704	−	0.380687i	$-0.875688\pi$
$257$		−	50287.9i		−	0.761373i	0.924704	−	0.380687i	$-0.124312\pi$
$258$	−10694.5	−	16129.9i	−0.160665	−	0.242322i
$259$	−44612.5			−0.665055
$260$	49778.4	+	21036.8i	0.736367	+	0.311196i
$261$		−	44116.9i		−	0.647626i
$262$	−33232.6	−	50122.8i	−0.484130	−	0.730185i
$263$	110188.			1.59303			0.796513	−	0.604621i	$-0.206675\pi$
$263$	110188.			1.59303			0.796513	+	0.604621i	$0.206675\pi$
$264$	−9902.76	−	52732.1i	−0.142085	−	0.756601i
$265$			198487.i			2.82645i
$266$	58481.6	−	38774.7i	0.826525	−	0.548005i
$267$		−	26737.6i		−	0.375059i
$268$	−21937.9	+	51910.6i	−0.305440	+	0.722747i
$269$	−97639.5			−1.34934			−0.674669	−	0.738120i	$-0.735714\pi$
$269$	−97639.5			−1.34934			−0.674669	+	0.738120i	$0.735714\pi$
$270$	88613.9	−	58753.1i	1.21555	−	0.805941i
$271$		−	52918.2i		−	0.720554i	−0.932845	−	0.360277i	$-0.882682\pi$
$271$		−	52918.2i		−	0.720554i	0.932845	−	0.360277i	$-0.117318\pi$
$272$	93520.0	−	90884.6i	1.26406	−	1.22844i
$273$		−	22097.2i		−	0.296491i
$274$	−24846.1	−	37473.9i	−0.330946	−	0.499147i
$275$	−147207.			−1.94654
$276$	65465.1	+	27666.2i	0.859393	+	0.363188i
$277$	30238.9			0.394100			0.197050	−	0.980393i	$-0.436864\pi$
$277$	30238.9			0.394100			0.197050	+	0.980393i	$0.436864\pi$
$278$	−80418.5	−	121291.i	−1.04056	−	1.56941i
$279$			28602.9i			0.367453i
$280$	−23220.3	−	123648.i	−0.296178	−	1.57714i
$281$			130615.i			1.65417i	0.562077	+	0.827085i	$0.310002\pi$
$281$			130615.i			1.65417i	−0.562077	+	0.827085i	$0.689998\pi$
$282$	24625.9	−	16327.5i	0.309666	−	0.205316i
$283$			77168.6i			0.963535i	0.876299	+	0.481768i	$0.160005\pi$
$283$			77168.6i			0.963535i	−0.876299	+	0.481768i	$0.839995\pi$
$284$	9425.76	−	22303.7i	0.116864	−	0.276529i
$285$	67165.4			0.826906
$286$	32247.4	+	48636.8i	0.394241	+	0.594611i
$287$	−33072.4	+	78532.2i	−0.401515	+	0.953420i
$288$	−55983.9	−	12179.3i	−0.674960	−	0.146838i
$289$	−175970.			−2.10689
$290$	−67587.9	−	101939.i	−0.803661	−	1.21212i
$291$		−	58427.4i		−	0.689971i
$292$	−45703.4	+	108146.i	−0.536022	+	1.26836i
$293$			63139.5i			0.735472i	0.929930	+	0.367736i	$0.119867\pi$
$293$			63139.5i			0.735472i	−0.929930	+	0.367736i	$0.880133\pi$
$294$	−2813.27	+	1865.27i	−0.0325475	+	0.0215797i
$295$		−	137752.i		−	1.58290i
$296$	10395.8	+	55357.6i	0.118652	+	0.631821i
$297$	114811.			1.30158
$298$	24281.1	+	36621.8i	0.273424	+	0.412389i
$299$	−77299.8			−0.864641
$300$	27395.7	−	64825.0i	0.304396	−	0.720277i
$301$		−	49003.6i		−	0.540872i
$302$	62238.7	−	41265.7i	0.682412	−	0.452455i
$303$		−	30488.7i		−	0.332088i
$304$	−61741.3	−	63531.6i	−0.668081	−	0.687453i
$305$	249106.			2.67784
$306$	62998.9	+	95017.7i	0.672807	+	1.01476i
$307$			27136.9i			0.287928i	0.989583	+	0.143964i	$0.0459849\pi$
$307$			27136.9i			0.287928i	−0.989583	+	0.143964i	$0.954015\pi$
$308$	52884.8	−	125139.i	0.557481	−	1.31914i
$309$		−	51962.9i		−	0.544222i
$310$	43820.1	+	66091.3i	0.455984	+	0.687735i
$311$	−81392.4			−0.841518			−0.420759	−	0.907173i	$-0.638236\pi$
$311$	−81392.4			−0.841518			−0.420759	+	0.907173i	$0.638236\pi$
$312$	−27419.4	+	5149.19i	−0.281675	+	0.0528969i
$313$			12220.3i			0.124737i	0.998053	+	0.0623683i	$0.0198654\pi$
$313$			12220.3i			0.124737i	−0.998053	+	0.0623683i	$0.980135\pi$
$314$	−96462.4	−	145489.i	−0.978361	−	1.47560i
$315$	109986.			1.10845
$316$	−48212.2	+	114082.i	−0.482817	+	1.14247i
$317$			11570.1i			0.115138i	0.998342	+	0.0575688i	$0.0183348\pi$
$317$			11570.1i			0.115138i	−0.998342	+	0.0575688i	$0.981665\pi$
$318$	−56624.0	−	85402.7i	−0.559946	−	0.844534i
$319$		−	132076.i		−	1.29790i
$320$	−148018.	+	57626.1i	−1.44549	+	0.562755i
$321$		−	36430.4i		−	0.353552i
$322$	99443.2	+	149984.i	0.959098	+	1.44655i
$323$			176282.i			1.68967i
$324$	6860.30	−	16233.2i	0.0653511	−	0.154637i
$325$			76543.9i			0.724676i
$326$	−52530.0	−	79228.0i	−0.494279	−	0.745493i
$327$		−	20486.2i		−	0.191587i
$328$	105154.	+	22738.0i	0.977410	+	0.211351i
$329$	74814.6			0.691185
$330$	108383.	−	71860.2i	0.995249	−	0.659873i
$331$	101137.			0.923110			0.461555	−	0.887111i	$-0.347292\pi$
$331$	101137.			0.923110			0.461555	+	0.887111i	$0.347292\pi$
$332$	50700.6	+	21426.6i	0.459978	+	0.194391i
$333$	−49241.1			−0.444058
$334$	−111656.	+	74030.5i	−1.00090	+	0.663618i
$335$	−136590.			−1.21711
$336$	45264.9	+	46577.5i	0.400944	+	0.412570i
$337$	−122847.			−1.08169			−0.540847	−	0.841121i	$-0.681896\pi$
$337$	−122847.			−1.08169			−0.540847	+	0.841121i	$0.681896\pi$
$338$	−69926.6	+	46363.0i	−0.612081	+	0.405824i
$339$	−29934.6			−0.260480
$340$	291137.	+	123037.i	2.51849	+	1.06434i
$341$			85630.2i			0.736408i
$342$	64549.1	−	42797.6i	0.551871	−	0.365904i
$343$	113163.			0.961869
$344$	−60806.3	+	11419.0i	−0.513844	+	0.0964968i
$345$			172255.i			1.44722i
$346$	1428.73	−	947.284i	0.0119344	−	0.00791276i
$347$	71706.0			0.595521			0.297760	−	0.954641i	$-0.403760\pi$
$347$	71706.0			0.595521			0.297760	+	0.954641i	$0.403760\pi$
$348$	58161.7	+	24579.7i	0.480263	+	0.202964i
$349$	85944.2			0.705612			0.352806	−	0.935697i	$-0.385228\pi$
$349$	85944.2			0.705612			0.352806	+	0.935697i	$0.385228\pi$
$350$	148518.	−	98470.8i	1.21239	−	0.803843i
$351$		−	59699.1i		−	0.484566i
$352$	−167602.	−	36461.9i	−1.35268	−	0.294276i
$353$	78698.5			0.631564			0.315782	−	0.948832i	$-0.397733\pi$
$353$	78698.5			0.631564			0.315782	+	0.948832i	$0.397733\pi$
