Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,4,Mod(1849,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1849");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.k (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: | \(123.904011012\) |
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 | 1849.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1849 |
Dual form | 2100.4.k.d.1849.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.0000 | −0.712663 | −0.356332 | − | 0.934360i | \(-0.615973\pi\) | ||||
−0.356332 | + | 0.934360i | \(0.615973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 39.0000i | − 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 101.000i | 1.44095i | 0.693482 | + | 0.720473i | \(0.256075\pi\) | ||||
−0.693482 | + | 0.720473i | \(0.743925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.0000 | 0.579577 | 0.289788 | − | 0.957091i | \(-0.406415\pi\) | ||||
0.289788 | + | 0.957091i | \(0.406415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 57.0000i | 0.516753i | 0.966044 | + | 0.258377i | \(0.0831875\pi\) | ||||
−0.966044 | + | 0.258377i | \(0.916812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 291.000 | 1.86336 | 0.931678 | − | 0.363284i | \(-0.118345\pi\) | ||||
0.931678 | + | 0.363284i | \(0.118345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −79.0000 | −0.457704 | −0.228852 | − | 0.973461i | \(-0.573497\pi\) | ||||
−0.228852 | + | 0.973461i | \(0.573497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0000i | 0.411456i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 322.000i | − 1.43072i | −0.698758 | − | 0.715358i | \(-0.746264\pi\) | ||||
0.698758 | − | 0.715358i | \(-0.253736\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −117.000 | −0.480384 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 455.000 | 1.73315 | 0.866574 | − | 0.499049i | \(-0.166317\pi\) | ||||
0.866574 | + | 0.499049i | \(0.166317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 307.000i | − 1.08877i | −0.838836 | − | 0.544384i | \(-0.816763\pi\) | ||||
0.838836 | − | 0.544384i | \(-0.183237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 508.000i | − 1.57658i | −0.615302 | − | 0.788292i | \(-0.710966\pi\) | ||||
0.615302 | − | 0.788292i | \(-0.289034\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 303.000 | 0.831931 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 31.0000i | − 0.0803430i | −0.999193 | − | 0.0401715i | \(-0.987210\pi\) | ||||
0.999193 | − | 0.0401715i | \(-0.0127904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 144.000i | − 0.334619i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −211.000 | −0.465591 | −0.232795 | − | 0.972526i | \(-0.574787\pi\) | ||||
−0.232795 | + | 0.972526i | \(0.574787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −797.000 | −1.67288 | −0.836438 | − | 0.548062i | \(-0.815366\pi\) | ||||
−0.836438 | + | 0.548062i | \(0.815366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 924.000i | 1.68484i | 0.538818 | + | 0.842422i | \(0.318871\pi\) | ||||
−0.538818 | + | 0.842422i | \(0.681129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 171.000 | 0.298348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 212.000 | 0.354363 | 0.177181 | − | 0.984178i | \(-0.443302\pi\) | ||||
0.177181 | + | 0.984178i | \(0.443302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22.0000i | 0.0352727i | 0.999844 | + | 0.0176363i | \(0.00561411\pi\) | ||||
−0.999844 | + | 0.0176363i | \(0.994386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 182.000i | 0.269361i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −874.000 | −1.24472 | −0.622359 | − | 0.782732i | \(-0.713825\pi\) | ||||
−0.622359 | + | 0.782732i | \(0.713825\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 587.000i | − 0.776285i | −0.921599 | − | 0.388142i | \(-0.873117\pi\) | ||||
0.921599 | − | 0.388142i | \(-0.126883\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 873.000i | − 1.07581i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 266.000 | 0.316808 | 0.158404 | − | 0.987374i | \(-0.449365\pi\) | ||||
0.158404 | + | 0.987374i | \(0.449365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −273.000 | −0.314485 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 237.000i | 0.264255i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1822.00i | − 1.90718i | −0.301114 | − | 0.953588i | \(-0.597359\pi\) | ||||
0.301114 | − | 0.953588i | \(-0.402641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 234.000 | 0.237554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1872.00 | −1.84427 | −0.922133 | − | 0.386872i | \(-0.873556\pi\) | ||||
−0.922133 | + | 0.386872i | \(0.873556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1595.00i | 1.52583i | 0.646501 | + | 0.762913i | \(0.276231\pi\) | ||||
−0.646501 | + | 0.762913i | \(0.723769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1026.00i | − 0.926983i | −0.886101 | − | 0.463491i | \(-0.846596\pi\) | ||||
0.886101 | − | 0.463491i | \(-0.153404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 588.000 | 0.516699 | 0.258349 | − | 0.966052i | \(-0.416821\pi\) | ||||
0.258349 | + | 0.966052i | \(0.416821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −966.000 | −0.826024 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 22.0000i | 0.0183149i | 0.999958 | + | 0.00915746i | \(0.00291495\pi\) | ||||
