Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(1,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, 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("315.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.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: | \(18.5856016518\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.70156 | −1.66225 | −0.831127 | − | 0.556083i | \(-0.812304\pi\) | ||||
−0.831127 | + | 0.556083i | \(0.812304\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.1047 | 1.76309 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −28.7016 | −1.26844 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −23.5078 | −0.743382 | ||||||||
\(11\) | −24.5969 | −0.674203 | −0.337102 | − | 0.941468i | \(-0.609447\pi\) | ||||
−0.337102 | + | 0.941468i | \(0.609447\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.0156 | −0.747045 | −0.373523 | − | 0.927621i | \(-0.621850\pi\) | ||||
−0.373523 | + | 0.927621i | \(0.621850\pi\) | |||||||
\(14\) | −32.9109 | −0.628273 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 22.1047 | 0.345386 | ||||||||
\(17\) | 18.4187 | 0.262777 | 0.131388 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131388 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −67.4031 | −0.813860 | −0.406930 | − | 0.913459i | \(-0.633401\pi\) | ||||
−0.406930 | + | 0.913459i | \(0.633401\pi\) | |||||||
\(20\) | 70.5234 | 0.788476 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 115.644 | 1.12070 | ||||||||
\(23\) | 145.675 | 1.32067 | 0.660333 | − | 0.750973i | \(-0.270415\pi\) | ||||
0.660333 | + | 0.750973i | \(0.270415\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 164.628 | 1.24178 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 98.7328 | 0.666384 | ||||||||
\(29\) | −214.419 | −1.37298 | −0.686492 | − | 0.727137i | \(-0.740851\pi\) | ||||
−0.686492 | + | 0.727137i | \(0.740851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −88.6594 | −0.513667 | −0.256834 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256834 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(32\) | 125.686 | 0.694323 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −86.5969 | −0.436801 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 162.125 | 0.720356 | 0.360178 | − | 0.932884i | \(-0.382716\pi\) | ||||
0.360178 | + | 0.932884i | \(0.382716\pi\) | |||||||
\(38\) | 316.900 | 1.35284 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −143.508 | −0.567264 | ||||||||
\(41\) | 337.769 | 1.28660 | 0.643300 | − | 0.765614i | \(-0.277565\pi\) | ||||
0.643300 | + | 0.765614i | \(0.277565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 122.156 | 0.433224 | 0.216612 | − | 0.976258i | \(-0.430499\pi\) | ||||
0.216612 | + | 0.976258i | \(0.430499\pi\) | |||||||
\(44\) | −346.931 | −1.18868 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −684.900 | −2.19528 | ||||||||
\(47\) | −354.219 | −1.09932 | −0.549661 | − | 0.835388i | \(-0.685243\pi\) | ||||
−0.549661 | + | 0.835388i | \(0.685243\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −117.539 | −0.332451 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −493.884 | −1.31710 | ||||||||
\(53\) | −676.691 | −1.75378 | −0.876892 | − | 0.480687i | \(-0.840387\pi\) | ||||
−0.876892 | + | 0.480687i | \(0.840387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −122.984 | −0.301513 | ||||||||
\(56\) | −200.911 | −0.479426 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1008.10 | 2.28225 | ||||||||
\(59\) | −501.319 | −1.10621 | −0.553103 | − | 0.833113i | \(-0.686556\pi\) | ||||
−0.553103 | + | 0.833113i | \(0.686556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −708.931 | −1.48802 | −0.744011 | − | 0.668167i | \(-0.767079\pi\) | ||||
−0.744011 | + | 0.668167i | \(0.767079\pi\) | |||||||
\(62\) | 416.837 | 0.853845 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −767.758 | −1.49953 | ||||||||
\(65\) | −175.078 | −0.334089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −907.956 | −1.65559 | −0.827795 | − | 0.561031i | \(-0.810405\pi\) | ||||
−0.827795 | + | 0.561031i | \(0.810405\pi\) | |||||||
\(68\) | 259.791 | 0.463298 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −164.555 | −0.280972 | ||||||||
\(71\) | −430.334 | −0.719314 | −0.359657 | − | 0.933085i | \(-0.617106\pi\) | ||||
−0.359657 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.3406 | 0.0662816 | 0.0331408 | − | 0.999451i | \(-0.489449\pi\) | ||||
0.0331408 | + | 0.999451i | \(0.489449\pi\) | |||||||
\(74\) | −762.241 | −1.19741 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −950.700 | −1.43490 | ||||||||
\(77\) | −172.178 | −0.254825 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 890.388 | 1.26806 | 0.634028 | − | 0.773310i | \(-0.281400\pi\) | ||||
0.634028 | + | 0.773310i | \(0.281400\pi\) | |||||||
\(80\) | 110.523 | 0.154461 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1588.04 | −2.13866 | ||||||||
\(83\) | 1057.15 | 1.39804 | 0.699020 | − | 0.715102i | \(-0.253620\pi\) | ||||
0.699020 | + | 0.715102i | \(0.253620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92.0937 | 0.117517 | ||||||||
\(86\) | −574.325 | −0.720129 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 705.969 | 0.855188 | ||||||||
\(89\) | −1473.72 | −1.75522 | −0.877610 | − | 0.479376i | \(-0.840863\pi\) | ||||
−0.877610 | + | 0.479376i | \(0.840863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −245.109 | −0.282356 | ||||||||
\(92\) | 2054.70 | 2.32845 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1665.38 | 1.82735 | ||||||||
\(95\) | −337.016 | −0.363969 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 555.034 | 0.580981 | 0.290491 | − | 0.956878i | \(-0.406181\pi\) | ||||
0.290491 | + | 0.956878i | \(0.406181\pi\) | |||||||
\(98\) | −230.377 | −0.237465 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 352.617 | 0.352617 | ||||||||
\(101\) | −1890.14 | −1.86214 | −0.931071 | − | 0.364838i | \(-0.881124\pi\) | ||||
−0.931071 | + | 0.364838i | \(0.881124\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 662.700 | 0.633959 | 0.316979 | − | 0.948432i | \(-0.397331\pi\) | ||||
0.316979 | + | 0.948432i | \(0.397331\pi\) | |||||||
\(104\) | 1005.00 | 0.947583 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3181.50 | 2.91523 | ||||||||
\(107\) | −1614.53 | −1.45872 | −0.729358 | − | 0.684132i | \(-0.760181\pi\) | ||||
−0.729358 | + | 0.684132i | \(0.760181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 217.206 | 0.190868 | 0.0954339 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954339 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(110\) | 578.219 | 0.501191 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 154.733 | 0.130544 | ||||||||
