Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.82843 | −1.35355 | −0.676777 | − | 0.736188i | \(-0.736624\pi\) | ||||
−0.676777 | + | 0.736188i | \(0.736624\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 6.65685 | 0.832107 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 11.4853 | 0.781474 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 5.14214 | 0.227252 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −19.1421 | −0.605327 | ||||||||
\(11\) | 48.5685 | 1.33127 | 0.665635 | − | 0.746278i | \(-0.268161\pi\) | ||||
0.665635 | + | 0.746278i | \(0.268161\pi\) | |||||||
\(12\) | −19.9706 | −0.480417 | ||||||||
\(13\) | −43.6569 | −0.931403 | −0.465701 | − | 0.884942i | \(-0.654198\pi\) | ||||
−0.465701 | + | 0.884942i | \(0.654198\pi\) | |||||||
\(14\) | 26.7990 | 0.511595 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −72.9411 | −1.13971 | ||||||||
\(17\) | −67.6569 | −0.965247 | −0.482623 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482623 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(18\) | −34.4558 | −0.451184 | ||||||||
\(19\) | −93.2548 | −1.12601 | −0.563003 | − | 0.826455i | \(-0.690354\pi\) | ||||
−0.563003 | + | 0.826455i | \(0.690354\pi\) | |||||||
\(20\) | 33.2843 | 0.372129 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | −185.941 | −1.80194 | ||||||||
\(23\) | −104.167 | −0.944357 | −0.472179 | − | 0.881503i | \(-0.656532\pi\) | ||||
−0.472179 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(24\) | −15.4264 | −0.131204 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 167.137 | 1.26070 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −46.5980 | −0.314507 | ||||||||
\(29\) | −58.7351 | −0.376098 | −0.188049 | − | 0.982160i | \(-0.560216\pi\) | ||||
−0.188049 | + | 0.982160i | \(0.560216\pi\) | |||||||
\(30\) | 57.4264 | 0.349486 | ||||||||
\(31\) | −9.08831 | −0.0526551 | −0.0263276 | − | 0.999653i | \(-0.508381\pi\) | ||||
−0.0263276 | + | 0.999653i | \(0.508381\pi\) | |||||||
\(32\) | 238.113 | 1.31540 | ||||||||
\(33\) | −145.706 | −0.768609 | ||||||||
\(34\) | 259.019 | 1.30651 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 59.9117 | 0.277369 | ||||||||
\(37\) | −252.676 | −1.12269 | −0.561347 | − | 0.827580i | \(-0.689717\pi\) | ||||
−0.561347 | + | 0.827580i | \(0.689717\pi\) | |||||||
\(38\) | 357.019 | 1.52411 | ||||||||
\(39\) | 130.971 | 0.537745 | ||||||||
\(40\) | 25.7107 | 0.101630 | ||||||||
\(41\) | 276.274 | 1.05236 | 0.526180 | − | 0.850373i | \(-0.323624\pi\) | ||||
0.526180 | + | 0.850373i | \(0.323624\pi\) | |||||||
\(42\) | −80.3970 | −0.295370 | ||||||||
\(43\) | −92.6375 | −0.328537 | −0.164268 | − | 0.986416i | \(-0.552526\pi\) | ||||
−0.164268 | + | 0.986416i | \(0.552526\pi\) | |||||||
\(44\) | 323.314 | 1.10776 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 398.794 | 1.27824 | ||||||||
\(47\) | −582.794 | −1.80871 | −0.904354 | − | 0.426784i | \(-0.859646\pi\) | ||||
−0.904354 | + | 0.426784i | \(0.859646\pi\) | |||||||
\(48\) | 218.823 | 0.658009 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −95.7107 | −0.270711 | ||||||||
\(51\) | 202.971 | 0.557286 | ||||||||
\(52\) | −290.617 | −0.775026 | ||||||||
\(53\) | 623.019 | 1.61468 | 0.807342 | − | 0.590083i | \(-0.200905\pi\) | ||||
0.807342 | + | 0.590083i | \(0.200905\pi\) | |||||||
\(54\) | 103.368 | 0.260491 | ||||||||
\(55\) | 242.843 | 0.595362 | ||||||||
\(56\) | −35.9949 | −0.0858933 | ||||||||
\(57\) | 279.765 | 0.650100 | ||||||||
\(58\) | 224.863 | 0.509068 | ||||||||
\(59\) | −524.999 | −1.15846 | −0.579229 | − | 0.815165i | \(-0.696646\pi\) | ||||
−0.579229 | + | 0.815165i | \(0.696646\pi\) | |||||||
\(60\) | −99.8528 | −0.214849 | ||||||||
\(61\) | −352.794 | −0.740502 | −0.370251 | − | 0.928932i | \(-0.620728\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(62\) | 34.7939 | 0.0712715 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −328.068 | −0.640758 | ||||||||
\(65\) | −218.284 | −0.416536 | ||||||||
\(66\) | 557.823 | 1.04035 | ||||||||
\(67\) | −736.520 | −1.34299 | −0.671494 | − | 0.741010i | \(-0.734347\pi\) | ||||
−0.671494 | + | 0.741010i | \(0.734347\pi\) | |||||||
\(68\) | −450.382 | −0.803188 | ||||||||
\(69\) | 312.500 | 0.545225 | ||||||||
\(70\) | 133.995 | 0.228792 | ||||||||
\(71\) | −492.264 | −0.822831 | −0.411415 | − | 0.911448i | \(-0.634965\pi\) | ||||
−0.411415 | + | 0.911448i | \(0.634965\pi\) | |||||||
\(72\) | 46.2792 | 0.0757508 | ||||||||
\(73\) | 1164.75 | 1.86745 | 0.933727 | − | 0.357987i | \(-0.116537\pi\) | ||||
0.933727 | + | 0.357987i | \(0.116537\pi\) | |||||||
\(74\) | 967.352 | 1.51963 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −620.784 | −0.936958 | ||||||||
\(77\) | −339.980 | −0.503173 | ||||||||
\(78\) | −501.411 | −0.727867 | ||||||||
\(79\) | −872.195 | −1.24215 | −0.621074 | − | 0.783752i | \(-0.713303\pi\) | ||||
−0.621074 | + | 0.783752i | \(0.713303\pi\) | |||||||
\(80\) | −364.706 | −0.509692 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1057.70 | −1.42443 | ||||||||
\(83\) | −529.588 | −0.700359 | −0.350180 | − | 0.936683i | \(-0.613879\pi\) | ||||
−0.350180 | + | 0.936683i | \(0.613879\pi\) | |||||||
\(84\) | 139.794 | 0.181581 | ||||||||
\(85\) | −338.284 | −0.431672 | ||||||||
\(86\) | 354.656 | 0.444692 | ||||||||
\(87\) | 176.205 | 0.217140 | ||||||||
\(88\) | 249.746 | 0.302534 | ||||||||
\(89\) | −385.216 | −0.458796 | −0.229398 | − | 0.973333i | \(-0.573676\pi\) | ||||
−0.229398 | + | 0.973333i | \(0.573676\pi\) | |||||||
\(90\) | −172.279 | −0.201776 | ||||||||
\(91\) | 305.598 | 0.352037 | ||||||||
\(92\) | −693.421 | −0.785806 | ||||||||
\(93\) | 27.2649 | 0.0304005 | ||||||||
\(94\) | 2231.18 | 2.44818 | ||||||||
\(95\) | −466.274 | −0.503565 | ||||||||
\(96\) | −714.338 | −0.759446 | ||||||||
\(97\) | −463.892 | −0.485579 | −0.242789 | − | 0.970079i | \(-0.578062\pi\) | ||||
−0.242789 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(98\) | −187.593 | −0.193365 | ||||||||
\(99\) | 437.117 | 0.443757 | ||||||||
\(100\) | 166.421 | 0.166421 | ||||||||
\(101\) | −432.725 | −0.426314 | −0.213157 | − | 0.977018i | \(-0.568375\pi\) | ||||
−0.213157 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(102\) | −777.058 | −0.754316 | ||||||||
\(103\) | 512.626 | 0.490393 | 0.245197 | − | 0.969473i | \(-0.421147\pi\) | ||||
0.245197 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(104\) | −224.489 | −0.211663 | ||||||||
\(105\) | 105.000 | 0.0975900 | ||||||||
\(106\) | −2385.18 | −2.18556 | ||||||||
\(107\) | 1963.09 | 1.77363 | 0.886817 | − | 0.462122i | \(-0.152912\pi\) | ||||
0.886817 | + | 0.462122i | \(0.152912\pi\) | |||||||
\(108\) | −179.735 | −0.160139 | ||||||||
\(109\) | 545.176 | 0.479068 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(110\) | −929.706 | −0.805854 | ||||||||
\(111\) | 758.029 | 0.648188 | ||||||||
\(112\) | 510.588 | 0.430768 | ||||||||
\(113\) | −231.823 | −0.192992 | −0.0964961 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964961 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(114\) | −1071.06 | −0.879945 | ||||||||
\(115\) | −520.833 | −0.422329 | ||||||||
\(116\) | −390.991 | −0.312953 | ||||||||
\(117\) | −392.912 | −0.310468 | ||||||||
