Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,4,Mod(1,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.153533511\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.192450 | −0.0962250 | − | 0.995360i | \(-0.530677\pi\) | ||||
−0.0962250 | + | 0.995360i | \(0.530677\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.136083 | ||||||||
\(7\) | 25.0000 | 1.34987 | 0.674937 | − | 0.737876i | \(-0.264171\pi\) | ||||
0.674937 | + | 0.737876i | \(0.264171\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.00000 | 0.246691 | 0.123346 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123346 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(12\) | −4.00000 | −0.0962250 | ||||||||
\(13\) | 76.0000 | 1.62143 | 0.810716 | − | 0.585440i | \(-0.199078\pi\) | ||||
0.810716 | + | 0.585440i | \(0.199078\pi\) | |||||||
\(14\) | −50.0000 | −0.954504 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 24.0000 | 0.342403 | 0.171202 | − | 0.985236i | \(-0.445235\pi\) | ||||
0.171202 | + | 0.985236i | \(0.445235\pi\) | |||||||
\(18\) | 52.0000 | 0.680918 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.0000 | −0.259783 | ||||||||
\(22\) | −18.0000 | −0.174437 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 8.00000 | 0.0680414 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −152.000 | −1.14653 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 100.000 | 0.674937 | ||||||||
\(29\) | 60.0000 | 0.384197 | 0.192099 | − | 0.981376i | \(-0.438471\pi\) | ||||
0.192099 | + | 0.981376i | \(0.438471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.0000 | 0.150637 | 0.0753184 | − | 0.997160i | \(-0.476003\pi\) | ||||
0.0753184 | + | 0.997160i | \(0.476003\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −9.00000 | −0.0474757 | ||||||||
\(34\) | −48.0000 | −0.242116 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | −37.0000 | −0.164399 | ||||||||
\(38\) | 80.0000 | 0.341519 | ||||||||
\(39\) | −76.0000 | −0.312045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 267.000 | 1.01703 | 0.508517 | − | 0.861052i | \(-0.330194\pi\) | ||||
0.508517 | + | 0.861052i | \(0.330194\pi\) | |||||||
\(42\) | 50.0000 | 0.183694 | ||||||||
\(43\) | 382.000 | 1.35475 | 0.677377 | − | 0.735636i | \(-0.263116\pi\) | ||||
0.677377 | + | 0.735636i | \(0.263116\pi\) | |||||||
\(44\) | 36.0000 | 0.123346 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −144.000 | −0.461557 | ||||||||
\(47\) | −267.000 | −0.828637 | −0.414319 | − | 0.910132i | \(-0.635980\pi\) | ||||
−0.414319 | + | 0.910132i | \(0.635980\pi\) | |||||||
\(48\) | −16.0000 | −0.0481125 | ||||||||
\(49\) | 282.000 | 0.822157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24.0000 | −0.0658955 | ||||||||
\(52\) | 304.000 | 0.810716 | ||||||||
\(53\) | −171.000 | −0.443182 | −0.221591 | − | 0.975140i | \(-0.571125\pi\) | ||||
−0.221591 | + | 0.975140i | \(0.571125\pi\) | |||||||
\(54\) | −106.000 | −0.267125 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −200.000 | −0.477252 | ||||||||
\(57\) | 40.0000 | 0.0929496 | ||||||||
\(58\) | −120.000 | −0.271668 | ||||||||
\(59\) | 396.000 | 0.873810 | 0.436905 | − | 0.899508i | \(-0.356075\pi\) | ||||
0.436905 | + | 0.899508i | \(0.356075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −898.000 | −1.88487 | −0.942435 | − | 0.334388i | \(-0.891470\pi\) | ||||
−0.942435 | + | 0.334388i | \(0.891470\pi\) | |||||||
\(62\) | −52.0000 | −0.106516 | ||||||||
\(63\) | −650.000 | −1.29988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 18.0000 | 0.0335704 | ||||||||
\(67\) | 676.000 | 1.23263 | 0.616317 | − | 0.787498i | \(-0.288624\pi\) | ||||
0.616317 | + | 0.787498i | \(0.288624\pi\) | |||||||
\(68\) | 96.0000 | 0.171202 | ||||||||
\(69\) | −72.0000 | −0.125620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21.0000 | −0.0351020 | −0.0175510 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175510 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(72\) | 208.000 | 0.340459 | ||||||||
\(73\) | 691.000 | 1.10788 | 0.553941 | − | 0.832556i | \(-0.313123\pi\) | ||||
0.553941 | + | 0.832556i | \(0.313123\pi\) | |||||||
\(74\) | 74.0000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −160.000 | −0.241490 | ||||||||
\(77\) | 225.000 | 0.333002 | ||||||||
\(78\) | 152.000 | 0.220649 | ||||||||
\(79\) | −394.000 | −0.561120 | −0.280560 | − | 0.959837i | \(-0.590520\pi\) | ||||
−0.280560 | + | 0.959837i | \(0.590520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | −534.000 | −0.719152 | ||||||||
\(83\) | −309.000 | −0.408640 | −0.204320 | − | 0.978904i | \(-0.565498\pi\) | ||||
−0.204320 | + | 0.978904i | \(0.565498\pi\) | |||||||
\(84\) | −100.000 | −0.129892 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −764.000 | −0.957956 | ||||||||
\(87\) | −60.0000 | −0.0739388 | ||||||||
\(88\) | −72.0000 | −0.0872185 | ||||||||
\(89\) | −918.000 | −1.09335 | −0.546673 | − | 0.837346i | \(-0.684106\pi\) | ||||
−0.546673 | + | 0.837346i | \(0.684106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1900.00 | 2.18873 | ||||||||
\(92\) | 288.000 | 0.326370 | ||||||||
\(93\) | −26.0000 | −0.0289900 | ||||||||
\(94\) | 534.000 | 0.585935 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 32.0000 | 0.0340207 | ||||||||
\(97\) | 766.000 | 0.801809 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(98\) | −564.000 | −0.581353 | ||||||||
\(99\) | −234.000 | −0.237554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1971.00 | 1.94180 | 0.970900 | − | 0.239485i | \(-0.0769785\pi\) | ||||
0.970900 | + | 0.239485i | \(0.0769785\pi\) | |||||||
\(102\) | 48.0000 | 0.0465952 | ||||||||
\(103\) | 34.0000 | 0.0325254 | 0.0162627 | − | 0.999868i | \(-0.494823\pi\) | ||||
0.0162627 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(104\) | −608.000 | −0.573263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 342.000 | 0.313377 | ||||||||
\(107\) | −2040.00 | −1.84312 | −0.921562 | − | 0.388231i | \(-0.873086\pi\) | ||||
−0.921562 | + | 0.388231i | \(0.873086\pi\) | |||||||
\(108\) | 212.000 | 0.188886 | ||||||||
\(109\) | −214.000 | −0.188050 | −0.0940251 | − | 0.995570i | \(-0.529973\pi\) | ||||
−0.0940251 | + | 0.995570i | \(0.529973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 37.0000 | 0.0316386 | ||||||||
\(112\) | 400.000 | 0.337468 | ||||||||
\(113\) | 66.0000 | 0.0549448 | 0.0274724 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274724 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(114\) | −80.0000 | −0.0657253 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 240.000 | 0.192099 | ||||||||
\(117\) | −1976.00 | −1.56138 | ||||||||
\(118\) | −792.000 | −0.617877 | ||||||||
\(119\) | 600.000 | 0.462201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1250.00 | −0.939144 | ||||||||
\(122\) | 1796.00 | 1.33280 | ||||||||
