Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 28x^{2} + 18x + 132 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.09331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09331 | −0.740097 | −0.370049 | − | 0.929012i | \(-0.620659\pi\) | ||||
−0.370049 | + | 0.929012i | \(0.620659\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −3.61805 | −0.452256 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 6.27993 | 0.427295 | ||||||||
\(7\) | 3.55562 | 0.191985 | 0.0959926 | − | 0.995382i | \(-0.469397\pi\) | ||||
0.0959926 | + | 0.995382i | \(0.469397\pi\) | |||||||
\(8\) | 24.3202 | 1.07481 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.4666 | 0.330982 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 10.8541 | 0.261110 | ||||||||
\(13\) | −10.2397 | −0.218460 | −0.109230 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109230 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(14\) | −7.44301 | −0.142088 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −21.9654 | −0.343209 | ||||||||
\(17\) | 45.8819 | 0.654589 | 0.327294 | − | 0.944922i | \(-0.393863\pi\) | ||||
0.327294 | + | 0.944922i | \(0.393863\pi\) | |||||||
\(18\) | −18.8398 | −0.246699 | ||||||||
\(19\) | −97.1404 | −1.17292 | −0.586461 | − | 0.809977i | \(-0.699479\pi\) | ||||
−0.586461 | + | 0.809977i | \(0.699479\pi\) | |||||||
\(20\) | 18.0902 | 0.202255 | ||||||||
\(21\) | −10.6668 | −0.110843 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.7760 | −0.143023 | −0.0715115 | − | 0.997440i | \(-0.522782\pi\) | ||||
−0.0715115 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(24\) | −72.9606 | −0.620542 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 21.4348 | 0.161681 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −12.8644 | −0.0868264 | ||||||||
\(29\) | −179.522 | −1.14953 | −0.574765 | − | 0.818319i | \(-0.694906\pi\) | ||||
−0.574765 | + | 0.818319i | \(0.694906\pi\) | |||||||
\(30\) | −31.3997 | −0.191092 | ||||||||
\(31\) | 79.6764 | 0.461622 | 0.230811 | − | 0.972999i | \(-0.425862\pi\) | ||||
0.230811 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(32\) | −148.581 | −0.820803 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −96.0452 | −0.484459 | ||||||||
\(35\) | −17.7781 | −0.0858584 | ||||||||
\(36\) | −32.5624 | −0.150752 | ||||||||
\(37\) | 235.295 | 1.04547 | 0.522733 | − | 0.852496i | \(-0.324912\pi\) | ||||
0.522733 | + | 0.852496i | \(0.324912\pi\) | |||||||
\(38\) | 203.345 | 0.868077 | ||||||||
\(39\) | 30.7190 | 0.126128 | ||||||||
\(40\) | −121.601 | −0.480670 | ||||||||
\(41\) | −144.425 | −0.550133 | −0.275067 | − | 0.961425i | \(-0.588700\pi\) | ||||
−0.275067 | + | 0.961425i | \(0.588700\pi\) | |||||||
\(42\) | 22.3290 | 0.0820344 | ||||||||
\(43\) | 229.458 | 0.813767 | 0.406884 | − | 0.913480i | \(-0.366615\pi\) | ||||
0.406884 | + | 0.913480i | \(0.366615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 33.0241 | 0.105851 | ||||||||
\(47\) | −138.515 | −0.429882 | −0.214941 | − | 0.976627i | \(-0.568956\pi\) | ||||
−0.214941 | + | 0.976627i | \(0.568956\pi\) | |||||||
\(48\) | 65.8961 | 0.198152 | ||||||||
\(49\) | −330.358 | −0.963142 | ||||||||
\(50\) | −52.3328 | −0.148019 | ||||||||
\(51\) | −137.646 | −0.377927 | ||||||||
\(52\) | 37.0476 | 0.0987997 | ||||||||
\(53\) | −1.77711 | −0.00460575 | −0.00230288 | − | 0.999997i | \(-0.500733\pi\) | ||||
−0.00230288 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(54\) | 56.5194 | 0.142432 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 86.4733 | 0.206348 | ||||||||
\(57\) | 291.421 | 0.677187 | ||||||||
\(58\) | 375.795 | 0.850764 | ||||||||
\(59\) | 95.7448 | 0.211270 | 0.105635 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105635 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(60\) | −54.2707 | −0.116772 | ||||||||
\(61\) | 527.720 | 1.10767 | 0.553833 | − | 0.832628i | \(-0.313165\pi\) | ||||
0.553833 | + | 0.832628i | \(0.313165\pi\) | |||||||
\(62\) | −166.787 | −0.341646 | ||||||||
\(63\) | 32.0005 | 0.0639951 | ||||||||
\(64\) | 486.750 | 0.950683 | ||||||||
\(65\) | 51.1984 | 0.0976981 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.52540 | 0.0118986 | 0.00594929 | − | 0.999982i | \(-0.498106\pi\) | ||||
0.00594929 | + | 0.999982i | \(0.498106\pi\) | |||||||
\(68\) | −166.003 | −0.296041 | ||||||||
\(69\) | 47.3281 | 0.0825744 | ||||||||
\(70\) | 37.2151 | 0.0635436 | ||||||||
\(71\) | 361.209 | 0.603769 | 0.301885 | − | 0.953344i | \(-0.402384\pi\) | ||||
0.301885 | + | 0.953344i | \(0.402384\pi\) | |||||||
\(72\) | 218.882 | 0.358270 | ||||||||
\(73\) | 505.985 | 0.811248 | 0.405624 | − | 0.914040i | \(-0.367054\pi\) | ||||
0.405624 | + | 0.914040i | \(0.367054\pi\) | |||||||
\(74\) | −492.546 | −0.773747 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 351.458 | 0.530461 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −64.3045 | −0.0933468 | ||||||||
\(79\) | −587.149 | −0.836195 | −0.418098 | − | 0.908402i | \(-0.637303\pi\) | ||||
−0.418098 | + | 0.908402i | \(0.637303\pi\) | |||||||
\(80\) | 109.827 | 0.153488 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 302.327 | 0.407152 | ||||||||
\(83\) | 907.928 | 1.20070 | 0.600350 | − | 0.799738i | \(-0.295028\pi\) | ||||
0.600350 | + | 0.799738i | \(0.295028\pi\) | |||||||
\(84\) | 38.5931 | 0.0501293 | ||||||||
\(85\) | −229.410 | −0.292741 | ||||||||
\(86\) | −480.327 | −0.602267 | ||||||||
\(87\) | 538.565 | 0.663681 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1541.60 | 1.83606 | 0.918030 | − | 0.396510i | \(-0.129779\pi\) | ||||
0.918030 | + | 0.396510i | \(0.129779\pi\) | |||||||
\(90\) | 94.1990 | 0.110327 | ||||||||
\(91\) | −36.4084 | −0.0419410 | ||||||||
\(92\) | 57.0784 | 0.0646830 | ||||||||
\(93\) | −239.029 | −0.266518 | ||||||||
\(94\) | 289.954 | 0.318154 | ||||||||
\(95\) | 485.702 | 0.524547 | ||||||||
\(96\) | 445.744 | 0.473891 | ||||||||
\(97\) | −913.677 | −0.956390 | −0.478195 | − | 0.878254i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878254i | \(0.658709\pi\) | |||||||
\(98\) | 691.541 | 0.712819 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −90.4512 | −0.0904512 | ||||||||
\(101\) | −419.835 | −0.413615 | −0.206808 | − | 0.978382i | \(-0.566307\pi\) | ||||
−0.206808 | + | 0.978382i | \(0.566307\pi\) | |||||||
\(102\) | 288.136 | 0.279703 | ||||||||
\(103\) | 481.611 | 0.460724 | 0.230362 | − | 0.973105i | \(-0.426009\pi\) | ||||
0.230362 | + | 0.973105i | \(0.426009\pi\) | |||||||
\(104\) | −249.031 | −0.234803 | ||||||||
\(105\) | 53.3342 | 0.0495704 | ||||||||
\(106\) | 3.72005 | 0.00340870 | ||||||||
\(107\) | −141.219 | −0.127590 | −0.0637949 | − | 0.997963i | \(-0.520320\pi\) | ||||
−0.0637949 | + | 0.997963i | \(0.520320\pi\) | |||||||
\(108\) | 97.6873 | 0.0870367 | ||||||||
\(109\) | 876.420 | 0.770145 | 0.385072 | − | 0.922886i | \(-0.374177\pi\) | ||||
0.385072 | + | 0.922886i | \(0.374177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −705.885 | −0.603600 | ||||||||
\(112\) | −78.1004 | −0.0658910 | ||||||||
