Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.35890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.35890 | 1.18755 | 0.593775 | − | 0.804631i | \(-0.297637\pi\) | ||||
0.593775 | + | 0.804631i | \(0.297637\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 3.28220 | 0.410275 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.0767 | 0.685632 | ||||||||
\(7\) | 30.4356 | 1.64337 | 0.821684 | − | 0.569944i | \(-0.193035\pi\) | ||||
0.821684 | + | 0.569944i | \(0.193035\pi\) | |||||||
\(8\) | −15.8466 | −0.700328 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 31.4356 | 0.861654 | 0.430827 | − | 0.902435i | \(-0.358222\pi\) | ||||
0.430827 | + | 0.902435i | \(0.358222\pi\) | |||||||
\(12\) | 9.84661 | 0.236873 | ||||||||
\(13\) | −60.7424 | −1.29592 | −0.647958 | − | 0.761676i | \(-0.724377\pi\) | ||||
−0.647958 | + | 0.761676i | \(0.724377\pi\) | |||||||
\(14\) | 102.230 | 1.95158 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.4848 | −1.24195 | ||||||||
\(17\) | −121.178 | −1.72882 | −0.864411 | − | 0.502786i | \(-0.832308\pi\) | ||||
−0.864411 | + | 0.502786i | \(0.832308\pi\) | |||||||
\(18\) | 30.2301 | 0.395850 | ||||||||
\(19\) | −14.4356 | −0.174303 | −0.0871514 | − | 0.996195i | \(-0.527776\pi\) | ||||
−0.0871514 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 91.3068 | 0.948799 | ||||||||
\(22\) | 105.589 | 1.02326 | ||||||||
\(23\) | 13.6932 | 0.124141 | 0.0620703 | − | 0.998072i | \(-0.480230\pi\) | ||||
0.0620703 | + | 0.998072i | \(0.480230\pi\) | |||||||
\(24\) | −47.5398 | −0.404334 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −204.028 | −1.53896 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 99.8958 | 0.674233 | ||||||||
\(29\) | −76.0492 | −0.486965 | −0.243482 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243482 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 183.049 | 1.06054 | 0.530268 | − | 0.847830i | \(-0.322091\pi\) | ||||
0.530268 | + | 0.847830i | \(0.322091\pi\) | |||||||
\(32\) | −140.208 | −0.774550 | ||||||||
\(33\) | 94.3068 | 0.497476 | ||||||||
\(34\) | −407.025 | −2.05306 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 29.5398 | 0.136758 | ||||||||
\(37\) | −37.3864 | −0.166116 | −0.0830580 | − | 0.996545i | \(-0.526469\pi\) | ||||
−0.0830580 | + | 0.996545i | \(0.526469\pi\) | |||||||
\(38\) | −48.4877 | −0.206993 | ||||||||
\(39\) | −182.227 | −0.748197 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −30.6627 | −0.116798 | −0.0583990 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0583990 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(42\) | 306.690 | 1.12675 | ||||||||
\(43\) | 327.564 | 1.16170 | 0.580850 | − | 0.814011i | \(-0.302720\pi\) | ||||
0.580850 | + | 0.814011i | \(0.302720\pi\) | |||||||
\(44\) | 103.178 | 0.353515 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 45.9941 | 0.147423 | ||||||||
\(47\) | −449.485 | −1.39498 | −0.697490 | − | 0.716594i | \(-0.745700\pi\) | ||||
−0.697490 | + | 0.716594i | \(0.745700\pi\) | |||||||
\(48\) | −238.454 | −0.717040 | ||||||||
\(49\) | 583.325 | 1.70066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −363.534 | −0.998136 | ||||||||
\(52\) | −199.369 | −0.531682 | ||||||||
\(53\) | −301.951 | −0.782569 | −0.391284 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391284 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(54\) | 90.6903 | 0.228544 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −482.301 | −1.15090 | ||||||||
\(57\) | −43.3068 | −0.100634 | ||||||||
\(58\) | −255.441 | −0.578295 | ||||||||
\(59\) | 340.970 | 0.752381 | 0.376190 | − | 0.926542i | \(-0.377234\pi\) | ||||
0.376190 | + | 0.926542i | \(0.377234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 619.098 | 1.29947 | 0.649733 | − | 0.760163i | \(-0.274881\pi\) | ||||
0.649733 | + | 0.760163i | \(0.274881\pi\) | |||||||
\(62\) | 614.844 | 1.25944 | ||||||||
\(63\) | 273.920 | 0.547789 | ||||||||
\(64\) | 164.932 | 0.322133 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 316.767 | 0.590778 | ||||||||
\(67\) | 256.890 | 0.468419 | 0.234210 | − | 0.972186i | \(-0.424750\pi\) | ||||
0.234210 | + | 0.972186i | \(0.424750\pi\) | |||||||
\(68\) | −397.731 | −0.709293 | ||||||||
\(69\) | 41.0796 | 0.0716726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 499.178 | 0.834388 | 0.417194 | − | 0.908818i | \(-0.363014\pi\) | ||||
0.417194 | + | 0.908818i | \(0.363014\pi\) | |||||||
\(72\) | −142.619 | −0.233443 | ||||||||
\(73\) | −19.1288 | −0.0306693 | −0.0153346 | − | 0.999882i | \(-0.504881\pi\) | ||||
−0.0153346 | + | 0.999882i | \(0.504881\pi\) | |||||||
\(74\) | −125.577 | −0.197271 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −47.3805 | −0.0715121 | ||||||||
\(77\) | 956.761 | 1.41601 | ||||||||
\(78\) | −612.083 | −0.888522 | ||||||||
\(79\) | 257.424 | 0.366613 | 0.183307 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183307 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −102.993 | −0.138703 | ||||||||
\(83\) | 914.909 | 1.20993 | 0.604965 | − | 0.796252i | \(-0.293187\pi\) | ||||
0.604965 | + | 0.796252i | \(0.293187\pi\) | |||||||
\(84\) | 299.687 | 0.389269 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1100.26 | 1.37958 | ||||||||
\(87\) | −228.148 | −0.281149 | ||||||||
\(88\) | −498.148 | −0.603440 | ||||||||
\(89\) | −1059.68 | −1.26209 | −0.631045 | − | 0.775746i | \(-0.717374\pi\) | ||||
−0.631045 | + | 0.775746i | \(0.717374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1848.73 | −2.12967 | ||||||||
\(92\) | 44.9439 | 0.0509318 | ||||||||
\(93\) | 549.148 | 0.612300 | ||||||||
\(94\) | −1509.77 | −1.65661 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −420.625 | −0.447186 | ||||||||
\(97\) | 521.000 | 0.545356 | 0.272678 | − | 0.962105i | \(-0.412091\pi\) | ||||
0.272678 | + | 0.962105i | \(0.412091\pi\) | |||||||
\(98\) | 1959.33 | 2.01962 | ||||||||
\(99\) | 282.920 | 0.287218 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 347.080 | 0.341938 | 0.170969 | − | 0.985276i | \(-0.445310\pi\) | ||||
0.170969 | + | 0.985276i | \(0.445310\pi\) | |||||||
\(102\) | −1221.07 | −1.18534 | ||||||||
\(103\) | −770.749 | −0.737322 | −0.368661 | − | 0.929564i | \(-0.620184\pi\) | ||||
−0.368661 | + | 0.929564i | \(0.620184\pi\) | |||||||
\(104\) | 962.561 | 0.907566 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1014.22 | −0.929339 | ||||||||
\(107\) | −1415.37 | −1.27878 | −0.639390 | − | 0.768883i | \(-0.720813\pi\) | ||||
−0.639390 | + | 0.768883i | \(0.720813\pi\) | |||||||
\(108\) | 88.6195 | 0.0789575 | ||||||||
\(109\) | 908.386 | 0.798235 | 0.399118 | − | 0.916900i | \(-0.369317\pi\) | ||||
0.399118 | + | 0.916900i | \(0.369317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −112.159 | −0.0959071 | ||||||||
\(112\) | −2419.17 | −2.04098 | ||||||||
\(113\) | −2049.94 | −1.70657 | −0.853283 | − | 0.521447i | \(-0.825392\pi\) | ||||
−0.853283 | + | 0.521447i | \(0.825392\pi\) | |||||||
