Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2672,2,Mod(1,2672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2672, 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("2672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2672 = 2^{4} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2672.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: | \(21.3360274201\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 668) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2672.1 |
$q$-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 | ||||||||
\(3\) | 1.30278 | 0.752158 | 0.376079 | − | 0.926588i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.302776 | 0.114438 | 0.0572192 | − | 0.998362i | \(-0.481777\pi\) | ||||
0.0572192 | + | 0.998362i | \(0.481777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.69722 | 0.748075 | 0.374038 | − | 0.927413i | \(-0.377973\pi\) | ||||
0.374038 | + | 0.927413i | \(0.377973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.90833 | −1.00913 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.30278 | 0.558505 | 0.279253 | − | 0.960218i | \(-0.409913\pi\) | ||||
0.279253 | + | 0.960218i | \(0.409913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.394449 | 0.0860758 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.30278 | 0.480162 | 0.240081 | − | 0.970753i | \(-0.422826\pi\) | ||||
0.240081 | + | 0.970753i | \(0.422826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60555 | −1.07879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.60555 | 1.41232 | 0.706158 | − | 0.708055i | \(-0.250427\pi\) | ||||
0.706158 | + | 0.708055i | \(0.250427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.60555 | −1.18639 | −0.593196 | − | 0.805058i | \(-0.702134\pi\) | ||||
−0.593196 | + | 0.805058i | \(0.702134\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.908327 | −0.153535 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.394449 | 0.0648470 | 0.0324235 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324235 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.51388 | 0.562671 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.21110 | −0.970011 | −0.485006 | − | 0.874511i | \(-0.661182\pi\) | ||||
−0.485006 | + | 0.874511i | \(0.661182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.60555 | −1.46483 | −0.732416 | − | 0.680857i | \(-0.761608\pi\) | ||||
−0.732416 | + | 0.680857i | \(0.761608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.90833 | 0.582619 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.60555 | −0.234194 | −0.117097 | − | 0.993120i | \(-0.537359\pi\) | ||||
−0.117097 | + | 0.993120i | \(0.537359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90833 | −0.986904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.60555 | −0.632621 | −0.316311 | − | 0.948656i | \(-0.602444\pi\) | ||||
−0.316311 | + | 0.948656i | \(0.602444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.60555 | −0.345114 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.81665 | −1.01764 | −0.508821 | − | 0.860872i | \(-0.669918\pi\) | ||||
−0.508821 | + | 0.860872i | \(0.669918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.81665 | 0.872783 | 0.436392 | − | 0.899757i | \(-0.356256\pi\) | ||||
0.436392 | + | 0.899757i | \(0.356256\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.394449 | −0.0496959 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.09167 | −1.00365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.21110 | −1.00315 | −0.501573 | − | 0.865115i | \(-0.667245\pi\) | ||||
−0.501573 | + | 0.865115i | \(0.667245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.90833 | −0.463833 | −0.231917 | − | 0.972736i | \(-0.574500\pi\) | ||||
−0.231917 | + | 0.972736i | \(0.574500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.09167 | −0.361853 | −0.180926 | − | 0.983497i | \(-0.557910\pi\) | ||||
−0.180926 | + | 0.983497i | \(0.557910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.21110 | 0.601726 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.39445 | −0.719432 | −0.359716 | − | 0.933062i | \(-0.617126\pi\) | ||||
−0.359716 | + | 0.933062i | \(0.617126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.60555 | 0.176232 | 0.0881161 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881161 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90833 | −0.749313 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.90833 | 1.06228 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8167 | −1.46456 | −0.732281 | − | 0.681002i | \(-0.761544\pi\) | ||||
−0.732281 | + | 0.681002i | \(0.761544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.816654 | 0.0856086 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.60555 | −0.892354 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.51388 | 0.458315 | 0.229157 | − | 0.973389i | \(-0.426403\pi\) | ||||
0.229157 | + | 0.973389i | \(0.426403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8167 | −1.07630 | −0.538149 | − | 0.842850i | \(-0.680876\pi\) | ||||
−0.538149 | + | 0.842850i | \(0.680876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.30278 | 0.325432 | 0.162716 | − | 0.986673i | \(-0.447975\pi\) | ||||
0.162716 | + | 0.986673i | \(0.447975\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.18335 | −0.115483 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.60555 | −0.735256 | −0.367628 | − | 0.929973i | \(-0.619830\pi\) | ||||
−0.367628 | + | 0.929973i | \(0.619830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.513878 | 0.0487752 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.42221 | 0.886366 | 0.443183 | − | 0.896431i | \(-0.353849\pi\) | ||||
