Newspace parameters
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(38.3512415037\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{105})\) |
|
|
Defining polynomial: |
\( x^{4} + 53x^{2} + 676 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.3 | ||
Root | \(-4.62348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.599 |
Dual form | 650.4.b.i.599.2 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | − 1.62348i | − 0.312438i | −0.987722 | − | 0.156219i | \(-0.950069\pi\) | ||||
0.987722 | − | 0.156219i | \(-0.0499306\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.24695 | 0.220927 | ||||||||
\(7\) | 2.62348i | 0.141654i | 0.997489 | + | 0.0708272i | \(0.0225639\pi\) | ||||
−0.997489 | + | 0.0708272i | \(0.977436\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 24.3643 | 0.902383 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.1174 | −1.40113 | −0.700567 | − | 0.713587i | \(-0.747069\pi\) | ||||
−0.700567 | + | 0.713587i | \(0.747069\pi\) | |||||||
\(12\) | 6.49390i | 0.156219i | ||||||||
\(13\) | − 13.0000i | − 0.277350i | ||||||||
\(14\) | −5.24695 | −0.100165 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 4.36433i | 0.0622650i | 0.999515 | + | 0.0311325i | \(0.00991138\pi\) | ||||
−0.999515 | + | 0.0311325i | \(0.990089\pi\) | |||||||
\(18\) | 48.7287i | 0.638081i | ||||||||
\(19\) | 47.4817 | 0.573318 | 0.286659 | − | 0.958033i | \(-0.407455\pi\) | ||||
0.286659 | + | 0.958033i | \(0.407455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.25915 | 0.0442582 | ||||||||
\(22\) | − 102.235i | − 0.990751i | ||||||||
\(23\) | 91.5991i | 0.830423i | 0.909725 | + | 0.415211i | \(0.136292\pi\) | ||||
−0.909725 | + | 0.415211i | \(0.863708\pi\) | |||||||
\(24\) | −12.9878 | −0.110464 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | − 83.3887i | − 0.594377i | ||||||||
\(28\) | − 10.4939i | − 0.0708272i | ||||||||
\(29\) | 139.988 | 0.896382 | 0.448191 | − | 0.893938i | \(-0.352068\pi\) | ||||
0.448191 | + | 0.893938i | \(0.352068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.1418 | 0.180427 | 0.0902133 | − | 0.995922i | \(-0.471245\pi\) | ||||
0.0902133 | + | 0.995922i | \(0.471245\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 82.9878i | 0.437767i | ||||||||
\(34\) | −8.72866 | −0.0440280 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −97.4573 | −0.451191 | ||||||||
\(37\) | − 377.482i | − 1.67723i | −0.544723 | − | 0.838616i | \(-0.683365\pi\) | ||||
0.544723 | − | 0.838616i | \(-0.316635\pi\) | |||||||
\(38\) | 94.9634i | 0.405397i | ||||||||
\(39\) | −21.1052 | −0.0866547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.71646 | −0.0293929 | −0.0146964 | − | 0.999892i | \(-0.504678\pi\) | ||||
−0.0146964 | + | 0.999892i | \(0.504678\pi\) | |||||||
\(42\) | 8.51830i | 0.0312953i | ||||||||
\(43\) | − 75.5991i | − 0.268111i | −0.990974 | − | 0.134055i | \(-0.957200\pi\) | ||||
0.990974 | − | 0.134055i | \(-0.0428000\pi\) | |||||||
\(44\) | 204.470 | 0.700567 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −183.198 | −0.587198 | ||||||||
\(47\) | 186.785i | 0.579689i | 0.957074 | + | 0.289845i | \(0.0936037\pi\) | ||||
−0.957074 | + | 0.289845i | \(0.906396\pi\) | |||||||
\(48\) | − 25.9756i | − 0.0781095i | ||||||||
\(49\) | 336.117 | 0.979934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.08538 | 0.0194539 | ||||||||
\(52\) | 52.0000i | 0.138675i | ||||||||
\(53\) | − 236.457i | − 0.612828i | −0.951898 | − | 0.306414i | \(-0.900871\pi\) | ||||
0.951898 | − | 0.306414i | \(-0.0991293\pi\) | |||||||
\(54\) | 166.777 | 0.420288 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 20.9878 | 0.0500824 | ||||||||
\(57\) | − 77.0854i | − 0.179126i | ||||||||
\(58\) | 279.976i | 0.633838i | ||||||||
\(59\) | 4.36433 | 0.00963029 | 0.00481514 | − | 0.999988i | \(-0.498467\pi\) | ||||
0.00481514 | + | 0.999988i | \(0.498467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 380.360 | 0.798362 | 0.399181 | − | 0.916872i | \(-0.369295\pi\) | ||||
0.399181 | + | 0.916872i | \(0.369295\pi\) | |||||||
\(62\) | 62.2835i | 0.127581i | ||||||||
\(63\) | 63.9192i | 0.127826i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −165.976 | −0.309548 | ||||||||
\(67\) | 98.2424i | 0.179138i | 0.995981 | + | 0.0895688i | \(0.0285489\pi\) | ||||
−0.995981 | + | 0.0895688i | \(0.971451\pi\) | |||||||
\(68\) | − 17.4573i | − 0.0311325i | ||||||||
\(69\) | 148.709 | 0.259456 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1168.46 | 1.95311 | 0.976554 | − | 0.215271i | \(-0.0690634\pi\) | ||||
0.976554 | + | 0.215271i | \(0.0690634\pi\) | |||||||
\(72\) | − 194.915i | − 0.319040i | ||||||||
\(73\) | 404.357i | 0.648307i | 0.946005 | + | 0.324153i | \(0.105079\pi\) | ||||
−0.946005 | + | 0.324153i | \(0.894921\pi\) | |||||||
\(74\) | 754.963 | 1.18598 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −189.927 | −0.286659 | ||||||||
\(77\) | − 134.105i | − 0.198477i | ||||||||
\(78\) | − 42.2104i | − 0.0612741i | ||||||||
\(79\) | 856.748 | 1.22015 | 0.610074 | − | 0.792344i | \(-0.291140\pi\) | ||||
0.610074 | + | 0.792344i | \(0.291140\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 522.457 | 0.716677 | ||||||||
\(82\) | − 15.4329i | − 0.0207839i | ||||||||
\(83\) | 920.898i | 1.21785i | 0.793227 | + | 0.608926i | \(0.208399\pi\) | ||||
−0.793227 | + | 0.608926i | \(0.791601\pi\) | |||||||
\(84\) | −17.0366 | −0.0221291 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 151.198 | 0.189583 | ||||||||
\(87\) | − 227.267i | − 0.280064i | ||||||||
\(88\) | 408.939i | 0.495376i | ||||||||
\(89\) | 1526.04 | 1.81753 | 0.908763 | − | 0.417312i | \(-0.137028\pi\) | ||||
0.908763 | + | 0.417312i | \(0.137028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.1052 | 0.0392878 | ||||||||
\(92\) | − 366.396i | − 0.415211i | ||||||||
\(93\) | − 50.5579i | − 0.0563721i | ||||||||
\(94\) | −373.570 | −0.409902 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 51.9512 | 0.0552318 | ||||||||
\(97\) | − 960.979i | − 1.00590i | −0.864315 | − | 0.502952i | \(-0.832247\pi\) | ||||
0.864315 | − | 0.502952i | \(-0.167753\pi\) | |||||||
\(98\) | 672.235i | 0.692918i | ||||||||
\(99\) | −1245.44 | −1.26436 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 848.854 | 0.836278 | 0.418139 | − | 0.908383i | \(-0.362682\pi\) | ||||
0.418139 | + | 0.908383i | \(0.362682\pi\) | |||||||
\(102\) | 14.1708i | 0.0137560i | ||||||||
\(103\) | 1819.89i | 1.74096i | 0.492203 | + | 0.870480i | \(0.336192\pi\) | ||||
−0.492203 | + | 0.870480i | \(0.663808\pi\) | |||||||
\(104\) | −104.000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 472.915 | 0.433335 | ||||||||
\(107\) | − 165.008i | − 0.149083i | −0.997218 | − | 0.0745415i | \(-0.976251\pi\) | ||||
0.997218 | − | 0.0745415i | \(-0.0237493\pi\) | |||||||
\(108\) | 333.555i | 0.297188i | ||||||||
\(109\) | −920.719 | −0.809073 | −0.404536 | − | 0.914522i | \(-0.632567\pi\) | ||||
−0.404536 | + | 0.914522i | \(0.632567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −612.832 | −0.524031 | ||||||||
\(112\) | 41.9756i | 0.0354136i | ||||||||
