Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43845 | 0.508568 | 0.254284 | − | 0.967130i | \(-0.418160\pi\) | ||||
0.254284 | + | 0.967130i | \(0.418160\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −5.93087 | −0.741359 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.31534 | 0.293622 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −20.0388 | −0.885599 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.61553 | 0.208743 | 0.104371 | − | 0.994538i | \(-0.466717\pi\) | ||||
0.104371 | + | 0.994538i | \(0.466717\pi\) | |||||||
\(12\) | −17.7926 | −0.428024 | ||||||||
\(13\) | −52.3542 | −1.11696 | −0.558478 | − | 0.829519i | \(-0.688615\pi\) | ||||
−0.558478 | + | 0.829519i | \(0.688615\pi\) | |||||||
\(14\) | 10.0691 | 0.192221 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.6222 | 0.290971 | ||||||||
\(17\) | 49.7235 | 0.709395 | 0.354697 | − | 0.934981i | \(-0.384584\pi\) | ||||
0.354697 | + | 0.934981i | \(0.384584\pi\) | |||||||
\(18\) | 12.9460 | 0.169523 | ||||||||
\(19\) | 140.600 | 1.69768 | 0.848840 | − | 0.528649i | \(-0.177301\pi\) | ||||
0.848840 | + | 0.528649i | \(0.177301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 10.9545 | 0.106160 | ||||||||
\(23\) | 23.4470 | 0.212566 | 0.106283 | − | 0.994336i | \(-0.466105\pi\) | ||||
0.106283 | + | 0.994336i | \(0.466105\pi\) | |||||||
\(24\) | −60.1165 | −0.511301 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −75.3087 | −0.568048 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −41.5161 | −0.280207 | ||||||||
\(29\) | 157.170 | 1.00641 | 0.503204 | − | 0.864168i | \(-0.332155\pi\) | ||||
0.503204 | + | 0.864168i | \(0.332155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.892 | 0.740971 | 0.370485 | − | 0.928838i | \(-0.379191\pi\) | ||||
0.370485 | + | 0.928838i | \(0.379191\pi\) | |||||||
\(32\) | 187.098 | 1.03358 | ||||||||
\(33\) | 22.8466 | 0.120518 | ||||||||
\(34\) | 71.5246 | 0.360776 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −53.3778 | −0.247120 | ||||||||
\(37\) | 115.477 | 0.513090 | 0.256545 | − | 0.966532i | \(-0.417416\pi\) | ||||
0.256545 | + | 0.966532i | \(0.417416\pi\) | |||||||
\(38\) | 202.246 | 0.863386 | ||||||||
\(39\) | −157.062 | −0.644875 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −188.617 | −0.718466 | −0.359233 | − | 0.933248i | \(-0.616962\pi\) | ||||
−0.359233 | + | 0.933248i | \(0.616962\pi\) | |||||||
\(42\) | 30.2074 | 0.110979 | ||||||||
\(43\) | −322.186 | −1.14262 | −0.571312 | − | 0.820733i | \(-0.693565\pi\) | ||||
−0.571312 | + | 0.820733i | \(0.693565\pi\) | |||||||
\(44\) | −45.1667 | −0.154753 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 33.7272 | 0.108104 | ||||||||
\(47\) | 76.6477 | 0.237877 | 0.118938 | − | 0.992902i | \(-0.462051\pi\) | ||||
0.118938 | + | 0.992902i | \(0.462051\pi\) | |||||||
\(48\) | 55.8665 | 0.167992 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 149.170 | 0.409569 | ||||||||
\(52\) | 310.506 | 0.828065 | ||||||||
\(53\) | 424.172 | 1.09933 | 0.549666 | − | 0.835385i | \(-0.314755\pi\) | ||||
0.549666 | + | 0.835385i | \(0.314755\pi\) | |||||||
\(54\) | 38.8381 | 0.0978739 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −140.272 | −0.334725 | ||||||||
\(57\) | 421.801 | 0.980157 | ||||||||
\(58\) | 226.081 | 0.511827 | ||||||||
\(59\) | 107.784 | 0.237835 | 0.118918 | − | 0.992904i | \(-0.462058\pi\) | ||||
0.118918 | + | 0.992904i | \(0.462058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 915.511 | 1.92163 | 0.960813 | − | 0.277197i | \(-0.0894053\pi\) | ||||
0.960813 | + | 0.277197i | \(0.0894053\pi\) | |||||||
\(62\) | 183.966 | 0.376834 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 120.153 | 0.234673 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 32.8636 | 0.0612914 | ||||||||
\(67\) | 451.723 | 0.823684 | 0.411842 | − | 0.911255i | \(-0.364886\pi\) | ||||
0.411842 | + | 0.911255i | \(0.364886\pi\) | |||||||
\(68\) | −294.903 | −0.525916 | ||||||||
\(69\) | 70.3409 | 0.122725 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 907.312 | 1.51659 | 0.758297 | − | 0.651909i | \(-0.226032\pi\) | ||||
0.758297 | + | 0.651909i | \(0.226032\pi\) | |||||||
\(72\) | −180.349 | −0.295200 | ||||||||
\(73\) | −755.956 | −1.21203 | −0.606014 | − | 0.795454i | \(-0.707232\pi\) | ||||
−0.606014 | + | 0.795454i | \(0.707232\pi\) | |||||||
\(74\) | 166.108 | 0.260941 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −833.882 | −1.25859 | ||||||||
\(77\) | 53.3087 | 0.0788973 | ||||||||
\(78\) | −225.926 | −0.327963 | ||||||||
\(79\) | 22.5834 | 0.0321624 | 0.0160812 | − | 0.999871i | \(-0.494881\pi\) | ||||
0.0160812 | + | 0.999871i | \(0.494881\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −271.316 | −0.365389 | ||||||||
\(83\) | −1112.25 | −1.47091 | −0.735454 | − | 0.677575i | \(-0.763031\pi\) | ||||
−0.735454 | + | 0.677575i | \(0.763031\pi\) | |||||||
\(84\) | −124.548 | −0.161778 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −463.447 | −0.581102 | ||||||||
\(87\) | 471.511 | 0.581050 | ||||||||
\(88\) | −152.606 | −0.184862 | ||||||||
\(89\) | 1518.81 | 1.80892 | 0.904458 | − | 0.426562i | \(-0.140275\pi\) | ||||
0.904458 | + | 0.426562i | \(0.140275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −366.479 | −0.422170 | ||||||||
\(92\) | −139.061 | −0.157588 | ||||||||
\(93\) | 383.676 | 0.427800 | ||||||||
\(94\) | 110.254 | 0.120977 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 561.293 | 0.596736 | ||||||||
\(97\) | 549.987 | 0.575698 | 0.287849 | − | 0.957676i | \(-0.407060\pi\) | ||||
0.287849 | + | 0.957676i | \(0.407060\pi\) | |||||||
\(98\) | 70.4839 | 0.0726526 | ||||||||
\(99\) | 68.5398 | 0.0695809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −533.299 | −0.525398 | −0.262699 | − | 0.964878i | \(-0.584613\pi\) | ||||
−0.262699 | + | 0.964878i | \(0.584613\pi\) | |||||||
\(102\) | 214.574 | 0.208294 | ||||||||
\(103\) | −1357.79 | −1.29890 | −0.649451 | − | 0.760404i | \(-0.725001\pi\) | ||||
−0.649451 | + | 0.760404i | \(0.725001\pi\) | |||||||
\(104\) | 1049.12 | 0.989176 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 610.149 | 0.559084 | ||||||||
\(107\) | −913.693 | −0.825515 | −0.412757 | − | 0.910841i | \(-0.635434\pi\) | ||||
−0.412757 | + | 0.910841i | \(0.635434\pi\) | |||||||
\(108\) | −160.133 | −0.142675 | ||||||||
\(109\) | −160.489 | −0.141028 | −0.0705139 | − | 0.997511i | \(-0.522464\pi\) | ||||
−0.0705139 | + | 0.997511i | \(0.522464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 346.432 | 0.296233 | ||||||||
\(112\) | 130.355 | 0.109977 | ||||||||
\(113\) | 1788.48 | 1.48891 | 0.744453 | − | 0.667675i | \(-0.232710\pi\) | ||||
0.744453 | + | 0.667675i | \(0.232710\pi\) | |||||||
\(114\) | 606.739 | 0.498476 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −932.157 | −0.746109 | ||||||||
\(117\) | −471.187 | −0.372319 | ||||||||
\(118\) | 155.042 | 0.120955 | ||||||||
\(119\) | 348.064 | 0.268126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1273.00 | −0.956427 | ||||||||
\(122\) | 1316.91 | 0.977277 | ||||||||
\(123\) | −565.852 | −0.414806 | ||||||||
\(124\) | −758.511 | −0.549325 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 90.6222 | 0.0640735 | ||||||||
\(127\) | 271.015 | 0.189360 | 0.0946799 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946799 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(128\) | −1323.95 | −0.914231 | ||||||||
\(129\) | −966.557 | −0.659694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −763.151 | −0.508984 | −0.254492 | − | 0.967075i | \(-0.581908\pi\) | ||||
−0.254492 | + | 0.967075i | \(0.581908\pi\) | |||||||
\(132\) | −135.500 | −0.0893468 | ||||||||
\(133\) | 984.203 | 0.641663 | ||||||||
\(134\) | 649.780 | 0.418899 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −996.400 | −0.628240 | ||||||||
\(137\) | 240.934 | 0.150251 | 0.0751254 | − | 0.997174i | \(-0.476064\pi\) | ||||
0.0751254 | + | 0.997174i | \(0.476064\pi\) | |||||||
\(138\) | 101.182 | 0.0624141 | ||||||||
\(139\) | −103.150 | −0.0629427 | −0.0314714 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314714 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 229.943 | 0.137338 | ||||||||
\(142\) | 1305.12 | 0.771291 | ||||||||
\(143\) | −398.705 | −0.233156 | ||||||||
\(144\) | 167.600 | 0.0969905 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1087.40 | −0.616398 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | −684.881 | −0.380384 | ||||||||
\(149\) | −3256.71 | −1.79061 | −0.895303 | − | 0.445458i | \(-0.853041\pi\) | ||||
−0.895303 | + | 0.445458i | \(0.853041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1471.04 | 0.792793 | 0.396396 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(152\) | −2817.47 | −1.50346 | ||||||||
\(153\) | 447.511 | 0.236465 | ||||||||
\(154\) | 76.6817 | 0.0401246 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 931.517 | 0.478084 | ||||||||
\(157\) | 1394.22 | 0.708730 | 0.354365 | − | 0.935107i | \(-0.384697\pi\) | ||||
0.354365 | + | 0.935107i | \(0.384697\pi\) | |||||||
\(158\) | 32.4850 | 0.0163567 | ||||||||
\(159\) | 1272.52 | 0.634699 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 164.129 | 0.0803426 | ||||||||
\(162\) | 116.514 | 0.0565075 | ||||||||
\(163\) | 3674.27 | 1.76559 | 0.882794 | − | 0.469760i | \(-0.155659\pi\) | ||||
0.882794 | + | 0.469760i | \(0.155659\pi\) | |||||||
\(164\) | 1118.67 | 0.532641 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1599.91 | −0.748056 | ||||||||
\(167\) | −4041.09 | −1.87251 | −0.936254 | − | 0.351325i | \(-0.885731\pi\) | ||||
−0.936254 | + | 0.351325i | \(0.885731\pi\) | |||||||
\(168\) | −420.815 | −0.193254 | ||||||||
\(169\) | 543.958 | 0.247591 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1265.40 | 0.565894 | ||||||||
\(172\) | 1910.84 | 0.847094 | ||||||||
\(173\) | −59.4582 | −0.0261302 | −0.0130651 | − | 0.999915i | \(-0.504159\pi\) | ||||
−0.0130651 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(174\) | 678.244 | 0.295503 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 141.818 | 0.0607381 | ||||||||
\(177\) | 323.352 | 0.137314 | ||||||||
\(178\) | 2184.73 | 0.919957 | ||||||||
\(179\) | −2973.32 | −1.24155 | −0.620773 | − | 0.783991i | \(-0.713181\pi\) | ||||
−0.620773 | + | 0.783991i | \(0.713181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −676.220 | −0.277696 | −0.138848 | − | 0.990314i | \(-0.544340\pi\) | ||||
−0.138848 | + | 0.990314i | \(0.544340\pi\) | |||||||
\(182\) | −527.161 | −0.214702 | ||||||||
\(183\) | 2746.53 | 1.10945 | ||||||||
\(184\) | −469.849 | −0.188249 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 551.898 | 0.217565 | ||||||||
\(187\) | 378.671 | 0.148081 | ||||||||
\(188\) | −454.588 | −0.176352 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5589 | 0.00627308 | 0.00313654 | − | 0.999995i | \(-0.499002\pi\) | ||||
0.00313654 | + | 0.999995i | \(0.499002\pi\) | |||||||
\(192\) | 360.458 | 0.135489 | ||||||||
\(193\) | −2694.68 | −1.00501 | −0.502506 | − | 0.864574i | \(-0.667589\pi\) | ||||
−0.502506 | + | 0.864574i | \(0.667589\pi\) | |||||||
\(194\) | 791.127 | 0.292781 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −290.613 | −0.105908 | ||||||||
\(197\) | −1027.38 | −0.371561 | −0.185781 | − | 0.982591i | \(-0.559481\pi\) | ||||
−0.185781 | + | 0.982591i | \(0.559481\pi\) | |||||||
\(198\) | 98.5908 | 0.0353866 | ||||||||
\(199\) | 2823.77 | 1.00589 | 0.502944 | − | 0.864319i | \(-0.332250\pi\) | ||||
0.502944 | + | 0.864319i | \(0.332250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1355.17 | 0.475554 | ||||||||
\(202\) | −767.123 | −0.267201 | ||||||||
\(203\) | 1100.19 | 0.380386 | ||||||||
\(204\) | −884.710 | −0.303638 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1953.11 | −0.660579 | ||||||||
\(207\) | 211.023 | 0.0708555 | ||||||||
\(208\) | −974.948 | −0.325002 | ||||||||
\(209\) | 1070.75 | 0.354378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5151.16 | 1.68067 | 0.840333 | − | 0.542071i | \(-0.182360\pi\) | ||||
0.840333 | + | 0.542071i | \(0.182360\pi\) | |||||||
\(212\) | −2515.71 | −0.814999 | ||||||||
\(213\) | 2721.94 | 0.875606 | ||||||||
\(214\) | −1314.30 | −0.419830 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −541.048 | −0.170434 | ||||||||
\(217\) | 895.244 | 0.280061 | ||||||||
\(218\) | −230.855 | −0.0717222 | ||||||||
\(219\) | −2267.87 | −0.699764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2603.23 | −0.792363 | ||||||||
\(222\) | 498.324 | 0.150655 | ||||||||
\(223\) | 114.496 | 0.0343822 | 0.0171911 | − | 0.999852i | \(-0.494528\pi\) | ||||
0.0171911 | + | 0.999852i | \(0.494528\pi\) | |||||||
\(224\) | 1309.68 | 0.390656 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2572.64 | 0.757209 | ||||||||
\(227\) | −4744.75 | −1.38731 | −0.693657 | − | 0.720306i | \(-0.744001\pi\) | ||||
−0.693657 | + | 0.720306i | \(0.744001\pi\) | |||||||
\(228\) | −2501.65 | −0.726648 | ||||||||
\(229\) | −5384.47 | −1.55378 | −0.776891 | − | 0.629635i | \(-0.783204\pi\) | ||||
−0.776891 | + | 0.629635i | \(0.783204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 159.926 | 0.0455514 | ||||||||
\(232\) | −3149.51 | −0.891274 | ||||||||
\(233\) | 1608.91 | 0.452373 | 0.226187 | − | 0.974084i | \(-0.427374\pi\) | ||||
0.226187 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(234\) | −677.778 | −0.189349 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −639.253 | −0.176321 | ||||||||
\(237\) | 67.7501 | 0.0185689 | ||||||||
\(238\) | 500.672 | 0.136360 | ||||||||
\(239\) | −3113.11 | −0.842554 | −0.421277 | − | 0.906932i | \(-0.638418\pi\) | ||||
−0.421277 | + | 0.906932i | \(0.638418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7136.38 | 1.90745 | 0.953724 | − | 0.300685i | \(-0.0972151\pi\) | ||||
0.953724 | + | 0.300685i | \(0.0972151\pi\) | |||||||
\(242\) | −1831.15 | −0.486408 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −5429.78 | −1.42461 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −813.948 | −0.210957 | ||||||||
\(247\) | −7361.01 | −1.89624 | ||||||||
\(248\) | −2562.81 | −0.656203 | ||||||||
\(249\) | −3336.75 | −0.849229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −225.504 | −0.0567079 | −0.0283539 | − | 0.999598i | \(-0.509027\pi\) | ||||
−0.0283539 | + | 0.999598i | \(0.509027\pi\) | |||||||
\(252\) | −373.645 | −0.0934024 | ||||||||
\(253\) | 178.561 | 0.0443717 | ||||||||
\(254\) | 389.841 | 0.0963024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2865.65 | −0.699621 | ||||||||
\(257\) | 4423.05 | 1.07355 | 0.536775 | − | 0.843725i | \(-0.319642\pi\) | ||||
0.536775 | + | 0.843725i | \(0.319642\pi\) | |||||||
\(258\) | −1390.34 | −0.335499 | ||||||||
\(259\) | 808.341 | 0.193930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1414.53 | 0.335469 | ||||||||
\(262\) | −1097.75 | −0.258853 | ||||||||
\(263\) | −6540.56 | −1.53349 | −0.766746 | − | 0.641950i | \(-0.778125\pi\) | ||||
−0.766746 | + | 0.641950i | \(0.778125\pi\) | |||||||
\(264\) | −457.819 | −0.106730 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1415.72 | 0.326329 | ||||||||
\(267\) | 4556.43 | 1.04438 | ||||||||
\(268\) | −2679.11 | −0.610645 | ||||||||
\(269\) | 2262.97 | 0.512920 | 0.256460 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256460 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1615.68 | 0.362160 | 0.181080 | − | 0.983468i | \(-0.442041\pi\) | ||||
0.181080 | + | 0.983468i | \(0.442041\pi\) | |||||||
\(272\) | 925.959 | 0.206414 | ||||||||
\(273\) | −1099.44 | −0.243740 | ||||||||
\(274\) | 346.571 | 0.0764127 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −417.183 | −0.0909835 | ||||||||
\(277\) | −4691.55 | −1.01765 | −0.508823 | − | 0.860871i | \(-0.669919\pi\) | ||||
−0.508823 | + | 0.860871i | \(0.669919\pi\) | |||||||
\(278\) | −148.375 | −0.0320107 | ||||||||
\(279\) | 1151.03 | 0.246990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8119.00 | −1.72363 | −0.861813 | − | 0.507226i | \(-0.830671\pi\) | ||||
−0.861813 | + | 0.507226i | \(0.830671\pi\) | |||||||
\(282\) | 330.761 | 0.0698459 | ||||||||
\(283\) | 3633.75 | 0.763265 | 0.381632 | − | 0.924314i | \(-0.375362\pi\) | ||||
0.381632 | + | 0.924314i | \(0.375362\pi\) | |||||||
\(284\) | −5381.15 | −1.12434 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −573.515 | −0.118576 | ||||||||
\(287\) | −1320.32 | −0.271554 | ||||||||
\(288\) | 1683.88 | 0.344526 | ||||||||
\(289\) | −2440.58 | −0.496759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1649.96 | 0.332379 | ||||||||
\(292\) | 4483.48 | 0.898547 | ||||||||
\(293\) | 7981.99 | 1.59151 | 0.795756 | − | 0.605618i | \(-0.207074\pi\) | ||||
0.795756 | + | 0.605618i | \(0.207074\pi\) | |||||||
\(294\) | 211.452 | 0.0419460 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2314.03 | −0.454392 | ||||||||
\(297\) | 205.619 | 0.0401725 | ||||||||
\(298\) | −4684.61 | −0.910645 | ||||||||
\(299\) | −1227.55 | −0.237427 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2255.30 | −0.431871 | ||||||||
\(302\) | 2116.02 | 0.403189 | ||||||||
\(303\) | −1599.90 | −0.303339 | ||||||||
\(304\) | 2618.28 | 0.493977 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 643.721 | 0.120259 | ||||||||
\(307\) | 7118.15 | 1.32330 | 0.661652 | − | 0.749811i | \(-0.269856\pi\) | ||||
0.661652 | + | 0.749811i | \(0.269856\pi\) | |||||||
\(308\) | −316.167 | −0.0584912 | ||||||||
\(309\) | −4073.36 | −0.749921 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9155.92 | −1.66940 | −0.834702 | − | 0.550703i | \(-0.814360\pi\) | ||||
−0.834702 | + | 0.550703i | \(0.814360\pi\) | |||||||
\(312\) | 3147.35 | 0.571101 | ||||||||
\(313\) | 6163.44 | 1.11303 | 0.556515 | − | 0.830838i | \(-0.312138\pi\) | ||||
0.556515 | + | 0.830838i | \(0.312138\pi\) | |||||||
\(314\) | 2005.51 | 0.360438 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −133.939 | −0.0238438 | ||||||||
\(317\) | −8658.37 | −1.53408 | −0.767038 | − | 0.641601i | \(-0.778270\pi\) | ||||
−0.767038 | + | 0.641601i | \(0.778270\pi\) | |||||||
\(318\) | 1830.45 | 0.322788 | ||||||||
\(319\) | 1196.94 | 0.210080 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2741.08 | −0.476611 | ||||||||
\(322\) | 236.090 | 0.0408597 | ||||||||
\(323\) | 6991.14 | 1.20433 | ||||||||
\(324\) | −480.400 | −0.0823732 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5285.24 | 0.897922 | ||||||||
\(327\) | −481.466 | −0.0814224 | ||||||||
\(328\) | 3779.67 | 0.636272 | ||||||||
\(329\) | 536.534 | 0.0899090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128.477 | −0.0213346 | −0.0106673 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106673 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(332\) | 6596.61 | 1.09047 | ||||||||
\(333\) | 1039.30 | 0.171030 | ||||||||
\(334\) | −5812.89 | −0.952297 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 391.066 | 0.0634952 | ||||||||
\(337\) | −7784.57 | −1.25832 | −0.629158 | − | 0.777277i | \(-0.716600\pi\) | ||||
−0.629158 | + | 0.777277i | \(0.716600\pi\) | |||||||
\(338\) | 782.455 | 0.125917 | ||||||||
\(339\) | 5365.45 | 0.859620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 973.965 | 0.154672 | ||||||||
\(342\) | 1820.22 | 0.287795 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 6456.22 | 1.01191 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −85.5274 | −0.0132890 | ||||||||
\(347\) | −3740.26 | −0.578638 | −0.289319 | − | 0.957233i | \(-0.593429\pi\) | ||||
−0.289319 | + | 0.957233i | \(0.593429\pi\) | |||||||
\(348\) | −2796.47 | −0.430766 | ||||||||
\(349\) | 5676.86 | 0.870703 | 0.435351 | − | 0.900261i | \(-0.356624\pi\) | ||||
0.435351 | + | 0.900261i | \(0.356624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1413.56 | −0.214958 | ||||||||
\(352\) | 1424.85 | 0.215752 | ||||||||
\(353\) | −909.564 | −0.137142 | −0.0685711 | − | 0.997646i | \(-0.521844\pi\) | ||||
−0.0685711 | + | 0.997646i | \(0.521844\pi\) | |||||||
\(354\) | 465.125 | 0.0698337 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9007.87 | −1.34106 | ||||||||
\(357\) | 1044.19 | 0.154803 | ||||||||
\(358\) | −4276.97 | −0.631410 | ||||||||
\(359\) | 2678.57 | 0.393788 | 0.196894 | − | 0.980425i | \(-0.436915\pi\) | ||||
0.196894 | + | 0.980425i | \(0.436915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12909.5 | 1.88212 | ||||||||
\(362\) | −972.706 | −0.141227 | ||||||||
\(363\) | −3819.01 | −0.552193 | ||||||||
\(364\) | 2173.54 | 0.312979 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3950.74 | 0.564231 | ||||||||
\(367\) | 716.898 | 0.101967 | 0.0509833 | − | 0.998700i | \(-0.483764\pi\) | ||||
0.0509833 | + | 0.998700i | \(0.483764\pi\) | |||||||
\(368\) | 436.633 | 0.0618508 | ||||||||
\(369\) | −1697.56 | −0.239489 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2969.21 | 0.415508 | ||||||||
\(372\) | −2275.53 | −0.317153 | ||||||||
\(373\) | 2006.15 | 0.278484 | 0.139242 | − | 0.990258i | \(-0.455533\pi\) | ||||
0.139242 | + | 0.990258i | \(0.455533\pi\) | |||||||
\(374\) | 544.698 | 0.0753092 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1535.93 | −0.210664 | ||||||||
\(377\) | −8228.53 | −1.12411 | ||||||||
\(378\) | 271.867 | 0.0369929 | ||||||||
\(379\) | 7277.53 | 0.986336 | 0.493168 | − | 0.869934i | \(-0.335839\pi\) | ||||
0.493168 | + | 0.869934i | \(0.335839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 813.045 | 0.109327 | ||||||||
\(382\) | 23.8191 | 0.00319029 | ||||||||
\(383\) | −5953.94 | −0.794339 | −0.397170 | − | 0.917745i | \(-0.630008\pi\) | ||||
−0.397170 | + | 0.917745i | \(0.630008\pi\) | |||||||
\(384\) | −3971.84 | −0.527831 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3876.16 | −0.511117 | ||||||||
\(387\) | −2899.67 | −0.380875 | ||||||||
\(388\) | −3261.90 | −0.426799 | ||||||||
\(389\) | 1867.98 | 0.243472 | 0.121736 | − | 0.992563i | \(-0.461154\pi\) | ||||
0.121736 | + | 0.992563i | \(0.461154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1165.86 | 0.150794 | ||||||||
\(392\) | −981.902 | −0.126514 | ||||||||
\(393\) | −2289.45 | −0.293862 | ||||||||
\(394\) | −1477.83 | −0.188964 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −406.500 | −0.0515844 | ||||||||
\(397\) | 2160.07 | 0.273075 | 0.136538 | − | 0.990635i | \(-0.456403\pi\) | ||||
0.136538 | + | 0.990635i | \(0.456403\pi\) | |||||||
\(398\) | 4061.85 | 0.511563 | ||||||||
\(399\) | 2952.61 | 0.370464 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1954.81 | 0.243438 | 0.121719 | − | 0.992565i | \(-0.461159\pi\) | ||||
0.121719 | + | 0.992565i | \(0.461159\pi\) | |||||||
\(402\) | 1949.34 | 0.241851 | ||||||||
\(403\) | −6695.68 | −0.827632 | ||||||||
\(404\) | 3162.93 | 0.389509 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1582.57 | 0.193452 | ||||||||
\(407\) | 879.420 | 0.107104 | ||||||||
\(408\) | −2989.20 | −0.362714 | ||||||||
\(409\) | 14895.1 | 1.80077 | 0.900384 | − | 0.435096i | \(-0.143286\pi\) | ||||
0.900384 | + | 0.435096i | \(0.143286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 722.801 | 0.0867474 | ||||||||
\(412\) | 8052.86 | 0.962952 | ||||||||
\(413\) | 754.489 | 0.0898934 | ||||||||
\(414\) | 303.545 | 0.0360348 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9795.34 | −1.15446 | ||||||||
\(417\) | −309.449 | −0.0363400 | ||||||||
\(418\) | 1540.21 | 0.180225 | ||||||||
\(419\) | 12608.9 | 1.47013 | 0.735067 | − | 0.677994i | \(-0.237151\pi\) | ||||
0.735067 | + | 0.677994i | \(0.237151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7862.86 | −0.910243 | −0.455122 | − | 0.890429i | \(-0.650404\pi\) | ||||
−0.455122 | + | 0.890429i | \(0.650404\pi\) | |||||||
\(422\) | 7409.67 | 0.854732 | ||||||||
\(423\) | 689.829 | 0.0792923 | ||||||||
\(424\) | −8499.91 | −0.973567 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3915.36 | 0.445305 | ||||||||
\(427\) | 6408.58 | 0.726307 | ||||||||
\(428\) | 5419.00 | 0.612002 | ||||||||
\(429\) | −1196.11 | −0.134613 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14291.0 | 1.59715 | 0.798575 | − | 0.601896i | \(-0.205588\pi\) | ||||
0.798575 | + | 0.601896i | \(0.205588\pi\) | |||||||
\(432\) | 502.799 | 0.0559975 | ||||||||
\(433\) | 13759.0 | 1.52705 | 0.763527 | − | 0.645776i | \(-0.223466\pi\) | ||||
0.763527 | + | 0.645776i | \(0.223466\pi\) | |||||||
\(434\) | 1287.76 | 0.142430 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 951.838 | 0.104552 | ||||||||
\(437\) | 3296.65 | 0.360870 | ||||||||
\(438\) | −3262.21 | −0.355878 | ||||||||
\(439\) | −6093.13 | −0.662436 | −0.331218 | − | 0.943554i | \(-0.607459\pi\) | ||||
−0.331218 | + | 0.943554i | \(0.607459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −3744.61 | −0.402970 | ||||||||
\(443\) | −13449.5 | −1.44244 | −0.721222 | − | 0.692704i | \(-0.756419\pi\) | ||||
−0.721222 | + | 0.692704i | \(0.756419\pi\) | |||||||
\(444\) | −2054.64 | −0.219615 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 164.697 | 0.0174857 | ||||||||
\(447\) | −9770.14 | −1.03381 | ||||||||
\(448\) | 841.068 | 0.0886981 | ||||||||
\(449\) | 6893.83 | 0.724588 | 0.362294 | − | 0.932064i | \(-0.381994\pi\) | ||||
0.362294 | + | 0.932064i | \(0.381994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1436.42 | −0.149974 | ||||||||
\(452\) | −10607.3 | −1.10381 | ||||||||
\(453\) | 4413.13 | 0.457719 | ||||||||
\(454\) | −6825.07 | −0.705543 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8452.40 | −0.868026 | ||||||||
\(457\) | 11820.1 | 1.20990 | 0.604948 | − | 0.796265i | \(-0.293194\pi\) | ||||
0.604948 | + | 0.796265i | \(0.293194\pi\) | |||||||
\(458\) | −7745.28 | −0.790203 | ||||||||
\(459\) | 1342.53 | 0.136523 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8443.38 | 0.853031 | 0.426516 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426516 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(462\) | 230.045 | 0.0231660 | ||||||||
\(463\) | 1269.74 | 0.127451 | 0.0637257 | − | 0.997967i | \(-0.479702\pi\) | ||||
0.0637257 | + | 0.997967i | \(0.479702\pi\) | |||||||
\(464\) | 2926.86 | 0.292836 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2314.33 | 0.230063 | ||||||||
\(467\) | 16481.8 | 1.63316 | 0.816579 | − | 0.577233i | \(-0.195868\pi\) | ||||
0.816579 | + | 0.577233i | \(0.195868\pi\) | |||||||
\(468\) | 2794.55 | 0.276022 | ||||||||
\(469\) | 3162.06 | 0.311323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4182.65 | 0.409186 | ||||||||
\(472\) | −2159.87 | −0.210627 | ||||||||
\(473\) | −2453.61 | −0.238514 | ||||||||
\(474\) | 97.4549 | 0.00944357 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2064.32 | −0.198778 | ||||||||
\(477\) | 3817.55 | 0.366444 | ||||||||
\(478\) | −4478.05 | −0.428496 | ||||||||
\(479\) | −1400.21 | −0.133564 | −0.0667822 | − | 0.997768i | \(-0.521273\pi\) | ||||
−0.0667822 | + | 0.997768i | \(0.521273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6045.72 | −0.573100 | ||||||||
\(482\) | 10265.3 | 0.970066 | ||||||||
\(483\) | 492.386 | 0.0463858 | ||||||||
\(484\) | 7550.02 | 0.709055 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 349.543 | 0.0326246 | ||||||||
\(487\) | 14165.9 | 1.31811 | 0.659055 | − | 0.752094i | \(-0.270956\pi\) | ||||
0.659055 | + | 0.752094i | \(0.270956\pi\) | |||||||
\(488\) | −18345.8 | −1.70179 | ||||||||
\(489\) | 11022.8 | 1.01936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4739.28 | 0.435603 | 0.217801 | − | 0.975993i | \(-0.430112\pi\) | ||||
0.217801 | + | 0.975993i | \(0.430112\pi\) | |||||||
\(492\) | 3356.00 | 0.307520 | ||||||||
\(493\) | 7815.06 | 0.713940 | ||||||||
\(494\) | −10588.4 | −0.964364 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2381.63 | 0.215601 | ||||||||
\(497\) | 6351.19 | 0.573219 | ||||||||
\(498\) | −4799.74 | −0.431890 | ||||||||
\(499\) | −11370.0 | −1.02003 | −0.510013 | − | 0.860167i | \(-0.670360\pi\) | ||||
−0.510013 | + | 0.860167i | \(0.670360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12123.3 | −1.08109 | ||||||||
\(502\) | −324.375 | −0.0288398 | ||||||||
\(503\) | −9212.48 | −0.816629 | −0.408314 | − | 0.912841i | \(-0.633883\pi\) | ||||
−0.408314 | + | 0.912841i | \(0.633883\pi\) | |||||||
\(504\) | −1262.45 | −0.111575 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 256.851 | 0.0225660 | ||||||||
\(507\) | 1631.87 | 0.142947 | ||||||||
\(508\) | −1607.36 | −0.140384 | ||||||||
\(509\) | −15938.3 | −1.38792 | −0.693960 | − | 0.720014i | \(-0.744136\pi\) | ||||
−0.693960 | + | 0.720014i | \(0.744136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5291.69 | −0.458103 | ||||||||
\(512\) | 6469.49 | 0.558426 | ||||||||
\(513\) | 3796.21 | 0.326719 | ||||||||
\(514\) | 6362.33 | 0.545973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5732.52 | 0.489070 | ||||||||
\(517\) | 583.713 | 0.0496550 | ||||||||
\(518\) | 1162.76 | 0.0986265 | ||||||||
\(519\) | −178.374 | −0.0150863 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6442.99 | 0.541790 | 0.270895 | − | 0.962609i | \(-0.412680\pi\) | ||||
0.270895 | + | 0.962609i | \(0.412680\pi\) | |||||||
\(522\) | 2034.73 | 0.170609 | ||||||||
\(523\) | −986.655 | −0.0824922 | −0.0412461 | − | 0.999149i | \(-0.513133\pi\) | ||||
−0.0412461 | + | 0.999149i | \(0.513133\pi\) | |||||||
\(524\) | 4526.15 | 0.377339 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9408.26 | −0.779885 | ||||||||
\(527\) | 6359.24 | 0.525641 | ||||||||
\(528\) | 425.453 | 0.0350672 | ||||||||
\(529\) | −11617.2 | −0.954815 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 970.057 | 0.0792785 | ||||||||
\(532\) | −5837.18 | −0.475703 | ||||||||
\(533\) | 9874.91 | 0.802495 | ||||||||
\(534\) | 6554.19 | 0.531137 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9052.01 | −0.729454 | ||||||||
\(537\) | −8919.97 | −0.716807 | ||||||||
\(538\) | 3255.16 | 0.260855 | ||||||||
\(539\) | 373.161 | 0.0298204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12681.1 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668097\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668097\pi\) | |||||||
\(542\) | 2324.06 | 0.184183 | ||||||||
\(543\) | −2028.66 | −0.160328 | ||||||||
\(544\) | 9303.14 | 0.733215 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1581.48 | −0.123958 | ||||||||
\(547\) | 14826.4 | 1.15892 | 0.579462 | − | 0.814999i | \(-0.303263\pi\) | ||||
0.579462 | + | 0.814999i | \(0.303263\pi\) | |||||||
\(548\) | −1428.95 | −0.111390 | ||||||||
\(549\) | 8239.60 | 0.640542 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22098.2 | 1.70856 | ||||||||
\(552\) | −1409.55 | −0.108685 | ||||||||
\(553\) | 158.083 | 0.0121562 | ||||||||
\(554\) | −6748.55 | −0.517542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 611.767 | 0.0466632 | ||||||||
\(557\) | −1926.46 | −0.146547 | −0.0732737 | − | 0.997312i | \(-0.523345\pi\) | ||||
−0.0732737 | + | 0.997312i | \(0.523345\pi\) | |||||||
\(558\) | 1655.69 | 0.125611 | ||||||||
\(559\) | 16867.8 | 1.27626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1136.01 | 0.0854946 | ||||||||
\(562\) | −11678.8 | −0.876581 | ||||||||
\(563\) | 18624.8 | 1.39422 | 0.697108 | − | 0.716966i | \(-0.254470\pi\) | ||||
0.697108 | + | 0.716966i | \(0.254470\pi\) | |||||||
\(564\) | −1363.76 | −0.101817 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5226.96 | 0.388172 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −18181.5 | −1.34309 | ||||||||
\(569\) | −20093.9 | −1.48045 | −0.740227 | − | 0.672357i | \(-0.765282\pi\) | ||||
−0.740227 | + | 0.672357i | \(0.765282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4535.25 | 0.332389 | 0.166195 | − | 0.986093i | \(-0.446852\pi\) | ||||
0.166195 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(572\) | 2364.66 | 0.172852 | ||||||||
\(573\) | 49.6766 | 0.00362176 | ||||||||
\(574\) | −1899.21 | −0.138104 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1081.37 | 0.0782243 | ||||||||
\(577\) | −10034.6 | −0.723994 | −0.361997 | − | 0.932179i | \(-0.617905\pi\) | ||||
−0.361997 | + | 0.932179i | \(0.617905\pi\) | |||||||
\(578\) | −3510.64 | −0.252636 | ||||||||
\(579\) | −8084.05 | −0.580244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7785.75 | −0.555951 | ||||||||
\(582\) | 2373.38 | 0.169037 | ||||||||
\(583\) | 3230.30 | 0.229477 | ||||||||
\(584\) | 15148.5 | 1.07337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11481.7 | 0.809391 | ||||||||
\(587\) | 11192.6 | 0.786999 | 0.393499 | − | 0.919325i | \(-0.371264\pi\) | ||||
0.393499 | + | 0.919325i | \(0.371264\pi\) | |||||||
\(588\) | −871.838 | −0.0611462 | ||||||||
\(589\) | 17981.7 | 1.25793 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3082.13 | −0.214521 | ||||||||
\(592\) | 2150.44 | 0.149295 | ||||||||
\(593\) | −20317.6 | −1.40699 | −0.703493 | − | 0.710703i | \(-0.748377\pi\) | ||||
−0.703493 | + | 0.710703i | \(0.748377\pi\) | |||||||
\(594\) | 295.772 | 0.0204305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19315.1 | 1.32748 | ||||||||
\(597\) | 8471.31 | 0.580750 | ||||||||
\(598\) | −1765.76 | −0.120748 | ||||||||
\(599\) | −26376.5 | −1.79919 | −0.899594 | − | 0.436727i | \(-0.856138\pi\) | ||||
−0.899594 | + | 0.436727i | \(0.856138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9266.13 | 0.628907 | 0.314454 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314454 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(602\) | −3244.13 | −0.219636 | ||||||||
\(603\) | 4065.51 | 0.274561 | ||||||||
\(604\) | −8724.56 | −0.587744 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2301.37 | −0.154268 | ||||||||
\(607\) | −11338.0 | −0.758149 | −0.379075 | − | 0.925366i | \(-0.623758\pi\) | ||||
−0.379075 | + | 0.925366i | \(0.623758\pi\) | |||||||
\(608\) | 26306.0 | 1.75469 | ||||||||
\(609\) | 3300.58 | 0.219616 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4012.83 | −0.265698 | ||||||||
\(612\) | −2654.13 | −0.175305 | ||||||||
\(613\) | −25712.5 | −1.69416 | −0.847078 | − | 0.531469i | \(-0.821640\pi\) | ||||
−0.847078 | + | 0.531469i | \(0.821640\pi\) | |||||||
\(614\) | 10239.1 | 0.672990 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1068.24 | −0.0698714 | ||||||||
\(617\) | −663.465 | −0.0432903 | −0.0216451 | − | 0.999766i | \(-0.506890\pi\) | ||||
−0.0216451 | + | 0.999766i | \(0.506890\pi\) | |||||||
\(618\) | −5859.32 | −0.381386 | ||||||||
\(619\) | −12768.7 | −0.829108 | −0.414554 | − | 0.910025i | \(-0.636062\pi\) | ||||
−0.414554 | + | 0.910025i | \(0.636062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 633.068 | 0.0409084 | ||||||||
\(622\) | −13170.3 | −0.849005 | ||||||||
\(623\) | 10631.7 | 0.683706 | ||||||||