\(113\) | 1658.20 | 1.38044 | 0.690221 | − | 0.723598i | \(-0.257513\pi\) | ||||
0.690221 | + | 0.723598i | \(0.257513\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 728.375 | 0.590620 | ||||||||
\(116\) | −3024.31 | −2.42069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2356.98 | 1.83879 | ||||||||
\(119\) | 128.931 | 0.0993202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −725.994 | −0.545450 | ||||||||
\(122\) | 3333.08 | 2.47347 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1250.51 | −0.905640 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1108.81 | −0.774734 | −0.387367 | − | 0.921926i | \(-0.626615\pi\) | ||||
−0.387367 | + | 0.921926i | \(0.626615\pi\) | |||||||
\(128\) | 2604.17 | 1.79827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 823.141 | 0.555340 | ||||||||
\(131\) | −185.488 | −0.123711 | −0.0618554 | − | 0.998085i | \(-0.519702\pi\) | ||||
−0.0618554 | + | 0.998085i | \(0.519702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −471.822 | −0.307610 | ||||||||
\(134\) | 4268.81 | 2.75201 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −528.647 | −0.333317 | ||||||||
\(137\) | 37.9907 | 0.0236917 | 0.0118458 | − | 0.999930i | \(-0.496229\pi\) | ||||
0.0118458 | + | 0.999930i | \(0.496229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.609 | 0.112040 | 0.0560199 | − | 0.998430i | \(-0.482159\pi\) | ||||
0.0560199 | + | 0.998430i | \(0.482159\pi\) | |||||||
\(140\) | 493.664 | 0.298016 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2023.24 | 1.19568 | ||||||||
\(143\) | 861.275 | 0.503660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1072.09 | −0.614018 | ||||||||
\(146\) | −194.366 | −0.110177 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2286.72 | 1.27005 | ||||||||
\(149\) | 1383.34 | 0.760587 | 0.380293 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380293 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 765.256 | 0.412422 | 0.206211 | − | 0.978508i | \(-0.433887\pi\) | ||||
0.206211 | + | 0.978508i | \(0.433887\pi\) | |||||||
\(152\) | 1934.57 | 1.03233 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 809.506 | 0.423584 | ||||||||
\(155\) | −443.297 | −0.229719 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2366.76 | −1.20311 | −0.601554 | − | 0.798832i | \(-0.705452\pi\) | ||||
−0.601554 | + | 0.798832i | \(0.705452\pi\) | |||||||
\(158\) | −4186.21 | −2.10783 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 628.430 | 0.310511 | ||||||||
\(161\) | 1019.72 | 0.499165 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3137.69 | −1.50775 | −0.753875 | − | 0.657018i | \(-0.771817\pi\) | ||||
−0.753875 | + | 0.657018i | \(0.771817\pi\) | |||||||
\(164\) | 4764.12 | 2.26839 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4970.26 | −2.32390 | ||||||||
\(167\) | −146.469 | −0.0678688 | −0.0339344 | − | 0.999424i | \(-0.510804\pi\) | ||||
−0.0339344 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −970.906 | −0.441924 | ||||||||
\(170\) | −432.984 | −0.195343 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1722.98 | 0.763812 | ||||||||
\(173\) | 1424.12 | 0.625860 | 0.312930 | − | 0.949776i | \(-0.398689\pi\) | ||||
0.312930 | + | 0.949776i | \(0.398689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | −543.706 | −0.232860 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6928.81 | 2.91762 | ||||||||
\(179\) | −1244.70 | −0.519737 | −0.259869 | − | 0.965644i | \(-0.583679\pi\) | ||||
−0.259869 | + | 0.965644i | \(0.583679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3879.09 | −1.59299 | −0.796493 | − | 0.604648i | \(-0.793314\pi\) | ||||
−0.796493 | + | 0.604648i | \(0.793314\pi\) | |||||||
\(182\) | 1152.40 | 0.469348 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4181.10 | −1.67519 | ||||||||
\(185\) | 810.625 | 0.322153 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −453.044 | −0.177165 | ||||||||
\(188\) | −4996.14 | −1.93820 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1584.50 | 0.605009 | ||||||||
\(191\) | −1574.90 | −0.596628 | −0.298314 | − | 0.954468i | \(-0.596424\pi\) | ||||
−0.298314 | + | 0.954468i | \(0.596424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4775.67 | −1.78114 | −0.890572 | − | 0.454843i | \(-0.849695\pi\) | ||||
−0.890572 | + | 0.454843i | \(0.849695\pi\) | |||||||
\(194\) | −2609.53 | −0.965738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 691.130 | 0.251869 | ||||||||
\(197\) | 2803.58 | 1.01394 | 0.506971 | − | 0.861963i | \(-0.330765\pi\) | ||||
0.506971 | + | 0.861963i | \(0.330765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4102.92 | 1.46155 | 0.730774 | − | 0.682620i | \(-0.239159\pi\) | ||||
0.730774 | + | 0.682620i | \(0.239159\pi\) | |||||||
\(200\) | −717.539 | −0.253688 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8886.63 | 3.09535 | ||||||||
\(203\) | −1500.93 | −0.518940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1688.84 | 0.575385 | ||||||||
\(206\) | −3115.72 | −1.05380 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −774.009 | −0.258019 | ||||||||
\(209\) | 1657.91 | 0.548707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −823.512 | −0.268687 | −0.134343 | − | 0.990935i | \(-0.542893\pi\) | ||||
−0.134343 | + | 0.990935i | \(0.542893\pi\) | |||||||
\(212\) | −9544.51 | −3.09207 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7590.82 | 2.42476 | ||||||||
\(215\) | 610.781 | 0.193744 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −620.616 | −0.194148 | ||||||||
\(218\) | −1021.21 | −0.317271 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1734.66 | −0.531593 | ||||||||
\(221\) | −644.944 | −0.196306 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 817.194 | 0.245396 | 0.122698 | − | 0.992444i | \(-0.460845\pi\) | ||||
0.122698 | + | 0.992444i | \(0.460845\pi\) | |||||||
\(224\) | 879.802 | 0.262430 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7796.12 | −2.29465 | ||||||||
\(227\) | −3655.85 | −1.06893 | −0.534465 | − | 0.845190i | \(-0.679487\pi\) | ||||
−0.534465 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 939.393 | 0.271078 | 0.135539 | − | 0.990772i | \(-0.456723\pi\) | ||||
0.135539 | + | 0.990772i | \(0.456723\pi\) | |||||||
\(230\) | −3424.50 | −0.981760 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6154.15 | 1.74155 | ||||||||
\(233\) | 7.64701 | 0.00215010 | 0.00107505 | − | 0.999999i | \(-0.499658\pi\) | ||||
0.00107505 | + | 0.999999i | \(0.499658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1771.09 | −0.491631 | ||||||||
\(236\) | −7070.94 | −1.95034 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −606.178 | −0.165095 | ||||||||
