Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 2x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.44504 | 1.02180 | 0.510899 | − | 0.859640i | \(-0.329312\pi\) | ||||
0.510899 | + | 0.859640i | \(0.329312\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0881460 | 0.0440730 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.35690 | −0.512858 | −0.256429 | − | 0.966563i | \(-0.582546\pi\) | ||||
−0.256429 | + | 0.966563i | \(0.582546\pi\) | |||||||
\(8\) | −2.76271 | −0.976765 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.85086 | −1.46259 | −0.731294 | − | 0.682062i | \(-0.761083\pi\) | ||||
−0.731294 | + | 0.682062i | \(0.761083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.198062 | −0.0549326 | −0.0274663 | − | 0.999623i | \(-0.508744\pi\) | ||||
−0.0274663 | + | 0.999623i | \(0.508744\pi\) | |||||||
\(14\) | −1.96077 | −0.524038 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.16852 | −1.04213 | ||||||||
\(17\) | −1.13706 | −0.275778 | −0.137889 | − | 0.990448i | \(-0.544032\pi\) | ||||
−0.137889 | + | 0.990448i | \(0.544032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.00969 | −1.49447 | ||||||||
\(23\) | 2.55496 | 0.532746 | 0.266373 | − | 0.963870i | \(-0.414175\pi\) | ||||
0.266373 | + | 0.963870i | \(0.414175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.286208 | −0.0561301 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.119605 | −0.0226032 | ||||||||
\(29\) | 10.2349 | 1.90057 | 0.950286 | − | 0.311377i | \(-0.100790\pi\) | ||||
0.950286 | + | 0.311377i | \(0.100790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.51573 | 0.451838 | 0.225919 | − | 0.974146i | \(-0.427461\pi\) | ||||
0.225919 | + | 0.974146i | \(0.427461\pi\) | |||||||
\(32\) | −0.498271 | −0.0880827 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.64310 | −0.281790 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.137063 | 0.0225331 | 0.0112665 | − | 0.999937i | \(-0.496414\pi\) | ||||
0.0112665 | + | 0.999937i | \(0.496414\pi\) | |||||||
\(38\) | −1.44504 | −0.234417 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7506 | 1.83514 | 0.917570 | − | 0.397575i | \(-0.130148\pi\) | ||||
0.917570 | + | 0.397575i | \(0.130148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59179 | 1.15774 | 0.578869 | − | 0.815421i | \(-0.303494\pi\) | ||||
0.578869 | + | 0.815421i | \(0.303494\pi\) | |||||||
\(44\) | −0.427583 | −0.0644606 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.69202 | 0.544359 | ||||||||
\(47\) | 2.69202 | 0.392672 | 0.196336 | − | 0.980537i | \(-0.437096\pi\) | ||||
0.196336 | + | 0.980537i | \(0.437096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15883 | −0.736976 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0174584 | −0.00242104 | ||||||||
\(53\) | 12.8780 | 1.76893 | 0.884465 | − | 0.466607i | \(-0.154524\pi\) | ||||
0.884465 | + | 0.466607i | \(0.154524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.74871 | 0.500942 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.7899 | 1.94200 | ||||||||
\(59\) | −5.82371 | −0.758182 | −0.379091 | − | 0.925359i | \(-0.623763\pi\) | ||||
−0.379091 | + | 0.925359i | \(0.623763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.58211 | −0.970789 | −0.485395 | − | 0.874295i | \(-0.661324\pi\) | ||||
−0.485395 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(62\) | 3.63533 | 0.461688 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.61702 | 0.952128 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.01507 | −0.979196 | −0.489598 | − | 0.871948i | \(-0.662856\pi\) | ||||
−0.489598 | + | 0.871948i | \(0.662856\pi\) | |||||||
\(68\) | −0.100228 | −0.0121544 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.82371 | 1.04718 | 0.523591 | − | 0.851970i | \(-0.324592\pi\) | ||||
0.523591 | + | 0.851970i | \(0.324592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9705 | 1.40104 | 0.700518 | − | 0.713635i | \(-0.252952\pi\) | ||||
0.700518 | + | 0.713635i | \(0.252952\pi\) | |||||||
\(74\) | 0.198062 | 0.0230243 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0881460 | −0.0101110 | ||||||||
\(77\) | 6.58211 | 0.750101 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7409 | 1.20845 | 0.604225 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604225 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.9801 | 1.87514 | ||||||||
\(83\) | 3.77479 | 0.414337 | 0.207169 | − | 0.978305i | \(-0.433575\pi\) | ||||
0.207169 | + | 0.978305i | \(0.433575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.9705 | 1.18298 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.4015 | 1.42860 | ||||||||
\(89\) | −9.36658 | −0.992856 | −0.496428 | − | 0.868078i | \(-0.665355\pi\) | ||||
−0.496428 | + | 0.868078i | \(0.665355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.268750 | 0.0281726 | ||||||||
\(92\) | 0.225209 | 0.0234797 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.89008 | 0.401232 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.198062 | −0.0201102 | −0.0100551 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100551 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(98\) | −7.45473 | −0.753042 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5090 | −1.14519 | −0.572595 | − | 0.819838i | \(-0.694063\pi\) | ||||
−0.572595 | + | 0.819838i | \(0.694063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1564 | −1.49341 | −0.746704 | − | 0.665156i | \(-0.768365\pi\) | ||||
−0.746704 | + | 0.665156i | \(0.768365\pi\) | |||||||
\(104\) | 0.547188 | 0.0536562 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.6093 | 1.80749 | ||||||||
\(107\) | 2.65279 | 0.256455 | 0.128228 | − | 0.991745i | \(-0.459071\pi\) | ||||
0.128228 | + | 0.991745i | \(0.459071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.49934 | −0.239393 | −0.119696 | − | 0.992811i | \(-0.538192\pi\) | ||||
−0.119696 | + | 0.992811i | \(0.538192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.65625 | 0.534465 | ||||||||
