Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | −15.0000 | −0.474342 | ||||||||
\(11\) | −45.0000 | −1.23346 | −0.616728 | − | 0.787177i | \(-0.711542\pi\) | ||||
−0.616728 | + | 0.787177i | \(0.711542\pi\) | |||||||
\(12\) | 2.00000 | 0.0481125 | ||||||||
\(13\) | −59.0000 | −1.25874 | −0.629371 | − | 0.777105i | \(-0.716688\pi\) | ||||
−0.629371 | + | 0.777105i | \(0.716688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0000 | −0.172133 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 54.0000 | 0.770407 | 0.385204 | − | 0.922832i | \(-0.374131\pi\) | ||||
0.385204 | + | 0.922832i | \(0.374131\pi\) | |||||||
\(18\) | −69.0000 | −0.903525 | ||||||||
\(19\) | 121.000 | 1.46102 | 0.730508 | − | 0.682904i | \(-0.239283\pi\) | ||||
0.730508 | + | 0.682904i | \(0.239283\pi\) | |||||||
\(20\) | −5.00000 | −0.0559017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −135.000 | −1.30828 | ||||||||
\(23\) | 69.0000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | −42.0000 | −0.357217 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −177.000 | −1.33510 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −162.000 | −1.03733 | −0.518666 | − | 0.854977i | \(-0.673571\pi\) | ||||
−0.518666 | + | 0.854977i | \(0.673571\pi\) | |||||||
\(30\) | −30.0000 | −0.182574 | ||||||||
\(31\) | 88.0000 | 0.509847 | 0.254924 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254924 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | −90.0000 | −0.474757 | ||||||||
\(34\) | 162.000 | 0.817140 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −23.0000 | −0.106481 | ||||||||
\(37\) | −259.000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 363.000 | 1.54964 | ||||||||
\(39\) | −118.000 | −0.484490 | ||||||||
\(40\) | 105.000 | 0.415049 | ||||||||
\(41\) | −195.000 | −0.742778 | −0.371389 | − | 0.928477i | \(-0.621118\pi\) | ||||
−0.371389 | + | 0.928477i | \(0.621118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −286.000 | −1.01429 | −0.507146 | − | 0.861860i | \(-0.669300\pi\) | ||||
−0.507146 | + | 0.861860i | \(0.669300\pi\) | |||||||
\(44\) | −45.0000 | −0.154182 | ||||||||
\(45\) | 115.000 | 0.380960 | ||||||||
\(46\) | 207.000 | 0.663489 | ||||||||
\(47\) | −45.0000 | −0.139658 | −0.0698290 | − | 0.997559i | \(-0.522245\pi\) | ||||
−0.0698290 | + | 0.997559i | \(0.522245\pi\) | |||||||
\(48\) | −142.000 | −0.426999 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 75.0000 | 0.212132 | ||||||||
\(51\) | 108.000 | 0.296530 | ||||||||
\(52\) | −59.0000 | −0.157343 | ||||||||
\(53\) | 597.000 | 1.54725 | 0.773625 | − | 0.633644i | \(-0.218441\pi\) | ||||
0.773625 | + | 0.633644i | \(0.218441\pi\) | |||||||
\(54\) | −300.000 | −0.756015 | ||||||||
\(55\) | 225.000 | 0.551618 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 242.000 | 0.562345 | ||||||||
\(58\) | −486.000 | −1.10026 | ||||||||
\(59\) | 360.000 | 0.794373 | 0.397187 | − | 0.917738i | \(-0.369987\pi\) | ||||
0.397187 | + | 0.917738i | \(0.369987\pi\) | |||||||
\(60\) | −10.0000 | −0.0215166 | ||||||||
\(61\) | −392.000 | −0.822794 | −0.411397 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411397 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(62\) | 264.000 | 0.540775 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 295.000 | 0.562927 | ||||||||
\(66\) | −270.000 | −0.503556 | ||||||||
\(67\) | −280.000 | −0.510559 | −0.255279 | − | 0.966867i | \(-0.582167\pi\) | ||||
−0.255279 | + | 0.966867i | \(0.582167\pi\) | |||||||
\(68\) | 54.0000 | 0.0963009 | ||||||||
\(69\) | 138.000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.0000 | 0.0802331 | 0.0401166 | − | 0.999195i | \(-0.487227\pi\) | ||||
0.0401166 | + | 0.999195i | \(0.487227\pi\) | |||||||
\(72\) | 483.000 | 0.790585 | ||||||||
\(73\) | −668.000 | −1.07101 | −0.535503 | − | 0.844533i | \(-0.679878\pi\) | ||||
−0.535503 | + | 0.844533i | \(0.679878\pi\) | |||||||
\(74\) | −777.000 | −1.22060 | ||||||||
\(75\) | 50.0000 | 0.0769800 | ||||||||
\(76\) | 121.000 | 0.182627 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −354.000 | −0.513880 | ||||||||
\(79\) | 782.000 | 1.11369 | 0.556847 | − | 0.830615i | \(-0.312011\pi\) | ||||
0.556847 | + | 0.830615i | \(0.312011\pi\) | |||||||
\(80\) | 355.000 | 0.496128 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | −585.000 | −0.787835 | ||||||||
\(83\) | −768.000 | −1.01565 | −0.507825 | − | 0.861460i | \(-0.669550\pi\) | ||||
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −270.000 | −0.344537 | ||||||||
\(86\) | −858.000 | −1.07582 | ||||||||
\(87\) | −324.000 | −0.399269 | ||||||||
\(88\) | 945.000 | 1.14474 | ||||||||
\(89\) | 1194.00 | 1.42206 | 0.711032 | − | 0.703159i | \(-0.248228\pi\) | ||||
0.711032 | + | 0.703159i | \(0.248228\pi\) | |||||||
\(90\) | 345.000 | 0.404069 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 69.0000 | 0.0781929 | ||||||||
\(93\) | 176.000 | 0.196240 | ||||||||
\(94\) | −135.000 | −0.148130 | ||||||||
\(95\) | −605.000 | −0.653386 | ||||||||
\(96\) | −90.0000 | −0.0956832 | ||||||||
\(97\) | −902.000 | −0.944167 | −0.472084 | − | 0.881554i | \(-0.656498\pi\) | ||||
−0.472084 | + | 0.881554i | \(0.656498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1035.00 | 1.05072 | ||||||||
\(100\) | 25.0000 | 0.0250000 | ||||||||
\(101\) | −684.000 | −0.673867 | −0.336933 | − | 0.941528i | \(-0.609390\pi\) | ||||
−0.336933 | + | 0.941528i | \(0.609390\pi\) | |||||||
\(102\) | 324.000 | 0.314517 | ||||||||
\(103\) | 1516.00 | 1.45025 | 0.725126 | − | 0.688616i | \(-0.241782\pi\) | ||||
0.725126 | + | 0.688616i | \(0.241782\pi\) | |||||||
\(104\) | 1239.00 | 1.16821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1791.00 | 1.64111 | ||||||||
\(107\) | −732.000 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(108\) | −100.000 | −0.0890973 | ||||||||
\(109\) | −1600.00 | −1.40598 | −0.702992 | − | 0.711198i | \(-0.748153\pi\) | ||||
−0.702992 | + | 0.711198i | \(0.748153\pi\) | |||||||
\(110\) | 675.000 | 0.585079 | ||||||||
\(111\) | −518.000 | −0.442940 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1392.00 | −1.15883 | −0.579417 | − | 0.815031i | \(-0.696720\pi\) | ||||
−0.579417 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(114\) | 726.000 | 0.596457 | ||||||||
\(115\) | −345.000 | −0.279751 | ||||||||
\(116\) | −162.000 | −0.129667 | ||||||||
\(117\) | 1357.00 | 1.07226 | ||||||||
\(118\) | 1080.00 | 0.842560 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 210.000 | 0.159752 | ||||||||
\(121\) | 694.000 | 0.521412 | ||||||||
\(122\) | −1176.00 | −0.872705 | ||||||||
\(123\) | −390.000 | −0.285895 | ||||||||
\(124\) | 88.0000 | 0.0637309 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 803.000 | 0.561061 | 0.280530 | − | 0.959845i | \(-0.409490\pi\) | ||||
0.280530 | + | 0.959845i | \(0.409490\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | −572.000 | −0.390401 | ||||||||
\(130\) | 885.000 | 0.597074 | ||||||||
\(131\) | −2019.00 | −1.34657 | −0.673286 | − | 0.739382i | \(-0.735118\pi\) | ||||
