Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, 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("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 31x^{4} + 9x^{3} + 230x^{2} + 32x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.691666\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.691666 | −0.244541 | −0.122270 | − | 0.992497i | \(-0.539018\pi\) | ||||
−0.122270 | + | 0.992497i | \(0.539018\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.52160 | −0.940200 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 2.07500 | 0.141186 | ||||||||
\(7\) | −14.5720 | −0.786816 | −0.393408 | − | 0.919364i | \(-0.628704\pi\) | ||||
−0.393408 | + | 0.919364i | \(0.628704\pi\) | |||||||
\(8\) | 10.7358 | 0.474458 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −3.45833 | −0.109362 | ||||||||
\(11\) | 36.8326 | 1.00959 | 0.504793 | − | 0.863240i | \(-0.331569\pi\) | ||||
0.504793 | + | 0.863240i | \(0.331569\pi\) | |||||||
\(12\) | 22.5648 | 0.542825 | ||||||||
\(13\) | −23.9199 | −0.510322 | −0.255161 | − | 0.966899i | \(-0.582128\pi\) | ||||
−0.255161 | + | 0.966899i | \(0.582128\pi\) | |||||||
\(14\) | 10.0790 | 0.192409 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 52.7472 | 0.824175 | ||||||||
\(17\) | 62.8914 | 0.897260 | 0.448630 | − | 0.893718i | \(-0.351912\pi\) | ||||
0.448630 | + | 0.893718i | \(0.351912\pi\) | |||||||
\(18\) | −6.22499 | −0.0815136 | ||||||||
\(19\) | −94.1599 | −1.13693 | −0.568467 | − | 0.822706i | \(-0.692463\pi\) | ||||
−0.568467 | + | 0.822706i | \(0.692463\pi\) | |||||||
\(20\) | −37.6080 | −0.420470 | ||||||||
\(21\) | 43.7161 | 0.454268 | ||||||||
\(22\) | −25.4759 | −0.246885 | ||||||||
\(23\) | 185.410 | 1.68090 | 0.840450 | − | 0.541889i | \(-0.182291\pi\) | ||||
0.840450 | + | 0.541889i | \(0.182291\pi\) | |||||||
\(24\) | −32.2073 | −0.273928 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 16.5446 | 0.124795 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 109.605 | 0.739764 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 10.3750 | 0.0631402 | ||||||||
\(31\) | −104.971 | −0.608174 | −0.304087 | − | 0.952644i | \(-0.598351\pi\) | ||||
−0.304087 | + | 0.952644i | \(0.598351\pi\) | |||||||
\(32\) | −122.370 | −0.676003 | ||||||||
\(33\) | −110.498 | −0.582885 | ||||||||
\(34\) | −43.4999 | −0.219417 | ||||||||
\(35\) | −72.8602 | −0.351875 | ||||||||
\(36\) | −67.6944 | −0.313400 | ||||||||
\(37\) | −259.799 | −1.15435 | −0.577173 | − | 0.816622i | \(-0.695844\pi\) | ||||
−0.577173 | + | 0.816622i | \(0.695844\pi\) | |||||||
\(38\) | 65.1272 | 0.278027 | ||||||||
\(39\) | 71.7597 | 0.294635 | ||||||||
\(40\) | 53.6788 | 0.212184 | ||||||||
\(41\) | 11.8069 | 0.0449740 | 0.0224870 | − | 0.999747i | \(-0.492842\pi\) | ||||
0.0224870 | + | 0.999747i | \(0.492842\pi\) | |||||||
\(42\) | −30.2369 | −0.111087 | ||||||||
\(43\) | −61.0501 | −0.216513 | −0.108256 | − | 0.994123i | \(-0.534527\pi\) | ||||
−0.108256 | + | 0.994123i | \(0.534527\pi\) | |||||||
\(44\) | −277.040 | −0.949213 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −128.242 | −0.411049 | ||||||||
\(47\) | 281.426 | 0.873409 | 0.436705 | − | 0.899605i | \(-0.356145\pi\) | ||||
0.436705 | + | 0.899605i | \(0.356145\pi\) | |||||||
\(48\) | −158.242 | −0.475838 | ||||||||
\(49\) | −130.656 | −0.380921 | ||||||||
\(50\) | −17.2916 | −0.0489082 | ||||||||
\(51\) | −188.674 | −0.518033 | ||||||||
\(52\) | 179.916 | 0.479805 | ||||||||
\(53\) | −170.846 | −0.442782 | −0.221391 | − | 0.975185i | \(-0.571060\pi\) | ||||
−0.221391 | + | 0.975185i | \(0.571060\pi\) | |||||||
\(54\) | 18.6750 | 0.0470619 | ||||||||
\(55\) | 184.163 | 0.451501 | ||||||||
\(56\) | −156.442 | −0.373311 | ||||||||
\(57\) | 282.480 | 0.656409 | ||||||||
\(58\) | 20.0583 | 0.0454101 | ||||||||
\(59\) | −636.987 | −1.40557 | −0.702785 | − | 0.711402i | \(-0.748060\pi\) | ||||
−0.702785 | + | 0.711402i | \(0.748060\pi\) | |||||||
\(60\) | 112.824 | 0.242759 | ||||||||
\(61\) | −379.603 | −0.796774 | −0.398387 | − | 0.917218i | \(-0.630430\pi\) | ||||
−0.398387 | + | 0.917218i | \(0.630430\pi\) | |||||||
\(62\) | 72.6051 | 0.148723 | ||||||||
\(63\) | −131.148 | −0.262272 | ||||||||
\(64\) | −337.339 | −0.658865 | ||||||||
\(65\) | −119.600 | −0.228223 | ||||||||
\(66\) | 76.4276 | 0.142539 | ||||||||
\(67\) | −623.333 | −1.13660 | −0.568300 | − | 0.822821i | \(-0.692399\pi\) | ||||
−0.568300 | + | 0.822821i | \(0.692399\pi\) | |||||||
\(68\) | −473.044 | −0.843603 | ||||||||
\(69\) | −556.231 | −0.970468 | ||||||||
\(70\) | 50.3949 | 0.0860477 | ||||||||
\(71\) | 298.898 | 0.499615 | 0.249808 | − | 0.968295i | \(-0.419633\pi\) | ||||
0.249808 | + | 0.968295i | \(0.419633\pi\) | |||||||
\(72\) | 96.6218 | 0.158153 | ||||||||
\(73\) | −524.124 | −0.840329 | −0.420165 | − | 0.907448i | \(-0.638028\pi\) | ||||
−0.420165 | + | 0.907448i | \(0.638028\pi\) | |||||||
\(74\) | 179.694 | 0.282284 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 708.233 | 1.06895 | ||||||||
\(77\) | −536.726 | −0.794358 | ||||||||
\(78\) | −49.6337 | −0.0720502 | ||||||||
\(79\) | 563.264 | 0.802179 | 0.401090 | − | 0.916039i | \(-0.368632\pi\) | ||||
0.401090 | + | 0.916039i | \(0.368632\pi\) | |||||||
\(80\) | 263.736 | 0.368582 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −8.16645 | −0.0109980 | ||||||||
\(83\) | −885.342 | −1.17083 | −0.585415 | − | 0.810734i | \(-0.699068\pi\) | ||||
−0.585415 | + | 0.810734i | \(0.699068\pi\) | |||||||
\(84\) | −328.815 | −0.427103 | ||||||||
\(85\) | 314.457 | 0.401267 | ||||||||
\(86\) | 42.2263 | 0.0529462 | ||||||||
\(87\) | 87.0000 | 0.107211 | ||||||||
\(88\) | 395.426 | 0.479006 | ||||||||
\(89\) | −447.652 | −0.533157 | −0.266579 | − | 0.963813i | \(-0.585893\pi\) | ||||
−0.266579 | + | 0.963813i | \(0.585893\pi\) | |||||||
\(90\) | −31.1250 | −0.0364540 | ||||||||
\(91\) | 348.562 | 0.401529 | ||||||||
\(92\) | −1394.58 | −1.58038 | ||||||||
\(93\) | 314.914 | 0.351130 | ||||||||
\(94\) | −194.653 | −0.213584 | ||||||||
\(95\) | −470.799 | −0.508453 | ||||||||
\(96\) | 367.109 | 0.390290 | ||||||||
\(97\) | −558.895 | −0.585022 | −0.292511 | − | 0.956262i | \(-0.594491\pi\) | ||||
−0.292511 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(98\) | 90.3702 | 0.0931507 | ||||||||
\(99\) | 331.493 | 0.336529 | ||||||||
\(100\) | −188.040 | −0.188040 | ||||||||
\(101\) | −1138.78 | −1.12191 | −0.560956 | − | 0.827846i | \(-0.689566\pi\) | ||||
−0.560956 | + | 0.827846i | \(0.689566\pi\) | |||||||
\(102\) | 130.500 | 0.126680 | ||||||||
\(103\) | 1008.31 | 0.964583 | 0.482292 | − | 0.876011i | \(-0.339805\pi\) | ||||
0.482292 | + | 0.876011i | \(0.339805\pi\) | |||||||
\(104\) | −256.798 | −0.242126 | ||||||||
\(105\) | 218.580 | 0.203155 | ||||||||
\(106\) | 118.168 | 0.108278 | ||||||||
\(107\) | 140.506 | 0.126946 | 0.0634730 | − | 0.997984i | \(-0.479782\pi\) | ||||
0.0634730 | + | 0.997984i | \(0.479782\pi\) | |||||||
\(108\) | 203.083 | 0.180942 | ||||||||
\(109\) | −850.530 | −0.747394 | −0.373697 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373697 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(110\) | −127.379 | −0.110410 | ||||||||
\(111\) | 779.398 | 0.666461 | ||||||||
