Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,4,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, 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("2475.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(146.029727264\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 825) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(13.6191\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 | \(0.589024\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.56155 | −0.695194 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.2670 | −1.31029 | −0.655147 | − | 0.755501i | \(-0.727394\pi\) | ||||
−0.655147 | + | 0.755501i | \(0.727394\pi\) | |||||||
\(8\) | 21.1771 | 0.935904 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −84.2360 | −1.79714 | −0.898571 | − | 0.438828i | \(-0.855394\pi\) | ||||
−0.898571 | + | 0.438828i | \(0.855394\pi\) | |||||||
\(14\) | 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 | \(0.594392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 120.887 | 1.45966 | 0.729828 | − | 0.683630i | \(-0.239600\pi\) | ||||
0.729828 | + | 0.683630i | \(0.239600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.1771 | −0.166462 | ||||||||
\(23\) | −9.94182 | −0.0901310 | −0.0450655 | − | 0.998984i | \(-0.514350\pi\) | ||||
−0.0450655 | + | 0.998984i | \(0.514350\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 131.539 | 0.992189 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 134.962 | 0.910909 | ||||||||
\(29\) | −196.860 | −1.26055 | −0.630275 | − | 0.776372i | \(-0.717058\pi\) | ||||
−0.630275 | + | 0.776372i | \(0.717058\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 63.9675 | 0.322657 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 253.477 | 1.12625 | 0.563126 | − | 0.826371i | \(-0.309599\pi\) | ||||
0.563126 | + | 0.826371i | \(0.309599\pi\) | |||||||
\(38\) | −188.772 | −0.805865 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 179.351 | 0.683170 | 0.341585 | − | 0.939851i | \(-0.389036\pi\) | ||||
0.341585 | + | 0.939851i | \(0.389036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 90.4851 | 0.320903 | 0.160452 | − | 0.987044i | \(-0.448705\pi\) | ||||
0.160452 | + | 0.987044i | \(0.448705\pi\) | |||||||
\(44\) | −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 | \(0.770029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 245.887 | 0.716873 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 468.483 | 1.24936 | ||||||||
\(53\) | 567.348 | 1.47040 | 0.735200 | − | 0.677850i | \(-0.237088\pi\) | ||||
0.735200 | + | 0.677850i | \(0.237088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −513.904 | −1.22631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 307.407 | 0.695939 | ||||||||
\(59\) | 491.696 | 1.08497 | 0.542487 | − | 0.840064i | \(-0.317483\pi\) | ||||
0.542487 | + | 0.840064i | \(0.317483\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −628.226 | −1.14552 | −0.572762 | − | 0.819722i | \(-0.694128\pi\) | ||||
−0.572762 | + | 0.819722i | \(0.694128\pi\) | |||||||
\(68\) | 227.824 | 0.406290 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −309.976 | −0.518133 | −0.259066 | − | 0.965859i | \(-0.583415\pi\) | ||||
−0.259066 | + | 0.965859i | \(0.583415\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1144.85 | 1.83554 | 0.917772 | − | 0.397109i | \(-0.129986\pi\) | ||||
0.917772 | + | 0.397109i | \(0.129986\pi\) | |||||||
\(74\) | −395.817 | −0.621795 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −672.322 | −1.01474 | ||||||||
\(77\) | −266.937 | −0.395069 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −87.4620 | −0.124560 | −0.0622800 | − | 0.998059i | \(-0.519837\pi\) | ||||
−0.0622800 | + | 0.998059i | \(0.519837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −280.067 | −0.377173 | ||||||||
\(83\) | 1040.13 | 1.37553 | 0.687764 | − | 0.725934i | \(-0.258592\pi\) | ||||
0.687764 | + | 0.725934i | \(0.258592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −141.297 | −0.177168 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 232.948 | 0.282186 | ||||||||
\(89\) | −390.723 | −0.465355 | −0.232677 | − | 0.972554i | \(-0.574749\pi\) | ||||
−0.232677 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2044.15 | 2.35479 | ||||||||
\(92\) | 55.2920 | 0.0626585 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 754.908 | 0.828328 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −165.548 | −0.173287 | −0.0866433 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866433 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(98\) | −383.966 | −0.395780 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1510.35 | −1.48798 | −0.743990 | − | 0.668191i | \(-0.767069\pi\) | ||||
−0.743990 | + | 0.668191i | \(0.767069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1245.78 | −1.19175 | −0.595876 | − | 0.803076i | \(-0.703195\pi\) | ||||