−0.673286 | + | 0.739382i | \(0.735118\pi\) | |||||||
\(132\) | −90.0000 | −0.0593447 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −840.000 | −0.541529 | ||||||||
\(135\) | 500.000 | 0.318764 | ||||||||
\(136\) | −1134.00 | −0.714998 | ||||||||
\(137\) | 60.0000 | 0.0374171 | 0.0187086 | − | 0.999825i | \(-0.494045\pi\) | ||||
0.0187086 | + | 0.999825i | \(0.494045\pi\) | |||||||
\(138\) | 414.000 | 0.255377 | ||||||||
\(139\) | 1708.00 | 1.04224 | 0.521118 | − | 0.853485i | \(-0.325515\pi\) | ||||
0.521118 | + | 0.853485i | \(0.325515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −90.0000 | −0.0537544 | ||||||||
\(142\) | 144.000 | 0.0851001 | ||||||||
\(143\) | 2655.00 | 1.55260 | ||||||||
\(144\) | 1633.00 | 0.945023 | ||||||||
\(145\) | 810.000 | 0.463909 | ||||||||
\(146\) | −2004.00 | −1.13597 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −259.000 | −0.143849 | ||||||||
\(149\) | −1086.00 | −0.597105 | −0.298552 | − | 0.954393i | \(-0.596504\pi\) | ||||
−0.298552 | + | 0.954393i | \(0.596504\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | −2866.00 | −1.54458 | −0.772291 | − | 0.635269i | \(-0.780889\pi\) | ||||
−0.772291 | + | 0.635269i | \(0.780889\pi\) | |||||||
\(152\) | −2541.00 | −1.35594 | ||||||||
\(153\) | −1242.00 | −0.656273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −440.000 | −0.228011 | ||||||||
\(156\) | −118.000 | −0.0605613 | ||||||||
\(157\) | 229.000 | 0.116409 | 0.0582044 | − | 0.998305i | \(-0.481462\pi\) | ||||
0.0582044 | + | 0.998305i | \(0.481462\pi\) | |||||||
\(158\) | 2346.00 | 1.18125 | ||||||||
\(159\) | 1194.00 | 0.595537 | ||||||||
\(160\) | 225.000 | 0.111174 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1263.00 | 0.612535 | ||||||||
\(163\) | −1228.00 | −0.590088 | −0.295044 | − | 0.955484i | \(-0.595334\pi\) | ||||
−0.295044 | + | 0.955484i | \(0.595334\pi\) | |||||||
\(164\) | −195.000 | −0.0928472 | ||||||||
\(165\) | 450.000 | 0.212318 | ||||||||
\(166\) | −2304.00 | −1.07726 | ||||||||
\(167\) | 1929.00 | 0.893835 | 0.446918 | − | 0.894575i | \(-0.352522\pi\) | ||||
0.446918 | + | 0.894575i | \(0.352522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1284.00 | 0.584433 | ||||||||
\(170\) | −810.000 | −0.365436 | ||||||||
\(171\) | −2783.00 | −1.24457 | ||||||||
\(172\) | −286.000 | −0.126787 | ||||||||
\(173\) | 699.000 | 0.307191 | 0.153595 | − | 0.988134i | \(-0.450915\pi\) | ||||
0.153595 | + | 0.988134i | \(0.450915\pi\) | |||||||
\(174\) | −972.000 | −0.423489 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3195.00 | 1.36836 | ||||||||
\(177\) | 720.000 | 0.305754 | ||||||||
\(178\) | 3582.00 | 1.50833 | ||||||||
\(179\) | 3117.00 | 1.30154 | 0.650770 | − | 0.759275i | \(-0.274446\pi\) | ||||
0.650770 | + | 0.759275i | \(0.274446\pi\) | |||||||
\(180\) | 115.000 | 0.0476200 | ||||||||
\(181\) | 1798.00 | 0.738366 | 0.369183 | − | 0.929357i | \(-0.379638\pi\) | ||||
0.369183 | + | 0.929357i | \(0.379638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −784.000 | −0.316694 | ||||||||
\(184\) | −1449.00 | −0.580553 | ||||||||
\(185\) | 1295.00 | 0.514650 | ||||||||
\(186\) | 528.000 | 0.208144 | ||||||||
\(187\) | −2430.00 | −0.950263 | ||||||||
\(188\) | −45.0000 | −0.0174572 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1815.00 | −0.693021 | ||||||||
\(191\) | −2388.00 | −0.904658 | −0.452329 | − | 0.891851i | \(-0.649407\pi\) | ||||
−0.452329 | + | 0.891851i | \(0.649407\pi\) | |||||||
\(192\) | 866.000 | 0.325511 | ||||||||
\(193\) | 272.000 | 0.101446 | 0.0507228 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507228 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(194\) | −2706.00 | −1.00144 | ||||||||
\(195\) | 590.000 | 0.216671 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2109.00 | −0.762741 | −0.381371 | − | 0.924422i | \(-0.624548\pi\) | ||||
−0.381371 | + | 0.924422i | \(0.624548\pi\) | |||||||
\(198\) | 3105.00 | 1.11446 | ||||||||
\(199\) | −1424.00 | −0.507260 | −0.253630 | − | 0.967301i | \(-0.581625\pi\) | ||||
−0.253630 | + | 0.967301i | \(0.581625\pi\) | |||||||
\(200\) | −525.000 | −0.185616 | ||||||||
\(201\) | −560.000 | −0.196514 | ||||||||
\(202\) | −2052.00 | −0.714744 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 108.000 | 0.0370662 | ||||||||
\(205\) | 975.000 | 0.332180 | ||||||||
\(206\) | 4548.00 | 1.53822 | ||||||||
\(207\) | −1587.00 | −0.532870 | ||||||||
\(208\) | 4189.00 | 1.39642 | ||||||||
\(209\) | −5445.00 | −1.80210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3625.00 | −1.18273 | −0.591363 | − | 0.806405i | \(-0.701410\pi\) | ||||
−0.591363 | + | 0.806405i | \(0.701410\pi\) | |||||||
\(212\) | 597.000 | 0.193406 | ||||||||
\(213\) | 96.0000 | 0.0308817 | ||||||||
\(214\) | −2196.00 | −0.701474 | ||||||||
\(215\) | 1430.00 | 0.453606 | ||||||||
\(216\) | 2100.00 | 0.661513 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4800.00 | −1.49127 | ||||||||
\(219\) | −1336.00 | −0.412231 | ||||||||
\(220\) | 225.000 | 0.0689523 | ||||||||
\(221\) | −3186.00 | −0.969745 | ||||||||
\(222\) | −1554.00 | −0.469809 | ||||||||
\(223\) | 4960.00 | 1.48944 | 0.744722 | − | 0.667374i | \(-0.232582\pi\) | ||||
0.744722 | + | 0.667374i | \(0.232582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −575.000 | −0.170370 | ||||||||
\(226\) | −4176.00 | −1.22913 | ||||||||
\(227\) | 1500.00 | 0.438584 | 0.219292 | − | 0.975659i | \(-0.429625\pi\) | ||||
0.219292 | + | 0.975659i | \(0.429625\pi\) | |||||||
\(228\) | 242.000 | 0.0702932 | ||||||||
\(229\) | −6092.00 | −1.75795 | −0.878975 | − | 0.476867i | \(-0.841772\pi\) | ||||
−0.878975 | + | 0.476867i | \(0.841772\pi\) | |||||||
\(230\) | −1035.00 | −0.296721 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3402.00 | 0.962725 | ||||||||
\(233\) | 138.000 | 0.0388012 | 0.0194006 | − | 0.999812i | \(-0.493824\pi\) | ||||
0.0194006 | + | 0.999812i | \(0.493824\pi\) | |||||||
\(234\) | 4071.00 | 1.13731 | ||||||||
\(235\) | 225.000 | 0.0624569 | ||||||||
\(236\) | 360.000 | 0.0992966 | ||||||||
\(237\) | 1564.00 | 0.428661 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5502.00 | −1.48910 | −0.744550 | − | 0.667567i | \(-0.767336\pi\) | ||||
−0.744550 | + | 0.667567i | \(0.767336\pi\) | |||||||
\(240\) | 710.000 | 0.190960 | ||||||||
\(241\) | −3551.00 | −0.949129 | −0.474564 | − | 0.880221i | \(-0.657394\pi\) | ||||
−0.474564 | + | 0.880221i | \(0.657394\pi\) | |||||||
\(242\) | 2082.00 | 0.553041 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | −392.000 | −0.102849 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1170.00 | −0.303238 | ||||||||
\(247\) | −7139.00 | −1.83904 | ||||||||
\(248\) | −1848.00 | −0.473178 | ||||||||
\(249\) | −1536.00 | −0.390924 | ||||||||
\(250\) | −375.000 | −0.0948683 | ||||||||
\(251\) | −7065.00 | −1.77665 | −0.888324 | − | 0.459216i | \(-0.848130\pi\) | ||||
−0.888324 | + | 0.459216i | \(0.848130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3105.00 | −0.771580 | ||||||||
\(254\) | 2409.00 | 0.595095 | ||||||||
\(255\) | −540.000 | −0.132612 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 4080.00 | 0.990286 | 0.495143 | − | 0.868812i | \(-0.335116\pi\) | ||||
0.495143 | + | 0.868812i | \(0.335116\pi\) | |||||||
\(258\) | −1716.00 | −0.414083 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 295.000 | 0.0703659 | ||||||||
\(261\) | 3726.00 | 0.883654 | ||||||||
\(262\) | −6057.00 | −1.42825 | ||||||||
\(263\) | −3288.00 | −0.770900 | −0.385450 | − | 0.922729i | \(-0.625954\pi\) | ||||
−0.385450 | + | 0.922729i | \(0.625954\pi\) | |||||||
\(264\) | 1890.00 | 0.440612 | ||||||||
\(265\) | −2985.00 | −0.691951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2388.00 | 0.547353 | ||||||||
\(268\) | −280.000 | −0.0638199 | ||||||||
\(269\) | 3264.00 | 0.739813 | 0.369906 | − | 0.929069i | \(-0.379390\pi\) | ||||
0.369906 | + | 0.929069i | \(0.379390\pi\) | |||||||
\(270\) | 1500.00 | 0.338100 | ||||||||
\(271\) | 2752.00 | 0.616871 | 0.308436 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308436 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(272\) | −3834.00 | −0.854671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 180.000 | 0.0396869 | ||||||||
\(275\) | −1125.00 | −0.246691 | ||||||||
\(276\) | 138.000 | 0.0300965 | ||||||||
\(277\) | −4690.00 | −1.01731 | −0.508655 | − | 0.860971i | \(-0.669857\pi\) | ||||
−0.508655 | + | 0.860971i | \(0.669857\pi\) | |||||||
\(278\) | 5124.00 | 1.10546 | ||||||||
\(279\) | −2024.00 | −0.434314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7821.00 | 1.66036 | 0.830181 | − | 0.557494i | \(-0.188237\pi\) | ||||
0.830181 | + | 0.557494i | \(0.188237\pi\) | |||||||
\(282\) | −270.000 | −0.0570151 | ||||||||
\(283\) | 658.000 | 0.138212 | 0.0691061 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691061 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(284\) | 48.0000 | 0.0100291 | ||||||||
\(285\) | −1210.00 | −0.251488 | ||||||||
\(286\) | 7965.00 | 1.64678 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1035.00 | 0.211764 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 2430.00 | 0.492050 | ||||||||
\(291\) | −1804.00 | −0.363410 | ||||||||
\(292\) | −668.000 | −0.133876 | ||||||||
\(293\) | 5997.00 | 1.19573 | 0.597864 | − | 0.801597i | \(-0.296016\pi\) | ||||
0.597864 | + | 0.801597i | \(0.296016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1800.00 | −0.355254 | ||||||||
\(296\) | 5439.00 | 1.06803 | ||||||||
\(297\) | 4500.00 | 0.879180 | ||||||||
\(298\) | −3258.00 | −0.633325 | ||||||||
\(299\) | −4071.00 | −0.787398 | ||||||||
\(300\) | 50.0000 | 0.00962250 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8598.00 | −1.63828 | ||||||||
\(303\) | −1368.00 | −0.259371 | ||||||||
\(304\) | −8591.00 | −1.62081 | ||||||||
\(305\) | 1960.00 | 0.367965 | ||||||||
\(306\) | −3726.00 | −0.696082 | ||||||||
\(307\) | 6226.00 | 1.15745 | 0.578724 | − | 0.815523i | \(-0.303551\pi\) | ||||
0.578724 | + | 0.815523i | \(0.303551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3032.00 | 0.558202 | ||||||||
\(310\) | −1320.00 | −0.241842 | ||||||||
\(311\) | −4680.00 | −0.853307 | −0.426653 | − | 0.904415i | \(-0.640308\pi\) | ||||
−0.426653 | + | 0.904415i | \(0.640308\pi\) | |||||||
\(312\) | 2478.00 | 0.449645 | ||||||||
\(313\) | −1028.00 | −0.185642 | −0.0928211 | − | 0.995683i | \(-0.529588\pi\) | ||||
−0.0928211 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(314\) | 687.000 | 0.123470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 782.000 | 0.139212 | ||||||||
\(317\) | 8622.00 | 1.52763 | 0.763817 | − | 0.645433i | \(-0.223323\pi\) | ||||
0.763817 | + | 0.645433i | \(0.223323\pi\) | |||||||
\(318\) | 3582.00 | 0.631662 | ||||||||
\(319\) | 7290.00 | 1.27950 | ||||||||
\(320\) | −2165.00 | −0.378210 | ||||||||
\(321\) | −1464.00 | −0.254556 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6534.00 | 1.12558 | ||||||||
\(324\) | 421.000 | 0.0721879 | ||||||||
\(325\) | −1475.00 | −0.251749 | ||||||||
\(326\) | −3684.00 | −0.625883 | ||||||||
\(327\) | −3200.00 | −0.541163 | ||||||||
\(328\) | 4095.00 | 0.689355 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1350.00 | 0.225197 | ||||||||
\(331\) | −1999.00 | −0.331949 | −0.165974 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165974 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(332\) | −768.000 | −0.126956 | ||||||||
\(333\) | 5957.00 | 0.980305 | ||||||||
\(334\) | 5787.00 | 0.948056 | ||||||||
\(335\) | 1400.00 | 0.228329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5114.00 | 0.826639 | 0.413319 | − | 0.910586i | \(-0.364369\pi\) | ||||
0.413319 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(338\) | 3852.00 | 0.619885 | ||||||||
\(339\) | −2784.00 | −0.446036 | ||||||||
\(340\) | −270.000 | −0.0430671 | ||||||||
\(341\) | −3960.00 | −0.628874 | ||||||||
\(342\) | −8349.00 | −1.32006 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6006.00 | 0.941342 | ||||||||
\(345\) | −690.000 | −0.107676 | ||||||||
\(346\) | 2097.00 | 0.325825 | ||||||||
\(347\) | 4320.00 | 0.668328 | 0.334164 | − | 0.942515i | \(-0.391546\pi\) | ||||
0.334164 | + | 0.942515i | \(0.391546\pi\) | |||||||
\(348\) | −324.000 | −0.0499087 | ||||||||
\(349\) | −7922.00 | −1.21506 | −0.607529 | − | 0.794298i | \(-0.707839\pi\) | ||||
−0.607529 | + | 0.794298i | \(0.707839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5900.00 | 0.897204 | ||||||||
\(352\) | 2025.00 | 0.306627 | ||||||||
\(353\) | −828.000 | −0.124844 | −0.0624221 | − | 0.998050i | \(-0.519882\pi\) | ||||
−0.0624221 | + | 0.998050i | \(0.519882\pi\) | |||||||
\(354\) | 2160.00 | 0.324301 | ||||||||
\(355\) | −240.000 | −0.0358813 | ||||||||
\(356\) | 1194.00 | 0.177758 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9351.00 | 1.38049 | ||||||||
\(359\) | −1350.00 | −0.198469 | −0.0992344 | − | 0.995064i | \(-0.531639\pi\) | ||||
−0.0992344 | + | 0.995064i | \(0.531639\pi\) | |||||||
\(360\) | −2415.00 | −0.353560 | ||||||||
\(361\) | 7782.00 | 1.13457 | ||||||||
\(362\) | 5394.00 | 0.783156 | ||||||||
\(363\) | 1388.00 | 0.200692 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3340.00 | 0.478969 | ||||||||
\(366\) | −2352.00 | −0.335904 | ||||||||
\(367\) | −2801.00 | −0.398395 | −0.199198 | − | 0.979959i | \(-0.563834\pi\) | ||||
−0.199198 | + | 0.979959i | \(0.563834\pi\) | |||||||
\(368\) | −4899.00 | −0.693962 | ||||||||
\(369\) | 4485.00 | 0.632737 | ||||||||
\(370\) | 3885.00 | 0.545869 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 176.000 | 0.0245300 | ||||||||
\(373\) | 6602.00 | 0.916457 | 0.458229 | − | 0.888834i | \(-0.348484\pi\) | ||||
0.458229 | + | 0.888834i | \(0.348484\pi\) | |||||||
\(374\) | −7290.00 | −1.00791 | ||||||||
\(375\) | −250.000 | −0.0344265 | ||||||||
\(376\) | 945.000 | 0.129613 | ||||||||
\(377\) | 9558.00 | 1.30573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8305.00 | −1.12559 | −0.562796 | − | 0.826596i | \(-0.690274\pi\) | ||||
−0.562796 | + | 0.826596i | \(0.690274\pi\) | |||||||
\(380\) | −605.000 | −0.0816733 | ||||||||
\(381\) | 1606.00 | 0.215952 | ||||||||
\(382\) | −7164.00 | −0.959534 | ||||||||
\(383\) | −945.000 | −0.126076 | −0.0630382 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630382 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(384\) | 3318.00 | 0.440940 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 816.000 | 0.107599 | ||||||||
\(387\) | 6578.00 | 0.864027 | ||||||||
\(388\) | −902.000 | −0.118021 | ||||||||
\(389\) | 12036.0 | 1.56876 | 0.784382 | − | 0.620278i | \(-0.212980\pi\) | ||||
0.784382 | + | 0.620278i | \(0.212980\pi\) | |||||||
\(390\) | 1770.00 | 0.229814 | ||||||||
\(391\) | 3726.00 | 0.481923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4038.00 | −0.518296 | ||||||||
\(394\) | −6327.00 | −0.809009 | ||||||||
\(395\) | −3910.00 | −0.498059 | ||||||||
\(396\) | 1035.00 | 0.131340 | ||||||||
\(397\) | 2698.00 | 0.341080 | 0.170540 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170540 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(398\) | −4272.00 | −0.538030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1775.00 | −0.221875 | ||||||||
\(401\) | 7053.00 | 0.878329 | 0.439165 | − | 0.898407i | \(-0.355274\pi\) | ||||
0.439165 | + | 0.898407i | \(0.355274\pi\) | |||||||
\(402\) | −1680.00 | −0.208435 | ||||||||
\(403\) | −5192.00 | −0.641767 | ||||||||
\(404\) | −684.000 | −0.0842333 | ||||||||
\(405\) | −2105.00 | −0.258267 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11655.0 | 1.41945 | ||||||||
\(408\) | −2268.00 | −0.275203 | ||||||||
\(409\) | 10870.0 | 1.31415 | 0.657074 | − | 0.753826i | \(-0.271794\pi\) | ||||
0.657074 | + | 0.753826i | \(0.271794\pi\) | |||||||
\(410\) | 2925.00 | 0.352330 | ||||||||
\(411\) | 120.000 | 0.0144019 | ||||||||
\(412\) | 1516.00 | 0.181281 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4761.00 | −0.565194 | ||||||||
\(415\) | 3840.00 | 0.454212 | ||||||||
\(416\) | 2655.00 | 0.312914 | ||||||||
\(417\) | 3416.00 | 0.401156 | ||||||||
\(418\) | −16335.0 | −1.91141 | ||||||||
\(419\) | 9729.00 | 1.13435 | 0.567175 | − | 0.823597i | \(-0.308036\pi\) | ||||
0.567175 | + | 0.823597i | \(0.308036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12550.0 | −1.45285 | −0.726425 | − | 0.687246i | \(-0.758819\pi\) | ||||
−0.726425 | + | 0.687246i | \(0.758819\pi\) | |||||||
\(422\) | −10875.0 | −1.25447 | ||||||||
\(423\) | 1035.00 | 0.118968 | ||||||||
\(424\) | −12537.0 | −1.43597 | ||||||||
\(425\) | 1350.00 | 0.154081 | ||||||||
\(426\) | 288.000 | 0.0327550 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −732.000 | −0.0826695 | ||||||||
\(429\) | 5310.00 | 0.597597 | ||||||||
\(430\) | 4290.00 | 0.481121 | ||||||||
\(431\) | 2988.00 | 0.333937 | 0.166969 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166969 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(432\) | 7100.00 | 0.790738 | ||||||||
\(433\) | −16616.0 | −1.84414 | −0.922072 | − | 0.387019i | \(-0.873505\pi\) | ||||
−0.922072 | + | 0.387019i | \(0.873505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1620.00 | 0.178559 | ||||||||
\(436\) | −1600.00 | −0.175748 | ||||||||
\(437\) | 8349.00 | 0.913929 | ||||||||
\(438\) | −4008.00 | −0.437237 | ||||||||
\(439\) | −7346.00 | −0.798646 | −0.399323 | − | 0.916810i | \(-0.630755\pi\) | ||||
−0.399323 | + | 0.916810i | \(0.630755\pi\) | |||||||
\(440\) | −4725.00 | −0.511944 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9558.00 | −1.02857 | ||||||||
\(443\) | 12.0000 | 0.00128699 | 0.000643496 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000643496 | 1.00000i | \(0.499795\pi\) | ||||||||
\(444\) | −518.000 | −0.0553675 | ||||||||
\(445\) | −5970.00 | −0.635967 | ||||||||
\(446\) | 14880.0 | 1.57979 | ||||||||
\(447\) | −2172.00 | −0.229826 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9669.00 | 1.01628 | 0.508138 | − | 0.861275i | \(-0.330334\pi\) | ||||
0.508138 | + | 0.861275i | \(0.330334\pi\) | |||||||
\(450\) | −1725.00 | −0.180705 | ||||||||
\(451\) | 8775.00 | 0.916183 | ||||||||
\(452\) | −1392.00 | −0.144854 | ||||||||
\(453\) | −5732.00 | −0.594510 | ||||||||
\(454\) | 4500.00 | 0.465188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5082.00 | −0.521900 | ||||||||
\(457\) | −9634.00 | −0.986126 | −0.493063 | − | 0.869994i | \(-0.664123\pi\) | ||||
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(458\) | −18276.0 | −1.86459 | ||||||||
\(459\) | −5400.00 | −0.549129 | ||||||||
\(460\) | −345.000 | −0.0349689 | ||||||||
\(461\) | 342.000 | 0.0345521 | 0.0172761 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172761 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2411.00 | 0.242006 | 0.121003 | − | 0.992652i | \(-0.461389\pi\) | ||||
0.121003 | + | 0.992652i | \(0.461389\pi\) | |||||||
\(464\) | 11502.0 | 1.15079 | ||||||||
\(465\) | −880.000 | −0.0877613 | ||||||||
\(466\) | 414.000 | 0.0411549 | ||||||||
\(467\) | 1206.00 | 0.119501 | 0.0597506 | − | 0.998213i | \(-0.480969\pi\) | ||||
0.0597506 | + | 0.998213i | \(0.480969\pi\) | |||||||
\(468\) | 1357.00 | 0.134033 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 675.000 | 0.0662456 | ||||||||
\(471\) | 458.000 | 0.0448058 | ||||||||
\(472\) | −7560.00 | −0.737240 | ||||||||
\(473\) | 12870.0 | 1.25109 | ||||||||
\(474\) | 4692.00 | 0.454664 | ||||||||
\(475\) | 3025.00 | 0.292203 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13731.0 | −1.31803 | ||||||||
\(478\) | −16506.0 | −1.57943 | ||||||||
\(479\) | 432.000 | 0.0412079 | 0.0206039 | − | 0.999788i | \(-0.493441\pi\) | ||||
0.0206039 | + | 0.999788i | \(0.493441\pi\) | |||||||
\(480\) | 450.000 | 0.0427908 | ||||||||
\(481\) | 15281.0 | 1.44855 | ||||||||
\(482\) | −10653.0 | −1.00670 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 694.000 | 0.0651766 | ||||||||
\(485\) | 4510.00 | 0.422244 | ||||||||
\(486\) | 10626.0 | 0.991780 | ||||||||
\(487\) | −11896.0 | −1.10690 | −0.553449 | − | 0.832883i | \(-0.686689\pi\) | ||||
−0.553449 | + | 0.832883i | \(0.686689\pi\) | |||||||
\(488\) | 8232.00 | 0.763617 | ||||||||
\(489\) | −2456.00 | −0.227125 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12276.0 | −1.12833 | −0.564163 | − | 0.825663i | \(-0.690801\pi\) | ||||
−0.564163 | + | 0.825663i | \(0.690801\pi\) | |||||||
\(492\) | −390.000 | −0.0357369 | ||||||||
\(493\) | −8748.00 | −0.799169 | ||||||||
\(494\) | −21417.0 | −1.95060 | ||||||||
\(495\) | −5175.00 | −0.469897 | ||||||||
\(496\) | −6248.00 | −0.565612 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4608.00 | −0.414637 | ||||||||
\(499\) | −10876.0 | −0.975705 | −0.487852 | − | 0.872926i | \(-0.662220\pi\) | ||||
−0.487852 | + | 0.872926i | \(0.662220\pi\) | |||||||
\(500\) | −125.000 | −0.0111803 | ||||||||
\(501\) | 3858.00 | 0.344037 | ||||||||
\(502\) | −21195.0 | −1.88442 | ||||||||
\(503\) | −12000.0 | −1.06372 | −0.531862 | − | 0.846831i | \(-0.678508\pi\) | ||||
−0.531862 | + | 0.846831i | \(0.678508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3420.00 | 0.301362 | ||||||||
\(506\) | −9315.00 | −0.818384 | ||||||||
\(507\) | 2568.00 | 0.224948 | ||||||||
\(508\) | 803.000 | 0.0701326 | ||||||||
\(509\) | 11682.0 | 1.01728 | 0.508640 | − | 0.860979i | \(-0.330148\pi\) | ||||
0.508640 | + | 0.860979i | \(0.330148\pi\) | |||||||
\(510\) | −1620.00 | −0.140656 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | −12100.0 | −1.04138 | ||||||||
\(514\) | 12240.0 | 1.05036 | ||||||||
\(515\) | −7580.00 | −0.648572 | ||||||||
\(516\) | −572.000 | −0.0488002 | ||||||||
\(517\) | 2025.00 | 0.172262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1398.00 | 0.118238 | ||||||||
\(520\) | −6195.00 | −0.522440 | ||||||||
\(521\) | −9609.00 | −0.808019 | −0.404010 | − | 0.914755i | \(-0.632384\pi\) | ||||
−0.404010 | + | 0.914755i | \(0.632384\pi\) | |||||||
\(522\) | 11178.0 | 0.937256 | ||||||||
\(523\) | −21188.0 | −1.77148 | −0.885742 | − | 0.464177i | \(-0.846350\pi\) | ||||
−0.885742 | + | 0.464177i | \(0.846350\pi\) | |||||||
\(524\) | −2019.00 | −0.168321 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9864.00 | −0.817663 | ||||||||
\(527\) | 4752.00 | 0.392790 | ||||||||
\(528\) | 6390.00 | 0.526684 | ||||||||
\(529\) | −7406.00 | −0.608696 | ||||||||
\(530\) | −8955.00 | −0.733925 | ||||||||
\(531\) | −8280.00 | −0.676688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11505.0 | 0.934966 | ||||||||
\(534\) | 7164.00 | 0.580555 | ||||||||
\(535\) | 3660.00 | 0.295767 | ||||||||
\(536\) | 5880.00 | 0.473838 | ||||||||
\(537\) | 6234.00 | 0.500963 | ||||||||
\(538\) | 9792.00 | 0.784690 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 500.000 | 0.0398455 | ||||||||
\(541\) | 8072.00 | 0.641483 | 0.320742 | − | 0.947167i | \(-0.396068\pi\) | ||||
0.320742 | + | 0.947167i | \(0.396068\pi\) | |||||||
\(542\) | 8256.00 | 0.654291 | ||||||||
\(543\) | 3596.00 | 0.284197 | ||||||||
\(544\) | −2430.00 | −0.191517 | ||||||||
\(545\) | 8000.00 | 0.628775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 344.000 | 0.0268892 | 0.0134446 | − | 0.999910i | \(-0.495720\pi\) | ||||
0.0134446 | + | 0.999910i | \(0.495720\pi\) | |||||||
\(548\) | 60.0000 | 0.00467714 | ||||||||
\(549\) | 9016.00 | 0.700899 | ||||||||
\(550\) | −3375.00 | −0.261655 | ||||||||
\(551\) | −19602.0 | −1.51556 | ||||||||
\(552\) | −2898.00 | −0.223455 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14070.0 | −1.07902 | ||||||||
\(555\) | 2590.00 | 0.198089 | ||||||||
\(556\) | 1708.00 | 0.130279 | ||||||||
\(557\) | 18363.0 | 1.39689 | 0.698443 | − | 0.715666i | \(-0.253877\pi\) | ||||
0.698443 | + | 0.715666i | \(0.253877\pi\) | |||||||
\(558\) | −6072.00 | −0.460660 | ||||||||
\(559\) | 16874.0 | 1.27673 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4860.00 | −0.365756 | ||||||||
\(562\) | 23463.0 | 1.76108 | ||||||||
\(563\) | 6294.00 | 0.471155 | 0.235578 | − | 0.971856i | \(-0.424302\pi\) | ||||
0.235578 | + | 0.971856i | \(0.424302\pi\) | |||||||
\(564\) | −90.0000 | −0.00671930 | ||||||||
\(565\) | 6960.00 | 0.518247 | ||||||||
\(566\) | 1974.00 | 0.146596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1008.00 | −0.0744626 | ||||||||
\(569\) | 11733.0 | 0.864452 | 0.432226 | − | 0.901765i | \(-0.357728\pi\) | ||||
0.432226 | + | 0.901765i | \(0.357728\pi\) | |||||||
\(570\) | −3630.00 | −0.266744 | ||||||||
\(571\) | 1052.00 | 0.0771013 | 0.0385506 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385506 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(572\) | 2655.00 | 0.194075 | ||||||||
\(573\) | −4776.00 | −0.348203 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1725.00 | 0.125109 | ||||||||
\(576\) | −9959.00 | −0.720414 | ||||||||
\(577\) | 13156.0 | 0.949205 | 0.474603 | − | 0.880200i | \(-0.342592\pi\) | ||||
0.474603 | + | 0.880200i | \(0.342592\pi\) | |||||||
\(578\) | −5991.00 | −0.431129 | ||||||||
\(579\) | 544.000 | 0.0390464 | ||||||||
\(580\) | 810.000 | 0.0579887 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5412.00 | −0.385455 | ||||||||
\(583\) | −26865.0 | −1.90846 | ||||||||
\(584\) | 14028.0 | 0.993977 | ||||||||
\(585\) | −6785.00 | −0.479530 | ||||||||
\(586\) | 17991.0 | 1.26826 | ||||||||
\(587\) | 13368.0 | 0.939960 | 0.469980 | − | 0.882677i | \(-0.344261\pi\) | ||||
0.469980 | + | 0.882677i | \(0.344261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10648.0 | 0.744895 | ||||||||
\(590\) | −5400.00 | −0.376804 | ||||||||
\(591\) | −4218.00 | −0.293579 | ||||||||
\(592\) | 18389.0 | 1.27666 | ||||||||
\(593\) | −26664.0 | −1.84647 | −0.923237 | − | 0.384231i | \(-0.874467\pi\) | ||||
−0.923237 | + | 0.384231i | \(0.874467\pi\) | |||||||
\(594\) | 13500.0 | 0.932511 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1086.00 | −0.0746381 | ||||||||
\(597\) | −2848.00 | −0.195244 | ||||||||
\(598\) | −12213.0 | −0.835162 | ||||||||
\(599\) | 7614.00 | 0.519365 | 0.259682 | − | 0.965694i | \(-0.416382\pi\) | ||||
0.259682 | + | 0.965694i | \(0.416382\pi\) | |||||||
\(600\) | −1050.00 | −0.0714435 | ||||||||
\(601\) | −6410.00 | −0.435057 | −0.217529 | − | 0.976054i | \(-0.569800\pi\) | ||||
−0.217529 | + | 0.976054i | \(0.569800\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6440.00 | 0.434921 | ||||||||
\(604\) | −2866.00 | −0.193073 | ||||||||
\(605\) | −3470.00 | −0.233183 | ||||||||
\(606\) | −4104.00 | −0.275105 | ||||||||
\(607\) | 21469.0 | 1.43558 | 0.717792 | − | 0.696257i | \(-0.245153\pi\) | ||||
0.717792 | + | 0.696257i | \(0.245153\pi\) | |||||||
\(608\) | −5445.00 | −0.363197 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5880.00 | 0.390286 | ||||||||
\(611\) | 2655.00 | 0.175793 | ||||||||
\(612\) | −1242.00 | −0.0820341 | ||||||||
\(613\) | 3737.00 | 0.246225 | 0.123113 | − | 0.992393i | \(-0.460712\pi\) | ||||
0.123113 | + | 0.992393i | \(0.460712\pi\) | |||||||
\(614\) | 18678.0 | 1.22766 | ||||||||
\(615\) | 1950.00 | 0.127856 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18078.0 | 1.17957 | 0.589784 | − | 0.807561i | \(-0.299213\pi\) | ||||
0.589784 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(618\) | 9096.00 | 0.592063 | ||||||||
\(619\) | −12287.0 | −0.797829 | −0.398915 | − | 0.916988i | \(-0.630613\pi\) | ||||
−0.398915 | + | 0.916988i | \(0.630613\pi\) | |||||||
\(620\) | −440.000 | −0.0285013 | ||||||||
\(621\) | −6900.00 | −0.445874 | ||||||||
\(622\) | −14040.0 | −0.905069 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8378.00 | 0.537481 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −3084.00 | −0.196903 | ||||||||
\(627\) | −10890.0 | −0.693628 | ||||||||
\(628\) | 229.000 | 0.0145511 | ||||||||
\(629\) | −13986.0 | −0.886579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9580.00 | −0.604396 | −0.302198 | − | 0.953245i | \(-0.597720\pi\) | ||||
−0.302198 | + | 0.953245i | \(0.597720\pi\) | |||||||
\(632\) | −16422.0 | −1.03360 | ||||||||
\(633\) | −7250.00 | −0.455232 | ||||||||
\(634\) | 25866.0 | 1.62030 | ||||||||
\(635\) | −4015.00 | −0.250914 | ||||||||
\(636\) | 1194.00 | 0.0744421 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21870.0 | 1.35712 | ||||||||
