Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, 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("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-4.88324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.88324 | 1.72649 | 0.863243 | − | 0.504788i | \(-0.168429\pi\) | ||||
0.863243 | + | 0.504788i | \(0.168429\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 15.8460 | 1.98076 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −14.6497 | −0.996787 | ||||||||
\(7\) | 5.48750 | 0.296297 | 0.148149 | − | 0.988965i | \(-0.452669\pi\) | ||||
0.148149 | + | 0.988965i | \(0.452669\pi\) | |||||||
\(8\) | 38.3141 | 1.69326 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 24.4162 | 0.772108 | ||||||||
\(11\) | 50.1324 | 1.37413 | 0.687067 | − | 0.726594i | \(-0.258898\pi\) | ||||
0.687067 | + | 0.726594i | \(0.258898\pi\) | |||||||
\(12\) | −47.5381 | −1.14359 | ||||||||
\(13\) | −20.7349 | −0.442371 | −0.221186 | − | 0.975232i | \(-0.570993\pi\) | ||||
−0.221186 | + | 0.975232i | \(0.570993\pi\) | |||||||
\(14\) | 26.7968 | 0.511553 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 60.3288 | 0.942637 | ||||||||
\(17\) | −18.8027 | −0.268255 | −0.134127 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134127 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(18\) | 43.9492 | 0.575496 | ||||||||
\(19\) | 78.8346 | 0.951890 | 0.475945 | − | 0.879475i | \(-0.342106\pi\) | ||||
0.475945 | + | 0.879475i | \(0.342106\pi\) | |||||||
\(20\) | 79.2302 | 0.885821 | ||||||||
\(21\) | −16.4625 | −0.171067 | ||||||||
\(22\) | 244.809 | 2.37243 | ||||||||
\(23\) | −6.33763 | −0.0574559 | −0.0287280 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287280 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(24\) | −114.942 | −0.977605 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −101.254 | −0.763748 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 86.9552 | 0.586892 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −73.2486 | −0.445777 | ||||||||
\(31\) | 310.950 | 1.80156 | 0.900778 | − | 0.434280i | \(-0.142997\pi\) | ||||
0.900778 | + | 0.434280i | \(0.142997\pi\) | |||||||
\(32\) | −11.9130 | −0.0658106 | ||||||||
\(33\) | −150.397 | −0.793357 | ||||||||
\(34\) | −91.8182 | −0.463138 | ||||||||
\(35\) | 27.4375 | 0.132508 | ||||||||
\(36\) | 142.614 | 0.660252 | ||||||||
\(37\) | −338.745 | −1.50512 | −0.752558 | − | 0.658525i | \(-0.771180\pi\) | ||||
−0.752558 | + | 0.658525i | \(0.771180\pi\) | |||||||
\(38\) | 384.969 | 1.64343 | ||||||||
\(39\) | 62.2047 | 0.255403 | ||||||||
\(40\) | 191.571 | 0.757250 | ||||||||
\(41\) | 353.526 | 1.34662 | 0.673312 | − | 0.739359i | \(-0.264871\pi\) | ||||
0.673312 | + | 0.739359i | \(0.264871\pi\) | |||||||
\(42\) | −80.3904 | −0.295345 | ||||||||
\(43\) | 507.609 | 1.80022 | 0.900112 | − | 0.435658i | \(-0.143484\pi\) | ||||
0.900112 | + | 0.435658i | \(0.143484\pi\) | |||||||
\(44\) | 794.400 | 2.72183 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −30.9482 | −0.0991969 | ||||||||
\(47\) | −112.771 | −0.349986 | −0.174993 | − | 0.984570i | \(-0.555990\pi\) | ||||
−0.174993 | + | 0.984570i | \(0.555990\pi\) | |||||||
\(48\) | −180.986 | −0.544232 | ||||||||
\(49\) | −312.887 | −0.912208 | ||||||||
\(50\) | 122.081 | 0.345297 | ||||||||
\(51\) | 56.4081 | 0.154877 | ||||||||
\(52\) | −328.566 | −0.876230 | ||||||||
\(53\) | −144.849 | −0.375406 | −0.187703 | − | 0.982226i | \(-0.560104\pi\) | ||||
−0.187703 | + | 0.982226i | \(0.560104\pi\) | |||||||
\(54\) | −131.848 | −0.332262 | ||||||||
\(55\) | 250.662 | 0.614532 | ||||||||
\(56\) | 210.249 | 0.501709 | ||||||||
\(57\) | −236.504 | −0.549574 | ||||||||
\(58\) | 141.614 | 0.320600 | ||||||||
\(59\) | −342.739 | −0.756285 | −0.378142 | − | 0.925747i | \(-0.623437\pi\) | ||||
−0.378142 | + | 0.925747i | \(0.623437\pi\) | |||||||
\(60\) | −237.691 | −0.511429 | ||||||||
\(61\) | 357.486 | 0.750350 | 0.375175 | − | 0.926954i | \(-0.377583\pi\) | ||||
0.375175 | + | 0.926954i | \(0.377583\pi\) | |||||||
\(62\) | 1518.44 | 3.11036 | ||||||||
\(63\) | 49.3875 | 0.0987657 | ||||||||
\(64\) | −540.804 | −1.05626 | ||||||||
\(65\) | −103.675 | −0.197834 | ||||||||
\(66\) | −734.426 | −1.36972 | ||||||||
\(67\) | −183.087 | −0.333844 | −0.166922 | − | 0.985970i | \(-0.553383\pi\) | ||||
−0.166922 | + | 0.985970i | \(0.553383\pi\) | |||||||
\(68\) | −297.949 | −0.531347 | ||||||||
\(69\) | 19.0129 | 0.0331722 | ||||||||
\(70\) | 133.984 | 0.228773 | ||||||||
\(71\) | −594.034 | −0.992942 | −0.496471 | − | 0.868053i | \(-0.665371\pi\) | ||||
−0.496471 | + | 0.868053i | \(0.665371\pi\) | |||||||
\(72\) | 344.827 | 0.564421 | ||||||||
\(73\) | −622.609 | −0.998231 | −0.499115 | − | 0.866536i | \(-0.666342\pi\) | ||||
−0.499115 | + | 0.866536i | \(0.666342\pi\) | |||||||
\(74\) | −1654.17 | −2.59856 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 1249.22 | 1.88546 | ||||||||
\(77\) | 275.102 | 0.407152 | ||||||||
\(78\) | 303.761 | 0.440950 | ||||||||
\(79\) | −1275.18 | −1.81607 | −0.908034 | − | 0.418897i | \(-0.862417\pi\) | ||||
−0.908034 | + | 0.418897i | \(0.862417\pi\) | |||||||
\(80\) | 301.644 | 0.421560 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1726.35 | 2.32493 | ||||||||
\(83\) | −739.108 | −0.977441 | −0.488720 | − | 0.872440i | \(-0.662536\pi\) | ||||
−0.488720 | + | 0.872440i | \(0.662536\pi\) | |||||||
\(84\) | −260.866 | −0.338842 | ||||||||
\(85\) | −94.0136 | −0.119967 | ||||||||
\(86\) | 2478.78 | 3.10806 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | 1920.78 | 2.32677 | ||||||||
\(89\) | 906.113 | 1.07919 | 0.539594 | − | 0.841925i | \(-0.318578\pi\) | ||||
0.539594 | + | 0.841925i | \(0.318578\pi\) | |||||||
\(90\) | 219.746 | 0.257369 | ||||||||
\(91\) | −113.783 | −0.131073 | ||||||||
\(92\) | −100.426 | −0.113806 | ||||||||
\(93\) | −932.849 | −1.04013 | ||||||||
\(94\) | −550.688 | −0.604246 | ||||||||
\(95\) | 394.173 | 0.425698 | ||||||||
\(96\) | 35.7390 | 0.0379958 | ||||||||
\(97\) | 76.0665 | 0.0796225 | 0.0398112 | − | 0.999207i | \(-0.487324\pi\) | ||||
0.0398112 | + | 0.999207i | \(0.487324\pi\) | |||||||
\(98\) | −1527.90 | −1.57491 | ||||||||
\(99\) | 451.192 | 0.458045 | ||||||||
\(100\) | 396.151 | 0.396151 | ||||||||
\(101\) | 653.553 | 0.643871 | 0.321935 | − | 0.946762i | \(-0.395667\pi\) | ||||
0.321935 | + | 0.946762i | \(0.395667\pi\) | |||||||
\(102\) | 275.455 | 0.267393 | ||||||||
\(103\) | 969.801 | 0.927741 | 0.463871 | − | 0.885903i | \(-0.346460\pi\) | ||||
0.463871 | + | 0.885903i | \(0.346460\pi\) | |||||||
\(104\) | −794.440 | −0.749050 | ||||||||
\(105\) | −82.3125 | −0.0765036 | ||||||||
\(106\) | −707.332 | −0.648133 | ||||||||
\(107\) | −1267.53 | −1.14520 | −0.572601 | − | 0.819835i | \(-0.694065\pi\) | ||||
−0.572601 | + | 0.819835i | \(0.694065\pi\) | |||||||
\(108\) | −427.843 | −0.381197 | ||||||||
\(109\) | −808.142 | −0.710146 | −0.355073 | − | 0.934838i | \(-0.615544\pi\) | ||||
−0.355073 | + | 0.934838i | \(0.615544\pi\) | |||||||
\(110\) | 1224.04 | 1.06098 | ||||||||
\(111\) | 1016.23 | 0.868980 | ||||||||
\(112\) | 331.054 | 0.279301 | ||||||||
