Newspace parameters
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(54.8717763053\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 26.0000 | 1.40387 | 0.701934 | − | 0.712242i | \(-0.252320\pi\) | ||||
0.701934 | + | 0.712242i | \(0.252320\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −48.0000 | −1.31569 | −0.657843 | − | 0.753155i | \(-0.728531\pi\) | ||||
−0.657843 | + | 0.753155i | \(0.728531\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −88.0000 | −1.87745 | −0.938723 | − | 0.344671i | \(-0.887990\pi\) | ||||
−0.938723 | + | 0.344671i | \(0.887990\pi\) | |||||||
\(14\) | 52.0000 | 0.992685 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −160.000 | −1.93192 | −0.965961 | − | 0.258688i | \(-0.916710\pi\) | ||||
−0.965961 | + | 0.258688i | \(0.916710\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 78.0000 | 0.810524 | ||||||||
\(22\) | −96.0000 | −0.930330 | ||||||||
\(23\) | −48.0000 | −0.435161 | −0.217580 | − | 0.976042i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976042i | \(0.569816\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −176.000 | −1.32756 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 104.000 | 0.701934 | ||||||||
\(29\) | −120.000 | −0.768395 | −0.384197 | − | 0.923251i | \(-0.625522\pi\) | ||||
−0.384197 | + | 0.923251i | \(0.625522\pi\) | |||||||
\(30\) | −30.0000 | −0.182574 | ||||||||
\(31\) | 31.0000 | 0.179605 | ||||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −144.000 | −0.759612 | ||||||||
\(34\) | −108.000 | −0.544760 | ||||||||
\(35\) | −130.000 | −0.627829 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −304.000 | −1.35074 | −0.675369 | − | 0.737480i | \(-0.736016\pi\) | ||||
−0.675369 | + | 0.737480i | \(0.736016\pi\) | |||||||
\(38\) | −320.000 | −1.36608 | ||||||||
\(39\) | −264.000 | −1.08394 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 162.000 | 0.617077 | 0.308538 | − | 0.951212i | \(-0.400160\pi\) | ||||
0.308538 | + | 0.951212i | \(0.400160\pi\) | |||||||
\(42\) | 156.000 | 0.573127 | ||||||||
\(43\) | 272.000 | 0.964642 | 0.482321 | − | 0.875995i | \(-0.339794\pi\) | ||||
0.482321 | + | 0.875995i | \(0.339794\pi\) | |||||||
\(44\) | −192.000 | −0.657843 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | −96.0000 | −0.307705 | ||||||||
\(47\) | 96.0000 | 0.297937 | 0.148969 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148969 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 333.000 | 0.970845 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | −162.000 | −0.444795 | ||||||||
\(52\) | −352.000 | −0.938723 | ||||||||
\(53\) | 582.000 | 1.50837 | 0.754187 | − | 0.656659i | \(-0.228031\pi\) | ||||
0.754187 | + | 0.656659i | \(0.228031\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 240.000 | 0.588393 | ||||||||
\(56\) | 208.000 | 0.496342 | ||||||||
\(57\) | −480.000 | −1.11540 | ||||||||
\(58\) | −240.000 | −0.543337 | ||||||||
\(59\) | 30.0000 | 0.0661978 | 0.0330989 | − | 0.999452i | \(-0.489462\pi\) | ||||
0.0330989 | + | 0.999452i | \(0.489462\pi\) | |||||||
\(60\) | −60.0000 | −0.129099 | ||||||||
\(61\) | −478.000 | −1.00331 | −0.501653 | − | 0.865069i | \(-0.667274\pi\) | ||||
−0.501653 | + | 0.865069i | \(0.667274\pi\) | |||||||
\(62\) | 62.0000 | 0.127000 | ||||||||
\(63\) | 234.000 | 0.467956 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 440.000 | 0.839620 | ||||||||
\(66\) | −288.000 | −0.537127 | ||||||||
\(67\) | −334.000 | −0.609024 | −0.304512 | − | 0.952509i | \(-0.598493\pi\) | ||||
−0.304512 | + | 0.952509i | \(0.598493\pi\) | |||||||
\(68\) | −216.000 | −0.385204 | ||||||||
\(69\) | −144.000 | −0.251240 | ||||||||
\(70\) | −260.000 | −0.443942 | ||||||||
\(71\) | 1062.00 | 1.77516 | 0.887579 | − | 0.460656i | \(-0.152386\pi\) | ||||
0.887579 | + | 0.460656i | \(0.152386\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 212.000 | 0.339900 | 0.169950 | − | 0.985453i | \(-0.445639\pi\) | ||||
0.169950 | + | 0.985453i | \(0.445639\pi\) | |||||||
\(74\) | −608.000 | −0.955116 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −640.000 | −0.965961 | ||||||||
\(77\) | −1248.00 | −1.84705 | ||||||||
\(78\) | −528.000 | −0.766464 | ||||||||
\(79\) | −640.000 | −0.911464 | −0.455732 | − | 0.890117i | \(-0.650622\pi\) | ||||
−0.455732 | + | 0.890117i | \(0.650622\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 324.000 | 0.436339 | ||||||||
\(83\) | 972.000 | 1.28543 | 0.642716 | − | 0.766105i | \(-0.277808\pi\) | ||||
0.642716 | + | 0.766105i | \(0.277808\pi\) | |||||||
\(84\) | 312.000 | 0.405262 | ||||||||
\(85\) | 270.000 | 0.344537 | ||||||||
\(86\) | 544.000 | 0.682105 | ||||||||
\(87\) | −360.000 | −0.443633 | ||||||||
\(88\) | −384.000 | −0.465165 | ||||||||
\(89\) | 120.000 | 0.142921 | 0.0714605 | − | 0.997443i | \(-0.477234\pi\) | ||||
0.0714605 | + | 0.997443i | \(0.477234\pi\) | |||||||
\(90\) | −90.0000 | −0.105409 | ||||||||
\(91\) | −2288.00 | −2.63569 | ||||||||
\(92\) | −192.000 | −0.217580 | ||||||||
\(93\) | 93.0000 | 0.103695 | ||||||||
\(94\) | 192.000 | 0.210673 | ||||||||
\(95\) | 800.000 | 0.863982 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 86.0000 | 0.0900204 | 0.0450102 | − | 0.998987i | \(-0.485668\pi\) | ||||
0.0450102 | + | 0.998987i | \(0.485668\pi\) | |||||||
\(98\) | 666.000 | 0.686491 | ||||||||
\(99\) | −432.000 | −0.438562 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1722.00 | 1.69649 | 0.848245 | − | 0.529605i | \(-0.177660\pi\) | ||||
0.848245 | + | 0.529605i | \(0.177660\pi\) | |||||||
\(102\) | −324.000 | −0.314517 | ||||||||
\(103\) | −1258.00 | −1.20344 | −0.601721 | − | 0.798707i | \(-0.705518\pi\) | ||||
−0.601721 | + | 0.798707i | \(0.705518\pi\) | |||||||
\(104\) | −704.000 | −0.663778 | ||||||||
\(105\) | −390.000 | −0.362477 | ||||||||
\(106\) | 1164.00 | 1.06658 | ||||||||
\(107\) | −1884.00 | −1.70218 | −0.851090 | − | 0.525021i | \(-0.824058\pi\) | ||||
−0.851090 | + | 0.525021i | \(0.824058\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −70.0000 | −0.0615118 | −0.0307559 | − | 0.999527i | \(-0.509791\pi\) | ||||
−0.0307559 | + | 0.999527i | \(0.509791\pi\) | |||||||
\(110\) | 480.000 | 0.416056 | ||||||||
\(111\) | −912.000 | −0.779849 | ||||||||
\(112\) | 416.000 | 0.350967 | ||||||||
\(113\) | −2178.00 | −1.81318 | −0.906589 | − | 0.422016i | \(-0.861323\pi\) | ||||
−0.906589 | + | 0.422016i | \(0.861323\pi\) | |||||||
\(114\) | −960.000 | −0.788704 | ||||||||
\(115\) | 240.000 | 0.194610 | ||||||||
\(116\) | −480.000 | −0.384197 | ||||||||
\(117\) | −792.000 | −0.625816 | ||||||||
\(118\) | 60.0000 | 0.0468089 | ||||||||
\(119\) | −1404.00 | −1.08155 | ||||||||
\(120\) | −120.000 | −0.0912871 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | −956.000 | −0.709444 | ||||||||
\(123\) | 486.000 | 0.356269 | ||||||||
\(124\) | 124.000 | 0.0898027 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 468.000 | 0.330895 | ||||||||
\(127\) | −2464.00 | −1.72161 | −0.860806 | − | 0.508934i | \(-0.830040\pi\) | ||||
