LMFDB - Embedded newform 92.5.g.a.3.45

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,5,Mod(3,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.g (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			3.45
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.45

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.99761 + 0.138197i) q^{2} +(8.69828 + 3.97237i) q^{3} +(15.9618 + 1.10492i) q^{4} +(17.8389 - 20.5871i) q^{5} +(34.2234 + 17.0821i) q^{6} +(0.355839 + 0.553696i) q^{7} +(63.6564 + 6.62289i) q^{8} +(6.83659 + 7.88985i) q^{9} +(74.1579 - 79.8341i) q^{10} +(-177.855 - 25.5717i) q^{11} +(134.451 + 73.0171i) q^{12} +(85.7828 + 55.1293i) q^{13} +(1.34599 + 2.26264i) q^{14} +(236.947 - 108.210i) q^{15} +(253.558 + 35.2729i) q^{16} +(-456.893 - 134.156i) q^{17} +(26.2397 + 32.4854i) q^{18} +(173.008 + 589.211i) q^{19} +(307.487 - 308.897i) q^{20} +(0.895700 + 6.22973i) q^{21} +(-707.461 - 126.805i) q^{22} +(164.776 + 502.683i) q^{23} +(527.392 + 310.475i) q^{24} +(-16.6587 - 115.864i) q^{25} +(335.308 + 232.240i) q^{26} +(-190.092 - 647.395i) q^{27} +(5.06804 + 9.23116i) q^{28} +(-144.384 - 42.3950i) q^{29} +(962.177 - 399.837i) q^{30} +(449.764 - 205.400i) q^{31} +(1008.75 + 176.048i) q^{32} +(-1445.45 - 928.935i) q^{33} +(-1807.94 - 599.445i) q^{34} +(17.7468 + 2.55160i) q^{35} +(100.407 + 133.490i) q^{36} +(-900.755 - 1039.53i) q^{37} +(610.192 + 2379.35i) q^{38} +(527.169 + 820.291i) q^{39} +(1271.90 - 1192.36i) q^{40} +(-808.382 + 932.923i) q^{41} +(2.71973 + 25.0278i) q^{42} +(1101.78 + 503.166i) q^{43} +(-2810.63 - 604.684i) q^{44} +284.386 q^{45} +(589.241 + 2032.30i) q^{46} -1008.92i q^{47} +(2065.40 + 1314.04i) q^{48} +(997.231 - 2183.63i) q^{49} +(-50.5830 - 465.481i) q^{50} +(-3441.27 - 2981.88i) q^{51} +(1308.34 + 974.745i) q^{52} +(-3691.19 + 2372.18i) q^{53} +(-670.447 - 2614.30i) q^{54} +(-3699.18 + 3205.35i) q^{55} +(18.9844 + 37.6030i) q^{56} +(-835.693 + 5812.37i) q^{57} +(-571.332 - 189.432i) q^{58} +(725.160 - 1128.37i) q^{59} +(3901.67 - 1465.42i) q^{60} +(-2143.38 - 4693.34i) q^{61} +(1826.37 - 758.955i) q^{62} +(-1.93585 + 6.59291i) q^{63} +(4008.27 + 843.179i) q^{64} +(2665.22 - 782.580i) q^{65} +(-5649.98 - 3913.28i) q^{66} +(-1583.80 + 227.717i) q^{67} +(-7144.61 - 2646.20i) q^{68} +(-563.576 + 5027.02i) q^{69} +(70.5921 + 12.6529i) q^{70} +(-857.416 + 123.278i) q^{71} +(382.939 + 547.517i) q^{72} +(6655.10 - 1954.11i) q^{73} +(-3457.21 - 4280.11i) q^{74} +(315.352 - 1073.99i) q^{75} +(2110.49 + 9596.03i) q^{76} +(-49.1288 - 107.577i) q^{77} +(1994.06 + 3352.06i) q^{78} +(-332.381 + 517.194i) q^{79} +(5249.36 - 4590.81i) q^{80} +(1038.56 - 7223.35i) q^{81} +(-3360.53 + 3617.75i) q^{82} +(-2573.69 + 2230.12i) q^{83} +(7.41366 + 100.427i) q^{84} +(-10912.3 + 7012.94i) q^{85} +(4334.96 + 2163.73i) q^{86} +(-1087.48 - 942.310i) q^{87} +(-11152.2 - 2805.71i) q^{88} +(1203.01 - 2634.23i) q^{89} +(1136.87 + 39.3013i) q^{90} +67.1148i q^{91} +(2074.70 + 8205.79i) q^{92} +4728.10 q^{93} +(139.430 - 4033.27i) q^{94} +(15216.4 + 6949.11i) q^{95} +(8075.09 + 5538.46i) q^{96} +(11078.7 - 12785.5i) q^{97} +(4288.32 - 8591.50i) q^{98} +(-1014.16 - 1578.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) $ 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.99761	+	0.138197i	0.999403	+	0.0345492i
$2$	3.99761	+	0.138197i	0.999403	+	0.0345492i
$3$	8.69828	+	3.97237i	0.966475	+	0.441374i	0.835185	−	0.549969i	$-0.185361\pi$
$3$	8.69828	+	3.97237i	0.966475	+	0.441374i	0.131291	+	0.991344i	$0.458088\pi$
$4$	15.9618	+	1.10492i	0.997613	+	0.0690572i
$5$	17.8389	−	20.5871i	0.713554	−	0.823486i	−0.276962	−	0.960881i	$-0.589328\pi$
$5$	17.8389	−	20.5871i	0.713554	−	0.823486i	0.990516	+	0.137395i	$0.0438731\pi$
$6$	34.2234	+	17.0821i	0.950649	+	0.474502i
$7$	0.355839	+	0.553696i	0.00726202	+	0.0112999i	0.844866	−	0.534979i	$-0.179680\pi$
$7$	0.355839	+	0.553696i	0.00726202	+	0.0112999i	−0.837604	+	0.546279i	$0.816044\pi$
$8$	63.6564	+	6.62289i	0.994631	+	0.103483i
$9$	6.83659	+	7.88985i	0.0844024	+	0.0974055i
$10$	74.1579	−	79.8341i	0.741579	−	0.798341i
$11$	−177.855	−	25.5717i	−1.46987	−	0.211336i	−0.639608	−	0.768702i	$-0.720903\pi$
$11$	−177.855	−	25.5717i	−1.46987	−	0.211336i	−0.830267	+	0.557366i	$0.811812\pi$
$12$	134.451	+	73.0171i	0.933688	+	0.507063i
$13$	85.7828	+	55.1293i	0.507591	+	0.326209i	0.769246	−	0.638953i	$-0.220632\pi$
$13$	85.7828	+	55.1293i	0.507591	+	0.326209i	−0.261655	+	0.965161i	$0.584268\pi$
$14$	1.34599	+	2.26264i	0.00686728	+	0.0115441i
$15$	236.947	−	108.210i	1.05310	−	0.480934i
$16$	253.558	+	35.2729i	0.990462	+	0.137785i
$17$	−456.893	−	134.156i	−1.58095	−	0.464208i	−0.630783	−	0.775960i	$-0.717266\pi$
$17$	−456.893	−	134.156i	−1.58095	−	0.464208i	−0.950164	+	0.311752i	$0.899084\pi$
$18$	26.2397	+	32.4854i	0.0809867	+	0.100263i
$19$	173.008	+	589.211i	0.479247	+	1.63216i	0.744239	+	0.667913i	$0.232812\pi$
$19$	173.008	+	589.211i	0.479247	+	1.63216i	−0.264993	+	0.964250i	$0.585370\pi$
$20$	307.487	−	308.897i	0.768718	−	0.772244i
$21$	0.895700	+	6.22973i	0.00203107	+	0.0141264i
$22$	−707.461	−	126.805i	−1.46170	−	0.261993i
$23$	164.776	+	502.683i	0.311486	+	0.950251i
$23$	164.776	+	502.683i	0.311486	+	0.950251i
$24$	527.392	+	310.475i	0.915612	+	0.539018i
$25$	−16.6587	−	115.864i	−0.0266539	−	0.185382i
$26$	335.308	+	232.240i	0.496017	+	0.343551i
$27$	−190.092	−	647.395i	−0.260758	−	0.888059i
$28$	5.06804	+	9.23116i	0.00646434	+	0.0117744i
$29$	−144.384	−	42.3950i	−0.171681	−	0.0504102i	0.194762	−	0.980851i	$-0.437607\pi$
$29$	−144.384	−	42.3950i	−0.171681	−	0.0504102i	−0.366443	+	0.930440i	$0.619425\pi$
$30$	962.177	−	399.837i	1.06909	−	0.444263i
$31$	449.764	−	205.400i	0.468017	−	0.213736i	−0.167425	−	0.985885i	$-0.553545\pi$
$31$	449.764	−	205.400i	0.468017	−	0.213736i	0.635442	+	0.772149i	$0.280818\pi$
$32$	1008.75	+	176.048i	0.985111	+	0.171922i
$33$	−1445.45	−	928.935i	−1.32732	−	0.853016i
$34$	−1807.94	−	599.445i	−1.56396	−	0.518551i
$35$	17.7468	+	2.55160i	0.0144872	+	0.00208294i
$36$	100.407	+	133.490i	0.0774743	+	0.103002i
$37$	−900.755	−	1039.53i	−0.657966	−	0.759333i	0.324478	−	0.945893i	$-0.394811\pi$
$37$	−900.755	−	1039.53i	−0.657966	−	0.759333i	−0.982443	+	0.186560i	$0.940266\pi$
$38$	610.192	+	2379.35i	0.422570	+	1.64775i
$39$	527.169	+	820.291i	0.346594	+	0.539310i
$40$	1271.90	−	1192.36i	0.794940	−	0.745224i
$41$	−808.382	+	932.923i	−0.480894	+	0.554981i	−0.943409	−	0.331630i	$-0.892401\pi$
$41$	−808.382	+	932.923i	−0.480894	+	0.554981i	0.462516	+	0.886611i	$0.346947\pi$
$42$	2.71973	+	25.0278i	0.00154180	+	0.0141881i
$43$	1101.78	+	503.166i	0.595879	+	0.272129i	0.690439	−	0.723390i	$-0.257417\pi$
$43$	1101.78	+	503.166i	0.595879	+	0.272129i	−0.0945602	+	0.995519i	$0.530144\pi$
$44$	−2810.63	−	604.684i	−1.45177	−	0.312337i
$45$	284.386			0.140438
$46$	589.241	+	2032.30i	0.278469	+	0.960445i
$47$		−	1008.92i		−	0.456732i	−0.973575	−	0.228366i	$-0.926662\pi$
$47$		−	1008.92i		−	0.456732i	0.973575	−	0.228366i	$-0.0733383\pi$
$48$	2065.40	+	1314.04i	0.896443	+	0.570330i
$49$	997.231	−	2183.63i	0.415340	−	0.909468i
$50$	−50.5830	−	465.481i	−0.0202332	−	0.186192i
$51$	−3441.27	−	2981.88i	−1.32306	−	1.14643i
$52$	1308.34	+	974.745i	0.483852	+	0.360483i
$53$	−3691.19	+	2372.18i	−1.31406	+	0.844494i	−0.994668	−	0.103129i	$-0.967114\pi$
$53$	−3691.19	+	2372.18i	−1.31406	+	0.844494i	−0.319390	+	0.947623i	$0.603478\pi$
$54$	−670.447	−	2614.30i	−0.229920	−	0.896538i
$55$	−3699.18	+	3205.35i	−1.22287	+	1.05962i
$56$	18.9844	+	37.6030i	0.00605369	+	0.0119908i
$57$	−835.693	+	5812.37i	−0.257216	+	1.78897i
$58$	−571.332	−	189.432i	−0.169837	−	0.0563116i
$59$	725.160	−	1128.37i	0.208319	−	0.324151i	−0.721333	−	0.692588i	$-0.756470\pi$
$59$	725.160	−	1128.37i	0.208319	−	0.324151i	0.929653	+	0.368437i	$0.120107\pi$
$60$	3901.67	−	1465.42i	1.08380	−	0.407062i
$61$	−2143.38	−	4693.34i	−0.576022	−	1.26131i	−0.943529	−	0.331291i	$-0.892516\pi$
$61$	−2143.38	−	4693.34i	−0.576022	−	1.26131i	0.367507	−	0.930021i	$-0.380212\pi$
$62$	1826.37	−	758.955i	0.475122	−	0.197439i
$63$	−1.93585	+	6.59291i	−0.000487743	+	0.00166110i
$64$	4008.27	+	843.179i	0.978583	+	0.205854i
$65$	2665.22	−	782.580i	0.630822	−	0.185226i
$66$	−5649.98	−	3913.28i	−1.29706	−	0.898365i
$67$	−1583.80	+	227.717i	−0.352819	+	0.0507277i	−0.316446	−	0.948611i	$-0.602490\pi$
$67$	−1583.80	+	227.717i	−0.352819	+	0.0507277i	−0.0363732	+	0.999338i	$0.511580\pi$
$68$	−7144.61	−	2646.20i	−1.54512	−	0.572275i
$69$	−563.576	+	5027.02i	−0.118373	+	1.05588i
$70$	70.5921	+	12.6529i	0.0144066	+	0.00258222i
$71$	−857.416	+	123.278i	−0.170088	+	0.0244550i	−0.226833	−	0.973934i	$-0.572837\pi$
$71$	−857.416	+	123.278i	−0.170088	+	0.0244550i	0.0567443	+	0.998389i	$0.481928\pi$
$72$	382.939	+	547.517i	0.0738695	+	0.105617i
$73$	6655.10	−	1954.11i	1.24885	−	0.366694i	0.410514	−	0.911854i	$-0.365349\pi$
$73$	6655.10	−	1954.11i	1.24885	−	0.366694i	0.838332	+	0.545160i	$0.183531\pi$
$74$	−3457.21	−	4280.11i	−0.631338	−	0.781612i
$75$	315.352	−	1073.99i	0.0560625	−	0.190931i
$76$	2110.49	+	9596.03i	0.365390	+	1.66136i
$77$	−49.1288	−	107.577i	−0.00828618	−	0.0181442i
$78$	1994.06	+	3352.06i	0.327754	+	0.550963i