\(118\) | 2009.92 | 1.56804 | ||||||||
\(119\) | 473.598 | 0.364829 | ||||||||
\(120\) | −77.1320 | −0.0586763 | ||||||||
\(121\) | 1027.90 | 0.772279 | ||||||||
\(122\) | 1350.65 | 1.00231 | ||||||||
\(123\) | −828.823 | −0.607581 | ||||||||
\(124\) | −60.4996 | −0.0438147 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 241.191 | 0.170532 | ||||||||
\(127\) | 2372.90 | 1.65796 | 0.828979 | − | 0.559280i | \(-0.188922\pi\) | ||||
0.828979 | + | 0.559280i | \(0.188922\pi\) | |||||||
\(128\) | −648.917 | −0.448099 | ||||||||
\(129\) | 277.913 | 0.189681 | ||||||||
\(130\) | 835.685 | 0.563804 | ||||||||
\(131\) | 1200.04 | 0.800364 | 0.400182 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400182 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(132\) | −969.941 | −0.639565 | ||||||||
\(133\) | 652.784 | 0.425591 | ||||||||
\(134\) | 2819.71 | 1.81781 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −347.901 | −0.219355 | ||||||||
\(137\) | 2781.25 | 1.73444 | 0.867221 | − | 0.497924i | \(-0.165904\pi\) | ||||
0.867221 | + | 0.497924i | \(0.165904\pi\) | |||||||
\(138\) | −1196.38 | −0.737991 | ||||||||
\(139\) | −1245.60 | −0.760078 | −0.380039 | − | 0.924971i | \(-0.624089\pi\) | ||||
−0.380039 | + | 0.924971i | \(0.624089\pi\) | |||||||
\(140\) | −232.990 | −0.140652 | ||||||||
\(141\) | 1748.38 | 1.04426 | ||||||||
\(142\) | 1884.60 | 1.11375 | ||||||||
\(143\) | −2120.35 | −1.23995 | ||||||||
\(144\) | −656.470 | −0.379902 | ||||||||
\(145\) | −293.675 | −0.168196 | ||||||||
\(146\) | −4459.17 | −2.52770 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −1682.03 | −0.934202 | ||||||||
\(149\) | 19.4046 | 0.0106690 | 0.00533452 | − | 0.999986i | \(-0.498302\pi\) | ||||
0.00533452 | + | 0.999986i | \(0.498302\pi\) | |||||||
\(150\) | 287.132 | 0.156295 | ||||||||
\(151\) | −2349.80 | −1.26638 | −0.633192 | − | 0.773995i | \(-0.718256\pi\) | ||||
−0.633192 | + | 0.773995i | \(0.718256\pi\) | |||||||
\(152\) | −479.529 | −0.255888 | ||||||||
\(153\) | −608.912 | −0.321749 | ||||||||
\(154\) | 1301.59 | 0.681071 | ||||||||
\(155\) | −45.4416 | −0.0235481 | ||||||||
\(156\) | 871.852 | 0.447462 | ||||||||
\(157\) | −3898.46 | −1.98172 | −0.990862 | − | 0.134880i | \(-0.956935\pi\) | ||||
−0.990862 | + | 0.134880i | \(0.956935\pi\) | |||||||
\(158\) | 3339.14 | 1.68131 | ||||||||
\(159\) | −1869.06 | −0.932239 | ||||||||
\(160\) | 1190.56 | 0.588264 | ||||||||
\(161\) | 729.166 | 0.356934 | ||||||||
\(162\) | −310.103 | −0.150395 | ||||||||
\(163\) | 1527.54 | 0.734024 | 0.367012 | − | 0.930216i | \(-0.380381\pi\) | ||||
0.367012 | + | 0.930216i | \(0.380381\pi\) | |||||||
\(164\) | 1839.12 | 0.875676 | ||||||||
\(165\) | −728.528 | −0.343732 | ||||||||
\(166\) | 2027.49 | 0.947974 | ||||||||
\(167\) | −998.518 | −0.462681 | −0.231340 | − | 0.972873i | \(-0.574311\pi\) | ||||
−0.231340 | + | 0.972873i | \(0.574311\pi\) | |||||||
\(168\) | 107.985 | 0.0495905 | ||||||||
\(169\) | −291.079 | −0.132489 | ||||||||
\(170\) | 1295.10 | 0.584290 | ||||||||
\(171\) | −839.294 | −0.375336 | ||||||||
\(172\) | −616.674 | −0.273378 | ||||||||
\(173\) | 685.253 | 0.301149 | 0.150575 | − | 0.988599i | \(-0.451888\pi\) | ||||
0.150575 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(174\) | −674.589 | −0.293911 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | −3542.64 | −1.51725 | ||||||||
\(177\) | 1575.00 | 0.668836 | ||||||||
\(178\) | 1474.77 | 0.621005 | ||||||||
\(179\) | 1025.58 | 0.428245 | 0.214122 | − | 0.976807i | \(-0.431311\pi\) | ||||
0.214122 | + | 0.976807i | \(0.431311\pi\) | |||||||
\(180\) | 299.558 | 0.124043 | ||||||||
\(181\) | 2899.40 | 1.19067 | 0.595333 | − | 0.803479i | \(-0.297020\pi\) | ||||
0.595333 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(182\) | −1169.96 | −0.476501 | ||||||||
\(183\) | 1058.38 | 0.427529 | ||||||||
\(184\) | −535.638 | −0.214608 | ||||||||
\(185\) | −1263.38 | −0.502084 | ||||||||
\(186\) | −104.382 | −0.0411486 | ||||||||
\(187\) | −3285.99 | −1.28500 | ||||||||
\(188\) | −3879.57 | −1.50504 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 1785.10 | 0.681603 | ||||||||
\(191\) | 1074.18 | 0.406939 | 0.203469 | − | 0.979081i | \(-0.434778\pi\) | ||||
0.203469 | + | 0.979081i | \(0.434778\pi\) | |||||||
\(192\) | 984.204 | 0.369942 | ||||||||
\(193\) | 898.999 | 0.335292 | 0.167646 | − | 0.985847i | \(-0.446383\pi\) | ||||
0.167646 | + | 0.985847i | \(0.446383\pi\) | |||||||
\(194\) | 1775.98 | 0.657257 | ||||||||
\(195\) | 654.853 | 0.240487 | ||||||||
\(196\) | 326.186 | 0.118872 | ||||||||
\(197\) | 3063.63 | 1.10799 | 0.553996 | − | 0.832519i | \(-0.313102\pi\) | ||||
0.553996 | + | 0.832519i | \(0.313102\pi\) | |||||||
\(198\) | −1673.47 | −0.600648 | ||||||||
\(199\) | −949.522 | −0.338240 | −0.169120 | − | 0.985595i | \(-0.554093\pi\) | ||||
−0.169120 | + | 0.985595i | \(0.554093\pi\) | |||||||
\(200\) | 128.553 | 0.0454505 | ||||||||
\(201\) | 2209.56 | 0.775375 | ||||||||
\(202\) | 1656.66 | 0.577039 | ||||||||
\(203\) | 411.145 | 0.142151 | ||||||||
\(204\) | 1351.15 | 0.463721 | ||||||||
\(205\) | 1381.37 | 0.470630 | ||||||||
\(206\) | −1962.55 | −0.663774 | ||||||||
\(207\) | −937.499 | −0.314786 | ||||||||
\(208\) | 3184.38 | 1.06152 | ||||||||
\(209\) | −4529.25 | −1.49902 | ||||||||
\(210\) | −401.985 | −0.132093 | ||||||||
\(211\) | 2306.64 | 0.752587 | 0.376294 | − | 0.926500i | \(-0.377198\pi\) | ||||
0.376294 | + | 0.926500i | \(0.377198\pi\) | |||||||
\(212\) | 4147.35 | 1.34359 | ||||||||
\(213\) | 1476.79 | 0.475062 | ||||||||
\(214\) | −7515.53 | −2.40071 | ||||||||
\(215\) | −463.188 | −0.146926 | ||||||||
\(216\) | −138.838 | −0.0437348 | ||||||||
\(217\) | 63.6182 | 0.0199018 | ||||||||
\(218\) | −2087.17 | −0.648444 | ||||||||
\(219\) | −3494.26 | −1.07817 | ||||||||
\(220\) | 1616.57 | 0.495405 | ||||||||
\(221\) | 2953.69 | 0.899033 | ||||||||
\(222\) | −2902.06 | −0.877357 | ||||||||
\(223\) | −3227.61 | −0.969222 | −0.484611 | − | 0.874730i | \(-0.661039\pi\) | ||||
−0.484611 | + | 0.874730i | \(0.661039\pi\) | |||||||
\(224\) | −1666.79 | −0.497174 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 887.519 | 0.261225 | ||||||||
\(227\) | −637.820 | −0.186492 | −0.0932458 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932458 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(228\) | 1862.35 | 0.540953 | ||||||||
\(229\) | 544.774 | 0.157204 | 0.0786019 | − | 0.996906i | \(-0.474954\pi\) | ||||
0.0786019 | + | 0.996906i | \(0.474954\pi\) | |||||||
\(230\) | 1993.97 | 0.571646 | ||||||||
\(231\) | 1019.94 | 0.290507 | ||||||||
\(232\) | −302.024 | −0.0854691 | ||||||||
\(233\) | −5748.54 | −1.61631 | −0.808154 | − | 0.588972i | \(-0.799533\pi\) | ||||
−0.808154 | + | 0.588972i | \(0.799533\pi\) | |||||||
\(234\) | 1504.23 | 0.420234 | ||||||||
\(235\) | −2913.97 | −0.808878 | ||||||||
\(236\) | −3494.84 | −0.963961 | ||||||||
\(237\) | 2616.59 | 0.717154 | ||||||||
\(238\) | −1813.14 | −0.493816 | ||||||||
\(239\) | −2678.10 | −0.724820 | −0.362410 | − | 0.932019i | \(-0.618046\pi\) | ||||
−0.362410 | + | 0.932019i | \(0.618046\pi\) | |||||||
\(240\) | 1094.12 | 0.294271 | ||||||||
