Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3030748.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 21x^{2} + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.42371\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.42371 | −1.56402 | −0.782008 | − | 0.623268i | \(-0.785805\pi\) | ||||
−0.782008 | + | 0.623268i | \(0.785805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.5692 | 1.44615 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −15.7890 | −0.697782 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.3775 | −0.640779 | −0.320390 | − | 0.947286i | \(-0.603814\pi\) | ||||
−0.320390 | + | 0.947286i | \(0.603814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56918 | −0.0761471 | −0.0380735 | − | 0.999275i | \(-0.512122\pi\) | ||||
−0.0380735 | + | 0.999275i | \(0.512122\pi\) | |||||||
\(14\) | 30.9659 | 0.591143 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −22.7075 | −0.354805 | ||||||||
\(17\) | 57.5082 | 0.820458 | 0.410229 | − | 0.911983i | \(-0.365449\pi\) | ||||
0.410229 | + | 0.911983i | \(0.365449\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −51.1384 | −0.617471 | −0.308735 | − | 0.951148i | \(-0.599906\pi\) | ||||
−0.308735 | + | 0.951148i | \(0.599906\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 103.415 | 1.00219 | ||||||||
\(23\) | 65.6390 | 0.595073 | 0.297537 | − | 0.954710i | \(-0.403835\pi\) | ||||
0.297537 | + | 0.954710i | \(0.403835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.7890 | 0.119095 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −80.9843 | −0.546592 | ||||||||
\(29\) | 41.6147 | 0.266471 | 0.133235 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133235 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −167.538 | −0.970666 | −0.485333 | − | 0.874329i | \(-0.661302\pi\) | ||||
−0.485333 | + | 0.874329i | \(0.661302\pi\) | |||||||
\(32\) | 226.763 | 1.25270 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −254.399 | −1.28321 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 224.538 | 0.997669 | 0.498835 | − | 0.866697i | \(-0.333761\pi\) | ||||
0.498835 | + | 0.866697i | \(0.333761\pi\) | |||||||
\(38\) | 226.221 | 0.965734 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 196.688 | 0.749208 | 0.374604 | − | 0.927185i | \(-0.377779\pi\) | ||||
0.374604 | + | 0.927185i | \(0.377779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −58.9685 | −0.209131 | −0.104565 | − | 0.994518i | \(-0.533345\pi\) | ||||
−0.104565 | + | 0.994518i | \(0.533345\pi\) | |||||||
\(44\) | −270.458 | −0.926661 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −290.368 | −0.930704 | ||||||||
\(47\) | 41.9282 | 0.130125 | 0.0650623 | − | 0.997881i | \(-0.479275\pi\) | ||||
0.0650623 | + | 0.997881i | \(0.479275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −41.2925 | −0.110120 | ||||||||
\(53\) | −33.3445 | −0.0864192 | −0.0432096 | − | 0.999066i | \(-0.513758\pi\) | ||||
−0.0432096 | + | 0.999066i | \(0.513758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 110.523 | 0.263737 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −184.091 | −0.416765 | ||||||||
\(59\) | −229.212 | −0.505777 | −0.252888 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252888 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −700.613 | −1.47056 | −0.735281 | − | 0.677762i | \(-0.762950\pi\) | ||||
−0.735281 | + | 0.677762i | \(0.762950\pi\) | |||||||
\(62\) | 741.138 | 1.51814 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −821.475 | −1.60444 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 453.890 | 0.827634 | 0.413817 | − | 0.910360i | \(-0.364195\pi\) | ||||
0.413817 | + | 0.910360i | \(0.364195\pi\) | |||||||
\(68\) | 665.322 | 1.18650 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 930.571 | 1.55547 | 0.777735 | − | 0.628592i | \(-0.216368\pi\) | ||||
0.777735 | + | 0.628592i | \(0.216368\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −370.182 | −0.593514 | −0.296757 | − | 0.954953i | \(-0.595905\pi\) | ||||
−0.296757 | + | 0.954953i | \(0.595905\pi\) | |||||||
\(74\) | −993.289 | −1.56037 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −591.629 | −0.892954 | ||||||||
\(77\) | 163.642 | 0.242192 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54.6007 | −0.0777602 | −0.0388801 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388801 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −870.091 | −1.17177 | ||||||||
\(83\) | −430.045 | −0.568718 | −0.284359 | − | 0.958718i | \(-0.591781\pi\) | ||||
−0.284359 | + | 0.958718i | \(0.591781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 260.859 | 0.327084 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 369.107 | 0.447124 | ||||||||
\(89\) | −737.202 | −0.878014 | −0.439007 | − | 0.898484i | \(-0.644670\pi\) | ||||
−0.439007 | + | 0.898484i | \(0.644670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.9843 | 0.0287809 | ||||||||
\(92\) | 759.390 | 0.860564 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −185.478 | −0.203517 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −150.371 | −0.157401 | −0.0787004 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0787004 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(98\) | −216.762 | −0.223431 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 134.423 | 0.132432 | 0.0662158 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662158 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 232.494 | 0.222411 | 0.111205 | − | 0.993797i | \(-0.464529\pi\) | ||||
0.111205 | + | 0.993797i | \(0.464529\pi\) | |||||||
\(104\) | 56.3538 | 0.0531340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 147.506 | 0.135161 | ||||||||
\(107\) | 1539.38 | 1.39082 | 0.695409 | − | 0.718614i | \(-0.255223\pi\) | ||||
0.695409 | + | 0.718614i | \(0.255223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −503.462 | −0.442412 | −0.221206 | − | 0.975227i | \(-0.570999\pi\) | ||||
−0.221206 | + | 0.975227i | \(0.570999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 158.953 | 0.134104 | ||||||||