$354$	39297.5	+	59270.2i	0.313588	+	0.472966i
$355$	58686.7			0.465675
$356$	−78733.5	−	33273.5i	−0.621240	−	0.262542i
$357$		−	129239.i		−	1.01404i
$358$	−13102.1	+	8687.03i	−0.102230	+	0.0677806i
$359$			136146.i			1.05637i	0.849128	+	0.528186i	$0.177128\pi$
$359$			136146.i			1.05637i	−0.849128	+	0.528186i	$0.822872\pi$
$360$	−25629.5	−	136476.i	−0.197758	−	1.05306i
$361$	−10566.0			−0.0810768
$362$	33586.8	+	50657.0i	0.256302	+	0.386565i
$363$	67147.0			0.509581
$364$	−65069.1	−	27498.8i	−0.491102	−	0.207545i
$365$	−284559.			−2.13592
$366$	−107182.	+	71064.3i	−0.800130	+	0.530505i
$367$		−	30125.9i		−	0.223670i	−0.993727	−	0.111835i	$-0.964327\pi$
$367$		−	30125.9i		−	0.223670i	0.993727	−	0.111835i	$-0.0356729\pi$
$368$	162936.	−	158345.i	1.20315	−	1.16925i
$369$	−36503.6	+	86680.0i	−0.268092	+	0.636599i
$370$	−113779.	+	75438.2i	−0.831111	+	0.551046i
$371$		−	259458.i		−	1.88503i
$372$	−37708.7	−	15936.1i	−0.272493	−	0.115158i
$373$	−173268.			−1.24538			−0.622688	−	0.782470i	$-0.713960\pi$
$373$	−173268.			−1.24538			−0.622688	+	0.782470i	$0.713960\pi$
$374$	188604.	+	284460.i	1.34836	+	2.03366i
$375$	49265.9			0.350335
$376$	−17433.7	−	92833.9i	−0.123314	−	0.656646i
$377$	−68676.1			−0.483196
$378$	−115834.	+	76800.5i	−0.810684	+	0.537503i
$379$			228441.i			1.59036i	0.606373	+	0.795180i	$0.292624\pi$
$379$			228441.i			1.59036i	−0.606373	+	0.795180i	$0.707376\pi$
$380$	83583.9	−	197781.i	0.578836	−	1.36967i
$381$		−	40968.8i		−	0.282230i
$382$	−118329.	+	78455.0i	−0.810896	+	0.537643i
$383$	−5588.45			−0.0380973			−0.0190487	−	0.999819i	$-0.506064\pi$
$383$	−5588.45			−0.0380973			−0.0190487	+	0.999819i	$0.506064\pi$
$384$	47248.0	−	67020.9i	0.320421	−	0.454514i
$385$	329272.			2.22143
$386$	16256.8	+	24519.1i	0.109109	+	0.164562i
$387$		−	54087.7i		−	0.361141i
$388$	−172050.	−	72709.9i	−1.14285	−	0.482981i
$389$	194859.			1.28772			0.643860	−	0.765143i	$-0.277332\pi$
$389$	194859.			1.28772			0.643860	+	0.765143i	$0.277332\pi$
$390$	−37365.6	−	56356.3i	−0.245664	−	0.370522i
$391$	−452100.			−2.95720
$392$	1991.63	+	10605.4i	0.0129610	+	0.0690169i
$393$			75248.1i			0.487204i
$394$	−6377.87	+	4228.68i	−0.0410850	+	0.0272403i
$395$	−300179.			−1.92392
$396$	58371.7	−	138122.i	0.372230	−	0.880790i
$397$		−	146045.i		−	0.926630i	−0.886194	−	0.463315i	$-0.846660\pi$
$397$		−	146045.i		−	0.926630i	0.886194	−	0.463315i	$-0.153340\pi$
$398$	145186.	−	96262.0i	0.916558	−	0.607699i
$399$	−87796.9			−0.551485
$400$	−156796.	−	161343.i	−0.979976	−	1.00839i
$401$	209088.			1.30029			0.650147	−	0.759809i	$-0.274707\pi$
$401$	209088.			1.30029			0.650147	+	0.759809i	$0.274707\pi$
$402$	58770.2	−	38966.0i	0.363668	−	0.241120i
$403$	44525.6			0.274157
$404$	−89779.2	−	37941.6i	−0.550064	−	0.232462i
$405$	42713.6			0.260409
$406$	88349.2	+	133252.i	0.535982	+	0.808391i
$407$	−147416.			−0.889931
$408$	−160367.	+	30115.9i	−0.963372	+	0.180915i
$409$	9946.03			0.0594570			0.0297285	−	0.999558i	$-0.490536\pi$
$409$	9946.03			0.0594570			0.0297285	+	0.999558i	$0.490536\pi$
$410$	48448.0	+	256211.i	0.288209	+	1.52416i
$411$			56258.7i			0.333047i
$412$	−153014.	−	64665.1i	−0.901439	−	0.380957i
$413$			180066.i			1.05568i
$414$	109760.	+	165545.i	0.640391	+	0.965865i
$415$			133406.i			0.774604i
$416$	−18959.3	+	87149.2i	−0.109556	+	0.503589i
$417$			182090.i			1.04717i
$418$	193245.	−	128126.i	1.10600	−	0.733304i
$419$			298912.i			1.70261i	0.524670	+	0.851306i	$0.324189\pi$
$419$			298912.i			1.70261i	−0.524670	+	0.851306i	$0.675811\pi$
$420$	−61278.6	+	145000.i	−0.347384	+	0.821998i
$421$		−	98837.3i		−	0.557643i	−0.960343	−	0.278822i	$-0.910056\pi$
$421$		−	98837.3i		−	0.557643i	0.960343	−	0.278822i	$-0.0899439\pi$
$422$	−226072.	+	149891.i	−1.26947	+	0.841689i
$423$	82576.6			0.461505
$424$	−321949.	+	60460.1i	−1.79083	+	0.336308i
$425$			447679.i			2.47850i
$426$	−25251.0	+	16742.0i	−0.139142	+	0.0922546i
$427$	−325625.			−1.78592
$428$	−107276.	−	45335.7i	−0.585617	−	0.247487i
$429$		−	73017.2i		−	0.396744i
$430$	−82863.3	−	124978.i	−0.448152	−	0.675922i
$431$		−	69477.1i		−	0.374013i	−0.982359	−	0.187007i	$-0.940121\pi$
$431$		−	69477.1i		−	0.374013i	0.982359	−	0.187007i	$-0.0598786\pi$
$432$	122290.	+	125836.i	0.655277	+	0.674278i
$433$	−107332.			−0.572469			−0.286235	−	0.958160i	$-0.592404\pi$
$433$	−107332.			−0.572469			−0.286235	+	0.958160i	$0.592404\pi$
$434$	−57280.5	−	86392.8i	−0.304108	−	0.458668i
$435$			153038.i			0.808764i
$436$	−60325.2	−	25494.0i	−0.317341	−	0.134111i
$437$			307129.i			1.60827i
$438$	122436.	−	81178.1i	0.638208	−	0.423147i
$439$	134157.			0.696118			0.348059	−	0.937473i	$-0.386841\pi$
$439$	134157.			0.696118			0.348059	+	0.937473i	$0.386841\pi$
$440$	−76728.5	−	408578.i	−0.396325	−	2.11042i
$441$	−9433.61			−0.0485066
$442$	147912.	−	98069.4i	0.757112	−	0.501983i
$443$		−	194105.i		−	0.989074i	−0.869157	−	0.494537i	$-0.835338\pi$
$443$		−	194105.i		−	0.989074i	0.869157	−	0.494537i	$-0.164662\pi$
$444$	27434.6	−	64917.2i	0.139166	−	0.329302i
$445$		−	207168.i		−	1.04617i
$446$	−51137.5	−	77127.8i	−0.257081	−	0.387741i
$447$		−	54979.4i		−	0.275160i
$448$	193485.	−	75327.3i	0.964034	−	0.375316i
$449$	−39666.9			−0.196759			−0.0983797	−	0.995149i	$-0.531366\pi$
$449$	−39666.9			−0.196759			−0.0983797	+	0.995149i	$0.531366\pi$
$450$	163927.	−	108687.i	0.809514	−	0.536727i