$79$	−332.381	+	517.194i	−0.0532576	+	0.0828704i	−0.866861	−	0.498549i	$-0.833866\pi$
$79$	−332.381	+	517.194i	−0.0532576	+	0.0828704i	0.813604	+	0.581420i	$0.197503\pi$
$80$	5249.36	−	4590.81i	0.820212	−	0.717315i
$81$	1038.56	−	7223.35i	0.158293	−	1.10095i
$82$	−3360.53	+	3617.75i	−0.499781	+	0.538035i
$83$	−2573.69	+	2230.12i	−0.373594	+	0.323721i	−0.821339	−	0.570440i	$-0.806773\pi$
$83$	−2573.69	+	2230.12i	−0.373594	+	0.323721i	0.447745	+	0.894161i	$0.352227\pi$
$84$	7.41366	+	100.427i	0.00105069	+	0.0142329i
$85$	−10912.3	+	7012.94i	−1.51036	+	0.970649i
$86$	4334.96	+	2163.73i	0.586122	+	0.292554i
$87$	−1087.48	−	942.310i	−0.143676	−	0.124496i
$88$	−11152.2	−	2805.71i	−1.44011	−	0.362308i
$89$	1203.01	−	2634.23i	0.151876	−	0.332563i	−0.818367	−	0.574697i	$-0.805120\pi$
$89$	1203.01	−	2634.23i	0.151876	−	0.332563i	0.970243	+	0.242134i	$0.0778474\pi$
$90$	1136.87	+	39.3013i	0.140354	+	0.00485202i
$91$			67.1148i			0.00810467i
$92$	2074.70	+	8205.79i	0.245120	+	0.969493i
$93$	4728.10			0.546664
$94$	139.430	−	4033.27i	0.0157797	−	0.456459i
$95$	15216.4	+	6949.11i	1.68603	+	0.769985i
$96$	8075.09	+	5538.46i	0.876203	+	0.600961i
$97$	11078.7	−	12785.5i	1.17746	−	1.35886i	0.257772	−	0.966206i	$-0.417012\pi$
$97$	11078.7	−	12785.5i	1.17746	−	1.35886i	0.919686	−	0.392654i	$-0.128443\pi$
$98$	4288.32	−	8591.50i	0.446514	−	0.894575i
$99$	−1014.16	−	1578.07i	−0.103476	−	0.161011i
$100$	−137.883	−	1867.80i	−0.0137883	−	0.186780i
$101$	2597.39	+	2997.54i	0.254621	+	0.293848i	0.868641	−	0.495442i	$-0.164994\pi$
$101$	2597.39	+	2997.54i	0.254621	+	0.293848i	−0.614020	+	0.789290i	$0.710449\pi$
$102$	−13344.8	−	12396.0i	−1.28266	−	1.19146i
$103$	14591.8	+	2097.98i	1.37542	+	0.197755i	0.790064	−	0.613025i	$-0.210047\pi$
$103$	14591.8	+	2097.98i	1.37542	+	0.197755i	0.585351	+	0.810780i	$0.300957\pi$
$104$	5095.51	+	4077.46i	0.471109	+	0.376984i
$105$	144.231	+	92.6914i	0.0130821	+	0.00840738i
$106$	−15083.8	+	8972.96i	−1.34245	+	0.798590i
$107$	13626.9	−	6223.21i	1.19023	−	0.543559i	0.280940	−	0.959725i	$-0.409354\pi$
$107$	13626.9	−	6223.21i	1.19023	−	0.543559i	0.909289	+	0.416166i	$0.136626\pi$
$108$	−2318.90	−	10543.6i	−0.198808	−	0.903946i
$109$	11127.4	+	3267.29i	0.936569	+	0.275001i	0.714184	−	0.699958i	$-0.246798\pi$
$109$	11127.4	+	3267.29i	0.936569	+	0.275001i	0.222384	+	0.974959i	$0.428616\pi$
$110$	−15230.8	+	12302.5i	−1.25875	+	1.01674i
$111$	−3705.63	−	12620.2i	−0.300757	−	1.02429i
$112$	70.6955	+	152.946i	0.00563580	+	0.0121927i
$113$	1706.57	+	11869.4i	0.133649	+	0.929551i	0.940741	+	0.339125i	$0.110131\pi$
$113$	1706.57	+	11869.4i	0.133649	+	0.929551i	−0.807092	+	0.590426i	$0.798960\pi$
$114$	−4144.03	+	23120.1i	−0.318870	+	1.77902i
$115$	13288.2	+	5575.02i	1.00478	+	0.421552i
$116$	−2257.79	−	836.232i	−0.167790	−	0.0621457i
$117$	151.501	+	1053.71i	0.0110673	+	0.0769749i
$118$	3054.85	−	4410.58i	0.219394	−	0.316761i
$119$	−88.2988	−	300.718i	−0.00623535	−	0.0212357i
$120$	15799.9	−	5318.99i	1.09721	−	0.369374i
$121$	16930.5	+	4971.24i	1.15638	+	0.339543i
$122$	−7919.79	−	19058.4i	−0.532101	−	1.28046i
$123$	−10737.5	+	4903.63i	−0.709726	+	0.324121i
$124$	7406.00	−	2781.61i	0.481659	−	0.180906i
$125$	11640.2	+	7480.72i	0.744975	+	0.478766i
$126$	−8.64991	+	26.0884i	−0.000544842	+	0.00164326i
$127$	−17517.4	−	2518.62i	−1.08608	−	0.156155i	−0.424056	−	0.905636i	$-0.639394\pi$
$127$	−17517.4	−	2518.62i	−1.08608	−	0.156155i	−0.662026	+	0.749481i	$0.730303\pi$
$128$	15907.0	+	3924.63i	0.970886	+	0.239541i
$129$	7584.83	+	8753.36i	0.455792	+	0.526012i
$130$	10762.7	−	2760.12i	0.636844	−	0.163321i
$131$	−2204.82	−	3430.77i	−0.128479	−	0.199917i	0.771055	−	0.636769i	$-0.219730\pi$
$131$	−2204.82	−	3430.77i	−0.128479	−	0.199917i	−0.899533	+	0.436853i	$0.856093\pi$
$132$	−22045.6	−	16424.6i	−1.26524	−	0.942641i
$133$	−264.681	+	305.458i	−0.0149630	+	0.0172683i
$134$	−6362.91	+	691.446i	−0.354361	+	0.0385078i
$135$	−16719.0	−	7635.33i	−0.917369	−	0.418948i
$136$	−28195.7	−	11565.8i	−1.52442	−	0.625316i
$137$	−20126.2			−1.07231			−0.536154	−	0.844120i	$-0.680123\pi$
$137$	−20126.2			−1.07231			−0.536154	+	0.844120i	$0.680123\pi$
$138$	−2947.68	+	20018.2i	−0.154782	+	1.05116i
$139$			17016.5i			0.880727i	0.897820	+	0.440363i	$0.145150\pi$
$139$			17016.5i			0.880727i	−0.897820	+	0.440363i	$0.854850\pi$
$140$	280.451	+	60.3369i	0.0143087	+	0.00307841i
$141$	4007.81	−	8775.87i	0.201590	−	0.441420i
$142$	−3444.65	+	374.325i	−0.170832	+	0.0185640i
$143$	−13847.1	−	11998.6i	−0.677155	−	0.586758i
$144$	1455.18	+	2241.68i	0.0701764	+	0.108106i
$145$	−3448.44	+	2216.18i	−0.164016	+	0.105407i
$146$	26874.6	−	6892.07i	1.26077	−	0.323329i
$147$	17348.4	−	15032.5i	0.802832	−	0.695658i
$148$	−13229.1	−	17588.0i	−0.603957	−	0.802957i
$149$	3522.54	−	24499.8i	0.158666	−	1.10355i	−0.742429	−	0.669924i	$-0.766327\pi$
$149$	3522.54	−	24499.8i	0.158666	−	1.10355i	0.901095	−	0.433621i	$-0.142764\pi$
$150$	1409.08	−	4249.81i	0.0626256	−	0.188881i
$151$	−9291.25	+	14457.5i	−0.407493	+	0.634072i	−0.982974	−	0.183743i	$-0.941179\pi$
$151$	−9291.25	+	14457.5i	−0.407493	+	0.634072i	0.575481	+	0.817815i	$0.304815\pi$
$152$	7110.78	+	38652.9i	0.307773	+	1.67299i
$153$	−2065.12	−	4521.99i	−0.0882192	−	0.193173i
$154$	−181.531	−	436.840i	−0.00765436	−	0.0184197i
$155$	3794.67	−	12923.5i	0.157947	−	0.537917i
$156$	7508.21	+	13675.8i	0.308523	+	0.561958i
$157$	−26022.6	+	7640.93i	−1.05573	+	0.309990i	−0.763129	−	0.646246i	$-0.776338\pi$
$157$	−26022.6	+	7640.93i	−1.05573	+	0.309990i	−0.292598	+	0.956235i	$0.594520\pi$
$158$	−1400.20	+	2021.61i	−0.0560889	+	0.0809809i
$159$	−41530.2	+	5971.14i	−1.64274	+	0.236191i
$160$	21619.3	−	17626.8i	0.844505	−	0.688549i
$161$	−219.700	+	270.110i	−0.00847575	+	0.0104205i
$162$	5150.01	−	28732.6i	0.196236	−	1.09483i
$163$	−1791.18	+	257.532i	−0.0674160	+	0.00969296i	−0.175940	−	0.984401i	$-0.556297\pi$
$163$	−1791.18	+	257.532i	−0.0674160	+	0.00969296i	0.108524	+	0.994094i	$0.465387\pi$
$164$	−13934.0	+	13997.9i	−0.518071	+	0.520447i
$165$	−44909.3	+	13186.6i	−1.64956	+	0.484355i
$166$	−10596.8	+	8559.46i	−0.384556	+	0.310621i
$167$	−13579.4	+	46247.3i	−0.486910	+	1.65826i	0.239420	+	0.970916i	$0.423043\pi$
$167$	−13579.4	+	46247.3i	−0.486910	+	1.65826i	−0.726330	+	0.687347i	$0.758775\pi$
$168$	15.7582	+	402.494i	0.000558326	+	0.0142607i
$169$	−7545.21	−	16521.7i	−0.264179	−	0.578471i
$170$	−44592.5	+	26527.0i	−1.54299	+	0.917888i
$171$	−3466.00	+	5393.20i	−0.118532	+	0.184440i
$172$	17030.4	+	9248.82i	0.575664	+	0.312629i
$173$	2651.21	−	18439.5i	0.0885832	−	0.616110i	−0.896372	−	0.443302i	$-0.853807\pi$
$173$	2651.21	−	18439.5i	0.0885832	−	0.616110i	0.984956	−	0.172808i	$-0.0552839\pi$
$174$	−4217.11	−	3917.28i	−0.139289	−	0.129386i
$175$	58.2255	−	50.4527i	0.00190124	−	0.00164744i
$176$	−44194.6	−	12757.4i	−1.42674	−	0.411847i
$177$	10790.0	−	6934.28i	0.344408	−	0.221337i
$178$	5173.22	−	10364.4i	0.163275	−	0.327117i
$179$	−18162.8	−	15738.2i	−0.566863	−	0.491189i	0.323632	−	0.946183i	$-0.395096\pi$
$179$	−18162.8	−	15738.2i	−0.566863	−	0.491189i	−0.890495	+	0.454994i	$0.849641\pi$
$180$	4539.32	+	314.223i	0.140102	+	0.00969824i
$181$	−10035.6	+	21974.9i	−0.306327	+	0.670763i	−0.998711	−	0.0507667i	$-0.983834\pi$
$181$	−10035.6	+	21974.9i	−0.306327	+	0.670763i	0.692383	+	0.721530i	$0.256561\pi$
$182$	−9.27505	+	268.299i	−0.000280010	+	0.00809983i
$183$		−	49338.3i		−	1.47327i
$184$	7159.82	+	33090.3i	0.211479	+	0.977383i
$185$	−37469.3			−1.09479
$186$	18901.1	+	653.409i	0.546338	+	0.0188868i
$187$	77830.1	+	35543.8i	2.22569	+	1.01644i
$188$	1114.77	−	16104.2i	0.0315406	−	0.455642i
$189$	290.818	−	335.622i	0.00814137	−	0.00939564i
$190$	59869.1	+	29882.7i	1.65842	+	0.827776i
$191$	−21883.8	−	34051.9i	−0.599869	−	0.933414i	−0.999857	−	0.0168939i	$-0.994622\pi$
$191$	−21883.8	−	34051.9i	−0.599869	−	0.933414i	0.399988	−	0.916520i	$-0.369014\pi$
$192$	31515.7	+	23256.6i	0.854917	+	0.630875i
$193$	39371.0	+	45436.6i	1.05697	+	1.21981i	0.974775	+	0.223190i	$0.0716471\pi$
$193$	39371.0	+	45436.6i	1.05697	+	1.21981i	0.0821934	+	0.996616i	$0.473807\pi$
$194$	46055.3	−	49580.5i	1.22370	−	1.31737i
$195$	26291.5	+	3780.15i	0.691428	+	0.0994123i
$196$	18330.3	−	33752.9i	0.477154	−	0.878614i
$197$	24572.4	+	15791.7i	0.633162	+	0.406909i	0.817479	−	0.575958i	$-0.195371\pi$
$197$	24572.4	+	15791.7i	0.633162	+	0.406909i	−0.184317	+	0.982867i	$0.559007\pi$
$198$	−3836.15	−	6448.67i	−0.0978510	−	0.164490i
$199$	19347.8	−	8835.83i	0.488568	−	0.223121i	−0.155871	−	0.987777i	$-0.549818\pi$
$199$	19347.8	−	8835.83i	0.488568	−	0.223121i	0.644439	+	0.764656i	$0.277091\pi$
$200$	−293.079	−	7485.80i	−0.00732697	−	0.187145i
$201$	−14681.0	−	4310.72i	−0.363381	−	0.106698i
$202$	9969.09	+	12342.0i	0.244316	+	0.302469i
$203$	−27.9035	−	95.0307i	−0.000677122	−	0.00230607i
$204$	−51634.1	−	51398.4i	−1.24073	−	1.23506i
$205$	4785.60	+	33284.6i	0.113875	+	0.792018i
$206$	58042.3	+	10403.5i	1.36776	+	0.245156i
$207$	−2839.59	+	4736.69i	−0.0662696	+	0.110544i
$208$	19806.4	+	17004.3i	0.457803	+	0.393036i
$209$	−15703.2	−	109218.i	−0.359497	−	2.50036i
$210$	563.768	+	390.476i	0.0127839	+	0.00885434i
$211$	5692.82	+	19388.0i	0.127868	+	0.435479i	0.998395	−	0.0566429i	$-0.0180397\pi$
