Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,4,Mod(1,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, 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("392.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.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: | \(23.1287487223\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1929.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 10x + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.90222\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.80445 | 0.539716 | 0.269858 | − | 0.962900i | \(-0.413023\pi\) | ||||
0.269858 | + | 0.962900i | \(0.413023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.69159 | −0.598514 | −0.299257 | − | 0.954173i | \(-0.596739\pi\) | ||||
−0.299257 | + | 0.954173i | \(0.596739\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.1351 | −0.708707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 31.4881 | 0.863093 | 0.431546 | − | 0.902091i | \(-0.357968\pi\) | ||||
0.431546 | + | 0.902091i | \(0.357968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.6837 | 0.398609 | 0.199304 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199304 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.7662 | −0.323028 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −87.9538 | −1.25482 | −0.627410 | − | 0.778689i | \(-0.715885\pi\) | ||||
−0.627410 | + | 0.778689i | \(0.715885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.0970 | 0.158140 | 0.0790700 | − | 0.996869i | \(-0.474805\pi\) | ||||
0.0790700 | + | 0.996869i | \(0.474805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.37681 | −0.0850087 | −0.0425043 | − | 0.999096i | \(-0.513534\pi\) | ||||
−0.0425043 | + | 0.999096i | \(0.513534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −80.2226 | −0.641781 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −129.383 | −0.922216 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.11923 | −0.0327799 | −0.0163900 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163900 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −257.412 | −1.49137 | −0.745685 | − | 0.666298i | \(-0.767878\pi\) | ||||
−0.745685 | + | 0.666298i | \(0.767878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 88.3067 | 0.465825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −380.215 | −1.68938 | −0.844688 | − | 0.535259i | \(-0.820214\pi\) | ||||
−0.844688 | + | 0.535259i | \(0.820214\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.3973 | 0.215136 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −217.959 | −0.830230 | −0.415115 | − | 0.909769i | \(-0.636259\pi\) | ||||
−0.415115 | + | 0.909769i | \(0.636259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 377.049 | 1.33720 | 0.668598 | − | 0.743624i | \(-0.266895\pi\) | ||||
0.668598 | + | 0.743624i | \(0.266895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 128.044 | 0.424171 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −357.710 | −1.11016 | −0.555079 | − | 0.831798i | \(-0.687312\pi\) | ||||
−0.555079 | + | 0.831798i | \(0.687312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −246.662 | −0.677246 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 764.390 | 1.98108 | 0.990538 | − | 0.137240i | \(-0.0438233\pi\) | ||||
0.990538 | + | 0.137240i | \(0.0438233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −210.706 | −0.516573 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 36.7298 | 0.0853506 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −450.671 | −0.994447 | −0.497224 | − | 0.867622i | \(-0.665647\pi\) | ||||
−0.497224 | + | 0.867622i | \(0.665647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −174.078 | −0.365383 | −0.182691 | − | 0.983170i | \(-0.558481\pi\) | ||||
−0.182691 | + | 0.983170i | \(0.558481\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −125.023 | −0.238573 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −497.234 | −0.906669 | −0.453334 | − | 0.891340i | \(-0.649766\pi\) | ||||
−0.453334 | + | 0.891340i | \(0.649766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −26.2967 | −0.0458805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 350.238 | 0.585432 | 0.292716 | − | 0.956199i | \(-0.405441\pi\) | ||||
0.292716 | + | 0.956199i | \(0.405441\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1062.69 | −1.70381 | −0.851903 | − | 0.523699i | \(-0.824552\pi\) | ||||
−0.851903 | + | 0.523699i | \(0.824552\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −224.980 | −0.346379 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 560.449 | 0.798170 | 0.399085 | − | 0.916914i | \(-0.369328\pi\) | ||||
0.399085 | + | 0.916914i | \(0.369328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 153.799 | 0.210972 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1105.27 | −1.46168 | −0.730840 | − | 0.682549i | \(-0.760871\pi\) | ||||
−0.730840 | + | 0.682549i | \(0.760871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 588.551 | 0.751027 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3566 | −0.0176918 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1206.71 | 1.43721 | 0.718604 | − | 0.695420i | \(-0.244782\pi\) | ||||
0.718604 | + | 0.695420i | \(0.244782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −721.897 | −0.804916 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −87.6398 | −0.0946490 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1442.99 | 1.51045 | 0.755226 | − | 0.655465i | \(-0.227527\pi\) | ||||
0.755226 | + | 0.655465i | \(0.227527\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −602.528 | −0.611680 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 311.922 | 0.307301 | 0.153651 | − | 0.988125i | \(-0.450897\pi\) | ||||
0.153651 | + | 0.988125i | \(0.450897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −581.632 | −0.556407 | −0.278203 | − | 0.960522i | \(-0.589739\pi\) | ||||
