Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, 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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} - 6230 x^{4} + 1488 x^{3} + 4720 x^{2} - 1440 x - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.49302\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-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 | ||||||||
\(3\) | 1.49302 | 0.861998 | 0.430999 | − | 0.902352i | \(-0.358161\pi\) | ||||
0.430999 | + | 0.902352i | \(0.358161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.02737 | 0.459453 | 0.229727 | − | 0.973255i | \(-0.426217\pi\) | ||||
0.229727 | + | 0.973255i | \(0.426217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.87698 | 1.46536 | 0.732681 | − | 0.680573i | \(-0.238269\pi\) | ||||
0.732681 | + | 0.680573i | \(0.238269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.770878 | −0.256959 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.61496 | −1.39146 | −0.695732 | − | 0.718301i | \(-0.744920\pi\) | ||||
−0.695732 | + | 0.718301i | \(0.744920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.62211 | −1.28194 | −0.640971 | − | 0.767565i | \(-0.721468\pi\) | ||||
−0.640971 | + | 0.767565i | \(0.721468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53389 | 0.396048 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47220 | 0.599596 | 0.299798 | − | 0.954003i | \(-0.403081\pi\) | ||||
0.299798 | + | 0.954003i | \(0.403081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.75700 | −1.77958 | −0.889789 | − | 0.456371i | \(-0.849149\pi\) | ||||
−0.889789 | + | 0.456371i | \(0.849149\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.78843 | 1.26314 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.50449 | 0.522221 | 0.261111 | − | 0.965309i | \(-0.415911\pi\) | ||||
0.261111 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94451 | −0.788903 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63001 | −1.08350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.13533 | −0.767911 | −0.383955 | − | 0.923352i | \(-0.625438\pi\) | ||||
−0.383955 | + | 0.923352i | \(0.625438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.95319 | 0.350804 | 0.175402 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175402 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.89025 | −1.19944 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.98309 | 0.673265 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50215 | −0.246951 | −0.123476 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123476 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.90092 | −1.10503 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.64140 | 1.03721 | 0.518606 | − | 0.855013i | \(-0.326451\pi\) | ||||
0.518606 | + | 0.855013i | \(0.326451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.59172 | 0.547732 | 0.273866 | − | 0.961768i | \(-0.411697\pi\) | ||||
0.273866 | + | 0.961768i | \(0.411697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.791976 | −0.118061 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.03098 | 1.14728 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.69105 | 0.516851 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4271 | −1.43227 | −0.716134 | − | 0.697963i | \(-0.754090\pi\) | ||||
−0.716134 | + | 0.697963i | \(0.754090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.74127 | −0.639312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.5814 | −1.53399 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.25042 | −0.683547 | −0.341773 | − | 0.939782i | \(-0.611028\pi\) | ||||
−0.341773 | + | 0.939782i | \(0.611028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7169 | −1.75627 | −0.878136 | − | 0.478412i | \(-0.841213\pi\) | ||||
−0.878136 | + | 0.478412i | \(0.841213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.98868 | −0.376538 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.74861 | −0.588992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.4380 | 1.88605 | 0.943023 | − | 0.332727i | \(-0.107969\pi\) | ||||
0.943023 | + | 0.332727i | \(0.107969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.73926 | 0.450154 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.38702 | −0.758000 | −0.379000 | − | 0.925397i | \(-0.623732\pi\) | ||||
−0.379000 | + | 0.925397i | \(0.623732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.34043 | 0.273927 | 0.136963 | − | 0.990576i | \(-0.456266\pi\) | ||||
0.136963 | + | 0.990576i | \(0.456266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.88926 | −0.680033 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.8921 | −2.03900 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0550 | −1.69382 | −0.846911 | − | 0.531735i | \(-0.821540\pi\) | ||||
−0.846911 | + | 0.531735i | \(0.821540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.09311 | −0.677012 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.24845 | 0.246799 | 0.123399 | − | 0.992357i | \(-0.460620\pi\) | ||||
0.123399 | + | 0.992357i | \(0.460620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.53986 | 0.275486 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.17414 | −0.661937 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.54414 | −0.799678 | −0.399839 | − | 0.916585i | \(-0.630934\pi\) | ||||
−0.399839 | + | 0.916585i | \(0.630934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.9198 | −1.87851 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.91616 | 0.302392 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.96930 | −0.817633 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.03188 | −0.307841 | −0.153921 | − | 0.988083i | \(-0.549190\pi\) | ||||
−0.153921 | + | 0.988083i | \(0.549190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.55757 | 0.357550 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.98951 | 0.993993 | 0.496997 | − | 0.867752i | \(-0.334436\pi\) | ||||
0.496997 | + | 0.867752i | \(0.334436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.03376 | −0.101859 | −0.0509296 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509296 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.94685 | 0.580353 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1575 | 0.981963 | 0.490982 | − | 0.871170i | \(-0.336638\pi\) | ||||
