LMFDB - Embedded newform 119.5.l.a.104.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(76,119)] 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("119.76"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			104.16
Character	$\chi$	$=$	119.104
Dual form			119.5.l.a.111.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07263 - 2.07263i) q^{2} +(3.92959 + 9.48686i) q^{3} -7.40839i q^{4} +(-2.20267 + 0.912377i) q^{5} +(11.5182 - 27.8074i) q^{6} +(40.6282 + 27.3925i) q^{7} +(-48.5170 + 48.5170i) q^{8} +(-17.2832 + 17.2832i) q^{9} +(6.45635 + 2.67431i) q^{10} +(-26.7132 - 11.0650i) q^{11} +(70.2824 - 29.1119i) q^{12} +33.9896 q^{13} +(-27.4327 - 140.982i) q^{14} +(-17.3112 - 17.3112i) q^{15} +82.5815 q^{16} +(287.101 + 33.0718i) q^{17} +71.6435 q^{18} +(-415.138 + 415.138i) q^{19} +(6.75925 + 16.3183i) q^{20} +(-100.217 + 493.075i) q^{21} +(32.4331 + 78.3003i) q^{22} +(789.775 + 327.135i) q^{23} +(-650.925 - 269.622i) q^{24} +(-437.922 + 437.922i) q^{25} +(-70.4480 - 70.4480i) q^{26} +(536.556 + 222.249i) q^{27} +(202.934 - 300.990i) q^{28} +(263.393 + 635.887i) q^{29} +71.7594i q^{30} +(-9.31714 - 22.4936i) q^{31} +(605.111 + 605.111i) q^{32} -296.905i q^{33} +(-526.510 - 663.601i) q^{34} +(-114.483 - 23.2685i) q^{35} +(128.041 + 128.041i) q^{36} +(1691.61 - 700.688i) q^{37} +1720.86 q^{38} +(133.565 + 322.455i) q^{39} +(62.6013 - 151.133i) q^{40} +(1669.52 + 691.538i) q^{41} +(1229.68 - 814.251i) q^{42} +(-1591.71 + 1591.71i) q^{43} +(-81.9737 + 197.902i) q^{44} +(22.3004 - 53.8380i) q^{45} +(-958.881 - 2314.94i) q^{46} +468.268 q^{47} +(324.511 + 783.439i) q^{48} +(900.302 + 2225.82i) q^{49} +1815.30 q^{50} +(814.443 + 2853.65i) q^{51} -251.809i q^{52} +(-3076.09 - 3076.09i) q^{53} +(-651.444 - 1572.72i) q^{54} +68.9359 q^{55} +(-3300.16 + 642.156i) q^{56} +(-5569.68 - 2307.04i) q^{57} +(772.043 - 1863.88i) q^{58} +(-3555.91 - 3555.91i) q^{59} +(-128.248 + 128.248i) q^{60} +(2034.97 + 842.914i) q^{61} +(-27.3099 + 65.9319i) q^{62} +(-1175.62 + 228.755i) q^{63} -3829.65i q^{64} +(-74.8681 + 31.0114i) q^{65} +(-615.376 + 615.376i) q^{66} -6988.76 q^{67} +(245.009 - 2126.96i) q^{68} +8777.99i q^{69} +(189.054 + 285.508i) q^{70} +(3136.47 - 1299.17i) q^{71} -1677.06i q^{72} +(1491.86 - 617.950i) q^{73} +(-4958.35 - 2053.82i) q^{74} +(-5875.36 - 2433.65i) q^{75} +(3075.51 + 3075.51i) q^{76} +(-782.213 - 1181.29i) q^{77} +(391.499 - 945.162i) q^{78} +(-10230.1 - 4237.44i) q^{79} +(-181.900 + 75.3454i) q^{80} +7943.40i q^{81} +(-2027.00 - 4893.60i) q^{82} +(-444.926 + 444.926i) q^{83} +(3652.89 + 742.445i) q^{84} +(-662.564 + 189.098i) q^{85} +6598.07 q^{86} +(-4997.55 + 4997.55i) q^{87} +(1832.88 - 759.206i) q^{88} +11679.8 q^{89} +(-157.807 + 65.3658i) q^{90} +(1380.94 + 931.061i) q^{91} +(2423.55 - 5850.96i) q^{92} +(176.781 - 176.781i) q^{93} +(-970.548 - 970.548i) q^{94} +(535.651 - 1293.18i) q^{95} +(-3362.77 + 8118.44i) q^{96} +(9585.87 - 3970.60i) q^{97} +(2747.30 - 6479.29i) q^{98} +(652.929 - 270.452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 8 q^{2} - 4 q^{7} + 120 q^{8} - 8 q^{9} - 128 q^{11} - 52 q^{14} - 504 q^{15} - 10256 q^{16} - 2064 q^{18} + 2824 q^{22} - 2672 q^{23} + 2224 q^{25} - 780 q^{28} - 8 q^{29} - 5888 q^{32} + 2104 q^{35}+ \cdots + 108752 q^{99}+O(q^{100}) $ 184 * q - 8 * q^2 - 4 * q^7 + 120 * q^8 - 8 * q^9 - 128 * q^11 - 52 * q^14 - 504 * q^15 - 10256 * q^16 - 2064 * q^18 + 2824 * q^22 - 2672 * q^23 + 2224 * q^25 - 780 * q^28 - 8 * q^29 - 5888 * q^32 + 2104 * q^35 + 1912 * q^36 - 8712 * q^37 - 4440 * q^39 + 17296 * q^42 - 2632 * q^43 + 3672 * q^44 + 3576 * q^46 + 4432 * q^49 + 2360 * q^50 + 22160 * q^51 - 16184 * q^53 - 22308 * q^56 - 8 * q^57 + 1528 * q^58 + 18040 * q^60 + 33740 * q^63 - 18472 * q^65 + 7616 * q^67 - 45296 * q^70 + 25528 * q^71 + 7984 * q^74 - 12184 * q^77 - 23704 * q^78 + 24728 * q^79 + 6800 * q^84 - 30656 * q^85 + 95480 * q^86 + 108000 * q^88 - 27544 * q^91 - 22848 * q^92 + 114464 * q^93 + 61936 * q^95 + 108752 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−2.07263	−	2.07263i	−0.518158	−	0.518158i	0.398856	−	0.917014i	$-0.369407\pi$
$2$	−2.07263	−	2.07263i	−0.518158	−	0.518158i	−0.917014	+	0.398856i	$0.869407\pi$
$3$	3.92959	+	9.48686i	0.436621	+	1.05410i	0.977108	+	0.212743i	$0.0682398\pi$
$3$	3.92959	+	9.48686i	0.436621	+	1.05410i	−0.540487	+	0.841352i	$0.681760\pi$
$4$		−	7.40839i		−	0.463025i
$5$	−2.20267	+	0.912377i	−0.0881069	+	0.0364951i	−0.426302	−	0.904581i	$-0.640184\pi$
$5$	−2.20267	+	0.912377i	−0.0881069	+	0.0364951i	0.338195	+	0.941076i	$0.390184\pi$
$6$	11.5182	−	27.8074i	0.319950	−	0.772427i
$7$	40.6282	+	27.3925i	0.829147	+	0.559031i
$7$	40.6282	+	27.3925i	0.829147	+	0.559031i
$8$	−48.5170	+	48.5170i	−0.758078	+	0.758078i
$9$	−17.2832	+	17.2832i	−0.213373	+	0.213373i
$10$	6.45635	+	2.67431i	0.0645635	+	0.0267431i
$11$	−26.7132	−	11.0650i	−0.220770	−	0.0914461i	0.269557	−	0.962984i	$-0.413123\pi$
$11$	−26.7132	−	11.0650i	−0.220770	−	0.0914461i	−0.490327	+	0.871538i	$0.663123\pi$
$12$	70.2824	−	29.1119i	0.488072	−	0.202166i
$13$	33.9896			0.201122			0.100561	−	0.994931i	$-0.467936\pi$
$13$	33.9896			0.201122			0.100561	+	0.994931i	$0.467936\pi$
$14$	−27.4327	−	140.982i	−0.139963	−	0.719295i
$15$	−17.3112	−	17.3112i	−0.0769386	−	0.0769386i
$16$	82.5815			0.322584
$17$	287.101	+	33.0718i	0.993431	+	0.114435i
$17$	287.101	+	33.0718i	0.993431	+	0.114435i
$18$	71.6435			0.221122
$19$	−415.138	+	415.138i	−1.14997	+	1.14997i	−0.163408	+	0.986558i	$0.552249\pi$
$19$	−415.138	+	415.138i	−1.14997	+	1.14997i	−0.986558	+	0.163408i	$0.947751\pi$
$20$	6.75925	+	16.3183i	0.0168981	+	0.0407957i
$21$	−100.217	+	493.075i	−0.227249	+	1.11808i
$22$	32.4331	+	78.3003i	0.0670105	+	0.161778i
$23$	789.775	+	327.135i	1.49296	+	0.618403i	0.971958	−	0.235153i	$-0.0755592\pi$
$23$	789.775	+	327.135i	1.49296	+	0.618403i	0.521000	+	0.853557i	$0.325559\pi$
$24$	−650.925	−	269.622i	−1.13008	−	0.468094i
$25$	−437.922	+	437.922i	−0.700676	+	0.700676i
$26$	−70.4480	−	70.4480i	−0.104213	−	0.104213i
$27$	536.556	+	222.249i	0.736017	+	0.304868i
$28$	202.934	−	300.990i	0.258845	−	0.383915i
$29$	263.393	+	635.887i	0.313190	+	0.756108i	0.999583	+	0.0288771i	$0.00919316\pi$
$29$	263.393	+	635.887i	0.313190	+	0.756108i	−0.686393	+	0.727231i	$0.740807\pi$
$30$			71.7594i			0.0797327i
$31$	−9.31714	−	22.4936i	−0.00969525	−	0.0234064i	0.918958	−	0.394356i	$-0.129032\pi$
$31$	−9.31714	−	22.4936i	−0.00969525	−	0.0234064i	−0.928653	+	0.370950i	$0.879032\pi$
$32$	605.111	+	605.111i	0.590929	+	0.590929i
$33$		−	296.905i		−	0.272640i
$34$	−526.510	−	663.601i	−0.455459	−	0.574050i
$35$	−114.483	−	23.2685i	−0.0934554	−	0.0189947i
$36$	128.041	+	128.041i	0.0987969	+	0.0987969i
$37$	1691.61	−	700.688i	1.23565	−	0.511824i	0.333300	−	0.942821i	$-0.391838\pi$
$37$	1691.61	−	700.688i	1.23565	−	0.511824i	0.902354	+	0.430996i	$0.141838\pi$
$38$	1720.86			1.19173
$39$	133.565	+	322.455i	0.0878141	+	0.212002i
$40$	62.6013	−	151.133i	0.0391258	−	0.0944580i
$41$	1669.52	+	691.538i	0.993171	+	0.411385i	0.819288	−	0.573382i	$-0.194369\pi$
$41$	1669.52	+	691.538i	0.993171	+	0.411385i	0.173882	+	0.984766i	$0.444369\pi$
$42$	1229.68	−	814.251i	0.697095	−	0.461594i
$43$	−1591.71	+	1591.71i	−0.860850	+	0.860850i	−0.991437	−	0.130587i	$-0.958314\pi$
$43$	−1591.71	+	1591.71i	−0.860850	+	0.860850i	0.130587	+	0.991437i	$0.458314\pi$
$44$	−81.9737	+	197.902i	−0.0423418	+	0.102222i
$45$	22.3004	−	53.8380i	0.0110126	−	0.0265867i
$46$	−958.881	−	2314.94i	−0.453157	−	1.09402i
$47$	468.268			0.211982			0.105991	−	0.994367i	$-0.466199\pi$
$47$	468.268			0.211982			0.105991	+	0.994367i	$0.466199\pi$
$48$	324.511	+	783.439i	0.140847	+	0.340034i
$49$	900.302	+	2225.82i	0.374969	+	0.927037i
$50$	1815.30			0.726122
$51$	814.443	+	2853.65i	0.313127	+	1.09714i
$52$		−	251.809i		−	0.0931245i
$53$	−3076.09	−	3076.09i	−1.09508	−	1.09508i	−0.994977	−	0.100105i	$-0.968082\pi$
$53$	−3076.09	−	3076.09i	−1.09508	−	1.09508i	−0.100105	−	0.994977i	$-0.531918\pi$
$54$	−651.444	−	1572.72i	−0.223403	−	0.539343i
$55$	68.9359			0.0227887
$56$	−3300.16	+	642.156i	−1.05235	+	0.204769i
$57$	−5569.68	−	2307.04i	−1.71427	−	0.710076i
$58$	772.043	−	1863.88i	0.229502	−	0.554066i
$59$	−3555.91	−	3555.91i	−1.02152	−	1.02152i	−0.999763	−	0.0217561i	$-0.993074\pi$
$59$	−3555.91	−	3555.91i	−1.02152	−	1.02152i	−0.0217561	−	0.999763i	$-0.506926\pi$
$60$	−128.248	+	128.248i	−0.0356244	+	0.0356244i
$61$	2034.97	+	842.914i	0.546889	+	0.226529i	0.638982	−	0.769222i	$-0.279356\pi$
$61$	2034.97	+	842.914i	0.546889	+	0.226529i	−0.0920931	+	0.995750i	$0.529356\pi$
$62$	−27.3099	+	65.9319i	−0.00710455	+	0.0171519i
$63$	−1175.62	+	228.755i	−0.296200	+	0.0576355i
$64$		−	3829.65i		−	0.934973i
$65$	−74.8681	+	31.0114i	−0.0177203	+	0.00733997i
$66$	−615.376	+	615.376i	−0.141271	+	0.141271i
$67$	−6988.76			−1.55686			−0.778432	−	0.627729i	$-0.783984\pi$
$67$	−6988.76			−1.55686			−0.778432	+	0.627729i	$0.783984\pi$
$68$	245.009	−	2126.96i	0.0529863	−	0.459983i