\(239\) | 889.115 | 0.240636 | 0.120318 | − | 0.992735i | \(-0.461609\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2140.23 | 0.572051 | 0.286026 | − | 0.958222i | \(-0.407666\pi\) | ||||
0.286026 | + | 0.958222i | \(0.407666\pi\) | |||||||
\(242\) | 3413.30 | 0.906676 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9999.25 | −2.62351 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2360.16 | 0.607990 | ||||||||
\(248\) | 2544.66 | 0.651557 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −587.695 | −0.148676 | ||||||||
\(251\) | 6749.81 | 1.69739 | 0.848693 | − | 0.528886i | \(-0.177390\pi\) | ||||
0.848693 | + | 0.528886i | \(0.177390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3583.15 | −0.890398 | ||||||||
\(254\) | 5213.15 | 1.28780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6101.62 | −1.48965 | ||||||||
\(257\) | −3068.64 | −0.744811 | −0.372405 | − | 0.928070i | \(-0.621467\pi\) | ||||
−0.372405 | + | 0.928070i | \(0.621467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1134.87 | 0.272269 | ||||||||
\(260\) | −2469.42 | −0.589027 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 872.081 | 0.205639 | ||||||||
\(263\) | 4674.12 | 1.09589 | 0.547944 | − | 0.836515i | \(-0.315411\pi\) | ||||
0.547944 | + | 0.836515i | \(0.315411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3383.45 | −0.784316 | ||||||||
\(266\) | 2218.30 | 0.511326 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12806.4 | −2.91895 | ||||||||
\(269\) | −2417.38 | −0.547919 | −0.273960 | − | 0.961741i | \(-0.588333\pi\) | ||||
−0.273960 | + | 0.961741i | \(0.588333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7724.30 | 1.73143 | 0.865715 | − | 0.500537i | \(-0.166864\pi\) | ||||
0.865715 | + | 0.500537i | \(0.166864\pi\) | |||||||
\(272\) | 407.141 | 0.0907593 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −178.616 | −0.0393816 | ||||||||
\(275\) | −614.922 | −0.134841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4576.17 | −0.992620 | −0.496310 | − | 0.868145i | \(-0.665312\pi\) | ||||
−0.496310 | + | 0.868145i | \(0.665312\pi\) | |||||||
\(278\) | −863.250 | −0.186239 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1004.55 | −0.214406 | ||||||||
\(281\) | 1358.56 | 0.288415 | 0.144208 | − | 0.989547i | \(-0.453937\pi\) | ||||
0.144208 | + | 0.989547i | \(0.453937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3885.04 | 0.816048 | 0.408024 | − | 0.912971i | \(-0.366218\pi\) | ||||
0.408024 | + | 0.912971i | \(0.366218\pi\) | |||||||
\(284\) | −6069.73 | −1.26821 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4049.34 | −0.837211 | ||||||||
\(287\) | 2364.38 | 0.486289 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4573.75 | −0.930948 | ||||||||
\(290\) | 5040.52 | 1.02065 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 583.097 | 0.116860 | ||||||||
\(293\) | 4033.91 | 0.804312 | 0.402156 | − | 0.915571i | \(-0.368261\pi\) | ||||
0.402156 | + | 0.915571i | \(0.368261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2506.59 | −0.494710 | ||||||||
\(296\) | −4653.24 | −0.913730 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6503.85 | −1.26429 | ||||||||
\(299\) | −5100.90 | −0.986598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 855.093 | 0.163743 | ||||||||
\(302\) | −3597.90 | −0.685549 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1489.92 | −0.281096 | ||||||||
\(305\) | −3544.66 | −0.665464 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4620.36 | −0.858950 | −0.429475 | − | 0.903079i | \(-0.641301\pi\) | ||||
−0.429475 | + | 0.903079i | \(0.641301\pi\) | |||||||
\(308\) | −2428.52 | −0.449278 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2084.19 | 0.381851 | ||||||||
\(311\) | −6675.89 | −1.21722 | −0.608609 | − | 0.793470i | \(-0.708272\pi\) | ||||
−0.608609 | + | 0.793470i | \(0.708272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2836.78 | 0.512283 | 0.256141 | − | 0.966639i | \(-0.417549\pi\) | ||||
0.256141 | + | 0.966639i | \(0.417549\pi\) | |||||||
\(314\) | 11127.5 | 1.99987 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12558.6 | 2.23569 | ||||||||
\(317\) | −4010.63 | −0.710597 | −0.355299 | − | 0.934753i | \(-0.615621\pi\) | ||||
−0.355299 | + | 0.934753i | \(0.615621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5274.03 | 0.925671 | ||||||||
\(320\) | −3838.79 | −0.670609 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4794.30 | −0.829739 | ||||||||
\(323\) | −1241.48 | −0.213863 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −875.391 | −0.149409 | ||||||||
\(326\) | 14752.1 | 2.50626 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9694.49 | −1.63198 | ||||||||
\(329\) | −2479.53 | −0.415504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11087.5 | 1.84117 | 0.920583 | − | 0.390546i | \(-0.127714\pi\) | ||||
0.920583 | + | 0.390546i | \(0.127714\pi\) | |||||||
\(332\) | 14910.8 | 2.46486 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 688.631 | 0.112815 | ||||||||
\(335\) | −4539.78 | −0.740402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12118.7 | 1.95890 | 0.979450 | − | 0.201689i | \(-0.0646431\pi\) | ||||
0.979450 | + | 0.201689i | \(0.0646431\pi\) | |||||||
\(338\) | 4564.78 | 0.734589 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1298.95 | 0.207193 | ||||||||
\(341\) | 2180.74 | 0.346316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −3506.07 | −0.549520 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6695.58 | −1.04034 | ||||||||
\(347\) | 6361.22 | 0.984116 | 0.492058 | − | 0.870562i | \(-0.336245\pi\) | ||||
0.492058 | + | 0.870562i | \(0.336245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3115.18 | −0.477799 | −0.238899 | − | 0.971044i | \(-0.576787\pi\) | ||||
−0.238899 | + | 0.971044i | \(0.576787\pi\) | |||||||
\(350\) | −822.773 | −0.125655 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3091.48 | −0.468115 | ||||||||
\(353\) | 11927.4 | 1.79839 | 0.899194 | − | 0.437550i | \(-0.144154\pi\) | ||||
0.899194 | + | 0.437550i | \(0.144154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2151.67 | −0.321687 | ||||||||
\(356\) | −20786.4 | −3.09460 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5852.02 | 0.863935 | ||||||||
\(359\) | 6143.95 | 0.903245 | 0.451623 | − | 0.892209i | \(-0.350845\pi\) | ||||
0.451623 | + | 0.892209i | \(0.350845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2315.82 | −0.337632 | ||||||||
\(362\) | 18237.8 | 2.64794 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3457.19 | −0.497819 | ||||||||
\(365\) | 206.703 | 0.0296420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1927.67 | −0.274178 | −0.137089 | − | 0.990559i | \(-0.543775\pi\) | ||||
