Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 92x^{3} - 28x^{2} + 1593x - 1782 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.17693\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −7.17693 | −1.38120 | −0.690600 | − | 0.723237i | \(-0.742654\pi\) | ||||
−0.690600 | + | 0.723237i | \(0.742654\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −18.7050 | −1.67302 | −0.836511 | − | 0.547949i | \(-0.815409\pi\) | ||||
−0.836511 | + | 0.547949i | \(0.815409\pi\) | |||||||
\(6\) | −14.3539 | −0.976656 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 24.5083 | 0.907714 | ||||||||
\(10\) | −37.4099 | −1.18301 | ||||||||
\(11\) | −36.8949 | −1.01129 | −0.505646 | − | 0.862741i | \(-0.668746\pi\) | ||||
−0.505646 | + | 0.862741i | \(0.668746\pi\) | |||||||
\(12\) | −28.7077 | −0.690600 | ||||||||
\(13\) | −22.7900 | −0.486216 | −0.243108 | − | 0.969999i | \(-0.578167\pi\) | ||||
−0.243108 | + | 0.969999i | \(0.578167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 134.244 | 2.31078 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −66.6941 | −0.951511 | −0.475756 | − | 0.879577i | \(-0.657825\pi\) | ||||
−0.475756 | + | 0.879577i | \(0.657825\pi\) | |||||||
\(18\) | 49.0166 | 0.641851 | ||||||||
\(19\) | 106.301 | 1.28353 | 0.641765 | − | 0.766901i | \(-0.278203\pi\) | ||||
0.641765 | + | 0.766901i | \(0.278203\pi\) | |||||||
\(20\) | −74.8199 | −0.836511 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −73.7897 | −0.715092 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −57.4154 | −0.488328 | ||||||||
\(25\) | 224.876 | 1.79901 | ||||||||
\(26\) | −45.5800 | −0.343807 | ||||||||
\(27\) | 17.8829 | 0.127465 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −199.773 | −1.27921 | −0.639603 | − | 0.768705i | \(-0.720901\pi\) | ||||
−0.639603 | + | 0.768705i | \(0.720901\pi\) | |||||||
\(30\) | 268.488 | 1.63397 | ||||||||
\(31\) | 262.034 | 1.51815 | 0.759075 | − | 0.651003i | \(-0.225651\pi\) | ||||
0.759075 | + | 0.651003i | \(0.225651\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 264.792 | 1.39680 | ||||||||
\(34\) | −133.388 | −0.672820 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 98.0331 | 0.453857 | ||||||||
\(37\) | 202.174 | 0.898302 | 0.449151 | − | 0.893456i | \(-0.351726\pi\) | ||||
0.449151 | + | 0.893456i | \(0.351726\pi\) | |||||||
\(38\) | 212.601 | 0.907593 | ||||||||
\(39\) | 163.562 | 0.671562 | ||||||||
\(40\) | −149.640 | −0.591503 | ||||||||
\(41\) | −44.4679 | −0.169383 | −0.0846917 | − | 0.996407i | \(-0.526991\pi\) | ||||
−0.0846917 | + | 0.996407i | \(0.526991\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18.2027 | −0.0645556 | −0.0322778 | − | 0.999479i | \(-0.510276\pi\) | ||||
−0.0322778 | + | 0.999479i | \(0.510276\pi\) | |||||||
\(44\) | −147.579 | −0.505646 | ||||||||
\(45\) | −458.426 | −1.51863 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 306.525 | 0.951305 | 0.475652 | − | 0.879633i | \(-0.342212\pi\) | ||||
0.475652 | + | 0.879633i | \(0.342212\pi\) | |||||||
\(48\) | −114.831 | −0.345300 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 449.751 | 1.27209 | ||||||||
\(51\) | 478.659 | 1.31423 | ||||||||
\(52\) | −91.1600 | −0.243108 | ||||||||
\(53\) | 300.565 | 0.778977 | 0.389488 | − | 0.921031i | \(-0.372652\pi\) | ||||
0.389488 | + | 0.921031i | \(0.372652\pi\) | |||||||
\(54\) | 35.7658 | 0.0901317 | ||||||||
\(55\) | 690.117 | 1.69192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −762.913 | −1.77281 | ||||||||
\(58\) | −399.547 | −0.904535 | ||||||||
\(59\) | −255.485 | −0.563750 | −0.281875 | − | 0.959451i | \(-0.590956\pi\) | ||||
−0.281875 | + | 0.959451i | \(0.590956\pi\) | |||||||
\(60\) | 536.977 | 1.15539 | ||||||||
\(61\) | −598.006 | −1.25519 | −0.627597 | − | 0.778538i | \(-0.715961\pi\) | ||||
−0.627597 | + | 0.778538i | \(0.715961\pi\) | |||||||
\(62\) | 524.068 | 1.07349 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 426.286 | 0.813451 | ||||||||
\(66\) | 529.584 | 0.987685 | ||||||||
\(67\) | −636.773 | −1.16111 | −0.580553 | − | 0.814222i | \(-0.697164\pi\) | ||||
−0.580553 | + | 0.814222i | \(0.697164\pi\) | |||||||
\(68\) | −266.776 | −0.475756 | ||||||||
\(69\) | −165.069 | −0.288000 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 320.916 | 0.536418 | 0.268209 | − | 0.963361i | \(-0.413568\pi\) | ||||
0.268209 | + | 0.963361i | \(0.413568\pi\) | |||||||
\(72\) | 196.066 | 0.320925 | ||||||||
\(73\) | 24.5948 | 0.0394330 | 0.0197165 | − | 0.999806i | \(-0.493724\pi\) | ||||
0.0197165 | + | 0.999806i | \(0.493724\pi\) | |||||||
\(74\) | 404.348 | 0.635196 | ||||||||
\(75\) | −1613.92 | −2.48479 | ||||||||
\(76\) | 425.203 | 0.641765 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 327.124 | 0.474866 | ||||||||
\(79\) | 1121.21 | 1.59678 | 0.798390 | − | 0.602141i | \(-0.205685\pi\) | ||||
0.798390 | + | 0.602141i | \(0.205685\pi\) | |||||||
\(80\) | −299.279 | −0.418256 | ||||||||
\(81\) | −790.068 | −1.08377 | ||||||||
\(82\) | −88.9358 | −0.119772 | ||||||||
\(83\) | 767.685 | 1.01523 | 0.507617 | − | 0.861583i | \(-0.330527\pi\) | ||||
0.507617 | + | 0.861583i | \(0.330527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1247.51 | 1.59190 | ||||||||
\(86\) | −36.4055 | −0.0456477 | ||||||||
\(87\) | 1433.76 | 1.76684 | ||||||||
\(88\) | −295.159 | −0.357546 | ||||||||
\(89\) | 807.439 | 0.961667 | 0.480833 | − | 0.876812i | \(-0.340334\pi\) | ||||
0.480833 | + | 0.876812i | \(0.340334\pi\) | |||||||
\(90\) | −916.853 | −1.07383 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −1880.60 | −2.09687 | ||||||||
\(94\) | 613.051 | 0.672674 | ||||||||
\(95\) | −1988.35 | −2.14737 | ||||||||
\(96\) | −229.662 | −0.244164 | ||||||||
\(97\) | −1170.29 | −1.22500 | −0.612500 | − | 0.790471i | \(-0.709836\pi\) | ||||
−0.612500 | + | 0.790471i | \(0.709836\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −904.230 | −0.917965 | ||||||||
\(100\) | 899.503 | 0.899503 | ||||||||
\(101\) | 554.631 | 0.546414 | 0.273207 | − | 0.961955i | \(-0.411916\pi\) | ||||
0.273207 | + | 0.961955i | \(0.411916\pi\) | |||||||
\(102\) | 957.317 | 0.929299 | ||||||||
\(103\) | 1018.33 | 0.974166 | 0.487083 | − | 0.873356i | \(-0.338061\pi\) | ||||
0.487083 | + | 0.873356i | \(0.338061\pi\) | |||||||
\(104\) | −182.320 | −0.171903 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 601.130 | 0.550820 | ||||||||
\(107\) | 1451.75 | 1.31164 | 0.655821 | − | 0.754916i | \(-0.272322\pi\) | ||||
0.655821 | + | 0.754916i | \(0.272322\pi\) | |||||||
\(108\) | 71.5317 | 0.0637327 | ||||||||
\(109\) | 1719.61 | 1.51109 | 0.755544 | − | 0.655098i | \(-0.227372\pi\) | ||||
0.755544 | + | 0.655098i | \(0.227372\pi\) | |||||||
\(110\) | 1380.23 | 1.19637 | ||||||||
\(111\) | −1450.99 | −1.24074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2162.47 | −1.80025 | −0.900126 | − | 0.435630i | \(-0.856525\pi\) | ||||
−0.900126 | + | 0.435630i | \(0.856525\pi\) | |||||||
