Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(13.2754297513\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | 0.323970 | 0.161985 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161985 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.0000 | 1.17864 | 0.589318 | − | 0.807901i | \(-0.299397\pi\) | ||||
0.589318 | + | 0.807901i | \(0.299397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | −6.00000 | −0.114541 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | −91.0000 | −1.29828 | −0.649139 | − | 0.760669i | \(-0.724871\pi\) | ||||
−0.649139 | + | 0.760669i | \(0.724871\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0000 | −0.422608 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −43.0000 | −0.416710 | ||||||||
\(23\) | −162.000 | −1.46867 | −0.734333 | − | 0.678789i | \(-0.762505\pi\) | ||||
−0.734333 | + | 0.678789i | \(0.762505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 28.0000 | 0.211202 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −42.0000 | −0.283473 | ||||||||
\(29\) | −160.000 | −1.02453 | −0.512263 | − | 0.858829i | \(-0.671193\pi\) | ||||
−0.512263 | + | 0.858829i | \(0.671193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.0000 | 0.243336 | 0.121668 | − | 0.992571i | \(-0.461176\pi\) | ||||
0.121668 | + | 0.992571i | \(0.461176\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 91.0000 | 0.459011 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −314.000 | −1.39517 | −0.697585 | − | 0.716502i | \(-0.745742\pi\) | ||||
−0.697585 | + | 0.716502i | \(0.745742\pi\) | |||||||
\(38\) | 35.0000 | 0.149414 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 203.000 | 0.773251 | 0.386625 | − | 0.922237i | \(-0.373641\pi\) | ||||
0.386625 | + | 0.922237i | \(0.373641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 92.0000 | 0.326276 | 0.163138 | − | 0.986603i | \(-0.447838\pi\) | ||||
0.163138 | + | 0.986603i | \(0.447838\pi\) | |||||||
\(44\) | −301.000 | −1.03131 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 162.000 | 0.519252 | ||||||||
\(47\) | −196.000 | −0.608288 | −0.304144 | − | 0.952626i | \(-0.598370\pi\) | ||||
−0.304144 | + | 0.952626i | \(0.598370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.000 | −0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 196.000 | 0.522698 | ||||||||
\(53\) | −82.0000 | −0.212520 | −0.106260 | − | 0.994338i | \(-0.533888\pi\) | ||||
−0.106260 | + | 0.994338i | \(0.533888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 90.0000 | 0.214763 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 160.000 | 0.362225 | ||||||||
\(59\) | 280.000 | 0.617846 | 0.308923 | − | 0.951087i | \(-0.400032\pi\) | ||||
0.308923 | + | 0.951087i | \(0.400032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −518.000 | −1.08726 | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(62\) | −42.0000 | −0.0860323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 141.000 | 0.257103 | 0.128551 | − | 0.991703i | \(-0.458967\pi\) | ||||
0.128551 | + | 0.991703i | \(0.458967\pi\) | |||||||
\(68\) | 637.000 | 1.13599 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −412.000 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −763.000 | −1.22332 | −0.611660 | − | 0.791121i | \(-0.709498\pi\) | ||||
−0.611660 | + | 0.791121i | \(0.709498\pi\) | |||||||
\(74\) | 314.000 | 0.493267 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 245.000 | 0.369782 | ||||||||
\(77\) | 258.000 | 0.381842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 510.000 | 0.726323 | 0.363161 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363161 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −203.000 | −0.273385 | ||||||||
\(83\) | −777.000 | −1.02755 | −0.513776 | − | 0.857924i | \(-0.671754\pi\) | ||||
−0.513776 | + | 0.857924i | \(0.671754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −92.0000 | −0.115356 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 645.000 | 0.781332 | ||||||||
\(89\) | 945.000 | 1.12550 | 0.562752 | − | 0.826626i | \(-0.309743\pi\) | ||||
0.562752 | + | 0.826626i | \(0.309743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −168.000 | −0.193530 | ||||||||
\(92\) | 1134.00 | 1.28508 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 196.000 | 0.215062 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1246.00 | 1.30425 | 0.652124 | − | 0.758112i | \(-0.273878\pi\) | ||||
0.652124 | + | 0.758112i | \(0.273878\pi\) | |||||||
\(98\) | 307.000 | 0.316446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1302.00 | −1.28271 | −0.641356 | − | 0.767244i | \(-0.721628\pi\) | ||||
−0.641356 | + | 0.767244i | \(0.721628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 532.000 | 0.508927 | 0.254464 | − | 0.967082i | \(-0.418101\pi\) | ||||
0.254464 | + | 0.967082i | \(0.418101\pi\) | |||||||
\(104\) | −420.000 | −0.396004 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 82.0000 | 0.0751372 | ||||||||
\(107\) | 1269.00 | 1.14653 | 0.573266 | − | 0.819370i | \(-0.305676\pi\) | ||||
0.573266 | + | 0.819370i | \(0.305676\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1070.00 | 0.940251 | 0.470126 | − | 0.882599i | \(-0.344209\pi\) | ||||
0.470126 | + | 0.882599i | \(0.344209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 246.000 | 0.207543 | ||||||||
\(113\) | 503.000 | 0.418746 | 0.209373 | − | 0.977836i | \(-0.432858\pi\) | ||||
0.209373 | + | 0.977836i | \(0.432858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1120.00 | 0.896460 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −280.000 | −0.218441 | ||||||||
\(119\) | −546.000 | −0.420603 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 518.000 | 0.389181 | ||||||||
\(122\) | 518.000 | 0.384406 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −294.000 | −0.212919 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −874.000 | −0.610669 | −0.305334 | − | 0.952245i | \(-0.598768\pi\) | ||||