\(123\) | −267.000 | −0.195728 | ||||||||
\(124\) | 104.000 | 0.0753184 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1300.00 | 0.919152 | ||||||||
\(127\) | −1433.00 | −1.00125 | −0.500623 | − | 0.865666i | \(-0.666896\pi\) | ||||
−0.500623 | + | 0.865666i | \(0.666896\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −382.000 | −0.260723 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1278.00 | 0.852362 | 0.426181 | − | 0.904638i | \(-0.359859\pi\) | ||||
0.426181 | + | 0.904638i | \(0.359859\pi\) | |||||||
\(132\) | −36.0000 | −0.0237379 | ||||||||
\(133\) | −1000.00 | −0.651962 | ||||||||
\(134\) | −1352.00 | −0.871605 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −192.000 | −0.121058 | ||||||||
\(137\) | 1770.00 | 1.10381 | 0.551903 | − | 0.833909i | \(-0.313902\pi\) | ||||
0.551903 | + | 0.833909i | \(0.313902\pi\) | |||||||
\(138\) | 144.000 | 0.0888268 | ||||||||
\(139\) | −844.000 | −0.515015 | −0.257508 | − | 0.966276i | \(-0.582901\pi\) | ||||
−0.257508 | + | 0.966276i | \(0.582901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 267.000 | 0.159471 | ||||||||
\(142\) | 42.0000 | 0.0248209 | ||||||||
\(143\) | 684.000 | 0.399993 | ||||||||
\(144\) | −416.000 | −0.240741 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1382.00 | −0.783391 | ||||||||
\(147\) | −282.000 | −0.158224 | ||||||||
\(148\) | −148.000 | −0.0821995 | ||||||||
\(149\) | −2553.00 | −1.40369 | −0.701845 | − | 0.712329i | \(-0.747640\pi\) | ||||
−0.701845 | + | 0.712329i | \(0.747640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3272.00 | 1.76339 | 0.881694 | − | 0.471822i | \(-0.156403\pi\) | ||||
0.881694 | + | 0.471822i | \(0.156403\pi\) | |||||||
\(152\) | 320.000 | 0.170759 | ||||||||
\(153\) | −624.000 | −0.329722 | ||||||||
\(154\) | −450.000 | −0.235468 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −304.000 | −0.156022 | ||||||||
\(157\) | 331.000 | 0.168259 | 0.0841295 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841295 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(158\) | 788.000 | 0.396772 | ||||||||
\(159\) | 171.000 | 0.0852905 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1800.00 | 0.881117 | ||||||||
\(162\) | −1298.00 | −0.629509 | ||||||||
\(163\) | 1732.00 | 0.832274 | 0.416137 | − | 0.909302i | \(-0.363384\pi\) | ||||
0.416137 | + | 0.909302i | \(0.363384\pi\) | |||||||
\(164\) | 1068.00 | 0.508517 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 618.000 | 0.288952 | ||||||||
\(167\) | −3666.00 | −1.69870 | −0.849352 | − | 0.527827i | \(-0.823007\pi\) | ||||
−0.849352 | + | 0.527827i | \(0.823007\pi\) | |||||||
\(168\) | 200.000 | 0.0918472 | ||||||||
\(169\) | 3579.00 | 1.62904 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1040.00 | 0.465092 | ||||||||
\(172\) | 1528.00 | 0.677377 | ||||||||
\(173\) | −2739.00 | −1.20371 | −0.601856 | − | 0.798604i | \(-0.705572\pi\) | ||||
−0.601856 | + | 0.798604i | \(0.705572\pi\) | |||||||
\(174\) | 120.000 | 0.0522826 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 144.000 | 0.0616728 | ||||||||
\(177\) | −396.000 | −0.168165 | ||||||||
\(178\) | 1836.00 | 0.773112 | ||||||||
\(179\) | −2448.00 | −1.02219 | −0.511095 | − | 0.859524i | \(-0.670760\pi\) | ||||
−0.511095 | + | 0.859524i | \(0.670760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −307.000 | −0.126073 | −0.0630363 | − | 0.998011i | \(-0.520078\pi\) | ||||
−0.0630363 | + | 0.998011i | \(0.520078\pi\) | |||||||
\(182\) | −3800.00 | −1.54766 | ||||||||
\(183\) | 898.000 | 0.362744 | ||||||||
\(184\) | −576.000 | −0.230779 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 52.0000 | 0.0204991 | ||||||||
\(187\) | 216.000 | 0.0844678 | ||||||||
\(188\) | −1068.00 | −0.414319 | ||||||||
\(189\) | 1325.00 | 0.509945 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5004.00 | −1.89569 | −0.947845 | − | 0.318732i | \(-0.896743\pi\) | ||||
−0.947845 | + | 0.318732i | \(0.896743\pi\) | |||||||
\(192\) | −64.0000 | −0.0240563 | ||||||||
\(193\) | 460.000 | 0.171562 | 0.0857812 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857812 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(194\) | −1532.00 | −0.566965 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1128.00 | 0.411079 | ||||||||
\(197\) | −69.0000 | −0.0249546 | −0.0124773 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124773 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(198\) | 468.000 | 0.167976 | ||||||||
\(199\) | −1006.00 | −0.358359 | −0.179180 | − | 0.983816i | \(-0.557344\pi\) | ||||
−0.179180 | + | 0.983816i | \(0.557344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −676.000 | −0.237221 | ||||||||
\(202\) | −3942.00 | −1.37306 | ||||||||
\(203\) | 1500.00 | 0.518618 | ||||||||
\(204\) | −96.0000 | −0.0329478 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −68.0000 | −0.0229990 | ||||||||
\(207\) | −1872.00 | −0.628565 | ||||||||
\(208\) | 1216.00 | 0.405358 | ||||||||
\(209\) | −360.000 | −0.119147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3353.00 | 1.09398 | 0.546991 | − | 0.837139i | \(-0.315773\pi\) | ||||
0.546991 | + | 0.837139i | \(0.315773\pi\) | |||||||
\(212\) | −684.000 | −0.221591 | ||||||||
\(213\) | 21.0000 | 0.00675538 | ||||||||
\(214\) | 4080.00 | 1.30329 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −424.000 | −0.133563 | ||||||||
\(217\) | 650.000 | 0.203340 | ||||||||
\(218\) | 428.000 | 0.132972 | ||||||||
\(219\) | −691.000 | −0.213212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1824.00 | 0.555183 | ||||||||
\(222\) | −74.0000 | −0.0223719 | ||||||||
\(223\) | 5677.00 | 1.70475 | 0.852377 | − | 0.522928i | \(-0.175160\pi\) | ||||
0.852377 | + | 0.522928i | \(0.175160\pi\) | |||||||
\(224\) | −800.000 | −0.238626 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −132.000 | −0.0388518 | ||||||||
\(227\) | −2076.00 | −0.607000 | −0.303500 | − | 0.952831i | \(-0.598155\pi\) | ||||
−0.303500 | + | 0.952831i | \(0.598155\pi\) | |||||||
\(228\) | 160.000 | 0.0464748 | ||||||||
\(229\) | 3671.00 | 1.05933 | 0.529665 | − | 0.848207i | \(-0.322318\pi\) | ||||
0.529665 | + | 0.848207i | \(0.322318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −225.000 | −0.0640862 | ||||||||
\(232\) | −480.000 | −0.135834 | ||||||||
\(233\) | 5742.00 | 1.61447 | 0.807234 | − | 0.590232i | \(-0.200964\pi\) | ||||
0.807234 | + | 0.590232i | \(0.200964\pi\) | |||||||
\(234\) | 3952.00 | 1.10406 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1584.00 | 0.436905 | ||||||||
\(237\) | 394.000 | 0.107988 | ||||||||
\(238\) | −1200.00 | −0.326825 | ||||||||
\(239\) | 3918.00 | 1.06039 | 0.530197 | − | 0.847874i | \(-0.322118\pi\) | ||||
0.530197 | + | 0.847874i | \(0.322118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2540.00 | 0.678904 | 0.339452 | − | 0.940623i | \(-0.389758\pi\) | ||||
