LMFDB - Embedded newform 164.5.d.f.163.10

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

$q$-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	$-0.917041\pi$
$13$		−	87.0973i		−	0.515368i	0.966229	−	0.257684i	$-0.0829594\pi$
$14$	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	$-0.656656\pi$
$17$		−	509.403i		−	1.76264i	0.472521	−	0.881319i	$-0.343344\pi$
$18$	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	$-0.683224\pi$
$23$		−	887.511i		−	1.67771i	0.544351	−	0.838857i	$-0.316776\pi$
$24$	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	$-0.844691\pi$
$29$		−	788.499i		−	0.937573i	0.883311	−	0.468787i	$-0.155309\pi$
$30$	−647.050	−	429.009i	−0.718945	−	0.476677i
$31$			511.217i			0.531964i	0.963978	+	0.265982i	$0.0856961\pi$
$31$			511.217i			0.531964i	−0.963978	+	0.265982i	$0.914304\pi$
$32$	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	$-0.915811\pi$
$43$		−	966.706i		−	0.522826i	0.965227	−	0.261413i	$-0.0841885\pi$
$44$	−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	$-0.635258\pi$
$53$		−	5118.39i		−	1.82214i	0.412253	−	0.911069i	$-0.364742\pi$
$54$	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	$0.170439\pi$
$59$			3552.21i			1.02046i	−0.860039	+	0.510228i	$0.829561\pi$
$60$	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	$-0.919673\pi$
$83$		−	3440.14i		−	0.499367i	0.968327	−	0.249684i	$-0.0803266\pi$
$84$	−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	$0.109486\pi$
$89$			5342.23i			0.674439i	−0.941426	+	0.337219i	$0.890514\pi$
$90$	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	$0.213014\pi$
$97$			11673.9i			1.24072i	−0.784317	+	0.620360i	$0.786986\pi$
$98$	−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	$0.0965142\pi$
$101$			6091.71i			0.597168i	−0.954383	+	0.298584i	$0.903486\pi$
$102$	−5635.45	+	8499.62i	−0.541661	+	0.816957i
$103$			10382.3i			0.978632i	0.872107	+	0.489316i	$0.162754\pi$
$103$			10382.3i			0.978632i	−0.872107	+	0.489316i	$0.837246\pi$
$104$	−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	$0.102972\pi$
$107$			7278.87i			0.635765i	−0.948130	+	0.317882i	$0.897028\pi$
$108$	−4269.13	−	10101.8i	−0.366009	−	0.866069i
$109$			4093.19i			0.344516i	0.985052	+	0.172258i	$0.0551062\pi$
$109$			4093.19i			0.344516i	−0.985052	+	0.172258i	$0.944894\pi$
$110$	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	$0.0816660\pi$
$127$			8185.66i			0.507512i	−0.967268	+	0.253756i	$0.918334\pi$
$128$	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	$-0.855669\pi$
$131$		−	15034.8i		−	0.876100i	0.898951	−	0.438050i	$-0.144331\pi$
$132$	−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	$-0.903198\pi$
$137$		−	11240.6i		−	0.598893i	0.954113	−	0.299446i	$-0.0968020\pi$
$138$	−9818.40	+	14808.5i	−0.515564	+	0.777596i
$139$		−	36382.1i		−	1.88304i	−0.336964	−	0.941518i	$-0.609400\pi$
$139$		−	36382.1i		−	1.88304i	0.336964	−	0.941518i	$-0.390600\pi$
$140$	−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	$0.0795759\pi$
$149$			10985.0i			0.494798i	−0.968914	+	0.247399i	$0.920424\pi$
$150$	−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	$-0.653994\pi$
$157$		−	43640.6i		−	1.77048i	0.465135	−	0.885240i	$-0.346006\pi$
$158$	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	$-0.852409\pi$
$163$		−	23765.1i		−	0.894467i	0.894417	−	0.447233i	$-0.147591\pi$
$164$	−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	$0.0744964\pi$
$181$			15195.0i			0.463813i	−0.972738	+	0.231907i	$0.925504\pi$
$182$	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	$0.0314760\pi$
$193$			7354.72i			0.197447i	−0.995115	+	0.0987237i	$0.968524\pi$
$194$	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	$-0.925273\pi$
$223$		−	23135.1i		−	0.465224i	0.972570	−	0.232612i	$-0.0747272\pi$
$224$	−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	$0.181271\pi$
$229$			56551.7i			1.07839i	−0.842182	+	0.539194i	$0.818729\pi$
$230$	−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	$-0.934406\pi$
$233$		−	22216.7i		−	0.409229i	0.978843	−	0.204615i	$-0.0655942\pi$
$234$	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	$0.0534947\pi$
