Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.37228 | −1.19228 | −0.596141 | − | 0.802880i | \(-0.703300\pi\) | ||||
−0.596141 | + | 0.802880i | \(0.703300\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 3.37228 | 0.421535 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.1168 | 0.688364 | ||||||||
\(7\) | 4.74456 | 0.256182 | 0.128091 | − | 0.991762i | \(-0.459115\pi\) | ||||
0.128091 | + | 0.991762i | \(0.459115\pi\) | |||||||
\(8\) | 15.6060 | 0.689693 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −10.1168 | −0.243373 | ||||||||
\(13\) | 15.0217 | 0.320483 | 0.160242 | − | 0.987078i | \(-0.448773\pi\) | ||||
0.160242 | + | 0.987078i | \(0.448773\pi\) | |||||||
\(14\) | −16.0000 | −0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.6060 | −1.24384 | ||||||||
\(17\) | −73.1684 | −1.04388 | −0.521940 | − | 0.852982i | \(-0.674791\pi\) | ||||
−0.521940 | + | 0.852982i | \(0.674791\pi\) | |||||||
\(18\) | −30.3505 | −0.397427 | ||||||||
\(19\) | −78.7011 | −0.950277 | −0.475138 | − | 0.879911i | \(-0.657602\pi\) | ||||
−0.475138 | + | 0.879911i | \(0.657602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.2337 | −0.147907 | ||||||||
\(22\) | −37.0951 | −0.359486 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | −46.8179 | −0.398194 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −50.6576 | −0.382106 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 16.0000 | 0.107990 | ||||||||
\(29\) | 243.125 | 1.55680 | 0.778399 | − | 0.627769i | \(-0.216032\pi\) | ||||
0.778399 | + | 0.627769i | \(0.216032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 278.717 | 1.61481 | 0.807405 | − | 0.589998i | \(-0.200871\pi\) | ||||
0.807405 | + | 0.589998i | \(0.200871\pi\) | |||||||
\(32\) | 143.606 | 0.793318 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 246.745 | 1.24460 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 30.3505 | 0.140512 | ||||||||
\(37\) | −102.380 | −0.454898 | −0.227449 | − | 0.973790i | \(-0.573039\pi\) | ||||
−0.227449 | + | 0.973790i | \(0.573039\pi\) | |||||||
\(38\) | 265.402 | 1.13300 | ||||||||
\(39\) | −45.0652 | −0.185031 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −241.255 | −0.918970 | −0.459485 | − | 0.888186i | \(-0.651966\pi\) | ||||
−0.459485 | + | 0.888186i | \(0.651966\pi\) | |||||||
\(42\) | 48.0000 | 0.176347 | ||||||||
\(43\) | 280.016 | 0.993071 | 0.496536 | − | 0.868016i | \(-0.334605\pi\) | ||||
0.496536 | + | 0.868016i | \(0.334605\pi\) | |||||||
\(44\) | 37.0951 | 0.127098 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 377.696 | 1.21061 | ||||||||
\(47\) | 169.870 | 0.527192 | 0.263596 | − | 0.964633i | \(-0.415091\pi\) | ||||
0.263596 | + | 0.964633i | \(0.415091\pi\) | |||||||
\(48\) | 238.818 | 0.718133 | ||||||||
\(49\) | −320.489 | −0.934371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 219.505 | 0.602684 | ||||||||
\(52\) | 50.6576 | 0.135095 | ||||||||
\(53\) | 409.652 | 1.06170 | 0.530849 | − | 0.847466i | \(-0.321873\pi\) | ||||
0.530849 | + | 0.847466i | \(0.321873\pi\) | |||||||
\(54\) | 91.0516 | 0.229455 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 74.0435 | 0.176687 | ||||||||
\(57\) | 236.103 | 0.548643 | ||||||||
\(58\) | −819.886 | −1.85614 | ||||||||
\(59\) | 196.000 | 0.432492 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −701.359 | −1.47213 | −0.736064 | − | 0.676912i | \(-0.763318\pi\) | ||||
−0.736064 | + | 0.676912i | \(0.763318\pi\) | |||||||
\(62\) | −939.913 | −1.92531 | ||||||||
\(63\) | 42.7011 | 0.0853941 | ||||||||
\(64\) | 152.568 | 0.297984 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 111.285 | 0.207550 | ||||||||
\(67\) | −900.587 | −1.64215 | −0.821076 | − | 0.570819i | \(-0.806626\pi\) | ||||
−0.821076 | + | 0.570819i | \(0.806626\pi\) | |||||||
\(68\) | −246.745 | −0.440032 | ||||||||
\(69\) | 336.000 | 0.586227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 756.500 | 1.26451 | 0.632254 | − | 0.774762i | \(-0.282130\pi\) | ||||
0.632254 | + | 0.774762i | \(0.282130\pi\) | |||||||
\(72\) | 140.454 | 0.229898 | ||||||||
\(73\) | 1019.81 | 1.63507 | 0.817536 | − | 0.575877i | \(-0.195339\pi\) | ||||
0.817536 | + | 0.575877i | \(0.195339\pi\) | |||||||
\(74\) | 345.255 | 0.542367 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −265.402 | −0.400575 | ||||||||
\(77\) | 52.1902 | 0.0772419 | ||||||||
\(78\) | 151.973 | 0.220609 | ||||||||
\(79\) | −327.549 | −0.466483 | −0.233241 | − | 0.972419i | \(-0.574933\pi\) | ||||
−0.233241 | + | 0.972419i | \(0.574933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 813.581 | 1.09567 | ||||||||
\(83\) | 756.619 | 1.00060 | 0.500300 | − | 0.865852i | \(-0.333223\pi\) | ||||
0.500300 | + | 0.865852i | \(0.333223\pi\) | |||||||
\(84\) | −48.0000 | −0.0623480 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −944.293 | −1.18402 | ||||||||
\(87\) | −729.375 | −0.898818 | ||||||||
\(88\) | 171.666 | 0.207950 | ||||||||
\(89\) | 508.978 | 0.606198 | 0.303099 | − | 0.952959i | \(-0.401979\pi\) | ||||
0.303099 | + | 0.952959i | \(0.401979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 71.2716 | 0.0821022 | ||||||||
\(92\) | −377.696 | −0.428016 | ||||||||
\(93\) | −836.152 | −0.932311 | ||||||||
\(94\) | −572.848 | −0.628561 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −430.818 | −0.458023 | ||||||||
\(97\) | −614.358 | −0.643079 | −0.321539 | − | 0.946896i | \(-0.604200\pi\) | ||||
−0.321539 | + | 0.946896i | \(0.604200\pi\) | |||||||
\(98\) | 1080.78 | 1.11403 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1015.92 | −1.00087 | −0.500434 | − | 0.865775i | \(-0.666826\pi\) | ||||
−0.500434 | + | 0.865775i | \(0.666826\pi\) | |||||||
\(102\) | −740.234 | −0.718569 | ||||||||
\(103\) | −1102.16 | −1.05436 | −0.527181 | − | 0.849753i | \(-0.676751\pi\) | ||||
−0.527181 | + | 0.849753i | \(0.676751\pi\) | |||||||
\(104\) | 234.429 | 0.221035 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1381.46 | −1.26584 | ||||||||
\(107\) | −1377.58 | −1.24463 | −0.622315 | − | 0.782767i | \(-0.713808\pi\) | ||||
−0.622315 | + | 0.782767i | \(0.713808\pi\) | |||||||
\(108\) | −91.0516 | −0.0811245 | ||||||||
\(109\) | 320.217 | 0.281388 | 0.140694 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140694 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 307.141 | 0.262636 | ||||||||
\(112\) | −377.696 | −0.318651 | ||||||||
\(113\) | 1629.45 | 1.35651 | 0.678254 | − | 0.734828i | \(-0.262737\pi\) | ||||
0.678254 | + | 0.734828i | \(0.262737\pi\) | |||||||
\(114\) | −796.206 | −0.654136 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 819.886 | 0.656245 | ||||||||
\(117\) | 135.196 | 0.106828 | ||||||||
\(118\) | −660.967 | −0.515652 | ||||||||
\(119\) | −347.152 | −0.267423 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2365.18 | 1.75519 | ||||||||
\(123\) | 723.766 | 0.530568 | ||||||||
