Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,4,Mod(1,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, 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("735.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.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: | \(43.3664038542\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 105) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.1 |
$q$-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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | \(-0.345802\pi\) | ||||
0.465701 | + | 0.884942i | \(0.345802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −72.9411 | −1.13971 | ||||||||
\(17\) | 67.6569 | 0.965247 | 0.482623 | − | 0.875828i | \(-0.339684\pi\) | ||||
0.482623 | + | 0.875828i | \(0.339684\pi\) | |||||||
\(18\) | −34.4558 | −0.451184 | ||||||||
\(19\) | 93.2548 | 1.12601 | 0.563003 | − | 0.826455i | \(-0.309646\pi\) | ||||
0.563003 | + | 0.826455i | \(0.309646\pi\) | |||||||
\(20\) | −33.2843 | −0.372129 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −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 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −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 | \(-0.491619\pi\) | ||||
0.0263276 | + | 0.999653i | \(0.491619\pi\) | |||||||
\(32\) | 238.113 | 1.31540 | ||||||||
\(33\) | 145.706 | 0.768609 | ||||||||
\(34\) | −259.019 | −1.30651 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.676376\pi\) | ||||
−0.526180 | + | 0.850373i | \(0.676376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −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 | \(-0.140354\pi\) | ||||
0.904354 | + | 0.426784i | \(0.140354\pi\) | |||||||
\(48\) | −218.823 | −0.658009 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 279.765 | 0.650100 | ||||||||
\(58\) | 224.863 | 0.509068 | ||||||||
\(59\) | 524.999 | 1.15846 | 0.579229 | − | 0.815165i | \(-0.303354\pi\) | ||||
0.579229 | + | 0.815165i | \(0.303354\pi\) | |||||||
\(60\) | −99.8528 | −0.214849 | ||||||||
\(61\) | 352.794 | 0.740502 | 0.370251 | − | 0.928932i | \(-0.379272\pi\) | ||||
0.370251 | + | 0.928932i | \(0.379272\pi\) | |||||||
\(62\) | −34.7939 | −0.0712715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(-0.883463\pi\) | ||||
−0.933727 | + | 0.357987i | \(0.883463\pi\) | |||||||
\(74\) | 967.352 | 1.51963 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 620.784 | 0.936958 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −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 | \(-0.386121\pi\) | ||||
0.350180 | + | 0.936683i | \(0.386121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −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 | \(-0.426324\pi\) | ||||
0.229398 | + | 0.973333i | \(0.426324\pi\) | |||||||
\(90\) | 172.279 | 0.201776 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −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 | \(-0.421938\pi\) | ||||
0.242789 | + | 0.970079i | \(0.421938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 437.117 | 0.443757 | ||||||||
\(100\) | 166.421 | 0.166421 | ||||||||
\(101\) | 432.725 | 0.426314 | 0.213157 | − | 0.977018i | \(-0.431625\pi\) | ||||
0.213157 | + | 0.977018i | \(0.431625\pi\) | |||||||
\(102\) | −777.058 | −0.754316 | ||||||||
\(103\) | −512.626 | −0.490393 | −0.245197 | − | 0.969473i | \(-0.578853\pi\) | ||||
−0.245197 | + | 0.969473i | \(0.578853\pi\) | |||||||
\(104\) | 224.489 | 0.211663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −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 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 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 | \(-0.631053\pi\) | ||||
−0.400182 | + | 0.916436i | \(0.631053\pi\) | |||||||
\(132\) | 969.941 | 0.639565 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | \(-0.375911\pi\) | ||||
0.380039 | + | 0.924971i | \(0.375911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −45.4416 | −0.0235481 | ||||||||
\(156\) | 871.852 | 0.447462 | ||||||||
\(157\) | 3898.46 | 1.98172 | 0.990862 | − | 0.134880i | \(-0.0430650\pi\) | ||||
0.990862 | + | 0.134880i | \(0.0430650\pi\) | |||||||
\(158\) | 3339.14 | 1.68131 | ||||||||
\(159\) | 1869.06 | 0.932239 | ||||||||
\(160\) | −1190.56 | −0.588264 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −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 | \(-0.425689\pi\) | ||||
0.231340 | + | 0.972873i | \(0.425689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −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 | \(-0.548112\pi\) | ||||
−0.150575 | + | 0.988599i | \(0.548112\pi\) | |||||||
\(174\) | 674.589 | 0.293911 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | \(-0.702980\pi\) | ||||
−0.595333 | + | 0.803479i | \(0.702980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 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 | \(-0.445907\pi\) | ||||
0.169120 | + | 0.985595i | \(0.445907\pi\) | |||||||
\(200\) | 128.553 | 0.0454505 | ||||||||
\(201\) | −2209.56 | −0.775375 | ||||||||
\(202\) | −1656.66 | −0.577039 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −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 | \(-0.338961\pi\) | ||||
0.484611 | + | 0.874730i | \(0.338961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 887.519 | 0.261225 | ||||||||
\(227\) | 637.820 | 0.186492 | 0.0932458 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932458 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(228\) | 1862.35 | 0.540953 | ||||||||
\(229\) | −544.774 | −0.157204 | −0.0786019 | − | 0.996906i | \(-0.525046\pi\) | ||||
−0.0786019 | + | 0.996906i | \(0.525046\pi\) | |||||||
\(230\) | −1993.97 | −0.571646 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −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 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(-0.404913\pi\) | ||||
0.294302 | + | 0.955713i | \(0.404913\pi\) | |||||||
\(242\) | −3935.25 | −1.04532 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2348.50 | 0.616177 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | \(-0.244683\pi\) | ||||
0.718820 | + | 0.695196i | \(0.244683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | \(-0.694350\pi\) | ||||
−0.573332 | + | 0.819323i | \(0.694350\pi\) | |||||||
\(258\) | 1063.97 | 0.256743 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1155.65 | 0.264886 | ||||||||
\(268\) | −4902.90 | −1.11751 | ||||||||
\(269\) | −4486.11 | −1.01681 | −0.508407 | − | 0.861117i | \(-0.669766\pi\) | ||||
−0.508407 | + | 0.861117i | \(0.669766\pi\) | |||||||
\(270\) | 516.838 | 0.116495 | ||||||||
\(271\) | −3827.68 | −0.857989 | −0.428994 | − | 0.903307i | \(-0.641132\pi\) | ||||
−0.428994 | + | 0.903307i | \(0.641132\pi\) | |||||||
\(272\) | −4934.97 | −1.10010 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.237797\pi\) | ||||
0.733688 | + | 0.679486i | \(0.237797\pi\) | |||||||
\(284\) | −3276.93 | −0.684683 | ||||||||
\(285\) | −1398.82 | −0.290734 | ||||||||
\(286\) | −8117.60 | −1.67834 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | \(-0.764090\pi\) | ||||
−0.737705 | + | 0.675123i | \(0.764090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 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 | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1537.88 | −0.283129 | ||||||||
\(310\) | 173.970 | 0.0318736 | ||||||||
\(311\) | −6189.25 | −1.12849 | −0.564244 | − | 0.825608i | \(-0.690832\pi\) | ||||
−0.564244 | + | 0.825608i | \(0.690832\pi\) | |||||||
\(312\) | 673.468 | 0.122204 | ||||||||
\(313\) | 2921.59 | 0.527598 | 0.263799 | − | 0.964578i | \(-0.415024\pi\) | ||||
0.263799 | + | 0.964578i | \(0.415024\pi\) | |||||||
\(314\) | −14925.0 | −2.68237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −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 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 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 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −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 | \(-0.720425\pi\) | ||||
−0.638451 | + | 0.769662i | \(0.720425\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1178.74 | 0.179248 | ||||||||
\(352\) | 11564.8 | 1.75115 | ||||||||
\(353\) | 8991.52 | 1.35572 | 0.677862 | − | 0.735189i | \(-0.262907\pi\) | ||||
0.677862 | + | 0.735189i | \(0.262907\pi\) | |||||||
\(354\) | −6029.76 | −0.905306 | ||||||||
\(355\) | 2461.32 | 0.367981 | ||||||||
\(356\) | 2564.33 | 0.381767 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −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 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5823.77 | 0.835150 | ||||||||
\(366\) | −4051.94 | −0.578684 | ||||||||
\(367\) | 7480.17 | 1.06393 | 0.531964 | − | 0.846767i | \(-0.321454\pi\) | ||||
0.531964 | + | 0.846767i | \(0.321454\pi\) | |||||||
\(368\) | 7598.02 | 1.07629 | ||||||||
\(369\) | −2486.47 | −0.350787 | ||||||||
\(370\) | −4836.76 | −0.679598 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 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 | \(-0.486041\pi\) | ||||
0.0438387 | + | 0.999039i | \(0.486041\pi\) | |||||||
\(384\) | −1946.75 | −0.258710 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −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 | \(-0.589868\pi\) | ||||
−0.278592 | + | 0.960410i | \(0.589868\pi\) | |||||||
\(398\) | −3635.18 | −0.457827 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −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 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12272.1 | −1.49461 | ||||||||
\(408\) | 1043.70 | 0.126645 | ||||||||
\(409\) | 3083.03 | 0.372729 | 0.186364 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186364 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(410\) | −5288.48 | −0.637023 | ||||||||
\(411\) | 8343.76 | 1.00138 | ||||||||
\(412\) | −3412.47 | −0.408060 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(-0.397763\pi\) | ||||
0.315692 | + | 0.948862i | \(0.397763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | \(-0.115495\pi\) | ||||
0.934893 | + | 0.354930i | \(0.115495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 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 | \(-0.651603\pi\) | ||||
−0.458473 | + | 0.888708i | \(0.651603\pi\) | |||||||
\(440\) | −1248.73 | −0.135297 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(-0.164827\pi\) | ||||
0.868900 | + | 0.494988i | \(0.164827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | \(-0.184723\pi\) | ||||
0.836284 | + | 0.548296i | \(0.184723\pi\) | |||||||
\(468\) | 2615.56 | 0.258342 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5607.17 | 0.538228 | ||||||||
\(478\) | 10252.9 | 0.981082 | ||||||||
\(479\) | −7329.12 | −0.699115 | −0.349558 | − | 0.936915i | \(-0.613668\pi\) | ||||
−0.349558 | + | 0.936915i | \(0.613668\pi\) | |||||||
\(480\) | −3571.69 | −0.339635 | ||||||||
\(481\) | −11031.0 | −1.04568 | ||||||||
\(482\) | −8430.80 | −0.796706 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −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 | \(-0.295836\pi\) | ||||
0.598317 | + | 0.801259i | \(0.295836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −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 | \(-0.439644\pi\) | ||||
0.188480 | + | 0.982077i | \(0.439644\pi\) | |||||||
\(510\) | 3885.29 | 0.337340 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −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 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2055.76 | −0.173869 | ||||||||
\(520\) | −1122.45 | −0.0946588 | ||||||||
\(521\) | −19395.7 | −1.63098 | −0.815490 | − | 0.578771i | \(-0.803532\pi\) | ||||
−0.815490 | + | 0.578771i | \(0.803532\pi\) | |||||||
\(522\) | 2023.77 | 0.169689 | ||||||||
\(523\) | −20413.8 | −1.70675 | −0.853377 | − | 0.521294i | \(-0.825450\pi\) | ||||
−0.853377 | + | 0.521294i | \(0.825450\pi\) | |||||||
\(524\) | −7988.47 | −0.665989 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9857.98 | 0.741897 | ||||||||
\(562\) | −20045.3 | −1.50456 | ||||||||
\(563\) | 2320.81 | 0.173731 | 0.0868654 | − | 0.996220i | \(-0.472315\pi\) | ||||
0.0868654 | + | 0.996220i | \(0.472315\pi\) | |||||||
\(564\) | 11638.7 | 0.868934 | ||||||||
\(565\) | 1159.12 | 0.0863087 | ||||||||
\(566\) | −26744.9 | −1.98617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2604.16 | −0.188871 | ||||||||
\(576\) | −2952.61 | −0.213586 | ||||||||
\(577\) | −8029.26 | −0.579311 | −0.289655 | − | 0.957131i | \(-0.593541\pi\) | ||||
−0.289655 | + | 0.957131i | \(0.593541\pi\) | |||||||
\(578\) | 1284.63 | 0.0924455 | ||||||||
\(579\) | 2697.00 | 0.193581 | ||||||||
\(580\) | 1954.95 | 0.139957 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −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 | \(-0.409072\pi\) | ||||
0.281789 | + | 0.959476i | \(0.409072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 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 | \(-0.646406\pi\) | ||||
−0.443901 | + | 0.896076i | \(0.646406\pi\) | |||||||
\(594\) | −5020.41 | −0.346784 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(-0.501163\pi\) | ||||
−0.00365347 | + | 0.999993i | \(0.501163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −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 | \(-0.411456\pi\) | ||||
0.274595 | + | 0.961560i | \(0.411456\pi\) | |||||||
\(608\) | 22205.2 | 1.48115 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −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 | \(-0.721892\pi\) | ||||
−0.641993 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(620\) | −302.498 | −0.0195945 | ||||||||
\(621\) | −2812.50 | −0.181742 | ||||||||
\(622\) | 23695.1 | 1.52747 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | \(-0.705286\pi\) | ||||
−0.601139 | + | 0.799144i | \(0.705286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1389.56 | 0.0848279 | ||||||||
\(646\) | −24154.8 | −1.47114 | ||||||||
\(647\) | −21650.0 | −1.31553 | −0.657765 | − | 0.753223i | \(-0.728498\pi\) | ||||
−0.657765 | + | 0.753223i | \(0.728498\pi\) | |||||||
\(648\) | 416.513 | 0.0252503 | ||||||||
\(649\) | 25498.4 | 1.54222 | ||||||||
\(650\) | −4178.43 | −0.252141 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 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 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(-0.122305\pi\) | ||||
0.927086 | + | 0.374849i | \(0.122305\pi\) | |||||||
\(662\) | 35444.2 | 2.08093 | ||||||||
\(663\) | 8861.06 | 0.519057 | ||||||||
\(664\) | 2723.21 | 0.159158 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | \(-0.684986\pi\) | ||||
−0.548985 | + | 0.835832i | \(0.684986\pi\) | |||||||
\(678\) | 2662.56 | 0.150818 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −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 | \(-0.339959\pi\) | ||||
0.481867 | + | 0.876245i | \(0.339959\pi\) | |||||||
\(692\) | −4561.63 | −0.250588 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −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 | \(-0.405677\pi\) | ||||
0.292006 | + | 0.956417i | \(0.405677\pi\) | |||||||
\(720\) | 3282.35 | 0.169897 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −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 | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950108i | \(0.399028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 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 | \(-0.265834\pi\) | ||||
0.671072 | + | 0.741392i | \(0.265834\pi\) | |||||||
\(734\) | −28637.3 | −1.44008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 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 | \(-0.608305\pi\) | ||||
−0.333723 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(762\) | −27253.4 | −1.29565 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.524972\pi\) | ||||
−0.0783701 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14172.9 | −0.662027 | ||||||||
\(772\) | 5984.51 | 0.278999 | ||||||||
\(773\) | 21074.6 | 0.980594 | 0.490297 | − | 0.871555i | \(-0.336888\pi\) | ||||
0.490297 | + | 0.871555i | \(0.336888\pi\) | |||||||
\(774\) | 3191.90 | 0.148231 | ||||||||
\(775\) | 227.208 | 0.0105310 | ||||||||
\(776\) | 2385.40 | 0.110349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19492.3 | −0.886254 | ||||||||
\(786\) | 13782.8 | 0.625464 | ||||||||
\(787\) | −21394.8 | −0.969048 | −0.484524 | − | 0.874778i | \(-0.661007\pi\) | ||||
−0.484524 | + | 0.874778i | \(0.661007\pi\) | |||||||
\(788\) | 20394.1 | 0.921968 | ||||||||
\(789\) | 17926.1 | 0.808853 | ||||||||
\(790\) | −16695.7 | −0.751906 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.651711\pi\) | ||||
−0.458773 | + | 0.888553i | \(0.651711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −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 | \(-0.664550\pi\) | ||||
−0.494230 | + | 0.869331i | \(0.664550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | \(-0.277068\pi\) | ||||
0.644494 | + | 0.764609i | \(0.277068\pi\) | |||||||
\(830\) | 10137.4 | 0.423947 | ||||||||
\(831\) | −10261.6 | −0.428365 | ||||||||
\(832\) | −14322.4 | −0.596804 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | \(-0.435512\pi\) | ||||
0.201212 | + | 0.979548i | \(0.435512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −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 | \(-0.661444\pi\) | ||||
−0.485723 | + | 0.874113i | \(0.661444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4196.47 | −0.167855 | ||||||||
\(856\) | 10094.5 | 0.403062 | ||||||||
\(857\) | −21036.7 | −0.838507 | −0.419254 | − | 0.907869i | \(-0.637708\pi\) | ||||
−0.419254 | + | 0.907869i | \(0.637708\pi\) | |||||||
\(858\) | −24352.8 | −0.968988 | ||||||||
\(859\) | 6179.19 | 0.245438 | 0.122719 | − | 0.992441i | \(-0.460839\pi\) | ||||
0.122719 | + | 0.992441i | \(0.460839\pi\) | |||||||
\(860\) | 3083.37 | 0.122258 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −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 | \(-0.333170\pi\) | ||||
0.500444 | + | 0.865769i | \(0.333170\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 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 | \(-0.421874\pi\) | ||||
0.242982 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(888\) | −3897.89 | −0.147302 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 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 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −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 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −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 | \(-0.351451\pi\) | ||||
0.449923 | + | 0.893067i | \(0.351451\pi\) | |||||||
\(930\) | 521.909 | 0.0184022 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −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 | \(-0.300750\pi\) | ||||
0.585878 | + | 0.810399i | \(0.300750\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8764.77 | 0.304609 | ||||||||
\(940\) | −19397.9 | −0.673073 | ||||||||
\(941\) | 19173.6 | 0.664232 | 0.332116 | − | 0.943239i | \(-0.392238\pi\) | ||||
0.332116 | + | 0.943239i | \(0.392238\pi\) | |||||||
\(942\) | −44774.9 | −1.54867 | ||||||||
\(943\) | 28778.5 | 0.993804 | ||||||||
\(944\) | −38294.0 | −1.32030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 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 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | \(-0.568664\pi\) | ||||
−0.214045 | + | 0.976824i | \(0.568664\pi\) | |||||||
\(972\) | 1617.62 | 0.0533797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4906.58 | 0.159689 | ||||||||
\(982\) | −43615.3 | −1.41733 | ||||||||
\(983\) | 1536.84 | 0.0498651 | 0.0249326 | − | 0.999689i | \(-0.492063\pi\) | ||||
0.0249326 | + | 0.999689i | \(0.492063\pi\) | |||||||
\(984\) | −4261.92 | −0.138074 | ||||||||
\(985\) | −15318.1 | −0.495509 | ||||||||
\(986\) | 15213.5 | 0.491376 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4747.61 | −0.151266 | ||||||||
\(996\) | 10576.2 | 0.336465 | ||||||||
\(997\) | 25894.9 | 0.822566 | 0.411283 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411283 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(998\) | −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 | 735.4.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 2205.4.a.bb.1.2 | 2 | |||
7.6 | odd | 2 | 105.4.a.e.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 315.4.a.k.1.2 | 2 | |||
28.27 | even | 2 | 1680.4.a.bo.1.1 | 2 | |||
35.13 | even | 4 | 525.4.d.l.274.4 | 4 | |||
35.27 | even | 4 | 525.4.d.l.274.1 | 4 | |||
35.34 | odd | 2 | 525.4.a.l.1.2 | 2 | |||
105.104 | even | 2 | 1575.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
315.4.a.k.1.2 | 2 | 21.20 | even | 2 | |||
525.4.a.l.1.2 | 2 | 35.34 | odd | 2 | |||
525.4.d.l.274.1 | 4 | 35.27 | even | 4 | |||
525.4.d.l.274.4 | 4 | 35.13 | even | 4 | |||
735.4.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1575.4.a.q.1.1 | 2 | 105.104 | even | 2 | |||
1680.4.a.bo.1.1 | 2 | 28.27 | even | 2 | |||
2205.4.a.bb.1.2 | 2 | 3.2 | odd | 2 |