$251$			21076.2i			0.334537i	−0.985911	+	0.167268i	$0.946505\pi$
$252$	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	$0.124312\pi$
$257$			50287.9i			0.761373i	−0.924704	+	0.380687i	$0.875688\pi$
$258$	−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	$0.117318\pi$
$271$			52918.2i			0.720554i	−0.932845	+	0.360277i	$0.882682\pi$
$272$	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	$-0.689998\pi$
$281$		−	130615.i		−	1.65417i	0.562077	−	0.827085i	$-0.310002\pi$
$282$	24625.9	+	16327.5i	0.309666	+	0.205316i
$283$		−	77168.6i		−	0.963535i	−0.876299	−	0.481768i	$-0.839995\pi$
$283$		−	77168.6i		−	0.963535i	0.876299	−	0.481768i	$-0.160005\pi$
$284$	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	$-0.880133\pi$
$293$		−	63139.5i		−	0.735472i	0.929930	−	0.367736i	$-0.119867\pi$
$294$	−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	$-0.954015\pi$
$307$		−	27136.9i		−	0.287928i	0.989583	−	0.143964i	$-0.0459849\pi$
$308$	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	$-0.980135\pi$
$313$		−	12220.3i		−	0.124737i	0.998053	−	0.0623683i	$-0.0198654\pi$
$314$	−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	$-0.981665\pi$
$317$		−	11570.1i		−	0.115138i	0.998342	−	0.0575688i	$-0.0183348\pi$
$318$	−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	$-0.822872\pi$
$359$		−	136146.i		−	1.05637i	0.849128	−	0.528186i	$-0.177128\pi$
$360$	−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	$0.0356729\pi$
$367$			30125.9i			0.223670i	−0.993727	+	0.111835i	$0.964327\pi$
$368$	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	$-0.707376\pi$
$379$		−	228441.i		−	1.59036i	0.606373	−	0.795180i	$-0.292624\pi$
$380$	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	$0.153340\pi$
$397$			146045.i			0.926630i	−0.886194	+	0.463315i	$0.846660\pi$
$398$	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	$-0.675811\pi$
$419$		−	298912.i		−	1.70261i	0.524670	−	0.851306i	$-0.324189\pi$
$420$	−61278.6	−	145000.i	−0.347384	−	0.821998i
$421$			98837.3i			0.557643i	0.960343	+	0.278822i	$0.0899439\pi$
$421$			98837.3i			0.557643i	−0.960343	+	0.278822i	$0.910056\pi$
$422$	−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	$0.0598786\pi$
$431$			69477.1i			0.374013i	−0.982359	+	0.187007i	$0.940121\pi$
$432$	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	$0.164662\pi$
$443$			194105.i			0.989074i	−0.869157	+	0.494537i	$0.835338\pi$
$444$	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	$-0.954153\pi$
$457$		−	59953.7i		−	0.287067i	0.989645	−	0.143534i	$-0.0458465\pi$
$458$	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	$-0.809585\pi$
$467$		−	245639.i		−	1.12632i	0.826347	−	0.563162i	$-0.190415\pi$
$468$	−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	$-0.821792\pi$
$487$		−	251905.i		−	1.06213i	0.847330	−	0.531066i	$-0.178208\pi$
$488$	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	$0.292724\pi$
$491$			383498.i			1.59074i	−0.606123	+	0.795371i	$0.707276\pi$
$492$	−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	$0.184683\pi$
$509$			284051.i			1.09638i	−0.836354	+	0.548190i	$0.815317\pi$
$510$	−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	$-0.986310\pi$
$521$		−	23341.8i		−	0.0859922i	0.999075	−	0.0429961i	$-0.0136903\pi$
$522$	97515.4	−	147077.i	0.357876	−	0.539763i
$523$		−	153104.i		−	0.559736i	−0.960038	−	0.279868i	$-0.909709\pi$
$523$		−	153104.i		−	0.559736i	0.960038	−	0.279868i	$-0.0902908\pi$
$524$	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	$0.0147365\pi$
$557$			28716.3i			0.0925589i	−0.998929	+	0.0462794i	$0.985264\pi$
$558$	−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	$-0.908044\pi$
$577$		−	189694.i		−	0.569774i	0.958561	−	0.284887i	$-0.0919560\pi$
$578$	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	$0.0334139\pi$
$593$			73691.7i			0.209560i	−0.994495	+	0.104780i	$0.966586\pi$
$594$	−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	$0.0231811\pi$
$599$			52213.5i			0.145522i	−0.997349	+	0.0727611i	$0.976819\pi$
$600$	51956.6	−	276668.i	0.144324	−	0.768523i