\(113\) | − 965.986i | − 0.804180i | −0.915600 | − | 0.402090i | \(-0.868284\pi\) | ||||
0.915600 | − | 0.402090i | \(-0.131716\pi\) | |||||||
\(114\) | 154.171 | 0.126662 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −559.951 | −0.448191 | ||||||||
\(117\) | − 316.736i | − 0.250276i | ||||||||
\(118\) | 8.72866i | 0.00680964i | ||||||||
\(119\) | −11.4497 | −0.00882011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1281.99 | 0.963175 | ||||||||
\(122\) | 760.719i | 0.564527i | ||||||||
\(123\) | 12.5275i | 0.00918345i | ||||||||
\(124\) | −124.567 | −0.0902133 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −127.838 | −0.0903869 | ||||||||
\(127\) | − 1105.46i | − 0.772393i | −0.922417 | − | 0.386196i | \(-0.873789\pi\) | ||||
0.922417 | − | 0.386196i | \(-0.126211\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | −122.733 | −0.0837679 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 700.020 | 0.466878 | 0.233439 | − | 0.972371i | \(-0.425002\pi\) | ||||
0.233439 | + | 0.972371i | \(0.425002\pi\) | |||||||
\(132\) | − 331.951i | − 0.218884i | ||||||||
\(133\) | 124.567i | 0.0812131i | ||||||||
\(134\) | −196.485 | −0.126669 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34.9146 | 0.0220140 | ||||||||
\(137\) | 1230.03i | 0.767070i | 0.923526 | + | 0.383535i | \(0.125293\pi\) | ||||
−0.923526 | + | 0.383535i | \(0.874707\pi\) | |||||||
\(138\) | 297.418i | 0.183463i | ||||||||
\(139\) | 1004.05 | 0.612679 | 0.306340 | − | 0.951922i | \(-0.400896\pi\) | ||||
0.306340 | + | 0.951922i | \(0.400896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 303.241 | 0.181117 | ||||||||
\(142\) | 2336.92i | 1.38106i | ||||||||
\(143\) | 664.526i | 0.388605i | ||||||||
\(144\) | 389.829 | 0.225596 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −808.713 | −0.458422 | ||||||||
\(147\) | − 545.678i | − 0.306169i | ||||||||
\(148\) | 1509.93i | 0.838616i | ||||||||
\(149\) | −2310.81 | −1.27053 | −0.635264 | − | 0.772295i | \(-0.719109\pi\) | ||||
−0.635264 | + | 0.772295i | \(0.719109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2268.83 | 1.22275 | 0.611374 | − | 0.791341i | \(-0.290617\pi\) | ||||
0.611374 | + | 0.791341i | \(0.290617\pi\) | |||||||
\(152\) | − 379.854i | − 0.202699i | ||||||||
\(153\) | 106.334i | 0.0561868i | ||||||||
\(154\) | 268.210 | 0.140344 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 84.4207 | 0.0433274 | ||||||||
\(157\) | − 1943.62i | − 0.988011i | −0.869459 | − | 0.494006i | \(-0.835532\pi\) | ||||
0.869459 | − | 0.494006i | \(-0.164468\pi\) | |||||||
\(158\) | 1713.50i | 0.862775i | ||||||||
\(159\) | −383.883 | −0.191471 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −240.308 | −0.117633 | ||||||||
\(162\) | 1044.91i | 0.506767i | ||||||||
\(163\) | − 311.814i | − 0.149835i | −0.997190 | − | 0.0749177i | \(-0.976131\pi\) | ||||
0.997190 | − | 0.0749177i | \(-0.0238694\pi\) | |||||||
\(164\) | 30.8658 | 0.0146964 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1841.80 | −0.861151 | ||||||||
\(167\) | 331.570i | 0.153639i | 0.997045 | + | 0.0768194i | \(0.0244765\pi\) | ||||
−0.997045 | + | 0.0768194i | \(0.975524\pi\) | |||||||
\(168\) | − 34.0732i | − 0.0156476i | ||||||||
\(169\) | −169.000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1156.86 | 0.517353 | ||||||||
\(172\) | 302.396i | 0.134055i | ||||||||
\(173\) | 234.096i | 0.102879i | 0.998676 | + | 0.0514393i | \(0.0163809\pi\) | ||||
−0.998676 | + | 0.0514393i | \(0.983619\pi\) | |||||||
\(174\) | 454.534 | 0.198035 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −817.878 | −0.350283 | ||||||||
\(177\) | − 7.08538i | − 0.00300887i | ||||||||
\(178\) | 3052.08i | 1.28519i | ||||||||
\(179\) | −21.5807 | −0.00901127 | −0.00450564 | − | 0.999990i | \(-0.501434\pi\) | ||||
−0.00450564 | + | 0.999990i | \(0.501434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1132.38 | 0.465024 | 0.232512 | − | 0.972594i | \(-0.425306\pi\) | ||||
0.232512 | + | 0.972594i | \(0.425306\pi\) | |||||||
\(182\) | 68.2104i | 0.0277807i | ||||||||
\(183\) | − 617.505i | − 0.249439i | ||||||||
\(184\) | 732.793 | 0.293599 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 101.116 | 0.0398611 | ||||||||
\(187\) | − 223.093i | − 0.0872416i | ||||||||
\(188\) | − 747.140i | − 0.289845i | ||||||||
\(189\) | 218.768 | 0.0841960 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1547.72 | −0.586331 | −0.293165 | − | 0.956062i | \(-0.594709\pi\) | ||||
−0.293165 | + | 0.956062i | \(0.594709\pi\) | |||||||
\(192\) | 103.902i | 0.0390547i | ||||||||
\(193\) | 1721.73i | 0.642140i | 0.947056 | + | 0.321070i | \(0.104042\pi\) | ||||
−0.947056 | + | 0.321070i | \(0.895958\pi\) | |||||||
\(194\) | 1921.96 | 0.711281 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1344.47 | −0.489967 | ||||||||
\(197\) | − 44.9786i | − 0.0162670i | −0.999967 | − | 0.00813349i | \(-0.997411\pi\) | ||||
0.999967 | − | 0.00813349i | \(-0.00258900\pi\) | |||||||
\(198\) | − 2490.88i | − 0.894036i | ||||||||
\(199\) | −2577.95 | −0.918323 | −0.459161 | − | 0.888353i | \(-0.651850\pi\) | ||||
−0.459161 | + | 0.888353i | \(0.651850\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 159.494 | 0.0559694 | ||||||||
\(202\) | 1697.71i | 0.591338i | ||||||||
\(203\) | 367.255i | 0.126976i | ||||||||
\(204\) | −28.3415 | −0.00972697 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3639.78 | −1.23105 | ||||||||
\(207\) | 2231.75i | 0.749359i | ||||||||
\(208\) | − 208.000i | − 0.0693375i | ||||||||
\(209\) | −2427.14 | −0.803296 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1434.93 | 0.468174 | 0.234087 | − | 0.972216i | \(-0.424790\pi\) | ||||
0.234087 | + | 0.972216i | \(0.424790\pi\) | |||||||
\(212\) | 945.829i | 0.306414i | ||||||||
\(213\) | − 1896.97i | − 0.610225i | ||||||||
\(214\) | 330.015 | 0.105418 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −667.110 | −0.210144 | ||||||||
\(217\) | 81.6997i | 0.0255582i | ||||||||
\(218\) | − 1841.44i | − 0.572101i | ||||||||
\(219\) | 656.463 | 0.202556 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 56.7363 | 0.0172692 | ||||||||
\(222\) | − 1225.66i | − 0.370546i | ||||||||
\(223\) | − 5222.63i | − 1.56831i | −0.620565 | − | 0.784155i | \(-0.713097\pi\) | ||||
0.620565 | − | 0.784155i | \(-0.286903\pi\) | |||||||
\(224\) | −83.9512 | −0.0250412 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1931.97 | 0.568641 | ||||||||
\(227\) | − 2349.65i | − 0.687011i | −0.939151 | − | 0.343506i | \(-0.888386\pi\) | ||||
0.939151 | − | 0.343506i | \(-0.111614\pi\) | |||||||
\(228\) | 308.342i | 0.0895632i | ||||||||
\(229\) | −317.860 | −0.0917238 | −0.0458619 | − | 0.998948i | \(-0.514603\pi\) | ||||
−0.0458619 | + | 0.998948i | \(0.514603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −217.716 | −0.0620117 | ||||||||
\(232\) | − 1119.90i | − 0.316919i | ||||||||
\(233\) | − 1295.68i | − 0.364303i | −0.983271 | − | 0.182151i | \(-0.941694\pi\) | ||||
0.983271 | − | 0.182151i | \(-0.0583061\pi\) | |||||||
\(234\) | 633.473 | 0.176972 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.4573 | −0.00481514 | ||||||||
