Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(-2.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.j.274.3 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.70156i | − 0.601593i | −0.953688 | − | 0.300797i | \(-0.902747\pi\) | ||||
0.953688 | − | 0.300797i | \(-0.0972525\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 5.10469 | 0.638086 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.10469 | −0.347330 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − 22.2984i | − 0.985461i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 37.4031 | 1.02522 | 0.512612 | − | 0.858620i | \(-0.328678\pi\) | ||||
0.512612 | + | 0.858620i | \(0.328678\pi\) | |||||||
\(12\) | − 15.3141i | − 0.368399i | ||||||||
\(13\) | − 29.0156i | − 0.619037i | −0.950893 | − | 0.309519i | \(-0.899832\pi\) | ||||
0.950893 | − | 0.309519i | \(-0.100168\pi\) | |||||||
\(14\) | 11.9109 | 0.227381 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.89531 | 0.0452393 | ||||||||
\(17\) | 58.4187i | 0.833449i | 0.909033 | + | 0.416724i | \(0.136822\pi\) | ||||
−0.909033 | + | 0.416724i | \(0.863178\pi\) | |||||||
\(18\) | 15.3141i | 0.200531i | ||||||||
\(19\) | 54.5969 | 0.659231 | 0.329615 | − | 0.944115i | \(-0.393081\pi\) | ||||
0.329615 | + | 0.944115i | \(0.393081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | − 63.6437i | − 0.616768i | ||||||||
\(23\) | − 161.675i | − 1.46572i | −0.680379 | − | 0.732860i | \(-0.738185\pi\) | ||||
0.680379 | − | 0.732860i | \(-0.261815\pi\) | |||||||
\(24\) | −66.8953 | −0.568956 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −49.3719 | −0.372409 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 35.7328i | 0.241174i | ||||||||
\(29\) | −137.581 | −0.880972 | −0.440486 | − | 0.897759i | \(-0.645194\pi\) | ||||
−0.440486 | + | 0.897759i | \(0.645194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 154.659 | 0.896053 | 0.448026 | − | 0.894020i | \(-0.352127\pi\) | ||||
0.448026 | + | 0.894020i | \(0.352127\pi\) | |||||||
\(32\) | − 183.314i | − 1.01268i | ||||||||
\(33\) | − 112.209i | − 0.591913i | ||||||||
\(34\) | 99.4031 | 0.501397 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −45.9422 | −0.212695 | ||||||||
\(37\) | − 350.125i | − 1.55568i | −0.628462 | − | 0.777840i | \(-0.716315\pi\) | ||||
0.628462 | − | 0.777840i | \(-0.283685\pi\) | |||||||
\(38\) | − 92.9000i | − 0.396589i | ||||||||
\(39\) | −87.0469 | −0.357401 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 353.769 | 1.34755 | 0.673773 | − | 0.738938i | \(-0.264673\pi\) | ||||
0.673773 | + | 0.738938i | \(0.264673\pi\) | |||||||
\(42\) | − 35.7328i | − 0.131278i | ||||||||
\(43\) | 518.156i | 1.83763i | 0.394689 | + | 0.918815i | \(0.370852\pi\) | ||||
−0.394689 | + | 0.918815i | \(0.629148\pi\) | |||||||
\(44\) | 190.931 | 0.654181 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −275.100 | −0.881767 | ||||||||
\(47\) | − 542.219i | − 1.68278i | −0.540427 | − | 0.841391i | \(-0.681737\pi\) | ||||
0.540427 | − | 0.841391i | \(-0.318263\pi\) | |||||||
\(48\) | − 8.68594i | − 0.0261189i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 175.256 | 0.481192 | ||||||||
\(52\) | − 148.116i | − 0.394999i | ||||||||
\(53\) | − 305.309i | − 0.791273i | −0.918407 | − | 0.395637i | \(-0.870524\pi\) | ||||
0.918407 | − | 0.395637i | \(-0.129476\pi\) | |||||||
\(54\) | 45.9422 | 0.115777 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 156.089 | 0.372469 | ||||||||
\(57\) | − 163.791i | − 0.380607i | ||||||||
\(58\) | 234.103i | 0.529987i | ||||||||
\(59\) | −14.6813 | −0.0323956 | −0.0161978 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161978 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −171.069 | −0.359067 | −0.179534 | − | 0.983752i | \(-0.557459\pi\) | ||||
−0.179534 | + | 0.983752i | \(0.557459\pi\) | |||||||
\(62\) | − 263.163i | − 0.539059i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | −288.758 | −0.563980 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −190.931 | −0.356091 | ||||||||
\(67\) | 551.956i | 1.00645i | 0.864155 | + | 0.503225i | \(0.167853\pi\) | ||||
−0.864155 | + | 0.503225i | \(0.832147\pi\) | |||||||
\(68\) | 298.209i | 0.531812i | ||||||||
\(69\) | −485.025 | −0.846234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.334 | −0.201142 | −0.100571 | − | 0.994930i | \(-0.532067\pi\) | ||||
−0.100571 | + | 0.994930i | \(0.532067\pi\) | |||||||
\(72\) | 200.686i | 0.328487i | ||||||||
\(73\) | − 284.659i | − 0.456395i | −0.973615 | − | 0.228198i | \(-0.926717\pi\) | ||||
0.973615 | − | 0.228198i | \(-0.0732832\pi\) | |||||||
\(74\) | −595.759 | −0.935887 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 278.700 | 0.420646 | ||||||||
\(77\) | 261.822i | 0.387498i | ||||||||
\(78\) | 148.116i | 0.215010i | ||||||||
\(79\) | −941.612 | −1.34101 | −0.670504 | − | 0.741906i | \(-0.733922\pi\) | ||||
−0.670504 | + | 0.741906i | \(0.733922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 601.959i | − 0.810674i | ||||||||
\(83\) | − 377.150i | − 0.498766i | −0.968405 | − | 0.249383i | \(-0.919772\pi\) | ||||
0.968405 | − | 0.249383i | \(-0.0802278\pi\) | |||||||
\(84\) | 107.198 | 0.139242 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 881.675 | 1.10551 | ||||||||
\(87\) | 412.744i | 0.508630i | ||||||||
\(88\) | − 834.031i | − 1.01032i | ||||||||
\(89\) | 677.725 | 0.807176 | 0.403588 | − | 0.914941i | \(-0.367763\pi\) | ||||
0.403588 | + | 0.914941i | \(0.367763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 203.109 | 0.233974 | ||||||||
\(92\) | − 825.300i | − 0.935255i | ||||||||
\(93\) | − 463.978i | − 0.517336i | ||||||||
\(94\) | −922.619 | −1.01235 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −549.942 | −0.584669 | ||||||||
\(97\) | − 1225.03i | − 1.28230i | −0.767414 | − | 0.641151i | \(-0.778457\pi\) | ||||
0.767414 | − | 0.641151i | \(-0.221543\pi\) | |||||||
\(98\) | 83.3765i | 0.0859419i | ||||||||
\(99\) | −336.628 | −0.341741 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −338.144 | −0.333134 | −0.166567 | − | 0.986030i | \(-0.553268\pi\) | ||||
−0.166567 | + | 0.986030i | \(0.553268\pi\) | |||||||
\(102\) | − 298.209i | − 0.289482i | ||||||||
\(103\) | 566.700i | 0.542122i | 0.962562 | + | 0.271061i | \(0.0873746\pi\) | ||||
−0.962562 | + | 0.271061i | \(0.912625\pi\) | |||||||
\(104\) | −647.003 | −0.610037 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −519.503 | −0.476024 | ||||||||
\(107\) | − 562.531i | − 0.508242i | −0.967172 | − | 0.254121i | \(-0.918214\pi\) | ||||
0.967172 | − | 0.254121i | \(-0.0817862\pi\) | |||||||
\(108\) | 137.827i | 0.122800i | ||||||||
\(109\) | −1830.79 | −1.60879 | −0.804396 | − | 0.594094i | \(-0.797511\pi\) | ||||
−0.804396 | + | 0.594094i | \(0.797511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1050.37 | −0.898173 | ||||||||
\(112\) | 20.2672i | 0.0170988i | ||||||||
\(113\) | 31.8032i | 0.0264761i | 0.999912 | + | 0.0132380i | \(0.00421392\pi\) | ||||
−0.999912 | + | 0.0132380i | \(0.995786\pi\) | |||||||