\(113\) | −1079.39 | −0.898585 | −0.449292 | − | 0.893385i | \(-0.648324\pi\) | ||||
−0.449292 | + | 0.893385i | \(0.648324\pi\) | |||||||
\(114\) | −610.035 | −0.501184 | ||||||||
\(115\) | 78.8801 | 0.0639618 | ||||||||
\(116\) | 649.518 | 0.519881 | ||||||||
\(117\) | −92.1571 | −0.0728199 | ||||||||
\(118\) | −200.424 | −0.156360 | ||||||||
\(119\) | 163.139 | 0.125671 | ||||||||
\(120\) | 364.803 | 0.277515 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1104.68 | −0.819781 | ||||||||
\(123\) | 433.276 | 0.317620 | ||||||||
\(124\) | −288.273 | −0.208771 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −66.9871 | −0.0473626 | ||||||||
\(127\) | 1542.46 | 1.07773 | 0.538863 | − | 0.842394i | \(-0.318854\pi\) | ||||
0.538863 | + | 0.842394i | \(0.318854\pi\) | |||||||
\(128\) | 169.731 | 0.117205 | ||||||||
\(129\) | −688.373 | −0.469829 | ||||||||
\(130\) | −107.174 | −0.0723061 | ||||||||
\(131\) | 1491.30 | 0.994623 | 0.497311 | − | 0.867572i | \(-0.334321\pi\) | ||||
0.497311 | + | 0.867572i | \(0.334321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −345.394 | −0.225184 | ||||||||
\(134\) | −13.6597 | −0.00880610 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 1115.86 | 0.703559 | ||||||||
\(137\) | 1735.30 | 1.08217 | 0.541084 | − | 0.840969i | \(-0.318014\pi\) | ||||
0.541084 | + | 0.840969i | \(0.318014\pi\) | |||||||
\(138\) | −99.0724 | −0.0611131 | ||||||||
\(139\) | −815.237 | −0.497464 | −0.248732 | − | 0.968572i | \(-0.580014\pi\) | ||||
−0.248732 | + | 0.968572i | \(0.580014\pi\) | |||||||
\(140\) | 64.3219 | 0.0388300 | ||||||||
\(141\) | 415.544 | 0.248192 | ||||||||
\(142\) | −756.123 | −0.446848 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −197.688 | −0.114403 | ||||||||
\(145\) | 897.609 | 0.514085 | ||||||||
\(146\) | −1059.18 | −0.600402 | ||||||||
\(147\) | 991.073 | 0.556070 | ||||||||
\(148\) | −851.308 | −0.472818 | ||||||||
\(149\) | 2493.44 | 1.37095 | 0.685473 | − | 0.728098i | \(-0.259595\pi\) | ||||
0.685473 | + | 0.728098i | \(0.259595\pi\) | |||||||
\(150\) | 156.998 | 0.0854591 | ||||||||
\(151\) | −1102.20 | −0.594010 | −0.297005 | − | 0.954876i | \(-0.595988\pi\) | ||||
−0.297005 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(152\) | −2362.47 | −1.26067 | ||||||||
\(153\) | 412.937 | 0.218196 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −398.382 | −0.206444 | ||||||||
\(156\) | −111.143 | −0.0570420 | ||||||||
\(157\) | −2485.15 | −1.26329 | −0.631646 | − | 0.775257i | \(-0.717620\pi\) | ||||
−0.631646 | + | 0.775257i | \(0.717620\pi\) | |||||||
\(158\) | 1229.09 | 0.618866 | ||||||||
\(159\) | 5.33133 | 0.00265913 | ||||||||
\(160\) | 742.906 | 0.367074 | ||||||||
\(161\) | −56.0935 | −0.0274583 | ||||||||
\(162\) | −169.558 | −0.0822330 | ||||||||
\(163\) | −688.813 | −0.330994 | −0.165497 | − | 0.986210i | \(-0.552923\pi\) | ||||
−0.165497 | + | 0.986210i | \(0.552923\pi\) | |||||||
\(164\) | 522.538 | 0.248801 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1900.58 | −0.888635 | ||||||||
\(167\) | 2216.01 | 1.02683 | 0.513414 | − | 0.858141i | \(-0.328381\pi\) | ||||
0.513414 | + | 0.858141i | \(0.328381\pi\) | |||||||
\(168\) | −259.420 | −0.119135 | ||||||||
\(169\) | −2092.15 | −0.952275 | ||||||||
\(170\) | 480.226 | 0.216657 | ||||||||
\(171\) | −874.263 | −0.390974 | ||||||||
\(172\) | −830.189 | −0.368031 | ||||||||
\(173\) | −2710.23 | −1.19107 | −0.595534 | − | 0.803330i | \(-0.703060\pi\) | ||||
−0.595534 | + | 0.803330i | \(0.703060\pi\) | |||||||
\(174\) | −1127.39 | −0.491189 | ||||||||
\(175\) | 88.8904 | 0.0383970 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −287.235 | −0.121977 | ||||||||
\(178\) | −3227.05 | −1.35886 | ||||||||
\(179\) | −1629.13 | −0.680263 | −0.340131 | − | 0.940378i | \(-0.610472\pi\) | ||||
−0.340131 | + | 0.940378i | \(0.610472\pi\) | |||||||
\(180\) | 162.812 | 0.0674183 | ||||||||
\(181\) | −1735.36 | −0.712644 | −0.356322 | − | 0.934363i | \(-0.615969\pi\) | ||||
−0.356322 | + | 0.934363i | \(0.615969\pi\) | |||||||
\(182\) | 76.2140 | 0.0310404 | ||||||||
\(183\) | −1583.16 | −0.639511 | ||||||||
\(184\) | −383.676 | −0.153723 | ||||||||
\(185\) | −1176.47 | −0.467547 | ||||||||
\(186\) | 500.362 | 0.197249 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 501.152 | 0.194416 | ||||||||
\(189\) | −96.0016 | −0.0369476 | ||||||||
\(190\) | −1016.73 | −0.388216 | ||||||||
\(191\) | −1890.92 | −0.716348 | −0.358174 | − | 0.933655i | \(-0.616600\pi\) | ||||
−0.358174 | + | 0.933655i | \(0.616600\pi\) | |||||||
\(192\) | −1460.25 | −0.548877 | ||||||||
\(193\) | 235.046 | 0.0876631 | 0.0438315 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438315 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(194\) | 1912.61 | 0.707822 | ||||||||
\(195\) | −153.595 | −0.0564060 | ||||||||
\(196\) | 1195.25 | 0.435586 | ||||||||
\(197\) | 2336.24 | 0.844923 | 0.422462 | − | 0.906381i | \(-0.361166\pi\) | ||||
0.422462 | + | 0.906381i | \(0.361166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4000.38 | −1.42502 | −0.712512 | − | 0.701660i | \(-0.752442\pi\) | ||||
−0.712512 | + | 0.701660i | \(0.752442\pi\) | |||||||
\(200\) | 608.005 | 0.214962 | ||||||||
\(201\) | −19.5762 | −0.00686964 | ||||||||
\(202\) | 878.846 | 0.306116 | ||||||||
\(203\) | −638.310 | −0.220693 | ||||||||
\(204\) | 498.009 | 0.170920 | ||||||||
\(205\) | 722.127 | 0.246027 | ||||||||
\(206\) | −1008.16 | −0.340980 | ||||||||
\(207\) | −141.984 | −0.0476743 | ||||||||
\(208\) | 224.918 | 0.0749773 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −111.645 | −0.0366869 | ||||||||
\(211\) | −626.154 | −0.204295 | −0.102147 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102147 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(212\) | 6.42967 | 0.00208298 | ||||||||
\(213\) | −1083.63 | −0.348586 | ||||||||
\(214\) | 295.615 | 0.0944289 | ||||||||
\(215\) | −1147.29 | −0.363928 | ||||||||
\(216\) | −656.645 | −0.206847 | ||||||||
\(217\) | 283.298 | 0.0886247 | ||||||||
\(218\) | −1834.62 | −0.569982 | ||||||||
\(219\) | −1517.96 | −0.468374 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −469.816 | −0.143001 | ||||||||
\(222\) | 1477.64 | 0.446723 | ||||||||
\(223\) | −296.977 | −0.0891795 | −0.0445897 | − | 0.999005i | \(-0.514198\pi\) | ||||
−0.0445897 | + | 0.999005i | \(0.514198\pi\) | |||||||
\(224\) | −528.298 | −0.157582 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 2259.49 | 0.665040 | ||||||||
\(227\) | 1216.15 | 0.355590 | 0.177795 | − | 0.984068i | \(-0.443104\pi\) | ||||
0.177795 | + | 0.984068i | \(0.443104\pi\) | |||||||
\(228\) | −1054.38 | −0.306262 | ||||||||
\(229\) | 4475.00 | 1.29134 | 0.645669 | − | 0.763617i | \(-0.276579\pi\) | ||||
0.645669 | + | 0.763617i | \(0.276579\pi\) | |||||||
\(230\) | −165.121 | −0.0473380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4366.00 | −1.23553 | ||||||||
\(233\) | −5653.07 | −1.58946 | −0.794732 | − | 0.606961i | \(-0.792388\pi\) | ||||
−0.794732 | + | 0.606961i | \(0.792388\pi\) | |||||||
\(234\) | 192.914 | 0.0538938 | ||||||||