\(237\) | − 1390.91i | − 0.381221i | ||||||||
\(238\) | − 22.8994i | − 0.00623676i | ||||||||
\(239\) | −2149.67 | −0.581801 | −0.290900 | − | 0.956753i | \(-0.593955\pi\) | ||||
−0.290900 | + | 0.956753i | \(0.593955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6687.39 | −1.78744 | −0.893719 | − | 0.448628i | \(-0.851913\pi\) | ||||
−0.893719 | + | 0.448628i | \(0.851913\pi\) | |||||||
\(242\) | 2563.97i | 0.681068i | ||||||||
\(243\) | − 3099.69i | − 0.818294i | ||||||||
\(244\) | −1521.44 | −0.399181 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −25.0550 | −0.00649368 | ||||||||
\(247\) | − 617.262i | − 0.159010i | ||||||||
\(248\) | − 249.134i | − 0.0637905i | ||||||||
\(249\) | 1495.05 | 0.380503 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 577.116 | 0.145128 | 0.0725642 | − | 0.997364i | \(-0.476882\pi\) | ||||
0.0725642 | + | 0.997364i | \(0.476882\pi\) | |||||||
\(252\) | − 255.677i | − 0.0639132i | ||||||||
\(253\) | − 4682.30i | − 1.16353i | ||||||||
\(254\) | 2210.92 | 0.546164 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4004.15i | 0.971876i | 0.873993 | + | 0.485938i | \(0.161522\pi\) | ||||
−0.873993 | + | 0.485938i | \(0.838478\pi\) | |||||||
\(258\) | − 245.466i | − 0.0592329i | ||||||||
\(259\) | 990.314 | 0.237587 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3410.71 | 0.808880 | ||||||||
\(262\) | 1400.04i | 0.330133i | ||||||||
\(263\) | 290.393i | 0.0680852i | 0.999420 | + | 0.0340426i | \(0.0108382\pi\) | ||||
−0.999420 | + | 0.0340426i | \(0.989162\pi\) | |||||||
\(264\) | 663.902 | 0.154774 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −249.134 | −0.0574263 | ||||||||
\(267\) | − 2477.49i | − 0.567864i | ||||||||
\(268\) | − 392.969i | − 0.0895688i | ||||||||
\(269\) | −1004.21 | −0.227612 | −0.113806 | − | 0.993503i | \(-0.536304\pi\) | ||||
−0.113806 | + | 0.993503i | \(0.536304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5506.55 | 1.23431 | 0.617157 | − | 0.786840i | \(-0.288284\pi\) | ||||
0.617157 | + | 0.786840i | \(0.288284\pi\) | |||||||
\(272\) | 69.8292i | 0.0155662i | ||||||||
\(273\) | − 55.3689i | − 0.0122750i | ||||||||
\(274\) | −2460.06 | −0.542400 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −594.835 | −0.129728 | ||||||||
\(277\) | 4208.88i | 0.912950i | 0.889736 | + | 0.456475i | \(0.150888\pi\) | ||||
−0.889736 | + | 0.456475i | \(0.849112\pi\) | |||||||
\(278\) | 2008.10i | 0.433230i | ||||||||
\(279\) | 758.748 | 0.162814 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6804.56 | −1.44458 | −0.722288 | − | 0.691592i | \(-0.756910\pi\) | ||||
−0.722288 | + | 0.691592i | \(0.756910\pi\) | |||||||
\(282\) | 606.482i | 0.128069i | ||||||||
\(283\) | − 3351.59i | − 0.703997i | −0.936001 | − | 0.351999i | \(-0.885502\pi\) | ||||
0.936001 | − | 0.351999i | \(-0.114498\pi\) | |||||||
\(284\) | −4673.84 | −0.976554 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1329.05 | −0.274785 | ||||||||
\(287\) | − 20.2439i | − 0.00416363i | ||||||||
\(288\) | 779.658i | 0.159520i | ||||||||
\(289\) | 4893.95 | 0.996123 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1560.13 | −0.314282 | ||||||||
\(292\) | − 1617.43i | − 0.324153i | ||||||||
\(293\) | − 3486.87i | − 0.695239i | −0.937636 | − | 0.347620i | \(-0.886990\pi\) | ||||
0.937636 | − | 0.347620i | \(-0.113010\pi\) | |||||||
\(294\) | 1091.36 | 0.216494 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3019.85 | −0.592991 | ||||||||
\(297\) | 4262.61i | 0.832801i | ||||||||
\(298\) | − 4621.62i | − 0.898399i | ||||||||
\(299\) | 1190.79 | 0.230318 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 198.332 | 0.0379790 | ||||||||
\(302\) | 4537.67i | 0.864614i | ||||||||
\(303\) | − 1378.09i | − 0.261285i | ||||||||
\(304\) | 759.707 | 0.143330 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −212.668 | −0.0397301 | ||||||||
\(307\) | − 8145.25i | − 1.51425i | −0.653271 | − | 0.757124i | \(-0.726604\pi\) | ||||
0.653271 | − | 0.757124i | \(-0.273396\pi\) | |||||||
\(308\) | 536.421i | 0.0992383i | ||||||||
\(309\) | 2954.54 | 0.543942 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −511.038 | −0.0931779 | −0.0465889 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465889 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(312\) | 168.841i | 0.0306371i | ||||||||
\(313\) | − 3285.96i | − 0.593397i | −0.954971 | − | 0.296699i | \(-0.904114\pi\) | ||||
0.954971 | − | 0.296699i | \(-0.0958857\pi\) | |||||||
\(314\) | 3887.24 | 0.698630 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3426.99 | −0.610074 | ||||||||
\(317\) | − 8375.89i | − 1.48403i | −0.670385 | − | 0.742014i | \(-0.733871\pi\) | ||||
0.670385 | − | 0.742014i | \(-0.266129\pi\) | |||||||
\(318\) | − 767.765i | − 0.135390i | ||||||||
\(319\) | −7155.81 | −1.25595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −267.886 | −0.0465792 | ||||||||
\(322\) | − 480.616i | − 0.0831791i | ||||||||
\(323\) | 207.226i | 0.0356977i | ||||||||
\(324\) | −2089.83 | −0.358338 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 623.628 | 0.105950 | ||||||||
\(327\) | 1494.77i | 0.252785i | ||||||||
\(328\) | 61.7317i | 0.0103920i | ||||||||
\(329\) | −490.026 | −0.0821155 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1475.80 | −0.245068 | −0.122534 | − | 0.992464i | \(-0.539102\pi\) | ||||
−0.122534 | + | 0.992464i | \(0.539102\pi\) | |||||||
\(332\) | − 3683.59i | − 0.608926i | ||||||||
\(333\) | − 9197.09i | − 1.51351i | ||||||||
\(334\) | −663.140 | −0.108639 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 68.1464 | 0.0110646 | ||||||||
\(337\) | − 9267.32i | − 1.49799i | −0.662575 | − | 0.748996i | \(-0.730536\pi\) | ||||
0.662575 | − | 0.748996i | \(-0.269464\pi\) | |||||||
\(338\) | − 338.000i | − 0.0543928i | ||||||||
\(339\) | −1568.25 | −0.251256 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1591.89 | −0.252802 | ||||||||
\(342\) | 2313.72i | 0.365823i | ||||||||
\(343\) | 1781.65i | 0.280466i | ||||||||
\(344\) | −604.793 | −0.0947914 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −468.192 | −0.0727461 | ||||||||
\(347\) | 12251.7i | 1.89541i | 0.319152 | + | 0.947703i | \(0.396602\pi\) | ||||
−0.319152 | + | 0.947703i | \(0.603398\pi\) | |||||||
\(348\) | 909.067i | 0.140032i | ||||||||
\(349\) | −9704.59 | −1.48847 | −0.744233 | − | 0.667920i | \(-0.767185\pi\) | ||||
−0.744233 | + | 0.667920i | \(0.767185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1084.05 | −0.164850 | ||||||||
\(352\) | − 1635.76i | − 0.247688i | ||||||||
\(353\) | − 10183.3i | − 1.53542i | −0.640797 | − | 0.767711i | \(-0.721396\pi\) | ||||
0.640797 | − | 0.767711i | \(-0.278604\pi\) | |||||||
\(354\) | 14.1708 | 0.00212759 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6104.16 | −0.908763 | ||||||||
\(357\) | 18.5883i | 0.00275574i | ||||||||
\(358\) | − 43.1614i | − 0.00637193i | ||||||||
\(359\) | −8393.64 | −1.23398 | −0.616991 | − | 0.786970i | \(-0.711649\pi\) | ||||
−0.616991 | + | 0.786970i | \(0.711649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4604.49 | −0.671306 | ||||||||