−0.595876 | + | 0.803076i | \(0.703195\pi\) | |||||||
\(104\) | −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 | \(0.580009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1380.30 | 1.21293 | 0.606463 | − | 0.795112i | \(-0.292588\pi\) | ||||
0.606463 | + | 0.795112i | \(0.292588\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −277.209 | −0.233873 | ||||||||
\(113\) | 1017.96 | 0.847445 | 0.423723 | − | 0.905792i | \(-0.360723\pi\) | ||||
0.423723 | + | 0.905792i | \(0.360723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1094.85 | 0.876326 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −767.810 | −0.599005 | ||||||||
\(119\) | 994.075 | 0.765770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −198.329 | −0.147179 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −840.477 | −0.608686 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1181.86 | 0.825770 | 0.412885 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412885 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(128\) | 1184.13 | 0.817683 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2615.26 | 1.74425 | 0.872124 | − | 0.489284i | \(-0.162742\pi\) | ||||
0.872124 | + | 0.489284i | \(0.162742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | \(0.546352\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2809.52 | 1.71439 | 0.857196 | − | 0.514990i | \(-0.172204\pi\) | ||||
0.857196 | + | 0.514990i | \(0.172204\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 484.045 | 0.286057 | ||||||||
\(143\) | −926.596 | −0.541859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1787.75 | −1.01339 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1409.72 | −0.782963 | ||||||||
\(149\) | 583.496 | 0.320818 | 0.160409 | − | 0.987051i | \(-0.448719\pi\) | ||||
0.160409 | + | 0.987051i | \(0.448719\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 416.836 | 0.218114 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 303.991 | 0.154529 | 0.0772647 | − | 0.997011i | \(-0.475381\pi\) | ||||
0.0772647 | + | 0.997011i | \(0.475381\pi\) | |||||||
\(158\) | 136.577 | 0.0687687 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 241.258 | 0.118098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −259.982 | −0.124929 | −0.0624643 | − | 0.998047i | \(-0.519896\pi\) | ||||
−0.0624643 | + | 0.998047i | \(0.519896\pi\) | |||||||
\(164\) | −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 | \(0.797064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4898.70 | 2.22972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −503.237 | −0.223090 | ||||||||
\(173\) | −3864.34 | −1.69827 | −0.849134 | − | 0.528177i | \(-0.822876\pi\) | ||||
−0.849134 | + | 0.528177i | \(0.822876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 125.656 | 0.0538164 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 610.135 | 0.256919 | ||||||||
\(179\) | −163.870 | −0.0684258 | −0.0342129 | − | 0.999415i | \(-0.510892\pi\) | ||||
−0.0342129 | + | 0.999415i | \(0.510892\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −210.539 | −0.0843539 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −450.605 | −0.176211 | ||||||||
\(188\) | 2688.65 | 1.04303 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2421.03 | −0.917171 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2275.44 | 0.848651 | 0.424326 | − | 0.905510i | \(-0.360511\pi\) | ||||
0.424326 | + | 0.905510i | \(0.360511\pi\) | |||||||
\(194\) | 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 | \(0.384803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1975.36 | −0.703665 | −0.351833 | − | 0.936063i | \(-0.614441\pi\) | ||||
−0.351833 | + | 0.936063i | \(0.614441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2358.50 | 0.821502 | ||||||||
\(203\) | 4777.19 | 1.65169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1945.35 | 0.657958 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 859.741 | 0.274629 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3667.29 | −1.14724 | ||||||||
\(218\) | −2155.41 | −0.669647 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3450.65 | 1.05030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5742.73 | −1.72449 | −0.862247 | − | 0.506489i | \(-0.830943\pi\) | ||||
−0.862247 | + | 0.506489i | \(0.830943\pi\) | |||||||
\(224\) | 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 | \(0.466753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4438.09 | 1.28069 | 0.640343 | − | 0.768089i | \(-0.278792\pi\) | ||||
0.640343 | + | 0.768089i | \(0.278792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4168.91 | −1.17975 | ||||||||
\(233\) | −614.179 | −0.172688 | −0.0863438 | − | 0.996265i | \(-0.527518\pi\) | ||||
−0.0863438 | + | 0.996265i | \(0.527518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2734.60 | −0.754267 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1552.30 | −0.422776 | ||||||||