$601$		−	269687.i		−	0.746639i	−0.927703	−	0.373320i	$-0.878219\pi$
$601$		−	269687.i		−	0.746639i	0.927703	−	0.373320i	$-0.121781\pi$
$602$	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	$0.253386\pi$
$607$			526578.i			1.42918i	−0.699546	+	0.714588i	$0.746614\pi$
$608$	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	$-0.825326\pi$
$619$		−	399732.i		−	1.04325i	0.853175	−	0.521625i	$-0.174674\pi$
$620$	−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	$-0.776734\pi$
$631$		−	513864.i		−	1.29059i	0.763932	−	0.645297i	$-0.223266\pi$
$632$	−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	$-0.827969\pi$
$641$		−	422816.i		−	1.02905i	0.857476	−	0.514523i	$-0.172031\pi$
$642$	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	$-0.940737\pi$
$647$		−	154976.i		−	0.370216i	0.982718	−	0.185108i	$-0.0592635\pi$
$648$	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	$0.0105189\pi$
$653$			28177.1i			0.0660799i	−0.999454	+	0.0330399i	$0.989481\pi$
$654$	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	$0.367275\pi$
$673$			828245.i			1.82864i	−0.404990	+	0.914321i	$0.632725\pi$
$674$	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	$0.210327\pi$
$709$			617009.i			1.22744i	−0.789525	+	0.613718i	$0.789673\pi$
$710$	−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	$-0.551600\pi$
$739$		−	1.07792e6i		−	1.97378i	0.161398	−	0.986889i	$-0.448400\pi$
$740$	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	$0.236522\pi$
$743$			746967.i			1.35308i	−0.736405	+	0.676540i	$0.763478\pi$
$744$	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	$0.0885118\pi$
$757$			314602.i			0.548997i	−0.961588	+	0.274498i	$0.911488\pi$
$758$	−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	$-0.792315\pi$
$773$		−	725572.i		−	1.21429i	0.794592	−	0.607144i	$-0.207685\pi$
$774$	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	$0.129678\pi$
$787$			490813.i			0.792441i	−0.918155	+	0.396220i	$0.870322\pi$
$788$	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	$-0.665665\pi$
$809$		−	1.13565e6i		−	1.73519i	0.497272	−	0.867595i	$-0.334335\pi$
$810$	−142399.	−	94413.6i	−0.217038	−	0.143901i
$811$		−	244636.i		−	0.371946i	−0.982555	−	0.185973i	$-0.940456\pi$
$811$		−	244636.i		−	0.371946i	0.982555	−	0.185973i	$-0.0595436\pi$
$812$	−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	$-0.882729\pi$
$859$		−	531482.i		−	0.720282i	0.932898	−	0.360141i	$-0.117271\pi$
$860$	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	$0.223949\pi$
$863$			963631.i			1.29387i	−0.762547	+	0.646933i	$0.776051\pi$
$864$	−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	$0.186025\pi$
$907$			907731.i			1.10342i	−0.834035	+	0.551712i	$0.813975\pi$
$908$	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	$-0.855282\pi$
$911$		−	728910.i		−	0.878288i	0.898417	−	0.439144i	$-0.144718\pi$
$912$	−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	$0.222000\pi$
$929$			1.10858e6i			1.28451i	−0.766493	+	0.642253i	$0.778000\pi$
$930$	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	$-0.953548\pi$
$937$		−	255343.i		−	0.290834i	0.989370	−	0.145417i	$-0.0464524\pi$
$938$	−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	$0.0766235\pi$
$947$			427601.i			0.476803i	−0.971167	+	0.238402i	$0.923377\pi$
$948$	−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	$-0.893666\pi$
$977$		−	625939.i		−	0.655757i	0.944720	−	0.327879i	$-0.106334\pi$
$978$	−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	$-0.996388\pi$
$983$		−	21929.6i		−	0.0226947i	0.999936	−	0.0113473i	$-0.00361205\pi$
$984$	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	$0.111756\pi$
$997$			683726.i			0.687846i	−0.938998	+	0.343923i	$0.888244\pi$
$998$	−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.163.10	yes	72
4.3	odd	2	inner	164.5.d.f.163.11	yes	72
41.40	even	2	inner	164.5.d.f.163.9	✓	72
164.163	odd	2	inner	164.5.d.f.163.12	yes	72

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

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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