\(114\) | −145.463 | −0.119508 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −249.609 | −0.199790 | ||||||||
\(117\) | −546.681 | −0.431972 | ||||||||
\(118\) | 1145.28 | 0.893490 | ||||||||
\(119\) | −3688.12 | −2.84109 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −342.803 | −0.257553 | ||||||||
\(122\) | 2079.49 | 1.54318 | ||||||||
\(123\) | −91.9882 | −0.0674333 | ||||||||
\(124\) | 600.804 | 0.435111 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 920.071 | 0.650527 | ||||||||
\(127\) | 281.644 | 0.196786 | 0.0983932 | − | 0.995148i | \(-0.468630\pi\) | ||||
0.0983932 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(128\) | 1675.66 | 1.15710 | ||||||||
\(129\) | 982.693 | 0.670708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 243.056 | 0.162106 | 0.0810531 | − | 0.996710i | \(-0.474172\pi\) | ||||
0.0810531 | + | 0.996710i | \(0.474172\pi\) | |||||||
\(132\) | 309.534 | 0.204102 | ||||||||
\(133\) | −439.356 | −0.286444 | ||||||||
\(134\) | 862.867 | 0.556271 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1920.26 | 1.21074 | ||||||||
\(137\) | 909.386 | 0.567110 | 0.283555 | − | 0.958956i | \(-0.408486\pi\) | ||||
0.283555 | + | 0.958956i | \(0.408486\pi\) | |||||||
\(138\) | 137.982 | 0.0851148 | ||||||||
\(139\) | −2049.52 | −1.25063 | −0.625317 | − | 0.780371i | \(-0.715030\pi\) | ||||
−0.625317 | + | 0.780371i | \(0.715030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1348.45 | −0.805392 | ||||||||
\(142\) | 1676.69 | 0.990877 | ||||||||
\(143\) | −1909.47 | −1.11663 | ||||||||
\(144\) | −715.363 | −0.413983 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −64.2517 | −0.0364213 | ||||||||
\(147\) | 1749.98 | 0.981875 | ||||||||
\(148\) | −122.710 | −0.0681533 | ||||||||
\(149\) | 3601.14 | 1.97998 | 0.989990 | − | 0.141136i | \(-0.0450753\pi\) | ||||
0.989990 | + | 0.141136i | \(0.0450753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1383.38 | 0.745550 | 0.372775 | − | 0.927922i | \(-0.378406\pi\) | ||||
0.372775 | + | 0.927922i | \(0.378406\pi\) | |||||||
\(152\) | 228.755 | 0.122069 | ||||||||
\(153\) | −1090.60 | −0.576274 | ||||||||
\(154\) | 3213.66 | 1.68159 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −598.106 | −0.306967 | ||||||||
\(157\) | −131.749 | −0.0669729 | −0.0334864 | − | 0.999439i | \(-0.510661\pi\) | ||||
−0.0334864 | + | 0.999439i | \(0.510661\pi\) | |||||||
\(158\) | 864.661 | 0.435372 | ||||||||
\(159\) | −905.852 | −0.451816 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 416.761 | 0.204009 | ||||||||
\(162\) | 272.071 | 0.131950 | ||||||||
\(163\) | 2897.74 | 1.39244 | 0.696222 | − | 0.717827i | \(-0.254863\pi\) | ||||
0.696222 | + | 0.717827i | \(0.254863\pi\) | |||||||
\(164\) | −100.641 | −0.0479193 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3073.09 | 1.43685 | ||||||||
\(167\) | 260.283 | 0.120607 | 0.0603034 | − | 0.998180i | \(-0.480793\pi\) | ||||
0.0603034 | + | 0.998180i | \(0.480793\pi\) | |||||||
\(168\) | −1446.90 | −0.664470 | ||||||||
\(169\) | 1492.64 | 0.679398 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −129.920 | −0.0581009 | ||||||||
\(172\) | 1075.13 | 0.476617 | ||||||||
\(173\) | −1935.83 | −0.850742 | −0.425371 | − | 0.905019i | \(-0.639856\pi\) | ||||
−0.425371 | + | 0.905019i | \(0.639856\pi\) | |||||||
\(174\) | −766.324 | −0.333879 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2498.65 | −1.07013 | ||||||||
\(177\) | 1022.91 | 0.434387 | ||||||||
\(178\) | −3559.36 | −1.49880 | ||||||||
\(179\) | 576.627 | 0.240777 | 0.120389 | − | 0.992727i | \(-0.461586\pi\) | ||||
0.120389 | + | 0.992727i | \(0.461586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1962.04 | −0.805733 | −0.402866 | − | 0.915259i | \(-0.631986\pi\) | ||||
−0.402866 | + | 0.915259i | \(0.631986\pi\) | |||||||
\(182\) | −6209.70 | −2.52909 | ||||||||
\(183\) | 1857.30 | 0.750247 | ||||||||
\(184\) | −216.991 | −0.0869390 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1844.53 | 0.727137 | ||||||||
\(187\) | −3809.30 | −1.48965 | ||||||||
\(188\) | −1475.30 | −0.572326 | ||||||||
\(189\) | 821.761 | 0.316266 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4318.75 | −1.63609 | −0.818047 | − | 0.575152i | \(-0.804943\pi\) | ||||
−0.818047 | + | 0.575152i | \(0.804943\pi\) | |||||||
\(192\) | 494.796 | 0.185984 | ||||||||
\(193\) | 2.97647 | 0.00111011 | 0.000555054 | − | 1.00000i | \(-0.499823\pi\) | ||||
0.000555054 | 1.00000i | \(0.499823\pi\) | ||||||||
\(194\) | 1749.99 | 0.647638 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1914.59 | 0.697738 | ||||||||
\(197\) | 569.705 | 0.206040 | 0.103020 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103020 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(198\) | 950.301 | 0.341086 | ||||||||
\(199\) | −3050.73 | −1.08674 | −0.543368 | − | 0.839494i | \(-0.682851\pi\) | ||||
−0.543368 | + | 0.839494i | \(0.682851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 770.670 | 0.270442 | ||||||||
\(202\) | 1165.81 | 0.406068 | ||||||||
\(203\) | −2314.60 | −0.800262 | ||||||||
\(204\) | −1193.19 | −0.409510 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2588.87 | −0.875607 | ||||||||
\(207\) | 123.239 | 0.0413802 | ||||||||
\(208\) | 4828.09 | 1.60946 | ||||||||
\(209\) | −453.792 | −0.150189 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −50.5104 | −0.0164800 | −0.00824000 | − | 0.999966i | \(-0.502623\pi\) | ||||
−0.00824000 | + | 0.999966i | \(0.502623\pi\) | |||||||
\(212\) | −991.064 | −0.321069 | ||||||||
\(213\) | 1497.53 | 0.481734 | ||||||||
\(214\) | −4754.10 | −1.51862 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −427.858 | −0.134778 | ||||||||
\(217\) | 5571.21 | 1.74285 | ||||||||
\(218\) | 3051.18 | 0.947944 | ||||||||
\(219\) | −57.3864 | −0.0177069 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7360.64 | 2.24041 | ||||||||
\(222\) | −376.732 | −0.113894 | ||||||||
\(223\) | 5453.55 | 1.63765 | 0.818827 | − | 0.574040i | \(-0.194625\pi\) | ||||
0.818827 | + | 0.574040i | \(0.194625\pi\) | |||||||
\(224\) | −4267.33 | −1.27287 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6885.54 | −2.02663 | ||||||||
\(227\) | −4777.14 | −1.39678 | −0.698392 | − | 0.715715i | \(-0.746101\pi\) | ||||
−0.698392 | + | 0.715715i | \(0.746101\pi\) | |||||||
\(228\) | −142.142 | −0.0412875 | ||||||||
\(229\) | −2085.51 | −0.601808 | −0.300904 | − | 0.953654i | \(-0.597288\pi\) | ||||
−0.300904 | + | 0.953654i | \(0.597288\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2870.28 | 0.817536 | ||||||||
\(232\) | 1205.12 | 0.341035 | ||||||||
\(233\) | 6484.53 | 1.82324 | 0.911622 | − | 0.411030i | \(-0.134831\pi\) | ||||
0.911622 | + | 0.411030i | \(0.134831\pi\) | |||||||
\(234\) | −1836.25 | −0.512988 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1119.13 | 0.308683 | ||||||||
\(237\) | 772.271 | 0.211664 | ||||||||
\(238\) | −12388.0 | −3.37394 | ||||||||