0.490982 | + | 0.871170i | \(0.336638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8459 | 1.51776 | 0.758880 | − | 0.651230i | \(-0.225747\pi\) | ||||
0.758880 | + | 0.651230i | \(0.225747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.24274 | −0.212871 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2294 | −1.33859 | −0.669293 | − | 0.742999i | \(-0.733403\pi\) | ||||
−0.669293 | + | 0.742999i | \(0.733403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.57303 | 0.239936 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.56308 | 0.329407 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.58467 | 0.878625 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2979 | 0.936172 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.91577 | 0.894075 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.18931 | −0.821917 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.4036 | −1.63305 | −0.816527 | − | 0.577308i | \(-0.804103\pi\) | ||||
−0.816527 | + | 0.577308i | \(0.804103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.36253 | 0.472144 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.07558 | −0.705567 | −0.352783 | − | 0.935705i | \(-0.614765\pi\) | ||||
−0.352783 | + | 0.935705i | \(0.614765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.0738 | −2.60773 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.78410 | −0.497816 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6236 | 1.07850 | 0.539252 | − | 0.842144i | \(-0.318707\pi\) | ||||
0.539252 | + | 0.842144i | \(0.318707\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.6425 | −1.92051 | −0.960257 | − | 0.279117i | \(-0.909958\pi\) | ||||
−0.960257 | + | 0.279117i | \(0.909958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.49302 | 0.125735 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.3309 | 1.78378 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.24850 | −0.352819 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.9904 | 0.988956 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.57979 | 0.129422 | 0.0647109 | − | 0.997904i | \(-0.479387\pi\) | ||||
0.0647109 | + | 0.997904i | \(0.479387\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.38147 | −0.356559 | −0.178279 | − | 0.983980i | \(-0.557053\pi\) | ||||
−0.178279 | + | 0.983980i | \(0.557053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.90576 | −0.154072 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00665 | 0.161178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4266 | 1.07156 | 0.535779 | − | 0.844358i | \(-0.320018\pi\) | ||||
0.535779 | + | 0.844358i | \(0.320018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.5679 | −1.23461 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.70984 | 0.765243 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.08897 | −0.633577 | −0.316789 | − | 0.948496i | \(-0.602605\pi\) | ||||
−0.316789 | + | 0.948496i | \(0.602605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.07883 | −0.551086 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.35268 | −0.336820 | −0.168410 | − | 0.985717i | \(-0.553863\pi\) | ||||
−0.168410 | + | 0.985717i | \(0.553863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.36390 | 0.643377 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.97971 | 0.457279 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.92311 | 0.374297 | 0.187149 | − | 0.982332i | \(-0.440075\pi\) | ||||
0.187149 | + | 0.982332i | \(0.440075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.2928 | −1.15603 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.83901 | −0.589216 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0083 | −1.19652 | −0.598260 | − | 0.801302i | \(-0.704141\pi\) | ||||
−0.598260 | + | 0.801302i | \(0.704141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8600 | 0.881550 | 0.440775 | − | 0.897618i | \(-0.354704\pi\) | ||||
0.440775 | + | 0.897618i | \(0.354704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.4797 | −1.51390 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.54326 | −0.113462 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.4091 | −0.834316 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.8275 | −1.58771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.29342 | −0.0935889 | −0.0467944 | − | 0.998905i | \(-0.514901\pi\) | ||||
−0.0467944 | + | 0.998905i | \(0.514901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.1614 | 0.947377 | 0.473688 | − | 0.880693i | \(-0.342922\pi\) | ||||
0.473688 | + | 0.880693i | \(0.342922\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.08979 | −0.507710 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.86306 | −0.631467 | −0.315734 | − | 0.948848i | \(-0.602251\pi\) | ||||
−0.315734 | + | 0.948848i | \(0.602251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7508 | 0.974772 | 0.487386 | − | 0.873187i | \(-0.337950\pi\) | ||||
0.487386 | + | 0.873187i | \(0.337950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.0492 | 1.62577 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0326 | −1.12527 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.82316 | 0.476550 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.93065 | −0.134190 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 35.7983 | 2.47622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.0838 | 1.93337 | 0.966683 | − | 0.255975i | \(-0.0823964\pi\) | ||||
0.966683 | + | 0.255975i | \(0.0823964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.53598 | −0.653395 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.69002 | 0.251657 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.57249 | 0.514054 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.49432 | 0.236124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4268 | −0.768648 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3016 | −0.957706 | −0.478853 | − | 0.877895i | \(-0.658947\pi\) | ||||
−0.478853 | + | 0.877895i | \(0.658947\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.04074 | 0.202716 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5207 | −0.764655 | −0.382328 | − | 0.924027i | \(-0.624877\pi\) | ||||
−0.382328 | + | 0.924027i | \(0.624877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.44069 | 0.293449 | 0.146725 | − | 0.989177i | \(-0.453127\pi\) | ||||