\(235\) | 692.573 | 0.192249 | ||||||||
\(236\) | −346.409 | −0.0955480 | ||||||||
\(237\) | 1761.45 | 0.482778 | ||||||||
\(238\) | −341.500 | −0.0930090 | ||||||||
\(239\) | −3769.86 | −1.02030 | −0.510151 | − | 0.860085i | \(-0.670411\pi\) | ||||
−0.510151 | + | 0.860085i | \(0.670411\pi\) | |||||||
\(240\) | −329.481 | −0.0886162 | ||||||||
\(241\) | 3873.99 | 1.03546 | 0.517730 | − | 0.855544i | \(-0.326777\pi\) | ||||
0.517730 | + | 0.855544i | \(0.326777\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1909.32 | −0.500949 | ||||||||
\(245\) | 1651.79 | 0.430730 | ||||||||
\(246\) | −906.982 | −0.235069 | ||||||||
\(247\) | 994.686 | 0.256236 | ||||||||
\(248\) | 1937.74 | 0.496157 | ||||||||
\(249\) | −2723.78 | −0.693224 | ||||||||
\(250\) | 261.664 | 0.0661963 | ||||||||
\(251\) | 3579.50 | 0.900144 | 0.450072 | − | 0.892992i | \(-0.351398\pi\) | ||||
0.450072 | + | 0.892992i | \(0.351398\pi\) | |||||||
\(252\) | −115.779 | −0.0289421 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3228.85 | −0.797622 | ||||||||
\(255\) | 688.229 | 0.169014 | ||||||||
\(256\) | −4249.30 | −1.03743 | ||||||||
\(257\) | −7366.86 | −1.78806 | −0.894031 | − | 0.448005i | \(-0.852135\pi\) | ||||
−0.894031 | + | 0.448005i | \(0.852135\pi\) | |||||||
\(258\) | 1440.98 | 0.347719 | ||||||||
\(259\) | 836.618 | 0.200714 | ||||||||
\(260\) | −185.238 | −0.0441845 | ||||||||
\(261\) | −1615.70 | −0.383177 | ||||||||
\(262\) | −3121.76 | −0.736118 | ||||||||
\(263\) | 1407.41 | 0.329978 | 0.164989 | − | 0.986295i | \(-0.447241\pi\) | ||||
0.164989 | + | 0.986295i | \(0.447241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.88555 | 0.00205975 | ||||||||
\(266\) | 723.017 | 0.166658 | ||||||||
\(267\) | −4624.80 | −1.06005 | ||||||||
\(268\) | −23.6092 | −0.00538120 | ||||||||
\(269\) | −2679.07 | −0.607233 | −0.303617 | − | 0.952794i | \(-0.598194\pi\) | ||||
−0.303617 | + | 0.952794i | \(0.598194\pi\) | |||||||
\(270\) | −282.597 | −0.0636974 | ||||||||
\(271\) | 4830.77 | 1.08284 | 0.541418 | − | 0.840754i | \(-0.317888\pi\) | ||||
0.541418 | + | 0.840754i | \(0.317888\pi\) | |||||||
\(272\) | −1007.81 | −0.224661 | ||||||||
\(273\) | 109.225 | 0.0242147 | ||||||||
\(274\) | −3632.53 | −0.800910 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −171.235 | −0.0373447 | ||||||||
\(277\) | −2302.39 | −0.499413 | −0.249706 | − | 0.968322i | \(-0.580334\pi\) | ||||
−0.249706 | + | 0.968322i | \(0.580334\pi\) | |||||||
\(278\) | 1706.54 | 0.368172 | ||||||||
\(279\) | 717.087 | 0.153874 | ||||||||
\(280\) | −432.366 | −0.0922815 | ||||||||
\(281\) | −813.238 | −0.172647 | −0.0863234 | − | 0.996267i | \(-0.527512\pi\) | ||||
−0.0863234 | + | 0.996267i | \(0.527512\pi\) | |||||||
\(282\) | −869.863 | −0.183686 | ||||||||
\(283\) | −6164.30 | −1.29480 | −0.647402 | − | 0.762149i | \(-0.724144\pi\) | ||||
−0.647402 | + | 0.762149i | \(0.724144\pi\) | |||||||
\(284\) | −1306.87 | −0.273058 | ||||||||
\(285\) | −1457.11 | −0.302847 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −513.521 | −0.105617 | ||||||||
\(288\) | −1337.23 | −0.273601 | ||||||||
\(289\) | −2807.85 | −0.571514 | ||||||||
\(290\) | −1878.98 | −0.380473 | ||||||||
\(291\) | 2741.03 | 0.552172 | ||||||||
\(292\) | −1830.68 | −0.366892 | ||||||||
\(293\) | 4264.64 | 0.850317 | 0.425158 | − | 0.905119i | \(-0.360218\pi\) | ||||
0.425158 | + | 0.905119i | \(0.360218\pi\) | |||||||
\(294\) | −2074.62 | −0.411546 | ||||||||
\(295\) | −478.724 | −0.0944827 | ||||||||
\(296\) | 5722.42 | 1.12368 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5219.56 | −1.01463 | ||||||||
\(299\) | 161.541 | 0.0312448 | ||||||||
\(300\) | 271.353 | 0.0522220 | ||||||||
\(301\) | 815.864 | 0.156231 | ||||||||
\(302\) | 2307.24 | 0.439625 | ||||||||
\(303\) | 1259.51 | 0.238801 | ||||||||
\(304\) | 2133.72 | 0.402557 | ||||||||
\(305\) | −2638.60 | −0.495363 | ||||||||
\(306\) | −864.407 | −0.161486 | ||||||||
\(307\) | 1442.87 | 0.268238 | 0.134119 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134119 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1444.83 | −0.265999 | ||||||||
\(310\) | 833.937 | 0.152789 | ||||||||
\(311\) | 6754.23 | 1.23150 | 0.615751 | − | 0.787940i | \(-0.288853\pi\) | ||||
0.615751 | + | 0.787940i | \(0.288853\pi\) | |||||||
\(312\) | 747.093 | 0.135563 | ||||||||
\(313\) | 760.144 | 0.137271 | 0.0686356 | − | 0.997642i | \(-0.478135\pi\) | ||||
0.0686356 | + | 0.997642i | \(0.478135\pi\) | |||||||
\(314\) | 5202.20 | 0.934959 | ||||||||
\(315\) | −160.003 | −0.0286195 | ||||||||
\(316\) | 2124.33 | 0.378174 | ||||||||
\(317\) | −3391.25 | −0.600856 | −0.300428 | − | 0.953804i | \(-0.597130\pi\) | ||||
−0.300428 | + | 0.953804i | \(0.597130\pi\) | |||||||
\(318\) | −11.1601 | −0.00196802 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2433.75 | −0.425158 | ||||||||
\(321\) | 423.656 | 0.0736640 | ||||||||
\(322\) | 117.421 | 0.0203218 | ||||||||
\(323\) | −4456.99 | −0.767782 | ||||||||
\(324\) | −293.062 | −0.0502506 | ||||||||
\(325\) | −255.992 | −0.0436919 | ||||||||
\(326\) | 1441.90 | 0.244968 | ||||||||
\(327\) | −2629.26 | −0.444643 | ||||||||
\(328\) | −3512.45 | −0.591289 | ||||||||
\(329\) | −492.505 | −0.0825309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3220.55 | −0.534797 | −0.267398 | − | 0.963586i | \(-0.586164\pi\) | ||||
−0.267398 | + | 0.963586i | \(0.586164\pi\) | |||||||
\(332\) | −3284.93 | −0.543023 | ||||||||
\(333\) | 2117.65 | 0.348489 | ||||||||
\(334\) | −4638.81 | −0.759953 | ||||||||
\(335\) | −32.6270 | −0.00532120 | ||||||||
\(336\) | 234.301 | 0.0380422 | ||||||||
\(337\) | −4386.18 | −0.708992 | −0.354496 | − | 0.935058i | \(-0.615348\pi\) | ||||
−0.354496 | + | 0.935058i | \(0.615348\pi\) | |||||||
\(338\) | 4379.52 | 0.704777 | ||||||||
\(339\) | 3238.16 | 0.518798 | ||||||||
\(340\) | 830.015 | 0.132394 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1830.11 | 0.289359 | ||||||||
\(343\) | −2394.20 | −0.376894 | ||||||||
\(344\) | 5580.46 | 0.874646 | ||||||||
\(345\) | −236.640 | −0.0369284 | ||||||||
\(346\) | 5673.35 | 0.881507 | ||||||||
\(347\) | 6501.60 | 1.00583 | 0.502916 | − | 0.864335i | \(-0.332260\pi\) | ||||
0.502916 | + | 0.864335i | \(0.332260\pi\) | |||||||
\(348\) | −1948.55 | −0.300154 | ||||||||
\(349\) | −1943.01 | −0.298014 | −0.149007 | − | 0.988836i | \(-0.547608\pi\) | ||||
−0.149007 | + | 0.988836i | \(0.547608\pi\) | |||||||
\(350\) | −186.075 | −0.0284176 | ||||||||
\(351\) | 276.471 | 0.0420426 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2124.76 | 0.320367 | 0.160183 | − | 0.987087i | \(-0.448791\pi\) | ||||
0.160183 | + | 0.987087i | \(0.448791\pi\) | |||||||
\(354\) | 601.271 | 0.0902746 | ||||||||
\(355\) | −1806.05 | −0.270014 | ||||||||
\(356\) | −5577.58 | −0.830369 | ||||||||
\(357\) | −489.416 | −0.0725564 | ||||||||
\(358\) | 3410.28 | 0.503461 | ||||||||
\(359\) | 6163.44 | 0.906112 | 0.453056 | − | 0.891482i | \(-0.350334\pi\) | ||||
0.453056 | + | 0.891482i | \(0.350334\pi\) | |||||||
\(360\) | −1094.41 | −0.160223 | ||||||||