\(239\) | −5191.00 | −1.40493 | −0.702464 | − | 0.711720i | \(-0.747917\pi\) | ||||
−0.702464 | + | 0.711720i | \(0.747917\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −706.360 | −0.185328 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10183.1 | −2.62321 | ||||||||
\(248\) | 3200.34 | 0.819442 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2612.91 | −0.657073 | −0.328537 | − | 0.944491i | \(-0.606555\pi\) | ||||
−0.328537 | + | 0.944491i | \(0.606555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | \(0.404536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6151.12 | −1.47572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4083.87 | −0.962986 | ||||||||
\(263\) | −7204.41 | −1.68914 | −0.844568 | − | 0.535449i | \(-0.820143\pi\) | ||||
−0.844568 | + | 0.535449i | \(0.820143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4580.93 | 1.05592 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3493.91 | 0.796361 | ||||||||
\(269\) | −5232.32 | −1.18595 | −0.592975 | − | 0.805221i | \(-0.702047\pi\) | ||||
−0.592975 | + | 0.805221i | \(0.702047\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 726.698 | 0.160224 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4940.23 | 1.07159 | 0.535793 | − | 0.844349i | \(-0.320013\pi\) | ||||
0.535793 | + | 0.844349i | \(0.320013\pi\) | |||||||
\(278\) | −4387.22 | −0.946503 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1766.97 | 0.375119 | 0.187559 | − | 0.982253i | \(-0.439942\pi\) | ||||
0.187559 | + | 0.982253i | \(0.439942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5304.29 | 1.11416 | 0.557080 | − | 0.830459i | \(-0.311922\pi\) | ||||
0.557080 | + | 0.830459i | \(0.311922\pi\) | |||||||
\(284\) | 1723.95 | 0.360203 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1446.93 | 0.299156 | ||||||||
\(287\) | −4352.32 | −0.895155 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3234.95 | −0.658446 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6367.15 | −1.27606 | ||||||||
\(293\) | 8356.39 | 1.66616 | 0.833081 | − | 0.553151i | \(-0.186575\pi\) | ||||
0.833081 | + | 0.553151i | \(0.186575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5367.90 | 1.05406 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −911.160 | −0.177121 | ||||||||
\(299\) | 837.459 | 0.161978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2195.80 | −0.420478 | ||||||||
\(302\) | −1943.09 | −0.370238 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1380.93 | 0.260533 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8558.29 | −1.59103 | −0.795517 | − | 0.605932i | \(-0.792800\pi\) | ||||
−0.795517 | + | 0.605932i | \(0.792800\pi\) | |||||||
\(308\) | 1484.58 | 0.274649 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6135.19 | −1.11863 | −0.559316 | − | 0.828954i | \(-0.688936\pi\) | ||||
−0.559316 | + | 0.828954i | \(0.688936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4088.62 | 0.738346 | 0.369173 | − | 0.929361i | \(-0.379641\pi\) | ||||
0.369173 | + | 0.929361i | \(0.379641\pi\) | |||||||
\(314\) | −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 | \(0.749027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2165.46 | −0.380070 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −376.737 | −0.0652011 | ||||||||
\(323\) | −4952.04 | −0.853062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 405.976 | 0.0689721 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5416.02 | 0.887280 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8267.16 | −1.33632 | −0.668161 | − | 0.744016i | \(-0.732918\pi\) | ||||
−0.668161 | + | 0.744016i | \(0.732918\pi\) | |||||||
\(338\) | −7649.58 | −1.23101 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1662.35 | 0.263992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | \(0.734085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3351.21 | 0.514000 | 0.257000 | − | 0.966411i | \(-0.417266\pi\) | ||||
0.257000 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2059.80 | −0.311897 | ||||||||
\(353\) | −36.5920 | −0.00551727 | −0.00275864 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275864 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2173.03 | 0.323512 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 255.892 | 0.0377773 | ||||||||
\(359\) | 12789.2 | 1.88019 | 0.940095 | − | 0.340912i | \(-0.110736\pi\) | ||||
0.940095 | + | 0.340912i | \(0.110736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7754.77 | 1.13060 | ||||||||
\(362\) | 4998.17 | 0.725686 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11368.7 | −1.63703 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1293.66 | 0.184001 | 0.0920005 | − | 0.995759i | \(-0.470674\pi\) | ||||
0.0920005 | + | 0.995759i | \(0.470674\pi\) | |||||||