\(239\) | 2234.62 | 0.604792 | 0.302396 | − | 0.953182i | \(-0.402214\pi\) | ||||
0.302396 | + | 0.953182i | \(0.402214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2393.01 | −0.639616 | −0.319808 | − | 0.947482i | \(-0.603618\pi\) | ||||
−0.319808 | + | 0.947482i | \(0.603618\pi\) | |||||||
\(242\) | −1151.44 | −0.305857 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2032.01 | 0.533139 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −308.979 | −0.0800805 | ||||||||
\(247\) | 876.852 | 0.225882 | ||||||||
\(248\) | −2900.71 | −0.742722 | ||||||||
\(249\) | 2744.73 | 0.698554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −612.661 | −0.154067 | −0.0770335 | − | 0.997029i | \(-0.524545\pi\) | ||||
−0.0770335 | + | 0.997029i | \(0.524545\pi\) | |||||||
\(252\) | 899.062 | 0.224744 | ||||||||
\(253\) | 430.454 | 0.106966 | ||||||||
\(254\) | 946.014 | 0.233694 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4308.91 | 1.05198 | ||||||||
\(257\) | −306.112 | −0.0742987 | −0.0371493 | − | 0.999310i | \(-0.511828\pi\) | ||||
−0.0371493 | + | 0.999310i | \(0.511828\pi\) | |||||||
\(258\) | 3300.77 | 0.796499 | ||||||||
\(259\) | −1137.88 | −0.272990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −684.443 | −0.162322 | ||||||||
\(262\) | 816.401 | 0.192509 | ||||||||
\(263\) | 283.839 | 0.0665484 | 0.0332742 | − | 0.999446i | \(-0.489407\pi\) | ||||
0.0332742 | + | 0.999446i | \(0.489407\pi\) | |||||||
\(264\) | −1494.44 | −0.348396 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1475.75 | −0.340166 | ||||||||
\(267\) | −3179.04 | −0.728668 | ||||||||
\(268\) | 843.165 | 0.192181 | ||||||||
\(269\) | 2426.21 | 0.549920 | 0.274960 | − | 0.961456i | \(-0.411335\pi\) | ||||
0.274960 | + | 0.961456i | \(0.411335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −174.946 | −0.0392148 | −0.0196074 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196074 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(272\) | 9631.80 | 2.14711 | ||||||||
\(273\) | −5546.19 | −1.22956 | ||||||||
\(274\) | 3054.54 | 0.673472 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 134.832 | 0.0294055 | ||||||||
\(277\) | −7807.07 | −1.69344 | −0.846718 | − | 0.532042i | \(-0.821425\pi\) | ||||
−0.846718 | + | 0.532042i | \(0.821425\pi\) | |||||||
\(278\) | −6884.14 | −1.48519 | ||||||||
\(279\) | 1647.44 | 0.353512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 584.171 | 0.124017 | 0.0620084 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620084 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(282\) | −4529.32 | −0.956444 | ||||||||
\(283\) | −5897.31 | −1.23872 | −0.619362 | − | 0.785106i | \(-0.712609\pi\) | ||||
−0.619362 | + | 0.785106i | \(0.712609\pi\) | |||||||
\(284\) | 1638.40 | 0.342329 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6413.73 | −1.32605 | ||||||||
\(287\) | −933.239 | −0.191942 | ||||||||
\(288\) | −1261.88 | −0.258183 | ||||||||
\(289\) | 9771.10 | 1.98883 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1563.00 | 0.314861 | ||||||||
\(292\) | −62.7846 | −0.0125828 | ||||||||
\(293\) | 1609.73 | 0.320960 | 0.160480 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160480 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(294\) | 5877.99 | 1.16603 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 592.448 | 0.116336 | ||||||||
\(297\) | 848.761 | 0.165825 | ||||||||
\(298\) | 12095.9 | 2.35133 | ||||||||
\(299\) | −831.758 | −0.160876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9969.62 | 1.90910 | ||||||||
\(302\) | 4646.64 | 0.885378 | ||||||||
\(303\) | 1041.24 | 0.197418 | ||||||||
\(304\) | 1147.41 | 0.216475 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3663.22 | −0.684354 | ||||||||
\(307\) | 234.473 | 0.0435898 | 0.0217949 | − | 0.999762i | \(-0.493062\pi\) | ||||
0.0217949 | + | 0.999762i | \(0.493062\pi\) | |||||||
\(308\) | 3140.28 | 0.580955 | ||||||||
\(309\) | −2312.25 | −0.425693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1795.25 | −0.327329 | −0.163665 | − | 0.986516i | \(-0.552331\pi\) | ||||
−0.163665 | + | 0.986516i | \(0.552331\pi\) | |||||||
\(312\) | 2887.68 | 0.523983 | ||||||||
\(313\) | −8440.61 | −1.52425 | −0.762127 | − | 0.647427i | \(-0.775845\pi\) | ||||
−0.762127 | + | 0.647427i | \(0.775845\pi\) | |||||||
\(314\) | −442.533 | −0.0795336 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 844.917 | 0.150412 | ||||||||
\(317\) | 10551.7 | 1.86953 | 0.934766 | − | 0.355264i | \(-0.115609\pi\) | ||||
0.934766 | + | 0.355264i | \(0.115609\pi\) | |||||||
\(318\) | −3042.67 | −0.536554 | ||||||||
\(319\) | −2390.65 | −0.419595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4246.12 | −0.738304 | ||||||||
\(322\) | 1399.86 | 0.242270 | ||||||||
\(323\) | 1749.28 | 0.301339 | ||||||||
\(324\) | 265.858 | 0.0455861 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9733.21 | 1.65360 | ||||||||
\(327\) | 2725.16 | 0.460861 | ||||||||
\(328\) | 485.900 | 0.0817968 | ||||||||
\(329\) | −13680.3 | −2.29247 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6743.17 | 1.11975 | 0.559876 | − | 0.828576i | \(-0.310849\pi\) | ||||
0.559876 | + | 0.828576i | \(0.310849\pi\) | |||||||
\(332\) | 3002.91 | 0.496405 | ||||||||
\(333\) | −336.478 | −0.0553720 | ||||||||
\(334\) | 874.265 | 0.143227 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7257.50 | −1.17836 | ||||||||
\(337\) | −8437.26 | −1.36382 | −0.681909 | − | 0.731437i | \(-0.738850\pi\) | ||||
−0.681909 | + | 0.731437i | \(0.738850\pi\) | |||||||
\(338\) | 5013.62 | 0.806819 | ||||||||
\(339\) | −6149.82 | −0.985287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5754.26 | 0.913814 | ||||||||
\(342\) | −436.389 | −0.0689978 | ||||||||
\(343\) | 7314.45 | 1.15144 | ||||||||
\(344\) | −5190.78 | −0.813571 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6502.25 | −1.01030 | ||||||||
\(347\) | −1848.85 | −0.286027 | −0.143013 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143013 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(348\) | −748.826 | −0.115349 | ||||||||
\(349\) | −1148.38 | −0.176136 | −0.0880678 | − | 0.996114i | \(-0.528069\pi\) | ||||
−0.0880678 | + | 0.996114i | \(0.528069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1640.04 | −0.249399 | ||||||||
\(352\) | −4407.54 | −0.667393 | ||||||||
\(353\) | −5753.60 | −0.867516 | −0.433758 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433758 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(354\) | 3435.85 | 0.515856 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3478.09 | −0.517804 | ||||||||
\(357\) | −11064.4 | −1.64030 | ||||||||
\(358\) | 1936.83 | 0.285935 | ||||||||
\(359\) | 5452.01 | 0.801521 | 0.400761 | − | 0.916183i | \(-0.368746\pi\) | ||||
0.400761 | + | 0.916183i | \(0.368746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6650.61 | −0.969619 | ||||||||
\(362\) | −6590.31 | −0.956848 | ||||||||
\(363\) | −1028.41 | −0.148698 | ||||||||
