Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 21x^{4} + 5x^{3} + 101x^{2} + 29x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.113318\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25118 | −0.442358 | −0.221179 | − | 0.975233i | \(-0.570990\pi\) | ||||
−0.221179 | + | 0.975233i | \(0.570990\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.43456 | −0.804320 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.67029 | −0.306167 | −0.153083 | − | 0.988213i | \(-0.548920\pi\) | ||||
−0.153083 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(8\) | 18.0602 | 0.798155 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.2537 | −0.582567 | −0.291283 | − | 0.956637i | \(-0.594082\pi\) | ||||
−0.291283 | + | 0.956637i | \(0.594082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.9479 | 0.873608 | 0.436804 | − | 0.899557i | \(-0.356110\pi\) | ||||
0.436804 | + | 0.899557i | \(0.356110\pi\) | |||||||
\(14\) | 7.09453 | 0.135435 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 28.8800 | 0.451250 | ||||||||
\(17\) | −59.1853 | −0.844384 | −0.422192 | − | 0.906506i | \(-0.638739\pi\) | ||||
−0.422192 | + | 0.906506i | \(0.638739\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.8800 | 0.264190 | 0.132095 | − | 0.991237i | \(-0.457830\pi\) | ||||
0.132095 | + | 0.991237i | \(0.457830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 26.5922 | 0.257703 | ||||||||
\(23\) | 98.7941 | 0.895652 | 0.447826 | − | 0.894121i | \(-0.352198\pi\) | ||||
0.447826 | + | 0.894121i | \(0.352198\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −51.2331 | −0.386447 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 36.4858 | 0.246256 | ||||||||
\(29\) | 159.643 | 1.02224 | 0.511120 | − | 0.859509i | \(-0.329231\pi\) | ||||
0.511120 | + | 0.859509i | \(0.329231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −69.4873 | −0.402590 | −0.201295 | − | 0.979531i | \(-0.564515\pi\) | ||||
−0.201295 | + | 0.979531i | \(0.564515\pi\) | |||||||
\(32\) | −180.615 | −0.997769 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 74.0512 | 0.373520 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −235.618 | −1.04690 | −0.523451 | − | 0.852056i | \(-0.675356\pi\) | ||||
−0.523451 | + | 0.852056i | \(0.675356\pi\) | |||||||
\(38\) | −27.3757 | −0.116866 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 491.487 | 1.87213 | 0.936066 | − | 0.351825i | \(-0.114439\pi\) | ||||
0.936066 | + | 0.351825i | \(0.114439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −95.3080 | −0.338008 | −0.169004 | − | 0.985615i | \(-0.554055\pi\) | ||||
−0.169004 | + | 0.985615i | \(0.554055\pi\) | |||||||
\(44\) | 136.758 | 0.468570 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −123.609 | −0.396199 | ||||||||
\(47\) | 548.796 | 1.70319 | 0.851597 | − | 0.524197i | \(-0.175634\pi\) | ||||
0.851597 | + | 0.524197i | \(0.175634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −310.848 | −0.906262 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −263.482 | −0.702660 | ||||||||
\(53\) | −509.829 | −1.32133 | −0.660664 | − | 0.750682i | \(-0.729725\pi\) | ||||
−0.660664 | + | 0.750682i | \(0.729725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −102.406 | −0.244368 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −199.742 | −0.452196 | ||||||||
\(59\) | −741.098 | −1.63530 | −0.817650 | − | 0.575715i | \(-0.804724\pi\) | ||||
−0.817650 | + | 0.575715i | \(0.804724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 387.157 | 0.812629 | 0.406314 | − | 0.913733i | \(-0.366814\pi\) | ||||
0.406314 | + | 0.913733i | \(0.366814\pi\) | |||||||
\(62\) | 86.9409 | 0.178089 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.05795 | −0.00987881 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1060.45 | −1.93364 | −0.966822 | − | 0.255451i | \(-0.917776\pi\) | ||||
−0.966822 | + | 0.255451i | \(0.917776\pi\) | |||||||
\(68\) | 380.831 | 0.679155 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 508.998 | 0.850802 | 0.425401 | − | 0.905005i | \(-0.360133\pi\) | ||||
0.425401 | + | 0.905005i | \(0.360133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −914.906 | −1.46687 | −0.733436 | − | 0.679758i | \(-0.762085\pi\) | ||||
−0.733436 | + | 0.679758i | \(0.762085\pi\) | |||||||
\(74\) | 294.800 | 0.463105 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −140.788 | −0.212493 | ||||||||
\(77\) | 120.515 | 0.178363 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 925.717 | 1.31837 | 0.659185 | − | 0.751981i | \(-0.270901\pi\) | ||||
0.659185 | + | 0.751981i | \(0.270901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −614.937 | −0.828152 | ||||||||
\(83\) | −708.964 | −0.937577 | −0.468788 | − | 0.883310i | \(-0.655309\pi\) | ||||
−0.468788 | + | 0.883310i | \(0.655309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 119.247 | 0.149520 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −383.846 | −0.464979 | ||||||||
\(89\) | −273.516 | −0.325760 | −0.162880 | − | 0.986646i | \(-0.552078\pi\) | ||||
−0.162880 | + | 0.986646i | \(0.552078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −232.186 | −0.267470 | ||||||||
\(92\) | −635.696 | −0.720390 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −686.641 | −0.753421 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1450.22 | −1.51802 | −0.759008 | − | 0.651081i | \(-0.774316\pi\) | ||||
−0.759008 | + | 0.651081i | \(0.774316\pi\) | |||||||
\(98\) | 388.926 | 0.400892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −676.246 | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1069.47 | −1.02308 | −0.511542 | − | 0.859258i | \(-0.670926\pi\) | ||||
−0.511542 | + | 0.859258i | \(0.670926\pi\) | |||||||
\(104\) | 739.527 | 0.697275 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 637.886 | 0.584499 | ||||||||
\(107\) | −209.566 | −0.189341 | −0.0946707 | − | 0.995509i | \(-0.530180\pi\) | ||||
−0.0946707 | + | 0.995509i | \(0.530180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −455.127 | −0.399938 | −0.199969 | − | 0.979802i | \(-0.564084\pi\) | ||||
−0.199969 | + | 0.979802i | \(0.564084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −163.758 | −0.138158 | ||||||||
\(113\) | 1130.83 | 0.941413 | 0.470706 | − | 0.882290i | \(-0.343999\pi\) | ||||
0.470706 | + | 0.882290i | \(0.343999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1027.23 | −0.822208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 927.245 | 0.723388 | ||||||||
\(119\) | 335.597 | 0.258522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −879.280 | −0.660616 | ||||||||
\(122\) | −484.402 | −0.359473 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 447.120 | 0.323811 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1277.62 | −0.892682 | −0.446341 | − | 0.894863i | \(-0.647273\pi\) | ||||
−0.446341 | + | 0.894863i | \(0.647273\pi\) | |||||||
\(128\) | 1451.25 | 1.00214 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1358.29 | −0.905909 | −0.452954 | − | 0.891534i | \(-0.649630\pi\) | ||||
−0.452954 | + | 0.891534i | \(0.649630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −124.066 | −0.0808862 | ||||||||
\(134\) | 1326.81 | 0.855363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1068.90 | −0.673949 | ||||||||
\(137\) | −956.545 | −0.596519 | −0.298260 | − | 0.954485i | \(-0.596406\pi\) | ||||
−0.298260 | + | 0.954485i | \(0.596406\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27.3274 | 0.0166754 | 0.00833769 | − | 0.999965i | \(-0.497346\pi\) | ||||
0.00833769 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −636.847 | −0.376359 | ||||||||
\(143\) | −870.295 | −0.508935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1144.71 | 0.648882 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1516.10 | 0.842044 | ||||||||
\(149\) | 216.410 | 0.118987 | 0.0594933 | − | 0.998229i | \(-0.481052\pi\) | ||||
0.0594933 | + | 0.998229i | \(0.481052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2675.41 | 1.44187 | 0.720933 | − | 0.693004i | \(-0.243713\pi\) | ||||
0.720933 | + | 0.693004i | \(0.243713\pi\) | |||||||
\(152\) | 395.156 | 0.210865 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −150.785 | −0.0789001 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −956.987 | −0.486471 | −0.243235 | − | 0.969967i | \(-0.578209\pi\) | ||||
−0.243235 | + | 0.969967i | \(0.578209\pi\) | |||||||
\(158\) | −1158.24 | −0.583192 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −560.191 | −0.274219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −478.098 | −0.229739 | −0.114870 | − | 0.993381i | \(-0.536645\pi\) | ||||
−0.114870 | + | 0.993381i | \(0.536645\pi\) | |||||||
\(164\) | −3162.50 | −1.50579 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 887.039 | 0.414744 | ||||||||
\(167\) | 2666.34 | 1.23549 | 0.617746 | − | 0.786377i | \(-0.288046\pi\) | ||||
0.617746 | + | 0.786377i | \(0.288046\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −520.269 | −0.236809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 613.265 | 0.271866 | ||||||||
\(173\) | 492.589 | 0.216479 | 0.108239 | − | 0.994125i | \(-0.465479\pi\) | ||||
0.108239 | + | 0.994125i | \(0.465479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −613.807 | −0.262883 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 342.217 | 0.144103 | ||||||||
\(179\) | −3890.48 | −1.62451 | −0.812257 | − | 0.583299i | \(-0.801762\pi\) | ||||
−0.812257 | + | 0.583299i | \(0.801762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4371.58 | −1.79523 | −0.897616 | − | 0.440779i | \(-0.854702\pi\) | ||||
−0.897616 | + | 0.440779i | \(0.854702\pi\) | |||||||
\(182\) | 290.506 | 0.118317 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1784.24 | 0.714869 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1257.91 | 0.491910 | ||||||||
\(188\) | −3531.26 | −1.36991 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 328.351 | 0.124391 | 0.0621954 | − | 0.998064i | \(-0.480190\pi\) | ||||
0.0621954 | + | 0.998064i | \(0.480190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −944.655 | −0.352320 | −0.176160 | − | 0.984362i | \(-0.556368\pi\) | ||||
−0.176160 | + | 0.984362i | \(0.556368\pi\) | |||||||
\(194\) | 1814.48 | 0.671506 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2000.17 | 0.728924 | ||||||||
\(197\) | −2757.66 | −0.997337 | −0.498668 | − | 0.866793i | \(-0.666177\pi\) | ||||
−0.498668 | + | 0.866793i | \(0.666177\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1529.88 | −0.544978 | −0.272489 | − | 0.962159i | \(-0.587847\pi\) | ||||
−0.272489 | + | 0.962159i | \(0.587847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 846.103 | 0.294711 | ||||||||
\(203\) | −905.222 | −0.312976 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1338.09 | 0.452569 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1182.57 | 0.394215 | ||||||||
\(209\) | −465.031 | −0.153908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −150.761 | −0.0491886 | −0.0245943 | − | 0.999698i | \(-0.507829\pi\) | ||||
−0.0245943 | + | 0.999698i | \(0.507829\pi\) | |||||||
\(212\) | 3280.52 | 1.06277 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 262.204 | 0.0837567 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 394.013 | 0.123260 | ||||||||
\(218\) | 569.444 | 0.176916 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2423.51 | −0.737661 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2573.87 | −0.772910 | −0.386455 | − | 0.922308i | \(-0.626301\pi\) | ||||
−0.386455 | + | 0.922308i | \(0.626301\pi\) | |||||||
\(224\) | 1024.14 | 0.305483 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1414.87 | −0.416441 | ||||||||
\(227\) | 2491.62 | 0.728523 | 0.364261 | − | 0.931297i | \(-0.381321\pi\) | ||||
0.364261 | + | 0.931297i | \(0.381321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1400.56 | 0.404154 | 0.202077 | − | 0.979370i | \(-0.435231\pi\) | ||||
0.202077 | + | 0.979370i | \(0.435231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2883.18 | 0.815906 | ||||||||
\(233\) | 3258.86 | 0.916289 | 0.458144 | − | 0.888878i | \(-0.348514\pi\) | ||||
0.458144 | + | 0.888878i | \(0.348514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4768.64 | 1.31530 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −419.892 | −0.114359 | ||||||||
\(239\) | 1660.80 | 0.449491 | 0.224746 | − | 0.974417i | \(-0.427845\pi\) | ||||
0.224746 | + | 0.974417i | \(0.427845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5966.20 | 1.59467 | 0.797337 | − | 0.603534i | \(-0.206241\pi\) | ||||
0.797337 | + | 0.603534i | \(0.206241\pi\) | |||||||
\(242\) | 1100.13 | 0.292229 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2491.18 | −0.653613 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 895.939 | 0.230799 | ||||||||
\(248\) | −1254.95 | −0.321329 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3051.45 | 0.767354 | 0.383677 | − | 0.923467i | \(-0.374658\pi\) | ||||
0.383677 | + | 0.923467i | \(0.374658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2099.74 | −0.521777 | ||||||||
\(254\) | 1598.53 | 0.394885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1775.31 | −0.433425 | ||||||||
\(257\) | −5559.16 | −1.34930 | −0.674652 | − | 0.738136i | \(-0.735706\pi\) | ||||
−0.674652 | + | 0.738136i | \(0.735706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1336.02 | 0.320527 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1699.46 | 0.400736 | ||||||||
\(263\) | 956.467 | 0.224252 | 0.112126 | − | 0.993694i | \(-0.464234\pi\) | ||||
0.112126 | + | 0.993694i | \(0.464234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 155.228 | 0.0357806 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6823.50 | 1.55527 | ||||||||
\(269\) | 4740.41 | 1.07445 | 0.537226 | − | 0.843438i | \(-0.319472\pi\) | ||||
0.537226 | + | 0.843438i | \(0.319472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3814.78 | −0.855097 | −0.427548 | − | 0.903992i | \(-0.640623\pi\) | ||||
−0.427548 | + | 0.903992i | \(0.640623\pi\) | |||||||
\(272\) | −1709.27 | −0.381028 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1196.81 | 0.263875 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1579.65 | 0.342642 | 0.171321 | − | 0.985215i | \(-0.445196\pi\) | ||||
0.171321 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(278\) | −34.1914 | −0.00737649 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7876.16 | −1.67207 | −0.836036 | − | 0.548674i | \(-0.815133\pi\) | ||||
−0.836036 | + | 0.548674i | \(0.815133\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 905.509 | 0.190201 | 0.0951006 | − | 0.995468i | \(-0.469683\pi\) | ||||
0.0951006 | + | 0.995468i | \(0.469683\pi\) | |||||||
\(284\) | −3275.18 | −0.684317 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1088.89 | 0.225131 | ||||||||
\(287\) | −2786.87 | −0.573184 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1410.11 | −0.287015 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5887.02 | 1.17983 | ||||||||
\(293\) | 7691.27 | 1.53355 | 0.766773 | − | 0.641919i | \(-0.221861\pi\) | ||||
0.766773 | + | 0.641919i | \(0.221861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4255.31 | −0.835590 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −270.767 | −0.0526346 | ||||||||
\(299\) | 4045.41 | 0.782449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 540.424 | 0.103487 | ||||||||
\(302\) | −3347.41 | −0.637821 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 631.893 | 0.119216 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8464.71 | 1.57364 | 0.786818 | − | 0.617185i | \(-0.211727\pi\) | ||||
0.786818 | + | 0.617185i | \(0.211727\pi\) | |||||||
\(308\) | −775.458 | −0.143460 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8388.01 | 1.52939 | 0.764695 | − | 0.644392i | \(-0.222889\pi\) | ||||
0.764695 | + | 0.644392i | \(0.222889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2384.69 | −0.430640 | −0.215320 | − | 0.976544i | \(-0.569080\pi\) | ||||
−0.215320 | + | 0.976544i | \(0.569080\pi\) | |||||||
\(314\) | 1197.36 | 0.215194 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5956.58 | −1.06039 | ||||||||
\(317\) | −3211.58 | −0.569023 | −0.284511 | − | 0.958673i | \(-0.591831\pi\) | ||||
−0.284511 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3393.01 | −0.595523 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 700.898 | 0.121303 | ||||||||
\(323\) | −1294.97 | −0.223078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 598.185 | 0.101627 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8876.35 | 1.49425 | ||||||||
\(329\) | −3111.83 | −0.521461 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7193.90 | 1.19460 | 0.597300 | − | 0.802018i | \(-0.296240\pi\) | ||||
0.597300 | + | 0.802018i | \(0.296240\pi\) | |||||||
\(332\) | 4561.87 | 0.754111 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3336.06 | −0.546530 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6913.84 | 1.11757 | 0.558785 | − | 0.829313i | \(-0.311268\pi\) | ||||
0.558785 | + | 0.829313i | \(0.311268\pi\) | |||||||
\(338\) | 650.948 | 0.104754 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1476.86 | 0.234536 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3707.50 | 0.583634 | ||||||||
\(344\) | −1721.28 | −0.269783 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −616.316 | −0.0957611 | ||||||||
\(347\) | 4009.84 | 0.620344 | 0.310172 | − | 0.950681i | \(-0.399613\pi\) | ||||
0.310172 | + | 0.950681i | \(0.399613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6884.76 | 1.05597 | 0.527984 | − | 0.849254i | \(-0.322948\pi\) | ||||
0.527984 | + | 0.849254i | \(0.322948\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3838.75 | 0.581267 | ||||||||
\(353\) | −7783.83 | −1.17363 | −0.586815 | − | 0.809721i | \(-0.699618\pi\) | ||||
−0.586815 | + | 0.809721i | \(0.699618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1759.96 | 0.262016 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4867.68 | 0.718617 | ||||||||
\(359\) | −8188.19 | −1.20378 | −0.601889 | − | 0.798580i | \(-0.705585\pi\) | ||||
−0.601889 | + | 0.798580i | \(0.705585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6380.27 | −0.930204 | ||||||||
\(362\) | 5469.62 | 0.794135 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1494.02 | 0.215131 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3688.79 | 0.524668 | 0.262334 | − | 0.964977i | \(-0.415508\pi\) | ||||
0.262334 | + | 0.964977i | \(0.415508\pi\) | |||||||
\(368\) | 2853.17 | 0.404162 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2890.87 | 0.404546 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4127.16 | −0.572912 | −0.286456 | − | 0.958093i | \(-0.592477\pi\) | ||||
−0.286456 | + | 0.958093i | \(0.592477\pi\) | |||||||
\(374\) | −1573.86 | −0.217600 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9911.36 | 1.35941 | ||||||||
\(377\) | 6537.05 | 0.893038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4145.52 | 0.561850 | 0.280925 | − | 0.959730i | \(-0.409359\pi\) | ||||
0.280925 | + | 0.959730i | \(0.409359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −410.825 | −0.0550253 | ||||||||
\(383\) | −9983.95 | −1.33200 | −0.666000 | − | 0.745952i | \(-0.731995\pi\) | ||||
−0.666000 | + | 0.745952i | \(0.731995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1181.93 | 0.155852 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9331.53 | 1.22097 | ||||||||
\(389\) | 7868.51 | 1.02558 | 0.512788 | − | 0.858515i | \(-0.328613\pi\) | ||||
0.512788 | + | 0.858515i | \(0.328613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5847.15 | −0.756274 | ||||||||
\(392\) | −5613.97 | −0.723337 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3450.32 | 0.441180 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8137.21 | −1.02870 | −0.514351 | − | 0.857580i | \(-0.671967\pi\) | ||||
−0.514351 | + | 0.857580i | \(0.671967\pi\) | |||||||
\(398\) | 1914.16 | 0.241075 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4204.86 | 0.523643 | 0.261822 | − | 0.965116i | \(-0.415677\pi\) | ||||
0.261822 | + | 0.965116i | \(0.415677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2845.36 | −0.351706 | ||||||||
\(404\) | 4351.34 | 0.535860 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1132.59 | 0.138447 | ||||||||
\(407\) | 5007.76 | 0.609891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8318.77 | −1.00571 | −0.502857 | − | 0.864370i | \(-0.667718\pi\) | ||||
−0.502857 | + | 0.864370i | \(0.667718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6881.54 | 0.822886 | ||||||||
\(413\) | 4202.24 | 0.500675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7395.82 | −0.871659 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 581.836 | 0.0680826 | ||||||||
\(419\) | −6938.90 | −0.809040 | −0.404520 | − | 0.914529i | \(-0.632561\pi\) | ||||
−0.404520 | + | 0.914529i | \(0.632561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9856.88 | 1.14108 | 0.570541 | − | 0.821269i | \(-0.306734\pi\) | ||||
0.570541 | + | 0.821269i | \(0.306734\pi\) | |||||||
\(422\) | 188.628 | 0.0217590 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9207.60 | −1.05462 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2195.29 | −0.248800 | ||||||||
\(428\) | 1348.47 | 0.152291 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3013.40 | −0.336775 | −0.168388 | − | 0.985721i | \(-0.553856\pi\) | ||||
−0.168388 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3902.19 | −0.433088 | −0.216544 | − | 0.976273i | \(-0.569479\pi\) | ||||
−0.216544 | + | 0.976273i | \(0.569479\pi\) | |||||||
\(434\) | −492.980 | −0.0545249 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2928.54 | 0.321678 | ||||||||
\(437\) | 2161.61 | 0.236622 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3169.12 | 0.344542 | 0.172271 | − | 0.985050i | \(-0.444890\pi\) | ||||
0.172271 | + | 0.985050i | \(0.444890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3032.24 | 0.326310 | ||||||||
\(443\) | −10732.6 | −1.15107 | −0.575534 | − | 0.817778i | \(-0.695206\pi\) | ||||
−0.575534 | + | 0.817778i | \(0.695206\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3220.36 | 0.341903 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.6800 | 0.00302456 | ||||||||
\(449\) | 294.508 | 0.0309547 | 0.0154774 | − | 0.999880i | \(-0.495073\pi\) | ||||
0.0154774 | + | 0.999880i | \(0.495073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10445.9 | −1.09064 | ||||||||
\(452\) | −7276.40 | −0.757197 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3117.46 | −0.322268 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5419.66 | −0.554751 | −0.277376 | − | 0.960762i | \(-0.589465\pi\) | ||||
−0.277376 | + | 0.960762i | \(0.589465\pi\) | |||||||
\(458\) | −1752.34 | −0.178781 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1002.66 | −0.101299 | −0.0506493 | − | 0.998717i | \(-0.516129\pi\) | ||||
−0.0506493 | + | 0.998717i | \(0.516129\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13615.3 | −1.36665 | −0.683323 | − | 0.730116i | \(-0.739466\pi\) | ||||
−0.683323 | + | 0.730116i | \(0.739466\pi\) | |||||||
\(464\) | 4610.49 | 0.461285 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4077.42 | −0.405328 | ||||||||
\(467\) | 1335.52 | 0.132336 | 0.0661678 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661678 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6013.04 | 0.592017 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13384.4 | −1.30522 | ||||||||
\(473\) | 2025.65 | 0.196912 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2159.42 | −0.207935 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2077.96 | −0.198836 | ||||||||
\(479\) | −13852.1 | −1.32134 | −0.660668 | − | 0.750678i | \(-0.729727\pi\) | ||||
−0.660668 | + | 0.750678i | \(0.729727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9648.07 | −0.914583 | ||||||||
\(482\) | −7464.77 | −0.705417 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5657.77 | 0.531346 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6113.26 | −0.568826 | −0.284413 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284413 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(488\) | 6992.12 | 0.648603 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16356.5 | −1.50338 | −0.751691 | − | 0.659515i | \(-0.770762\pi\) | ||||
−0.751691 | + | 0.659515i | \(0.770762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9448.51 | −0.863164 | ||||||||
\(494\) | −1120.98 | −0.102096 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2006.79 | −0.181669 | ||||||||
\(497\) | −2886.17 | −0.260487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9262.82 | −0.830983 | −0.415492 | − | 0.909597i | \(-0.636390\pi\) | ||||
−0.415492 | + | 0.909597i | \(0.636390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3817.90 | −0.339445 | ||||||||
\(503\) | 12498.5 | 1.10792 | 0.553959 | − | 0.832544i | \(-0.313116\pi\) | ||||
0.553959 | + | 0.832544i | \(0.313116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2627.15 | 0.230812 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8220.93 | 0.718002 | ||||||||
\(509\) | 7370.25 | 0.641809 | 0.320904 | − | 0.947112i | \(-0.396013\pi\) | ||||
0.320904 | + | 0.947112i | \(0.396013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5187.78 | 0.449107 | ||||||||
\(512\) | −9388.79 | −0.810410 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6955.49 | 0.596875 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11664.0 | −0.992224 | ||||||||
\(518\) | −1671.60 | −0.141787 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5426.50 | −0.456313 | −0.228157 | − | 0.973624i | \(-0.573270\pi\) | ||||
−0.228157 | + | 0.973624i | \(0.573270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19681.7 | −1.64555 | −0.822773 | − | 0.568371i | \(-0.807574\pi\) | ||||
−0.822773 | + | 0.568371i | \(0.807574\pi\) | |||||||
\(524\) | 8739.97 | 0.728640 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1196.71 | −0.0991996 | ||||||||
\(527\) | 4112.62 | 0.339941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2406.73 | −0.197808 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 798.308 | 0.0650583 | ||||||||
\(533\) | 20125.4 | 1.63551 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19151.9 | −1.54335 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5931.09 | −0.475293 | ||||||||
\(539\) | 6606.67 | 0.527958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16726.1 | 1.32923 | 0.664613 | − | 0.747188i | \(-0.268596\pi\) | ||||
0.664613 | + | 0.747188i | \(0.268596\pi\) | |||||||
\(542\) | 4772.96 | 0.378259 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10689.8 | 0.842500 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19292.6 | −1.50803 | −0.754014 | − | 0.656859i | \(-0.771885\pi\) | ||||
−0.754014 | + | 0.656859i | \(0.771885\pi\) | |||||||
\(548\) | 6154.94 | 0.479792 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3492.99 | 0.270066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5249.08 | −0.403641 | ||||||||
\(554\) | −1976.42 | −0.151570 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −175.840 | −0.0134123 | ||||||||
\(557\) | −7161.62 | −0.544789 | −0.272395 | − | 0.962186i | \(-0.587816\pi\) | ||||
−0.272395 | + | 0.962186i | \(0.587816\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3902.66 | −0.295286 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9854.47 | 0.739655 | ||||||||
\(563\) | −17096.8 | −1.27983 | −0.639914 | − | 0.768446i | \(-0.721030\pi\) | ||||
−0.639914 | + | 0.768446i | \(0.721030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1132.95 | −0.0841369 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9192.60 | 0.679072 | ||||||||
\(569\) | −11508.9 | −0.847942 | −0.423971 | − | 0.905676i | \(-0.639364\pi\) | ||||
−0.423971 | + | 0.905676i | \(0.639364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10695.3 | 0.783863 | 0.391931 | − | 0.919994i | \(-0.371807\pi\) | ||||
0.391931 | + | 0.919994i | \(0.371807\pi\) | |||||||
\(572\) | 5599.96 | 0.409347 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3486.87 | 0.253553 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23047.9 | −1.66291 | −0.831453 | − | 0.555595i | \(-0.812491\pi\) | ||||
−0.831453 | + | 0.555595i | \(0.812491\pi\) | |||||||
\(578\) | 1764.29 | 0.126963 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4020.03 | 0.287055 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10835.8 | 0.769762 | ||||||||
\(584\) | −16523.4 | −1.17079 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9623.14 | −0.678376 | ||||||||
\(587\) | −12449.5 | −0.875378 | −0.437689 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437689 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1520.38 | −0.106360 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6804.65 | −0.472414 | ||||||||
\(593\) | −18331.7 | −1.26946 | −0.634732 | − | 0.772732i | \(-0.718890\pi\) | ||||
−0.634732 | + | 0.772732i | \(0.718890\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1392.50 | −0.0957032 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5061.53 | −0.346122 | ||||||||
\(599\) | 23905.9 | 1.63067 | 0.815333 | − | 0.578992i | \(-0.196554\pi\) | ||||
0.815333 | + | 0.578992i | \(0.196554\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16524.6 | −1.12155 | −0.560777 | − | 0.827967i | \(-0.689498\pi\) | ||||
−0.560777 | + | 0.827967i | \(0.689498\pi\) | |||||||
\(602\) | −676.165 | −0.0457782 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17215.1 | −1.15972 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2610.92 | −0.174587 | −0.0872933 | − | 0.996183i | \(-0.527822\pi\) | ||||
−0.0872933 | + | 0.996183i | \(0.527822\pi\) | |||||||
\(608\) | −3951.86 | −0.263600 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22472.0 | 1.48792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5036.27 | −0.331832 | −0.165916 | − | 0.986140i | \(-0.553058\pi\) | ||||
−0.165916 | + | 0.986140i | \(0.553058\pi\) | |||||||
\(614\) | −10590.8 | −0.696110 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2176.52 | 0.142361 | ||||||||
\(617\) | 15805.7 | 1.03130 | 0.515650 | − | 0.856800i | \(-0.327551\pi\) | ||||
0.515650 | + | 0.856800i | \(0.327551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5929.52 | −0.385020 | −0.192510 | − | 0.981295i | \(-0.561663\pi\) | ||||
−0.192510 | + | 0.981295i | \(0.561663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10494.9 | −0.676538 | ||||||||
\(623\) | 1550.92 | 0.0997370 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2983.66 | 0.190497 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6157.79 | 0.391278 | ||||||||
\(629\) | 13945.1 | 0.883988 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12427.8 | 0.784060 | 0.392030 | − | 0.919952i | \(-0.371773\pi\) | ||||
0.392030 | + | 0.919952i | \(0.371773\pi\) | |||||||
\(632\) | 16718.6 | 1.05226 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4018.25 | 0.251712 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12728.6 | −0.791718 | ||||||||
\(638\) | 4245.25 | 0.263434 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28418.8 | 1.75113 | 0.875566 | − | 0.483098i | \(-0.160489\pi\) | ||||
0.875566 | + | 0.483098i | \(0.160489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13882.4 | 0.851431 | 0.425715 | − | 0.904857i | \(-0.360022\pi\) | ||||
0.425715 | + | 0.904857i | \(0.360022\pi\) | |||||||
\(644\) | 3604.58 | 0.220559 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1620.24 | 0.0986802 | ||||||||
\(647\) | 13037.5 | 0.792207 | 0.396104 | − | 0.918206i | \(-0.370362\pi\) | ||||
0.396104 | + | 0.918206i | \(0.370362\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15751.1 | 0.952672 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3076.35 | 0.184784 | ||||||||
\(653\) | −4574.74 | −0.274155 | −0.137078 | − | 0.990560i | \(-0.543771\pi\) | ||||
−0.137078 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14194.1 | 0.844798 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3893.45 | 0.230672 | ||||||||
\(659\) | 7182.71 | 0.424581 | 0.212290 | − | 0.977207i | \(-0.431908\pi\) | ||||
0.212290 | + | 0.977207i | \(0.431908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1611.10 | 0.0948026 | 0.0474013 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474013 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(662\) | −9000.84 | −0.528441 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12804.0 | −0.748332 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15771.8 | 0.915571 | ||||||||
\(668\) | −17156.7 | −0.993731 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8228.52 | −0.473410 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17721.1 | −1.01501 | −0.507503 | − | 0.861650i | \(-0.669431\pi\) | ||||
−0.507503 | + | 0.861650i | \(0.669431\pi\) | |||||||
\(674\) | −8650.44 | −0.494365 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3347.70 | 0.190470 | ||||||||
\(677\) | −12774.3 | −0.725196 | −0.362598 | − | 0.931946i | \(-0.618110\pi\) | ||||
−0.362598 | + | 0.931946i | \(0.618110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8223.17 | 0.464766 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1847.82 | −0.103749 | ||||||||
\(683\) | 7065.27 | 0.395820 | 0.197910 | − | 0.980220i | \(-0.436585\pi\) | ||||
0.197910 | + | 0.980220i | \(0.436585\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4638.74 | −0.258175 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2752.49 | −0.152526 | ||||||||
\(689\) | −20876.4 | −1.15432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26270.4 | −1.44627 | −0.723136 | − | 0.690706i | \(-0.757300\pi\) | ||||
−0.723136 | + | 0.690706i | \(0.757300\pi\) | |||||||
\(692\) | −3169.59 | −0.174118 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5017.01 | −0.274414 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29088.8 | −1.58080 | ||||||||
\(698\) | −8614.05 | −0.467116 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32274.9 | −1.73895 | −0.869476 | − | 0.493975i | \(-0.835544\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5155.32 | −0.276581 | ||||||||
\(704\) | 107.500 | 0.00575507 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9738.94 | 0.519164 | ||||||||
\(707\) | 3834.51 | 0.203977 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13697.1 | −0.725539 | −0.362770 | − | 0.931879i | \(-0.618169\pi\) | ||||
−0.362770 | + | 0.931879i | \(0.618169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4939.76 | −0.260007 | ||||||||
\(713\) | −6864.94 | −0.360580 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25033.5 | 1.30663 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10244.9 | 0.532501 | ||||||||
\(719\) | −6826.36 | −0.354076 | −0.177038 | − | 0.984204i | \(-0.556651\pi\) | ||||
−0.177038 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6064.18 | 0.313234 | ||||||||
\(722\) | 7982.84 | 0.411483 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28129.2 | 1.44394 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22413.2 | 1.14341 | 0.571706 | − | 0.820458i | \(-0.306282\pi\) | ||||
0.571706 | + | 0.820458i | \(0.306282\pi\) | |||||||
\(728\) | −4193.33 | −0.213482 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5640.83 | 0.285408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −167.208 | −0.00842562 | −0.00421281 | − | 0.999991i | \(-0.501341\pi\) | ||||
−0.00421281 | + | 0.999991i | \(0.501341\pi\) | |||||||
\(734\) | −4615.33 | −0.232091 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17843.7 | −0.893653 | ||||||||
\(737\) | 22538.4 | 1.12648 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27695.8 | 1.37863 | 0.689313 | − | 0.724463i | \(-0.257912\pi\) | ||||
0.689313 | + | 0.724463i | \(0.257912\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3616.99 | −0.178954 | ||||||||
\(743\) | 35379.4 | 1.74689 | 0.873447 | − | 0.486919i | \(-0.161879\pi\) | ||||
0.873447 | + | 0.486919i | \(0.161879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5163.81 | 0.253432 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8094.07 | −0.395653 | ||||||||
\(749\) | 1188.30 | 0.0579700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5408.34 | −0.262787 | −0.131394 | − | 0.991330i | \(-0.541945\pi\) | ||||
−0.131394 | + | 0.991330i | \(0.541945\pi\) | |||||||
\(752\) | 15849.2 | 0.768566 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8179.00 | −0.395042 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 701.285 | 0.0336706 | 0.0168353 | − | 0.999858i | \(-0.494641\pi\) | ||||
0.0168353 | + | 0.999858i | \(0.494641\pi\) | |||||||
\(758\) | −5186.78 | −0.248539 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23271.0 | 1.10850 | 0.554252 | − | 0.832349i | \(-0.313004\pi\) | ||||
0.554252 | + | 0.832349i | \(0.313004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2580.70 | 0.122448 | ||||||||
\(764\) | −2112.79 | −0.100050 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12491.7 | 0.589221 | ||||||||
\(767\) | −30346.4 | −1.42861 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10456.3 | −0.490332 | −0.245166 | − | 0.969481i | \(-0.578842\pi\) | ||||
−0.245166 | + | 0.969481i | \(0.578842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6078.44 | 0.283378 | ||||||||
\(773\) | −18324.8 | −0.852650 | −0.426325 | − | 0.904570i | \(-0.640192\pi\) | ||||
−0.426325 | + | 0.904570i | \(0.640192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26191.3 | −1.21161 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9844.89 | −0.453672 | ||||||||
\(779\) | 10753.7 | 0.494598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10818.1 | −0.495649 | ||||||||
\(782\) | 7315.82 | 0.334544 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8977.28 | −0.408950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14839.7 | 0.672147 | 0.336073 | − | 0.941836i | \(-0.390901\pi\) | ||||
0.336073 | + | 0.941836i | \(0.390901\pi\) | |||||||
\(788\) | 17744.3 | 0.802178 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6412.14 | −0.288229 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15853.3 | 0.709919 | ||||||||
\(794\) | 10181.1 | 0.455055 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9844.13 | 0.438337 | ||||||||
\(797\) | −38086.1 | −1.69269 | −0.846347 | − | 0.532631i | \(-0.821203\pi\) | ||||
−0.846347 | + | 0.532631i | \(0.821203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32480.6 | −1.43815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5261.03 | −0.231638 | ||||||||
\(803\) | 19445.2 | 0.854551 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3560.05 | 0.155580 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12213.1 | −0.531753 | ||||||||
\(809\) | 37170.3 | 1.61537 | 0.807686 | − | 0.589612i | \(-0.200719\pi\) | ||||
0.807686 | + | 0.589612i | \(0.200719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37402.9 | 1.61947 | 0.809736 | − | 0.586794i | \(-0.199610\pi\) | ||||
0.809736 | + | 0.586794i | \(0.199610\pi\) | |||||||
\(812\) | 5824.70 | 0.251733 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6265.60 | −0.269790 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2085.34 | −0.0892983 | ||||||||
\(818\) | 10408.3 | 0.444885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15002.4 | −0.637743 | −0.318872 | − | 0.947798i | \(-0.603304\pi\) | ||||
−0.318872 | + | 0.947798i | \(0.603304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11648.5 | −0.493366 | −0.246683 | − | 0.969096i | \(-0.579341\pi\) | ||||
−0.246683 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(824\) | −19314.8 | −0.816579 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5257.74 | −0.221477 | ||||||||
\(827\) | −46483.9 | −1.95454 | −0.977269 | − | 0.212003i | \(-0.932001\pi\) | ||||
−0.977269 | + | 0.212003i | \(0.932001\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1565.64 | 0.0655933 | 0.0327967 | − | 0.999462i | \(-0.489559\pi\) | ||||
0.0327967 | + | 0.999462i | \(0.489559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −207.113 | −0.00863021 | ||||||||
\(833\) | 18397.6 | 0.765233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2992.27 | 0.123791 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8681.79 | 0.357885 | ||||||||
\(839\) | 32926.2 | 1.35487 | 0.677436 | − | 0.735582i | \(-0.263091\pi\) | ||||
0.677436 | + | 0.735582i | \(0.263091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1096.90 | 0.0449754 | ||||||||
\(842\) | −12332.7 | −0.504766 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 970.078 | 0.0395633 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4985.77 | 0.202259 | ||||||||
\(848\) | −14723.8 | −0.596248 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23277.7 | −0.937660 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14963.0 | −0.600613 | −0.300306 | − | 0.953843i | \(-0.597089\pi\) | ||||
−0.300306 | + | 0.953843i | \(0.597089\pi\) | |||||||
\(854\) | 2746.70 | 0.110059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3784.81 | −0.151124 | ||||||||
\(857\) | 21868.7 | 0.871668 | 0.435834 | − | 0.900027i | \(-0.356454\pi\) | ||||
0.435834 | + | 0.900027i | \(0.356454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13542.5 | 0.537909 | 0.268954 | − | 0.963153i | \(-0.413322\pi\) | ||||
0.268954 | + | 0.963153i | \(0.413322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3770.29 | 0.148975 | ||||||||
\(863\) | −2080.25 | −0.0820539 | −0.0410269 | − | 0.999158i | \(-0.513063\pi\) | ||||
−0.0410269 | + | 0.999158i | \(0.513063\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4882.33 | 0.191580 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2535.30 | −0.0991401 | ||||||||
\(869\) | −19674.9 | −0.768039 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43423.1 | −1.68925 | ||||||||
\(872\) | −8219.67 | −0.319212 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2704.56 | −0.104672 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28076.9 | 1.08106 | 0.540530 | − | 0.841325i | \(-0.318224\pi\) | ||||
0.540530 | + | 0.841325i | \(0.318224\pi\) | |||||||
\(878\) | −3965.13 | −0.152411 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2105.32 | 0.0805110 | 0.0402555 | − | 0.999189i | \(-0.487183\pi\) | ||||
0.0402555 | + | 0.999189i | \(0.487183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23829.7 | 0.908190 | 0.454095 | − | 0.890953i | \(-0.349963\pi\) | ||||
0.454095 | + | 0.890953i | \(0.349963\pi\) | |||||||
\(884\) | 15594.2 | 0.593315 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13428.4 | 0.509184 | ||||||||
\(887\) | 12634.7 | 0.478277 | 0.239139 | − | 0.970985i | \(-0.423135\pi\) | ||||
0.239139 | + | 0.970985i | \(0.423135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7244.48 | 0.273310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16561.7 | 0.621667 | ||||||||
\(893\) | 12007.6 | 0.449967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8229.01 | −0.306821 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −368.481 | −0.0136931 | ||||||||
\(899\) | −11093.2 | −0.411544 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30174.3 | 1.11571 | ||||||||
\(902\) | 13069.7 | 0.482454 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20423.0 | 0.751393 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31942.7 | 1.16939 | 0.584697 | − | 0.811252i | \(-0.301213\pi\) | ||||
0.584697 | + | 0.811252i | \(0.301213\pi\) | |||||||
\(908\) | −16032.5 | −0.585965 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22605.6 | −0.822128 | −0.411064 | − | 0.911607i | \(-0.634843\pi\) | ||||
−0.411064 | + | 0.911607i | \(0.634843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15068.1 | 0.546201 | ||||||||
\(914\) | 6780.96 | 0.245398 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9011.95 | −0.325069 | ||||||||
\(917\) | 7701.87 | 0.277359 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45168.0 | 1.62128 | 0.810638 | − | 0.585547i | \(-0.199120\pi\) | ||||
0.810638 | + | 0.585547i | \(0.199120\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1254.51 | 0.0448102 | ||||||||
\(923\) | 20842.4 | 0.743268 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17035.2 | 0.604547 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28834.0 | −1.01996 | ||||||||
\(929\) | −32891.6 | −1.16161 | −0.580806 | − | 0.814042i | \(-0.697262\pi\) | ||||
−0.580806 | + | 0.814042i | \(0.697262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6801.34 | −0.239425 | ||||||||
\(932\) | −20969.3 | −0.736989 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1670.98 | −0.0585397 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34702.8 | 1.20992 | 0.604958 | − | 0.796257i | \(-0.293190\pi\) | ||||
0.604958 | + | 0.796257i | \(0.293190\pi\) | |||||||
\(938\) | −7523.37 | −0.261884 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27172.9 | 0.941351 | 0.470675 | − | 0.882306i | \(-0.344010\pi\) | ||||
0.470675 | + | 0.882306i | \(0.344010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48556.0 | 1.67678 | ||||||||
\(944\) | −21402.9 | −0.737929 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2534.44 | −0.0871056 | ||||||||
\(947\) | 39846.1 | 1.36729 | 0.683645 | − | 0.729815i | \(-0.260394\pi\) | ||||
0.683645 | + | 0.729815i | \(0.260394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37463.5 | −1.28147 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6060.95 | 0.206341 | ||||||||
\(953\) | −45983.5 | −1.56301 | −0.781507 | − | 0.623896i | \(-0.785549\pi\) | ||||
−0.781507 | + | 0.623896i | \(0.785549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10686.5 | −0.361534 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17331.5 | 0.584503 | ||||||||
\(959\) | 5423.88 | 0.182634 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24962.5 | −0.837921 | ||||||||
\(962\) | 12071.4 | 0.404573 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −38389.8 | −1.28263 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52188.1 | 1.73553 | 0.867765 | − | 0.496976i | \(-0.165556\pi\) | ||||
0.867765 | + | 0.496976i | \(0.165556\pi\) | |||||||
\(968\) | −15880.0 | −0.527274 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2777.37 | −0.0917921 | −0.0458961 | − | 0.998946i | \(-0.514614\pi\) | ||||
−0.0458961 | + | 0.998946i | \(0.514614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −154.954 | −0.00510545 | ||||||||
\(974\) | 7648.77 | 0.251625 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11181.1 | 0.366698 | ||||||||
\(977\) | 33242.3 | 1.08855 | 0.544275 | − | 0.838907i | \(-0.316805\pi\) | ||||
0.544275 | + | 0.838907i | \(0.316805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5813.24 | 0.189777 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20464.9 | 0.665033 | ||||||||
\(983\) | −18130.3 | −0.588268 | −0.294134 | − | 0.955764i | \(-0.595031\pi\) | ||||
−0.294134 | + | 0.955764i | \(0.595031\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11821.8 | 0.381827 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5764.97 | −0.185636 | ||||||||
\(989\) | −9415.87 | −0.302737 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30597.2 | 0.980778 | 0.490389 | − | 0.871504i | \(-0.336855\pi\) | ||||
0.490389 | + | 0.871504i | \(0.336855\pi\) | |||||||
\(992\) | 12550.5 | 0.401692 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3611.10 | 0.115229 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23839.4 | −0.757273 | −0.378637 | − | 0.925545i | \(-0.623607\pi\) | ||||
−0.378637 | + | 0.925545i | \(0.623607\pi\) | |||||||
\(998\) | 11589.4 | 0.367592 | ||||||||
\(999\) | 0 | 0 |
(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 | 675.4.a.bb.1.3 | 6 | ||
3.2 | odd | 2 | inner | 675.4.a.bb.1.4 | 6 | ||
5.2 | odd | 4 | 135.4.b.c.109.5 | ✓ | 12 | ||
5.3 | odd | 4 | 135.4.b.c.109.7 | yes | 12 | ||
5.4 | even | 2 | 675.4.a.bc.1.4 | 6 | |||
15.2 | even | 4 | 135.4.b.c.109.8 | yes | 12 | ||
15.8 | even | 4 | 135.4.b.c.109.6 | yes | 12 | ||
15.14 | odd | 2 | 675.4.a.bc.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.b.c.109.5 | ✓ | 12 | 5.2 | odd | 4 | ||
135.4.b.c.109.6 | yes | 12 | 15.8 | even | 4 | ||
135.4.b.c.109.7 | yes | 12 | 5.3 | odd | 4 | ||
135.4.b.c.109.8 | yes | 12 | 15.2 | even | 4 | ||
675.4.a.bb.1.3 | 6 | 1.1 | even | 1 | trivial | ||
675.4.a.bb.1.4 | 6 | 3.2 | odd | 2 | inner | ||
675.4.a.bc.1.3 | 6 | 15.14 | odd | 2 | |||
675.4.a.bc.1.4 | 6 | 5.4 | even | 2 |