\(361\) | 2577.25 | 0.375747 | ||||||||
\(362\) | 3632.66 | 0.527426 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 131.727 | 0.0189681 | ||||||||
\(365\) | −2529.93 | −0.362801 | ||||||||
\(366\) | 3314.05 | 0.473301 | ||||||||
\(367\) | −12573.5 | −1.78837 | −0.894184 | − | 0.447699i | \(-0.852244\pi\) | ||||
−0.894184 | + | 0.447699i | \(0.852244\pi\) | |||||||
\(368\) | 346.526 | 0.0490868 | ||||||||
\(369\) | −1299.83 | −0.183378 | ||||||||
\(370\) | 2462.73 | 0.346030 | ||||||||
\(371\) | −6.31872 | −0.000884236 0 | ||||||||
\(372\) | 864.818 | 0.120534 | ||||||||
\(373\) | −6379.88 | −0.885624 | −0.442812 | − | 0.896614i | \(-0.646019\pi\) | ||||
−0.442812 | + | 0.896614i | \(0.646019\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | −3368.70 | −0.462041 | ||||||||
\(377\) | 1838.25 | 0.251126 | ||||||||
\(378\) | 200.961 | 0.0273448 | ||||||||
\(379\) | 6409.71 | 0.868720 | 0.434360 | − | 0.900739i | \(-0.356975\pi\) | ||||
0.434360 | + | 0.900739i | \(0.356975\pi\) | |||||||
\(380\) | −1757.29 | −0.237229 | ||||||||
\(381\) | −4627.38 | −0.622225 | ||||||||
\(382\) | 3958.29 | 0.530167 | ||||||||
\(383\) | −6122.43 | −0.816818 | −0.408409 | − | 0.912799i | \(-0.633916\pi\) | ||||
−0.408409 | + | 0.912799i | \(0.633916\pi\) | |||||||
\(384\) | −509.192 | −0.0676682 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −492.024 | −0.0648792 | ||||||||
\(387\) | 2065.12 | 0.271256 | ||||||||
\(388\) | 3305.72 | 0.432533 | ||||||||
\(389\) | −7544.33 | −0.983323 | −0.491662 | − | 0.870786i | \(-0.663610\pi\) | ||||
−0.491662 | + | 0.870786i | \(0.663610\pi\) | |||||||
\(390\) | 321.523 | 0.0417460 | ||||||||
\(391\) | −723.835 | −0.0936212 | ||||||||
\(392\) | −8034.36 | −1.03520 | ||||||||
\(393\) | −4473.90 | −0.574246 | ||||||||
\(394\) | −4890.47 | −0.625326 | ||||||||
\(395\) | 2935.74 | 0.373958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5341.07 | −0.675216 | −0.337608 | − | 0.941287i | \(-0.609618\pi\) | ||||
−0.337608 | + | 0.941287i | \(0.609618\pi\) | |||||||
\(398\) | 8374.05 | 1.05466 | ||||||||
\(399\) | 1036.18 | 0.130010 | ||||||||
\(400\) | −549.134 | −0.0686418 | ||||||||
\(401\) | 14413.2 | 1.79492 | 0.897458 | − | 0.441100i | \(-0.145412\pi\) | ||||
0.897458 | + | 0.441100i | \(0.145412\pi\) | |||||||
\(402\) | 40.9791 | 0.00508421 | ||||||||
\(403\) | −815.860 | −0.100846 | ||||||||
\(404\) | 1518.98 | 0.187060 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 1336.18 | 0.163334 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3347.57 | −0.406200 | ||||||||
\(409\) | −13192.8 | −1.59496 | −0.797482 | − | 0.603342i | \(-0.793835\pi\) | ||||
−0.797482 | + | 0.603342i | \(0.793835\pi\) | |||||||
\(410\) | −1511.64 | −0.182084 | ||||||||
\(411\) | −5205.91 | −0.624790 | ||||||||
\(412\) | −1742.49 | −0.208365 | ||||||||
\(413\) | 340.432 | 0.0405607 | ||||||||
\(414\) | 297.217 | 0.0352837 | ||||||||
\(415\) | −4539.64 | −0.536969 | ||||||||
\(416\) | 1521.42 | 0.179312 | ||||||||
\(417\) | 2445.71 | 0.287211 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4648.27 | −0.541964 | −0.270982 | − | 0.962584i | \(-0.587348\pi\) | ||||
−0.270982 | + | 0.962584i | \(0.587348\pi\) | |||||||
\(420\) | −192.966 | −0.0224185 | ||||||||
\(421\) | −14885.8 | −1.72326 | −0.861628 | − | 0.507541i | \(-0.830555\pi\) | ||||
−0.861628 | + | 0.507541i | \(0.830555\pi\) | |||||||
\(422\) | 1310.74 | 0.151198 | ||||||||
\(423\) | −1246.63 | −0.143294 | ||||||||
\(424\) | −43.2197 | −0.00495031 | ||||||||
\(425\) | 1147.05 | 0.130918 | ||||||||
\(426\) | 2268.37 | 0.257988 | ||||||||
\(427\) | 1876.37 | 0.212656 | ||||||||
\(428\) | 510.935 | 0.0577033 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2401.63 | 0.269342 | ||||||||
\(431\) | −1795.56 | −0.200671 | −0.100336 | − | 0.994954i | \(-0.531992\pi\) | ||||
−0.100336 | + | 0.994954i | \(0.531992\pi\) | |||||||
\(432\) | 593.065 | 0.0660506 | ||||||||
\(433\) | 14633.7 | 1.62414 | 0.812069 | − | 0.583561i | \(-0.198341\pi\) | ||||
0.812069 | + | 0.583561i | \(0.198341\pi\) | |||||||
\(434\) | −593.032 | −0.0655909 | ||||||||
\(435\) | −2692.83 | −0.296807 | ||||||||
\(436\) | −3170.93 | −0.348302 | ||||||||
\(437\) | 1532.49 | 0.167755 | ||||||||
\(438\) | 3177.55 | 0.346642 | ||||||||
\(439\) | −7081.49 | −0.769889 | −0.384944 | − | 0.922940i | \(-0.625779\pi\) | ||||
−0.384944 | + | 0.922940i | \(0.625779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2973.22 | −0.321047 | ||||||||
\(442\) | 983.472 | 0.105835 | ||||||||
\(443\) | 14206.1 | 1.52360 | 0.761798 | − | 0.647815i | \(-0.224317\pi\) | ||||
0.761798 | + | 0.647815i | \(0.224317\pi\) | |||||||
\(444\) | 2553.92 | 0.272982 | ||||||||
\(445\) | −7708.00 | −0.821111 | ||||||||
\(446\) | 621.664 | 0.0660015 | ||||||||
\(447\) | −7480.33 | −0.791516 | ||||||||
\(448\) | 1730.69 | 0.182517 | ||||||||
\(449\) | 4005.28 | 0.420982 | 0.210491 | − | 0.977596i | \(-0.432494\pi\) | ||||
0.210491 | + | 0.977596i | \(0.432494\pi\) | |||||||
\(450\) | −470.995 | −0.0493398 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3905.27 | 0.406390 | ||||||||
\(453\) | 3306.59 | 0.342952 | ||||||||
\(454\) | −2545.79 | −0.263171 | ||||||||
\(455\) | 182.042 | 0.0187566 | ||||||||
\(456\) | 7087.42 | 0.727848 | ||||||||
\(457\) | −18169.7 | −1.85983 | −0.929916 | − | 0.367771i | \(-0.880121\pi\) | ||||
−0.929916 | + | 0.367771i | \(0.880121\pi\) | |||||||
\(458\) | −9367.57 | −0.955716 | ||||||||
\(459\) | −1238.81 | −0.125976 | ||||||||
\(460\) | −285.392 | −0.0289271 | ||||||||
\(461\) | −2485.00 | −0.251059 | −0.125529 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125529 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16228.3 | −1.62893 | −0.814463 | − | 0.580215i | \(-0.802969\pi\) | ||||
−0.814463 | + | 0.580215i | \(0.802969\pi\) | |||||||
\(464\) | 3943.26 | 0.394529 | ||||||||
\(465\) | 1195.15 | 0.119190 | ||||||||
\(466\) | 11833.6 | 1.17636 | ||||||||
\(467\) | −10523.4 | −1.04275 | −0.521376 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521376 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(468\) | 333.429 | 0.0329332 | ||||||||
\(469\) | 23.2018 | 0.00228435 | ||||||||
\(470\) | −1449.77 | −0.142283 | ||||||||
\(471\) | 7455.46 | 0.729362 | ||||||||
\(472\) | 2328.53 | 0.227075 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3687.26 | −0.357302 | ||||||||
\(475\) | −2428.51 | −0.234585 | ||||||||
\(476\) | −590.243 | −0.0568356 | ||||||||
\(477\) | −15.9940 | −0.00153525 | ||||||||
\(478\) | 7891.50 | 0.755123 | ||||||||
\(479\) | 3980.01 | 0.379648 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(480\) | −2228.72 | −0.211930 | ||||||||
\(481\) | −2409.34 | −0.228392 | ||||||||
\(482\) | −8109.47 | −0.766341 | ||||||||
\(483\) | 168.280 | 0.0158531 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4568.38 | 0.427711 | ||||||||
\(486\) | 508.675 | 0.0474773 | ||||||||
\(487\) | −1101.38 | −0.102481 | −0.0512406 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512406 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(488\) | 12834.3 | 1.19053 | ||||||||