\(364\) | −6067.91 | −0.873749 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6238.47 | 0.890956 | ||||||||
\(367\) | 8385.93 | 1.19276 | 0.596379 | − | 0.802703i | \(-0.296606\pi\) | ||||
0.596379 | + | 0.802703i | \(0.296606\pi\) | |||||||
\(368\) | −1088.40 | −0.154176 | ||||||||
\(369\) | −275.965 | −0.0389327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9190.05 | −1.28605 | ||||||||
\(372\) | 1802.41 | 0.251212 | ||||||||
\(373\) | 2728.30 | 0.378730 | 0.189365 | − | 0.981907i | \(-0.439357\pi\) | ||||
0.189365 | + | 0.981907i | \(0.439357\pi\) | |||||||
\(374\) | −12795.1 | −1.76903 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7122.81 | 0.976944 | ||||||||
\(377\) | 4619.41 | 0.631065 | ||||||||
\(378\) | 2760.21 | 0.375582 | ||||||||
\(379\) | 3348.99 | 0.453895 | 0.226947 | − | 0.973907i | \(-0.427125\pi\) | ||||
0.226947 | + | 0.973907i | \(0.427125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 844.932 | 0.113615 | ||||||||
\(382\) | −14506.2 | −1.94294 | ||||||||
\(383\) | 10430.3 | 1.39155 | 0.695774 | − | 0.718261i | \(-0.255062\pi\) | ||||
0.695774 | + | 0.718261i | \(0.255062\pi\) | |||||||
\(384\) | 5026.97 | 0.668051 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.99766 | 0.00131831 | ||||||||
\(387\) | 2948.08 | 0.387233 | ||||||||
\(388\) | 1710.03 | 0.223746 | ||||||||
\(389\) | 9827.23 | 1.28088 | 0.640438 | − | 0.768010i | \(-0.278753\pi\) | ||||
0.640438 | + | 0.768010i | \(0.278753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1659.32 | −0.214617 | ||||||||
\(392\) | −9243.73 | −1.19102 | ||||||||
\(393\) | 729.168 | 0.0935921 | ||||||||
\(394\) | 1913.58 | 0.244682 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 928.602 | 0.117838 | ||||||||
\(397\) | −436.382 | −0.0551672 | −0.0275836 | − | 0.999619i | \(-0.508781\pi\) | ||||
−0.0275836 | + | 0.999619i | \(0.508781\pi\) | |||||||
\(398\) | −10247.1 | −1.29055 | ||||||||
\(399\) | −1318.07 | −0.165378 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14501.5 | −1.80591 | −0.902955 | − | 0.429736i | \(-0.858607\pi\) | ||||
−0.902955 | + | 0.429736i | \(0.858607\pi\) | |||||||
\(402\) | 2588.60 | 0.321163 | ||||||||
\(403\) | −11118.8 | −1.37436 | ||||||||
\(404\) | 1139.19 | 0.140289 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7774.51 | −0.950351 | ||||||||
\(407\) | −1175.26 | −0.143134 | ||||||||
\(408\) | 5760.78 | 0.699022 | ||||||||
\(409\) | −12058.4 | −1.45782 | −0.728911 | − | 0.684609i | \(-0.759973\pi\) | ||||
−0.728911 | + | 0.684609i | \(0.759973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2728.16 | 0.327421 | ||||||||
\(412\) | −2529.76 | −0.302505 | ||||||||
\(413\) | 10377.6 | 1.23644 | ||||||||
\(414\) | 413.947 | 0.0491410 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8516.60 | 1.00375 | ||||||||
\(417\) | −6148.57 | −0.722054 | ||||||||
\(418\) | −1524.24 | −0.178356 | ||||||||
\(419\) | 6042.95 | 0.704577 | 0.352288 | − | 0.935892i | \(-0.385404\pi\) | ||||
0.352288 | + | 0.935892i | \(0.385404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9994.67 | −1.15703 | −0.578516 | − | 0.815671i | \(-0.696368\pi\) | ||||
−0.578516 | + | 0.815671i | \(0.696368\pi\) | |||||||
\(422\) | −169.659 | −0.0195708 | ||||||||
\(423\) | −4045.36 | −0.464994 | ||||||||
\(424\) | 4784.90 | 0.548054 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5030.07 | 0.572083 | ||||||||
\(427\) | 18842.6 | 2.13550 | ||||||||
\(428\) | −4645.55 | −0.524652 | ||||||||
\(429\) | −5728.42 | −0.644687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9327.32 | 1.04242 | 0.521208 | − | 0.853430i | \(-0.325482\pi\) | ||||
0.521208 | + | 0.853430i | \(0.325482\pi\) | |||||||
\(432\) | −2146.09 | −0.239013 | ||||||||
\(433\) | −7861.22 | −0.872485 | −0.436243 | − | 0.899829i | \(-0.643691\pi\) | ||||
−0.436243 | + | 0.899829i | \(0.643691\pi\) | |||||||
\(434\) | 18713.1 | 2.06972 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2981.51 | 0.327496 | ||||||||
\(437\) | −197.670 | −0.0216380 | ||||||||
\(438\) | −192.755 | −0.0210279 | ||||||||
\(439\) | 7412.06 | 0.805828 | 0.402914 | − | 0.915238i | \(-0.367997\pi\) | ||||
0.402914 | + | 0.915238i | \(0.367997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5249.93 | 0.566886 | ||||||||
\(442\) | 24723.6 | 2.66060 | ||||||||
\(443\) | −3043.66 | −0.326430 | −0.163215 | − | 0.986591i | \(-0.552186\pi\) | ||||
−0.163215 | + | 0.986591i | \(0.552186\pi\) | |||||||
\(444\) | −368.129 | −0.0393483 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18317.9 | 1.94480 | ||||||||
\(447\) | 10803.4 | 1.14314 | ||||||||
\(448\) | 5019.81 | 0.529383 | ||||||||
\(449\) | −9547.87 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −963.902 | −0.100639 | ||||||||
\(452\) | −6728.31 | −0.700162 | ||||||||
\(453\) | 4150.14 | 0.430443 | ||||||||
\(454\) | −16045.9 | −1.65875 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 686.266 | 0.0704766 | ||||||||
\(457\) | 13401.9 | 1.37180 | 0.685901 | − | 0.727695i | \(-0.259408\pi\) | ||||
0.685901 | + | 0.727695i | \(0.259408\pi\) | |||||||
\(458\) | −7005.00 | −0.714677 | ||||||||
\(459\) | −3271.81 | −0.332712 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4137.03 | −0.417962 | −0.208981 | − | 0.977920i | \(-0.567015\pi\) | ||||
−0.208981 | + | 0.977920i | \(0.567015\pi\) | |||||||
\(462\) | 9640.99 | 0.970865 | ||||||||
\(463\) | −13976.3 | −1.40288 | −0.701439 | − | 0.712729i | \(-0.747459\pi\) | ||||
−0.701439 | + | 0.712729i | \(0.747459\pi\) | |||||||
\(464\) | 6044.75 | 0.604786 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21780.9 | 2.16519 | ||||||||
\(467\) | −10796.5 | −1.06982 | −0.534908 | − | 0.844910i | \(-0.679654\pi\) | ||||
−0.534908 | + | 0.844910i | \(0.679654\pi\) | |||||||
\(468\) | −1794.32 | −0.177227 | ||||||||
\(469\) | 7818.60 | 0.769785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −395.248 | −0.0386668 | ||||||||
\(472\) | −5403.21 | −0.526913 | ||||||||
\(473\) | 10297.2 | 1.00098 | ||||||||
\(474\) | 2593.98 | 0.251362 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12105.2 | −1.16563 | ||||||||
\(477\) | −2717.56 | −0.260856 | ||||||||
\(478\) | 7505.85 | 0.718221 | ||||||||
\(479\) | 14568.4 | 1.38966 | 0.694830 | − | 0.719174i | \(-0.255479\pi\) | ||||
0.694830 | + | 0.719174i | \(0.255479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2270.94 | 0.215272 | ||||||||
\(482\) | −8037.89 | −0.759577 | ||||||||
\(483\) | 1250.28 | 0.117784 | ||||||||
\(484\) | −1125.15 | −0.105668 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 816.212 | 0.0761814 | ||||||||
\(487\) | −11456.6 | −1.06601 | −0.533004 | − | 0.846113i | \(-0.678937\pi\) | ||||
−0.533004 | + | 0.846113i | \(0.678937\pi\) | |||||||
\(488\) | −9810.61 | −0.910052 | ||||||||
\(489\) | 8693.21 | 0.803928 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19666.5 | −1.80761 | −0.903804 | − | 0.427948i | \(-0.859237\pi\) | ||||
−0.903804 | + | 0.427948i | \(0.859237\pi\) | |||||||
