Properties

Label 2646.2.e.f.2125.1
Level $2646$
Weight $2$
Character 2646.2125
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2125.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2125
Dual form 2646.2.e.f.1549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(3.00000 - 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} +(3.00000 - 5.19615i) q^{58} +5.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +8.00000 q^{67} +(3.00000 - 5.19615i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-3.00000 - 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} -21.0000 q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - 3q^{5} + 2q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - 3q^{5} + 2q^{8} - 3q^{10} - 6q^{11} - 2q^{13} + 2q^{16} + 6q^{17} + 7q^{19} - 3q^{20} - 6q^{22} + 3q^{23} - 4q^{25} - 2q^{26} + 6q^{29} + 4q^{31} + 2q^{32} + 6q^{34} - 2q^{37} + 7q^{38} - 3q^{40} - 2q^{43} - 6q^{44} + 3q^{46} - 4q^{50} - 2q^{52} + 6q^{53} + 36q^{55} + 6q^{58} + 10q^{61} + 4q^{62} + 2q^{64} + 12q^{65} + 16q^{67} + 6q^{68} - 6q^{71} - 2q^{73} - 2q^{74} + 7q^{76} + 10q^{79} - 3q^{80} + 12q^{83} + 18q^{85} - 2q^{86} - 6q^{88} + 3q^{92} - 42q^{95} - 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 3.00000 5.19615i 0.514496 0.891133i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 3.50000 + 6.06218i 0.567775 + 0.983415i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) −3.00000 5.19615i −0.452267 0.783349i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) 18.0000 2.42712
\(56\) 0 0
\(57\) 0 0
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 0 0
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) −21.0000 −2.15455
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 18.0000 1.71623
\(111\) 0 0
\(112\) 0 0
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 0 0
\(115\) 4.50000 + 7.79423i 0.419627 + 0.726816i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 5.00000 0.452679
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 6.00000 0.526235
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) 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
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 −0.251754
\(143\) −6.00000 + 10.3923i −0.501745 + 0.869048i
\(144\) 0 0
\(145\) 9.00000 + 15.5885i 0.747409 + 1.29455i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −11.5000 19.9186i −0.935857 1.62095i −0.773099 0.634285i \(-0.781294\pi\)
−0.162758 0.986666i \(-0.552039\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.00000 + 5.19615i −0.240966 + 0.417365i
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 5.00000 0.397779
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 9.00000 + 15.5885i 0.690268 + 1.19558i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) 0 0
\(178\) 0 0
\(179\) 9.00000 15.5885i 0.672692 1.16514i −0.304446 0.952529i \(-0.598471\pi\)
0.977138 0.212607i \(-0.0681952\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.50000 2.59808i 0.110581 0.191533i
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −36.0000 −2.63258
\(188\) 0 0
\(189\) 0 0
\(190\) −21.0000 −1.52350
\(191\) 9.00000 0.651217 0.325609 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) 0 0
\(193\) 17.0000 1.22369 0.611843 0.790979i \(-0.290428\pi\)
0.611843 + 0.790979i \(0.290428\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i \(-0.998611\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 0 0
\(202\) 4.50000 + 7.79423i 0.316619 + 0.548400i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 5.00000 8.66025i 0.348367 0.603388i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 21.0000 36.3731i 1.45260 2.51598i
\(210\) 0 0
\(211\) −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i \(-0.255467\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) 0 0
\(218\) 5.00000 8.66025i 0.338643 0.586546i
