Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, 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("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.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: | \(59.4086991038\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 465) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-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 | ||||||||
\(7\) | 1.17009 | 0.442251 | 0.221126 | − | 0.975245i | \(-0.429027\pi\) | ||||
0.221126 | + | 0.975245i | \(0.429027\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0917087 | 0.0254354 | 0.0127177 | − | 0.999919i | \(-0.495952\pi\) | ||||
0.0127177 | + | 0.999919i | \(0.495952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.04945 | −1.46721 | −0.733603 | − | 0.679578i | \(-0.762163\pi\) | ||||
−0.733603 | + | 0.679578i | \(0.762163\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.17009 | −0.255334 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.70928 | 0.356409 | 0.178204 | − | 0.983994i | \(-0.442971\pi\) | ||||
0.178204 | + | 0.983994i | \(0.442971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.95774 | 1.47772 | 0.738858 | − | 0.673862i | \(-0.235366\pi\) | ||||
0.738858 | + | 0.673862i | \(0.235366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.17009 | 0.197781 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.35350 | −0.551313 | −0.275656 | − | 0.961256i | \(-0.588895\pi\) | ||||
−0.275656 | + | 0.961256i | \(0.588895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0917087 | −0.0146852 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.68035 | −0.730947 | −0.365474 | − | 0.930822i | \(-0.619093\pi\) | ||||
−0.365474 | + | 0.930822i | \(0.619093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.738205 | 0.112575 | 0.0562876 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562876 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.12783 | 1.33143 | 0.665715 | − | 0.746206i | \(-0.268127\pi\) | ||||
0.665715 | + | 0.746206i | \(0.268127\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.63090 | −0.804414 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.04945 | 0.847092 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.97107 | 0.682829 | 0.341415 | − | 0.939913i | \(-0.389094\pi\) | ||||
0.341415 | + | 0.939913i | \(0.389094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0361 | −1.43678 | −0.718390 | − | 0.695641i | \(-0.755121\pi\) | ||||
−0.718390 | + | 0.695641i | \(0.755121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.26180 | −0.417630 | −0.208815 | − | 0.977955i | \(-0.566961\pi\) | ||||
−0.208815 | + | 0.977955i | \(0.566961\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.17009 | 0.147417 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0917087 | 0.0113751 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.85043 | −0.470405 | −0.235203 | − | 0.971946i | \(-0.575575\pi\) | ||||
−0.235203 | + | 0.971946i | \(0.575575\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.70928 | −0.205773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.21953 | 0.144732 | 0.0723661 | − | 0.997378i | \(-0.476945\pi\) | ||||
0.0723661 | + | 0.997378i | \(0.476945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.66701 | 0.897356 | 0.448678 | − | 0.893693i | \(-0.351895\pi\) | ||||
0.448678 | + | 0.893693i | \(0.351895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.34017 | −0.266687 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.52586 | −0.396690 | −0.198345 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198345 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5464 | −1.37714 | −0.688572 | − | 0.725168i | \(-0.741762\pi\) | ||||
−0.688572 | + | 0.725168i | \(0.741762\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.04945 | −0.656155 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.95774 | −0.853159 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.77432 | −0.612077 | −0.306038 | − | 0.952019i | \(-0.599004\pi\) | ||||
−0.306038 | + | 0.952019i | \(0.599004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.107307 | 0.0112488 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9421 | 1.38729 | 0.693647 | − | 0.720315i | \(-0.256003\pi\) | ||||
0.693647 | + | 0.720315i | \(0.256003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.77205 | −0.667270 | −0.333635 | − | 0.942702i | \(-0.608275\pi\) | ||||
−0.333635 | + | 0.942702i | \(0.608275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17009 | −0.114189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.630898 | −0.0609912 | −0.0304956 | − | 0.999535i | \(-0.509709\pi\) | ||||
−0.0304956 | + | 0.999535i | \(0.509709\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.8660 | −1.13656 | −0.568280 | − | 0.822835i | \(-0.692391\pi\) | ||||
−0.568280 | + | 0.822835i | \(0.692391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.35350 | 0.318301 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75872 | 0.353591 | 0.176795 | − | 0.984248i | \(-0.443427\pi\) | ||||
0.176795 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70928 | 0.159391 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0917087 | 0.00847848 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.07838 | −0.648874 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.68035 | 0.422013 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.18342 | 0.371218 | 0.185609 | − | 0.982624i | \(-0.440574\pi\) | ||||
0.185609 | + | 0.982624i | \(0.440574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.738205 | −0.0649953 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.695944 | 0.0608049 | 0.0304025 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304025 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.20620 | 0.701103 | 0.350552 | − | 0.936543i | \(-0.385994\pi\) | ||||