−0.137089 | + | 0.990559i | \(0.543775\pi\) | |||||||
\(368\) | 3220.10 | 0.456139 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3811.20 | −0.535500 | ||||||||
\(371\) | −4736.83 | −0.662868 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10452.0 | 1.45090 | 0.725449 | − | 0.688276i | \(-0.241632\pi\) | ||||
0.725449 | + | 0.688276i | \(0.241632\pi\) | |||||||
\(374\) | 2130.01 | 0.294493 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10166.6 | 1.39443 | ||||||||
\(377\) | 7508.01 | 1.02568 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7066.43 | 0.957726 | 0.478863 | − | 0.877890i | \(-0.341049\pi\) | ||||
0.478863 | + | 0.877890i | \(0.341049\pi\) | |||||||
\(380\) | −4753.50 | −0.641709 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7404.51 | 0.991747 | ||||||||
\(383\) | −7168.04 | −0.956318 | −0.478159 | − | 0.878273i | \(-0.658696\pi\) | ||||
−0.478159 | + | 0.878273i | \(0.658696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −860.891 | −0.113961 | ||||||||
\(386\) | 22453.1 | 2.96071 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7828.58 | 1.02432 | ||||||||
\(389\) | 7414.06 | 0.966344 | 0.483172 | − | 0.875525i | \(-0.339485\pi\) | ||||
0.483172 | + | 0.875525i | \(0.339485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2683.15 | 0.347040 | ||||||||
\(392\) | −1406.38 | −0.181206 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13181.2 | −1.68543 | ||||||||
\(395\) | 4451.94 | 0.567092 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8936.01 | −1.12969 | −0.564843 | − | 0.825198i | \(-0.691063\pi\) | ||||
−0.564843 | + | 0.825198i | \(0.691063\pi\) | |||||||
\(398\) | −19290.1 | −2.42946 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 552.617 | 0.0690771 | ||||||||
\(401\) | −1782.91 | −0.222031 | −0.111015 | − | 0.993819i | \(-0.535410\pi\) | ||||
−0.111015 | + | 0.993819i | \(0.535410\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3104.46 | 0.383733 | ||||||||
\(404\) | −26659.9 | −3.28312 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7056.72 | 0.862609 | ||||||||
\(407\) | −3987.77 | −0.485667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8759.92 | −1.05905 | −0.529524 | − | 0.848295i | \(-0.677629\pi\) | ||||
−0.529524 | + | 0.848295i | \(0.677629\pi\) | |||||||
\(410\) | −7940.20 | −0.956436 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9347.17 | 1.11772 | ||||||||
\(413\) | −3509.23 | −0.418106 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5285.75 | 0.625222 | ||||||||
\(416\) | −4400.97 | −0.518691 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7794.75 | −0.912090 | ||||||||
\(419\) | 3212.74 | 0.374588 | 0.187294 | − | 0.982304i | \(-0.440028\pi\) | ||||
0.187294 | + | 0.982304i | \(0.440028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15757.8 | 1.82420 | 0.912101 | − | 0.409965i | \(-0.134459\pi\) | ||||
0.912101 | + | 0.409965i | \(0.134459\pi\) | |||||||
\(422\) | 3871.79 | 0.446626 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19422.1 | 2.22457 | ||||||||
\(425\) | 460.469 | 0.0525553 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4962.52 | −0.562419 | ||||||||
\(428\) | −22772.5 | −2.57184 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2871.63 | −0.322051 | ||||||||
\(431\) | 405.917 | 0.0453650 | 0.0226825 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226825 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7845.25 | −0.870713 | −0.435357 | − | 0.900258i | \(-0.643378\pi\) | ||||
−0.435357 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(434\) | 2917.86 | 0.322723 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3063.63 | 0.336516 | ||||||||
\(437\) | −9818.95 | −1.07484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 423.029 | 0.0459911 | 0.0229955 | − | 0.999736i | \(-0.492680\pi\) | ||||
0.0229955 | + | 0.999736i | \(0.492680\pi\) | |||||||
\(440\) | 3529.84 | 0.382452 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3032.24 | 0.326310 | ||||||||
\(443\) | 16058.7 | 1.72229 | 0.861143 | − | 0.508362i | \(-0.169749\pi\) | ||||
0.861143 | + | 0.508362i | \(0.169749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7368.62 | −0.784958 | ||||||||
\(446\) | −3842.09 | −0.407911 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5374.30 | −0.566768 | ||||||||
\(449\) | −2186.75 | −0.229842 | −0.114921 | − | 0.993375i | \(-0.536662\pi\) | ||||
−0.114921 | + | 0.993375i | \(0.536662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8308.05 | −0.867430 | ||||||||
\(452\) | 23388.3 | 2.43384 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17188.2 | 1.77683 | ||||||||
\(455\) | −1225.55 | −0.126274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5799.22 | −0.593602 | −0.296801 | − | 0.954939i | \(-0.595920\pi\) | ||||
−0.296801 | + | 0.954939i | \(0.595920\pi\) | |||||||
\(458\) | −4416.62 | −0.450600 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10273.5 | 1.04131 | ||||||||
\(461\) | −9873.35 | −0.997500 | −0.498750 | − | 0.866746i | \(-0.666207\pi\) | ||||
−0.498750 | + | 0.866746i | \(0.666207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6181.84 | −0.620506 | −0.310253 | − | 0.950654i | \(-0.600414\pi\) | ||||
−0.310253 | + | 0.950654i | \(0.600414\pi\) | |||||||
\(464\) | −4739.66 | −0.474209 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.9529 | −0.00357400 | ||||||||
\(467\) | −6145.50 | −0.608950 | −0.304475 | − | 0.952520i | \(-0.598481\pi\) | ||||
−0.304475 | + | 0.952520i | \(0.598481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6355.69 | −0.625754 | ||||||||
\(470\) | 8326.91 | 0.817216 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14388.6 | 1.40316 | ||||||||
\(473\) | −3004.66 | −0.292081 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1685.08 | −0.162772 | ||||||||
\(476\) | 1818.53 | 0.175110 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4180.23 | −0.399999 | ||||||||
\(479\) | −10879.4 | −1.03777 | −0.518887 | − | 0.854843i | \(-0.673653\pi\) | ||||
−0.518887 | + | 0.854843i | \(0.673653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5676.91 | −0.538139 | ||||||||
\(482\) | −10062.4 | −0.950894 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10239.9 | −0.961675 | ||||||||
\(485\) | 2775.17 | 0.259823 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8087.51 | 0.752526 | 0.376263 | − | 0.926513i | \(-0.377209\pi\) | ||||
0.376263 | + | 0.926513i | \(0.377209\pi\) | |||||||
\(488\) | 20347.4 | 1.88747 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1151.88 | −0.106197 | ||||||||
\(491\) | 6959.90 | 0.639707 | 0.319853 | − | 0.947467i | \(-0.396366\pi\) | ||||