\(219\) 0 0
\(220\) 18.0000 1.21356
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 14.0000 24.2487i 0.937509 1.62381i 0.167412 0.985887i \(-0.446459\pi\)
0.770097 0.637927i \(-0.220208\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.50000 + 12.9904i 0.498893 + 0.864107i
\(227\) −7.50000 12.9904i −0.497792 0.862202i 0.502204 0.864749i \(-0.332523\pi\)
−0.999997 + 0.00254715i \(0.999189\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) 4.50000 + 7.79423i 0.296721 + 0.513936i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 4.50000 + 7.79423i 0.294805 + 0.510617i 0.974939 0.222470i \(-0.0714120\pi\)
−0.680135 + 0.733087i \(0.738079\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i \(-0.249619\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) −12.5000 + 21.6506i −0.803530 + 1.39176i
\(243\) 0 0
\(244\) 5.00000 0.320092
\(245\) 0 0
\(246\) 0 0
\(247\) 7.00000 12.1244i 0.445399 0.771454i
\(248\) 2.00000 0.127000
\(249\) 0 0
\(250\) −3.00000 −0.189737
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 17.0000 1.06667
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) −4.50000 + 7.79423i −0.278011 + 0.481529i
\(263\) −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i \(-0.942499\pi\)
0.336270 0.941766i \(-0.390834\pi\)
\(264\) 0 0
\(265\) 9.00000 + 15.5885i 0.552866 + 0.957591i
\(266\) 0 0
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 0 0
\(271\) 14.0000 + 24.2487i 0.850439 + 1.47300i 0.880812 + 0.473466i \(0.156997\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 3.00000 5.19615i 0.181902 0.315063i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) −12.0000 + 20.7846i −0.723627 + 1.25336i
\(276\) 0 0
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) −2.50000 4.33013i −0.149940 0.259704i
\(279\) 0 0
\(280\) 0 0
\(281\) −13.5000 + 23.3827i −0.805342 + 1.39489i 0.110717 + 0.993852i \(0.464685\pi\)
−0.916060 + 0.401042i \(0.868648\pi\)
\(282\) 0 0
\(283\) −19.0000 −1.12943 −0.564716 0.825285i \(-0.691014\pi\)
−0.564716 + 0.825285i \(0.691014\pi\)
\(284\) −3.00000 −0.178017
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 9.00000 + 15.5885i 0.528498 + 0.915386i
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −1.50000 2.59808i −0.0876309 0.151781i 0.818878 0.573967i \(-0.194596\pi\)
−0.906509 + 0.422186i \(0.861263\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 0 0
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) −11.5000 19.9186i −0.661751 1.14619i
\(303\) 0 0
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) −7.50000 + 12.9904i −0.429449 + 0.743827i
\(306\) 0 0
\(307\) −25.0000 −1.42683 −0.713413 0.700744i \(-0.752851\pi\)
−0.713413 + 0.700744i \(0.752851\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −36.0000 −2.01561
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) 42.0000 2.33694
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) −1.00000 1.73205i −0.0553849 0.0959294i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 26.0000 1.42909 0.714545 0.699590i \(-0.246634\pi\)
0.714545 + 0.699590i \(0.246634\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 0 0
\(334\) 0 0
\(335\) −12.0000 + 20.7846i −0.655630 + 1.13558i
\(336\) 0 0
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) 9.00000 + 15.5885i 0.488094 + 0.845403i
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.00000 + 1.73205i −0.0539164 + 0.0933859i
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 24.0000 1.28839 0.644194 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) 0 0
\(349\) −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i \(0.411649\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.00000 5.19615i −0.159901 0.276956i
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 0 0
\(355\) 4.50000 7.79423i 0.238835 0.413675i
\(356\) 0 0
\(357\) 0 0
