Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.23612.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 20x + 26 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.26150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.26150 | 1.86022 | 0.930110 | − | 0.367281i | \(-0.119711\pi\) | ||||
0.930110 | + | 0.367281i | \(0.119711\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 19.6833 | 2.46042 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 15.7845 | 1.07400 | ||||||||
\(7\) | 10.3207 | 0.557266 | 0.278633 | − | 0.960398i | \(-0.410119\pi\) | ||||
0.278633 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(8\) | 61.4719 | 2.71670 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 59.0500 | 1.42052 | ||||||||
\(13\) | −63.9817 | −1.36502 | −0.682512 | − | 0.730874i | \(-0.739113\pi\) | ||||
−0.682512 | + | 0.730874i | \(0.739113\pi\) | |||||||
\(14\) | 54.3024 | 1.03664 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 165.967 | 2.59324 | ||||||||
\(17\) | −17.1461 | −0.244620 | −0.122310 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122310 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(18\) | 47.3535 | 0.620073 | ||||||||
\(19\) | 90.2104 | 1.08925 | 0.544623 | − | 0.838681i | \(-0.316673\pi\) | ||||
0.544623 | + | 0.838681i | \(0.316673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30.9621 | 0.321738 | ||||||||
\(22\) | 57.8765 | 0.560877 | ||||||||
\(23\) | 212.605 | 1.92744 | 0.963721 | − | 0.266913i | \(-0.0860036\pi\) | ||||
0.963721 | + | 0.266913i | \(0.0860036\pi\) | |||||||
\(24\) | 184.416 | 1.56849 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −336.639 | −2.53925 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 203.146 | 1.37111 | ||||||||
\(29\) | 57.5461 | 0.368484 | 0.184242 | − | 0.982881i | \(-0.441017\pi\) | ||||
0.184242 | + | 0.982881i | \(0.441017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −141.704 | −0.820991 | −0.410496 | − | 0.911863i | \(-0.634644\pi\) | ||||
−0.410496 | + | 0.911863i | \(0.634644\pi\) | |||||||
\(32\) | 381.462 | 2.10730 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −90.2140 | −0.455046 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 177.150 | 0.820139 | ||||||||
\(37\) | 257.963 | 1.14619 | 0.573093 | − | 0.819490i | \(-0.305743\pi\) | ||||
0.573093 | + | 0.819490i | \(0.305743\pi\) | |||||||
\(38\) | 474.642 | 2.02624 | ||||||||
\(39\) | −191.945 | −0.788097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −225.914 | −0.860533 | −0.430266 | − | 0.902702i | \(-0.641580\pi\) | ||||
−0.430266 | + | 0.902702i | \(0.641580\pi\) | |||||||
\(42\) | 162.907 | 0.598503 | ||||||||
\(43\) | 347.445 | 1.23221 | 0.616103 | − | 0.787666i | \(-0.288711\pi\) | ||||
0.616103 | + | 0.787666i | \(0.288711\pi\) | |||||||
\(44\) | 216.517 | 0.741844 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1118.62 | 3.58547 | ||||||||
\(47\) | −404.364 | −1.25495 | −0.627473 | − | 0.778638i | \(-0.715911\pi\) | ||||
−0.627473 | + | 0.778638i | \(0.715911\pi\) | |||||||
\(48\) | 497.902 | 1.49721 | ||||||||
\(49\) | −236.483 | −0.689455 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −51.4382 | −0.141231 | ||||||||
\(52\) | −1259.37 | −3.35853 | ||||||||
\(53\) | −259.568 | −0.672726 | −0.336363 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336363 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(54\) | 142.060 | 0.358000 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 634.433 | 1.51392 | ||||||||
\(57\) | 270.631 | 0.628877 | ||||||||
\(58\) | 302.779 | 0.685462 | ||||||||
\(59\) | −853.067 | −1.88237 | −0.941185 | − | 0.337891i | \(-0.890287\pi\) | ||||
−0.941185 | + | 0.337891i | \(0.890287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −203.699 | −0.427558 | −0.213779 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213779 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(62\) | −745.573 | −1.52722 | ||||||||
\(63\) | 92.8864 | 0.185755 | ||||||||
\(64\) | 679.320 | 1.32680 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 173.629 | 0.323823 | ||||||||
\(67\) | −266.890 | −0.486653 | −0.243327 | − | 0.969944i | \(-0.578239\pi\) | ||||
−0.243327 | + | 0.969944i | \(0.578239\pi\) | |||||||
\(68\) | −337.492 | −0.601866 | ||||||||
\(69\) | 637.814 | 1.11281 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 92.4460 | 0.154526 | 0.0772629 | − | 0.997011i | \(-0.475382\pi\) | ||||
0.0772629 | + | 0.997011i | \(0.475382\pi\) | |||||||
\(72\) | 553.247 | 0.905566 | ||||||||
\(73\) | 242.026 | 0.388040 | 0.194020 | − | 0.980998i | \(-0.437847\pi\) | ||||
0.194020 | + | 0.980998i | \(0.437847\pi\) | |||||||
\(74\) | 1357.27 | 2.13216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1775.64 | 2.68000 | ||||||||
\(77\) | 113.528 | 0.168022 | ||||||||
\(78\) | −1009.92 | −1.46603 | ||||||||
\(79\) | −1021.60 | −1.45492 | −0.727460 | − | 0.686150i | \(-0.759299\pi\) | ||||
−0.727460 | + | 0.686150i | \(0.759299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1188.65 | −1.60078 | ||||||||
\(83\) | −706.415 | −0.934206 | −0.467103 | − | 0.884203i | \(-0.654702\pi\) | ||||
−0.467103 | + | 0.884203i | \(0.654702\pi\) | |||||||
\(84\) | 609.438 | 0.791609 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1828.08 | 2.29217 | ||||||||
\(87\) | 172.638 | 0.212745 | ||||||||
\(88\) | 676.191 | 0.819116 | ||||||||
\(89\) | −440.218 | −0.524304 | −0.262152 | − | 0.965027i | \(-0.584432\pi\) | ||||
−0.262152 | + | 0.965027i | \(0.584432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −660.336 | −0.760682 | ||||||||
\(92\) | 4184.77 | 4.74231 | ||||||||
\(93\) | −425.111 | −0.473999 | ||||||||
\(94\) | −2127.56 | −2.33448 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1144.38 | 1.21665 | ||||||||
\(97\) | 197.761 | 0.207006 | 0.103503 | − | 0.994629i | \(-0.466995\pi\) | ||||
0.103503 | + | 0.994629i | \(0.466995\pi\) | |||||||
\(98\) | −1244.25 | −1.28254 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1400.62 | 1.37987 | 0.689937 | − | 0.723870i | \(-0.257638\pi\) | ||||
0.689937 | + | 0.723870i | \(0.257638\pi\) | |||||||
\(102\) | −270.642 | −0.262721 | ||||||||
\(103\) | 1345.70 | 1.28734 | 0.643669 | − | 0.765304i | \(-0.277411\pi\) | ||||
0.643669 | + | 0.765304i | \(0.277411\pi\) | |||||||
\(104\) | −3933.07 | −3.70836 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1365.72 | −1.25142 | ||||||||
\(107\) | 889.178 | 0.803366 | 0.401683 | − | 0.915779i | \(-0.368425\pi\) | ||||
0.401683 | + | 0.915779i | \(0.368425\pi\) | |||||||
\(108\) | 531.450 | 0.473508 | ||||||||
\(109\) | 1256.29 | 1.10395 | 0.551974 | − | 0.833861i | \(-0.313875\pi\) | ||||
0.551974 | + | 0.833861i | \(0.313875\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 773.890 | 0.661751 | ||||||||
\(112\) | 1712.90 | 1.44512 | ||||||||
\(113\) | 2394.01 | 1.99301 | 0.996504 | − | 0.0835448i | \(-0.0266242\pi\) | ||||
