Properties

Label 147.2.e.c.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.c.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 −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 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 \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 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 \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) −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 \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 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 \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) −1.00000 1.73205i −0.129099 0.223607i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 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 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 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 \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 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 \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) −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 \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 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 \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 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 −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 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 \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 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 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) −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 \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 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 −0.991082 0.133250i \(-0.957459\pi\)
0.610939 + 0.791677i \(0.290792\pi\)
\(174\) −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 \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 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 \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) 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 \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 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 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 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 0.896435 0.443176i \(-0.146148\pi\)
−0.832019 + 0.554747i \(0.812815\pi\)
\(242\) 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 \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 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 \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) −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 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) −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 \(-0.964041\pi\)
0.399188 0.916869i \(-0.369292\pi\)
\(284\) 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 \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 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 \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) −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 \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 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 0.967857 0.251500i \(-0.0809239\pi\)
−0.701734 + 0.712439i \(0.747591\pi\)
\(354\) 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 −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) 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 \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) −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 \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 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 \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 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 \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 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 \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 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 \(-0.519989\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(468\) −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 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) −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 \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 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 −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 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 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) −1.00000 1.73205i −0.0437688 0.0758098i
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 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 0.905088 0.425223i \(-0.139804\pi\)
−0.820798 + 0.571218i \(0.806471\pi\)
\(564\) 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 \(0.0836092\pi\)
−0.257982 + 0.966150i \(0.583058\pi\)
\(578\) 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 \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 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 −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 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 \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) 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 −0.981454 0.191700i \(-0.938600\pi\)
0.656744 + 0.754114i \(0.271933\pi\)
\(608\) 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 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 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 \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 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 \(-0.878670\pi\)
0.141950 0.989874i \(-0.454663\pi\)
\(648\) −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 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) −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 −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) −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 −0.610704 0.791859i \(-0.709113\pi\)
0.991122 + 0.132956i \(0.0424468\pi\)
\(692\) −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 \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) −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 \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 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 −0.982986 0.183679i \(-0.941199\pi\)
0.650564 + 0.759452i \(0.274533\pi\)
\(734\) 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 −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 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 \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 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 0.964014 0.265852i \(-0.0856532\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(774\) −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 \(-0.879732\pi\)
0.145251 0.989395i \(-0.453601\pi\)
\(788\) 11.0000 + 19.0526i 0.391859 + 0.678719i
\(789\) 8.00000 13.8564i 0.284808 0.493301i
\(790\) 32.0000 1.13851
\(791\) 0 0
\(792\) 12.0000 0.426401
\(793\) −2.00000 + 3.46410i −0.0710221 + 0.123014i
\(794\) 9.00000 + 15.5885i 0.319398 + 0.553214i
\(795\) 6.00000 + 10.3923i 0.212798 + 0.368577i
\(796\) −12.0000 + 20.7846i −0.425329 + 0.736691i
\(797\) 26.0000 0.920967 0.460484 0.887668i \(-0.347676\pi\)
0.460484 + 0.887668i \(0.347676\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.50000 + 4.33013i −0.0883883 + 0.153093i
\(801\) −7.00000 12.1244i −0.247333 0.428393i
\(802\) −15.0000