Properties

Label 2646.2.h.a.667.1
Level $2646$
Weight $2$
Character 2646.667
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.h (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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.a.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} -3.00000 q^{23} +4.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-1.00000 + 1.73205i) q^{37} +7.00000 q^{38} -3.00000 q^{40} +(-1.00000 + 1.73205i) q^{43} +(-3.00000 + 5.19615i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{52} +(3.00000 + 5.19615i) q^{53} -18.0000 q^{55} -6.00000 q^{58} +(2.50000 + 4.33013i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{68} -3.00000 q^{71} +(1.00000 + 1.73205i) q^{73} +2.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(-2.50000 - 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-6.00000 + 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +2.00000 q^{86} +6.00000 q^{88} +(1.50000 - 2.59808i) q^{92} +(10.5000 - 18.1865i) q^{95} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 6 q^{5} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} - 6 q^{5} + 2 q^{8} + 3 q^{10} + 12 q^{11} + 2 q^{13} - q^{16} - 6 q^{17} - 7 q^{19} + 3 q^{20} - 6 q^{22} - 6 q^{23} + 8 q^{25} + 2 q^{26} + 6 q^{29} + 2 q^{31} - q^{32} - 6 q^{34} - 2 q^{37} + 14 q^{38} - 6 q^{40} - 2 q^{43} - 6 q^{44} + 3 q^{46} - 4 q^{50} - 4 q^{52} + 6 q^{53} - 36 q^{55} - 12 q^{58} + 5 q^{61} - 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} + 12 q^{68} - 6 q^{71} + 2 q^{73} + 4 q^{74} - 7 q^{76} - 5 q^{79} + 3 q^{80} - 12 q^{83} + 18 q^{85} + 4 q^{86} + 12 q^{88} + 3 q^{92} + 21 q^{95} + 2 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 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
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 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 \(0.219235\pi\)
\(38\) 7.00000 1.13555
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 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
\(58\) −6.00000 −0.787839
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 6.00000 0.727607
\(69\) 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 \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 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 \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) 2.00000 0.215666
\(87\) 0 0
\(88\) 6.00000 0.639602
\(89\) 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
\(95\) 10.5000 18.1865i 1.07728 1.86590i
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 9.00000 0.895533 0.447767 0.894150i \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 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 \(0.674364\pi\)
\(110\) 9.00000 + 15.5885i 0.858116 + 1.48630i
\(111\) 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
\(115\) 9.00000 0.839254
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 2.50000 4.33013i 0.226339 0.392031i
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) −9.00000 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.50000 + 2.59808i 0.125877 + 0.218026i
\(143\) 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
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 23.0000 1.87171 0.935857 0.352381i \(-0.114628\pi\)
0.935857 + 0.352381i \(0.114628\pi\)
\(152\) −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
\(157\) −6.50000 + 11.2583i −0.518756 + 0.898513i 0.481006 + 0.876717i \(0.340272\pi\)
−0.999762 + 0.0217953i \(0.993062\pi\)
\(158\) −2.50000 + 4.33013i −0.198889 + 0.344486i
\(159\) 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
\(166\) 12.0000 0.931381
\(167\) 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
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 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 \(-0.120568\pi\)
0.929118 + 0.369784i \(0.120568\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.00000 −0.221163
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 0 0
\(187\) −18.0000 31.1769i −1.31629 2.27988i
\(188\) 0 0
\(189\) 0 0
\(190\) −21.0000 −1.52350
\(191\) −4.50000 7.79423i −0.325609 0.563971i 0.656027 0.754738i \(-0.272236\pi\)
−0.981635 + 0.190767i \(0.938902\pi\)
\(192\) 0 0
\(193\) −8.50000 + 14.7224i −0.611843 + 1.05974i 0.379086 + 0.925361i \(0.376238\pi\)
−0.990930 + 0.134382i \(0.957095\pi\)
\(194\) −2.00000 −0.143592
\(195\) 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 \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) 4.00000 0.282843