0.350552 | + | 0.936543i | \(0.385994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.49693 | 0.381424 | 0.190712 | − | 0.981646i | \(-0.438920\pi\) | ||||
0.190712 | + | 0.981646i | \(0.438920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.12783 | −0.768702 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.183417 | −0.0153381 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.95774 | 0.660854 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.63090 | 0.464429 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3607 | 1.09455 | 0.547275 | − | 0.836953i | \(-0.315665\pi\) | ||||
0.547275 | + | 0.836953i | \(0.315665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8660 | −1.12840 | −0.564201 | − | 0.825638i | \(-0.690816\pi\) | ||||
−0.564201 | + | 0.825638i | \(0.690816\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.04945 | −0.489069 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0989 | −1.60407 | −0.802033 | − | 0.597279i | \(-0.796248\pi\) | ||||
−0.802033 | + | 0.597279i | \(0.796248\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97107 | −0.394232 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.06505 | −0.318399 | −0.159200 | − | 0.987246i | \(-0.550891\pi\) | ||||
−0.159200 | + | 0.987246i | \(0.550891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.91548 | −0.302989 | −0.151494 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151494 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9916 | −0.999353 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0722 | 1.22195 | 0.610975 | − | 0.791650i | \(-0.290778\pi\) | ||||
0.610975 | + | 0.791650i | \(0.290778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.17009 | 0.0884502 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0361 | 0.829525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9421 | −1.64003 | −0.820016 | − | 0.572340i | \(-0.806036\pi\) | ||||
−0.820016 | + | 0.572340i | \(0.806036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.94214 | 0.293017 | 0.146509 | − | 0.989209i | \(-0.453196\pi\) | ||||
0.146509 | + | 0.989209i | \(0.453196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.26180 | 0.241119 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.35350 | −0.246555 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0989 | 0.884759 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.17009 | −0.0851113 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.3184 | −1.68726 | −0.843631 | − | 0.536923i | \(-0.819587\pi\) | ||||
−0.843631 | + | 0.536923i | \(0.819587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2557 | −0.738218 | −0.369109 | − | 0.929386i | \(-0.620337\pi\) | ||||
−0.369109 | + | 0.929386i | \(0.620337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0917087 | −0.00656740 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.9916 | 1.70933 | 0.854665 | − | 0.519180i | \(-0.173763\pi\) | ||||
0.854665 | + | 0.519180i | \(0.173763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.1217 | 1.14284 | 0.571418 | − | 0.820659i | \(-0.306394\pi\) | ||||
0.571418 | + | 0.820659i | \(0.306394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.85043 | 0.271589 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.31124 | 0.653521 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.68035 | −0.326890 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.70928 | 0.118803 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4391 | −1.26940 | −0.634699 | − | 0.772759i | \(-0.718876\pi\) | ||||
−0.634699 | + | 0.772759i | \(0.718876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.21953 | −0.0835611 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.738205 | 0.0503451 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17009 | −0.0794306 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.66701 | −0.518089 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.554787 | −0.0373190 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.2762 | 1.02297 | 0.511484 | − | 0.859293i | \(-0.329096\pi\) | ||||
0.511484 | + | 0.859293i | \(0.329096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7815 | 1.31294 | 0.656472 | − | 0.754350i | \(-0.272048\pi\) | ||||
0.656472 | + | 0.754350i | \(0.272048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4329 | 1.68066 | 0.840328 | − | 0.542079i | \(-0.182363\pi\) | ||||
0.840328 | + | 0.542079i | \(0.182363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.34017 | 0.153972 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.2062 | −1.06170 | −0.530852 | − | 0.847465i | \(-0.678128\pi\) | ||||
−0.530852 | + | 0.847465i | \(0.678128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.12783 | 0.595434 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.52586 | 0.229029 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7587 | −1.27809 | −0.639043 | − | 0.769171i | \(-0.720669\pi\) | ||||
−0.639043 | + | 0.769171i | \(0.720669\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.65368 | −0.557433 | −0.278716 | − | 0.960373i | \(-0.589909\pi\) | ||||
−0.278716 | + | 0.960373i | \(0.589909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.63090 | −0.359745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.5464 | 0.795094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.9360 | 1.19523 | 0.597615 | − | 0.801783i | \(-0.296115\pi\) | ||||
0.597615 | + | 0.801783i | \(0.296115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.41855 | −0.214922 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.04945 | 0.378831 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.1012 | −0.817228 | −0.408614 | − | 0.912707i | \(-0.633988\pi\) | ||||
−0.408614 | + | 0.912707i | \(0.633988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.92389 | −0.243819 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.95774 | 0.492572 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.49693 | −0.523943 | −0.261972 | − | 0.965076i | \(-0.584373\pi\) | ||||
−0.261972 | + | 0.965076i | \(0.584373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.97107 | 0.305370 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.77432 | 0.353383 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.8010 | 1.32923 | 0.664615 | − | 0.747186i | \(-0.268596\pi\) | ||||
0.664615 | + | 0.747186i | \(0.268596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3402 | −0.628121 | −0.314060 | − | 0.949403i | \(-0.601689\pi\) | ||||
−0.314060 | + | 0.949403i | \(0.601689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.107307 | −0.00649452 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.646496 | −0.0388442 | −0.0194221 | − | 0.999811i | \(-0.506183\pi\) | ||||
−0.0194221 | + | 0.999811i | \(0.506183\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3874 | −1.03724 | −0.518621 | − | 0.855004i | \(-0.673555\pi\) | ||||
−0.518621 | + | 0.855004i | \(0.673555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.92881 | −0.174100 | −0.0870498 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870498 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.47641 | −0.323262 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.5958 | 1.15270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.9916 | −1.86897 | −0.934484 | − | 0.356004i | \(-0.884139\pi\) | ||||
−0.934484 | + | 0.356004i | \(0.884139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0361 | −0.642548 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.156755 | 0.00906540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.863763 | 0.0497865 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.9421 | −0.800955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.26180 | −0.186770 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.66701 | 0.323434 | 0.161717 | − | 0.986837i | \(-0.448297\pi\) | ||||
0.161717 | + | 0.986837i | \(0.448297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.77205 | 0.385249 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2401 | 0.920889 | 0.460444 | − | 0.887689i | \(-0.347690\pi\) | ||||
0.460444 | + | 0.887689i | \(0.347690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.42574 | 0.419728 | 0.209864 | − | 0.977731i | \(-0.432698\pi\) | ||||
0.209864 | + | 0.977731i | \(0.432698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.17009 | 0.0659269 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2534 | −0.744384 | −0.372192 | − | 0.928156i | \(-0.621394\pi\) | ||||
−0.372192 | + | 0.928156i | \(0.621394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.9155 | −0.891096 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.630898 | 0.0352133 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0917087 | 0.00508709 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.8660 | 0.656193 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6803 | 0.588827 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.62475 | −0.199235 | −0.0996173 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996173 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.35350 | −0.183771 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.85043 | −0.210372 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3268 | 0.725959 | 0.362980 | − | 0.931797i | \(-0.381759\pi\) | ||||
0.362980 | + | 0.931797i | \(0.381759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.75872 | −0.204146 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7792 | −0.798004 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.70928 | −0.0920243 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.2290 | −0.871218 | −0.435609 | − | 0.900136i | \(-0.643467\pi\) | ||||
−0.435609 | + | 0.900136i | \(0.643467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.38962 | 0.127913 | 0.0639567 | − | 0.997953i | \(-0.479628\pi\) | ||||
0.0639567 | + | 0.997953i | \(0.479628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0917087 | −0.00489505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.2062 | −1.92706 | −0.963531 | − | 0.267597i | \(-0.913770\pi\) | ||||
−0.963531 | + | 0.267597i | \(0.913770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.21953 | 0.0647262 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.07838 | 0.374627 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.382433 | −0.0201841 | −0.0100920 | − | 0.999949i | \(-0.503212\pi\) | ||||
−0.0100920 | + | 0.999949i | \(0.503212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.66701 | 0.401310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.63317 | 0.398448 | 0.199224 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199224 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.68035 | −0.243649 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.81658 | 0.301982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5486 | −0.908634 | −0.454317 | − | 0.890840i | \(-0.650117\pi\) | ||||
−0.454317 | + | 0.890840i | \(0.650117\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.729794 | 0.0375863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.68649 | −0.394828 | −0.197414 | − | 0.980320i | \(-0.563254\pi\) | ||||
−0.197414 | + | 0.980320i | \(0.563254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.18342 | −0.214323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.92389 | 0.302697 | 0.151348 | − | 0.988480i | \(-0.451638\pi\) | ||||
