Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,4,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(144.554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 92x^{4} + 26x^{3} + 2116x^{2} + 80x - 7800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.44232\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −6.44232 | −1.23983 | −0.619913 | − | 0.784671i | \(-0.712832\pi\) | ||||
−0.619913 | + | 0.784671i | \(0.712832\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −12.8846 | −0.876689 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 14.5035 | 0.537168 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.3846 | 1.32623 | 0.663114 | − | 0.748518i | \(-0.269234\pi\) | ||||
0.663114 | + | 0.748518i | \(0.269234\pi\) | |||||||
\(12\) | −25.7693 | −0.619913 | ||||||||
\(13\) | −93.4871 | −1.99451 | −0.997256 | − | 0.0740250i | \(-0.976416\pi\) | ||||
−0.997256 | + | 0.0740250i | \(0.976416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 20.2793 | 0.289320 | 0.144660 | − | 0.989481i | \(-0.453791\pi\) | ||||
0.144660 | + | 0.989481i | \(0.453791\pi\) | |||||||
\(18\) | 29.0071 | 0.379835 | ||||||||
\(19\) | 31.0581 | 0.375011 | 0.187506 | − | 0.982264i | \(-0.439960\pi\) | ||||
0.187506 | + | 0.982264i | \(0.439960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 96.7692 | 0.937785 | ||||||||
\(23\) | 21.0487 | 0.190825 | 0.0954123 | − | 0.995438i | \(-0.469583\pi\) | ||||
0.0954123 | + | 0.995438i | \(0.469583\pi\) | |||||||
\(24\) | −51.5386 | −0.438345 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −186.974 | −1.41033 | ||||||||
\(27\) | 80.5063 | 0.573831 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 69.5116 | 0.445103 | 0.222551 | − | 0.974921i | \(-0.428562\pi\) | ||||
0.222551 | + | 0.974921i | \(0.428562\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −161.116 | −0.933462 | −0.466731 | − | 0.884399i | \(-0.654568\pi\) | ||||
−0.466731 | + | 0.884399i | \(0.654568\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −311.709 | −1.64429 | ||||||||
\(34\) | 40.5585 | 0.204580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 58.0141 | 0.268584 | ||||||||
\(37\) | −162.582 | −0.722386 | −0.361193 | − | 0.932491i | \(-0.617630\pi\) | ||||
−0.361193 | + | 0.932491i | \(0.617630\pi\) | |||||||
\(38\) | 62.1162 | 0.265173 | ||||||||
\(39\) | 602.274 | 2.47285 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 365.073 | 1.39060 | 0.695302 | − | 0.718717i | \(-0.255270\pi\) | ||||
0.695302 | + | 0.718717i | \(0.255270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −254.518 | −0.902644 | −0.451322 | − | 0.892361i | \(-0.649047\pi\) | ||||
−0.451322 | + | 0.892361i | \(0.649047\pi\) | |||||||
\(44\) | 193.538 | 0.663114 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 42.0975 | 0.134933 | ||||||||
\(47\) | −468.802 | −1.45493 | −0.727466 | − | 0.686144i | \(-0.759302\pi\) | ||||
−0.727466 | + | 0.686144i | \(0.759302\pi\) | |||||||
\(48\) | −103.077 | −0.309956 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −130.646 | −0.358707 | ||||||||
\(52\) | −373.949 | −0.997256 | ||||||||
\(53\) | 587.150 | 1.52172 | 0.760861 | − | 0.648915i | \(-0.224777\pi\) | ||||
0.760861 | + | 0.648915i | \(0.224777\pi\) | |||||||
\(54\) | 161.013 | 0.405760 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −200.086 | −0.464949 | ||||||||
\(58\) | 139.023 | 0.314735 | ||||||||
\(59\) | −536.945 | −1.18482 | −0.592409 | − | 0.805637i | \(-0.701823\pi\) | ||||
−0.592409 | + | 0.805637i | \(0.701823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 625.824 | 1.31358 | 0.656791 | − | 0.754072i | \(-0.271913\pi\) | ||||
0.656791 | + | 0.754072i | \(0.271913\pi\) | |||||||
\(62\) | −322.232 | −0.660057 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −623.419 | −1.16269 | ||||||||
\(67\) | 123.074 | 0.224416 | 0.112208 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112208 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(68\) | 81.1171 | 0.144660 | ||||||||
\(69\) | −135.603 | −0.236589 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 210.060 | 0.351121 | 0.175560 | − | 0.984469i | \(-0.443826\pi\) | ||||
0.175560 | + | 0.984469i | \(0.443826\pi\) | |||||||
\(72\) | 116.028 | 0.189917 | ||||||||
\(73\) | 141.783 | 0.227322 | 0.113661 | − | 0.993520i | \(-0.463742\pi\) | ||||
0.113661 | + | 0.993520i | \(0.463742\pi\) | |||||||
\(74\) | −325.164 | −0.510804 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 124.232 | 0.187506 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1204.55 | 1.74857 | ||||||||
\(79\) | 513.424 | 0.731198 | 0.365599 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365599 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −910.243 | −1.24862 | ||||||||
\(82\) | 730.146 | 0.983306 | ||||||||
\(83\) | 117.376 | 0.155225 | 0.0776125 | − | 0.996984i | \(-0.475270\pi\) | ||||
0.0776125 | + | 0.996984i | \(0.475270\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −509.037 | −0.638266 | ||||||||
\(87\) | −447.816 | −0.551850 | ||||||||
\(88\) | 387.077 | 0.468892 | ||||||||
\(89\) | 61.2589 | 0.0729598 | 0.0364799 | − | 0.999334i | \(-0.488386\pi\) | ||||
0.0364799 | + | 0.999334i | \(0.488386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 84.1950 | 0.0954123 | ||||||||
\(93\) | 1037.96 | 1.15733 | ||||||||
\(94\) | −937.604 | −1.02879 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −206.154 | −0.219172 | ||||||||
\(97\) | 436.654 | 0.457067 | 0.228533 | − | 0.973536i | \(-0.426607\pi\) | ||||
0.228533 | + | 0.973536i | \(0.426607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 701.748 | 0.712407 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1768.21 | −1.74201 | −0.871007 | − | 0.491271i | \(-0.836532\pi\) | ||||
−0.871007 | + | 0.491271i | \(0.836532\pi\) | |||||||
\(102\) | −261.291 | −0.253644 | ||||||||
\(103\) | 849.407 | 0.812568 | 0.406284 | − | 0.913747i | \(-0.366824\pi\) | ||||
0.406284 | + | 0.913747i | \(0.366824\pi\) | |||||||
\(104\) | −747.897 | −0.705167 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1174.30 | 1.07602 | ||||||||
\(107\) | −1282.58 | −1.15880 | −0.579399 | − | 0.815044i | \(-0.696713\pi\) | ||||
−0.579399 | + | 0.815044i | \(0.696713\pi\) | |||||||
\(108\) | 322.025 | 0.286916 | ||||||||
\(109\) | −598.398 | −0.525836 | −0.262918 | − | 0.964818i | \(-0.584685\pi\) | ||||
−0.262918 | + | 0.964818i | \(0.584685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1047.40 | 0.895633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −860.218 | −0.716128 | −0.358064 | − | 0.933697i | \(-0.616563\pi\) | ||||
−0.358064 | + | 0.933697i | \(0.616563\pi\) | |||||||