\(114\) | −278.700 | −0.228971 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −702.309 | −0.562136 | ||||||||
\(117\) | 261.141i | 0.206346i | ||||||||
\(118\) | 24.9811i | 0.0194890i | ||||||||
\(119\) | −408.931 | −0.315014 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67.9937 | 0.0510847 | ||||||||
\(122\) | 291.084i | 0.216012i | ||||||||
\(123\) | − 1061.31i | − 0.778006i | ||||||||
\(124\) | 789.488 | 0.571759 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −107.198 | −0.0757936 | ||||||||
\(127\) | 2220.81i | 1.55169i | 0.630921 | + | 0.775847i | \(0.282677\pi\) | ||||
−0.630921 | + | 0.775847i | \(0.717323\pi\) | |||||||
\(128\) | − 975.173i | − 0.673390i | ||||||||
\(129\) | 1554.47 | 1.06096 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 646.512 | 0.431191 | 0.215596 | − | 0.976483i | \(-0.430831\pi\) | ||||
0.215596 | + | 0.976483i | \(0.430831\pi\) | |||||||
\(132\) | − 572.794i | − 0.377692i | ||||||||
\(133\) | 382.178i | 0.249166i | ||||||||
\(134\) | 939.188 | 0.605474 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1302.65 | 0.821331 | ||||||||
\(137\) | − 896.009i | − 0.558768i | −0.960179 | − | 0.279384i | \(-0.909870\pi\) | ||||
0.960179 | − | 0.279384i | \(-0.0901303\pi\) | |||||||
\(138\) | 825.300i | 0.509088i | ||||||||
\(139\) | 2313.61 | 1.41178 | 0.705891 | − | 0.708320i | \(-0.250547\pi\) | ||||
0.705891 | + | 0.708320i | \(0.250547\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1626.66 | −0.971554 | ||||||||
\(142\) | 204.756i | 0.121005i | ||||||||
\(143\) | − 1085.27i | − 0.634652i | ||||||||
\(144\) | −26.0578 | −0.0150798 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −484.366 | −0.274564 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − 1787.28i | − 0.992658i | ||||||||
\(149\) | −819.337 | −0.450488 | −0.225244 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225244 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534.744 | 0.288191 | 0.144095 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144095 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(152\) | − 1217.43i | − 0.649646i | ||||||||
\(153\) | − 525.769i | − 0.277816i | ||||||||
\(154\) | 445.506 | 0.233116 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −444.347 | −0.228053 | ||||||||
\(157\) | 1564.76i | 0.795423i | 0.917511 | + | 0.397711i | \(0.130195\pi\) | ||||
−0.917511 | + | 0.397711i | \(0.869805\pi\) | |||||||
\(158\) | 1602.21i | 0.806741i | ||||||||
\(159\) | −915.928 | −0.456842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1131.72 | 0.553990 | ||||||||
\(162\) | − 137.827i | − 0.0668437i | ||||||||
\(163\) | 1114.31i | 0.535455i | 0.963495 | + | 0.267728i | \(0.0862727\pi\) | ||||
−0.963495 | + | 0.267728i | \(0.913727\pi\) | |||||||
\(164\) | 1805.88 | 0.859850 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −641.744 | −0.300054 | ||||||||
\(167\) | − 1774.47i | − 0.822231i | −0.911583 | − | 0.411115i | \(-0.865139\pi\) | ||||
0.911583 | − | 0.411115i | \(-0.134861\pi\) | |||||||
\(168\) | − 468.267i | − 0.215045i | ||||||||
\(169\) | 1355.09 | 0.616793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −491.372 | −0.219744 | ||||||||
\(172\) | 2645.02i | 1.17257i | ||||||||
\(173\) | 4215.88i | 1.85276i | 0.376590 | + | 0.926380i | \(0.377097\pi\) | ||||
−0.376590 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(174\) | 702.309 | 0.305988 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 108.294 | 0.0463804 | ||||||||
\(177\) | 44.0438i | 0.0187036i | ||||||||
\(178\) | − 1153.19i | − 0.485592i | ||||||||
\(179\) | 2430.70 | 1.01497 | 0.507483 | − | 0.861662i | \(-0.330576\pi\) | ||||
0.507483 | + | 0.861662i | \(0.330576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2700.91 | −1.10916 | −0.554578 | − | 0.832132i | \(-0.687120\pi\) | ||||
−0.554578 | + | 0.832132i | \(0.687120\pi\) | |||||||
\(182\) | − 345.603i | − 0.140757i | ||||||||
\(183\) | 513.206i | 0.207308i | ||||||||
\(184\) | −3605.10 | −1.44441 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −789.488 | −0.311226 | ||||||||
\(187\) | 2185.04i | 0.854472i | ||||||||
\(188\) | − 2767.86i | − 1.07376i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3611.10 | 1.36801 | 0.684005 | − | 0.729478i | \(-0.260237\pi\) | ||||
0.684005 | + | 0.729478i | \(0.260237\pi\) | |||||||
\(192\) | 866.273i | 0.325614i | ||||||||
\(193\) | 4468.33i | 1.66651i | 0.552886 | + | 0.833257i | \(0.313526\pi\) | ||||
−0.552886 | + | 0.833257i | \(0.686474\pi\) | |||||||
\(194\) | −2084.47 | −0.771425 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −250.130 | −0.0911551 | ||||||||
\(197\) | − 434.422i | − 0.157113i | −0.996910 | − | 0.0785566i | \(-0.974969\pi\) | ||||
0.996910 | − | 0.0785566i | \(-0.0250311\pi\) | |||||||
\(198\) | 572.794i | 0.205589i | ||||||||
\(199\) | 468.915 | 0.167038 | 0.0835189 | − | 0.996506i | \(-0.473384\pi\) | ||||
0.0835189 | + | 0.996506i | \(0.473384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1655.87 | 0.581074 | ||||||||
\(202\) | 575.372i | 0.200411i | ||||||||
\(203\) | − 963.069i | − 0.332976i | ||||||||
\(204\) | 894.628 | 0.307042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 964.275 | 0.326137 | ||||||||
\(207\) | 1455.07i | 0.488573i | ||||||||
\(208\) | − 84.0093i | − 0.0280048i | ||||||||
\(209\) | 2042.09 | 0.675859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3735.51 | 1.21878 | 0.609392 | − | 0.792869i | \(-0.291414\pi\) | ||||
0.609392 | + | 0.792869i | \(0.291414\pi\) | |||||||
\(212\) | − 1558.51i | − 0.504900i | ||||||||
\(213\) | 361.003i | 0.116129i | ||||||||
\(214\) | −957.182 | −0.305755 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 602.058 | 0.189652 | ||||||||
\(217\) | 1082.62i | 0.338676i | ||||||||
\(218\) | 3115.21i | 0.967838i | ||||||||
\(219\) | −853.978 | −0.263500 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1695.06 | 0.515936 | ||||||||
\(222\) | 1787.28i | 0.540334i | ||||||||
\(223\) | − 842.806i | − 0.253087i | −0.991961 | − | 0.126544i | \(-0.959612\pi\) | ||||
0.991961 | − | 0.126544i | \(-0.0403884\pi\) | |||||||
\(224\) | 1283.20 | 0.382756 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.1152 | 0.0159278 | ||||||||
\(227\) | 992.150i | 0.290094i | 0.989425 | + | 0.145047i | \(0.0463333\pi\) | ||||
−0.989425 | + | 0.145047i | \(0.953667\pi\) | |||||||
\(228\) | − 836.100i | − 0.242860i | ||||||||
\(229\) | 6411.39 | 1.85012 | 0.925059 | − | 0.379825i | \(-0.124016\pi\) | ||||
0.925059 | + | 0.379825i | \(0.124016\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 785.466 | 0.223722 | ||||||||
\(232\) | 3067.85i | 0.868164i | ||||||||
\(233\) | 2274.35i | 0.639476i | 0.947506 | + | 0.319738i | \(0.103595\pi\) | ||||
−0.947506 | + | 0.319738i | \(0.896405\pi\) | |||||||
\(234\) | 444.347 | 0.124136 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −74.9433 | −0.0206712 | ||||||||
\(237\) | 2824.84i | 0.774232i | ||||||||
\(238\) | 695.822i | 0.189510i | ||||||||
\(239\) | −2863.12 | −0.774893 | −0.387447 | − | 0.921892i | \(-0.626643\pi\) | ||||