0.443183 | + | 0.896431i | \(0.353849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.90833 | −0.644205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.51388 | −0.324858 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.697224 | 0.0639145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.09167 | −0.729602 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2111 | −1.26103 | −0.630516 | − | 0.776176i | \(-0.717157\pi\) | ||||
−0.630516 | + | 0.776176i | \(0.717157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.5139 | −1.10179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0278 | 1.74983 | 0.874917 | − | 0.484274i | \(-0.160916\pi\) | ||||
0.874917 | + | 0.484274i | \(0.160916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.605551 | −0.0525080 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.8167 | 1.44735 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.78890 | −0.238272 | −0.119136 | − | 0.992878i | \(-0.538012\pi\) | ||||
−0.119136 | + | 0.992878i | \(0.538012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.90833 | −0.501138 | −0.250569 | − | 0.968099i | \(-0.580618\pi\) | ||||
−0.250569 | + | 0.968099i | \(0.580618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09167 | −0.176151 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.8167 | −1.89482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.00000 | −0.742307 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5139 | 1.43479 | 0.717396 | − | 0.696665i | \(-0.245334\pi\) | ||||
0.717396 | + | 0.696665i | \(0.245334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5139 | −1.58802 | −0.794008 | − | 0.607907i | \(-0.792009\pi\) | ||||
−0.794008 | + | 0.607907i | \(0.792009\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.8167 | 1.59171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.816654 | 0.0651761 | 0.0325880 | − | 0.999469i | \(-0.489625\pi\) | ||||
0.0325880 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.697224 | 0.0549490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.39445 | 0.422526 | 0.211263 | − | 0.977429i | \(-0.432242\pi\) | ||||
0.211263 | + | 0.977429i | \(0.432242\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.72498 | −0.440383 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.60555 | 0.199251 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.78890 | 0.440122 | 0.220061 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220061 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21110 | 0.0915507 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1833 | −0.765427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.908327 | −0.0678915 | −0.0339458 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339458 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.21110 | −0.535997 | −0.267999 | − | 0.963419i | \(-0.586362\pi\) | ||||
−0.267999 | + | 0.963419i | \(0.586362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.88057 | 0.656471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.18335 | −0.0870013 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.69722 | −0.123455 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3028 | 0.817840 | 0.408920 | − | 0.912570i | \(-0.365905\pi\) | ||||
0.408920 | + | 0.912570i | \(0.365905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.90833 | 0.425291 | 0.212645 | − | 0.977129i | \(-0.431792\pi\) | ||||
0.212645 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.5416 | −0.754902 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.69722 | 0.263416 | 0.131708 | − | 0.991289i | \(-0.457954\pi\) | ||||
0.131708 | + | 0.991289i | \(0.457954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6972 | 0.758306 | 0.379153 | − | 0.925334i | \(-0.376215\pi\) | ||||
0.379153 | + | 0.925334i | \(0.376215\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6972 | −0.754524 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.30278 | 0.161623 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.6333 | 1.30141 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.00000 | −0.208514 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5139 | −0.930334 | −0.465167 | − | 0.885223i | \(-0.654006\pi\) | ||||
−0.465167 | + | 0.885223i | \(0.654006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.09167 | −0.348876 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.8167 | 1.96528 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.02776 | −0.272171 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.21110 | 0.417804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.513878 | 0.0344118 | 0.0172059 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172059 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.21110 | −0.347407 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.18335 | −0.0785414 | −0.0392707 | − | 0.999229i | \(-0.512503\pi\) | ||||
−0.0392707 | + | 0.999229i | \(0.512503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.69722 | 0.574729 | 0.287364 | − | 0.957821i | \(-0.407221\pi\) | ||||
0.287364 | + | 0.957821i | \(0.407221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.90833 | 0.452580 | 0.226290 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226290 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.81665 | 0.314204 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.33053 | −0.541126 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0917 | −0.717461 | −0.358730 | − | 0.933441i | \(-0.616790\pi\) | ||||
−0.358730 | + | 0.933441i | \(0.616790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.69722 | 0.173743 | 0.0868717 | − | 0.996220i | \(-0.472313\pi\) | ||||