\(113\) | −1220.10 | −1.01572 | −0.507862 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507862 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(114\) | −1154.91 | −0.948832 | ||||||||
\(115\) | −31.6881 | −0.0256951 | ||||||||
\(116\) | 459.535 | 0.367817 | ||||||||
\(117\) | −186.614 | −0.147457 | ||||||||
\(118\) | −1673.68 | −1.30572 | ||||||||
\(119\) | −103.180 | −0.0794831 | ||||||||
\(120\) | −574.712 | −0.437198 | ||||||||
\(121\) | 1182.26 | 0.888247 | ||||||||
\(122\) | 1745.69 | 1.29547 | ||||||||
\(123\) | −1060.58 | −0.777473 | ||||||||
\(124\) | 4927.32 | 3.56844 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 241.171 | 0.170518 | ||||||||
\(127\) | 814.733 | 0.569258 | 0.284629 | − | 0.958638i | \(-0.408130\pi\) | ||||
0.284629 | + | 0.958638i | \(0.408130\pi\) | |||||||
\(128\) | −2545.57 | −1.75781 | ||||||||
\(129\) | −1522.83 | −1.03936 | ||||||||
\(130\) | −506.268 | −0.341559 | ||||||||
\(131\) | −1493.91 | −0.996363 | −0.498181 | − | 0.867073i | \(-0.665999\pi\) | ||||
−0.498181 | + | 0.867073i | \(0.665999\pi\) | |||||||
\(132\) | −2383.20 | −1.57145 | ||||||||
\(133\) | 432.605 | 0.282042 | ||||||||
\(134\) | −894.056 | −0.576378 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −720.410 | −0.454225 | ||||||||
\(137\) | −1608.72 | −1.00323 | −0.501615 | − | 0.865091i | \(-0.667261\pi\) | ||||
−0.501615 | + | 0.865091i | \(0.667261\pi\) | |||||||
\(138\) | 92.8445 | 0.0572714 | ||||||||
\(139\) | 51.5725 | 0.0314700 | 0.0157350 | − | 0.999876i | \(-0.494991\pi\) | ||||
0.0157350 | + | 0.999876i | \(0.494991\pi\) | |||||||
\(140\) | 434.776 | 0.262466 | ||||||||
\(141\) | 338.313 | 0.202064 | ||||||||
\(142\) | −2900.81 | −1.71430 | ||||||||
\(143\) | −1039.49 | −0.607878 | ||||||||
\(144\) | 542.959 | 0.314212 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | −3040.35 | −1.72343 | ||||||||
\(147\) | 938.662 | 0.526664 | ||||||||
\(148\) | −5367.77 | −2.98127 | ||||||||
\(149\) | −608.330 | −0.334472 | −0.167236 | − | 0.985917i | \(-0.553484\pi\) | ||||
−0.167236 | + | 0.985917i | \(0.553484\pi\) | |||||||
\(150\) | −366.243 | −0.199357 | ||||||||
\(151\) | −341.568 | −0.184082 | −0.0920412 | − | 0.995755i | \(-0.529339\pi\) | ||||
−0.0920412 | + | 0.995755i | \(0.529339\pi\) | |||||||
\(152\) | 3020.48 | 1.61180 | ||||||||
\(153\) | −169.224 | −0.0894182 | ||||||||
\(154\) | 1343.39 | 0.702943 | ||||||||
\(155\) | 1554.75 | 0.805680 | ||||||||
\(156\) | 985.699 | 0.505891 | ||||||||
\(157\) | −358.378 | −0.182176 | −0.0910882 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910882 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(158\) | −6227.03 | −3.13542 | ||||||||
\(159\) | 434.547 | 0.216741 | ||||||||
\(160\) | −59.5650 | −0.0294314 | ||||||||
\(161\) | −34.7777 | −0.0170240 | ||||||||
\(162\) | 395.543 | 0.191832 | ||||||||
\(163\) | −1667.36 | −0.801213 | −0.400606 | − | 0.916250i | \(-0.631201\pi\) | ||||
−0.400606 | + | 0.916250i | \(0.631201\pi\) | |||||||
\(164\) | 5602.00 | 2.66733 | ||||||||
\(165\) | −751.986 | −0.354800 | ||||||||
\(166\) | −3609.24 | −1.68754 | ||||||||
\(167\) | −1832.30 | −0.849029 | −0.424514 | − | 0.905421i | \(-0.639555\pi\) | ||||
−0.424514 | + | 0.905421i | \(0.639555\pi\) | |||||||
\(168\) | −630.746 | −0.289662 | ||||||||
\(169\) | −1767.06 | −0.804308 | ||||||||
\(170\) | −459.091 | −0.207122 | ||||||||
\(171\) | 709.512 | 0.317297 | ||||||||
\(172\) | 8043.60 | 3.56580 | ||||||||
\(173\) | 2034.77 | 0.894224 | 0.447112 | − | 0.894478i | \(-0.352453\pi\) | ||||
0.447112 | + | 0.894478i | \(0.352453\pi\) | |||||||
\(174\) | −424.842 | −0.185099 | ||||||||
\(175\) | 137.188 | 0.0592594 | ||||||||
\(176\) | 3024.43 | 1.29531 | ||||||||
\(177\) | 1028.22 | 0.436641 | ||||||||
\(178\) | 4424.77 | 1.86320 | ||||||||
\(179\) | −332.198 | −0.138713 | −0.0693566 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693566 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(180\) | 713.072 | 0.295274 | ||||||||
\(181\) | −843.391 | −0.346347 | −0.173173 | − | 0.984891i | \(-0.555402\pi\) | ||||
−0.173173 | + | 0.984891i | \(0.555402\pi\) | |||||||
\(182\) | −555.629 | −0.226296 | ||||||||
\(183\) | −1072.46 | −0.433215 | ||||||||
\(184\) | −242.821 | −0.0972879 | ||||||||
\(185\) | −1693.72 | −0.673109 | ||||||||
\(186\) | −4555.33 | −1.79577 | ||||||||
\(187\) | −942.625 | −0.368618 | ||||||||
\(188\) | −1786.97 | −0.693236 | ||||||||
\(189\) | −148.163 | −0.0570224 | ||||||||
\(190\) | 1924.84 | 0.734962 | ||||||||
\(191\) | 2438.81 | 0.923908 | 0.461954 | − | 0.886904i | \(-0.347148\pi\) | ||||
0.461954 | + | 0.886904i | \(0.347148\pi\) | |||||||
\(192\) | 1622.41 | 0.609831 | ||||||||
\(193\) | 4095.03 | 1.52729 | 0.763645 | − | 0.645637i | \(-0.223408\pi\) | ||||
0.763645 | + | 0.645637i | \(0.223408\pi\) | |||||||
\(194\) | 371.451 | 0.137467 | ||||||||
\(195\) | 311.024 | 0.114220 | ||||||||
\(196\) | −4958.03 | −1.80686 | ||||||||
\(197\) | 3226.76 | 1.16699 | 0.583495 | − | 0.812117i | \(-0.301685\pi\) | ||||
0.583495 | + | 0.812117i | \(0.301685\pi\) | |||||||
\(198\) | 2203.28 | 0.790809 | ||||||||
\(199\) | −4218.74 | −1.50281 | −0.751404 | − | 0.659842i | \(-0.770623\pi\) | ||||
−0.751404 | + | 0.659842i | \(0.770623\pi\) | |||||||
\(200\) | 957.853 | 0.338652 | ||||||||
\(201\) | 549.260 | 0.192745 | ||||||||
\(202\) | 3191.46 | 1.11163 | ||||||||
\(203\) | 159.138 | 0.0550210 | ||||||||
\(204\) | 893.846 | 0.306773 | ||||||||
\(205\) | 1767.63 | 0.602228 | ||||||||
\(206\) | 4735.77 | 1.60173 | ||||||||
\(207\) | −57.0387 | −0.0191520 | ||||||||
\(208\) | −1250.91 | −0.416996 | ||||||||
\(209\) | 3952.17 | 1.30803 | ||||||||
\(210\) | −401.952 | −0.132082 | ||||||||
\(211\) | −2798.33 | −0.913010 | −0.456505 | − | 0.889721i | \(-0.650899\pi\) | ||||
−0.456505 | + | 0.889721i | \(0.650899\pi\) | |||||||
\(212\) | −2295.28 | −0.743588 | ||||||||
\(213\) | 1782.10 | 0.573276 | ||||||||
\(214\) | −6189.64 | −1.97717 | ||||||||
\(215\) | 2538.05 | 0.805085 | ||||||||
\(216\) | −1034.48 | −0.325868 | ||||||||
\(217\) | 1706.34 | 0.533796 | ||||||||
\(218\) | −3946.35 | −1.22606 | ||||||||
\(219\) | 1867.83 | 0.576329 | ||||||||
\(220\) | 3972.00 | 1.21724 | ||||||||
\(221\) | 389.872 | 0.118668 | ||||||||
\(222\) | 4962.52 | 1.50028 | ||||||||
\(223\) | 2496.01 | 0.749529 | 0.374764 | − | 0.927120i | \(-0.377724\pi\) | ||||
0.374764 | + | 0.927120i | \(0.377724\pi\) | |||||||
\(224\) | −65.3725 | −0.0194995 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −5958.02 | −1.75364 | ||||||||
\(227\) | 3409.57 | 0.996920 | 0.498460 | − | 0.866913i | \(-0.333899\pi\) | ||||
0.498460 | + | 0.866913i | \(0.333899\pi\) | |||||||
\(228\) | −3747.65 | −1.08857 | ||||||||
\(229\) | 4794.47 | 1.38353 | 0.691763 | − | 0.722125i | \(-0.256834\pi\) | ||||
0.691763 | + | 0.722125i | \(0.256834\pi\) | |||||||
\(230\) | −154.741 | −0.0443622 | ||||||||
\(231\) | −825.305 | −0.235069 | ||||||||
\(232\) | 1111.11 | 0.314431 | ||||||||
\(233\) | 1989.36 | 0.559345 | 0.279672 | − | 0.960095i | \(-0.409774\pi\) | ||||
0.279672 | + | 0.960095i | \(0.409774\pi\) | |||||||
\(234\) | −911.282 | −0.254583 | ||||||||
\(235\) | −563.855 | −0.156518 | ||||||||
\(236\) | −5431.06 | −1.49802 | ||||||||