\(124\) | 939.913 | 0.680699 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | −2291.26 | −1.60091 | −0.800457 | − | 0.599390i | \(-0.795410\pi\) | ||||
−0.800457 | + | 0.599390i | \(0.795410\pi\) | |||||||
\(128\) | −1663.35 | −1.14860 | ||||||||
\(129\) | −840.049 | −0.573350 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1147.41 | −0.765267 | −0.382633 | − | 0.923900i | \(-0.624983\pi\) | ||||
−0.382633 | + | 0.923900i | \(0.624983\pi\) | |||||||
\(132\) | −111.285 | −0.0733799 | ||||||||
\(133\) | −373.402 | −0.243444 | ||||||||
\(134\) | 3037.03 | 1.95791 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1141.86 | −0.719956 | ||||||||
\(137\) | −1268.60 | −0.791121 | −0.395561 | − | 0.918440i | \(-0.629450\pi\) | ||||
−0.395561 | + | 0.918440i | \(0.629450\pi\) | |||||||
\(138\) | −1133.09 | −0.698947 | ||||||||
\(139\) | −486.288 | −0.296737 | −0.148368 | − | 0.988932i | \(-0.547402\pi\) | ||||
−0.148368 | + | 0.988932i | \(0.547402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −509.609 | −0.304374 | ||||||||
\(142\) | −2551.13 | −1.50765 | ||||||||
\(143\) | 165.239 | 0.0966294 | ||||||||
\(144\) | −716.454 | −0.414614 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3439.10 | −1.94947 | ||||||||
\(147\) | 961.467 | 0.539459 | ||||||||
\(148\) | −345.255 | −0.191756 | ||||||||
\(149\) | 2354.11 | 1.29434 | 0.647169 | − | 0.762346i | \(-0.275953\pi\) | ||||
0.647169 | + | 0.762346i | \(0.275953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −570.070 | −0.307229 | −0.153615 | − | 0.988131i | \(-0.549091\pi\) | ||||
−0.153615 | + | 0.988131i | \(0.549091\pi\) | |||||||
\(152\) | −1228.21 | −0.655399 | ||||||||
\(153\) | −658.516 | −0.347960 | ||||||||
\(154\) | −176.000 | −0.0920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −151.973 | −0.0779971 | ||||||||
\(157\) | 2072.67 | 1.05361 | 0.526807 | − | 0.849985i | \(-0.323389\pi\) | ||||
0.526807 | + | 0.849985i | \(0.323389\pi\) | |||||||
\(158\) | 1104.59 | 0.556179 | ||||||||
\(159\) | −1228.96 | −0.612972 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −531.391 | −0.260121 | ||||||||
\(162\) | −273.155 | −0.132476 | ||||||||
\(163\) | −2676.51 | −1.28614 | −0.643069 | − | 0.765808i | \(-0.722339\pi\) | ||||
−0.643069 | + | 0.765808i | \(0.722339\pi\) | |||||||
\(164\) | −813.581 | −0.387378 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2551.53 | −1.19300 | ||||||||
\(167\) | 1188.12 | 0.550536 | 0.275268 | − | 0.961368i | \(-0.411233\pi\) | ||||
0.275268 | + | 0.961368i | \(0.411233\pi\) | |||||||
\(168\) | −222.130 | −0.102010 | ||||||||
\(169\) | −1971.35 | −0.897290 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −708.310 | −0.316759 | ||||||||
\(172\) | 944.293 | 0.418615 | ||||||||
\(173\) | −807.147 | −0.354718 | −0.177359 | − | 0.984146i | \(-0.556755\pi\) | ||||
−0.177359 | + | 0.984146i | \(0.556755\pi\) | |||||||
\(174\) | 2459.66 | 1.07164 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −875.666 | −0.375033 | ||||||||
\(177\) | −588.000 | −0.249699 | ||||||||
\(178\) | −1716.42 | −0.722758 | ||||||||
\(179\) | −1950.39 | −0.814408 | −0.407204 | − | 0.913337i | \(-0.633496\pi\) | ||||
−0.407204 | + | 0.913337i | \(0.633496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1061.61 | 0.435959 | 0.217980 | − | 0.975953i | \(-0.430053\pi\) | ||||
0.217980 | + | 0.975953i | \(0.430053\pi\) | |||||||
\(182\) | −240.348 | −0.0978889 | ||||||||
\(183\) | 2104.08 | 0.849933 | ||||||||
\(184\) | −1747.87 | −0.700297 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2819.74 | 1.11158 | ||||||||
\(187\) | −804.853 | −0.314742 | ||||||||
\(188\) | 572.848 | 0.222230 | ||||||||
\(189\) | −128.103 | −0.0493023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2136.41 | 0.809348 | 0.404674 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404674 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(192\) | −457.704 | −0.172041 | ||||||||
\(193\) | −3947.76 | −1.47236 | −0.736181 | − | 0.676784i | \(-0.763373\pi\) | ||||
−0.736181 | + | 0.676784i | \(0.763373\pi\) | |||||||
\(194\) | 2071.79 | 0.766731 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1080.78 | −0.393870 | ||||||||
\(197\) | −923.886 | −0.334133 | −0.167066 | − | 0.985946i | \(-0.553429\pi\) | ||||
−0.167066 | + | 0.985946i | \(0.553429\pi\) | |||||||
\(198\) | −333.856 | −0.119829 | ||||||||
\(199\) | −476.152 | −0.169616 | −0.0848078 | − | 0.996397i | \(-0.527028\pi\) | ||||
−0.0848078 | + | 0.996397i | \(0.527028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2701.76 | 0.948097 | ||||||||
\(202\) | 3425.96 | 1.19332 | ||||||||
\(203\) | 1153.52 | 0.398824 | ||||||||
\(204\) | 740.234 | 0.254053 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3716.80 | 1.25710 | ||||||||
\(207\) | −1008.00 | −0.338458 | ||||||||
\(208\) | −1195.82 | −0.398631 | ||||||||
\(209\) | −865.712 | −0.286519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4918.24 | −1.60467 | −0.802336 | − | 0.596872i | \(-0.796410\pi\) | ||||
−0.802336 | + | 0.596872i | \(0.796410\pi\) | |||||||
\(212\) | 1381.46 | 0.447543 | ||||||||
\(213\) | −2269.50 | −0.730064 | ||||||||
\(214\) | 4645.57 | 1.48395 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −421.361 | −0.132731 | ||||||||
\(217\) | 1322.39 | 0.413686 | ||||||||
\(218\) | −1079.86 | −0.335494 | ||||||||
\(219\) | −3059.44 | −0.944010 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1099.12 | −0.334546 | ||||||||
\(222\) | −1035.77 | −0.313136 | ||||||||
\(223\) | −2100.29 | −0.630700 | −0.315350 | − | 0.948975i | \(-0.602122\pi\) | ||||
−0.315350 | + | 0.948975i | \(0.602122\pi\) | |||||||
\(224\) | 681.348 | 0.203234 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5494.95 | −1.61734 | ||||||||
\(227\) | 2257.16 | 0.659970 | 0.329985 | − | 0.943986i | \(-0.392956\pi\) | ||||
0.329985 | + | 0.943986i | \(0.392956\pi\) | |||||||
\(228\) | 796.206 | 0.231272 | ||||||||
\(229\) | −5311.07 | −1.53260 | −0.766301 | − | 0.642482i | \(-0.777905\pi\) | ||||
−0.766301 | + | 0.642482i | \(0.777905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −156.571 | −0.0445956 | ||||||||
\(232\) | 3794.20 | 1.07371 | ||||||||
\(233\) | −2466.27 | −0.693435 | −0.346718 | − | 0.937970i | \(-0.612704\pi\) | ||||
−0.346718 | + | 0.937970i | \(0.612704\pi\) | |||||||
\(234\) | −455.918 | −0.127369 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 660.967 | 0.182311 | ||||||||
\(237\) | 982.646 | 0.269324 | ||||||||
\(238\) | 1170.70 | 0.318844 | ||||||||
\(239\) | 1429.40 | 0.386863 | 0.193432 | − | 0.981114i | \(-0.438038\pi\) | ||||
0.193432 | + | 0.981114i | \(0.438038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −978.989 | −0.261669 | −0.130835 | − | 0.991404i | \(-0.541766\pi\) | ||||
−0.130835 | + | 0.991404i | \(0.541766\pi\) | |||||||
\(242\) | −408.046 | −0.108389 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2365.18 | −0.620553 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2440.74 | −0.632586 | ||||||||