−0.999958 | + | 0.00915746i | \(0.997085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 351.000i | 0.277350i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 707.000 | 0.544627 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.000 | −0.492111 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1365.00i | − 1.00063i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1750.00i | 1.22274i | 0.791347 | + | 0.611368i | \(0.209380\pi\) | ||||
−0.791347 | + | 0.611368i | \(0.790620\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −921.000 | −0.628601 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1664.00 | 1.10980 | 0.554902 | − | 0.831916i | \(-0.312756\pi\) | ||||
0.554902 | + | 0.831916i | \(0.312756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 336.000i | − 0.219059i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1080.00i | − 0.673508i | −0.941593 | − | 0.336754i | \(-0.890671\pi\) | ||||
0.941593 | − | 0.336754i | \(-0.109329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 896.000 | 0.546746 | 0.273373 | − | 0.961908i | \(-0.411861\pi\) | ||||
0.273373 | + | 0.961908i | \(0.411861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1524.00 | −0.910241 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1014.00i | 0.592972i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 591.000 | 0.324944 | 0.162472 | − | 0.986713i | \(-0.448053\pi\) | ||||
0.162472 | + | 0.986713i | \(0.448053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1606.00 | −0.865526 | −0.432763 | − | 0.901508i | \(-0.642461\pi\) | ||||
−0.432763 | + | 0.901508i | \(0.642461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 909.000i | − 0.480316i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3554.00i | − 1.80662i | −0.428983 | − | 0.903312i | \(-0.641128\pi\) | ||||
0.428983 | − | 0.903312i | \(-0.358872\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −93.0000 | −0.0463860 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 399.000 | 0.195314 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2897.00i | − 1.39209i | −0.717999 | − | 0.696045i | \(-0.754942\pi\) | ||||
0.717999 | − | 0.696045i | \(-0.245058\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 66.0000i | 0.0305822i | 0.999883 | + | 0.0152911i | \(0.00486750\pi\) | ||||
−0.999883 | + | 0.0152911i | \(0.995132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 676.000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −432.000 | −0.193192 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1672.00i | 0.734797i | 0.930064 | + | 0.367398i | \(0.119751\pi\) | ||||
−0.930064 | + | 0.367398i | \(0.880249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 633.000i | 0.268809i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4710.00 | −1.96671 | −0.983357 | − | 0.181682i | \(-0.941846\pi\) | ||||
−0.983357 | + | 0.181682i | \(0.941846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2842.00 | 1.16710 | 0.583548 | − | 0.812079i | \(-0.301664\pi\) | ||||
0.583548 | + | 0.812079i | \(0.301664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2391.00i | 0.965835i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2626.00i | − 1.02691i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4197.00 | −1.58997 | −0.794985 | − | 0.606629i | \(-0.792521\pi\) | ||||
−0.794985 | + | 0.606629i | \(0.792521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2662.00i | 0.992824i | 0.868087 | + | 0.496412i | \(0.165349\pi\) | ||||
−0.868087 | + | 0.496412i | \(0.834651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3601.00i | − 1.30234i | −0.758933 | − | 0.651169i | \(-0.774279\pi\) | ||||
0.758933 | − | 0.651169i | \(-0.225721\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1840.00 | 0.655448 | 0.327724 | − | 0.944774i | \(-0.393718\pi\) | ||||
0.327724 | + | 0.944774i | \(0.393718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2772.00 | 0.972745 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2037.00i | − 0.704283i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 513.000i | − 0.172251i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1248.00 | −0.413043 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1733.00 | −0.565425 | −0.282712 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282712 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 636.000i | − 0.204592i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 553.000i | 0.172996i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 66.0000 | 0.0203647 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3939.00 | 1.19894 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4727.00i | 1.41948i | 0.704465 | + | 0.709738i | \(0.251187\pi\) | ||||
−0.704465 | + | 0.709738i | \(0.748813\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2863.00i | − 0.837110i | −0.908191 | − | 0.418555i | \(-0.862537\pi\) | ||||
0.908191 | − | 0.418555i | \(-0.137463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5578.00 | −1.60963 | −0.804814 | − | 0.593528i | \(-0.797735\pi\) | ||||
−0.804814 | + | 0.593528i | \(0.797735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 546.000 | 0.155516 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5016.00i | 1.41034i | 0.709039 | + | 0.705170i | \(0.249129\pi\) | ||||
−0.709039 | + | 0.705170i | \(0.750871\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2622.00i | 0.718638i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2992.00 | −0.809776 | −0.404888 | − | 0.914366i | \(-0.632689\pi\) | ||||