\(489\) | 2066.44 | 0.191099 | ||||||||
\(490\) | −3457.71 | −0.318782 | ||||||||
\(491\) | 2319.62 | 0.213204 | 0.106602 | − | 0.994302i | \(-0.466003\pi\) | ||||
0.106602 | + | 0.994302i | \(0.466003\pi\) | |||||||
\(492\) | −1567.61 | −0.143645 | ||||||||
\(493\) | −8236.81 | −0.752469 | ||||||||
\(494\) | −2082.19 | −0.189640 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1750.12 | −0.158433 | ||||||||
\(497\) | 1284.32 | 0.115915 | ||||||||
\(498\) | 5701.73 | 0.513053 | ||||||||
\(499\) | −3583.35 | −0.321469 | −0.160734 | − | 0.986998i | \(-0.551386\pi\) | ||||
−0.160734 | + | 0.986998i | \(0.551386\pi\) | |||||||
\(500\) | 452.256 | 0.0404510 | ||||||||
\(501\) | −6648.04 | −0.592839 | ||||||||
\(502\) | −7493.01 | −0.666194 | ||||||||
\(503\) | −11119.5 | −0.985674 | −0.492837 | − | 0.870122i | \(-0.664040\pi\) | ||||
−0.492837 | + | 0.870122i | \(0.664040\pi\) | |||||||
\(504\) | 778.259 | 0.0687826 | ||||||||
\(505\) | 2099.18 | 0.184974 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6276.45 | 0.549796 | ||||||||
\(508\) | −5580.69 | −0.487408 | ||||||||
\(509\) | 8984.01 | 0.782336 | 0.391168 | − | 0.920319i | \(-0.372071\pi\) | ||||
0.391168 | + | 0.920319i | \(0.372071\pi\) | |||||||
\(510\) | −1440.68 | −0.125087 | ||||||||
\(511\) | 1799.09 | 0.155748 | ||||||||
\(512\) | 7537.26 | 0.650591 | ||||||||
\(513\) | 2622.79 | 0.225729 | ||||||||
\(514\) | 15421.1 | 1.32334 | ||||||||
\(515\) | −2408.06 | −0.206042 | ||||||||
\(516\) | 2490.57 | 0.212483 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1751.30 | −0.148548 | ||||||||
\(519\) | 8130.68 | 0.687664 | ||||||||
\(520\) | 1245.15 | 0.105007 | ||||||||
\(521\) | −16931.5 | −1.42376 | −0.711882 | − | 0.702299i | \(-0.752157\pi\) | ||||
−0.711882 | + | 0.702299i | \(0.752157\pi\) | |||||||
\(522\) | 3382.16 | 0.283588 | ||||||||
\(523\) | −18323.2 | −1.53197 | −0.765983 | − | 0.642861i | \(-0.777747\pi\) | ||||
−0.765983 | + | 0.642861i | \(0.777747\pi\) | |||||||
\(524\) | −5395.60 | −0.449824 | ||||||||
\(525\) | −266.671 | −0.0221685 | ||||||||
\(526\) | −2946.14 | −0.244216 | ||||||||
\(527\) | 3655.71 | 0.302173 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11918.1 | −0.979544 | ||||||||
\(530\) | −18.6002 | −0.00152442 | ||||||||
\(531\) | 861.704 | 0.0704233 | ||||||||
\(532\) | 1249.65 | 0.101841 | ||||||||
\(533\) | 1478.87 | 0.120182 | ||||||||
\(534\) | 9681.15 | 0.784540 | ||||||||
\(535\) | 706.093 | 0.0570599 | ||||||||
\(536\) | 158.699 | 0.0127887 | ||||||||
\(537\) | 4887.39 | 0.392750 | ||||||||
\(538\) | 5608.13 | 0.449412 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −488.436 | −0.0389240 | ||||||||
\(541\) | 13422.3 | 1.06667 | 0.533335 | − | 0.845904i | \(-0.320939\pi\) | ||||
0.533335 | + | 0.845904i | \(0.320939\pi\) | |||||||
\(542\) | −10112.3 | −0.801404 | ||||||||
\(543\) | 5206.09 | 0.411445 | ||||||||
\(544\) | −6817.19 | −0.537288 | ||||||||
\(545\) | −4382.10 | −0.344419 | ||||||||
\(546\) | −228.642 | −0.0179212 | ||||||||
\(547\) | 13824.7 | 1.08063 | 0.540314 | − | 0.841463i | \(-0.318305\pi\) | ||||
0.540314 | + | 0.841463i | \(0.318305\pi\) | |||||||
\(548\) | −6278.41 | −0.489417 | ||||||||
\(549\) | 4749.48 | 0.369222 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17438.8 | 1.34831 | ||||||||
\(552\) | 1151.03 | 0.0887518 | ||||||||
\(553\) | −2087.68 | −0.160537 | ||||||||
\(554\) | 4819.63 | 0.369614 | ||||||||
\(555\) | 3529.42 | 0.269938 | ||||||||
\(556\) | 2949.56 | 0.224981 | ||||||||
\(557\) | −5443.20 | −0.414067 | −0.207034 | − | 0.978334i | \(-0.566381\pi\) | ||||
−0.207034 | + | 0.978334i | \(0.566381\pi\) | |||||||
\(558\) | −1501.09 | −0.113882 | ||||||||
\(559\) | −2349.57 | −0.177775 | ||||||||
\(560\) | 390.502 | 0.0294674 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1702.36 | 0.127775 | ||||||||
\(563\) | −16823.2 | −1.25935 | −0.629675 | − | 0.776858i | \(-0.716812\pi\) | ||||
−0.629675 | + | 0.776858i | \(0.716812\pi\) | |||||||
\(564\) | −1503.46 | −0.112246 | ||||||||
\(565\) | 5396.93 | 0.401859 | ||||||||
\(566\) | 12903.8 | 0.958281 | ||||||||
\(567\) | 288.005 | 0.0213317 | ||||||||
\(568\) | 8784.67 | 0.648938 | ||||||||
\(569\) | 19196.0 | 1.41430 | 0.707151 | − | 0.707063i | \(-0.249980\pi\) | ||||
0.707151 | + | 0.707063i | \(0.249980\pi\) | |||||||
\(570\) | 3050.18 | 0.224137 | ||||||||
\(571\) | 17350.0 | 1.27159 | 0.635794 | − | 0.771859i | \(-0.280673\pi\) | ||||
0.635794 | + | 0.771859i | \(0.280673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5672.77 | 0.413583 | ||||||||
\(574\) | 1074.96 | 0.0781672 | ||||||||
\(575\) | −394.401 | −0.0286046 | ||||||||
\(576\) | 4380.75 | 0.316894 | ||||||||
\(577\) | −19192.4 | −1.38473 | −0.692367 | − | 0.721545i | \(-0.743432\pi\) | ||||
−0.692367 | + | 0.721545i | \(0.743432\pi\) | |||||||
\(578\) | 5877.70 | 0.422976 | ||||||||
\(579\) | −705.138 | −0.0506123 | ||||||||
\(580\) | −3247.59 | −0.232498 | ||||||||
\(581\) | 3228.24 | 0.230517 | ||||||||
\(582\) | −5737.83 | −0.408661 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12305.7 | 0.871938 | ||||||||
\(585\) | 460.786 | 0.0325660 | ||||||||
\(586\) | −8927.22 | −0.629317 | ||||||||
\(587\) | −11943.4 | −0.839789 | −0.419895 | − | 0.907573i | \(-0.637933\pi\) | ||||
−0.419895 | + | 0.907573i | \(0.637933\pi\) | |||||||
\(588\) | −3585.75 | −0.251486 | ||||||||
\(589\) | −7739.79 | −0.541447 | ||||||||
\(590\) | 1002.12 | 0.0699264 | ||||||||
\(591\) | −7008.71 | −0.487817 | ||||||||
\(592\) | −5168.34 | −0.358813 | ||||||||
\(593\) | −13925.2 | −0.964315 | −0.482158 | − | 0.876085i | \(-0.660147\pi\) | ||||
−0.482158 | + | 0.876085i | \(0.660147\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −815.693 | −0.0562019 | ||||||||
\(596\) | −9021.40 | −0.620018 | ||||||||
\(597\) | 12001.1 | 0.822738 | ||||||||
\(598\) | −338.157 | −0.0231242 | ||||||||
\(599\) | 9438.13 | 0.643792 | 0.321896 | − | 0.946775i | \(-0.395680\pi\) | ||||
0.321896 | + | 0.946775i | \(0.395680\pi\) | |||||||
\(600\) | −1824.01 | −0.124108 | ||||||||
\(601\) | 18515.0 | 1.25664 | 0.628321 | − | 0.777954i | \(-0.283742\pi\) | ||||
0.628321 | + | 0.777954i | \(0.283742\pi\) | |||||||
\(602\) | −1707.86 | −0.115626 | ||||||||
\(603\) | 58.7286 | 0.00396619 | ||||||||
\(604\) | 3987.80 | 0.268644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2636.54 | −0.176736 | ||||||||
\(607\) | −22935.8 | −1.53366 | −0.766832 | − | 0.641848i | \(-0.778168\pi\) | ||||
−0.766832 | + | 0.641848i | \(0.778168\pi\) | |||||||
\(608\) | 14433.2 | 0.962738 | ||||||||
\(609\) | 1914.93 | 0.127417 | ||||||||
\(610\) | 5523.41 | 0.366617 | ||||||||
\(611\) | 1418.35 | 0.0939118 | ||||||||
\(612\) | −1494.03 | −0.0986805 | ||||||||
\(613\) | 5076.32 | 0.334471 | 0.167235 | − | 0.985917i | \(-0.446516\pi\) | ||||
0.167235 | + | 0.985917i | \(0.446516\pi\) | |||||||
\(614\) | −3020.38 | −0.198522 | ||||||||
\(615\) | −2166.38 | −0.142044 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11305.1 | 0.737643 | 0.368822 | − | 0.929500i | \(-0.379761\pi\) | ||||