$451$	−109283.	+	259499.i	−0.537280	+	1.27580i
$452$	−37252.1	+	88147.8i	−0.182337	+	0.431454i
$453$	−93437.4			−0.455328
$454$	−279228.	+	185135.i	−1.35471	+	0.898206i
$455$		−	171213.i		−	0.827018i
$456$	20458.9	+	108943.i	0.0983902	+	0.523926i
$457$			59953.7i			0.287067i	0.989645	+	0.143534i	$0.0458465\pi$
$457$			59953.7i			0.287067i	−0.989645	+	0.143534i	$0.954153\pi$
$458$	125001.	+	188532.i	0.595913	+	0.898781i
$459$		−	349160.i		−	1.65729i
$460$	507236.	+	214363.i	2.39715	+	1.01306i
$461$	16349.7			0.0769323			0.0384661	−	0.999260i	$-0.487753\pi$
$461$	16349.7			0.0769323			0.0384661	+	0.999260i	$0.487753\pi$
$462$	−141675.	+	93933.8i	−0.663757	+	0.440087i
$463$	67510.9			0.314928			0.157464	−	0.987525i	$-0.449668\pi$
$463$	67510.9			0.314928			0.157464	+	0.987525i	$0.449668\pi$
$464$	144759.	−	140679.i	0.672370	−	0.653423i
$465$		−	99221.2i		−	0.458879i
$466$	−49107.4	−	74065.8i	−0.226139	−	0.341072i
$467$			245639.i			1.12632i	0.826347	+	0.563162i	$0.190415\pi$
$467$			245639.i			1.12632i	−0.826347	+	0.563162i	$0.809585\pi$
$468$	−71820.1	−	30351.8i	−0.327910	−	0.138578i
$469$	178547.			0.811720
$470$	190806.	−	126509.i	0.863766	−	0.572697i
$471$			218419.i			0.984573i
$472$	223435.	−	41959.8i	1.00292	−	0.188343i
$473$		−	161926.i		−	0.723759i
$474$	129157.	−	85634.3i	0.574860	−	0.381146i
$475$	304126.			1.34792
$476$	−380567.	−	160831.i	−1.67964	−	0.709834i
$477$		−	286377.i		−	1.25864i
$478$	−66961.6	+	44397.1i	−0.293069	+	0.194312i
$479$	−124581.			−0.542978			−0.271489	−	0.962442i	$-0.587516\pi$
$479$	−124581.			−0.542978			−0.271489	+	0.962442i	$0.587516\pi$
$480$	194204.	+	42249.0i	0.842898	+	0.183373i
$481$			76652.8i			0.331313i
$482$	−203061.	+	134634.i	−0.874042	+	0.579510i
$483$		−	225168.i		−	0.965188i
$484$	83561.0	−	197726.i	0.356708	−	0.844060i
$485$		−	452707.i		−	1.92457i
$486$	−203470.	+	134905.i	−0.861446	+	0.571159i
$487$			251905.i			1.06213i	0.847330	+	0.531066i	$0.178208\pi$
$487$			251905.i			1.06213i	−0.847330	+	0.531066i	$0.821792\pi$
$488$	75878.7	+	404053.i	0.318625	+	1.69667i
$489$			118943.i			0.497417i
$490$	−21797.8	+	14452.4i	−0.0907863	+	0.0601934i
$491$		−	383498.i		−	1.59074i	−0.606123	−	0.795371i	$-0.707276\pi$
$491$		−	383498.i		−	1.59074i	0.606123	−	0.795371i	$-0.292724\pi$
$492$	−93936.9	−	96418.4i	−0.388067	−	0.398318i
$493$	−401663.			−1.65260
$494$	−66622.2	−	100483.i	−0.273002	−	0.411753i
$495$	363434.			1.48325
$496$	−93853.1	+	91208.4i	−0.381492	+	0.370742i
$497$	−76713.8			−0.310571
$498$	−38057.8	−	57400.4i	−0.153456	−	0.231449i
$499$	16542.9			0.0664369			0.0332185	−	0.999448i	$-0.489424\pi$
$499$	16542.9			0.0664369			0.0332185	+	0.999448i	$0.489424\pi$
$500$	61308.8	−	145072.i	0.245235	−	0.580288i
$501$	167626.			0.667831
$502$	46586.4	+	70263.6i	0.184864	+	0.278820i
$503$	248213.			0.981045			0.490523	−	0.871428i	$-0.336806\pi$
$503$	248213.			0.981045			0.490523	+	0.871428i	$0.336806\pi$
$504$	33502.2	+	178399.i	0.131890	+	0.702312i
$505$		−	236232.i		−	0.926309i
$506$	328597.	+	495604.i	1.28340	+	1.93568i
$507$	104979.			0.408401
$508$	−120640.	−	50983.6i	−0.467480	−	0.197562i
$509$		−	284051.i		−	1.09638i	−0.836354	−	0.548190i	$-0.815317\pi$
$509$		−	284051.i		−	1.09638i	0.836354	−	0.548190i	$-0.184683\pi$
$510$	−218539.	−	329609.i	−0.840210	−	1.26724i
$511$	371968.			1.42450
$512$	−138557.	−	222534.i	−0.528553	−	0.848900i
$513$	−237197.			−0.901312
$514$	111156.	+	167650.i	0.420732	+	0.634566i
$515$		−	402618.i		−	1.51803i
$516$	71306.8	+	30134.9i	0.267813	+	0.113180i
$517$	247215.			0.924897
$518$	148729.	−	98610.9i	0.554289	−	0.367507i
$519$	−2144.92			−0.00796300
$520$	−212451.	+	39897.0i	−0.785690	+	0.147548i
$521$			23341.8i			0.0859922i	0.999075	+	0.0429961i	$0.0136903\pi$
$521$			23341.8i			0.0859922i	−0.999075	+	0.0429961i	$0.986310\pi$
$522$	97515.4	+	147077.i	0.357876	+	0.539763i
$523$			153104.i			0.559736i	0.960038	+	0.279868i	$0.0902908\pi$
$523$			153104.i			0.559736i	−0.960038	+	0.279868i	$0.909709\pi$
$524$	221581.	+	93642.4i	0.806995	+	0.341044i
$525$	−222966.			−0.808947
$526$	−367345.	+	243558.i	−1.32771	+	0.880301i
$527$	260415.			0.937660
$528$	149572.	+	153909.i	0.536516	+	0.552073i
$529$	−507835.			−1.81473
$530$	−438734.	−	661717.i	−1.56189	−	2.35570i
$531$			198748.i			0.704877i
$532$	−109259.	+	258534.i	−0.386041	+	0.913469i
$533$	134933.	+	56824.6i	0.474969	+	0.200024i
$534$	59100.3	+	89137.6i	0.207256	+	0.312592i
$535$		−	282269.i		−	0.986180i
$536$	−41605.8	−	221550.i	−0.144819	−	0.771157i
$537$	19669.9			0.0682110
$538$	325510.	−	215821.i	1.12461	−	0.745639i
$539$	−28242.0			−0.0972115
$540$	−165554.	+	391742.i	−0.567743	+	1.34342i
$541$	−134041.			−0.457976			−0.228988	−	0.973429i	$-0.573542\pi$
$541$	−134041.			−0.457976			−0.228988	+	0.973429i	$0.573542\pi$
$542$	116970.	+	176418.i	0.398175	+	0.600545i
$543$		−	76050.1i		−	0.257929i
$544$	−110887.	+	509706.i	−0.374698	+	1.72235i
$545$		−	158731.i		−	0.534403i
$546$	48843.3	+	73667.5i	0.163840	+	0.247110i
$547$	−12489.2			−0.0417406			−0.0208703	−	0.999782i	$-0.506644\pi$
$547$	−12489.2			−0.0417406			−0.0208703	+	0.999782i	$0.506644\pi$
$548$	165664.	+	70011.1i	0.551653	+	0.233134i
$549$	−359409.			−1.19246
$550$	490757.	−	325384.i	1.62234	−	1.07565i
$551$			272865.i			0.898762i
$552$	−279400.	+	52469.7i	−0.916956	+	0.172199i
$553$	392387.			1.28311