−0.860806 | + | 0.508934i | \(0.830040\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 816.000 | 0.556936 | ||||||||
\(130\) | 880.000 | 0.593701 | ||||||||
\(131\) | −1458.00 | −0.972413 | −0.486206 | − | 0.873844i | \(-0.661620\pi\) | ||||
−0.486206 | + | 0.873844i | \(0.661620\pi\) | |||||||
\(132\) | −576.000 | −0.379806 | ||||||||
\(133\) | −4160.00 | −2.71216 | ||||||||
\(134\) | −668.000 | −0.430645 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −432.000 | −0.272380 | ||||||||
\(137\) | 966.000 | 0.602416 | 0.301208 | − | 0.953559i | \(-0.402610\pi\) | ||||
0.301208 | + | 0.953559i | \(0.402610\pi\) | |||||||
\(138\) | −288.000 | −0.177654 | ||||||||
\(139\) | 980.000 | 0.598004 | 0.299002 | − | 0.954253i | \(-0.403346\pi\) | ||||
0.299002 | + | 0.954253i | \(0.403346\pi\) | |||||||
\(140\) | −520.000 | −0.313914 | ||||||||
\(141\) | 288.000 | 0.172014 | ||||||||
\(142\) | 2124.00 | 1.25523 | ||||||||
\(143\) | 4224.00 | 2.47013 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 600.000 | 0.343636 | ||||||||
\(146\) | 424.000 | 0.240346 | ||||||||
\(147\) | 999.000 | 0.560518 | ||||||||
\(148\) | −1216.00 | −0.675369 | ||||||||
\(149\) | −30.0000 | −0.0164946 | −0.00824730 | − | 0.999966i | \(-0.502625\pi\) | ||||
−0.00824730 | + | 0.999966i | \(0.502625\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | 1832.00 | 0.987325 | 0.493662 | − | 0.869654i | \(-0.335658\pi\) | ||||
0.493662 | + | 0.869654i | \(0.335658\pi\) | |||||||
\(152\) | −1280.00 | −0.683038 | ||||||||
\(153\) | −486.000 | −0.256802 | ||||||||
\(154\) | −2496.00 | −1.30606 | ||||||||
\(155\) | −155.000 | −0.0803219 | ||||||||
\(156\) | −1056.00 | −0.541972 | ||||||||
\(157\) | 3566.00 | 1.81272 | 0.906362 | − | 0.422501i | \(-0.138848\pi\) | ||||
0.906362 | + | 0.422501i | \(0.138848\pi\) | |||||||
\(158\) | −1280.00 | −0.644502 | ||||||||
\(159\) | 1746.00 | 0.870860 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | −1248.00 | −0.610908 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −1798.00 | −0.863989 | −0.431995 | − | 0.901876i | \(-0.642190\pi\) | ||||
−0.431995 | + | 0.901876i | \(0.642190\pi\) | |||||||
\(164\) | 648.000 | 0.308538 | ||||||||
\(165\) | 720.000 | 0.339709 | ||||||||
\(166\) | 1944.00 | 0.908938 | ||||||||
\(167\) | −864.000 | −0.400349 | −0.200175 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200175 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(168\) | 624.000 | 0.286563 | ||||||||
\(169\) | 5547.00 | 2.52481 | ||||||||
\(170\) | 540.000 | 0.243624 | ||||||||
\(171\) | −1440.00 | −0.643974 | ||||||||
\(172\) | 1088.00 | 0.482321 | ||||||||
\(173\) | 1482.00 | 0.651297 | 0.325648 | − | 0.945491i | \(-0.394417\pi\) | ||||
0.325648 | + | 0.945491i | \(0.394417\pi\) | |||||||
\(174\) | −720.000 | −0.313696 | ||||||||
\(175\) | 650.000 | 0.280774 | ||||||||
\(176\) | −768.000 | −0.328921 | ||||||||
\(177\) | 90.0000 | 0.0382193 | ||||||||
\(178\) | 240.000 | 0.101060 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −180.000 | −0.0745356 | ||||||||
\(181\) | −358.000 | −0.147016 | −0.0735081 | − | 0.997295i | \(-0.523419\pi\) | ||||
−0.0735081 | + | 0.997295i | \(0.523419\pi\) | |||||||
\(182\) | −4576.00 | −1.86371 | ||||||||
\(183\) | −1434.00 | −0.579259 | ||||||||
\(184\) | −384.000 | −0.153852 | ||||||||
\(185\) | 1520.00 | 0.604068 | ||||||||
\(186\) | 186.000 | 0.0733236 | ||||||||
\(187\) | 2592.00 | 1.01361 | ||||||||
\(188\) | 384.000 | 0.148969 | ||||||||
\(189\) | 702.000 | 0.270175 | ||||||||
\(190\) | 1600.00 | 0.610927 | ||||||||
\(191\) | 1722.00 | 0.652354 | 0.326177 | − | 0.945309i | \(-0.394240\pi\) | ||||
0.326177 | + | 0.945309i | \(0.394240\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −418.000 | −0.155898 | −0.0779490 | − | 0.996957i | \(-0.524837\pi\) | ||||
−0.0779490 | + | 0.996957i | \(0.524837\pi\) | |||||||
\(194\) | 172.000 | 0.0636540 | ||||||||
\(195\) | 1320.00 | 0.484755 | ||||||||
\(196\) | 1332.00 | 0.485423 | ||||||||
\(197\) | −54.0000 | −0.0195296 | −0.00976482 | − | 0.999952i | \(-0.503108\pi\) | ||||
−0.00976482 | + | 0.999952i | \(0.503108\pi\) | |||||||
\(198\) | −864.000 | −0.310110 | ||||||||
\(199\) | −1720.00 | −0.612701 | −0.306351 | − | 0.951919i | \(-0.599108\pi\) | ||||
−0.306351 | + | 0.951919i | \(0.599108\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | −1002.00 | −0.351620 | ||||||||
\(202\) | 3444.00 | 1.19960 | ||||||||
\(203\) | −3120.00 | −1.07872 | ||||||||
\(204\) | −648.000 | −0.222397 | ||||||||
\(205\) | −810.000 | −0.275965 | ||||||||
\(206\) | −2516.00 | −0.850961 | ||||||||
\(207\) | −432.000 | −0.145054 | ||||||||
\(208\) | −1408.00 | −0.469362 | ||||||||
\(209\) | 7680.00 | 2.54180 | ||||||||
\(210\) | −780.000 | −0.256310 | ||||||||
\(211\) | −2488.00 | −0.811758 | −0.405879 | − | 0.913927i | \(-0.633035\pi\) | ||||
−0.405879 | + | 0.913927i | \(0.633035\pi\) | |||||||
\(212\) | 2328.00 | 0.754187 | ||||||||
\(213\) | 3186.00 | 1.02489 | ||||||||
\(214\) | −3768.00 | −1.20362 | ||||||||
\(215\) | −1360.00 | −0.431401 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 806.000 | 0.252142 | ||||||||
\(218\) | −140.000 | −0.0434954 | ||||||||
\(219\) | 636.000 | 0.196242 | ||||||||
\(220\) | 960.000 | 0.294196 | ||||||||
\(221\) | 4752.00 | 1.44640 | ||||||||
\(222\) | −1824.00 | −0.551436 | ||||||||
\(223\) | −3148.00 | −0.945317 | −0.472658 | − | 0.881246i | \(-0.656706\pi\) | ||||
−0.472658 | + | 0.881246i | \(0.656706\pi\) | |||||||
\(224\) | 832.000 | 0.248171 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −4356.00 | −1.28211 | ||||||||
\(227\) | 1536.00 | 0.449110 | 0.224555 | − | 0.974461i | \(-0.427907\pi\) | ||||
0.224555 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(228\) | −1920.00 | −0.557698 | ||||||||
\(229\) | −2770.00 | −0.799331 | −0.399665 | − | 0.916661i | \(-0.630874\pi\) | ||||
−0.399665 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(230\) | 480.000 | 0.137610 | ||||||||
\(231\) | −3744.00 | −1.06639 | ||||||||
\(232\) | −960.000 | −0.271668 | ||||||||
\(233\) | −2598.00 | −0.730475 | −0.365237 | − | 0.930914i | \(-0.619012\pi\) | ||||
−0.365237 | + | 0.930914i | \(0.619012\pi\) | |||||||
\(234\) | −1584.00 | −0.442518 | ||||||||
\(235\) | −480.000 | −0.133241 | ||||||||
\(236\) | 120.000 | 0.0330989 | ||||||||
\(237\) | −1920.00 | −0.526234 | ||||||||
\(238\) | −2808.00 | −0.764771 | ||||||||
\(239\) | −5340.00 | −1.44525 | −0.722627 | − | 0.691238i | \(-0.757066\pi\) | ||||
−0.722627 | + | 0.691238i | \(0.757066\pi\) | |||||||
\(240\) | −240.000 | −0.0645497 | ||||||||
\(241\) | 3002.00 | 0.802389 | 0.401195 | − | 0.915993i | \(-0.368595\pi\) | ||||
0.401195 | + | 0.915993i | \(0.368595\pi\) | |||||||
\(242\) | 1946.00 | 0.516916 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1912.00 | −0.501653 | ||||||||
\(245\) | −1665.00 | −0.434175 | ||||||||
\(246\) | 972.000 | 0.251921 | ||||||||
\(247\) | 14080.0 | 3.62708 | ||||||||
\(248\) | 248.000 | 0.0635001 | ||||||||