$211$	5692.82	+	19388.0i	0.127868	+	0.435479i	−0.870526	+	0.492122i	$0.836221\pi$
$212$	−61539.1	+	33785.9i	−1.36924	+	0.751733i
$213$	−7947.75	−	2333.67i	−0.175180	−	0.0514375i
$214$	55335.2	−	22994.8i	1.20830	−	0.502113i
$215$	30013.3	−	13706.6i	0.649286	−	0.296519i
$216$	−7812.96	−	42469.8i	−0.167459	−	0.910275i
$217$	273.773	+	175.943i	0.00581395	+	0.00373640i
$218$	44031.4	+	14599.1i	0.926509	+	0.307195i
$219$	65650.4	+	9439.10i	1.36883	+	0.196808i
$220$	−62587.1	+	47075.9i	−1.29312	+	0.972643i
$221$	−31797.7	−	36696.5i	−0.651045	−	0.751346i
$222$	−13069.6	−	50962.9i	−0.265190	−	1.03407i
$223$	33972.6	+	52862.3i	0.683154	+	1.06301i	0.993659	+	0.112437i	$0.0358655\pi$
$223$	33972.6	+	52862.3i	0.683154	+	1.06301i	−0.310505	+	0.950572i	$0.600498\pi$
$224$	261.476	+	621.188i	0.00521119	+	0.0123802i
$225$	800.259	−	923.548i	0.0158076	−	0.0182429i
$226$	5181.87	+	47685.2i	0.101454	+	0.933613i
$227$	−444.623	−	203.053i	−0.00862860	−	0.00394055i	0.411096	−	0.911592i	$-0.365146\pi$
$227$	−444.623	−	203.053i	−0.00862860	−	0.00394055i	−0.419725	+	0.907651i	$0.637873\pi$
$228$	−19761.4	+	91852.6i	−0.380143	+	1.76694i
$229$	3769.85			0.0718875			0.0359437	−	0.999354i	$-0.488556\pi$
$229$	3769.85			0.0718875			0.0359437	+	0.999354i	$0.488556\pi$
$230$	52350.7	+	24123.2i	0.989616	+	0.456014i
$231$		−	1130.89i		−	0.0211932i
$232$	−8910.19	−	3654.95i	−0.165543	−	0.0679056i
$233$	−8601.84	+	18835.4i	−0.158445	+	0.346947i	−0.972160	−	0.234317i	$-0.924715\pi$
$233$	−8601.84	+	18835.4i	−0.158445	+	0.346947i	0.813715	+	0.581264i	$0.197442\pi$
$234$	460.021	+	4233.26i	0.00840129	+	0.0773113i
$235$	−20770.8	−	17998.0i	−0.376112	−	0.325903i
$236$	12821.6	−	17209.6i	0.230207	−	0.308992i
$237$	−4945.63	+	3178.36i	−0.0880490	+	0.0565857i
$238$	−311.426	−	1214.36i	−0.00549795	−	0.0214384i
$239$	−55599.9	+	48177.6i	−0.973371	+	0.843430i	−0.987683	−	0.156467i	$-0.949989\pi$
$239$	−55599.9	+	48177.6i	−0.973371	+	0.843430i	0.0143126	+	0.999898i	$0.495444\pi$
$240$	63896.8	−	19079.8i	1.10932	−	0.331246i
$241$	−2366.92	+	16462.3i	−0.0407521	+	0.283437i	0.959248	+	0.282567i	$0.0911860\pi$
$241$	−2366.92	+	16462.3i	−0.0407521	+	0.283437i	−1.00000		0.000869972i	$0.999723\pi$
$242$	66994.6	+	22212.8i	1.14395	+	0.379292i
$243$	8179.98	−	12728.3i	0.138529	−	0.215555i
$244$	−29026.4	−	77282.5i	−0.487544	−	1.29808i
$245$	−27165.3	−	59483.7i	−0.452566	−	0.990981i
$246$	−43601.8	+	18118.9i	−0.720501	+	0.299407i
$247$	−17641.7	+	60082.0i	−0.289165	+	0.984805i
$248$	29990.7	−	10096.3i	0.487622	−	0.164157i
$249$	−31245.5	+	9174.51i	−0.503952	+	0.147974i
$250$	45499.3	+	31513.7i	0.727989	+	0.504219i
$251$	−2475.57	+	355.933i	−0.0392941	+	0.00564964i	−0.161934	−	0.986802i	$-0.551773\pi$
$251$	−2475.57	+	355.933i	−0.0392941	+	0.00564964i	0.122640	+	0.992451i	$0.460864\pi$
$252$	−38.1843	+	103.096i	−0.000601290	+	0.00162345i
$253$	−16451.8	−	93618.2i	−0.257022	−	1.46258i
$254$	−69679.7	−	12489.3i	−1.08004	−	0.193585i
$255$	−122777.	+	17652.6i	−1.88814	+	0.271474i
$256$	63047.6	+	17887.5i	0.962031	+	0.272941i
$257$	−88637.7	+	26026.4i	−1.34200	+	0.394046i	−0.872382	−	0.488824i	$-0.837426\pi$
$257$	−88637.7	+	26026.4i	−1.34200	+	0.394046i	−0.469616	+	0.882871i	$0.655608\pi$
$258$	29111.5	+	36040.7i	0.437346	+	0.541445i
$259$	255.058	−	868.649i	0.00380224	−	0.0129493i
$260$	43406.4	−	9546.54i	0.642107	−	0.141221i
$261$	−652.605	−	1429.01i	−0.00958008	−	0.0209775i
$262$	−8339.89	−	14019.6i	−0.121495	−	0.204236i
$263$	27892.0	−	43400.9i	0.403245	−	0.627461i	−0.578942	−	0.815369i	$-0.696534\pi$
$263$	27892.0	−	43400.9i	0.403245	−	0.627461i	0.982187	+	0.187908i	$0.0601706\pi$
$264$	−85860.0	−	68705.7i	−1.23192	−	0.985791i
$265$	−17010.1	+	118308.i	−0.242223	+	1.68470i
$266$	−1100.31	+	1184.53i	−0.0155507	+	0.0167410i
$267$	20928.3	−	18134.4i	0.293569	−	0.254379i
$268$	−25532.0	+	1884.80i	−0.355480	+	0.0262419i
$269$	44338.2	−	28494.4i	0.612736	−	0.393781i	−0.197146	−	0.980374i	$-0.563167\pi$
$269$	44338.2	−	28494.4i	0.612736	−	0.393781i	0.809882	+	0.586593i	$0.199531\pi$
$270$	−65781.1	−	32833.6i	−0.902347	−	0.450392i
$271$	−85111.8	−	73749.8i	−1.15891	−	1.00421i	−0.999857	−	0.0169358i	$-0.994609\pi$
$271$	−85111.8	−	73749.8i	−1.15891	−	1.00421i	−0.159058	−	0.987269i	$-0.550846\pi$
$272$	−111117.	−	50132.3i	−1.50191	−	0.677610i
$273$	−266.605	+	583.783i	−0.00357719	+	0.00783296i
$274$	−80456.5	−	2781.37i	−1.07167	−	0.0370474i
$275$			21032.9i			0.278121i
$276$	−14550.1	+	79617.7i	−0.191007	+	1.04518i
$277$	102576.			1.33686			0.668430	−	0.743775i	$-0.266967\pi$
$277$	102576.			1.33686			0.668430	+	0.743775i	$0.266967\pi$
$278$	−2351.63	+	68025.5i	−0.0304284	+	0.880201i
$279$	4695.43	+	2144.33i	0.0603208	+	0.0275476i
$280$	1112.80	+	279.961i	0.0141938	+	0.00357093i
$281$	74786.3	−	86308.0i	0.947129	−	1.09305i	−0.0484222	−	0.998827i	$-0.515419\pi$
$281$	74786.3	−	86308.0i	0.947129	−	1.09305i	0.995552	−	0.0942185i	$-0.0300352\pi$
$282$	17234.5	−	34528.7i	0.216720	−	0.434192i
$283$	−19132.2	−	29770.3i	−0.238887	−	0.371715i	0.701023	−	0.713139i	$-0.252727\pi$
$283$	−19132.2	−	29770.3i	−0.238887	−	0.371715i	−0.939909	+	0.341424i	$0.889091\pi$
$284$	−13822.1	+	1020.36i	−0.171371	+	0.0126508i
$285$	104752.	+	120891.i	1.28966	+	1.48834i
$286$	−53697.3	−	49879.5i	−0.656479	−	0.609803i
$287$	−804.210	−	115.628i	−0.00976350	−	0.00140378i
$288$	5507.44	+	9162.48i	0.0663995	+	0.110466i
$289$	120491.	+	77435.1i	1.44265	+	0.927134i
$290$	−14091.8	+	8382.85i	−0.167560	+	0.0996772i
$291$	147154.	−	67203.2i	1.73775	−	0.793604i
$292$	108387.	−	23837.9i	1.27119	−	0.279577i
$293$	36201.8	+	10629.8i	0.421691	+	0.123820i	0.485692	−	0.874130i	$-0.338568\pi$
$293$	36201.8	+	10629.8i	0.421691	+	0.123820i	−0.0640006	+	0.997950i	$0.520386\pi$
$294$	71429.6	−	57696.5i	0.826387	−	0.667505i
$295$	−10293.9	−	35057.8i	−0.118287	−	0.402848i
$296$	−50454.1	−	72138.1i	−0.575855	−	0.823344i
$297$	17253.9	+	120003.i	0.195602	+	1.36044i
$298$	17467.5	−	97453.9i	0.196698	−	1.09740i
$299$	−13577.6	+	52205.5i	−0.151873	+	0.583948i
$300$	6220.25	−	16794.4i	0.0691139	−	0.186604i
$301$	113.455	+	789.098i	0.00125225	+	0.00870960i
$302$	−39140.8	+	56511.3i	−0.429157	+	0.619615i
$303$	10685.4	+	36391.2i	0.116388	+	0.396380i
$304$	23084.4	+	155502.i	0.249788	+	1.68263i
$305$	−134858.	−	39597.9i	−1.44970	−	0.425669i
$306$	−7630.64	−	18362.6i	−0.0814926	−	0.196106i
$307$	−122195.	+	55804.6i	−1.29651	+	0.592098i	−0.939675	−	0.342069i	$-0.888872\pi$
$307$	−122195.	+	55804.6i	−1.29651	+	0.592098i	−0.356838	+	0.934166i	$0.616145\pi$
$308$	−665.320	−	1771.41i	−0.00701341	−	0.0186731i
$309$	118589.	+	76212.8i	1.24202	+	0.798198i
$310$	16955.6	−	51138.6i	0.176437	−	0.532139i
$311$	−78420.3	−	11275.1i	−0.810789	−	0.116574i	−0.275563	−	0.961283i	$-0.588864\pi$
$311$	−78420.3	−	11275.1i	−0.810789	−	0.116574i	−0.535226	+	0.844709i	$0.679773\pi$
$312$	28125.0	+	55708.1i	0.288924	+	0.572281i
$313$	−47157.4	−	54422.6i	−0.481350	−	0.555508i	0.462183	−	0.886784i	$-0.347066\pi$
$313$	−47157.4	−	54422.6i	−0.481350	−	0.555508i	−0.943534	+	0.331276i	$0.892521\pi$
$314$	−105084.	+	26949.2i	−1.06581	+	0.273330i
$315$	101.196	+	157.464i	0.00101986	+	0.00158694i
$316$	−5876.85	+	7888.10i	−0.0588533	+	0.0789948i
$317$	17661.6	−	20382.6i	0.175757	−	0.202834i	−0.661036	−	0.750355i	$-0.729883\pi$
$317$	17661.6	−	20382.6i	0.175757	−	0.202834i	0.836792	+	0.547521i	$0.184428\pi$
$318$	−166847.	+	18131.0i	−1.64992	+	0.179294i
$319$	24595.3	+	11232.3i	0.241697	+	0.110379i
$320$	88861.7	−	67477.6i	0.867790	−	0.658960i
$321$	143252.			1.39024
$322$	−915.603	+	1049.43i	−0.00883071	+	0.0101215i
$323$		−	292417.i		−	2.80283i
$324$	24558.5	−	114150.i	0.233944	−	1.08739i
$325$	4958.45	−	10857.5i	0.0469439	−	0.102793i
$326$	−7196.02	+	781.979i	−0.0677106	+	0.00735800i
$327$	83810.1	+	72621.9i	0.783792	+	0.679160i
$328$	−57637.4	+	54032.7i	−0.535743	+	0.502237i
$329$	558.636	−	359.013i	0.00516104	−	0.00331680i
$330$	−181352.	+	46508.4i	−1.66531	+	0.427075i
$331$	124552.	−	107925.i	1.13683	−	0.985067i	0.136843	−	0.990593i	$-0.456304\pi$
$331$	124552.	−	107925.i	1.13683	−	0.985067i	0.999985	+	0.00552556i	$0.00175885\pi$
$332$	−43544.8	+	32753.0i	−0.395058	+	0.297149i
$333$	2043.61	−	14213.6i	0.0184294	−	0.128179i
$334$	−60676.5	+	183002.i	−0.543911	+	1.64045i
$335$	−23565.2	+	36668.2i	−0.209982	+	0.326738i
$336$	7.37166	+	1611.19i	6.52960e−5	+	0.0142715i
$337$	−23408.9	−	51258.3i	−0.206120	−	0.451340i	0.778134	−	0.628098i	$-0.216166\pi$
$337$	−23408.9	−	51258.3i	−0.206120	−	0.451340i	−0.984254	+	0.176758i	$0.943439\pi$
$338$	−27879.6	−	67090.1i	−0.244035	−	0.587253i
$339$	−32305.6	+	110023.i	−0.281111	+	0.957377i
$340$	−181929.	+	99881.9i	−1.57378	+	0.864031i
$341$	−85245.2	+	25030.2i	−0.733096	+	0.215256i
$342$	−14601.1	+	21080.9i	−0.124834	+	0.180234i
$343$	3128.13	−	449.757i	0.0265887	−	0.00382287i
$344$	66803.0	+	39326.7i	0.564519	+	0.332331i
$345$	93438.5	+	101279.i	0.785033	+	0.850904i
$346$	13146.8	−	73347.8i	0.109816	−	0.612681i
$347$	57565.6	−	8276.68i	0.478084	−	0.0687381i	0.100940	−	0.994893i	$-0.467815\pi$
$347$	57565.6	−	8276.68i	0.478084	−	0.0687381i	0.377144	+	0.926154i	$0.376906\pi$
$348$	−16317.0	−	16242.5i	−0.134736	−	0.134121i
