LMFDB - Embedded newform 36.5.f.a.7.14

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			7.14
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29332 - 3.78514i) q^{2} +(8.65442 - 2.47004i) q^{3} +(-12.6546 - 9.79083i) q^{4} +(-10.5756 - 18.3175i) q^{5} +(1.84350 - 35.9528i) q^{6} +(38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 - 42.7535i) q^{9} +O(q^{10})$	\(q+(1.29332 - 3.78514i) q^{2} +(8.65442 - 2.47004i) q^{3} +(-12.6546 - 9.79083i) q^{4} +(-10.5756 - 18.3175i) q^{5} +(1.84350 - 35.9528i) 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} +(-133.702 - 53.4765i) q^{12} +(14.5519 + 25.2046i) q^{13} +(134.419 - 117.408i) q^{14} +(-136.770 - 132.405i) q^{15} +(64.2793 + 247.799i) q^{16} +402.841 q^{17} +(-72.8504 - 315.704i) q^{18} +644.741i q^{19} +(-45.5130 + 335.344i) q^{20} +(389.517 + 97.6292i) q^{21} +(-204.165 + 178.327i) q^{22} +(335.527 - 193.717i) q^{23} +(-375.336 + 436.920i) 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} +(-678.059 + 346.453i) q^{30} +(-1090.90 + 629.833i) q^{31} +(1021.09 + 77.1774i) q^{32} +(-591.628 - 148.287i) q^{33} +(521.004 - 1524.81i) q^{34} -943.733i q^{35} +(-1289.20 - 132.558i) q^{36} -1402.04 q^{37} +(2440.44 + 833.859i) q^{38} +(188.194 + 182.187i) q^{39} +(1210.46 + 605.982i) q^{40} +(-774.166 - 1340.89i) q^{41} +(873.312 - 1348.11i) 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} +(1168.37 + 1985.78i) q^{48} +(-205.097 - 355.239i) q^{49} +(-467.404 - 535.125i) q^{50} +(3486.36 - 995.034i) q^{51} +(62.6253 - 461.430i) q^{52} +906.566 q^{53} +(-1410.28 - 2552.29i) q^{54} +1433.41i q^{55} +(-2850.53 + 169.681i) q^{56} +(1592.54 + 5579.86i) q^{57} +(1906.22 + 2182.40i) q^{58} +(-3916.45 + 2261.16i) q^{59} +(434.426 + 3014.63i) 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} +(-1326.45 + 2047.62i) q^{66} +(-58.7165 + 33.9000i) q^{67} +(-5097.81 - 3944.15i) q^{68} +(2425.30 - 2505.27i) q^{69} +(-3572.16 - 1220.55i) q^{70} +1315.04i q^{71} +(-2169.11 + 4708.38i) q^{72} +9470.72 q^{73} +(-1813.29 + 5306.91i) q^{74} +(388.665 - 1550.68i) q^{75} +(6312.55 - 8158.96i) q^{76} +(-1511.89 - 2618.67i) q^{77} +(933.001 - 476.716i) 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} +(-3973.33 - 5049.16i) q^{84} +(-4260.28 - 7379.03i) q^{85} +(5638.88 - 4925.26i) q^{86} +(-1585.10 + 6324.16i) q^{87} +(4329.61 - 257.724i) q^{88} +8083.40 q^{89} +(-5012.45 + 4673.19i) q^{90} +1298.56i q^{91} +(-6142.62 - 833.676i) q^{92} +(-7885.41 + 8145.41i) q^{93} +(-12560.2 + 10970.7i) q^{94} +(11810.0 - 6818.52i) q^{95} +(9027.55 - 1854.20i) 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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.29332	−	3.78514i	0.323331	−	0.946286i
$2$	1.29332	−	3.78514i	0.323331	−	0.946286i
$3$	8.65442	−	2.47004i	0.961602	−	0.274449i
$3$	8.65442	−	2.47004i	0.961602	−	0.274449i
$4$	−12.6546	−	9.79083i	−0.790914	−	0.611927i
$5$	−10.5756	−	18.3175i	−0.423024	−	0.732698i	0.573210	−	0.819409i	$-0.305698\pi$
$5$	−10.5756	−	18.3175i	−0.423024	−	0.732698i	−0.996234	+	0.0867102i	$0.972365\pi$
$6$	1.84350	−	35.9528i	0.0512083	−	0.998688i
$7$	38.6407	+	22.3092i	0.788586	+	0.455290i	0.839464	−	0.543415i	$-0.182869\pi$
$7$	38.6407	+	22.3092i	0.788586	+	0.455290i	−0.0508787	+	0.998705i	$0.516202\pi$
$8$	−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	$-0.423681\pi$
$11$	−58.6904	−	33.8849i	−0.485045	−	0.280041i	−0.722516	+	0.691354i	$0.757015\pi$
$12$	−133.702	−	53.4765i	−0.928487	−	0.371364i
$13$	14.5519	+	25.2046i	0.0861058	+	0.149140i	0.905862	−	0.423573i	$-0.139224\pi$
$13$	14.5519	+	25.2046i	0.0861058	+	0.149140i	−0.819756	+	0.572713i	$0.805891\pi$
$14$	134.419	−	117.408i	0.685809	−	0.599018i
$15$	−136.770	−	132.405i	−0.607868	−	0.588466i
$16$	64.2793	+	247.799i	0.251091	+	0.967963i
$17$	402.841			1.39391			0.696957	−	0.717113i	$-0.254537\pi$
$17$	402.841			1.39391			0.696957	+	0.717113i	$0.254537\pi$
$18$	−72.8504	−	315.704i	−0.224847	−	0.974394i
$19$			644.741i			1.78599i	0.450070	+	0.892993i	$0.351399\pi$
$19$			644.741i			1.78599i	−0.450070	+	0.892993i	$0.648601\pi$
$20$	−45.5130	+	335.344i	−0.113782	+	0.838361i
$21$	389.517	+	97.6292i	0.883259	+	0.221381i
$22$	−204.165	+	178.327i	−0.421828	+	0.368445i
$23$	335.527	−	193.717i	0.634267	−	0.366194i	−0.148136	−	0.988967i	$-0.547327\pi$
$23$	335.527	−	193.717i	0.634267	−	0.366194i	0.782403	+	0.622773i	$0.213994\pi$
$24$	−375.336	+	436.920i	−0.651625	+	0.758541i
$25$	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	−0.996933	−	0.0782617i	$-0.975063\pi$
$29$	−362.210	+	627.366i	−0.430690	+	0.745977i	0.566243	+	0.824238i	$0.308396\pi$
$30$	−678.059	+	346.453i	−0.753399	+	0.384948i
$31$	−1090.90	+	629.833i	−1.13517	+	0.655393i	−0.945231	−	0.326402i	$-0.894164\pi$
$31$	−1090.90	+	629.833i	−1.13517	+	0.655393i	−0.189944	+	0.981795i	$0.560831\pi$
$32$	1021.09	+	77.1774i	0.997156	+	0.0753685i
$33$	−591.628	−	148.287i	−0.543277	−	0.136168i
$34$	521.004	−	1524.81i	0.450695	−	1.31904i
$35$		−	943.733i		−	0.770394i
$36$	−1289.20	−	132.558i	−0.994755	−	0.102282i
$37$	−1402.04			−1.02413			−0.512066	−	0.858946i	$-0.671120\pi$
$37$	−1402.04			−1.02413			−0.512066	+	0.858946i	$0.671120\pi$
$38$	2440.44	+	833.859i	1.69005	+	0.577464i
$39$	188.194	+	182.187i	0.123731	+	0.119781i
$40$	1210.46	+	605.982i	0.756540	+	0.378739i
$41$	−774.166	−	1340.89i	−0.460539	−	0.797677i	0.538449	−	0.842658i	$-0.319010\pi$
$41$	−774.166	−	1340.89i	−0.460539	−	0.797677i	−0.998988	+	0.0449815i	$0.985677\pi$
$42$	873.312	−	1348.11i	0.495075	−	0.764236i
$43$	1620.98	+	935.875i	0.876681	+	0.506152i	0.869563	−	0.493823i	$-0.164401\pi$
$43$	1620.98	+	935.875i	0.876681	+	0.506152i	0.00711825	+	0.999975i	$0.497734\pi$
$44$	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	−0.982679	−	0.185316i	$-0.940669\pi$
$47$	−3610.63	−	2084.60i	−1.63451	−	0.943683i	−0.651828	−	0.758367i	$-0.725998\pi$
$48$	1168.37	+	1985.78i	0.507106	+	0.861884i
$49$	−205.097	−	355.239i	−0.0854217	−	0.147955i
$50$	−467.404	−	535.125i	−0.186962	−	0.214050i
$51$	3486.36	−	995.034i	1.34039	−	0.382558i
$52$	62.6253	−	461.430i	0.0231602	−	0.170647i
$53$	906.566			0.322736			0.161368	−	0.986894i	$-0.448409\pi$
$53$	906.566			0.322736			0.161368	+	0.986894i	$0.448409\pi$
$54$	−1410.28	−	2552.29i	−0.483634	−	0.875270i
$55$			1433.41i			0.473855i
$56$	−2850.53	+	169.681i	−0.908971	+	0.0541073i
$57$	1592.54	+	5579.86i	0.490162	+	1.71741i
$58$	1906.22	+	2182.40i	0.566652	+	0.648753i
$59$	−3916.45	+	2261.16i	−1.12509	+	0.649573i	−0.942696	−	0.333652i	$-0.891719\pi$
$59$	−3916.45	+	2261.16i	−1.12509	+	0.649573i	−0.182397	+	0.983225i	$0.558386\pi$
$60$	434.426	+	3014.63i	0.120674	+	0.837397i
$61$	−1314.22	+	2276.30i	−0.353190	+	0.611743i	−0.986806	−	0.161904i	$-0.948236\pi$
$61$	−1314.22	+	2276.30i	−0.353190	+	0.611743i	0.633617	+	0.773647i	$0.281570\pi$
$62$	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
$66$	−1326.45	+	2047.62i	−0.304512	+	0.470068i
$67$	−58.7165	+	33.9000i	−0.0130801	+	0.00755179i	−0.506526	−	0.862225i	$-0.669070\pi$
$67$	−58.7165	+	33.9000i	−0.0130801	+	0.00755179i	0.493446	+	0.869777i	$0.335737\pi$
$68$	−5097.81	−	3944.15i	−1.10247	−	0.852974i
$69$	2425.30	−	2505.27i	0.509410	−	0.526206i
$70$	−3572.16	−	1220.55i	−0.729013	−	0.249092i
$71$			1315.04i			0.260869i	0.991457	+	0.130434i	$0.0416372\pi$
$71$			1315.04i			0.260869i	−0.991457	+	0.130434i	$0.958363\pi$
$72$	−2169.11	+	4708.38i	−0.418423	+	0.908252i
$73$	9470.72			1.77720			0.888602	−	0.458680i	$-0.151678\pi$
$73$	9470.72			1.77720			0.888602	+	0.458680i	$0.151678\pi$
$74$	−1813.29	+	5306.91i	−0.331133	+	0.969121i
$75$	388.665	−	1550.68i	0.0690960	−	0.275677i
$76$	6312.55	−	8158.96i	1.09289	−	1.41256i