\(639\) | −1104.00 | −0.0683467 | ||||||||
\(640\) | −8295.00 | −0.512326 | ||||||||
\(641\) | 10779.0 | 0.664189 | 0.332094 | − | 0.943246i | \(-0.392245\pi\) | ||||
0.332094 | + | 0.943246i | \(0.392245\pi\) | |||||||
\(642\) | −4392.00 | −0.269998 | ||||||||
\(643\) | −8882.00 | −0.544746 | −0.272373 | − | 0.962192i | \(-0.587809\pi\) | ||||
−0.272373 | + | 0.962192i | \(0.587809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2860.00 | 0.174593 | ||||||||
\(646\) | 19602.0 | 1.19386 | ||||||||
\(647\) | 11019.0 | 0.669554 | 0.334777 | − | 0.942297i | \(-0.391339\pi\) | ||||
0.334777 | + | 0.942297i | \(0.391339\pi\) | |||||||
\(648\) | −8841.00 | −0.535968 | ||||||||
\(649\) | −16200.0 | −0.979824 | ||||||||
\(650\) | −4425.00 | −0.267020 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1228.00 | −0.0737610 | ||||||||
\(653\) | 22323.0 | 1.33777 | 0.668887 | − | 0.743364i | \(-0.266771\pi\) | ||||
0.668887 | + | 0.743364i | \(0.266771\pi\) | |||||||
\(654\) | −9600.00 | −0.573990 | ||||||||
\(655\) | 10095.0 | 0.602205 | ||||||||
\(656\) | 13845.0 | 0.824019 | ||||||||
\(657\) | 15364.0 | 0.912339 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11856.0 | −0.700826 | −0.350413 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350413 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(660\) | 450.000 | 0.0265397 | ||||||||
\(661\) | 33244.0 | 1.95619 | 0.978095 | − | 0.208158i | \(-0.0667470\pi\) | ||||
0.978095 | + | 0.208158i | \(0.0667470\pi\) | |||||||
\(662\) | −5997.00 | −0.352085 | ||||||||
\(663\) | −6372.00 | −0.373255 | ||||||||
\(664\) | 16128.0 | 0.942602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17871.0 | 1.03977 | ||||||||
\(667\) | −11178.0 | −0.648896 | ||||||||
\(668\) | 1929.00 | 0.111729 | ||||||||
\(669\) | 9920.00 | 0.573288 | ||||||||
\(670\) | 4200.00 | 0.242179 | ||||||||
\(671\) | 17640.0 | 1.01488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12322.0 | −0.705763 | −0.352881 | − | 0.935668i | \(-0.614798\pi\) | ||||
−0.352881 | + | 0.935668i | \(0.614798\pi\) | |||||||
\(674\) | 15342.0 | 0.876783 | ||||||||
\(675\) | −2500.00 | −0.142556 | ||||||||
\(676\) | 1284.00 | 0.0730542 | ||||||||
\(677\) | 12597.0 | 0.715129 | 0.357564 | − | 0.933889i | \(-0.383607\pi\) | ||||
0.357564 | + | 0.933889i | \(0.383607\pi\) | |||||||
\(678\) | −8352.00 | −0.473092 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5670.00 | 0.319757 | ||||||||
\(681\) | 3000.00 | 0.168811 | ||||||||
\(682\) | −11880.0 | −0.667022 | ||||||||
\(683\) | −8340.00 | −0.467235 | −0.233617 | − | 0.972329i | \(-0.575056\pi\) | ||||
−0.233617 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(684\) | −2783.00 | −0.155571 | ||||||||
\(685\) | −300.000 | −0.0167334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12184.0 | −0.676636 | ||||||||
\(688\) | 20306.0 | 1.12523 | ||||||||
\(689\) | −35223.0 | −1.94759 | ||||||||
\(690\) | −2070.00 | −0.114208 | ||||||||
\(691\) | 20200.0 | 1.11208 | 0.556038 | − | 0.831157i | \(-0.312321\pi\) | ||||
0.556038 | + | 0.831157i | \(0.312321\pi\) | |||||||
\(692\) | 699.000 | 0.0383988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12960.0 | 0.708869 | ||||||||
\(695\) | −8540.00 | −0.466102 | ||||||||
\(696\) | 6804.00 | 0.370553 | ||||||||
\(697\) | −10530.0 | −0.572241 | ||||||||
\(698\) | −23766.0 | −1.28876 | ||||||||
\(699\) | 276.000 | 0.0149346 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 474.000 | 0.0255388 | 0.0127694 | − | 0.999918i | \(-0.495935\pi\) | ||||
0.0127694 | + | 0.999918i | \(0.495935\pi\) | |||||||
\(702\) | 17700.0 | 0.951629 | ||||||||
\(703\) | −31339.0 | −1.68133 | ||||||||
\(704\) | −19485.0 | −1.04314 | ||||||||
\(705\) | 450.000 | 0.0240397 | ||||||||
\(706\) | −2484.00 | −0.132417 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 720.000 | 0.0382193 | ||||||||
\(709\) | −25126.0 | −1.33093 | −0.665463 | − | 0.746431i | \(-0.731766\pi\) | ||||
−0.665463 | + | 0.746431i | \(0.731766\pi\) | |||||||
\(710\) | −720.000 | −0.0380579 | ||||||||
\(711\) | −17986.0 | −0.948703 | ||||||||
\(712\) | −25074.0 | −1.31979 | ||||||||
\(713\) | 6072.00 | 0.318932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13275.0 | −0.694345 | ||||||||
\(716\) | 3117.00 | 0.162692 | ||||||||
\(717\) | −11004.0 | −0.573155 | ||||||||
\(718\) | −4050.00 | −0.210508 | ||||||||
\(719\) | 7296.00 | 0.378435 | 0.189218 | − | 0.981935i | \(-0.439405\pi\) | ||||
0.189218 | + | 0.981935i | \(0.439405\pi\) | |||||||
\(720\) | −8165.00 | −0.422627 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 23346.0 | 1.20339 | ||||||||
\(723\) | −7102.00 | −0.365320 | ||||||||
\(724\) | 1798.00 | 0.0922958 | ||||||||
\(725\) | −4050.00 | −0.207467 | ||||||||
\(726\) | 4164.00 | 0.212866 | ||||||||
\(727\) | 15421.0 | 0.786703 | 0.393352 | − | 0.919388i | \(-0.371316\pi\) | ||||
0.393352 | + | 0.919388i | \(0.371316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 10020.0 | 0.508023 | ||||||||
\(731\) | −15444.0 | −0.781419 | ||||||||
\(732\) | −784.000 | −0.0395867 | ||||||||
\(733\) | 29167.0 | 1.46972 | 0.734862 | − | 0.678217i | \(-0.237247\pi\) | ||||
0.734862 | + | 0.678217i | \(0.237247\pi\) | |||||||
\(734\) | −8403.00 | −0.422562 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3105.00 | −0.155505 | ||||||||
\(737\) | 12600.0 | 0.629752 | ||||||||
\(738\) | 13455.0 | 0.671118 | ||||||||
\(739\) | −13381.0 | −0.666073 | −0.333037 | − | 0.942914i | \(-0.608073\pi\) | ||||
−0.333037 | + | 0.942914i | \(0.608073\pi\) | |||||||
\(740\) | 1295.00 | 0.0643313 | ||||||||
\(741\) | −14278.0 | −0.707848 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5487.00 | 0.270927 | 0.135463 | − | 0.990782i | \(-0.456748\pi\) | ||||
0.135463 | + | 0.990782i | \(0.456748\pi\) | |||||||
\(744\) | −3696.00 | −0.182126 | ||||||||
\(745\) | 5430.00 | 0.267033 | ||||||||
\(746\) | 19806.0 | 0.972050 | ||||||||
\(747\) | 17664.0 | 0.865183 | ||||||||
\(748\) | −2430.00 | −0.118783 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −750.000 | −0.0365148 | ||||||||
\(751\) | 6638.00 | 0.322535 | 0.161268 | − | 0.986911i | \(-0.448442\pi\) | ||||
0.161268 | + | 0.986911i | \(0.448442\pi\) | |||||||
\(752\) | 3195.00 | 0.154933 | ||||||||
\(753\) | −14130.0 | −0.683832 | ||||||||
\(754\) | 28674.0 | 1.38494 | ||||||||
\(755\) | 14330.0 | 0.690758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14846.0 | 0.712797 | 0.356398 | − | 0.934334i | \(-0.384005\pi\) | ||||
0.356398 | + | 0.934334i | \(0.384005\pi\) | |||||||
\(758\) | −24915.0 | −1.19387 | ||||||||
\(759\) | −6210.00 | −0.296981 | ||||||||
\(760\) | 12705.0 | 0.606393 | ||||||||
\(761\) | 3651.00 | 0.173914 | 0.0869571 | − | 0.996212i | \(-0.472286\pi\) | ||||
0.0869571 | + | 0.996212i | \(0.472286\pi\) | |||||||
\(762\) | 4818.00 | 0.229052 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2388.00 | −0.113082 | ||||||||
\(765\) | 6210.00 | 0.293494 | ||||||||
\(766\) | −2835.00 | −0.133724 | ||||||||
\(767\) | −21240.0 | −0.999911 | ||||||||
\(768\) | 3026.00 | 0.142176 | ||||||||
