Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,4,Mod(1,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, 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("693.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.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: | \(40.8883236340\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 43x^{6} + 57x^{5} + 560x^{4} - 439x^{3} - 2246x^{2} + 384x + 1056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.778078\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.221922 | 0.0784611 | 0.0392306 | − | 0.999230i | \(-0.487509\pi\) | ||||
0.0392306 | + | 0.999230i | \(0.487509\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.95075 | −0.993844 | ||||||||
\(5\) | 15.1615 | 1.35609 | 0.678043 | − | 0.735022i | \(-0.262828\pi\) | ||||
0.678043 | + | 0.735022i | \(0.262828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −3.53982 | −0.156439 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.36467 | 0.106400 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.8013 | 0.806477 | 0.403239 | − | 0.915095i | \(-0.367884\pi\) | ||||
0.403239 | + | 0.915095i | \(0.367884\pi\) | |||||||
\(14\) | 1.55345 | 0.0296555 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.8204 | 0.981569 | ||||||||
\(17\) | −61.7617 | −0.881142 | −0.440571 | − | 0.897718i | \(-0.645224\pi\) | ||||
−0.440571 | + | 0.897718i | \(0.645224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.5657 | 0.658855 | 0.329427 | − | 0.944181i | \(-0.393144\pi\) | ||||
0.329427 | + | 0.944181i | \(0.393144\pi\) | |||||||
\(20\) | −120.545 | −1.34774 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.44114 | 0.0236569 | ||||||||
\(23\) | 24.4988 | 0.222102 | 0.111051 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111051 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.871 | 0.838972 | ||||||||
\(26\) | 8.38893 | 0.0632771 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −55.6553 | −0.375638 | ||||||||
\(29\) | −16.2692 | −0.104176 | −0.0520882 | − | 0.998642i | \(-0.516588\pi\) | ||||
−0.0520882 | + | 0.998642i | \(0.516588\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −190.027 | −1.10096 | −0.550481 | − | 0.834848i | \(-0.685556\pi\) | ||||
−0.550481 | + | 0.834848i | \(0.685556\pi\) | |||||||
\(32\) | 42.2597 | 0.233454 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.7063 | −0.0691354 | ||||||||
\(35\) | 106.131 | 0.512553 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 170.813 | 0.758958 | 0.379479 | − | 0.925200i | \(-0.376103\pi\) | ||||
0.379479 | + | 0.925200i | \(0.376103\pi\) | |||||||
\(38\) | 12.1093 | 0.0516945 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −53.6690 | −0.212145 | ||||||||
\(41\) | 78.0123 | 0.297158 | 0.148579 | − | 0.988901i | \(-0.452530\pi\) | ||||
0.148579 | + | 0.988901i | \(0.452530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.5205 | 0.161437 | 0.0807186 | − | 0.996737i | \(-0.474278\pi\) | ||||
0.0807186 | + | 0.996737i | \(0.474278\pi\) | |||||||
\(44\) | −87.4583 | −0.299655 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.43681 | 0.0174264 | ||||||||
\(47\) | 273.595 | 0.849105 | 0.424553 | − | 0.905403i | \(-0.360431\pi\) | ||||
0.424553 | + | 0.905403i | \(0.360431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 23.2732 | 0.0658267 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −300.549 | −0.801512 | ||||||||
\(53\) | −163.247 | −0.423088 | −0.211544 | − | 0.977368i | \(-0.567849\pi\) | ||||
−0.211544 | + | 0.977368i | \(0.567849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 166.777 | 0.408876 | ||||||||
\(56\) | −24.7787 | −0.0591285 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.61049 | −0.00817379 | ||||||||
\(59\) | 650.249 | 1.43483 | 0.717417 | − | 0.696644i | \(-0.245324\pi\) | ||||
0.717417 | + | 0.696644i | \(0.245324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 257.506 | 0.540496 | 0.270248 | − | 0.962791i | \(-0.412894\pi\) | ||||
0.270248 | + | 0.962791i | \(0.412894\pi\) | |||||||
\(62\) | −42.1710 | −0.0863827 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −493.185 | −0.963252 | ||||||||
\(65\) | 573.125 | 1.09365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −399.767 | −0.728945 | −0.364473 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364473 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(68\) | 491.052 | 0.875717 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 23.5527 | 0.0402155 | ||||||||
\(71\) | 198.479 | 0.331763 | 0.165881 | − | 0.986146i | \(-0.446953\pi\) | ||||
0.165881 | + | 0.986146i | \(0.446953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −226.479 | −0.363114 | −0.181557 | − | 0.983380i | \(-0.558114\pi\) | ||||
−0.181557 | + | 0.983380i | \(0.558114\pi\) | |||||||
\(74\) | 37.9071 | 0.0595487 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −433.839 | −0.654799 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 138.641 | 0.197447 | 0.0987234 | − | 0.995115i | \(-0.468524\pi\) | ||||
0.0987234 | + | 0.995115i | \(0.468524\pi\) | |||||||
\(80\) | 952.453 | 1.33109 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.3126 | 0.0233154 | ||||||||
\(83\) | 490.784 | 0.649043 | 0.324521 | − | 0.945878i | \(-0.394797\pi\) | ||||
0.324521 | + | 0.945878i | \(0.394797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −936.401 | −1.19491 | ||||||||
\(86\) | 10.1020 | 0.0126666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −38.9380 | −0.0471682 | ||||||||
\(89\) | 221.276 | 0.263542 | 0.131771 | − | 0.991280i | \(-0.457934\pi\) | ||||
0.131771 | + | 0.991280i | \(0.457934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 264.609 | 0.304820 | ||||||||
\(92\) | −194.784 | −0.220735 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 60.7167 | 0.0666218 | ||||||||
\(95\) | 827.299 | 0.893464 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1598.94 | 1.67369 | 0.836846 | − | 0.547438i | \(-0.184397\pi\) | ||||
0.836846 | + | 0.547438i | \(0.184397\pi\) | |||||||
\(98\) | 10.8742 | 0.0112087 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −833.807 | −0.833807 | ||||||||
\(101\) | 1770.89 | 1.74465 | 0.872326 | − | 0.488924i | \(-0.162611\pi\) | ||||
0.872326 | + | 0.488924i | \(0.162611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1159.21 | 1.10893 | 0.554466 | − | 0.832206i | \(-0.312923\pi\) | ||||
0.554466 | + | 0.832206i | \(0.312923\pi\) | |||||||
\(104\) | −133.810 | −0.126165 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36.2280 | −0.0331960 | ||||||||
\(107\) | 1334.93 | 1.20610 | 0.603050 | − | 0.797703i | \(-0.293952\pi\) | ||||
0.603050 | + | 0.797703i | \(0.293952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 382.778 | 0.336362 | 0.168181 | − | 0.985756i | \(-0.446211\pi\) | ||||
0.168181 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(110\) | 37.0113 | 0.0320808 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 439.743 | 0.370998 | ||||||||
\(113\) | 641.007 | 0.533636 | 0.266818 | − | 0.963747i | \(-0.414028\pi\) | ||||
0.266818 | + | 0.963747i | \(0.414028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 371.438 | 0.301190 | ||||||||
\(116\) | 129.352 | 0.103535 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 144.304 | 0.112579 | ||||||||
\(119\) | −432.332 | −0.333040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 57.1462 | 0.0424080 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1510.86 | 1.09418 | ||||||||
\(125\) | −305.179 | −0.218368 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −574.823 | −0.401632 | −0.200816 | − | 0.979629i | \(-0.564359\pi\) | ||||
−0.200816 | + | 0.979629i | \(0.564359\pi\) | |||||||
\(128\) | −447.526 | −0.309032 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 127.189 | 0.0858093 | ||||||||
\(131\) | −733.130 | −0.488961 | −0.244480 | − | 0.969654i | \(-0.578617\pi\) | ||||
−0.244480 | + | 0.969654i | \(0.578617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 381.960 | 0.249024 | ||||||||
\(134\) | −88.7170 | −0.0571939 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 218.625 | 0.137845 | ||||||||
\(137\) | −700.501 | −0.436846 | −0.218423 | − | 0.975854i | \(-0.570091\pi\) | ||||
−0.218423 | + | 0.975854i | \(0.570091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 619.481 | 0.378012 | 0.189006 | − | 0.981976i | \(-0.439473\pi\) | ||||
0.189006 | + | 0.981976i | \(0.439473\pi\) | |||||||
\(140\) | −843.818 | −0.509397 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 44.0469 | 0.0260305 | ||||||||
\(143\) | 415.815 | 0.243162 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −246.666 | −0.141272 | ||||||||
\(146\) | −50.2605 | −0.0284904 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1358.09 | −0.754286 | ||||||||
\(149\) | 2598.45 | 1.42868 | 0.714339 | − | 0.699800i | \(-0.246727\pi\) | ||||
0.714339 | + | 0.699800i | \(0.246727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2195.71 | −1.18334 | −0.591669 | − | 0.806181i | \(-0.701531\pi\) | ||||
−0.591669 | + | 0.806181i | \(0.701531\pi\) | |||||||
\(152\) | −193.153 | −0.103071 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.0880 | 0.00894148 | ||||||||
\(155\) | −2881.09 | −1.49300 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1585.74 | −0.806090 | −0.403045 | − | 0.915180i | \(-0.632048\pi\) | ||||
−0.403045 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(158\) | 30.7674 | 0.0154919 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 640.722 | 0.316584 | ||||||||
\(161\) | 171.491 | 0.0839467 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2688.22 | 1.29176 | 0.645882 | − | 0.763437i | \(-0.276490\pi\) | ||||
0.645882 | + | 0.763437i | \(0.276490\pi\) | |||||||
\(164\) | −620.256 | −0.295329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 108.916 | 0.0509246 | ||||||||
\(167\) | 2366.77 | 1.09668 | 0.548342 | − | 0.836254i | \(-0.315259\pi\) | ||||
0.548342 | + | 0.836254i | \(0.315259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −768.059 | −0.349594 | ||||||||
\(170\) | −207.808 | −0.0937536 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −361.922 | −0.160443 | ||||||||
\(173\) | −960.924 | −0.422299 | −0.211149 | − | 0.977454i | \(-0.567721\pi\) | ||||
−0.211149 | + | 0.977454i | \(0.567721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 734.100 | 0.317102 | ||||||||
\(176\) | 691.025 | 0.295954 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 49.1060 | 0.0206778 | ||||||||
\(179\) | 1270.38 | 0.530464 | 0.265232 | − | 0.964185i | \(-0.414552\pi\) | ||||
0.265232 | + | 0.964185i | \(0.414552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1066.57 | −0.437999 | −0.218999 | − | 0.975725i | \(-0.570279\pi\) | ||||
−0.218999 | + | 0.975725i | \(0.570279\pi\) | |||||||
\(182\) | 58.7225 | 0.0239165 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −86.7212 | −0.0347455 | ||||||||
\(185\) | 2589.78 | 1.02921 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −679.379 | −0.265674 | ||||||||
\(188\) | −2175.29 | −0.843878 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 183.596 | 0.0701022 | ||||||||
\(191\) | −946.790 | −0.358677 | −0.179339 | − | 0.983787i | \(-0.557396\pi\) | ||||
−0.179339 | + | 0.983787i | \(0.557396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3405.75 | −1.27022 | −0.635108 | − | 0.772424i | \(-0.719044\pi\) | ||||
−0.635108 | + | 0.772424i | \(0.719044\pi\) | |||||||
\(194\) | 354.840 | 0.131320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −389.587 | −0.141978 | ||||||||
\(197\) | −3923.90 | −1.41912 | −0.709558 | − | 0.704647i | \(-0.751106\pi\) | ||||
−0.709558 | + | 0.704647i | \(0.751106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2560.58 | −0.912136 | −0.456068 | − | 0.889945i | \(-0.650743\pi\) | ||||
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(200\) | −371.226 | −0.131248 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 392.998 | 0.136887 | ||||||||
\(203\) | −113.884 | −0.0393749 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1182.78 | 0.402972 | ||||||||
\(206\) | 257.253 | 0.0870081 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2374.70 | 0.791613 | ||||||||
\(209\) | 600.223 | 0.198652 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5739.00 | −1.87246 | −0.936230 | − | 0.351387i | \(-0.885710\pi\) | ||||
−0.936230 | + | 0.351387i | \(0.885710\pi\) | |||||||
\(212\) | 1297.93 | 0.420483 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 296.250 | 0.0946321 | ||||||||
\(215\) | 690.159 | 0.218923 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1330.19 | −0.416124 | ||||||||
\(218\) | 84.9468 | 0.0263914 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1326.00 | −0.406359 | ||||||||
\(221\) | −2334.67 | −0.710621 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2730.77 | 0.820025 | 0.410012 | − | 0.912080i | \(-0.365524\pi\) | ||||
0.410012 | + | 0.912080i | \(0.365524\pi\) | |||||||
\(224\) | 295.818 | 0.0882374 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 142.253 | 0.0418697 | ||||||||
\(227\) | 2118.19 | 0.619336 | 0.309668 | − | 0.950845i | \(-0.399782\pi\) | ||||
0.309668 | + | 0.950845i | \(0.399782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2821.55 | −0.814207 | −0.407104 | − | 0.913382i | \(-0.633461\pi\) | ||||
−0.407104 | + | 0.913382i | \(0.633461\pi\) | |||||||
\(230\) | 82.4302 | 0.0236317 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 57.5900 | 0.0162973 | ||||||||