−0.278203 | + | 0.960522i | \(0.589739\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1175.48 | −1.06203 | −0.531016 | − | 0.847361i | \(-0.678190\pi\) | ||||
−0.531016 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 337.052 | 0.296181 | 0.148091 | − | 0.988974i | \(-0.452687\pi\) | ||||
0.148091 | + | 0.988974i | \(0.452687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1066.29 | −0.911783 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1168.16 | −0.972487 | −0.486243 | − | 0.873823i | \(-0.661633\pi\) | ||||
−0.486243 | + | 0.873823i | \(0.661633\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 62.7457 | 0.0508789 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −357.513 | −0.282497 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −339.499 | −0.255071 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −611.253 | −0.448088 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1373.27 | 0.982629 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23.4734 | 0.0164010 | 0.00820049 | − | 0.999966i | \(-0.497390\pi\) | ||||
0.00820049 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1057.41 | 0.721706 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −373.982 | −0.249427 | −0.124713 | − | 0.992193i | \(-0.539801\pi\) | ||||
−0.124713 | + | 0.992193i | \(0.539801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 865.780 | 0.551959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1138.14 | 0.709764 | 0.354882 | − | 0.934911i | \(-0.384521\pi\) | ||||
0.354882 | + | 0.934911i | \(0.384521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1229.46 | −0.750224 | −0.375112 | − | 0.926979i | \(-0.622396\pi\) | ||||
−0.375112 | + | 0.926979i | \(0.622396\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1003.18 | −0.599170 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 588.313 | 0.344037 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.2558 | 0.0196192 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2962.76 | 1.62898 | 0.814492 | − | 0.580175i | \(-0.197016\pi\) | ||||
0.814492 | + | 0.580175i | \(0.197016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2597.70 | −1.39999 | −0.699993 | − | 0.714149i | \(-0.746814\pi\) | ||||
−0.699993 | + | 0.714149i | \(0.746814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1683.00 | 0.889299 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1722.49 | 0.892606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1364.98 | 0.693870 | 0.346935 | − | 0.937889i | \(-0.387222\pi\) | ||||
0.346935 | + | 0.937889i | \(0.387222\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2143.69 | 1.06922 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3317.48 | 1.59414 | 0.797071 | − | 0.603886i | \(-0.206382\pi\) | ||||
0.797071 | + | 0.603886i | \(0.206382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −590.912 | −0.278803 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3803.96 | 1.76263 | 0.881315 | − | 0.472530i | \(-0.156659\pi\) | ||||
0.881315 | + | 0.472530i | \(0.156659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1847.92 | −0.841111 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −250.612 | −0.112075 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2522.30 | 1.10848 | 0.554239 | − | 0.832358i | \(-0.313009\pi\) | ||||
0.554239 | + | 0.832358i | \(0.313009\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1263.88 | −0.536719 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −187.036 | −0.0780992 | −0.0390496 | − | 0.999237i | \(-0.512433\pi\) | ||||
−0.0390496 | + | 0.999237i | \(0.512433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −457.654 | −0.187940 | −0.0939701 | − | 0.995575i | \(-0.529956\pi\) | ||||
−0.0939701 | + | 0.995575i | \(0.529956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −488.191 | −0.197203 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2544.24 | 1.01112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2769.50 | −1.08303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2891.60 | 1.09544 | 0.547719 | − | 0.836663i | \(-0.315496\pi\) | ||||
0.547719 | + | 0.836663i | \(0.315496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1147.89 | 0.428120 | 0.214060 | − | 0.976821i | \(-0.431331\pi\) | ||||
0.214060 | + | 0.976821i | \(0.431331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −350.621 | −0.128762 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1638.22 | 0.592481 | 0.296240 | − | 0.955113i | \(-0.404267\pi\) | ||||
0.296240 | + | 0.955113i | \(0.404267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5311.28 | 1.89199 | 0.945996 | − | 0.324179i | \(-0.105088\pi\) | ||||
0.945996 | + | 0.324179i | \(0.105088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1394.47 | −0.489344 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1458.49 | 0.496904 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 179.426 | 0.0602462 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 412.400 | 0.136489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1505.74 | −0.491277 | −0.245639 | − | 0.969361i | \(-0.578998\pi\) | ||||
−0.245639 | + | 0.969361i | \(0.578998\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 982.225 | 0.315967 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2523.06 | −0.800331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2980.24 | −0.919571 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1643.30 | −0.500182 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2520.23 | −0.756802 | −0.378401 | − | 0.925642i | \(-0.623526\pi\) | ||||
−0.378401 | + | 0.925642i | \(0.623526\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1535.07 | 0.454834 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1538.04 | −0.449705 | −0.224853 | − | 0.974393i | \(-0.572190\pi\) | ||||
−0.224853 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 571.683 | 0.164969 | 0.0824845 | − | 0.996592i | \(-0.473715\pi\) | ||||