−0.387447 | + | 0.921892i | \(0.626643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5364.23 | −1.43378 | −0.716889 | − | 0.697187i | \(-0.754435\pi\) | ||||
−0.716889 | + | 0.697187i | \(0.754435\pi\) | |||||||
\(242\) | − 115.696i | − 0.0307322i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −873.252 | −0.229116 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1805.88 | −0.468043 | ||||||||
\(247\) | − 1584.16i | − 0.408088i | ||||||||
\(248\) | − 3448.66i | − 0.883025i | ||||||||
\(249\) | −1131.45 | −0.287963 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5569.81 | 1.40065 | 0.700325 | − | 0.713824i | \(-0.253039\pi\) | ||||
0.700325 | + | 0.713824i | \(0.253039\pi\) | |||||||
\(252\) | − 321.595i | − 0.0803913i | ||||||||
\(253\) | − 6047.15i | − 1.50269i | ||||||||
\(254\) | 3778.85 | 0.933489 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3969.38 | −0.969087 | ||||||||
\(257\) | 2095.36i | 0.508580i | 0.967128 | + | 0.254290i | \(0.0818418\pi\) | ||||
−0.967128 | + | 0.254290i | \(0.918158\pi\) | |||||||
\(258\) | − 2645.02i | − 0.638264i | ||||||||
\(259\) | 2450.87 | 0.587992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1238.23 | 0.293657 | ||||||||
\(262\) | − 1100.08i | − 0.259402i | ||||||||
\(263\) | 7465.88i | 1.75044i | 0.483724 | + | 0.875220i | \(0.339284\pi\) | ||||
−0.483724 | + | 0.875220i | \(0.660716\pi\) | |||||||
\(264\) | −2502.09 | −0.583308 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 650.300 | 0.149896 | ||||||||
\(267\) | − 2033.17i | − 0.466023i | ||||||||
\(268\) | 2817.56i | 0.642202i | ||||||||
\(269\) | 6521.38 | 1.47812 | 0.739062 | − | 0.673637i | \(-0.235269\pi\) | ||||
0.739062 | + | 0.673637i | \(0.235269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2409.70 | 0.540144 | 0.270072 | − | 0.962840i | \(-0.412952\pi\) | ||||
0.270072 | + | 0.962840i | \(0.412952\pi\) | |||||||
\(272\) | 169.141i | 0.0377046i | ||||||||
\(273\) | − 609.328i | − 0.135085i | ||||||||
\(274\) | −1524.62 | −0.336151 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2475.90 | −0.539970 | ||||||||
\(277\) | − 2219.83i | − 0.481503i | −0.970587 | − | 0.240752i | \(-0.922606\pi\) | ||||
0.970587 | − | 0.240752i | \(-0.0773939\pi\) | |||||||
\(278\) | − 3936.75i | − 0.849319i | ||||||||
\(279\) | −1391.93 | −0.298684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5838.56 | 1.23950 | 0.619749 | − | 0.784800i | \(-0.287234\pi\) | ||||
0.619749 | + | 0.784800i | \(0.287234\pi\) | |||||||
\(282\) | 2767.86i | 0.584480i | ||||||||
\(283\) | 3645.04i | 0.765636i | 0.923824 | + | 0.382818i | \(0.125046\pi\) | ||||
−0.923824 | + | 0.382818i | \(0.874954\pi\) | |||||||
\(284\) | −614.269 | −0.128346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1846.66 | −0.381802 | ||||||||
\(287\) | 2476.38i | 0.509325i | ||||||||
\(288\) | 1649.83i | 0.337559i | ||||||||
\(289\) | 1500.25 | 0.305363 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3675.10 | −0.740338 | ||||||||
\(292\) | − 1453.10i | − 0.291219i | ||||||||
\(293\) | − 3777.91i | − 0.753268i | −0.926362 | − | 0.376634i | \(-0.877081\pi\) | ||||
0.926362 | − | 0.376634i | \(-0.122919\pi\) | |||||||
\(294\) | 250.130 | 0.0496186 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7807.24 | −1.53306 | ||||||||
\(297\) | 1009.88i | 0.197304i | ||||||||
\(298\) | 1394.15i | 0.271011i | ||||||||
\(299\) | −4691.10 | −0.907336 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3627.09 | −0.694559 | ||||||||
\(302\) | − 909.900i | − 0.173374i | ||||||||
\(303\) | 1014.43i | 0.192335i | ||||||||
\(304\) | 158.075 | 0.0298231 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −894.628 | −0.167132 | ||||||||
\(307\) | − 4799.64i | − 0.892281i | −0.894963 | − | 0.446140i | \(-0.852798\pi\) | ||||
0.894963 | − | 0.446140i | \(-0.147202\pi\) | |||||||
\(308\) | 1336.52i | 0.247257i | ||||||||
\(309\) | 1700.10 | 0.312994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 580.113 | 0.105772 | 0.0528861 | − | 0.998601i | \(-0.483158\pi\) | ||||
0.0528861 | + | 0.998601i | \(0.483158\pi\) | |||||||
\(312\) | 1941.01i | 0.352205i | ||||||||
\(313\) | 6114.78i | 1.10424i | 0.833764 | + | 0.552121i | \(0.186182\pi\) | ||||
−0.833764 | + | 0.552121i | \(0.813818\pi\) | |||||||
\(314\) | 2662.53 | 0.478521 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4806.64 | −0.855679 | ||||||||
\(317\) | − 4300.63i | − 0.761979i | −0.924579 | − | 0.380989i | \(-0.875583\pi\) | ||||
0.924579 | − | 0.380989i | \(-0.124417\pi\) | |||||||
\(318\) | 1558.51i | 0.274833i | ||||||||
\(319\) | −5145.97 | −0.903194 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1687.59 | −0.293434 | ||||||||
\(322\) | − 1925.70i | − 0.333277i | ||||||||
\(323\) | 3189.48i | 0.549435i | ||||||||
\(324\) | 413.480 | 0.0708984 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1896.06 | 0.322126 | ||||||||
\(327\) | 5492.38i | 0.928836i | ||||||||
\(328\) | − 7888.49i | − 1.32795i | ||||||||
\(329\) | 3795.53 | 0.636032 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6687.54 | −1.11051 | −0.555257 | − | 0.831679i | \(-0.687380\pi\) | ||||
−0.555257 | + | 0.831679i | \(0.687380\pi\) | |||||||
\(332\) | − 1925.23i | − 0.318256i | ||||||||
\(333\) | 3151.12i | 0.518560i | ||||||||
\(334\) | −3019.37 | −0.494648 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 60.8016 | 0.00987202 | ||||||||
\(337\) | 5869.28i | 0.948723i | 0.880330 | + | 0.474362i | \(0.157321\pi\) | ||||
−0.880330 | + | 0.474362i | \(0.842679\pi\) | |||||||
\(338\) | − 2305.78i | − 0.371058i | ||||||||
\(339\) | 95.4097 | 0.0152860 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5784.74 | 0.918655 | ||||||||
\(342\) | 836.100i | 0.132196i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | 11554.1 | 1.81091 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7173.58 | 1.11461 | ||||||||
\(347\) | 1937.22i | 0.299699i | 0.988709 | + | 0.149850i | \(0.0478790\pi\) | ||||
−0.988709 | + | 0.149850i | \(0.952121\pi\) | |||||||
\(348\) | 2106.93i | 0.324549i | ||||||||
\(349\) | 9748.82 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 783.422 | 0.119134 | ||||||||
\(352\) | − 6856.52i | − 1.03822i | ||||||||
\(353\) | 4576.61i | 0.690052i | 0.938593 | + | 0.345026i | \(0.112130\pi\) | ||||
−0.938593 | + | 0.345026i | \(0.887870\pi\) | |||||||
\(354\) | 74.9433 | 0.0112520 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3459.57 | 0.515048 | ||||||||
\(357\) | 1226.79i | 0.181873i | ||||||||
\(358\) | − 4135.98i | − 0.610596i | ||||||||
\(359\) | −10849.9 | −1.59509 | −0.797546 | − | 0.603258i | \(-0.793869\pi\) | ||||
−0.797546 | + | 0.603258i | \(0.793869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3878.18 | −0.565415 | ||||||||
\(362\) | 4595.77i | 0.667261i | ||||||||
\(363\) | − 203.981i | − 0.0294938i | ||||||||
\(364\) | 1036.81 | 0.149296 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 873.252 | 0.124715 | ||||||||
\(367\) | 11467.7i | 1.63108i | 0.578699 | + | 0.815541i | \(0.303561\pi\) | ||||
−0.578699 | + | 0.815541i | \(0.696439\pi\) | |||||||