\(113\) | 267.084 | 0.222347 | 0.111173 | − | 0.993801i | \(-0.464539\pi\) | ||||
0.111173 | + | 0.993801i | \(0.464539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 481.448 | 0.385356 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1013.97 | 0.791043 | ||||||||
\(119\) | −402.557 | −0.310104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −784.494 | −0.589402 | ||||||||
\(122\) | 3099.31 | 2.29998 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1938.27 | −1.40373 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 296.412 | 0.207105 | 0.103552 | − | 0.994624i | \(-0.466979\pi\) | ||||
0.103552 | + | 0.994624i | \(0.466979\pi\) | |||||||
\(128\) | 1819.86 | 1.25667 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2768.20 | 1.84625 | 0.923123 | − | 0.384504i | \(-0.125627\pi\) | ||||
0.923123 | + | 0.384504i | \(0.125627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 357.969 | 0.233382 | ||||||||
\(134\) | −2007.88 | −1.29443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −907.997 | −0.572500 | ||||||||
\(137\) | 813.962 | 0.507602 | 0.253801 | − | 0.967256i | \(-0.418319\pi\) | ||||
0.253801 | + | 0.967256i | \(0.418319\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 99.1631 | 0.0605101 | 0.0302550 | − | 0.999542i | \(-0.490368\pi\) | ||||
0.0302550 | + | 0.999542i | \(0.490368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4116.57 | −2.43278 | ||||||||
\(143\) | 83.4384 | 0.0487935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1637.58 | 0.928266 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2597.72 | 1.44278 | ||||||||
\(149\) | −1427.06 | −0.784624 | −0.392312 | − | 0.919832i | \(-0.628325\pi\) | ||||
−0.392312 | + | 0.919832i | \(0.628325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1719.54 | 0.926718 | 0.463359 | − | 0.886171i | \(-0.346644\pi\) | ||||
0.463359 | + | 0.886171i | \(0.346644\pi\) | |||||||
\(152\) | 807.423 | 0.430860 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −723.906 | −0.378792 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3270.08 | −1.66230 | −0.831149 | − | 0.556049i | \(-0.812317\pi\) | ||||
−0.831149 | + | 0.556049i | \(0.812317\pi\) | |||||||
\(158\) | 241.537 | 0.121618 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −459.473 | −0.224917 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 891.324 | 0.428306 | 0.214153 | − | 0.976800i | \(-0.431301\pi\) | ||||
0.214153 | + | 0.976800i | \(0.431301\pi\) | |||||||
\(164\) | 2275.52 | 1.08347 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1902.39 | 0.889484 | ||||||||
\(167\) | 1598.41 | 0.740649 | 0.370324 | − | 0.928902i | \(-0.379246\pi\) | ||||
0.370324 | + | 0.928902i | \(0.379246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2184.26 | −0.994202 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −682.217 | −0.302434 | ||||||||
\(173\) | 2492.49 | 1.09538 | 0.547690 | − | 0.836681i | \(-0.315507\pi\) | ||||
0.547690 | + | 0.836681i | \(0.315507\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 530.845 | 0.227352 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3261.16 | 1.37323 | ||||||||
\(179\) | −1410.34 | −0.588904 | −0.294452 | − | 0.955666i | \(-0.595137\pi\) | ||||
−0.294452 | + | 0.955666i | \(0.595137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2039.16 | 0.837399 | 0.418700 | − | 0.908125i | \(-0.362486\pi\) | ||||
0.418700 | + | 0.908125i | \(0.362486\pi\) | |||||||
\(182\) | −110.523 | −0.0450138 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1036.37 | −0.415231 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1344.40 | −0.525732 | ||||||||
\(188\) | 485.075 | 0.188179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2576.79 | −0.976178 | −0.488089 | − | 0.872794i | \(-0.662306\pi\) | ||||
−0.488089 | + | 0.872794i | \(0.662306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2873.61 | 1.07175 | 0.535874 | − | 0.844298i | \(-0.319982\pi\) | ||||
0.535874 | + | 0.844298i | \(0.319982\pi\) | |||||||
\(194\) | 665.198 | 0.246178 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 566.890 | 0.206592 | ||||||||
\(197\) | −1489.82 | −0.538810 | −0.269405 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269405 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1311.18 | 0.467071 | 0.233536 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233536 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −594.648 | −0.207125 | ||||||||
\(203\) | −291.303 | −0.100716 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1028.48 | −0.347854 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 81.0472 | 0.0270174 | ||||||||
\(209\) | 1195.49 | 0.395662 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2671.37 | 0.871585 | 0.435793 | − | 0.900047i | \(-0.356468\pi\) | ||||
0.435793 | + | 0.900047i | \(0.356468\pi\) | |||||||
\(212\) | −385.768 | −0.124975 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6809.77 | −2.17526 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1172.76 | 0.366877 | ||||||||
\(218\) | 2227.17 | 0.691940 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −205.257 | −0.0624755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3321.87 | 0.997529 | 0.498764 | − | 0.866738i | \(-0.333787\pi\) | ||||
0.498764 | + | 0.866738i | \(0.333787\pi\) | |||||||
\(224\) | −1587.34 | −0.473477 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1181.50 | −0.347754 | ||||||||
\(227\) | −1756.95 | −0.513712 | −0.256856 | − | 0.966450i | \(-0.582687\pi\) | ||||
−0.256856 | + | 0.966450i | \(0.582687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2654.65 | 0.766045 | 0.383023 | − | 0.923739i | \(-0.374883\pi\) | ||||
0.383023 | + | 0.923739i | \(0.374883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −657.054 | −0.185938 | ||||||||
\(233\) | −4379.70 | −1.23143 | −0.615716 | − | 0.787968i | \(-0.711133\pi\) | ||||
−0.615716 | + | 0.787968i | \(0.711133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2651.79 | −0.731427 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1780.80 | 0.485008 | ||||||||