\(362\) | 2264.77i | 0.328822i | ||||||||
\(363\) | − 2081.27i | − 0.300933i | ||||||||
\(364\) | −136.421 | −0.0196439 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1235.01 | 0.176380 | ||||||||
\(367\) | 1694.93i | 0.241075i | 0.992709 | + | 0.120538i | \(0.0384618\pi\) | ||||
−0.992709 | + | 0.120538i | \(0.961538\pi\) | |||||||
\(368\) | 1465.59i | 0.207606i | ||||||||
\(369\) | −188.006 | −0.0265236 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 620.340 | 0.0868098 | ||||||||
\(372\) | 202.232i | 0.0281861i | ||||||||
\(373\) | 4925.86i | 0.683784i | 0.939739 | + | 0.341892i | \(0.111068\pi\) | ||||
−0.939739 | + | 0.341892i | \(0.888932\pi\) | |||||||
\(374\) | 446.186 | 0.0616891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1494.28 | 0.204951 | ||||||||
\(377\) | − 1819.84i | − 0.248612i | ||||||||
\(378\) | 437.537i | 0.0595356i | ||||||||
\(379\) | −4563.89 | −0.618552 | −0.309276 | − | 0.950972i | \(-0.600087\pi\) | ||||
−0.309276 | + | 0.950972i | \(0.600087\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1794.69 | −0.241325 | ||||||||
\(382\) | − 3095.44i | − 0.414598i | ||||||||
\(383\) | 6385.74i | 0.851948i | 0.904735 | + | 0.425974i | \(0.140068\pi\) | ||||
−0.904735 | + | 0.425974i | \(0.859932\pi\) | |||||||
\(384\) | −207.805 | −0.0276159 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3443.46 | −0.454061 | ||||||||
\(387\) | − 1841.92i | − 0.241938i | ||||||||
\(388\) | 3843.91i | 0.502952i | ||||||||
\(389\) | 12304.3 | 1.60374 | 0.801870 | − | 0.597498i | \(-0.203838\pi\) | ||||
0.801870 | + | 0.597498i | \(0.203838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −399.768 | −0.0517063 | ||||||||
\(392\) | − 2688.94i | − 0.346459i | ||||||||
\(393\) | − 1136.46i | − 0.145870i | ||||||||
\(394\) | 89.9572 | 0.0115025 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4981.76 | 0.632179 | ||||||||
\(397\) | − 3593.57i | − 0.454298i | −0.973860 | − | 0.227149i | \(-0.927060\pi\) | ||||
0.973860 | − | 0.227149i | \(-0.0729404\pi\) | |||||||
\(398\) | − 5155.91i | − 0.649352i | ||||||||
\(399\) | 202.232 | 0.0253740 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5943.15 | 0.740116 | 0.370058 | − | 0.929009i | \(-0.379338\pi\) | ||||
0.370058 | + | 0.929009i | \(0.379338\pi\) | |||||||
\(402\) | 318.988i | 0.0395763i | ||||||||
\(403\) | − 404.843i | − 0.0500414i | ||||||||
\(404\) | −3395.41 | −0.418139 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −734.509 | −0.0897859 | ||||||||
\(407\) | 19295.9i | 2.35003i | ||||||||
\(408\) | − 56.6830i | − 0.00687801i | ||||||||
\(409\) | 3673.76 | 0.444146 | 0.222073 | − | 0.975030i | \(-0.428718\pi\) | ||||
0.222073 | + | 0.975030i | \(0.428718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1996.92 | 0.239662 | ||||||||
\(412\) | − 7279.55i | − 0.870480i | ||||||||
\(413\) | 11.4497i | 0.00136417i | ||||||||
\(414\) | −4463.50 | −0.529877 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | − 1630.05i | − 0.191424i | ||||||||
\(418\) | − 4854.28i | − 0.568016i | ||||||||
\(419\) | 6367.72 | 0.742443 | 0.371221 | − | 0.928544i | \(-0.378939\pi\) | ||||
0.371221 | + | 0.928544i | \(0.378939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5184.48 | −0.600180 | −0.300090 | − | 0.953911i | \(-0.597017\pi\) | ||||
−0.300090 | + | 0.953911i | \(0.597017\pi\) | |||||||
\(422\) | 2869.86i | 0.331049i | ||||||||
\(423\) | 4550.89i | 0.523102i | ||||||||
\(424\) | −1891.66 | −0.216668 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3793.93 | 0.431495 | ||||||||
\(427\) | 997.864i | 0.113091i | ||||||||
\(428\) | 660.030i | 0.0745415i | ||||||||
\(429\) | 1078.84 | 0.121415 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6252.06 | 0.698727 | 0.349363 | − | 0.936987i | \(-0.386398\pi\) | ||||
0.349363 | + | 0.936987i | \(0.386398\pi\) | |||||||
\(432\) | − 1334.22i | − 0.148594i | ||||||||
\(433\) | 13563.3i | 1.50533i | 0.658402 | + | 0.752667i | \(0.271233\pi\) | ||||
−0.658402 | + | 0.752667i | \(0.728767\pi\) | |||||||
\(434\) | −163.399 | −0.0180724 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3682.88 | 0.404536 | ||||||||
\(437\) | 4349.28i | 0.476097i | ||||||||
\(438\) | 1312.93i | 0.143228i | ||||||||
\(439\) | −4955.82 | −0.538789 | −0.269394 | − | 0.963030i | \(-0.586824\pi\) | ||||
−0.269394 | + | 0.963030i | \(0.586824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8189.27 | 0.884275 | ||||||||
\(442\) | 113.473i | 0.0122112i | ||||||||
\(443\) | 10721.6i | 1.14988i | 0.818194 | + | 0.574942i | \(0.194975\pi\) | ||||
−0.818194 | + | 0.574942i | \(0.805025\pi\) | |||||||
\(444\) | 2451.33 | 0.262016 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10445.3 | 1.10896 | ||||||||
\(447\) | 3751.54i | 0.396961i | ||||||||
\(448\) | − 167.902i | − 0.0177068i | ||||||||
\(449\) | 3704.31 | 0.389348 | 0.194674 | − | 0.980868i | \(-0.437635\pi\) | ||||
0.194674 | + | 0.980868i | \(0.437635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 394.445 | 0.0411834 | ||||||||
\(452\) | 3863.94i | 0.402090i | ||||||||
\(453\) | − 3683.40i | − 0.382033i | ||||||||
\(454\) | 4699.30 | 0.485790 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −616.683 | −0.0633308 | ||||||||
\(457\) | 6710.74i | 0.686904i | 0.939170 | + | 0.343452i | \(0.111596\pi\) | ||||
−0.939170 | + | 0.343452i | \(0.888404\pi\) | |||||||
\(458\) | − 635.719i | − 0.0648585i | ||||||||
\(459\) | 363.936 | 0.0370089 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −977.491 | −0.0987555 | −0.0493777 | − | 0.998780i | \(-0.515724\pi\) | ||||
−0.0493777 | + | 0.998780i | \(0.515724\pi\) | |||||||
\(462\) | − 435.433i | − 0.0438489i | ||||||||
\(463\) | 14489.1i | 1.45435i | 0.686452 | + | 0.727176i | \(0.259167\pi\) | ||||
−0.686452 | + | 0.727176i | \(0.740833\pi\) | |||||||
\(464\) | 2239.80 | 0.224096 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2591.35 | 0.257601 | ||||||||
\(467\) | 14849.7i | 1.47144i | 0.677285 | + | 0.735721i | \(0.263156\pi\) | ||||
−0.677285 | + | 0.735721i | \(0.736844\pi\) | |||||||
\(468\) | 1266.95i | 0.125138i | ||||||||
\(469\) | −257.736 | −0.0253756 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3155.42 | −0.308692 | ||||||||
\(472\) | − 34.9146i | − 0.00340482i | ||||||||
\(473\) | 3864.43i | 0.375659i | ||||||||
\(474\) | 2781.82 | 0.269564 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 45.7988 | 0.00441005 | ||||||||
\(477\) | − 5761.12i | − 0.553006i | ||||||||
\(478\) | − 4299.33i | − 0.411395i | ||||||||
\(479\) | −8109.85 | −0.773588 | −0.386794 | − | 0.922166i | \(-0.626418\pi\) | ||||
−0.386794 | + | 0.922166i | \(0.626418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4907.26 | −0.465181 | ||||||||
\(482\) | − 13374.8i | − 1.26391i | ||||||||
\(483\) | 390.134i | 0.0367530i | ||||||||
\(484\) | −5127.94 | −0.481588 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6199.38 | 0.578621 | ||||||||
\(487\) | 1215.92i | 0.113138i | 0.998399 | + | 0.0565692i | \(0.0180162\pi\) | ||||
−0.998399 | + | 0.0565692i | \(0.981984\pi\) | |||||||