0.0868717 | + | 0.996220i | \(0.472313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3944 | 0.795104 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7250 | 1.32407 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.39445 | −0.343241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.09167 | 0.132554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3944 | 0.656092 | 0.328046 | − | 0.944662i | \(-0.393610\pi\) | ||||
0.328046 | + | 0.944662i | \(0.393610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.00000 | −0.563602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1194 | 1.19264 | 0.596319 | − | 0.802748i | \(-0.296629\pi\) | ||||
0.596319 | + | 0.802748i | \(0.296629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.119429 | 0.00742099 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.90833 | −0.613310 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2111 | −0.752969 | −0.376484 | − | 0.926423i | \(-0.622867\pi\) | ||||
−0.376484 | + | 0.926423i | \(0.622867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.8167 | 0.848750 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.30278 | 0.323316 | 0.161658 | − | 0.986847i | \(-0.448316\pi\) | ||||
0.161658 | + | 0.986847i | \(0.448316\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4222 | −0.876087 | −0.438043 | − | 0.898954i | \(-0.644328\pi\) | ||||
−0.438043 | + | 0.898954i | \(0.644328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.06392 | 0.0643912 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.5139 | 1.53298 | 0.766490 | − | 0.642256i | \(-0.222001\pi\) | ||||
0.766490 | + | 0.642256i | \(0.222001\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.60555 | 0.515201 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4222 | −0.920012 | −0.460006 | − | 0.887916i | \(-0.652153\pi\) | ||||
−0.460006 | + | 0.887916i | \(0.652153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4222 | 0.619536 | 0.309768 | − | 0.950812i | \(-0.399749\pi\) | ||||
0.309768 | + | 0.950812i | \(0.399749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.81665 | 0.463019 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.88057 | −0.111007 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.6972 | −0.688072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.88057 | 0.344725 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.4500 | 1.36531 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.21110 | 0.359197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.90833 | −0.167633 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.0917 | −0.809545 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.4500 | −1.17096 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9361 | −1.48025 | −0.740125 | − | 0.672469i | \(-0.765234\pi\) | ||||
−0.740125 | + | 0.672469i | \(0.765234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.30278 | 0.244776 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.21110 | −0.352199 | −0.176100 | − | 0.984372i | \(-0.556348\pi\) | ||||
−0.176100 | + | 0.984372i | \(0.556348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5139 | 0.594280 | 0.297140 | − | 0.954834i | \(-0.403967\pi\) | ||||
0.297140 | + | 0.954834i | \(0.403967\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.18335 | 0.0666740 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.5416 | 1.60306 | 0.801529 | − | 0.597956i | \(-0.204020\pi\) | ||||
0.801529 | + | 0.597956i | \(0.204020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.90833 | −0.553029 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.60555 | −0.256260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.7889 | 0.598460 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.60555 | 0.144087 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.486122 | −0.0268008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.18335 | −0.504762 | −0.252381 | − | 0.967628i | \(-0.581214\pi\) | ||||
−0.252381 | + | 0.967628i | \(0.581214\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.513878 | −0.0281604 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.6333 | 1.34586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6056 | 1.50377 | 0.751885 | − | 0.659294i | \(-0.229145\pi\) | ||||
0.751885 | + | 0.659294i | \(0.229145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.2750 | 0.666688 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.21110 | −0.227378 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.00000 | −0.484544 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.9083 | −1.17610 | −0.588050 | − | 0.808824i | \(-0.700104\pi\) | ||||
−0.588050 | + | 0.808824i | \(0.700104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.4500 | −1.95112 | −0.975561 | − | 0.219729i | \(-0.929483\pi\) | ||||
−0.975561 | + | 0.219729i | \(0.929483\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.1194 | −0.807015 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.18335 | −0.222657 | −0.111329 | − | 0.993784i | \(-0.535511\pi\) | ||||
−0.111329 | + | 0.993784i | \(0.535511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7250 | 0.622297 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.908327 | 0.0480738 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.18335 | −0.0624546 | −0.0312273 | − | 0.999512i | \(-0.509942\pi\) | ||||
−0.0312273 | + | 0.999512i | \(0.509942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.3305 | −0.752158 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.27502 | 0.485477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.8167 | −0.982221 | −0.491111 | − | 0.871097i | \(-0.663409\pi\) | ||||
−0.491111 | + | 0.871097i | \(0.663409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.09167 | 0.421236 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.39445 | −0.0723962 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4861 | −0.853619 | −0.426810 | − | 0.904342i | \(-0.640363\pi\) | ||||