\(358\) 9.00000 15.5885i 0.475665 0.823876i
\(359\) −1.50000 2.59808i −0.0791670 0.137121i 0.823724 0.566991i \(-0.191893\pi\)
−0.902891 + 0.429870i \(0.858559\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −25.0000 −1.31397
\(363\) 0 0
\(364\) 0 0
\(365\) −3.00000 5.19615i −0.157027 0.271979i
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) −36.0000 −1.86152
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) −21.0000 −1.07728
\(381\) 0 0
\(382\) 9.00000 0.460480
\(383\) −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i \(-0.985440\pi\)
0.539076 + 0.842257i \(0.318774\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.0000 0.865277
\(387\) 0 0
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0 0
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) −7.50000 + 12.9904i −0.377366 + 0.653617i
\(396\) 0 0
\(397\) −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i \(-0.940407\pi\)
0.330075 0.943955i \(-0.392926\pi\)
\(398\) −7.00000 + 12.1244i −0.350878 + 0.607739i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 4.50000 + 7.79423i 0.223883 + 0.387777i
\(405\) 0 0
\(406\) 0 0
\(407\) −6.00000 + 10.3923i −0.297409 + 0.515127i
\(408\) 0 0
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) 0 0
\(415\) 18.0000 + 31.1769i 0.883585 + 1.53041i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) 21.0000 36.3731i 1.02714 1.77906i
\(419\) 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i \(-0.0472572\pi\)
−0.622601 + 0.782540i \(0.713924\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −4.00000 6.92820i −0.194717 0.337260i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) −24.0000 −1.16417
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) −3.00000 5.19615i −0.144673 0.250581i
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 21.0000 1.00457
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 18.0000 0.858116
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −18.0000 −0.855206 −0.427603 0.903967i \(-0.640642\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 14.0000 24.2487i 0.662919 1.14821i
\(447\) 0 0
\(448\) 0 0
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 0 0
\(454\) −7.50000 12.9904i −0.351992 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) 29.0000 1.35656 0.678281 0.734802i \(-0.262725\pi\)
0.678281 + 0.734802i \(0.262725\pi\)
\(458\) 0.500000 0.866025i 0.0233635 0.0404667i
\(459\) 0 0
\(460\) 4.50000 + 7.79423i 0.209814 + 0.363408i
\(461\) −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i \(0.445654\pi\)
−0.938386 + 0.345589i \(0.887679\pi\)
\(462\) 0 0
\(463\) 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i \(-0.0689855\pi\)
−0.674526 + 0.738251i \(0.735652\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) 4.50000 + 7.79423i 0.208458 + 0.361061i
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.0000 0.551761
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 0 0
\(477\) 0 0
\(478\) −7.50000 12.9904i −0.343042 0.594166i
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −4.00000 6.92820i −0.182195 0.315571i
\(483\) 0 0
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 0 0
\(487\) −14.5000 + 25.1147i −0.657058 + 1.13806i 0.324316 + 0.945949i \(0.394866\pi\)
−0.981374 + 0.192109i \(0.938467\pi\)
\(488\) 5.00000 0.226339
\(489\) 0 0
\(490\) 0 0
\(491\) 9.00000 + 15.5885i 0.406164 + 0.703497i 0.994456 0.105151i \(-0.0335327\pi\)
−0.588292 + 0.808649i \(0.700199\pi\)
\(492\) 0 0
\(493\) −18.0000 31.1769i −0.810679 1.40414i
\(494\) 7.00000 12.1244i 0.314945 0.545501i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i \(0.420813\pi\)
−0.962472 + 0.271380i \(0.912520\pi\)
\(500\) −3.00000 −0.134164
\(501\) 0 0
\(502\) −3.00000 −0.133897
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −27.0000 −1.20148
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) 17.0000 0.754253