\(249\) | 2916.00 | 0.742145 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 2352.00 | 0.591462 | 0.295731 | − | 0.955271i | \(-0.404437\pi\) | ||||
0.295731 | + | 0.955271i | \(0.404437\pi\) | |||||||
\(252\) | 936.000 | 0.233978 | ||||||||
\(253\) | 2304.00 | 0.572535 | ||||||||
\(254\) | −4928.00 | −1.21736 | ||||||||
\(255\) | 810.000 | 0.198918 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −294.000 | −0.0713588 | −0.0356794 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356794 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(258\) | 1632.00 | 0.393813 | ||||||||
\(259\) | −7904.00 | −1.89626 | ||||||||
\(260\) | 1760.00 | 0.419810 | ||||||||
\(261\) | −1080.00 | −0.256132 | ||||||||
\(262\) | −2916.00 | −0.687600 | ||||||||
\(263\) | −2448.00 | −0.573955 | −0.286977 | − | 0.957937i | \(-0.592650\pi\) | ||||
−0.286977 | + | 0.957937i | \(0.592650\pi\) | |||||||
\(264\) | −1152.00 | −0.268563 | ||||||||
\(265\) | −2910.00 | −0.674566 | ||||||||
\(266\) | −8320.00 | −1.91779 | ||||||||
\(267\) | 360.000 | 0.0825155 | ||||||||
\(268\) | −1336.00 | −0.304512 | ||||||||
\(269\) | −8400.00 | −1.90393 | −0.951965 | − | 0.306208i | \(-0.900940\pi\) | ||||
−0.951965 | + | 0.306208i | \(0.900940\pi\) | |||||||
\(270\) | −270.000 | −0.0608581 | ||||||||
\(271\) | −3688.00 | −0.826679 | −0.413340 | − | 0.910577i | \(-0.635638\pi\) | ||||
−0.413340 | + | 0.910577i | \(0.635638\pi\) | |||||||
\(272\) | −864.000 | −0.192602 | ||||||||
\(273\) | −6864.00 | −1.52171 | ||||||||
\(274\) | 1932.00 | 0.425972 | ||||||||
\(275\) | −1200.00 | −0.263137 | ||||||||
\(276\) | −576.000 | −0.125620 | ||||||||
\(277\) | −9124.00 | −1.97909 | −0.989545 | − | 0.144223i | \(-0.953932\pi\) | ||||
−0.989545 | + | 0.144223i | \(0.953932\pi\) | |||||||
\(278\) | 1960.00 | 0.422852 | ||||||||
\(279\) | 279.000 | 0.0598684 | ||||||||
\(280\) | −1040.00 | −0.221971 | ||||||||
\(281\) | 6702.00 | 1.42280 | 0.711402 | − | 0.702786i | \(-0.248061\pi\) | ||||
0.711402 | + | 0.702786i | \(0.248061\pi\) | |||||||
\(282\) | 576.000 | 0.121632 | ||||||||
\(283\) | 6482.00 | 1.36154 | 0.680768 | − | 0.732499i | \(-0.261646\pi\) | ||||
0.680768 | + | 0.732499i | \(0.261646\pi\) | |||||||
\(284\) | 4248.00 | 0.887579 | ||||||||
\(285\) | 2400.00 | 0.498820 | ||||||||
\(286\) | 8448.00 | 1.74665 | ||||||||
\(287\) | 4212.00 | 0.866294 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 1200.00 | 0.242988 | ||||||||
\(291\) | 258.000 | 0.0519733 | ||||||||
\(292\) | 848.000 | 0.169950 | ||||||||
\(293\) | 4062.00 | 0.809913 | 0.404957 | − | 0.914336i | \(-0.367287\pi\) | ||||
0.404957 | + | 0.914336i | \(0.367287\pi\) | |||||||
\(294\) | 1998.00 | 0.396346 | ||||||||
\(295\) | −150.000 | −0.0296045 | ||||||||
\(296\) | −2432.00 | −0.477558 | ||||||||
\(297\) | −1296.00 | −0.253204 | ||||||||
\(298\) | −60.0000 | −0.0116634 | ||||||||
\(299\) | 4224.00 | 0.816991 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | 7072.00 | 1.35423 | ||||||||
\(302\) | 3664.00 | 0.698144 | ||||||||
\(303\) | 5166.00 | 0.979468 | ||||||||
\(304\) | −2560.00 | −0.482980 | ||||||||
\(305\) | 2390.00 | 0.448692 | ||||||||
\(306\) | −972.000 | −0.181587 | ||||||||
\(307\) | 5006.00 | 0.930643 | 0.465322 | − | 0.885142i | \(-0.345939\pi\) | ||||
0.465322 | + | 0.885142i | \(0.345939\pi\) | |||||||
\(308\) | −4992.00 | −0.923525 | ||||||||
\(309\) | −3774.00 | −0.694807 | ||||||||
\(310\) | −310.000 | −0.0567962 | ||||||||
\(311\) | −438.000 | −0.0798608 | −0.0399304 | − | 0.999202i | \(-0.512714\pi\) | ||||
−0.0399304 | + | 0.999202i | \(0.512714\pi\) | |||||||
\(312\) | −2112.00 | −0.383232 | ||||||||
\(313\) | 10292.0 | 1.85859 | 0.929294 | − | 0.369340i | \(-0.120416\pi\) | ||||
0.929294 | + | 0.369340i | \(0.120416\pi\) | |||||||
\(314\) | 7132.00 | 1.28179 | ||||||||
\(315\) | −1170.00 | −0.209276 | ||||||||
\(316\) | −2560.00 | −0.455732 | ||||||||
\(317\) | −8874.00 | −1.57228 | −0.786141 | − | 0.618047i | \(-0.787924\pi\) | ||||
−0.786141 | + | 0.618047i | \(0.787924\pi\) | |||||||
\(318\) | 3492.00 | 0.615791 | ||||||||
\(319\) | 5760.00 | 1.01097 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | −5652.00 | −0.982754 | ||||||||
\(322\) | −2496.00 | −0.431977 | ||||||||
\(323\) | 8640.00 | 1.48837 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −2200.00 | −0.375489 | ||||||||
\(326\) | −3596.00 | −0.610933 | ||||||||
\(327\) | −210.000 | −0.0355138 | ||||||||
\(328\) | 1296.00 | 0.218170 | ||||||||
\(329\) | 2496.00 | 0.418264 | ||||||||
\(330\) | 1440.00 | 0.240210 | ||||||||
\(331\) | −9508.00 | −1.57887 | −0.789436 | − | 0.613832i | \(-0.789627\pi\) | ||||
−0.789436 | + | 0.613832i | \(0.789627\pi\) | |||||||
\(332\) | 3888.00 | 0.642716 | ||||||||
\(333\) | −2736.00 | −0.450246 | ||||||||
\(334\) | −1728.00 | −0.283090 | ||||||||
\(335\) | 1670.00 | 0.272364 | ||||||||
\(336\) | 1248.00 | 0.202631 | ||||||||
\(337\) | −3304.00 | −0.534066 | −0.267033 | − | 0.963687i | \(-0.586043\pi\) | ||||
−0.267033 | + | 0.963687i | \(0.586043\pi\) | |||||||
\(338\) | 11094.0 | 1.78531 | ||||||||
\(339\) | −6534.00 | −1.04684 | ||||||||
\(340\) | 1080.00 | 0.172268 | ||||||||
\(341\) | −1488.00 | −0.236304 | ||||||||
\(342\) | −2880.00 | −0.455358 | ||||||||
\(343\) | −260.000 | −0.0409291 | ||||||||
\(344\) | 2176.00 | 0.341052 | ||||||||
\(345\) | 720.000 | 0.112358 | ||||||||
\(346\) | 2964.00 | 0.460536 | ||||||||
\(347\) | −5724.00 | −0.885534 | −0.442767 | − | 0.896637i | \(-0.646003\pi\) | ||||
−0.442767 | + | 0.896637i | \(0.646003\pi\) | |||||||
\(348\) | −1440.00 | −0.221816 | ||||||||
\(349\) | 10010.0 | 1.53531 | 0.767655 | − | 0.640864i | \(-0.221424\pi\) | ||||
0.767655 | + | 0.640864i | \(0.221424\pi\) | |||||||
\(350\) | 1300.00 | 0.198537 | ||||||||
\(351\) | −2376.00 | −0.361315 | ||||||||
\(352\) | −1536.00 | −0.232583 | ||||||||
\(353\) | −7758.00 | −1.16974 | −0.584868 | − | 0.811129i | \(-0.698854\pi\) | ||||
−0.584868 | + | 0.811129i | \(0.698854\pi\) | |||||||
\(354\) | 180.000 | 0.0270251 | ||||||||
\(355\) | −5310.00 | −0.793875 | ||||||||
\(356\) | 480.000 | 0.0714605 | ||||||||
\(357\) | −4212.00 | −0.624433 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8730.00 | 1.28343 | 0.641716 | − | 0.766943i | \(-0.278223\pi\) | ||||
0.641716 | + | 0.766943i | \(0.278223\pi\) | |||||||
\(360\) | −360.000 | −0.0527046 | ||||||||
\(361\) | 18741.0 | 2.73232 | ||||||||
\(362\) | −716.000 | −0.103956 | ||||||||
\(363\) | 2919.00 | 0.422060 | ||||||||
\(364\) | −9152.00 | −1.31784 | ||||||||
\(365\) | −1060.00 | −0.152008 | ||||||||
\(366\) | −2868.00 | −0.409598 | ||||||||
\(367\) | −5404.00 | −0.768628 | −0.384314 | − | 0.923202i | \(-0.625562\pi\) | ||||
−0.384314 | + | 0.923202i | \(0.625562\pi\) | |||||||
\(368\) | −768.000 | −0.108790 | ||||||||
\(369\) | 1458.00 | 0.205692 | ||||||||
\(370\) | 3040.00 | 0.427141 | ||||||||
\(371\) | 15132.0 | 2.11756 | ||||||||
\(372\) | 372.000 | 0.0518476 | ||||||||
\(373\) | −9538.00 | −1.32402 | −0.662009 | − | 0.749496i | \(-0.730296\pi\) | ||||