\(247\) | −1182.23 | −0.304548 | ||||||||
\(248\) | 4349.65 | 1.11372 | ||||||||
\(249\) | −2269.86 | −0.577696 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6530.63 | −1.64227 | −0.821135 | − | 0.570734i | \(-0.806659\pi\) | ||||
−0.821135 | + | 0.570734i | \(0.806659\pi\) | |||||||
\(252\) | 144.000 | 0.0359966 | ||||||||
\(253\) | −1232.00 | −0.306147 | ||||||||
\(254\) | 7726.76 | 1.90874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4388.74 | 1.07147 | ||||||||
\(257\) | −8130.26 | −1.97335 | −0.986676 | − | 0.162696i | \(-0.947981\pi\) | ||||
−0.986676 | + | 0.162696i | \(0.947981\pi\) | |||||||
\(258\) | 2832.88 | 0.683595 | ||||||||
\(259\) | −485.750 | −0.116537 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2188.12 | 0.518933 | ||||||||
\(262\) | 3869.40 | 0.912414 | ||||||||
\(263\) | 4549.42 | 1.06665 | 0.533326 | − | 0.845910i | \(-0.320942\pi\) | ||||
0.533326 | + | 0.845910i | \(0.320942\pi\) | |||||||
\(264\) | −514.997 | −0.120060 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1259.22 | 0.290254 | ||||||||
\(267\) | −1526.93 | −0.349988 | ||||||||
\(268\) | −3037.03 | −0.692225 | ||||||||
\(269\) | −29.1522 | −0.00660760 | −0.00330380 | − | 0.999995i | \(-0.501052\pi\) | ||||
−0.00330380 | + | 0.999995i | \(0.501052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7711.22 | 1.72850 | 0.864250 | − | 0.503063i | \(-0.167794\pi\) | ||||
0.864250 | + | 0.503063i | \(0.167794\pi\) | |||||||
\(272\) | 5824.64 | 1.29842 | ||||||||
\(273\) | −213.815 | −0.0474017 | ||||||||
\(274\) | 4278.07 | 0.943239 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1133.09 | 0.247115 | ||||||||
\(277\) | −1127.52 | −0.244571 | −0.122286 | − | 0.992495i | \(-0.539022\pi\) | ||||
−0.122286 | + | 0.992495i | \(0.539022\pi\) | |||||||
\(278\) | 1639.90 | 0.353794 | ||||||||
\(279\) | 2508.46 | 0.538270 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1872.47 | −0.397517 | −0.198758 | − | 0.980049i | \(-0.563691\pi\) | ||||
−0.198758 | + | 0.980049i | \(0.563691\pi\) | |||||||
\(282\) | 1718.54 | 0.362900 | ||||||||
\(283\) | −2124.48 | −0.446245 | −0.223123 | − | 0.974790i | \(-0.571625\pi\) | ||||
−0.223123 | + | 0.974790i | \(0.571625\pi\) | |||||||
\(284\) | 2551.13 | 0.533034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −557.233 | −0.115209 | ||||||||
\(287\) | −1144.65 | −0.235424 | ||||||||
\(288\) | 1292.45 | 0.264439 | ||||||||
\(289\) | 440.621 | 0.0896846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1843.07 | 0.371282 | ||||||||
\(292\) | 3439.10 | 0.689241 | ||||||||
\(293\) | 3324.19 | 0.662802 | 0.331401 | − | 0.943490i | \(-0.392479\pi\) | ||||
0.331401 | + | 0.943490i | \(0.392479\pi\) | |||||||
\(294\) | −3242.34 | −0.643187 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1597.75 | −0.313740 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | −7938.73 | −1.54322 | ||||||||
\(299\) | −1682.44 | −0.325411 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1328.55 | 0.254407 | ||||||||
\(302\) | 1922.44 | 0.366304 | ||||||||
\(303\) | 3047.75 | 0.577851 | ||||||||
\(304\) | 6265.07 | 1.18200 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2220.70 | 0.414866 | ||||||||
\(307\) | 1698.94 | 0.315843 | 0.157921 | − | 0.987452i | \(-0.449521\pi\) | ||||
0.157921 | + | 0.987452i | \(0.449521\pi\) | |||||||
\(308\) | 176.000 | 0.0325602 | ||||||||
\(309\) | 3306.49 | 0.608736 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6928.83 | 1.26334 | 0.631668 | − | 0.775239i | \(-0.282370\pi\) | ||||
0.631668 | + | 0.775239i | \(0.282370\pi\) | |||||||
\(312\) | −703.287 | −0.127615 | ||||||||
\(313\) | 3560.75 | 0.643020 | 0.321510 | − | 0.946906i | \(-0.395810\pi\) | ||||
0.321510 | + | 0.946906i | \(0.395810\pi\) | |||||||
\(314\) | −6989.64 | −1.25620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1104.59 | −0.196639 | ||||||||
\(317\) | −332.750 | −0.0589561 | −0.0294780 | − | 0.999565i | \(-0.509385\pi\) | ||||
−0.0294780 | + | 0.999565i | \(0.509385\pi\) | |||||||
\(318\) | 4144.39 | 0.730835 | ||||||||
\(319\) | 2674.37 | 0.469393 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4132.73 | 0.718587 | ||||||||
\(322\) | 1792.00 | 0.310137 | ||||||||
\(323\) | 5758.43 | 0.991975 | ||||||||
\(324\) | 273.155 | 0.0468372 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9025.94 | 1.53344 | ||||||||
\(327\) | −960.652 | −0.162459 | ||||||||
\(328\) | −3765.02 | −0.633807 | ||||||||
\(329\) | 805.957 | 0.135057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −541.445 | −0.0899108 | −0.0449554 | − | 0.998989i | \(-0.514315\pi\) | ||||
−0.0449554 | + | 0.998989i | \(0.514315\pi\) | |||||||
\(332\) | 2551.53 | 0.421788 | ||||||||
\(333\) | −921.423 | −0.151633 | ||||||||
\(334\) | −4006.67 | −0.656393 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1133.09 | 0.183973 | ||||||||
\(337\) | −816.531 | −0.131986 | −0.0659930 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659930 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(338\) | 6647.94 | 1.06982 | ||||||||
\(339\) | −4888.34 | −0.783180 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3065.89 | 0.486883 | ||||||||
\(342\) | 2388.62 | 0.377666 | ||||||||
\(343\) | −3147.97 | −0.495552 | ||||||||
\(344\) | 4369.92 | 0.684914 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2721.93 | 0.422924 | ||||||||
\(347\) | −6260.53 | −0.968539 | −0.484269 | − | 0.874919i | \(-0.660914\pi\) | ||||
−0.484269 | + | 0.874919i | \(0.660914\pi\) | |||||||
\(348\) | −2459.66 | −0.378884 | ||||||||
\(349\) | −12768.5 | −1.95840 | −0.979198 | − | 0.202906i | \(-0.934961\pi\) | ||||
−0.979198 | + | 0.202906i | \(0.934961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −405.587 | −0.0616771 | ||||||||
\(352\) | 1579.67 | 0.239194 | ||||||||
\(353\) | 2649.28 | 0.399453 | 0.199727 | − | 0.979852i | \(-0.435995\pi\) | ||||
0.199727 | + | 0.979852i | \(0.435995\pi\) | |||||||
\(354\) | 1982.90 | 0.297712 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1716.42 | 0.255534 | ||||||||
\(357\) | 1041.46 | 0.154397 | ||||||||
\(358\) | 6577.27 | 0.971004 | ||||||||
\(359\) | −3203.91 | −0.471020 | −0.235510 | − | 0.971872i | \(-0.575676\pi\) | ||||
−0.235510 | + | 0.971872i | \(0.575676\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −665.143 | −0.0969737 | ||||||||
\(362\) | −3580.04 | −0.519786 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 240.348 | 0.0346089 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7095.54 | −1.01336 | ||||||||
\(367\) | 8429.40 | 1.19894 | 0.599470 | − | 0.800397i | \(-0.295378\pi\) | ||||
0.599470 | + | 0.800397i | \(0.295378\pi\) | |||||||
\(368\) | 8915.87 | 1.26297 | ||||||||
\(369\) | −2171.30 | −0.306323 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1943.62 | 0.271988 | ||||||||
\(372\) | −2819.74 | −0.393002 | ||||||||