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 9.00000 15.5885i 0.396973 0.687577i
\(515\) 15.0000 + 25.9808i 0.660979 + 1.14485i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 6.00000 0.263117
\(521\) 12.0000 20.7846i 0.525730 0.910590i −0.473821 0.880621i \(-0.657126\pi\)
0.999551 0.0299693i \(-0.00954094\pi\)
\(522\) 0 0
\(523\) 6.50000 + 11.2583i 0.284225 + 0.492292i 0.972421 0.233233i \(-0.0749303\pi\)
−0.688196 + 0.725525i \(0.741597\pi\)
\(524\) −4.50000 + 7.79423i −0.196583 + 0.340492i
\(525\) 0 0
\(526\) −10.5000 18.1865i −0.457822 0.792971i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 9.00000 + 15.5885i 0.390935 + 0.677119i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 36.0000 1.55642
\(536\) 8.00000 0.345547
\(537\) 0 0
\(538\) −4.50000 + 7.79423i −0.194009 + 0.336033i
\(539\) 0 0
\(540\) 0 0
\(541\) −19.0000 32.9090i −0.816874 1.41487i −0.907975 0.419025i \(-0.862372\pi\)
0.0911008 0.995842i \(-0.470961\pi\)
\(542\) 14.0000 + 24.2487i 0.601351 + 1.04157i
\(543\) 0 0
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 15.0000 + 25.9808i 0.642529 + 1.11289i
\(546\) 0 0
\(547\) −16.0000 + 27.7128i −0.684111 + 1.18491i 0.289605 + 0.957146i \(0.406476\pi\)
−0.973715 + 0.227768i \(0.926857\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 0 0
\(550\) −12.0000 + 20.7846i −0.511682 + 0.886259i
\(551\) 42.0000 1.78926
\(552\) 0 0
\(553\) 0 0
\(554\) 8.00000 + 13.8564i 0.339887 + 0.588702i
\(555\) 0 0
\(556\) −2.50000 4.33013i −0.106024 0.183638i
\(557\) −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i \(0.336450\pi\)
−0.999952 + 0.00979220i \(0.996883\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) 33.0000 1.39078 0.695392 0.718631i \(-0.255231\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(564\) 0 0
\(565\) −45.0000 −1.89316
\(566\) −19.0000 −0.798630
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −6.00000 + 10.3923i −0.250873 + 0.434524i
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 2.00000 3.46410i 0.0832611 0.144212i −0.821388 0.570370i \(-0.806800\pi\)
0.904649 + 0.426158i \(0.140133\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0 0
\(580\) 9.00000 + 15.5885i 0.373705 + 0.647275i
\(581\) 0 0
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) −1.50000 2.59808i −0.0619644 0.107326i
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) 7.00000 + 12.1244i 0.288430 + 0.499575i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) −6.00000 −0.245358
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i \(-0.925505\pi\)
0.687203 + 0.726465i \(0.258838\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −11.5000 19.9186i −0.467928 0.810476i
\(605\) −37.5000 64.9519i −1.52459 2.64067i
\(606\) 0 0
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) −7.50000 + 12.9904i −0.303666 + 0.525965i
\(611\) 0 0
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) −25.0000 −1.00892
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i \(0.153988\pi\)
−0.0398207 + 0.999207i \(0.512679\pi\)
\(618\) 0 0
\(619\) 3.50000 + 6.06218i 0.140677 + 0.243659i 0.927752 0.373198i \(-0.121739\pi\)
−0.787075 + 0.616858i \(0.788405\pi\)
\(620\) −3.00000 + 5.19615i −0.120483 + 0.208683i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) −13.0000 −0.518756
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 5.00000 0.198889
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) −25.5000 + 44.1673i −1.01194 + 1.75273i
\(636\) 0 0
\(637\) 0 0
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i \(0.0123508\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 42.0000 1.65247
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −4.00000 + 6.92820i −0.156893 + 0.271746i
\(651\) 0 0
\(652\) −1.00000 1.73205i −0.0391630 0.0678323i