\(368\) | −113.568 | −0.0160874 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13767.8 | −1.92666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8638.61 | −1.19917 | −0.599585 | − | 0.800311i | \(-0.704668\pi\) | ||||
−0.599585 | + | 0.800311i | \(0.704668\pi\) | |||||||
\(374\) | 703.643 | 0.0972848 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10237.7 | −1.40418 | ||||||||
\(377\) | 16582.7 | 2.26539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1853.53 | 0.251212 | 0.125606 | − | 0.992080i | \(-0.459912\pi\) | ||||
0.125606 | + | 0.992080i | \(0.459912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3780.57 | 0.506363 | ||||||||
\(383\) | −3888.44 | −0.518773 | −0.259387 | − | 0.965774i | \(-0.583520\pi\) | ||||
−0.259387 | + | 0.965774i | \(0.583520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3553.22 | −0.468534 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 920.701 | 0.120468 | ||||||||
\(389\) | 10791.1 | 1.40651 | 0.703255 | − | 0.710938i | \(-0.251729\pi\) | ||||
0.703255 | + | 0.710938i | \(0.251729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 407.257 | 0.0526749 | ||||||||
\(392\) | 5207.18 | 0.670924 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3057.42 | −0.390941 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2875.92 | −0.363573 | −0.181787 | − | 0.983338i | \(-0.558188\pi\) | ||||
−0.181787 | + | 0.983338i | \(0.558188\pi\) | |||||||
\(398\) | 3084.63 | 0.388488 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7615.88 | −0.948426 | −0.474213 | − | 0.880410i | \(-0.657267\pi\) | ||||
−0.474213 | + | 0.880410i | \(0.657267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12730.0 | −1.57351 | ||||||||
\(404\) | 8399.92 | 1.03443 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7459.84 | −0.911886 | ||||||||
\(407\) | 2788.24 | 0.339578 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3791.51 | −0.458382 | −0.229191 | − | 0.973381i | \(-0.573608\pi\) | ||||
−0.229191 | + | 0.973381i | \(0.573608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6928.48 | 0.828500 | ||||||||
\(413\) | −11932.0 | −1.42163 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15773.6 | 1.85905 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2076.49 | −0.242978 | ||||||||
\(419\) | −8806.66 | −1.02681 | −0.513405 | − | 0.858146i | \(-0.671616\pi\) | ||||
−0.513405 | + | 0.858146i | \(0.671616\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12014.8 | 1.37615 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3082.10 | −0.349305 | ||||||||
\(428\) | 3062.01 | 0.345813 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9017.97 | −1.00784 | −0.503922 | − | 0.863749i | \(-0.668110\pi\) | ||||
−0.503922 | + | 0.863749i | \(0.668110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13799.1 | −1.53150 | −0.765751 | − | 0.643137i | \(-0.777633\pi\) | ||||
−0.765751 | + | 0.643137i | \(0.777633\pi\) | |||||||
\(434\) | 5726.67 | 0.633385 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7676.62 | −0.843219 | ||||||||
\(437\) | −1201.84 | −0.131560 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 464.472 | 0.0504967 | 0.0252483 | − | 0.999681i | \(-0.491962\pi\) | ||||
0.0252483 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5388.37 | −0.579861 | ||||||||
\(443\) | −5796.17 | −0.621635 | −0.310818 | − | 0.950470i | \(-0.600603\pi\) | ||||
−0.310818 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8967.58 | 0.952079 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4878.20 | −0.514449 | ||||||||
\(449\) | 8955.57 | 0.941291 | 0.470645 | − | 0.882323i | \(-0.344021\pi\) | ||||
0.470645 | + | 0.882323i | \(0.344021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1972.87 | 0.205984 | ||||||||
\(452\) | −5661.42 | −0.589139 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1113.64 | −0.115122 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10067.8 | −1.03053 | −0.515267 | − | 0.857030i | \(-0.672307\pi\) | ||||
−0.515267 | + | 0.857030i | \(0.672307\pi\) | |||||||
\(458\) | −6930.31 | −0.707057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8293.06 | 0.837844 | 0.418922 | − | 0.908022i | \(-0.362408\pi\) | ||||
0.418922 | + | 0.908022i | \(0.362408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9901.59 | 0.993879 | 0.496939 | − | 0.867785i | \(-0.334457\pi\) | ||||
0.496939 | + | 0.867785i | \(0.334457\pi\) | |||||||
\(464\) | −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 | \(0.318130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15245.2 | 1.50097 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10412.7 | 1.01543 | ||||||||
\(473\) | 995.336 | 0.0967560 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5528.60 | −0.532359 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8106.02 | 0.775650 | ||||||||
\(479\) | −5725.15 | −0.546114 | −0.273057 | − | 0.961998i | \(-0.588035\pi\) | ||||
−0.273057 | + | 0.961998i | \(0.588035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21351.9 | −2.02403 | ||||||||
