Properties

Label 2646.2.e.f.1549.1
Level $2646$
Weight $2$
Character 2646.1549
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 1549.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1549
Dual form 2646.2.e.f.2125.1

$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 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 −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) −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 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 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 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 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 −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) −1.00000 1.73205i −0.152499 0.264135i 0.779647 0.626219i \(-0.215399\pi\)
−0.932145 + 0.362084i \(0.882065\pi\)
\(44\) −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 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 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 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −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 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 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 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0 0
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) −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 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 18.0000 1.71623
\(111\) 0 0
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) 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 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) 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 −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 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 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −11.5000 + 19.9186i −0.935857 + 1.62095i −0.162758 + 0.986666i \(0.552039\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 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 −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 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 0.977138 + 0.212607i \(0.0681952\pi\)
−0.304446 + 0.952529i \(0.598471\pi\)
\(180\) 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 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −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 −0.970229 0.242190i \(-0.922134\pi\)
0.694857 + 0.719148i \(0.255467\pi\)
\(212\) 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 0.770097 + 0.637927i \(0.220208\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.50000 12.9904i 0.498893 0.864107i
\(227\) −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i \(-0.999189\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) 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 −0.680135 0.733087i \(-0.738079\pi\)
0.974939 + 0.222470i \(0.0714120\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i \(-0.994563\pi\)
0.514719 + 0.857359i \(0.327896\pi\)
\(240\) 0 0
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) −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 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 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 0.336270 + 0.941766i \(0.390834\pi\)
−0.983728 + 0.179664i \(0.942499\pi\)
\(264\) 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 0.695606 0.718423i \(-0.255136\pi\)
−0.969976 + 0.243201i \(0.921803\pi\)
\(270\) 0 0
\(271\) 14.0000 24.2487i 0.850439 1.47300i −0.0303728 0.999539i \(-0.509669\pi\)
0.880812 0.473466i \(-0.156997\pi\)
\(272\) 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 −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −2.50000 + 4.33013i −0.149940 + 0.259704i
\(279\) 0 0
\(280\) 0 0
\(281\) −13.5000 23.3827i −0.805342 1.39489i −0.916060 0.401042i \(-0.868648\pi\)
0.110717 0.993852i \(-0.464685\pi\)
\(282\) 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 −0.906509 0.422186i \(-0.861263\pi\)
0.818878 + 0.573967i \(0.194596\pi\)
\(294\) 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 −0.393730 0.919226i \(-0.628816\pi\)
0.992938 0.118633i \(-0.0378512\pi\)
\(338\) 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 −0.969885 0.243563i \(-0.921684\pi\)
0.274011 0.961727i \(-0.411649\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.00000 + 5.19615i −0.159901 + 0.276956i
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 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 −0.902891 0.429870i \(-0.858559\pi\)
0.823724 + 0.566991i \(0.191893\pi\)
\(360\) 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 −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 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 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) −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 0.539076 0.842257i \(-0.318774\pi\)
−0.998954 + 0.0457244i \(0.985440\pi\)
\(384\) 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 −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 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 0.330075 + 0.943955i \(0.392926\pi\)
−0.982526 + 0.186124i \(0.940407\pi\)
\(398\) −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 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 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 −0.622601 0.782540i \(-0.713924\pi\)
0.989000 + 0.147918i \(0.0472572\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) −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 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 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 −0.938386 0.345589i \(-0.887679\pi\)
0.169904 0.985461i \(-0.445654\pi\)
\(462\) 0 0
\(463\) 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i \(-0.735652\pi\)
0.976607 + 0.215032i \(0.0689855\pi\)
\(464\) 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 −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 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 −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) 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 −0.981374 0.192109i \(-0.938467\pi\)
0.324316 0.945949i \(-0.394866\pi\)
\(488\) 5.00000 0.226339
\(489\) 0 0
\(490\) 0 0
\(491\) 9.00000 15.5885i 0.406164 0.703497i −0.588292 0.808649i \(-0.700199\pi\)
0.994456 + 0.105151i \(0.0335327\pi\)
\(492\) 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 −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) −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 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 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 0.999551 + 0.0299693i \(0.00954094\pi\)
−0.473821 + 0.880621i \(0.657126\pi\)
\(522\) 0 0
\(523\) 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i \(-0.741597\pi\)
0.972421 + 0.233233i \(0.0749303\pi\)
\(524\) −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 0.0911008 + 0.995842i \(0.470961\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) 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 −0.973715 0.227768i \(-0.926857\pi\)
0.289605 0.957146i \(-0.406476\pi\)
\(548\) 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 −0.999952 0.00979220i \(-0.996883\pi\)
0.491496 0.870880i \(-0.336450\pi\)
\(558\) 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 0.904649 0.426158i \(-0.140133\pi\)
−0.821388 + 0.570370i \(0.806800\pi\)
\(578\) −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 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 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 0.687203 0.726465i \(-0.258838\pi\)
−0.972739 + 0.231903i \(0.925505\pi\)
\(602\) 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 0.998154 0.0607380i \(-0.0193454\pi\)
−0.551678 + 0.834058i \(0.686012\pi\)
\(608\) 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 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) −25.0000 −1.00892
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 36.3731i 0.845428 1.46432i −0.0398207 0.999207i \(-0.512679\pi\)
0.885249 0.465118i \(-0.153988\pi\)
\(618\) 0 0
\(619\) 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i \(-0.788405\pi\)
0.927752 + 0.373198i \(0.121739\pi\)
\(620\) −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 −0.466029 0.884769i \(-0.654316\pi\)
0.999247 0.0387913i \(-0.0123508\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 42.0000 1.65247
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 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 −0.966910 0.255119i \(-0.917885\pi\)
0.262515 0.964928i \(-0.415448\pi\)
\(654\) 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 0.907122 + 0.420869i \(0.138275\pi\)
−0.0890776 + 0.996025i \(0.528392\pi\)
\(660\) 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 0.963679 + 0.267063i \(0.0860531\pi\)
−0.250557 + 0.968102i \(0.580614\pi\)
\(674\) 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 0.802905 0.596107i \(-0.203287\pi\)
−0.917697 + 0.397282i \(0.869953\pi\)
\(684\) 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 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) 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 0.782267 0.622944i \(-0.214063\pi\)
−0.930618 + 0.365991i \(0.880730\pi\)
\(728\) 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 −0.999136 0.0415715i \(-0.986764\pi\)
0.463566 0.886062i \(-0.346570\pi\)
\(734\) −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 0.521475 0.853266i \(-0.325382\pi\)
−0.999688 + 0.0249776i \(0.992049\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 31.1769i 0.660356 1.14377i −0.320166 0.947361i \(-0.603739\pi\)
0.980522 0.196409i \(-0.0629279\pi\)
\(744\) 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 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) 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 −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 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 −0.964193 0.265200i \(-0.914562\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 17.0000 0.611843
\(773\) −25.5000 44.1673i −0.917171 1.58859i −0.803691 0.595047i \(-0.797133\pi\)
−0.113480 0.993540i \(-0.536200\pi\)
\(774\) 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 −0.248108