Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, 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("1225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | −0.874032 | −0.504623 | −0.252311 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.333851 | −0.136294 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 1.62054 | 0.467811 | ||||||||
\(13\) | 4.03631 | 1.11947 | 0.559735 | − | 0.828671i | \(-0.310903\pi\) | ||||
0.559735 | + | 0.828671i | \(0.310903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −7.40492 | −1.79596 | −0.897978 | − | 0.440040i | \(-0.854964\pi\) | ||||
−0.897978 | + | 0.440040i | \(0.854964\pi\) | |||||||
\(18\) | −0.854102 | −0.201314 | ||||||||
\(19\) | −4.24264 | −0.973329 | −0.486664 | − | 0.873589i | \(-0.661786\pi\) | ||||
−0.486664 | + | 0.873589i | \(0.661786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.854102 | 0.182095 | ||||||||
\(23\) | 3.76393 | 0.784834 | 0.392417 | − | 0.919787i | \(-0.371639\pi\) | ||||
0.392417 | + | 0.919787i | \(0.371639\pi\) | |||||||
\(24\) | 1.28669 | 0.262645 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.54173 | 0.302359 | ||||||||
\(27\) | 4.57649 | 0.880746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23607 | 0.415227 | 0.207614 | − | 0.978211i | \(-0.433430\pi\) | ||||
0.207614 | + | 0.978211i | \(0.433430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86474 | −1.23294 | −0.616472 | − | 0.787377i | \(-0.711438\pi\) | ||||
−0.616472 | + | 0.787377i | \(0.711438\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | −1.95440 | −0.340217 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.14590 | 0.690983 | ||||||||
\(37\) | 10.7082 | 1.76042 | 0.880209 | − | 0.474586i | \(-0.157402\pi\) | ||||
0.880209 | + | 0.474586i | \(0.157402\pi\) | |||||||
\(38\) | −1.62054 | −0.262887 | ||||||||
\(39\) | −3.52786 | −0.564910 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.78282 | 0.746951 | 0.373476 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373476 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | −4.14590 | −0.625018 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.43769 | 0.211976 | ||||||||
\(47\) | 9.48683 | 1.38380 | 0.691898 | − | 0.721995i | \(-0.256775\pi\) | ||||
0.691898 | + | 0.721995i | \(0.256775\pi\) | |||||||
\(48\) | −2.74962 | −0.396873 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.47214 | 0.906280 | ||||||||
\(52\) | −7.48373 | −1.03781 | ||||||||
\(53\) | 9.70820 | 1.33352 | 0.666762 | − | 0.745271i | \(-0.267680\pi\) | ||||
0.666762 | + | 0.745271i | \(0.267680\pi\) | |||||||
\(54\) | 1.74806 | 0.237881 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.70820 | 0.491164 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | 13.1893 | 1.71710 | 0.858550 | − | 0.512730i | \(-0.171366\pi\) | ||||
0.858550 | + | 0.512730i | \(0.171366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.03476 | 0.388561 | 0.194280 | − | 0.980946i | \(-0.437763\pi\) | ||||
0.194280 | + | 0.980946i | \(0.437763\pi\) | |||||||
\(62\) | −2.62210 | −0.333007 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.746512 | −0.0918893 | ||||||||
\(67\) | 8.70820 | 1.06388 | 0.531938 | − | 0.846783i | \(-0.321464\pi\) | ||||
0.531938 | + | 0.846783i | \(0.321464\pi\) | |||||||
\(68\) | 13.7295 | 1.66494 | ||||||||
\(69\) | −3.28980 | −0.396045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.47214 | −0.886779 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(72\) | 3.29180 | 0.387942 | ||||||||
\(73\) | −2.62210 | −0.306893 | −0.153447 | − | 0.988157i | \(-0.549037\pi\) | ||||
−0.153447 | + | 0.988157i | \(0.549037\pi\) | |||||||
\(74\) | 4.09017 | 0.475473 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.86629 | 0.902325 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.34752 | −0.152577 | ||||||||
\(79\) | −4.70820 | −0.529714 | −0.264857 | − | 0.964288i | \(-0.585325\pi\) | ||||
−0.264857 | + | 0.964288i | \(0.585325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 1.82688 | 0.201745 | ||||||||
\(83\) | −6.86474 | −0.753503 | −0.376751 | − | 0.926314i | \(-0.622959\pi\) | ||||
−0.376751 | + | 0.926314i | \(0.622959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.90983 | 0.205942 | ||||||||
\(87\) | −1.95440 | −0.209533 | ||||||||
\(88\) | −3.29180 | −0.350907 | ||||||||
\(89\) | −7.94510 | −0.842179 | −0.421089 | − | 0.907019i | \(-0.638352\pi\) | ||||
−0.421089 | + | 0.907019i | \(0.638352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.97871 | −0.727581 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 3.62365 | 0.373751 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.62365 | −0.369837 | ||||||||
\(97\) | 10.1058 | 1.02609 | 0.513046 | − | 0.858361i | \(-0.328517\pi\) | ||||
0.513046 | + | 0.858361i | \(0.328517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1074 | −1.10523 | −0.552613 | − | 0.833438i | \(-0.686369\pi\) | ||||
−0.552613 | + | 0.833438i | \(0.686369\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | −9.48683 | −0.934765 | −0.467383 | − | 0.884055i | \(-0.654803\pi\) | ||||
−0.467383 | + | 0.884055i | \(0.654803\pi\) | |||||||
\(104\) | −5.94200 | −0.582661 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.70820 | 0.360173 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | −8.48528 | −0.816497 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.35931 | −0.888347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.76393 | 0.918513 | 0.459257 | − | 0.888304i | \(-0.348116\pi\) | ||||
0.459257 | + | 0.888304i | \(0.348116\pi\) | |||||||
\(114\) | 1.41641 | 0.132659 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.14590 | −0.384937 | ||||||||
\(117\) | −9.02546 | −0.834404 | ||||||||
\(118\) | 5.03786 | 0.463773 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 1.15917 | 0.104947 | ||||||||
\(123\) | −4.18034 | −0.376929 | ||||||||
\(124\) | 12.7279 | 1.14300 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | 0.621150 | 0.310575 | − | 0.950549i | \(-0.399478\pi\) | ||||
0.310575 | + | 0.950549i | \(0.399478\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | −4.37016 | −0.384771 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8098 | 1.29394 | 0.646971 | − | 0.762515i | \(-0.276036\pi\) | ||||