$69$			8777.99i			1.84373i
$70$	189.054	+	285.508i	0.0385824	+	0.0582669i
$71$	3136.47	−	1299.17i	0.622192	−	0.257721i	−0.0492393	−	0.998787i	$-0.515680\pi$
$71$	3136.47	−	1299.17i	0.622192	−	0.257721i	0.671432	+	0.741066i	$0.265680\pi$
$72$		−	1677.06i		−	0.323507i
$73$	1491.86	−	617.950i	0.279952	−	0.115960i	−0.238290	−	0.971194i	$-0.576587\pi$
$73$	1491.86	−	617.950i	0.279952	−	0.115960i	0.518242	+	0.855234i	$0.326587\pi$
$74$	−4958.35	−	2053.82i	−0.905470	−	0.375058i
$75$	−5875.36	−	2433.65i	−1.04451	−	0.432650i
$76$	3075.51	+	3075.51i	0.532463	+	0.532463i
$77$	−782.213	−	1181.29i	−0.131930	−	0.199240i
$78$	391.499	−	945.162i	0.0643489	−	0.155352i
$79$	−10230.1	−	4237.44i	−1.63917	−	0.678968i	−0.642960	−	0.765900i	$-0.722294\pi$
$79$	−10230.1	−	4237.44i	−1.63917	−	0.678968i	−0.996214	+	0.0869319i	$0.972294\pi$
$80$	−181.900	+	75.3454i	−0.0284219	+	0.0117727i
$81$			7943.40i			1.21070i
$82$	−2027.00	−	4893.60i	−0.301457	−	0.727782i
$83$	−444.926	+	444.926i	−0.0645850	+	0.0645850i	−0.738662	−	0.674077i	$-0.764542\pi$
$83$	−444.926	+	444.926i	−0.0645850	+	0.0645850i	0.674077	+	0.738662i	$0.264542\pi$
$84$	3652.89	+	742.445i	0.517700	+	0.105222i
$85$	−662.564	+	189.098i	−0.0917044	+	0.0261728i
$86$	6598.07			0.892113
$87$	−4997.55	+	4997.55i	−0.660265	+	0.660265i
$88$	1832.88	−	759.206i	0.236685	−	0.0980379i
$89$	11679.8			1.47453			0.737266	−	0.675602i	$-0.236116\pi$
$89$	11679.8			1.47453			0.737266	+	0.675602i	$0.236116\pi$
$90$	−157.807	+	65.3658i	−0.0194824	+	0.00806986i
$91$	1380.94	+	931.061i	0.166760	+	0.112433i
$92$	2423.55	−	5850.96i	0.286336	−	0.691276i
$93$	176.781	−	176.781i	0.0204394	−	0.0204394i
$94$	−970.548	−	970.548i	−0.109840	−	0.109840i
$95$	535.651	−	1293.18i	0.0593519	−	0.143288i
$96$	−3362.77	+	8118.44i	−0.364883	+	0.880907i
$97$	9585.87	−	3970.60i	1.01880	−	0.422000i	0.190141	−	0.981757i	$-0.439106\pi$
$97$	9585.87	−	3970.60i	1.01880	−	0.422000i	0.828657	+	0.559757i	$0.189106\pi$
$98$	2747.30	−	6479.29i	0.286058	−	0.674645i
$99$	652.929	−	270.452i	0.0666186	−	0.0275943i
$100$	3244.30	+	3244.30i	0.324430	+	0.324430i
$101$		−	12712.2i		−	1.24617i	−0.782153	−	0.623086i	$-0.785879\pi$
$101$		−	12712.2i		−	1.24617i	0.782153	−	0.623086i	$-0.214121\pi$
$102$	4226.53	−	7602.61i	0.406241	−	0.730739i
$103$		−	16076.1i		−	1.51533i	−0.652646	−	0.757663i	$-0.726341\pi$
$103$		−	16076.1i		−	1.51533i	0.652646	−	0.757663i	$-0.273659\pi$
$104$	−1649.08	+	1649.08i	−0.152466	+	0.152466i
$105$	−229.126	−	1177.52i	−0.0207824	−	0.106804i
$106$			12751.2i			1.13485i
$107$	3939.88	+	9511.71i	0.344124	+	0.830790i	0.997290	+	0.0735744i	$0.0234406\pi$
$107$	3939.88	+	9511.71i	0.344124	+	0.830790i	−0.653165	+	0.757215i	$0.726559\pi$
$108$	1646.51	−	3975.02i	0.141161	−	0.340794i
$109$	1247.32	−	3011.31i	0.104985	−	0.253456i	−0.862654	−	0.505794i	$-0.831200\pi$
$109$	1247.32	−	3011.31i	0.104985	−	0.253456i	0.967639	+	0.252338i	$0.0811996\pi$
$110$	−142.879	−	142.879i	−0.0118082	−	0.0118082i
$111$	13294.7	+	13294.7i	1.07902	+	1.07902i
$112$	3355.14	+	2262.11i	0.267469	+	0.180334i
$113$	−837.958	−	347.093i	−0.0656244	−	0.0271825i	0.349630	−	0.936888i	$-0.386307\pi$
$113$	−837.958	−	347.093i	−0.0656244	−	0.0271825i	−0.415254	+	0.909705i	$0.636307\pi$
$114$	6762.26	+	16325.5i	0.520334	+	1.25620i
$115$	−2038.09			−0.154109
$116$	4710.90	−	1951.32i	0.350097	−	0.145015i
$117$	−587.450	+	587.450i	−0.0429140	+	0.0429140i
$118$			14740.2i			1.05862i
$119$	10758.5	+	9208.07i	0.759727	+	0.650242i
$120$	1679.77			0.116651
$121$	−9761.59	−	9761.59i	−0.666730	−	0.666730i
$122$	−2470.70	−	5964.80i	−0.165997	−	0.400753i
$123$			18556.0i			1.22652i
$124$	−166.641	+	69.0250i	−0.0108377	+	0.00448914i
$125$	1135.28	−	2740.82i	0.0726582	−	0.175412i
$126$	2910.75	+	1962.49i	0.183342	+	0.123614i
$127$	−7461.30	+	7461.30i	−0.462601	+	0.462601i	−0.899507	−	0.436906i	$-0.856074\pi$
$127$	−7461.30	+	7461.30i	−0.462601	+	0.462601i	0.436906	+	0.899507i	$0.356074\pi$
$128$	1744.32	−	1744.32i	0.106465	−	0.106465i
$129$	−21355.1	−	8845.58i	−1.28328	−	0.531553i
$130$	219.449	+	90.8988i	0.0129852	+	0.00537863i
$131$	−20681.6	+	8566.61i	−1.20515	+	0.499191i	−0.892660	−	0.450730i	$-0.851164\pi$
$131$	−20681.6	+	8566.61i	−1.20515	+	0.499191i	−0.312492	+	0.949920i	$0.601164\pi$
$132$	−2199.59			−0.126239
$133$	−28238.0	+	5494.64i	−1.59636	+	0.310625i
$134$	14485.1	+	14485.1i	0.806701	+	0.806701i
$135$	−1384.63			−0.0759744
$136$	−15533.8	+	12324.8i	−0.839849	+	0.666347i
$137$	18360.6			0.978239			0.489119	−	0.872217i	$-0.337318\pi$
$137$	18360.6			0.978239			0.489119	+	0.872217i	$0.337318\pi$
$138$	18193.5	−	18193.5i	0.955342	−	0.955342i
$139$	3466.23	+	8368.21i	0.179402	+	0.433115i	0.987841	−	0.155465i	$-0.0496874\pi$
$139$	3466.23	+	8368.21i	0.179402	+	0.433115i	−0.808439	+	0.588579i	$0.799687\pi$
$140$	−172.382	+	848.134i	−0.00879500	+	0.0432722i
$141$	1840.10	+	4442.39i	0.0925557	+	0.223449i
$142$	−9193.45	−	3808.05i	−0.455934	−	0.188854i
$143$	−907.973	−	376.095i	−0.0444018	−	0.0183918i
$144$	−1427.27	+	1427.27i	−0.0688307	+	0.0688307i
$145$	−1160.34	−	1160.34i	−0.0551885	−	0.0551885i
$146$	−4372.86	−	1811.30i	−0.205145	−	0.0849737i
$147$	−17578.2	+	17287.6i	−0.813466	+	0.800017i
$148$	−5190.97	−	12532.1i	−0.236987	−	0.572138i
$149$		−	18544.4i		−	0.835295i	−0.908609	−	0.417647i	$-0.862855\pi$
$149$		−	18544.4i		−	0.835295i	0.908609	−	0.417647i	$-0.137145\pi$
$150$	7133.39	+	17221.5i	0.317040	+	0.765402i
$151$	3404.83	+	3404.83i	0.149328	+	0.149328i	0.777818	−	0.628490i	$-0.216327\pi$
$151$	3404.83	+	3404.83i	0.149328	+	0.149328i	−0.628490	+	0.777818i	$0.716327\pi$
$152$		−	40282.5i		−	1.74353i
$153$	−5533.62	+	4390.45i	−0.236389	+	0.187554i
$154$	−827.145	+	4069.62i	−0.0348771	+	0.171598i
$155$	41.0452	+	41.0452i	0.00170844	+	0.00170844i
$156$	2388.87	−	989.504i	0.0981621	−	0.0406601i
$157$	33203.7			1.34706			0.673530	−	0.739159i	$-0.264777\pi$
$157$	33203.7			1.34706			0.673530	+	0.739159i	$0.264777\pi$
$158$	12420.5	+	29985.9i	0.497538	+	1.20116i
$159$	17094.7	−	41270.1i	0.676186	−	1.63246i
$160$	−1884.95	−	780.772i	−0.0736309	−	0.0304989i
$161$	23126.1	+	34924.8i	0.892175	+	1.34736i
$162$	16463.7	−	16463.7i	0.627333	−	0.627333i
$163$	−3495.39	+	8438.62i	−0.131559	+	0.317611i	−0.975908	−	0.218182i	$-0.929987\pi$
$163$	−3495.39	+	8438.62i	−0.131559	+	0.317611i	0.844349	+	0.535793i	$0.179987\pi$
$164$	5123.18	−	12368.5i	0.190481	−	0.459862i
$165$	270.890	+	653.985i	0.00995003	+	0.0240215i
$166$	1844.34			0.0669305
$167$	9788.69	+	23632.0i	0.350988	+	0.847359i	0.996499	+	0.0836081i	$0.0266444\pi$
$167$	9788.69	+	23632.0i	0.350988	+	0.847359i	−0.645511	+	0.763751i	$0.723356\pi$
$168$	−19060.3	−	28784.7i	−0.675323	−	1.01987i
$169$	−27405.7			−0.959550
$170$	1765.18	+	981.321i	0.0610790	+	0.0339557i
$171$		−	14349.8i		−	0.490744i
$172$	11792.0	+	11792.0i	0.398595	+	0.398595i
$173$	1281.31	+	3093.36i	0.0428117	+	0.103357i	0.943839	−	0.330406i	$-0.107186\pi$
$173$	1281.31	+	3093.36i	0.0428117	+	0.103357i	−0.901027	+	0.433763i	$0.857186\pi$
$174$	20716.1			0.684243
$175$	−29787.8	+	5796.21i	−0.972663	+	0.189264i
$176$	−2206.02	−	913.762i	−0.0712170	−	0.0294990i
$177$	19761.2	−	47707.7i	0.630763	−	1.52280i
$178$	−24207.9	−	24207.9i	−0.764041	−	0.764041i
$179$	42409.2	−	42409.2i	1.32359	−	1.32359i	0.412748	−	0.910845i	$-0.364569\pi$
$179$	42409.2	−	42409.2i	1.32359	−	1.32359i	0.910845	−	0.412748i	$-0.135431\pi$
$180$	−398.853	−	165.210i	−0.0123103	−	0.00509909i
$181$	−18158.4	+	43838.2i	−0.554268	+	1.33812i	0.359977	+	0.932961i	$0.382785\pi$
$181$	−18158.4	+	43838.2i	−0.554268	+	1.33812i	−0.914245	+	0.405161i	$0.867215\pi$
$182$	−932.429	−	4791.92i	−0.0281497	−	0.144666i
$183$			22617.8i			0.675380i
$184$	−54189.1	+	22445.9i	−1.60058	+	0.662980i
$185$	−3086.77	+	3086.77i	−0.0901905	+	0.0901905i
$186$	−732.803			−0.0211817
$187$	−7303.47	−	4060.23i	−0.208856	−	0.116109i
$188$		−	3469.11i		−	0.0981528i
$189$	15711.4	+	23727.2i	0.439836	+	0.664237i
$190$	−3790.48	+	1570.07i	−0.105000	+	0.0434922i
$191$		−	3240.00i		−	0.0888132i	−0.999014	−	0.0444066i	$-0.985860\pi$
$191$		−	3240.00i		−	0.0888132i	0.999014	−	0.0444066i	$-0.0141397\pi$
$192$	36331.3	−	15048.9i	0.985550	−	0.408228i
$193$	−25037.5	−	10370.9i	−0.672167	−	0.278421i	0.0203813	−	0.999792i	$-0.493512\pi$
$193$	−25037.5	−	10370.9i	−0.672167	−	0.278421i	−0.692548	+	0.721372i	$0.743512\pi$
$194$	−28097.6	−	11638.4i	−0.746561	−	0.309236i
$195$	−588.401	−	588.401i	−0.0154741	−	0.0154741i
$196$	16489.7	−	6669.79i	0.429241	−	0.173620i
$197$	3241.04	−	7824.55i	0.0835125	−	0.201617i	−0.876607	−	0.481207i	$-0.840199\pi$
$197$	3241.04	−	7824.55i	0.0835125	−	0.201617i	0.960119	+	0.279590i	$0.0901985\pi$
$198$	−1913.83	−	792.734i	−0.0488172	−	0.0202207i
$199$	5544.33	−	2296.54i	0.140005	−	0.0579919i	−0.311581	−	0.950220i	$-0.600859\pi$
$199$	5544.33	−	2296.54i	0.140005	−	0.0579919i	0.451586	+	0.892228i	$0.350859\pi$
$200$		−	42493.3i		−	1.06233i
$201$	−27462.9	−	66301.4i	−0.679759	−	1.64108i
