Properties

Label 882.2.g.j.667.1
Level $882$
Weight $2$
Character 882.667
Analytic conductor $7.043$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
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 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.2.g.j.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-2.00000 - 3.46410i) q^{11} -6.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} -2.00000 q^{20} -4.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +2.00000 q^{29} +(0.500000 + 0.866025i) q^{32} -2.00000 q^{34} +(5.00000 - 8.66025i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-4.00000 - 6.92820i) q^{46} +1.00000 q^{50} +(3.00000 + 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} -8.00000 q^{55} +(1.00000 - 1.73205i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{68} -8.00000 q^{71} +(5.00000 + 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +4.00000 q^{76} +(1.00000 + 1.73205i) q^{80} +(-3.00000 + 5.19615i) q^{82} -4.00000 q^{83} -4.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(2.00000 + 3.46410i) q^{88} +(3.00000 - 5.19615i) q^{89} -8.00000 q^{92} +(4.00000 + 6.92820i) q^{95} +14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 2q^{5} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 2q^{5} - 2q^{8} - 2q^{10} - 4q^{11} - 12q^{13} - q^{16} - 2q^{17} - 4q^{19} - 4q^{20} - 8q^{22} + 8q^{23} + q^{25} - 6q^{26} + 4q^{29} + q^{32} - 4q^{34} + 10q^{37} + 4q^{38} - 2q^{40} - 12q^{41} - 8q^{43} - 4q^{44} - 8q^{46} + 2q^{50} + 6q^{52} + 6q^{53} - 16q^{55} + 2q^{58} - 4q^{59} + 6q^{61} + 2q^{64} - 12q^{65} - 4q^{67} - 2q^{68} - 16q^{71} + 10q^{73} - 10q^{74} + 8q^{76} + 2q^{80} - 6q^{82} - 8q^{83} - 8q^{85} - 4q^{86} + 4q^{88} + 6q^{89} - 16q^{92} + 8q^{95} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
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
\(3\) 0 0
\(4\) −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 \(0.0190830\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −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 0
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) −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
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 0 0
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 0 0
\(40\) −1.00000 + 1.73205i −0.158114 + 0.273861i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 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
\(45\) 0 0
\(46\) −4.00000 6.92820i −0.589768 1.02151i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 3.00000 + 5.19615i 0.416025 + 0.720577i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 1.00000 1.73205i 0.131306 0.227429i
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) 0 0
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 2.00000 + 3.46410i 0.213201 + 0.369274i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0 0
\(103\) 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
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −8.00000 13.8564i −0.746004 1.29212i
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −3.00000 5.19615i −0.271607 0.470438i
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) 10.0000 17.3205i 0.873704 1.51330i 0.0155672 0.999879i \(-0.495045\pi\)
0.858137 0.513421i \(-0.171622\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i \(-0.0261741\pi\)
−0.569442 + 0.822031i \(0.692841\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) 12.0000 + 20.7846i 1.00349 + 1.73810i
\(144\) 0 0
\(145\) 2.00000 3.46410i 0.166091 0.287678i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.00000 8.66025i −0.399043 0.691164i 0.594565 0.804048i \(-0.297324\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) −2.00000 + 3.46410i −0.155230 + 0.268866i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) −2.00000 + 3.46410i −0.153393 + 0.265684i
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 + 6.92820i −0.294884 + 0.510754i
\(185\) −10.0000 17.3205i −0.735215 1.27343i
\(186\) 0 0
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 7.00000 12.1244i 0.502571 0.870478i
\(195\) 0 0
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) 0 0
\(208\) 3.00000 5.19615i 0.208013 0.360288i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 4.00000 + 6.92820i 0.269680 + 0.467099i
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 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 \(0.963710\pi\)
\(228\) 0 0
\(229\) −1.00000 + 1.73205i −0.0660819 + 0.114457i −0.897173 0.441679i \(-0.854383\pi\)
0.831092 + 0.556136i \(0.187717\pi\)
\(230\) −16.0000 −1.05501
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −11.0000 + 19.0526i −0.720634 + 1.24817i 0.240112 + 0.970745i \(0.422816\pi\)
−0.960746 + 0.277429i \(0.910518\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 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 0
\(244\) −6.00000 −0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 12.0000 20.7846i 0.763542 1.32249i
\(248\) 0 0
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 25.9808i 0.935674 1.62064i 0.162247 0.986750i \(-0.448126\pi\)
0.773427 0.633885i \(-0.218541\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −10.0000 17.3205i −0.617802 1.07006i
