Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 14x^{6} + 28x^{5} + 43x^{4} - 90x^{3} - 23x^{2} + 82x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.17253\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.585733 | −0.261948 | −0.130974 | − | 0.991386i | \(-0.541810\pi\) | ||||
−0.130974 | + | 0.991386i | \(0.541810\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.49689 | −0.565770 | −0.282885 | − | 0.959154i | \(-0.591291\pi\) | ||||
−0.282885 | + | 0.959154i | \(0.591291\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.585733 | 0.185225 | ||||||||
\(11\) | −3.18036 | −0.958914 | −0.479457 | − | 0.877565i | \(-0.659166\pi\) | ||||
−0.479457 | + | 0.877565i | \(0.659166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.04779 | −1.67735 | −0.838677 | − | 0.544629i | \(-0.816671\pi\) | ||||
−0.838677 | + | 0.544629i | \(0.816671\pi\) | |||||||
\(14\) | 1.49689 | 0.400060 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.54325 | 1.10190 | 0.550949 | − | 0.834539i | \(-0.314266\pi\) | ||||
0.550949 | + | 0.834539i | \(0.314266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74794 | 1.08925 | 0.544626 | − | 0.838679i | \(-0.316672\pi\) | ||||
0.544626 | + | 0.838679i | \(0.316672\pi\) | |||||||
\(20\) | −0.585733 | −0.130974 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.18036 | 0.678054 | ||||||||
\(23\) | 1.06929 | 0.222962 | 0.111481 | − | 0.993767i | \(-0.464441\pi\) | ||||
0.111481 | + | 0.993767i | \(0.464441\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65692 | −0.931383 | ||||||||
\(26\) | 6.04779 | 1.18607 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.49689 | −0.282885 | ||||||||
\(29\) | 10.4462 | 1.93980 | 0.969901 | − | 0.243499i | \(-0.0782953\pi\) | ||||
0.969901 | + | 0.243499i | \(0.0782953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.42013 | −1.15309 | −0.576545 | − | 0.817066i | \(-0.695599\pi\) | ||||
−0.576545 | + | 0.817066i | \(0.695599\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.54325 | −0.779160 | ||||||||
\(35\) | 0.876775 | 0.148202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.98632 | −1.64174 | −0.820871 | − | 0.571114i | \(-0.806511\pi\) | ||||
−0.820871 | + | 0.571114i | \(0.806511\pi\) | |||||||
\(38\) | −4.74794 | −0.770217 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.585733 | 0.0926125 | ||||||||
\(41\) | 3.37739 | 0.527459 | 0.263730 | − | 0.964597i | \(-0.415047\pi\) | ||||
0.263730 | + | 0.964597i | \(0.415047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53155 | −0.233559 | −0.116779 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116779 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(44\) | −3.18036 | −0.479457 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.06929 | −0.157658 | ||||||||
\(47\) | −13.0787 | −1.90772 | −0.953862 | − | 0.300246i | \(-0.902931\pi\) | ||||
−0.953862 | + | 0.300246i | \(0.902931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.75933 | −0.679904 | ||||||||
\(50\) | 4.65692 | 0.658588 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.04779 | −0.838677 | ||||||||
\(53\) | −7.71455 | −1.05967 | −0.529837 | − | 0.848099i | \(-0.677747\pi\) | ||||
−0.529837 | + | 0.848099i | \(0.677747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.86284 | 0.251185 | ||||||||
\(56\) | 1.49689 | 0.200030 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.4462 | −1.37165 | ||||||||
\(59\) | −3.21453 | −0.418496 | −0.209248 | − | 0.977863i | \(-0.567102\pi\) | ||||
−0.209248 | + | 0.977863i | \(0.567102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.85140 | 0.749195 | 0.374597 | − | 0.927188i | \(-0.377781\pi\) | ||||
0.374597 | + | 0.927188i | \(0.377781\pi\) | |||||||
\(62\) | 6.42013 | 0.815357 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.54239 | 0.439379 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3418 | 1.38562 | 0.692812 | − | 0.721119i | \(-0.256372\pi\) | ||||
0.692812 | + | 0.721119i | \(0.256372\pi\) | |||||||
\(68\) | 4.54325 | 0.550949 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.876775 | −0.104795 | ||||||||
\(71\) | 15.3383 | 1.82032 | 0.910161 | − | 0.414255i | \(-0.135958\pi\) | ||||
0.910161 | + | 0.414255i | \(0.135958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9439 | 1.74905 | 0.874523 | − | 0.484983i | \(-0.161174\pi\) | ||||
0.874523 | + | 0.484983i | \(0.161174\pi\) | |||||||
\(74\) | 9.98632 | 1.16089 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.74794 | 0.544626 | ||||||||
\(77\) | 4.76063 | 0.542525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50495 | 0.506846 | 0.253423 | − | 0.967356i | \(-0.418444\pi\) | ||||
0.253423 | + | 0.967356i | \(0.418444\pi\) | |||||||
\(80\) | −0.585733 | −0.0654869 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.37739 | −0.372970 | ||||||||
\(83\) | 1.09046 | 0.119694 | 0.0598469 | − | 0.998208i | \(-0.480939\pi\) | ||||
0.0598469 | + | 0.998208i | \(0.480939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.66113 | −0.288640 | ||||||||
\(86\) | 1.53155 | 0.165151 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.18036 | 0.339027 | ||||||||
\(89\) | 4.43131 | 0.469718 | 0.234859 | − | 0.972029i | \(-0.424537\pi\) | ||||
0.234859 | + | 0.972029i | \(0.424537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.05285 | 0.948997 | ||||||||
\(92\) | 1.06929 | 0.111481 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.0787 | 1.34896 | ||||||||
\(95\) | −2.78102 | −0.285327 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.60980 | −0.772658 | −0.386329 | − | 0.922361i | \(-0.626257\pi\) | ||||
−0.386329 | + | 0.922361i | \(0.626257\pi\) | |||||||
\(98\) | 4.75933 | 0.480765 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.65692 | −0.465692 | ||||||||
\(101\) | 11.3248 | 1.12686 | 0.563431 | − | 0.826163i | \(-0.309481\pi\) | ||||
0.563431 | + | 0.826163i | \(0.309481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8368 | −1.56045 | −0.780224 | − | 0.625501i | \(-0.784895\pi\) | ||||
−0.780224 | + | 0.625501i | \(0.784895\pi\) | |||||||
\(104\) | 6.04779 | 0.593034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.71455 | 0.749303 | ||||||||
\(107\) | 8.73169 | 0.844125 | 0.422062 | − | 0.906567i | \(-0.361306\pi\) | ||||
0.422062 | + | 0.906567i | \(0.361306\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.93898 | −0.185720 | −0.0928601 | − | 0.995679i | \(-0.529601\pi\) | ||||
−0.0928601 | + | 0.995679i | \(0.529601\pi\) | |||||||
\(110\) | −1.86284 | −0.177615 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.49689 | −0.141442 | ||||||||