\(653\) −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i \(0.415448\pi\)
−0.966910 + 0.255119i \(0.917885\pi\)
\(654\) 0 0
\(655\) −13.5000 23.3827i −0.527489 0.913637i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.0000 36.3731i 0.818044 1.41689i −0.0890776 0.996025i \(-0.528392\pi\)
0.907122 0.420869i \(-0.138275\pi\)
\(660\) 0 0
\(661\) 5.00000 0.194477 0.0972387 0.995261i \(-0.468999\pi\)
0.0972387 + 0.995261i \(0.468999\pi\)
\(662\) 26.0000 1.01052
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) −12.0000 + 20.7846i −0.463600 + 0.802980i
\(671\) −15.0000 25.9808i −0.579069 1.00298i
\(672\) 0 0
\(673\) 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i \(-0.580614\pi\)
0.963679 0.267063i \(-0.0860531\pi\)
\(674\) 11.0000 + 19.0526i 0.423704 + 0.733877i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 9.00000 + 15.5885i 0.345134 + 0.597790i
\(681\) 0 0
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) −3.00000 + 5.19615i −0.114792 + 0.198825i −0.917697 0.397282i \(-0.869953\pi\)
0.802905 + 0.596107i \(0.203287\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) 47.0000 1.78796 0.893982 0.448103i \(-0.147900\pi\)
0.893982 + 0.448103i \(0.147900\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 15.0000 0.568982
\(696\) 0 0
\(697\) 0 0
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 7.00000 12.1244i 0.264010 0.457279i
\(704\) −3.00000 5.19615i −0.113067 0.195837i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 0 0
\(708\) 0 0
\(709\) −52.0000 −1.95290 −0.976450 0.215742i \(-0.930783\pi\)
−0.976450 + 0.215742i \(0.930783\pi\)
\(710\) 4.50000 7.79423i 0.168882 0.292512i
\(711\) 0 0
\(712\) 0 0
\(713\) 3.00000 5.19615i 0.112351 0.194597i
\(714\) 0 0
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) 9.00000 15.5885i 0.336346 0.582568i
\(717\) 0 0
\(718\) −1.50000 2.59808i −0.0559795 0.0969593i
\(719\) −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) −25.0000 −0.929118
\(725\) −24.0000 −0.891338
\(726\) 0 0
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) −14.5000 + 25.1147i −0.535570 + 0.927634i 0.463566 + 0.886062i \(0.346570\pi\)
−0.999136 + 0.0415715i \(0.986764\pi\)
\(734\) −4.00000 6.92820i −0.147643 0.255725i
\(735\) 0 0
\(736\) 1.50000 2.59808i 0.0552907 0.0957664i
\(737\) −24.0000 41.5692i −0.884051 1.53122i
\(738\) 0 0
\(739\) −13.0000 + 22.5167i −0.478213 + 0.828289i −0.999688 0.0249776i \(-0.992049\pi\)
0.521475 + 0.853266i \(0.325382\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) 0 0
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) −7.00000 + 12.1244i −0.256288 + 0.443904i
\(747\) 0 0
\(748\) −36.0000 −1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i \(-0.641977\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −12.0000 −0.437014
\(755\) 69.0000 2.51117
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 2.00000 0.0726433
\(759\) 0 0
\(760\) −21.0000 −0.761750
\(761\) −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 9.00000 0.325609
\(765\) 0 0
\(766\) −9.00000 + 15.5885i −0.325183 + 0.563234i
\(767\) 0 0
\(768\) 0 0
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 17.0000 0.611843
\(773\) −25.5000 + 44.1673i −0.917171 + 1.58859i −0.113480 + 0.993540i \(0.536200\pi\)
−0.803691 + 0.595047i \(0.797133\pi\)
\(774\) 0 0
\(775\) −4.00000 6.92820i −0.143684 0.248868i
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) 12.0000 + 20.7846i 0.430221 + 0.745164i
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) −9.00000 15.5885i −0.321839 0.557442i
\(783\) 0 0
\(784\) 0 0
\(785\) 19.5000 33.7750i 0.695985 1.20548i
\(786\) 0 0
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) −7.50000 + 12.9904i −0.266838 + 0.462177i
\(791\) 0 0
\(792\) 0 0
\(793\) −5.00000 8.66025i −0.177555 0.307535i
\(794\) −13.0000 22.5167i −0.461353 0.799086i
\(795\) 0 0
\(796\) −7.00000 + 12.1244i −0.2481