\(113\) | 8.52781 | 0.802229 | 0.401114 | − | 0.916028i | \(-0.368623\pi\) | ||||
0.401114 | + | 0.916028i | \(0.368623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.902165 | 0.0837639 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.41550 | −0.774710 | ||||||||
\(119\) | 1.54288 | 0.141435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.5308 | 1.13916 | ||||||||
\(122\) | −10.9565 | −0.991951 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.221751 | 0.0199139 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.4088 | −1.81099 | −0.905494 | − | 0.424359i | \(-0.860499\pi\) | ||||
−0.905494 | + | 0.424359i | \(0.860499\pi\) | |||||||
\(128\) | 12.0035 | 1.06097 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2131 | 1.15444 | 0.577218 | − | 0.816590i | \(-0.304138\pi\) | ||||
0.577218 | + | 0.816590i | \(0.304138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.35690 | 0.117658 | ||||||||
\(134\) | −11.5821 | −1.00054 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.14138 | 0.269371 | ||||||||
\(137\) | −6.86054 | −0.586136 | −0.293068 | − | 0.956092i | \(-0.594676\pi\) | ||||
−0.293068 | + | 0.956092i | \(0.594676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.28621 | 0.363551 | 0.181776 | − | 0.983340i | \(-0.441816\pi\) | ||||
0.181776 | + | 0.983340i | \(0.441816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7506 | 1.07001 | ||||||||
\(143\) | 0.960771 | 0.0803437 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.2978 | 1.43158 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0120816 | 0.000993100 0 | ||||||||
\(149\) | 15.3545 | 1.25789 | 0.628945 | − | 0.777450i | \(-0.283487\pi\) | ||||
0.628945 | + | 0.777450i | \(0.283487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2295 | −0.832467 | −0.416233 | − | 0.909258i | \(-0.636650\pi\) | ||||
−0.416233 | + | 0.909258i | \(0.636650\pi\) | |||||||
\(152\) | 2.76271 | 0.224085 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.51142 | 0.766452 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.17092 | −0.253067 | −0.126533 | − | 0.991962i | \(-0.540385\pi\) | ||||
−0.126533 | + | 0.991962i | \(0.540385\pi\) | |||||||
\(158\) | 15.5211 | 1.23479 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.46681 | −0.273223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.63773 | 0.363255 | 0.181627 | − | 0.983367i | \(-0.441864\pi\) | ||||
0.181627 | + | 0.983367i | \(0.441864\pi\) | |||||||
\(164\) | 1.03577 | 0.0808801 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.45473 | 0.423369 | ||||||||
\(167\) | −19.6286 | −1.51891 | −0.759454 | − | 0.650560i | \(-0.774534\pi\) | ||||
−0.759454 | + | 0.650560i | \(0.774534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9608 | −0.996982 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.669186 | 0.0510250 | ||||||||
\(173\) | 20.5646 | 1.56350 | 0.781751 | − | 0.623591i | \(-0.214327\pi\) | ||||
0.781751 | + | 0.623591i | \(0.214327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.2209 | 1.52421 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.5351 | −1.01450 | ||||||||
\(179\) | −6.92154 | −0.517340 | −0.258670 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258670 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6461 | −1.31162 | −0.655812 | − | 0.754925i | \(-0.727673\pi\) | ||||
−0.655812 | + | 0.754925i | \(0.727673\pi\) | |||||||
\(182\) | 0.388355 | 0.0287868 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.05861 | −0.520367 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.51573 | 0.403350 | ||||||||
\(188\) | 0.237291 | 0.0173062 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.92931 | −0.501387 | −0.250694 | − | 0.968066i | \(-0.580659\pi\) | ||||
−0.250694 | + | 0.968066i | \(0.580659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0368 | 1.51426 | 0.757132 | − | 0.653262i | \(-0.226600\pi\) | ||||
0.757132 | + | 0.653262i | \(0.226600\pi\) | |||||||
\(194\) | −0.286208 | −0.0205486 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.454731 | −0.0324808 | ||||||||
\(197\) | 21.5646 | 1.53642 | 0.768209 | − | 0.640199i | \(-0.221148\pi\) | ||||
0.768209 | + | 0.640199i | \(0.221148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9909 | 1.55889 | 0.779447 | − | 0.626468i | \(-0.215500\pi\) | ||||
0.779447 | + | 0.626468i | \(0.215500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.6310 | −1.17015 | ||||||||
\(203\) | −13.8877 | −0.974725 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.9017 | −1.52596 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.825627 | 0.0572469 | ||||||||
\(209\) | 4.85086 | 0.335541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.6233 | −1.41976 | −0.709882 | − | 0.704321i | \(-0.751252\pi\) | ||||
−0.709882 | + | 0.704321i | \(0.751252\pi\) | |||||||
\(212\) | 1.13514 | 0.0779620 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.83340 | 0.262046 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.41358 | −0.231729 | ||||||||
\(218\) | −3.61165 | −0.244611 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.225209 | 0.0151492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.97716 | −0.534190 | −0.267095 | − | 0.963670i | \(-0.586064\pi\) | ||||
−0.267095 | + | 0.963670i | \(0.586064\pi\) | |||||||
\(224\) | 0.676102 | 0.0451740 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3230 | 0.819717 | ||||||||
\(227\) | 19.7942 | 1.31379 | 0.656893 | − | 0.753984i | \(-0.271871\pi\) | ||||
0.656893 | + | 0.753984i | \(0.271871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.03385 | −0.266564 | −0.133282 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133282 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −28.2760 | −1.85641 | ||||||||
\(233\) | 26.8159 | 1.75677 | 0.878385 | − | 0.477953i | \(-0.158621\pi\) | ||||
0.878385 | + | 0.477953i | \(0.158621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.513337 | −0.0334154 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.22952 | 0.144518 | ||||||||
