LMFDB - Embedded newform 36.5.f.a.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.63137 + 3.01262i) q^{2} +(-8.65442 - 2.47004i) q^{3} +(-2.15179 + 15.8546i) q^{4} +(-10.5756 + 18.3175i) q^{5} +(-15.3317 - 32.5721i) q^{6} +(-38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 + 42.7535i) q^{9} +O(q^{10})$	\(q+(2.63137 + 3.01262i) q^{2} +(-8.65442 - 2.47004i) q^{3} +(-2.15179 + 15.8546i) q^{4} +(-10.5756 + 18.3175i) q^{5} +(-15.3317 - 32.5721i) q^{6} +(-38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 + 42.7535i) q^{9} +(-83.0119 + 16.3397i) q^{10} +(58.6904 - 33.8849i) q^{11} +(57.7841 - 131.898i) q^{12} +(14.5519 - 25.2046i) q^{13} +(-168.887 - 57.7061i) q^{14} +(136.770 - 132.405i) q^{15} +(-246.740 - 68.2318i) q^{16} +402.841 q^{17} +(52.2322 + 319.762i) q^{18} +644.741i q^{19} +(-267.660 - 207.088i) q^{20} +(389.517 - 97.6292i) q^{21} +(256.519 + 87.6483i) q^{22} +(-335.527 - 193.717i) q^{23} +(549.409 - 172.990i) q^{24} +(88.8138 + 153.830i) q^{25} +(114.223 - 22.4833i) q^{26} +(-489.802 - 539.940i) q^{27} +(-270.558 - 660.639i) q^{28} +(-362.210 - 627.366i) q^{29} +(758.779 + 63.6318i) q^{30} +(1090.90 + 629.833i) q^{31} +(-443.706 - 922.876i) q^{32} +(-591.628 + 148.287i) q^{33} +(1060.02 + 1213.61i) q^{34} -943.733i q^{35} +(-825.880 + 998.768i) q^{36} -1402.04 q^{37} +(-1942.36 + 1696.55i) q^{38} +(-188.194 + 182.187i) q^{39} +(-80.4363 - 1351.28i) q^{40} +(-774.166 + 1340.89i) q^{41} +(1319.08 + 916.570i) q^{42} +(-1620.98 + 935.875i) q^{43} +(410.944 + 1003.43i) q^{44} +(-1510.71 + 808.057i) q^{45} +(-299.300 - 1520.56i) q^{46} +(3610.63 - 2084.60i) q^{47} +(1966.85 + 1199.96i) q^{48} +(-205.097 + 355.239i) q^{49} +(-229.730 + 672.346i) q^{50} +(-3486.36 - 995.034i) q^{51} +(368.297 + 284.950i) q^{52} +906.566 q^{53} +(337.786 - 2896.37i) q^{54} +1433.41i q^{55} +(1278.32 - 2553.48i) q^{56} +(1592.54 - 5579.86i) q^{57} +(936.910 - 2742.03i) q^{58} +(3916.45 + 2261.16i) q^{59} +(1804.93 + 2453.35i) q^{60} +(-1314.22 - 2276.30i) q^{61} +(973.119 + 4943.80i) q^{62} +(-3612.19 - 117.200i) q^{63} +(1612.72 - 3765.15i) q^{64} +(307.789 + 533.107i) q^{65} +(-2003.52 - 1392.16i) q^{66} +(58.7165 + 33.9000i) q^{67} +(-866.831 + 6386.91i) q^{68} +(2425.30 + 2505.27i) q^{69} +(2843.11 - 2483.31i) q^{70} +1315.04i q^{71} +(-5182.11 + 140.062i) q^{72} +9470.72 q^{73} +(-3689.27 - 4223.80i) q^{74} +(-388.665 - 1550.68i) q^{75} +(-10222.1 - 1387.35i) q^{76} +(-1511.89 + 2618.67i) q^{77} +(-1044.07 - 87.5566i) q^{78} +(3783.95 - 2184.67i) q^{79} +(3859.25 - 3798.05i) q^{80} +(2905.28 + 5882.69i) q^{81} +(-6076.73 + 1196.12i) q^{82} +(659.925 - 381.008i) q^{83} +(709.715 + 6385.74i) q^{84} +(-4260.28 + 7379.03i) q^{85} +(-7084.84 - 2420.78i) q^{86} +(1585.10 + 6324.16i) q^{87} +(-1941.61 + 3878.41i) q^{88} +8083.40 q^{89} +(-6409.62 - 2424.91i) q^{90} +1298.56i q^{91} +(3793.29 - 4902.82i) q^{92} +(-7885.41 - 8145.41i) q^{93} +(15781.0 + 5392.11i) q^{94} +(-11810.0 - 6818.52i) q^{95} +(1560.48 + 9082.93i) q^{96} +(-3332.71 - 5772.42i) q^{97} +(-1609.89 + 316.884i) q^{98} +(5486.47 + 178.012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.63137	+	3.01262i	0.657842	+	0.753156i
$2$	2.63137	+	3.01262i	0.657842	+	0.753156i
$3$	−8.65442	−	2.47004i	−0.961602	−	0.274449i
$3$	−8.65442	−	2.47004i	−0.961602	−	0.274449i
$4$	−2.15179	+	15.8546i	−0.134487	+	0.990915i
$5$	−10.5756	+	18.3175i	−0.423024	+	0.732698i	−0.996234	−	0.0867102i	$-0.972365\pi$
$5$	−10.5756	+	18.3175i	−0.423024	+	0.732698i	0.573210	+	0.819409i	$0.305698\pi$
$6$	−15.3317	−	32.5721i	−0.425879	−	0.904780i
$7$	−38.6407	+	22.3092i	−0.788586	+	0.455290i	−0.839464	−	0.543415i	$-0.817131\pi$
$7$	−38.6407	+	22.3092i	−0.788586	+	0.455290i	0.0508787	+	0.998705i	$0.483798\pi$
$8$	−53.4262	+	35.2369i	−0.834785	+	0.550576i
$9$	68.7978	+	42.7535i	0.849356	+	0.527821i
$10$	−83.0119	+	16.3397i	−0.830119	+	0.163397i
$11$	58.6904	−	33.8849i	0.485045	−	0.280041i	−0.237472	−	0.971394i	$-0.576319\pi$
$11$	58.6904	−	33.8849i	0.485045	−	0.280041i	0.722516	+	0.691354i	$0.242985\pi$
$12$	57.7841	−	131.898i	0.401279	−	0.915956i
$13$	14.5519	−	25.2046i	0.0861058	−	0.149140i	−0.819756	−	0.572713i	$-0.805891\pi$
$13$	14.5519	−	25.2046i	0.0861058	−	0.149140i	0.905862	+	0.423573i	$0.139224\pi$
$14$	−168.887	−	57.7061i	−0.861669	−	0.294419i
$15$	136.770	−	132.405i	0.607868	−	0.588466i
$16$	−246.740	−	68.2318i	−0.963826	−	0.266531i
$17$	402.841			1.39391			0.696957	−	0.717113i	$-0.254537\pi$
$17$	402.841			1.39391			0.696957	+	0.717113i	$0.254537\pi$
$18$	52.2322	+	319.762i	0.161211	+	0.986920i
$19$			644.741i			1.78599i	0.450070	+	0.892993i	$0.351399\pi$
$19$			644.741i			1.78599i	−0.450070	+	0.892993i	$0.648601\pi$
$20$	−267.660	−	207.088i	−0.669151	−	0.517719i
$21$	389.517	−	97.6292i	0.883259	−	0.221381i
$22$	256.519	+	87.6483i	0.529997	+	0.181092i
$23$	−335.527	−	193.717i	−0.634267	−	0.366194i	0.148136	−	0.988967i	$-0.452673\pi$
$23$	−335.527	−	193.717i	−0.634267	−	0.366194i	−0.782403	+	0.622773i	$0.786006\pi$
$24$	549.409	−	172.990i	0.953836	−	0.300329i
$25$	88.8138	+	153.830i	0.142102	+	0.246128i
$26$	114.223	−	22.4833i	0.168969	−	0.0332593i
$27$	−489.802	−	539.940i	−0.671882	−	0.740658i
$28$	−270.558	−	660.639i	−0.345099	−	0.842652i
$29$	−362.210	−	627.366i	−0.430690	−	0.745977i	0.566243	−	0.824238i	$-0.308396\pi$
$29$	−362.210	−	627.366i	−0.430690	−	0.745977i	−0.996933	+	0.0782617i	$0.975063\pi$
$30$	758.779	+	63.6318i	0.843088	+	0.0707020i
$31$	1090.90	+	629.833i	1.13517	+	0.655393i	0.945231	−	0.326402i	$-0.105836\pi$
$31$	1090.90	+	629.833i	1.13517	+	0.655393i	0.189944	+	0.981795i	$0.439169\pi$
$32$	−443.706	−	922.876i	−0.433307	−	0.901246i
$33$	−591.628	+	148.287i	−0.543277	+	0.136168i
$34$	1060.02	+	1213.61i	0.916976	+	1.04983i
$35$		−	943.733i		−	0.770394i
$36$	−825.880	+	998.768i	−0.637253	+	0.770654i
$37$	−1402.04			−1.02413			−0.512066	−	0.858946i	$-0.671120\pi$
$37$	−1402.04			−1.02413			−0.512066	+	0.858946i	$0.671120\pi$
$38$	−1942.36	+	1696.55i	−1.34513	+	1.17490i
$39$	−188.194	+	182.187i	−0.123731	+	0.119781i
$40$	−80.4363	−	1351.28i	−0.0502727	−	0.844552i
$41$	−774.166	+	1340.89i	−0.460539	+	0.797677i	−0.998988	−	0.0449815i	$-0.985677\pi$
$41$	−774.166	+	1340.89i	−0.460539	+	0.797677i	0.538449	+	0.842658i	$0.319010\pi$
$42$	1319.08	+	916.570i	0.747780	+	0.519598i
$43$	−1620.98	+	935.875i	−0.876681	+	0.506152i	−0.869563	−	0.493823i	$-0.835599\pi$
$43$	−1620.98	+	935.875i	−0.876681	+	0.506152i	−0.00711825	+	0.999975i	$0.502266\pi$
$44$	410.944	+	1003.43i	0.212264	+	0.518300i
$45$	−1510.71	+	808.057i	−0.746031	+	0.399041i
$46$	−299.300	−	1520.56i	−0.141446	−	0.718599i
$47$	3610.63	−	2084.60i	1.63451	−	0.943683i	0.651828	−	0.758367i	$-0.274002\pi$
$47$	3610.63	−	2084.60i	1.63451	−	0.943683i	0.982679	−	0.185316i	$-0.0593310\pi$
$48$	1966.85	+	1199.96i	0.853668	+	0.520817i
$49$	−205.097	+	355.239i	−0.0854217	+	0.147955i
$50$	−229.730	+	672.346i	−0.0918920	+	0.268938i
$51$	−3486.36	−	995.034i	−1.34039	−	0.382558i
$52$	368.297	+	284.950i	0.136205	+	0.105381i
$53$	906.566			0.322736			0.161368	−	0.986894i	$-0.448409\pi$
$53$	906.566			0.322736			0.161368	+	0.986894i	$0.448409\pi$
$54$	337.786	−	2896.37i	0.115839	−	0.993268i
$55$			1433.41i			0.473855i
$56$	1278.32	−	2553.48i	0.407627	−	0.814246i
$57$	1592.54	−	5579.86i	0.490162	−	1.71741i
$58$	936.910	−	2742.03i	0.278511	−	0.815111i
$59$	3916.45	+	2261.16i	1.12509	+	0.649573i	0.942696	−	0.333652i	$-0.108281\pi$
$59$	3916.45	+	2261.16i	1.12509	+	0.649573i	0.182397	+	0.983225i	$0.441614\pi$
$60$	1804.93	+	2453.35i	0.501369	+	0.681487i
$61$	−1314.22	−	2276.30i	−0.353190	−	0.611743i	0.633617	−	0.773647i	$-0.281570\pi$
$61$	−1314.22	−	2276.30i	−0.353190	−	0.611743i	−0.986806	+	0.161904i	$0.948236\pi$
$62$	973.119	+	4943.80i	0.253153	+	1.28611i
$63$	−3612.19	−	117.200i	−0.910101	−	0.0295289i
$64$	1612.72	−	3765.15i	0.393731	−	0.919226i
$65$	307.789	+	533.107i	0.0728496	+	0.126179i
$66$	−2003.52	−	1392.16i	−0.459946	−	0.319595i
$67$	58.7165	+	33.9000i	0.0130801	+	0.00755179i	0.506526	−	0.862225i	$-0.330930\pi$
$67$	58.7165	+	33.9000i	0.0130801	+	0.00755179i	−0.493446	+	0.869777i	$0.664263\pi$
$68$	−866.831	+	6386.91i	−0.187463	+	1.38125i
$69$	2425.30	+	2505.27i	0.509410	+	0.526206i
$70$	2843.11	−	2483.31i	0.580227	−	0.506798i
$71$			1315.04i			0.260869i	0.991457	+	0.130434i	$0.0416372\pi$
$71$			1315.04i			0.260869i	−0.991457	+	0.130434i	$0.958363\pi$
$72$	−5182.11	+	140.062i	−0.999635	+	0.0270181i
$73$	9470.72			1.77720			0.888602	−	0.458680i	$-0.151678\pi$
$73$	9470.72			1.77720			0.888602	+	0.458680i	$0.151678\pi$
$74$	−3689.27	−	4223.80i	−0.673717	−	0.771330i
$75$	−388.665	−	1550.68i	−0.0690960	−	0.275677i
$76$	−10222.1	−	1387.35i	−1.76976	−	0.240192i
$77$	−1511.89	+	2618.67i	−0.255000	+	0.441672i
$78$	−1044.07	−	87.5566i	−0.171609	−	0.0143913i
$79$	3783.95	−	2184.67i	0.606305	−	0.350050i	−0.165213	−	0.986258i	$-0.552831\pi$
$79$	3783.95	−	2184.67i	0.606305	−	0.350050i	0.771518	+	0.636207i	$0.219498\pi$
$80$	3859.25	−	3798.05i	0.603008	−	0.593445i
$81$	2905.28	+	5882.69i	0.442810	+	0.896616i
$82$	−6076.73	+	1196.12i	−0.903737	+	0.177888i
$83$	659.925	−	381.008i	0.0957940	−	0.0553067i	−0.451338	−	0.892353i	$-0.649053\pi$
$83$	659.925	−	381.008i	0.0957940	−	0.0553067i	0.547132	+	0.837047i	$0.315720\pi$
$84$	709.715	+	6385.74i	0.100583	+	0.905008i
$85$	−4260.28	+	7379.03i	−0.589659	+	1.02132i
$86$	−7084.84	−	2420.78i	−0.957929	−	0.327309i
$87$	1585.10	+	6324.16i	0.209420	+	0.835535i
$88$	−1941.61	+	3878.41i	−0.250724	+	0.500828i
$89$	8083.40			1.02050			0.510251	−	0.860025i	$-0.329552\pi$
$89$	8083.40			1.02050			0.510251	+	0.860025i	$0.329552\pi$
$90$	−6409.62	−	2424.91i	−0.791311	−	0.299372i
$91$			1298.56i			0.156813i
$92$	3793.29	−	4902.82i	0.448168	−	0.579256i
$93$	−7885.41	−	8145.41i	−0.911714	−	0.941775i
$94$	15781.0	+	5392.11i	1.78599	+	0.610244i
$95$	−11810.0	−	6818.52i	−1.30859	−	0.755514i
$96$	1560.48	+	9082.93i	0.169322	+	0.985561i
$97$	−3332.71	−	5772.42i	−0.354204	−	0.613500i	0.632777	−	0.774334i	$-0.281915\pi$
$97$	−3332.71	−	5772.42i	−0.354204	−	0.613500i	−0.986981	+	0.160834i	$0.948582\pi$
$98$	−1609.89	+	316.884i	−0.167627	+	0.0329950i
$99$	5486.47	+	178.012i	0.559787	+	0.0181627i
$100$	−2630.03	+	1077.10i	−0.263003	+	0.107710i
$101$	−4643.04	−	8041.97i	−0.455155	−	0.788352i	0.543542	−	0.839382i	$-0.317083\pi$
$101$	−4643.04	−	8041.97i	−0.455155	−	0.788352i	−0.998697	+	0.0510303i	$0.983749\pi$
$102$	−6176.23	−	13121.4i	−0.593640	−	1.26119i
$103$	−9792.48	−	5653.69i	−0.923035	−	0.532915i	−0.0384332	−	0.999261i	$-0.512237\pi$
$103$	−9792.48	−	5653.69i	−0.923035	−	0.532915i	−0.884602	+	0.466346i	$0.845570\pi$
$104$	110.679	+	1859.35i	0.0102329	+	0.171907i
$105$	−2331.06	+	8167.45i	−0.211434	+	0.740812i
$106$	2385.51	+	2731.14i	0.212310	+	0.243071i
$107$			6261.61i			0.546913i	0.961884	+	0.273456i	$0.0881669\pi$
$107$			6261.61i			0.546913i	−0.961884	+	0.273456i	$0.911833\pi$
$108$	9614.51	−	6603.80i	0.824289	−	0.566169i
$109$	3452.85			0.290620			0.145310	−	0.989386i	$-0.453582\pi$
$109$	3452.85			0.290620			0.145310	+	0.989386i	$0.453582\pi$
$110$	−4318.33	+	3771.84i	−0.356887	+	0.311722i
$111$	12133.8	+	3463.08i	0.984806	+	0.281072i
$112$	11056.4	−	2868.04i	0.881409	−	0.228639i
$113$	1272.55	−	2204.13i	0.0996597	−	0.172616i	−0.811884	−	0.583819i	$-0.801558\pi$
$113$	1272.55	−	2204.13i	0.0996597	−	0.172616i	0.911544	+	0.411203i	$0.134891\pi$
$114$	21000.6	−	9884.95i	1.61592	−	0.760615i
$115$	7096.79	−	4097.33i	0.536619	−	0.309817i
$116$	10726.1	−	4392.75i	0.797122	−	0.326453i
$117$	2078.72	−	1111.88i	0.151853	−	0.0812241i
$118$	3493.59	+	17748.7i	0.250904	+	1.27469i
$119$	−15566.1	+	8987.07i	−1.09922	+	0.634636i
$120$	−2641.60	+	11893.2i	−0.183444	+	0.825920i
$121$	−5024.12	+	8702.04i	−0.343154	+	0.594361i
$122$	3399.42	−	9949.02i	0.228394	−	0.668437i
$123$	10012.0	−	9692.44i	0.661776	−	0.640653i
$124$	−12333.2	+	15940.6i	−0.802106	+	1.03672i
$125$	−16976.5			−1.08650
$126$	−9151.93	−	11190.6i	−0.576463	−	0.704873i
$127$		−	530.060i		−	0.0328638i	−0.999865	−	0.0164319i	$-0.994769\pi$
$127$		−	530.060i		−	0.0328638i	0.999865	−	0.0164319i	$-0.00523067\pi$
$128$	15586.6	−	5048.97i	0.951333	−	0.308164i
$129$	16340.3	−	4095.56i	0.981931	−	0.246112i
$130$	−796.142	+	2330.05i	−0.0471090	+	0.137873i
$131$	−802.198	−	463.149i	−0.0467454	−	0.0269885i	0.476445	−	0.879204i	$-0.341925\pi$
$131$	−802.198	−	463.149i	−0.0467454	−	0.0269885i	−0.523191	+	0.852216i	$0.675258\pi$
$132$	−1077.97	−	9699.14i	−0.0618669	−	0.556654i
$133$	−14383.7	−	24913.2i	−0.813142	−	1.40840i
$134$	52.3769	+	266.094i	0.00291696	+	0.0148192i
$135$	15070.3	−	3261.74i	0.826901	−	0.178971i
$136$	−21522.3	+	14194.9i	−1.16362	+	0.767456i
$137$	−834.113	−	1444.73i	−0.0444410	−	0.0769741i	0.842949	−	0.537993i	$-0.180817\pi$
$137$	−834.113	−	1444.73i	−0.0444410	−	0.0769741i	−0.887390	+	0.461019i	$0.847484\pi$
$138$	−1165.57	+	13898.8i	−0.0612038	+	0.729826i
$139$	717.766	+	414.402i	0.0371495	+	0.0214483i	0.518460	−	0.855102i	$-0.326506\pi$
$139$	717.766	+	414.402i	0.0371495	+	0.0214483i	−0.481310	+	0.876550i	$0.659839\pi$
$140$	14962.5	+	2030.72i	0.763395	+	0.103608i
$141$	−36396.9	+	9122.57i	−1.83074	+	0.458859i
$142$	−3961.72	+	3460.36i	−0.196475	+	0.171611i
$143$		−	1972.36i		−	0.0964525i
$144$	−14058.0	−	15243.2i	−0.677951	−	0.735107i
$145$	15322.3			0.728768
$146$	24920.9	+	28531.7i	1.16912	+	1.33851i
$147$	2652.45	−	2567.79i	0.122748	−	0.118830i
$148$	3016.89	−	22228.8i	0.137732	−	1.01483i
$149$	−1561.38	+	2704.39i	−0.0703292	+	0.121814i	−0.899046	−	0.437855i	$-0.855738\pi$
$149$	−1561.38	+	2704.39i	−0.0703292	+	0.121814i	0.828716	+	0.559669i	$0.189072\pi$
$150$	3648.90	−	5251.32i	0.162173	−	0.233392i
$151$	−7932.37	+	4579.76i	−0.347896	+	0.200858i	−0.663758	−	0.747947i	$-0.731040\pi$
$151$	−7932.37	+	4579.76i	−0.347896	+	0.200858i	0.315862	+	0.948805i	$0.397706\pi$
$152$	−22718.7	−	34446.1i	−0.983322	−	1.49091i
$153$	27714.6	+	17222.9i	1.18393	+	0.735737i
$154$	−11867.4	+	2335.94i	−0.500397	+	0.0984963i
$155$	−23073.9	+	13321.7i	−0.960411	+	0.554494i
$156$	−2483.56	−	3375.78i	−0.102053	−	0.138716i
$157$	−10551.8	+	18276.3i	−0.428084	+	0.741463i	−0.996703	−	0.0811381i	$-0.974145\pi$
$157$	−10551.8	+	18276.3i	−0.428084	+	0.741463i	0.568619	+	0.822601i	$0.307478\pi$
$158$	16538.5	+	5650.96i	0.662496	+	0.226364i
$159$	−7845.80	−	2239.25i	−0.310344	−	0.0885746i
$160$	21597.2	+	1632.39i	0.843641	+	0.0637653i
$161$	17286.7			0.666898
$162$	−10077.5	+	24232.0i	−0.383992	+	0.923336i
$163$		−	42771.0i		−	1.60981i	−0.593405	−	0.804904i	$-0.702217\pi$
$163$		−	42771.0i		−	1.60981i	0.593405	−	0.804904i	$-0.297783\pi$
$164$	−19593.6	−	15159.5i	−0.728494	−	0.563632i
$165$	3540.59	−	12405.3i	0.130049	−	0.455660i
$166$	2884.34	+	985.532i	0.104672	+	0.0357647i
$167$	9568.12	+	5524.16i	0.343079	+	0.198077i	0.661633	−	0.749828i	$-0.269864\pi$
$167$	9568.12	+	5524.16i	0.343079	+	0.198077i	−0.318554	+	0.947905i	$0.603197\pi$
$168$	−17370.3	+	18941.3i	−0.615444	+	0.671107i
$169$	13857.0	+	24001.0i	0.485172	+	0.840342i
$170$	−33440.6	+	6582.32i	−1.15711	+	0.227762i
$171$	−27564.9	+	44356.8i	−0.942681	+	1.51694i
$172$	−11349.9	−	27713.9i	−0.383651	−	0.936787i
$173$	10967.8	+	18996.8i	0.366461	+	0.634729i	0.989009	−	0.147852i	$-0.0472360\pi$
$173$	10967.8	+	18996.8i	0.366461	+	0.634729i	−0.622549	+	0.782581i	$0.713903\pi$
$174$	−14881.3	+	21416.5i	−0.491523	+	0.707376i
$175$	−6863.66	−	3962.73i	−0.224119	−	0.129395i
$176$	−16793.3	+	4356.20i	−0.542138	+	0.140631i
$177$	−28309.4	−	29242.8i	−0.903617	−	0.933411i
$178$	21270.4	+	24352.2i	0.671329	+	0.768597i
$179$			11479.2i			0.358265i	0.983825	+	0.179133i	$0.0573291\pi$
$179$			11479.2i			0.358265i	−0.983825	+	0.179133i	$0.942671\pi$
$180$	−9560.72	−	25690.6i	−0.295084	−	0.792919i
$181$	45472.2			1.38800			0.693999	−	0.719976i	$-0.255847\pi$
$181$	45472.2			1.38800			0.693999	+	0.719976i	$0.255847\pi$
$182$	−3912.08	+	3417.00i	−0.118104	+	0.103158i
$183$	5751.26	+	22946.2i	0.171736	+	0.685186i
$184$	24751.9	−	1473.38i	0.731094	−	0.0435190i
$185$	14827.4	−	25681.7i	0.433232	−	0.750379i
$186$	3789.62	−	45189.4i	0.109539	−	1.30620i
$187$	23642.9	−	13650.2i	0.676111	−	0.390353i
$188$	25281.2	+	61730.8i	0.715290	+	1.74657i
$189$	30971.9	+	9936.56i	0.867051	+	0.278171i
$190$	−10534.9	−	53521.2i	−0.291825	−	1.48258i
$191$	60657.0	−	35020.3i	1.66270	−	0.959961i	0.691283	−	0.722584i	$-0.257046\pi$
$191$	60657.0	−	35020.3i	1.66270	−	0.959961i	0.971418	−	0.237376i	$-0.0762875\pi$
$192$	−23257.2	+	28601.7i	−0.630893	+	0.775870i
$193$	17426.4	−	30183.5i	0.467836	−	0.810316i	−0.531488	−	0.847066i	$-0.678367\pi$
$193$	17426.4	−	30183.5i	0.467836	−	0.810316i	0.999325	+	0.0367497i	$0.0117004\pi$
$194$	8620.54	−	25229.6i	0.229050	−	0.670357i
$195$	−1346.94	−	5373.98i	−0.0354225	−	0.141328i
$196$	−5190.87	−	4016.15i	−0.135122	−	0.104544i
$197$	−30858.0			−0.795124			−0.397562	−	0.917575i	$-0.630144\pi$
$197$	−30858.0			−0.795124			−0.397562	+	0.917575i	$0.630144\pi$
$198$	13900.6	+	16997.1i	0.354572	+	0.433555i
$199$			34262.5i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$199$			34262.5i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$200$	−10165.5	−	5089.04i	−0.254137	−	0.127226i
$201$	−424.422	−	438.416i	−0.0105052	−	0.0108516i
$202$	12009.9	−	35149.1i	0.294331	−	0.861414i
$203$	27992.1	+	16161.2i	0.679272	+	0.392178i
$204$	23277.8	−	53133.8i	0.559348	−	1.27676i
$205$	−16374.5	−	28361.5i	−0.389638	−	0.674872i
$206$	−8735.19	−	44378.0i	−0.205844	−	1.04576i
$207$	−14801.5	−	27672.2i	−0.345433	−	0.645808i
$208$	−5310.28	+	5226.07i	−0.122741	+	0.120795i
$209$	21847.0	+	37840.1i	0.500149	+	0.866283i
$210$	−30739.3	+	14469.0i	−0.697037	+	0.328095i
$211$	14989.6	+	8654.27i	0.336687	+	0.194386i	0.658806	−	0.752313i	$-0.271062\pi$
$211$	14989.6	+	8654.27i	0.336687	+	0.194386i	−0.322119	+	0.946699i	$0.604395\pi$
$212$	−1950.74	+	14373.3i	−0.0434038	+	0.319804i
$213$	3248.20	−	11380.9i	0.0715952	−	0.250852i
$214$	−18863.9	+	16476.6i	−0.411911	+	0.359782i
$215$		−	39589.7i		−	0.856457i
$216$	45194.1	+	11587.9i	0.968666	+	0.248368i
$217$	−56204.3			−1.19358
$218$	9085.73	+	10402.1i	0.191182	+	0.218882i
$219$	−81963.5	−	23393.0i	−1.70896	−	0.487751i
$220$	−22726.2	−	3084.41i	−0.469550	−	0.0637274i
$221$	5862.10	−	10153.5i	0.120024	−	0.207888i
$222$	21495.5	+	45667.2i	0.436156	+	0.926613i
$223$	−55484.8	+	32034.1i	−1.11574	+	0.644174i	−0.940311	−	0.340317i	$-0.889466\pi$
$223$	−55484.8	+	32034.1i	−1.11574	+	0.644174i	−0.175432	+	0.984492i	$0.556132\pi$
$224$	37733.8	+	25761.9i	0.752028	+	0.513430i
$225$	−466.578	+	14380.3i	−0.00921636	+	0.284055i
$226$	9988.77	−	1966.15i	0.195567	−	0.0384946i
$227$	−11857.8	+	6846.11i	−0.230119	+	0.132859i	−0.610627	−	0.791918i	$-0.709083\pi$
$227$	−11857.8	+	6846.11i	−0.230119	+	0.132859i	0.380508	+	0.924778i	$0.375749\pi$
$228$	85039.8	+	37255.8i	1.63588	+	0.716678i
$229$	−32996.2	+	57151.0i	−0.629205	+	1.08982i	0.358506	+	0.933527i	$0.383286\pi$
$229$	−32996.2	+	57151.0i	−0.629205	+	1.08982i	−0.987711	+	0.156288i	$0.950047\pi$
$230$	31018.0	+	10598.4i	0.586352	+	0.200347i
$231$	19552.8	−	18928.7i	0.366424	−	0.354728i
$232$	41458.0	+	20754.7i	0.770250	+	0.385602i
$233$	−63342.4			−1.16676			−0.583381	−	0.812198i	$-0.698271\pi$
$233$	−63342.4			−1.16676			−0.583381	+	0.812198i	$0.698271\pi$
$234$	8819.55	+	3336.65i	0.161070	+	0.0609367i
$235$			88183.3i			1.59680i
$236$	−44277.3	+	57228.4i	−0.794982	+	1.02751i
$237$	−38144.1	+	9560.49i	−0.679095	+	0.170209i
$238$	−68034.7	−	23246.4i	−1.20109	−	0.410394i
$239$	−275.008	−	158.776i	−0.00481448	−	0.00277964i	0.497591	−	0.867412i	$-0.334218\pi$
$239$	−275.008	−	158.776i	−0.00481448	−	0.00277964i	−0.502405	+	0.864632i	$0.667551\pi$
$240$	−42780.9	+	23337.4i	−0.742724	+	0.405163i
$241$	−12752.6	−	22088.2i	−0.219566	−	0.380300i	0.735109	−	0.677949i	$-0.237131\pi$
$241$	−12752.6	−	22088.2i	−0.219566	−	0.380300i	−0.954675	+	0.297649i	$0.903798\pi$
$242$	−39436.3	+	7762.48i	−0.673388	+	0.132547i
$243$	−10613.0	−	58087.4i	−0.179732	−	0.983716i
$244$	38917.8	−	15938.4i	0.653685	−	0.267710i
$245$	−4338.05	−	7513.73i	−0.0722708	−	0.125177i
$246$	55545.0	+	4658.05i	0.917856	+	0.0769721i
$247$	16250.4	+	9382.19i	0.266361	+	0.153784i
$248$	−80476.2	+	4790.41i	−1.30847	+	0.0778878i
$249$	−6652.37	+	1667.36i	−0.107295	+	0.0268924i
$250$	−44671.5	−	51143.9i	−0.714744	−	0.818302i
$251$		−	40987.7i		−	0.650588i	−0.945613	−	0.325294i	$-0.894537\pi$
$251$		−	40987.7i		−	0.650588i	0.945613	−	0.325294i	$-0.105463\pi$
$252$	9630.86	−	57017.8i	0.151657	−	0.897862i
$253$	−26256.3			−0.410197
$254$	1596.87	−	1394.78i	0.0247516	−	0.0216192i
$255$	55096.8	−	53338.1i	0.847317	−	0.820271i
$256$	56224.8	+	33671.0i	0.857923	+	0.513778i
$257$	−15479.1	+	26810.5i	−0.234357	+	0.405919i	−0.959086	−	0.283116i	$-0.908632\pi$
$257$	−15479.1	+	26810.5i	−0.234357	+	0.405919i	0.724728	+	0.689035i	$0.241965\pi$
$258$	55335.7	+	38450.3i	0.831316	+	0.577643i
$259$	54175.6	−	31278.3i	0.807615	−	0.466277i
$260$	−9114.52	+	3732.76i	−0.134830	+	0.0552183i
$261$	1902.85	−	58647.2i	0.0279334	−	0.860926i
$262$	−715.585	−	3635.44i	−0.0104246	−	0.0529607i
$263$	13311.8	−	7685.54i	0.192453	−	0.111113i	−0.400678	−	0.916219i	$-0.631225\pi$
$263$	13311.8	−	7685.54i	0.192453	−	0.111113i	0.593130	+	0.805107i	$0.297892\pi$
$264$	26383.3	−	28769.5i	0.378548	−	0.412786i
$265$	−9587.47	+	16606.0i	−0.136525	+	0.236468i
$266$	37205.5	−	108889.i	0.525828	−	1.53893i
$267$	−69957.1	−	19966.3i	−0.981317	−	0.280076i
$268$	−663.818	+	857.983i	−0.00924228	+	0.0119456i
$269$	76105.5			1.05175			0.525873	−	0.850563i	$-0.323739\pi$
$269$	76105.5			1.05175			0.525873	+	0.850563i	$0.323739\pi$
$270$	49481.8	+	36818.2i	0.678763	+	0.505051i
$271$			78076.4i			1.06312i	0.847021	+	0.531559i	$0.178394\pi$
$271$			78076.4i			1.06312i	−0.847021	+	0.531559i	$0.821606\pi$
$272$	−99396.9	−	27486.6i	−1.34349	−	0.371521i
$273$	3207.51	−	11238.3i	0.0430370	−	0.150791i
$274$	2157.56	−	6314.48i	0.0287383	−	0.0841078i
$275$	10425.0	+	6018.90i	0.137852	+	0.0795887i
$276$	−44938.9	+	33061.5i	−0.589935	+	0.434014i
$277$	−2369.97	−	4104.90i	−0.0308875	−	0.0534987i	0.850168	−	0.526511i	$-0.176500\pi$
$277$	−2369.97	−	4104.90i	−0.0308875	−	0.0534987i	−0.881056	+	0.473012i	$0.843167\pi$
$278$	640.269	+	3252.80i	0.00828463	+	0.0420890i
$279$	48124.2	+	89971.1i	0.618237	+	1.15583i
$280$	33254.2	+	50420.1i	0.424161	+	0.643113i
$281$	−21604.6	−	37420.3i	−0.273612	−	0.473909i	0.696172	−	0.717875i	$-0.254885\pi$
$281$	−21604.6	−	37420.3i	−0.273612	−	0.473909i	−0.969784	+	0.243966i	$0.921552\pi$
$282$	−123257.	−	85645.3i	−1.54993	−	1.07697i
$283$	31277.1	+	18057.8i	0.390529	+	0.225472i	0.682389	−	0.730989i	$-0.260941\pi$
$283$	31277.1	+	18057.8i	0.390529	+	0.225472i	−0.291860	+	0.956461i	$0.594274\pi$
$284$	−20849.5	−	2829.69i	−0.258499	−	0.0350835i
$285$	85366.8	+	88181.5i	1.05099	+	1.08564i
$286$	5941.97	−	5190.00i	0.0726438	−	0.0634505i
$287$		−	69084.1i		−	0.838715i
$288$	8930.19	−	82461.9i	0.107665	−	0.994187i
$289$	78760.1			0.942997
$290$	40318.7	+	46160.4i	0.479414	+	0.548876i
$291$	14584.5	+	58188.8i	0.172229	+	0.687153i
$292$	−20379.0	+	150155.i	−0.239011	+	1.76106i
$293$	48046.7	−	83219.2i	0.559665	−	0.969368i	−0.437859	−	0.899043i	$-0.644263\pi$
$293$	48046.7	−	83219.2i	0.559665	−	0.969368i	0.997524	−	0.0703243i	$-0.0224034\pi$
$294$	14715.4	+	1234.04i	0.170246	+	0.0142770i
$295$	−82837.5	+	47826.3i	−0.951882	+	0.549569i
$296$	74905.5	−	49403.4i	0.854929	−	0.563862i
$297$	−47042.5	−	15092.4i	−0.533307	−	0.171098i
$298$	−12255.9	+	2412.40i	−0.138010	+	0.0271654i
$299$	−9765.10	+	5637.88i	−0.109228	+	0.0630628i
$300$	25421.9	−	2825.40i	0.282465	−	0.0313934i
$301$	41757.3	−	72325.7i	0.460892	−	0.798288i
$302$	−34670.1	−	11846.2i	−0.380138	−	0.129887i
$303$	20318.8	+	81067.1i	0.221316	+	0.882997i
$304$	43991.9	−	159083.i	0.476020	−	1.72138i
$305$	55594.6			0.597631
$306$	21041.3	+	128813.i	0.224714	+	1.37568i
$307$		−	140641.i		−	1.49223i	−0.665817	−	0.746115i	$-0.731917\pi$
$307$		−	140641.i		−	1.49223i	0.665817	−	0.746115i	$-0.268083\pi$
$308$	−38264.9	−	29605.4i	−0.403366	−	0.312082i
$309$	70783.4	+	73117.2i	0.741334	+	0.765778i
$310$	−100849.	−	34458.6i	−1.04942	−	0.358570i
$311$	−141564.	−	81731.8i	−1.46363	−	0.845027i	−0.464453	−	0.885598i	$-0.653749\pi$
$311$	−141564.	−	81731.8i	−1.46363	−	0.845027i	−0.999177	+	0.0405712i	$0.987082\pi$
$312$	3634.80	−	16365.0i	0.0373398	−	0.168115i
$313$	25645.1	+	44418.7i	0.261768	+	0.453395i	0.966712	−	0.255868i	$-0.0823611\pi$
$313$	25645.1	+	44418.7i	0.261768	+	0.453395i	−0.704944	+	0.709263i	$0.749028\pi$
$314$	−82825.4	+	16303.0i	−0.840049	+	0.165352i
$315$	40347.9	−	64926.7i	0.406630	−	0.654338i
$316$	26494.8	+	64694.1i	0.265330	+	0.647874i
$317$	14025.0	+	24292.0i	0.139568	+	0.241738i	0.927333	−	0.374237i	$-0.122095\pi$
$317$	14025.0	+	24292.0i	0.139568	+	0.241738i	−0.787765	+	0.615975i	$0.788762\pi$
$318$	−13899.2	−	29528.7i	−0.137447	−	0.292005i
$319$	−42516.5	−	24546.9i	−0.417808	−	0.241221i
$320$	51912.4	+	69359.7i	0.506957	+	0.677340i
$321$	15466.4	−	54190.5i	0.150100	−	0.525912i
$322$	45487.6	+	52078.2i	0.438714	+	0.502278i
$323$			259728.i			2.48951i
$324$	−99519.6	+	33403.8i	−0.948022	+	0.318204i
$325$	5169.63			0.0489433
$326$	128853.	−	112546.i	1.21244	−	1.05900i
$327$	−29882.4	−	8528.68i	−0.279460	−	0.0797602i
$328$	−5888.19	−	98918.1i	−0.0547311	−	0.919450i
$329$	−93011.4	+	161101.i	−0.859299	+	1.48835i
$330$	46689.2	−	21976.6i	0.428735	−	0.201805i
$331$	97678.0	−	56394.4i	0.891540	−	0.514731i	0.0170938	−	0.999854i	$-0.494559\pi$
$331$	97678.0	−	56394.4i	0.891540	−	0.514731i	0.874446	+	0.485123i	$0.161225\pi$
$332$	4620.72	+	11282.7i	0.0419212	+	0.102362i
$333$	−96457.0	−	59941.9i	−0.869852	−	0.540558i
$334$	8535.06	+	43361.2i	0.0765092	+	0.388695i
$335$	−1241.92	+	717.024i	−0.0110664	+	0.00638917i
$336$	−102771.	−	2488.50i	−0.910314	−	0.0220424i
$337$	10409.8	−	18030.3i	0.0916606	−	0.158761i	−0.816549	−	0.577276i	$-0.804116\pi$
$337$	10409.8	−	18030.3i	0.0916606	−	0.158761i	0.908210	+	0.418515i	$0.137449\pi$
$338$	−35843.1	+	104901.i	−0.313742	+	0.918222i
$339$	−16457.5	+	15932.2i	−0.143207	+	0.138636i
$340$	−107825.	−	83423.4i	−0.932739	−	0.721656i
$341$	85367.4			0.734147
$342$	−206164.	+	33676.3i	−1.76263	+	0.287920i
$343$		−	125431.i		−	1.06615i
$344$	53625.7	−	107119.i	0.453165	−	0.905208i
$345$	−71539.2	+	17930.7i	−0.601043	+	0.150646i
$346$	−28369.8	+	83029.5i	−0.236976	+	0.693554i
$347$	139615.	+	80606.6i	1.15950	+	0.669440i	0.951185	−	0.308621i	$-0.0998676\pi$
$347$	139615.	+	80606.6i	1.15950	+	0.669440i	0.208318	+	0.978061i	$0.433201\pi$
$348$	−103678.	+	11522.9i	−0.856108	+	0.0951485i
$349$	110742.	+	191811.i	0.909205	+	1.57479i	0.815171	+	0.579220i	$0.196643\pi$
$349$	110742.	+	191811.i	0.909205	+	1.57479i	0.0940341	+	0.995569i	$0.470024\pi$
$350$	−6122.59	−	31105.0i	−0.0499803	−	0.253919i
$351$	−20736.5	+	4488.12i	−0.168314	+	0.0364292i
$352$	−57312.9	−	39129.0i	−0.462559	−	0.315801i
$353$	−109395.	−	189477.i	−0.877904	−	1.52057i	−0.853637	−	0.520869i	$-0.825608\pi$
$353$	−109395.	−	189477.i	−0.877904	−	1.52057i	−0.0242676	−	0.999705i	$-0.507725\pi$
$354$	13605.1	−	162234.i	0.108566	−	1.29460i
$355$	−24088.2	−	13907.3i	−0.191138	−	0.110354i
$356$	−17393.8	+	128159.i	−0.137244	+	1.01123i
$357$	156914.	−	39329.1i	1.23119	−	0.308587i
$358$	−34582.4	+	30206.0i	−0.269830	+	0.235682i
$359$			924.606i			0.00717411i	0.999994	+	0.00358705i	$0.00114180\pi$
$359$			924.606i			0.00717411i	−0.999994	+	0.00358705i	$0.998858\pi$
$360$	52238.3	−	96404.3i	0.403073	−	0.743860i
$361$	−285370.			−2.18975
$362$	119654.	+	136991.i	0.913084	+	1.04538i
$363$	64975.2	−	62901.3i	0.493100	−	0.477360i
$364$	−20588.3	−	2794.24i	−0.155388	−	0.0210893i
$365$	−100158.	+	173479.i	−0.751799	+	1.30215i
$366$	−53994.5	+	77706.3i	−0.403076	+	0.580088i
$367$	−35332.0	+	20398.9i	−0.262323	+	0.151452i	−0.625394	−	0.780309i	$-0.715062\pi$
$367$	−35332.0	+	20398.9i	−0.262323	+	0.151452i	0.363071	+	0.931762i	$0.381728\pi$
$368$	69570.1	+	70691.2i	0.513721	+	0.521999i
$369$	−110589.	+	59152.3i	−0.812192	+	0.434429i
$370$	116386.	−	22908.9i	0.850150	−	0.167340i
$371$	−35030.3	+	20224.8i	−0.254505	+	0.146939i
$372$	146110.	−	107493.i	1.05583	−	0.776775i
$373$	117265.	−	203109.i	0.842851	−	1.45986i	−0.0446228	−	0.999004i	$-0.514209\pi$
$373$	117265.	−	203109.i	0.842851	−	1.45986i	0.887474	−	0.460858i	$-0.152458\pi$
$374$	103336.	+	35308.4i	0.738771	+	0.252426i
$375$	146922.	+	41932.7i	1.04478	+	0.298188i
$376$	−119447.	+	238599.i	−0.844892	+	1.68769i
$377$	−21083.4			−0.148340
$378$	51563.5	+	119453.i	0.360876	+	0.836017i
$379$		−	185553.i		−	1.29178i	−0.763428	−	0.645892i	$-0.776485\pi$
$379$		−	185553.i		−	1.29178i	0.763428	−	0.645892i	$-0.223515\pi$
$380$	133518.	−	172572.i	0.924639	−	1.19509i
$381$	−1309.27	+	4587.36i	−0.00901944	+	0.0316019i
$382$	265114.	+	90585.2i	1.81679	+	0.620770i
$383$	−52190.3	−	30132.1i	−0.355789	−	0.205415i	0.311443	−	0.950265i	$-0.399188\pi$
$383$	−52190.3	−	30132.1i	−0.355789	−	0.205415i	−0.667232	+	0.744850i	$0.732521\pi$
$384$	−147364.	+	5196.21i	−0.999379	+	0.0352390i
$385$	−31978.3	−	55388.1i	−0.215742	−	0.373675i
$386$	136787.	−	26924.6i	0.918056	−	0.180707i
$387$	−151532.	−	4916.56i	−1.01177	−	0.0328276i
$388$	98691.0	−	40417.8i	0.655562	−	0.268479i
$389$	6004.66	+	10400.4i	0.0396816	+	0.0687306i	0.885184	−	0.465241i	$-0.154032\pi$
$389$	6004.66	+	10400.4i	0.0396816	+	0.0687306i	−0.845502	+	0.533971i	$0.820699\pi$
$390$	12645.5	−	18198.8i	0.0831392	−	0.119650i
$391$	−135164.	−	78037.0i	−0.884113	−	0.510443i
$392$	−1559.94	−	26206.1i	−0.0101516	−	0.170542i
$393$	5798.56	+	5989.75i	0.0375435	+	0.0387814i
$394$	−81198.7	−	92963.4i	−0.523066	−	0.598852i
$395$			92416.5i			0.592318i
$396$	−14628.1	+	86603.0i	−0.0932818	+	0.552259i
$397$	32276.3			0.204787			0.102394	−	0.994744i	$-0.467350\pi$
$397$	32276.3			0.204787			0.102394	+	0.994744i	$0.467350\pi$
$398$	−103220.	+	90157.2i	−0.651624	+	0.569160i
$399$	62945.5	+	251138.i	0.395384	+	1.57749i
$400$	−11417.8	−	44015.9i	−0.0713611	−	0.275099i
$401$	93863.1	−	162576.i	0.583722	−	1.01104i	−0.411311	−	0.911495i	$-0.634929\pi$
$401$	93863.1	−	162576.i	0.583722	−	1.01104i	0.995033	−	0.0995418i	$-0.0317377\pi$
$402$	203.971	−	2432.26i	0.00126217	−	0.0150507i
$403$	31749.4	−	18330.5i	0.195490	−	0.112866i
$404$	137494.	−	56309.0i	0.842402	−	0.344997i
$405$	−138481.	−	8995.70i	−0.844268	−	0.0548435i
$406$	24969.8	+	126856.i	0.151483	+	0.769588i
$407$	−82286.0	+	47507.9i	−0.496749	+	0.286798i
$408$	221325.	−	69687.4i	1.32957	−	0.418633i
$409$	67272.0	−	116518.i	0.402149	−	0.696543i	−0.591836	−	0.806059i	$-0.701597\pi$
$409$	67272.0	−	116518.i	0.402149	−	0.696543i	0.993985	+	0.109515i	$0.0349299\pi$
$410$	42355.1	−	123960.i	0.251964	−	0.737417i
$411$	3650.23	+	14563.6i	0.0216091	+	0.0862152i
$412$	110709.	−	143091.i	0.652210	−	0.842980i
$413$	−201779.			−1.18298
$414$	44417.9	−	117407.i	0.259154	−	0.685005i
$415$			16117.5i			0.0935841i
$416$	−29717.5	−	2246.15i	−0.171722	−	0.0129793i
$417$	−5188.25	−	5359.32i	−0.0298366	−	0.0308204i
$418$	−56510.5	+	165388.i	−0.323427	+	0.946568i
$419$	−73320.7	−	42331.7i	−0.417637	−	0.241123i	0.276429	−	0.961034i	$-0.410849\pi$
$419$	−73320.7	−	42331.7i	−0.417637	−	0.241123i	−0.694066	+	0.719912i	$0.744182\pi$
$420$	−124476.	−	54532.8i	−0.705647	−	0.309143i
$421$	57849.8	+	100199.i	0.326391	+	0.565325i	0.981793	−	0.189955i	$-0.0608341\pi$
$421$	57849.8	+	100199.i	0.326391	+	0.565325i	−0.655402	+	0.755280i	$0.727501\pi$
$422$	13371.2	+	67930.7i	0.0750837	+	0.381453i
$423$	337527.	+	10951.3i	1.88637	+	0.0612047i
$424$	−48434.4	+	31944.6i	−0.269415	+	0.177691i
$425$	35777.9	+	61969.1i	0.198078	+	0.343081i
$426$	42833.6	−	20161.7i	0.236029	−	0.111099i
$427$	101565.	+	58638.4i	0.557041	+	0.321608i
$428$	−99275.5	−	13473.7i	−0.541944	−	0.0735527i
$429$	−4871.80	+	17069.6i	−0.0264713	+	0.0927489i
$430$	119269.	−	104175.i	0.645045	−	0.563413i
$431$		−	294896.i		−	1.58750i	−0.608241	−	0.793752i	$-0.708125\pi$
$431$		−	294896.i		−	1.58750i	0.608241	−	0.793752i	$-0.291875\pi$
$432$	84012.4	+	166645.i	0.450169	+	0.892943i
$433$	−151284.			−0.806895			−0.403447	−	0.915003i	$-0.632188\pi$
$433$	−151284.			−0.806895			−0.403447	+	0.915003i	$0.632188\pi$
$434$	−147894.	−	169322.i	−0.785185	−	0.898949i
$435$	−132606.	−	37846.8i	−0.700784	−	0.200010i
$436$	−7429.82	+	54743.7i	−0.0390846	+	0.287979i
$437$	124897.	−	216328.i	0.654017	−	1.13279i
$438$	−145202.	−	308481.i	−0.756874	−	1.60798i
$439$	17332.7	−	10007.1i	0.0899369	−	0.0519251i	−0.454357	−	0.890820i	$-0.650131\pi$
$439$	17332.7	−	10007.1i	0.0899369	−	0.0519251i	0.544294	+	0.838895i	$0.316798\pi$
$440$	−50509.0	−	76581.8i	−0.260893	−	0.395567i
$441$	−29298.0	+	15671.0i	−0.150647	+	0.0805788i
$442$	46013.9	−	9057.19i	0.235529	−	0.0463606i
$443$	−33466.7	+	19322.0i	−0.170532	+	0.0984567i	−0.582837	−	0.812589i	$-0.698057\pi$
$443$	−33466.7	+	19322.0i	−0.170532	+	0.0984567i	0.412305	+	0.911046i	$0.364724\pi$
$444$	−81015.4	+	184925.i	−0.410962	+	0.938059i
$445$	−85486.7	+	148067.i	−0.431696	+	0.747720i
$446$	−242508.	−	82861.0i	−1.21915	−	0.416563i
$447$	20192.8	−	19548.2i	0.101060	−	0.0978345i
$448$	21680.7	+	181467.i	0.108023	+	0.904150i
$449$	79457.9			0.394135			0.197067	−	0.980390i	$-0.436858\pi$
$449$	79457.9			0.394135			0.197067	+	0.980390i	$0.436858\pi$
$450$	−44550.1	+	36434.2i	−0.220000	+	0.179922i
$451$			104930.i			0.515878i
$452$	32207.4	+	24918.7i	0.157645	+	0.121969i
$453$	79962.2	−	20041.8i	0.389662	−	0.0976655i
$454$	−51827.0	−	17708.5i	−0.251446	−	0.0859151i
$455$	−23786.4	−	13733.1i	−0.114896	−	0.0663354i
$456$	111534.	+	354227.i	0.536384	+	1.70354i
$457$	131776.	+	228243.i	0.630963	+	1.09286i	0.987355	+	0.158524i	$0.0506735\pi$
$457$	131776.	+	228243.i	0.630963	+	1.09286i	−0.356392	+	0.934337i	$0.615993\pi$
$458$	−259000.	+	50980.5i	−1.23472	+	0.243037i
$459$	−197312.	−	217510.i	−0.936546	−	1.03241i
$460$	49691.0	+	121334.i	0.234834	+	0.573411i
$461$	100305.	+	173733.i	0.471976	+	0.817487i	0.999486	−	0.0320624i	$-0.0102075\pi$
$461$	100305.	+	173733.i	0.471976	+	0.817487i	−0.527510	+	0.849549i	$0.676874\pi$
$462$	108475.	+	9096.84i	0.508215	+	0.0426193i
$463$	205297.	+	118528.i	0.957679	+	0.552916i	0.895458	−	0.445146i	$-0.146848\pi$
$463$	205297.	+	118528.i	0.957679	+	0.552916i	0.0622210	+	0.998062i	$0.480182\pi$
$464$	46565.2	+	179510.i	0.216285	+	0.833784i
$465$	232596.	−	58298.2i	1.07571	−	0.269618i
$466$	−166677.	−	190827.i	−0.767546	−	0.878754i
$467$			230464.i			1.05674i	0.849014	+	0.528371i	$0.177197\pi$
$467$			230464.i			1.05674i	−0.849014	+	0.528371i	$0.822803\pi$
$468$	13155.4	+	35349.9i	0.0600639	+	0.161398i
$469$	−3025.13			−0.0137530
$470$	−265663.	+	232043.i	−1.20264	+	1.05044i
$471$	136463.	−	132107.i	0.615140	−	0.595505i
$472$	−288918.	+	17198.1i	−1.29685	+	0.0771961i
$473$	−63424.1	+	109854.i	−0.283486	+	0.491013i
$474$	−129173.	−	89756.6i	−0.574932	−	0.399493i
$475$	−99180.5	+	57261.9i	−0.439581	+	0.253792i
$476$	−108992.	−	266133.i	−0.481039	−	1.17459i
$477$	62369.7	+	38758.9i	0.274118	+	0.170347i
$478$	−245.315	−	1246.29i	−0.00107366	−	0.00545461i
$479$	−2079.74	+	1200.74i	−0.00906438	+	0.00523332i	−0.504525	−	0.863397i	$-0.668332\pi$
$479$	−2079.74	+	1200.74i	−0.00906438	+	0.00523332i	0.495461	+	0.868630i	$0.334999\pi$
$480$	−182879.	−	67473.4i	−0.793746	−	0.292853i
$481$	−20402.3	+	35337.7i	−0.0881836	+	0.152739i
$482$	32986.6	−	96541.1i	0.141985	−	0.415545i
$483$	−149606.	−	42698.8i	−0.641290	−	0.183029i
$484$	−127157.	−	98380.7i	−0.542812	−	0.419971i
$485$	140981.			0.599347
$486$	147069.	−	184822.i	0.622656	−	0.782496i
$487$			405227.i			1.70860i	0.519781	+	0.854300i	$0.326014\pi$
$487$			405227.i			1.70860i	−0.519781	+	0.854300i	$0.673986\pi$
$488$	150423.	+	75304.9i	0.631649	+	0.316216i
$489$	−105646.	+	370158.i	−0.441810	+	1.54799i
$490$	11221.0	−	32840.3i	0.0467347	−	0.136778i