−0.305334 | + | 0.952245i | \(0.598768\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1092.00 | −0.728309 | −0.364155 | − | 0.931339i | \(-0.618642\pi\) | ||||
−0.364155 | + | 0.931339i | \(0.618642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −210.000 | −0.136912 | ||||||||
\(134\) | −141.000 | −0.0908996 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1365.00 | −0.860645 | ||||||||
\(137\) | −411.000 | −0.256307 | −0.128154 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128154 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −595.000 | −0.363074 | −0.181537 | − | 0.983384i | \(-0.558107\pi\) | ||||
−0.181537 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 412.000 | 0.243481 | ||||||||
\(143\) | −1204.00 | −0.704081 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 763.000 | 0.432509 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2198.00 | 1.22077 | ||||||||
\(149\) | 3200.00 | 1.75942 | 0.879712 | − | 0.475507i | \(-0.157735\pi\) | ||||
0.879712 | + | 0.475507i | \(0.157735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 202.000 | 0.108864 | 0.0544322 | − | 0.998517i | \(-0.482665\pi\) | ||||
0.0544322 | + | 0.998517i | \(0.482665\pi\) | |||||||
\(152\) | −525.000 | −0.280152 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −258.000 | −0.135002 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 406.000 | 0.206384 | 0.103192 | − | 0.994661i | \(-0.467094\pi\) | ||||
0.103192 | + | 0.994661i | \(0.467094\pi\) | |||||||
\(158\) | −510.000 | −0.256794 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −972.000 | −0.475803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3803.00 | −1.82745 | −0.913724 | − | 0.406336i | \(-0.866806\pi\) | ||||
−0.913724 | + | 0.406336i | \(0.866806\pi\) | |||||||
\(164\) | −1421.00 | −0.676594 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 777.000 | 0.363295 | ||||||||
\(167\) | −4116.00 | −1.90722 | −0.953610 | − | 0.301046i | \(-0.902664\pi\) | ||||
−0.953610 | + | 0.301046i | \(0.902664\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −644.000 | −0.285492 | ||||||||
\(173\) | −1512.00 | −0.664481 | −0.332241 | − | 0.943195i | \(-0.607805\pi\) | ||||
−0.332241 | + | 0.943195i | \(0.607805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1763.00 | 0.755063 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −945.000 | −0.397926 | ||||||||
\(179\) | −2585.00 | −1.07940 | −0.539698 | − | 0.841859i | \(-0.681462\pi\) | ||||
−0.539698 | + | 0.841859i | \(0.681462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2758.00 | −1.13260 | −0.566300 | − | 0.824199i | \(-0.691626\pi\) | ||||
−0.566300 | + | 0.824199i | \(0.691626\pi\) | |||||||
\(182\) | 168.000 | 0.0684230 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2430.00 | −0.973598 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3913.00 | −1.53020 | ||||||||
\(188\) | 1372.00 | 0.532252 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2378.00 | 0.900869 | 0.450435 | − | 0.892809i | \(-0.351269\pi\) | ||||
0.450435 | + | 0.892809i | \(0.351269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3067.00 | 1.14387 | 0.571937 | − | 0.820298i | \(-0.306192\pi\) | ||||
0.571937 | + | 0.820298i | \(0.306192\pi\) | |||||||
\(194\) | −1246.00 | −0.461122 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2149.00 | 0.783163 | ||||||||
\(197\) | −2346.00 | −0.848455 | −0.424227 | − | 0.905556i | \(-0.639454\pi\) | ||||
−0.424227 | + | 0.905556i | \(0.639454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4900.00 | 1.74549 | 0.872743 | − | 0.488180i | \(-0.162339\pi\) | ||||
0.872743 | + | 0.488180i | \(0.162339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1302.00 | 0.453507 | ||||||||
\(203\) | −960.000 | −0.331915 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −532.000 | −0.179933 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1148.00 | −0.382690 | ||||||||
\(209\) | −1505.00 | −0.498101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4307.00 | 1.40524 | 0.702621 | − | 0.711564i | \(-0.252013\pi\) | ||||
0.702621 | + | 0.711564i | \(0.252013\pi\) | |||||||
\(212\) | 574.000 | 0.185955 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1269.00 | −0.405360 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 252.000 | 0.0788335 | ||||||||
\(218\) | −1070.00 | −0.332429 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2548.00 | 0.775552 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2212.00 | 0.664244 | 0.332122 | − | 0.943236i | \(-0.392235\pi\) | ||||
0.332122 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(224\) | −966.000 | −0.288141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −503.000 | −0.148049 | ||||||||
\(227\) | −476.000 | −0.139177 | −0.0695886 | − | 0.997576i | \(-0.522169\pi\) | ||||
−0.0695886 | + | 0.997576i | \(0.522169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2940.00 | −0.848387 | −0.424194 | − | 0.905572i | \(-0.639442\pi\) | ||||
−0.424194 | + | 0.905572i | \(0.639442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2400.00 | −0.679171 | ||||||||
\(233\) | −1002.00 | −0.281730 | −0.140865 | − | 0.990029i | \(-0.544988\pi\) | ||||
−0.140865 | + | 0.990029i | \(0.544988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1960.00 | −0.540615 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 546.000 | 0.148706 | ||||||||
\(239\) | −2480.00 | −0.671204 | −0.335602 | − | 0.942004i | \(-0.608940\pi\) | ||||
−0.335602 | + | 0.942004i | \(0.608940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1897.00 | 0.507039 | 0.253520 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253520 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(242\) | −518.000 | −0.137596 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3626.00 | 0.951356 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 980.000 | 0.252453 | ||||||||
\(248\) | 630.000 | 0.161311 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2373.00 | 0.596743 | 0.298371 | − | 0.954450i | \(-0.403557\pi\) | ||||