$349$	−77011.2	+	22612.5i	−0.632270	+	0.185651i	−0.582136	−	0.813091i	$-0.697783\pi$
$349$	−77011.2	+	22612.5i	−0.632270	+	0.185651i	−0.0501340	+	0.998742i	$0.515965\pi$
$350$	239.735	−	193.644i	0.00195702	−	0.00158077i
$351$	19383.8	−	66015.0i	0.157334	−	0.535832i
$352$	−174910.	−	57106.5i	−1.41166	−	0.460893i
$353$	−77597.0	−	169914.i	−0.622724	−	1.36358i	−0.913521	−	0.406791i	$-0.866648\pi$
$353$	−77597.0	−	169914.i	−0.622724	−	1.36358i	0.290797	−	0.956785i	$-0.406079\pi$
$354$	44092.3	−	26229.4i	0.351849	−	0.209306i
$355$	−12757.4	+	19850.9i	−0.101229	+	0.157515i
$356$	22112.8	−	40717.8i	0.174479	−	0.321280i
$357$	426.516	−	2966.49i	0.00334656	−	0.0232759i
$358$	−70433.0	−	65425.2i	−0.549554	−	0.510481i
$359$	−127508.	+	110487.i	−0.989350	+	0.857277i	−0.989763	−	0.142723i	$-0.954414\pi$
$359$	−127508.	+	110487.i	−0.989350	+	0.857277i	0.000412702		1.00000i	$0.499869\pi$
$360$	18103.0	+	1883.46i	0.139684	+	0.0145329i
$361$	−207605.	+	133420.i	−1.59303	+	1.02378i
$362$	−43155.3	+	86460.1i	−0.329319	+	0.659779i
$363$	127519.	+	110495.i	0.967743	+	0.838554i
$364$	−74.1561	+	1071.27i	−0.000559686	+	0.00808532i
$365$	78489.8	−	171869.i	0.589152	−	1.29006i
$366$	6818.40	−	197235.i	0.0509003	−	1.47239i
$367$		−	59959.7i		−	0.445172i	−0.974913	−	0.222586i	$-0.928550\pi$
$367$		−	59959.7i		−	0.445172i	0.974913	−	0.222586i	$-0.0714497\pi$
$368$	24049.2	+	133272.i	0.177585	+	0.984106i
$369$	−12887.2			−0.0946468
$370$	−149788.	−	5178.14i	−1.09414	−	0.0378243i
$371$	−2626.94	−	1199.68i	−0.0190854	−	0.00871603i
$372$	75469.0	+	5224.15i	0.545359	+	0.0377511i
$373$	141638.	−	163459.i	1.01803	−	1.17487i	0.0335426	−	0.999437i	$-0.489321\pi$
$373$	141638.	−	163459.i	1.01803	−	1.17487i	0.984491	−	0.175436i	$-0.0561335\pi$
$374$	306223.	+	152846.i	2.18924	+	1.09273i
$375$	71533.8	+	111309.i	0.508684	+	0.791528i
$376$	6681.98	−	64224.3i	0.0472639	−	0.454280i
$377$	−10048.5	−	11596.5i	−0.0706996	−	0.0815917i
$378$	1208.96	−	1301.50i	0.00846112	−	0.00910876i
$379$	114214.	+	16421.5i	0.795135	+	0.114323i	0.527898	−	0.849308i	$-0.322980\pi$
$379$	114214.	+	16421.5i	0.795135	+	0.114323i	0.267237	+	0.963631i	$0.413889\pi$
$380$	235204.	+	127733.i	1.62883	+	0.884579i
$381$	−142366.	−	91493.3i	−0.980748	−	0.630289i
$382$	−82777.1	−	139150.i	−0.567262	−	0.953582i
$383$	−224622.	+	102581.i	−1.53128	+	0.699311i	−0.989939	−	0.141494i	$-0.954809\pi$
$383$	−224622.	+	102581.i	−1.53128	+	0.699311i	−0.541338	+	0.840805i	$0.682082\pi$
$384$	122773.	+	97326.1i	0.832611	+	0.660035i
$385$	−3091.10	−	907.630i	−0.0208541	−	0.00612332i
$386$	151111.	+	187079.i	1.01419	+	1.25560i
$387$	3562.52	+	12132.8i	0.0237868	+	0.0810103i
$388$	190963.	−	191839.i	1.26849	−	1.27430i
$389$	36443.4	+	253469.i	0.240835	+	1.67504i	0.647963	+	0.761672i	$0.275621\pi$
$389$	36443.4	+	253469.i	0.240835	+	1.67504i	−0.407128	+	0.913371i	$0.633470\pi$
$390$	104581.	+	18745.0i	0.687580	+	0.123241i
$391$	−7847.10	−	251778.i	−0.0513281	−	1.64689i
$392$	77942.1	−	132398.i	0.507224	−	0.861605i
$393$	−5549.86	−	38600.1i	−0.0359333	−	0.249922i
$394$	96048.6	+	66525.0i	0.618726	+	0.428541i
$395$	4718.26	+	16068.9i	0.0302404	+	0.102989i
$396$	−14444.3	−	26309.4i	−0.0921096	−	0.167773i
$397$	297598.	+	87382.6i	1.88820	+	0.554427i	0.994361	+	0.106045i	$0.0338186\pi$
$397$	297598.	+	87382.6i	1.88820	+	0.554427i	0.893842	+	0.448382i	$0.148000\pi$
$398$	78566.0	−	32648.4i	0.495985	−	0.206109i
$399$	−3515.66	+	1605.55i	−0.0220832	+	0.0100850i
$400$	−137.102	−	29965.8i	−0.000856887	−	0.187286i
$401$	115785.	+	74410.4i	0.720050	+	0.462748i	0.848654	−	0.528948i	$-0.177413\pi$
$401$	115785.	+	74410.4i	0.720050	+	0.462748i	−0.128604	+	0.991696i	$0.541050\pi$
$402$	−58093.0	−	19261.4i	−0.359478	−	0.119189i
$403$	49905.6	+	7175.34i	0.307284	+	0.0441807i
$404$	38146.9	+	50716.1i	0.233720	+	0.310730i
$405$	−130181.	−	150237.i	−0.793668	−	0.915942i
$406$	−98.4145	−	383.752i	−0.000597045	−	0.00232808i
$407$	133621.	+	207919.i	0.806653	+	1.25518i
$408$	−199310.	−	212607.i	−1.19732	−	1.27719i
$409$	151066.	−	174339.i	0.903065	−	1.04219i	−0.0958393	−	0.995397i	$-0.530553\pi$
$409$	151066.	−	174339.i	0.903065	−	1.04219i	0.998904	−	0.0467960i	$-0.0149011\pi$
$410$	14531.1	+	133720.i	0.0864434	+	0.795480i
$411$	−175063.	−	79948.5i	−1.03636	−	0.473289i
$412$	230593.	+	49610.2i	1.35848	+	0.292265i
$413$	882.815			0.00517571
$414$	−12006.2	+	18543.0i	−0.0700492	+	0.108188i
$415$			92767.7i			0.538642i
$416$	76828.3	+	70713.7i	0.443950	+	0.408618i
$417$	−67595.9	+	148014.i	−0.388730	+	0.851201i
$418$	−47681.7	−	438782.i	−0.272897	−	2.51129i
$419$	112324.	+	97329.4i	0.639801	+	0.554391i	0.913201	−	0.407510i	$-0.133603\pi$
$419$	112324.	+	97329.4i	0.639801	+	0.554391i	−0.273400	+	0.961901i	$0.588148\pi$
$420$	2199.76	+	1638.88i	0.0124703	+	0.00929072i
$421$	−255279.	+	164058.i	−1.44029	+	0.925621i	−0.440685	+	0.897662i	$0.645264\pi$
$421$	−255279.	+	164058.i	−1.44029	+	0.925621i	−0.999609	+	0.0279586i	$0.991099\pi$
$422$	20078.3	+	78292.2i	0.112746	+	0.439637i
$423$	7960.23	−	6897.58i	0.0444882	−	0.0385493i
$424$	−250679.	+	126558.i	−1.39439	+	0.703978i
$425$	−7932.57	+	55172.3i	−0.0439174	+	0.305452i
$426$	−31449.5	−	10427.5i	−0.173298	−	0.0574592i
$427$	1835.99	−	2856.85i	0.0100696	−	0.0156687i
$428$	224387.	−	84277.1i	1.22492	−	0.460068i
$429$	−72783.3	−	159373.i	−0.395474	−	0.865966i
$430$	121876.	−	50645.9i	0.659143	−	0.273910i
$431$	37157.8	−	126548.i	0.200030	−	0.681240i	−0.796983	−	0.604002i	$-0.793572\pi$
$431$	37157.8	−	126548.i	0.200030	−	0.681240i	0.997013	−	0.0772377i	$-0.0246100\pi$
$432$	−25364.0	−	170858.i	−0.135910	−	0.915517i
$433$	−153157.	+	44970.9i	−0.816884	+	0.239859i	−0.663374	−	0.748288i	$-0.730876\pi$
$433$	−153157.	+	44970.9i	−0.816884	+	0.239859i	−0.153510	+	0.988147i	$0.549058\pi$
$434$	1070.12	+	741.187i	0.00568139	+	0.00393504i
$435$	−38798.9	+	5578.45i	−0.205041	+	0.0294805i
$436$	174003.	+	64446.7i	0.915342	+	0.339022i
$437$	−267679.	+	184056.i	−1.40169	+	0.963800i
$438$	261140.	+	46806.5i	1.36121	+	0.243982i
$439$	−364434.	+	52397.6i	−1.89099	+	0.271883i	−0.987607	−	0.156949i	$-0.949834\pi$
$439$	−364434.	+	52397.6i	−1.89099	+	0.271883i	−0.903384	+	0.428832i	$0.858925\pi$
$440$	−256705.	+	179542.i	−1.32595	+	0.927386i
$441$	24046.2	−	7060.60i	0.123643	−	0.0363048i
$442$	−122043.	−	151093.i	−0.624698	−	0.773390i
$443$	63730.0	−	217044.i	0.324740	−	1.10596i	−0.621746	−	0.783219i	$-0.713576\pi$
$443$	63730.0	−	217044.i	0.324740	−	1.10596i	0.946486	−	0.322745i	$-0.104606\pi$
$444$	−45204.3	−	205536.i	−0.229305	−	1.04261i
$445$	−32770.9	−	71758.2i	−0.165489	−	0.362369i
$446$	128504.	+	216018.i	0.646020	+	1.08598i
$447$	127962.	−	199113.i	0.640423	−	0.996518i
$448$	959.435	+	2519.40i	0.00478035	+	0.0125528i
$449$	29923.8	−	208125.i	0.148431	−	1.03236i	−0.770359	−	0.637611i	$-0.779923\pi$
$449$	29923.8	−	208125.i	0.148431	−	1.03236i	0.918789	−	0.394748i	$-0.129168\pi$
$450$	3326.76	−	3581.39i	0.0164284	−	0.0176859i
$451$	167631.	−	145253.i	0.824141	−	0.714122i
$452$	14125.2	+	191343.i	0.0691380	+	0.936561i
$453$	−138248.	+	88846.8i	−0.673695	+	0.432958i
$454$	−1749.37	−	873.171i	−0.00848731	−	0.00423631i
$455$	1381.70	+	1197.25i	0.00667408	+	0.00578312i
$456$	−91692.0	+	364460.i	−0.440962	+	1.75275i
$457$	−36058.6	+	78957.3i	−0.172654	+	0.378059i	−0.976101	−	0.217317i	$-0.930270\pi$
$457$	−36058.6	+	78957.3i	−0.172654	+	0.378059i	0.803447	+	0.595376i	$0.202997\pi$
$458$	15070.4	+	520.982i	0.0718445	+	0.00248366i
$459$			321293.i			1.52502i
$460$	205944.	+	103670.i	0.973270	+	0.489933i
$461$	48117.5			0.226413			0.113206	−	0.993571i	$-0.463888\pi$
$461$	48117.5			0.226413			0.113206	+	0.993571i	$0.463888\pi$
$462$	156.286	−	4520.87i	0.000732210	−	0.0211806i
$463$	−284142.	−	129763.i	−1.32548	−	0.605326i	−0.378197	−	0.925725i	$-0.623456\pi$
$463$	−284142.	−	129763.i	−1.32548	−	0.605326i	−0.947283	+	0.320399i	$0.896183\pi$
$464$	−35114.4	−	15842.4i	−0.163098	−	0.0735845i
$465$	84343.9	−	97338.1i	0.390075	−	0.450170i
$466$	−36989.8	+	74107.9i	−0.170338	+	0.341266i
$467$	218213.	+	339545.i	1.00057	+	1.55691i	0.819209	+	0.573495i	$0.194413\pi$
$467$	218213.	+	339545.i	1.00057	+	1.55691i	0.181357	+	0.983417i	$0.441951\pi$
$468$	1253.96	+	16986.5i	0.00572523	+	0.0775554i
$469$	−689.666	−	795.916i	−0.00313540	−	0.00361844i
$470$	−80546.3	−	74819.5i	−0.364628	−	0.338703i
$471$	−256705.	−	36908.6i	−1.15716	−	0.166374i
$472$	53634.2	−	67025.4i	0.240745	−	0.300854i
$473$	−183090.	−	117665.i	−0.818357	−	0.525926i
$474$	−20209.9	+	12022.4i	−0.0899515	+	0.0535099i
$475$	65386.1	−	29860.8i	0.289800	−	0.132347i
$476$	−1077.14	−	4897.57i	−0.00475399	−	0.0216156i
$477$	−43951.3	−	12905.3i	−0.193168	−	0.0567192i
$478$	−228925.	+	184912.i	−1.00193	+	0.809298i
$479$	51309.5	+	174744.i	0.223628	+	0.761608i	0.992504	+	0.122210i	$0.0389982\pi$
$479$	51309.5	+	174744.i	0.223628	+	0.761608i	−0.768876	+	0.639398i	$0.779184\pi$
$480$	258071.	−	67443.2i	1.12010	−	0.292722i
$481$	−19961.0	−	138831.i	−0.0862762	−	0.600064i
$482$	−11737.1	+	65482.8i	−0.0505203	+	0.281860i
$483$	−2983.99	+	1476.76i	−0.0127909	+	0.00633018i
$484$	264749.	+	98056.8i	1.13017	+	0.418588i
$485$	−65585.6	−	456158.i	−0.278821	−	1.93924i