\(201\) 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 \(0.922134\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 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
\(220\) 9.00000 15.5885i 0.606780 1.05097i
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) −14.0000 + 24.2487i −0.937509 + 1.62381i −0.167412 + 0.985887i \(0.553541\pi\)
−0.770097 + 0.637927i \(0.779792\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.50000 12.9904i 0.498893 0.864107i
\(227\) −15.0000 −0.995585 −0.497792 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) 0 0
\(229\) 1.00000 0.0660819 0.0330409 0.999454i \(-0.489481\pi\)
0.0330409 + 0.999454i \(0.489481\pi\)
\(230\) −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 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) −12.5000 21.6506i −0.803530 1.39176i
\(243\) 0 0
\(244\) −5.00000 −0.320092
\(245\) 0 0
\(246\) 0 0
\(247\) −14.0000 −0.890799
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) 0 0
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) −8.50000 14.7224i −0.533337 0.923768i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) 4.50000 + 7.79423i 0.278011 + 0.481529i
\(263\) 21.0000 1.29492 0.647458 0.762101i \(-0.275832\pi\)
0.647458 + 0.762101i \(0.275832\pi\)
\(264\) 0 0
\(265\) −9.00000 15.5885i −0.552866 0.957591i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 4.50000 + 7.79423i 0.274370 + 0.475223i 0.969976 0.243201i \(-0.0781974\pi\)
−0.695606 + 0.718423i \(0.744864\pi\)
\(270\) 0 0
\(271\) −14.0000 + 24.2487i −0.850439 + 1.47300i 0.0303728 + 0.999539i \(0.490331\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 24.0000 1.44725
\(276\) 0 0
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) 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
\(283\) −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i \(0.357681\pi\)
−0.997076 + 0.0764162i \(0.975652\pi\)
\(284\) 1.50000 2.59808i 0.0890086 0.154167i
\(285\) 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
\(290\) 18.0000 1.05700
\(291\) 0 0
\(292\) −2.00000 −0.117041
\(293\) 1.50000 + 2.59808i 0.0876309 + 0.151781i 0.906509 0.422186i \(-0.138737\pi\)
−0.818878 + 0.573967i \(0.805404\pi\)
\(294\) 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
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) −11.5000 19.9186i −0.661751 1.14619i
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) −7.50000 12.9904i −0.429449 0.743827i
\(306\) 0 0
\(307\) 25.0000 1.42683 0.713413 0.700744i \(-0.247149\pi\)
0.713413 + 0.700744i \(0.247149\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.00000 0.340777
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) −3.00000 −0.167705
\(321\) 0 0
\(322\) 0 0
\(323\) 42.0000 2.33694
\(324\) 0 0
\(325\) 4.00000 + 6.92820i 0.221880 + 0.384308i
\(326\) 2.00000 0.110770
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0000 22.5167i −0.714545 1.23763i −0.963135 0.269019i \(-0.913301\pi\)
0.248590 0.968609i \(-0.420033\pi\)
\(332\) −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 \(0.628816\pi\)
\(338\) −9.00000 −0.489535
\(339\) 0 0
\(340\) −18.0000 −0.976187
\(341\) 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
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −12.0000 + 20.7846i −0.644194 + 1.11578i 0.340293 + 0.940319i \(0.389474\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(348\) 0 0
\(349\) 13.0000 22.5167i 0.695874 1.20529i −0.274011 0.961727i \(-0.588351\pi\)
0.969885 0.243563i \(-0.0783162\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.00000 + 5.19615i −0.159901 + 0.276956i
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 9.00000 0.477670
\(356\) 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
\(362\) −12.5000 21.6506i −0.656985 1.13793i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.00000 5.19615i −0.157027 0.271979i
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) −18.0000 + 31.1769i −0.930758 + 1.61212i
\(375\) 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 \(0.483642\pi\)
\(380\) 10.5000 + 18.1865i 0.538639 + 0.932949i
\(381\) 0 0
\(382\) −4.50000 + 7.79423i −0.230240 + 0.398787i
\(383\) −18.0000 −0.919757 −0.459879 0.887982i \(-0.652107\pi\)
−0.459879 + 0.887982i \(0.652107\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.0000 0.865277
\(387\) 0 0
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) 9.00000 + 15.5885i 0.455150 + 0.788342i
\(392\) 0 0
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 7.50000 + 12.9904i 0.377366 + 0.653617i
\(396\) 0 0
\(397\) 13.0000 22.5167i 0.652451 1.13008i −0.330075 0.943955i \(-0.607074\pi\)
