Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,4,Mod(49,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(35.4011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.49 |
Dual form | 600.4.f.h.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 19.0000i | − 1.02590i | −0.858417 | − | 0.512952i | \(-0.828552\pi\) | ||||
0.858417 | − | 0.512952i | \(-0.171448\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.0000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.0213346i | −0.999943 | − | 0.0106673i | \(-0.996604\pi\) | ||||
0.999943 | − | 0.0106673i | \(-0.00339558\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 58.0000i | − 0.827474i | −0.910396 | − | 0.413737i | \(-0.864223\pi\) | ||||
0.910396 | − | 0.413737i | \(-0.135777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.0000 | 0.639949 | 0.319975 | − | 0.947426i | \(-0.396326\pi\) | ||||
0.319975 | + | 0.947426i | \(0.396326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −57.0000 | −0.592306 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 58.0000i | − 0.525819i | −0.964821 | − | 0.262909i | \(-0.915318\pi\) | ||||
0.964821 | − | 0.262909i | \(-0.0846821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.0000 | −0.140872 | −0.0704362 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704362 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.0000 | −0.202780 | −0.101390 | − | 0.994847i | \(-0.532329\pi\) | ||||
−0.101390 | + | 0.994847i | \(0.532329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 66.0000i | − 0.348155i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 270.000i | − 1.19967i | −0.800124 | − | 0.599834i | \(-0.795233\pi\) | ||||
0.800124 | − | 0.599834i | \(-0.204767\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | −0.0123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −468.000 | −1.78267 | −0.891333 | − | 0.453349i | \(-0.850229\pi\) | ||||
−0.891333 | + | 0.453349i | \(0.850229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 431.000i | 1.52853i | 0.644901 | + | 0.764266i | \(0.276899\pi\) | ||||
−0.644901 | + | 0.764266i | \(0.723101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 230.000i | − 0.713807i | −0.934141 | − | 0.356904i | \(-0.883832\pi\) | ||||
0.934141 | − | 0.356904i | \(-0.116168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.0000 | −0.0524781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −174.000 | −0.477743 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 159.000i | − 0.369475i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −446.000 | −0.984140 | −0.492070 | − | 0.870556i | \(-0.663760\pi\) | ||||
−0.492070 | + | 0.870556i | \(0.663760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 127.000 | 0.266569 | 0.133284 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133284 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 171.000i | 0.341968i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 811.000i | − 1.47880i | −0.673268 | − | 0.739399i | \(-0.735110\pi\) | ||||
0.673268 | − | 0.739399i | \(-0.264890\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −174.000 | −0.303582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.0000 | 0.0601748 | 0.0300874 | − | 0.999547i | \(-0.490421\pi\) | ||||
0.0300874 | + | 0.999547i | \(0.490421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 522.000i | − 0.836924i | −0.908234 | − | 0.418462i | \(-0.862569\pi\) | ||||
0.908234 | − | 0.418462i | \(-0.137431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 418.000i | − 0.618643i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1368.00 | −1.94825 | −0.974127 | − | 0.226002i | \(-0.927434\pi\) | ||||
−0.974127 | + | 0.226002i | \(0.927434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1138.00i | 1.50496i | 0.658615 | + | 0.752480i | \(0.271143\pi\) | ||||
−0.658615 | + | 0.752480i | \(0.728857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 66.0000i | 0.0813327i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −144.000 | −0.171505 | −0.0857526 | − | 0.996316i | \(-0.527329\pi\) | ||||
−0.0857526 | + | 0.996316i | \(0.527329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.0000 | −0.0218873 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 105.000i | 0.117075i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1079.00i | − 1.12944i | −0.825282 | − | 0.564721i | \(-0.808984\pi\) | ||||
0.825282 | − | 0.564721i | \(-0.191016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −198.000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1440.00 | −1.41867 | −0.709333 | − | 0.704873i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704873i | \(0.751004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 124.000i | − 0.118622i | −0.998240 | − | 0.0593111i | \(-0.981110\pi\) | ||||
0.998240 | − | 0.0593111i | \(-0.0188904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 432.000i | − 0.390309i | −0.980773 | − | 0.195154i | \(-0.937479\pi\) | ||||
0.980773 | − | 0.195154i | \(-0.0625208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −701.000 | −0.615997 | −0.307998 | − | 0.951387i | \(-0.599659\pi\) | ||||
−0.307998 | + | 0.951387i | \(0.599659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −810.000 | −0.692629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1044.00i | 0.869126i | 0.900641 | + | 0.434563i | \(0.143097\pi\) | ||||