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) −2.00000 + 3.46410i −0.122169 + 0.211604i
\(269\) −11.0000 19.0526i −0.670682 1.16166i −0.977711 0.209955i \(-0.932668\pi\)
0.307029 0.951700i \(-0.400665\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 0 0
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −2.00000 3.46410i −0.117444 0.203419i
\(291\) 0 0
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) −5.00000 + 8.66025i −0.290619 + 0.503367i
\(297\) 0 0
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) −24.0000 + 41.5692i −1.38796 + 2.40401i
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) −6.00000 10.3923i −0.343559 0.595062i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.00000 + 6.92820i 0.226819 + 0.392862i 0.956864 0.290537i \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 0 0
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 1.00000 1.73205i 0.0559017 0.0968246i
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −3.00000 5.19615i −0.166410 0.288231i
\(326\) 10.0000 + 17.3205i 0.553849 + 0.959294i
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) 0 0
\(334\) −4.00000 + 6.92820i −0.218870 + 0.379094i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 0 0
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 11.0000 + 19.0526i 0.591364 + 1.02427i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.00000 3.46410i 0.106600 0.184637i
\(353\) 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i \(0.127637\pi\)
−0.122308 + 0.992492i \(0.539030\pi\)
\(354\) 0 0
\(355\) −8.00000 + 13.8564i −0.424596 + 0.735422i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −4.00000 + 6.92820i −0.211112 + 0.365657i −0.952063 0.305903i \(-0.901042\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 9.00000 15.5885i 0.473029 0.819311i
\(363\) 0 0
\(364\) 0 0
\(365\) 20.0000 1.04685
\(366\) 0 0
\(367\) 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i \(0.147978\pi\)
−0.0586798 + 0.998277i \(0.518689\pi\)
\(368\) 4.00000 + 6.92820i 0.208514 + 0.361158i
\(369\) 0 0
\(370\) −20.0000 −1.03975
\(371\) 0 0
\(372\) 0 0
\(373\) −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 4.00000 6.92820i 0.205196 0.355409i
\(381\) 0 0
\(382\) 0 0
\(383\) 8.00000 13.8564i 0.408781 0.708029i −0.585973 0.810331i \(-0.699287\pi\)
0.994753 + 0.102302i \(0.0326207\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 8.66025i 0.251896 0.436297i
\(395\) 0 0
\(396\) 0 0
\(397\) 3.00000 5.19615i 0.150566 0.260787i −0.780870 0.624694i \(-0.785224\pi\)
0.931436 + 0.363906i \(0.118557\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 1.73205i 0.0497519 0.0861727i
\(405\) 0 0
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) 6.00000 + 10.3923i 0.296319 + 0.513239i
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 0 0
\(418\) 8.00000 13.8564i 0.391293 0.677739i
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 16.0000 + 27.7128i 0.765384 + 1.32568i
\(438\) 0 0
\(439\) −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 8.00000 0.381385
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 0 0
\(448\) 0 0
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) −7.00000 12.1244i −0.329252 0.570282i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 1.00000 + 1.73205i 0.0467269 + 0.0809334i
\(459\) 0 0
\(460\) −8.00000 + 13.8564i −0.373002 + 0.646058i
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) 11.0000 + 19.0526i 0.509565 + 0.882593i
\(467\) −14.0000 + 24.2487i −0.647843 + 1.12210i 0.335794 + 0.941935i \(0.390995\pi\)
−0.983637 + 0.180161i \(0.942338\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) −30.0000 + 51.9615i −1.36788 + 2.36924i
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 14.0000 24.2487i 0.635707 1.10108i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) −2.00000 3.46410i −0.0900755 0.156015i
\(494\) −12.0000 20.7846i −0.539906 0.935144i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 22.0000 38.1051i 0.984855 1.70582i 0.342277 0.939599i \(-0.388802\pi\)
0.642578 0.766220i \(-0.277865\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) 0 0
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) −16.0000 + 27.7128i −0.711287 + 1.23198i
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 25.9808i −0.661622 1.14596i
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) 3.00000 + 5.19615i 0.131432 + 0.227648i 0.924229 0.381839i \(-0.124709\pi\)
−0.792797 + 0.609486i \(0.791376\pi\)
\(522\) 0 0
\(523\) 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i \(-0.689279\pi\)
0.997478 + 0.0709788i \(0.0226123\pi\)
\(524\) −20.0000 −0.873704
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 6.00000 10.3923i 0.260623 0.451413i
\(531\) 0 0
\(532\) 0 0
\(533\) 36.0000 1.55933
\(534\) 0 0
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −22.0000 −0.948487
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0000 + 25.9808i −0.644900 + 1.11700i 0.339424 + 0.940633i \(0.389768\pi\)
−0.984325 + 0.176367i \(0.943566\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 5.00000 8.66025i 0.213589 0.369948i
\(549\) 0 0