\(112\) | −768.634 | −0.648474 | ||||||||
\(113\) | 1851.23 | 1.54115 | 0.770573 | − | 0.637352i | \(-0.219970\pi\) | ||||
0.770573 | + | 0.637352i | \(0.219970\pi\) | |||||||
\(114\) | −195.381 | −0.160519 | ||||||||
\(115\) | 927.051 | 0.751721 | ||||||||
\(116\) | 218.126 | 0.174591 | ||||||||
\(117\) | −215.279 | −0.170107 | ||||||||
\(118\) | 440.582 | 0.343719 | ||||||||
\(119\) | −916.456 | −0.705978 | ||||||||
\(120\) | −161.036 | −0.122505 | ||||||||
\(121\) | 25.6407 | 0.0192643 | ||||||||
\(122\) | 262.558 | 0.194844 | ||||||||
\(123\) | −35.4208 | −0.0259657 | ||||||||
\(124\) | 789.552 | 0.571805 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 90.7108 | 0.0641362 | ||||||||
\(127\) | 903.124 | 0.631018 | 0.315509 | − | 0.948923i | \(-0.397825\pi\) | ||||
0.315509 | + | 0.948923i | \(0.397825\pi\) | |||||||
\(128\) | 1212.28 | 0.837122 | ||||||||
\(129\) | 183.150 | 0.125004 | ||||||||
\(130\) | 82.7229 | 0.0558098 | ||||||||
\(131\) | −685.958 | −0.457499 | −0.228750 | − | 0.973485i | \(-0.573464\pi\) | ||||
−0.228750 | + | 0.973485i | \(0.573464\pi\) | |||||||
\(132\) | 831.120 | 0.548028 | ||||||||
\(133\) | 1372.10 | 0.894558 | ||||||||
\(134\) | 431.138 | 0.277945 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 675.187 | 0.425712 | ||||||||
\(137\) | −1152.95 | −0.718999 | −0.359500 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359500 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(138\) | 384.726 | 0.237319 | ||||||||
\(139\) | −438.465 | −0.267555 | −0.133777 | − | 0.991011i | \(-0.542711\pi\) | ||||
−0.133777 | + | 0.991011i | \(0.542711\pi\) | |||||||
\(140\) | 548.025 | 0.330833 | ||||||||
\(141\) | −844.279 | −0.504263 | ||||||||
\(142\) | −206.738 | −0.122176 | ||||||||
\(143\) | −881.032 | −0.515214 | ||||||||
\(144\) | 474.725 | 0.274725 | ||||||||
\(145\) | −145.000 | −0.0830455 | ||||||||
\(146\) | 362.518 | 0.205495 | ||||||||
\(147\) | 391.968 | 0.219925 | ||||||||
\(148\) | 1954.11 | 1.08532 | ||||||||
\(149\) | −405.570 | −0.222991 | −0.111495 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111495 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(150\) | 51.8749 | 0.0282371 | ||||||||
\(151\) | −78.9559 | −0.0425519 | −0.0212760 | − | 0.999774i | \(-0.506773\pi\) | ||||
−0.0212760 | + | 0.999774i | \(0.506773\pi\) | |||||||
\(152\) | −1010.88 | −0.539428 | ||||||||
\(153\) | 566.023 | 0.299087 | ||||||||
\(154\) | 371.235 | 0.194253 | ||||||||
\(155\) | −524.856 | −0.271984 | ||||||||
\(156\) | −539.748 | −0.277015 | ||||||||
\(157\) | 314.869 | 0.160059 | 0.0800296 | − | 0.996792i | \(-0.474499\pi\) | ||||
0.0800296 | + | 0.996792i | \(0.474499\pi\) | |||||||
\(158\) | −389.590 | −0.196166 | ||||||||
\(159\) | 512.537 | 0.255640 | ||||||||
\(160\) | −611.848 | −0.302318 | ||||||||
\(161\) | −2701.80 | −1.32256 | ||||||||
\(162\) | −56.0249 | −0.0271712 | ||||||||
\(163\) | 816.812 | 0.392501 | 0.196251 | − | 0.980554i | \(-0.437123\pi\) | ||||
0.196251 | + | 0.980554i | \(0.437123\pi\) | |||||||
\(164\) | −88.8070 | −0.0422845 | ||||||||
\(165\) | −552.489 | −0.260674 | ||||||||
\(166\) | 612.361 | 0.286316 | ||||||||
\(167\) | −1364.36 | −0.632200 | −0.316100 | − | 0.948726i | \(-0.602374\pi\) | ||||
−0.316100 | + | 0.948726i | \(0.602374\pi\) | |||||||
\(168\) | 469.325 | 0.215531 | ||||||||
\(169\) | −1624.84 | −0.739571 | ||||||||
\(170\) | −217.499 | −0.0981261 | ||||||||
\(171\) | −847.439 | −0.378978 | ||||||||
\(172\) | 459.194 | 0.203565 | ||||||||
\(173\) | 430.857 | 0.189350 | 0.0946748 | − | 0.995508i | \(-0.469819\pi\) | ||||
0.0946748 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(174\) | −60.1749 | −0.0262175 | ||||||||
\(175\) | −364.301 | −0.157363 | ||||||||
\(176\) | 1942.82 | 0.832076 | ||||||||
\(177\) | 1910.96 | 0.811506 | ||||||||
\(178\) | 309.625 | 0.130379 | ||||||||
\(179\) | −3192.64 | −1.33312 | −0.666561 | − | 0.745451i | \(-0.732234\pi\) | ||||
−0.666561 | + | 0.745451i | \(0.732234\pi\) | |||||||
\(180\) | −338.472 | −0.140157 | ||||||||
\(181\) | −621.160 | −0.255085 | −0.127543 | − | 0.991833i | \(-0.540709\pi\) | ||||
−0.127543 | + | 0.991833i | \(0.540709\pi\) | |||||||
\(182\) | −241.088 | −0.0981903 | ||||||||
\(183\) | 1138.81 | 0.460017 | ||||||||
\(184\) | 1990.52 | 0.797517 | ||||||||
\(185\) | −1299.00 | −0.516239 | ||||||||
\(186\) | −217.815 | −0.0858655 | ||||||||
\(187\) | 2316.46 | 0.905861 | ||||||||
\(188\) | −2116.78 | −0.821179 | ||||||||
\(189\) | 393.445 | 0.151423 | ||||||||
\(190\) | 325.636 | 0.124337 | ||||||||
\(191\) | 2943.37 | 1.11505 | 0.557526 | − | 0.830160i | \(-0.311751\pi\) | ||||
0.557526 | + | 0.830160i | \(0.311751\pi\) | |||||||
\(192\) | 1012.02 | 0.380396 | ||||||||
\(193\) | 3259.79 | 1.21578 | 0.607889 | − | 0.794022i | \(-0.292017\pi\) | ||||
0.607889 | + | 0.794022i | \(0.292017\pi\) | |||||||
\(194\) | 386.568 | 0.143062 | ||||||||
\(195\) | 358.799 | 0.131765 | ||||||||
\(196\) | 982.741 | 0.358142 | ||||||||
\(197\) | 2372.35 | 0.857983 | 0.428992 | − | 0.903308i | \(-0.358869\pi\) | ||||
0.428992 | + | 0.903308i | \(0.358869\pi\) | |||||||
\(198\) | −229.283 | −0.0822950 | ||||||||
\(199\) | −1828.75 | −0.651441 | −0.325721 | − | 0.945466i | \(-0.605607\pi\) | ||||
−0.325721 | + | 0.945466i | \(0.605607\pi\) | |||||||
\(200\) | 268.394 | 0.0948916 | ||||||||
\(201\) | 1870.00 | 0.656216 | ||||||||
\(202\) | 787.657 | 0.274353 | ||||||||
\(203\) | 422.589 | 0.146108 | ||||||||
\(204\) | 1419.13 | 0.487055 | ||||||||
\(205\) | 59.0347 | 0.0201130 | ||||||||
\(206\) | −697.416 | −0.235880 | ||||||||
\(207\) | 1668.69 | 0.560300 | ||||||||
\(208\) | −1261.71 | −0.420595 | ||||||||
\(209\) | −3468.15 | −1.14783 | ||||||||
\(210\) | −151.185 | −0.0496797 | ||||||||
\(211\) | 4223.45 | 1.37798 | 0.688991 | − | 0.724770i | \(-0.258054\pi\) | ||||
0.688991 | + | 0.724770i | \(0.258054\pi\) | |||||||
\(212\) | 1285.03 | 0.416304 | ||||||||
\(213\) | −896.694 | −0.288453 | ||||||||
\(214\) | −97.1832 | −0.0310435 | ||||||||
\(215\) | −305.251 | −0.0968275 | ||||||||
\(216\) | −289.865 | −0.0913095 | ||||||||
\(217\) | 1529.65 | 0.478521 | ||||||||
\(218\) | 588.282 | 0.182768 | ||||||||
\(219\) | 1572.37 | 0.485164 | ||||||||
\(220\) | −1385.20 | −0.424501 | ||||||||
\(221\) | −1504.36 | −0.457891 | ||||||||
\(222\) | −539.083 | −0.162977 | ||||||||
\(223\) | −327.670 | −0.0983964 | −0.0491982 | − | 0.998789i | \(-0.515667\pi\) | ||||
−0.0491982 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(224\) | 1783.17 | 0.531889 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −1280.44 | −0.376873 | ||||||||
\(227\) | 3662.12 | 1.07076 | 0.535382 | − | 0.844610i | \(-0.320168\pi\) | ||||
0.535382 | + | 0.844610i | \(0.320168\pi\) | |||||||
\(228\) | −2124.70 | −0.617156 | ||||||||
\(229\) | −6562.57 | −1.89374 | −0.946871 | − | 0.321613i | \(-0.895775\pi\) | ||||
−0.946871 | + | 0.321613i | \(0.895775\pi\) | |||||||
\(230\) | −641.210 | −0.183827 | ||||||||
\(231\) | 1610.18 | 0.458623 | ||||||||
\(232\) | −311.337 | −0.0881046 | ||||||||
\(233\) | 2490.28 | 0.700189 | 0.350094 | − | 0.936714i | \(-0.386150\pi\) | ||||
0.350094 | + | 0.936714i | \(0.386150\pi\) | |||||||
\(234\) | 148.901 | 0.0415982 | ||||||||