−0.900641 | + | 0.434563i | \(0.856903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000i | 0.00711154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1102.00 | −0.848909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −847.000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1404.00i | 1.02922i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 504.000i | 0.352148i | 0.984377 | + | 0.176074i | \(0.0563398\pi\) | ||||
−0.984377 | + | 0.176074i | \(0.943660\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1293.00 | 0.882498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 72.0000 | 0.0480204 | 0.0240102 | − | 0.999712i | \(-0.492357\pi\) | ||||
0.0240102 | + | 0.999712i | \(0.492357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1007.00i | − 0.656526i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1850.00i | − 1.15369i | −0.816852 | − | 0.576847i | \(-0.804283\pi\) | ||||
0.816852 | − | 0.576847i | \(-0.195717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1836.00 | −1.12034 | −0.560171 | − | 0.828377i | \(-0.689265\pi\) | ||||
−0.560171 | + | 0.828377i | \(0.689265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −690.000 | −0.412117 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 22.0000i | − 0.0128653i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.0000i | 0.0302983i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2398.00 | 1.31847 | 0.659234 | − | 0.751938i | \(-0.270881\pi\) | ||||
0.659234 | + | 0.751938i | \(0.270881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1871.00 | 1.00834 | 0.504172 | − | 0.863604i | \(-0.331798\pi\) | ||||
0.504172 | + | 0.863604i | \(0.331798\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 522.000i | 0.275825i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3293.00i | − 1.67395i | −0.547242 | − | 0.836975i | \(-0.684322\pi\) | ||||
0.547242 | − | 0.836975i | \(-0.315678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1102.00 | −0.539440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 883.000i | − 0.424306i | −0.977236 | − | 0.212153i | \(-0.931952\pi\) | ||||
0.977236 | − | 0.212153i | \(-0.0680475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4104.00i | 1.90166i | 0.309715 | + | 0.950830i | \(0.399766\pi\) | ||||
−0.309715 | + | 0.950830i | \(0.600234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2196.00 | 0.999545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −477.000 | −0.213316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1706.00i | − 0.749739i | −0.927078 | − | 0.374869i | \(-0.877688\pi\) | ||||
0.927078 | − | 0.374869i | \(-0.122312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1338.00i | 0.568193i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −662.000 | −0.276426 | −0.138213 | − | 0.990403i | \(-0.544136\pi\) | ||||
−0.138213 | + | 0.990403i | \(0.544136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4121.00 | 1.69233 | 0.846164 | − | 0.532922i | \(-0.178906\pi\) | ||||
0.846164 | + | 0.532922i | \(0.178906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 381.000i | − 0.153903i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1276.00i | − 0.498986i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 513.000 | 0.197435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −958.000 | −0.362924 | −0.181462 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181462 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 3187.00i | − 1.18863i | −0.804233 | − | 0.594314i | \(-0.797424\pi\) | ||||
0.804233 | − | 0.594314i | \(-0.202576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2282.00i | − 0.825308i | −0.910888 | − | 0.412654i | \(-0.864602\pi\) | ||||
0.910888 | − | 0.412654i | \(-0.135398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1043.00 | −0.371539 | −0.185770 | − | 0.982593i | \(-0.559478\pi\) | ||||
−0.185770 | + | 0.982593i | \(0.559478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2433.00 | −0.853784 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 418.000i | 0.144521i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 522.000i | 0.175273i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1166.00 | 0.385904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4139.00 | 1.35043 | 0.675214 | − | 0.737621i | \(-0.264051\pi\) | ||||
0.675214 | + | 0.737621i | \(0.264051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 108.000i | − 0.0347420i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 665.000i | 0.208033i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1566.00 | −0.483199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −58.0000 | −0.0176539 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 413.000i | − 0.124020i | −0.998076 | − | 0.0620101i | \(-0.980249\pi\) | ||||
0.998076 | − | 0.0620101i | \(-0.0197511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5652.00i | 1.65258i | 0.563242 | + | 0.826292i | \(0.309554\pi\) | ||||
−0.563242 | + | 0.826292i | \(0.690446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4391.00 | 1.26710 | 0.633549 | − | 0.773703i | \(-0.281597\pi\) | ||||
0.633549 | + | 0.773703i | \(0.281597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1254.00 | −0.357174 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2052.00i | 0.576957i | 0.957486 | + | 0.288479i | \(0.0931494\pi\) | ||||
−0.957486 | + | 0.288479i | \(0.906851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4104.00i | 1.12482i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4320.00 | 1.16919 | 0.584597 | − | 0.811324i | \(-0.301252\pi\) | ||||
0.584597 | + | 0.811324i | \(0.301252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4265.00 | 1.13997 | 0.569985 | − | 0.821655i | \(-0.306949\pi\) | ||||