−0.426810 | + | 0.904342i | \(0.640363\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.90833 | 0.201825 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.5139 | 1.05652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0277564 | 0.00142575 | 0.000712875 | − | 1.00000i | \(-0.499773\pi\) | ||||
0.000712875 | 1.00000i | \(0.499773\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.5139 | −0.948495 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8444 | 1.42278 | 0.711391 | − | 0.702796i | \(-0.248065\pi\) | ||||
0.711391 | + | 0.702796i | \(0.248065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5139 | 0.636116 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.81665 | −0.244214 | −0.122107 | − | 0.992517i | \(-0.538965\pi\) | ||||
−0.122107 | + | 0.992517i | \(0.538965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.30278 | 0.268173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.0917 | 1.31615 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.1833 | 0.965219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.11943 | 0.156560 | 0.0782798 | − | 0.996931i | \(-0.475057\pi\) | ||||
0.0782798 | + | 0.996931i | \(0.475057\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.788897 | −0.0394943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.6972 | −1.08351 | −0.541754 | − | 0.840537i | \(-0.682240\pi\) | ||||
−0.541754 | + | 0.840537i | \(0.682240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.8167 | −0.887511 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.1833 | 0.506015 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0917 | 0.944022 | 0.472011 | − | 0.881593i | \(-0.343528\pi\) | ||||
0.472011 | + | 0.881593i | \(0.343528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.63331 | −0.179218 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.36669 | −0.116457 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.81665 | −0.236440 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.69722 | −0.376935 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2111 | 0.596551 | 0.298276 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298276 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6056 | 0.614357 | 0.307178 | − | 0.951652i | \(-0.400615\pi\) | ||||
0.307178 | + | 0.951652i | \(0.400615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.09167 | 0.101701 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.21110 | 0.446804 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.06392 | 0.0998799 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0278 | −0.820198 | −0.410099 | − | 0.912041i | \(-0.634506\pi\) | ||||
−0.410099 | + | 0.912041i | \(0.634506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.3305 | −1.40954 | −0.704768 | − | 0.709438i | \(-0.748949\pi\) | ||||
−0.704768 | + | 0.709438i | \(0.748949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −29.7250 | −1.42520 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.60555 | −0.220313 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.2111 | 1.06008 | 0.530039 | − | 0.847973i | \(-0.322177\pi\) | ||||
0.530039 | + | 0.847973i | \(0.322177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.275019 | −0.0130666 | −0.00653328 | − | 0.999979i | \(-0.502080\pi\) | ||||
−0.00653328 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.4500 | 1.96492 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.8167 | 1.07919 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.97224 | 0.187462 | 0.0937309 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937309 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.4222 | −1.19444 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.44996 | −0.114856 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.88057 | 0.321860 | 0.160930 | − | 0.986966i | \(-0.448551\pi\) | ||||
0.160930 | + | 0.986966i | \(0.448551\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9083 | −0.602509 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.6972 | −1.01054 | −0.505270 | − | 0.862961i | \(-0.668607\pi\) | ||||
−0.505270 | + | 0.862961i | \(0.668607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.78890 | −0.0831371 | −0.0415686 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415686 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.8167 | 1.19722 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1194 | 0.607095 | 0.303547 | − | 0.952816i | \(-0.401829\pi\) | ||||
0.303547 | + | 0.952816i | \(0.401829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.48612 | −0.114798 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.06392 | 0.0490227 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | −0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.63331 | −0.166010 | −0.0830050 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830050 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06392 | 0.0485104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.908327 | 0.0413303 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5416 | −0.614894 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.8167 | −1.39644 | −0.698218 | − | 0.715885i | \(-0.746023\pi\) | ||||
−0.698218 | + | 0.715885i | \(0.746023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.02776 | 0.317806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.633308 | −0.0285808 | −0.0142904 | − | 0.999898i | \(-0.504549\pi\) | ||||
−0.0142904 | + | 0.999898i | \(0.504549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.5139 | 0.788785 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.18335 | −0.0530803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.669468 | −0.0299695 | −0.0149848 | − | 0.999888i | \(-0.504770\pi\) | ||||
−0.0149848 | + | 0.999888i | \(0.504770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.30278 | 0.0582037 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.486122 | 0.0216751 | 0.0108376 | − | 0.999941i | \(-0.496550\pi\) | ||||
0.0108376 | + | 0.999941i | \(0.496550\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.4500 | 1.44400 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.45837 | −0.331238 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.9083 | 1.10404 | 0.552021 | − | 0.833830i | \(-0.313857\pi\) | ||||
0.552021 | + | 0.833830i | \(0.313857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.936083 | −0.0414099 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.2111 | 0.494982 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.90833 | −0.436613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.54163 | 0.331041 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.8167 | −1.91964 | −0.959821 | − | 0.280612i | \(-0.909463\pi\) | ||||
−0.959821 | + | 0.280612i | \(0.909463\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.81665 | 0.385525 | 0.192763 | − | 0.981245i | \(-0.438255\pi\) | ||||
0.192763 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.57779 | 0.0688606 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.2111 | −0.662606 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6972 | −0.769445 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1833 | 0.441920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.7527 | −0.725642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.8167 | 0.986450 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.18335 | −0.0510652 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.6056 | −1.53080 | −0.765401 | − | 0.643554i | \(-0.777459\pi\) | ||||
−0.765401 | + | 0.643554i | \(0.777459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.39445 | −0.403154 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.3583 | 1.46905 | 0.734527 | − | 0.678579i | \(-0.237404\pi\) | ||||
0.734527 | + | 0.678579i | \(0.237404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.88057 | −0.379014 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.2111 | −0.648015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.93608 | −0.0823306 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.54163 | −0.0654387 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8167 | 0.458316 | 0.229158 | − | 0.973389i | \(-0.426403\pi\) | ||||
0.229158 | + | 0.973389i | \(0.426403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9083 | −1.09581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.5139 | −0.990992 | −0.495496 | − | 0.868610i | \(-0.665014\pi\) | ||||
−0.495496 | + | 0.868610i | \(0.665014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.2666 | −1.18919 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.02776 | −0.0431617 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.2111 | 1.51805 | 0.759024 | − | 0.651062i | \(-0.225676\pi\) | ||||
0.759024 | + | 0.651062i | \(0.225676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5416 | 0.608548 | 0.304274 | − | 0.952584i | \(-0.401586\pi\) | ||||
0.304274 | + | 0.952584i | \(0.401586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.7250 | 0.615145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.21110 | 0.384130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.5139 | −1.02053 | −0.510263 | − | 0.860018i | \(-0.670452\pi\) | ||||
−0.510263 | + | 0.860018i | \(0.670452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.69722 | 0.319886 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.486122 | 0.0201677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.5416 | 0.435843 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.9083 | 1.77102 | 0.885508 | − | 0.464624i | \(-0.153810\pi\) | ||||
0.885508 | + | 0.464624i | \(0.153810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2111 | 0.544354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.81665 | 0.198131 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.3944 | −1.16602 | −0.583010 | − | 0.812465i | \(-0.698125\pi\) | ||||
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.09167 | −0.0857502 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9361 | 0.570366 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.0917 | 1.06608 | 0.533038 | − | 0.846091i | \(-0.321050\pi\) | ||||
0.533038 | + | 0.846091i | \(0.321050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5416 | 1.00107 | 0.500537 | − | 0.865715i | \(-0.333136\pi\) | ||||
0.500537 | + | 0.865715i | \(0.333136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.6972 | 0.435625 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.0000 | 1.34164 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7250 | −0.557080 | −0.278540 | − | 0.960425i | \(-0.589850\pi\) | ||||
−0.278540 | + | 0.960425i | \(0.589850\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.00000 | 0.121566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.33053 | −0.175195 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.3305 | −1.54816 | −0.774078 | − | 0.633090i | \(-0.781786\pi\) | ||||
−0.774078 | + | 0.633090i | \(0.781786\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.2750 | 0.978863 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.4500 | −1.54794 | −0.773969 | − | 0.633224i | \(-0.781731\pi\) | ||||
−0.773969 | + | 0.633224i | \(0.781731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.0278 | −1.00595 | −0.502975 | − | 0.864301i | \(-0.667761\pi\) | ||||
−0.502975 | + | 0.864301i | \(0.667761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.9083 | −0.517993 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.18335 | −0.167602 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.908327 | 0.0362174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9361 | 1.35097 | 0.675487 | − | 0.737372i | \(-0.263933\pi\) | ||||
0.675487 | + | 0.737372i | \(0.263933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.6056 | −0.699758 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.6333 | 1.69185 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6333 | −0.738279 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.09167 | 0.201423 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3028 | −0.446433 | −0.223216 | − | 0.974769i | \(-0.571656\pi\) | ||||
−0.223216 | + | 0.974769i | \(0.571656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5139 | 0.493499 | 0.246750 | − | 0.969079i | \(-0.420637\pi\) | ||||
0.246750 | + | 0.969079i | \(0.420637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.5416 | 1.47820 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.9361 | 1.41279 | 0.706397 | − | 0.707816i | \(-0.250320\pi\) | ||||
0.706397 | + | 0.707816i | \(0.250320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.60555 | −0.102120 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1194 | −0.513403 | −0.256701 | − | 0.966491i | \(-0.582636\pi\) | ||||
−0.256701 | + | 0.966491i | \(0.582636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.0833 | −2.34765 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.02776 | 0.157138 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.8167 | 0.771947 | 0.385974 | − | 0.922510i | \(-0.373866\pi\) | ||||
0.385974 | + | 0.922510i | \(0.373866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.1194 | −1.48267 | −0.741337 | − | 0.671133i | \(-0.765808\pi\) | ||||
−0.741337 | + | 0.671133i | \(0.765808\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.09167 | 0.314255 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.81665 | 0.0704468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.5139 | 0.678140 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.669468 | 0.0258831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.6333 | 1.60485 | 0.802423 | − | 0.596756i | \(-0.203544\pi\) | ||||
0.802423 | + | 0.596756i | \(0.203544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.4222 | −0.863031 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8167 | −0.531017 | −0.265509 | − | 0.964108i | \(-0.585540\pi\) | ||||
−0.265509 | + | 0.964108i | \(0.585540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.36669 | 0.0524488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.54163 | −0.0590756 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.5416 | 1.89566 | 0.947829 | − | 0.318779i | \(-0.103273\pi\) | ||||
0.947829 | + | 0.318779i | \(0.103273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.36669 | 0.319675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3305 | 0.432287 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.4222 | −0.473248 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.4500 | 1.61487 | 0.807436 | − | 0.589955i | \(-0.200854\pi\) | ||||
0.807436 | + | 0.589955i | \(0.200854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.7250 | 0.672347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3028 | −0.541756 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | 0.340411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.02776 | 0.303204 | 0.151602 | − | 0.988442i | \(-0.451557\pi\) | ||||
0.151602 | + | 0.988442i | \(0.451557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.788897 | −0.0297538 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.27502 | 0.236331 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.27502 | −0.123170 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.1472 | 1.88332 | 0.941659 | − | 0.336570i | \(-0.109267\pi\) | ||||
0.941659 | + | 0.336570i | \(0.109267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.33053 | 0.312419 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.2111 | −0.569660 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.4500 | −0.539644 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.8806 | 0.853301 | 0.426651 | − | 0.904417i | \(-0.359693\pi\) | ||||
0.426651 | + | 0.904417i | \(0.359693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | 0.0372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.51388 | 0.130683 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.4222 | 1.12985 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.7250 | −1.06535 | −0.532675 | − | 0.846320i | \(-0.678813\pi\) | ||||
−0.532675 | + | 0.846320i | \(0.678813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.1194 | −0.818117 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.0000 | 0.995910 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.93608 | 0.144791 | 0.0723956 | − | 0.997376i | \(-0.476936\pi\) | ||||
0.0723956 | + | 0.997376i | \(0.476936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.02776 | −0.258171 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.1194 | −1.91208 | −0.956038 | − | 0.293242i | \(-0.905266\pi\) | ||||
−0.956038 | + | 0.293242i | \(0.905266\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.5416 | −1.92498 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.09167 | −0.0765303 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.30278 | −0.0841416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6056 | 0.861379 | 0.430689 | − | 0.902500i | \(-0.358270\pi\) | ||||
0.430689 | + | 0.902500i | \(0.358270\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.5416 | 0.493485 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 58.5416 | 2.13055 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7250 | 0.825953 | 0.412977 | − | 0.910742i | \(-0.364489\pi\) | ||||
0.412977 | + | 0.910742i | \(0.364489\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.69722 | −0.134024 | −0.0670121 | − | 0.997752i | \(-0.521347\pi\) | ||||
−0.0670121 | + | 0.997752i | \(0.521347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.605551 | 0.0219224 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | 0.325396 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.0833 | −0.761273 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8167 | −0.534302 | −0.267151 | − | 0.963655i | \(-0.586082\pi\) | ||||
−0.267151 | + | 0.963655i | \(0.586082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.9083 | 0.897051 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6056 | 0.381455 | 0.190728 | − | 0.981643i | \(-0.438915\pi\) | ||||
0.190728 | + | 0.981643i | \(0.438915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.4222 | −0.949114 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.155590 | 0.00558175 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.4222 | 0.445072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.6333 | −1.52359 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.44996 | −0.0874429 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.4500 | −1.54882 | −0.774412 | − | 0.632682i | \(-0.781954\pi\) | ||||
−0.774412 | + | 0.632682i | \(0.781954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.9083 | −0.566351 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.85281 | 0.101434 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.3860 | 0.652908 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.0000 | 0.638394 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.6333 | 1.29762 | 0.648809 | − | 0.760951i | \(-0.275267\pi\) | ||||
0.648809 | + | 0.760951i | \(0.275267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.69722 | −0.130798 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.09167 | −0.0737218 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.90833 | 0.243185 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.7250 | 0.834126 | 0.417063 | − | 0.908878i | \(-0.363059\pi\) | ||||
0.417063 | + | 0.908878i | \(0.363059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8444 | 1.32890 | 0.664448 | − | 0.747334i | \(-0.268667\pi\) | ||||
0.664448 | + | 0.747334i | \(0.268667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.7889 | −0.658955 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1833 | −0.566878 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.2111 | 0.672111 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06392 | −0.0371763 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7250 | 0.513905 | 0.256953 | − | 0.966424i | \(-0.417282\pi\) | ||||
0.256953 | + | 0.966424i | \(0.417282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3028 | 0.742568 | 0.371284 | − | 0.928519i | \(-0.378918\pi\) | ||||
0.371284 | + | 0.928519i | \(0.378918\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.45837 | −0.0507123 | −0.0253562 | − | 0.999678i | \(-0.508072\pi\) | ||||
−0.0253562 | + | 0.999678i | \(0.508072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8722 | 1.31535 | 0.657677 | − | 0.753300i | \(-0.271539\pi\) | ||||
0.657677 | + | 0.753300i | \(0.271539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.2389 | 1.15304 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.9083 | −0.551191 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.00000 | −0.103819 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.0278 | 1.27987 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.3944 | −1.39457 | −0.697286 | − | 0.716793i | \(-0.745609\pi\) | ||||
−0.697286 | + | 0.716793i | \(0.745609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8444 | 0.994635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.0917 | −0.691994 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.1749 | 0.590836 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.33053 | −0.114438 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5778 | 0.465989 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.908327 | 0.0311370 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.7250 | 1.39440 | 0.697198 | − | 0.716878i | \(-0.254430\pi\) | ||||
0.697198 | + | 0.716878i | \(0.254430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.81665 | −0.267324 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.5416 | 0.872486 | 0.436243 | − | 0.899829i | \(-0.356309\pi\) | ||||
0.436243 | + | 0.899829i | \(0.356309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3944 | 1.41236 | 0.706180 | − | 0.708032i | \(-0.250417\pi\) | ||||
0.706180 | + | 0.708032i | \(0.250417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.44996 | −0.0834945 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5139 | 0.391937 | 0.195968 | − | 0.980610i | \(-0.437215\pi\) | ||||
0.195968 | + | 0.980610i | \(0.437215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.3667 | −0.590485 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.2389 | −0.517539 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.1472 | −0.750429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.88057 | −0.199027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.908327 | 0.0307071 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.5139 | 0.658937 | 0.329468 | − | 0.944167i | \(-0.393130\pi\) | ||||
0.329468 | + | 0.944167i | \(0.393130\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.4500 | 0.790948 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.7889 | −0.498251 | −0.249125 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249125 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.9361 | 0.940124 | 0.470062 | − | 0.882633i | \(-0.344232\pi\) | ||||
0.470062 | + | 0.882633i | \(0.344232\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.5500 | 1.02693 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.8167 | −0.363188 | −0.181594 | − | 0.983374i | \(-0.558126\pi\) | ||||
−0.181594 | + | 0.983374i | \(0.558126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.30278 | −0.144310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.21110 | 0.107455 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.72498 | 0.0910861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.09167 | 0.270173 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −50.2389 | −1.67556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6056 | −0.353322 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.78890 | −0.126087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.6333 | 0.719115 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.63331 | 0.153846 | 0.0769232 | − | 0.997037i | \(-0.475490\pi\) | ||||
0.0769232 | + | 0.997037i | \(0.475490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.0917 | 0.467391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.18335 | −0.237995 | −0.118997 | − | 0.992895i | \(-0.537968\pi\) | ||||
−0.118997 | + | 0.992895i | \(0.537968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.6417 | −0.880748 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.06392 | 0.200248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0916731 | 0.00302402 | 0.00151201 | − | 0.999999i | \(-0.499519\pi\) | ||||
0.00151201 | + | 0.999999i | \(0.499519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.7889 | −1.11338 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5416 | −0.346982 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.57779 | 0.0518776 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.30278 | −0.141322 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.4861 | 0.508083 | 0.254042 | − | 0.967193i | \(-0.418240\pi\) | ||||
0.254042 | + | 0.967193i | \(0.418240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8167 | 0.452823 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.09167 | −0.264909 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.4500 | −1.68080 | −0.840398 | − | 0.541969i | \(-0.817679\pi\) | ||||
−0.840398 | + | 0.541969i | \(0.817679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6972 | 0.446992 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.2389 | 1.93113 | 0.965566 | − | 0.260159i | \(-0.0837750\pi\) | ||||
0.965566 | + | 0.260159i | \(0.0837750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.3028 | −0.465762 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.09167 | 0.165632 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0917 | −0.457918 | −0.228959 | − | 0.973436i | \(-0.573532\pi\) | ||||
−0.228959 | + | 0.973436i | \(0.573532\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.33894 | −0.270693 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.1833 | 1.20575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.3583 | 1.37212 | 0.686060 | − | 0.727545i | \(-0.259339\pi\) | ||||
0.686060 | + | 0.727545i | \(0.259339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.9083 | −1.09725 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.844410 | −0.0272674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6333 | 0.407526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.90833 | 0.319291 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.7250 | −0.570587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.4861 | 0.819578 | 0.409789 | − | 0.912180i | \(-0.365602\pi\) | ||||
0.409789 | + | 0.912180i | \(0.365602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | −0.192748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4777 | −1.58782 | −0.793908 | − | 0.608038i | \(-0.791957\pi\) | ||||
−0.793908 | + | 0.608038i | \(0.791957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78890 | −0.0573494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.0555 | 0.450137 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.5694 | −1.36192 | −0.680958 | − | 0.732323i | \(-0.738436\pi\) | ||||
−0.680958 | + | 0.732323i | \(0.738436\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.60555 | −0.0831888 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.2666 | 0.997250 | 0.498625 | − | 0.866818i | \(-0.333838\pi\) | ||||
0.498625 | + | 0.866818i | \(0.333838\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0917 | −0.353410 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.633308 | −0.0201584 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.1194 | −0.703357 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6333 | 0.623673 | 0.311836 | − | 0.950136i | \(-0.399056\pi\) | ||||
0.311836 | + | 0.950136i | \(0.399056\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.9638 | −0.379661 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0917 | −1.01737 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.7889 | −0.785072 | −0.392536 | − | 0.919737i | \(-0.628402\pi\) | ||||
−0.392536 | + | 0.919737i | \(0.628402\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.21110 | −0.0699562 |
(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 | 2672.2.a.c.1.2 | 2 | ||
4.3 | odd | 2 | 668.2.a.a.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 6012.2.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.a.a.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
2672.2.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6012.2.a.a.1.1 | 2 | 12.11 | even | 2 |