\(113\) | 11.9224 | 1.12156 | 0.560781 | − | 0.827964i | \(-0.310501\pi\) | ||||
0.560781 | + | 0.827964i | \(0.310501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.626318 | −0.0584044 | ||||||||
\(116\) | 10.4462 | 0.969901 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.21453 | 0.295921 | ||||||||
\(119\) | −6.80072 | −0.623421 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.885329 | −0.0804845 | ||||||||
\(122\) | −5.85140 | −0.529761 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.42013 | −0.576545 | ||||||||
\(125\) | 5.65637 | 0.505921 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.46517 | 0.218748 | 0.109374 | − | 0.994001i | \(-0.465115\pi\) | ||||
0.109374 | + | 0.994001i | \(0.465115\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.54239 | −0.310688 | ||||||||
\(131\) | 1.07564 | 0.0939791 | 0.0469895 | − | 0.998895i | \(-0.485037\pi\) | ||||
0.0469895 | + | 0.998895i | \(0.485037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.10712 | −0.616266 | ||||||||
\(134\) | −11.3418 | −0.979784 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.54325 | −0.389580 | ||||||||
\(137\) | −7.49845 | −0.640636 | −0.320318 | − | 0.947310i | \(-0.603790\pi\) | ||||
−0.320318 | + | 0.947310i | \(0.603790\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50751 | −0.551960 | −0.275980 | − | 0.961163i | \(-0.589002\pi\) | ||||
−0.275980 | + | 0.961163i | \(0.589002\pi\) | |||||||
\(140\) | 0.876775 | 0.0741010 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.3383 | −1.28716 | ||||||||
\(143\) | 19.2341 | 1.60844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.11865 | −0.508127 | ||||||||
\(146\) | −14.9439 | −1.23676 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.98632 | −0.820871 | ||||||||
\(149\) | 13.2807 | 1.08800 | 0.543999 | − | 0.839086i | \(-0.316909\pi\) | ||||
0.543999 | + | 0.839086i | \(0.316909\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.77304 | 0.225667 | 0.112833 | − | 0.993614i | \(-0.464007\pi\) | ||||
0.112833 | + | 0.993614i | \(0.464007\pi\) | |||||||
\(152\) | −4.74794 | −0.385109 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.76063 | −0.383623 | ||||||||
\(155\) | 3.76048 | 0.302049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.97992 | 0.317633 | 0.158816 | − | 0.987308i | \(-0.449232\pi\) | ||||
0.158816 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(158\) | −4.50495 | −0.358394 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.585733 | 0.0463062 | ||||||||
\(161\) | −1.60060 | −0.126145 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0742 | 1.33735 | 0.668677 | − | 0.743553i | \(-0.266861\pi\) | ||||
0.668677 | + | 0.743553i | \(0.266861\pi\) | |||||||
\(164\) | 3.37739 | 0.263730 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.09046 | −0.0846362 | ||||||||
\(167\) | 3.88787 | 0.300853 | 0.150426 | − | 0.988621i | \(-0.451935\pi\) | ||||
0.150426 | + | 0.988621i | \(0.451935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.5757 | 1.81352 | ||||||||
\(170\) | 2.66113 | 0.204099 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.53155 | −0.116779 | ||||||||
\(173\) | 6.81516 | 0.518147 | 0.259074 | − | 0.965858i | \(-0.416583\pi\) | ||||
0.259074 | + | 0.965858i | \(0.416583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.97088 | 0.526949 | ||||||||
\(176\) | −3.18036 | −0.239728 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.43131 | −0.332141 | ||||||||
\(179\) | −1.64779 | −0.123162 | −0.0615808 | − | 0.998102i | \(-0.519614\pi\) | ||||
−0.0615808 | + | 0.998102i | \(0.519614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1341 | 1.19924 | 0.599621 | − | 0.800284i | \(-0.295318\pi\) | ||||
0.599621 | + | 0.800284i | \(0.295318\pi\) | |||||||
\(182\) | −9.05285 | −0.671042 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.06929 | −0.0788291 | ||||||||
\(185\) | 5.84932 | 0.430050 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4491 | −1.05663 | ||||||||
\(188\) | −13.0787 | −0.953862 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.78102 | 0.201757 | ||||||||
\(191\) | −0.988248 | −0.0715071 | −0.0357536 | − | 0.999361i | \(-0.511383\pi\) | ||||
−0.0357536 | + | 0.999361i | \(0.511383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2266 | 1.16801 | 0.584006 | − | 0.811749i | \(-0.301484\pi\) | ||||
0.584006 | + | 0.811749i | \(0.301484\pi\) | |||||||
\(194\) | 7.60980 | 0.546351 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.75933 | −0.339952 | ||||||||
\(197\) | −21.1776 | −1.50884 | −0.754422 | − | 0.656389i | \(-0.772083\pi\) | ||||
−0.754422 | + | 0.656389i | \(0.772083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.43075 | −0.384975 | −0.192488 | − | 0.981299i | \(-0.561656\pi\) | ||||
−0.192488 | + | 0.981299i | \(0.561656\pi\) | |||||||
\(200\) | 4.65692 | 0.329294 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.3248 | −0.796812 | ||||||||
\(203\) | −15.6367 | −1.09748 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.97825 | −0.138167 | ||||||||
\(206\) | 15.8368 | 1.10340 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.04779 | −0.419339 | ||||||||
\(209\) | −15.1001 | −1.04450 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70251 | 0.599105 | 0.299553 | − | 0.954080i | \(-0.403163\pi\) | ||||
0.299553 | + | 0.954080i | \(0.403163\pi\) | |||||||
\(212\) | −7.71455 | −0.529837 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.73169 | −0.596886 | ||||||||
\(215\) | 0.897078 | 0.0611802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.61020 | 0.652383 | ||||||||
\(218\) | 1.93898 | 0.131324 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.86284 | 0.125593 | ||||||||
\(221\) | −27.4766 | −1.84827 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | 1.49689 | 0.100015 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.9224 | −0.793064 | ||||||||
\(227\) | 5.33837 | 0.354320 | 0.177160 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177160 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9242 | −1.11838 | −0.559191 | − | 0.829039i | \(-0.688888\pi\) | ||||
−0.559191 | + | 0.829039i | \(0.688888\pi\) | |||||||
\(230\) | 0.626318 | 0.0412982 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.4462 | −0.685824 | ||||||||
\(233\) | 16.5149 | 1.08193 | 0.540963 | − | 0.841046i | \(-0.318060\pi\) | ||||
0.540963 | + | 0.841046i | \(0.318060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.66062 | 0.499724 | ||||||||
\(236\) | −3.21453 | −0.209248 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.80072 | 0.440825 | ||||||||
