Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("405.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08613 | 1.47512 | 0.737558 | − | 0.675283i | \(-0.235979\pi\) | ||||
0.737558 | + | 0.675283i | \(0.235979\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.35194 | 1.17597 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.08613 | 1.54441 | 0.772206 | − | 0.635372i | \(-0.219153\pi\) | ||||
0.772206 | + | 0.635372i | \(0.219153\pi\) | |||||||
\(8\) | 0.734191 | 0.259576 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.08613 | −0.659692 | ||||||||
\(11\) | 1.35194 | 0.407625 | 0.203813 | − | 0.979010i | \(-0.434667\pi\) | ||||
0.203813 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.648061 | 0.179740 | 0.0898699 | − | 0.995954i | \(-0.471355\pi\) | ||||
0.0898699 | + | 0.995954i | \(0.471355\pi\) | |||||||
\(14\) | 8.52420 | 2.27819 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.17226 | −0.793065 | ||||||||
\(17\) | 1.35194 | 0.327893 | 0.163947 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.648061 | 0.148675 | 0.0743377 | − | 0.997233i | \(-0.476316\pi\) | ||||
0.0743377 | + | 0.997233i | \(0.476316\pi\) | |||||||
\(20\) | −2.35194 | −0.525910 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.82032 | 0.601294 | ||||||||
\(23\) | −4.79001 | −0.998786 | −0.499393 | − | 0.866376i | \(-0.666444\pi\) | ||||
−0.499393 | + | 0.866376i | \(0.666444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.35194 | 0.265137 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.61033 | 1.81618 | ||||||||
\(29\) | −3.87614 | −0.719781 | −0.359890 | − | 0.932995i | \(-0.617186\pi\) | ||||
−0.359890 | + | 0.932995i | \(0.617186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.69646 | −1.38233 | −0.691163 | − | 0.722699i | \(-0.742901\pi\) | ||||
−0.691163 | + | 0.722699i | \(0.742901\pi\) | |||||||
\(32\) | −8.08613 | −1.42944 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.82032 | 0.483681 | ||||||||
\(35\) | −4.08613 | −0.690682 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52420 | 1.23697 | 0.618485 | − | 0.785796i | \(-0.287747\pi\) | ||||
0.618485 | + | 0.785796i | \(0.287747\pi\) | |||||||
\(38\) | 1.35194 | 0.219313 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.734191 | −0.116086 | ||||||||
\(41\) | 0.179679 | 0.0280611 | 0.0140306 | − | 0.999902i | \(-0.495534\pi\) | ||||
0.0140306 | + | 0.999902i | \(0.495534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.820321 | −0.125098 | −0.0625489 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625489 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(44\) | 3.17968 | 0.479355 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.99258 | −1.47333 | ||||||||
\(47\) | −10.9065 | −1.59087 | −0.795435 | − | 0.606039i | \(-0.792757\pi\) | ||||
−0.795435 | + | 0.606039i | \(0.792757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.69646 | 1.38521 | ||||||||
\(50\) | 2.08613 | 0.295023 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.52420 | 0.211368 | ||||||||
\(53\) | −4.17226 | −0.573104 | −0.286552 | − | 0.958065i | \(-0.592509\pi\) | ||||
−0.286552 | + | 0.958065i | \(0.592509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.35194 | −0.182295 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.08613 | −1.06176 | ||||||||
\(59\) | −4.17226 | −0.543182 | −0.271591 | − | 0.962413i | \(-0.587550\pi\) | ||||
−0.271591 | + | 0.962413i | \(0.587550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.82032 | −0.489142 | −0.244571 | − | 0.969631i | \(-0.578647\pi\) | ||||
−0.244571 | + | 0.969631i | \(0.578647\pi\) | |||||||
\(62\) | −16.0558 | −2.03909 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.5242 | −1.31552 | ||||||||
\(65\) | −0.648061 | −0.0803820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.14195 | 0.994697 | 0.497349 | − | 0.867551i | \(-0.334307\pi\) | ||||
0.497349 | + | 0.867551i | \(0.334307\pi\) | |||||||
\(68\) | 3.17968 | 0.385593 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.52420 | −1.01884 | ||||||||
\(71\) | 6.11644 | 0.725888 | 0.362944 | − | 0.931811i | \(-0.381772\pi\) | ||||
0.362944 | + | 0.931811i | \(0.381772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3445 | −1.44482 | −0.722408 | − | 0.691467i | \(-0.756965\pi\) | ||||
−0.722408 | + | 0.691467i | \(0.756965\pi\) | |||||||
\(74\) | 15.6965 | 1.82468 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.52420 | 0.174838 | ||||||||
\(77\) | 5.52420 | 0.629541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3445 | 1.16385 | 0.581925 | − | 0.813243i | \(-0.302300\pi\) | ||||
0.581925 | + | 0.813243i | \(0.302300\pi\) | |||||||
\(80\) | 3.17226 | 0.354669 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.374833 | 0.0413934 | ||||||||
\(83\) | 12.2584 | 1.34553 | 0.672767 | − | 0.739855i | \(-0.265106\pi\) | ||||
0.672767 | + | 0.739855i | \(0.265106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.35194 | −0.146638 | ||||||||
\(86\) | −1.71130 | −0.184534 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.992582 | 0.105810 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.64806 | 0.277592 | ||||||||
\(92\) | −11.2658 | −1.17454 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.7523 | −2.34672 | ||||||||
\(95\) | −0.648061 | −0.0664896 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5800 | −1.37884 | −0.689421 | − | 0.724361i | \(-0.742135\pi\) | ||||
−0.689421 | + | 0.724361i | \(0.742135\pi\) | |||||||
\(98\) | 20.2281 | 2.04334 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.35194 | 0.235194 | ||||||||
\(101\) | 1.46838 | 0.146109 | 0.0730547 | − | 0.997328i | \(-0.476725\pi\) | ||||
0.0730547 | + | 0.997328i | \(0.476725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.52420 | 0.741381 | 0.370691 | − | 0.928756i | \(-0.379121\pi\) | ||||
0.370691 | + | 0.928756i | \(0.379121\pi\) | |||||||
\(104\) | 0.475800 | 0.0466561 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.70388 | −0.845395 | ||||||||
\(107\) | −1.20999 | −0.116974 | −0.0584871 | − | 0.998288i | \(-0.518628\pi\) | ||||
−0.0584871 | + | 0.998288i | \(0.518628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1042 | 1.35094 | 0.675469 | − | 0.737388i | \(-0.263941\pi\) | ||||
0.675469 | + | 0.737388i | \(0.263941\pi\) | |||||||
\(110\) | −2.82032 | −0.268907 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.9623 | −1.22482 | ||||||||
\(113\) | 11.9245 | 1.12177 | 0.560883 | − | 0.827895i | \(-0.310462\pi\) | ||||
0.560883 | + | 0.827895i | \(0.310462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.79001 | 0.446671 | ||||||||
\(116\) | −9.11644 | −0.846440 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.70388 | −0.801257 | ||||||||
\(119\) | 5.52420 | 0.506403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.17226 | −0.833842 | ||||||||
\(122\) | −7.96969 | −0.721542 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.1016 | −1.62557 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.07871 | −0.628134 | −0.314067 | − | 0.949401i | \(-0.601692\pi\) | ||||
−0.314067 | + | 0.949401i | \(0.601692\pi\) | |||||||
\(128\) | −5.78259 | −0.511114 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.35194 | −0.118573 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64806 | 0.229616 | ||||||||
\(134\) | 16.9852 | 1.46729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.992582 | 0.0851132 | ||||||||
\(137\) | 7.46838 | 0.638067 | 0.319033 | − | 0.947743i | \(-0.396642\pi\) | ||||
0.319033 | + | 0.947743i | \(0.396642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | −9.61033 | −0.812221 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7597 | 1.07077 | ||||||||
\(143\) | 0.876139 | 0.0732664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87614 | 0.321896 | ||||||||
\(146\) | −25.7523 | −2.13127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.6965 | 1.45464 | ||||||||
\(149\) | 10.5848 | 0.867143 | 0.433571 | − | 0.901119i | \(-0.357253\pi\) | ||||
0.433571 | + | 0.901119i | \(0.357253\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6965 | 1.44012 | 0.720059 | − | 0.693913i | \(-0.244115\pi\) | ||||
0.720059 | + | 0.693913i | \(0.244115\pi\) | |||||||
\(152\) | 0.475800 | 0.0385925 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.5242 | 0.928646 | ||||||||
\(155\) | 7.69646 | 0.618195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53162 | −0.202045 | −0.101023 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101023 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(158\) | 21.5800 | 1.71681 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.08613 | 0.639265 | ||||||||
\(161\) | −19.5726 | −1.54254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.47580 | 0.663876 | 0.331938 | − | 0.943301i | \(-0.392298\pi\) | ||||
0.331938 | + | 0.943301i | \(0.392298\pi\) | |||||||
\(164\) | 0.422594 | 0.0329990 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.5726 | 1.98482 | ||||||||
\(167\) | −12.7342 | −0.985401 | −0.492701 | − | 0.870199i | \(-0.663990\pi\) | ||||
−0.492701 | + | 0.870199i | \(0.663990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5800 | −0.967694 | ||||||||
\(170\) | −2.82032 | −0.216309 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.92935 | −0.147111 | ||||||||
\(173\) | −23.0484 | −1.75234 | −0.876169 | − | 0.482005i | \(-0.839909\pi\) | ||||
−0.876169 | + | 0.482005i | \(0.839909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.08613 | 0.308882 | ||||||||
\(176\) | −4.28870 | −0.323273 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.25839 | 0.469086 | ||||||||
\(179\) | −2.22808 | −0.166534 | −0.0832672 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832672 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.468382 | 0.0348146 | 0.0174073 | − | 0.999848i | \(-0.494459\pi\) | ||||
0.0174073 | + | 0.999848i | \(0.494459\pi\) | |||||||
\(182\) | 5.52420 | 0.409481 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.51678 | −0.259261 | ||||||||
\(185\) | −7.52420 | −0.553190 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.82774 | 0.133658 | ||||||||
\(188\) | −25.6513 | −1.87081 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.35194 | −0.0980800 | ||||||||
\(191\) | 20.2281 | 1.46365 | 0.731826 | − | 0.681491i | \(-0.238668\pi\) | ||||
0.731826 | + | 0.681491i | \(0.238668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9293 | −1.43455 | −0.717273 | − | 0.696792i | \(-0.754610\pi\) | ||||
−0.717273 | + | 0.696792i | \(0.754610\pi\) | |||||||
\(194\) | −28.3297 | −2.03395 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.8055 | 1.62896 | ||||||||
\(197\) | 15.5800 | 1.11003 | 0.555015 | − | 0.831840i | \(-0.312712\pi\) | ||||
0.555015 | + | 0.831840i | \(0.312712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.58482 | 0.254121 | 0.127061 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127061 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(200\) | 0.734191 | 0.0519151 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.06324 | 0.215529 | ||||||||
\(203\) | −15.8384 | −1.11164 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.179679 | −0.0125493 | ||||||||
\(206\) | 15.6965 | 1.09362 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.05582 | −0.142545 | ||||||||
\(209\) | 0.876139 | 0.0606038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9926 | 1.03213 | 0.516066 | − | 0.856549i | \(-0.327396\pi\) | ||||
0.516066 | + | 0.856549i | \(0.327396\pi\) | |||||||
\(212\) | −9.81290 | −0.673953 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.52420 | −0.172551 | ||||||||
\(215\) | 0.820321 | 0.0559454 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.4487 | −2.13488 | ||||||||
\(218\) | 29.4232 | 1.99279 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.17968 | −0.214374 | ||||||||
\(221\) | 0.876139 | 0.0589355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8310 | −1.79674 | −0.898368 | − | 0.439244i | \(-0.855246\pi\) | ||||
−0.898368 | + | 0.439244i | \(0.855246\pi\) | |||||||
\(224\) | −33.0410 | −2.20764 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.8761 | 1.65474 | ||||||||
\(227\) | −1.35194 | −0.0897314 | −0.0448657 | − | 0.998993i | \(-0.514286\pi\) | ||||
−0.0448657 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.23550 | −0.544217 | −0.272108 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(230\) | 9.99258 | 0.658891 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.84583 | −0.186838 | ||||||||
\(233\) | −8.58744 | −0.562582 | −0.281291 | − | 0.959623i | \(-0.590763\pi\) | ||||
−0.281291 | + | 0.959623i | \(0.590763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9065 | 0.711458 | ||||||||
\(236\) | −9.81290 | −0.638766 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5242 | 0.747003 | ||||||||
\(239\) | 23.9245 | 1.54755 | 0.773775 | − | 0.633461i | \(-0.218366\pi\) | ||||
0.773775 | + | 0.633461i | \(0.218366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.24030 | −0.401973 | −0.200987 | − | 0.979594i | \(-0.564415\pi\) | ||||
−0.200987 | + | 0.979594i | \(0.564415\pi\) | |||||||
\(242\) | −19.1345 | −1.23001 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.98516 | −0.575216 | ||||||||
\(245\) | −9.69646 | −0.619484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.419983 | 0.0267229 | ||||||||
\(248\) | −5.65067 | −0.358818 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.08613 | −0.131938 | ||||||||
\(251\) | 28.5726 | 1.80349 | 0.901743 | − | 0.432272i | \(-0.142288\pi\) | ||||
0.901743 | + | 0.432272i | \(0.142288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47580 | −0.407130 | ||||||||
\(254\) | −14.7671 | −0.926571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.98516 | 0.561573 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.7449 | 1.91039 | ||||||||
\(260\) | −1.52420 | −0.0945268 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.5168 | 0.773289 | ||||||||
\(263\) | −31.8687 | −1.96511 | −0.982555 | − | 0.185974i | \(-0.940456\pi\) | ||||
−0.982555 | + | 0.185974i | \(0.940456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.17226 | 0.256300 | ||||||||
\(266\) | 5.52420 | 0.338710 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.1494 | 1.16973 | ||||||||
\(269\) | 31.4971 | 1.92041 | 0.960207 | − | 0.279289i | \(-0.0900987\pi\) | ||||
0.960207 | + | 0.279289i | \(0.0900987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.24030 | −0.196834 | −0.0984172 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984172 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(272\) | −4.28870 | −0.260041 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.5800 | 0.941223 | ||||||||
\(275\) | 1.35194 | 0.0815250 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.58482 | −0.335560 | −0.167780 | − | 0.985824i | \(-0.553660\pi\) | ||||
−0.167780 | + | 0.985824i | \(0.553660\pi\) | |||||||
\(278\) | 16.6890 | 1.00094 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | 24.1042 | 1.43794 | 0.718969 | − | 0.695043i | \(-0.244615\pi\) | ||||
0.718969 | + | 0.695043i | \(0.244615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5423 | −0.626674 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(284\) | 14.3855 | 0.853622 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.82774 | 0.108077 | ||||||||
\(287\) | 0.734191 | 0.0433379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1723 | −0.892486 | ||||||||
\(290\) | 8.08613 | 0.474834 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.0336 | −1.69906 | ||||||||
\(293\) | −18.9926 | −1.10956 | −0.554779 | − | 0.831998i | \(-0.687197\pi\) | ||||
−0.554779 | + | 0.831998i | \(0.687197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.17226 | 0.242918 | ||||||||
\(296\) | 5.52420 | 0.321088 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.0813 | 1.27914 | ||||||||
\(299\) | −3.10422 | −0.179521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.35194 | −0.193203 | ||||||||
\(302\) | 36.9171 | 2.12434 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.05582 | −0.117909 | ||||||||
\(305\) | 3.82032 | 0.218751 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4791 | 1.68246 | 0.841229 | − | 0.540679i | \(-0.181833\pi\) | ||||
0.841229 | + | 0.540679i | \(0.181833\pi\) | |||||||
\(308\) | 12.9926 | 0.740321 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.0558 | 0.911909 | ||||||||
\(311\) | 9.41256 | 0.533738 | 0.266869 | − | 0.963733i | \(-0.414011\pi\) | ||||
0.266869 | + | 0.963733i | \(0.414011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6210 | 0.656858 | 0.328429 | − | 0.944529i | \(-0.393481\pi\) | ||||
0.328429 | + | 0.944529i | \(0.393481\pi\) | |||||||
\(314\) | −5.28128 | −0.298040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.3297 | 1.36865 | ||||||||
\(317\) | 9.17968 | 0.515582 | 0.257791 | − | 0.966201i | \(-0.417005\pi\) | ||||
0.257791 | + | 0.966201i | \(0.417005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.24030 | −0.293401 | ||||||||
\(320\) | 10.5242 | 0.588321 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −40.8310 | −2.27542 | ||||||||
\(323\) | 0.876139 | 0.0487497 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.648061 | 0.0359479 | ||||||||
\(326\) | 17.6816 | 0.979295 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.131919 | 0.00728398 | ||||||||
\(329\) | −44.5652 | −2.45696 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.22066 | −0.396883 | −0.198442 | − | 0.980113i | \(-0.563588\pi\) | ||||
−0.198442 | + | 0.980113i | \(0.563588\pi\) | |||||||
\(332\) | 28.8310 | 1.58231 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.5652 | −1.45358 | ||||||||
\(335\) | −8.14195 | −0.444842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.28390 | 0.124412 | 0.0622059 | − | 0.998063i | \(-0.480186\pi\) | ||||
0.0622059 | + | 0.998063i | \(0.480186\pi\) | |||||||
\(338\) | −26.2436 | −1.42746 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.17968 | −0.172442 | ||||||||
\(341\) | −10.4051 | −0.563470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0181 | 0.594921 | ||||||||
\(344\) | −0.602272 | −0.0324724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0820 | −2.58490 | ||||||||
\(347\) | 0.708686 | 0.0380443 | 0.0190221 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190221 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3445 | −1.14255 | −0.571273 | − | 0.820760i | \(-0.693550\pi\) | ||||
−0.571273 | + | 0.820760i | \(0.693550\pi\) | |||||||
\(350\) | 8.52420 | 0.455638 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.9320 | −0.582675 | ||||||||
\(353\) | 10.0968 | 0.537398 | 0.268699 | − | 0.963224i | \(-0.413406\pi\) | ||||
0.268699 | + | 0.963224i | \(0.413406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.11644 | −0.324627 | ||||||||
\(356\) | 7.05582 | 0.373958 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.64806 | −0.245658 | ||||||||
\(359\) | −30.5578 | −1.61278 | −0.806388 | − | 0.591386i | \(-0.798581\pi\) | ||||
−0.806388 | + | 0.591386i | \(0.798581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | 0.977106 | 0.0513555 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.22808 | 0.326440 | ||||||||
\(365\) | 12.3445 | 0.646142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.17968 | −0.374776 | −0.187388 | − | 0.982286i | \(-0.560002\pi\) | ||||
−0.187388 | + | 0.982286i | \(0.560002\pi\) | |||||||
\(368\) | 15.1952 | 0.792102 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.6965 | −0.816020 | ||||||||
\(371\) | −17.0484 | −0.885109 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.9245 | −1.13521 | −0.567605 | − | 0.823301i | \(-0.692130\pi\) | ||||
−0.567605 | + | 0.823301i | \(0.692130\pi\) | |||||||
\(374\) | 3.81290 | 0.197161 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00742 | −0.412951 | ||||||||
\(377\) | −2.51197 | −0.129373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3929 | −0.893414 | −0.446707 | − | 0.894680i | \(-0.647403\pi\) | ||||
−0.446707 | + | 0.894680i | \(0.647403\pi\) | |||||||
\(380\) | −1.52420 | −0.0781898 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 42.1984 | 2.15906 | ||||||||
\(383\) | −0.475800 | −0.0243123 | −0.0121561 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121561 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.52420 | −0.281539 | ||||||||
\(386\) | −41.5752 | −2.11612 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −31.9394 | −1.62148 | ||||||||
\(389\) | 5.58744 | 0.283294 | 0.141647 | − | 0.989917i | \(-0.454760\pi\) | ||||
0.141647 | + | 0.989917i | \(0.454760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.47580 | −0.327495 | ||||||||
\(392\) | 7.11905 | 0.359567 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.5019 | 1.63742 | ||||||||
\(395\) | −10.3445 | −0.520489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.75228 | 0.188321 | 0.0941607 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941607 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(398\) | 7.47841 | 0.374859 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.17226 | −0.158613 | ||||||||
\(401\) | −23.5652 | −1.17679 | −0.588394 | − | 0.808574i | \(-0.700240\pi\) | ||||
−0.588394 | + | 0.808574i | \(0.700240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.98777 | −0.248459 | ||||||||
\(404\) | 3.45355 | 0.171820 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.0410 | −1.63980 | ||||||||
\(407\) | 10.1723 | 0.504220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.04840 | 0.0518400 | 0.0259200 | − | 0.999664i | \(-0.491748\pi\) | ||||
0.0259200 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(410\) | −0.374833 | −0.0185117 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.6965 | 0.871842 | ||||||||
\(413\) | −17.0484 | −0.838897 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.2584 | −0.601741 | ||||||||
\(416\) | −5.24030 | −0.256927 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.82774 | 0.0893977 | ||||||||
\(419\) | 25.9197 | 1.26626 | 0.633131 | − | 0.774045i | \(-0.281769\pi\) | ||||
0.633131 | + | 0.774045i | \(0.281769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64064 | 0.372382 | 0.186191 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186191 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(422\) | 31.2765 | 1.52252 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.06324 | −0.148764 | ||||||||
\(425\) | 1.35194 | 0.0655787 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6103 | −0.755437 | ||||||||
\(428\) | −2.84583 | −0.137558 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.71130 | 0.0825261 | ||||||||
\(431\) | −7.98516 | −0.384632 | −0.192316 | − | 0.981333i | \(-0.561600\pi\) | ||||
−0.192316 | + | 0.981333i | \(0.561600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5120 | −0.601287 | −0.300644 | − | 0.953737i | \(-0.597201\pi\) | ||||
−0.300644 | + | 0.953737i | \(0.597201\pi\) | |||||||
\(434\) | −65.6062 | −3.14920 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.1723 | 1.58866 | ||||||||
\(437\) | −3.10422 | −0.148495 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.76450 | −0.418307 | −0.209153 | − | 0.977883i | \(-0.567071\pi\) | ||||
−0.209153 | + | 0.977883i | \(0.567071\pi\) | |||||||
\(440\) | −0.992582 | −0.0473195 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.82774 | 0.0869367 | ||||||||
\(443\) | −3.67095 | −0.174412 | −0.0872062 | − | 0.996190i | \(-0.527794\pi\) | ||||
−0.0872062 | + | 0.996190i | \(0.527794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | −0.142214 | ||||||||
\(446\) | −55.9729 | −2.65040 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −43.0032 | −2.03171 | ||||||||
\(449\) | −28.1723 | −1.32953 | −0.664766 | − | 0.747052i | \(-0.731469\pi\) | ||||
−0.664766 | + | 0.747052i | \(0.731469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.242915 | 0.0114384 | ||||||||
\(452\) | 28.0458 | 1.31916 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.82032 | −0.132364 | ||||||||
\(455\) | −2.64806 | −0.124143 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2616 | 1.64947 | 0.824735 | − | 0.565519i | \(-0.191324\pi\) | ||||
0.824735 | + | 0.565519i | \(0.191324\pi\) | |||||||
\(458\) | −17.1803 | −0.802784 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.2658 | 0.525271 | ||||||||
\(461\) | −34.6768 | −1.61506 | −0.807530 | − | 0.589826i | \(-0.799196\pi\) | ||||
−0.807530 | + | 0.589826i | \(0.799196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.44874 | 0.346172 | 0.173086 | − | 0.984907i | \(-0.444626\pi\) | ||||
0.173086 | + | 0.984907i | \(0.444626\pi\) | |||||||
\(464\) | 12.2961 | 0.570833 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9145 | −0.829874 | ||||||||
\(467\) | −29.9655 | −1.38664 | −0.693319 | − | 0.720630i | \(-0.743852\pi\) | ||||
−0.693319 | + | 0.720630i | \(0.743852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.2691 | 1.53622 | ||||||||
\(470\) | 22.7523 | 1.04948 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.06324 | −0.140997 | ||||||||
\(473\) | −1.10902 | −0.0509930 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.648061 | 0.0297351 | ||||||||
\(476\) | 12.9926 | 0.595514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 49.9097 | 2.28282 | ||||||||
\(479\) | 7.98516 | 0.364851 | 0.182426 | − | 0.983220i | \(-0.441605\pi\) | ||||
0.182426 | + | 0.983220i | \(0.441605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.87614 | 0.222333 | ||||||||
\(482\) | −13.0181 | −0.592958 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.5726 | −0.980573 | ||||||||
\(485\) | 13.5800 | 0.616637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9442 | −0.541243 | −0.270621 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270621 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(488\) | −2.80485 | −0.126969 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.2281 | −0.913811 | ||||||||
\(491\) | 9.22066 | 0.416123 | 0.208061 | − | 0.978116i | \(-0.433285\pi\) | ||||
0.208061 | + | 0.978116i | \(0.433285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.24030 | −0.236011 | ||||||||
\(494\) | 0.876139 | 0.0394193 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.4152 | 1.09627 | ||||||||
\(497\) | 24.9926 | 1.12107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1723 | 1.35070 | 0.675348 | − | 0.737499i | \(-0.263993\pi\) | ||||
0.675348 | + | 0.737499i | \(0.263993\pi\) | |||||||
\(500\) | −2.35194 | −0.105182 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 59.6062 | 2.66035 | ||||||||
\(503\) | 10.5981 | 0.472546 | 0.236273 | − | 0.971687i | \(-0.424074\pi\) | ||||
0.236273 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.46838 | −0.0653421 | ||||||||
\(506\) | −13.5094 | −0.600564 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.6487 | −0.738667 | ||||||||
\(509\) | −28.7523 | −1.27442 | −0.637211 | − | 0.770689i | \(-0.719912\pi\) | ||||