$554$	−100810.	+	66839.6i	−0.328462	+	0.217778i
$555$	170814.			0.554545
$556$	536198.	+	226602.i	1.73450	+	0.733018i
$557$		−	28716.3i		−	0.0925589i	−0.998929	−	0.0462794i	$-0.985264\pi$
$557$		−	28716.3i		−	0.0925589i	0.998929	−	0.0462794i	$-0.0147365\pi$
$558$	−63223.4	−	95356.1i	−0.203053	−	0.306253i
$559$	−84197.5			−0.269448
$560$	350721.	+	360891.i	1.11837	+	1.15080i
$561$		−	427053.i		−	1.35693i
$562$	−288709.	−	435443.i	−0.914088	−	1.37867i
$563$	367469.			1.15932			0.579662	−	0.814857i	$-0.303185\pi$
$563$	367469.			1.15932			0.579662	+	0.814857i	$0.303185\pi$
$564$	−46007.5	+	108865.i	−0.144634	+	0.342240i
$565$	−231939.			−0.726570
$566$	−170572.	−	257264.i	−0.532446	−	0.803057i
$567$	−55834.2			−0.173674
$568$	17876.2	+	95190.6i	0.0554088	+	0.295051i
$569$	46051.4			0.142239			0.0711195	−	0.997468i	$-0.477343\pi$
$569$	46051.4			0.142239			0.0711195	+	0.997468i	$0.477343\pi$
$570$	−223916.	+	148461.i	−0.689184	+	0.456945i
$571$	535306.			1.64184			0.820918	−	0.571046i	$-0.193462\pi$
$571$	535306.			1.64184			0.820918	+	0.571046i	$0.193462\pi$
$572$	−215012.	−	90866.2i	−0.657160	−	0.277722i
$573$	177645.			0.541057
$574$	−63329.9	−	334913.i	−0.192214	−	1.01650i
$575$			779973.i			2.35909i
$576$	213560.	−	83142.6i	0.643686	−	0.250599i
$577$			189694.i			0.569774i	0.958561	+	0.284887i	$0.0919560\pi$
$577$			189694.i			0.569774i	−0.958561	+	0.284887i	$0.908044\pi$
$578$	586648.	−	388961.i	1.75599	−	1.16426i
$579$		−	36809.9i		−	0.109801i
$580$	450648.	+	190448.i	1.33962	+	0.566137i
$581$		−	174385.i		−	0.516604i
$582$	129147.	+	194785.i	0.381275	+	0.575055i
$583$		−	857343.i		−	2.52242i
$584$	−86677.7	−	461558.i	−0.254145	−	1.35332i
$585$		−	188977.i		−	0.552200i
$586$	−139563.	−	210494.i	−0.406419	−	0.612978i
$587$	−414832.			−1.20392			−0.601958	−	0.798527i	$-0.705613\pi$
$587$	−414832.			−1.20392			−0.601958	+	0.798527i	$0.705613\pi$
$588$	5255.92	−	12436.8i	0.0152018	−	0.0359712i
$589$		−	176910.i		−	0.509943i
$590$	304485.	+	459237.i	0.874706	+	1.31927i
$591$	9574.94			0.0274133
$592$	−157019.	−	161572.i	−0.448032	−	0.461024i
$593$		−	73691.7i		−	0.209560i	−0.994495	−	0.104780i	$-0.966586\pi$
$593$		−	73691.7i		−	0.209560i	0.994495	−	0.104780i	$-0.0334139\pi$
$594$	−382757.	+	253777.i	−1.08480	+	0.719250i
$595$		−	1.00137e6i		−	2.82853i
$596$	−161897.	−	68419.1i	−0.455770	−	0.192613i
$597$	−217965.			−0.611558
$598$	257702.	−	170862.i	0.720634	−	0.477797i
$599$		−	52213.5i		−	0.145522i	−0.997349	−	0.0727611i	$-0.976819\pi$
$599$		−	52213.5i		−	0.145522i	0.997349	−	0.0727611i	$-0.0231811\pi$
$600$	51956.6	+	276668.i	0.144324	+	0.768523i
$601$			269687.i			0.746639i	0.927703	+	0.373320i	$0.121781\pi$
$601$			269687.i			0.746639i	−0.927703	+	0.373320i	$0.878219\pi$
$602$	108317.	+	163368.i	0.298884	+	0.450790i
$603$	197071.			0.541986
$604$	−116278.	+	275143.i	−0.318731	+	0.754196i
$605$	520268.			1.42140
$606$	67391.7	+	101643.i	0.183510	+	0.276778i
$607$		−	526578.i		−	1.42918i	−0.699546	−	0.714588i	$-0.746614\pi$
$607$		−	526578.i		−	1.42918i	0.699546	−	0.714588i	$-0.253386\pi$
$608$	346262.	+	75329.4i	0.936695	+	0.203778i
$609$		−	200048.i		−	0.539385i
$610$	−830468.	+	550620.i	−2.23184	+	1.47976i
$611$		−	128546.i		−	0.344330i
$612$	−420051.	−	177518.i	−1.12150	−	0.473957i
$613$	667438.			1.77619			0.888097	−	0.459657i	$-0.152028\pi$
$613$	667438.			1.77619			0.888097	+	0.459657i	$0.152028\pi$
$614$	−59983.0	−	90469.0i	−0.159108	−	0.239973i
$615$	126628.	−	300686.i	0.334796	−	0.794993i
$616$	100298.	+	534083.i	0.264319	+	1.40750i
$617$	148685.			0.390569			0.195285	−	0.980747i	$-0.437437\pi$
$617$	148685.			0.390569			0.195285	+	0.980747i	$0.437437\pi$
$618$	114858.	+	173234.i	0.300735	+	0.453581i
$619$			399732.i			1.04325i	0.853175	+	0.521625i	$0.174674\pi$
$619$			399732.i			1.04325i	−0.853175	+	0.521625i	$0.825326\pi$
$620$	−292174.	−	123476.i	−0.760079	−	0.321217i
$621$		−	608326.i		−	1.57744i
$622$	271346.	−	179909.i	0.701362	−	0.465020i
$623$			270805.i			0.697718i
$624$	80028.9	−	77773.8i	0.205531	−	0.199739i
$625$	−167549.			−0.428925
$626$	−27011.6	−	40740.1i	−0.0689290	−	0.103962i
$627$	−290113.			−0.737960
$628$	643172.	+	271811.i	1.63083	+	0.689203i
$629$			448316.i			1.13314i
$630$	−366671.	+	243111.i	−0.923837	+	0.612525i
$631$			513864.i			1.29059i	0.763932	+	0.645297i	$0.223266\pi$
$631$			513864.i			1.29059i	−0.763932	+	0.645297i	$0.776734\pi$
$632$	−91435.8	−	486894.i	−0.228919	−	1.21899i
$633$	339397.			0.847033
$634$	−25574.3	−	38572.2i	−0.0636246	−	0.0959613i
$635$		−	317434.i		−	0.787238i
$636$	377546.	+	159554.i	0.933373	+	0.394452i
$637$			14685.1i			0.0361909i
$638$	291938.	+	440313.i	0.717215	+	1.08173i
$639$	−84672.9			−0.207368
$640$	366086.	−	519291.i	0.893766	−	1.26780i
$641$			422816.i			1.02905i	0.857476	+	0.514523i	$0.172031\pi$
$641$			422816.i			1.02905i	−0.857476	+	0.514523i	$0.827969\pi$
$642$	80525.1	+	121451.i	0.195371	+	0.294668i
$643$	−150514.			−0.364045			−0.182023	−	0.983294i	$-0.558264\pi$
$643$	−150514.			−0.364045			−0.182023	+	0.983294i	$0.558264\pi$
$644$	−663047.	−	280210.i	−1.59872	−	0.675634i
$645$			187626.i			0.450997i
$646$	−389651.	−	587688.i	−0.933707	−	1.40826i
$647$			154976.i			0.370216i	0.982718	+	0.185108i	$0.0592635\pi$
$647$			154976.i			0.370216i	−0.982718	+	0.185108i	$0.940737\pi$
$648$	13010.7	+	69282.0i	0.0309850	+	0.164995i