−0.662009 | + | 0.749496i | \(0.730296\pi\) | |||||||
\(374\) | 5184.00 | 0.716733 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 768.000 | 0.105337 | ||||||||
\(377\) | 10560.0 | 1.44262 | ||||||||
\(378\) | 1404.00 | 0.191042 | ||||||||
\(379\) | −5440.00 | −0.737293 | −0.368646 | − | 0.929570i | \(-0.620179\pi\) | ||||
−0.368646 | + | 0.929570i | \(0.620179\pi\) | |||||||
\(380\) | 3200.00 | 0.431991 | ||||||||
\(381\) | −7392.00 | −0.993973 | ||||||||
\(382\) | 3444.00 | 0.461284 | ||||||||
\(383\) | 6672.00 | 0.890139 | 0.445070 | − | 0.895496i | \(-0.353179\pi\) | ||||
0.445070 | + | 0.895496i | \(0.353179\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 6240.00 | 0.826026 | ||||||||
\(386\) | −836.000 | −0.110236 | ||||||||
\(387\) | 2448.00 | 0.321547 | ||||||||
\(388\) | 344.000 | 0.0450102 | ||||||||
\(389\) | −10440.0 | −1.36074 | −0.680371 | − | 0.732867i | \(-0.738182\pi\) | ||||
−0.680371 | + | 0.732867i | \(0.738182\pi\) | |||||||
\(390\) | 2640.00 | 0.342773 | ||||||||
\(391\) | 2592.00 | 0.335251 | ||||||||
\(392\) | 2664.00 | 0.343246 | ||||||||
\(393\) | −4374.00 | −0.561423 | ||||||||
\(394\) | −108.000 | −0.0138095 | ||||||||
\(395\) | 3200.00 | 0.407619 | ||||||||
\(396\) | −1728.00 | −0.219281 | ||||||||
\(397\) | −6334.00 | −0.800741 | −0.400371 | − | 0.916353i | \(-0.631119\pi\) | ||||
−0.400371 | + | 0.916353i | \(0.631119\pi\) | |||||||
\(398\) | −3440.00 | −0.433245 | ||||||||
\(399\) | −12480.0 | −1.56587 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 10212.0 | 1.27173 | 0.635864 | − | 0.771801i | \(-0.280644\pi\) | ||||
0.635864 | + | 0.771801i | \(0.280644\pi\) | |||||||
\(402\) | −2004.00 | −0.248633 | ||||||||
\(403\) | −2728.00 | −0.337199 | ||||||||
\(404\) | 6888.00 | 0.848245 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | −6240.00 | −0.762773 | ||||||||
\(407\) | 14592.0 | 1.77715 | ||||||||
\(408\) | −1296.00 | −0.157259 | ||||||||
\(409\) | 8030.00 | 0.970802 | 0.485401 | − | 0.874292i | \(-0.338674\pi\) | ||||
0.485401 | + | 0.874292i | \(0.338674\pi\) | |||||||
\(410\) | −1620.00 | −0.195137 | ||||||||
\(411\) | 2898.00 | 0.347805 | ||||||||
\(412\) | −5032.00 | −0.601721 | ||||||||
\(413\) | 780.000 | 0.0929329 | ||||||||
\(414\) | −864.000 | −0.102568 | ||||||||
\(415\) | −4860.00 | −0.574863 | ||||||||
\(416\) | −2816.00 | −0.331889 | ||||||||
\(417\) | 2940.00 | 0.345258 | ||||||||
\(418\) | 15360.0 | 1.79733 | ||||||||
\(419\) | 7530.00 | 0.877958 | 0.438979 | − | 0.898497i | \(-0.355340\pi\) | ||||
0.438979 | + | 0.898497i | \(0.355340\pi\) | |||||||
\(420\) | −1560.00 | −0.181239 | ||||||||
\(421\) | −4078.00 | −0.472089 | −0.236045 | − | 0.971742i | \(-0.575851\pi\) | ||||
−0.236045 | + | 0.971742i | \(0.575851\pi\) | |||||||
\(422\) | −4976.00 | −0.574000 | ||||||||
\(423\) | 864.000 | 0.0993123 | ||||||||
\(424\) | 4656.00 | 0.533291 | ||||||||
\(425\) | −1350.00 | −0.154081 | ||||||||
\(426\) | 6372.00 | 0.724705 | ||||||||
\(427\) | −12428.0 | −1.40851 | ||||||||
\(428\) | −7536.00 | −0.851090 | ||||||||
\(429\) | 12672.0 | 1.42613 | ||||||||
\(430\) | −2720.00 | −0.305047 | ||||||||
\(431\) | 15882.0 | 1.77496 | 0.887481 | − | 0.460843i | \(-0.152453\pi\) | ||||
0.887481 | + | 0.460843i | \(0.152453\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 4772.00 | 0.529625 | 0.264813 | − | 0.964300i | \(-0.414690\pi\) | ||||
0.264813 | + | 0.964300i | \(0.414690\pi\) | |||||||
\(434\) | 1612.00 | 0.178291 | ||||||||
\(435\) | 1800.00 | 0.198399 | ||||||||
\(436\) | −280.000 | −0.0307559 | ||||||||
\(437\) | 7680.00 | 0.840696 | ||||||||
\(438\) | 1272.00 | 0.138764 | ||||||||
\(439\) | −1960.00 | −0.213088 | −0.106544 | − | 0.994308i | \(-0.533979\pi\) | ||||
−0.106544 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(440\) | 1920.00 | 0.208028 | ||||||||
\(441\) | 2997.00 | 0.323615 | ||||||||
\(442\) | 9504.00 | 1.02276 | ||||||||
\(443\) | −4128.00 | −0.442725 | −0.221363 | − | 0.975192i | \(-0.571050\pi\) | ||||
−0.221363 | + | 0.975192i | \(0.571050\pi\) | |||||||
\(444\) | −3648.00 | −0.389924 | ||||||||
\(445\) | −600.000 | −0.0639162 | ||||||||
\(446\) | −6296.00 | −0.668440 | ||||||||
\(447\) | −90.0000 | −0.00952316 | ||||||||
\(448\) | 1664.00 | 0.175484 | ||||||||
\(449\) | −14820.0 | −1.55768 | −0.778841 | − | 0.627222i | \(-0.784192\pi\) | ||||
−0.778841 | + | 0.627222i | \(0.784192\pi\) | |||||||
\(450\) | 450.000 | 0.0471405 | ||||||||
\(451\) | −7776.00 | −0.811879 | ||||||||
\(452\) | −8712.00 | −0.906589 | ||||||||
\(453\) | 5496.00 | 0.570032 | ||||||||
\(454\) | 3072.00 | 0.317569 | ||||||||
\(455\) | 11440.0 | 1.17872 | ||||||||
\(456\) | −3840.00 | −0.394352 | ||||||||
\(457\) | 8516.00 | 0.871689 | 0.435844 | − | 0.900022i | \(-0.356450\pi\) | ||||
0.435844 | + | 0.900022i | \(0.356450\pi\) | |||||||
\(458\) | −5540.00 | −0.565212 | ||||||||
\(459\) | −1458.00 | −0.148265 | ||||||||
\(460\) | 960.000 | 0.0973048 | ||||||||
\(461\) | 13692.0 | 1.38330 | 0.691649 | − | 0.722234i | \(-0.256885\pi\) | ||||
0.691649 | + | 0.722234i | \(0.256885\pi\) | |||||||
\(462\) | −7488.00 | −0.754055 | ||||||||
\(463\) | −4288.00 | −0.430411 | −0.215205 | − | 0.976569i | \(-0.569042\pi\) | ||||
−0.215205 | + | 0.976569i | \(0.569042\pi\) | |||||||
\(464\) | −1920.00 | −0.192099 | ||||||||
\(465\) | −465.000 | −0.0463739 | ||||||||
\(466\) | −5196.00 | −0.516524 | ||||||||
\(467\) | −324.000 | −0.0321048 | −0.0160524 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160524 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(468\) | −3168.00 | −0.312908 | ||||||||
\(469\) | −8684.00 | −0.854989 | ||||||||
\(470\) | −960.000 | −0.0942160 | ||||||||
\(471\) | 10698.0 | 1.04658 | ||||||||
\(472\) | 240.000 | 0.0234044 | ||||||||
\(473\) | −13056.0 | −1.26917 | ||||||||
\(474\) | −3840.00 | −0.372103 | ||||||||
\(475\) | −4000.00 | −0.386384 | ||||||||
\(476\) | −5616.00 | −0.540775 | ||||||||
\(477\) | 5238.00 | 0.502791 | ||||||||
\(478\) | −10680.0 | −1.02195 | ||||||||
\(479\) | −8970.00 | −0.855636 | −0.427818 | − | 0.903865i | \(-0.640718\pi\) | ||||
−0.427818 | + | 0.903865i | \(0.640718\pi\) | |||||||
\(480\) | −480.000 | −0.0456435 | ||||||||
\(481\) | 26752.0 | 2.53594 | ||||||||
\(482\) | 6004.00 | 0.567375 | ||||||||
\(483\) | −3744.00 | −0.352708 | ||||||||
\(484\) | 3892.00 | 0.365515 | ||||||||
\(485\) | −430.000 | −0.0402583 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 14216.0 | 1.32277 | 0.661384 | − | 0.750047i | \(-0.269969\pi\) | ||||
0.661384 | + | 0.750047i | \(0.269969\pi\) | |||||||
\(488\) | −3824.00 | −0.354722 | ||||||||
\(489\) | −5394.00 | −0.498824 | ||||||||
\(490\) | −3330.00 | −0.307008 | ||||||||
\(491\) | −8268.00 | −0.759938 | −0.379969 | − | 0.924999i | \(-0.624065\pi\) | ||||
−0.379969 | + | 0.924999i | \(0.624065\pi\) | |||||||
\(492\) | 1944.00 | 0.178135 | ||||||||
\(493\) | 6480.00 | 0.591977 | ||||||||
\(494\) | 28160.0 | 2.56473 | ||||||||
\(495\) | 2160.00 | 0.196131 | ||||||||