\(482\) | 552.334 | 0.0521953 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −672.948 | −0.0631995 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16620.3 | −1.54648 | −0.773242 | − | 0.634111i | \(-0.781366\pi\) | ||||
−0.773242 | + | 0.634111i | \(0.781366\pi\) | |||||||
\(488\) | 2689.65 | 0.249498 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9769.75 | 0.897969 | 0.448985 | − | 0.893540i | \(-0.351786\pi\) | ||||
0.448985 | + | 0.893540i | \(0.351786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8064.17 | 0.736698 | ||||||||
\(494\) | 15901.4 | 1.44825 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1726.32 | 0.156278 | ||||||||
\(497\) | 7522.20 | 0.678907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1886.64 | −0.169254 | −0.0846270 | − | 0.996413i | \(-0.526970\pi\) | ||||
−0.0846270 | + | 0.996413i | \(0.526970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4080.20 | 0.362765 | ||||||||
\(503\) | −2920.56 | −0.258889 | −0.129445 | − | 0.991587i | \(-0.541319\pi\) | ||||
−0.129445 | + | 0.991587i | \(0.541319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 170.771 | 0.0150034 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6572.96 | −0.574070 | ||||||||
\(509\) | −7956.30 | −0.692842 | −0.346421 | − | 0.938079i | \(-0.612603\pi\) | ||||
−0.346421 | + | 0.938079i | \(0.612603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27782.1 | −2.40510 | ||||||||
\(512\) | −4074.36 | −0.351686 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3801.41 | −0.326212 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5317.78 | −0.452371 | ||||||||
\(518\) | 9605.30 | 0.814735 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20260.6 | −1.70371 | −0.851853 | − | 0.523780i | \(-0.824521\pi\) | ||||
−0.851853 | + | 0.523780i | \(0.824521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3457.70 | −0.289091 | −0.144546 | − | 0.989498i | \(-0.546172\pi\) | ||||
−0.144546 | + | 0.989498i | \(0.546172\pi\) | |||||||
\(524\) | −14544.9 | −1.21259 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11250.1 | 0.932559 | ||||||||
\(527\) | −6190.60 | −0.511702 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12068.2 | −0.991876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16315.2 | 1.32961 | ||||||||
\(533\) | −15107.8 | −1.22775 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13304.0 | −1.07210 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7670.71 | 0.604557 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17068.8 | −1.33421 | −0.667103 | − | 0.744965i | \(-0.732466\pi\) | ||||
−0.667103 | + | 0.744965i | \(0.732466\pi\) | |||||||
\(548\) | 2588.17 | 0.201754 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23797.9 | −1.83997 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.560475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7622.10 | −0.576709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2759.21 | −0.207100 | ||||||||
\(563\) | 18839.1 | 1.41025 | 0.705126 | − | 0.709082i | \(-0.250890\pi\) | ||||
0.705126 | + | 0.709082i | \(0.250890\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8282.92 | −0.615119 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6564.40 | −0.484922 | ||||||||
\(569\) | −25785.9 | −1.89983 | −0.949914 | − | 0.312513i | \(-0.898829\pi\) | ||||
−0.949914 | + | 0.312513i | \(0.898829\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6796.38 | 0.494208 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8872.77 | 0.640170 | 0.320085 | − | 0.947389i | \(-0.396289\pi\) | ||||
0.320085 | + | 0.947389i | \(0.396289\pi\) | |||||||
\(578\) | 5051.54 | 0.363523 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25240.8 | −1.80235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.371856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18268.8 | 1.27802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2895.54 | 0.201023 | ||||||||
\(593\) | −6643.23 | −0.460042 | −0.230021 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230021 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3245.14 | −0.223031 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1307.74 | −0.0894270 | ||||||||
\(599\) | −26138.0 | −1.78292 | −0.891462 | − | 0.453096i | \(-0.850320\pi\) | ||||
−0.891462 | + | 0.453096i | \(0.850320\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6920.40 | −0.466204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4043.74 | 0.270396 | 0.135198 | − | 0.990819i | \(-0.456833\pi\) | ||||
0.135198 | + | 0.990819i | \(0.456833\pi\) | |||||||
\(608\) | −22636.7 | −1.50994 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40722.6 | 2.69633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5443.62 | 0.358671 | 0.179336 | − | 0.983788i | \(-0.442605\pi\) | ||||
0.179336 | + | 0.983788i | \(0.442605\pi\) | |||||||