\(114\) | −1525.83 | −1.25357 | ||||||||
\(115\) | −430.214 | −0.348849 | ||||||||
\(116\) | −799.093 | −0.639603 | ||||||||
\(117\) | −558.544 | −0.441345 | ||||||||
\(118\) | −510.969 | −0.398631 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1073.95 | 0.816984 | ||||||||
\(121\) | 30.2313 | 0.0227132 | ||||||||
\(122\) | −1196.01 | −0.887556 | ||||||||
\(123\) | 319.143 | 0.233952 | ||||||||
\(124\) | 1048.14 | 0.759075 | ||||||||
\(125\) | −1868.17 | −1.33675 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1462.69 | 1.02199 | 0.510994 | − | 0.859584i | \(-0.329278\pi\) | ||||
0.510994 | + | 0.859584i | \(0.329278\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 130.640 | 0.0891642 | ||||||||
\(130\) | 852.573 | 0.575197 | ||||||||
\(131\) | −1970.02 | −1.31390 | −0.656952 | − | 0.753932i | \(-0.728155\pi\) | ||||
−0.656952 | + | 0.753932i | \(0.728155\pi\) | |||||||
\(132\) | 1059.17 | 0.698399 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1273.55 | −0.821027 | ||||||||
\(135\) | −334.499 | −0.213253 | ||||||||
\(136\) | −533.553 | −0.336410 | ||||||||
\(137\) | −2064.12 | −1.28722 | −0.643611 | − | 0.765353i | \(-0.722565\pi\) | ||||
−0.643611 | + | 0.765353i | \(0.722565\pi\) | |||||||
\(138\) | −330.139 | −0.203647 | ||||||||
\(139\) | −9.19537 | −0.00561108 | −0.00280554 | − | 0.999996i | \(-0.500893\pi\) | ||||
−0.00280554 | + | 0.999996i | \(0.500893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2199.91 | −1.31394 | ||||||||
\(142\) | 641.831 | 0.379305 | ||||||||
\(143\) | 840.834 | 0.491707 | ||||||||
\(144\) | 392.132 | 0.226928 | ||||||||
\(145\) | 3736.75 | 2.14014 | ||||||||
\(146\) | 49.1897 | 0.0278833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 808.696 | 0.449151 | ||||||||
\(149\) | −619.044 | −0.340363 | −0.170181 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170181 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(150\) | −3227.83 | −1.75701 | ||||||||
\(151\) | 162.870 | 0.0877758 | 0.0438879 | − | 0.999036i | \(-0.486026\pi\) | ||||
0.0438879 | + | 0.999036i | \(0.486026\pi\) | |||||||
\(152\) | 850.406 | 0.453796 | ||||||||
\(153\) | −1634.56 | −0.863700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4901.33 | −2.53990 | ||||||||
\(156\) | 654.249 | 0.335781 | ||||||||
\(157\) | 1320.45 | 0.671234 | 0.335617 | − | 0.941999i | \(-0.391055\pi\) | ||||
0.335617 | + | 0.941999i | \(0.391055\pi\) | |||||||
\(158\) | 2242.41 | 1.12909 | ||||||||
\(159\) | −2157.13 | −1.07592 | ||||||||
\(160\) | −598.559 | −0.295751 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1580.14 | −0.766341 | ||||||||
\(163\) | −2193.25 | −1.05392 | −0.526960 | − | 0.849890i | \(-0.676668\pi\) | ||||
−0.526960 | + | 0.849890i | \(0.676668\pi\) | |||||||
\(164\) | −177.872 | −0.0846917 | ||||||||
\(165\) | −4952.92 | −2.33687 | ||||||||
\(166\) | 1535.37 | 0.717878 | ||||||||
\(167\) | −2117.18 | −0.981030 | −0.490515 | − | 0.871433i | \(-0.663191\pi\) | ||||
−0.490515 | + | 0.871433i | \(0.663191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1677.62 | −0.763594 | ||||||||
\(170\) | 2495.02 | 1.12564 | ||||||||
\(171\) | 2605.25 | 1.16508 | ||||||||
\(172\) | −72.8109 | −0.0322778 | ||||||||
\(173\) | 2576.00 | 1.13208 | 0.566040 | − | 0.824378i | \(-0.308475\pi\) | ||||
0.566040 | + | 0.824378i | \(0.308475\pi\) | |||||||
\(174\) | 2867.52 | 1.24934 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −590.318 | −0.252823 | ||||||||
\(177\) | 1833.59 | 0.778652 | ||||||||
\(178\) | 1614.88 | 0.680001 | ||||||||
\(179\) | −3008.14 | −1.25608 | −0.628042 | − | 0.778179i | \(-0.716144\pi\) | ||||
−0.628042 | + | 0.778179i | \(0.716144\pi\) | |||||||
\(180\) | −1833.71 | −0.759313 | ||||||||
\(181\) | −202.379 | −0.0831090 | −0.0415545 | − | 0.999136i | \(-0.513231\pi\) | ||||
−0.0415545 | + | 0.999136i | \(0.513231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4291.85 | 1.73367 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −3781.66 | −1.50288 | ||||||||
\(186\) | −3761.19 | −1.48271 | ||||||||
\(187\) | 2460.67 | 0.962257 | ||||||||
\(188\) | 1226.10 | 0.475652 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3976.70 | −1.51842 | ||||||||
\(191\) | 4260.13 | 1.61389 | 0.806943 | − | 0.590629i | \(-0.201120\pi\) | ||||
0.806943 | + | 0.590629i | \(0.201120\pi\) | |||||||
\(192\) | −459.323 | −0.172650 | ||||||||
\(193\) | 2071.29 | 0.772510 | 0.386255 | − | 0.922392i | \(-0.373768\pi\) | ||||
0.386255 | + | 0.922392i | \(0.373768\pi\) | |||||||
\(194\) | −2340.58 | −0.866206 | ||||||||
\(195\) | −3059.43 | −1.12354 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4143.04 | −1.49837 | −0.749187 | − | 0.662359i | \(-0.769555\pi\) | ||||
−0.749187 | + | 0.662359i | \(0.769555\pi\) | |||||||
\(198\) | −1808.46 | −0.649099 | ||||||||
\(199\) | −1113.48 | −0.396647 | −0.198323 | − | 0.980137i | \(-0.563550\pi\) | ||||
−0.198323 | + | 0.980137i | \(0.563550\pi\) | |||||||
\(200\) | 1799.01 | 0.636045 | ||||||||
\(201\) | 4570.07 | 1.60372 | ||||||||
\(202\) | 1109.26 | 0.386373 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1914.63 | 0.657114 | ||||||||
\(205\) | 831.770 | 0.283382 | ||||||||
\(206\) | 2036.66 | 0.688840 | ||||||||
\(207\) | 563.690 | 0.189271 | ||||||||
\(208\) | −364.640 | −0.121554 | ||||||||
\(209\) | −3921.95 | −1.29802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1213.02 | 0.395772 | 0.197886 | − | 0.980225i | \(-0.436592\pi\) | ||||
0.197886 | + | 0.980225i | \(0.436592\pi\) | |||||||
\(212\) | 1202.26 | 0.389488 | ||||||||
\(213\) | −2303.19 | −0.740901 | ||||||||
\(214\) | 2903.50 | 0.927471 | ||||||||
\(215\) | 340.481 | 0.108003 | ||||||||
\(216\) | 143.063 | 0.0450659 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3439.22 | 1.06850 | ||||||||
\(219\) | −176.515 | −0.0544649 | ||||||||
\(220\) | 2760.47 | 0.845958 | ||||||||
\(221\) | 1519.96 | 0.462640 | ||||||||
\(222\) | −2901.97 | −0.877332 | ||||||||
\(223\) | 3263.55 | 0.980016 | 0.490008 | − | 0.871718i | \(-0.336994\pi\) | ||||
0.490008 | + | 0.871718i | \(0.336994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5511.32 | 1.63298 | ||||||||
\(226\) | −4324.95 | −1.27297 | ||||||||
\(227\) | −6282.29 | −1.83687 | −0.918436 | − | 0.395569i | \(-0.870547\pi\) | ||||
−0.918436 | + | 0.395569i | \(0.870547\pi\) | |||||||
\(228\) | −3051.65 | −0.886406 | ||||||||
\(229\) | 2034.66 | 0.587136 | 0.293568 | − | 0.955938i | \(-0.405157\pi\) | ||||
0.293568 | + | 0.955938i | \(0.405157\pi\) | |||||||
\(230\) | −860.428 | −0.246674 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1598.19 | −0.452268 | ||||||||
\(233\) | 1687.13 | 0.474368 | 0.237184 | − | 0.971465i | \(-0.423776\pi\) | ||||
0.237184 | + | 0.971465i | \(0.423776\pi\) | |||||||
\(234\) | −1117.09 | −0.312078 | ||||||||
\(235\) | −5733.55 | −1.59155 | ||||||||
\(236\) | −1021.94 | −0.281875 | ||||||||