0.996504 | + | 0.0835448i | \(0.0266242\pi\) | |||||||
\(114\) | 1423.93 | 1.16985 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1132.70 | 0.906626 | ||||||||
\(117\) | −575.835 | −0.455008 | ||||||||
\(118\) | −4488.41 | −3.50162 | ||||||||
\(119\) | −176.960 | −0.136318 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1071.76 | −0.795352 | ||||||||
\(123\) | −677.742 | −0.496829 | ||||||||
\(124\) | −2789.20 | −2.01998 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 488.721 | 0.345546 | ||||||||
\(127\) | −2065.57 | −1.44322 | −0.721612 | − | 0.692298i | \(-0.756598\pi\) | ||||
−0.721612 | + | 0.692298i | \(0.756598\pi\) | |||||||
\(128\) | 522.548 | 0.360837 | ||||||||
\(129\) | 1042.33 | 0.711414 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 785.526 | 0.523907 | 0.261953 | − | 0.965081i | \(-0.415633\pi\) | ||||
0.261953 | + | 0.965081i | \(0.415633\pi\) | |||||||
\(132\) | 649.550 | 0.428304 | ||||||||
\(133\) | 931.035 | 0.607000 | ||||||||
\(134\) | −1404.24 | −0.905282 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1054.00 | −0.664558 | ||||||||
\(137\) | −1276.24 | −0.795885 | −0.397942 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397942 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(138\) | 3355.86 | 2.07007 | ||||||||
\(139\) | −2703.21 | −1.64952 | −0.824760 | − | 0.565482i | \(-0.808690\pi\) | ||||
−0.824760 | + | 0.565482i | \(0.808690\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1213.09 | −0.724544 | ||||||||
\(142\) | 486.405 | 0.287452 | ||||||||
\(143\) | −703.798 | −0.411570 | ||||||||
\(144\) | 1493.71 | 0.864413 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1273.42 | 0.721840 | ||||||||
\(147\) | −709.449 | −0.398057 | ||||||||
\(148\) | 5077.58 | 2.82010 | ||||||||
\(149\) | −2400.99 | −1.32011 | −0.660056 | − | 0.751217i | \(-0.729467\pi\) | ||||
−0.660056 | + | 0.751217i | \(0.729467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2517.30 | −1.35665 | −0.678326 | − | 0.734761i | \(-0.737294\pi\) | ||||
−0.678326 | + | 0.734761i | \(0.737294\pi\) | |||||||
\(152\) | 5545.40 | 2.95916 | ||||||||
\(153\) | −154.315 | −0.0815399 | ||||||||
\(154\) | 597.326 | 0.312558 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3778.12 | −1.93905 | ||||||||
\(157\) | −1391.42 | −0.707310 | −0.353655 | − | 0.935376i | \(-0.615061\pi\) | ||||
−0.353655 | + | 0.935376i | \(0.615061\pi\) | |||||||
\(158\) | −5375.13 | −2.70647 | ||||||||
\(159\) | −778.705 | −0.388398 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2194.23 | 1.07410 | ||||||||
\(162\) | 426.181 | 0.206691 | ||||||||
\(163\) | 2720.53 | 1.30729 | 0.653644 | − | 0.756802i | \(-0.273239\pi\) | ||||
0.653644 | + | 0.756802i | \(0.273239\pi\) | |||||||
\(164\) | −4446.74 | −2.11727 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3716.80 | −1.73783 | ||||||||
\(167\) | −2950.25 | −1.36705 | −0.683525 | − | 0.729927i | \(-0.739554\pi\) | ||||
−0.683525 | + | 0.729927i | \(0.739554\pi\) | |||||||
\(168\) | 1903.30 | 0.874064 | ||||||||
\(169\) | 1896.65 | 0.863292 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 811.894 | 0.363082 | ||||||||
\(172\) | 6838.88 | 3.03174 | ||||||||
\(173\) | −537.049 | −0.236018 | −0.118009 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118009 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(174\) | 908.336 | 0.395752 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1825.64 | 0.781891 | ||||||||
\(177\) | −2559.20 | −1.08679 | ||||||||
\(178\) | −2316.21 | −0.975320 | ||||||||
\(179\) | 2891.25 | 1.20728 | 0.603638 | − | 0.797259i | \(-0.293717\pi\) | ||||
0.603638 | + | 0.797259i | \(0.293717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 435.209 | 0.178723 | 0.0893615 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893615 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(182\) | −3474.36 | −1.41504 | ||||||||
\(183\) | −611.098 | −0.246851 | ||||||||
\(184\) | 13069.2 | 5.23628 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2236.72 | −0.881743 | ||||||||
\(187\) | −188.607 | −0.0737556 | ||||||||
\(188\) | −7959.23 | −3.08769 | ||||||||
\(189\) | 278.659 | 0.107246 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3779.49 | −1.43180 | −0.715901 | − | 0.698202i | \(-0.753984\pi\) | ||||
−0.715901 | + | 0.698202i | \(0.753984\pi\) | |||||||
\(192\) | 2037.96 | 0.766027 | ||||||||
\(193\) | −3751.91 | −1.39932 | −0.699660 | − | 0.714476i | \(-0.746665\pi\) | ||||
−0.699660 | + | 0.714476i | \(0.746665\pi\) | |||||||
\(194\) | 1040.52 | 0.385076 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4654.78 | −1.69635 | ||||||||
\(197\) | 3920.73 | 1.41797 | 0.708986 | − | 0.705223i | \(-0.249153\pi\) | ||||
0.708986 | + | 0.705223i | \(0.249153\pi\) | |||||||
\(198\) | 520.888 | 0.186959 | ||||||||
\(199\) | −597.084 | −0.212694 | −0.106347 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106347 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −800.669 | −0.280969 | ||||||||
\(202\) | 7369.37 | 2.56687 | ||||||||
\(203\) | 593.917 | 0.205344 | ||||||||
\(204\) | −1012.48 | −0.347488 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7080.40 | 2.39473 | ||||||||
\(207\) | 1913.44 | 0.642480 | ||||||||
\(208\) | −10618.9 | −3.53984 | ||||||||
\(209\) | 992.314 | 0.328420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4384.55 | −1.43054 | −0.715272 | − | 0.698846i | \(-0.753697\pi\) | ||||
−0.715272 | + | 0.698846i | \(0.753697\pi\) | |||||||
\(212\) | −5109.17 | −1.65519 | ||||||||
\(213\) | 277.338 | 0.0892155 | ||||||||
\(214\) | 4678.41 | 1.49444 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1659.74 | 0.522829 | ||||||||
\(217\) | −1462.48 | −0.457510 | ||||||||
\(218\) | 6609.95 | 2.05359 | ||||||||
\(219\) | 726.077 | 0.224035 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1097.03 | 0.333912 | ||||||||
\(222\) | 4071.82 | 1.23100 | ||||||||
\(223\) | 2333.03 | 0.700587 | 0.350294 | − | 0.936640i | \(-0.386082\pi\) | ||||
0.350294 | + | 0.936640i | \(0.386082\pi\) | |||||||
\(224\) | 3936.95 | 1.17433 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12596.1 | 3.70743 | ||||||||
\(227\) | 2120.00 | 0.619864 | 0.309932 | − | 0.950759i | \(-0.399694\pi\) | ||||
0.309932 | + | 0.950759i | \(0.399694\pi\) | |||||||
\(228\) | 5326.93 | 1.54730 | ||||||||
\(229\) | 2347.12 | 0.677301 | 0.338651 | − | 0.940912i | \(-0.390030\pi\) | ||||
0.338651 | + | 0.940912i | \(0.390030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 340.583 | 0.0970075 | ||||||||
\(232\) | 3537.47 | 1.00106 | ||||||||
\(233\) | 375.499 | 0.105578 | 0.0527891 | − | 0.998606i | \(-0.483189\pi\) | ||||
0.0527891 | + | 0.998606i | \(0.483189\pi\) | |||||||
\(234\) | −3029.75 | −0.846415 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16791.2 | −4.63142 | ||||||||
\(237\) | −3064.79 | −0.839998 | ||||||||
\(238\) | −931.072 | −0.253582 | ||||||||
\(239\) | −1428.15 | −0.386524 | −0.193262 | − | 0.981147i | \(-0.561907\pi\) | ||||
−0.193262 | + | 0.981147i | \(0.561907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 190.819 | 0.0510032 | 0.0255016 | − | 0.999675i | \(-0.491882\pi\) | ||||
0.0255016 | + | 0.999675i | \(0.491882\pi\) | |||||||
\(242\) | 636.641 | 0.169111 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −4009.49 | −1.05197 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3565.94 | −0.924211 | ||||||||
\(247\) | −5771.81 | −1.48685 | ||||||||
\(248\) | −8710.79 | −2.23039 | ||||||||
\(249\) | −2119.24 | −0.539364 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6294.80 | −1.58297 | −0.791483 | − | 0.611191i | \(-0.790691\pi\) | ||||
−0.791483 | + | 0.611191i | \(0.790691\pi\) | |||||||
\(252\) | 1828.31 | 0.457036 | ||||||||
\(253\) | 2338.65 | 0.581145 | ||||||||
\(254\) | −10868.0 | −2.68471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2685.18 | −0.655561 | ||||||||
\(257\) | −4459.44 | −1.08238 | −0.541191 | − | 0.840900i | \(-0.682026\pi\) | ||||
−0.541191 | + | 0.840900i | \(0.682026\pi\) | |||||||
\(258\) | 5484.24 | 1.32339 | ||||||||
\(259\) | 2662.36 | 0.638731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 517.915 | 0.122828 | ||||||||
\(262\) | 4133.04 | 0.974581 | ||||||||
\(263\) | 4416.65 | 1.03552 | 0.517761 | − | 0.855525i | \(-0.326766\pi\) | ||||
0.517761 | + | 0.855525i | \(0.326766\pi\) | |||||||
\(264\) | 2028.57 | 0.472917 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4898.64 | 1.12915 | ||||||||
\(267\) | −1320.65 | −0.302707 | ||||||||
\(268\) | −5253.28 | −1.19737 | ||||||||
\(269\) | 1914.86 | 0.434020 | 0.217010 | − | 0.976169i | \(-0.430370\pi\) | ||||
0.217010 | + | 0.976169i | \(0.430370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6088.34 | 1.36472 | 0.682362 | − | 0.731014i | \(-0.260953\pi\) | ||||
0.682362 | + | 0.731014i | \(0.260953\pi\) | |||||||
\(272\) | −2845.69 | −0.634357 | ||||||||
\(273\) | −1981.01 | −0.439180 | ||||||||
\(274\) | −6714.91 | −1.48052 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12554.3 | 2.73798 | ||||||||
\(277\) | 832.321 | 0.180539 | 0.0902696 | − | 0.995917i | \(-0.471227\pi\) | ||||
0.0902696 | + | 0.995917i | \(0.471227\pi\) | |||||||
\(278\) | −14222.9 | −3.06847 | ||||||||
\(279\) | −1275.33 | −0.273664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2545.32 | −0.540360 | −0.270180 | − | 0.962810i | \(-0.587083\pi\) | ||||
−0.270180 | + | 0.962810i | \(0.587083\pi\) | |||||||
\(282\) | −6382.67 | −1.34781 | ||||||||
\(283\) | 5911.71 | 1.24175 | 0.620874 | − | 0.783911i | \(-0.286778\pi\) | ||||
0.620874 | + | 0.783911i | \(0.286778\pi\) | |||||||
\(284\) | 1819.65 | 0.380198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3703.03 | −0.765611 | ||||||||
\(287\) | −2331.59 | −0.479545 | ||||||||
\(288\) | 3433.15 | 0.702433 | ||||||||
\(289\) | −4619.01 | −0.940161 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 593.282 | 0.119515 | ||||||||
\(292\) | 4763.87 | 0.954742 | ||||||||
\(293\) | 6871.03 | 1.37000 | 0.685000 | − | 0.728543i | \(-0.259802\pi\) | ||||
0.685000 | + | 0.728543i | \(0.259802\pi\) | |||||||
\(294\) | −3732.76 | −0.740473 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15857.5 | 3.11384 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −12632.8 | −2.45570 | ||||||||
\(299\) | −13602.8 | −2.63100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3585.88 | 0.686666 | ||||||||
\(302\) | −13244.7 | −2.52367 | ||||||||
\(303\) | 4201.87 | 0.796670 | ||||||||
\(304\) | 14972.0 | 2.82468 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −811.926 | −0.151682 | ||||||||
\(307\) | −200.179 | −0.0372144 | −0.0186072 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186072 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(308\) | 2234.61 | 0.413404 | ||||||||
\(309\) | 4037.10 | 0.743245 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5734.93 | 1.04565 | 0.522827 | − | 0.852439i | \(-0.324878\pi\) | ||||
0.522827 | + | 0.852439i | \(0.324878\pi\) | |||||||
\(312\) | −11799.2 | −2.14102 | ||||||||
\(313\) | 3077.36 | 0.555727 | 0.277864 | − | 0.960621i | \(-0.410374\pi\) | ||||
0.277864 | + | 0.960621i | \(0.410374\pi\) | |||||||
\(314\) | −7320.97 | −1.31575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20108.5 | −3.57971 | ||||||||
\(317\) | −2142.38 | −0.379584 | −0.189792 | − | 0.981824i | \(-0.560781\pi\) | ||||
−0.189792 | + | 0.981824i | \(0.560781\pi\) | |||||||
\(318\) | −4097.15 | −0.722506 | ||||||||
\(319\) | 633.007 | 0.111102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2667.54 | 0.463823 | ||||||||
\(322\) | 11544.9 | 1.99806 | ||||||||
\(323\) | −1546.75 | −0.266451 | ||||||||
\(324\) | 1594.35 | 0.273380 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14314.0 | 2.43184 | ||||||||
\(327\) | 3768.86 | 0.637365 | ||||||||
\(328\) | −13887.4 | −2.33781 | ||||||||
\(329\) | −4173.32 | −0.699339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1618.23 | −0.268719 | −0.134359 | − | 0.990933i | \(-0.542898\pi\) | ||||
−0.134359 | + | 0.990933i | \(0.542898\pi\) | |||||||
\(332\) | −13904.6 | −2.29854 | ||||||||
\(333\) | 2321.67 | 0.382062 | ||||||||
\(334\) | −15522.7 | −2.54301 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5138.70 | 0.834343 | ||||||||
\(337\) | −2406.47 | −0.388988 | −0.194494 | − | 0.980904i | \(-0.562306\pi\) | ||||
−0.194494 | + | 0.980904i | \(0.562306\pi\) | |||||||
\(338\) | 9979.23 | 1.60591 | ||||||||
\(339\) | 7182.04 | 1.15066 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1558.74 | −0.247538 | ||||||||
\(342\) | 4271.78 | 0.675413 | ||||||||
\(343\) | −5980.67 | −0.941475 | ||||||||
\(344\) | 21358.1 | 3.34753 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2825.68 | −0.439045 | ||||||||
\(347\) | 6612.89 | 1.02305 | 0.511525 | − | 0.859268i | \(-0.329081\pi\) | ||||
0.511525 | + | 0.859268i | \(0.329081\pi\) | |||||||
\(348\) | 3398.10 | 0.523441 | ||||||||
\(349\) | 349.871 | 0.0536623 | 0.0268311 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268311 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1727.50 | −0.262699 | ||||||||
\(352\) | 4196.08 | 0.635374 | ||||||||
\(353\) | −1723.29 | −0.259835 | −0.129917 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129917 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(354\) | −13465.2 | −2.02166 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8664.97 | −1.29001 | ||||||||
\(357\) | −530.879 | −0.0787033 | ||||||||
\(358\) | 15212.3 | 2.24580 | ||||||||
\(359\) | 5875.74 | 0.863816 | 0.431908 | − | 0.901918i | \(-0.357841\pi\) | ||||
0.431908 | + | 0.901918i | \(0.357841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1278.92 | 0.186458 | ||||||||
\(362\) | 2289.85 | 0.332464 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | −12997.6 | −1.87159 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3215.29 | −0.459197 | ||||||||