$649$			595004.i			1.41264i
$650$	−169192.	−	255182.i	−0.400453	−	0.603981i
$651$			129699.i			0.306038i
$652$	350249.	+	148018.i	0.823913	+	0.348193i
$653$		−	28177.1i		−	0.0660799i	−0.999454	−	0.0330399i	$-0.989481\pi$
$653$		−	28177.1i		−	0.0660799i	0.999454	−	0.0330399i	$-0.0105189\pi$
$654$	45282.4	+	68296.8i	0.105870	+	0.159678i
$655$			583037.i			1.35898i
$656$	−400821.	+	156626.i	−0.931414	+	0.363963i
$657$	410560.			0.951142
$658$	−249417.	+	165369.i	−0.576068	+	0.381946i
$659$	−44942.2			−0.103487			−0.0517433	−	0.998660i	$-0.516478\pi$
$659$	−44942.2			−0.103487			−0.0517433	+	0.998660i	$0.516478\pi$
$660$	−202487.	+	479135.i	−0.464846	+	1.09994i
$661$	−756780.			−1.73207			−0.866037	−	0.499979i	$-0.833341\pi$
$661$	−756780.			−1.73207			−0.866037	+	0.499979i	$0.833341\pi$
$662$	−337170.	+	223551.i	−0.769366	+	0.510107i
$663$	−222057.			−0.505170
$664$	−216387.	+	40636.1i	−0.490788	+	0.0921670i
$665$	−680268.			−1.53828
$666$	164160.	−	108842.i	0.370099	−	0.245385i
$667$	−699802.			−1.57298
$668$	208602.	−	493606.i	0.467484	−	1.10618i
$669$			115790.i			0.258713i
$670$	455363.	−	301916.i	1.01440	−	0.672569i
$671$	−1.07598e6			−2.38980
$672$	−253858.	−	55226.9i	−0.562150	−	0.122296i
$673$		−	828245.i		−	1.82864i	−0.404990	−	0.914321i	$-0.632725\pi$
$673$		−	828245.i		−	1.82864i	0.404990	−	0.914321i	$-0.367275\pi$
$674$	409547.	−	271539.i	0.901537	−	0.597740i
$675$	−602378.			−1.32209
$676$	130641.	−	309129.i	0.285882	−	0.676467i
$677$	−649862.			−1.41789			−0.708947	−	0.705261i	$-0.750830\pi$
$677$	−649862.			−1.41789			−0.708947	+	0.705261i	$0.750830\pi$
$678$	99796.0	−	66167.1i	0.217097	−	0.143940i
$679$			591767.i			1.28354i
$680$	−1.24255e6	+	233344.i	−2.68718	+	0.504636i
$681$	419198.			0.903909
$682$	−189276.	−	285474.i	−0.406936	−	0.613758i
$683$	117208.			0.251255			0.125627	−	0.992078i	$-0.459906\pi$
$683$	117208.			0.251255			0.125627	+	0.992078i	$0.459906\pi$
$684$	−120594.	+	285357.i	−0.257760	+	0.609924i
$685$			435903.i			0.928985i
$686$	−377262.	+	250134.i	−0.801669	+	0.531525i
$687$		−	283038.i		−	0.599697i
$688$	177475.	−	172474.i	0.374939	−	0.364374i
$689$	−445798.			−0.939073
$690$	−380751.	−	574264.i	−0.799728	−	1.20618i
$691$	215585.			0.451504			0.225752	−	0.974185i	$-0.427516\pi$
$691$	215585.			0.451504			0.225752	+	0.974185i	$0.427516\pi$
$692$	−2669.25	+	6316.10i	−0.00557412	+	0.0131898i
$693$	−475072.			−0.989219
$694$	−239053.	+	158498.i	−0.496336	+	0.329082i
$695$			1.41087e6i			2.92091i
$696$	−248230.	+	46616.1i	−0.512432	+	0.0962315i
$697$	789179.	+	332348.i	1.62446	+	0.684112i
$698$	−286521.	+	189970.i	−0.588092	+	0.389918i
$699$			111193.i			0.227575i
$700$	−277470.	+	656563.i	−0.566265	+	1.33992i
$701$	−342937.			−0.697877			−0.348938	−	0.937146i	$-0.613458\pi$
$701$	−342937.			−0.697877			−0.348938	+	0.937146i	$0.613458\pi$
$702$	131958.	+	199025.i	0.267770	+	0.403861i
$703$	304558.			0.616254
$704$	639347.	−	248909.i	1.29000	−	0.502222i
$705$	−286452.			−0.576333
$706$	−262365.	+	173954.i	−0.526376	+	0.349000i
$707$			308796.i			0.617779i
$708$	−262020.	−	110732.i	−0.522719	−	0.220906i
$709$		−	617009.i		−	1.22744i	−0.789525	−	0.613718i	$-0.789673\pi$
$709$		−	617009.i		−	1.22744i	0.789525	−	0.613718i	$-0.210327\pi$
$710$	−195650.	+	129720.i	−0.388117	+	0.257330i
$711$	433097.			0.856734
$712$	336029.	−	63104.2i	0.662852	−	0.124480i
$713$	453711.			0.892483
$714$	285668.	+	430857.i	0.560357	+	0.845155i
$715$		−	565752.i		−	1.10666i
$716$	24478.2	−	57921.6i	0.0477478	−	0.112983i
$717$	100528.			0.195545
$718$	−300936.	−	453884.i	−0.583748	−	0.880433i
$719$	−9869.50			−0.0190914			−0.00954569	−	0.999954i	$-0.503039\pi$
$719$	−9869.50			−0.0190914			−0.00954569	+	0.999954i	$0.503039\pi$
$720$	387109.	+	398334.i	0.746738	+	0.768391i
$721$			526292.i			1.01241i
$722$	35224.9	−	23354.9i	0.0675734	−	0.0448027i
$723$	304850.			0.583190
$724$	−223943.	−	94640.4i	−0.427229	−	0.180551i
$725$			692959.i			1.31835i
$726$	−223854.	+	148421.i	−0.424710	+	0.281593i
$727$	572649.			1.08348			0.541738	−	0.840547i	$-0.317766\pi$
$727$	572649.			1.08348			0.541738	+	0.840547i	$0.317766\pi$
$728$	277710.	−	52152.3i	0.523997	−	0.0984035i
$729$	216247.			0.406906
$730$	948660.	−	628984.i	1.78018	−	1.18030i
$731$	−492443.			−0.921554
$732$	200244.	−	473828.i	0.373713	−	0.884297i
$733$	272369.			0.506933			0.253466	−	0.967344i	$-0.418429\pi$
$733$	272369.			0.506933			0.253466	+	0.967344i	$0.418429\pi$
$734$	66589.9	+	100434.i	0.123599	+	0.186418i
$735$	32724.5			0.0605756
$736$	−193193.	+	888040.i	−0.356645	+	1.63937i
$737$	589984.			1.08619
$738$	−69900.4	−	369661.i	−0.128342	−	0.678720i
$739$			1.07792e6i			1.97378i	0.161398	+	0.986889i	$0.448400\pi$
$739$			1.07792e6i			1.97378i	−0.161398	+	0.986889i	$0.551600\pi$
$740$	212569.	−	502991.i	0.388183	−	0.918537i
$741$			150852.i			0.274735i
$742$	573501.	+	864979.i	1.04166	+	1.57108i
$743$		−	746967.i		−	1.35308i	−0.736405	−	0.676540i	$-0.763478\pi$
$743$		−	746967.i		−	1.35308i	0.736405	−	0.676540i	$-0.236522\pi$
$744$	160938.	−	30223.2i	0.290745	−	0.0546002i
$745$		−	425991.i		−	0.767517i
$746$	577640.	−	382989.i	1.03796	−	0.688190i
$747$		−	192478.i		−	0.344937i
$748$	−1.25753e6	−	531446.i	−2.24759	−	0.949852i
$749$			368975.i			0.657709i
$750$	−164242.	+	108897.i	−0.291986	+	0.193594i
$751$	−219919.			−0.389926			−0.194963	−	0.980811i	$-0.562459\pi$