\(492\) | −301.924 | −0.0276662 | ||||||||
\(493\) | 9215.48 | 0.841875 | ||||||||
\(494\) | 2945.26 | 0.268246 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14549.6 | −1.31713 | ||||||||
\(497\) | 15192.8 | 1.37121 | ||||||||
\(498\) | 9219.26 | 0.829568 | ||||||||
\(499\) | 8379.31 | 0.751722 | 0.375861 | − | 0.926676i | \(-0.377347\pi\) | ||||
0.375861 | + | 0.926676i | \(0.377347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 780.850 | 0.0696323 | ||||||||
\(502\) | −2057.87 | −0.182962 | ||||||||
\(503\) | −15678.1 | −1.38976 | −0.694881 | − | 0.719124i | \(-0.744543\pi\) | ||||
−0.694881 | + | 0.719124i | \(0.744543\pi\) | |||||||
\(504\) | −4340.71 | −0.383632 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1445.85 | 0.127028 | ||||||||
\(507\) | 4477.91 | 0.392251 | ||||||||
\(508\) | 924.413 | 0.0807366 | ||||||||
\(509\) | −17037.3 | −1.48363 | −0.741813 | − | 0.670606i | \(-0.766034\pi\) | ||||
−0.741813 | + | 0.670606i | \(0.766034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −582.197 | −0.0504009 | ||||||||
\(512\) | 1067.93 | 0.0921798 | ||||||||
\(513\) | −389.761 | −0.0335446 | ||||||||
\(514\) | −1028.20 | −0.0882334 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3225.40 | 0.275175 | ||||||||
\(517\) | −14129.8 | −1.20199 | ||||||||
\(518\) | −3822.02 | −0.324189 | ||||||||
\(519\) | −5807.49 | −0.491176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8776.12 | −0.737982 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(522\) | −2298.97 | −0.192765 | ||||||||
\(523\) | 11120.4 | 0.929753 | 0.464877 | − | 0.885375i | \(-0.346099\pi\) | ||||
0.464877 | + | 0.885375i | \(0.346099\pi\) | |||||||
\(524\) | 797.759 | 0.0665082 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 953.385 | 0.0790296 | ||||||||
\(527\) | −22181.5 | −1.83348 | ||||||||
\(528\) | −7495.95 | −0.617840 | ||||||||
\(529\) | −11979.5 | −0.984589 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3068.73 | 0.250794 | ||||||||
\(532\) | −1442.06 | −0.117521 | ||||||||
\(533\) | 1862.53 | 0.151360 | ||||||||
\(534\) | −10678.1 | −0.865330 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4070.83 | −0.328047 | ||||||||
\(537\) | 1729.88 | 0.139013 | ||||||||
\(538\) | 8149.39 | 0.653058 | ||||||||
\(539\) | 18337.2 | 1.46538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21730.6 | 1.72693 | 0.863467 | − | 0.504405i | \(-0.168288\pi\) | ||||
0.863467 | + | 0.504405i | \(0.168288\pi\) | |||||||
\(542\) | −587.626 | −0.0465695 | ||||||||
\(543\) | −5886.13 | −0.465190 | ||||||||
\(544\) | 16990.2 | 1.33906 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18629.1 | −1.46017 | ||||||||
\(547\) | −6926.17 | −0.541392 | −0.270696 | − | 0.962665i | \(-0.587254\pi\) | ||||
−0.270696 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(548\) | 2984.79 | 0.232671 | ||||||||
\(549\) | 5571.89 | 0.433155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1097.82 | 0.0848793 | ||||||||
\(552\) | −650.973 | −0.0501943 | ||||||||
\(553\) | 7834.85 | 0.602480 | ||||||||
\(554\) | −26223.2 | −2.01104 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6726.95 | −0.513104 | ||||||||
\(557\) | −6589.22 | −0.501246 | −0.250623 | − | 0.968085i | \(-0.580636\pi\) | ||||
−0.250623 | + | 0.968085i | \(0.580636\pi\) | |||||||
\(558\) | 5533.59 | 0.419813 | ||||||||
\(559\) | −19897.0 | −1.50547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11427.9 | −0.860047 | ||||||||
\(562\) | 1962.17 | 0.147276 | ||||||||
\(563\) | 3839.63 | 0.287426 | 0.143713 | − | 0.989619i | \(-0.454096\pi\) | ||||
0.143713 | + | 0.989619i | \(0.454096\pi\) | |||||||
\(564\) | −4425.90 | −0.330433 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19808.5 | −1.47105 | ||||||||
\(567\) | 2465.28 | 0.182596 | ||||||||
\(568\) | −7910.28 | −0.584345 | ||||||||
\(569\) | −20874.0 | −1.53794 | −0.768968 | − | 0.639287i | \(-0.779229\pi\) | ||||
−0.768968 | + | 0.639287i | \(0.779229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21175.9 | 1.55199 | 0.775994 | − | 0.630740i | \(-0.217248\pi\) | ||||
0.775994 | + | 0.630740i | \(0.217248\pi\) | |||||||
\(572\) | −6267.28 | −0.458126 | ||||||||
\(573\) | −12956.3 | −0.944599 | ||||||||
\(574\) | −3134.66 | −0.227941 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1484.39 | 0.107378 | ||||||||
\(577\) | −14924.2 | −1.07678 | −0.538391 | − | 0.842695i | \(-0.680968\pi\) | ||||
−0.538391 | + | 0.842695i | \(0.680968\pi\) | |||||||
\(578\) | 32820.1 | 2.36183 | ||||||||
\(579\) | 8.92941 | 0.000640922 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27845.8 | 1.98836 | ||||||||
\(582\) | 5249.96 | 0.373914 | ||||||||
\(583\) | −9492.00 | −0.674303 | ||||||||
\(584\) | 303.127 | 0.0214785 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5406.92 | 0.381156 | ||||||||
\(587\) | 25218.0 | 1.77318 | 0.886592 | − | 0.462552i | \(-0.153066\pi\) | ||||
0.886592 | + | 0.462552i | \(0.153066\pi\) | |||||||
\(588\) | 5743.78 | 0.402839 | ||||||||
\(589\) | −2642.42 | −0.184854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1709.11 | 0.118957 | ||||||||
\(592\) | 2971.65 | 0.206308 | ||||||||
\(593\) | 5011.77 | 0.347063 | 0.173532 | − | 0.984828i | \(-0.444482\pi\) | ||||
0.173532 | + | 0.984828i | \(0.444482\pi\) | |||||||
\(594\) | 2850.90 | 0.196926 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11819.7 | 0.812337 | ||||||||
\(597\) | −9152.19 | −0.627428 | ||||||||
\(598\) | −2793.79 | −0.191048 | ||||||||
\(599\) | 4943.41 | 0.337199 | 0.168600 | − | 0.985685i | \(-0.446075\pi\) | ||||
0.168600 | + | 0.985685i | \(0.446075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24334.8 | −1.65164 | −0.825821 | − | 0.563932i | \(-0.809288\pi\) | ||||
−0.825821 | + | 0.563932i | \(0.809288\pi\) | |||||||
\(602\) | 33486.9 | 2.26715 | ||||||||
\(603\) | 2312.01 | 0.156140 | ||||||||
\(604\) | 4540.54 | 0.305881 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3497.42 | 0.234444 | ||||||||
\(607\) | 28973.8 | 1.93741 | 0.968707 | − | 0.248207i | \(-0.0798415\pi\) | ||||
0.968707 | + | 0.248207i | \(0.0798415\pi\) | |||||||
\(608\) | 2023.99 | 0.135006 | ||||||||
\(609\) | −6943.81 | −0.462032 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27302.8 | 1.80778 | ||||||||
\(612\) | −3579.58 | −0.236431 | ||||||||
\(613\) | 15139.1 | 0.997490 | 0.498745 | − | 0.866749i | \(-0.333794\pi\) | ||||
0.498745 | + | 0.866749i | \(0.333794\pi\) | |||||||
\(614\) | 787.571 | 0.0517651 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15161.4 | −0.991673 | ||||||||
\(617\) | 13894.8 | 0.906617 | 0.453309 | − | 0.891354i | \(-0.350244\pi\) | ||||
0.453309 | + | 0.891354i | \(0.350244\pi\) | |||||||
\(618\) | −7766.61 | −0.505532 | ||||||||
\(619\) | −4589.69 | −0.298021 | −0.149011 | − | 0.988836i | \(-0.547609\pi\) | ||||
−0.149011 | + | 0.988836i | \(0.547609\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 369.717 | 0.0238909 | ||||||||
\(622\) | −6030.07 | −0.388720 | ||||||||