$77$	−1511.89	−	2618.67i	−0.255000	−	0.441672i
$78$	933.001	−	476.716i	0.153353	−	0.0783556i
$79$	−3783.95	−	2184.67i	−0.606305	−	0.350050i	0.165213	−	0.986258i	$-0.447169\pi$
$79$	−3783.95	−	2184.67i	−0.606305	−	0.350050i	−0.771518	+	0.636207i	$0.780502\pi$
$80$	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	$-0.350947\pi$
$83$	−659.925	−	381.008i	−0.0957940	−	0.0553067i	−0.547132	+	0.837047i	$0.684280\pi$
$84$	−3973.33	−	5049.16i	−0.563113	−	0.715584i
$85$	−4260.28	−	7379.03i	−0.589659	−	1.02132i
$86$	5638.88	−	4925.26i	0.762422	−	0.665936i
$87$	−1585.10	+	6324.16i	−0.209420	+	0.835535i
$88$	4329.61	−	257.724i	0.559092	−	0.0332804i
$89$	8083.40			1.02050			0.510251	−	0.860025i	$-0.329552\pi$
$89$	8083.40			1.02050			0.510251	+	0.860025i	$0.329552\pi$
$90$	−5012.45	+	4673.19i	−0.618821	+	0.576937i
$91$			1298.56i			0.156813i
$92$	−6142.62	−	833.676i	−0.725734	−	0.0984967i
$93$	−7885.41	+	8145.41i	−0.911714	+	0.941775i
$94$	−12560.2	+	10970.7i	−1.42148	+	1.24159i
$95$	11810.0	−	6818.52i	1.30859	−	0.755514i
$96$	9027.55	−	1854.20i	0.979551	−	0.201194i
$97$	−3332.71	+	5772.42i	−0.354204	+	0.613500i	−0.986981	−	0.160834i	$-0.948582\pi$
$97$	−3332.71	+	5772.42i	−0.354204	+	0.613500i	0.632777	+	0.774334i	$0.281915\pi$
$98$	−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	−0.998697	−	0.0510303i	$-0.983749\pi$
$101$	−4643.04	+	8041.97i	−0.455155	+	0.788352i	0.543542	+	0.839382i	$0.317083\pi$
$102$	742.638	−	14483.3i	0.0713800	−	1.39209i
$103$	9792.48	−	5653.69i	0.923035	−	0.532915i	0.0384332	−	0.999261i	$-0.487763\pi$
$103$	9792.48	−	5653.69i	0.923035	−	0.532915i	0.884602	+	0.466346i	$0.154430\pi$
$104$	−1665.58	−	833.824i	−0.153993	−	0.0770917i
$105$	−2331.06	−	8167.45i	−0.211434	−	0.740812i
$106$	1172.48	−	3431.48i	0.104351	−	0.305401i
$107$			6261.61i			0.546913i	0.961884	+	0.273456i	$0.0881669\pi$
$107$			6261.61i			0.546913i	−0.961884	+	0.273456i	$0.911833\pi$
$108$	−11484.7	+	2037.17i	−0.984630	+	0.174655i
$109$	3452.85			0.290620			0.145310	−	0.989386i	$-0.453582\pi$
$109$	3452.85			0.290620			0.145310	+	0.989386i	$0.453582\pi$
$110$	5425.67	+	1853.87i	0.448403	+	0.153212i
$111$	−12133.8	+	3463.08i	−0.984806	+	0.281072i
$112$	−3044.40	+	11009.1i	−0.242697	+	0.877641i
$113$	1272.55	+	2204.13i	0.0996597	+	0.172616i	0.911544	−	0.411203i	$-0.134891\pi$
$113$	1272.55	+	2204.13i	0.0996597	+	0.172616i	−0.811884	+	0.583819i	$0.801558\pi$
$114$	23180.2	+	1188.58i	1.78364	+	0.0914573i
$115$	−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
$120$	11972.7	+	2254.52i	0.831435	+	0.156564i
$121$	−5024.12	−	8702.04i	−0.343154	−	0.594361i
$122$	6916.39	+	7918.50i	0.464687	+	0.532014i
$123$	−10012.0	−	9692.44i	−0.661776	−	0.640653i
$124$	19971.6	+	2710.54i	1.29888	+	0.176284i
$125$	−16976.5			−1.08650
$126$	4228.11	−	13824.2i	0.266321	−	0.870764i
$127$		−	530.060i		−	0.0328638i	−0.999865	−	0.0164319i	$-0.994769\pi$
$127$		−	530.060i		−	0.0328638i	0.999865	−	0.0164319i	$-0.00523067\pi$
$128$	−12165.9	−	10973.9i	−0.742545	−	0.669796i
$129$	16340.3	+	4095.56i	0.981931	+	0.246112i
$130$	−1619.82	−	1854.51i	−0.0958471	−	0.109734i
$131$	802.198	−	463.149i	0.0467454	−	0.0269885i	−0.476445	−	0.879204i	$-0.658075\pi$
$131$	802.198	−	463.149i	0.0467454	−	0.0269885i	0.523191	+	0.852216i	$0.324742\pi$
$132$	6034.99	+	7669.04i	0.346361	+	0.440143i
$133$	−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	−0.887390	−	0.461019i	$-0.847484\pi$
$137$	−834.113	+	1444.73i	−0.0444410	+	0.0769741i	0.842949	+	0.537993i	$0.180817\pi$
$138$	−6346.10	−	12420.2i	−0.333234	−	0.652187i
$139$	−717.766	+	414.402i	−0.0371495	+	0.0214483i	−0.518460	−	0.855102i	$-0.673494\pi$
$139$	−717.766	+	414.402i	−0.0371495	+	0.0214483i	0.481310	+	0.876550i	$0.340161\pi$
$140$	−9239.93	+	11942.6i	−0.471425	+	0.609316i
$141$	−36396.9	−	9122.57i	−1.83074	−	0.458859i
$142$	4977.62	+	1700.77i	0.246857	+	0.0843470i
$143$		−	1972.36i		−	0.0964525i
$144$	15016.5	+	14299.8i	0.724177	+	0.689614i
$145$	15322.3			0.728768
$146$	12248.7	−	35848.0i	0.574625	−	1.68174i
$147$	−2652.45	−	2567.79i	−0.122748	−	0.118830i
$148$	17742.2	+	13727.1i	0.810000	+	0.626693i
$149$	−1561.38	−	2704.39i	−0.0703292	−	0.121814i	0.828716	−	0.559669i	$-0.189072\pi$
$149$	−1561.38	−	2704.39i	−0.0703292	−	0.121814i	−0.899046	+	0.437855i	$0.855738\pi$
$150$	−5366.89	−	3476.69i	−0.238528	−	0.154519i
$151$	7932.37	+	4579.76i	0.347896	+	0.200858i	0.663758	−	0.747947i	$-0.268960\pi$
$151$	7932.37	+	4579.76i	0.347896	+	0.200858i	−0.315862	+	0.948805i	$0.602294\pi$
$152$	−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
$156$	−597.765	−	4148.09i	−0.0245630	−	0.170451i
$157$	−10551.8	−	18276.3i	−0.428084	−	0.741463i	0.568619	−	0.822601i	$-0.307478\pi$
$157$	−10551.8	−	18276.3i	−0.428084	−	0.741463i	−0.996703	+	0.0811381i	$0.974145\pi$
$158$	−13163.1	+	11497.3i	−0.527285	+	0.460556i
$159$	7845.80	−	2239.25i	0.310344	−	0.0885746i
$160$	−9384.91	−	19519.9i	−0.366598	−	0.762497i
$161$	17286.7			0.666898
$162$	−18509.4	−	18605.1i	−0.705281	−	0.708928i
$163$		−	42771.0i		−	1.60981i	−0.593405	−	0.804904i	$-0.702217\pi$
$163$		−	42771.0i		−	1.60981i	0.593405	−	0.804904i	$-0.297783\pi$
$164$	−3331.69	+	24548.2i	−0.123873	+	0.912710i
$165$	3540.59	+	12405.3i	0.130049	+	0.455660i
$166$	−2295.66	+	2005.14i	−0.0833091	+	0.0727661i
$167$	−9568.12	+	5524.16i	−0.343079	+	0.198077i	−0.661633	−	0.749828i	$-0.730136\pi$
$167$	−9568.12	+	5524.16i	−0.343079	+	0.198077i	0.318554	+	0.947905i	$0.396803\pi$
$168$	−24250.6	+	8509.42i	−0.859219	+	0.301496i
$169$	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	−0.622549	−	0.782581i	$-0.713903\pi$
$173$	10967.8	−	18996.8i	0.366461	−	0.634729i	0.989009	+	0.147852i	$0.0472360\pi$
$174$	21887.8	+	14179.0i	0.722943	+	0.468325i
$175$	6863.66	−	3962.73i	0.224119	−	0.129395i
$176$	4624.06	−	16721.5i	0.149279	−	0.539821i
$177$	−28309.4	+	29242.8i	−0.903617	+	0.933411i
$178$	10454.4	−	30596.8i	0.329960	−	0.965687i
$179$			11479.2i			0.358265i	0.983825	+	0.179133i	$0.0573291\pi$
$179$			11479.2i			0.358265i	−0.983825	+	0.179133i	$0.942671\pi$
$180$	11206.0	+	25016.8i	0.345863	+	0.772123i
$181$	45472.2			1.38800			0.693999	−	0.719976i	$-0.255847\pi$
$181$	45472.2			1.38800			0.693999	+	0.719976i	$0.255847\pi$
$182$	4915.25	+	1679.46i	0.148389	+	0.0507023i
$183$	−5751.26	+	22946.2i	−0.171736	+	0.685186i
$184$	−11100.0	+	22172.5i	−0.327858	+	0.654905i
$185$	14827.4	+	25681.7i	0.433232	+	0.750379i
$186$	20633.2	+	40382.1i	0.596403	+	1.16725i
$187$	−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	−0.971418	−	0.237376i	$-0.923713\pi$
$191$	−60657.0	−	35020.3i	−1.66270	−	0.959961i	−0.691283	−	0.722584i	$-0.742954\pi$
$192$	4657.12	−	36568.6i	0.126332	−	0.991988i
$193$	17426.4	+	30183.5i	0.467836	+	0.810316i	0.999325	−	0.0367497i	$-0.0117004\pi$
$193$	17426.4	+	30183.5i	0.467836	+	0.810316i	−0.531488	+	0.847066i	$0.678367\pi$
$194$	17539.2	+	20080.4i	0.466021	+	0.533542i
$195$	1346.94	−	5373.98i	0.0354225	−	0.141328i
$196$	−882.655	+	6503.50i	−0.0229762	+	0.169291i
$197$	−30858.0			−0.795124			−0.397562	−	0.917575i	$-0.630144\pi$
$197$	−30858.0			−0.795124			−0.397562	+	0.917575i	$0.630144\pi$
$198$	−6421.98	+	20997.3i	−0.163809	+	0.535591i
$199$			34262.5i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$199$			34262.5i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$200$	675.504	+	11348.1i	0.0168876	+	0.283702i
$201$	−424.422	+	438.416i	−0.0105052	+	0.0108516i
$202$	24435.1	+	27975.4i	0.598840	+	0.685605i
$203$	−27992.1	+	16161.2i	−0.679272	+	0.392178i
$204$	−53860.7	−	21542.5i	−1.29423	−	0.517650i
$205$	−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
$210$	−33929.8	−	1739.77i	−0.769383	−	0.0394506i