\(614\) | 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 | \(0.502439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4517.44 | −0.293330 | −0.146665 | − | 0.989186i | \(-0.546854\pi\) | ||||
−0.146665 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9580.42 | 0.617588 | ||||||||
\(623\) | 9481.68 | 0.609752 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6384.59 | −0.407635 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12425.9 | 0.778386 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20712.6 | −1.28832 | ||||||||
\(638\) | 3381.47 | 0.209834 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8233.77 | 0.507355 | 0.253677 | − | 0.967289i | \(-0.418360\pi\) | ||||
0.253677 | + | 0.967289i | \(0.418360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4844.30 | 0.297108 | 0.148554 | − | 0.988904i | \(-0.452538\pi\) | ||||
0.148554 | + | 0.988904i | \(0.452538\pi\) | |||||||
\(644\) | −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 | \(0.861712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5408.66 | 0.327132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1445.90 | 0.0868497 | ||||||||
\(653\) | −4212.65 | −0.252456 | −0.126228 | − | 0.992001i | \(-0.540287\pi\) | ||||
−0.126228 | + | 0.992001i | \(0.540287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2048.78 | 0.121938 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18319.4 | −1.08535 | ||||||||
\(659\) | −14549.4 | −0.860039 | −0.430020 | − | 0.902820i | \(-0.641493\pi\) | ||||
−0.430020 | + | 0.902820i | \(0.641493\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22026.9 | 1.28736 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1957.14 | 0.113615 | ||||||||
\(668\) | 19289.5 | 1.11726 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1397.09 | 0.0803784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8223.98 | 0.471042 | 0.235521 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235521 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(674\) | 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 | \(0.585686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4017.34 | 0.227057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2595.85 | −0.145748 | ||||||||
\(683\) | −561.238 | −0.0314424 | −0.0157212 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157212 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3680.01 | −0.204815 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13543.4 | 0.740779 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7346.96 | −0.399263 | ||||||||
\(698\) | −5233.09 | −0.283775 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2782.39 | 0.149914 | 0.0749569 | − | 0.997187i | \(-0.476118\pi\) | ||||
0.0749569 | + | 0.997187i | \(0.476118\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30642.1 | 1.64394 | ||||||||
\(704\) | 2211.24 | 0.118380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.1404 | 0.00304604 | ||||||||
\(707\) | 36651.8 | 1.94969 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4824.70 | 0.255565 | 0.127783 | − | 0.991802i | \(-0.459214\pi\) | ||||
0.127783 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8274.37 | −0.435527 | ||||||||
\(713\) | −1502.43 | −0.0789153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 911.371 | 0.0475692 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19971.0 | −1.03804 | ||||||||
\(719\) | −20717.6 | −1.07460 | −0.537298 | − | 0.843392i | \(-0.680555\pi\) | ||||
−0.537298 | + | 0.843392i | \(0.680555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30231.4 | 1.56155 | ||||||||
\(722\) | −12109.5 | −0.624195 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17801.3 | 0.913783 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22731.2 | 1.15963 | 0.579816 | − | 0.814747i | \(-0.303124\pi\) | ||||
0.579816 | + | 0.814747i | \(0.303124\pi\) | |||||||
\(728\) | 43289.2 | 2.20385 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3706.64 | −0.187544 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24311.8 | −1.22507 | −0.612536 | − | 0.790443i | \(-0.709851\pi\) | ||||
−0.612536 | + | 0.790443i | \(0.709851\pi\) | |||||||
\(734\) | −2020.11 | −0.101586 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1861.65 | 0.0932357 | ||||||||
\(737\) | −6910.49 | −0.345388 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16033.9 | 0.798126 | 0.399063 | − | 0.916924i | \(-0.369335\pi\) | ||||
0.399063 | + | 0.916924i | \(0.369335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21499.2 | 1.06369 | ||||||||
\(743\) | 19512.2 | 0.963435 | 0.481718 | − | 0.876326i | \(-0.340013\pi\) | ||||
0.481718 | + | 0.876326i | \(0.340013\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13489.7 | 0.662053 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25894.7 | −1.25070 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20208.6 | 0.970270 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(758\) | −2894.38 | −0.138692 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3529.19 | −0.168112 | −0.0840558 | − | 0.996461i | \(-0.526787\pi\) | ||||