0.319853 | + | 0.947467i | \(0.396366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3949.32 | −0.360788 | ||||||||
\(494\) | −11096.4 | −1.01063 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1959.79 | −0.177413 | ||||||||
\(497\) | −3012.34 | −0.271875 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18632.0 | 1.67151 | 0.835756 | − | 0.549101i | \(-0.185030\pi\) | ||||
0.835756 | + | 0.549101i | \(0.185030\pi\) | |||||||
\(500\) | 1763.09 | 0.157695 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31734.6 | −2.82149 | ||||||||
\(503\) | −4627.62 | −0.410209 | −0.205105 | − | 0.978740i | \(-0.565753\pi\) | ||||
−0.205105 | + | 0.978740i | \(0.565753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9450.72 | −0.832775 | ||||||||
\(506\) | 16846.4 | 1.48007 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15639.4 | −1.36592 | ||||||||
\(509\) | 11351.8 | 0.988528 | 0.494264 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494264 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 289.384 | 0.0250521 | ||||||||
\(512\) | 7853.76 | 0.677911 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14427.4 | 1.23806 | ||||||||
\(515\) | 3313.50 | 0.283515 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8712.67 | 0.741166 | ||||||||
\(518\) | −5335.68 | −0.452580 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5025.02 | 0.423772 | ||||||||
\(521\) | −19096.1 | −1.60579 | −0.802893 | − | 0.596123i | \(-0.796707\pi\) | ||||
−0.802893 | + | 0.596123i | \(0.796707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3145.11 | −0.262956 | −0.131478 | − | 0.991319i | \(-0.541972\pi\) | ||||
−0.131478 | + | 0.991319i | \(0.541972\pi\) | |||||||
\(524\) | −2616.24 | −0.218113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21975.7 | −1.82164 | ||||||||
\(527\) | −1632.99 | −0.134980 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9054.20 | 0.744160 | ||||||||
\(530\) | 15907.5 | 1.30373 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6654.90 | −0.542343 | ||||||||
\(533\) | −11827.2 | −0.961148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8072.66 | −0.652358 | ||||||||
\(536\) | 26059.8 | 2.10002 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11365.5 | 0.910781 | ||||||||
\(539\) | −1205.25 | −0.0963148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8776.12 | 0.697440 | 0.348720 | − | 0.937227i | \(-0.386616\pi\) | ||||
0.348720 | + | 0.937227i | \(0.386616\pi\) | |||||||
\(542\) | −36316.3 | −2.87808 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2314.98 | 0.182452 | ||||||||
\(545\) | 1086.03 | 0.0853587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13695.1 | −1.07049 | −0.535247 | − | 0.844696i | \(-0.679781\pi\) | ||||
−0.535247 | + | 0.844696i | \(0.679781\pi\) | |||||||
\(548\) | 535.847 | 0.0417705 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2891.09 | 0.224139 | ||||||||
\(551\) | 14452.5 | 1.11742 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6232.71 | 0.479280 | ||||||||
\(554\) | 21515.2 | 1.64999 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2589.75 | 0.197536 | ||||||||
\(557\) | −7850.44 | −0.597188 | −0.298594 | − | 0.954380i | \(-0.596518\pi\) | ||||
−0.298594 | + | 0.954380i | \(0.596518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4277.38 | −0.323638 | ||||||||
\(560\) | 773.664 | 0.0583808 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6387.33 | −0.479419 | ||||||||
\(563\) | 4948.81 | 0.370457 | 0.185229 | − | 0.982695i | \(-0.440697\pi\) | ||||
0.185229 | + | 0.982695i | \(0.440697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8290.98 | 0.617353 | ||||||||
\(566\) | −18265.7 | −1.35648 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12351.3 | 0.912408 | ||||||||
\(569\) | 8115.76 | 0.597945 | 0.298972 | − | 0.954262i | \(-0.403356\pi\) | ||||
0.298972 | + | 0.954262i | \(0.403356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5656.42 | 0.414560 | 0.207280 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207280 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(572\) | 12148.0 | 0.887996 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11116.3 | −0.808336 | ||||||||
\(575\) | 3641.87 | 0.264133 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9536.77 | −0.688078 | −0.344039 | − | 0.938955i | \(-0.611795\pi\) | ||||
−0.344039 | + | 0.938955i | \(0.611795\pi\) | |||||||
\(578\) | 21503.8 | 1.54747 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15121.5 | −1.08257 | ||||||||
\(581\) | 7400.05 | 0.528409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16644.5 | 1.18241 | ||||||||
\(584\) | −1186.54 | −0.0840743 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18965.7 | −1.33697 | ||||||||
\(587\) | 13089.6 | 0.920383 | 0.460191 | − | 0.887820i | \(-0.347781\pi\) | ||||
0.460191 | + | 0.887820i | \(0.347781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5975.92 | 0.418053 | ||||||||
\(590\) | 11784.9 | 0.822334 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3583.72 | 0.248801 | ||||||||
\(593\) | −4281.96 | −0.296524 | −0.148262 | − | 0.988948i | \(-0.547368\pi\) | ||||
−0.148262 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 644.656 | 0.0444173 | ||||||||
\(596\) | 19511.5 | 1.34098 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23982.2 | 1.63997 | ||||||||
\(599\) | −3699.92 | −0.252378 | −0.126189 | − | 0.992006i | \(-0.540275\pi\) | ||||
−0.126189 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17286.1 | −1.17323 | −0.586616 | − | 0.809865i | \(-0.699540\pi\) | ||||
−0.586616 | + | 0.809865i | \(0.699540\pi\) | |||||||
\(602\) | −4020.28 | −0.272183 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10793.7 | 0.727135 | ||||||||
\(605\) | −3629.97 | −0.243933 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14456.7 | 0.966689 | 0.483344 | − | 0.875430i | \(-0.339422\pi\) | ||||
0.483344 | + | 0.875430i | \(0.339422\pi\) | |||||||
\(608\) | −8471.63 | −0.565082 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16665.4 | 1.10617 | ||||||||
\(611\) | 12403.2 | 0.821243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17981.9 | 1.18480 | 0.592400 | − | 0.805644i | \(-0.298181\pi\) | ||||
0.592400 | + | 0.805644i | \(0.298181\pi\) | |||||||
\(614\) | 21722.9 | 1.42779 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4941.78 | 0.323231 | ||||||||
\(617\) | −19614.7 | −1.27983 | −0.639916 | − | 0.768445i | \(-0.721031\pi\) | ||||
−0.639916 | + | 0.768445i | \(0.721031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10462.9 | −0.679385 | −0.339692 | − | 0.940537i | \(-0.610323\pi\) | ||||
−0.339692 | + | 0.940537i | \(0.610323\pi\) | |||||||