$486$	34459.4	−	49752.4i	0.145893	−	0.210640i
$487$	48603.6	+	165529.i	0.204932	+	0.697936i	0.996249	+	0.0865294i	$0.0275776\pi$
$487$	48603.6	+	165529.i	0.204932	+	0.697936i	−0.791317	+	0.611406i	$0.790604\pi$
$488$	−105356.	−	312957.i	−0.442405	−	1.31415i
$489$	−16603.2	−	4875.13i	−0.0694341	−	0.0203877i
$490$	−100376.	−	241547.i	−0.418058	−	1.00603i
$491$	143385.	−	65481.5i	0.594757	−	0.271616i	−0.0952103	−	0.995457i	$-0.530352\pi$
$491$	143385.	−	65481.5i	0.594757	−	0.271616i	0.689967	+	0.723841i	$0.257625\pi$
$492$	−176807.	+	66406.8i	−0.730415	+	0.274336i
$493$	60280.6	+	38740.0i	0.248018	+	0.159392i
$494$	−78827.7	+	237746.i	−0.323017	+	0.974227i
$495$	−50579.5	−	7272.24i	−0.206426	−	0.0296796i
$496$	121287.	−	36216.5i	0.493002	−	0.147212i
$497$	−373.361	−	430.881i	−0.00151153	−	0.00174439i
$498$	−126175.	+	32358.1i	−0.508764	+	0.130474i
$499$	−100623.	−	156573.i	−0.404108	−	0.628804i	0.578240	−	0.815867i	$-0.303740\pi$
$499$	−100623.	−	156573.i	−0.404108	−	0.628804i	−0.982348	+	0.187062i	$0.940103\pi$
$500$	177533.	+	132267.i	0.710134	+	0.529069i
$501$	−301829.	+	348329.i	−1.20250	+	1.38776i
$502$	−9945.56	+	1080.77i	−0.0394659	+	0.00428869i
$503$	−127409.	−	58185.8i	−0.503575	−	0.229975i	0.147396	−	0.989078i	$-0.452911\pi$
$503$	−127409.	−	58185.8i	−0.503575	−	0.229975i	−0.650971	+	0.759102i	$0.725638\pi$
$504$	−166.894	+	406.860i	−0.000657020	+	0.00160171i
$505$	108045.			0.423665
$506$	−52830.0	−	376523.i	−0.206338	−	1.47058i
$507$		−	173683.i		−	0.675680i
$508$	−276827.	−	59557.0i	−1.07271	−	0.230784i
$509$	−37786.7	+	82741.4i	−0.145849	+	0.319365i	−0.968431	−	0.249282i	$-0.919806\pi$
$509$	−37786.7	+	82741.4i	−0.145849	+	0.319365i	0.822582	+	0.568647i	$0.192533\pi$
$510$	−493253.	+	53600.9i	−1.89640	+	0.206078i
$511$	3450.13	+	2989.55i	0.0132128	+	0.0114489i
$512$	249568.	+	80220.1i	0.952027	+	0.306016i
$513$	348565.	−	224009.i	1.32449	−	0.851198i
$514$	−357936.	+	91793.9i	−1.35481	+	0.347446i
$515$	303492.	−	262977.i	1.14428	−	0.991526i
$516$	111396.	+	148100.i	0.418379	+	0.556232i
$517$	−25799.8	+	179441.i	−0.0965239	+	0.671339i
$518$	1139.67	−	3437.27i	0.00424736	−	0.0128102i
$519$	96309.6	−	149861.i	0.357549	−	0.556356i
$520$	174841.	−	32164.7i	0.646603	−	0.118952i
$521$	58378.8	+	127832.i	0.215070	+	0.470938i	0.986162	−	0.165787i	$-0.0530163\pi$
$521$	58378.8	+	127832.i	0.215070	+	0.470938i	−0.771092	+	0.636724i	$0.780289\pi$
$522$	−2411.38	−	5802.80i	−0.00884961	−	0.0212959i
$523$	−80149.2	+	272963.i	−0.293019	+	0.997931i	0.673039	+	0.739607i	$0.264988\pi$
$523$	−80149.2	+	272963.i	−0.293019	+	0.997931i	−0.966058	+	0.258324i	$0.916830\pi$
$524$	−31402.2	−	57197.4i	−0.114366	−	0.208312i
$525$	706.879	−	207.558i	0.00256464	−	0.000753046i
$526$	117499.	−	169645.i	0.424682	−	0.613155i
$527$	−233050.	+	33507.5i	−0.839127	+	0.120648i
$528$	−333740.	−	286524.i	−1.19713	−	1.02776i
$529$	−225539.	+	165660.i	−0.805954	+	0.591979i
$530$	−84349.7	+	470599.i	−0.300284	+	1.67533i
$531$	13860.3	−	1992.81i	0.0491568	−	0.00706768i
$532$	−4562.29	+	4583.21i	−0.0161198	+	0.0161937i
$533$	−120777.	+	35463.2i	−0.425137	+	0.124831i
$534$	86169.2	−	69602.2i	0.302183	−	0.244085i
$535$	114971.	−	391555.i	0.401680	−	1.36800i
$536$	−102327.	+	4006.26i	−0.356174	+	0.0139447i
$537$	−95467.5	−	209045.i	−0.331060	−	0.724921i
$538$	181185.	−	107782.i	0.625975	−	0.372377i
$539$	−233202.	+	362869.i	−0.802701	+	1.24903i
$540$	−258430.	−	140347.i	−0.886247	−	0.481299i
$541$	−64244.9	+	446833.i	−0.219505	+	1.52669i	0.520367	+	0.853943i	$0.325795\pi$
$541$	−64244.9	+	446833.i	−0.219505	+	1.52669i	−0.739872	+	0.672748i	$0.765114\pi$
$542$	−330052.	−	306585.i	−1.12353	−	1.04365i
$543$	−174585.	+	151278.i	−0.592116	+	0.513071i
$544$	−437275.	−	215766.i	−1.47760	−	0.729096i
$545$	265764.	−	170796.i	0.894752	−	0.575023i
$546$	−1146.46	+	2296.89i	−0.00384568	+	0.00770470i
$547$	−228332.	−	197851.i	−0.763118	−	0.661245i	0.183712	−	0.982980i	$-0.441189\pi$
$547$	−228332.	−	197851.i	−0.763118	−	0.661245i	−0.946830	+	0.321735i	$0.895734\pi$
$548$	−321250.	−	22237.7i	−1.06975	−	0.0740506i
$549$	22376.4	−	48997.4i	0.0742412	−	0.162565i
$550$	−2906.68	+	84081.5i	−0.00960888	+	0.277955i
$551$		−	92407.3i		−	0.304371i
$552$	−69168.7	+	316270.i	−0.227003	+	1.03796i
$553$	−404.643			−0.00132319
$554$	410059.	+	14175.7i	1.33606	+	0.0461875i
$555$	−325919.	−	148842.i	−1.05809	−	0.483214i
$556$	−18801.8	+	271614.i	−0.0608205	+	0.878624i
$557$	93718.9	−	108157.i	0.302076	−	0.348615i	−0.584336	−	0.811512i	$-0.698645\pi$
$557$	93718.9	−	108157.i	0.302076	−	0.348615i	0.886412	+	0.462898i	$0.153190\pi$
$558$	18474.2	+	9221.10i	0.0593331	+	0.0296152i
$559$	66774.6	+	103903.i	0.213692	+	0.332511i
$560$	4409.84	+	1272.96i	0.0140620	+	0.00405918i
$561$	535795.	+	618340.i	1.70244	+	1.96472i
$562$	310894.	−	334691.i	0.984328	−	1.05967i
$563$	326224.	+	46903.9i	1.02920	+	0.147976i	0.636169	−	0.771550i	$-0.280518\pi$
$563$	326224.	+	46903.9i	1.02920	+	0.147976i	0.393029	+	0.919526i	$0.371427\pi$
$564$	73668.4	−	135650.i	0.231592	−	0.426445i
$565$	274801.	+	176604.i	0.860838	+	0.553227i
$566$	−72369.0	−	121654.i	−0.225902	−	0.379747i
$567$	4369.10	−	1995.30i	0.0135902	−	0.00620644i
$568$	−55396.5	+	2168.85i	−0.171706	+	0.00672252i
$569$	86306.3	+	25341.8i	0.266574	+	0.0782732i	0.412288	−	0.911054i	$-0.364730\pi$
$569$	86306.3	+	25341.8i	0.266574	+	0.0782732i	−0.145714	+	0.989327i	$0.546548\pi$
$570$	402053.	+	497750.i	1.23747	+	1.53201i
$571$	86354.4	+	294096.i	0.264857	+	0.902022i	0.979315	+	0.202343i	$0.0648555\pi$
$571$	86354.4	+	294096.i	0.264857	+	0.902022i	−0.714457	+	0.699679i	$0.753326\pi$
$572$	−207768.	−	206819.i	−0.635019	−	0.632120i
$573$	−55084.8	−	383123.i	−0.167773	−	1.16689i
$574$	−3198.94	−	573.375i	−0.00970918	−	0.00174026i
$575$	55497.8	−	27465.6i	0.167857	−	0.0830717i
$576$	20750.4	+	37389.2i	0.0625434	+	0.112694i
$577$	−56272.4	−	391383.i	−0.169022	−	1.17557i	−0.880911	−	0.473282i	$-0.843069\pi$
$577$	−56272.4	−	391383.i	−0.169022	−	1.17557i	0.711889	−	0.702292i	$-0.247840\pi$
$578$	470977.	+	326207.i	1.40976	+	0.976423i
$579$	161969.	+	551616.i	0.483142	+	1.64543i
$580$	−57492.0	+	31563.9i	−0.170904	+	0.0938286i
$581$	−2150.63	−	631.481i	−0.00637108	−	0.00187072i
$582$	597554.	−	248316.i	1.76413	−	0.733092i
$583$	717157.	−	327514.i	2.10997	−	0.963592i
$584$	436582.	−	80315.8i	1.28009	−	0.235492i
$585$	24395.5	+	15678.0i	0.0712849	+	0.0458120i
$586$	143252.	+	47496.8i	0.417162	+	0.138315i
$587$	−643866.	−	92573.9i	−1.86861	−	0.268666i	−0.887315	−	0.461165i	$-0.847432\pi$
$587$	−643866.	−	92573.9i	−1.86861	−	0.268666i	−0.981297	+	0.192499i	$0.938341\pi$
$588$	293521.	−	220777.i	0.848955	−	0.638556i
$589$	198837.	+	229470.i	0.573148	+	0.661448i
$590$	−36306.2	−	141570.i	−0.104298	−	0.406694i
$591$	151007.	+	234971.i	0.432337	+	0.672729i
$592$	−191727.	−	295353.i	−0.547066	−	0.842748i
$593$	77382.1	−	89303.7i	0.220055	−	0.253957i	−0.634978	−	0.772530i	$-0.718991\pi$
$593$	77382.1	−	89303.7i	0.220055	−	0.253957i	0.855033	+	0.518573i	$0.173536\pi$
$594$	52390.2	+	482111.i	0.148483	+	1.36639i
$595$	−7766.08	−	3546.65i	−0.0219365	−	0.0100181i
$596$	83296.3	−	387169.i	0.234495	−	1.08995i
$597$	203392.			0.570669
$598$	−61492.6	+	206821.i	−0.171957	+	0.578352i
$599$		−	304909.i		−	0.849799i	−0.905241	−	0.424899i	$-0.860309\pi$
$599$		−	304909.i		−	0.849799i	0.905241	−	0.424899i	$-0.139691\pi$
$600$	27187.1	−	66277.8i	0.0755197	−	0.184105i
$601$	−207042.	+	453358.i	−0.573204	+	1.25514i	0.371870	+	0.928285i	$0.378717\pi$
$601$	−207042.	+	453358.i	−0.573204	+	1.25514i	−0.945074	+	0.326856i	$0.894011\pi$
$602$	344.499	+	3170.19i	0.000950593	+	0.00874766i
$603$	−12624.5	−	10939.2i	−0.0347199	−	0.0300850i
$604$	−164279.	+	220501.i	−0.450308	+	0.604418i
$605$	404365.	−	259869.i	1.10475	−	0.709977i
$606$	37687.1	+	146955.i	0.102624	+	0.400164i
$607$	−159623.	+	138314.i	−0.433230	+	0.375396i	−0.844000	−	0.536343i	$-0.819805\pi$
$607$	−159623.	+	138314.i	−0.433230	+	0.375396i	0.410770	+	0.911739i	$0.365260\pi$
$608$	70792.8	+	624826.i	0.191506	+	1.69025i
$609$	134.784	−	937.446i	0.000363417	−	0.00252762i
$610$	−533637.	−	176934.i	−1.43412	−	0.475501i
$611$	55621.1	−	86548.1i	0.148990	−	0.231833i
$612$	−27966.7	−	74460.9i	−0.0746686	−	0.198804i
$613$	−212289.	−	464849.i	−0.564947	−	1.23706i	−0.949445	−	0.313935i	$-0.898353\pi$
$613$	−212289.	−	464849.i	−0.564947	−	1.23706i	0.384498	−	0.923126i	$-0.374375\pi$
$614$	−496200.	+	206198.i	−1.31620	+	0.546951i
$615$	−90592.2	+	308529.i	−0.239519	+	0.815728i
$616$	−2414.89	−	7173.34i	−0.00636408	−	0.0189043i
$617$	−450233.	+	132200.i	−1.18268	+	0.347266i	−0.813207	−	0.581975i	$-0.802280\pi$
$617$	−450233.	+	132200.i	−1.18268	+	0.347266i	−0.369473	+	0.929241i	$0.620462\pi$
$618$	463542.	+	321058.i	1.21370	+	0.840633i
$619$	352797.	−	50724.6i	0.920755	−	0.132385i	0.334393	−	0.942434i	$-0.391469\pi$
$619$	352797.	−	50724.6i	0.920755	−	0.132385i	0.586362	+	0.810049i	$0.300560\pi$
$620$	74849.1	−	202089.i	0.194717	−	0.525726i
$621$	294112.	−	202231.i	0.762657	−	0.524403i
$622$	−311936.	−	55911.1i	−0.806277	−	0.144516i
$623$	1886.64	−	271.258i	0.00486086	−	0.000698886i
$624$	104734.	+	226586.i	0.268979	+	0.581922i
$625$	431851.	−	126803.i	1.10554	−	0.324615i