\(624\) | −2924.84 | −0.187640 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8865.78 | 0.566051 | ||||||||
\(627\) | 3212.24 | 0.204600 | ||||||||
\(628\) | −8268.92 | −0.525423 | ||||||||
\(629\) | 5741.93 | 0.363984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14937.6 | −0.942400 | −0.471200 | − | 0.882026i | \(-0.656179\pi\) | ||||
−0.471200 | + | 0.882026i | \(0.656179\pi\) | |||||||
\(632\) | −452.544 | −0.0284829 | ||||||||
\(633\) | 15453.5 | 0.970333 | ||||||||
\(634\) | −12454.6 | −0.780182 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7547.13 | −0.470540 | ||||||||
\(637\) | −2565.35 | −0.159565 | ||||||||
\(638\) | 1721.73 | 0.106840 | ||||||||
\(639\) | 8165.81 | 0.505531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10903.0 | 0.671829 | 0.335914 | − | 0.941893i | \(-0.390955\pi\) | ||||
0.335914 | + | 0.941893i | \(0.390955\pi\) | |||||||
\(642\) | −3942.90 | −0.242389 | ||||||||
\(643\) | 7623.47 | 0.467559 | 0.233779 | − | 0.972290i | \(-0.424891\pi\) | ||||
0.233779 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(644\) | −973.426 | −0.0595627 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10056.4 | 0.612482 | ||||||||
\(647\) | −5384.84 | −0.327202 | −0.163601 | − | 0.986527i | \(-0.552311\pi\) | ||||
−0.163601 | + | 0.986527i | \(0.552311\pi\) | |||||||
\(648\) | −1623.14 | −0.0983999 | ||||||||
\(649\) | 820.833 | 0.0496464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2685.73 | 0.161693 | ||||||||
\(652\) | −21791.6 | −1.30893 | ||||||||
\(653\) | −297.318 | −0.0178177 | −0.00890883 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00890883 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(654\) | −692.564 | −0.0414088 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3512.47 | −0.209053 | ||||||||
\(657\) | −6803.61 | −0.404009 | ||||||||
\(658\) | 771.776 | 0.0457248 | ||||||||
\(659\) | 10324.7 | 0.610309 | 0.305155 | − | 0.952303i | \(-0.401292\pi\) | ||||
0.305155 | + | 0.952303i | \(0.401292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4272.98 | 0.251437 | 0.125718 | − | 0.992066i | \(-0.459876\pi\) | ||||
0.125718 | + | 0.992066i | \(0.459876\pi\) | |||||||
\(662\) | −184.808 | −0.0108501 | ||||||||
\(663\) | −7809.69 | −0.457471 | ||||||||
\(664\) | 22288.2 | 1.30263 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1494.97 | 0.0869804 | ||||||||
\(667\) | 3685.17 | 0.213928 | ||||||||
\(668\) | 23967.2 | 1.38820 | ||||||||
\(669\) | 343.488 | 0.0198506 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6972.10 | 0.401125 | ||||||||
\(672\) | 3929.05 | 0.225545 | ||||||||
\(673\) | 23033.4 | 1.31927 | 0.659637 | − | 0.751584i | \(-0.270710\pi\) | ||||
0.659637 | + | 0.751584i | \(0.270710\pi\) | |||||||
\(674\) | −11197.7 | −0.639940 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3226.15 | −0.183554 | ||||||||
\(677\) | −5113.50 | −0.290292 | −0.145146 | − | 0.989410i | \(-0.546365\pi\) | ||||
−0.145146 | + | 0.989410i | \(0.546365\pi\) | |||||||
\(678\) | 7717.91 | 0.437175 | ||||||||
\(679\) | 3849.91 | 0.217593 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14234.2 | −0.800966 | ||||||||
\(682\) | 1401.00 | 0.0786613 | ||||||||
\(683\) | −1341.02 | −0.0751286 | −0.0375643 | − | 0.999294i | \(-0.511960\pi\) | ||||
−0.0375643 | + | 0.999294i | \(0.511960\pi\) | |||||||
\(684\) | −7504.94 | −0.419530 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 493.387 | 0.0274601 | ||||||||
\(687\) | −16153.4 | −0.897076 | ||||||||
\(688\) | −5999.80 | −0.332471 | ||||||||
\(689\) | −22207.2 | −1.22790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16809.3 | −0.925404 | −0.462702 | − | 0.886514i | \(-0.653120\pi\) | ||||
−0.462702 | + | 0.886514i | \(0.653120\pi\) | |||||||
\(692\) | 352.639 | 0.0193718 | ||||||||
\(693\) | 479.778 | 0.0262991 | ||||||||
\(694\) | −5380.16 | −0.294277 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9448.53 | −0.514577 | ||||||||
\(697\) | −9378.71 | −0.509676 | ||||||||
\(698\) | 8165.86 | 0.442812 | ||||||||
\(699\) | 4826.72 | 0.261178 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13467.0 | 0.725592 | 0.362796 | − | 0.931869i | \(-0.381822\pi\) | ||||
0.362796 | + | 0.931869i | \(0.381822\pi\) | |||||||
\(702\) | −2033.33 | −0.109321 | ||||||||
\(703\) | 16236.1 | 0.871064 | ||||||||
\(704\) | 915.025 | 0.0489863 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1308.36 | −0.0697461 | ||||||||
\(707\) | −3733.09 | −0.198582 | ||||||||
\(708\) | −1917.76 | −0.101799 | ||||||||
\(709\) | 35514.3 | 1.88119 | 0.940597 | − | 0.339525i | \(-0.110266\pi\) | ||||
0.940597 | + | 0.339525i | \(0.110266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 203.250 | 0.0107208 | ||||||||
\(712\) | −30435.2 | −1.60198 | ||||||||
\(713\) | 2998.68 | 0.157506 | ||||||||
\(714\) | 1502.02 | 0.0787277 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17634.4 | 0.920431 | ||||||||
\(717\) | −9339.34 | −0.486449 | ||||||||
\(718\) | 3852.99 | 0.200268 | ||||||||
\(719\) | 4993.61 | 0.259013 | 0.129506 | − | 0.991579i | \(-0.458661\pi\) | ||||
0.129506 | + | 0.991579i | \(0.458661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9504.51 | −0.490938 | ||||||||
\(722\) | 18569.6 | 0.957186 | ||||||||
\(723\) | 21409.1 | 1.10127 | ||||||||
\(724\) | 4010.57 | 0.205872 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5493.45 | −0.280828 | ||||||||
\(727\) | 4223.35 | 0.215454 | 0.107727 | − | 0.994181i | \(-0.465643\pi\) | ||||
0.107727 | + | 0.994181i | \(0.465643\pi\) | |||||||
\(728\) | 7343.81 | 0.373873 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16020.2 | −0.810572 | ||||||||
\(732\) | −16289.3 | −0.822502 | ||||||||
\(733\) | −19030.9 | −0.958968 | −0.479484 | − | 0.877551i | \(-0.659176\pi\) | ||||
−0.479484 | + | 0.877551i | \(0.659176\pi\) | |||||||
\(734\) | 1031.22 | 0.0518570 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4386.87 | 0.219704 | ||||||||
\(737\) | 3440.11 | 0.171938 | ||||||||
\(738\) | −2441.85 | −0.121796 | ||||||||
\(739\) | −27772.5 | −1.38245 | −0.691224 | − | 0.722641i | \(-0.742928\pi\) | ||||
−0.691224 | + | 0.722641i | \(0.742928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22083.0 | −1.09479 | ||||||||
\(742\) | 4271.05 | 0.211314 | ||||||||
\(743\) | −26880.7 | −1.32726 | −0.663631 | − | 0.748060i | \(-0.730985\pi\) | ||||
−0.663631 | + | 0.748060i | \(0.730985\pi\) | |||||||
\(744\) | −7688.42 | −0.378859 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2885.74 | 0.141628 | ||||||||
\(747\) | −10010.2 | −0.490302 | ||||||||
\(748\) | −2245.85 | −0.109781 | ||||||||
\(749\) | −6395.85 | −0.312015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35166.6 | −1.70872 | −0.854360 | − | 0.519681i | \(-0.826051\pi\) | ||||
−0.854360 | + | 0.519681i | \(0.826051\pi\) | |||||||
\(752\) | 1427.35 | 0.0692154 | ||||||||
\(753\) | −676.512 | −0.0327403 | ||||||||
