Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2280,2,Mod(1,2280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2280.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: | \(18.2058916609\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2280.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.77801 | −1.04999 | −0.524994 | − | 0.851106i | \(-0.675932\pi\) | ||||
−0.524994 | + | 0.851106i | \(0.675932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.778008 | −0.234578 | −0.117289 | − | 0.993098i | \(-0.537420\pi\) | ||||
−0.117289 | + | 0.993098i | \(0.537420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.50466 | −1.52672 | −0.763360 | − | 0.645974i | \(-0.776452\pi\) | ||||
−0.763360 | + | 0.645974i | \(0.776452\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.00933 | −1.70001 | −0.850006 | − | 0.526773i | \(-0.823402\pi\) | ||||
−0.850006 | + | 0.526773i | \(0.823402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.77801 | 0.606211 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.27334 | −0.265510 | −0.132755 | − | 0.991149i | \(-0.542382\pi\) | ||||
−0.132755 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.23132 | 1.52852 | 0.764259 | − | 0.644909i | \(-0.223105\pi\) | ||||
0.764259 | + | 0.644909i | \(0.223105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00933 | 0.899702 | 0.449851 | − | 0.893104i | \(-0.351477\pi\) | ||||
0.449851 | + | 0.893104i | \(0.351477\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.778008 | 0.135434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.77801 | 0.469569 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.51399 | 1.39969 | 0.699846 | − | 0.714294i | \(-0.253252\pi\) | ||||
0.699846 | + | 0.714294i | \(0.253252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.50466 | 0.881452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.06068 | 1.41504 | 0.707520 | − | 0.706693i | \(-0.249814\pi\) | ||||
0.707520 | + | 0.706693i | \(0.249814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5140 | −1.60337 | −0.801684 | − | 0.597747i | \(-0.796063\pi\) | ||||
−0.801684 | + | 0.597747i | \(0.796063\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.72666 | −0.981184 | −0.490592 | − | 0.871389i | \(-0.663219\pi\) | ||||
−0.490592 | + | 0.871389i | \(0.663219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.717328 | 0.102475 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.00933 | 0.981502 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.72666 | 1.19870 | 0.599349 | − | 0.800488i | \(-0.295426\pi\) | ||||
0.599349 | + | 0.800488i | \(0.295426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.778008 | 0.104907 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.29200 | −0.688960 | −0.344480 | − | 0.938794i | \(-0.611945\pi\) | ||||
−0.344480 | + | 0.938794i | \(0.611945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.73599 | −0.990491 | −0.495246 | − | 0.868753i | \(-0.664922\pi\) | ||||
−0.495246 | + | 0.868753i | \(0.664922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.77801 | −0.349996 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.50466 | 0.682770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45331 | −0.177550 | −0.0887752 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887752 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.27334 | 0.153293 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4626 | −1.47904 | −0.739522 | − | 0.673133i | \(-0.764948\pi\) | ||||
−0.739522 | + | 0.673133i | \(0.764948\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.5653 | 1.70474 | 0.852372 | − | 0.522935i | \(-0.175163\pi\) | ||||
0.852372 | + | 0.522935i | \(0.175163\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16131 | 0.246304 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.28267 | 0.256821 | 0.128410 | − | 0.991721i | \(-0.459013\pi\) | ||||
0.128410 | + | 0.991721i | \(0.459013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.45331 | 0.379050 | 0.189525 | − | 0.981876i | \(-0.439305\pi\) | ||||
0.189525 | + | 0.981876i | \(0.439305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.00933 | 0.760268 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.23132 | −0.882490 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.51399 | −0.266483 | −0.133241 | − | 0.991084i | \(-0.542539\pi\) | ||||
−0.133241 | + | 0.991084i | \(0.542539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2920 | 1.60304 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00933 | −0.519443 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.51399 | 0.864465 | 0.432233 | − | 0.901762i | \(-0.357726\pi\) | ||||
0.432233 | + | 0.901762i | \(0.357726\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.778008 | −0.0781927 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5560 | 1.54788 | 0.773941 | − | 0.633258i | \(-0.218283\pi\) | ||||
0.773941 | + | 0.633258i | \(0.218283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.45331 | −0.143199 | −0.0715996 | − | 0.997433i | \(-0.522810\pi\) | ||||
−0.0715996 | + | 0.997433i | \(0.522810\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.77801 | −0.271106 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.0187 | 1.35523 | 0.677617 | − | 0.735415i | \(-0.263013\pi\) | ||||
0.677617 | + | 0.735415i | \(0.263013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.29200 | −0.698447 | −0.349224 | − | 0.937039i | \(-0.613555\pi\) | ||||
−0.349224 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.51399 | −0.808112 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7360 | 1.85661 | 0.928303 | − | 0.371825i | \(-0.121268\pi\) | ||||
0.928303 | + | 0.371825i | \(0.121268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.27334 | 0.118740 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.50466 | −0.508906 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.4720 | 1.78499 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3947 | −0.944973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.06068 | −0.816974 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.45331 | 0.128961 | 0.0644803 | − | 0.997919i | \(-0.479461\pi\) | ||||