\(368\) | − 468.100i | − 0.0663081i | ||||||||
\(369\) | −3183.92 | −0.449182 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2137.17 | 0.299073 | ||||||||
\(372\) | − 2368.46i | − 0.330105i | ||||||||
\(373\) | − 539.982i | − 0.0749576i | −0.999297 | − | 0.0374788i | \(-0.988067\pi\) | ||||
0.999297 | − | 0.0374788i | \(-0.0119327\pi\) | |||||||
\(374\) | 3717.99 | 0.514044 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12090.6 | −1.65832 | ||||||||
\(377\) | 3992.01i | 0.545355i | ||||||||
\(378\) | 321.595i | 0.0437595i | ||||||||
\(379\) | −8577.57 | −1.16253 | −0.581267 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581267 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6662.44 | 0.895871 | ||||||||
\(382\) | − 6144.51i | − 0.822985i | ||||||||
\(383\) | − 8627.96i | − 1.15109i | −0.817770 | − | 0.575546i | \(-0.804790\pi\) | ||||
0.817770 | − | 0.575546i | \(-0.195210\pi\) | |||||||
\(384\) | −2925.52 | −0.388782 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7603.13 | 1.00256 | ||||||||
\(387\) | − 4663.41i | − 0.612543i | ||||||||
\(388\) | − 6253.42i | − 0.818219i | ||||||||
\(389\) | −9234.06 | −1.20356 | −0.601781 | − | 0.798661i | \(-0.705542\pi\) | ||||
−0.601781 | + | 0.798661i | \(0.705542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9444.85 | 1.22160 | ||||||||
\(392\) | 1092.62i | 0.140780i | ||||||||
\(393\) | − 1939.54i | − 0.248948i | ||||||||
\(394\) | −739.196 | −0.0945182 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1718.38 | −0.218060 | ||||||||
\(397\) | 11618.0i | 1.46874i | 0.678747 | + | 0.734372i | \(0.262523\pi\) | ||||
−0.678747 | + | 0.734372i | \(0.737477\pi\) | |||||||
\(398\) | − 797.889i | − 0.100489i | ||||||||
\(399\) | 1146.53 | 0.143856 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11157.1 | 1.38942 | 0.694711 | − | 0.719289i | \(-0.255532\pi\) | ||||
0.694711 | + | 0.719289i | \(0.255532\pi\) | |||||||
\(402\) | − 2817.56i | − 0.349570i | ||||||||
\(403\) | − 4487.54i | − 0.554690i | ||||||||
\(404\) | −1726.12 | −0.212568 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1638.72 | −0.200316 | ||||||||
\(407\) | − 13095.8i | − 1.59492i | ||||||||
\(408\) | − 3907.94i | − 0.474196i | ||||||||
\(409\) | 7428.08 | 0.898031 | 0.449015 | − | 0.893524i | \(-0.351775\pi\) | ||||
0.449015 | + | 0.893524i | \(0.351775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2688.03 | −0.322605 | ||||||||
\(412\) | 2892.83i | 0.345921i | ||||||||
\(413\) | − 102.769i | − 0.0122444i | ||||||||
\(414\) | 2475.90 | 0.293922 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5318.97 | −0.626885 | ||||||||
\(417\) | − 6940.83i | − 0.815093i | ||||||||
\(418\) | − 3474.75i | − 0.406592i | ||||||||
\(419\) | −9644.74 | −1.12453 | −0.562263 | − | 0.826959i | \(-0.690069\pi\) | ||||
−0.562263 | + | 0.826959i | \(0.690069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9918.18 | 1.14818 | 0.574088 | − | 0.818793i | \(-0.305357\pi\) | ||||
0.574088 | + | 0.818793i | \(0.305357\pi\) | |||||||
\(422\) | − 6356.21i | − 0.733212i | ||||||||
\(423\) | 4879.97i | 0.560927i | ||||||||
\(424\) | −6807.92 | −0.779769 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 614.269 | 0.0698625 | ||||||||
\(427\) | − 1197.48i | − 0.135715i | ||||||||
\(428\) | − 2871.54i | − 0.324302i | ||||||||
\(429\) | −3255.82 | −0.366417 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16324.1 | −1.82437 | −0.912185 | − | 0.409779i | \(-0.865606\pi\) | ||||
−0.912185 | + | 0.409779i | \(0.865606\pi\) | |||||||
\(432\) | 78.1735i | 0.00870630i | ||||||||
\(433\) | 5168.75i | 0.573659i | 0.957982 | + | 0.286829i | \(0.0926012\pi\) | ||||
−0.957982 | + | 0.286829i | \(0.907399\pi\) | |||||||
\(434\) | 1842.14 | 0.203745 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9345.63 | −1.02655 | ||||||||
\(437\) | − 8826.95i | − 0.966248i | ||||||||
\(438\) | 1453.10i | 0.158520i | ||||||||
\(439\) | −18339.0 | −1.99378 | −0.996892 | − | 0.0787782i | \(-0.974898\pi\) | ||||
−0.996892 | + | 0.0787782i | \(0.974898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 2884.24i | − 0.310383i | ||||||||
\(443\) | 1613.28i | 0.173023i | 0.996251 | + | 0.0865113i | \(0.0275719\pi\) | ||||
−0.996251 | + | 0.0865113i | \(0.972428\pi\) | |||||||
\(444\) | −5361.83 | −0.573111 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1434.09 | −0.152256 | ||||||||
\(447\) | 2458.01i | 0.260089i | ||||||||
\(448\) | − 2021.30i | − 0.213164i | ||||||||
\(449\) | 886.750 | 0.0932034 | 0.0466017 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466017 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13232.1 | 1.38154 | ||||||||
\(452\) | 162.345i | 0.0168940i | ||||||||
\(453\) | − 1604.23i | − 0.166387i | ||||||||
\(454\) | 1688.21 | 0.174518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3652.28 | −0.375073 | ||||||||
\(457\) | 7391.22i | 0.756557i | 0.925692 | + | 0.378279i | \(0.123484\pi\) | ||||
−0.925692 | + | 0.378279i | \(0.876516\pi\) | |||||||
\(458\) | − 10909.4i | − 1.11302i | ||||||||
\(459\) | −1577.31 | −0.160397 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7133.35 | −0.720679 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(462\) | − 1336.52i | − 0.134590i | ||||||||
\(463\) | − 14461.8i | − 1.45162i | −0.687897 | − | 0.725808i | \(-0.741466\pi\) | ||||
0.687897 | − | 0.725808i | \(-0.258534\pi\) | |||||||
\(464\) | −398.341 | −0.0398546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3869.95 | 0.384704 | ||||||||
\(467\) | − 16393.5i | − 1.62441i | −0.583370 | − | 0.812206i | \(-0.698266\pi\) | ||||
0.583370 | − | 0.812206i | \(-0.301734\pi\) | |||||||
\(468\) | 1333.04i | 0.131666i | ||||||||
\(469\) | −3863.69 | −0.380403 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4694.28 | 0.459238 | ||||||||
\(472\) | 327.370i | 0.0319246i | ||||||||
\(473\) | 19380.7i | 1.88398i | ||||||||
\(474\) | 4806.64 | 0.465772 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2087.47 | −0.201006 | ||||||||
\(477\) | 2747.78i | 0.263758i | ||||||||
\(478\) | 4871.77i | 0.466171i | ||||||||
\(479\) | 12991.4 | 1.23923 | 0.619617 | − | 0.784904i | \(-0.287288\pi\) | ||||
0.619617 | + | 0.784904i | \(0.287288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10159.1 | −0.963025 | ||||||||
\(482\) | 9127.57i | 0.862551i | ||||||||
\(483\) | − 3395.17i | − 0.319846i | ||||||||
\(484\) | 347.087 | 0.0325964 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −413.480 | −0.0385922 | ||||||||
\(487\) | − 12863.5i | − 1.19692i | −0.801152 | − | 0.598461i | \(-0.795779\pi\) | ||||
0.801152 | − | 0.598461i | \(-0.204221\pi\) | |||||||
\(488\) | 3814.57i | 0.353847i | ||||||||
\(489\) | 3342.92 | 0.309145 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4898.10 | −0.450200 | −0.225100 | − | 0.974336i | \(-0.572271\pi\) | ||||
−0.225100 | + | 0.974336i | \(0.572271\pi\) | |||||||
\(492\) | − 5417.63i | − 0.496435i | ||||||||
\(493\) | − 8037.32i | − 0.734245i | ||||||||
\(494\) | −2695.55 | −0.245503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 447.787 | 0.0405368 | ||||||||
