Newspace parameters
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(20.6506685020\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
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 | 99.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.99 |
Dual form | 350.4.c.a.99.2 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 10.0000i | − 1.92450i | −0.272166 | − | 0.962250i | \(-0.587740\pi\) | ||||
0.272166 | − | 0.962250i | \(-0.412260\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −20.0000 | −1.36083 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −73.0000 | −2.70370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.00000 | 0.246691 | 0.123346 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123346 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(12\) | 40.0000i | 0.962250i | ||||||||
\(13\) | 52.0000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 96.0000i | 1.36961i | 0.728725 | + | 0.684806i | \(0.240113\pi\) | ||||
−0.728725 | + | 0.684806i | \(0.759887\pi\) | |||||||
\(18\) | 146.000i | 1.91181i | ||||||||
\(19\) | 10.0000 | 0.120745 | 0.0603726 | − | 0.998176i | \(-0.480771\pi\) | ||||
0.0603726 | + | 0.998176i | \(0.480771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 70.0000 | 0.727393 | ||||||||
\(22\) | − 18.0000i | − 0.174437i | ||||||||
\(23\) | − 75.0000i | − 0.679938i | −0.940437 | − | 0.339969i | \(-0.889583\pi\) | ||||
0.940437 | − | 0.339969i | \(-0.110417\pi\) | |||||||
\(24\) | 80.0000 | 0.680414 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 104.000 | 0.784465 | ||||||||
\(27\) | 460.000i | 3.27878i | ||||||||
\(28\) | − 28.0000i | − 0.188982i | ||||||||
\(29\) | −189.000 | −1.21022 | −0.605111 | − | 0.796141i | \(-0.706871\pi\) | ||||
−0.605111 | + | 0.796141i | \(0.706871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −232.000 | −1.34414 | −0.672071 | − | 0.740486i | \(-0.734595\pi\) | ||||
−0.672071 | + | 0.740486i | \(0.734595\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | − 90.0000i | − 0.474757i | ||||||||
\(34\) | 192.000 | 0.968463 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 292.000 | 1.35185 | ||||||||
\(37\) | 305.000i | 1.35518i | 0.735439 | + | 0.677590i | \(0.236976\pi\) | ||||
−0.735439 | + | 0.677590i | \(0.763024\pi\) | |||||||
\(38\) | − 20.0000i | − 0.0853797i | ||||||||
\(39\) | 520.000 | 2.13504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −438.000 | −1.66839 | −0.834196 | − | 0.551467i | \(-0.814068\pi\) | ||||
−0.834196 | + | 0.551467i | \(0.814068\pi\) | |||||||
\(42\) | − 140.000i | − 0.514344i | ||||||||
\(43\) | − 353.000i | − 1.25191i | −0.779860 | − | 0.625953i | \(-0.784710\pi\) | ||||
0.779860 | − | 0.625953i | \(-0.215290\pi\) | |||||||
\(44\) | −36.0000 | −0.123346 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −150.000 | −0.480789 | ||||||||
\(47\) | − 486.000i | − 1.50831i | −0.656699 | − | 0.754153i | \(-0.728048\pi\) | ||||
0.656699 | − | 0.754153i | \(-0.271952\pi\) | |||||||
\(48\) | − 160.000i | − 0.481125i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 960.000 | 2.63582 | ||||||||
\(52\) | − 208.000i | − 0.554700i | ||||||||
\(53\) | 354.000i | 0.917465i | 0.888574 | + | 0.458732i | \(0.151696\pi\) | ||||
−0.888574 | + | 0.458732i | \(0.848304\pi\) | |||||||
\(54\) | 920.000 | 2.31845 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | − 100.000i | − 0.232374i | ||||||||
\(58\) | 378.000i | 0.855756i | ||||||||
\(59\) | 672.000 | 1.48283 | 0.741415 | − | 0.671047i | \(-0.234155\pi\) | ||||
0.741415 | + | 0.671047i | \(0.234155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 206.000 | 0.432387 | 0.216193 | − | 0.976351i | \(-0.430636\pi\) | ||||
0.216193 | + | 0.976351i | \(0.430636\pi\) | |||||||
\(62\) | 464.000i | 0.950453i | ||||||||
\(63\) | − 511.000i | − 1.02190i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −180.000 | −0.335704 | ||||||||
\(67\) | 599.000i | 1.09223i | 0.837710 | + | 0.546116i | \(0.183894\pi\) | ||||
−0.837710 | + | 0.546116i | \(0.816106\pi\) | |||||||
\(68\) | − 384.000i | − 0.684806i | ||||||||
\(69\) | −750.000 | −1.30854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −471.000 | −0.787288 | −0.393644 | − | 0.919263i | \(-0.628786\pi\) | ||||
−0.393644 | + | 0.919263i | \(0.628786\pi\) | |||||||
\(72\) | − 584.000i | − 0.955904i | ||||||||
\(73\) | − 614.000i | − 0.984428i | −0.870474 | − | 0.492214i | \(-0.836188\pi\) | ||||
0.870474 | − | 0.492214i | \(-0.163812\pi\) | |||||||
\(74\) | 610.000 | 0.958258 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.0603726 | ||||||||
\(77\) | 63.0000i | 0.0932405i | ||||||||
\(78\) | − 1040.00i | − 1.50970i | ||||||||
\(79\) | −743.000 | −1.05815 | −0.529076 | − | 0.848574i | \(-0.677461\pi\) | ||||
−0.529076 | + | 0.848574i | \(0.677461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2629.00 | 3.60631 | ||||||||
\(82\) | 876.000i | 1.17973i | ||||||||
\(83\) | − 996.000i | − 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | −280.000 | −0.363696 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −706.000 | −0.885232 | ||||||||
\(87\) | 1890.00i | 2.32907i | ||||||||
\(88\) | 72.0000i | 0.0872185i | ||||||||
\(89\) | −180.000 | −0.214382 | −0.107191 | − | 0.994238i | \(-0.534186\pi\) | ||||
−0.107191 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −364.000 | −0.419314 | ||||||||
\(92\) | 300.000i | 0.339969i | ||||||||
\(93\) | 2320.00i | 2.58680i | ||||||||
\(94\) | −972.000 | −1.06653 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −320.000 | −0.340207 | ||||||||
\(97\) | − 184.000i | − 0.192602i | −0.995352 | − | 0.0963009i | \(-0.969299\pi\) | ||||
0.995352 | − | 0.0963009i | \(-0.0307011\pi\) | |||||||
\(98\) | 98.0000i | 0.101015i | ||||||||
\(99\) | −657.000 | −0.666980 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −726.000 | −0.715245 | −0.357622 | − | 0.933866i | \(-0.616412\pi\) | ||||
−0.357622 | + | 0.933866i | \(0.616412\pi\) | |||||||
\(102\) | − 1920.00i | − 1.86381i | ||||||||
\(103\) | 1798.00i | 1.72002i | 0.510276 | + | 0.860011i | \(0.329543\pi\) | ||||
−0.510276 | + | 0.860011i | \(0.670457\pi\) | |||||||
\(104\) | −416.000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 708.000 | 0.648746 | ||||||||
\(107\) | 876.000i | 0.791459i | 0.918367 | + | 0.395730i | \(0.129508\pi\) | ||||
−0.918367 | + | 0.395730i | \(0.870492\pi\) | |||||||
\(108\) | − 1840.00i | − 1.63939i | ||||||||
\(109\) | 691.000 | 0.607209 | 0.303605 | − | 0.952798i | \(-0.401810\pi\) | ||||
0.303605 | + | 0.952798i | \(0.401810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3050.00 | 2.60805 | ||||||||
\(112\) | 112.000i | 0.0944911i | ||||||||
\(113\) | 1521.00i | 1.26623i | 0.774059 | + | 0.633113i | \(0.218223\pi\) | ||||
−0.774059 | + | 0.633113i | \(0.781777\pi\) | |||||||
\(114\) | −200.000 | −0.164313 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 756.000 | 0.605111 | ||||||||
\(117\) | − 3796.00i | − 2.99949i | ||||||||
\(118\) | − 1344.00i | − 1.04852i | ||||||||