0.646971 | + | 0.762515i | \(0.276036\pi\) | |||||||
\(132\) | 3.62365 | 0.315398 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.32624 | 0.287343 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.9010 | 0.934757 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | −1.25659 | −0.106968 | ||||||||
\(139\) | 19.5927 | 1.66183 | 0.830914 | − | 0.556401i | \(-0.187818\pi\) | ||||
0.830914 | + | 0.556401i | \(0.187818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.29180 | −0.698295 | ||||||||
\(142\) | −2.85410 | −0.239511 | ||||||||
\(143\) | 9.02546 | 0.754747 | ||||||||
\(144\) | −7.03444 | −0.586203 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00155 | −0.0828890 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.8541 | −1.63200 | ||||||||
\(149\) | 9.65248 | 0.790762 | 0.395381 | − | 0.918517i | \(-0.370613\pi\) | ||||
0.395381 | + | 0.918517i | \(0.370613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.41641 | 0.684918 | 0.342459 | − | 0.939533i | \(-0.388740\pi\) | ||||
0.342459 | + | 0.939533i | \(0.388740\pi\) | |||||||
\(152\) | 6.24574 | 0.506597 | ||||||||
\(153\) | 16.5579 | 1.33863 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.54102 | 0.523701 | ||||||||
\(157\) | 5.45052 | 0.434999 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(158\) | −1.79837 | −0.143071 | ||||||||
\(159\) | −8.48528 | −0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.03444 | 0.0812734 | ||||||||
\(163\) | −2.29180 | −0.179507 | −0.0897537 | − | 0.995964i | \(-0.528608\pi\) | ||||
−0.0897537 | + | 0.995964i | \(0.528608\pi\) | |||||||
\(164\) | −8.86784 | −0.692462 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.62210 | −0.203514 | ||||||||
\(167\) | −14.2697 | −1.10422 | −0.552110 | − | 0.833772i | \(-0.686177\pi\) | ||||
−0.552110 | + | 0.833772i | \(0.686177\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.29180 | 0.253215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.48683 | 0.725476 | ||||||||
\(172\) | −9.27051 | −0.706870 | ||||||||
\(173\) | −4.24264 | −0.322562 | −0.161281 | − | 0.986909i | \(-0.551563\pi\) | ||||
−0.161281 | + | 0.986909i | \(0.551563\pi\) | |||||||
\(174\) | −0.746512 | −0.0565930 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.03444 | 0.530241 | ||||||||
\(177\) | −11.5279 | −0.866487 | ||||||||
\(178\) | −3.03476 | −0.227465 | ||||||||
\(179\) | 3.70820 | 0.277164 | 0.138582 | − | 0.990351i | \(-0.455746\pi\) | ||||
0.138582 | + | 0.990351i | \(0.455746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1074 | −0.825605 | −0.412802 | − | 0.910821i | \(-0.635450\pi\) | ||||
−0.412802 | + | 0.910821i | \(0.635450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.65248 | −0.196077 | ||||||||
\(184\) | −5.54102 | −0.408489 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.29180 | 0.168043 | ||||||||
\(187\) | −16.5579 | −1.21083 | ||||||||
\(188\) | −17.5896 | −1.28285 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.1246 | −1.67324 | −0.836619 | − | 0.547785i | \(-0.815471\pi\) | ||||
−0.836619 | + | 0.547785i | \(0.815471\pi\) | |||||||
\(192\) | 4.11512 | 0.296983 | ||||||||
\(193\) | −10.7082 | −0.770793 | −0.385397 | − | 0.922751i | \(-0.625935\pi\) | ||||
−0.385397 | + | 0.922751i | \(0.625935\pi\) | |||||||
\(194\) | 3.86008 | 0.277138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.94427 | −0.423512 | −0.211756 | − | 0.977323i | \(-0.567918\pi\) | ||||
−0.211756 | + | 0.977323i | \(0.567918\pi\) | |||||||
\(198\) | −1.90983 | −0.135726 | ||||||||
\(199\) | −25.2495 | −1.78989 | −0.894945 | − | 0.446176i | \(-0.852786\pi\) | ||||
−0.894945 | + | 0.446176i | \(0.852786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.61125 | −0.536856 | ||||||||
\(202\) | −4.24264 | −0.298511 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.62365 | −0.252472 | ||||||||
\(207\) | −8.41641 | −0.584981 | ||||||||
\(208\) | 12.6978 | 0.880435 | ||||||||
\(209\) | −9.48683 | −0.656218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.41641 | 0.510567 | 0.255283 | − | 0.966866i | \(-0.417831\pi\) | ||||
0.255283 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(212\) | −18.0000 | −1.23625 | ||||||||
\(213\) | 6.53089 | 0.447489 | ||||||||
\(214\) | 2.29180 | 0.156664 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.73722 | −0.458410 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.381966 | −0.0258700 | ||||||||
\(219\) | 2.29180 | 0.154865 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.8885 | −2.01052 | ||||||||
\(222\) | −3.57494 | −0.239934 | ||||||||
\(223\) | 5.86319 | 0.392628 | 0.196314 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196314 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.72949 | 0.248082 | ||||||||
\(227\) | 26.4574 | 1.75604 | 0.878020 | − | 0.478625i | \(-0.158865\pi\) | ||||
0.878020 | + | 0.478625i | \(0.158865\pi\) | |||||||
\(228\) | −6.87539 | −0.455334 | ||||||||
\(229\) | 7.07107 | 0.467269 | 0.233635 | − | 0.972324i | \(-0.424938\pi\) | ||||
0.233635 | + | 0.972324i | \(0.424938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.29180 | −0.216117 | ||||||||
\(233\) | 4.52786 | 0.296630 | 0.148315 | − | 0.988940i | \(-0.452615\pi\) | ||||
0.148315 | + | 0.988940i | \(0.452615\pi\) | |||||||
\(234\) | −3.44742 | −0.225365 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −24.4543 | −1.59184 | ||||||||
\(237\) | 4.11512 | 0.267306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.1246 | 1.88391 | 0.941957 | − | 0.335733i | \(-0.108984\pi\) | ||||
0.941957 | + | 0.335733i | \(0.108984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7310 | 0.948909 | 0.474454 | − | 0.880280i | \(-0.342645\pi\) | ||||
0.474454 | + | 0.880280i | \(0.342645\pi\) | |||||||
\(242\) | −2.29180 | −0.147322 | ||||||||
\(243\) | −16.0965 | −1.03259 | ||||||||
\(244\) | −5.62675 | −0.360216 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.59675 | −0.101805 | ||||||||
\(247\) | −17.1246 | −1.08961 | ||||||||
\(248\) | 10.1058 | 0.641721 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5687 | 0.730213 | 0.365106 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365106 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.41641 | 0.529135 | ||||||||
\(254\) | 2.67376 | 0.167767 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −12.1089 | −0.755334 | −0.377667 | − | 0.925941i | \(-0.623274\pi\) | ||||
−0.377667 | + | 0.925941i | \(0.623274\pi\) | |||||||
\(258\) | −1.66925 | −0.103923 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | 5.65685 | 0.349482 | ||||||||
\(263\) | 29.9443 | 1.84644 | 0.923221 | − | 0.384268i | \(-0.125546\pi\) | ||||
0.923221 | + | 0.384268i | \(0.125546\pi\) | |||||||
\(264\) | 2.87714 | 0.177075 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.94427 | 0.424983 | ||||||||
\(268\) | −16.1459 | −0.986268 | ||||||||
\(269\) | 15.3500 | 0.935907 | 0.467954 | − | 0.883753i | \(-0.344991\pi\) | ||||
0.467954 | + | 0.883753i | \(0.344991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.44897 | 0.270256 | 0.135128 | − | 0.990828i | \(-0.456855\pi\) | ||||
0.135128 | + | 0.990828i | \(0.456855\pi\) | |||||||
\(272\) | −23.2951 | −1.41247 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.29180 | −0.138452 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.09962 | 0.367154 | ||||||||
\(277\) | −24.0000 | −1.44202 | −0.721010 | − | 0.692925i | \(-0.756322\pi\) | ||||
−0.721010 | + | 0.692925i | \(0.756322\pi\) | |||||||
\(278\) | 7.48373 | 0.448844 | ||||||||
\(279\) | 15.3500 | 0.918982 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.5967 | −1.46732 | −0.733659 | − | 0.679517i | \(-0.762189\pi\) | ||||
−0.733659 | + | 0.679517i | \(0.762189\pi\) | |||||||
\(282\) | −3.16718 | −0.188603 | ||||||||
\(283\) | 20.8005 | 1.23646 | 0.618232 | − | 0.785996i | \(-0.287849\pi\) | ||||
0.618232 | + | 0.785996i | \(0.287849\pi\) | |||||||
\(284\) | 13.8541 | 0.822090 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.44742 | 0.203850 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.27051 | −0.546270 | ||||||||
\(289\) | 37.8328 | 2.22546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.83282 | −0.517789 | ||||||||
\(292\) | 4.86163 | 0.284506 | ||||||||
\(293\) | −18.4335 | −1.07690 | −0.538448 | − | 0.842659i | \(-0.680989\pi\) | ||||
−0.538448 | + | 0.842659i | \(0.680989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.7639 | −0.916260 | ||||||||
\(297\) | 10.2333 | 0.593799 | ||||||||
\(298\) | 3.68692 | 0.213577 | ||||||||
\(299\) | 15.1924 | 0.878599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.21478 | 0.184990 | ||||||||
\(303\) | 9.70820 | 0.557722 | ||||||||
\(304\) | −13.3469 | −0.765498 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.32456 | 0.361551 | ||||||||
\(307\) | −14.5548 | −0.830686 | −0.415343 | − | 0.909665i | \(-0.636338\pi\) | ||||
−0.415343 | + | 0.909665i | \(0.636338\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.29180 | 0.471704 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.56564 | 0.542418 | 0.271209 | − | 0.962520i | \(-0.412577\pi\) | ||||
0.271209 | + | 0.962520i | \(0.412577\pi\) | |||||||
\(312\) | 5.19350 | 0.294024 | ||||||||
\(313\) | −21.2132 | −1.19904 | −0.599521 | − | 0.800359i | \(-0.704642\pi\) | ||||
−0.599521 | + | 0.800359i | \(0.704642\pi\) | |||||||
\(314\) | 2.08191 | 0.117489 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.72949 | 0.491072 | ||||||||
\(317\) | −11.9443 | −0.670857 | −0.335429 | − | 0.942066i | \(-0.608881\pi\) | ||||
−0.335429 | + | 0.942066i | \(0.608881\pi\) | |||||||
\(318\) | −3.24109 | −0.181751 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.24419 | −0.292702 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.4164 | 1.74806 | ||||||||
\(324\) | −5.02129 | −0.278960 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.875388 | −0.0484833 | ||||||||
\(327\) | 0.874032 | 0.0483341 | ||||||||
\(328\) | −7.04096 | −0.388772 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.29180 | −0.0710035 | −0.0355018 | − | 0.999370i | \(-0.511303\pi\) | ||||
−0.0355018 | + | 0.999370i | \(0.511303\pi\) | |||||||
\(332\) | 12.7279 | 0.698535 | ||||||||
\(333\) | −23.9443 | −1.31214 | ||||||||
\(334\) | −5.45052 | −0.298239 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1246 | −1.25968 | −0.629839 | − | 0.776726i | \(-0.716879\pi\) | ||||
−0.629839 | + | 0.776726i | \(0.716879\pi\) | |||||||
\(338\) | 1.25735 | 0.0683911 | ||||||||
\(339\) | −8.53399 | −0.463503 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3500 | −0.831250 | ||||||||
\(342\) | 3.62365 | 0.195944 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.36068 | −0.396861 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.62054 | −0.0871210 | ||||||||
\(347\) | 27.6525 | 1.48446 | 0.742231 | − | 0.670144i | \(-0.233768\pi\) | ||||
0.742231 | + | 0.670144i | \(0.233768\pi\) | |||||||
\(348\) | 3.62365 | 0.194248 | ||||||||
\(349\) | 1.00155 | 0.0536118 | 0.0268059 | − | 0.999641i | \(-0.491466\pi\) | ||||
0.0268059 | + | 0.999641i | \(0.491466\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.4721 | 0.985970 | ||||||||
\(352\) | 9.27051 | 0.494120 | ||||||||
\(353\) | 12.1089 | 0.644493 | 0.322247 | − | 0.946656i | \(-0.395562\pi\) | ||||
0.322247 | + | 0.946656i | \(0.395562\pi\) | |||||||
\(354\) | −4.40325 | −0.234030 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.7310 | 0.780743 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.41641 | 0.0748595 | ||||||||
\(359\) | 0.0557281 | 0.00294122 | 0.00147061 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00147061 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −4.24264 | −0.222988 | ||||||||
\(363\) | 5.24419 | 0.275249 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.01316 | −0.0529585 | ||||||||
\(367\) | 8.69161 | 0.453698 | 0.226849 | − | 0.973930i | \(-0.427158\pi\) | ||||
0.226849 | + | 0.973930i | \(0.427158\pi\) | |||||||
\(368\) | 11.8409 | 0.617252 | ||||||||
\(369\) | −10.6947 | −0.556745 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.1246 | −0.576784 | ||||||||
\(373\) | −16.1246 | −0.834901 | −0.417450 | − | 0.908700i | \(-0.637076\pi\) | ||||
−0.417450 | + | 0.908700i | \(0.637076\pi\) | |||||||
\(374\) | −6.32456 | −0.327035 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.9659 | −0.720237 | ||||||||
\(377\) | 9.02546 | 0.464835 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.11822 | −0.313446 | ||||||||
\(382\) | −8.83282 | −0.451926 | ||||||||
\(383\) | 13.1893 | 0.673941 | 0.336971 | − | 0.941515i | \(-0.390598\pi\) | ||||
0.336971 | + | 0.941515i | \(0.390598\pi\) | |||||||
\(384\) | 8.81913 | 0.450049 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.09017 | −0.208184 | ||||||||
\(387\) | −11.1803 | −0.568329 | ||||||||
\(388\) | −18.7372 | −0.951239 | ||||||||
\(389\) | 27.7639 | 1.40769 | 0.703844 | − | 0.710355i | \(-0.251466\pi\) | ||||
0.703844 | + | 0.710355i | \(0.251466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.8716 | −1.40953 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.9443 | −0.652952 | ||||||||
\(394\) | −2.27051 | −0.114387 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.27051 | 0.465861 | ||||||||
\(397\) | −9.89949 | −0.496841 | −0.248421 | − | 0.968652i | \(-0.579912\pi\) | ||||
−0.248421 | + | 0.968652i | \(0.579912\pi\) | |||||||
\(398\) | −9.64446 | −0.483433 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.0689 | 1.15201 | 0.576003 | − | 0.817448i | \(-0.304612\pi\) | ||||
0.576003 | + | 0.817448i | \(0.304612\pi\) | |||||||
\(402\) | −2.90724 | −0.145000 | ||||||||
\(403\) | −27.7082 | −1.38024 | ||||||||
\(404\) | 20.5942 | 1.02460 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9443 | 1.18687 | ||||||||
\(408\) | −9.52786 | −0.471700 | ||||||||
\(409\) | 14.7310 | 0.728402 | 0.364201 | − | 0.931320i | \(-0.381342\pi\) | ||||
0.364201 | + | 0.931320i | \(0.381342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.24419 | 0.258677 | ||||||||
\(412\) | 17.5896 | 0.866575 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.21478 | −0.157998 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.7341 | 0.820458 | ||||||||
\(417\) | −17.1246 | −0.838596 | ||||||||
\(418\) | −3.62365 | −0.177238 | ||||||||
\(419\) | −4.86163 | −0.237506 | −0.118753 | − | 0.992924i | \(-0.537890\pi\) | ||||
−0.118753 | + | 0.992924i | \(0.537890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.29180 | −0.452854 | −0.226427 | − | 0.974028i | \(-0.572705\pi\) | ||||
−0.226427 | + | 0.974028i | \(0.572705\pi\) | |||||||
\(422\) | 2.83282 | 0.137899 | ||||||||
\(423\) | −21.2132 | −1.03142 | ||||||||
\(424\) | −14.2918 | −0.694071 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.49458 | 0.120863 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.1246 | −0.537728 | ||||||||
\(429\) | −7.88854 | −0.380862 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.76393 | 0.325807 | 0.162904 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162904 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(432\) | 14.3972 | 0.692684 | ||||||||
\(433\) | 32.7031 | 1.57161 | 0.785806 | − | 0.618473i | \(-0.212248\pi\) | ||||
0.785806 | + | 0.618473i | \(0.212248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.85410 | 0.0887954 | ||||||||
\(437\) | −15.9690 | −0.763901 | ||||||||
\(438\) | 0.875388 | 0.0418277 | ||||||||
\(439\) | −17.7658 | −0.847915 | −0.423957 | − | 0.905682i | \(-0.639359\pi\) | ||||
−0.423957 | + | 0.905682i | \(0.639359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.4164 | −0.543023 | ||||||||
\(443\) | 20.1803 | 0.958797 | 0.479398 | − | 0.877597i | \(-0.340855\pi\) | ||||
0.479398 | + | 0.877597i | \(0.340855\pi\) | |||||||
\(444\) | 17.3531 | 0.823543 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.23954 | 0.106045 | ||||||||
\(447\) | −8.43657 | −0.399036 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5967 | −0.594477 | −0.297239 | − | 0.954803i | \(-0.596066\pi\) | ||||
−0.297239 | + | 0.954803i | \(0.596066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6947 | 0.503594 | ||||||||
\(452\) | −18.1033 | −0.851509 | ||||||||
\(453\) | −7.35621 | −0.345625 | ||||||||
\(454\) | 10.1058 | 0.474290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.45898 | −0.255640 | ||||||||
\(457\) | 7.29180 | 0.341096 | 0.170548 | − | 0.985349i | \(-0.445446\pi\) | ||||
0.170548 | + | 0.985349i | \(0.445446\pi\) | |||||||
\(458\) | 2.70091 | 0.126205 | ||||||||
\(459\) | −33.8885 | −1.58178 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.4009 | 1.55564 | 0.777819 | − | 0.628489i | \(-0.216326\pi\) | ||||
0.777819 | + | 0.628489i | \(0.216326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 7.03444 | 0.326566 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.72949 | 0.0801171 | ||||||||
\(467\) | 9.64446 | 0.446292 | 0.223146 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223146 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(468\) | 16.7341 | 0.773535 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.76393 | −0.219510 | ||||||||
\(472\) | −19.4164 | −0.893714 | ||||||||
\(473\) | 11.1803 | 0.514073 | ||||||||
\(474\) | 1.57184 | 0.0721968 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.7082 | −0.993950 | ||||||||
\(478\) | 11.1246 | 0.508828 | ||||||||
\(479\) | 9.02546 | 0.412384 | 0.206192 | − | 0.978512i | \(-0.433893\pi\) | ||||
0.206192 | + | 0.978512i | \(0.433893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.2216 | 1.97074 | ||||||||
\(482\) | 5.62675 | 0.256291 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1246 | 0.505664 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.14833 | −0.278894 | ||||||||
\(487\) | 28.7082 | 1.30089 | 0.650446 | − | 0.759552i | \(-0.274582\pi\) | ||||
0.650446 | + | 0.759552i | \(0.274582\pi\) | |||||||
\(488\) | −4.46758 | −0.202238 | ||||||||
\(489\) | 2.00310 | 0.0905835 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.47214 | 0.337213 | 0.168606 | − | 0.985683i | \(-0.446073\pi\) | ||||
0.168606 | + | 0.985683i | \(0.446073\pi\) | |||||||
\(492\) | 7.75078 | 0.349432 | ||||||||
\(493\) | −16.5579 | −0.745730 | ||||||||
\(494\) | −6.54102 | −0.294294 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5958 | −0.969678 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.29180 | 0.102698 | ||||||||
\(499\) | −25.4164 | −1.13779 | −0.568897 | − | 0.822409i | \(-0.692630\pi\) | ||||
−0.568897 | + | 0.822409i | \(0.692630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4721 | 0.557214 | ||||||||
\(502\) | 4.41887 | 0.197224 | ||||||||
\(503\) | −16.8918 | −0.753166 | −0.376583 | − | 0.926383i | \(-0.622901\pi\) | ||||
−0.376583 | + | 0.926383i | \(0.622901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.21478 | 0.142914 | ||||||||
\(507\) | −2.87714 | −0.127778 | ||||||||
\(508\) | −12.9787 | −0.575837 | ||||||||
\(509\) | −5.78437 | −0.256388 | −0.128194 | − | 0.991749i | \(-0.540918\pi\) | ||||
−0.128194 | + | 0.991749i | \(0.540918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | −19.4164 | −0.857255 | ||||||||
\(514\) | −4.62520 | −0.204009 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.10272 | 0.356702 | ||||||||
\(517\) | 21.2132 | 0.932956 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.70820 | 0.162772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.0230 | −1.57820 | −0.789099 | − | 0.614266i | \(-0.789452\pi\) | ||||
−0.789099 | + | 0.614266i | \(0.789452\pi\) | |||||||
\(522\) | −1.90983 | −0.0835910 | ||||||||
\(523\) | 3.24109 | 0.141723 | 0.0708615 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708615 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(524\) | −27.4589 | −1.19955 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.4377 | 0.498707 | ||||||||
\(527\) | 50.8328 | 2.21431 | ||||||||
\(528\) | −6.14833 | −0.267572 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.4922 | −1.27985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3050 | 0.836190 | ||||||||
\(534\) | 2.65248 | 0.114784 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.8197 | −0.553725 | ||||||||
\(537\) | −3.24109 | −0.139863 | ||||||||
\(538\) | 5.86319 | 0.252780 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.70820 | −0.374395 | −0.187197 | − | 0.982322i | \(-0.559940\pi\) | ||||
−0.187197 | + | 0.982322i | \(0.559940\pi\) | |||||||
\(542\) | 1.69936 | 0.0729936 | ||||||||
\(543\) | 9.70820 | 0.416619 | ||||||||
\(544\) | −30.7000 | −1.31625 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0000 | 1.23995 | 0.619975 | − | 0.784621i | \(-0.287143\pi\) | ||||
0.619975 | + | 0.784621i | \(0.287143\pi\) | |||||||
\(548\) | 11.1246 | 0.475220 | ||||||||
\(549\) | −6.78593 | −0.289616 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.48683 | −0.404153 | ||||||||
\(552\) | 4.84303 | 0.206133 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.16718 | −0.389476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.3268 | −1.54060 | ||||||||
\(557\) | 24.5967 | 1.04220 | 0.521099 | − | 0.853496i | \(-0.325522\pi\) | ||||
0.521099 | + | 0.853496i | \(0.325522\pi\) | |||||||
\(558\) | 5.86319 | 0.248208 | ||||||||
\(559\) | 20.1815 | 0.853589 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4721 | 0.611014 | ||||||||
\(562\) | −9.39512 | −0.396309 | ||||||||
\(563\) | 13.8083 | 0.581950 | 0.290975 | − | 0.956731i | \(-0.406020\pi\) | ||||
0.290975 | + | 0.956731i | \(0.406020\pi\) | |||||||
\(564\) | 15.3738 | 0.647355 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.94510 | 0.333957 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.0000 | 0.461550 | ||||||||
\(569\) | −29.9443 | −1.25533 | −0.627665 | − | 0.778484i | \(-0.715989\pi\) | ||||
−0.627665 | + | 0.778484i | \(0.715989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4164 | 1.10549 | 0.552746 | − | 0.833350i | \(-0.313580\pi\) | ||||
0.552746 | + | 0.833350i | \(0.313580\pi\) | |||||||
\(572\) | −16.7341 | −0.699689 | ||||||||
\(573\) | 20.2117 | 0.844354 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.5279 | 0.438661 | ||||||||
\(577\) | −42.1900 | −1.75639 | −0.878196 | − | 0.478301i | \(-0.841253\pi\) | ||||
−0.878196 | + | 0.478301i | \(0.841253\pi\) | |||||||
\(578\) | 14.4508 | 0.601076 | ||||||||
\(579\) | 9.35931 | 0.388960 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.37384 | −0.139850 | ||||||||
\(583\) | 21.7082 | 0.899062 | ||||||||
\(584\) | 3.86008 | 0.159731 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.04096 | −0.290860 | ||||||||
\(587\) | −5.86319 | −0.242000 | −0.121000 | − | 0.992653i | \(-0.538610\pi\) | ||||
−0.121000 | + | 0.992653i | \(0.538610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1246 | 1.20006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.19548 | 0.213714 | ||||||||
\(592\) | 33.6869 | 1.38452 | ||||||||
\(593\) | 30.7000 | 1.26070 | 0.630350 | − | 0.776311i | \(-0.282912\pi\) | ||||
0.630350 | + | 0.776311i | \(0.282912\pi\) | |||||||
\(594\) | 3.90879 | 0.160380 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.8967 | −0.733076 | ||||||||
\(597\) | 22.0689 | 0.903219 | ||||||||
\(598\) | 5.80298 | 0.237301 | ||||||||
\(599\) | −6.81966 | −0.278644 | −0.139322 | − | 0.990247i | \(-0.544492\pi\) | ||||
−0.139322 | + | 0.990247i | \(0.544492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4621 | 1.20178 | 0.600891 | − | 0.799331i | \(-0.294813\pi\) | ||||
0.600891 | + | 0.799331i | \(0.294813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.4721 | −0.792967 | ||||||||
\(604\) | −15.6049 | −0.634953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.70820 | 0.150635 | ||||||||
\(607\) | 45.2247 | 1.83562 | 0.917808 | − | 0.397025i | \(-0.129958\pi\) | ||||
0.917808 | + | 0.397025i | \(0.129958\pi\) | |||||||
\(608\) | −17.5896 | −0.713351 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.2918 | 1.54912 | ||||||||
\(612\) | −30.7000 | −1.24098 | ||||||||
\(613\) | 14.4164 | 0.582273 | 0.291137 | − | 0.956681i | \(-0.405967\pi\) | ||||
0.291137 | + | 0.956681i | \(0.405967\pi\) | |||||||
\(614\) | −5.55944 | −0.224361 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.3607 | 0.779432 | 0.389716 | − | 0.920935i | \(-0.372573\pi\) | ||||
0.389716 | + | 0.920935i | \(0.372573\pi\) | |||||||
\(618\) | 3.16718 | 0.127403 | ||||||||
\(619\) | 9.28050 | 0.373015 | 0.186507 | − | 0.982454i | \(-0.440283\pi\) | ||||
0.186507 | + | 0.982454i | \(0.440283\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.2256 | 0.691240 | ||||||||
\(622\) | 3.65375 | 0.146502 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.0983 | −0.444288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.10272 | −0.323850 | ||||||||
\(627\) | 8.29180 | 0.331142 | ||||||||
\(628\) | −10.1058 | −0.403266 | ||||||||
\(629\) | −79.2934 | −3.16163 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.1246 | −1.11962 | −0.559812 | − | 0.828620i | \(-0.689126\pi\) | ||||
−0.559812 | + | 0.828620i | \(0.689126\pi\) | |||||||
\(632\) | 6.93112 | 0.275705 | ||||||||
\(633\) | −6.48218 | −0.257643 | ||||||||
\(634\) | −4.56231 | −0.181192 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.7326 | 0.623837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.90983 | 0.0756109 | ||||||||
\(639\) | 16.7082 | 0.660966 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5279 | −0.652811 | −0.326406 | − | 0.945230i | \(-0.605838\pi\) | ||||
−0.326406 | + | 0.945230i | \(0.605838\pi\) | |||||||
\(642\) | −2.00310 | −0.0790562 | ||||||||
\(643\) | −22.2148 | −0.876064 | −0.438032 | − | 0.898959i | \(-0.644324\pi\) | ||||
−0.438032 | + | 0.898959i | \(0.644324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | −19.0525 | −0.749030 | −0.374515 | − | 0.927221i | \(-0.622191\pi\) | ||||
−0.374515 | + | 0.927221i | \(0.622191\pi\) | |||||||
\(648\) | −3.98684 | −0.156618 | ||||||||
\(649\) | 29.4922 | 1.15767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.24922 | 0.166412 | ||||||||
\(653\) | 1.41641 | 0.0554283 | 0.0277142 | − | 0.999616i | \(-0.491177\pi\) | ||||
0.0277142 | + | 0.999616i | \(0.491177\pi\) | |||||||
\(654\) | 0.333851 | 0.0130546 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.0463 | 0.587458 | ||||||||
\(657\) | 5.86319 | 0.228745 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.83282 | −0.344078 | −0.172039 | − | 0.985090i | \(-0.555035\pi\) | ||||
−0.172039 | + | 0.985090i | \(0.555035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9752 | −0.776946 | −0.388473 | − | 0.921460i | \(-0.626997\pi\) | ||||
−0.388473 | + | 0.921460i | \(0.626997\pi\) | |||||||
\(662\) | −0.493422 | −0.0191774 | ||||||||
\(663\) | 26.1235 | 1.01455 | ||||||||
\(664\) | 10.1058 | 0.392182 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.14590 | −0.354396 | ||||||||
\(667\) | 8.41641 | 0.325885 | ||||||||
\(668\) | 26.4574 | 1.02367 | ||||||||
\(669\) | −5.12461 | −0.198129 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.78593 | 0.261968 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.1246 | −1.58524 | −0.792619 | − | 0.609718i | \(-0.791283\pi\) | ||||
−0.792619 | + | 0.609718i | \(0.791283\pi\) | |||||||
\(674\) | −8.83282 | −0.340227 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.10333 | −0.234743 | ||||||||
\(677\) | 13.8083 | 0.530696 | 0.265348 | − | 0.964153i | \(-0.414513\pi\) | ||||
0.265348 | + | 0.964153i | \(0.414513\pi\) | |||||||
\(678\) | −3.25969 | −0.125188 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.1246 | −0.886137 | ||||||||
\(682\) | −5.86319 | −0.224513 | ||||||||
\(683\) | 41.0689 | 1.57146 | 0.785729 | − | 0.618571i | \(-0.212288\pi\) | ||||
0.785729 | + | 0.618571i | \(0.212288\pi\) | |||||||
\(684\) | −17.5896 | −0.672553 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.18034 | −0.235795 | ||||||||
\(688\) | 15.7295 | 0.599681 | ||||||||
\(689\) | 39.1853 | 1.49284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79677 | −0.0683524 | −0.0341762 | − | 0.999416i | \(-0.510881\pi\) | ||||
−0.0341762 | + | 0.999416i | \(0.510881\pi\) | |||||||
\(692\) | 7.86629 | 0.299031 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.5623 | 0.400940 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.87714 | 0.109058 | ||||||||
\(697\) | −35.4164 | −1.34149 | ||||||||
\(698\) | 0.382559 | 0.0144801 | ||||||||
\(699\) | −3.95750 | −0.149686 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.4164 | 1.18658 | 0.593291 | − | 0.804988i | \(-0.297828\pi\) | ||||
0.593291 | + | 0.804988i | \(0.297828\pi\) | |||||||
\(702\) | 7.05573 | 0.266301 | ||||||||
\(703\) | −45.4311 | −1.71346 | ||||||||
\(704\) | −10.5279 | −0.396784 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.62520 | 0.174072 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.3738 | 0.803278 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.5279 | 0.394826 | ||||||||
\(712\) | 11.6963 | 0.438336 | ||||||||
\(713\) | −25.8384 | −0.967656 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.87539 | −0.256945 | ||||||||
\(717\) | −25.4558 | −0.950666 | ||||||||
\(718\) | 0.0212862 | 0.000794395 0 | ||||||||
\(719\) | −1.54173 | −0.0574969 | −0.0287485 | − | 0.999587i | \(-0.509152\pi\) | ||||
−0.0287485 | + | 0.999587i | \(0.509152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.381966 | −0.0142153 | ||||||||
\(723\) | −12.8754 | −0.478841 | ||||||||
\(724\) | 20.5942 | 0.765378 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00310 | 0.0743421 | ||||||||
\(727\) | −5.65685 | −0.209801 | −0.104901 | − | 0.994483i | \(-0.533452\pi\) | ||||
−0.104901 | + | 0.994483i | \(0.533452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94427 | 0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.0246 | −1.36940 | ||||||||
\(732\) | 4.91796 | 0.181773 | ||||||||
\(733\) | 6.48218 | 0.239425 | 0.119712 | − | 0.992809i | \(-0.461803\pi\) | ||||
0.119712 | + | 0.992809i | \(0.461803\pi\) | |||||||
\(734\) | 3.31990 | 0.122540 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.6049 | 0.575203 | ||||||||
\(737\) | 19.4721 | 0.717265 | ||||||||
\(738\) | −4.08502 | −0.150372 | ||||||||
\(739\) | −7.29180 | −0.268233 | −0.134117 | − | 0.990966i | \(-0.542820\pi\) | ||||
−0.134117 | + | 0.990966i | \(0.542820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9675 | 0.549843 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.7082 | 1.23663 | 0.618317 | − | 0.785929i | \(-0.287815\pi\) | ||||
0.618317 | + | 0.785929i | \(0.287815\pi\) | |||||||
\(744\) | −8.83282 | −0.323827 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.15905 | −0.225499 | ||||||||
\(747\) | 15.3500 | 0.561628 | ||||||||
\(748\) | 30.7000 | 1.12250 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8328 | 0.979143 | 0.489572 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489572 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(752\) | 29.8446 | 1.08832 | ||||||||
\(753\) | −10.1115 | −0.368482 | ||||||||
\(754\) | 3.44742 | 0.125548 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.4164 | −0.451282 | −0.225641 | − | 0.974211i | \(-0.572448\pi\) | ||||
−0.225641 | + | 0.974211i | \(0.572448\pi\) | |||||||
\(758\) | −7.25735 | −0.263599 | ||||||||
\(759\) | −7.35621 | −0.267014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.9148 | −1.91816 | −0.959080 | − | 0.283136i | \(-0.908625\pi\) | ||||
−0.959080 | + | 0.283136i | \(0.908625\pi\) | |||||||
\(762\) | −2.33695 | −0.0846589 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 42.8754 | 1.55118 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.03786 | 0.182025 | ||||||||
\(767\) | 53.2361 | 1.92224 | ||||||||
\(768\) | −4.86163 | −0.175429 | ||||||||
\(769\) | −8.69161 | −0.313428 | −0.156714 | − | 0.987644i | \(-0.550090\pi\) | ||||
−0.156714 | + | 0.987644i | \(0.550090\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5836 | 0.381159 | ||||||||
\(772\) | 19.8541 | 0.714565 | ||||||||
\(773\) | −15.3500 | −0.552102 | −0.276051 | − | 0.961143i | \(-0.589026\pi\) | ||||
−0.276051 | + | 0.961143i | \(0.589026\pi\) | |||||||
\(774\) | −4.27051 | −0.153500 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.8771 | −0.534059 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6049 | 0.380203 | ||||||||
\(779\) | −20.2918 | −0.727029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.7082 | −0.597867 | ||||||||
\(782\) | −10.6460 | −0.380700 | ||||||||
\(783\) | 10.2333 | 0.365710 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.94427 | −0.176356 | ||||||||
\(787\) | 16.3516 | 0.582871 | 0.291435 | − | 0.956591i | \(-0.405867\pi\) | ||||
0.291435 | + | 0.956591i | \(0.405867\pi\) | |||||||
\(788\) | 11.0213 | 0.392617 | ||||||||
\(789\) | −26.1723 | −0.931757 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.36068 | 0.261550 | ||||||||
\(793\) | 12.2492 | 0.434983 | ||||||||
\(794\) | −3.78127 | −0.134192 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 46.8152 | 1.65932 | ||||||||
\(797\) | 39.0277 | 1.38243 | 0.691216 | − | 0.722648i | \(-0.257075\pi\) | ||||
0.691216 | + | 0.722648i | \(0.257075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −70.2492 | −2.48524 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.7658 | 0.627723 | ||||||||
\(802\) | 8.81153 | 0.311146 | ||||||||
\(803\) | −5.86319 | −0.206907 | ||||||||
\(804\) | 14.1120 | 0.497693 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.5836 | −0.372791 | ||||||||
\(807\) | −13.4164 | −0.472280 | ||||||||
\(808\) | 16.3516 | 0.575246 | ||||||||
\(809\) | 29.0689 | 1.02201 | 0.511004 | − | 0.859578i | \(-0.329274\pi\) | ||||
0.511004 | + | 0.859578i | \(0.329274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.07107 | −0.248299 | −0.124149 | − | 0.992264i | \(-0.539620\pi\) | ||||
−0.124149 | + | 0.992264i | \(0.539620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.88854 | −0.136377 | ||||||||
\(814\) | 9.14590 | 0.320564 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.3607 | 0.712766 | ||||||||
\(817\) | −21.2132 | −0.742156 | ||||||||
\(818\) | 5.62675 | 0.196735 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5836 | 0.369370 | 0.184685 | − | 0.982798i | \(-0.440874\pi\) | ||||
0.184685 | + | 0.982798i | \(0.440874\pi\) | |||||||
\(822\) | 2.00310 | 0.0698662 | ||||||||
\(823\) | −29.5410 | −1.02974 | −0.514868 | − | 0.857270i | \(-0.672159\pi\) | ||||
−0.514868 | + | 0.857270i | \(0.672159\pi\) | |||||||
\(824\) | 13.9659 | 0.486525 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.47214 | −0.0511912 | −0.0255956 | − | 0.999672i | \(-0.508148\pi\) | ||||
−0.0255956 | + | 0.999672i | \(0.508148\pi\) | |||||||
\(828\) | 15.6049 | 0.542307 | ||||||||
\(829\) | −10.0757 | −0.349944 | −0.174972 | − | 0.984573i | \(-0.555984\pi\) | ||||
−0.174972 | + | 0.984573i | \(0.555984\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.9768 | 0.727676 | ||||||||
\(832\) | −19.0038 | −0.658837 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.54102 | −0.226497 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.5896 | 0.608348 | ||||||||
\(837\) | −31.4164 | −1.08591 | ||||||||
\(838\) | −1.85698 | −0.0641483 | ||||||||
\(839\) | 31.3190 | 1.08125 | 0.540626 | − | 0.841263i | \(-0.318187\pi\) | ||||
0.540626 | + | 0.841263i | \(0.318187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0000 | −0.827586 | ||||||||
\(842\) | −3.54915 | −0.122312 | ||||||||
\(843\) | 21.4983 | 0.740442 | ||||||||
\(844\) | −13.7508 | −0.473321 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.10272 | −0.278577 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.5410 | 1.04878 | ||||||||
\(849\) | −18.1803 | −0.623948 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.3050 | 1.38164 | ||||||||
\(852\) | −12.1089 | −0.414845 | ||||||||
\(853\) | 22.2148 | 0.760619 | 0.380309 | − | 0.924859i | \(-0.375818\pi\) | ||||
0.380309 | + | 0.924859i | \(0.375818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.83282 | −0.301899 | ||||||||
\(857\) | −20.6730 | −0.706177 | −0.353088 | − | 0.935590i | \(-0.614869\pi\) | ||||
−0.353088 | + | 0.935590i | \(0.614869\pi\) | |||||||
\(858\) | −3.01316 | −0.102867 | ||||||||
\(859\) | −39.7742 | −1.35708 | −0.678539 | − | 0.734564i | \(-0.737387\pi\) | ||||
−0.678539 | + | 0.734564i | \(0.737387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.58359 | 0.0879975 | ||||||||
\(863\) | −1.36068 | −0.0463181 | −0.0231590 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231590 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(864\) | 18.9737 | 0.645497 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.4915 | 0.424478 | ||||||||
\(867\) | −33.0671 | −1.12302 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5279 | −0.357133 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.1490 | 1.19098 | ||||||||
\(872\) | 1.47214 | 0.0498528 | ||||||||
\(873\) | −22.5973 | −0.764803 | ||||||||
\(874\) | −6.09962 | −0.206323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.24922 | −0.143568 | ||||||||
\(877\) | −38.2918 | −1.29302 | −0.646511 | − | 0.762905i | \(-0.723773\pi\) | ||||
−0.646511 | + | 0.762905i | \(0.723773\pi\) | |||||||
\(878\) | −6.78593 | −0.229014 | ||||||||
\(879\) | 16.1115 | 0.543426 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.62054 | 0.0545975 | 0.0272988 | − | 0.999627i | \(-0.491309\pi\) | ||||
0.0272988 | + | 0.999627i | \(0.491309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7082 | −1.10072 | −0.550359 | − | 0.834928i | \(-0.685509\pi\) | ||||
−0.550359 | + | 0.834928i | \(0.685509\pi\) | |||||||
\(884\) | 55.4164 | 1.86386 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.70820 | 0.258962 | ||||||||
\(887\) | 24.9945 | 0.839232 | 0.419616 | − | 0.907702i | \(-0.362165\pi\) | ||||
0.419616 | + | 0.907702i | \(0.362165\pi\) | |||||||
\(888\) | 13.7782 | 0.462366 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.05573 | 0.202875 | ||||||||
\(892\) | −10.8709 | −0.363986 | ||||||||
\(893\) | −40.2492 | −1.34689 | ||||||||
\(894\) | −3.22248 | −0.107776 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.2786 | −0.443361 | ||||||||
\(898\) | −4.81153 | −0.160563 | ||||||||
\(899\) | −15.3500 | −0.511952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −71.8885 | −2.39495 | ||||||||
\(902\) | 4.08502 | 0.136016 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.3738 | −0.478067 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.80982 | −0.0933501 | ||||||||
\(907\) | −14.8328 | −0.492516 | −0.246258 | − | 0.969204i | \(-0.579201\pi\) | ||||
−0.246258 | + | 0.969204i | \(0.579201\pi\) | |||||||
\(908\) | −49.0547 | −1.62794 | ||||||||
\(909\) | 24.8369 | 0.823786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.7639 | 0.721071 | 0.360536 | − | 0.932745i | \(-0.382594\pi\) | ||||
0.360536 | + | 0.932745i | \(0.382594\pi\) | |||||||
\(912\) | 11.6656 | 0.386288 | ||||||||
\(913\) | −15.3500 | −0.508011 | ||||||||
\(914\) | 2.78522 | 0.0921268 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1105 | −0.433182 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.9443 | −0.427225 | ||||||||
\(919\) | 31.8328 | 1.05007 | 0.525034 | − | 0.851081i | \(-0.324053\pi\) | ||||
0.525034 | + | 0.851081i | \(0.324053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.7214 | 0.419183 | ||||||||
\(922\) | 12.7580 | 0.420163 | ||||||||
\(923\) | −30.1599 | −0.992724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.34752 | −0.175731 | ||||||||
\(927\) | 21.2132 | 0.696733 | ||||||||
\(928\) | 9.27051 | 0.304319 | ||||||||
\(929\) | 47.0516 | 1.54371 | 0.771857 | − | 0.635797i | \(-0.219328\pi\) | ||||
0.771857 | + | 0.635797i | \(0.219328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.39512 | −0.274991 | ||||||||
\(933\) | −8.36068 | −0.273716 | ||||||||
\(934\) | 3.68385 | 0.120539 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.2867 | 0.434290 | ||||||||
\(937\) | 28.4906 | 0.930747 | 0.465374 | − | 0.885114i | \(-0.345920\pi\) | ||||
0.465374 | + | 0.885114i | \(0.345920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.5410 | 0.605063 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.62365 | −0.118128 | −0.0590638 | − | 0.998254i | \(-0.518812\pi\) | ||||
−0.0590638 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(942\) | −1.81966 | −0.0592877 | ||||||||
\(943\) | 18.0022 | 0.586233 | ||||||||
\(944\) | 41.4922 | 1.35046 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.27051 | 0.138846 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −7.62985 | −0.247806 | ||||||||
\(949\) | −10.5836 | −0.343558 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.4397 | 0.338530 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.5967 | −1.18548 | −0.592742 | − | 0.805392i | \(-0.701955\pi\) | ||||
−0.592742 | + | 0.805392i | \(0.701955\pi\) | |||||||
\(954\) | −8.29180 | −0.268457 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −54.0000 | −1.74648 | ||||||||
\(957\) | −4.37016 | −0.141267 | ||||||||
\(958\) | 3.44742 | 0.111381 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1246 | 0.520149 | ||||||||
\(962\) | 16.5092 | 0.532278 | ||||||||
\(963\) | −13.4164 | −0.432338 | ||||||||
\(964\) | −27.3128 | −0.879687 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.2492 | −1.48727 | −0.743637 | − | 0.668583i | \(-0.766901\pi\) | ||||
−0.743637 | + | 0.668583i | \(0.766901\pi\) | |||||||
\(968\) | 8.83282 | 0.283897 | ||||||||
\(969\) | −27.4589 | −0.882108 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7279 | 0.408458 | 0.204229 | − | 0.978923i | \(-0.434531\pi\) | ||||
0.204229 | + | 0.978923i | \(0.434531\pi\) | |||||||
\(972\) | 29.8446 | 0.957266 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.9656 | 0.351359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.54704 | 0.305593 | ||||||||
\(977\) | −27.7639 | −0.888247 | −0.444123 | − | 0.895966i | \(-0.646485\pi\) | ||||
−0.444123 | + | 0.895966i | \(0.646485\pi\) | |||||||
\(978\) | 0.765117 | 0.0244658 | ||||||||
\(979\) | −17.7658 | −0.567797 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.23607 | 0.0713922 | ||||||||
\(982\) | 2.85410 | 0.0910781 | ||||||||
\(983\) | −8.10272 | −0.258437 | −0.129218 | − | 0.991616i | \(-0.541247\pi\) | ||||
−0.129218 | + | 0.991616i | \(0.541247\pi\) | |||||||
\(984\) | 6.15403 | 0.196183 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.32456 | −0.201415 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.7508 | 1.01013 | ||||||||
\(989\) | 18.8197 | 0.598430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00000 | −0.158830 | −0.0794151 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794151 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(992\) | −28.4605 | −0.903622 | ||||||||
\(993\) | 1.12907 | 0.0358300 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.1246 | −0.352497 | ||||||||
\(997\) | 48.6722 | 1.54146 | 0.770731 | − | 0.637160i | \(-0.219891\pi\) | ||||
0.770731 | + | 0.637160i | \(0.219891\pi\) | |||||||
\(998\) | −9.70820 | −0.307308 | ||||||||
\(999\) | 49.0060 | 1.55048 |
(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 | 1225.2.a.bc.1.1 | yes | 4 | |
5.2 | odd | 4 | 1225.2.b.n.99.6 | 8 | |||
5.3 | odd | 4 | 1225.2.b.n.99.3 | 8 | |||
5.4 | even | 2 | 1225.2.a.ba.1.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 1225.2.a.bc.1.2 | yes | 4 | |
35.13 | even | 4 | 1225.2.b.n.99.4 | 8 | |||
35.27 | even | 4 | 1225.2.b.n.99.5 | 8 | |||
35.34 | odd | 2 | 1225.2.a.ba.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1225.2.a.ba.1.3 | ✓ | 4 | 35.34 | odd | 2 | ||
1225.2.a.ba.1.4 | yes | 4 | 5.4 | even | 2 | ||
1225.2.a.bc.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1225.2.a.bc.1.2 | yes | 4 | 7.6 | odd | 2 | inner | |
1225.2.b.n.99.3 | 8 | 5.3 | odd | 4 | |||
1225.2.b.n.99.4 | 8 | 35.13 | even | 4 | |||
1225.2.b.n.99.5 | 8 | 35.27 | even | 4 | |||
1225.2.b.n.99.6 | 8 | 5.2 | odd | 4 |