\(237\) | −8046.82 | −2.20547 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6511.95 | −1.76244 | −0.881220 | − | 0.472707i | \(-0.843277\pi\) | ||||
−0.881220 | + | 0.472707i | \(0.843277\pi\) | |||||||
\(240\) | 2147.91 | 0.577695 | ||||||||
\(241\) | −3163.26 | −0.845492 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(242\) | 60.4625 | 0.0160607 | ||||||||
\(243\) | 5187.42 | 1.36944 | ||||||||
\(244\) | −2392.02 | −0.627597 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 638.286 | 0.165429 | ||||||||
\(247\) | −2422.60 | −0.624073 | ||||||||
\(248\) | 2096.27 | 0.536747 | ||||||||
\(249\) | −5509.62 | −1.40224 | ||||||||
\(250\) | −3736.34 | −0.945228 | ||||||||
\(251\) | −518.424 | −0.130369 | −0.0651845 | − | 0.997873i | \(-0.520764\pi\) | ||||
−0.0651845 | + | 0.997873i | \(0.520764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −848.582 | −0.210869 | ||||||||
\(254\) | 2925.37 | 0.722654 | ||||||||
\(255\) | −8953.29 | −2.19873 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5445.71 | −1.32177 | −0.660884 | − | 0.750488i | \(-0.729818\pi\) | ||||
−0.660884 | + | 0.750488i | \(0.729818\pi\) | |||||||
\(258\) | 261.279 | 0.0630486 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1705.15 | 0.406726 | ||||||||
\(261\) | −4896.10 | −1.16115 | ||||||||
\(262\) | −3940.04 | −0.929071 | ||||||||
\(263\) | 5094.98 | 1.19456 | 0.597281 | − | 0.802032i | \(-0.296248\pi\) | ||||
0.597281 | + | 0.802032i | \(0.296248\pi\) | |||||||
\(264\) | 2118.33 | 0.493843 | ||||||||
\(265\) | −5622.05 | −1.30325 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5794.93 | −1.32825 | ||||||||
\(268\) | −2547.09 | −0.580553 | ||||||||
\(269\) | −7694.70 | −1.74407 | −0.872034 | − | 0.489446i | \(-0.837199\pi\) | ||||
−0.872034 | + | 0.489446i | \(0.837199\pi\) | |||||||
\(270\) | −668.999 | −0.150792 | ||||||||
\(271\) | 898.571 | 0.201418 | 0.100709 | − | 0.994916i | \(-0.467889\pi\) | ||||
0.100709 | + | 0.994916i | \(0.467889\pi\) | |||||||
\(272\) | −1067.11 | −0.237878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4128.24 | −0.910204 | ||||||||
\(275\) | −8296.76 | −1.81932 | ||||||||
\(276\) | −660.277 | −0.144000 | ||||||||
\(277\) | −3660.31 | −0.793959 | −0.396979 | − | 0.917828i | \(-0.629942\pi\) | ||||
−0.396979 | + | 0.917828i | \(0.629942\pi\) | |||||||
\(278\) | −18.3907 | −0.00396764 | ||||||||
\(279\) | 6422.00 | 1.37805 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3392.36 | 0.720183 | 0.360092 | − | 0.932917i | \(-0.382745\pi\) | ||||
0.360092 | + | 0.932917i | \(0.382745\pi\) | |||||||
\(282\) | −4399.82 | −0.929097 | ||||||||
\(283\) | −8150.68 | −1.71204 | −0.856021 | − | 0.516942i | \(-0.827070\pi\) | ||||
−0.856021 | + | 0.516942i | \(0.827070\pi\) | |||||||
\(284\) | 1283.66 | 0.268209 | ||||||||
\(285\) | 14270.3 | 2.96595 | ||||||||
\(286\) | 1681.67 | 0.347689 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 784.265 | 0.160463 | ||||||||
\(289\) | −464.898 | −0.0946261 | ||||||||
\(290\) | 7473.51 | 1.51331 | ||||||||
\(291\) | 8399.09 | 1.69197 | ||||||||
\(292\) | 98.3794 | 0.0197165 | ||||||||
\(293\) | −6020.89 | −1.20049 | −0.600246 | − | 0.799816i | \(-0.704931\pi\) | ||||
−0.600246 | + | 0.799816i | \(0.704931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4778.83 | 0.943167 | ||||||||
\(296\) | 1617.39 | 0.317598 | ||||||||
\(297\) | −659.788 | −0.128905 | ||||||||
\(298\) | −1238.09 | −0.240673 | ||||||||
\(299\) | −524.170 | −0.101383 | ||||||||
\(300\) | −6455.67 | −1.24239 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 325.739 | 0.0620669 | ||||||||
\(303\) | −3980.54 | −0.754707 | ||||||||
\(304\) | 1700.81 | 0.320882 | ||||||||
\(305\) | 11185.7 | 2.09997 | ||||||||
\(306\) | −3269.11 | −0.610728 | ||||||||
\(307\) | −2860.72 | −0.531824 | −0.265912 | − | 0.963997i | \(-0.585673\pi\) | ||||
−0.265912 | + | 0.963997i | \(0.585673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7308.49 | −1.34552 | ||||||||
\(310\) | −9802.67 | −1.79598 | ||||||||
\(311\) | −1380.64 | −0.251732 | −0.125866 | − | 0.992047i | \(-0.540171\pi\) | ||||
−0.125866 | + | 0.992047i | \(0.540171\pi\) | |||||||
\(312\) | 1308.50 | 0.237433 | ||||||||
\(313\) | −298.973 | −0.0539902 | −0.0269951 | − | 0.999636i | \(-0.508594\pi\) | ||||
−0.0269951 | + | 0.999636i | \(0.508594\pi\) | |||||||
\(314\) | 2640.91 | 0.474634 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4484.83 | 0.798390 | ||||||||
\(317\) | −2343.58 | −0.415232 | −0.207616 | − | 0.978210i | \(-0.566570\pi\) | ||||
−0.207616 | + | 0.978210i | \(0.566570\pi\) | |||||||
\(318\) | −4314.26 | −0.760792 | ||||||||
\(319\) | 7370.61 | 1.29365 | ||||||||
\(320\) | −1197.12 | −0.209128 | ||||||||
\(321\) | −10419.1 | −1.81164 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7089.63 | −1.22129 | ||||||||
\(324\) | −3160.27 | −0.541885 | ||||||||
\(325\) | −5124.92 | −0.874706 | ||||||||
\(326\) | −4386.51 | −0.745234 | ||||||||
\(327\) | −12341.5 | −2.08712 | ||||||||
\(328\) | −355.743 | −0.0598861 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −9905.84 | −1.65242 | ||||||||
\(331\) | 1886.83 | 0.313322 | 0.156661 | − | 0.987652i | \(-0.449927\pi\) | ||||
0.156661 | + | 0.987652i | \(0.449927\pi\) | |||||||
\(332\) | 3070.74 | 0.507617 | ||||||||
\(333\) | 4954.93 | 0.815402 | ||||||||
\(334\) | −4234.35 | −0.693693 | ||||||||
\(335\) | 11910.8 | 1.94256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10943.8 | 1.76898 | 0.884488 | − | 0.466564i | \(-0.154508\pi\) | ||||
0.884488 | + | 0.466564i | \(0.154508\pi\) | |||||||
\(338\) | −3355.23 | −0.539942 | ||||||||
\(339\) | 15519.9 | 2.48651 | ||||||||
\(340\) | 4990.04 | 0.795950 | ||||||||
\(341\) | −9667.70 | −1.53529 | ||||||||
\(342\) | 5210.50 | 0.823834 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −145.622 | −0.0228238 | ||||||||
\(345\) | 3087.62 | 0.481831 | ||||||||
\(346\) | 5152.00 | 0.800501 | ||||||||
\(347\) | 10567.0 | 1.63477 | 0.817385 | − | 0.576091i | \(-0.195423\pi\) | ||||
0.817385 | + | 0.576091i | \(0.195423\pi\) | |||||||
\(348\) | 5735.03 | 0.883420 | ||||||||
\(349\) | −1332.92 | −0.204440 | −0.102220 | − | 0.994762i | \(-0.532595\pi\) | ||||
−0.102220 | + | 0.994762i | \(0.532595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −407.552 | −0.0619758 | ||||||||
\(352\) | −1180.64 | −0.178773 | ||||||||
\(353\) | 3880.43 | 0.585083 | 0.292541 | − | 0.956253i | \(-0.405499\pi\) | ||||
0.292541 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(354\) | 3667.19 | 0.550590 | ||||||||
\(355\) | −6002.72 | −0.897440 | ||||||||
\(356\) | 3229.76 | 0.480833 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6016.29 | −0.888186 | ||||||||
\(359\) | −12612.1 | −1.85415 | −0.927073 | − | 0.374880i | \(-0.877684\pi\) | ||||
−0.927073 | + | 0.374880i | \(0.877684\pi\) | |||||||
\(360\) | −3667.41 | −0.536915 | ||||||||
\(361\) | 4440.85 | 0.647448 | ||||||||
\(362\) | −404.758 | −0.0587669 | ||||||||