\(119\) | −672.000 | −0.517665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1250.00 | −0.939144 | ||||||||
\(122\) | − 412.000i | − 0.305744i | ||||||||
\(123\) | 4380.00i | 3.21082i | ||||||||
\(124\) | 928.000 | 0.672071 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1022.00 | −0.722595 | ||||||||
\(127\) | 1031.00i | 0.720366i | 0.932882 | + | 0.360183i | \(0.117286\pi\) | ||||
−0.932882 | + | 0.360183i | \(0.882714\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −3530.00 | −2.40930 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1116.00 | −0.744316 | −0.372158 | − | 0.928169i | \(-0.621382\pi\) | ||||
−0.372158 | + | 0.928169i | \(0.621382\pi\) | |||||||
\(132\) | 360.000i | 0.237379i | ||||||||
\(133\) | 70.0000i | 0.0456374i | ||||||||
\(134\) | 1198.00 | 0.772324 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −768.000 | −0.484231 | ||||||||
\(137\) | − 1398.00i | − 0.871819i | −0.899991 | − | 0.435909i | \(-0.856427\pi\) | ||||
0.899991 | − | 0.435909i | \(-0.143573\pi\) | |||||||
\(138\) | 1500.00i | 0.925279i | ||||||||
\(139\) | −674.000 | −0.411280 | −0.205640 | − | 0.978628i | \(-0.565928\pi\) | ||||
−0.205640 | + | 0.978628i | \(0.565928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4860.00 | −2.90274 | ||||||||
\(142\) | 942.000i | 0.556696i | ||||||||
\(143\) | 468.000i | 0.273679i | ||||||||
\(144\) | −1168.00 | −0.675926 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1228.00 | −0.696096 | ||||||||
\(147\) | 490.000i | 0.274929i | ||||||||
\(148\) | − 1220.00i | − 0.677590i | ||||||||
\(149\) | 1281.00 | 0.704320 | 0.352160 | − | 0.935940i | \(-0.385447\pi\) | ||||
0.352160 | + | 0.935940i | \(0.385447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 953.000 | 0.513603 | 0.256801 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256801 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(152\) | 80.0000i | 0.0426898i | ||||||||
\(153\) | − 7008.00i | − 3.70303i | ||||||||
\(154\) | 126.000 | 0.0659310 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2080.00 | −1.06752 | ||||||||
\(157\) | 650.000i | 0.330418i | 0.986259 | + | 0.165209i | \(0.0528299\pi\) | ||||
−0.986259 | + | 0.165209i | \(0.947170\pi\) | |||||||
\(158\) | 1486.00i | 0.748227i | ||||||||
\(159\) | 3540.00 | 1.76566 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 525.000 | 0.256993 | ||||||||
\(162\) | − 5258.00i | − 2.55005i | ||||||||
\(163\) | − 932.000i | − 0.447852i | −0.974606 | − | 0.223926i | \(-0.928113\pi\) | ||||
0.974606 | − | 0.223926i | \(-0.0718874\pi\) | |||||||
\(164\) | 1752.00 | 0.834196 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1992.00 | −0.931381 | ||||||||
\(167\) | − 180.000i | − 0.0834061i | −0.999130 | − | 0.0417030i | \(-0.986722\pi\) | ||||
0.999130 | − | 0.0417030i | \(-0.0132783\pi\) | |||||||
\(168\) | 560.000i | 0.257172i | ||||||||
\(169\) | −507.000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −730.000 | −0.326459 | ||||||||
\(172\) | 1412.00i | 0.625953i | ||||||||
\(173\) | 834.000i | 0.366519i | 0.983065 | + | 0.183260i | \(0.0586649\pi\) | ||||
−0.983065 | + | 0.183260i | \(0.941335\pi\) | |||||||
\(174\) | 3780.00 | 1.64690 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 144.000 | 0.0616728 | ||||||||
\(177\) | − 6720.00i | − 2.85371i | ||||||||
\(178\) | 360.000i | 0.151591i | ||||||||
\(179\) | 648.000 | 0.270580 | 0.135290 | − | 0.990806i | \(-0.456803\pi\) | ||||
0.135290 | + | 0.990806i | \(0.456803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2914.00 | −1.19666 | −0.598331 | − | 0.801249i | \(-0.704169\pi\) | ||||
−0.598331 | + | 0.801249i | \(0.704169\pi\) | |||||||
\(182\) | 728.000i | 0.296500i | ||||||||
\(183\) | − 2060.00i | − 0.832129i | ||||||||
\(184\) | 600.000 | 0.240394 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4640.00 | 1.82915 | ||||||||
\(187\) | 864.000i | 0.337871i | ||||||||
\(188\) | 1944.00i | 0.754153i | ||||||||
\(189\) | −3220.00 | −1.23926 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −876.000 | −0.331859 | −0.165930 | − | 0.986138i | \(-0.553062\pi\) | ||||
−0.165930 | + | 0.986138i | \(0.553062\pi\) | |||||||
\(192\) | 640.000i | 0.240563i | ||||||||
\(193\) | 601.000i | 0.224150i | 0.993700 | + | 0.112075i | \(0.0357497\pi\) | ||||
−0.993700 | + | 0.112075i | \(0.964250\pi\) | |||||||
\(194\) | −368.000 | −0.136190 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | − 2013.00i | − 0.728022i | −0.931395 | − | 0.364011i | \(-0.881407\pi\) | ||||
0.931395 | − | 0.364011i | \(-0.118593\pi\) | |||||||
\(198\) | 1314.00i | 0.471626i | ||||||||
\(199\) | −326.000 | −0.116128 | −0.0580641 | − | 0.998313i | \(-0.518493\pi\) | ||||
−0.0580641 | + | 0.998313i | \(0.518493\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5990.00 | 2.10200 | ||||||||
\(202\) | 1452.00i | 0.505754i | ||||||||
\(203\) | − 1323.00i | − 0.457421i | ||||||||
\(204\) | −3840.00 | −1.31791 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3596.00 | 1.21624 | ||||||||
\(207\) | 5475.00i | 1.83835i | ||||||||
\(208\) | 832.000i | 0.277350i | ||||||||
\(209\) | 90.0000 | 0.0297867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5956.00 | −1.94326 | −0.971630 | − | 0.236505i | \(-0.923998\pi\) | ||||
−0.971630 | + | 0.236505i | \(0.923998\pi\) | |||||||
\(212\) | − 1416.00i | − 0.458732i | ||||||||
\(213\) | 4710.00i | 1.51514i | ||||||||
\(214\) | 1752.00 | 0.559646 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3680.00 | −1.15922 | ||||||||
\(217\) | − 1624.00i | − 0.508038i | ||||||||
\(218\) | − 1382.00i | − 0.429362i | ||||||||
\(219\) | −6140.00 | −1.89453 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4992.00 | −1.51945 | ||||||||
\(222\) | − 6100.00i | − 1.84417i | ||||||||
\(223\) | 3118.00i | 0.936308i | 0.883647 | + | 0.468154i | \(0.155081\pi\) | ||||
−0.883647 | + | 0.468154i | \(0.844919\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3042.00 | 0.895358 | ||||||||
\(227\) | − 6.00000i | − 0.00175433i | −1.00000 | 0.000877167i | \(-0.999721\pi\) | |||||
1.00000 | 0.000877167i | \(-0.000279211\pi\) | ||||||||
\(228\) | 400.000i | 0.116187i | ||||||||
\(229\) | 586.000 | 0.169100 | 0.0845502 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845502 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 630.000 | 0.179441 | ||||||||
\(232\) | − 1512.00i | − 0.427878i | ||||||||
\(233\) | − 1293.00i | − 0.363550i | −0.983340 | − | 0.181775i | \(-0.941816\pi\) | ||||
0.983340 | − | 0.181775i | \(-0.0581843\pi\) | |||||||
\(234\) | −7592.00 | −2.12096 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2688.00 | −0.741415 | ||||||||
\(237\) | 7430.00i | 2.03642i | ||||||||
\(238\) | 1344.00i | 0.366044i | ||||||||
\(239\) | 5376.00 | 1.45500 | 0.727499 | − | 0.686109i | \(-0.240683\pi\) | ||||
0.727499 | + | 0.686109i | \(0.240683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −670.000 | −0.179081 | −0.0895404 | − | 0.995983i | \(-0.528540\pi\) | ||||
−0.0895404 | + | 0.995983i | \(0.528540\pi\) | |||||||