0.569985 | + | 0.821655i | \(0.306949\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 53.0000i | − 0.0136531i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3414.00 | 0.868889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2412.00 | −0.606550 | −0.303275 | − | 0.952903i | \(-0.598080\pi\) | ||||
−0.303275 | + | 0.952903i | \(0.598080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1276.00i | − 0.317081i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6948.00i | 1.68640i | 0.537601 | + | 0.843199i | \(0.319331\pi\) | ||||
−0.537601 | + | 0.843199i | \(0.680669\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5130.00 | −1.23074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 198.000 | 0.0469574 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3564.00i | 0.835611i | 0.908537 | + | 0.417805i | \(0.137201\pi\) | ||||
−0.908537 | + | 0.417805i | \(0.862799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 432.000i | 0.0990186i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1534.00 | 0.347694 | 0.173847 | − | 0.984773i | \(-0.444380\pi\) | ||||
0.173847 | + | 0.984773i | \(0.444380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7704.00 | 1.72688 | 0.863440 | − | 0.504451i | \(-0.168305\pi\) | ||||
0.863440 | + | 0.504451i | \(0.168305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 57.0000i | 0.0126366i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4877.00i | 1.05787i | 0.848662 | + | 0.528936i | \(0.177409\pi\) | ||||
−0.848662 | + | 0.528936i | \(0.822591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 315.000 | 0.0675934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3758.00 | −0.797806 | −0.398903 | − | 0.916993i | \(-0.630609\pi\) | ||||
−0.398903 | + | 0.916993i | \(0.630609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 935.000i | − 0.196396i | −0.995167 | − | 0.0981978i | \(-0.968692\pi\) | ||||
0.995167 | − | 0.0981978i | \(-0.0313078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8892.00i | 1.82884i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1549.00 | 0.315286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3237.00 | −0.652084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6214.00i | − 1.23900i | −0.784998 | − | 0.619498i | \(-0.787336\pi\) | ||||
0.784998 | − | 0.619498i | \(-0.212664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 594.000i | 0.116052i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −58.0000 | −0.0112181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8189.00 | 1.56813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4320.00i | 0.819068i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3905.00i | − 0.725961i | −0.931797 | − | 0.362981i | \(-0.881759\pi\) | ||||
0.931797 | − | 0.362981i | \(-0.118241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −372.000 | −0.0684865 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9662.00 | 1.76168 | 0.880839 | − | 0.473416i | \(-0.156979\pi\) | ||||
0.880839 | + | 0.473416i | \(0.156979\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5147.00i | − 0.929475i | −0.885449 | − | 0.464737i | \(-0.846149\pi\) | ||||
0.885449 | − | 0.464737i | \(-0.153851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9216.00i | − 1.63288i | −0.577432 | − | 0.816439i | \(-0.695945\pi\) | ||||
0.577432 | − | 0.816439i | \(-0.304055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −484.000 | −0.0849492 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1296.00 | −0.225345 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3074.00i | − 0.529542i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2103.00i | 0.355646i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4370.00 | −0.732298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2196.00 | 0.364662 | 0.182331 | − | 0.983237i | \(-0.441636\pi\) | ||||
0.182331 | + | 0.983237i | \(0.441636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2430.00i | 0.399889i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2521.00i | 0.407500i | 0.979023 | + | 0.203750i | \(0.0653130\pi\) | ||||
−0.979023 | + | 0.203750i | \(0.934687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3132.00 | 0.501790 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −770.000 | −0.122281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6175.00i | − 0.972066i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7034.00i | 1.08820i | 0.839021 | + | 0.544099i | \(0.183129\pi\) | ||||
−0.839021 | + | 0.544099i | \(0.816871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7362.00 | −1.12917 | −0.564583 | − | 0.825376i | \(-0.690963\pi\) | ||||
−0.564583 | + | 0.825376i | \(0.690963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0000 | 0.00410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9382.00i | 1.41460i | 0.706914 | + | 0.707300i | \(0.250087\pi\) | ||||
−0.706914 | + | 0.707300i | \(0.749913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3306.00i | 0.490118i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10116.0 | 1.48719 | 0.743596 | − | 0.668629i | \(-0.233119\pi\) | ||||
0.743596 | + | 0.668629i | \(0.233119\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4050.00 | −0.590465 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2541.00i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3277.00i | − 0.466098i | −0.972465 | − | 0.233049i | \(-0.925130\pi\) | ||||
0.972465 | − | 0.233049i | \(-0.0748703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4212.00 | 0.594222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 10891.0i | − 1.51184i | −0.654667 | − | 0.755918i | \(-0.727191\pi\) | ||||