0.339452 | + | 0.940623i | \(0.389758\pi\) | |||||||
\(242\) | 2500.00 | 0.664075 | ||||||||
\(243\) | −2080.00 | −0.549103 | ||||||||
\(244\) | −3592.00 | −0.942435 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 534.000 | 0.138401 | ||||||||
\(247\) | −3040.00 | −0.783120 | ||||||||
\(248\) | −208.000 | −0.0532581 | ||||||||
\(249\) | 309.000 | 0.0786429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 444.000 | 0.111654 | 0.0558268 | − | 0.998440i | \(-0.482221\pi\) | ||||
0.0558268 | + | 0.998440i | \(0.482221\pi\) | |||||||
\(252\) | −2600.00 | −0.649939 | ||||||||
\(253\) | 648.000 | 0.161025 | ||||||||
\(254\) | 2866.00 | 0.707988 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5034.00 | 1.22184 | 0.610919 | − | 0.791693i | \(-0.290800\pi\) | ||||
0.610919 | + | 0.791693i | \(0.290800\pi\) | |||||||
\(258\) | 764.000 | 0.184359 | ||||||||
\(259\) | −925.000 | −0.221918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1560.00 | −0.369968 | ||||||||
\(262\) | −2556.00 | −0.602711 | ||||||||
\(263\) | 393.000 | 0.0921423 | 0.0460711 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460711 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(264\) | 72.0000 | 0.0167852 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2000.00 | 0.461007 | ||||||||
\(267\) | 918.000 | 0.210415 | ||||||||
\(268\) | 2704.00 | 0.616317 | ||||||||
\(269\) | −1566.00 | −0.354947 | −0.177473 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177473 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3431.00 | 0.769072 | 0.384536 | − | 0.923110i | \(-0.374362\pi\) | ||||
0.384536 | + | 0.923110i | \(0.374362\pi\) | |||||||
\(272\) | 384.000 | 0.0856008 | ||||||||
\(273\) | −1900.00 | −0.421221 | ||||||||
\(274\) | −3540.00 | −0.780508 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −288.000 | −0.0628100 | ||||||||
\(277\) | 4450.00 | 0.965251 | 0.482626 | − | 0.875827i | \(-0.339683\pi\) | ||||
0.482626 | + | 0.875827i | \(0.339683\pi\) | |||||||
\(278\) | 1688.00 | 0.364171 | ||||||||
\(279\) | −676.000 | −0.145058 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 318.000 | 0.0675099 | 0.0337550 | − | 0.999430i | \(-0.489253\pi\) | ||||
0.0337550 | + | 0.999430i | \(0.489253\pi\) | |||||||
\(282\) | −534.000 | −0.112763 | ||||||||
\(283\) | 7936.00 | 1.66695 | 0.833474 | − | 0.552559i | \(-0.186349\pi\) | ||||
0.833474 | + | 0.552559i | \(0.186349\pi\) | |||||||
\(284\) | −84.0000 | −0.0175510 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1368.00 | −0.282838 | ||||||||
\(287\) | 6675.00 | 1.37287 | ||||||||
\(288\) | 832.000 | 0.170229 | ||||||||
\(289\) | −4337.00 | −0.882760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −766.000 | −0.154308 | ||||||||
\(292\) | 2764.00 | 0.553941 | ||||||||
\(293\) | 1698.00 | 0.338560 | 0.169280 | − | 0.985568i | \(-0.445856\pi\) | ||||
0.169280 | + | 0.985568i | \(0.445856\pi\) | |||||||
\(294\) | 564.000 | 0.111881 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 296.000 | 0.0581238 | ||||||||
\(297\) | 477.000 | 0.0931931 | ||||||||
\(298\) | 5106.00 | 0.992559 | ||||||||
\(299\) | 5472.00 | 1.05837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9550.00 | 1.82875 | ||||||||
\(302\) | −6544.00 | −1.24690 | ||||||||
\(303\) | −1971.00 | −0.373700 | ||||||||
\(304\) | −640.000 | −0.120745 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1248.00 | 0.233148 | ||||||||
\(307\) | 1189.00 | 0.221042 | 0.110521 | − | 0.993874i | \(-0.464748\pi\) | ||||
0.110521 | + | 0.993874i | \(0.464748\pi\) | |||||||
\(308\) | 900.000 | 0.166501 | ||||||||
\(309\) | −34.0000 | −0.00625952 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3984.00 | −0.726405 | −0.363202 | − | 0.931710i | \(-0.618317\pi\) | ||||
−0.363202 | + | 0.931710i | \(0.618317\pi\) | |||||||
\(312\) | 608.000 | 0.110324 | ||||||||
\(313\) | 6010.00 | 1.08532 | 0.542660 | − | 0.839952i | \(-0.317417\pi\) | ||||
0.542660 | + | 0.839952i | \(0.317417\pi\) | |||||||
\(314\) | −662.000 | −0.118977 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1576.00 | −0.280560 | ||||||||
\(317\) | 6234.00 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(318\) | −342.000 | −0.0603095 | ||||||||
\(319\) | 540.000 | 0.0947780 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2040.00 | 0.354709 | ||||||||
\(322\) | −3600.00 | −0.623044 | ||||||||
\(323\) | −960.000 | −0.165374 | ||||||||
\(324\) | 2596.00 | 0.445130 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3464.00 | −0.588507 | ||||||||
\(327\) | 214.000 | 0.0361903 | ||||||||
\(328\) | −2136.00 | −0.359576 | ||||||||
\(329\) | −6675.00 | −1.11856 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10316.0 | 1.71305 | 0.856524 | − | 0.516108i | \(-0.172620\pi\) | ||||
0.856524 | + | 0.516108i | \(0.172620\pi\) | |||||||
\(332\) | −1236.00 | −0.204320 | ||||||||
\(333\) | 962.000 | 0.158310 | ||||||||
\(334\) | 7332.00 | 1.20117 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −400.000 | −0.0649458 | ||||||||
\(337\) | 4507.00 | 0.728522 | 0.364261 | − | 0.931297i | \(-0.381322\pi\) | ||||
0.364261 | + | 0.931297i | \(0.381322\pi\) | |||||||
\(338\) | −7158.00 | −1.15190 | ||||||||
\(339\) | −66.0000 | −0.0105741 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 234.000 | 0.0371607 | ||||||||
\(342\) | −2080.00 | −0.328870 | ||||||||
\(343\) | −1525.00 | −0.240065 | ||||||||
\(344\) | −3056.00 | −0.478978 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5478.00 | 0.851153 | ||||||||
\(347\) | −5136.00 | −0.794568 | −0.397284 | − | 0.917696i | \(-0.630047\pi\) | ||||
−0.397284 | + | 0.917696i | \(0.630047\pi\) | |||||||
\(348\) | −240.000 | −0.0369694 | ||||||||
\(349\) | −6658.00 | −1.02119 | −0.510594 | − | 0.859822i | \(-0.670574\pi\) | ||||
−0.510594 | + | 0.859822i | \(0.670574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4028.00 | 0.612532 | ||||||||
\(352\) | −288.000 | −0.0436092 | ||||||||
\(353\) | 1302.00 | 0.196313 | 0.0981565 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981565 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(354\) | 792.000 | 0.118911 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3672.00 | −0.546673 | ||||||||
\(357\) | −600.000 | −0.0889506 | ||||||||
\(358\) | 4896.00 | 0.722798 | ||||||||
\(359\) | −2949.00 | −0.433544 | −0.216772 | − | 0.976222i | \(-0.569553\pi\) | ||||
−0.216772 | + | 0.976222i | \(0.569553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | 614.000 | 0.0891468 | ||||||||
\(363\) | 1250.00 | 0.180738 | ||||||||
\(364\) | 7600.00 | 1.09436 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1796.00 | −0.256498 | ||||||||
\(367\) | 7672.00 | 1.09121 | 0.545606 | − | 0.838042i | \(-0.316299\pi\) | ||||
0.545606 | + | 0.838042i | \(0.316299\pi\) | |||||||