\(235\) | 1407.13 | 0.390601 | ||||||||
\(236\) | 4791.16 | 1.32152 | ||||||||
\(237\) | −1689.79 | −0.463138 | ||||||||
\(238\) | 633.881 | 0.172640 | ||||||||
\(239\) | −3584.40 | −0.970106 | −0.485053 | − | 0.874485i | \(-0.661200\pi\) | ||||
−0.485053 | + | 0.874485i | \(0.661200\pi\) | |||||||
\(240\) | −791.208 | −0.212801 | ||||||||
\(241\) | −6543.94 | −1.74910 | −0.874548 | − | 0.484938i | \(-0.838842\pi\) | ||||
−0.874548 | + | 0.484938i | \(0.838842\pi\) | |||||||
\(242\) | −17.7348 | −0.00471090 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 2855.22 | 0.749126 | ||||||||
\(245\) | −653.279 | −0.170353 | ||||||||
\(246\) | 24.4994 | 0.00634968 | ||||||||
\(247\) | 2252.29 | 0.580203 | ||||||||
\(248\) | −1126.95 | −0.288553 | ||||||||
\(249\) | 2656.03 | 0.675979 | ||||||||
\(250\) | −86.4582 | −0.0218724 | ||||||||
\(251\) | 528.100 | 0.132802 | 0.0664011 | − | 0.997793i | \(-0.478848\pi\) | ||||
0.0664011 | + | 0.997793i | \(0.478848\pi\) | |||||||
\(252\) | 986.445 | 0.246588 | ||||||||
\(253\) | 6829.14 | 1.69701 | ||||||||
\(254\) | −624.660 | −0.154310 | ||||||||
\(255\) | −943.371 | −0.231671 | ||||||||
\(256\) | 1860.22 | 0.454155 | ||||||||
\(257\) | 5020.78 | 1.21863 | 0.609314 | − | 0.792929i | \(-0.291445\pi\) | ||||
0.609314 | + | 0.792929i | \(0.291445\pi\) | |||||||
\(258\) | −126.679 | −0.0305685 | ||||||||
\(259\) | 3785.81 | 0.908257 | ||||||||
\(260\) | 899.579 | 0.214575 | ||||||||
\(261\) | −261.000 | −0.0618984 | ||||||||
\(262\) | 474.453 | 0.111877 | ||||||||
\(263\) | −422.212 | −0.0989913 | −0.0494957 | − | 0.998774i | \(-0.515761\pi\) | ||||
−0.0494957 | + | 0.998774i | \(0.515761\pi\) | |||||||
\(264\) | −1186.28 | −0.276554 | ||||||||
\(265\) | −854.228 | −0.198018 | ||||||||
\(266\) | −949.035 | −0.218756 | ||||||||
\(267\) | 1342.96 | 0.307818 | ||||||||
\(268\) | 4688.46 | 1.06863 | ||||||||
\(269\) | −1777.19 | −0.402815 | −0.201407 | − | 0.979508i | \(-0.564551\pi\) | ||||
−0.201407 | + | 0.979508i | \(0.564551\pi\) | |||||||
\(270\) | 93.3749 | 0.0210467 | ||||||||
\(271\) | −1465.51 | −0.328499 | −0.164250 | − | 0.986419i | \(-0.552520\pi\) | ||||
−0.164250 | + | 0.986419i | \(0.552520\pi\) | |||||||
\(272\) | 3317.35 | 0.739499 | ||||||||
\(273\) | −1045.68 | −0.231823 | ||||||||
\(274\) | 797.454 | 0.175825 | ||||||||
\(275\) | 920.815 | 0.201917 | ||||||||
\(276\) | 4183.74 | 0.912434 | ||||||||
\(277\) | −6081.50 | −1.31914 | −0.659570 | − | 0.751643i | \(-0.729262\pi\) | ||||
−0.659570 | + | 0.751643i | \(0.729262\pi\) | |||||||
\(278\) | 303.271 | 0.0654281 | ||||||||
\(279\) | −944.742 | −0.202725 | ||||||||
\(280\) | −782.209 | −0.166950 | ||||||||
\(281\) | −1194.50 | −0.253587 | −0.126794 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126794 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(282\) | 583.959 | 0.123313 | ||||||||
\(283\) | 3827.53 | 0.803968 | 0.401984 | − | 0.915647i | \(-0.368321\pi\) | ||||
0.401984 | + | 0.915647i | \(0.368321\pi\) | |||||||
\(284\) | −2248.19 | −0.469738 | ||||||||
\(285\) | 1412.40 | 0.293555 | ||||||||
\(286\) | 609.380 | 0.125991 | ||||||||
\(287\) | −172.051 | −0.0353862 | ||||||||
\(288\) | −1101.33 | −0.225334 | ||||||||
\(289\) | −957.668 | −0.194925 | ||||||||
\(290\) | 100.292 | 0.0203080 | ||||||||
\(291\) | 1676.68 | 0.337763 | ||||||||
\(292\) | 3942.25 | 0.790077 | ||||||||
\(293\) | −6821.00 | −1.36002 | −0.680012 | − | 0.733201i | \(-0.738025\pi\) | ||||
−0.680012 | + | 0.733201i | \(0.738025\pi\) | |||||||
\(294\) | −271.111 | −0.0537806 | ||||||||
\(295\) | −3184.93 | −0.628590 | ||||||||
\(296\) | −2789.14 | −0.547688 | ||||||||
\(297\) | −994.480 | −0.194295 | ||||||||
\(298\) | 280.519 | 0.0545303 | ||||||||
\(299\) | −4434.99 | −0.857801 | ||||||||
\(300\) | 564.120 | 0.108565 | ||||||||
\(301\) | 889.624 | 0.170356 | ||||||||
\(302\) | 54.6111 | 0.0104057 | ||||||||
\(303\) | 3416.35 | 0.647736 | ||||||||
\(304\) | −4966.67 | −0.937034 | ||||||||
\(305\) | −1898.02 | −0.356328 | ||||||||
\(306\) | −391.499 | −0.0731389 | ||||||||
\(307\) | −7350.74 | −1.36654 | −0.683272 | − | 0.730164i | \(-0.739444\pi\) | ||||
−0.683272 | + | 0.730164i | \(0.739444\pi\) | |||||||
\(308\) | 4037.04 | 0.746856 | ||||||||
\(309\) | −3024.94 | −0.556902 | ||||||||
\(310\) | 363.025 | 0.0665111 | ||||||||
\(311\) | 3393.14 | 0.618673 | 0.309337 | − | 0.950953i | \(-0.399893\pi\) | ||||
0.309337 | + | 0.950953i | \(0.399893\pi\) | |||||||
\(312\) | 770.395 | 0.139792 | ||||||||
\(313\) | −10732.3 | −1.93810 | −0.969049 | − | 0.246867i | \(-0.920599\pi\) | ||||
−0.969049 | + | 0.246867i | \(0.920599\pi\) | |||||||
\(314\) | −217.784 | −0.0391410 | ||||||||
\(315\) | −655.741 | −0.117292 | ||||||||
\(316\) | −4236.65 | −0.754209 | ||||||||
\(317\) | −8721.17 | −1.54520 | −0.772602 | − | 0.634890i | \(-0.781045\pi\) | ||||
−0.772602 | + | 0.634890i | \(0.781045\pi\) | |||||||
\(318\) | −354.504 | −0.0625145 | ||||||||
\(319\) | −1068.15 | −0.187475 | ||||||||
\(320\) | −1686.70 | −0.294654 | ||||||||
\(321\) | −421.518 | −0.0732923 | ||||||||
\(322\) | 1868.75 | 0.323420 | ||||||||
\(323\) | −5921.85 | −1.02013 | ||||||||
\(324\) | −609.249 | −0.104467 | ||||||||
\(325\) | −597.998 | −0.102064 | ||||||||
\(326\) | −564.961 | −0.0959825 | ||||||||
\(327\) | 2551.59 | 0.431508 | ||||||||
\(328\) | 126.756 | 0.0213383 | ||||||||
\(329\) | −4100.95 | −0.687212 | ||||||||
\(330\) | 382.138 | 0.0637454 | ||||||||
\(331\) | −6093.02 | −1.01179 | −0.505895 | − | 0.862595i | \(-0.668838\pi\) | ||||
−0.505895 | + | 0.862595i | \(0.668838\pi\) | |||||||
\(332\) | 6659.18 | 1.10081 | ||||||||
\(333\) | −2338.20 | −0.384782 | ||||||||
\(334\) | 943.682 | 0.154599 | ||||||||
\(335\) | −3116.66 | −0.508303 | ||||||||
\(336\) | 2305.90 | 0.374397 | ||||||||
\(337\) | −6306.92 | −1.01947 | −0.509733 | − | 0.860333i | \(-0.670256\pi\) | ||||
−0.509733 | + | 0.860333i | \(0.670256\pi\) | |||||||
\(338\) | 1123.85 | 0.180855 | ||||||||
\(339\) | −5553.70 | −0.889781 | ||||||||
\(340\) | −2365.22 | −0.377271 | ||||||||
\(341\) | −3866.37 | −0.614004 | ||||||||
\(342\) | 586.144 | 0.0926756 | ||||||||
\(343\) | 6902.13 | 1.08653 | ||||||||
\(344\) | −655.419 | −0.102726 | ||||||||
\(345\) | −2781.15 | −0.434007 | ||||||||
\(346\) | −298.009 | −0.0463037 | ||||||||
\(347\) | 11395.7 | 1.76298 | 0.881491 | − | 0.472201i | \(-0.156540\pi\) | ||||
0.881491 | + | 0.472201i | \(0.156540\pi\) | |||||||
\(348\) | −654.379 | −0.100800 | ||||||||
\(349\) | 8835.08 | 1.35510 | 0.677552 | − | 0.735475i | \(-0.263041\pi\) | ||||
0.677552 | + | 0.735475i | \(0.263041\pi\) | |||||||
\(350\) | 251.974 | 0.0384817 | ||||||||
\(351\) | 645.837 | 0.0982115 | ||||||||
\(352\) | −4507.19 | −0.682483 | ||||||||
\(353\) | −3390.75 | −0.511251 | −0.255626 | − | 0.966776i | \(-0.582281\pi\) | ||||
−0.255626 | + | 0.966776i | \(0.582281\pi\) | |||||||
\(354\) | −1321.75 | −0.198446 | ||||||||
\(355\) | 1494.49 | 0.223435 | ||||||||
\(356\) | 3367.06 | 0.501274 | ||||||||
\(357\) | 2749.37 | 0.407597 | ||||||||
\(358\) | 2208.24 | 0.326003 | ||||||||
\(359\) | −5160.27 | −0.758632 | −0.379316 | − | 0.925267i | \(-0.623841\pi\) | ||||
−0.379316 | + | 0.925267i | \(0.623841\pi\) | |||||||
\(360\) | 483.109 | 0.0707280 | ||||||||
\(361\) | 2007.08 | 0.292620 | ||||||||
\(362\) | 429.635 | 0.0623788 | ||||||||
\(363\) | −76.9222 | −0.0111222 | ||||||||
\(364\) | −2621.74 | −0.377518 | ||||||||
\(365\) | −2620.62 | −0.375807 | ||||||||
\(366\) | −787.675 | −0.112493 | ||||||||
\(367\) | 1110.17 | 0.157902 | 0.0789512 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789512 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(368\) | 9779.88 | 1.38536 | ||||||||
\(369\) | 106.262 | 0.0149913 | ||||||||
\(370\) | 898.472 | 0.126241 | ||||||||
\(371\) | 2489.57 | 0.348388 | ||||||||
\(372\) | −2368.66 | −0.330132 | ||||||||
\(373\) | 5801.22 | 0.805297 | 0.402648 | − | 0.915355i | \(-0.368090\pi\) | ||||
0.402648 | + | 0.915355i | \(0.368090\pi\) | |||||||
\(374\) | −1602.21 | −0.221520 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 3021.32 | 0.414396 | ||||||||
\(377\) | 693.677 | 0.0947644 | ||||||||
\(378\) | −272.132 | −0.0370290 | ||||||||
\(379\) | −12664.5 | −1.71644 | −0.858219 | − | 0.513284i | \(-0.828429\pi\) | ||||
−0.858219 | + | 0.513284i | \(0.828429\pi\) | |||||||
\(380\) | 3541.16 | 0.478047 | ||||||||
\(381\) | −2709.37 | −0.364318 | ||||||||
\(382\) | −2035.83 | −0.272675 | ||||||||
\(383\) | −13408.3 | −1.78885 | −0.894427 | − | 0.447215i | \(-0.852416\pi\) | ||||
−0.894427 | + | 0.447215i | \(0.852416\pi\) | |||||||
\(384\) | −3636.85 | −0.483313 | ||||||||
\(385\) | −2683.63 | −0.355248 | ||||||||
\(386\) | −2254.69 | −0.297307 | ||||||||
\(387\) | −549.451 | −0.0721710 | ||||||||
\(388\) | 4203.78 | 0.550038 | ||||||||
\(389\) | −4676.56 | −0.609540 | −0.304770 | − | 0.952426i | \(-0.598580\pi\) | ||||
−0.304770 | + | 0.952426i | \(0.598580\pi\) | |||||||
\(390\) | −248.169 | −0.0322218 | ||||||||
\(391\) | 11660.7 | 1.50820 | ||||||||
\(392\) | −1402.69 | −0.180731 | ||||||||
\(393\) | 2057.87 | 0.264137 | ||||||||
\(394\) | −1640.87 | −0.209812 | ||||||||
\(395\) | 2816.32 | 0.358745 | ||||||||
\(396\) | −2493.36 | −0.316404 | ||||||||
\(397\) | −5913.71 | −0.747608 | −0.373804 | − | 0.927508i | \(-0.621947\pi\) | ||||
−0.373804 | + | 0.927508i | \(0.621947\pi\) | |||||||
\(398\) | 1264.89 | 0.159304 | ||||||||
\(399\) | −4116.30 | −0.516473 | ||||||||
\(400\) | 1318.68 | 0.164835 | ||||||||
\(401\) | 7756.80 | 0.965975 | 0.482987 | − | 0.875627i | \(-0.339552\pi\) | ||||
0.482987 | + | 0.875627i | \(0.339552\pi\) | |||||||
\(402\) | −1293.41 | −0.160472 | ||||||||
\(403\) | 2510.90 | 0.310365 | ||||||||
\(404\) | 8565.46 | 1.05482 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −292.290 | −0.0357294 | ||||||||
\(407\) | −9569.09 | −1.16541 | ||||||||
\(408\) | −2025.56 | −0.245785 | ||||||||
\(409\) | 7674.37 | 0.927808 | 0.463904 | − | 0.885886i | \(-0.346448\pi\) | ||||
0.463904 | + | 0.885886i | \(0.346448\pi\) | |||||||
\(410\) | −40.8323 | −0.00491844 | ||||||||
\(411\) | 3458.84 | 0.415114 | ||||||||
\(412\) | −7584.13 | −0.906901 | ||||||||
\(413\) | 9282.19 | 1.10592 | ||||||||
\(414\) | −1154.18 | −0.137016 | ||||||||
\(415\) | −4426.71 | −0.523611 | ||||||||
\(416\) | 2927.07 | 0.344979 | ||||||||
\(417\) | 1315.39 | 0.154473 | ||||||||
\(418\) | 2398.80 | 0.280692 | ||||||||
\(419\) | 11316.2 | 1.31940 | 0.659702 | − | 0.751527i | \(-0.270682\pi\) | ||||
0.659702 | + | 0.751527i | \(0.270682\pi\) | |||||||
\(420\) | −1644.07 | −0.191006 | ||||||||
\(421\) | −15960.8 | −1.84770 | −0.923851 | − | 0.382753i | \(-0.874976\pi\) | ||||
−0.923851 | + | 0.382753i | \(0.874976\pi\) | |||||||
\(422\) | −2921.21 | −0.336973 | ||||||||
\(423\) | 2532.84 | 0.291136 | ||||||||
\(424\) | −1834.16 | −0.210081 | ||||||||
\(425\) | 1572.29 | 0.179452 | ||||||||
\(426\) | 620.213 | 0.0705385 | ||||||||
\(427\) | 5531.59 | 0.626914 | ||||||||
\(428\) | −1056.83 | −0.119355 | ||||||||
\(429\) | 2643.10 | 0.297459 | ||||||||
\(430\) | 211.131 | 0.0236783 | ||||||||
\(431\) | 9181.83 | 1.02616 | 0.513078 | − | 0.858342i | \(-0.328505\pi\) | ||||
0.513078 | + | 0.858342i | \(0.328505\pi\) | |||||||
\(432\) | −1424.18 | −0.158613 | ||||||||
\(433\) | 312.822 | 0.0347188 | 0.0173594 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173594 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(434\) | −1058.00 | −0.117018 | ||||||||
\(435\) | 435.000 | 0.0479463 | ||||||||
\(436\) | 6397.34 | 0.702700 | ||||||||
\(437\) | −17458.2 | −1.91107 | ||||||||
\(438\) | −1087.56 | −0.118642 | ||||||||
\(439\) | −8018.14 | −0.871720 | −0.435860 | − | 0.900014i | \(-0.643556\pi\) | ||||
−0.435860 | + | 0.900014i | \(0.643556\pi\) | |||||||
\(440\) | 1977.13 | 0.214218 | ||||||||
\(441\) | −1175.90 | −0.126974 | ||||||||
\(442\) | 1040.51 | 0.111973 | ||||||||
\(443\) | 553.480 | 0.0593603 | 0.0296802 | − | 0.999559i | \(-0.490551\pi\) | ||||
0.0296802 | + | 0.999559i | \(0.490551\pi\) | |||||||
\(444\) | −5862.32 | −0.626607 | ||||||||
\(445\) | −2238.26 | −0.238435 | ||||||||
\(446\) | 226.638 | 0.0240619 | ||||||||
\(447\) | 1216.71 | 0.128744 | ||||||||
\(448\) | 4915.71 | 0.518406 | ||||||||
\(449\) | −12055.2 | −1.26708 | −0.633540 | − | 0.773710i | \(-0.718399\pi\) | ||||
−0.633540 | + | 0.773710i | \(0.718399\pi\) | |||||||
\(450\) | −155.625 | −0.0163027 | ||||||||
\(451\) | 434.880 | 0.0454051 | ||||||||
\(452\) | −13924.2 | −1.44899 | ||||||||
\(453\) | 236.868 | 0.0245674 | ||||||||
\(454\) | −2532.96 | −0.261845 | ||||||||
\(455\) | 1742.81 | 0.179569 | ||||||||
\(456\) | 3032.63 | 0.311439 | ||||||||
\(457\) | −268.261 | −0.0274589 | −0.0137295 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137295 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(458\) | 4539.11 | 0.463097 | ||||||||
\(459\) | −1698.07 | −0.172678 | ||||||||
\(460\) | −6972.91 | −0.706768 | ||||||||
\(461\) | 3621.49 | 0.365877 | 0.182939 | − | 0.983124i | \(-0.441439\pi\) | ||||
0.182939 | + | 0.983124i | \(0.441439\pi\) | |||||||
\(462\) | −1113.70 | −0.112152 | ||||||||
\(463\) | −7751.51 | −0.778063 | −0.389031 | − | 0.921225i | \(-0.627190\pi\) | ||||
−0.389031 | + | 0.921225i | \(0.627190\pi\) | |||||||
\(464\) | −1529.67 | −0.153046 | ||||||||
\(465\) | 1574.57 | 0.157030 | ||||||||
\(466\) | −1722.44 | −0.171225 | ||||||||
\(467\) | 8838.90 | 0.875836 | 0.437918 | − | 0.899015i | \(-0.355716\pi\) | ||||
0.437918 | + | 0.899015i | \(0.355716\pi\) | |||||||
\(468\) | 1619.24 | 0.159935 | ||||||||
\(469\) | 9083.22 | 0.894295 | ||||||||
\(470\) | −973.265 | −0.0955178 | ||||||||
\(471\) | −944.607 | −0.0924102 | ||||||||
\(472\) | −6838.54 | −0.666884 | ||||||||
\(473\) | −2248.63 | −0.218588 | ||||||||
\(474\) | 1168.77 | 0.113256 | ||||||||
\(475\) | −2354.00 | −0.227387 | ||||||||
\(476\) | 6893.21 | 0.663760 | ||||||||
\(477\) | −1537.61 | −0.147594 | ||||||||
\(478\) | 2479.20 | 0.237230 | ||||||||
\(479\) | −9904.02 | −0.944731 | −0.472366 | − | 0.881403i | \(-0.656600\pi\) | ||||
−0.472366 | + | 0.881403i | \(0.656600\pi\) | |||||||
\(480\) | 1835.54 | 0.174543 | ||||||||
\(481\) | 6214.38 | 0.589088 | ||||||||
\(482\) | 4526.22 | 0.427726 | ||||||||
\(483\) | 8105.41 | 0.763580 | ||||||||
\(484\) | −192.859 | −0.0181123 | ||||||||
\(485\) | −2794.47 | −0.261630 | ||||||||
\(486\) | 168.075 | 0.0156873 | ||||||||
\(487\) | 799.412 | 0.0743836 | 0.0371918 | − | 0.999308i | \(-0.488159\pi\) | ||||
0.0371918 | + | 0.999308i | \(0.488159\pi\) | |||||||
\(488\) | −4075.33 | −0.378036 | ||||||||
\(489\) | −2450.44 | −0.226611 | ||||||||
\(490\) | 451.851 | 0.0416583 | ||||||||
\(491\) | −10013.3 | −0.920351 | −0.460176 | − | 0.887828i | \(-0.652214\pi\) | ||||
−0.460176 | + | 0.887828i | \(0.652214\pi\) | |||||||
\(492\) | 266.421 | 0.0244130 | ||||||||
\(493\) | −1823.85 | −0.166617 | ||||||||
\(494\) | −1557.84 | −0.141883 | ||||||||
\(495\) | 1657.47 | 0.150500 | ||||||||
\(496\) | −5536.94 | −0.501242 | ||||||||
\(497\) | −4355.55 | −0.393105 | ||||||||
\(498\) | −1837.08 | −0.165304 | ||||||||
\(499\) | 2556.35 | 0.229335 | 0.114667 | − | 0.993404i | \(-0.463420\pi\) | ||||
0.114667 | + | 0.993404i | \(0.463420\pi\) | |||||||
\(500\) | −940.200 | −0.0840940 | ||||||||
\(501\) | 4093.08 | 0.365001 | ||||||||
\(502\) | −365.269 | −0.0324756 | ||||||||
\(503\) | 11520.2 | 1.02120 | 0.510598 | − | 0.859820i | \(-0.329424\pi\) | ||||
0.510598 | + | 0.859820i | \(0.329424\pi\) | |||||||
\(504\) | −1407.98 | −0.124437 | ||||||||
\(505\) | −5693.91 | −0.501734 | ||||||||
\(506\) | −4723.48 | −0.414989 | ||||||||
\(507\) | 4874.51 | 0.426992 | ||||||||
\(508\) | −6792.94 | −0.593283 | ||||||||
\(509\) | 8055.10 | 0.701446 | 0.350723 | − | 0.936479i | \(-0.385936\pi\) | ||||
0.350723 | + | 0.936479i | \(0.385936\pi\) | |||||||
\(510\) | 652.498 | 0.0566531 | ||||||||
\(511\) | 7637.55 | 0.661184 | ||||||||
\(512\) | −10984.9 | −0.948181 | ||||||||
\(513\) | 2542.32 | 0.218803 | ||||||||
\(514\) | −3472.70 | −0.298004 | ||||||||
\(515\) | 5041.57 | 0.431375 | ||||||||
\(516\) | −1377.58 | −0.117529 | ||||||||
\(517\) | 10365.7 | 0.881782 | ||||||||
\(518\) | −2618.51 | −0.222106 | ||||||||
\(519\) | −1292.57 | −0.109321 | ||||||||
\(520\) | −1283.99 | −0.108282 | ||||||||
\(521\) | 22383.5 | 1.88222 | 0.941111 | − | 0.338097i | \(-0.109783\pi\) | ||||
0.941111 | + | 0.338097i | \(0.109783\pi\) | |||||||
\(522\) | 180.525 | 0.0151367 | ||||||||
\(523\) | 5260.45 | 0.439816 | 0.219908 | − | 0.975521i | \(-0.429424\pi\) | ||||
0.219908 | + | 0.975521i | \(0.429424\pi\) | |||||||
\(524\) | 5159.50 | 0.430141 | ||||||||
\(525\) | 1092.90 | 0.0908537 | ||||||||
\(526\) | 292.030 | 0.0242074 | ||||||||
\(527\) | −6601.79 | −0.545690 | ||||||||
\(528\) | −5828.45 | −0.480399 | ||||||||
\(529\) | 22210.0 | 1.82543 | ||||||||
\(530\) | 590.840 | 0.0484235 | ||||||||
\(531\) | −5732.88 | −0.468523 | ||||||||
\(532\) | −10320.4 | −0.841063 | ||||||||
\(533\) | −282.421 | −0.0229512 | ||||||||
\(534\) | −928.876 | −0.0752742 | ||||||||
\(535\) | 702.530 | 0.0567720 | ||||||||
\(536\) | −6691.95 | −0.539269 | ||||||||
\(537\) | 9577.91 | 0.769678 | ||||||||
\(538\) | 1229.22 | 0.0985046 | ||||||||
\(539\) | −4812.40 | −0.384573 | ||||||||
\(540\) | 1015.42 | 0.0809195 | ||||||||
\(541\) | −15052.8 | −1.19625 | −0.598123 | − | 0.801404i | \(-0.704087\pi\) | ||||
−0.598123 | + | 0.801404i | \(0.704087\pi\) | |||||||
\(542\) | 1013.64 | 0.0803315 | ||||||||
\(543\) | 1863.48 | 0.147274 | ||||||||
\(544\) | −7695.99 | −0.606550 | ||||||||
\(545\) | −4252.65 | −0.334245 | ||||||||
\(546\) | 723.264 | 0.0566902 | ||||||||
\(547\) | 13743.0 | 1.07424 | 0.537121 | − | 0.843505i | \(-0.319512\pi\) | ||||
0.537121 | + | 0.843505i | \(0.319512\pi\) | |||||||
\(548\) | 8672.00 | 0.676003 | ||||||||
\(549\) | −3416.43 | −0.265591 | ||||||||
\(550\) | −636.896 | −0.0493770 | ||||||||
\(551\) | 2730.64 | 0.211123 | ||||||||
\(552\) | −5971.56 | −0.460446 | ||||||||
\(553\) | −8207.90 | −0.631167 | ||||||||
\(554\) | 4206.36 | 0.322584 | ||||||||
\(555\) | 3896.99 | 0.298051 | ||||||||
\(556\) | 3297.96 | 0.251555 | ||||||||
\(557\) | 23296.7 | 1.77219 | 0.886097 | − | 0.463500i | \(-0.153407\pi\) | ||||
0.886097 | + | 0.463500i | \(0.153407\pi\) | |||||||
\(558\) | 653.446 | 0.0495745 | ||||||||
\(559\) | 1460.31 | 0.110491 | ||||||||
\(560\) | −3843.17 | −0.290006 | ||||||||
\(561\) | −6949.37 | −0.522999 | ||||||||
\(562\) | 826.196 | 0.0620124 | ||||||||
\(563\) | 6823.79 | 0.510814 | 0.255407 | − | 0.966834i | \(-0.417791\pi\) | ||||
0.255407 | + | 0.966834i | \(0.417791\pi\) | |||||||
\(564\) | 6350.33 | 0.474108 | ||||||||
\(565\) | 9256.17 | 0.689221 | ||||||||
\(566\) | −2647.37 | −0.196603 | ||||||||
\(567\) | −1180.33 | −0.0874240 | ||||||||
\(568\) | 3208.90 | 0.237046 | ||||||||
\(569\) | 17974.8 | 1.32433 | 0.662166 | − | 0.749358i | \(-0.269638\pi\) | ||||
0.662166 | + | 0.749358i | \(0.269638\pi\) | |||||||
\(570\) | −976.907 | −0.0717862 | ||||||||
\(571\) | 22031.6 | 1.61470 | 0.807350 | − | 0.590072i | \(-0.200901\pi\) | ||||
0.807350 | + | 0.590072i | \(0.200901\pi\) | |||||||
\(572\) | 6626.77 | 0.484404 | ||||||||
\(573\) | −8830.11 | −0.643775 | ||||||||
\(574\) | 119.002 | 0.00865338 | ||||||||
\(575\) | 4635.26 | 0.336180 | ||||||||
\(576\) | −3036.05 | −0.219622 | ||||||||
\(577\) | 14520.1 | 1.04762 | 0.523811 | − | 0.851834i | \(-0.324510\pi\) | ||||
0.523811 | + | 0.851834i | \(0.324510\pi\) | |||||||
\(578\) | 662.386 | 0.0476672 | ||||||||
\(579\) | −9779.38 | −0.701929 | ||||||||
\(580\) | 1090.63 | 0.0780793 | ||||||||
\(581\) | 12901.2 | 0.921227 | ||||||||
\(582\) | −1159.71 | −0.0825968 | ||||||||
\(583\) | −6292.69 | −0.447027 | ||||||||
\(584\) | −5626.87 | −0.398701 | ||||||||
\(585\) | −1076.40 | −0.0760743 | ||||||||
\(586\) | 4717.85 | 0.332581 | ||||||||
\(587\) | −998.184 | −0.0701865 | −0.0350932 | − | 0.999384i | \(-0.511173\pi\) | ||||
−0.0350932 | + | 0.999384i | \(0.511173\pi\) | |||||||
\(588\) | −2948.22 | −0.206773 | ||||||||
\(589\) | 9884.08 | 0.691454 | ||||||||
\(590\) | 2202.91 | 0.153716 | ||||||||
\(591\) | −7117.04 | −0.495357 | ||||||||
\(592\) | −13703.7 | −0.951383 | ||||||||
\(593\) | 3431.22 | 0.237611 | 0.118806 | − | 0.992918i | \(-0.462093\pi\) | ||||
0.118806 | + | 0.992918i | \(0.462093\pi\) | |||||||
\(594\) | 687.848 | 0.0475130 | ||||||||
\(595\) | −4582.28 | −0.315723 | ||||||||
\(596\) | 3050.54 | 0.209656 | ||||||||
\(597\) | 5486.26 | 0.376110 | ||||||||
\(598\) | 3067.53 | 0.209767 | ||||||||
\(599\) | −21059.5 | −1.43651 | −0.718255 | − | 0.695780i | \(-0.755059\pi\) | ||||
−0.718255 | + | 0.695780i | \(0.755059\pi\) | |||||||
\(600\) | −805.182 | −0.0547857 | ||||||||
\(601\) | 8534.75 | 0.579267 | 0.289634 | − | 0.957138i | \(-0.406467\pi\) | ||||
0.289634 | + | 0.957138i | \(0.406467\pi\) | |||||||
\(602\) | −615.323 | −0.0416589 | ||||||||
\(603\) | −5609.99 | −0.378867 | ||||||||
\(604\) | 593.874 | 0.0400073 | ||||||||
\(605\) | 128.204 | 0.00861524 | ||||||||
\(606\) | −2362.97 | −0.158398 | ||||||||
\(607\) | −17101.7 | −1.14355 | −0.571776 | − | 0.820409i | \(-0.693746\pi\) | ||||
−0.571776 | + | 0.820409i | \(0.693746\pi\) | |||||||
\(608\) | 11522.3 | 0.768571 | ||||||||
\(609\) | −1267.77 | −0.0843555 | ||||||||
\(610\) | 1312.79 | 0.0871367 | ||||||||
\(611\) | −6731.69 | −0.445720 | ||||||||
\(612\) | −4257.40 | −0.281201 | ||||||||
\(613\) | −1048.59 | −0.0690897 | −0.0345449 | − | 0.999403i | \(-0.510998\pi\) | ||||
−0.0345449 | + | 0.999403i | \(0.510998\pi\) | |||||||
\(614\) | 5084.26 | 0.334176 | ||||||||
\(615\) | −177.104 | −0.0116122 | ||||||||
\(616\) | −5762.16 | −0.376890 | ||||||||
\(617\) | 2212.12 | 0.144338 | 0.0721689 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721689 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(618\) | 2092.25 | 0.136185 | ||||||||
\(619\) | 25602.7 | 1.66246 | 0.831228 | − | 0.555932i | \(-0.187638\pi\) | ||||
0.831228 | + | 0.555932i | \(0.187638\pi\) | |||||||
\(620\) | 3947.76 | 0.255719 | ||||||||
\(621\) | −5006.08 | −0.323489 | ||||||||
\(622\) | −2346.92 | −0.151291 | ||||||||
\(623\) | 6523.19 | 0.419496 | ||||||||
\(624\) | 3785.13 | 0.242831 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 7423.16 | 0.473944 | ||||||||
\(627\) | 10404.5 | 0.662702 | ||||||||
\(628\) | −2368.32 | −0.150488 | ||||||||
\(629\) | −16339.2 | −1.03575 | ||||||||
\(630\) | 453.554 | 0.0286826 | ||||||||
\(631\) | −25127.0 | −1.58524 | −0.792622 | − | 0.609713i | \(-0.791285\pi\) | ||||
−0.792622 | + | 0.609713i | \(0.791285\pi\) | |||||||
\(632\) | 6047.07 | 0.380600 | ||||||||
\(633\) | −12670.3 | −0.795578 | ||||||||
\(634\) | 6032.14 | 0.377866 | ||||||||
\(635\) | 4515.62 | 0.282200 | ||||||||
\(636\) | −3855.10 | −0.240353 | ||||||||
\(637\) | 3125.28 | 0.194392 | ||||||||
\(638\) | 738.800 | 0.0458454 | ||||||||
\(639\) | 2690.08 | 0.166538 | ||||||||
\(640\) | 6061.41 | 0.374372 | ||||||||
\(641\) | 2231.80 | 0.137521 | 0.0687605 | − | 0.997633i | \(-0.478096\pi\) | ||||
0.0687605 | + | 0.997633i | \(0.478096\pi\) | |||||||
\(642\) | 291.550 | 0.0179230 | ||||||||
\(643\) | −15105.0 | −0.926415 | −0.463207 | − | 0.886250i | \(-0.653301\pi\) | ||||
−0.463207 | + | 0.886250i | \(0.653301\pi\) | |||||||
\(644\) | 20321.9 | 1.24347 | ||||||||
\(645\) | 915.752 | 0.0559034 | ||||||||
\(646\) | 4095.94 | 0.249462 | ||||||||
\(647\) | 21013.9 | 1.27688 | 0.638441 | − | 0.769671i | \(-0.279580\pi\) | ||||
0.638441 | + | 0.769671i | \(0.279580\pi\) | |||||||
\(648\) | 869.596 | 0.0527176 | ||||||||
\(649\) | −23461.9 | −1.41904 | ||||||||
\(650\) | 413.614 | 0.0249589 | ||||||||
\(651\) | −4588.94 | −0.276274 | ||||||||
\(652\) | −6143.73 | −0.369029 | ||||||||
\(653\) | 25780.5 | 1.54498 | 0.772489 | − | 0.635028i | \(-0.219011\pi\) | ||||
0.772489 | + | 0.635028i | \(0.219011\pi\) | |||||||
\(654\) | −1764.85 | −0.105521 | ||||||||
\(655\) | −3429.79 | −0.204600 | ||||||||
\(656\) | 622.783 | 0.0370665 | ||||||||
\(657\) | −4717.11 | −0.280110 | ||||||||
\(658\) | 2836.49 | 0.168051 | ||||||||
\(659\) | 14065.8 | 0.831448 | 0.415724 | − | 0.909491i | \(-0.363528\pi\) | ||||
0.415724 | + | 0.909491i | \(0.363528\pi\) | |||||||
\(660\) | 4155.60 | 0.245086 | ||||||||
\(661\) | −13363.3 | −0.786342 | −0.393171 | − | 0.919465i | \(-0.628622\pi\) | ||||
−0.393171 | + | 0.919465i | \(0.628622\pi\) | |||||||
\(662\) | 4214.33 | 0.247424 | ||||||||
\(663\) | 4513.07 | 0.264364 | ||||||||
\(664\) | −9504.81 | −0.555510 | ||||||||
\(665\) | 6860.50 | 0.400058 | ||||||||
\(666\) | 1617.25 | 0.0940948 | ||||||||
\(667\) | −5376.90 | −0.312135 | ||||||||
\(668\) | 10262.2 | 0.594395 | ||||||||
\(669\) | 983.010 | 0.0568092 | ||||||||
\(670\) | 2155.69 | 0.124301 | ||||||||
\(671\) | −13981.8 | −0.804412 | ||||||||
\(672\) | −5349.52 | −0.307087 | ||||||||
\(673\) | −17727.5 | −1.01537 | −0.507686 | − | 0.861542i | \(-0.669499\pi\) | ||||
−0.507686 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(674\) | 4362.28 | 0.249301 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 12221.4 | 0.695345 | ||||||||
\(677\) | 15776.1 | 0.895605 | 0.447803 | − | 0.894132i | \(-0.352207\pi\) | ||||
0.447803 | + | 0.894132i | \(0.352207\pi\) | |||||||
\(678\) | 3841.31 | 0.217588 | ||||||||
\(679\) | 8144.23 | 0.460305 | ||||||||
\(680\) | 3375.94 | 0.190384 | ||||||||
\(681\) | −10986.4 | −0.618206 | ||||||||
\(682\) | 2674.23 | 0.150149 | ||||||||
\(683\) | 14482.3 | 0.811350 | 0.405675 | − | 0.914018i | \(-0.367037\pi\) | ||||
0.405675 | + | 0.914018i | \(0.367037\pi\) | |||||||
\(684\) | 6374.09 | 0.356315 | ||||||||
\(685\) | −5764.73 | −0.321546 | ||||||||
\(686\) | −4773.97 | −0.265701 | ||||||||
\(687\) | 19687.7 | 1.09335 | ||||||||
\(688\) | −3220.22 | −0.178445 | ||||||||
\(689\) | 4086.61 | 0.225961 | ||||||||
\(690\) | 1923.63 | 0.106132 | ||||||||
\(691\) | 19721.5 | 1.08573 | 0.542867 | − | 0.839819i | \(-0.317339\pi\) | ||||
0.542867 | + | 0.839819i | \(0.317339\pi\) | |||||||
\(692\) | −3240.74 | −0.178026 | ||||||||
\(693\) | −4830.53 | −0.264786 | ||||||||
\(694\) | −7882.04 | −0.431121 | ||||||||
\(695\) | −2192.32 | −0.119654 | ||||||||
\(696\) | 934.011 | 0.0508672 | ||||||||
\(697\) | 742.555 | 0.0403533 | ||||||||
\(698\) | −6110.92 | −0.331378 | ||||||||
\(699\) | −7470.85 | −0.404254 | ||||||||
\(700\) | 2740.12 | 0.147953 | ||||||||
\(701\) | 2004.45 | 0.107998 | 0.0539992 | − | 0.998541i | \(-0.482803\pi\) | ||||
0.0539992 | + | 0.998541i | \(0.482803\pi\) | |||||||
\(702\) | −446.704 | −0.0240167 | ||||||||
\(703\) | 24462.7 | 1.31241 | ||||||||
\(704\) | −12425.1 | −0.665181 | ||||||||
\(705\) | −4221.39 | −0.225513 | ||||||||
\(706\) | 2345.27 | 0.125022 | ||||||||
\(707\) | 16594.4 | 0.882738 | ||||||||
\(708\) | −14373.5 | −0.762978 | ||||||||
\(709\) | 10037.8 | 0.531705 | 0.265853 | − | 0.964014i | \(-0.414347\pi\) | ||||
0.265853 | + | 0.964014i | \(0.414347\pi\) | |||||||
\(710\) | −1033.69 | −0.0546389 | ||||||||
\(711\) | 5069.38 | 0.267393 | ||||||||
\(712\) | −4805.88 | −0.252961 | ||||||||
\(713\) | −19462.8 | −1.02228 | ||||||||
\(714\) | −1901.64 | −0.0996740 | ||||||||
\(715\) | −4405.16 | −0.230411 | ||||||||
\(716\) | 24013.7 | 1.25340 | ||||||||
\(717\) | 10753.2 | 0.560091 | ||||||||
\(718\) | 3569.18 | 0.185516 | ||||||||
\(719\) | 10367.8 | 0.537768 | 0.268884 | − | 0.963173i | \(-0.413345\pi\) | ||||
0.268884 | + | 0.963173i | \(0.413345\pi\) | |||||||
\(720\) | 2373.63 | 0.122861 | ||||||||
\(721\) | −14693.2 | −0.758949 | ||||||||
\(722\) | −1388.23 | −0.0715576 | ||||||||
\(723\) | 19631.8 | 1.00984 | ||||||||
\(724\) | 4672.11 | 0.239831 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | 53.2044 | 0.00271984 | ||||||||
\(727\) | −32648.0 | −1.66554 | −0.832770 | − | 0.553619i | \(-0.813246\pi\) | ||||
−0.832770 | + | 0.553619i | \(0.813246\pi\) | |||||||
\(728\) | 3742.07 | 0.190509 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1812.59 | 0.0919001 | ||||||||
\(731\) | −3839.53 | −0.194268 | ||||||||
\(732\) | −8565.66 | −0.432508 | ||||||||
\(733\) | 21036.1 | 1.06001 | 0.530004 | − | 0.847995i | \(-0.322191\pi\) | ||||
0.530004 | + | 0.847995i | \(0.322191\pi\) | |||||||
\(734\) | −767.863 | −0.0386136 | ||||||||
\(735\) | 1959.84 | 0.0983534 | ||||||||
\(736\) | −22688.6 | −1.13629 | ||||||||
\(737\) | −22959.0 | −1.14750 | ||||||||
\(738\) | −73.4981 | −0.00366599 | ||||||||
\(739\) | 24591.3 | 1.22410 | 0.612048 | − | 0.790820i | \(-0.290346\pi\) | ||||
0.612048 | + | 0.790820i | \(0.290346\pi\) | |||||||
\(740\) | 9770.54 | 0.485368 | ||||||||
\(741\) | −6756.88 | −0.334980 | ||||||||
\(742\) | −1721.95 | −0.0851950 | ||||||||
\(743\) | 3352.77 | 0.165547 | 0.0827734 | − | 0.996568i | \(-0.473622\pi\) | ||||
0.0827734 | + | 0.996568i | \(0.473622\pi\) | |||||||