\(239\) | −932.890 | −0.252484 | −0.126242 | − | 0.991999i | \(-0.540292\pi\) | ||||
−0.126242 | + | 0.991999i | \(0.540292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6451.43 | −1.72437 | −0.862184 | − | 0.506595i | \(-0.830904\pi\) | ||||
−0.862184 | + | 0.506595i | \(0.830904\pi\) | |||||||
\(242\) | 3470.37 | 0.921834 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8105.52 | −2.12665 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 182.522 | 0.0470186 | ||||||||
\(248\) | 2645.25 | 0.677313 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5085.23 | 1.27879 | 0.639396 | − | 0.768878i | \(-0.279185\pi\) | ||||
0.639396 | + | 0.768878i | \(0.279185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1534.47 | −0.381311 | ||||||||
\(254\) | −1311.24 | −0.323915 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1478.71 | −0.361013 | ||||||||
\(257\) | −4817.11 | −1.16919 | −0.584597 | − | 0.811324i | \(-0.698747\pi\) | ||||
−0.584597 | + | 0.811324i | \(0.698747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1571.76 | −0.377084 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12245.7 | −2.88756 | ||||||||
\(263\) | −8001.67 | −1.87606 | −0.938030 | − | 0.346553i | \(-0.887352\pi\) | ||||
−0.938030 | + | 0.346553i | \(0.887352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1583.55 | −0.365013 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5251.13 | 1.19688 | ||||||||
\(269\) | −3477.43 | −0.788188 | −0.394094 | − | 0.919070i | \(-0.628942\pi\) | ||||
−0.394094 | + | 0.919070i | \(0.628942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4589.09 | −1.02866 | −0.514331 | − | 0.857592i | \(-0.671960\pi\) | ||||
−0.514331 | + | 0.857592i | \(0.671960\pi\) | |||||||
\(272\) | −1305.87 | −0.291103 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3600.73 | −0.793898 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1920.87 | 0.416657 | 0.208329 | − | 0.978059i | \(-0.433198\pi\) | ||||
0.208329 | + | 0.978059i | \(0.433198\pi\) | |||||||
\(278\) | −438.668 | −0.0946388 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −392.063 | −0.0832331 | −0.0416166 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416166 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7701.96 | −1.61779 | −0.808894 | − | 0.587955i | \(-0.799933\pi\) | ||||
−0.808894 | + | 0.587955i | \(0.799933\pi\) | |||||||
\(284\) | 10765.9 | 2.24944 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −369.107 | −0.0763138 | ||||||||
\(287\) | −1376.82 | −0.283174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1605.81 | −0.326849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4282.70 | −0.858309 | ||||||||
\(293\) | −6657.73 | −1.32747 | −0.663735 | − | 0.747968i | \(-0.731030\pi\) | ||||
−0.663735 | + | 0.747968i | \(0.731030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3545.23 | −0.696155 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6312.88 | 1.22716 | ||||||||
\(299\) | −234.277 | −0.0453131 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 412.780 | 0.0790439 | ||||||||
\(302\) | −7606.75 | −1.44940 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1161.23 | 0.219082 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5082.53 | 0.944870 | 0.472435 | − | 0.881366i | \(-0.343375\pi\) | ||||
0.472435 | + | 0.881366i | \(0.343375\pi\) | |||||||
\(308\) | 1893.21 | 0.350245 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2627.30 | −0.479038 | −0.239519 | − | 0.970892i | \(-0.576990\pi\) | ||||
−0.239519 | + | 0.970892i | \(0.576990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2378.77 | −0.429571 | −0.214786 | − | 0.976661i | \(-0.568905\pi\) | ||||
−0.214786 | + | 0.976661i | \(0.568905\pi\) | |||||||
\(314\) | 14465.9 | 2.59986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −631.685 | −0.112453 | ||||||||
\(317\) | −7116.78 | −1.26094 | −0.630470 | − | 0.776213i | \(-0.717138\pi\) | ||||
−0.630470 | + | 0.776213i | \(0.717138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −972.846 | −0.170749 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2032.57 | 0.351773 | ||||||||
\(323\) | −2940.87 | −0.506609 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3942.96 | −0.669878 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3105.51 | −0.522784 | ||||||||
\(329\) | −293.497 | −0.0491825 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9616.07 | −1.59682 | −0.798410 | − | 0.602115i | \(-0.794325\pi\) | ||||
−0.798410 | + | 0.602115i | \(0.794325\pi\) | |||||||
\(332\) | −4975.27 | −0.822449 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7070.88 | −1.15839 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11052.0 | 1.78648 | 0.893238 | − | 0.449584i | \(-0.148428\pi\) | ||||
0.893238 | + | 0.449584i | \(0.148428\pi\) | |||||||
\(338\) | 9662.53 | 1.55495 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3916.61 | 0.621983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 931.054 | 0.145927 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11026.1 | −1.71319 | ||||||||
\(347\) | −2320.86 | −0.359050 | −0.179525 | − | 0.983753i | \(-0.557456\pi\) | ||||
−0.179525 | + | 0.983753i | \(0.557456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7462.68 | −1.14461 | −0.572304 | − | 0.820042i | \(-0.693950\pi\) | ||||
−0.572304 | + | 0.820042i | \(0.693950\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5301.16 | −0.802706 | ||||||||
\(353\) | −9430.78 | −1.42195 | −0.710977 | − | 0.703216i | \(-0.751747\pi\) | ||||
−0.710977 | + | 0.703216i | \(0.751747\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8528.82 | −1.26974 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6238.94 | 0.921056 | ||||||||
\(359\) | −7449.39 | −1.09516 | −0.547582 | − | 0.836752i | \(-0.684451\pi\) | ||||
−0.547582 | + | 0.836752i | \(0.684451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4243.87 | −0.618730 | ||||||||