\(623\) | −32252.0 | −2.07408 | ||||||||
\(624\) | 14484.3 | 0.929223 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28351.2 | −1.81013 | ||||||||
\(627\) | −1361.37 | −0.0867114 | ||||||||
\(628\) | −432.428 | −0.0274773 | ||||||||
\(629\) | 4530.41 | 0.287185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3005.77 | 0.189632 | 0.0948160 | − | 0.995495i | \(-0.469774\pi\) | ||||
0.0948160 | + | 0.995495i | \(0.469774\pi\) | |||||||
\(632\) | −4079.29 | −0.256749 | ||||||||
\(633\) | −151.531 | −0.00951473 | ||||||||
\(634\) | 35442.0 | 2.22016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2973.19 | −0.185369 | ||||||||
\(637\) | −35432.6 | −2.20391 | ||||||||
\(638\) | −8029.96 | −0.498290 | ||||||||
\(639\) | 4492.60 | 0.278129 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5631.47 | −0.347004 | −0.173502 | − | 0.984834i | \(-0.555508\pi\) | ||||
−0.173502 | + | 0.984834i | \(0.555508\pi\) | |||||||
\(642\) | −14262.3 | −0.876773 | ||||||||
\(643\) | 11305.1 | 0.693358 | 0.346679 | − | 0.937984i | \(-0.387309\pi\) | ||||
0.346679 | + | 0.937984i | \(0.387309\pi\) | |||||||
\(644\) | 1367.89 | 0.0836997 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5875.64 | 0.357855 | ||||||||
\(647\) | −8614.30 | −0.523436 | −0.261718 | − | 0.965144i | \(-0.584289\pi\) | ||||
−0.261718 | + | 0.965144i | \(0.584289\pi\) | |||||||
\(648\) | −1283.58 | −0.0778142 | ||||||||
\(649\) | 10718.6 | 0.648291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16713.6 | 1.00623 | ||||||||
\(652\) | 9510.96 | 0.571285 | ||||||||
\(653\) | 12639.8 | 0.757479 | 0.378739 | − | 0.925503i | \(-0.376358\pi\) | ||||
0.378739 | + | 0.925503i | \(0.376358\pi\) | |||||||
\(654\) | 9153.53 | 0.547296 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2437.22 | 0.145057 | ||||||||
\(657\) | −172.159 | −0.0102231 | ||||||||
\(658\) | −45950.9 | −2.72242 | ||||||||
\(659\) | 13640.4 | 0.806306 | 0.403153 | − | 0.915133i | \(-0.367914\pi\) | ||||
0.403153 | + | 0.915133i | \(0.367914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17052.0 | −1.00340 | −0.501699 | − | 0.865042i | \(-0.667291\pi\) | ||||
−0.501699 | + | 0.865042i | \(0.667291\pi\) | |||||||
\(662\) | 22649.6 | 1.32976 | ||||||||
\(663\) | 22081.9 | 1.29350 | ||||||||
\(664\) | −14498.2 | −0.847348 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1130.20 | −0.0657570 | ||||||||
\(667\) | −1041.36 | −0.0604521 | ||||||||
\(668\) | 854.302 | 0.0494820 | ||||||||
\(669\) | 16360.7 | 0.945500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19461.7 | 1.11969 | ||||||||
\(672\) | −12802.0 | −0.734892 | ||||||||
\(673\) | −16419.7 | −0.940467 | −0.470234 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470234 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(674\) | −28339.9 | −1.61960 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4899.14 | 0.278740 | ||||||||
\(677\) | −8670.47 | −0.492221 | −0.246110 | − | 0.969242i | \(-0.579153\pi\) | ||||
−0.246110 | + | 0.969242i | \(0.579153\pi\) | |||||||
\(678\) | −20656.6 | −1.17008 | ||||||||
\(679\) | 15856.9 | 0.896220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14331.4 | −0.806434 | ||||||||
\(682\) | 19328.0 | 1.08520 | ||||||||
\(683\) | 5973.36 | 0.334647 | 0.167324 | − | 0.985902i | \(-0.446488\pi\) | ||||
0.167324 | + | 0.985902i | \(0.446488\pi\) | |||||||
\(684\) | −426.425 | −0.0238374 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24568.5 | 1.36739 | ||||||||
\(687\) | −6256.52 | −0.347454 | ||||||||
\(688\) | −26036.4 | −1.44277 | ||||||||
\(689\) | 18341.2 | 1.01414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15316.3 | −0.843212 | −0.421606 | − | 0.906779i | \(-0.638533\pi\) | ||||
−0.421606 | + | 0.906779i | \(0.638533\pi\) | |||||||
\(692\) | −6353.78 | −0.349038 | ||||||||
\(693\) | 8610.85 | 0.472005 | ||||||||
\(694\) | −6210.09 | −0.339671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3615.36 | 0.196897 | ||||||||
\(697\) | 3715.65 | 0.201923 | ||||||||
\(698\) | −3857.29 | −0.209170 | ||||||||
\(699\) | 19453.6 | 1.05265 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34583.1 | 1.86332 | 0.931660 | − | 0.363333i | \(-0.118361\pi\) | ||||
0.931660 | + | 0.363333i | \(0.118361\pi\) | |||||||
\(702\) | −5508.74 | −0.296174 | ||||||||
\(703\) | 539.695 | 0.0289545 | ||||||||
\(704\) | 5184.74 | 0.277567 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19325.8 | −1.03022 | ||||||||
\(707\) | 10563.6 | 0.561929 | ||||||||
\(708\) | 3357.39 | 0.178218 | ||||||||
\(709\) | 11194.1 | 0.592955 | 0.296477 | − | 0.955040i | \(-0.404188\pi\) | ||||
0.296477 | + | 0.955040i | \(0.404188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2316.81 | 0.122204 | ||||||||
\(712\) | 16792.4 | 0.883877 | ||||||||
\(713\) | 2506.53 | 0.131655 | ||||||||
\(714\) | −37164.1 | −1.94794 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1892.61 | 0.0987850 | ||||||||
\(717\) | 6703.85 | 0.349177 | ||||||||
\(718\) | 18312.8 | 0.951847 | ||||||||
\(719\) | −15491.9 | −0.803549 | −0.401774 | − | 0.915739i | \(-0.631606\pi\) | ||||
−0.401774 | + | 0.915739i | \(0.631606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23458.2 | −1.21169 | ||||||||
\(722\) | −22338.7 | −1.15147 | ||||||||
\(723\) | −7179.04 | −0.369283 | ||||||||
\(724\) | −6439.83 | −0.330572 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3454.33 | −0.176587 | ||||||||
\(727\) | −6272.72 | −0.320003 | −0.160002 | − | 0.987117i | \(-0.551150\pi\) | ||||
−0.160002 | + | 0.987117i | \(0.551150\pi\) | |||||||
\(728\) | 29296.1 | 1.49146 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39693.6 | −2.00837 | ||||||||
\(732\) | 6096.02 | 0.307808 | ||||||||
\(733\) | 24980.5 | 1.25877 | 0.629383 | − | 0.777095i | \(-0.283308\pi\) | ||||
0.629383 | + | 0.777095i | \(0.283308\pi\) | |||||||
\(734\) | 28167.5 | 1.41646 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1919.90 | −0.0961530 | ||||||||
\(737\) | 8075.49 | 0.403615 | ||||||||
\(738\) | −926.938 | −0.0462345 | ||||||||
\(739\) | −30660.7 | −1.52621 | −0.763107 | − | 0.646272i | \(-0.776327\pi\) | ||||
−0.763107 | + | 0.646272i | \(0.776327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2630.56 | 0.130413 | ||||||||
\(742\) | −30868.5 | −1.52725 | ||||||||
\(743\) | −17205.7 | −0.849551 | −0.424776 | − | 0.905299i | \(-0.639647\pi\) | ||||
−0.424776 | + | 0.905299i | \(0.639647\pi\) | |||||||
\(744\) | −8702.12 | −0.428811 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9164.09 | 0.449760 | ||||||||
\(747\) | 8234.18 | 0.403310 | ||||||||
\(748\) | −12502.9 | −0.611165 | ||||||||
\(749\) | −43077.8 | −2.10151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18397.1 | 0.893901 | 0.446950 | − | 0.894559i | \(-0.352510\pi\) | ||||
0.446950 | + | 0.894559i | \(0.352510\pi\) | |||||||
\(752\) | 35727.2 | 1.73250 | ||||||||
\(753\) | −1837.98 | −0.0889506 | ||||||||
\(754\) | 15516.1 | 0.749422 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2697.19 | 0.129756 | ||||||||