\(488\) | − 3042.88i | − 0.282264i | ||||||||
\(489\) | −506.222 | −0.0468143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12639.4 | −1.16173 | −0.580866 | − | 0.814000i | \(-0.697286\pi\) | ||||
−0.580866 | + | 0.814000i | \(0.697286\pi\) | |||||||
\(492\) | − 50.1099i | − 0.00459173i | ||||||||
\(493\) | 610.953i | 0.0558132i | ||||||||
\(494\) | 1234.52 | 0.112437 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 498.268 | 0.0451067 | ||||||||
\(497\) | 3065.43i | 0.276666i | ||||||||
\(498\) | 2990.11i | 0.269056i | ||||||||
\(499\) | −2658.21 | −0.238473 | −0.119236 | − | 0.992866i | \(-0.538045\pi\) | ||||
−0.119236 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 538.296 | 0.0480026 | ||||||||
\(502\) | 1154.23i | 0.102621i | ||||||||
\(503\) | 18698.8i | 1.65753i | 0.559599 | + | 0.828764i | \(0.310955\pi\) | ||||
−0.559599 | + | 0.828764i | \(0.689045\pi\) | |||||||
\(504\) | 511.354 | 0.0451935 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9364.61 | 0.822742 | ||||||||
\(507\) | 274.367i | 0.0240337i | ||||||||
\(508\) | 4421.85i | 0.386196i | ||||||||
\(509\) | 20005.8 | 1.74212 | 0.871062 | − | 0.491173i | \(-0.163432\pi\) | ||||
0.871062 | + | 0.491173i | \(0.163432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1060.82 | −0.0918354 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | − 3959.44i | − 0.340767i | ||||||||
\(514\) | −8008.30 | −0.687220 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 490.933 | 0.0418840 | ||||||||
\(517\) | − 9547.96i | − 0.812222i | ||||||||
\(518\) | 1980.63i | 0.168000i | ||||||||
\(519\) | 380.049 | 0.0321432 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9981.25 | −0.839321 | −0.419661 | − | 0.907681i | \(-0.637851\pi\) | ||||
−0.419661 | + | 0.907681i | \(0.637851\pi\) | |||||||
\(522\) | 6821.42i | 0.571964i | ||||||||
\(523\) | 398.152i | 0.0332887i | 0.999861 | + | 0.0166443i | \(0.00529831\pi\) | ||||
−0.999861 | + | 0.0166443i | \(0.994702\pi\) | |||||||
\(524\) | −2800.08 | −0.233439 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −580.786 | −0.0481435 | ||||||||
\(527\) | 135.913i | 0.0112343i | ||||||||
\(528\) | 1327.80i | 0.109442i | ||||||||
\(529\) | 3776.61 | 0.310398 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 106.334 | 0.00869020 | ||||||||
\(532\) | − 498.268i | − 0.0406065i | ||||||||
\(533\) | 100.314i | 0.00815212i | ||||||||
\(534\) | 4954.98 | 0.401541 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 785.939 | 0.0633347 | ||||||||
\(537\) | 35.0358i | 0.00281546i | ||||||||
\(538\) | − 2008.41i | − 0.160946i | ||||||||
\(539\) | −17181.4 | −1.37302 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7263.34 | 0.577219 | 0.288609 | − | 0.957447i | \(-0.406807\pi\) | ||||
0.288609 | + | 0.957447i | \(0.406807\pi\) | |||||||
\(542\) | 11013.1i | 0.872792i | ||||||||
\(543\) | − 1838.40i | − 0.145291i | ||||||||
\(544\) | −139.658 | −0.0110070 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 110.738 | 0.00867975 | ||||||||
\(547\) | − 16741.6i | − 1.30863i | −0.756222 | − | 0.654315i | \(-0.772957\pi\) | ||||
0.756222 | − | 0.654315i | \(-0.227043\pi\) | |||||||
\(548\) | − 4920.12i | − 0.383535i | ||||||||
\(549\) | 9267.21 | 0.720428 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6646.86 | 0.513912 | ||||||||
\(552\) | − 1189.67i | − 0.0917314i | ||||||||
\(553\) | 2247.66i | 0.172839i | ||||||||
\(554\) | −8417.76 | −0.645553 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4016.20 | −0.306340 | ||||||||
\(557\) | 6000.76i | 0.456482i | 0.973605 | + | 0.228241i | \(0.0732974\pi\) | ||||
−0.973605 | + | 0.228241i | \(0.926703\pi\) | |||||||
\(558\) | 1517.50i | 0.115127i | ||||||||
\(559\) | −982.788 | −0.0743605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −362.186 | −0.0272576 | ||||||||
\(562\) | − 13609.1i | − 1.02147i | ||||||||
\(563\) | − 147.660i | − 0.0110535i | −0.999985 | − | 0.00552674i | \(-0.998241\pi\) | ||||
0.999985 | − | 0.00552674i | \(-0.00175923\pi\) | |||||||
\(564\) | −1212.96 | −0.0905585 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6703.18 | 0.497801 | ||||||||
\(567\) | 1370.65i | 0.101520i | ||||||||
\(568\) | − 9347.68i | − 0.690528i | ||||||||
\(569\) | 19161.2 | 1.41174 | 0.705868 | − | 0.708343i | \(-0.250557\pi\) | ||||
0.705868 | + | 0.708343i | \(0.250557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20439.8 | 1.49804 | 0.749019 | − | 0.662549i | \(-0.230525\pi\) | ||||
0.749019 | + | 0.662549i | \(0.230525\pi\) | |||||||
\(572\) | − 2658.10i | − 0.194302i | ||||||||
\(573\) | 2512.69i | 0.183192i | ||||||||
\(574\) | 40.4879 | 0.00294413 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1559.32 | −0.112798 | ||||||||
\(577\) | − 22889.0i | − 1.65144i | −0.564081 | − | 0.825720i | \(-0.690769\pi\) | ||||
0.564081 | − | 0.825720i | \(-0.309231\pi\) | |||||||
\(578\) | 9787.91i | 0.704365i | ||||||||
\(579\) | 2795.19 | 0.200629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2415.95 | −0.172514 | ||||||||
\(582\) | − 3120.25i | − 0.222231i | ||||||||
\(583\) | 12087.1i | 0.858655i | ||||||||
\(584\) | 3234.85 | 0.229211 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6973.74 | 0.491608 | ||||||||
\(587\) | 1492.73i | 0.104960i | 0.998622 | + | 0.0524799i | \(0.0167126\pi\) | ||||
−0.998622 | + | 0.0524799i | \(0.983287\pi\) | |||||||
\(588\) | 2182.71i | 0.153084i | ||||||||
\(589\) | 1478.66 | 0.103442 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −73.0217 | −0.00508242 | ||||||||
\(592\) | − 6039.71i | − 0.419308i | ||||||||
\(593\) | 23920.6i | 1.65650i | 0.560360 | + | 0.828249i | \(0.310663\pi\) | ||||
−0.560360 | + | 0.828249i | \(0.689337\pi\) | |||||||
\(594\) | −8525.23 | −0.588879 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9243.23 | 0.635264 | ||||||||
\(597\) | 4185.24i | 0.286919i | ||||||||
\(598\) | 2381.58i | 0.162859i | ||||||||
\(599\) | 23867.0 | 1.62801 | 0.814005 | − | 0.580857i | \(-0.197283\pi\) | ||||
0.814005 | + | 0.580857i | \(0.197283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6618.71 | −0.449222 | −0.224611 | − | 0.974448i | \(-0.572111\pi\) | ||||
−0.224611 | + | 0.974448i | \(0.572111\pi\) | |||||||
\(602\) | 396.665i | 0.0268552i | ||||||||
\(603\) | 2393.61i | 0.161651i | ||||||||
\(604\) | −9075.34 | −0.611374 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2756.19 | 0.184756 | ||||||||
\(607\) | − 13982.7i | − 0.934994i | −0.883995 | − | 0.467497i | \(-0.845156\pi\) | ||||
0.883995 | − | 0.467497i | \(-0.154844\pi\) | |||||||
\(608\) | 1519.41i | 0.101349i | ||||||||
\(609\) | 596.229 | 0.0396723 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2428.21 | 0.160777 | ||||||||
\(612\) | − 425.336i | − 0.0280934i | ||||||||
\(613\) | − 4043.90i | − 0.266446i | −0.991086 | − | 0.133223i | \(-0.957467\pi\) | ||||
0.991086 | − | 0.133223i | \(-0.0425327\pi\) | |||||||
\(614\) | 16290.5 | 1.07074 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1072.84 | −0.0701721 | ||||||||
\(617\) | 2871.83i | 0.187384i | 0.995601 | + | 0.0936918i | \(0.0298668\pi\) | ||||
