Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.91035289.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 285x^{2} + 286x + 19616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(13.6191\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −0.552092 | −0.276046 | − | 0.961144i | \(-0.589024\pi\) | ||||
−0.276046 | + | 0.961144i | \(0.589024\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −5.56155 | −0.695194 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.68466 | 0.318751 | ||||||||
\(7\) | 24.2670 | 1.31029 | 0.655147 | − | 0.755501i | \(-0.272606\pi\) | ||||
0.655147 | + | 0.755501i | \(0.272606\pi\) | |||||||
\(8\) | 21.1771 | 0.935904 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 16.6847 | 0.401371 | ||||||||
\(13\) | 84.2360 | 1.79714 | 0.898571 | − | 0.438828i | \(-0.144606\pi\) | ||||
0.898571 | + | 0.438828i | \(0.144606\pi\) | |||||||
\(14\) | −37.8942 | −0.723404 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | −40.9641 | −0.584426 | −0.292213 | − | 0.956353i | \(-0.594392\pi\) | ||||
−0.292213 | + | 0.956353i | \(0.594392\pi\) | |||||||
\(18\) | −14.0540 | −0.184031 | ||||||||
\(19\) | 120.887 | 1.45966 | 0.729828 | − | 0.683630i | \(-0.239600\pi\) | ||||
0.729828 | + | 0.683630i | \(0.239600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −72.8010 | −0.756499 | ||||||||
\(22\) | 17.1771 | 0.166462 | ||||||||
\(23\) | −9.94182 | −0.0901310 | −0.0450655 | − | 0.998984i | \(-0.514350\pi\) | ||||
−0.0450655 | + | 0.998984i | \(0.514350\pi\) | |||||||
\(24\) | −63.5312 | −0.540344 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −131.539 | −0.992189 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −134.962 | −0.910909 | ||||||||
\(29\) | 196.860 | 1.26055 | 0.630275 | − | 0.776372i | \(-0.282942\pi\) | ||||
0.630275 | + | 0.776372i | \(0.282942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 151.123 | 0.875562 | 0.437781 | − | 0.899082i | \(-0.355764\pi\) | ||||
0.437781 | + | 0.899082i | \(0.355764\pi\) | |||||||
\(32\) | −187.255 | −1.03445 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 63.9675 | 0.322657 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −50.0540 | −0.231731 | ||||||||
\(37\) | −253.477 | −1.12625 | −0.563126 | − | 0.826371i | \(-0.690401\pi\) | ||||
−0.563126 | + | 0.826371i | \(0.690401\pi\) | |||||||
\(38\) | −188.772 | −0.805865 | ||||||||
\(39\) | −252.708 | −1.03758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −179.351 | −0.683170 | −0.341585 | − | 0.939851i | \(-0.610964\pi\) | ||||
−0.341585 | + | 0.939851i | \(0.610964\pi\) | |||||||
\(42\) | 113.683 | 0.417657 | ||||||||
\(43\) | −90.4851 | −0.320903 | −0.160452 | − | 0.987044i | \(-0.551295\pi\) | ||||
−0.160452 | + | 0.987044i | \(0.551295\pi\) | |||||||
\(44\) | 61.1771 | 0.209609 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.5247 | 0.0497606 | ||||||||
\(47\) | −483.434 | −1.50034 | −0.750172 | − | 0.661243i | \(-0.770029\pi\) | ||||
−0.750172 | + | 0.661243i | \(0.770029\pi\) | |||||||
\(48\) | −34.2699 | −0.103051 | ||||||||
\(49\) | 245.887 | 0.716873 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 122.892 | 0.337419 | ||||||||
\(52\) | −468.483 | −1.24936 | ||||||||
\(53\) | 567.348 | 1.47040 | 0.735200 | − | 0.677850i | \(-0.237088\pi\) | ||||
0.735200 | + | 0.677850i | \(0.237088\pi\) | |||||||
\(54\) | 42.1619 | 0.106250 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 513.904 | 1.22631 | ||||||||
\(57\) | −362.662 | −0.842733 | ||||||||
\(58\) | −307.407 | −0.695939 | ||||||||
\(59\) | −491.696 | −1.08497 | −0.542487 | − | 0.840064i | \(-0.682517\pi\) | ||||
−0.542487 | + | 0.840064i | \(0.682517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 127.008 | 0.266585 | 0.133292 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133292 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(62\) | −235.986 | −0.483391 | ||||||||
\(63\) | 218.403 | 0.436765 | ||||||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −51.5312 | −0.0961069 | ||||||||
\(67\) | 628.226 | 1.14552 | 0.572762 | − | 0.819722i | \(-0.305872\pi\) | ||||
0.572762 | + | 0.819722i | \(0.305872\pi\) | |||||||
\(68\) | 227.824 | 0.406290 | ||||||||
\(69\) | 29.8255 | 0.0520372 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 309.976 | 0.518133 | 0.259066 | − | 0.965859i | \(-0.416585\pi\) | ||||
0.259066 | + | 0.965859i | \(0.416585\pi\) | |||||||
\(72\) | 190.594 | 0.311968 | ||||||||
\(73\) | −1144.85 | −1.83554 | −0.917772 | − | 0.397109i | \(-0.870014\pi\) | ||||
−0.917772 | + | 0.397109i | \(0.870014\pi\) | |||||||
\(74\) | 395.817 | 0.621795 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −672.322 | −1.01474 | ||||||||
\(77\) | −266.937 | −0.395069 | ||||||||
\(78\) | 394.617 | 0.572840 | ||||||||
\(79\) | −87.4620 | −0.124560 | −0.0622800 | − | 0.998059i | \(-0.519837\pi\) | ||||
−0.0622800 | + | 0.998059i | \(0.519837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 280.067 | 0.377173 | ||||||||
\(83\) | 1040.13 | 1.37553 | 0.687764 | − | 0.725934i | \(-0.258592\pi\) | ||||
0.687764 | + | 0.725934i | \(0.258592\pi\) | |||||||
\(84\) | 404.887 | 0.525914 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 141.297 | 0.177168 | ||||||||
\(87\) | −590.579 | −0.727778 | ||||||||
\(88\) | −232.948 | −0.282186 | ||||||||
\(89\) | 390.723 | 0.465355 | 0.232677 | − | 0.972554i | \(-0.425251\pi\) | ||||
0.232677 | + | 0.972554i | \(0.425251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2044.15 | 2.35479 | ||||||||
\(92\) | 55.2920 | 0.0626585 | ||||||||
\(93\) | −453.368 | −0.505506 | ||||||||
\(94\) | 754.908 | 0.828328 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 561.764 | 0.597238 | ||||||||
\(97\) | 165.548 | 0.173287 | 0.0866433 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866433 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(98\) | −383.966 | −0.395780 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1510.35 | 1.48798 | 0.743990 | − | 0.668191i | \(-0.232931\pi\) | ||||
0.743990 | + | 0.668191i | \(0.232931\pi\) | |||||||
\(102\) | −191.903 | −0.186286 | ||||||||
\(103\) | 1245.78 | 1.19175 | 0.595876 | − | 0.803076i | \(-0.296805\pi\) | ||||
0.595876 | + | 0.803076i | \(0.296805\pi\) | |||||||
\(104\) | 1783.87 | 1.68195 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −885.944 | −0.811797 | ||||||||
\(107\) | −550.568 | −0.497434 | −0.248717 | − | 0.968576i | \(-0.580009\pi\) | ||||
−0.248717 | + | 0.968576i | \(0.580009\pi\) | |||||||
\(108\) | 150.162 | 0.133790 | ||||||||
\(109\) | 1380.30 | 1.21293 | 0.606463 | − | 0.795112i | \(-0.292588\pi\) | ||||
0.606463 | + | 0.795112i | \(0.292588\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 760.430 | 0.650242 | ||||||||
\(112\) | 277.209 | 0.233873 | ||||||||
\(113\) | 1017.96 | 0.847445 | 0.423723 | − | 0.905792i | \(-0.360723\pi\) | ||||
0.423723 | + | 0.905792i | \(0.360723\pi\) | |||||||
