Properties

Label 147.2.e.b.79.1
Level $147$
Weight $2$
Character 147.79
Analytic conductor $1.174$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17380090971\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.2.e.b.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} -2.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(-1.50000 - 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(2.50000 + 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{33} +6.00000 q^{34} -1.00000 q^{36} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{39} +(3.00000 - 5.19615i) q^{40} +2.00000 q^{41} -4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{45} -1.00000 q^{48} +1.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} -8.00000 q^{55} +4.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(3.00000 + 5.19615i) q^{73} +(3.00000 + 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -12.0000 q^{83} +12.0000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(7.00000 - 12.1244i) q^{89} +2.00000 q^{90} +(4.00000 + 6.92820i) q^{95} +(2.50000 - 4.33013i) q^{96} +18.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} + q^{4} + 2q^{5} - 2q^{6} + 6q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} + q^{4} + 2q^{5} - 2q^{6} + 6q^{8} - q^{9} - 2q^{10} - 4q^{11} + q^{12} - 4q^{13} - 4q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + 4q^{20} - 8q^{22} - 3q^{24} + q^{25} - 2q^{26} + 2q^{27} - 4q^{29} - 2q^{30} + 5q^{32} - 4q^{33} + 12q^{34} - 2q^{36} - 6q^{37} + 4q^{38} + 2q^{39} + 6q^{40} + 4q^{41} - 8q^{43} + 4q^{44} + 2q^{45} - 2q^{48} + 2q^{50} + 6q^{51} - 2q^{52} - 6q^{53} + q^{54} - 16q^{55} + 8q^{57} - 2q^{58} - 12q^{59} - 2q^{60} + 2q^{61} + 14q^{64} - 4q^{65} + 4q^{66} - 4q^{67} - 6q^{68} - 3q^{72} + 6q^{73} + 6q^{74} + q^{75} - 8q^{76} + 4q^{78} + 16q^{79} - 2q^{80} - q^{81} + 2q^{82} - 24q^{83} + 24q^{85} - 4q^{86} + 2q^{87} - 12q^{88} + 14q^{89} + 4q^{90} + 8q^{95} + 5q^{96} + 36q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −1.50000 2.59808i −0.306186 0.530330i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 2.50000 + 4.33013i 0.441942 + 0.765466i
\(33\) −2.00000 + 3.46410i −0.348155 + 0.603023i
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 1.00000 + 1.73205i 0.160128 + 0.277350i
\(40\) 3.00000 5.19615i 0.474342 0.821584i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) −1.00000 1.73205i −0.129099 0.223607i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 2.00000 + 3.46410i 0.246183 + 0.426401i
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i \(-0.0524664\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 1.00000 + 1.73205i 0.107211 + 0.185695i
\(88\) −6.00000 10.3923i −0.639602 1.10782i
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 2.50000 4.33013i 0.255155 0.441942i
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −2.00000 + 3.46410i −0.193347 + 0.334887i −0.946357 0.323122i \(-0.895268\pi\)
0.753010 + 0.658009i \(0.228601\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 2.00000 3.46410i 0.187317 0.324443i
\(115\) 0 0
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −6.00000 −0.547723
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.50000 + 2.59808i −0.132583 + 0.229640i
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 1.00000 1.73205i 0.0860663 0.149071i
\(136\) 9.00000 + 15.5885i 0.771744 + 1.33670i
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 + 6.92820i 0.334497 + 0.579365i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −2.00000 + 3.46410i −0.166091 + 0.287678i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −6.00000 + 10.3923i −0.486664 + 0.842927i
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i \(-0.141236\pi\)
−0.823359 + 0.567521i \(0.807902\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 10.0000 0.790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 4.00000 + 6.92820i 0.311400 + 0.539360i
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 6.00000 10.3923i 0.460179 0.797053i
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 5.00000 8.66025i 0.380143 0.658427i −0.610939 0.791677i \(-0.709208\pi\)
0.991082 + 0.133250i \(0.0425415\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) −7.00000 12.1244i −0.524672 0.908759i
\(179\) 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) −1.00000 + 1.73205i −0.0745356 + 0.129099i
\(181\) −26.0000 −1.93256 −0.966282 0.257485i \(-0.917106\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0 0
\(185\) 6.00000 + 10.3923i 0.441129 + 0.764057i
\(186\) 0 0
\(187\) 12.0000 20.7846i 0.877527 1.51992i