\(367\) | 5368.28 | 0.763548 | 0.381774 | − | 0.924256i | \(-0.375313\pi\) | ||||
0.381774 | + | 0.924256i | \(0.375313\pi\) | |||||||
\(368\) | 35285.5 | 4.99832 | ||||||||
\(369\) | −2033.23 | −0.286844 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2678.93 | −0.374887 | ||||||||
\(372\) | −8367.60 | −1.16624 | ||||||||
\(373\) | −10393.9 | −1.44282 | −0.721412 | − | 0.692506i | \(-0.756507\pi\) | ||||
−0.721412 | + | 0.692506i | \(0.756507\pi\) | |||||||
\(374\) | −992.354 | −0.137202 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24857.0 | −3.40931 | ||||||||
\(377\) | −3681.90 | −0.502990 | ||||||||
\(378\) | 1466.16 | 0.199501 | ||||||||
\(379\) | 10918.9 | 1.47986 | 0.739928 | − | 0.672686i | \(-0.234860\pi\) | ||||
0.739928 | + | 0.672686i | \(0.234860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6196.70 | −0.833246 | ||||||||
\(382\) | −19885.8 | −2.66347 | ||||||||
\(383\) | 11663.6 | 1.55609 | 0.778044 | − | 0.628210i | \(-0.216212\pi\) | ||||
0.778044 | + | 0.628210i | \(0.216212\pi\) | |||||||
\(384\) | 1567.64 | 0.208329 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19740.7 | −2.60304 | ||||||||
\(387\) | 3127.00 | 0.410735 | ||||||||
\(388\) | 3892.59 | 0.509321 | ||||||||
\(389\) | −5827.00 | −0.759487 | −0.379744 | − | 0.925092i | \(-0.623988\pi\) | ||||
−0.379744 | + | 0.925092i | \(0.623988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3645.34 | −0.471490 | ||||||||
\(392\) | −14537.1 | −1.87304 | ||||||||
\(393\) | 2356.58 | 0.302478 | ||||||||
\(394\) | 20628.9 | 2.63774 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1948.65 | 0.247281 | ||||||||
\(397\) | −7366.99 | −0.931332 | −0.465666 | − | 0.884961i | \(-0.654185\pi\) | ||||
−0.465666 | + | 0.884961i | \(0.654185\pi\) | |||||||
\(398\) | −3141.55 | −0.395658 | ||||||||
\(399\) | 2793.11 | 0.350452 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14604.2 | 1.81870 | 0.909349 | − | 0.416035i | \(-0.136581\pi\) | ||||
0.909349 | + | 0.416035i | \(0.136581\pi\) | |||||||
\(402\) | −4212.72 | −0.522665 | ||||||||
\(403\) | 9066.43 | 1.12067 | ||||||||
\(404\) | 27569.0 | 3.39507 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3124.89 | 0.381985 | ||||||||
\(407\) | 2837.60 | 0.345588 | ||||||||
\(408\) | −3162.00 | −0.383683 | ||||||||
\(409\) | 12581.2 | 1.52103 | 0.760515 | − | 0.649320i | \(-0.224946\pi\) | ||||
0.760515 | + | 0.649320i | \(0.224946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3828.71 | −0.459504 | ||||||||
\(412\) | 26487.9 | 3.16739 | ||||||||
\(413\) | −8804.26 | −1.04898 | ||||||||
\(414\) | 10067.6 | 1.19516 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24406.6 | −2.87651 | ||||||||
\(417\) | −8109.63 | −0.952351 | ||||||||
\(418\) | 5221.06 | 0.610934 | ||||||||
\(419\) | −3776.01 | −0.440263 | −0.220131 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220131 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12683.4 | 1.46830 | 0.734148 | − | 0.678989i | \(-0.237582\pi\) | ||||
0.734148 | + | 0.678989i | \(0.237582\pi\) | |||||||
\(422\) | −23069.3 | −2.66113 | ||||||||
\(423\) | −3639.27 | −0.418316 | ||||||||
\(424\) | −15956.2 | −1.82759 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1459.21 | 0.165960 | ||||||||
\(427\) | −2102.32 | −0.238263 | ||||||||
\(428\) | 17502.0 | 1.97662 | ||||||||
\(429\) | −2111.39 | −0.237620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14152.6 | 1.58168 | 0.790841 | − | 0.612022i | \(-0.209644\pi\) | ||||
0.790841 | + | 0.612022i | \(0.209644\pi\) | |||||||
\(432\) | 4481.12 | 0.499069 | ||||||||
\(433\) | 10950.2 | 1.21532 | 0.607661 | − | 0.794197i | \(-0.292108\pi\) | ||||
0.607661 | + | 0.794197i | \(0.292108\pi\) | |||||||
\(434\) | −7694.84 | −0.851070 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24727.9 | 2.71618 | ||||||||
\(437\) | 19179.2 | 2.09946 | ||||||||
\(438\) | 3820.25 | 0.416755 | ||||||||
\(439\) | −11221.0 | −1.21993 | −0.609964 | − | 0.792429i | \(-0.708816\pi\) | ||||
−0.609964 | + | 0.792429i | \(0.708816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2128.35 | −0.229818 | ||||||||
\(442\) | 5772.04 | 0.621149 | ||||||||
\(443\) | −9647.11 | −1.03465 | −0.517323 | − | 0.855790i | \(-0.673071\pi\) | ||||
−0.517323 | + | 0.855790i | \(0.673071\pi\) | |||||||
\(444\) | 15232.7 | 1.62818 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12275.2 | 1.30325 | ||||||||
\(447\) | −7202.96 | −0.762167 | ||||||||
\(448\) | 7011.07 | 0.739379 | ||||||||
\(449\) | 6482.03 | 0.681305 | 0.340652 | − | 0.940189i | \(-0.389352\pi\) | ||||
0.340652 | + | 0.940189i | \(0.389352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2485.05 | −0.259460 | ||||||||
\(452\) | 47122.2 | 4.90363 | ||||||||
\(453\) | −7551.89 | −0.783264 | ||||||||
\(454\) | 11154.4 | 1.15308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16636.2 | 1.70847 | ||||||||
\(457\) | −11319.8 | −1.15868 | −0.579342 | − | 0.815085i | \(-0.696690\pi\) | ||||
−0.579342 | + | 0.815085i | \(0.696690\pi\) | |||||||
\(458\) | 12349.4 | 1.25993 | ||||||||
\(459\) | −462.944 | −0.0470771 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8406.73 | −0.849329 | −0.424664 | − | 0.905351i | \(-0.639608\pi\) | ||||
−0.424664 | + | 0.905351i | \(0.639608\pi\) | |||||||
\(462\) | 1791.98 | 0.180455 | ||||||||
\(463\) | −9758.56 | −0.979523 | −0.489761 | − | 0.871857i | \(-0.662916\pi\) | ||||
−0.489761 | + | 0.871857i | \(0.662916\pi\) | |||||||
\(464\) | 9550.78 | 0.955568 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1975.68 | 0.196399 | ||||||||
\(467\) | 16388.7 | 1.62394 | 0.811969 | − | 0.583701i | \(-0.198396\pi\) | ||||
0.811969 | + | 0.583701i | \(0.198396\pi\) | |||||||
\(468\) | −11334.4 | −1.11951 | ||||||||
\(469\) | −2754.49 | −0.271195 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4174.27 | −0.408365 | ||||||||
\(472\) | −52439.6 | −5.11384 | ||||||||
\(473\) | 3821.89 | 0.371524 | ||||||||
\(474\) | −16125.4 | −1.56258 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3483.16 | −0.335400 | ||||||||
\(477\) | −2336.11 | −0.224242 | ||||||||
\(478\) | −7514.20 | −0.719020 | ||||||||
\(479\) | 13829.0 | 1.31913 | 0.659567 | − | 0.751646i | \(-0.270740\pi\) | ||||
0.659567 | + | 0.751646i | \(0.270740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16504.9 | −1.56457 | ||||||||
\(482\) | 1004.00 | 0.0948771 | ||||||||
\(483\) | 6582.69 | 0.620130 | ||||||||
\(484\) | 2381.68 | 0.223674 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1278.54 | 0.119333 | ||||||||
\(487\) | −13264.4 | −1.23423 | −0.617113 | − | 0.786875i | \(-0.711698\pi\) | ||||
−0.617113 | + | 0.786875i | \(0.711698\pi\) | |||||||
\(488\) | −12521.8 | −1.16155 | ||||||||
\(489\) | 8161.58 | 0.754763 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7468.22 | −0.686428 | −0.343214 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343214 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(492\) | −13340.2 | −1.22241 | ||||||||
\(493\) | −986.690 | −0.0901385 | ||||||||
\(494\) | −30368.4 | −2.76586 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23518.2 | −2.12903 | ||||||||
\(497\) | 954.109 | 0.0861119 | ||||||||
\(498\) | −11150.4 | −1.00334 | ||||||||
\(499\) | −5276.64 | −0.473377 | −0.236688 | − | 0.971586i | \(-0.576062\pi\) | ||||
−0.236688 | + | 0.971586i | \(0.576062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8850.76 | −0.789267 | ||||||||
\(502\) | −33120.1 | −2.94466 | ||||||||
\(503\) | 10956.8 | 0.971253 | 0.485626 | − | 0.874166i | \(-0.338592\pi\) | ||||
0.485626 | + | 0.874166i | \(0.338592\pi\) | |||||||
\(504\) | 5709.90 | 0.504641 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12304.8 | 1.08106 | ||||||||
\(507\) | 5689.96 | 0.498422 | ||||||||
\(508\) | −40657.3 | −3.55093 | ||||||||
\(509\) | 12734.4 | 1.10892 | 0.554462 | − | 0.832209i | \(-0.312924\pi\) | ||||
0.554462 | + | 0.832209i | \(0.312924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2497.87 | 0.216242 | ||||||||
\(512\) | −18308.4 | −1.58032 | ||||||||
\(513\) | 2435.68 | 0.209626 | ||||||||
\(514\) | −23463.3 | −2.01347 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 20516.6 | 1.75038 | ||||||||
\(517\) | −4448.00 | −0.378381 | ||||||||
\(518\) | 14008.0 | 1.18818 | ||||||||
\(519\) | −1611.15 | −0.136265 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5650.70 | −0.475166 | −0.237583 | − | 0.971367i | \(-0.576355\pi\) | ||||
−0.237583 | + | 0.971367i | \(0.576355\pi\) | |||||||
\(522\) | 2725.01 | 0.228487 | ||||||||
\(523\) | −14103.2 | −1.17914 | −0.589572 | − | 0.807716i | \(-0.700703\pi\) | ||||
−0.589572 | + | 0.807716i | \(0.700703\pi\) | |||||||
\(524\) | 15461.8 | 1.28903 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23238.2 | 1.92630 | ||||||||
\(527\) | 2429.66 | 0.200830 | ||||||||
\(528\) | 5476.92 | 0.451425 | ||||||||
\(529\) | 33033.8 | 2.71503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7677.60 | −0.627457 | ||||||||
\(532\) | 18325.9 | 1.49347 | ||||||||
\(533\) | 14454.4 | 1.17465 | ||||||||
\(534\) | −6948.62 | −0.563102 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16406.2 | −1.32209 | ||||||||
\(537\) | 8673.75 | 0.697021 | ||||||||
\(538\) | 10075.0 | 0.807372 | ||||||||
\(539\) | −2601.31 | −0.207878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6391.90 | −0.507965 | −0.253983 | − | 0.967209i | \(-0.581741\pi\) | ||||
−0.253983 | + | 0.967209i | \(0.581741\pi\) | |||||||
\(542\) | 32033.8 | 2.53869 | ||||||||
\(543\) | 1305.63 | 0.103186 | ||||||||
\(544\) | −6540.57 | −0.515486 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10423.1 | −0.816971 | ||||||||
\(547\) | −20786.7 | −1.62482 | −0.812409 | − | 0.583088i | \(-0.801844\pi\) | ||||
−0.812409 | + | 0.583088i | \(0.801844\pi\) | |||||||
\(548\) | −25120.6 | −1.95821 | ||||||||
\(549\) | −1833.29 | −0.142519 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5191.26 | 0.401370 | ||||||||
\(552\) | 39207.6 | 3.02317 | ||||||||
\(553\) | −10543.6 | −0.810777 | ||||||||
\(554\) | 4379.26 | 0.335843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −53208.2 | −4.05851 | ||||||||
\(557\) | 15125.9 | 1.15064 | 0.575320 | − | 0.817928i | \(-0.304877\pi\) | ||||
0.575320 | + | 0.817928i | \(0.304877\pi\) | |||||||
\(558\) | −6710.16 | −0.509075 | ||||||||
\(559\) | −22230.1 | −1.68199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −565.820 | −0.0425828 | ||||||||
\(562\) | −13392.2 | −1.00519 | ||||||||
\(563\) | −8706.42 | −0.651744 | −0.325872 | − | 0.945414i | \(-0.605658\pi\) | ||||
−0.325872 | + | 0.945414i | \(0.605658\pi\) | |||||||
\(564\) | −23877.7 | −1.78268 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31104.4 | 2.30992 | ||||||||
\(567\) | 835.977 | 0.0619184 | ||||||||
\(568\) | 5682.83 | 0.419800 | ||||||||
\(569\) | 7067.76 | 0.520731 | 0.260366 | − | 0.965510i | \(-0.416157\pi\) | ||||
0.260366 | + | 0.965510i | \(0.416157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3326.42 | −0.243794 | −0.121897 | − | 0.992543i | \(-0.538898\pi\) | ||||
−0.121897 | + | 0.992543i | \(0.538898\pi\) | |||||||
\(572\) | −13853.1 | −1.01264 | ||||||||
\(573\) | −11338.5 | −0.826651 | ||||||||
\(574\) | −12267.7 | −0.892060 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6113.88 | 0.442266 | ||||||||
\(577\) | 3308.06 | 0.238676 | 0.119338 | − | 0.992854i | \(-0.461923\pi\) | ||||
0.119338 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(578\) | −24302.9 | −1.74891 | ||||||||
\(579\) | −11255.7 | −0.807897 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7290.70 | −0.520601 | ||||||||
\(582\) | 3121.55 | 0.222324 | ||||||||
\(583\) | −2855.25 | −0.202834 | ||||||||
\(584\) | 14877.8 | 1.05419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36151.9 | 2.54850 | ||||||||
\(587\) | 5694.88 | 0.400431 | 0.200215 | − | 0.979752i | \(-0.435836\pi\) | ||||
0.200215 | + | 0.979752i | \(0.435836\pi\) | |||||||
\(588\) | −13964.3 | −0.979387 | ||||||||
\(589\) | −12783.1 | −0.894262 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11762.2 | 0.818666 | ||||||||
\(592\) | 42813.5 | 2.97234 | ||||||||
\(593\) | 3907.69 | 0.270606 | 0.135303 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135303 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(594\) | 1562.66 | 0.107941 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −47259.5 | −3.24803 | ||||||||
\(597\) | −1791.25 | −0.122799 | ||||||||
\(598\) | −71571.1 | −4.89425 | ||||||||
\(599\) | 10727.2 | 0.731720 | 0.365860 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365860 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3348.98 | 0.227301 | 0.113650 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113650 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(602\) | 18867.1 | 1.27735 | ||||||||
\(603\) | −2402.01 | −0.162218 | ||||||||
\(604\) | −49548.8 | −3.33793 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22108.1 | 1.48198 | ||||||||
\(607\) | 21539.9 | 1.44032 | 0.720162 | − | 0.693806i | \(-0.244068\pi\) | ||||
0.720162 | + | 0.693806i | \(0.244068\pi\) | |||||||
\(608\) | 34411.8 | 2.29537 | ||||||||
\(609\) | 1781.75 | 0.118555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25871.9 | 1.71303 | ||||||||
\(612\) | −3037.43 | −0.200622 | ||||||||
\(613\) | 9284.33 | 0.611730 | 0.305865 | − | 0.952075i | \(-0.401054\pi\) | ||||
0.305865 | + | 0.952075i | \(0.401054\pi\) | |||||||
\(614\) | −1053.24 | −0.0692270 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6978.77 | 0.456465 | ||||||||
\(617\) | 20711.3 | 1.35139 | 0.675695 | − | 0.737181i | \(-0.263844\pi\) | ||||
0.675695 | + | 0.737181i | \(0.263844\pi\) | |||||||
\(618\) | 21241.2 | 1.38260 | ||||||||
\(619\) | −13282.9 | −0.862496 | −0.431248 | − | 0.902233i | \(-0.641927\pi\) | ||||