\(754\) | −11836.3 | −0.571688 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1120.93 | −0.0539259 | ||||||||
\(757\) | −14589.2 | −0.700467 | −0.350233 | − | 0.936662i | \(-0.613898\pi\) | ||||
−0.350233 | + | 0.936662i | \(0.613898\pi\) | |||||||
\(758\) | 10468.3 | 0.501619 | ||||||||
\(759\) | 535.683 | 0.0256180 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −782.826 | −0.0372897 | −0.0186448 | − | 0.999826i | \(-0.505935\pi\) | ||||
−0.0186448 | + | 0.999826i | \(0.505935\pi\) | |||||||
\(762\) | 1169.52 | 0.0556002 | ||||||||
\(763\) | −1123.42 | −0.0533035 | ||||||||
\(764\) | −98.2085 | −0.00465060 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8564.42 | −0.403975 | ||||||||
\(767\) | −5642.95 | −0.265652 | ||||||||
\(768\) | −8596.95 | −0.403927 | ||||||||
\(769\) | −16548.4 | −0.776008 | −0.388004 | − | 0.921658i | \(-0.626835\pi\) | ||||
−0.388004 | + | 0.921658i | \(0.626835\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13269.2 | 0.619815 | ||||||||
\(772\) | 15981.8 | 0.745075 | ||||||||
\(773\) | −5744.94 | −0.267310 | −0.133655 | − | 0.991028i | \(-0.542671\pi\) | ||||
−0.133655 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(774\) | −4171.02 | −0.193701 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11021.1 | −0.509837 | ||||||||
\(777\) | 2425.02 | 0.111966 | ||||||||
\(778\) | 2687.00 | 0.123822 | ||||||||
\(779\) | −26519.7 | −1.21973 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6909.66 | 0.316578 | ||||||||
\(782\) | 1677.03 | 0.0766888 | ||||||||
\(783\) | 4243.60 | 0.193683 | ||||||||
\(784\) | 912.486 | 0.0415673 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3293.26 | −0.149449 | ||||||||
\(787\) | 34744.3 | 1.57370 | 0.786848 | − | 0.617146i | \(-0.211711\pi\) | ||||
0.786848 | + | 0.617146i | \(0.211711\pi\) | |||||||
\(788\) | 6093.24 | 0.275460 | ||||||||
\(789\) | −19621.7 | −0.885362 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12519.4 | 0.562753 | ||||||||
\(792\) | −1373.46 | −0.0616207 | ||||||||
\(793\) | −47930.8 | −2.14637 | ||||||||
\(794\) | 3107.15 | 0.138877 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16747.4 | −0.745724 | ||||||||
\(797\) | −21748.7 | −0.966600 | −0.483300 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483300 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(798\) | 4247.17 | 0.188406 | ||||||||
\(799\) | 3811.19 | 0.168749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13669.3 | 0.602972 | ||||||||
\(802\) | 2811.89 | 0.123805 | ||||||||
\(803\) | −5757.01 | −0.253002 | ||||||||
\(804\) | −8037.34 | −0.352556 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9631.38 | −0.420907 | ||||||||
\(807\) | 6788.90 | 0.296134 | ||||||||
\(808\) | 10686.7 | 0.465292 | ||||||||
\(809\) | −42350.6 | −1.84050 | −0.920252 | − | 0.391325i | \(-0.872017\pi\) | ||||
−0.920252 | + | 0.391325i | \(0.872017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18910.7 | −0.818796 | −0.409398 | − | 0.912356i | \(-0.634261\pi\) | ||||
−0.409398 | + | 0.912356i | \(0.634261\pi\) | |||||||
\(812\) | −6525.10 | −0.282003 | ||||||||
\(813\) | 4847.03 | 0.209093 | ||||||||
\(814\) | 1265.00 | 0.0544696 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2777.88 | 0.119173 | ||||||||
\(817\) | −45299.4 | −1.93981 | ||||||||
\(818\) | 21425.8 | 0.915813 | ||||||||
\(819\) | −3298.31 | −0.140723 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6593.42 | 0.280283 | 0.140141 | − | 0.990132i | \(-0.455244\pi\) | ||||
0.140141 | + | 0.990132i | \(0.455244\pi\) | |||||||
\(822\) | 1039.71 | 0.0441169 | ||||||||
\(823\) | −26762.4 | −1.13351 | −0.566755 | − | 0.823886i | \(-0.691801\pi\) | ||||
−0.566755 | + | 0.823886i | \(0.691801\pi\) | |||||||
\(824\) | 27208.5 | 1.15031 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1085.29 | 0.0457169 | ||||||||
\(827\) | 24016.7 | 1.00985 | 0.504924 | − | 0.863164i | \(-0.331521\pi\) | ||||
0.504924 | + | 0.863164i | \(0.331521\pi\) | |||||||
\(828\) | −1251.55 | −0.0525293 | ||||||||
\(829\) | −28422.3 | −1.19077 | −0.595383 | − | 0.803442i | \(-0.703000\pi\) | ||||
−0.595383 | + | 0.803442i | \(0.703000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14074.7 | −0.587538 | ||||||||
\(832\) | −6290.49 | −0.262120 | ||||||||
\(833\) | 2436.45 | 0.101342 | ||||||||
\(834\) | −445.126 | −0.0184814 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6350.46 | −0.262721 | ||||||||
\(837\) | 3453.09 | 0.142600 | ||||||||
\(838\) | 18137.3 | 0.747663 | ||||||||
\(839\) | 6637.09 | 0.273108 | 0.136554 | − | 0.990633i | \(-0.456397\pi\) | ||||
0.136554 | + | 0.990633i | \(0.456397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 313.546 | 0.0128560 | ||||||||
\(842\) | −11310.3 | −0.462921 | ||||||||
\(843\) | −24357.0 | −0.995136 | ||||||||
\(844\) | −30550.9 | −1.24598 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 992.283 | 0.0403255 | ||||||||
\(847\) | −8911.03 | −0.361495 | ||||||||
\(848\) | 7899.01 | 0.319874 | ||||||||
\(849\) | 10901.2 | 0.440671 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2707.59 | 0.109066 | ||||||||
\(852\) | −16143.5 | −0.649138 | ||||||||
\(853\) | 1406.88 | 0.0564720 | 0.0282360 | − | 0.999601i | \(-0.491011\pi\) | ||||
0.0282360 | + | 0.999601i | \(0.491011\pi\) | |||||||
\(854\) | 9218.40 | 0.369376 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18309.3 | 0.731075 | ||||||||
\(857\) | −27943.4 | −1.11380 | −0.556901 | − | 0.830579i | \(-0.688010\pi\) | ||||
−0.556901 | + | 0.830579i | \(0.688010\pi\) | |||||||
\(858\) | −1720.55 | −0.0684598 | ||||||||
\(859\) | 1936.63 | 0.0769233 | 0.0384616 | − | 0.999260i | \(-0.487754\pi\) | ||||
0.0384616 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3960.97 | −0.156782 | ||||||||
\(862\) | 20556.8 | 0.812259 | ||||||||
\(863\) | −7947.70 | −0.313491 | −0.156746 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156746 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(864\) | 5051.63 | 0.198912 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19791.6 | 0.776611 | ||||||||
\(867\) | −7321.73 | −0.286804 | ||||||||
\(868\) | −5309.58 | −0.207625 | ||||||||
\(869\) | 171.984 | 0.00671365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23649.6 | −0.920019 | ||||||||
\(872\) | 3216.00 | 0.124894 | ||||||||
\(873\) | 4949.88 | 0.191899 | ||||||||
\(874\) | 4742.06 | 0.183527 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13450.4 | 0.518776 | ||||||||
\(877\) | −38655.0 | −1.48835 | −0.744177 | − | 0.667983i | \(-0.767158\pi\) | ||||
−0.744177 | + | 0.667983i | \(0.767158\pi\) | |||||||
\(878\) | −8764.65 | −0.336893 | ||||||||
\(879\) | 23946.0 | 0.918859 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18879.4 | −0.721978 | −0.360989 | − | 0.932570i | \(-0.617561\pi\) | ||||
−0.360989 | + | 0.932570i | \(0.617561\pi\) | |||||||
\(882\) | 634.355 | 0.0242175 | ||||||||
\(883\) | 35098.1 | 1.33765 | 0.668825 | − | 0.743420i | \(-0.266798\pi\) | ||||
0.668825 | + | 0.743420i | \(0.266798\pi\) | |||||||
\(884\) | 15439.4 | 0.587425 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19346.3 | −0.733581 | ||||||||
\(887\) | 48816.4 | 1.84791 | 0.923954 | − | 0.382504i | \(-0.124938\pi\) | ||||
0.923954 | + | 0.382504i | \(0.124938\pi\) | |||||||
\(888\) | −6942.08 | −0.262344 | ||||||||
\(889\) | 1897.11 | 0.0715713 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 616.858 | 0.0231936 | ||||||||
\(892\) | −679.062 | −0.0254895 | ||||||||
\(893\) | 10776.7 | 0.403839 | ||||||||
\(894\) | −14053.8 | −0.525761 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9267.63 | −0.345547 | ||||||||
\(897\) | −3682.64 | −0.137079 | ||||||||
\(898\) | 9916.41 | 0.368502 | ||||||||
\(899\) | 20100.8 | 0.745718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21091.3 | 0.779860 | ||||||||
\(902\) | −2066.22 | −0.0762721 | ||||||||
\(903\) | −6765.90 | −0.249341 | ||||||||
\(904\) | −35839.1 | −1.31857 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6348.05 | 0.232781 | ||||||||
\(907\) | 6010.83 | 0.220051 | 0.110026 | − | 0.993929i | \(-0.464907\pi\) | ||||
0.110026 | + | 0.993929i | \(0.464907\pi\) | |||||||
\(908\) | 28140.5 | 1.02850 | ||||||||
\(909\) | −4799.69 | −0.175133 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25780.1 | 0.937576 | 0.468788 | − | 0.883311i | \(-0.344691\pi\) | ||||
0.468788 | + | 0.883311i | \(0.344691\pi\) | |||||||
\(912\) | 7854.85 | 0.285198 | ||||||||
\(913\) | −8470.37 | −0.307041 | ||||||||
\(914\) | 17002.6 | 0.615314 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31934.6 | 1.15191 | ||||||||
\(917\) | −5342.06 | −0.192378 | ||||||||
\(918\) | 1931.16 | 0.0694313 | ||||||||
\(919\) | 26731.8 | 0.959522 | 0.479761 | − | 0.877399i | \(-0.340723\pi\) | ||||
0.479761 | + | 0.877399i | \(0.340723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21354.4 | 0.764010 | ||||||||
\(922\) | 12145.4 | 0.433824 | ||||||||
\(923\) | −47501.6 | −1.69397 | ||||||||
\(924\) | −948.501 | −0.0337699 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1826.46 | 0.0648177 | ||||||||
\(927\) | −12220.1 | −0.432967 | ||||||||
\(928\) | 29406.2 | 1.04020 | ||||||||
\(929\) | −30464.6 | −1.07590 | −0.537949 | − | 0.842977i | \(-0.680801\pi\) | ||||
−0.537949 | + | 0.842977i | \(0.680801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6889.42 | 0.242526 | ||||||||
\(932\) | −9542.22 | −0.335371 | ||||||||
\(933\) | −27467.7 | −0.963830 | ||||||||
\(934\) | 23708.1 | 0.830572 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9442.04 | 0.329725 | ||||||||
\(937\) | 28533.4 | 0.994819 | 0.497409 | − | 0.867516i | \(-0.334285\pi\) | ||||
0.497409 | + | 0.867516i | \(0.334285\pi\) | |||||||
\(938\) | 4548.46 | 0.158329 | ||||||||
\(939\) | 18490.3 | 0.642608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34455.8 | 1.19365 | 0.596827 | − | 0.802370i | \(-0.296428\pi\) | ||||
0.596827 | + | 0.802370i | \(0.296428\pi\) | |||||||
\(942\) | 6016.52 | 0.208099 | ||||||||
\(943\) | −4422.50 | −0.152722 | ||||||||
\(944\) | 2007.17 | 0.0692033 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3529.39 | −0.121301 | ||||||||
\(947\) | −2477.68 | −0.0850198 | −0.0425099 | − | 0.999096i | \(-0.513535\pi\) | ||||
−0.0425099 | + | 0.999096i | \(0.513535\pi\) | |||||||
\(948\) | −401.817 | −0.0137662 | ||||||||
\(949\) | 39577.5 | 1.35378 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25975.1 | −0.885699 | ||||||||
\(952\) | −6974.80 | −0.237452 | ||||||||
\(953\) | −41690.6 | −1.41709 | −0.708547 | − | 0.705663i | \(-0.750649\pi\) | ||||
−0.708547 | + | 0.705663i | \(0.750649\pi\) | |||||||
\(954\) | 5491.35 | 0.186361 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18463.5 | 0.624635 | ||||||||
\(957\) | 3590.81 | 0.121290 | ||||||||
\(958\) | −2014.13 | −0.0679266 | ||||||||
\(959\) | 1686.54 | 0.0567895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13434.6 | −0.450962 | ||||||||
\(962\) | −8696.44 | −0.291460 | ||||||||
\(963\) | −8223.24 | −0.275172 | ||||||||
\(964\) | −42325.0 | −1.41410 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 708.271 | 0.0235903 | ||||||||
\(967\) | 20641.3 | 0.686430 | 0.343215 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343215 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(968\) | 25509.5 | 0.847010 | ||||||||
\(969\) | 20973.4 | 0.695318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6626.17 | 0.218995 | 0.109497 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109497 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(972\) | −1441.20 | −0.0475582 | ||||||||
\(973\) | −722.048 | −0.0237901 | ||||||||
\(974\) | 20377.0 | 0.670349 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17048.8 | 0.559138 | ||||||||
\(977\) | −41961.0 | −1.37405 | −0.687027 | − | 0.726632i | \(-0.741085\pi\) | ||||
−0.687027 | + | 0.726632i | \(0.741085\pi\) | |||||||
\(978\) | 15855.7 | 0.518415 | ||||||||
\(979\) | 11566.5 | 0.377598 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1444.40 | −0.0470093 | ||||||||
\(982\) | 6817.21 | 0.221533 | ||||||||
\(983\) | 16781.7 | 0.544510 | 0.272255 | − | 0.962225i | \(-0.412231\pi\) | ||||
0.272255 | + | 0.962225i | \(0.412231\pi\) | |||||||
\(984\) | 11339.0 | 0.367352 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11241.6 | 0.363087 | ||||||||
\(987\) | 1609.60 | 0.0519090 | ||||||||
\(988\) | 43657.2 | 1.40579 | ||||||||
\(989\) | −7554.27 | −0.242884 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50319.8 | 1.61298 | 0.806489 | − | 0.591250i | \(-0.201365\pi\) | ||||
0.806489 | + | 0.591250i | \(0.201365\pi\) | |||||||
\(992\) | 23928.3 | 0.765851 | ||||||||
\(993\) | −385.432 | −0.0123176 | ||||||||
\(994\) | 9135.85 | 0.291521 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19789.8 | 0.629583 | ||||||||
\(997\) | −12949.5 | −0.411348 | −0.205674 | − | 0.978621i | \(-0.565939\pi\) | ||||
−0.205674 | + | 0.978621i | \(0.565939\pi\) | |||||||
\(998\) | −16355.2 | −0.518753 | ||||||||
\(999\) | 3117.89 | 0.0987443 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 525.4.a.p.1.1 | 2 | ||
3.2 | odd | 2 | 1575.4.a.m.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.i.274.3 | 4 | |||
5.3 | odd | 4 | 525.4.d.i.274.2 | 4 | |||
5.4 | even | 2 | 105.4.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 315.4.a.m.1.1 | 2 | |||
20.19 | odd | 2 | 1680.4.a.bk.1.1 | 2 | |||
35.34 | odd | 2 | 735.4.a.k.1.2 | 2 | |||
105.104 | even | 2 | 2205.4.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
315.4.a.m.1.1 | 2 | 15.14 | odd | 2 | |||
525.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
525.4.d.i.274.2 | 4 | 5.3 | odd | 4 | |||
525.4.d.i.274.3 | 4 | 5.2 | odd | 4 | |||
735.4.a.k.1.2 | 2 | 35.34 | odd | 2 | |||
1575.4.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
1680.4.a.bk.1.1 | 2 | 20.19 | odd | 2 | |||
2205.4.a.bh.1.1 | 2 | 105.104 | even | 2 |