\(373\) | 9388.53 | 1.30327 | 0.651635 | − | 0.758533i | \(-0.274083\pi\) | ||||
0.651635 | + | 0.758533i | \(0.274083\pi\) | |||||||
\(374\) | 2714.19 | 0.375261 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2650.98 | 0.363600 | ||||||||
\(377\) | 3652.16 | 0.498928 | ||||||||
\(378\) | 432.000 | 0.0587822 | ||||||||
\(379\) | −14264.5 | −1.93329 | −0.966647 | − | 0.256112i | \(-0.917558\pi\) | ||||
−0.966647 | + | 0.256112i | \(0.917558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6873.77 | 0.924288 | ||||||||
\(382\) | −7204.58 | −0.964970 | ||||||||
\(383\) | −13462.2 | −1.79605 | −0.898026 | − | 0.439942i | \(-0.854999\pi\) | ||||
−0.898026 | + | 0.439942i | \(0.854999\pi\) | |||||||
\(384\) | 4990.05 | 0.663144 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13313.0 | 1.75547 | ||||||||
\(387\) | 2520.15 | 0.331024 | ||||||||
\(388\) | −2071.79 | −0.271080 | ||||||||
\(389\) | −941.881 | −0.122764 | −0.0613821 | − | 0.998114i | \(-0.519551\pi\) | ||||
−0.0613821 | + | 0.998114i | \(0.519551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8194.87 | 1.05993 | ||||||||
\(392\) | −5001.54 | −0.644429 | ||||||||
\(393\) | 3442.24 | 0.441827 | ||||||||
\(394\) | 3115.60 | 0.398380 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 333.856 | 0.0423659 | ||||||||
\(397\) | 847.839 | 0.107183 | 0.0535917 | − | 0.998563i | \(-0.482933\pi\) | ||||
0.0535917 | + | 0.998563i | \(0.482933\pi\) | |||||||
\(398\) | 1605.72 | 0.202230 | ||||||||
\(399\) | 1120.21 | 0.140553 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12203.6 | 1.51975 | 0.759875 | − | 0.650069i | \(-0.225260\pi\) | ||||
0.759875 | + | 0.650069i | \(0.225260\pi\) | |||||||
\(402\) | −9111.10 | −1.13040 | ||||||||
\(403\) | 4186.82 | 0.517520 | ||||||||
\(404\) | −3425.96 | −0.421901 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3890.00 | −0.475511 | ||||||||
\(407\) | −1126.18 | −0.137157 | ||||||||
\(408\) | 3425.59 | 0.415667 | ||||||||
\(409\) | 8759.53 | 1.05900 | 0.529500 | − | 0.848310i | \(-0.322380\pi\) | ||||
0.529500 | + | 0.848310i | \(0.322380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3805.79 | 0.456754 | ||||||||
\(412\) | −3716.80 | −0.444451 | ||||||||
\(413\) | 929.934 | 0.110797 | ||||||||
\(414\) | 3399.26 | 0.403537 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2157.21 | 0.254245 | ||||||||
\(417\) | 1458.86 | 0.171321 | ||||||||
\(418\) | 2919.42 | 0.341612 | ||||||||
\(419\) | −11188.4 | −1.30451 | −0.652256 | − | 0.757999i | \(-0.726177\pi\) | ||||
−0.652256 | + | 0.757999i | \(0.726177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14082.3 | −1.63023 | −0.815116 | − | 0.579298i | \(-0.803327\pi\) | ||||
−0.815116 | + | 0.579298i | \(0.803327\pi\) | |||||||
\(422\) | 16585.7 | 1.91322 | ||||||||
\(423\) | 1528.83 | 0.175731 | ||||||||
\(424\) | 6393.02 | 0.732246 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7653.39 | 0.870441 | ||||||||
\(427\) | −3327.64 | −0.377133 | ||||||||
\(428\) | −4645.57 | −0.524655 | ||||||||
\(429\) | −495.718 | −0.0557890 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5616.05 | −0.627647 | −0.313823 | − | 0.949481i | \(-0.601610\pi\) | ||||
−0.313823 | + | 0.949481i | \(0.601610\pi\) | |||||||
\(432\) | 2149.36 | 0.239378 | ||||||||
\(433\) | −7195.75 | −0.798627 | −0.399314 | − | 0.916814i | \(-0.630752\pi\) | ||||
−0.399314 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(434\) | −4459.48 | −0.493230 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1079.86 | 0.118615 | ||||||||
\(437\) | 8814.52 | 0.964887 | ||||||||
\(438\) | 10317.3 | 1.12553 | ||||||||
\(439\) | 101.959 | 0.0110848 | 0.00554240 | − | 0.999985i | \(-0.498236\pi\) | ||||
0.00554240 | + | 0.999985i | \(0.498236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2884.40 | −0.311457 | ||||||||
\(442\) | 3706.53 | 0.398873 | ||||||||
\(443\) | −4953.74 | −0.531285 | −0.265642 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265642 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(444\) | 1035.77 | 0.110710 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7082.78 | 0.751972 | ||||||||
\(447\) | −7062.34 | −0.747287 | ||||||||
\(448\) | 723.869 | 0.0763383 | ||||||||
\(449\) | −11602.0 | −1.21945 | −0.609723 | − | 0.792615i | \(-0.708719\pi\) | ||||
−0.609723 | + | 0.792615i | \(0.708719\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2653.81 | −0.277080 | ||||||||
\(452\) | 5494.95 | 0.571816 | ||||||||
\(453\) | 1710.21 | 0.177379 | ||||||||
\(454\) | −7611.79 | −0.786870 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3684.62 | 0.378395 | ||||||||
\(457\) | 3530.68 | 0.361397 | 0.180698 | − | 0.983539i | \(-0.442164\pi\) | ||||
0.180698 | + | 0.983539i | \(0.442164\pi\) | |||||||
\(458\) | 17910.4 | 1.82729 | ||||||||
\(459\) | 1975.55 | 0.200895 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11566.3 | 1.16854 | 0.584271 | − | 0.811559i | \(-0.301381\pi\) | ||||
0.584271 | + | 0.811559i | \(0.301381\pi\) | |||||||
\(462\) | 528.000 | 0.0531705 | ||||||||
\(463\) | −10888.5 | −1.09294 | −0.546470 | − | 0.837479i | \(-0.684029\pi\) | ||||
−0.546470 | + | 0.837479i | \(0.684029\pi\) | |||||||
\(464\) | −19354.2 | −1.93641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8316.94 | 0.826770 | ||||||||
\(467\) | −10688.0 | −1.05906 | −0.529529 | − | 0.848292i | \(-0.677631\pi\) | ||||
−0.529529 | + | 0.848292i | \(0.677631\pi\) | |||||||
\(468\) | 455.918 | 0.0450317 | ||||||||
\(469\) | −4272.89 | −0.420690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6218.02 | −0.608304 | ||||||||
\(472\) | 3058.77 | 0.298287 | ||||||||
\(473\) | 3080.18 | 0.299422 | ||||||||
\(474\) | −3313.76 | −0.321110 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1170.70 | −0.112728 | ||||||||
\(477\) | 3686.87 | 0.353900 | ||||||||
\(478\) | −4820.35 | −0.461250 | ||||||||
\(479\) | 2341.90 | 0.223391 | 0.111696 | − | 0.993742i | \(-0.464372\pi\) | ||||
0.111696 | + | 0.993742i | \(0.464372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1537.93 | −0.145787 | ||||||||
\(482\) | 3301.43 | 0.311983 | ||||||||
\(483\) | 1594.17 | 0.150181 | ||||||||
\(484\) | 408.046 | 0.0383214 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 819.464 | 0.0764849 | ||||||||
\(487\) | −6748.91 | −0.627972 | −0.313986 | − | 0.949428i | \(-0.601665\pi\) | ||||
−0.313986 | + | 0.949428i | \(0.601665\pi\) | |||||||
\(488\) | −10945.4 | −1.01532 | ||||||||
\(489\) | 8029.53 | 0.742552 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7361.40 | 0.676609 | 0.338305 | − | 0.941037i | \(-0.390147\pi\) | ||||
0.338305 | + | 0.941037i | \(0.390147\pi\) | |||||||
\(492\) | 2440.74 | 0.223653 | ||||||||
\(493\) | −17789.1 | −1.62511 | ||||||||
\(494\) | 3986.80 | 0.363107 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22187.6 | −2.00857 | ||||||||
\(497\) | 3589.26 | 0.323944 | ||||||||
\(498\) | 7654.60 | 0.688777 | ||||||||