−0.431248 | + | 0.902233i | \(0.641927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5740.33 | 0.370936 | ||||||||
\(622\) | 30174.3 | 1.94515 | ||||||||
\(623\) | −4543.36 | −0.292177 | ||||||||
\(624\) | −31856.6 | −2.04373 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16191.5 | 1.03378 | ||||||||
\(627\) | 2976.94 | 0.189613 | ||||||||
\(628\) | −27387.9 | −1.74028 | ||||||||
\(629\) | −4423.06 | −0.280380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14789.9 | −0.933086 | −0.466543 | − | 0.884498i | \(-0.654501\pi\) | ||||
−0.466543 | + | 0.884498i | \(0.654501\pi\) | |||||||
\(632\) | −62799.5 | −3.95258 | ||||||||
\(633\) | −13153.6 | −0.825925 | ||||||||
\(634\) | −11272.1 | −0.706109 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15327.5 | −0.955622 | ||||||||
\(637\) | 15130.6 | 0.941123 | ||||||||
\(638\) | 3330.57 | 0.206675 | ||||||||
\(639\) | 832.014 | 0.0515086 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5808.52 | −0.357914 | −0.178957 | − | 0.983857i | \(-0.557272\pi\) | ||||
−0.178957 | + | 0.983857i | \(0.557272\pi\) | |||||||
\(642\) | 14035.2 | 0.862813 | ||||||||
\(643\) | 18891.2 | 1.15862 | 0.579311 | − | 0.815106i | \(-0.303322\pi\) | ||||
0.579311 | + | 0.815106i | \(0.303322\pi\) | |||||||
\(644\) | 43189.8 | 2.64273 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8138.24 | −0.495657 | ||||||||
\(647\) | 243.046 | 0.0147684 | 0.00738418 | − | 0.999973i | \(-0.497650\pi\) | ||||
0.00738418 | + | 0.999973i | \(0.497650\pi\) | |||||||
\(648\) | 4979.22 | 0.301855 | ||||||||
\(649\) | −9383.74 | −0.567556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4387.44 | −0.264144 | ||||||||
\(652\) | 53549.0 | 3.21648 | ||||||||
\(653\) | 15920.4 | 0.954081 | 0.477041 | − | 0.878881i | \(-0.341709\pi\) | ||||
0.477041 | + | 0.878881i | \(0.341709\pi\) | |||||||
\(654\) | 19829.8 | 1.18564 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −37494.4 | −2.23157 | ||||||||
\(657\) | 2178.23 | 0.129347 | ||||||||
\(658\) | −21957.9 | −1.30092 | ||||||||
\(659\) | −7476.38 | −0.441940 | −0.220970 | − | 0.975281i | \(-0.570922\pi\) | ||||
−0.220970 | + | 0.975281i | \(0.570922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14920.1 | −0.877948 | −0.438974 | − | 0.898500i | \(-0.644658\pi\) | ||||
−0.438974 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(662\) | −8514.30 | −0.499876 | ||||||||
\(663\) | 3291.10 | 0.192784 | ||||||||
\(664\) | −43424.7 | −2.53796 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12215.5 | 0.710720 | ||||||||
\(667\) | 12234.6 | 0.710232 | ||||||||
\(668\) | −58070.8 | −3.36351 | ||||||||
\(669\) | 6999.08 | 0.404484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2240.69 | −0.128914 | ||||||||
\(672\) | 11810.9 | 0.677997 | ||||||||
\(673\) | −563.692 | −0.0322864 | −0.0161432 | − | 0.999870i | \(-0.505139\pi\) | ||||
−0.0161432 | + | 0.999870i | \(0.505139\pi\) | |||||||
\(674\) | −12661.6 | −0.723602 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37332.5 | 2.12406 | ||||||||
\(677\) | −13280.2 | −0.753914 | −0.376957 | − | 0.926231i | \(-0.623030\pi\) | ||||
−0.376957 | + | 0.926231i | \(0.623030\pi\) | |||||||
\(678\) | 37788.3 | 2.14049 | ||||||||
\(679\) | 2041.03 | 0.115357 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6359.99 | 0.357879 | ||||||||
\(682\) | −8201.30 | −0.460475 | ||||||||
\(683\) | −6856.80 | −0.384141 | −0.192070 | − | 0.981381i | \(-0.561520\pi\) | ||||
−0.192070 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(684\) | 15980.8 | 0.893334 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31467.3 | −1.75135 | ||||||||
\(687\) | 7041.36 | 0.391040 | ||||||||
\(688\) | 57664.5 | 3.19541 | ||||||||
\(689\) | 16607.6 | 0.918287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28374.6 | −1.56211 | −0.781057 | − | 0.624460i | \(-0.785319\pi\) | ||||
−0.781057 | + | 0.624460i | \(0.785319\pi\) | |||||||
\(692\) | −10570.9 | −0.580702 | ||||||||
\(693\) | 1021.75 | 0.0560073 | ||||||||
\(694\) | 34793.7 | 1.90310 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10612.4 | 0.577963 | ||||||||
\(697\) | 3873.54 | 0.210503 | ||||||||
\(698\) | 1840.84 | 0.0998237 | ||||||||
\(699\) | 1126.50 | 0.0609556 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 667.753 | 0.0359781 | 0.0179891 | − | 0.999838i | \(-0.494274\pi\) | ||||
0.0179891 | + | 0.999838i | \(0.494274\pi\) | |||||||
\(702\) | −9089.26 | −0.488678 | ||||||||
\(703\) | 23271.0 | 1.24848 | ||||||||
\(704\) | 7472.52 | 0.400044 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9067.10 | −0.483349 | ||||||||
\(707\) | 14455.4 | 0.768956 | ||||||||
\(708\) | −50373.6 | −2.67395 | ||||||||
\(709\) | 23667.8 | 1.25368 | 0.626842 | − | 0.779147i | \(-0.284347\pi\) | ||||
0.626842 | + | 0.779147i | \(0.284347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9194.37 | −0.484973 | ||||||||
\(712\) | −27061.0 | −1.42438 | ||||||||
\(713\) | −30126.9 | −1.58241 | ||||||||
\(714\) | −2793.22 | −0.146405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 56909.5 | 2.97040 | ||||||||
\(717\) | −4284.45 | −0.223160 | ||||||||
\(718\) | 30915.2 | 1.60689 | ||||||||
\(719\) | 11835.5 | 0.613896 | 0.306948 | − | 0.951726i | \(-0.400692\pi\) | ||||
0.306948 | + | 0.951726i | \(0.400692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13888.6 | 0.717390 | ||||||||
\(722\) | 6729.01 | 0.346853 | ||||||||
\(723\) | 572.458 | 0.0294467 | ||||||||
\(724\) | 8566.38 | 0.439733 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1909.92 | 0.0976362 | ||||||||
\(727\) | −15633.2 | −0.797530 | −0.398765 | − | 0.917053i | \(-0.630561\pi\) | ||||
−0.398765 | + | 0.917053i | \(0.630561\pi\) | |||||||
\(728\) | −40592.1 | −2.06654 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5957.31 | −0.301422 | ||||||||
\(732\) | −12028.5 | −0.607356 | ||||||||
\(733\) | 14870.7 | 0.749335 | 0.374668 | − | 0.927159i | \(-0.377757\pi\) | ||||
0.374668 | + | 0.927159i | \(0.377757\pi\) | |||||||
\(734\) | 28245.2 | 1.42037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 81100.6 | 4.06169 | ||||||||
\(737\) | −2935.79 | −0.146731 | ||||||||
\(738\) | −10697.8 | −0.533593 | ||||||||
\(739\) | 20850.3 | 1.03788 | 0.518939 | − | 0.854812i | \(-0.326327\pi\) | ||||
0.518939 | + | 0.854812i | \(0.326327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17315.4 | −0.858432 | ||||||||
\(742\) | −14095.2 | −0.697372 | ||||||||
\(743\) | 29254.7 | 1.44448 | 0.722242 | − | 0.691641i | \(-0.243112\pi\) | ||||
0.722242 | + | 0.691641i | \(0.243112\pi\) | |||||||
\(744\) | −26132.4 | −1.28771 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −54687.2 | −2.68397 | ||||||||
\(747\) | −6357.73 | −0.311402 | ||||||||
\(748\) | −3712.41 | −0.181470 | ||||||||
\(749\) | 9176.95 | 0.447688 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10936.8 | 0.531411 | 0.265705 | − | 0.964054i | \(-0.414395\pi\) | ||||