$491$	−111325.	−	64273.4i	−0.461773	−	0.266605i	0.251016	−	0.967983i	$-0.419235\pi$
$491$	−111325.	−	64273.4i	−0.461773	−	0.266605i	−0.712790	+	0.701378i	$0.752569\pi$
$492$	132126.	+	179593.i	0.545832	+	0.741924i
$493$	−145913.	−	252729.i	−0.600345	−	1.03983i
$494$	14495.9	+	73644.5i	0.0594006	+	0.301777i
$495$	−61283.4	+	98615.6i	−0.250111	+	0.402472i
$496$	−226194.	−	229839.i	−0.919429	−	0.934244i
$497$	−29337.5	−	50814.1i	−0.118771	−	0.205717i
$498$	−22528.0	−	15653.6i	−0.0908371	−	0.0631185i
$499$	111377.	+	64303.6i	0.447296	+	0.258246i	0.706687	−	0.707526i	$-0.250189\pi$
$499$	111377.	+	64303.6i	0.447296	+	0.258246i	−0.259392	+	0.965772i	$0.583522\pi$
$500$	36530.0	−	269157.i	0.146120	−	1.07663i
$501$	−69161.6	−	71442.0i	−0.275543	−	0.284628i
$502$	123480.	−	107854.i	0.489994	−	0.427984i
$503$		−	368128.i		−	1.45500i	−0.686109	−	0.727499i	$-0.740683\pi$
$503$		−	368128.i		−	1.45500i	0.686109	−	0.727499i	$-0.259317\pi$
$504$	197116.	−	121021.i	0.775997	−	0.476430i
$505$	196411.			0.770165
$506$	−69090.0	−	79100.3i	−0.269845	−	0.308942i
$507$	−60640.7	−	241942.i	−0.235911	−	0.941229i
$508$	8403.92	+	1140.58i	0.0325653	+	0.00441976i
$509$	40698.4	−	70491.6i	0.157087	−	0.272083i	−0.776730	−	0.629834i	$-0.783123\pi$
$509$	40698.4	−	70491.6i	0.157087	−	0.272083i	0.933817	+	0.357751i	$0.116456\pi$
$510$	305667.	+	25633.5i	1.17519	+	0.0985526i
$511$	−365955.	+	211284.i	−1.40148	+	0.809143i
$512$	46510.3	+	257985.i	0.177423	+	0.984135i
$513$	348121.	−	315795.i	1.32281	−	1.19997i
$514$	−121501.	+	23915.8i	−0.459890	+	0.0905230i
$515$	207123.	−	119582.i	0.780931	−	0.450871i
$516$	29772.7	+	267883.i	0.111820	+	1.00611i
$517$	141273.	−	244692.i	0.528539	−	0.915457i
$518$	236786.	+	80906.0i	0.882463	+	0.301523i
$519$	−47997.1	−	191497.i	−0.178189	−	0.710931i
$520$	−35229.1	−	17636.4i	−0.130285	−	0.0652232i
$521$	−17832.5			−0.0656956			−0.0328478	−	0.999460i	$-0.510458\pi$
$521$	−17832.5			−0.0656956			−0.0328478	+	0.999460i	$0.510458\pi$
$522$	181689.	−	148590.i	0.666787	−	0.545316i
$523$			51996.2i			0.190094i	0.995473	+	0.0950470i	$0.0303001\pi$
$523$			51996.2i			0.190094i	−0.995473	+	0.0950470i	$0.969700\pi$
$524$	9069.23	−	11722.0i	0.0330299	−	0.0426911i
$525$	49612.8	+	51248.6i	0.180001	+	0.185936i
$526$	58181.8	+	19879.8i	0.210289	+	0.0718522i
$527$	439461.	+	253723.i	1.58234	+	0.913562i
$528$	156096.	+	3779.72i	0.559917	+	0.0135579i
$529$	−64868.3	−	112355.i	−0.231804	−	0.401496i
$530$	−75255.7	+	14813.0i	−0.267909	+	0.0527342i
$531$	172770.	+	323005.i	0.612746	+	1.14557i
$532$	425941.	−	174440.i	1.50497	−	0.616343i
$533$	22531.1	+	39025.1i	0.0793101	+	0.137369i
$534$	−123932.	−	263293.i	−0.434611	−	0.923330i
$535$	−114697.	−	66220.2i	−0.400722	−	0.231357i
$536$	−4331.53	+	257.838i	−0.0150769	+	0.000897465i
$537$	28354.0	−	99345.6i	0.0983255	−	0.344508i
$538$	200262.	+	229277.i	0.691884	+	0.792129i
$539$			27798.8i			0.0956862i
$540$	19285.7	+	245952.i	0.0661374	+	0.843458i
$541$	−329819.			−1.12689			−0.563444	−	0.826154i	$-0.690524\pi$
$541$	−329819.			−1.12689			−0.563444	+	0.826154i	$0.690524\pi$
$542$	−235215.	+	205448.i	−0.800693	+	0.699364i
$543$	−393535.	−	112318.i	−1.33470	−	0.380934i
$544$	−178743.	−	371773.i	−0.603993	−	1.25626i
$545$	−36515.9	+	63247.5i	−0.122939	+	0.212936i
$546$	42296.9	−	19909.1i	0.141881	−	0.0667832i
$547$	306032.	−	176688.i	1.02280	−	0.590517i	0.107890	−	0.994163i	$-0.465591\pi$
$547$	306032.	−	176688.i	1.02280	−	0.590517i	0.914915	+	0.403646i	$0.132257\pi$
$548$	24700.5	−	10115.8i	0.0822516	−	0.0336853i
$549$	6904.18	−	212792.i	0.0229069	−	0.706008i
$550$	9299.45	+	47244.6i	0.0307420	+	0.156181i
$551$	404489.	−	233532.i	1.33230	−	0.769206i
$552$	−217853.	−	48387.0i	−0.714965	−	0.158800i
$553$	−97476.3	+	168834.i	−0.318749	+	0.552090i
$554$	6130.27	−	17941.3i	0.0199738	−	0.0584568i
$555$	−191757.	+	185636.i	−0.622537	+	0.602666i
$556$	−8114.69	+	10488.2i	−0.0262496	+	0.0339275i
$557$	−381405.			−1.22935			−0.614676	−	0.788780i	$-0.710713\pi$
$557$	−381405.			−1.22935			−0.614676	+	0.788780i	$0.710713\pi$
$558$	−144416.	+	381727.i	−0.463819	+	1.22598i
$559$			54475.0i			0.174330i
$560$	−64392.6	+	232856.i	−0.205334	+	0.742526i
$561$	−238332.	+	59735.9i	−0.757281	+	0.189806i
$562$	55883.6	−	163553.i	0.176934	−	0.517830i
$563$	203807.	+	117668.i	0.642988	+	0.371229i	0.785765	−	0.618526i	$-0.212270\pi$
$563$	203807.	+	117668.i	0.642988	+	0.371229i	−0.142776	+	0.989755i	$0.545603\pi$
$564$	−66316.5	−	596690.i	−0.208480	−	1.87582i
$565$	26916.0	+	46619.9i	0.0843168	+	0.146041i
$566$	27900.1	+	141743.i	0.0870909	+	0.442454i
$567$	−243500.	−	162497.i	−0.757414	−	0.505451i
$568$	−46337.9	−	70257.6i	−0.143628	−	0.217769i
$569$	110971.	+	192208.i	0.342757	+	0.593673i	0.984944	−	0.172875i	$-0.0553058\pi$
$569$	110971.	+	192208.i	0.342757	+	0.593673i	−0.642186	+	0.766549i	$0.721972\pi$
$570$	−41026.1	+	489216.i	−0.126273	+	1.50574i
$571$	34588.3	+	19969.5i	0.106086	+	0.0612486i	0.552104	−	0.833775i	$-0.313825\pi$
$571$	34588.3	+	19969.5i	0.106086	+	0.0612486i	−0.446018	+	0.895024i	$0.647158\pi$
$572$	31271.0	+	4244.10i	0.0955763	+	0.0129716i
$573$	−611452.	+	153255.i	−1.86232	+	0.466773i
$574$	208124.	−	181786.i	0.631683	−	0.551742i
$575$		−	68818.8i		−	0.208148i
$576$	271925.	−	190084.i	0.819605	−	0.572930i
$577$	511135.			1.53527			0.767634	−	0.640889i	$-0.221434\pi$
$577$	511135.			1.53527			0.767634	+	0.640889i	$0.221434\pi$
$578$	207247.	+	237274.i	0.620343	+	0.710224i
$579$	−225370.	+	218176.i	−0.672262	+	0.650804i
$580$	−32970.5	+	242930.i	−0.0980098	+	0.722147i
$581$	−17000.0	+	29444.8i	−0.0503612	+	0.0872281i
$582$	−136924.	+	197054.i	−0.404234	+	0.581754i
$583$	53206.7	−	30718.9i	0.156541	−	0.0903793i
$584$	−505985.	+	333719.i	−1.48358	+	0.978486i
$585$	−1616.95	+	49835.7i	−0.00472483	+	0.145623i
$586$	377137.	−	74234.1i	1.09826	−	0.216176i
$587$	−60509.5	+	34935.2i	−0.175609	+	0.101388i	−0.585228	−	0.810869i	$-0.698995\pi$
$587$	−60509.5	+	34935.2i	−0.175609	+	0.101388i	0.409619	+	0.912257i	$0.365662\pi$
$588$	35003.9	+	47579.1i	0.101242	+	0.137614i
$589$	−406079.	+	703350.i	−1.17052	+	2.02741i
$590$	−362059.	−	123710.i	−1.04010	−	0.355385i
$591$	267058.	+	76220.4i	0.764592	+	0.218221i
$592$	345938.	+	95663.4i	0.987085	+	0.272962i
$593$	206980.			0.588599			0.294299	−	0.955713i	$-0.404914\pi$
$593$	206980.			0.588599			0.294299	+	0.955713i	$0.404914\pi$
$594$	−78318.5	−	181435.i	−0.221968	−	0.514219i
$595$		−	380174.i		−	1.07386i
$596$	−39517.3	−	30574.4i	−0.111249	−	0.0860726i
$597$	84629.6	−	296522.i	0.237451	−	0.831970i
$598$	−42680.4	−	14583.2i	−0.119351	−	0.0407803i
$599$	−241159.	−	139233.i	−0.672123	−	0.388051i	0.124757	−	0.992187i	$-0.460185\pi$
$599$	−241159.	−	139233.i	−0.672123	−	0.388051i	−0.796881	+	0.604137i	$0.793518\pi$
$600$	75406.1	+	69151.8i	0.209462	+	0.192088i
$601$	−213736.	−	370201.i	−0.591737	−	1.02492i	−0.993999	−	0.109393i	$-0.965109\pi$
$601$	−213736.	−	370201.i	−0.591737	−	1.02492i	0.402262	−	0.915525i	$-0.368224\pi$
$602$	327769.	−	64516.8i	0.904430	−	0.178024i
$603$	2590.22	+	4842.58i	0.00712365	+	0.0133181i
$604$	−55541.6	−	135620.i	−0.152246	−	0.371748i
$605$	−106266.	−	184058.i	−0.290325	−	0.502857i
$606$	−190758.	+	274530.i	−0.519443	+	0.747558i
$607$	−361479.	−	208700.i	−0.981082	−	0.566428i	−0.0784853	−	0.996915i	$-0.525008\pi$
$607$	−361479.	−	208700.i	−0.981082	−	0.566428i	−0.902597	+	0.430487i	$0.858342\pi$
$608$	595016.	−	286076.i	1.60961	−	0.773880i
$609$	−202336.	−	209008.i	−0.545556	−	0.563544i
$610$	146290.	+	167486.i	0.393147	+	0.450109i
$611$		−	121339.i		−	0.325026i
$612$	−332699.	+	402345.i	−0.888277	+	1.07423i
$613$	−23327.6			−0.0620796			−0.0310398	−	0.999518i	$-0.509882\pi$
$613$	−23327.6			−0.0620796			−0.0310398	+	0.999518i	$0.509882\pi$
$614$	423699.	−	370079.i	1.12388	−	0.981652i
$615$	71657.8	+	285898.i	0.189458	+	0.755894i
$616$	−11499.2	−	193180.i	−0.0303045	−	0.509098i
$617$	−39385.7	+	68218.0i	−0.103459	+	0.179196i	−0.913108	−	0.407719i	$-0.866324\pi$
$617$	−39385.7	+	68218.0i	−0.103459	+	0.179196i	0.809649	+	0.586915i	$0.199658\pi$
$618$	−34017.5	+	405642.i	−0.0890687	+	1.06210i
$619$	382655.	−	220926.i	0.998679	−	0.576587i	0.0908215	−	0.995867i	$-0.471051\pi$
$619$	382655.	−	220926.i	0.998679	−	0.576587i	0.907857	+	0.419280i	$0.137717\pi$
$620$	−161561.	−	394494.i	−0.420293	−	1.02626i
$621$	59746.4	+	276047.i	0.154928	+	0.715814i
$622$	−126279.	−	641545.i	−0.326401	−	1.65824i
$623$	−312348.	+	180334.i	−0.804753	+	0.464625i
$624$	58866.0	−	32112.0i	0.151180	−	0.0824703i
$625$	124028.	−	214823.i	0.317512	−	0.549947i
$626$	−66334.9	+	194141.i	−0.169275	+	0.495415i
$627$	−95606.4	−	381447.i	−0.243193	−	0.970285i
$628$	−267059.	−	206623.i	−0.677155	−	0.523912i
$629$	−564798.			−1.42755
$630$	301770.	−	49293.3i	0.760317	−	0.124196i
$631$			211599.i			0.531440i	0.964050	+	0.265720i	$0.0856097\pi$
$631$			211599.i			0.531440i	−0.964050	+	0.265720i	$0.914390\pi$
$632$	−125181.	+	250053.i	−0.313405	+	0.626034i
$633$	−108350.	−	111923.i	−0.270410	−	0.279325i