\(114\) | 566.316 | 0.465267 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1094.85 | −0.876326 | ||||||||
\(117\) | 758.124 | 0.599048 | ||||||||
\(118\) | 767.810 | 0.599005 | ||||||||
\(119\) | −994.075 | −0.765770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −198.329 | −0.147179 | ||||||||
\(123\) | 538.054 | 0.394429 | ||||||||
\(124\) | −840.477 | −0.608686 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −341.048 | −0.241135 | ||||||||
\(127\) | −1181.86 | −0.825770 | −0.412885 | − | 0.910783i | \(-0.635479\pi\) | ||||
−0.412885 | + | 0.910783i | \(0.635479\pi\) | |||||||
\(128\) | 1184.13 | 0.817683 | ||||||||
\(129\) | 271.455 | 0.185274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2615.26 | −1.74425 | −0.872124 | − | 0.489284i | \(-0.837258\pi\) | ||||
−0.872124 | + | 0.489284i | \(0.837258\pi\) | |||||||
\(132\) | −183.531 | −0.121018 | ||||||||
\(133\) | 2933.58 | 1.91258 | ||||||||
\(134\) | −981.009 | −0.632435 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −867.499 | −0.546966 | ||||||||
\(137\) | −465.369 | −0.290213 | −0.145106 | − | 0.989416i | \(-0.546352\pi\) | ||||
−0.145106 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(138\) | −46.5740 | −0.0287293 | ||||||||
\(139\) | 2809.52 | 1.71439 | 0.857196 | − | 0.514990i | \(-0.172204\pi\) | ||||
0.857196 | + | 0.514990i | \(0.172204\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1450.30 | 0.866224 | ||||||||
\(142\) | −484.045 | −0.286057 | ||||||||
\(143\) | −926.596 | −0.541859 | ||||||||
\(144\) | 102.810 | 0.0594963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1787.75 | 1.01339 | ||||||||
\(147\) | −737.662 | −0.413887 | ||||||||
\(148\) | 1409.72 | 0.782963 | ||||||||
\(149\) | −583.496 | −0.320818 | −0.160409 | − | 0.987051i | \(-0.551281\pi\) | ||||
−0.160409 | + | 0.987051i | \(0.551281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1244.33 | 0.670610 | 0.335305 | − | 0.942110i | \(-0.391161\pi\) | ||||
0.335305 | + | 0.942110i | \(0.391161\pi\) | |||||||
\(152\) | 2560.04 | 1.36610 | ||||||||
\(153\) | −368.676 | −0.194809 | ||||||||
\(154\) | 416.836 | 0.218114 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1405.45 | 0.721320 | ||||||||
\(157\) | −303.991 | −0.154529 | −0.0772647 | − | 0.997011i | \(-0.524619\pi\) | ||||
−0.0772647 | + | 0.997011i | \(0.524619\pi\) | |||||||
\(158\) | 136.577 | 0.0687687 | ||||||||
\(159\) | −1702.04 | −0.848936 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −241.258 | −0.118098 | ||||||||
\(162\) | −126.486 | −0.0613436 | ||||||||
\(163\) | 259.982 | 0.124929 | 0.0624643 | − | 0.998047i | \(-0.480104\pi\) | ||||
0.0624643 | + | 0.998047i | \(0.480104\pi\) | |||||||
\(164\) | 997.472 | 0.474936 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1624.21 | −0.759419 | ||||||||
\(167\) | −3468.36 | −1.60712 | −0.803562 | − | 0.595222i | \(-0.797064\pi\) | ||||
−0.803562 | + | 0.595222i | \(0.797064\pi\) | |||||||
\(168\) | −1541.71 | −0.708010 | ||||||||
\(169\) | 4898.70 | 2.22972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1087.99 | 0.486552 | ||||||||
\(172\) | 503.237 | 0.223090 | ||||||||
\(173\) | −3864.34 | −1.69827 | −0.849134 | − | 0.528177i | \(-0.822876\pi\) | ||||
−0.849134 | + | 0.528177i | \(0.822876\pi\) | |||||||
\(174\) | 922.220 | 0.401801 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −125.656 | −0.0538164 | ||||||||
\(177\) | 1475.09 | 0.626410 | ||||||||
\(178\) | −610.135 | −0.256919 | ||||||||
\(179\) | 163.870 | 0.0684258 | 0.0342129 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342129 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3200.77 | −1.31443 | −0.657214 | − | 0.753704i | \(-0.728265\pi\) | ||||
−0.657214 | + | 0.753704i | \(0.728265\pi\) | |||||||
\(182\) | −3192.05 | −1.30006 | ||||||||
\(183\) | −381.023 | −0.153913 | ||||||||
\(184\) | −210.539 | −0.0843539 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 707.958 | 0.279086 | ||||||||
\(187\) | 450.605 | 0.176211 | ||||||||
\(188\) | 2688.65 | 1.04303 | ||||||||
\(189\) | −655.209 | −0.252166 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2421.03 | 0.917171 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(192\) | −603.065 | −0.226680 | ||||||||
\(193\) | −2275.44 | −0.848651 | −0.424326 | − | 0.905510i | \(-0.639489\pi\) | ||||
−0.424326 | + | 0.905510i | \(0.639489\pi\) | |||||||
\(194\) | −258.511 | −0.0956702 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1367.52 | −0.498366 | ||||||||
\(197\) | 1957.94 | 0.708107 | 0.354054 | − | 0.935225i | \(-0.384803\pi\) | ||||
0.354054 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(198\) | 154.594 | 0.0554874 | ||||||||
\(199\) | −1975.36 | −0.703665 | −0.351833 | − | 0.936063i | \(-0.614441\pi\) | ||||
−0.351833 | + | 0.936063i | \(0.614441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1884.68 | −0.661368 | ||||||||
\(202\) | −2358.50 | −0.821502 | ||||||||
\(203\) | 4777.19 | 1.65169 | ||||||||
\(204\) | −683.471 | −0.234571 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1945.35 | −0.657958 | ||||||||
\(207\) | −89.4764 | −0.0300437 | ||||||||
\(208\) | 962.252 | 0.320770 | ||||||||
\(209\) | −1329.76 | −0.440103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1179.92 | 0.384973 | 0.192486 | − | 0.981300i | \(-0.438345\pi\) | ||||
0.192486 | + | 0.981300i | \(0.438345\pi\) | |||||||
\(212\) | −3155.34 | −1.02221 | ||||||||
\(213\) | −929.929 | −0.299144 | ||||||||
\(214\) | 859.741 | 0.274629 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −571.781 | −0.180115 | ||||||||
\(217\) | 3667.29 | 1.14724 | ||||||||
\(218\) | −2155.41 | −0.669647 | ||||||||
\(219\) | 3434.55 | 1.05975 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3450.65 | −1.05030 | ||||||||
\(222\) | −1187.45 | −0.358993 | ||||||||
\(223\) | 5742.73 | 1.72449 | 0.862247 | − | 0.506489i | \(-0.169057\pi\) | ||||
0.862247 | + | 0.506489i | \(0.169057\pi\) | |||||||
\(224\) | −4544.11 | −1.35543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1589.59 | −0.467868 | ||||||||
\(227\) | 713.160 | 0.208520 | 0.104260 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104260 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(228\) | 2016.97 | 0.585863 | ||||||||
\(229\) | 4438.09 | 1.28069 | 0.640343 | − | 0.768089i | \(-0.278792\pi\) | ||||
0.640343 | + | 0.768089i | \(0.278792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 800.811 | 0.228093 | ||||||||
\(232\) | 4168.91 | 1.17975 | ||||||||
\(233\) | −614.179 | −0.172688 | −0.0863438 | − | 0.996265i | \(-0.527518\pi\) | ||||
−0.0863438 | + | 0.996265i | \(0.527518\pi\) | |||||||
\(234\) | −1183.85 | −0.330730 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2734.60 | 0.754267 | ||||||||
\(237\) | 262.386 | 0.0719148 | ||||||||
\(238\) | 1552.30 | 0.422776 | ||||||||
\(239\) | 5191.00 | 1.40493 | 0.702464 | − | 0.711720i | \(-0.252083\pi\) | ||||