−0.637211 | + | 0.770689i | \(0.719912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −50.4413 | −2.23139 | ||||||||
\(512\) | 30.3094 | 1.33950 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.5503 | 1.65627 | ||||||||
\(515\) | −7.52420 | −0.331556 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7449 | −0.648478 | ||||||||
\(518\) | 64.1378 | 2.81805 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.475800 | −0.0208652 | ||||||||
\(521\) | 36.0942 | 1.58132 | 0.790658 | − | 0.612259i | \(-0.209739\pi\) | ||||
0.790658 | + | 0.612259i | \(0.209739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1297 | 0.486669 | 0.243334 | − | 0.969942i | \(-0.421759\pi\) | ||||
0.243334 | + | 0.969942i | \(0.421759\pi\) | |||||||
\(524\) | 14.1116 | 0.616470 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −66.4823 | −2.89877 | ||||||||
\(527\) | −10.4051 | −0.453255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0558176 | −0.00242685 | ||||||||
\(530\) | 8.70388 | 0.378072 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.22808 | 0.270021 | ||||||||
\(533\) | 0.116443 | 0.00504370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.20999 | 0.0523125 | ||||||||
\(536\) | 5.97774 | 0.258199 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 65.7071 | 2.83284 | ||||||||
\(539\) | 13.1090 | 0.564646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7374 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(542\) | −6.75970 | −0.290354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.9320 | −0.468704 | ||||||||
\(545\) | −14.1042 | −0.604158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.71455 | −0.116066 | −0.0580328 | − | 0.998315i | \(-0.518483\pi\) | ||||
−0.0580328 | + | 0.998315i | \(0.518483\pi\) | |||||||
\(548\) | 17.5652 | 0.750347 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.82032 | 0.120259 | ||||||||
\(551\) | −2.51197 | −0.107014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2691 | 1.79746 | ||||||||
\(554\) | −11.6507 | −0.494990 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.8155 | 0.797956 | ||||||||
\(557\) | 8.93676 | 0.378663 | 0.189331 | − | 0.981913i | \(-0.439368\pi\) | ||||
0.189331 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.531618 | −0.0224850 | ||||||||
\(560\) | 12.9623 | 0.547756 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 50.2845 | 2.12113 | ||||||||
\(563\) | 9.36261 | 0.394587 | 0.197293 | − | 0.980344i | \(-0.436785\pi\) | ||||
0.197293 | + | 0.980344i | \(0.436785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.9245 | −0.501669 | ||||||||
\(566\) | −21.9926 | −0.924417 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.49064 | 0.188423 | ||||||||
\(569\) | −35.8735 | −1.50390 | −0.751948 | − | 0.659222i | \(-0.770886\pi\) | ||||
−0.751948 | + | 0.659222i | \(0.770886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 2.06063 | 0.0861591 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.53162 | 0.0639285 | ||||||||
\(575\) | −4.79001 | −0.199757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35675 | 0.0564821 | 0.0282411 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282411 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(578\) | −31.6513 | −1.31652 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.11644 | 0.378540 | ||||||||
\(581\) | 50.0894 | 2.07806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.64064 | −0.233612 | ||||||||
\(584\) | −9.06324 | −0.375039 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.6210 | −1.63673 | ||||||||
\(587\) | −28.7900 | −1.18829 | −0.594145 | − | 0.804358i | \(-0.702510\pi\) | ||||
−0.594145 | + | 0.804358i | \(0.702510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.98777 | −0.205518 | ||||||||
\(590\) | 8.70388 | 0.358333 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.8687 | −0.980998 | ||||||||
\(593\) | −30.9171 | −1.26961 | −0.634807 | − | 0.772671i | \(-0.718920\pi\) | ||||
−0.634807 | + | 0.772671i | \(0.718920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.52420 | −0.226470 | ||||||||
\(596\) | 24.8949 | 1.01973 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.47580 | −0.264815 | ||||||||
\(599\) | −1.39292 | −0.0569132 | −0.0284566 | − | 0.999595i | \(-0.509059\pi\) | ||||
−0.0284566 | + | 0.999595i | \(0.509059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.82513 | 0.359985 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(602\) | −6.99258 | −0.284996 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 41.6210 | 1.69353 | ||||||||
\(605\) | 9.17226 | 0.372905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.15678 | −0.0875412 | −0.0437706 | − | 0.999042i | \(-0.513937\pi\) | ||||
−0.0437706 | + | 0.999042i | \(0.513937\pi\) | |||||||
\(608\) | −5.24030 | −0.212522 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.96969 | 0.322683 | ||||||||
\(611\) | −7.06804 | −0.285942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.57521 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(614\) | 61.4971 | 2.48182 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.05582 | 0.163414 | ||||||||
\(617\) | 37.6768 | 1.51681 | 0.758406 | − | 0.651783i | \(-0.225979\pi\) | ||||
0.758406 | + | 0.651783i | \(0.225979\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1042 | 0.687477 | 0.343738 | − | 0.939065i | \(-0.388307\pi\) | ||||
0.343738 | + | 0.939065i | \(0.388307\pi\) | |||||||
\(620\) | 18.1016 | 0.726978 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.6358 | 0.787325 | ||||||||
\(623\) | 12.2584 | 0.491122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.2429 | 0.968942 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.95421 | −0.237599 | ||||||||
\(629\) | 10.1723 | 0.405595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1090 | 1.31805 | 0.659025 | − | 0.752121i | \(-0.270969\pi\) | ||||
0.659025 | + | 0.752121i | \(0.270969\pi\) | |||||||
\(632\) | 7.59485 | 0.302107 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.1500 | 0.760544 | ||||||||
\(635\) | 7.07871 | 0.280910 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.28390 | 0.248977 | ||||||||
\(638\) | −10.9320 | −0.432800 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.78259 | 0.228577 | ||||||||
\(641\) | 23.1526 | 0.914473 | 0.457237 | − | 0.889345i | \(-0.348839\pi\) | ||||
0.457237 | + | 0.889345i | \(0.348839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.0639 | 1.69827 | 0.849137 | − | 0.528173i | \(-0.177123\pi\) | ||||
0.849137 | + | 0.528173i | \(0.177123\pi\) | |||||||
\(644\) | −46.0336 | −1.81398 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.82774 | 0.0719115 | ||||||||
\(647\) | 20.6439 | 0.811595 | 0.405798 | − | 0.913963i | \(-0.366994\pi\) | ||||
0.405798 | + | 0.913963i | \(0.366994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.64064 | −0.221415 | ||||||||
\(650\) | 1.35194 | 0.0530274 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.9346 | 0.780698 | ||||||||
\(653\) | −6.83516 | −0.267480 | −0.133740 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133740 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00000 | −0.234439 | ||||||||
\(656\) | −0.569988 | −0.0222543 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −92.9688 | −3.62430 | ||||||||
\(659\) | 26.8613 | 1.04637 | 0.523184 | − | 0.852220i | \(-0.324744\pi\) | ||||
0.523184 | + | 0.852220i | \(0.324744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.12125 | −0.0825071 | −0.0412535 | − | 0.999149i | \(-0.513135\pi\) | ||||
−0.0412535 | + | 0.999149i | \(0.513135\pi\) | |||||||
\(662\) | −15.0632 | −0.585449 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | −2.64806 | −0.102687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5667 | 0.718907 | ||||||||
\(668\) | −29.9500 | −1.15880 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.9852 | −0.656194 | ||||||||
\(671\) | −5.16484 | −0.199387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.8203 | 1.34222 | 0.671112 | − | 0.741356i | \(-0.265817\pi\) | ||||
0.671112 | + | 0.741356i | \(0.265817\pi\) | |||||||
\(674\) | 4.76450 | 0.183522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.5874 | −1.13798 | ||||||||
\(677\) | 24.6842 | 0.948692 | 0.474346 | − | 0.880338i | \(-0.342685\pi\) | ||||
0.474346 | + | 0.880338i | \(0.342685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −55.4897 | −2.12950 | ||||||||
\(680\) | −0.992582 | −0.0380638 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.7065 | −0.831184 | ||||||||
\(683\) | 38.4610 | 1.47167 | 0.735834 | − | 0.677162i | \(-0.236790\pi\) | ||||
0.735834 | + | 0.677162i | \(0.236790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.46838 | −0.285352 | ||||||||
\(686\) | 22.9852 | 0.877578 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.60227 | 0.0992107 | ||||||||
\(689\) | −2.70388 | −0.103010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.480608 | 0.0182832 | 0.00914159 | − | 0.999958i | \(-0.497090\pi\) | ||||
0.00914159 | + | 0.999958i | \(0.497090\pi\) | |||||||
\(692\) | −54.2084 | −2.06070 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.47841 | 0.0561197 | ||||||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.242915 | 0.00920105 | ||||||||
\(698\) | −44.5274 | −1.68539 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.61033 | 0.363236 | ||||||||
\(701\) | 18.1797 | 0.686637 | 0.343318 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343318 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.87614 | 0.183907 | ||||||||
\(704\) | −14.2281 | −0.536241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.0632 | 0.792725 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.18710 | 0.269917 | 0.134959 | − | 0.990851i | \(-0.456910\pi\) | ||||
0.134959 | + | 0.990851i | \(0.456910\pi\) | |||||||
\(710\) | −12.7597 | −0.478863 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.20257 | 0.0825449 | ||||||||
\(713\) | 36.8661 | 1.38065 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.876139 | −0.0327657 | ||||||||
\(716\) | −5.24030 | −0.195839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −63.7475 | −2.37903 | ||||||||
\(719\) | −12.5168 | −0.466797 | −0.233399 | − | 0.972381i | \(-0.574985\pi\) | ||||
−0.233399 | + | 0.972381i | \(0.574985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.7449 | 1.14500 | ||||||||
\(722\) | −38.7603 | −1.44251 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.10161 | 0.0409409 | ||||||||
\(725\) | −3.87614 | −0.143956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.42584 | 0.312497 | 0.156249 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156249 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(728\) | 1.94418 | 0.0720562 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.7523 | 0.953135 | ||||||||
\(731\) | −1.10902 | −0.0410187 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | −14.9777 | −0.552839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.7326 | 1.42770 | ||||||||
\(737\) | 11.0074 | 0.405463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81290 | −0.0666887 | −0.0333444 | − | 0.999444i | \(-0.510616\pi\) | ||||
−0.0333444 | + | 0.999444i | \(0.510616\pi\) | |||||||
\(740\) | −17.6965 | −0.650535 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −35.5652 | −1.30564 | ||||||||
\(743\) | −20.1371 | −0.738760 | −0.369380 | − | 0.929278i | \(-0.620430\pi\) | ||||
−0.369380 | + | 0.929278i | \(0.620430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5848 | −0.387798 | ||||||||
\(746\) | −45.7374 | −1.67457 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.29873 | 0.157177 | ||||||||
\(749\) | −4.94418 | −0.180656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2132 | 0.445668 | 0.222834 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222834 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(752\) | 34.5981 | 1.26166 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.24030 | −0.190841 | ||||||||
\(755\) | −17.6965 | −0.644040 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.9533 | 1.92462 | 0.962310 | − | 0.271955i | \(-0.0876701\pi\) | ||||
0.962310 | + | 0.271955i | \(0.0876701\pi\) | |||||||
\(758\) | −36.2839 | −1.31789 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.475800 | −0.0172591 | ||||||||
\(761\) | 18.4535 | 0.668940 | 0.334470 | − | 0.942406i | \(-0.391443\pi\) | ||||
0.334470 | + | 0.942406i | \(0.391443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.6317 | 2.08641 | ||||||||
\(764\) | 47.5752 | 1.72121 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.992582 | −0.0358634 | ||||||||
\(767\) | −2.70388 | −0.0976314 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.45355 | −0.160599 | −0.0802995 | − | 0.996771i | \(-0.525588\pi\) | ||||
−0.0802995 | + | 0.996771i | \(0.525588\pi\) | |||||||
\(770\) | −11.5242 | −0.415303 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −46.8726 | −1.68698 | ||||||||
\(773\) | −38.9368 | −1.40046 | −0.700229 | − | 0.713918i | \(-0.746919\pi\) | ||||
−0.700229 | + | 0.713918i | \(0.746919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.69646 | −0.276465 | ||||||||
\(776\) | −9.97033 | −0.357914 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.6561 | 0.417892 | ||||||||
\(779\) | 0.116443 | 0.00417200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.26906 | 0.295890 | ||||||||
\(782\) | −13.5094 | −0.483094 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30.7597 | −1.09856 | ||||||||
\(785\) | 2.53162 | 0.0903573 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2281 | 1.22010 | 0.610050 | − | 0.792363i | \(-0.291150\pi\) | ||||
0.610050 | + | 0.792363i | \(0.291150\pi\) | |||||||
\(788\) | 36.6433 | 1.30536 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.5800 | −0.767783 | ||||||||
\(791\) | 48.7252 | 1.73247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47580 | −0.0879183 | ||||||||
\(794\) | 7.82774 | 0.277796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.43129 | 0.298839 | ||||||||
\(797\) | −23.9655 | −0.848902 | −0.424451 | − | 0.905451i | \(-0.639533\pi\) | ||||
−0.424451 | + | 0.905451i | \(0.639533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7449 | −0.521636 | ||||||||
\(800\) | −8.08613 | −0.285888 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −49.1600 | −1.73590 | ||||||||
\(803\) | −16.6890 | −0.588943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5726 | 0.689843 | ||||||||
\(806\) | −10.4051 | −0.366506 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.07807 | 0.0379265 | ||||||||
\(809\) | 0.283896 | 0.00998124 | 0.00499062 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499062 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4413 | 1.13917 | 0.569584 | − | 0.821933i | \(-0.307104\pi\) | ||||
0.569584 | + | 0.821933i | \(0.307104\pi\) | |||||||
\(812\) | −37.2510 | −1.30725 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.2207 | 0.743784 | ||||||||
\(815\) | −8.47580 | −0.296894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.531618 | −0.0185990 | ||||||||
\(818\) | 2.18710 | 0.0764701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.422594 | −0.0147576 | ||||||||
\(821\) | −41.6694 | −1.45427 | −0.727136 | − | 0.686493i | \(-0.759149\pi\) | ||||
−0.727136 | + | 0.686493i | \(0.759149\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3626 | −0.674938 | −0.337469 | − | 0.941337i | \(-0.609571\pi\) | ||||
−0.337469 | + | 0.941337i | \(0.609571\pi\) | |||||||
\(824\) | 5.52420 | 0.192445 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.5652 | −1.23747 | ||||||||
\(827\) | −18.8097 | −0.654076 | −0.327038 | − | 0.945011i | \(-0.606050\pi\) | ||||
−0.327038 | + | 0.945011i | \(0.606050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1016 | −1.14967 | −0.574833 | − | 0.818271i | \(-0.694933\pi\) | ||||
−0.574833 | + | 0.818271i | \(0.694933\pi\) | |||||||
\(830\) | −25.5726 | −0.887638 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.82032 | −0.236452 | ||||||||
\(833\) | 13.1090 | 0.454201 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7342 | 0.440685 | ||||||||
\(836\) | 2.06063 | 0.0712682 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.0719 | 1.86788 | ||||||||
\(839\) | 39.6965 | 1.37047 | 0.685237 | − | 0.728320i | \(-0.259699\pi\) | ||||
0.685237 | + | 0.728320i | \(0.259699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9755 | −0.481915 | ||||||||
\(842\) | 15.9394 | 0.549307 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.2616 | 1.21376 | ||||||||
\(845\) | 12.5800 | 0.432766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.4791 | −1.28780 | ||||||||
\(848\) | 13.2355 | 0.454509 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.82032 | 0.0967362 | ||||||||
\(851\) | −36.0410 | −1.23547 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.11644 | −0.140944 | −0.0704722 | − | 0.997514i | \(-0.522451\pi\) | ||||
−0.0704722 | + | 0.997514i | \(0.522451\pi\) | |||||||
\(854\) | −32.5652 | −1.11436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.888365 | −0.0303637 | ||||||||
\(857\) | −14.7449 | −0.503675 | −0.251837 | − | 0.967770i | \(-0.581035\pi\) | ||||
−0.251837 | + | 0.967770i | \(0.581035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.8539 | −1.29156 | −0.645779 | − | 0.763524i | \(-0.723467\pi\) | ||||
−0.645779 | + | 0.763524i | \(0.723467\pi\) | |||||||
\(860\) | 1.92935 | 0.0657901 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.6581 | −0.567377 | ||||||||
\(863\) | −26.7704 | −0.911274 | −0.455637 | − | 0.890166i | \(-0.650588\pi\) | ||||
−0.455637 | + | 0.890166i | \(0.650588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0484 | 0.783669 | ||||||||
\(866\) | −26.1016 | −0.886969 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −73.9655 | −2.51055 | ||||||||
\(869\) | 13.9852 | 0.474414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.27648 | 0.178787 | ||||||||
\(872\) | 10.3552 | 0.350671 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.47580 | −0.219047 | ||||||||
\(875\) | −4.08613 | −0.138136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9681 | −1.58600 | −0.793001 | − | 0.609221i | \(-0.791482\pi\) | ||||
−0.793001 | + | 0.609221i | \(0.791482\pi\) | |||||||
\(878\) | −18.2839 | −0.617052 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.28870 | 0.144572 | ||||||||
\(881\) | 19.8055 | 0.667264 | 0.333632 | − | 0.942703i | \(-0.391726\pi\) | ||||
0.333632 | + | 0.942703i | \(0.391726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.20257 | −0.208733 | −0.104367 | − | 0.994539i | \(-0.533282\pi\) | ||||
−0.104367 | + | 0.994539i | \(0.533282\pi\) | |||||||
\(884\) | 2.06063 | 0.0693063 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.65809 | −0.257279 | ||||||||
\(887\) | −13.4274 | −0.450848 | −0.225424 | − | 0.974261i | \(-0.572377\pi\) | ||||
−0.225424 | + | 0.974261i | \(0.572377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.9245 | −0.970098 | ||||||||
\(890\) | −6.25839 | −0.209782 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −63.1049 | −2.11291 | ||||||||
\(893\) | −7.06804 | −0.236523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.22808 | 0.0744764 | ||||||||
\(896\) | −23.6284 | −0.789370 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −58.7710 | −1.96121 | ||||||||
\(899\) | 29.8325 | 0.994971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64064 | −0.187917 | ||||||||
\(902\) | 0.506752 | 0.0168730 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.75489 | 0.291183 | ||||||||
\(905\) | −0.468382 | −0.0155695 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.673566 | 0.0223654 | 0.0111827 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111827 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(908\) | −3.17968 | −0.105521 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.52420 | −0.183125 | ||||||||
\(911\) | 7.90970 | 0.262060 | 0.131030 | − | 0.991378i | \(-0.458172\pi\) | ||||
0.131030 | + | 0.991378i | \(0.458172\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5726 | 0.548473 | ||||||||
\(914\) | 73.5604 | 2.43316 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.3694 | −0.639983 | ||||||||
\(917\) | 24.5168 | 0.809615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.58263 | −0.283115 | −0.141557 | − | 0.989930i | \(-0.545211\pi\) | ||||
−0.141557 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(920\) | 3.51678 | 0.115945 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −72.3404 | −2.38240 | ||||||||
\(923\) | 3.96383 | 0.130471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.52420 | 0.247394 | ||||||||
\(926\) | 15.5390 | 0.510644 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.3430 | 1.02888 | ||||||||
\(929\) | −29.6162 | −0.971676 | −0.485838 | − | 0.874049i | \(-0.661485\pi\) | ||||
−0.485838 | + | 0.874049i | \(0.661485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.28390 | 0.205946 | ||||||||
\(932\) | −20.1971 | −0.661579 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −62.5120 | −2.04545 | ||||||||
\(935\) | −1.82774 | −0.0597735 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2058 | −0.496753 | −0.248376 | − | 0.968664i | \(-0.579897\pi\) | ||||
−0.248376 | + | 0.968664i | \(0.579897\pi\) | |||||||
\(938\) | 69.4036 | 2.26611 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.6513 | 0.836654 | ||||||||
\(941\) | −5.65287 | −0.184278 | −0.0921391 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921391 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.860663 | −0.0280270 | ||||||||
\(944\) | 13.2355 | 0.430779 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.31357 | −0.0752206 | ||||||||
\(947\) | 40.3962 | 1.31270 | 0.656350 | − | 0.754457i | \(-0.272100\pi\) | ||||
0.656350 | + | 0.754457i | \(0.272100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 1.35194 | 0.0438627 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.05582 | 0.131450 | ||||||||
\(953\) | 22.9320 | 0.742839 | 0.371419 | − | 0.928465i | \(-0.378871\pi\) | ||||
0.371419 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2281 | −0.654565 | ||||||||
\(956\) | 56.2691 | 1.81987 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.6581 | 0.538198 | ||||||||
\(959\) | 30.5168 | 0.985438 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2355 | 0.910822 | ||||||||
\(962\) | 10.1723 | 0.327967 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.6768 | −0.472708 | ||||||||
\(965\) | 19.9293 | 0.641548 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3700 | 0.333478 | 0.166739 | − | 0.986001i | \(-0.446676\pi\) | ||||
0.166739 | + | 0.986001i | \(0.446676\pi\) | |||||||
\(968\) | −6.73419 | −0.216445 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.3297 | 0.909611 | ||||||||
\(971\) | −48.0410 | −1.54171 | −0.770854 | − | 0.637012i | \(-0.780170\pi\) | ||||
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.6890 | 1.04796 | ||||||||
\(974\) | −24.9171 | −0.798396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.1191 | 0.387921 | ||||||||
\(977\) | −27.0532 | −0.865509 | −0.432754 | − | 0.901512i | \(-0.642458\pi\) | ||||
−0.432754 | + | 0.901512i | \(0.642458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.05582 | 0.129624 | ||||||||
\(980\) | −22.8055 | −0.728494 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.2355 | 0.613829 | ||||||||
\(983\) | 22.4817 | 0.717054 | 0.358527 | − | 0.933519i | \(-0.383279\pi\) | ||||
0.358527 | + | 0.933519i | \(0.383279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5800 | −0.496421 | ||||||||
\(986\) | −10.9320 | −0.348144 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.987774 | 0.0314253 | ||||||||
\(989\) | 3.92935 | 0.124946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5316 | −0.842805 | −0.421402 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421402 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(992\) | 62.2346 | 1.97595 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 52.1378 | 1.65371 | ||||||||
\(995\) | −3.58482 | −0.113647 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3659 | −0.898356 | −0.449178 | − | 0.893442i | \(-0.648283\pi\) | ||||
−0.449178 | + | 0.893442i | \(0.648283\pi\) | |||||||
\(998\) | 62.9433 | 1.99243 | ||||||||
\(999\) | 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 | 405.2.a.i.1.3 | 3 | ||
3.2 | odd | 2 | 405.2.a.j.1.1 | 3 | |||
4.3 | odd | 2 | 6480.2.a.bs.1.1 | 3 | |||
5.2 | odd | 4 | 2025.2.b.m.649.5 | 6 | |||
5.3 | odd | 4 | 2025.2.b.m.649.2 | 6 | |||
5.4 | even | 2 | 2025.2.a.o.1.1 | 3 | |||
9.2 | odd | 6 | 45.2.e.b.31.3 | yes | 6 | ||
9.4 | even | 3 | 135.2.e.b.46.1 | 6 | |||
9.5 | odd | 6 | 45.2.e.b.16.3 | ✓ | 6 | ||
9.7 | even | 3 | 135.2.e.b.91.1 | 6 | |||
12.11 | even | 2 | 6480.2.a.bv.1.1 | 3 | |||
15.2 | even | 4 | 2025.2.b.l.649.2 | 6 | |||
15.8 | even | 4 | 2025.2.b.l.649.5 | 6 | |||
15.14 | odd | 2 | 2025.2.a.n.1.3 | 3 | |||
36.7 | odd | 6 | 2160.2.q.k.1441.3 | 6 | |||
36.11 | even | 6 | 720.2.q.i.481.3 | 6 | |||
36.23 | even | 6 | 720.2.q.i.241.3 | 6 | |||
36.31 | odd | 6 | 2160.2.q.k.721.3 | 6 | |||
45.2 | even | 12 | 225.2.k.b.49.2 | 12 | |||
45.4 | even | 6 | 675.2.e.b.451.3 | 6 | |||
45.7 | odd | 12 | 675.2.k.b.199.5 | 12 | |||
45.13 | odd | 12 | 675.2.k.b.424.5 | 12 | |||
45.14 | odd | 6 | 225.2.e.b.151.1 | 6 | |||
45.22 | odd | 12 | 675.2.k.b.424.2 | 12 | |||
45.23 | even | 12 | 225.2.k.b.124.2 | 12 | |||
45.29 | odd | 6 | 225.2.e.b.76.1 | 6 | |||
45.32 | even | 12 | 225.2.k.b.124.5 | 12 | |||
45.34 | even | 6 | 675.2.e.b.226.3 | 6 | |||
45.38 | even | 12 | 225.2.k.b.49.5 | 12 | |||
45.43 | odd | 12 | 675.2.k.b.199.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.3 | ✓ | 6 | 9.5 | odd | 6 | ||
45.2.e.b.31.3 | yes | 6 | 9.2 | odd | 6 | ||
135.2.e.b.46.1 | 6 | 9.4 | even | 3 | |||
135.2.e.b.91.1 | 6 | 9.7 | even | 3 | |||
225.2.e.b.76.1 | 6 | 45.29 | odd | 6 | |||
225.2.e.b.151.1 | 6 | 45.14 | odd | 6 | |||
225.2.k.b.49.2 | 12 | 45.2 | even | 12 | |||
225.2.k.b.49.5 | 12 | 45.38 | even | 12 | |||
225.2.k.b.124.2 | 12 | 45.23 | even | 12 | |||
225.2.k.b.124.5 | 12 | 45.32 | even | 12 | |||
405.2.a.i.1.3 | 3 | 1.1 | even | 1 | trivial | ||
405.2.a.j.1.1 | 3 | 3.2 | odd | 2 | |||
675.2.e.b.226.3 | 6 | 45.34 | even | 6 | |||
675.2.e.b.451.3 | 6 | 45.4 | even | 6 | |||
675.2.k.b.199.2 | 12 | 45.43 | odd | 12 | |||
675.2.k.b.199.5 | 12 | 45.7 | odd | 12 | |||
675.2.k.b.424.2 | 12 | 45.22 | odd | 12 | |||
675.2.k.b.424.5 | 12 | 45.13 | odd | 12 | |||
720.2.q.i.241.3 | 6 | 36.23 | even | 6 | |||
720.2.q.i.481.3 | 6 | 36.11 | even | 6 | |||
2025.2.a.n.1.3 | 3 | 15.14 | odd | 2 | |||
2025.2.a.o.1.1 | 3 | 5.4 | even | 2 | |||
2025.2.b.l.649.2 | 6 | 15.2 | even | 4 | |||
2025.2.b.l.649.5 | 6 | 15.8 | even | 4 | |||
2025.2.b.m.649.2 | 6 | 5.3 | odd | 4 | |||
2025.2.b.m.649.5 | 6 | 5.2 | odd | 4 | |||
2160.2.q.k.721.3 | 6 | 36.31 | odd | 6 | |||
2160.2.q.k.1441.3 | 6 | 36.7 | odd | 6 | |||
6480.2.a.bs.1.1 | 3 | 4.3 | odd | 2 | |||
6480.2.a.bv.1.1 | 3 | 12.11 | even | 2 |