0.654667 | − | 0.755918i | \(-0.272809\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.0000i | 0.00300546i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2591.00 | 0.351163 | 0.175581 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175581 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1512.00 | 0.203313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 612.000i | 0.0816494i | 0.999166 | + | 0.0408247i | \(0.0129985\pi\) | ||||
−0.999166 | + | 0.0408247i | \(0.987001\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3879.00i | − 0.509511i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3708.00 | −0.483298 | −0.241649 | − | 0.970364i | \(-0.577688\pi\) | ||||
−0.241649 | + | 0.970364i | \(0.577688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3364.00 | −0.435102 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 216.000i | − 0.0277246i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3833.00i | − 0.484566i | −0.970206 | − | 0.242283i | \(-0.922104\pi\) | ||||
0.970206 | − | 0.242283i | \(-0.0778963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3021.00 | −0.379046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9288.00 | −1.15666 | −0.578330 | − | 0.815803i | \(-0.696295\pi\) | ||||
−0.578330 | + | 0.815803i | \(0.696295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.0000i | 0.00432624i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5940.00i | − 0.723427i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 755.000 | 0.0912771 | 0.0456386 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456386 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5550.00 | −0.666086 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8474.00i | 1.00963i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5508.00i | 0.646830i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9576.00 | 1.11651 | 0.558256 | − | 0.829669i | \(-0.311471\pi\) | ||||
0.558256 | + | 0.829669i | \(0.311471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9414.00 | 1.08981 | 0.544905 | − | 0.838498i | \(-0.316566\pi\) | ||||
0.544905 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2070.00i | 0.237936i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2413.00i | − 0.273474i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −66.0000 | −0.00742776 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2254.00 | −0.251906 | −0.125953 | − | 0.992036i | \(-0.540199\pi\) | ||||
−0.125953 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6301.00i | 0.699323i | 0.936876 | + | 0.349661i | \(0.113703\pi\) | ||||
−0.936876 | + | 0.349661i | \(0.886297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3074.00i | − 0.336497i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3779.00 | 0.410847 | 0.205423 | − | 0.978673i | \(-0.434143\pi\) | ||||
0.205423 | + | 0.978673i | \(0.434143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 162.000 | 0.0174927 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7632.00i | − 0.818527i | −0.912416 | − | 0.409263i | \(-0.865786\pi\) | ||||
0.912416 | − | 0.409263i | \(-0.134214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 7194.00i | − 0.761218i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2988.00 | −0.314059 | −0.157029 | − | 0.987594i | \(-0.550192\pi\) | ||||
−0.157029 | + | 0.987594i | \(0.550192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10296.0 | −1.07499 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5613.00i | − 0.582167i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1370.00i | − 0.140232i | −0.997539 | − | 0.0701159i | \(-0.977663\pi\) | ||||
0.997539 | − | 0.0701159i | \(-0.0223369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1566.00 | 0.159248 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7992.00 | −0.807429 | −0.403714 | − | 0.914885i | \(-0.632281\pi\) | ||||
−0.403714 | + | 0.914885i | \(0.632281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3096.00i | 0.310763i | 0.987855 | + | 0.155382i | \(0.0496607\pi\) | ||||
−0.987855 | + | 0.155382i | \(0.950339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8338.00i | − 0.826203i | −0.910685 | − | 0.413101i | \(-0.864446\pi\) | ||||
0.910685 | − | 0.413101i | \(-0.135554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15409.0 | −1.51710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9879.00 | −0.966455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9482.00i | 0.921740i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4918.00 | −0.469121 | −0.234561 | − | 0.972101i | \(-0.575365\pi\) | ||||
−0.234561 | + | 0.972101i | \(0.575365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −270.000 | −0.0255945 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3306.00i | 0.311446i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 19637.0i | − 1.82718i | −0.406635 | − | 0.913591i | \(-0.633298\pi\) | ||||
0.406635 | − | 0.913591i | \(-0.366702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2649.00 | −0.244973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3096.00 | 0.284563 | 0.142282 | − | 0.989826i | \(-0.454556\pi\) | ||||
0.142282 | + | 0.989826i | \(0.454556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1276.00i | 0.116568i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 684.000i | − 0.0617336i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6875.00 | −0.616768 | −0.308384 | − | 0.951262i | \(-0.599788\pi\) | ||||