\(114\) | −400.172 | −0.328768 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 278.046 | 0.222551 | ||||||||
\(117\) | −1355.89 | −1.07139 | ||||||||
\(118\) | −1073.89 | −0.837793 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1010.07 | 0.758881 | ||||||||
\(122\) | 1251.65 | 0.928843 | ||||||||
\(123\) | −2351.92 | −1.72411 | ||||||||
\(124\) | −644.465 | −0.466731 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −971.435 | −0.678748 | −0.339374 | − | 0.940652i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940652i | \(0.610215\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1639.69 | 1.11912 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149.593 | −0.0997713 | −0.0498856 | − | 0.998755i | \(-0.515886\pi\) | ||||
−0.0498856 | + | 0.998755i | \(0.515886\pi\) | |||||||
\(132\) | −1246.84 | −0.822146 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 246.147 | 0.158686 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 162.234 | 0.102290 | ||||||||
\(137\) | 495.245 | 0.308844 | 0.154422 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154422 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(138\) | −271.206 | −0.167294 | ||||||||
\(139\) | 466.520 | 0.284674 | 0.142337 | − | 0.989818i | \(-0.454538\pi\) | ||||
0.142337 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3020.17 | 1.80386 | ||||||||
\(142\) | 420.121 | 0.248280 | ||||||||
\(143\) | −4523.34 | −2.64518 | ||||||||
\(144\) | 232.056 | 0.134292 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 283.567 | 0.160741 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −650.327 | −0.361193 | ||||||||
\(149\) | −178.554 | −0.0981723 | −0.0490862 | − | 0.998795i | \(-0.515631\pi\) | ||||
−0.0490862 | + | 0.998795i | \(0.515631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 831.668 | 0.448213 | 0.224107 | − | 0.974565i | \(-0.428054\pi\) | ||||
0.224107 | + | 0.974565i | \(0.428054\pi\) | |||||||
\(152\) | 248.465 | 0.132587 | ||||||||
\(153\) | 294.121 | 0.155413 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2409.10 | 1.23642 | ||||||||
\(157\) | −167.697 | −0.0852462 | −0.0426231 | − | 0.999091i | \(-0.513571\pi\) | ||||
−0.0426231 | + | 0.999091i | \(0.513571\pi\) | |||||||
\(158\) | 1026.85 | 0.517035 | ||||||||
\(159\) | −3782.61 | −1.88667 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1820.49 | −0.882907 | ||||||||
\(163\) | 1612.09 | 0.774655 | 0.387327 | − | 0.921942i | \(-0.373398\pi\) | ||||
0.387327 | + | 0.921942i | \(0.373398\pi\) | |||||||
\(164\) | 1460.29 | 0.695302 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 234.752 | 0.109761 | ||||||||
\(167\) | 1590.69 | 0.737073 | 0.368536 | − | 0.929613i | \(-0.379859\pi\) | ||||
0.368536 | + | 0.929613i | \(0.379859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6542.84 | 2.97808 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 450.452 | 0.201444 | ||||||||
\(172\) | −1018.07 | −0.451322 | ||||||||
\(173\) | −1742.41 | −0.765739 | −0.382870 | − | 0.923802i | \(-0.625064\pi\) | ||||
−0.382870 | + | 0.923802i | \(0.625064\pi\) | |||||||
\(174\) | −895.632 | −0.390217 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 774.154 | 0.331557 | ||||||||
\(177\) | 3459.17 | 1.46897 | ||||||||
\(178\) | 122.518 | 0.0515904 | ||||||||
\(179\) | −2429.37 | −1.01441 | −0.507205 | − | 0.861825i | \(-0.669321\pi\) | ||||
−0.507205 | + | 0.861825i | \(0.669321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2628.61 | −1.07946 | −0.539732 | − | 0.841837i | \(-0.681474\pi\) | ||||
−0.539732 | + | 0.841837i | \(0.681474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4031.76 | −1.62861 | ||||||||
\(184\) | 168.390 | 0.0674667 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2075.92 | 0.818356 | ||||||||
\(187\) | 981.204 | 0.383705 | ||||||||
\(188\) | −1875.21 | −0.727466 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1124.82 | 0.426122 | 0.213061 | − | 0.977039i | \(-0.431657\pi\) | ||||
0.213061 | + | 0.977039i | \(0.431657\pi\) | |||||||
\(192\) | −412.309 | −0.154978 | ||||||||
\(193\) | −2216.08 | −0.826514 | −0.413257 | − | 0.910615i | \(-0.635609\pi\) | ||||
−0.413257 | + | 0.910615i | \(0.635609\pi\) | |||||||
\(194\) | 873.308 | 0.323195 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3125.56 | 1.13039 | 0.565194 | − | 0.824958i | \(-0.308801\pi\) | ||||
0.565194 | + | 0.824958i | \(0.308801\pi\) | |||||||
\(198\) | 1403.50 | 0.503748 | ||||||||
\(199\) | −4539.34 | −1.61701 | −0.808506 | − | 0.588488i | \(-0.799724\pi\) | ||||
−0.808506 | + | 0.588488i | \(0.799724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −792.881 | −0.278236 | ||||||||
\(202\) | −3536.42 | −1.23179 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −522.582 | −0.179353 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1698.81 | 0.574573 | ||||||||
\(207\) | 305.281 | 0.102505 | ||||||||
\(208\) | −1495.79 | −0.498628 | ||||||||
\(209\) | 1502.73 | 0.497350 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2520.40 | 0.822331 | 0.411165 | − | 0.911561i | \(-0.365122\pi\) | ||||
0.411165 | + | 0.911561i | \(0.365122\pi\) | |||||||
\(212\) | 2348.60 | 0.760861 | ||||||||
\(213\) | −1353.28 | −0.435329 | ||||||||
\(214\) | −2565.15 | −0.819394 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 644.051 | 0.202880 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1196.80 | −0.371822 | ||||||||
\(219\) | −913.415 | −0.281839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1895.85 | −0.577053 | ||||||||
\(222\) | 2094.81 | 0.633308 | ||||||||
\(223\) | −5800.58 | −1.74186 | −0.870931 | − | 0.491405i | \(-0.836484\pi\) | ||||
−0.870931 | + | 0.491405i | \(0.836484\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1720.44 | −0.506379 | ||||||||
\(227\) | −6626.47 | −1.93751 | −0.968753 | − | 0.248026i | \(-0.920218\pi\) | ||||
−0.968753 | + | 0.248026i | \(0.920218\pi\) | |||||||
\(228\) | −800.345 | −0.232474 | ||||||||
\(229\) | −507.845 | −0.146547 | −0.0732736 | − | 0.997312i | \(-0.523345\pi\) | ||||
−0.0732736 | + | 0.997312i | \(0.523345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 556.093 | 0.157368 | ||||||||
\(233\) | −6307.82 | −1.77356 | −0.886779 | − | 0.462193i | \(-0.847063\pi\) | ||||
−0.886779 | + | 0.462193i | \(0.847063\pi\) | |||||||
\(234\) | −2711.79 | −0.757586 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2147.78 | −0.592409 | ||||||||
\(237\) | −3307.64 | −0.906559 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4615.12 | −1.24907 | −0.624535 | − | 0.780997i | \(-0.714711\pi\) | ||||
−0.624535 | + | 0.780997i | \(0.714711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1550.70 | −0.414480 | −0.207240 | − | 0.978290i | \(-0.566448\pi\) | ||||