\(363\) | −216.968 | −0.0313715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −460.046 | −0.0659723 | ||||||||
\(366\) | 8583.69 | 1.22589 | ||||||||
\(367\) | 5092.93 | 0.724384 | 0.362192 | − | 0.932104i | \(-0.382029\pi\) | ||||
0.362192 | + | 0.932104i | \(0.382029\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −1089.83 | −0.153752 | ||||||||
\(370\) | −7563.31 | −1.06270 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7522.39 | −1.04843 | ||||||||
\(373\) | −12578.8 | −1.74612 | −0.873062 | − | 0.487609i | \(-0.837869\pi\) | ||||
−0.873062 | + | 0.487609i | \(0.837869\pi\) | |||||||
\(374\) | 4921.34 | 0.680418 | ||||||||
\(375\) | 13407.7 | 1.84633 | ||||||||
\(376\) | 2452.20 | 0.336337 | ||||||||
\(377\) | 4552.84 | 0.621971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3831.85 | 0.519338 | 0.259669 | − | 0.965698i | \(-0.416387\pi\) | ||||
0.259669 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(380\) | −7953.41 | −1.07369 | ||||||||
\(381\) | −10497.6 | −1.41157 | ||||||||
\(382\) | 8520.27 | 1.14119 | ||||||||
\(383\) | 7165.67 | 0.956002 | 0.478001 | − | 0.878359i | \(-0.341362\pi\) | ||||
0.478001 | + | 0.878359i | \(0.341362\pi\) | |||||||
\(384\) | −918.647 | −0.122082 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4142.57 | 0.546247 | ||||||||
\(387\) | −446.118 | −0.0585980 | ||||||||
\(388\) | −4681.16 | −0.612500 | ||||||||
\(389\) | 10808.2 | 1.40873 | 0.704364 | − | 0.709839i | \(-0.251232\pi\) | ||||
0.704364 | + | 0.709839i | \(0.251232\pi\) | |||||||
\(390\) | −6118.85 | −0.794462 | ||||||||
\(391\) | −1533.96 | −0.198404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14138.7 | 1.81477 | ||||||||
\(394\) | −8286.08 | −1.05951 | ||||||||
\(395\) | −20972.1 | −2.67145 | ||||||||
\(396\) | −3616.92 | −0.458982 | ||||||||
\(397\) | 12829.0 | 1.62183 | 0.810917 | − | 0.585162i | \(-0.198969\pi\) | ||||
0.810917 | + | 0.585162i | \(0.198969\pi\) | |||||||
\(398\) | −2226.97 | −0.280472 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3598.01 | 0.449751 | ||||||||
\(401\) | 10168.2 | 1.26628 | 0.633139 | − | 0.774038i | \(-0.281766\pi\) | ||||
0.633139 | + | 0.774038i | \(0.281766\pi\) | |||||||
\(402\) | 9140.14 | 1.13400 | ||||||||
\(403\) | −5971.75 | −0.738149 | ||||||||
\(404\) | 2218.52 | 0.273207 | ||||||||
\(405\) | 14778.2 | 1.81317 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7459.18 | −0.908447 | ||||||||
\(408\) | 3829.27 | 0.464650 | ||||||||
\(409\) | −1594.36 | −0.192753 | −0.0963766 | − | 0.995345i | \(-0.530725\pi\) | ||||
−0.0963766 | + | 0.995345i | \(0.530725\pi\) | |||||||
\(410\) | 1663.54 | 0.200382 | ||||||||
\(411\) | 14814.0 | 1.77791 | ||||||||
\(412\) | 4073.32 | 0.487083 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1127.38 | 0.133835 | ||||||||
\(415\) | −14359.5 | −1.69851 | ||||||||
\(416\) | −729.280 | −0.0859517 | ||||||||
\(417\) | 65.9945 | 0.00775003 | ||||||||
\(418\) | −7843.90 | −0.917842 | ||||||||
\(419\) | −8355.45 | −0.974201 | −0.487101 | − | 0.873346i | \(-0.661945\pi\) | ||||
−0.487101 | + | 0.873346i | \(0.661945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1727.23 | −0.199952 | −0.0999762 | − | 0.994990i | \(-0.531877\pi\) | ||||
−0.0999762 | + | 0.994990i | \(0.531877\pi\) | |||||||
\(422\) | 2426.04 | 0.279853 | ||||||||
\(423\) | 7512.41 | 0.863513 | ||||||||
\(424\) | 2404.52 | 0.275410 | ||||||||
\(425\) | −14997.9 | −1.71177 | ||||||||
\(426\) | −4606.38 | −0.523896 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5806.99 | 0.655821 | ||||||||
\(429\) | −6034.61 | −0.679146 | ||||||||
\(430\) | 680.963 | 0.0763696 | ||||||||
\(431\) | 5240.54 | 0.585680 | 0.292840 | − | 0.956161i | \(-0.405400\pi\) | ||||
0.292840 | + | 0.956161i | \(0.405400\pi\) | |||||||
\(432\) | 286.127 | 0.0318664 | ||||||||
\(433\) | 6074.43 | 0.674177 | 0.337088 | − | 0.941473i | \(-0.390558\pi\) | ||||
0.337088 | + | 0.941473i | \(0.390558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26818.4 | −2.95596 | ||||||||
\(436\) | 6878.44 | 0.755544 | ||||||||
\(437\) | 2444.92 | 0.267634 | ||||||||
\(438\) | −353.031 | −0.0385125 | ||||||||
\(439\) | 10981.3 | 1.19388 | 0.596938 | − | 0.802288i | \(-0.296384\pi\) | ||||
0.596938 | + | 0.802288i | \(0.296384\pi\) | |||||||
\(440\) | 5520.94 | 0.598183 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3039.92 | 0.327136 | ||||||||
\(443\) | 4102.85 | 0.440028 | 0.220014 | − | 0.975497i | \(-0.429390\pi\) | ||||
0.220014 | + | 0.975497i | \(0.429390\pi\) | |||||||
\(444\) | −5803.95 | −0.620368 | ||||||||
\(445\) | −15103.1 | −1.60889 | ||||||||
\(446\) | 6527.10 | 0.692976 | ||||||||
\(447\) | 4442.83 | 0.470109 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16448.6 | 1.72886 | 0.864429 | − | 0.502754i | \(-0.167680\pi\) | ||||
0.864429 | + | 0.502754i | \(0.167680\pi\) | |||||||
\(450\) | 11022.6 | 1.15469 | ||||||||
\(451\) | 1640.64 | 0.171296 | ||||||||
\(452\) | −8649.89 | −0.900126 | ||||||||
\(453\) | −1168.90 | −0.121236 | ||||||||
\(454\) | −12564.6 | −1.29886 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6103.30 | −0.626783 | ||||||||
\(457\) | 14213.7 | 1.45490 | 0.727452 | − | 0.686159i | \(-0.240704\pi\) | ||||
0.727452 | + | 0.686159i | \(0.240704\pi\) | |||||||
\(458\) | 4069.32 | 0.415168 | ||||||||
\(459\) | −1192.68 | −0.121285 | ||||||||
\(460\) | −1720.86 | −0.174425 | ||||||||
\(461\) | 6087.14 | 0.614982 | 0.307491 | − | 0.951551i | \(-0.400511\pi\) | ||||
0.307491 | + | 0.951551i | \(0.400511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5359.06 | 0.537919 | 0.268959 | − | 0.963151i | \(-0.413320\pi\) | ||||
0.268959 | + | 0.963151i | \(0.413320\pi\) | |||||||
\(464\) | −3196.37 | −0.319801 | ||||||||
\(465\) | 35176.5 | 3.50811 | ||||||||
\(466\) | 3374.27 | 0.335429 | ||||||||
\(467\) | 17780.9 | 1.76188 | 0.880942 | − | 0.473224i | \(-0.156910\pi\) | ||||
0.880942 | + | 0.473224i | \(0.156910\pi\) | |||||||
\(468\) | −2234.18 | −0.220673 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11467.1 | −1.12540 | ||||||||
\(471\) | −9476.80 | −0.927108 | ||||||||
\(472\) | −2043.88 | −0.199316 | ||||||||
\(473\) | 671.587 | 0.0652846 | ||||||||
\(474\) | −16093.6 | −1.55950 | ||||||||
\(475\) | 23904.5 | 2.30908 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7366.33 | 0.707088 | ||||||||
\(478\) | −13023.9 | −1.24623 | ||||||||
\(479\) | 12340.2 | 1.17711 | 0.588555 | − | 0.808457i | \(-0.299697\pi\) | ||||
0.588555 | + | 0.808457i | \(0.299697\pi\) | |||||||
\(480\) | 4295.81 | 0.408492 | ||||||||
\(481\) | −4607.55 | −0.436769 | ||||||||
\(482\) | −6326.52 | −0.597853 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 120.925 | 0.0113566 | ||||||||
\(485\) | 21890.2 | 2.04945 | ||||||||
\(486\) | 10374.8 | 0.968338 | ||||||||
\(487\) | −14345.9 | −1.33486 | −0.667428 | − | 0.744674i | \(-0.732605\pi\) | ||||
−0.667428 | + | 0.744674i | \(0.732605\pi\) | |||||||