\(497\) | − 842.340i | − 0.0760244i | ||||||||
\(498\) | 1925.23i | 0.173236i | ||||||||
\(499\) | −10308.0 | −0.924746 | −0.462373 | − | 0.886686i | \(-0.653002\pi\) | ||||
−0.462373 | + | 0.886686i | \(0.653002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5323.41 | −0.474715 | ||||||||
\(502\) | − 9477.37i | − 0.842621i | ||||||||
\(503\) | 15119.6i | 1.34026i | 0.742244 | + | 0.670130i | \(0.233762\pi\) | ||||
−0.742244 | + | 0.670130i | \(0.766238\pi\) | |||||||
\(504\) | −1404.80 | −0.124156 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10289.6 | −0.904009 | ||||||||
\(507\) | − 4065.28i | − 0.356105i | ||||||||
\(508\) | 11336.6i | 0.990114i | ||||||||
\(509\) | −14183.8 | −1.23514 | −0.617571 | − | 0.786515i | \(-0.711883\pi\) | ||||
−0.617571 | + | 0.786515i | \(0.711883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1992.62 | 0.172501 | ||||||||
\(512\) | − 1047.24i | − 0.0903943i | ||||||||
\(513\) | 1474.12i | 0.126869i | ||||||||
\(514\) | 3565.39 | 0.305958 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7935.07 | 0.676981 | ||||||||
\(517\) | − 20280.7i | − 1.72523i | ||||||||
\(518\) | − 4170.32i | − 0.353732i | ||||||||
\(519\) | 12647.6 | 1.06969 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7464.08 | −0.627653 | −0.313827 | − | 0.949480i | \(-0.601611\pi\) | ||||
−0.313827 | + | 0.949480i | \(0.601611\pi\) | |||||||
\(522\) | − 2106.93i | − 0.176662i | ||||||||
\(523\) | 16642.9i | 1.39148i | 0.718295 | + | 0.695739i | \(0.244923\pi\) | ||||
−0.718295 | + | 0.695739i | \(0.755077\pi\) | |||||||
\(524\) | 3300.24 | 0.275137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12703.7 | 1.05305 | ||||||||
\(527\) | 9035.01i | 0.746814i | ||||||||
\(528\) | − 324.881i | − 0.0267777i | ||||||||
\(529\) | −13971.8 | −1.14834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 132.132 | 0.0107985 | ||||||||
\(532\) | 1950.90i | 0.158989i | ||||||||
\(533\) | − 10264.8i | − 0.834181i | ||||||||
\(534\) | −3459.57 | −0.280356 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12307.8 | 0.991818 | ||||||||
\(537\) | − 7292.09i | − 0.585991i | ||||||||
\(538\) | − 11096.5i | − 0.889230i | ||||||||
\(539\) | −1832.75 | −0.146461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 67.8755 | 0.00539408 | 0.00269704 | − | 0.999996i | \(-0.499142\pi\) | ||||
0.00269704 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(542\) | − 4100.26i | − 0.324947i | ||||||||
\(543\) | 8102.74i | 0.640372i | ||||||||
\(544\) | 10709.0 | 0.844014 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1036.81 | −0.0812662 | ||||||||
\(547\) | − 9212.91i | − 0.720138i | −0.932926 | − | 0.360069i | \(-0.882753\pi\) | ||||
0.932926 | − | 0.360069i | \(-0.117247\pi\) | |||||||
\(548\) | − 4573.85i | − 0.356542i | ||||||||
\(549\) | 1539.62 | 0.119689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7511.51 | −0.580764 | ||||||||
\(552\) | 10815.3i | 0.833931i | ||||||||
\(553\) | − 6591.29i | − 0.506854i | ||||||||
\(554\) | −3777.17 | −0.289669 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11810.2 | 0.900838 | ||||||||
\(557\) | 16699.6i | 1.27035i | 0.772370 | + | 0.635173i | \(0.219071\pi\) | ||||
−0.772370 | + | 0.635173i | \(0.780929\pi\) | |||||||
\(558\) | 2368.46i | 0.179686i | ||||||||
\(559\) | 15034.6 | 1.13756 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6555.13 | 0.493329 | ||||||||
\(562\) | − 9934.67i | − 0.745674i | ||||||||
\(563\) | − 14772.8i | − 1.10586i | −0.833227 | − | 0.552931i | \(-0.813509\pi\) | ||||
0.833227 | − | 0.552931i | \(-0.186491\pi\) | |||||||
\(564\) | −8303.57 | −0.619935 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6202.26 | 0.460601 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 2683.27i | 0.198217i | ||||||||
\(569\) | −5663.76 | −0.417289 | −0.208644 | − | 0.977992i | \(-0.566905\pi\) | ||||
−0.208644 | + | 0.977992i | \(0.566905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5579.58 | 0.408929 | 0.204464 | − | 0.978874i | \(-0.434455\pi\) | ||||
0.204464 | + | 0.978874i | \(0.434455\pi\) | |||||||
\(572\) | − 5539.99i | − 0.404962i | ||||||||
\(573\) | − 10833.3i | − 0.789821i | ||||||||
\(574\) | 4213.72 | 0.306406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2598.82 | 0.187993 | ||||||||
\(577\) | − 2301.23i | − 0.166034i | −0.996548 | − | 0.0830170i | \(-0.973544\pi\) | ||||
0.996548 | − | 0.0830170i | \(-0.0264556\pi\) | |||||||
\(578\) | − 2552.77i | − 0.183704i | ||||||||
\(579\) | 13405.0 | 0.962162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2640.05 | 0.188516 | ||||||||
\(582\) | 6253.42i | 0.445382i | ||||||||
\(583\) | − 11419.5i | − 0.811232i | ||||||||
\(584\) | −6347.46 | −0.449760 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6428.34 | −0.453161 | ||||||||
\(587\) | − 16470.4i | − 1.15810i | −0.815291 | − | 0.579052i | \(-0.803423\pi\) | ||||
0.815291 | − | 0.579052i | \(-0.196577\pi\) | |||||||
\(588\) | 750.389i | 0.0526284i | ||||||||
\(589\) | 8443.92 | 0.590706 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1303.27 | −0.0907093 | ||||||||
\(592\) | − 1013.72i | − 0.0703779i | ||||||||
\(593\) | 13570.0i | 0.939715i | 0.882742 | + | 0.469858i | \(0.155695\pi\) | ||||
−0.882742 | + | 0.469858i | \(0.844305\pi\) | |||||||
\(594\) | 1718.38 | 0.118697 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4182.46 | −0.287450 | ||||||||
\(597\) | − 1406.75i | − 0.0964393i | ||||||||
\(598\) | 7982.20i | 0.545847i | ||||||||
\(599\) | −27814.1 | −1.89725 | −0.948625 | − | 0.316403i | \(-0.897525\pi\) | ||||
−0.948625 | + | 0.316403i | \(0.897525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20646.1 | 1.40128 | 0.700641 | − | 0.713514i | \(-0.252898\pi\) | ||||
0.700641 | + | 0.713514i | \(0.252898\pi\) | |||||||
\(602\) | 6171.72i | 0.417842i | ||||||||
\(603\) | − 4967.61i | − 0.335483i | ||||||||
\(604\) | 2729.70 | 0.183891 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1726.12 | 0.115707 | ||||||||
\(607\) | 3315.28i | 0.221686i | 0.993838 | + | 0.110843i | \(0.0353550\pi\) | ||||
−0.993838 | + | 0.110843i | \(0.964645\pi\) | |||||||
\(608\) | − 10008.4i | − 0.667588i | ||||||||
\(609\) | −2889.21 | −0.192244 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15732.8 | −1.04170 | ||||||||
\(612\) | − 2683.88i | − 0.177271i | ||||||||
\(613\) | 11113.9i | 0.732278i | 0.930560 | + | 0.366139i | \(0.119320\pi\) | ||||
−0.930560 | + | 0.366139i | \(0.880680\pi\) | |||||||
\(614\) | −8166.89 | −0.536790 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5838.22 | 0.381865 | ||||||||
\(617\) | 7871.34i | 0.513595i | 0.966465 | + | 0.256797i | \(0.0826673\pi\) | ||||
−0.966465 | + | 0.256797i | \(0.917333\pi\) | |||||||
\(618\) | − 2892.83i | − 0.188295i | ||||||||
\(619\) | 19107.1 | 1.24068 | 0.620339 | − | 0.784334i | \(-0.286995\pi\) | ||||
0.620339 | + | 0.784334i | \(0.286995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4365.22 | 0.282078 | ||||||||
\(622\) | − 987.098i | − 0.0636319i | ||||||||
\(623\) | 4744.07i | 0.305084i | ||||||||
