LMFDB - Embedded newform 164.5.d.f.163.9

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			163.9
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(-5599.44 + 3722.69i) 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	$-0.589689\pi$
$3$	−5.00494			−0.556105			−0.278052	+	0.960566i	$0.589689\pi$
$4$	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	$-0.326953\pi$
$7$	50.6913			1.03452			0.517258	+	0.855830i	$0.326953\pi$
$8$	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	$-0.256659\pi$
$11$	167.503			1.38432			0.692160	+	0.721744i	$0.256659\pi$
$12$	−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	$-0.659110\pi$
$19$	−346.056			−0.958605			−0.479302	+	0.877650i	$0.659110\pi$
$20$	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	$0.155309\pi$
$29$			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	$0.0856961\pi$
$31$			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	$-0.391580\pi$
$47$	1475.89			0.668124			0.334062	+	0.942551i	$0.391580\pi$
$48$	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	$0.170439\pi$
$59$			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	$-0.371673\pi$
$67$	3522.24			0.784638			0.392319	+	0.919829i	$0.371673\pi$
$68$	−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	$-0.547961\pi$
$71$	−1513.35			−0.300209			−0.150104	+	0.988670i	$0.547961\pi$
$72$	−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	$-0.287072\pi$
$79$	7740.71			1.24030			0.620150	+	0.784483i	$0.287072\pi$
$80$	−6918.77	+	7119.39i	−1.08106	+	1.11241i
$81$	1101.45			0.167879
$82$	−5599.44	+	3722.69i	−0.832755	+	0.553642i
$83$		−	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	$-0.890514\pi$
$89$		−	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	$0.162754\pi$
$103$			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	$-0.944894\pi$
$109$		−	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	$0.0816660\pi$
$127$			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	$0.0968020\pi$
$137$			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	$-0.609400\pi$
$139$		−	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	$-0.920424\pi$
$149$		−	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	$-0.365742\pi$
$151$	18669.0			0.818780			0.409390	+	0.912359i	$0.365742\pi$
$152$	−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	$-0.852409\pi$
$163$		−	23765.1i		−	0.894467i	0.894417	−	0.447233i	$-0.147591\pi$
$164$	26896.0	−	33.7573i	0.999999	−	0.00125510i
$165$	−32510.3			−1.19413
$166$	−7604.04	+	11468.7i	−0.275949	+	0.416197i
$167$	−33492.2			−1.20091			−0.600455	−	0.799659i	$-0.705014\pi$
$167$	−33492.2			−1.20091			−0.600455	+	0.799659i	$0.705014\pi$
$168$	−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	$-0.519534\pi$
$179$	−3930.10			−0.122658			−0.0613292	+	0.998118i	$0.519534\pi$
$180$	−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	$-0.661716\pi$
$191$	−35493.8			−0.972940			−0.486470	+	0.873697i	$0.661716\pi$
$192$	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	$-0.314682\pi$
$199$	43549.9			1.09972			0.549858	+	0.835258i	$0.314682\pi$
$200$	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	$-0.775574\pi$
$211$	−67812.3			−1.52315			−0.761577	+	0.648075i	$0.775574\pi$
$212$	−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	$-0.802011\pi$
$227$	−83756.8			−1.62543			−0.812715	+	0.582662i	$0.802011\pi$
$228$	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	$-0.556257\pi$
$239$	−20085.7			−0.351634			−0.175817	+	0.984423i	$0.556257\pi$
$240$	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
$246$	28024.9	−	18631.8i	0.463099	−	0.307883i
$247$		−	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	$-0.875688\pi$
$257$		−	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	$-0.793325\pi$
$263$	−110188.			−1.59303			−0.796513	+	0.604621i	$0.793325\pi$
$264$	−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	$0.310002\pi$
$281$			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	$-0.839995\pi$
$283$		−	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	$0.119867\pi$
$293$			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	$-0.954015\pi$
$307$		−	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	$-0.361764\pi$
$311$	81392.4			0.841518			0.420759	+	0.907173i	$0.361764\pi$
$312$	−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
$328$	−89740.3	−	59337.9i	−0.834142	−	0.551550i
$329$	74814.6			0.691185
$330$	108383.	+	71860.2i	0.995249	+	0.659873i
$331$	−101137.			−0.923110			−0.461555	−	0.887111i	$-0.652708\pi$
$331$	−101137.			−0.923110			−0.461555	+	0.887111i	$0.652708\pi$
$332$	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	$-0.596240\pi$
$347$	−71706.0			−0.595521			−0.297760	+	0.954641i	$0.596240\pi$
$348$	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	$-0.493936\pi$
$383$	5588.45			0.0380973			0.0190487	+	0.999819i	$0.493936\pi$
$384$	−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	$0.490536\pi$
$410$	−217142.	+	144363.i	−1.29175	+	0.858793i
$411$		−	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	$-0.910056\pi$
$421$		−	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	$0.0598786\pi$
$431$			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	$-0.613159\pi$
$439$	−134157.			−0.696118			−0.348059	+	0.937473i	$0.613159\pi$
$440$	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	$0.0458465\pi$
$457$			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	$-0.550332\pi$
$463$	−67510.9			−0.314928			−0.157464	+	0.987525i	$0.550332\pi$