\(237\) | 3825.55 | 1.04851 | ||||||||
\(238\) | −503.852 | −0.137226 | ||||||||
\(239\) | 2574.69 | 0.696832 | 0.348416 | − | 0.937340i | \(-0.386720\pi\) | ||||
0.348416 | + | 0.937340i | \(0.386720\pi\) | |||||||
\(240\) | −904.932 | −0.243388 | ||||||||
\(241\) | −3683.44 | −0.984528 | −0.492264 | − | 0.870446i | \(-0.663831\pi\) | ||||
−0.492264 | + | 0.870446i | \(0.663831\pi\) | |||||||
\(242\) | 5773.24 | 1.53355 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 5664.73 | 1.48626 | ||||||||
\(245\) | −1564.44 | −0.407952 | ||||||||
\(246\) | −5179.06 | −1.34230 | ||||||||
\(247\) | −1634.63 | −0.421089 | ||||||||
\(248\) | 11913.8 | 3.05050 | ||||||||
\(249\) | 2217.32 | 0.564326 | ||||||||
\(250\) | 610.405 | 0.154422 | ||||||||
\(251\) | 4631.27 | 1.16463 | 0.582317 | − | 0.812962i | \(-0.302146\pi\) | ||||
0.582317 | + | 0.812962i | \(0.302146\pi\) | |||||||
\(252\) | 782.597 | 0.195631 | ||||||||
\(253\) | −317.720 | −0.0789522 | ||||||||
\(254\) | 3978.54 | 0.982817 | ||||||||
\(255\) | 282.041 | 0.0692630 | ||||||||
\(256\) | −8104.22 | −1.97857 | ||||||||
\(257\) | −1609.98 | −0.390770 | −0.195385 | − | 0.980727i | \(-0.562596\pi\) | ||||
−0.195385 | + | 0.980727i | \(0.562596\pi\) | |||||||
\(258\) | −7436.33 | −1.79444 | ||||||||
\(259\) | −1858.86 | −0.445962 | ||||||||
\(260\) | −1642.83 | −0.391862 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | −7295.12 | −1.72021 | ||||||||
\(263\) | −2868.22 | −0.672479 | −0.336239 | − | 0.941777i | \(-0.609155\pi\) | ||||
−0.336239 | + | 0.941777i | \(0.609155\pi\) | |||||||
\(264\) | −5762.34 | −1.34336 | ||||||||
\(265\) | −724.244 | −0.167887 | ||||||||
\(266\) | 2112.52 | 0.486942 | ||||||||
\(267\) | −2718.34 | −0.623070 | ||||||||
\(268\) | −2901.20 | −0.661264 | ||||||||
\(269\) | −554.047 | −0.125579 | −0.0627896 | − | 0.998027i | \(-0.520000\pi\) | ||||
−0.0627896 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(270\) | −659.238 | −0.148592 | ||||||||
\(271\) | −1826.02 | −0.409309 | −0.204655 | − | 0.978834i | \(-0.565607\pi\) | ||||
−0.204655 | + | 0.978834i | \(0.565607\pi\) | |||||||
\(272\) | −1134.35 | −0.252867 | ||||||||
\(273\) | 341.348 | 0.0756752 | ||||||||
\(274\) | −7855.79 | −1.73206 | ||||||||
\(275\) | 1253.31 | 0.274827 | ||||||||
\(276\) | 301.279 | 0.0657060 | ||||||||
\(277\) | 1470.00 | 0.318859 | 0.159429 | − | 0.987209i | \(-0.449035\pi\) | ||||
0.159429 | + | 0.987209i | \(0.449035\pi\) | |||||||
\(278\) | 251.841 | 0.0543325 | ||||||||
\(279\) | 2798.55 | 0.600519 | ||||||||
\(280\) | 1051.24 | 0.224371 | ||||||||
\(281\) | 7826.43 | 1.66151 | 0.830757 | − | 0.556635i | \(-0.187908\pi\) | ||||
0.830757 | + | 0.556635i | \(0.187908\pi\) | |||||||
\(282\) | 1652.06 | 0.348861 | ||||||||
\(283\) | −6796.87 | −1.42767 | −0.713837 | − | 0.700312i | \(-0.753044\pi\) | ||||
−0.713837 | + | 0.700312i | \(0.753044\pi\) | |||||||
\(284\) | −9413.10 | −1.96678 | ||||||||
\(285\) | −1182.52 | −0.245777 | ||||||||
\(286\) | −5076.08 | −1.04949 | ||||||||
\(287\) | 1939.98 | 0.399001 | ||||||||
\(288\) | −107.217 | −0.0219369 | ||||||||
\(289\) | −4559.46 | −0.928039 | ||||||||
\(290\) | 708.070 | 0.143377 | ||||||||
\(291\) | −228.199 | −0.0459701 | ||||||||
\(292\) | −9865.89 | −1.97725 | ||||||||
\(293\) | 3631.49 | 0.724074 | 0.362037 | − | 0.932164i | \(-0.382081\pi\) | ||||
0.362037 | + | 0.932164i | \(0.382081\pi\) | |||||||
\(294\) | 4583.71 | 0.909277 | ||||||||
\(295\) | −1713.69 | −0.338221 | ||||||||
\(296\) | −12978.7 | −2.54856 | ||||||||
\(297\) | −1353.57 | −0.264452 | ||||||||
\(298\) | −2970.62 | −0.577461 | ||||||||
\(299\) | 131.410 | 0.0254169 | ||||||||
\(300\) | −1188.45 | −0.228718 | ||||||||
\(301\) | 2785.50 | 0.533401 | ||||||||
\(302\) | −1667.96 | −0.317816 | ||||||||
\(303\) | −1960.66 | −0.371739 | ||||||||
\(304\) | 4756.00 | 0.897287 | ||||||||
\(305\) | 1787.43 | 0.335567 | ||||||||
\(306\) | −826.364 | −0.154379 | ||||||||
\(307\) | −9080.77 | −1.68817 | −0.844083 | − | 0.536213i | \(-0.819854\pi\) | ||||
−0.844083 | + | 0.536213i | \(0.819854\pi\) | |||||||
\(308\) | 4359.27 | 0.806469 | ||||||||
\(309\) | −2909.40 | −0.535632 | ||||||||
\(310\) | 7592.21 | 1.39100 | ||||||||
\(311\) | 2657.69 | 0.484577 | 0.242289 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242289 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(312\) | 2383.32 | 0.432464 | ||||||||
\(313\) | −530.474 | −0.0957960 | −0.0478980 | − | 0.998852i | \(-0.515252\pi\) | ||||
−0.0478980 | + | 0.998852i | \(0.515252\pi\) | |||||||
\(314\) | −1750.05 | −0.314525 | ||||||||
\(315\) | 246.938 | 0.0441694 | ||||||||
\(316\) | −20206.6 | −3.59719 | ||||||||
\(317\) | 2393.66 | 0.424106 | 0.212053 | − | 0.977258i | \(-0.431985\pi\) | ||||
0.212053 | + | 0.977258i | \(0.431985\pi\) | |||||||
\(318\) | 2122.00 | 0.374200 | ||||||||
\(319\) | 1453.84 | 0.255170 | ||||||||
\(320\) | −2704.02 | −0.472373 | ||||||||
\(321\) | 3802.58 | 0.661182 | ||||||||
\(322\) | −169.828 | −0.0293918 | ||||||||
\(323\) | −1482.31 | −0.255349 | ||||||||
\(324\) | 1283.53 | 0.220084 | ||||||||
\(325\) | −518.373 | −0.0884743 | ||||||||
\(326\) | −8142.12 | −1.38328 | ||||||||
\(327\) | 2424.43 | 0.410003 | ||||||||
\(328\) | 13545.1 | 2.28019 | ||||||||
\(329\) | −618.830 | −0.103700 | ||||||||
\(330\) | −3672.13 | −0.612558 | ||||||||
\(331\) | −7984.54 | −1.32589 | −0.662945 | − | 0.748668i | \(-0.730694\pi\) | ||||
−0.662945 | + | 0.748668i | \(0.730694\pi\) | |||||||
\(332\) | −11711.9 | −1.93607 | ||||||||
\(333\) | −3048.70 | −0.501706 | ||||||||
\(334\) | −8947.57 | −1.46584 | ||||||||
\(335\) | −915.433 | −0.149300 | ||||||||
\(336\) | −993.163 | −0.161254 | ||||||||
\(337\) | 9704.45 | 1.56865 | 0.784325 | − | 0.620350i | \(-0.213010\pi\) | ||||
0.784325 | + | 0.620350i | \(0.213010\pi\) | |||||||
\(338\) | −8629.00 | −1.38863 | ||||||||
\(339\) | 3660.29 | 0.586429 | ||||||||
\(340\) | −1489.74 | −0.237626 | ||||||||
\(341\) | 15588.7 | 2.47558 | ||||||||
\(342\) | 3464.72 | 0.547808 | ||||||||
\(343\) | −3599.18 | −0.566582 | ||||||||
\(344\) | 19448.6 | 3.04825 | ||||||||
\(345\) | 95.0644 | 0.0148351 | ||||||||
\(346\) | 9936.27 | 1.54387 | ||||||||
\(347\) | 5514.04 | 0.853053 | 0.426526 | − | 0.904475i | \(-0.359737\pi\) | ||||
0.426526 | + | 0.904475i | \(0.359737\pi\) | |||||||
\(348\) | −1378.61 | −0.212359 | ||||||||
\(349\) | 2521.06 | 0.386674 | 0.193337 | − | 0.981132i | \(-0.438069\pi\) | ||||
0.193337 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(350\) | 669.920 | 0.102311 | ||||||||
\(351\) | 559.842 | 0.0851344 | ||||||||
\(352\) | −597.227 | −0.0904326 | ||||||||
\(353\) | 5721.03 | 0.862606 | 0.431303 | − | 0.902207i | \(-0.358054\pi\) | ||||
0.431303 | + | 0.902207i | \(0.358054\pi\) | |||||||
\(354\) | 5021.03 | 0.753855 | ||||||||
\(355\) | −2970.17 | −0.444057 | ||||||||
\(356\) | 14358.3 | 2.13761 | ||||||||
\(357\) | 309.540 | 0.0458896 | ||||||||
\(358\) | −1622.20 | −0.239486 | ||||||||
\(359\) | 6403.95 | 0.941470 | 0.470735 | − | 0.882275i | \(-0.343989\pi\) | ||||
0.470735 | + | 0.882275i | \(0.343989\pi\) | |||||||
\(360\) | 1724.14 | 0.252417 | ||||||||