$626$	−180996.	−	224077.i	−0.461871	−	0.571807i
$627$	297264.	−	1.01239e6i	0.756149	−	2.57521i
$628$	−423811.	+	93210.3i	−1.07461	+	0.236344i
$629$	272090.	+	595795.i	0.687720	+	1.50590i
$630$	382.780	+	643.464i	0.000964426	+	0.00162122i
$631$	−51997.8	+	80910.1i	−0.130595	+	0.203210i	−0.900393	−	0.435078i	$-0.856721\pi$
$631$	−51997.8	+	80910.1i	−0.130595	+	0.203210i	0.769798	+	0.638288i	$0.220357\pi$
$632$	−24583.5	+	30721.4i	−0.0615473	+	0.0769143i
$633$	−27498.4	+	191256.i	−0.0686279	+	0.477317i
$634$	73421.1	−	79040.9i	0.182660	−	0.196641i
$635$	−364342.	+	315704.i	−0.903569	+	0.782947i
$636$	−669494.	+	49422.8i	−1.65513	+	0.122184i
$637$	205927.	−	132341.i	0.507499	−	0.326150i
$638$	96770.2	+	48301.3i	0.237739	+	0.118664i
$639$	−6834.45	−	5922.08i	−0.0167379	−	0.0145035i
$640$	364560.	−	257469.i	0.890038	−	0.628586i
$641$	231833.	−	507644.i	0.564234	−	1.23550i	−0.385577	−	0.922676i	$-0.625997\pi$
$641$	231833.	−	507644.i	0.564234	−	1.23550i	0.949811	−	0.312825i	$-0.101275\pi$
$642$	572665.	+	19796.9i	1.38941	+	0.0480317i
$643$			221615.i			0.536014i	0.963417	+	0.268007i	$0.0863651\pi$
$643$			221615.i			0.536014i	−0.963417	+	0.268007i	$0.913635\pi$
$644$	−3805.25	+	4068.69i	−0.00917513	+	0.00981032i
$645$	315511.			0.758395
$646$	40411.1	−	1.16897e6i	0.0968357	−	2.80116i
$647$	397384.	+	181479.i	0.949297	+	0.433529i	0.829025	−	0.559211i	$-0.188896\pi$
$647$	397384.	+	181479.i	0.949297	+	0.433529i	0.120272	+	0.992741i	$0.461623\pi$
$648$	113951.	−	452934.i	0.271373	−	1.07866i
$649$	−157828.	+	182143.i	−0.374708	+	0.432437i
$650$	21322.4	−	42718.8i	0.0504673	−	0.101110i
$651$	1682.44	+	2617.93i	0.00396989	+	0.00617727i
$652$	−28874.9	+	2131.58i	−0.0679244	+	0.00501426i
$653$	−335172.	−	386809.i	−0.786034	−	0.907132i	0.211495	−	0.977379i	$-0.432167\pi$
$653$	−335172.	−	386809.i	−0.786034	−	0.907132i	−0.997530	+	0.0702469i	$0.977621\pi$
$654$	325004.	+	301896.i	0.759860	+	0.705834i
$655$	−109961.	−	15810.0i	−0.256305	−	0.0368511i
$656$	−237879.	+	208036.i	−0.552775	+	0.483428i
$657$	60915.9	+	39148.3i	0.141124	+	0.0906946i
$658$	2282.82	−	1357.99i	0.00527255	−	0.00313651i
$659$	507451.	−	231745.i	1.16848	−	0.533629i	0.265841	−	0.964017i	$-0.414350\pi$
$659$	507451.	−	231745.i	1.16848	−	0.533629i	0.902644	+	0.430388i	$0.141623\pi$
$660$	−731403.	+	160860.i	−1.67907	+	0.369284i
$661$	−271083.	−	79597.0i	−0.620438	−	0.182177i	−0.0436182	−	0.999048i	$-0.513888\pi$
$661$	−271083.	−	79597.0i	−0.620438	−	0.182177i	−0.576820	+	0.816871i	$0.695707\pi$
$662$	512826.	−	414229.i	1.17018	−	0.945203i
$663$	−130813.	−	445508.i	−0.297594	−	1.01351i
$664$	−178602.	+	124916.i	−0.405088	+	0.283323i
$665$	1566.90	+	10898.1i	0.00354323	+	0.0246437i
$666$	10133.9	−	56538.2i	0.0228468	−	0.127466i
$667$	−2479.78	−	79565.0i	−0.00557393	−	0.178842i
$668$	−267852.	+	723186.i	−0.600262	+	1.62068i
$669$	85514.0	+	594763.i	0.191067	+	1.32890i
$670$	−99272.1	+	143329.i	−0.221145	+	0.319289i
$671$	261194.	+	889543.i	0.580119	+	1.97570i
$672$	−193.193	+	6441.95i	−0.000427812	+	0.0142652i
$673$	160498.	+	47126.5i	0.354356	+	0.104048i	0.454066	−	0.890968i	$-0.349973\pi$
$673$	160498.	+	47126.5i	0.354356	+	0.104048i	−0.0997096	+	0.995017i	$0.531791\pi$
$674$	−86495.9	−	208146.i	−0.190404	−	0.458192i
$675$	−71842.9	+	32809.6i	−0.157680	+	0.0720100i
$676$	−102180.	−	272053.i	−0.223601	−	0.595334i
$677$	−24037.0	−	15447.6i	−0.0524449	−	0.0337043i	0.514156	−	0.857697i	$-0.328105\pi$
$677$	−24037.0	−	15447.6i	−0.0524449	−	0.0337043i	−0.566601	+	0.823993i	$0.691742\pi$
$678$	−144350.	+	435364.i	−0.314020	+	0.947094i
$679$	11021.5	+	1584.66i	0.0239057	+	0.00343713i
$680$	−741087.	+	374147.i	−1.60270	+	0.809142i
$681$	−3060.86	−	3532.42i	−0.00660007	−	0.00761689i
$682$	−344236.	+	88280.6i	−0.740096	+	0.189800i
$683$	−472679.	−	735503.i	−1.01327	−	1.57668i	−0.800283	−	0.599623i	$-0.795317\pi$
$683$	−472679.	−	735503.i	−1.01327	−	1.57668i	−0.212987	−	0.977055i	$-0.568319\pi$
$684$	−61282.7	+	82255.6i	−0.130986	+	0.175814i
$685$	−359028.	+	414340.i	−0.765150	+	0.883030i
$686$	12567.2	−	1365.66i	0.0267049	−	0.00290197i
$687$	32791.2	+	14975.2i	0.0694774	+	0.0317293i
$688$	261618.	+	166445.i	0.552701	+	0.351636i
$689$	−447417.			−0.942485
$690$	359535.	+	417786.i	0.755166	+	0.877518i
$691$			457193.i			0.957510i	0.877948	+	0.478755i	$0.158912\pi$
$691$			457193.i			0.957510i	−0.877948	+	0.478755i	$0.841088\pi$
$692$	62692.2	−	291399.i	0.130919	−	0.608522i
$693$	512.893	−	1123.08i	0.00106797	−	0.00233853i
$694$	231269.	−	25131.6i	0.480173	−	0.0521796i
$695$	350322.	+	303555.i	0.725266	+	0.628446i
$696$	−62984.5	−	67186.4i	−0.130021	−	0.138696i
$697$	494502.	−	317797.i	1.01789	−	0.654160i
$698$	−310986.	+	79753.4i	−0.638307	+	0.163696i
$699$	−149642.	+	129666.i	−0.306267	+	0.265382i
$700$	985.130	−	740.982i	0.00201047	−	0.00151221i
$701$	42333.5	−	294436.i	0.0861486	−	0.599177i	−0.900320	−	0.435228i	$-0.856668\pi$
$701$	42333.5	−	294436.i	0.0861486	−	0.599177i	0.986469	−	0.163949i	$-0.0524231\pi$
$702$	86611.8	−	261224.i	0.175753	−	0.530076i
$703$	456663.	−	710581.i	0.924028	−	1.43782i
$704$	−691330.	−	252462.i	−1.39489	−	0.509390i
$705$	−109175.	−	239061.i	−0.219658	−	0.480984i
$706$	−286721.	−	689973.i	−0.575242	−	1.38428i
$707$	−735.477	+	2504.81i	−0.00147140	+	0.00501112i
$708$	179889.	−	98761.6i	0.358871	−	0.197025i
$709$	−194765.	+	57188.3i	−0.387453	+	0.113766i	−0.469657	−	0.882849i	$-0.655622\pi$
$709$	−194765.	+	57188.3i	−0.387453	+	0.113766i	0.0822038	+	0.996616i	$0.473804\pi$
$710$	−53742.4	+	77593.1i	−0.106611	+	0.153924i
$711$	−6352.94	+	913.414i	−0.0125671	+	0.00180688i
$712$	94025.6	−	159718.i	0.185475	−	0.315061i
$713$	177361.	+	192244.i	0.348883	+	0.378158i
$714$	2115.01	−	11799.9i	0.00414873	−	0.0231463i
$715$	−494034.	+	71031.4i	−0.966374	+	0.138944i
$716$	−272522.	−	271278.i	−0.531589	−	0.529162i
$717$	−675003.	+	198199.i	−1.31301	+	0.385534i
$718$	−524998.	+	424062.i	−1.01838	+	0.822584i
$719$	−119124.	+	405698.i	−0.230430	+	0.784774i	0.760376	+	0.649484i	$0.225015\pi$
$719$	−119124.	+	405698.i	−0.230430	+	0.784774i	−0.990806	+	0.135290i	$0.956803\pi$
$720$	72108.5	+	10031.1i	0.139098	+	0.0193502i
$721$	4030.68	+	8825.96i	0.00775368	+	0.0169782i
$722$	−848362.	+	504669.i	−1.62745	+	0.968128i
$723$	−85982.6	+	133791.i	−0.164488	+	0.255948i
$724$	−184466.	+	339670.i	−0.351917	+	0.648008i
$725$	−2506.79	+	17435.1i	−0.00476916	+	0.0331703i
$726$	494500.	+	459341.i	0.938194	+	0.871489i
$727$	−497362.	+	430966.i	−0.941030	+	0.815407i	−0.982980	−	0.183713i	$-0.941188\pi$
$727$	−497362.	+	430966.i	−0.941030	+	0.815407i	0.0419501	+	0.999120i	$0.486643\pi$
$728$	−444.494	+	4272.28i	−0.000838693	+	0.00806116i
$729$	−375559.	+	241357.i	−0.706680	+	0.454155i
$730$	337523.	−	676217.i	0.633371	−	1.26894i
$731$	−435894.	−	377704.i	−0.815729	−	0.706833i
$732$	54514.6	−	787528.i	0.101740	−	1.46975i
$733$	65223.7	−	142820.i	0.121394	−	0.265816i	−0.839173	−	0.543865i	$-0.816960\pi$
$733$	65223.7	−	142820.i	0.121394	−	0.265816i	0.960567	+	0.278049i	$0.0896877\pi$
$734$	8286.25	−	239696.i	0.0153803	−	0.444906i
$735$		−	625316.i		−	1.15751i
$736$	77721.8	+	536091.i	0.143479	+	0.989653i
$737$	287510.			0.529321
$738$	−51518.0	−	1780.97i	−0.0945903	−	0.00326997i
$739$	−60193.6	−	27489.5i	−0.110220	−	0.0503359i	0.359542	−	0.933129i	$-0.382933\pi$
$739$	−60193.6	−	27489.5i	−0.110220	−	0.0503359i	−0.469762	+	0.882793i	$0.655660\pi$
$740$	−598078.	−	41400.4i	−1.09218	−	0.0756034i
$741$	−392120.	+	452531.i	−0.714139	+	0.824160i
$742$	−10335.7	−	5158.90i	−0.0187729	−	0.00937021i
$743$	189331.	+	294604.i	0.342960	+	0.533656i	0.969296	−	0.245897i	$-0.0790826\pi$
$743$	189331.	+	294604.i	0.342960	+	0.533656i	−0.626336	+	0.779553i	$0.715446\pi$
$744$	300974.	+	31313.7i	0.543729	+	0.0565703i
$745$	−441543.	−	509568.i	−0.795537	−	0.918099i
$746$	588803.	−	633871.i	1.05802	−	1.13900i
$747$	−35190.6	−	5059.64i	−0.0630645	−	0.00906731i
$748$	1.20304e6	+	653339.i	2.15018	+	1.16771i
$749$	8294.76	+	5330.72i	0.0147856	+	0.00950216i
$750$	270582.	+	454855.i	0.481034	+	0.808631i
$751$	547678.	−	250116.i	0.971059	−	0.443468i	0.134241	−	0.990949i	$-0.457140\pi$
$751$	547678.	−	250116.i	0.971059	−	0.443468i	0.836818	+	0.547481i	$0.184413\pi$
$752$	35587.5	−	255820.i	0.0629307	−	0.452376i
$753$	−22947.1	−	6737.87i	−0.0404704	−	0.0118832i
$754$	−38567.3	−	47747.2i	−0.0678385	−	0.0839856i
$755$	131893.	+	449185.i	0.231381	+	0.788010i
$756$	5012.81	−	5035.80i	0.00877077	−	0.00881099i
$757$	−46726.2	−	324988.i	−0.0815396	−	0.567121i	−0.989105	−	0.147210i	$-0.952971\pi$
$757$	−46726.2	−	324988.i	−0.0815396	−	0.567121i	0.907566	−	0.419910i	$-0.137939\pi$
$758$	454314.	+	81430.8i	0.790711	+	0.141726i
$759$	228784.	−	879669.i	0.397139	−	1.52699i
$760$	922600.	+	543132.i	1.59730	+	0.940326i
$761$	51178.6	+	355955.i	0.0883729	+	0.614647i	0.985090	+	0.172042i	$0.0550365\pi$
$761$	51178.6	+	355955.i	0.0883729	+	0.614647i	−0.896717	+	0.442605i	$0.854054\pi$
$762$	−556481.	−	385429.i	−0.958387	−	0.663796i
$763$	2150.47	+	7323.82i	0.00369389	+	0.0125802i
$764$	−311681.	−	567709.i	−0.533978	−	0.972611i
$765$	−129934.	−	38152.2i	−0.222025	−	0.0651923i
$766$	−912126.	+	379038.i	−1.55452	+	0.645989i