\(769\) | −29855.0 | −1.40000 | −0.699999 | − | 0.714144i | \(-0.746816\pi\) | ||||
−0.699999 | + | 0.714144i | \(0.746816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8160.00 | 0.381161 | ||||||||
\(772\) | 272.000 | 0.0126807 | ||||||||
\(773\) | 6519.00 | 0.303327 | 0.151664 | − | 0.988432i | \(-0.451537\pi\) | ||||
0.151664 | + | 0.988432i | \(0.451537\pi\) | |||||||
\(774\) | 19734.0 | 0.916439 | ||||||||
\(775\) | 2200.00 | 0.101969 | ||||||||
\(776\) | 18942.0 | 0.876261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36108.0 | 1.66393 | ||||||||
\(779\) | −23595.0 | −1.08521 | ||||||||
\(780\) | 590.000 | 0.0270838 | ||||||||
\(781\) | −2160.00 | −0.0989640 | ||||||||
\(782\) | 11178.0 | 0.511157 | ||||||||
\(783\) | 16200.0 | 0.739388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1145.00 | −0.0520596 | ||||||||
\(786\) | −12114.0 | −0.549735 | ||||||||
\(787\) | −35114.0 | −1.59044 | −0.795222 | − | 0.606319i | \(-0.792646\pi\) | ||||
−0.795222 | + | 0.606319i | \(0.792646\pi\) | |||||||
\(788\) | −2109.00 | −0.0953427 | ||||||||
\(789\) | −6576.00 | −0.296720 | ||||||||
\(790\) | −11730.0 | −0.528272 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −21735.0 | −0.975151 | ||||||||
\(793\) | 23128.0 | 1.03569 | ||||||||
\(794\) | 8094.00 | 0.361770 | ||||||||
\(795\) | −5970.00 | −0.266332 | ||||||||
\(796\) | −1424.00 | −0.0634075 | ||||||||
\(797\) | −20910.0 | −0.929323 | −0.464661 | − | 0.885488i | \(-0.653824\pi\) | ||||
−0.464661 | + | 0.885488i | \(0.653824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2430.00 | −0.107594 | ||||||||
\(800\) | −1125.00 | −0.0497184 | ||||||||
\(801\) | −27462.0 | −1.21139 | ||||||||
\(802\) | 21159.0 | 0.931609 | ||||||||
\(803\) | 30060.0 | 1.32104 | ||||||||
\(804\) | −560.000 | −0.0245643 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15576.0 | −0.680696 | ||||||||
\(807\) | 6528.00 | 0.284754 | ||||||||
\(808\) | 14364.0 | 0.625401 | ||||||||
\(809\) | 4431.00 | 0.192566 | 0.0962829 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962829 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(810\) | −6315.00 | −0.273934 | ||||||||
\(811\) | 9577.00 | 0.414666 | 0.207333 | − | 0.978270i | \(-0.433522\pi\) | ||||
0.207333 | + | 0.978270i | \(0.433522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5504.00 | 0.237434 | ||||||||
\(814\) | 34965.0 | 1.50556 | ||||||||
\(815\) | 6140.00 | 0.263895 | ||||||||
\(816\) | −7668.00 | −0.328963 | ||||||||
\(817\) | −34606.0 | −1.48190 | ||||||||
\(818\) | 32610.0 | 1.39387 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 975.000 | 0.0415225 | ||||||||
\(821\) | −10938.0 | −0.464968 | −0.232484 | − | 0.972600i | \(-0.574685\pi\) | ||||
−0.232484 | + | 0.972600i | \(0.574685\pi\) | |||||||
\(822\) | 360.000 | 0.0152755 | ||||||||
\(823\) | 11540.0 | 0.488772 | 0.244386 | − | 0.969678i | \(-0.421414\pi\) | ||||
0.244386 | + | 0.969678i | \(0.421414\pi\) | |||||||
\(824\) | −31836.0 | −1.34595 | ||||||||
\(825\) | −2250.00 | −0.0949514 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18762.0 | −0.788898 | −0.394449 | − | 0.918918i | \(-0.629065\pi\) | ||||
−0.394449 | + | 0.918918i | \(0.629065\pi\) | |||||||
\(828\) | −1587.00 | −0.0666088 | ||||||||
\(829\) | 39610.0 | 1.65948 | 0.829742 | − | 0.558147i | \(-0.188488\pi\) | ||||
0.829742 | + | 0.558147i | \(0.188488\pi\) | |||||||
\(830\) | 11520.0 | 0.481765 | ||||||||
\(831\) | −9380.00 | −0.391563 | ||||||||
\(832\) | −25547.0 | −1.06452 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10248.0 | 0.425491 | ||||||||
\(835\) | −9645.00 | −0.399735 | ||||||||
\(836\) | −5445.00 | −0.225262 | ||||||||
\(837\) | −8800.00 | −0.363408 | ||||||||
\(838\) | 29187.0 | 1.20316 | ||||||||
\(839\) | −39162.0 | −1.61147 | −0.805734 | − | 0.592277i | \(-0.798229\pi\) | ||||
−0.805734 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1855.00 | 0.0760589 | ||||||||
\(842\) | −37650.0 | −1.54098 | ||||||||
\(843\) | 15642.0 | 0.639074 | ||||||||
\(844\) | −3625.00 | −0.147841 | ||||||||
\(845\) | −6420.00 | −0.261367 | ||||||||
\(846\) | 3105.00 | 0.126185 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −42387.0 | −1.71648 | ||||||||
\(849\) | 1316.00 | 0.0531979 | ||||||||
\(850\) | 4050.00 | 0.163428 | ||||||||
\(851\) | −17871.0 | −0.719871 | ||||||||
\(852\) | 96.0000 | 0.00386022 | ||||||||
\(853\) | 11527.0 | 0.462693 | 0.231346 | − | 0.972871i | \(-0.425687\pi\) | ||||
0.231346 | + | 0.972871i | \(0.425687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13915.0 | 0.556588 | ||||||||
\(856\) | 15372.0 | 0.613790 | ||||||||
\(857\) | 41826.0 | 1.66715 | 0.833576 | − | 0.552405i | \(-0.186290\pi\) | ||||
0.833576 | + | 0.552405i | \(0.186290\pi\) | |||||||
\(858\) | 15930.0 | 0.633848 | ||||||||
\(859\) | −35192.0 | −1.39783 | −0.698915 | − | 0.715205i | \(-0.746333\pi\) | ||||
−0.698915 | + | 0.715205i | \(0.746333\pi\) | |||||||
\(860\) | 1430.00 | 0.0567007 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8964.00 | 0.354194 | ||||||||
\(863\) | −9063.00 | −0.357483 | −0.178742 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178742 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(864\) | 4500.00 | 0.177191 | ||||||||
\(865\) | −3495.00 | −0.137380 | ||||||||
\(866\) | −49848.0 | −1.95601 | ||||||||
\(867\) | −3994.00 | −0.156451 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35190.0 | −1.37369 | ||||||||
\(870\) | 4860.00 | 0.189390 | ||||||||
\(871\) | 16520.0 | 0.642662 | ||||||||
\(872\) | 33600.0 | 1.30486 | ||||||||
\(873\) | 20746.0 | 0.804291 | ||||||||
\(874\) | 25047.0 | 0.969368 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1336.00 | −0.0515288 | ||||||||
\(877\) | 28439.0 | 1.09500 | 0.547501 | − | 0.836805i | \(-0.315579\pi\) | ||||
0.547501 | + | 0.836805i | \(0.315579\pi\) | |||||||
\(878\) | −22038.0 | −0.847092 | ||||||||
\(879\) | 11994.0 | 0.460236 | ||||||||
\(880\) | −15975.0 | −0.611951 | ||||||||
\(881\) | 9303.00 | 0.355762 | 0.177881 | − | 0.984052i | \(-0.443076\pi\) | ||||
0.177881 | + | 0.984052i | \(0.443076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14728.0 | −0.561310 | −0.280655 | − | 0.959809i | \(-0.590552\pi\) | ||||
−0.280655 | + | 0.959809i | \(0.590552\pi\) | |||||||
\(884\) | −3186.00 | −0.121218 | ||||||||
\(885\) | −3600.00 | −0.136737 | ||||||||
\(886\) | 36.0000 | 0.00136506 | ||||||||
\(887\) | 17016.0 | 0.644128 | 0.322064 | − | 0.946718i | \(-0.395623\pi\) | ||||
0.322064 | + | 0.946718i | \(0.395623\pi\) | |||||||
\(888\) | 10878.0 | 0.411083 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17910.0 | −0.674544 | ||||||||
\(891\) | −18945.0 | −0.712325 | ||||||||
\(892\) | 4960.00 | 0.186181 | ||||||||
\(893\) | −5445.00 | −0.204043 | ||||||||
\(894\) | −6516.00 | −0.243767 | ||||||||
\(895\) | −15585.0 | −0.582066 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8142.00 | −0.303070 | ||||||||
\(898\) | 29007.0 | 1.07792 | ||||||||
\(899\) | −14256.0 | −0.528881 | ||||||||
\(900\) | −575.000 | −0.0212963 | ||||||||