−0.207240 | + | 0.978290i | \(0.566448\pi\) | |||||||
\(242\) | 2020.14 | 0.536610 | ||||||||
\(243\) | 3690.41 | 0.974238 | ||||||||
\(244\) | 2503.30 | 0.656791 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4703.83 | −1.21913 | ||||||||
\(247\) | −2903.53 | −0.747965 | ||||||||
\(248\) | −1288.93 | −0.330029 | ||||||||
\(249\) | −756.173 | −0.192452 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −762.543 | −0.191758 | −0.0958790 | − | 0.995393i | \(-0.530566\pi\) | ||||
−0.0958790 | + | 0.995393i | \(0.530566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1018.44 | 0.253077 | ||||||||
\(254\) | −1942.87 | −0.479947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2302.36 | −0.558822 | −0.279411 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279411 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(258\) | 3279.38 | 0.791338 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1008.16 | 0.239095 | ||||||||
\(262\) | −299.187 | −0.0705490 | ||||||||
\(263\) | −4833.50 | −1.13326 | −0.566628 | − | 0.823974i | \(-0.691752\pi\) | ||||
−0.566628 | + | 0.823974i | \(0.691752\pi\) | |||||||
\(264\) | −2493.67 | −0.581345 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −394.649 | −0.0904575 | ||||||||
\(268\) | 492.295 | 0.112208 | ||||||||
\(269\) | −4830.35 | −1.09484 | −0.547420 | − | 0.836858i | \(-0.684390\pi\) | ||||
−0.547420 | + | 0.836858i | \(0.684390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5950.37 | 1.33380 | 0.666899 | − | 0.745149i | \(-0.267621\pi\) | ||||
0.666899 | + | 0.745149i | \(0.267621\pi\) | |||||||
\(272\) | 324.468 | 0.0723301 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 990.491 | 0.218386 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −542.411 | −0.118295 | ||||||||
\(277\) | −7668.90 | −1.66346 | −0.831732 | − | 0.555177i | \(-0.812651\pi\) | ||||
−0.831732 | + | 0.555177i | \(0.812651\pi\) | |||||||
\(278\) | 933.040 | 0.201295 | ||||||||
\(279\) | −2336.75 | −0.501426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6314.18 | −1.34047 | −0.670235 | − | 0.742149i | \(-0.733807\pi\) | ||||
−0.670235 | + | 0.742149i | \(0.733807\pi\) | |||||||
\(282\) | 6040.35 | 1.27552 | ||||||||
\(283\) | −6122.72 | −1.28607 | −0.643035 | − | 0.765836i | \(-0.722325\pi\) | ||||
−0.643035 | + | 0.765836i | \(0.722325\pi\) | |||||||
\(284\) | 840.242 | 0.175560 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9046.68 | −1.87042 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 464.113 | 0.0949587 | ||||||||
\(289\) | −4501.75 | −0.916294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2813.07 | −0.566683 | ||||||||
\(292\) | 567.134 | 0.113661 | ||||||||
\(293\) | 1646.67 | 0.328326 | 0.164163 | − | 0.986433i | \(-0.447508\pi\) | ||||
0.164163 | + | 0.986433i | \(0.447508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1300.65 | −0.255402 | ||||||||
\(297\) | 3895.27 | 0.761031 | ||||||||
\(298\) | −357.107 | −0.0694183 | ||||||||
\(299\) | −1967.79 | −0.380602 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1663.34 | 0.316934 | ||||||||
\(303\) | 11391.4 | 2.15979 | ||||||||
\(304\) | 496.929 | 0.0937528 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 588.242 | 0.109894 | ||||||||
\(307\) | 7890.42 | 1.46687 | 0.733436 | − | 0.679758i | \(-0.237915\pi\) | ||||
0.733436 | + | 0.679758i | \(0.237915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5472.15 | −1.00744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3436.98 | 0.626667 | 0.313333 | − | 0.949643i | \(-0.398554\pi\) | ||||
0.313333 | + | 0.949643i | \(0.398554\pi\) | |||||||
\(312\) | 4818.19 | 0.874284 | ||||||||
\(313\) | −7209.81 | −1.30199 | −0.650995 | − | 0.759082i | \(-0.725648\pi\) | ||||
−0.650995 | + | 0.759082i | \(0.725648\pi\) | |||||||
\(314\) | −335.393 | −0.0602782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2053.69 | 0.365599 | ||||||||
\(317\) | −885.804 | −0.156945 | −0.0784727 | − | 0.996916i | \(-0.525004\pi\) | ||||
−0.0784727 | + | 0.996916i | \(0.525004\pi\) | |||||||
\(318\) | −7565.22 | −1.33408 | ||||||||
\(319\) | 3363.29 | 0.590308 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8262.77 | 1.43671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 629.835 | 0.108498 | ||||||||
\(324\) | −3640.97 | −0.624309 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3224.18 | 0.547764 | ||||||||
\(327\) | 3855.08 | 0.651945 | ||||||||
\(328\) | 2920.58 | 0.491653 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1766.18 | −0.293288 | −0.146644 | − | 0.989189i | \(-0.546847\pi\) | ||||
−0.146644 | + | 0.989189i | \(0.546847\pi\) | |||||||
\(332\) | 469.504 | 0.0776125 | ||||||||
\(333\) | −2358.01 | −0.388042 | ||||||||
\(334\) | 3181.38 | 0.521189 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7521.34 | −1.21577 | −0.607883 | − | 0.794026i | \(-0.707981\pi\) | ||||
−0.607883 | + | 0.794026i | \(0.707981\pi\) | |||||||
\(338\) | 13085.7 | 2.10582 | ||||||||
\(339\) | 5541.80 | 0.887874 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7795.54 | −1.23798 | ||||||||
\(342\) | 900.904 | 0.142442 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2036.15 | −0.319133 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3484.82 | −0.541459 | ||||||||
\(347\) | −4658.53 | −0.720700 | −0.360350 | − | 0.932817i | \(-0.617343\pi\) | ||||
−0.360350 | + | 0.932817i | \(0.617343\pi\) | |||||||
\(348\) | −1791.26 | −0.275925 | ||||||||
\(349\) | 7198.15 | 1.10403 | 0.552017 | − | 0.833833i | \(-0.313858\pi\) | ||||
0.552017 | + | 0.833833i | \(0.313858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7526.30 | −1.14451 | ||||||||
\(352\) | 1548.31 | 0.234446 | ||||||||
\(353\) | −3640.08 | −0.548844 | −0.274422 | − | 0.961609i | \(-0.588486\pi\) | ||||
−0.274422 | + | 0.961609i | \(0.588486\pi\) | |||||||
\(354\) | 6918.34 | 1.03872 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 245.035 | 0.0364799 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4858.73 | −0.717296 | ||||||||
\(359\) | −5469.89 | −0.804150 | −0.402075 | − | 0.915607i | \(-0.631711\pi\) | ||||
−0.402075 | + | 0.915607i | \(0.631711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5894.40 | −0.859367 | ||||||||
\(362\) | −5257.22 | −0.763296 | ||||||||
\(363\) | −6507.20 | −0.940880 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8063.52 | −1.15160 | ||||||||
\(367\) | −65.0871 | −0.00925754 | −0.00462877 | − | 0.999989i | \(-0.501473\pi\) | ||||
−0.00462877 | + | 0.999989i | \(0.501473\pi\) | |||||||
\(368\) | 336.780 | 0.0477062 | ||||||||