−0.404888 | + | 0.914366i | \(0.632689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1574.00 | −0.420706 | −0.210353 | − | 0.977625i | \(-0.567461\pi\) | ||||
−0.210353 | + | 0.977625i | \(0.567461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1872.00i | − 0.482237i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1761.00 | −0.448188 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5697.00 | −1.43264 | −0.716318 | − | 0.697774i | \(-0.754174\pi\) | ||||
−0.716318 | + | 0.697774i | \(0.754174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1482.00i | − 0.368271i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2599.00i | − 0.630822i | −0.948955 | − | 0.315411i | \(-0.897858\pi\) | ||||
0.948955 | − | 0.315411i | \(-0.102142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2254.00 | −0.540760 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2619.00 | −0.621119 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1115.00i | − 0.261421i | −0.991421 | − | 0.130711i | \(-0.958274\pi\) | ||||
0.991421 | − | 0.130711i | \(-0.0417259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 798.000i | − 0.182909i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4194.00 | −0.950605 | −0.475302 | − | 0.879822i | \(-0.657661\pi\) | ||||
−0.475302 | + | 0.879822i | \(0.657661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3972.00 | −0.890339 | −0.445169 | − | 0.895446i | \(-0.646857\pi\) | ||||
−0.445169 | + | 0.895446i | \(0.646857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 819.000i | 0.181568i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1842.00i | 0.399549i | 0.979842 | + | 0.199774i | \(0.0640209\pi\) | ||||
−0.979842 | + | 0.199774i | \(0.935979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 711.000 | 0.152568 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2680.00 | −0.568952 | −0.284476 | − | 0.958683i | \(-0.591820\pi\) | ||||
−0.284476 | + | 0.958683i | \(0.591820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2680.00i | 0.562931i | 0.959571 | + | 0.281465i | \(0.0908205\pi\) | ||||
−0.959571 | + | 0.281465i | \(0.909180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3185.00i | − 0.655068i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5288.00 | −1.07633 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5466.00 | −1.10111 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5656.00i | − 1.12774i | −0.825864 | − | 0.563869i | \(-0.809312\pi\) | ||||
0.825864 | − | 0.563869i | \(-0.190688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 702.000i | − 0.137152i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2223.00 | 0.429965 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2149.00 | −0.411516 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5616.00i | 1.06479i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6998.00i | − 1.30097i | −0.759520 | − | 0.650484i | \(-0.774566\pi\) | ||||
0.759520 | − | 0.650484i | \(-0.225434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4785.00 | 0.880936 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5610.00 | 1.02287 | 0.511437 | − | 0.859321i | \(-0.329113\pi\) | ||||
0.511437 | + | 0.859321i | \(0.329113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 166.000i | 0.0299772i | 0.999888 | + | 0.0149886i | \(0.00477120\pi\) | ||||
−0.999888 | + | 0.0149886i | \(0.995229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5333.00i | − 0.944893i | −0.881359 | − | 0.472447i | \(-0.843371\pi\) | ||||
0.881359 | − | 0.472447i | \(-0.156629\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7566.00 | −1.32795 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3078.00 | −0.535194 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4848.00i | 0.835139i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1764.00i | − 0.298316i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3556.00 | −0.595892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6481.00 | 1.07622 | 0.538109 | − | 0.842875i | \(-0.319139\pi\) | ||||
0.538109 | + | 0.842875i | \(0.319139\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2898.00i | 0.476905i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 9221.00i | − 1.49050i | −0.666783 | − | 0.745252i | \(-0.732329\pi\) | ||||
0.666783 | − | 0.745252i | \(-0.267671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 66.0000 | 0.0105741 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2054.00 | 0.326189 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1910.00i | − 0.295488i | −0.989026 | − | 0.147744i | \(-0.952799\pi\) | ||||
0.989026 | − | 0.147744i | \(-0.0472011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3409.00 | −0.522864 | −0.261432 | − | 0.965222i | \(-0.584195\pi\) | ||||
−0.261432 | + | 0.965222i | \(0.584195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1053.00 | 0.160128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2130.00i | 0.321157i | 0.987023 | + | 0.160579i | \(0.0513360\pi\) | ||||
−0.987023 | + | 0.160579i | \(0.948664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2121.00i | − 0.314440i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −647.000 | −0.0951180 | −0.0475590 | − | 0.998868i | \(-0.515144\pi\) | ||||
−0.0475590 | + | 0.998868i | \(0.515144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4555.00 | −0.664091 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1965.00i | 0.284121i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11503.0i | 1.63611i | 0.575141 | + | 0.818054i | \(0.304947\pi\) | ||||
