Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-4.79301\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.79301 | 1.69459 | 0.847293 | − | 0.531125i | \(-0.178231\pi\) | ||||
0.847293 | + | 0.531125i | \(0.178231\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 14.9730 | 1.87162 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.3790 | −0.978370 | ||||||||
\(7\) | −0.140520 | −0.00758737 | −0.00379368 | − | 0.999993i | \(-0.501208\pi\) | ||||
−0.00379368 | + | 0.999993i | \(0.501208\pi\) | |||||||
\(8\) | 33.4216 | 1.47704 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47.3504 | 1.29788 | 0.648940 | − | 0.760839i | \(-0.275212\pi\) | ||||
0.648940 | + | 0.760839i | \(0.275212\pi\) | |||||||
\(12\) | −44.9190 | −1.08058 | ||||||||
\(13\) | −34.3424 | −0.732682 | −0.366341 | − | 0.930481i | \(-0.619390\pi\) | ||||
−0.366341 | + | 0.930481i | \(0.619390\pi\) | |||||||
\(14\) | −0.673515 | −0.0128575 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 40.4065 | 0.631352 | ||||||||
\(17\) | −16.5164 | −0.235636 | −0.117818 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117818 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(18\) | 43.1371 | 0.564862 | ||||||||
\(19\) | 91.0020 | 1.09881 | 0.549403 | − | 0.835558i | \(-0.314855\pi\) | ||||
0.549403 | + | 0.835558i | \(0.314855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.421560 | 0.00438057 | ||||||||
\(22\) | 226.951 | 2.19937 | ||||||||
\(23\) | 161.582 | 1.46487 | 0.732436 | − | 0.680835i | \(-0.238383\pi\) | ||||
0.732436 | + | 0.680835i | \(0.238383\pi\) | |||||||
\(24\) | −100.265 | −0.852771 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −164.604 | −1.24159 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −2.10400 | −0.0142007 | ||||||||
\(29\) | −12.3327 | −0.0789698 | −0.0394849 | − | 0.999220i | \(-0.512572\pi\) | ||||
−0.0394849 | + | 0.999220i | \(0.512572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −333.038 | −1.92953 | −0.964765 | − | 0.263115i | \(-0.915250\pi\) | ||||
−0.964765 | + | 0.263115i | \(0.915250\pi\) | |||||||
\(32\) | −73.7042 | −0.407162 | ||||||||
\(33\) | −142.051 | −0.749332 | ||||||||
\(34\) | −79.1633 | −0.399306 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 134.757 | 0.623875 | ||||||||
\(37\) | 281.402 | 1.25033 | 0.625166 | − | 0.780492i | \(-0.285031\pi\) | ||||
0.625166 | + | 0.780492i | \(0.285031\pi\) | |||||||
\(38\) | 436.174 | 1.86202 | ||||||||
\(39\) | 103.027 | 0.423014 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 125.610 | 0.478462 | 0.239231 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239231 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(42\) | 2.02054 | 0.00742325 | ||||||||
\(43\) | 529.821 | 1.87900 | 0.939500 | − | 0.342549i | \(-0.111290\pi\) | ||||
0.939500 | + | 0.342549i | \(0.111290\pi\) | |||||||
\(44\) | 708.977 | 2.42914 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 774.463 | 2.48235 | ||||||||
\(47\) | −75.0713 | −0.232985 | −0.116492 | − | 0.993192i | \(-0.537165\pi\) | ||||
−0.116492 | + | 0.993192i | \(0.537165\pi\) | |||||||
\(48\) | −121.220 | −0.364511 | ||||||||
\(49\) | −342.980 | −0.999942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 49.5492 | 0.136045 | ||||||||
\(52\) | −514.208 | −1.37130 | ||||||||
\(53\) | 249.426 | 0.646438 | 0.323219 | − | 0.946324i | \(-0.395235\pi\) | ||||
0.323219 | + | 0.946324i | \(0.395235\pi\) | |||||||
\(54\) | −129.411 | −0.326123 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.69641 | −0.0112069 | ||||||||
\(57\) | −273.006 | −0.634395 | ||||||||
\(58\) | −59.1108 | −0.133821 | ||||||||
\(59\) | −268.564 | −0.592611 | −0.296305 | − | 0.955093i | \(-0.595755\pi\) | ||||
−0.296305 | + | 0.955093i | \(0.595755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 369.848 | 0.776297 | 0.388149 | − | 0.921597i | \(-0.373115\pi\) | ||||
0.388149 | + | 0.921597i | \(0.373115\pi\) | |||||||
\(62\) | −1596.26 | −3.26975 | ||||||||
\(63\) | −1.26468 | −0.00252912 | ||||||||
\(64\) | −676.517 | −1.32132 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −680.854 | −1.26981 | ||||||||
\(67\) | 176.506 | 0.321846 | 0.160923 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160923 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(68\) | −247.300 | −0.441022 | ||||||||
\(69\) | −484.745 | −0.845745 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 722.104 | 1.20701 | 0.603507 | − | 0.797358i | \(-0.293770\pi\) | ||||
0.603507 | + | 0.797358i | \(0.293770\pi\) | |||||||
\(72\) | 300.795 | 0.492347 | ||||||||
\(73\) | 2.44271 | 0.00391641 | 0.00195820 | − | 0.999998i | \(-0.499377\pi\) | ||||
0.00195820 | + | 0.999998i | \(0.499377\pi\) | |||||||
\(74\) | 1348.77 | 2.11879 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1362.57 | 2.05655 | ||||||||
\(77\) | −6.65368 | −0.00984750 | ||||||||
\(78\) | 493.811 | 0.716834 | ||||||||
\(79\) | 607.662 | 0.865409 | 0.432705 | − | 0.901536i | \(-0.357559\pi\) | ||||
0.432705 | + | 0.901536i | \(0.357559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 602.049 | 0.810795 | ||||||||
\(83\) | 1268.55 | 1.67761 | 0.838807 | − | 0.544429i | \(-0.183253\pi\) | ||||
0.838807 | + | 0.544429i | \(0.183253\pi\) | |||||||
\(84\) | 6.31201 | 0.00819878 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2539.44 | 3.18413 | ||||||||
\(87\) | 36.9981 | 0.0455933 | ||||||||
\(88\) | 1582.53 | 1.91702 | ||||||||
\(89\) | −1337.53 | −1.59301 | −0.796507 | − | 0.604629i | \(-0.793321\pi\) | ||||
−0.796507 | + | 0.604629i | \(0.793321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82579 | 0.00555913 | ||||||||
\(92\) | 2419.36 | 2.74169 | ||||||||
\(93\) | 999.114 | 1.11401 | ||||||||
\(94\) | −359.818 | −0.394812 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 221.113 | 0.235075 | ||||||||
\(97\) | 1431.21 | 1.49812 | 0.749059 | − | 0.662503i | \(-0.230506\pi\) | ||||
0.749059 | + | 0.662503i | \(0.230506\pi\) | |||||||
\(98\) | −1643.91 | −1.69449 | ||||||||
\(99\) | 426.154 | 0.432627 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −374.102 | −0.368559 | −0.184280 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184280 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(102\) | 237.490 | 0.230539 | ||||||||
\(103\) | 2017.87 | 1.93035 | 0.965177 | − | 0.261597i | \(-0.0842493\pi\) | ||||
0.965177 | + | 0.261597i | \(0.0842493\pi\) | |||||||
\(104\) | −1147.78 | −1.08220 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1195.50 | 1.09545 | ||||||||
\(107\) | −1679.71 | −1.51761 | −0.758804 | − | 0.651319i | \(-0.774216\pi\) | ||||
−0.758804 | + | 0.651319i | \(0.774216\pi\) | |||||||
\(108\) | −404.271 | −0.360194 | ||||||||
\(109\) | 20.2283 | 0.0177754 | 0.00888772 | − | 0.999961i | \(-0.497171\pi\) | ||||
0.00888772 | + | 0.999961i | \(0.497171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −844.207 | −0.721879 | ||||||||
\(112\) | −5.67792 | −0.00479030 | ||||||||