0.298371 | + | 0.954450i | \(0.403557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6966.00 | −1.73102 | ||||||||
\(254\) | 874.000 | 0.215904 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 4494.00 | 1.09077 | 0.545385 | − | 0.838185i | \(-0.316383\pi\) | ||||
0.545385 | + | 0.838185i | \(0.316383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1884.00 | −0.451993 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1092.00 | 0.257496 | ||||||||
\(263\) | −722.000 | −0.169279 | −0.0846396 | − | 0.996412i | \(-0.526974\pi\) | ||||
−0.0846396 | + | 0.996412i | \(0.526974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 210.000 | 0.0484057 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −987.000 | −0.224965 | ||||||||
\(269\) | 6160.00 | 1.39621 | 0.698107 | − | 0.715993i | \(-0.254026\pi\) | ||||
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7238.00 | −1.62243 | −0.811213 | − | 0.584751i | \(-0.801192\pi\) | ||||
−0.811213 | + | 0.584751i | \(0.801192\pi\) | |||||||
\(272\) | −3731.00 | −0.831710 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 411.000 | 0.0906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1776.00 | 0.385233 | 0.192616 | − | 0.981274i | \(-0.438303\pi\) | ||||
0.192616 | + | 0.981274i | \(0.438303\pi\) | |||||||
\(278\) | 595.000 | 0.128366 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4542.00 | −0.964246 | −0.482123 | − | 0.876104i | \(-0.660134\pi\) | ||||
−0.482123 | + | 0.876104i | \(0.660134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7077.00 | 1.48652 | 0.743258 | − | 0.669005i | \(-0.233280\pi\) | ||||
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(284\) | 2884.00 | 0.602584 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1204.00 | 0.248930 | ||||||||
\(287\) | 1218.00 | 0.250510 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3368.00 | 0.685528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5341.00 | 1.07041 | ||||||||
\(293\) | 4158.00 | 0.829054 | 0.414527 | − | 0.910037i | \(-0.363947\pi\) | ||||
0.414527 | + | 0.910037i | \(0.363947\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4710.00 | −0.924876 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3200.00 | −0.622050 | ||||||||
\(299\) | 4536.00 | 0.877337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 552.000 | 0.105703 | ||||||||
\(302\) | −202.000 | −0.0384894 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1435.00 | −0.270733 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2569.00 | −0.477591 | −0.238796 | − | 0.971070i | \(-0.576753\pi\) | ||||
−0.238796 | + | 0.971070i | \(0.576753\pi\) | |||||||
\(308\) | −1806.00 | −0.334112 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2982.00 | −0.543710 | −0.271855 | − | 0.962338i | \(-0.587637\pi\) | ||||
−0.271855 | + | 0.962338i | \(0.587637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2422.00 | 0.437379 | 0.218689 | − | 0.975795i | \(-0.429822\pi\) | ||||
0.218689 | + | 0.975795i | \(0.429822\pi\) | |||||||
\(314\) | −406.000 | −0.0729679 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3570.00 | −0.635532 | ||||||||
\(317\) | 9484.00 | 1.68036 | 0.840181 | − | 0.542307i | \(-0.182449\pi\) | ||||
0.840181 | + | 0.542307i | \(0.182449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6880.00 | −1.20754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 972.000 | 0.168222 | ||||||||
\(323\) | 3185.00 | 0.548663 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3803.00 | 0.646100 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3045.00 | 0.512598 | ||||||||
\(329\) | −1176.00 | −0.197067 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −183.000 | −0.0303885 | −0.0151942 | − | 0.999885i | \(-0.504837\pi\) | ||||
−0.0151942 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(332\) | 5439.00 | 0.899108 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4116.00 | 0.674304 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2861.00 | 0.462459 | 0.231229 | − | 0.972899i | \(-0.425725\pi\) | ||||
0.231229 | + | 0.972899i | \(0.425725\pi\) | |||||||
\(338\) | 1413.00 | 0.227388 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1806.00 | 0.286805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3900.00 | −0.613936 | ||||||||
\(344\) | 1380.00 | 0.216292 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1512.00 | 0.234930 | ||||||||
\(347\) | 629.000 | 0.0973098 | 0.0486549 | − | 0.998816i | \(-0.484507\pi\) | ||||
0.0486549 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5950.00 | 0.912597 | 0.456298 | − | 0.889827i | \(-0.349175\pi\) | ||||
0.456298 | + | 0.889827i | \(0.349175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6923.00 | −1.04829 | ||||||||
\(353\) | 11718.0 | 1.76682 | 0.883408 | − | 0.468604i | \(-0.155243\pi\) | ||||
0.883408 | + | 0.468604i | \(0.155243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6615.00 | −0.984815 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2585.00 | 0.381624 | ||||||||
\(359\) | −8070.00 | −1.18640 | −0.593201 | − | 0.805054i | \(-0.702136\pi\) | ||||
−0.593201 | + | 0.805054i | \(0.702136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5634.00 | −0.821403 | ||||||||
\(362\) | 2758.00 | 0.400434 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1176.00 | 0.169338 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8316.00 | 1.18281 | 0.591406 | − | 0.806374i | \(-0.298573\pi\) | ||||
0.591406 | + | 0.806374i | \(0.298573\pi\) | |||||||
\(368\) | −6642.00 | −0.940865 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −492.000 | −0.0688500 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12062.0 | 1.67439 | 0.837194 | − | 0.546906i | \(-0.184195\pi\) | ||||
0.837194 | + | 0.546906i | \(0.184195\pi\) | |||||||
\(374\) | 3913.00 | 0.541006 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2940.00 | −0.403242 | ||||||||
\(377\) | 4480.00 | 0.612021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1735.00 | 0.235148 | 0.117574 | − | 0.993064i | \(-0.462488\pi\) | ||||