\(496\) | 496.000 | 0.0449013 | ||||||||
\(497\) | 27612.0 | 2.49209 | ||||||||
\(498\) | 5832.00 | 0.524775 | ||||||||
\(499\) | −11860.0 | −1.06398 | −0.531990 | − | 0.846750i | \(-0.678556\pi\) | ||||
−0.531990 | + | 0.846750i | \(0.678556\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | −2592.00 | −0.231142 | ||||||||
\(502\) | 4704.00 | 0.418227 | ||||||||
\(503\) | −3768.00 | −0.334010 | −0.167005 | − | 0.985956i | \(-0.553410\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553410\pi\) | |||||||
\(504\) | 1872.00 | 0.165447 | ||||||||
\(505\) | −8610.00 | −0.758693 | ||||||||
\(506\) | 4608.00 | 0.404843 | ||||||||
\(507\) | 16641.0 | 1.45770 | ||||||||
\(508\) | −9856.00 | −0.860806 | ||||||||
\(509\) | −3420.00 | −0.297817 | −0.148908 | − | 0.988851i | \(-0.547576\pi\) | ||||
−0.148908 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(510\) | 1620.00 | 0.140656 | ||||||||
\(511\) | 5512.00 | 0.477175 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −4320.00 | −0.371799 | ||||||||
\(514\) | −588.000 | −0.0504583 | ||||||||
\(515\) | 6290.00 | 0.538195 | ||||||||
\(516\) | 3264.00 | 0.278468 | ||||||||
\(517\) | −4608.00 | −0.391992 | ||||||||
\(518\) | −15808.0 | −1.34086 | ||||||||
\(519\) | 4446.00 | 0.376026 | ||||||||
\(520\) | 3520.00 | 0.296850 | ||||||||
\(521\) | −15198.0 | −1.27800 | −0.638999 | − | 0.769208i | \(-0.720651\pi\) | ||||
−0.638999 | + | 0.769208i | \(0.720651\pi\) | |||||||
\(522\) | −2160.00 | −0.181112 | ||||||||
\(523\) | −208.000 | −0.0173904 | −0.00869522 | − | 0.999962i | \(-0.502768\pi\) | ||||
−0.00869522 | + | 0.999962i | \(0.502768\pi\) | |||||||
\(524\) | −5832.00 | −0.486206 | ||||||||
\(525\) | 1950.00 | 0.162105 | ||||||||
\(526\) | −4896.00 | −0.405847 | ||||||||
\(527\) | −1674.00 | −0.138369 | ||||||||
\(528\) | −2304.00 | −0.189903 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | −5820.00 | −0.476990 | ||||||||
\(531\) | 270.000 | 0.0220659 | ||||||||
\(532\) | −16640.0 | −1.35608 | ||||||||
\(533\) | −14256.0 | −1.15853 | ||||||||
\(534\) | 720.000 | 0.0583473 | ||||||||
\(535\) | 9420.00 | 0.761238 | ||||||||
\(536\) | −2672.00 | −0.215322 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16800.0 | −1.34628 | ||||||||
\(539\) | −15984.0 | −1.27733 | ||||||||
\(540\) | −540.000 | −0.0430331 | ||||||||
\(541\) | −22918.0 | −1.82130 | −0.910649 | − | 0.413182i | \(-0.864417\pi\) | ||||
−0.910649 | + | 0.413182i | \(0.864417\pi\) | |||||||
\(542\) | −7376.00 | −0.584550 | ||||||||
\(543\) | −1074.00 | −0.0848798 | ||||||||
\(544\) | −1728.00 | −0.136190 | ||||||||
\(545\) | 350.000 | 0.0275089 | ||||||||
\(546\) | −13728.0 | −1.07601 | ||||||||
\(547\) | 23906.0 | 1.86864 | 0.934321 | − | 0.356434i | \(-0.116007\pi\) | ||||
0.934321 | + | 0.356434i | \(0.116007\pi\) | |||||||
\(548\) | 3864.00 | 0.301208 | ||||||||
\(549\) | −4302.00 | −0.334435 | ||||||||
\(550\) | −2400.00 | −0.186066 | ||||||||
\(551\) | 19200.0 | 1.48448 | ||||||||
\(552\) | −1152.00 | −0.0888268 | ||||||||
\(553\) | −16640.0 | −1.27957 | ||||||||
\(554\) | −18248.0 | −1.39943 | ||||||||
\(555\) | 4560.00 | 0.348759 | ||||||||
\(556\) | 3920.00 | 0.299002 | ||||||||
\(557\) | 18846.0 | 1.43363 | 0.716814 | − | 0.697265i | \(-0.245600\pi\) | ||||
0.716814 | + | 0.697265i | \(0.245600\pi\) | |||||||
\(558\) | 558.000 | 0.0423334 | ||||||||
\(559\) | −23936.0 | −1.81106 | ||||||||
\(560\) | −2080.00 | −0.156957 | ||||||||
\(561\) | 7776.00 | 0.585210 | ||||||||
\(562\) | 13404.0 | 1.00607 | ||||||||
\(563\) | 19452.0 | 1.45614 | 0.728068 | − | 0.685505i | \(-0.240419\pi\) | ||||
0.728068 | + | 0.685505i | \(0.240419\pi\) | |||||||
\(564\) | 1152.00 | 0.0860070 | ||||||||
\(565\) | 10890.0 | 0.810877 | ||||||||
\(566\) | 12964.0 | 0.962752 | ||||||||
\(567\) | 2106.00 | 0.155985 | ||||||||
\(568\) | 8496.00 | 0.627613 | ||||||||
\(569\) | 23940.0 | 1.76383 | 0.881913 | − | 0.471412i | \(-0.156256\pi\) | ||||
0.881913 | + | 0.471412i | \(0.156256\pi\) | |||||||
\(570\) | 4800.00 | 0.352719 | ||||||||
\(571\) | −9628.00 | −0.705638 | −0.352819 | − | 0.935692i | \(-0.614777\pi\) | ||||
−0.352819 | + | 0.935692i | \(0.614777\pi\) | |||||||
\(572\) | 16896.0 | 1.23507 | ||||||||
\(573\) | 5166.00 | 0.376637 | ||||||||
\(574\) | 8424.00 | 0.612563 | ||||||||
\(575\) | −1200.00 | −0.0870321 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −23374.0 | −1.68643 | −0.843217 | − | 0.537573i | \(-0.819341\pi\) | ||||
−0.843217 | + | 0.537573i | \(0.819341\pi\) | |||||||
\(578\) | −3994.00 | −0.287420 | ||||||||
\(579\) | −1254.00 | −0.0900077 | ||||||||
\(580\) | 2400.00 | 0.171818 | ||||||||
\(581\) | 25272.0 | 1.80458 | ||||||||
\(582\) | 516.000 | 0.0367507 | ||||||||
\(583\) | −27936.0 | −1.98455 | ||||||||
\(584\) | 1696.00 | 0.120173 | ||||||||
\(585\) | 3960.00 | 0.279873 | ||||||||
\(586\) | 8124.00 | 0.572695 | ||||||||
\(587\) | −11244.0 | −0.790613 | −0.395306 | − | 0.918549i | \(-0.629362\pi\) | ||||
−0.395306 | + | 0.918549i | \(0.629362\pi\) | |||||||
\(588\) | 3996.00 | 0.280259 | ||||||||
\(589\) | −4960.00 | −0.346983 | ||||||||
\(590\) | −300.000 | −0.0209336 | ||||||||
\(591\) | −162.000 | −0.0112754 | ||||||||
\(592\) | −4864.00 | −0.337684 | ||||||||
\(593\) | −5298.00 | −0.366885 | −0.183442 | − | 0.983030i | \(-0.558724\pi\) | ||||
−0.183442 | + | 0.983030i | \(0.558724\pi\) | |||||||
\(594\) | −2592.00 | −0.179042 | ||||||||
\(595\) | 7020.00 | 0.483684 | ||||||||
\(596\) | −120.000 | −0.00824730 | ||||||||
\(597\) | −5160.00 | −0.353743 | ||||||||
\(598\) | 8448.00 | 0.577700 | ||||||||
\(599\) | −2430.00 | −0.165755 | −0.0828774 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828774 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(600\) | 600.000 | 0.0408248 | ||||||||
\(601\) | 2702.00 | 0.183389 | 0.0916946 | − | 0.995787i | \(-0.470772\pi\) | ||||
0.0916946 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(602\) | 14144.0 | 0.957585 | ||||||||
\(603\) | −3006.00 | −0.203008 | ||||||||
\(604\) | 7328.00 | 0.493662 | ||||||||
\(605\) | −4865.00 | −0.326926 | ||||||||
\(606\) | 10332.0 | 0.692589 | ||||||||
\(607\) | 8366.00 | 0.559416 | 0.279708 | − | 0.960085i | \(-0.409762\pi\) | ||||
0.279708 | + | 0.960085i | \(0.409762\pi\) | |||||||
\(608\) | −5120.00 | −0.341519 | ||||||||
\(609\) | −9360.00 | −0.622802 | ||||||||
\(610\) | 4780.00 | 0.317273 | ||||||||
\(611\) | −8448.00 | −0.559361 | ||||||||
\(612\) | −1944.00 | −0.128401 | ||||||||
\(613\) | −6028.00 | −0.397176 | −0.198588 | − | 0.980083i | \(-0.563635\pi\) | ||||
−0.198588 | + | 0.980083i | \(0.563635\pi\) | |||||||
\(614\) | 10012.0 | 0.658064 | ||||||||
\(615\) | −2430.00 | −0.159329 | ||||||||
\(616\) | −9984.00 | −0.653031 | ||||||||
\(617\) | −5634.00 | −0.367612 | −0.183806 | − | 0.982963i | \(-0.558842\pi\) | ||||
−0.183806 | + | 0.982963i | \(0.558842\pi\) | |||||||
\(618\) | −7548.00 | −0.491303 | ||||||||
\(619\) | −10420.0 | −0.676600 | −0.338300 | − | 0.941038i | \(-0.609852\pi\) | ||||