\(188\) 0 0
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) −3.50000 6.06218i −0.252591 0.437500i
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 9.00000 15.5885i 0.646162 1.11919i
\(195\) 4.00000 0.286446
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 1.50000 + 2.59808i 0.106066 + 0.183712i
\(201\) −2.00000 + 3.46410i −0.141069 + 0.244339i
\(202\) −14.0000 −0.985037
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 3.00000 0.204124
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) 3.00000 5.19615i 0.202721 0.351123i
\(220\) −4.00000 6.92820i −0.269680 0.467099i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 3.00000 5.19615i 0.201347 0.348743i
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) −7.00000 + 12.1244i −0.465633 + 0.806500i
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) 0 0
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 2.50000 + 4.33013i 0.160706 + 0.278351i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 4.00000 6.92820i 0.254514 0.440831i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −6.00000 10.3923i −0.375735 0.650791i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −13.0000 + 22.5167i −0.810918 + 1.40455i 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) −4.00000 −0.248069
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) 2.00000 + 3.46410i 0.123560 + 0.214013i
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) −6.00000 + 10.3923i −0.369274 + 0.639602i
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) −14.0000 −0.856786
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 6.00000 10.3923i 0.359856 0.623289i
\(279\) 0 0
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) 0 0
\(285\) 4.00000 6.92820i 0.236940 0.410391i
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 2.00000 + 3.46410i 0.117444 + 0.203419i
\(291\) −9.00000 15.5885i −0.527589 0.913812i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) −9.00000 + 15.5885i −0.523114 + 0.906061i
\(297\) −2.00000 3.46410i −0.116052 0.201008i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −7.00000 + 12.1244i −0.402139 + 0.696526i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i \(0.429392\pi\)
−0.954810 + 0.297218i \(0.903941\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 7.00000 12.1244i 0.391312 0.677772i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 9.00000 15.5885i 0.497701 0.862044i
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) −4.00000 + 6.92820i −0.218870 + 0.379094i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 7.00000 + 12.1244i 0.380188 + 0.658505i
\(340\) 6.00000 + 10.3923i 0.325396 + 0.563602i
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) −5.00000 8.66025i −0.268802 0.465578i
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) −1.00000 + 1.73205i −0.0536056 + 0.0928477i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 10.0000 17.3205i 0.533002 0.923186i
\(353\) −5.00000 8.66025i −0.266123 0.460939i 0.701734 0.712439i \(-0.252409\pi\)
−0.967857 + 0.251500i \(0.919076\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 0 0
\(356\) 14.0000 0.741999
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i \(0.486738\pi\)
−0.886100 + 0.463494i \(0.846596\pi\)
\(360\) 3.00000 + 5.19615i 0.158114 + 0.273861i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) −12.0000 20.7846i −0.620505 1.07475i
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) −4.00000 + 6.92820i −0.205196 + 0.355409i
\(381\) 0 0
\(382\) −4.00000 6.92820i −0.204658 0.354478i
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 9.00000 + 15.5885i 0.456906 + 0.791384i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 2.00000 3.46410i 0.101274 0.175412i
\(391\) 0 0
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 11.0000 19.0526i 0.554172 0.959854i
\(395\) −16.0000 27.7128i −0.805047 1.39438i
\(396\) 2.00000 + 3.46410i 0.100504 + 0.174078i
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) 2.00000 + 3.46410i 0.0997509 + 0.172774i
\(403\) 0 0
\(404\) 7.00000 12.1244i 0.348263 0.603209i
\(405\) −2.00000 −0.0993808
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 9.00000 15.5885i 0.445566 0.771744i
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) −2.00000 3.46410i −0.0987730 0.171080i
\(411\) 3.00000 5.19615i 0.147979 0.256307i
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) −5.00000 8.66025i −0.245145 0.424604i
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 8.00000 13.8564i 0.391293 0.677739i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) 2.00000 3.46410i 0.0973585 0.168630i