\(239\) | −3.36227 | −0.217487 | −0.108744 | − | 0.994070i | \(-0.534683\pi\) | ||||
−0.108744 | + | 0.994070i | \(0.534683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.7506 | 1.78758 | 0.893788 | − | 0.448491i | \(-0.148038\pi\) | ||||
0.893788 | + | 0.448491i | \(0.148038\pi\) | |||||||
\(242\) | 18.1075 | 1.16400 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.668332 | −0.0427856 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.198062 | 0.0126024 | ||||||||
\(248\) | −6.95023 | −0.441340 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.59419 | 0.353102 | 0.176551 | − | 0.984291i | \(-0.443506\pi\) | ||||
0.176551 | + | 0.984291i | \(0.443506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3937 | −0.779187 | ||||||||
\(254\) | −29.4916 | −1.85047 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.11146 | 0.131966 | ||||||||
\(257\) | 10.4668 | 0.652902 | 0.326451 | − | 0.945214i | \(-0.394147\pi\) | ||||
0.326451 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.185981 | −0.0115563 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.0935 | 1.17960 | ||||||||
\(263\) | 15.4795 | 0.954506 | 0.477253 | − | 0.878766i | \(-0.341633\pi\) | ||||
0.477253 | + | 0.878766i | \(0.341633\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.96077 | 0.120223 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.706496 | −0.0431561 | ||||||||
\(269\) | −9.13036 | −0.556688 | −0.278344 | − | 0.960481i | \(-0.589785\pi\) | ||||
−0.278344 | + | 0.960481i | \(0.589785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.44265 | 0.452109 | 0.226054 | − | 0.974115i | \(-0.427417\pi\) | ||||
0.226054 | + | 0.974115i | \(0.427417\pi\) | |||||||
\(272\) | 4.73987 | 0.287397 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.91377 | −0.598913 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4155 | 0.685891 | 0.342946 | − | 0.939355i | \(-0.388575\pi\) | ||||
0.342946 | + | 0.939355i | \(0.388575\pi\) | |||||||
\(278\) | 6.19375 | 0.371476 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5060 | −1.28294 | −0.641471 | − | 0.767147i | \(-0.721676\pi\) | ||||
−0.641471 | + | 0.767147i | \(0.721676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.45712 | 0.324392 | 0.162196 | − | 0.986759i | \(-0.448142\pi\) | ||||
0.162196 | + | 0.986759i | \(0.448142\pi\) | |||||||
\(284\) | 0.777775 | 0.0461524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.38835 | 0.0820951 | ||||||||
\(287\) | −15.9444 | −0.941167 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7071 | −0.923946 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.05515 | 0.0617479 | ||||||||
\(293\) | 7.39075 | 0.431772 | 0.215886 | − | 0.976419i | \(-0.430736\pi\) | ||||
0.215886 | + | 0.976419i | \(0.430736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.378666 | −0.0220095 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.1879 | 1.28531 | ||||||||
\(299\) | −0.506041 | −0.0292651 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3013 | −0.593756 | ||||||||
\(302\) | −14.7821 | −0.850613 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.16852 | 0.239081 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2131 | 1.83850 | 0.919250 | − | 0.393674i | \(-0.128796\pi\) | ||||
0.919250 | + | 0.393674i | \(0.128796\pi\) | |||||||
\(308\) | 0.580186 | 0.0330592 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.8442 | −0.841735 | −0.420867 | − | 0.907122i | \(-0.638274\pi\) | ||||
−0.420867 | + | 0.907122i | \(0.638274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1491 | 0.743234 | 0.371617 | − | 0.928386i | \(-0.378804\pi\) | ||||
0.371617 | + | 0.928386i | \(0.378804\pi\) | |||||||
\(314\) | −4.58211 | −0.258583 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.946771 | 0.0532600 | ||||||||
\(317\) | −5.13467 | −0.288392 | −0.144196 | − | 0.989549i | \(-0.546060\pi\) | ||||
−0.144196 | + | 0.989549i | \(0.546060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −49.6480 | −2.77975 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00969 | −0.279179 | ||||||||
\(323\) | 1.13706 | 0.0632679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.70171 | 0.371173 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −32.4636 | −1.79250 | ||||||||
\(329\) | −3.65279 | −0.201385 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00969 | 0.110462 | 0.0552312 | − | 0.998474i | \(-0.482410\pi\) | ||||
0.0552312 | + | 0.998474i | \(0.482410\pi\) | |||||||
\(332\) | 0.332733 | 0.0182611 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.3642 | −1.55202 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.31873 | 0.0718359 | 0.0359180 | − | 0.999355i | \(-0.488564\pi\) | ||||
0.0359180 | + | 0.999355i | \(0.488564\pi\) | |||||||
\(338\) | −18.7289 | −1.01872 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2034 | −0.660853 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4983 | 0.890823 | ||||||||
\(344\) | −20.9739 | −1.13084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.7168 | 1.59758 | ||||||||
\(347\) | 12.0151 | 0.645003 | 0.322501 | − | 0.946569i | \(-0.395476\pi\) | ||||
0.322501 | + | 0.946569i | \(0.395476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5579 | −0.565154 | −0.282577 | − | 0.959245i | \(-0.591189\pi\) | ||||
−0.282577 | + | 0.959245i | \(0.591189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.41704 | 0.128829 | ||||||||
\(353\) | −1.01102 | −0.0538110 | −0.0269055 | − | 0.999638i | \(-0.508565\pi\) | ||||
−0.0269055 | + | 0.999638i | \(0.508565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.825627 | −0.0437581 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0019 | −0.528618 | ||||||||
\(359\) | 5.14244 | 0.271408 | 0.135704 | − | 0.990749i | \(-0.456670\pi\) | ||||
0.135704 | + | 0.990749i | \(0.456670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −25.4993 | −1.34022 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0236892 | 0.00124165 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.5308 | 1.54149 | 0.770747 | − | 0.637141i | \(-0.219883\pi\) | ||||
0.770747 | + | 0.637141i | \(0.219883\pi\) | |||||||
\(368\) | −10.6504 | −0.555190 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.4741 | −0.907210 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.78986 | −0.455121 | −0.227561 | − | 0.973764i | \(-0.573075\pi\) | ||||
−0.227561 | + | 0.973764i | \(0.573075\pi\) | |||||||
\(374\) | 7.97046 | 0.412143 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.43727 | −0.383548 | ||||||||
\(377\) | −2.02715 | −0.104403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1511 | 0.983724 | 0.491862 | − | 0.870673i | \(-0.336316\pi\) | ||||
0.491862 | + | 0.870673i | \(0.336316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0131 | −0.512317 | ||||||||
\(383\) | −6.99894 | −0.357629 | −0.178814 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178814 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.3991 | 1.54727 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0174584 | −0.000886316 0 | ||||||||
\(389\) | −8.08575 | −0.409964 | −0.204982 | − | 0.978766i | \(-0.565714\pi\) | ||||
−0.204982 | + | 0.978766i | \(0.565714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.90515 | −0.146920 | ||||||||
\(392\) | 14.2524 | 0.719853 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.1618 | 1.56991 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7006 | 0.888370 | 0.444185 | − | 0.895935i | \(-0.353493\pi\) | ||||
0.444185 | + | 0.895935i | \(0.353493\pi\) | |||||||
\(398\) | 31.7778 | 1.59288 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5418 | 0.776121 | 0.388061 | − | 0.921634i | \(-0.373145\pi\) | ||||
0.388061 | + | 0.921634i | \(0.373145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.498271 | −0.0248207 | ||||||||
\(404\) | −1.01447 | −0.0504720 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0683 | −0.995973 | ||||||||
\(407\) | −0.664874 | −0.0329566 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1661 | 0.651023 | 0.325512 | − | 0.945538i | \(-0.394463\pi\) | ||||
0.325512 | + | 0.945538i | \(0.394463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.33598 | −0.0658190 | ||||||||
\(413\) | 7.90217 | 0.388840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.0986887 | 0.00483861 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.00969 | 0.342855 | ||||||||
\(419\) | 25.1739 | 1.22983 | 0.614913 | − | 0.788595i | \(-0.289191\pi\) | ||||
0.614913 | + | 0.788595i | \(0.289191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9420 | 1.31307 | 0.656536 | − | 0.754295i | \(-0.272021\pi\) | ||||
0.656536 | + | 0.754295i | \(0.272021\pi\) | |||||||
\(422\) | −29.8015 | −1.45071 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −35.5782 | −1.72783 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2881 | 0.497877 | ||||||||
\(428\) | 0.233833 | 0.0113027 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.9487 | −0.912726 | −0.456363 | − | 0.889794i | \(-0.650848\pi\) | ||||
−0.456363 | + | 0.889794i | \(0.650848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.68904 | 0.177284 | 0.0886419 | − | 0.996064i | \(-0.471747\pi\) | ||||
0.0886419 | + | 0.996064i | \(0.471747\pi\) | |||||||
\(434\) | −4.93277 | −0.236781 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.220306 | −0.0105508 | ||||||||
\(437\) | −2.55496 | −0.122220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.6926 | −1.22624 | −0.613121 | − | 0.789989i | \(-0.710086\pi\) | ||||
−0.613121 | + | 0.789989i | \(0.710086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.325437 | 0.0154795 | ||||||||
\(443\) | −27.3653 | −1.30016 | −0.650081 | − | 0.759865i | \(-0.725265\pi\) | ||||
−0.650081 | + | 0.759865i | \(0.725265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.5273 | −0.545835 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.3355 | −0.488307 | ||||||||
\(449\) | −7.55794 | −0.356681 | −0.178341 | − | 0.983969i | \(-0.557073\pi\) | ||||
−0.178341 | + | 0.983969i | \(0.557073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −57.0006 | −2.68405 | ||||||||
\(452\) | 0.751692 | 0.0353566 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.6034 | 1.34242 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.85623 | 0.367499 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(458\) | −5.82908 | −0.272375 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.87907 | −0.180666 | −0.0903331 | − | 0.995912i | \(-0.528793\pi\) | ||||
−0.0903331 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0954 | 0.608597 | 0.304298 | − | 0.952577i | \(-0.401578\pi\) | ||||
0.304298 | + | 0.952577i | \(0.401578\pi\) | |||||||
\(464\) | −42.6644 | −1.98065 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.7502 | 1.79507 | ||||||||
\(467\) | 6.44026 | 0.298020 | 0.149010 | − | 0.988836i | \(-0.452391\pi\) | ||||
0.149010 | + | 0.988836i | \(0.452391\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8756 | 0.502189 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.0892 | 0.740566 | ||||||||
\(473\) | −36.8267 | −1.69329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.135998 | 0.00623348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.85862 | −0.222228 | ||||||||
\(479\) | −5.69096 | −0.260026 | −0.130013 | − | 0.991512i | \(-0.541502\pi\) | ||||
−0.130013 | + | 0.991512i | \(0.541502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0271471 | −0.00123780 | ||||||||
\(482\) | 40.1008 | 1.82654 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.10454 | 0.0502063 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9632 | 0.587417 | 0.293709 | − | 0.955895i | \(-0.405110\pi\) | ||||
0.293709 | + | 0.955895i | \(0.405110\pi\) | |||||||
\(488\) | 20.9472 | 0.948233 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.6045 | 0.884737 | 0.442369 | − | 0.896833i | \(-0.354138\pi\) | ||||
0.442369 | + | 0.896833i | \(0.354138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6377 | −0.524137 | ||||||||