\(757\) | 22305.1 | 1.07093 | 0.535465 | − | 0.844557i | \(-0.320136\pi\) | ||||
0.535465 | + | 0.844557i | \(0.320136\pi\) | |||||||
\(758\) | 11248.9 | 0.539023 | ||||||||
\(759\) | 1291.36 | 0.0617569 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14458.5 | 0.688727 | 0.344364 | − | 0.938836i | \(-0.388095\pi\) | ||||
0.344364 | + | 0.938836i | \(0.388095\pi\) | |||||||
\(762\) | 2838.04 | 0.134923 | ||||||||
\(763\) | 27647.3 | 1.31179 | ||||||||
\(764\) | −14175.0 | −0.671249 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35034.3 | 1.65253 | ||||||||
\(767\) | −20711.3 | −0.975022 | ||||||||
\(768\) | 12926.7 | 0.607361 | ||||||||
\(769\) | −39897.6 | −1.87093 | −0.935463 | − | 0.353424i | \(-0.885017\pi\) | ||||
−0.935463 | + | 0.353424i | \(0.885017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −918.337 | −0.0428964 | ||||||||
\(772\) | 9.76938 | 0.000455450 0 | ||||||||
\(773\) | 20070.2 | 0.933863 | 0.466931 | − | 0.884294i | \(-0.345359\pi\) | ||||
0.466931 | + | 0.884294i | \(0.345359\pi\) | |||||||
\(774\) | 9902.30 | 0.459859 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8256.08 | −0.381928 | ||||||||
\(777\) | −3413.63 | −0.157611 | ||||||||
\(778\) | 33008.7 | 1.52110 | ||||||||
\(779\) | 442.635 | 0.0203582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15692.0 | 0.718953 | ||||||||
\(782\) | −5573.47 | −0.254868 | ||||||||
\(783\) | −2053.33 | −0.0937164 | ||||||||
\(784\) | −46365.5 | −2.11213 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2449.20 | 0.111145 | ||||||||
\(787\) | 10733.0 | 0.486137 | 0.243069 | − | 0.970009i | \(-0.421846\pi\) | ||||
0.243069 | + | 0.970009i | \(0.421846\pi\) | |||||||
\(788\) | 1869.89 | 0.0845329 | ||||||||
\(789\) | 851.516 | 0.0384218 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −62391.1 | −2.80452 | ||||||||
\(792\) | −4483.33 | −0.201147 | ||||||||
\(793\) | −37605.5 | −1.68400 | ||||||||
\(794\) | −1465.76 | −0.0655139 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10013.1 | −0.445861 | ||||||||
\(797\) | −14335.8 | −0.637140 | −0.318570 | − | 0.947899i | \(-0.603203\pi\) | ||||
−0.318570 | + | 0.947899i | \(0.603203\pi\) | |||||||
\(798\) | −4427.26 | −0.196395 | ||||||||
\(799\) | 54467.7 | 2.41167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9537.13 | −0.420697 | ||||||||
\(802\) | −48709.0 | −2.14461 | ||||||||
\(803\) | −601.325 | −0.0264263 | ||||||||
\(804\) | 2529.49 | 0.110956 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37347.1 | −1.63213 | ||||||||
\(807\) | 7278.63 | 0.317497 | ||||||||
\(808\) | −5500.03 | −0.239468 | ||||||||
\(809\) | 20920.7 | 0.909187 | 0.454593 | − | 0.890699i | \(-0.349785\pi\) | ||||
0.454593 | + | 0.890699i | \(0.349785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12816.5 | 0.554931 | 0.277465 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277465 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(812\) | −7596.99 | −0.328328 | ||||||||
\(813\) | −524.838 | −0.0226407 | ||||||||
\(814\) | −3947.59 | −0.169979 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 28895.4 | 1.23963 | ||||||||
\(817\) | −4728.59 | −0.202488 | ||||||||
\(818\) | −40502.9 | −1.73124 | ||||||||
\(819\) | −16638.6 | −0.709889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7253.55 | 0.308344 | 0.154172 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154172 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(822\) | 9163.61 | 0.388829 | ||||||||
\(823\) | 35288.1 | 1.49461 | 0.747307 | − | 0.664479i | \(-0.231346\pi\) | ||||
0.747307 | + | 0.664479i | \(0.231346\pi\) | |||||||
\(824\) | 12213.8 | 0.516367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34857.3 | 1.46833 | ||||||||
\(827\) | −32205.9 | −1.35418 | −0.677092 | − | 0.735899i | \(-0.736760\pi\) | ||||
−0.677092 | + | 0.735899i | \(0.736760\pi\) | |||||||
\(828\) | 404.495 | 0.0169773 | ||||||||
\(829\) | 29993.3 | 1.25659 | 0.628294 | − | 0.777976i | \(-0.283754\pi\) | ||||
0.628294 | + | 0.777976i | \(0.283754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23421.2 | −0.977706 | ||||||||
\(832\) | −10018.4 | −0.417457 | ||||||||
\(833\) | −70686.2 | −2.94013 | ||||||||
\(834\) | −20652.4 | −0.857476 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1489.44 | −0.0616187 | ||||||||
\(837\) | 4942.33 | 0.204100 | ||||||||
\(838\) | 20297.7 | 0.836720 | ||||||||
\(839\) | −35608.7 | −1.46526 | −0.732628 | − | 0.680629i | \(-0.761706\pi\) | ||||
−0.732628 | + | 0.680629i | \(0.761706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18605.5 | −0.762865 | ||||||||
\(842\) | −33571.1 | −1.37403 | ||||||||
\(843\) | 1752.51 | 0.0716011 | ||||||||
\(844\) | −165.785 | −0.00676134 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13588.0 | −0.552203 | ||||||||
\(847\) | −10433.4 | −0.423255 | ||||||||
\(848\) | 24000.5 | 0.971911 | ||||||||
\(849\) | −17691.9 | −0.715177 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −511.940 | −0.0206217 | ||||||||
\(852\) | 4915.21 | 0.197644 | ||||||||
\(853\) | −11229.3 | −0.450744 | −0.225372 | − | 0.974273i | \(-0.572360\pi\) | ||||
−0.225372 | + | 0.974273i | \(0.572360\pi\) | |||||||
\(854\) | 63290.5 | 2.53601 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22428.9 | 0.895565 | ||||||||
\(857\) | 22136.1 | 0.882327 | 0.441164 | − | 0.897427i | \(-0.354566\pi\) | ||||
0.441164 | + | 0.897427i | \(0.354566\pi\) | |||||||
\(858\) | −19241.2 | −0.765598 | ||||||||
\(859\) | −820.727 | −0.0325994 | −0.0162997 | − | 0.999867i | \(-0.505189\pi\) | ||||
−0.0162997 | + | 0.999867i | \(0.505189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2799.72 | −0.110818 | ||||||||
\(862\) | 31329.5 | 1.23792 | ||||||||
\(863\) | −245.223 | −0.00967264 | −0.00483632 | − | 0.999988i | \(-0.501539\pi\) | ||||
−0.00483632 | + | 0.999988i | \(0.501539\pi\) | |||||||
\(864\) | −3785.63 | −0.149062 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26405.0 | −1.03612 | ||||||||
\(867\) | 29313.3 | 1.14825 | ||||||||
\(868\) | 18285.8 | 0.715048 | ||||||||
\(869\) | 8092.27 | 0.315894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15604.1 | −0.607032 | ||||||||
\(872\) | −14394.8 | −0.559026 | ||||||||
\(873\) | 4689.00 | 0.181785 | ||||||||
\(874\) | −663.952 | −0.0256963 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −188.354 | −0.00726471 | ||||||||
\(877\) | 37727.8 | 1.45265 | 0.726326 | − | 0.687350i | \(-0.241226\pi\) | ||||
0.726326 | + | 0.687350i | \(0.241226\pi\) | |||||||
\(878\) | 24896.4 | 0.956961 | ||||||||
\(879\) | 4829.19 | 0.185306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21738.8 | 0.831326 | 0.415663 | − | 0.909519i | \(-0.363550\pi\) | ||||
0.415663 | + | 0.909519i | \(0.363550\pi\) | |||||||
\(882\) | 17634.0 | 0.673205 | ||||||||
\(883\) | −44340.4 | −1.68989 | −0.844946 | − | 0.534852i | \(-0.820368\pi\) | ||||
−0.844946 | + | 0.534852i | \(0.820368\pi\) | |||||||