0.0644803 | + | 0.997919i | \(0.479461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.5140 | 0.925705 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7873 | 1.37935 | 0.689673 | − | 0.724121i | \(-0.257754\pi\) | ||||
0.689673 | + | 0.724121i | \(0.257754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.77801 | −0.240884 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.282672 | −0.0241503 | −0.0120752 | − | 0.999927i | \(-0.503844\pi\) | ||||
−0.0120752 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4626 | 1.39634 | 0.698172 | − | 0.715931i | \(-0.253997\pi\) | ||||
0.698172 | + | 0.715931i | \(0.253997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.72666 | 0.566487 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.28267 | 0.358135 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.23132 | −0.683574 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.717328 | −0.0591642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5747 | −1.75572 | −0.877861 | − | 0.478916i | \(-0.841030\pi\) | ||||
−0.877861 | + | 0.478916i | \(0.841030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.00933 | −0.566671 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.00933 | −0.402359 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8387 | −1.10445 | −0.552224 | − | 0.833696i | \(-0.686221\pi\) | ||||
−0.552224 | + | 0.833696i | \(0.686221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.72666 | −0.692069 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.53736 | 0.278783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.6167 | 1.45817 | 0.729086 | − | 0.684422i | \(-0.239945\pi\) | ||||
0.729086 | + | 0.684422i | \(0.239945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.778008 | −0.0605678 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.73599 | −0.753393 | −0.376697 | − | 0.926337i | \(-0.622940\pi\) | ||||
−0.376697 | + | 0.926337i | \(0.622940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.3013 | 1.33087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.82936 | 0.367169 | 0.183585 | − | 0.983004i | \(-0.441230\pi\) | ||||
0.183585 | + | 0.983004i | \(0.441230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.77801 | −0.209998 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.29200 | 0.397771 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.8387 | 1.78179 | 0.890894 | − | 0.454212i | \(-0.150079\pi\) | ||||
0.890894 | + | 0.454212i | \(0.150079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7267 | −1.09462 | −0.547312 | − | 0.836929i | \(-0.684349\pi\) | ||||
−0.547312 | + | 0.836929i | \(0.684349\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.73599 | 0.571860 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.51399 | −0.625961 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.45331 | 0.398786 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.77801 | 0.202070 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.22199 | −0.233135 | −0.116568 | − | 0.993183i | \(-0.537189\pi\) | ||||
−0.116568 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50466 | 0.396234 | 0.198117 | − | 0.980178i | \(-0.436517\pi\) | ||||
0.198117 | + | 0.980178i | \(0.436517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.50466 | −0.394197 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.17997 | 0.440305 | 0.220152 | − | 0.975466i | \(-0.429345\pi\) | ||||
0.220152 | + | 0.975466i | \(0.429345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0280 | −1.20708 | −0.603541 | − | 0.797332i | \(-0.706244\pi\) | ||||
−0.603541 | + | 0.797332i | \(0.706244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.45331 | 0.102509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.8667 | −1.60493 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.06068 | −0.632825 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.27334 | −0.0885035 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.778008 | −0.0538159 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.56534 | 0.589663 | 0.294831 | − | 0.955549i | \(-0.404737\pi\) | ||||
0.294831 | + | 0.955549i | \(0.404737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4626 | 0.853926 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.5140 | 0.717048 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.9160 | −0.944677 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.5653 | −0.984235 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.5840 | 2.59544 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.98134 | −0.132681 | −0.0663403 | − | 0.997797i | \(-0.521132\pi\) | ||||
−0.0663403 | + | 0.997797i | \(0.521132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.282672 | 0.0187616 | 0.00938081 | − | 0.999956i | \(-0.497014\pi\) | ||||
0.00938081 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.26401 | 0.281774 | 0.140887 | − | 0.990026i | \(-0.455005\pi\) | ||||
0.140887 | + | 0.990026i | \(0.455005\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.16131 | −0.142204 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.62395 | −0.433950 | −0.216975 | − | 0.976177i | \(-0.569619\pi\) | ||||
−0.216975 | + | 0.976177i | \(0.569619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.72666 | 0.438799 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.28267 | −0.148275 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.21266 | 0.272495 | 0.136247 | − | 0.990675i | \(-0.456496\pi\) | ||||
0.136247 | + | 0.990675i | \(0.456496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1120 | −1.61761 | −0.808804 | − | 0.588078i | \(-0.799885\pi\) | ||||
−0.808804 | + | 0.588078i | \(0.799885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.717328 | −0.0458284 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.50466 | −0.350253 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.45331 | −0.218845 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.3340 | −1.40971 | −0.704856 | − | 0.709351i | \(-0.748988\pi\) | ||||