−0.338300 | + | 0.941038i | \(0.609852\pi\) | |||||||
\(620\) | −620.000 | −0.0401610 | ||||||||
\(621\) | −1296.00 | −0.0837467 | ||||||||
\(622\) | −876.000 | −0.0564701 | ||||||||
\(623\) | 3120.00 | 0.200642 | ||||||||
\(624\) | −4224.00 | −0.270986 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 20584.0 | 1.31422 | ||||||||
\(627\) | 23040.0 | 1.46751 | ||||||||
\(628\) | 14264.0 | 0.906362 | ||||||||
\(629\) | 16416.0 | 1.04062 | ||||||||
\(630\) | −2340.00 | −0.147981 | ||||||||
\(631\) | −7408.00 | −0.467366 | −0.233683 | − | 0.972313i | \(-0.575078\pi\) | ||||
−0.233683 | + | 0.972313i | \(0.575078\pi\) | |||||||
\(632\) | −5120.00 | −0.322251 | ||||||||
\(633\) | −7464.00 | −0.468669 | ||||||||
\(634\) | −17748.0 | −1.11177 | ||||||||
\(635\) | 12320.0 | 0.769928 | ||||||||
\(636\) | 6984.00 | 0.435430 | ||||||||
\(637\) | −29304.0 | −1.82271 | ||||||||
\(638\) | 11520.0 | 0.714861 | ||||||||
\(639\) | 9558.00 | 0.591719 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −13428.0 | −0.827417 | −0.413708 | − | 0.910409i | \(-0.635767\pi\) | ||||
−0.413708 | + | 0.910409i | \(0.635767\pi\) | |||||||
\(642\) | −11304.0 | −0.694912 | ||||||||
\(643\) | −5848.00 | −0.358667 | −0.179333 | − | 0.983788i | \(-0.557394\pi\) | ||||
−0.179333 | + | 0.983788i | \(0.557394\pi\) | |||||||
\(644\) | −4992.00 | −0.305454 | ||||||||
\(645\) | −4080.00 | −0.249070 | ||||||||
\(646\) | 17280.0 | 1.05243 | ||||||||
\(647\) | 9456.00 | 0.574581 | 0.287290 | − | 0.957844i | \(-0.407246\pi\) | ||||
0.287290 | + | 0.957844i | \(0.407246\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −1440.00 | −0.0870954 | ||||||||
\(650\) | −4400.00 | −0.265511 | ||||||||
\(651\) | 2418.00 | 0.145574 | ||||||||
\(652\) | −7192.00 | −0.431995 | ||||||||
\(653\) | −378.000 | −0.0226528 | −0.0113264 | − | 0.999936i | \(-0.503605\pi\) | ||||
−0.0113264 | + | 0.999936i | \(0.503605\pi\) | |||||||
\(654\) | −420.000 | −0.0251121 | ||||||||
\(655\) | 7290.00 | 0.434876 | ||||||||
\(656\) | 2592.00 | 0.154269 | ||||||||
\(657\) | 1908.00 | 0.113300 | ||||||||
\(658\) | 4992.00 | 0.295757 | ||||||||
\(659\) | 6330.00 | 0.374176 | 0.187088 | − | 0.982343i | \(-0.440095\pi\) | ||||
0.187088 | + | 0.982343i | \(0.440095\pi\) | |||||||
\(660\) | 2880.00 | 0.169854 | ||||||||
\(661\) | 2702.00 | 0.158995 | 0.0794974 | − | 0.996835i | \(-0.474668\pi\) | ||||
0.0794974 | + | 0.996835i | \(0.474668\pi\) | |||||||
\(662\) | −19016.0 | −1.11643 | ||||||||
\(663\) | 14256.0 | 0.835079 | ||||||||
\(664\) | 7776.00 | 0.454469 | ||||||||
\(665\) | 20800.0 | 1.21292 | ||||||||
\(666\) | −5472.00 | −0.318372 | ||||||||
\(667\) | 5760.00 | 0.334375 | ||||||||
\(668\) | −3456.00 | −0.200175 | ||||||||
\(669\) | −9444.00 | −0.545779 | ||||||||
\(670\) | 3340.00 | 0.192590 | ||||||||
\(671\) | 22944.0 | 1.32003 | ||||||||
\(672\) | 2496.00 | 0.143282 | ||||||||
\(673\) | 2312.00 | 0.132424 | 0.0662118 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662118 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(674\) | −6608.00 | −0.377642 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 22188.0 | 1.26240 | ||||||||
\(677\) | 6486.00 | 0.368209 | 0.184104 | − | 0.982907i | \(-0.441062\pi\) | ||||
0.184104 | + | 0.982907i | \(0.441062\pi\) | |||||||
\(678\) | −13068.0 | −0.740226 | ||||||||
\(679\) | 2236.00 | 0.126377 | ||||||||
\(680\) | 2160.00 | 0.121812 | ||||||||
\(681\) | 4608.00 | 0.259294 | ||||||||
\(682\) | −2976.00 | −0.167092 | ||||||||
\(683\) | 9552.00 | 0.535135 | 0.267567 | − | 0.963539i | \(-0.413780\pi\) | ||||
0.267567 | + | 0.963539i | \(0.413780\pi\) | |||||||
\(684\) | −5760.00 | −0.321987 | ||||||||
\(685\) | −4830.00 | −0.269408 | ||||||||
\(686\) | −520.000 | −0.0289412 | ||||||||
\(687\) | −8310.00 | −0.461494 | ||||||||
\(688\) | 4352.00 | 0.241161 | ||||||||
\(689\) | −51216.0 | −2.83189 | ||||||||
\(690\) | 1440.00 | 0.0794491 | ||||||||
\(691\) | −26548.0 | −1.46155 | −0.730777 | − | 0.682617i | \(-0.760842\pi\) | ||||
−0.730777 | + | 0.682617i | \(0.760842\pi\) | |||||||
\(692\) | 5928.00 | 0.325648 | ||||||||
\(693\) | −11232.0 | −0.615683 | ||||||||
\(694\) | −11448.0 | −0.626167 | ||||||||
\(695\) | −4900.00 | −0.267435 | ||||||||
\(696\) | −2880.00 | −0.156848 | ||||||||
\(697\) | −8748.00 | −0.475400 | ||||||||
\(698\) | 20020.0 | 1.08563 | ||||||||
\(699\) | −7794.00 | −0.421740 | ||||||||
\(700\) | 2600.00 | 0.140387 | ||||||||
\(701\) | −20658.0 | −1.11304 | −0.556521 | − | 0.830834i | \(-0.687864\pi\) | ||||
−0.556521 | + | 0.830834i | \(0.687864\pi\) | |||||||
\(702\) | −4752.00 | −0.255488 | ||||||||
\(703\) | 48640.0 | 2.60952 | ||||||||
\(704\) | −3072.00 | −0.164461 | ||||||||
\(705\) | −1440.00 | −0.0769270 | ||||||||
\(706\) | −15516.0 | −0.827128 | ||||||||
\(707\) | 44772.0 | 2.38165 | ||||||||
\(708\) | 360.000 | 0.0191096 | ||||||||
\(709\) | −23530.0 | −1.24639 | −0.623193 | − | 0.782068i | \(-0.714165\pi\) | ||||
−0.623193 | + | 0.782068i | \(0.714165\pi\) | |||||||
\(710\) | −10620.0 | −0.561354 | ||||||||
\(711\) | −5760.00 | −0.303821 | ||||||||
\(712\) | 960.000 | 0.0505302 | ||||||||
\(713\) | −1488.00 | −0.0781571 | ||||||||
\(714\) | −8424.00 | −0.441541 | ||||||||
\(715\) | −21120.0 | −1.10468 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16020.0 | −0.834418 | ||||||||
\(718\) | 17460.0 | 0.907523 | ||||||||
\(719\) | 120.000 | 0.00622426 | 0.00311213 | − | 0.999995i | \(-0.499009\pi\) | ||||
0.00311213 | + | 0.999995i | \(0.499009\pi\) | |||||||
\(720\) | −720.000 | −0.0372678 | ||||||||
\(721\) | −32708.0 | −1.68947 | ||||||||
\(722\) | 37482.0 | 1.93204 | ||||||||
\(723\) | 9006.00 | 0.463260 | ||||||||
\(724\) | −1432.00 | −0.0735081 | ||||||||
\(725\) | −3000.00 | −0.153679 | ||||||||
\(726\) | 5838.00 | 0.298441 | ||||||||
\(727\) | 24626.0 | 1.25630 | 0.628148 | − | 0.778094i | \(-0.283813\pi\) | ||||
0.628148 | + | 0.778094i | \(0.283813\pi\) | |||||||
\(728\) | −18304.0 | −0.931856 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2120.00 | −0.107486 | ||||||||
\(731\) | −14688.0 | −0.743167 | ||||||||
\(732\) | −5736.00 | −0.289629 | ||||||||
\(733\) | −26998.0 | −1.36043 | −0.680214 | − | 0.733013i | \(-0.738113\pi\) | ||||
−0.680214 | + | 0.733013i | \(0.738113\pi\) | |||||||
\(734\) | −10808.0 | −0.543502 | ||||||||
\(735\) | −4995.00 | −0.250671 | ||||||||
\(736\) | −1536.00 | −0.0769262 | ||||||||
\(737\) | 16032.0 | 0.801284 | ||||||||
\(738\) | 2916.00 | 0.145446 | ||||||||
\(739\) | 3620.00 | 0.180195 | 0.0900973 | − | 0.995933i | \(-0.471282\pi\) | ||||
0.0900973 | + | 0.995933i | \(0.471282\pi\) | |||||||
\(740\) | 6080.00 | 0.302034 | ||||||||
\(741\) | 42240.0 | 2.09410 | ||||||||
\(742\) | 30264.0 | 1.49734 | ||||||||
\(743\) | 20952.0 | 1.03453 | 0.517264 | − | 0.855826i | \(-0.326951\pi\) | ||||
0.517264 | + | 0.855826i | \(0.326951\pi\) | |||||||
\(744\) | 744.000 | 0.0366618 | ||||||||
\(745\) | 150.000 | 0.00737661 | ||||||||
\(746\) | −19076.0 | −0.936222 | ||||||||
\(747\) | 8748.00 | 0.428477 | ||||||||