\(369\) | 5294.84 | 0.746988 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4151.85 | 0.578665 | ||||||||
\(373\) | 10153.4 | 1.40944 | 0.704721 | − | 0.709484i | \(-0.251072\pi\) | ||||
0.704721 | + | 0.709484i | \(0.251072\pi\) | |||||||
\(374\) | 1962.41 | 0.271320 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3750.41 | −0.514396 | ||||||||
\(377\) | −6498.44 | −0.887763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1453.96 | 0.197057 | 0.0985287 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985287 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6258.30 | 0.841529 | ||||||||
\(382\) | 2249.65 | 0.301314 | ||||||||
\(383\) | 577.301 | 0.0770201 | 0.0385101 | − | 0.999258i | \(-0.487739\pi\) | ||||
0.0385101 | + | 0.999258i | \(0.487739\pi\) | |||||||
\(384\) | −824.617 | −0.109586 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4432.16 | −0.584433 | ||||||||
\(387\) | −3691.41 | −0.484871 | ||||||||
\(388\) | 1746.62 | 0.228533 | ||||||||
\(389\) | −2071.00 | −0.269933 | −0.134966 | − | 0.990850i | \(-0.543093\pi\) | ||||
−0.134966 | + | 0.990850i | \(0.543093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 426.853 | 0.0552094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 963.729 | 0.123699 | ||||||||
\(394\) | 6251.11 | 0.799306 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2806.99 | 0.356203 | ||||||||
\(397\) | −5033.42 | −0.636322 | −0.318161 | − | 0.948037i | \(-0.603065\pi\) | ||||
−0.318161 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(398\) | −9078.68 | −1.14340 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4946.88 | −0.616048 | −0.308024 | − | 0.951379i | \(-0.599668\pi\) | ||||
−0.308024 | + | 0.951379i | \(0.599668\pi\) | |||||||
\(402\) | −1585.76 | −0.196743 | ||||||||
\(403\) | 15062.3 | 1.86180 | ||||||||
\(404\) | −7072.83 | −0.871007 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7866.46 | −0.958049 | ||||||||
\(408\) | −1045.16 | −0.126822 | ||||||||
\(409\) | 9389.84 | 1.13520 | 0.567601 | − | 0.823304i | \(-0.307872\pi\) | ||||
0.567601 | + | 0.823304i | \(0.307872\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3190.53 | −0.382913 | ||||||||
\(412\) | 3397.63 | 0.406284 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 610.562 | 0.0724819 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2991.59 | −0.352583 | ||||||||
\(417\) | −3005.47 | −0.352946 | ||||||||
\(418\) | 3005.47 | 0.351680 | ||||||||
\(419\) | −8423.77 | −0.982167 | −0.491084 | − | 0.871112i | \(-0.663399\pi\) | ||||
−0.491084 | + | 0.871112i | \(0.663399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5680.15 | 0.657562 | 0.328781 | − | 0.944406i | \(-0.393362\pi\) | ||||
0.328781 | + | 0.944406i | \(0.393362\pi\) | |||||||
\(422\) | 5040.81 | 0.581476 | ||||||||
\(423\) | −6799.28 | −0.781542 | ||||||||
\(424\) | 4697.20 | 0.538010 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2706.55 | −0.307824 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5130.31 | −0.579399 | ||||||||
\(429\) | 29140.8 | 3.27956 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12348.4 | 1.38005 | 0.690023 | − | 0.723787i | \(-0.257600\pi\) | ||||
0.690023 | + | 0.723787i | \(0.257600\pi\) | |||||||
\(432\) | 1288.10 | 0.143458 | ||||||||
\(433\) | −9031.93 | −1.00242 | −0.501209 | − | 0.865326i | \(-0.667111\pi\) | ||||
−0.501209 | + | 0.865326i | \(0.667111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2393.59 | −0.262918 | ||||||||
\(437\) | 653.734 | 0.0715614 | ||||||||
\(438\) | −1826.83 | −0.199291 | ||||||||
\(439\) | 10657.4 | 1.15866 | 0.579329 | − | 0.815094i | \(-0.303315\pi\) | ||||
0.579329 | + | 0.815094i | \(0.303315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3791.70 | −0.408038 | ||||||||
\(443\) | −901.320 | −0.0966660 | −0.0483330 | − | 0.998831i | \(-0.515391\pi\) | ||||
−0.0483330 | + | 0.998831i | \(0.515391\pi\) | |||||||
\(444\) | 4189.62 | 0.447816 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11601.2 | −1.23168 | ||||||||
\(447\) | 1150.30 | 0.121717 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7771.88 | −0.816877 | −0.408438 | − | 0.912786i | \(-0.633926\pi\) | ||||
−0.408438 | + | 0.912786i | \(0.633926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17663.9 | 1.84426 | ||||||||
\(452\) | −3440.87 | −0.358064 | ||||||||
\(453\) | −5357.87 | −0.555706 | ||||||||
\(454\) | −13252.9 | −1.37002 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1600.69 | −0.164384 | ||||||||
\(457\) | 2760.35 | 0.282547 | 0.141273 | − | 0.989971i | \(-0.454880\pi\) | ||||
0.141273 | + | 0.989971i | \(0.454880\pi\) | |||||||
\(458\) | −1015.69 | −0.103625 | ||||||||
\(459\) | 1632.61 | 0.166021 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16482.3 | 1.66520 | 0.832602 | − | 0.553872i | \(-0.186850\pi\) | ||||
0.832602 | + | 0.553872i | \(0.186850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9949.16 | 0.998653 | 0.499327 | − | 0.866414i | \(-0.333581\pi\) | ||||
0.499327 | + | 0.866414i | \(0.333581\pi\) | |||||||
\(464\) | 1112.19 | 0.111276 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12615.6 | −1.25410 | ||||||||
\(467\) | −2101.55 | −0.208240 | −0.104120 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104120 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(468\) | −5423.57 | −0.535694 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1080.36 | 0.105690 | ||||||||
\(472\) | −4295.56 | −0.418896 | ||||||||
\(473\) | −12314.8 | −1.19711 | ||||||||
\(474\) | −6615.28 | −0.641034 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8515.74 | 0.817420 | ||||||||
\(478\) | −9230.25 | −0.883225 | ||||||||
\(479\) | 8009.97 | 0.764060 | 0.382030 | − | 0.924150i | \(-0.375225\pi\) | ||||
0.382030 | + | 0.924150i | \(0.375225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15199.3 | 1.44081 | ||||||||
\(482\) | −3101.41 | −0.293082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4040.28 | 0.379441 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7380.82 | 0.688890 | ||||||||
\(487\) | 5382.59 | 0.500839 | 0.250420 | − | 0.968137i | \(-0.419431\pi\) | ||||
0.250420 | + | 0.968137i | \(0.419431\pi\) | |||||||
\(488\) | 5006.59 | 0.464422 | ||||||||
\(489\) | −10385.6 | −0.960437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3456.93 | −0.317737 | −0.158869 | − | 0.987300i | \(-0.550785\pi\) | ||||
−0.158869 | + | 0.987300i | \(0.550785\pi\) | |||||||
\(492\) | −9407.67 | −0.862054 | ||||||||
\(493\) | 1409.64 | 0.128777 | ||||||||
\(494\) | −5807.06 | −0.528891 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2577.86 | −0.233365 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1512.35 | −0.136084 | ||||||||
\(499\) | −12098.2 | −1.08535 | −0.542674 | − | 0.839943i | \(-0.682588\pi\) | ||||
−0.542674 | + | 0.839943i | \(0.682588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10247.7 | −0.913842 | ||||||||
\(502\) | −1525.09 | −0.135593 | ||||||||
\(503\) | −1508.10 | −0.133684 | −0.0668418 | − | 0.997764i | \(-0.521292\pi\) | ||||
−0.0668418 | + | 0.997764i | \(0.521292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2036.87 | 0.178952 | ||||||||
\(507\) | −42151.1 | −3.69230 | ||||||||
\(508\) | −3885.74 | −0.339374 | ||||||||
\(509\) | 10363.5 | 0.902460 | 0.451230 | − | 0.892408i | \(-0.350985\pi\) | ||||
0.451230 | + | 0.892408i | \(0.350985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 2500.37 | 0.215193 | ||||||||
\(514\) | −4604.72 | −0.395147 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6558.76 | 0.559561 | ||||||||
\(517\) | −22682.8 | −1.92957 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11225.2 | 0.949383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4650.70 | −0.391077 | −0.195538 | − | 0.980696i | \(-0.562645\pi\) | ||||
−0.195538 | + | 0.980696i | \(0.562645\pi\) | |||||||
\(522\) | 2016.33 | 0.169066 | ||||||||
\(523\) | −6457.71 | −0.539916 | −0.269958 | − | 0.962872i | \(-0.587010\pi\) | ||||
−0.269958 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(524\) | −598.374 | −0.0498856 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9667.00 | −0.801333 | ||||||||
\(527\) | −3267.32 | −0.270069 | ||||||||
\(528\) | −4987.35 | −0.411073 | ||||||||
\(529\) | −11724.0 | −0.963586 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7787.59 | −0.636446 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34129.6 | −2.77358 | ||||||||
\(534\) | −789.299 | −0.0639631 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 984.590 | 0.0793429 | ||||||||
\(537\) | 15650.8 | 1.25769 | ||||||||
\(538\) | −9660.70 | −0.774168 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23030.2 | −1.83021 | −0.915106 | − | 0.403214i | \(-0.867893\pi\) | ||||
−0.915106 | + | 0.403214i | \(0.867893\pi\) | |||||||
\(542\) | 11900.7 | 0.943137 | ||||||||
\(543\) | 16934.4 | 1.33835 | ||||||||
\(544\) | 648.936 | 0.0511451 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6553.72 | −0.512280 | −0.256140 | − | 0.966640i | \(-0.582451\pi\) | ||||
−0.256140 | + | 0.966640i | \(0.582451\pi\) | |||||||
\(548\) | 1980.98 | 0.154422 | ||||||||
\(549\) | 9076.66 | 0.705614 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2158.90 | 0.166919 | ||||||||
\(552\) | −1084.82 | −0.0836469 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15337.8 | −1.17625 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1866.08 | 0.142337 | ||||||||
\(557\) | 5254.73 | 0.399731 | 0.199865 | − | 0.979823i | \(-0.435949\pi\) | ||||
0.199865 | + | 0.979823i | \(0.435949\pi\) | |||||||
\(558\) | −4673.51 | −0.354561 | ||||||||
\(559\) | 23794.2 | 1.80034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6321.24 | −0.475727 | ||||||||
\(562\) | −12628.4 | −0.947856 | ||||||||
\(563\) | −9759.11 | −0.730546 | −0.365273 | − | 0.930900i | \(-0.619024\pi\) | ||||
−0.365273 | + | 0.930900i | \(0.619024\pi\) | |||||||
\(564\) | 12080.7 | 0.901931 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12245.4 | −0.909389 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1680.48 | 0.124140 | ||||||||
\(569\) | 4063.44 | 0.299382 | 0.149691 | − | 0.988733i | \(-0.452172\pi\) | ||||
0.149691 | + | 0.988733i | \(0.452172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23907.0 | −1.75215 | −0.876075 | − | 0.482175i | \(-0.839847\pi\) | ||||
−0.876075 | + | 0.482175i | \(0.839847\pi\) | |||||||
\(572\) | −18093.4 | −1.32259 | ||||||||
\(573\) | −7246.48 | −0.528317 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 928.226 | 0.0671460 | ||||||||
\(577\) | 15145.4 | 1.09274 | 0.546369 | − | 0.837545i | \(-0.316010\pi\) | ||||
0.546369 | + | 0.837545i | \(0.316010\pi\) | |||||||
\(578\) | −9003.50 | −0.647918 | ||||||||
\(579\) | 14276.7 | 1.02473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5626.13 | −0.400706 | ||||||||
\(583\) | 28409.0 | 2.01815 | ||||||||
\(584\) | 1134.27 | 0.0803704 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3293.34 | 0.232162 | ||||||||
\(587\) | 10865.9 | 0.764025 | 0.382013 | − | 0.924157i | \(-0.375231\pi\) | ||||
0.382013 | + | 0.924157i | \(0.375231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5003.96 | −0.350059 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20135.8 | −1.40149 | ||||||||
\(592\) | −2601.31 | −0.180596 | ||||||||
\(593\) | 4578.29 | 0.317045 | 0.158523 | − | 0.987355i | \(-0.449327\pi\) | ||||
0.158523 | + | 0.987355i | \(0.449327\pi\) | |||||||
\(594\) | 7790.53 | 0.538130 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −714.214 | −0.0490862 | ||||||||
\(597\) | 29243.9 | 2.00481 | ||||||||
\(598\) | −3935.57 | −0.269126 | ||||||||
\(599\) | −20561.5 | −1.40254 | −0.701270 | − | 0.712896i | \(-0.747383\pi\) | ||||
−0.701270 | + | 0.712896i | \(0.747383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1254.44 | 0.0851406 | 0.0425703 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425703 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1785.00 | 0.120549 | ||||||||
\(604\) | 3326.67 | 0.224107 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22782.7 | 1.52720 | ||||||||
\(607\) | −10861.4 | −0.726277 | −0.363139 | − | 0.931735i | \(-0.618295\pi\) | ||||
−0.363139 | + | 0.931735i | \(0.618295\pi\) | |||||||
\(608\) | 993.859 | 0.0662933 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43826.9 | 2.90188 | ||||||||
\(612\) | 1176.48 | 0.0777067 | ||||||||
\(613\) | −21385.7 | −1.40907 | −0.704536 | − | 0.709668i | \(-0.748845\pi\) | ||||
−0.704536 | + | 0.709668i | \(0.748845\pi\) | |||||||
\(614\) | 15780.8 | 1.03724 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11863.3 | 0.774066 | 0.387033 | − | 0.922066i | \(-0.373500\pi\) | ||||
0.387033 | + | 0.922066i | \(0.373500\pi\) | |||||||
\(618\) | −10944.3 | −0.712370 | ||||||||
\(619\) | 8098.60 | 0.525864 | 0.262932 | − | 0.964814i | \(-0.415310\pi\) | ||||
0.262932 | + | 0.964814i | \(0.415310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1694.56 | 0.109501 | ||||||||
\(622\) | 6873.96 | 0.443120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9636.39 | 0.618212 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14419.6 | −0.920645 | ||||||||
\(627\) | −9681.10 | −0.616628 | ||||||||
\(628\) | −670.787 | −0.0426231 | ||||||||
\(629\) | −3297.04 | −0.209001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28405.4 | 1.79208 | 0.896038 | − | 0.443977i | \(-0.146433\pi\) | ||||
0.896038 | + | 0.443977i | \(0.146433\pi\) | |||||||
\(632\) | 4107.39 | 0.258518 | ||||||||
\(633\) | −16237.3 | −1.01955 | ||||||||
\(634\) | −1771.61 | −0.110977 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15130.4 | −0.943335 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6726.58 | 0.417411 | ||||||||
\(639\) | 3046.62 | 0.188611 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4854.85 | 0.299150 | 0.149575 | − | 0.988750i | \(-0.452209\pi\) | ||||
0.149575 | + | 0.988750i | \(0.452209\pi\) | |||||||
\(642\) | 16525.5 | 1.01591 | ||||||||
\(643\) | 23838.8 | 1.46207 | 0.731033 | − | 0.682342i | \(-0.239038\pi\) | ||||
0.731033 | + | 0.682342i | \(0.239038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1259.67 | 0.0767199 | ||||||||
\(647\) | 16912.8 | 1.02768 | 0.513841 | − | 0.857886i | \(-0.328222\pi\) | ||||
0.513841 | + | 0.857886i | \(0.328222\pi\) | |||||||
\(648\) | −7281.94 | −0.441453 | ||||||||
\(649\) | −25979.9 | −1.57134 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6448.37 | 0.387327 | ||||||||
\(653\) | −14301.5 | −0.857059 | −0.428530 | − | 0.903528i | \(-0.640968\pi\) | ||||
−0.428530 | + | 0.903528i | \(0.640968\pi\) | |||||||
\(654\) | 7710.15 | 0.460995 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5841.17 | 0.347651 | ||||||||
\(657\) | 2056.36 | 0.122110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8601.03 | −0.508420 | −0.254210 | − | 0.967149i | \(-0.581815\pi\) | ||||
−0.254210 | + | 0.967149i | \(0.581815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 794.288 | 0.0467386 | 0.0233693 | − | 0.999727i | \(-0.492561\pi\) | ||||
0.0233693 | + | 0.999727i | \(0.492561\pi\) | |||||||
\(662\) | −3532.37 | −0.207386 | ||||||||
\(663\) | 12213.7 | 0.715445 | ||||||||
\(664\) | 939.007 | 0.0548803 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4716.02 | −0.274387 | ||||||||
\(667\) | 1463.13 | 0.0849366 | ||||||||
\(668\) | 6362.75 | 0.368536 | ||||||||
\(669\) | 37369.2 | 2.15961 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30280.3 | 1.74211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3100.85 | −0.177606 | −0.0888031 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888031 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(674\) | −15042.7 | −0.859677 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26171.4 | 1.48904 | ||||||||
\(677\) | 3236.73 | 0.183748 | 0.0918742 | − | 0.995771i | \(-0.470714\pi\) | ||||
0.0918742 | + | 0.995771i | \(0.470714\pi\) | |||||||
\(678\) | 11083.6 | 0.627822 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42689.8 | 2.40217 | ||||||||
\(682\) | −15591.1 | −0.875386 | ||||||||
\(683\) | −9415.00 | −0.527460 | −0.263730 | − | 0.964597i | \(-0.584953\pi\) | ||||
−0.263730 | + | 0.964597i | \(0.584953\pi\) | |||||||
\(684\) | 1801.81 | 0.100722 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3271.70 | 0.181693 | ||||||||
\(688\) | −4072.29 | −0.225661 | ||||||||
\(689\) | −54891.0 | −3.03509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22798.5 | 1.25513 | 0.627565 | − | 0.778564i | \(-0.284052\pi\) | ||||
0.627565 | + | 0.778564i | \(0.284052\pi\) | |||||||
\(692\) | −6969.63 | −0.382870 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9317.06 | −0.509612 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3582.53 | −0.195108 | ||||||||
\(697\) | 7403.41 | 0.402330 | ||||||||
\(698\) | 14396.3 | 0.780670 | ||||||||
\(699\) | 40637.0 | 2.19890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33797.9 | 1.82101 | 0.910506 | − | 0.413496i | \(-0.135692\pi\) | ||||
0.910506 | + | 0.413496i | \(0.135692\pi\) | |||||||
\(702\) | −15052.6 | −0.809294 | ||||||||
\(703\) | −5049.48 | −0.270903 | ||||||||
\(704\) | 3096.62 | 0.165779 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7280.16 | −0.388091 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13836.7 | 0.734484 | ||||||||
\(709\) | −26226.1 | −1.38920 | −0.694599 | − | 0.719397i | \(-0.744418\pi\) | ||||
−0.694599 | + | 0.719397i | \(0.744418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7446.45 | 0.392776 | ||||||||
\(712\) | 490.071 | 0.0257952 | ||||||||
\(713\) | −3391.29 | −0.178128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9717.47 | −0.507205 | ||||||||
\(717\) | 29732.1 | 1.54863 | ||||||||
\(718\) | −10939.8 | −0.568620 | ||||||||
\(719\) | 8593.89 | 0.445755 | 0.222878 | − | 0.974846i | \(-0.428455\pi\) | ||||
0.222878 | + | 0.974846i | \(0.428455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11788.8 | −0.607664 | ||||||||
\(723\) | 9990.14 | 0.513883 | ||||||||
\(724\) | −10514.4 | −0.539732 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13014.4 | −0.665303 | ||||||||
\(727\) | −26368.9 | −1.34521 | −0.672606 | − | 0.740001i | \(-0.734825\pi\) | ||||
−0.672606 | + | 0.740001i | \(0.734825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 801.754 | 0.0407333 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5161.45 | −0.261153 | ||||||||
\(732\) | −16127.0 | −0.814307 | ||||||||
\(733\) | −16495.5 | −0.831207 | −0.415604 | − | 0.909546i | \(-0.636430\pi\) | ||||
−0.415604 | + | 0.909546i | \(0.636430\pi\) | |||||||
\(734\) | −130.174 | −0.00654607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 673.560 | 0.0337333 | ||||||||
\(737\) | 5954.87 | 0.297626 | ||||||||
\(738\) | 10589.7 | 0.528200 | ||||||||
\(739\) | 8670.04 | 0.431573 | 0.215786 | − | 0.976441i | \(-0.430768\pi\) | ||||
0.215786 | + | 0.976441i | \(0.430768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18705.5 | 0.927346 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30923.0 | 1.52686 | 0.763430 | − | 0.645891i | \(-0.223514\pi\) | ||||
0.763430 | + | 0.645891i | \(0.223514\pi\) | |||||||
\(744\) | 8303.70 | 0.409178 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20306.8 | 0.996627 | ||||||||
\(747\) | 1702.36 | 0.0833819 | ||||||||
\(748\) | 3924.82 | 0.191852 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13168.0 | 0.639822 | 0.319911 | − | 0.947448i | \(-0.396347\pi\) | ||||
0.319911 | + | 0.947448i | \(0.396347\pi\) | |||||||
\(752\) | −7500.83 | −0.363733 | ||||||||
\(753\) | 4912.55 | 0.237747 | ||||||||
\(754\) | −12996.9 | −0.627743 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31713.3 | −1.52264 | −0.761321 | − | 0.648375i | \(-0.775449\pi\) | ||||
−0.761321 | + | 0.648375i | \(0.775449\pi\) | |||||||
\(758\) | 2907.91 | 0.139341 | ||||||||
\(759\) | −6561.09 | −0.313771 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 818.651 | 0.0389962 | 0.0194981 | − | 0.999810i | \(-0.493793\pi\) | ||||