\(361\) | −644.098 | −0.0939055 | ||||||||
\(362\) | −4118.48 | −0.597963 | ||||||||
\(363\) | −3546.77 | −0.512830 | ||||||||
\(364\) | −1803.01 | −0.259624 | ||||||||
\(365\) | −3113.04 | −0.446422 | ||||||||
\(366\) | −5237.06 | −0.747939 | ||||||||
\(367\) | 13350.7 | 1.89891 | 0.949456 | − | 0.313899i | \(-0.101635\pi\) | ||||
0.949456 | + | 0.313899i | \(0.101635\pi\) | |||||||
\(368\) | −382.341 | −0.0541601 | ||||||||
\(369\) | 3181.74 | 0.448874 | ||||||||
\(370\) | −8270.87 | −1.16211 | ||||||||
\(371\) | −794.858 | −0.111232 | ||||||||
\(372\) | −14782.0 | −2.06024 | ||||||||
\(373\) | −1367.05 | −0.189767 | −0.0948837 | − | 0.995488i | \(-0.530248\pi\) | ||||
−0.0948837 | + | 0.995488i | \(0.530248\pi\) | |||||||
\(374\) | −4603.07 | −0.636414 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −4320.72 | −0.592617 | ||||||||
\(377\) | −601.312 | −0.0821463 | ||||||||
\(378\) | −723.513 | −0.0984484 | ||||||||
\(379\) | 9882.96 | 1.33945 | 0.669727 | − | 0.742607i | \(-0.266411\pi\) | ||||
0.669727 | + | 0.742607i | \(0.266411\pi\) | |||||||
\(380\) | 6246.09 | 0.843204 | ||||||||
\(381\) | −2444.20 | −0.328662 | ||||||||
\(382\) | 11909.3 | 1.59511 | ||||||||
\(383\) | 13225.8 | 1.76450 | 0.882252 | − | 0.470777i | \(-0.156026\pi\) | ||||
0.882252 | + | 0.470777i | \(0.156026\pi\) | |||||||
\(384\) | 7636.72 | 1.01487 | ||||||||
\(385\) | 1375.51 | 0.182084 | ||||||||
\(386\) | 19997.0 | 2.63684 | ||||||||
\(387\) | 4568.48 | 0.600075 | ||||||||
\(388\) | 1205.35 | 0.157713 | ||||||||
\(389\) | −8442.16 | −1.10035 | −0.550173 | − | 0.835051i | \(-0.685438\pi\) | ||||
−0.550173 | + | 0.835051i | \(0.685438\pi\) | |||||||
\(390\) | 1518.80 | 0.197199 | ||||||||
\(391\) | 119.165 | 0.0154128 | ||||||||
\(392\) | −11988.0 | −1.54461 | ||||||||
\(393\) | 4481.73 | 0.575250 | ||||||||
\(394\) | 15757.0 | 2.01479 | ||||||||
\(395\) | −6375.92 | −0.812170 | ||||||||
\(396\) | 7149.60 | 0.907275 | ||||||||
\(397\) | −2268.55 | −0.286789 | −0.143394 | − | 0.989666i | \(-0.545802\pi\) | ||||
−0.143394 | + | 0.989666i | \(0.545802\pi\) | |||||||
\(398\) | −20601.1 | −2.59458 | ||||||||
\(399\) | −1297.82 | −0.162837 | ||||||||
\(400\) | 1508.22 | 0.188527 | ||||||||
\(401\) | 8294.00 | 1.03287 | 0.516437 | − | 0.856325i | \(-0.327258\pi\) | ||||
0.516437 | + | 0.856325i | \(0.327258\pi\) | |||||||
\(402\) | 2682.17 | 0.332772 | ||||||||
\(403\) | −6447.51 | −0.796957 | ||||||||
\(404\) | 10356.2 | 1.27535 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 777.107 | 0.0949930 | ||||||||
\(407\) | −16982.1 | −2.06823 | ||||||||
\(408\) | 2161.23 | 0.262247 | ||||||||
\(409\) | 9913.01 | 1.19845 | 0.599226 | − | 0.800580i | \(-0.295475\pi\) | ||||
0.599226 | + | 0.800580i | \(0.295475\pi\) | |||||||
\(410\) | 8631.77 | 1.03974 | ||||||||
\(411\) | 4826.17 | 0.579216 | ||||||||
\(412\) | 15367.5 | 1.83763 | ||||||||
\(413\) | −1880.78 | −0.224085 | ||||||||
\(414\) | −278.534 | −0.0330656 | ||||||||
\(415\) | −3695.54 | −0.437125 | ||||||||
\(416\) | 247.015 | 0.0291127 | ||||||||
\(417\) | −154.718 | −0.0181692 | ||||||||
\(418\) | 19299.4 | 2.25829 | ||||||||
\(419\) | −13332.1 | −1.55446 | −0.777228 | − | 0.629219i | \(-0.783375\pi\) | ||||
−0.777228 | + | 0.629219i | \(0.783375\pi\) | |||||||
\(420\) | −1304.33 | −0.151535 | ||||||||
\(421\) | −2848.13 | −0.329714 | −0.164857 | − | 0.986317i | \(-0.552716\pi\) | ||||
−0.164857 | + | 0.986317i | \(0.552716\pi\) | |||||||
\(422\) | −13664.9 | −1.57630 | ||||||||
\(423\) | −1014.94 | −0.116662 | ||||||||
\(424\) | −5549.76 | −0.635661 | ||||||||
\(425\) | −470.068 | −0.0536509 | ||||||||
\(426\) | 8702.44 | 0.989752 | ||||||||
\(427\) | 1961.70 | 0.222326 | ||||||||
\(428\) | −20085.3 | −2.26836 | ||||||||
\(429\) | 3118.47 | 0.350958 | ||||||||
\(430\) | 12393.9 | 1.38997 | ||||||||
\(431\) | 12669.7 | 1.41595 | 0.707977 | − | 0.706235i | \(-0.249608\pi\) | ||||
0.707977 | + | 0.706235i | \(0.249608\pi\) | |||||||
\(432\) | −1628.88 | −0.181411 | ||||||||
\(433\) | −14545.6 | −1.61436 | −0.807178 | − | 0.590308i | \(-0.799006\pi\) | ||||
−0.807178 | + | 0.590308i | \(0.799006\pi\) | |||||||
\(434\) | 8332.45 | 0.921591 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | −12805.9 | −1.40663 | ||||||||
\(437\) | −499.625 | −0.0546917 | ||||||||
\(438\) | 9121.05 | 0.995024 | ||||||||
\(439\) | 11489.4 | 1.24911 | 0.624557 | − | 0.780979i | \(-0.285280\pi\) | ||||
0.624557 | + | 0.780979i | \(0.285280\pi\) | |||||||
\(440\) | 9603.90 | 1.04056 | ||||||||
\(441\) | −2815.99 | −0.304069 | ||||||||
\(442\) | 1903.84 | 0.204879 | ||||||||
\(443\) | −11125.7 | −1.19322 | −0.596611 | − | 0.802531i | \(-0.703486\pi\) | ||||
−0.596611 | + | 0.802531i | \(0.703486\pi\) | |||||||
\(444\) | 16103.3 | 1.72124 | ||||||||
\(445\) | 4530.57 | 0.482628 | ||||||||
\(446\) | 12188.6 | 1.29405 | ||||||||
\(447\) | 1824.99 | 0.193107 | ||||||||
\(448\) | −2967.66 | −0.312966 | ||||||||
\(449\) | −6676.79 | −0.701776 | −0.350888 | − | 0.936418i | \(-0.614120\pi\) | ||||
−0.350888 | + | 0.936418i | \(0.614120\pi\) | |||||||
\(450\) | 1098.73 | 0.115099 | ||||||||
\(451\) | 17723.1 | 1.85044 | ||||||||
\(452\) | −19333.7 | −2.01190 | ||||||||
\(453\) | 1024.70 | 0.106280 | ||||||||
\(454\) | 16649.7 | 1.72117 | ||||||||
\(455\) | −568.914 | −0.0586178 | ||||||||
\(456\) | −9061.44 | −0.930572 | ||||||||
\(457\) | −10826.9 | −1.10823 | −0.554114 | − | 0.832441i | \(-0.686943\pi\) | ||||
−0.554114 | + | 0.832441i | \(0.686943\pi\) | |||||||
\(458\) | 23412.6 | 2.38864 | ||||||||
\(459\) | 507.673 | 0.0516256 | ||||||||
\(460\) | −502.132 | −0.0508957 | ||||||||
\(461\) | −4114.21 | −0.415657 | −0.207829 | − | 0.978165i | \(-0.566640\pi\) | ||||
−0.207829 | + | 0.978165i | \(0.566640\pi\) | |||||||
\(462\) | −4030.16 | −0.405844 | ||||||||
\(463\) | −6107.19 | −0.613014 | −0.306507 | − | 0.951868i | \(-0.599160\pi\) | ||||
−0.306507 | + | 0.951868i | \(0.599160\pi\) | |||||||
\(464\) | 1749.54 | 0.175043 | ||||||||
\(465\) | −4664.25 | −0.465160 | ||||||||
\(466\) | 9714.53 | 0.965701 | ||||||||
\(467\) | −1409.31 | −0.139647 | −0.0698235 | − | 0.997559i | \(-0.522244\pi\) | ||||
−0.0698235 | + | 0.997559i | \(0.522244\pi\) | |||||||
\(468\) | −2957.10 | −0.292077 | ||||||||
\(469\) | −1004.69 | −0.0989172 | ||||||||
\(470\) | −2753.44 | −0.270227 | ||||||||
\(471\) | 1075.13 | 0.105180 | ||||||||
\(472\) | −13131.7 | −1.28059 | ||||||||
\(473\) | 25447.7 | 2.47375 | ||||||||
\(474\) | 18681.1 | 1.81023 | ||||||||
\(475\) | 1970.87 | 0.190378 | ||||||||
\(476\) | −1634.99 | −0.157437 | ||||||||
\(477\) | −1303.64 | −0.125135 | ||||||||
\(478\) | 12572.8 | 1.20307 | ||||||||
\(479\) | 12633.9 | 1.20513 | 0.602566 | − | 0.798069i | \(-0.294145\pi\) | ||||
0.602566 | + | 0.798069i | \(0.294145\pi\) | |||||||
\(480\) | 178.695 | 0.0169922 | ||||||||
\(481\) | 7023.84 | 0.665821 | ||||||||
\(482\) | −17987.1 | −1.69977 | ||||||||
\(483\) | 104.333 | 0.00982883 | ||||||||
\(484\) | 18734.1 | 1.75940 | ||||||||
\(485\) | 380.332 | 0.0356083 | ||||||||
\(486\) | −1186.63 | −0.110754 | ||||||||
\(487\) | −17024.7 | −1.58411 | −0.792056 | − | 0.610449i | \(-0.790989\pi\) | ||||
−0.792056 | + | 0.610449i | \(0.790989\pi\) | |||||||