0.368822 | + | 0.929500i | \(0.379761\pi\) | |||||||
\(618\) | 3024.49 | 0.196865 | ||||||||
\(619\) | −13500.7 | −0.876638 | −0.438319 | − | 0.898819i | \(-0.644426\pi\) | ||||
−0.438319 | + | 0.898819i | \(0.644426\pi\) | |||||||
\(620\) | 1441.36 | 0.0933654 | ||||||||
\(621\) | 425.953 | 0.0275248 | ||||||||
\(622\) | −14138.7 | −0.911432 | ||||||||
\(623\) | 5481.34 | 0.352496 | ||||||||
\(624\) | −674.755 | −0.0432882 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −1591.22 | −0.101594 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8991.40 | 0.571331 | ||||||||
\(629\) | 10795.8 | 0.684350 | ||||||||
\(630\) | 334.936 | 0.0211812 | ||||||||
\(631\) | 7201.91 | 0.454364 | 0.227182 | − | 0.973852i | \(-0.427049\pi\) | ||||
0.227182 | + | 0.973852i | \(0.427049\pi\) | |||||||
\(632\) | −14279.6 | −0.898752 | ||||||||
\(633\) | 1878.46 | 0.117950 | ||||||||
\(634\) | 7098.93 | 0.444692 | ||||||||
\(635\) | −7712.30 | −0.481973 | ||||||||
\(636\) | −19.2890 | −0.00120261 | ||||||||
\(637\) | 3382.76 | 0.210408 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3250.88 | 0.201256 | ||||||||
\(640\) | −848.653 | −0.0524156 | ||||||||
\(641\) | −10896.8 | −0.671446 | −0.335723 | − | 0.941961i | \(-0.608981\pi\) | ||||
−0.335723 | + | 0.941961i | \(0.608981\pi\) | |||||||
\(642\) | −886.844 | −0.0545186 | ||||||||
\(643\) | −24156.4 | −1.48155 | −0.740774 | − | 0.671754i | \(-0.765541\pi\) | ||||
−0.740774 | + | 0.671754i | \(0.765541\pi\) | |||||||
\(644\) | 202.949 | 0.0124182 | ||||||||
\(645\) | 3441.87 | 0.210114 | ||||||||
\(646\) | 9329.87 | 0.568233 | ||||||||
\(647\) | 6293.32 | 0.382405 | 0.191202 | − | 0.981551i | \(-0.438761\pi\) | ||||
0.191202 | + | 0.981551i | \(0.438761\pi\) | |||||||
\(648\) | 1969.94 | 0.119423 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 535.871 | 0.0323363 | ||||||||
\(651\) | −849.895 | −0.0511675 | ||||||||
\(652\) | 2492.16 | 0.149694 | ||||||||
\(653\) | 900.311 | 0.0539539 | 0.0269770 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269770 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(654\) | 5503.86 | 0.329079 | ||||||||
\(655\) | −7456.50 | −0.444809 | ||||||||
\(656\) | 3172.36 | 0.188811 | ||||||||
\(657\) | 4553.87 | 0.270416 | ||||||||
\(658\) | 1030.97 | 0.0610809 | ||||||||
\(659\) | −24626.9 | −1.45573 | −0.727865 | − | 0.685720i | \(-0.759487\pi\) | ||||
−0.727865 | + | 0.685720i | \(0.759487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30979.4 | 1.82293 | 0.911467 | − | 0.411373i | \(-0.134951\pi\) | ||||
0.911467 | + | 0.411373i | \(0.134951\pi\) | |||||||
\(662\) | 6741.62 | 0.395802 | ||||||||
\(663\) | 1409.45 | 0.0825618 | ||||||||
\(664\) | 22081.0 | 1.29052 | ||||||||
\(665\) | 1726.97 | 0.100705 | ||||||||
\(666\) | −4432.91 | −0.257916 | ||||||||
\(667\) | 2832.14 | 0.164409 | ||||||||
\(668\) | −8017.64 | −0.464389 | ||||||||
\(669\) | 890.930 | 0.0514878 | ||||||||
\(670\) | 68.2985 | 0.00393821 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1584.89 | 0.0909800 | ||||||||
\(673\) | 1125.07 | 0.0644402 | 0.0322201 | − | 0.999481i | \(-0.489742\pi\) | ||||
0.0322201 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(674\) | 9181.63 | 0.524723 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 7569.49 | 0.430672 | ||||||||
\(677\) | 16409.3 | 0.931551 | 0.465776 | − | 0.884903i | \(-0.345775\pi\) | ||||
0.465776 | + | 0.884903i | \(0.345775\pi\) | |||||||
\(678\) | −6778.47 | −0.383961 | ||||||||
\(679\) | −3248.68 | −0.183613 | ||||||||
\(680\) | −5579.29 | −0.314641 | ||||||||
\(681\) | −3648.46 | −0.205300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24830.7 | 1.39110 | 0.695548 | − | 0.718479i | \(-0.255161\pi\) | ||||
0.695548 | + | 0.718479i | \(0.255161\pi\) | |||||||
\(684\) | 3163.13 | 0.176820 | ||||||||
\(685\) | −8676.52 | −0.483960 | ||||||||
\(686\) | 5011.81 | 0.278938 | ||||||||
\(687\) | −13425.0 | −0.745554 | ||||||||
\(688\) | −5040.13 | −0.279292 | ||||||||
\(689\) | 18.1970 | 0.00100617 | ||||||||
\(690\) | 495.362 | 0.0273306 | ||||||||
\(691\) | 33267.5 | 1.83148 | 0.915741 | − | 0.401768i | \(-0.131604\pi\) | ||||
0.915741 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(692\) | 9805.73 | 0.538668 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13609.9 | −0.744414 | ||||||||
\(695\) | 4076.18 | 0.222473 | ||||||||
\(696\) | 13098.0 | 0.713332 | ||||||||
\(697\) | −6626.52 | −0.360111 | ||||||||
\(698\) | 4067.33 | 0.220560 | ||||||||
\(699\) | 16959.2 | 0.917677 | ||||||||
\(700\) | −321.610 | −0.0173653 | ||||||||
\(701\) | 15590.4 | 0.840000 | 0.420000 | − | 0.907524i | \(-0.362030\pi\) | ||||
0.420000 | + | 0.907524i | \(0.362030\pi\) | |||||||
\(702\) | −578.741 | −0.0311156 | ||||||||
\(703\) | −22856.6 | −1.22625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2077.72 | −0.110995 | ||||||||
\(706\) | −4447.78 | −0.237103 | ||||||||
\(707\) | −1492.77 | −0.0794080 | ||||||||
\(708\) | 1039.23 | 0.0551647 | ||||||||
\(709\) | −33594.5 | −1.77950 | −0.889752 | − | 0.456443i | \(-0.849123\pi\) | ||||
−0.889752 | + | 0.456443i | \(0.849123\pi\) | |||||||
\(710\) | 3780.62 | 0.199837 | ||||||||
\(711\) | −5284.34 | −0.278732 | ||||||||
\(712\) | 37492.0 | 1.97342 | ||||||||
\(713\) | −1256.98 | −0.0660226 | ||||||||
\(714\) | 1024.50 | 0.0536988 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5894.27 | 0.307653 | ||||||||
\(717\) | 11309.6 | 0.589072 | ||||||||
\(718\) | −12902.0 | −0.670611 | ||||||||
\(719\) | 9329.98 | 0.483935 | 0.241968 | − | 0.970284i | \(-0.422207\pi\) | ||||
0.241968 | + | 0.970284i | \(0.422207\pi\) | |||||||
\(720\) | 988.442 | 0.0511626 | ||||||||
\(721\) | 1712.42 | 0.0884521 | ||||||||
\(722\) | −5394.99 | −0.278090 | ||||||||
\(723\) | −11622.0 | −0.597823 | ||||||||
\(724\) | 6278.62 | 0.322297 | ||||||||
\(725\) | −4488.04 | −0.229906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7667.73 | −0.391170 | −0.195585 | − | 0.980687i | \(-0.562660\pi\) | ||||
−0.195585 | + | 0.980687i | \(0.562660\pi\) | |||||||
\(728\) | −885.458 | −0.0450787 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5295.92 | 0.268508 | ||||||||
\(731\) | 10528.0 | 0.532683 | ||||||||
\(732\) | 5727.95 | 0.289223 | ||||||||
\(733\) | 27923.5 | 1.40706 | 0.703531 | − | 0.710664i | \(-0.251606\pi\) | ||||
0.703531 | + | 0.710664i | \(0.251606\pi\) | |||||||
\(734\) | 26320.2 | 1.32357 | ||||||||
\(735\) | −4955.36 | −0.248682 | ||||||||
\(736\) | 2344.02 | 0.117394 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2720.95 | 0.135717 | ||||||||
\(739\) | −8329.33 | −0.414614 | −0.207307 | − | 0.978276i | \(-0.566470\pi\) | ||||
−0.207307 | + | 0.978276i | \(0.566470\pi\) | |||||||
\(740\) | 4256.54 | 0.211451 | ||||||||
\(741\) | −2984.06 | −0.147938 | ||||||||
\(742\) | 13.2271 | 0.000654421 0 | ||||||||
\(743\) | −10423.0 | −0.514646 | −0.257323 | − | 0.966325i | \(-0.582841\pi\) | ||||
−0.257323 | + | 0.966325i | \(0.582841\pi\) | |||||||
\(744\) | −5813.23 | −0.286456 | ||||||||