\(242\) | 2500.00i | 0.664075i | ||||||||
\(243\) | − 13870.0i | − 3.66157i | ||||||||
\(244\) | −824.000 | −0.216193 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8760.00 | 2.27040 | ||||||||
\(247\) | 520.000i | 0.133955i | ||||||||
\(248\) | − 1856.00i | − 0.475226i | ||||||||
\(249\) | −9960.00 | −2.53490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1380.00 | 0.347031 | 0.173516 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173516 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(252\) | 2044.00i | 0.510952i | ||||||||
\(253\) | − 675.000i | − 0.167735i | ||||||||
\(254\) | 2062.00 | 0.509376 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 3576.00i | − 0.867956i | −0.900923 | − | 0.433978i | \(-0.857110\pi\) | ||||
0.900923 | − | 0.433978i | \(-0.142890\pi\) | |||||||
\(258\) | 7060.00i | 1.70363i | ||||||||
\(259\) | −2135.00 | −0.512210 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13797.0 | 3.27208 | ||||||||
\(262\) | 2232.00i | 0.526311i | ||||||||
\(263\) | 5919.00i | 1.38776i | 0.720090 | + | 0.693881i | \(0.244100\pi\) | ||||
−0.720090 | + | 0.693881i | \(0.755900\pi\) | |||||||
\(264\) | 720.000 | 0.167852 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 140.000 | 0.0322705 | ||||||||
\(267\) | 1800.00i | 0.412578i | ||||||||
\(268\) | − 2396.00i | − 0.546116i | ||||||||
\(269\) | 1764.00 | 0.399825 | 0.199913 | − | 0.979814i | \(-0.435934\pi\) | ||||
0.199913 | + | 0.979814i | \(0.435934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −340.000 | −0.0762123 | −0.0381061 | − | 0.999274i | \(-0.512132\pi\) | ||||
−0.0381061 | + | 0.999274i | \(0.512132\pi\) | |||||||
\(272\) | 1536.00i | 0.342403i | ||||||||
\(273\) | 3640.00i | 0.806970i | ||||||||
\(274\) | −2796.00 | −0.616469 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3000.00 | 0.654271 | ||||||||
\(277\) | 4706.00i | 1.02078i | 0.859943 | + | 0.510390i | \(0.170499\pi\) | ||||
−0.859943 | + | 0.510390i | \(0.829501\pi\) | |||||||
\(278\) | 1348.00i | 0.290819i | ||||||||
\(279\) | 16936.0 | 3.63416 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6681.00 | 1.41835 | 0.709173 | − | 0.705035i | \(-0.249069\pi\) | ||||
0.709173 | + | 0.705035i | \(0.249069\pi\) | |||||||
\(282\) | 9720.00i | 2.05254i | ||||||||
\(283\) | 226.000i | 0.0474710i | 0.999718 | + | 0.0237355i | \(0.00755596\pi\) | ||||
−0.999718 | + | 0.0237355i | \(0.992444\pi\) | |||||||
\(284\) | 1884.00 | 0.393644 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 936.000 | 0.193520 | ||||||||
\(287\) | − 3066.00i | − 0.630593i | ||||||||
\(288\) | 2336.00i | 0.477952i | ||||||||
\(289\) | −4303.00 | −0.875840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1840.00 | −0.370662 | ||||||||
\(292\) | 2456.00i | 0.492214i | ||||||||
\(293\) | − 4320.00i | − 0.861355i | −0.902506 | − | 0.430678i | \(-0.858275\pi\) | ||||
0.902506 | − | 0.430678i | \(-0.141725\pi\) | |||||||
\(294\) | 980.000 | 0.194404 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2440.00 | −0.479129 | ||||||||
\(297\) | 4140.00i | 0.808846i | ||||||||
\(298\) | − 2562.00i | − 0.498029i | ||||||||
\(299\) | 3900.00 | 0.754324 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2471.00 | 0.473176 | ||||||||
\(302\) | − 1906.00i | − 0.363172i | ||||||||
\(303\) | 7260.00i | 1.37649i | ||||||||
\(304\) | 160.000 | 0.0301863 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14016.0 | −2.61844 | ||||||||
\(307\) | − 6604.00i | − 1.22772i | −0.789415 | − | 0.613860i | \(-0.789616\pi\) | ||||
0.789415 | − | 0.613860i | \(-0.210384\pi\) | |||||||
\(308\) | − 252.000i | − 0.0466202i | ||||||||
\(309\) | 17980.0 | 3.31018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6036.00 | 1.10055 | 0.550274 | − | 0.834984i | \(-0.314523\pi\) | ||||
0.550274 | + | 0.834984i | \(0.314523\pi\) | |||||||
\(312\) | 4160.00i | 0.754851i | ||||||||
\(313\) | − 9146.00i | − 1.65164i | −0.563936 | − | 0.825819i | \(-0.690713\pi\) | ||||
0.563936 | − | 0.825819i | \(-0.309287\pi\) | |||||||
\(314\) | 1300.00 | 0.233641 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2972.00 | 0.529076 | ||||||||
\(317\) | − 4449.00i | − 0.788267i | −0.919053 | − | 0.394134i | \(-0.871045\pi\) | ||||
0.919053 | − | 0.394134i | \(-0.128955\pi\) | |||||||
\(318\) | − 7080.00i | − 1.24851i | ||||||||
\(319\) | −1701.00 | −0.298551 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8760.00 | 1.52316 | ||||||||
\(322\) | − 1050.00i | − 0.181721i | ||||||||
\(323\) | 960.000i | 0.165374i | ||||||||
\(324\) | −10516.0 | −1.80316 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1864.00 | −0.316679 | ||||||||
\(327\) | − 6910.00i | − 1.16857i | ||||||||
\(328\) | − 3504.00i | − 0.589866i | ||||||||
\(329\) | 3402.00 | 0.570086 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10081.0 | −1.67402 | −0.837012 | − | 0.547185i | \(-0.815700\pi\) | ||||
−0.837012 | + | 0.547185i | \(0.815700\pi\) | |||||||
\(332\) | 3984.00i | 0.658586i | ||||||||
\(333\) | − 22265.0i | − 3.66401i | ||||||||
\(334\) | −360.000 | −0.0589770 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1120.00 | 0.181848 | ||||||||
\(337\) | 7778.00i | 1.25725i | 0.777707 | + | 0.628627i | \(0.216383\pi\) | ||||
−0.777707 | + | 0.628627i | \(0.783617\pi\) | |||||||
\(338\) | 1014.00i | 0.163178i | ||||||||
\(339\) | 15210.0 | 2.43685 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2088.00 | −0.331588 | ||||||||
\(342\) | 1460.00i | 0.230841i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | 2824.00 | 0.442616 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1668.00 | 0.259168 | ||||||||
\(347\) | 1017.00i | 0.157336i | 0.996901 | + | 0.0786678i | \(0.0250666\pi\) | ||||
−0.996901 | + | 0.0786678i | \(0.974933\pi\) | |||||||
\(348\) | − 7560.00i | − 1.16454i | ||||||||
\(349\) | −10370.0 | −1.59053 | −0.795263 | − | 0.606265i | \(-0.792667\pi\) | ||||
−0.795263 | + | 0.606265i | \(0.792667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23920.0 | −3.63748 | ||||||||
\(352\) | − 288.000i | − 0.0436092i | ||||||||
\(353\) | 9432.00i | 1.42214i | 0.703122 | + | 0.711069i | \(0.251789\pi\) | ||||
−0.703122 | + | 0.711069i | \(0.748211\pi\) | |||||||
\(354\) | −13440.0 | −2.01788 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 720.000 | 0.107191 | ||||||||
\(357\) | 6720.00i | 0.996247i | ||||||||
\(358\) | − 1296.00i | − 0.191329i | ||||||||
\(359\) | −7557.00 | −1.11098 | −0.555492 | − | 0.831522i | \(-0.687470\pi\) | ||||
−0.555492 | + | 0.831522i | \(0.687470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6759.00 | −0.985421 | ||||||||
\(362\) | 5828.00i | 0.846168i | ||||||||
\(363\) | 12500.0i | 1.80738i | ||||||||
\(364\) | 1456.00 | 0.209657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4120.00 | −0.588404 | ||||||||
\(367\) | − 11662.0i | − 1.65872i | −0.558712 | − | 0.829362i | \(-0.688704\pi\) | ||||
0.558712 | − | 0.829362i | \(-0.311296\pi\) | |||||||
\(368\) | − 1200.00i | − 0.169985i | ||||||||
