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: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 76 x^{10} + 86 x^{9} + 2070 x^{8} - 2627 x^{7} - 23872 x^{6} + 33784 x^{5} + \cdots + 9680 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 11^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.95717\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.95717 | 1.04552 | 0.522759 | − | 0.852481i | \(-0.324903\pi\) | ||||
0.522759 | + | 0.852481i | \(0.324903\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0.744851 | 0.0931063 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −8.87151 | −0.603630 | ||||||||
\(7\) | −13.4337 | −0.725352 | −0.362676 | − | 0.931915i | \(-0.618137\pi\) | ||||
−0.362676 | + | 0.931915i | \(0.618137\pi\) | |||||||
\(8\) | −21.4547 | −0.948173 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −14.7858 | −0.467570 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.23455 | −0.0537550 | ||||||||
\(13\) | −13.8516 | −0.295519 | −0.147760 | − | 0.989023i | \(-0.547206\pi\) | ||||
−0.147760 | + | 0.989023i | \(0.547206\pi\) | |||||||
\(14\) | −39.7257 | −0.758368 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −69.4040 | −1.08444 | ||||||||
\(17\) | −25.6449 | −0.365871 | −0.182935 | − | 0.983125i | \(-0.558560\pi\) | ||||
−0.182935 | + | 0.983125i | \(0.558560\pi\) | |||||||
\(18\) | 26.6145 | 0.348506 | ||||||||
\(19\) | −38.1498 | −0.460640 | −0.230320 | − | 0.973115i | \(-0.573977\pi\) | ||||
−0.230320 | + | 0.973115i | \(0.573977\pi\) | |||||||
\(20\) | −3.72425 | −0.0416384 | ||||||||
\(21\) | 40.3011 | 0.418782 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −62.5445 | −0.567019 | −0.283509 | − | 0.958969i | \(-0.591499\pi\) | ||||
−0.283509 | + | 0.958969i | \(0.591499\pi\) | |||||||
\(24\) | 64.3641 | 0.547428 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −40.9616 | −0.308970 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −10.0061 | −0.0675349 | ||||||||
\(29\) | −53.6490 | −0.343530 | −0.171765 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171765 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(30\) | 44.3575 | 0.269951 | ||||||||
\(31\) | −220.673 | −1.27852 | −0.639258 | − | 0.768993i | \(-0.720758\pi\) | ||||
−0.639258 | + | 0.768993i | \(0.720758\pi\) | |||||||
\(32\) | −33.6018 | −0.185625 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −75.8363 | −0.382524 | ||||||||
\(35\) | 67.1685 | 0.324387 | ||||||||
\(36\) | 6.70366 | 0.0310354 | ||||||||
\(37\) | −162.917 | −0.723876 | −0.361938 | − | 0.932202i | \(-0.617885\pi\) | ||||
−0.361938 | + | 0.932202i | \(0.617885\pi\) | |||||||
\(38\) | −112.815 | −0.481607 | ||||||||
\(39\) | 41.5549 | 0.170618 | ||||||||
\(40\) | 107.274 | 0.424036 | ||||||||
\(41\) | −17.8559 | −0.0680152 | −0.0340076 | − | 0.999422i | \(-0.510827\pi\) | ||||
−0.0340076 | + | 0.999422i | \(0.510827\pi\) | |||||||
\(42\) | 119.177 | 0.437844 | ||||||||
\(43\) | −259.519 | −0.920380 | −0.460190 | − | 0.887821i | \(-0.652219\pi\) | ||||
−0.460190 | + | 0.887821i | \(0.652219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | −184.955 | −0.592828 | ||||||||
\(47\) | 20.5710 | 0.0638422 | 0.0319211 | − | 0.999490i | \(-0.489837\pi\) | ||||
0.0319211 | + | 0.999490i | \(0.489837\pi\) | |||||||
\(48\) | 208.212 | 0.626100 | ||||||||
\(49\) | −162.535 | −0.473864 | ||||||||
\(50\) | 73.9292 | 0.209103 | ||||||||
\(51\) | 76.9347 | 0.211236 | ||||||||
\(52\) | −10.3174 | −0.0275147 | ||||||||
\(53\) | 123.088 | 0.319008 | 0.159504 | − | 0.987197i | \(-0.449010\pi\) | ||||
0.159504 | + | 0.987197i | \(0.449010\pi\) | |||||||
\(54\) | −79.8436 | −0.201210 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 288.216 | 0.687759 | ||||||||
\(57\) | 114.449 | 0.265951 | ||||||||
\(58\) | −158.649 | −0.359167 | ||||||||
\(59\) | −697.175 | −1.53838 | −0.769191 | − | 0.639019i | \(-0.779340\pi\) | ||||
−0.769191 | + | 0.639019i | \(0.779340\pi\) | |||||||
\(60\) | 11.1728 | 0.0240400 | ||||||||
\(61\) | 829.186 | 1.74043 | 0.870216 | − | 0.492670i | \(-0.163979\pi\) | ||||
0.870216 | + | 0.492670i | \(0.163979\pi\) | |||||||
\(62\) | −652.566 | −1.33671 | ||||||||
\(63\) | −120.903 | −0.241784 | ||||||||
\(64\) | 455.866 | 0.890363 | ||||||||
\(65\) | 69.2581 | 0.132160 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 445.977 | 0.813206 | 0.406603 | − | 0.913605i | \(-0.366713\pi\) | ||||
0.406603 | + | 0.913605i | \(0.366713\pi\) | |||||||
\(68\) | −19.1016 | −0.0340649 | ||||||||
\(69\) | 187.633 | 0.327368 | ||||||||
\(70\) | 198.629 | 0.339153 | ||||||||
\(71\) | 718.238 | 1.20055 | 0.600276 | − | 0.799793i | \(-0.295057\pi\) | ||||
0.600276 | + | 0.799793i | \(0.295057\pi\) | |||||||
\(72\) | −193.092 | −0.316058 | ||||||||
\(73\) | 268.461 | 0.430424 | 0.215212 | − | 0.976567i | \(-0.430956\pi\) | ||||
0.215212 | + | 0.976567i | \(0.430956\pi\) | |||||||
\(74\) | −481.773 | −0.756825 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −28.4159 | −0.0428885 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 122.885 | 0.178384 | ||||||||
\(79\) | −368.090 | −0.524219 | −0.262110 | − | 0.965038i | \(-0.584418\pi\) | ||||
−0.262110 | + | 0.965038i | \(0.584418\pi\) | |||||||
\(80\) | 347.020 | 0.484975 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −52.8030 | −0.0711111 | ||||||||
\(83\) | 525.631 | 0.695126 | 0.347563 | − | 0.937657i | \(-0.387009\pi\) | ||||
0.347563 | + | 0.937657i | \(0.387009\pi\) | |||||||
\(84\) | 30.0183 | 0.0389913 | ||||||||
\(85\) | 128.224 | 0.163622 | ||||||||
\(86\) | −767.443 | −0.962273 | ||||||||
\(87\) | 160.947 | 0.198337 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1188.65 | 1.41569 | 0.707845 | − | 0.706367i | \(-0.249667\pi\) | ||||
0.707845 | + | 0.706367i | \(0.249667\pi\) | |||||||
\(90\) | −133.073 | −0.155857 | ||||||||
\(91\) | 186.079 | 0.214355 | ||||||||
\(92\) | −46.5863 | −0.0527930 | ||||||||
\(93\) | 662.018 | 0.738151 | ||||||||
\(94\) | 60.8318 | 0.0667481 | ||||||||
\(95\) | 190.749 | 0.206005 | ||||||||
\(96\) | 100.805 | 0.107171 | ||||||||
\(97\) | 296.908 | 0.310789 | 0.155394 | − | 0.987853i | \(-0.450335\pi\) | ||||
0.155394 | + | 0.987853i | \(0.450335\pi\) | |||||||
\(98\) | −480.645 | −0.495433 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.6213 | 0.0186213 | ||||||||
\(101\) | −246.716 | −0.243061 | −0.121531 | − | 0.992588i | \(-0.538780\pi\) | ||||
−0.121531 | + | 0.992588i | \(0.538780\pi\) | |||||||
\(102\) | 227.509 | 0.220850 | ||||||||
\(103\) | −213.327 | −0.204075 | −0.102038 | − | 0.994781i | \(-0.532536\pi\) | ||||
−0.102038 | + | 0.994781i | \(0.532536\pi\) | |||||||
\(104\) | 297.182 | 0.280203 | ||||||||
\(105\) | −201.506 | −0.187285 | ||||||||
\(106\) | 363.992 | 0.333529 | ||||||||
\(107\) | 79.8372 | 0.0721322 | 0.0360661 | − | 0.999349i | \(-0.488517\pi\) | ||||
0.0360661 | + | 0.999349i | \(0.488517\pi\) | |||||||
\(108\) | −20.1110 | −0.0179183 | ||||||||
\(109\) | −814.199 | −0.715469 | −0.357735 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357735 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 488.751 | 0.417930 | ||||||||