$767$	124413.	−	56817.3i	0.211482	−	0.0965806i
$768$	477350.	+	406039.i	0.809310	+	0.688407i
$769$	−613186.	−	394070.i	−1.03691	−	0.666379i	−0.0926861	−	0.995695i	$-0.529545\pi$
$769$	−613186.	−	394070.i	−1.03691	−	0.666379i	−0.944220	+	0.329317i	$0.893182\pi$
$770$	−12231.6	−	4055.53i	−0.0206301	−	0.00684016i
$771$	−874381.	−	125717.i	−1.47093	−	0.211488i
$772$	578229.	+	768751.i	0.970209	+	1.28989i
$773$	101139.	+	116721.i	0.169262	+	0.195339i	0.834043	−	0.551700i	$-0.186021\pi$
$773$	101139.	+	116721.i	0.169262	+	0.195339i	−0.664781	+	0.747038i	$0.731475\pi$
$774$	12564.8	+	48994.7i	0.0209737	+	0.0817837i
$775$	−31290.9	−	48689.7i	−0.0520973	−	0.0810650i
$776$	789908.	−	740506.i	1.31176	−	1.22972i
$777$	5669.16	−	6542.56i	0.00939024	−	0.0108369i
$778$	110658.	+	1.01831e6i	0.182820	+	1.68236i
$779$	−689545.	−	314905.i	−1.13629	−	0.518925i
$780$	415484.	+	89388.0i	0.682912	+	0.146923i
$781$	155648.			0.255177
$782$	3425.31	−	1.00760e6i	0.00560127	−	1.64768i
$783$			101532.i			0.165608i
$784$	329879.	−	518503.i	0.536689	−	0.843566i
$785$	−306909.	+	672037.i	−0.498047	+	1.09057i
$786$	−16851.8	−	155075.i	−0.0272772	−	0.251014i
$787$	−395138.	−	342389.i	−0.637968	−	0.552802i	0.274687	−	0.961534i	$-0.411426\pi$
$787$	−395138.	−	342389.i	−0.637968	−	0.552802i	−0.912655	+	0.408731i	$0.865971\pi$
$788$	374771.	+	279215.i	0.603551	+	0.449662i
$789$	415017.	−	266715.i	0.666671	−	0.428444i
$790$	16641.1	+	64889.4i	0.0266642	+	0.103973i
$791$	−5964.80	+	5168.53i	−0.00953329	+	0.00826064i
$792$	−54106.7	−	107171.i	−0.0862582	−	0.170855i
$793$	74875.6	−	520771.i	0.119068	−	0.828134i
$794$	1.17760e6	+	390449.i	1.86792	+	0.619332i
$795$	−617922.	+	961506.i	−0.977687	+	1.52131i
$796$	318588.	−	119658.i	0.502810	−	0.188850i
$797$	9408.54	+	20601.8i	0.0148117	+	0.0324331i	0.916893	−	0.399132i	$-0.130689\pi$
$797$	9408.54	+	20601.8i	0.0148117	+	0.0324331i	−0.902082	+	0.431566i	$0.857961\pi$
$798$	−14276.1	+	5932.51i	−0.0224184	+	0.00931607i
$799$	−135353.	+	460969.i	−0.212018	+	0.722069i
$800$	3593.10	−	119811.i	0.00561422	−	0.187204i
$801$	29008.2	−	8517.56i	0.0452121	−	0.0132755i
$802$	452580.	+	313465.i	0.703633	+	0.487349i
$803$	−1.23361e6	+	177367.i	−1.91314	+	0.275068i
$804$	−229571.	−	85028.0i	−0.355145	−	0.131538i
$805$	1641.60	+	9341.44i	0.00253323	+	0.0144153i
$806$	198512.	+	35581.0i	0.305574	+	0.0547707i
$807$	498856.	−	71724.7i	0.765999	−	0.110134i
$808$	145488.	+	208015.i	0.222845	+	0.318619i
$809$	251488.	−	73843.6i	0.384256	−	0.112828i	−0.0838988	−	0.996474i	$-0.526737\pi$
$809$	251488.	−	73843.6i	0.384256	−	0.112828i	0.468154	+	0.883647i	$0.344919\pi$
$810$	−499653.	−	618581.i	−0.761549	−	0.942816i
$811$	−35223.3	+	119959.i	−0.0535535	+	0.182387i	−0.981926	−	0.189264i	$-0.939390\pi$
$811$	−35223.3	+	119959.i	−0.0535535	+	0.182387i	0.928373	+	0.371650i	$0.121208\pi$
$812$	−340.390	−	1547.69i	−0.000516255	−	0.00234732i
$813$	−447365.	−	979592.i	−0.676832	−	1.48205i
$814$	505432.	+	849644.i	0.762806	+	1.28230i
$815$	−26650.7	+	41469.3i	−0.0401230	+	0.0624326i
$816$	−767383.	−	877463.i	−1.15248	−	1.31780i
$817$	−105854.	+	736233.i	−0.158586	+	1.10299i
$818$	627995.	−	676063.i	0.938533	−	1.01037i
$819$	−529.525	+	458.836i	−0.000789440	+	0.000684053i
$820$	39610.1	+	536569.i	0.0589086	+	0.797991i
$821$	130648.	−	83962.2i	0.193828	−	0.124565i	−0.440128	−	0.897935i	$-0.645067\pi$
$821$	130648.	−	83962.2i	0.193828	−	0.124565i	0.633955	+	0.773370i	$0.281430\pi$
$822$	−688785.	−	343796.i	−1.01939	−	0.508812i
$823$	130946.	+	113466.i	0.193328	+	0.167519i	0.746146	−	0.665783i	$-0.231902\pi$
$823$	130946.	+	113466.i	0.193328	+	0.167519i	−0.552818	+	0.833302i	$0.686448\pi$
$824$	914965.	+	230190.i	1.34757	+	0.339025i
$825$	−83550.6	+	182950.i	−0.122756	+	0.268797i
$826$	3529.15	+	122.002i	0.00517262	+	0.000178817i
$827$		−	1.00903e6i		−	1.47534i	−0.675162	−	0.737669i	$-0.735926\pi$
$827$		−	1.00903e6i		−	1.47534i	0.675162	−	0.737669i	$-0.264074\pi$
$828$	−50558.5	+	72468.7i	−0.0737452	+	0.105704i
$829$	488397.			0.710663			0.355331	−	0.934740i	$-0.384368\pi$
$829$	488397.			0.710663			0.355331	+	0.934740i	$0.384368\pi$
$830$	−12820.2	+	370849.i	−0.0186097	+	0.538321i
$831$	892233.	+	407469.i	1.29204	+	0.590056i
$832$	297357.	+	293304.i	0.429568	+	0.423712i
$833$	−748576.	+	863903.i	−1.07881	+	1.24502i
$834$	−290677.	+	582363.i	−0.417907	+	0.837262i
$835$	709858.	+	1.10456e6i	1.01812	+	1.58422i
$836$	−129975.	−	1.76067e6i	−0.185971	−	2.51922i
$837$	−218472.	−	252130.i	−0.311849	−	0.359893i
$838$	435578.	+	404608.i	0.620266	+	0.576165i
$839$	254160.	+	36542.7i	0.361064	+	0.0519131i	0.320460	−	0.947262i	$-0.396163\pi$
$839$	254160.	+	36542.7i	0.361064	+	0.0519131i	0.0406041	+	0.999175i	$0.487072\pi$
$840$	8567.31	+	6855.62i	0.0121419	+	0.00971602i
$841$	−575953.	−	370143.i	−0.814320	−	0.523332i
$842$	−1.04318e6	+	620561.i	−1.47141	+	0.875307i
$843$	993359.	−	453652.i	1.39782	−	0.638363i
$844$	69445.6	+	315757.i	0.0974899	+	0.443269i
$845$	−474733.	−	139394.i	−0.664869	−	0.195223i
$846$	32775.1	−	26473.8i	0.0457935	−	0.0369892i
$847$	3271.97	+	11143.3i	0.00456082	+	0.0155327i
$848$	−1.01961e6	+	471288.i	−1.41788	+	0.655382i
$849$	−48158.6	−	334951.i	−0.0668126	−	0.464692i
$850$	−39336.0	+	219461.i	−0.0544443	+	0.303752i
$851$	374129.	−	624083.i	0.516610	−	0.861754i
$852$	−124282.	−	46031.2i	−0.171210	−	0.0634122i
$853$	5712.60	+	39732.0i	0.00785119	+	0.0546062i	0.993370	−	0.114958i	$-0.0366732\pi$
$853$	5712.60	+	39732.0i	0.00785119	+	0.0546062i	−0.985519	+	0.169564i	$0.945764\pi$
$854$	7734.38	−	11166.9i	0.0106050	−	0.0153114i
$855$	49201.1	+	167564.i	0.0673043	+	0.229217i
$856$	908657.	−	305897.i	1.24009	−	0.417473i
$857$	249693.	+	73316.6i	0.339974	+	0.0998253i	0.447263	−	0.894403i	$-0.352399\pi$
$857$	249693.	+	73316.6i	0.339974	+	0.0998253i	−0.107289	+	0.994228i	$0.534217\pi$
$858$	−268935.	−	647171.i	−0.365319	−	0.879113i
$859$	−221555.	+	101181.i	−0.300259	+	0.137124i	−0.559848	−	0.828596i	$-0.689140\pi$
$859$	−221555.	+	101181.i	−0.300259	+	0.137124i	0.259589	+	0.965719i	$0.416413\pi$
$860$	494210.	−	185620.i	0.668213	−	0.250973i
$861$	−6535.93	−	4200.38i	−0.00881659	−	0.00566608i
$862$	166031.	−	500754.i	0.223447	−	0.673922i
$863$	266808.	+	38361.2i	0.358243	+	0.0515075i	0.319087	−	0.947726i	$-0.396624\pi$
$863$	266808.	+	38361.2i	0.358243	+	0.0515075i	0.0391562	+	0.999233i	$0.487533\pi$
$864$	−77783.5	−	686527.i	−0.104198	−	0.919666i
$865$	−332323.	−	383521.i	−0.444149	−	0.512575i
$866$	−618476.	+	158610.i	−0.824683	+	0.211493i
$867$	740467.	+	1.15219e6i	0.985071	+	1.53280i
$868$	4175.51	+	3110.87i	0.00554204	+	0.00412897i
$869$	72341.0	−	83486.0i	0.0957955	−	0.110554i
$870$	−155874.	+	16938.6i	−0.205937	+	0.0223789i
$871$	−148417.	−	67779.8i	−0.195636	−	0.0893437i
$872$	686690.	+	281679.i	0.903083	+	0.370444i
$873$	176616.			0.231741
$874$	−1.09551e6	+	698792.i	−1.43415	+	0.914797i
$875$			9107.08i			0.0118950i
$876$	1.03747e6	+	223203.i	1.35197	+	0.290865i
$877$	213656.	−	467842.i	0.277790	−	0.608275i	−0.718386	−	0.695645i	$-0.755119\pi$
$877$	213656.	−	467842.i	0.277790	−	0.608275i	0.996176	+	0.0873694i	$0.0278460\pi$
$878$	−1.46411e6	+	159102.i	−1.89926	+	0.206389i
$879$	272668.	+	236268.i	0.352903	+	0.305792i
$880$	−1.05102e6	+	682263.i	−1.35720	+	0.881022i
$881$	−1.13904e6	+	732017.i	−1.46753	+	0.943126i	−0.469341	+	0.883017i	$0.655508\pi$
$881$	−1.13904e6	+	732017.i	−1.46753	+	0.943126i	−0.998192	+	0.0601086i	$0.980855\pi$
$882$	97103.1	−	24902.4i	0.124823	−	0.0320114i
$883$	526676.	−	456368.i	0.675495	−	0.585320i	−0.248079	−	0.968740i	$-0.579799\pi$
$883$	526676.	−	456368.i	0.675495	−	0.585320i	0.923574	+	0.383420i	$0.125254\pi$
$884$	−467002.	−	620876.i	−0.597605	−	0.794512i
$885$	49723.4	−	345834.i	0.0634855	−	0.441551i
$886$	284763.	−	858852.i	0.362757	−	1.09408i
$887$	637556.	−	992057.i	0.810347	−	1.26092i	−0.151804	−	0.988411i	$-0.548508\pi$
$887$	637556.	−	992057.i	0.810347	−	1.26092i	0.962152	−	0.272514i	$-0.0878553\pi$
$888$	−152305.	−	827900.i	−0.193147	−	1.04991i
$889$	−4838.82	−	10595.5i	−0.00612261	−	0.0134066i
$890$	−121088.	−	291390.i	−0.152870	−	0.367870i
$891$	−369426.	+	1.25815e6i	−0.465342	+	1.58481i
$892$	483855.	+	881315.i	0.608115	+	1.10765i
$893$	594467.	−	174551.i	0.745461	−	0.218887i
$894$	539061.	−	778294.i	0.674470	−	0.973797i
$895$	−648009.	+	93169.6i	−0.808974	+	0.116313i
$896$	3487.28	+	10204.2i	0.00434380	+	0.0127105i
$897$	−325481.	+	400163.i	−0.404521	+	0.497338i
$898$	148386.	−	827866.i	0.184009	−	1.02661i
$899$	−73646.7	+	10588.8i	−0.0911242	+	0.0131017i
$900$	13794.0	−	13857.3i	0.0170296	−	0.0171077i
$901$	2.00472e6	−	588640.i	2.46948	−	0.725103i
$902$	690198.	−	557500.i	0.848321	−	0.685223i
$903$	−2147.73	+	7314.48i	−0.00263392	+	0.00897032i
$904$	30023.9	+	766868.i	0.0367393	+	0.938391i
$905$	273376.	+	598611.i	0.333783	+	0.730882i
$906$	−564942.	+	336070.i	−0.688252	+	0.409424i
$907$	−372068.	+	578949.i	−0.452280	+	0.703762i	−0.990265	−	0.139193i	$-0.955549\pi$
$907$	−372068.	+	578949.i	−0.452280	+	0.703762i	0.537985	+	0.842954i	$0.319186\pi$
$908$	−6872.63	−	3732.36i	−0.00833588	−	0.00452701i
$909$	−5892.89	+	40986.0i	−0.00713182	+	0.0496029i