\(620\) | −6252.56 | −0.405014 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31387.1 | 2.02332 | ||||||||
\(623\) | −10316.1 | −0.663411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −13337.3 | −0.851544 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33382.4 | −2.12118 | ||||||||
\(629\) | 2986.14 | 0.189293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24481.9 | 1.54454 | 0.772272 | − | 0.635292i | \(-0.219120\pi\) | ||||
0.772272 | + | 0.635292i | \(0.219120\pi\) | |||||||
\(632\) | −25555.5 | −1.60846 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18856.2 | 1.18119 | ||||||||
\(635\) | −5544.06 | −0.346471 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1715.77 | −0.106721 | ||||||||
\(638\) | −24796.2 | −1.53870 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13020.9 | 0.804211 | ||||||||
\(641\) | 1109.39 | 0.0683595 | 0.0341797 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341797 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30112.5 | 1.84684 | 0.923422 | − | 0.383787i | \(-0.125380\pi\) | ||||
0.923422 | + | 0.383787i | \(0.125380\pi\) | |||||||
\(644\) | 14382.9 | 0.880071 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5836.90 | 0.355495 | ||||||||
\(647\) | 4260.27 | 0.258869 | 0.129435 | − | 0.991588i | \(-0.458684\pi\) | ||||
0.129435 | + | 0.991588i | \(0.458684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12330.9 | 0.745808 | ||||||||
\(650\) | 4115.70 | 0.248356 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44256.2 | −2.65829 | ||||||||
\(653\) | 10576.8 | 0.633844 | 0.316922 | − | 0.948452i | \(-0.397351\pi\) | ||||
0.316922 | + | 0.948452i | \(0.397351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −927.438 | −0.0553252 | ||||||||
\(656\) | 7466.27 | 0.444373 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11657.7 | 0.690674 | ||||||||
\(659\) | −3394.70 | −0.200666 | −0.100333 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100333 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33174.4 | −1.95210 | −0.976048 | − | 0.217554i | \(-0.930192\pi\) | ||||
−0.976048 | + | 0.217554i | \(0.930192\pi\) | |||||||
\(662\) | −52128.7 | −3.06048 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30341.9 | −1.77333 | ||||||||
\(665\) | −2359.11 | −0.137567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31235.4 | −1.81326 | ||||||||
\(668\) | −2065.89 | −0.119658 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21344.1 | 1.23074 | ||||||||
\(671\) | 17437.5 | 1.00323 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 753.881 | 0.0431797 | 0.0215899 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215899 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(674\) | −56976.9 | −3.25619 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13694.3 | −0.779149 | ||||||||
\(677\) | −15668.8 | −0.889511 | −0.444756 | − | 0.895652i | \(-0.646709\pi\) | ||||
−0.444756 | + | 0.895652i | \(0.646709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3885.24 | 0.219590 | ||||||||
\(680\) | −2643.23 | −0.149064 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10252.9 | −0.575665 | ||||||||
\(683\) | 11557.4 | 0.647485 | 0.323742 | − | 0.946145i | \(-0.395059\pi\) | ||||
0.323742 | + | 0.946145i | \(0.395059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 189.953 | 0.0105952 | ||||||||
\(686\) | −1612.64 | −0.0897532 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2700.22 | 0.149630 | ||||||||
\(689\) | 23694.7 | 1.31016 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18503.1 | −1.01866 | −0.509328 | − | 0.860572i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(692\) | 20086.8 | 1.10344 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29907.7 | −1.63585 | ||||||||
\(695\) | 918.046 | 0.0501057 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6221.28 | 0.338088 | ||||||||
\(698\) | 14646.2 | 0.794223 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2468.32 | 0.133277 | ||||||||
\(701\) | −22580.4 | −1.21662 | −0.608311 | − | 0.793699i | \(-0.708153\pi\) | ||||
−0.608311 | + | 0.793699i | \(0.708153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10927.7 | −0.586269 | ||||||||
\(704\) | 18884.4 | 1.01099 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −56077.4 | −2.98938 | ||||||||
\(707\) | −13231.0 | −0.703823 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27426.6 | −1.45279 | −0.726394 | − | 0.687278i | \(-0.758805\pi\) | ||||
−0.726394 | + | 0.687278i | \(0.758805\pi\) | |||||||
\(710\) | 10116.2 | 0.534725 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 42298.2 | 2.22639 | ||||||||
\(713\) | −12915.5 | −0.678383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4306.37 | 0.225244 | ||||||||
\(716\) | −17556.1 | −0.916342 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28886.1 | −1.50142 | ||||||||
\(719\) | −19383.0 | −1.00538 | −0.502688 | − | 0.864468i | \(-0.667656\pi\) | ||||
−0.502688 | + | 0.864468i | \(0.667656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4638.90 | 0.239614 | ||||||||
\(722\) | 10888.0 | 0.561230 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −54713.3 | −2.80857 | ||||||||
\(725\) | −5360.47 | −0.274597 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12317.3 | −0.628368 | −0.314184 | − | 0.949362i | \(-0.601731\pi\) | ||||
−0.314184 | + | 0.949362i | \(0.601731\pi\) | |||||||
\(728\) | 7035.02 | 0.358153 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −971.828 | −0.0492726 | ||||||||
\(731\) | 2249.96 | 0.113841 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1234.02 | 0.0621822 | 0.0310911 | − | 0.999517i | \(-0.490102\pi\) | ||||
0.0310911 | + | 0.999517i | \(0.490102\pi\) | |||||||
\(734\) | 9063.05 | 0.455754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18309.3 | 0.916970 | ||||||||
\(737\) | 22332.9 | 1.11620 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15257.3 | −0.759473 | −0.379736 | − | 0.925095i | \(-0.623985\pi\) | ||||
−0.379736 | + | 0.925095i | \(0.623985\pi\) | |||||||
\(740\) | 11433.6 | 0.567984 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22270.5 | 1.10186 | ||||||||
\(743\) | 35565.1 | 1.75606 | 0.878032 | − | 0.478602i | \(-0.158856\pi\) | ||||
0.878032 | + | 0.478602i | \(0.158856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6916.69 | 0.340145 | ||||||||
\(746\) | −49140.8 | −2.41176 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6390.04 | −0.312357 | ||||||||
\(749\) | −11301.7 | −0.551343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14266.7 | 0.693209 | 0.346605 | − | 0.938011i | \(-0.387335\pi\) | ||||
0.346605 | + | 0.938011i | \(0.387335\pi\) | |||||||