$634$	−36277.7	+	106173.i	−0.0902530	+	0.264142i
$635$	9709.36	+	5605.70i	0.0240793	+	0.0139022i
$636$	52385.1	−	119574.i	0.129507	−	0.295612i
$637$	5969.11	+	10338.8i	0.0147106	+	0.0254795i
$638$	−37926.0	−	192678.i	−0.0931743	−	0.473360i
$639$	−56222.6	+	90471.9i	−0.137692	+	0.221570i
$640$	−72353.7	+	338903.i	−0.176645	+	0.827401i
$641$	2552.74	+	4421.47i	0.00621284	+	0.0107610i	0.869115	−	0.494610i	$-0.164689\pi$
$641$	2552.74	+	4421.47i	0.00621284	+	0.0107610i	−0.862902	+	0.505371i	$0.831356\pi$
$642$	203953.	−	96000.8i	0.494836	−	0.232919i
$643$	−69127.8	−	39911.0i	−0.167198	−	0.0965318i	0.414066	−	0.910247i	$-0.364108\pi$
$643$	−69127.8	−	39911.0i	−0.167198	−	0.0965318i	−0.581264	+	0.813715i	$0.697442\pi$
$644$	−37197.3	+	274074.i	−0.0896891	+	0.660839i
$645$	−97788.2	+	342626.i	−0.235054	+	0.823570i
$646$	−782463.	+	683441.i	−1.87499	+	1.63771i
$647$			531516.i			1.26972i	0.772628	+	0.634859i	$0.218942\pi$
$647$			531516.i			1.26972i	−0.772628	+	0.634859i	$0.781058\pi$
$648$	−362506.	−	211917.i	−0.863306	−	0.504680i
$649$	306477.			0.727627
$650$	13603.2	+	15574.2i	0.0321969	+	0.0368619i
$651$	486416.	+	138827.i	1.14775	+	0.327576i
$652$	678119.	+	92034.3i	1.59518	+	0.216498i
$653$	235615.	−	408097.i	0.552556	−	0.957055i	−0.445533	−	0.895265i	$-0.646986\pi$
$653$	235615.	−	408097.i	0.552556	−	0.957055i	0.998089	−	0.0617897i	$-0.0196808\pi$
$654$	−52937.9	−	112467.i	−0.123769	−	0.262947i
$655$	16967.4	−	9796.15i	0.0395488	−	0.0228335i
$656$	282509.	−	278029.i	0.656485	−	0.646074i
$657$	651564.	+	404906.i	1.50948	+	0.938045i
$658$	−730082.	+	143707.i	−1.68624	+	0.331913i
$659$	−309469.	+	178672.i	−0.712601	+	0.411420i	−0.812023	−	0.583625i	$-0.801634\pi$
$659$	−309469.	+	178672.i	−0.712601	+	0.411420i	0.0994224	+	0.995045i	$0.468300\pi$
$660$	189064.	+	82828.5i	0.434031	+	0.190148i
$661$	282792.	−	489809.i	0.647237	−	1.12105i	−0.336543	−	0.941668i	$-0.609258\pi$
$661$	282792.	−	489809.i	0.647237	−	1.12105i	0.983780	−	0.179380i	$-0.0574090\pi$
$662$	426922.	+	145872.i	0.974165	+	0.332857i
$663$	−75812.5	+	73392.6i	−0.172470	+	0.166965i
$664$	−21831.8	+	43609.5i	−0.0495168	+	0.0989111i
$665$	608463.			1.37591
$666$	−73231.4	−	448318.i	−0.165101	−	1.01074i
$667$			280664.i			0.630864i
$668$	−108172.	+	139812.i	−0.242417	+	0.313323i
$669$	559314.	−	140187.i	1.24969	−	0.313225i
$670$	−5428.08	−	1854.69i	−0.0120920	−	0.00413163i
$671$	−154264.	−	89064.5i	−0.342626	−	0.197815i
$672$	−262931.	−	316158.i	−0.582241	−	0.700108i
$673$	158119.	+	273870.i	0.349103	+	0.604663i	0.986090	−	0.166211i	$-0.0531532\pi$
$673$	158119.	+	273870.i	0.349103	+	0.604663i	−0.636988	+	0.770874i	$0.719820\pi$
$674$	81710.5	−	16083.6i	0.179870	−	0.0354049i
$675$	39557.8	−	123300.i	0.0868210	−	0.270618i
$676$	−410345.	+	168052.i	−0.897957	+	0.367749i
$677$	300914.	+	521198.i	0.656545	+	1.13717i	0.981504	+	0.191441i	$0.0613161\pi$
$677$	300914.	+	521198.i	0.656545	+	1.13717i	−0.324959	+	0.945728i	$0.605351\pi$
$678$	−91303.4	−	7656.78i	−0.198622	−	0.0166566i
$679$	257556.	+	148700.i	0.558641	+	0.322531i
$680$	−32403.1	−	544353.i	−0.0700758	−	1.17723i
$681$	119533.	−	29959.8i	0.257746	−	0.0646018i
$682$	224633.	+	257180.i	0.482953	+	0.552927i
$683$		−	385277.i		−	0.825909i	−0.910752	−	0.412955i	$-0.864497\pi$
$683$		−	385277.i		−	0.825909i	0.910752	−	0.412955i	$-0.135503\pi$
$684$	−643947.	−	532479.i	−1.37638	−	1.13813i
$685$	35285.0			0.0751984
$686$	377877.	−	330056.i	0.802975	−	0.701357i
$687$	426728.	−	413107.i	0.904144	−	0.875284i
$688$	463817.	−	120315.i	0.979873	−	0.254180i
$689$	13192.2	−	22849.6i	0.0277895	−	0.0481328i
$690$	−242264.	−	168338.i	−0.508852	−	0.353578i
$691$	−397767.	+	229651.i	−0.833053	+	0.480963i	−0.854897	−	0.518798i	$-0.826380\pi$
$691$	−397767.	+	229651.i	−0.833053	+	0.480963i	0.0218438	+	0.999761i	$0.493046\pi$
$692$	−324788.	+	133014.i	−0.678247	+	0.277769i
$693$	−215972.	+	115520.i	−0.449709	+	0.240543i
$694$	124541.	+	632712.i	0.258578	+	1.31367i
$695$	−15181.6	+	8765.10i	−0.0314303	+	0.0181463i
$696$	−307529.	−	282022.i	−0.634846	−	0.582190i
$697$	−311866.	+	540168.i	−0.641952	+	1.11189i
$698$	−286451.	+	838349.i	−0.587948	+	1.72074i
$699$	548191.	+	156458.i	1.12196	+	0.320217i
$700$	77596.9	−	100294.i	0.158361	−	0.204681i
$701$	−127011.			−0.258467			−0.129234	−	0.991614i	$-0.541252\pi$
$701$	−127011.			−0.258467			−0.129234	+	0.991614i	$0.541252\pi$
$702$	−68086.4	−	50661.4i	−0.138161	−	0.102802i
$703$		−	903950.i		−	1.82908i
$704$	−32930.3	−	275625.i	−0.0664432	−	0.556126i
$705$	217816.	−	763175.i	0.438240	−	1.53549i
$706$	282966.	−	828150.i	0.567707	−	1.66150i
$707$	358820.	+	207165.i	0.717857	+	0.414455i
$708$	524551.	−	385911.i	1.04646	−	0.769876i
$709$	−247408.	−	428523.i	−0.492177	−	0.852475i	0.507783	−	0.861485i	$-0.330465\pi$
$709$	−247408.	−	428523.i	−0.492177	−	0.852475i	−0.999959	+	0.00901014i	$0.997132\pi$
$710$	−21487.4	−	109164.i	−0.0426253	−	0.216552i
$711$	353730.	+	11477.0i	0.699733	+	0.0227033i
$712$	−431865.	+	284834.i	−0.851900	+	0.561864i
$713$	−244018.	−	422652.i	−0.480002	−	0.831388i
$714$	531381.	+	369232.i	1.04234	+	0.724275i
$715$	36128.6	+	20858.8i	0.0706706	+	0.0408017i
$716$	−181998.	−	24700.8i	−0.355011	−	0.0481820i
$717$	1987.85	+	2053.39i	0.00386674	+	0.00399423i
$718$	−2785.49	+	2432.98i	−0.00540322	+	0.00471943i
$719$			614613.i			1.18890i	0.804134	+	0.594448i	$0.202629\pi$
$719$			614613.i			1.18890i	−0.804134	+	0.594448i	$0.797371\pi$
$720$	427888.	−	96301.0i	0.825401	−	0.185766i
$721$	504518.			0.970523
$722$	−750914.	−	859712.i	−1.44051	−	1.64922i
$723$	55807.8	+	222660.i	0.106762	+	0.425957i
$724$	−97846.7	+	720945.i	−0.186668	+	1.37539i
$725$	64338.5	−	111438.i	0.122404	−	0.212010i
$726$	360472.	+	30229.4i	0.683908	+	0.0573531i
$727$	−286999.	+	165699.i	−0.543014	+	0.313509i	−0.746299	−	0.665610i	$-0.768171\pi$
$727$	−286999.	+	165699.i	−0.543014	+	0.313509i	0.203286	+	0.979119i	$0.434838\pi$
$728$	−45757.4	−	69377.4i	−0.0863373	−	0.130905i
$729$	−51629.3	+	528927.i	−0.0971495	+	0.995270i
$730$	−786182.	+	154749.i	−1.47529	+	0.290390i
$731$	−652999.	+	377009.i	−1.22202	+	0.705532i
$732$	−376179.	+	41808.8i	−0.702057	+	0.0780271i
$733$	25808.4	−	44701.5i	0.0480345	−	0.0831982i	−0.841008	−	0.541022i	$-0.818038\pi$
$733$	25808.4	−	44701.5i	0.0480345	−	0.0831982i	0.889043	+	0.457824i	$0.151371\pi$
$734$	−154426.	−	52764.9i	−0.286634	−	0.0979383i
$735$	18984.1	+	75742.1i	0.0351411	+	0.140205i
$736$	−29901.1	+	395603.i	−0.0551990	+	0.730305i
$737$	4594.79			0.00845923
$738$	−469204.	−	177511.i	−0.861487	−	0.325921i
$739$		−	228968.i		−	0.419263i	−0.977780	−	0.209631i	$-0.932774\pi$
$739$		−	228968.i		−	0.419263i	0.977780	−	0.209631i	$-0.0672264\pi$
$740$	375269.	+	290344.i	0.685298	+	0.530212i
$741$	−117464.	−	121337.i	−0.213928	−	0.220981i
$742$	−153107.	−	52314.4i	−0.278092	−	0.0950196i
$743$	−910009.	−	525394.i	−1.64842	−	0.951716i	−0.977700	−	0.210005i	$-0.932652\pi$
$743$	−910009.	−	525394.i	−1.64842	−	0.951716i	−0.670720	−	0.741711i	$-0.734015\pi$
$744$	708307.	+	157321.i	1.27960	+	0.284211i
$745$	−33025.0	−	57201.0i	−0.0595018	−	0.103060i
$746$	920459.	−	181179.i	1.65397	−	0.325560i
$747$	61690.8	+	2001.60i	0.110555	+	0.00358704i
$748$	165545.	+	404223.i	0.295878	+	0.722466i
$749$	−139692.	−	241953.i	−0.249004	−	0.431288i
$750$	260278.	+	552961.i	0.462717	+	0.983041i
$751$	−233295.	−	134693.i	−0.413643	−	0.238817i	0.278711	−	0.960375i	$-0.410093\pi$
$751$	−233295.	−	134693.i	−0.413643	−	0.238817i	−0.692354	+	0.721558i	$0.743426\pi$
$752$	−1.03312e6	+	267993.i	−1.82690	+	0.473901i
$753$	−101241.	+	354724.i	−0.178553	+	0.625606i
$754$	−55478.1	−	63516.2i	−0.0975840	−	0.111723i
$755$		−	193735.i		−	0.339870i
$756$	−224186.	+	469667.i	−0.392251	+	0.821764i
$757$	−476176.			−0.830952			−0.415476	−	0.909604i	$-0.636385\pi$
$757$	−476176.			−0.830952			−0.415476	+	0.909604i	$0.636385\pi$
$758$	559002.	−	488259.i	0.972915	−	0.849791i
$759$	227233.	+	64854.1i	0.394446	+	0.112578i
$760$	871228.	−	51860.6i	1.50836	−	0.0897863i
$761$	−242197.	+	419498.i	−0.418215	+	0.724370i	−0.995760	−	0.0919890i	$-0.970678\pi$
$761$	−242197.	+	419498.i	−0.418215	+	0.724370i	0.577545	+	0.816359i	$0.304011\pi$
$762$	−17265.2	+	8126.71i	−0.0297345	+	0.0139960i
$763$	−133421.	+	77030.4i	−0.229178	+	0.132316i
$764$	424714.	+	1.03705e6i	0.727628	+	1.77670i
$765$	−608577.	+	325519.i	−1.03990	+	0.556229i
$766$	−46555.3	−	236518.i	−0.0793436	−	0.403095i
$767$	113983.	−	65808.4i	0.193754	−	0.111864i
$768$	−403424.	−	430280.i	−0.683974	−	0.729506i
$769$	−251061.	+	434851.i	−0.424549	+	0.735340i	−0.996378	−	0.0850327i	$-0.972901\pi$
$769$	−251061.	+	434851.i	−0.424549	+	0.735340i	0.571830	+	0.820372i	$0.306234\pi$
$770$	82716.6	−	242085.i	0.139512	−	0.408307i
$771$	200185.	−	193796.i	0.336762	−	0.326013i
$772$	441050.	+	341238.i	0.740037	+	0.572563i
$773$	435529.			0.728884			0.364442	−	0.931226i	$-0.381260\pi$
$773$	435529.			0.728884			0.364442	+	0.931226i	$0.381260\pi$