−0.575141 | + | 0.818054i | \(0.695053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4095.00 | −0.577716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −217.000 | −0.0303668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3692.00i | − 0.512505i | −0.966610 | − | 0.256253i | \(-0.917512\pi\) | ||||
0.966610 | − | 0.256253i | \(-0.0824879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 11349.0i | − 1.55041i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8103.00 | −1.09821 | −0.549107 | − | 0.835752i | \(-0.685032\pi\) | ||||
−0.549107 | + | 0.835752i | \(0.685032\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5250.00 | 0.705947 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 2664.00i | − 0.355415i | −0.984083 | − | 0.177708i | \(-0.943132\pi\) | ||||
0.984083 | − | 0.177708i | \(-0.0568681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2763.00i | 0.362923i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2050.00 | 0.267196 | 0.133598 | − | 0.991036i | \(-0.457347\pi\) | ||||
0.133598 | + | 0.991036i | \(0.457347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5757.00 | −0.744614 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 4992.00i | − 0.640746i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1213.00i | 0.153347i | 0.997056 | + | 0.0766735i | \(0.0244299\pi\) | ||||
−0.997056 | + | 0.0766735i | \(0.975570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1008.00 | −0.126474 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10876.0 | 1.35442 | 0.677209 | − | 0.735791i | \(-0.263189\pi\) | ||||
0.677209 | + | 0.735791i | \(0.263189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3081.00i | 0.380833i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8372.00i | 1.01962i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12534.0 | 1.51532 | 0.757661 | − | 0.652649i | \(-0.226342\pi\) | ||||
0.757661 | + | 0.652649i | \(0.226342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3240.00 | −0.388850 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1477.00i | 0.175977i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 2688.00i | − 0.315664i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4569.00 | −0.532721 | −0.266361 | − | 0.963873i | \(-0.585821\pi\) | ||||
−0.266361 | + | 0.963873i | \(0.585821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9262.00 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4572.00i | 0.525528i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5579.00i | 0.632287i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3042.00 | 0.342352 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9429.00 | −1.05378 | −0.526890 | − | 0.849934i | \(-0.676642\pi\) | ||||
−0.526890 | + | 0.849934i | \(0.676642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 418.000i | 0.0463921i | 0.999731 | + | 0.0231961i | \(0.00738420\pi\) | ||||
−0.999731 | + | 0.0231961i | \(0.992616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2736.00i | 0.299498i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 419.000 | 0.0455530 | 0.0227765 | − | 0.999741i | \(-0.492749\pi\) | ||||
0.0227765 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9628.00i | − 1.03260i | −0.856409 | − | 0.516298i | \(-0.827310\pi\) | ||||
0.856409 | − | 0.516298i | \(-0.172690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1773.00i | − 0.187606i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14052.0 | −1.47696 | −0.738480 | − | 0.674276i | \(-0.764456\pi\) | ||||
−0.738480 | + | 0.674276i | \(0.764456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11830.0 | −1.23515 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4818.00i | 0.499712i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 12089.0i | − 1.23742i | −0.785621 | − | 0.618708i | \(-0.787656\pi\) | ||||
0.785621 | − | 0.618708i | \(-0.212344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2727.00 | −0.277310 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2744.00 | −0.277225 | −0.138613 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138613 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 592.000i | 0.0594224i | 0.999559 | + | 0.0297112i | \(0.00945876\pi\) | ||||
−0.999559 | + | 0.0297112i | \(0.990541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3361.00i | − 0.333038i | −0.986038 | − | 0.166519i | \(-0.946747\pi\) | ||||
0.986038 | − | 0.166519i | \(-0.0532526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6468.00 | 0.636811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10662.0 | −1.04306 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7982.00i | 0.775925i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 279.000i | 0.0267810i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8604.00 | −0.820724 | −0.410362 | − | 0.911923i | \(-0.634598\pi\) | ||||
−0.410362 | + | 0.911923i | \(0.634598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12558.0 | −1.19043 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1197.00i | − 0.112765i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9826.00i | − 0.914289i | −0.889393 | − | 0.457144i | \(-0.848872\pi\) | ||||
0.889393 | − | 0.457144i | \(-0.151128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8691.00 | −0.803723 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4758.00 | 0.437323 | 0.218661 | − | 0.975801i | \(-0.429831\pi\) | ||||