\(368\) | 1152.00 | 0.163185 | ||||||||
\(369\) | −6942.00 | −0.979366 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4275.00 | −0.598240 | ||||||||
\(372\) | −104.000 | −0.0144950 | ||||||||
\(373\) | 9709.00 | 1.34776 | 0.673878 | − | 0.738843i | \(-0.264627\pi\) | ||||
0.673878 | + | 0.738843i | \(0.264627\pi\) | |||||||
\(374\) | −432.000 | −0.0597278 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2136.00 | 0.292968 | ||||||||
\(377\) | 4560.00 | 0.622949 | ||||||||
\(378\) | −2650.00 | −0.360585 | ||||||||
\(379\) | −3991.00 | −0.540907 | −0.270454 | − | 0.962733i | \(-0.587174\pi\) | ||||
−0.270454 | + | 0.962733i | \(0.587174\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1433.00 | 0.192690 | ||||||||
\(382\) | 10008.0 | 1.34046 | ||||||||
\(383\) | 6042.00 | 0.806088 | 0.403044 | − | 0.915181i | \(-0.367952\pi\) | ||||
0.403044 | + | 0.915181i | \(0.367952\pi\) | |||||||
\(384\) | 128.000 | 0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −920.000 | −0.121313 | ||||||||
\(387\) | −9932.00 | −1.30458 | ||||||||
\(388\) | 3064.00 | 0.400905 | ||||||||
\(389\) | 4728.00 | 0.616245 | 0.308122 | − | 0.951347i | \(-0.400299\pi\) | ||||
0.308122 | + | 0.951347i | \(0.400299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1728.00 | 0.223501 | ||||||||
\(392\) | −2256.00 | −0.290677 | ||||||||
\(393\) | −1278.00 | −0.164037 | ||||||||
\(394\) | 138.000 | 0.0176455 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −936.000 | −0.118777 | ||||||||
\(397\) | 13051.0 | 1.64990 | 0.824951 | − | 0.565205i | \(-0.191203\pi\) | ||||
0.824951 | + | 0.565205i | \(0.191203\pi\) | |||||||
\(398\) | 2012.00 | 0.253398 | ||||||||
\(399\) | 1000.00 | 0.125470 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1098.00 | 0.136737 | 0.0683685 | − | 0.997660i | \(-0.478221\pi\) | ||||
0.0683685 | + | 0.997660i | \(0.478221\pi\) | |||||||
\(402\) | 1352.00 | 0.167740 | ||||||||
\(403\) | 1976.00 | 0.244247 | ||||||||
\(404\) | 7884.00 | 0.970900 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3000.00 | −0.366718 | ||||||||
\(407\) | −333.000 | −0.0405558 | ||||||||
\(408\) | 192.000 | 0.0232976 | ||||||||
\(409\) | −1996.00 | −0.241310 | −0.120655 | − | 0.992694i | \(-0.538500\pi\) | ||||
−0.120655 | + | 0.992694i | \(0.538500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1770.00 | −0.212427 | ||||||||
\(412\) | 136.000 | 0.0162627 | ||||||||
\(413\) | 9900.00 | 1.17953 | ||||||||
\(414\) | 3744.00 | 0.444463 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2432.00 | −0.286631 | ||||||||
\(417\) | 844.000 | 0.0991148 | ||||||||
\(418\) | 720.000 | 0.0842496 | ||||||||
\(419\) | −7023.00 | −0.818845 | −0.409422 | − | 0.912345i | \(-0.634270\pi\) | ||||
−0.409422 | + | 0.912345i | \(0.634270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3404.00 | 0.394064 | 0.197032 | − | 0.980397i | \(-0.436870\pi\) | ||||
0.197032 | + | 0.980397i | \(0.436870\pi\) | |||||||
\(422\) | −6706.00 | −0.773562 | ||||||||
\(423\) | 6942.00 | 0.797947 | ||||||||
\(424\) | 1368.00 | 0.156689 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −42.0000 | −0.00477678 | ||||||||
\(427\) | −22450.0 | −2.54434 | ||||||||
\(428\) | −8160.00 | −0.921562 | ||||||||
\(429\) | −684.000 | −0.0769786 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2712.00 | 0.303092 | 0.151546 | − | 0.988450i | \(-0.451575\pi\) | ||||
0.151546 | + | 0.988450i | \(0.451575\pi\) | |||||||
\(432\) | 848.000 | 0.0944431 | ||||||||
\(433\) | −1043.00 | −0.115758 | −0.0578792 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578792 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(434\) | −1300.00 | −0.143783 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −856.000 | −0.0940251 | ||||||||
\(437\) | −2880.00 | −0.315261 | ||||||||
\(438\) | 1382.00 | 0.150764 | ||||||||
\(439\) | 8612.00 | 0.936283 | 0.468142 | − | 0.883653i | \(-0.344924\pi\) | ||||
0.468142 | + | 0.883653i | \(0.344924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7332.00 | −0.791707 | ||||||||
\(442\) | −3648.00 | −0.392574 | ||||||||
\(443\) | 4935.00 | 0.529275 | 0.264638 | − | 0.964348i | \(-0.414748\pi\) | ||||
0.264638 | + | 0.964348i | \(0.414748\pi\) | |||||||
\(444\) | 148.000 | 0.0158193 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11354.0 | −1.20544 | ||||||||
\(447\) | 2553.00 | 0.270140 | ||||||||
\(448\) | 1600.00 | 0.168734 | ||||||||
\(449\) | 1290.00 | 0.135588 | 0.0677938 | − | 0.997699i | \(-0.478404\pi\) | ||||
0.0677938 | + | 0.997699i | \(0.478404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2403.00 | 0.250893 | ||||||||
\(452\) | 264.000 | 0.0274724 | ||||||||
\(453\) | −3272.00 | −0.339364 | ||||||||
\(454\) | 4152.00 | 0.429214 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −320.000 | −0.0328627 | ||||||||
\(457\) | 5038.00 | 0.515684 | 0.257842 | − | 0.966187i | \(-0.416989\pi\) | ||||
0.257842 | + | 0.966187i | \(0.416989\pi\) | |||||||
\(458\) | −7342.00 | −0.749059 | ||||||||
\(459\) | 1272.00 | 0.129350 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1074.00 | 0.108506 | 0.0542529 | − | 0.998527i | \(-0.482722\pi\) | ||||
0.0542529 | + | 0.998527i | \(0.482722\pi\) | |||||||
\(462\) | 450.000 | 0.0453158 | ||||||||
\(463\) | −14762.0 | −1.48175 | −0.740873 | − | 0.671645i | \(-0.765588\pi\) | ||||
−0.740873 | + | 0.671645i | \(0.765588\pi\) | |||||||
\(464\) | 960.000 | 0.0960493 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11484.0 | −1.14160 | ||||||||
\(467\) | −9702.00 | −0.961360 | −0.480680 | − | 0.876896i | \(-0.659610\pi\) | ||||
−0.480680 | + | 0.876896i | \(0.659610\pi\) | |||||||
\(468\) | −7904.00 | −0.780689 | ||||||||
\(469\) | 16900.0 | 1.66390 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −331.000 | −0.0323815 | ||||||||
\(472\) | −3168.00 | −0.308939 | ||||||||
\(473\) | 3438.00 | 0.334206 | ||||||||
\(474\) | −788.000 | −0.0763587 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2400.00 | 0.231100 | ||||||||
\(477\) | 4446.00 | 0.426768 | ||||||||
\(478\) | −7836.00 | −0.749812 | ||||||||
\(479\) | 5136.00 | 0.489916 | 0.244958 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244958 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2812.00 | −0.266562 | ||||||||
\(482\) | −5080.00 | −0.480057 | ||||||||
\(483\) | −1800.00 | −0.169571 | ||||||||
\(484\) | −5000.00 | −0.469572 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4160.00 | 0.388275 | ||||||||
\(487\) | −1772.00 | −0.164881 | −0.0824404 | − | 0.996596i | \(-0.526271\pi\) | ||||
−0.0824404 | + | 0.996596i | \(0.526271\pi\) | |||||||
\(488\) | 7184.00 | 0.666402 | ||||||||
\(489\) | −1732.00 | −0.160171 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12264.0 | 1.12722 | 0.563612 | − | 0.826040i | \(-0.309411\pi\) | ||||