0.0194981 | + | 0.999810i | \(0.493793\pi\) | |||||||
\(762\) | 12516.6 | 0.595051 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4499.29 | 0.213061 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1154.60 | 0.0544615 | ||||||||
\(767\) | 50197.4 | 2.36313 | ||||||||
\(768\) | −1649.23 | −0.0774891 | ||||||||
\(769\) | −28514.9 | −1.33716 | −0.668578 | − | 0.743642i | \(-0.733097\pi\) | ||||
−0.668578 | + | 0.743642i | \(0.733097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14832.6 | 0.692842 | ||||||||
\(772\) | −8864.33 | −0.413257 | ||||||||
\(773\) | 28791.0 | 1.33964 | 0.669819 | − | 0.742525i | \(-0.266372\pi\) | ||||
0.669819 | + | 0.742525i | \(0.266372\pi\) | |||||||
\(774\) | −7382.83 | −0.342856 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3493.23 | 0.161598 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4142.00 | −0.190871 | ||||||||
\(779\) | 11338.5 | 0.521493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10163.7 | 0.465666 | ||||||||
\(782\) | 853.706 | 0.0390390 | ||||||||
\(783\) | 5596.12 | 0.255414 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1927.46 | 0.0874684 | ||||||||
\(787\) | 7485.80 | 0.339059 | 0.169530 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169530 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(788\) | 12502.2 | 0.565194 | ||||||||
\(789\) | 31139.0 | 1.40504 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5613.98 | 0.251874 | ||||||||
\(793\) | −58506.5 | −2.61996 | ||||||||
\(794\) | −10066.8 | −0.449948 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18157.4 | −0.808506 | ||||||||
\(797\) | 2323.41 | 0.103261 | 0.0516307 | − | 0.998666i | \(-0.483558\pi\) | ||||
0.0516307 | + | 0.998666i | \(0.483558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9506.96 | −0.420941 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 888.469 | 0.0391917 | ||||||||
\(802\) | −9893.76 | −0.435612 | ||||||||
\(803\) | 6860.14 | 0.301481 | ||||||||
\(804\) | −3171.52 | −0.139118 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30124.6 | 1.31649 | ||||||||
\(807\) | 31118.7 | 1.35741 | ||||||||
\(808\) | −14145.7 | −0.615895 | ||||||||
\(809\) | −9103.69 | −0.395635 | −0.197818 | − | 0.980239i | \(-0.563385\pi\) | ||||
−0.197818 | + | 0.980239i | \(0.563385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4516.19 | 0.195542 | 0.0977711 | − | 0.995209i | \(-0.468829\pi\) | ||||
0.0977711 | + | 0.995209i | \(0.468829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38334.2 | −1.65368 | ||||||||
\(814\) | −15732.9 | −0.677443 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2090.33 | −0.0896767 | ||||||||
\(817\) | −7904.86 | −0.338502 | ||||||||
\(818\) | 18779.7 | 0.802709 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6046.44 | −0.257031 | −0.128515 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128515 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(822\) | −6381.06 | −0.270760 | ||||||||
\(823\) | 44591.3 | 1.88864 | 0.944322 | − | 0.329022i | \(-0.106719\pi\) | ||||
0.944322 | + | 0.329022i | \(0.106719\pi\) | |||||||
\(824\) | 6795.25 | 0.287286 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17170.6 | 0.721982 | 0.360991 | − | 0.932569i | \(-0.382439\pi\) | ||||
0.360991 | + | 0.932569i | \(0.382439\pi\) | |||||||
\(828\) | 1221.12 | 0.0512524 | ||||||||
\(829\) | 30509.9 | 1.27823 | 0.639115 | − | 0.769111i | \(-0.279301\pi\) | ||||
0.639115 | + | 0.769111i | \(0.279301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49405.5 | 2.06241 | ||||||||
\(832\) | −5983.18 | −0.249314 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6010.95 | −0.249571 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6010.93 | 0.248675 | ||||||||
\(837\) | −12970.9 | −0.535650 | ||||||||
\(838\) | −16847.5 | −0.694497 | ||||||||
\(839\) | 34089.6 | 1.40275 | 0.701373 | − | 0.712794i | \(-0.252571\pi\) | ||||
0.701373 | + | 0.712794i | \(0.252571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19557.1 | −0.801884 | ||||||||
\(842\) | 11360.3 | 0.464966 | ||||||||
\(843\) | 40678.0 | 1.66195 | ||||||||
\(844\) | 10081.6 | 0.411165 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13598.6 | −0.552634 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9394.40 | 0.380430 | ||||||||
\(849\) | 39444.6 | 1.59450 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3422.14 | −0.137849 | ||||||||
\(852\) | −5413.11 | −0.217664 | ||||||||
\(853\) | 5078.39 | 0.203846 | 0.101923 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101923 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10260.6 | −0.409697 | ||||||||
\(857\) | 85.5262 | 0.00340901 | 0.00170450 | − | 0.999999i | \(-0.499457\pi\) | ||||
0.00170450 | + | 0.999999i | \(0.499457\pi\) | |||||||
\(858\) | 58281.6 | 2.31900 | ||||||||
\(859\) | −32320.1 | −1.28376 | −0.641878 | − | 0.766807i | \(-0.721844\pi\) | ||||
−0.641878 | + | 0.766807i | \(0.721844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24696.7 | 0.975840 | ||||||||
\(863\) | 20936.2 | 0.825813 | 0.412907 | − | 0.910773i | \(-0.364514\pi\) | ||||
0.412907 | + | 0.910773i | \(0.364514\pi\) | |||||||
\(864\) | 2576.20 | 0.101440 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18063.9 | −0.708816 | ||||||||
\(867\) | 29001.7 | 1.13604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24841.8 | 0.969736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11505.8 | −0.447600 | ||||||||
\(872\) | −4787.19 | −0.185911 | ||||||||
\(873\) | 6333.02 | 0.245522 | ||||||||
\(874\) | 1307.47 | 0.0506015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3653.66 | −0.140920 | ||||||||
\(877\) | −24078.1 | −0.927093 | −0.463546 | − | 0.886073i | \(-0.653423\pi\) | ||||
−0.463546 | + | 0.886073i | \(0.653423\pi\) | |||||||
\(878\) | 21314.8 | 0.819295 | ||||||||
\(879\) | −10608.4 | −0.407067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23196.8 | −0.887081 | −0.443541 | − | 0.896254i | \(-0.646278\pi\) | ||||
−0.443541 | + | 0.896254i | \(0.646278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31800.2 | 1.21196 | 0.605981 | − | 0.795479i | \(-0.292781\pi\) | ||||
0.605981 | + | 0.795479i | \(0.292781\pi\) | |||||||
\(884\) | −7583.40 | −0.288526 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1802.64 | −0.0683532 | ||||||||
\(887\) | 34200.2 | 1.29462 | 0.647311 | − | 0.762226i | \(-0.275893\pi\) | ||||
0.647311 | + | 0.762226i | \(0.275893\pi\) | |||||||
\(888\) | 8379.24 | 0.316654 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44041.8 | −1.65595 | ||||||||
\(892\) | −23202.3 | −0.870931 | ||||||||
\(893\) | −14560.1 | −0.545616 | ||||||||