−0.995601 | + | 0.0936918i | \(0.970133\pi\) | |||||||
\(618\) | 5909.09i | 0.384625i | ||||||||
\(619\) | −26324.3 | −1.70931 | −0.854656 | − | 0.519195i | \(-0.826232\pi\) | ||||
−0.854656 | + | 0.519195i | \(0.826232\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7638.33 | 0.493584 | ||||||||
\(622\) | − 1022.08i | − 0.0658867i | ||||||||
\(623\) | 4003.53i | 0.257461i | ||||||||
\(624\) | −337.683 | −0.0216637 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6571.91 | 0.419595 | ||||||||
\(627\) | 3940.40i | 0.250980i | ||||||||
\(628\) | 7774.48i | 0.494006i | ||||||||
\(629\) | 1647.45 | 0.104433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17428.2 | −1.09953 | −0.549766 | − | 0.835319i | \(-0.685283\pi\) | ||||
−0.549766 | + | 0.835319i | \(0.685283\pi\) | |||||||
\(632\) | − 6853.99i | − 0.431388i | ||||||||
\(633\) | − 2329.57i | − 0.146275i | ||||||||
\(634\) | 16751.8 | 1.04937 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1535.53 | 0.0957354 | ||||||||
\(637\) | − 4369.53i | − 0.271785i | ||||||||
\(638\) | − 14311.6i | − 0.888092i | ||||||||
\(639\) | 28468.8 | 1.76245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22541.7 | 1.38899 | 0.694496 | − | 0.719496i | \(-0.255627\pi\) | ||||
0.694496 | + | 0.719496i | \(0.255627\pi\) | |||||||
\(642\) | − 535.772i | − 0.0329365i | ||||||||
\(643\) | 21498.3i | 1.31852i | 0.751913 | + | 0.659262i | \(0.229131\pi\) | ||||
−0.751913 | + | 0.659262i | \(0.770869\pi\) | |||||||
\(644\) | 961.232 | 0.0588165 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −414.451 | −0.0252421 | ||||||||
\(647\) | − 8290.26i | − 0.503746i | −0.967760 | − | 0.251873i | \(-0.918953\pi\) | ||||
0.967760 | − | 0.251873i | \(-0.0810466\pi\) | |||||||
\(648\) | − 4179.66i | − 0.253383i | ||||||||
\(649\) | −223.093 | −0.0134933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 132.637 | 0.00798536 | ||||||||
\(652\) | 1247.26i | 0.0749177i | ||||||||
\(653\) | 8650.10i | 0.518383i | 0.965826 | + | 0.259192i | \(0.0834562\pi\) | ||||
−0.965826 | + | 0.259192i | \(0.916544\pi\) | |||||||
\(654\) | −2989.53 | −0.178746 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −123.463 | −0.00734822 | ||||||||
\(657\) | 9851.88i | 0.585020i | ||||||||
\(658\) | − 980.052i | − 0.0580644i | ||||||||
\(659\) | 29128.3 | 1.72182 | 0.860908 | − | 0.508761i | \(-0.169896\pi\) | ||||
0.860908 | + | 0.508761i | \(0.169896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14221.5 | −0.836839 | −0.418420 | − | 0.908254i | \(-0.637416\pi\) | ||||
−0.418420 | + | 0.908254i | \(0.637416\pi\) | |||||||
\(662\) | − 2951.61i | − 0.173289i | ||||||||
\(663\) | − 92.1099i | − 0.00539555i | ||||||||
\(664\) | 7367.18 | 0.430576 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18394.2 | 1.07021 | ||||||||
\(667\) | 12822.8i | 0.744376i | ||||||||
\(668\) | − 1326.28i | − 0.0768194i | ||||||||
\(669\) | −8478.81 | −0.490000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19443.0 | −1.11861 | ||||||||
\(672\) | 136.293i | 0.00782382i | ||||||||
\(673\) | − 33065.1i | − 1.89386i | −0.321444 | − | 0.946929i | \(-0.604168\pi\) | ||||
0.321444 | − | 0.946929i | \(-0.395832\pi\) | |||||||
\(674\) | 18534.6 | 1.05924 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | − 24785.0i | − 1.40704i | −0.710675 | − | 0.703520i | \(-0.751610\pi\) | ||||
0.710675 | − | 0.703520i | \(-0.248390\pi\) | |||||||
\(678\) | − 3136.51i | − 0.177665i | ||||||||
\(679\) | 2521.10 | 0.142491 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3814.60 | −0.214648 | ||||||||
\(682\) | − 3183.77i | − 0.178758i | ||||||||
\(683\) | 8376.31i | 0.469269i | 0.972084 | + | 0.234634i | \(0.0753893\pi\) | ||||
−0.972084 | + | 0.234634i | \(0.924611\pi\) | |||||||
\(684\) | −4627.44 | −0.258676 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3563.30 | −0.198320 | ||||||||
\(687\) | 516.037i | 0.0286580i | ||||||||
\(688\) | − 1209.59i | − 0.0670276i | ||||||||
\(689\) | −3073.95 | −0.169968 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1387.54 | −0.0763883 | −0.0381942 | − | 0.999270i | \(-0.512161\pi\) | ||||
−0.0381942 | + | 0.999270i | \(0.512161\pi\) | |||||||
\(692\) | − 936.384i | − 0.0514393i | ||||||||
\(693\) | − 3267.38i | − 0.179102i | ||||||||
\(694\) | −24503.4 | −1.34026 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1818.13 | −0.0990175 | ||||||||
\(697\) | − 33.6772i | − 0.00183015i | ||||||||
\(698\) | − 19409.2i | − 1.05250i | ||||||||
\(699\) | −2103.50 | −0.113822 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23975.7 | −1.29180 | −0.645898 | − | 0.763424i | \(-0.723517\pi\) | ||||
−0.645898 | + | 0.763424i | \(0.723517\pi\) | |||||||
\(702\) | − 2168.11i | − 0.116567i | ||||||||
\(703\) | − 17923.5i | − 0.961588i | ||||||||
\(704\) | 3271.51 | 0.175142 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20366.7 | 1.08571 | ||||||||
\(707\) | 2226.95i | 0.118462i | ||||||||
\(708\) | 28.3415i | 0.00150443i | ||||||||
\(709\) | 6875.84 | 0.364214 | 0.182107 | − | 0.983279i | \(-0.441708\pi\) | ||||
0.182107 | + | 0.983279i | \(0.441708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20874.1 | 1.10104 | ||||||||
\(712\) | − 12208.3i | − 0.642593i | ||||||||
\(713\) | 2852.56i | 0.149830i | ||||||||
\(714\) | −37.1766 | −0.00194860 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 86.3228 | 0.00450564 | ||||||||
\(717\) | 3489.93i | 0.181777i | ||||||||
\(718\) | − 16787.3i | − 0.872557i | ||||||||
\(719\) | −35132.8 | −1.82230 | −0.911149 | − | 0.412078i | \(-0.864803\pi\) | ||||
−0.911149 | + | 0.412078i | \(0.864803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4774.43 | −0.246615 | ||||||||
\(722\) | − 9208.98i | − 0.474685i | ||||||||
\(723\) | 10856.8i | 0.558463i | ||||||||
\(724\) | −4529.53 | −0.232512 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4162.55 | 0.212791 | ||||||||
\(727\) | 21820.6i | 1.11318i | 0.830788 | + | 0.556589i | \(0.187890\pi\) | ||||
−0.830788 | + | 0.556589i | \(0.812110\pi\) | |||||||
\(728\) | − 272.841i | − 0.0138904i | ||||||||
\(729\) | 9074.07 | 0.461011 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 329.939 | 0.0166939 | ||||||||
\(732\) | 2470.02i | 0.124719i | ||||||||
\(733\) | 39336.5i | 1.98216i | 0.133258 | + | 0.991081i | \(0.457456\pi\) | ||||
−0.133258 | + | 0.991081i | \(0.542544\pi\) | |||||||
\(734\) | −3389.86 | −0.170466 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2931.17 | −0.146799 | ||||||||
\(737\) | − 5021.89i | − 0.250996i | ||||||||
\(738\) | − 376.013i | − 0.0187550i | ||||||||
\(739\) | −16015.2 | −0.797198 | −0.398599 | − | 0.917125i | \(-0.630503\pi\) | ||||
−0.398599 | + | 0.917125i | \(0.630503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1002.11 | −0.0496807 | ||||||||
\(742\) | 1240.68i | 0.0613838i | ||||||||
\(743\) | − 7885.18i | − 0.389340i | −0.980869 | − | 0.194670i | \(-0.937636\pi\) | ||||
0.980869 | − | 0.194670i | \(-0.0623635\pi\) | |||||||
\(744\) | −404.463 | −0.0199306 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9851.72 | −0.483508 | ||||||||
\(747\) | 22437.1i | 1.09897i | ||||||||