0.117574 | + | 0.993064i | \(0.462488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2378.00 | −0.318505 | ||||||||
\(383\) | −7602.00 | −1.01421 | −0.507107 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507107 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3067.00 | −0.404420 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8722.00 | −1.14122 | ||||||||
\(389\) | −3030.00 | −0.394928 | −0.197464 | − | 0.980310i | \(-0.563271\pi\) | ||||
−0.197464 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14742.0 | 1.90674 | ||||||||
\(392\) | −4605.00 | −0.593336 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2346.00 | 0.299974 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1204.00 | −0.152209 | −0.0761046 | − | 0.997100i | \(-0.524248\pi\) | ||||
−0.0761046 | + | 0.997100i | \(0.524248\pi\) | |||||||
\(398\) | −4900.00 | −0.617123 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1077.00 | −0.134122 | −0.0670609 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670609 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1176.00 | −0.145362 | ||||||||
\(404\) | 9114.00 | 1.12237 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 960.000 | 0.117350 | ||||||||
\(407\) | −13502.0 | −1.64440 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3955.00 | −0.478147 | −0.239074 | − | 0.971001i | \(-0.576844\pi\) | ||||
−0.239074 | + | 0.971001i | \(0.576844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3724.00 | −0.445311 | ||||||||
\(413\) | 1680.00 | 0.200163 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4508.00 | 0.531305 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1505.00 | 0.176105 | ||||||||
\(419\) | −6265.00 | −0.730466 | −0.365233 | − | 0.930916i | \(-0.619011\pi\) | ||||
−0.365233 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3788.00 | −0.438517 | −0.219259 | − | 0.975667i | \(-0.570364\pi\) | ||||
−0.219259 | + | 0.975667i | \(0.570364\pi\) | |||||||
\(422\) | −4307.00 | −0.496828 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1230.00 | −0.140882 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3108.00 | −0.352240 | ||||||||
\(428\) | −8883.00 | −1.00321 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15258.0 | 1.70523 | 0.852613 | − | 0.522544i | \(-0.175017\pi\) | ||||
0.852613 | + | 0.522544i | \(0.175017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13573.0 | −1.50641 | −0.753206 | − | 0.657784i | \(-0.771494\pi\) | ||||
−0.753206 | + | 0.657784i | \(0.771494\pi\) | |||||||
\(434\) | −252.000 | −0.0278719 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7490.00 | −0.822720 | ||||||||
\(437\) | 5670.00 | 0.620670 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8120.00 | −0.882794 | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2548.00 | −0.274199 | ||||||||
\(443\) | 6183.00 | 0.663122 | 0.331561 | − | 0.943434i | \(-0.392425\pi\) | ||||
0.331561 | + | 0.943434i | \(0.392425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2212.00 | −0.234846 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1002.00 | −0.105670 | ||||||||
\(449\) | 1975.00 | 0.207586 | 0.103793 | − | 0.994599i | \(-0.466902\pi\) | ||||
0.103793 | + | 0.994599i | \(0.466902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8729.00 | 0.911380 | ||||||||
\(452\) | −3521.00 | −0.366402 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 476.000 | 0.0492066 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11831.0 | 1.21101 | 0.605504 | − | 0.795842i | \(-0.292971\pi\) | ||||
0.605504 | + | 0.795842i | \(0.292971\pi\) | |||||||
\(458\) | 2940.00 | 0.299950 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1932.00 | −0.195189 | −0.0975946 | − | 0.995226i | \(-0.531115\pi\) | ||||
−0.0975946 | + | 0.995226i | \(0.531115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9228.00 | −0.926267 | −0.463133 | − | 0.886289i | \(-0.653275\pi\) | ||||
−0.463133 | + | 0.886289i | \(0.653275\pi\) | |||||||
\(464\) | −6560.00 | −0.656337 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1002.00 | 0.0996068 | ||||||||
\(467\) | −13916.0 | −1.37892 | −0.689460 | − | 0.724324i | \(-0.742152\pi\) | ||||
−0.689460 | + | 0.724324i | \(0.742152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 846.000 | 0.0832935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4200.00 | 0.409578 | ||||||||
\(473\) | 3956.00 | 0.384560 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3822.00 | 0.368027 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2480.00 | 0.237307 | ||||||||
\(479\) | −2310.00 | −0.220348 | −0.110174 | − | 0.993912i | \(-0.535141\pi\) | ||||
−0.110174 | + | 0.993912i | \(0.535141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8792.00 | 0.833432 | ||||||||
\(482\) | −1897.00 | −0.179266 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3626.00 | −0.340533 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17114.0 | −1.59242 | −0.796211 | − | 0.605019i | \(-0.793165\pi\) | ||||
−0.796211 | + | 0.605019i | \(0.793165\pi\) | |||||||
\(488\) | −7770.00 | −0.720761 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17228.0 | 1.58348 | 0.791740 | − | 0.610858i | \(-0.209175\pi\) | ||||
0.791740 | + | 0.610858i | \(0.209175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14560.0 | 1.33012 | ||||||||
\(494\) | −980.000 | −0.0892556 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1722.00 | 0.155887 | ||||||||
\(497\) | −2472.00 | −0.223107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12500.0 | −1.12140 | −0.560698 | − | 0.828020i | \(-0.689467\pi\) | ||||
−0.560698 | + | 0.828020i | \(0.689467\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2373.00 | −0.210980 | ||||||||
\(503\) | 868.000 | 0.0769428 | 0.0384714 | − | 0.999260i | \(-0.487751\pi\) | ||||
0.0384714 | + | 0.999260i | \(0.487751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6966.00 | 0.612009 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6118.00 | 0.534335 | ||||||||