0.702464 | + | 0.711720i | \(0.252083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −353.708 | −0.0945408 | −0.0472704 | − | 0.998882i | \(-0.515052\pi\) | ||||
−0.0472704 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(242\) | −188.948 | −0.0501902 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −706.360 | −0.185328 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −840.200 | −0.217761 | ||||||||
\(247\) | 10183.1 | 2.62321 | ||||||||
\(248\) | 3200.34 | 0.819442 | ||||||||
\(249\) | −3120.38 | −0.794162 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2612.91 | 0.657073 | 0.328537 | − | 0.944491i | \(-0.393445\pi\) | ||||
0.328537 | + | 0.944491i | \(0.393445\pi\) | |||||||
\(252\) | −1214.66 | −0.303636 | ||||||||
\(253\) | 109.360 | 0.0271755 | ||||||||
\(254\) | 1845.53 | 0.455901 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | 2434.38 | 0.590866 | 0.295433 | − | 0.955364i | \(-0.404536\pi\) | ||||
0.295433 | + | 0.955364i | \(0.404536\pi\) | |||||||
\(258\) | −423.892 | −0.102288 | ||||||||
\(259\) | −6151.12 | −1.47572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1771.74 | 0.420183 | ||||||||
\(262\) | 4083.87 | 0.962986 | ||||||||
\(263\) | −7204.41 | −1.68914 | −0.844568 | − | 0.535449i | \(-0.820143\pi\) | ||||
−0.844568 | + | 0.535449i | \(0.820143\pi\) | |||||||
\(264\) | 698.844 | 0.162920 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4580.93 | −1.05592 | ||||||||
\(267\) | −1172.17 | −0.268673 | ||||||||
\(268\) | −3493.91 | −0.796361 | ||||||||
\(269\) | 5232.32 | 1.18595 | 0.592975 | − | 0.805221i | \(-0.297953\pi\) | ||||
0.592975 | + | 0.805221i | \(0.297953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6231.13 | 1.39673 | 0.698366 | − | 0.715741i | \(-0.253911\pi\) | ||||
0.698366 | + | 0.715741i | \(0.253911\pi\) | |||||||
\(272\) | −467.944 | −0.104314 | ||||||||
\(273\) | −6132.46 | −1.35954 | ||||||||
\(274\) | 726.698 | 0.160224 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −165.876 | −0.0361759 | ||||||||
\(277\) | −4940.23 | −1.07159 | −0.535793 | − | 0.844349i | \(-0.679987\pi\) | ||||
−0.535793 | + | 0.844349i | \(0.679987\pi\) | |||||||
\(278\) | −4387.22 | −0.946503 | ||||||||
\(279\) | 1360.10 | 0.291854 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1766.97 | −0.375119 | −0.187559 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187559 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(282\) | −2264.72 | −0.478235 | ||||||||
\(283\) | −5304.29 | −1.11416 | −0.557080 | − | 0.830459i | \(-0.688078\pi\) | ||||
−0.557080 | + | 0.830459i | \(0.688078\pi\) | |||||||
\(284\) | −1723.95 | −0.360203 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1446.93 | 0.299156 | ||||||||
\(287\) | −4352.32 | −0.895155 | ||||||||
\(288\) | −1685.29 | −0.344815 | ||||||||
\(289\) | −3234.95 | −0.658446 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −496.643 | −0.100047 | ||||||||
\(292\) | 6367.15 | 1.27606 | ||||||||
\(293\) | 8356.39 | 1.66616 | 0.833081 | − | 0.553151i | \(-0.186575\pi\) | ||||
0.833081 | + | 0.553151i | \(0.186575\pi\) | |||||||
\(294\) | 1151.90 | 0.228504 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5367.90 | −1.05406 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | 911.160 | 0.177121 | ||||||||
\(299\) | −837.459 | −0.161978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2195.80 | −0.420478 | ||||||||
\(302\) | −1943.09 | −0.370238 | ||||||||
\(303\) | −4531.06 | −0.859085 | ||||||||
\(304\) | 1380.93 | 0.260533 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 575.708 | 0.107552 | ||||||||
\(307\) | 8558.29 | 1.59103 | 0.795517 | − | 0.605932i | \(-0.207200\pi\) | ||||
0.795517 | + | 0.605932i | \(0.207200\pi\) | |||||||
\(308\) | 1484.58 | 0.274649 | ||||||||
\(309\) | −3737.35 | −0.688059 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6135.19 | 1.11863 | 0.559316 | − | 0.828954i | \(-0.311064\pi\) | ||||
0.559316 | + | 0.828954i | \(0.311064\pi\) | |||||||
\(312\) | −5351.62 | −0.971076 | ||||||||
\(313\) | −4088.62 | −0.738346 | −0.369173 | − | 0.929361i | \(-0.620359\pi\) | ||||
−0.369173 | + | 0.929361i | \(0.620359\pi\) | |||||||
\(314\) | 474.698 | 0.0853145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 486.425 | 0.0865934 | ||||||||
\(317\) | −7957.42 | −1.40988 | −0.704942 | − | 0.709265i | \(-0.749027\pi\) | ||||
−0.704942 | + | 0.709265i | \(0.749027\pi\) | |||||||
\(318\) | 2657.83 | 0.468691 | ||||||||
\(319\) | −2165.46 | −0.380070 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1651.70 | 0.287194 | ||||||||
\(322\) | 376.737 | 0.0652011 | ||||||||
\(323\) | −4952.04 | −0.853062 | ||||||||
\(324\) | −450.486 | −0.0772438 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −405.976 | −0.0689721 | ||||||||
\(327\) | −4140.91 | −0.700283 | ||||||||
\(328\) | −3798.14 | −0.639382 | ||||||||
\(329\) | −11731.5 | −1.96589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3113.97 | −0.517097 | −0.258549 | − | 0.965998i | \(-0.583244\pi\) | ||||
−0.258549 | + | 0.965998i | \(0.583244\pi\) | |||||||
\(332\) | −5784.72 | −0.956259 | ||||||||
\(333\) | −2281.29 | −0.375417 | ||||||||
\(334\) | 5416.02 | 0.887280 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −831.627 | −0.135027 | ||||||||
\(337\) | 8267.16 | 1.33632 | 0.668161 | − | 0.744016i | \(-0.267082\pi\) | ||||
0.668161 | + | 0.744016i | \(0.267082\pi\) | |||||||
\(338\) | −7649.58 | −1.23101 | ||||||||
\(339\) | −3053.87 | −0.489273 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1662.35 | −0.263992 | ||||||||
\(342\) | −1698.95 | −0.268622 | ||||||||
\(343\) | −2356.63 | −0.370980 | ||||||||
\(344\) | −1916.21 | −0.300335 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6034.37 | 0.937601 | ||||||||
\(347\) | −8673.03 | −1.34177 | −0.670883 | − | 0.741563i | \(-0.734085\pi\) | ||||
−0.670883 | + | 0.741563i | \(0.734085\pi\) | |||||||
\(348\) | 3284.54 | 0.505947 | ||||||||
\(349\) | 3351.21 | 0.514000 | 0.257000 | − | 0.966411i | \(-0.417266\pi\) | ||||
0.257000 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2274.37 | −0.345860 | ||||||||
\(352\) | 2059.80 | 0.311897 | ||||||||
\(353\) | −36.5920 | −0.00551727 | −0.00275864 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275864 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(354\) | −2303.43 | −0.345836 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2173.03 | −0.323512 | ||||||||
\(357\) | 2982.22 | 0.442118 | ||||||||
\(358\) | −255.892 | −0.0377773 | ||||||||
\(359\) | −12789.2 | −1.88019 | −0.940095 | − | 0.340912i | \(-0.889264\pi\) | ||||
−0.940095 | + | 0.340912i | \(0.889264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7754.77 | 1.13060 | ||||||||
\(362\) | 4998.17 | 0.725686 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −11368.7 | −1.63703 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 594.988 | 0.0849741 | ||||||||