0.982526 0.186124i \(-0.0595926\pi\)
\(398\) 7.00000 12.1244i 0.350878 0.607739i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) −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
\(409\) 16.0000 27.7128i 0.791149 1.37031i −0.134107 0.990967i \(-0.542817\pi\)
0.925256 0.379344i \(-0.123850\pi\)
\(410\) 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
\(416\) −2.00000 −0.0980581
\(417\) 0 0
\(418\) 42.0000 2.05429
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) 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
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) −6.00000 −0.289346
\(431\) 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 \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 10.5000 18.1865i 0.502283 0.869980i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −18.0000 −0.858116
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i \(-0.0260248\pi\)
−0.569057 + 0.822298i \(0.692691\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 28.0000 1.32584
\(447\) 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
\(452\) −15.0000 −0.705541
\(453\) 0 0
\(454\) 7.50000 + 12.9904i 0.351992 + 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) −14.5000 25.1147i −0.678281 1.17482i −0.975498 0.220008i \(-0.929392\pi\)
0.297217 0.954810i \(-0.403942\pi\)
\(458\) −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 \(-0.554346\pi\)
0.938386 0.345589i \(-0.112321\pi\)
\(462\) 0 0
\(463\) 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i \(-0.0689855\pi\)
−0.674526 + 0.738251i \(0.735652\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −9.00000 −0.416917
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 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
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 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 \(-0.394866\pi\)
\(488\) 2.50000 + 4.33013i 0.113170 + 0.196016i
\(489\) 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
\(493\) −36.0000 −1.62136
\(494\) 7.00000 + 12.1244i 0.314945 + 0.545501i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 0 0
\(502\) −1.50000 2.59808i −0.0669483 0.115958i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) −27.0000 −1.20148
\(506\) 9.00000 + 15.5885i 0.400099 + 0.692991i
\(507\) 0 0
\(508\) −8.50000 + 14.7224i −0.377127 + 0.653202i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −9.00000 15.5885i −0.396973 0.687577i
\(515\) −30.0000 −1.32196
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −12.0000 20.7846i −0.525730 0.910590i −0.999551 0.0299693i \(-0.990459\pi\)
0.473821 0.880621i \(-0.342874\pi\)
\(522\) 0 0
\(523\) −6.50000 + 11.2583i −0.284225 + 0.492292i −0.972421 0.233233i \(-0.925070\pi\)
0.688196 + 0.725525i \(0.258403\pi\)
\(524\) 4.50000 7.79423i 0.196583 0.340492i
\(525\) 0 0
\(526\) −10.5000 18.1865i −0.457822 0.792971i
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −9.00000 + 15.5885i −0.390935 + 0.677119i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 18.0000 31.1769i 0.778208 1.34790i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 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 \(0.862372\pi\)
\(542\) 28.0000 1.20270
\(543\) 0 0
\(544\) 6.00000 0.257248
\(545\) −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
\(551\) 21.0000 + 36.3731i 0.894630 + 1.54954i
\(552\) 0 0
\(553\) 0 0
\(554\) 8.00000 + 13.8564i 0.339887 + 0.588702i
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) −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
\(562\) 27.0000 1.13893
\(563\) 16.5000 28.5788i 0.695392 1.20445i −0.274656 0.961542i \(-0.588564\pi\)
0.970048 0.242912i \(-0.0781026\pi\)
\(564\) 0 0
\(565\) −22.5000 38.9711i −0.946582 1.63953i
\(566\) 19.0000 0.798630
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −12.0000 −0.501745
\(573\) 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 \(-0.193200\pi\)
−0.904649 + 0.426158i \(0.859867\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) −9.00000 15.5885i −0.373705 0.647275i
\(581\) 0 0
\(582\) 0 0
\(583\) 18.0000 + 31.1769i 0.745484 + 1.29122i
\(584\) 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 \(-0.813614\pi\)
0.895320 + 0.445424i \(0.146947\pi\)
\(588\) 0 0
\(589\) 7.00000 + 12.1244i 0.288430 + 0.499575i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 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
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) 7.00000 12.1244i 0.285536 0.494563i −0.687203 0.726465i \(-0.741162\pi\)