$464$	−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	$-0.412484\pi$
$479$	124581.			0.542978			0.271489	+	0.962442i	$0.412484\pi$
$480$	−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	$0.707276\pi$
$492$	−134613.	+	168.953i	−0.556105	+	0.000697969i
$493$	−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	$-0.510576\pi$
$499$	−16542.9			−0.0664369			−0.0332185	+	0.999448i	$0.510576\pi$
$500$	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	$-0.663194\pi$
$503$	−248213.			−0.981045			−0.490523	+	0.871428i	$0.663194\pi$
$504$	−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	$-0.909709\pi$
$523$		−	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	$-0.493356\pi$
$547$	12489.2			0.0417406			0.0208703	+	0.999782i	$0.493356\pi$
$548$	−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	$-0.696815\pi$
$563$	−367469.			−1.15932			−0.579662	+	0.814857i	$0.696815\pi$
$564$	−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	$-0.806538\pi$
$571$	−535306.			−1.64184			−0.820918	+	0.571046i	$0.806538\pi$
$572$	−215012.	+	90866.2i	−0.657160	+	0.277722i
$573$	177645.			0.541057
$574$	−283843.	+	188708.i	−0.861498	+	0.572751i
$575$		−	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	$-0.294387\pi$
$587$	414832.			1.20392			0.601958	+	0.798527i	$0.294387\pi$
$588$	−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	$0.0231811\pi$
$599$			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	$0.121781\pi$
$601$			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	$0.253386\pi$
$607$			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	$0.172031\pi$
$641$			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	$-0.441736\pi$
$643$	150514.			0.364045			0.182023	+	0.983294i	$0.441736\pi$
$644$	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	$-0.989481\pi$
$653$		−	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
$656$	168016.	+	396181.i	0.390431	+	0.920632i
$657$	410560.			0.951142
$658$	−249417.	−	165369.i	−0.576068	−	0.381946i
$659$	44942.2			0.103487			0.0517433	−	0.998660i	$-0.483522\pi$
$659$	44942.2			0.103487			0.0517433	+	0.998660i	$0.483522\pi$
$660$	−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	$-0.540094\pi$
$683$	−117208.			−0.251255			−0.125627	+	0.992078i	$0.540094\pi$
$684$	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	$-0.572484\pi$
$691$	−215585.			−0.451504			−0.225752	+	0.974185i	$0.572484\pi$
$692$	−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	$-0.496961\pi$
$719$	9869.50			0.0190914			0.00954569	+	0.999954i	$0.496961\pi$
$720$	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	$-0.682234\pi$
$727$	−572649.			−1.08348			−0.541738	+	0.840547i	$0.682234\pi$
$728$	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
$738$	313292.	−	208286.i	0.575223	−	0.382427i
$739$		−	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	$-0.437541\pi$
$751$	219919.			0.389926			0.194963	+	0.980811i	$0.437541\pi$
$752$	−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	$0.129678\pi$
$787$			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	$0.334335\pi$
$809$			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	$-0.940456\pi$
$811$		−	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
$820$	1.04301e6	−	1309.08i	1.55117	−	0.00194688i
$821$	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	$-0.325687\pi$
$823$	705312.			1.04131			0.520657	+	0.853766i	$0.325687\pi$
$824$	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	$-0.373672\pi$
$827$	528726.			0.773072			0.386536	+	0.922274i	$0.373672\pi$
$828$	−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	$-0.259672\pi$
$839$	964790.			1.37059			0.685297	+	0.728264i	$0.259672\pi$
$840$	−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	$-0.414957\pi$
$883$	411683.			0.528009			0.264005	+	0.964521i	$0.414957\pi$
$884$	−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	$-0.493861\pi$
$887$	30346.1			0.0385705			0.0192853	+	0.999814i	$0.493861\pi$
$888$	−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
$902$	−937922.	+	623560.i	−1.15280	+	0.766417i
$903$			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	$-0.824575\pi$
$919$	−1.43903e6			−1.70388			−0.851942	+	0.523636i	$0.824575\pi$
$920$	−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	$0.0766235\pi$
$947$			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	$-0.319324\pi$
$967$	1.00544e6			1.07524			0.537618	+	0.843188i	$0.319324\pi$
$968$	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	$-0.631167\pi$
$971$	−755235.			−0.801021			−0.400510	+	0.916292i	$0.631167\pi$
$972$	−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	$-0.996388\pi$
$983$		−	21929.6i		−	0.0226947i	0.999936	−	0.0113473i	$-0.00361205\pi$
$984$	449145.	+	296983.i	0.463870	+	0.306720i
$985$	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	$-0.384439\pi$
$991$	697516.			0.710243			0.355122	+	0.934820i	$0.384439\pi$
$992$	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.163.9	✓	72
4.3	odd	2	inner	164.5.d.f.163.12	yes	72
41.40	even	2	inner	164.5.d.f.163.10	yes	72
164.163	odd	2	inner	164.5.d.f.163.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.9	✓	72	1.1	even	1	trivial
164.5.d.f.163.10	yes	72	41.40	even	2	inner
164.5.d.f.163.11	yes	72	164.163	odd	2	inner
164.5.d.f.163.12	yes	72	4.3	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} +(-5599.44 + 3722.69i) 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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