$774$	−383925.	−	469446.i	−0.640862	−	0.783617i
$775$			223752.i			0.372531i
$776$	381456.	+	190964.i	0.633463	+	0.317124i
$777$	−546117.	+	136880.i	−0.904573	+	0.226724i
$778$	−15531.9	+	45457.0i	−0.0256606	+	0.0751004i
$779$	−864530.	−	499136.i	−1.42464	−	0.822516i
$780$	88100.9	−	9791.59i	0.144808	−	0.0160940i
$781$	44560.0	+	77180.2i	0.0730539	+	0.126533i
$782$	−120571.	−	612543.i	−0.197164	−	1.00167i
$783$	−161329.	+	502857.i	−0.263141	+	0.820202i
$784$	74844.3	−	73657.4i	0.121766	−	0.119835i
$785$	−223184.	−	386566.i	−0.362179	−	0.627313i
$786$	−2786.70	+	33230.1i	−0.00451072	+	0.0537881i
$787$	−371945.	−	214742.i	−0.600522	−	0.346711i	0.168725	−	0.985663i	$-0.446035\pi$
$787$	−371945.	−	214742.i	−0.600522	−	0.346711i	−0.769247	+	0.638952i	$0.779368\pi$
$788$	66399.9	−	489242.i	0.106934	−	0.787900i
$789$	−134189.	+	33633.3i	−0.215557	+	0.0540276i
$790$	−278416.	+	243182.i	−0.446108	+	0.389652i
$791$			113559.i			0.181496i
$792$	−299394.	+	183816.i	−0.477301	+	0.293043i
$793$	−76497.5			−0.121647
$794$	84930.9	+	97236.4i	0.134718	+	0.154237i
$795$	123991.	−	120034.i	0.196181	−	0.189919i
$796$	−543219.	−	73725.7i	−0.857332	−	0.116357i
$797$	−362714.	+	628240.i	−0.571016	+	0.989028i	0.425446	+	0.904984i	$0.360117\pi$
$797$	−362714.	+	628240.i	−0.571016	+	0.989028i	−0.996462	+	0.0840446i	$0.973216\pi$
$798$	−590951.	+	850467.i	−0.927994	+	1.33552i
$799$	1.45451e6	−	839761.i	2.27836	−	1.31541i
$800$	102559.	−	150220.i	0.160248	−	0.234718i
$801$	556120.	+	345594.i	0.866769	+	0.538643i
$802$	736768.	−	145023.i	1.14547	−	0.225469i
$803$	555840.	−	320914.i	0.862023	−	0.497689i
$804$	7864.21	−	5785.69i	0.0121659	−	0.00895041i
$805$	−182817.	+	316648.i	−0.282114	+	0.488635i
$806$	138767.	+	47414.6i	0.213608	+	0.0729863i
$807$	−658648.	−	187984.i	−1.01136	−	0.288651i
$808$	531434.	+	266046.i	0.814004	+	0.407506i
$809$	144295.			0.220473			0.110237	−	0.993905i	$-0.464839\pi$
$809$	144295.			0.220473			0.110237	+	0.993905i	$0.464839\pi$
$810$	−337294.	−	440862.i	−0.514089	−	0.671943i
$811$			321928.i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$811$			321928.i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$812$	−316464.	+	409029.i	−0.479968	+	0.620358i
$813$	192852.	−	675706.i	0.291771	−	1.02230i
$814$	−359648.	−	122886.i	−0.542787	−	0.185462i
$815$	783456.	+	452328.i	1.17950	+	0.680987i
$816$	792329.	+	483395.i	1.18994	+	0.725975i
$817$	−603397.	−	1.04511e6i	−0.903980	−	1.56574i
$818$	528044.	−	103938.i	0.789156	−	0.155334i
$819$	−55518.2	+	89338.4i	−0.0827689	+	0.133190i
$820$	484896.	−	198584.i	0.721142	−	0.295336i
$821$	−453891.	−	786162.i	−0.673388	−	1.16634i	−0.976937	−	0.213527i	$-0.931505\pi$
$821$	−453891.	−	786162.i	−0.673388	−	1.16634i	0.303549	−	0.952816i	$-0.401828\pi$
$822$	−34269.4	+	49318.9i	−0.0507181	+	0.0729910i
$823$	730902.	+	421987.i	1.07909	+	0.623016i	0.930652	−	0.365905i	$-0.119241\pi$
$823$	730902.	+	421987.i	1.07909	+	0.623016i	0.148443	+	0.988921i	$0.452574\pi$
$824$	722394.	−	43001.1i	1.06395	−	0.0633323i
$825$	−75355.7	−	77840.3i	−0.110715	−	0.114366i
$826$	−530955.	−	607885.i	−0.778212	−	0.890966i
$827$			658309.i			0.962540i	0.876572	+	0.481270i	$0.159824\pi$
$827$			658309.i			0.962540i	−0.876572	+	0.481270i	$0.840176\pi$
$828$	470583.	−	175127.i	0.686397	−	0.255442i
$829$	1.22965e6			1.78925			0.894625	−	0.446818i	$-0.147443\pi$
$829$	1.22965e6			1.78925			0.894625	+	0.446818i	$0.147443\pi$
$830$	−48556.0	+	42411.2i	−0.0704834	+	0.0615636i
$831$	10371.4	+	41379.4i	0.0150188	+	0.0599215i
$832$	−71430.9	−	95438.0i	−0.103190	−	0.137872i
$833$	−82621.7	+	143105.i	−0.119071	+	0.206236i
$834$	2493.40	−	29732.6i	0.00358476	−	0.0427465i
$835$	−202377.	+	116842.i	−0.290261	+	0.167582i
$836$	−646952.	+	264952.i	−0.925677	+	0.379101i
$837$	−194254.	−	897515.i	−0.277281	−	1.28112i
$838$	−65404.3	−	332278.i	−0.0931362	−	0.473166i
$839$	45546.9	−	26296.5i	0.0647045	−	0.0373572i	−0.467299	−	0.884099i	$-0.654773\pi$
$839$	45546.9	−	26296.5i	0.0647045	−	0.0373572i	0.532003	+	0.846742i	$0.321439\pi$
$840$	−163256.	−	518495.i	−0.231372	−	0.734829i
$841$	91248.2	−	158047.i	0.129013	−	0.223456i
$842$	−149637.	+	437940.i	−0.211064	+	0.617718i
$843$	94545.8	+	377215.i	0.133042	+	0.530804i
$844$	−169465.	+	219033.i	−0.237900	+	0.307486i
$845$	−586183.			−0.820956
$846$	855166.	+	1.04566e6i	1.19484	+	1.46100i
$847$		−	448337.i		−	0.624939i
$848$	−223686.	−	61856.6i	−0.311062	−	0.0860191i
$849$	−226081.	−	233535.i	−0.313653	−	0.323994i
$850$	−92544.7	+	270849.i	−0.128090	+	0.374877i
$851$	470421.	+	271598.i	0.649572	+	0.375031i
$852$	173451.	+	75988.4i	0.238944	+	0.104681i
$853$	322258.	+	558168.i	0.442900	+	0.767126i	0.997903	−	0.0647226i	$-0.0206163\pi$
$853$	322258.	+	558168.i	0.442900	+	0.767126i	−0.555003	+	0.831848i	$0.687283\pi$
$854$	90598.9	+	460276.i	0.124224	+	0.631106i
$855$	−520988.	−	974019.i	−0.712681	−	1.33240i
$856$	−220639.	−	334534.i	−0.301117	−	0.456555i
$857$	−175819.	−	304528.i	−0.239390	−	0.414635i	0.721150	−	0.692779i	$-0.243614\pi$
$857$	−175819.	−	304528.i	−0.239390	−	0.414635i	−0.960539	+	0.278144i	$0.910281\pi$
$858$	−64243.8	+	30239.5i	−0.0872683	+	0.0410771i
$859$	−658817.	−	380368.i	−0.892851	−	0.515487i	−0.0179767	−	0.999838i	$-0.505722\pi$
$859$	−658817.	−	380368.i	−0.892851	−	0.515487i	−0.874874	+	0.484351i	$0.839056\pi$
$860$	627681.	+	85188.9i	0.848676	+	0.115182i
$861$	−170641.	+	597883.i	−0.230184	+	0.806510i
$862$	888412.	−	775981.i	1.19564	−	1.04433i
$863$		−	363360.i		−	0.487883i	−0.969790	−	0.243942i	$-0.921559\pi$
$863$		−	363360.i		−	0.487883i	0.969790	−	0.243942i	$-0.0784406\pi$
$864$	−280970.	+	691601.i	−0.376385	+	0.926463i
$865$	−463964.			−0.620086
$866$	−398084.	−	455761.i	−0.530809	−	0.607717i
$867$	−681622.	−	194541.i	−0.906788	−	0.258805i
$868$	120940.	−	891100.i	0.160521	−	1.18273i
$869$	148054.	−	256438.i	0.196057	−	0.339580i
$870$	−234917.	−	499080.i	−0.310367	−	0.659374i
$871$	1708.87	−	986.617i	0.00225254	−	0.00130051i
$872$	−184473.	+	121668.i	−0.242605	+	0.160008i
$873$	17508.2	−	539615.i	0.0229727	−	0.708036i
$874$	980365.	−	192971.i	1.28341	−	0.252621i
$875$	655985.	−	378733.i	0.856796	−	0.494672i
$876$	547257.	−	1.24917e6i	0.713154	−	1.62784i
$877$	−36035.0	+	62414.4i	−0.0468516	+	0.0811494i	−0.888500	−	0.458876i	$-0.848252\pi$
$877$	−36035.0	+	62414.4i	−0.0468516	+	0.0811494i	0.841649	+	0.540026i	$0.181585\pi$
$878$	75756.3	+	25884.7i	0.0982720	+	0.0335780i
$879$	−621371.	+	601537.i	−0.804216	+	0.778546i
$880$	97804.3	−	353680.i	0.126297	−	0.456714i
$881$	1.34754e6			1.73616			0.868082	−	0.496422i	$-0.165353\pi$
$881$	1.34754e6			1.73616			0.868082	+	0.496422i	$0.165353\pi$
$882$	−124305.	−	47027.5i	−0.159790	−	0.0604525i
$883$			675925.i			0.866916i	0.901174	+	0.433458i	$0.142707\pi$
$883$			675925.i			0.866916i	−0.901174	+	0.433458i	$0.857293\pi$
$884$	148365.	+	114790.i	0.189858	+	0.146892i
$885$	835043.	−	209296.i	1.06616	−	0.267224i
$886$	−146273.	−	49979.2i	−0.186336	−	0.0636681i
$887$	888008.	+	512692.i	1.12868	+	0.651642i	0.943602	−	0.331082i	$-0.107414\pi$
$887$	888008.	+	512692.i	1.12868	+	0.651642i	0.185075	+	0.982724i	$0.440747\pi$
$888$	−770291.	+	242538.i	−0.976853	+	0.307577i
$889$	11825.2	+	20481.9i	0.0149626	+	0.0259159i
$890$	−671018.	+	132081.i	−0.847138	+	0.166747i
$891$	369846.	+	246813.i	0.465871	+	0.310894i
$892$	−388498.	−	948622.i	−0.488269	−	1.19224i
$893$	1.34402e6	+	2.32792e6i	1.68540	+	2.91921i
$894$	112026.	+	9394.59i	0.140166	+	0.0117545i
$895$	−210269.	−	121399.i	−0.262500	−	0.151555i
$896$	−489640.	+	542821.i	−0.609904	+	0.676147i
$897$	98437.0	−	24672.4i	0.122341	−	0.0306638i
$898$	209083.	+	239377.i	0.259278	+	0.296845i
$899$		−	912528.i		−	1.12908i
$900$	−226990.	−	38340.8i	−0.280235	−	0.0473343i
$901$	365202.			0.449867
$902$	−316115.	+	276110.i	−0.388537	+	0.339367i
$903$	−540032.	+	522795.i	−0.662284	+	0.641144i
$904$	9678.86	+	162599.i	0.0118437	+	0.198967i
$905$	−480895.	+	832935.i	−0.587156	+	1.01698i
$906$	270789.	+	188159.i	0.329894	+	0.229228i
$907$	−1.39930e6	+	807885.i	−1.70097	+	0.982053i	−0.756181	+	0.654363i	$0.772937\pi$
$907$	−1.39930e6	+	807885.i	−1.70097	+	0.982053i	−0.944785	+	0.327690i	$0.893730\pi$
$908$	−83027.1	−	202733.i	−0.100704	−	0.245896i
$909$	24391.9	−	751776.i	0.0295201	−	0.909831i
$910$	−21218.2	−	107796.i	−0.0256227	−	0.130173i
$911$	246841.	−	142514.i	0.297427	−	0.171719i	−0.343860	−	0.939021i	$-0.611734\pi$
$911$	246841.	−	142514.i	0.297427	−	0.171719i	0.641286	+	0.767302i	$0.278401\pi$
$912$	−773665.	+	1.26811e6i	−0.930173	+	1.52464i
$913$	25820.8	−	44723.0i	0.0309762	−	0.0536524i
$914$	−340858.	+	997583.i	−0.408020	+	1.19414i
$915$	−481139.	−	137321.i	−0.574683	−	0.164019i
$916$	−835108.	−	646119.i	−0.995295	−	0.770055i
$917$	41330.0			0.0491503
$918$	136074.	−	1.16678e6i	0.161469	−	1.38453i
$919$			662333.i			0.784233i	0.919916	+	0.392117i	$0.128257\pi$
$919$			662333.i			0.784233i	−0.919916	+	0.392117i	$0.871743\pi$
$920$	−234777.	+	468974.i	−0.277384	+	0.554081i