0.0824845 | + | 0.996592i | \(0.473715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1604.20 | −0.451051 | −0.225525 | − | 0.974237i | \(-0.572410\pi\) | ||||
−0.225525 | + | 0.974237i | \(0.572410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2393.65 | 0.664445 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1571.75 | 0.430785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4699.38 | −1.27187 | −0.635936 | − | 0.771742i | \(-0.719386\pi\) | ||||
−0.635936 | + | 0.771742i | \(0.719386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −872.607 | −0.233235 | −0.116617 | − | 0.993177i | \(-0.537205\pi\) | ||||
−0.116617 | + | 0.993177i | \(0.537205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3924.67 | 1.03608 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 244.700 | 0.0630360 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3099.68 | −0.788892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3126.30 | 0.786176 | 0.393088 | − | 0.919501i | \(-0.371407\pi\) | ||||
0.393088 | + | 0.919501i | \(0.371407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −295.258 | −0.0733704 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1650.56 | 0.405341 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 904.015 | 0.219420 | 0.109710 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109710 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 97.9569 | 0.0232313 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −92.6368 | −0.0217195 | −0.0108598 | − | 0.999941i | \(-0.503457\pi\) | ||||
−0.0108598 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5114.98 | −1.18570 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3384.16 | 0.775683 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4051.78 | −0.918368 | −0.459184 | − | 0.888341i | \(-0.651858\pi\) | ||||
−0.459184 | + | 0.888341i | \(0.651858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2791.30 | 0.625680 | 0.312840 | − | 0.949806i | \(-0.398720\pi\) | ||||
0.312840 | + | 0.949806i | \(0.398720\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2526.06 | −0.553917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2580.66 | −0.559773 | −0.279886 | − | 0.960033i | \(-0.590297\pi\) | ||||
−0.279886 | + | 0.960033i | \(0.590297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4925.59 | 1.05694 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −919.487 | −0.195203 | −0.0976014 | − | 0.995226i | \(-0.531117\pi\) | ||||
−0.0976014 | + | 0.995226i | \(0.531117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8272.00 | −1.73752 | −0.868762 | − | 0.495229i | \(-0.835084\pi\) | ||||
−0.868762 | + | 0.495229i | \(0.835084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −245.781 | −0.0510835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2822.88 | 0.574573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4046.80 | 0.815215 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2859.38 | −0.570126 | −0.285063 | − | 0.958509i | \(-0.592014\pi\) | ||||
−0.285063 | + | 0.958509i | \(0.592014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3015.71 | 0.595191 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4074.04 | −0.795958 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −175.193 | −0.0338852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 874.770 | 0.165855 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1164.86 | 0.218687 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3542.86 | −0.658638 | −0.329319 | − | 0.944219i | \(-0.606819\pi\) | ||||
−0.329319 | + | 0.944219i | \(0.606819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1631.15 | −0.300301 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −622.549 | −0.113510 | −0.0567548 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567548 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7064.85 | −1.27581 | −0.637905 | − | 0.770115i | \(-0.720199\pi\) | ||||
−0.637905 | + | 0.770115i | \(0.720199\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6459.21 | −1.14443 | −0.572217 | − | 0.820103i | \(-0.693916\pi\) | ||||
−0.572217 | + | 0.820103i | \(0.693916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −161.195 | −0.0282921 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3296.56 | −0.573196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1151.93 | −0.198437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1498.85 | −0.255820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 945.245 | 0.159854 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8335.22 | −1.38412 | −0.692062 | − | 0.721838i | \(-0.743298\pi\) | ||||
−0.692062 | + | 0.721838i | \(0.743298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7275.44 | 1.19727 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3327.29 | 0.542654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5853.18 | 0.946122 | 0.473061 | − | 0.881030i | \(-0.343149\pi\) | ||||
0.473061 | + | 0.881030i | \(0.343149\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3276.03 | −0.524866 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8105.41 | −1.28719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 175.967 | 0.0274601 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7175.81 | 1.11014 | 0.555069 | − | 0.831805i | \(-0.312692\pi\) | ||||
0.555069 | + | 0.831805i | \(0.312692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10302.4 | −1.58016 | −0.790081 | − | 0.613003i | \(-0.789961\pi\) | ||||
−0.790081 | + | 0.613003i | \(0.789961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2417.35 | −0.367604 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1101.12 | 0.166025 | 0.0830124 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830124 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2343.65 | −0.350389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5632.93 | −0.828119 | −0.414060 | − | 0.910250i | \(-0.635889\pi\) | ||||