\(748\) | 10368.0 | 0.506807 | ||||||||
\(749\) | −48984.0 | −2.38963 | ||||||||
\(750\) | −750.000 | −0.0365148 | ||||||||
\(751\) | 8672.00 | 0.421366 | 0.210683 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210683 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(752\) | 1536.00 | 0.0744843 | ||||||||
\(753\) | 7056.00 | 0.341481 | ||||||||
\(754\) | 21120.0 | 1.02009 | ||||||||
\(755\) | −9160.00 | −0.441545 | ||||||||
\(756\) | 2808.00 | 0.135087 | ||||||||
\(757\) | 21176.0 | 1.01672 | 0.508359 | − | 0.861146i | \(-0.330252\pi\) | ||||
0.508359 | + | 0.861146i | \(0.330252\pi\) | |||||||
\(758\) | −10880.0 | −0.521345 | ||||||||
\(759\) | 6912.00 | 0.330553 | ||||||||
\(760\) | 6400.00 | 0.305464 | ||||||||
\(761\) | 27132.0 | 1.29242 | 0.646212 | − | 0.763158i | \(-0.276352\pi\) | ||||
0.646212 | + | 0.763158i | \(0.276352\pi\) | |||||||
\(762\) | −14784.0 | −0.702845 | ||||||||
\(763\) | −1820.00 | −0.0863544 | ||||||||
\(764\) | 6888.00 | 0.326177 | ||||||||
\(765\) | 2430.00 | 0.114846 | ||||||||
\(766\) | 13344.0 | 0.629423 | ||||||||
\(767\) | −2640.00 | −0.124283 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −6850.00 | −0.321219 | −0.160609 | − | 0.987018i | \(-0.551346\pi\) | ||||
−0.160609 | + | 0.987018i | \(0.551346\pi\) | |||||||
\(770\) | 12480.0 | 0.584088 | ||||||||
\(771\) | −882.000 | −0.0411990 | ||||||||
\(772\) | −1672.00 | −0.0779490 | ||||||||
\(773\) | 7422.00 | 0.345344 | 0.172672 | − | 0.984979i | \(-0.444760\pi\) | ||||
0.172672 | + | 0.984979i | \(0.444760\pi\) | |||||||
\(774\) | 4896.00 | 0.227368 | ||||||||
\(775\) | 775.000 | 0.0359211 | ||||||||
\(776\) | 688.000 | 0.0318270 | ||||||||
\(777\) | −23712.0 | −1.09480 | ||||||||
\(778\) | −20880.0 | −0.962191 | ||||||||
\(779\) | −25920.0 | −1.19214 | ||||||||
\(780\) | 5280.00 | 0.242377 | ||||||||
\(781\) | −50976.0 | −2.33555 | ||||||||
\(782\) | 5184.00 | 0.237058 | ||||||||
\(783\) | −3240.00 | −0.147878 | ||||||||
\(784\) | 5328.00 | 0.242711 | ||||||||
\(785\) | −17830.0 | −0.810675 | ||||||||
\(786\) | −8748.00 | −0.396986 | ||||||||
\(787\) | −1204.00 | −0.0545336 | −0.0272668 | − | 0.999628i | \(-0.508680\pi\) | ||||
−0.0272668 | + | 0.999628i | \(0.508680\pi\) | |||||||
\(788\) | −216.000 | −0.00976482 | ||||||||
\(789\) | −7344.00 | −0.331373 | ||||||||
\(790\) | 6400.00 | 0.288230 | ||||||||
\(791\) | −56628.0 | −2.54546 | ||||||||
\(792\) | −3456.00 | −0.155055 | ||||||||
\(793\) | 42064.0 | 1.88365 | ||||||||
\(794\) | −12668.0 | −0.566210 | ||||||||
\(795\) | −8730.00 | −0.389461 | ||||||||
\(796\) | −6880.00 | −0.306351 | ||||||||
\(797\) | 37266.0 | 1.65625 | 0.828124 | − | 0.560545i | \(-0.189408\pi\) | ||||
0.828124 | + | 0.560545i | \(0.189408\pi\) | |||||||
\(798\) | −24960.0 | −1.10724 | ||||||||
\(799\) | −5184.00 | −0.229533 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | 1080.00 | 0.0476404 | ||||||||
\(802\) | 20424.0 | 0.899248 | ||||||||
\(803\) | −10176.0 | −0.447202 | ||||||||
\(804\) | −4008.00 | −0.175810 | ||||||||
\(805\) | 6240.00 | 0.273206 | ||||||||
\(806\) | −5456.00 | −0.238436 | ||||||||
\(807\) | −25200.0 | −1.09923 | ||||||||
\(808\) | 13776.0 | 0.599799 | ||||||||
\(809\) | −25860.0 | −1.12384 | −0.561922 | − | 0.827190i | \(-0.689938\pi\) | ||||
−0.561922 | + | 0.827190i | \(0.689938\pi\) | |||||||
\(810\) | −810.000 | −0.0351364 | ||||||||
\(811\) | −5128.00 | −0.222033 | −0.111016 | − | 0.993819i | \(-0.535411\pi\) | ||||
−0.111016 | + | 0.993819i | \(0.535411\pi\) | |||||||
\(812\) | −12480.0 | −0.539362 | ||||||||
\(813\) | −11064.0 | −0.477283 | ||||||||
\(814\) | 29184.0 | 1.25663 | ||||||||
\(815\) | 8990.00 | 0.386388 | ||||||||
\(816\) | −2592.00 | −0.111199 | ||||||||
\(817\) | −43520.0 | −1.86361 | ||||||||
\(818\) | 16060.0 | 0.686461 | ||||||||
\(819\) | −20592.0 | −0.878563 | ||||||||
\(820\) | −3240.00 | −0.137983 | ||||||||
\(821\) | 8592.00 | 0.365241 | 0.182621 | − | 0.983183i | \(-0.441542\pi\) | ||||
0.182621 | + | 0.983183i | \(0.441542\pi\) | |||||||
\(822\) | 5796.00 | 0.245935 | ||||||||
\(823\) | 39392.0 | 1.66843 | 0.834216 | − | 0.551438i | \(-0.185921\pi\) | ||||
0.834216 | + | 0.551438i | \(0.185921\pi\) | |||||||
\(824\) | −10064.0 | −0.425481 | ||||||||
\(825\) | −3600.00 | −0.151922 | ||||||||
\(826\) | 1560.00 | 0.0657135 | ||||||||
\(827\) | −22044.0 | −0.926898 | −0.463449 | − | 0.886123i | \(-0.653388\pi\) | ||||
−0.463449 | + | 0.886123i | \(0.653388\pi\) | |||||||
\(828\) | −1728.00 | −0.0725268 | ||||||||
\(829\) | −21310.0 | −0.892795 | −0.446397 | − | 0.894835i | \(-0.647293\pi\) | ||||
−0.446397 | + | 0.894835i | \(0.647293\pi\) | |||||||
\(830\) | −9720.00 | −0.406489 | ||||||||
\(831\) | −27372.0 | −1.14263 | ||||||||
\(832\) | −5632.00 | −0.234681 | ||||||||
\(833\) | −17982.0 | −0.747946 | ||||||||
\(834\) | 5880.00 | 0.244134 | ||||||||
\(835\) | 4320.00 | 0.179042 | ||||||||
\(836\) | 30720.0 | 1.27090 | ||||||||
\(837\) | 837.000 | 0.0345651 | ||||||||
\(838\) | 15060.0 | 0.620810 | ||||||||
\(839\) | −14070.0 | −0.578963 | −0.289482 | − | 0.957184i | \(-0.593483\pi\) | ||||
−0.289482 | + | 0.957184i | \(0.593483\pi\) | |||||||
\(840\) | −3120.00 | −0.128155 | ||||||||
\(841\) | −9989.00 | −0.409570 | ||||||||
\(842\) | −8156.00 | −0.333817 | ||||||||
\(843\) | 20106.0 | 0.821456 | ||||||||
\(844\) | −9952.00 | −0.405879 | ||||||||
\(845\) | −27735.0 | −1.12913 | ||||||||
\(846\) | 1728.00 | 0.0702244 | ||||||||
\(847\) | 25298.0 | 1.02627 | ||||||||
\(848\) | 9312.00 | 0.377094 | ||||||||
\(849\) | 19446.0 | 0.786084 | ||||||||
\(850\) | −2700.00 | −0.108952 | ||||||||
\(851\) | 14592.0 | 0.587788 | ||||||||
\(852\) | 12744.0 | 0.512444 | ||||||||
\(853\) | −22918.0 | −0.919927 | −0.459963 | − | 0.887938i | \(-0.652137\pi\) | ||||
−0.459963 | + | 0.887938i | \(0.652137\pi\) | |||||||
\(854\) | −24856.0 | −0.995966 | ||||||||
\(855\) | 7200.00 | 0.287994 | ||||||||
\(856\) | −15072.0 | −0.601811 | ||||||||
\(857\) | −25914.0 | −1.03291 | −0.516456 | − | 0.856314i | \(-0.672749\pi\) | ||||
−0.516456 | + | 0.856314i | \(0.672749\pi\) | |||||||
\(858\) | 25344.0 | 1.00843 | ||||||||
\(859\) | −31900.0 | −1.26707 | −0.633535 | − | 0.773714i | \(-0.718397\pi\) | ||||
−0.633535 | + | 0.773714i | \(0.718397\pi\) | |||||||
\(860\) | −5440.00 | −0.215701 | ||||||||
\(861\) | 12636.0 | 0.500155 | ||||||||
\(862\) | 31764.0 | 1.25509 | ||||||||
\(863\) | 7752.00 | 0.305772 | 0.152886 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152886 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −7410.00 | −0.291269 | ||||||||
\(866\) | 9544.00 | 0.374502 | ||||||||
\(867\) | −5991.00 | −0.234677 | ||||||||
\(868\) | 3224.00 | 0.126071 | ||||||||
\(869\) | 30720.0 | 1.19920 | ||||||||
\(870\) | 3600.00 | 0.140289 | ||||||||
\(871\) | 29392.0 | 1.14341 | ||||||||
\(872\) | −560.000 | −0.0217477 | ||||||||
\(873\) | 774.000 | 0.0300068 | ||||||||
\(874\) | 15360.0 | 0.594462 | ||||||||
\(875\) | −3250.00 | −0.125566 | ||||||||
\(876\) | 2544.00 | 0.0981208 | ||||||||