\(367\) | −1293.66 | −0.184001 | −0.0920005 | − | 0.995759i | \(-0.529326\pi\) | ||||
−0.0920005 | + | 0.995759i | \(0.529326\pi\) | |||||||
\(368\) | −113.568 | −0.0160874 | ||||||||
\(369\) | −1614.16 | −0.227723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13767.8 | 1.92666 | ||||||||
\(372\) | 2521.43 | 0.351425 | ||||||||
\(373\) | 8638.61 | 1.19917 | 0.599585 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599585 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(374\) | −703.643 | −0.0972848 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10237.7 | −1.40418 | ||||||||
\(377\) | 16582.7 | 2.26539 | ||||||||
\(378\) | 1023.14 | 0.139219 | ||||||||
\(379\) | 1853.53 | 0.251212 | 0.125606 | − | 0.992080i | \(-0.459912\pi\) | ||||
0.125606 | + | 0.992080i | \(0.459912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3545.57 | 0.476758 | ||||||||
\(382\) | −3780.57 | −0.506363 | ||||||||
\(383\) | −3888.44 | −0.518773 | −0.259387 | − | 0.965774i | \(-0.583520\pi\) | ||||
−0.259387 | + | 0.965774i | \(0.583520\pi\) | |||||||
\(384\) | −3552.39 | −0.472090 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3553.22 | 0.468534 | ||||||||
\(387\) | −814.366 | −0.106968 | ||||||||
\(388\) | −920.701 | −0.120468 | ||||||||
\(389\) | −10791.1 | −1.40651 | −0.703255 | − | 0.710938i | \(-0.748271\pi\) | ||||
−0.703255 | + | 0.710938i | \(0.748271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 407.257 | 0.0526749 | ||||||||
\(392\) | 5207.18 | 0.670924 | ||||||||
\(393\) | 7845.79 | 1.00704 | ||||||||
\(394\) | −3057.42 | −0.390941 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 550.594 | 0.0698696 | ||||||||
\(397\) | 2875.92 | 0.363573 | 0.181787 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181787 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(398\) | 3084.63 | 0.388488 | ||||||||
\(399\) | −8800.73 | −1.10423 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7615.88 | 0.948426 | 0.474213 | − | 0.880410i | \(-0.342733\pi\) | ||||
0.474213 | + | 0.880410i | \(0.342733\pi\) | |||||||
\(402\) | 2943.03 | 0.365136 | ||||||||
\(403\) | 12730.0 | 1.57351 | ||||||||
\(404\) | −8399.92 | −1.03443 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7459.84 | −0.911886 | ||||||||
\(407\) | 2788.24 | 0.339578 | ||||||||
\(408\) | 2602.50 | 0.315791 | ||||||||
\(409\) | −3791.51 | −0.458382 | −0.229191 | − | 0.973381i | \(-0.573608\pi\) | ||||
−0.229191 | + | 0.973381i | \(0.573608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1396.11 | 0.167554 | ||||||||
\(412\) | −6928.48 | −0.828500 | ||||||||
\(413\) | −11932.0 | −1.42163 | ||||||||
\(414\) | 139.722 | 0.0165869 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15773.6 | −1.85905 | ||||||||
\(417\) | −8428.57 | −0.989805 | ||||||||
\(418\) | 2076.49 | 0.242978 | ||||||||
\(419\) | 8806.66 | 1.02681 | 0.513405 | − | 0.858146i | \(-0.328384\pi\) | ||||
0.513405 | + | 0.858146i | \(0.328384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7730.71 | −0.894945 | −0.447473 | − | 0.894298i | \(-0.647676\pi\) | ||||
−0.447473 | + | 0.894298i | \(0.647676\pi\) | |||||||
\(422\) | −1842.51 | −0.212541 | ||||||||
\(423\) | −4350.91 | −0.500114 | ||||||||
\(424\) | 12014.8 | 1.37615 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1452.13 | 0.165155 | ||||||||
\(427\) | 3082.10 | 0.349305 | ||||||||
\(428\) | 3062.01 | 0.345813 | ||||||||
\(429\) | 2779.79 | 0.312842 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9017.97 | 1.00784 | 0.503922 | − | 0.863749i | \(-0.331890\pi\) | ||||
0.503922 | + | 0.863749i | \(0.331890\pi\) | |||||||
\(432\) | −308.429 | −0.0343502 | ||||||||
\(433\) | 13799.1 | 1.53150 | 0.765751 | − | 0.643137i | \(-0.222367\pi\) | ||||
0.765751 | + | 0.643137i | \(0.222367\pi\) | |||||||
\(434\) | −5726.67 | −0.633385 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7676.62 | −0.843219 | ||||||||
\(437\) | −1201.84 | −0.131560 | ||||||||
\(438\) | −5363.24 | −0.585081 | ||||||||
\(439\) | 464.472 | 0.0504967 | 0.0252483 | − | 0.999681i | \(-0.491962\pi\) | ||||
0.0252483 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2212.99 | 0.238958 | ||||||||
\(442\) | 5388.37 | 0.579861 | ||||||||
\(443\) | −5796.17 | −0.621635 | −0.310818 | − | 0.950470i | \(-0.600603\pi\) | ||||
−0.310818 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(444\) | −4229.17 | −0.452044 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8967.58 | −0.952079 | ||||||||
\(447\) | 1750.49 | 0.185224 | ||||||||
\(448\) | 4878.20 | 0.514449 | ||||||||
\(449\) | −8955.57 | −0.941291 | −0.470645 | − | 0.882323i | \(-0.655979\pi\) | ||||
−0.470645 | + | 0.882323i | \(0.655979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1972.87 | 0.205984 | ||||||||
\(452\) | −5661.42 | −0.589139 | ||||||||
\(453\) | −3732.99 | −0.387177 | ||||||||
\(454\) | −1113.64 | −0.115122 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7680.13 | −0.788717 | ||||||||
\(457\) | 10067.8 | 1.03053 | 0.515267 | − | 0.857030i | \(-0.327693\pi\) | ||||
0.515267 | + | 0.857030i | \(0.327693\pi\) | |||||||
\(458\) | −6930.31 | −0.707057 | ||||||||
\(459\) | 1106.03 | 0.112473 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8293.06 | −0.837844 | −0.418922 | − | 0.908022i | \(-0.637592\pi\) | ||||
−0.418922 | + | 0.908022i | \(0.637592\pi\) | |||||||
\(462\) | −1250.51 | −0.125928 | ||||||||
\(463\) | −9901.59 | −0.993879 | −0.496939 | − | 0.867785i | \(-0.665543\pi\) | ||||
−0.496939 | + | 0.867785i | \(0.665543\pi\) | |||||||
\(464\) | 2248.79 | 0.224994 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 959.073 | 0.0953395 | ||||||||
\(467\) | 10915.0 | 1.08156 | 0.540779 | − | 0.841165i | \(-0.318130\pi\) | ||||
0.540779 | + | 0.841165i | \(0.318130\pi\) | |||||||
\(468\) | −4216.35 | −0.416454 | ||||||||
\(469\) | 15245.2 | 1.50097 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 911.973 | 0.0892176 | ||||||||
\(472\) | −10412.7 | −1.01543 | ||||||||
\(473\) | 995.336 | 0.0967560 | ||||||||
\(474\) | −409.730 | −0.0397036 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5528.60 | 0.532359 | ||||||||
\(477\) | 5106.13 | 0.490134 | ||||||||
\(478\) | −8106.02 | −0.775650 | ||||||||
\(479\) | 5725.15 | 0.546114 | 0.273057 | − | 0.961998i | \(-0.411965\pi\) | ||||
0.273057 | + | 0.961998i | \(0.411965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21351.9 | −2.02403 | ||||||||
\(482\) | 552.334 | 0.0521953 | ||||||||
\(483\) | 723.775 | 0.0681840 | ||||||||
\(484\) | −672.948 | −0.0631995 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 379.457 | 0.0354167 | ||||||||
\(487\) | 16620.3 | 1.54648 | 0.773242 | − | 0.634111i | \(-0.218634\pi\) | ||||
0.773242 | + | 0.634111i | \(0.218634\pi\) | |||||||
\(488\) | 2689.65 | 0.249498 | ||||||||