\(901\) | 32238.0 | 1.19201 | ||||||||
\(902\) | 26325.0 | 0.971759 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29232.0 | 1.07549 | ||||||||
\(905\) | −8990.00 | −0.330207 | ||||||||
\(906\) | −17196.0 | −0.630573 | ||||||||
\(907\) | −24922.0 | −0.912372 | −0.456186 | − | 0.889884i | \(-0.650785\pi\) | ||||
−0.456186 | + | 0.889884i | \(0.650785\pi\) | |||||||
\(908\) | 1500.00 | 0.0548230 | ||||||||
\(909\) | 15732.0 | 0.574035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30714.0 | 1.11701 | 0.558507 | − | 0.829500i | \(-0.311374\pi\) | ||||
0.558507 | + | 0.829500i | \(0.311374\pi\) | |||||||
\(912\) | −17182.0 | −0.623852 | ||||||||
\(913\) | 34560.0 | 1.25276 | ||||||||
\(914\) | −28902.0 | −1.04594 | ||||||||
\(915\) | 3920.00 | 0.141630 | ||||||||
\(916\) | −6092.00 | −0.219744 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16200.0 | −0.582440 | ||||||||
\(919\) | 17426.0 | 0.625496 | 0.312748 | − | 0.949836i | \(-0.398750\pi\) | ||||
0.312748 | + | 0.949836i | \(0.398750\pi\) | |||||||
\(920\) | 7245.00 | 0.259631 | ||||||||
\(921\) | 12452.0 | 0.445502 | ||||||||
\(922\) | 1026.00 | 0.0366481 | ||||||||
\(923\) | −2832.00 | −0.100993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6475.00 | −0.230159 | ||||||||
\(926\) | 7233.00 | 0.256686 | ||||||||
\(927\) | −34868.0 | −1.23540 | ||||||||
\(928\) | 7290.00 | 0.257873 | ||||||||
\(929\) | −26649.0 | −0.941147 | −0.470573 | − | 0.882361i | \(-0.655953\pi\) | ||||
−0.470573 | + | 0.882361i | \(0.655953\pi\) | |||||||
\(930\) | −2640.00 | −0.0930850 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 138.000 | 0.00485015 | ||||||||
\(933\) | −9360.00 | −0.328438 | ||||||||
\(934\) | 3618.00 | 0.126750 | ||||||||
\(935\) | 12150.0 | 0.424971 | ||||||||
\(936\) | −28497.0 | −0.995143 | ||||||||
\(937\) | −27686.0 | −0.965274 | −0.482637 | − | 0.875820i | \(-0.660321\pi\) | ||||
−0.482637 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2056.00 | −0.0714537 | ||||||||
\(940\) | 225.000 | 0.00780712 | ||||||||
\(941\) | 17808.0 | 0.616923 | 0.308461 | − | 0.951237i | \(-0.400186\pi\) | ||||
0.308461 | + | 0.951237i | \(0.400186\pi\) | |||||||
\(942\) | 1374.00 | 0.0475237 | ||||||||
\(943\) | −13455.0 | −0.464640 | ||||||||
\(944\) | −25560.0 | −0.881258 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38610.0 | 1.32698 | ||||||||
\(947\) | −6906.00 | −0.236974 | −0.118487 | − | 0.992956i | \(-0.537804\pi\) | ||||
−0.118487 | + | 0.992956i | \(0.537804\pi\) | |||||||
\(948\) | 1564.00 | 0.0535827 | ||||||||
\(949\) | 39412.0 | 1.34812 | ||||||||
\(950\) | 9075.00 | 0.309928 | ||||||||
\(951\) | 17244.0 | 0.587986 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20940.0 | −0.711766 | −0.355883 | − | 0.934530i | \(-0.615820\pi\) | ||||
−0.355883 | + | 0.934530i | \(0.615820\pi\) | |||||||
\(954\) | −41193.0 | −1.39798 | ||||||||
\(955\) | 11940.0 | 0.404575 | ||||||||
\(956\) | −5502.00 | −0.186137 | ||||||||
\(957\) | 14580.0 | 0.492481 | ||||||||
\(958\) | 1296.00 | 0.0437076 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4330.00 | −0.145573 | ||||||||
\(961\) | −22047.0 | −0.740056 | ||||||||
\(962\) | 45843.0 | 1.53642 | ||||||||
\(963\) | 16836.0 | 0.563377 | ||||||||
\(964\) | −3551.00 | −0.118641 | ||||||||
\(965\) | −1360.00 | −0.0453678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9176.00 | 0.305150 | 0.152575 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152575 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(968\) | −14574.0 | −0.483911 | ||||||||
\(969\) | 13068.0 | 0.433235 | ||||||||
\(970\) | 13530.0 | 0.447858 | ||||||||
\(971\) | −29763.0 | −0.983666 | −0.491833 | − | 0.870689i | \(-0.663673\pi\) | ||||
−0.491833 | + | 0.870689i | \(0.663673\pi\) | |||||||
\(972\) | 3542.00 | 0.116882 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −35688.0 | −1.17404 | ||||||||
\(975\) | −2950.00 | −0.0968981 | ||||||||
\(976\) | 27832.0 | 0.912788 | ||||||||
\(977\) | −38490.0 | −1.26039 | −0.630197 | − | 0.776436i | \(-0.717026\pi\) | ||||
−0.630197 | + | 0.776436i | \(0.717026\pi\) | |||||||
\(978\) | −7368.00 | −0.240903 | ||||||||
\(979\) | −53730.0 | −1.75405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36800.0 | 1.19769 | ||||||||
\(982\) | −36828.0 | −1.19677 | ||||||||
\(983\) | 12609.0 | 0.409120 | 0.204560 | − | 0.978854i | \(-0.434424\pi\) | ||||
0.204560 | + | 0.978854i | \(0.434424\pi\) | |||||||
\(984\) | 8190.00 | 0.265333 | ||||||||
\(985\) | 10545.0 | 0.341108 | ||||||||
\(986\) | −26244.0 | −0.847646 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7139.00 | −0.229880 | ||||||||
\(989\) | −19734.0 | −0.634484 | ||||||||
\(990\) | −15525.0 | −0.498401 | ||||||||
\(991\) | 19820.0 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −3960.00 | −0.126744 | ||||||||
\(993\) | −3998.00 | −0.127767 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7120.00 | 0.226853 | ||||||||
\(996\) | −1536.00 | −0.0488655 | ||||||||
\(997\) | −46034.0 | −1.46230 | −0.731149 | − | 0.682218i | \(-0.761016\pi\) | ||||
−0.731149 | + | 0.682218i | \(0.761016\pi\) | |||||||
\(998\) | −32628.0 | −1.03489 | ||||||||
\(999\) | 25900.0 | 0.820260 |
(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 | 245.4.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 2205.4.a.g.1.1 | 1 | |||
5.4 | even | 2 | 1225.4.a.a.1.1 | 1 | |||
7.2 | even | 3 | 245.4.e.a.116.1 | 2 | |||
7.3 | odd | 6 | 35.4.e.a.16.1 | yes | 2 | ||
7.4 | even | 3 | 245.4.e.a.226.1 | 2 | |||
7.5 | odd | 6 | 35.4.e.a.11.1 | ✓ | 2 | ||
7.6 | odd | 2 | 245.4.a.e.1.1 | 1 | |||
21.5 | even | 6 | 315.4.j.b.46.1 | 2 | |||
21.17 | even | 6 | 315.4.j.b.226.1 | 2 | |||
21.20 | even | 2 | 2205.4.a.e.1.1 | 1 | |||
28.3 | even | 6 | 560.4.q.b.401.1 | 2 | |||
28.19 | even | 6 | 560.4.q.b.81.1 | 2 | |||
35.3 | even | 12 | 175.4.k.b.149.2 | 4 | |||
35.12 | even | 12 | 175.4.k.b.74.2 | 4 | |||
35.17 | even | 12 | 175.4.k.b.149.1 | 4 | |||
35.19 | odd | 6 | 175.4.e.b.151.1 | 2 | |||
35.24 | odd | 6 | 175.4.e.b.51.1 | 2 | |||
35.33 | even | 12 | 175.4.k.b.74.1 | 4 | |||
35.34 | odd | 2 | 1225.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.a.11.1 | ✓ | 2 | 7.5 | odd | 6 | ||
35.4.e.a.16.1 | yes | 2 | 7.3 | odd | 6 | ||
175.4.e.b.51.1 | 2 | 35.24 | odd | 6 | |||
175.4.e.b.151.1 | 2 | 35.19 | odd | 6 | |||
175.4.k.b.74.1 | 4 | 35.33 | even | 12 | |||
175.4.k.b.74.2 | 4 | 35.12 | even | 12 | |||
175.4.k.b.149.1 | 4 | 35.17 | even | 12 | |||
175.4.k.b.149.2 | 4 | 35.3 | even | 12 | |||
245.4.a.e.1.1 | 1 | 7.6 | odd | 2 | |||
245.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
245.4.e.a.116.1 | 2 | 7.2 | even | 3 | |||
245.4.e.a.226.1 | 2 | 7.4 | even | 3 | |||
315.4.j.b.46.1 | 2 | 21.5 | even | 6 | |||
315.4.j.b.226.1 | 2 | 21.17 | even | 6 | |||
560.4.q.b.81.1 | 2 | 28.19 | even | 6 | |||
560.4.q.b.401.1 | 2 | 28.3 | even | 6 | |||
1225.4.a.a.1.1 | 1 | 5.4 | even | 2 | |||
1225.4.a.b.1.1 | 1 | 35.34 | odd | 2 | |||
2205.4.a.e.1.1 | 1 | 21.20 | even | 2 | |||
2205.4.a.g.1.1 | 1 | 3.2 | odd | 2 |