\(494\) | 0.286208 | 0.0128771 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.4869 | −0.470875 | ||||||||
\(497\) | −11.9729 | −0.537056 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.49827 | 0.246136 | 0.123068 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123068 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.08383 | 0.360799 | ||||||||
\(503\) | −35.6939 | −1.59151 | −0.795757 | − | 0.605616i | \(-0.792927\pi\) | ||||
−0.795757 | + | 0.605616i | \(0.792927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.9095 | −0.796173 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.79895 | −0.0798157 | ||||||||
\(509\) | 16.4450 | 0.728914 | 0.364457 | − | 0.931220i | \(-0.381255\pi\) | ||||
0.364457 | + | 0.931220i | \(0.381255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.2427 | −0.718533 | ||||||||
\(512\) | −20.9558 | −0.926123 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.1250 | 0.667134 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.0586 | −0.574317 | ||||||||
\(518\) | −0.268750 | −0.0118082 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.5435 | 1.16289 | 0.581445 | − | 0.813586i | \(-0.302487\pi\) | ||||
0.581445 | + | 0.813586i | \(0.302487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1685 | 1.05682 | 0.528408 | − | 0.848991i | \(-0.322789\pi\) | ||||
0.528408 | + | 0.848991i | \(0.322789\pi\) | |||||||
\(524\) | 1.16468 | 0.0508795 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.3685 | 0.975313 | ||||||||
\(527\) | −2.86054 | −0.124607 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.4722 | −0.716182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.119605 | 0.00518553 | ||||||||
\(533\) | −2.32736 | −0.100809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.1433 | 0.956445 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.1938 | −0.568823 | ||||||||
\(539\) | 25.0248 | 1.07789 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.80386 | 0.421501 | 0.210750 | − | 0.977540i | \(-0.432409\pi\) | ||||
0.210750 | + | 0.977540i | \(0.432409\pi\) | |||||||
\(542\) | 10.7549 | 0.461964 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.566566 | 0.0242913 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.1739 | −0.905331 | −0.452665 | − | 0.891681i | \(-0.649527\pi\) | ||||
−0.452665 | + | 0.891681i | \(0.649527\pi\) | |||||||
\(548\) | −0.604729 | −0.0258328 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2349 | −0.436021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.5743 | −0.619764 | ||||||||
\(554\) | 16.4959 | 0.700843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.377812 | 0.0160228 | ||||||||
\(557\) | 24.4077 | 1.03419 | 0.517094 | − | 0.855928i | \(-0.327014\pi\) | ||||
0.517094 | + | 0.855928i | \(0.327014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.50365 | −0.0635975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.0771 | −1.31091 | ||||||||
\(563\) | 14.4849 | 0.610464 | 0.305232 | − | 0.952278i | \(-0.401266\pi\) | ||||
0.305232 | + | 0.952278i | \(0.401266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.88577 | 0.331464 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.3773 | −1.02285 | ||||||||
\(569\) | −0.811626 | −0.0340251 | −0.0170126 | − | 0.999855i | \(-0.505416\pi\) | ||||
−0.0170126 | + | 0.999855i | \(0.505416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.6588 | −1.57597 | −0.787985 | − | 0.615694i | \(-0.788876\pi\) | ||||
−0.787985 | + | 0.615694i | \(0.788876\pi\) | |||||||
\(572\) | 0.0846882 | 0.00354099 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.0403 | −0.961683 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.89307 | −0.370223 | −0.185112 | − | 0.982718i | \(-0.559265\pi\) | ||||
−0.185112 | + | 0.982718i | \(0.559265\pi\) | |||||||
\(578\) | −22.6974 | −0.944087 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.12200 | −0.212496 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −62.4693 | −2.58721 | ||||||||
\(584\) | −33.0709 | −1.36848 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6799 | 0.441184 | ||||||||
\(587\) | 20.3327 | 0.839222 | 0.419611 | − | 0.907704i | \(-0.362167\pi\) | ||||
0.419611 | + | 0.907704i | \(0.362167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.51573 | −0.103659 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.571352 | −0.0234824 | ||||||||
\(593\) | 17.0049 | 0.698308 | 0.349154 | − | 0.937065i | \(-0.386469\pi\) | ||||
0.349154 | + | 0.937065i | \(0.386469\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.35344 | 0.0554390 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.731250 | −0.0299030 | ||||||||
\(599\) | 12.4004 | 0.506668 | 0.253334 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253334 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.73125 | −0.396946 | −0.198473 | − | 0.980106i | \(-0.563598\pi\) | ||||
−0.198473 | + | 0.980106i | \(0.563598\pi\) | |||||||
\(602\) | −14.8858 | −0.606699 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.901691 | −0.0366893 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4282 | 0.950920 | 0.475460 | − | 0.879737i | \(-0.342282\pi\) | ||||
0.475460 | + | 0.879737i | \(0.342282\pi\) | |||||||
\(608\) | 0.498271 | 0.0202076 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.533188 | −0.0215705 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.1424 | −1.13666 | −0.568331 | − | 0.822800i | \(-0.692411\pi\) | ||||
−0.568331 | + | 0.822800i | \(0.692411\pi\) | |||||||
\(614\) | 46.5493 | 1.87858 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.1844 | −0.732672 | ||||||||
\(617\) | 36.4805 | 1.46865 | 0.734326 | − | 0.678797i | \(-0.237498\pi\) | ||||
0.734326 | + | 0.678797i | \(0.237498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.2097 | −1.53578 | −0.767888 | − | 0.640584i | \(-0.778692\pi\) | ||||
−0.767888 | + | 0.640584i | \(0.778692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.4504 | −0.860083 | ||||||||
\(623\) | 12.7095 | 0.509195 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.0011 | 0.759435 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.279503 | −0.0111534 | ||||||||
\(629\) | −0.155850 | −0.00621413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5235 | −0.498553 | −0.249276 | − | 0.968432i | \(-0.580193\pi\) | ||||
−0.249276 | + | 0.968432i | \(0.580193\pi\) | |||||||
\(632\) | −29.6741 | −1.18037 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.41981 | −0.294678 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.02177 | 0.0404840 | ||||||||
\(638\) | −71.7434 | −2.84035 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.3564 | −1.47549 | −0.737745 | − | 0.675080i | \(-0.764109\pi\) | ||||
−0.737745 | + | 0.675080i | \(0.764109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5483 | 0.573727 | 0.286864 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286864 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(644\) | −0.305586 | −0.0120418 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64310 | 0.0646471 | ||||||||
\(647\) | −23.4403 | −0.921532 | −0.460766 | − | 0.887522i | \(-0.652425\pi\) | ||||
−0.460766 | + | 0.887522i | \(0.652425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.2500 | 1.10891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.408797 | 0.0160097 | ||||||||
\(653\) | 27.1903 | 1.06404 | 0.532019 | − | 0.846732i | \(-0.321433\pi\) | ||||
0.532019 | + | 0.846732i | \(0.321433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −48.9828 | −1.91246 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.27844 | −0.205775 | ||||||||
\(659\) | −2.71486 | −0.105756 | −0.0528779 | − | 0.998601i | \(-0.516839\pi\) | ||||
−0.0528779 | + | 0.998601i | \(0.516839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.41311 | −0.366128 | −0.183064 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183064 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(662\) | 2.90408 | 0.112870 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4286 | −0.404710 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.1497 | 1.01252 | ||||||||
\(668\) | −1.73019 | −0.0669429 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.7797 | 1.41986 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.8001 | 1.72692 | 0.863459 | − | 0.504419i | \(-0.168293\pi\) | ||||
0.863459 | + | 0.504419i | \(0.168293\pi\) | |||||||
\(674\) | 1.90562 | 0.0734019 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.14244 | −0.0439400 | ||||||||
\(677\) | −32.9197 | −1.26521 | −0.632604 | − | 0.774475i | \(-0.718014\pi\) | ||||
−0.632604 | + | 0.774475i | \(0.718014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.268750 | 0.0103137 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.6345 | −0.675259 | ||||||||
\(683\) | 20.3448 | 0.778473 | 0.389236 | − | 0.921138i | \(-0.372739\pi\) | ||||
0.389236 | + | 0.921138i | \(0.372739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.8407 | 0.910242 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31.6466 | −1.20651 | ||||||||
\(689\) | −2.55065 | −0.0971719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.1473 | −1.75553 | −0.877764 | − | 0.479094i | \(-0.840965\pi\) | ||||
−0.877764 | + | 0.479094i | \(0.840965\pi\) | |||||||
\(692\) | 1.81269 | 0.0689082 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.3623 | 0.659063 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.3612 | −0.506092 | ||||||||
\(698\) | −15.2567 | −0.577473 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1933 | −0.498303 | −0.249152 | − | 0.968464i | \(-0.580152\pi\) | ||||
−0.249152 | + | 0.968464i | \(0.580152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.137063 | −0.00516944 | ||||||||
\(704\) | −36.9491 | −1.39257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.46096 | −0.0549840 | ||||||||
\(707\) | 15.6165 | 0.587321 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.1860 | 1.54677 | 0.773386 | − | 0.633935i | \(-0.218562\pi\) | ||||
0.773386 | + | 0.633935i | \(0.218562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.8771 | 0.969787 | ||||||||
\(713\) | 6.42758 | 0.240715 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.610106 | −0.0228007 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.43104 | 0.277324 | ||||||||
\(719\) | 35.6256 | 1.32861 | 0.664306 | − | 0.747461i | \(-0.268727\pi\) | ||||
0.664306 | + | 0.747461i | \(0.268727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5657 | 0.765907 | ||||||||
\(722\) | 1.44504 | 0.0537789 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.55543 | −0.0578072 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0116 | −0.742189 | −0.371095 | − | 0.928595i | \(-0.621017\pi\) | ||||
−0.371095 | + | 0.928595i | \(0.621017\pi\) | |||||||
\(728\) | −0.742478 | −0.0275181 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.63235 | −0.319279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9952 | 0.701604 | 0.350802 | − | 0.936450i | \(-0.385909\pi\) | ||||
0.350802 | + | 0.936450i | \(0.385909\pi\) | |||||||
\(734\) | 42.6732 | 1.57510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.27306 | −0.0469257 | ||||||||
\(737\) | 38.8799 | 1.43216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.1704 | 1.77198 | 0.885989 | − | 0.463706i | \(-0.153481\pi\) | ||||
0.885989 | + | 0.463706i | \(0.153481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.2508 | −0.926987 | ||||||||
\(743\) | −13.2446 | −0.485897 | −0.242948 | − | 0.970039i | \(-0.578115\pi\) | ||||
−0.242948 | + | 0.970039i | \(0.578115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.7017 | −0.465043 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.486189 | 0.0177768 | ||||||||
\(749\) | −3.59956 | −0.131525 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0562 | 0.439937 | 0.219969 | − | 0.975507i | \(-0.429404\pi\) | ||||
0.219969 | + | 0.975507i | \(0.429404\pi\) | |||||||
\(752\) | −11.2218 | −0.409215 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.92931 | −0.106679 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0054 | −0.545380 | −0.272690 | − | 0.962102i | \(-0.587913\pi\) | ||||
−0.272690 | + | 0.962102i | \(0.587913\pi\) | |||||||
\(758\) | 27.6741 | 1.00517 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.3967 | −1.60938 | −0.804690 | − | 0.593695i | \(-0.797668\pi\) | ||||
−0.804690 | + | 0.593695i | \(0.797668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.39134 | 0.122775 | ||||||||
\(764\) | −0.610791 | −0.0220976 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1138 | −0.365425 | ||||||||
\(767\) | 1.15346 | 0.0416489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.7211 | −1.43238 | −0.716190 | − | 0.697906i | \(-0.754115\pi\) | ||||
−0.716190 | + | 0.697906i | \(0.754115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.85431 | 0.0667382 | ||||||||
\(773\) | −1.72779 | −0.0621444 | −0.0310722 | − | 0.999517i | \(-0.509892\pi\) | ||||
−0.0310722 | + | 0.999517i | \(0.509892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.547188 | 0.0196429 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.6843 | −0.418901 | ||||||||
\(779\) | −11.7506 | −0.421010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.8025 | −1.53159 | ||||||||
\(782\) | −4.19806 | −0.150122 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.5047 | 0.768025 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.6329 | −1.51970 | −0.759850 | − | 0.650098i | \(-0.774728\pi\) | ||||
−0.759850 | + | 0.650098i | \(0.774728\pi\) | |||||||
\(788\) | 1.90084 | 0.0677145 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.5714 | −0.411430 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.50173 | 0.0533280 | ||||||||
\(794\) | 25.5782 | 0.907735 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.93841 | 0.0687051 | ||||||||
\(797\) | 38.5864 | 1.36680 | 0.683401 | − | 0.730044i | \(-0.260500\pi\) | ||||
0.683401 | + | 0.730044i | \(0.260500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.06100 | −0.108290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.4586 | 0.793040 | ||||||||
\(803\) | −58.0670 | −2.04914 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.720023 | −0.0253617 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.7961 | 1.11858 | ||||||||
\(809\) | 8.38298 | 0.294730 | 0.147365 | − | 0.989082i | \(-0.452921\pi\) | ||||
0.147365 | + | 0.989082i | \(0.452921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.340765 | −0.0119659 | −0.00598295 | − | 0.999982i | \(-0.501904\pi\) | ||||
−0.00598295 | + | 0.999982i | \(0.501904\pi\) | |||||||
\(812\) | −1.22414 | −0.0429590 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.960771 | −0.0336750 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.59179 | −0.265603 | ||||||||
\(818\) | 19.0256 | 0.665215 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.7506 | 1.17791 | 0.588953 | − | 0.808168i | \(-0.299540\pi\) | ||||
0.588953 | + | 0.808168i | \(0.299540\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.2669 | −1.29904 | −0.649522 | − | 0.760343i | \(-0.725031\pi\) | ||||
−0.649522 | + | 0.760343i | \(0.725031\pi\) | |||||||
\(824\) | 41.8728 | 1.45871 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.4190 | 0.397316 | ||||||||
\(827\) | −21.1691 | −0.736122 | −0.368061 | − | 0.929802i | \(-0.619978\pi\) | ||||
−0.368061 | + | 0.929802i | \(0.619978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.0374 | −1.07797 | −0.538987 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538987 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.50864 | −0.0523028 | ||||||||
\(833\) | 5.86592 | 0.203242 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.427583 | 0.0147883 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.3773 | 1.25663 | ||||||||
\(839\) | −33.2403 | −1.14758 | −0.573791 | − | 0.819002i | \(-0.694528\pi\) | ||||
−0.573791 | + | 0.819002i | \(0.694528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.7531 | 2.61218 | ||||||||
\(842\) | 38.9323 | 1.34170 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.81786 | −0.0625732 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0030 | −0.584229 | ||||||||
\(848\) | −53.6822 | −1.84346 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.350191 | 0.0120044 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3086 | 0.832310 | 0.416155 | − | 0.909294i | \(-0.363377\pi\) | ||||
0.416155 | + | 0.909294i | \(0.363377\pi\) | |||||||
\(854\) | 14.8668 | 0.508731 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.32889 | −0.250496 | ||||||||
\(857\) | −57.3889 | −1.96037 | −0.980185 | − | 0.198087i | \(-0.936527\pi\) | ||||
−0.980185 | + | 0.198087i | \(0.936527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8135 | −0.471312 | −0.235656 | − | 0.971837i | \(-0.575724\pi\) | ||||
−0.235656 | + | 0.971837i | \(0.575724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.3817 | −0.932623 | ||||||||
\(863\) | −9.01938 | −0.307023 | −0.153512 | − | 0.988147i | \(-0.549058\pi\) | ||||
−0.153512 | + | 0.988147i | \(0.549058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.33081 | 0.181148 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.300894 | −0.0102130 | ||||||||
\(869\) | −52.1027 | −1.76746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.58748 | 0.0537898 | ||||||||
\(872\) | 6.90494 | 0.233831 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.69202 | −0.124884 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37675 | 0.0802570 | 0.0401285 | − | 0.999195i | \(-0.487223\pi\) | ||||
0.0401285 | + | 0.999195i | \(0.487223\pi\) | |||||||
\(878\) | −37.1269 | −1.25297 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.99330 | 0.269301 | 0.134650 | − | 0.990893i | \(-0.457009\pi\) | ||||
0.134650 | + | 0.990893i | \(0.457009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.76377 | 0.0593557 | 0.0296779 | − | 0.999560i | \(-0.490552\pi\) | ||||
0.0296779 | + | 0.999560i | \(0.490552\pi\) | |||||||
\(884\) | 0.0198513 | 0.000667672 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.5439 | −1.32850 | ||||||||
\(887\) | 45.9197 | 1.54183 | 0.770917 | − | 0.636936i | \(-0.219798\pi\) | ||||
0.770917 | + | 0.636936i | \(0.219798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.6926 | 0.928780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.703155 | −0.0235434 | ||||||||
\(893\) | −2.69202 | −0.0900851 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.2874 | −0.544125 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.9215 | −0.364457 | ||||||||
\(899\) | 25.7482 | 0.858752 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.6431 | −0.487833 | ||||||||
\(902\) | −82.3682 | −2.74256 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.5599 | −0.783589 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.0549 | −1.82807 | −0.914034 | − | 0.405638i | \(-0.867049\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867049\pi\) | |||||||
\(908\) | 1.74478 | 0.0579024 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8998 | −1.71952 | −0.859758 | − | 0.510702i | \(-0.829386\pi\) | ||||
−0.859758 | + | 0.510702i | \(0.829386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.3110 | −0.606004 | ||||||||
\(914\) | 11.3526 | 0.375510 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.355568 | −0.0117483 | ||||||||
\(917\) | −17.9288 | −0.592062 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.4614 | 0.378078 | 0.189039 | − | 0.981970i | \(-0.439463\pi\) | ||||
0.189039 | + | 0.981970i | \(0.439463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.60541 | −0.184604 | ||||||||
\(923\) | −1.74764 | −0.0575244 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.9235 | 0.621864 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.09975 | −0.167408 | ||||||||
\(929\) | −36.5295 | −1.19849 | −0.599246 | − | 0.800565i | \(-0.704533\pi\) | ||||
−0.599246 | + | 0.800565i | \(0.704533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.15883 | 0.169074 | ||||||||
\(932\) | 2.36372 | 0.0774261 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.30644 | 0.304516 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7845 | 1.59372 | 0.796860 | − | 0.604164i | \(-0.206493\pi\) | ||||
0.796860 | + | 0.604164i | \(0.206493\pi\) | |||||||
\(938\) | 15.7157 | 0.513136 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.1817 | 0.592705 | 0.296353 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296353 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0224 | 0.977663 | ||||||||
\(944\) | 24.2763 | 0.790125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.2161 | −1.73021 | ||||||||
\(947\) | −7.55150 | −0.245391 | −0.122695 | − | 0.992444i | \(-0.539154\pi\) | ||||
−0.122695 | + | 0.992444i | \(0.539154\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.37090 | −0.0769626 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.26252 | −0.138149 | ||||||||
\(953\) | 13.8592 | 0.448944 | 0.224472 | − | 0.974481i | \(-0.427934\pi\) | ||||
0.224472 | + | 0.974481i | \(0.427934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.296371 | −0.00958532 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.22367 | −0.265695 | ||||||||
\(959\) | 9.30904 | 0.300605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.6711 | −0.795842 | ||||||||
\(962\) | −0.0392287 | −0.00126478 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.44611 | 0.0787838 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.89977 | −0.157566 | −0.0787830 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787830 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(968\) | −34.6189 | −1.11269 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5133 | −0.465755 | −0.232878 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232878 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.81594 | −0.186450 | ||||||||
\(974\) | 18.7323 | 0.600222 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.6062 | 1.01169 | ||||||||
\(977\) | −19.6644 | −0.629120 | −0.314560 | − | 0.949238i | \(-0.601857\pi\) | ||||
−0.314560 | + | 0.949238i | \(0.601857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.4359 | 1.45214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.3293 | 0.904023 | ||||||||
\(983\) | −15.4397 | −0.492449 | −0.246224 | − | 0.969213i | \(-0.579190\pi\) | ||||
−0.246224 | + | 0.969213i | \(0.579190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.8170 | −0.535562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0174584 | 0.000555426 0 | ||||||||
\(989\) | 19.3967 | 0.616780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9377 | 0.379213 | 0.189606 | − | 0.981860i | \(-0.439279\pi\) | ||||
0.189606 | + | 0.981860i | \(0.439279\pi\) | |||||||
\(992\) | −1.25352 | −0.0397991 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.3013 | −0.548763 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9390 | −0.568134 | −0.284067 | − | 0.958804i | \(-0.591684\pi\) | ||||
−0.284067 | + | 0.958804i | \(0.591684\pi\) | |||||||
\(998\) | 7.94523 | 0.251502 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4275.2.a.bn.1.2 | 3 | ||
3.2 | odd | 2 | 475.2.a.d.1.2 | ✓ | 3 | ||
5.4 | even | 2 | 4275.2.a.z.1.2 | 3 | |||
12.11 | even | 2 | 7600.2.a.bw.1.3 | 3 | |||
15.2 | even | 4 | 475.2.b.c.324.2 | 6 | |||
15.8 | even | 4 | 475.2.b.c.324.5 | 6 | |||
15.14 | odd | 2 | 475.2.a.h.1.2 | yes | 3 | ||
57.56 | even | 2 | 9025.2.a.be.1.2 | 3 | |||
60.59 | even | 2 | 7600.2.a.bn.1.1 | 3 | |||
285.284 | even | 2 | 9025.2.a.w.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.d.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
475.2.a.h.1.2 | yes | 3 | 15.14 | odd | 2 | ||
475.2.b.c.324.2 | 6 | 15.2 | even | 4 | |||
475.2.b.c.324.5 | 6 | 15.8 | even | 4 | |||
4275.2.a.z.1.2 | 3 | 5.4 | even | 2 | |||
4275.2.a.bn.1.2 | 3 | 1.1 | even | 1 | trivial | ||
7600.2.a.bn.1.1 | 3 | 60.59 | even | 2 | |||
7600.2.a.bw.1.3 | 3 | 12.11 | even | 2 | |||
9025.2.a.w.1.2 | 3 | 285.284 | even | 2 | |||
9025.2.a.be.1.2 | 3 | 57.56 | even | 2 |