\(744\) | 3380.84 | 0.166596 | ||||||||
\(745\) | −2027.85 | −0.0997244 | ||||||||
\(746\) | −4012.50 | −0.196928 | ||||||||
\(747\) | −7968.08 | −0.390277 | ||||||||
\(748\) | −17423.4 | −0.851690 | ||||||||
\(749\) | −2047.46 | −0.0998831 | ||||||||
\(750\) | 259.375 | 0.0126280 | ||||||||
\(751\) | 10898.0 | 0.529525 | 0.264762 | − | 0.964314i | \(-0.414706\pi\) | ||||
0.264762 | + | 0.964314i | \(0.414706\pi\) | |||||||
\(752\) | 14844.5 | 0.719843 | ||||||||
\(753\) | −1584.30 | −0.0766734 | ||||||||
\(754\) | −479.793 | −0.0231738 | ||||||||
\(755\) | −394.779 | −0.0190298 | ||||||||
\(756\) | −2959.33 | −0.142368 | ||||||||
\(757\) | −34910.6 | −1.67615 | −0.838075 | − | 0.545555i | \(-0.816319\pi\) | ||||
−0.838075 | + | 0.545555i | \(0.816319\pi\) | |||||||
\(758\) | 8759.58 | 0.419739 | ||||||||
\(759\) | −20487.4 | −0.979771 | ||||||||
\(760\) | −5054.39 | −0.241239 | ||||||||
\(761\) | −17093.2 | −0.814229 | −0.407115 | − | 0.913377i | \(-0.633465\pi\) | ||||
−0.407115 | + | 0.913377i | \(0.633465\pi\) | |||||||
\(762\) | 1873.98 | 0.0890907 | ||||||||
\(763\) | 12393.9 | 0.588062 | ||||||||
\(764\) | −22138.8 | −1.04837 | ||||||||
\(765\) | 2830.11 | 0.133756 | ||||||||
\(766\) | 9274.05 | 0.437448 | ||||||||
\(767\) | 15236.7 | 0.717293 | ||||||||
\(768\) | −5580.65 | −0.262206 | ||||||||
\(769\) | 29371.4 | 1.37732 | 0.688660 | − | 0.725084i | \(-0.258199\pi\) | ||||
0.688660 | + | 0.725084i | \(0.258199\pi\) | |||||||
\(770\) | 1856.17 | 0.0868726 | ||||||||
\(771\) | −15062.3 | −0.703575 | ||||||||
\(772\) | −24518.9 | −1.14307 | ||||||||
\(773\) | −25646.0 | −1.19330 | −0.596651 | − | 0.802501i | \(-0.703502\pi\) | ||||
−0.596651 | + | 0.802501i | \(0.703502\pi\) | |||||||
\(774\) | 380.036 | 0.0176487 | ||||||||
\(775\) | −2624.28 | −0.121635 | ||||||||
\(776\) | −6000.16 | −0.277568 | ||||||||
\(777\) | −11357.4 | −0.524382 | ||||||||
\(778\) | 3234.62 | 0.149057 | ||||||||
\(779\) | −1111.74 | −0.0511325 | ||||||||
\(780\) | −2698.74 | −0.123885 | ||||||||
\(781\) | 11009.2 | 0.504405 | ||||||||
\(782\) | −8065.32 | −0.368817 | ||||||||
\(783\) | 783.000 | 0.0357371 | ||||||||
\(784\) | −6891.74 | −0.313946 | ||||||||
\(785\) | 1574.35 | 0.0715806 | ||||||||
\(786\) | −1423.36 | −0.0645923 | ||||||||
\(787\) | 18188.7 | 0.823834 | 0.411917 | − | 0.911221i | \(-0.364859\pi\) | ||||
0.411917 | + | 0.911221i | \(0.364859\pi\) | |||||||
\(788\) | −17843.8 | −0.806676 | ||||||||
\(789\) | 1266.64 | 0.0571527 | ||||||||
\(790\) | −1947.95 | −0.0877279 | ||||||||
\(791\) | −26976.2 | −1.21260 | ||||||||
\(792\) | 3558.83 | 0.159669 | ||||||||
\(793\) | 9080.07 | 0.406611 | ||||||||
\(794\) | 4090.31 | 0.182821 | ||||||||
\(795\) | 2562.68 | 0.114326 | ||||||||
\(796\) | 13755.1 | 0.612485 | ||||||||
\(797\) | 12068.7 | 0.536379 | 0.268190 | − | 0.963366i | \(-0.413575\pi\) | ||||
0.268190 | + | 0.963366i | \(0.413575\pi\) | |||||||
\(798\) | 2847.11 | 0.126299 | ||||||||
\(799\) | 17699.3 | 0.783675 | ||||||||
\(800\) | −3059.24 | −0.135201 | ||||||||
\(801\) | −4028.87 | −0.177719 | ||||||||
\(802\) | −5365.11 | −0.236220 | ||||||||
\(803\) | −19304.8 | −0.848385 | ||||||||
\(804\) | −14065.4 | −0.616974 | ||||||||
\(805\) | −13509.0 | −0.591466 | ||||||||
\(806\) | −1736.71 | −0.0758968 | ||||||||
\(807\) | 5331.57 | 0.232565 | ||||||||
\(808\) | −12225.7 | −0.532300 | ||||||||
\(809\) | −18274.6 | −0.794191 | −0.397096 | − | 0.917777i | \(-0.629982\pi\) | ||||
−0.397096 | + | 0.917777i | \(0.629982\pi\) | |||||||
\(810\) | −280.125 | −0.0121513 | ||||||||
\(811\) | −30620.5 | −1.32581 | −0.662903 | − | 0.748705i | \(-0.730676\pi\) | ||||
−0.662903 | + | 0.748705i | \(0.730676\pi\) | |||||||
\(812\) | −3178.54 | −0.137371 | ||||||||
\(813\) | 4396.53 | 0.189659 | ||||||||
\(814\) | 6618.61 | 0.284990 | ||||||||
\(815\) | 4084.06 | 0.175532 | ||||||||
\(816\) | −9952.05 | −0.426950 | ||||||||
\(817\) | 5748.47 | 0.246161 | ||||||||
\(818\) | −5308.10 | −0.226887 | ||||||||
\(819\) | 3137.05 | 0.133843 | ||||||||
\(820\) | −444.035 | −0.0189102 | ||||||||
\(821\) | −10076.0 | −0.428326 | −0.214163 | − | 0.976798i | \(-0.568702\pi\) | ||||
−0.214163 | + | 0.976798i | \(0.568702\pi\) | |||||||
\(822\) | −2392.36 | −0.101512 | ||||||||
\(823\) | 37593.9 | 1.59227 | 0.796137 | − | 0.605116i | \(-0.206873\pi\) | ||||
0.796137 | + | 0.605116i | \(0.206873\pi\) | |||||||
\(824\) | 10825.0 | 0.457654 | ||||||||
\(825\) | −2762.45 | −0.116577 | ||||||||
\(826\) | −6420.18 | −0.270444 | ||||||||
\(827\) | 34830.2 | 1.46453 | 0.732264 | − | 0.681021i | \(-0.238464\pi\) | ||||
0.732264 | + | 0.681021i | \(0.238464\pi\) | |||||||
\(828\) | −12551.2 | −0.526794 | ||||||||
\(829\) | −19925.3 | −0.834784 | −0.417392 | − | 0.908727i | \(-0.637056\pi\) | ||||
−0.417392 | + | 0.908727i | \(0.637056\pi\) | |||||||
\(830\) | 3061.80 | 0.128044 | ||||||||
\(831\) | 18244.5 | 0.761606 | ||||||||
\(832\) | 8069.12 | 0.336233 | ||||||||
\(833\) | −8217.14 | −0.341785 | ||||||||
\(834\) | −909.814 | −0.0377749 | ||||||||
\(835\) | −6821.81 | −0.282729 | ||||||||
\(836\) | 26086.1 | 1.07919 | ||||||||
\(837\) | 2834.22 | 0.117043 | ||||||||
\(838\) | −7827.00 | −0.322648 | ||||||||
\(839\) | 26090.0 | 1.07357 | 0.536786 | − | 0.843718i | \(-0.319638\pi\) | ||||
0.536786 | + | 0.843718i | \(0.319638\pi\) | |||||||
\(840\) | 2346.63 | 0.0963885 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 11039.5 | 0.451838 | ||||||||
\(843\) | 3583.51 | 0.146409 | ||||||||
\(844\) | −31767.1 | −1.29558 | ||||||||
\(845\) | −8124.19 | −0.330746 | ||||||||
\(846\) | −1751.88 | −0.0711947 | ||||||||
\(847\) | −373.637 | −0.0151574 | ||||||||
\(848\) | −9011.63 | −0.364930 | ||||||||
\(849\) | −11482.6 | −0.464171 | ||||||||
\(850\) | −1087.50 | −0.0438833 | ||||||||
\(851\) | −48169.5 | −1.94034 | ||||||||
\(852\) | 6744.57 | 0.271203 | ||||||||
\(853\) | −37626.4 | −1.51032 | −0.755160 | − | 0.655540i | \(-0.772441\pi\) | ||||
−0.755160 | + | 0.655540i | \(0.772441\pi\) | |||||||
\(854\) | −3826.01 | −0.153306 | ||||||||
\(855\) | −4237.19 | −0.169484 | ||||||||
\(856\) | 1508.44 | 0.0602306 | ||||||||
\(857\) | 25833.1 | 1.02969 | 0.514844 | − | 0.857284i | \(-0.327850\pi\) | ||||
0.514844 | + | 0.857284i | \(0.327850\pi\) | |||||||
\(858\) | −1828.14 | −0.0727409 | ||||||||
\(859\) | 49111.2 | 1.95070 | 0.975351 | − | 0.220661i | \(-0.0708215\pi\) | ||||
0.975351 | + | 0.220661i | \(0.0708215\pi\) | |||||||
\(860\) | 2295.97 | 0.0910372 | ||||||||
\(861\) | 516.153 | 0.0204303 | ||||||||
\(862\) | −6350.76 | −0.250937 | ||||||||
\(863\) | 14549.3 | 0.573886 | 0.286943 | − | 0.957948i | \(-0.407361\pi\) | ||||
0.286943 | + | 0.957948i | \(0.407361\pi\) | |||||||
\(864\) | 3303.98 | 0.130097 | ||||||||
\(865\) | 2154.29 | 0.0846797 | ||||||||
\(866\) | −216.368 | −0.00849017 | ||||||||
\(867\) | 2873.00 | 0.112540 | ||||||||
\(868\) | −11505.4 | −0.449905 | ||||||||
\(869\) | 20746.5 | 0.809869 | ||||||||
\(870\) | −300.875 | −0.0117248 | ||||||||
\(871\) | 14910.1 | 0.580032 | ||||||||
\(872\) | −9131.08 | −0.354607 | ||||||||
\(873\) | −5030.05 | −0.195007 | ||||||||
\(874\) | 12075.2 | 0.467335 | ||||||||
\(875\) | −1821.50 | −0.0703749 | ||||||||
\(876\) | −11826.7 | −0.456151 | ||||||||