\(748\) | 892.372i | 0.0436208i | ||||||||
\(749\) | 432.893 | 0.0211183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22509.9 | −1.09374 | −0.546870 | − | 0.837218i | \(-0.684181\pi\) | ||||
−0.546870 | + | 0.837218i | \(0.684181\pi\) | |||||||
\(752\) | 2988.56i | 0.144922i | ||||||||
\(753\) | − 936.933i | − 0.0453436i | ||||||||
\(754\) | 3639.68 | 0.175795 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −875.073 | −0.0420980 | ||||||||
\(757\) | − 11376.9i | − 0.546234i | −0.961981 | − | 0.273117i | \(-0.911945\pi\) | ||||
0.961981 | − | 0.273117i | \(-0.0880546\pi\) | |||||||
\(758\) | − 9127.78i | − 0.437382i | ||||||||
\(759\) | −7601.61 | −0.363532 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1967.75 | −0.0937329 | −0.0468665 | − | 0.998901i | \(-0.514924\pi\) | ||||
−0.0468665 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(762\) | − 3589.38i | − 0.170642i | ||||||||
\(763\) | − 2415.48i | − 0.114609i | ||||||||
\(764\) | 6190.88 | 0.293165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12771.5 | −0.602418 | ||||||||
\(767\) | − 56.7363i | − 0.00267096i | ||||||||
\(768\) | − 415.610i | − 0.0195274i | ||||||||
\(769\) | 29055.2 | 1.36250 | 0.681248 | − | 0.732053i | \(-0.261438\pi\) | ||||
0.681248 | + | 0.732053i | \(0.261438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6500.64 | 0.303651 | ||||||||
\(772\) | − 6886.93i | − 0.321070i | ||||||||
\(773\) | − 17339.6i | − 0.806809i | −0.915022 | − | 0.403404i | \(-0.867827\pi\) | ||||
0.915022 | − | 0.403404i | \(-0.132173\pi\) | |||||||
\(774\) | 3683.84 | 0.171076 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7687.83 | −0.355640 | ||||||||
\(777\) | − 1607.75i | − 0.0742313i | ||||||||
\(778\) | 24608.7i | 1.13402i | ||||||||
\(779\) | −366.391 | −0.0168515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59728.6 | −2.73657 | ||||||||
\(782\) | − 799.537i | − 0.0365619i | ||||||||
\(783\) | − 11673.4i | − 0.532789i | ||||||||
\(784\) | 5377.88 | 0.244984 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2272.93 | 0.103146 | ||||||||
\(787\) | − 20499.1i | − 0.928482i | −0.885709 | − | 0.464241i | \(-0.846327\pi\) | ||||
0.885709 | − | 0.464241i | \(-0.153673\pi\) | |||||||
\(788\) | 179.914i | 0.00813349i | ||||||||
\(789\) | 471.446 | 0.0212724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2534.24 | 0.113916 | ||||||||
\(792\) | 9963.52i | 0.447018i | ||||||||
\(793\) | − 4944.68i | − 0.221426i | ||||||||
\(794\) | 7187.14 | 0.321237 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10311.8 | 0.459161 | ||||||||
\(797\) | 20639.2i | 0.917289i | 0.888620 | + | 0.458644i | \(0.151665\pi\) | ||||
−0.888620 | + | 0.458644i | \(0.848335\pi\) | |||||||
\(798\) | 404.463i | 0.0179422i | ||||||||
\(799\) | −815.191 | −0.0360944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37180.9 | 1.64010 | ||||||||
\(802\) | 11886.3i | 0.523341i | ||||||||
\(803\) | − 20669.7i | − 0.908364i | ||||||||
\(804\) | −637.976 | −0.0279847 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 809.686 | 0.0353846 | ||||||||
\(807\) | 1630.31i | 0.0711146i | ||||||||
\(808\) | − 6790.83i | − 0.295669i | ||||||||
\(809\) | 24472.6 | 1.06355 | 0.531773 | − | 0.846887i | \(-0.321526\pi\) | ||||
0.531773 | + | 0.846887i | \(0.321526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −928.998 | −0.0402238 | −0.0201119 | − | 0.999798i | \(-0.506402\pi\) | ||||
−0.0201119 | + | 0.999798i | \(0.506402\pi\) | |||||||
\(812\) | − 1469.02i | − 0.0634882i | ||||||||
\(813\) | − 8939.75i | − 0.385647i | ||||||||
\(814\) | −38591.7 | −1.66172 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 113.366 | 0.00486349 | ||||||||
\(817\) | − 3589.57i | − 0.153713i | ||||||||
\(818\) | 7347.52i | 0.314059i | ||||||||
\(819\) | 830.950 | 0.0354527 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3761.43 | 0.159896 | 0.0799481 | − | 0.996799i | \(-0.474525\pi\) | ||||
0.0799481 | + | 0.996799i | \(0.474525\pi\) | |||||||
\(822\) | 3993.85i | 0.169466i | ||||||||
\(823\) | 5718.32i | 0.242197i | 0.992640 | + | 0.121098i | \(0.0386417\pi\) | ||||
−0.992640 | + | 0.121098i | \(0.961358\pi\) | |||||||
\(824\) | 14559.1 | 0.615523 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.8994 | −0.000964616 0 | ||||||||
\(827\) | 30541.0i | 1.28418i | 0.766630 | + | 0.642089i | \(0.221932\pi\) | ||||
−0.766630 | + | 0.642089i | \(0.778068\pi\) | |||||||
\(828\) | − 8927.00i | − 0.374680i | ||||||||
\(829\) | 41273.1 | 1.72916 | 0.864581 | − | 0.502493i | \(-0.167584\pi\) | ||||
0.864581 | + | 0.502493i | \(0.167584\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6833.02 | 0.285240 | ||||||||
\(832\) | 832.000i | 0.0346688i | ||||||||
\(833\) | 1466.93i | 0.0610156i | ||||||||
\(834\) | 3260.10 | 0.135357 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9708.56 | 0.401648 | ||||||||
\(837\) | − 2596.87i | − 0.107241i | ||||||||
\(838\) | 12735.4i | 0.524986i | ||||||||
\(839\) | −38391.2 | −1.57975 | −0.789875 | − | 0.613268i | \(-0.789855\pi\) | ||||
−0.789875 | + | 0.613268i | \(0.789855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4792.41 | −0.196499 | ||||||||
\(842\) | − 10369.0i | − 0.424392i | ||||||||
\(843\) | 11047.0i | 0.451341i | ||||||||
\(844\) | −5739.72 | −0.234087 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9101.78 | −0.369889 | ||||||||
\(847\) | 3363.26i | 0.136438i | ||||||||
\(848\) | − 3783.32i | − 0.153207i | ||||||||
\(849\) | −5441.22 | −0.219955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34577.0 | 1.39281 | ||||||||
\(852\) | 7587.87i | 0.305113i | ||||||||
\(853\) | − 10176.9i | − 0.408498i | −0.978919 | − | 0.204249i | \(-0.934525\pi\) | ||||
0.978919 | − | 0.204249i | \(-0.0654752\pi\) | |||||||
\(854\) | −1995.73 | −0.0799677 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1320.06 | −0.0527088 | ||||||||
\(857\) | 20605.8i | 0.821331i | 0.911786 | + | 0.410666i | \(0.134704\pi\) | ||||
−0.911786 | + | 0.410666i | \(0.865296\pi\) | |||||||
\(858\) | 2157.68i | 0.0858532i | ||||||||
\(859\) | −23472.9 | −0.932345 | −0.466173 | − | 0.884694i | \(-0.654367\pi\) | ||||
−0.466173 | + | 0.884694i | \(0.654367\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.8655 | −0.00130088 | ||||||||
\(862\) | 12504.1i | 0.494074i | ||||||||
\(863\) | − 22922.3i | − 0.904153i | −0.891979 | − | 0.452076i | \(-0.850683\pi\) | ||||
0.891979 | − | 0.452076i | \(-0.149317\pi\) | |||||||
\(864\) | 2668.44 | 0.105072 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27126.6 | −1.06443 | ||||||||
\(867\) | − 7945.21i | − 0.311227i | ||||||||
\(868\) | − 326.799i | − 0.0127791i | ||||||||
\(869\) | −43794.7 | −1.70959 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1277.15 | 0.0496838 | ||||||||
\(872\) | 7365.76i | 0.286050i | ||||||||
\(873\) | − 23413.6i | − 0.907709i | ||||||||
\(874\) | −8698.56 | −0.336651 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2625.85 | −0.101278 | ||||||||
\(877\) | 12732.4i | 0.490243i | 0.969492 | + | 0.245122i | \(0.0788279\pi\) | ||||
−0.969492 | + | 0.245122i | \(0.921172\pi\) | |||||||