\(624\) | −252.028 | −0.0161686 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10404.7 | 0.664305 | ||||||||
\(627\) | − 6126.28i | − 0.390208i | ||||||||
\(628\) | 7987.60i | 0.507548i | ||||||||
\(629\) | 20453.9 | 1.29658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25769.9 | −1.62580 | −0.812902 | − | 0.582401i | \(-0.802113\pi\) | ||||
−0.812902 | + | 0.582401i | \(0.802113\pi\) | |||||||
\(632\) | 20996.5i | 1.32151i | ||||||||
\(633\) | − 11206.5i | − 0.703665i | ||||||||
\(634\) | −7317.79 | −0.458401 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4675.53 | −0.291504 | ||||||||
\(637\) | 1421.77i | 0.0884339i | ||||||||
\(638\) | 8756.19i | 0.543355i | ||||||||
\(639\) | 1083.01 | 0.0670472 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1954.61 | −0.120440 | −0.0602202 | − | 0.998185i | \(-0.519180\pi\) | ||||
−0.0602202 | + | 0.998185i | \(0.519180\pi\) | |||||||
\(642\) | 2871.54i | 0.176528i | ||||||||
\(643\) | 19396.5i | 1.18961i | 0.803868 | + | 0.594807i | \(0.202772\pi\) | ||||
−0.803868 | + | 0.594807i | \(0.797228\pi\) | |||||||
\(644\) | 5777.10 | 0.353493 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5427.10 | 0.330536 | ||||||||
\(647\) | 31264.3i | 1.89973i | 0.312661 | + | 0.949865i | \(0.398780\pi\) | ||||
−0.312661 | + | 0.949865i | \(0.601220\pi\) | |||||||
\(648\) | − 1806.17i | − 0.109496i | ||||||||
\(649\) | −549.126 | −0.0332127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3247.85 | 0.195535 | ||||||||
\(652\) | 5688.18i | 0.341666i | ||||||||
\(653\) | − 6442.75i | − 0.386102i | −0.981189 | − | 0.193051i | \(-0.938162\pi\) | ||||
0.981189 | − | 0.193051i | \(-0.0618382\pi\) | |||||||
\(654\) | 9345.63 | 0.558781 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1024.27 | 0.0609620 | ||||||||
\(657\) | 2561.93i | 0.152132i | ||||||||
\(658\) | − 6458.33i | − 0.382632i | ||||||||
\(659\) | 3584.70 | 0.211897 | 0.105949 | − | 0.994372i | \(-0.466212\pi\) | ||||
0.105949 | + | 0.994372i | \(0.466212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6294.43 | 0.370386 | 0.185193 | − | 0.982702i | \(-0.440709\pi\) | ||||
0.185193 | + | 0.982702i | \(0.440709\pi\) | |||||||
\(662\) | 11379.3i | 0.668078i | ||||||||
\(663\) | − 5085.17i | − 0.297876i | ||||||||
\(664\) | −8409.85 | −0.491514 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5361.83 | 0.311962 | ||||||||
\(667\) | 22243.4i | 1.29126i | ||||||||
\(668\) | − 9058.11i | − 0.524654i | ||||||||
\(669\) | −2528.42 | −0.146120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6398.51 | −0.368125 | ||||||||
\(672\) | − 3849.60i | − 0.220984i | ||||||||
\(673\) | 10233.9i | 0.586162i | 0.956088 | + | 0.293081i | \(0.0946806\pi\) | ||||
−0.956088 | + | 0.293081i | \(0.905319\pi\) | |||||||
\(674\) | 9986.94 | 0.570745 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6917.33 | 0.393567 | ||||||||
\(677\) | − 7100.75i | − 0.403108i | −0.979477 | − | 0.201554i | \(-0.935401\pi\) | ||||
0.979477 | − | 0.201554i | \(-0.0645992\pi\) | |||||||
\(678\) | − 162.345i | − 0.00919593i | ||||||||
\(679\) | 8575.24 | 0.484665 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2976.45 | 0.167486 | ||||||||
\(682\) | − 9843.10i | − 0.552657i | ||||||||
\(683\) | 35274.6i | 1.97620i | 0.153813 | + | 0.988100i | \(0.450845\pi\) | ||||
−0.153813 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(684\) | −2508.30 | −0.140215 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −583.636 | −0.0324830 | ||||||||
\(687\) | − 19234.2i | − 1.06817i | ||||||||
\(688\) | 1500.22i | 0.0831330i | ||||||||
\(689\) | −8858.74 | −0.489828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4945.12 | 0.272245 | 0.136122 | − | 0.990692i | \(-0.456536\pi\) | ||||
0.136122 | + | 0.990692i | \(0.456536\pi\) | |||||||
\(692\) | 21520.8i | 1.18222i | ||||||||
\(693\) | − 2356.40i | − 0.129166i | ||||||||
\(694\) | 3296.31 | 0.180297 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9203.54 | 0.501235 | ||||||||
\(697\) | 20666.7i | 1.12311i | ||||||||
\(698\) | − 16588.2i | − 0.899532i | ||||||||
\(699\) | 6823.06 | 0.369201 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15300.4 | −0.824379 | −0.412190 | − | 0.911098i | \(-0.635236\pi\) | ||||
−0.412190 | + | 0.911098i | \(0.635236\pi\) | |||||||
\(702\) | − 1333.04i | − 0.0716701i | ||||||||
\(703\) | − 19115.7i | − 1.02555i | ||||||||
\(704\) | −10800.4 | −0.578206 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7787.38 | 0.415130 | ||||||||
\(707\) | − 2367.01i | − 0.125913i | ||||||||
\(708\) | 224.830i | 0.0119345i | ||||||||
\(709\) | 28297.4 | 1.49892 | 0.749458 | − | 0.662052i | \(-0.230314\pi\) | ||||
0.749458 | + | 0.662052i | \(0.230314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8474.51 | 0.447003 | ||||||||
\(712\) | − 15112.2i | − 0.795441i | ||||||||
\(713\) | − 25004.5i | − 1.31336i | ||||||||
\(714\) | 2087.47 | 0.109414 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12407.9 | 0.647635 | ||||||||
\(717\) | 8589.35i | 0.447385i | ||||||||
\(718\) | 18461.9i | 0.959597i | ||||||||
\(719\) | −8548.96 | −0.443425 | −0.221712 | − | 0.975112i | \(-0.571165\pi\) | ||||
−0.221712 | + | 0.975112i | \(0.571165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3966.90 | −0.204903 | ||||||||
\(722\) | 6598.97i | 0.340150i | ||||||||
\(723\) | 16092.7i | 0.827792i | ||||||||
\(724\) | −13787.3 | −0.707737 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −347.087 | −0.0177432 | ||||||||
\(727\) | 14345.3i | 0.731827i | 0.930649 | + | 0.365913i | \(0.119243\pi\) | ||||
−0.930649 | + | 0.365913i | \(0.880757\pi\) | |||||||
\(728\) | − 4529.02i | − 0.230572i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30270.0 | −1.53157 | ||||||||
\(732\) | 2619.76i | 0.132280i | ||||||||
\(733\) | 22624.0i | 1.14002i | 0.821637 | + | 0.570012i | \(0.193061\pi\) | ||||
−0.821637 | + | 0.570012i | \(0.806939\pi\) | |||||||
\(734\) | 19512.9 | 0.981248 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29637.3 | −1.48430 | ||||||||
\(737\) | 20644.9i | 1.03184i | ||||||||
\(738\) | 5417.63i | 0.270225i | ||||||||
\(739\) | −14837.3 | −0.738566 | −0.369283 | − | 0.929317i | \(-0.620397\pi\) | ||||
−0.369283 | + | 0.929317i | \(0.620397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4752.49 | −0.235610 | ||||||||
\(742\) | − 3636.52i | − 0.179920i | ||||||||
\(743\) | − 13073.1i | − 0.645497i | −0.946485 | − | 0.322749i | \(-0.895393\pi\) | ||||
0.946485 | − | 0.322749i | \(-0.104607\pi\) | |||||||
\(744\) | −10346.0 | −0.509815 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −918.813 | −0.0450940 | ||||||||
\(747\) | 3394.35i | 0.166255i | ||||||||
\(748\) | 11154.0i | 0.545226i | ||||||||
\(749\) | 3937.72 | 0.192098 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16213.3 | 0.787791 | 0.393895 | − | 0.919155i | \(-0.371127\pi\) | ||||
0.393895 | + | 0.919155i | \(0.371127\pi\) | |||||||
\(752\) | − 1569.89i | − 0.0761278i | ||||||||
\(753\) | − 16709.4i | − 0.808665i | ||||||||