0.218661 | + | 0.975801i | \(0.429831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29391.0i | 2.68500i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1484.00i | − 0.133937i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20631.0 | 1.85084 | 0.925421 | − | 0.378940i | \(-0.123711\pi\) | ||||
0.925421 | + | 0.378940i | \(0.123711\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 198.000 | 0.0176567 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 7566.00i | − 0.670678i | −0.942097 | − | 0.335339i | \(-0.891149\pi\) | ||||
0.942097 | − | 0.335339i | \(-0.108851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2028.00i | − 0.177646i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12028.0 | −1.04741 | −0.523705 | − | 0.851900i | \(-0.675451\pi\) | ||||
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 154.000 | 0.0133318 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1296.00i | 0.111540i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13208.0i | 1.12357i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5016.00 | 0.424235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21317.0 | 1.79254 | 0.896271 | − | 0.443506i | \(-0.146266\pi\) | ||||
0.896271 | + | 0.443506i | \(0.146266\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15416.0i | 1.28890i | 0.764647 | + | 0.644450i | \(0.222914\pi\) | ||||
−0.764647 | + | 0.644450i | \(0.777086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 7979.00i | − 0.659527i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8918.00 | 0.732966 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1899.00 | 0.155197 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17745.0i | − 1.44207i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14130.0i | 1.13548i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1274.00 | 0.101809 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17520.0 | 1.39232 | 0.696159 | − | 0.717888i | \(-0.254891\pi\) | ||||
0.696159 | + | 0.717888i | \(0.254891\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8526.00i | − 0.673823i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 17379.0i | − 1.35845i | −0.733930 | − | 0.679225i | \(-0.762316\pi\) | ||||
0.733930 | − | 0.679225i | \(-0.237684\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7173.00 | 0.557625 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13968.0 | 1.07996 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6118.00i | 0.470459i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15830.0i | − 1.20420i | −0.798421 | − | 0.602099i | \(-0.794331\pi\) | ||||
0.798421 | − | 0.602099i | \(-0.205669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11973.0 | −0.905910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7878.00 | −0.592887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7343.00i | − 0.549681i | −0.961490 | − | 0.274841i | \(-0.911375\pi\) | ||||
0.961490 | − | 0.274841i | \(-0.0886251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10806.0 | 0.796153 | 0.398077 | − | 0.917352i | \(-0.369678\pi\) | ||||
0.398077 | + | 0.917352i | \(0.369678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1593.00 | −0.116751 | −0.0583756 | − | 0.998295i | \(-0.518592\pi\) | ||||
−0.0583756 | + | 0.998295i | \(0.518592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12591.0i | 0.917970i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9314.00i | − 0.672005i | −0.941861 | − | 0.336003i | \(-0.890925\pi\) | ||||
0.941861 | − | 0.336003i | \(-0.109075\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7986.00 | 0.573207 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4109.00 | −0.293408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 806.000i | 0.0572575i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3083.00i | 0.216779i | 0.994109 | + | 0.108389i | \(0.0345693\pi\) | ||||
−0.994109 | + | 0.108389i | \(0.965431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3792.00 | −0.265274 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10803.0 | −0.751905 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 18882.0i | − 1.30757i | −0.756679 | − | 0.653787i | \(-0.773179\pi\) | ||||
0.756679 | − | 0.653787i | \(-0.226821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5520.00i | − 0.378423i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1707.00 | −0.116438 | −0.0582188 | − | 0.998304i | \(-0.518542\pi\) | ||||
−0.0582188 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1440.00 | 0.0977352 | 0.0488676 | − | 0.998805i | \(-0.484439\pi\) | ||||
0.0488676 | + | 0.998805i | \(0.484439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8316.00i | − 0.561615i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8284.00i | 0.553933i | 0.960880 | + | 0.276966i | \(0.0893291\pi\) | ||||
−0.960880 | + | 0.276966i | \(0.910671\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6111.00 | −0.406618 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19812.0 | −1.31180 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24042.0i | − 1.58409i | −0.610463 | − | 0.792045i | \(-0.709016\pi\) | ||||
0.610463 | − | 0.792045i | \(-0.290984\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 862.000i | − 0.0562444i | −0.999604 | − | 0.0281222i | \(-0.991047\pi\) | ||||
0.999604 | − | 0.0281222i | \(-0.00895276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9890.00 | −0.642185 | −0.321093 | − | 0.947048i | \(-0.604050\pi\) | ||||