\(241\) | −2202.16 | −0.588604 | −0.294302 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294302 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(242\) | −3935.25 | −1.04532 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2348.50 | −0.616177 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 3173.09 | 0.822393 | ||||||||
\(247\) | 4071.21 | 1.04877 | ||||||||
\(248\) | −46.7333 | −0.0119660 | ||||||||
\(249\) | 1588.76 | 0.404353 | ||||||||
\(250\) | −478.553 | −0.121065 | ||||||||
\(251\) | −5716.90 | −1.43764 | −0.718820 | − | 0.695196i | \(-0.755317\pi\) | ||||
−0.718820 | + | 0.695196i | \(0.755317\pi\) | |||||||
\(252\) | −419.382 | −0.104836 | ||||||||
\(253\) | −5059.22 | −1.25719 | ||||||||
\(254\) | −9084.47 | −2.24413 | ||||||||
\(255\) | 1014.85 | 0.249226 | ||||||||
\(256\) | 5108.88 | 1.24728 | ||||||||
\(257\) | 4724.29 | 1.14666 | 0.573332 | − | 0.819323i | \(-0.305650\pi\) | ||||
0.573332 | + | 0.819323i | \(0.305650\pi\) | |||||||
\(258\) | −1063.97 | −0.256743 | ||||||||
\(259\) | 1768.73 | 0.424339 | ||||||||
\(260\) | −1453.09 | −0.346602 | ||||||||
\(261\) | −528.616 | −0.125366 | ||||||||
\(262\) | −4594.25 | −1.08334 | ||||||||
\(263\) | 5975.36 | 1.40097 | 0.700487 | − | 0.713665i | \(-0.252966\pi\) | ||||
0.700487 | + | 0.713665i | \(0.252966\pi\) | |||||||
\(264\) | −749.238 | −0.174668 | ||||||||
\(265\) | 3115.10 | 0.722109 | ||||||||
\(266\) | −2499.14 | −0.576059 | ||||||||
\(267\) | 1155.65 | 0.264886 | ||||||||
\(268\) | −4902.90 | −1.11751 | ||||||||
\(269\) | 4486.11 | 1.01681 | 0.508407 | − | 0.861117i | \(-0.330234\pi\) | ||||
0.508407 | + | 0.861117i | \(0.330234\pi\) | |||||||
\(270\) | 516.838 | 0.116495 | ||||||||
\(271\) | 3827.68 | 0.857989 | 0.428994 | − | 0.903307i | \(-0.358868\pi\) | ||||
0.428994 | + | 0.903307i | \(0.358868\pi\) | |||||||
\(272\) | 4934.97 | 1.10010 | ||||||||
\(273\) | −916.794 | −0.203249 | ||||||||
\(274\) | −10647.8 | −2.34766 | ||||||||
\(275\) | 1214.21 | 0.266254 | ||||||||
\(276\) | 2080.26 | 0.453685 | ||||||||
\(277\) | −3420.54 | −0.741950 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(278\) | 4768.71 | 1.02881 | ||||||||
\(279\) | −81.7948 | −0.0175517 | ||||||||
\(280\) | −179.975 | −0.0384127 | ||||||||
\(281\) | 5235.92 | 1.11156 | 0.555781 | − | 0.831329i | \(-0.312419\pi\) | ||||
0.555781 | + | 0.831329i | \(0.312419\pi\) | |||||||
\(282\) | −6693.55 | −1.41346 | ||||||||
\(283\) | −6985.88 | −1.46738 | −0.733688 | − | 0.679486i | \(-0.762203\pi\) | ||||
−0.733688 | + | 0.679486i | \(0.762203\pi\) | |||||||
\(284\) | −3276.93 | −0.684683 | ||||||||
\(285\) | 1398.82 | 0.290734 | ||||||||
\(286\) | 8117.60 | 1.67834 | ||||||||
\(287\) | −1933.92 | −0.397755 | ||||||||
\(288\) | 2143.01 | 0.438466 | ||||||||
\(289\) | −335.550 | −0.0682984 | ||||||||
\(290\) | 1124.31 | 0.227662 | ||||||||
\(291\) | 1391.68 | 0.280349 | ||||||||
\(292\) | 7753.59 | 1.55392 | ||||||||
\(293\) | 7399.70 | 1.47541 | 0.737705 | − | 0.675123i | \(-0.235910\pi\) | ||||
0.737705 | + | 0.675123i | \(0.235910\pi\) | |||||||
\(294\) | 562.779 | 0.111639 | ||||||||
\(295\) | −2625.00 | −0.518078 | ||||||||
\(296\) | −1299.30 | −0.255135 | ||||||||
\(297\) | −1311.35 | −0.256203 | ||||||||
\(298\) | −74.2892 | −0.0144411 | ||||||||
\(299\) | 4547.58 | 0.879577 | ||||||||
\(300\) | −499.264 | −0.0960834 | ||||||||
\(301\) | 648.463 | 0.124175 | ||||||||
\(302\) | 8996.04 | 1.71412 | ||||||||
\(303\) | 1298.17 | 0.246133 | ||||||||
\(304\) | 6802.11 | 1.28332 | ||||||||
\(305\) | −1763.97 | −0.331163 | ||||||||
\(306\) | 2331.17 | 0.435504 | ||||||||
\(307\) | 2668.64 | 0.496116 | 0.248058 | − | 0.968745i | \(-0.420208\pi\) | ||||
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(308\) | −2263.20 | −0.418693 | ||||||||
\(309\) | −1537.88 | −0.283129 | ||||||||
\(310\) | 173.970 | 0.0318736 | ||||||||
\(311\) | 6189.25 | 1.12849 | 0.564244 | − | 0.825608i | \(-0.309168\pi\) | ||||
0.564244 | + | 0.825608i | \(0.309168\pi\) | |||||||
\(312\) | 673.468 | 0.122204 | ||||||||
\(313\) | −2921.59 | −0.527598 | −0.263799 | − | 0.964578i | \(-0.584976\pi\) | ||||
−0.263799 | + | 0.964578i | \(0.584976\pi\) | |||||||
\(314\) | 14925.0 | 2.68237 | ||||||||
\(315\) | −315.000 | −0.0563436 | ||||||||
\(316\) | −5806.08 | −1.03360 | ||||||||
\(317\) | 9825.56 | 1.74088 | 0.870439 | − | 0.492276i | \(-0.163835\pi\) | ||||
0.870439 | + | 0.492276i | \(0.163835\pi\) | |||||||
\(318\) | 7155.55 | 1.26183 | ||||||||
\(319\) | −2852.68 | −0.500687 | ||||||||
\(320\) | −1640.34 | −0.286556 | ||||||||
\(321\) | −5889.26 | −1.02401 | ||||||||
\(322\) | −2791.56 | −0.483129 | ||||||||
\(323\) | 6309.33 | 1.08687 | ||||||||
\(324\) | 539.205 | 0.0924563 | ||||||||
\(325\) | −1091.42 | −0.186281 | ||||||||
\(326\) | −5848.07 | −0.993541 | ||||||||
\(327\) | −1635.53 | −0.276590 | ||||||||
\(328\) | 1420.64 | 0.239151 | ||||||||
\(329\) | 4079.56 | 0.683627 | ||||||||
\(330\) | 2789.12 | 0.465260 | ||||||||
\(331\) | −9258.17 | −1.53739 | −0.768693 | − | 0.639618i | \(-0.779093\pi\) | ||||
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(332\) | −3525.39 | −0.582774 | ||||||||
\(333\) | −2274.09 | −0.374232 | ||||||||
\(334\) | 3822.75 | 0.626263 | ||||||||
\(335\) | −3682.60 | −0.600603 | ||||||||
\(336\) | −1531.76 | −0.248704 | ||||||||
\(337\) | −3693.98 | −0.597103 | −0.298552 | − | 0.954394i | \(-0.596503\pi\) | ||||
−0.298552 | + | 0.954394i | \(0.596503\pi\) | |||||||
\(338\) | 1114.38 | 0.179331 | ||||||||
\(339\) | 695.470 | 0.111424 | ||||||||
\(340\) | −2251.91 | −0.359197 | ||||||||
\(341\) | −441.406 | −0.0700982 | ||||||||
\(342\) | 3213.17 | 0.508037 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −476.355 | −0.0746608 | ||||||||
\(345\) | 1562.50 | 0.243832 | ||||||||
\(346\) | −2623.44 | −0.407622 | ||||||||
\(347\) | 3832.83 | 0.592960 | 0.296480 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296480 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(348\) | 1172.97 | 0.180684 | ||||||||
\(349\) | 8325.22 | 1.27690 | 0.638451 | − | 0.769662i | \(-0.279575\pi\) | ||||
0.638451 | + | 0.769662i | \(0.279575\pi\) | |||||||
\(350\) | 669.975 | 0.102319 | ||||||||
\(351\) | 1178.74 | 0.179248 | ||||||||
\(352\) | 11564.8 | 1.75115 | ||||||||
\(353\) | −8991.52 | −1.35572 | −0.677862 | − | 0.735189i | \(-0.737093\pi\) | ||||
−0.677862 | + | 0.735189i | \(0.737093\pi\) | |||||||
\(354\) | −6029.76 | −0.905306 | ||||||||
\(355\) | −2461.32 | −0.367981 | ||||||||
\(356\) | −2564.33 | −0.381767 | ||||||||
\(357\) | −1420.79 | −0.210634 | ||||||||
\(358\) | −3926.38 | −0.579652 | ||||||||
\(359\) | −12893.8 | −1.89557 | −0.947783 | − | 0.318917i | \(-0.896681\pi\) | ||||
−0.947783 | + | 0.318917i | \(0.896681\pi\) | |||||||
\(360\) | 231.396 | 0.0338768 | ||||||||
\(361\) | 1837.46 | 0.267891 | ||||||||
\(362\) | −11100.1 | −1.61163 | ||||||||
\(363\) | −3083.71 | −0.445875 | ||||||||
\(364\) | 2034.32 | 0.292932 | ||||||||
\(365\) | 5823.77 | 0.835150 | ||||||||
\(366\) | −4051.94 | −0.578684 | ||||||||
\(367\) | −7480.17 | −1.06393 | −0.531964 | − | 0.846767i | \(-0.678546\pi\) | ||||
−0.531964 | + | 0.846767i | \(0.678546\pi\) | |||||||
\(368\) | 7598.02 | 1.07629 | ||||||||
\(369\) | 2486.47 | 0.350787 | ||||||||
\(370\) | 4836.76 | 0.679598 | ||||||||
\(371\) | −4361.14 | −0.610293 | ||||||||
\(372\) | 181.499 | 0.0252964 | ||||||||
\(373\) | −3523.32 | −0.489090 | −0.244545 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244545 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(374\) | 12580.2 | 1.73932 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −2996.81 | −0.411033 | ||||||||
\(377\) | 2564.19 | 0.350298 | ||||||||
\(378\) | −723.573 | −0.0984565 | ||||||||
\(379\) | 13515.4 | 1.83177 | 0.915886 | − | 0.401438i | \(-0.131490\pi\) | ||||
0.915886 | + | 0.401438i | \(0.131490\pi\) | |||||||
\(380\) | −3103.92 | −0.419020 | ||||||||
\(381\) | −7118.69 | −0.957222 | ||||||||
\(382\) | −4112.44 | −0.550813 | ||||||||
\(383\) | −657.182 | −0.0876774 | −0.0438387 | − | 0.999039i | \(-0.513959\pi\) | ||||
−0.0438387 | + | 0.999039i | \(0.513959\pi\) | |||||||
\(384\) | 1946.75 | 0.258710 | ||||||||
\(385\) | −1699.90 | −0.225026 | ||||||||
\(386\) | −3441.75 | −0.453836 | ||||||||
\(387\) | −833.738 | −0.109512 | ||||||||
\(388\) | −3088.06 | −0.404053 | ||||||||
\(389\) | −9741.87 | −1.26975 | −0.634875 | − | 0.772615i | \(-0.718948\pi\) | ||||
−0.634875 | + | 0.772615i | \(0.718948\pi\) | |||||||
\(390\) | −2507.06 | −0.325512 | ||||||||
\(391\) | 7047.58 | 0.911538 | ||||||||
\(392\) | 251.965 | 0.0324646 | ||||||||
\(393\) | −3600.11 | −0.462091 | ||||||||
\(394\) | −11728.9 | −1.49973 | ||||||||
\(395\) | −4360.98 | −0.555505 | ||||||||
\(396\) | 2909.82 | 0.369253 | ||||||||
\(397\) | 4407.42 | 0.557184 | 0.278592 | − | 0.960410i | \(-0.410132\pi\) | ||||
0.278592 | + | 0.960410i | \(0.410132\pi\) | |||||||
\(398\) | 3635.18 | 0.457827 | ||||||||
\(399\) | −1958.35 | −0.245715 | ||||||||
\(400\) | −1823.53 | −0.227941 | ||||||||
\(401\) | −11569.5 | −1.44078 | −0.720391 | − | 0.693568i | \(-0.756037\pi\) | ||||
−0.720391 | + | 0.693568i | \(0.756037\pi\) | |||||||
\(402\) | −8459.14 | −1.04951 | ||||||||
\(403\) | 396.767 | 0.0490431 | ||||||||
\(404\) | −2880.59 | −0.354739 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −1574.04 | −0.192410 | ||||||||
\(407\) | −12272.1 | −1.49461 | ||||||||
\(408\) | 1043.70 | 0.126645 | ||||||||
\(409\) | −3083.03 | −0.372729 | −0.186364 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186364 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(410\) | −5288.48 | −0.637023 | ||||||||
\(411\) | −8343.76 | −1.00138 | ||||||||
\(412\) | 3412.47 | 0.408060 | ||||||||
\(413\) | 3674.99 | 0.437856 | ||||||||
\(414\) | 3589.15 | 0.426079 | ||||||||
\(415\) | −2647.94 | −0.313210 | ||||||||
\(416\) | −10395.3 | −1.22517 | ||||||||
\(417\) | 3736.81 | 0.438831 | ||||||||
\(418\) | 17339.9 | 2.02900 | ||||||||
\(419\) | −5415.21 | −0.631385 | −0.315692 | − | 0.948862i | \(-0.602237\pi\) | ||||
−0.315692 | + | 0.948862i | \(0.602237\pi\) | |||||||
\(420\) | 698.970 | 0.0812053 | ||||||||
\(421\) | 4188.34 | 0.484863 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(422\) | −8830.82 | −1.01867 | ||||||||
\(423\) | −5245.15 | −0.602902 | ||||||||
\(424\) | 3203.65 | 0.366941 | ||||||||
\(425\) | −1691.42 | −0.193049 | ||||||||
\(426\) | −5653.79 | −0.643021 | ||||||||
\(427\) | 2469.56 | 0.279884 | ||||||||
\(428\) | 13068.0 | 1.47585 | ||||||||
\(429\) | 6361.05 | 0.715884 | ||||||||
\(430\) | 1773.28 | 0.198872 | ||||||||
\(431\) | −9108.41 | −1.01795 | −0.508975 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508975 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(432\) | 1969.41 | 0.219336 | ||||||||
\(433\) | −16847.0 | −1.86979 | −0.934893 | − | 0.354930i | \(-0.884505\pi\) | ||||
−0.934893 | + | 0.354930i | \(0.884505\pi\) | |||||||
\(434\) | −243.558 | −0.0269381 | ||||||||
\(435\) | 881.026 | 0.0971080 | ||||||||
\(436\) | 3629.16 | 0.398635 | ||||||||
\(437\) | 9714.03 | 1.06335 | ||||||||
\(438\) | 13377.5 | 1.45937 | ||||||||
\(439\) | 8434.14 | 0.916946 | 0.458473 | − | 0.888708i | \(-0.348397\pi\) | ||||
0.458473 | + | 0.888708i | \(0.348397\pi\) | |||||||
\(440\) | 1248.73 | 0.135297 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −11308.0 | −1.21689 | ||||||||
\(443\) | −4298.49 | −0.461010 | −0.230505 | − | 0.973071i | \(-0.574038\pi\) | ||||
−0.230505 | + | 0.973071i | \(0.574038\pi\) | |||||||
\(444\) | 5046.09 | 0.539362 | ||||||||
\(445\) | −1926.08 | −0.205180 | ||||||||
\(446\) | 12356.7 | 1.31189 | ||||||||
\(447\) | −58.2139 | −0.00615978 | ||||||||
\(448\) | 2296.48 | 0.242184 | ||||||||
\(449\) | 10545.0 | 1.10835 | 0.554173 | − | 0.832402i | \(-0.313035\pi\) | ||||
0.554173 | + | 0.832402i | \(0.313035\pi\) | |||||||
\(450\) | −861.396 | −0.0902369 | ||||||||
\(451\) | 13418.2 | 1.40098 | ||||||||
\(452\) | −1543.21 | −0.160590 | ||||||||
\(453\) | 7049.40 | 0.731147 | ||||||||
\(454\) | 2441.85 | 0.252426 | ||||||||
\(455\) | 1527.99 | 0.157436 | ||||||||
\(456\) | 1438.59 | 0.147737 | ||||||||
\(457\) | 11952.4 | 1.22344 | 0.611719 | − | 0.791075i | \(-0.290478\pi\) | ||||
0.611719 | + | 0.791075i | \(0.290478\pi\) | |||||||
\(458\) | −2085.63 | −0.212784 | ||||||||
\(459\) | 1826.74 | 0.185762 | ||||||||
\(460\) | −3467.11 | −0.351423 | ||||||||
\(461\) | −17200.9 | −1.73780 | −0.868900 | − | 0.494988i | \(-0.835173\pi\) | ||||
−0.868900 | + | 0.494988i | \(0.835173\pi\) | |||||||
\(462\) | −3904.76 | −0.393217 | ||||||||
\(463\) | −10368.7 | −1.04076 | −0.520381 | − | 0.853934i | \(-0.674210\pi\) | ||||
−0.520381 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(464\) | 4284.20 | 0.428640 | ||||||||
\(465\) | 136.325 | 0.0135955 | ||||||||
\(466\) | 22007.9 | 2.18776 | ||||||||
\(467\) | −16879.5 | −1.67257 | −0.836284 | − | 0.548296i | \(-0.815277\pi\) | ||||
−0.836284 | + | 0.548296i | \(0.815277\pi\) | |||||||
\(468\) | −2615.56 | −0.258342 | ||||||||
\(469\) | 5155.64 | 0.507602 | ||||||||
\(470\) | 11155.9 | 1.09486 | ||||||||
\(471\) | 11695.4 | 1.14415 | ||||||||
\(472\) | −2699.62 | −0.263263 | ||||||||
\(473\) | −4499.27 | −0.437371 | ||||||||
\(474\) | −10017.4 | −0.970706 | ||||||||
\(475\) | −2331.37 | −0.225201 | ||||||||
\(476\) | 3152.67 | 0.303577 | ||||||||
\(477\) | 5607.17 | 0.538228 | ||||||||
\(478\) | 10252.9 | 0.981082 | ||||||||
\(479\) | 7329.12 | 0.699115 | 0.349558 | − | 0.936915i | \(-0.386332\pi\) | ||||
0.349558 | + | 0.936915i | \(0.386332\pi\) | |||||||
\(480\) | −3571.69 | −0.339635 | ||||||||
\(481\) | 11031.0 | 1.04568 | ||||||||
\(482\) | 8430.80 | 0.796706 | ||||||||
\(483\) | −2187.50 | −0.206076 | ||||||||
\(484\) | 6842.60 | 0.642619 | ||||||||
\(485\) | −2319.46 | −0.217157 | ||||||||
\(486\) | 930.308 | 0.0868305 | ||||||||
\(487\) | −17209.5 | −1.60131 | −0.800655 | − | 0.599125i | \(-0.795515\pi\) | ||||
−0.800655 | + | 0.599125i | \(0.795515\pi\) | |||||||
\(488\) | −1814.11 | −0.168281 | ||||||||
\(489\) | −4582.61 | −0.423789 | ||||||||
\(490\) | −937.965 | −0.0864754 | ||||||||
\(491\) | 11392.5 | 1.04712 | 0.523560 | − | 0.851989i | \(-0.324604\pi\) | ||||
0.523560 | + | 0.851989i | \(0.324604\pi\) | |||||||
\(492\) | −5517.35 | −0.505572 | ||||||||
\(493\) | 3973.83 | 0.363027 | ||||||||
\(494\) | −15586.3 | −1.41956 | ||||||||
\(495\) | 2185.58 | 0.198454 | ||||||||
\(496\) | 662.912 | 0.0600113 | ||||||||
\(497\) | 3445.85 | 0.311001 | ||||||||
\(498\) | −6082.47 | −0.547313 | ||||||||
\(499\) | 19079.4 | 1.71164 | 0.855822 | − | 0.517271i | \(-0.173052\pi\) | ||||
0.855822 | + | 0.517271i | \(0.173052\pi\) | |||||||
\(500\) | 832.107 | 0.0744259 | ||||||||
\(501\) | 2995.55 | 0.267129 | ||||||||
\(502\) | 21886.7 | 1.94592 | ||||||||
\(503\) | −13499.4 | −1.19663 | −0.598317 | − | 0.801259i | \(-0.704164\pi\) | ||||
−0.598317 | + | 0.801259i | \(0.704164\pi\) | |||||||
\(504\) | −323.955 | −0.0286311 | ||||||||
\(505\) | −2163.62 | −0.190654 | ||||||||
\(506\) | 19368.8 | 1.70168 | ||||||||
\(507\) | 873.237 | 0.0764928 | ||||||||
\(508\) | 15796.0 | 1.37960 | ||||||||
\(509\) | −4328.85 | −0.376960 | −0.188480 | − | 0.982077i | \(-0.560356\pi\) | ||||
−0.188480 | + | 0.982077i | \(0.560356\pi\) | |||||||
\(510\) | −3885.29 | −0.337340 | ||||||||
\(511\) | −8153.27 | −0.705831 | ||||||||
\(512\) | −14367.6 | −1.24017 | ||||||||
\(513\) | 2517.88 | 0.216700 | ||||||||
\(514\) | −18086.6 | −1.55207 | ||||||||
\(515\) | 2563.13 | 0.219311 | ||||||||
\(516\) | 1850.02 | 0.157835 | ||||||||
\(517\) | −28305.5 | −2.40788 | ||||||||
\(518\) | −6771.47 | −0.574365 | ||||||||
\(519\) | −2055.76 | −0.173869 | ||||||||
\(520\) | −1122.45 | −0.0946588 | ||||||||
\(521\) | 19395.7 | 1.63098 | 0.815490 | − | 0.578771i | \(-0.196468\pi\) | ||||
0.815490 | + | 0.578771i | \(0.196468\pi\) | |||||||
\(522\) | 2023.77 | 0.169689 | ||||||||
\(523\) | 20413.8 | 1.70675 | 0.853377 | − | 0.521294i | \(-0.174550\pi\) | ||||
0.853377 | + | 0.521294i | \(0.174550\pi\) | |||||||
\(524\) | 7988.47 | 0.665989 | ||||||||
\(525\) | 525.000 | 0.0436436 | ||||||||
\(526\) | −22876.2 | −1.89629 | ||||||||
\(527\) | 614.887 | 0.0508252 | ||||||||
\(528\) | 10627.9 | 0.875987 | ||||||||
\(529\) | −1316.34 | −0.108189 | ||||||||
\(530\) | −11925.9 | −0.977413 | ||||||||
\(531\) | −4724.99 | −0.386153 | ||||||||
\(532\) | 4345.49 | 0.354137 | ||||||||
\(533\) | −12061.3 | −0.980171 | ||||||||
\(534\) | −4424.32 | −0.358537 | ||||||||
\(535\) | 9815.43 | 0.793193 | ||||||||
\(536\) | −3787.28 | −0.305197 | ||||||||
\(537\) | −3076.75 | −0.247247 | ||||||||
\(538\) | −17174.8 | −1.37631 | ||||||||
\(539\) | 2379.86 | 0.190181 | ||||||||
\(540\) | −898.675 | −0.0716163 | ||||||||
\(541\) | −4919.18 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(542\) | −14654.0 | −1.16133 | ||||||||
\(543\) | −8698.19 | −0.687431 | ||||||||
\(544\) | −16110.0 | −1.26969 | ||||||||
\(545\) | 2725.88 | 0.214246 | ||||||||
\(546\) | 3509.88 | 0.275108 | ||||||||
\(547\) | 15334.2 | 1.19862 | 0.599308 | − | 0.800518i | \(-0.295442\pi\) | ||||
0.599308 | + | 0.800518i | \(0.295442\pi\) | |||||||
\(548\) | 18514.4 | 1.44324 | ||||||||
\(549\) | −3175.15 | −0.246834 | ||||||||
\(550\) | −4648.53 | −0.360389 | ||||||||
\(551\) | 5477.33 | 0.423488 | ||||||||
\(552\) | 1606.92 | 0.123904 | ||||||||
\(553\) | 6105.37 | 0.469487 | ||||||||
\(554\) | 13095.3 | 1.00427 | ||||||||
\(555\) | 3790.14 | 0.289879 | ||||||||
\(556\) | −8291.81 | −0.632466 | ||||||||
\(557\) | −8613.78 | −0.655256 | −0.327628 | − | 0.944807i | \(-0.606249\pi\) | ||||
−0.327628 | + | 0.944807i | \(0.606249\pi\) | |||||||
\(558\) | 313.145 | 0.0237572 | ||||||||
\(559\) | 4044.26 | 0.306000 | ||||||||
\(560\) | 2552.94 | 0.192645 | ||||||||
\(561\) | 9857.98 | 0.741897 | ||||||||
\(562\) | −20045.3 | −1.50456 | ||||||||
\(563\) | −2320.81 | −0.173731 | −0.0868654 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868654 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(564\) | 11638.7 | 0.868934 | ||||||||
\(565\) | −1159.12 | −0.0863087 | ||||||||
\(566\) | 26744.9 | 1.98617 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −2531.29 | −0.186990 | ||||||||
\(569\) | −1736.04 | −0.127906 | −0.0639529 | − | 0.997953i | \(-0.520371\pi\) | ||||
−0.0639529 | + | 0.997953i | \(0.520371\pi\) | |||||||
\(570\) | −5355.29 | −0.393524 | ||||||||
\(571\) | 23897.8 | 1.75148 | 0.875738 | − | 0.482786i | \(-0.160375\pi\) | ||||
0.875738 | + | 0.482786i | \(0.160375\pi\) | |||||||
\(572\) | −14114.9 | −1.03177 | ||||||||
\(573\) | −3222.55 | −0.234946 | ||||||||
\(574\) | 7403.87 | 0.538382 | ||||||||
\(575\) | −2604.16 | −0.188871 | ||||||||
\(576\) | −2952.61 | −0.213586 | ||||||||
\(577\) | 8029.26 | 0.579311 | 0.289655 | − | 0.957131i | \(-0.406459\pi\) | ||||
0.289655 | + | 0.957131i | \(0.406459\pi\) | |||||||
\(578\) | 1284.63 | 0.0924455 | ||||||||
\(579\) | −2697.00 | −0.193581 | ||||||||
\(580\) | −1954.95 | −0.139957 | ||||||||
\(581\) | 3707.12 | 0.264711 | ||||||||
\(582\) | −5327.93 | −0.379467 | ||||||||
\(583\) | 30259.1 | 2.14958 | ||||||||
\(584\) | 5989.32 | 0.424383 | ||||||||
\(585\) | −1964.56 | −0.138845 | ||||||||
\(586\) | −28329.2 | −1.99705 | ||||||||
\(587\) | −8015.14 | −0.563578 | −0.281789 | − | 0.959476i | \(-0.590928\pi\) | ||||
−0.281789 | + | 0.959476i | \(0.590928\pi\) | |||||||
\(588\) | −978.558 | −0.0686310 | ||||||||
\(589\) | 847.529 | 0.0592900 | ||||||||
\(590\) | 10049.6 | 0.701247 | ||||||||
\(591\) | −9190.88 | −0.639700 | ||||||||
\(592\) | 18430.5 | 1.27954 | ||||||||
\(593\) | 12820.3 | 0.887801 | 0.443901 | − | 0.896076i | \(-0.353594\pi\) | ||||
0.443901 | + | 0.896076i | \(0.353594\pi\) | |||||||
\(594\) | 5020.41 | 0.346784 | ||||||||
\(595\) | 2367.99 | 0.163157 | ||||||||
\(596\) | 129.174 | 0.00887779 | ||||||||
\(597\) | 2848.57 | 0.195283 | ||||||||
\(598\) | −17410.1 | −1.19055 | ||||||||
\(599\) | −15330.5 | −1.04572 | −0.522860 | − | 0.852418i | \(-0.675135\pi\) | ||||
−0.522860 | + | 0.852418i | \(0.675135\pi\) | |||||||
\(600\) | −385.660 | −0.0262409 | ||||||||
\(601\) | 107.658 | 0.00730694 | 0.00365347 | − | 0.999993i | \(-0.498837\pi\) | ||||
0.00365347 | + | 0.999993i | \(0.498837\pi\) | |||||||
\(602\) | −2482.59 | −0.168078 | ||||||||
\(603\) | −6628.68 | −0.447663 | ||||||||
\(604\) | −15642.3 | −1.05377 | ||||||||
\(605\) | 5139.52 | 0.345374 | ||||||||
\(606\) | −4969.97 | −0.333154 | ||||||||
\(607\) | −8213.06 | −0.549189 | −0.274595 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274595 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(608\) | −22205.2 | −1.48115 | ||||||||
\(609\) | −1233.44 | −0.0820712 | ||||||||
\(610\) | 6753.23 | 0.448246 | ||||||||
\(611\) | 25443.0 | 1.68463 | ||||||||
\(612\) | −4053.44 | −0.267729 | ||||||||
\(613\) | 1242.60 | 0.0818732 | 0.0409366 | − | 0.999162i | \(-0.486966\pi\) | ||||
0.0409366 | + | 0.999162i | \(0.486966\pi\) | |||||||
\(614\) | −10216.7 | −0.671519 | ||||||||
\(615\) | −4144.11 | −0.271718 | ||||||||
\(616\) | −1748.22 | −0.114347 | ||||||||
\(617\) | −13170.6 | −0.859367 | −0.429683 | − | 0.902980i | \(-0.641375\pi\) | ||||
−0.429683 | + | 0.902980i | \(0.641375\pi\) | |||||||
\(618\) | 5887.65 | 0.383230 | ||||||||
\(619\) | 19774.1 | 1.28399 | 0.641993 | − | 0.766711i | \(-0.278108\pi\) | ||||
0.641993 | + | 0.766711i | \(0.278108\pi\) | |||||||
\(620\) | −302.498 | −0.0195945 | ||||||||
\(621\) | 2812.50 | 0.181742 | ||||||||
\(622\) | −23695.1 | −1.52747 | ||||||||
\(623\) | 2696.51 | 0.173409 | ||||||||
\(624\) | −9553.14 | −0.612871 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 11185.1 | 0.714132 | ||||||||
\(627\) | 13587.8 | 0.865459 | ||||||||
\(628\) | −25951.5 | −1.64901 | ||||||||
\(629\) | 17095.3 | 1.08368 | ||||||||
\(630\) | 1205.95 | 0.0762641 | ||||||||
\(631\) | −14308.8 | −0.902735 | −0.451367 | − | 0.892338i | \(-0.649064\pi\) | ||||
−0.451367 | + | 0.892338i | \(0.649064\pi\) | |||||||
\(632\) | −4484.95 | −0.282281 | ||||||||
\(633\) | −6919.93 | −0.434507 | ||||||||
\(634\) | −37616.4 | −2.35637 | ||||||||
\(635\) | 11864.5 | 0.741461 | ||||||||
\(636\) | −12442.0 | −0.775722 | ||||||||
\(637\) | −2139.19 | −0.133058 | ||||||||
\(638\) | 10921.3 | 0.677707 | ||||||||
\(639\) | −4430.38 | −0.274277 | ||||||||
\(640\) | −3244.58 | −0.200396 | ||||||||
\(641\) | 11537.5 | 0.710925 | 0.355463 | − | 0.934691i | \(-0.384323\pi\) | ||||
0.355463 | + | 0.934691i | \(0.384323\pi\) | |||||||
\(642\) | 22546.6 | 1.38605 | ||||||||
\(643\) | 19603.0 | 1.20228 | 0.601139 | − | 0.799144i | \(-0.294714\pi\) | ||||
0.601139 | + | 0.799144i | \(0.294714\pi\) | |||||||
\(644\) | 4853.95 | 0.297007 | ||||||||
\(645\) | 1389.56 | 0.0848279 | ||||||||
\(646\) | −24154.8 | −1.47114 | ||||||||
\(647\) | 21650.0 | 1.31553 | 0.657765 | − | 0.753223i | \(-0.271502\pi\) | ||||
0.657765 | + | 0.753223i | \(0.271502\pi\) | |||||||
\(648\) | 416.513 | 0.0252503 | ||||||||
\(649\) | −25498.4 | −1.54222 | ||||||||
\(650\) | 4178.43 | 0.252141 | ||||||||
\(651\) | −190.855 | −0.0114903 | ||||||||
\(652\) | 10168.6 | 0.610787 | ||||||||
\(653\) | −2927.33 | −0.175429 | −0.0877145 | − | 0.996146i | \(-0.527956\pi\) | ||||
−0.0877145 | + | 0.996146i | \(0.527956\pi\) | |||||||
\(654\) | 6261.50 | 0.374379 | ||||||||
\(655\) | 6000.18 | 0.357934 | ||||||||
\(656\) | −20151.7 | −1.19938 | ||||||||
\(657\) | 10482.8 | 0.622484 | ||||||||
\(658\) | −15618.3 | −0.925326 | ||||||||
\(659\) | −4778.76 | −0.282480 | −0.141240 | − | 0.989975i | \(-0.545109\pi\) | ||||
−0.141240 | + | 0.989975i | \(0.545109\pi\) | |||||||
\(660\) | −4849.71 | −0.286022 | ||||||||
\(661\) | −31510.3 | −1.85417 | −0.927086 | − | 0.374849i | \(-0.877695\pi\) | ||||
−0.927086 | + | 0.374849i | \(0.877695\pi\) | |||||||
\(662\) | 35444.2 | 2.08093 | ||||||||
\(663\) | −8861.06 | −0.519057 | ||||||||
\(664\) | −2723.21 | −0.159158 | ||||||||
\(665\) | 3263.92 | 0.190330 | ||||||||
\(666\) | 8706.17 | 0.506542 | ||||||||
\(667\) | 6118.23 | 0.355170 | ||||||||
\(668\) | −6646.99 | −0.385000 | ||||||||
\(669\) | 9682.82 | 0.559581 | ||||||||
\(670\) | 14098.6 | 0.812948 | ||||||||
\(671\) | −17134.7 | −0.985808 | ||||||||
\(672\) | 5000.37 | 0.287044 | ||||||||
\(673\) | −8992.15 | −0.515040 | −0.257520 | − | 0.966273i | \(-0.582905\pi\) | ||||
−0.257520 | + | 0.966273i | \(0.582905\pi\) | |||||||
\(674\) | 14142.1 | 0.808211 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −1937.67 | −0.110245 | ||||||||
\(677\) | 19340.8 | 1.09797 | 0.548985 | − | 0.835832i | \(-0.315014\pi\) | ||||
0.548985 | + | 0.835832i | \(0.315014\pi\) | |||||||
\(678\) | −2662.56 | −0.150818 | ||||||||
\(679\) | 3247.25 | 0.183531 | ||||||||
\(680\) | −1739.50 | −0.0980984 | ||||||||
\(681\) | 1913.46 | 0.107671 | ||||||||
\(682\) | 1689.89 | 0.0948816 | ||||||||
\(683\) | −4255.14 | −0.238387 | −0.119194 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119194 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(684\) | −5587.05 | −0.312319 | ||||||||
\(685\) | 13906.3 | 0.775666 | ||||||||
\(686\) | 1313.15 | 0.0730850 | ||||||||
\(687\) | −1634.32 | −0.0907616 | ||||||||
\(688\) | 6757.08 | 0.374435 | ||||||||
\(689\) | −27199.1 | −1.50392 | ||||||||
\(690\) | −5981.91 | −0.330040 | ||||||||
\(691\) | −17505.5 | −0.963733 | −0.481867 | − | 0.876245i | \(-0.660041\pi\) | ||||
−0.481867 | + | 0.876245i | \(0.660041\pi\) | |||||||
\(692\) | 4561.63 | 0.250588 | ||||||||
\(693\) | −3059.82 | −0.167724 | ||||||||
\(694\) | −14673.7 | −0.802603 | ||||||||
\(695\) | −6228.02 | −0.339917 | ||||||||
\(696\) | 906.071 | 0.0493456 | ||||||||
\(697\) | −18691.8 | −1.01579 | ||||||||
\(698\) | −31872.5 | −1.72836 | ||||||||
\(699\) | 17245.6 | 0.933175 | ||||||||
\(700\) | −1164.95 | −0.0629014 | ||||||||
\(701\) | −3240.77 | −0.174611 | −0.0873054 | − | 0.996182i | \(-0.527826\pi\) | ||||
−0.0873054 | + | 0.996182i | \(0.527826\pi\) | |||||||
\(702\) | −4512.70 | −0.242622 | ||||||||
\(703\) | 23563.3 | 1.26416 | ||||||||
\(704\) | −15933.8 | −0.853022 | ||||||||
\(705\) | 8741.91 | 0.467006 | ||||||||
\(706\) | 34423.4 | 1.83504 | ||||||||
\(707\) | 3029.07 | 0.161132 | ||||||||
\(708\) | 10484.5 | 0.556543 | ||||||||
\(709\) | 19949.3 | 1.05672 | 0.528358 | − | 0.849022i | \(-0.322808\pi\) | ||||
0.528358 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(710\) | 9422.99 | 0.498082 | ||||||||
\(711\) | −7849.76 | −0.414049 | ||||||||
\(712\) | −1980.83 | −0.104262 | ||||||||
\(713\) | 946.698 | 0.0497253 | ||||||||
\(714\) | 5439.41 | 0.285105 | ||||||||
\(715\) | −10601.7 | −0.554522 | ||||||||
\(716\) | 6827.17 | 0.356345 | ||||||||
\(717\) | 8034.30 | 0.418475 | ||||||||
\(718\) | 49362.9 | 2.56575 | ||||||||
\(719\) | −11259.4 | −0.584011 | −0.292006 | − | 0.956417i | \(-0.594323\pi\) | ||||
−0.292006 | + | 0.956417i | \(0.594323\pi\) | |||||||
\(720\) | −3282.35 | −0.169897 | ||||||||
\(721\) | −3588.38 | −0.185351 | ||||||||
\(722\) | −7034.60 | −0.362605 | ||||||||
\(723\) | 6606.47 | 0.339830 | ||||||||
\(724\) | 19300.9 | 0.990761 | ||||||||
\(725\) | −1468.38 | −0.0752195 | ||||||||
\(726\) | 11805.8 | 0.603516 | ||||||||
\(727\) | −12228.5 | −0.623840 | −0.311920 | − | 0.950108i | \(-0.600972\pi\) | ||||
−0.311920 | + | 0.950108i | \(0.600972\pi\) | |||||||
\(728\) | 1571.43 | 0.0800013 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −22295.9 | −1.13042 | ||||||||
\(731\) | 6267.56 | 0.317119 | ||||||||
\(732\) | 7045.49 | 0.355750 | ||||||||
\(733\) | −26635.1 | −1.34214 | −0.671072 | − | 0.741392i | \(-0.734166\pi\) | ||||
−0.671072 | + | 0.741392i | \(0.734166\pi\) | |||||||
\(734\) | 28637.3 | 1.44008 | ||||||||
\(735\) | −735.000 | −0.0368856 | ||||||||
\(736\) | −24803.4 | −1.24221 | ||||||||
\(737\) | −35771.7 | −1.78788 | ||||||||
\(738\) | −9519.26 | −0.474809 | ||||||||
\(739\) | −6074.00 | −0.302349 | −0.151174 | − | 0.988507i | \(-0.548306\pi\) | ||||
−0.151174 | + | 0.988507i | \(0.548306\pi\) | |||||||
\(740\) | −8410.14 | −0.417788 | ||||||||
\(741\) | −12213.6 | −0.605505 | ||||||||
\(742\) | 16696.3 | 0.826065 | ||||||||
\(743\) | −4016.87 | −0.198337 | −0.0991686 | − | 0.995071i | \(-0.531618\pi\) | ||||
−0.0991686 | + | 0.995071i | \(0.531618\pi\) | |||||||
\(744\) | 140.200 | 0.00690858 | ||||||||
\(745\) | 97.0231 | 0.00477134 | ||||||||
\(746\) | 13488.8 | 0.662010 | ||||||||
\(747\) | −4766.29 | −0.233453 | ||||||||
\(748\) | −21874.4 | −1.06926 | ||||||||
\(749\) | −13741.6 | −0.670370 | ||||||||
\(750\) | 1435.66 | 0.0698972 | ||||||||
\(751\) | −23913.2 | −1.16192 | −0.580962 | − | 0.813931i | \(-0.697324\pi\) | ||||
−0.580962 | + | 0.813931i | \(0.697324\pi\) | |||||||
\(752\) | 42509.6 | 2.06139 | ||||||||
\(753\) | 17150.7 | 0.830022 | ||||||||
\(754\) | −9816.81 | −0.474147 | ||||||||
\(755\) | −11749.0 | −0.566344 | ||||||||
\(756\) | 1258.15 | 0.0605269 | ||||||||
\(757\) | 31044.9 | 1.49055 | 0.745275 | − | 0.666758i | \(-0.232318\pi\) | ||||
0.745275 | + | 0.666758i | \(0.232318\pi\) | |||||||
\(758\) | −51742.9 | −2.47940 | ||||||||
\(759\) | 15177.6 | 0.725842 | ||||||||
\(760\) | −2397.65 | −0.114436 | ||||||||
\(761\) | 14011.8 | 0.667446 | 0.333723 | − | 0.942671i | \(-0.391695\pi\) | ||||
0.333723 | + | 0.942671i | \(0.391695\pi\) | |||||||
\(762\) | 27253.4 | 1.29565 | ||||||||
\(763\) | −3816.23 | −0.181071 | ||||||||
\(764\) | 7150.69 | 0.338616 | ||||||||
\(765\) | −3044.56 | −0.143891 | ||||||||
\(766\) | 2515.97 | 0.118676 | ||||||||
\(767\) | 22919.8 | 1.07899 | ||||||||
\(768\) | −15326.6 | −0.720120 | ||||||||
\(769\) | 3342.49 | 0.156740 | 0.0783701 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783701 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(770\) | 6507.94 | 0.304584 | ||||||||
\(771\) | −14172.9 | −0.662027 | ||||||||
\(772\) | 5984.51 | 0.278999 | ||||||||
\(773\) | −21074.6 | −0.980594 | −0.490297 | − | 0.871555i | \(-0.663112\pi\) | ||||
−0.490297 | + | 0.871555i | \(0.663112\pi\) | |||||||
\(774\) | 3191.90 | 0.148231 | ||||||||
\(775\) | −227.208 | −0.0105310 | ||||||||
\(776\) | −2385.40 | −0.110349 | ||||||||
\(777\) | −5306.20 | −0.244992 | ||||||||
\(778\) | 37296.0 | 1.71867 | ||||||||
\(779\) | −25763.9 | −1.18496 | ||||||||
\(780\) | 4359.26 | 0.200111 | ||||||||
\(781\) | −23908.5 | −1.09541 | ||||||||
\(782\) | −26981.1 | −1.23382 | ||||||||
\(783\) | 1585.85 | 0.0723800 | ||||||||
\(784\) | −3574.12 | −0.162815 | ||||||||
\(785\) | −19492.3 | −0.886254 | ||||||||
\(786\) | 13782.8 | 0.625464 | ||||||||
\(787\) | 21394.8 | 0.969048 | 0.484524 | − | 0.874778i | \(-0.338993\pi\) | ||||
0.484524 | + | 0.874778i | \(0.338993\pi\) | |||||||
\(788\) | 20394.1 | 0.921968 | ||||||||
\(789\) | −17926.1 | −0.808853 | ||||||||
\(790\) | 16695.7 | 0.751906 | ||||||||
\(791\) | 1622.76 | 0.0729442 | ||||||||
\(792\) | 2247.71 | 0.100845 | ||||||||
\(793\) | 15401.9 | 0.689706 | ||||||||
\(794\) | −16873.5 | −0.754179 | ||||||||
\(795\) | −9345.29 | −0.416910 | ||||||||
\(796\) | −6320.83 | −0.281452 | ||||||||
\(797\) | 20645.0 | 0.917547 | 0.458773 | − | 0.888553i | \(-0.348289\pi\) | ||||
0.458773 | + | 0.888553i | \(0.348289\pi\) | |||||||
\(798\) | 7497.41 | 0.332588 | ||||||||
\(799\) | 39430.0 | 1.74585 | ||||||||
\(800\) | 5952.82 | 0.263080 | ||||||||
\(801\) | −3466.95 | −0.152932 | ||||||||
\(802\) | 44293.0 | 1.95017 | ||||||||
\(803\) | 56570.4 | 2.48608 | ||||||||
\(804\) | 14708.7 | 0.645194 | ||||||||
\(805\) | 3645.83 | 0.159626 | ||||||||
\(806\) | −1518.99 | −0.0663825 | ||||||||
\(807\) | −13458.3 | −0.587058 | ||||||||
\(808\) | −2225.13 | −0.0968810 | ||||||||
\(809\) | −15939.0 | −0.692688 | −0.346344 | − | 0.938108i | \(-0.612577\pi\) | ||||
−0.346344 | + | 0.938108i | \(0.612577\pi\) | |||||||
\(810\) | −1550.51 | −0.0672586 | ||||||||
\(811\) | 22829.2 | 0.988460 | 0.494230 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494230 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(812\) | 2736.94 | 0.118285 | ||||||||
\(813\) | −11483.0 | −0.495360 | ||||||||
\(814\) | 46982.9 | 2.02303 | ||||||||
\(815\) | 7637.69 | 0.328266 | ||||||||
\(816\) | −14804.9 | −0.635141 | ||||||||
\(817\) | 8638.90 | 0.369935 | ||||||||
\(818\) | 11803.2 | 0.504508 | ||||||||
\(819\) | 2750.38 | 0.117346 | ||||||||
\(820\) | 9195.58 | 0.391614 | ||||||||
\(821\) | −5700.22 | −0.242313 | −0.121157 | − | 0.992633i | \(-0.538660\pi\) | ||||
−0.121157 | + | 0.992633i | \(0.538660\pi\) | |||||||
\(822\) | 31943.5 | 1.35542 | ||||||||
\(823\) | −32438.0 | −1.37390 | −0.686948 | − | 0.726707i | \(-0.741050\pi\) | ||||
−0.686948 | + | 0.726707i | \(0.741050\pi\) | |||||||
\(824\) | 2635.99 | 0.111443 | ||||||||
\(825\) | −3642.64 | −0.153722 | ||||||||
\(826\) | −14069.4 | −0.592662 | ||||||||
\(827\) | −12762.6 | −0.536638 | −0.268319 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268319 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(828\) | −6240.79 | −0.261935 | ||||||||
\(829\) | −30766.7 | −1.28899 | −0.644494 | − | 0.764609i | \(-0.722932\pi\) | ||||
−0.644494 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(830\) | 10137.4 | 0.423947 | ||||||||
\(831\) | 10261.6 | 0.428365 | ||||||||
\(832\) | 14322.4 | 0.596804 | ||||||||
\(833\) | −3315.19 | −0.137892 | ||||||||
\(834\) | −14306.1 | −0.593981 | ||||||||
\(835\) | −4992.59 | −0.206917 | ||||||||
\(836\) | −30150.6 | −1.24734 | ||||||||
\(837\) | 245.384 | 0.0101335 | ||||||||
\(838\) | 20731.7 | 0.854613 | ||||||||
\(839\) | −9779.71 | −0.402423 | −0.201212 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201212 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(840\) | 539.924 | 0.0221776 | ||||||||
\(841\) | −20939.2 | −0.858551 | ||||||||
\(842\) | −16034.8 | −0.656288 | ||||||||
\(843\) | −15707.8 | −0.641760 | ||||||||
\(844\) | 15355.0 | 0.626233 | ||||||||
\(845\) | −1455.40 | −0.0592510 | ||||||||
\(846\) | 20080.7 | 0.816061 | ||||||||
\(847\) | −7195.32 | −0.291894 | ||||||||
\(848\) | −45443.7 | −1.84026 | ||||||||
\(849\) | 20957.6 | 0.847190 | ||||||||
\(850\) | 6475.48 | 0.261303 | ||||||||
\(851\) | 26320.4 | 1.06023 | ||||||||
\(852\) | 9830.79 | 0.395302 | ||||||||
\(853\) | 24201.5 | 0.971445 | 0.485723 | − | 0.874113i | \(-0.338556\pi\) | ||||
0.485723 | + | 0.874113i | \(0.338556\pi\) | |||||||
\(854\) | −9454.52 | −0.378837 | ||||||||
\(855\) | −4196.47 | −0.167855 | ||||||||
\(856\) | 10094.5 | 0.403062 | ||||||||
\(857\) | 21036.7 | 0.838507 | 0.419254 | − | 0.907869i | \(-0.362292\pi\) | ||||
0.419254 | + | 0.907869i | \(0.362292\pi\) | |||||||
\(858\) | −24352.8 | −0.968988 | ||||||||
\(859\) | −6179.19 | −0.245438 | −0.122719 | − | 0.992441i | \(-0.539161\pi\) | ||||
−0.122719 | + | 0.992441i | \(0.539161\pi\) | |||||||
\(860\) | −3083.37 | −0.122258 | ||||||||
\(861\) | 5801.76 | 0.229644 | ||||||||
\(862\) | 34870.9 | 1.37785 | ||||||||
\(863\) | 50256.2 | 1.98232 | 0.991160 | − | 0.132671i | \(-0.0423555\pi\) | ||||
0.991160 | + | 0.132671i | \(0.0423555\pi\) | |||||||
\(864\) | −6429.04 | −0.253149 | ||||||||
\(865\) | 3426.27 | 0.134678 | ||||||||
\(866\) | 64497.7 | 2.53085 | ||||||||
\(867\) | 1006.65 | 0.0394321 | ||||||||
\(868\) | 423.497 | 0.0165604 | ||||||||
\(869\) | −42361.2 | −1.65363 | ||||||||
\(870\) | −3372.94 | −0.131441 | ||||||||
\(871\) | 32154.1 | 1.25086 | ||||||||
\(872\) | 2803.37 | 0.108869 | ||||||||
\(873\) | −4175.03 | −0.161860 | ||||||||
\(874\) | −37189.5 | −1.43930 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | −23260.8 | −0.897156 | ||||||||
\(877\) | −9175.95 | −0.353306 | −0.176653 | − | 0.984273i | \(-0.556527\pi\) | ||||
−0.176653 | + | 0.984273i | \(0.556527\pi\) | |||||||
\(878\) | −32289.5 | −1.24114 | ||||||||
\(879\) | −22199.1 | −0.851828 | ||||||||
\(880\) | −17713.2 | −0.678537 | ||||||||
\(881\) | −26172.7 | −1.00089 | −0.500444 | − | 0.865769i | \(-0.666830\pi\) | ||||
−0.500444 | + | 0.865769i | \(0.666830\pi\) | |||||||
\(882\) | −1688.34 | −0.0644549 | ||||||||
\(883\) | 18615.5 | 0.709471 | 0.354736 | − | 0.934967i | \(-0.384571\pi\) | ||||
0.354736 | + | 0.934967i | \(0.384571\pi\) | |||||||
\(884\) | 19662.3 | 0.748092 | ||||||||
\(885\) | 7874.99 | 0.299113 | ||||||||
\(886\) | 16456.4 | 0.624001 | ||||||||
\(887\) | −12837.8 | −0.485964 | −0.242982 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242982 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(888\) | 3897.89 | 0.147302 | ||||||||
\(889\) | −16610.3 | −0.626649 | ||||||||
\(890\) | 7373.86 | 0.277722 | ||||||||
\(891\) | 3934.05 | 0.147919 | ||||||||
\(892\) | −21485.7 | −0.806496 | ||||||||
\(893\) | 54348.4 | 2.03662 | ||||||||
\(894\) | 222.868 | 0.00833759 | ||||||||
\(895\) | 5127.92 | 0.191517 | ||||||||
\(896\) | 4542.42 | 0.169366 | ||||||||
\(897\) | −13642.7 | −0.507824 | ||||||||
\(898\) | −40370.6 | −1.50020 | ||||||||
\(899\) | 533.803 | 0.0198035 | ||||||||
\(900\) | 1497.79 | 0.0554738 | ||||||||
\(901\) | −42151.5 | −1.55857 | ||||||||
\(902\) | −51370.7 | −1.89630 | ||||||||
\(903\) | −1945.39 | −0.0716926 | ||||||||
\(904\) | −1192.07 | −0.0438579 | ||||||||
\(905\) | 14497.0 | 0.532482 | ||||||||
\(906\) | −26988.1 | −0.989647 | ||||||||
\(907\) | −26766.1 | −0.979885 | −0.489942 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489942 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(908\) | −4245.87 | −0.155181 | ||||||||
\(909\) | −3894.52 | −0.142105 | ||||||||
\(910\) | −5849.80 | −0.213098 | ||||||||
\(911\) | 5022.67 | 0.182666 | 0.0913328 | − | 0.995820i | \(-0.470887\pi\) | ||||
0.0913328 | + | 0.995820i | \(0.470887\pi\) | |||||||
\(912\) | −20406.3 | −0.740923 | ||||||||
\(913\) | −25721.3 | −0.932367 | ||||||||
\(914\) | −45759.0 | −1.65599 | ||||||||
\(915\) | 5291.91 | 0.191197 | ||||||||
\(916\) | 3626.48 | 0.130810 | ||||||||
\(917\) | −8400.26 | −0.302509 | ||||||||
\(918\) | −6993.52 | −0.251439 | ||||||||
\(919\) | 9541.79 | 0.342497 | 0.171248 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171248 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(920\) | −2678.19 | −0.0959754 | ||||||||
\(921\) | −8005.93 | −0.286432 | ||||||||
\(922\) | 65852.4 | 2.35220 | ||||||||
\(923\) | 21490.7 | 0.766387 | ||||||||
\(924\) | 6789.59 | 0.241733 | ||||||||
\(925\) | −6316.90 | −0.224539 | ||||||||
\(926\) | 39695.7 | 1.40873 | ||||||||
\(927\) | 4613.63 | 0.163464 | ||||||||
\(928\) | −13985.6 | −0.494718 | ||||||||
\(929\) | −25479.6 | −0.899846 | −0.449923 | − | 0.893067i | \(-0.648549\pi\) | ||||
−0.449923 | + | 0.893067i | \(0.648549\pi\) | |||||||
\(930\) | −521.909 | −0.0184022 | ||||||||
\(931\) | −4569.49 | −0.160858 | ||||||||
\(932\) | −38267.2 | −1.34494 | ||||||||
\(933\) | −18567.7 | −0.651533 | ||||||||
\(934\) | 64621.9 | 2.26391 | ||||||||
\(935\) | −16430.0 | −0.574671 | ||||||||
\(936\) | −2020.41 | −0.0705545 | ||||||||
\(937\) | −33608.3 | −1.17176 | −0.585878 | − | 0.810399i | \(-0.699250\pi\) | ||||
−0.585878 | + | 0.810399i | \(0.699250\pi\) | |||||||
\(938\) | −19738.0 | −0.687066 | ||||||||
\(939\) | 8764.77 | 0.304609 | ||||||||
\(940\) | −19397.9 | −0.673073 | ||||||||
\(941\) | −19173.6 | −0.664232 | −0.332116 | − | 0.943239i | \(-0.607762\pi\) | ||||
−0.332116 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(942\) | −44774.9 | −1.54867 | ||||||||
\(943\) | −28778.5 | −0.993804 | ||||||||
\(944\) | 38294.0 | 1.32030 | ||||||||
\(945\) | 945.000 | 0.0325300 | ||||||||
\(946\) | 17225.1 | 0.592005 | ||||||||
\(947\) | −979.315 | −0.0336045 | −0.0168023 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168023 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(948\) | 17418.2 | 0.596749 | ||||||||
\(949\) | −50849.5 | −1.73935 | ||||||||
\(950\) | 8925.48 | 0.304822 | ||||||||
\(951\) | −29476.7 | −1.00510 | ||||||||
\(952\) | 2435.31 | 0.0829083 | ||||||||
\(953\) | 3048.61 | 0.103624 | 0.0518122 | − | 0.998657i | \(-0.483500\pi\) | ||||
0.0518122 | + | 0.998657i | \(0.483500\pi\) | |||||||
\(954\) | −21466.7 | −0.728521 | ||||||||
\(955\) | 5370.92 | 0.181989 | ||||||||
\(956\) | −17827.7 | −0.603127 | ||||||||
\(957\) | 8558.03 | 0.289072 | ||||||||
\(958\) | −28059.0 | −0.946290 | ||||||||
\(959\) | −19468.8 | −0.655557 | ||||||||
\(960\) | 4921.02 | 0.165443 | ||||||||
\(961\) | −29708.4 | −0.997227 | ||||||||
\(962\) | −42231.6 | −1.41538 | ||||||||
\(963\) | 17667.8 | 0.591211 | ||||||||
\(964\) | −14659.4 | −0.489781 | ||||||||
\(965\) | 4495.00 | 0.149947 | ||||||||
\(966\) | 8374.67 | 0.278934 | ||||||||
\(967\) | −14467.9 | −0.481133 | −0.240567 | − | 0.970633i | \(-0.577333\pi\) | ||||
−0.240567 | + | 0.970633i | \(0.577333\pi\) | |||||||
\(968\) | 5285.62 | 0.175502 | ||||||||
\(969\) | −18928.0 | −0.627507 | ||||||||
\(970\) | 8879.89 | 0.293934 | ||||||||
\(971\) | 12952.8 | 0.428090 | 0.214045 | − | 0.976824i | \(-0.431336\pi\) | ||||
0.214045 | + | 0.976824i | \(0.431336\pi\) | |||||||
\(972\) | −1617.62 | −0.0533797 | ||||||||
\(973\) | 8719.23 | 0.287282 | ||||||||
\(974\) | 65885.4 | 2.16746 | ||||||||
\(975\) | 3274.26 | 0.107549 | ||||||||
\(976\) | 25733.2 | 0.843954 | ||||||||
\(977\) | 47244.2 | 1.54706 | 0.773529 | − | 0.633760i | \(-0.218489\pi\) | ||||
0.773529 | + | 0.633760i | \(0.218489\pi\) | |||||||
\(978\) | 17544.2 | 0.573621 | ||||||||
\(979\) | −18709.4 | −0.610781 | ||||||||
\(980\) | 1630.93 | 0.0531614 | ||||||||
\(981\) | 4906.58 | 0.159689 | ||||||||
\(982\) | −43615.3 | −1.41733 | ||||||||
\(983\) | −1536.84 | −0.0498651 | −0.0249326 | − | 0.999689i | \(-0.507937\pi\) | ||||
−0.0249326 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(984\) | −4261.92 | −0.138074 | ||||||||
\(985\) | 15318.1 | 0.495509 | ||||||||
\(986\) | −15213.5 | −0.491376 | ||||||||
\(987\) | −12238.7 | −0.394692 | ||||||||
\(988\) | 27101.5 | 0.872685 | ||||||||
\(989\) | 9649.73 | 0.310256 | ||||||||
\(990\) | −8367.35 | −0.268618 | ||||||||
\(991\) | 3785.22 | 0.121334 | 0.0606668 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606668 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(992\) | −2164.04 | −0.0692625 | ||||||||
\(993\) | 27774.5 | 0.887610 | ||||||||
\(994\) | −13192.2 | −0.420956 | ||||||||
\(995\) | −4747.61 | −0.151266 | ||||||||
\(996\) | 10576.2 | 0.336465 | ||||||||
\(997\) | −25894.9 | −0.822566 | −0.411283 | − | 0.911508i | \(-0.634919\pi\) | ||||
−0.411283 | + | 0.911508i | \(0.634919\pi\) | |||||||
\(998\) | −73044.0 | −2.31680 | ||||||||
\(999\) | 6822.26 | 0.216063 |
(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 | 105.4.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.4.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 1680.4.a.bo.1.1 | 2 | |||
5.2 | odd | 4 | 525.4.d.l.274.1 | 4 | |||
5.3 | odd | 4 | 525.4.d.l.274.4 | 4 | |||
5.4 | even | 2 | 525.4.a.l.1.2 | 2 | |||
7.6 | odd | 2 | 735.4.a.o.1.1 | 2 | |||
15.14 | odd | 2 | 1575.4.a.q.1.1 | 2 | |||
21.20 | even | 2 | 2205.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.4.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
525.4.a.l.1.2 | 2 | 5.4 | even | 2 | |||
525.4.d.l.274.1 | 4 | 5.2 | odd | 4 | |||
525.4.d.l.274.4 | 4 | 5.3 | odd | 4 | |||
735.4.a.o.1.1 | 2 | 7.6 | odd | 2 | |||
1575.4.a.q.1.1 | 2 | 15.14 | odd | 2 | |||
1680.4.a.bo.1.1 | 2 | 4.3 | odd | 2 | |||
2205.4.a.bb.1.2 | 2 | 21.20 | even | 2 |