\(877\) | 501.781 | 0.0193203 | 0.00966017 | − | 0.999953i | \(-0.496925\pi\) | ||||
0.00966017 | + | 0.999953i | \(0.496925\pi\) | |||||||
\(878\) | 5545.88 | 0.213171 | ||||||||
\(879\) | 20463.0 | 0.785210 | ||||||||
\(880\) | 9714.09 | 0.372116 | ||||||||
\(881\) | 1569.47 | 0.0600189 | 0.0300095 | − | 0.999550i | \(-0.490446\pi\) | ||||
0.0300095 | + | 0.999550i | \(0.490446\pi\) | |||||||
\(882\) | 813.332 | 0.0310502 | ||||||||
\(883\) | −26159.0 | −0.996967 | −0.498483 | − | 0.866899i | \(-0.666110\pi\) | ||||
−0.498483 | + | 0.866899i | \(0.666110\pi\) | |||||||
\(884\) | 11315.2 | 0.430509 | ||||||||
\(885\) | 9554.80 | 0.362917 | ||||||||
\(886\) | −382.823 | −0.0145160 | ||||||||
\(887\) | −29723.0 | −1.12514 | −0.562571 | − | 0.826749i | \(-0.690188\pi\) | ||||
−0.562571 | + | 0.826749i | \(0.690188\pi\) | |||||||
\(888\) | 8367.43 | 0.316208 | ||||||||
\(889\) | −13160.4 | −0.496495 | ||||||||
\(890\) | 1548.13 | 0.0583071 | ||||||||
\(891\) | 2983.44 | 0.112176 | ||||||||
\(892\) | 2464.60 | 0.0925123 | ||||||||
\(893\) | −26499.1 | −0.993009 | ||||||||
\(894\) | −841.557 | −0.0314831 | ||||||||
\(895\) | −15963.2 | −0.596190 | ||||||||
\(896\) | −17665.4 | −0.658661 | ||||||||
\(897\) | 13305.0 | 0.495251 | ||||||||
\(898\) | 8338.16 | 0.309853 | ||||||||
\(899\) | 3044.17 | 0.112935 | ||||||||
\(900\) | −1692.36 | −0.0626800 | ||||||||
\(901\) | −10744.7 | −0.397290 | ||||||||
\(902\) | −300.792 | −0.0111034 | ||||||||
\(903\) | −2668.87 | −0.0983549 | ||||||||
\(904\) | 19874.4 | 0.731209 | ||||||||
\(905\) | −3105.80 | −0.114078 | ||||||||
\(906\) | −163.833 | −0.00600772 | ||||||||
\(907\) | −9772.21 | −0.357752 | −0.178876 | − | 0.983872i | \(-0.557246\pi\) | ||||
−0.178876 | + | 0.983872i | \(0.557246\pi\) | |||||||
\(908\) | −27545.0 | −1.00673 | ||||||||
\(909\) | −10249.0 | −0.373971 | ||||||||
\(910\) | −1205.44 | −0.0439120 | ||||||||
\(911\) | −49823.7 | −1.81200 | −0.906001 | − | 0.423275i | \(-0.860880\pi\) | ||||
−0.906001 | + | 0.423275i | \(0.860880\pi\) | |||||||
\(912\) | 14900.0 | 0.540997 | ||||||||
\(913\) | −32609.4 | −1.18205 | ||||||||
\(914\) | 185.547 | 0.00671483 | ||||||||
\(915\) | 5694.05 | 0.205726 | ||||||||
\(916\) | 49361.0 | 1.78050 | ||||||||
\(917\) | 9995.80 | 0.359968 | ||||||||
\(918\) | 1174.50 | 0.0422267 | ||||||||
\(919\) | 28235.9 | 1.01351 | 0.506756 | − | 0.862090i | \(-0.330845\pi\) | ||||
0.506756 | + | 0.862090i | \(0.330845\pi\) | |||||||
\(920\) | 9952.60 | 0.356660 | ||||||||
\(921\) | 22052.2 | 0.788974 | ||||||||
\(922\) | −2504.86 | −0.0894720 | ||||||||
\(923\) | −7149.61 | −0.254965 | ||||||||
\(924\) | −12111.1 | −0.431197 | ||||||||
\(925\) | −6494.99 | −0.230869 | ||||||||
\(926\) | 5361.45 | 0.190268 | ||||||||
\(927\) | 9074.82 | 0.321528 | ||||||||
\(928\) | 3548.72 | 0.125531 | ||||||||
\(929\) | −22846.1 | −0.806842 | −0.403421 | − | 0.915014i | \(-0.632179\pi\) | ||||
−0.403421 | + | 0.915014i | \(0.632179\pi\) | |||||||
\(930\) | −1089.08 | −0.0384002 | ||||||||
\(931\) | 12302.5 | 0.433082 | ||||||||
\(932\) | −18730.9 | −0.658317 | ||||||||
\(933\) | −10179.4 | −0.357191 | ||||||||
\(934\) | −6113.56 | −0.214178 | ||||||||
\(935\) | 11582.3 | 0.405113 | ||||||||
\(936\) | −2311.18 | −0.0807088 | ||||||||
\(937\) | −45416.9 | −1.58346 | −0.791732 | − | 0.610868i | \(-0.790820\pi\) | ||||
−0.791732 | + | 0.610868i | \(0.790820\pi\) | |||||||
\(938\) | −6282.55 | −0.218692 | ||||||||
\(939\) | 32196.9 | 1.11896 | ||||||||
\(940\) | −10583.9 | −0.367243 | ||||||||
\(941\) | −39333.3 | −1.36262 | −0.681311 | − | 0.731994i | \(-0.738590\pi\) | ||||
−0.681311 | + | 0.731994i | \(0.738590\pi\) | |||||||
\(942\) | 653.352 | 0.0225981 | ||||||||
\(943\) | 2189.13 | 0.0755968 | ||||||||
\(944\) | −33599.3 | −1.15844 | ||||||||
\(945\) | 1967.22 | 0.0677183 | ||||||||
\(946\) | 1555.30 | 0.0534538 | ||||||||
\(947\) | 31274.8 | 1.07317 | 0.536587 | − | 0.843845i | \(-0.319713\pi\) | ||||
0.536587 | + | 0.843845i | \(0.319713\pi\) | |||||||
\(948\) | 12709.9 | 0.435443 | ||||||||
\(949\) | 12537.0 | 0.428839 | ||||||||
\(950\) | 1628.18 | 0.0556054 | ||||||||
\(951\) | 26163.5 | 0.892124 | ||||||||
\(952\) | −9838.85 | −0.334957 | ||||||||
\(953\) | −34174.1 | −1.16160 | −0.580802 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580802 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(954\) | 1063.51 | 0.0360928 | ||||||||
\(955\) | 14716.8 | 0.498666 | ||||||||
\(956\) | 26960.4 | 0.912093 | ||||||||
\(957\) | 3204.44 | 0.108239 | ||||||||
\(958\) | 6850.27 | 0.231025 | ||||||||
\(959\) | 16800.8 | 0.565720 | ||||||||
\(960\) | 5060.09 | 0.170118 | ||||||||
\(961\) | −18772.0 | −0.630124 | ||||||||
\(962\) | −4298.27 | −0.144056 | ||||||||
\(963\) | 1264.55 | 0.0423153 | ||||||||
\(964\) | 49220.9 | 1.64450 | ||||||||
\(965\) | 16299.0 | 0.543712 | ||||||||
\(966\) | −5606.24 | −0.186726 | ||||||||
\(967\) | 37894.7 | 1.26020 | 0.630098 | − | 0.776515i | \(-0.283015\pi\) | ||||
0.630098 | + | 0.776515i | \(0.283015\pi\) | |||||||
\(968\) | 275.273 | 0.00914008 | ||||||||
\(969\) | 17765.5 | 0.588970 | ||||||||
\(970\) | 1932.84 | 0.0639792 | ||||||||
\(971\) | −39869.1 | −1.31767 | −0.658837 | − | 0.752286i | \(-0.728951\pi\) | ||||
−0.658837 | + | 0.752286i | \(0.728951\pi\) | |||||||
\(972\) | 1827.75 | 0.0603138 | ||||||||
\(973\) | 6389.33 | 0.210516 | ||||||||
\(974\) | −552.926 | −0.0181898 | ||||||||
\(975\) | 1793.99 | 0.0589269 | ||||||||
\(976\) | −20023.0 | −0.656681 | ||||||||
\(977\) | −34257.3 | −1.12179 | −0.560894 | − | 0.827887i | \(-0.689543\pi\) | ||||
−0.560894 | + | 0.827887i | \(0.689543\pi\) | |||||||
\(978\) | 1694.88 | 0.0554155 | ||||||||
\(979\) | −16488.2 | −0.538268 | ||||||||
\(980\) | 4913.71 | 0.160166 | ||||||||
\(981\) | −7654.77 | −0.249131 | ||||||||
\(982\) | 6925.83 | 0.225063 | ||||||||
\(983\) | 8665.65 | 0.281171 | 0.140586 | − | 0.990069i | \(-0.455101\pi\) | ||||
0.140586 | + | 0.990069i | \(0.455101\pi\) | |||||||
\(984\) | −380.269 | −0.0123197 | ||||||||
\(985\) | 11861.7 | 0.383702 | ||||||||
\(986\) | 1261.50 | 0.0407446 | ||||||||
\(987\) | 12302.9 | 0.396762 | ||||||||
\(988\) | −16940.9 | −0.545507 | ||||||||
\(989\) | −11319.3 | −0.363937 | ||||||||
\(990\) | −1146.41 | −0.0368034 | ||||||||
\(991\) | 22129.9 | 0.709362 | 0.354681 | − | 0.934987i | \(-0.384589\pi\) | ||||
0.354681 | + | 0.934987i | \(0.384589\pi\) | |||||||
\(992\) | 12845.3 | 0.411127 | ||||||||
\(993\) | 18279.0 | 0.584157 | ||||||||
\(994\) | 3012.59 | 0.0961302 | ||||||||
\(995\) | −9143.76 | −0.291333 | ||||||||
\(996\) | −19977.6 | −0.635555 | ||||||||
\(997\) | −14159.7 | −0.449791 | −0.224895 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224895 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(998\) | −1768.14 | −0.0560817 | ||||||||
\(999\) | 7014.59 | 0.222154 |
(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 | 435.4.a.g.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 1305.4.a.i.1.4 | 6 | |||
5.4 | even | 2 | 2175.4.a.l.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.g.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1305.4.a.i.1.4 | 6 | 3.2 | odd | 2 | |||
2175.4.a.l.1.4 | 6 | 5.4 | even | 2 |