−0.704856 | + | 0.709351i | \(0.748988\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.990671 | 0.0622830 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.00933 | −0.438941 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.829359 | −0.0517340 | −0.0258670 | − | 0.999665i | \(-0.508235\pi\) | ||||
−0.0258670 | + | 0.999665i | \(0.508235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.6519 | −1.46966 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23132 | 0.509506 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.73599 | 0.353696 | 0.176848 | − | 0.984238i | \(-0.443410\pi\) | ||||
0.176848 | + | 0.984238i | \(0.443410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.72666 | −0.536074 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.51399 | 0.153854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1379 | −0.922977 | −0.461488 | − | 0.887146i | \(-0.652684\pi\) | ||||
−0.461488 | + | 0.887146i | \(0.652684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.6680 | −1.49848 | −0.749239 | − | 0.662300i | \(-0.769580\pi\) | ||||
−0.749239 | + | 0.662300i | \(0.769580\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.2920 | −0.925514 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.778008 | −0.0469156 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.28267 | −0.257321 | −0.128660 | − | 0.991689i | \(-0.541068\pi\) | ||||
−0.128660 | + | 0.991689i | \(0.541068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00933 | 0.299901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.5140 | 1.82031 | 0.910156 | − | 0.414265i | \(-0.135961\pi\) | ||||
0.910156 | + | 0.414265i | \(0.135961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.5233 | 1.04165 | 0.520827 | − | 0.853662i | \(-0.325624\pi\) | ||||
0.520827 | + | 0.853662i | \(0.325624\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.1706 | −1.48578 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.1307 | 1.89004 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.51399 | −0.499099 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.71733 | 0.334010 | 0.167005 | − | 0.985956i | \(-0.446590\pi\) | ||||
0.167005 | + | 0.985956i | \(0.446590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.29200 | 0.308112 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.778008 | 0.0451446 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.00933 | 0.405360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.2080 | 1.68352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5560 | −0.893670 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.73599 | 0.442961 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.46264 | −0.482988 | −0.241494 | − | 0.970402i | \(-0.577637\pi\) | ||||
−0.241494 | + | 0.970402i | \(0.577637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.45331 | 0.0826761 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2313 | −0.580165 | −0.290082 | − | 0.957002i | \(-0.593683\pi\) | ||||
−0.290082 | + | 0.957002i | \(0.593683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.1400 | 1.70361 | 0.851807 | − | 0.523855i | \(-0.175507\pi\) | ||||
0.851807 | + | 0.523855i | \(0.175507\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.77801 | 0.156523 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.83869 | 0.440265 | 0.220132 | − | 0.975470i | \(-0.429351\pi\) | ||||
0.220132 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.40403 | −0.358557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0187 | −0.782445 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.00933 | −0.390009 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.50466 | −0.305344 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.29200 | 0.403249 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.6867 | 1.03023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.29200 | −0.400805 | −0.200402 | − | 0.979714i | \(-0.564225\pi\) | ||||
−0.200402 | + | 0.979714i | \(0.564225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.51399 | 0.466564 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.45331 | 0.0794030 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4953 | −0.571717 | −0.285859 | − | 0.958272i | \(-0.592279\pi\) | ||||
−0.285859 | + | 0.958272i | \(0.592279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.7360 | −1.07191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.89730 | −0.211050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4533 | 0.942390 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.27334 | −0.0685545 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.43466 | −0.291748 | −0.145874 | − | 0.989303i | \(-0.546599\pi\) | ||||
−0.145874 | + | 0.989303i | \(0.546599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.43466 | −0.0767954 | −0.0383977 | − | 0.999263i | \(-0.512225\pi\) | ||||
−0.0383977 | + | 0.999263i | \(0.512225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.50466 | 0.293817 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.73599 | −0.305296 | −0.152648 | − | 0.988281i | \(-0.548780\pi\) | ||||
−0.152648 | + | 0.988281i | \(0.548780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4626 | 0.661448 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.4720 | −1.03057 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7780 | 1.51885 | 0.759423 | − | 0.650598i | \(-0.225482\pi\) | ||||
0.759423 | + | 0.650598i | \(0.225482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3947 | 0.545580 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.5653 | −0.762385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.9087 | −1.66562 | −0.832810 | − | 0.553559i | \(-0.813269\pi\) | ||||
−0.832810 | + | 0.553559i | \(0.813269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.06068 | 0.471680 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.2427 | −1.25862 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.5233 | −1.21799 | −0.608996 | − | 0.793174i | \(-0.708427\pi\) | ||||