\(489\) | −779.946 | −0.0721276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9769.75 | −0.897969 | −0.448985 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448985 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(492\) | −2992.42 | −0.274204 | ||||||||
\(493\) | −8064.17 | −0.736698 | ||||||||
\(494\) | −15901.4 | −1.44825 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1726.32 | 0.156278 | ||||||||
\(497\) | 7522.20 | 0.678907 | ||||||||
\(498\) | 4872.64 | 0.438450 | ||||||||
\(499\) | −1886.64 | −0.169254 | −0.0846270 | − | 0.996413i | \(-0.526970\pi\) | ||||
−0.0846270 | + | 0.996413i | \(0.526970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10405.1 | 0.927873 | ||||||||
\(502\) | −4080.20 | −0.362765 | ||||||||
\(503\) | −2920.56 | −0.258889 | −0.129445 | − | 0.991587i | \(-0.541319\pi\) | ||||
−0.129445 | + | 0.991587i | \(0.541319\pi\) | |||||||
\(504\) | 4625.14 | 0.408770 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −170.771 | −0.0150034 | ||||||||
\(507\) | −14696.1 | −1.28733 | ||||||||
\(508\) | 6572.96 | 0.574070 | ||||||||
\(509\) | 7956.30 | 0.692842 | 0.346421 | − | 0.938079i | \(-0.387397\pi\) | ||||
0.346421 | + | 0.938079i | \(0.387397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27782.1 | −2.40510 | ||||||||
\(512\) | −4074.36 | −0.351686 | ||||||||
\(513\) | −3263.96 | −0.280911 | ||||||||
\(514\) | −3801.41 | −0.326212 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1509.71 | −0.128801 | ||||||||
\(517\) | 5317.78 | 0.452371 | ||||||||
\(518\) | 9605.30 | 0.814735 | ||||||||
\(519\) | 11593.0 | 0.980496 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20260.6 | 1.70371 | 0.851853 | − | 0.523780i | \(-0.175479\pi\) | ||||
0.851853 | + | 0.523780i | \(0.175479\pi\) | |||||||
\(522\) | −2766.66 | −0.231980 | ||||||||
\(523\) | 3457.70 | 0.289091 | 0.144546 | − | 0.989498i | \(-0.453828\pi\) | ||||
0.144546 | + | 0.989498i | \(0.453828\pi\) | |||||||
\(524\) | 14544.9 | 1.21259 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11250.1 | 0.932559 | ||||||||
\(527\) | −6190.60 | −0.511702 | ||||||||
\(528\) | 376.969 | 0.0310709 | ||||||||
\(529\) | −12068.2 | −0.991876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4425.27 | −0.361658 | ||||||||
\(532\) | −16315.2 | −1.32961 | ||||||||
\(533\) | −15107.8 | −1.22775 | ||||||||
\(534\) | 1830.40 | 0.148332 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13304.0 | 1.07210 | ||||||||
\(537\) | −491.610 | −0.0395056 | ||||||||
\(538\) | −8170.55 | −0.654753 | ||||||||
\(539\) | −2704.76 | −0.216145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3020.10 | −0.240008 | −0.120004 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120004 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(542\) | −9730.24 | −0.771125 | ||||||||
\(543\) | 9602.32 | 0.758885 | ||||||||
\(544\) | 7670.71 | 0.604557 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9576.16 | 0.750590 | ||||||||
\(547\) | 17068.8 | 1.33421 | 0.667103 | − | 0.744965i | \(-0.267534\pi\) | ||||
0.667103 | + | 0.744965i | \(0.267534\pi\) | |||||||
\(548\) | 2588.17 | 0.201754 | ||||||||
\(549\) | 1143.07 | 0.0888616 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23797.9 | 1.83997 | ||||||||
\(552\) | 631.616 | 0.0487018 | ||||||||
\(553\) | −2122.44 | −0.163210 | ||||||||
\(554\) | 7714.42 | 0.591614 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15625.3 | −1.19184 | ||||||||
\(557\) | −4965.05 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(558\) | −2123.87 | −0.161130 | ||||||||
\(559\) | −7622.10 | −0.576709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1351.81 | −0.101736 | ||||||||
\(562\) | 2759.21 | 0.207100 | ||||||||
\(563\) | 18839.1 | 1.41025 | 0.705126 | − | 0.709082i | \(-0.250890\pi\) | ||||
0.705126 | + | 0.709082i | \(0.250890\pi\) | |||||||
\(564\) | −8065.94 | −0.602194 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8282.92 | 0.615119 | ||||||||
\(567\) | 1965.63 | 0.145588 | ||||||||
\(568\) | 6564.40 | 0.484922 | ||||||||
\(569\) | 25785.9 | 1.89983 | 0.949914 | − | 0.312513i | \(-0.101171\pi\) | ||||
0.949914 | + | 0.312513i | \(0.101171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1732.89 | 0.127004 | 0.0635018 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635018 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(572\) | 5153.31 | 0.376697 | ||||||||
\(573\) | −7263.09 | −0.529529 | ||||||||
\(574\) | 6796.38 | 0.494208 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1809.20 | 0.130874 | ||||||||
\(577\) | −8872.77 | −0.640170 | −0.320085 | − | 0.947389i | \(-0.603711\pi\) | ||||
−0.320085 | + | 0.947389i | \(0.603711\pi\) | |||||||
\(578\) | 5051.54 | 0.363523 | ||||||||
\(579\) | 6826.32 | 0.489969 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25240.8 | 1.80235 | ||||||||
\(582\) | 775.534 | 0.0552352 | ||||||||
\(583\) | −6240.83 | −0.443343 | ||||||||
\(584\) | −24244.6 | −1.71789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13048.9 | −0.919875 | ||||||||
\(587\) | 11144.0 | 0.783582 | 0.391791 | − | 0.920054i | \(-0.371856\pi\) | ||||
0.391791 | + | 0.920054i | \(0.371856\pi\) | |||||||
\(588\) | 4102.55 | 0.287732 | ||||||||
\(589\) | 18268.8 | 1.27802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5873.81 | −0.408826 | ||||||||
\(592\) | −2895.54 | −0.201023 | ||||||||
\(593\) | −6643.23 | −0.460042 | −0.230021 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230021 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(594\) | −463.781 | −0.0320356 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3245.14 | 0.223031 | ||||||||
\(597\) | 5926.07 | 0.406261 | ||||||||
\(598\) | 1307.74 | 0.0894270 | ||||||||
\(599\) | 26138.0 | 1.78292 | 0.891462 | − | 0.453096i | \(-0.149680\pi\) | ||||
0.891462 | + | 0.453096i | \(0.149680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8628.54 | 0.585633 | 0.292817 | − | 0.956169i | \(-0.405407\pi\) | ||||
0.292817 | + | 0.956169i | \(0.405407\pi\) | |||||||
\(602\) | 3428.86 | 0.232143 | ||||||||
\(603\) | 5654.04 | 0.381841 | ||||||||
\(604\) | −6920.40 | −0.466204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7075.50 | 0.474294 | ||||||||
\(607\) | −4043.74 | −0.270396 | −0.135198 | − | 0.990819i | \(-0.543167\pi\) | ||||
−0.135198 | + | 0.990819i | \(0.543167\pi\) | |||||||
\(608\) | −22636.7 | −1.50994 | ||||||||
\(609\) | −14331.6 | −0.953604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40722.6 | −2.69633 | ||||||||
\(612\) | 2050.41 | 0.135430 | ||||||||
\(613\) | −5443.62 | −0.358671 | −0.179336 | − | 0.983788i | \(-0.557395\pi\) | ||||
−0.179336 | + | 0.983788i | \(0.557395\pi\) | |||||||
\(614\) | −13364.2 | −0.878397 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5652.95 | −0.369746 | ||||||||
\(617\) | −234.868 | −0.0153248 | −0.00766241 | − | 0.999971i | \(-0.502439\pi\) | ||||
−0.00766241 | + | 0.999971i | \(0.502439\pi\) | |||||||