\(113\) | 642.520 | 0.534896 | 0.267448 | − | 0.963572i | \(-0.413820\pi\) | ||||
0.267448 | + | 0.963572i | \(0.413820\pi\) | |||||||
\(114\) | −1308.52 | −1.07504 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −184.657 | −0.147802 | ||||||||
\(117\) | −309.081 | −0.244227 | ||||||||
\(118\) | −1287.23 | −1.00423 | ||||||||
\(119\) | 2.32088 | 0.00178786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 911.063 | 0.684495 | ||||||||
\(122\) | 1772.69 | 1.31550 | ||||||||
\(123\) | −376.829 | −0.276240 | ||||||||
\(124\) | −4986.58 | −3.61135 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.06163 | −0.00428582 | ||||||||
\(127\) | 1185.91 | 0.828603 | 0.414302 | − | 0.910140i | \(-0.364026\pi\) | ||||
0.414302 | + | 0.910140i | \(0.364026\pi\) | |||||||
\(128\) | −2652.92 | −1.83193 | ||||||||
\(129\) | −1589.46 | −1.08484 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −223.094 | −0.148793 | −0.0743963 | − | 0.997229i | \(-0.523703\pi\) | ||||
−0.0743963 | + | 0.997229i | \(0.523703\pi\) | |||||||
\(132\) | −2126.93 | −1.40247 | ||||||||
\(133\) | −12.7876 | −0.00833704 | ||||||||
\(134\) | 845.997 | 0.545396 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −552.005 | −0.348045 | ||||||||
\(137\) | 1579.55 | 0.985035 | 0.492517 | − | 0.870303i | \(-0.336077\pi\) | ||||
0.492517 | + | 0.870303i | \(0.336077\pi\) | |||||||
\(138\) | −2323.39 | −1.43319 | ||||||||
\(139\) | 1565.25 | 0.955128 | 0.477564 | − | 0.878597i | \(-0.341520\pi\) | ||||
0.477564 | + | 0.878597i | \(0.341520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 225.214 | 0.134514 | ||||||||
\(142\) | 3461.05 | 2.04539 | ||||||||
\(143\) | −1626.13 | −0.950934 | ||||||||
\(144\) | 363.659 | 0.210451 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.7080 | 0.00663669 | ||||||||
\(147\) | 1028.94 | 0.577317 | ||||||||
\(148\) | 4213.43 | 2.34015 | ||||||||
\(149\) | 192.635 | 0.105915 | 0.0529574 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529574 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1052.83 | 0.567406 | 0.283703 | − | 0.958912i | \(-0.408437\pi\) | ||||
0.283703 | + | 0.958912i | \(0.408437\pi\) | |||||||
\(152\) | 3041.44 | 1.62298 | ||||||||
\(153\) | −148.648 | −0.0785454 | ||||||||
\(154\) | −31.8912 | −0.0166874 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1542.62 | 0.791723 | ||||||||
\(157\) | −2045.26 | −1.03968 | −0.519838 | − | 0.854265i | \(-0.674008\pi\) | ||||
−0.519838 | + | 0.854265i | \(0.674008\pi\) | |||||||
\(158\) | 2912.53 | 1.46651 | ||||||||
\(159\) | −748.277 | −0.373221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.7054 | −0.0111145 | ||||||||
\(162\) | 388.234 | 0.188287 | ||||||||
\(163\) | −848.013 | −0.407494 | −0.203747 | − | 0.979024i | \(-0.565312\pi\) | ||||
−0.203747 | + | 0.979024i | \(0.565312\pi\) | |||||||
\(164\) | 1880.75 | 0.895500 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6080.20 | 2.84286 | ||||||||
\(167\) | −1972.45 | −0.913968 | −0.456984 | − | 0.889475i | \(-0.651070\pi\) | ||||
−0.456984 | + | 0.889475i | \(0.651070\pi\) | |||||||
\(168\) | 14.0892 | 0.00647028 | ||||||||
\(169\) | −1017.60 | −0.463177 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 819.018 | 0.366268 | ||||||||
\(172\) | 7933.01 | 3.51678 | ||||||||
\(173\) | −2707.65 | −1.18993 | −0.594967 | − | 0.803750i | \(-0.702835\pi\) | ||||
−0.594967 | + | 0.803750i | \(0.702835\pi\) | |||||||
\(174\) | 177.332 | 0.0772617 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1913.26 | 0.819419 | ||||||||
\(177\) | 805.692 | 0.342144 | ||||||||
\(178\) | −6410.82 | −2.69950 | ||||||||
\(179\) | 3132.25 | 1.30791 | 0.653953 | − | 0.756535i | \(-0.273109\pi\) | ||||
0.653953 | + | 0.756535i | \(0.273109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 317.051 | 0.130200 | 0.0651000 | − | 0.997879i | \(-0.479263\pi\) | ||||
0.0651000 | + | 0.997879i | \(0.479263\pi\) | |||||||
\(182\) | 23.1301 | 0.00942042 | ||||||||
\(183\) | −1109.54 | −0.448195 | ||||||||
\(184\) | 5400.32 | 2.16368 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4788.77 | 1.88779 | ||||||||
\(187\) | −782.059 | −0.305828 | ||||||||
\(188\) | −1124.04 | −0.436059 | ||||||||
\(189\) | 3.79404 | 0.00146019 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1679.46 | 0.636237 | 0.318119 | − | 0.948051i | \(-0.396949\pi\) | ||||
0.318119 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(192\) | 2029.55 | 0.762866 | ||||||||
\(193\) | 1449.62 | 0.540653 | 0.270326 | − | 0.962769i | \(-0.412868\pi\) | ||||
0.270326 | + | 0.962769i | \(0.412868\pi\) | |||||||
\(194\) | 6859.82 | 2.53869 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5135.44 | −1.87152 | ||||||||
\(197\) | 1060.62 | 0.383586 | 0.191793 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191793 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(198\) | 2042.56 | 0.733124 | ||||||||
\(199\) | −183.077 | −0.0652159 | −0.0326080 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326080 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −529.519 | −0.185818 | ||||||||
\(202\) | −1793.07 | −0.624556 | ||||||||
\(203\) | 1.73299 | 0.000599173 0 | ||||||||
\(204\) | 741.900 | 0.254624 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9671.67 | 3.27115 | ||||||||
\(207\) | 1454.23 | 0.488291 | ||||||||
\(208\) | −1387.66 | −0.462580 | ||||||||
\(209\) | 4308.98 | 1.42612 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4904.73 | −1.60026 | −0.800131 | − | 0.599825i | \(-0.795237\pi\) | ||||
−0.800131 | + | 0.599825i | \(0.795237\pi\) | |||||||
\(212\) | 3734.65 | 1.20989 | ||||||||
\(213\) | −2166.31 | −0.696870 | ||||||||
\(214\) | −8050.90 | −2.57172 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −902.384 | −0.284257 | ||||||||
\(217\) | 46.7985 | 0.0146400 | ||||||||
\(218\) | 96.9547 | 0.0301220 | ||||||||
\(219\) | −7.32813 | −0.00226114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 567.212 | 0.172646 | ||||||||
\(222\) | −4046.30 | −1.22329 | ||||||||
\(223\) | 4837.42 | 1.45263 | 0.726317 | − | 0.687360i | \(-0.241230\pi\) | ||||
0.726317 | + | 0.687360i | \(0.241230\pi\) | |||||||
\(224\) | 10.3569 | 0.00308929 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3079.61 | 0.906428 | ||||||||
\(227\) | 44.8176 | 0.0131042 | 0.00655209 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655209 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(228\) | −4087.72 | −1.18735 | ||||||||
\(229\) | −4159.78 | −1.20038 | −0.600188 | − | 0.799859i | \(-0.704908\pi\) | ||||
−0.600188 | + | 0.799859i | \(0.704908\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.9610 | 0.00568546 | ||||||||
\(232\) | −412.179 | −0.116642 | ||||||||
\(233\) | −2945.40 | −0.828152 | −0.414076 | − | 0.910242i | \(-0.635895\pi\) | ||||
−0.414076 | + | 0.910242i | \(0.635895\pi\) | |||||||
\(234\) | −1481.43 | −0.413864 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4021.21 | −1.10914 | ||||||||
\(237\) | −1822.99 | −0.499644 | ||||||||
\(238\) | 11.1240 | 0.00302968 | ||||||||
\(239\) | 2174.54 | 0.588533 | 0.294266 | − | 0.955723i | \(-0.404925\pi\) | ||||
0.294266 | + | 0.955723i | \(0.404925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2300.69 | 0.614939 | 0.307470 | − | 0.951558i | \(-0.400518\pi\) | ||||
0.307470 | + | 0.951558i | \(0.400518\pi\) | |||||||
\(242\) | 4366.74 | 1.15994 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 5537.72 | 1.45294 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1806.15 | −0.468112 | ||||||||
\(247\) | −3125.23 | −0.805074 | ||||||||
\(248\) | −11130.7 | −2.85000 | ||||||||
\(249\) | −3805.66 | −0.968571 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3368.55 | 0.847096 | 0.423548 | − | 0.905874i | \(-0.360785\pi\) | ||||
0.423548 | + | 0.905874i | \(0.360785\pi\) | |||||||
\(252\) | −18.9360 | −0.00473357 | ||||||||
\(253\) | 7650.95 | 1.90123 | ||||||||
\(254\) | 5684.09 | 1.40414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7303.36 | −1.78305 | ||||||||
\(257\) | −404.905 | −0.0982772 | −0.0491386 | − | 0.998792i | \(-0.515648\pi\) | ||||
−0.0491386 | + | 0.998792i | \(0.515648\pi\) | |||||||
\(258\) | −7618.33 | −1.83836 | ||||||||
\(259\) | −39.5427 | −0.00948672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −110.994 | −0.0263233 | ||||||||
\(262\) | −1069.29 | −0.252142 | ||||||||
\(263\) | 1514.70 | 0.355135 | 0.177567 | − | 0.984109i | \(-0.443177\pi\) | ||||
0.177567 | + | 0.984109i | \(0.443177\pi\) | |||||||
\(264\) | −4747.59 | −1.10679 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −61.2912 | −0.0141278 | ||||||||
\(267\) | 4012.60 | 0.919727 | ||||||||
\(268\) | 2642.83 | 0.602374 | ||||||||
\(269\) | −1891.88 | −0.428811 | −0.214405 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214405 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2094.31 | −0.469448 | −0.234724 | − | 0.972062i | \(-0.575419\pi\) | ||||
−0.234724 | + | 0.972062i | \(0.575419\pi\) | |||||||
\(272\) | −667.370 | −0.148769 | ||||||||
\(273\) | −14.4774 | −0.00320956 | ||||||||
\(274\) | 7570.79 | 1.66923 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7258.08 | −1.58292 | ||||||||
\(277\) | 1492.73 | 0.323789 | 0.161894 | − | 0.986808i | \(-0.448240\pi\) | ||||
0.161894 | + | 0.986808i | \(0.448240\pi\) | |||||||
\(278\) | 7502.27 | 1.61855 | ||||||||
\(279\) | −2997.34 | −0.643176 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2069.49 | 0.439344 | 0.219672 | − | 0.975574i | \(-0.429501\pi\) | ||||
0.219672 | + | 0.975574i | \(0.429501\pi\) | |||||||
\(282\) | 1079.45 | 0.227945 | ||||||||
\(283\) | −3398.90 | −0.713935 | −0.356967 | − | 0.934117i | \(-0.616189\pi\) | ||||
−0.356967 | + | 0.934117i | \(0.616189\pi\) | |||||||
\(284\) | 10812.1 | 2.25908 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7794.05 | −1.61144 | ||||||||
\(287\) | −17.6507 | −0.00363026 | ||||||||
\(288\) | −663.338 | −0.135721 | ||||||||
\(289\) | −4640.21 | −0.944476 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4293.64 | −0.864939 | ||||||||
\(292\) | 36.5747 | 0.00733004 | ||||||||
\(293\) | −7677.60 | −1.53082 | −0.765410 | − | 0.643543i | \(-0.777464\pi\) | ||||
−0.765410 | + | 0.643543i | \(0.777464\pi\) | |||||||
\(294\) | 4931.73 | 0.978314 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9404.93 | 1.84679 | ||||||||
\(297\) | −1278.46 | −0.249777 | ||||||||
\(298\) | 923.304 | 0.179482 | ||||||||
\(299\) | −5549.09 | −1.07329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −74.4505 | −0.0142567 | ||||||||
\(302\) | 5046.24 | 0.961518 | ||||||||
\(303\) | 1122.31 | 0.212788 | ||||||||
\(304\) | 3677.07 | 0.693732 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −712.470 | −0.133102 | ||||||||
\(307\) | 4507.90 | 0.838043 | 0.419022 | − | 0.907976i | \(-0.362373\pi\) | ||||
0.419022 | + | 0.907976i | \(0.362373\pi\) | |||||||
\(308\) | −99.6255 | −0.0184308 | ||||||||
\(309\) | −6053.61 | −1.11449 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7065.19 | 1.28820 | 0.644100 | − | 0.764941i | \(-0.277232\pi\) | ||||
0.644100 | + | 0.764941i | \(0.277232\pi\) | |||||||
\(312\) | 3443.34 | 0.624809 | ||||||||
\(313\) | −2063.81 | −0.372694 | −0.186347 | − | 0.982484i | \(-0.559665\pi\) | ||||
−0.186347 | + | 0.982484i | \(0.559665\pi\) | |||||||
\(314\) | −9802.94 | −1.76182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9098.52 | 1.61972 | ||||||||
\(317\) | −8596.49 | −1.52311 | −0.761557 | − | 0.648098i | \(-0.775565\pi\) | ||||
−0.761557 | + | 0.648098i | \(0.775565\pi\) | |||||||
\(318\) | −3586.50 | −0.632456 | ||||||||
\(319\) | −583.959 | −0.102493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5039.14 | 0.876192 | ||||||||
\(322\) | −108.827 | −0.0188345 | ||||||||
\(323\) | −1503.03 | −0.258918 | ||||||||
\(324\) | 1212.81 | 0.207958 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4064.54 | −0.690533 | ||||||||
\(327\) | −60.6850 | −0.0102627 | ||||||||
\(328\) | 4198.08 | 0.706708 | ||||||||
\(329\) | 10.5490 | 0.00176774 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 259.628 | 0.0431131 | 0.0215566 | − | 0.999768i | \(-0.493138\pi\) | ||||
0.0215566 | + | 0.999768i | \(0.493138\pi\) | |||||||
\(332\) | 18994.1 | 3.13986 | ||||||||
\(333\) | 2532.62 | 0.416777 | ||||||||
\(334\) | −9453.97 | −1.54880 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.0338 | 0.00276568 | ||||||||
\(337\) | −6721.19 | −1.08643 | −0.543215 | − | 0.839594i | \(-0.682793\pi\) | ||||
−0.543215 | + | 0.839594i | \(0.682793\pi\) | |||||||
\(338\) | −4877.38 | −0.784894 | ||||||||
\(339\) | −1927.56 | −0.308822 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15769.5 | −2.50430 | ||||||||
\(342\) | 3925.57 | 0.620673 | ||||||||
\(343\) | 96.3940 | 0.0151743 | ||||||||
\(344\) | 17707.5 | 2.77536 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12977.8 | −2.01645 | ||||||||
\(347\) | 7139.56 | 1.10453 | 0.552264 | − | 0.833669i | \(-0.313764\pi\) | ||||
0.552264 | + | 0.833669i | \(0.313764\pi\) | |||||||
\(348\) | 553.972 | 0.0853334 | ||||||||
\(349\) | −11473.4 | −1.75976 | −0.879879 | − | 0.475198i | \(-0.842376\pi\) | ||||
−0.879879 | + | 0.475198i | \(0.842376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 927.244 | 0.141005 | ||||||||
\(352\) | −3489.92 | −0.528448 | ||||||||
\(353\) | −59.6020 | −0.00898667 | −0.00449333 | − | 0.999990i | \(-0.501430\pi\) | ||||
−0.00449333 | + | 0.999990i | \(0.501430\pi\) | |||||||
\(354\) | 3861.69 | 0.579793 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20026.9 | −2.98152 | ||||||||
\(357\) | −6.96265 | −0.00103222 | ||||||||
\(358\) | 15012.9 | 2.21636 | ||||||||
\(359\) | −7801.88 | −1.14698 | −0.573492 | − | 0.819211i | \(-0.694412\pi\) | ||||
−0.573492 | + | 0.819211i | \(0.694412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1422.37 | 0.207373 | ||||||||
\(362\) | 1519.63 | 0.220635 | ||||||||
\(363\) | −2733.19 | −0.395193 | ||||||||
\(364\) | 72.2565 | 0.0104046 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5318.06 | −0.759506 | ||||||||
\(367\) | 1583.29 | 0.225197 | 0.112599 | − | 0.993641i | \(-0.464083\pi\) | ||||
0.112599 | + | 0.993641i | \(0.464083\pi\) | |||||||
\(368\) | 6528.94 | 0.924850 | ||||||||
\(369\) | 1130.49 | 0.159487 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.0493 | −0.00490477 | ||||||||
\(372\) | 14959.7 | 2.08502 | ||||||||
\(373\) | 11181.2 | 1.55212 | 0.776059 | − | 0.630661i | \(-0.217216\pi\) | ||||
0.776059 | + | 0.630661i | \(0.217216\pi\) | |||||||
\(374\) | −3748.42 | −0.518252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2509.01 | −0.344128 | ||||||||
\(377\) | 423.534 | 0.0578598 | ||||||||
\(378\) | 18.1849 | 0.00247442 | ||||||||
\(379\) | −11723.0 | −1.58885 | −0.794423 | − | 0.607365i | \(-0.792227\pi\) | ||||
−0.794423 | + | 0.607365i | \(0.792227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3557.73 | −0.478394 | ||||||||
\(382\) | 8049.67 | 1.07816 | ||||||||
\(383\) | 9272.02 | 1.23702 | 0.618509 | − | 0.785778i | \(-0.287737\pi\) | ||||
0.618509 | + | 0.785778i | \(0.287737\pi\) | |||||||
\(384\) | 7958.77 | 1.05767 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6948.05 | 0.916183 | ||||||||
\(387\) | 4768.39 | 0.626333 | ||||||||
\(388\) | 21429.5 | 2.80391 | ||||||||
\(389\) | −1341.15 | −0.174805 | −0.0874023 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874023 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2668.74 | −0.345177 | ||||||||
\(392\) | −11463.0 | −1.47696 | ||||||||
\(393\) | 669.283 | 0.0859054 | ||||||||
\(394\) | 5083.59 | 0.650019 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6380.80 | 0.809715 | ||||||||
\(397\) | −11366.3 | −1.43692 | −0.718459 | − | 0.695569i | \(-0.755152\pi\) | ||||
−0.718459 | + | 0.695569i | \(0.755152\pi\) | |||||||
\(398\) | −877.490 | −0.110514 | ||||||||
\(399\) | 38.3628 | 0.00481339 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12421.7 | −1.54690 | −0.773451 | − | 0.633856i | \(-0.781471\pi\) | ||||
−0.773451 | + | 0.633856i | \(0.781471\pi\) | |||||||
\(402\) | −2537.99 | −0.314884 | ||||||||
\(403\) | 11437.3 | 1.41373 | ||||||||
\(404\) | −5601.42 | −0.689805 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.30625 | 0.00101535 | ||||||||
\(407\) | 13324.5 | 1.62278 | ||||||||
\(408\) | 1656.02 | 0.200944 | ||||||||
\(409\) | 12917.8 | 1.56172 | 0.780860 | − | 0.624706i | \(-0.214781\pi\) | ||||
0.780860 | + | 0.624706i | \(0.214781\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4738.64 | −0.568710 | ||||||||
\(412\) | 30213.5 | 3.61290 | ||||||||
\(413\) | 37.7386 | 0.00449636 | ||||||||
\(414\) | 6970.16 | 0.827451 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2531.18 | 0.298320 | ||||||||
\(417\) | −4695.75 | −0.551443 | ||||||||
\(418\) | 20653.0 | 2.41668 | ||||||||
\(419\) | −4162.80 | −0.485361 | −0.242680 | − | 0.970106i | \(-0.578027\pi\) | ||||
−0.242680 | + | 0.970106i | \(0.578027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14947.3 | −1.73037 | −0.865186 | − | 0.501451i | \(-0.832800\pi\) | ||||
−0.865186 | + | 0.501451i | \(0.832800\pi\) | |||||||
\(422\) | −23508.4 | −2.71178 | ||||||||
\(423\) | −675.642 | −0.0776615 | ||||||||
\(424\) | 8336.21 | 0.954817 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10383.2 | −1.18091 | ||||||||
\(427\) | −51.9710 | −0.00589005 | ||||||||
\(428\) | −25150.4 | −2.84039 | ||||||||
\(429\) | 4878.38 | 0.549022 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12762.9 | −1.42638 | −0.713188 | − | 0.700973i | \(-0.752749\pi\) | ||||
−0.713188 | + | 0.700973i | \(0.752749\pi\) | |||||||
\(432\) | −1090.98 | −0.121504 | ||||||||
\(433\) | −777.497 | −0.0862913 | −0.0431456 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431456 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(434\) | 224.306 | 0.0248088 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 302.879 | 0.0332689 | ||||||||
\(437\) | 14704.2 | 1.60961 | ||||||||
\(438\) | −35.1239 | −0.00383170 | ||||||||
\(439\) | 9936.45 | 1.08028 | 0.540138 | − | 0.841577i | \(-0.318372\pi\) | ||||
0.540138 | + | 0.841577i | \(0.318372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3086.82 | −0.333314 | ||||||||
\(442\) | 2718.66 | 0.292564 | ||||||||
\(443\) | −7139.86 | −0.765745 | −0.382873 | − | 0.923801i | \(-0.625065\pi\) | ||||
−0.382873 | + | 0.923801i | \(0.625065\pi\) | |||||||
\(444\) | −12640.3 | −1.35109 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23185.8 | 2.46162 | ||||||||
\(447\) | −577.906 | −0.0611499 | ||||||||
\(448\) | 95.0642 | 0.0100254 | ||||||||
\(449\) | 10438.2 | 1.09712 | 0.548560 | − | 0.836111i | \(-0.315176\pi\) | ||||
0.548560 | + | 0.836111i | \(0.315176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5947.67 | 0.620986 | ||||||||
\(452\) | 9620.45 | 1.00112 | ||||||||
\(453\) | −3158.50 | −0.327592 | ||||||||
\(454\) | 214.811 | 0.0222062 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9124.31 | −0.937029 | ||||||||
\(457\) | −5039.76 | −0.515864 | −0.257932 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257932 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(458\) | −19937.9 | −2.03414 | ||||||||
\(459\) | 445.943 | 0.0453482 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1832.68 | 0.185155 | 0.0925775 | − | 0.995705i | \(-0.470489\pi\) | ||||
0.0925775 | + | 0.995705i | \(0.470489\pi\) | |||||||
\(462\) | 95.6736 | 0.00963450 | ||||||||
\(463\) | −1887.49 | −0.189458 | −0.0947290 | − | 0.995503i | \(-0.530198\pi\) | ||||
−0.0947290 | + | 0.995503i | \(0.530198\pi\) | |||||||
\(464\) | −498.321 | −0.0498577 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14117.3 | −1.40337 | ||||||||
\(467\) | 3944.31 | 0.390837 | 0.195419 | − | 0.980720i | \(-0.437393\pi\) | ||||
0.195419 | + | 0.980720i | \(0.437393\pi\) | |||||||
\(468\) | −4627.87 | −0.457101 | ||||||||
\(469\) | −24.8027 | −0.00244196 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6135.77 | 0.600257 | ||||||||
\(472\) | −8975.85 | −0.875311 | ||||||||
\(473\) | 25087.3 | 2.43872 | ||||||||
\(474\) | −8737.60 | −0.846690 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 34.7506 | 0.00334620 | ||||||||
\(477\) | 2244.83 | 0.215479 | ||||||||
\(478\) | 10422.6 | 0.997320 | ||||||||
\(479\) | −10759.1 | −1.02630 | −0.513150 | − | 0.858299i | \(-0.671522\pi\) | ||||
−0.513150 | + | 0.858299i | \(0.671522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9664.02 | −0.916095 | ||||||||
\(482\) | 11027.2 | 1.04207 | ||||||||
\(483\) | 68.1163 | 0.00641698 | ||||||||
\(484\) | 13641.3 | 1.28112 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1164.70 | −0.108708 | ||||||||
\(487\) | −3191.34 | −0.296948 | −0.148474 | − | 0.988916i | \(-0.547436\pi\) | ||||
−0.148474 | + | 0.988916i | \(0.547436\pi\) | |||||||
\(488\) | 12360.9 | 1.14662 | ||||||||
\(489\) | 2544.04 | 0.235267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 933.900 | 0.0858377 | 0.0429189 | − | 0.999079i | \(-0.486334\pi\) | ||||
0.0429189 | + | 0.999079i | \(0.486334\pi\) | |||||||
\(492\) | −5642.25 | −0.517017 | ||||||||
\(493\) | 203.692 | 0.0186082 | ||||||||
\(494\) | −14979.3 | −1.36427 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13456.9 | −1.21821 | ||||||||
\(497\) | −101.470 | −0.00915806 | ||||||||
\(498\) | −18240.6 | −1.64133 | ||||||||
\(499\) | 5499.10 | 0.493333 | 0.246667 | − | 0.969100i | \(-0.420665\pi\) | ||||
0.246667 | + | 0.969100i | \(0.420665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5917.34 | 0.527679 | ||||||||
\(502\) | 16145.5 | 1.43548 | ||||||||
\(503\) | 11172.5 | 0.990374 | 0.495187 | − | 0.868787i | \(-0.335100\pi\) | ||||
0.495187 | + | 0.868787i | \(0.335100\pi\) | |||||||
\(504\) | −42.2677 | −0.00373562 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 36671.1 | 3.22180 | ||||||||
\(507\) | 3052.80 | 0.267416 | ||||||||
\(508\) | 17756.6 | 1.55083 | ||||||||
\(509\) | −8576.81 | −0.746877 | −0.373439 | − | 0.927655i | \(-0.621821\pi\) | ||||
−0.373439 | + | 0.927655i | \(0.621821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.343250 | −2.97152e−5 0 | ||||||||
\(512\) | −13781.7 | −1.18960 | ||||||||
\(513\) | −2457.05 | −0.211465 | ||||||||
\(514\) | −1940.71 | −0.166539 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −23799.0 | −2.03041 | ||||||||
\(517\) | −3554.66 | −0.302386 | ||||||||
\(518\) | −189.529 | −0.0160761 | ||||||||
\(519\) | 8122.94 | 0.687008 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19732.4 | −1.65929 | −0.829647 | − | 0.558289i | \(-0.811458\pi\) | ||||
−0.829647 | + | 0.558289i | \(0.811458\pi\) | |||||||
\(522\) | −531.997 | −0.0446071 | ||||||||
\(523\) | −16353.7 | −1.36730 | −0.683651 | − | 0.729809i | \(-0.739609\pi\) | ||||
−0.683651 | + | 0.729809i | \(0.739609\pi\) | |||||||
\(524\) | −3340.39 | −0.278484 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7259.98 | 0.601807 | ||||||||
\(527\) | 5500.59 | 0.454667 | ||||||||
\(528\) | −5739.79 | −0.473092 | ||||||||
\(529\) | 13941.6 | 1.14585 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2417.08 | −0.197537 | ||||||||
\(532\) | −191.469 | −0.0156038 | ||||||||
\(533\) | −4313.73 | −0.350560 | ||||||||
\(534\) | 19232.5 | 1.55856 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5899.13 | 0.475380 | ||||||||
\(537\) | −9396.75 | −0.755120 | ||||||||
\(538\) | −9067.82 | −0.726657 | ||||||||
\(539\) | −16240.3 | −1.29781 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14238.7 | 1.13155 | 0.565776 | − | 0.824559i | \(-0.308577\pi\) | ||||
0.565776 | + | 0.824559i | \(0.308577\pi\) | |||||||
\(542\) | −10038.1 | −0.795521 | ||||||||
\(543\) | −951.153 | −0.0751710 | ||||||||
\(544\) | 1217.33 | 0.0959421 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −69.3903 | −0.00543888 | ||||||||
\(547\) | −7018.76 | −0.548630 | −0.274315 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274315 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(548\) | 23650.5 | 1.84361 | ||||||||
\(549\) | 3328.63 | 0.258766 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1122.30 | −0.0867725 | ||||||||
\(552\) | −16201.0 | −1.24920 | ||||||||
\(553\) | −85.3887 | −0.00656618 | ||||||||
\(554\) | 7154.68 | 0.548688 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 23436.5 | 1.78764 | ||||||||
\(557\) | −6144.57 | −0.467421 | −0.233711 | − | 0.972306i | \(-0.575087\pi\) | ||||
−0.233711 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(558\) | −14366.3 | −1.08992 | ||||||||
\(559\) | −18195.3 | −1.37671 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2346.18 | 0.176570 | ||||||||
\(562\) | 9919.12 | 0.744507 | ||||||||
\(563\) | −17169.5 | −1.28527 | −0.642635 | − | 0.766172i | \(-0.722159\pi\) | ||||
−0.642635 | + | 0.766172i | \(0.722159\pi\) | |||||||
\(564\) | 3372.12 | 0.251759 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16291.0 | −1.20982 | ||||||||
\(567\) | −11.3821 | −0.000843041 0 | ||||||||
\(568\) | 24133.9 | 1.78281 | ||||||||
\(569\) | −15575.2 | −1.14754 | −0.573768 | − | 0.819018i | \(-0.694519\pi\) | ||||
−0.573768 | + | 0.819018i | \(0.694519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21207.6 | −1.55431 | −0.777156 | − | 0.629308i | \(-0.783339\pi\) | ||||
−0.777156 | + | 0.629308i | \(0.783339\pi\) | |||||||
\(572\) | −24348.0 | −1.77979 | ||||||||
\(573\) | −5038.37 | −0.367332 | ||||||||
\(574\) | −84.5999 | −0.00615180 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6088.65 | −0.440441 | ||||||||
\(577\) | 2071.25 | 0.149441 | 0.0747205 | − | 0.997205i | \(-0.476194\pi\) | ||||
0.0747205 | + | 0.997205i | \(0.476194\pi\) | |||||||
\(578\) | −22240.6 | −1.60050 | ||||||||
\(579\) | −4348.86 | −0.312146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −178.257 | −0.0127287 | ||||||||
\(582\) | −20579.5 | −1.46571 | ||||||||
\(583\) | 11810.4 | 0.839000 | ||||||||
\(584\) | 81.6394 | 0.00578470 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36798.9 | −2.59411 | ||||||||
\(587\) | −20730.6 | −1.45766 | −0.728828 | − | 0.684697i | \(-0.759935\pi\) | ||||
−0.728828 | + | 0.684697i | \(0.759935\pi\) | |||||||
\(588\) | 15406.3 | 1.08052 | ||||||||
\(589\) | −30307.1 | −2.12018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3181.87 | −0.221463 | ||||||||
\(592\) | 11370.5 | 0.789399 | ||||||||
\(593\) | 1924.00 | 0.133236 | 0.0666182 | − | 0.997779i | \(-0.478779\pi\) | ||||
0.0666182 | + | 0.997779i | \(0.478779\pi\) | |||||||
\(594\) | −6127.68 | −0.423269 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2884.33 | 0.198233 | ||||||||
\(597\) | 549.230 | 0.0376524 | ||||||||
\(598\) | −26596.9 | −1.81878 | ||||||||
\(599\) | −8088.34 | −0.551720 | −0.275860 | − | 0.961198i | \(-0.588963\pi\) | ||||
−0.275860 | + | 0.961198i | \(0.588963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19953.8 | 1.35430 | 0.677149 | − | 0.735846i | \(-0.263215\pi\) | ||||
0.677149 | + | 0.735846i | \(0.263215\pi\) | |||||||
\(602\) | −356.842 | −0.0241592 | ||||||||
\(603\) | 1588.56 | 0.107282 | ||||||||
\(604\) | 15764.0 | 1.06197 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5379.22 | 0.360588 | ||||||||
\(607\) | 3633.68 | 0.242976 | 0.121488 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121488 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(608\) | −6707.23 | −0.447392 | ||||||||
\(609\) | −5.19897 | −0.000345933 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2578.13 | 0.170704 | ||||||||
\(612\) | −2225.70 | −0.147007 | ||||||||
\(613\) | 1581.91 | 0.104230 | 0.0521148 | − | 0.998641i | \(-0.483404\pi\) | ||||
0.0521148 | + | 0.998641i | \(0.483404\pi\) | |||||||
\(614\) | 21606.4 | 1.42014 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −222.377 | −0.0145452 | ||||||||
\(617\) | −4454.03 | −0.290620 | −0.145310 | − | 0.989386i | \(-0.546418\pi\) | ||||
−0.145310 | + | 0.989386i | \(0.546418\pi\) | |||||||
\(618\) | −29015.0 | −1.88860 | ||||||||
\(619\) | −2630.26 | −0.170790 | −0.0853951 | − | 0.996347i | \(-0.527215\pi\) | ||||
−0.0853951 | + | 0.996347i | \(0.527215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4362.70 | −0.281915 | ||||||||
\(622\) | 33863.6 | 2.18297 | ||||||||
\(623\) | 187.950 | 0.0120868 | ||||||||
\(624\) | 4162.97 | 0.267071 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9891.85 | −0.631562 | ||||||||
\(627\) | −12927.0 | −0.823370 | ||||||||
\(628\) | −30623.6 | −1.94588 | ||||||||
\(629\) | −4647.75 | −0.294623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16896.4 | −1.06599 | −0.532993 | − | 0.846120i | \(-0.678933\pi\) | ||||
−0.532993 | + | 0.846120i | \(0.678933\pi\) | |||||||
\(632\) | 20309.1 | 1.27825 | ||||||||
\(633\) | 14714.2 | 0.923912 | ||||||||
\(634\) | −41203.1 | −2.58105 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11203.9 | −0.698530 | ||||||||
\(637\) | 11778.8 | 0.732640 | ||||||||
\(638\) | −2798.92 | −0.173684 | ||||||||
\(639\) | 6498.93 | 0.402338 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28804.5 | 1.77490 | 0.887448 | − | 0.460908i | \(-0.152476\pi\) | ||||
0.887448 | + | 0.460908i | \(0.152476\pi\) | |||||||
\(642\) | 24152.7 | 1.48478 | ||||||||
\(643\) | −10219.9 | −0.626801 | −0.313400 | − | 0.949621i | \(-0.601468\pi\) | ||||
−0.313400 | + | 0.949621i | \(0.601468\pi\) | |||||||
\(644\) | −339.968 | −0.0208022 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7204.03 | −0.438759 | ||||||||
\(647\) | 1792.38 | 0.108912 | 0.0544558 | − | 0.998516i | \(-0.482658\pi\) | ||||
0.0544558 | + | 0.998516i | \(0.482658\pi\) | |||||||
\(648\) | 2707.15 | 0.164116 | ||||||||
\(649\) | −12716.6 | −0.769138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −140.396 | −0.00845243 | ||||||||
\(652\) | −12697.3 | −0.762675 | ||||||||
\(653\) | 13405.4 | 0.803359 | 0.401679 | − | 0.915780i | \(-0.368427\pi\) | ||||
0.401679 | + | 0.915780i | \(0.368427\pi\) | |||||||
\(654\) | −290.864 | −0.0173910 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5075.44 | 0.302077 | ||||||||
\(657\) | 21.9844 | 0.00130547 | ||||||||
\(658\) | 50.5616 | 0.00299559 | ||||||||
\(659\) | −15441.6 | −0.912778 | −0.456389 | − | 0.889780i | \(-0.650858\pi\) | ||||
−0.456389 | + | 0.889780i | \(0.650858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4356.59 | 0.256356 | 0.128178 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128178 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(662\) | 1244.40 | 0.0730589 | ||||||||
\(663\) | −1701.64 | −0.0996774 | ||||||||
\(664\) | 42397.2 | 2.47791 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12138.9 | 0.706265 | ||||||||
\(667\) | −1992.74 | −0.115681 | ||||||||
\(668\) | −29533.4 | −1.71060 | ||||||||
\(669\) | −14512.3 | −0.838679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17512.4 | 1.00754 | ||||||||
\(672\) | −31.0707 | −0.00178360 | ||||||||
\(673\) | 17617.2 | 1.00905 | 0.504527 | − | 0.863396i | \(-0.331667\pi\) | ||||
0.504527 | + | 0.863396i | \(0.331667\pi\) | |||||||
\(674\) | −32214.8 | −1.84105 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15236.5 | −0.866894 | ||||||||
\(677\) | −3294.63 | −0.187036 | −0.0935178 | − | 0.995618i | \(-0.529811\pi\) | ||||
−0.0935178 | + | 0.995618i | \(0.529811\pi\) | |||||||
\(678\) | −9238.83 | −0.523326 | ||||||||
\(679\) | −201.114 | −0.0113668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −134.453 | −0.00756570 | ||||||||
\(682\) | −75583.4 | −4.24375 | ||||||||
\(683\) | −4829.50 | −0.270565 | −0.135282 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135282 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(684\) | 12263.2 | 0.685517 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 462.018 | 0.0257142 | ||||||||
\(687\) | 12479.3 | 0.693037 | ||||||||
\(688\) | 21408.2 | 1.18631 | ||||||||
\(689\) | −8565.87 | −0.473634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23330.5 | 1.28442 | 0.642211 | − | 0.766528i | \(-0.278017\pi\) | ||||
0.642211 | + | 0.766528i | \(0.278017\pi\) | |||||||
\(692\) | −40541.5 | −2.22711 | ||||||||
\(693\) | −59.8831 | −0.00328250 | ||||||||
\(694\) | 34220.0 | 1.87172 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1236.54 | 0.0673432 | ||||||||
\(697\) | −2074.62 | −0.112743 | ||||||||
\(698\) | −54992.0 | −2.98206 | ||||||||
\(699\) | 8836.19 | 0.478134 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27619.7 | 1.48813 | 0.744066 | − | 0.668106i | \(-0.232895\pi\) | ||||
0.744066 | + | 0.668106i | \(0.232895\pi\) | |||||||
\(702\) | 4444.30 | 0.238945 | ||||||||
\(703\) | 25608.2 | 1.37387 | ||||||||
\(704\) | −32033.4 | −1.71492 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −285.673 | −0.0152287 | ||||||||
\(707\) | 52.5688 | 0.00279640 | ||||||||
\(708\) | 12063.6 | 0.640365 | ||||||||
\(709\) | 25819.3 | 1.36765 | 0.683826 | − | 0.729645i | \(-0.260315\pi\) | ||||
0.683826 | + | 0.729645i | \(0.260315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5468.96 | 0.288470 | ||||||||
\(712\) | −44702.6 | −2.35295 | ||||||||
\(713\) | −53812.8 | −2.82651 | ||||||||
\(714\) | −33.3721 | −0.00174919 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 46899.1 | 2.44791 | ||||||||
\(717\) | −6523.62 | −0.339790 | ||||||||
\(718\) | −37394.5 | −1.94366 | ||||||||
\(719\) | −16339.0 | −0.847484 | −0.423742 | − | 0.905783i | \(-0.639284\pi\) | ||||
−0.423742 | + | 0.905783i | \(0.639284\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −283.551 | −0.0146463 | ||||||||
\(722\) | 6817.44 | 0.351411 | ||||||||
\(723\) | −6902.06 | −0.355035 | ||||||||
\(724\) | 4747.20 | 0.243685 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13100.2 | −0.669689 | ||||||||
\(727\) | 7287.52 | 0.371773 | 0.185887 | − | 0.982571i | \(-0.440484\pi\) | ||||
0.185887 | + | 0.982571i | \(0.440484\pi\) | |||||||
\(728\) | 161.286 | 0.00821106 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8750.74 | −0.442760 | ||||||||
\(732\) | −16613.2 | −0.838853 | ||||||||
\(733\) | 12030.1 | 0.606197 | 0.303098 | − | 0.952959i | \(-0.401979\pi\) | ||||
0.303098 | + | 0.952959i | \(0.401979\pi\) | |||||||
\(734\) | 7588.76 | 0.381616 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11909.2 | −0.596440 | ||||||||
\(737\) | 8357.64 | 0.417718 | ||||||||
\(738\) | 5418.44 | 0.270265 | ||||||||
\(739\) | −15163.0 | −0.754778 | −0.377389 | − | 0.926055i | \(-0.623178\pi\) | ||||
−0.377389 | + | 0.926055i | \(0.623178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9375.68 | 0.464810 | ||||||||
\(742\) | −167.992 | −0.00831155 | ||||||||
\(743\) | 22772.8 | 1.12443 | 0.562216 | − | 0.826991i | \(-0.309949\pi\) | ||||
0.562216 | + | 0.826991i | \(0.309949\pi\) | |||||||
\(744\) | 33392.0 | 1.64545 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 53591.6 | 2.63020 | ||||||||
\(747\) | 11417.0 | 0.559205 | ||||||||
\(748\) | −11709.8 | −0.572394 | ||||||||