$202$	−26347.7	+	26347.7i	−0.645714	+	0.645714i
$203$	−6717.35	+	33049.9i	−0.163007	+	0.802008i
$204$	21141.0	−	6033.71i	0.508001	−	0.144985i
$205$	−4308.35			−0.102519
$206$	−33319.8	+	33319.8i	−0.785179	+	0.785179i
$207$	−19303.8	+	7995.89i	−0.450507	+	0.186606i
$208$	2806.91			0.0648788
$209$	15683.2	−	6496.18i	0.359039	−	0.148719i
$210$	−1965.67	+	2915.46i	−0.0445730	+	0.0661101i
$211$	7240.63	−	17480.4i	0.162634	−	0.392633i	−0.821464	−	0.570261i	$-0.806842\pi$
$211$	7240.63	−	17480.4i	0.162634	−	0.392633i	0.984098	+	0.177627i	$0.0568422\pi$
$212$	−22788.9	+	22788.9i	−0.507050	+	0.507050i
$213$	24650.1	+	24650.1i	0.543324	+	0.543324i
$214$	11548.4	−	27880.2i	0.252170	−	0.608791i
$215$	2053.78	−	4958.26i	0.0444300	−	0.107264i
$216$	−36814.9	+	15249.3i	−0.789072	+	0.326844i
$217$	237.616	−	1169.09i	0.00504611	−	0.0248273i
$218$	−8826.57	+	3656.09i	−0.185729	+	0.0769314i
$219$	11724.8	+	11724.8i	0.244465	+	0.244465i
$220$		−	510.704i		−	0.0105517i
$221$	9758.48	+	1124.10i	0.199801	+	0.0230155i
$222$		−	55109.8i		−	1.11821i
$223$	−26198.8	+	26198.8i	−0.526831	+	0.526831i	−0.919626	−	0.392795i	$-0.871508\pi$
$223$	−26198.8	+	26198.8i	−0.526831	+	0.526831i	0.392795	+	0.919626i	$0.371508\pi$
$224$	8009.07	+	41160.1i	0.159619	+	0.820314i
$225$		−	15137.4i		−	0.299011i
$226$	1017.38	+	2456.18i	0.0199190	+	0.0480886i
$227$	20073.4	−	48461.4i	0.389555	−	0.940469i	−0.600479	−	0.799640i	$-0.705023\pi$
$227$	20073.4	−	48461.4i	0.389555	−	0.940469i	0.990034	−	0.140828i	$-0.0449765\pi$
$228$	−17091.4	+	41262.4i	−0.328782	+	0.793751i
$229$	1118.91	+	1118.91i	0.0213366	+	0.0213366i	0.717695	−	0.696358i	$-0.245197\pi$
$229$	1118.91	+	1118.91i	0.0213366	+	0.0213366i	−0.696358	+	0.717695i	$0.745197\pi$
$230$	4224.20	+	4224.20i	0.0798526	+	0.0798526i
$231$	8132.98	−	12062.7i	0.152414	−	0.226059i
$232$	−43630.4	−	18072.3i	−0.810612	−	0.335766i
$233$	−15873.7	−	38322.5i	−0.292392	−	0.705897i	0.707608	−	0.706606i	$-0.249774\pi$
$233$	−15873.7	−	38322.5i	−0.292392	−	0.705897i	−1.00000		0.000708433i	$0.999774\pi$
$234$	2435.14			0.0444725
$235$	−1031.44	+	427.237i	−0.0186771	+	0.00773630i
$236$	−26343.6	+	26343.6i	−0.472989	+	0.472989i
$237$		−	113703.i		−	2.02430i
$238$	−3213.46	−	41383.4i	−0.0567308	−	0.730587i
$239$	40458.3			0.708291			0.354146	−	0.935190i	$-0.384772\pi$
$239$	40458.3			0.708291			0.354146	+	0.935190i	$0.384772\pi$
$240$	−1429.58	−	1429.58i	−0.0248191	−	0.0248191i
$241$	23854.7	+	57590.3i	0.410714	+	0.991551i	0.984947	+	0.172859i	$0.0553004\pi$
$241$	23854.7	+	57590.3i	0.410714	+	0.991551i	−0.574233	+	0.818692i	$0.694700\pi$
$242$			40464.4i			0.690943i
$243$	−31896.8	+	13212.1i	−0.540175	+	0.223748i
$244$	6244.64	−	15075.9i	0.104888	−	0.253223i
$245$	−4013.85	−	4081.33i	−0.0668697	−	0.0679938i
$246$	38459.7	−	38459.7i	0.635529	−	0.635529i
$247$	−14110.4	+	14110.4i	−0.231284	+	0.231284i
$248$	1543.36	+	639.280i	0.0250936	+	0.0103941i
$249$	−5969.33	−	2472.58i	−0.0962779	−	0.0398796i
$250$	−8033.74	+	3327.68i	−0.128540	+	0.0532429i
$251$	−37721.1			−0.598738			−0.299369	−	0.954137i	$-0.596776\pi$
$251$	−37721.1			−0.598738			−0.299369	+	0.954137i	$0.596776\pi$
$252$	1694.71	+	8709.42i	0.0266867	+	0.137148i
$253$	−17477.7	−	17477.7i	−0.273050	−	0.273050i
$254$	30929.1			0.479401
$255$	−4397.55	−	5542.58i	−0.0676287	−	0.0852376i
$256$	−68505.0			−1.04530
$257$	−29427.2	+	29427.2i	−0.445535	+	0.445535i	−0.893867	−	0.448332i	$-0.852018\pi$
$257$	−29427.2	+	29427.2i	−0.445535	+	0.445535i	0.448332	+	0.893867i	$0.352018\pi$
$258$	25927.7	+	62594.9i	0.389515	+	0.940372i
$259$	87920.6	+	17869.7i	1.31066	+	0.266390i
$260$	229.744	+	554.652i	0.00339859	+	0.00820491i
$261$	−15542.4	−	6437.89i	−0.228159	−	0.0945067i
$262$	60620.8	+	25110.0i	0.883119	+	0.365800i
$263$	−29442.6	+	29442.6i	−0.425662	+	0.425662i	−0.887148	−	0.461485i	$-0.847317\pi$
$263$	−29442.6	+	29442.6i	−0.425662	+	0.425662i	0.461485	+	0.887148i	$0.347317\pi$
$264$	14405.0	+	14405.0i	0.206683	+	0.206683i
$265$	9582.16	+	3969.06i	0.136449	+	0.0565192i
$266$	69915.3	+	47138.6i	0.988119	+	0.666213i
$267$	45896.7	+	110804.i	0.643811	+	1.55430i
$268$			51775.5i			0.720866i
$269$	−32163.3	−	77649.1i	−0.444484	−	1.07308i	−0.974358	−	0.225003i	$-0.927761\pi$
$269$	−32163.3	−	77649.1i	−0.444484	−	1.07308i	0.529874	−	0.848077i	$-0.322239\pi$
$270$	2869.83	+	2869.83i	0.0393667	+	0.0393667i
$271$		−	87647.1i		−	1.19344i	−0.802451	−	0.596718i	$-0.796471\pi$
$271$		−	87647.1i		−	1.19344i	0.802451	−	0.596718i	$-0.203529\pi$
$272$	23709.3	+	2731.12i	0.320465	+	0.0369149i
$273$	−3406.33	+	16759.5i	−0.0457048	+	0.224872i
$274$	−38054.7	−	38054.7i	−0.506882	−	0.506882i
$275$	16543.9	−	6852.72i	0.218763	−	0.0906145i
$276$	65030.8			0.853691
$277$	−36880.6	−	89037.6i	−0.480660	−	1.16042i	−0.959296	−	0.282403i	$-0.908868\pi$
$277$	−36880.6	−	89037.6i	−0.480660	−	1.16042i	0.478635	−	0.878014i	$-0.341132\pi$
$278$	10160.0	−	24528.4i	0.131463	−	0.317381i
$279$	549.791	+	227.731i	0.00706300	+	0.00292559i
$280$	6683.28	−	4425.45i	0.0852459	−	0.0564471i
$281$	−77613.5	+	77613.5i	−0.982935	+	0.982935i	−0.999857	−	0.0169220i	$-0.994613\pi$
$281$	−77613.5	+	77613.5i	−0.982935	+	0.982935i	0.0169220	+	0.999857i	$0.494613\pi$
$282$	5393.60	−	13021.3i	0.0678235	−	0.163740i
$283$	−1396.26	+	3370.87i	−0.0174339	+	0.0420891i	−0.932357	−	0.361540i	$-0.882251\pi$
$283$	−1396.26	+	3370.87i	−0.0174339	+	0.0420891i	0.914923	+	0.403629i	$0.132251\pi$
$284$	−9624.75	−	23236.2i	−0.119331	−	0.288090i
$285$	14373.1			0.176954
$286$	1102.39	+	2661.40i	0.0134773	+	0.0325370i
$287$	48886.6	+	73828.3i	0.593508	+	0.896311i
$288$	−20916.5			−0.252176
$289$	81333.5	+	18989.9i	0.973809	+	0.227367i
$290$			4809.90i			0.0571927i
$291$	75337.0	+	75337.0i	0.889656	+	0.889656i
$292$	−4578.01	−	11052.3i	−0.0536922	−	0.129624i
$293$	75144.8			0.875314			0.437657	−	0.899142i	$-0.355808\pi$
$293$	75144.8			0.875314			0.437657	+	0.899142i	$0.355808\pi$
$294$	72263.9	+	602.351i	0.836039	+	0.00696875i
$295$	11076.8	+	4588.17i	0.127283	+	0.0527225i
$296$	−48076.5	+	116067.i	−0.548719	+	1.32472i
$297$	−11874.0	−	11874.0i	−0.134612	−	0.134612i
$298$	−38435.7	+	38435.7i	−0.432815	+	0.432815i
$299$	26844.2	+	11119.2i	0.300267	+	0.124375i
$300$	−18029.5	+	43527.0i	−0.200327	+	0.483633i
$301$	−108269.	+	21067.4i	−1.19501	+	0.232530i
$302$		−	14113.9i		−	0.154751i
$303$	120599.	−	49953.7i	1.31358	−	0.544104i
$304$	−34282.7	+	34282.7i	−0.370961	+	0.370961i
$305$	−5251.44			−0.0564519
$306$	20568.9	+	2369.38i	0.219669	+	0.0253041i
$307$		−	102525.i		−	1.08781i	−0.839148	−	0.543903i	$-0.816946\pi$
$307$		−	102525.i		−	1.08781i	0.839148	−	0.543903i	$-0.183054\pi$
$308$	−8751.48	+	5794.94i	−0.0922529	+	0.0610868i
$309$	152512.	−	63172.4i	1.59730	−	0.661623i
$310$		−	170.143i		−	0.00177048i
$311$	22451.7	−	9299.78i	0.232128	−	0.0961506i	−0.263588	−	0.964635i	$-0.584906\pi$
$311$	22451.7	−	9299.78i	0.232128	−	0.0961506i	0.495716	+	0.868485i	$0.334906\pi$
$312$	−22124.7	−	9164.36i	−0.227284	−	0.0941441i
$313$	−60335.9	−	24991.9i	−0.615867	−	0.255100i	0.0528679	−	0.998602i	$-0.483164\pi$
$313$	−60335.9	−	24991.9i	−0.615867	−	0.255100i	−0.668735	+	0.743501i	$0.733164\pi$
$314$	−68819.1	−	68819.1i	−0.697990	−	0.697990i
$315$	2380.79	−	1576.48i	0.0239938	−	0.0158879i
$316$	−31392.6	+	75788.5i	−0.314379	+	0.758978i
$317$	61763.3	+	25583.2i	0.614627	+	0.254587i	0.668206	−	0.743977i	$-0.267063\pi$
$317$	61763.3	+	25583.2i	0.614627	+	0.254587i	−0.0535783	+	0.998564i	$0.517063\pi$
$318$	−120969.	+	50106.9i	−1.19624	+	0.495500i
$319$		−	19901.0i		−	0.195566i
$320$	3494.08	+	8435.46i	0.0341219	+	0.0823775i
$321$	−74754.2	+	74754.2i	−0.725480	+	0.725480i
$322$	24454.5	−	120318.i	0.235856	−	1.16043i
$323$	−132916.	+	105457.i	−1.27401	+	1.01082i
$324$	58847.8			0.560583
$325$	−14884.8	+	14884.8i	−0.140921	+	0.140921i
$326$	24734.8	−	10245.5i	0.232741	−	0.0964046i
$327$	33469.3			0.313005
$328$	−114551.	+	47448.7i	−1.06476	+	0.441039i
$329$	19024.9	+	12827.0i	0.175764	+	0.118504i
$330$	794.017	−	1916.93i	0.00729125	−	0.0176026i
$331$	69219.8	−	69219.8i	0.631792	−	0.631792i	−0.316725	−	0.948517i	$-0.602583\pi$
$331$	69219.8	−	69219.8i	0.631792	−	0.631792i	0.948517	+	0.316725i	$0.102583\pi$
$332$	3296.19	+	3296.19i	0.0299044	+	0.0299044i
$333$	−17126.3	+	41346.6i	−0.154446	+	0.372864i
$334$	28692.1	−	69268.8i	0.257199	−	0.620933i
$335$	15393.9	−	6376.38i	0.137170	−	0.0568178i
$336$	−8276.05	+	40718.9i	−0.0733068	+	0.360676i
$337$	130684.	−	54131.3i	1.15070	−	0.476638i	0.275935	−	0.961176i	$-0.411013\pi$
$337$	130684.	−	54131.3i	1.15070	−	0.476638i	0.874770	+	0.484539i	$0.161013\pi$
$338$	56801.9	+	56801.9i	0.497198	+	0.497198i
$339$		−	9313.52i		−	0.0810428i
$340$	1400.92	+	4908.54i	0.0121186	+	0.0424614i
$341$			703.969i			0.00605404i
$342$	−29741.9	+	29741.9i	−0.254283	+	0.254283i
$343$	−24393.0	+	115092.i	−0.207337	+	0.978269i
$344$		−	154450.i		−	1.30518i
$345$	−8008.83	−	19335.0i	−0.0672870	−	0.162445i
$346$	3755.71	−	9067.08i	0.0313718	−	0.0757382i