\(112\) | 932.353 | 0.786599 | ||||||||
\(113\) | 1918.61 | 1.59723 | 0.798616 | − | 0.601840i | \(-0.205566\pi\) | ||||
0.798616 | + | 0.601840i | \(0.205566\pi\) | |||||||
\(114\) | 338.446 | 0.278056 | ||||||||
\(115\) | 312.722 | 0.253578 | ||||||||
\(116\) | −39.9605 | −0.0319848 | ||||||||
\(117\) | −124.665 | −0.0985064 | ||||||||
\(118\) | −2061.67 | −1.60840 | ||||||||
\(119\) | 344.506 | 0.265385 | ||||||||
\(120\) | −321.821 | −0.244817 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2452.04 | 1.81965 | ||||||||
\(123\) | 53.5677 | 0.0392686 | ||||||||
\(124\) | −164.368 | −0.119038 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −357.532 | −0.252789 | ||||||||
\(127\) | −569.156 | −0.397673 | −0.198837 | − | 0.980033i | \(-0.563716\pi\) | ||||
−0.198837 | + | 0.980033i | \(0.563716\pi\) | |||||||
\(128\) | 1616.89 | 1.11652 | ||||||||
\(129\) | 778.558 | 0.531381 | ||||||||
\(130\) | 204.808 | 0.138176 | ||||||||
\(131\) | −2730.18 | −1.82089 | −0.910445 | − | 0.413629i | \(-0.864261\pi\) | ||||
−0.910445 | + | 0.413629i | \(0.864261\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 512.493 | 0.334126 | ||||||||
\(134\) | 1318.83 | 0.850221 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 550.204 | 0.346909 | ||||||||
\(137\) | −1193.11 | −0.744048 | −0.372024 | − | 0.928223i | \(-0.621336\pi\) | ||||
−0.372024 | + | 0.928223i | \(0.621336\pi\) | |||||||
\(138\) | 554.864 | 0.342269 | ||||||||
\(139\) | 1266.67 | 0.772930 | 0.386465 | − | 0.922304i | \(-0.373696\pi\) | ||||
0.386465 | + | 0.922304i | \(0.373696\pi\) | |||||||
\(140\) | 50.0305 | 0.0302025 | ||||||||
\(141\) | −61.7129 | −0.0368593 | ||||||||
\(142\) | 2123.95 | 1.25520 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −624.636 | −0.361479 | ||||||||
\(145\) | 268.245 | 0.153631 | ||||||||
\(146\) | 793.885 | 0.450016 | ||||||||
\(147\) | 487.606 | 0.273586 | ||||||||
\(148\) | −121.349 | −0.0673974 | ||||||||
\(149\) | 849.490 | 0.467067 | 0.233533 | − | 0.972349i | \(-0.424971\pi\) | ||||
0.233533 | + | 0.972349i | \(0.424971\pi\) | |||||||
\(150\) | −221.788 | −0.120726 | ||||||||
\(151\) | 2887.11 | 1.55596 | 0.777979 | − | 0.628290i | \(-0.216245\pi\) | ||||
0.777979 | + | 0.628290i | \(0.216245\pi\) | |||||||
\(152\) | 818.492 | 0.436766 | ||||||||
\(153\) | −230.804 | −0.121957 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1103.36 | 0.571769 | ||||||||
\(156\) | 30.9522 | 0.0158856 | ||||||||
\(157\) | 753.269 | 0.382913 | 0.191457 | − | 0.981501i | \(-0.438679\pi\) | ||||
0.191457 | + | 0.981501i | \(0.438679\pi\) | |||||||
\(158\) | −1088.50 | −0.548080 | ||||||||
\(159\) | −369.264 | −0.184180 | ||||||||
\(160\) | 168.009 | 0.0830141 | ||||||||
\(161\) | 840.204 | 0.411288 | ||||||||
\(162\) | 239.531 | 0.116169 | ||||||||
\(163\) | 1263.95 | 0.607361 | 0.303681 | − | 0.952774i | \(-0.401784\pi\) | ||||
0.303681 | + | 0.952774i | \(0.401784\pi\) | |||||||
\(164\) | −13.3000 | −0.00633265 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1554.38 | 0.726766 | ||||||||
\(167\) | 3454.82 | 1.60085 | 0.800426 | − | 0.599432i | \(-0.204607\pi\) | ||||
0.800426 | + | 0.599432i | \(0.204607\pi\) | |||||||
\(168\) | −864.649 | −0.397078 | ||||||||
\(169\) | −2005.13 | −0.912668 | ||||||||
\(170\) | 379.181 | 0.171070 | ||||||||
\(171\) | −343.348 | −0.153547 | ||||||||
\(172\) | −193.303 | −0.0856932 | ||||||||
\(173\) | 277.970 | 0.122160 | 0.0610799 | − | 0.998133i | \(-0.480546\pi\) | ||||
0.0610799 | + | 0.998133i | \(0.480546\pi\) | |||||||
\(174\) | 475.948 | 0.207365 | ||||||||
\(175\) | −335.843 | −0.145070 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2091.53 | 0.888185 | ||||||||
\(178\) | 3515.03 | 1.48013 | ||||||||
\(179\) | −3518.02 | −1.46899 | −0.734495 | − | 0.678614i | \(-0.762581\pi\) | ||||
−0.734495 | + | 0.678614i | \(0.762581\pi\) | |||||||
\(180\) | −33.5183 | −0.0138795 | ||||||||
\(181\) | 183.046 | 0.0751697 | 0.0375849 | − | 0.999293i | \(-0.488034\pi\) | ||||
0.0375849 | + | 0.999293i | \(0.488034\pi\) | |||||||
\(182\) | 550.266 | 0.224112 | ||||||||
\(183\) | −2487.56 | −1.00484 | ||||||||
\(184\) | 1341.87 | 0.537632 | ||||||||
\(185\) | 814.585 | 0.323727 | ||||||||
\(186\) | 1957.70 | 0.771750 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 15.3223 | 0.00594411 | ||||||||
\(189\) | 362.710 | 0.139594 | ||||||||
\(190\) | 564.077 | 0.215381 | ||||||||
\(191\) | 3628.53 | 1.37462 | 0.687308 | − | 0.726367i | \(-0.258792\pi\) | ||||
0.687308 | + | 0.726367i | \(0.258792\pi\) | |||||||
\(192\) | −1367.60 | −0.514051 | ||||||||
\(193\) | 3896.63 | 1.45329 | 0.726647 | − | 0.687011i | \(-0.241078\pi\) | ||||
0.726647 | + | 0.687011i | \(0.241078\pi\) | |||||||
\(194\) | 878.009 | 0.324935 | ||||||||
\(195\) | −207.774 | −0.0763027 | ||||||||
\(196\) | −121.065 | −0.0441198 | ||||||||
\(197\) | −4224.29 | −1.52776 | −0.763878 | − | 0.645361i | \(-0.776707\pi\) | ||||
−0.763878 | + | 0.645361i | \(0.776707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2242.23 | 0.798732 | 0.399366 | − | 0.916791i | \(-0.369230\pi\) | ||||
0.399366 | + | 0.916791i | \(0.369230\pi\) | |||||||
\(200\) | −536.368 | −0.189635 | ||||||||
\(201\) | −1337.93 | −0.469505 | ||||||||
\(202\) | −729.582 | −0.254125 | ||||||||
\(203\) | 720.705 | 0.249180 | ||||||||
\(204\) | 57.3049 | 0.0196674 | ||||||||
\(205\) | 89.2796 | 0.0304173 | ||||||||
\(206\) | −630.845 | −0.213364 | ||||||||
\(207\) | −562.900 | −0.189006 | ||||||||
\(208\) | 961.358 | 0.320472 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −595.886 | −0.195810 | ||||||||
\(211\) | −4156.66 | −1.35619 | −0.678096 | − | 0.734974i | \(-0.737195\pi\) | ||||
−0.678096 | + | 0.734974i | \(0.737195\pi\) | |||||||
\(212\) | 91.6823 | 0.0297017 | ||||||||
\(213\) | −2154.71 | −0.693139 | ||||||||
\(214\) | 236.092 | 0.0754155 | ||||||||
\(215\) | 1297.60 | 0.411606 | ||||||||
\(216\) | 579.277 | 0.182476 | ||||||||
\(217\) | 2964.45 | 0.927374 | ||||||||
\(218\) | −2407.73 | −0.748036 | ||||||||
\(219\) | −805.383 | −0.248506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 355.223 | 0.108122 | ||||||||
\(222\) | 1445.32 | 0.436953 | ||||||||
\(223\) | −3686.16 | −1.10692 | −0.553461 | − | 0.832875i | \(-0.686693\pi\) | ||||
−0.553461 | + | 0.832875i | \(0.686693\pi\) | |||||||
\(224\) | 451.396 | 0.134644 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 5673.64 | 1.66993 | ||||||||
\(227\) | 4852.44 | 1.41880 | 0.709400 | − | 0.704806i | \(-0.248966\pi\) | ||||
0.709400 | + | 0.704806i | \(0.248966\pi\) | |||||||
\(228\) | 85.2477 | 0.0247617 | ||||||||
\(229\) | −6525.07 | −1.88292 | −0.941460 | − | 0.337124i | \(-0.890546\pi\) | ||||
−0.941460 | + | 0.337124i | \(0.890546\pi\) | |||||||
\(230\) | 924.773 | 0.265121 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1151.02 | 0.325726 | ||||||||
\(233\) | 949.548 | 0.266983 | 0.133491 | − | 0.991050i | \(-0.457381\pi\) | ||||
0.133491 | + | 0.991050i | \(0.457381\pi\) | |||||||
\(234\) | −368.654 | −0.102990 | ||||||||
\(235\) | −102.855 | −0.0285511 | ||||||||
\(236\) | −519.291 | −0.143233 | ||||||||
\(237\) | 1104.27 | 0.302658 | ||||||||
\(238\) | 1018.76 | 0.277465 | ||||||||
\(239\) | −5268.44 | −1.42589 | −0.712943 | − | 0.701222i | \(-0.752638\pi\) | ||||
−0.712943 | + | 0.701222i | \(0.752638\pi\) | |||||||
\(240\) | −1041.06 | −0.280001 | ||||||||
\(241\) | 1128.47 | 0.301622 | 0.150811 | − | 0.988563i | \(-0.451811\pi\) | ||||
0.150811 | + | 0.988563i | \(0.451811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 617.620 | 0.162045 | ||||||||
\(245\) | 812.677 | 0.211919 | ||||||||
\(246\) | 158.409 | 0.0410560 | ||||||||
\(247\) | 528.436 | 0.136128 | ||||||||
\(248\) | 4734.47 | 1.21225 | ||||||||
\(249\) | −1576.89 | −0.401331 | ||||||||
\(250\) | −369.646 | −0.0935139 | ||||||||
\(251\) | 2186.48 | 0.549837 | 0.274919 | − | 0.961467i | \(-0.411349\pi\) | ||||
0.274919 | + | 0.961467i | \(0.411349\pi\) | |||||||
\(252\) | −90.0550 | −0.0225116 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1683.09 | −0.415774 | ||||||||
\(255\) | −384.673 | −0.0944674 | ||||||||
\(256\) | 1134.48 | 0.276973 | ||||||||
\(257\) | 338.497 | 0.0821591 | 0.0410796 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410796 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(258\) | 2302.33 | 0.555568 | ||||||||
\(259\) | 2188.58 | 0.525065 | ||||||||
\(260\) | 51.5870 | 0.0123050 | ||||||||
\(261\) | −482.841 | −0.114510 | ||||||||
\(262\) | −8073.60 | −1.90377 | ||||||||
\(263\) | −3560.56 | −0.834803 | −0.417402 | − | 0.908722i | \(-0.637059\pi\) | ||||
−0.417402 | + | 0.908722i | \(0.637059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −615.440 | −0.142665 | ||||||||
\(266\) | 1515.53 | 0.349335 | ||||||||
\(267\) | −3565.95 | −0.817349 | ||||||||
\(268\) | 332.186 | 0.0757146 | ||||||||
\(269\) | 7224.32 | 1.63745 | 0.818726 | − | 0.574184i | \(-0.194680\pi\) | ||||
0.818726 | + | 0.574184i | \(0.194680\pi\) | |||||||
\(270\) | 399.218 | 0.0899838 | ||||||||
\(271\) | −844.801 | −0.189365 | −0.0946826 | − | 0.995508i | \(-0.530184\pi\) | ||||
−0.0946826 | + | 0.995508i | \(0.530184\pi\) | |||||||
\(272\) | 1779.86 | 0.396764 | ||||||||
\(273\) | −558.236 | −0.123758 | ||||||||
\(274\) | −3528.24 | −0.777915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 139.759 | 0.0304801 | ||||||||
\(277\) | 3237.43 | 0.702231 | 0.351116 | − | 0.936332i | \(-0.385802\pi\) | ||||
0.351116 | + | 0.936332i | \(0.385802\pi\) | |||||||
\(278\) | 3745.75 | 0.808111 | ||||||||
\(279\) | −1986.05 | −0.426172 | ||||||||
\(280\) | −1441.08 | −0.307575 | ||||||||
\(281\) | −5492.06 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698109\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698109\pi\) | |||||||
\(282\) | −182.495 | −0.0385370 | ||||||||
\(283\) | −3736.57 | −0.784862 | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392431 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(284\) | 534.980 | 0.111779 | ||||||||
\(285\) | −572.247 | −0.118937 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 239.871 | 0.0493350 | ||||||||
\(288\) | −302.416 | −0.0618751 | ||||||||
\(289\) | −4255.34 | −0.866139 | ||||||||
\(290\) | 793.246 | 0.160624 | ||||||||
\(291\) | −890.725 | −0.179434 | ||||||||
\(292\) | 199.963 | 0.0400752 | ||||||||
\(293\) | 9509.23 | 1.89602 | 0.948012 | − | 0.318234i | \(-0.103090\pi\) | ||||
0.948012 | + | 0.318234i | \(0.103090\pi\) | |||||||
\(294\) | 1441.93 | 0.286039 | ||||||||
\(295\) | 3485.88 | 0.687985 | ||||||||
\(296\) | 3495.34 | 0.686359 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2512.09 | 0.488326 | ||||||||
\(299\) | 866.343 | 0.167565 | ||||||||
\(300\) | −55.8638 | −0.0107510 | ||||||||
\(301\) | 3486.31 | 0.667599 | ||||||||
\(302\) | 8537.68 | 1.62678 | ||||||||
\(303\) | 740.149 | 0.140332 | ||||||||
\(304\) | 2647.75 | 0.499535 | ||||||||
\(305\) | −4145.93 | −0.778345 | ||||||||
\(306\) | −682.527 | −0.127508 | ||||||||
\(307\) | 6485.38 | 1.20567 | 0.602834 | − | 0.797867i | \(-0.294038\pi\) | ||||
0.602834 | + | 0.797867i | \(0.294038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 639.982 | 0.117823 | ||||||||
\(310\) | 3262.83 | 0.597795 | ||||||||
\(311\) | −10727.9 | −1.95602 | −0.978008 | − | 0.208569i | \(-0.933119\pi\) | ||||
−0.978008 | + | 0.208569i | \(0.933119\pi\) | |||||||
\(312\) | −891.547 | −0.161775 | ||||||||
\(313\) | −8221.69 | −1.48472 | −0.742360 | − | 0.670001i | \(-0.766294\pi\) | ||||
−0.742360 | + | 0.670001i | \(0.766294\pi\) | |||||||
\(314\) | 2227.54 | 0.400343 | ||||||||
\(315\) | 604.517 | 0.108129 | ||||||||
\(316\) | −274.172 | −0.0488081 | ||||||||
\(317\) | 3456.12 | 0.612351 | 0.306176 | − | 0.951975i | \(-0.400951\pi\) | ||||
0.306176 | + | 0.951975i | \(0.400951\pi\) | |||||||
\(318\) | −1091.98 | −0.192563 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2279.33 | −0.398183 | ||||||||
\(321\) | −239.511 | −0.0416456 | ||||||||
\(322\) | 2484.63 | 0.430009 | ||||||||
\(323\) | 978.347 | 0.168535 | ||||||||
\(324\) | 60.3329 | 0.0103451 | ||||||||
\(325\) | −346.291 | −0.0591038 | ||||||||
\(326\) | 3737.70 | 0.635006 | ||||||||
\(327\) | 2442.60 | 0.413076 | ||||||||
\(328\) | 383.093 | 0.0644902 | ||||||||
\(329\) | −276.344 | −0.0463081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9266.82 | 1.53882 | 0.769411 | − | 0.638753i | \(-0.220550\pi\) | ||||
0.769411 | + | 0.638753i | \(0.220550\pi\) | |||||||
\(332\) | 391.516 | 0.0647207 | ||||||||
\(333\) | −1466.25 | −0.241292 | ||||||||
\(334\) | 10216.5 | 1.67372 | ||||||||
\(335\) | −2229.89 | −0.363677 | ||||||||
\(336\) | −2797.06 | −0.454143 | ||||||||
\(337\) | 7306.41 | 1.18102 | 0.590512 | − | 0.807029i | \(-0.298926\pi\) | ||||
0.590512 | + | 0.807029i | \(0.298926\pi\) | |||||||
\(338\) | −5929.52 | −0.954211 | ||||||||
\(339\) | −5755.82 | −0.922163 | ||||||||
\(340\) | 95.5081 | 0.0152343 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1015.34 | −0.160536 | ||||||||
\(343\) | 6791.22 | 1.06907 | ||||||||
\(344\) | 5567.91 | 0.872679 | ||||||||
\(345\) | −938.167 | −0.146404 | ||||||||
\(346\) | 822.003 | 0.127720 | ||||||||
\(347\) | −684.673 | −0.105923 | −0.0529614 | − | 0.998597i | \(-0.516866\pi\) | ||||
−0.0529614 | + | 0.998597i | \(0.516866\pi\) | |||||||
\(348\) | 119.882 | 0.0184665 | ||||||||
\(349\) | −3392.79 | −0.520378 | −0.260189 | − | 0.965558i | \(-0.583785\pi\) | ||||
−0.260189 | + | 0.965558i | \(0.583785\pi\) | |||||||
\(350\) | −993.144 | −0.151674 | ||||||||
\(351\) | 373.994 | 0.0568727 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10934.4 | −1.64866 | −0.824331 | − | 0.566108i | \(-0.808448\pi\) | ||||
−0.824331 | + | 0.566108i | \(0.808448\pi\) | |||||||
\(354\) | 6185.00 | 0.928612 | ||||||||
\(355\) | −3591.19 | −0.536903 | ||||||||
\(356\) | 885.366 | 0.131810 | ||||||||
\(357\) | −1033.52 | −0.153220 | ||||||||
\(358\) | −10403.4 | −1.53585 | ||||||||
\(359\) | 2575.42 | 0.378622 | 0.189311 | − | 0.981917i | \(-0.439375\pi\) | ||||
0.189311 | + | 0.981917i | \(0.439375\pi\) | |||||||
\(360\) | 965.462 | 0.141345 | ||||||||
\(361\) | −5403.59 | −0.787811 | ||||||||
\(362\) | 541.299 | 0.0785912 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 138.601 | 0.0199578 | ||||||||
\(365\) | −1342.30 | −0.192492 | ||||||||
\(366\) | −7356.13 | −1.05058 | ||||||||
\(367\) | −1398.59 | −0.198925 | −0.0994626 | − | 0.995041i | \(-0.531712\pi\) | ||||
−0.0994626 | + | 0.995041i | \(0.531712\pi\) | |||||||
\(368\) | 4340.84 | 0.614896 | ||||||||
\(369\) | −160.703 | −0.0226717 | ||||||||
\(370\) | 2408.87 | 0.338462 | ||||||||
\(371\) | −1653.53 | −0.231393 | ||||||||
\(372\) | 493.105 | 0.0687266 | ||||||||
\(373\) | 623.943 | 0.0866127 | 0.0433063 | − | 0.999062i | \(-0.486211\pi\) | ||||
0.0433063 | + | 0.999062i | \(0.486211\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | −441.344 | −0.0605334 | ||||||||
\(377\) | 743.126 | 0.101520 | ||||||||
\(378\) | 1072.60 | 0.145948 | ||||||||
\(379\) | −5504.16 | −0.745988 | −0.372994 | − | 0.927834i | \(-0.621669\pi\) | ||||
−0.372994 | + | 0.927834i | \(0.621669\pi\) | |||||||
\(380\) | 142.079 | 0.0191803 | ||||||||
\(381\) | 1707.47 | 0.229597 | ||||||||
\(382\) | 10730.2 | 1.43718 | ||||||||
\(383\) | −7440.83 | −0.992711 | −0.496356 | − | 0.868119i | \(-0.665329\pi\) | ||||
−0.496356 | + | 0.868119i | \(0.665329\pi\) | |||||||
\(384\) | −4850.66 | −0.644620 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11523.0 | 1.51944 | ||||||||
\(387\) | −2335.67 | −0.306793 | ||||||||
\(388\) | 221.153 | 0.0289364 | ||||||||
\(389\) | 6043.79 | 0.787744 | 0.393872 | − | 0.919165i | \(-0.371135\pi\) | ||||
0.393872 | + | 0.919165i | \(0.371135\pi\) | |||||||
\(390\) | −614.424 | −0.0797758 | ||||||||
\(391\) | 1603.95 | 0.207455 | ||||||||
\(392\) | 3487.15 | 0.449305 | ||||||||
\(393\) | 8190.53 | 1.05129 | ||||||||
\(394\) | −12491.9 | −1.59730 | ||||||||
\(395\) | 1840.45 | 0.234438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5697.21 | −0.720239 | −0.360119 | − | 0.932906i | \(-0.617264\pi\) | ||||
−0.360119 | + | 0.932906i | \(0.617264\pi\) | |||||||
\(398\) | 6630.67 | 0.835089 | ||||||||
\(399\) | −1537.48 | −0.192908 | ||||||||
\(400\) | −1735.10 | −0.216888 | ||||||||
\(401\) | 15823.4 | 1.97053 | 0.985266 | − | 0.171027i | \(-0.0547086\pi\) | ||||
0.985266 | + | 0.171027i | \(0.0547086\pi\) | |||||||
\(402\) | −3956.49 | −0.490875 | ||||||||
\(403\) | 3056.67 | 0.377826 | ||||||||
\(404\) | −183.767 | −0.0226306 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 2131.25 | 0.260522 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1650.61 | −0.200288 | ||||||||
\(409\) | −3371.10 | −0.407555 | −0.203778 | − | 0.979017i | \(-0.565322\pi\) | ||||
−0.203778 | + | 0.979017i | \(0.565322\pi\) | |||||||
\(410\) | 264.015 | 0.0318019 | ||||||||
\(411\) | 3579.34 | 0.429576 | ||||||||
\(412\) | −158.897 | −0.0190007 | ||||||||
\(413\) | 9365.65 | 1.11587 | ||||||||
\(414\) | −1664.59 | −0.197609 | ||||||||
\(415\) | −2628.15 | −0.310870 | ||||||||
\(416\) | 465.439 | 0.0548558 | ||||||||
\(417\) | −3800.00 | −0.446251 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −713.843 | −0.0832304 | −0.0416152 | − | 0.999134i | \(-0.513250\pi\) | ||||
−0.0416152 | + | 0.999134i | \(0.513250\pi\) | |||||||
\(420\) | −150.092 | −0.0174374 | ||||||||
\(421\) | −1067.26 | −0.123551 | −0.0617754 | − | 0.998090i | \(-0.519676\pi\) | ||||
−0.0617754 | + | 0.998090i | \(0.519676\pi\) | |||||||
\(422\) | −12292.0 | −1.41792 | ||||||||
\(423\) | 185.139 | 0.0212807 | ||||||||
\(424\) | −2640.82 | −0.302475 | ||||||||
\(425\) | −641.122 | −0.0731741 | ||||||||
\(426\) | −6371.85 | −0.724689 | ||||||||
\(427\) | −11139.0 | −1.26243 | ||||||||
\(428\) | 59.4668 | 0.00671597 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3837.21 | 0.430342 | ||||||||
\(431\) | 4779.89 | 0.534197 | 0.267099 | − | 0.963669i | \(-0.413935\pi\) | ||||
0.267099 | + | 0.963669i | \(0.413935\pi\) | |||||||
\(432\) | 1873.91 | 0.208700 | ||||||||
\(433\) | 9747.37 | 1.08182 | 0.540911 | − | 0.841080i | \(-0.318080\pi\) | ||||
0.540911 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(434\) | 8766.39 | 0.969585 | ||||||||
\(435\) | −804.735 | −0.0886991 | ||||||||
\(436\) | −606.457 | −0.0666147 | ||||||||
\(437\) | 2386.06 | 0.261191 | ||||||||
\(438\) | −2381.65 | −0.259817 | ||||||||
\(439\) | 16880.1 | 1.83517 | 0.917587 | − | 0.397536i | \(-0.130134\pi\) | ||||
0.917587 | + | 0.397536i | \(0.130134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1462.82 | −0.157955 | ||||||||
\(442\) | 1050.46 | 0.113043 | ||||||||
\(443\) | −3952.86 | −0.423941 | −0.211971 | − | 0.977276i | \(-0.567988\pi\) | ||||
−0.211971 | + | 0.977276i | \(0.567988\pi\) | |||||||
\(444\) | 364.047 | 0.0389119 | ||||||||
\(445\) | −5943.24 | −0.633116 | ||||||||
\(446\) | −10900.6 | −1.15731 | ||||||||
\(447\) | −2548.47 | −0.269661 | ||||||||
\(448\) | −6123.97 | −0.645827 | ||||||||
\(449\) | −2612.11 | −0.274550 | −0.137275 | − | 0.990533i | \(-0.543834\pi\) | ||||
−0.137275 | + | 0.990533i | \(0.543834\pi\) | |||||||
\(450\) | 665.363 | 0.0697012 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1429.08 | 0.148713 | ||||||||
\(453\) | −8661.33 | −0.898333 | ||||||||
\(454\) | 14349.5 | 1.48338 | ||||||||
\(455\) | −930.393 | −0.0958626 | ||||||||
\(456\) | −2455.48 | −0.252167 | ||||||||
\(457\) | 8039.48 | 0.822913 | 0.411456 | − | 0.911429i | \(-0.365020\pi\) | ||||
0.411456 | + | 0.911429i | \(0.365020\pi\) | |||||||
\(458\) | −19295.7 | −1.96863 | ||||||||
\(459\) | 692.412 | 0.0704118 | ||||||||
\(460\) | 232.932 | 0.0236098 | ||||||||
\(461\) | −2749.59 | −0.277790 | −0.138895 | − | 0.990307i | \(-0.544355\pi\) | ||||
−0.138895 | + | 0.990307i | \(0.544355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17487.3 | −1.75530 | −0.877650 | − | 0.479303i | \(-0.840890\pi\) | ||||
−0.877650 | + | 0.479303i | \(0.840890\pi\) | |||||||
\(464\) | 3723.46 | 0.372537 | ||||||||
\(465\) | −3310.09 | −0.330111 | ||||||||
\(466\) | 2807.98 | 0.279135 | ||||||||
\(467\) | 4642.11 | 0.459982 | 0.229991 | − | 0.973193i | \(-0.426130\pi\) | ||||
0.229991 | + | 0.973193i | \(0.426130\pi\) | |||||||
\(468\) | −92.8565 | −0.00917157 | ||||||||
\(469\) | −5991.13 | −0.589861 | ||||||||
\(470\) | −304.159 | −0.0298507 | ||||||||
\(471\) | −2259.81 | −0.221075 | ||||||||
\(472\) | 14957.7 | 1.45865 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3265.51 | 0.316434 | ||||||||
\(475\) | −953.745 | −0.0921280 | ||||||||
\(476\) | 256.606 | 0.0247090 | ||||||||
\(477\) | 1107.79 | 0.106336 | ||||||||
\(478\) | −15579.7 | −1.49079 | ||||||||
\(479\) | −8868.05 | −0.845911 | −0.422956 | − | 0.906150i | \(-0.639007\pi\) | ||||
−0.422956 | + | 0.906150i | \(0.639007\pi\) | |||||||
\(480\) | −504.026 | −0.0479282 | ||||||||
\(481\) | 2256.67 | 0.213919 | ||||||||
\(482\) | 3337.07 | 0.315351 | ||||||||
\(483\) | −2520.61 | −0.237457 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1484.54 | −0.138989 | ||||||||
\(486\) | −718.592 | −0.0670700 | ||||||||
\(487\) | −1960.53 | −0.182423 | −0.0912117 | − | 0.995832i | \(-0.529074\pi\) | ||||
−0.0912117 | + | 0.995832i | \(0.529074\pi\) | |||||||
\(488\) | −17789.9 | −1.65023 | ||||||||
\(489\) | −3791.84 | −0.350660 | ||||||||
\(490\) | 2403.22 | 0.221565 | ||||||||
\(491\) | 13106.9 | 1.20470 | 0.602348 | − | 0.798234i | \(-0.294232\pi\) | ||||
0.602348 | + | 0.798234i | \(0.294232\pi\) | |||||||
\(492\) | 39.9000 | 0.00365616 | ||||||||
\(493\) | 1375.82 | 0.125688 | ||||||||
\(494\) | 1562.68 | 0.142324 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15315.6 | 1.38647 | ||||||||
\(497\) | −9648.60 | −0.870823 | ||||||||
\(498\) | −4663.14 | −0.419599 | ||||||||
\(499\) | −8815.60 | −0.790863 | −0.395431 | − | 0.918496i | \(-0.629405\pi\) | ||||
−0.395431 | + | 0.918496i | \(0.629405\pi\) | |||||||
\(500\) | −93.1063 | −0.00832768 | ||||||||
\(501\) | −10364.5 | −0.924252 | ||||||||
\(502\) | 6465.78 | 0.574864 | ||||||||
\(503\) | −14750.9 | −1.30757 | −0.653787 | − | 0.756679i | \(-0.726821\pi\) | ||||
−0.653787 | + | 0.756679i | \(0.726821\pi\) | |||||||
\(504\) | 2593.95 | 0.229253 | ||||||||
\(505\) | 1233.58 | 0.108700 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6015.40 | 0.526929 | ||||||||
\(508\) | −423.937 | −0.0370259 | ||||||||
\(509\) | 6003.97 | 0.522832 | 0.261416 | − | 0.965226i | \(-0.415811\pi\) | ||||
0.261416 | + | 0.965226i | \(0.415811\pi\) | |||||||
\(510\) | −1137.54 | −0.0987673 | ||||||||
\(511\) | −3606.43 | −0.312209 | ||||||||
\(512\) | −9580.24 | −0.826935 | ||||||||
\(513\) | 1030.04 | 0.0886502 | ||||||||
\(514\) | 1000.99 | 0.0858988 | ||||||||
\(515\) | 1066.64 | 0.0912653 | ||||||||
\(516\) | 579.909 | 0.0494750 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6472.00 | 0.548964 | ||||||||
\(519\) | −833.909 | −0.0705289 | ||||||||
\(520\) | −1485.91 | −0.125311 | ||||||||
\(521\) | −6769.02 | −0.569206 | −0.284603 | − | 0.958645i | \(-0.591862\pi\) | ||||
−0.284603 | + | 0.958645i | \(0.591862\pi\) | |||||||
\(522\) | −1427.84 | −0.119722 | ||||||||
\(523\) | 18106.8 | 1.51387 | 0.756937 | − | 0.653488i | \(-0.226695\pi\) | ||||
0.756937 | + | 0.653488i | \(0.226695\pi\) | |||||||
\(524\) | −2033.57 | −0.169536 | ||||||||
\(525\) | 1007.53 | 0.0837564 | ||||||||
\(526\) | −10529.2 | −0.872801 | ||||||||
\(527\) | 5659.13 | 0.467771 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8255.19 | −0.678490 | ||||||||
\(530\) | −1819.96 | −0.149159 | ||||||||
\(531\) | −6274.58 | −0.512794 | ||||||||
\(532\) | 381.731 | 0.0311093 | ||||||||
\(533\) | 247.333 | 0.0200998 | ||||||||
\(534\) | −10545.1 | −0.854553 | ||||||||
\(535\) | −399.186 | −0.0322585 | ||||||||
\(536\) | −9568.31 | −0.771060 | ||||||||
\(537\) | 10554.1 | 0.848122 | ||||||||
\(538\) | 21363.6 | 1.71199 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 100.555 | 0.00801332 | ||||||||
\(541\) | −14549.7 | −1.15627 | −0.578134 | − | 0.815941i | \(-0.696219\pi\) | ||||
−0.578134 | + | 0.815941i | \(0.696219\pi\) | |||||||
\(542\) | −2498.22 | −0.197985 | ||||||||
\(543\) | −549.139 | −0.0433992 | ||||||||
\(544\) | 861.713 | 0.0679148 | ||||||||
\(545\) | 4071.00 | 0.319968 | ||||||||
\(546\) | −1650.80 | −0.129391 | ||||||||
\(547\) | 7927.94 | 0.619697 | 0.309849 | − | 0.950786i | \(-0.399722\pi\) | ||||
0.309849 | + | 0.950786i | \(0.399722\pi\) | |||||||
\(548\) | −888.691 | −0.0692756 | ||||||||
\(549\) | 7462.67 | 0.580144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2046.70 | 0.158244 | ||||||||
\(552\) | −4025.62 | −0.310402 | ||||||||
\(553\) | 4944.81 | 0.380244 | ||||||||
\(554\) | 9573.62 | 0.734195 | ||||||||
\(555\) | −2443.76 | −0.186904 | ||||||||
\(556\) | 943.477 | 0.0719647 | ||||||||
\(557\) | 12856.6 | 0.978013 | 0.489006 | − | 0.872280i | \(-0.337360\pi\) | ||||
0.489006 | + | 0.872280i | \(0.337360\pi\) | |||||||
\(558\) | −5873.10 | −0.445570 | ||||||||
\(559\) | 3594.76 | 0.271990 | ||||||||
\(560\) | −4661.77 | −0.351778 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16241.0 | −1.21901 | ||||||||
\(563\) | 9751.32 | 0.729963 | 0.364981 | − | 0.931015i | \(-0.381075\pi\) | ||||
0.364981 | + | 0.931015i | \(0.381075\pi\) | |||||||
\(564\) | −45.9669 | −0.00343183 | ||||||||
\(565\) | −9593.03 | −0.714304 | ||||||||
\(566\) | −11049.7 | −0.820587 | ||||||||
\(567\) | −1088.13 | −0.0805947 | ||||||||
\(568\) | −15409.6 | −1.13833 | ||||||||
\(569\) | 3962.75 | 0.291963 | 0.145982 | − | 0.989287i | \(-0.453366\pi\) | ||||
0.145982 | + | 0.989287i | \(0.453366\pi\) | |||||||
\(570\) | −1692.23 | −0.124350 | ||||||||
\(571\) | −19004.4 | −1.39283 | −0.696416 | − | 0.717638i | \(-0.745223\pi\) | ||||
−0.696416 | + | 0.717638i | \(0.745223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10885.6 | −0.793634 | ||||||||
\(574\) | 709.340 | 0.0515806 | ||||||||
\(575\) | −1563.61 | −0.113404 | ||||||||
\(576\) | 4102.79 | 0.296788 | ||||||||
\(577\) | 10410.7 | 0.751134 | 0.375567 | − | 0.926795i | \(-0.377448\pi\) | ||||
0.375567 | + | 0.926795i | \(0.377448\pi\) | |||||||
\(578\) | −12583.8 | −0.905563 | ||||||||
\(579\) | −11689.9 | −0.839060 | ||||||||
\(580\) | 199.803 | 0.0143041 | ||||||||
\(581\) | −7061.17 | −0.504211 | ||||||||
\(582\) | −2634.03 | −0.187601 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5759.75 | −0.408117 | ||||||||
\(585\) | 623.323 | 0.0440534 | ||||||||
\(586\) | 28120.4 | 1.98233 | ||||||||
\(587\) | −1636.78 | −0.115089 | −0.0575445 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575445 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(588\) | 363.194 | 0.0254726 | ||||||||
\(589\) | 8418.61 | 0.588935 | ||||||||
\(590\) | 10308.3 | 0.719300 | ||||||||
\(591\) | 12672.9 | 0.882050 | ||||||||
\(592\) | 11307.1 | 0.784998 | ||||||||
\(593\) | −11586.5 | −0.802361 | −0.401181 | − | 0.915999i | \(-0.631400\pi\) | ||||
−0.401181 | + | 0.915999i | \(0.631400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1722.53 | −0.118684 | ||||||||
\(596\) | 632.743 | 0.0434869 | ||||||||
\(597\) | −6726.70 | −0.461148 | ||||||||
\(598\) | 2561.92 | 0.175192 | ||||||||
\(599\) | 7828.53 | 0.533998 | 0.266999 | − | 0.963697i | \(-0.413968\pi\) | ||||
0.266999 | + | 0.963697i | \(0.413968\pi\) | |||||||
\(600\) | 1609.10 | 0.109486 | ||||||||
\(601\) | 15473.7 | 1.05023 | 0.525113 | − | 0.851032i | \(-0.324023\pi\) | ||||
0.525113 | + | 0.851032i | \(0.324023\pi\) | |||||||
\(602\) | 10309.6 | 0.697987 | ||||||||
\(603\) | 4013.80 | 0.271069 | ||||||||
\(604\) | 2150.47 | 0.144870 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2188.75 | 0.146719 | ||||||||
\(607\) | −20781.3 | −1.38960 | −0.694799 | − | 0.719204i | \(-0.744507\pi\) | ||||
−0.694799 | + | 0.719204i | \(0.744507\pi\) | |||||||
\(608\) | 1281.90 | 0.0855064 | ||||||||
\(609\) | −2162.12 | −0.143864 | ||||||||
\(610\) | −12260.2 | −0.813773 | ||||||||
\(611\) | −284.941 | −0.0188666 | ||||||||
\(612\) | −171.915 | −0.0113550 | ||||||||
\(613\) | −15758.2 | −1.03829 | −0.519143 | − | 0.854688i | \(-0.673749\pi\) | ||||
−0.519143 | + | 0.854688i | \(0.673749\pi\) | |||||||
\(614\) | 19178.4 | 1.26055 | ||||||||
\(615\) | −267.839 | −0.0175615 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14137.0 | −0.922421 | −0.461211 | − | 0.887291i | \(-0.652585\pi\) | ||||
−0.461211 | + | 0.887291i | \(0.652585\pi\) | |||||||
\(618\) | 1892.53 | 0.123186 | ||||||||
\(619\) | −22204.7 | −1.44181 | −0.720907 | − | 0.693032i | \(-0.756275\pi\) | ||||
−0.720907 | + | 0.693032i | \(0.756275\pi\) | |||||||
\(620\) | 821.841 | 0.0532354 | ||||||||
\(621\) | 1688.70 | 0.109123 | ||||||||
\(622\) | −31724.1 | −2.04505 | ||||||||
\(623\) | −15968.0 | −1.02687 | ||||||||
\(624\) | −2884.07 | −0.185025 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −24312.9 | −1.55230 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 561.073 | 0.0356517 | ||||||||
\(629\) | 4177.99 | 0.264845 | ||||||||
\(630\) | 1787.66 | 0.113051 | ||||||||
\(631\) | 14169.5 | 0.893947 | 0.446973 | − | 0.894547i | \(-0.352502\pi\) | ||||
0.446973 | + | 0.894547i | \(0.352502\pi\) | |||||||
\(632\) | 7897.26 | 0.497051 | ||||||||
\(633\) | 12470.0 | 0.782998 | ||||||||
\(634\) | 10220.3 | 0.640224 | ||||||||
\(635\) | 2845.78 | 0.177845 | ||||||||
\(636\) | −275.047 | −0.0171483 | ||||||||
\(637\) | 2251.38 | 0.140036 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6464.14 | 0.400184 | ||||||||
\(640\) | −8084.43 | −0.499321 | ||||||||
\(641\) | 4233.79 | 0.260881 | 0.130440 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130440 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(642\) | −708.276 | −0.0435412 | ||||||||
\(643\) | −20028.5 | −1.22838 | −0.614189 | − | 0.789159i | \(-0.710517\pi\) | ||||
−0.614189 | + | 0.789159i | \(0.710517\pi\) | |||||||
\(644\) | 625.827 | 0.0382935 | ||||||||
\(645\) | −3892.79 | −0.237641 | ||||||||
\(646\) | 2893.14 | 0.176206 | ||||||||
\(647\) | 22677.1 | 1.37794 | 0.688971 | − | 0.724789i | \(-0.258063\pi\) | ||||
0.688971 | + | 0.724789i | \(0.258063\pi\) | |||||||
\(648\) | −1737.83 | −0.105353 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1024.04 | −0.0617941 | ||||||||
\(651\) | −8893.36 | −0.535419 | ||||||||
\(652\) | 941.451 | 0.0565492 | ||||||||
\(653\) | −24678.8 | −1.47895 | −0.739476 | − | 0.673183i | \(-0.764926\pi\) | ||||
−0.739476 | + | 0.673183i | \(0.764926\pi\) | |||||||
\(654\) | 7223.18 | 0.431879 | ||||||||
\(655\) | 13650.9 | 0.814327 | ||||||||
\(656\) | 1239.27 | 0.0737583 | ||||||||
\(657\) | 2416.15 | 0.143475 | ||||||||
\(658\) | −817.197 | −0.0484159 | ||||||||
\(659\) | −9281.04 | −0.548616 | −0.274308 | − | 0.961642i | \(-0.588449\pi\) | ||||
−0.274308 | + | 0.961642i | \(0.588449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13001.3 | 0.765040 | 0.382520 | − | 0.923947i | \(-0.375056\pi\) | ||||
0.382520 | + | 0.923947i | \(0.375056\pi\) | |||||||
\(662\) | 27403.6 | 1.60887 | ||||||||
\(663\) | −1065.67 | −0.0624241 | ||||||||
\(664\) | −11277.3 | −0.659100 | ||||||||
\(665\) | −2562.47 | −0.149426 | ||||||||
\(666\) | −4335.96 | −0.252275 | ||||||||
\(667\) | 3355.45 | 0.194788 | ||||||||
\(668\) | 2573.33 | 0.149049 | ||||||||
\(669\) | 11058.5 | 0.639082 | ||||||||
\(670\) | −6594.15 | −0.380230 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1354.19 | −0.0777365 | ||||||||
\(673\) | 5807.93 | 0.332659 | 0.166329 | − | 0.986070i | \(-0.446809\pi\) | ||||
0.166329 | + | 0.986070i | \(0.446809\pi\) | |||||||
\(674\) | 21606.3 | 1.23478 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −1493.52 | −0.0849752 | ||||||||
\(677\) | −2910.87 | −0.165249 | −0.0826245 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826245 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(678\) | −17020.9 | −0.964137 | ||||||||
\(679\) | −3988.58 | −0.225431 | ||||||||
\(680\) | −2751.02 | −0.155142 | ||||||||
\(681\) | −14557.3 | −0.819144 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21234.7 | −1.18964 | −0.594819 | − | 0.803860i | \(-0.702776\pi\) | ||||
−0.594819 | + | 0.803860i | \(0.702776\pi\) | |||||||
\(684\) | −255.743 | −0.0142962 | ||||||||
\(685\) | 5965.57 | 0.332748 | ||||||||
\(686\) | 20082.8 | 1.11773 | ||||||||
\(687\) | 19575.2 | 1.08710 | ||||||||
\(688\) | 18011.7 | 0.998094 | ||||||||
\(689\) | −1704.97 | −0.0942731 | ||||||||
\(690\) | −2774.32 | −0.153067 | ||||||||
\(691\) | 16554.8 | 0.911398 | 0.455699 | − | 0.890134i | \(-0.349389\pi\) | ||||
0.455699 | + | 0.890134i | \(0.349389\pi\) | |||||||
\(692\) | 207.046 | 0.0113738 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2024.70 | −0.110744 | ||||||||
\(695\) | −6333.33 | −0.345665 | ||||||||
\(696\) | −3453.07 | −0.188058 | ||||||||
\(697\) | 457.913 | 0.0248848 | ||||||||
\(698\) | −10033.1 | −0.544065 | ||||||||
\(699\) | −2848.64 | −0.154143 | ||||||||
\(700\) | −250.153 | −0.0135070 | ||||||||
\(701\) | 11287.6 | 0.608172 | 0.304086 | − | 0.952645i | \(-0.401649\pi\) | ||||
0.304086 | + | 0.952645i | \(0.401649\pi\) | |||||||
\(702\) | 1105.96 | 0.0594614 | ||||||||
\(703\) | 6215.25 | 0.333446 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 308.564 | 0.0164840 | ||||||||
\(706\) | −32334.8 | −1.72370 | ||||||||
\(707\) | 3314.32 | 0.176305 | ||||||||
\(708\) | 1557.87 | 0.0826956 | ||||||||
\(709\) | −5742.74 | −0.304193 | −0.152097 | − | 0.988366i | \(-0.548603\pi\) | ||||
−0.152097 | + | 0.988366i | \(0.548603\pi\) | |||||||
\(710\) | −10619.8 | −0.561341 | ||||||||
\(711\) | −3312.81 | −0.174740 | ||||||||
\(712\) | −25502.1 | −1.34232 | ||||||||
\(713\) | 13801.9 | 0.724942 | ||||||||
\(714\) | −3056.29 | −0.160194 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2620.40 | −0.136772 | ||||||||
\(717\) | 15805.3 | 0.823236 | ||||||||
\(718\) | 7615.95 | 0.395856 | ||||||||
\(719\) | 13803.5 | 0.715971 | 0.357986 | − | 0.933727i | \(-0.383464\pi\) | ||||
0.357986 | + | 0.933727i | \(0.383464\pi\) | |||||||
\(720\) | 3123.18 | 0.161658 | ||||||||
\(721\) | 2865.78 | 0.148026 | ||||||||
\(722\) | −15979.3 | −0.823670 | ||||||||
\(723\) | −3385.40 | −0.174142 | ||||||||
\(724\) | 136.342 | 0.00699878 | ||||||||
\(725\) | −1341.23 | −0.0687060 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28815.2 | 1.47001 | 0.735005 | − | 0.678062i | \(-0.237180\pi\) | ||||
0.735005 | + | 0.678062i | \(0.237180\pi\) | |||||||
\(728\) | −3992.26 | −0.203246 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3969.42 | −0.201253 | ||||||||
\(731\) | 6655.35 | 0.336740 | ||||||||
\(732\) | −1852.86 | −0.0935569 | ||||||||
\(733\) | −7588.75 | −0.382397 | −0.191198 | − | 0.981551i | \(-0.561237\pi\) | ||||
−0.191198 | + | 0.981551i | \(0.561237\pi\) | |||||||
\(734\) | −4135.85 | −0.207980 | ||||||||
\(735\) | −2438.03 | −0.122351 | ||||||||
\(736\) | 2101.60 | 0.105253 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −475.227 | −0.0237037 | ||||||||
\(739\) | 10493.0 | 0.522316 | 0.261158 | − | 0.965296i | \(-0.415896\pi\) | ||||
0.261158 | + | 0.965296i | \(0.415896\pi\) | |||||||
\(740\) | 606.745 | 0.0301410 | ||||||||
\(741\) | −1585.31 | −0.0785935 | ||||||||
\(742\) | −4889.77 | −0.241926 | ||||||||
\(743\) | −6109.24 | −0.301650 | −0.150825 | − | 0.988560i | \(-0.548193\pi\) | ||||
−0.150825 | + | 0.988560i | \(0.548193\pi\) | |||||||
\(744\) | −14203.4 | −0.699895 | ||||||||
\(745\) | −4247.45 | −0.208879 | ||||||||
\(746\) | 1845.10 | 0.0905551 | ||||||||
\(747\) | 4730.68 | 0.231709 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1072.51 | −0.0523213 | ||||||||
\(750\) | 1108.94 | 0.0539903 | ||||||||
\(751\) | 10119.0 | 0.491673 | 0.245837 | − | 0.969311i | \(-0.420937\pi\) | ||||
0.245837 | + | 0.969311i | \(0.420937\pi\) | |||||||
\(752\) | −1427.71 | −0.0692329 | ||||||||
\(753\) | −6559.43 | −0.317449 | ||||||||
\(754\) | 2197.55 | 0.106141 | ||||||||
\(755\) | −14435.6 | −0.695846 | ||||||||
\(756\) | 270.165 | 0.0129971 | ||||||||
\(757\) | 19631.9 | 0.942579 | 0.471290 | − | 0.881978i | \(-0.343789\pi\) | ||||
0.471290 | + | 0.881978i | \(0.343789\pi\) | |||||||
\(758\) | −16276.7 | −0.779944 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4092.46 | −0.195328 | ||||||||
\(761\) | −37652.9 | −1.79358 | −0.896791 | − | 0.442454i | \(-0.854108\pi\) | ||||
−0.896791 | + | 0.442454i | \(0.854108\pi\) | |||||||
\(762\) | 5049.28 | 0.240047 | ||||||||
\(763\) | 10937.7 | 0.518967 | ||||||||
\(764\) | 2702.72 | 0.127985 | ||||||||
\(765\) | 1154.02 | 0.0545408 | ||||||||
\(766\) | −22003.8 | −1.03790 | ||||||||
\(767\) | 9657.01 | 0.454621 | ||||||||
\(768\) | −3403.44 | −0.159910 | ||||||||
\(769\) | 8180.02 | 0.383588 | 0.191794 | − | 0.981435i | \(-0.438569\pi\) | ||||
0.191794 | + | 0.981435i | \(0.438569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1015.49 | −0.0474346 | ||||||||
\(772\) | 2902.41 | 0.135311 | ||||||||
\(773\) | −1141.76 | −0.0531258 | −0.0265629 | − | 0.999647i | \(-0.508456\pi\) | ||||
−0.0265629 | + | 0.999647i | \(0.508456\pi\) | |||||||
\(774\) | −6906.98 | −0.320758 | ||||||||
\(775\) | −5516.82 | −0.255703 | ||||||||
\(776\) | −6370.08 | −0.294681 | ||||||||
\(777\) | −6565.74 | −0.303146 | ||||||||
\(778\) | 17872.5 | 0.823600 | ||||||||
\(779\) | 681.199 | 0.0313305 | ||||||||
\(780\) | −154.761 | −0.00710427 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4743.14 | 0.216898 | ||||||||
\(783\) | 1448.52 | 0.0661124 | ||||||||
\(784\) | 11280.6 | 0.513876 | ||||||||
\(785\) | −3766.34 | −0.171244 | ||||||||
\(786\) | 24220.8 | 1.09914 | ||||||||
\(787\) | 39228.0 | 1.77678 | 0.888390 | − | 0.459089i | \(-0.151824\pi\) | ||||
0.888390 | + | 0.459089i | \(0.151824\pi\) | |||||||
\(788\) | −3146.46 | −0.142244 | ||||||||
\(789\) | 10681.7 | 0.481974 | ||||||||
\(790\) | 5442.52 | 0.245109 | ||||||||
\(791\) | −25774.0 | −1.15856 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11485.6 | −0.514331 | ||||||||
\(794\) | −16847.6 | −0.753022 | ||||||||
\(795\) | 1846.32 | 0.0823676 | ||||||||
\(796\) | 1670.13 | 0.0743671 | ||||||||
\(797\) | 24547.6 | 1.09099 | 0.545495 | − | 0.838114i | \(-0.316342\pi\) | ||||
0.545495 | + | 0.838114i | \(0.316342\pi\) | |||||||
\(798\) | −4546.59 | −0.201689 | ||||||||
\(799\) | −527.540 | −0.0233580 | ||||||||
\(800\) | −840.044 | −0.0371250 | ||||||||
\(801\) | 10697.8 | 0.471897 | ||||||||
\(802\) | 46792.5 | 2.06023 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −996.559 | −0.0437139 | ||||||||
\(805\) | −4201.02 | −0.183934 | ||||||||
\(806\) | 9039.10 | 0.395023 | ||||||||
\(807\) | −21673.0 | −0.945384 | ||||||||
\(808\) | 5293.23 | 0.230464 | ||||||||
\(809\) | 699.945 | 0.0304187 | 0.0152094 | − | 0.999884i | \(-0.495159\pi\) | ||||
0.0152094 | + | 0.999884i | \(0.495159\pi\) | |||||||
\(810\) | −1197.65 | −0.0519522 | ||||||||
\(811\) | 33739.5 | 1.46086 | 0.730428 | − | 0.682990i | \(-0.239321\pi\) | ||||
0.730428 | + | 0.682990i | \(0.239321\pi\) | |||||||
\(812\) | 536.818 | 0.0232003 | ||||||||
\(813\) | 2534.40 | 0.109330 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6319.73 | −0.271620 | ||||||||
\(816\) | −5339.58 | −0.229072 | ||||||||
\(817\) | 9900.61 | 0.423964 | ||||||||
\(818\) | −9968.91 | −0.426106 | ||||||||
\(819\) | 1674.71 | 0.0714518 | ||||||||
\(820\) | 66.4999 | 0.00283205 | ||||||||
\(821\) | −32297.4 | −1.37294 | −0.686472 | − | 0.727156i | \(-0.740842\pi\) | ||||
−0.686472 | + | 0.727156i | \(0.740842\pi\) | |||||||
\(822\) | 10584.7 | 0.449129 | ||||||||
\(823\) | −10124.4 | −0.428817 | −0.214408 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214408 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(824\) | 4576.87 | 0.193499 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27695.8 | 1.16666 | ||||||||
\(827\) | 6914.26 | 0.290728 | 0.145364 | − | 0.989378i | \(-0.453565\pi\) | ||||
0.145364 | + | 0.989378i | \(0.453565\pi\) | |||||||
\(828\) | −419.277 | −0.0175977 | ||||||||
\(829\) | −2321.74 | −0.0972707 | −0.0486354 | − | 0.998817i | \(-0.515487\pi\) | ||||
−0.0486354 | + | 0.998817i | \(0.515487\pi\) | |||||||
\(830\) | −7771.90 | −0.325020 | ||||||||
\(831\) | −9712.28 | −0.405433 | ||||||||
\(832\) | −6314.48 | −0.263119 | ||||||||
\(833\) | 4168.21 | 0.173373 | ||||||||
\(834\) | −11237.2 | −0.466563 | ||||||||
\(835\) | −17274.1 | −0.715923 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5958.16 | 0.246050 | ||||||||
\(838\) | −2110.96 | −0.0870188 | ||||||||
\(839\) | −30540.6 | −1.25671 | −0.628354 | − | 0.777927i | \(-0.716271\pi\) | ||||
−0.628354 | + | 0.777927i | \(0.716271\pi\) | |||||||
\(840\) | 4323.24 | 0.177579 | ||||||||
\(841\) | −21510.8 | −0.881987 | ||||||||
\(842\) | −3156.06 | −0.129175 | ||||||||
\(843\) | 16476.2 | 0.673155 | ||||||||
\(844\) | −3096.09 | −0.126270 | ||||||||
\(845\) | 10025.7 | 0.408158 | ||||||||
\(846\) | 547.486 | 0.0222494 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8542.81 | −0.345945 | ||||||||
\(849\) | 11209.7 | 0.453140 | ||||||||
\(850\) | −1895.91 | −0.0765048 | ||||||||
\(851\) | 10189.6 | 0.410451 | ||||||||
\(852\) | −1604.94 | −0.0645356 | ||||||||
\(853\) | 16368.5 | 0.657029 | 0.328515 | − | 0.944499i | \(-0.393452\pi\) | ||||
0.328515 | + | 0.944499i | \(0.393452\pi\) | |||||||
\(854\) | −32940.0 | −1.31989 | ||||||||
\(855\) | 1716.74 | 0.0686682 | ||||||||
\(856\) | −1712.88 | −0.0683938 | ||||||||
\(857\) | 29094.5 | 1.15969 | 0.579843 | − | 0.814728i | \(-0.303114\pi\) | ||||
0.579843 | + | 0.814728i | \(0.303114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34464.5 | −1.36893 | −0.684467 | − | 0.729044i | \(-0.739965\pi\) | ||||
−0.684467 | + | 0.729044i | \(0.739965\pi\) | |||||||
\(860\) | 966.516 | 0.0383232 | ||||||||
\(861\) | −719.613 | −0.0284836 | ||||||||
\(862\) | 14134.9 | 0.558513 | ||||||||
\(863\) | −34844.9 | −1.37443 | −0.687215 | − | 0.726454i | \(-0.741167\pi\) | ||||
−0.687215 | + | 0.726454i | \(0.741167\pi\) | |||||||
\(864\) | 907.247 | 0.0357236 | ||||||||
\(865\) | −1389.85 | −0.0546315 | ||||||||
\(866\) | 28824.6 | 1.13106 | ||||||||
\(867\) | 12766.0 | 0.500065 | ||||||||
\(868\) | 2208.07 | 0.0863444 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2379.74 | −0.0927364 | ||||||||
\(871\) | −6177.51 | −0.240318 | ||||||||
\(872\) | 17468.4 | 0.678389 | ||||||||
\(873\) | 2672.18 | 0.103596 | ||||||||
\(874\) | 7055.98 | 0.273080 | ||||||||
\(875\) | 1679.21 | 0.0648775 | ||||||||
\(876\) | −599.890 | −0.0231375 | ||||||||
\(877\) | 45487.0 | 1.75141 | 0.875704 | − | 0.482848i | \(-0.160398\pi\) | ||||