\(499\) | 10381.7 | 0.931359 | 0.465680 | − | 0.884953i | \(-0.345810\pi\) | ||||
0.465680 | + | 0.884953i | \(0.345810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3564.36 | −0.317852 | ||||||||
\(502\) | 22023.1 | 1.95805 | ||||||||
\(503\) | −19149.0 | −1.69744 | −0.848721 | − | 0.528840i | \(-0.822627\pi\) | ||||
−0.848721 | + | 0.528840i | \(0.822627\pi\) | |||||||
\(504\) | 666.391 | 0.0588957 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4154.65 | 0.365013 | ||||||||
\(507\) | 5914.04 | 0.518051 | ||||||||
\(508\) | −7726.76 | −0.674841 | ||||||||
\(509\) | 16073.2 | 1.39967 | 0.699836 | − | 0.714303i | \(-0.253256\pi\) | ||||
0.699836 | + | 0.714303i | \(0.253256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4838.58 | 0.418877 | ||||||||
\(512\) | −1493.27 | −0.128894 | ||||||||
\(513\) | 2124.93 | 0.182881 | ||||||||
\(514\) | 27417.5 | 2.35279 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2832.88 | −0.241687 | ||||||||
\(517\) | 1868.56 | 0.158954 | ||||||||
\(518\) | 1638.09 | 0.138945 | ||||||||
\(519\) | 2421.44 | 0.204797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18955.3 | −1.59395 | −0.796975 | − | 0.604012i | \(-0.793568\pi\) | ||||
−0.796975 | + | 0.604012i | \(0.793568\pi\) | |||||||
\(522\) | −7378.97 | −0.618714 | ||||||||
\(523\) | 4442.19 | 0.371402 | 0.185701 | − | 0.982606i | \(-0.440544\pi\) | ||||
0.185701 | + | 0.982606i | \(0.440544\pi\) | |||||||
\(524\) | −3869.40 | −0.322587 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15341.9 | −1.27175 | ||||||||
\(527\) | −20393.3 | −1.68567 | ||||||||
\(528\) | 2627.00 | 0.216525 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1764.00 | 0.144164 | ||||||||
\(532\) | −1259.22 | −0.102620 | ||||||||
\(533\) | −3624.08 | −0.294515 | ||||||||
\(534\) | 5149.25 | 0.417285 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14054.5 | −1.13258 | ||||||||
\(537\) | 5851.17 | 0.470199 | ||||||||
\(538\) | 98.3096 | 0.00787812 | ||||||||
\(539\) | −3525.38 | −0.281723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2180.90 | 0.173316 | 0.0866580 | − | 0.996238i | \(-0.472381\pi\) | ||||
0.0866580 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(542\) | −26004.4 | −2.06086 | ||||||||
\(543\) | −3184.82 | −0.251701 | ||||||||
\(544\) | −10507.4 | −0.828129 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 721.044 | 0.0565162 | ||||||||
\(547\) | −8225.04 | −0.642920 | −0.321460 | − | 0.946923i | \(-0.604174\pi\) | ||||
−0.321460 | + | 0.946923i | \(0.604174\pi\) | |||||||
\(548\) | −4278.07 | −0.333485 | ||||||||
\(549\) | −6312.23 | −0.490709 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19134.2 | −1.47939 | ||||||||
\(552\) | 5243.61 | 0.404316 | ||||||||
\(553\) | −1554.08 | −0.119505 | ||||||||
\(554\) | 3802.32 | 0.291598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1639.90 | −0.125085 | ||||||||
\(557\) | 25181.9 | 1.91561 | 0.957804 | − | 0.287423i | \(-0.0927986\pi\) | ||||
0.957804 | + | 0.287423i | \(0.0927986\pi\) | |||||||
\(558\) | −8459.22 | −0.641769 | ||||||||
\(559\) | 4206.33 | 0.318263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2414.56 | 0.181716 | ||||||||
\(562\) | 6314.50 | 0.473952 | ||||||||
\(563\) | 4504.50 | 0.337197 | 0.168599 | − | 0.985685i | \(-0.446076\pi\) | ||||
0.168599 | + | 0.985685i | \(0.446076\pi\) | |||||||
\(564\) | −1718.54 | −0.128304 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7164.36 | 0.532050 | ||||||||
\(567\) | 384.310 | 0.0284647 | ||||||||
\(568\) | 11805.9 | 0.872122 | ||||||||
\(569\) | −13447.0 | −0.990732 | −0.495366 | − | 0.868684i | \(-0.664966\pi\) | ||||
−0.495366 | + | 0.868684i | \(0.664966\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2605.52 | −0.190959 | −0.0954795 | − | 0.995431i | \(-0.530438\pi\) | ||||
−0.0954795 | + | 0.995431i | \(0.530438\pi\) | |||||||
\(572\) | 557.233 | 0.0407327 | ||||||||
\(573\) | −6409.24 | −0.467277 | ||||||||
\(574\) | 3860.09 | 0.280691 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1373.11 | 0.0993281 | ||||||||
\(577\) | −6339.65 | −0.457406 | −0.228703 | − | 0.973496i | \(-0.573448\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573448\pi\) | |||||||
\(578\) | −1485.90 | −0.106929 | ||||||||
\(579\) | 11843.3 | 0.850069 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3589.83 | 0.256336 | ||||||||
\(582\) | −6215.37 | −0.442672 | ||||||||
\(583\) | 4506.17 | 0.320114 | ||||||||
\(584\) | 15915.2 | 1.12770 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11210.1 | −0.790247 | ||||||||
\(587\) | 13370.6 | 0.940140 | 0.470070 | − | 0.882629i | \(-0.344229\pi\) | ||||
0.470070 | + | 0.882629i | \(0.344229\pi\) | |||||||
\(588\) | 3242.34 | 0.227401 | ||||||||
\(589\) | −21935.3 | −1.53452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2771.66 | 0.192912 | ||||||||
\(592\) | 8150.09 | 0.565822 | ||||||||
\(593\) | −14319.3 | −0.991608 | −0.495804 | − | 0.868434i | \(-0.665127\pi\) | ||||
−0.495804 | + | 0.868434i | \(0.665127\pi\) | |||||||
\(594\) | 1001.57 | 0.0691832 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7938.73 | 0.545609 | ||||||||
\(597\) | 1428.46 | 0.0979276 | ||||||||
\(598\) | 5673.65 | 0.387981 | ||||||||
\(599\) | −5788.63 | −0.394853 | −0.197427 | − | 0.980318i | \(-0.563258\pi\) | ||||
−0.197427 | + | 0.980318i | \(0.563258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23968.1 | 1.62675 | 0.813375 | − | 0.581739i | \(-0.197628\pi\) | ||||
0.813375 | + | 0.581739i | \(0.197628\pi\) | |||||||
\(602\) | −4480.26 | −0.303325 | ||||||||
\(603\) | −8105.28 | −0.547384 | ||||||||
\(604\) | −1922.44 | −0.129508 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10277.9 | −0.688961 | ||||||||
\(607\) | 23526.6 | 1.57317 | 0.786585 | − | 0.617482i | \(-0.211847\pi\) | ||||
0.786585 | + | 0.617482i | \(0.211847\pi\) | |||||||
\(608\) | −11301.9 | −0.753872 | ||||||||
\(609\) | −3460.56 | −0.230261 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2551.74 | 0.168956 | ||||||||
\(612\) | −2220.70 | −0.146677 | ||||||||
\(613\) | −1228.07 | −0.0809159 | −0.0404579 | − | 0.999181i | \(-0.512882\pi\) | ||||
−0.0404579 | + | 0.999181i | \(0.512882\pi\) | |||||||
\(614\) | −5729.31 | −0.376573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 814.478 | 0.0532732 | ||||||||
\(617\) | 9844.90 | 0.642368 | 0.321184 | − | 0.947017i | \(-0.395919\pi\) | ||||
0.321184 | + | 0.947017i | \(0.395919\pi\) | |||||||
\(618\) | −11150.4 | −0.725785 | ||||||||
\(619\) | −6551.68 | −0.425419 | −0.212709 | − | 0.977115i | \(-0.568229\pi\) | ||||
−0.212709 | + | 0.977115i | \(0.568229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3024.00 | 0.195409 | ||||||||
\(622\) | −23365.9 | −1.50625 | ||||||||
\(623\) | 2414.88 | 0.155297 | ||||||||
\(624\) | 3587.46 | 0.230150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12007.8 | −0.766661 | ||||||||