$211$	−14989.6	+	8654.27i	−0.336687	+	0.194386i	−0.658806	−	0.752313i	$-0.728938\pi$
$211$	−14989.6	+	8654.27i	−0.336687	+	0.194386i	0.322119	+	0.946699i	$0.395605\pi$
$212$	−11472.3	−	8876.03i	−0.255257	−	0.197491i
$213$	3248.20	+	11380.9i	0.0715952	+	0.250852i
$214$	23701.1	+	8098.28i	0.517536	+	0.176834i
$215$		−	39589.7i		−	0.856457i
$216$	−7142.47	+	46106.0i	−0.153088	+	0.988213i
$217$	−56204.3			−1.19358
$218$	4465.65	−	13069.5i	0.0939663	−	0.275009i
$219$	81963.5	−	23393.0i	1.70896	−	0.487751i
$220$	14034.3	−	18139.3i	0.289965	−	0.374779i
$221$	5862.10	+	10153.5i	0.120024	+	0.207888i
$222$	−2584.65	+	50407.1i	−0.0524440	+	1.02279i
$223$	55484.8	+	32034.1i	1.11574	+	0.644174i	0.940311	−	0.340317i	$-0.110534\pi$
$223$	55484.8	+	32034.1i	1.11574	+	0.644174i	0.175432	+	0.984492i	$0.443868\pi$
$224$	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	$-0.290917\pi$
$227$	11857.8	+	6846.11i	0.230119	+	0.132859i	−0.380508	+	0.924778i	$0.624251\pi$
$228$	34478.5	−	86203.3i	0.663252	−	1.65827i
$229$	−32996.2	−	57151.0i	−0.629205	−	1.08982i	−0.987711	−	0.156288i	$-0.950047\pi$
$229$	−32996.2	−	57151.0i	−0.629205	−	1.08982i	0.358506	−	0.933527i	$-0.383286\pi$
$230$	−24687.4	+	21563.2i	−0.466681	+	0.407622i
$231$	−19552.8	−	18928.7i	−0.366424	−	0.354728i
$232$	−2754.91	−	46281.0i	−0.0511838	−	0.859857i
$233$	−63342.4			−1.16676			−0.583381	−	0.812198i	$-0.698271\pi$
$233$	−63342.4			−1.16676			−0.583381	+	0.812198i	$0.698271\pi$
$234$	6897.07	−	6430.25i	0.125960	−	0.117435i
$235$			88183.3i			1.59680i
$236$	71699.9	+	9731.11i	1.28734	+	0.174718i
$237$	−38144.1	−	9560.49i	−0.679095	−	0.170209i
$238$	54149.3	−	47296.6i	0.955959	−	0.834980i
$239$	275.008	−	158.776i	0.00481448	−	0.00277964i	−0.497591	−	0.867412i	$-0.665782\pi$
$239$	275.008	−	158.776i	0.00481448	−	0.00277964i	0.502405	+	0.864632i	$0.332449\pi$
$240$	24018.2	−	42402.4i	0.416983	−	0.736153i
$241$	−12752.6	+	22088.2i	−0.219566	+	0.380300i	−0.954675	−	0.297649i	$-0.903798\pi$
$241$	−12752.6	+	22088.2i	−0.219566	+	0.380300i	0.735109	+	0.677949i	$0.237131\pi$
$242$	−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
$246$	−49636.0	+	25361.5i	−0.820214	+	0.419087i
$247$	−16250.4	+	9382.19i	−0.266361	+	0.153784i
$248$	36089.5	−	72089.6i	0.586783	−	1.17211i
$249$	−6652.37	−	1667.36i	−0.107295	−	0.0268924i
$250$	−21956.1	+	64258.6i	−0.351298	+	1.02814i
$251$		−	40987.7i		−	0.650588i	−0.945613	−	0.325294i	$-0.894537\pi$
$251$		−	40987.7i		−	0.650588i	0.945613	−	0.325294i	$-0.105463\pi$
$252$	−46858.4	−	33883.2i	−0.737882	−	0.533561i
$253$	−26256.3			−0.410197
$254$	−2006.35	−	685.539i	−0.0310986	−	0.0106259i
$255$	−55096.8	−	53338.1i	−0.847317	−	0.820271i
$256$	−57272.3	+	31856.6i	−0.873907	+	0.486094i
$257$	−15479.1	−	26810.5i	−0.234357	−	0.405919i	0.724728	−	0.689035i	$-0.241965\pi$
$257$	−15479.1	−	26810.5i	−0.234357	−	0.405919i	−0.959086	+	0.283116i	$0.908632\pi$
$258$	36635.6	−	56553.5i	0.550381	−	0.849611i
$259$	−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	$-0.368775\pi$
$263$	−13311.8	−	7685.54i	−0.192453	−	0.111113i	−0.593130	+	0.805107i	$0.702108\pi$
$264$	36833.6	−	12924.7i	0.528490	−	0.185445i
$265$	−9587.47	−	16606.0i	−0.136525	−	0.236468i
$266$	75697.5	+	86665.1i	1.06984	+	1.22485i
$267$	69957.1	−	19966.3i	0.981317	−	0.280076i
$268$	1074.94	+	145.891i	0.0149664	+	0.00203124i
$269$	76105.5			1.05175			0.525873	−	0.850563i	$-0.323739\pi$
$269$	76105.5			1.05175			0.525873	+	0.850563i	$0.323739\pi$
$270$	−31836.9	+	52824.7i	−0.436720	+	0.724618i
$271$			78076.4i			1.06312i	0.847021	+	0.531559i	$0.178394\pi$
$271$			78076.4i			1.06312i	−0.847021	+	0.531559i	$0.821606\pi$
$272$	25894.4	+	99823.5i	0.349999	+	1.34926i
$273$	3207.51	+	11238.3i	0.0430370	+	0.150791i
$274$	4389.72	+	5025.74i	0.0584704	+	0.0669420i
$275$	−10425.0	+	6018.90i	−0.137852	+	0.0795887i
$276$	−55220.0	+	7957.53i	−0.724900	+	0.104462i
$277$	−2369.97	+	4104.90i	−0.0308875	+	0.0534987i	−0.881056	−	0.473012i	$-0.843167\pi$
$277$	−2369.97	+	4104.90i	−0.0308875	+	0.0534987i	0.850168	+	0.526511i	$0.176500\pi$
$278$	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	−0.969784	−	0.243966i	$-0.921552\pi$
$281$	−21604.6	+	37420.3i	−0.273612	+	0.473909i	0.696172	+	0.717875i	$0.254885\pi$
$282$	−81603.2	+	125969.i	−1.02615	+	1.58404i
$283$	−31277.1	+	18057.8i	−0.390529	+	0.225472i	−0.682389	−	0.730989i	$-0.739059\pi$
$283$	−31277.1	+	18057.8i	−0.390529	+	0.225472i	0.291860	+	0.956461i	$0.405726\pi$
$284$	12875.3	−	16641.3i	0.159633	−	0.206325i
$285$	85366.8	−	88181.5i	1.05099	−	1.08564i
$286$	−7465.66	−	2550.90i	−0.0912717	−	0.0311861i
$287$		−	69084.1i		−	0.838715i
$288$	73548.2	−	38345.4i	0.886721	−	0.462305i
$289$	78760.1			0.942997
$290$	19816.7	−	57997.3i	0.235633	−	0.689623i
$291$	−14584.5	+	58188.8i	−0.172229	+	0.687153i
$292$	−119848.	−	92726.2i	−1.40562	−	1.08752i
$293$	48046.7	+	83219.2i	0.559665	+	0.969368i	0.997524	+	0.0703243i	$0.0224034\pi$
$293$	48046.7	+	83219.2i	0.559665	+	0.969368i	−0.437859	+	0.899043i	$0.644263\pi$
$294$	−13149.9	+	6718.94i	−0.152135	+	0.0777331i
$295$	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
$300$	−20100.9	+	15818.0i	−0.223343	+	0.175755i
$301$	41757.3	+	72325.7i	0.460892	+	0.798288i
$302$	27594.2	−	24102.1i	0.302554	−	0.264265i
$303$	−20318.8	+	81067.1i	−0.221316	+	0.882997i
$304$	−159766.	+	41443.5i	−1.72877	+	0.448445i
$305$	55594.6			0.597631
$306$	−29347.1	−	127178.i	−0.313417	−	1.35822i
$307$		−	140641.i		−	1.49223i	−0.665817	−	0.746115i	$-0.731917\pi$
$307$		−	140641.i		−	1.49223i	0.665817	−	0.746115i	$-0.268083\pi$
$308$	−6506.56	+	47941.0i	−0.0685883	+	0.505366i
$309$	70783.4	−	73117.2i	0.741334	−	0.765778i
$310$	80266.6	−	70108.7i	0.835240	−	0.729539i
$311$	141564.	−	81731.8i	1.46363	−	0.845027i	0.464453	−	0.885598i	$-0.346251\pi$
$311$	141564.	−	81731.8i	1.46363	−	0.845027i	0.999177	+	0.0405712i	$0.0129178\pi$
$312$	−16474.2	−	3102.20i	−0.169237	−	0.0318684i
$313$	25645.1	−	44418.7i	0.261768	−	0.453395i	−0.704944	−	0.709263i	$-0.749028\pi$
$313$	25645.1	−	44418.7i	0.261768	−	0.453395i	0.966712	+	0.255868i	$0.0823611\pi$
$314$	−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	−0.787765	−	0.615975i	$-0.788762\pi$
$317$	14025.0	−	24292.0i	0.139568	−	0.241738i	0.927333	+	0.374237i	$0.122095\pi$
$318$	1671.25	−	32593.6i	0.0165268	−	0.322313i
$319$	42516.5	−	24546.9i	0.417808	−	0.241221i
$320$	−86023.4	+	10277.7i	−0.840073	+	0.100368i
$321$	15466.4	+	54190.5i	0.150100	+	0.525912i
$322$	22357.2	−	65432.5i	0.215629	−	0.631076i
$323$			259728.i			2.48951i
$324$	−94361.6	+	45998.3i	−0.898888	+	0.438179i
$325$	5169.63			0.0489433
$326$	−161894.	−	55316.7i	−1.52334	−	0.520500i
$327$	29882.4	−	8528.68i	0.279460	−	0.0797602i
$328$	88609.7	+	44359.7i	0.823633	+	0.412327i
$329$	−93011.4	−	161101.i	−0.859299	−	1.48835i
$330$	51535.1	+	2642.49i	0.473234	+	0.0242653i
$331$	−97678.0	−	56394.4i	−0.891540	−	0.514731i	−0.0170938	−	0.999854i	$-0.505441\pi$
$331$	−97678.0	−	56394.4i	−0.891540	−	0.514731i	−0.874446	+	0.485123i	$0.838775\pi$
$332$	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
$336$	845.525	+	102797.i	0.00748942	+	0.910550i
$337$	10409.8	+	18030.3i	0.0916606	+	0.158761i	0.908210	−	0.418515i	$-0.137449\pi$
$337$	10409.8	+	18030.3i	0.0916606	+	0.158761i	−0.816549	+	0.577276i	$0.804116\pi$
$338$	−72925.7	−	83491.7i	−0.638333	−	0.730819i
$339$	16457.5	+	15932.2i	0.143207	+	0.138636i
$340$	−18334.5	+	135091.i	−0.158603	+	1.16860i
$341$	85367.4			0.734147
$342$	203547.	−	46969.6i	1.74025	−	0.401573i
$343$		−	125431.i		−	1.06615i
$344$	−119580.	+	7118.12i	−1.01052	+	0.0601518i
$345$	−71539.2	−	17930.7i	−0.601043	−	0.150646i
$346$	−57720.7	−	66083.7i	−0.482147	−	0.552004i