$347$	−2562.32	+	6185.99i	−0.0212801	+	0.0513748i	−0.934162	−	0.356848i	$-0.883851\pi$
$347$	−2562.32	+	6185.99i	−0.0212801	+	0.0513748i	0.912882	+	0.408223i	$0.133851\pi$
$348$	37023.8	+	37023.8i	0.305719	+	0.305719i
$349$	54543.3	+	54543.3i	0.447807	+	0.447807i	0.894625	−	0.446818i	$-0.147443\pi$
$349$	54543.3	+	54543.3i	0.447807	+	0.447807i	−0.446818	+	0.894625i	$0.647443\pi$
$350$	73752.5	+	49725.7i	0.602062	+	0.405924i
$351$	18237.4	+	7554.16i	0.148029	+	0.0613158i
$352$	−9468.92	−	22860.0i	−0.0764214	−	0.184498i
$353$	64539.5			0.517936			0.258968	−	0.965886i	$-0.416618\pi$
$353$	64539.5			0.517936			0.258968	+	0.965886i	$0.416618\pi$
$354$	−139838.	+	57922.8i	−1.11588	+	0.462214i
$355$	−5723.29	+	5723.29i	−0.0454139	+	0.0454139i
$356$		−	86528.3i		−	0.682745i
$357$	−45079.3	+	138248.i	−0.353704	+	1.08473i
$358$	−175798.			−1.37166
$359$	−27416.9	−	27416.9i	−0.212730	−	0.212730i	0.592696	−	0.805426i	$-0.298064\pi$
$359$	−27416.9	−	27416.9i	−0.212730	−	0.212730i	−0.805426	+	0.592696i	$0.798064\pi$
$360$	1530.11	+	3694.01i	0.0118064	+	0.0285032i
$361$		−	214358.i		−	1.64485i
$362$	128496.	−	53224.9i	0.980557	−	0.406160i
$363$	54247.8	−	130966.i	0.411689	−	0.993905i
$364$	6897.67	−	10230.5i	0.0520594	−	0.0772139i
$365$	−2722.28	+	2722.28i	−0.0204337	+	0.0204337i
$366$	46878.4	−	46878.4i	0.349954	−	0.349954i
$367$	45606.9	+	18891.0i	0.338609	+	0.140257i	0.545508	−	0.838106i	$-0.316337\pi$
$367$	45606.9	+	18891.0i	0.338609	+	0.140257i	−0.206898	+	0.978362i	$0.566337\pi$
$368$	65220.8	+	27015.3i	0.481604	+	0.199487i
$369$	−40806.7	+	16902.7i	−0.299694	+	0.124137i
$370$	12795.5			0.0934659
$371$	−40714.2	−	209238.i	−0.295800	−	1.52017i
$372$	−1309.66	−	1309.66i	−0.00946396	−	0.00946396i
$373$	−206826.			−1.48658			−0.743290	−	0.668969i	$-0.766736\pi$
$373$	−206826.			−1.48658			−0.743290	+	0.668969i	$0.766736\pi$
$374$	6722.05	+	23552.8i	0.0480572	+	0.168383i
$375$	30463.0			0.216626
$376$	−22719.0	+	22719.0i	−0.160699	+	0.160699i
$377$	8952.64	+	21613.6i	0.0629895	+	0.152070i
$378$	16613.9	−	81741.6i	0.116275	−	0.572084i
$379$	−7066.06	−	17059.0i	−0.0491925	−	0.118761i	0.897373	−	0.441273i	$-0.145473\pi$
$379$	−7066.06	−	17059.0i	−0.0491925	−	0.118761i	−0.946566	+	0.322512i	$0.895473\pi$
$380$	−9580.35	−	3968.31i	−0.0663459	−	0.0274814i
$381$	−100104.	−	41464.5i	−0.689607	−	0.285645i
$382$	−6715.32	+	6715.32i	−0.0460193	+	0.0460193i
$383$	142050.	+	142050.i	0.968378	+	0.968378i	0.999515	−	0.0311374i	$-0.00991293\pi$
$383$	142050.	+	142050.i	0.968378	+	0.968378i	−0.0311374	+	0.999515i	$0.509913\pi$
$384$	23402.6	+	9693.68i	0.158709	+	0.0657395i
$385$	2800.74	+	1888.33i	0.0188952	+	0.0127396i
$386$	30398.6	+	73388.7i	0.204023	+	0.492555i
$387$		−	55019.8i		−	0.367364i
$388$	−29415.7	−	71015.8i	−0.195396	−	0.471728i
$389$	−192882.	−	192882.i	−1.27466	−	1.27466i	−0.943618	−	0.331038i	$-0.892601\pi$
$389$	−192882.	−	192882.i	−1.27466	−	1.27466i	−0.331038	−	0.943618i	$-0.607399\pi$
$390$			2439.08i			0.0160360i
$391$	215927.	+	120040.i	1.41238	+	0.785188i
$392$	−151670.	−	64310.0i	−0.987022	−	0.418510i
$393$	−162540.	−	162540.i	−1.05239	−	1.05239i
$394$	−22934.9	+	9499.95i	−0.147742	+	0.0611968i
$395$	26399.7			0.169202
$396$	−2003.61	−	4837.15i	−0.0127768	−	0.0308460i
$397$	−53829.2	+	129955.i	−0.341537	+	0.824542i	0.656024	+	0.754740i	$0.272237\pi$
$397$	−53829.2	+	129955.i	−0.341537	+	0.824542i	−0.997561	+	0.0698025i	$0.977763\pi$
$398$	−16251.2	−	6731.48i	−0.102594	−	0.0424956i
$399$	−163090.	−	246298.i	−1.02443	−	1.54709i
$400$	−36164.3	+	36164.3i	−0.226027	+	0.226027i
$401$	21098.2	−	50935.7i	0.131207	−	0.316762i	−0.844599	−	0.535399i	$-0.820161\pi$
$401$	21098.2	−	50935.7i	0.131207	−	0.316762i	0.975806	+	0.218637i	$0.0701611\pi$
$402$	−80497.8	+	194339.i	−0.498118	+	1.20256i
$403$	−316.686	−	764.548i	−0.00194993	−	0.00470755i
$404$	−94177.0			−0.577008
$405$	−7247.37	−	17496.7i	−0.0441845	−	0.106671i
$406$	82423.0	−	54577.8i	0.500030	−	0.331103i
$407$	−52941.5			−0.319600
$408$	−177965.	−	98936.2i	−1.06909	−	0.594340i
$409$		−	266754.i		−	1.59464i	−0.603554	−	0.797322i	$-0.706249\pi$
$409$		−	266754.i		−	1.59464i	0.603554	−	0.797322i	$-0.293751\pi$
$410$	8929.62	+	8929.62i	0.0531209	+	0.0531209i
$411$	72149.4	+	174184.i	0.427119	+	1.03116i
$412$	−119098.			−0.701633
$413$	−47065.0	−	241875.i	−0.275929	−	1.41805i
$414$	56582.2	+	23437.1i	0.330126	+	0.136742i
$415$	574.086	−	1385.97i	0.00333335	−	0.00804742i
$416$	20567.5	+	20567.5i	0.118849	+	0.118849i
$417$	−65767.2	+	65767.2i	−0.378214	+	0.378214i
$418$	−45969.6	−	19041.3i	−0.263099	−	0.108979i
$419$	−56720.2	+	136935.i	−0.323080	+	0.779984i	0.675992	+	0.736909i	$0.263715\pi$
$419$	−56720.2	+	136935.i	−0.323080	+	0.779984i	−0.999072	+	0.0430747i	$0.986285\pi$
$420$	−8723.52	+	1697.45i	−0.0494531	+	0.00962275i
$421$			250881.i			1.41548i	0.706474	+	0.707739i	$0.250285\pi$
$421$			250881.i			1.41548i	−0.706474	+	0.707739i	$0.749715\pi$
$422$	−51237.7	+	21223.3i	−0.287716	+	0.119176i
$423$	−8093.17	+	8093.17i	−0.0452312	+	0.0452312i
$424$	298485.			1.66032
$425$	−140211.	+	111245.i	−0.776255	+	0.615891i
$426$		−	102181.i		−	0.563055i
$427$	59587.8	+	89989.1i	0.326815	+	0.493553i
$428$	70466.5	−	29188.2i	0.384676	−	0.159338i
$429$		−	10091.7i		−	0.0548340i
$430$	−14533.4	+	6019.92i	−0.0786013	+	0.0325577i
$431$	208543.	+	86381.2i	1.12264	+	0.465013i	0.865273	−	0.501301i	$-0.167145\pi$
$431$	208543.	+	86381.2i	1.12264	+	0.465013i	0.257367	+	0.966314i	$0.417145\pi$
$432$	44309.6	+	18353.6i	0.237427	+	0.0983456i
$433$	−40199.8	−	40199.8i	−0.214411	−	0.214411i	0.591727	−	0.806138i	$-0.298446\pi$
$433$	−40199.8	−	40199.8i	−0.214411	−	0.214411i	−0.806138	+	0.591727i	$0.798446\pi$
$434$	−2915.59	+	1930.61i	−0.0154791	+	0.0102498i
$435$	6448.31	−	15567.6i	0.0340775	−	0.0822703i
$436$	−22308.9	−	9240.66i	−0.117356	−	0.0486105i
$437$	−463672.	+	192059.i	−2.42800	+	1.00571i
$438$		−	48602.4i		−	0.253343i
$439$	146080.	+	352668.i	0.757986	+	1.82994i	0.506987	+	0.861954i	$0.330759\pi$
$439$	146080.	+	352668.i	0.757986	+	1.82994i	0.251000	+	0.967987i	$0.419241\pi$
$440$	−3344.56	+	3344.56i	−0.0172756	+	0.0172756i
$441$	−54029.3	−	22909.1i	−0.277813	−	0.117796i
$442$	−17895.9	−	22555.6i	−0.0916028	−	0.115454i
$443$	−254248.			−1.29554			−0.647768	−	0.761838i	$-0.724297\pi$
$443$	−254248.			−1.29554			−0.647768	+	0.761838i	$0.724297\pi$
$444$	98492.0	−	98492.0i	0.499614	−	0.499614i
$445$	−25726.7	+	10656.4i	−0.129916	+	0.0538132i
$446$	108601.			0.545964
$447$	175928.	−	72871.7i	0.880480	−	0.364707i
$448$	104904.	−	155592.i	0.522678	−	0.775230i
$449$	39963.5	−	96480.4i	0.198231	−	0.478571i	−0.793239	−	0.608911i	$-0.791607\pi$
$449$	39963.5	−	96480.4i	0.198231	−	0.478571i	0.991469	+	0.130340i	$0.0416068\pi$
$450$	−31374.3	+	31374.3i	−0.154935	+	0.154935i
$451$	−36946.4	−	36946.4i	−0.181643	−	0.181643i
$452$	−2571.40	+	6207.92i	−0.0125862	+	0.0303857i
$453$	−18921.6	+	45680.7i	−0.0922063	+	0.222606i
$454$	−142047.	+	58838.0i	−0.689162	+	0.285460i
$455$	−3891.23	−	790.887i	−0.0187960	−	0.00382025i
$456$	382154.	−	158294.i	1.83785	−	0.761261i
$457$	5096.68	+	5096.68i	0.0244037	+	0.0244037i	0.719203	−	0.694800i	$-0.244507\pi$
$457$	5096.68	+	5096.68i	0.0244037	+	0.0244037i	−0.694800	+	0.719203i	$0.744507\pi$
$458$		−	4638.18i		−	0.0221114i
$459$	146696.	+	81552.9i	0.696294	+	0.387092i
$460$			15098.9i			0.0713560i
$461$	289339.	−	289339.i	1.36146	−	1.36146i	0.489398	−	0.872061i	$-0.337217\pi$
$461$	289339.	−	289339.i	1.36146	−	1.36146i	0.872061	−	0.489398i	$-0.162783\pi$
$462$	−41858.3	+	8144.93i	−0.196109	+	0.0381596i
$463$		−	121720.i		−	0.567805i	−0.958853	−	0.283902i	$-0.908371\pi$
$463$		−	121720.i		−	0.567805i	0.958853	−	0.283902i	$-0.0916292\pi$
$464$	21751.4	+	52512.5i	0.101030	+	0.243908i
$465$	−228.099	+	550.681i	−0.00105492	+	0.00254679i
$466$	−46528.1	+	112329.i	−0.214261	+	0.517272i
$467$	−107021.	−	107021.i	−0.490719	−	0.490719i	0.417813	−	0.908533i	$-0.362797\pi$
$467$	−107021.	−	107021.i	−0.490719	−	0.490719i	−0.908533	+	0.417813i	$0.862797\pi$
$468$	4352.06	+	4352.06i	0.0198702	+	0.0198702i
$469$	−283941.	−	191440.i	−1.29087	−	0.870334i
$470$	3023.30	+	1252.29i	0.0136863	+	0.00566905i
$471$	130477.	+	314999.i	0.588155	+	1.41993i
$472$	345044.			1.54878
$473$	60132.0	−	24907.5i	0.268772	−	0.111329i
$474$	−235664.	+	235664.i	−1.04891	+	1.04891i
$475$		−	363597.i		−	1.61151i
$476$	68217.0	−	79703.2i	0.301078	−	0.351772i
$477$	106329.			0.467322
$478$	−83855.2	−	83855.2i	−0.367007	−	0.367007i
$479$	59030.5	+	142512.i	0.257280	+	0.621128i	0.998757	−	0.0498500i	$-0.0158743\pi$
$479$	59030.5	+	142512.i	0.257280	+	0.621128i	−0.741477	+	0.670978i	$0.765874\pi$
$480$		−	20950.4i		−	0.0909304i
$481$	57497.2	−	23816.1i	0.248517	−	0.102939i
$482$	69921.5	−	168805.i	0.300965	−	0.726595i
$483$	−240451.	+	356634.i	−1.03070	+	1.52872i
$484$	−72317.7	+	72317.7i	−0.308712	+	0.308712i
$485$	−17491.8	+	17491.8i	−0.0743622	+	0.0743622i
$486$	93494.1	+	38726.5i	0.395833	+	0.163959i
$487$	223989.	+	92779.4i	0.944429	+	0.391195i	0.801134	−	0.598485i	$-0.204230\pi$
$487$	223989.	+	92779.4i	0.944429	+	0.391195i	0.143295	+	0.989680i	$0.454230\pi$
$488$	−139626.	+	57835.2i	−0.586311	+	0.242858i
$489$	−93791.4			−0.392234
$490$	−139.855	+	16778.3i	−0.000582485	+	0.0698806i
$491$	68314.1	+	68314.1i	0.283366	+	0.283366i	0.834450	−	0.551084i	$-0.185786\pi$
$491$	68314.1	+	68314.1i	0.283366	+	0.283366i	−0.551084	+	0.834450i	$0.685786\pi$
$492$	137470.			0.567907
$493$	54590.6	+	191275.i	0.224607	+	0.786981i
$494$	58491.3			0.239683
$495$	−1191.43	+	1191.43i	−0.00486250	+	0.00486250i
$496$	−769.423	−	1857.55i	−0.00312753	−	0.00755053i
$497$	163017.	+	33132.9i	0.659963	+	0.134136i
$498$	7247.48	+	17497.0i	0.0292232	+	0.0705511i
$499$	104309.	+	43206.2i	0.418910	+	0.173518i	0.582174	−	0.813064i	$-0.302202\pi$
$499$	104309.	+	43206.2i	0.418910	+	0.173518i	−0.163264	+	0.986582i	$0.552202\pi$
$500$	−20305.1	−	8410.64i	−0.0812203	−	0.0336425i
$501$	−185728.	+	185728.i	−0.739949	+	0.739949i
$502$	78182.0	+	78182.0i	0.310241	+	0.310241i
$503$	376653.	+	156015.i	1.48869	+	0.616637i	0.971032	−	0.238949i	$-0.0768030\pi$
$503$	376653.	+	156015.i	1.48869	+	0.616637i	0.517661	+	0.855586i	$0.326803\pi$
$504$	45938.8	−	68135.9i	0.180850	−	0.268235i
$505$	11598.3	+	28000.8i	0.0454791	+	0.109796i
$506$			72449.6i			0.282967i
$507$	−107693.	−	259994.i	−0.418959	−	1.01146i
$508$	55276.2	+	55276.2i	0.214196	+	0.214196i
$509$			30427.6i			0.117444i	0.998274	+	0.0587222i	$0.0187026\pi$
$509$			30427.6i			0.117444i	−0.998274	+	0.0587222i	$0.981297\pi$
$510$	−2373.21	+	20602.2i	−0.00912423	+	0.0792089i
$511$	77538.9	+	15759.7i	0.296946	+	0.0603539i
$512$	114077.	+	114077.i	0.435168	+	0.435168i
$513$	−315009.	+	130481.i	−1.19698	+	0.495807i
$514$	121983.			0.461715
$515$	14667.5	+	35410.4i	0.0553020	+	0.133511i
$516$	−65531.5	+	158207.i	−0.246122	+	0.594192i
$517$	−12509.0	−	5181.38i	−0.0467994	−	0.0193849i
$518$	−145190.	−	219265.i	−0.541099	−	0.817163i
$519$	−24311.2	+	24311.2i	−0.0902552	+	0.0902552i
$520$	2127.79	−	5136.95i	0.00786906	−	0.0189976i
$521$	60981.3	−	147222.i	0.224658	−	0.542372i	−0.770854	−	0.637012i	$-0.780170\pi$
$521$	60981.3	−	147222.i	0.224658	−	0.542372i	0.995512	+	0.0946404i	$0.0301701\pi$
$522$	18870.4	+	45557.1i	0.0692532	+	0.167192i
$523$	412804.			1.50918			0.754589	−	0.656197i	$-0.227836\pi$
$523$	412804.			1.50918			0.754589	+	0.656197i	$0.227836\pi$
$524$	63464.8	+	153218.i	0.231137	+	0.558015i
$525$	−172042.	−	259816.i	−0.624187	−	0.942643i
$526$	122048.			0.441121
$527$	−1931.06	−	6766.07i	−0.00695304	−	0.0243621i
$528$		−	24518.9i		−	0.0879494i
$529$	318849.	+	318849.i	1.13939	+	1.13939i
$530$	−11633.9	−	28086.7i	−0.0414165	−	0.0999882i
$531$	122915.			0.435929
$532$	40706.5	+	209198.i	0.143827	+	0.739153i
$533$	56746.4	+	23505.1i	0.199749	+	0.0827386i
$534$	134530.	−	324783.i	0.471776	−	1.13897i
$535$	−17356.5	−	17356.5i	−0.0606395	−	0.0606395i
$536$	339074.	−	339074.i	1.18022	−	1.18022i
$537$	568981.	+	235680.i	1.97310	+	0.817285i
$538$	−94275.4	+	227601.i	−0.325712	+	0.786338i
$539$	578.650	−	69420.6i	0.00199177	−	0.238952i
$540$			10257.9i			0.0351780i
$541$	−181607.	+	75224.3i	−0.620496	+	0.257018i	−0.670709	−	0.741721i	$-0.734010\pi$
$541$	−181607.	+	75224.3i	−0.620496	+	0.257018i	0.0502127	+	0.998739i	$0.484010\pi$
$542$	−181660.	+	181660.i	−0.618388	+	0.618388i
$543$	−487242.			−1.65251
$544$	153716.	+	193740.i	0.519423	+	0.654670i
$545$			7770.95i			0.0261626i
$546$	41796.3	−	27676.1i	0.140201	−	0.0928367i
$547$	−171174.	+	70902.6i	−0.572089	+	0.236967i	−0.649924	−	0.759999i	$-0.725199\pi$
$547$	−171174.	+	70902.6i	−0.572089	+	0.236967i	0.0778351	+	0.996966i	$0.475199\pi$
$548$		−	136022.i		−	0.452948i
$549$	−49739.1	+	20602.6i	−0.165026	+	0.0683562i
$550$	−48492.6	−	20086.3i	−0.160306	−	0.0664010i
$551$	−373325.	−	154636.i	−1.22966	−	0.509341i
$552$	−425882.	−	425882.i	−1.39769	−	1.39769i
$553$	−299556.	−	452387.i	−0.979552	−	1.47931i
$554$	−108102.	+	260982.i	−0.352221	+	0.850337i
$555$	−41413.5	−	17154.0i	−0.134448	−	0.0556904i
$556$	61995.0	−	25679.2i	0.200543	−	0.0830675i
$557$			50990.3i			0.164353i	0.996618	+	0.0821764i	$0.0261871\pi$
$557$			50990.3i			0.164353i	−0.996618	+	0.0821764i	$0.973813\pi$
$558$	−667.512	−	1611.52i	−0.00214383	−	0.00517567i
$559$	−54101.7	+	54101.7i	−0.173136	+	0.173136i
$560$	−9454.17	−	1921.54i	−0.0301472	−	0.00612738i
$561$	9819.19	−	85242.0i	0.0311997	−	0.270849i
$562$	321729.			1.01863
$563$	73255.9	−	73255.9i	0.231114	−	0.231114i	−0.582044	−	0.813157i	$-0.697747\pi$
$563$	73255.9	−	73255.9i	0.231114	−	0.231114i	0.813157	+	0.582044i	$0.197747\pi$
$564$	32911.0	−	13632.2i	0.103462	−	0.0428556i
$565$	2162.43			0.00677399
$566$	9880.52	−	4092.64i	0.0308423	−	0.0127753i
$567$	−217589.	+	322726.i	−0.676818	+	1.00385i
$568$	−89140.4	+	215204.i	−0.276298	+	0.667043i
$569$	−35366.9	+	35366.9i	−0.109238	+	0.109238i	−0.759613	−	0.650375i	$-0.774612\pi$
$569$	−35366.9	+	35366.9i	−0.109238	+	0.109238i	0.650375	+	0.759613i	$0.274612\pi$
$570$	−29790.1	−	29790.1i	−0.0916900	−	0.0916900i
$571$	145521.	−	351319.i	0.446328	−	1.07753i	−0.527359	−	0.849643i	$-0.676818\pi$
$571$	145521.	−	351319.i	0.446328	−	1.07753i	0.973687	−	0.227889i	$-0.0731823\pi$
$572$	−2786.26	+	6726.62i	−0.00851587	+	0.0205591i
$573$	30737.4	−	12731.8i	0.0936176	−	0.0387777i
$574$	51694.8	−	254343.i	0.156900	−	0.771962i
$575$	−489120.	+	202600.i	−1.47938	+	0.612779i
$576$	66188.6	+	66188.6i	0.199498	+	0.199498i
$577$			196256.i			0.589483i	0.955577	+	0.294742i	$0.0952336\pi$
$577$			196256.i			0.589483i	−0.955577	+	0.294742i	$0.904766\pi$
$578$	−129215.	−	207934.i	−0.386775	−	0.622399i
$579$		−	278281.i		−	0.830092i
$580$	−8596.23	+	8596.23i	−0.0255536	+	0.0255536i
$581$	−30264.2	+	5888.91i	−0.0896555	+	0.0174455i
$582$		−	312292.i		−	0.921965i
$583$	48135.4	+	116209.i	0.141621	+	0.341903i
$584$	−42399.6	+	102362.i	−0.124319	+	0.300132i
$585$	757.984	−	1829.94i	0.00221487	−	0.00534717i
$586$	−155748.	−	155748.i	−0.453551	−	0.453551i
$587$	−202120.	−	202120.i	−0.586588	−	0.586588i	0.350118	−	0.936706i	$-0.386142\pi$
$587$	−202120.	−	202120.i	−0.586588	−	0.586588i	−0.936706	+	0.350118i	$0.886142\pi$
$588$	128073.	+	130226.i	0.370428	+	0.376655i
$589$	13205.8	+	5470.03i	0.0380658	+	0.0157674i
$590$	−13448.6	−	32467.8i	−0.0386343	−	0.0932715i
$591$	86966.4			0.248987
$592$	139696.	−	57863.8i	0.398602	−	0.165106i
$593$	−342931.	+	342931.i	−0.975209	+	0.975209i	−0.999700	−	0.0244913i	$-0.992203\pi$
$593$	−342931.	+	342931.i	−0.975209	+	0.975209i	0.0244913	+	0.999700i	$0.492203\pi$
$594$			49220.8i			0.139500i
$595$	−32098.7	−	10466.6i	−0.0906678	−	0.0295645i
$596$	−137384.			−0.386762
$597$	43573.8	+	43573.8i	0.122258	+	0.122258i
$598$	−32592.0	−	78684.1i	−0.0911400	−	0.220031i
$599$			595754.i			1.66040i	0.557463	+	0.830202i	$0.311775\pi$
$599$			595754.i			1.66040i	−0.557463	+	0.830202i	$0.688225\pi$
$600$	403128.	−	166981.i	1.11980	−	0.463837i
$601$	8883.88	−	21447.6i	0.0245954	−	0.0593785i	−0.911105	−	0.412175i	$-0.864769\pi$
$601$	8883.88	−	21447.6i	0.0245954	−	0.0593785i	0.935700	+	0.352797i	$0.114769\pi$
$602$	268068.	+	180738.i	0.739693	+	0.498718i
$603$	120788.	−	120788.i	0.332192	−	0.332192i
$604$	25224.3	−	25224.3i	0.0691425	−	0.0691425i
$605$	30407.8	+	12595.3i	0.0830758	+	0.0344111i
$606$	−353493.	−	146421.i	−0.962576	−	0.398712i
$607$	−613992.	+	254324.i	−1.66642	+	0.690255i	−0.998540	−	0.0540103i	$-0.982800\pi$
$607$	−613992.	+	254324.i	−1.66642	+	0.690255i	−0.667884	+	0.744266i	$0.732800\pi$
$608$	−502409.			−1.35910
$609$	−339937.	+	66146.0i	−0.916565	+	0.178348i
$610$	10884.3	+	10884.3i	0.0292510	+	0.0292510i
$611$	15916.3			0.0426343
$612$	32526.2	+	40995.2i	0.0868420	+	0.109454i
$613$	−358982.			−0.955327			−0.477664	−	0.878543i	$-0.658516\pi$
$613$	−358982.			−0.955327			−0.477664	+	0.878543i	$0.658516\pi$
$614$	−212496.	+	212496.i	−0.563656	+	0.563656i
$615$	−16930.0	−	40872.7i	−0.0447618	−	0.108065i
$616$	95263.4	+	19362.1i	0.251052	+	0.0510260i
$617$	−136643.	−	329886.i	−0.358936	−	0.866549i	−0.995450	−	0.0952836i	$-0.969624\pi$
$617$	−136643.	−	329886.i	−0.358936	−	0.866549i	0.636514	−	0.771265i	$-0.280376\pi$
$618$	−447034.	−	185167.i	−1.17048	−	0.484828i
$619$	−212195.	−	87893.8i	−0.553800	−	0.229391i	0.0881911	−	0.996104i	$-0.471891\pi$
$619$	−212195.	−	87893.8i	−0.553800	−	0.229391i	−0.641991	+	0.766712i	$0.721891\pi$
$620$	304.079	−	304.079i	0.000791048	−	0.000791048i
$621$	351053.	+	351053.i	0.910311	+	0.910311i
$622$	−65809.0	−	27259.0i	−0.170100	−	0.0704578i
$623$	474528.	+	319938.i	1.22260	+	0.824309i
$624$	11030.0	+	26628.8i	0.0283274	+	0.0683884i
$625$		−	379999.i		−	0.972799i
$626$	73255.0	+	176853.i	0.186934	+	0.451299i
$627$	123257.	+	123257.i	0.313527	+	0.313527i
$628$		−	245986.i		−	0.623722i
$629$	508837.	−	145224.i	1.28611	−	0.367060i
$630$	−8201.95	−	1667.03i	−0.0206650	−	0.00420014i
$631$	−42005.5	−	42005.5i	−0.105499	−	0.105499i	0.652387	−	0.757886i	$-0.273768\pi$