\(239\) | 14.8861 | 0.962903 | 0.481451 | − | 0.876473i | \(-0.340110\pi\) | ||||
0.481451 | + | 0.876473i | \(0.340110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.70313 | 0.109708 | 0.0548541 | − | 0.998494i | \(-0.482531\pi\) | ||||
0.0548541 | + | 0.998494i | \(0.482531\pi\) | |||||||
\(242\) | 0.885329 | 0.0569111 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.85140 | 0.374597 | ||||||||
\(245\) | 2.78770 | 0.178099 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.7145 | −1.82706 | ||||||||
\(248\) | 6.42013 | 0.407679 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.65637 | −0.357740 | ||||||||
\(251\) | 28.4403 | 1.79514 | 0.897569 | − | 0.440873i | \(-0.145331\pi\) | ||||
0.897569 | + | 0.440873i | \(0.145331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.40072 | −0.213802 | ||||||||
\(254\) | −2.46517 | −0.154678 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.2851 | 1.07821 | 0.539106 | − | 0.842238i | \(-0.318762\pi\) | ||||
0.539106 | + | 0.842238i | \(0.318762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9484 | 0.928848 | ||||||||
\(260\) | 3.54239 | 0.219690 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.07564 | −0.0664532 | ||||||||
\(263\) | −3.84344 | −0.236996 | −0.118498 | − | 0.992954i | \(-0.537808\pi\) | ||||
−0.118498 | + | 0.992954i | \(0.537808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.51866 | 0.277579 | ||||||||
\(266\) | 7.10712 | 0.435766 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.3418 | 0.692812 | ||||||||
\(269\) | −1.43863 | −0.0877150 | −0.0438575 | − | 0.999038i | \(-0.513965\pi\) | ||||
−0.0438575 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.44794 | −0.513176 | −0.256588 | − | 0.966521i | \(-0.582598\pi\) | ||||
−0.256588 | + | 0.966521i | \(0.582598\pi\) | |||||||
\(272\) | 4.54325 | 0.275475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.49845 | 0.452998 | ||||||||
\(275\) | 14.8107 | 0.893116 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1492 | 1.21065 | 0.605324 | − | 0.795979i | \(-0.293043\pi\) | ||||
0.605324 | + | 0.795979i | \(0.293043\pi\) | |||||||
\(278\) | 6.50751 | 0.390294 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.876775 | −0.0523973 | ||||||||
\(281\) | 0.863739 | 0.0515264 | 0.0257632 | − | 0.999668i | \(-0.491798\pi\) | ||||
0.0257632 | + | 0.999668i | \(0.491798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7643 | 0.877646 | 0.438823 | − | 0.898573i | \(-0.355395\pi\) | ||||
0.438823 | + | 0.898573i | \(0.355395\pi\) | |||||||
\(284\) | 15.3383 | 0.910161 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.2341 | −1.13734 | ||||||||
\(287\) | −5.05556 | −0.298421 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.64108 | 0.214181 | ||||||||
\(290\) | 6.11865 | 0.359300 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.9439 | 0.874523 | ||||||||
\(293\) | −27.7810 | −1.62298 | −0.811491 | − | 0.584364i | \(-0.801344\pi\) | ||||
−0.811491 | + | 0.584364i | \(0.801344\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.88285 | 0.109624 | ||||||||
\(296\) | 9.98632 | 0.580443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.2807 | −0.769331 | ||||||||
\(299\) | −6.46684 | −0.373987 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.29255 | 0.132141 | ||||||||
\(302\) | −2.77304 | −0.159570 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.74794 | 0.272313 | ||||||||
\(305\) | −3.42735 | −0.196250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.5648 | −1.40199 | −0.700994 | − | 0.713167i | \(-0.747260\pi\) | ||||
−0.700994 | + | 0.713167i | \(0.747260\pi\) | |||||||
\(308\) | 4.76063 | 0.271262 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.76048 | −0.213581 | ||||||||
\(311\) | 23.3167 | 1.32217 | 0.661083 | − | 0.750313i | \(-0.270097\pi\) | ||||
0.661083 | + | 0.750313i | \(0.270097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.8040 | 1.91071 | 0.955357 | − | 0.295453i | \(-0.0954704\pi\) | ||||
0.955357 | + | 0.295453i | \(0.0954704\pi\) | |||||||
\(314\) | −3.97992 | −0.224600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.50495 | 0.253423 | ||||||||
\(317\) | 28.4355 | 1.59709 | 0.798547 | − | 0.601932i | \(-0.205602\pi\) | ||||
0.798547 | + | 0.601932i | \(0.205602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.2225 | −1.86010 | ||||||||
\(320\) | −0.585733 | −0.0327435 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.60060 | 0.0891982 | ||||||||
\(323\) | 21.5710 | 1.20024 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.1640 | 1.56226 | ||||||||
\(326\) | −17.0742 | −0.945652 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.37739 | −0.186485 | ||||||||
\(329\) | 19.5773 | 1.07933 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.1657 | −1.82295 | −0.911475 | − | 0.411356i | \(-0.865055\pi\) | ||||
−0.911475 | + | 0.411356i | \(0.865055\pi\) | |||||||
\(332\) | 1.09046 | 0.0598469 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.88787 | −0.212735 | ||||||||
\(335\) | −6.64327 | −0.362961 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.40874 | 0.349107 | 0.174553 | − | 0.984648i | \(-0.444152\pi\) | ||||
0.174553 | + | 0.984648i | \(0.444152\pi\) | |||||||
\(338\) | −23.5757 | −1.28235 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.66113 | −0.144320 | ||||||||
\(341\) | 20.4183 | 1.10571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6024 | 0.950439 | ||||||||
\(344\) | 1.53155 | 0.0825756 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.81516 | −0.366385 | ||||||||
\(347\) | −30.3873 | −1.63128 | −0.815639 | − | 0.578562i | \(-0.803614\pi\) | ||||
−0.815639 | + | 0.578562i | \(0.803614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1951 | 0.706319 | 0.353159 | − | 0.935563i | \(-0.385107\pi\) | ||||
0.353159 | + | 0.935563i | \(0.385107\pi\) | |||||||
\(350\) | −6.97088 | −0.372609 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.18036 | 0.169514 | ||||||||
\(353\) | 16.0690 | 0.855265 | 0.427633 | − | 0.903953i | \(-0.359348\pi\) | ||||
0.427633 | + | 0.903953i | \(0.359348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.98414 | −0.476829 | ||||||||
\(356\) | 4.43131 | 0.234859 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.64779 | 0.0870884 | ||||||||
\(359\) | 10.4685 | 0.552507 | 0.276253 | − | 0.961085i | \(-0.410907\pi\) | ||||
0.276253 | + | 0.961085i | \(0.410907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.54291 | 0.186469 | ||||||||