0.265705 | + | 0.964054i | \(0.414395\pi\) | |||||||
\(752\) | −67111.2 | −3.25438 | ||||||||
\(753\) | −18884.4 | −0.913926 | ||||||||
\(754\) | −19372.3 | −0.935672 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5484.94 | 0.263870 | ||||||||
\(757\) | 8476.34 | 0.406972 | 0.203486 | − | 0.979078i | \(-0.434773\pi\) | ||||
0.203486 | + | 0.979078i | \(0.434773\pi\) | |||||||
\(758\) | 57449.6 | 2.75286 | ||||||||
\(759\) | 7015.96 | 0.335524 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 913.964 | 0.0435364 | 0.0217682 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217682 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(762\) | −32603.9 | −1.55002 | ||||||||
\(763\) | 12965.8 | 0.615193 | ||||||||
\(764\) | −74393.0 | −3.52283 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 61367.9 | 2.89466 | ||||||||
\(767\) | 54580.6 | 2.56948 | ||||||||
\(768\) | −8055.53 | −0.378488 | ||||||||
\(769\) | 32215.2 | 1.51067 | 0.755337 | − | 0.655337i | \(-0.227473\pi\) | ||||
0.755337 | + | 0.655337i | \(0.227473\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13378.3 | −0.624914 | ||||||||
\(772\) | −73850.2 | −3.44291 | ||||||||
\(773\) | −72.6900 | −0.00338225 | −0.00169112 | − | 0.999999i | \(-0.500538\pi\) | ||||
−0.00169112 | + | 0.999999i | \(0.500538\pi\) | |||||||
\(774\) | 16452.7 | 0.764058 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12156.7 | 0.562373 | ||||||||
\(777\) | 7987.09 | 0.368771 | ||||||||
\(778\) | −30658.7 | −1.41281 | ||||||||
\(779\) | −20379.8 | −0.937332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1016.91 | 0.0465913 | ||||||||
\(782\) | −19179.9 | −0.877075 | ||||||||
\(783\) | 1553.75 | 0.0709148 | ||||||||
\(784\) | −39248.5 | −1.78792 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12399.1 | 0.562675 | ||||||||
\(787\) | −487.318 | −0.0220724 | −0.0110362 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110362 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(788\) | 77173.1 | 3.48880 | ||||||||
\(789\) | 13249.9 | 0.597859 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24707.9 | 1.11064 | ||||||||
\(792\) | 6085.72 | 0.273039 | ||||||||
\(793\) | 13033.0 | 0.583627 | ||||||||
\(794\) | −38761.4 | −1.73248 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11752.6 | −0.523317 | ||||||||
\(797\) | −31379.9 | −1.39465 | −0.697324 | − | 0.716756i | \(-0.745626\pi\) | ||||
−0.697324 | + | 0.716756i | \(0.745626\pi\) | |||||||
\(798\) | 14695.9 | 0.651917 | ||||||||
\(799\) | 6933.25 | 0.306985 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3961.96 | −0.174768 | ||||||||
\(802\) | 76839.8 | 3.38318 | ||||||||
\(803\) | 2662.28 | 0.116999 | ||||||||
\(804\) | −15759.8 | −0.691302 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47703.0 | 2.08470 | ||||||||
\(807\) | 5744.59 | 0.250581 | ||||||||
\(808\) | 86099.0 | 3.74870 | ||||||||
\(809\) | 1824.26 | 0.0792802 | 0.0396401 | − | 0.999214i | \(-0.487379\pi\) | ||||
0.0396401 | + | 0.999214i | \(0.487379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4364.52 | −0.188976 | −0.0944878 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944878 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(812\) | 11690.3 | 0.505232 | ||||||||
\(813\) | 18265.0 | 0.787924 | ||||||||
\(814\) | 14930.0 | 0.642870 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8537.06 | −0.366246 | ||||||||
\(817\) | 31343.1 | 1.34218 | ||||||||
\(818\) | 66196.1 | 2.82945 | ||||||||
\(819\) | −5943.02 | −0.253561 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3306.16 | 0.140543 | 0.0702714 | − | 0.997528i | \(-0.477613\pi\) | ||||
0.0702714 | + | 0.997528i | \(0.477613\pi\) | |||||||
\(822\) | −20144.7 | −0.854779 | ||||||||
\(823\) | 19183.7 | 0.812519 | 0.406259 | − | 0.913758i | \(-0.366833\pi\) | ||||
0.406259 | + | 0.913758i | \(0.366833\pi\) | |||||||
\(824\) | 82722.8 | 3.49731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −46323.6 | −1.95134 | ||||||||
\(827\) | −20646.4 | −0.868131 | −0.434066 | − | 0.900881i | \(-0.642921\pi\) | ||||
−0.434066 | + | 0.900881i | \(0.642921\pi\) | |||||||
\(828\) | 37663.0 | 1.58077 | ||||||||
\(829\) | 5345.44 | 0.223950 | 0.111975 | − | 0.993711i | \(-0.464282\pi\) | ||||
0.111975 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2496.96 | 0.104234 | ||||||||
\(832\) | −43464.0 | −1.81111 | ||||||||
\(833\) | 4054.75 | 0.168654 | ||||||||
\(834\) | −42668.8 | −1.77158 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19532.1 | 0.808051 | ||||||||
\(837\) | −3826.00 | −0.158000 | ||||||||
\(838\) | −19867.5 | −0.818985 | ||||||||
\(839\) | 29284.9 | 1.20504 | 0.602519 | − | 0.798105i | \(-0.294164\pi\) | ||||
0.602519 | + | 0.798105i | \(0.294164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21077.4 | −0.864219 | ||||||||
\(842\) | 66733.8 | 2.73135 | ||||||||
\(843\) | −7635.97 | −0.311977 | ||||||||
\(844\) | −86302.6 | −3.51974 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19148.0 | −0.778159 | ||||||||
\(847\) | 1248.81 | 0.0506605 | ||||||||
\(848\) | −43079.9 | −1.74454 | ||||||||
\(849\) | 17735.1 | 0.716923 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54844.2 | 2.20921 | ||||||||
\(852\) | 5458.94 | 0.219507 | ||||||||
\(853\) | 8070.62 | 0.323954 | 0.161977 | − | 0.986795i | \(-0.448213\pi\) | ||||
0.161977 | + | 0.986795i | \(0.448213\pi\) | |||||||
\(854\) | −11061.4 | −0.443222 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54659.5 | 2.18250 | ||||||||
\(857\) | 11344.2 | 0.452169 | 0.226085 | − | 0.974108i | \(-0.427407\pi\) | ||||
0.226085 | + | 0.974108i | \(0.427407\pi\) | |||||||
\(858\) | −11109.1 | −0.442026 | ||||||||
\(859\) | 25470.6 | 1.01170 | 0.505848 | − | 0.862623i | \(-0.331180\pi\) | ||||
0.505848 | + | 0.862623i | \(0.331180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6994.78 | −0.276866 | ||||||||
\(862\) | 74463.6 | 2.94228 | ||||||||
\(863\) | 14558.4 | 0.574243 | 0.287122 | − | 0.957894i | \(-0.407302\pi\) | ||||
0.287122 | + | 0.957894i | \(0.407302\pi\) | |||||||
\(864\) | 10299.5 | 0.405550 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 57614.6 | 2.26077 | ||||||||
\(867\) | −13857.0 | −0.542802 | ||||||||
\(868\) | −28786.5 | −1.12567 | ||||||||
\(869\) | −11237.6 | −0.438675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17076.0 | 0.664294 | ||||||||
\(872\) | 77226.3 | 2.99910 | ||||||||
\(873\) | 1779.85 | 0.0690019 | ||||||||
\(874\) | 100911. | 3.90546 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14291.6 | 0.551220 | ||||||||
\(877\) | −185.528 | −0.00714350 | −0.00357175 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357175 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(878\) | −59039.1 | −2.26933 | ||||||||
\(879\) | 20613.1 | 0.790969 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18950.1 | 0.724681 | 0.362340 | − | 0.932046i | \(-0.381978\pi\) | ||||