\(369\) | 31974.0 | 4.51084 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2478.00 | −0.346769 | ||||||||
\(372\) | − 9280.00i | − 1.29340i | ||||||||
\(373\) | 2377.00i | 0.329964i | 0.986297 | + | 0.164982i | \(0.0527565\pi\) | ||||
−0.986297 | + | 0.164982i | \(0.947243\pi\) | |||||||
\(374\) | 1728.00 | 0.238911 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3888.00 | 0.533267 | ||||||||
\(377\) | − 9828.00i | − 1.34262i | ||||||||
\(378\) | 6440.00i | 0.876291i | ||||||||
\(379\) | −4427.00 | −0.599999 | −0.300000 | − | 0.953939i | \(-0.596987\pi\) | ||||
−0.300000 | + | 0.953939i | \(0.596987\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10310.0 | 1.38634 | ||||||||
\(382\) | 1752.00i | 0.234660i | ||||||||
\(383\) | − 4608.00i | − 0.614772i | −0.951585 | − | 0.307386i | \(-0.900546\pi\) | ||||
0.951585 | − | 0.307386i | \(-0.0994543\pi\) | |||||||
\(384\) | 1280.00 | 0.170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1202.00 | 0.158498 | ||||||||
\(387\) | 25769.0i | 3.38479i | ||||||||
\(388\) | 736.000i | 0.0963009i | ||||||||
\(389\) | 699.000 | 0.0911072 | 0.0455536 | − | 0.998962i | \(-0.485495\pi\) | ||||
0.0455536 | + | 0.998962i | \(0.485495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7200.00 | 0.931252 | ||||||||
\(392\) | − 392.000i | − 0.0505076i | ||||||||
\(393\) | 11160.0i | 1.43244i | ||||||||
\(394\) | −4026.00 | −0.514789 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2628.00 | 0.333490 | ||||||||
\(397\) | − 7630.00i | − 0.964581i | −0.876011 | − | 0.482291i | \(-0.839805\pi\) | ||||
0.876011 | − | 0.482291i | \(-0.160195\pi\) | |||||||
\(398\) | 652.000i | 0.0821151i | ||||||||
\(399\) | 700.000 | 0.0878292 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5601.00 | 0.697508 | 0.348754 | − | 0.937214i | \(-0.386605\pi\) | ||||
0.348754 | + | 0.937214i | \(0.386605\pi\) | |||||||
\(402\) | − 11980.0i | − 1.48634i | ||||||||
\(403\) | − 12064.0i | − 1.49119i | ||||||||
\(404\) | 2904.00 | 0.357622 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2646.00 | −0.323445 | ||||||||
\(407\) | 2745.00i | 0.334311i | ||||||||
\(408\) | 7680.00i | 0.931904i | ||||||||
\(409\) | −4670.00 | −0.564588 | −0.282294 | − | 0.959328i | \(-0.591095\pi\) | ||||
−0.282294 | + | 0.959328i | \(0.591095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13980.0 | −1.67782 | ||||||||
\(412\) | − 7192.00i | − 0.860011i | ||||||||
\(413\) | 4704.00i | 0.560457i | ||||||||
\(414\) | 10950.0 | 1.29991 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1664.00 | 0.196116 | ||||||||
\(417\) | 6740.00i | 0.791509i | ||||||||
\(418\) | − 180.000i | − 0.0210624i | ||||||||
\(419\) | −36.0000 | −0.00419741 | −0.00209871 | − | 0.999998i | \(-0.500668\pi\) | ||||
−0.00209871 | + | 0.999998i | \(0.500668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5495.00 | 0.636128 | 0.318064 | − | 0.948069i | \(-0.396967\pi\) | ||||
0.318064 | + | 0.948069i | \(0.396967\pi\) | |||||||
\(422\) | 11912.0i | 1.37409i | ||||||||
\(423\) | 35478.0i | 4.07801i | ||||||||
\(424\) | −2832.00 | −0.324373 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9420.00 | 1.07136 | ||||||||
\(427\) | 1442.00i | 0.163427i | ||||||||
\(428\) | − 3504.00i | − 0.395730i | ||||||||
\(429\) | 4680.00 | 0.526696 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2700.00 | 0.301750 | 0.150875 | − | 0.988553i | \(-0.451791\pi\) | ||||
0.150875 | + | 0.988553i | \(0.451791\pi\) | |||||||
\(432\) | 7360.00i | 0.819695i | ||||||||
\(433\) | − 15104.0i | − 1.67633i | −0.545415 | − | 0.838166i | \(-0.683628\pi\) | ||||
0.545415 | − | 0.838166i | \(-0.316372\pi\) | |||||||
\(434\) | −3248.00 | −0.359237 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2764.00 | −0.303605 | ||||||||
\(437\) | − 750.000i | − 0.0820992i | ||||||||
\(438\) | 12280.0i | 1.33964i | ||||||||
\(439\) | −14948.0 | −1.62512 | −0.812562 | − | 0.582875i | \(-0.801928\pi\) | ||||
−0.812562 | + | 0.582875i | \(0.801928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3577.00 | 0.386243 | ||||||||
\(442\) | 9984.00i | 1.07441i | ||||||||
\(443\) | − 4980.00i | − 0.534101i | −0.963682 | − | 0.267051i | \(-0.913951\pi\) | ||||
0.963682 | − | 0.267051i | \(-0.0860491\pi\) | |||||||
\(444\) | −12200.0 | −1.30402 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6236.00 | 0.662070 | ||||||||
\(447\) | − 12810.0i | − 1.35546i | ||||||||
\(448\) | − 448.000i | − 0.0472456i | ||||||||
\(449\) | −12375.0 | −1.30070 | −0.650348 | − | 0.759637i | \(-0.725377\pi\) | ||||
−0.650348 | + | 0.759637i | \(0.725377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3942.00 | −0.411578 | ||||||||
\(452\) | − 6084.00i | − 0.633113i | ||||||||
\(453\) | − 9530.00i | − 0.988429i | ||||||||
\(454\) | −12.0000 | −0.00124050 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 800.000 | 0.0821567 | ||||||||
\(457\) | 10835.0i | 1.10906i | 0.832164 | + | 0.554529i | \(0.187102\pi\) | ||||
−0.832164 | + | 0.554529i | \(0.812898\pi\) | |||||||
\(458\) | − 1172.00i | − 0.119572i | ||||||||
\(459\) | −44160.0 | −4.49066 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5700.00 | 0.575869 | 0.287934 | − | 0.957650i | \(-0.407032\pi\) | ||||
0.287934 | + | 0.957650i | \(0.407032\pi\) | |||||||
\(462\) | − 1260.00i | − 0.126884i | ||||||||
\(463\) | − 6128.00i | − 0.615102i | −0.951532 | − | 0.307551i | \(-0.900491\pi\) | ||||
0.951532 | − | 0.307551i | \(-0.0995095\pi\) | |||||||
\(464\) | −3024.00 | −0.302555 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2586.00 | −0.257069 | ||||||||
\(467\) | − 9810.00i | − 0.972061i | −0.873942 | − | 0.486031i | \(-0.838444\pi\) | ||||
0.873942 | − | 0.486031i | \(-0.161556\pi\) | |||||||
\(468\) | 15184.0i | 1.49974i | ||||||||
\(469\) | −4193.00 | −0.412825 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6500.00 | 0.635890 | ||||||||
\(472\) | 5376.00i | 0.524259i | ||||||||
\(473\) | − 3177.00i | − 0.308834i | ||||||||
\(474\) | 14860.0 | 1.43996 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2688.00 | 0.258833 | ||||||||
\(477\) | − 25842.0i | − 2.48055i | ||||||||
\(478\) | − 10752.0i | − 1.02884i | ||||||||
\(479\) | 204.000 | 0.0194593 | 0.00972964 | − | 0.999953i | \(-0.496903\pi\) | ||||
0.00972964 | + | 0.999953i | \(0.496903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15860.0 | −1.50344 | ||||||||
\(482\) | 1340.00i | 0.126629i | ||||||||
\(483\) | − 5250.00i | − 0.494582i | ||||||||
\(484\) | 5000.00 | 0.469572 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27740.0 | −2.58912 | ||||||||
\(487\) | 15401.0i | 1.43303i | 0.697571 | + | 0.716515i | \(0.254264\pi\) | ||||
−0.697571 | + | 0.716515i | \(0.745736\pi\) | |||||||
\(488\) | 1648.00i | 0.152872i | ||||||||
\(489\) | −9320.00 | −0.861892 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3897.00 | 0.358186 | 0.179093 | − | 0.983832i | \(-0.442684\pi\) | ||||
0.179093 | + | 0.983832i | \(0.442684\pi\) | |||||||
\(492\) | − 17520.0i | − 1.60541i | ||||||||
\(493\) | − 18144.0i | − 1.65753i | ||||||||