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) −4.00000 + 6.92820i −0.170406 + 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −1.00000 1.73205i −0.0423714 0.0733893i 0.844062 0.536246i \(-0.180158\pi\)
−0.886433 + 0.462856i \(0.846825\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) −13.0000 + 22.5167i −0.548372 + 0.949808i
\(563\) −22.0000 38.1051i −0.927189 1.60594i −0.788002 0.615673i \(-0.788884\pi\)
−0.139188 0.990266i \(-0.544449\pi\)
\(564\) 0 0
\(565\) 14.0000 24.2487i 0.588984 1.02015i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) 12.0000 20.7846i 0.501745 0.869048i
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) 17.0000 + 29.4449i 0.707719 + 1.22581i 0.965701 + 0.259656i \(0.0836092\pi\)
−0.257982 + 0.966150i \(0.583058\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) 0 0
\(586\) 15.0000 25.9808i 0.619644 1.07326i
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −4.00000 + 6.92820i −0.164677 + 0.285230i
\(591\) 0 0
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) −9.00000 + 15.5885i −0.369586 + 0.640141i −0.989501 0.144528i \(-0.953834\pi\)
0.619915 + 0.784669i \(0.287167\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 24.0000 + 41.5692i 0.981433 + 1.69989i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 24.0000 41.5692i 0.974130 1.68724i 0.291353 0.956616i \(-0.405895\pi\)
0.682777 0.730627i \(-0.260772\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −12.0000 −0.485866
\(611\) 0 0
\(612\) 0 0
\(613\) 21.0000 + 36.3731i 0.848182 + 1.46909i 0.882829 + 0.469695i \(0.155636\pi\)
−0.0346469 + 0.999400i \(0.511031\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 0 0
\(628\) −5.00000 + 8.66025i −0.199522 + 0.345582i
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 6.92820i 0.157378 0.272587i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 0 0
\(649\) −8.00000 + 13.8564i −0.314027 + 0.543912i
\(650\) −6.00000 −0.235339
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 0 0
\(655\) −20.0000 34.6410i −0.781465 1.35354i
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) 0 0
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 0 0
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 4.00000 + 6.92820i 0.154765 + 0.268060i
\(669\) 0 0
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 9.00000 15.5885i 0.346667 0.600445i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) 0 0
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0 0
\(685\) 20.0000 0.764161
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −2.00000 + 3.46410i −0.0760836 + 0.131781i −0.901557 0.432660i \(-0.857575\pi\)
0.825473 + 0.564441i \(0.190908\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −4.00000 + 6.92820i −0.151729 + 0.262802i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) −11.0000 + 19.0526i −0.416356 + 0.721150i
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 20.0000 + 34.6410i 0.754314 + 1.30651i
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 8.00000 + 13.8564i 0.300235 + 0.520022i
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 48.0000 1.79510
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 0 0
\(718\) 4.00000 + 6.92820i 0.149279 + 0.258558i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) −9.00000 15.5885i −0.334482 0.579340i
\(725\) 1.00000 + 1.73205i 0.0371391 + 0.0643268i
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 10.0000 17.3205i 0.370117 0.641061i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) 3.00000 5.19615i 0.110808 0.191924i −0.805289 0.592883i \(-0.797990\pi\)
0.916096 + 0.400959i \(0.131323\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) −8.00000 + 13.8564i −0.294684 + 0.510407i
\(738\) 0 0
\(739\) 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i \(-0.0958281\pi\)
−0.734311 + 0.678813i \(0.762495\pi\)
\(740\) −10.0000 + 17.3205i −0.367607 + 0.636715i
\(741\) 0 0
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) 0 0
\(748\) 8.00000 0.292509
\(749\) 0 0
\(750\) 0 0
\(751\) −24.0000 + 41.5692i −0.875772 + 1.51688i −0.0198348 + 0.999803i \(0.506314\pi\)
−0.855938 + 0.517079i \(0.827019\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) 11.0000 19.0526i 0.398750 0.690655i −0.594822 0.803857i \(-0.702778\pi\)
0.993572 + 0.113203i \(0.0361109\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −8.00000 13.8564i −0.289052 0.500652i
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −0.0359908 + 0.0623379i
\(773\) 1.00000 + 1.73205i 0.0359675 + 0.0622975i 0.883449 0.468528i \(-0.155215\pi\)
−0.847481 + 0.530825i \(0.821882\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) 16.0000 + 27.7128i 0.572525 + 0.991642i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) 0 0
\(784\) 0 0
\(785\) −20.0000 −0.713831
\(786\) 0 0
\(787\) −18.0000 31.1769i −0.641631 1.11134i −0.985069 0.172162i \(-0.944925\pi\)
0.343438 0.939175i \(-0.388408\pi\)
\(788\) −5.00000 8.66025i −0.178118 0.308509i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −18.0000 + 31.1769i −0.639199 + 1.10712i
\(794\) −3.00000 5.19615i −0.106466 0.184405i
\(795\) 0 0
\(796\) 4.00000 6.92820i 0.141776 0.245564i
\(797\)