$910$	5358.05	+	4977.09i	0.00647029	+	0.00601025i
$911$	−102820.	+	89093.7i	−0.123891	+	0.107352i	−0.714603	−	0.699531i	$-0.753392\pi$
$911$	−102820.	+	89093.7i	−0.123891	+	0.107352i	0.590712	+	0.806883i	$0.298847\pi$
$912$	−416916.	+	1.44430e6i	−0.501255	+	1.73647i
$913$	514771.	−	330823.i	0.617551	−	0.396876i
$914$	−155060.	+	310658.i	−0.185612	+	0.371869i
$915$	−1.01573e6	−	880139.i	−1.21322	−	1.05126i
$916$	60173.6	+	4165.36i	0.0717158	+	0.00496435i
$917$	1115.04	−	2441.60i	0.00132603	−	0.00290360i
$918$	−44401.6	+	1.28440e6i	−0.0526882	+	1.52411i
$919$			226168.i			0.267794i	0.990995	+	0.133897i	$0.0427491\pi$
$919$			226168.i			0.267794i	−0.990995	+	0.133897i	$0.957251\pi$
$920$	808957.	+	442892.i	0.955762	+	0.523266i
$921$	−1.28456e6			−1.51438
$922$	192355.	+	6649.69i	0.226278	+	0.00782239i
$923$	−80347.8	−	36693.6i	−0.0943128	−	0.0430712i
$924$	1249.54	−	18051.1i	0.00146355	−	0.0211426i
$925$	−105438.	+	121682.i	−0.123229	+	0.142214i
$926$	−1.11796e6	−	558010.i	−1.30377	−	0.650759i
$927$	83205.3	+	129470.i	0.0968259	+	0.150664i
$928$	−138184.	−	68184.6i	−0.160458	−	0.0791754i
$929$	−559613.	−	645828.i	−0.648420	−	0.748316i	0.332420	−	0.943131i	$-0.392135\pi$
$929$	−559613.	−	645828.i	−0.648420	−	0.748316i	−0.980840	+	0.194815i	$0.937589\pi$
$930$	350626.	−	377464.i	0.405395	−	0.436425i
$931$	1.45915e6	+	209794.i	1.68345	+	0.242044i
$932$	−158112.	+	291143.i	−0.182026	+	0.335177i
$933$	−637332.	−	409589.i	−0.732154	−	0.470527i
$934$	825405.	+	1.38753e6i	0.946179	+	1.59055i
$935$	2.12015e6	−	968238.i	2.42517	−	1.10754i
$936$	2665.37	+	68078.7i	0.00304233	+	0.0777069i
$937$	463505.	+	136097.i	0.527928	+	0.155014i	0.534826	−	0.844963i	$-0.320377\pi$
$937$	463505.	+	136097.i	0.527928	+	0.155014i	−0.00689735	+	0.999976i	$0.502196\pi$
$938$	−2647.02	−	3277.07i	−0.00300851	−	0.00372461i
$939$	−194002.	−	660709.i	−0.220026	−	0.749341i
$940$	−311653.	−	310230.i	−0.352708	−	0.351098i
$941$	215624.	+	1.49970e6i	0.243511	+	1.69366i	0.634228	+	0.773146i	$0.281318\pi$
$941$	215624.	+	1.49970e6i	0.243511	+	1.69366i	−0.390717	+	0.920511i	$0.627773\pi$
$942$	−1.02111e6	−	183022.i	−1.15072	−	0.206253i
$943$	−602166.	−	252637.i	−0.677163	−	0.284101i
$944$	223671.	−	260529.i	0.250996	−	0.292357i
$945$	−1721.63	−	11974.2i	−0.00192787	−	0.0134086i
$946$	−715663.	−	495681.i	−0.799698	−	0.553886i
$947$	−45349.1	−	154445.i	−0.0505672	−	0.172216i	0.930338	−	0.366704i	$-0.119514\pi$
$947$	−45349.1	−	154445.i	−0.0505672	−	0.172216i	−0.980905	+	0.194488i	$0.937696\pi$
$948$	−82452.9	+	45267.9i	−0.0917465	+	0.0503702i
$949$	678622.	+	199261.i	0.753521	+	0.221254i
$950$	265515.	−	110336.i	0.294199	−	0.122256i
$951$	234593.	−	107135.i	0.259390	−	0.118460i
$952$	−3629.16	−	19727.4i	−0.00400435	−	0.0217669i
$953$	1.23321e6	+	792534.i	1.35784	+	0.872634i	0.998172	−	0.0604450i	$-0.0192520\pi$
$953$	1.23321e6	+	792534.i	1.35784	+	0.872634i	0.359673	+	0.933079i	$0.382888\pi$
$954$	−173917.	−	57664.2i	−0.191093	−	0.0633592i
$955$	−1.09141e6	−	156922.i	−1.19669	−	0.172058i
$956$	−940707.	+	707568.i	−1.02929	+	0.774199i
$957$	169318.	+	195403.i	0.184875	+	0.213357i
$958$	180966.	+	705650.i	0.197182	+	0.768880i
$959$	−7161.67	−	11143.8i	−0.00778712	−	0.0121170i
$960$	1.04099e6	−	233947.i	1.12955	−	0.253849i
$961$	−444679.	+	513187.i	−0.481504	+	0.555685i
$962$	−60610.1	−	557753.i	−0.0654930	−	0.602687i
$963$	142262.	+	64968.9i	0.153404	+	0.0700572i
$964$	−55969.8	+	260153.i	−0.0602282	+	0.279946i
$965$	1.63774e6			1.75870
$966$	−12132.9	+	5491.14i	−0.0130020	+	0.00588448i
$967$		−	728547.i		−	0.779120i	−0.921001	−	0.389560i	$-0.872627\pi$
$967$		−	728547.i		−	0.779120i	0.921001	−	0.389560i	$-0.127373\pi$
$968$	1.04481e6	+	428580.i	1.11503	+	0.457385i
$969$	1.16159e6	−	2.54352e6i	1.23710	−	2.70887i
$970$	−199146.	−	1.83261e6i	−0.211655	−	1.94772i
$971$	465105.	+	403016.i	0.493302	+	0.427449i	0.865654	−	0.500643i	$-0.166903\pi$
$971$	465105.	+	403016.i	0.493302	+	0.427449i	−0.372352	+	0.928092i	$0.621449\pi$
$972$	144631.	−	194128.i	0.153084	−	0.205474i
$973$	−9421.99	+	6055.14i	−0.00995215	+	0.00639586i
$974$	171423.	+	668436.i	0.180697	+	0.704599i
$975$	86260.0	−	74744.7i	0.0907403	−	0.0786269i
$976$	−377924.	−	1.26564e6i	−0.396738	−	1.32865i
$977$	1247.60	−	8677.27i	0.00130703	−	0.00909063i	−0.989157	−	0.146859i	$-0.953084\pi$
$977$	1247.60	−	8677.27i	0.00130703	−	0.00909063i	0.990465	+	0.137768i	$0.0439928\pi$
$978$	−65699.3	−	21783.4i	−0.0686883	−	0.0227744i
$979$	−281323.	+	437747.i	−0.293522	+	0.456728i
$980$	−367882.	−	979482.i	−0.383051	−	1.01987i
$981$	50294.9	+	110130.i	0.0522620	+	0.114438i
$982$	582245.	−	241954.i	0.603786	−	0.250906i
$983$	−145411.	+	495225.i	−0.150484	+	0.512502i	−0.999884	−	0.0152485i	$-0.995146\pi$
$983$	−145411.	+	495225.i	−0.150484	+	0.512502i	0.849400	+	0.527750i	$0.176964\pi$
$984$	−715984.	+	241034.i	−0.739457	+	0.248937i
$985$	763450.	−	224169.i	0.786879	−	0.231049i
$986$	235625.	+	163198.i	0.242363	+	0.167865i
$987$	6285.30	−	903.690i	0.00645196	−	0.000927652i
$988$	−347978.	+	939524.i	−0.356483	+	0.962485i
$989$	−71386.2	+	636756.i	−0.0729830	+	0.650999i
$990$	−201192.	−	36061.5i	−0.205277	−	0.0367937i
$991$	−688569.	+	99001.3i	−0.701133	+	0.100808i	−0.483656	−	0.875258i	$-0.660692\pi$
$991$	−688569.	+	99001.3i	−0.701133	+	0.100808i	−0.217476	+	0.976066i	$0.569782\pi$
$992$	489861.	−	128018.i	0.497794	−	0.130091i
$993$	1.51211e6	−	443994.i	1.53350	−	0.450276i
$994$	−1433.00	−	1774.09i	−0.00145036	−	0.00179557i
$995$	163238.	−	555936.i	0.164882	−	0.561538i
$996$	−508872.	+	111918.i	−0.512968	+	0.112819i
$997$	243651.	+	533522.i	0.245120	+	0.536737i	0.991702	−	0.128555i	$-0.0410340\pi$
$997$	243651.	+	533522.i	0.245120	+	0.536737i	−0.746583	+	0.665293i	$0.768307\pi$
$998$	−380615.	−	639824.i	−0.382142	−	0.642391i
$999$	−501758.	+	780750.i	−0.502763	+	0.782314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.3.45	yes	460
4.3	odd	2	inner	92.5.g.a.3.6	✓	460
23.8	even	11	inner	92.5.g.a.31.6	yes	460
92.31	odd	22	inner	92.5.g.a.31.45	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.6	✓	460	4.3	odd	2	inner
92.5.g.a.3.45	yes	460	1.1	even	1	trivial
92.5.g.a.31.6	yes	460	23.8	even	11	inner
92.5.g.a.31.45	yes	460	92.31	odd	22	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(3.99761 + 0.138197i) q^{2} +(8.69828 + 3.97237i) q^{3} +(15.9618 + 1.10492i) q^{4} +(17.8389 - 20.5871i) q^{5} +(34.2234 + 17.0821i) q^{6} +(0.355839 + 0.553696i) q^{7} +(63.6564 + 6.62289i) q^{8} +(6.83659 + 7.88985i) q^{9} +(74.1579 - 79.8341i) q^{10} +(-177.855 - 25.5717i) q^{11} +(134.451 + 73.0171i) q^{12} +(85.7828 + 55.1293i) q^{13} +(1.34599 + 2.26264i) q^{14} +(236.947 - 108.210i) q^{15} +(253.558 + 35.2729i) q^{16} +(-456.893 - 134.156i) q^{17} +(26.2397 + 32.4854i) q^{18} +(173.008 + 589.211i) q^{19} +(307.487 - 308.897i) q^{20} +(0.895700 + 6.22973i) q^{21} +(-707.461 - 126.805i) q^{22} +(164.776 + 502.683i) q^{23} +(527.392 + 310.475i) q^{24} +(-16.6587 - 115.864i) q^{25} +(335.308 + 232.240i) q^{26} +(-190.092 - 647.395i) q^{27} +(5.06804 + 9.23116i) q^{28} +(-144.384 - 42.3950i) q^{29} +(962.177 - 399.837i) q^{30} +(449.764 - 205.400i) q^{31} +(1008.75 + 176.048i) q^{32} +(-1445.45 - 928.935i) q^{33} +(-1807.94 - 599.445i) q^{34} +(17.7468 + 2.55160i) q^{35} +(100.407 + 133.490i) q^{36} +(-900.755 - 1039.53i) q^{37} +(610.192 + 2379.35i) q^{38} +(527.169 + 820.291i) q^{39} +(1271.90 - 1192.36i) q^{40} +(-808.382 + 932.923i) q^{41} +(2.71973 + 25.0278i) q^{42} +(1101.78 + 503.166i) q^{43} +(-2810.63 - 604.684i) q^{44} +284.386 q^{45} +(589.241 + 2032.30i) q^{46} -1008.92i q^{47} +(2065.40 + 1314.04i) q^{48} +(997.231 - 2183.63i) q^{49} +(-50.5830 - 465.481i) q^{50} +(-3441.27 - 2981.88i) q^{51} +(1308.34 + 974.745i) q^{52} +(-3691.19 + 2372.18i) q^{53} +(-670.447 - 2614.30i) q^{54} +(-3699.18 + 3205.35i) q^{55} +(18.9844 + 37.6030i) q^{56} +(-835.693 + 5812.37i) q^{57} +(-571.332 - 189.432i) q^{58} +(725.160 - 1128.37i) q^{59} +(3901.67 - 1465.42i) q^{60} +(-2143.38 - 4693.34i) q^{61} +(1826.37 - 758.955i) q^{62} +(-1.93585 + 6.59291i) q^{63} +(4008.27 + 843.179i) q^{64} +(2665.22 - 782.580i) q^{65} +(-5649.98 - 3913.28i) q^{66} +(-1583.80 + 227.717i) q^{67} +(-7144.61 - 2646.20i) q^{68} +(-563.576 + 5027.02i) q^{69} +(70.5921 + 12.6529i) q^{70} +(-857.416 + 123.278i) q^{71} +(382.939 + 547.517i) q^{72} +(6655.10 - 1954.11i) q^{73} +(-3457.21 - 4280.11i) q^{74} +(315.352 - 1073.99i) q^{75} +(2110.49 + 9596.03i) q^{76} +(-49.1288 - 107.577i) q^{77} +(1994.06 + 3352.06i) q^{78} +(-332.381 + 517.194i) q^{79} +(5249.36 - 4590.81i) q^{80} +(1038.56 - 7223.35i) q^{81} +(-3360.53 + 3617.75i) q^{82} +(-2573.69 + 2230.12i) q^{83} +(7.41366 + 100.427i) q^{84} +(-10912.3 + 7012.94i) q^{85} +(4334.96 + 2163.73i) q^{86} +(-1087.48 - 942.310i) q^{87} +(-11152.2 - 2805.71i) q^{88} +(1203.01 - 2634.23i) q^{89} +(1136.87 + 39.3013i) q^{90} +67.1148i q^{91} +(2074.70 + 8205.79i) q^{92} +4728.10 q^{93} +(139.430 - 4033.27i) q^{94} +(15216.4 + 6949.11i) q^{95} +(8075.09 + 5538.46i) q^{96} +(11078.7 - 12785.5i) q^{97} +(4288.32 - 8591.50i) q^{98} +(-1014.16 - 1578.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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