0.362340 | + | 0.932046i | \(0.381978\pi\) | |||||||
\(882\) | −11198.3 | −0.427513 | ||||||||
\(883\) | −21258.3 | −0.810189 | −0.405095 | − | 0.914275i | \(-0.632761\pi\) | ||||
−0.405095 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(884\) | 21593.3 | 0.821563 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50758.2 | −1.92467 | ||||||||
\(887\) | −35707.4 | −1.35168 | −0.675839 | − | 0.737049i | \(-0.736219\pi\) | ||||
−0.675839 | + | 0.737049i | \(0.736219\pi\) | |||||||
\(888\) | 47572.5 | 1.79778 | ||||||||
\(889\) | −21318.1 | −0.804259 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 45921.8 | 1.72374 | ||||||||
\(893\) | −36477.8 | −1.36695 | ||||||||
\(894\) | −37898.4 | −1.41780 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5393.06 | 0.201082 | ||||||||
\(897\) | −40808.4 | −1.51901 | ||||||||
\(898\) | 34105.2 | 1.26738 | ||||||||
\(899\) | −8154.49 | −0.302522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4450.58 | 0.164562 | ||||||||
\(902\) | −13075.1 | −0.482653 | ||||||||
\(903\) | 10757.6 | 0.396447 | ||||||||
\(904\) | 147165. | 5.41440 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −39734.2 | −1.45704 | ||||||||
\(907\) | 6542.52 | 0.239516 | 0.119758 | − | 0.992803i | \(-0.461788\pi\) | ||||
0.119758 | + | 0.992803i | \(0.461788\pi\) | |||||||
\(908\) | 41728.6 | 1.52512 | ||||||||
\(909\) | 12605.6 | 0.459958 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31171.2 | 1.13364 | 0.566821 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566821 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(912\) | 44915.9 | 1.63083 | ||||||||
\(913\) | −7770.56 | −0.281674 | ||||||||
\(914\) | −59559.2 | −2.15541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46199.2 | 1.66644 | ||||||||
\(917\) | 8107.19 | 0.291955 | ||||||||
\(918\) | −2435.78 | −0.0875737 | ||||||||
\(919\) | 12031.9 | 0.431877 | 0.215938 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215938 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −600.537 | −0.0214857 | ||||||||
\(922\) | −44232.0 | −1.57994 | ||||||||
\(923\) | −5914.85 | −0.210931 | ||||||||
\(924\) | 6703.82 | 0.238679 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −51344.7 | −1.82213 | ||||||||
\(927\) | 12111.3 | 0.429113 | ||||||||
\(928\) | 21951.6 | 0.776506 | ||||||||
\(929\) | −12546.2 | −0.443085 | −0.221542 | − | 0.975151i | \(-0.571109\pi\) | ||||
−0.221542 | + | 0.975151i | \(0.571109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21333.2 | −0.750986 | ||||||||
\(932\) | 7391.07 | 0.259767 | ||||||||
\(933\) | 17204.8 | 0.603708 | ||||||||
\(934\) | 86229.1 | 3.02088 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −35397.7 | −1.23612 | ||||||||
\(937\) | −17909.8 | −0.624427 | −0.312214 | − | 0.950012i | \(-0.601070\pi\) | ||||
−0.312214 | + | 0.950012i | \(0.601070\pi\) | |||||||
\(938\) | −14492.7 | −0.504483 | ||||||||
\(939\) | 9232.08 | 0.320849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 829.893 | 0.0287500 | 0.0143750 | − | 0.999897i | \(-0.495424\pi\) | ||||
0.0143750 | + | 0.999897i | \(0.495424\pi\) | |||||||
\(942\) | −21962.9 | −0.759650 | ||||||||
\(943\) | −48030.4 | −1.65863 | ||||||||
\(944\) | −141581. | −4.88144 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20108.9 | 0.691116 | ||||||||
\(947\) | 17654.9 | 0.605814 | 0.302907 | − | 0.953020i | \(-0.402043\pi\) | ||||
0.302907 | + | 0.953020i | \(0.402043\pi\) | |||||||
\(948\) | −60325.4 | −2.06675 | ||||||||
\(949\) | −15485.2 | −0.529685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6427.14 | −0.219153 | ||||||||
\(952\) | −10878.0 | −0.370335 | ||||||||
\(953\) | −30736.6 | −1.04476 | −0.522380 | − | 0.852713i | \(-0.674956\pi\) | ||||
−0.522380 | + | 0.852713i | \(0.674956\pi\) | |||||||
\(954\) | −12291.5 | −0.417139 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28110.8 | −0.951012 | ||||||||
\(957\) | 1899.02 | 0.0641449 | ||||||||
\(958\) | 72761.5 | 2.45388 | ||||||||
\(959\) | −13171.7 | −0.443519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9711.08 | −0.325974 | ||||||||
\(962\) | −86840.6 | −2.91045 | ||||||||
\(963\) | 8002.61 | 0.267789 | ||||||||
\(964\) | 3755.97 | 0.125489 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 34634.8 | 1.15358 | ||||||||
\(967\) | −23645.2 | −0.786327 | −0.393163 | − | 0.919469i | \(-0.628619\pi\) | ||||
−0.393163 | + | 0.919469i | \(0.628619\pi\) | |||||||
\(968\) | 7438.10 | 0.246973 | ||||||||
\(969\) | −4640.26 | −0.153836 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27402.0 | 0.905635 | 0.452818 | − | 0.891603i | \(-0.350419\pi\) | ||||
0.452818 | + | 0.891603i | \(0.350419\pi\) | |||||||
\(972\) | 4783.05 | 0.157836 | ||||||||
\(973\) | −27899.1 | −0.919222 | ||||||||
\(974\) | −69790.6 | −2.29593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33807.5 | −1.10876 | ||||||||
\(977\) | 49118.7 | 1.60844 | 0.804220 | − | 0.594332i | \(-0.202584\pi\) | ||||
0.804220 | + | 0.594332i | \(0.202584\pi\) | |||||||
\(978\) | 42942.1 | 1.40403 | ||||||||
\(979\) | −4842.40 | −0.158084 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11306.6 | 0.367983 | ||||||||
\(982\) | −39294.0 | −1.27691 | ||||||||
\(983\) | −52630.5 | −1.70768 | −0.853842 | − | 0.520533i | \(-0.825733\pi\) | ||||
−0.853842 | + | 0.520533i | \(0.825733\pi\) | |||||||
\(984\) | −41662.1 | −1.34973 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5191.47 | −0.167677 | ||||||||
\(987\) | −12520.0 | −0.403764 | ||||||||
\(988\) | −113609. | −3.65827 | ||||||||
\(989\) | 73868.4 | 2.37500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45472.7 | 1.45761 | 0.728803 | − | 0.684724i | \(-0.240077\pi\) | ||||
0.728803 | + | 0.684724i | \(0.240077\pi\) | |||||||
\(992\) | −54054.5 | −1.73007 | ||||||||
\(993\) | −4854.68 | −0.155145 | ||||||||
\(994\) | 5020.04 | 0.160187 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −41713.8 | −1.32706 | ||||||||
\(997\) | −55068.1 | −1.74927 | −0.874637 | − | 0.484779i | \(-0.838900\pi\) | ||||
−0.874637 | + | 0.484779i | \(0.838900\pi\) | |||||||
\(998\) | −27763.0 | −0.880585 | ||||||||
\(999\) | 6965.01 | 0.220584 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.4.a.s.1.3 | 3 | ||
3.2 | odd | 2 | 2475.4.a.s.1.1 | 3 | |||
5.2 | odd | 4 | 825.4.c.l.199.6 | 6 | |||
5.3 | odd | 4 | 825.4.c.l.199.1 | 6 | |||
5.4 | even | 2 | 165.4.a.d.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 495.4.a.l.1.3 | 3 | |||
55.54 | odd | 2 | 1815.4.a.s.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.d.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
495.4.a.l.1.3 | 3 | 15.14 | odd | 2 | |||
825.4.a.s.1.3 | 3 | 1.1 | even | 1 | trivial | ||
825.4.c.l.199.1 | 6 | 5.3 | odd | 4 | |||
825.4.c.l.199.6 | 6 | 5.2 | odd | 4 | |||
1815.4.a.s.1.3 | 3 | 55.54 | odd | 2 | |||
2475.4.a.s.1.1 | 3 | 3.2 | odd | 2 |