\(754\) | 6792.65 | 0.328082 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −964.786 | −0.0464139 | ||||||||
\(757\) | 19903.9i | 0.955642i | 0.878457 | + | 0.477821i | \(0.158573\pi\) | ||||
−0.878457 | + | 0.477821i | \(0.841427\pi\) | |||||||
\(758\) | 14595.3i | 0.699372i | ||||||||
\(759\) | −18141.4 | −0.867580 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30125.5 | −1.43502 | −0.717509 | − | 0.696549i | \(-0.754718\pi\) | ||||
−0.717509 | + | 0.696549i | \(0.754718\pi\) | |||||||
\(762\) | − 11336.6i | − 0.538950i | ||||||||
\(763\) | − 12815.6i | − 0.608066i | ||||||||
\(764\) | 18433.5 | 0.872907 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14681.0 | −0.692489 | ||||||||
\(767\) | 425.986i | 0.0200541i | ||||||||
\(768\) | 11908.1i | 0.559503i | ||||||||
\(769\) | 36049.1 | 1.69046 | 0.845230 | − | 0.534402i | \(-0.179463\pi\) | ||||
0.845230 | + | 0.534402i | \(0.179463\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6286.09 | 0.293629 | ||||||||
\(772\) | 22809.4i | 1.06338i | ||||||||
\(773\) | 9644.77i | 0.448769i | 0.974501 | + | 0.224384i | \(0.0720371\pi\) | ||||
−0.974501 | + | 0.224384i | \(0.927963\pi\) | |||||||
\(774\) | −7935.07 | −0.368502 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27316.4 | −1.26366 | ||||||||
\(777\) | − 7352.62i | − 0.339477i | ||||||||
\(778\) | 15712.3i | 0.724054i | ||||||||
\(779\) | 19314.7 | 0.888344 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4500.88 | −0.206215 | ||||||||
\(782\) | − 16071.0i | − 0.734908i | ||||||||
\(783\) | − 3714.69i | − 0.169543i | ||||||||
\(784\) | −141.870 | −0.00646275 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3300.24 | −0.149766 | ||||||||
\(787\) | − 25218.6i | − 1.14224i | −0.820865 | − | 0.571122i | \(-0.806508\pi\) | ||||
0.820865 | − | 0.571122i | \(-0.193492\pi\) | |||||||
\(788\) | − 2217.59i | − 0.100252i | ||||||||
\(789\) | 22397.6 | 1.01062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −222.623 | −0.0100070 | ||||||||
\(792\) | 7506.28i | 0.336773i | ||||||||
\(793\) | 4963.67i | 0.222276i | ||||||||
\(794\) | 19768.8 | 0.883586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2393.67 | 0.106584 | ||||||||
\(797\) | 32042.3i | 1.42409i | 0.702135 | + | 0.712044i | \(0.252230\pi\) | ||||
−0.702135 | + | 0.712044i | \(0.747770\pi\) | |||||||
\(798\) | − 1950.90i | − 0.0865427i | ||||||||
\(799\) | 31675.7 | 1.40251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6099.52 | −0.269059 | ||||||||
\(802\) | − 18984.5i | − 0.835867i | ||||||||
\(803\) | − 10647.1i | − 0.467908i | ||||||||
\(804\) | 8452.69 | 0.370775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7635.82 | −0.333698 | ||||||||
\(807\) | − 19564.1i | − 0.853396i | ||||||||
\(808\) | 7540.07i | 0.328291i | ||||||||
\(809\) | −3427.90 | −0.148972 | −0.0744860 | − | 0.997222i | \(-0.523732\pi\) | ||||
−0.0744860 | + | 0.997222i | \(0.523732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23094.4 | 0.999943 | 0.499972 | − | 0.866042i | \(-0.333344\pi\) | ||||
0.499972 | + | 0.866042i | \(0.333344\pi\) | |||||||
\(812\) | − 4916.16i | − 0.212467i | ||||||||
\(813\) | − 7229.11i | − 0.311852i | ||||||||
\(814\) | −22283.3 | −0.959494 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 507.422 | 0.0217688 | ||||||||
\(817\) | 28289.7i | 1.21142i | ||||||||
\(818\) | − 12639.3i | − 0.540249i | ||||||||
\(819\) | −1827.98 | −0.0779914 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 474.741 | 0.0201810 | 0.0100905 | − | 0.999949i | \(-0.496788\pi\) | ||||
0.0100905 | + | 0.999949i | \(0.496788\pi\) | |||||||
\(822\) | 4573.85i | 0.194077i | ||||||||
\(823\) | − 24159.8i | − 1.02328i | −0.859201 | − | 0.511638i | \(-0.829039\pi\) | ||||
0.859201 | − | 0.511638i | \(-0.170961\pi\) | |||||||
\(824\) | 12636.5 | 0.534240 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −174.868 | −0.00736613 | ||||||||
\(827\) | − 7566.35i | − 0.318147i | −0.987267 | − | 0.159074i | \(-0.949149\pi\) | ||||
0.987267 | − | 0.159074i | \(-0.0508507\pi\) | |||||||
\(828\) | 7427.70i | 0.311752i | ||||||||
\(829\) | 10580.9 | 0.443295 | 0.221648 | − | 0.975127i | \(-0.428857\pi\) | ||||
0.221648 | + | 0.975127i | \(0.428857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6659.48 | −0.277996 | ||||||||
\(832\) | 8378.49i | 0.349125i | ||||||||
\(833\) | − 2862.52i | − 0.119064i | ||||||||
\(834\) | −11810.2 | −0.490354 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10424.2 | 0.431256 | ||||||||
\(837\) | 4175.80i | 0.172445i | ||||||||
\(838\) | 16411.1i | 0.676507i | ||||||||
\(839\) | −15315.6 | −0.630218 | −0.315109 | − | 0.949055i | \(-0.602041\pi\) | ||||
−0.315109 | + | 0.949055i | \(0.602041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5460.40 | −0.223888 | ||||||||
\(842\) | − 16876.4i | − 0.690735i | ||||||||
\(843\) | − 17515.7i | − 0.715625i | ||||||||
\(844\) | 19068.6 | 0.777688 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8303.57 | 0.337450 | ||||||||
\(847\) | 475.956i | 0.0193082i | ||||||||
\(848\) | − 883.966i | − 0.0357966i | ||||||||
\(849\) | 10935.1 | 0.442040 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56606.4 | −2.28019 | ||||||||
\(852\) | 1842.81i | 0.0741004i | ||||||||
\(853\) | − 18598.2i | − 0.746528i | −0.927725 | − | 0.373264i | \(-0.878239\pi\) | ||||
0.927725 | − | 0.373264i | \(-0.121761\pi\) | |||||||
\(854\) | −2037.59 | −0.0816450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12543.6 | −0.500853 | ||||||||
\(857\) | 41775.3i | 1.66513i | 0.553926 | + | 0.832566i | \(0.313129\pi\) | ||||
−0.553926 | + | 0.832566i | \(0.686871\pi\) | |||||||
\(858\) | 5539.99i | 0.220434i | ||||||||
\(859\) | −32414.7 | −1.28752 | −0.643758 | − | 0.765229i | \(-0.722626\pi\) | ||||
−0.643758 | + | 0.765229i | \(0.722626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7429.14 | 0.294059 | ||||||||
\(862\) | 27776.4i | 1.09753i | ||||||||
\(863\) | 31299.7i | 1.23459i | 0.786730 | + | 0.617297i | \(0.211772\pi\) | ||||
−0.786730 | + | 0.617297i | \(0.788228\pi\) | |||||||
\(864\) | 4949.48 | 0.194890 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8794.94 | 0.345109 | ||||||||
\(867\) | − 4500.75i | − 0.176302i | ||||||||
\(868\) | 5526.41i | 0.216104i | ||||||||
\(869\) | −35219.2 | −1.37483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16015.4 | 0.623030 | ||||||||
\(872\) | 40823.8i | 1.58540i | ||||||||
\(873\) | 11025.3i | 0.427434i | ||||||||
\(874\) | −15019.6 | −0.581288 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4359.29 | −0.168136 | ||||||||
\(877\) | − 19973.0i | − 0.769031i | −0.923119 | − | 0.384515i | \(-0.874369\pi\) | ||||
0.923119 | − | 0.384515i | \(-0.125631\pi\) | |||||||
\(878\) | 31204.9i | 1.19945i | ||||||||
\(879\) | −11333.7 | −0.434900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17367.9 | 0.664176 | 0.332088 | − | 0.943248i | \(-0.392247\pi\) | ||||
0.332088 | + | 0.943248i | \(0.392247\pi\) | |||||||
\(882\) | − 750.389i | − 0.0286473i | ||||||||
\(883\) | 14364.2i | 0.547446i | 0.961809 | + | 0.273723i | \(0.0882551\pi\) | ||||