\(745\) | −12467.2 | −0.613106 | ||||||||
\(746\) | 13355.1 | 0.655448 | ||||||||
\(747\) | 8171.35 | 0.400233 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −502.119 | −0.0244954 | ||||||||
\(750\) | −784.992 | −0.0382185 | ||||||||
\(751\) | −36541.4 | −1.77552 | −0.887760 | − | 0.460307i | \(-0.847739\pi\) | ||||
−0.887760 | + | 0.460307i | \(0.847739\pi\) | |||||||
\(752\) | 3042.52 | 0.147539 | ||||||||
\(753\) | −10738.5 | −0.519698 | ||||||||
\(754\) | −3848.02 | −0.185858 | ||||||||
\(755\) | 5510.98 | 0.265649 | ||||||||
\(756\) | 347.338 | 0.0167098 | ||||||||
\(757\) | −17114.6 | −0.821718 | −0.410859 | − | 0.911699i | \(-0.634771\pi\) | ||||
−0.410859 | + | 0.911699i | \(0.634771\pi\) | |||||||
\(758\) | −13417.5 | −0.642937 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11812.4 | 0.563789 | ||||||||
\(761\) | 23597.4 | 1.12405 | 0.562027 | − | 0.827119i | \(-0.310022\pi\) | ||||
0.562027 | + | 0.827119i | \(0.310022\pi\) | |||||||
\(762\) | 9686.54 | 0.460507 | ||||||||
\(763\) | 3116.21 | 0.147856 | ||||||||
\(764\) | 6841.45 | 0.323972 | ||||||||
\(765\) | −2064.69 | −0.0975803 | ||||||||
\(766\) | 12816.2 | 0.604525 | ||||||||
\(767\) | −980.396 | −0.0461539 | ||||||||
\(768\) | 12747.9 | 0.598958 | ||||||||
\(769\) | −9769.32 | −0.458116 | −0.229058 | − | 0.973413i | \(-0.573564\pi\) | ||||
−0.229058 | + | 0.973413i | \(0.573564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22100.6 | 1.03234 | ||||||||
\(772\) | −850.407 | −0.0396461 | ||||||||
\(773\) | 4933.64 | 0.229561 | 0.114781 | − | 0.993391i | \(-0.463384\pi\) | ||||
0.114781 | + | 0.993391i | \(0.463384\pi\) | |||||||
\(774\) | −4322.94 | −0.200756 | ||||||||
\(775\) | 1991.91 | 0.0923245 | ||||||||
\(776\) | −22220.8 | −1.02794 | ||||||||
\(777\) | −2509.85 | −0.115882 | ||||||||
\(778\) | 15792.6 | 0.727755 | ||||||||
\(779\) | 14029.5 | 0.645264 | ||||||||
\(780\) | 555.714 | 0.0255100 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1515.21 | 0.0692888 | ||||||||
\(783\) | 4847.09 | 0.221227 | ||||||||
\(784\) | 7256.43 | 0.330559 | ||||||||
\(785\) | 12425.8 | 0.564961 | ||||||||
\(786\) | 9365.27 | 0.424998 | ||||||||
\(787\) | 5524.93 | 0.250245 | 0.125122 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125122 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(788\) | −8452.61 | −0.382121 | ||||||||
\(789\) | −4222.22 | −0.190513 | ||||||||
\(790\) | −6145.43 | −0.276765 | ||||||||
\(791\) | −3837.88 | −0.172515 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5403.68 | −0.241980 | ||||||||
\(794\) | 11180.5 | 0.499725 | ||||||||
\(795\) | −26.6567 | −0.00118920 | ||||||||
\(796\) | 14473.6 | 0.644475 | ||||||||
\(797\) | −29994.7 | −1.33308 | −0.666541 | − | 0.745468i | \(-0.732226\pi\) | ||||
−0.666541 | + | 0.745468i | \(0.732226\pi\) | |||||||
\(798\) | −2169.05 | −0.0962200 | ||||||||
\(799\) | −6355.32 | −0.281396 | ||||||||
\(800\) | −3714.53 | −0.164161 | ||||||||
\(801\) | 13874.4 | 0.612020 | ||||||||
\(802\) | −30171.3 | −1.32841 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 70.8276 | 0.00310684 | ||||||||
\(805\) | 280.467 | 0.0122797 | ||||||||
\(806\) | 1707.85 | 0.0746358 | ||||||||
\(807\) | 8037.21 | 0.350586 | ||||||||
\(808\) | −10210.5 | −0.444558 | ||||||||
\(809\) | −6020.90 | −0.261661 | −0.130830 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130830 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(810\) | 847.791 | 0.0367757 | ||||||||
\(811\) | 25351.3 | 1.09766 | 0.548831 | − | 0.835933i | \(-0.315073\pi\) | ||||
0.548831 | + | 0.835933i | \(0.315073\pi\) | |||||||
\(812\) | 2309.44 | 0.0998095 | ||||||||
\(813\) | −14492.3 | −0.625176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3444.07 | 0.148025 | ||||||||
\(816\) | 3023.44 | 0.129708 | ||||||||
\(817\) | −22289.6 | −0.954486 | ||||||||
\(818\) | 27616.6 | 1.18043 | ||||||||
\(819\) | −327.675 | −0.0139803 | ||||||||
\(820\) | −2612.69 | −0.111267 | ||||||||
\(821\) | 16072.6 | 0.683238 | 0.341619 | − | 0.939839i | \(-0.389025\pi\) | ||||
0.341619 | + | 0.939839i | \(0.389025\pi\) | |||||||
\(822\) | 10897.6 | 0.462405 | ||||||||
\(823\) | −19242.3 | −0.815000 | −0.407500 | − | 0.913205i | \(-0.633599\pi\) | ||||
−0.407500 | + | 0.913205i | \(0.633599\pi\) | |||||||
\(824\) | 11712.9 | 0.495191 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −712.630 | −0.0300188 | ||||||||
\(827\) | 40811.2 | 1.71602 | 0.858008 | − | 0.513636i | \(-0.171702\pi\) | ||||
0.858008 | + | 0.513636i | \(0.171702\pi\) | |||||||
\(828\) | 513.706 | 0.0215610 | ||||||||
\(829\) | −3445.06 | −0.144333 | −0.0721663 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721663 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(830\) | 9502.88 | 0.397410 | ||||||||
\(831\) | 6907.18 | 0.288336 | ||||||||
\(832\) | −4984.16 | −0.207686 | ||||||||
\(833\) | −15157.4 | −0.630461 | ||||||||
\(834\) | −5119.63 | −0.212564 | ||||||||
\(835\) | −11080.1 | −0.459211 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2151.26 | −0.0888393 | ||||||||
\(838\) | 9730.28 | 0.401106 | ||||||||
\(839\) | 18299.8 | 0.753015 | 0.376508 | − | 0.926414i | \(-0.377125\pi\) | ||||
0.376508 | + | 0.926414i | \(0.377125\pi\) | |||||||
\(840\) | 1297.10 | 0.0532788 | ||||||||
\(841\) | 7839.07 | 0.321418 | ||||||||
\(842\) | 31160.7 | 1.27538 | ||||||||
\(843\) | 2439.72 | 0.0996776 | ||||||||
\(844\) | 2265.46 | 0.0923936 | ||||||||
\(845\) | 10460.7 | 0.425870 | ||||||||
\(846\) | 2609.59 | 0.106051 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 39.0349 | 0.00158073 | ||||||||
\(849\) | 18492.9 | 0.747555 | ||||||||
\(850\) | −2401.13 | −0.0968919 | ||||||||
\(851\) | −3712.02 | −0.149526 | ||||||||
\(852\) | 3920.61 | 0.157650 | ||||||||
\(853\) | 13253.4 | 0.531990 | 0.265995 | − | 0.963974i | \(-0.414299\pi\) | ||||
0.265995 | + | 0.963974i | \(0.414299\pi\) | |||||||
\(854\) | −3927.83 | −0.157386 | ||||||||
\(855\) | 4371.32 | 0.174849 | ||||||||
\(856\) | −3434.46 | −0.137135 | ||||||||
\(857\) | −14698.3 | −0.585862 | −0.292931 | − | 0.956134i | \(-0.594631\pi\) | ||||
−0.292931 | + | 0.956134i | \(0.594631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28131.1 | 1.11737 | 0.558685 | − | 0.829380i | \(-0.311306\pi\) | ||||
0.558685 | + | 0.829380i | \(0.311306\pi\) | |||||||
\(860\) | 4150.95 | 0.164588 | ||||||||
\(861\) | 1540.56 | 0.0609783 | ||||||||
\(862\) | 3758.68 | 0.148516 | ||||||||
\(863\) | −38137.0 | −1.50429 | −0.752144 | − | 0.658999i | \(-0.770980\pi\) | ||||
−0.752144 | + | 0.658999i | \(0.770980\pi\) | |||||||
\(864\) | 4011.69 | 0.157964 | ||||||||
\(865\) | 13551.1 | 0.532662 | ||||||||
\(866\) | −30632.9 | −1.20202 | ||||||||
\(867\) | 8423.54 | 0.329964 | ||||||||
\(868\) | −1024.99 | −0.0400810 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5636.93 | 0.219666 | ||||||||
\(871\) | −66.8180 | −0.00259936 | ||||||||
\(872\) | 21314.7 | 0.827760 | ||||||||
\(873\) | −8223.09 | −0.318797 | ||||||||
\(874\) | −3207.98 | −0.124155 | ||||||||
\(875\) | −444.452 | −0.0171717 | ||||||||