$921$	−347389.	+	1.21717e6i	−0.409541	+	1.43493i
$922$	−259453.	+	759336.i	−0.305209	+	0.893249i
$923$	33145.1	+	19136.3i	0.0389059	+	0.0224623i
$924$	258034.	+	350733.i	0.302226	+	0.410802i
$925$	−124520.	−	215675.i	−0.145531	−	0.252067i
$926$	183131.	+	930373.i	0.213570	+	1.08501i
$927$	−431986.	−	807624.i	−0.502702	−	0.939832i
$928$	−418267.	+	612641.i	−0.485688	+	0.711394i
$929$	−620275.	−	1.07435e6i	−0.718708	−	1.24484i	−0.961512	−	0.274764i	$-0.911400\pi$
$929$	−620275.	−	1.07435e6i	−0.718708	−	1.24484i	0.242803	−	0.970076i	$-0.421933\pi$
$930$	787677.	+	547320.i	0.910714	+	0.632813i
$931$	−229037.	−	132235.i	−0.264245	−	0.152562i
$932$	136300.	−	1.00427e6i	0.156914	−	1.15616i
$933$	1.02327e6	+	1.05701e6i	1.17551	+	1.21427i
$934$	−694300.	+	606435.i	−0.795891	+	0.695169i
$935$			577438.i			0.660514i
$936$	−71879.2	+	132651.i	−0.0820449	+	0.151412i
$937$	−593717.			−0.676239			−0.338119	−	0.941103i	$-0.609791\pi$
$937$	−593717.			−0.676239			−0.338119	+	0.941103i	$0.609791\pi$
$938$	−7960.23	−	9113.57i	−0.00904732	−	0.0103582i
$939$	−112228.	−	447762.i	−0.127283	−	0.507828i
$940$	−1.39812e6	−	189752.i	−1.58229	−	0.214749i
$941$	613509.	−	1.06263e6i	0.692854	−	1.20006i	−0.278044	−	0.960568i	$-0.589686\pi$
$941$	613509.	−	1.06263e6i	0.692854	−	1.20006i	0.970899	−	0.239491i	$-0.0769804\pi$
$942$	757075.	+	63488.9i	0.853173	+	0.0715478i
$943$	519507.	−	299938.i	0.584209	−	0.337293i
$944$	−812060.	−	825145.i	−0.911264	−	0.925947i
$945$	−509559.	+	462242.i	−0.570599	+	0.517614i
$946$	−497840.	+	97992.9i	−0.556298	+	0.109500i
$947$	1.48474e6	−	857213.i	1.65558	−	0.955848i	0.680857	−	0.732416i	$-0.261607\pi$
$947$	1.48474e6	−	857213.i	1.65558	−	0.955848i	0.974720	−	0.223431i	$-0.0717258\pi$
$948$	−69500.0	−	625333.i	−0.0773335	−	0.695817i
$949$	137817.	−	238706.i	0.153027	−	0.265051i
$950$	−433489.	−	148116.i	−0.480320	−	0.164118i
$951$	−61375.9	−	244875.i	−0.0678636	−	0.270760i
$952$	514960.	−	1.02865e6i	0.568198	−	1.13499i
$953$	−1.23751e6			−1.36258			−0.681290	−	0.732014i	$-0.738581\pi$
$953$	−1.23751e6			−1.36258			−0.681290	+	0.732014i	$0.738581\pi$
$954$	47352.0	+	289885.i	0.0520285	+	0.318515i
$955$			1.48144e6i			1.62434i
$956$	3109.09	−	4018.50i	0.00340187	−	0.00439691i
$957$	307324.	+	317457.i	0.335562	+	0.346626i
$958$	−9089.93	−	3105.89i	−0.00990443	−	0.00338419i
$959$	64461.5	+	37216.8i	0.0700911	+	0.0404671i
$960$	−277951.	−	728493.i	−0.301596	−	0.790466i
$961$	331619.	+	574381.i	0.359081	+	0.621947i
$962$	−160145.	+	31522.3i	−0.173047	+	0.0340619i
$963$	−267706.	+	430785.i	−0.288672	+	0.464523i
$964$	377642.	−	154659.i	0.406374	−	0.166426i
$965$	368589.	+	638416.i	0.395811	+	0.685565i
$966$	−265033.	−	563063.i	−0.284018	−	0.603396i
$967$	858506.	+	495659.i	0.918101	+	0.530066i	0.883029	−	0.469319i	$-0.155501\pi$
$967$	858506.	+	495659.i	0.918101	+	0.530066i	0.0350720	+	0.999385i	$0.488834\pi$
$968$	−38212.7	−	641952.i	−0.0407809	−	0.685096i
$969$	641539.	−	2.24780e6i	0.683244	−	2.39392i
$970$	370974.	+	424724.i	0.394276	+	0.451402i
$971$		−	1.45182e6i		−	1.53984i	−0.638141	−	0.769920i	$-0.720296\pi$
$971$		−	1.45182e6i		−	1.53984i	0.638141	−	0.769920i	$-0.279704\pi$
$972$	943792.	−	43272.7i	0.998951	−	0.0458017i
$973$	−36980.0			−0.0390608
$974$	−1.22080e6	+	1.06630e6i	−1.28684	+	1.12399i
$975$	−44740.1	−	12769.2i	−0.0470639	−	0.0134324i
$976$	168954.	+	651324.i	0.177366	+	0.683750i
$977$	−306090.	+	530163.i	−0.320671	+	0.555418i	−0.980627	−	0.195886i	$-0.937242\pi$
$977$	−306090.	+	530163.i	−0.320671	+	0.555418i	0.659956	+	0.751304i	$0.270575\pi$
$978$	−1.39314e6	+	655750.i	−1.45652	+	0.685584i
$979$	474418.	−	273905.i	0.494989	−	0.285782i
$980$	128462.	−	52610.3i	0.133759	−	0.0547796i
$981$	237549.	+	147621.i	0.246839	+	0.153395i
$982$	−99305.1	−	504507.i	−0.102979	−	0.523171i
$983$	−1.04512e6	+	603401.i	−1.08158	+	0.624452i	−0.931323	−	0.364195i	$-0.881344\pi$
$983$	−1.04512e6	+	603401.i	−1.08158	+	0.624452i	−0.150259	+	0.988647i	$0.548011\pi$
$984$	−193373.	+	870623.i	−0.199713	+	0.899166i
$985$	326341.	−	565239.i	0.336356	−	0.582586i
$986$	377426.	−	1.10460e6i	0.388220	−	1.13620i
$987$	1.20288e6	−	1.16449e6i	1.23478	−	1.19537i
$988$	−183719.	+	237456.i	−0.188209	+	0.243260i
$989$	725178.			0.741399
$990$	−458351.	+	74870.3i	−0.467657	+	0.0763905i
$991$		−	860509.i		−	0.876210i	−0.898924	−	0.438105i	$-0.855650\pi$
$991$		−	860509.i		−	0.876210i	0.898924	−	0.438105i	$-0.144350\pi$
$992$	97217.8	−	1.28623e6i	0.0987921	−	1.30706i
$993$	−984642.	+	246792.i	−0.998573	+	0.250284i
$994$	75885.8	−	222093.i	0.0768047	−	0.224783i
$995$	−627601.	−	362346.i	−0.633924	−	0.365996i
$996$	−12120.9	−	109059.i	−0.0122184	−	0.109936i
$997$	243483.	+	421725.i	0.244951	+	0.424267i	0.962118	−	0.272634i	$-0.0878949\pi$
$997$	243483.	+	421725.i	0.244951	+	0.424267i	−0.717167	+	0.696901i	$0.754562\pi$
$998$	99351.8	+	504744.i	0.0997504	+	0.506769i
$999$	686720.	+	757015.i	0.688095	+	0.758531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.17	yes	44
3.2	odd	2		108.5.f.a.91.6		44
4.3	odd	2	inner	36.5.f.a.31.14	yes	44
9.2	odd	6		108.5.f.a.19.9		44
9.4	even	3		324.5.d.f.163.2		22
9.5	odd	6		324.5.d.e.163.21		22
9.7	even	3	inner	36.5.f.a.7.14	✓	44
12.11	even	2		108.5.f.a.91.9		44
36.7	odd	6	inner	36.5.f.a.7.17	yes	44
36.11	even	6		108.5.f.a.19.6		44
36.23	even	6		324.5.d.e.163.22		22
36.31	odd	6		324.5.d.f.163.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.14	✓	44	9.7	even	3	inner
36.5.f.a.7.17	yes	44	36.7	odd	6	inner
36.5.f.a.31.14	yes	44	4.3	odd	2	inner
36.5.f.a.31.17	yes	44	1.1	even	1	trivial
108.5.f.a.19.6		44	36.11	even	6
108.5.f.a.19.9		44	9.2	odd	6
108.5.f.a.91.6		44	3.2	odd	2
108.5.f.a.91.9		44	12.11	even	2
324.5.d.e.163.21		22	9.5	odd	6
324.5.d.e.163.22		22	36.23	even	6
324.5.d.f.163.1		22	36.31	odd	6
324.5.d.f.163.2		22	9.4	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.63137 + 3.01262i) q^{2} +(-8.65442 - 2.47004i) q^{3} +(-2.15179 + 15.8546i) q^{4} +(-10.5756 + 18.3175i) q^{5} +(-15.3317 - 32.5721i) q^{6} +(-38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 + 42.7535i) q^{9} +O(q^{10})\)	\(q+(2.63137 + 3.01262i) q^{2} +(-8.65442 - 2.47004i) q^{3} +(-2.15179 + 15.8546i) q^{4} +(-10.5756 + 18.3175i) q^{5} +(-15.3317 - 32.5721i) q^{6} +(-38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 + 42.7535i) q^{9} +(-83.0119 + 16.3397i) q^{10} +(58.6904 - 33.8849i) q^{11} +(57.7841 - 131.898i) q^{12} +(14.5519 - 25.2046i) q^{13} +(-168.887 - 57.7061i) q^{14} +(136.770 - 132.405i) q^{15} +(-246.740 - 68.2318i) q^{16} +402.841 q^{17} +(52.2322 + 319.762i) q^{18} +644.741i q^{19} +(-267.660 - 207.088i) q^{20} +(389.517 - 97.6292i) q^{21} +(256.519 + 87.6483i) q^{22} +(-335.527 - 193.717i) q^{23} +(549.409 - 172.990i) q^{24} +(88.8138 + 153.830i) q^{25} +(114.223 - 22.4833i) q^{26} +(-489.802 - 539.940i) q^{27} +(-270.558 - 660.639i) q^{28} +(-362.210 - 627.366i) q^{29} +(758.779 + 63.6318i) q^{30} +(1090.90 + 629.833i) q^{31} +(-443.706 - 922.876i) q^{32} +(-591.628 + 148.287i) q^{33} +(1060.02 + 1213.61i) q^{34} -943.733i q^{35} +(-825.880 + 998.768i) q^{36} -1402.04 q^{37} +(-1942.36 + 1696.55i) q^{38} +(-188.194 + 182.187i) q^{39} +(-80.4363 - 1351.28i) q^{40} +(-774.166 + 1340.89i) q^{41} +(1319.08 + 916.570i) q^{42} +(-1620.98 + 935.875i) q^{43} +(410.944 + 1003.43i) q^{44} +(-1510.71 + 808.057i) q^{45} +(-299.300 - 1520.56i) q^{46} +(3610.63 - 2084.60i) q^{47} +(1966.85 + 1199.96i) q^{48} +(-205.097 + 355.239i) q^{49} +(-229.730 + 672.346i) q^{50} +(-3486.36 - 995.034i) q^{51} +(368.297 + 284.950i) q^{52} +906.566 q^{53} +(337.786 - 2896.37i) q^{54} +1433.41i q^{55} +(1278.32 - 2553.48i) q^{56} +(1592.54 - 5579.86i) q^{57} +(936.910 - 2742.03i) q^{58} +(3916.45 + 2261.16i) q^{59} +(1804.93 + 2453.35i) q^{60} +(-1314.22 - 2276.30i) q^{61} +(973.119 + 4943.80i) q^{62} +(-3612.19 - 117.200i) q^{63} +(1612.72 - 3765.15i) q^{64} +(307.789 + 533.107i) q^{65} +(-2003.52 - 1392.16i) q^{66} +(58.7165 + 33.9000i) q^{67} +(-866.831 + 6386.91i) q^{68} +(2425.30 + 2505.27i) q^{69} +(2843.11 - 2483.31i) q^{70} +1315.04i q^{71} +(-5182.11 + 140.062i) q^{72} +9470.72 q^{73} +(-3689.27 - 4223.80i) q^{74} +(-388.665 - 1550.68i) q^{75} +(-10222.1 - 1387.35i) q^{76} +(-1511.89 + 2618.67i) q^{77} +(-1044.07 - 87.5566i) q^{78} +(3783.95 - 2184.67i) q^{79} +(3859.25 - 3798.05i) q^{80} +(2905.28 + 5882.69i) q^{81} +(-6076.73 + 1196.12i) q^{82} +(659.925 - 381.008i) q^{83} +(709.715 + 6385.74i) q^{84} +(-4260.28 + 7379.03i) q^{85} +(-7084.84 - 2420.78i) q^{86} +(1585.10 + 6324.16i) q^{87} +(-1941.61 + 3878.41i) q^{88} +8083.40 q^{89} +(-6409.62 - 2424.91i) q^{90} +1298.56i q^{91} +(3793.29 - 4902.82i) q^{92} +(-7885.41 - 8145.41i) q^{93} +(15781.0 + 5392.11i) q^{94} +(-11810.0 - 6818.52i) q^{95} +(1560.48 + 9082.93i) q^{96} +(-3332.71 - 5772.42i) q^{97} +(-1609.89 + 316.884i) q^{98} +(5486.47 + 178.012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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