\(423\) 0 0
\(424\) −9.00000 15.5885i −0.437079 0.757042i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 4.00000 6.92820i 0.193122 0.334497i
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 4.00000 0.191785
\(436\) −9.00000 + 15.5885i −0.431022 + 0.746552i
\(437\) 0 0
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) −24.0000 −1.14416
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 3.00000 + 5.19615i 0.142374 + 0.246598i
\(445\) −14.0000 24.2487i −0.663664 1.14950i
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −4.00000 6.92820i −0.188353 0.326236i
\(452\) −7.00000 12.1244i −0.329252 0.570282i
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) 3.00000 + 5.19615i 0.140028 + 0.242536i
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 1.00000 1.73205i 0.0460776 0.0798087i
\(472\) −18.0000 31.1769i −0.828517 1.43503i
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) −8.00000 + 13.8564i −0.367452 + 0.636446i
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 12.0000 20.7846i 0.548867 0.950666i
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) −5.00000 8.66025i −0.228218 0.395285i
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) 18.0000 31.1769i 0.817338 1.41567i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i \(-0.108650\pi\)
−0.761052 + 0.648691i \(0.775317\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 1.00000 1.73205i 0.0450835 0.0780869i
\(493\) −6.00000 10.3923i −0.270226 0.468046i
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) 4.00000 6.92820i 0.179787 0.311400i
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) 4.00000 + 6.92820i 0.178707 + 0.309529i
\(502\) −10.0000 + 17.3205i −0.446322 + 0.773052i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −28.0000 −1.24598
\(506\) 0 0
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) 0 0
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) −12.0000 −0.531369
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) −2.00000 + 3.46410i −0.0883022 + 0.152944i
\(514\) 13.0000 + 22.5167i 0.573405 + 0.993167i
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) −10.0000 −0.438951
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) −1.00000 1.73205i −0.0437688 0.0758098i
\(523\) 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i \(-0.689279\pi\)
0.997478 + 0.0709788i \(0.0226123\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 0 0
\(528\) 2.00000 + 3.46410i 0.0870388 + 0.150756i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −6.00000 + 10.3923i −0.260623 + 0.451413i
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) −7.00000 + 12.1244i −0.302920 + 0.524672i
\(535\) 4.00000 + 6.92820i 0.172935 + 0.299532i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 2.00000 3.46410i 0.0863064 0.149487i
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) 2.00000 0.0860663
\(541\) 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i \(-0.572440\pi\)
0.956504 0.291718i \(-0.0942267\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 13.0000 + 22.5167i 0.557883 + 0.966282i
\(544\) −15.0000 + 25.9808i −0.643120 + 1.11392i
\(545\) 36.0000 1.54207
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) −22.0000 −0.934690
\(555\) 6.00000 10.3923i 0.254686 0.441129i
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) −11.0000 + 19.0526i −0.464007 + 0.803684i
\(563\) −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i \(-0.193529\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(564\) 0 0
\(565\) −14.0000 + 24.2487i −0.588984 + 1.02015i
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) −4.00000 6.92820i −0.167542 0.290191i
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) −4.00000 + 6.92820i −0.167248 + 0.289683i
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) 0 0
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) −17.0000 29.4449i −0.707719 1.22581i −0.965701 0.259656i \(-0.916391\pi\)
0.257982 0.966150i \(-0.416942\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) −18.0000 −0.746124
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) 9.00000 + 15.5885i 0.372423 + 0.645055i
\(585\) −2.00000 3.46410i −0.0826898 0.143223i
\(586\) 7.00000 12.1244i 0.289167 0.500853i
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −12.0000 + 20.7846i −0.494032 + 0.855689i
\(591\) −11.0000 19.0526i −0.452480 0.783718i
\(592\) 3.00000 + 5.19615i 0.123299 + 0.213561i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) 0 0
\(599\) −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i \(-0.729446\pi\)