\(494\) | 1040.00 | 0.0947203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3712.00 | −0.336036 | ||||||||
\(497\) | − 3297.00i | − 0.297567i | ||||||||
\(498\) | 19920.0i | 1.79244i | ||||||||
\(499\) | −8132.00 | −0.729536 | −0.364768 | − | 0.931098i | \(-0.618852\pi\) | ||||
−0.364768 | + | 0.931098i | \(0.618852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1800.00 | −0.160515 | ||||||||
\(502\) | − 2760.00i | − 0.245388i | ||||||||
\(503\) | 10998.0i | 0.974904i | 0.873150 | + | 0.487452i | \(0.162074\pi\) | ||||
−0.873150 | + | 0.487452i | \(0.837926\pi\) | |||||||
\(504\) | 4088.00 | 0.361298 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1350.00 | −0.118606 | ||||||||
\(507\) | 5070.00i | 0.444116i | ||||||||
\(508\) | − 4124.00i | − 0.360183i | ||||||||
\(509\) | −5940.00 | −0.517261 | −0.258631 | − | 0.965976i | \(-0.583271\pi\) | ||||
−0.258631 | + | 0.965976i | \(0.583271\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4298.00 | 0.372079 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 4600.00i | 0.395897i | ||||||||
\(514\) | −7152.00 | −0.613738 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14120.0 | 1.20465 | ||||||||
\(517\) | − 4374.00i | − 0.372086i | ||||||||
\(518\) | 4270.00i | 0.362187i | ||||||||
\(519\) | 8340.00 | 0.705367 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17022.0 | 1.43138 | 0.715688 | − | 0.698420i | \(-0.246113\pi\) | ||||
0.715688 | + | 0.698420i | \(0.246113\pi\) | |||||||
\(522\) | − 27594.0i | − 2.31371i | ||||||||
\(523\) | 15748.0i | 1.31666i | 0.752730 | + | 0.658329i | \(0.228736\pi\) | ||||
−0.752730 | + | 0.658329i | \(0.771264\pi\) | |||||||
\(524\) | 4464.00 | 0.372158 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11838.0 | 0.981295 | ||||||||
\(527\) | − 22272.0i | − 1.84096i | ||||||||
\(528\) | − 1440.00i | − 0.118689i | ||||||||
\(529\) | 6542.00 | 0.537684 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −49056.0 | −4.00913 | ||||||||
\(532\) | − 280.000i | − 0.0228187i | ||||||||
\(533\) | − 22776.0i | − 1.85092i | ||||||||
\(534\) | 3600.00 | 0.291736 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4792.00 | −0.386162 | ||||||||
\(537\) | − 6480.00i | − 0.520731i | ||||||||
\(538\) | − 3528.00i | − 0.282719i | ||||||||
\(539\) | −441.000 | −0.0352416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3373.00 | −0.268053 | −0.134026 | − | 0.990978i | \(-0.542791\pi\) | ||||
−0.134026 | + | 0.990978i | \(0.542791\pi\) | |||||||
\(542\) | 680.000i | 0.0538902i | ||||||||
\(543\) | 29140.0i | 2.30298i | ||||||||
\(544\) | 3072.00 | 0.242116 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7280.00 | 0.570614 | ||||||||
\(547\) | − 14389.0i | − 1.12473i | −0.826888 | − | 0.562367i | \(-0.809891\pi\) | ||||
0.826888 | − | 0.562367i | \(-0.190109\pi\) | |||||||
\(548\) | 5592.00i | 0.435909i | ||||||||
\(549\) | −15038.0 | −1.16905 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1890.00 | −0.146128 | ||||||||
\(552\) | − 6000.00i | − 0.462639i | ||||||||
\(553\) | − 5201.00i | − 0.399944i | ||||||||
\(554\) | 9412.00 | 0.721801 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2696.00 | 0.205640 | ||||||||
\(557\) | − 4929.00i | − 0.374952i | −0.982269 | − | 0.187476i | \(-0.939969\pi\) | ||||
0.982269 | − | 0.187476i | \(-0.0600307\pi\) | |||||||
\(558\) | − 33872.0i | − 2.56974i | ||||||||
\(559\) | 18356.0 | 1.38887 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8640.00 | 0.650234 | ||||||||
\(562\) | − 13362.0i | − 1.00292i | ||||||||
\(563\) | − 15678.0i | − 1.17362i | −0.809724 | − | 0.586811i | \(-0.800383\pi\) | ||||
0.809724 | − | 0.586811i | \(-0.199617\pi\) | |||||||
\(564\) | 19440.0 | 1.45137 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 452.000 | 0.0335671 | ||||||||
\(567\) | 18403.0i | 1.36306i | ||||||||
\(568\) | − 3768.00i | − 0.278348i | ||||||||
\(569\) | 14499.0 | 1.06824 | 0.534121 | − | 0.845408i | \(-0.320643\pi\) | ||||
0.534121 | + | 0.845408i | \(0.320643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9457.00 | −0.693105 | −0.346553 | − | 0.938031i | \(-0.612648\pi\) | ||||
−0.346553 | + | 0.938031i | \(0.612648\pi\) | |||||||
\(572\) | − 1872.00i | − 0.136840i | ||||||||
\(573\) | 8760.00i | 0.638664i | ||||||||
\(574\) | −6132.00 | −0.445897 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4672.00 | 0.337963 | ||||||||
\(577\) | 10370.0i | 0.748195i | 0.927389 | + | 0.374098i | \(0.122048\pi\) | ||||
−0.927389 | + | 0.374098i | \(0.877952\pi\) | |||||||
\(578\) | 8606.00i | 0.619312i | ||||||||
\(579\) | 6010.00 | 0.431377 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6972.00 | 0.497844 | ||||||||
\(582\) | 3680.00i | 0.262098i | ||||||||
\(583\) | 3186.00i | 0.226330i | ||||||||
\(584\) | 4912.00 | 0.348048 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8640.00 | −0.609070 | ||||||||
\(587\) | − 12126.0i | − 0.852630i | −0.904575 | − | 0.426315i | \(-0.859812\pi\) | ||||
0.904575 | − | 0.426315i | \(-0.140188\pi\) | |||||||
\(588\) | − 1960.00i | − 0.137464i | ||||||||
\(589\) | −2320.00 | −0.162299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20130.0 | −1.40108 | ||||||||
\(592\) | 4880.00i | 0.338795i | ||||||||
\(593\) | − 1068.00i | − 0.0739587i | −0.999316 | − | 0.0369793i | \(-0.988226\pi\) | ||||
0.999316 | − | 0.0369793i | \(-0.0117736\pi\) | |||||||
\(594\) | 8280.00 | 0.571940 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5124.00 | −0.352160 | ||||||||
\(597\) | 3260.00i | 0.223489i | ||||||||
\(598\) | − 7800.00i | − 0.533387i | ||||||||
\(599\) | −3375.00 | −0.230215 | −0.115107 | − | 0.993353i | \(-0.536721\pi\) | ||||
−0.115107 | + | 0.993353i | \(0.536721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27448.0 | −1.86294 | −0.931470 | − | 0.363817i | \(-0.881473\pi\) | ||||
−0.931470 | + | 0.363817i | \(0.881473\pi\) | |||||||
\(602\) | − 4942.00i | − 0.334586i | ||||||||
\(603\) | − 43727.0i | − 2.95307i | ||||||||
\(604\) | −3812.00 | −0.256801 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14520.0 | 0.973325 | ||||||||
\(607\) | 3884.00i | 0.259714i | 0.991533 | + | 0.129857i | \(0.0414519\pi\) | ||||
−0.991533 | + | 0.129857i | \(0.958548\pi\) | |||||||
\(608\) | − 320.000i | − 0.0213449i | ||||||||
\(609\) | −13230.0 | −0.880306 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25272.0 | 1.67332 | ||||||||
\(612\) | 28032.0i | 1.85151i | ||||||||
\(613\) | 3643.00i | 0.240032i | 0.992772 | + | 0.120016i | \(0.0382945\pi\) | ||||
−0.992772 | + | 0.120016i | \(0.961705\pi\) | |||||||
\(614\) | −13208.0 | −0.868129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −504.000 | −0.0329655 | ||||||||
\(617\) | 30369.0i | 1.98154i | 0.135555 | + | 0.990770i | \(0.456718\pi\) | ||||
−0.135555 | + | 0.990770i | \(0.543282\pi\) | |||||||
\(618\) | − 35960.0i | − 2.34065i | ||||||||
\(619\) | 10888.0 | 0.706988 | 0.353494 | − | 0.935437i | \(-0.384993\pi\) | ||||
0.353494 | + | 0.935437i | \(0.384993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34500.0 | 2.22937 | ||||||||