0.146725 | + | 0.989177i | \(0.453127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.7134 | −1.75761 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.0449 | 1.24767 | 0.623835 | − | 0.781556i | \(-0.285574\pi\) | ||||
0.623835 | + | 0.781556i | \(0.285574\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02737 | 0.0670181 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.4775 | −1.46007 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.40019 | 0.284625 | 0.142312 | − | 0.989822i | \(-0.454546\pi\) | ||||
0.142312 | + | 0.989822i | \(0.454546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.39750 | 0.154437 | 0.0772183 | − | 0.997014i | \(-0.475396\pi\) | ||||
0.0772183 | + | 0.997014i | \(0.475396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79287 | 0.499913 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.25077 | 0.527123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.8537 | 2.28132 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.35698 | 0.212740 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.8883 | 1.94965 | 0.974827 | − | 0.222965i | \(-0.0715734\pi\) | ||||
0.974827 | + | 0.222965i | \(0.0715734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5581 | −0.726652 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.79207 | 0.237469 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3108 | 1.07982 | 0.539910 | − | 0.841723i | \(-0.318458\pi\) | ||||
0.539910 | + | 0.841723i | \(0.318458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.82379 | −0.361873 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.18783 | 0.197322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.8884 | −0.671410 | −0.335705 | − | 0.941967i | \(-0.608975\pi\) | ||||
−0.335705 | + | 0.941967i | \(0.608975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7124 | −0.658060 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.2636 | −0.689321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00374 | −0.183141 | −0.0915707 | − | 0.995799i | \(-0.529189\pi\) | ||||
−0.0915707 | + | 0.995799i | \(0.529189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3228 | −1.35601 | −0.678006 | − | 0.735056i | \(-0.737156\pi\) | ||||
−0.678006 | + | 0.735056i | \(0.737156\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.7547 | −1.61927 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.2038 | 1.09773 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.97377 | 0.539182 | 0.269591 | − | 0.962975i | \(-0.413112\pi\) | ||||
0.269591 | + | 0.962975i | \(0.413112\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50567 | −0.0901423 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.000716445 0 | 4.27395e−5 0 | 2.13698e−5 | − | 1.00000i | \(-0.499993\pi\) | ||||
2.13698e−5 | 1.00000i | \(0.499993\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.30795 | 0.493857 | 0.246928 | − | 0.969034i | \(-0.420579\pi\) | ||||
0.246928 | + | 0.969034i | \(0.420579\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.8984 | −0.704798 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.7486 | 1.51989 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8882 | −0.640484 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.52668 | −0.265358 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.58037 | 0.442850 | 0.221425 | − | 0.975177i | \(-0.428929\pi\) | ||||
0.221425 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.39412 | −0.314058 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.9823 | 1.50765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5760 | −0.669458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.9250 | 0.802626 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.9146 | 0.856820 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.0923 | −0.806924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.4123 | −0.822556 | −0.411278 | − | 0.911510i | \(-0.634917\pi\) | ||||
−0.411278 | + | 0.911510i | \(0.634917\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.54343 | −0.0878024 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6197 | 1.33935 | 0.669676 | − | 0.742654i | \(-0.266433\pi\) | ||||
0.669676 | + | 0.742654i | \(0.266433\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6649 | 0.602813 | 0.301407 | − | 0.953496i | \(-0.402544\pi\) | ||||
0.301407 | + | 0.953496i | \(0.402544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.07047 | −0.173002 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.8725 | −1.56548 | −0.782739 | − | 0.622350i | \(-0.786178\pi\) | ||||
−0.782739 | + | 0.622350i | \(0.786178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0844 | 1.06852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.1654 | 0.846451 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.1769 | −1.06703 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.2320 | 1.01133 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.6583 | 1.30831 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.87698 | 0.213745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.0287 | 1.48563 | 0.742815 | − | 0.669496i | \(-0.233490\pi\) | ||||
0.742815 | + | 0.669496i | \(0.233490\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.15797 | 0.0634564 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8605 | 0.866550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7556 | 0.803788 | 0.401894 | − | 0.915686i | \(-0.368352\pi\) | ||||
0.401894 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.2448 | −1.15386 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.01391 | −0.488131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.99709 | 0.215823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.84160 | 0.206825 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.30950 | −0.0702977 | −0.0351489 | − | 0.999382i | \(-0.511191\pi\) | ||||
−0.0351489 | + | 0.999382i | \(0.511191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.680695 | 0.0364368 | 0.0182184 | − | 0.999834i | \(-0.494201\pi\) | ||||
0.0182184 | + | 0.999834i | \(0.494201\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.0225 | 1.38898 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0211 | −0.639818 | −0.319909 | − | 0.947448i | \(-0.603652\pi\) | ||||
−0.319909 | + | 0.947448i | \(0.603652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.56183 | −0.348266 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.3101 | 0.757373 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.1639 | −1.32810 | −0.664051 | − | 0.747687i | \(-0.731164\pi\) | ||||