−0.961809 | + | 0.273723i | \(0.911745\pi\) | |||||||
\(884\) | 8652.73 | 0.329211 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2745.09 | 0.104089 | ||||||||
\(887\) | − 33738.1i | − 1.27713i | −0.769568 | − | 0.638564i | \(-0.779529\pi\) | ||||
0.769568 | − | 0.638564i | \(-0.220471\pi\) | |||||||
\(888\) | 23421.7i | 0.885114i | ||||||||
\(889\) | −15545.7 | −0.586485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3029.65 | 0.113914 | ||||||||
\(892\) | − 4302.26i | − 0.161491i | ||||||||
\(893\) | − 29603.4i | − 1.10934i | ||||||||
\(894\) | 4182.46 | 0.156468 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6826.21 | 0.254518 | ||||||||
\(897\) | 14073.3i | 0.523850i | ||||||||
\(898\) | − 1508.86i | − 0.0560705i | ||||||||
\(899\) | −21278.2 | −0.789398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17835.8 | 0.659485 | ||||||||
\(902\) | − 22515.2i | − 0.831123i | ||||||||
\(903\) | 10881.3i | 0.401004i | ||||||||
\(904\) | 709.162 | 0.0260911 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2729.70 | −0.100097 | ||||||||
\(907\) | − 32998.6i | − 1.20805i | −0.796966 | − | 0.604024i | \(-0.793563\pi\) | ||||
0.796966 | − | 0.604024i | \(-0.206437\pi\) | |||||||
\(908\) | 5064.62i | 0.185105i | ||||||||
\(909\) | 3043.29 | 0.111045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33446.3 | 1.21638 | 0.608192 | − | 0.793790i | \(-0.291895\pi\) | ||||
0.608192 | + | 0.793790i | \(0.291895\pi\) | |||||||
\(912\) | − 474.225i | − 0.0172184i | ||||||||
\(913\) | − 14106.6i | − 0.511347i | ||||||||
\(914\) | 12576.6 | 0.455139 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32728.2 | 1.18053 | ||||||||
\(917\) | 4525.59i | 0.162975i | ||||||||
\(918\) | 2683.88i | 0.0964939i | ||||||||
\(919\) | −41708.7 | −1.49711 | −0.748554 | − | 0.663074i | \(-0.769252\pi\) | ||||
−0.748554 | + | 0.663074i | \(0.769252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14398.9 | −0.515158 | ||||||||
\(922\) | 12137.8i | 0.433556i | ||||||||
\(923\) | 3491.58i | 0.124514i | ||||||||
\(924\) | 4009.56 | 0.142754 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24607.7 | −0.873283 | ||||||||
\(927\) | − 5100.30i | − 0.180707i | ||||||||
\(928\) | 25220.6i | 0.892140i | ||||||||
\(929\) | −49024.6 | −1.73137 | −0.865686 | − | 0.500587i | \(-0.833117\pi\) | ||||
−0.865686 | + | 0.500587i | \(0.833117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2675.25 | −0.0941758 | ||||||||
\(932\) | 11609.9i | 0.408040i | ||||||||
\(933\) | − 1740.34i | − 0.0610677i | ||||||||
\(934\) | −27894.6 | −0.977235 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5823.03 | 0.203346 | ||||||||
\(937\) | − 5447.58i | − 0.189930i | −0.995481 | − | 0.0949651i | \(-0.969726\pi\) | ||||
0.995481 | − | 0.0949651i | \(-0.0302739\pi\) | |||||||
\(938\) | 6574.31i | 0.228848i | ||||||||
\(939\) | 18344.4 | 0.637535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4125.75 | 0.142928 | 0.0714642 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714642 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(942\) | − 7987.60i | − 0.276274i | ||||||||
\(943\) | − 57195.5i | − 1.97513i | ||||||||
\(944\) | −42.5069 | −0.00146555 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32977.4 | 1.13339 | ||||||||
\(947\) | 17332.3i | 0.594747i | 0.954761 | + | 0.297374i | \(0.0961107\pi\) | ||||
−0.954761 | + | 0.297374i | \(0.903889\pi\) | |||||||
\(948\) | 14419.9i | 0.494026i | ||||||||
\(949\) | −8259.57 | −0.282526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12901.9 | −0.439929 | ||||||||
\(952\) | 9118.53i | 0.310434i | ||||||||
\(953\) | − 56839.4i | − 1.93201i | −0.258517 | − | 0.966007i | \(-0.583234\pi\) | ||||
0.258517 | − | 0.966007i | \(-0.416766\pi\) | |||||||
\(954\) | 4675.53 | 0.158675 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14615.3 | −0.494449 | ||||||||
\(957\) | 15437.9i | 0.521459i | ||||||||
\(958\) | − 22105.7i | − 0.745515i | ||||||||
\(959\) | 6272.07 | 0.211195 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5871.48 | −0.197089 | ||||||||
\(962\) | 17286.3i | 0.579349i | ||||||||
\(963\) | 5062.78i | 0.169414i | ||||||||
\(964\) | −27382.7 | −0.914873 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5777.10 | −0.192417 | ||||||||
\(967\) | − 13284.2i | − 0.441769i | −0.975300 | − | 0.220884i | \(-0.929106\pi\) | ||||
0.975300 | − | 0.220884i | \(-0.0708943\pi\) | |||||||
\(968\) | − 1516.15i | − 0.0503420i | ||||||||
\(969\) | 9568.44 | 0.317216 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12153.0 | 0.401658 | 0.200829 | − | 0.979626i | \(-0.435636\pi\) | ||||
0.200829 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(972\) | − 1240.44i | − 0.0409332i | ||||||||
\(973\) | 16195.3i | 0.533604i | ||||||||
\(974\) | −21888.1 | −0.720060 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −495.298 | −0.0162440 | ||||||||
\(977\) | − 37999.3i | − 1.24433i | −0.782888 | − | 0.622163i | \(-0.786254\pi\) | ||||
0.782888 | − | 0.622163i | \(-0.213746\pi\) | |||||||
\(978\) | − 5688.18i | − 0.185980i | ||||||||
\(979\) | 25349.0 | 0.827537 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16477.1 | 0.536264 | ||||||||
\(982\) | 8334.42i | 0.270837i | ||||||||
\(983\) | − 22375.0i | − 0.725993i | −0.931791 | − | 0.362996i | \(-0.881754\pi\) | ||||
0.931791 | − | 0.362996i | \(-0.118246\pi\) | |||||||
\(984\) | −23665.5 | −0.766695 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13676.0 | −0.441717 | ||||||||
\(987\) | − 11386.6i | − 0.367213i | ||||||||
\(988\) | − 8086.65i | − 0.260395i | ||||||||
\(989\) | 83772.9 | 2.69345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18985.3 | 0.608564 | 0.304282 | − | 0.952582i | \(-0.401583\pi\) | ||||
0.304282 | + | 0.952582i | \(0.401583\pi\) | |||||||
\(992\) | − 28351.2i | − 0.907412i | ||||||||
\(993\) | 20062.6i | 0.641156i | ||||||||
\(994\) | −1433.29 | −0.0457358 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5775.70 | −0.183745 | ||||||||
\(997\) | − 56476.5i | − 1.79401i | −0.442019 | − | 0.897006i | \(-0.645738\pi\) | ||||
0.442019 | − | 0.897006i | \(-0.354262\pi\) | |||||||
\(998\) | 17539.6i | 0.556321i | ||||||||
\(999\) | 9453.37 | 0.299391 |
(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 | 525.4.d.j.274.2 | 4 | ||
5.2 | odd | 4 | 525.4.a.i.1.2 | 2 | |||
5.3 | odd | 4 | 105.4.a.g.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 525.4.d.j.274.3 | 4 | ||
15.2 | even | 4 | 1575.4.a.y.1.1 | 2 | |||
15.8 | even | 4 | 315.4.a.g.1.2 | 2 | |||
20.3 | even | 4 | 1680.4.a.y.1.1 | 2 | |||
35.13 | even | 4 | 735.4.a.q.1.1 | 2 | |||
105.83 | odd | 4 | 2205.4.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.g.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
315.4.a.g.1.2 | 2 | 15.8 | even | 4 | |||
525.4.a.i.1.2 | 2 | 5.2 | odd | 4 | |||
525.4.d.j.274.2 | 4 | 1.1 | even | 1 | trivial | ||
525.4.d.j.274.3 | 4 | 5.4 | even | 2 | inner | ||
735.4.a.q.1.1 | 2 | 35.13 | even | 4 | |||
1575.4.a.y.1.1 | 2 | 15.2 | even | 4 | |||
1680.4.a.y.1.1 | 2 | 20.3 | even | 4 | |||
2205.4.a.v.1.2 | 2 | 105.83 | odd | 4 |