\(618\) | 5836.06 | 0.379872 | ||||||||
\(619\) | −4517.44 | −0.293330 | −0.146665 | − | 0.989186i | \(-0.546854\pi\) | ||||
−0.146665 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 268.429 | 0.0173457 | ||||||||
\(622\) | −9580.42 | −0.617588 | ||||||||
\(623\) | 9481.68 | 0.609752 | ||||||||
\(624\) | −2886.76 | −0.185197 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6384.59 | 0.407635 | ||||||||
\(627\) | 3989.29 | 0.254094 | ||||||||
\(628\) | 1690.66 | 0.107428 | ||||||||
\(629\) | 10383.4 | 0.658211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26533.3 | 1.67397 | 0.836983 | − | 0.547229i | \(-0.184317\pi\) | ||||
0.836983 | + | 0.547229i | \(0.184317\pi\) | |||||||
\(632\) | −1852.19 | −0.116576 | ||||||||
\(633\) | −3539.77 | −0.222264 | ||||||||
\(634\) | 12425.9 | 0.778386 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9466.01 | 0.590175 | ||||||||
\(637\) | 20712.6 | 1.28832 | ||||||||
\(638\) | 3381.47 | 0.209834 | ||||||||
\(639\) | 2789.79 | 0.172711 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8233.77 | −0.507355 | −0.253677 | − | 0.967289i | \(-0.581640\pi\) | ||||
−0.253677 | + | 0.967289i | \(0.581640\pi\) | |||||||
\(642\) | −2579.22 | −0.158557 | ||||||||
\(643\) | −4844.30 | −0.297108 | −0.148554 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148554 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(644\) | 1341.77 | 0.0821012 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7732.87 | 0.470969 | ||||||||
\(647\) | −29856.8 | −1.81421 | −0.907104 | − | 0.420907i | \(-0.861712\pi\) | ||||
−0.907104 | + | 0.420907i | \(0.861712\pi\) | |||||||
\(648\) | 1715.34 | 0.103989 | ||||||||
\(649\) | 5408.66 | 0.327132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11001.9 | −0.662362 | ||||||||
\(652\) | −1445.90 | −0.0868497 | ||||||||
\(653\) | −4212.65 | −0.252456 | −0.126228 | − | 0.992001i | \(-0.540287\pi\) | ||||
−0.126228 | + | 0.992001i | \(0.540287\pi\) | |||||||
\(654\) | 6466.24 | 0.386621 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2048.78 | −0.121938 | ||||||||
\(657\) | −10303.7 | −0.611848 | ||||||||
\(658\) | 18319.4 | 1.08535 | ||||||||
\(659\) | 14549.4 | 0.860039 | 0.430020 | − | 0.902820i | \(-0.358507\pi\) | ||||
0.430020 | + | 0.902820i | \(0.358507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2494.86 | 0.146806 | 0.0734029 | − | 0.997302i | \(-0.476614\pi\) | ||||
0.0734029 | + | 0.997302i | \(0.476614\pi\) | |||||||
\(662\) | 4862.63 | 0.285485 | ||||||||
\(663\) | 10351.9 | 0.606389 | ||||||||
\(664\) | 22026.9 | 1.28736 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3562.35 | 0.207265 | ||||||||
\(667\) | −1957.14 | −0.113615 | ||||||||
\(668\) | 19289.5 | 1.11726 | ||||||||
\(669\) | −17228.2 | −0.995637 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1397.09 | −0.0803784 | ||||||||
\(672\) | 13632.3 | 0.782557 | ||||||||
\(673\) | −8223.98 | −0.471042 | −0.235521 | − | 0.971869i | \(-0.575680\pi\) | ||||
−0.235521 | + | 0.971869i | \(0.575680\pi\) | |||||||
\(674\) | −12909.6 | −0.737773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27244.4 | −1.55009 | ||||||||
\(677\) | −9369.49 | −0.531904 | −0.265952 | − | 0.963986i | \(-0.585686\pi\) | ||||
−0.265952 | + | 0.963986i | \(0.585686\pi\) | |||||||
\(678\) | 4768.78 | 0.270124 | ||||||||
\(679\) | 4017.34 | 0.227057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2139.48 | −0.120389 | ||||||||
\(682\) | 2595.85 | 0.145748 | ||||||||
\(683\) | −561.238 | −0.0314424 | −0.0157212 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157212 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(684\) | −6050.90 | −0.338248 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3680.01 | 0.204815 | ||||||||
\(687\) | −13314.3 | −0.739405 | ||||||||
\(688\) | −1033.64 | −0.0572777 | ||||||||
\(689\) | 47791.1 | 2.64252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11456.5 | 0.630720 | 0.315360 | − | 0.948972i | \(-0.397875\pi\) | ||||
0.315360 | + | 0.948972i | \(0.397875\pi\) | |||||||
\(692\) | 21491.7 | 1.18063 | ||||||||
\(693\) | −2402.43 | −0.131690 | ||||||||
\(694\) | 13543.4 | 0.740779 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12506.7 | −0.681130 | ||||||||
\(697\) | 7346.96 | 0.399263 | ||||||||
\(698\) | −5233.09 | −0.283775 | ||||||||
\(699\) | 1842.54 | 0.0997012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2782.39 | −0.149914 | −0.0749569 | − | 0.997187i | \(-0.523882\pi\) | ||||
−0.0749569 | + | 0.997187i | \(0.523882\pi\) | |||||||
\(702\) | 3551.55 | 0.190947 | ||||||||
\(703\) | −30642.1 | −1.64394 | ||||||||
\(704\) | −2211.24 | −0.118380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.1404 | 0.00304604 | ||||||||
\(707\) | 36651.8 | 1.94969 | ||||||||
\(708\) | −8203.79 | −0.435476 | ||||||||
\(709\) | 4824.70 | 0.255565 | 0.127783 | − | 0.991802i | \(-0.459214\pi\) | ||||
0.127783 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −787.158 | −0.0415200 | ||||||||
\(712\) | 8274.37 | 0.435527 | ||||||||
\(713\) | −1502.43 | −0.0789153 | ||||||||
\(714\) | −4656.90 | −0.244090 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −911.371 | −0.0475692 | ||||||||
\(717\) | −15573.0 | −0.811135 | ||||||||
\(718\) | 19971.0 | 1.03804 | ||||||||
\(719\) | 20717.6 | 1.07460 | 0.537298 | − | 0.843392i | \(-0.319445\pi\) | ||||
0.537298 | + | 0.843392i | \(0.319445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30231.4 | 1.56155 | ||||||||
\(722\) | −12109.5 | −0.624195 | ||||||||
\(723\) | 1061.12 | 0.0545832 | ||||||||
\(724\) | 17801.3 | 0.913783 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 566.844 | 0.0289773 | ||||||||
\(727\) | −22731.2 | −1.15963 | −0.579816 | − | 0.814747i | \(-0.696876\pi\) | ||||
−0.579816 | + | 0.814747i | \(0.696876\pi\) | |||||||
\(728\) | 43289.2 | 2.20385 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3706.64 | 0.187544 | ||||||||
\(732\) | 2119.08 | 0.106999 | ||||||||
\(733\) | 24311.8 | 1.22507 | 0.612536 | − | 0.790443i | \(-0.290149\pi\) | ||||
0.612536 | + | 0.790443i | \(0.290149\pi\) | |||||||
\(734\) | 2020.11 | 0.101586 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1861.65 | 0.0932357 | ||||||||
\(737\) | −6910.49 | −0.345388 | ||||||||
\(738\) | 2520.60 | 0.125724 | ||||||||
\(739\) | 16033.9 | 0.798126 | 0.399063 | − | 0.916924i | \(-0.369335\pi\) | ||||
0.399063 | + | 0.916924i | \(0.369335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30549.2 | −1.51451 | ||||||||
\(742\) | −21499.2 | −1.06369 | ||||||||
\(743\) | 19512.2 | 0.963435 | 0.481718 | − | 0.876326i | \(-0.340013\pi\) | ||||
0.481718 | + | 0.876326i | \(0.340013\pi\) | |||||||
\(744\) | −9601.01 | −0.473105 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13489.7 | −0.662053 | ||||||||
\(747\) | 9361.15 | 0.458509 | ||||||||
\(748\) | −2506.06 | −0.122501 | ||||||||