−0.321093 | + | 0.947048i | \(0.604050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1539.00 | −0.0994492 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1862.00i | − 0.119742i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3744.00i | 0.238470i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32522.0 | 2.06159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21646.0 | −1.36563 | −0.682816 | − | 0.730590i | \(-0.739245\pi\) | ||||
−0.682816 | + | 0.730590i | \(0.739245\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5199.00i | 0.326448i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1911.00i | 0.118864i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1908.00 | −0.118121 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19658.0 | 1.21130 | 0.605651 | − | 0.795731i | \(-0.292913\pi\) | ||||
0.605651 | + | 0.795731i | \(0.292913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23818.0i | − 1.46079i | −0.683023 | − | 0.730397i | \(-0.739335\pi\) | ||||
0.683023 | − | 0.730397i | \(-0.260665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 28490.0i | − 1.73116i | −0.500775 | − | 0.865578i | \(-0.666951\pi\) | ||||
0.500775 | − | 0.865578i | \(-0.333049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5486.00 | 0.331809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1659.00 | 0.0998792 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11002.0i | 0.659329i | 0.944098 | + | 0.329664i | \(0.106936\pi\) | ||||
−0.944098 | + | 0.329664i | \(0.893064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 198.000i | − 0.0117576i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11506.0 | −0.680137 | −0.340068 | − | 0.940401i | \(-0.610450\pi\) | ||||
−0.340068 | + | 0.940401i | \(0.610450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8398.00 | 0.494167 | 0.247083 | − | 0.968994i | \(-0.420528\pi\) | ||||
0.247083 | + | 0.968994i | \(0.420528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 11817.0i | − 0.692209i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16587.0i | 0.962895i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14181.0 | 0.819535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20722.0 | 1.19220 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1901.00i | 0.108883i | 0.998517 | + | 0.0544414i | \(0.0173378\pi\) | ||||
−0.998517 | + | 0.0544414i | \(0.982662\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 19896.0i | − 1.12949i | −0.825265 | − | 0.564745i | \(-0.808974\pi\) | ||||
0.825265 | − | 0.564745i | \(-0.191026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12754.0 | −0.720845 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8589.00 | −0.483306 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 15662.0i | − 0.877437i | −0.898624 | − | 0.438719i | \(-0.855432\pi\) | ||||
0.898624 | − | 0.438719i | \(-0.144568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16734.0i | 0.929319i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1209.00 | −0.0668494 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1162.00 | 0.0639719 | 0.0319859 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319859 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1638.00i | − 0.0897871i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45955.0i | 2.49737i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15048.0 | 0.814260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13501.0 | 0.727426 | 0.363713 | − | 0.931511i | \(-0.381509\pi\) | ||||
0.363713 | + | 0.931511i | \(0.381509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 15456.0i | − 0.829209i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13104.0i | 0.697067i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20672.0 | 1.09500 | 0.547499 | − | 0.836806i | \(-0.315580\pi\) | ||||
0.547499 | + | 0.836806i | \(0.315580\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7866.00 | 0.414906 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4503.00i | − 0.236520i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8976.00i | 0.467524i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7098.00 | 0.368165 | 0.184083 | − | 0.982911i | \(-0.441069\pi\) | ||||
0.184083 | + | 0.982911i | \(0.441069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11165.0 | 0.576708 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4722.00i | 0.242895i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4053.00i | 0.206764i | 0.994642 | + | 0.103382i | \(0.0329664\pi\) | ||||
−0.994642 | + | 0.103382i | \(0.967034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31007.0 | 1.56886 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10331.0i | 0.520579i | 0.965531 | + | 0.260289i | \(0.0838180\pi\) | ||||
−0.965531 | + | 0.260289i | \(0.916182\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 24024.0i | − 1.20073i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8969.00 | 0.446455 | 0.223227 | − | 0.974766i | \(-0.428341\pi\) | ||||
0.223227 | + | 0.974766i | \(0.428341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5616.00 | −0.278420 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 11613.0i | − 0.573405i | −0.958020 | − | 0.286702i | \(-0.907441\pi\) | ||||
0.958020 | − | 0.286702i | \(-0.0925591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5283.00i | 0.258762i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7182.00 | −0.350367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32476.0 | −1.57798 | −0.788992 | − | 0.614403i | \(-0.789397\pi\) | ||||