\(622\) | − 12072.0i | − 0.778204i | ||||||||
\(623\) | − 1260.00i | − 0.0810286i | ||||||||
\(624\) | 8320.00 | 0.533761 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18292.0 | −1.16788 | ||||||||
\(627\) | − 900.000i | − 0.0573246i | ||||||||
\(628\) | − 2600.00i | − 0.165209i | ||||||||
\(629\) | −29280.0 | −1.85607 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28499.0 | 1.79798 | 0.898992 | − | 0.437966i | \(-0.144301\pi\) | ||||
0.898992 | + | 0.437966i | \(0.144301\pi\) | |||||||
\(632\) | − 5944.00i | − 0.374113i | ||||||||
\(633\) | 59560.0i | 3.73981i | ||||||||
\(634\) | −8898.00 | −0.557389 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14160.0 | −0.882831 | ||||||||
\(637\) | − 2548.00i | − 0.158486i | ||||||||
\(638\) | 3402.00i | 0.211107i | ||||||||
\(639\) | 34383.0 | 2.12859 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5817.00 | 0.358436 | 0.179218 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179218 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(642\) | − 17520.0i | − 1.07704i | ||||||||
\(643\) | − 22376.0i | − 1.37235i | −0.727435 | − | 0.686177i | \(-0.759288\pi\) | ||||
0.727435 | − | 0.686177i | \(-0.240712\pi\) | |||||||
\(644\) | −2100.00 | −0.128496 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1920.00 | 0.116937 | ||||||||
\(647\) | 3018.00i | 0.183385i | 0.995787 | + | 0.0916923i | \(0.0292276\pi\) | ||||
−0.995787 | + | 0.0916923i | \(0.970772\pi\) | |||||||
\(648\) | 21032.0i | 1.27502i | ||||||||
\(649\) | 6048.00 | 0.365801 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16240.0 | −0.977720 | ||||||||
\(652\) | 3728.00i | 0.223926i | ||||||||
\(653\) | 29682.0i | 1.77878i | 0.457145 | + | 0.889392i | \(0.348872\pi\) | ||||
−0.457145 | + | 0.889392i | \(0.651128\pi\) | |||||||
\(654\) | −13820.0 | −0.826307 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7008.00 | −0.417098 | ||||||||
\(657\) | 44822.0i | 2.66160i | ||||||||
\(658\) | − 6804.00i | − 0.403112i | ||||||||
\(659\) | −2052.00 | −0.121297 | −0.0606484 | − | 0.998159i | \(-0.519317\pi\) | ||||
−0.0606484 | + | 0.998159i | \(0.519317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14222.0 | 0.836871 | 0.418435 | − | 0.908247i | \(-0.362579\pi\) | ||||
0.418435 | + | 0.908247i | \(0.362579\pi\) | |||||||
\(662\) | 20162.0i | 1.18371i | ||||||||
\(663\) | 49920.0i | 2.92418i | ||||||||
\(664\) | 7968.00 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −44530.0 | −2.59084 | ||||||||
\(667\) | 14175.0i | 0.822876i | ||||||||
\(668\) | 720.000i | 0.0417030i | ||||||||
\(669\) | 31180.0 | 1.80193 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1854.00 | 0.106666 | ||||||||
\(672\) | − 2240.00i | − 0.128586i | ||||||||
\(673\) | − 20942.0i | − 1.19949i | −0.800192 | − | 0.599744i | \(-0.795269\pi\) | ||||
0.800192 | − | 0.599744i | \(-0.204731\pi\) | |||||||
\(674\) | 15556.0 | 0.889013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2028.00 | 0.115385 | ||||||||
\(677\) | 13074.0i | 0.742208i | 0.928591 | + | 0.371104i | \(0.121021\pi\) | ||||
−0.928591 | + | 0.371104i | \(0.878979\pi\) | |||||||
\(678\) | − 30420.0i | − 1.72312i | ||||||||
\(679\) | 1288.00 | 0.0727966 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.0000 | −0.00337622 | ||||||||
\(682\) | 4176.00i | 0.234468i | ||||||||
\(683\) | 31383.0i | 1.75818i | 0.476656 | + | 0.879090i | \(0.341849\pi\) | ||||
−0.476656 | + | 0.879090i | \(0.658151\pi\) | |||||||
\(684\) | 2920.00 | 0.163230 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | − 5860.00i | − 0.325434i | ||||||||
\(688\) | − 5648.00i | − 0.312977i | ||||||||
\(689\) | −18408.0 | −1.01784 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −622.000 | −0.0342431 | −0.0171216 | − | 0.999853i | \(-0.505450\pi\) | ||||
−0.0171216 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(692\) | − 3336.00i | − 0.183260i | ||||||||
\(693\) | − 4599.00i | − 0.252095i | ||||||||
\(694\) | 2034.00 | 0.111253 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15120.0 | −0.823451 | ||||||||
\(697\) | − 42048.0i | − 2.28505i | ||||||||
\(698\) | 20740.0i | 1.12467i | ||||||||
\(699\) | −12930.0 | −0.699653 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7782.00 | 0.419290 | 0.209645 | − | 0.977778i | \(-0.432769\pi\) | ||||
0.209645 | + | 0.977778i | \(0.432769\pi\) | |||||||
\(702\) | 47840.0i | 2.57209i | ||||||||
\(703\) | 3050.00i | 0.163631i | ||||||||
\(704\) | −576.000 | −0.0308364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18864.0 | 1.00560 | ||||||||
\(707\) | − 5082.00i | − 0.270337i | ||||||||
\(708\) | 26880.0i | 1.42685i | ||||||||
\(709\) | −7502.00 | −0.397382 | −0.198691 | − | 0.980062i | \(-0.563669\pi\) | ||||
−0.198691 | + | 0.980062i | \(0.563669\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 54239.0 | 2.86093 | ||||||||
\(712\) | − 1440.00i | − 0.0757953i | ||||||||
\(713\) | 17400.0i | 0.913934i | ||||||||
\(714\) | 13440.0 | 0.704453 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2592.00 | −0.135290 | ||||||||
\(717\) | − 53760.0i | − 2.80015i | ||||||||
\(718\) | 15114.0i | 0.785584i | ||||||||
\(719\) | 20814.0 | 1.07960 | 0.539799 | − | 0.841794i | \(-0.318500\pi\) | ||||
0.539799 | + | 0.841794i | \(0.318500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12586.0 | −0.650107 | ||||||||
\(722\) | 13518.0i | 0.696798i | ||||||||
\(723\) | 6700.00i | 0.344641i | ||||||||
\(724\) | 11656.0 | 0.598331 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25000.0 | 1.27801 | ||||||||
\(727\) | 14360.0i | 0.732576i | 0.930501 | + | 0.366288i | \(0.119372\pi\) | ||||
−0.930501 | + | 0.366288i | \(0.880628\pi\) | |||||||
\(728\) | − 2912.00i | − 0.148250i | ||||||||
\(729\) | −67717.0 | −3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33888.0 | 1.71463 | ||||||||
\(732\) | 8240.00i | 0.416064i | ||||||||
\(733\) | 1588.00i | 0.0800193i | 0.999199 | + | 0.0400096i | \(0.0127389\pi\) | ||||
−0.999199 | + | 0.0400096i | \(0.987261\pi\) | |||||||
\(734\) | −23324.0 | −1.17289 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2400.00 | −0.120197 | ||||||||
\(737\) | 5391.00i | 0.269444i | ||||||||
\(738\) | − 63948.0i | − 3.18965i | ||||||||
\(739\) | −2957.00 | −0.147192 | −0.0735961 | − | 0.997288i | \(-0.523448\pi\) | ||||
−0.0735961 | + | 0.997288i | \(0.523448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5200.00 | 0.257796 | ||||||||
\(742\) | 4956.00i | 0.245203i | ||||||||
\(743\) | 12384.0i | 0.611474i | 0.952116 | + | 0.305737i | \(0.0989028\pi\) | ||||
−0.952116 | + | 0.305737i | \(0.901097\pi\) | |||||||
\(744\) | −18560.0 | −0.914573 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4754.00 | 0.233319 | ||||||||
\(747\) | 72708.0i | 3.56124i | ||||||||
\(748\) | − 3456.00i | − 0.168936i | ||||||||
\(749\) | −6132.00 | −0.299143 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20236.0 | −0.983252 | −0.491626 | − | 0.870806i | \(-0.663597\pi\) | ||||