\(749\) | −13360.6 | −0.651785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8393.65 | 0.407841 | 0.203920 | − | 0.978987i | \(-0.434632\pi\) | ||||
0.203920 | + | 0.978987i | \(0.434632\pi\) | |||||||
\(752\) | −5522.41 | −0.267795 | ||||||||
\(753\) | −7838.73 | −0.379361 | ||||||||
\(754\) | −25894.7 | −1.25070 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3643.98 | 0.175305 | ||||||||
\(757\) | −20208.6 | −0.970270 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(758\) | −2894.38 | −0.138692 | ||||||||
\(759\) | −328.080 | −0.0156898 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3529.19 | 0.168112 | 0.0840558 | − | 0.996461i | \(-0.473213\pi\) | ||||
0.0840558 | + | 0.996461i | \(0.473213\pi\) | |||||||
\(762\) | −5536.59 | −0.263215 | ||||||||
\(763\) | 33495.8 | 1.58929 | ||||||||
\(764\) | −13464.7 | −0.637612 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6072.01 | 0.286411 | ||||||||
\(767\) | −41418.5 | −1.94985 | ||||||||
\(768\) | 10371.8 | 0.487317 | ||||||||
\(769\) | −26692.6 | −1.25171 | −0.625853 | − | 0.779941i | \(-0.715249\pi\) | ||||
−0.625853 | + | 0.779941i | \(0.715249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7303.14 | −0.341136 | ||||||||
\(772\) | 12655.0 | 0.589977 | ||||||||
\(773\) | −32009.0 | −1.48937 | −0.744684 | − | 0.667417i | \(-0.767400\pi\) | ||||
−0.744684 | + | 0.667417i | \(0.767400\pi\) | |||||||
\(774\) | 1271.67 | 0.0590561 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3505.81 | 0.162180 | ||||||||
\(777\) | 18453.4 | 0.852008 | ||||||||
\(778\) | 16850.9 | 0.776523 | ||||||||
\(779\) | −21681.3 | −0.997194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3409.74 | −0.156223 | ||||||||
\(782\) | −635.954 | −0.0290814 | ||||||||
\(783\) | −5315.21 | −0.242593 | ||||||||
\(784\) | 2808.84 | 0.127954 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12251.6 | −0.555980 | ||||||||
\(787\) | −8180.18 | −0.370511 | −0.185255 | − | 0.982690i | \(-0.559311\pi\) | ||||
−0.185255 | + | 0.982690i | \(0.559311\pi\) | |||||||
\(788\) | −10889.2 | −0.492272 | ||||||||
\(789\) | 21613.2 | 0.975223 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24702.8 | 1.11040 | ||||||||
\(792\) | −2096.53 | −0.0940619 | ||||||||
\(793\) | 10698.6 | 0.479091 | ||||||||
\(794\) | −4490.91 | −0.200726 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10986.1 | 0.489184 | ||||||||
\(797\) | 25471.0 | 1.13203 | 0.566015 | − | 0.824395i | \(-0.308484\pi\) | ||||
0.566015 | + | 0.824395i | \(0.308484\pi\) | |||||||
\(798\) | 13742.8 | 0.609636 | ||||||||
\(799\) | 19803.4 | 0.876840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3516.51 | 0.155118 | ||||||||
\(802\) | −11892.6 | −0.523619 | ||||||||
\(803\) | 12593.4 | 0.553437 | ||||||||
\(804\) | 10481.7 | 0.459779 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19878.5 | −0.868723 | ||||||||
\(807\) | −15697.0 | −0.684708 | ||||||||
\(808\) | 31984.9 | 1.39261 | ||||||||
\(809\) | 12381.1 | 0.538067 | 0.269034 | − | 0.963131i | \(-0.413296\pi\) | ||||
0.269034 | + | 0.963131i | \(0.413296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29129.5 | 1.26125 | 0.630627 | − | 0.776086i | \(-0.282798\pi\) | ||||
0.630627 | + | 0.776086i | \(0.282798\pi\) | |||||||
\(812\) | −26568.6 | −1.14825 | ||||||||
\(813\) | −18693.4 | −0.806403 | ||||||||
\(814\) | −4353.99 | −0.187478 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1403.83 | 0.0602255 | ||||||||
\(817\) | −10938.5 | −0.468409 | ||||||||
\(818\) | 5920.64 | 0.253069 | ||||||||
\(819\) | 18397.4 | 0.784929 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5279.00 | −0.224407 | −0.112204 | − | 0.993685i | \(-0.535791\pi\) | ||||
−0.112204 | + | 0.993685i | \(0.535791\pi\) | |||||||
\(822\) | −2180.09 | −0.0925055 | ||||||||
\(823\) | −19991.7 | −0.846738 | −0.423369 | − | 0.905957i | \(-0.639153\pi\) | ||||
−0.423369 | + | 0.905957i | \(0.639153\pi\) | |||||||
\(824\) | 26382.0 | 1.11537 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18632.4 | 0.784874 | ||||||||
\(827\) | −9918.83 | −0.417063 | −0.208532 | − | 0.978016i | \(-0.566868\pi\) | ||||
−0.208532 | + | 0.978016i | \(0.566868\pi\) | |||||||
\(828\) | 497.628 | 0.0208862 | ||||||||
\(829\) | −5671.76 | −0.237622 | −0.118811 | − | 0.992917i | \(-0.537908\pi\) | ||||
−0.118811 | + | 0.992917i | \(0.537908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14820.7 | 0.618681 | ||||||||
\(832\) | 16933.3 | 0.705595 | ||||||||
\(833\) | −10072.5 | −0.418959 | ||||||||
\(834\) | 13161.7 | 0.546464 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7395.54 | 0.305957 | ||||||||
\(837\) | −4080.31 | −0.168502 | ||||||||
\(838\) | −13752.1 | −0.566894 | ||||||||
\(839\) | −29160.1 | −1.19990 | −0.599951 | − | 0.800036i | \(-0.704813\pi\) | ||||
−0.599951 | + | 0.800036i | \(0.704813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14364.7 | 0.588984 | ||||||||
\(842\) | 12071.9 | 0.494092 | ||||||||
\(843\) | 5300.90 | 0.216575 | ||||||||
\(844\) | −6562.21 | −0.267631 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6794.17 | 0.276109 | ||||||||
\(847\) | 2936.31 | 0.119118 | ||||||||
\(848\) | 6480.98 | 0.262450 | ||||||||
\(849\) | 15912.9 | 0.643260 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2520.02 | 0.101510 | ||||||||
\(852\) | 5171.85 | 0.207963 | ||||||||
\(853\) | −18361.2 | −0.737017 | −0.368508 | − | 0.929624i | \(-0.620131\pi\) | ||||
−0.368508 | + | 0.929624i | \(0.620131\pi\) | |||||||
\(854\) | −4812.86 | −0.192849 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11659.4 | −0.465550 | ||||||||
\(857\) | −1755.28 | −0.0699642 | −0.0349821 | − | 0.999388i | \(-0.511137\pi\) | ||||
−0.0349821 | + | 0.999388i | \(0.511137\pi\) | |||||||
\(858\) | −4340.78 | −0.172718 | ||||||||
\(859\) | −31317.3 | −1.24392 | −0.621962 | − | 0.783047i | \(-0.713664\pi\) | ||||
−0.621962 | + | 0.783047i | \(0.713664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13057.0 | 0.516818 | ||||||||
\(862\) | −14082.0 | −0.556422 | ||||||||
\(863\) | 42862.3 | 1.69067 | 0.845336 | − | 0.534235i | \(-0.179400\pi\) | ||||
0.845336 | + | 0.534235i | \(0.179400\pi\) | |||||||
\(864\) | 5055.88 | 0.199079 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21548.0 | −0.845530 | ||||||||
\(867\) | 9704.84 | 0.380154 | ||||||||
\(868\) | −20395.9 | −0.797558 | ||||||||
\(869\) | 962.082 | 0.0375563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52919.3 | 2.05867 | ||||||||
\(872\) | 29230.8 | 1.13518 | ||||||||
\(873\) | 1489.93 | 0.0577622 | ||||||||
\(874\) | 1876.74 | 0.0726335 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19101.4 | −0.736733 | ||||||||
\(877\) | −38306.6 | −1.47494 | −0.737471 | − | 0.675379i | \(-0.763980\pi\) | ||||
−0.737471 | + | 0.675379i | \(0.763980\pi\) | |||||||
\(878\) | −725.298 | −0.0278788 | ||||||||