\(876\) | 5492.03 | 0.211825 | ||||||||
\(877\) | 23653.1 | 0.910728 | 0.455364 | − | 0.890305i | \(-0.349509\pi\) | ||||
0.455364 | + | 0.890305i | \(0.349509\pi\) | |||||||
\(878\) | 14823.8 | 0.569793 | ||||||||
\(879\) | −12793.9 | −0.490931 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4181.89 | 0.159922 | 0.0799612 | − | 0.996798i | \(-0.474520\pi\) | ||||
0.0799612 | + | 0.996798i | \(0.474520\pi\) | |||||||
\(882\) | 6223.87 | 0.237606 | ||||||||
\(883\) | −20102.5 | −0.766142 | −0.383071 | − | 0.923719i | \(-0.625134\pi\) | ||||
−0.383071 | + | 0.923719i | \(0.625134\pi\) | |||||||
\(884\) | 1699.82 | 0.0646731 | ||||||||
\(885\) | 1436.17 | 0.0545496 | ||||||||
\(886\) | −29737.8 | −1.12761 | ||||||||
\(887\) | −7941.42 | −0.300617 | −0.150308 | − | 0.988639i | \(-0.548027\pi\) | ||||
−0.150308 | + | 0.988639i | \(0.548027\pi\) | |||||||
\(888\) | −17167.3 | −0.648756 | ||||||||
\(889\) | 5484.39 | 0.206907 | ||||||||
\(890\) | 16135.3 | 0.607702 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1074.47 | 0.0403319 | ||||||||
\(893\) | 13455.4 | 0.504218 | ||||||||
\(894\) | 15658.7 | 0.585799 | ||||||||
\(895\) | 8145.66 | 0.304223 | ||||||||
\(896\) | 603.497 | 0.0225016 | ||||||||
\(897\) | −484.624 | −0.0180392 | ||||||||
\(898\) | −8384.30 | −0.311568 | ||||||||
\(899\) | −14303.6 | −0.530649 | ||||||||
\(900\) | −814.060 | −0.0301504 | ||||||||
\(901\) | −81.5373 | −0.00301487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2447.59 | −0.0902002 | ||||||||
\(904\) | −26250.9 | −0.965808 | ||||||||
\(905\) | 8676.82 | 0.318704 | ||||||||
\(906\) | −6921.72 | −0.253818 | ||||||||
\(907\) | −9541.21 | −0.349295 | −0.174647 | − | 0.984631i | \(-0.555879\pi\) | ||||
−0.174647 | + | 0.984631i | \(0.555879\pi\) | |||||||
\(908\) | −4400.10 | −0.160818 | ||||||||
\(909\) | −3778.52 | −0.137872 | ||||||||
\(910\) | −381.070 | −0.0138817 | ||||||||
\(911\) | 54124.8 | 1.96842 | 0.984212 | − | 0.176993i | \(-0.0566369\pi\) | ||||
0.984212 | + | 0.176993i | \(0.0566369\pi\) | |||||||
\(912\) | −6401.17 | −0.232417 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 38034.9 | 1.37646 | ||||||||
\(915\) | 7915.80 | 0.285998 | ||||||||
\(916\) | −16190.8 | −0.584015 | ||||||||
\(917\) | 5302.49 | 0.190953 | ||||||||
\(918\) | 2593.22 | 0.0932342 | ||||||||
\(919\) | 4785.90 | 0.171787 | 0.0858935 | − | 0.996304i | \(-0.472626\pi\) | ||||
0.0858935 | + | 0.996304i | \(0.472626\pi\) | |||||||
\(920\) | 1918.38 | 0.0687469 | ||||||||
\(921\) | −4328.62 | −0.154867 | ||||||||
\(922\) | 5201.88 | 0.185808 | ||||||||
\(923\) | −3698.66 | −0.131899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5882.37 | 0.209093 | ||||||||
\(926\) | 33970.9 | 1.20556 | ||||||||
\(927\) | 4334.50 | 0.153575 | ||||||||
\(928\) | 26673.6 | 0.943537 | ||||||||
\(929\) | −42417.2 | −1.49802 | −0.749011 | − | 0.662558i | \(-0.769471\pi\) | ||||
−0.749011 | + | 0.662558i | \(0.769471\pi\) | |||||||
\(930\) | −2501.81 | −0.0882125 | ||||||||
\(931\) | 32091.1 | 1.12969 | ||||||||
\(932\) | 20453.1 | 0.718844 | ||||||||
\(933\) | −20262.7 | −0.711008 | ||||||||
\(934\) | 22028.8 | 0.771738 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2241.28 | −0.0782676 | ||||||||
\(937\) | 43632.1 | 1.52124 | 0.760618 | − | 0.649200i | \(-0.224896\pi\) | ||||
0.760618 | + | 0.649200i | \(0.224896\pi\) | |||||||
\(938\) | −48.5686 | −0.00169064 | ||||||||
\(939\) | −2280.43 | −0.0792536 | ||||||||
\(940\) | −2505.76 | −0.0869457 | ||||||||
\(941\) | −41150.7 | −1.42558 | −0.712792 | − | 0.701376i | \(-0.752570\pi\) | ||||
−0.712792 | + | 0.701376i | \(0.752570\pi\) | |||||||
\(942\) | −15606.6 | −0.539799 | ||||||||
\(943\) | 2278.46 | 0.0786817 | ||||||||
\(944\) | −2103.07 | −0.0725097 | ||||||||
\(945\) | 480.008 | 0.0165235 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40605.3 | −1.39334 | −0.696671 | − | 0.717390i | \(-0.745336\pi\) | ||||
−0.696671 | + | 0.717390i | \(0.745336\pi\) | |||||||
\(948\) | −6373.00 | −0.218339 | ||||||||
\(949\) | −5181.13 | −0.177225 | ||||||||
\(950\) | 5083.63 | 0.173615 | ||||||||
\(951\) | 10173.7 | 0.346904 | ||||||||
\(952\) | 3967.56 | 0.135073 | ||||||||
\(953\) | −18063.2 | −0.613981 | −0.306990 | − | 0.951713i | \(-0.599322\pi\) | ||||
−0.306990 | + | 0.951713i | \(0.599322\pi\) | |||||||
\(954\) | 33.4804 | 0.00113623 | ||||||||
\(955\) | 9454.61 | 0.320360 | ||||||||
\(956\) | 13639.5 | 0.461438 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8331.41 | −0.280977 | ||||||||
\(959\) | 6170.07 | 0.207760 | ||||||||
\(960\) | 7301.24 | 0.245465 | ||||||||
\(961\) | −23442.7 | −0.786905 | ||||||||
\(962\) | 5043.51 | 0.169032 | ||||||||
\(963\) | −1270.97 | −0.0425300 | ||||||||
\(964\) | −14016.3 | −0.468293 | ||||||||
\(965\) | −1175.23 | −0.0392041 | ||||||||
\(966\) | −352.263 | −0.0117328 | ||||||||
\(967\) | −39800.2 | −1.32357 | −0.661783 | − | 0.749696i | \(-0.730200\pi\) | ||||
−0.661783 | + | 0.749696i | \(0.730200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13371.0 | 0.443279 | ||||||||
\(970\) | −9563.05 | −0.316547 | ||||||||
\(971\) | −27405.4 | −0.905748 | −0.452874 | − | 0.891575i | \(-0.649601\pi\) | ||||
−0.452874 | + | 0.891575i | \(0.649601\pi\) | |||||||
\(972\) | 879.185 | 0.0290122 | ||||||||
\(973\) | −2898.67 | −0.0955057 | ||||||||
\(974\) | 2305.53 | 0.0758461 | ||||||||
\(975\) | 767.976 | 0.0252256 | ||||||||
\(976\) | −11591.6 | −0.380161 | ||||||||
\(977\) | 6513.88 | 0.213303 | 0.106652 | − | 0.994296i | \(-0.465987\pi\) | ||||
0.106652 | + | 0.994296i | \(0.465987\pi\) | |||||||
\(978\) | −4325.70 | −0.141432 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5976.25 | −0.194800 | ||||||||
\(981\) | 7887.78 | 0.256715 | ||||||||
\(982\) | −4855.69 | −0.157792 | ||||||||
\(983\) | −2650.01 | −0.0859838 | −0.0429919 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429919 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(984\) | 10537.4 | 0.341381 | ||||||||
\(985\) | −11681.2 | −0.377861 | ||||||||
\(986\) | 17242.2 | 0.556900 | ||||||||
\(987\) | 1477.51 | 0.0476492 | ||||||||
\(988\) | −3598.82 | −0.115884 | ||||||||
\(989\) | −3619.93 | −0.116387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10091.7 | −0.323486 | −0.161743 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161743 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(992\) | −11838.4 | −0.378901 | ||||||||
\(993\) | 9661.66 | 0.308765 | ||||||||
\(994\) | −2688.48 | −0.0857882 | ||||||||
\(995\) | 20001.9 | 0.637290 | ||||||||
\(996\) | 9854.78 | 0.313515 | ||||||||
\(997\) | −3007.33 | −0.0955297 | −0.0477648 | − | 0.998859i | \(-0.515210\pi\) | ||||
−0.0477648 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(998\) | 7501.07 | 0.237918 | ||||||||
\(999\) | −6352.96 | −0.201200 |
(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 | 1815.4.a.w.1.2 | yes | 4 | |
11.10 | odd | 2 | 1815.4.a.u.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.u.1.3 | ✓ | 4 | 11.10 | odd | 2 | ||
1815.4.a.w.1.2 | yes | 4 | 1.1 | even | 1 | trivial |