\(749\) | 236.034 | 0.0115147 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27855.5 | −1.35348 | −0.676739 | − | 0.736223i | \(-0.736608\pi\) | ||||
−0.676739 | + | 0.736223i | \(0.736608\pi\) | |||||||
\(752\) | −3033.37 | −0.147095 | ||||||||
\(753\) | −10105.6 | −0.489071 | ||||||||
\(754\) | 2030.01 | 0.0980484 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 56.8081 | 0.00273293 | ||||||||
\(757\) | −302.235 | −0.0145111 | −0.00725557 | − | 0.999974i | \(-0.502310\pi\) | ||||
−0.00725557 | + | 0.999974i | \(0.502310\pi\) | |||||||
\(758\) | −56188.7 | −2.69244 | ||||||||
\(759\) | −22952.9 | −1.09768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4497.19 | −0.214222 | −0.107111 | − | 0.994247i | \(-0.534160\pi\) | ||||
−0.107111 | + | 0.994247i | \(0.534160\pi\) | |||||||
\(762\) | −17052.3 | −0.810680 | ||||||||
\(763\) | −2.84249 | −0.000134869 0 | ||||||||
\(764\) | 25146.5 | 1.19080 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 44440.9 | 2.09623 | ||||||||
\(767\) | 9223.13 | 0.434195 | ||||||||
\(768\) | 21910.1 | 1.02944 | ||||||||
\(769\) | 2438.76 | 0.114362 | 0.0571808 | − | 0.998364i | \(-0.481789\pi\) | ||||
0.0571808 | + | 0.998364i | \(0.481789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1214.71 | 0.0567404 | ||||||||
\(772\) | 21705.1 | 1.01190 | ||||||||
\(773\) | 37464.5 | 1.74321 | 0.871607 | − | 0.490205i | \(-0.163078\pi\) | ||||
0.871607 | + | 0.490205i | \(0.163078\pi\) | |||||||
\(774\) | 22855.0 | 1.06138 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 47833.4 | 2.21278 | ||||||||
\(777\) | 118.628 | 0.00547716 | ||||||||
\(778\) | −6428.15 | −0.296222 | ||||||||
\(779\) | 11430.7 | 0.525736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34191.9 | 1.56656 | ||||||||
\(782\) | −12791.3 | −0.584932 | ||||||||
\(783\) | 332.983 | 0.0151978 | ||||||||
\(784\) | −13858.6 | −0.631315 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3207.88 | 0.145574 | ||||||||
\(787\) | −30317.8 | −1.37321 | −0.686603 | − | 0.727033i | \(-0.740899\pi\) | ||||
−0.686603 | + | 0.727033i | \(0.740899\pi\) | |||||||
\(788\) | 15880.7 | 0.717928 | ||||||||
\(789\) | −4544.10 | −0.205037 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −90.2870 | −0.00405845 | ||||||||
\(792\) | 14242.8 | 0.639008 | ||||||||
\(793\) | −12701.4 | −0.568779 | ||||||||
\(794\) | −54478.7 | −2.43498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2741.21 | −0.122060 | ||||||||
\(797\) | 23627.1 | 1.05008 | 0.525041 | − | 0.851077i | \(-0.324050\pi\) | ||||
0.525041 | + | 0.851077i | \(0.324050\pi\) | |||||||
\(798\) | 183.874 | 0.00815671 | ||||||||
\(799\) | 1239.91 | 0.0548996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12037.8 | −0.531005 | ||||||||
\(802\) | −59537.2 | −2.62136 | ||||||||
\(803\) | 115.663 | 0.00508303 | ||||||||
\(804\) | −7928.48 | −0.347781 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 54819.2 | 2.39569 | ||||||||
\(807\) | 5675.65 | 0.247574 | ||||||||
\(808\) | −12503.1 | −0.544378 | ||||||||
\(809\) | −30566.8 | −1.32839 | −0.664197 | − | 0.747558i | \(-0.731226\pi\) | ||||
−0.664197 | + | 0.747558i | \(0.731226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36976.4 | 1.60101 | 0.800504 | − | 0.599328i | \(-0.204565\pi\) | ||||
0.800504 | + | 0.599328i | \(0.204565\pi\) | |||||||
\(812\) | 25.9481 | 0.00112143 | ||||||||
\(813\) | 6282.94 | 0.271036 | ||||||||
\(814\) | 63864.6 | 2.74994 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2002.11 | 0.0858920 | ||||||||
\(817\) | 48214.8 | 2.06466 | ||||||||
\(818\) | 61915.1 | 2.64647 | ||||||||
\(819\) | 43.4321 | 0.00185304 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9499.03 | −0.403798 | −0.201899 | − | 0.979406i | \(-0.564711\pi\) | ||||
−0.201899 | + | 0.979406i | \(0.564711\pi\) | |||||||
\(822\) | −22712.4 | −0.963728 | ||||||||
\(823\) | 4753.25 | 0.201322 | 0.100661 | − | 0.994921i | \(-0.467904\pi\) | ||||
0.100661 | + | 0.994921i | \(0.467904\pi\) | |||||||
\(824\) | 67440.5 | 2.85121 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 180.882 | 0.00761947 | ||||||||
\(827\) | −13224.0 | −0.556039 | −0.278020 | − | 0.960575i | \(-0.589678\pi\) | ||||
−0.278020 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(828\) | 21774.2 | 0.913897 | ||||||||
\(829\) | −10210.7 | −0.427782 | −0.213891 | − | 0.976858i | \(-0.568614\pi\) | ||||
−0.213891 | + | 0.976858i | \(0.568614\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4478.19 | −0.186939 | ||||||||
\(832\) | 23233.2 | 0.968109 | ||||||||
\(833\) | 5664.80 | 0.235623 | ||||||||
\(834\) | −22506.8 | −0.934469 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 64518.4 | 2.66916 | ||||||||
\(837\) | 8992.03 | 0.371338 | ||||||||
\(838\) | −19952.4 | −0.822485 | ||||||||
\(839\) | −6722.41 | −0.276619 | −0.138310 | − | 0.990389i | \(-0.544167\pi\) | ||||
−0.138310 | + | 0.990389i | \(0.544167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24236.9 | −0.993764 | ||||||||
\(842\) | −71642.6 | −2.93227 | ||||||||
\(843\) | −6208.48 | −0.253655 | ||||||||
\(844\) | −73438.4 | −2.99509 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3238.36 | −0.131604 | ||||||||
\(847\) | −128.023 | −0.00519351 | ||||||||
\(848\) | 10078.4 | 0.408130 | ||||||||
\(849\) | 10196.7 | 0.412191 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45469.4 | 1.83158 | ||||||||
\(852\) | −32436.2 | −1.30428 | ||||||||
\(853\) | 3785.52 | 0.151950 | 0.0759752 | − | 0.997110i | \(-0.475793\pi\) | ||||
0.0759752 | + | 0.997110i | \(0.475793\pi\) | |||||||
\(854\) | −249.098 | −0.00998121 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −56138.8 | −2.24157 | ||||||||
\(857\) | −13421.7 | −0.534979 | −0.267489 | − | 0.963561i | \(-0.586194\pi\) | ||||
−0.267489 | + | 0.963561i | \(0.586194\pi\) | |||||||
\(858\) | 23382.1 | 0.930365 | ||||||||
\(859\) | 491.965 | 0.0195409 | 0.00977045 | − | 0.999952i | \(-0.496890\pi\) | ||||
0.00977045 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.9520 | 0.00209593 | ||||||||
\(862\) | −61172.8 | −2.41712 | ||||||||
\(863\) | 8088.10 | 0.319029 | 0.159515 | − | 0.987196i | \(-0.449007\pi\) | ||||
0.159515 | + | 0.987196i | \(0.449007\pi\) | |||||||
\(864\) | 1990.01 | 0.0783583 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3726.55 | −0.146228 | ||||||||
\(867\) | 13920.6 | 0.545293 | ||||||||
\(868\) | 700.714 | 0.0274007 | ||||||||
\(869\) | 28773.1 | 1.12320 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6061.64 | −0.235811 | ||||||||
\(872\) | 676.064 | 0.0262551 | ||||||||
\(873\) | 12880.9 | 0.499373 | ||||||||
\(874\) | 70477.7 | 2.72762 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −109.724 | −0.00423200 | ||||||||
\(877\) | −12000.4 | −0.462058 | −0.231029 | − | 0.972947i | \(-0.574209\pi\) | ||||
−0.231029 | + | 0.972947i | \(0.574209\pi\) | |||||||
\(878\) | 47625.6 | 1.83062 | ||||||||