\(879\) | −25069.2 | −0.961959 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12994.5 | −0.496931 | −0.248466 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248466 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(882\) | −3455.69 | −0.131927 | ||||||||
\(883\) | 4256.48 | 0.162222 | 0.0811110 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811110 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(884\) | 19191.0 | 0.730160 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9051.03 | 0.343200 | ||||||||
\(887\) | −38188.8 | −1.44561 | −0.722804 | − | 0.691053i | \(-0.757147\pi\) | ||||
−0.722804 | + | 0.691053i | \(0.757147\pi\) | |||||||
\(888\) | 16103.7 | 0.608563 | ||||||||
\(889\) | −28680.1 | −1.08200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | −31938.5 | −1.19886 | ||||||||
\(893\) | −58441.1 | −2.18999 | ||||||||
\(894\) | −2733.48 | −0.102261 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 28735.3 | 1.07141 | ||||||||
\(897\) | 2512.38 | 0.0935182 | ||||||||
\(898\) | 13984.6 | 0.519679 | ||||||||
\(899\) | 29750.0 | 1.10369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23240.9 | −0.859341 | ||||||||
\(902\) | −3080.73 | −0.113722 | ||||||||
\(903\) | 6587.40 | 0.242763 | ||||||||
\(904\) | 21557.3 | 0.793127 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5829.26 | 0.213757 | ||||||||
\(907\) | 31257.8 | 1.14432 | 0.572161 | − | 0.820142i | \(-0.306105\pi\) | ||||
0.572161 | + | 0.820142i | \(0.306105\pi\) | |||||||
\(908\) | −3966.28 | −0.144962 | ||||||||
\(909\) | 13593.2 | 0.495993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35781.4 | −1.30131 | −0.650653 | − | 0.759375i | \(-0.725505\pi\) | ||||
−0.650653 | + | 0.759375i | \(0.725505\pi\) | |||||||
\(912\) | −4142.80 | −0.150419 | ||||||||
\(913\) | −11441.4 | −0.414737 | ||||||||
\(914\) | −15721.5 | −0.568950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24682.7 | −0.890326 | ||||||||
\(917\) | −63464.6 | −2.28548 | ||||||||
\(918\) | −1727.12 | −0.0620954 | ||||||||
\(919\) | 31489.1 | 1.13028 | 0.565140 | − | 0.824995i | \(-0.308822\pi\) | ||||
0.565140 | + | 0.824995i | \(0.308822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25674.9 | −0.918583 | ||||||||
\(922\) | 12950.0 | 0.462567 | ||||||||
\(923\) | 26111.2 | 0.931159 | ||||||||
\(924\) | −4453.75 | −0.158569 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15461.9 | 0.548713 | ||||||||
\(927\) | 11212.0 | 0.397251 | ||||||||
\(928\) | −36862.9 | −1.30397 | ||||||||
\(929\) | −40466.1 | −1.42912 | −0.714559 | − | 0.699575i | \(-0.753373\pi\) | ||||
−0.714559 | + | 0.699575i | \(0.753373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29724.7 | 1.04639 | ||||||||
\(932\) | 3415.79 | 0.120051 | ||||||||
\(933\) | −18405.6 | −0.645843 | ||||||||
\(934\) | −17044.4 | −0.597120 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16054.8 | 0.560651 | ||||||||
\(937\) | −39041.1 | −1.36117 | −0.680586 | − | 0.732668i | \(-0.738275\pi\) | ||||
−0.680586 | + | 0.732668i | \(0.738275\pi\) | |||||||
\(938\) | −23806.1 | −0.828676 | ||||||||
\(939\) | 12265.9 | 0.426284 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10842.0 | 0.375598 | 0.187799 | − | 0.982207i | \(-0.439865\pi\) | ||||
0.187799 | + | 0.982207i | \(0.439865\pi\) | |||||||
\(942\) | −1424.09 | −0.0492563 | ||||||||
\(943\) | 1783.08 | 0.0615748 | ||||||||
\(944\) | −5616.79 | −0.193656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1554.27 | −0.0534182 | ||||||||
\(947\) | 17810.1 | 0.611142 | 0.305571 | − | 0.952169i | \(-0.401153\pi\) | ||||
0.305571 | + | 0.952169i | \(0.401153\pi\) | |||||||
\(948\) | −1459.27 | −0.0499947 | ||||||||
\(949\) | −96437.6 | −3.29873 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23872.3 | 0.813997 | ||||||||
\(952\) | −21051.6 | −0.716687 | ||||||||
\(953\) | 45621.7 | 1.55071 | 0.775357 | − | 0.631523i | \(-0.217570\pi\) | ||||
0.775357 | + | 0.631523i | \(0.217570\pi\) | |||||||
\(954\) | −7973.49 | −0.270599 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28870.0 | −0.976697 | ||||||||
\(957\) | 6496.37 | 0.219433 | ||||||||
\(958\) | −8940.12 | −0.301506 | ||||||||
\(959\) | −11293.1 | −0.380264 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6952.93 | −0.233390 | ||||||||
\(962\) | 33342.0 | 1.11745 | ||||||||
\(963\) | −4955.11 | −0.165811 | ||||||||
\(964\) | 1967.17 | 0.0657242 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1130.21 | −0.0376439 | ||||||||
\(967\) | 41111.6 | 1.36718 | 0.683588 | − | 0.729868i | \(-0.260419\pi\) | ||||
0.683588 | + | 0.729868i | \(0.260419\pi\) | |||||||
\(968\) | 2562.43 | 0.0850821 | ||||||||
\(969\) | 14856.1 | 0.492515 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22030.1 | 0.728093 | 0.364046 | − | 0.931381i | \(-0.381395\pi\) | ||||
0.364046 | + | 0.931381i | \(0.381395\pi\) | |||||||
\(972\) | 1351.46 | 0.0445967 | ||||||||
\(973\) | 68178.7 | 2.24636 | ||||||||
\(974\) | −25953.5 | −0.853802 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1450.85 | 0.0475825 | ||||||||
\(977\) | 34593.0 | 1.13278 | 0.566391 | − | 0.824137i | \(-0.308339\pi\) | ||||
0.566391 | + | 0.824137i | \(0.308339\pi\) | |||||||
\(978\) | 1217.93 | 0.0398211 | ||||||||
\(979\) | −4297.95 | −0.140310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12422.7 | 0.404309 | ||||||||
\(982\) | 15256.0 | 0.495762 | ||||||||
\(983\) | 20638.9 | 0.669663 | 0.334831 | − | 0.942278i | \(-0.391321\pi\) | ||||
0.334831 | + | 0.942278i | \(0.391321\pi\) | |||||||
\(984\) | 11394.4 | 0.369147 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12592.6 | 0.406725 | ||||||||
\(987\) | 35194.5 | 1.13501 | ||||||||
\(988\) | −56633.7 | −1.82364 | ||||||||
\(989\) | 899.586 | 0.0289233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35229.7 | −1.12927 | −0.564636 | − | 0.825340i | \(-0.690983\pi\) | ||||
−0.564636 | + | 0.825340i | \(0.690983\pi\) | |||||||
\(992\) | −28298.4 | −0.905722 | ||||||||
\(993\) | 9341.91 | 0.298546 | ||||||||
\(994\) | −11746.3 | −0.374819 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17354.2 | 0.552096 | ||||||||
\(997\) | −29366.2 | −0.932834 | −0.466417 | − | 0.884565i | \(-0.654455\pi\) | ||||
−0.466417 | + | 0.884565i | \(0.654455\pi\) | |||||||
\(998\) | 2946.09 | 0.0934439 | ||||||||
\(999\) | 6843.87 | 0.216747 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.4.a.v.1.2 | yes | 4 | |
3.2 | odd | 2 | 2475.4.a.bb.1.4 | 4 | |||
5.2 | odd | 4 | 825.4.c.q.199.4 | 8 | |||
5.3 | odd | 4 | 825.4.c.q.199.5 | 8 | |||
5.4 | even | 2 | 825.4.a.u.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 2475.4.a.bd.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.u.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
825.4.a.v.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
825.4.c.q.199.4 | 8 | 5.2 | odd | 4 | |||
825.4.c.q.199.5 | 8 | 5.3 | odd | 4 | |||
2475.4.a.bb.1.4 | 4 | 3.2 | odd | 2 | |||
2475.4.a.bd.1.1 | 4 | 15.14 | odd | 2 |