−0.788992 | + | 0.614403i | \(0.789397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17091.0i | 0.827132i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29914.0i | 1.43625i | 0.695913 | + | 0.718126i | \(0.255000\pi\) | ||||
−0.695913 | + | 0.718126i | \(0.745000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4446.00 | −0.212621 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3090.00 | −0.147191 | −0.0735955 | − | 0.997288i | \(-0.523447\pi\) | ||||
−0.0735955 | + | 0.997288i | \(0.523447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4116.00i | − 0.195294i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8229.00i | 0.387395i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7760.00 | 0.363892 | 0.181946 | − | 0.983309i | \(-0.441760\pi\) | ||||
0.181946 | + | 0.983309i | \(0.441760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7797.00 | −0.364205 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34020.0i | 1.58294i | 0.611207 | + | 0.791471i | \(0.290684\pi\) | ||||
−0.611207 | + | 0.791471i | \(0.709316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6762.00i | 0.312208i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21840.0 | 1.00449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5512.00 | −0.252541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7857.00i | 0.358603i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15154.0i | 0.686381i | 0.939266 | + | 0.343190i | \(0.111508\pi\) | ||||
−0.939266 | + | 0.343190i | \(0.888492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3345.00 | −0.150932 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 154.000 | 0.00692239 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31083.0i | 1.39192i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13386.0i | 0.594927i | 0.954733 | + | 0.297463i | \(0.0961406\pi\) | ||||
−0.954733 | + | 0.297463i | \(0.903859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51308.0 | 2.27177 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2394.00 | −0.105603 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 572.000i | − 0.0251375i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12582.0i | 0.548832i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36468.0 | −1.58485 | −0.792427 | − | 0.609967i | \(-0.791183\pi\) | ||||
−0.792427 | + | 0.609967i | \(0.791183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38422.0 | −1.66360 | −0.831800 | − | 0.555076i | \(-0.812689\pi\) | ||||
−0.831800 | + | 0.555076i | \(0.812689\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11916.0i | 0.514037i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 14736.0i | − 0.631025i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2457.00 | 0.104828 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19194.0 | 0.815926 | 0.407963 | − | 0.912998i | \(-0.366239\pi\) | ||||
0.407963 | + | 0.912998i | \(0.366239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 7426.00i | − 0.314525i | −0.987557 | − | 0.157263i | \(-0.949733\pi\) | ||||
0.987557 | − | 0.157263i | \(-0.0502669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33170.0i | 1.39472i | 0.716721 | + | 0.697360i | \(0.245642\pi\) | ||||
−0.716721 | + | 0.697360i | \(0.754358\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16397.0 | −0.686962 | −0.343481 | − | 0.939160i | \(-0.611606\pi\) | ||||
−0.343481 | + | 0.939160i | \(0.611606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5526.00 | 0.230680 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4949.00i | − 0.205850i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2133.00i | − 0.0880851i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14996.0 | −0.617067 | −0.308534 | − | 0.951213i | \(-0.599838\pi\) | ||||
−0.308534 | + | 0.951213i | \(0.599838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60292.0 | 2.47210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8040.00i | 0.328484i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4585.00i | 0.186001i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8040.00 | 0.325008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18354.0 | 0.739327 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21053.0i | − 0.845066i | −0.906348 | − | 0.422533i | \(-0.861141\pi\) | ||||
0.906348 | − | 0.422533i | \(-0.138859\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6390.00i | 0.254700i | 0.991858 | + | 0.127350i | \(0.0406472\pi\) | ||||
−0.991858 | + | 0.127350i | \(0.959353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22176.0 | −0.880833 | −0.440416 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440416 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9555.00 | −0.378204 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 42472.0i | − 1.67528i | −0.546225 | − | 0.837638i | \(-0.683936\pi\) | ||||
0.546225 | − | 0.837638i | \(-0.316064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15864.0i | 0.621418i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22724.0 | 0.887064 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36036.0 | 1.40188 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16398.0i | 0.635725i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3472.00i | − 0.133684i | −0.997764 | − | 0.0668421i | \(-0.978708\pi\) | ||||
0.997764 | − | 0.0668421i | \(-0.0212924\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16968.0 | −0.651099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32639.0 | 1.24817 | 0.624084 | − | 0.781357i | \(-0.285472\pi\) | ||||