\(752\) | −7829.89 | −0.379690 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −35299.4 | −1.70494 | ||||||||
\(755\) | 3826.28 | 0.184441 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15927.9 | −0.764744 | −0.382372 | − | 0.924009i | \(-0.624893\pi\) | ||||
−0.382372 | + | 0.924009i | \(0.624893\pi\) | |||||||
\(758\) | −33223.3 | −1.59198 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9672.87 | 0.461674 | ||||||||
\(761\) | 2566.48 | 0.122253 | 0.0611266 | − | 0.998130i | \(-0.480531\pi\) | ||||
0.0611266 | + | 0.998130i | \(0.480531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1520.44 | 0.0721413 | ||||||||
\(764\) | −22213.5 | −1.05191 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33701.0 | 1.58964 | ||||||||
\(767\) | 17554.0 | 0.826386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14433.1 | 0.676816 | 0.338408 | − | 0.940999i | \(-0.390112\pi\) | ||||
0.338408 | + | 0.940999i | \(0.390112\pi\) | |||||||
\(770\) | 4047.53 | 0.189432 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −67359.4 | −3.14031 | ||||||||
\(773\) | 29443.2 | 1.36999 | 0.684993 | − | 0.728550i | \(-0.259805\pi\) | ||||
0.684993 | + | 0.728550i | \(0.259805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2216.48 | −0.102733 | ||||||||
\(776\) | −15930.4 | −0.736941 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34857.7 | −1.60631 | ||||||||
\(779\) | −22766.7 | −1.04711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10584.9 | 0.484964 | ||||||||
\(782\) | −12615.0 | −0.576869 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1083.13 | 0.0493408 | ||||||||
\(785\) | −11833.8 | −0.538046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26390.6 | 1.19533 | 0.597664 | − | 0.801747i | \(-0.296096\pi\) | ||||
0.597664 | + | 0.801747i | \(0.296096\pi\) | |||||||
\(788\) | 39543.6 | 1.78767 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20931.1 | −0.942650 | ||||||||
\(791\) | 11607.4 | 0.521758 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24823.7 | 1.11162 | ||||||||
\(794\) | 42013.2 | 1.87783 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 57870.3 | 2.57683 | ||||||||
\(797\) | 3738.33 | 0.166146 | 0.0830730 | − | 0.996543i | \(-0.473527\pi\) | ||||
0.0830730 | + | 0.996543i | \(0.473527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6524.26 | −0.288876 | ||||||||
\(800\) | 3142.15 | 0.138865 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8382.48 | 0.369072 | ||||||||
\(803\) | −1016.85 | −0.0446873 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5098.62 | 0.223233 | ||||||||
\(806\) | −14595.8 | −0.637861 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 54250.1 | 2.36202 | ||||||||
\(809\) | −43204.1 | −1.87760 | −0.938798 | − | 0.344468i | \(-0.888059\pi\) | ||||
−0.938798 | + | 0.344468i | \(0.888059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30192.4 | −1.30727 | −0.653637 | − | 0.756809i | \(-0.726758\pi\) | ||||
−0.653637 | + | 0.756809i | \(0.726758\pi\) | |||||||
\(812\) | −21170.2 | −0.914935 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18748.7 | 0.807301 | ||||||||
\(815\) | −15688.5 | −0.674286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8233.71 | −0.352584 | ||||||||
\(818\) | 41185.3 | 1.76041 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23820.6 | 1.01445 | ||||||||
\(821\) | 40274.7 | 1.71206 | 0.856028 | − | 0.516929i | \(-0.172925\pi\) | ||||
0.856028 | + | 0.516929i | \(0.172925\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25184.2 | 1.06667 | 0.533334 | − | 0.845905i | \(-0.320939\pi\) | ||||
0.533334 | + | 0.845905i | \(0.320939\pi\) | |||||||
\(824\) | −19020.5 | −0.804140 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16498.9 | 0.694999 | ||||||||
\(827\) | 38941.7 | 1.63741 | 0.818703 | − | 0.574218i | \(-0.194694\pi\) | ||||
0.818703 | + | 0.574218i | \(0.194694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8327.05 | −0.348867 | −0.174433 | − | 0.984669i | \(-0.555809\pi\) | ||||
−0.174433 | + | 0.984669i | \(0.555809\pi\) | |||||||
\(830\) | −24851.3 | −1.03928 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26883.5 | 1.12021 | ||||||||
\(833\) | 902.519 | 0.0375395 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −732.343 | −0.0303518 | ||||||||
\(836\) | 23384.2 | 0.967418 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15104.9 | −0.622660 | ||||||||
\(839\) | −8784.41 | −0.361468 | −0.180734 | − | 0.983532i | \(-0.557847\pi\) | ||||
−0.180734 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21586.4 | 0.885087 | ||||||||
\(842\) | −74086.4 | −3.03229 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11615.4 | −0.473718 | ||||||||
\(845\) | −4854.53 | −0.197634 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5081.96 | −0.206161 | ||||||||
\(848\) | −14958.0 | −0.605732 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2164.92 | −0.0873602 | ||||||||
\(851\) | 23617.6 | 0.951350 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9076.15 | −0.364316 | −0.182158 | − | 0.983269i | \(-0.558308\pi\) | ||||
−0.182158 | + | 0.983269i | \(0.558308\pi\) | |||||||
\(854\) | 23331.6 | 0.934884 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46339.6 | 1.85030 | ||||||||
\(857\) | −36396.7 | −1.45074 | −0.725372 | − | 0.688357i | \(-0.758332\pi\) | ||||
−0.725372 | + | 0.688357i | \(0.758332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8915.27 | 0.354115 | 0.177058 | − | 0.984200i | \(-0.443342\pi\) | ||||
0.177058 | + | 0.984200i | \(0.443342\pi\) | |||||||
\(860\) | 8614.88 | 0.341587 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1908.44 | −0.0754081 | ||||||||
\(863\) | 6148.26 | 0.242514 | 0.121257 | − | 0.992621i | \(-0.461308\pi\) | ||||
0.121257 | + | 0.992621i | \(0.461308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7120.59 | 0.279893 | ||||||||
\(866\) | 36884.9 | 1.44735 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8753.59 | −0.342300 | ||||||||
\(869\) | −21900.8 | −0.854928 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31792.6 | 1.23680 | ||||||||
\(872\) | −6234.16 | −0.242105 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 46164.4 | 1.78665 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14287.0 | −0.550101 | −0.275050 | − | 0.961430i | \(-0.588694\pi\) | ||||
−0.275050 | + | 0.961430i | \(0.588694\pi\) | |||||||
\(878\) | −1988.90 | −0.0764488 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2718.53 | −0.104138 | ||||||||
\(881\) | 13315.9 | 0.509221 | 0.254610 | − | 0.967044i | \(-0.418053\pi\) | ||||
0.254610 | + | 0.967044i | \(0.418053\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5271.78 | −0.200917 | −0.100458 | − | 0.994941i | \(-0.532031\pi\) | ||||
−0.100458 | + | 0.994941i | \(0.532031\pi\) | |||||||
\(884\) | −9096.73 | −0.346104 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −75501.1 | −2.86288 | ||||||||
\(887\) | −2606.07 | −0.0986507 | −0.0493253 | − | 0.998783i | \(-0.515707\pi\) | ||||
−0.0493253 | + | 0.998783i | \(0.515707\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7761.69 | −0.292822 | ||||||||
\(890\) | 34644.0 | 1.30480 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11526.3 | 0.432654 | ||||||||
\(893\) | 23875.4 | 0.894694 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6223.48 | −0.232434 | ||||||||
\(896\) | 18229.2 | 0.679682 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10281.1 | 0.382056 | ||||||||
\(899\) | 19010.2 | 0.705258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12463.8 | −0.460854 | ||||||||
\(902\) | 39060.8 | 1.44189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47592.8 | −1.75101 | ||||||||
\(905\) | −19395.4 | −0.712405 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18610.6 | 0.681317 | 0.340659 | − | 0.940187i | \(-0.389350\pi\) | ||||
0.340659 | + | 0.940187i | \(0.389350\pi\) | |||||||
\(908\) | −51564.6 | −1.88462 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5761.98 | 0.209899 | ||||||||
\(911\) | −41091.7 | −1.49443 | −0.747216 | − | 0.664581i | \(-0.768610\pi\) | ||||
−0.747216 | + | 0.664581i | \(0.768610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26002.6 | −0.942563 | ||||||||
\(914\) | 27265.4 | 0.986716 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13249.8 | 0.477934 | ||||||||
\(917\) | −1298.41 | −0.0467583 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38891.3 | 1.39598 | 0.697990 | − | 0.716107i | \(-0.254078\pi\) | ||||
0.697990 | + | 0.716107i | \(0.254078\pi\) | |||||||
\(920\) | −20905.5 | −0.749167 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46420.2 | 1.65810 | ||||||||
\(923\) | 15068.4 | 0.537360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4053.12 | 0.144071 | ||||||||
\(926\) | 29064.3 | 1.03144 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26949.4 | −0.953295 | ||||||||
\(929\) | −18699.4 | −0.660396 | −0.330198 | − | 0.943912i | \(-0.607115\pi\) | ||||
−0.330198 | + | 0.943912i | \(0.607115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3302.75 | −0.116266 | ||||||||
\(932\) | 107.859 | 0.00379080 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28893.4 | 1.01223 | ||||||||
\(935\) | −2265.22 | −0.0792305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21509.6 | 0.749933 | 0.374967 | − | 0.927038i | \(-0.377654\pi\) | ||||
0.374967 | + | 0.927038i | \(0.377654\pi\) | |||||||
\(938\) | 29881.7 | 1.04016 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24980.7 | −0.866788 | ||||||||
\(941\) | 11241.7 | 0.389448 | 0.194724 | − | 0.980858i | \(-0.437619\pi\) | ||||
0.194724 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49204.5 | 1.69917 | ||||||||
\(944\) | −11081.5 | −0.382068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14126.6 | 0.485513 | ||||||||
\(947\) | 36556.3 | 1.25441 | 0.627203 | − | 0.778856i | \(-0.284200\pi\) | ||||
0.627203 | + | 0.778856i | \(0.284200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1447.57 | −0.0495153 | ||||||||
\(950\) | 7922.50 | 0.270568 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3700.53 | −0.125982 | ||||||||
\(953\) | 36633.4 | 1.24520 | 0.622598 | − | 0.782542i | \(-0.286077\pi\) | ||||
0.622598 | + | 0.782542i | \(0.286077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7874.52 | −0.266820 | ||||||||
\(956\) | 12540.7 | 0.424263 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 51150.3 | 1.72504 | ||||||||
\(959\) | 265.935 | 0.00895462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21930.5 | −0.736146 | ||||||||
\(962\) | 26690.3 | 0.894523 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30187.3 | 1.00858 | ||||||||
\(965\) | −23878.4 | −0.796551 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35515.8 | −1.18109 | −0.590544 | − | 0.807006i | \(-0.701087\pi\) | ||||
−0.590544 | + | 0.807006i | \(0.701087\pi\) | |||||||
\(968\) | 20837.2 | 0.691871 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13047.6 | −0.431891 | ||||||||
\(971\) | 39661.0 | 1.31080 | 0.655398 | − | 0.755283i | \(-0.272501\pi\) | ||||
0.655398 | + | 0.755283i | \(0.272501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1285.26 | 0.0423471 | ||||||||
\(974\) | −38023.9 | −1.25089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15670.7 | −0.513942 | ||||||||
\(977\) | −50325.3 | −1.64795 | −0.823977 | − | 0.566624i | \(-0.808249\pi\) | ||||
−0.823977 | + | 0.566624i | \(0.808249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36249.0 | 1.18337 | ||||||||
\(980\) | 3455.65 | 0.112639 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32722.4 | −1.06335 | ||||||||
\(983\) | −51189.0 | −1.66091 | −0.830456 | − | 0.557084i | \(-0.811920\pi\) | ||||
−0.830456 | + | 0.557084i | \(0.811920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14017.9 | 0.453449 | ||||||||
\(986\) | 18568.0 | 0.599721 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33289.3 | 1.07194 | ||||||||
\(989\) | 17795.1 | 0.572145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55137.3 | −1.76740 | −0.883700 | − | 0.468054i | \(-0.844955\pi\) | ||||
−0.883700 | + | 0.468054i | \(0.844955\pi\) | |||||||
\(992\) | −11143.2 | −0.356651 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14162.7 | 0.451925 | ||||||||
\(995\) | 20514.6 | 0.653624 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41606.5 | 1.32166 | 0.660828 | − | 0.750537i | \(-0.270205\pi\) | ||||
0.660828 | + | 0.750537i | \(0.270205\pi\) | |||||||
\(998\) | −87599.6 | −2.77848 | ||||||||
\(999\) | 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 | 315.4.a.g.1.1 | 2 | ||
3.2 | odd | 2 | 105.4.a.g.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 1575.4.a.y.1.2 | 2 | |||
7.6 | odd | 2 | 2205.4.a.v.1.1 | 2 | |||
12.11 | even | 2 | 1680.4.a.y.1.2 | 2 | |||
15.2 | even | 4 | 525.4.d.j.274.4 | 4 | |||
15.8 | even | 4 | 525.4.d.j.274.1 | 4 | |||
15.14 | odd | 2 | 525.4.a.i.1.1 | 2 | |||
21.20 | even | 2 | 735.4.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.g.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
315.4.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
525.4.a.i.1.1 | 2 | 15.14 | odd | 2 | |||
525.4.d.j.274.1 | 4 | 15.8 | even | 4 | |||
525.4.d.j.274.4 | 4 | 15.2 | even | 4 | |||
735.4.a.q.1.2 | 2 | 21.20 | even | 2 | |||
1575.4.a.y.1.2 | 2 | 5.4 | even | 2 | |||
1680.4.a.y.1.2 | 2 | 12.11 | even | 2 | |||
2205.4.a.v.1.1 | 2 | 7.6 | odd | 2 |