\(362\) | −9020.63 | −1.30971 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 289.047 | 0.0416214 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12464.6 | −1.77287 | −0.886436 | − | 0.462850i | \(-0.846827\pi\) | ||||
−0.886436 | + | 0.462850i | \(0.846827\pi\) | |||||||
\(368\) | −1490.50 | −0.211135 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 233.411 | 0.0326634 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8335.42 | −1.15708 | −0.578541 | − | 0.815653i | \(-0.696378\pi\) | ||||
−0.578541 | + | 0.815653i | \(0.696378\pi\) | |||||||
\(374\) | 5947.21 | 0.822254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −662.004 | −0.0907986 | ||||||||
\(377\) | −148.530 | −0.0202910 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11976.6 | −1.62321 | −0.811603 | − | 0.584209i | \(-0.801405\pi\) | ||||
−0.811603 | + | 0.584209i | \(0.801405\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11399.0 | 1.52676 | ||||||||
\(383\) | −1607.28 | −0.214434 | −0.107217 | − | 0.994236i | \(-0.534194\pi\) | ||||
−0.107217 | + | 0.994236i | \(0.534194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12712.0 | −1.67623 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1739.67 | −0.227625 | ||||||||
\(389\) | 10021.6 | 1.30621 | 0.653103 | − | 0.757269i | \(-0.273467\pi\) | ||||
0.653103 | + | 0.757269i | \(0.273467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3774.78 | 0.488233 | ||||||||
\(392\) | −773.661 | −0.0996831 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6590.54 | 0.842708 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1247.17 | −0.157666 | −0.0788331 | − | 0.996888i | \(-0.525119\pi\) | ||||
−0.0788331 | + | 0.996888i | \(0.525119\pi\) | |||||||
\(398\) | −5800.28 | −0.730507 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5115.73 | −0.637075 | −0.318538 | − | 0.947910i | \(-0.603192\pi\) | ||||
−0.318538 | + | 0.947910i | \(0.603192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 597.972 | 0.0739134 | ||||||||
\(404\) | 1555.16 | 0.191516 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1288.64 | 0.157522 | ||||||||
\(407\) | −5249.12 | −0.639286 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11412.9 | 1.37979 | 0.689894 | − | 0.723911i | \(-0.257657\pi\) | ||||
0.689894 | + | 0.723911i | \(0.257657\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2689.76 | 0.321639 | ||||||||
\(413\) | 1604.48 | 0.191166 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −809.359 | −0.0953897 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5288.48 | −0.618823 | ||||||||
\(419\) | 10144.2 | 1.18276 | 0.591381 | − | 0.806393i | \(-0.298583\pi\) | ||||
0.591381 | + | 0.806393i | \(0.298583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −195.217 | −0.0225993 | −0.0112996 | − | 0.999936i | \(-0.503597\pi\) | ||||
−0.0112996 | + | 0.999936i | \(0.503597\pi\) | |||||||
\(422\) | −11817.3 | −1.36317 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 526.476 | 0.0603017 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4904.29 | 0.555820 | ||||||||
\(428\) | 17809.4 | 2.01133 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8432.54 | 0.942415 | 0.471208 | − | 0.882022i | \(-0.343818\pi\) | ||||
0.471208 | + | 0.882022i | \(0.343818\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3039.89 | −0.337386 | −0.168693 | − | 0.985669i | \(-0.553955\pi\) | ||||
−0.168693 | + | 0.985669i | \(0.553955\pi\) | |||||||
\(434\) | −5187.96 | −0.573802 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5824.65 | −0.639793 | ||||||||
\(437\) | −3356.67 | −0.367440 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8748.73 | −0.951148 | −0.475574 | − | 0.879676i | \(-0.657760\pi\) | ||||
−0.475574 | + | 0.879676i | \(0.657760\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 907.997 | 0.0977127 | ||||||||
\(443\) | −2184.85 | −0.234324 | −0.117162 | − | 0.993113i | \(-0.537380\pi\) | ||||
−0.117162 | + | 0.993113i | \(0.537380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14695.0 | −1.56015 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5750.32 | 0.606422 | ||||||||
\(449\) | −12511.6 | −1.31505 | −0.657525 | − | 0.753432i | \(-0.728397\pi\) | ||||
−0.657525 | + | 0.753432i | \(0.728397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4598.07 | −0.480077 | ||||||||
\(452\) | 3089.95 | 0.321546 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7772.22 | 0.803455 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10709.8 | −1.09625 | −0.548123 | − | 0.836397i | \(-0.684658\pi\) | ||||
−0.548123 | + | 0.836397i | \(0.684658\pi\) | |||||||
\(458\) | −11743.4 | −1.19811 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 73.0989 | 0.00738515 | 0.00369258 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369258 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2307.72 | 0.231639 | 0.115820 | − | 0.993270i | \(-0.463051\pi\) | ||||
0.115820 | + | 0.993270i | \(0.463051\pi\) | |||||||
\(464\) | −944.967 | −0.0945452 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19374.5 | 1.92598 | ||||||||
\(467\) | −977.511 | −0.0968604 | −0.0484302 | − | 0.998827i | \(-0.515422\pi\) | ||||
−0.0484302 | + | 0.998827i | \(0.515422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3177.23 | −0.312816 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3619.02 | 0.352922 | ||||||||
\(473\) | 1378.53 | 0.134007 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4657.26 | −0.448456 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4126.83 | 0.394889 | ||||||||
\(479\) | 8973.08 | 0.855930 | 0.427965 | − | 0.903795i | \(-0.359231\pi\) | ||||
0.427965 | + | 0.903795i | \(0.359231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −801.415 | −0.0759696 | ||||||||
\(482\) | 28539.2 | 2.69694 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9075.95 | −0.852362 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17259.1 | 1.60592 | 0.802961 | − | 0.596031i | \(-0.203257\pi\) | ||||
0.802961 | + | 0.596031i | \(0.203257\pi\) | |||||||