$751$	−219919.			−0.389926			−0.194963	+	0.980811i	$0.562459\pi$
$752$	263319.	+	270954.i	0.465636	+	0.479138i
$753$		−	105485.i		−	0.186038i
$754$	228952.	−	151801.i	0.402719	−	0.267012i
$755$	−723971.			−1.27007
$756$	216408.	−	512075.i	0.378642	−	0.895962i
$757$		−	314602.i		−	0.548997i	−0.961588	−	0.274498i	$-0.911488\pi$
$757$		−	314602.i		−	0.548997i	0.961588	−	0.274498i	$-0.0885118\pi$
$758$	−504943.	−	761576.i	−0.878827	−	1.32548i
$759$		−	744037.i		−	1.29155i
$760$	158519.	+	844113.i	0.274445	+	1.46141i
$761$	−582433.			−1.00572			−0.502860	−	0.864368i	$-0.667719\pi$
$761$	−582433.			−1.00572			−0.502860	+	0.864368i	$0.667719\pi$
$762$	90556.8	+	136582.i	0.155959	+	0.235224i
$763$			207489.i			0.356407i
$764$	221070.	−	523106.i	0.378741	−	0.896196i
$765$		−	1.10526e6i		−	1.88861i
$766$	18630.8	−	12352.6i	0.0317522	−	0.0210524i
$767$	309388.			0.525911
$768$	−9373.22	+	327870.i	−0.0158916	+	0.555878i
$769$	378869.			0.640673			0.320336	−	0.947304i	$-0.396204\pi$
$769$	378869.			0.640673			0.320336	+	0.947304i	$0.396204\pi$
$770$	−1.09773e6	+	727818.i	−1.85145	+	1.22756i
$771$		−	251688.i		−	0.423403i
$772$	−108393.	−	45808.1i	−0.181873	−	0.0768613i
$773$			725572.i			1.21429i	0.794592	+	0.607144i	$0.207685\pi$
$773$			725572.i			1.21429i	−0.794592	+	0.607144i	$0.792315\pi$
$774$	119555.	+	180317.i	0.199565	+	0.300993i
$775$		−	449274.i		−	0.748011i
$776$	734296.	−	137896.i	1.21940	−	0.228997i
$777$	−223283.			−0.369840
$778$	−649621.	+	430714.i	−1.07325	+	0.711590i
$779$	225777.	−	536119.i	0.372052	−	0.883459i
$780$	249138.	+	105288.i	0.409498	+	0.173058i
$781$	−253491.			−0.415585
$782$	1.50721e6	−	999316.i	2.46468	−	1.63414i
$783$		−	540461.i		−	0.881537i
$784$	−30081.7	−	30954.0i	−0.0489408	−	0.0503599i
$785$			1.69235e6i			2.74632i
$786$	−166327.	−	250862.i	−0.269227	−	0.406059i
$787$		−	490813.i		−	0.792441i	−0.918155	−	0.396220i	$-0.870322\pi$
$787$		−	490813.i		−	0.792441i	0.918155	−	0.396220i	$-0.129678\pi$
$788$	11915.5	−	28195.1i	0.0191894	−	0.0454068i
$789$	551485.			0.885890
$790$	1.00074e6	−	663511.i	1.60349	−	1.06315i
$791$	303185.			0.484568
$792$	110703.	+	589494.i	0.176486	+	0.939787i
$793$			559486.i			0.889698i
$794$	322816.	+	486885.i	0.512052	+	0.772299i
$795$			993418.i			1.57180i
$796$	−271246.	+	641836.i	−0.428092	+	1.01297i
$797$	198660.			0.312748			0.156374	−	0.987698i	$-0.450020\pi$
$797$	198660.			0.312748			0.156374	+	0.987698i	$0.450020\pi$
$798$	292697.	−	194065.i	0.459635	−	0.304748i
$799$		−	751820.i		−	1.17766i
$800$	879356.	+	191304.i	1.37399	+	0.298912i
$801$			298901.i			0.465867i
$802$	−697058.	+	462166.i	−1.08373	+	0.718537i
$803$	1.22912e6			1.90617
$804$	−109798.	+	259809.i	−0.169856	+	0.401923i
$805$		−	1.74464e6i		−	2.69225i
$806$	−148439.	+	98418.8i	−0.228496	+	0.151498i
$807$	−488680.			−0.750374
$808$	383171.	−	71957.2i	0.586908	−	0.110218i
$809$			1.13565e6i			1.73519i	0.497272	+	0.867595i	$0.334335\pi$
$809$			1.13565e6i			1.73519i	−0.497272	+	0.867595i	$0.665665\pi$
$810$	−142399.	+	94413.6i	−0.217038	+	0.143901i
$811$			244636.i			0.371946i	0.982555	+	0.185973i	$0.0595436\pi$
$811$			244636.i			0.371946i	−0.982555	+	0.185973i	$0.940456\pi$
$812$	−589076.	−	248949.i	−0.893428	−	0.377571i
$813$		−	264853.i		−	0.400704i
$814$	491456.	−	325847.i	0.741712	−	0.491773i
$815$			921593.i			1.38747i
$816$	468062.	−	454872.i	0.702948	−	0.683139i
$817$			334535.i			0.501184i
$818$	−33158.0	+	21984.6i	−0.0495544	+	0.0328557i
$819$			247026.i			0.368277i
$820$	−727842.	−	747068.i	−1.08245	−	1.11105i
$821$	1.32452e6			1.96505			0.982525	−	0.186131i	$-0.0595948\pi$
$821$	1.32452e6			1.96505			0.982525	+	0.186131i	$0.0595948\pi$
$822$	−124353.	−	187555.i	−0.184041	−	0.277578i
$823$	−705312.			−1.04131			−0.520657	−	0.853766i	$-0.674313\pi$
$823$	−705312.			−1.04131			−0.520657	+	0.853766i	$0.674313\pi$
$824$	653052.	−	122639.i	0.961819	−	0.180624i
$825$	−736762.			−1.08248
$826$	−398015.	−	600303.i	−0.583364	−	0.879854i
$827$	−528726.			−0.773072			−0.386536	−	0.922274i	$-0.626328\pi$
$827$	−528726.			−0.773072			−0.386536	+	0.922274i	$0.626328\pi$
$828$	−731838.	−	309282.i	−1.06747	−	0.451122i
$829$	−80601.3			−0.117282			−0.0586412	−	0.998279i	$-0.518677\pi$
$829$	−80601.3			−0.117282			−0.0586412	+	0.998279i	$0.518677\pi$
$830$	−294879.	−	444749.i	−0.428043	−	0.645593i
$831$	151344.			0.219161
$832$	−129427.	−	332445.i	−0.186972	−	0.480256i
$833$			85888.4i			0.123778i
$834$	−402490.	−	607053.i	−0.578659	−	0.872759i
$835$	1.29880e6			1.86282
$836$	−361031.	+	854290.i	−0.516574	+	1.22234i
$837$			350403.i			0.500170i
$838$	−660711.	−	996513.i	−0.940857	−	1.41904i
$839$	−964790.			−1.37059			−0.685297	−	0.728264i	$-0.740328\pi$
$839$	−964790.			−1.37059			−0.685297	+	0.728264i	$0.740328\pi$
$840$	−116216.	−	618851.i	−0.164706	−	0.877057i
$841$	85550.2			0.120956
$842$	218468.	+	329503.i	0.308152	+	0.464767i
$843$			653720.i			0.919892i
$844$	422362.	−	999414.i	0.592925	−	1.40301i
$845$	813398.			1.13917
$846$	−275294.	+	182526.i	−0.384641	+	0.255026i
$847$	−680081.			−0.947968
$848$	939672.	−	913193.i	1.30673	−	1.26990i
$849$			386224.i			0.535827i
$850$	−989544.	−	1.49247e6i	−1.36961	−	2.06571i
$851$			781083.i			1.07854i
$852$	47175.4	−	111629.i	0.0649885	−	0.153779i