$347$	−139615.	+	80606.6i	−1.15950	+	0.669440i	−0.951185	−	0.308621i	$-0.900132\pi$
$347$	−139615.	+	80606.6i	−1.15950	+	0.669440i	−0.208318	+	0.978061i	$0.566799\pi$
$348$	81977.6	−	64510.5i	0.676919	−	0.532687i
$349$	110742.	−	191811.i	0.909205	−	1.57479i	0.0940341	−	0.995569i	$-0.470024\pi$
$349$	110742.	−	191811.i	0.909205	−	1.57479i	0.815171	−	0.579220i	$-0.196643\pi$
$350$	−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	−0.0242676	+	0.999705i	$0.507725\pi$
$353$	−109395.	+	189477.i	−0.877904	+	1.52057i	−0.853637	+	0.520869i	$0.825608\pi$
$354$	74075.1	+	144976.i	0.591107	+	1.15688i
$355$	24088.2	−	13907.3i	0.191138	−	0.110354i
$356$	−102292.	−	79143.2i	−0.807130	−	0.624473i
$357$	156914.	+	39329.1i	1.23119	+	0.308587i
$358$	43450.3	+	14846.3i	0.339021	+	0.115838i
$359$			924.606i			0.00717411i	0.999994	+	0.00358705i	$0.00114180\pi$
$359$			924.606i			0.00717411i	−0.999994	+	0.00358705i	$0.998858\pi$
$360$	109185.	−	10061.4i	0.842478	−	0.0776339i
$361$	−285370.			−2.18975
$362$	58810.2	−	172119.i	0.448782	−	1.31344i
$363$	−64975.2	−	62901.3i	−0.493100	−	0.477360i
$364$	12714.0	−	16432.9i	0.0959578	−	0.124025i
$365$	−100158.	−	173479.i	−0.751799	−	1.30215i
$366$	79416.4	+	51446.2i	0.592854	+	0.384053i
$367$	35332.0	+	20398.9i	0.262323	+	0.151452i	0.625394	−	0.780309i	$-0.284938\pi$
$367$	35332.0	+	20398.9i	0.262323	+	0.151452i	−0.363071	+	0.931762i	$0.618272\pi$
$368$	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
$372$	179537.	−	25872.4i	1.29739	−	0.186961i
$373$	117265.	+	203109.i	0.842851	+	1.45986i	0.887474	+	0.460858i	$0.152458\pi$
$373$	117265.	+	203109.i	0.842851	+	1.45986i	−0.0446228	+	0.999004i	$0.514209\pi$
$374$	−82246.1	+	71837.7i	−0.587993	+	0.513581i
$375$	−146922.	+	41932.7i	−1.04478	+	0.298188i
$376$	266357.	−	15855.1i	1.88403	−	0.112149i
$377$	−21083.4			−0.148340
$378$	2445.40	−	130084.i	0.0171146	−	0.910420i
$379$		−	185553.i		−	1.29178i	−0.763428	−	0.645892i	$-0.776485\pi$
$379$		−	185553.i		−	1.29178i	0.763428	−	0.645892i	$-0.223515\pi$
$380$	−216210.	−	29344.1i	−1.49730	−	0.203214i
$381$	−1309.27	−	4587.36i	−0.00901944	−	0.0316019i
$382$	−211006.	+	184303.i	−1.44600	+	1.26301i
$383$	52190.3	−	30132.1i	0.355789	−	0.205415i	−0.311443	−	0.950265i	$-0.600812\pi$
$383$	52190.3	−	30132.1i	0.355789	−	0.205415i	0.667232	+	0.744850i	$0.267479\pi$
$384$	−132394.	−	64922.9i	−0.897857	−	0.440287i
$385$	−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	−0.845502	−	0.533971i	$-0.820699\pi$
$389$	6004.66	−	10400.4i	0.0396816	−	0.0687306i	0.885184	+	0.465241i	$0.154032\pi$
$390$	−18599.3	−	12048.7i	−0.122283	−	0.0792154i
$391$	135164.	−	78037.0i	0.884113	−	0.510443i
$392$	23475.1	+	11752.1i	0.152769	+	0.0764792i
$393$	5798.56	−	5989.75i	0.0375435	−	0.0387814i
$394$	−39909.3	+	116802.i	−0.257088	+	0.752415i
$395$			92416.5i			0.592318i
$396$	71172.1	+	51464.4i	0.453858	+	0.328183i
$397$	32276.3			0.204787			0.102394	−	0.994744i	$-0.467350\pi$
$397$	32276.3			0.204787			0.102394	+	0.994744i	$0.467350\pi$
$398$	129688.	+	44312.4i	0.818719	+	0.279743i
$399$	−62945.5	+	251138.i	−0.395384	+	1.57749i
$400$	43827.8	+	12119.9i	0.273924	+	0.0757491i
$401$	93863.1	+	162576.i	0.583722	+	1.01104i	0.995033	+	0.0995418i	$0.0317377\pi$
$401$	93863.1	+	162576.i	0.583722	+	1.01104i	−0.411311	+	0.911495i	$0.634929\pi$
$402$	1110.55	+	2173.51i	0.00687207	+	0.0134496i
$403$	−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
$408$	−151201.	+	176009.i	−0.908310	+	1.05734i
$409$	67272.0	+	116518.i	0.402149	+	0.696543i	0.993985	−	0.109515i	$-0.0349299\pi$
$409$	67272.0	+	116518.i	0.402149	+	0.696543i	−0.591836	+	0.806059i	$0.701597\pi$
$410$	86174.8	+	98660.5i	0.512640	+	0.586916i
$411$	−3650.23	+	14563.6i	−0.0216091	+	0.0862152i
$412$	−179275.	−	24331.1i	−1.05615	−	0.143340i
$413$	−201779.			−1.18298
$414$	−85600.3	−	91814.8i	−0.499430	−	0.535688i
$415$			16117.5i			0.0935841i
$416$	12913.5	+	26859.2i	0.0746205	+	0.155205i
$417$	−5188.25	+	5359.32i	−0.0298366	+	0.0308204i
$418$	−114975.	−	131634.i	−0.658038	−	0.753380i
$419$	73320.7	−	42331.7i	0.417637	−	0.241123i	−0.276429	−	0.961034i	$-0.589151\pi$
$419$	73320.7	−	42331.7i	0.417637	−	0.241123i	0.694066	+	0.719912i	$0.255818\pi$
$420$	−50467.5	+	126179.i	−0.286097	+	0.715301i
$421$	57849.8	−	100199.i	0.326391	−	0.565325i	−0.655402	−	0.755280i	$-0.727501\pi$
$421$	57849.8	−	100199.i	0.326391	−	0.565325i	0.981793	+	0.189955i	$0.0608341\pi$
$422$	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
$426$	47279.3	+	2424.28i	0.260527	+	0.0133587i
$427$	−101565.	+	58638.4i	−0.557041	+	0.321608i
$428$	61306.3	−	79238.3i	0.334671	−	0.432561i
$429$	−4871.80	−	17069.6i	−0.0264713	−	0.0927489i
$430$	−149853.	−	51202.3i	−0.810453	−	0.276919i
$431$		−	294896.i		−	1.58750i	−0.608241	−	0.793752i	$-0.708125\pi$
$431$		−	294896.i		−	1.58750i	0.608241	−	0.793752i	$-0.291875\pi$
$432$	165281.	+	86665.3i	0.885634	+	0.464384i
$433$	−151284.			−0.806895			−0.403447	−	0.915003i	$-0.632188\pi$
$433$	−151284.			−0.806895			−0.403447	+	0.915003i	$0.632188\pi$
$434$	−72690.4	+	212742.i	−0.385920	+	1.12947i
$435$	132606.	−	37846.8i	0.700784	−	0.200010i
$436$	−43694.6	−	33806.3i	−0.229855	−	0.177838i
$437$	124897.	+	216328.i	0.654017	+	1.13279i
$438$	17459.3	−	340498.i	0.0910076	−	1.77487i
$439$	−17332.7	−	10007.1i	−0.0899369	−	0.0519251i	0.454357	−	0.890820i	$-0.349869\pi$
$439$	−17332.7	−	10007.1i	−0.0899369	−	0.0519251i	−0.544294	+	0.838895i	$0.683202\pi$
$440$	−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	$-0.301943\pi$
$443$	33466.7	+	19322.0i	0.170532	+	0.0984567i	−0.412305	+	0.911046i	$0.635276\pi$
$444$	187455.	+	74975.9i	0.950893	+	0.380326i
$445$	−85486.7	−	148067.i	−0.431696	−	0.747720i
$446$	193014.	−	168587.i	0.970327	−	0.847530i
$447$	−20192.8	−	19548.2i	−0.101060	−	0.0978345i
$448$	146314.	−	109509.i	0.729005	−	0.545626i
$449$	79457.9			0.394135			0.197067	−	0.980390i	$-0.436858\pi$
$449$	79457.9			0.394135			0.197067	+	0.980390i	$0.436858\pi$
$450$	−55034.8	−	16832.3i	−0.271777	−	0.0831223i
$451$			104930.i			0.515878i
$452$	5476.55	−	40351.8i	0.0268059	−	0.197509i
$453$	79962.2	+	20041.8i	0.389662	+	0.0976655i
$454$	41249.5	−	36029.3i	0.200128	−	0.174801i
$455$	23786.4	−	13733.1i	0.114896	−	0.0663354i
$456$	−281700.	−	241995.i	−1.35474	−	1.16379i
$457$	131776.	−	228243.i	0.630963	−	1.09286i	−0.356392	−	0.934337i	$-0.615993\pi$
$457$	131776.	−	228243.i	0.630963	−	1.09286i	0.987355	−	0.158524i	$-0.0506735\pi$
$458$	−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	−0.527510	−	0.849549i	$-0.676874\pi$
$461$	100305.	−	173733.i	0.471976	−	0.817487i	0.999486	+	0.0320624i	$0.0102075\pi$
$462$	−96935.8	+	49529.2i	−0.454151	+	0.232048i
$463$	−205297.	+	118528.i	−0.957679	+	0.552916i	−0.895458	−	0.445146i	$-0.853152\pi$
$463$	−205297.	+	118528.i	−0.957679	+	0.552916i	−0.0622210	+	0.998062i	$0.519818\pi$
$464$	−178743.	−	49428.5i	−0.830220	−	0.229584i
$465$	232596.	+	58298.2i	1.07571	+	0.269618i
$466$	−81922.2	+	239760.i	−0.377250	+	1.10409i
$467$			230464.i			1.05674i	0.849014	+	0.528371i	$0.177197\pi$
$467$			230464.i			1.05674i	−0.849014	+	0.528371i	$0.822803\pi$
$468$	−15419.3	−	34422.8i	−0.0703999	−	0.157165i
$469$	−3025.13			−0.0137530
$470$	333787.	+	114050.i	1.51103	+	0.516295i
$471$	−136463.	−	132107.i	−0.615140	−	0.595505i
$472$	129565.	−	258809.i	0.581571	−	1.16170i
$473$	−63424.1	−	109854.i	−0.283486	−	0.491013i
$474$	−85520.5	+	132016.i	−0.380639	+	0.587584i
$475$	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	$-0.331668\pi$
$479$	2079.74	+	1200.74i	0.00906438	+	0.00523332i	−0.495461	+	0.868630i	$0.665001\pi$
$480$	−129436.	−	145752.i	−0.561788	−	0.632606i
$481$	−20402.3	−	35337.7i	−0.0881836	−	0.152739i
$482$	67113.8	+	76837.7i	0.288880	+	0.330735i
$483$	149606.	−	42698.8i	0.641290	−	0.183029i
$484$	−21621.7	+	159311.i	−0.0922997	+	0.680074i
$485$	140981.			0.599347
$486$	−206143.	−	115297.i	−0.872764	−	0.488143i
$487$			405227.i			1.70860i	0.519781	+	0.854300i	$0.326014\pi$
$487$			405227.i			1.70860i	−0.519781	+	0.854300i	$0.673986\pi$
$488$	−9995.75	−	167923.i	−0.0419736	−	0.705132i
$489$	−105646.	−	370158.i	−0.441810	−	1.54799i
$490$	22830.0	+	26137.8i	0.0950855	+	0.108862i
$491$	111325.	−	64273.4i	0.461773	−	0.266605i	−0.251016	−	0.967983i	$-0.580765\pi$
$491$	111325.	−	64273.4i	0.461773	−	0.266605i	0.712790	+	0.701378i	$0.247431\pi$
$492$	31801.3	+	220680.i	0.131376	+	0.911660i
$493$	−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
$498$	−14914.9	+	23023.7i	−0.0601396	+	0.0928361i
$499$	−111377.	+	64303.6i	−0.447296	+	0.258246i	−0.706687	−	0.707526i	$-0.749811\pi$
$499$	−111377.	+	64303.6i	−0.447296	+	0.258246i	0.259392	+	0.965772i	$0.416478\pi$
$500$	214832.	+	166214.i	0.859326	+	0.664857i
$501$	−69161.6	+	71442.0i	−0.275543	+	0.284628i
$502$	−155144.	−	53010.3i	−0.615642	−	0.210355i
$503$		−	368128.i		−	1.45500i	−0.686109	−	0.727499i	$-0.740683\pi$
$503$		−	368128.i		−	1.45500i	0.686109	−	0.727499i	$-0.259317\pi$
$504$	−188856.	+	133544.i	−0.743481	+	0.525731i
$505$	196411.			0.770165
$506$	−33957.9	+	99383.8i	−0.132629	+	0.388163i
$507$	60640.7	−	241942.i	0.235911	−	0.941229i
$508$	−5189.73	+	6707.72i	−0.0201102	+	0.0259925i
$509$	40698.4	+	70491.6i	0.157087	+	0.272083i	0.933817	−	0.357751i	$-0.116456\pi$
$509$	40698.4	+	70491.6i	0.157087	+	0.272083i	−0.776730	+	0.629834i	$0.783123\pi$
$510$	−273150.	+	139566.i	−1.05017	+	0.536585i
$511$	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
$516$	−166682.	−	211813.i	−0.626020	−	0.795524i
$517$	141273.	+	244692.i	0.528539	+	0.915457i
$518$	−188460.	+	164610.i	−0.702358	+	0.613473i
$519$	47997.1	−	191497.i	0.178189	−	0.710931i
$520$	2341.00	+	39327.4i	0.00865754	+	0.145442i
$521$	−17832.5			−0.0656956			−0.0328478	−	0.999460i	$-0.510458\pi$
$521$	−17832.5			−0.0656956			−0.0328478	+	0.999460i	$0.510458\pi$
$522$	224449.	+	68647.2i	0.823714	+	0.251931i
$523$			51996.2i			0.190094i	0.995473	+	0.0950470i	$0.0303001\pi$
$523$			51996.2i			0.190094i	−0.995473	+	0.0950470i	$0.969700\pi$
$524$	−14686.1	−	1993.20i	−0.0534866	−	0.00725920i
$525$	49612.8	−	51248.6i	0.180001	−	0.185936i
$526$	−46307.3	+	40447.0i	−0.167370	+	0.146189i
$527$	−439461.	+	253723.i	−1.58234	+	0.913562i
$528$	−1284.25	−	156136.i	−0.00460660	−	0.560062i
$529$	−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
$534$	14901.7	−	290621.i	0.0522582	−	1.01916i
$535$	114697.	−	66220.2i	0.400722	−	0.231357i
$536$	1942.47	−	3880.13i	0.00676122	−	0.0135057i
$537$	28354.0	+	99345.6i	0.0983255	+	0.344508i
$538$	98429.0	−	288070.i	0.340062	−	0.995253i
$539$			27798.8i			0.0956862i
$540$	158774.	+	188827.i	0.544491	+	0.647554i
$541$	−329819.			−1.12689			−0.563444	−	0.826154i	$-0.690524\pi$
$541$	−329819.			−1.12689			−0.563444	+	0.826154i	$0.690524\pi$
$542$	295530.	+	100978.i	1.00601	+	0.343739i
$543$	393535.	−	112318.i	1.33470	−	0.380934i
$544$	411336.	+	31090.2i	1.38995	+	0.105057i
$545$	−36515.9	−	63247.5i	−0.122939	−	0.212936i
$546$	46687.0	+	2393.90i	0.156607	+	0.00803010i
$547$	−306032.	−	176688.i	−1.02280	−	0.590517i	−0.107890	−	0.994163i	$-0.534409\pi$
$547$	−306032.	−	176688.i	−1.02280	−	0.590517i	−0.914915	+	0.403646i	$0.867743\pi$
$548$	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
$552$	−41296.9	+	219307.i	−0.135531	+	0.719738i
$553$	−97476.3	−	168834.i	−0.318749	−	0.552090i
$554$	12472.5	+	14279.6i	0.0406382	+	0.0465262i
$555$	191757.	+	185636.i	0.622537	+	0.602666i
$556$	13140.4	+	1783.42i	0.0425069	+	0.00576903i
$557$	−381405.			−1.22935			−0.614676	−	0.788780i	$-0.710713\pi$
$557$	−381405.			−1.22935			−0.614676	+	0.788780i	$0.710713\pi$
$558$	278313.	+	298519.i	0.893852	+	0.958744i
$559$			54475.0i			0.174330i
$560$	233856.	−	60662.5i	0.745713	−	0.193439i
$561$	−238332.	−	59735.9i	−0.757281	−	0.189806i
$562$	113700.	+	130173.i	0.359987	+	0.412144i
$563$	−203807.	+	117668.i	−0.642988	+	0.371229i	−0.785765	−	0.618526i	$-0.787730\pi$
$563$	−203807.	+	117668.i	−0.642988	+	0.371229i	0.142776	+	0.989755i	$0.454397\pi$
$564$	371272.	+	471799.i	1.16717	+	1.48320i
$565$	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	−0.642186	−	0.766549i	$-0.721972\pi$
$569$	110971.	−	192208.i	0.342757	−	0.593673i	0.984944	+	0.172875i	$0.0553058\pi$
$570$	−223373.	−	437173.i	−0.687512	−	1.34556i
$571$	−34588.3	+	19969.5i	−0.106086	+	0.0612486i	−0.552104	−	0.833775i	$-0.686175\pi$
$571$	−34588.3	+	19969.5i	−0.106086	+	0.0612486i	0.446018	+	0.895024i	$0.352842\pi$
$572$	−19311.0	+	24959.5i	−0.0590219	+	0.0762857i
$573$	−611452.	−	153255.i	−1.86232	−	0.466773i
$574$	−261493.	−	89348.1i	−0.793664	−	0.271182i
$575$		−	68818.8i		−	0.208148i
$576$	−50021.4	−	327983.i	−0.150769	−	0.988569i
$577$	511135.			1.53527			0.767634	−	0.640889i	$-0.221434\pi$
$577$	511135.			1.53527			0.767634	+	0.640889i	$0.221434\pi$
$578$	101862.	−	298118.i	0.304900	−	0.892345i
$579$	225370.	+	218176.i	0.672262	+	0.650804i
$580$	−193899.	−	150018.i	−0.576393	−	0.445953i
$581$	−17000.0	−	29444.8i	−0.0503612	−	0.0872281i
$582$	201391.	+	130462.i	0.594557	+	0.385156i
$583$	−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	$-0.301005\pi$
$587$	60509.5	+	34935.2i	0.175609	+	0.101388i	−0.409619	+	0.912257i	$0.634338\pi$
$588$	8425.04	+	58464.1i	0.0243678	+	0.169097i
$589$	−406079.	−	703350.i	−1.17052	−	2.02741i
$590$	288165.	−	251697.i	0.827823	−	0.723060i
$591$	−267058.	+	76220.4i	−0.764592	+	0.218221i
$592$	−90121.9	−	347423.i	−0.257150	−	0.991322i
$593$	206980.			0.588599			0.294299	−	0.955713i	$-0.404914\pi$
$593$	206980.			0.588599			0.294299	+	0.955713i	$0.404914\pi$
$594$	−3714.26	+	197582.i	−0.0105269	+	0.559982i
$595$		−	380174.i		−	1.07386i
$596$	−6719.53	+	49510.2i	−0.0189167	+	0.139381i
$597$	84629.6	+	296522.i	0.237451	+	0.831970i
$598$	33969.6	−	29670.7i	0.0949923	−	0.0829708i
$599$	241159.	−	139233.i	0.672123	−	0.388051i	−0.124757	−	0.992187i	$-0.539815\pi$
$599$	241159.	−	139233.i	0.672123	−	0.388051i	0.796881	+	0.604137i	$0.206482\pi$
$600$	33876.3	+	96542.5i	0.0941009	+	0.268174i
$601$	−213736.	+	370201.i	−0.591737	+	1.02492i	0.402262	+	0.915525i	$0.368224\pi$
$601$	−213736.	+	370201.i	−0.591737	+	1.02492i	−0.993999	+	0.109393i	$0.965109\pi$
$602$	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
$606$	280572.	+	181755.i	0.764009	+	0.494928i
$607$	361479.	−	208700.i	0.981082	−	0.566428i	0.0784853	−	0.996915i	$-0.474992\pi$
$607$	361479.	−	208700.i	0.981082	−	0.566428i	0.902597	+	0.430487i	$0.141658\pi$
$608$	−49759.4	+	658337.i	−0.134607	+	1.78091i
$609$	−202336.	+	209008.i	−0.545556	+	0.563544i
$610$	71901.8	−	210434.i	0.193232	−	0.565530i
$611$		−	121339.i		−	0.325026i
$612$	−519344.	−	53399.8i	−1.38660	−	0.142573i
$613$	−23327.6			−0.0620796			−0.0310398	−	0.999518i	$-0.509882\pi$
$613$	−23327.6			−0.0620796			−0.0310398	+	0.999518i	$0.509882\pi$
$614$	−532347.	−	181895.i	−1.41208	−	0.482484i
$615$	−71657.8	+	285898.i	−0.189458	+	0.755894i
$616$	173049.	+	86631.5i	0.456044	+	0.228305i
$617$	−39385.7	−	68218.0i	−0.103459	−	0.179196i	0.809649	−	0.586915i	$-0.199658\pi$
$617$	−39385.7	−	68218.0i	−0.103459	−	0.179196i	−0.913108	+	0.407719i	$0.866324\pi$
$618$	−185213.	−	362489.i	−0.484948	−	0.949114i
$619$	−382655.	−	220926.i	−0.998679	−	0.576587i	−0.0908215	−	0.995867i	$-0.528949\pi$
$619$	−382655.	−	220926.i	−0.998679	−	0.576587i	−0.907857	+	0.419280i	$0.862283\pi$
$620$	−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
$624$	−33048.8	+	58345.2i	−0.0848762	+	0.149843i
$625$	124028.	+	214823.i	0.317512	+	0.549947i
$626$	−134964.	−	154518.i	−0.344404	−	0.394304i
$627$	95606.4	−	381447.i	0.243193	−	0.970285i
$628$	−45410.7	+	334591.i	−0.115143	+	0.848390i
$629$	−564798.			−1.42755
$630$	−297940.	+	68751.3i	−0.750667	+	0.173221i
$631$			211599.i			0.531440i	0.964050	+	0.265720i	$0.0856097\pi$
$631$			211599.i			0.531440i	−0.964050	+	0.265720i	$0.914390\pi$
$632$	279143.	−	16616.2i	0.698864	−	0.0416005i
$633$	−108350.	+	111923.i	−0.270410	+	0.279325i
$634$	−73809.9	−	84504.1i	−0.183627	−	0.210232i
$635$	−9709.36	+	5605.70i	−0.0240793	+	0.0139022i
$636$	−121210.	−	48479.9i	−0.299656	−	0.119853i
$637$	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	−0.862902	−	0.505371i	$-0.831356\pi$
$641$	2552.74	−	4421.47i	0.00621284	−	0.0107610i	0.869115	+	0.494610i	$0.164689\pi$
$642$	225122.	+	11543.3i	0.546195	+	0.0280065i
$643$	69127.8	−	39911.0i	0.167198	−	0.0965318i	−0.414066	−	0.910247i	$-0.635892\pi$
$643$	69127.8	−	39911.0i	0.167198	−	0.0965318i	0.581264	+	0.813715i	$0.302558\pi$
$644$	−218756.	−	169251.i	−0.527459	−	0.408093i
$645$	−97788.2	−	342626.i	−0.235054	−	0.823570i
$646$	983109.	+	335913.i	2.35579	+	0.804936i
$647$			531516.i			1.26972i	0.772628	+	0.634859i	$0.218942\pi$
$647$			531516.i			1.26972i	−0.772628	+	0.634859i	$0.781058\pi$
$648$	52069.9	+	416663.i	0.124004	+	0.992282i
$649$	306477.			0.727627
$650$	6686.01	−	19567.8i	0.0158249	−	0.0463143i
$651$	−486416.	+	138827.i	−1.14775	+	0.327576i
$652$	−418763.	+	541251.i	−0.985085	+	1.27322i
$653$	235615.	+	408097.i	0.552556	+	0.957055i	0.998089	+	0.0617897i	$0.0196808\pi$
$653$	235615.	+	408097.i	0.552556	+	0.957055i	−0.445533	+	0.895265i	$0.646986\pi$
$654$	6365.33	−	124140.i	0.0148821	−	0.290238i
$655$	−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	$-0.198366\pi$
$659$	309469.	+	178672.i	0.712601	+	0.411420i	−0.0994224	+	0.995045i	$0.531700\pi$
$660$	76653.8	−	191650.i	0.175973	−	0.439969i
$661$	282792.	+	489809.i	0.647237	+	1.12105i	0.983780	+	0.179380i	$0.0574090\pi$
$661$	282792.	+	489809.i	0.647237	+	1.12105i	−0.336543	+	0.941668i	$0.609258\pi$
$662$	−339790.	+	296789.i	−0.775345	+	0.677223i
$663$	75812.5	+	73392.6i	0.172470	+	0.166965i
$664$	48682.8	−	2897.89i	0.110418	−	0.00657272i
$665$	608463.			1.37591
$666$	102139.	+	442628.i	0.230273	+	0.997907i
$667$			280664.i			0.630864i
$668$	175167.	+	23773.7i	0.392554	+	0.0532775i
$669$	559314.	+	140187.i	1.24969	+	0.313225i
$670$	4320.25	−	3773.51i	0.00962408	−	0.00840613i
$671$	154264.	−	89064.5i	0.342626	−	0.197815i
$672$	390197.	+	129750.i	0.864062	+	0.287322i
$673$	158119.	−	273870.i	0.349103	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$673$	158119.	−	273870.i	0.349103	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$674$	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	−0.324959	−	0.945728i	$-0.605351\pi$
$677$	300914.	−	521198.i	0.656545	−	1.13717i	0.981504	−	0.191441i	$-0.0613161\pi$
$678$	81590.5	−	41688.6i	0.177493	−	0.0906896i
$679$	−257556.	+	148700.i	−0.558641	+	0.322531i
$680$	487625.	+	244115.i	1.05455	+	0.527929i
$681$	119533.	+	29959.8i	0.257746	+	0.0646018i
$682$	110408.	−	323128.i	0.237372	−	0.694713i
$683$		−	385277.i		−	0.825909i	−0.910752	−	0.412955i	$-0.864497\pi$
$683$		−	385277.i		−	0.825909i	0.910752	−	0.412955i	$-0.135503\pi$
$684$	85465.5	−	831202.i	0.182675	−	1.77662i
$685$	35285.0			0.0751984
$686$	−474775.	−	162223.i	−1.00888	−	0.344718i
$687$	−426728.	−	413107.i	−0.904144	−	0.875284i
$688$	−127713.	+	461835.i	−0.269810	+	0.975685i
$689$	13192.2	+	22849.6i	0.0277895	+	0.0481328i
$690$	−160393.	+	247596.i	−0.336890	+	0.520050i
$691$	397767.	+	229651.i	0.833053	+	0.480963i	0.854897	−	0.518798i	$-0.173620\pi$
$691$	397767.	+	229651.i	0.833053	+	0.480963i	−0.0218438	+	0.999761i	$0.506954\pi$
$692$	−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
$696$	−138158.	−	393730.i	−0.285205	−	0.812793i
$697$	−311866.	−	540168.i	−0.641952	−	1.11189i
$698$	−582807.	−	667248.i	−1.19623	−	1.36955i
$699$	−548191.	+	156458.i	−1.12196	+	0.320217i
$700$	−125655.	−	17054.0i	−0.256440	−	0.0348040i
$701$	−127011.			−0.258467			−0.129234	−	0.991614i	$-0.541252\pi$
$701$	−127011.			−0.258467			−0.129234	+	0.991614i	$0.541252\pi$
$702$	43807.2	−	72686.1i	0.0888937	−	0.147495i
$703$		−	903950.i		−	1.82908i
$704$	−222233.	+	166331.i	−0.448398	+	0.335605i
$705$	217816.	+	763175.i	0.438240	+	1.53549i
$706$	575716.	+	659130.i	1.15504	+	1.32240i
$707$	−358820.	+	207165.i	−0.717857	+	0.414455i
$708$	644557.	−	92884.5i	1.28586	−	0.185301i
$709$	−247408.	+	428523.i	−0.492177	+	0.852475i	−0.999959	−	0.00901014i	$-0.997132\pi$
$709$	−247408.	+	428523.i	−0.492177	+	0.852475i	0.507783	+	0.861485i	$0.330465\pi$
$710$	−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
$714$	351806.	−	543076.i	0.690092	−	1.06528i
$715$	−36128.6	+	20858.8i	−0.0706706	+	0.0408017i
$716$	112391.	−	145265.i	0.219232	−	0.283357i
$717$	1987.85	−	2053.39i	0.00386674	−	0.00399423i
$718$	3499.77	+	1195.82i	0.00678876	+	0.00231961i
$719$			614613.i			1.18890i	0.804134	+	0.594448i	$0.202629\pi$
$719$			614613.i			1.18890i	−0.804134	+	0.594448i	$0.797371\pi$
$720$	103128.	−	426294.i	0.198935	−	0.822326i
$721$	504518.			0.970523
$722$	−369076.	+	1.08017e6i	−0.708013	+	2.07213i
$723$	−55807.8	+	222660.i	−0.106762	+	0.425957i
$724$	−575434.	−	445210.i	−1.09779	−	0.849353i
$725$	64338.5	+	111438.i	0.122404	+	0.212010i
$726$	−322124.	+	164589.i	−0.611153	+	0.312268i
$727$	286999.	+	165699.i	0.543014	+	0.313509i	0.746299	−	0.665610i	$-0.231829\pi$
$727$	286999.	+	165699.i	0.543014	+	0.313509i	−0.203286	+	0.979119i	$0.565162\pi$
$728$	−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
$732$	297442.	−	234066.i	0.555112	−	0.436833i
$733$	25808.4	+	44701.5i	0.0480345	+	0.0831982i	0.889043	−	0.457824i	$-0.151371\pi$
$733$	25808.4	+	44701.5i	0.0480345	+	0.0831982i	−0.841008	+	0.541022i	$0.818038\pi$
$734$	122909.	−	107354.i	0.228134	−	0.199263i
$735$	−18984.1	+	75742.1i	−0.0351411	+	0.140205i
$736$	357553.	−	171906.i	0.660062	−	0.317349i
$737$	4594.79			0.00845923
$738$	−366927.	+	342092.i	−0.673701	+	0.628101i
$739$		−	228968.i		−	0.419263i	−0.977780	−	0.209631i	$-0.932774\pi$
$739$		−	228968.i		−	0.419263i	0.977780	−	0.209631i	$-0.0672264\pi$
$740$	63810.8	−	470165.i	0.116528	−	0.858592i
$741$	−117464.	+	121337.i	−0.213928	+	0.220981i
$742$	121859.	−	106438.i	0.221335	−	0.193325i
$743$	910009.	−	525394.i	1.64842	−	0.951716i	0.670720	−	0.741711i	$-0.265985\pi$
$743$	910009.	−	525394.i	1.64842	−	0.951716i	0.977700	−	0.210005i	$-0.0673480\pi$
$744$	134269.	−	713036.i	0.242566	−	1.28815i
$745$	−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
$750$	−31296.2	+	610353.i	−0.0556377	+	1.08507i
$751$	233295.	−	134693.i	0.413643	−	0.238817i	−0.278711	−	0.960375i	$-0.589907\pi$
$751$	233295.	−	134693.i	0.413643	−	0.238817i	0.692354	+	0.721558i	$0.256574\pi$
$752$	284472.	−	1.02870e6i	0.503041	−	1.81909i
$753$	−101241.	−	354724.i	−0.178553	−	0.625606i
$754$	−27267.6	+	79803.5i	−0.0479627	+	0.140372i
$755$		−	193735.i		−	0.339870i
$756$	−489225.	−	177497.i	−0.855984	−	0.310562i
$757$	−476176.			−0.830952			−0.415476	−	0.909604i	$-0.636385\pi$
$757$	−476176.			−0.830952			−0.415476	+	0.909604i	$0.636385\pi$
$758$	−702346.	−	239980.i	−1.22240	−	0.417674i
$759$	−227233.	+	64854.1i	−0.394446	+	0.112578i
$760$	−390701.	+	780436.i	−0.676422	+	1.35117i
$761$	−242197.	−	419498.i	−0.418215	−	0.724370i	0.577545	−	0.816359i	$-0.304011\pi$
$761$	−242197.	−	419498.i	−0.418215	−	0.724370i	−0.995760	+	0.0919890i	$0.970678\pi$
$762$	−19057.1	−	977.166i	−0.0328207	−	0.00168290i
$763$	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
$768$	−416971.	+	417166.i	−0.706942	+	0.707271i
$769$	−251061.	−	434851.i	−0.424549	−	0.735340i	0.571830	−	0.820372i	$-0.306234\pi$
$769$	−251061.	−	434851.i	−0.424549	−	0.735340i	−0.996378	+	0.0850327i	$0.972901\pi$
$770$	168293.	+	192677.i	0.283848	+	0.324974i
$771$	−200185.	−	193796.i	−0.336762	−	0.326013i
$772$	74996.1	−	552580.i	0.125836	−	0.927172i
$773$	435529.			0.728884			0.364442	−	0.931226i	$-0.381260\pi$
$773$	435529.			0.728884			0.364442	+	0.931226i	$0.381260\pi$
$774$	177370.	−	579929.i	0.296073	−	0.968039i
$775$			223752.i			0.372531i
$776$	−25348.1	−	425833.i	−0.0420941	−	0.707157i
$777$	−546117.	−	136880.i	−0.904573	−	0.226724i
$778$	−31601.0	−	36179.6i	−0.0522085	−	0.0597729i
$779$	864530.	−	499136.i	1.42464	−	0.822516i
$780$	−69660.8	+	54818.1i	−0.114498	+	0.0901020i
$781$	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
$786$	−15172.6	−	29695.0i	−0.0245593	−	0.0480661i
$787$	371945.	−	214742.i	0.600522	−	0.346711i	−0.168725	−	0.985663i	$-0.553965\pi$
$787$	371945.	−	214742.i	0.600522	−	0.346711i	0.769247	+	0.638952i	$0.220632\pi$
$788$	390496.	+	302125.i	0.628875	+	0.486558i
$789$	−134189.	−	33633.3i	−0.215557	−	0.0540276i
$790$	349810.	+	119524.i	0.560503	+	0.191515i
$791$			113559.i			0.181496i
$792$	286849.	−	202837.i	0.457302	−	0.323367i
$793$	−76497.5			−0.121647
$794$	41743.7	−	122171.i	0.0662140	−	0.193787i
$795$	−123991.	−	120034.i	−0.196181	−	0.189919i
$796$	335458.	−	433579.i	0.529434	−	0.684292i
$797$	−362714.	−	628240.i	−0.571016	−	0.989028i	−0.996462	−	0.0840446i	$-0.973216\pi$
$797$	−362714.	−	628240.i	−0.571016	−	0.989028i	0.425446	−	0.904984i	$-0.360117\pi$
$798$	869184.	+	563060.i	1.36492	+	0.884197i
$799$	−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
$804$	9663.37	−	1392.55i	0.0149492	−	0.00215426i
$805$	−182817.	−	316648.i	−0.282114	−	0.488635i
$806$	−110446.	+	96468.7i	−0.170012	+	0.148497i
$807$	658648.	−	187984.i	1.01136	−	0.288651i
$808$	−35314.2	−	593258.i	−0.0540912	−	0.908701i
$809$	144295.			0.220473			0.110237	−	0.993905i	$-0.464839\pi$
$809$	144295.			0.220473			0.110237	+	0.993905i	$0.464839\pi$
$810$	−145051.	+	535805.i	−0.221080	+	0.816651i
$811$			321928.i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$811$			321928.i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$812$	512462.	+	69551.3i	0.777230	+	0.105486i
$813$	192852.	+	675706.i	0.291771	+	1.02230i
$814$	286247.	−	250021.i	0.432008	−	0.377336i
$815$	−783456.	+	452328.i	−1.17950	+	0.680987i
$816$	470669.	+	799954.i	0.706862	+	1.20139i
$817$	−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	0.303549	+	0.952816i	$0.401828\pi$
$821$	−453891.	+	786162.i	−0.673388	+	1.16634i	−0.976937	+	0.213527i	$0.931505\pi$
$822$	50404.2	+	32652.0i	0.0745974	+	0.0483244i
$823$	−730902.	+	421987.i	−1.07909	+	0.623016i	−0.930652	−	0.365905i	$-0.880759\pi$
$823$	−730902.	+	421987.i	−1.07909	+	0.623016i	−0.148443	+	0.988921i	$0.547426\pi$
$824$	−323957.	+	647112.i	−0.477126	+	0.953070i
$825$	−75355.7	+	77840.3i	−0.110715	+	0.114366i
$826$	−260966.	+	763763.i	−0.382493	+	1.11943i
$827$			658309.i			0.962540i	0.876572	+	0.481270i	$0.159824\pi$
$827$			658309.i			0.962540i	−0.876572	+	0.481270i	$0.840176\pi$
$828$	−458241.	+	205263.i	−0.668395	+	0.299399i
$829$	1.22965e6			1.78925			0.894625	−	0.446818i	$-0.147443\pi$
$829$	1.22965e6			1.78925			0.894625	+	0.446818i	$0.147443\pi$
$830$	61007.1	+	20845.2i	0.0885573	+	0.0302586i
$831$	−10371.4	+	41379.4i	−0.0150188	+	0.0599215i
$832$	118367.	−	14141.9i	0.170996	−	0.0204297i
$833$	−82621.7	−	143105.i	−0.119071	−	0.206236i
$834$	13575.7	+	26569.6i	0.0195178	+	0.0381991i
$835$	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	$-0.345227\pi$
$839$	−45546.9	−	26296.5i	−0.0647045	−	0.0373572i	−0.532003	+	0.846742i	$0.678561\pi$
$840$	412335.	+	354217.i	0.584375	+	0.502008i
$841$	91248.2	+	158047.i	0.129013	+	0.223456i
$842$	−304449.	−	348559.i	−0.429427	−	0.491646i
$843$	−94545.8	+	377215.i	−0.133042	+	0.530804i
$844$	274421.	+	37244.4i	0.385241	+	0.0522849i
$845$	−586183.			−0.820956
$846$	−395079.	+	1.29175e6i	−0.552006	+	1.80484i
$847$		−	448337.i		−	0.624939i
$848$	58273.4	+	224646.i	0.0810362	+	0.312397i
$849$	−226081.	+	233535.i	−0.313653	+	0.323994i
$850$	−188290.	−	215570.i	−0.260608	−	0.298367i
$851$	−470421.	+	271598.i	−0.649572	+	0.375031i
$852$	70323.7	−	175824.i	0.0968774	−	0.242213i
$853$	322258.	−	558168.i	0.442900	−	0.767126i	−0.555003	−	0.831848i	$-0.687283\pi$
$853$	322258.	−	558168.i	0.442900	−	0.767126i	0.997903	+	0.0647226i	$0.0206163\pi$
$854$	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	−0.960539	−	0.278144i	$-0.910281\pi$
$857$	−175819.	+	304528.i	−0.239390	+	0.414635i	0.721150	+	0.692779i	$0.243614\pi$
$858$	−70911.7	−	3636.04i	−0.0963260	−	0.00493917i
$859$	658817.	−	380368.i	0.892851	−	0.515487i	0.0179767	−	0.999838i	$-0.494278\pi$
$859$	658817.	−	380368.i	0.892851	−	0.515487i	0.874874	+	0.484351i	$0.160944\pi$
$860$	−387616.	+	500993.i	−0.524089	+	0.677384i
$861$	−170641.	−	597883.i	−0.230184	−	0.806510i
$862$	−1.11623e6	−	381396.i	−1.50223	−	0.513289i
$863$		−	363360.i		−	0.487883i	−0.969790	−	0.243942i	$-0.921559\pi$
$863$		−	363360.i		−	0.487883i	0.969790	−	0.243942i	$-0.0784406\pi$
$864$	541802.	−	513524.i	0.725793	−	0.687913i
$865$	−463964.			−0.620086
$866$	−195659.	+	572631.i	−0.260894	+	0.763553i
$867$	681622.	−	194541.i	0.906788	−	0.258805i
$868$	711245.	+	550287.i	0.944017	+	0.730382i
$869$	148054.	+	256438.i	0.196057	+	0.339580i
$870$	28246.7	−	550881.i	0.0373190	−	0.727812i
$871$	−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
$876$	−1.26626e6	−	506460.i	−1.65011	−	0.659990i
$877$	−36035.0	−	62414.4i	−0.0468516	−	0.0811494i	0.841649	−	0.540026i	$-0.181585\pi$
$877$	−36035.0	−	62414.4i	−0.0468516	−	0.0811494i	−0.888500	+	0.458876i	$0.848252\pi$
$878$	−60295.0	+	52664.5i	−0.0782154	+	0.0683171i
$879$	621371.	+	601537.i	0.804216	+	0.778546i
$880$	−355198.	+	92138.7i	−0.458675	+	0.118981i
$881$	1.34754e6			1.73616			0.868082	−	0.496422i	$-0.165353\pi$
$881$	1.34754e6			1.73616			0.868082	+	0.496422i	$0.165353\pi$
$882$	−97208.9	+	90629.3i	−0.124959	+	0.116502i
$883$			675925.i			0.866916i	0.901174	+	0.433458i	$0.142707\pi$
$883$			675925.i			0.866916i	−0.901174	+	0.433458i	$0.857293\pi$
$884$	25228.0	−	185883.i	0.0322834	−	0.237867i
$885$	835043.	+	209296.i	1.06616	+	0.267224i
$886$	116420.	−	101687.i	0.148306	−	0.129538i
$887$	−888008.	+	512692.i	−1.12868	+	0.651642i	−0.943602	−	0.331082i	$-0.892586\pi$
$887$	−888008.	+	512692.i	−1.12868	+	0.651642i	−0.185075	+	0.982724i	$0.559253\pi$
$888$	526235.	−	612577.i	0.667350	−	0.776845i
$889$	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
$894$	−100109.	+	51150.3i	−0.125255	+	0.0639990i
$895$	210269.	−	121399.i	0.262500	−	0.151555i
$896$	−225277.	−	695452.i	−0.280608	−	0.866265i
$897$	98437.0	+	24672.4i	0.122341	+	0.0306638i
$898$	102765.	−	300760.i	0.127436	−	0.372964i
$899$		−	912528.i		−	1.12908i
$900$	−134890.	+	186545.i	−0.166531	+	0.230303i
$901$	365202.			0.449867
$902$	397176.	+	135709.i	0.488169	+	0.166799i
$903$	540032.	+	522795.i	0.662284	+	0.641144i
$904$	−145654.	−	72917.5i	−0.178232	−	0.0892267i
$905$	−480895.	−	832935.i	−0.587156	−	1.01698i
$906$	179278.	−	276748.i	0.218409	−	0.337154i
$907$	1.39930e6	+	807885.i	1.70097	+	0.982053i	0.944785	+	0.327690i	$0.106270\pi$
$907$	1.39930e6	+	807885.i	1.70097	+	0.982053i	0.756181	+	0.654363i	$0.227063\pi$
$908$	−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	$-0.388266\pi$
$911$	−246841.	−	142514.i	−0.297427	−	0.171719i	−0.641286	+	0.767302i	$0.721599\pi$
$912$	−1.28031e6	+	753298.i	−1.53931	+	0.905684i
$913$	25820.8	+	44723.0i	0.0309762	+	0.0536524i
$914$	−693503.	−	793983.i	−0.830149	−	0.950427i
$915$	481139.	−	137321.i	0.574683	−	0.164019i
$916$	−142002.	+	1.04628e6i	−0.169240	+	1.24698i
$917$	41330.0			0.0491503
$918$	−568118.	−	1.02817e6i	−0.674145	−	1.22005i
$919$			662333.i			0.784233i	0.919916	+	0.392117i	$0.128257\pi$
$919$			662333.i			0.784233i	−0.919916	+	0.392117i	$0.871743\pi$
$920$	523532.	−	31163.7i	0.618540	−	0.0368191i
$921$	−347389.	−	1.21717e6i	−0.409541	−	1.43493i
$922$	−527878.	−	604361.i	−0.620972	−	0.710943i
$923$	−33145.1	+	19136.3i	−0.0389059	+	0.0224623i
$924$	62105.8	+	430973.i	0.0727425	+	0.504785i
$925$	−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	0.242803	+	0.970076i	$0.421933\pi$
$929$	−620275.	+	1.07435e6i	−0.718708	+	1.24484i	−0.961512	+	0.274764i	$0.911400\pi$
$930$	521489.	−	805011.i	0.602947	−	0.930757i
$931$	229037.	−	132235.i	0.264245	−	0.152562i
$932$	801574.	+	620174.i	0.922809	+	0.713973i
$933$	1.02327e6	−	1.05701e6i	1.17551	−	1.21427i
$934$	872338.	+	298064.i	0.999980	+	0.341677i
$935$			577438.i			0.660514i
$936$	−150237.	+	13844.3i	−0.171485	+	0.0158023i
$937$	−593717.			−0.676239			−0.338119	−	0.941103i	$-0.609791\pi$
$937$	−593717.			−0.676239			−0.338119	+	0.941103i	$0.609791\pi$
$938$	−3912.47	+	11450.5i	−0.00444677	+	0.0130143i
$939$	112228.	−	447762.i	0.127283	−	0.507828i
$940$	863388.	−	1.11593e6i	0.977125	−	1.26293i
$941$	613509.	+	1.06263e6i	0.692854	+	1.20006i	0.970899	+	0.239491i	$0.0769804\pi$
$941$	613509.	+	1.06263e6i	0.692854	+	1.20006i	−0.278044	+	0.960568i	$0.589686\pi$
$942$	−676537.	+	345675.i	−0.762412	+	0.389553i
$943$	−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	−0.974720	−	0.223431i	$-0.928274\pi$
$947$	−1.48474e6	−	857213.i	−1.65558	−	0.955848i	−0.680857	−	0.732416i	$-0.738393\pi$
$948$	389094.	+	494447.i	0.432950	+	0.550178i
$949$	137817.	+	238706.i	0.153027	+	0.265051i
$950$	345017.	−	301354.i	0.382290	−	0.333911i
$951$	61375.9	−	244875.i	0.0678636	−	0.270760i
$952$	−1.14831e6	+	68354.3i	−1.26703	+	0.0754210i
$953$	−1.23751e6			−1.36258			−0.681290	−	0.732014i	$-0.738581\pi$
$953$	−1.23751e6			−1.36258			−0.681290	+	0.732014i	$0.738581\pi$
$954$	−66043.7	−	286206.i	−0.0725662	−	0.314472i
$955$			1.48144e6i			1.62434i
$956$	−5034.67	−	683.305i	−0.00550877	−	0.000747651i
$957$	307324.	−	317457.i	0.335562	−	0.346626i
$958$	7234.74	−	6319.17i	0.00788301	−	0.00688540i
$959$	−64461.5	+	37216.8i	−0.0700911	+	0.0404671i
$960$	−719096.	+	301428.i	−0.780269	+	0.327071i
$961$	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
$966$	31868.0	−	621503.i	0.0341507	−	0.666023i
$967$	−858506.	+	495659.i	−0.918101	+	0.530066i	−0.883029	−	0.469319i	$-0.844499\pi$
$967$	−858506.	+	495659.i	−0.918101	+	0.530066i	−0.0350720	+	0.999385i	$0.511166\pi$
$968$	575053.	+	287883.i	0.613701	+	0.307231i
$969$	641539.	+	2.24780e6i	0.683244	+	2.39392i
$970$	182335.	−	533635.i	0.193787	−	0.567154i
$971$		−	1.45182e6i		−	1.53984i	−0.638141	−	0.769920i	$-0.720296\pi$
$971$		−	1.45182e6i		−	1.53984i	0.638141	−	0.769920i	$-0.279704\pi$
$972$	−703027.	+	631165.i	−0.744114	+	0.668052i
$973$	−36980.0			−0.0390608
$974$	1.53384e6	+	524089.i	1.61682	+	0.552443i
$975$	44740.1	−	12769.2i	0.0470639	−	0.0134324i
$976$	−648540.	−	179343.i	−0.680828	−	0.188272i
$977$	−306090.	−	530163.i	−0.320671	−	0.555418i	0.659956	−	0.751304i	$-0.270575\pi$
$977$	−306090.	−	530163.i	−0.320671	−	0.555418i	−0.980627	+	0.195886i	$0.937242\pi$
$978$	−1.53774e6	−	78848.3i	−1.60770	−	0.0824355i
$979$	−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	$-0.118656\pi$
$983$	1.04512e6	+	603401.i	1.08158	+	0.624452i	0.150259	+	0.988647i	$0.451989\pi$
$984$	876435.	+	165038.i	0.905169	+	0.170449i
$985$	326341.	+	565239.i	0.336356	+	0.582586i
$986$	767903.	+	879163.i	0.789864	+	0.904306i
$987$	−1.20288e6	−	1.16449e6i	−1.23478	−	1.19537i
$988$	297503.	+	40377.1i	0.304773	+	0.0413638i
$989$	725178.			0.741399
$990$	452534.	−	104425.i	0.461722	−	0.106545i
$991$		−	860509.i		−	0.876210i	−0.898924	−	0.438105i	$-0.855650\pi$
$991$		−	860509.i		−	0.876210i	0.898924	−	0.438105i	$-0.144350\pi$
$992$	−1.16252e6	+	558922.i	−1.18134	+	0.567973i
$993$	−984642.	−	246792.i	−0.998573	−	0.250284i
$994$	154396.	+	176766.i	0.156265	+	0.178906i
$995$	627601.	−	362346.i	0.633924	−	0.365996i
$996$	67858.4	+	86232.0i	0.0684046	+	0.0869260i
$997$	243483.	−	421725.i	0.244951	−	0.424267i	−0.717167	−	0.696901i	$-0.754562\pi$
$997$	243483.	−	421725.i	0.244951	−	0.424267i	0.962118	+	0.272634i	$0.0878949\pi$
$998$	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.7.14	✓	44
3.2	odd	2		108.5.f.a.19.9		44
4.3	odd	2	inner	36.5.f.a.7.17	yes	44
9.2	odd	6		324.5.d.e.163.21		22
9.4	even	3	inner	36.5.f.a.31.17	yes	44
9.5	odd	6		108.5.f.a.91.6		44
9.7	even	3		324.5.d.f.163.2		22
12.11	even	2		108.5.f.a.19.6		44
36.7	odd	6		324.5.d.f.163.1		22
36.11	even	6		324.5.d.e.163.22		22
36.23	even	6		108.5.f.a.91.9		44
36.31	odd	6	inner	36.5.f.a.31.14	yes	44

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

\(f(q)\)	\(=\)	\(q+(1.29332 - 3.78514i) q^{2} +(8.65442 - 2.47004i) q^{3} +(-12.6546 - 9.79083i) q^{4} +(-10.5756 - 18.3175i) q^{5} +(1.84350 - 35.9528i) q^{6} +(38.6407 + 22.3092i) q^{7} +(-53.4262 + 35.2369i) q^{8} +(68.7978 - 42.7535i) q^{9} +O(q^{10})\)	\(q+(1.29332 - 3.78514i) q^{2} +(8.65442 - 2.47004i) q^{3} +(-12.6546 - 9.79083i) q^{4} +(-10.5756 - 18.3175i) q^{5} +(1.84350 - 35.9528i) 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} +(-133.702 - 53.4765i) q^{12} +(14.5519 + 25.2046i) q^{13} +(134.419 - 117.408i) q^{14} +(-136.770 - 132.405i) q^{15} +(64.2793 + 247.799i) q^{16} +402.841 q^{17} +(-72.8504 - 315.704i) q^{18} +644.741i q^{19} +(-45.5130 + 335.344i) q^{20} +(389.517 + 97.6292i) q^{21} +(-204.165 + 178.327i) q^{22} +(335.527 - 193.717i) q^{23} +(-375.336 + 436.920i) 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} +(-678.059 + 346.453i) q^{30} +(-1090.90 + 629.833i) q^{31} +(1021.09 + 77.1774i) q^{32} +(-591.628 - 148.287i) q^{33} +(521.004 - 1524.81i) q^{34} -943.733i q^{35} +(-1289.20 - 132.558i) q^{36} -1402.04 q^{37} +(2440.44 + 833.859i) q^{38} +(188.194 + 182.187i) q^{39} +(1210.46 + 605.982i) q^{40} +(-774.166 - 1340.89i) q^{41} +(873.312 - 1348.11i) 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} +(1168.37 + 1985.78i) q^{48} +(-205.097 - 355.239i) q^{49} +(-467.404 - 535.125i) q^{50} +(3486.36 - 995.034i) q^{51} +(62.6253 - 461.430i) q^{52} +906.566 q^{53} +(-1410.28 - 2552.29i) q^{54} +1433.41i q^{55} +(-2850.53 + 169.681i) q^{56} +(1592.54 + 5579.86i) q^{57} +(1906.22 + 2182.40i) q^{58} +(-3916.45 + 2261.16i) q^{59} +(434.426 + 3014.63i) 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} +(-1326.45 + 2047.62i) q^{66} +(-58.7165 + 33.9000i) q^{67} +(-5097.81 - 3944.15i) q^{68} +(2425.30 - 2505.27i) q^{69} +(-3572.16 - 1220.55i) q^{70} +1315.04i q^{71} +(-2169.11 + 4708.38i) q^{72} +9470.72 q^{73} +(-1813.29 + 5306.91i) q^{74} +(388.665 - 1550.68i) q^{75} +(6312.55 - 8158.96i) q^{76} +(-1511.89 - 2618.67i) q^{77} +(933.001 - 476.716i) 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} +(-3973.33 - 5049.16i) q^{84} +(-4260.28 - 7379.03i) q^{85} +(5638.88 - 4925.26i) q^{86} +(-1585.10 + 6324.16i) q^{87} +(4329.61 - 257.724i) q^{88} +8083.40 q^{89} +(-5012.45 + 4673.19i) q^{90} +1298.56i q^{91} +(-6142.62 - 833.676i) q^{92} +(-7885.41 + 8145.41i) q^{93} +(-12560.2 + 10970.7i) q^{94} +(11810.0 - 6818.52i) q^{95} +(9027.55 - 1854.20i) 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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