$631$	−42005.5	−	42005.5i	−0.105499	−	0.105499i	−0.757886	+	0.652387i	$0.773768\pi$
$632$	701921.	−	290745.i	1.75733	−	0.727911i
$633$	194287.			0.484882
$634$	−74988.0	−	181037.i	−0.186558	−	0.450390i
$635$	9627.28	−	23242.3i	0.0238757	−	0.0576411i
$636$	−305745.	−	126644.i	−0.755867	−	0.313091i
$637$	30600.9	+	75654.7i	0.0754147	+	0.186448i
$638$	−41247.5	+	41247.5i	−0.101334	+	0.101334i
$639$	−31754.5	+	76662.1i	−0.0777684	+	0.187750i
$640$	−2250.69	+	5433.65i	−0.00549485	+	0.0132657i
$641$	−251015.	−	606004.i	−0.610919	−	1.47489i	−0.861993	−	0.506921i	$-0.830784\pi$
$641$	−251015.	−	606004.i	−0.610919	−	1.47489i	0.251074	−	0.967968i	$-0.419216\pi$
$642$	309876.			0.751826
$643$	−3193.92	−	7710.81i	−0.00772507	−	0.0186500i	0.919970	−	0.391989i	$-0.128213\pi$
$643$	−3193.92	−	7710.81i	−0.00772507	−	0.0186500i	−0.927695	+	0.373339i	$0.878213\pi$
$644$	258737.	−	171327.i	0.623859	−	0.413099i
$645$	55108.8			0.132465
$646$	494061.	+	56911.8i	1.18390	+	0.136376i
$647$			311945.i			0.745195i	0.927993	+	0.372598i	$0.121533\pi$
$647$			311945.i			0.745195i	−0.927993	+	0.372598i	$0.878467\pi$
$648$	−385390.	−	385390.i	−0.917804	−	0.917804i
$649$	55643.7	+	134336.i	0.132107	+	0.318935i
$650$	61701.5			0.146039
$651$	12024.7	−	2339.82i	0.0283736	−	0.00552103i
$652$	62516.6	+	25895.2i	0.147062	+	0.0609150i
$653$	84834.6	−	204809.i	0.198951	−	0.480311i	−0.792645	−	0.609684i	$-0.791296\pi$
$653$	84834.6	−	204809.i	0.198951	−	0.480311i	0.991596	+	0.129373i	$0.0412965\pi$
$654$	−69369.6	−	69369.6i	−0.162186	−	0.162186i
$655$	37738.9	−	37738.9i	0.0879643	−	0.0879643i
$656$	137871.	+	57108.2i	0.320381	+	0.132706i
$657$	−15104.0	+	36464.3i	−0.0349914	+	0.0844768i
$658$	−12845.9	−	66017.3i	−0.0296696	−	0.152478i
$659$		−	628081.i		−	1.44625i	−0.690715	−	0.723127i	$-0.742704\pi$
$659$		−	628081.i		−	1.44625i	0.690715	−	0.723127i	$-0.257296\pi$
$660$	4844.98	−	2006.86i	0.0111225	−	0.00460711i
$661$	368537.	−	368537.i	0.843488	−	0.843488i	−0.145823	−	0.989311i	$-0.546583\pi$
$661$	368537.	−	368537.i	0.843488	−	0.843488i	0.989311	+	0.145823i	$0.0465830\pi$
$662$	−286934.			−0.654736
$663$	27682.6	+	96994.5i	0.0629767	+	0.220658i
$664$		−	43172.9i		−	0.0979209i
$665$	57185.8	−	37866.6i	0.129314	−	0.0856274i
$666$	121193.	−	50199.7i	0.273230	−	0.113176i
$667$			588373.i			1.32252i
$668$	175075.	−	72518.5i	0.392348	−	0.162516i
$669$	−351495.	−	145594.i	−0.785356	−	0.325305i
$670$	−45121.9	−	18690.1i	−0.100517	−	0.0416353i
$671$	−45033.9	−	45033.9i	−0.100022	−	0.100022i
$672$	−359007.	+	237723.i	−0.794996	+	0.526420i
$673$	162205.	−	391598.i	0.358125	−	0.864591i	−0.637439	−	0.770501i	$-0.720006\pi$
$673$	162205.	−	391598.i	0.358125	−	0.864591i	0.995564	−	0.0940895i	$-0.0299940\pi$
$674$	−383055.	−	158667.i	−0.843221	−	0.349273i
$675$	−332298.	+	137642.i	−0.729323	+	0.302096i
$676$			203032.i			0.444295i
$677$	−9045.25	−	21837.2i	−0.0197353	−	0.0476452i	0.913705	−	0.406379i	$-0.133209\pi$
$677$	−9045.25	−	21837.2i	−0.0197353	−	0.0476452i	−0.933440	+	0.358734i	$0.883209\pi$
$678$	−19303.5	+	19303.5i	−0.0419930	+	0.0419930i
$679$	498221.	+	101263.i	1.08064	+	0.219639i
$680$	22971.1	−	41320.1i	0.0496781	−	0.0893601i
$681$	538627.			1.16143
$682$	1459.07	−	1459.07i	0.00313695	−	0.00313695i
$683$	−146537.	+	60697.4i	−0.314127	+	0.130115i	−0.534176	−	0.845373i	$-0.679378\pi$
$683$	−146537.	+	60697.4i	−0.314127	+	0.130115i	0.220050	+	0.975489i	$0.429378\pi$
$684$	−106309.			−0.227226
$685$	−40442.3	+	16751.8i	−0.0861896	+	0.0357009i
$686$	289102.	−	187986.i	0.614332	−	0.399465i
$687$	−6218.09	+	15011.8i	−0.0131748	+	0.0318067i
$688$	−131446.	+	131446.i	−0.277696	+	0.277696i
$689$	−104555.	−	104555.i	−0.220245	−	0.220245i
$690$	−23475.0	+	56673.8i	−0.0493070	+	0.119038i
$691$	330490.	−	797873.i	0.692153	−	1.67100i	−0.0482445	−	0.998836i	$-0.515363\pi$
$691$	330490.	−	797873.i	0.692153	−	1.67100i	0.740397	−	0.672169i	$-0.234637\pi$
$692$	22916.8	−	9492.45i	0.0478566	−	0.0198229i
$693$	33935.7	+	6897.37i	0.0706627	+	0.0143621i
$694$	18132.0	−	7510.53i	0.0376467	−	0.0155938i
$695$	−15269.9	−	15269.9i	−0.0316131	−	0.0316131i
$696$		−	484932.i		−	1.00106i
$697$	456451.	+	253756.i	0.939569	+	0.522336i
$698$		−	226097.i		−	0.464070i
$699$	301183.	−	301183.i	0.616419	−	0.616419i
$700$	42940.6	+	220680.i	0.0876339	+	0.450367i
$701$			463348.i			0.942913i	0.881889	+	0.471456i	$0.156272\pi$
$701$			463348.i			0.942913i	−0.881889	+	0.471456i	$0.843728\pi$
$702$	−22142.3	−	53456.3i	−0.0449313	−	0.108474i
$703$	−411369.	+	993134.i	−0.832380	+	2.00954i
$704$	−42375.0	+	102302.i	−0.0854996	+	0.206414i
$705$	−8106.27	−	8106.27i	−0.0163096	−	0.0163096i
$706$	−133767.	−	133767.i	−0.268373	−	0.268373i
$707$	348219.	−	516474.i	0.696648	−	1.03326i
$708$	−353437.	−	146398.i	−0.705092	−	0.292059i
$709$	74421.0	+	179668.i	0.148048	+	0.357420i	0.980455	−	0.196746i	$-0.0630374\pi$
$709$	74421.0	+	179668.i	0.148048	+	0.357420i	−0.832406	+	0.554166i	$0.813037\pi$
$710$	23724.5			0.0470632
$711$	250045.	−	103572.i	0.494629	−	0.204882i
$712$	−566667.	+	566667.i	−1.11781	+	1.11781i
$713$		−	20812.8i		−	0.0409404i
$714$	379971.	−	193105.i	0.745338	−	0.378789i
$715$	2343.11			0.00458332
$716$	−314184.	−	314184.i	−0.612856	−	0.612856i
$717$	158984.	+	383822.i	0.309254	+	0.746606i
$718$			113650.i			0.220456i
$719$	−346901.	+	143691.i	−0.671039	+	0.277954i	−0.692075	−	0.721825i	$-0.743303\pi$
$719$	−346901.	+	143691.i	−0.671039	+	0.277954i	0.0210362	+	0.999779i	$0.493303\pi$
$720$	1841.60	−	4446.02i	0.00355248	−	0.00857644i
$721$	440365.	−	653143.i	0.847114	−	1.25643i
$722$	−444286.	+	444286.i	−0.852291	+	0.852291i
$723$	−452612.	+	452612.i	−0.865863	+	0.865863i
$724$	324771.	+	134524.i	0.619583	+	0.256640i
$725$	−393815.	−	163123.i	−0.749232	−	0.310342i
$726$	−383880.	+	159008.i	−0.728319	+	0.301680i
$727$	−592580.			−1.12119			−0.560593	−	0.828091i	$-0.689427\pi$
$727$	−592580.			−1.12119			−0.560593	+	0.828091i	$0.689427\pi$
$728$	−112171.	+	21826.7i	−0.211650	+	0.0411836i
$729$	204281.	+	204281.i	0.384390	+	0.384390i
$730$	11284.6			0.0211758
$731$	−509624.	+	404342.i	−0.953707	+	0.756683i
$732$	167562.			0.312718
$733$	332520.	−	332520.i	0.618886	−	0.618886i	−0.326360	−	0.945246i	$-0.605822\pi$
$733$	332520.	−	332520.i	0.618886	−	0.618886i	0.945246	+	0.326360i	$0.105822\pi$
$734$	−55372.3	−	133681.i	−0.102778	−	0.248128i
$735$	22946.2	−	54116.8i	0.0424753	−	0.100175i
$736$	279948.	+	675854.i	0.516799	+	1.24766i
$737$	186692.	+	77330.5i	0.343709	+	0.142369i
$738$	119610.	+	49544.2i	0.219612	+	0.0909661i
$739$	−256375.	+	256375.i	−0.469447	+	0.469447i	−0.901736	−	0.432288i	$-0.857706\pi$
$739$	−256375.	+	256375.i	−0.469447	+	0.469447i	0.432288	+	0.901736i	$0.357706\pi$
$740$	22868.0	+	22868.0i	0.0417604	+	0.0417604i
$741$	−189311.	−	78415.3i	−0.344779	−	0.142812i
$742$	−349287.	+	518058.i	−0.634417	+	0.940959i
$743$	−72085.3	−	174029.i	−0.130578	−	0.315242i	0.845046	−	0.534694i	$-0.179573\pi$
$743$	−72085.3	−	174029.i	−0.130578	−	0.315242i	−0.975623	+	0.219452i	$0.929573\pi$
$744$			17153.7i			0.0309894i
$745$	16919.5	+	40847.2i	0.0304841	+	0.0735952i
$746$	428675.	+	428675.i	0.770284	+	0.770284i
$747$		−	15379.5i		−	0.0275614i
$748$	−30079.7	+	54107.0i	−0.0537615	+	0.0967052i
$749$	−100479.	+	494367.i	−0.179107	+	0.881223i
$750$	−63138.5	−	63138.5i	−0.112246	−	0.112246i
$751$	540265.	−	223785.i	0.957915	−	0.396781i	0.151715	−	0.988424i	$-0.451520\pi$
$751$	540265.	−	223785.i	0.957915	−	0.396781i	0.806200	+	0.591643i	$0.201520\pi$
$752$	38670.3			0.0683819
$753$	−148228.	−	357855.i	−0.261422	−	0.631127i
$754$	26241.5	−	63352.5i	0.0461578	−	0.111435i
$755$	−10606.2	−	4393.23i	−0.0186066	−	0.00770709i
$756$	175780.	−	116396.i	0.307558	−	0.203655i
$757$	404237.	−	404237.i	0.705415	−	0.705415i	−0.260153	−	0.965568i	$-0.583773\pi$
$757$	404237.	−	404237.i	0.705415	−	0.705415i	0.965568	+	0.260153i	$0.0837729\pi$
$758$	−20711.6	+	50002.3i	−0.0360476	+	0.0870265i
$759$	97128.3	−	234488.i	0.168602	−	0.407041i
$760$	36752.8	+	88729.1i	0.0636302	+	0.153617i
$761$	349912.			0.604212			0.302106	−	0.953274i	$-0.402310\pi$
$761$	349912.			0.604212			0.302106	+	0.953274i	$0.402310\pi$
$762$	121538.	+	293420.i	0.209316	+	0.505335i
$763$	133164.	−	88176.6i	0.228737	−	0.151462i
$764$	−24003.2			−0.0411227
$765$	8183.01	−	14719.5i	0.0139827	−	0.0251518i
$766$		−	588836.i		−	1.00355i
$767$	−120864.	−	120864.i	−0.205450	−	0.205450i
$768$	−269196.	−	649898.i	−0.456401	−	1.10185i
$769$	−78039.5			−0.131966			−0.0659830	−	0.997821i	$-0.521018\pi$
$769$	−78039.5			−0.131966			−0.0659830	+	0.997821i	$0.521018\pi$
$770$	−1891.10	−	9718.72i	−0.00318958	−	0.0163918i
$771$	−394808.	−	163535.i	−0.664167	−	0.275107i
$772$	−76831.6	+	185488.i	−0.128916	+	0.311230i
$773$	−413397.	−	413397.i	−0.691843	−	0.691843i	0.270794	−	0.962637i	$-0.412714\pi$
$773$	−413397.	−	413397.i	−0.691843	−	0.691843i	−0.962637	+	0.270794i	$0.912714\pi$
$774$	−114036.	+	114036.i	−0.190353	+	0.190353i
$775$	13930.6	+	5770.25i	0.0231935	+	0.00960708i
$776$	−272436.	+	657719.i	−0.452419	+	1.09224i
$777$	175964.	+	904312.i	0.291462	+	1.49788i
$778$			799547.i			1.32095i
$779$	−980165.	+	405998.i	−1.61519	+	0.669035i
$780$	−4359.10	+	4359.10i	−0.00716487	+	0.00716487i
$781$	−98160.6			−0.160929
$782$	−198737.	−	696336.i	−0.324986	−	1.13869i
$783$			399728.i			0.651990i
$784$	74348.2	+	183811.i	0.120959	+	0.299047i
$785$	−73136.9	+	30294.3i	−0.118685	+	0.0491611i
$786$			673773.i			1.09061i
$787$	739521.	−	306320.i	1.19399	−	0.494567i	0.304938	−	0.952372i	$-0.401364\pi$
$787$	739521.	−	306320.i	1.19399	−	0.494567i	0.889053	+	0.457805i	$0.151364\pi$
$788$	−57967.4	−	24010.9i	−0.0933536	−	0.0386683i
$789$	−395016.	−	163621.i	−0.634542	−	0.262836i
$790$	−54716.8	−	54716.8i	−0.0876731	−	0.0876731i
$791$	−24537.0	−	37055.5i	−0.0392164	−	0.0592243i
$792$	−18556.6	+	44799.6i	−0.0295834	+	0.0714207i
$793$	69168.1	+	28650.3i	0.109992	+	0.0455600i
$794$	380918.	−	157781.i	0.604213	−	0.250273i
$795$			106501.i			0.168508i
$796$	−17013.6	−	41074.5i	−0.0268516	−	0.0648256i
$797$	630727.	−	630727.i	0.992944	−	0.992944i	−0.00703105	−	0.999975i	$-0.502238\pi$
$797$	630727.	−	630727.i	0.992944	−	0.992944i	0.999975	+	0.00703105i	$0.00223807\pi$
$798$	−172459.	+	848512.i	−0.270819	+	1.33245i
$799$	134440.	+	15486.5i	0.210589	+	0.0242582i
$800$	−529983.			−0.828099
$801$	−201864.	+	201864.i	−0.314625	+	0.314625i
$802$	−149300.	+	61842.0i	−0.232119	+	0.0961468i
$803$	−46690.1			−0.0724091
$804$	−491187.	+	203456.i	−0.759861	+	0.314745i
$805$	−82803.8	−	55828.3i	−0.127779	−	0.0861514i
$806$	−928.253	+	2241.00i	−0.00142888	+	0.00344963i
$807$	610258.	−	610258.i	0.937058	−	0.937058i
$808$	616758.	+	616758.i	0.944695	+	0.944695i
$809$	−174682.	+	421720.i	−0.266902	+	0.644358i	−0.999334	−	0.0364815i	$-0.988385\pi$
$809$	−174682.	+	421720.i	−0.266902	+	0.644358i	0.732432	+	0.680840i	$0.238385\pi$
$810$	−21243.1	+	51285.4i	−0.0323778	+	0.0781670i
$811$	790222.	−	327321.i	1.20145	−	0.497659i	0.309986	−	0.950741i	$-0.399676\pi$
$811$	790222.	−	327321.i	1.20145	−	0.497659i	0.891469	+	0.453082i	$0.149676\pi$
$812$	244847.	+	49764.8i	0.371349	+	0.0754762i
$813$	831496.	−	344417.i	1.25799	−	0.521078i
$814$	109728.	+	109728.i	0.165603	+	0.165603i
$815$		−	21776.6i		−	0.0327850i
$816$	67257.9	+	235659.i	0.101010	+	0.353918i
$817$		−	1.32156e6i		−	1.97990i
$818$	−552882.	+	552882.i	−0.826277	+	0.826277i
$819$	−39958.8	+	7775.31i	−0.0595723	+	0.0115918i
$820$			31917.9i			0.0474687i
$821$	423165.	+	1.02161e6i	0.627803	+	1.51565i	0.842346	+	0.538937i	$0.181174\pi$
$821$	423165.	+	1.02161e6i	0.627803	+	1.51565i	−0.214543	+	0.976715i	$0.568826\pi$
$822$	211480.	−	510559.i	0.312987	−	0.755618i
$823$	437091.	−	1.05523e6i	0.645315	−	1.55793i	−0.174100	−	0.984728i	$-0.555701\pi$
$823$	437091.	−	1.05523e6i	0.645315	−	1.55793i	0.819415	−	0.573201i	$-0.194299\pi$
$824$	779964.	+	779964.i	1.14874	+	1.14874i
$825$	130022.	+	130022.i	0.191033	+	0.191033i
$826$	−403770.	+	598867.i	−0.591799	+	0.877749i
$827$	314427.	+	130240.i	0.459736	+	0.190429i	0.600517	−	0.799612i	$-0.294961\pi$
$827$	314427.	+	130240.i	0.459736	+	0.190429i	−0.140781	+	0.990041i	$0.544961\pi$
$828$	59236.7	+	143010.i	0.0864033	+	0.208596i
$829$	47339.3			0.0688831			0.0344415	−	0.999407i	$-0.489035\pi$
$829$	47339.3			0.0688831			0.0344415	+	0.999407i	$0.489035\pi$
$830$	−4062.47	+	1682.73i	−0.00589704	+	0.00244263i
$831$	699762.	−	699762.i	1.01332	−	1.01332i
$832$		−	130168.i		−	0.188044i
$833$	184866.	+	668810.i	0.266420	+	0.963857i
$834$	272622.			0.391949
$835$	−43122.6	−	43122.6i	−0.0618489	−	0.0618489i
$836$	−48126.3	−	116187.i	−0.0688604	−	0.166244i
$837$		−	14139.8i		−	0.0201833i
$838$	401375.	−	166255.i	0.571561	−	0.236748i
$839$	−122994.	+	296934.i	−0.174727	+	0.421828i	−0.986846	−	0.161664i	$-0.948314\pi$
$839$	−122994.	+	296934.i	−0.174727	+	0.421828i	0.812119	+	0.583492i	$0.198314\pi$
$840$	68246.1	+	46013.2i	0.0967207	+	0.0652114i
$841$	165147.	−	165147.i	0.233495	−	0.233495i
$842$	519984.	−	519984.i	0.733442	−	0.733442i
$843$	−1.04130e6	−	431320.i	−1.46528	−	0.606938i
$844$	−129502.	−	53641.4i	−0.181799	−	0.0753036i
$845$	60365.8	−	25004.3i	0.0845430	−	0.0350188i
$846$	33548.3			0.0468738
$847$	−129201.	−	663990.i	−0.180095	−	0.925539i
$848$	−254028.	−	254028.i	−0.353256	−	0.353256i
$849$	−37465.7			−0.0519779
$850$	521176.	+	60035.3i	0.721352	+	0.0830939i
$851$	1.56521e6			2.16129
$852$	182617.	−	182617.i	0.251572	−	0.251572i
$853$	263072.	+	635113.i	0.361557	+	0.872877i	0.995073	+	0.0991468i	$0.0316113\pi$
$853$	263072.	+	635113.i	0.361557	+	0.872877i	−0.633515	+	0.773730i	$0.718389\pi$
$854$	63010.7	−	310018.i	0.0863970	−	0.425080i
$855$	13092.5	+	31608.0i	0.0179097	+	0.0432379i
$856$	−652631.	−	270328.i	−0.890676	−	0.368930i
$857$	−561891.	−	232743.i	−0.765051	−	0.316895i	−0.0341853	−	0.999416i	$-0.510884\pi$
$857$	−561891.	−	232743.i	−0.765051	−	0.316895i	−0.730866	+	0.682521i	$0.760884\pi$
$858$	−20916.4	+	20916.4i	−0.0284127	+	0.0284127i
$859$	−340106.	−	340106.i	−0.460923	−	0.460923i	0.438035	−	0.898958i	$-0.355675\pi$
$859$	−340106.	−	340106.i	−0.460923	−	0.460923i	−0.898958	+	0.438035i	$0.855675\pi$
$860$	−36732.7	−	15215.2i	−0.0496657	−	0.0205722i
$861$	−508294.	+	753895.i	−0.685660	+	1.01696i
$862$	−253196.	−	611269.i	−0.340755	−	0.822655i
$863$		−	311447.i		−	0.418179i	−0.977896	−	0.209090i	$-0.932950\pi$
$863$		−	311447.i		−	0.418179i	0.977896	−	0.209090i	$-0.0670500\pi$
$864$	190191.	+	459161.i	0.254778	+	0.615089i
$865$	−5644.62	−	5644.62i	−0.00754401	−	0.00754401i
$866$			166639.i			0.222198i
$867$	139452.	+	846222.i	0.185519	+	1.12576i
$868$	−8661.10	−	1760.35i	−0.0114956	−	0.00233647i
$869$	226391.	+	226391.i	0.299792	+	0.299792i
$870$	−45630.9	+	18900.9i	−0.0602865	+	0.0249715i
$871$	−237545.			−0.313120
$872$	85583.1	+	206616.i	0.112552	+	0.271726i
$873$	−97049.9	+	234299.i	−0.127340	+	0.307427i
$874$	1.35909e6	+	562953.i	1.77920	+	0.736969i
$875$	121203.	−	80256.3i	0.158305	−	0.104825i
$876$	86861.9	−	86861.9i	0.113193	−	0.113193i
$877$	413108.	−	997331.i	0.537112	−	1.29670i	−0.389619	−	0.920976i	$-0.627393\pi$
$877$	413108.	−	997331.i	0.537112	−	1.29670i	0.926731	−	0.375726i	$-0.122607\pi$
$878$	428181.	−	1.03372e6i	0.555442	−	1.34096i
$879$	295288.	+	712889.i	0.382180	+	0.922665i
$880$	5692.83			0.00735128
$881$	84795.5	+	204715.i	0.109250	+	0.263753i	0.969044	−	0.246888i	$-0.0794081\pi$
$881$	84795.5	+	204715.i	0.109250	+	0.263753i	−0.859794	+	0.510641i	$0.829408\pi$
$882$	64500.7	+	159465.i	0.0829139	+	0.204988i
$883$	−121921.			−0.156372			−0.0781859	−	0.996939i	$-0.524913\pi$
$883$	−121921.			−0.156372			−0.0781859	+	0.996939i	$0.524913\pi$
$884$	8327.76	−	72294.6i	0.0106567	−	0.0925127i
$885$			123114.i			0.157189i
$886$	526962.	+	526962.i	0.671292	+	0.671292i
$887$	−349705.	−	844263.i	−0.444483	−	1.07308i	−0.974359	−	0.225001i	$-0.927762\pi$
$887$	−349705.	−	844263.i	−0.444483	−	1.07308i	0.529876	−	0.848075i	$-0.322238\pi$
$888$	−1.29003e6			−1.63597
$889$	−507523.	+	98755.5i	−0.642173	+	0.124956i
$890$	75408.7	+	31235.3i	0.0952010	+	0.0394335i
$891$	87893.5	−	212194.i	0.110714	−	0.267287i
$892$	194091.	+	194091.i	0.243936	+	0.243936i
$893$	−194396.	+	194396.i	−0.243772	+	0.243772i
$894$	−515670.	−	213598.i	−0.645204	−	0.267252i
$895$	−54720.5	+	132107.i	−0.0683131	+	0.164922i
$896$	118650.	−	23087.3i	0.147792	−	0.0287579i
$897$			298361.i			0.370815i
$898$	−282798.	+	117139.i	−0.350690	+	0.145261i
$899$	11849.3	−	11849.3i	0.0146613	−	0.0146613i
$900$	−112144.			−0.138449
$901$	−781417.	−	984880.i	−0.962572	−	1.21320i
$902$			153153.i			0.188240i
$903$	−625317.	−	944350.i	−0.766876	−	1.15813i
$904$	57495.1	−	23815.3i	0.0703549	−	0.0291419i
$905$		−	113129.i		−	0.138126i
$906$	133897.	−	55461.8i	0.163122	−	0.0675675i
$907$	436221.	+	180689.i	0.530264	+	0.219642i	0.631719	−	0.775198i	$-0.282350\pi$
$907$	436221.	+	180689.i	0.530264	+	0.219642i	−0.101455	+	0.994840i	$0.532350\pi$
$908$	−359021.	−	148711.i	−0.435460	−	0.180373i
$909$	219708.	+	219708.i	0.265899	+	0.265899i
$910$	6425.88	+	9704.31i	0.00775978	+	0.0117188i
$911$	−288347.	+	696131.i	−0.347439	+	0.838792i	0.649482	+	0.760377i	$0.274986\pi$
$911$	−288347.	+	696131.i	−0.347439	+	0.838792i	−0.996921	+	0.0784149i	$0.975014\pi$
$912$	−459952.	−	190518.i	−0.552997	−	0.229059i
$913$	16808.5	−	6962.31i	0.0201645	−	0.00835241i
$914$		−	21127.1i		−	0.0252899i
$915$	−20636.0	−	49819.6i	−0.0246481	−	0.0595057i
$916$	8289.33	−	8289.33i	0.00987935	−	0.00987935i
$917$	−1.07492e6	−	218476.i	−1.27831	−	0.259815i
$918$	−135018.	−	473076.i	−0.160216	−	0.561365i
$919$	−901882.			−1.06787			−0.533935	−	0.845525i	$-0.679287\pi$
$919$	−901882.			−1.06787			−0.533935	+	0.845525i	$0.679287\pi$
$920$	98881.8	−	98881.8i	0.116826	−	0.116826i
$921$	972638.	−	402880.i	1.14665	−	0.474959i
$922$	−1.19938e6			−1.41090
$923$	106608.	−	44158.3i	0.125137	−	0.0518333i
$924$	−89365.5	−	60252.3i	−0.104671	−	0.0705716i
$925$	−433947.	+	1.04764e6i	−0.507170	+	1.22442i
$926$	−252280.	+	252280.i	−0.294213	+	0.294213i
$927$	277847.	+	277847.i	0.323330	+	0.323330i
$928$	−225400.	+	544164.i	−0.261733	+	0.631879i
$929$	447628.	−	1.08067e6i	0.518664	−	1.25217i	−0.420060	−	0.907496i	$-0.637991\pi$
$929$	447628.	−	1.08067e6i	0.518664	−	1.25217i	0.938724	−	0.344669i	$-0.112009\pi$
$930$	1614.12	−	668.592i	0.00186626	−	0.000773028i
$931$	−1.29777e6	−	550272.i	−1.49726	−	0.634860i
$932$	−283908.	+	117598.i	−0.326848	+	0.135385i
$933$	176451.	+	176451.i	0.202704	+	0.202704i
$934$			443628.i			0.508540i
$935$	19791.6	+	2279.83i	0.0226390	+	0.00260783i
$936$		−	57002.6i		−	0.0650643i
$937$	−44867.1	+	44867.1i	−0.0511032	+	0.0511032i	−0.732197	−	0.681093i	$-0.761505\pi$
$937$	−44867.1	+	44867.1i	−0.0511032	+	0.0511032i	0.681093	+	0.732197i	$0.261505\pi$
$938$	191721.	+	985289.i	0.217903	+	1.11984i
$939$		−	670606.i		−	0.760564i
$940$	3165.14	+	7641.32i	0.00358209	+	0.00864794i
$941$	193922.	−	468169.i	0.219002	−	0.528717i	−0.775749	−	0.631041i	$-0.782628\pi$
$941$	193922.	−	468169.i	0.219002	−	0.528717i	0.994751	+	0.102324i	$0.0326278\pi$
$942$	382446.	−	923307.i	0.430992	−	1.04051i
$943$	1.09232e6	+	1.09232e6i	1.22836	+	1.22836i
$944$	−293652.	−	293652.i	−0.329526	−	0.329526i
$945$	−56255.1	−	37928.6i	−0.0629939	−	0.0424720i
$946$	−176256.	−	73007.5i	−0.196952	−	0.0815803i
$947$	−242127.	−	584546.i	−0.269987	−	0.651806i	0.729495	−	0.683986i	$-0.239755\pi$
$947$	−242127.	−	584546.i	−0.269987	−	0.651806i	−0.999482	+	0.0321797i	$0.989755\pi$
$948$	−842355.			−0.937299
$949$	50707.9	−	21003.9i	0.0563045	−	0.0233221i
$950$	−753602.	+	753602.i	−0.835016	+	0.835016i
$951$			686471.i			0.759034i
$952$	−968718.	+	75221.9i	−1.06887	+	0.0829985i
$953$	−212699.			−0.234196			−0.117098	−	0.993120i	$-0.537359\pi$
$953$	−212699.			−0.234196			−0.117098	+	0.993120i	$0.537359\pi$
$954$	−220381.	−	220381.i	−0.242147	−	0.242147i
$955$	2956.10	+	7136.65i	0.00324125	+	0.00782506i
$956$		−	299731.i		−	0.327956i
$957$	188798.	−	78202.8i	0.206146	−	0.0853883i
$958$	173027.	−	417724.i	0.188531	−	0.455154i
$959$	745957.	+	502942.i	0.811104	+	0.546865i
$960$	−66295.7	+	66295.7i	−0.0719355	+	0.0719355i
$961$	652609.	−	652609.i	0.706653	−	0.706653i
$962$	−168533.	−	69808.5i	−0.182110	−	0.0754324i
$963$	−232487.	−	96299.1i	−0.250695	−	0.103841i
$964$	426651.	−	176725.i	0.459112	−	0.190171i
$965$	64611.7			0.0693835
$966$	1.23754e6	−	240804.i	1.32619	−	0.258054i
$967$	−952759.	−	952759.i	−1.01890	−	1.01890i	−0.999818	−	0.0190782i	$-0.993927\pi$
$967$	−952759.	−	952759.i	−1.01890	−	1.01890i	−0.0190782	−	0.999818i	$-0.506073\pi$
$968$	947206.			1.01087
$969$	−1.52276e6	−	846553.i	−1.62176	−	0.901584i
$970$	72508.3			0.0770627
$971$	−946347.	+	946347.i	−1.00372	+	1.00372i	−0.00372524	+	0.999993i	$0.501186\pi$
$971$	−946347.	+	946347.i	−1.00372	+	1.00372i	−0.999993	+	0.00372524i	$0.998814\pi$
$972$	97880.3	+	236304.i	0.103601	+	0.250114i
$973$	−88399.7	+	434934.i	−0.0933738	+	0.459407i
$974$	−271950.	−	656545.i	−0.286662	−	0.692064i
$975$	−199701.	−	82719.1i	−0.210074	−	0.0870154i
$976$	168051.	+	69609.1i	0.176418	+	0.0730745i
$977$	−39530.1	+	39530.1i	−0.0414132	+	0.0414132i	−0.727510	−	0.686097i	$-0.759323\pi$
$977$	−39530.1	+	39530.1i	−0.0414132	+	0.0414132i	0.686097	+	0.727510i	$0.259323\pi$
$978$	194395.	+	194395.i	0.203239	+	0.203239i
$979$	−312004.	−	129236.i	−0.325533	−	0.134840i
$980$	−30236.1	+	29736.2i	−0.0314828	+	0.0309623i
$981$	30487.3	+	73602.8i	0.0316797	+	0.0764815i
$982$		−	283180.i		−	0.293657i
$983$	−335633.	−	810290.i	−0.347342	−	0.838559i	−0.996932	−	0.0782736i	$-0.975059\pi$
$983$	−335633.	−	810290.i	−0.347342	−	0.838559i	0.649589	−	0.760285i	$-0.274941\pi$
$984$	−900279.	−	900279.i	−0.929795	−	0.929795i
$985$			20192.0i			0.0208116i
$986$	283296.	−	509589.i	0.291398	−	0.524163i
$987$	−46928.3	+	230891.i	−0.0481727	+	0.237014i
$988$	104535.	+	104535.i	0.107090	+	0.107090i
$989$	−1.77780e6	+	736389.i	−1.81757	+	0.752860i
$990$	4938.81			0.00503909
$991$	−483850.	−	1.16812e6i	−0.492678	−	1.18943i	−0.953352	−	0.301861i	$-0.902392\pi$
$991$	−483850.	−	1.16812e6i	−0.492678	−	1.18943i	0.460674	−	0.887570i	$-0.347608\pi$
$992$	7973.19	−	19249.0i	0.00810231	−	0.0195607i
$993$	928683.	+	384673.i	0.941823	+	0.390116i
$994$	−269201.	−	406546.i	−0.272461	−	0.411469i
$995$	−10117.0	+	10117.0i	−0.0102190	+	0.0102190i
$996$	−18317.8	+	44223.1i	−0.0184652	+	0.0445790i
$997$	−73072.3	+	176412.i	−0.0735127	+	0.177475i	−0.956364	−	0.292176i	$-0.905621\pi$
$997$	−73072.3	+	176412.i	−0.0735127	+	0.177475i	0.882852	+	0.469652i	$0.155621\pi$
$998$	−126644.	−	305745.i	−0.127152	−	0.306972i
$999$	1.06337e6			1.06550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.l.a.104.16	yes	184
7.6	odd	2	inner	119.5.l.a.104.15	✓	184
17.9	even	8	inner	119.5.l.a.111.15	yes	184
119.111	odd	8	inner	119.5.l.a.111.16	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.l.a.104.15	✓	184	7.6	odd	2	inner
119.5.l.a.104.16	yes	184	1.1	even	1	trivial
119.5.l.a.111.15	yes	184	17.9	even	8	inner
119.5.l.a.111.16	yes	184	119.111	odd	8	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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07263 - 2.07263i) q^{2} +(3.92959 + 9.48686i) q^{3} -7.40839i q^{4} +(-2.20267 + 0.912377i) q^{5} +(11.5182 - 27.8074i) q^{6} +(40.6282 + 27.3925i) q^{7} +(-48.5170 + 48.5170i) q^{8} +(-17.2832 + 17.2832i) q^{9} +(6.45635 + 2.67431i) q^{10} +(-26.7132 - 11.0650i) q^{11} +(70.2824 - 29.1119i) q^{12} +33.9896 q^{13} +(-27.4327 - 140.982i) q^{14} +(-17.3112 - 17.3112i) q^{15} +82.5815 q^{16} +(287.101 + 33.0718i) q^{17} +71.6435 q^{18} +(-415.138 + 415.138i) q^{19} +(6.75925 + 16.3183i) q^{20} +(-100.217 + 493.075i) q^{21} +(32.4331 + 78.3003i) q^{22} +(789.775 + 327.135i) q^{23} +(-650.925 - 269.622i) q^{24} +(-437.922 + 437.922i) q^{25} +(-70.4480 - 70.4480i) q^{26} +(536.556 + 222.249i) q^{27} +(202.934 - 300.990i) q^{28} +(263.393 + 635.887i) q^{29} +71.7594i q^{30} +(-9.31714 - 22.4936i) q^{31} +(605.111 + 605.111i) q^{32} -296.905i q^{33} +(-526.510 - 663.601i) q^{34} +(-114.483 - 23.2685i) q^{35} +(128.041 + 128.041i) q^{36} +(1691.61 - 700.688i) q^{37} +1720.86 q^{38} +(133.565 + 322.455i) q^{39} +(62.6013 - 151.133i) q^{40} +(1669.52 + 691.538i) q^{41} +(1229.68 - 814.251i) q^{42} +(-1591.71 + 1591.71i) q^{43} +(-81.9737 + 197.902i) q^{44} +(22.3004 - 53.8380i) q^{45} +(-958.881 - 2314.94i) q^{46} +468.268 q^{47} +(324.511 + 783.439i) q^{48} +(900.302 + 2225.82i) q^{49} +1815.30 q^{50} +(814.443 + 2853.65i) q^{51} -251.809i q^{52} +(-3076.09 - 3076.09i) q^{53} +(-651.444 - 1572.72i) q^{54} +68.9359 q^{55} +(-3300.16 + 642.156i) q^{56} +(-5569.68 - 2307.04i) q^{57} +(772.043 - 1863.88i) q^{58} +(-3555.91 - 3555.91i) q^{59} +(-128.248 + 128.248i) q^{60} +(2034.97 + 842.914i) q^{61} +(-27.3099 + 65.9319i) q^{62} +(-1175.62 + 228.755i) q^{63} -3829.65i q^{64} +(-74.8681 + 31.0114i) q^{65} +(-615.376 + 615.376i) q^{66} -6988.76 q^{67} +(245.009 - 2126.96i) q^{68} +8777.99i q^{69} +(189.054 + 285.508i) q^{70} +(3136.47 - 1299.17i) q^{71} -1677.06i q^{72} +(1491.86 - 617.950i) q^{73} +(-4958.35 - 2053.82i) q^{74} +(-5875.36 - 2433.65i) q^{75} +(3075.51 + 3075.51i) q^{76} +(-782.213 - 1181.29i) q^{77} +(391.499 - 945.162i) q^{78} +(-10230.1 - 4237.44i) q^{79} +(-181.900 + 75.3454i) q^{80} +7943.40i q^{81} +(-2027.00 - 4893.60i) q^{82} +(-444.926 + 444.926i) q^{83} +(3652.89 + 742.445i) q^{84} +(-662.564 + 189.098i) q^{85} +6598.07 q^{86} +(-4997.55 + 4997.55i) q^{87} +(1832.88 - 759.206i) q^{88} +11679.8 q^{89} +(-157.807 + 65.3658i) q^{90} +(1380.94 + 931.061i) q^{91} +(2423.55 - 5850.96i) q^{92} +(176.781 - 176.781i) q^{93} +(-970.548 - 970.548i) q^{94} +(535.651 - 1293.18i) q^{95} +(-3362.77 + 8118.44i) q^{96} +(9585.87 - 3970.60i) q^{97} +(2747.30 - 6479.29i) q^{98} +(652.929 - 270.452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 8 q^{2} - 4 q^{7} + 120 q^{8} - 8 q^{9} - 128 q^{11} - 52 q^{14} - 504 q^{15} - 10256 q^{16} - 2064 q^{18} + 2824 q^{22} - 2672 q^{23} + 2224 q^{25} - 780 q^{28} - 8 q^{29} - 5888 q^{32} + 2104 q^{35}+ \cdots + 108752 q^{99}+O(q^{100}) \) 184 * q - 8 * q^2 - 4 * q^7 + 120 * q^8 - 8 * q^9 - 128 * q^11 - 52 * q^14 - 504 * q^15 - 10256 * q^16 - 2064 * q^18 + 2824 * q^22 - 2672 * q^23 + 2224 * q^25 - 780 * q^28 - 8 * q^29 - 5888 * q^32 + 2104 * q^35 + 1912 * q^36 - 8712 * q^37 - 4440 * q^39 + 17296 * q^42 - 2632 * q^43 + 3672 * q^44 + 3576 * q^46 + 4432 * q^49 + 2360 * q^50 + 22160 * q^51 - 16184 * q^53 - 22308 * q^56 - 8 * q^57 + 1528 * q^58 + 18040 * q^60 + 33740 * q^63 - 18472 * q^65 + 7616 * q^67 - 45296 * q^70 + 25528 * q^71 + 7984 * q^74 - 12184 * q^77 - 23704 * q^78 + 24728 * q^79 + 6800 * q^84 - 30656 * q^85 + 95480 * q^86 + 108000 * q^88 - 27544 * q^91 - 22848 * q^92 + 114464 * q^93 + 61936 * q^95 + 108752 * q^99

Introduction

L-functions

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