\(878\) | − 9911.63i | − 0.380981i | ||||||||
\(879\) | −5660.85 | −0.217219 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32910.4 | 1.25855 | 0.629273 | − | 0.777184i | \(-0.283353\pi\) | ||||
0.629273 | + | 0.777184i | \(0.283353\pi\) | |||||||
\(882\) | 16378.5i | 0.625277i | ||||||||
\(883\) | − 17053.9i | − 0.649952i | −0.945722 | − | 0.324976i | \(-0.894644\pi\) | ||||
0.945722 | − | 0.324976i | \(-0.105356\pi\) | |||||||
\(884\) | −226.945 | −0.00863460 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21443.2 | −0.813090 | ||||||||
\(887\) | 7601.23i | 0.287739i | 0.989597 | + | 0.143869i | \(0.0459545\pi\) | ||||
−0.989597 | + | 0.143869i | \(0.954046\pi\) | |||||||
\(888\) | 4902.66i | 0.185273i | ||||||||
\(889\) | 2900.15 | 0.109413 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26706.6 | −1.00416 | ||||||||
\(892\) | 20890.5i | 0.784155i | ||||||||
\(893\) | 8868.87i | 0.332347i | ||||||||
\(894\) | −7503.08 | −0.280694 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 335.805 | 0.0125206 | ||||||||
\(897\) | − 1933.22i | − 0.0719601i | ||||||||
\(898\) | 7408.63i | 0.275311i | ||||||||
\(899\) | 4359.47 | 0.161731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1031.98 | 0.0381578 | ||||||||
\(902\) | 788.890i | 0.0291210i | ||||||||
\(903\) | − 321.988i | − 0.0118661i | ||||||||
\(904\) | −7727.89 | −0.284321 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7366.79 | 0.270138 | ||||||||
\(907\) | − 49076.2i | − 1.79664i | −0.439347 | − | 0.898318i | \(-0.644790\pi\) | ||||
0.439347 | − | 0.898318i | \(-0.355210\pi\) | |||||||
\(908\) | 9398.59i | 0.343506i | ||||||||
\(909\) | 20681.7 | 0.754643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22427.3 | −0.815642 | −0.407821 | − | 0.913062i | \(-0.633711\pi\) | ||||
−0.407821 | + | 0.913062i | \(0.633711\pi\) | |||||||
\(912\) | − 1233.37i | − 0.0447816i | ||||||||
\(913\) | − 47073.9i | − 1.70637i | ||||||||
\(914\) | −13421.5 | −0.485715 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1271.44 | 0.0458619 | ||||||||
\(917\) | 1836.48i | 0.0661353i | ||||||||
\(918\) | 727.871i | 0.0261692i | ||||||||
\(919\) | −47062.8 | −1.68929 | −0.844645 | − | 0.535327i | \(-0.820188\pi\) | ||||
−0.844645 | + | 0.535327i | \(0.820188\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13223.6 | −0.473109 | ||||||||
\(922\) | − 1954.98i | − 0.0698307i | ||||||||
\(923\) | − 15190.0i | − 0.541695i | ||||||||
\(924\) | 870.866 | 0.0310058 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28978.2 | −1.02838 | ||||||||
\(927\) | 44340.4i | 1.57101i | ||||||||
\(928\) | 4479.61i | 0.158459i | ||||||||
\(929\) | −18074.8 | −0.638338 | −0.319169 | − | 0.947698i | \(-0.603404\pi\) | ||||
−0.319169 | + | 0.947698i | \(0.603404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15959.4 | 0.561814 | ||||||||
\(932\) | 5182.70i | 0.182151i | ||||||||
\(933\) | 829.658i | 0.0291123i | ||||||||
\(934\) | −29699.4 | −1.04047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2533.89 | −0.0884859 | ||||||||
\(937\) | − 39939.1i | − 1.39248i | −0.717809 | − | 0.696241i | \(-0.754855\pi\) | ||||
0.717809 | − | 0.696241i | \(-0.245145\pi\) | |||||||
\(938\) | − 515.473i | − 0.0179433i | ||||||||
\(939\) | −5334.67 | −0.185400 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12975.7 | −0.449518 | −0.224759 | − | 0.974414i | \(-0.572159\pi\) | ||||
−0.224759 | + | 0.974414i | \(0.572159\pi\) | |||||||
\(942\) | − 6310.84i | − 0.218278i | ||||||||
\(943\) | − 706.821i | − 0.0244085i | ||||||||
\(944\) | 69.8292 | 0.00240757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7728.85 | −0.265631 | ||||||||
\(947\) | 43713.9i | 1.50001i | 0.661432 | + | 0.750005i | \(0.269949\pi\) | ||||
−0.661432 | + | 0.750005i | \(0.730051\pi\) | |||||||
\(948\) | 5563.64i | 0.190610i | ||||||||
\(949\) | 5256.64 | 0.179808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13598.0 | −0.463667 | ||||||||
\(952\) | 91.5976i | 0.00311838i | ||||||||
\(953\) | − 13116.8i | − 0.445850i | −0.974836 | − | 0.222925i | \(-0.928439\pi\) | ||||
0.974836 | − | 0.222925i | \(-0.0715606\pi\) | |||||||
\(954\) | 11522.2 | 0.391034 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8598.66 | 0.290900 | ||||||||
\(957\) | 11617.3i | 0.392407i | ||||||||
\(958\) | − 16219.7i | − 0.547009i | ||||||||
\(959\) | −3226.95 | −0.108659 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28821.2 | −0.967446 | ||||||||
\(962\) | − 9814.52i | − 0.328932i | ||||||||
\(963\) | − 4020.30i | − 0.134530i | ||||||||
\(964\) | 26749.5 | 0.893719 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −780.268 | −0.0259883 | ||||||||
\(967\) | 20837.0i | 0.692941i | 0.938061 | + | 0.346471i | \(0.112620\pi\) | ||||
−0.938061 | + | 0.346471i | \(0.887380\pi\) | |||||||
\(968\) | − 10255.9i | − 0.340534i | ||||||||
\(969\) | 336.426 | 0.0111533 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36214.0 | 1.19687 | 0.598436 | − | 0.801170i | \(-0.295789\pi\) | ||||
0.598436 | + | 0.801170i | \(0.295789\pi\) | |||||||
\(972\) | 12398.8i | 0.409147i | ||||||||
\(973\) | 2634.10i | 0.0867887i | ||||||||
\(974\) | −2431.83 | −0.0800010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6085.76 | 0.199590 | ||||||||
\(977\) | − 4171.16i | − 0.136589i | −0.997665 | − | 0.0682943i | \(-0.978244\pi\) | ||||
0.997665 | − | 0.0682943i | \(-0.0217557\pi\) | |||||||
\(978\) | − 1012.44i | − 0.0331027i | ||||||||
\(979\) | −78007.1 | −2.54660 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22432.7 | −0.730093 | ||||||||
\(982\) | − 25278.9i | − 0.821468i | ||||||||
\(983\) | 45275.4i | 1.46903i | 0.678590 | + | 0.734517i | \(0.262591\pi\) | ||||
−0.678590 | + | 0.734517i | \(0.737409\pi\) | |||||||
\(984\) | 100.220 | 0.00324684 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1221.91 | −0.0394659 | ||||||||
\(987\) | 795.545i | 0.0256560i | ||||||||
\(988\) | 2469.05i | 0.0795050i | ||||||||
\(989\) | 6924.81 | 0.222645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2463.81 | −0.0789764 | −0.0394882 | − | 0.999220i | \(-0.512573\pi\) | ||||
−0.0394882 | + | 0.999220i | \(0.512573\pi\) | |||||||
\(992\) | 996.537i | 0.0318952i | ||||||||
\(993\) | 2395.93i | 0.0765686i | ||||||||
\(994\) | −6130.85 | −0.195633 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5980.22 | −0.190252 | ||||||||
\(997\) | − 29662.7i | − 0.942253i | −0.882066 | − | 0.471127i | \(-0.843848\pi\) | ||||
0.882066 | − | 0.471127i | \(-0.156152\pi\) | |||||||
\(998\) | − 5316.42i | − 0.168626i | ||||||||
\(999\) | −31477.7 | −0.996908 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 650.4.b.i.599.3 | 4 | ||
5.2 | odd | 4 | 650.4.a.m.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 650.4.a.p.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 650.4.b.i.599.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
650.4.a.m.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
650.4.a.p.1.2 | yes | 2 | 5.3 | odd | 4 | ||
650.4.b.i.599.2 | 4 | 5.4 | even | 2 | inner | ||
650.4.b.i.599.3 | 4 | 1.1 | even | 1 | trivial |