\(233\) | 6838.94 | 1.92289 | 0.961445 | − | 0.274996i | \(-0.0886765\pi\) | ||||
0.961445 | + | 0.274996i | \(0.0886765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4148.12 | 1.15146 | ||||||||
\(236\) | −5169.96 | −1.42600 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −95.9438 | −0.0261307 | ||||||||
\(239\) | 3473.80 | 0.940174 | 0.470087 | − | 0.882620i | \(-0.344223\pi\) | ||||
0.470087 | + | 0.882620i | \(0.344223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1672.96 | 0.447156 | 0.223578 | − | 0.974686i | \(-0.428226\pi\) | ||||
0.223578 | + | 0.974686i | \(0.428226\pi\) | |||||||
\(242\) | 26.8525 | 0.00713283 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2047.37 | −0.537169 | ||||||||
\(245\) | 742.914 | 0.193727 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2062.66 | 0.531351 | ||||||||
\(248\) | 672.660 | 0.172234 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −67.7258 | −0.0171334 | ||||||||
\(251\) | −4468.56 | −1.12372 | −0.561859 | − | 0.827233i | \(-0.689914\pi\) | ||||
−0.561859 | + | 0.827233i | \(0.689914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 269.487 | 0.0669663 | ||||||||
\(254\) | −127.566 | −0.0315125 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3846.17 | 0.939005 | ||||||||
\(257\) | 643.728 | 0.156244 | 0.0781219 | − | 0.996944i | \(-0.475108\pi\) | ||||
0.0781219 | + | 0.996944i | \(0.475108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1195.69 | 0.286859 | ||||||||
\(260\) | −4556.78 | −1.08692 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −162.697 | −0.0383644 | ||||||||
\(263\) | −4100.67 | −0.961438 | −0.480719 | − | 0.876875i | \(-0.659624\pi\) | ||||
−0.480719 | + | 0.876875i | \(0.659624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2475.07 | −0.573744 | ||||||||
\(266\) | 84.7652 | 0.0195387 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3178.45 | 0.724458 | ||||||||
\(269\) | 1869.88 | 0.423823 | 0.211912 | − | 0.977289i | \(-0.432031\pi\) | ||||
0.211912 | + | 0.977289i | \(0.432031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5446.72 | 1.22090 | 0.610451 | − | 0.792054i | \(-0.290988\pi\) | ||||
0.610451 | + | 0.792054i | \(0.290988\pi\) | |||||||
\(272\) | −3879.90 | −0.864902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −155.456 | −0.0342754 | ||||||||
\(275\) | 1153.59 | 0.252960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2570.87 | −0.557648 | −0.278824 | − | 0.960342i | \(-0.589945\pi\) | ||||
−0.278824 | + | 0.960342i | \(0.589945\pi\) | |||||||
\(278\) | 137.476 | 0.0296593 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −375.683 | −0.0801834 | ||||||||
\(281\) | −6127.68 | −1.30088 | −0.650439 | − | 0.759559i | \(-0.725415\pi\) | ||||
−0.650439 | + | 0.759559i | \(0.725415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1634.83 | −0.343395 | −0.171698 | − | 0.985150i | \(-0.554925\pi\) | ||||
−0.171698 | + | 0.985150i | \(0.554925\pi\) | |||||||
\(284\) | −1578.06 | −0.329720 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 92.2783 | 0.0190788 | ||||||||
\(287\) | 546.086 | 0.112315 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1098.49 | −0.223589 | ||||||||
\(290\) | −54.7404 | −0.0110844 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1800.68 | 0.360879 | ||||||||
\(293\) | −5802.05 | −1.15686 | −0.578429 | − | 0.815733i | \(-0.696334\pi\) | ||||
−0.578429 | + | 0.815733i | \(0.696334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9858.75 | 1.94576 | ||||||||
\(296\) | −604.646 | −0.118731 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 576.652 | 0.112096 | ||||||||
\(299\) | 926.086 | 0.179120 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 318.643 | 0.0610176 | ||||||||
\(302\) | −487.275 | −0.0928461 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3427.84 | 0.646712 | ||||||||
\(305\) | 3904.18 | 0.732960 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1012.73 | 0.188273 | 0.0941365 | − | 0.995559i | \(-0.469991\pi\) | ||||
0.0941365 | + | 0.995559i | \(0.469991\pi\) | |||||||
\(308\) | −612.208 | −0.113259 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −639.377 | −0.117142 | ||||||||
\(311\) | 5612.02 | 1.02324 | 0.511621 | − | 0.859211i | \(-0.329045\pi\) | ||||
0.511621 | + | 0.859211i | \(0.329045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9363.85 | −1.69098 | −0.845489 | − | 0.533994i | \(-0.820691\pi\) | ||||
−0.845489 | + | 0.533994i | \(0.820691\pi\) | |||||||
\(314\) | −351.911 | −0.0632467 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1102.30 | −0.196231 | ||||||||
\(317\) | −7870.51 | −1.39449 | −0.697243 | − | 0.716835i | \(-0.745590\pi\) | ||||
−0.697243 | + | 0.716835i | \(0.745590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −178.961 | −0.0314103 | ||||||||
\(320\) | −7477.43 | −1.30625 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 38.0577 | 0.00658655 | ||||||||
\(323\) | −3370.07 | −0.580544 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3964.28 | 0.676612 | ||||||||
\(326\) | 596.574 | 0.101353 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −276.149 | −0.0464872 | ||||||||
\(329\) | 1915.17 | 0.320932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9672.26 | −1.60615 | −0.803075 | − | 0.595878i | \(-0.796804\pi\) | ||||
−0.803075 | + | 0.595878i | \(0.796804\pi\) | |||||||
\(332\) | −3902.10 | −0.645047 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 525.238 | 0.0860471 | ||||||||
\(335\) | −6061.08 | −0.988513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3705.97 | 0.599042 | 0.299521 | − | 0.954090i | \(-0.403173\pi\) | ||||
0.299521 | + | 0.954090i | \(0.403173\pi\) | |||||||
\(338\) | −170.449 | −0.0274296 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7445.09 | 1.18755 | ||||||||
\(341\) | −2090.29 | −0.331952 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −161.134 | −0.0252551 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −213.250 | −0.0331340 | ||||||||
\(347\) | 4360.40 | 0.674578 | 0.337289 | − | 0.941401i | \(-0.390490\pi\) | ||||
0.337289 | + | 0.941401i | \(0.390490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5327.66 | −0.817144 | −0.408572 | − | 0.912726i | \(-0.633973\pi\) | ||||
−0.408572 | + | 0.912726i | \(0.633973\pi\) | |||||||
\(350\) | 162.913 | 0.0248802 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 464.857 | 0.0703891 | ||||||||
\(353\) | −8697.75 | −1.31143 | −0.655715 | − | 0.755009i | \(-0.727633\pi\) | ||||
−0.655715 | + | 0.755009i | \(0.727633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3009.25 | 0.449899 | ||||||||
\(356\) | −1759.31 | −0.261920 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 281.926 | 0.0416208 | ||||||||
\(359\) | 1904.47 | 0.279984 | 0.139992 | − | 0.990153i | \(-0.455292\pi\) | ||||
0.139992 | + | 0.990153i | \(0.455292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3881.58 | −0.565910 | ||||||||
\(362\) | −236.696 | −0.0343659 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2103.84 | −0.302943 | ||||||||
\(365\) | −3433.76 | −0.492414 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11523.2 | 1.63898 | 0.819492 | − | 0.573090i | \(-0.194256\pi\) | ||||
0.819492 | + | 0.573090i | \(0.194256\pi\) | |||||||
\(368\) | 1539.02 | 0.218009 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 574.729 | 0.0807533 | ||||||||
\(371\) | −1142.73 | −0.159912 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8410.72 | −1.16753 | −0.583767 | − | 0.811921i | \(-0.698422\pi\) | ||||
−0.583767 | + | 0.811921i | \(0.698422\pi\) | |||||||
\(374\) | −150.769 | −0.0208451 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −968.477 | −0.132833 | ||||||||
\(377\) | −614.997 | −0.0840158 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1474.83 | −0.199886 | −0.0999429 | − | 0.994993i | \(-0.531866\pi\) | ||||
−0.0999429 | + | 0.994993i | \(0.531866\pi\) | |||||||
\(380\) | −6577.65 | −0.887964 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −210.113 | −0.0281422 | ||||||||
\(383\) | −14807.8 | −1.97558 | −0.987788 | − | 0.155805i | \(-0.950203\pi\) | ||||
−0.987788 | + | 0.155805i | \(0.950203\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1167.44 | 0.154540 | ||||||||
\(386\) | −755.811 | −0.0996625 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12712.8 | −1.66339 | ||||||||
\(389\) | 7886.38 | 1.02791 | 0.513953 | − | 0.857818i | \(-0.328181\pi\) | ||||
0.513953 | + | 0.857818i | \(0.328181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1513.09 | −0.195703 | ||||||||
\(392\) | −173.451 | −0.0223485 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −870.797 | −0.111346 | ||||||||
\(395\) | 2102.00 | 0.267755 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9140.36 | −1.15552 | −0.577760 | − | 0.816207i | \(-0.696073\pi\) | ||||
−0.577760 | + | 0.816207i | \(0.696073\pi\) | |||||||
\(398\) | −568.249 | −0.0715672 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6588.07 | 0.823509 | ||||||||
\(401\) | 3110.82 | 0.387399 | 0.193700 | − | 0.981061i | \(-0.437951\pi\) | ||||
0.193700 | + | 0.981061i | \(0.437951\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7183.27 | −0.887901 | ||||||||
\(404\) | −14079.9 | −1.73391 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.2734 | −0.00308940 | ||||||||
\(407\) | 1878.94 | 0.228835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4395.82 | 0.531441 | 0.265721 | − | 0.964050i | \(-0.414390\pi\) | ||||
0.265721 | + | 0.964050i | \(0.414390\pi\) | |||||||
\(410\) | 262.485 | 0.0316176 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9216.56 | −1.10211 | ||||||||
\(413\) | 4551.74 | 0.542316 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7441.03 | 0.880158 | ||||||||
\(416\) | 1597.48 | 0.188276 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 133.202 | 0.0155865 | ||||||||
\(419\) | 13680.4 | 1.59506 | 0.797532 | − | 0.603277i | \(-0.206139\pi\) | ||||
0.797532 | + | 0.603277i | \(0.206139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4972.96 | 0.575694 | 0.287847 | − | 0.957676i | \(-0.407060\pi\) | ||||
0.287847 | + | 0.957676i | \(0.407060\pi\) | |||||||
\(422\) | −1273.61 | −0.146915 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 577.863 | 0.0661876 | ||||||||
\(425\) | −6477.04 | −0.739253 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1802.54 | 0.204288 | ||||||||
\(428\) | −10613.7 | −1.19868 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 153.161 | 0.0171770 | ||||||||
\(431\) | 11287.7 | 1.26151 | 0.630753 | − | 0.775984i | \(-0.282746\pi\) | ||||
0.630753 | + | 0.775984i | \(0.282746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1261.97 | 0.140061 | 0.0700303 | − | 0.997545i | \(-0.477690\pi\) | ||||
0.0700303 | + | 0.997545i | \(0.477690\pi\) | |||||||
\(434\) | −295.197 | −0.0326496 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3043.37 | −0.334292 | ||||||||
\(437\) | 1336.79 | 0.146333 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7735.83 | −0.841027 | −0.420514 | − | 0.907286i | \(-0.638150\pi\) | ||||
−0.420514 | + | 0.907286i | \(0.638150\pi\) | |||||||
\(440\) | −590.359 | −0.0639642 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −518.115 | −0.0557561 | ||||||||
\(443\) | −6696.73 | −0.718219 | −0.359110 | − | 0.933295i | \(-0.616920\pi\) | ||||
−0.359110 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3354.88 | 0.357386 | ||||||||
\(446\) | 606.016 | 0.0643401 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3452.30 | −0.364075 | ||||||||
\(449\) | 11839.5 | 1.24442 | 0.622208 | − | 0.782852i | \(-0.286236\pi\) | ||||
0.622208 | + | 0.782852i | \(0.286236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 858.135 | 0.0895965 | ||||||||
\(452\) | −5096.49 | −0.530351 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 470.073 | 0.0485938 | ||||||||
\(455\) | 4011.88 | 0.413362 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9116.78 | −0.933183 | −0.466592 | − | 0.884473i | \(-0.654518\pi\) | ||||
−0.466592 | + | 0.884473i | \(0.654518\pi\) | |||||||
\(458\) | −626.163 | −0.0638836 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2953.21 | −0.299336 | ||||||||
\(461\) | 9601.92 | 0.970078 | 0.485039 | − | 0.874492i | \(-0.338805\pi\) | ||||
0.485039 | + | 0.874492i | \(0.338805\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10049.0 | 1.00867 | 0.504337 | − | 0.863507i | \(-0.331737\pi\) | ||||
0.504337 | + | 0.863507i | \(0.331737\pi\) | |||||||
\(464\) | −1022.04 | −0.102256 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1517.71 | 0.150872 | ||||||||
\(467\) | 53.2684 | 0.00527831 | 0.00263915 | − | 0.999997i | \(-0.499160\pi\) | ||||
0.00263915 | + | 0.999997i | \(0.499160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2798.37 | −0.275515 | ||||||||
\(470\) | 920.557 | 0.0903449 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2301.76 | −0.224464 | ||||||||
\(473\) | 500.725 | 0.0486752 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5722.39 | 0.552761 | ||||||||
\(476\) | 3437.36 | 0.330990 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 770.912 | 0.0737671 | ||||||||
\(479\) | −1553.49 | −0.148185 | −0.0740926 | − | 0.997251i | \(-0.523606\pi\) | ||||
−0.0740926 | + | 0.997251i | \(0.523606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6456.95 | 0.612083 | ||||||||
\(482\) | 371.266 | 0.0350844 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −962.041 | −0.0903494 | ||||||||
\(485\) | 24242.4 | 2.26967 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4340.19 | −0.403845 | −0.201923 | − | 0.979401i | \(-0.564719\pi\) | ||||
−0.201923 | + | 0.979401i | \(0.564719\pi\) | |||||||
\(488\) | −911.525 | −0.0845549 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 164.869 | 0.0152000 | ||||||||
\(491\) | −304.844 | −0.0280192 | −0.0140096 | − | 0.999902i | \(-0.504460\pi\) | ||||
−0.0140096 | + | 0.999902i | \(0.504460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1004.81 | 0.0917941 | ||||||||
\(494\) | 457.748 | 0.0416904 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11937.6 | −1.08067 | ||||||||
\(497\) | 1389.36 | 0.125395 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14238.0 | 1.27732 | 0.638658 | − | 0.769491i | \(-0.279490\pi\) | ||||
0.638658 | + | 0.769491i | \(0.279490\pi\) | |||||||
\(500\) | 2426.40 | 0.217024 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −991.671 | −0.0881682 | ||||||||
\(503\) | −863.867 | −0.0765764 | −0.0382882 | − | 0.999267i | \(-0.512190\pi\) | ||||
−0.0382882 | + | 0.999267i | \(0.512190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26849.3 | 2.36590 | ||||||||
\(506\) | 59.8049 | 0.00525425 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4570.28 | 0.399160 | ||||||||
\(509\) | −15882.5 | −1.38307 | −0.691533 | − | 0.722345i | \(-0.743064\pi\) | ||||
−0.691533 | + | 0.722345i | \(0.743064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1585.35 | −0.137244 | ||||||||
\(512\) | 4433.76 | 0.382708 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 142.857 | 0.0122591 | ||||||||
\(515\) | 17575.3 | 1.50381 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3009.55 | 0.256015 | ||||||||
\(518\) | 265.349 | 0.0225073 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2028.76 | −0.171090 | ||||||||
\(521\) | −3222.11 | −0.270946 | −0.135473 | − | 0.990781i | \(-0.543255\pi\) | ||||
−0.135473 | + | 0.990781i | \(0.543255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15897.9 | −1.32919 | −0.664595 | − | 0.747203i | \(-0.731396\pi\) | ||||
−0.664595 | + | 0.747203i | \(0.731396\pi\) | |||||||
\(524\) | 5828.94 | 0.485951 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −910.028 | −0.0754355 | ||||||||
\(527\) | 11736.4 | 0.970104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11566.8 | −0.950671 | ||||||||
\(530\) | −549.271 | −0.0450166 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3036.87 | −0.247491 | ||||||||
\(533\) | 2948.97 | 0.239651 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20239.6 | 1.63558 | ||||||||
\(536\) | 1415.10 | 0.114036 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 414.966 | 0.0332537 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5790.34 | 0.460159 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(542\) | 1208.74 | 0.0957934 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2610.03 | −0.205706 | ||||||||
\(545\) | 5803.50 | 0.456137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −394.656 | −0.0308487 | −0.0154244 | − | 0.999881i | \(-0.504910\pi\) | ||||
−0.0154244 | + | 0.999881i | \(0.504910\pi\) | |||||||
\(548\) | 5569.51 | 0.434156 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 256.006 | 0.0198475 | ||||||||
\(551\) | −887.740 | −0.0686370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 970.485 | 0.0746279 | ||||||||
\(554\) | −570.531 | −0.0437537 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4925.34 | −0.375685 | ||||||||
\(557\) | 20388.5 | 1.55097 | 0.775484 | − | 0.631367i | \(-0.217506\pi\) | ||||
0.775484 | + | 0.631367i | \(0.217506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1720.73 | 0.130196 | ||||||||
\(560\) | 6667.17 | 0.503106 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1359.86 | −0.102068 | ||||||||
\(563\) | −9186.83 | −0.687707 | −0.343853 | − | 0.939023i | \(-0.611732\pi\) | ||||
−0.343853 | + | 0.939023i | \(0.611732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9718.64 | 0.723657 | ||||||||
\(566\) | −362.805 | −0.0269432 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −702.580 | −0.0519007 | ||||||||
\(569\) | 20287.6 | 1.49473 | 0.747364 | − | 0.664415i | \(-0.231319\pi\) | ||||
0.747364 | + | 0.664415i | \(0.231319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16177.3 | 1.18564 | 0.592818 | − | 0.805337i | \(-0.298015\pi\) | ||||
0.592818 | + | 0.805337i | \(0.298015\pi\) | |||||||
\(572\) | −3306.04 | −0.241665 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 121.188 | 0.00881237 | ||||||||
\(575\) | 2569.22 | 0.186337 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3080.98 | −0.222293 | −0.111146 | − | 0.993804i | \(-0.535452\pi\) | ||||
−0.111146 | + | 0.993804i | \(0.535452\pi\) | |||||||
\(578\) | −243.779 | −0.0175430 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1961.18 | 0.140402 | ||||||||
\(581\) | 3435.49 | 0.245315 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1795.71 | −0.127566 | ||||||||
\(584\) | 801.693 | 0.0568053 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1287.60 | −0.0907684 | ||||||||
\(587\) | −13470.3 | −0.947154 | −0.473577 | − | 0.880752i | \(-0.657037\pi\) | ||||
−0.473577 | + | 0.880752i | \(0.657037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10369.0 | −0.725374 | ||||||||
\(590\) | 2187.87 | 0.152666 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10730.5 | 0.744970 | ||||||||
\(593\) | −9759.61 | −0.675850 | −0.337925 | − | 0.941173i | \(-0.609725\pi\) | ||||
−0.337925 | + | 0.941173i | \(0.609725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6554.81 | −0.451632 | ||||||||
\(596\) | −20659.6 | −1.41988 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 205.519 | 0.0140540 | ||||||||
\(599\) | 26993.6 | 1.84128 | 0.920642 | − | 0.390407i | \(-0.127666\pi\) | ||||
0.920642 | + | 0.390407i | \(0.127666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 921.111 | 0.0625173 | 0.0312587 | − | 0.999511i | \(-0.490048\pi\) | ||||
0.0312587 | + | 0.999511i | \(0.490048\pi\) | |||||||
\(602\) | 70.7138 | 0.00478751 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17457.5 | 1.17605 | ||||||||
\(605\) | 1834.54 | 0.123281 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8954.12 | 0.598742 | 0.299371 | − | 0.954137i | \(-0.403223\pi\) | ||||
0.299371 | + | 0.954137i | \(0.403223\pi\) | |||||||
\(608\) | 2305.93 | 0.153812 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 866.423 | 0.0575089 | ||||||||
\(611\) | 10342.3 | 0.684784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3495.30 | 0.230300 | 0.115150 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115150 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(614\) | 224.748 | 0.0147721 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −272.566 | −0.0178279 | ||||||||
\(617\) | 703.452 | 0.0458994 | 0.0229497 | − | 0.999737i | \(-0.492694\pi\) | ||||
0.0229497 | + | 0.999737i | \(0.492694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22343.8 | −1.45084 | −0.725421 | − | 0.688305i | \(-0.758355\pi\) | ||||
−0.725421 | + | 0.688305i | \(0.758355\pi\) | |||||||
\(620\) | 22906.9 | 1.48381 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1245.43 | 0.0802848 | ||||||||
\(623\) | 1548.93 | 0.0996095 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17735.9 | −1.13510 | ||||||||
\(626\) | −2078.04 | −0.132676 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12607.8 | 0.801127 | ||||||||
\(629\) | −10549.7 | −0.668750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2517.59 | −0.158833 | −0.0794166 | − | 0.996842i | \(-0.525306\pi\) | ||||
−0.0794166 | + | 0.996842i | \(0.525306\pi\) | |||||||
\(632\) | −490.762 | −0.0308884 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1746.64 | −0.109413 | ||||||||
\(635\) | −8715.19 | −0.544649 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1852.27 | 0.115211 | ||||||||
\(638\) | −39.7153 | −0.00246449 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6785.18 | −0.419075 | ||||||||
\(641\) | −27413.1 | −1.68916 | −0.844581 | − | 0.535427i | \(-0.820151\pi\) | ||||
−0.844581 | + | 0.535427i | \(0.820151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14594.3 | −0.895090 | −0.447545 | − | 0.894261i | \(-0.647702\pi\) | ||||
−0.447545 | + | 0.894261i | \(0.647702\pi\) | |||||||
\(644\) | −1363.49 | −0.0834299 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −747.892 | −0.0455502 | ||||||||
\(647\) | 30744.2 | 1.86813 | 0.934065 | − | 0.357102i | \(-0.116235\pi\) | ||||
0.934065 | + | 0.357102i | \(0.116235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7152.73 | 0.432618 | ||||||||
\(650\) | 879.760 | 0.0530877 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21373.4 | −1.28381 | ||||||||
\(653\) | −963.185 | −0.0577218 | −0.0288609 | − | 0.999583i | \(-0.509188\pi\) | ||||
−0.0288609 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11115.4 | −0.663074 | ||||||||
\(656\) | 4900.77 | 0.291681 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 425.017 | 0.0251807 | ||||||||
\(659\) | 19165.9 | 1.13292 | 0.566461 | − | 0.824088i | \(-0.308312\pi\) | ||||
0.566461 | + | 0.824088i | \(0.308312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1337.15 | 0.0786825 | 0.0393412 | − | 0.999226i | \(-0.487474\pi\) | ||||
0.0393412 | + | 0.999226i | \(0.487474\pi\) | |||||||
\(662\) | −2146.48 | −0.126020 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1737.29 | −0.101536 | ||||||||
\(665\) | 5791.09 | 0.337698 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −398.575 | −0.0231378 | ||||||||
\(668\) | −18817.6 | −1.08993 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1345.08 | −0.0775599 | ||||||||
\(671\) | 2832.57 | 0.162966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25541.2 | −1.46291 | −0.731456 | − | 0.681889i | \(-0.761159\pi\) | ||||
−0.731456 | + | 0.681889i | \(0.761159\pi\) | |||||||
\(674\) | 822.436 | 0.0470016 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6106.64 | 0.347442 | ||||||||
\(677\) | −28339.6 | −1.60883 | −0.804417 | − | 0.594065i | \(-0.797522\pi\) | ||||
−0.804417 | + | 0.594065i | \(0.797522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11192.6 | 0.632596 | ||||||||
\(680\) | 3314.69 | 0.186930 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −463.882 | −0.0260454 | ||||||||
\(683\) | 29608.1 | 1.65875 | 0.829373 | − | 0.558696i | \(-0.188698\pi\) | ||||
0.829373 | + | 0.558696i | \(0.188698\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10620.7 | −0.592401 | ||||||||
\(686\) | 76.1191 | 0.00423650 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2859.61 | 0.158462 | ||||||||
\(689\) | −6170.94 | −0.341211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9526.18 | −0.524447 | −0.262224 | − | 0.965007i | \(-0.584456\pi\) | ||||
−0.262224 | + | 0.965007i | \(0.584456\pi\) | |||||||
\(692\) | 7640.07 | 0.419699 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 967.667 | 0.0529282 | ||||||||
\(695\) | 9392.27 | 0.512617 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4818.17 | −0.261838 | ||||||||
\(698\) | −1182.32 | −0.0641141 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5836.65 | −0.315149 | ||||||||
\(701\) | 9000.24 | 0.484928 | 0.242464 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242464 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9320.53 | 0.500043 | ||||||||
\(704\) | −5425.04 | −0.290432 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1930.22 | −0.102896 | ||||||||
\(707\) | 12396.2 | 0.659417 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26507.1 | −1.40409 | −0.702043 | − | 0.712135i | \(-0.747728\pi\) | ||||
−0.702043 | + | 0.712135i | \(0.747728\pi\) | |||||||
\(710\) | 667.817 | 0.0352996 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −783.278 | −0.0412283 | ||||||||
\(713\) | −4655.42 | −0.244526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6304.38 | 0.329749 | ||||||||
\(716\) | −10100.5 | −0.527198 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 422.643 | 0.0219678 | ||||||||
\(719\) | −1142.82 | −0.0592766 | −0.0296383 | − | 0.999561i | \(-0.509436\pi\) | ||||
−0.0296383 | + | 0.999561i | \(0.509436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8114.44 | 0.419137 | ||||||||
\(722\) | −861.407 | −0.0444020 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8480.06 | 0.435302 | ||||||||
\(725\) | −1706.17 | −0.0874010 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8756.51 | 0.446714 | 0.223357 | − | 0.974737i | \(-0.428298\pi\) | ||||
0.223357 | + | 0.974737i | \(0.428298\pi\) | |||||||
\(728\) | −936.669 | −0.0476858 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −762.026 | −0.0386354 | ||||||||
\(731\) | −2811.42 | −0.142249 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21531.5 | 1.08497 | 0.542485 | − | 0.840065i | \(-0.317483\pi\) | ||||
0.542485 | + | 0.840065i | \(0.317483\pi\) | |||||||
\(734\) | 2557.25 | 0.128597 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1035.31 | 0.0518507 | ||||||||
\(737\) | −4397.44 | −0.219785 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29052.5 | −1.44616 | −0.723082 | − | 0.690762i | \(-0.757275\pi\) | ||||
−0.723082 | + | 0.690762i | \(0.757275\pi\) | |||||||
\(740\) | −20590.7 | −1.02288 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −253.596 | −0.0125469 | ||||||||
\(743\) | −21077.0 | −1.04070 | −0.520349 | − | 0.853954i | \(-0.674198\pi\) | ||||
−0.520349 | + | 0.853954i | \(0.674198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39396.4 | 1.93741 | ||||||||
\(746\) | −1866.52 | −0.0916061 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5401.57 | 0.264039 | ||||||||
\(749\) | 9344.53 | 0.455863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20376.3 | −0.990068 | −0.495034 | − | 0.868874i | \(-0.664844\pi\) | ||||
−0.495034 | + | 0.868874i | \(0.664844\pi\) | |||||||
\(752\) | 17187.4 | 0.833456 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −136.481 | −0.00659198 | ||||||||
\(755\) | −33290.2 | −1.60471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4174.74 | 0.200441 | 0.100220 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100220 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(758\) | −327.296 | −0.0156833 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2928.49 | −0.139773 | ||||||||
\(761\) | −33842.9 | −1.61210 | −0.806048 | − | 0.591850i | \(-0.798398\pi\) | ||||
−0.806048 | + | 0.591850i | \(0.798398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2679.45 | 0.127133 | ||||||||
\(764\) | 7527.69 | 0.356469 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3286.18 | −0.155006 | ||||||||
\(767\) | 24580.3 | 1.15716 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35288.8 | 1.65481 | 0.827403 | − | 0.561608i | \(-0.189817\pi\) | ||||
0.827403 | + | 0.561608i | \(0.189817\pi\) | |||||||
\(770\) | 259.079 | 0.0121254 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27078.3 | 1.26240 | ||||||||
\(773\) | 7889.49 | 0.367096 | 0.183548 | − | 0.983011i | \(-0.441242\pi\) | ||||
0.183548 | + | 0.983011i | \(0.441242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19928.4 | −0.923676 | ||||||||
\(776\) | −5659.97 | −0.261831 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1750.16 | 0.0806507 | ||||||||
\(779\) | 4256.80 | 0.195784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2183.27 | 0.100030 | ||||||||
\(782\) | −335.787 | −0.0153551 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3078.20 | 0.140224 | ||||||||
\(785\) | −24042.3 | −1.09313 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29792.1 | −1.34940 | −0.674698 | − | 0.738094i | \(-0.735726\pi\) | ||||
−0.674698 | + | 0.738094i | \(0.735726\pi\) | |||||||
\(788\) | 31197.9 | 1.41038 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 466.480 | 0.0210084 | ||||||||
\(791\) | 4487.05 | 0.201696 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9734.08 | 0.435898 | ||||||||
\(794\) | −2028.44 | −0.0906634 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20358.6 | 0.906520 | ||||||||
\(797\) | 9484.68 | 0.421537 | 0.210768 | − | 0.977536i | \(-0.432403\pi\) | ||||
0.210768 | + | 0.977536i | \(0.432403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16897.7 | −0.748182 | ||||||||
\(800\) | 4431.84 | 0.195862 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 690.359 | 0.0303958 | ||||||||
\(803\) | −2491.27 | −0.109483 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2600.07 | 0.113839 | ||||||||
\(806\) | −1594.12 | −0.0696657 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6268.62 | −0.272932 | ||||||||
\(809\) | −4355.71 | −0.189294 | −0.0946469 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946469 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24779.5 | 1.07290 | 0.536452 | − | 0.843931i | \(-0.319764\pi\) | ||||
0.536452 | + | 0.843931i | \(0.319764\pi\) | |||||||
\(812\) | 905.466 | 0.0391325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 416.978 | 0.0179546 | ||||||||
\(815\) | 40757.5 | 1.75174 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2483.86 | 0.106364 | ||||||||
\(818\) | 975.528 | 0.0416975 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9404.02 | −0.400491 | ||||||||
\(821\) | −11432.8 | −0.486001 | −0.243001 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243001 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −294.772 | −0.0124850 | −0.00624248 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624248 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(824\) | −4103.38 | −0.173480 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1010.13 | 0.0425507 | ||||||||
\(827\) | 5247.79 | 0.220657 | 0.110329 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110329 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7639.88 | −0.320077 | −0.160039 | − | 0.987111i | \(-0.551162\pi\) | ||||
−0.160039 | + | 0.987111i | \(0.551162\pi\) | |||||||
\(830\) | 1651.33 | 0.0690582 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18643.1 | −0.776841 | ||||||||
\(833\) | −3026.32 | −0.125877 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35883.8 | 1.48720 | ||||||||
\(836\) | −4772.22 | −0.197429 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3035.98 | 0.125150 | ||||||||
\(839\) | 6424.79 | 0.264372 | 0.132186 | − | 0.991225i | \(-0.457800\pi\) | ||||
0.132186 | + | 0.991225i | \(0.457800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24124.3 | −0.989147 | ||||||||
\(842\) | 1103.61 | 0.0451696 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45629.4 | 1.86093 | ||||||||
\(845\) | −11644.9 | −0.474080 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | −10255.2 | −0.415290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1437.40 | −0.0580027 | ||||||||
\(851\) | 4184.71 | 0.168566 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8879.93 | −0.356440 | −0.178220 | − | 0.983991i | \(-0.557034\pi\) | ||||
−0.178220 | + | 0.983991i | \(0.557034\pi\) | |||||||
\(854\) | 400.023 | 0.0160287 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4725.42 | −0.188682 | ||||||||
\(857\) | 33495.3 | 1.33510 | 0.667549 | − | 0.744566i | \(-0.267344\pi\) | ||||
0.667549 | + | 0.744566i | \(0.267344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8626.96 | 0.342664 | 0.171332 | − | 0.985213i | \(-0.445193\pi\) | ||||
0.171332 | + | 0.985213i | \(0.445193\pi\) | |||||||
\(860\) | −5487.28 | −0.217575 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2504.98 | 0.0989792 | ||||||||
\(863\) | 31254.6 | 1.23281 | 0.616407 | − | 0.787428i | \(-0.288588\pi\) | ||||
0.616407 | + | 0.787428i | \(0.288588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14569.1 | −0.572674 | ||||||||
\(866\) | 280.058 | 0.0109893 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10576.0 | 0.413563 | ||||||||
\(869\) | 1525.05 | 0.0595324 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15111.7 | −0.587878 | ||||||||
\(872\) | −1354.96 | −0.0526203 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 296.663 | 0.0114815 | ||||||||
\(875\) | −2136.25 | −0.0825354 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17993.1 | 0.692798 | 0.346399 | − | 0.938087i | \(-0.387404\pi\) | ||||
0.346399 | + | 0.938087i | \(0.387404\pi\) | |||||||
\(878\) | −1716.75 | −0.0659880 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10477.0 | 0.401340 | ||||||||
\(881\) | −21216.5 | −0.811353 | −0.405677 | − | 0.914017i | \(-0.632964\pi\) | ||||
−0.405677 | + | 0.914017i | \(0.632964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25621.2 | −0.976470 | −0.488235 | − | 0.872712i | \(-0.662359\pi\) | ||||
−0.488235 | + | 0.872712i | \(0.662359\pi\) | |||||||
\(884\) | 18562.4 | 0.706246 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1486.15 | −0.0563523 | ||||||||
\(887\) | 9821.44 | 0.371783 | 0.185892 | − | 0.982570i | \(-0.440483\pi\) | ||||
0.185892 | + | 0.982570i | \(0.440483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4023.76 | −0.151803 | ||||||||
\(890\) | 744.521 | 0.0280409 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21711.6 | −0.814977 | ||||||||
\(893\) | 14928.9 | 0.559437 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19260.9 | 0.719355 | ||||||||
\(896\) | −3132.69 | −0.116803 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2627.45 | 0.0976382 | ||||||||
\(899\) | 3091.58 | 0.114694 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10082.4 | 0.372801 | ||||||||
\(902\) | 190.439 | 0.00702984 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2269.05 | −0.0834817 | ||||||||
\(905\) | −16170.9 | −0.593964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42843.2 | −1.56845 | −0.784226 | − | 0.620475i | \(-0.786940\pi\) | ||||
−0.784226 | + | 0.620475i | \(0.786940\pi\) | |||||||
\(908\) | −16841.2 | −0.615524 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 890.323 | 0.0324329 | ||||||||
\(911\) | −41062.3 | −1.49336 | −0.746681 | − | 0.665182i | \(-0.768354\pi\) | ||||
−0.746681 | + | 0.665182i | \(0.768354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5398.62 | 0.195694 | ||||||||
\(914\) | −2023.21 | −0.0732186 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22433.5 | 0.809195 | ||||||||
\(917\) | −5131.91 | −0.184810 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48794.4 | 1.75144 | 0.875722 | − | 0.482815i | \(-0.160386\pi\) | ||||
0.875722 | + | 0.482815i | \(0.160386\pi\) | |||||||
\(920\) | −1314.82 | −0.0471179 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2130.87 | 0.0761134 | ||||||||
\(923\) | 7502.78 | 0.267559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17913.4 | 0.636745 | ||||||||
\(926\) | 2230.09 | 0.0791417 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −687.532 | −0.0243204 | ||||||||
\(929\) | −20643.0 | −0.729038 | −0.364519 | − | 0.931196i | \(-0.618767\pi\) | ||||
−0.364519 | + | 0.931196i | \(0.618767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2673.72 | 0.0941221 | ||||||||
\(932\) | −54374.7 | −1.91105 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.8214 | 0.000414142 0 | ||||||||
\(935\) | −10300.4 | −0.360277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42485.1 | 1.48124 | 0.740622 | − | 0.671921i | \(-0.234531\pi\) | ||||
0.740622 | + | 0.671921i | \(0.234531\pi\) | |||||||
\(938\) | −621.019 | −0.0216173 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −32980.6 | −1.14437 | ||||||||
\(941\) | 1787.96 | 0.0619404 | 0.0309702 | − | 0.999520i | \(-0.490140\pi\) | ||||
0.0309702 | + | 0.999520i | \(0.490140\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1911.21 | 0.0659994 | ||||||||
\(944\) | 40848.9 | 1.40839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 111.122 | 0.00381911 | ||||||||
\(947\) | 4409.90 | 0.151323 | 0.0756613 | − | 0.997134i | \(-0.475893\pi\) | ||||
0.0756613 | + | 0.997134i | \(0.475893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8561.20 | −0.292843 | ||||||||
\(950\) | 1269.92 | 0.0433702 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1530.38 | 0.0521006 | ||||||||
\(953\) | −50160.0 | −1.70497 | −0.852487 | − | 0.522748i | \(-0.824907\pi\) | ||||
−0.852487 | + | 0.522748i | \(0.824907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14354.8 | −0.486397 | ||||||||
\(956\) | −27619.3 | −0.934386 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −344.753 | −0.0116268 | ||||||||
\(959\) | −4903.51 | −0.165112 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6319.17 | 0.212117 | ||||||||
\(962\) | 1432.94 | 0.0480247 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13301.3 | −0.444404 | ||||||||
\(965\) | −51636.4 | −1.72252 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15711.7 | 0.522497 | 0.261248 | − | 0.965272i | \(-0.415866\pi\) | ||||
0.261248 | + | 0.965272i | \(0.415866\pi\) | |||||||
\(968\) | −428.318 | −0.0142218 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5379.92 | 0.178081 | ||||||||
\(971\) | −21930.3 | −0.724795 | −0.362397 | − | 0.932024i | \(-0.618042\pi\) | ||||
−0.362397 | + | 0.932024i | \(0.618042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4336.37 | 0.142875 | ||||||||
\(974\) | −963.181 | −0.0316862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16176.7 | 0.530535 | ||||||||
\(977\) | −46329.0 | −1.51709 | −0.758544 | − | 0.651621i | \(-0.774089\pi\) | ||||
−0.758544 | + | 0.651621i | \(0.774089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2434.04 | 0.0794609 | ||||||||
\(980\) | −5906.73 | −0.192534 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −67.6515 | −0.00219842 | ||||||||
\(983\) | −29563.1 | −0.959224 | −0.479612 | − | 0.877481i | \(-0.659223\pi\) | ||||
−0.479612 | + | 0.877481i | \(0.659223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59492.2 | −1.92445 | ||||||||
\(986\) | 222.990 | 0.00720227 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16399.7 | −0.528080 | ||||||||
\(989\) | 1115.20 | 0.0358556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39722.4 | −1.27328 | −0.636642 | − | 0.771160i | \(-0.719677\pi\) | ||||
−0.636642 | + | 0.771160i | \(0.719677\pi\) | |||||||
\(992\) | −8030.48 | −0.257024 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 308.328 | 0.00983860 | ||||||||
\(995\) | −38822.3 | −1.23694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38762.1 | −1.23130 | −0.615652 | − | 0.788018i | \(-0.711107\pi\) | ||||
−0.615652 | + | 0.788018i | \(0.711107\pi\) | |||||||
\(998\) | 3159.72 | 0.100220 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 693.4.a.u.1.4 | yes | 8 | |
3.2 | odd | 2 | 693.4.a.r.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.4.a.r.1.5 | ✓ | 8 | 3.2 | odd | 2 | ||
693.4.a.u.1.4 | yes | 8 | 1.1 | even | 1 | trivial |