−0.0840558 | + | 0.996461i | \(0.526787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33495.8 | −1.58929 | ||||||||
\(764\) | 13464.7 | 0.637612 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6072.01 | 0.286411 | ||||||||
\(767\) | −41418.5 | −1.94985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26692.6 | −1.25171 | −0.625853 | − | 0.779941i | \(-0.715249\pi\) | ||||
−0.625853 | + | 0.779941i | \(0.715249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12655.0 | −0.589977 | ||||||||
\(773\) | −32009.0 | −1.48937 | −0.744684 | − | 0.667417i | \(-0.767400\pi\) | ||||
−0.744684 | + | 0.667417i | \(0.767400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3505.81 | −0.162180 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16850.9 | −0.776523 | ||||||||
\(779\) | 21681.3 | 0.997194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3409.74 | −0.156223 | ||||||||
\(782\) | −635.954 | −0.0290814 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2808.84 | 0.127954 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8180.18 | 0.370511 | 0.185255 | − | 0.982690i | \(-0.440689\pi\) | ||||
0.185255 | + | 0.982690i | \(0.440689\pi\) | |||||||
\(788\) | −10889.2 | −0.492272 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24702.8 | −1.11040 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | \(0.308484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19803.4 | 0.876840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11892.6 | 0.523619 | ||||||||
\(803\) | 12593.4 | 0.553437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19878.5 | 0.868723 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −31984.9 | −1.39261 | ||||||||
\(809\) | −12381.1 | −0.538067 | −0.269034 | − | 0.963131i | \(-0.586704\pi\) | ||||
−0.269034 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4353.99 | −0.187478 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10938.5 | 0.468409 | ||||||||
\(818\) | 5920.64 | 0.253069 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5279.00 | 0.224407 | 0.112204 | − | 0.993685i | \(-0.464209\pi\) | ||||
0.112204 | + | 0.993685i | \(0.464209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19991.7 | 0.846738 | 0.423369 | − | 0.905957i | \(-0.360847\pi\) | ||||
0.423369 | + | 0.905957i | \(0.360847\pi\) | |||||||
\(824\) | −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 | \(0.566868\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5671.76 | −0.237622 | −0.118811 | − | 0.992917i | \(-0.537908\pi\) | ||||
−0.118811 | + | 0.992917i | \(0.537908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16933.3 | −0.705595 | ||||||||
\(833\) | −10072.5 | −0.418959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7395.54 | −0.305957 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13752.1 | 0.566894 | ||||||||
\(839\) | 29160.1 | 1.19990 | 0.599951 | − | 0.800036i | \(-0.295187\pi\) | ||||
0.599951 | + | 0.800036i | \(0.295187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14364.7 | 0.588984 | ||||||||
\(842\) | 12071.9 | 0.494092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6562.21 | −0.267631 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2936.31 | −0.119118 | ||||||||
\(848\) | 6480.98 | 0.262450 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2520.02 | −0.101510 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18361.2 | 0.737017 | 0.368508 | − | 0.929624i | \(-0.379869\pi\) | ||||
0.368508 | + | 0.929624i | \(0.379869\pi\) | |||||||
\(854\) | 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 | \(0.511137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31317.3 | −1.24392 | −0.621962 | − | 0.783047i | \(-0.713664\pi\) | ||||
−0.621962 | + | 0.783047i | \(0.713664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14082.0 | 0.556422 | ||||||||
\(863\) | 42862.3 | 1.69067 | 0.845336 | − | 0.534235i | \(-0.179400\pi\) | ||||
0.845336 | + | 0.534235i | \(0.179400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21548.0 | 0.845530 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20395.9 | 0.797558 | ||||||||
\(869\) | −962.082 | −0.0375563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52919.3 | 2.05867 | ||||||||
\(872\) | 29230.8 | 1.13518 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1876.74 | 0.0726335 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38306.6 | 1.47494 | 0.737471 | − | 0.675379i | \(-0.236020\pi\) | ||||
0.737471 | + | 0.675379i | \(0.236020\pi\) | |||||||
\(878\) | −725.298 | −0.0278788 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12994.5 | 0.496931 | 0.248466 | − | 0.968641i | \(-0.420074\pi\) | ||||