0.563612 | + | 0.826040i | \(0.309411\pi\) | |||||||
\(492\) | −1068.00 | −0.0978641 | ||||||||
\(493\) | 1440.00 | 0.131550 | ||||||||
\(494\) | 6080.00 | 0.553749 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 416.000 | 0.0376592 | ||||||||
\(497\) | −525.000 | −0.0473832 | ||||||||
\(498\) | −618.000 | −0.0556089 | ||||||||
\(499\) | −6586.00 | −0.590841 | −0.295421 | − | 0.955367i | \(-0.595460\pi\) | ||||
−0.295421 | + | 0.955367i | \(0.595460\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3666.00 | 0.326916 | ||||||||
\(502\) | −888.000 | −0.0789510 | ||||||||
\(503\) | 6408.00 | 0.568029 | 0.284015 | − | 0.958820i | \(-0.408334\pi\) | ||||
0.284015 | + | 0.958820i | \(0.408334\pi\) | |||||||
\(504\) | 5200.00 | 0.459576 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1296.00 | −0.113862 | ||||||||
\(507\) | −3579.00 | −0.313509 | ||||||||
\(508\) | −5732.00 | −0.500623 | ||||||||
\(509\) | 6501.00 | 0.566113 | 0.283057 | − | 0.959103i | \(-0.408652\pi\) | ||||
0.283057 | + | 0.959103i | \(0.408652\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17275.0 | 1.49550 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −2120.00 | −0.182457 | ||||||||
\(514\) | −10068.0 | −0.863970 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1528.00 | −0.130361 | ||||||||
\(517\) | −2403.00 | −0.204417 | ||||||||
\(518\) | 1850.00 | 0.156920 | ||||||||
\(519\) | 2739.00 | 0.231655 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9615.00 | 0.808524 | 0.404262 | − | 0.914643i | \(-0.367528\pi\) | ||||
0.404262 | + | 0.914643i | \(0.367528\pi\) | |||||||
\(522\) | 3120.00 | 0.261607 | ||||||||
\(523\) | −590.000 | −0.0493287 | −0.0246643 | − | 0.999696i | \(-0.507852\pi\) | ||||
−0.0246643 | + | 0.999696i | \(0.507852\pi\) | |||||||
\(524\) | 5112.00 | 0.426181 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −786.000 | −0.0651544 | ||||||||
\(527\) | 624.000 | 0.0515785 | ||||||||
\(528\) | −144.000 | −0.0118689 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10296.0 | −0.841447 | ||||||||
\(532\) | −4000.00 | −0.325981 | ||||||||
\(533\) | 20292.0 | 1.64905 | ||||||||
\(534\) | −1836.00 | −0.148786 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5408.00 | −0.435802 | ||||||||
\(537\) | 2448.00 | 0.196721 | ||||||||
\(538\) | 3132.00 | 0.250985 | ||||||||
\(539\) | 2538.00 | 0.202819 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13070.0 | 1.03868 | 0.519338 | − | 0.854569i | \(-0.326179\pi\) | ||||
0.519338 | + | 0.854569i | \(0.326179\pi\) | |||||||
\(542\) | −6862.00 | −0.543816 | ||||||||
\(543\) | 307.000 | 0.0242627 | ||||||||
\(544\) | −768.000 | −0.0605289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3800.00 | 0.297848 | ||||||||
\(547\) | 6928.00 | 0.541535 | 0.270768 | − | 0.962645i | \(-0.412722\pi\) | ||||
0.270768 | + | 0.962645i | \(0.412722\pi\) | |||||||
\(548\) | 7080.00 | 0.551903 | ||||||||
\(549\) | 23348.0 | 1.81506 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2400.00 | −0.185560 | ||||||||
\(552\) | 576.000 | 0.0444134 | ||||||||
\(553\) | −9850.00 | −0.757441 | ||||||||
\(554\) | −8900.00 | −0.682536 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3376.00 | −0.257508 | ||||||||
\(557\) | −1860.00 | −0.141491 | −0.0707457 | − | 0.997494i | \(-0.522538\pi\) | ||||
−0.0707457 | + | 0.997494i | \(0.522538\pi\) | |||||||
\(558\) | 1352.00 | 0.102571 | ||||||||
\(559\) | 29032.0 | 2.19664 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −216.000 | −0.0162558 | ||||||||
\(562\) | −636.000 | −0.0477367 | ||||||||
\(563\) | −1536.00 | −0.114982 | −0.0574908 | − | 0.998346i | \(-0.518310\pi\) | ||||
−0.0574908 | + | 0.998346i | \(0.518310\pi\) | |||||||
\(564\) | 1068.00 | 0.0797357 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15872.0 | −1.17871 | ||||||||
\(567\) | 16225.0 | 1.20174 | ||||||||
\(568\) | 168.000 | 0.0124104 | ||||||||
\(569\) | −1254.00 | −0.0923909 | −0.0461954 | − | 0.998932i | \(-0.514710\pi\) | ||||
−0.0461954 | + | 0.998932i | \(0.514710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14789.0 | 1.08389 | 0.541944 | − | 0.840414i | \(-0.317688\pi\) | ||||
0.541944 | + | 0.840414i | \(0.317688\pi\) | |||||||
\(572\) | 2736.00 | 0.199996 | ||||||||
\(573\) | 5004.00 | 0.364826 | ||||||||
\(574\) | −13350.0 | −0.970763 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1664.00 | −0.120370 | ||||||||
\(577\) | −15932.0 | −1.14949 | −0.574747 | − | 0.818331i | \(-0.694899\pi\) | ||||
−0.574747 | + | 0.818331i | \(0.694899\pi\) | |||||||
\(578\) | 8674.00 | 0.624206 | ||||||||
\(579\) | −460.000 | −0.0330172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7725.00 | −0.551613 | ||||||||
\(582\) | 1532.00 | 0.109112 | ||||||||
\(583\) | −1539.00 | −0.109329 | ||||||||
\(584\) | −5528.00 | −0.391696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3396.00 | −0.239398 | ||||||||
\(587\) | 9546.00 | 0.671219 | 0.335610 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335610 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(588\) | −1128.00 | −0.0791121 | ||||||||
\(589\) | −1040.00 | −0.0727546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 69.0000 | 0.00480251 | ||||||||
\(592\) | −592.000 | −0.0410997 | ||||||||
\(593\) | −8793.00 | −0.608913 | −0.304456 | − | 0.952526i | \(-0.598475\pi\) | ||||
−0.304456 | + | 0.952526i | \(0.598475\pi\) | |||||||
\(594\) | −954.000 | −0.0658975 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10212.0 | −0.701845 | ||||||||
\(597\) | 1006.00 | 0.0689662 | ||||||||
\(598\) | −10944.0 | −0.748384 | ||||||||
\(599\) | 25875.0 | 1.76498 | 0.882491 | − | 0.470330i | \(-0.155865\pi\) | ||||
0.882491 | + | 0.470330i | \(0.155865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19478.0 | 1.32200 | 0.661002 | − | 0.750384i | \(-0.270132\pi\) | ||||
0.661002 | + | 0.750384i | \(0.270132\pi\) | |||||||
\(602\) | −19100.0 | −1.29312 | ||||||||
\(603\) | −17576.0 | −1.18698 | ||||||||
\(604\) | 13088.0 | 0.881694 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3942.00 | 0.264246 | ||||||||
\(607\) | 13696.0 | 0.915821 | 0.457911 | − | 0.888998i | \(-0.348598\pi\) | ||||
0.457911 | + | 0.888998i | \(0.348598\pi\) | |||||||
\(608\) | 1280.00 | 0.0853797 | ||||||||
\(609\) | −1500.00 | −0.0998080 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20292.0 | −1.34358 | ||||||||
\(612\) | −2496.00 | −0.164861 | ||||||||
\(613\) | −7049.00 | −0.464448 | −0.232224 | − | 0.972662i | \(-0.574600\pi\) | ||||
−0.232224 | + | 0.972662i | \(0.574600\pi\) | |||||||
\(614\) | −2378.00 | −0.156300 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1800.00 | −0.117734 | ||||||||
\(617\) | 12069.0 | 0.787487 | 0.393744 | − | 0.919220i | \(-0.371180\pi\) | ||||
0.393744 | + | 0.919220i | \(0.371180\pi\) | |||||||
\(618\) | 68.0000 | 0.00442615 | ||||||||