−0.664051 | + | 0.747687i | \(0.731164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.1711 | 2.16690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3750 | 0.806978 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40449 | 0.125857 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.22700 | −0.325047 | −0.162523 | − | 0.986705i | \(-0.551963\pi\) | ||||
−0.162523 | + | 0.986705i | \(0.551963\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.11971 | −0.266521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.4256 | −2.09879 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.3793 | 1.93543 | 0.967713 | − | 0.252053i | \(-0.0811059\pi\) | ||||
0.967713 | + | 0.252053i | \(0.0811059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7199 | −0.708491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.1139 | 0.984417 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3685 | −0.892160 | −0.446080 | − | 0.894993i | \(-0.647180\pi\) | ||||
−0.446080 | + | 0.894993i | \(0.647180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.4770 | −1.40769 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.4596 | −1.45422 | −0.727109 | − | 0.686522i | \(-0.759136\pi\) | ||||
−0.727109 | + | 0.686522i | \(0.759136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.3818 | −0.936823 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.76878 | −0.140745 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.0883 | −1.37343 | −0.686714 | − | 0.726927i | \(-0.740948\pi\) | ||||
−0.686714 | + | 0.726927i | \(0.740948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.19159 | 0.313122 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0570 | −0.608197 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4670 | −0.778231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1195 | 0.658450 | 0.329225 | − | 0.944252i | \(-0.393213\pi\) | ||||
0.329225 | + | 0.944252i | \(0.393213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44.9009 | −2.24785 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.8177 | −1.68878 | −0.844388 | − | 0.535732i | \(-0.820036\pi\) | ||||
−0.844388 | + | 0.535732i | \(0.820036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.02787 | −0.449710 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.25987 | −0.311055 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.93235 | 0.343624 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5302 | −0.767918 | −0.383959 | − | 0.923350i | \(-0.625440\pi\) | ||||
−0.383959 | + | 0.923350i | \(0.625440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.8473 | 0.929669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.3558 | −1.00164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.30998 | 0.113393 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.8058 | −1.65548 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3311 | −1.53062 | −0.765312 | − | 0.643660i | \(-0.777415\pi\) | ||||
−0.765312 | + | 0.643660i | \(0.777415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.17748 | −0.154861 | −0.0774305 | − | 0.996998i | \(-0.524672\pi\) | ||||
−0.0774305 | + | 0.996998i | \(0.524672\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.770878 | −0.0374814 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.75162 | −0.473023 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −53.1802 | −2.57357 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.8475 | 1.53761 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6392 | −1.33133 | −0.665666 | − | 0.746249i | \(-0.731853\pi\) | ||||
−0.665666 | + | 0.746249i | \(0.731853\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.8153 | 1.52894 | 0.764472 | − | 0.644657i | \(-0.223000\pi\) | ||||
0.764472 | + | 0.644657i | \(0.223000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.34312 | −0.304129 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.4273 | −0.929334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6534 | 0.603912 | 0.301956 | − | 0.953322i | \(-0.402361\pi\) | ||||
0.301956 | + | 0.953322i | \(0.402361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.19091 | −0.294805 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.8285 | −0.847060 | −0.423530 | − | 0.905882i | \(-0.639209\pi\) | ||||
−0.423530 | + | 0.905882i | \(0.639209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.75062 | −0.367414 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.35867 | 0.111561 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.0083 | 0.897055 | 0.448527 | − | 0.893769i | \(-0.351949\pi\) | ||||
0.448527 | + | 0.893769i | \(0.351949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.6498 | −1.44324 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.54164 | −0.307353 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.4103 | −0.863087 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.57180 | 0.354194 | 0.177097 | − | 0.984193i | \(-0.443329\pi\) | ||||
0.177097 | + | 0.984193i | \(0.443329\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.9185 | −0.649660 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.04187 | 0.0950995 | 0.0475498 | − | 0.998869i | \(-0.484859\pi\) | ||||
0.0475498 | + | 0.998869i | \(0.484859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.29998 | −0.199837 | −0.0999184 | − | 0.994996i | \(-0.531858\pi\) | ||||
−0.0999184 | + | 0.994996i | \(0.531858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.99598 | 0.138935 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6015 | 1.04587 | 0.522936 | − | 0.852372i | \(-0.324837\pi\) | ||||
0.522936 | + | 0.852372i | \(0.324837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 59.8527 | 2.76374 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0462 | 0.923681 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.5757 | −0.762150 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.5976 | 1.40391 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.03800 | 0.368035 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.92055 | −0.179134 | −0.0895672 | − | 0.995981i | \(-0.528548\pi\) | ||||
−0.0895672 | + | 0.995981i | \(0.528548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.94308 | 0.316577 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.4970 | 0.659638 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.11486 | −0.141439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6655 | 0.709870 | 0.354935 | − | 0.934891i | \(-0.384503\pi\) | ||||