−0.608996 | + | 0.793174i | \(0.708427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.3107 | −2.33362 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2920 | 1.40190 | 0.700948 | − | 0.713212i | \(-0.252761\pi\) | ||||
0.700948 | + | 0.713212i | \(0.252761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45331 | −0.0744555 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.65872 | 0.289147 | 0.144574 | − | 0.989494i | \(-0.453819\pi\) | ||||
0.144574 | + | 0.989494i | \(0.453819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.16131 | −0.110151 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5140 | −0.534456 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.9253 | 1.56797 | 0.783987 | − | 0.620777i | \(-0.213183\pi\) | ||||
0.783987 | + | 0.620777i | \(0.213183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.92528 | 0.451371 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7873 | −0.796366 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.28267 | −0.114854 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1893 | −0.561575 | −0.280787 | − | 0.959770i | \(-0.590596\pi\) | ||||
−0.280787 | + | 0.959770i | \(0.590596\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.77801 | 0.139074 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.60737 | −0.379894 | −0.189947 | − | 0.981794i | \(-0.560832\pi\) | ||||
−0.189947 | + | 0.981794i | \(0.560832\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.5747 | −1.37359 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.62395 | −0.328337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6680 | −0.923076 | −0.461538 | − | 0.887121i | \(-0.652702\pi\) | ||||
−0.461538 | + | 0.887121i | \(0.652702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.282672 | 0.0139432 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.7012 | 0.723400 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.45331 | −0.169516 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.4626 | −0.806179 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.8994 | 1.50953 | 0.754766 | − | 0.655994i | \(-0.227750\pi\) | ||||
0.754766 | + | 0.655994i | \(0.227750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7360 | −1.05935 | −0.529674 | − | 0.848202i | \(-0.677686\pi\) | ||||
−0.529674 | + | 0.848202i | \(0.677686\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.72666 | −0.327061 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.00933 | −0.340002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.4906 | 1.04000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.28267 | −0.206769 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.1400 | 1.16278 | 0.581392 | − | 0.813624i | \(-0.302508\pi\) | ||||
0.581392 | + | 0.813624i | \(0.302508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.53265 | −0.313939 | −0.156970 | − | 0.987603i | \(-0.550172\pi\) | ||||
−0.156970 | + | 0.987603i | \(0.550172\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.23132 | 0.394662 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.27334 | −0.0609123 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.2080 | 1.29856 | 0.649282 | − | 0.760547i | \(-0.275069\pi\) | ||||
0.649282 | + | 0.760547i | \(0.275069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.717328 | 0.0341585 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.1587 | −1.71795 | −0.858975 | − | 0.512017i | \(-0.828898\pi\) | ||||
−0.858975 | + | 0.512017i | \(0.828898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.51399 | 0.119175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0000 | −0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.6540 | −1.82420 | −0.912098 | − | 0.409973i | \(-0.865538\pi\) | ||||
−0.912098 | + | 0.409973i | \(0.865538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.04928 | −0.331938 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.5747 | 1.01367 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.2920 | −0.716900 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.1587 | 1.87854 | 0.939272 | − | 0.343174i | \(-0.111502\pi\) | ||||
0.939272 | + | 0.343174i | \(0.111502\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.00933 | 0.327167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.9253 | −1.06774 | −0.533868 | − | 0.845568i | \(-0.679262\pi\) | ||||
−0.533868 | + | 0.845568i | \(0.679262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.11929 | −0.237914 | −0.118957 | − | 0.992899i | \(-0.537955\pi\) | ||||
−0.118957 | + | 0.992899i | \(0.537955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.00933 | 0.232302 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.0280 | 1.62090 | 0.810451 | − | 0.585807i | \(-0.199222\pi\) | ||||
0.810451 | + | 0.585807i | \(0.199222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.03731 | 0.186426 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8387 | 0.637653 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.17997 | 0.376115 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.72666 | 0.399566 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.8153 | −1.86490 | −0.932450 | − | 0.361299i | \(-0.882333\pi\) | ||||
−0.932450 | + | 0.361299i | \(0.882333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.8667 | −2.13694 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.53736 | −0.160955 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.51399 | −0.386601 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.9160 | −0.993107 | −0.496553 | − | 0.868006i | \(-0.665401\pi\) | ||||
−0.496553 | + | 0.868006i | \(0.665401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.6167 | −0.841876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9927 | −0.721742 | −0.360871 | − | 0.932616i | \(-0.617521\pi\) | ||||
−0.360871 | + | 0.932616i | \(0.617521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −57.6960 | −2.59850 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.778008 | 0.0349689 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.6213 | 1.55298 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.668047 | −0.0299059 | −0.0149530 | − | 0.999888i | \(-0.504760\pi\) | ||||