−0.491626 | + | 0.870806i | \(0.663597\pi\) | |||||||
\(752\) | − 7776.00i | − 0.377077i | ||||||||
\(753\) | − 13800.0i | − 0.667862i | ||||||||
\(754\) | −19656.0 | −0.949376 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12880.0 | 0.619631 | ||||||||
\(757\) | 37601.0i | 1.80533i | 0.430348 | + | 0.902663i | \(0.358391\pi\) | ||||
−0.430348 | + | 0.902663i | \(0.641609\pi\) | |||||||
\(758\) | 8854.00i | 0.424264i | ||||||||
\(759\) | −6750.00 | −0.322806 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13392.0 | −0.637923 | −0.318962 | − | 0.947768i | \(-0.603334\pi\) | ||||
−0.318962 | + | 0.947768i | \(0.603334\pi\) | |||||||
\(762\) | − 20620.0i | − 0.980294i | ||||||||
\(763\) | 4837.00i | 0.229503i | ||||||||
\(764\) | 3504.00 | 0.165930 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9216.00 | −0.434710 | ||||||||
\(767\) | 34944.0i | 1.64505i | ||||||||
\(768\) | − 2560.00i | − 0.120281i | ||||||||
\(769\) | −22430.0 | −1.05182 | −0.525908 | − | 0.850541i | \(-0.676274\pi\) | ||||
−0.525908 | + | 0.850541i | \(0.676274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35760.0 | −1.67038 | ||||||||
\(772\) | − 2404.00i | − 0.112075i | ||||||||
\(773\) | − 34704.0i | − 1.61477i | −0.590026 | − | 0.807384i | \(-0.700882\pi\) | ||||
0.590026 | − | 0.807384i | \(-0.299118\pi\) | |||||||
\(774\) | 51538.0 | 2.39340 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1472.00 | 0.0680950 | ||||||||
\(777\) | 21350.0i | 0.985749i | ||||||||
\(778\) | − 1398.00i | − 0.0644225i | ||||||||
\(779\) | −4380.00 | −0.201450 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4239.00 | −0.194217 | ||||||||
\(782\) | − 14400.0i | − 0.658495i | ||||||||
\(783\) | − 86940.0i | − 3.96805i | ||||||||
\(784\) | −784.000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22320.0 | 1.01289 | ||||||||
\(787\) | 37646.0i | 1.70513i | 0.522624 | + | 0.852564i | \(0.324953\pi\) | ||||
−0.522624 | + | 0.852564i | \(0.675047\pi\) | |||||||
\(788\) | 8052.00i | 0.364011i | ||||||||
\(789\) | 59190.0 | 2.67075 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10647.0 | −0.478589 | ||||||||
\(792\) | − 5256.00i | − 0.235813i | ||||||||
\(793\) | 10712.0i | 0.479690i | ||||||||
\(794\) | −15260.0 | −0.682062 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1304.00 | 0.0580641 | ||||||||
\(797\) | − 8988.00i | − 0.399462i | −0.979851 | − | 0.199731i | \(-0.935993\pi\) | ||||
0.979851 | − | 0.199731i | \(-0.0640068\pi\) | |||||||
\(798\) | − 1400.00i | − 0.0621046i | ||||||||
\(799\) | 46656.0 | 2.06580 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13140.0 | 0.579624 | ||||||||
\(802\) | − 11202.0i | − 0.493212i | ||||||||
\(803\) | − 5526.00i | − 0.242850i | ||||||||
\(804\) | −23960.0 | −1.05100 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24128.0 | −1.05443 | ||||||||
\(807\) | − 17640.0i | − 0.769464i | ||||||||
\(808\) | − 5808.00i | − 0.252877i | ||||||||
\(809\) | 28029.0 | 1.21811 | 0.609053 | − | 0.793130i | \(-0.291550\pi\) | ||||
0.609053 | + | 0.793130i | \(0.291550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8078.00 | 0.349762 | 0.174881 | − | 0.984590i | \(-0.444046\pi\) | ||||
0.174881 | + | 0.984590i | \(0.444046\pi\) | |||||||
\(812\) | 5292.00i | 0.228710i | ||||||||
\(813\) | 3400.00i | 0.146671i | ||||||||
\(814\) | 5490.00 | 0.236394 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15360.0 | 0.658955 | ||||||||
\(817\) | − 3530.00i | − 0.151162i | ||||||||
\(818\) | 9340.00i | 0.399224i | ||||||||
\(819\) | 26572.0 | 1.13370 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35574.0 | −1.51223 | −0.756115 | − | 0.654439i | \(-0.772905\pi\) | ||||
−0.756115 | + | 0.654439i | \(0.772905\pi\) | |||||||
\(822\) | 27960.0i | 1.18640i | ||||||||
\(823\) | − 6599.00i | − 0.279498i | −0.990187 | − | 0.139749i | \(-0.955370\pi\) | ||||
0.990187 | − | 0.139749i | \(-0.0446295\pi\) | |||||||
\(824\) | −14384.0 | −0.608119 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9408.00 | 0.396303 | ||||||||
\(827\) | − 663.000i | − 0.0278776i | −0.999903 | − | 0.0139388i | \(-0.995563\pi\) | ||||
0.999903 | − | 0.0139388i | \(-0.00443700\pi\) | |||||||
\(828\) | − 21900.0i | − 0.919176i | ||||||||
\(829\) | 22564.0 | 0.945332 | 0.472666 | − | 0.881242i | \(-0.343292\pi\) | ||||
0.472666 | + | 0.881242i | \(0.343292\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 47060.0 | 1.96449 | ||||||||
\(832\) | − 3328.00i | − 0.138675i | ||||||||
\(833\) | − 4704.00i | − 0.195659i | ||||||||
\(834\) | 13480.0 | 0.559681 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −360.000 | −0.0148934 | ||||||||
\(837\) | − 106720.i | − 4.40715i | ||||||||
\(838\) | 72.0000i | 0.00296802i | ||||||||
\(839\) | 294.000 | 0.0120977 | 0.00604887 | − | 0.999982i | \(-0.498075\pi\) | ||||
0.00604887 | + | 0.999982i | \(0.498075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11332.0 | 0.464636 | ||||||||
\(842\) | − 10990.0i | − 0.449810i | ||||||||
\(843\) | − 66810.0i | − 2.72961i | ||||||||
\(844\) | 23824.0 | 0.971630 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 70956.0 | 2.88359 | ||||||||
\(847\) | − 8750.00i | − 0.354963i | ||||||||
\(848\) | 5664.00i | 0.229366i | ||||||||
\(849\) | 2260.00 | 0.0913581 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22875.0 | 0.921439 | ||||||||
\(852\) | − 18840.0i | − 0.757568i | ||||||||
\(853\) | 28852.0i | 1.15812i | 0.815286 | + | 0.579058i | \(0.196580\pi\) | ||||
−0.815286 | + | 0.579058i | \(0.803420\pi\) | |||||||
\(854\) | 2884.00 | 0.115560 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7008.00 | −0.279823 | ||||||||
\(857\) | − 7422.00i | − 0.295835i | −0.989000 | − | 0.147918i | \(-0.952743\pi\) | ||||
0.989000 | − | 0.147918i | \(-0.0472570\pi\) | |||||||
\(858\) | − 9360.00i | − 0.372430i | ||||||||
\(859\) | −8138.00 | −0.323242 | −0.161621 | − | 0.986853i | \(-0.551672\pi\) | ||||
−0.161621 | + | 0.986853i | \(0.551672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30660.0 | −1.21358 | ||||||||
\(862\) | − 5400.00i | − 0.213370i | ||||||||
\(863\) | 32199.0i | 1.27007i | 0.772485 | + | 0.635033i | \(0.219013\pi\) | ||||
−0.772485 | + | 0.635033i | \(0.780987\pi\) | |||||||
\(864\) | 14720.0 | 0.579612 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30208.0 | −1.18535 | ||||||||
\(867\) | 43030.0i | 1.68555i | ||||||||
\(868\) | 6496.00i | 0.254019i | ||||||||
\(869\) | −6687.00 | −0.261037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31148.0 | −1.21172 | ||||||||
\(872\) | 5528.00i | 0.214681i | ||||||||
\(873\) | 13432.0i | 0.520738i | ||||||||
\(874\) | −1500.00 | −0.0580529 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24560.0 | 0.947267 | ||||||||
\(877\) | − 11158.0i | − 0.429622i | −0.976656 | − | 0.214811i | \(-0.931086\pi\) | ||||
0.976656 | − | 0.214811i | \(-0.0689136\pi\) | |||||||
\(878\) | 29896.0i | 1.14914i | ||||||||
\(879\) | −43200.0 | −1.65768 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16272.0 | 0.622267 | 0.311134 | − | 0.950366i | \(-0.399291\pi\) | ||||