\(884\) | 24159.1 | 0.919184 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10223.3 | −0.387652 | ||||||||
\(887\) | −681.008 | −0.0257790 | −0.0128895 | − | 0.999917i | \(-0.504103\pi\) | ||||
−0.0128895 | + | 0.999917i | \(0.504103\pi\) | |||||||
\(888\) | 1777.34 | 0.0671664 | ||||||||
\(889\) | 8572.00 | 0.323392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2546.28 | 0.0957393 | ||||||||
\(892\) | 17899.7 | 0.671889 | ||||||||
\(893\) | 6488.58 | 0.243149 | ||||||||
\(894\) | 36287.6 | 1.35754 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50999.6 | 1.90154 | ||||||||
\(897\) | −2495.28 | −0.0928816 | ||||||||
\(898\) | −32070.3 | −1.19176 | ||||||||
\(899\) | −13920.7 | −0.516443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36589.8 | 1.35292 | ||||||||
\(902\) | −3237.65 | −0.119514 | ||||||||
\(903\) | 29908.9 | 1.10222 | ||||||||
\(904\) | 32484.6 | 1.19516 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13939.9 | 0.511173 | ||||||||
\(907\) | 5348.01 | 0.195786 | 0.0978929 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978929 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(908\) | −15679.5 | −0.573066 | ||||||||
\(909\) | 3123.72 | 0.113979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14488.7 | 0.526930 | 0.263465 | − | 0.964669i | \(-0.415135\pi\) | ||||
0.263465 | + | 0.964669i | \(0.415135\pi\) | |||||||
\(912\) | 3442.23 | 0.124982 | ||||||||
\(913\) | 28760.7 | 1.04254 | ||||||||
\(914\) | 45015.6 | 1.62908 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6845.05 | −0.246907 | ||||||||
\(917\) | 7397.56 | 0.266400 | ||||||||
\(918\) | −10989.7 | −0.395112 | ||||||||
\(919\) | −22546.9 | −0.809308 | −0.404654 | − | 0.914470i | \(-0.632608\pi\) | ||||
−0.404654 | + | 0.914470i | \(0.632608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 703.419 | 0.0251666 | ||||||||
\(922\) | −13895.9 | −0.496351 | ||||||||
\(923\) | −30321.3 | −1.08130 | ||||||||
\(924\) | 9420.85 | 0.335415 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −46944.9 | −1.66599 | ||||||||
\(927\) | −6936.74 | −0.245774 | ||||||||
\(928\) | 10662.7 | 0.377178 | ||||||||
\(929\) | −13980.7 | −0.493747 | −0.246874 | − | 0.969048i | \(-0.579403\pi\) | ||||
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8420.65 | −0.296429 | ||||||||
\(932\) | 21283.5 | 0.748032 | ||||||||
\(933\) | −5385.75 | −0.188984 | ||||||||
\(934\) | −36264.5 | −1.27046 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8663.05 | 0.302522 | ||||||||
\(937\) | 26362.6 | 0.919133 | 0.459567 | − | 0.888143i | \(-0.348005\pi\) | ||||
0.459567 | + | 0.888143i | \(0.348005\pi\) | |||||||
\(938\) | 26261.9 | 0.914159 | ||||||||
\(939\) | −25321.8 | −0.880029 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14715.6 | −0.509792 | −0.254896 | − | 0.966968i | \(-0.582041\pi\) | ||||
−0.254896 | + | 0.966968i | \(0.582041\pi\) | |||||||
\(942\) | −1327.60 | −0.0459188 | ||||||||
\(943\) | −419.871 | −0.0144994 | ||||||||
\(944\) | −27101.9 | −0.934419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34587.2 | 1.18872 | ||||||||
\(947\) | −11818.2 | −0.405532 | −0.202766 | − | 0.979227i | \(-0.564993\pi\) | ||||
−0.202766 | + | 0.979227i | \(0.564993\pi\) | |||||||
\(948\) | 2534.75 | 0.0868406 | ||||||||
\(949\) | 1161.93 | 0.0397448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31655.1 | 1.07937 | ||||||||
\(952\) | 58444.2 | 1.98969 | ||||||||
\(953\) | −43832.3 | −1.48989 | −0.744945 | − | 0.667125i | \(-0.767524\pi\) | ||||
−0.744945 | + | 0.667125i | \(0.767524\pi\) | |||||||
\(954\) | −9128.00 | −0.309780 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7334.46 | 0.248131 | ||||||||
\(957\) | −7171.95 | −0.242253 | ||||||||
\(958\) | 48933.8 | 1.65029 | ||||||||
\(959\) | 27677.7 | 0.931971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3716.00 | 0.124736 | ||||||||
\(962\) | 7627.86 | 0.255647 | ||||||||
\(963\) | −12738.4 | −0.426260 | ||||||||
\(964\) | −7854.36 | −0.262419 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4199.58 | 0.139875 | ||||||||
\(967\) | 10696.2 | 0.355706 | 0.177853 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(968\) | 5432.27 | 0.180372 | ||||||||
\(969\) | 5247.83 | 0.173978 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27933.0 | 0.923187 | 0.461593 | − | 0.887092i | \(-0.347278\pi\) | ||||
0.461593 | + | 0.887092i | \(0.347278\pi\) | |||||||
\(972\) | 797.575 | 0.0263192 | ||||||||
\(973\) | −62378.4 | −2.05525 | ||||||||
\(974\) | −38481.4 | −1.26594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −49208.9 | −1.61387 | ||||||||
\(977\) | 24341.7 | 0.797094 | 0.398547 | − | 0.917148i | \(-0.369515\pi\) | ||||
0.398547 | + | 0.917148i | \(0.369515\pi\) | |||||||
\(978\) | 29199.6 | 0.954704 | ||||||||
\(979\) | −33311.7 | −1.08748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8175.48 | 0.266078 | ||||||||
\(982\) | −66057.7 | −2.14662 | ||||||||
\(983\) | 12553.0 | 0.407301 | 0.203651 | − | 0.979044i | \(-0.434719\pi\) | ||||
0.203651 | + | 0.979044i | \(0.434719\pi\) | |||||||
\(984\) | 1457.70 | 0.0472254 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30953.9 | 0.999769 | ||||||||
\(987\) | −41041.0 | −1.32356 | ||||||||
\(988\) | 2878.01 | 0.0926737 | ||||||||
\(989\) | 4485.41 | 0.144214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45631.8 | −1.46271 | −0.731353 | − | 0.681999i | \(-0.761111\pi\) | ||||
−0.731353 | + | 0.681999i | \(0.761111\pi\) | |||||||
\(992\) | −25665.0 | −0.821437 | ||||||||
\(993\) | 20229.5 | 0.646490 | ||||||||
\(994\) | 51031.0 | 1.62838 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9008.74 | 0.286599 | ||||||||
\(997\) | −34499.0 | −1.09588 | −0.547941 | − | 0.836517i | \(-0.684588\pi\) | ||||
−0.547941 | + | 0.836517i | \(0.684588\pi\) | |||||||
\(998\) | 28145.3 | 0.892708 | ||||||||
\(999\) | −1009.43 | −0.0319690 |
(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 | 75.4.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 225.4.a.n.1.1 | 2 | |||
4.3 | odd | 2 | 1200.4.a.bl.1.1 | 2 | |||
5.2 | odd | 4 | 75.4.b.c.49.3 | 4 | |||
5.3 | odd | 4 | 75.4.b.c.49.2 | 4 | |||
5.4 | even | 2 | 75.4.a.e.1.1 | yes | 2 | ||
15.2 | even | 4 | 225.4.b.h.199.2 | 4 | |||
15.8 | even | 4 | 225.4.b.h.199.3 | 4 | |||
15.14 | odd | 2 | 225.4.a.j.1.2 | 2 | |||
20.3 | even | 4 | 1200.4.f.v.49.2 | 4 | |||
20.7 | even | 4 | 1200.4.f.v.49.3 | 4 | |||
20.19 | odd | 2 | 1200.4.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
75.4.a.e.1.1 | yes | 2 | 5.4 | even | 2 | ||
75.4.b.c.49.2 | 4 | 5.3 | odd | 4 | |||
75.4.b.c.49.3 | 4 | 5.2 | odd | 4 | |||
225.4.a.j.1.2 | 2 | 15.14 | odd | 2 | |||
225.4.a.n.1.1 | 2 | 3.2 | odd | 2 | |||
225.4.b.h.199.2 | 4 | 15.2 | even | 4 | |||
225.4.b.h.199.3 | 4 | 15.8 | even | 4 | |||
1200.4.a.bl.1.1 | 2 | 4.3 | odd | 2 | |||
1200.4.a.bu.1.2 | 2 | 20.19 | odd | 2 | |||
1200.4.f.v.49.2 | 4 | 20.3 | even | 4 | |||
1200.4.f.v.49.3 | 4 | 20.7 | even | 4 |