−0.0149530 | + | 0.999888i | \(0.504760\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.73599 | 0.434972 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4881 | 0.556816 | 0.278408 | − | 0.960463i | \(-0.410193\pi\) | ||||
0.278408 | + | 0.960463i | \(0.410193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5560 | −0.692234 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.3013 | −0.768379 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.32469 | −0.0587161 | −0.0293580 | − | 0.999569i | \(-0.509346\pi\) | ||||
−0.0293580 | + | 0.999569i | \(0.509346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.4626 | −1.78996 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.45331 | 0.0640406 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.23339 | 0.230164 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.82936 | −0.211985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.3272 | 1.41628 | 0.708141 | − | 0.706071i | \(-0.249534\pi\) | ||||
0.708141 | + | 0.706071i | \(0.249534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.2334 | 1.45319 | 0.726597 | − | 0.687063i | \(-0.241101\pi\) | ||||
0.726597 | + | 0.687063i | \(0.241101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.77801 | 0.121242 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.1120 | −1.52950 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3786 | −0.929504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.29200 | −0.229653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.8760 | −2.16037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0187 | −0.606079 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.8387 | −1.02872 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.558087 | −0.0240385 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0934 | 0.476941 | 0.238471 | − | 0.971150i | \(-0.423354\pi\) | ||||
0.238471 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.7267 | 0.631981 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.29200 | 0.312355 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.55602 | −0.237558 | −0.118779 | − | 0.992921i | \(-0.537898\pi\) | ||||
−0.118779 | + | 0.992921i | \(0.537898\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.73599 | −0.330164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.23132 | 0.350666 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.34128 | −0.269659 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.51399 | 0.361399 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.2427 | 1.28143 | 0.640713 | − | 0.767781i | \(-0.278639\pi\) | ||||
0.640713 | + | 0.767781i | \(0.278639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 57.8760 | 2.44789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.45331 | −0.230239 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.8853 | 1.38595 | 0.692976 | − | 0.720961i | \(-0.256299\pi\) | ||||
0.692976 | + | 0.720961i | \(0.256299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.7360 | −0.830299 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.77801 | −0.116665 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.48601 | −0.397674 | −0.198837 | − | 0.980033i | \(-0.563716\pi\) | ||||
−0.198837 | + | 0.980033i | \(0.563716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.0653 | −1.88592 | −0.942962 | − | 0.332900i | \(-0.891973\pi\) | ||||
−0.942962 | + | 0.332900i | \(0.891973\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.22199 | 0.134601 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.27334 | −0.0531021 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.6680 | −1.44325 | −0.721625 | − | 0.692284i | \(-0.756604\pi\) | ||||
−0.721625 | + | 0.692284i | \(0.756604\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.50466 | −0.228766 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.59333 | −0.397998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.78941 | −0.281189 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.50466 | 0.227590 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.3879 | −1.46062 | −0.730308 | − | 0.683118i | \(-0.760623\pi\) | ||||
−0.730308 | + | 0.683118i | \(0.760623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00933 | 0.206406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.17997 | −0.254210 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.2080 | 1.03517 | 0.517583 | − | 0.855633i | \(-0.326832\pi\) | ||||
0.517583 | + | 0.855633i | \(0.326832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.4720 | −0.798273 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.0280 | 0.696909 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6027 | 1.33211 | 0.666054 | − | 0.745903i | \(-0.267982\pi\) | ||||
0.666054 | + | 0.745903i | \(0.267982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.89730 | 0.240556 | 0.120278 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120278 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.45331 | −0.0591835 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3947 | 0.422605 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.46264 | 0.343488 | 0.171744 | − | 0.985142i | \(-0.445060\pi\) | ||||
0.171744 | + | 0.985142i | \(0.445060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.8667 | 0.926604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.0280 | 1.49799 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.4413 | 1.87575 | 0.937874 | − | 0.346976i | \(-0.112791\pi\) | ||||
0.937874 | + | 0.346976i | \(0.112791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.06068 | 0.365362 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.42533 | 0.178157 | 0.0890785 | − | 0.996025i | \(-0.471608\pi\) | ||||
0.0890785 | + | 0.996025i | \(0.471608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9907 | 1.16523 | 0.582617 | − | 0.812747i | \(-0.302029\pi\) | ||||
0.582617 | + | 0.812747i | \(0.302029\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.27334 | 0.0510975 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.98389 | 0.279804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.778008 | 0.0310706 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −59.6774 | −2.37949 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.98134 | −0.0788760 | −0.0394380 | − | 0.999222i | \(-0.512557\pi\) | ||||
−0.0394380 | + | 0.999222i | \(0.512557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.56534 | −0.340442 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.45331 | −0.0576730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.94865 | −0.156451 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4626 | −0.493014 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.17271 | −0.164812 | −0.0824061 | − | 0.996599i | \(-0.526260\pi\) | ||||
−0.0824061 | + | 0.996599i | \(0.526260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.6167 | −0.576426 | −0.288213 | − | 0.957566i | \(-0.593061\pi\) | ||||
−0.288213 | + | 0.957566i | \(0.593061\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.5140 | −0.413988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.17064 | 0.0460226 | 0.0230113 | − | 0.999735i | \(-0.492675\pi\) | ||||
0.0230113 | + | 0.999735i | \(0.492675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.11722 | 0.161615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.9160 | 0.545409 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.6519 | −0.690774 | −0.345387 | − | 0.938460i | \(-0.612252\pi\) | ||||
−0.345387 | + | 0.938460i | \(0.612252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.7873 | −0.616862 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.5653 | 0.568248 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.5067 | 1.11046 | 0.555232 | − | 0.831695i | \(-0.312629\pi\) | ||||
0.555232 | + | 0.831695i | \(0.312629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5161 | 1.14804 | 0.574021 | − | 0.818841i | \(-0.305383\pi\) | ||||
0.574021 | + | 0.818841i | \(0.305383\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −38.5840 | −1.49848 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.77801 | 0.107727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4813 | −0.405838 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.98134 | 0.0766031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.01866 | 0.232348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.50466 | 0.0580005 | 0.0290003 | − | 0.999579i | \(-0.490768\pi\) | ||||
0.0290003 | + | 0.999579i | \(0.490768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.85735 | −0.378849 | −0.189424 | − | 0.981895i | \(-0.560662\pi\) | ||||
−0.189424 | + | 0.981895i | \(0.560662\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.6519 | −0.907678 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.282672 | −0.0108320 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.65872 | 0.0634691 | 0.0317346 | − | 0.999496i | \(-0.489897\pi\) | ||||
0.0317346 | + | 0.999496i | \(0.489897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.282672 | 0.0108004 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.26401 | −0.162682 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.0373 | −1.83008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.2147 | 0.730963 | 0.365481 | − | 0.930819i | \(-0.380904\pi\) | ||||
0.365481 | + | 0.930819i | \(0.380904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.16131 | 0.0821015 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4626 | −0.624464 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −63.5093 | −2.40559 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.62395 | 0.250541 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.5653 | 1.30552 | 0.652758 | − | 0.757567i | \(-0.273612\pi\) | ||||
0.652758 | + | 0.757567i | \(0.273612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.51399 | 0.321111 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.72666 | −0.253341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.2147 | −1.62526 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.84802 | 0.106960 | 0.0534798 | − | 0.998569i | \(-0.482969\pi\) | ||||
0.0534798 | + | 0.998569i | \(0.482969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28267 | 0.0856069 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.37860 | −0.238880 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.28267 | −0.160163 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.21266 | −0.157325 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.12862 | −0.228559 | −0.114279 | − | 0.993449i | \(-0.536456\pi\) | ||||
−0.114279 | + | 0.993449i | \(0.536456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.03731 | 0.150357 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.1120 | 0.933927 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.23132 | 0.305704 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.6753 | −0.395925 | −0.197963 | − | 0.980210i | \(-0.563432\pi\) | ||||
−0.197963 | + | 0.980210i | \(0.563432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.6960 | 2.72575 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.6426 | 1.50117 | 0.750585 | − | 0.660774i | \(-0.229772\pi\) | ||||
0.750585 | + | 0.660774i | \(0.229772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.717328 | 0.0264590 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.13069 | 0.0416495 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2241 | 0.964668 | 0.482334 | − | 0.875987i | \(-0.339789\pi\) | ||||
0.482334 | + | 0.875987i | \(0.339789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.50466 | 0.202219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.56534 | −0.314232 | −0.157116 | − | 0.987580i | \(-0.550220\pi\) | ||||
−0.157116 | + | 0.987580i | \(0.550220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.45331 | 0.126350 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38.9439 | −1.42298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.3693 | −1.50959 | −0.754793 | − | 0.655963i | \(-0.772263\pi\) | ||||
−0.754793 | + | 0.655963i | \(0.772263\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.3340 | 0.813897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.5747 | 0.785183 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1986 | 1.24297 | 0.621485 | − | 0.783426i | \(-0.286530\pi\) | ||||
0.621485 | + | 0.783426i | \(0.286530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.990671 | −0.0359591 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.2572 | 0.733361 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.00933 | 0.253423 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.1307 | 1.05185 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.5840 | −0.886522 | −0.443261 | − | 0.896393i | \(-0.646178\pi\) | ||||
−0.443261 | + | 0.896393i | \(0.646178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.829359 | 0.0298686 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.2173 | 1.51845 | 0.759225 | − | 0.650828i | \(-0.225578\pi\) | ||||
0.759225 | + | 0.650828i | \(0.225578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00933 | 0.179940 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.6519 | 0.848509 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.06068 | 0.324633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.69603 | 0.346951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.23132 | −0.294163 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.8387 | 0.493924 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.8226 | 0.884829 | 0.442415 | − | 0.896811i | \(-0.354122\pi\) | ||||
0.442415 | + | 0.896811i | \(0.354122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.73599 | −0.204206 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54.8267 | −1.94941 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.5840 | 1.51220 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.72666 | 0.309503 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.1706 | 0.395684 | 0.197842 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197842 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.1493 | 1.66802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.51399 | −0.0888276 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.3320 | −0.399896 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.53736 | −0.124675 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1379 | 0.532881 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.9066 | 0.875670 | 0.437835 | − | 0.899055i | \(-0.355745\pi\) | ||||
0.437835 | + | 0.899055i | \(0.355745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6774 | 1.53372 | 0.766860 | − | 0.641814i | \(-0.221818\pi\) | ||||
0.766860 | + | 0.641814i | \(0.221818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.6680 | 0.865146 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6167 | −0.652114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5140 | −0.367838 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2920 | 0.534346 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8039 | −0.586461 | −0.293230 | − | 0.956042i | \(-0.594730\pi\) | ||||
−0.293230 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.33402 | 0.290506 | 0.145253 | − | 0.989395i | \(-0.453600\pi\) | ||||
0.145253 | + | 0.989395i | \(0.453600\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.778008 | 0.0270868 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.7173 | −0.407451 | −0.203726 | − | 0.979028i | \(-0.565305\pi\) | ||||
−0.203726 | + | 0.979028i | \(0.565305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.2173 | 0.563250 | 0.281625 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281625 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.28267 | 0.148564 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.02799 | −0.174209 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.73599 | 0.336928 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00933 | −0.173148 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.6120 | −1.22946 | −0.614731 | − | 0.788737i | \(-0.710736\pi\) | ||||
−0.614731 | + | 0.788737i | \(0.710736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.7546 | 1.33637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.5140 | −1.05096 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.3013 | −0.595184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.8766 | 0.992211 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.5233 | −0.601399 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8412 | −0.371633 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.3854 | −0.834939 | −0.417470 | − | 0.908691i | \(-0.637083\pi\) | ||||
−0.417470 | + | 0.908691i | \(0.637083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.2733 | −1.34155 | −0.670776 | − | 0.741660i | \(-0.734039\pi\) | ||||
−0.670776 | + | 0.741660i | \(0.734039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4720 | 0.527897 | 0.263948 | − | 0.964537i | \(-0.414975\pi\) | ||||
0.263948 | + | 0.964537i | \(0.414975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.1706 | 0.857813 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65872 | 0.192625 | 0.0963125 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963125 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.82936 | −0.164203 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.1307 | −1.09122 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.77594 | −0.0602445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.51399 | 0.288155 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.77801 | 0.0939138 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.06068 | −0.103352 | −0.0516759 | − | 0.998664i | \(-0.516456\pi\) | ||||
−0.0516759 | + | 0.998664i | \(0.516456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.71733 | −0.192841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6867 | 0.427426 | 0.213713 | − | 0.976896i | \(-0.431444\pi\) | ||||
0.213713 | + | 0.976896i | \(0.431444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.0793 | −0.911292 | −0.455646 | − | 0.890161i | \(-0.650592\pi\) | ||||
−0.455646 | + | 0.890161i | \(0.650592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.29200 | −0.177889 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.8880 | −0.432736 | −0.216368 | − | 0.976312i | \(-0.569421\pi\) | ||||
−0.216368 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.03731 | −0.135407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.778008 | −0.0260642 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.72666 | −0.225099 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.8387 | −0.796839 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.00933 | −0.234035 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.2334 | 1.37521 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61.1680 | −2.03780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.2080 | −0.971980 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.7267 | 0.489531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5560 | −0.450120 | −0.225060 | − | 0.974345i | \(-0.572258\pi\) | ||||
−0.225060 | + | 0.974345i | \(0.572258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5560 | 0.515960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.0934 | −0.566329 | −0.283164 | − | 0.959071i | \(-0.591384\pi\) | ||||
−0.283164 | + | 0.959071i | \(0.591384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.68670 | −0.0889169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.73599 | −0.255744 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.8573 | −1.44830 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7708 | 0.817112 | 0.408556 | − | 0.912733i | \(-0.366033\pi\) | ||||
0.408556 | + | 0.912733i | \(0.366033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.46264 | 0.278854 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.6027 | 2.25808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.51399 | 0.279938 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.45331 | −0.0477331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.57467 | 0.0516634 | 0.0258317 | − | 0.999666i | \(-0.491777\pi\) | ||||
0.0258317 | + | 0.999666i | \(0.491777\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.717328 | 0.0235095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.2313 | 0.334958 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.45331 | −0.178342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5933 | −0.901435 | −0.450717 | − | 0.892667i | \(-0.648832\pi\) | ||||
−0.450717 | + | 0.892667i | \(0.648832\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.1400 | −0.983582 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.3713 | 1.70726 | 0.853628 | − | 0.520882i | \(-0.174397\pi\) | ||||
0.853628 | + | 0.520882i | \(0.174397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5374 | −0.375708 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.77801 | −0.0903686 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.2427 | −1.50269 | −0.751343 | − | 0.659912i | \(-0.770594\pi\) | ||||
−0.751343 | + | 0.659912i | \(0.770594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.1773 | −2.60267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.83869 | −0.254187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1893 | 1.20468 | 0.602340 | − | 0.798240i | \(-0.294235\pi\) | ||||
0.602340 | + | 0.798240i | \(0.294235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.22199 | 0.104261 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.40403 | 0.207013 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.785266 | 0.0253576 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.90663 | −0.190536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.0187 | 0.451745 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.50466 | −0.177201 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.2500 | 1.35867 | 0.679334 | − | 0.733829i | \(-0.262269\pi\) | ||||
0.679334 | + | 0.733829i | \(0.262269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.00933 | 0.225172 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.73599 | −0.248260 | −0.124130 | − | 0.992266i | \(-0.539614\pi\) | ||||
−0.124130 | + | 0.992266i | \(0.539614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.7333 | −1.46614 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.50466 | 0.176290 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.9880 | −1.24734 | −0.623669 | − | 0.781689i | \(-0.714359\pi\) | ||||
−0.623669 | + | 0.781689i | \(0.714359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.95591 | 0.0625110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.29200 | −0.232816 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.39470 | −0.235854 | −0.117927 | − | 0.993022i | \(-0.537625\pi\) | ||||
−0.117927 | + | 0.993022i | \(0.537625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.17997 | −0.196910 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.6867 | −0.594804 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.3879 | 0.425711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6613 | 1.41871 | 0.709356 | − | 0.704850i | \(-0.248986\pi\) | ||||
0.709356 | + | 0.704850i | \(0.248986\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.29200 | 0.231405 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0280 | 0.539823 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.74531 | −0.276967 | −0.138483 | − | 0.990365i | \(-0.544223\pi\) | ||||
−0.138483 | + | 0.990365i | \(0.544223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.51399 | −0.269371 |
(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 | 2280.2.a.r.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 6840.2.a.bk.1.2 | 3 | |||
4.3 | odd | 2 | 4560.2.a.bt.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.r.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4560.2.a.bt.1.2 | 3 | 4.3 | odd | 2 | |||
6840.2.a.bk.1.2 | 3 | 3.2 | odd | 2 |