$853$	−497645.			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$853$	−497645.			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$854$	1.08557e6	−	719756.i	1.48847	−	0.986892i
$855$	−750846.			−1.02711
$856$	457844.	−	85980.4i	0.624842	−	0.117342i
$857$	817172.			1.11263			0.556317	−	0.830970i	$-0.312214\pi$
$857$	817172.			1.11263			0.556317	+	0.830970i	$0.312214\pi$
$858$	161396.	+	243425.i	0.219239	+	0.330666i
$859$			531482.i			0.720282i	0.932898	+	0.360141i	$0.117271\pi$
$859$			531482.i			0.720282i	−0.932898	+	0.360141i	$0.882729\pi$
$860$	552499.	+	233491.i	0.747024	+	0.315699i
$861$	−165525.	+	393049.i	−0.223284	+	0.530201i
$862$	153571.	+	231623.i	0.206678	+	0.311721i
$863$		−	963631.i		−	1.29387i	−0.762547	−	0.646933i	$-0.776051\pi$
$863$		−	963631.i		−	1.29387i	0.762547	−	0.646933i	$-0.223949\pi$
$864$	−685838.	−	149204.i	−0.918743	−	0.199873i
$865$	−16619.3			−0.0222116
$866$	357822.	−	237244.i	0.477124	−	0.316344i
$867$	−880720.			−1.17165
$868$	381923.	+	161404.i	0.506916	+	0.214228i
$869$	1.29659e6			1.71697
$870$	−338274.	−	510199.i	−0.446920	−	0.674063i
$871$		−	306777.i		−	0.404377i
$872$	257464.	−	48350.1i	0.338597	−	0.0635864i
$873$			653163.i			0.857024i
$874$	−678873.	−	1.02390e6i	−0.888721	−	1.34041i
$875$	−498977.			−0.651724
$876$	−228743.	+	541263.i	−0.298084	+	0.705342i
$877$	−316018.			−0.410878			−0.205439	−	0.978670i	$-0.565862\pi$
$877$	−316018.			−0.410878			−0.205439	+	0.978670i	$0.565862\pi$
$878$	−447251.	+	296538.i	−0.580179	+	0.384672i
$879$			316010.i			0.408999i
$880$	1.15891e6	+	1.19252e6i	1.49653	+	1.53992i
$881$	−131632.			−0.169594			−0.0847969	−	0.996398i	$-0.527024\pi$
$881$	−131632.			−0.169594			−0.0847969	+	0.996398i	$0.527024\pi$
$882$	31449.7	−	20851.9i	0.0404278	−	0.0268046i
$883$	−411683.			−0.528009			−0.264005	−	0.964521i	$-0.585043\pi$
$883$	−411683.			−0.528009			−0.264005	+	0.964521i	$0.585043\pi$
$884$	−276339.	+	653887.i	−0.353621	+	0.836755i
$885$		−	689441.i		−	0.880260i
$886$	429046.	+	647106.i	0.546559	+	0.824343i
$887$	−30346.1			−0.0385705			−0.0192853	−	0.999814i	$-0.506139\pi$
$887$	−30346.1			−0.0385705			−0.0192853	+	0.999814i	$0.506139\pi$
$888$	52030.5	+	277062.i	0.0659831	+	0.351359i
$889$			414942.i			0.525029i
$890$	457921.	+	690655.i	0.578110	+	0.871930i
$891$	−184497.			−0.232398
$892$	340964.	+	144095.i	0.428528	+	0.181100i
$893$	−510740.			−0.640467
$894$	121526.	+	183290.i	0.152052	+	0.229332i
$895$	152406.			0.190264
$896$	−478539.	+	678803.i	−0.596075	+	0.845528i
$897$	−386881.			−0.480831
$898$	132241.	−	87679.1i	0.163989	−	0.108729i
$899$	403094.			0.498755
$900$	−306257.	+	724682.i	−0.378096	+	0.894669i
$901$	−2.60732e6			−3.21177
$902$	−209265.	−	1.10668e6i	−0.257208	−	1.36021i
$903$		−	245260.i		−	0.300782i
$904$	−70649.7	−	376208.i	−0.0864516	−	0.460354i
$905$		−	589251.i		−	0.719454i
$906$	311501.	−	206533.i	0.379493	−	0.251612i
$907$		−	907731.i		−	1.10342i	−0.834035	−	0.551712i	$-0.813975\pi$
$907$		−	907731.i		−	1.10342i	0.834035	−	0.551712i	$-0.186025\pi$
$908$	521670.	−	1.23440e6i	0.632739	−	1.49722i
$909$			340834.i			0.412492i
$910$	378447.	+	570790.i	0.457007	+	0.689277i
$911$			728910.i			0.878288i	0.898417	+	0.439144i	$0.144718\pi$
$911$			728910.i			0.878288i	−0.898417	+	0.439144i	$0.855282\pi$
$912$	−309012.	−	317972.i	−0.371523	−	0.382296i
$913$		−	576233.i		−	0.691284i
$914$	−132521.	−	199874.i	−0.158632	−	0.239256i
$915$	1.24676e6			1.48916
$916$	−833456.	−	352227.i	−0.993326	−	0.419789i
$917$		−	762131.i		−	0.906340i
$918$	771777.	+	1.16403e6i	0.915813	+	1.38127i
$919$	1.43903e6			1.70388			0.851942	−	0.523636i	$-0.175425\pi$
$919$	1.43903e6			1.70388			0.851942	+	0.523636i	$0.175425\pi$
$920$	−2.16485e6	+	406545.i	−2.55771	+	0.480323i
$921$			135819.i			0.160118i
$922$	−54506.7	+	36139.2i	−0.0641191	+	0.0425125i
$923$			131809.i			0.154718i
$924$	264686.	−	626313.i	0.310018	−	0.733579i
$925$	773445.			0.903954
$926$	−225068.	+	149225.i	−0.262477	+	0.174028i
$927$			580896.i			0.675987i
$928$	−171640.	+	788969.i	−0.199307	+	0.916144i
$929$		−	1.10858e6i		−	1.28451i	−0.766493	−	0.642253i	$-0.778000\pi$
$929$		−	1.10858e6i		−	1.28451i	0.766493	−	0.642253i	$-0.222000\pi$
$930$	219317.	+	330783.i	0.253575	+	0.382453i
$931$	58347.3			0.0673164
$932$	327428.	+	138374.i	0.376950	+	0.159303i
$933$	−407365.			−0.467972
$934$	−542956.	−	818910.i	−0.622402	−	0.938734i
$935$		−	3.30889e6i		−	3.78494i
$936$	306523.	−	57563.1i	0.349873	−	0.0657041i
$937$			255343.i			0.290834i	0.989370	+	0.145417i	$0.0464524\pi$
$937$			255343.i			0.290834i	−0.989370	+	0.145417i	$0.953548\pi$
$938$	−595239.	+	394657.i	−0.676527	+	0.448553i
$939$			61162.1i			0.0693667i
$940$	−356475.	+	843509.i	−0.403435	+	0.954627i
$941$	−110751.			−0.125074			−0.0625372	−	0.998043i	$-0.519919\pi$
$941$	−110751.			−0.125074			−0.0625372	+	0.998043i	$0.519919\pi$
$942$	−482789.	−	728163.i	−0.544071	−	0.820591i
$943$	1.37495e6	+	579036.i	1.54620	+	0.651152i
$944$	−652141.	+	633764.i	−0.731809	+	0.711187i
$945$	1.34740e6			1.50880
$946$	357918.	+	539828.i	0.399946	+	0.603216i
$947$		−	427601.i		−	0.476803i	−0.971167	−	0.238402i	$-0.923377\pi$
$947$		−	427601.i		−	0.476803i	0.971167	−	0.238402i	$-0.0766235\pi$
$948$	−241299.	+	570975.i	−0.268497	+	0.635331i
$949$		−	639111.i		−	0.709650i
$950$	−1.01389e6	+	672234.i	−1.12343	+	0.744858i
$951$			57907.5i			0.0640285i
$952$	1.62423e6	−	305021.i	1.79215	−	0.336555i