\(619\) | −18415.0 | −1.19574 | −0.597869 | − | 0.801594i | \(-0.703986\pi\) | ||||
−0.597869 | + | 0.801594i | \(0.703986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3816.00 | 0.246587 | ||||||||
\(622\) | 7968.00 | 0.513646 | ||||||||
\(623\) | −22950.0 | −1.47588 | ||||||||
\(624\) | −1216.00 | −0.0780112 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12020.0 | −0.767437 | ||||||||
\(627\) | 360.000 | 0.0229298 | ||||||||
\(628\) | 1324.00 | 0.0841295 | ||||||||
\(629\) | −888.000 | −0.0562907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10250.0 | 0.646666 | 0.323333 | − | 0.946285i | \(-0.395197\pi\) | ||||
0.323333 | + | 0.946285i | \(0.395197\pi\) | |||||||
\(632\) | 3152.00 | 0.198386 | ||||||||
\(633\) | −3353.00 | −0.210537 | ||||||||
\(634\) | −12468.0 | −0.781021 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 684.000 | 0.0426452 | ||||||||
\(637\) | 21432.0 | 1.33307 | ||||||||
\(638\) | −1080.00 | −0.0670182 | ||||||||
\(639\) | 546.000 | 0.0338019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1569.00 | −0.0966798 | −0.0483399 | − | 0.998831i | \(-0.515393\pi\) | ||||
−0.0483399 | + | 0.998831i | \(0.515393\pi\) | |||||||
\(642\) | −4080.00 | −0.250817 | ||||||||
\(643\) | −27596.0 | −1.69250 | −0.846252 | − | 0.532783i | \(-0.821146\pi\) | ||||
−0.846252 | + | 0.532783i | \(0.821146\pi\) | |||||||
\(644\) | 7200.00 | 0.440559 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1920.00 | 0.116937 | ||||||||
\(647\) | 9126.00 | 0.554529 | 0.277264 | − | 0.960794i | \(-0.410572\pi\) | ||||
0.277264 | + | 0.960794i | \(0.410572\pi\) | |||||||
\(648\) | −5192.00 | −0.314755 | ||||||||
\(649\) | 3564.00 | 0.215561 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −650.000 | −0.0391329 | ||||||||
\(652\) | 6928.00 | 0.416137 | ||||||||
\(653\) | 14250.0 | 0.853975 | 0.426987 | − | 0.904258i | \(-0.359575\pi\) | ||||
0.426987 | + | 0.904258i | \(0.359575\pi\) | |||||||
\(654\) | −428.000 | −0.0255904 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4272.00 | 0.254259 | ||||||||
\(657\) | −17966.0 | −1.06685 | ||||||||
\(658\) | 13350.0 | 0.790938 | ||||||||
\(659\) | −5985.00 | −0.353782 | −0.176891 | − | 0.984230i | \(-0.556604\pi\) | ||||
−0.176891 | + | 0.984230i | \(0.556604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16846.0 | −0.991276 | −0.495638 | − | 0.868529i | \(-0.665066\pi\) | ||||
−0.495638 | + | 0.868529i | \(0.665066\pi\) | |||||||
\(662\) | −20632.0 | −1.21131 | ||||||||
\(663\) | −1824.00 | −0.106845 | ||||||||
\(664\) | 2472.00 | 0.144476 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1924.00 | −0.111942 | ||||||||
\(667\) | 4320.00 | 0.250781 | ||||||||
\(668\) | −14664.0 | −0.849352 | ||||||||
\(669\) | −5677.00 | −0.328080 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8082.00 | −0.464981 | ||||||||
\(672\) | 800.000 | 0.0459236 | ||||||||
\(673\) | −2297.00 | −0.131564 | −0.0657822 | − | 0.997834i | \(-0.520954\pi\) | ||||
−0.0657822 | + | 0.997834i | \(0.520954\pi\) | |||||||
\(674\) | −9014.00 | −0.515143 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14316.0 | 0.814520 | ||||||||
\(677\) | −27999.0 | −1.58950 | −0.794748 | − | 0.606939i | \(-0.792397\pi\) | ||||
−0.794748 | + | 0.606939i | \(0.792397\pi\) | |||||||
\(678\) | 132.000 | 0.00747703 | ||||||||
\(679\) | 19150.0 | 1.08234 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2076.00 | 0.116817 | ||||||||
\(682\) | −468.000 | −0.0262766 | ||||||||
\(683\) | 28872.0 | 1.61751 | 0.808753 | − | 0.588149i | \(-0.200143\pi\) | ||||
0.808753 | + | 0.588149i | \(0.200143\pi\) | |||||||
\(684\) | 4160.00 | 0.232546 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3050.00 | 0.169752 | ||||||||
\(687\) | −3671.00 | −0.203868 | ||||||||
\(688\) | 6112.00 | 0.338689 | ||||||||
\(689\) | −12996.0 | −0.718590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7720.00 | −0.425011 | −0.212506 | − | 0.977160i | \(-0.568162\pi\) | ||||
−0.212506 | + | 0.977160i | \(0.568162\pi\) | |||||||
\(692\) | −10956.0 | −0.601856 | ||||||||
\(693\) | −5850.00 | −0.320668 | ||||||||
\(694\) | 10272.0 | 0.561844 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 480.000 | 0.0261413 | ||||||||
\(697\) | 6408.00 | 0.348236 | ||||||||
\(698\) | 13316.0 | 0.722089 | ||||||||
\(699\) | −5742.00 | −0.310704 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31740.0 | −1.71013 | −0.855067 | − | 0.518518i | \(-0.826484\pi\) | ||||
−0.855067 | + | 0.518518i | \(0.826484\pi\) | |||||||
\(702\) | −8056.00 | −0.433126 | ||||||||
\(703\) | 1480.00 | 0.0794015 | ||||||||
\(704\) | 576.000 | 0.0308364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2604.00 | −0.138814 | ||||||||
\(707\) | 49275.0 | 2.62118 | ||||||||
\(708\) | −1584.00 | −0.0840824 | ||||||||
\(709\) | −33184.0 | −1.75776 | −0.878880 | − | 0.477044i | \(-0.841708\pi\) | ||||
−0.878880 | + | 0.477044i | \(0.841708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10244.0 | 0.540338 | ||||||||
\(712\) | 7344.00 | 0.386556 | ||||||||
\(713\) | 1872.00 | 0.0983267 | ||||||||
\(714\) | 1200.00 | 0.0628976 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9792.00 | −0.511095 | ||||||||
\(717\) | −3918.00 | −0.204073 | ||||||||
\(718\) | 5898.00 | 0.306562 | ||||||||
\(719\) | −23703.0 | −1.22945 | −0.614724 | − | 0.788742i | \(-0.710732\pi\) | ||||
−0.614724 | + | 0.788742i | \(0.710732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 850.000 | 0.0439052 | ||||||||
\(722\) | 10518.0 | 0.542160 | ||||||||
\(723\) | −2540.00 | −0.130655 | ||||||||
\(724\) | −1228.00 | −0.0630363 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2500.00 | −0.127801 | ||||||||
\(727\) | −25730.0 | −1.31262 | −0.656309 | − | 0.754492i | \(-0.727883\pi\) | ||||
−0.656309 | + | 0.754492i | \(0.727883\pi\) | |||||||
\(728\) | −15200.0 | −0.773832 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9168.00 | 0.463872 | ||||||||
\(732\) | 3592.00 | 0.181372 | ||||||||
\(733\) | −26021.0 | −1.31120 | −0.655599 | − | 0.755110i | \(-0.727584\pi\) | ||||
−0.655599 | + | 0.755110i | \(0.727584\pi\) | |||||||
\(734\) | −15344.0 | −0.771604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2304.00 | −0.115389 | ||||||||
\(737\) | 6084.00 | 0.304080 | ||||||||
\(738\) | 13884.0 | 0.692516 | ||||||||
\(739\) | −2563.00 | −0.127580 | −0.0637899 | − | 0.997963i | \(-0.520319\pi\) | ||||
−0.0637899 | + | 0.997963i | \(0.520319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3040.00 | 0.150711 | ||||||||
\(742\) | 8550.00 | 0.423019 | ||||||||
\(743\) | 3807.00 | 0.187975 | 0.0939874 | − | 0.995573i | \(-0.470039\pi\) | ||||
0.0939874 | + | 0.995573i | \(0.470039\pi\) | |||||||
\(744\) | 208.000 | 0.0102495 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19418.0 | −0.953007 | ||||||||