\(627\) | 2597.14 | 0.165422 | ||||||||
\(628\) | 6989.64 | 0.444135 | ||||||||
\(629\) | 7491.01 | 0.474859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26440.5 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(632\) | −5111.72 | −0.321730 | ||||||||
\(633\) | 14754.7 | 0.926458 | ||||||||
\(634\) | 1122.13 | 0.0702923 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4144.39 | −0.258389 | ||||||||
\(637\) | −4814.31 | −0.299450 | ||||||||
\(638\) | −9018.74 | −0.559648 | ||||||||
\(639\) | 6808.50 | 0.421502 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27927.2 | −1.72084 | −0.860421 | − | 0.509584i | \(-0.829799\pi\) | ||||
−0.860421 | + | 0.509584i | \(0.829799\pi\) | |||||||
\(642\) | −13936.7 | −0.856758 | ||||||||
\(643\) | 16737.7 | 1.02655 | 0.513274 | − | 0.858225i | \(-0.328432\pi\) | ||||
0.513274 | + | 0.858225i | \(0.328432\pi\) | |||||||
\(644\) | −1792.00 | −0.109650 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19419.1 | −1.18271 | ||||||||
\(647\) | −7818.70 | −0.475092 | −0.237546 | − | 0.971376i | \(-0.576343\pi\) | ||||
−0.237546 | + | 0.971376i | \(0.576343\pi\) | |||||||
\(648\) | 1264.08 | 0.0766325 | ||||||||
\(649\) | 2156.00 | 0.130401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3967.17 | −0.238842 | ||||||||
\(652\) | −9025.94 | −0.542152 | ||||||||
\(653\) | −19747.6 | −1.18344 | −0.591719 | − | 0.806144i | \(-0.701550\pi\) | ||||
−0.591719 | + | 0.806144i | \(0.701550\pi\) | |||||||
\(654\) | 3239.59 | 0.193697 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19205.4 | 1.14305 | ||||||||
\(657\) | 9178.33 | 0.545024 | ||||||||
\(658\) | −2717.91 | −0.161026 | ||||||||
\(659\) | 7867.72 | 0.465072 | 0.232536 | − | 0.972588i | \(-0.425298\pi\) | ||||
0.232536 | + | 0.972588i | \(0.425298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4227.41 | 0.248755 | 0.124378 | − | 0.992235i | \(-0.460307\pi\) | ||||
0.124378 | + | 0.992235i | \(0.460307\pi\) | |||||||
\(662\) | 1825.90 | 0.107199 | ||||||||
\(663\) | 3297.35 | 0.193150 | ||||||||
\(664\) | 11807.8 | 0.690106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3107.30 | 0.180789 | ||||||||
\(667\) | −27230.0 | −1.58073 | ||||||||
\(668\) | 4006.67 | 0.232070 | ||||||||
\(669\) | 6300.88 | 0.364135 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7714.94 | −0.443863 | ||||||||
\(672\) | −2044.04 | −0.117337 | ||||||||
\(673\) | −29397.6 | −1.68379 | −0.841897 | − | 0.539638i | \(-0.818561\pi\) | ||||
−0.841897 | + | 0.539638i | \(0.818561\pi\) | |||||||
\(674\) | 2753.57 | 0.157364 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6647.94 | −0.378239 | ||||||||
\(677\) | −5737.14 | −0.325696 | −0.162848 | − | 0.986651i | \(-0.552068\pi\) | ||||
−0.162848 | + | 0.986651i | \(0.552068\pi\) | |||||||
\(678\) | 16484.8 | 0.933771 | ||||||||
\(679\) | −2914.86 | −0.164745 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6771.49 | −0.381034 | ||||||||
\(682\) | −10339.0 | −0.580502 | ||||||||
\(683\) | −32097.6 | −1.79821 | −0.899107 | − | 0.437729i | \(-0.855783\pi\) | ||||
−0.899107 | + | 0.437729i | \(0.855783\pi\) | |||||||
\(684\) | −2388.62 | −0.133525 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10615.8 | 0.590837 | ||||||||
\(687\) | 15933.2 | 0.884848 | ||||||||
\(688\) | −22291.0 | −1.23523 | ||||||||
\(689\) | 6153.69 | 0.340257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16456.2 | −0.905965 | −0.452983 | − | 0.891519i | \(-0.649640\pi\) | ||||
−0.452983 | + | 0.891519i | \(0.649640\pi\) | |||||||
\(692\) | −2721.93 | −0.149526 | ||||||||
\(693\) | 469.712 | 0.0257473 | ||||||||
\(694\) | 21112.3 | 1.15477 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11382.6 | −0.619909 | ||||||||
\(697\) | 17652.3 | 0.959294 | ||||||||
\(698\) | 43058.9 | 2.33496 | ||||||||
\(699\) | 7398.80 | 0.400355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27238.1 | 1.46758 | 0.733788 | − | 0.679379i | \(-0.237751\pi\) | ||||
0.733788 | + | 0.679379i | \(0.237751\pi\) | |||||||
\(702\) | 1367.75 | 0.0735364 | ||||||||
\(703\) | 8057.44 | 0.432279 | ||||||||
\(704\) | 1678.25 | 0.0898457 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8934.12 | −0.476261 | ||||||||
\(707\) | −4820.09 | −0.256405 | ||||||||
\(708\) | −1982.90 | −0.105257 | ||||||||
\(709\) | 28761.4 | 1.52349 | 0.761747 | − | 0.647875i | \(-0.224342\pi\) | ||||
0.761747 | + | 0.647875i | \(0.224342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2947.94 | −0.155494 | ||||||||
\(712\) | 7943.10 | 0.418090 | ||||||||
\(713\) | −31216.3 | −1.63964 | ||||||||
\(714\) | −3512.09 | −0.184085 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6577.27 | −0.343302 | ||||||||
\(717\) | −4288.21 | −0.223356 | ||||||||
\(718\) | 10804.5 | 0.561588 | ||||||||
\(719\) | −27272.0 | −1.41456 | −0.707282 | − | 0.706931i | \(-0.750079\pi\) | ||||
−0.707282 | + | 0.706931i | \(0.750079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5229.28 | −0.270109 | ||||||||
\(722\) | 2243.05 | 0.115620 | ||||||||
\(723\) | 2936.97 | 0.151075 | ||||||||
\(724\) | 3580.04 | 0.183772 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1224.14 | 0.0625785 | ||||||||
\(727\) | −3979.75 | −0.203027 | −0.101514 | − | 0.994834i | \(-0.532369\pi\) | ||||
−0.101514 | + | 0.994834i | \(0.532369\pi\) | |||||||
\(728\) | 1112.26 | 0.0566253 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20488.3 | −1.03665 | ||||||||
\(732\) | 7095.54 | 0.358277 | ||||||||
\(733\) | −9342.48 | −0.470767 | −0.235384 | − | 0.971903i | \(-0.575635\pi\) | ||||
−0.235384 | + | 0.971903i | \(0.575635\pi\) | |||||||
\(734\) | −28426.3 | −1.42947 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16083.9 | −0.805515 | ||||||||
\(737\) | −9906.45 | −0.495127 | ||||||||
\(738\) | 7322.23 | 0.365224 | ||||||||
\(739\) | −28928.0 | −1.43997 | −0.719983 | − | 0.693992i | \(-0.755850\pi\) | ||||
−0.719983 | + | 0.693992i | \(0.755850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3546.68 | 0.175831 | ||||||||
\(742\) | −6554.43 | −0.324287 | ||||||||
\(743\) | −4857.04 | −0.239822 | −0.119911 | − | 0.992785i | \(-0.538261\pi\) | ||||
−0.119911 | + | 0.992785i | \(0.538261\pi\) | |||||||
\(744\) | −13049.0 | −0.643008 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31660.8 | −1.55386 | ||||||||
\(747\) | 6809.57 | 0.333533 | ||||||||
\(748\) | −2714.19 | −0.132675 | ||||||||
\(749\) | −6536.00 | −0.318852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14355.4 | 0.697517 | 0.348759 | − | 0.937213i | \(-0.386603\pi\) | ||||
0.348759 | + | 0.937213i | \(0.386603\pi\) | |||||||
\(752\) | −13522.6 | −0.655744 | ||||||||
\(753\) | 19591.9 | 0.948165 | ||||||||
\(754\) | −12316.1 | −0.594863 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | 17714.9 | 0.850538 | 0.425269 | − | 0.905067i | \(-0.360179\pi\) | ||||
0.425269 | + | 0.905067i | \(0.360179\pi\) | |||||||
\(758\) | 48103.9 | 2.30503 | ||||||||
\(759\) | 3696.00 | 0.176754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7945.82 | −0.378497 | −0.189248 | − | 0.981929i | \(-0.560605\pi\) | ||||
−0.189248 | + | 0.981929i | \(0.560605\pi\) | |||||||
\(762\) | −23180.3 | −1.10201 | ||||||||
\(763\) | 1519.29 | 0.0720866 | ||||||||
\(764\) | 7204.58 | 0.341168 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45398.4 | 2.14140 | ||||||||
\(767\) | 2944.26 | 0.138606 | ||||||||
\(768\) | −13166.2 | −0.618613 | ||||||||
\(769\) | 27308.1 | 1.28057 | 0.640284 | − | 0.768139i | \(-0.278817\pi\) | ||||
0.640284 | + | 0.768139i | \(0.278817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24390.8 | 1.13932 | ||||||||
\(772\) | −13313.0 | −0.620653 | ||||||||
\(773\) | 18872.6 | 0.878136 | 0.439068 | − | 0.898454i | \(-0.355309\pi\) | ||||
0.439068 | + | 0.898454i | \(0.355309\pi\) | |||||||
\(774\) | −8498.64 | −0.394674 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9587.65 | −0.443527 | ||||||||
\(777\) | 1457.25 | 0.0672826 | ||||||||
\(778\) | 3176.29 | 0.146369 | ||||||||
\(779\) | 18987.1 | 0.873276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8321.50 | 0.381263 | ||||||||
\(782\) | −27635.4 | −1.26373 | ||||||||
\(783\) | −6564.37 | −0.299606 | ||||||||
\(784\) | 25512.8 | 1.16221 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11608.2 | −0.526782 | ||||||||
\(787\) | 14512.1 | 0.657307 | 0.328654 | − | 0.944450i | \(-0.393405\pi\) | ||||
0.328654 | + | 0.944450i | \(0.393405\pi\) | |||||||
\(788\) | −3115.60 | −0.140849 | ||||||||
\(789\) | −13648.3 | −0.615832 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7731.01 | 0.347513 | ||||||||
\(792\) | 1544.99 | 0.0693167 | ||||||||
\(793\) | −10535.6 | −0.471792 | ||||||||
\(794\) | −2859.15 | −0.127793 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1605.72 | −0.0714989 | ||||||||
\(797\) | −29108.9 | −1.29371 | −0.646856 | − | 0.762612i | \(-0.723917\pi\) | ||||
−0.646856 | + | 0.762612i | \(0.723917\pi\) | |||||||
\(798\) | −3777.65 | −0.167578 | ||||||||
\(799\) | −12429.1 | −0.550325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4580.80 | 0.202066 | ||||||||
\(802\) | −41154.0 | −1.81197 | ||||||||
\(803\) | 11218.0 | 0.492993 | ||||||||
\(804\) | 9111.10 | 0.399656 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14119.1 | −0.617029 | ||||||||
\(807\) | 87.4567 | 0.00381490 | ||||||||
\(808\) | −15854.4 | −0.690291 | ||||||||
\(809\) | −3000.83 | −0.130413 | −0.0652063 | − | 0.997872i | \(-0.520771\pi\) | ||||
−0.0652063 | + | 0.997872i | \(0.520771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6239.39 | 0.270154 | 0.135077 | − | 0.990835i | \(-0.456872\pi\) | ||||
0.135077 | + | 0.990835i | \(0.456872\pi\) | |||||||
\(812\) | 3890.00 | 0.168118 | ||||||||
\(813\) | −23133.7 | −0.997950 | ||||||||
\(814\) | 3797.81 | 0.163530 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17473.9 | −0.749645 | ||||||||
\(817\) | −22037.6 | −0.943693 | ||||||||
\(818\) | −29539.6 | −1.26263 | ||||||||
\(819\) | 641.445 | 0.0273674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14922.4 | 0.634342 | 0.317171 | − | 0.948368i | \(-0.397267\pi\) | ||||
0.317171 | + | 0.948368i | \(0.397267\pi\) | |||||||
\(822\) | −12834.2 | −0.544580 | ||||||||
\(823\) | 25737.8 | 1.09011 | 0.545057 | − | 0.838399i | \(-0.316508\pi\) | ||||
0.545057 | + | 0.838399i | \(0.316508\pi\) | |||||||
\(824\) | −17200.3 | −0.727186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3136.00 | −0.132101 | ||||||||
\(827\) | −27043.4 | −1.13711 | −0.568555 | − | 0.822645i | \(-0.692497\pi\) | ||||
−0.568555 | + | 0.822645i | \(0.692497\pi\) | |||||||
\(828\) | −3399.26 | −0.142672 | ||||||||
\(829\) | −9795.41 | −0.410384 | −0.205192 | − | 0.978722i | \(-0.565782\pi\) | ||||
−0.205192 | + | 0.978722i | \(0.565782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3382.56 | 0.141203 | ||||||||
\(832\) | 2291.84 | 0.0954990 | ||||||||
\(833\) | 23449.7 | 0.975370 | ||||||||
\(834\) | −4919.70 | −0.204263 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2919.42 | −0.120778 | ||||||||
\(837\) | −7525.37 | −0.310770 | ||||||||
\(838\) | 37730.5 | 1.55535 | ||||||||
\(839\) | 28875.5 | 1.18819 | 0.594095 | − | 0.804395i | \(-0.297510\pi\) | ||||
0.594095 | + | 0.804395i | \(0.297510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34720.7 | 1.42362 | ||||||||
\(842\) | 47489.3 | 1.94369 | ||||||||
\(843\) | 5617.41 | 0.229506 | ||||||||
\(844\) | −16585.7 | −0.676426 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5155.63 | −0.209520 | ||||||||
\(847\) | 574.092 | 0.0232893 | ||||||||
\(848\) | −32610.7 | −1.32059 | ||||||||
\(849\) | 6373.45 | 0.257640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11466.6 | 0.461892 | ||||||||
\(852\) | −7653.39 | −0.307747 | ||||||||
\(853\) | 47157.1 | 1.89288 | 0.946441 | − | 0.322878i | \(-0.104650\pi\) | ||||
0.946441 | + | 0.322878i | \(0.104650\pi\) | |||||||
\(854\) | 11221.7 | 0.449649 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21498.4 | −0.858412 | ||||||||
\(857\) | −5021.31 | −0.200145 | −0.100073 | − | 0.994980i | \(-0.531908\pi\) | ||||
−0.100073 | + | 0.994980i | \(0.531908\pi\) | |||||||
\(858\) | 1671.70 | 0.0665162 | ||||||||
\(859\) | −22921.1 | −0.910428 | −0.455214 | − | 0.890382i | \(-0.650437\pi\) | ||||
−0.455214 | + | 0.890382i | \(0.650437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3433.95 | 0.135922 | ||||||||
\(862\) | 18938.9 | 0.748332 | ||||||||
\(863\) | 19488.1 | 0.768693 | 0.384347 | − | 0.923189i | \(-0.374427\pi\) | ||||
0.384347 | + | 0.923189i | \(0.374427\pi\) | |||||||
\(864\) | −3877.36 | −0.152674 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24266.1 | 0.952188 | ||||||||
\(867\) | −1321.86 | −0.0517794 | ||||||||
\(868\) | 4459.48 | 0.174383 | ||||||||
\(869\) | −3603.04 | −0.140650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13528.4 | −0.526282 | ||||||||
\(872\) | 4997.30 | 0.194071 | ||||||||
\(873\) | −5529.22 | −0.214360 | ||||||||
\(874\) | −29725.0 | −1.15042 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10317.3 | −0.397933 | ||||||||
\(877\) | 8455.67 | 0.325573 | 0.162787 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162787 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(878\) | −343.834 | −0.0132162 | ||||||||
\(879\) | −9972.56 | −0.382669 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11291.2 | −0.431794 | −0.215897 | − | 0.976416i | \(-0.569268\pi\) | ||||
−0.215897 | + | 0.976416i | \(0.569268\pi\) | |||||||
\(882\) | 9727.02 | 0.371344 | ||||||||
\(883\) | −31818.1 | −1.21264 | −0.606322 | − | 0.795219i | \(-0.707356\pi\) | ||||
−0.606322 | + | 0.795219i | \(0.707356\pi\) | |||||||
\(884\) | −3706.53 | −0.141023 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16705.4 | 0.633441 | ||||||||
\(887\) | −17481.1 | −0.661732 | −0.330866 | − | 0.943678i | \(-0.607341\pi\) | ||||