\(509\) | −13370.0 | −1.16427 | −0.582136 | − | 0.813091i | \(-0.697783\pi\) | ||||
−0.582136 | + | 0.813091i | \(0.697783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4578.00 | −0.396319 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4494.00 | −0.385646 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8428.00 | −0.716950 | ||||||||
\(518\) | 1884.00 | 0.159803 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21637.0 | −1.81945 | −0.909726 | − | 0.415210i | \(-0.863708\pi\) | ||||
−0.909726 | + | 0.415210i | \(0.863708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 287.000 | 0.0239955 | 0.0119977 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119977 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(524\) | 7644.00 | 0.637270 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 722.000 | 0.0598492 | ||||||||
\(527\) | −3822.00 | −0.315918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1470.00 | 0.119798 | ||||||||
\(533\) | −5684.00 | −0.461916 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2115.00 | 0.170437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6160.00 | −0.493637 | ||||||||
\(539\) | −13201.0 | −1.05493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5328.00 | −0.423417 | −0.211709 | − | 0.977333i | \(-0.567903\pi\) | ||||
−0.211709 | + | 0.977333i | \(0.567903\pi\) | |||||||
\(542\) | 7238.00 | 0.573614 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14651.0 | 1.15470 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 71.0000 | 0.00554980 | 0.00277490 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277490 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(548\) | 2877.00 | 0.224269 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5600.00 | 0.432973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3060.00 | 0.235306 | ||||||||
\(554\) | −1776.00 | −0.136200 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4165.00 | 0.317689 | ||||||||
\(557\) | 18444.0 | 1.40305 | 0.701524 | − | 0.712646i | \(-0.252503\pi\) | ||||
0.701524 | + | 0.712646i | \(0.252503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2576.00 | −0.194907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4542.00 | 0.340912 | ||||||||
\(563\) | −672.000 | −0.0503045 | −0.0251522 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251522 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7077.00 | −0.525563 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6180.00 | −0.456526 | ||||||||
\(569\) | 10935.0 | 0.805657 | 0.402829 | − | 0.915275i | \(-0.368027\pi\) | ||||
0.402829 | + | 0.915275i | \(0.368027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13588.0 | −0.995867 | −0.497934 | − | 0.867215i | \(-0.665908\pi\) | ||||
−0.497934 | + | 0.867215i | \(0.665908\pi\) | |||||||
\(572\) | 8428.00 | 0.616071 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1218.00 | −0.0885685 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8701.00 | 0.627777 | 0.313889 | − | 0.949460i | \(-0.398368\pi\) | ||||
0.313889 | + | 0.949460i | \(0.398368\pi\) | |||||||
\(578\) | −3368.00 | −0.242371 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4662.00 | −0.332896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3526.00 | −0.250484 | ||||||||
\(584\) | −11445.0 | −0.810955 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4158.00 | −0.293115 | ||||||||
\(587\) | −11361.0 | −0.798839 | −0.399420 | − | 0.916768i | \(-0.630788\pi\) | ||||
−0.399420 | + | 0.916768i | \(0.630788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1470.00 | −0.102836 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12874.0 | −0.893781 | ||||||||
\(593\) | −11417.0 | −0.790624 | −0.395312 | − | 0.918547i | \(-0.629364\pi\) | ||||
−0.395312 | + | 0.918547i | \(0.629364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22400.0 | −1.53950 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4536.00 | −0.310185 | ||||||||
\(599\) | 21050.0 | 1.43586 | 0.717930 | − | 0.696116i | \(-0.245090\pi\) | ||||
0.717930 | + | 0.696116i | \(0.245090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7427.00 | 0.504083 | 0.252041 | − | 0.967716i | \(-0.418898\pi\) | ||||
0.252041 | + | 0.967716i | \(0.418898\pi\) | |||||||
\(602\) | −552.000 | −0.0373718 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1414.00 | −0.0952564 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4144.00 | −0.277100 | −0.138550 | − | 0.990355i | \(-0.544244\pi\) | ||||
−0.138550 | + | 0.990355i | \(0.544244\pi\) | |||||||
\(608\) | 5635.00 | 0.375871 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5488.00 | 0.363373 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30122.0 | 1.98469 | 0.992346 | − | 0.123489i | \(-0.0394084\pi\) | ||||
0.992346 | + | 0.123489i | \(0.0394084\pi\) | |||||||
\(614\) | 2569.00 | 0.168854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3870.00 | 0.253128 | ||||||||
\(617\) | 11934.0 | 0.778679 | 0.389339 | − | 0.921094i | \(-0.372703\pi\) | ||||
0.389339 | + | 0.921094i | \(0.372703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8540.00 | 0.554526 | 0.277263 | − | 0.960794i | \(-0.410573\pi\) | ||||
0.277263 | + | 0.960794i | \(0.410573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2982.00 | 0.192230 | ||||||||
\(623\) | 5670.00 | 0.364629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2422.00 | −0.154637 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2842.00 | −0.180586 | ||||||||
\(629\) | 28574.0 | 1.81132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3158.00 | −0.199236 | −0.0996181 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996181 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(632\) | 7650.00 | 0.481488 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9484.00 | −0.594097 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8596.00 | 0.534672 | ||||||||
\(638\) | 6880.00 | 0.426931 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4278.00 | 0.263605 | 0.131803 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131803 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11508.0 | −0.705803 | −0.352901 | − | 0.935661i | \(-0.614805\pi\) | ||||
−0.352901 | + | 0.935661i | \(0.614805\pi\) | |||||||
\(644\) | 6804.00 | 0.416328 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3185.00 | −0.193982 | ||||||||
\(647\) | 8204.00 | 0.498505 | 0.249252 | − | 0.968439i | \(-0.419815\pi\) | ||||
0.249252 | + | 0.968439i | \(0.419815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12040.0 | 0.728215 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26621.0 | 1.59902 | ||||||||
\(653\) | 5518.00 | 0.330683 | 0.165342 | − | 0.986236i | \(-0.447127\pi\) | ||||
0.165342 | + | 0.986236i | \(0.447127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8323.00 | 0.495364 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1176.00 | 0.0696736 | ||||||||
\(659\) | −13295.0 | −0.785887 | −0.392944 | − | 0.919563i | \(-0.628543\pi\) | ||||
−0.392944 | + | 0.919563i | \(0.628543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9968.00 | −0.586551 | −0.293276 | − | 0.956028i | \(-0.594745\pi\) | ||||
−0.293276 | + | 0.956028i | \(0.594745\pi\) | |||||||
\(662\) | 183.000 | 0.0107440 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11655.0 | −0.681177 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25920.0 | 1.50469 | ||||||||
\(668\) | 28812.0 | 1.66882 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22274.0 | −1.28149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15738.0 | −0.901419 | −0.450710 | − | 0.892671i | \(-0.648829\pi\) | ||||
−0.450710 | + | 0.892671i | \(0.648829\pi\) | |||||||
\(674\) | −2861.00 | −0.163504 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9891.00 | 0.562756 | ||||||||
\(677\) | 19824.0 | 1.12540 | 0.562702 | − | 0.826660i | \(-0.309762\pi\) | ||||
0.562702 | + | 0.826660i | \(0.309762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7476.00 | 0.422537 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1806.00 | −0.101401 | ||||||||
\(683\) | 11073.0 | 0.620346 | 0.310173 | − | 0.950680i | \(-0.399613\pi\) | ||||
0.310173 | + | 0.950680i | \(0.399613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3900.00 | 0.217059 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3772.00 | 0.209021 | ||||||||
\(689\) | 2296.00 | 0.126953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6503.00 | −0.358011 | −0.179006 | − | 0.983848i | \(-0.557288\pi\) | ||||
−0.179006 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(692\) | 10584.0 | 0.581421 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −629.000 | −0.0344042 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18473.0 | −1.00389 | ||||||||
\(698\) | −5950.00 | −0.322652 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10148.0 | 0.546768 | 0.273384 | − | 0.961905i | \(-0.411857\pi\) | ||||
0.273384 | + | 0.961905i | \(0.411857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10990.0 | 0.589610 | ||||||||
\(704\) | −7181.00 | −0.384438 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11718.0 | −0.624664 | ||||||||
\(707\) | −7812.00 | −0.415559 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9980.00 | −0.528641 | −0.264321 | − | 0.964435i | \(-0.585148\pi\) | ||||
−0.264321 | + | 0.964435i | \(0.585148\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14175.0 | 0.746110 | ||||||||
\(713\) | −6804.00 | −0.357380 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18095.0 | 0.944472 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8070.00 | 0.419456 | ||||||||
\(719\) | 27510.0 | 1.42691 | 0.713456 | − | 0.700700i | \(-0.247129\pi\) | ||||
0.713456 | + | 0.700700i | \(0.247129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3192.00 | 0.164877 | ||||||||
\(722\) | 5634.00 | 0.290410 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19306.0 | 0.991025 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17024.0 | −0.868480 | −0.434240 | − | 0.900797i | \(-0.642983\pi\) | ||||
−0.434240 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(728\) | −2520.00 | −0.128293 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8372.00 | −0.423597 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34748.0 | −1.75095 | −0.875475 | − | 0.483263i | \(-0.839451\pi\) | ||||
−0.875475 | + | 0.483263i | \(0.839451\pi\) | |||||||
\(734\) | −8316.00 | −0.418187 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26082.0 | 1.30624 | ||||||||
\(737\) | 6063.00 | 0.303030 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12020.0 | −0.598326 | −0.299163 | − | 0.954202i | \(-0.596707\pi\) | ||||
−0.299163 | + | 0.954202i | \(0.596707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 492.000 | 0.0243422 | ||||||||
\(743\) | −28642.0 | −1.41423 | −0.707115 | − | 0.707098i | \(-0.750004\pi\) | ||||
−0.707115 | + | 0.707098i | \(0.750004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12062.0 | −0.591986 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27391.0 | 1.33892 | ||||||||
\(749\) | 7614.00 | 0.371441 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8752.00 | 0.425253 | 0.212627 | − | 0.977134i | \(-0.431798\pi\) | ||||
0.212627 | + | 0.977134i | \(0.431798\pi\) | |||||||
\(752\) | −8036.00 | −0.389685 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4480.00 | −0.216382 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10256.0 | 0.492418 | 0.246209 | − | 0.969217i | \(-0.420815\pi\) | ||||
0.246209 | + | 0.969217i | \(0.420815\pi\) | |||||||
\(758\) | −1735.00 | −0.0831373 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33957.0 | −1.61753 | −0.808765 | − | 0.588132i | \(-0.799864\pi\) | ||||
−0.808765 | + | 0.588132i | \(0.799864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6420.00 | 0.304613 | ||||||||
\(764\) | −16646.0 | −0.788261 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7602.00 | 0.358579 | ||||||||
\(767\) | −7840.00 | −0.369082 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27965.0 | 1.31137 | 0.655685 | − | 0.755034i | \(-0.272380\pi\) | ||||
0.655685 | + | 0.755034i | \(0.272380\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21469.0 | −1.00089 | ||||||||
\(773\) | −9912.00 | −0.461203 | −0.230601 | − | 0.973048i | \(-0.574069\pi\) | ||||
−0.230601 | + | 0.973048i | \(0.574069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18690.0 | 0.864603 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3030.00 | 0.139628 | ||||||||
\(779\) | −7105.00 | −0.326782 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17716.0 | −0.811688 | ||||||||
\(782\) | −14742.0 | −0.674134 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12587.0 | −0.573387 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25564.0 | −1.15789 | −0.578944 | − | 0.815367i | \(-0.696535\pi\) | ||||
−0.578944 | + | 0.815367i | \(0.696535\pi\) | |||||||
\(788\) | 16422.0 | 0.742398 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3018.00 | 0.135661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14504.0 | 0.649498 | ||||||||
\(794\) | 1204.00 | 0.0538141 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34300.0 | −1.52730 | ||||||||
\(797\) | −12446.0 | −0.553149 | −0.276575 | − | 0.960992i | \(-0.589199\pi\) | ||||
−0.276575 | + | 0.960992i | \(0.589199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17836.0 | 0.789728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1077.00 | 0.0474192 | ||||||||
\(803\) | −32809.0 | −1.44185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1176.00 | 0.0513931 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19530.0 | −0.850325 | ||||||||
\(809\) | −33970.0 | −1.47629 | −0.738147 | − | 0.674640i | \(-0.764299\pi\) | ||||
−0.738147 | + | 0.674640i | \(0.764299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18732.0 | 0.811060 | 0.405530 | − | 0.914082i | \(-0.367087\pi\) | ||||
0.405530 | + | 0.914082i | \(0.367087\pi\) | |||||||
\(812\) | 6720.00 | 0.290426 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13502.0 | 0.581382 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3220.00 | −0.137887 | ||||||||
\(818\) | 3955.00 | 0.169051 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6162.00 | −0.261943 | −0.130972 | − | 0.991386i | \(-0.541810\pi\) | ||||
−0.130972 | + | 0.991386i | \(0.541810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25388.0 | −1.07530 | −0.537649 | − | 0.843169i | \(-0.680687\pi\) | ||||
−0.537649 | + | 0.843169i | \(0.680687\pi\) | |||||||
\(824\) | 7980.00 | 0.337374 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1680.00 | −0.0707684 | ||||||||
\(827\) | −25201.0 | −1.05964 | −0.529821 | − | 0.848109i | \(-0.677741\pi\) | ||||
−0.529821 | + | 0.848109i | \(0.677741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19740.0 | −0.827019 | −0.413509 | − | 0.910500i | \(-0.635697\pi\) | ||||
−0.413509 | + | 0.910500i | \(0.635697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4676.00 | 0.194845 | ||||||||
\(833\) | 27937.0 | 1.16202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10535.0 | 0.435838 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6265.00 | 0.258259 | ||||||||
\(839\) | −29680.0 | −1.22130 | −0.610648 | − | 0.791902i | \(-0.709091\pi\) | ||||
−0.610648 | + | 0.791902i | \(0.709091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1211.00 | 0.0496535 | ||||||||
\(842\) | 3788.00 | 0.155039 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30149.0 | −1.22959 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3108.00 | 0.126083 | ||||||||
\(848\) | −3362.00 | −0.136146 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50868.0 | 2.04904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1218.00 | −0.0488904 | −0.0244452 | − | 0.999701i | \(-0.507782\pi\) | ||||
−0.0244452 | + | 0.999701i | \(0.507782\pi\) | |||||||
\(854\) | 3108.00 | 0.124536 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19035.0 | 0.760050 | ||||||||
\(857\) | −38731.0 | −1.54379 | −0.771894 | − | 0.635752i | \(-0.780690\pi\) | ||||
−0.771894 | + | 0.635752i | \(0.780690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23555.0 | −0.935607 | −0.467803 | − | 0.883833i | \(-0.654954\pi\) | ||||
−0.467803 | + | 0.883833i | \(0.654954\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15258.0 | −0.602888 | ||||||||
\(863\) | −24872.0 | −0.981058 | −0.490529 | − | 0.871425i | \(-0.663196\pi\) | ||||
−0.490529 | + | 0.871425i | \(0.663196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13573.0 | 0.532597 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1764.00 | −0.0689793 | ||||||||
\(869\) | 21930.0 | 0.856069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3948.00 | −0.153585 | ||||||||
\(872\) | 16050.0 | 0.623305 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5670.00 | −0.219440 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17124.0 | −0.659335 | −0.329667 | − | 0.944097i | \(-0.606937\pi\) | ||||
−0.329667 | + | 0.944097i | \(0.606937\pi\) | |||||||
\(878\) | 8120.00 | 0.312115 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 658.000 | 0.0251630 | 0.0125815 | − | 0.999921i | \(-0.495995\pi\) | ||||
0.0125815 | + | 0.999921i | \(0.495995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33727.0 | 1.28540 | 0.642698 | − | 0.766120i | \(-0.277815\pi\) | ||||
0.642698 | + | 0.766120i | \(0.277815\pi\) | |||||||
\(884\) | −17836.0 | −0.678608 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6183.00 | −0.234449 | ||||||||
\(887\) | −36036.0 | −1.36412 | −0.682058 | − | 0.731298i | \(-0.738915\pi\) | ||||
−0.682058 | + | 0.731298i | \(0.738915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5244.00 | −0.197838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15484.0 | −0.581214 | ||||||||
\(893\) | 6860.00 | 0.257067 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8730.00 | 0.325501 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1975.00 | −0.0733927 | ||||||||
\(899\) | −6720.00 | −0.249304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7462.00 | 0.275910 | ||||||||