0.311134 | + | 0.950366i | \(0.399291\pi\) | |||||||
\(882\) | − 7154.00i | − 0.273115i | ||||||||
\(883\) | − 9071.00i | − 0.345712i | −0.984947 | − | 0.172856i | \(-0.944701\pi\) | ||||
0.984947 | − | 0.172856i | \(-0.0552995\pi\) | |||||||
\(884\) | 19968.0 | 0.759725 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9960.00 | −0.377667 | ||||||||
\(887\) | − 30138.0i | − 1.14085i | −0.821349 | − | 0.570426i | \(-0.806778\pi\) | ||||
0.821349 | − | 0.570426i | \(-0.193222\pi\) | |||||||
\(888\) | 24400.0i | 0.922084i | ||||||||
\(889\) | −7217.00 | −0.272273 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23661.0 | 0.889645 | ||||||||
\(892\) | − 12472.0i | − 0.468154i | ||||||||
\(893\) | − 4860.00i | − 0.182121i | ||||||||
\(894\) | −25620.0 | −0.958457 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | − 39000.0i | − 1.45170i | ||||||||
\(898\) | 24750.0i | 0.919731i | ||||||||
\(899\) | 43848.0 | 1.62671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33984.0 | −1.25657 | ||||||||
\(902\) | 7884.00i | 0.291029i | ||||||||
\(903\) | − 24710.0i | − 0.910628i | ||||||||
\(904\) | −12168.0 | −0.447679 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −19060.0 | −0.698925 | ||||||||
\(907\) | 25844.0i | 0.946126i | 0.881029 | + | 0.473063i | \(0.156852\pi\) | ||||
−0.881029 | + | 0.473063i | \(0.843148\pi\) | |||||||
\(908\) | 24.0000i | 0 0.000877167i | ||||||||
\(909\) | 52998.0 | 1.93381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40815.0 | 1.48437 | 0.742185 | − | 0.670195i | \(-0.233790\pi\) | ||||
0.742185 | + | 0.670195i | \(0.233790\pi\) | |||||||
\(912\) | − 1600.00i | − 0.0580935i | ||||||||
\(913\) | − 8964.00i | − 0.324934i | ||||||||
\(914\) | 21670.0 | 0.784223 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2344.00 | −0.0845502 | ||||||||
\(917\) | − 7812.00i | − 0.281325i | ||||||||
\(918\) | 88320.0i | 3.17538i | ||||||||
\(919\) | 5389.00 | 0.193435 | 0.0967175 | − | 0.995312i | \(-0.469166\pi\) | ||||
0.0967175 | + | 0.995312i | \(0.469166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −66040.0 | −2.36275 | ||||||||
\(922\) | − 11400.0i | − 0.407201i | ||||||||
\(923\) | − 24492.0i | − 0.873417i | ||||||||
\(924\) | −2520.00 | −0.0897207 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12256.0 | −0.434943 | ||||||||
\(927\) | − 131254.i | − 4.65043i | ||||||||
\(928\) | 6048.00i | 0.213939i | ||||||||
\(929\) | −43662.0 | −1.54198 | −0.770992 | − | 0.636844i | \(-0.780239\pi\) | ||||
−0.770992 | + | 0.636844i | \(0.780239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −490.000 | −0.0172493 | ||||||||
\(932\) | 5172.00i | 0.181775i | ||||||||
\(933\) | − 60360.0i | − 2.11800i | ||||||||
\(934\) | −19620.0 | −0.687351 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30368.0 | 1.06048 | ||||||||
\(937\) | − 11950.0i | − 0.416638i | −0.978061 | − | 0.208319i | \(-0.933201\pi\) | ||||
0.978061 | − | 0.208319i | \(-0.0667992\pi\) | |||||||
\(938\) | 8386.00i | 0.291911i | ||||||||
\(939\) | −91460.0 | −3.17858 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8448.00 | −0.292664 | −0.146332 | − | 0.989236i | \(-0.546747\pi\) | ||||
−0.146332 | + | 0.989236i | \(0.546747\pi\) | |||||||
\(942\) | − 13000.0i | − 0.449642i | ||||||||
\(943\) | 32850.0i | 1.13440i | ||||||||
\(944\) | 10752.0 | 0.370707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6354.00 | −0.218379 | ||||||||
\(947\) | 25692.0i | 0.881603i | 0.897605 | + | 0.440801i | \(0.145306\pi\) | ||||
−0.897605 | + | 0.440801i | \(0.854694\pi\) | |||||||
\(948\) | − 29720.0i | − 1.01821i | ||||||||
\(949\) | 31928.0 | 1.09213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44490.0 | −1.51702 | ||||||||
\(952\) | − 5376.00i | − 0.183022i | ||||||||
\(953\) | − 47547.0i | − 1.61616i | −0.589074 | − | 0.808079i | \(-0.700507\pi\) | ||||
0.589074 | − | 0.808079i | \(-0.299493\pi\) | |||||||
\(954\) | −51684.0 | −1.75402 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21504.0 | −0.727499 | ||||||||
\(957\) | 17010.0i | 0.574561i | ||||||||
\(958\) | − 408.000i | − 0.0137598i | ||||||||
\(959\) | 9786.00 | 0.329517 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24033.0 | 0.806720 | ||||||||
\(962\) | 31720.0i | 1.06309i | ||||||||
\(963\) | − 63948.0i | − 2.13987i | ||||||||
\(964\) | 2680.00 | 0.0895404 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −10500.0 | −0.349723 | ||||||||
\(967\) | 51608.0i | 1.71624i | 0.513452 | + | 0.858119i | \(0.328367\pi\) | ||||
−0.513452 | + | 0.858119i | \(0.671633\pi\) | |||||||
\(968\) | − 10000.0i | − 0.332037i | ||||||||
\(969\) | 9600.00 | 0.318263 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11754.0 | −0.388469 | −0.194235 | − | 0.980955i | \(-0.562222\pi\) | ||||
−0.194235 | + | 0.980955i | \(0.562222\pi\) | |||||||
\(972\) | 55480.0i | 1.83078i | ||||||||
\(973\) | − 4718.00i | − 0.155449i | ||||||||
\(974\) | 30802.0 | 1.01331 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3296.00 | 0.108097 | ||||||||
\(977\) | 12765.0i | 0.418003i | 0.977915 | + | 0.209001i | \(0.0670213\pi\) | ||||
−0.977915 | + | 0.209001i | \(0.932979\pi\) | |||||||
\(978\) | 18640.0i | 0.609449i | ||||||||
\(979\) | −1620.00 | −0.0528860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50443.0 | −1.64171 | ||||||||
\(982\) | − 7794.00i | − 0.253275i | ||||||||
\(983\) | 32112.0i | 1.04193i | 0.853579 | + | 0.520963i | \(0.174427\pi\) | ||||
−0.853579 | + | 0.520963i | \(0.825573\pi\) | |||||||
\(984\) | −35040.0 | −1.13520 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36288.0 | −1.17205 | ||||||||
\(987\) | − 34020.0i | − 1.09713i | ||||||||
\(988\) | − 2080.00i | − 0.0669773i | ||||||||
\(989\) | −26475.0 | −0.851219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42505.0 | −1.36248 | −0.681239 | − | 0.732061i | \(-0.738559\pi\) | ||||
−0.681239 | + | 0.732061i | \(0.738559\pi\) | |||||||
\(992\) | 7424.00i | 0.237613i | ||||||||
\(993\) | 100810.i | 3.22166i | ||||||||
\(994\) | −6594.00 | −0.210411 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 39840.0 | 1.26745 | ||||||||
\(997\) | 59654.0i | 1.89495i | 0.319836 | + | 0.947473i | \(0.396372\pi\) | ||||
−0.319836 | + | 0.947473i | \(0.603628\pi\) | |||||||
\(998\) | 16264.0i | 0.515860i | ||||||||
\(999\) | −140300. | −4.44334 |
(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 | 350.4.c.a.99.1 | 2 | ||
5.2 | odd | 4 | 350.4.a.k.1.1 | yes | 1 | ||
5.3 | odd | 4 | 350.4.a.j.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 350.4.c.a.99.2 | 2 | ||
35.13 | even | 4 | 2450.4.a.a.1.1 | 1 | |||
35.27 | even | 4 | 2450.4.a.bp.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.4.a.j.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
350.4.a.k.1.1 | yes | 1 | 5.2 | odd | 4 | ||
350.4.c.a.99.1 | 2 | 1.1 | even | 1 | trivial | ||
350.4.c.a.99.2 | 2 | 5.4 | even | 2 | inner | ||
2450.4.a.a.1.1 | 1 | 35.13 | even | 4 | |||
2450.4.a.bp.1.1 | 1 | 35.27 | even | 4 |