\(488\) | −4784.05 | −0.443778 | ||||||||
\(489\) | 15740.8 | 1.45567 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −839.846 | −0.0771929 | −0.0385964 | − | 0.999255i | \(-0.512289\pi\) | ||||
−0.0385964 | + | 0.999255i | \(0.512289\pi\) | |||||||
\(492\) | 1276.57 | 0.116976 | ||||||||
\(493\) | 13323.7 | 1.21718 | ||||||||
\(494\) | −4845.19 | −0.441286 | ||||||||
\(495\) | 16913.6 | 1.53578 | ||||||||
\(496\) | 4192.54 | 0.379538 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11019.2 | −0.991534 | ||||||||
\(499\) | −10473.4 | −0.939587 | −0.469794 | − | 0.882776i | \(-0.655672\pi\) | ||||
−0.469794 | + | 0.882776i | \(0.655672\pi\) | |||||||
\(500\) | −7472.69 | −0.668377 | ||||||||
\(501\) | 15194.8 | 1.35500 | ||||||||
\(502\) | −1036.85 | −0.0921849 | ||||||||
\(503\) | −21797.3 | −1.93219 | −0.966097 | − | 0.258180i | \(-0.916877\pi\) | ||||
−0.966097 | + | 0.258180i | \(0.916877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10374.3 | −0.914163 | ||||||||
\(506\) | −1697.16 | −0.149107 | ||||||||
\(507\) | 12040.1 | 1.05468 | ||||||||
\(508\) | 5850.74 | 0.510994 | ||||||||
\(509\) | −18466.3 | −1.60806 | −0.804031 | − | 0.594587i | \(-0.797316\pi\) | ||||
−0.804031 | + | 0.594587i | \(0.797316\pi\) | |||||||
\(510\) | −17906.6 | −1.55474 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1900.97 | 0.163606 | ||||||||
\(514\) | −10891.4 | −0.934631 | ||||||||
\(515\) | −19047.8 | −1.62980 | ||||||||
\(516\) | 522.559 | 0.0445821 | ||||||||
\(517\) | −11309.2 | −0.962048 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18487.8 | −1.56363 | ||||||||
\(520\) | 3410.29 | 0.287598 | ||||||||
\(521\) | −970.557 | −0.0816139 | −0.0408070 | − | 0.999167i | \(-0.512993\pi\) | ||||
−0.0408070 | + | 0.999167i | \(0.512993\pi\) | |||||||
\(522\) | −9792.20 | −0.821059 | ||||||||
\(523\) | −2501.73 | −0.209164 | −0.104582 | − | 0.994516i | \(-0.533350\pi\) | ||||
−0.104582 | + | 0.994516i | \(0.533350\pi\) | |||||||
\(524\) | −7880.08 | −0.656952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10190.0 | 0.844683 | ||||||||
\(527\) | −17476.1 | −1.44454 | ||||||||
\(528\) | 4236.67 | 0.349199 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −11244.1 | −0.921534 | ||||||||
\(531\) | −6261.49 | −0.511724 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1013.42 | 0.0823570 | ||||||||
\(534\) | −11589.9 | −0.939218 | ||||||||
\(535\) | −27154.9 | −2.19441 | ||||||||
\(536\) | −5094.18 | −0.410513 | ||||||||
\(537\) | 21589.2 | 1.73490 | ||||||||
\(538\) | −15389.4 | −1.23324 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1338.00 | −0.106626 | ||||||||
\(541\) | −5519.57 | −0.438641 | −0.219321 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219321 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(542\) | 1797.14 | 0.142424 | ||||||||
\(543\) | 1452.46 | 0.114790 | ||||||||
\(544\) | −2134.21 | −0.168205 | ||||||||
\(545\) | −32165.2 | −2.52809 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15172.9 | −1.18601 | −0.593004 | − | 0.805199i | \(-0.702058\pi\) | ||||
−0.593004 | + | 0.805199i | \(0.702058\pi\) | |||||||
\(548\) | −8256.47 | −0.643611 | ||||||||
\(549\) | −14656.1 | −1.13936 | ||||||||
\(550\) | −16593.5 | −1.28645 | ||||||||
\(551\) | −21236.1 | −1.64190 | ||||||||
\(552\) | −1320.55 | −0.101823 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7320.61 | −0.561413 | ||||||||
\(555\) | 27140.7 | 2.07578 | ||||||||
\(556\) | −36.7815 | −0.00280554 | ||||||||
\(557\) | −2907.15 | −0.221149 | −0.110574 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110574 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(558\) | 12844.0 | 0.974426 | ||||||||
\(559\) | 414.840 | 0.0313880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17660.0 | −1.32907 | ||||||||
\(562\) | 6784.73 | 0.509246 | ||||||||
\(563\) | −1318.69 | −0.0987141 | −0.0493570 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493570 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(564\) | −8799.64 | −0.656971 | ||||||||
\(565\) | 40449.0 | 3.01186 | ||||||||
\(566\) | −16301.4 | −1.21060 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2567.33 | 0.189652 | ||||||||
\(569\) | −2920.60 | −0.215181 | −0.107591 | − | 0.994195i | \(-0.534314\pi\) | ||||
−0.107591 | + | 0.994195i | \(0.534314\pi\) | |||||||
\(570\) | 28540.5 | 2.09725 | ||||||||
\(571\) | 11200.3 | 0.820873 | 0.410436 | − | 0.911889i | \(-0.365376\pi\) | ||||
0.410436 | + | 0.911889i | \(0.365376\pi\) | |||||||
\(572\) | 3363.34 | 0.245854 | ||||||||
\(573\) | −30574.7 | −2.22910 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5172.14 | 0.375119 | ||||||||
\(576\) | 1568.53 | 0.113464 | ||||||||
\(577\) | 3416.96 | 0.246534 | 0.123267 | − | 0.992374i | \(-0.460663\pi\) | ||||
0.123267 | + | 0.992374i | \(0.460663\pi\) | |||||||
\(578\) | −929.796 | −0.0669108 | ||||||||
\(579\) | −14865.5 | −1.06699 | ||||||||
\(580\) | 14947.0 | 1.07007 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16798.2 | 1.19640 | ||||||||
\(583\) | −11089.3 | −0.787773 | ||||||||
\(584\) | 196.759 | 0.0139417 | ||||||||
\(585\) | 10447.5 | 0.738381 | ||||||||
\(586\) | −12041.8 | −0.848876 | ||||||||
\(587\) | 16614.4 | 1.16823 | 0.584114 | − | 0.811671i | \(-0.301442\pi\) | ||||
0.584114 | + | 0.811671i | \(0.301442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27854.4 | 1.94859 | ||||||||
\(590\) | 9557.66 | 0.666920 | ||||||||
\(591\) | 29734.3 | 2.06955 | ||||||||
\(592\) | 3234.78 | 0.224576 | ||||||||
\(593\) | 16559.0 | 1.14671 | 0.573354 | − | 0.819308i | \(-0.305642\pi\) | ||||
0.573354 | + | 0.819308i | \(0.305642\pi\) | |||||||
\(594\) | −1319.58 | −0.0911496 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2476.18 | −0.170181 | ||||||||
\(597\) | 7991.39 | 0.547849 | ||||||||
\(598\) | −1048.34 | −0.0716887 | ||||||||
\(599\) | 10995.8 | 0.750043 | 0.375021 | − | 0.927016i | \(-0.377635\pi\) | ||||
0.375021 | + | 0.927016i | \(0.377635\pi\) | |||||||
\(600\) | −12911.3 | −0.878505 | ||||||||
\(601\) | −9311.94 | −0.632016 | −0.316008 | − | 0.948756i | \(-0.602343\pi\) | ||||
−0.316008 | + | 0.948756i | \(0.602343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15606.2 | −1.05395 | ||||||||
\(604\) | 651.479 | 0.0438879 | ||||||||
\(605\) | −565.475 | −0.0379997 | ||||||||
\(606\) | −7961.09 | −0.533659 | ||||||||
\(607\) | 19247.2 | 1.28702 | 0.643510 | − | 0.765438i | \(-0.277477\pi\) | ||||
0.643510 | + | 0.765438i | \(0.277477\pi\) | |||||||
\(608\) | 3401.62 | 0.226898 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22371.4 | 1.48490 | ||||||||
\(611\) | −6985.72 | −0.462540 | ||||||||
\(612\) | −6538.23 | −0.431850 | ||||||||
\(613\) | −10419.4 | −0.686517 | −0.343259 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343259 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(614\) | −5721.44 | −0.376057 | ||||||||
\(615\) | −5969.56 | −0.391408 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15890.0 | 1.03681 | 0.518403 | − | 0.855137i | \(-0.326527\pi\) | ||||
0.518403 | + | 0.855137i | \(0.326527\pi\) | |||||||
\(618\) | −14617.0 | −0.951425 | ||||||||
\(619\) | 2325.59 | 0.151007 | 0.0755035 | − | 0.997146i | \(-0.475944\pi\) | ||||
0.0755035 | + | 0.997146i | \(0.475944\pi\) | |||||||
\(620\) | −19605.3 | −1.26995 | ||||||||
\(621\) | 411.307 | 0.0265784 | ||||||||
\(622\) | −2761.28 | −0.178002 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2617.00 | 0.167891 | ||||||||
\(625\) | 6834.62 | 0.437416 | ||||||||
\(626\) | −597.945 | −0.0381768 | ||||||||
\(627\) | 28147.6 | 1.79283 | ||||||||
\(628\) | 5281.82 | 0.335617 | ||||||||
\(629\) | −13483.8 | −0.854745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25002.0 | 1.57736 | 0.788678 | − | 0.614806i | \(-0.210766\pi\) | ||||
0.788678 | + | 0.614806i | \(0.210766\pi\) | |||||||
\(632\) | 8969.65 | 0.564547 | ||||||||
\(633\) | −8705.77 | −0.546640 | ||||||||
\(634\) | −4687.15 | −0.293613 | ||||||||
\(635\) | −27359.5 | −1.70981 | ||||||||
\(636\) | −8628.53 | −0.537961 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14741.2 | 0.914750 | ||||||||
\(639\) | 7865.09 | 0.486914 | ||||||||
\(640\) | −2394.24 | −0.147876 | ||||||||
\(641\) | −23855.1 | −1.46992 | −0.734960 | − | 0.678110i | \(-0.762799\pi\) | ||||
−0.734960 | + | 0.678110i | \(0.762799\pi\) | |||||||
\(642\) | −20838.2 | −1.28102 | ||||||||
\(643\) | −28805.3 | −1.76667 | −0.883337 | − | 0.468738i | \(-0.844709\pi\) | ||||
−0.883337 | + | 0.468738i | \(0.844709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2443.61 | −0.149174 | ||||||||
\(646\) | −14179.3 | −0.863585 | ||||||||
\(647\) | −32498.4 | −1.97472 | −0.987360 | − | 0.158492i | \(-0.949337\pi\) | ||||
−0.987360 | + | 0.158492i | \(0.949337\pi\) | |||||||
\(648\) | −6320.54 | −0.383170 | ||||||||
\(649\) | 9426.07 | 0.570116 | ||||||||
\(650\) | −10249.8 | −0.618510 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8773.02 | −0.526960 | ||||||||
\(653\) | 16341.1 | 0.979290 | 0.489645 | − | 0.871922i | \(-0.337126\pi\) | ||||
0.489645 | + | 0.871922i | \(0.337126\pi\) | |||||||
\(654\) | −24683.0 | −1.47581 | ||||||||
\(655\) | 36849.2 | 2.19819 | ||||||||
\(656\) | −711.486 | −0.0423458 | ||||||||
\(657\) | 602.777 | 0.0357939 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5445.43 | 0.321887 | 0.160944 | − | 0.986964i | \(-0.448546\pi\) | ||||
0.160944 | + | 0.986964i | \(0.448546\pi\) | |||||||
\(660\) | −19811.7 | −1.16844 | ||||||||
\(661\) | −17006.6 | −1.00073 | −0.500363 | − | 0.865816i | \(-0.666800\pi\) | ||||
−0.500363 | + | 0.865816i | \(0.666800\pi\) | |||||||
\(662\) | 3773.66 | 0.221552 | ||||||||
\(663\) | −10908.6 | −0.638999 | ||||||||
\(664\) | 6141.48 | 0.358939 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9909.87 | 0.576576 | ||||||||
\(667\) | −4594.79 | −0.266733 | ||||||||
\(668\) | −8468.70 | −0.490515 | ||||||||
\(669\) | −23422.3 | −1.35360 | ||||||||
\(670\) | 23821.6 | 1.37360 | ||||||||
\(671\) | 22063.4 | 1.26937 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20763.5 | −1.18926 | −0.594631 | − | 0.803999i | \(-0.702702\pi\) | ||||
−0.594631 | + | 0.803999i | \(0.702702\pi\) | |||||||
\(674\) | 21887.5 | 1.25085 | ||||||||
\(675\) | 4021.43 | 0.229311 | ||||||||
\(676\) | −6710.46 | −0.381797 | ||||||||
\(677\) | 18958.9 | 1.07629 | 0.538146 | − | 0.842851i | \(-0.319125\pi\) | ||||
0.538146 | + | 0.842851i | \(0.319125\pi\) | |||||||
\(678\) | 31039.8 | 1.75823 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9980.08 | 0.562822 | ||||||||
\(681\) | 45087.5 | 2.53709 | ||||||||
\(682\) | −19335.4 | −1.08562 | ||||||||
\(683\) | 22546.4 | 1.26312 | 0.631562 | − | 0.775325i | \(-0.282414\pi\) | ||||
0.631562 | + | 0.775325i | \(0.282414\pi\) | |||||||
\(684\) | 10421.0 | 0.582539 | ||||||||
\(685\) | 38609.3 | 2.15355 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14602.6 | −0.810952 | ||||||||
\(688\) | −291.244 | −0.0161389 | ||||||||
\(689\) | −6849.88 | −0.378751 | ||||||||
\(690\) | 6175.23 | 0.340706 | ||||||||
\(691\) | −27690.6 | −1.52446 | −0.762228 | − | 0.647309i | \(-0.775894\pi\) | ||||
−0.762228 | + | 0.647309i | \(0.775894\pi\) | |||||||
\(692\) | 10304.0 | 0.566040 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21134.0 | 1.15596 | ||||||||
\(695\) | 171.999 | 0.00938747 | ||||||||
\(696\) | 11470.1 | 0.624672 | ||||||||
\(697\) | 2965.75 | 0.161170 | ||||||||
\(698\) | −2665.84 | −0.144561 | ||||||||
\(699\) | −12108.4 | −0.655198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2135.07 | 0.115036 | 0.0575182 | − | 0.998344i | \(-0.481681\pi\) | ||||
0.0575182 | + | 0.998344i | \(0.481681\pi\) | |||||||
\(702\) | −815.104 | −0.0438235 | ||||||||
\(703\) | 21491.2 | 1.15300 | ||||||||
\(704\) | −2361.27 | −0.126412 | ||||||||
\(705\) | 41149.2 | 2.19826 | ||||||||
\(706\) | 7760.85 | 0.413716 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7334.37 | 0.389326 | ||||||||
\(709\) | −18765.6 | −0.994016 | −0.497008 | − | 0.867746i | \(-0.665568\pi\) | ||||
−0.497008 | + | 0.867746i | \(0.665568\pi\) | |||||||
\(710\) | −12005.4 | −0.634586 | ||||||||
\(711\) | 27478.8 | 1.44942 | ||||||||
\(712\) | 6459.51 | 0.340001 | ||||||||
\(713\) | 6026.78 | 0.316556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15727.8 | −0.822637 | ||||||||
\(716\) | −12032.6 | −0.628042 | ||||||||
\(717\) | 46735.8 | 2.43428 | ||||||||
\(718\) | −25224.1 | −1.31108 | ||||||||
\(719\) | −24563.0 | −1.27405 | −0.637027 | − | 0.770842i | \(-0.719836\pi\) | ||||
−0.637027 | + | 0.770842i | \(0.719836\pi\) | |||||||
\(720\) | −7334.82 | −0.379657 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8881.70 | 0.457815 | ||||||||
\(723\) | 22702.5 | 1.16779 | ||||||||
\(724\) | −809.517 | −0.0415545 | ||||||||
\(725\) | −44924.2 | −2.30130 | ||||||||
\(726\) | −433.935 | −0.0221830 | ||||||||
\(727\) | −1895.61 | −0.0967045 | −0.0483522 | − | 0.998830i | \(-0.515397\pi\) | ||||
−0.0483522 | + | 0.998830i | \(0.515397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15897.9 | −0.807697 | ||||||||
\(730\) | −920.091 | −0.0466495 | ||||||||
\(731\) | 1214.01 | 0.0614254 | ||||||||
\(732\) | 17167.4 | 0.866837 | ||||||||
\(733\) | 8040.15 | 0.405143 | 0.202571 | − | 0.979268i | \(-0.435070\pi\) | ||||
0.202571 | + | 0.979268i | \(0.435070\pi\) | |||||||
\(734\) | 10185.9 | 0.512217 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 23493.6 | 1.17422 | ||||||||
\(738\) | −2179.66 | −0.108719 | ||||||||
\(739\) | 7025.86 | 0.349730 | 0.174865 | − | 0.984592i | \(-0.444051\pi\) | ||||
0.174865 | + | 0.984592i | \(0.444051\pi\) | |||||||
\(740\) | −15126.6 | −0.751440 | ||||||||
\(741\) | 17386.8 | 0.861970 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35267.7 | 1.74138 | 0.870691 | − | 0.491830i | \(-0.163672\pi\) | ||||
0.870691 | + | 0.491830i | \(0.163672\pi\) | |||||||
\(744\) | −15044.8 | −0.741355 | ||||||||
\(745\) | 11579.2 | 0.569435 | ||||||||
\(746\) | −25157.5 | −1.23470 | ||||||||
\(747\) | 18814.6 | 0.921542 | ||||||||
\(748\) | 9842.68 | 0.481128 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26815.5 | 1.30555 | ||||||||
\(751\) | −26262.0 | −1.27605 | −0.638026 | − | 0.770015i | \(-0.720249\pi\) | ||||
−0.638026 | + | 0.770015i | \(0.720249\pi\) | |||||||
\(752\) | 4904.41 | 0.237826 | ||||||||
\(753\) | 3720.69 | 0.180066 | ||||||||
\(754\) | 9105.67 | 0.439800 | ||||||||
\(755\) | −3046.47 | −0.146851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20312.0 | 0.975234 | 0.487617 | − | 0.873058i | \(-0.337866\pi\) | ||||
0.487617 | + | 0.873058i | \(0.337866\pi\) | |||||||
\(758\) | 7663.70 | 0.367227 | ||||||||
\(759\) | 6090.21 | 0.291252 | ||||||||
\(760\) | −15906.8 | −0.759212 | ||||||||
\(761\) | −5976.37 | −0.284682 | −0.142341 | − | 0.989818i | \(-0.545463\pi\) | ||||
−0.142341 | + | 0.989818i | \(0.545463\pi\) | |||||||
\(762\) | −20995.2 | −0.998130 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17040.5 | 0.806943 | ||||||||
\(765\) | 30574.3 | 1.44499 | ||||||||
\(766\) | 14331.3 | 0.675995 | ||||||||
\(767\) | 5822.50 | 0.274104 | ||||||||
\(768\) | −1837.29 | −0.0863250 | ||||||||
\(769\) | −20927.5 | −0.981360 | −0.490680 | − | 0.871340i | \(-0.663252\pi\) | ||||
−0.490680 | + | 0.871340i | \(0.663252\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39083.5 | 1.82563 | ||||||||
\(772\) | 8285.15 | 0.386255 | ||||||||
\(773\) | −15071.3 | −0.701262 | −0.350631 | − | 0.936514i | \(-0.614033\pi\) | ||||
−0.350631 | + | 0.936514i | \(0.614033\pi\) | |||||||
\(774\) | −892.235 | −0.0414350 | ||||||||
\(775\) | 58925.0 | 2.73116 | ||||||||
\(776\) | −9362.33 | −0.433103 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21616.3 | 0.996121 | ||||||||
\(779\) | −4726.97 | −0.217409 | ||||||||
\(780\) | −12237.7 | −0.561769 | ||||||||
\(781\) | −11840.1 | −0.542476 | ||||||||
\(782\) | −3067.93 | −0.140293 | ||||||||
\(783\) | −3572.53 | −0.163055 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24699.0 | −1.12299 | ||||||||
\(786\) | 28277.4 | 1.28323 | ||||||||
\(787\) | 9818.43 | 0.444713 | 0.222357 | − | 0.974965i | \(-0.428625\pi\) | ||||
0.222357 | + | 0.974965i | \(0.428625\pi\) | |||||||
\(788\) | −16572.2 | −0.749187 | ||||||||
\(789\) | −36566.3 | −1.64993 | ||||||||
\(790\) | −41944.3 | −1.88900 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7233.84 | −0.324550 | ||||||||
\(793\) | 13628.6 | 0.610296 | ||||||||
\(794\) | 25658.0 | 1.14681 | ||||||||
\(795\) | 40349.1 | 1.80004 | ||||||||
\(796\) | −4453.93 | −0.198323 | ||||||||
\(797\) | 25841.3 | 1.14849 | 0.574244 | − | 0.818684i | \(-0.305296\pi\) | ||||
0.574244 | + | 0.818684i | \(0.305296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20443.4 | −0.905177 | ||||||||
\(800\) | 7196.02 | 0.318022 | ||||||||
\(801\) | 19788.9 | 0.872918 | ||||||||
\(802\) | 20336.5 | 0.895393 | ||||||||
\(803\) | −907.423 | −0.0398783 | ||||||||
\(804\) | 18280.3 | 0.801861 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11943.5 | −0.521950 | ||||||||
\(807\) | 55224.3 | 2.40891 | ||||||||
\(808\) | 4437.05 | 0.193187 | ||||||||
\(809\) | −44965.3 | −1.95414 | −0.977068 | − | 0.212926i | \(-0.931701\pi\) | ||||
−0.977068 | + | 0.212926i | \(0.931701\pi\) | |||||||
\(810\) | 29556.4 | 1.28211 | ||||||||
\(811\) | 23927.0 | 1.03599 | 0.517997 | − | 0.855382i | \(-0.326678\pi\) | ||||
0.517997 | + | 0.855382i | \(0.326678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6448.98 | −0.278199 | ||||||||
\(814\) | −14918.4 | −0.642369 | ||||||||
\(815\) | 41024.8 | 1.76323 | ||||||||
\(816\) | 7658.54 | 0.328557 | ||||||||
\(817\) | −1934.96 | −0.0828590 | ||||||||
\(818\) | −3188.72 | −0.136297 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3327.08 | 0.141691 | ||||||||
\(821\) | −45775.0 | −1.94587 | −0.972934 | − | 0.231082i | \(-0.925773\pi\) | ||||
−0.972934 | + | 0.231082i | \(0.925773\pi\) | |||||||
\(822\) | 29628.0 | 1.25717 | ||||||||
\(823\) | 187.951 | 0.00796060 | 0.00398030 | − | 0.999992i | \(-0.498733\pi\) | ||||
0.00398030 | + | 0.999992i | \(0.498733\pi\) | |||||||
\(824\) | 8146.65 | 0.344420 | ||||||||
\(825\) | 59545.2 | 2.51285 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11598.2 | −0.487676 | −0.243838 | − | 0.969816i | \(-0.578406\pi\) | ||||
−0.243838 | + | 0.969816i | \(0.578406\pi\) | |||||||
\(828\) | 2254.76 | 0.0946357 | ||||||||
\(829\) | 4238.86 | 0.177590 | 0.0887948 | − | 0.996050i | \(-0.471698\pi\) | ||||
0.0887948 | + | 0.996050i | \(0.471698\pi\) | |||||||
\(830\) | −28719.0 | −1.20103 | ||||||||
\(831\) | 26269.8 | 1.09662 | ||||||||
\(832\) | −1458.56 | −0.0607770 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 131.989 | 0.00548010 | ||||||||
\(835\) | 39601.7 | 1.64129 | ||||||||
\(836\) | −15687.8 | −0.649012 | ||||||||
\(837\) | 4685.93 | 0.193512 | ||||||||
\(838\) | −16710.9 | −0.688864 | ||||||||
\(839\) | 30548.4 | 1.25703 | 0.628514 | − | 0.777798i | \(-0.283663\pi\) | ||||
0.628514 | + | 0.777798i | \(0.283663\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15520.4 | 0.636368 | ||||||||
\(842\) | −3454.46 | −0.141388 | ||||||||
\(843\) | −24346.7 | −0.994717 | ||||||||
\(844\) | 4852.09 | 0.197886 | ||||||||
\(845\) | 31379.7 | 1.27751 | ||||||||
\(846\) | 15024.8 | 0.610596 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4809.04 | 0.194744 | ||||||||
\(849\) | 58496.8 | 2.36467 | ||||||||
\(850\) | −29995.8 | −1.21041 | ||||||||
\(851\) | 4650.00 | 0.187309 | ||||||||
\(852\) | −9212.75 | −0.370450 | ||||||||
\(853\) | −7956.01 | −0.319354 | −0.159677 | − | 0.987169i | \(-0.551045\pi\) | ||||
−0.159677 | + | 0.987169i | \(0.551045\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48731.1 | −1.94920 | ||||||||
\(856\) | 11614.0 | 0.463736 | ||||||||
\(857\) | −32534.3 | −1.29679 | −0.648396 | − | 0.761303i | \(-0.724560\pi\) | ||||
−0.648396 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(858\) | −12069.2 | −0.480229 | ||||||||
\(859\) | 818.271 | 0.0325018 | 0.0162509 | − | 0.999868i | \(-0.494827\pi\) | ||||
0.0162509 | + | 0.999868i | \(0.494827\pi\) | |||||||
\(860\) | 1361.93 | 0.0540015 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10481.1 | 0.414138 | ||||||||
\(863\) | −20161.0 | −0.795238 | −0.397619 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397619 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(864\) | 572.253 | 0.0225329 | ||||||||
\(865\) | −48184.0 | −1.89400 | ||||||||
\(866\) | 12148.9 | 0.476715 | ||||||||
\(867\) | 3336.54 | 0.130698 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41366.8 | −1.61481 | ||||||||
\(870\) | −53636.8 | −2.09018 | ||||||||
\(871\) | 14512.1 | 0.564549 | ||||||||
\(872\) | 13756.9 | 0.534250 | ||||||||
\(873\) | −28681.8 | −1.11195 | ||||||||
\(874\) | 4889.83 | 0.189246 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −706.061 | −0.0272324 | ||||||||
\(877\) | −33048.9 | −1.27250 | −0.636250 | − | 0.771483i | \(-0.719515\pi\) | ||||
−0.636250 | + | 0.771483i | \(0.719515\pi\) | |||||||
\(878\) | 21962.7 | 0.844197 | ||||||||
\(879\) | 43211.5 | 1.65812 | ||||||||
\(880\) | 11041.9 | 0.422979 | ||||||||
\(881\) | −15531.2 | −0.593938 | −0.296969 | − | 0.954887i | \(-0.595976\pi\) | ||||
−0.296969 | + | 0.954887i | \(0.595976\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22079.1 | −0.841474 | −0.420737 | − | 0.907183i | \(-0.638228\pi\) | ||||
−0.420737 | + | 0.907183i | \(0.638228\pi\) | |||||||
\(884\) | 6079.84 | 0.231320 | ||||||||
\(885\) | −34297.3 | −1.30270 | ||||||||
\(886\) | 8205.70 | 0.311147 | ||||||||
\(887\) | −8427.81 | −0.319028 | −0.159514 | − | 0.987196i | \(-0.550993\pi\) | ||||
−0.159514 | + | 0.987196i | \(0.550993\pi\) | |||||||
\(888\) | −11607.9 | −0.438666 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −30206.2 | −1.13766 | ||||||||
\(891\) | 29149.4 | 1.09601 | ||||||||
\(892\) | 13054.2 | 0.490008 | ||||||||
\(893\) | 32583.9 | 1.22103 | ||||||||
\(894\) | 8885.67 | 0.332417 | ||||||||
\(895\) | 56267.2 | 2.10146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3761.93 | 0.140030 | ||||||||
\(898\) | 32897.2 | 1.22249 | ||||||||
\(899\) | −52347.4 | −1.94203 | ||||||||
\(900\) | 22045.3 | 0.816491 | ||||||||
\(901\) | −20045.9 | −0.741205 | ||||||||
\(902\) | 3281.27 | 0.121125 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17299.8 | −0.636485 | ||||||||
\(905\) | 3785.50 | 0.139043 | ||||||||
\(906\) | −2337.81 | −0.0857268 | ||||||||
\(907\) | −28182.9 | −1.03175 | −0.515876 | − | 0.856663i | \(-0.672533\pi\) | ||||
−0.515876 | + | 0.856663i | \(0.672533\pi\) | |||||||
\(908\) | −25129.1 | −0.918436 | ||||||||
\(909\) | 13593.0 | 0.495988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48586.1 | −1.76699 | −0.883496 | − | 0.468439i | \(-0.844816\pi\) | ||||
−0.883496 | + | 0.468439i | \(0.844816\pi\) | |||||||
\(912\) | −12206.6 | −0.443203 | ||||||||
\(913\) | −28323.6 | −1.02670 | ||||||||
\(914\) | 28427.5 | 1.02877 | ||||||||
\(915\) | −80278.8 | −2.90048 | ||||||||
\(916\) | 8138.64 | 0.293568 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2385.37 | −0.0857614 | ||||||||
\(919\) | −48873.3 | −1.75428 | −0.877139 | − | 0.480236i | \(-0.840551\pi\) | ||||
−0.877139 | + | 0.480236i | \(0.840551\pi\) | |||||||
\(920\) | −3441.71 | −0.123337 | ||||||||
\(921\) | 20531.2 | 0.734556 | ||||||||
\(922\) | 12174.3 | 0.434858 | ||||||||
\(923\) | −7313.67 | −0.260815 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45464.0 | 1.61605 | ||||||||
\(926\) | 10718.1 | 0.380366 | ||||||||
\(927\) | 24957.5 | 0.884264 | ||||||||
\(928\) | −6392.75 | −0.226134 | ||||||||
\(929\) | −36236.5 | −1.27974 | −0.639872 | − | 0.768482i | \(-0.721012\pi\) | ||||
−0.639872 | + | 0.768482i | \(0.721012\pi\) | |||||||
\(930\) | 70353.0 | 2.48061 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6748.53 | 0.237184 | ||||||||
\(933\) | 9908.74 | 0.347693 | ||||||||
\(934\) | 35561.7 | 1.24584 | ||||||||
\(935\) | −46026.7 | −1.60988 | ||||||||
\(936\) | −4468.35 | −0.156039 | ||||||||
\(937\) | 37238.1 | 1.29831 | 0.649154 | − | 0.760657i | \(-0.275123\pi\) | ||||
0.649154 | + | 0.760657i | \(0.275123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2145.70 | 0.0745713 | ||||||||
\(940\) | −22934.2 | −0.795777 | ||||||||
\(941\) | 7961.47 | 0.275809 | 0.137905 | − | 0.990446i | \(-0.455963\pi\) | ||||
0.137905 | + | 0.990446i | \(0.455963\pi\) | |||||||
\(942\) | −18953.6 | −0.655565 | ||||||||
\(943\) | −1022.76 | −0.0353189 | ||||||||
\(944\) | −4087.75 | −0.140938 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1343.17 | 0.0461632 | ||||||||
\(947\) | 5376.57 | 0.184493 | 0.0922465 | − | 0.995736i | \(-0.470595\pi\) | ||||
0.0922465 | + | 0.995736i | \(0.470595\pi\) | |||||||
\(948\) | −32187.3 | −1.10274 | ||||||||
\(949\) | −560.517 | −0.0191730 | ||||||||
\(950\) | 47808.9 | 1.63276 | ||||||||
\(951\) | 16819.7 | 0.573518 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19459.6 | −0.661448 | −0.330724 | − | 0.943728i | \(-0.607293\pi\) | ||||
−0.330724 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(954\) | 14732.7 | 0.499987 | ||||||||
\(955\) | −79685.6 | −2.70007 | ||||||||
\(956\) | −26047.8 | −0.881220 | ||||||||
\(957\) | −52898.3 | −1.78679 | ||||||||
\(958\) | 24680.3 | 0.832343 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8591.63 | 0.288847 | ||||||||
\(961\) | 38870.7 | 1.30478 | ||||||||
\(962\) | −9215.09 | −0.308842 | ||||||||
\(963\) | 35579.8 | 1.19060 | ||||||||
\(964\) | −12653.0 | −0.422746 | ||||||||
\(965\) | −38743.4 | −1.29243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7286.78 | −0.242324 | −0.121162 | − | 0.992633i | \(-0.538662\pi\) | ||||
−0.121162 | + | 0.992633i | \(0.538662\pi\) | |||||||
\(968\) | 241.850 | 0.00803033 | ||||||||
\(969\) | 50881.8 | 1.68685 | ||||||||
\(970\) | 43780.5 | 1.44918 | ||||||||
\(971\) | 1401.06 | 0.0463050 | 0.0231525 | − | 0.999732i | \(-0.492630\pi\) | ||||
0.0231525 | + | 0.999732i | \(0.492630\pi\) | |||||||
\(972\) | 20749.7 | 0.684718 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −28691.8 | −0.943886 | ||||||||
\(975\) | 36781.2 | 1.20814 | ||||||||
\(976\) | −9568.10 | −0.313799 | ||||||||
\(977\) | 28822.9 | 0.943833 | 0.471917 | − | 0.881643i | \(-0.343562\pi\) | ||||
0.471917 | + | 0.881643i | \(0.343562\pi\) | |||||||
\(978\) | 31481.7 | 1.02932 | ||||||||
\(979\) | −29790.4 | −0.972527 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42144.6 | 1.37164 | ||||||||
\(982\) | −1679.69 | −0.0545836 | ||||||||
\(983\) | −8699.13 | −0.282257 | −0.141129 | − | 0.989991i | \(-0.545073\pi\) | ||||
−0.141129 | + | 0.989991i | \(0.545073\pi\) | |||||||
\(984\) | 2553.14 | 0.0827146 | ||||||||
\(985\) | 77495.5 | 2.50681 | ||||||||
\(986\) | 26647.4 | 0.860676 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9690.38 | −0.312037 | ||||||||
\(989\) | −418.663 | −0.0134608 | ||||||||
\(990\) | 33827.2 | 1.08596 | ||||||||
\(991\) | 40870.4 | 1.31008 | 0.655041 | − | 0.755593i | \(-0.272651\pi\) | ||||
0.655041 | + | 0.755593i | \(0.272651\pi\) | |||||||
\(992\) | 8385.08 | 0.268374 | ||||||||
\(993\) | −13541.6 | −0.432760 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20827.7 | 0.663599 | ||||||||
\(996\) | −22038.5 | −0.701120 | ||||||||
\(997\) | 36867.5 | 1.17112 | 0.585560 | − | 0.810629i | \(-0.300875\pi\) | ||||
0.585560 | + | 0.810629i | \(0.300875\pi\) | |||||||
\(998\) | −20946.8 | −0.664389 | ||||||||
\(999\) | 3615.46 | 0.114503 |
(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 | 2254.4.a.l.1.2 | 5 | ||
7.6 | odd | 2 | 322.4.a.h.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.a.h.1.4 | ✓ | 5 | 7.6 | odd | 2 | ||
2254.4.a.l.1.2 | 5 | 1.1 | even | 1 | trivial |