\(894\) | 2300.60 | 0.0860666 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12677.1 | 0.471880 | ||||||||
\(898\) | −15543.8 | −0.577619 | ||||||||
\(899\) | −11199.4 | −0.415486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11907.0 | 0.440265 | ||||||||
\(902\) | 35327.8 | 1.30409 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6881.74 | −0.253190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10715.7 | −0.392944 | ||||||||
\(907\) | −4793.39 | −0.175482 | −0.0877409 | − | 0.996143i | \(-0.527965\pi\) | ||||
−0.0877409 | + | 0.996143i | \(0.527965\pi\) | |||||||
\(908\) | −26505.9 | −0.968753 | ||||||||
\(909\) | −25645.3 | −0.935753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25153.4 | −0.914787 | −0.457393 | − | 0.889264i | \(-0.651217\pi\) | ||||
−0.457393 | + | 0.889264i | \(0.651217\pi\) | |||||||
\(912\) | −3201.38 | −0.116237 | ||||||||
\(913\) | 5679.19 | 0.205864 | ||||||||
\(914\) | 5520.70 | 0.199791 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2031.38 | −0.0732736 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3265.22 | 0.117395 | ||||||||
\(919\) | −20437.0 | −0.733573 | −0.366786 | − | 0.930305i | \(-0.619542\pi\) | ||||
−0.366786 | + | 0.930305i | \(0.619542\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −50832.6 | −1.81867 | ||||||||
\(922\) | 32964.7 | 1.17748 | ||||||||
\(923\) | −19637.9 | −0.700315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19898.3 | 0.706155 | ||||||||
\(927\) | 12319.4 | 0.436485 | ||||||||
\(928\) | 2224.37 | 0.0786838 | ||||||||
\(929\) | −1282.13 | −0.0452802 | −0.0226401 | − | 0.999744i | \(-0.507207\pi\) | ||||
−0.0226401 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25231.3 | −0.886779 | ||||||||
\(933\) | −22142.1 | −0.776957 | ||||||||
\(934\) | −4203.11 | −0.147248 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10847.1 | −0.378793 | ||||||||
\(937\) | −16878.5 | −0.588472 | −0.294236 | − | 0.955733i | \(-0.595065\pi\) | ||||
−0.294236 | + | 0.955733i | \(0.595065\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46447.9 | 1.61424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14931.6 | −0.517275 | −0.258637 | − | 0.965974i | \(-0.583274\pi\) | ||||
−0.258637 | + | 0.965974i | \(0.583274\pi\) | |||||||
\(942\) | 2160.71 | 0.0747344 | ||||||||
\(943\) | 7684.33 | 0.265362 | ||||||||
\(944\) | −8591.11 | −0.296204 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24629.5 | −0.846486 | ||||||||
\(947\) | −37545.7 | −1.28835 | −0.644177 | − | 0.764877i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764877i | \(0.722800\pi\) | |||||||
\(948\) | −13230.6 | −0.453279 | ||||||||
\(949\) | −13254.9 | −0.453396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5706.63 | 0.194585 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −437.260 | −0.0148628 | −0.00743140 | − | 0.999972i | \(-0.502366\pi\) | ||||
−0.00743140 | + | 0.999972i | \(0.502366\pi\) | |||||||
\(954\) | 17031.5 | 0.578003 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18460.5 | −0.624535 | ||||||||
\(957\) | −21667.4 | −0.731879 | ||||||||
\(958\) | 16019.9 | 0.540272 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3832.58 | −0.128649 | ||||||||
\(962\) | 30398.6 | 1.01881 | ||||||||
\(963\) | −18601.9 | −0.622469 | ||||||||
\(964\) | −6202.82 | −0.207240 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52372.7 | 1.74167 | 0.870834 | − | 0.491577i | \(-0.163579\pi\) | ||||
0.870834 | + | 0.491577i | \(0.163579\pi\) | |||||||
\(968\) | 8080.57 | 0.268305 | ||||||||
\(969\) | −4057.60 | −0.134519 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40759.4 | −1.34710 | −0.673548 | − | 0.739144i | \(-0.735231\pi\) | ||||
−0.673548 | + | 0.739144i | \(0.735231\pi\) | |||||||
\(972\) | 14761.6 | 0.487119 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10765.2 | 0.354147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10013.2 | 0.328396 | ||||||||
\(977\) | 37637.9 | 1.23249 | 0.616246 | − | 0.787554i | \(-0.288653\pi\) | ||||
0.616246 | + | 0.787554i | \(0.288653\pi\) | |||||||
\(978\) | −20771.2 | −0.679132 | ||||||||
\(979\) | 2963.99 | 0.0967614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8678.89 | −0.282462 | ||||||||
\(982\) | −6913.86 | −0.224674 | ||||||||
\(983\) | 8799.74 | 0.285522 | 0.142761 | − | 0.989757i | \(-0.454402\pi\) | ||||
0.142761 | + | 0.989757i | \(0.454402\pi\) | |||||||
\(984\) | −18815.3 | −0.609564 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2819.29 | 0.0910592 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11614.1 | −0.373982 | ||||||||
\(989\) | −5357.29 | −0.172247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43972.1 | −1.40950 | −0.704752 | − | 0.709454i | \(-0.748942\pi\) | ||||
−0.704752 | + | 0.709454i | \(0.748942\pi\) | |||||||
\(992\) | −5155.72 | −0.165014 | ||||||||
\(993\) | 11378.3 | 0.363626 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3024.69 | −0.0962260 | ||||||||
\(997\) | −10052.7 | −0.319329 | −0.159664 | − | 0.987171i | \(-0.551041\pi\) | ||||
−0.159664 | + | 0.987171i | \(0.551041\pi\) | |||||||
\(998\) | −24196.3 | −0.767457 | ||||||||
\(999\) | −13088.9 | −0.414528 |
(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 | 2450.4.a.cx.1.2 | 6 | ||
5.2 | odd | 4 | 490.4.c.e.99.11 | 12 | |||
5.3 | odd | 4 | 490.4.c.e.99.2 | 12 | |||
5.4 | even | 2 | 2450.4.a.cw.1.5 | 6 | |||
7.3 | odd | 6 | 350.4.e.n.51.2 | 12 | |||
7.5 | odd | 6 | 350.4.e.n.151.2 | 12 | |||
7.6 | odd | 2 | 2450.4.a.cy.1.5 | 6 | |||
35.3 | even | 12 | 70.4.i.a.9.11 | yes | 24 | ||
35.12 | even | 12 | 70.4.i.a.39.11 | yes | 24 | ||
35.13 | even | 4 | 490.4.c.f.99.5 | 12 | |||
35.17 | even | 12 | 70.4.i.a.9.2 | ✓ | 24 | ||
35.19 | odd | 6 | 350.4.e.o.151.5 | 12 | |||
35.24 | odd | 6 | 350.4.e.o.51.5 | 12 | |||
35.27 | even | 4 | 490.4.c.f.99.8 | 12 | |||
35.33 | even | 12 | 70.4.i.a.39.2 | yes | 24 | ||
35.34 | odd | 2 | 2450.4.a.cv.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.i.a.9.2 | ✓ | 24 | 35.17 | even | 12 | ||
70.4.i.a.9.11 | yes | 24 | 35.3 | even | 12 | ||
70.4.i.a.39.2 | yes | 24 | 35.33 | even | 12 | ||
70.4.i.a.39.11 | yes | 24 | 35.12 | even | 12 | ||
350.4.e.n.51.2 | 12 | 7.3 | odd | 6 | |||
350.4.e.n.151.2 | 12 | 7.5 | odd | 6 | |||
350.4.e.o.51.5 | 12 | 35.24 | odd | 6 | |||
350.4.e.o.151.5 | 12 | 35.19 | odd | 6 | |||
490.4.c.e.99.2 | 12 | 5.3 | odd | 4 | |||
490.4.c.e.99.11 | 12 | 5.2 | odd | 4 | |||
490.4.c.f.99.5 | 12 | 35.13 | even | 4 | |||
490.4.c.f.99.8 | 12 | 35.27 | even | 4 | |||
2450.4.a.cv.1.2 | 6 | 35.34 | odd | 2 | |||
2450.4.a.cw.1.5 | 6 | 5.4 | even | 2 | |||
2450.4.a.cx.1.2 | 6 | 1.1 | even | 1 | trivial | ||
2450.4.a.cy.1.5 | 6 | 7.6 | odd | 2 |