−0.308384 | + | 0.951262i | \(0.599788\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12312.0 | 1.09792 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 11268.0i | − 0.998838i | −0.866361 | − | 0.499419i | \(-0.833547\pi\) | ||||
0.866361 | − | 0.499419i | \(-0.166453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6588.00i | − 0.577087i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16078.0 | −1.40009 | −0.700044 | − | 0.714100i | \(-0.746836\pi\) | ||||
−0.700044 | + | 0.714100i | \(0.746836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9918.00 | −0.858604 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1431.00i | 0.123158i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5060.00i | − 0.430442i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5118.00 | −0.432862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17366.0 | −1.46030 | −0.730152 | − | 0.683285i | \(-0.760551\pi\) | ||||
−0.730152 | + | 0.683285i | \(0.760551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4913.00i | 0.410766i | 0.978682 | + | 0.205383i | \(0.0658440\pi\) | ||||
−0.978682 | + | 0.205383i | \(0.934156\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2030.00i | 0.167795i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8803.00 | 0.723514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4014.00 | 0.328047 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 468.000i | 0.0380325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1986.00i | 0.159594i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −396.000 | −0.0316455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17605.0 | 1.39907 | 0.699536 | − | 0.714597i | \(-0.253390\pi\) | ||||
0.699536 | + | 0.714597i | \(0.253390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 12363.0i | − 0.977067i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 14560.0i | − 1.13810i | −0.822303 | − | 0.569050i | \(-0.807311\pi\) | ||||
0.822303 | − | 0.569050i | \(-0.192689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1143.00 | −0.0888562 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1166.00 | −0.0901511 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25992.0i | 1.99872i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20614.0i | − 1.56812i | −0.620685 | − | 0.784060i | \(-0.713145\pi\) | ||||
0.620685 | − | 0.784060i | \(-0.286855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 431.000 | 0.0326107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3828.00 | −0.288090 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3442.00i | − 0.257661i | −0.991667 | − | 0.128830i | \(-0.958878\pi\) | ||||
0.991667 | − | 0.128830i | \(-0.0411223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1539.00i | − 0.113989i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22082.0 | −1.62693 | −0.813467 | − | 0.581611i | \(-0.802423\pi\) | ||||
−0.813467 | + | 0.581611i | \(0.802423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 451.000 | 0.0330539 | 0.0165269 | − | 0.999863i | \(-0.494739\pi\) | ||||
0.0165269 | + | 0.999863i | \(0.494739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2874.00i | 0.209534i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20987.0i | 1.51421i | 0.653292 | + | 0.757106i | \(0.273387\pi\) | ||||
−0.653292 | + | 0.757106i | \(0.726613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9561.00 | −0.686255 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21622.0 | 1.54394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3888.00i | 0.273381i | 0.990614 | + | 0.136691i | \(0.0436467\pi\) | ||||
−0.990614 | + | 0.136691i | \(0.956353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1855.00 | −0.129769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6846.00 | −0.476492 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11268.0i | 0.780306i | 0.920750 | + | 0.390153i | \(0.127578\pi\) | ||||
−0.920750 | + | 0.390153i | \(0.872422\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3129.00i | 0.214508i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3996.00 | 0.272575 | 0.136287 | − | 0.990669i | \(-0.456483\pi\) | ||||
0.136287 | + | 0.990669i | \(0.456483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24965.0 | −1.69442 | −0.847208 | − | 0.531262i | \(-0.821718\pi\) | ||||
−0.847208 | + | 0.531262i | \(0.821718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7299.00i | 0.492932i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4176.00i | 0.279240i | 0.990205 | + | 0.139620i | \(0.0445881\pi\) | ||||
−0.990205 | + | 0.139620i | \(0.955412\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1254.00 | 0.0834395 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −230.000 | −0.0152288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9558.00i | 0.629762i | 0.949131 | + | 0.314881i | \(0.101965\pi\) | ||||
−0.949131 | + | 0.314881i | \(0.898035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 9000.00i | − 0.587239i | −0.955922 | − | 0.293619i | \(-0.905140\pi\) | ||||
0.955922 | − | 0.293619i | \(-0.0948598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15625.0 | 1.01457 | 0.507287 | − | 0.861777i | \(-0.330648\pi\) | ||||
0.507287 | + | 0.861777i | \(0.330648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1566.00 | 0.101194 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2736.00i | 0.175948i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3498.00i | − 0.222802i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15660.0 | −0.992695 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31175.0 | −1.96681 | −0.983405 | − | 0.181424i | \(-0.941929\pi\) | ||||
−0.983405 | + | 0.181424i | \(0.941929\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 12417.0i | − 0.779671i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000i | 0.00111960i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −324.000 | −0.0200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6732.00 | −0.414817 | −0.207409 | − | 0.978254i | \(-0.566503\pi\) | ||||
−0.207409 | + | 0.978254i | \(0.566503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6228.00i | 0.381973i | 0.981593 | + | 0.190986i | \(0.0611686\pi\) | ||||
−0.981593 | + | 0.190986i | \(0.938831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 396.000i | − 0.0240624i | −0.999928 | − | 0.0120312i | \(-0.996170\pi\) | ||||
0.999928 | − | 0.0120312i | \(-0.00382974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9812.00 | −0.593459 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1995.00 | 0.120108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4702.00i | 0.281782i | 0.990025 | + | 0.140891i | \(0.0449967\pi\) | ||||
−0.990025 | + | 0.140891i | \(0.955003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4698.00i | 0.278975i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22140.0 | 1.30873 | 0.654364 | − | 0.756180i | \(-0.272936\pi\) | ||||
0.654364 | + | 0.756180i | \(0.272936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13518.0 | −0.795445 | −0.397723 | − | 0.917506i | \(-0.630199\pi\) | ||||
−0.397723 | + | 0.917506i | \(0.630199\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 174.000i | 0.0101925i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1276.00i | 0.0740733i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1239.00 | −0.0716032 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2794.00 | 0.160747 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11250.0i | 0.644362i | 0.946678 | + | 0.322181i | \(0.104416\pi\) | ||||
−0.946678 | + | 0.322181i | \(0.895584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15170.0i | − 0.861197i | −0.902544 | − | 0.430599i | \(-0.858302\pi\) | ||||
0.902544 | − | 0.430599i | \(-0.141698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20501.0 | −1.15870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16956.0 | 0.954119 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22680.0i | − 1.27061i | −0.772262 | − | 0.635305i | \(-0.780875\pi\) | ||||
0.772262 | − | 0.635305i | \(-0.219125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 13173.0i | − 0.731559i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 128.000 | 0.00704682 | 0.00352341 | − | 0.999994i | \(-0.498878\pi\) | ||||
0.00352341 | + | 0.999994i | \(0.498878\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3762.00i | 0.206214i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27144.0i | 1.47511i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6156.00 | 0.333106 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25682.0 | 1.38373 | 0.691866 | − | 0.722026i | \(-0.256789\pi\) | ||||
0.691866 | + | 0.722026i | \(0.256789\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 14310.0i | − 0.767727i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27360.0i | 1.45542i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4951.00 | 0.262255 | 0.131127 | − | 0.991366i | \(-0.458140\pi\) | ||||
0.131127 | + | 0.991366i | \(0.458140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12312.0 | 0.649418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2030.00i | 0.106626i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 12960.0i | − 0.675035i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22190.0 | 1.15097 | 0.575485 | − | 0.817812i | \(-0.304813\pi\) | ||||
0.575485 | + | 0.817812i | \(0.304813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2356.00 | −0.121695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 12795.0i | − 0.658162i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7685.00i | 0.392051i | 0.980599 | + | 0.196025i | \(0.0628035\pi\) | ||||
−0.980599 | + | 0.196025i | \(0.937197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24998.0 | 1.26482 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 29574.0i | − 1.49023i | −0.666934 | − | 0.745116i | \(-0.732394\pi\) | ||||
0.666934 | − | 0.745116i | \(-0.267606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 17842.0i | − 0.891748i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32580.0 | 1.62175 | 0.810876 | − | 0.585218i | \(-0.198991\pi\) | ||||
0.810876 | + | 0.585218i | \(0.198991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −159.000 | −0.00788261 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3060.00i | 0.151091i | 0.997142 | + | 0.0755454i | \(0.0240698\pi\) | ||||
−0.997142 | + | 0.0755454i | \(0.975930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10242.0i | − 0.501654i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8208.00 | −0.400419 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7992.00 | −0.388325 | −0.194163 | − | 0.980969i | \(-0.562199\pi\) | ||||
−0.194163 | + | 0.980969i | \(0.562199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7236.00i | 0.350192i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22841.0i | 1.09666i | 0.836263 | + | 0.548329i | \(0.184736\pi\) | ||||
−0.836263 | + | 0.548329i | \(0.815264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3828.00 | −0.183067 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17172.0 | −0.817982 | −0.408991 | − | 0.912538i | \(-0.634119\pi\) | ||||