\(879\) | 23032.8 | 0.883820 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2285.38 | −0.0873964 | −0.0436982 | − | 0.999045i | \(-0.513914\pi\) | ||||
−0.0436982 | + | 0.999045i | \(0.513914\pi\) | |||||||
\(882\) | −14795.2 | −0.564830 | ||||||||
\(883\) | −19226.6 | −0.732759 | −0.366379 | − | 0.930466i | \(-0.619403\pi\) | ||||
−0.366379 | + | 0.930466i | \(0.619403\pi\) | |||||||
\(884\) | 8492.87 | 0.323129 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34221.5 | −1.29762 | ||||||||
\(887\) | −14952.8 | −0.566028 | −0.283014 | − | 0.959116i | \(-0.591334\pi\) | ||||
−0.283014 | + | 0.959116i | \(0.591334\pi\) | |||||||
\(888\) | −28214.8 | −1.06625 | ||||||||
\(889\) | −166.644 | −0.00628692 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3835.38 | 0.144209 | ||||||||
\(892\) | 72430.6 | 2.71879 | ||||||||
\(893\) | −6831.64 | −0.256005 | ||||||||
\(894\) | −2769.91 | −0.103624 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 372.789 | 0.0138996 | ||||||||
\(897\) | 16647.3 | 0.619662 | ||||||||
\(898\) | 50030.2 | 1.85916 | ||||||||
\(899\) | 4107.26 | 0.152375 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4119.61 | −0.152324 | ||||||||
\(902\) | 28507.3 | 1.05231 | ||||||||
\(903\) | 223.352 | 0.00823109 | ||||||||
\(904\) | 21474.1 | 0.790064 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15138.7 | −0.555133 | ||||||||
\(907\) | −48744.8 | −1.78450 | −0.892251 | − | 0.451540i | \(-0.850875\pi\) | ||||
−0.892251 | + | 0.451540i | \(0.850875\pi\) | |||||||
\(908\) | 671.053 | 0.0245261 | ||||||||
\(909\) | −3366.92 | −0.122853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35064.7 | −1.27524 | −0.637621 | − | 0.770350i | \(-0.720081\pi\) | ||||
−0.637621 | + | 0.770350i | \(0.720081\pi\) | |||||||
\(912\) | −11031.2 | −0.400527 | ||||||||
\(913\) | 60066.6 | 2.17734 | ||||||||
\(914\) | −24155.6 | −0.874177 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −62284.4 | −2.24665 | ||||||||
\(917\) | 31.3492 | 0.00112894 | ||||||||
\(918\) | 2137.41 | 0.0768465 | ||||||||
\(919\) | −20159.6 | −0.723617 | −0.361808 | − | 0.932253i | \(-0.617841\pi\) | ||||
−0.361808 | + | 0.932253i | \(0.617841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13523.7 | −0.483845 | ||||||||
\(922\) | 8784.07 | 0.313761 | ||||||||
\(923\) | −24798.8 | −0.884357 | ||||||||
\(924\) | 298.877 | 0.0106410 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9046.76 | −0.321053 | ||||||||
\(927\) | 18160.8 | 0.643451 | ||||||||
\(928\) | 908.972 | 0.0321535 | ||||||||
\(929\) | 22221.8 | 0.784793 | 0.392397 | − | 0.919796i | \(-0.371646\pi\) | ||||
0.392397 | + | 0.919796i | \(0.371646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31211.9 | −1.09874 | ||||||||
\(932\) | −44101.4 | −1.54999 | ||||||||
\(933\) | −21195.6 | −0.743743 | ||||||||
\(934\) | 18905.2 | 0.662308 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10330.0 | −0.360734 | ||||||||
\(937\) | −8123.54 | −0.283228 | −0.141614 | − | 0.989922i | \(-0.545229\pi\) | ||||
−0.141614 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(938\) | −118.880 | −0.00413812 | ||||||||
\(939\) | 6191.42 | 0.215175 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41826.3 | −1.44899 | −0.724494 | − | 0.689281i | \(-0.757927\pi\) | ||||
−0.724494 | + | 0.689281i | \(0.757927\pi\) | |||||||
\(942\) | 29408.8 | 1.01719 | ||||||||
\(943\) | 20296.2 | 0.700885 | ||||||||
\(944\) | −10851.7 | −0.374146 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 120244. | 4.13262 | ||||||||
\(947\) | −32843.5 | −1.12700 | −0.563501 | − | 0.826115i | \(-0.690546\pi\) | ||||
−0.563501 | + | 0.826115i | \(0.690546\pi\) | |||||||
\(948\) | −27295.6 | −0.935146 | ||||||||
\(949\) | −83.8885 | −0.00286948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25789.5 | 0.879370 | ||||||||
\(952\) | 77.5678 | 0.00264074 | ||||||||
\(953\) | 12579.4 | 0.427583 | 0.213791 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213791 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(954\) | 10759.5 | 0.365149 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 32559.4 | 1.10151 | ||||||||
\(957\) | 1751.88 | 0.0591746 | ||||||||
\(958\) | −51568.8 | −1.73916 | ||||||||
\(959\) | −221.958 | −0.00747382 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81123.3 | 2.72308 | ||||||||
\(962\) | −46319.8 | −1.55240 | ||||||||
\(963\) | −15117.4 | −0.505870 | ||||||||
\(964\) | 34448.2 | 1.15093 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 326.482 | 0.0108741 | ||||||||
\(967\) | −41883.1 | −1.39283 | −0.696417 | − | 0.717637i | \(-0.745223\pi\) | ||||
−0.696417 | + | 0.717637i | \(0.745223\pi\) | |||||||
\(968\) | 30449.2 | 1.01103 | ||||||||
\(969\) | 4509.08 | 0.149487 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55390.3 | 1.83065 | 0.915323 | − | 0.402720i | \(-0.131935\pi\) | ||||
0.915323 | + | 0.402720i | \(0.131935\pi\) | |||||||
\(972\) | −3638.44 | −0.120065 | ||||||||
\(973\) | −219.949 | −0.00724691 | ||||||||
\(974\) | −15296.2 | −0.503204 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14944.2 | 0.490117 | ||||||||
\(977\) | 35463.4 | 1.16128 | 0.580642 | − | 0.814159i | \(-0.302802\pi\) | ||||
0.580642 | + | 0.814159i | \(0.302802\pi\) | |||||||
\(978\) | 12193.6 | 0.398680 | ||||||||
\(979\) | −63332.8 | −2.06754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 182.055 | 0.00592515 | ||||||||
\(982\) | 4476.20 | 0.145459 | ||||||||
\(983\) | 34670.9 | 1.12495 | 0.562477 | − | 0.826813i | \(-0.309849\pi\) | ||||
0.562477 | + | 0.826813i | \(0.309849\pi\) | |||||||
\(984\) | −12594.2 | −0.408018 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 976.298 | 0.0315331 | ||||||||
\(987\) | −31.6471 | −0.00102060 | ||||||||
\(988\) | −46794.0 | −1.50680 | ||||||||
\(989\) | 85609.3 | 2.75250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37280.3 | −1.19500 | −0.597501 | − | 0.801868i | \(-0.703840\pi\) | ||||
−0.597501 | + | 0.801868i | \(0.703840\pi\) | |||||||
\(992\) | 24546.3 | 0.785631 | ||||||||
\(993\) | −778.884 | −0.0248914 | ||||||||
\(994\) | −486.347 | −0.0155191 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −56982.2 | −1.81280 | ||||||||
\(997\) | 34383.2 | 1.09220 | 0.546101 | − | 0.837719i | \(-0.316111\pi\) | ||||
0.546101 | + | 0.837719i | \(0.316111\pi\) | |||||||
\(998\) | 26357.3 | 0.835996 | ||||||||
\(999\) | −7597.86 | −0.240626 |
(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 | 1875.4.a.f.1.13 | 14 | ||
5.4 | even | 2 | 1875.4.a.g.1.2 | 14 | |||
25.4 | even | 10 | 75.4.g.b.16.7 | ✓ | 28 | ||
25.19 | even | 10 | 75.4.g.b.61.7 | yes | 28 | ||
75.29 | odd | 10 | 225.4.h.a.91.1 | 28 | |||
75.44 | odd | 10 | 225.4.h.a.136.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.7 | ✓ | 28 | 25.4 | even | 10 | ||
75.4.g.b.61.7 | yes | 28 | 25.19 | even | 10 | ||
225.4.h.a.91.1 | 28 | 75.29 | odd | 10 | |||
225.4.h.a.136.1 | 28 | 75.44 | odd | 10 | |||
1875.4.a.f.1.13 | 14 | 1.1 | even | 1 | trivial | ||
1875.4.a.g.1.2 | 14 | 5.4 | even | 2 |