$953$	−1.11045e6			−1.22268			−0.611340	−	0.791368i	$-0.709369\pi$
$953$	−1.11045e6			−1.22268			−0.611340	+	0.791368i	$0.709369\pi$
$954$	633002.	+	954721.i	0.695518	+	1.04901i
$955$	1.37643e6			1.50920
$956$	125102.	−	296022.i	0.136882	−	0.323898i
$957$		−	661031.i		−	0.721769i
$958$	415329.	−	275373.i	0.452544	−	0.300047i
$959$		−	569801.i		−	0.619564i
$960$	−740822.	+	288415.i	−0.803844	+	0.312951i
$961$	662178.			0.717015
$962$	−169432.	−	255545.i	−0.183082	−	0.276132i
$963$			407257.i			0.439153i
$964$	379370.	−	897685.i	0.408234	−	0.965984i
$965$		−	285211.i		−	0.306275i
$966$	497707.	+	750664.i	0.533359	+	0.804435i
$967$	−1.00544e6			−1.07524			−0.537618	−	0.843188i	$-0.680676\pi$
$967$	−1.00544e6			−1.07524			−0.537618	+	0.843188i	$0.680676\pi$
$968$	158476.	+	843881.i	0.169127	+	0.900597i
$969$			882282.i			0.939636i
$970$	1.00066e6	+	1.50923e6i	1.06351	+	1.60403i
$971$	755235.			0.801021			0.400510	−	0.916292i	$-0.368833\pi$
$971$	755235.			0.801021			0.400510	+	0.916292i	$0.368833\pi$
$972$	380135.	−	899494.i	0.402351	−	0.952063i
$973$		−	1.84426e6i		−	1.94803i
$974$	−556807.	−	839799.i	−0.586930	−	0.885233i
$975$			383098.i			0.402996i
$976$	−1.14608e6	−	1.17931e6i	−1.20313	−	1.23802i
$977$			625939.i			0.655757i	0.944720	+	0.327879i	$0.106334\pi$
$977$			625939.i			0.655757i	−0.944720	+	0.327879i	$0.893666\pi$
$978$	−262910.	−	396532.i	−0.274871	−	0.414572i
$979$			894838.i			0.933639i
$980$	40723.9	−	96363.0i	0.0424031	−	0.100336i
$981$			229016.i			0.237973i
$982$	847677.	+	1.27850e6i	0.879038	+	1.32580i
$983$			21929.6i			0.0226947i	0.999936	+	0.0113473i	$0.00361205\pi$
$983$			21929.6i			0.0226947i	−0.999936	+	0.0113473i	$0.996388\pi$
$984$	526288.	+	113802.i	0.543543	+	0.117533i
$985$	74188.5			0.0764652
$986$	1.33906e6	−	887831.i	1.37736	−	0.913222i
$987$	374443.			0.384371
$988$	444210.	+	187727.i	0.455066	+	0.192315i
$989$	−857962.			−0.877154
$990$	−1.21161e6	+	803329.i	−1.23622	+	0.819640i
$991$	−697516.			−0.710243			−0.355122	−	0.934820i	$-0.615561\pi$
$991$	−697516.			−0.710243			−0.355122	+	0.934820i	$0.615561\pi$
$992$	111282.	−	511522.i	0.113084	−	0.519805i
$993$	506185.			0.513346
$994$	255748.	−	169567.i	0.258845	−	0.171620i
$995$	−1.68883e6			−1.70585
$996$	253754.	+	107239.i	0.255796	+	0.108102i
$997$		−	683726.i		−	0.687846i	−0.938998	−	0.343923i	$-0.888244\pi$
$997$		−	683726.i		−	0.687846i	0.938998	−	0.343923i	$-0.111756\pi$
$998$	−55150.5	+	36566.1i	−0.0553718	+	0.0367128i
$999$	−603235.			−0.604443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.5.d.f.163.12	yes	72
4.3	odd	2	inner	164.5.d.f.163.9	✓	72
41.40	even	2	inner	164.5.d.f.163.11	yes	72
164.163	odd	2	inner	164.5.d.f.163.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.9	✓	72	4.3	odd	2	inner
164.5.d.f.163.10	yes	72	164.163	odd	2	inner
164.5.d.f.163.11	yes	72	41.40	even	2	inner
164.5.d.f.163.12	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.33380 + 2.21038i) q^{2} +5.00494 q^{3} +(6.22840 - 14.7379i) q^{4} +38.7793 q^{5} +(-16.6855 + 11.0629i) q^{6} -50.6913 q^{7} +(11.8123 + 62.9005i) q^{8} -55.9505 q^{9} +(-129.282 + 85.7171i) q^{10} -167.503 q^{11} +(31.1728 - 73.7626i) q^{12} +87.0973i q^{13} +(168.994 - 112.047i) q^{14} +194.088 q^{15} +(-178.414 - 183.588i) q^{16} +509.403i q^{17} +(186.528 - 123.672i) q^{18} +346.056 q^{19} +(241.533 - 571.527i) q^{20} -253.707 q^{21} +(558.420 - 370.245i) q^{22} +887.511i q^{23} +(59.1200 + 314.813i) q^{24} +878.832 q^{25} +(-192.519 - 290.365i) q^{26} -685.430 q^{27} +(-315.725 + 747.085i) q^{28} +788.499i q^{29} +(-647.050 + 429.009i) q^{30} -511.217i q^{31} +(1000.60 + 217.680i) q^{32} -838.341 q^{33} +(-1125.98 - 1698.24i) q^{34} -1965.77 q^{35} +(-348.482 + 824.596i) q^{36} +880.083 q^{37} +(-1153.68 + 764.918i) q^{38} +435.917i q^{39} +(458.073 + 2439.23i) q^{40} +(652.427 - 1549.23i) q^{41} +(845.808 - 560.790i) q^{42} +966.706i q^{43} +(-1043.27 + 2468.64i) q^{44} -2169.72 q^{45} +(-1961.74 - 2958.78i) q^{46} -1475.89 q^{47} +(-892.953 - 918.846i) q^{48} +168.606 q^{49} +(-2929.85 + 1942.56i) q^{50} +2549.53i q^{51} +(1283.63 + 542.476i) q^{52} +5118.39i q^{53} +(2285.08 - 1515.06i) q^{54} -6495.63 q^{55} +(-598.782 - 3188.51i) q^{56} +1731.99 q^{57} +(-1742.89 - 2628.70i) q^{58} -3552.21i q^{59} +(1208.86 - 2860.46i) q^{60} +6423.69 q^{61} +(1129.99 + 1704.29i) q^{62} +2836.20 q^{63} +(-3816.94 + 1486.00i) q^{64} +3377.57i q^{65} +(2794.86 - 1853.06i) q^{66} -3522.24 q^{67} +(7507.55 + 3172.76i) q^{68} +4441.94i q^{69} +(6553.48 - 4345.11i) q^{70} +1513.35 q^{71} +(-660.906 - 3519.31i) q^{72} -7337.90 q^{73} +(-2934.02 + 1945.32i) q^{74} +4398.51 q^{75} +(2155.38 - 5100.16i) q^{76} +8490.92 q^{77} +(-963.544 - 1453.26i) q^{78} -7740.71 q^{79} +(-6918.77 - 7119.39i) q^{80} +1101.45 q^{81} +(1249.33 + 6606.92i) q^{82} +3440.14i q^{83} +(-1580.19 + 3739.12i) q^{84} +19754.3i q^{85} +(-2136.79 - 3222.80i) q^{86} +3946.39i q^{87} +(-1978.60 - 10536.0i) q^{88} -5342.23i q^{89} +(7233.41 - 4795.92i) q^{90} -4415.07i q^{91} +(13080.1 + 5527.77i) q^{92} -2558.61i q^{93} +(4920.30 - 3262.28i) q^{94} +13419.8 q^{95} +(5007.93 + 1089.47i) q^{96} -11673.9i q^{97} +(-562.099 + 372.685i) q^{98} +9371.86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) \) 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

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