\(488\) | 13696.7 | 1.27054 | ||||||||
\(489\) | 5002.08 | 0.462580 | ||||||||
\(490\) | −7639.52 | −0.704323 | ||||||||
\(491\) | −3792.47 | −0.348578 | −0.174289 | − | 0.984695i | \(-0.555763\pi\) | ||||
−0.174289 | + | 0.984695i | \(0.555763\pi\) | |||||||
\(492\) | −16806.0 | −1.53998 | ||||||||
\(493\) | −545.279 | −0.0498136 | ||||||||
\(494\) | −7982.29 | −0.727004 | ||||||||
\(495\) | 2255.96 | 0.204844 | ||||||||
\(496\) | 18759.2 | 1.69821 | ||||||||
\(497\) | −3259.76 | −0.294206 | ||||||||
\(498\) | 10827.7 | 0.974301 | ||||||||
\(499\) | 6484.19 | 0.581708 | 0.290854 | − | 0.956767i | \(-0.406061\pi\) | ||||
0.290854 | + | 0.956767i | \(0.406061\pi\) | |||||||
\(500\) | 1980.76 | 0.177164 | ||||||||
\(501\) | 5496.91 | 0.490187 | ||||||||
\(502\) | 22615.6 | 2.01073 | ||||||||
\(503\) | −8781.60 | −0.778434 | −0.389217 | − | 0.921146i | \(-0.627254\pi\) | ||||
−0.389217 | + | 0.921146i | \(0.627254\pi\) | |||||||
\(504\) | 1892.24 | 0.167236 | ||||||||
\(505\) | 3267.76 | 0.287948 | ||||||||
\(506\) | −1551.51 | −0.136310 | ||||||||
\(507\) | 5301.19 | 0.464367 | ||||||||
\(508\) | 12910.3 | 1.12756 | ||||||||
\(509\) | 21343.3 | 1.85860 | 0.929299 | − | 0.369328i | \(-0.120412\pi\) | ||||
0.929299 | + | 0.369328i | \(0.120412\pi\) | |||||||
\(510\) | 1377.27 | 0.119582 | ||||||||
\(511\) | −3416.57 | −0.295773 | ||||||||
\(512\) | −19210.3 | −1.65817 | ||||||||
\(513\) | −2128.54 | −0.183191 | ||||||||
\(514\) | −7861.93 | −0.674659 | ||||||||
\(515\) | 4849.01 | 0.414898 | ||||||||
\(516\) | −24130.8 | −2.05872 | ||||||||
\(517\) | −5653.48 | −0.480928 | ||||||||
\(518\) | −9077.28 | −0.769947 | ||||||||
\(519\) | −6104.31 | −0.516280 | ||||||||
\(520\) | −3972.20 | −0.334985 | ||||||||
\(521\) | 7007.06 | 0.589223 | 0.294611 | − | 0.955617i | \(-0.404810\pi\) | ||||
0.294611 | + | 0.955617i | \(0.404810\pi\) | |||||||
\(522\) | 1274.53 | 0.106867 | ||||||||
\(523\) | −5901.85 | −0.493441 | −0.246721 | − | 0.969087i | \(-0.579353\pi\) | ||||
−0.246721 | + | 0.969087i | \(0.579353\pi\) | |||||||
\(524\) | −23672.6 | −1.97355 | ||||||||
\(525\) | −411.563 | −0.0342134 | ||||||||
\(526\) | −14006.2 | −1.16103 | ||||||||
\(527\) | −5846.70 | −0.483276 | ||||||||
\(528\) | −9073.28 | −0.747848 | ||||||||
\(529\) | −12126.8 | −0.996699 | ||||||||
\(530\) | −3536.66 | −0.289854 | ||||||||
\(531\) | −3084.65 | −0.252095 | ||||||||
\(532\) | 6855.08 | 0.558657 | ||||||||
\(533\) | −7330.34 | −0.595707 | ||||||||
\(534\) | −13274.3 | −1.07572 | ||||||||
\(535\) | −6337.64 | −0.512149 | ||||||||
\(536\) | −7014.80 | −0.565286 | ||||||||
\(537\) | 996.595 | 0.0800861 | ||||||||
\(538\) | −2705.54 | −0.216811 | ||||||||
\(539\) | −15685.8 | −1.25350 | ||||||||
\(540\) | −2139.22 | −0.170476 | ||||||||
\(541\) | 7826.71 | 0.621990 | 0.310995 | − | 0.950412i | \(-0.399338\pi\) | ||||
0.310995 | + | 0.950412i | \(0.399338\pi\) | |||||||
\(542\) | −8916.90 | −0.706667 | ||||||||
\(543\) | 2530.17 | 0.199963 | ||||||||
\(544\) | 223.997 | 0.0176540 | ||||||||
\(545\) | −4040.71 | −0.317587 | ||||||||
\(546\) | 1666.89 | 0.130652 | ||||||||
\(547\) | 4256.78 | 0.332737 | 0.166368 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166368 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(548\) | −25491.9 | −1.98716 | ||||||||
\(549\) | 3217.37 | 0.250117 | ||||||||
\(550\) | 6120.21 | 0.474485 | ||||||||
\(551\) | 2286.20 | 0.176762 | ||||||||
\(552\) | 728.462 | 0.0561692 | ||||||||
\(553\) | −6997.57 | −0.538096 | ||||||||
\(554\) | 7178.38 | 0.550506 | ||||||||
\(555\) | 5081.17 | 0.388620 | ||||||||
\(556\) | 817.221 | 0.0623343 | ||||||||
\(557\) | −11138.6 | −0.847324 | −0.423662 | − | 0.905820i | \(-0.639256\pi\) | ||||
−0.423662 | + | 0.905820i | \(0.639256\pi\) | |||||||
\(558\) | 13666.0 | 1.03679 | ||||||||
\(559\) | −10525.2 | −0.796368 | ||||||||
\(560\) | 1655.27 | 0.124907 | ||||||||
\(561\) | 2827.88 | 0.212822 | ||||||||
\(562\) | 38218.3 | 2.86858 | ||||||||
\(563\) | 16458.1 | 1.23202 | 0.616009 | − | 0.787739i | \(-0.288748\pi\) | ||||
0.616009 | + | 0.787739i | \(0.288748\pi\) | |||||||
\(564\) | 5360.92 | 0.400240 | ||||||||
\(565\) | −6100.48 | −0.454246 | ||||||||
\(566\) | −33190.7 | −2.46486 | ||||||||
\(567\) | 444.488 | 0.0329219 | ||||||||
\(568\) | −22759.9 | −1.68131 | ||||||||
\(569\) | 2449.68 | 0.180485 | 0.0902423 | − | 0.995920i | \(-0.471236\pi\) | ||||
0.0902423 | + | 0.995920i | \(0.471236\pi\) | |||||||
\(570\) | −5774.53 | −0.424331 | ||||||||
\(571\) | 156.880 | 0.0114978 | 0.00574888 | − | 0.999983i | \(-0.498170\pi\) | ||||
0.00574888 | + | 0.999983i | \(0.498170\pi\) | |||||||
\(572\) | −16471.8 | −1.20406 | ||||||||
\(573\) | −7316.44 | −0.533419 | ||||||||
\(574\) | 9473.37 | 0.688869 | ||||||||
\(575\) | −158.441 | −0.0114912 | ||||||||
\(576\) | −4867.24 | −0.352086 | ||||||||
\(577\) | −20318.3 | −1.46597 | −0.732984 | − | 0.680246i | \(-0.761873\pi\) | ||||
−0.732984 | + | 0.680246i | \(0.761873\pi\) | |||||||
\(578\) | −22264.9 | −1.60225 | ||||||||
\(579\) | −12285.1 | −0.881781 | ||||||||
\(580\) | 2297.68 | 0.164493 | ||||||||
\(581\) | −4055.85 | −0.289613 | ||||||||
\(582\) | −1114.35 | −0.0793667 | ||||||||
\(583\) | −7261.62 | −0.515859 | ||||||||
\(584\) | −23854.7 | −1.69027 | ||||||||
\(585\) | −933.071 | −0.0659448 | ||||||||
\(586\) | 17733.4 | 1.25010 | ||||||||
\(587\) | −9510.91 | −0.668752 | −0.334376 | − | 0.942440i | \(-0.608525\pi\) | ||||
−0.334376 | + | 0.942440i | \(0.608525\pi\) | |||||||
\(588\) | 14874.1 | 1.04319 | ||||||||
\(589\) | 24513.6 | 1.71488 | ||||||||
\(590\) | −8368.38 | −0.583934 | ||||||||
\(591\) | −9680.27 | −0.673762 | ||||||||
\(592\) | −20436.1 | −1.41878 | ||||||||
\(593\) | −15977.2 | −1.10641 | −0.553207 | − | 0.833044i | \(-0.686596\pi\) | ||||
−0.553207 | + | 0.833044i | \(0.686596\pi\) | |||||||
\(594\) | −6609.83 | −0.456574 | ||||||||
\(595\) | −515.900 | −0.0355459 | ||||||||
\(596\) | −9639.62 | −0.662507 | ||||||||
\(597\) | 12656.2 | 0.867647 | ||||||||
\(598\) | 641.707 | 0.0438819 | ||||||||
\(599\) | −4002.17 | −0.272995 | −0.136498 | − | 0.990640i | \(-0.543585\pi\) | ||||
−0.136498 | + | 0.990640i | \(0.543585\pi\) | |||||||
\(600\) | −2873.56 | −0.195521 | ||||||||
\(601\) | −1574.81 | −0.106885 | −0.0534425 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534425 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(602\) | 13602.3 | 0.920910 | ||||||||
\(603\) | −1647.78 | −0.111281 | ||||||||
\(604\) | −5412.51 | −0.364622 | ||||||||
\(605\) | 5911.28 | 0.397236 | ||||||||
\(606\) | −9574.37 | −0.641802 | ||||||||
\(607\) | −8803.52 | −0.588672 | −0.294336 | − | 0.955702i | \(-0.595098\pi\) | ||||
−0.294336 | + | 0.955702i | \(0.595098\pi\) | |||||||
\(608\) | −939.156 | −0.0626444 | ||||||||
\(609\) | −477.413 | −0.0317664 | ||||||||
\(610\) | 8728.44 | 0.579351 | ||||||||
\(611\) | 2338.29 | 0.154824 | ||||||||
\(612\) | −2681.54 | −0.177116 | ||||||||
\(613\) | 16874.2 | 1.11181 | 0.555907 | − | 0.831245i | \(-0.312371\pi\) | ||||
0.555907 | + | 0.831245i | \(0.312371\pi\) | |||||||
\(614\) | −44343.6 | −2.91460 | ||||||||
\(615\) | −5302.90 | −0.347697 | ||||||||
\(616\) | 10540.3 | 0.689415 | ||||||||
\(617\) | 4592.02 | 0.299624 | 0.149812 | − | 0.988715i | \(-0.452133\pi\) | ||||
0.149812 | + | 0.988715i | \(0.452133\pi\) | |||||||
\(618\) | −14207.3 | −0.924761 | ||||||||
\(619\) | 4982.48 | 0.323526 | 0.161763 | − | 0.986830i | \(-0.448282\pi\) | ||||
0.161763 | + | 0.986830i | \(0.448282\pi\) | |||||||
\(620\) | 24636.6 | 1.59586 | ||||||||
\(621\) | 171.116 | 0.0110574 | ||||||||
\(622\) | 12978.1 | 0.836616 | ||||||||
\(623\) | 4972.30 | 0.319761 | ||||||||
\(624\) | 3752.74 | 0.240753 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2590.43 | −0.165391 | ||||||||
\(627\) | −11856.5 | −0.755189 | ||||||||
\(628\) | −5678.88 | −0.360847 | ||||||||
\(629\) | 6369.32 | 0.403755 | ||||||||
\(630\) | 1205.86 | 0.0762578 | ||||||||
\(631\) | 20584.3 | 1.29865 | 0.649325 | − | 0.760511i | \(-0.275051\pi\) | ||||
0.649325 | + | 0.760511i | \(0.275051\pi\) | |||||||
\(632\) | −48857.6 | −3.07508 | ||||||||
\(633\) | 8394.99 | 0.527126 | ||||||||
\(634\) | 11688.8 | 0.732213 | ||||||||
\(635\) | 4073.66 | 0.254580 | ||||||||
\(636\) | 6885.84 | 0.429310 | ||||||||
\(637\) | 6487.69 | 0.403535 | ||||||||
\(638\) | 7099.45 | 0.440548 | ||||||||
\(639\) | −5346.31 | −0.330981 | ||||||||
\(640\) | −12727.9 | −0.786115 | ||||||||
\(641\) | 4840.03 | 0.298237 | 0.149118 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149118 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(642\) | 18568.9 | 1.14152 | ||||||||
\(643\) | 1340.16 | 0.0821941 | 0.0410970 | − | 0.999155i | \(-0.486915\pi\) | ||||
0.0410970 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(644\) | −551.090 | −0.0337205 | ||||||||
\(645\) | −7614.14 | −0.464816 | ||||||||
\(646\) | −7238.46 | −0.440856 | ||||||||
\(647\) | 15752.3 | 0.957169 | 0.478585 | − | 0.878041i | \(-0.341150\pi\) | ||||
0.478585 | + | 0.878041i | \(0.341150\pi\) | |||||||
\(648\) | 3103.44 | 0.188140 | ||||||||
\(649\) | −17182.3 | −1.03924 | ||||||||
\(650\) | −2531.34 | −0.152750 | ||||||||
\(651\) | −5119.01 | −0.308187 | ||||||||
\(652\) | −26421.1 | −1.58701 | ||||||||
\(653\) | 2290.66 | 0.137275 | 0.0686373 | − | 0.997642i | \(-0.478135\pi\) | ||||
0.0686373 | + | 0.997642i | \(0.478135\pi\) | |||||||
\(654\) | 11839.1 | 0.707865 | ||||||||
\(655\) | −7469.55 | −0.445587 | ||||||||
\(656\) | 21327.8 | 1.26938 | ||||||||
\(657\) | −5603.48 | −0.332744 | ||||||||
\(658\) | −3021.90 | −0.179036 | ||||||||
\(659\) | −3003.49 | −0.177541 | −0.0887704 | − | 0.996052i | \(-0.528294\pi\) | ||||
−0.0887704 | + | 0.996052i | \(0.528294\pi\) | |||||||
\(660\) | −11916.0 | −0.702772 | ||||||||
\(661\) | 8104.71 | 0.476909 | 0.238454 | − | 0.971154i | \(-0.423359\pi\) | ||||
0.238454 | + | 0.971154i | \(0.423359\pi\) | |||||||
\(662\) | −38990.4 | −2.28913 | ||||||||
\(663\) | −1169.62 | −0.0685131 | ||||||||
\(664\) | −28318.3 | −1.65506 | ||||||||
\(665\) | 2163.03 | 0.126133 | ||||||||
\(666\) | −14887.6 | −0.866188 | ||||||||
\(667\) | −183.791 | −0.0106693 | ||||||||
\(668\) | −29034.7 | −1.68172 | ||||||||
\(669\) | −7488.02 | −0.432741 | ||||||||
\(670\) | −4470.28 | −0.257764 | ||||||||
\(671\) | 17921.6 | 1.03108 | ||||||||
\(672\) | 196.118 | 0.0112580 | ||||||||
\(673\) | 5747.03 | 0.329170 | 0.164585 | − | 0.986363i | \(-0.447371\pi\) | ||||
0.164585 | + | 0.986363i | \(0.447371\pi\) | |||||||
\(674\) | 47389.2 | 2.70825 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −28001.0 | −1.59314 | ||||||||
\(677\) | 25714.2 | 1.45979 | 0.729895 | − | 0.683559i | \(-0.239569\pi\) | ||||
0.729895 | + | 0.683559i | \(0.239569\pi\) | |||||||
\(678\) | 17874.1 | 1.01246 | ||||||||
\(679\) | 417.415 | 0.0235919 | ||||||||
\(680\) | −3602.05 | −0.203136 | ||||||||
\(681\) | −10228.7 | −0.575572 | ||||||||
\(682\) | 76123.2 | 4.27406 | ||||||||
\(683\) | 4007.09 | 0.224490 | 0.112245 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112245 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(684\) | 11243.0 | 0.628487 | ||||||||
\(685\) | −8043.62 | −0.448658 | ||||||||
\(686\) | −17575.7 | −0.978196 | ||||||||
\(687\) | −14383.4 | −0.798779 | ||||||||
\(688\) | 30623.4 | 1.69696 | ||||||||
\(689\) | 3003.43 | 0.166069 | ||||||||
\(690\) | 464.223 | 0.0256125 | ||||||||
\(691\) | −27863.7 | −1.53399 | −0.766993 | − | 0.641655i | \(-0.778248\pi\) | ||||
−0.766993 | + | 0.641655i | \(0.778248\pi\) | |||||||
\(692\) | 32243.1 | 1.77124 | ||||||||
\(693\) | 2475.91 | 0.135717 | ||||||||
\(694\) | 26926.4 | 1.47278 | ||||||||
\(695\) | 257.863 | 0.0140738 | ||||||||
\(696\) | −3333.33 | −0.181537 | ||||||||
\(697\) | −6647.26 | −0.361238 | ||||||||
\(698\) | 12311.0 | 0.667588 | ||||||||
\(699\) | −5968.08 | −0.322938 | ||||||||
\(700\) | 2173.88 | 0.117378 | ||||||||
\(701\) | 12916.0 | 0.695906 | 0.347953 | − | 0.937512i | \(-0.386877\pi\) | ||||
0.347953 | + | 0.937512i | \(0.386877\pi\) | |||||||
\(702\) | 2733.85 | 0.146983 | ||||||||
\(703\) | −26704.8 | −1.43271 | ||||||||
\(704\) | −27111.8 | −1.45144 | ||||||||
\(705\) | 1691.56 | 0.0903659 | ||||||||
\(706\) | 27937.2 | 1.48928 | ||||||||
\(707\) | 3586.37 | 0.190777 | ||||||||
\(708\) | 16293.2 | 0.864880 | ||||||||
\(709\) | −30250.8 | −1.60239 | −0.801193 | − | 0.598406i | \(-0.795801\pi\) | ||||
−0.801193 | + | 0.598406i | \(0.795801\pi\) | |||||||
\(710\) | −14504.1 | −0.766659 | ||||||||
\(711\) | −11476.7 | −0.605356 | ||||||||
\(712\) | 34716.9 | 1.82735 | ||||||||
\(713\) | −1970.68 | −0.103510 | ||||||||
\(714\) | 1511.56 | 0.0792277 | ||||||||
\(715\) | −5197.45 | −0.271851 | ||||||||
\(716\) | −5264.03 | −0.274757 | ||||||||
\(717\) | −7724.07 | −0.402316 | ||||||||
\(718\) | 31272.1 | 1.62544 | ||||||||
\(719\) | 6161.35 | 0.319582 | 0.159791 | − | 0.987151i | \(-0.448918\pi\) | ||||
0.159791 | + | 0.987151i | \(0.448918\pi\) | |||||||
\(720\) | 2714.80 | 0.140520 | ||||||||
\(721\) | 5321.78 | 0.274887 | ||||||||
\(722\) | −3145.29 | −0.162127 | ||||||||
\(723\) | 11050.3 | 0.568417 | ||||||||
\(724\) | −13364.4 | −0.686029 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | −17319.7 | −0.885393 | ||||||||
\(727\) | −35454.3 | −1.80870 | −0.904352 | − | 0.426786i | \(-0.859646\pi\) | ||||
−0.904352 | + | 0.426786i | \(0.859646\pi\) | |||||||
\(728\) | −4359.49 | −0.221941 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −15201.7 | −0.770742 | ||||||||
\(731\) | −9544.43 | −0.482919 | ||||||||
\(732\) | −16994.2 | −0.858092 | ||||||||
\(733\) | −26681.1 | −1.34446 | −0.672231 | − | 0.740342i | \(-0.734664\pi\) | ||||
−0.672231 | + | 0.740342i | \(0.734664\pi\) | |||||||
\(734\) | 65194.7 | 3.27845 | ||||||||
\(735\) | 4693.31 | 0.235531 | ||||||||
\(736\) | 75.5001 | 0.00378121 | ||||||||
\(737\) | −9178.57 | −0.458747 | ||||||||
\(738\) | 15537.2 | 0.774976 | ||||||||
\(739\) | −28886.6 | −1.43791 | −0.718953 | − | 0.695059i | \(-0.755378\pi\) | ||||
−0.718953 | + | 0.695059i | \(0.755378\pi\) | |||||||
\(740\) | −26838.8 | −1.33326 | ||||||||
\(741\) | 4903.89 | 0.243116 | ||||||||
\(742\) | −3881.48 | −0.192040 | ||||||||
\(743\) | −16398.0 | −0.809669 | −0.404834 | − | 0.914390i | \(-0.632671\pi\) | ||||
−0.404834 | + | 0.914390i | \(0.632671\pi\) | |||||||
\(744\) | −35741.3 | −1.76121 | ||||||||
\(745\) | −3041.65 | −0.149580 | ||||||||
\(746\) | −6675.64 | −0.327631 | ||||||||
\(747\) | −6651.97 | −0.325814 | ||||||||
\(748\) | −14936.9 | −0.730142 | ||||||||
\(749\) | −6955.56 | −0.339320 | ||||||||
\(750\) | −1831.22 | −0.0891554 | ||||||||
\(751\) | −5905.21 | −0.286930 | −0.143465 | − | 0.989655i | \(-0.545824\pi\) | ||||
−0.143465 | + | 0.989655i | \(0.545824\pi\) | |||||||
\(752\) | −6803.33 | −0.329910 | ||||||||
\(753\) | −13893.8 | −0.672402 | ||||||||
\(754\) | −2936.35 | −0.141824 | ||||||||
\(755\) | −1707.84 | −0.0823241 | ||||||||
\(756\) | −2347.79 | −0.112947 | ||||||||
\(757\) | −12439.0 | −0.597229 | −0.298614 | − | 0.954374i | \(-0.596524\pi\) | ||||
−0.298614 | + | 0.954374i | \(0.596524\pi\) | |||||||
\(758\) | 48260.9 | 2.31255 | ||||||||
\(759\) | 953.161 | 0.0455831 | ||||||||
\(760\) | 15102.4 | 0.720818 | ||||||||
\(761\) | 14270.0 | 0.679748 | 0.339874 | − | 0.940471i | \(-0.389616\pi\) | ||||
0.339874 | + | 0.940471i | \(0.389616\pi\) | |||||||
\(762\) | −11935.6 | −0.567430 | ||||||||
\(763\) | −4434.68 | −0.210414 | ||||||||
\(764\) | 38645.6 | 1.83004 | ||||||||
\(765\) | −846.122 | −0.0399890 | ||||||||
\(766\) | 64584.6 | 3.04639 | ||||||||
\(767\) | 7106.66 | 0.334559 | ||||||||
\(768\) | 24312.7 | 1.14233 | ||||||||
\(769\) | −15143.9 | −0.710147 | −0.355074 | − | 0.934838i | \(-0.615544\pi\) | ||||
−0.355074 | + | 0.934838i | \(0.615544\pi\) | |||||||
\(770\) | 6716.94 | 0.314366 | ||||||||
\(771\) | 4829.95 | 0.225611 | ||||||||
\(772\) | 64890.1 | 3.02519 | ||||||||
\(773\) | −40617.2 | −1.88991 | −0.944955 | − | 0.327202i | \(-0.893894\pi\) | ||||
−0.944955 | + | 0.327202i | \(0.893894\pi\) | |||||||
\(774\) | 22309.0 | 1.03602 | ||||||||
\(775\) | 7773.74 | 0.360311 | ||||||||
\(776\) | 2914.42 | 0.134822 | ||||||||
\(777\) | 5576.59 | 0.257476 | ||||||||
\(778\) | −41225.1 | −1.89973 | ||||||||
\(779\) | 27870.1 | 1.28184 | ||||||||
\(780\) | 4928.49 | 0.226241 | ||||||||
\(781\) | −29780.4 | −1.36444 | ||||||||
\(782\) | 581.910 | 0.0266100 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | −18876.1 | −0.859881 | ||||||||
\(785\) | −1791.89 | −0.0814718 | ||||||||
\(786\) | 21885.4 | 0.993162 | ||||||||
\(787\) | 43878.2 | 1.98741 | 0.993703 | − | 0.112048i | \(-0.0357412\pi\) | ||||
0.993703 | + | 0.112048i | \(0.0357412\pi\) | |||||||
\(788\) | 51131.3 | 2.31152 | ||||||||
\(789\) | 8604.66 | 0.388256 | ||||||||
\(790\) | −31135.1 | −1.40220 | ||||||||
\(791\) | −6695.27 | −0.300956 | ||||||||
\(792\) | 17287.0 | 0.775590 | ||||||||
\(793\) | −7412.43 | −0.331933 | ||||||||
\(794\) | −11077.9 | −0.495137 | ||||||||
\(795\) | 2172.73 | 0.0969294 | ||||||||
\(796\) | −66850.4 | −2.97670 | ||||||||
\(797\) | 14556.0 | 0.646925 | 0.323463 | − | 0.946241i | \(-0.395153\pi\) | ||||
0.323463 | + | 0.946241i | \(0.395153\pi\) | |||||||
\(798\) | −6337.55 | −0.281136 | ||||||||
\(799\) | 2120.40 | 0.0938853 | ||||||||
\(800\) | −297.825 | −0.0131621 | ||||||||
\(801\) | 8155.02 | 0.359730 | ||||||||
\(802\) | 40501.6 | 1.78324 | ||||||||
\(803\) | −31212.9 | −1.37170 | ||||||||
\(804\) | 8703.59 | 0.381781 | ||||||||
\(805\) | −173.889 | −0.00761338 | ||||||||
\(806\) | −31484.8 | −1.37593 | ||||||||
\(807\) | 1662.14 | 0.0725032 | ||||||||
\(808\) | 25040.3 | 1.09024 | ||||||||
\(809\) | −14030.7 | −0.609755 | −0.304878 | − | 0.952392i | \(-0.598616\pi\) | ||||
−0.304878 | + | 0.952392i | \(0.598616\pi\) | |||||||
\(810\) | 1977.71 | 0.0857898 | ||||||||
\(811\) | 30195.7 | 1.30741 | 0.653707 | − | 0.756747i | \(-0.273213\pi\) | ||||
0.653707 | + | 0.756747i | \(0.273213\pi\) | |||||||
\(812\) | 2521.70 | 0.108983 | ||||||||
\(813\) | 5478.06 | 0.236315 | ||||||||
\(814\) | −82927.7 | −3.57078 | ||||||||
\(815\) | −8336.80 | −0.358313 | ||||||||
\(816\) | 3403.04 | 0.145993 | ||||||||
\(817\) | 40017.2 | 1.71362 | ||||||||
\(818\) | 48407.6 | 2.06911 | ||||||||
\(819\) | −1024.05 | −0.0436911 | ||||||||
\(820\) | 28010.0 | 1.19287 | ||||||||
\(821\) | 31237.5 | 1.32789 | 0.663944 | − | 0.747782i | \(-0.268881\pi\) | ||||
0.663944 | + | 0.747782i | \(0.268881\pi\) | |||||||
\(822\) | 23567.4 | 1.00001 | ||||||||
\(823\) | −22306.9 | −0.944798 | −0.472399 | − | 0.881385i | \(-0.656612\pi\) | ||||
−0.472399 | + | 0.881385i | \(0.656612\pi\) | |||||||
\(824\) | 37157.1 | 1.57091 | ||||||||
\(825\) | −3759.93 | −0.158671 | ||||||||
\(826\) | −9184.30 | −0.386880 | ||||||||
\(827\) | 41561.9 | 1.74758 | 0.873790 | − | 0.486304i | \(-0.161655\pi\) | ||||
0.873790 | + | 0.486304i | \(0.161655\pi\) | |||||||
\(828\) | −903.837 | −0.0379354 | ||||||||
\(829\) | 42423.6 | 1.77736 | 0.888681 | − | 0.458527i | \(-0.151623\pi\) | ||||
0.888681 | + | 0.458527i | \(0.151623\pi\) | |||||||
\(830\) | −18046.2 | −0.754690 | ||||||||
\(831\) | −4410.01 | −0.184093 | ||||||||
\(832\) | 11213.5 | 0.467259 | ||||||||
\(833\) | 5883.13 | 0.244704 | ||||||||
\(834\) | −755.524 | −0.0313689 | ||||||||
\(835\) | −9161.51 | −0.379697 | ||||||||
\(836\) | 62626.3 | 2.59088 | ||||||||
\(837\) | −8395.64 | −0.346710 | ||||||||
\(838\) | −65104.0 | −2.68375 | ||||||||
\(839\) | −31547.4 | −1.29814 | −0.649068 | − | 0.760730i | \(-0.724841\pi\) | ||||
−0.649068 | + | 0.760730i | \(0.724841\pi\) | |||||||
\(840\) | −3153.73 | −0.129541 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −13908.1 | −0.569247 | ||||||||
\(843\) | −23479.3 | −0.959276 | ||||||||
\(844\) | −44342.5 | −1.80845 | ||||||||
\(845\) | −8835.32 | −0.359697 | ||||||||
\(846\) | −4956.19 | −0.201415 | ||||||||
\(847\) | 6487.63 | 0.263185 | ||||||||
\(848\) | −8738.56 | −0.353872 | ||||||||
\(849\) | 20390.6 | 0.824268 | ||||||||
\(850\) | −2295.45 | −0.0926276 | ||||||||
\(851\) | 2146.84 | 0.0864779 | ||||||||
\(852\) | 28239.3 | 1.13552 | ||||||||
\(853\) | −5030.77 | −0.201935 | −0.100967 | − | 0.994890i | \(-0.532194\pi\) | ||||
−0.100967 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(854\) | 9579.46 | 0.383844 | ||||||||
\(855\) | 3547.56 | 0.141899 | ||||||||
\(856\) | −48564.2 | −1.93912 | ||||||||
\(857\) | −16655.5 | −0.663875 | −0.331937 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331937 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(858\) | 15228.2 | 0.605925 | ||||||||
\(859\) | 33206.7 | 1.31897 | 0.659486 | − | 0.751717i | \(-0.270774\pi\) | ||||
0.659486 | + | 0.751717i | \(0.270774\pi\) | |||||||
\(860\) | 40218.0 | 1.59468 | ||||||||
\(861\) | −5819.93 | −0.230363 | ||||||||
\(862\) | 61869.0 | 2.44463 | ||||||||
\(863\) | −12156.5 | −0.479504 | −0.239752 | − | 0.970834i | \(-0.577066\pi\) | ||||
−0.239752 | + | 0.970834i | \(0.577066\pi\) | |||||||
\(864\) | 321.651 | 0.0126653 | ||||||||
\(865\) | 10173.9 | 0.399909 | ||||||||
\(866\) | −71029.6 | −2.78716 | ||||||||
\(867\) | 13678.4 | 0.535804 | ||||||||
\(868\) | 27038.7 | 1.05732 | ||||||||
\(869\) | −63928.0 | −2.49552 | ||||||||
\(870\) | −2124.21 | −0.0827787 | ||||||||
\(871\) | 3796.28 | 0.147683 | ||||||||
\(872\) | −30963.3 | −1.20246 | ||||||||
\(873\) | 684.598 | 0.0265408 | ||||||||
\(874\) | −2439.79 | −0.0944246 | ||||||||
\(875\) | 685.938 | 0.0265016 | ||||||||