−0.408991 | + | 0.912538i | \(0.634119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13319.0i | 0.631953i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 446.000i | 0.0209963i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30869.0 | 1.44755 | 0.723774 | − | 0.690037i | \(-0.242406\pi\) | ||||
0.723774 | + | 0.690037i | \(0.242406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20844.0 | 0.973642 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 34884.0i | − 1.62314i | −0.584252 | − | 0.811572i | \(-0.698612\pi\) | ||||
0.584252 | − | 0.811572i | \(-0.301388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15390.0i | 0.710570i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24804.0 | −1.14082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 792.000 | 0.0362868 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 594.000i | − 0.0271109i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5039.00i | 0.228235i | 0.993467 | + | 0.114118i | \(0.0364040\pi\) | ||||
−0.993467 | + | 0.114118i | \(0.963596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10692.0 | 0.482440 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19836.0 | 0.891640 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 127.000i | − 0.00568714i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 540.000i | 0.0239997i | 0.999928 | + | 0.0119999i | \(0.00381977\pi\) | ||||
−0.999928 | + | 0.0119999i | \(0.996180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13340.0 | −0.590657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1296.00 | 0.0571684 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11484.0i | − 0.504684i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4602.00i | − 0.200741i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41328.0 | 1.79606 | 0.898032 | − | 0.439931i | \(-0.144997\pi\) | ||||
0.898032 | + | 0.439931i | \(0.144997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12853.0 | −0.556510 | −0.278255 | − | 0.960507i | \(-0.589756\pi\) | ||||
−0.278255 | + | 0.960507i | \(0.589756\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 23112.0i | − 0.997015i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22843.0i | 0.978183i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 171.000 | 0.00729576 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29470.0 | 1.25275 | 0.626376 | − | 0.779521i | \(-0.284537\pi\) | ||||
0.626376 | + | 0.779521i | \(0.284537\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24407.0i | 1.03375i | 0.856062 | + | 0.516874i | \(0.172904\pi\) | ||||
−0.856062 | + | 0.516874i | \(0.827096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15048.0i | 0.632733i | 0.948637 | + | 0.316367i | \(0.102463\pi\) | ||||
−0.948637 | + | 0.316367i | \(0.897537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28406.0 | 1.19009 | 0.595043 | − | 0.803694i | \(-0.297135\pi\) | ||||
0.595043 | + | 0.803694i | \(0.297135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14631.0 | 0.610763 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1044.00i | 0.0434243i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 945.000i | − 0.0390251i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26914.0 | 1.10748 | 0.553739 | − | 0.832690i | \(-0.313200\pi\) | ||||
0.553739 | + | 0.832690i | \(0.313200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23905.0 | −0.980155 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11274.0i | 0.460614i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16093.0i | 0.652848i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2805.00 | −0.113389 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15660.0 | −0.630808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21275.0i | − 0.853977i | −0.904257 | − | 0.426988i | \(-0.859575\pi\) | ||||
0.904257 | − | 0.426988i | \(-0.140425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39132.0i | 1.55977i | 0.625922 | + | 0.779885i | \(0.284723\pi\) | ||||
−0.625922 | + | 0.779885i | \(0.715277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 448.000 | 0.0177946 | 0.00889730 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889730 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26676.0 | 1.05588 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26856.0i | 1.05932i | 0.848212 | + | 0.529658i | \(0.177680\pi\) | ||||
−0.848212 | + | 0.529658i | \(0.822320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4647.00i | − 0.182030i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30096.0 | −1.17484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −811.000 | −0.0315496 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9711.00i | 0.376481i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3653.00i | − 0.140653i | −0.997524 | − | 0.0703267i | \(-0.977596\pi\) | ||||
0.997524 | − | 0.0703267i | \(-0.0224042\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18642.0 | −0.715335 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6552.00 | −0.250559 | −0.125280 | − | 0.992121i | \(-0.539983\pi\) | ||||
−0.125280 | + | 0.992121i | \(0.539983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4481.00i | − 0.170779i | −0.996348 | − | 0.0853894i | \(-0.972787\pi\) | ||||
0.996348 | − | 0.0853894i | \(-0.0272134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 14666.0i | − 0.555170i | −0.960701 | − | 0.277585i | \(-0.910466\pi\) | ||||