0.248466 | + | 0.968641i | \(0.420074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4256.48 | −0.162222 | −0.0811110 | − | 0.996705i | \(-0.525847\pi\) | ||||
−0.0811110 | + | 0.996705i | \(0.525847\pi\) | |||||||
\(884\) | −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 | \(0.757147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28680.1 | −1.08200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31938.5 | 1.19886 | ||||||||
\(893\) | −58441.1 | −2.18999 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28735.3 | −1.07141 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13984.6 | −0.519679 | ||||||||
\(899\) | −29750.0 | −1.10369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23240.9 | −0.859341 | ||||||||
\(902\) | −3080.73 | −0.113722 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21557.3 | 0.793127 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31257.8 | −1.14432 | −0.572161 | − | 0.820142i | \(-0.693895\pi\) | ||||
−0.572161 | + | 0.820142i | \(0.693895\pi\) | |||||||
\(908\) | −3966.28 | −0.144962 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35781.4 | 1.30131 | 0.650653 | − | 0.759375i | \(-0.274495\pi\) | ||||
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11441.4 | 0.414737 | ||||||||
\(914\) | 15721.5 | 0.568950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24682.7 | −0.890326 | ||||||||
\(917\) | −63464.6 | −2.28548 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31489.1 | 1.13028 | 0.565140 | − | 0.824995i | \(-0.308822\pi\) | ||||
0.565140 | + | 0.824995i | \(0.308822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12950.0 | −0.462567 | ||||||||
\(923\) | 26111.2 | 0.931159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15461.9 | −0.548713 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36862.9 | 1.30397 | ||||||||
\(929\) | 40466.1 | 1.42912 | 0.714559 | − | 0.699575i | \(-0.246627\pi\) | ||||
0.714559 | + | 0.699575i | \(0.246627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29724.7 | 1.04639 | ||||||||
\(932\) | 3415.79 | 0.120051 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17044.4 | −0.597120 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39041.1 | 1.36117 | 0.680586 | − | 0.732668i | \(-0.261725\pi\) | ||||
0.680586 | + | 0.732668i | \(0.261725\pi\) | |||||||
\(938\) | −23806.1 | −0.828676 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10842.0 | −0.375598 | −0.187799 | − | 0.982207i | \(-0.560135\pi\) | ||||
−0.187799 | + | 0.982207i | \(0.560135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(0.401153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −96437.6 | −3.29873 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21051.6 | 0.716687 | ||||||||
\(953\) | 45621.7 | 1.55071 | 0.775357 | − | 0.631523i | \(-0.217570\pi\) | ||||
0.775357 | + | 0.631523i | \(0.217570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28870.0 | 0.976697 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8940.12 | 0.301506 | ||||||||
\(959\) | 11293.1 | 0.380264 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6952.93 | −0.233390 | ||||||||
\(962\) | 33342.0 | 1.11745 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1967.17 | 0.0657242 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41111.6 | −1.36718 | −0.683588 | − | 0.729868i | \(-0.739581\pi\) | ||||
−0.683588 | + | 0.729868i | \(0.739581\pi\) | |||||||
\(968\) | 2562.43 | 0.0850821 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22030.1 | −0.728093 | −0.364046 | − | 0.931381i | \(-0.618605\pi\) | ||||
−0.364046 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | \(0.308339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4297.95 | −0.140310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15256.0 | −0.495762 | ||||||||
\(983\) | 20638.9 | 0.669663 | 0.334831 | − | 0.942278i | \(-0.391321\pi\) | ||||
0.334831 | + | 0.942278i | \(0.391321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12592.6 | −0.406725 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11746.3 | −0.374819 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29366.2 | 0.932834 | 0.466417 | − | 0.884565i | \(-0.345545\pi\) | ||||
0.466417 | + | 0.884565i | \(0.345545\pi\) | |||||||
\(998\) | 2946.09 | 0.0934439 | ||||||||
\(999\) | 0 | 0 |
(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 | 2475.4.a.bd.1.1 | 4 | ||
3.2 | odd | 2 | 825.4.a.u.1.3 | ✓ | 4 | ||
5.4 | even | 2 | 2475.4.a.bb.1.4 | 4 | |||
15.2 | even | 4 | 825.4.c.q.199.5 | 8 | |||
15.8 | even | 4 | 825.4.c.q.199.4 | 8 | |||
15.14 | odd | 2 | 825.4.a.v.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.u.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
825.4.a.v.1.2 | yes | 4 | 15.14 | odd | 2 | ||
825.4.c.q.199.4 | 8 | 15.8 | even | 4 | |||
825.4.c.q.199.5 | 8 | 15.2 | even | 4 | |||
2475.4.a.bb.1.4 | 4 | 5.4 | even | 2 | |||
2475.4.a.bd.1.1 | 4 | 1.1 | even | 1 | trivial |