\(876\) | 29597.7 | 1.14157 | ||||||||
\(877\) | 10910.0 | 0.420075 | 0.210037 | − | 0.977693i | \(-0.432641\pi\) | ||||
0.210037 | + | 0.977693i | \(0.432641\pi\) | |||||||
\(878\) | 56105.7 | 2.15658 | ||||||||
\(879\) | −10894.5 | −0.418044 | ||||||||
\(880\) | 15122.1 | 0.579281 | ||||||||
\(881\) | −10796.4 | −0.412871 | −0.206435 | − | 0.978460i | \(-0.566186\pi\) | ||||
−0.206435 | + | 0.978460i | \(0.566186\pi\) | |||||||
\(882\) | −13751.1 | −0.524972 | ||||||||
\(883\) | −23778.3 | −0.906232 | −0.453116 | − | 0.891452i | \(-0.649688\pi\) | ||||
−0.453116 | + | 0.891452i | \(0.649688\pi\) | |||||||
\(884\) | 6177.94 | 0.235053 | ||||||||
\(885\) | 5141.08 | 0.195272 | ||||||||
\(886\) | −54329.4 | −2.06008 | ||||||||
\(887\) | −26229.5 | −0.992897 | −0.496449 | − | 0.868066i | \(-0.665363\pi\) | ||||
−0.496449 | + | 0.868066i | \(0.665363\pi\) | |||||||
\(888\) | 38936.2 | 1.47141 | ||||||||
\(889\) | 4470.85 | 0.168670 | ||||||||
\(890\) | 22123.8 | 0.833251 | ||||||||
\(891\) | 4060.72 | 0.152682 | ||||||||
\(892\) | 39551.8 | 1.48463 | ||||||||
\(893\) | −8890.26 | −0.333148 | ||||||||
\(894\) | 8911.86 | 0.333397 | ||||||||
\(895\) | −1660.99 | −0.0620344 | ||||||||
\(896\) | −13968.8 | −0.520833 | ||||||||
\(897\) | −394.230 | −0.0146744 | ||||||||
\(898\) | −32604.4 | −1.21161 | ||||||||
\(899\) | 9017.54 | 0.334540 | ||||||||
\(900\) | 3565.36 | 0.132050 | ||||||||
\(901\) | 2723.55 | 0.100704 | ||||||||
\(902\) | 86546.3 | 3.19476 | ||||||||
\(903\) | −8356.51 | −0.307959 | ||||||||
\(904\) | −46746.9 | −1.71989 | ||||||||
\(905\) | −4216.96 | −0.154891 | ||||||||
\(906\) | 5003.88 | 0.183491 | ||||||||
\(907\) | 53019.1 | 1.94098 | 0.970491 | − | 0.241136i | \(-0.0775201\pi\) | ||||
0.970491 | + | 0.241136i | \(0.0775201\pi\) | |||||||
\(908\) | 54028.1 | 1.97465 | ||||||||
\(909\) | 5881.98 | 0.214624 | ||||||||
\(910\) | −2778.14 | −0.101203 | ||||||||
\(911\) | −16886.9 | −0.614147 | −0.307074 | − | 0.951686i | \(-0.599350\pi\) | ||||
−0.307074 | + | 0.951686i | \(0.599350\pi\) | |||||||
\(912\) | −14268.0 | −0.518049 | ||||||||
\(913\) | −37053.2 | −1.34314 | ||||||||
\(914\) | −52870.3 | −1.91334 | ||||||||
\(915\) | −5362.28 | −0.193739 | ||||||||
\(916\) | 75973.4 | 2.74043 | ||||||||
\(917\) | −8197.83 | −0.295219 | ||||||||
\(918\) | 2479.09 | 0.0891309 | ||||||||
\(919\) | −54865.8 | −1.96937 | −0.984687 | − | 0.174330i | \(-0.944224\pi\) | ||||
−0.984687 | + | 0.174330i | \(0.944224\pi\) | |||||||
\(920\) | −1214.10 | −0.0435085 | ||||||||
\(921\) | 27242.3 | 0.974663 | ||||||||
\(922\) | −20090.7 | −0.717626 | ||||||||
\(923\) | 12317.2 | 0.439249 | ||||||||
\(924\) | −13077.8 | −0.465615 | ||||||||
\(925\) | −8468.62 | −0.301023 | ||||||||
\(926\) | −29822.9 | −1.05836 | ||||||||
\(927\) | 8728.21 | 0.309247 | ||||||||
\(928\) | −345.477 | −0.0122207 | ||||||||
\(929\) | 27835.6 | 0.983053 | 0.491527 | − | 0.870863i | \(-0.336439\pi\) | ||||
0.491527 | + | 0.870863i | \(0.336439\pi\) | |||||||
\(930\) | −22776.6 | −0.803092 | ||||||||
\(931\) | −24666.4 | −0.868322 | ||||||||
\(932\) | 31523.5 | 1.10793 | ||||||||
\(933\) | −7973.06 | −0.279771 | ||||||||
\(934\) | −6882.01 | −0.241099 | ||||||||
\(935\) | −4713.13 | −0.164851 | ||||||||
\(936\) | −7149.96 | −0.249683 | ||||||||
\(937\) | −38996.7 | −1.35962 | −0.679811 | − | 0.733387i | \(-0.737938\pi\) | ||||
−0.679811 | + | 0.733387i | \(0.737938\pi\) | |||||||
\(938\) | −4906.13 | −0.170779 | ||||||||
\(939\) | 1591.42 | 0.0553079 | ||||||||
\(940\) | −8934.87 | −0.310025 | ||||||||
\(941\) | 15686.8 | 0.543437 | 0.271718 | − | 0.962377i | \(-0.412408\pi\) | ||||
0.271718 | + | 0.962377i | \(0.412408\pi\) | |||||||
\(942\) | 5250.14 | 0.181591 | ||||||||
\(943\) | −2240.52 | −0.0773715 | ||||||||
\(944\) | −20677.0 | −0.712902 | ||||||||
\(945\) | −740.813 | −0.0255012 | ||||||||
\(946\) | 124267. | 4.27090 | ||||||||
\(947\) | −54527.1 | −1.87106 | −0.935530 | − | 0.353248i | \(-0.885077\pi\) | ||||
−0.935530 | + | 0.353248i | \(0.885077\pi\) | |||||||
\(948\) | 60619.8 | 2.07684 | ||||||||
\(949\) | 12909.7 | 0.441589 | ||||||||
\(950\) | 9624.22 | 0.328685 | ||||||||
\(951\) | −7180.99 | −0.244858 | ||||||||
\(952\) | −3953.25 | −0.134586 | ||||||||
\(953\) | 48998.7 | 1.66550 | 0.832752 | − | 0.553647i | \(-0.186764\pi\) | ||||
0.832752 | + | 0.553647i | \(0.186764\pi\) | |||||||
\(954\) | −6365.99 | −0.216044 | ||||||||
\(955\) | 12194.1 | 0.413184 | ||||||||
\(956\) | 40798.6 | 1.38025 | ||||||||
\(957\) | −4361.52 | −0.147323 | ||||||||
\(958\) | 61694.4 | 2.08064 | ||||||||
\(959\) | −8827.88 | −0.297254 | ||||||||
\(960\) | 8112.07 | 0.272725 | ||||||||
\(961\) | 66898.8 | 2.24560 | ||||||||
\(962\) | 34299.1 | 1.14953 | ||||||||
\(963\) | −11407.7 | −0.381734 | ||||||||
\(964\) | −58368.0 | −1.95011 | ||||||||
\(965\) | 20475.2 | 0.683025 | ||||||||
\(966\) | 509.484 | 0.0169693 | ||||||||
\(967\) | −18866.1 | −0.627395 | −0.313698 | − | 0.949523i | \(-0.601568\pi\) | ||||
−0.313698 | + | 0.949523i | \(0.601568\pi\) | |||||||
\(968\) | 45297.1 | 1.50403 | ||||||||
\(969\) | 4446.92 | 0.147426 | ||||||||
\(970\) | 1857.25 | 0.0614772 | ||||||||
\(971\) | 49921.4 | 1.64990 | 0.824950 | − | 0.565205i | \(-0.191203\pi\) | ||||
0.824950 | + | 0.565205i | \(0.191203\pi\) | |||||||
\(972\) | −3850.59 | −0.127066 | ||||||||
\(973\) | 283.004 | 0.00932446 | ||||||||
\(974\) | −83135.6 | −2.73495 | ||||||||
\(975\) | 1555.12 | 0.0510806 | ||||||||
\(976\) | 21566.7 | 0.707308 | ||||||||
\(977\) | −2591.52 | −0.0848618 | −0.0424309 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424309 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(978\) | 24426.4 | 0.798639 | ||||||||
\(979\) | 45425.6 | 1.48295 | ||||||||
\(980\) | −24790.1 | −0.808053 | ||||||||
\(981\) | −7273.28 | −0.236715 | ||||||||
\(982\) | −18519.6 | −0.601815 | ||||||||
\(983\) | 18566.6 | 0.602423 | 0.301211 | − | 0.953557i | \(-0.402609\pi\) | ||||
0.301211 | + | 0.953557i | \(0.402609\pi\) | |||||||
\(984\) | −40635.2 | −1.31647 | ||||||||
\(985\) | 16133.8 | 0.521894 | ||||||||
\(986\) | −2662.73 | −0.0860026 | ||||||||
\(987\) | 1856.49 | 0.0598711 | ||||||||
\(988\) | −25902.4 | −0.834074 | ||||||||
\(989\) | −3217.04 | −0.103434 | ||||||||
\(990\) | 11016.4 | 0.353660 | ||||||||
\(991\) | −34558.3 | −1.10775 | −0.553875 | − | 0.832600i | \(-0.686851\pi\) | ||||
−0.553875 | + | 0.832600i | \(0.686851\pi\) | |||||||
\(992\) | −3704.34 | −0.118561 | ||||||||
\(993\) | 23953.6 | 0.765503 | ||||||||
\(994\) | −15918.2 | −0.507943 | ||||||||
\(995\) | −21093.7 | −0.672076 | ||||||||
\(996\) | 35135.8 | 1.11779 | ||||||||
\(997\) | −11238.6 | −0.357000 | −0.178500 | − | 0.983940i | \(-0.557124\pi\) | ||||
−0.178500 | + | 0.983940i | \(0.557124\pi\) | |||||||
\(998\) | 31663.9 | 1.00431 | ||||||||
\(999\) | 9146.11 | 0.289660 |
(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 | 435.4.a.i.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.n.1.1 | 7 | |||
5.4 | even | 2 | 2175.4.a.n.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.i.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.n.1.1 | 7 | 3.2 | odd | 2 | |||
2175.4.a.n.1.1 | 7 | 5.4 | even | 2 |