0.354935 | + | 0.934891i | \(0.384503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0770 | −0.546142 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6893 | 0.708046 | 0.354023 | − | 0.935237i | \(-0.384813\pi\) | ||||
0.354023 | + | 0.935237i | \(0.384813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2233 | −0.460436 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.65494 | 0.164277 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.7624 | −1.11074 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.5705 | −1.05516 | −0.527581 | − | 0.849505i | \(-0.676901\pi\) | ||||
−0.527581 | + | 0.849505i | \(0.676901\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.49866 | −0.290339 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.2356 | −1.66025 | −0.830126 | − | 0.557576i | \(-0.811731\pi\) | ||||
−0.830126 | + | 0.557576i | \(0.811731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2629 | 0.456693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.4875 | 0.554589 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.78382 | 0.389336 | 0.194668 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194668 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.07381 | 0.401402 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 43.6720 | 1.92817 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.06205 | −0.0467995 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.61496 | −0.202966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.35033 | 0.322644 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0774 | 0.791987 | 0.395994 | − | 0.918253i | \(-0.370400\pi\) | ||||
0.395994 | + | 0.918253i | \(0.370400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3059 | −0.756735 | −0.378368 | − | 0.925655i | \(-0.623515\pi\) | ||||
−0.378368 | + | 0.925655i | \(0.623515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.8325 | −0.996493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.82868 | 0.210341 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7275 | −0.727285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.04744 | 0.175644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.6973 | −1.32965 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4355 | 0.451166 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.9009 | −1.03140 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.0627 | −1.59640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3028 | 1.13085 | 0.565423 | − | 0.824801i | \(-0.308713\pi\) | ||||
0.565423 | + | 0.824801i | \(0.308713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.7073 | 0.759894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.2796 | 0.697340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.26305 | 0.267789 | 0.133894 | − | 0.990996i | \(-0.457252\pi\) | ||||
0.133894 | + | 0.990996i | \(0.457252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5741 | 0.451290 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.0777 | 1.36656 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −58.3680 | −2.48206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.30412 | −0.0978044 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.5741 | −0.998868 | −0.499434 | − | 0.866352i | \(-0.666459\pi\) | ||||
−0.499434 | + | 0.866352i | \(0.666459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.6013 | −0.702161 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0341 | −0.719179 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1171 | 0.637110 | 0.318555 | − | 0.947904i | \(-0.396802\pi\) | ||||
0.318555 | + | 0.947904i | \(0.396802\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.6188 | −0.615017 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.6229 | −0.992068 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.8408 | 1.58637 | 0.793184 | − | 0.608982i | \(-0.208422\pi\) | ||||
0.793184 | + | 0.608982i | \(0.208422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5876 | 0.987110 | 0.493555 | − | 0.869715i | \(-0.335697\pi\) | ||||
0.493555 | + | 0.869715i | \(0.335697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.93111 | −0.0806734 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.87898 | −0.411982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0045 | −0.416492 | −0.208246 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208246 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6503 | 0.816637 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.71718 | 0.361650 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.1206 | 1.99295 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.66060 | 0.151347 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.48325 | −0.102495 | −0.0512473 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512473 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.1509 | −0.624283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2328 | −0.544323 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.16410 | −0.253129 | −0.126565 | − | 0.991958i | \(-0.540395\pi\) | ||||
−0.126565 | + | 0.991958i | \(0.540395\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.84698 | 0.403687 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.5304 | 0.840251 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.4563 | 1.89815 | 0.949077 | − | 0.315044i | \(-0.102019\pi\) | ||||
0.949077 | + | 0.315044i | \(0.102019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.0275 | 1.30643 | 0.653215 | − | 0.757172i | \(-0.273420\pi\) | ||||
0.653215 | + | 0.757172i | \(0.273420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.9008 | −0.484637 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.5797 | 0.430127 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.7903 | −1.69621 | −0.848107 | − | 0.529825i | \(-0.822258\pi\) | ||||
−0.848107 | + | 0.529825i | \(0.822258\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.9370 | −0.969977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.62211 | −0.186991 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.2969 | −0.981343 | −0.490672 | − | 0.871345i | \(-0.663249\pi\) | ||||
−0.490672 | + | 0.871345i | \(0.663249\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.1871 | 0.410785 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.6303 | 1.91752 | 0.958761 | − | 0.284212i | \(-0.0917319\pi\) | ||||
0.958761 | + | 0.284212i | \(0.0917319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.1133 | −1.12997 | −0.564984 | − | 0.825102i | \(-0.691118\pi\) | ||||
−0.564984 | + | 0.825102i | \(0.691118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.1003 | −0.565825 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.2485 | −1.17182 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.2818 | 0.411271 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 53.4477 | 2.13450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.71360 | −0.148071 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0142 | −0.478277 | −0.239138 | − | 0.970986i | \(-0.576865\pi\) | ||||
−0.239138 | + | 0.970986i | \(0.576865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.9298 | 1.66656 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.9072 | −0.750311 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.1201 | −1.47075 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.92362 | 0.194775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.1072 | −0.952175 | −0.476088 | − | 0.879398i | \(-0.657945\pi\) | ||||
−0.476088 | + | 0.879398i | \(0.657945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8324 | −0.466623 | −0.233312 | − | 0.972402i | \(-0.574956\pi\) | ||||
−0.233312 | + | 0.972402i | \(0.574956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.50929 | 0.216928 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.4896 | −1.23798 | −0.618991 | − | 0.785398i | \(-0.712458\pi\) | ||||
−0.618991 | + | 0.785398i | \(0.712458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.2305 | 0.951131 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3059 | 0.443114 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.8703 | −0.855849 | −0.427925 | − | 0.903814i | \(-0.640755\pi\) | ||||
−0.427925 | + | 0.903814i | \(0.640755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.29659 | −0.324175 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.80419 | −0.0703881 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.6467 | −0.687418 | −0.343709 | − | 0.939076i | \(-0.611683\pi\) | ||||
−0.343709 | + | 0.939076i | \(0.611683\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0644 | 0.780415 | 0.390208 | − | 0.920727i | \(-0.372403\pi\) | ||||
0.390208 | + | 0.920727i | \(0.372403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.0604 | −0.662573 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30.8968 | −1.19813 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3569 | −0.401019 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.3526 | −0.825541 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 63.3031 | 2.44379 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −51.7534 | −1.99495 | −0.997474 | − | 0.0710349i | \(-0.977370\pi\) | ||||
−0.997474 | + | 0.0710349i | \(0.977370\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.2077 | 0.854774 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3687 | −0.859700 | −0.429850 | − | 0.902900i | \(-0.641433\pi\) | ||||
−0.429850 | + | 0.902900i | \(0.641433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.7546 | −0.451098 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.2007 | −0.659131 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.3522 | −0.740491 | −0.370245 | − | 0.928934i | \(-0.620726\pi\) | ||||
−0.370245 | + | 0.928934i | \(0.620726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9691 | 0.495522 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.63006 | 0.252953 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.1951 | 1.83609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.24792 | −0.161598 | −0.0807992 | − | 0.996730i | \(-0.525747\pi\) | ||||
−0.0807992 | + | 0.996730i | \(0.525747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.7926 | 0.523939 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.2622 | −0.882386 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4189 | 0.621908 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.4345 | 1.07549 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.6059 | −0.438349 | −0.219174 | − | 0.975686i | \(-0.570336\pi\) | ||||
−0.219174 | + | 0.975686i | \(0.570336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.6521 | 0.439469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.53389 | 0.0577695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.7291 | 1.45656 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3715 | 1.74152 | 0.870759 | − | 0.491711i | \(-0.163628\pi\) | ||||
0.870759 | + | 0.491711i | \(0.163628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6056 | 0.435243 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.89174 | 0.183197 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.9147 | 0.819562 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.56959 | 0.245346 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.77255 | −0.364455 | −0.182227 | − | 0.983256i | \(-0.558331\pi\) | ||||
−0.182227 | + | 0.983256i | \(0.558331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00786 | −0.149260 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.57953 | 0.133124 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.3119 | 0.605807 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.76248 | −0.287894 | −0.143947 | − | 0.989585i | \(-0.545980\pi\) | ||||
−0.143947 | + | 0.989585i | \(0.545980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9143 | 1.10794 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.87945 | 0.328418 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8115 | 1.21192 | 0.605961 | − | 0.795494i | \(-0.292789\pi\) | ||||
0.605961 | + | 0.795494i | \(0.292789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.3186 | 0.454379 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −71.2456 | −2.62437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9710 | −0.477146 | −0.238573 | − | 0.971125i | \(-0.576680\pi\) | ||||
−0.238573 | + | 0.971125i | \(0.576680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.5305 | 1.96649 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.8415 | −0.544483 | −0.272241 | − | 0.962229i | \(-0.587765\pi\) | ||||
−0.272241 | + | 0.962229i | \(0.587765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.62303 | 0.0594632 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.73328 | −0.0634173 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.3805 | 1.43893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.3413 | 1.76400 | 0.882000 | − | 0.471250i | \(-0.156197\pi\) | ||||
0.882000 | + | 0.471250i | \(0.156197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.1170 | 1.68060 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.50138 | −0.163822 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.4744 | −1.79818 | −0.899089 | − | 0.437767i | \(-0.855770\pi\) | ||||
−0.899089 | + | 0.437767i | \(0.855770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.2565 | −0.626373 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.9920 | −1.92096 | −0.960480 | − | 0.278350i | \(-0.910213\pi\) | ||||
−0.960480 | + | 0.278350i | \(0.910213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 61.4342 | 2.22407 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.95792 | −0.0707888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.2680 | 0.876268 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.5342 | −0.920786 | −0.460393 | − | 0.887715i | \(-0.652291\pi\) | ||||
−0.460393 | + | 0.887715i | \(0.652291\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.8455 | 0.930803 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0208 | 0.540260 | 0.270130 | − | 0.962824i | \(-0.412933\pi\) | ||||
0.270130 | + | 0.962824i | \(0.412933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.70440 | −0.276750 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.69506 | −0.311934 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.5174 | −1.84580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.4759 | 1.05473 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.2819 | 0.832029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7941 | 0.492331 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7354 | 0.739136 | 0.369568 | − | 0.929204i | \(-0.379506\pi\) | ||||
0.369568 | + | 0.929204i | \(0.379506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.2567 | −0.578754 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55.1670 | −1.96151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.4011 | 2.25144 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.9939 | −0.567247 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.5536 | −0.798890 | −0.399445 | − | 0.916757i | \(-0.630797\pi\) | ||||
−0.399445 | + | 0.916757i | \(0.630797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.47220 | 0.0874601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.81562 | 0.205485 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8010 | −0.381159 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.97559 | 0.351593 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.48466 | −0.157868 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.0902 | 1.09307 | 0.546537 | − | 0.837435i | \(-0.315946\pi\) | ||||
0.546537 | + | 0.837435i | \(0.315946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.3496 | 1.80313 | 0.901564 | − | 0.432647i | \(-0.142420\pi\) | ||||
0.901564 | + | 0.432647i | \(0.142420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.3285 | −1.16888 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.31035 | −0.291099 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.8610 | −0.974733 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.8140 | 0.482700 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.0087 | 1.60571 | 0.802857 | − | 0.596171i | \(-0.203312\pi\) | ||||
0.802857 | + | 0.596171i | \(0.203312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9780 | −0.487243 | −0.243622 | − | 0.969870i | \(-0.578336\pi\) | ||||
−0.243622 | + | 0.969870i | \(0.578336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 27.1787 | 0.946241 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.26566 | 0.252652 | 0.126326 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126326 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.19459 | 0.249878 | 0.124939 | − | 0.992164i | \(-0.460126\pi\) | ||||
0.124939 | + | 0.992164i | \(0.460126\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.3981 | 0.464774 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.8542 | 0.687906 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.47180 | −0.154753 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.9965 | −0.380095 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4530 | 0.360879 | 0.180439 | − | 0.983586i | \(-0.442248\pi\) | ||||
0.180439 | + | 0.983586i | \(0.442248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8991 | −0.410313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.00106967 | 3.68414e−5 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.59280 | 0.295601 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.9247 | 1.37183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.4040 | 0.425703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.76210 | −0.128963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.43910 | 0.0835131 | 0.0417566 | − | 0.999128i | \(-0.486705\pi\) | ||||
0.0417566 | + | 0.999128i | \(0.486705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.14336 | 0.210098 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.5827 | −1.35212 | −0.676060 | − | 0.736847i | \(-0.736314\pi\) | ||||
−0.676060 | + | 0.736847i | \(0.736314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.6196 | 1.38592 | 0.692962 | − | 0.720975i | \(-0.256306\pi\) | ||||
0.692962 | + | 0.720975i | \(0.256306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.4432 | 1.31014 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.4721 | −1.03728 | −0.518642 | − | 0.854992i | \(-0.673562\pi\) | ||||
−0.518642 | + | 0.854992i | \(0.673562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.05785 | 0.171972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.2564 | −0.552096 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.4783 | 2.35689 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −71.3559 | −2.41780 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.33721 | 0.0791027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.6268 | −1.20441 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.2267 | 1.32459 | 0.662295 | − | 0.749243i | \(-0.269583\pi\) | ||||
0.662295 | + | 0.749243i | \(0.269583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3177 | 0.381736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.4238 | 1.02500 | 0.512501 | − | 0.858687i | \(-0.328719\pi\) | ||||
0.512501 | + | 0.858687i | \(0.328719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.3525 | 1.02144 | 0.510721 | − | 0.859747i | \(-0.329379\pi\) | ||||
0.510721 | + | 0.859747i | \(0.329379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.05355 | −0.270717 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.20845 | −0.275613 | −0.137806 | − | 0.990459i | \(-0.544005\pi\) | ||||
−0.137806 | + | 0.990459i | \(0.544005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −71.3503 | −2.39301 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.1195 | 0.942038 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.75700 | −0.259578 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4465 | −0.549745 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.2833 | −0.577071 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.07709 | −0.269386 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.7778 | −0.858783 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.7904 | 0.691862 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.1846 | 0.405031 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.22770 | 0.306401 | 0.153200 | − | 0.988195i | \(-0.451042\pi\) | ||||
0.153200 | + | 0.988195i | \(0.451042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.70069 | −0.255416 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.7976 | −0.589660 | −0.294830 | − | 0.955550i | \(-0.595263\pi\) | ||||
−0.294830 | + | 0.955550i | \(0.595263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3765 | −0.343412 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.0402 | −0.695567 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.3089 | −1.03391 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.1369 | 1.65386 | 0.826931 | − | 0.562303i | \(-0.190085\pi\) | ||||
0.826931 | + | 0.562303i | \(0.190085\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.5180 | −0.709041 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5215 | 0.971713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.92523 | 0.194821 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.796901 | 0.0261737 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.7399 | −1.73034 | −0.865170 | − | 0.501479i | \(-0.832790\pi\) | ||||
−0.865170 | + | 0.501479i | \(0.832790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −62.2963 | −2.04168 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.2648 | 1.15452 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.7214 | −0.383329 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7772 | −0.450080 | −0.225040 | − | 0.974349i | \(-0.572251\pi\) | ||||
−0.225040 | + | 0.974349i | \(0.572251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9229 | 0.519624 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5400 | 0.734784 | 0.367392 | − | 0.930066i | \(-0.380251\pi\) | ||||
0.367392 | + | 0.930066i | \(0.380251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.6333 | 0.541654 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.4248 | −0.729480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.7961 | −1.87812 | −0.939060 | − | 0.343753i | \(-0.888302\pi\) | ||||
−0.939060 | + | 0.343753i | \(0.888302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8177 | −0.351158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.6144 | −1.34944 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.1887 | −0.653977 | −0.326989 | − | 0.945028i | \(-0.606034\pi\) | ||||
−0.326989 | + | 0.945028i | \(0.606034\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.32882 | −0.0429997 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.4934 | 0.921062 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.9413 | 1.58040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1850 | −0.876937 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.83020 | −0.252325 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.5216 | 0.435275 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.1154 | −1.00060 | −0.500301 | − | 0.865851i | \(-0.666777\pi\) | ||||
−0.500301 | + | 0.865851i | \(0.666777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.6315 | −0.919777 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4477 | −0.880840 | −0.440420 | − | 0.897792i | \(-0.645170\pi\) | ||||
−0.440420 | + | 0.897792i | \(0.645170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −87.7846 | −2.81425 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.2208 | 0.871763 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.65464 | −0.116922 | −0.0584611 | − | 0.998290i | \(-0.518619\pi\) | ||||
−0.0584611 | + | 0.998290i | \(0.518619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.8160 | 1.11272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2152 | −0.390003 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.0031 | −0.382841 | −0.191420 | − | 0.981508i | \(-0.561309\pi\) | ||||
−0.191420 | + | 0.981508i | \(0.561309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.10563 | −0.290129 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.78843 | 0.184248 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.99542 | 0.286038 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.9133 | −1.10906 | −0.554529 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554529 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.3545 | 1.28061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1272 | 0.447862 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.2808 | −1.21236 | −0.606182 | − | 0.795326i | \(-0.707300\pi\) | ||||
−0.606182 | + | 0.795326i | \(0.707300\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.45710 | 0.267571 |
(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 | 6016.2.a.m.1.10 | ✓ | 13 | |
4.3 | odd | 2 | 6016.2.a.o.1.4 | yes | 13 | ||
8.3 | odd | 2 | 6016.2.a.n.1.10 | yes | 13 | ||
8.5 | even | 2 | 6016.2.a.p.1.4 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.10 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.n.1.10 | yes | 13 | 8.3 | odd | 2 | ||
6016.2.a.o.1.4 | yes | 13 | 4.3 | odd | 2 | ||
6016.2.a.p.1.4 | yes | 13 | 8.5 | even | 2 |