−0.330866 | + | 0.943678i | \(0.607341\pi\) | |||||||
\(888\) | 4793.24 | 0.181138 | ||||||||
\(889\) | −10871.0 | −0.410126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −7082.78 | −0.265862 | ||||||||
\(893\) | −13368.9 | −0.500978 | ||||||||
\(894\) | 23816.2 | 0.890976 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7891.87 | −0.294251 | ||||||||
\(897\) | 5047.31 | 0.187876 | ||||||||
\(898\) | 39125.1 | 1.45392 | ||||||||
\(899\) | 67763.1 | 2.51393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29973.6 | −1.10829 | ||||||||
\(902\) | 8949.39 | 0.330357 | ||||||||
\(903\) | −3985.66 | −0.146882 | ||||||||
\(904\) | 25429.1 | 0.935574 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5767.31 | −0.211486 | ||||||||
\(907\) | −10607.4 | −0.388326 | −0.194163 | − | 0.980969i | \(-0.562199\pi\) | ||||
−0.194163 | + | 0.980969i | \(0.562199\pi\) | |||||||
\(908\) | 7611.79 | 0.278201 | ||||||||
\(909\) | −9143.26 | −0.333623 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41249.2 | −1.50016 | −0.750080 | − | 0.661347i | \(-0.769985\pi\) | ||||
−0.750080 | + | 0.661347i | \(0.769985\pi\) | |||||||
\(912\) | −18795.2 | −0.682425 | ||||||||
\(913\) | 8322.81 | 0.301692 | ||||||||
\(914\) | −11906.5 | −0.430887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17910.4 | −0.646045 | ||||||||
\(917\) | −5443.97 | −0.196048 | ||||||||
\(918\) | −6662.10 | −0.239523 | ||||||||
\(919\) | −13858.1 | −0.497429 | −0.248714 | − | 0.968577i | \(-0.580008\pi\) | ||||
−0.248714 | + | 0.968577i | \(0.580008\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5096.83 | −0.182352 | ||||||||
\(922\) | −39004.9 | −1.39323 | ||||||||
\(923\) | 11363.9 | 0.405253 | ||||||||
\(924\) | −528.000 | −0.0187986 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36719.0 | 1.30309 | ||||||||
\(927\) | −9919.47 | −0.351454 | ||||||||
\(928\) | 34914.2 | 1.23504 | ||||||||
\(929\) | 20893.7 | 0.737890 | 0.368945 | − | 0.929451i | \(-0.379719\pi\) | ||||
0.368945 | + | 0.929451i | \(0.379719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25222.8 | 0.887911 | ||||||||
\(932\) | −8316.94 | −0.292307 | ||||||||
\(933\) | −20786.5 | −0.729388 | ||||||||
\(934\) | 36042.9 | 1.26270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2109.86 | 0.0736784 | ||||||||
\(937\) | −3203.52 | −0.111691 | −0.0558454 | − | 0.998439i | \(-0.517785\pi\) | ||||
−0.0558454 | + | 0.998439i | \(0.517785\pi\) | |||||||
\(938\) | 14409.4 | 0.501581 | ||||||||
\(939\) | −10682.2 | −0.371248 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19951.6 | 0.691182 | 0.345591 | − | 0.938385i | \(-0.387678\pi\) | ||||
0.345591 | + | 0.938385i | \(0.387678\pi\) | |||||||
\(942\) | 20968.9 | 0.725270 | ||||||||
\(943\) | 27020.6 | 0.933099 | ||||||||
\(944\) | −15602.8 | −0.537952 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10387.2 | −0.356996 | ||||||||
\(947\) | 38216.7 | 1.31138 | 0.655689 | − | 0.755031i | \(-0.272378\pi\) | ||||
0.655689 | + | 0.755031i | \(0.272378\pi\) | |||||||
\(948\) | 3313.76 | 0.113529 | ||||||||
\(949\) | 15319.4 | 0.524014 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 998.249 | 0.0340383 | ||||||||
\(952\) | −5417.65 | −0.184440 | ||||||||
\(953\) | 47661.4 | 1.62004 | 0.810022 | − | 0.586399i | \(-0.199455\pi\) | ||||
0.810022 | + | 0.586399i | \(0.199455\pi\) | |||||||
\(954\) | −12433.2 | −0.421948 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4820.35 | 0.163077 | ||||||||
\(957\) | −8023.12 | −0.271004 | ||||||||
\(958\) | −7897.56 | −0.266345 | ||||||||
\(959\) | −6018.94 | −0.202671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47892.3 | 1.60761 | ||||||||
\(962\) | 5186.34 | 0.173819 | ||||||||
\(963\) | −12398.2 | −0.414876 | ||||||||
\(964\) | −3301.43 | −0.110303 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5376.00 | −0.179058 | ||||||||
\(967\) | −18933.2 | −0.629628 | −0.314814 | − | 0.949153i | \(-0.601942\pi\) | ||||
−0.314814 | + | 0.949153i | \(0.601942\pi\) | |||||||
\(968\) | 1888.32 | 0.0626994 | ||||||||
\(969\) | −17275.3 | −0.572717 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40660.3 | −1.34382 | −0.671911 | − | 0.740632i | \(-0.734526\pi\) | ||||
−0.671911 | + | 0.740632i | \(0.734526\pi\) | |||||||
\(972\) | −819.464 | −0.0270415 | ||||||||
\(973\) | −2307.23 | −0.0760188 | ||||||||
\(974\) | 22759.2 | 0.748720 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55832.3 | 1.83110 | ||||||||
\(977\) | 22502.8 | 0.736876 | 0.368438 | − | 0.929652i | \(-0.379893\pi\) | ||||
0.368438 | + | 0.929652i | \(0.379893\pi\) | |||||||
\(978\) | −27077.8 | −0.885331 | ||||||||
\(979\) | 5598.76 | 0.182775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2881.96 | 0.0937959 | ||||||||
\(982\) | −24824.7 | −0.806709 | ||||||||
\(983\) | 4435.20 | 0.143907 | 0.0719536 | − | 0.997408i | \(-0.477077\pi\) | ||||
0.0719536 | + | 0.997408i | \(0.477077\pi\) | |||||||
\(984\) | 11295.1 | 0.365929 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59989.8 | 1.93759 | ||||||||
\(987\) | −2417.87 | −0.0779753 | ||||||||
\(988\) | −3986.80 | −0.128378 | ||||||||
\(989\) | −31361.8 | −1.00834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7362.76 | 0.236010 | 0.118005 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118005 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(992\) | 40025.5 | 1.28106 | ||||||||
\(993\) | 1624.33 | 0.0519101 | ||||||||
\(994\) | −12104.0 | −0.386233 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7654.60 | −0.243519 | ||||||||
\(997\) | 53480.1 | 1.69883 | 0.849413 | − | 0.527728i | \(-0.176956\pi\) | ||||
0.849413 | + | 0.527728i | \(0.176956\pi\) | |||||||
\(998\) | −35010.0 | −1.11044 | ||||||||
\(999\) | 2764.27 | 0.0875452 |
(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 | 825.4.a.k.1.1 | 2 | ||
3.2 | odd | 2 | 2475.4.a.o.1.2 | 2 | |||
5.2 | odd | 4 | 825.4.c.i.199.1 | 4 | |||
5.3 | odd | 4 | 825.4.c.i.199.4 | 4 | |||
5.4 | even | 2 | 33.4.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 99.4.a.e.1.1 | 2 | |||
20.19 | odd | 2 | 528.4.a.o.1.1 | 2 | |||
35.34 | odd | 2 | 1617.4.a.j.1.2 | 2 | |||
40.19 | odd | 2 | 2112.4.a.bh.1.2 | 2 | |||
40.29 | even | 2 | 2112.4.a.ba.1.2 | 2 | |||
55.54 | odd | 2 | 363.4.a.j.1.1 | 2 | |||
60.59 | even | 2 | 1584.4.a.x.1.2 | 2 | |||
165.164 | even | 2 | 1089.4.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
99.4.a.e.1.1 | 2 | 15.14 | odd | 2 | |||
363.4.a.j.1.1 | 2 | 55.54 | odd | 2 | |||
528.4.a.o.1.1 | 2 | 20.19 | odd | 2 | |||
825.4.a.k.1.1 | 2 | 1.1 | even | 1 | trivial | ||
825.4.c.i.199.1 | 4 | 5.2 | odd | 4 | |||
825.4.c.i.199.4 | 4 | 5.3 | odd | 4 | |||
1089.4.a.t.1.2 | 2 | 165.164 | even | 2 | |||
1584.4.a.x.1.2 | 2 | 60.59 | even | 2 | |||
1617.4.a.j.1.2 | 2 | 35.34 | odd | 2 | |||
2112.4.a.ba.1.2 | 2 | 40.29 | even | 2 | |||
2112.4.a.bh.1.2 | 2 | 40.19 | odd | 2 | |||
2475.4.a.o.1.2 | 2 | 3.2 | odd | 2 |