0.972739 + 0.231903i \(0.0744951\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −11.5000 + 19.9186i −0.467928 + 0.810476i
\(605\) −75.0000 −3.04918
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) −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 \(0.884985\pi\)
\(614\) −12.5000 21.6506i −0.504459 0.873749i
\(615\) 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
\(619\) 7.00000 0.281354 0.140677 0.990056i \(-0.455072\pi\)
0.140677 + 0.990056i \(0.455072\pi\)
\(620\) −3.00000 5.19615i −0.120483 0.208683i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 0 0
\(628\) −6.50000 11.2583i −0.259378 0.449256i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −2.50000 4.33013i −0.0994447 0.172243i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −51.0000 −2.02387
\(636\) 0 0
\(637\) 0 0
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) −27.0000 −1.06644 −0.533218 0.845978i \(-0.679017\pi\)
−0.533218 + 0.845978i \(0.679017\pi\)
\(642\) 0 0
\(643\) −2.00000 3.46410i −0.0788723 0.136611i 0.823891 0.566748i \(-0.191799\pi\)
−0.902764 + 0.430137i \(0.858465\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −21.0000 36.3731i −0.826234 1.43108i
\(647\) 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
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 0 0
\(655\) 27.0000 1.05498
\(656\) 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
\(661\) 2.50000 4.33013i 0.0972387 0.168422i −0.813302 0.581842i \(-0.802332\pi\)
0.910541 + 0.413419i \(0.135666\pi\)
\(662\) −13.0000 + 22.5167i −0.505259 + 0.875135i
\(663\) 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
\(670\) −24.0000 −0.927201
\(671\) 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
\(677\) −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i \(-0.867705\pi\)
0.107772 0.994176i \(-0.465628\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 9.00000 + 15.5885i 0.345134 + 0.597790i
\(681\) 0 0
\(682\) −12.0000 −0.459504
\(683\) −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
\(688\) 2.00000 0.0762493
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 23.5000 + 40.7032i 0.893982 + 1.54842i 0.835059 + 0.550160i \(0.185433\pi\)
0.0589228 + 0.998263i \(0.481233\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) −7.50000 12.9904i −0.284491 0.492753i
\(696\) 0 0
\(697\) 0 0
\(698\) −26.0000 −0.984115
\(699\) 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
\(704\) 6.00000 0.226134
\(705\) 0 0
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) 0 0
\(708\) 0 0
\(709\) 26.0000 + 45.0333i 0.976450 + 1.69126i 0.675063 + 0.737760i \(0.264116\pi\)
0.301388 + 0.953502i \(0.402550\pi\)
\(710\) −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
\(716\) −18.0000 −0.672692
\(717\) 0 0
\(718\) 3.00000 0.111959
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) −12.5000 + 21.6506i −0.464559 + 0.804640i
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0 0
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3.00000 + 5.19615i −0.111035 + 0.192318i
\(731\) 12.0000 0.443836
\(732\) 0 0
\(733\) −29.0000 −1.07114 −0.535570 0.844491i \(-0.679903\pi\)
−0.535570 + 0.844491i \(0.679903\pi\)
\(734\) 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 \(0.992049\pi\)
\(740\) 3.00000 + 5.19615i 0.110282 + 0.191014i
\(741\) 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
\(745\) −18.0000 −0.659469
\(746\) −7.00000 12.1244i −0.256288 0.443904i
\(747\) 0 0
\(748\) 36.0000 1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) −31.0000 −1.13121 −0.565603 0.824678i \(-0.691357\pi\)
−0.565603 + 0.824678i \(0.691357\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) −69.0000 −2.51117
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −1.00000 1.73205i −0.0363216 0.0629109i
\(759\) 0 0
\(760\) 10.5000 18.1865i 0.380875 0.659695i
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 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 \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.50000 14.7224i −0.305922 0.529872i
\(773\) 25.5000 + 44.1673i 0.917171 + 1.58859i 0.803691 + 0.595047i \(0.202867\pi\)
0.113480 + 0.993540i \(0.463800\pi\)
\(774\) 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
\(781\) −18.0000 −0.644091
\(782\) 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
\(787\) 10.0000 17.3205i 0.356462 0.617409i −0.630905 0.775860i \(-0.717316\pi\)
0.987367 + 0.158450i \(0.0506498\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 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
\(794\) −26.0000 −0.922705