\(902\) | −8729.00 | −0.322222 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7545.00 | 0.277592 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39156.0 | 1.43347 | 0.716733 | − | 0.697348i | \(-0.245637\pi\) | ||||
0.716733 | + | 0.697348i | \(0.245637\pi\) | |||||||
\(908\) | 3332.00 | 0.121780 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43532.0 | −1.58318 | −0.791591 | − | 0.611051i | \(-0.790747\pi\) | ||||
−0.791591 | + | 0.611051i | \(0.790747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33411.0 | −1.21111 | ||||||||
\(914\) | −11831.0 | −0.428156 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20580.0 | 0.742339 | ||||||||
\(917\) | −6552.00 | −0.235950 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28610.0 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1932.00 | 0.0690098 | ||||||||
\(923\) | 11536.0 | 0.411389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9228.00 | 0.327485 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25760.0 | 0.911221 | ||||||||
\(929\) | 24290.0 | 0.857835 | 0.428918 | − | 0.903344i | \(-0.358895\pi\) | ||||
0.428918 | + | 0.903344i | \(0.358895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10745.0 | 0.378253 | ||||||||
\(932\) | 7014.00 | 0.246514 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13916.0 | 0.487522 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34461.0 | 1.20149 | 0.600743 | − | 0.799442i | \(-0.294872\pi\) | ||||
0.600743 | + | 0.799442i | \(0.294872\pi\) | |||||||
\(938\) | −846.000 | −0.0294487 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40628.0 | 1.40748 | 0.703738 | − | 0.710460i | \(-0.251513\pi\) | ||||
0.703738 | + | 0.710460i | \(0.251513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32886.0 | −1.13565 | ||||||||
\(944\) | 11480.0 | 0.395807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3956.00 | −0.135963 | ||||||||
\(947\) | 20904.0 | 0.717306 | 0.358653 | − | 0.933471i | \(-0.383236\pi\) | ||||
0.358653 | + | 0.933471i | \(0.383236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21364.0 | 0.730774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8190.00 | −0.278823 | ||||||||
\(953\) | −1807.00 | −0.0614213 | −0.0307106 | − | 0.999528i | \(-0.509777\pi\) | ||||
−0.0307106 | + | 0.999528i | \(0.509777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17360.0 | 0.587304 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2310.00 | 0.0779047 | ||||||||
\(959\) | −2466.00 | −0.0830358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28027.0 | −0.940787 | ||||||||
\(962\) | −8792.00 | −0.294663 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13279.0 | −0.443660 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57584.0 | −1.91497 | −0.957485 | − | 0.288482i | \(-0.906849\pi\) | ||||
−0.957485 | + | 0.288482i | \(0.906849\pi\) | |||||||
\(968\) | 7770.00 | 0.257993 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27237.0 | −0.900182 | −0.450091 | − | 0.892983i | \(-0.648608\pi\) | ||||
−0.450091 | + | 0.892983i | \(0.648608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3570.00 | −0.117625 | ||||||||
\(974\) | 17114.0 | 0.563006 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21238.0 | −0.696528 | ||||||||
\(977\) | 13649.0 | 0.446950 | 0.223475 | − | 0.974710i | \(-0.428260\pi\) | ||||
0.223475 | + | 0.974710i | \(0.428260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40635.0 | 1.32656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17228.0 | −0.559845 | ||||||||
\(983\) | −16002.0 | −0.519211 | −0.259606 | − | 0.965715i | \(-0.583593\pi\) | ||||
−0.259606 | + | 0.965715i | \(0.583593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −14560.0 | −0.470269 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6860.00 | −0.220896 | ||||||||
\(989\) | −14904.0 | −0.479191 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37022.0 | 1.18672 | 0.593362 | − | 0.804936i | \(-0.297800\pi\) | ||||
0.593362 | + | 0.804936i | \(0.297800\pi\) | |||||||
\(992\) | −6762.00 | −0.216425 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2472.00 | 0.0788804 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18396.0 | 0.584360 | 0.292180 | − | 0.956363i | \(-0.405619\pi\) | ||||
0.292180 | + | 0.956363i | \(0.405619\pi\) | |||||||
\(998\) | 12500.0 | 0.396474 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 25.4.a.b.1.1 | yes | 1 | ||
5.2 | odd | 4 | 225.4.b.f.199.1 | 2 | |||
5.3 | odd | 4 | 225.4.b.f.199.2 | 2 | |||
5.4 | even | 2 | 225.4.a.e.1.1 | 1 | |||
12.11 | even | 2 | 400.4.a.c.1.1 | 1 | |||
15.2 | even | 4 | 25.4.b.b.24.2 | 2 | |||
15.8 | even | 4 | 25.4.b.b.24.1 | 2 | |||
15.14 | odd | 2 | 25.4.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 1225.4.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 1600.4.a.i.1.1 | 1 | |||
24.11 | even | 2 | 1600.4.a.bs.1.1 | 1 | |||
60.23 | odd | 4 | 400.4.c.e.49.1 | 2 | |||
60.47 | odd | 4 | 400.4.c.e.49.2 | 2 | |||
60.59 | even | 2 | 400.4.a.s.1.1 | 1 | |||
105.104 | even | 2 | 1225.4.a.h.1.1 | 1 | |||
120.29 | odd | 2 | 1600.4.a.bt.1.1 | 1 | |||
120.59 | even | 2 | 1600.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.4.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
25.4.a.b.1.1 | yes | 1 | 3.2 | odd | 2 | ||
25.4.b.b.24.1 | 2 | 15.8 | even | 4 | |||
25.4.b.b.24.2 | 2 | 15.2 | even | 4 | |||
225.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.4.a.e.1.1 | 1 | 5.4 | even | 2 | |||
225.4.b.f.199.1 | 2 | 5.2 | odd | 4 | |||
225.4.b.f.199.2 | 2 | 5.3 | odd | 4 | |||
400.4.a.c.1.1 | 1 | 12.11 | even | 2 | |||
400.4.a.s.1.1 | 1 | 60.59 | even | 2 | |||
400.4.c.e.49.1 | 2 | 60.23 | odd | 4 | |||
400.4.c.e.49.2 | 2 | 60.47 | odd | 4 | |||
1225.4.a.h.1.1 | 1 | 105.104 | even | 2 | |||
1225.4.a.i.1.1 | 1 | 21.20 | even | 2 | |||
1600.4.a.h.1.1 | 1 | 120.59 | even | 2 | |||
1600.4.a.i.1.1 | 1 | 24.5 | odd | 2 | |||
1600.4.a.bs.1.1 | 1 | 24.11 | even | 2 | |||
1600.4.a.bt.1.1 | 1 | 120.29 | odd | 2 |