\(362\) | −16.1341 | −0.847992 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.05285 | 0.474498 | ||||||||
\(365\) | −8.75311 | −0.458159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.1262 | 1.36378 | 0.681888 | − | 0.731457i | \(-0.261159\pi\) | ||||
0.681888 | + | 0.731457i | \(0.261159\pi\) | |||||||
\(368\) | 1.06929 | 0.0557406 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.84932 | −0.304091 | ||||||||
\(371\) | 11.5478 | 0.599532 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.2059 | −1.35689 | −0.678446 | − | 0.734650i | \(-0.737346\pi\) | ||||
−0.678446 | + | 0.734650i | \(0.737346\pi\) | |||||||
\(374\) | 14.4491 | 0.747147 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.0787 | 0.674482 | ||||||||
\(377\) | −63.1761 | −3.25374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.9269 | 1.69134 | 0.845670 | − | 0.533706i | \(-0.179201\pi\) | ||||
0.845670 | + | 0.533706i | \(0.179201\pi\) | |||||||
\(380\) | −2.78102 | −0.142663 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.988248 | 0.0505632 | ||||||||
\(383\) | −20.5468 | −1.04989 | −0.524946 | − | 0.851136i | \(-0.675914\pi\) | ||||
−0.524946 | + | 0.851136i | \(0.675914\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.78846 | −0.142113 | ||||||||
\(386\) | −16.2266 | −0.825910 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.60980 | −0.386329 | ||||||||
\(389\) | −22.5931 | −1.14551 | −0.572757 | − | 0.819725i | \(-0.694126\pi\) | ||||
−0.572757 | + | 0.819725i | \(0.694126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.85804 | 0.245682 | ||||||||
\(392\) | 4.75933 | 0.240383 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.1776 | 1.06691 | ||||||||
\(395\) | −2.63870 | −0.132767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.21751 | 0.362236 | 0.181118 | − | 0.983461i | \(-0.442028\pi\) | ||||
0.181118 | + | 0.983461i | \(0.442028\pi\) | |||||||
\(398\) | 5.43075 | 0.272219 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.65692 | −0.232846 | ||||||||
\(401\) | 11.3770 | 0.568143 | 0.284071 | − | 0.958803i | \(-0.408315\pi\) | ||||
0.284071 | + | 0.958803i | \(0.408315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.8276 | 1.93414 | ||||||||
\(404\) | 11.3248 | 0.563431 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.6367 | 0.776037 | ||||||||
\(407\) | 31.7601 | 1.57429 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.13979 | 0.105806 | 0.0529030 | − | 0.998600i | \(-0.483153\pi\) | ||||
0.0529030 | + | 0.998600i | \(0.483153\pi\) | |||||||
\(410\) | 1.97825 | 0.0976986 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.8368 | −0.780224 | ||||||||
\(413\) | 4.81178 | 0.236772 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.638719 | −0.0313535 | ||||||||
\(416\) | 6.04779 | 0.296517 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.1001 | 0.738572 | ||||||||
\(419\) | −33.3352 | −1.62853 | −0.814266 | − | 0.580493i | \(-0.802860\pi\) | ||||
−0.814266 | + | 0.580493i | \(0.802860\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1838 | −1.22738 | −0.613691 | − | 0.789546i | \(-0.710316\pi\) | ||||
−0.613691 | + | 0.789546i | \(0.710316\pi\) | |||||||
\(422\) | −8.70251 | −0.423631 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.71455 | 0.374652 | ||||||||
\(425\) | −21.1575 | −1.02629 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.75888 | −0.423872 | ||||||||
\(428\) | 8.73169 | 0.422062 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.897078 | −0.0432609 | ||||||||
\(431\) | 21.3427 | 1.02804 | 0.514020 | − | 0.857778i | \(-0.328156\pi\) | ||||
0.514020 | + | 0.857778i | \(0.328156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4723 | 1.51246 | 0.756231 | − | 0.654305i | \(-0.227039\pi\) | ||||
0.756231 | + | 0.654305i | \(0.227039\pi\) | |||||||
\(434\) | −9.61020 | −0.461305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.93898 | −0.0928601 | ||||||||
\(437\) | 5.07692 | 0.242862 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.30672 | 0.396458 | 0.198229 | − | 0.980156i | \(-0.436481\pi\) | ||||
0.198229 | + | 0.980156i | \(0.436481\pi\) | |||||||
\(440\) | −1.86284 | −0.0888074 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.4766 | 1.30693 | ||||||||
\(443\) | −5.18961 | −0.246566 | −0.123283 | − | 0.992372i | \(-0.539342\pi\) | ||||
−0.123283 | + | 0.992372i | \(0.539342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.59556 | −0.123041 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.49689 | −0.0707212 | ||||||||
\(449\) | 12.2820 | 0.579623 | 0.289811 | − | 0.957084i | \(-0.406407\pi\) | ||||
0.289811 | + | 0.957084i | \(0.406407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7413 | −0.505788 | ||||||||
\(452\) | 11.9224 | 0.560781 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.33837 | −0.250542 | ||||||||
\(455\) | −5.30255 | −0.248587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.6297 | 1.71347 | 0.856733 | − | 0.515760i | \(-0.172490\pi\) | ||||
0.856733 | + | 0.515760i | \(0.172490\pi\) | |||||||
\(458\) | 16.9242 | 0.790815 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.626318 | −0.0292022 | ||||||||
\(461\) | 23.3611 | 1.08804 | 0.544018 | − | 0.839074i | \(-0.316902\pi\) | ||||
0.544018 | + | 0.839074i | \(0.316902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6070 | −1.46890 | −0.734451 | − | 0.678661i | \(-0.762560\pi\) | ||||
−0.734451 | + | 0.678661i | \(0.762560\pi\) | |||||||
\(464\) | 10.4462 | 0.484951 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.5149 | −0.765037 | ||||||||
\(467\) | −41.2962 | −1.91096 | −0.955479 | − | 0.295058i | \(-0.904661\pi\) | ||||
−0.955479 | + | 0.295058i | \(0.904661\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9774 | −0.783944 | ||||||||
\(470\) | −7.66062 | −0.353358 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.21453 | 0.147961 | ||||||||
\(473\) | 4.87087 | 0.223963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.1108 | −1.01451 | ||||||||
\(476\) | −6.80072 | −0.311711 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.8861 | −0.680875 | ||||||||
\(479\) | −18.4305 | −0.842112 | −0.421056 | − | 0.907035i | \(-0.638340\pi\) | ||||
−0.421056 | + | 0.907035i | \(0.638340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 60.3952 | 2.75378 | ||||||||
\(482\) | −1.70313 | −0.0775754 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.885329 | −0.0402422 | ||||||||
\(485\) | 4.45731 | 0.202396 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4137 | −0.471891 | −0.235945 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235945 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(488\) | −5.85140 | −0.264880 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.78770 | −0.125935 | ||||||||
\(491\) | −23.7037 | −1.06973 | −0.534867 | − | 0.844936i | \(-0.679638\pi\) | ||||
−0.534867 | + | 0.844936i | \(0.679638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.4594 | 2.13747 | ||||||||
\(494\) | 28.7145 | 1.29193 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.42013 | −0.288272 | ||||||||
\(497\) | −22.9597 | −1.02988 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.2061 | −1.08361 | −0.541807 | − | 0.840503i | \(-0.682260\pi\) | ||||
−0.541807 | + | 0.840503i | \(0.682260\pi\) | |||||||
\(500\) | 5.65637 | 0.252961 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.4403 | −1.26935 | ||||||||
\(503\) | 3.47026 | 0.154731 | 0.0773657 | − | 0.997003i | \(-0.475349\pi\) | ||||
0.0773657 | + | 0.997003i | \(0.475349\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.63332 | −0.295179 | ||||||||
\(506\) | 3.40072 | 0.151181 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.46517 | 0.109374 | ||||||||
\(509\) | 1.53550 | 0.0680600 | 0.0340300 | − | 0.999421i | \(-0.489166\pi\) | ||||
0.0340300 | + | 0.999421i | \(0.489166\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.3693 | −0.989558 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.2851 | −0.762411 | ||||||||
\(515\) | 9.27614 | 0.408755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.5949 | 1.82934 | ||||||||
\(518\) | −14.9484 | −0.656795 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.54239 | −0.155344 | ||||||||
\(521\) | −16.9837 | −0.744068 | −0.372034 | − | 0.928219i | \(-0.621340\pi\) | ||||
−0.372034 | + | 0.928219i | \(0.621340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.10471 | −0.0920326 | −0.0460163 | − | 0.998941i | \(-0.514653\pi\) | ||||
−0.0460163 | + | 0.998941i | \(0.514653\pi\) | |||||||
\(524\) | 1.07564 | 0.0469895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.84344 | 0.167582 | ||||||||
\(527\) | −29.1682 | −1.27059 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8566 | −0.950288 | ||||||||
\(530\) | −4.51866 | −0.196278 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.10712 | −0.308133 | ||||||||
\(533\) | −20.4257 | −0.884736 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.11444 | −0.221116 | ||||||||
\(536\) | −11.3418 | −0.489892 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.43863 | 0.0620239 | ||||||||
\(539\) | 15.1364 | 0.651970 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3108 | 0.572277 | 0.286138 | − | 0.958188i | \(-0.407628\pi\) | ||||
0.286138 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(542\) | 8.44794 | 0.362870 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.54325 | −0.194790 | ||||||||
\(545\) | 1.13572 | 0.0486490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.3342 | −0.484617 | −0.242308 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242308 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(548\) | −7.49845 | −0.320318 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.8107 | −0.631529 | ||||||||
\(551\) | 49.5977 | 2.11293 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.74340 | −0.286758 | ||||||||
\(554\) | −20.1492 | −0.856058 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.50751 | −0.275980 | ||||||||
\(557\) | 37.7363 | 1.59894 | 0.799470 | − | 0.600706i | \(-0.205114\pi\) | ||||
0.799470 | + | 0.600706i | \(0.205114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.26248 | 0.391761 | ||||||||
\(560\) | 0.876775 | 0.0370505 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.863739 | −0.0364346 | ||||||||
\(563\) | −18.2752 | −0.770209 | −0.385105 | − | 0.922873i | \(-0.625835\pi\) | ||||
−0.385105 | + | 0.922873i | \(0.625835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.98332 | −0.293790 | ||||||||
\(566\) | −14.7643 | −0.620590 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.3383 | −0.643581 | ||||||||
\(569\) | 12.2166 | 0.512146 | 0.256073 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256073 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.810246 | 0.0339077 | 0.0169539 | − | 0.999856i | \(-0.494603\pi\) | ||||
0.0169539 | + | 0.999856i | \(0.494603\pi\) | |||||||
\(572\) | 19.2341 | 0.804219 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.05556 | 0.211015 | ||||||||
\(575\) | −4.97959 | −0.207663 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9944 | −0.832376 | −0.416188 | − | 0.909279i | \(-0.636634\pi\) | ||||
−0.416188 | + | 0.909279i | \(0.636634\pi\) | |||||||
\(578\) | −3.64108 | −0.151449 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.11865 | −0.254063 | ||||||||
\(581\) | −1.63230 | −0.0677191 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.5350 | 1.01614 | ||||||||
\(584\) | −14.9439 | −0.618381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.7810 | 1.14762 | ||||||||
\(587\) | 15.1575 | 0.625617 | 0.312808 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312808 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.4824 | −1.25600 | ||||||||
\(590\) | −1.88285 | −0.0775159 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.98632 | −0.410435 | ||||||||
\(593\) | −10.1080 | −0.415085 | −0.207542 | − | 0.978226i | \(-0.566546\pi\) | ||||
−0.207542 | + | 0.978226i | \(0.566546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.98341 | 0.163304 | ||||||||
\(596\) | 13.2807 | 0.543999 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.46684 | 0.264449 | ||||||||
\(599\) | 13.7754 | 0.562849 | 0.281424 | − | 0.959583i | \(-0.409193\pi\) | ||||
0.281424 | + | 0.959583i | \(0.409193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.92779 | −0.364172 | −0.182086 | − | 0.983283i | \(-0.558285\pi\) | ||||
−0.182086 | + | 0.983283i | \(0.558285\pi\) | |||||||
\(602\) | −2.29255 | −0.0934375 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.77304 | 0.112833 | ||||||||
\(605\) | 0.518566 | 0.0210827 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3237 | 0.500204 | 0.250102 | − | 0.968219i | \(-0.419536\pi\) | ||||
0.250102 | + | 0.968219i | \(0.419536\pi\) | |||||||
\(608\) | −4.74794 | −0.192554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.42735 | 0.138770 | ||||||||
\(611\) | 79.0972 | 3.19993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9032 | −1.08661 | −0.543306 | − | 0.839535i | \(-0.682828\pi\) | ||||
−0.543306 | + | 0.839535i | \(0.682828\pi\) | |||||||
\(614\) | 24.5648 | 0.991355 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.76063 | −0.191811 | ||||||||
\(617\) | 1.35067 | 0.0543758 | 0.0271879 | − | 0.999630i | \(-0.491345\pi\) | ||||
0.0271879 | + | 0.999630i | \(0.491345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.41979 | 0.378613 | 0.189307 | − | 0.981918i | \(-0.439376\pi\) | ||||
0.189307 | + | 0.981918i | \(0.439376\pi\) | |||||||
\(620\) | 3.76048 | 0.151024 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.3167 | −0.934913 | ||||||||
\(623\) | −6.63317 | −0.265752 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9715 | 0.798859 | ||||||||
\(626\) | −33.8040 | −1.35108 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.97992 | 0.158816 | ||||||||
\(629\) | −45.3703 | −1.80903 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.1621 | −1.28035 | −0.640177 | − | 0.768228i | \(-0.721139\pi\) | ||||
−0.640177 | + | 0.768228i | \(0.721139\pi\) | |||||||
\(632\) | −4.50495 | −0.179197 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.4355 | −1.12932 | ||||||||
\(635\) | −1.44393 | −0.0573006 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.7834 | 1.14044 | ||||||||
\(638\) | 33.2225 | 1.31529 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.585733 | 0.0231531 | ||||||||
\(641\) | 10.5434 | 0.416441 | 0.208220 | − | 0.978082i | \(-0.433233\pi\) | ||||
0.208220 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.5228 | 1.67694 | 0.838468 | − | 0.544951i | \(-0.183452\pi\) | ||||
0.838468 | + | 0.544951i | \(0.183452\pi\) | |||||||
\(644\) | −1.60060 | −0.0630727 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.5710 | −0.848701 | ||||||||
\(647\) | 5.84286 | 0.229707 | 0.114853 | − | 0.993382i | \(-0.463360\pi\) | ||||
0.114853 | + | 0.993382i | \(0.463360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2233 | 0.401301 | ||||||||
\(650\) | −28.1640 | −1.10468 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.0742 | 0.668677 | ||||||||
\(653\) | 5.00429 | 0.195833 | 0.0979164 | − | 0.995195i | \(-0.468782\pi\) | ||||
0.0979164 | + | 0.995195i | \(0.468782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.630037 | −0.0246176 | ||||||||
\(656\) | 3.37739 | 0.131865 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.5773 | −0.763203 | ||||||||
\(659\) | 31.8454 | 1.24052 | 0.620261 | − | 0.784395i | \(-0.287027\pi\) | ||||
0.620261 | + | 0.784395i | \(0.287027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9484 | 0.737005 | 0.368503 | − | 0.929627i | \(-0.379871\pi\) | ||||
0.368503 | + | 0.929627i | \(0.379871\pi\) | |||||||
\(662\) | 33.1657 | 1.28902 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.09046 | −0.0423181 | ||||||||
\(665\) | 4.16287 | 0.161429 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1700 | 0.432503 | ||||||||
\(668\) | 3.88787 | 0.150426 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.64327 | 0.256652 | ||||||||
\(671\) | −18.6095 | −0.718413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.9693 | 1.00104 | 0.500521 | − | 0.865725i | \(-0.333142\pi\) | ||||
0.500521 | + | 0.865725i | \(0.333142\pi\) | |||||||
\(674\) | −6.40874 | −0.246856 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.5757 | 0.906759 | ||||||||
\(677\) | −42.6732 | −1.64006 | −0.820032 | − | 0.572317i | \(-0.806045\pi\) | ||||
−0.820032 | + | 0.572317i | \(0.806045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.3910 | 0.437146 | ||||||||
\(680\) | 2.66113 | 0.102050 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.4183 | −0.781857 | ||||||||
\(683\) | −43.2949 | −1.65663 | −0.828317 | − | 0.560260i | \(-0.810701\pi\) | ||||
−0.828317 | + | 0.560260i | \(0.810701\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.39209 | 0.167813 | ||||||||
\(686\) | −17.6024 | −0.672062 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.53155 | −0.0583897 | ||||||||
\(689\) | 46.6559 | 1.77745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.8538 | −0.755273 | −0.377636 | − | 0.925954i | \(-0.623263\pi\) | ||||
−0.377636 | + | 0.925954i | \(0.623263\pi\) | |||||||
\(692\) | 6.81516 | 0.259074 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3873 | 1.15349 | ||||||||
\(695\) | 3.81166 | 0.144584 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.3443 | 0.581207 | ||||||||
\(698\) | −13.1951 | −0.499443 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.97088 | 0.263474 | ||||||||
\(701\) | 27.2877 | 1.03064 | 0.515321 | − | 0.856997i | \(-0.327673\pi\) | ||||
0.515321 | + | 0.856997i | \(0.327673\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.4144 | −1.78827 | ||||||||
\(704\) | −3.18036 | −0.119864 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0690 | −0.604764 | ||||||||
\(707\) | −16.9520 | −0.637545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.4005 | −0.916382 | −0.458191 | − | 0.888854i | \(-0.651502\pi\) | ||||
−0.458191 | + | 0.888854i | \(0.651502\pi\) | |||||||
\(710\) | 8.98414 | 0.337169 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.43131 | −0.166070 | ||||||||
\(713\) | −6.86498 | −0.257095 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2661 | −0.421327 | ||||||||
\(716\) | −1.64779 | −0.0615808 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.4685 | −0.390681 | ||||||||
\(719\) | 5.73870 | 0.214018 | 0.107009 | − | 0.994258i | \(-0.465873\pi\) | ||||
0.107009 | + | 0.994258i | \(0.465873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7059 | 0.882854 | ||||||||
\(722\) | −3.54291 | −0.131853 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.1341 | 0.599621 | ||||||||
\(725\) | −48.6469 | −1.80670 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.25441 | 0.120699 | 0.0603497 | − | 0.998177i | \(-0.480778\pi\) | ||||
0.0603497 | + | 0.998177i | \(0.480778\pi\) | |||||||
\(728\) | −9.05285 | −0.335521 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.75311 | 0.323967 | ||||||||
\(731\) | −6.95820 | −0.257358 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.2895 | 1.45119 | 0.725595 | − | 0.688122i | \(-0.241564\pi\) | ||||
0.725595 | + | 0.688122i | \(0.241564\pi\) | |||||||
\(734\) | −26.1262 | −0.964335 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.06929 | −0.0394145 | ||||||||
\(737\) | −36.0710 | −1.32869 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.5580 | 0.829809 | 0.414904 | − | 0.909865i | \(-0.363815\pi\) | ||||
0.414904 | + | 0.909865i | \(0.363815\pi\) | |||||||
\(740\) | 5.84932 | 0.215025 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5478 | −0.423933 | ||||||||
\(743\) | 16.1152 | 0.591210 | 0.295605 | − | 0.955310i | \(-0.404479\pi\) | ||||
0.295605 | + | 0.955310i | \(0.404479\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.77895 | −0.284999 | ||||||||
\(746\) | 26.2059 | 0.959467 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.4491 | −0.528313 | ||||||||
\(749\) | −13.0704 | −0.477580 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6657 | 0.425688 | 0.212844 | − | 0.977086i | \(-0.431727\pi\) | ||||
0.212844 | + | 0.977086i | \(0.431727\pi\) | |||||||
\(752\) | −13.0787 | −0.476931 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 63.1761 | 2.30074 | ||||||||
\(755\) | −1.62426 | −0.0591128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.1726 | 1.60548 | 0.802741 | − | 0.596328i | \(-0.203374\pi\) | ||||
0.802741 | + | 0.596328i | \(0.203374\pi\) | |||||||
\(758\) | −32.9269 | −1.19596 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.78102 | 0.100878 | ||||||||
\(761\) | −4.55042 | −0.164953 | −0.0824763 | − | 0.996593i | \(-0.526283\pi\) | ||||
−0.0824763 | + | 0.996593i | \(0.526283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.90243 | 0.105075 | ||||||||
\(764\) | −0.988248 | −0.0357536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.5468 | 0.742386 | ||||||||
\(767\) | 19.4408 | 0.701966 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.5915 | 0.454063 | 0.227031 | − | 0.973887i | \(-0.427098\pi\) | ||||
0.227031 | + | 0.973887i | \(0.427098\pi\) | |||||||
\(770\) | 2.78846 | 0.100489 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.2266 | 0.584006 | ||||||||
\(773\) | 37.3896 | 1.34481 | 0.672405 | − | 0.740183i | \(-0.265261\pi\) | ||||
0.672405 | + | 0.740183i | \(0.265261\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.8980 | 1.07397 | ||||||||
\(776\) | 7.60980 | 0.273176 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.5931 | 0.810001 | ||||||||
\(779\) | 16.0356 | 0.574536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.7813 | −1.74553 | ||||||||
\(782\) | −4.85804 | −0.173723 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.75933 | −0.169976 | ||||||||
\(785\) | −2.33117 | −0.0832031 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.6138 | −0.734803 | −0.367402 | − | 0.930062i | \(-0.619753\pi\) | ||||
−0.367402 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(788\) | −21.1776 | −0.754422 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.63870 | 0.0938806 | ||||||||
\(791\) | −17.8464 | −0.634546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.3880 | −1.25667 | ||||||||
\(794\) | −7.21751 | −0.256140 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.43075 | −0.192488 | ||||||||
\(797\) | −23.8712 | −0.845560 | −0.422780 | − | 0.906232i | \(-0.638946\pi\) | ||||
−0.422780 | + | 0.906232i | \(0.638946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.4197 | −2.10212 | ||||||||
\(800\) | 4.65692 | 0.164647 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.3770 | −0.401738 | ||||||||
\(803\) | −47.5268 | −1.67718 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.937527 | 0.0330435 | ||||||||
\(806\) | −38.8276 | −1.36764 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.3248 | −0.398406 | ||||||||
\(809\) | 12.5712 | 0.441978 | 0.220989 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220989 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.4170 | 1.10320 | 0.551600 | − | 0.834109i | \(-0.314018\pi\) | ||||
0.551600 | + | 0.834109i | \(0.314018\pi\) | |||||||
\(812\) | −15.6367 | −0.548741 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −31.7601 | −1.11319 | ||||||||
\(815\) | −10.0009 | −0.350316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.27170 | −0.254404 | ||||||||
\(818\) | −2.13979 | −0.0748162 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.97825 | −0.0690833 | ||||||||
\(821\) | −34.9424 | −1.21950 | −0.609748 | − | 0.792595i | \(-0.708730\pi\) | ||||
−0.609748 | + | 0.792595i | \(0.708730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4458 | −0.573263 | −0.286632 | − | 0.958041i | \(-0.592536\pi\) | ||||
−0.286632 | + | 0.958041i | \(0.592536\pi\) | |||||||
\(824\) | 15.8368 | 0.551701 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.81178 | −0.167423 | ||||||||
\(827\) | −5.00885 | −0.174175 | −0.0870874 | − | 0.996201i | \(-0.527756\pi\) | ||||
−0.0870874 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1491 | −0.421954 | −0.210977 | − | 0.977491i | \(-0.567665\pi\) | ||||
−0.210977 | + | 0.977491i | \(0.567665\pi\) | |||||||
\(830\) | 0.638719 | 0.0221703 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.04779 | −0.209669 | ||||||||
\(833\) | −21.6228 | −0.749186 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.27726 | −0.0788077 | ||||||||
\(836\) | −15.1001 | −0.522249 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.3352 | 1.15155 | ||||||||
\(839\) | −28.3298 | −0.978053 | −0.489026 | − | 0.872269i | \(-0.662648\pi\) | ||||
−0.489026 | + | 0.872269i | \(0.662648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.1222 | 2.76283 | ||||||||
\(842\) | 25.1838 | 0.867890 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.70251 | 0.299553 | ||||||||
\(845\) | −13.8091 | −0.475047 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32524 | 0.0455357 | ||||||||
\(848\) | −7.71455 | −0.264919 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.1575 | 0.725697 | ||||||||
\(851\) | −10.6783 | −0.366046 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.7850 | −1.19101 | −0.595507 | − | 0.803350i | \(-0.703049\pi\) | ||||
−0.595507 | + | 0.803350i | \(0.703049\pi\) | |||||||
\(854\) | 8.75888 | 0.299723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.73169 | −0.298443 | ||||||||
\(857\) | −29.5698 | −1.01008 | −0.505042 | − | 0.863095i | \(-0.668523\pi\) | ||||
−0.505042 | + | 0.863095i | \(0.668523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1666 | 0.449240 | 0.224620 | − | 0.974446i | \(-0.427886\pi\) | ||||
0.224620 | + | 0.974446i | \(0.427886\pi\) | |||||||
\(860\) | 0.897078 | 0.0305901 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.3427 | −0.726934 | ||||||||
\(863\) | −26.5705 | −0.904469 | −0.452235 | − | 0.891899i | \(-0.649373\pi\) | ||||
−0.452235 | + | 0.891899i | \(0.649373\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.99186 | −0.135727 | ||||||||
\(866\) | −31.4723 | −1.06947 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.61020 | 0.326192 | ||||||||
\(869\) | −14.3273 | −0.486022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.5929 | −2.32418 | ||||||||
\(872\) | 1.93898 | 0.0656620 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.07692 | −0.171729 | ||||||||
\(875\) | −8.46695 | −0.286235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.8177 | −1.81730 | −0.908648 | − | 0.417563i | \(-0.862884\pi\) | ||||
−0.908648 | + | 0.417563i | \(0.862884\pi\) | |||||||
\(878\) | −8.30672 | −0.280338 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.86284 | 0.0627963 | ||||||||
\(881\) | 16.5945 | 0.559082 | 0.279541 | − | 0.960134i | \(-0.409818\pi\) | ||||
0.279541 | + | 0.960134i | \(0.409818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.7445 | −1.74134 | −0.870671 | − | 0.491866i | \(-0.836315\pi\) | ||||
−0.870671 | + | 0.491866i | \(0.836315\pi\) | |||||||
\(884\) | −27.4766 | −0.924137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.18961 | 0.174348 | ||||||||
\(887\) | 39.9001 | 1.33972 | 0.669858 | − | 0.742489i | \(-0.266355\pi\) | ||||
0.669858 | + | 0.742489i | \(0.266355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.69007 | −0.123761 | ||||||||
\(890\) | 2.59556 | 0.0870034 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | −62.0968 | −2.07799 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.965164 | 0.0322619 | ||||||||
\(896\) | 1.49689 | 0.0500075 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.2820 | −0.409855 | ||||||||
\(899\) | −67.0657 | −2.23677 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.0491 | −1.16765 | ||||||||
\(902\) | 10.7413 | 0.357646 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.9224 | −0.396532 | ||||||||
\(905\) | −9.45030 | −0.314138 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9406 | 0.894549 | 0.447275 | − | 0.894397i | \(-0.352395\pi\) | ||||
0.447275 | + | 0.894397i | \(0.352395\pi\) | |||||||
\(908\) | 5.33837 | 0.177160 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.30255 | 0.175778 | ||||||||
\(911\) | −19.2901 | −0.639111 | −0.319555 | − | 0.947568i | \(-0.603534\pi\) | ||||
−0.319555 | + | 0.947568i | \(0.603534\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46806 | −0.114776 | ||||||||
\(914\) | −36.6297 | −1.21160 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.9242 | −0.559191 | ||||||||
\(917\) | −1.61011 | −0.0531705 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0123 | 1.51781 | 0.758903 | − | 0.651204i | \(-0.225736\pi\) | ||||
0.758903 | + | 0.651204i | \(0.225736\pi\) | |||||||
\(920\) | 0.626318 | 0.0206491 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.3611 | −0.769358 | ||||||||
\(923\) | −92.7628 | −3.05332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.5055 | 1.52909 | ||||||||
\(926\) | 31.6070 | 1.03867 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.4462 | −0.342912 | ||||||||
\(929\) | 40.9071 | 1.34212 | 0.671059 | − | 0.741404i | \(-0.265840\pi\) | ||||
0.671059 | + | 0.741404i | \(0.265840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5970 | −0.740587 | ||||||||
\(932\) | 16.5149 | 0.540963 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 41.2962 | 1.35125 | ||||||||
\(935\) | 8.46333 | 0.276781 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4636 | −1.12588 | −0.562938 | − | 0.826499i | \(-0.690329\pi\) | ||||
−0.562938 | + | 0.826499i | \(0.690329\pi\) | |||||||
\(938\) | 16.9774 | 0.554332 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.66062 | 0.249862 | ||||||||
\(941\) | −12.9895 | −0.423445 | −0.211723 | − | 0.977330i | \(-0.567907\pi\) | ||||
−0.211723 | + | 0.977330i | \(0.567907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.61140 | 0.117604 | ||||||||
\(944\) | −3.21453 | −0.104624 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.87087 | −0.158366 | ||||||||
\(947\) | 1.02790 | 0.0334022 | 0.0167011 | − | 0.999861i | \(-0.494684\pi\) | ||||
0.0167011 | + | 0.999861i | \(0.494684\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −90.3773 | −2.93377 | ||||||||
\(950\) | 22.1108 | 0.717367 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.80072 | 0.220413 | ||||||||
\(953\) | 55.1750 | 1.78729 | 0.893647 | − | 0.448770i | \(-0.148138\pi\) | ||||
0.893647 | + | 0.448770i | \(0.148138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.578849 | 0.0187311 | ||||||||
\(956\) | 14.8861 | 0.481451 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.4305 | 0.595463 | ||||||||
\(959\) | 11.2243 | 0.362452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.2181 | 0.329615 | ||||||||
\(962\) | −60.3952 | −1.94722 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.70313 | 0.0548541 | ||||||||
\(965\) | −9.50442 | −0.305958 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.2258 | −1.77594 | −0.887971 | − | 0.459899i | \(-0.847886\pi\) | ||||
−0.887971 | + | 0.459899i | \(0.847886\pi\) | |||||||
\(968\) | 0.885329 | 0.0284556 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.45731 | −0.143115 | ||||||||
\(971\) | 52.7978 | 1.69436 | 0.847180 | − | 0.531305i | \(-0.178298\pi\) | ||||
0.847180 | + | 0.531305i | \(0.178298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.74100 | 0.312282 | ||||||||
\(974\) | 10.4137 | 0.333677 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.85140 | 0.187299 | ||||||||
\(977\) | 24.8695 | 0.795647 | 0.397824 | − | 0.917462i | \(-0.369766\pi\) | ||||
0.397824 | + | 0.917462i | \(0.369766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0931 | −0.450419 | ||||||||
\(980\) | 2.78770 | 0.0890497 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.7037 | 0.756417 | ||||||||
\(983\) | −29.7887 | −0.950111 | −0.475056 | − | 0.879956i | \(-0.657572\pi\) | ||||
−0.475056 | + | 0.879956i | \(0.657572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4044 | 0.395238 | ||||||||
\(986\) | −47.4594 | −1.51142 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.7145 | −0.913530 | ||||||||
\(989\) | −1.63767 | −0.0520748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.9480 | 0.506604 | 0.253302 | − | 0.967387i | \(-0.418483\pi\) | ||||
0.253302 | + | 0.967387i | \(0.418483\pi\) | |||||||
\(992\) | 6.42013 | 0.203839 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.9597 | 0.728237 | ||||||||
\(995\) | 3.18097 | 0.100843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.9344 | 0.821352 | 0.410676 | − | 0.911781i | \(-0.365293\pi\) | ||||
0.410676 | + | 0.911781i | \(0.365293\pi\) | |||||||
\(998\) | 24.2061 | 0.766231 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4014.2.a.x.1.3 | ✓ | 8 | |
3.2 | odd | 2 | 4014.2.a.y.1.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.a.x.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4014.2.a.y.1.6 | yes | 8 | 3.2 | odd | 2 |