0.624084 | + | 0.781357i | \(0.285472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 45513.0i | − 1.73458i | −0.497803 | − | 0.867290i | \(-0.665860\pi\) | ||||
0.497803 | − | 0.867290i | \(-0.334140\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27626.0i | 1.04576i | 0.852406 | + | 0.522881i | \(0.175143\pi\) | ||||
−0.852406 | + | 0.522881i | \(0.824857\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12250.0 | 0.462151 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2106.00 | −0.0791848 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 24384.0i | − 0.913751i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 6669.00i | − 0.248240i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22989.0 | −0.852865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3131.00 | 0.115770 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6447.00i | 0.237589i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11561.0i | 0.423238i | 0.977352 | + | 0.211619i | \(0.0678736\pi\) | ||||
−0.977352 | + | 0.211619i | \(0.932126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16848.0 | 0.614756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25773.0 | 0.937319 | 0.468659 | − | 0.883379i | \(-0.344737\pi\) | ||||
0.468659 | + | 0.883379i | \(0.344737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15262.0i | 0.553229i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 11648.0i | − 0.419467i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13240.0 | 0.475242 | 0.237621 | − | 0.971358i | \(-0.423632\pi\) | ||||
0.237621 | + | 0.971358i | \(0.423632\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20994.0 | −0.751114 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 8268.00i | − 0.294848i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 14355.0i | − 0.508608i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30653.0 | 1.08255 | 0.541277 | − | 0.840844i | \(-0.317941\pi\) | ||||
0.541277 | + | 0.840844i | \(0.317941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2352.00 | −0.0827967 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16830.0i | − 0.590557i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 19030.0i | − 0.663482i | −0.943370 | − | 0.331741i | \(-0.892364\pi\) | ||||
0.943370 | − | 0.331741i | \(-0.107636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 498.000 | 0.0173074 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5320.00 | −0.184301 | −0.0921504 | − | 0.995745i | \(-0.529374\pi\) | ||||
−0.0921504 | + | 0.995745i | \(0.529374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25935.0i | 0.895610i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 14524.0i | − 0.498381i | −0.968455 | − | 0.249190i | \(-0.919836\pi\) | ||||
0.968455 | − | 0.249190i | \(-0.0801645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 858.000 | 0.0293486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15999.0 | −0.545534 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8688.00i | − 0.295312i | −0.989039 | − | 0.147656i | \(-0.952827\pi\) | ||||
0.989039 | − | 0.147656i | \(-0.0471728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22698.0i | 0.766690i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7560.00 | −0.254562 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23550.0 | −0.790507 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9234.00i | 0.308994i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19672.0i | 0.654197i | 0.944990 | + | 0.327099i | \(0.106071\pi\) | ||||
−0.944990 | + | 0.327099i | \(0.893929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14544.0 | 0.482168 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45996.0 | 1.52017 | 0.760083 | − | 0.649826i | \(-0.225158\pi\) | ||||
0.760083 | + | 0.649826i | \(0.225158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6272.00i | − 0.206651i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32454.0i | 1.06274i | 0.847140 | + | 0.531369i | \(0.178322\pi\) | ||||
−0.847140 | + | 0.531369i | \(0.821678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6916.00 | −0.225778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5292.00 | −0.172233 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34048.0i | 1.10474i | 0.833598 | + | 0.552372i | \(0.186277\pi\) | ||||
−0.833598 | + | 0.552372i | \(0.813723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10668.0i | 0.344039i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17499.0 | 0.562625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14804.0 | −0.474535 | −0.237268 | − | 0.971444i | \(-0.576252\pi\) | ||||
−0.237268 | + | 0.971444i | \(0.576252\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 19443.0i | − 0.621354i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35546.0i | 1.12914i | 0.825385 | + | 0.564570i | \(0.190958\pi\) | ||||
−0.825385 | + | 0.564570i | \(0.809042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8694.00 | 0.275341 |
(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 | 2100.4.k.d.1849.1 | 2 | ||
5.2 | odd | 4 | 2100.4.a.e.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 2100.4.a.j.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 2100.4.k.d.1849.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.4.a.e.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
2100.4.a.j.1.1 | yes | 1 | 5.3 | odd | 4 | ||
2100.4.k.d.1849.1 | 2 | 1.1 | even | 1 | trivial | ||
2100.4.k.d.1849.2 | 2 | 5.4 | even | 2 | inner |