\(488\) | 11062.0 | 1.02613 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2612.25 | 0.240100 | 0.120050 | − | 0.992768i | \(-0.461695\pi\) | ||||
0.120050 | + | 0.992768i | \(0.461695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2393.18 | 0.218628 | ||||||||
\(494\) | −807.423 | −0.0735378 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3804.37 | 0.344397 | ||||||||
\(497\) | −6513.99 | −0.587913 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16056.2 | 1.44043 | 0.720215 | − | 0.693751i | \(-0.244043\pi\) | ||||
0.720215 | + | 0.693751i | \(0.244043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22495.6 | −2.00005 | ||||||||
\(503\) | −20352.4 | −1.80411 | −0.902054 | − | 0.431623i | \(-0.857941\pi\) | ||||
−0.902054 | + | 0.431623i | \(0.857941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6788.07 | 0.596376 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3429.24 | 0.299504 | ||||||||
\(509\) | −19740.3 | −1.71900 | −0.859502 | − | 0.511133i | \(-0.829226\pi\) | ||||
−0.859502 | + | 0.511133i | \(0.829226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2591.28 | 0.224327 | ||||||||
\(512\) | −8017.47 | −0.692042 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21309.5 | 1.82864 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −980.175 | −0.0833812 | ||||||||
\(518\) | 6953.02 | 0.589765 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19115.6 | 1.60742 | 0.803712 | − | 0.595019i | \(-0.202855\pi\) | ||||
0.803712 | + | 0.595019i | \(0.202855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4696.30 | −0.392648 | −0.196324 | − | 0.980539i | \(-0.562900\pi\) | ||||
−0.196324 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(524\) | 32025.7 | 2.66994 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35397.0 | 2.93419 | ||||||||
\(527\) | −9634.79 | −0.796391 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7858.52 | −0.645888 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4141.40 | 0.337505 | ||||||||
\(533\) | −702.016 | −0.0570500 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7166.46 | −0.577508 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15383.1 | 1.23274 | ||||||||
\(539\) | −1145.50 | −0.0915399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1302.32 | −0.103496 | −0.0517478 | − | 0.998660i | \(-0.516479\pi\) | ||||
−0.0517478 | + | 0.998660i | \(0.516479\pi\) | |||||||
\(542\) | 20300.8 | 1.60885 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13040.8 | 1.02779 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13145.9 | 1.02757 | 0.513784 | − | 0.857920i | \(-0.328243\pi\) | ||||
0.513784 | + | 0.857920i | \(0.328243\pi\) | |||||||
\(548\) | 9416.87 | 0.734067 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2128.11 | −0.164538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 382.205 | 0.0293906 | ||||||||
\(554\) | −8497.38 | −0.651659 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1147.24 | 0.0875065 | ||||||||
\(557\) | −5167.96 | −0.393130 | −0.196565 | − | 0.980491i | \(-0.562979\pi\) | ||||
−0.196565 | + | 0.980491i | \(0.562979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 210.469 | 0.0159247 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1734.37 | 0.130178 | ||||||||
\(563\) | −1444.18 | −0.108108 | −0.0540542 | − | 0.998538i | \(-0.517214\pi\) | ||||
−0.0540542 | + | 0.998538i | \(0.517214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 34071.2 | 2.53025 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14692.8 | −1.08538 | ||||||||
\(569\) | −22883.1 | −1.68596 | −0.842980 | − | 0.537945i | \(-0.819201\pi\) | ||||
−0.842980 | + | 0.537945i | \(0.819201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6611.79 | 0.484580 | 0.242290 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242290 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(572\) | 965.313 | 0.0705626 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6090.64 | 0.442889 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16695.5 | −1.20458 | −0.602291 | − | 0.798277i | \(-0.705745\pi\) | ||||
−0.602291 | + | 0.798277i | \(0.705745\pi\) | |||||||
\(578\) | 7103.63 | 0.511197 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3010.31 | 0.214955 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 779.510 | 0.0553756 | ||||||||
\(584\) | 5844.81 | 0.414144 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29451.9 | 2.07619 | ||||||||
\(587\) | 16504.8 | 1.16052 | 0.580261 | − | 0.814431i | \(-0.302951\pi\) | ||||
0.580261 | + | 0.814431i | \(0.302951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8567.60 | 0.599358 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5098.70 | −0.353978 | ||||||||
\(593\) | −16410.8 | −1.13644 | −0.568222 | − | 0.822875i | \(-0.692369\pi\) | ||||
−0.568222 | + | 0.822875i | \(0.692369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16509.9 | −1.13468 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1036.37 | 0.0708704 | ||||||||
\(599\) | 6879.60 | 0.469270 | 0.234635 | − | 0.972084i | \(-0.424610\pi\) | ||||
0.234635 | + | 0.972084i | \(0.424610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −979.314 | −0.0664676 | −0.0332338 | − | 0.999448i | \(-0.510581\pi\) | ||||
−0.0332338 | + | 0.999448i | \(0.510581\pi\) | |||||||
\(602\) | −1826.02 | −0.123626 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19893.7 | 1.34017 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5654.83 | 0.378126 | 0.189063 | − | 0.981965i | \(-0.439455\pi\) | ||||
0.189063 | + | 0.981965i | \(0.439455\pi\) | |||||||
\(608\) | −11596.3 | −0.773507 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −149.649 | −0.00990861 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8619.72 | 0.567940 | 0.283970 | − | 0.958833i | \(-0.408348\pi\) | ||||
0.283970 | + | 0.958833i | \(0.408348\pi\) | |||||||
\(614\) | −22483.6 | −1.47779 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2583.75 | −0.168997 | ||||||||
\(617\) | 7061.35 | 0.460744 | 0.230372 | − | 0.973103i | \(-0.426006\pi\) | ||||
0.230372 | + | 0.973103i | \(0.426006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5725.08 | 0.371745 | 0.185873 | − | 0.982574i | \(-0.440489\pi\) | ||||
0.185873 | + | 0.982574i | \(0.440489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11622.4 | 0.749223 | ||||||||
\(623\) | 5160.41 | 0.331858 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10523.0 | 0.671857 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37832.2 | −2.40393 | ||||||||
\(629\) | 12912.8 | 0.818546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3621.56 | −0.228482 | −0.114241 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114241 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(632\) | 862.090 | 0.0542597 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31482.5 | 1.97213 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −174.890 | −0.0108782 | ||||||||
\(638\) | 4303.58 | 0.267054 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20656.0 | 1.27280 | 0.636398 | − | 0.771361i | \(-0.280424\pi\) | ||||
0.636398 | + | 0.771361i | \(0.280424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15856.5 | −0.972504 | −0.486252 | − | 0.873819i | \(-0.661636\pi\) | ||||
−0.486252 | + | 0.873819i | \(0.661636\pi\) | |||||||
\(644\) | −5315.73 | −0.325262 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13009.6 | 0.792344 | ||||||||
\(647\) | 5476.66 | 0.332782 | 0.166391 | − | 0.986060i | \(-0.446789\pi\) | ||||
0.166391 | + | 0.986060i | \(0.446789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5358.39 | 0.324091 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10311.9 | 0.619394 | ||||||||
\(653\) | 18293.1 | 1.09627 | 0.548135 | − | 0.836390i | \(-0.315338\pi\) | ||||
0.548135 | + | 0.836390i | \(0.315338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4466.31 | −0.265823 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1298.35 | 0.0769222 | ||||||||
\(659\) | −32480.3 | −1.91996 | −0.959979 | − | 0.280073i | \(-0.909641\pi\) | ||||
−0.959979 | + | 0.280073i | \(0.909641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19403.4 | −1.14176 | −0.570880 | − | 0.821034i | \(-0.693398\pi\) | ||||
−0.570880 | + | 0.821034i | \(0.693398\pi\) | |||||||
\(662\) | 42538.7 | 2.49745 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6789.98 | 0.396841 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2731.55 | 0.158570 | ||||||||
\(668\) | 18492.2 | 1.07109 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16378.6 | 0.942306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3449.20 | 0.197559 | 0.0987793 | − | 0.995109i | \(-0.468506\pi\) | ||||
0.0987793 | + | 0.995109i | \(0.468506\pi\) | |||||||
\(674\) | −48890.9 | −2.79408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25270.1 | −1.43776 | ||||||||
\(677\) | 23683.0 | 1.34448 | 0.672239 | − | 0.740334i | \(-0.265333\pi\) | ||||
0.672239 | + | 0.740334i | \(0.265333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1052.60 | 0.0594919 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17325.9 | −0.972792 | ||||||||
\(683\) | −14101.5 | −0.790012 | −0.395006 | − | 0.918679i | \(-0.629258\pi\) | ||||
−0.395006 | + | 0.918679i | \(0.629258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1517.33 | 0.0844489 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1339.03 | 0.0742006 | ||||||||
\(689\) | 119.012 | 0.00658057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1327.04 | 0.0730577 | 0.0365289 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365289 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(692\) | 28836.1 | 1.58408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10266.8 | 0.561560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11311.2 | 0.614694 | ||||||||
\(698\) | 33012.7 | 1.79019 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9073.19 | 0.488858 | 0.244429 | − | 0.969667i | \(-0.421399\pi\) | ||||
0.244429 | + | 0.969667i | \(0.421399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11482.5 | −0.616032 | ||||||||
\(704\) | 19204.0 | 1.02809 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41719.0 | 2.22396 | ||||||||
\(707\) | −940.961 | −0.0500544 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13479.5 | −0.714010 | −0.357005 | − | 0.934102i | \(-0.616202\pi\) | ||||
−0.357005 | + | 0.934102i | \(0.616202\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11639.7 | 0.612662 | ||||||||
\(713\) | −10997.0 | −0.577618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16316.5 | −0.851642 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32953.9 | 1.71285 | ||||||||
\(719\) | −26389.8 | −1.36881 | −0.684404 | − | 0.729103i | \(-0.739938\pi\) | ||||
−0.684404 | + | 0.729103i | \(0.739938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1627.46 | −0.0840633 | ||||||||
\(722\) | 18773.6 | 0.967704 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23591.4 | 1.21100 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7983.43 | 0.407275 | 0.203638 | − | 0.979046i | \(-0.434724\pi\) | ||||
0.203638 | + | 0.979046i | \(0.434724\pi\) | |||||||
\(728\) | −394.476 | −0.0200828 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3391.17 | −0.171583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24350.2 | −1.22700 | −0.613502 | − | 0.789693i | \(-0.710240\pi\) | ||||
−0.613502 | + | 0.789693i | \(0.710240\pi\) | |||||||
\(734\) | 55139.5 | 2.77280 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14884.5 | 0.745450 | ||||||||
\(737\) | −10610.8 | −0.530331 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1936.37 | 0.0963880 | 0.0481940 | − | 0.998838i | \(-0.484653\pi\) | ||||
0.0481940 | + | 0.998838i | \(0.484653\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1032.54 | −0.0510861 | ||||||||
\(743\) | 27212.0 | 1.34362 | 0.671811 | − | 0.740722i | \(-0.265517\pi\) | ||||
0.671811 | + | 0.740722i | \(0.265517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36873.5 | 1.80970 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15553.6 | −0.760287 | ||||||||
\(749\) | −10775.7 | −0.525680 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13542.6 | −0.658026 | −0.329013 | − | 0.944325i | \(-0.606716\pi\) | ||||
−0.329013 | + | 0.944325i | \(0.606716\pi\) | |||||||
\(752\) | −952.086 | −0.0461689 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 657.054 | 0.0317354 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6328.67 | 0.303857 | 0.151928 | − | 0.988392i | \(-0.451452\pi\) | ||||
0.151928 | + | 0.988392i | \(0.451452\pi\) | |||||||
\(758\) | 52980.8 | 2.53872 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26036.0 | −1.24021 | −0.620107 | − | 0.784517i | \(-0.712911\pi\) | ||||
−0.620107 | + | 0.784517i | \(0.712911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3524.24 | 0.167216 | ||||||||
\(764\) | −29811.4 | −1.41170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7110.15 | 0.335379 | ||||||||
\(767\) | 818.097 | 0.0385134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6092.16 | −0.285681 | −0.142841 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142841 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 33245.3 | 1.54990 | ||||||||
\(773\) | −16076.6 | −0.748040 | −0.374020 | − | 0.927421i | \(-0.622021\pi\) | ||||
−0.374020 | + | 0.927421i | \(0.622021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2374.21 | 0.109831 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44332.5 | −2.04293 | ||||||||
\(779\) | −10058.3 | −0.462614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21754.4 | −0.996713 | ||||||||
\(782\) | −16698.5 | −0.763604 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1112.67 | −0.0506865 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41683.3 | 1.88799 | 0.943995 | − | 0.329961i | \(-0.107036\pi\) | ||||
0.943995 | + | 0.329961i | \(0.107036\pi\) | |||||||
\(788\) | −17236.0 | −0.779199 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1869.59 | −0.0840392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2500.61 | 0.111979 | ||||||||
\(794\) | 5517.10 | 0.246593 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15169.3 | 0.675454 | ||||||||
\(797\) | 37247.7 | 1.65543 | 0.827717 | − | 0.561145i | \(-0.189639\pi\) | ||||
0.827717 | + | 0.561145i | \(0.189639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2411.21 | 0.106762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22630.5 | 0.996396 | ||||||||
\(803\) | 8653.92 | 0.380312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2645.25 | −0.115602 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2122.40 | −0.0924083 | ||||||||
\(809\) | 12084.0 | 0.525156 | 0.262578 | − | 0.964911i | \(-0.415427\pi\) | ||||
0.262578 | + | 0.964911i | \(0.415427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43963.8 | −1.90355 | −0.951775 | − | 0.306796i | \(-0.900743\pi\) | ||||
−0.951775 | + | 0.306796i | \(0.900743\pi\) | |||||||
\(812\) | −3370.13 | −0.145651 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23220.6 | 0.999854 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3015.55 | 0.129132 | ||||||||
\(818\) | −50487.4 | −2.15801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6761.26 | 0.287417 | 0.143709 | − | 0.989620i | \(-0.454097\pi\) | ||||
0.143709 | + | 0.989620i | \(0.454097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21729.5 | −0.920343 | −0.460172 | − | 0.887830i | \(-0.652212\pi\) | ||||
−0.460172 | + | 0.887830i | \(0.652212\pi\) | |||||||
\(824\) | −3670.84 | −0.155194 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7097.76 | −0.298986 | ||||||||
\(827\) | −27297.7 | −1.14780 | −0.573902 | − | 0.818924i | \(-0.694571\pi\) | ||||
−0.573902 | + | 0.818924i | \(0.694571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14194.9 | −0.594703 | −0.297352 | − | 0.954768i | \(-0.596103\pi\) | ||||
−0.297352 | + | 0.954768i | \(0.596103\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2931.99 | 0.122174 | ||||||||
\(833\) | 2817.90 | 0.117208 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13830.8 | 0.572186 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44875.0 | −1.84986 | ||||||||
\(839\) | 30955.4 | 1.27378 | 0.636889 | − | 0.770955i | \(-0.280221\pi\) | ||||
0.636889 | + | 0.770955i | \(0.280221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22657.2 | −0.928993 | ||||||||
\(842\) | 863.583 | 0.0353457 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30905.5 | 1.26044 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5491.46 | 0.222773 | ||||||||
\(848\) | 757.171 | 0.0306620 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14738.4 | 0.593686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21925.6 | −0.880094 | −0.440047 | − | 0.897975i | \(-0.645038\pi\) | ||||
−0.440047 | + | 0.897975i | \(0.645038\pi\) | |||||||
\(854\) | −21695.1 | −0.869312 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24305.3 | −0.970487 | ||||||||
\(857\) | 28288.5 | 1.12756 | 0.563780 | − | 0.825925i | \(-0.309347\pi\) | ||||
0.563780 | + | 0.825925i | \(0.309347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12483.8 | −0.495858 | −0.247929 | − | 0.968778i | \(-0.579750\pi\) | ||||
−0.247929 | + | 0.968778i | \(0.579750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37303.1 | −1.47395 | ||||||||
\(863\) | −13344.0 | −0.526346 | −0.263173 | − | 0.964749i | \(-0.584769\pi\) | ||||
−0.263173 | + | 0.964749i | \(0.584769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13447.6 | 0.527677 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13567.9 | 0.530559 | ||||||||
\(869\) | 1276.43 | 0.0498271 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1620.01 | −0.0630219 | ||||||||
\(872\) | 7949.17 | 0.308707 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14848.9 | 0.574683 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19198.7 | 0.739219 | 0.369609 | − | 0.929187i | \(-0.379492\pi\) | ||||
0.369609 | + | 0.929187i | \(0.379492\pi\) | |||||||
\(878\) | 38701.8 | 1.48761 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31063.7 | 1.18793 | 0.593963 | − | 0.804492i | \(-0.297562\pi\) | ||||
0.593963 | + | 0.804492i | \(0.297562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37100.6 | −1.41397 | −0.706985 | − | 0.707229i | \(-0.749945\pi\) | ||||
−0.706985 | + | 0.707229i | \(0.749945\pi\) | |||||||
\(884\) | −2374.65 | −0.0903487 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9665.15 | 0.366487 | ||||||||
\(887\) | −4568.24 | −0.172927 | −0.0864636 | − | 0.996255i | \(-0.527557\pi\) | ||||
−0.0864636 | + | 0.996255i | \(0.527557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2074.88 | −0.0782782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38431.3 | 1.44257 | ||||||||
\(893\) | −2144.14 | −0.0803481 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12739.0 | −0.474977 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 55347.5 | 2.05676 | ||||||||
\(899\) | −6972.03 | −0.258654 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1917.58 | −0.0709033 | ||||||||
\(902\) | 20340.5 | 0.750849 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4216.99 | −0.155150 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 776.485 | 0.0284264 | 0.0142132 | − | 0.999899i | \(-0.495476\pi\) | ||||
0.0142132 | + | 0.999899i | \(0.495476\pi\) | |||||||
\(908\) | −20326.4 | −0.742904 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24605.9 | −0.894872 | −0.447436 | − | 0.894316i | \(-0.647663\pi\) | ||||
−0.447436 | + | 0.894316i | \(0.647663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10053.4 | 0.364423 | ||||||||
\(914\) | 47377.2 | 1.71455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30712.1 | 1.10781 | ||||||||
\(917\) | −19377.4 | −0.697816 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −156.897 | −0.00563173 | −0.00281587 | − | 0.999996i | \(-0.500896\pi\) | ||||
−0.00281587 | + | 0.999996i | \(0.500896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −323.368 | −0.0115505 | ||||||||
\(923\) | −3321.37 | −0.118445 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10208.7 | −0.362287 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9436.69 | 0.333809 | ||||||||
\(929\) | 2740.94 | 0.0968002 | 0.0484001 | − | 0.998828i | \(-0.484588\pi\) | ||||
0.0484001 | + | 0.998828i | \(0.484588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2505.78 | −0.0882101 | ||||||||
\(932\) | −50669.5 | −1.78083 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4324.22 | 0.151491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15341.1 | 0.534870 | 0.267435 | − | 0.963576i | \(-0.413824\pi\) | ||||
0.267435 | + | 0.963576i | \(0.413824\pi\) | |||||||
\(938\) | 14055.1 | 0.489250 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40269.2 | −1.39505 | −0.697523 | − | 0.716563i | \(-0.745714\pi\) | ||||
−0.697523 | + | 0.716563i | \(0.745714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12910.4 | 0.445834 | ||||||||
\(944\) | 5204.83 | 0.179452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6098.23 | −0.209588 | ||||||||
\(947\) | −10173.6 | −0.349100 | −0.174550 | − | 0.984648i | \(-0.555847\pi\) | ||||
−0.174550 | + | 0.984648i | \(0.555847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1321.25 | 0.0451944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6355.98 | 0.216385 | ||||||||
\(953\) | −15239.9 | −0.518015 | −0.259007 | − | 0.965875i | \(-0.583395\pi\) | ||||
−0.259007 | + | 0.965875i | \(0.583395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10792.8 | −0.365129 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −39694.3 | −1.33869 | ||||||||
\(959\) | −5697.73 | −0.191855 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1722.13 | −0.0578069 | ||||||||
\(962\) | 3545.23 | 0.118818 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −74637.7 | −2.49369 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35689.8 | −1.18687 | −0.593437 | − | 0.804881i | \(-0.702229\pi\) | ||||
−0.593437 | + | 0.804881i | \(0.702229\pi\) | |||||||
\(968\) | 12386.4 | 0.411274 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22841.5 | 0.754913 | 0.377456 | − | 0.926027i | \(-0.376799\pi\) | ||||
0.377456 | + | 0.926027i | \(0.376799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −694.142 | −0.0228707 | ||||||||
\(974\) | −76349.2 | −2.51169 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15909.2 | 0.521763 | ||||||||
\(977\) | 14487.1 | 0.474394 | 0.237197 | − | 0.971462i | \(-0.423771\pi\) | ||||
0.237197 | + | 0.971462i | \(0.423771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17233.9 | 0.562613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11555.8 | −0.375520 | ||||||||
\(983\) | −35291.6 | −1.14509 | −0.572547 | − | 0.819872i | \(-0.694045\pi\) | ||||
−0.572547 | + | 0.819872i | \(0.694045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10586.7 | −0.341938 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2111.63 | 0.0679958 | ||||||||
\(989\) | −3870.64 | −0.124448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29615.5 | −0.949310 | −0.474655 | − | 0.880172i | \(-0.657427\pi\) | ||||
−0.474655 | + | 0.880172i | \(0.657427\pi\) | |||||||
\(992\) | −37991.4 | −1.21596 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28816.0 | 0.919505 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45868.5 | 1.45704 | 0.728520 | − | 0.685025i | \(-0.240209\pi\) | ||||
0.728520 | + | 0.685025i | \(0.240209\pi\) | |||||||
\(998\) | −71027.9 | −2.25286 | ||||||||
\(999\) | 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 | 1575.4.a.bh.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1575.4.a.bh.1.4 | yes | 4 | |
5.4 | even | 2 | 1575.4.a.bi.1.4 | yes | 4 | ||
15.14 | odd | 2 | 1575.4.a.bi.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.4.a.bh.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1575.4.a.bh.1.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1575.4.a.bi.1.1 | yes | 4 | 15.14 | odd | 2 | ||
1575.4.a.bi.1.4 | yes | 4 | 5.4 | even | 2 |