−0.320607 0.947212i \(-0.603887\pi\)
\(600\) 1.50000 2.59808i 0.0612372 0.106066i
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 7.00000 + 12.1244i 0.284356 + 0.492518i
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −20.0000 −0.811107
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) 0 0
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) 2.00000 3.46410i 0.0807134 0.139800i
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 4.00000 6.92820i 0.160904 0.278693i
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 13.0000 + 22.5167i 0.519584 + 0.899947i
\(627\) −8.00000 13.8564i −0.319489 0.553372i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −36.0000 −1.43541
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 24.0000 41.5692i 0.954669 1.65353i
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) 3.00000 + 5.19615i 0.118585 + 0.205396i
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 2.00000 3.46410i 0.0789337 0.136717i
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) 20.0000 + 34.6410i 0.786281 + 1.36188i 0.928231 + 0.372005i \(0.121330\pi\)
−0.141950 + 0.989874i \(0.545337\pi\)
\(648\) −1.50000 2.59808i −0.0589256 0.102062i
\(649\) −24.0000 + 41.5692i −0.942082 + 1.63173i
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) −9.00000 15.5885i −0.351928 0.609557i
\(655\) 4.00000 + 6.92820i 0.156293 + 0.270707i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) −36.0000 −1.39707
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 0 0
\(668\) −4.00000 6.92820i −0.154765 0.268060i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) 14.0000 0.537667
\(679\) 0 0
\(680\) 36.0000 1.38054
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) 0 0
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 10.0000 0.380143
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 12.0000 20.7846i 0.455186 0.788405i
\(696\) 3.00000 + 5.19615i 0.113715 + 0.196960i
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −1.00000 + 1.73205i −0.0377426 + 0.0653720i
\(703\) −12.0000 20.7846i −0.452589 0.783906i
\(704\) −14.0000 24.2487i −0.527645 0.913908i
\(705\) 0 0
\(706\) −10.0000 −0.376355
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −3.00000 + 5.19615i −0.112667 + 0.195146i −0.916845 0.399244i \(-0.869273\pi\)
0.804178 + 0.594389i \(0.202606\pi\)
\(710\) 0 0
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) 21.0000 36.3731i 0.787008 1.36314i
\(713\) 0 0
\(714\) 0 0
\(715\) 16.0000 0.598366
\(716\) −2.00000 + 3.46410i −0.0747435 + 0.129460i
\(717\) −12.0000 20.7846i −0.448148 0.776215i
\(718\) 16.0000 + 27.7128i 0.597115 + 1.03423i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −1.00000 + 1.73205i −0.0371904 + 0.0644157i
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) −1.00000 1.73205i −0.0371391 0.0643268i
\(726\) 2.50000 4.33013i 0.0927837 0.160706i
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.00000 10.3923i 0.222070 0.384636i
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) 9.00000 15.5885i 0.332423 0.575773i −0.650564 0.759452i \(-0.725467\pi\)
0.982986 + 0.183679i \(0.0588007\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.00000 + 13.8564i −0.294684 + 0.510407i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) −18.0000 31.1769i −0.662141 1.14686i −0.980052 0.198741i \(-0.936315\pi\)
0.317911 0.948120i \(-0.397019\pi\)
\(740\) −6.00000 + 10.3923i −0.220564 + 0.382029i
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) −12.0000 −0.438178
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 0 0
\(753\) 10.0000 + 17.3205i 0.364420 + 0.631194i
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) 0 0
\(760\) 12.0000 + 20.7846i 0.435286 + 0.753937i
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) −6.00000 + 10.3923i −0.216930 + 0.375735i
\(766\) 0 0
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 8.50000 14.7224i 0.306717 0.531250i
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) 1.00000 1.73205i 0.0359908 0.0623379i
\(773\) −7.00000 12.1244i −0.251773 0.436083i 0.712241 0.701935i \(-0.247680\pi\)
−0.964014 + 0.265852i \(0.914347\pi\)
\(774\) −2.00000 3.46410i −0.0718885 0.124515i
\(775\) 0 0
\(776\) 54.0000 1.93849
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −4.00000 + 6.92820i −0.143315 + 0.248229i
\(780\) 2.00000 + 3.46410i 0.0716115 + 0.124035i
\(781\) 0 0
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 4.00000 0.142766
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) 22.0000 + 38.1051i 0.784215 + 1.35830i 0.929467 + 0.368906i