−0.414060 | + | 0.910250i | \(0.635889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6687.47 | −0.974992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −952.106 | −0.137666 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7111.05 | 1.01975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3196.46 | 0.454643 | 0.227322 | − | 0.973820i | \(-0.427003\pi\) | ||||
0.227322 | + | 0.973820i | \(0.427003\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4170.66 | 0.588390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 915.394 | 0.127071 | 0.0635353 | − | 0.997980i | \(-0.479762\pi\) | ||||
0.0635353 | + | 0.997980i | \(0.479762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3851.25 | 0.530340 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −95.6460 | −0.0130664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11767.5 | 1.59487 | 0.797437 | − | 0.603402i | \(-0.206188\pi\) | ||||
0.797437 | + | 0.603402i | \(0.206188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 65.8298 | 0.00885187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8415.12 | 1.12270 | 0.561348 | − | 0.827580i | \(-0.310283\pi\) | ||||
0.561348 | + | 0.827580i | \(0.310283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7214.86 | −0.947680 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3362.38 | −0.438251 | −0.219125 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219125 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 824.726 | 0.106671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1048.81 | −0.134620 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3750.29 | −0.477716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4863.44 | −0.614834 | −0.307417 | − | 0.951575i | \(-0.599465\pi\) | ||||
−0.307417 | + | 0.951575i | \(0.599465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3738.85 | 0.465609 | 0.232805 | − | 0.972524i | \(-0.425210\pi\) | ||||
0.232805 | + | 0.972524i | \(0.425210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4809.39 | −0.594474 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1029.16 | −0.126270 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11972.2 | −1.45809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14013.3 | −1.69416 | −0.847081 | − | 0.531464i | \(-0.821642\pi\) | ||||
−0.847081 | + | 0.531464i | \(0.821642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3191.85 | 0.383071 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7396.03 | 0.874836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3447.95 | −0.404908 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8043.46 | −0.937826 | −0.468913 | − | 0.883244i | \(-0.655354\pi\) | ||||
−0.468913 | + | 0.883244i | \(0.655354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1832.27 | 0.212112 | 0.106056 | − | 0.994360i | \(-0.466178\pi\) | ||||
0.106056 | + | 0.994360i | \(0.466178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6844.82 | 0.786777 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7055.89 | 0.805319 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1649.89 | 0.185682 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2863.25 | 0.319996 | 0.159998 | − | 0.987117i | \(-0.448851\pi\) | ||||
0.159998 | + | 0.987117i | \(0.448851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6856.23 | −0.760946 | −0.380473 | − | 0.924792i | \(-0.624239\pi\) | ||||
−0.380473 | + | 0.924792i | \(0.624239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 96.0685 | 0.0105888 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −122.808 | −0.0134433 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4074.42 | −0.442964 | −0.221482 | − | 0.975164i | \(-0.571089\pi\) | ||||
−0.221482 | + | 0.975164i | \(0.571089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2497.92 | −0.267901 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8074.84 | −0.860189 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8308.89 | 0.879188 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9529.68 | 1.00163 | 0.500817 | − | 0.865553i | \(-0.333033\pi\) | ||||
0.500817 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6863.11 | −0.716566 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7285.11 | −0.755595 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10551.9 | 1.08008 | 0.540041 | − | 0.841639i | \(-0.318409\pi\) | ||||
0.540041 | + | 0.841639i | \(0.318409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11379.8 | 1.15722 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13103.5 | 1.32384 | 0.661922 | − | 0.749573i | \(-0.269741\pi\) | ||||
0.661922 | + | 0.749573i | \(0.269741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −816.035 | −0.0819101 | −0.0409550 | − | 0.999161i | \(-0.513040\pi\) | ||||
−0.0409550 | + | 0.999161i | \(0.513040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4830.64 | 0.481754 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4588.33 | −0.454652 | −0.227326 | − | 0.973819i | \(-0.572998\pi\) | ||||
−0.227326 | + | 0.973819i | \(0.572998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3828.03 | 0.374493 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11872.6 | 1.15412 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1050.68 | −0.101491 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14626.7 | −1.40400 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17381.5 | 1.65800 | 0.829001 | − | 0.559247i | \(-0.188910\pi\) | ||||
0.829001 | + | 0.559247i | \(0.188910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7103.80 | −0.673400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9655.93 | −0.904027 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16352.5 | −1.52156 | −0.760781 | − | 0.649008i | \(-0.775184\pi\) | ||||
−0.760781 | + | 0.649008i | \(0.775184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9303.70 | 0.860384 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13094.7 | −1.20358 | −0.601789 | − | 0.798655i | \(-0.705545\pi\) | ||||
−0.601789 | + | 0.798655i | \(0.705545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 450.256 | 0.0411329 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4031.87 | 0.366099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9761.05 | −0.875681 | −0.437840 | − | 0.899053i | \(-0.644256\pi\) | ||||
−0.437840 | + | 0.899053i | \(0.644256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10668.0 | 0.951319 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14229.0 | 1.26131 | 0.630657 | − | 0.776061i | \(-0.282785\pi\) | ||||
0.630657 | + | 0.776061i | \(0.282785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2087.26 | −0.183924 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5182.39 | −0.453961 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20320.3 | 1.76951 | 0.884757 | − | 0.466053i | \(-0.154324\pi\) | ||||
0.884757 | + | 0.466053i | \(0.154324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1694.53 | −0.145839 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3892.04 | 0.333017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11263.6 | −0.958170 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7073.65 | 0.598263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20185.4 | 1.69738 | 0.848692 | − | 0.528888i | \(-0.177391\pi\) | ||||
0.848692 | + | 0.528888i | \(0.177391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2710.67 | −0.226634 | −0.113317 | − | 0.993559i | \(-0.536148\pi\) | ||||
−0.113317 | + | 0.993559i | \(0.536148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22640.3 | 1.87140 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12079.1 | −0.992774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8623.63 | 0.704771 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4072.27 | −0.330937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7865.80 | 0.635642 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −524.533 | −0.0421514 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3656.67 | 0.290596 | 0.145298 | − | 0.989388i | \(-0.453586\pi\) | ||||
0.145298 | + | 0.989388i | \(0.453586\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1283.47 | −0.101434 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2255.42 | −0.177269 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 787.130 | 0.0615269 | 0.0307635 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307635 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3330.99 | 0.258949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −67.0466 | −0.00518381 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7135.19 | 0.545715 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12457.4 | −0.947640 | −0.473820 | − | 0.880622i | \(-0.657125\pi\) | ||||
−0.473820 | + | 0.880622i | \(0.657125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7044.66 | 0.533018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7766.91 | −0.584526 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15918.7 | −1.19164 | −0.595820 | − | 0.803118i | \(-0.703173\pi\) | ||||
−0.595820 | + | 0.803118i | \(0.703173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7816.83 | 0.582047 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7816.50 | −0.575896 | −0.287948 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287948 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21837.8 | −1.60050 | −0.800248 | − | 0.599670i | \(-0.795299\pi\) | ||||
−0.800248 | + | 0.599670i | \(0.795299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8109.32 | 0.591225 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 752.232 | 0.0545569 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15184.6 | 1.09557 | 0.547785 | − | 0.836619i | \(-0.315471\pi\) | ||||
0.547785 | + | 0.836619i | \(0.315471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3219.20 | 0.231063 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24069.2 | 1.70985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2392.33 | 0.169078 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21861.6 | −1.53718 | −0.768591 | − | 0.639740i | \(-0.779042\pi\) | ||||
−0.768591 | + | 0.639740i | \(0.779042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3371.32 | −0.235845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4594.31 | 0.319771 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −273.502 | −0.0189399 | −0.00946997 | − | 0.999955i | \(-0.503014\pi\) | ||||
−0.00946997 | + | 0.999955i | \(0.503014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14895.2 | 1.02114 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2443.63 | −0.166684 | −0.0833421 | − | 0.996521i | \(-0.526559\pi\) | ||||
−0.0833421 | + | 0.996521i | \(0.526559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1107.14 | −0.0751431 | −0.0375716 | − | 0.999294i | \(-0.511962\pi\) | ||||
−0.0375716 | + | 0.999294i | \(0.511962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9514.62 | 0.642562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2271.79 | 0.152663 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1418.86 | −0.0948759 | −0.0474379 | − | 0.998874i | \(-0.515106\pi\) | ||||
−0.0474379 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6683.34 | −0.442519 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9402.98 | 0.619548 | 0.309774 | − | 0.950810i | \(-0.399747\pi\) | ||||
0.309774 | + | 0.950810i | \(0.399747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4090.26 | 0.268187 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11223.0 | −0.732284 | −0.366142 | − | 0.930559i | \(-0.619322\pi\) | ||||
−0.366142 | + | 0.930559i | \(0.619322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15879.1 | 1.03108 | 0.515538 | − | 0.856867i | \(-0.327592\pi\) | ||||
0.515538 | + | 0.856867i | \(0.327592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1213.20 | 0.0783964 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 838.493 | 0.0536636 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1156.55 | 0.0736655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33441.3 | 2.11986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9079.04 | −0.572791 | −0.286395 | − | 0.958112i | \(-0.592457\pi\) | ||||
−0.286395 | + | 0.958112i | \(0.592457\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4222.77 | −0.265150 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −157.074 | −0.00981622 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6701.84 | −0.414900 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9935.15 | 0.612192 | 0.306096 | − | 0.952001i | \(-0.400977\pi\) | ||||
0.306096 | + | 0.952001i | \(0.400977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21282.8 | −1.30531 | −0.652653 | − | 0.757657i | \(-0.726344\pi\) | ||||
−0.652653 | + | 0.757657i | \(0.726344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7075.78 | −0.431951 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6876.14 | 0.417819 | 0.208910 | − | 0.977935i | \(-0.433009\pi\) | ||||
0.208910 | + | 0.977935i | \(0.433009\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14190.8 | −0.858300 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1402.24 | −0.0840335 | −0.0420168 | − | 0.999117i | \(-0.513378\pi\) | ||||
−0.0420168 | + | 0.999117i | \(0.513378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2502.53 | 0.149286 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20334.6 | 1.20750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19975.7 | 1.18079 | 0.590395 | − | 0.807114i | \(-0.298972\pi\) | ||||
0.590395 | + | 0.807114i | \(0.298972\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 656.831 | 0.0386502 | 0.0193251 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193251 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4608.55 | −0.269956 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0020 | 0.00278658 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7067.84 | −0.408458 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5481.37 | −0.315359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14668.1 | 0.840140 | 0.420070 | − | 0.907492i | \(-0.362006\pi\) | ||||
0.420070 | + | 0.907492i | \(0.362006\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10379.5 | 0.591861 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19210.1 | 1.09055 | 0.545276 | − | 0.838257i | \(-0.316425\pi\) | ||||
0.545276 | + | 0.838257i | \(0.316425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4313.34 | −0.242713 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18446.0 | 1.03341 | 0.516704 | − | 0.856164i | \(-0.327159\pi\) | ||||
0.516704 | + | 0.856164i | \(0.327159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7615.95 | −0.424804 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1603.25 | 0.0890364 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14281.6 | 0.789674 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24902.0 | −1.37093 | −0.685467 | − | 0.728103i | \(-0.740402\pi\) | ||||
−0.685467 | + | 0.728103i | \(0.740402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8227.02 | 0.449020 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19170.3 | 1.04179 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4498.90 | −0.243439 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22637.7 | 1.21970 | 0.609852 | − | 0.792515i | \(-0.291229\pi\) | ||||
0.609852 | + | 0.792515i | \(0.291229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4979.67 | −0.267158 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6712.87 | 0.358612 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.98987 | 0.000370254 0 | 0.000185127 | − | 1.00000i | \(-0.499941\pi\) | ||||
0.000185127 | 1.00000i | \(0.499941\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10724.2 | −0.565668 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2413.70 | 0.126779 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3936.75 | −0.205911 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13179.1 | −0.686449 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19019.6 | −0.986525 | −0.493262 | − | 0.869881i | \(-0.664196\pi\) | ||||
−0.493262 | + | 0.869881i | \(0.664196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2447.18 | −0.125880 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 410.678 | 0.0210375 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33880.6 | −1.72842 | −0.864210 | − | 0.503130i | \(-0.832182\pi\) | ||||
−0.864210 | + | 0.503130i | \(0.832182\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6853.96 | 0.348217 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33162.9 | −1.67794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10445.4 | −0.526344 | −0.263172 | − | 0.964749i | \(-0.584769\pi\) | ||||
−0.263172 | + | 0.964749i | \(0.584769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15657.0 | −0.782540 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25674.5 | −1.27801 | −0.639007 | − | 0.769201i | \(-0.720655\pi\) | ||||
−0.639007 | + | 0.769201i | \(0.720655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 686.248 | 0.0340215 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30646.2 | −1.51319 | −0.756596 | − | 0.653883i | \(-0.773139\pi\) | ||||
−0.756596 | + | 0.653883i | \(0.773139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19825.6 | −0.974970 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21149.5 | 1.03590 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8711.90 | −0.423305 | −0.211652 | − | 0.977345i | \(-0.567884\pi\) | ||||
−0.211652 | + | 0.977345i | \(0.567884\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8767.54 | 0.424312 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17382.8 | 0.837912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18830.7 | −0.904114 | −0.452057 | − | 0.891989i | \(-0.649310\pi\) | ||||
−0.452057 | + | 0.891989i | \(0.649310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −828.035 | −0.0395992 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21800.6 | 1.03846 | 0.519232 | − | 0.854633i | \(-0.326218\pi\) | ||||
0.519232 | + | 0.854633i | \(0.326218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11262.0 | −0.532258 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8420.19 | −0.396395 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4412.21 | 0.206903 | 0.103452 | − | 0.994634i | \(-0.467011\pi\) | ||||
0.103452 | + | 0.994634i | \(0.467011\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2535.26 | 0.118424 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30446.8 | −1.41668 | −0.708342 | − | 0.705870i | \(-0.750556\pi\) | ||||
−0.708342 | + | 0.705870i | \(0.750556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20650.2 | 0.957133 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2854.61 | −0.131292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11028.3 | 0.505282 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 662.343 | 0.0302302 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9133.92 | −0.415291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11212.0 | −0.507834 | −0.253917 | − | 0.967226i | \(-0.581719\pi\) | ||||
−0.253917 | + | 0.967226i | \(0.581719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −259.795 | −0.0117224 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3252.41 | −0.145645 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14344.7 | −0.639942 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11809.3 | −0.524852 | −0.262426 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262426 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31462.0 | 1.39305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23090.6 | −1.01856 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33461.9 | −1.47054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11363.0 | −0.495658 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14327.7 | 0.622662 | 0.311331 | − | 0.950302i | \(-0.399225\pi\) | ||||
0.311331 | + | 0.950302i | \(0.399225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32413.9 | −1.40346 | −0.701730 | − | 0.712443i | \(-0.747589\pi\) | ||||
−0.701730 | + | 0.712443i | \(0.747589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7828.05 | 0.337690 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22199.2 | −0.954117 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4938.21 | 0.211464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2406.16 | 0.102285 | 0.0511423 | − | 0.998691i | \(-0.483714\pi\) | ||||
0.0511423 | + | 0.998691i | \(0.483714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1960.36 | −0.0830303 | −0.0415152 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415152 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7084.19 | −0.298958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17517.2 | 0.736557 | 0.368278 | − | 0.929716i | \(-0.379947\pi\) | ||||
0.368278 | + | 0.929716i | \(0.379947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33498.7 | 1.40345 | 0.701724 | − | 0.712449i | \(-0.252414\pi\) | ||||
0.701724 | + | 0.712449i | \(0.252414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7237.33 | −0.302118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25454.5 | −1.05496 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 33304.8 | 1.37537 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1609.45 | −0.0662268 | −0.0331134 | − | 0.999452i | \(-0.510542\pi\) | ||||
−0.0331134 | + | 0.999452i | \(0.510542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24362.8 | −0.998925 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2578.65 | −0.105354 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12365.5 | 0.503417 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23198.4 | −0.937770 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3565.20 | 0.143612 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20446.9 | −0.820739 | −0.410369 | − | 0.911919i | \(-0.634600\pi\) | ||||
−0.410369 | + | 0.911919i | \(0.634600\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1676.99 | 0.0670784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5784.22 | −0.230554 | −0.115277 | − | 0.993333i | \(-0.536776\pi\) | ||||
−0.115277 | + | 0.993333i | \(0.536776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32361.3 | 1.28539 | 0.642697 | − | 0.766120i | \(-0.277815\pi\) | ||||
0.642697 | + | 0.766120i | \(0.277815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28831.3 | −1.13723 | −0.568614 | − | 0.822604i | \(-0.692520\pi\) | ||||
−0.568614 | + | 0.822604i | \(0.692520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16878.2 | −0.663440 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7916.60 | 0.310106 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17647.5 | 0.688895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9290.16 | −0.361406 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27611.8 | −1.07047 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13105.4 | −0.504604 | −0.252302 | − | 0.967649i | \(-0.581188\pi\) | ||||
−0.252302 | + | 0.967649i | \(0.581188\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8018.98 | −0.307706 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3089.10 | −0.118132 | −0.0590661 | − | 0.998254i | \(-0.518812\pi\) | ||||
−0.0590661 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1601.96 | 0.0610536 | 0.0305268 | − | 0.999534i | \(-0.490282\pi\) | ||||
0.0305268 | + | 0.999534i | \(0.490282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8457.39 | 0.321234 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22570.4 | −0.854387 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4842.83 | 0.182089 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4684.93 | −0.175560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1251.57 | 0.0467435 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −491.320 | −0.0182884 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1317.75 | 0.0488870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −67231.0 | −2.48589 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3062.44 | 0.112485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48344.3 | 1.76984 | 0.884920 | − | 0.465743i | \(-0.154213\pi\) | ||||
0.884920 | + | 0.465743i | \(0.154213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5968.66 | −0.217787 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14697.9 | 0.534539 | 0.267269 | − | 0.963622i | \(-0.413879\pi\) | ||||
0.267269 | + | 0.963622i | \(0.413879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34802.9 | −1.26157 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3266.78 | 0.118029 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15330.6 | 0.550282 | 0.275141 | − | 0.961404i | \(-0.411276\pi\) | ||||
0.275141 | + | 0.961404i | \(0.411276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9935.77 | −0.355477 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6543.74 | 0.233358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30501.8 | 1.08421 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11129.6 | 0.394329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55910.3 | 1.97455 | 0.987275 | − | 0.159020i | \(-0.0508335\pi\) | ||||
0.987275 | + | 0.159020i | \(0.0508335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1745.90 | −0.0612629 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18532.4 | 0.648206 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18627.7 | 0.649457 | 0.324728 | − | 0.945807i | \(-0.394727\pi\) | ||||
0.324728 | + | 0.945807i | \(0.394727\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19813.0 | −0.688575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40564.7 | 1.40528 | 0.702641 | − | 0.711545i | \(-0.252004\pi\) | ||||
0.702641 | + | 0.711545i | \(0.252004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2043.76 | 0.0705767 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26690.1 | 0.915852 | 0.457926 | − | 0.888990i | \(-0.348592\pi\) | ||||
0.457926 | + | 0.888990i | \(0.348592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19854.9 | −0.679153 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18114.5 | −0.617669 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7182.06 | −0.244123 | −0.122062 | − | 0.992523i | \(-0.538951\pi\) | ||||
−0.122062 | + | 0.992523i | \(0.538951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19349.4 | −0.655635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −452.062 | −0.0152697 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36469.7 | 1.22419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22492.8 | 0.752670 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7681.22 | −0.256236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18129.4 | 0.602898 | 0.301449 | − | 0.953482i | \(-0.402530\pi\) | ||||
0.301449 | + | 0.953482i | \(0.402530\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3230.53 | −0.107100 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20976.0 | −0.693257 | −0.346629 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346629 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4203.45 | −0.138070 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44694.7 | −1.46357 | −0.731786 | − | 0.681534i | \(-0.761313\pi\) | ||||
−0.731786 | + | 0.681534i | \(0.761313\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37997.1 | 1.24044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6449.52 | −0.209906 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15426.2 | 0.500529 | 0.250265 | − | 0.968177i | \(-0.419482\pi\) | ||||
0.250265 | + | 0.968177i | \(0.419482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10962.3 | −0.354608 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3535.51 | −0.113673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28248.1 | 0.905479 | 0.452739 | − | 0.891643i | \(-0.350447\pi\) | ||||
0.452739 | + | 0.891643i | \(0.350447\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23375.7 | −0.747034 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35540.9 | −1.13238 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37121.5 | −1.17919 | −0.589594 | − | 0.807700i | \(-0.700712\pi\) | ||||
−0.589594 | + | 0.807700i | \(0.700712\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49193.4 | 1.55797 |
(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 | 392.4.a.i.1.3 | 3 | ||
4.3 | odd | 2 | 784.4.a.be.1.1 | 3 | |||
7.2 | even | 3 | 56.4.i.b.25.1 | yes | 6 | ||
7.3 | odd | 6 | 392.4.i.m.177.3 | 6 | |||
7.4 | even | 3 | 56.4.i.b.9.1 | ✓ | 6 | ||
7.5 | odd | 6 | 392.4.i.m.361.3 | 6 | |||
7.6 | odd | 2 | 392.4.a.l.1.1 | 3 | |||
21.2 | odd | 6 | 504.4.s.h.361.2 | 6 | |||
21.11 | odd | 6 | 504.4.s.h.289.2 | 6 | |||
28.11 | odd | 6 | 112.4.i.e.65.3 | 6 | |||
28.23 | odd | 6 | 112.4.i.e.81.3 | 6 | |||
28.27 | even | 2 | 784.4.a.bb.1.3 | 3 | |||
56.11 | odd | 6 | 448.4.i.m.65.1 | 6 | |||
56.37 | even | 6 | 448.4.i.j.193.3 | 6 | |||
56.51 | odd | 6 | 448.4.i.m.193.1 | 6 | |||
56.53 | even | 6 | 448.4.i.j.65.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.4.i.b.9.1 | ✓ | 6 | 7.4 | even | 3 | ||
56.4.i.b.25.1 | yes | 6 | 7.2 | even | 3 | ||
112.4.i.e.65.3 | 6 | 28.11 | odd | 6 | |||
112.4.i.e.81.3 | 6 | 28.23 | odd | 6 | |||
392.4.a.i.1.3 | 3 | 1.1 | even | 1 | trivial | ||
392.4.a.l.1.1 | 3 | 7.6 | odd | 2 | |||
392.4.i.m.177.3 | 6 | 7.3 | odd | 6 | |||
392.4.i.m.361.3 | 6 | 7.5 | odd | 6 | |||
448.4.i.j.65.3 | 6 | 56.53 | even | 6 | |||
448.4.i.j.193.3 | 6 | 56.37 | even | 6 | |||
448.4.i.m.65.1 | 6 | 56.11 | odd | 6 | |||
448.4.i.m.193.1 | 6 | 56.51 | odd | 6 | |||
504.4.s.h.289.2 | 6 | 21.11 | odd | 6 | |||
504.4.s.h.361.2 | 6 | 21.2 | odd | 6 | |||
784.4.a.bb.1.3 | 3 | 28.27 | even | 2 | |||
784.4.a.be.1.1 | 3 | 4.3 | odd | 2 |