\(747\) | 8034.00 | 0.393506 | ||||||||
\(748\) | 864.000 | 0.0422339 | ||||||||
\(749\) | −51000.0 | −2.48798 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15109.0 | −0.734135 | −0.367067 | − | 0.930194i | \(-0.619638\pi\) | ||||
−0.367067 | + | 0.930194i | \(0.619638\pi\) | |||||||
\(752\) | −4272.00 | −0.207159 | ||||||||
\(753\) | −444.000 | −0.0214877 | ||||||||
\(754\) | −9120.00 | −0.440492 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5300.00 | 0.254972 | ||||||||
\(757\) | −23804.0 | −1.14289 | −0.571447 | − | 0.820639i | \(-0.693618\pi\) | ||||
−0.571447 | + | 0.820639i | \(0.693618\pi\) | |||||||
\(758\) | 7982.00 | 0.382479 | ||||||||
\(759\) | −648.000 | −0.0309893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35487.0 | −1.69041 | −0.845205 | − | 0.534441i | \(-0.820522\pi\) | ||||
−0.845205 | + | 0.534441i | \(0.820522\pi\) | |||||||
\(762\) | −2866.00 | −0.136252 | ||||||||
\(763\) | −5350.00 | −0.253844 | ||||||||
\(764\) | −20016.0 | −0.947845 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12084.0 | −0.569990 | ||||||||
\(767\) | 30096.0 | 1.41682 | ||||||||
\(768\) | −256.000 | −0.0120281 | ||||||||
\(769\) | 11576.0 | 0.542836 | 0.271418 | − | 0.962462i | \(-0.412507\pi\) | ||||
0.271418 | + | 0.962462i | \(0.412507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5034.00 | −0.235143 | ||||||||
\(772\) | 1840.00 | 0.0857812 | ||||||||
\(773\) | −36021.0 | −1.67605 | −0.838024 | − | 0.545633i | \(-0.816289\pi\) | ||||
−0.838024 | + | 0.545633i | \(0.816289\pi\) | |||||||
\(774\) | 19864.0 | 0.922476 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6128.00 | −0.283482 | ||||||||
\(777\) | 925.000 | 0.0427081 | ||||||||
\(778\) | −9456.00 | −0.435751 | ||||||||
\(779\) | −10680.0 | −0.491208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −189.000 | −0.00865935 | ||||||||
\(782\) | −3456.00 | −0.158039 | ||||||||
\(783\) | 3180.00 | 0.145139 | ||||||||
\(784\) | 4512.00 | 0.205539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2556.00 | 0.115992 | ||||||||
\(787\) | −4847.00 | −0.219539 | −0.109769 | − | 0.993957i | \(-0.535011\pi\) | ||||
−0.109769 | + | 0.993957i | \(0.535011\pi\) | |||||||
\(788\) | −276.000 | −0.0124773 | ||||||||
\(789\) | −393.000 | −0.0177328 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1650.00 | 0.0741685 | ||||||||
\(792\) | 1872.00 | 0.0839882 | ||||||||
\(793\) | −68248.0 | −3.05619 | ||||||||
\(794\) | −26102.0 | −1.16666 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4024.00 | −0.179180 | ||||||||
\(797\) | 10176.0 | 0.452261 | 0.226131 | − | 0.974097i | \(-0.427392\pi\) | ||||
0.226131 | + | 0.974097i | \(0.427392\pi\) | |||||||
\(798\) | −2000.00 | −0.0887208 | ||||||||
\(799\) | −6408.00 | −0.283728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23868.0 | 1.05285 | ||||||||
\(802\) | −2196.00 | −0.0966876 | ||||||||
\(803\) | 6219.00 | 0.273305 | ||||||||
\(804\) | −2704.00 | −0.118610 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3952.00 | −0.172709 | ||||||||
\(807\) | 1566.00 | 0.0683096 | ||||||||
\(808\) | −15768.0 | −0.686530 | ||||||||
\(809\) | −23568.0 | −1.02424 | −0.512118 | − | 0.858915i | \(-0.671139\pi\) | ||||
−0.512118 | + | 0.858915i | \(0.671139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6629.00 | 0.287023 | 0.143512 | − | 0.989649i | \(-0.454161\pi\) | ||||
0.143512 | + | 0.989649i | \(0.454161\pi\) | |||||||
\(812\) | 6000.00 | 0.259309 | ||||||||
\(813\) | −3431.00 | −0.148008 | ||||||||
\(814\) | 666.000 | 0.0286773 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −384.000 | −0.0164739 | ||||||||
\(817\) | −15280.0 | −0.654320 | ||||||||
\(818\) | 3992.00 | 0.170632 | ||||||||
\(819\) | −49400.0 | −2.10766 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37605.0 | 1.59857 | 0.799284 | − | 0.600954i | \(-0.205213\pi\) | ||||
0.799284 | + | 0.600954i | \(0.205213\pi\) | |||||||
\(822\) | 3540.00 | 0.150209 | ||||||||
\(823\) | −12632.0 | −0.535023 | −0.267511 | − | 0.963555i | \(-0.586201\pi\) | ||||
−0.267511 | + | 0.963555i | \(0.586201\pi\) | |||||||
\(824\) | −272.000 | −0.0114995 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19800.0 | −0.834056 | ||||||||
\(827\) | 9744.00 | 0.409712 | 0.204856 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204856 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(828\) | −7488.00 | −0.314283 | ||||||||
\(829\) | −22264.0 | −0.932763 | −0.466382 | − | 0.884584i | \(-0.654443\pi\) | ||||
−0.466382 | + | 0.884584i | \(0.654443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4450.00 | −0.185763 | ||||||||
\(832\) | 4864.00 | 0.202679 | ||||||||
\(833\) | 6768.00 | 0.281509 | ||||||||
\(834\) | −1688.00 | −0.0700847 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1440.00 | −0.0595735 | ||||||||
\(837\) | 1378.00 | 0.0569064 | ||||||||
\(838\) | 14046.0 | 0.579011 | ||||||||
\(839\) | 16416.0 | 0.675499 | 0.337749 | − | 0.941236i | \(-0.390334\pi\) | ||||
0.337749 | + | 0.941236i | \(0.390334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20789.0 | −0.852392 | ||||||||
\(842\) | −6808.00 | −0.278645 | ||||||||
\(843\) | −318.000 | −0.0129923 | ||||||||
\(844\) | 13412.0 | 0.546991 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13884.0 | −0.564234 | ||||||||
\(847\) | −31250.0 | −1.26772 | ||||||||
\(848\) | −2736.00 | −0.110796 | ||||||||
\(849\) | −7936.00 | −0.320804 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2664.00 | −0.107310 | ||||||||
\(852\) | 84.0000 | 0.00337769 | ||||||||
\(853\) | 7540.00 | 0.302655 | 0.151327 | − | 0.988484i | \(-0.451645\pi\) | ||||
0.151327 | + | 0.988484i | \(0.451645\pi\) | |||||||
\(854\) | 44900.0 | 1.79912 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16320.0 | 0.651643 | ||||||||
\(857\) | 3282.00 | 0.130818 | 0.0654090 | − | 0.997859i | \(-0.479165\pi\) | ||||
0.0654090 | + | 0.997859i | \(0.479165\pi\) | |||||||
\(858\) | 1368.00 | 0.0544321 | ||||||||
\(859\) | 12404.0 | 0.492688 | 0.246344 | − | 0.969182i | \(-0.420771\pi\) | ||||
0.246344 | + | 0.969182i | \(0.420771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6675.00 | −0.264208 | ||||||||
\(862\) | −5424.00 | −0.214318 | ||||||||
\(863\) | −39528.0 | −1.55915 | −0.779576 | − | 0.626307i | \(-0.784566\pi\) | ||||
−0.779576 | + | 0.626307i | \(0.784566\pi\) | |||||||
\(864\) | −1696.00 | −0.0667814 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2086.00 | 0.0818535 | ||||||||
\(867\) | 4337.00 | 0.169887 | ||||||||
\(868\) | 2600.00 | 0.101670 | ||||||||
\(869\) | −3546.00 | −0.138423 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51376.0 | 1.99863 | ||||||||
\(872\) | 1712.00 | 0.0664858 | ||||||||
\(873\) | −19916.0 | −0.772113 | ||||||||
\(874\) | 5760.00 | 0.222923 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2764.00 | −0.106606 | ||||||||
