Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(1,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, 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("4410.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.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: | \(35.2140272914\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.41421 | 1.02942 | 0.514712 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514712 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.17157 | −0.324936 | −0.162468 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162468 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.41421 | 0.828068 | 0.414034 | − | 0.910261i | \(-0.364119\pi\) | ||||
0.414034 | + | 0.910261i | \(0.364119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.82843 | −1.10772 | −0.553859 | − | 0.832611i | \(-0.686845\pi\) | ||||
−0.553859 | + | 0.832611i | \(0.686845\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.41421 | −0.727913 | ||||||||
\(23\) | −3.65685 | −0.762507 | −0.381253 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381253 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.17157 | 0.229764 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.41421 | 1.00539 | 0.502697 | − | 0.864463i | \(-0.332341\pi\) | ||||
0.502697 | + | 0.864463i | \(0.332341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.41421 | −1.33163 | −0.665816 | − | 0.746116i | \(-0.731916\pi\) | ||||
−0.665816 | + | 0.746116i | \(0.731916\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.41421 | −0.585533 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.41421 | −0.561293 | −0.280647 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280647 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(38\) | 4.82843 | 0.783274 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.07107 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(44\) | 3.41421 | 0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.65685 | 0.539174 | ||||||||
\(47\) | 2.58579 | 0.377176 | 0.188588 | − | 0.982056i | \(-0.439609\pi\) | ||||
0.188588 | + | 0.982056i | \(0.439609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.17157 | −0.162468 | ||||||||
\(53\) | 6.48528 | 0.890822 | 0.445411 | − | 0.895326i | \(-0.353058\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.41421 | −0.460372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.41421 | −0.710921 | ||||||||
\(59\) | −0.828427 | −0.107852 | −0.0539260 | − | 0.998545i | \(-0.517174\pi\) | ||||
−0.0539260 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65685 | 0.212138 | 0.106069 | − | 0.994359i | \(-0.466173\pi\) | ||||
0.106069 | + | 0.994359i | \(0.466173\pi\) | |||||||
\(62\) | 7.41421 | 0.941606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.17157 | 0.145316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.89949 | 0.720738 | 0.360369 | − | 0.932810i | \(-0.382651\pi\) | ||||
0.360369 | + | 0.932810i | \(0.382651\pi\) | |||||||
\(68\) | 3.41421 | 0.414034 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4853 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713756\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8284 | −1.50145 | −0.750727 | − | 0.660613i | \(-0.770297\pi\) | ||||
−0.750727 | + | 0.660613i | \(0.770297\pi\) | |||||||
\(74\) | 3.41421 | 0.396894 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.82843 | −0.553859 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.65685 | 0.403832 | ||||||||
\(83\) | 0.485281 | 0.0532666 | 0.0266333 | − | 0.999645i | \(-0.491521\pi\) | ||||
0.0266333 | + | 0.999645i | \(0.491521\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.41421 | −0.370323 | ||||||||
\(86\) | 7.07107 | 0.762493 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.41421 | −0.363956 | ||||||||
\(89\) | 14.4853 | 1.53544 | 0.767718 | − | 0.640787i | \(-0.221392\pi\) | ||||
0.767718 | + | 0.640787i | \(0.221392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.65685 | −0.381253 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.58579 | −0.266704 | ||||||||
\(95\) | 4.82843 | 0.495386 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4853 | −1.47076 | −0.735379 | − | 0.677656i | \(-0.762996\pi\) | ||||
−0.735379 | + | 0.677656i | \(0.762996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.65685 | 0.960893 | 0.480446 | − | 0.877024i | \(-0.340475\pi\) | ||||
0.480446 | + | 0.877024i | \(0.340475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.65685 | −0.557386 | −0.278693 | − | 0.960380i | \(-0.589901\pi\) | ||||
−0.278693 | + | 0.960380i | \(0.589901\pi\) | |||||||
\(104\) | 1.17157 | 0.114882 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.48528 | −0.629906 | ||||||||
\(107\) | −10.8284 | −1.04682 | −0.523412 | − | 0.852080i | \(-0.675341\pi\) | ||||
−0.523412 | + | 0.852080i | \(0.675341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4853 | 1.38744 | 0.693719 | − | 0.720246i | \(-0.255971\pi\) | ||||
0.693719 | + | 0.720246i | \(0.255971\pi\) | |||||||
\(110\) | 3.41421 | 0.325532 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.34315 | −0.408569 | −0.204284 | − | 0.978912i | \(-0.565487\pi\) | ||||
−0.204284 | + | 0.978912i | \(0.565487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.65685 | 0.341003 | ||||||||
\(116\) | 5.41421 | 0.502697 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.828427 | 0.0762629 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | −1.65685 | −0.150005 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.41421 | −0.665816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.17157 | −0.102754 | ||||||||
\(131\) | −6.48528 | −0.566622 | −0.283311 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283311 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.89949 | −0.509639 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.41421 | −0.292766 | ||||||||
\(137\) | 4.48528 | 0.383203 | 0.191602 | − | 0.981473i | \(-0.438632\pi\) | ||||
0.191602 | + | 0.981473i | \(0.438632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.31371 | 0.111427 | 0.0557137 | − | 0.998447i | \(-0.482257\pi\) | ||||
0.0557137 | + | 0.998447i | \(0.482257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.4853 | 0.879905 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.41421 | −0.449626 | ||||||||
\(146\) | 12.8284 | 1.06169 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.41421 | −0.280647 | ||||||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.17157 | 0.258099 | 0.129049 | − | 0.991638i | \(-0.458807\pi\) | ||||
0.129049 | + | 0.991638i | \(0.458807\pi\) | |||||||
\(152\) | 4.82843 | 0.391637 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.41421 | 0.595524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | −13.6569 | −1.08648 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07107 | 0.553849 | 0.276924 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276924 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(164\) | −3.65685 | −0.285552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.485281 | −0.0376651 | ||||||||
\(167\) | −6.58579 | −0.509623 | −0.254812 | − | 0.966991i | \(-0.582013\pi\) | ||||
−0.254812 | + | 0.966991i | \(0.582013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | 3.41421 | 0.261858 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.07107 | −0.539164 | ||||||||
\(173\) | −20.1421 | −1.53138 | −0.765689 | − | 0.643211i | \(-0.777602\pi\) | ||||
−0.765689 | + | 0.643211i | \(0.777602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41421 | 0.257356 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.4853 | −1.08572 | ||||||||
\(179\) | 10.7279 | 0.801843 | 0.400921 | − | 0.916113i | \(-0.368690\pi\) | ||||
0.400921 | + | 0.916113i | \(0.368690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.51472 | −0.261247 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.65685 | 0.269587 | ||||||||
\(185\) | 3.41421 | 0.251018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6569 | 0.852434 | ||||||||
\(188\) | 2.58579 | 0.188588 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.82843 | −0.350291 | ||||||||
\(191\) | −9.31371 | −0.673916 | −0.336958 | − | 0.941520i | \(-0.609398\pi\) | ||||
−0.336958 | + | 0.941520i | \(0.609398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1421 | 1.44986 | 0.724931 | − | 0.688821i | \(-0.241871\pi\) | ||||
0.724931 | + | 0.688821i | \(0.241871\pi\) | |||||||
\(194\) | 14.4853 | 1.03998 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.343146 | −0.0244481 | −0.0122241 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122241 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2426 | −1.29319 | −0.646593 | − | 0.762835i | \(-0.723807\pi\) | ||||
−0.646593 | + | 0.762835i | \(0.723807\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.65685 | −0.679454 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | 5.65685 | 0.394132 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.17157 | −0.0812340 | ||||||||
\(209\) | −16.4853 | −1.14031 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.7990 | −1.63839 | −0.819195 | − | 0.573515i | \(-0.805579\pi\) | ||||
−0.819195 | + | 0.573515i | \(0.805579\pi\) | |||||||
\(212\) | 6.48528 | 0.445411 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.8284 | 0.740216 | ||||||||
\(215\) | 7.07107 | 0.482243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.4853 | −0.981067 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.41421 | −0.230186 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8284 | 0.725125 | 0.362563 | − | 0.931959i | \(-0.381902\pi\) | ||||
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.34315 | 0.288902 | ||||||||
\(227\) | −24.9706 | −1.65735 | −0.828677 | − | 0.559727i | \(-0.810906\pi\) | ||||
−0.828677 | + | 0.559727i | \(0.810906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.17157 | 0.341747 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(230\) | −3.65685 | −0.241126 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.41421 | −0.355461 | ||||||||
\(233\) | −23.6569 | −1.54981 | −0.774906 | − | 0.632076i | \(-0.782203\pi\) | ||||
−0.774906 | + | 0.632076i | \(0.782203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58579 | −0.168678 | ||||||||
\(236\) | −0.828427 | −0.0539260 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6569 | 1.27150 | 0.635748 | − | 0.771897i | \(-0.280692\pi\) | ||||
0.635748 | + | 0.771897i | \(0.280692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0711 | −1.22848 | −0.614238 | − | 0.789121i | \(-0.710536\pi\) | ||||
−0.614238 | + | 0.789121i | \(0.710536\pi\) | |||||||
\(242\) | −0.656854 | −0.0422242 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.65685 | 0.106069 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.65685 | 0.359937 | ||||||||
\(248\) | 7.41421 | 0.470803 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −14.3431 | −0.905331 | −0.452666 | − | 0.891680i | \(-0.649527\pi\) | ||||
−0.452666 | + | 0.891680i | \(0.649527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4853 | −0.784943 | ||||||||
\(254\) | 14.1421 | 0.887357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.89949 | 0.243244 | 0.121622 | − | 0.992577i | \(-0.461190\pi\) | ||||
0.121622 | + | 0.992577i | \(0.461190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.17157 | 0.0726579 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.48528 | 0.400662 | ||||||||
\(263\) | 10.0000 | 0.616626 | 0.308313 | − | 0.951285i | \(-0.400236\pi\) | ||||
0.308313 | + | 0.951285i | \(0.400236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.48528 | −0.398388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.89949 | 0.360369 | ||||||||
\(269\) | −14.9706 | −0.912771 | −0.456386 | − | 0.889782i | \(-0.650856\pi\) | ||||
−0.456386 | + | 0.889782i | \(0.650856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.75736 | −0.106752 | −0.0533760 | − | 0.998574i | \(-0.516998\pi\) | ||||
−0.0533760 | + | 0.998574i | \(0.516998\pi\) | |||||||
\(272\) | 3.41421 | 0.207017 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.48528 | −0.270966 | ||||||||
\(275\) | 3.41421 | 0.205885 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.4142 | −1.88750 | −0.943749 | − | 0.330664i | \(-0.892727\pi\) | ||||
−0.943749 | + | 0.330664i | \(0.892727\pi\) | |||||||
\(278\) | −1.31371 | −0.0787910 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4558 | 1.27995 | 0.639974 | − | 0.768396i | \(-0.278945\pi\) | ||||
0.639974 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9706 | 0.889908 | 0.444954 | − | 0.895554i | \(-0.353220\pi\) | ||||
0.444954 | + | 0.895554i | \(0.353220\pi\) | |||||||
\(284\) | −10.4853 | −0.622187 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.34315 | −0.314303 | ||||||||
\(290\) | 5.41421 | 0.317934 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.8284 | −0.750727 | ||||||||
\(293\) | 25.3137 | 1.47884 | 0.739421 | − | 0.673243i | \(-0.235099\pi\) | ||||
0.739421 | + | 0.673243i | \(0.235099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.828427 | 0.0482329 | ||||||||
\(296\) | 3.41421 | 0.198447 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.7279 | 0.737309 | ||||||||
\(299\) | 4.28427 | 0.247766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.17157 | −0.182504 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.82843 | −0.276929 | ||||||||
\(305\) | −1.65685 | −0.0948712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.6274 | −1.51971 | −0.759853 | − | 0.650094i | \(-0.774729\pi\) | ||||
−0.759853 | + | 0.650094i | \(0.774729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.41421 | −0.421099 | ||||||||
\(311\) | 21.4558 | 1.21665 | 0.608325 | − | 0.793688i | \(-0.291842\pi\) | ||||
0.608325 | + | 0.793688i | \(0.291842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.65685 | −0.432791 | −0.216395 | − | 0.976306i | \(-0.569430\pi\) | ||||
−0.216395 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6569 | 0.768258 | ||||||||
\(317\) | −14.9706 | −0.840831 | −0.420415 | − | 0.907332i | \(-0.638116\pi\) | ||||
−0.420415 | + | 0.907332i | \(0.638116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4853 | 1.03498 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.4853 | −0.917266 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.17157 | −0.0649872 | ||||||||
\(326\) | −7.07107 | −0.391630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.65685 | 0.201916 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.7990 | 0.868391 | 0.434196 | − | 0.900819i | \(-0.357033\pi\) | ||||
0.434196 | + | 0.900819i | \(0.357033\pi\) | |||||||
\(332\) | 0.485281 | 0.0266333 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.58579 | 0.360358 | ||||||||
\(335\) | −5.89949 | −0.322324 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.4853 | −1.44275 | −0.721373 | − | 0.692547i | \(-0.756488\pi\) | ||||
−0.721373 | + | 0.692547i | \(0.756488\pi\) | |||||||
\(338\) | 11.6274 | 0.632448 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.41421 | −0.185162 | ||||||||
\(341\) | −25.3137 | −1.37081 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.07107 | 0.381246 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1421 | 1.08285 | ||||||||
\(347\) | −17.6569 | −0.947870 | −0.473935 | − | 0.880560i | \(-0.657167\pi\) | ||||
−0.473935 | + | 0.880560i | \(0.657167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4853 | 1.09655 | 0.548276 | − | 0.836297i | \(-0.315284\pi\) | ||||
0.548276 | + | 0.836297i | \(0.315284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.41421 | −0.181978 | ||||||||
\(353\) | 11.8995 | 0.633346 | 0.316673 | − | 0.948535i | \(-0.397434\pi\) | ||||
0.316673 | + | 0.948535i | \(0.397434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4853 | 0.556501 | ||||||||
\(356\) | 14.4853 | 0.767718 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7279 | −0.566988 | ||||||||
\(359\) | 32.8284 | 1.73262 | 0.866309 | − | 0.499508i | \(-0.166486\pi\) | ||||
0.866309 | + | 0.499508i | \(0.166486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | 3.51472 | 0.184730 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.8284 | 0.671471 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.485281 | 0.0253315 | 0.0126657 | − | 0.999920i | \(-0.495968\pi\) | ||||
0.0126657 | + | 0.999920i | \(0.495968\pi\) | |||||||
\(368\) | −3.65685 | −0.190627 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.41421 | −0.177497 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.7574 | 1.12655 | 0.563277 | − | 0.826268i | \(-0.309541\pi\) | ||||
0.563277 | + | 0.826268i | \(0.309541\pi\) | |||||||
\(374\) | −11.6569 | −0.602762 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.58579 | −0.133352 | ||||||||
\(377\) | −6.34315 | −0.326689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.48528 | 0.230393 | 0.115197 | − | 0.993343i | \(-0.463250\pi\) | ||||
0.115197 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(380\) | 4.82843 | 0.247693 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.31371 | 0.476531 | ||||||||
\(383\) | −29.6985 | −1.51752 | −0.758761 | − | 0.651369i | \(-0.774195\pi\) | ||||
−0.758761 | + | 0.651369i | \(0.774195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.1421 | −1.02521 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.4853 | −0.735379 | ||||||||
\(389\) | −16.0416 | −0.813343 | −0.406671 | − | 0.913574i | \(-0.633311\pi\) | ||||
−0.406671 | + | 0.913574i | \(0.633311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4853 | −0.631408 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.343146 | 0.0172874 | ||||||||
\(395\) | −13.6569 | −0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.34315 | −0.418730 | −0.209365 | − | 0.977838i | \(-0.567140\pi\) | ||||
−0.209365 | + | 0.977838i | \(0.567140\pi\) | |||||||
\(398\) | 18.2426 | 0.914421 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −4.97056 | −0.248218 | −0.124109 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124109 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.68629 | 0.432695 | ||||||||
\(404\) | 9.65685 | 0.480446 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.6569 | −0.577809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.8701 | −1.32864 | −0.664319 | − | 0.747449i | \(-0.731279\pi\) | ||||
−0.664319 | + | 0.747449i | \(0.731279\pi\) | |||||||
\(410\) | −3.65685 | −0.180599 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.65685 | −0.278693 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.485281 | −0.0238215 | ||||||||
\(416\) | 1.17157 | 0.0574411 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.4853 | 0.806321 | ||||||||
\(419\) | −40.2843 | −1.96802 | −0.984008 | − | 0.178126i | \(-0.942997\pi\) | ||||
−0.984008 | + | 0.178126i | \(0.942997\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.82843 | 0.430271 | 0.215136 | − | 0.976584i | \(-0.430981\pi\) | ||||
0.215136 | + | 0.976584i | \(0.430981\pi\) | |||||||
\(422\) | 23.7990 | 1.15852 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.48528 | −0.314953 | ||||||||
\(425\) | 3.41421 | 0.165614 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.8284 | −0.523412 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.07107 | −0.340997 | ||||||||
\(431\) | 16.1421 | 0.777539 | 0.388770 | − | 0.921335i | \(-0.372900\pi\) | ||||
0.388770 | + | 0.921335i | \(0.372900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8284 | −1.57763 | −0.788817 | − | 0.614628i | \(-0.789306\pi\) | ||||
−0.788817 | + | 0.614628i | \(0.789306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4853 | 0.693719 | ||||||||
\(437\) | 17.6569 | 0.844642 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.2426 | −0.679764 | −0.339882 | − | 0.940468i | \(-0.610387\pi\) | ||||
−0.339882 | + | 0.940468i | \(0.610387\pi\) | |||||||
\(440\) | 3.41421 | 0.162766 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | 0.970563 | 0.0461128 | 0.0230564 | − | 0.999734i | \(-0.492660\pi\) | ||||
0.0230564 | + | 0.999734i | \(0.492660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4853 | −0.686668 | ||||||||
\(446\) | −10.8284 | −0.512741 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.8284 | 1.83243 | 0.916213 | − | 0.400691i | \(-0.131230\pi\) | ||||
0.916213 | + | 0.400691i | \(0.131230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.4853 | −0.587909 | ||||||||
\(452\) | −4.34315 | −0.204284 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.9706 | 1.17193 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.142136 | 0.00664882 | 0.00332441 | − | 0.999994i | \(-0.498942\pi\) | ||||
0.00332441 | + | 0.999994i | \(0.498942\pi\) | |||||||
\(458\) | −5.17157 | −0.241652 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.65685 | 0.170502 | ||||||||
\(461\) | −2.68629 | −0.125113 | −0.0625565 | − | 0.998041i | \(-0.519925\pi\) | ||||
−0.0625565 | + | 0.998041i | \(0.519925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.0000 | 1.67306 | 0.836531 | − | 0.547920i | \(-0.184580\pi\) | ||||
0.836531 | + | 0.547920i | \(0.184580\pi\) | |||||||
\(464\) | 5.41421 | 0.251349 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.6569 | 1.09588 | ||||||||
\(467\) | −38.8284 | −1.79677 | −0.898383 | − | 0.439214i | \(-0.855257\pi\) | ||||
−0.898383 | + | 0.439214i | \(0.855257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.58579 | 0.119273 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.828427 | 0.0381314 | ||||||||
\(473\) | −24.1421 | −1.11006 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.82843 | −0.221543 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.6569 | −0.899084 | ||||||||
\(479\) | −30.8284 | −1.40859 | −0.704293 | − | 0.709909i | \(-0.748736\pi\) | ||||
−0.704293 | + | 0.709909i | \(0.748736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 19.0711 | 0.868663 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.656854 | 0.0298570 | ||||||||
\(485\) | 14.4853 | 0.657743 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.17157 | −0.415604 | −0.207802 | − | 0.978171i | \(-0.566631\pi\) | ||||
−0.207802 | + | 0.978171i | \(0.566631\pi\) | |||||||
\(488\) | −1.65685 | −0.0750023 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9289 | −0.854251 | −0.427125 | − | 0.904192i | \(-0.640474\pi\) | ||||
−0.427125 | + | 0.904192i | \(0.640474\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.4853 | 0.832535 | ||||||||
\(494\) | −5.65685 | −0.254514 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.41421 | −0.332908 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.1127 | −1.39280 | −0.696398 | − | 0.717656i | \(-0.745215\pi\) | ||||
−0.696398 | + | 0.717656i | \(0.745215\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.3431 | 0.640166 | ||||||||
\(503\) | −25.4142 | −1.13316 | −0.566582 | − | 0.824005i | \(-0.691735\pi\) | ||||
−0.566582 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.65685 | −0.429724 | ||||||||
\(506\) | 12.4853 | 0.555038 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.1421 | −0.627456 | ||||||||
\(509\) | 35.5980 | 1.57785 | 0.788926 | − | 0.614488i | \(-0.210637\pi\) | ||||
0.788926 | + | 0.614488i | \(0.210637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.89949 | −0.171999 | ||||||||
\(515\) | 5.65685 | 0.249271 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.82843 | 0.388274 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.17157 | −0.0513769 | ||||||||
\(521\) | −20.8284 | −0.912510 | −0.456255 | − | 0.889849i | \(-0.650810\pi\) | ||||
−0.456255 | + | 0.889849i | \(0.650810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6274 | −1.07688 | −0.538441 | − | 0.842663i | \(-0.680986\pi\) | ||||
−0.538441 | + | 0.842663i | \(0.680986\pi\) | |||||||
\(524\) | −6.48528 | −0.283311 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0000 | −0.436021 | ||||||||
\(527\) | −25.3137 | −1.10268 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 6.48528 | 0.281703 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.28427 | 0.185572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8284 | 0.468154 | ||||||||
\(536\) | −5.89949 | −0.254819 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.9706 | 0.645427 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.9411 | −1.88918 | −0.944588 | − | 0.328258i | \(-0.893539\pi\) | ||||
−0.944588 | + | 0.328258i | \(0.893539\pi\) | |||||||
\(542\) | 1.75736 | 0.0754850 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.41421 | −0.146383 | ||||||||
\(545\) | −14.4853 | −0.620481 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.27208 | −0.310932 | −0.155466 | − | 0.987841i | \(-0.549688\pi\) | ||||
−0.155466 | + | 0.987841i | \(0.549688\pi\) | |||||||
\(548\) | 4.48528 | 0.191602 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.41421 | −0.145583 | ||||||||
\(551\) | −26.1421 | −1.11369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 31.4142 | 1.33466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.31371 | 0.0557137 | ||||||||
\(557\) | 6.68629 | 0.283307 | 0.141654 | − | 0.989916i | \(-0.454758\pi\) | ||||
0.141654 | + | 0.989916i | \(0.454758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.28427 | 0.350387 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.4558 | −0.905060 | ||||||||
\(563\) | 15.7990 | 0.665848 | 0.332924 | − | 0.942954i | \(-0.391965\pi\) | ||||
0.332924 | + | 0.942954i | \(0.391965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.34315 | 0.182718 | ||||||||
\(566\) | −14.9706 | −0.629260 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.4853 | 0.439953 | ||||||||
\(569\) | 0.686292 | 0.0287708 | 0.0143854 | − | 0.999897i | \(-0.495421\pi\) | ||||
0.0143854 | + | 0.999897i | \(0.495421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.68629 | −0.196115 | −0.0980576 | − | 0.995181i | \(-0.531263\pi\) | ||||
−0.0980576 | + | 0.995181i | \(0.531263\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.65685 | −0.152501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.6274 | 1.52482 | 0.762410 | − | 0.647095i | \(-0.224016\pi\) | ||||
0.762410 | + | 0.647095i | \(0.224016\pi\) | |||||||
\(578\) | 5.34315 | 0.222246 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.41421 | −0.224813 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.1421 | 0.917034 | ||||||||
\(584\) | 12.8284 | 0.530844 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.3137 | −1.04570 | ||||||||
\(587\) | 10.1421 | 0.418611 | 0.209305 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209305 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.7990 | 1.47507 | ||||||||
\(590\) | −0.828427 | −0.0341058 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.41421 | −0.140323 | ||||||||
\(593\) | −39.6985 | −1.63022 | −0.815111 | − | 0.579305i | \(-0.803324\pi\) | ||||
−0.815111 | + | 0.579305i | \(0.803324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.7279 | −0.521356 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.28427 | −0.175197 | ||||||||
\(599\) | 32.6274 | 1.33312 | 0.666560 | − | 0.745451i | \(-0.267766\pi\) | ||||
0.666560 | + | 0.745451i | \(0.267766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.3848 | 1.89207 | 0.946037 | − | 0.324058i | \(-0.105047\pi\) | ||||
0.946037 | + | 0.324058i | \(0.105047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.17157 | 0.129049 | ||||||||
\(605\) | −0.656854 | −0.0267049 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.1127 | 1.26283 | 0.631413 | − | 0.775447i | \(-0.282475\pi\) | ||||
0.631413 | + | 0.775447i | \(0.282475\pi\) | |||||||
\(608\) | 4.82843 | 0.195819 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.65685 | 0.0670841 | ||||||||
\(611\) | −3.02944 | −0.122558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4142 | 0.784133 | 0.392066 | − | 0.919937i | \(-0.371760\pi\) | ||||
0.392066 | + | 0.919937i | \(0.371760\pi\) | |||||||
\(614\) | 26.6274 | 1.07460 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1127 | 1.57462 | 0.787309 | − | 0.616559i | \(-0.211474\pi\) | ||||
0.787309 | + | 0.616559i | \(0.211474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.828427 | −0.0332973 | −0.0166486 | − | 0.999861i | \(-0.505300\pi\) | ||||
−0.0166486 | + | 0.999861i | \(0.505300\pi\) | |||||||
\(620\) | 7.41421 | 0.297762 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.4558 | −0.860301 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.65685 | 0.306029 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | −0.399043 | ||||||||
\(629\) | −11.6569 | −0.464789 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4558 | 0.615287 | 0.307644 | − | 0.951502i | \(-0.400460\pi\) | ||||
0.307644 | + | 0.951502i | \(0.400460\pi\) | |||||||
\(632\) | −13.6569 | −0.543240 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.9706 | 0.594557 | ||||||||
\(635\) | 14.1421 | 0.561214 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.4853 | −0.731839 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −18.6274 | −0.735739 | −0.367869 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367869 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.97056 | −0.274892 | −0.137446 | − | 0.990509i | \(-0.543889\pi\) | ||||
−0.137446 | + | 0.990509i | \(0.543889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.4853 | 0.648605 | ||||||||
\(647\) | −13.6152 | −0.535270 | −0.267635 | − | 0.963520i | \(-0.586242\pi\) | ||||
−0.267635 | + | 0.963520i | \(0.586242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.82843 | −0.111025 | ||||||||
\(650\) | 1.17157 | 0.0459529 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.07107 | 0.276924 | ||||||||
\(653\) | −45.1127 | −1.76540 | −0.882698 | − | 0.469940i | \(-0.844275\pi\) | ||||
−0.882698 | + | 0.469940i | \(0.844275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.48528 | 0.253401 | ||||||||
\(656\) | −3.65685 | −0.142776 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.5858 | 1.11354 | 0.556772 | − | 0.830665i | \(-0.312040\pi\) | ||||
0.556772 | + | 0.830665i | \(0.312040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3431 | 0.869048 | 0.434524 | − | 0.900660i | \(-0.356917\pi\) | ||||
0.434524 | + | 0.900660i | \(0.356917\pi\) | |||||||
\(662\) | −15.7990 | −0.614045 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.485281 | −0.0188326 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.7990 | −0.766620 | ||||||||
\(668\) | −6.58579 | −0.254812 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.89949 | 0.227917 | ||||||||
\(671\) | 5.65685 | 0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9706 | 0.422884 | 0.211442 | − | 0.977391i | \(-0.432184\pi\) | ||||
0.211442 | + | 0.977391i | \(0.432184\pi\) | |||||||
\(674\) | 26.4853 | 1.02017 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6274 | −0.447208 | ||||||||
\(677\) | −15.4558 | −0.594016 | −0.297008 | − | 0.954875i | \(-0.595989\pi\) | ||||
−0.297008 | + | 0.954875i | \(0.595989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.41421 | 0.130929 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 25.3137 | 0.969312 | ||||||||
\(683\) | −26.3431 | −1.00799 | −0.503996 | − | 0.863706i | \(-0.668137\pi\) | ||||
−0.503996 | + | 0.863706i | \(0.668137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.48528 | −0.171374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.07107 | −0.269582 | ||||||||
\(689\) | −7.59798 | −0.289460 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02944 | 0.0391616 | 0.0195808 | − | 0.999808i | \(-0.493767\pi\) | ||||
0.0195808 | + | 0.999808i | \(0.493767\pi\) | |||||||
\(692\) | −20.1421 | −0.765689 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.6569 | 0.670245 | ||||||||
\(695\) | −1.31371 | −0.0498318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | −20.4853 | −0.775379 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.75736 | −0.292991 | −0.146496 | − | 0.989211i | \(-0.546799\pi\) | ||||
−0.146496 | + | 0.989211i | \(0.546799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.4853 | 0.621754 | ||||||||
\(704\) | 3.41421 | 0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8995 | −0.447843 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1127 | 0.792904 | 0.396452 | − | 0.918055i | \(-0.370241\pi\) | ||||
0.396452 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(710\) | −10.4853 | −0.393506 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.4853 | −0.542859 | ||||||||
\(713\) | 27.1127 | 1.01538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 10.7279 | 0.400921 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.8284 | −1.22515 | ||||||||
\(719\) | 33.4558 | 1.24769 | 0.623846 | − | 0.781547i | \(-0.285569\pi\) | ||||
0.623846 | + | 0.781547i | \(0.285569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.31371 | −0.160540 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.51472 | −0.130623 | ||||||||
\(725\) | 5.41421 | 0.201079 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4558 | −0.499050 | −0.249525 | − | 0.968368i | \(-0.580274\pi\) | ||||
−0.249525 | + | 0.968368i | \(0.580274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.8284 | −0.474801 | ||||||||
\(731\) | −24.1421 | −0.892929 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.97056 | 0.257464 | 0.128732 | − | 0.991679i | \(-0.458909\pi\) | ||||
0.128732 | + | 0.991679i | \(0.458909\pi\) | |||||||
\(734\) | −0.485281 | −0.0179121 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.65685 | 0.134793 | ||||||||
\(737\) | 20.1421 | 0.741945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.82843 | −0.104045 | −0.0520227 | − | 0.998646i | \(-0.516567\pi\) | ||||
−0.0520227 | + | 0.998646i | \(0.516567\pi\) | |||||||
\(740\) | 3.41421 | 0.125509 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.6569 | −1.67499 | −0.837494 | − | 0.546447i | \(-0.815980\pi\) | ||||
−0.837494 | + | 0.546447i | \(0.815980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.7279 | 0.466315 | ||||||||
\(746\) | −21.7574 | −0.796594 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.6569 | 0.426217 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.7990 | −1.52527 | −0.762633 | − | 0.646831i | \(-0.776094\pi\) | ||||
−0.762633 | + | 0.646831i | \(0.776094\pi\) | |||||||
\(752\) | 2.58579 | 0.0942939 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.34315 | 0.231004 | ||||||||
\(755\) | −3.17157 | −0.115425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3553 | 0.776173 | 0.388087 | − | 0.921623i | \(-0.373136\pi\) | ||||
0.388087 | + | 0.921623i | \(0.373136\pi\) | |||||||
\(758\) | −4.48528 | −0.162913 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.82843 | −0.175145 | ||||||||
\(761\) | −8.62742 | −0.312744 | −0.156372 | − | 0.987698i | \(-0.549980\pi\) | ||||
−0.156372 | + | 0.987698i | \(0.549980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.31371 | −0.336958 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.6985 | 1.07305 | ||||||||
\(767\) | 0.970563 | 0.0350450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.9289 | 0.466229 | 0.233115 | − | 0.972449i | \(-0.425108\pi\) | ||||
0.233115 | + | 0.972449i | \(0.425108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.1421 | 0.724931 | ||||||||
\(773\) | 18.9706 | 0.682324 | 0.341162 | − | 0.940005i | \(-0.389180\pi\) | ||||
0.341162 | + | 0.940005i | \(0.389180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.41421 | −0.266326 | ||||||||
\(776\) | 14.4853 | 0.519991 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.0416 | 0.575120 | ||||||||
\(779\) | 17.6569 | 0.632622 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.7990 | −1.28099 | ||||||||
\(782\) | 12.4853 | 0.446473 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.02944 | 0.107988 | 0.0539939 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539939 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(788\) | −0.343146 | −0.0122241 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6569 | 0.485889 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.94113 | −0.0689314 | ||||||||
\(794\) | 8.34315 | 0.296087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.2426 | −0.646593 | ||||||||
\(797\) | 7.85786 | 0.278340 | 0.139170 | − | 0.990269i | \(-0.455557\pi\) | ||||
0.139170 | + | 0.990269i | \(0.455557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.82843 | 0.312327 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.97056 | 0.175517 | ||||||||
\(803\) | −43.7990 | −1.54563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.68629 | −0.305962 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.65685 | −0.339727 | ||||||||
\(809\) | 16.4853 | 0.579592 | 0.289796 | − | 0.957088i | \(-0.406413\pi\) | ||||
0.289796 | + | 0.957088i | \(0.406413\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.6274 | 0.864786 | 0.432393 | − | 0.901685i | \(-0.357669\pi\) | ||||
0.432393 | + | 0.901685i | \(0.357669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.6569 | 0.408573 | ||||||||
\(815\) | −7.07107 | −0.247689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1421 | 1.19448 | ||||||||
\(818\) | 26.8701 | 0.939490 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.65685 | 0.127703 | ||||||||
\(821\) | −28.9289 | −1.00963 | −0.504813 | − | 0.863229i | \(-0.668439\pi\) | ||||
−0.504813 | + | 0.863229i | \(0.668439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3431 | 0.360539 | 0.180270 | − | 0.983617i | \(-0.442303\pi\) | ||||
0.180270 | + | 0.983617i | \(0.442303\pi\) | |||||||
\(824\) | 5.65685 | 0.197066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7990 | −0.827572 | −0.413786 | − | 0.910374i | \(-0.635794\pi\) | ||||
−0.413786 | + | 0.910374i | \(0.635794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | 0.485281 | 0.0168444 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.17157 | −0.0406170 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.58579 | 0.227911 | ||||||||
\(836\) | −16.4853 | −0.570155 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 40.2843 | 1.39160 | ||||||||
\(839\) | −24.2843 | −0.838386 | −0.419193 | − | 0.907897i | \(-0.637687\pi\) | ||||
−0.419193 | + | 0.907897i | \(0.637687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.313708 | 0.0108175 | ||||||||
\(842\) | −8.82843 | −0.304248 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.7990 | −0.819195 | ||||||||
\(845\) | 11.6274 | 0.399995 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.48528 | 0.222705 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.41421 | −0.117107 | ||||||||
\(851\) | 12.4853 | 0.427990 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.6569 | 1.76870 | 0.884349 | − | 0.466827i | \(-0.154603\pi\) | ||||
0.884349 | + | 0.466827i | \(0.154603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.8284 | 0.370108 | ||||||||
\(857\) | 51.8995 | 1.77285 | 0.886426 | − | 0.462869i | \(-0.153180\pi\) | ||||
0.886426 | + | 0.462869i | \(0.153180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.9706 | −1.05670 | −0.528351 | − | 0.849026i | \(-0.677189\pi\) | ||||
−0.528351 | + | 0.849026i | \(0.677189\pi\) | |||||||
\(860\) | 7.07107 | 0.241121 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.1421 | −0.549803 | ||||||||
\(863\) | −28.9706 | −0.986169 | −0.493085 | − | 0.869981i | \(-0.664131\pi\) | ||||
−0.493085 | + | 0.869981i | \(0.664131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.1421 | 0.684853 | ||||||||
\(866\) | 32.8284 | 1.11556 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6274 | 1.58173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.91169 | −0.234194 | ||||||||
\(872\) | −14.4853 | −0.490534 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.6569 | −0.597252 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5563 | −1.40326 | −0.701629 | − | 0.712542i | \(-0.747544\pi\) | ||||
−0.701629 | + | 0.712542i | \(0.747544\pi\) | |||||||
\(878\) | 14.2426 | 0.480666 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.41421 | −0.115093 | ||||||||
\(881\) | 52.1421 | 1.75671 | 0.878357 | − | 0.478006i | \(-0.158640\pi\) | ||||
0.878357 | + | 0.478006i | \(0.158640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5269 | 0.690786 | 0.345393 | − | 0.938458i | \(-0.387746\pi\) | ||||
0.345393 | + | 0.938458i | \(0.387746\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.970563 | −0.0326067 | ||||||||
\(887\) | 45.8995 | 1.54115 | 0.770577 | − | 0.637347i | \(-0.219968\pi\) | ||||
0.770577 | + | 0.637347i | \(0.219968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.4853 | 0.485548 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.8284 | 0.362563 | ||||||||
\(893\) | −12.4853 | −0.417804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7279 | −0.358595 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.8284 | −1.29572 | ||||||||
\(899\) | −40.1421 | −1.33882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.1421 | 0.737661 | ||||||||
\(902\) | 12.4853 | 0.415714 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.34315 | 0.144451 | ||||||||
\(905\) | 3.51472 | 0.116833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.3259 | −1.87027 | −0.935135 | − | 0.354290i | \(-0.884722\pi\) | ||||
−0.935135 | + | 0.354290i | \(0.884722\pi\) | |||||||
\(908\) | −24.9706 | −0.828677 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.5980 | −0.848099 | −0.424049 | − | 0.905639i | \(-0.639392\pi\) | ||||
−0.424049 | + | 0.905639i | \(0.639392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65685 | 0.0548339 | ||||||||
\(914\) | −0.142136 | −0.00470143 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.17157 | 0.170874 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.4558 | −0.641789 | −0.320895 | − | 0.947115i | \(-0.603984\pi\) | ||||
−0.320895 | + | 0.947115i | \(0.603984\pi\) | |||||||
\(920\) | −3.65685 | −0.120563 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.68629 | 0.0884683 | ||||||||
\(923\) | 12.2843 | 0.404342 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.41421 | −0.112259 | ||||||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.41421 | −0.177730 | ||||||||
\(929\) | 52.9117 | 1.73598 | 0.867988 | − | 0.496585i | \(-0.165413\pi\) | ||||
0.867988 | + | 0.496585i | \(0.165413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.6569 | −0.774906 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.8284 | 1.27050 | ||||||||
\(935\) | −11.6569 | −0.381220 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9706 | 0.619741 | 0.309871 | − | 0.950779i | \(-0.399714\pi\) | ||||
0.309871 | + | 0.950779i | \(0.399714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.58579 | −0.0843391 | ||||||||
\(941\) | 56.0000 | 1.82555 | 0.912774 | − | 0.408465i | \(-0.133936\pi\) | ||||
0.912774 | + | 0.408465i | \(0.133936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3726 | 0.435471 | ||||||||
\(944\) | −0.828427 | −0.0269630 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.1421 | 0.784929 | ||||||||
\(947\) | 38.6274 | 1.25522 | 0.627611 | − | 0.778527i | \(-0.284033\pi\) | ||||
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.0294 | 0.487876 | ||||||||
\(950\) | 4.82843 | 0.156655 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.1716 | −1.46325 | −0.731625 | − | 0.681707i | \(-0.761238\pi\) | ||||
−0.731625 | + | 0.681707i | \(0.761238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.31371 | 0.301385 | ||||||||
\(956\) | 19.6569 | 0.635748 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.8284 | 0.996021 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.0711 | −0.614238 | ||||||||
\(965\) | −20.1421 | −0.648398 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9706 | 1.31752 | 0.658762 | − | 0.752351i | \(-0.271080\pi\) | ||||
0.658762 | + | 0.752351i | \(0.271080\pi\) | |||||||
\(968\) | −0.656854 | −0.0211121 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.4853 | −0.465094 | ||||||||
\(971\) | 9.65685 | 0.309903 | 0.154952 | − | 0.987922i | \(-0.450478\pi\) | ||||
0.154952 | + | 0.987922i | \(0.450478\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.17157 | 0.293876 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.65685 | 0.0530346 | ||||||||
\(977\) | 29.3137 | 0.937829 | 0.468914 | − | 0.883244i | \(-0.344645\pi\) | ||||
0.468914 | + | 0.883244i | \(0.344645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.4558 | 1.58062 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.9289 | 0.604046 | ||||||||
\(983\) | 14.3848 | 0.458803 | 0.229402 | − | 0.973332i | \(-0.426323\pi\) | ||||
0.229402 | + | 0.973332i | \(0.426323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.343146 | 0.0109335 | ||||||||
\(986\) | −18.4853 | −0.588691 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.65685 | 0.179969 | ||||||||
\(989\) | 25.8579 | 0.822232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1421 | −0.385708 | −0.192854 | − | 0.981227i | \(-0.561774\pi\) | ||||
−0.192854 | + | 0.981227i | \(0.561774\pi\) | |||||||
\(992\) | 7.41421 | 0.235402 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.2426 | 0.578331 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.34315 | 0.264230 | 0.132115 | − | 0.991234i | \(-0.457823\pi\) | ||||
0.132115 | + | 0.991234i | \(0.457823\pi\) | |||||||
\(998\) | 31.1127 | 0.984855 | ||||||||
\(999\) | 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 | 4410.2.a.bp.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4410.2.a.bx.1.1 | yes | 2 | ||
7.6 | odd | 2 | 4410.2.a.bs.1.2 | yes | 2 | ||
21.20 | even | 2 | 4410.2.a.bu.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.a.bp.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4410.2.a.bs.1.2 | yes | 2 | 7.6 | odd | 2 | ||
4410.2.a.bu.1.1 | yes | 2 | 21.20 | even | 2 | ||
4410.2.a.bx.1.1 | yes | 2 | 3.2 | odd | 2 |