0.151348 | + | 0.988480i | \(0.451638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.34017 | −0.119266 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.738205 | 0.0375251 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.7636 | −1.45837 | −0.729187 | − | 0.684314i | \(-0.760102\pi\) | ||||
−0.729187 | + | 0.684314i | \(0.760102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3402 | −0.522925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.695944 | −0.0351057 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.52586 | −0.177405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.41855 | 0.472704 | 0.236352 | − | 0.971668i | \(-0.424048\pi\) | ||||
0.236352 | + | 0.971668i | \(0.424048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9721 | 0.697734 | 0.348867 | − | 0.937172i | \(-0.386566\pi\) | ||||
0.348867 | + | 0.937172i | \(0.386566\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0917087 | −0.00456834 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.70701 | 0.332454 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.73820 | 0.234289 | 0.117145 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117145 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.20620 | −0.404782 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.9132 | −0.635418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5464 | −0.615877 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.49693 | −0.220216 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.3123 | −1.48085 | −0.740426 | − | 0.672138i | \(-0.765376\pi\) | ||||
−0.740426 | + | 0.672138i | \(0.765376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.9916 | −1.65665 | −0.828324 | − | 0.560249i | \(-0.810706\pi\) | ||||
−0.828324 | + | 0.560249i | \(0.810706\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.12783 | 0.443810 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.04945 | −0.293441 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.81658 | −0.184697 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.183417 | 0.00885548 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6381 | −0.801428 | −0.400714 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400714 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8976 | −1.58096 | −0.790479 | − | 0.612489i | \(-0.790168\pi\) | ||||
−0.790479 | + | 0.612489i | \(0.790168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.95774 | −0.381544 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.5113 | 1.36077 | 0.680385 | − | 0.732855i | \(-0.261813\pi\) | ||||
0.680385 | + | 0.732855i | \(0.261813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.63090 | −0.268138 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0494 | 0.952578 | 0.476289 | − | 0.879289i | \(-0.341982\pi\) | ||||
0.476289 | + | 0.879289i | \(0.341982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.77432 | −0.273729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.3607 | −0.631939 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.7308 | −1.49747 | −0.748735 | − | 0.662869i | \(-0.769339\pi\) | ||||
−0.748735 | + | 0.662869i | \(0.769339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.36069 | 0.440778 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8660 | 0.651483 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.107307 | 0.00503064 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.7864 | −1.81435 | −0.907176 | − | 0.420751i | \(-0.861767\pi\) | ||||
−0.907176 | + | 0.420751i | \(0.861767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.04945 | 0.282364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.324575 | −0.0151169 | −0.00755847 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00755847 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8371 | −0.782486 | −0.391243 | − | 0.920287i | \(-0.627955\pi\) | ||||
−0.391243 | + | 0.920287i | \(0.627955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.0700 | 1.43775 | 0.718873 | − | 0.695141i | \(-0.244658\pi\) | ||||
0.718873 | + | 0.695141i | \(0.244658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.50534 | −0.208037 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0989 | 0.926108 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.47641 | −0.0678854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.97107 | 0.227610 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.3123 | 1.38500 | 0.692502 | − | 0.721416i | \(-0.256508\pi\) | ||||
0.692502 | + | 0.721416i | \(0.256508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.307546 | −0.0140229 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | −0.0910032 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.92777 | −0.268613 | −0.134306 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134306 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.06505 | 0.183828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1194 | 0.501812 | 0.250906 | − | 0.968011i | \(-0.419271\pi\) | ||||
0.250906 | + | 0.968011i | \(0.419271\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.1399 | −2.16811 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.42696 | 0.0640080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.482553 | 0.0216020 | 0.0108010 | − | 0.999942i | \(-0.496562\pi\) | ||||
0.0108010 | + | 0.999942i | \(0.496562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.91548 | 0.174931 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.1795 | −1.25646 | −0.628232 | − | 0.778026i | \(-0.716221\pi\) | ||||
−0.628232 | + | 0.778026i | \(0.716221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9421 | 0.620417 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9916 | 0.576977 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.8359 | −1.36678 | −0.683388 | − | 0.730055i | \(-0.739494\pi\) | ||||
−0.683388 | + | 0.730055i | \(0.739494\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.97107 | 0.396857 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.77205 | −0.298412 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.2557 | −0.802883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0722 | −0.705493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0472 | −1.27258 | −0.636290 | − | 0.771450i | \(-0.719532\pi\) | ||||
−0.636290 | + | 0.771450i | \(0.719532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5958 | −0.725685 | −0.362842 | − | 0.931851i | \(-0.618194\pi\) | ||||
−0.362842 | + | 0.931851i | \(0.618194\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.17009 | −0.0510668 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.04945 | 0.263518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0784 | −0.872973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0361 | −0.478927 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.429229 | −0.0185920 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.630898 | −0.0272761 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.9421 | 0.946873 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2618 | 0.485080 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.6370 | −0.500315 | −0.250158 | − | 0.968205i | \(-0.580482\pi\) | ||||
−0.250158 | + | 0.968205i | \(0.580482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.94214 | −0.169173 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8660 | −0.508285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.9821 | 0.555076 | 0.277538 | − | 0.960715i | \(-0.410482\pi\) | ||||
0.277538 | + | 0.960715i | \(0.410482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.26180 | −0.139210 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.12556 | −0.175437 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.35350 | 0.142348 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.9337 | 1.94627 | 0.973137 | − | 0.230225i | \(-0.0739464\pi\) | ||||
0.973137 | + | 0.230225i | \(0.0739464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0676998 | 0.00286340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0989 | −0.510816 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.2017 | 0.851399 | 0.425699 | − | 0.904865i | \(-0.360028\pi\) | ||||
0.425699 | + | 0.904865i | \(0.360028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.75872 | 0.158131 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.17009 | 0.0491390 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.1883 | 0.888261 | 0.444131 | − | 0.895962i | \(-0.353513\pi\) | ||||
0.444131 | + | 0.895962i | \(0.353513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.299135 | −0.0125184 | −0.00625921 | − | 0.999980i | \(-0.501992\pi\) | ||||
−0.00625921 | + | 0.999980i | \(0.501992\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.3184 | 0.974141 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70928 | 0.0712817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7009 | 0.820158 | 0.410079 | − | 0.912050i | \(-0.365501\pi\) | ||||
0.410079 | + | 0.912050i | \(0.365501\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2557 | 0.426210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6803 | −0.609043 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.94214 | −0.411761 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0917087 | 0.00379169 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.6598 | 0.563801 | 0.281901 | − | 0.959444i | \(-0.409035\pi\) | ||||
0.281901 | + | 0.959444i | \(0.409035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.9916 | −0.986882 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.4846 | 1.49824 | 0.749122 | − | 0.662432i | \(-0.230476\pi\) | ||||
0.749122 | + | 0.662432i | \(0.230476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.07838 | −0.290185 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.1217 | −0.659817 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1038 | −1.51602 | −0.758010 | − | 0.652242i | \(-0.773828\pi\) | ||||
−0.758010 | + | 0.652242i | \(0.773828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8638 | −1.09580 | −0.547898 | − | 0.836545i | \(-0.684572\pi\) | ||||
−0.547898 | + | 0.836545i | \(0.684572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.85043 | −0.156802 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.88777 | −0.279566 | −0.139783 | − | 0.990182i | \(-0.544641\pi\) | ||||
−0.139783 | + | 0.990182i | \(0.544641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.31124 | −0.377311 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.837101 | 0.0338655 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4729 | 1.15001 | 0.575005 | − | 0.818150i | \(-0.305000\pi\) | ||||
0.575005 | + | 0.818150i | \(0.305000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.68035 | 0.188730 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.20394 | 0.209503 | 0.104751 | − | 0.994498i | \(-0.466595\pi\) | ||||
0.104751 | + | 0.994498i | \(0.466595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0494 | −0.564695 | −0.282348 | − | 0.959312i | \(-0.591113\pi\) | ||||
−0.282348 | + | 0.959312i | \(0.591113\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70928 | −0.0685909 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.75646 | −0.270692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.2868 | 0.808890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.15061 | 0.125424 | 0.0627120 | − | 0.998032i | \(-0.480025\pi\) | ||||
0.0627120 | + | 0.998032i | \(0.480025\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.4391 | 0.732887 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.18342 | 0.166014 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.516403 | −0.0204606 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.21953 | 0.0482441 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.19448 | 0.165672 | 0.0828360 | − | 0.996563i | \(-0.473602\pi\) | ||||
0.0828360 | + | 0.996563i | \(0.473602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0722 | 1.50142 | 0.750711 | − | 0.660631i | \(-0.229711\pi\) | ||||
0.750711 | + | 0.660631i | \(0.229711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.738205 | −0.0290668 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.20847 | 0.204766 | 0.102383 | − | 0.994745i | \(-0.467353\pi\) | ||||
0.102383 | + | 0.994745i | \(0.467353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0722 | 0.866411 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.17009 | 0.0458593 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.6658 | 1.00438 | 0.502190 | − | 0.864757i | \(-0.332528\pi\) | ||||
0.502190 | + | 0.864757i | \(0.332528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.695944 | 0.0271928 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.66701 | 0.299119 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.9721 | 0.466367 | 0.233184 | − | 0.972433i | \(-0.425086\pi\) | ||||
0.233184 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.9504 | 1.43720 | 0.718601 | − | 0.695422i | \(-0.244783\pi\) | ||||
0.718601 | + | 0.695422i | \(0.244783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.554787 | 0.0215462 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6020 | 0.526670 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.2762 | −0.590611 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.52359 | 0.251840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8853 | −0.805070 | −0.402535 | − | 0.915405i | \(-0.631871\pi\) | ||||
−0.402535 | + | 0.915405i | \(0.631871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.1110 | −1.19569 | −0.597847 | − | 0.801611i | \(-0.703977\pi\) | ||||
−0.597847 | + | 0.801611i | \(0.703977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.0410 | −0.538846 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.7815 | −0.758029 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.1545 | −1.03904 | −0.519519 | − | 0.854459i | \(-0.673889\pi\) | ||||
−0.519519 | + | 0.854459i | \(0.673889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.20620 | 0.313543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.4329 | −0.970327 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.455891 | 0.0173680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.3234 | −1.61006 | −0.805028 | − | 0.593237i | \(-0.797850\pi\) | ||||
−0.805028 | + | 0.593237i | \(0.797850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.34017 | −0.0888958 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.49693 | 0.170578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.3135 | 1.07245 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.2062 | 0.612975 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.69472 | −0.328395 | −0.164198 | − | 0.986427i | \(-0.552503\pi\) | ||||
−0.164198 | + | 0.986427i | \(0.552503\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.12783 | −0.343774 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.3135 | 0.613533 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.3074 | −1.17577 | −0.587886 | − | 0.808943i | \(-0.700040\pi\) | ||||
−0.587886 | + | 0.808943i | \(0.700040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.52586 | −0.132230 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.70928 | −0.0640129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.183417 | −0.00685942 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.7587 | 0.737903 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.5236 | −0.765401 | −0.382700 | − | 0.923873i | \(-0.625006\pi\) | ||||
−0.382700 | + | 0.923873i | \(0.625006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.92389 | −0.295101 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.65368 | 0.321834 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.95774 | 0.295543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7971 | −1.17929 | −0.589645 | − | 0.807663i | \(-0.700732\pi\) | ||||
−0.589645 | + | 0.807663i | \(0.700732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.46573 | −0.165171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1978 | 0.376664 | 0.188332 | − | 0.982105i | \(-0.439692\pi\) | ||||
0.188332 | + | 0.982105i | \(0.439692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.63090 | 0.207699 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.70086 | 0.283665 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.3835 | −1.52232 | −0.761158 | − | 0.648567i | \(-0.775369\pi\) | ||||
−0.761158 | + | 0.648567i | \(0.775369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.8987 | 0.876757 | 0.438378 | − | 0.898791i | \(-0.355553\pi\) | ||||
0.438378 | + | 0.898791i | \(0.355553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3607 | 0.489498 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5464 | −0.459048 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.738205 | −0.0269734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.6475 | −1.88465 | −0.942323 | − | 0.334706i | \(-0.891363\pi\) | ||||
−0.942323 | + | 0.334706i | \(0.891363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9360 | −0.690066 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.8660 | −0.504637 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.687534 | −0.0249888 | −0.0124944 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124944 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.41855 | 0.124086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.1555 | −1.16564 | −0.582819 | − | 0.812602i | \(-0.698050\pi\) | ||||
−0.582819 | + | 0.812602i | \(0.698050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8843 | −0.502645 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.04945 | −0.218718 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.01211 | −0.0365451 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.2206 | −1.23403 | −0.617013 | − | 0.786953i | \(-0.711657\pi\) | ||||
−0.617013 | + | 0.786953i | \(0.711657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1012 | 0.471827 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.20781 | 0.331182 | 0.165591 | − | 0.986195i | \(-0.447047\pi\) | ||||
0.165591 | + | 0.986195i | \(0.447047\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.92389 | 0.140769 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.43907 | −0.0872768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.95774 | −0.284386 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0989 | −0.717360 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.4908 | 1.26511 | 0.632555 | − | 0.774515i | \(-0.282006\pi\) | ||||
0.632555 | + | 0.774515i | \(0.282006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.49693 | 0.302499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.39803 | 0.156376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.299135 | −0.0106226 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.97107 | −0.176306 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.89884 | 0.244369 | 0.122185 | − | 0.992507i | \(-0.461010\pi\) | ||||
0.122185 | + | 0.992507i | \(0.461010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.2183 | −1.95348 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.77432 | −0.204026 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.3340 | −0.541126 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.8010 | −0.767431 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.2278 | 1.97686 | 0.988432 | − | 0.151668i | \(-0.0484644\pi\) | ||||
0.988432 | + | 0.151668i | \(0.0484644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.7070 | −1.21873 | −0.609364 | − | 0.792891i | \(-0.708575\pi\) | ||||
−0.609364 | + | 0.792891i | \(0.708575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3402 | 0.362646 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.06505 | −0.142392 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.107307 | 0.00374962 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.2651 | 1.09116 | 0.545580 | − | 0.838059i | \(-0.316309\pi\) | ||||
0.545580 | + | 0.838059i | \(0.316309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.5523 | 1.55300 | 0.776499 | − | 0.630119i | \(-0.216994\pi\) | ||||
0.776499 | + | 0.630119i | \(0.216994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.97107 | 0.103314 | 0.0516571 | − | 0.998665i | \(-0.483550\pi\) | ||||
0.0516571 | + | 0.998665i | \(0.483550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.2823 | −1.05175 | −0.525874 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525874 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.646496 | 0.0224267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.0638 | 1.18024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.91548 | −0.135501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.8687 | 1.65261 | 0.826305 | − | 0.563223i | \(-0.190439\pi\) | ||||
0.826305 | + | 0.563223i | \(0.190439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.3256 | 1.18364 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3874 | 0.598852 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9916 | −0.446924 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.19061 | −0.281433 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.92881 | 0.100517 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.73206 | −0.196493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.8531 | −1.63846 | −0.819229 | − | 0.573466i | \(-0.805598\pi\) | ||||
−0.819229 | + | 0.573466i | \(0.805598\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.13170 | 0.106977 | 0.0534884 | − | 0.998568i | \(-0.482966\pi\) | ||||
0.0534884 | + | 0.998568i | \(0.482966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4703 | 0.630197 | 0.315099 | − | 0.949059i | \(-0.397962\pi\) | ||||
0.315099 | + | 0.949059i | \(0.397962\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.47641 | 0.186636 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.9130 | 1.63098 | 0.815489 | − | 0.578772i | \(-0.196468\pi\) | ||||
0.815489 | + | 0.578772i | \(0.196468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0722 | 0.546472 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.5958 | −0.665509 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.05172 | 0.239213 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.353118 | −0.0119650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0000 | −0.406138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.17009 | 0.0395561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.8104 | 1.51314 | 0.756571 | − | 0.653912i | \(-0.226873\pi\) | ||||
0.756571 | + | 0.653912i | \(0.226873\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.9916 | 1.07905 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4501 | −0.823746 | −0.411873 | − | 0.911241i | \(-0.635125\pi\) | ||||
−0.411873 | + | 0.911241i | \(0.635125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8043 | −1.33952 | −0.669761 | − | 0.742577i | \(-0.733603\pi\) | ||||
−0.669761 | + | 0.742577i | \(0.733603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0361 | 0.370975 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9588 | −0.569420 | −0.284710 | − | 0.958614i | \(-0.591897\pi\) | ||||
−0.284710 | + | 0.958614i | \(0.591897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.89496 | 0.164172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.9421 | −0.733445 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.156755 | −0.00523391 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.95774 | −0.265405 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.0722 | −1.00185 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.863763 | −0.0287442 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.94214 | 0.131041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.72487 | 0.123682 | 0.0618412 | − | 0.998086i | \(-0.480303\pi\) | ||||
0.0618412 | + | 0.998086i | \(0.480303\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.9421 | 0.462432 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.5523 | 1.87366 | 0.936831 | − | 0.349781i | \(-0.113744\pi\) | ||||
0.936831 | + | 0.349781i | \(0.113744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.0928 | 0.830449 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.26180 | 0.107832 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.814315 | 0.0268911 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.9770 | 1.35171 | 0.675854 | − | 0.737036i | \(-0.263775\pi\) | ||||
0.675854 | + | 0.737036i | \(0.263775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.66701 | −0.186734 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.111842 | 0.00368132 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.35350 | −0.110263 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.77205 | −0.222423 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.2713 | 1.32126 | 0.660628 | − | 0.750713i | \(-0.270290\pi\) | ||||
0.660628 | + | 0.750713i | \(0.270290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.2401 | −0.531675 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0989 | 0.395676 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.9405 | −0.945446 | −0.472723 | − | 0.881211i | \(-0.656729\pi\) | ||||
−0.472723 | + | 0.881211i | \(0.656729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.42574 | −0.242330 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.7431 | 1.49118 | 0.745592 | − | 0.666403i | \(-0.232167\pi\) | ||||
0.745592 | + | 0.666403i | \(0.232167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.17009 | −0.0380629 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.7093 | 1.87530 | 0.937650 | − | 0.347582i | \(-0.112997\pi\) | ||||
0.937650 | + | 0.347582i | \(0.112997\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.703132 | 0.0228246 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.2534 | 0.429770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.89269 | −0.126097 | −0.0630483 | − | 0.998010i | \(-0.520082\pi\) | ||||
−0.0630483 | + | 0.998010i | \(0.520082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.3184 | −0.754567 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9155 | 0.514474 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.60197 | 0.310064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.630898 | −0.0203304 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.2557 | −0.330141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1317 | −0.743865 | −0.371933 | − | 0.928260i | \(-0.621305\pi\) | ||||
−0.371933 | + | 0.928260i | \(0.621305\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.51414 | 0.112774 | 0.0563870 | − | 0.998409i | \(-0.482042\pi\) | ||||
0.0563870 | + | 0.998409i | \(0.482042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.26180 | 0.168685 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0917087 | −0.00293703 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.5174 | 1.20029 | 0.600145 | − | 0.799891i | \(-0.295110\pi\) | ||||
0.600145 | + | 0.799891i | \(0.295110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5486 | 0.369096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8660 | −0.378853 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.2434 | −1.79388 | −0.896942 | − | 0.442147i | \(-0.854217\pi\) | ||||
−0.896942 | + | 0.442147i | \(0.854217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9916 | 0.764436 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6803 | −0.339959 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.26180 | 0.0401228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.4284 | −1.95134 | −0.975669 | − | 0.219251i | \(-0.929639\pi\) | ||||
−0.975669 | + | 0.219251i | \(0.929639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.62475 | 0.115028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.1217 | 0.511092 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.6307 | 1.57182 | 0.785910 | − | 0.618340i | \(-0.212195\pi\) | ||||
0.785910 | + | 0.618340i | \(0.212195\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35350 | 0.106100 |
(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 | 7440.2.a.bp.1.3 | 3 | ||
4.3 | odd | 2 | 465.2.a.f.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 1395.2.a.i.1.1 | 3 | |||
20.3 | even | 4 | 2325.2.c.o.1024.1 | 6 | |||
20.7 | even | 4 | 2325.2.c.o.1024.6 | 6 | |||
20.19 | odd | 2 | 2325.2.a.q.1.1 | 3 | |||
60.59 | even | 2 | 6975.2.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.a.f.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
1395.2.a.i.1.1 | 3 | 12.11 | even | 2 | |||
2325.2.a.q.1.1 | 3 | 20.19 | odd | 2 | |||
2325.2.c.o.1024.1 | 6 | 20.3 | even | 4 | |||
2325.2.c.o.1024.6 | 6 | 20.7 | even | 4 | |||
6975.2.a.be.1.3 | 3 | 60.59 | even | 2 | |||
7440.2.a.bp.1.3 | 3 | 1.1 | even | 1 | trivial |