0.875704 | + | 0.482848i | \(0.160398\pi\) | |||||||
\(878\) | 49917.2 | 1.91871 | ||||||||
\(879\) | −28527.7 | −1.09467 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16896.5 | 0.646149 | 0.323075 | − | 0.946373i | \(-0.395284\pi\) | ||||
0.323075 | + | 0.946373i | \(0.395284\pi\) | |||||||
\(882\) | −4325.80 | −0.165144 | ||||||||
\(883\) | 47599.3 | 1.81409 | 0.907047 | − | 0.421029i | \(-0.138331\pi\) | ||||
0.907047 | + | 0.421029i | \(0.138331\pi\) | |||||||
\(884\) | 264.588 | 0.0100668 | ||||||||
\(885\) | −10457.6 | −0.397208 | ||||||||
\(886\) | −11689.3 | −0.443238 | ||||||||
\(887\) | −45471.8 | −1.72130 | −0.860650 | − | 0.509197i | \(-0.829942\pi\) | ||||
−0.860650 | + | 0.509197i | \(0.829942\pi\) | |||||||
\(888\) | −10486.0 | −0.396270 | ||||||||
\(889\) | 7645.88 | 0.288453 | ||||||||
\(890\) | −17575.2 | −0.661934 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2745.64 | −0.103061 | ||||||||
\(893\) | −784.778 | −0.0294083 | ||||||||
\(894\) | −7536.26 | −0.281935 | ||||||||
\(895\) | 17590.1 | 0.656952 | ||||||||
\(896\) | −21720.8 | −0.809867 | ||||||||
\(897\) | −2599.03 | −0.0967436 | ||||||||
\(898\) | −7724.45 | −0.287047 | ||||||||
\(899\) | 11838.9 | 0.439209 | ||||||||
\(900\) | 167.591 | 0.00620709 | ||||||||
\(901\) | −3156.58 | −0.116716 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10458.9 | −0.385439 | ||||||||
\(904\) | −41163.1 | −1.51445 | ||||||||
\(905\) | −915.231 | −0.0336169 | ||||||||
\(906\) | −25613.0 | −0.939223 | ||||||||
\(907\) | 3514.39 | 0.128659 | 0.0643293 | − | 0.997929i | \(-0.479509\pi\) | ||||
0.0643293 | + | 0.997929i | \(0.479509\pi\) | |||||||
\(908\) | 3614.34 | 0.132099 | ||||||||
\(909\) | −2220.45 | −0.0810205 | ||||||||
\(910\) | −2751.33 | −0.100226 | ||||||||
\(911\) | −15794.1 | −0.574405 | −0.287203 | − | 0.957870i | \(-0.592725\pi\) | ||||
−0.287203 | + | 0.957870i | \(0.592725\pi\) | |||||||
\(912\) | −7943.24 | −0.288407 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23774.1 | 0.860369 | ||||||||
\(915\) | 12437.8 | 0.449378 | ||||||||
\(916\) | −4860.20 | −0.175312 | ||||||||
\(917\) | 36676.4 | 1.32079 | ||||||||
\(918\) | 2047.58 | 0.0736168 | ||||||||
\(919\) | 21882.5 | 0.785459 | 0.392730 | − | 0.919654i | \(-0.371531\pi\) | ||||
0.392730 | + | 0.919654i | \(0.371531\pi\) | |||||||
\(920\) | −6709.37 | −0.240436 | ||||||||
\(921\) | −19456.1 | −0.696093 | ||||||||
\(922\) | −8131.02 | −0.290435 | ||||||||
\(923\) | −9948.76 | −0.354786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4072.93 | −0.144775 | ||||||||
\(926\) | −51712.9 | −1.83520 | ||||||||
\(927\) | −1919.95 | −0.0680251 | ||||||||
\(928\) | 1802.70 | 0.0637679 | ||||||||
\(929\) | −100.426 | −0.00354668 | −0.00177334 | − | 0.999998i | \(-0.500564\pi\) | ||||
−0.00177334 | + | 0.999998i | \(0.500564\pi\) | |||||||
\(930\) | −9788.50 | −0.345137 | ||||||||
\(931\) | 6200.69 | 0.218281 | ||||||||
\(932\) | 707.272 | 0.0248578 | ||||||||
\(933\) | 32183.6 | 1.12931 | ||||||||
\(934\) | 13727.5 | 0.480919 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2674.64 | 0.0934011 | ||||||||
\(937\) | 48135.4 | 1.67825 | 0.839123 | − | 0.543942i | \(-0.183069\pi\) | ||||
0.839123 | + | 0.543942i | \(0.183069\pi\) | |||||||
\(938\) | −17716.8 | −0.616709 | ||||||||
\(939\) | 24665.1 | 0.857204 | ||||||||
\(940\) | −76.6115 | −0.00265829 | ||||||||
\(941\) | 10466.4 | 0.362588 | 0.181294 | − | 0.983429i | \(-0.441971\pi\) | ||||
0.181294 | + | 0.983429i | \(0.441971\pi\) | |||||||
\(942\) | −6682.63 | −0.231138 | ||||||||
\(943\) | 1116.79 | 0.0385659 | ||||||||
\(944\) | 48386.8 | 1.66828 | ||||||||
\(945\) | −1813.55 | −0.0624284 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9541.38 | −0.327406 | −0.163703 | − | 0.986510i | \(-0.552344\pi\) | ||||
−0.163703 | + | 0.986510i | \(0.552344\pi\) | |||||||
\(948\) | 822.516 | 0.0281794 | ||||||||
\(949\) | −3718.62 | −0.127199 | ||||||||
\(950\) | −2820.38 | −0.0963214 | ||||||||
\(951\) | −10368.4 | −0.353541 | ||||||||
\(952\) | −7391.28 | −0.251631 | ||||||||
\(953\) | 17051.3 | 0.579586 | 0.289793 | − | 0.957089i | \(-0.406414\pi\) | ||||
0.289793 | + | 0.957089i | \(0.406414\pi\) | |||||||
\(954\) | 3275.93 | 0.111176 | ||||||||
\(955\) | −18142.7 | −0.614747 | ||||||||
\(956\) | −3924.20 | −0.132759 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26224.3 | −0.884415 | ||||||||
\(959\) | 16027.9 | 0.539697 | ||||||||
\(960\) | 6837.99 | 0.229891 | ||||||||
\(961\) | 18905.4 | 0.634601 | ||||||||
\(962\) | 6673.34 | 0.223656 | ||||||||
\(963\) | 718.534 | 0.0240441 | ||||||||
\(964\) | 840.540 | 0.0280830 | ||||||||
\(965\) | −19483.2 | −0.649933 | ||||||||
\(966\) | −7453.88 | −0.248266 | ||||||||
\(967\) | 2160.46 | 0.0718468 | 0.0359234 | − | 0.999355i | \(-0.488563\pi\) | ||||
0.0359234 | + | 0.999355i | \(0.488563\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2935.04 | −0.0973035 | ||||||||
\(970\) | −4390.04 | −0.145315 | ||||||||
\(971\) | −45614.5 | −1.50756 | −0.753779 | − | 0.657128i | \(-0.771771\pi\) | ||||
−0.753779 | + | 0.657128i | \(0.771771\pi\) | |||||||
\(972\) | −180.999 | −0.00597277 | ||||||||
\(973\) | −17016.0 | −0.560646 | ||||||||
\(974\) | −5797.62 | −0.190727 | ||||||||
\(975\) | 1038.87 | 0.0341236 | ||||||||
\(976\) | −57548.8 | −1.88739 | ||||||||
\(977\) | 19116.0 | 0.625972 | 0.312986 | − | 0.949758i | \(-0.398671\pi\) | ||||
0.312986 | + | 0.949758i | \(0.398671\pi\) | |||||||
\(978\) | −11213.1 | −0.366621 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 605.323 | 0.0197310 | ||||||||
\(981\) | −7327.80 | −0.238490 | ||||||||
\(982\) | 38759.3 | 1.25953 | ||||||||
\(983\) | −24497.3 | −0.794854 | −0.397427 | − | 0.917634i | \(-0.630097\pi\) | ||||
−0.397427 | + | 0.917634i | \(0.630097\pi\) | |||||||
\(984\) | −1149.28 | −0.0372334 | ||||||||
\(985\) | 21121.4 | 0.683233 | ||||||||
\(986\) | 4068.54 | 0.131409 | ||||||||
\(987\) | 829.033 | 0.0267360 | ||||||||
\(988\) | 393.606 | 0.0126744 | ||||||||
\(989\) | 16231.5 | 0.521872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19625.0 | 0.629072 | 0.314536 | − | 0.949246i | \(-0.398151\pi\) | ||||
0.314536 | + | 0.949246i | \(0.398151\pi\) | |||||||
\(992\) | 7414.99 | 0.237325 | ||||||||
\(993\) | −27800.5 | −0.888440 | ||||||||
\(994\) | −28532.5 | −0.910460 | ||||||||
\(995\) | −11211.2 | −0.357204 | ||||||||
\(996\) | −1174.55 | −0.0373665 | ||||||||
\(997\) | 2468.28 | 0.0784064 | 0.0392032 | − | 0.999231i | \(-0.487518\pi\) | ||||
0.0392032 | + | 0.999231i | \(0.487518\pi\) | |||||||
\(998\) | −26069.2 | −0.826861 | ||||||||
\(999\) | 4398.76 | 0.139310 |
(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.bj.1.9 | 12 | ||
11.3 | even | 5 | 165.4.m.b.31.5 | yes | 24 | ||
11.4 | even | 5 | 165.4.m.b.16.5 | ✓ | 24 | ||
11.10 | odd | 2 | 1815.4.a.bm.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.m.b.16.5 | ✓ | 24 | 11.4 | even | 5 | ||
165.4.m.b.31.5 | yes | 24 | 11.3 | even | 5 | ||
1815.4.a.bj.1.9 | 12 | 1.1 | even | 1 | trivial | ||
1815.4.a.bm.1.4 | 12 | 11.10 | odd | 2 |