\(877\) | 28706.0 | 1.10528 | 0.552641 | − | 0.833419i | \(-0.313620\pi\) | ||||
0.552641 | + | 0.833419i | \(0.313620\pi\) | |||||||
\(878\) | −3920.00 | −0.150676 | ||||||||
\(879\) | 12186.0 | 0.467604 | ||||||||
\(880\) | 3840.00 | 0.147098 | ||||||||
\(881\) | −43608.0 | −1.66764 | −0.833820 | − | 0.552036i | \(-0.813851\pi\) | ||||
−0.833820 | + | 0.552036i | \(0.813851\pi\) | |||||||
\(882\) | 5994.00 | 0.228830 | ||||||||
\(883\) | −32668.0 | −1.24503 | −0.622517 | − | 0.782606i | \(-0.713890\pi\) | ||||
−0.622517 | + | 0.782606i | \(0.713890\pi\) | |||||||
\(884\) | 19008.0 | 0.723199 | ||||||||
\(885\) | −450.000 | −0.0170922 | ||||||||
\(886\) | −8256.00 | −0.313054 | ||||||||
\(887\) | 32316.0 | 1.22330 | 0.611649 | − | 0.791129i | \(-0.290507\pi\) | ||||
0.611649 | + | 0.791129i | \(0.290507\pi\) | |||||||
\(888\) | −7296.00 | −0.275718 | ||||||||
\(889\) | −64064.0 | −2.41692 | ||||||||
\(890\) | −1200.00 | −0.0451956 | ||||||||
\(891\) | −3888.00 | −0.146187 | ||||||||
\(892\) | −12592.0 | −0.472658 | ||||||||
\(893\) | −15360.0 | −0.575591 | ||||||||
\(894\) | −180.000 | −0.00673389 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3328.00 | 0.124086 | ||||||||
\(897\) | 12672.0 | 0.471690 | ||||||||
\(898\) | −29640.0 | −1.10145 | ||||||||
\(899\) | −3720.00 | −0.138008 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −31428.0 | −1.16206 | ||||||||
\(902\) | −15552.0 | −0.574085 | ||||||||
\(903\) | 21216.0 | 0.781865 | ||||||||
\(904\) | −17424.0 | −0.641055 | ||||||||
\(905\) | 1790.00 | 0.0657476 | ||||||||
\(906\) | 10992.0 | 0.403074 | ||||||||
\(907\) | 45206.0 | 1.65495 | 0.827476 | − | 0.561502i | \(-0.189776\pi\) | ||||
0.827476 | + | 0.561502i | \(0.189776\pi\) | |||||||
\(908\) | 6144.00 | 0.224555 | ||||||||
\(909\) | 15498.0 | 0.565496 | ||||||||
\(910\) | 22880.0 | 0.833478 | ||||||||
\(911\) | −1368.00 | −0.0497518 | −0.0248759 | − | 0.999691i | \(-0.507919\pi\) | ||||
−0.0248759 | + | 0.999691i | \(0.507919\pi\) | |||||||
\(912\) | −7680.00 | −0.278849 | ||||||||
\(913\) | −46656.0 | −1.69122 | ||||||||
\(914\) | 17032.0 | 0.616377 | ||||||||
\(915\) | 7170.00 | 0.259052 | ||||||||
\(916\) | −11080.0 | −0.399665 | ||||||||
\(917\) | −37908.0 | −1.36514 | ||||||||
\(918\) | −2916.00 | −0.104839 | ||||||||
\(919\) | −8260.00 | −0.296488 | −0.148244 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148244 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(920\) | 1920.00 | 0.0688049 | ||||||||
\(921\) | 15018.0 | 0.537307 | ||||||||
\(922\) | 27384.0 | 0.978139 | ||||||||
\(923\) | −93456.0 | −3.33276 | ||||||||
\(924\) | −14976.0 | −0.533197 | ||||||||
\(925\) | −7600.00 | −0.270148 | ||||||||
\(926\) | −8576.00 | −0.304346 | ||||||||
\(927\) | −11322.0 | −0.401147 | ||||||||
\(928\) | −3840.00 | −0.135834 | ||||||||
\(929\) | 9120.00 | 0.322086 | 0.161043 | − | 0.986947i | \(-0.448514\pi\) | ||||
0.161043 | + | 0.986947i | \(0.448514\pi\) | |||||||
\(930\) | −930.000 | −0.0327913 | ||||||||
\(931\) | −53280.0 | −1.87560 | ||||||||
\(932\) | −10392.0 | −0.365237 | ||||||||
\(933\) | −1314.00 | −0.0461076 | ||||||||
\(934\) | −648.000 | −0.0227015 | ||||||||
\(935\) | −12960.0 | −0.453302 | ||||||||
\(936\) | −6336.00 | −0.221259 | ||||||||
\(937\) | −27274.0 | −0.950910 | −0.475455 | − | 0.879740i | \(-0.657717\pi\) | ||||
−0.475455 | + | 0.879740i | \(0.657717\pi\) | |||||||
\(938\) | −17368.0 | −0.604569 | ||||||||
\(939\) | 30876.0 | 1.07306 | ||||||||
\(940\) | −1920.00 | −0.0666207 | ||||||||
\(941\) | 49392.0 | 1.71109 | 0.855544 | − | 0.517731i | \(-0.173223\pi\) | ||||
0.855544 | + | 0.517731i | \(0.173223\pi\) | |||||||
\(942\) | 21396.0 | 0.740042 | ||||||||
\(943\) | −7776.00 | −0.268527 | ||||||||
\(944\) | 480.000 | 0.0165494 | ||||||||
\(945\) | −3510.00 | −0.120826 | ||||||||
\(946\) | −26112.0 | −0.897436 | ||||||||
\(947\) | −25164.0 | −0.863485 | −0.431742 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431742 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(948\) | −7680.00 | −0.263117 | ||||||||
\(949\) | −18656.0 | −0.638145 | ||||||||
\(950\) | −8000.00 | −0.273215 | ||||||||
\(951\) | −26622.0 | −0.907758 | ||||||||
\(952\) | −11232.0 | −0.382386 | ||||||||
\(953\) | −21138.0 | −0.718496 | −0.359248 | − | 0.933242i | \(-0.616967\pi\) | ||||
−0.359248 | + | 0.933242i | \(0.616967\pi\) | |||||||
\(954\) | 10476.0 | 0.355527 | ||||||||
\(955\) | −8610.00 | −0.291741 | ||||||||
\(956\) | −21360.0 | −0.722627 | ||||||||
\(957\) | 17280.0 | 0.583681 | ||||||||
\(958\) | −17940.0 | −0.605026 | ||||||||
\(959\) | 25116.0 | 0.845712 | ||||||||
\(960\) | −960.000 | −0.0322749 | ||||||||
\(961\) | 961.000 | 0.0322581 | ||||||||
\(962\) | 53504.0 | 1.79318 | ||||||||
\(963\) | −16956.0 | −0.567393 | ||||||||
\(964\) | 12008.0 | 0.401195 | ||||||||
\(965\) | 2090.00 | 0.0697197 | ||||||||
\(966\) | −7488.00 | −0.249402 | ||||||||
\(967\) | 21356.0 | 0.710199 | 0.355100 | − | 0.934828i | \(-0.384447\pi\) | ||||
0.355100 | + | 0.934828i | \(0.384447\pi\) | |||||||
\(968\) | 7784.00 | 0.258458 | ||||||||
\(969\) | 25920.0 | 0.859309 | ||||||||
\(970\) | −860.000 | −0.0284669 | ||||||||
\(971\) | 31242.0 | 1.03255 | 0.516274 | − | 0.856424i | \(-0.327319\pi\) | ||||
0.516274 | + | 0.856424i | \(0.327319\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 25480.0 | 0.839518 | ||||||||
\(974\) | 28432.0 | 0.935339 | ||||||||
\(975\) | −6600.00 | −0.216789 | ||||||||
\(976\) | −7648.00 | −0.250826 | ||||||||
\(977\) | 7686.00 | 0.251686 | 0.125843 | − | 0.992050i | \(-0.459836\pi\) | ||||
0.125843 | + | 0.992050i | \(0.459836\pi\) | |||||||
\(978\) | −10788.0 | −0.352722 | ||||||||
\(979\) | −5760.00 | −0.188039 | ||||||||
\(980\) | −6660.00 | −0.217088 | ||||||||
\(981\) | −630.000 | −0.0205039 | ||||||||
\(982\) | −16536.0 | −0.537357 | ||||||||
\(983\) | −35928.0 | −1.16574 | −0.582871 | − | 0.812564i | \(-0.698071\pi\) | ||||
−0.582871 | + | 0.812564i | \(0.698071\pi\) | |||||||
\(984\) | 3888.00 | 0.125960 | ||||||||
\(985\) | 270.000 | 0.00873392 | ||||||||
\(986\) | 12960.0 | 0.418591 | ||||||||
\(987\) | 7488.00 | 0.241485 | ||||||||
\(988\) | 56320.0 | 1.81354 | ||||||||
\(989\) | −13056.0 | −0.419774 | ||||||||
\(990\) | 4320.00 | 0.138685 | ||||||||
\(991\) | −8968.00 | −0.287465 | −0.143733 | − | 0.989617i | \(-0.545911\pi\) | ||||
−0.143733 | + | 0.989617i | \(0.545911\pi\) | |||||||
\(992\) | 992.000 | 0.0317500 | ||||||||
\(993\) | −28524.0 | −0.911563 | ||||||||
\(994\) | 55224.0 | 1.76217 | ||||||||
\(995\) | 8600.00 | 0.274008 | ||||||||
\(996\) | 11664.0 | 0.371072 | ||||||||
\(997\) | 34526.0 | 1.09674 | 0.548370 | − | 0.836236i | \(-0.315249\pi\) | ||||
0.548370 | + | 0.836236i | \(0.315249\pi\) | |||||||
\(998\) | −23720.0 | −0.752348 | ||||||||
\(999\) | −8208.00 | −0.259950 |
(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 | 930.4.a.c.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.4.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |