Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.95835 | −1.13065 | −0.565326 | − | 0.824867i | \(-0.691250\pi\) | ||||
−0.565326 | + | 0.824867i | \(0.691250\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.337153 | 0.150780 | 0.0753898 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753898 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.830729 | −0.313986 | −0.156993 | − | 0.987600i | \(-0.550180\pi\) | ||||
−0.156993 | + | 0.987600i | \(0.550180\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.835124 | 0.278375 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.82988 | 1.75777 | 0.878887 | − | 0.477029i | \(-0.158286\pi\) | ||||
0.878887 | + | 0.477029i | \(0.158286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14912 | 1.15076 | 0.575379 | − | 0.817887i | \(-0.304855\pi\) | ||||
0.575379 | + | 0.817887i | \(0.304855\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.660263 | −0.170479 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.44743 | −1.07866 | −0.539330 | − | 0.842095i | \(-0.681322\pi\) | ||||
−0.539330 | + | 0.842095i | \(0.681322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.68929 | −0.387550 | −0.193775 | − | 0.981046i | \(-0.562073\pi\) | ||||
−0.193775 | + | 0.981046i | \(0.562073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.62686 | 0.355009 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.61850 | 1.38005 | 0.690026 | − | 0.723784i | \(-0.257599\pi\) | ||||
0.690026 | + | 0.723784i | \(0.257599\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88633 | −0.977266 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.23958 | 0.815907 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.73612 | −1.25087 | −0.625433 | − | 0.780278i | \(-0.715078\pi\) | ||||
−0.625433 | + | 0.780278i | \(0.715078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.271306 | −0.0487279 | −0.0243640 | − | 0.999703i | \(-0.507756\pi\) | ||||
−0.0243640 | + | 0.999703i | \(0.507756\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.4169 | −1.98743 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.280083 | −0.0473427 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.23650 | −0.696476 | −0.348238 | − | 0.937406i | \(-0.613220\pi\) | ||||
−0.348238 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.12541 | −1.30111 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.53349 | −1.33271 | −0.666354 | − | 0.745636i | \(-0.732146\pi\) | ||||
−0.666354 | + | 0.745636i | \(0.732146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.824655 | 0.125759 | 0.0628794 | − | 0.998021i | \(-0.479972\pi\) | ||||
0.0628794 | + | 0.998021i | \(0.479972\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.281565 | 0.0419732 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.45594 | −1.23343 | −0.616713 | − | 0.787188i | \(-0.711536\pi\) | ||||
−0.616713 | + | 0.787188i | \(0.711536\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.30989 | −0.901413 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.70961 | 1.21959 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.66412 | −0.365945 | −0.182973 | − | 0.983118i | \(-0.558572\pi\) | ||||
−0.182973 | + | 0.983118i | \(0.558572\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.96556 | 0.265037 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.30822 | 0.438184 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.99137 | 0.780010 | 0.390005 | − | 0.920813i | \(-0.372473\pi\) | ||||
0.390005 | + | 0.920813i | \(0.372473\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.2825 | 1.95672 | 0.978359 | − | 0.206914i | \(-0.0663421\pi\) | ||||
0.978359 | + | 0.206914i | \(0.0663421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.693761 | −0.0874057 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.39889 | 0.173511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.68864 | −1.06149 | −0.530743 | − | 0.847533i | \(-0.678087\pi\) | ||||
−0.530743 | + | 0.847533i | \(0.678087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9613 | −1.56036 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4284 | 1.35630 | 0.678150 | − | 0.734924i | \(-0.262782\pi\) | ||||
0.678150 | + | 0.734924i | \(0.262782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3274 | 1.55986 | 0.779930 | − | 0.625867i | \(-0.215255\pi\) | ||||
0.779930 | + | 0.625867i | \(0.215255\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.56913 | 1.10495 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.84305 | −0.551916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2656 | −1.15497 | −0.577487 | − | 0.816400i | \(-0.695966\pi\) | ||||
−0.577487 | + | 0.816400i | \(0.695966\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8079 | −1.20088 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.4136 | −1.69186 | −0.845931 | − | 0.533293i | \(-0.820954\pi\) | ||||
−0.845931 | + | 0.533293i | \(0.820954\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.49947 | −0.162640 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.1917 | 1.41430 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.23120 | −0.448506 | −0.224253 | − | 0.974531i | \(-0.571994\pi\) | ||||
−0.224253 | + | 0.974531i | \(0.571994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.44679 | −0.361322 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.531311 | 0.0550944 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.569550 | −0.0584346 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3532 | −1.15274 | −0.576371 | − | 0.817188i | \(-0.695532\pi\) | ||||
−0.576371 | + | 0.817188i | \(0.695532\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.86867 | 0.489320 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2476 | 1.71620 | 0.858099 | − | 0.513484i | \(-0.171645\pi\) | ||||
0.858099 | + | 0.513484i | \(0.171645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.88423 | 0.875389 | 0.437695 | − | 0.899124i | \(-0.355795\pi\) | ||||
0.437695 | + | 0.899124i | \(0.355795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.548500 | 0.0535281 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9665 | 1.35019 | 0.675096 | − | 0.737730i | \(-0.264102\pi\) | ||||
0.675096 | + | 0.737730i | \(0.264102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.83880 | −0.367691 | −0.183845 | − | 0.982955i | \(-0.558855\pi\) | ||||
−0.183845 | + | 0.982955i | \(0.558855\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.29653 | 0.787472 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.39443 | −0.883754 | −0.441877 | − | 0.897076i | \(-0.645687\pi\) | ||||
−0.441877 | + | 0.897076i | \(0.645687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.23145 | 0.208084 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.46503 | 0.320342 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.69461 | 0.338684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.9875 | 2.08977 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.7115 | 1.50683 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.33321 | −0.298131 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.13992 | −0.189887 | −0.0949436 | − | 0.995483i | \(-0.530267\pi\) | ||||
−0.0949436 | + | 0.995483i | \(0.530267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.61496 | −0.142189 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.91725 | 0.779104 | 0.389552 | − | 0.921005i | \(-0.372630\pi\) | ||||
0.389552 | + | 0.921005i | \(0.372630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.40334 | 0.121685 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.42939 | 0.123022 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0499 | 1.02949 | 0.514746 | − | 0.857343i | \(-0.327886\pi\) | ||||
0.514746 | + | 0.857343i | \(0.327886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.30684 | −0.619758 | −0.309879 | − | 0.950776i | \(-0.600289\pi\) | ||||
−0.309879 | + | 0.950776i | \(0.600289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5597 | 1.39458 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.1888 | 2.02277 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.27111 | −0.188605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.3570 | 1.01918 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.54557 | −0.208542 | −0.104271 | − | 0.994549i | \(-0.533251\pi\) | ||||
−0.104271 | + | 0.994549i | \(0.533251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.49133 | −0.121363 | −0.0606815 | − | 0.998157i | \(-0.519327\pi\) | ||||
−0.0606815 | + | 0.998157i | \(0.519327\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.71415 | −0.300272 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0914716 | −0.00734718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.7688 | −1.57772 | −0.788862 | − | 0.614571i | \(-0.789329\pi\) | ||||
−0.788862 | + | 0.614571i | \(0.789329\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.21727 | 0.413757 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.49818 | −0.433317 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.08030 | 0.397920 | 0.198960 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198960 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.84926 | −0.299664 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.2333 | −1.33355 | −0.666775 | − | 0.745259i | \(-0.732326\pi\) | ||||
−0.666775 | + | 0.745259i | \(0.732326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.21516 | 0.324243 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.41077 | −0.107884 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6750 | −0.887630 | −0.443815 | − | 0.896118i | \(-0.646375\pi\) | ||||
−0.443815 | + | 0.896118i | \(0.646375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.05921 | 0.306848 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7332 | −0.881920 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.74740 | −0.504324 | −0.252162 | − | 0.967685i | \(-0.581142\pi\) | ||||
−0.252162 | + | 0.967685i | \(0.581142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.68546 | 0.571256 | 0.285628 | − | 0.958341i | \(-0.407798\pi\) | ||||
0.285628 | + | 0.958341i | \(0.407798\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.9284 | −2.21237 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.42835 | −0.105014 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.9280 | −1.89604 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.52194 | −0.256183 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.61634 | 0.623456 | 0.311728 | − | 0.950171i | \(-0.399092\pi\) | ||||
0.311728 | + | 0.950171i | \(0.399092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.20122 | 0.590337 | 0.295168 | − | 0.955445i | \(-0.404624\pi\) | ||||
0.295168 | + | 0.955445i | \(0.404624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.73951 | −0.196180 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.7837 | 0.839557 | 0.419778 | − | 0.907627i | \(-0.362108\pi\) | ||||
0.419778 | + | 0.907627i | \(0.362108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.19649 | 0.297481 | 0.148741 | − | 0.988876i | \(-0.452478\pi\) | ||||
0.148741 | + | 0.988876i | \(0.452478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.0154 | 1.20017 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.59589 | 0.392755 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.87710 | −0.200945 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.52727 | 0.384172 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.84836 | −0.681225 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0815 | −1.31362 | −0.656811 | − | 0.754055i | \(-0.728095\pi\) | ||||
−0.656811 | + | 0.754055i | \(0.728095\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.3808 | −1.53350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.278035 | 0.0189619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.225381 | 0.0152999 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.0998 | −1.76366 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4529 | −1.24128 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5825 | 0.775621 | 0.387810 | − | 0.921739i | \(-0.373231\pi\) | ||||
0.387810 | + | 0.921739i | \(0.373231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.08069 | −0.272046 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.0726 | −1.92962 | −0.964808 | − | 0.262955i | \(-0.915303\pi\) | ||||
−0.964808 | + | 0.262955i | \(0.915303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1259 | −1.26387 | −0.631937 | − | 0.775020i | \(-0.717740\pi\) | ||||
−0.631937 | + | 0.775020i | \(0.717740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.48437 | 0.624026 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.6549 | −1.68071 | −0.840353 | − | 0.542040i | \(-0.817652\pi\) | ||||
−0.840353 | + | 0.542040i | \(0.817652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.85095 | −0.185975 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.1037 | 1.30587 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.56292 | 0.165781 | 0.0828906 | − | 0.996559i | \(-0.473585\pi\) | ||||
0.0828906 | + | 0.996559i | \(0.473585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.98525 | 0.449959 | 0.224980 | − | 0.974363i | \(-0.427768\pi\) | ||||
0.224980 | + | 0.974363i | \(0.427768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.44696 | 0.541873 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.12740 | −0.135915 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.00906 | −0.445976 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.1852 | 1.91291 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.29264 | 0.207829 | 0.103915 | − | 0.994586i | \(-0.466863\pi\) | ||||
0.103915 | + | 0.994586i | \(0.466863\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.5850 | 2.42582 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.93647 | 0.183889 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.8611 | 0.927013 | 0.463506 | − | 0.886094i | \(-0.346591\pi\) | ||||
0.463506 | + | 0.886094i | \(0.346591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.51938 | 0.218684 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.62550 | −0.348210 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.92149 | −0.550122 | −0.275061 | − | 0.961427i | \(-0.588698\pi\) | ||||
−0.275061 | + | 0.961427i | \(0.588698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.898217 | −0.0551770 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.28615 | 0.507104 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3663 | −0.753984 | −0.376992 | − | 0.926217i | \(-0.623042\pi\) | ||||
−0.376992 | + | 0.926217i | \(0.623042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.33563 | 0.202625 | 0.101313 | − | 0.994855i | \(-0.467696\pi\) | ||||
0.101313 | + | 0.994855i | \(0.467696\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.75001 | 0.408529 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.4867 | −1.71781 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8733 | −0.653312 | −0.326656 | − | 0.945143i | \(-0.605922\pi\) | ||||
−0.326656 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.226574 | −0.0135646 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7151 | −0.758517 | −0.379258 | − | 0.925291i | \(-0.623821\pi\) | ||||
−0.379258 | + | 0.925291i | \(0.623821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.8004 | 1.71201 | 0.856003 | − | 0.516970i | \(-0.172940\pi\) | ||||
0.856003 | + | 0.516970i | \(0.172940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.11538 | 0.0660692 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.08902 | 0.418451 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.77961 | 0.163507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.2335 | 1.30335 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.2273 | −1.53221 | −0.766107 | − | 0.642713i | \(-0.777809\pi\) | ||||
−0.766107 | + | 0.642713i | \(0.777809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.02001 | 0.117610 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.7162 | 1.43418 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.4609 | 1.58811 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.685065 | −0.0394865 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.7767 | −1.94042 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.15253 | 0.295033 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5057 | 1.05618 | 0.528089 | − | 0.849189i | \(-0.322909\pi\) | ||||
0.528089 | + | 0.849189i | \(0.322909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.3984 | −0.989761 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.98655 | −0.509581 | −0.254790 | − | 0.966996i | \(-0.582006\pi\) | ||||
−0.254790 | + | 0.966996i | \(0.582006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.26787 | −0.0716641 | −0.0358320 | − | 0.999358i | \(-0.511408\pi\) | ||||
−0.0358320 | + | 0.999358i | \(0.511408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.233904 | −0.0131790 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.1367 | −1.01866 | −0.509330 | − | 0.860572i | \(-0.670107\pi\) | ||||
−0.509330 | + | 0.860572i | \(0.670107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.2708 | −2.19874 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.3513 | −1.52660 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.51299 | 0.418034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.2739 | −1.12460 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.51771 | 0.415730 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.02459 | 0.387278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8368 | −1.09033 | −0.545166 | − | 0.838328i | \(-0.683533\pi\) | ||||
−0.545166 | + | 0.838328i | \(0.683533\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.53800 | −0.193881 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.92940 | −0.160050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.953395 | −0.0519347 | −0.0259674 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259674 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.3976 | 0.999218 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.58168 | −0.0856527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0569 | 0.597017 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.36995 | −0.235270 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.867113 | −0.0465491 | −0.0232745 | − | 0.999729i | \(-0.507409\pi\) | ||||
−0.0232745 | + | 0.999729i | \(0.507409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.67195 | 0.464199 | 0.232100 | − | 0.972692i | \(-0.425440\pi\) | ||||
0.232100 | + | 0.972692i | \(0.425440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.5905 | 0.938912 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.8386 | 1.85427 | 0.927136 | − | 0.374725i | \(-0.122263\pi\) | ||||
0.927136 | + | 0.374725i | \(0.122263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.85312 | 0.204502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.23532 | −0.382934 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.92500 | −0.259931 | −0.129966 | − | 0.991518i | \(-0.541487\pi\) | ||||
−0.129966 | + | 0.991518i | \(0.541487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1463 | −0.849805 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −45.0175 | −2.36281 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.49339 | 0.235195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.8092 | 0.616435 | 0.308218 | − | 0.951316i | \(-0.400267\pi\) | ||||
0.308218 | + | 0.951316i | \(0.400267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.12652 | −0.370992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.21316 | 0.114902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6256 | 0.964399 | 0.482199 | − | 0.876062i | \(-0.339838\pi\) | ||||
0.482199 | + | 0.876062i | \(0.339838\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.52758 | 0.337083 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.9490 | −1.43944 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00820 | −0.411354 | −0.205677 | − | 0.978620i | \(-0.565940\pi\) | ||||
−0.205677 | + | 0.978620i | \(0.565940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.19071 | 0.214696 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.3412 | −1.75476 | −0.877378 | − | 0.479800i | \(-0.840709\pi\) | ||||
−0.877378 | + | 0.479800i | \(0.840709\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.63285 | −0.0832177 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.688689 | 0.0350081 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.0751 | −1.77838 | −0.889190 | − | 0.457539i | \(-0.848731\pi\) | ||||
−0.889190 | + | 0.457539i | \(0.848731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.4353 | −1.48861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.4631 | −0.880896 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.46109 | −0.174146 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9832 | 0.651608 | 0.325804 | − | 0.945437i | \(-0.394365\pi\) | ||||
0.325804 | + | 0.945437i | \(0.394365\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.74823 | −0.137584 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6205 | 0.929862 | 0.464931 | − | 0.885347i | \(-0.346079\pi\) | ||||
0.464931 | + | 0.885347i | \(0.346079\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12568 | −0.0560741 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.64393 | −0.181069 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.6983 | −1.22425 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.0572 | −1.33789 | −0.668946 | − | 0.743311i | \(-0.733254\pi\) | ||||
−0.668946 | + | 0.743311i | \(0.733254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.5979 | −1.16400 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.97720 | −0.244912 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.19675 | −0.255098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3093 | 0.700731 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.16488 | −0.350027 | −0.175014 | − | 0.984566i | \(-0.555997\pi\) | ||||
−0.175014 | + | 0.984566i | \(0.555997\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5823 | −0.954381 | −0.477190 | − | 0.878800i | \(-0.658345\pi\) | ||||
−0.477190 | + | 0.878800i | \(0.658345\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.06176 | −0.343354 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.7316 | 1.05414 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.6956 | −0.614382 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −47.3702 | −2.28705 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.1575 | −0.922785 | −0.461392 | − | 0.887196i | \(-0.652650\pi\) | ||||
−0.461392 | + | 0.887196i | \(0.652650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6346 | −1.42415 | −0.712074 | − | 0.702104i | \(-0.752244\pi\) | ||||
−0.712074 | + | 0.702104i | \(0.752244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.44762 | 0.213247 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.1806 | −0.534839 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.4331 | 1.69113 | 0.845564 | − | 0.533874i | \(-0.179264\pi\) | ||||
0.845564 | + | 0.533874i | \(0.179264\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.26954 | −0.250931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.25789 | 0.154787 | 0.0773936 | − | 0.997001i | \(-0.475340\pi\) | ||||
0.0773936 | + | 0.997001i | \(0.475340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.42656 | −0.0676255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.98512 | 0.235788 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6219 | 0.501280 | 0.250640 | − | 0.968080i | \(-0.419359\pi\) | ||||
0.250640 | + | 0.968080i | \(0.419359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −49.7492 | −2.34260 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.92055 | 0.137219 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.16210 | −0.0544799 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1742 | −1.31794 | −0.658968 | − | 0.752171i | \(-0.729007\pi\) | ||||
−0.658968 | + | 0.752171i | \(0.729007\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.8552 | −0.880086 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.6957 | 1.42964 | 0.714820 | − | 0.699308i | \(-0.246508\pi\) | ||||
0.714820 | + | 0.699308i | \(0.246508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.89086 | 0.180824 | 0.0904118 | − | 0.995904i | \(-0.471182\pi\) | ||||
0.0904118 | + | 0.995904i | \(0.471182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.179133 | 0.00830710 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.3849 | −1.49859 | −0.749297 | − | 0.662234i | \(-0.769608\pi\) | ||||
−0.749297 | + | 0.662234i | \(0.769608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.21790 | 0.333292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.7142 | 1.78386 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.80764 | 0.221056 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.25442 | 0.378739 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.22487 | −0.101870 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8962 | 0.772008 | 0.386004 | − | 0.922497i | \(-0.373855\pi\) | ||||
0.386004 | + | 0.922497i | \(0.373855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5777 | −0.801475 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7673 | 0.489931 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.82777 | −0.173810 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4159 | −1.01576 | −0.507880 | − | 0.861428i | \(-0.669571\pi\) | ||||
−0.507880 | + | 0.861428i | \(0.669571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.94899 | −0.449909 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.05607 | 0.137919 | 0.0689593 | − | 0.997619i | \(-0.478032\pi\) | ||||
0.0689593 | + | 0.997619i | \(0.478032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.9584 | 1.34926 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.64149 | 0.0737795 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.49389 | −0.425859 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0137 | 1.47790 | 0.738948 | − | 0.673763i | \(-0.235323\pi\) | ||||
0.738948 | + | 0.673763i | \(0.235323\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.7487 | 1.50778 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.81508 | 0.258768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.25475 | −0.366606 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.8182 | −1.05572 | −0.527862 | − | 0.849330i | \(-0.677006\pi\) | ||||
−0.527862 | + | 0.849330i | \(0.677006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0715 | −0.489774 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.16188 | −0.316205 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.99535 | 0.131991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.2971 | −2.16808 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.8636 | 1.00360 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.5560 | 1.77679 | 0.888396 | − | 0.459077i | \(-0.151820\pi\) | ||||
0.888396 | + | 0.459077i | \(0.151820\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2705 | −1.01755 | −0.508774 | − | 0.860900i | \(-0.669901\pi\) | ||||
−0.508774 | + | 0.860900i | \(0.669901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.94935 | −0.346938 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.20661 | 0.0525609 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8045 | 0.904545 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.00354 | 0.217135 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −35.4064 | −1.53362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.70885 | 0.203581 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.2138 | 0.570216 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.7859 | −1.58448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.2040 | −1.04061 | −0.520305 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520305 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0508 | −0.645891 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.29427 | −0.0554402 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.59891 | 0.111121 | 0.0555607 | − | 0.998455i | \(-0.482305\pi\) | ||||
0.0555607 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7627 | 0.544701 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3793 | 0.484773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.52795 | 0.362645 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.79720 | 0.118735 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.0709 | 1.23178 | 0.615888 | − | 0.787834i | \(-0.288798\pi\) | ||||
0.615888 | + | 0.787834i | \(0.288798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.42159 | 0.144718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 50.7760 | 2.14376 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.1925 | −1.31461 | −0.657304 | − | 0.753625i | \(-0.728303\pi\) | ||||
−0.657304 | + | 0.753625i | \(0.728303\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.16736 | −0.133252 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.97846 | 0.377060 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.64159 | −0.278430 | −0.139215 | − | 0.990262i | \(-0.544458\pi\) | ||||
−0.139215 | + | 0.990262i | \(0.544458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7632 | −0.659670 | −0.329835 | − | 0.944039i | \(-0.606993\pi\) | ||||
−0.329835 | + | 0.944039i | \(0.606993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.8738 | −0.704912 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.3402 | −1.34868 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.3843 | −1.47307 | −0.736534 | − | 0.676400i | \(-0.763539\pi\) | ||||
−0.736534 | + | 0.676400i | \(0.763539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0608 | −0.667466 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8045 | 0.531221 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.5315 | −0.643249 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.16825 | 0.0483010 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.3362 | 0.880640 | 0.440320 | − | 0.897841i | \(-0.354865\pi\) | ||||
0.440320 | + | 0.897841i | \(0.354865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.458314 | 0.0188845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.0767 | −0.949247 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.1255 | −1.81202 | −0.906009 | − | 0.423258i | \(-0.860887\pi\) | ||||
−0.906009 | + | 0.423258i | \(0.860887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.24565 | 0.0510666 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.21819 | −0.336348 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.83858 | −0.197699 | −0.0988495 | − | 0.995102i | \(-0.531516\pi\) | ||||
−0.0988495 | + | 0.995102i | \(0.531516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.72151 | −0.396549 | −0.198274 | − | 0.980147i | \(-0.563534\pi\) | ||||
−0.198274 | + | 0.980147i | \(0.563534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.25609 | −0.295491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.75031 | 0.315095 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.5935 | 1.72882 | 0.864408 | − | 0.502791i | \(-0.167693\pi\) | ||||
0.864408 | + | 0.502791i | \(0.167693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.9587 | −0.444069 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.0847 | −1.41937 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5162 | −0.465134 | −0.232567 | − | 0.972580i | \(-0.574712\pi\) | ||||
−0.232567 | + | 0.972580i | \(0.574712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.63435 | 0.227199 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.1232 | 1.37375 | 0.686875 | − | 0.726776i | \(-0.258982\pi\) | ||||
0.686875 | + | 0.726776i | \(0.258982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.13729 | −0.367259 | −0.183629 | − | 0.982996i | \(-0.558785\pi\) | ||||
−0.183629 | + | 0.982996i | \(0.558785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.0596 | 1.12599 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.51498 | 0.140825 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3078 | 0.932313 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.2865 | 0.770229 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.8415 | 0.751260 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3463 | 0.690543 | 0.345272 | − | 0.938503i | \(-0.387787\pi\) | ||||
0.345272 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.3682 | 1.48525 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.721481 | −0.0286311 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.1805 | −1.03731 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.54412 | 0.377560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.45039 | 0.175780 | 0.0878899 | − | 0.996130i | \(-0.471988\pi\) | ||||
0.0878899 | + | 0.996130i | \(0.471988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.21021 | 0.323779 | 0.161889 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161889 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.544490 | −0.0214393 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1289 | 0.909292 | 0.454646 | − | 0.890672i | \(-0.349766\pi\) | ||||
0.454646 | + | 0.890672i | \(0.349766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.9290 | 1.37108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.441375 | −0.0172989 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.34044 | 0.208988 | 0.104494 | − | 0.994526i | \(-0.466678\pi\) | ||||
0.104494 | + | 0.994526i | \(0.466678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00648 | 0.117473 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1301 | 0.434225 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.7109 | −1.00156 | −0.500778 | − | 0.865576i | \(-0.666953\pi\) | ||||
−0.500778 | + | 0.865576i | \(0.666953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.28360 | −0.283299 | −0.141650 | − | 0.989917i | \(-0.545241\pi\) | ||||
−0.141650 | + | 0.989917i | \(0.545241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.1372 | 1.40345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.473141 | 0.0183476 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.5830 | −1.72626 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.6825 | −0.876958 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 89.0949 | 3.43947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.3831 | −1.40247 | −0.701233 | − | 0.712932i | \(-0.747367\pi\) | ||||
−0.701233 | + | 0.712932i | \(0.747367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.7160 | −0.797358 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.9056 | −1.14937 | −0.574684 | − | 0.818376i | \(-0.694875\pi\) | ||||
−0.574684 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.43142 | 0.361945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 56.9342 | 2.18172 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.12594 | −0.196139 | −0.0980694 | − | 0.995180i | \(-0.531267\pi\) | ||||
−0.0980694 | + | 0.995180i | \(0.531267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.06266 | 0.155226 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.4551 | 1.42900 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0537 | −0.421114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5616 | −1.08653 | −0.543267 | − | 0.839560i | \(-0.682813\pi\) | ||||
−0.543267 | + | 0.839560i | \(0.682813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.04455 | −0.153640 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.46353 | −0.0934469 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.9521 | 1.43754 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 50.2411 | 1.90029 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.07775 | 0.342862 | 0.171431 | − | 0.985196i | \(-0.445161\pi\) | ||||
0.171431 | + | 0.985196i | \(0.445161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.15667 | 0.269919 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.58315 | 0.210274 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.3281 | −0.538862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.17002 | 0.0814968 | 0.0407484 | − | 0.999169i | \(-0.487026\pi\) | ||||
0.0407484 | + | 0.999169i | \(0.487026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.57307 | −0.321515 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.79564 | −0.0672471 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.15535 | 0.304993 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.01908 | −0.187441 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.4247 | −0.426069 | −0.213034 | − | 0.977045i | \(-0.568335\pi\) | ||||
−0.213034 | + | 0.977045i | \(0.568335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.38039 | −0.274860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.6795 | −0.508748 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.9149 | 1.22243 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.4513 | 1.38899 | 0.694496 | − | 0.719497i | \(-0.255628\pi\) | ||||
0.694496 | + | 0.719497i | \(0.255628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.8817 | 0.588212 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.66759 | −0.135651 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3356 | −1.23128 | −0.615639 | − | 0.788028i | \(-0.711102\pi\) | ||||
−0.615639 | + | 0.788028i | \(0.711102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.16619 | 0.153672 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.6537 | −1.86585 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.1025 | −1.07055 | −0.535277 | − | 0.844677i | \(-0.679793\pi\) | ||||
−0.535277 | + | 0.844677i | \(0.679793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7262 | 0.504244 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.7059 | 0.759627 | 0.379814 | − | 0.925063i | \(-0.375988\pi\) | ||||
0.379814 | + | 0.925063i | \(0.375988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.858249 | −0.0314438 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.8723 | −0.470971 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6024 | −0.423941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8005 | −0.941472 | −0.470736 | − | 0.882274i | \(-0.656012\pi\) | ||||
−0.470736 | + | 0.882274i | \(0.656012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.44813 | −0.234983 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.502808 | −0.0182991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.7420 | −1.66252 | −0.831261 | − | 0.555882i | \(-0.812381\pi\) | ||||
−0.831261 | + | 0.555882i | \(0.812381\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −75.5629 | −2.74276 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2372 | −0.552348 | −0.276174 | − | 0.961108i | \(-0.589067\pi\) | ||||
−0.276174 | + | 0.961108i | \(0.589067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.18900 | 0.115450 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.25224 | −0.0452748 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.8589 | 0.897603 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.5754 | 1.53531 | 0.767654 | − | 0.640865i | \(-0.221424\pi\) | ||||
0.767654 | + | 0.640865i | \(0.221424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.1033 | −1.04813 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.1472 | −1.40803 | −0.704013 | − | 0.710187i | \(-0.748610\pi\) | ||||
−0.704013 | + | 0.710187i | \(0.748610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.32569 | 0.0476201 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.89216 | −0.247255 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.4155 | 0.516490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.6261 | 2.38407 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.5583 | −1.02059 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.66512 | −0.237888 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.22182 | −0.114845 | −0.0574227 | − | 0.998350i | \(-0.518288\pi\) | ||||
−0.0574227 | + | 0.998350i | \(0.518288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.4714 | 0.621997 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.80422 | 0.277486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.4087 | 2.25171 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.75902 | 0.0623860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.1582 | 1.52874 | 0.764371 | − | 0.644777i | \(-0.223050\pi\) | ||||
0.764371 | + | 0.644777i | \(0.223050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.6072 | 1.33045 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.53357 | −0.124853 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77.6974 | 2.74188 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.85373 | −0.0653354 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.2174 | 0.852494 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.5555 | 1.39070 | 0.695348 | − | 0.718673i | \(-0.255250\pi\) | ||||
0.695348 | + | 0.718673i | \(0.255250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7483 | −0.693455 | −0.346728 | − | 0.937966i | \(-0.612707\pi\) | ||||
−0.346728 | + | 0.937966i | \(0.612707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.53232 | −0.229099 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.71284 | 0.0599982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.39308 | −0.0487378 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.87850 | −0.100583 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9925 | −0.942046 | −0.471023 | − | 0.882121i | \(-0.656115\pi\) | ||||
−0.471023 | + | 0.882121i | \(0.656115\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.4789 | −1.65501 | −0.827505 | − | 0.561458i | \(-0.810241\pi\) | ||||
−0.827505 | + | 0.561458i | \(0.810241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 55.7868 | 1.94225 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.5127 | 1.75650 | 0.878249 | − | 0.478204i | \(-0.158712\pi\) | ||||
0.878249 | + | 0.478204i | \(0.158712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.6321 | −1.13336 | −0.566679 | − | 0.823939i | \(-0.691772\pi\) | ||||
−0.566679 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.2937 | 0.738669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.0628 | 0.972318 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.81025 | −0.201072 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.15022 | −0.0397575 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.2513 | 0.630103 | 0.315052 | − | 0.949075i | \(-0.397978\pi\) | ||||
0.315052 | + | 0.949075i | \(0.397978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3754 | 0.564668 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.9005 | 0.857619 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.42116 | 0.0488893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0964 | −0.656159 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −56.4012 | −1.93568 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.0392 | −0.961173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.54962 | −0.292734 | −0.146367 | − | 0.989230i | \(-0.546758\pi\) | ||||
−0.146367 | + | 0.989230i | \(0.546758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.475645 | −0.0162667 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.2767 | −1.64910 | −0.824551 | − | 0.565788i | \(-0.808572\pi\) | ||||
−0.824551 | + | 0.565788i | \(0.808572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.1046 | −1.77779 | −0.888893 | − | 0.458114i | \(-0.848525\pi\) | ||||
−0.888893 | + | 0.458114i | \(0.848525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8828 | −0.473123 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.5867 | −1.07522 | −0.537612 | − | 0.843192i | \(-0.680673\pi\) | ||||
−0.537612 | + | 0.843192i | \(0.680673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.93625 | −0.133837 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.44344 | −0.184869 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.8474 | −2.03018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0502 | −1.22151 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.48132 | −0.320894 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.76899 | 0.0936090 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.58569 | 0.0873126 | 0.0436563 | − | 0.999047i | \(-0.486099\pi\) | ||||
0.0436563 | + | 0.999047i | \(0.486099\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.3621 | 1.73240 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.1813 | 1.42113 | 0.710563 | − | 0.703634i | \(-0.248441\pi\) | ||||
0.710563 | + | 0.703634i | \(0.248441\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0086 | 1.04352 | 0.521761 | − | 0.853091i | \(-0.325275\pi\) | ||||
0.521761 | + | 0.853091i | \(0.325275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.95588 | −0.132976 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.8971 | −1.84326 | −0.921631 | − | 0.388067i | \(-0.873143\pi\) | ||||
−0.921631 | + | 0.388067i | \(0.873143\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.77769 | 0.0596219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −63.0090 | −2.11088 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.2845 | 0.478014 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.27491 | −0.0760418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53.7780 | −1.79560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.82755 | 0.0609522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8485 | 0.394730 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.34159 | 0.0446455 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.59118 | 0.0861337 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0123 | 0.465272 | 0.232636 | − | 0.972564i | \(-0.425265\pi\) | ||||
0.232636 | + | 0.972564i | \(0.425265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4039 | 0.477746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.9212 | 0.925070 | 0.462535 | − | 0.886601i | \(-0.346940\pi\) | ||||
0.462535 | + | 0.886601i | \(0.346940\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −89.8594 | −2.97391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.0904 | −0.333580 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.40782 | −0.244628 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4349 | 0.575126 | 0.287563 | − | 0.957762i | \(-0.407155\pi\) | ||||
0.287563 | + | 0.957762i | \(0.407155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.2407 | −1.19417 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.4177 | 1.56077 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.7009 | 0.680642 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.41944 | 0.243686 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.571374 | −0.0187462 | −0.00937309 | − | 0.999956i | \(-0.502984\pi\) | ||||
−0.00937309 | + | 0.999956i | \(0.502984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.6592 | 0.349342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.5988 | 0.576159 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.74170 | −0.285884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3397 | −0.664469 | −0.332234 | − | 0.943197i | \(-0.607802\pi\) | ||||
−0.332234 | + | 0.943197i | \(0.607802\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48292 | 0.0810271 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.0177050 | −0.000577166 0 | −0.000288583 | − | 1.00000i | \(-0.500092\pi\) | ||||
−0.000288583 | 1.00000i | \(0.500092\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.4789 | −1.83921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.18743 | −0.0386272 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6708 | 0.509233 | 0.254616 | − | 0.967042i | \(-0.418051\pi\) | ||||
0.254616 | + | 0.967042i | \(0.418051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.2971 | 1.79502 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.5180 | 1.15175 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.4298 | −0.758964 | −0.379482 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379482 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.90503 | 0.0940045 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 76.9058 | 2.48601 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0102 | −0.323246 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9264 | −0.997626 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6638 | 0.375859 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.76507 | 0.0890108 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3559 | −0.815390 | −0.407695 | − | 0.913118i | \(-0.633667\pi\) | ||||
−0.407695 | + | 0.913118i | \(0.633667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.7131 | −0.472651 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0972 | −0.324034 | −0.162017 | − | 0.986788i | \(-0.551800\pi\) | ||||
−0.162017 | + | 0.986788i | \(0.551800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.07000 | 0.194595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.7034 | 1.27153 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.26710 | −0.104524 | −0.0522619 | − | 0.998633i | \(-0.516643\pi\) | ||||
−0.0522619 | + | 0.998633i | \(0.516643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.6674 | −0.788372 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.20588 | −0.102356 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.2017 | 0.803809 | 0.401905 | − | 0.915682i | \(-0.368348\pi\) | ||||
0.401905 | + | 0.915682i | \(0.368348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.97293 | 0.126588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.7566 | −0.437877 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.45798 | 0.173554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.06526 | −0.287967 | −0.143984 | − | 0.989580i | \(-0.545991\pi\) | ||||
−0.143984 | + | 0.989580i | \(0.545991\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.8474 | 1.23279 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.41486 | 0.0448541 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8356 | −0.564860 | −0.282430 | − | 0.959288i | \(-0.591140\pi\) | ||||
−0.282430 | + | 0.959288i | \(0.591140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.9610 | −0.568260 |
(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 | 8048.2.a.v.1.6 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.23 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.23 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.6 | 28 | 1.1 | even | 1 | trivial |