0.960701 | − | 0.277585i | \(-0.0895341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9576.00 | 0.361270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1782.00 | 0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 12190.0i | − 0.456800i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 174.000i | 0.00647680i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 770.000 | 0.0285661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 24567.0i | − 0.905358i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51804.0i | 1.89650i | 0.317528 | + | 0.948249i | \(0.397147\pi\) | ||||
−0.317528 | + | 0.948249i | \(0.602853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12960.0 | 0.472889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31198.0 | 1.13462 | 0.567308 | − | 0.823505i | \(-0.307985\pi\) | ||||
0.567308 | + | 0.823505i | \(0.307985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25036.0i | 0.907525i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1368.00i | − 0.0492643i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27001.0 | 0.969185 | 0.484592 | − | 0.874740i | \(-0.338968\pi\) | ||||
0.484592 | + | 0.874740i | \(0.338968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11715.0 | −0.419134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 36.0000i | − 0.00128381i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1116.00i | 0.0395407i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22694.0 | 0.801470 | 0.400735 | − | 0.916194i | \(-0.368755\pi\) | ||||
0.400735 | + | 0.916194i | \(0.368755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −954.000 | −0.0335833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 28986.0i | − 1.01711i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29503.0i | 1.02862i | 0.857603 | + | 0.514312i | \(0.171953\pi\) | ||||
−0.857603 | + | 0.514312i | \(0.828047\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15441.0 | −0.536633 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14566.0 | 0.504610 | 0.252305 | − | 0.967648i | \(-0.418811\pi\) | ||||
0.252305 | + | 0.967648i | \(0.418811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27144.0i | 0.937360i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42322.0i | 1.45225i | 0.687563 | + | 0.726125i | \(0.258681\pi\) | ||||
−0.687563 | + | 0.726125i | \(0.741319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −522.000 | −0.0178555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27648.0 | −0.942742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 43416.0i | − 1.47574i | −0.674942 | − | 0.737871i | \(-0.735831\pi\) | ||||
0.674942 | − | 0.737871i | \(-0.264169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1452.00i | 0.0490454i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35150.0 | −1.18358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28566.0 | −0.958880 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3888.00i | 0.130103i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21528.0i | 0.715919i | 0.933737 | + | 0.357960i | \(0.116527\pi\) | ||||
−0.933737 | + | 0.357960i | \(0.883473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9222.00 | −0.305731 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27050.0 | 0.894002 | 0.447001 | − | 0.894533i | \(-0.352492\pi\) | ||||
0.447001 | + | 0.894533i | \(0.352492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34884.0i | 1.14936i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24934.0i | − 0.816489i | −0.912873 | − | 0.408244i | \(-0.866141\pi\) | ||||
0.912873 | − | 0.408244i | \(-0.133859\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3168.00 | −0.103422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6309.00 | 0.205332 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 8388.00i | − 0.272162i | −0.990698 | − | 0.136081i | \(-0.956549\pi\) | ||||
0.990698 | − | 0.136081i | \(-0.0434508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13110.0i | 0.422792i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24998.0 | 0.803731 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29033.0 | 0.930639 | 0.465320 | − | 0.885143i | \(-0.345939\pi\) | ||||
0.465320 | + | 0.885143i | \(0.345939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 6588.00i | − 0.210538i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 25326.0i | − 0.804496i | −0.915531 | − | 0.402248i | \(-0.868229\pi\) | ||||
0.915531 | − | 0.402248i | \(-0.131771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7290.00 | 0.230876 |
(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 | 600.4.f.h.49.1 | 2 | ||
3.2 | odd | 2 | 1800.4.f.g.649.1 | 2 | |||
4.3 | odd | 2 | 1200.4.f.f.49.2 | 2 | |||
5.2 | odd | 4 | 600.4.a.g.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 600.4.a.j.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 600.4.f.h.49.2 | 2 | ||
15.2 | even | 4 | 1800.4.a.bf.1.1 | 1 | |||
15.8 | even | 4 | 1800.4.a.g.1.1 | 1 | |||
15.14 | odd | 2 | 1800.4.f.g.649.2 | 2 | |||
20.3 | even | 4 | 1200.4.a.n.1.1 | 1 | |||
20.7 | even | 4 | 1200.4.a.x.1.1 | 1 | |||
20.19 | odd | 2 | 1200.4.f.f.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.g.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
600.4.a.j.1.1 | yes | 1 | 5.3 | odd | 4 | ||
600.4.f.h.49.1 | 2 | 1.1 | even | 1 | trivial | ||
600.4.f.h.49.2 | 2 | 5.4 | even | 2 | inner | ||
1200.4.a.n.1.1 | 1 | 20.3 | even | 4 | |||
1200.4.a.x.1.1 | 1 | 20.7 | even | 4 | |||
1200.4.f.f.49.1 | 2 | 20.19 | odd | 2 | |||
1200.4.f.f.49.2 | 2 | 4.3 | odd | 2 | |||
1800.4.a.g.1.1 | 1 | 15.8 | even | 4 | |||
1800.4.a.bf.1.1 | 1 | 15.2 | even | 4 | |||
1800.4.f.g.649.1 | 2 | 3.2 | odd | 2 | |||
1800.4.f.g.649.2 | 2 | 15.14 | odd | 2 |