\(877\) | 6586.00 | 0.253584 | 0.126792 | − | 0.991929i | \(-0.459532\pi\) | ||||
0.126792 | + | 0.991929i | \(0.459532\pi\) | |||||||
\(878\) | −17224.0 | −0.662052 | ||||||||
\(879\) | −1698.00 | −0.0651560 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41550.0 | −1.58894 | −0.794469 | − | 0.607304i | \(-0.792251\pi\) | ||||
−0.794469 | + | 0.607304i | \(0.792251\pi\) | |||||||
\(882\) | 14664.0 | 0.559822 | ||||||||
\(883\) | 23944.0 | 0.912548 | 0.456274 | − | 0.889839i | \(-0.349184\pi\) | ||||
0.456274 | + | 0.889839i | \(0.349184\pi\) | |||||||
\(884\) | 7296.00 | 0.277592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9870.00 | −0.374254 | ||||||||
\(887\) | −6369.00 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(888\) | −296.000 | −0.0111859 | ||||||||
\(889\) | −35825.0 | −1.35155 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5841.00 | 0.219619 | ||||||||
\(892\) | 22708.0 | 0.852377 | ||||||||
\(893\) | 10680.0 | 0.400216 | ||||||||
\(894\) | −5106.00 | −0.191018 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3200.00 | −0.119313 | ||||||||
\(897\) | −5472.00 | −0.203684 | ||||||||
\(898\) | −2580.00 | −0.0958750 | ||||||||
\(899\) | 1560.00 | 0.0578742 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4104.00 | −0.151747 | ||||||||
\(902\) | −4806.00 | −0.177408 | ||||||||
\(903\) | −9550.00 | −0.351943 | ||||||||
\(904\) | −528.000 | −0.0194259 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6544.00 | 0.239967 | ||||||||
\(907\) | 22246.0 | 0.814406 | 0.407203 | − | 0.913338i | \(-0.366504\pi\) | ||||
0.407203 | + | 0.913338i | \(0.366504\pi\) | |||||||
\(908\) | −8304.00 | −0.303500 | ||||||||
\(909\) | −51246.0 | −1.86988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31770.0 | −1.15542 | −0.577710 | − | 0.816242i | \(-0.696053\pi\) | ||||
−0.577710 | + | 0.816242i | \(0.696053\pi\) | |||||||
\(912\) | 640.000 | 0.0232374 | ||||||||
\(913\) | −2781.00 | −0.100808 | ||||||||
\(914\) | −10076.0 | −0.364644 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14684.0 | 0.529665 | ||||||||
\(917\) | 31950.0 | 1.15058 | ||||||||
\(918\) | −2544.00 | −0.0914646 | ||||||||
\(919\) | 21176.0 | 0.760100 | 0.380050 | − | 0.924966i | \(-0.375907\pi\) | ||||
0.380050 | + | 0.924966i | \(0.375907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1189.00 | −0.0425395 | ||||||||
\(922\) | −2148.00 | −0.0767252 | ||||||||
\(923\) | −1596.00 | −0.0569155 | ||||||||
\(924\) | −900.000 | −0.0320431 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 29524.0 | 1.04775 | ||||||||
\(927\) | −884.000 | −0.0313208 | ||||||||
\(928\) | −1920.00 | −0.0679171 | ||||||||
\(929\) | 38766.0 | 1.36908 | 0.684538 | − | 0.728977i | \(-0.260004\pi\) | ||||
0.684538 | + | 0.728977i | \(0.260004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11280.0 | −0.397086 | ||||||||
\(932\) | 22968.0 | 0.807234 | ||||||||
\(933\) | 3984.00 | 0.139797 | ||||||||
\(934\) | 19404.0 | 0.679784 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15808.0 | 0.552031 | ||||||||
\(937\) | 37849.0 | 1.31961 | 0.659804 | − | 0.751438i | \(-0.270639\pi\) | ||||
0.659804 | + | 0.751438i | \(0.270639\pi\) | |||||||
\(938\) | −33800.0 | −1.17656 | ||||||||
\(939\) | −6010.00 | −0.208870 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6114.00 | −0.211807 | −0.105904 | − | 0.994376i | \(-0.533774\pi\) | ||||
−0.105904 | + | 0.994376i | \(0.533774\pi\) | |||||||
\(942\) | 662.000 | 0.0228972 | ||||||||
\(943\) | 19224.0 | 0.663860 | ||||||||
\(944\) | 6336.00 | 0.218453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6876.00 | −0.236319 | ||||||||
\(947\) | 6912.00 | 0.237180 | 0.118590 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118590 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(948\) | 1576.00 | 0.0539938 | ||||||||
\(949\) | 52516.0 | 1.79636 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6234.00 | −0.212567 | ||||||||
\(952\) | −4800.00 | −0.163413 | ||||||||
\(953\) | −50223.0 | −1.70712 | −0.853559 | − | 0.520997i | \(-0.825560\pi\) | ||||
−0.853559 | + | 0.520997i | \(0.825560\pi\) | |||||||
\(954\) | −8892.00 | −0.301771 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15672.0 | 0.530197 | ||||||||
\(957\) | −540.000 | −0.0182400 | ||||||||
\(958\) | −10272.0 | −0.346423 | ||||||||
\(959\) | 44250.0 | 1.49000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29115.0 | −0.977309 | ||||||||
\(962\) | 5624.00 | 0.188488 | ||||||||
\(963\) | 53040.0 | 1.77486 | ||||||||
\(964\) | 10160.0 | 0.339452 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3600.00 | 0.119905 | ||||||||
\(967\) | 47266.0 | 1.57184 | 0.785921 | − | 0.618326i | \(-0.212189\pi\) | ||||
0.785921 | + | 0.618326i | \(0.212189\pi\) | |||||||
\(968\) | 10000.0 | 0.332037 | ||||||||
\(969\) | 960.000 | 0.0318263 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31860.0 | 1.05297 | 0.526486 | − | 0.850184i | \(-0.323509\pi\) | ||||
0.526486 | + | 0.850184i | \(0.323509\pi\) | |||||||
\(972\) | −8320.00 | −0.274552 | ||||||||
\(973\) | −21100.0 | −0.695205 | ||||||||
\(974\) | 3544.00 | 0.116588 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14368.0 | −0.471218 | ||||||||
\(977\) | −47004.0 | −1.53919 | −0.769596 | − | 0.638531i | \(-0.779543\pi\) | ||||
−0.769596 | + | 0.638531i | \(0.779543\pi\) | |||||||
\(978\) | 3464.00 | 0.113258 | ||||||||
\(979\) | −8262.00 | −0.269719 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5564.00 | 0.181085 | ||||||||
\(982\) | −24528.0 | −0.797067 | ||||||||
\(983\) | −2589.00 | −0.0840043 | −0.0420022 | − | 0.999118i | \(-0.513374\pi\) | ||||
−0.0420022 | + | 0.999118i | \(0.513374\pi\) | |||||||
\(984\) | 2136.00 | 0.0692004 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2880.00 | −0.0930202 | ||||||||
\(987\) | 6675.00 | 0.215266 | ||||||||
\(988\) | −12160.0 | −0.391560 | ||||||||
\(989\) | 27504.0 | 0.884304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4142.00 | 0.132770 | 0.0663849 | − | 0.997794i | \(-0.478853\pi\) | ||||
0.0663849 | + | 0.997794i | \(0.478853\pi\) | |||||||
\(992\) | −832.000 | −0.0266291 | ||||||||
\(993\) | −10316.0 | −0.329676 | ||||||||
\(994\) | 1050.00 | 0.0335050 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1236.00 | 0.0393214 | ||||||||
\(997\) | 13120.0 | 0.416765 | 0.208382 | − | 0.978047i | \(-0.433180\pi\) | ||||
0.208382 | + | 0.978047i | \(0.433180\pi\) | |||||||
\(998\) | 13172.0 | 0.417788 | ||||||||
\(999\) | −1961.00 | −0.0621054 |
(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 | 1850.4.a.b.1.1 | 1 | ||
5.4 | even | 2 | 370.4.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.4.a.b.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1850.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |