Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.596863 | 0.344599 | 0.172300 | − | 0.985045i | \(-0.444880\pi\) | ||||
0.172300 | + | 0.985045i | \(0.444880\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.74289 | 1.67387 | 0.836936 | − | 0.547301i | \(-0.184345\pi\) | ||||
0.836936 | + | 0.547301i | \(0.184345\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.10831 | −0.418903 | −0.209451 | − | 0.977819i | \(-0.567168\pi\) | ||||
−0.209451 | + | 0.977819i | \(0.567168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.64375 | −0.881251 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.05435 | 1.22243 | 0.611216 | − | 0.791464i | \(-0.290681\pi\) | ||||
0.611216 | + | 0.791464i | \(0.290681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.28166 | −1.74222 | −0.871110 | − | 0.491088i | \(-0.836599\pi\) | ||||
−0.871110 | + | 0.491088i | \(0.836599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23399 | 0.576815 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.42667 | 0.831089 | 0.415545 | − | 0.909573i | \(-0.363591\pi\) | ||||
0.415545 | + | 0.909573i | \(0.363591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.55414 | −1.04479 | −0.522395 | − | 0.852704i | \(-0.674961\pi\) | ||||
−0.522395 | + | 0.852704i | \(0.674961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.661511 | −0.144353 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.12930 | 1.48656 | 0.743281 | − | 0.668980i | \(-0.233269\pi\) | ||||
0.743281 | + | 0.668980i | \(0.233269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.00922 | 1.80184 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.36855 | −0.648278 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.58996 | −1.40942 | −0.704710 | − | 0.709495i | \(-0.748923\pi\) | ||||
−0.704710 | + | 0.709495i | \(0.748923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1526 | −1.82347 | −0.911735 | − | 0.410779i | \(-0.865257\pi\) | ||||
−0.911735 | + | 0.410779i | \(0.865257\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41989 | 0.421249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.14829 | −0.701189 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9132 | −1.79413 | −0.897063 | − | 0.441902i | \(-0.854304\pi\) | ||||
−0.897063 | + | 0.441902i | \(0.854304\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.74929 | −0.600368 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.41002 | 0.688730 | 0.344365 | − | 0.938836i | \(-0.388094\pi\) | ||||
0.344365 | + | 0.938836i | \(0.388094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.01601 | −1.37493 | −0.687464 | − | 0.726218i | \(-0.741276\pi\) | ||||
−0.687464 | + | 0.726218i | \(0.741276\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.89528 | −1.47510 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.789928 | −0.115223 | −0.0576115 | − | 0.998339i | \(-0.518348\pi\) | ||||
−0.0576115 | + | 0.998339i | \(0.518348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.77164 | −0.824521 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.04525 | 0.286393 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.5917 | −1.72960 | −0.864799 | − | 0.502117i | \(-0.832555\pi\) | ||||
−0.864799 | + | 0.502117i | \(0.832555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1750 | 2.04620 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.71820 | −0.360034 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.67098 | −0.477921 | −0.238961 | − | 0.971029i | \(-0.576807\pi\) | ||||
−0.238961 | + | 0.971029i | \(0.576807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4825 | −1.59823 | −0.799113 | − | 0.601181i | \(-0.794697\pi\) | ||||
−0.799113 | + | 0.601181i | \(0.794697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.93010 | 0.369158 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −23.5116 | −2.91625 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.33923 | 1.01880 | 0.509400 | − | 0.860530i | \(-0.329867\pi\) | ||||
0.509400 | + | 0.860530i | \(0.329867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.25522 | 0.512268 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.5483 | 1.96392 | 0.981961 | − | 0.189084i | \(-0.0605517\pi\) | ||||
0.981961 | + | 0.189084i | \(0.0605517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9080 | 1.62780 | 0.813902 | − | 0.581002i | \(-0.197339\pi\) | ||||
0.813902 | + | 0.581002i | \(0.197339\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.37727 | 0.620914 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.49349 | −0.512080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.08841 | −0.122456 | −0.0612280 | − | 0.998124i | \(-0.519502\pi\) | ||||
−0.0612280 | + | 0.998124i | \(0.519502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.92070 | 0.657855 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.85350 | 0.971798 | 0.485899 | − | 0.874015i | \(-0.338492\pi\) | ||||
0.485899 | + | 0.874015i | \(0.338492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8256 | 1.39114 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.53017 | −0.485685 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8450 | −1.46757 | −0.733784 | − | 0.679383i | \(-0.762248\pi\) | ||||
−0.733784 | + | 0.679383i | \(0.762248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.96204 | 0.729820 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.05974 | −0.628366 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.0456 | −1.74884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.23701 | 0.734807 | 0.367403 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367403 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.7187 | −1.07727 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.3018 | −1.22407 | −0.612036 | − | 0.790830i | \(-0.709649\pi\) | ||||
−0.612036 | + | 0.790830i | \(0.709649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.52046 | 0.445414 | 0.222707 | − | 0.974885i | \(-0.428511\pi\) | ||||
0.222707 | + | 0.974885i | \(0.428511\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.47596 | −0.241629 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.6723 | −1.61177 | −0.805886 | − | 0.592071i | \(-0.798310\pi\) | ||||
−0.805886 | + | 0.592071i | \(0.798310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.13728 | −0.204714 | −0.102357 | − | 0.994748i | \(-0.532638\pi\) | ||||
−0.102357 | + | 0.994748i | \(0.532638\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.51372 | −0.618255 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.98985 | 0.375334 | 0.187667 | − | 0.982233i | \(-0.439907\pi\) | ||||
0.187667 | + | 0.982233i | \(0.439907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.6842 | 2.48831 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.6072 | 1.53533 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.79782 | −0.348145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.43776 | 0.494342 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.63218 | 0.237336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15.0061 | 1.34218 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6610 | 0.946008 | 0.473004 | − | 0.881060i | \(-0.343170\pi\) | ||||
0.473004 | + | 0.881060i | \(0.343170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.38132 | −0.473799 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.97324 | 0.783996 | 0.391998 | − | 0.919966i | \(-0.371784\pi\) | ||||
0.391998 | + | 0.919966i | \(0.371784\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.04740 | 0.437665 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.6081 | −1.08513 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.1837 | −1.29723 | −0.648614 | − | 0.761117i | \(-0.724651\pi\) | ||||
−0.648614 | + | 0.761117i | \(0.724651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0272 | 0.935315 | 0.467657 | − | 0.883910i | \(-0.345098\pi\) | ||||
0.467657 | + | 0.883910i | \(0.345098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.471479 | −0.0397057 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.4681 | −2.12975 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.4084 | −2.35919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.44488 | −0.284129 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.53804 | 0.453694 | 0.226847 | − | 0.973930i | \(-0.427158\pi\) | ||||
0.226847 | + | 0.973930i | \(0.427158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.05565 | 0.574181 | 0.287090 | − | 0.957903i | \(-0.407312\pi\) | ||||
0.287090 | + | 0.957903i | \(0.407312\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.05927 | −0.732398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −38.0002 | −3.05225 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7281 | −1.17543 | −0.587714 | − | 0.809069i | \(-0.699972\pi\) | ||||
−0.587714 | + | 0.809069i | \(0.699972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.51551 | −0.596018 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.90149 | −0.622724 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3357 | −0.966206 | −0.483103 | − | 0.875563i | \(-0.660490\pi\) | ||||
−0.483103 | + | 0.875563i | \(0.660490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.05739 | 0.705117 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.22308 | −0.636321 | −0.318160 | − | 0.948037i | \(-0.603065\pi\) | ||||
−0.318160 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.4593 | 2.03533 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0400 | 0.920723 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.10789 | −0.312317 | −0.156158 | − | 0.987732i | \(-0.549911\pi\) | ||||
−0.156158 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.98503 | −0.754797 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.19107 | −0.164691 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.4420 | −0.855218 | −0.427609 | − | 0.903964i | \(-0.640644\pi\) | ||||
−0.427609 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.82949 | −0.210315 | −0.105157 | − | 0.994456i | \(-0.533535\pi\) | ||||
−0.105157 | + | 0.994456i | \(0.533535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.45037 | −0.550747 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40.8471 | −3.00314 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8929 | 1.01595 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.73340 | 0.271565 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8684 | 0.858770 | 0.429385 | − | 0.903122i | \(-0.358730\pi\) | ||||
0.429385 | + | 0.903122i | \(0.358730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.58302 | 0.185930 | 0.0929649 | − | 0.995669i | \(-0.470366\pi\) | ||||
0.0929649 | + | 0.995669i | \(0.470366\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.0332 | −1.00494 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0693 | 1.14489 | 0.572444 | − | 0.819944i | \(-0.305995\pi\) | ||||
0.572444 | + | 0.819944i | \(0.305995\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.5167 | −1.31261 | −0.656305 | − | 0.754495i | \(-0.727882\pi\) | ||||
−0.656305 | + | 0.754495i | \(0.727882\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.97738 | 0.351077 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.41204 | 0.590410 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.5062 | 1.15285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.8481 | −1.31003 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.4641 | −1.27719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0114 | −0.826900 | −0.413450 | − | 0.910527i | \(-0.635676\pi\) | ||||
−0.413450 | + | 0.910527i | \(0.635676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.87707 | 0.676766 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.7459 | −2.30145 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.2523 | 0.763856 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.30115 | 0.560940 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.5252 | −1.44794 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.53206 | 0.303489 | 0.151745 | − | 0.988420i | \(-0.451511\pi\) | ||||
0.151745 | + | 0.988420i | \(0.451511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.8182 | −1.58788 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.77728 | −0.582568 | −0.291284 | − | 0.956637i | \(-0.594083\pi\) | ||||
−0.291284 | + | 0.956637i | \(0.594083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7649 | −1.43827 | −0.719133 | − | 0.694873i | \(-0.755461\pi\) | ||||
−0.719133 | + | 0.694873i | \(0.755461\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.68200 | −0.176462 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.4379 | 1.01137 | 0.505685 | − | 0.862718i | \(-0.331240\pi\) | ||||
0.505685 | + | 0.862718i | \(0.331240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.95662 | −0.192868 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.649634 | −0.0421983 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.89595 | −0.381377 | −0.190689 | − | 0.981651i | \(-0.561072\pi\) | ||||
−0.190689 | + | 0.981651i | \(0.561072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6126 | 1.13453 | 0.567264 | − | 0.823536i | \(-0.308002\pi\) | ||||
0.567264 | + | 0.823536i | \(0.308002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6395 | 0.874974 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.6026 | −1.38014 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.6075 | 1.82025 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.28433 | 0.334881 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2226 | 1.15020 | 0.575101 | − | 0.818082i | \(-0.304963\pi\) | ||||
0.575101 | + | 0.818082i | \(0.304963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.9047 | 1.81722 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.65515 | 0.479384 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00865 | 0.125296 | 0.0626479 | − | 0.998036i | \(-0.480045\pi\) | ||||
0.0626479 | + | 0.998036i | \(0.480045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0953 | 0.751564 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0660 | 1.24205 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0383 | 1.60559 | 0.802794 | − | 0.596256i | \(-0.203346\pi\) | ||||
0.802794 | + | 0.596256i | \(0.203346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −47.1292 | −2.89513 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.26358 | −0.505723 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7113 | 1.56764 | 0.783822 | − | 0.620985i | \(-0.213267\pi\) | ||||
0.783822 | + | 0.620985i | \(0.213267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3375 | 1.35691 | 0.678453 | − | 0.734644i | \(-0.262651\pi\) | ||||
0.678453 | + | 0.734644i | \(0.262651\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.15539 | 0.251496 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 36.5266 | 2.20263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0231 | 0.722396 | 0.361198 | − | 0.932489i | \(-0.382368\pi\) | ||||
0.361198 | + | 0.932489i | \(0.382368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.8411 | 1.60694 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.165606 | −0.00987924 | −0.00493962 | − | 0.999988i | \(-0.501572\pi\) | ||||
−0.00493962 | + | 0.999988i | \(0.501572\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.10918 | 0.541484 | 0.270742 | − | 0.962652i | \(-0.412731\pi\) | ||||
0.270742 | + | 0.962652i | \(0.412731\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.1739 | −0.602650 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.88768 | −0.288511 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.25794 | −0.309291 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.31950 | 0.253214 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.00724 | −0.234105 | −0.117053 | − | 0.993126i | \(-0.537345\pi\) | ||||
−0.117053 | + | 0.993126i | \(0.537345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7401 | −0.799979 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.6573 | −0.792476 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −44.7838 | −2.58992 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.99255 | 0.575961 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.34248 | −0.421814 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −46.7208 | −2.67522 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.30062 | 0.302522 | 0.151261 | − | 0.988494i | \(-0.451667\pi\) | ||||
0.151261 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.69809 | 0.153489 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9719 | −0.678862 | −0.339431 | − | 0.940631i | \(-0.610235\pi\) | ||||
−0.339431 | + | 0.940631i | \(0.610235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9937 | −1.13011 | −0.565056 | − | 0.825053i | \(-0.691145\pi\) | ||||
−0.565056 | + | 0.825053i | \(0.691145\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.9671 | 0.617924 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.46272 | −0.531479 | −0.265740 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265740 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.7724 | −1.72292 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.95108 | −0.555415 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6055 | −0.868314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −56.5929 | −3.13921 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.27567 | −0.0705444 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.875487 | 0.0482672 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7619 | −0.701459 | −0.350730 | − | 0.936477i | \(-0.614066\pi\) | ||||
−0.350730 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.8519 | 1.58108 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.2128 | 1.70534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.84959 | 0.318648 | 0.159324 | − | 0.987226i | \(-0.449069\pi\) | ||||
0.159324 | + | 0.987226i | \(0.449069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.38140 | 0.129340 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.1624 | −2.22907 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.1550 | 0.764296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.9268 | 0.857470 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7771 | 0.578548 | 0.289274 | − | 0.957246i | \(-0.406586\pi\) | ||||
0.289274 | + | 0.957246i | \(0.406586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.48714 | 0.400777 | 0.200389 | − | 0.979716i | \(-0.435780\pi\) | ||||
0.200389 | + | 0.979716i | \(0.435780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.1601 | 1.12944 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8339 | −1.00243 | −0.501215 | − | 0.865323i | \(-0.667113\pi\) | ||||
−0.501215 | + | 0.865323i | \(0.667113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 61.9385 | 3.28735 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.26678 | −0.119971 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.4047 | 1.02414 | 0.512070 | − | 0.858944i | \(-0.328879\pi\) | ||||
0.512070 | + | 0.858944i | \(0.328879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.74015 | 0.0915867 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.24560 | 0.170350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.0560 | 2.72473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7684 | 0.562108 | 0.281054 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281054 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.6590 | −0.606944 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.9555 | 0.724533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6677 | −0.655910 | −0.327955 | − | 0.944693i | \(-0.606359\pi\) | ||||
−0.327955 | + | 0.944693i | \(0.606359\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.95658 | 0.462516 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 47.6776 | 2.45552 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0510 | −1.38952 | −0.694759 | − | 0.719243i | \(-0.744489\pi\) | ||||
−0.694759 | + | 0.719243i | \(0.744489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.36314 | 0.325993 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0428 | −1.27963 | −0.639813 | − | 0.768531i | \(-0.720988\pi\) | ||||
−0.639813 | + | 0.768531i | \(0.720988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.8186 | −0.857156 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.8361 | 1.21166 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2476 | 0.773085 | 0.386543 | − | 0.922272i | \(-0.373669\pi\) | ||||
0.386543 | + | 0.922272i | \(0.373669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4297 | 1.23546 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.35580 | 0.270164 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.07381 | −0.204976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.9551 | 0.600007 | 0.300004 | − | 0.953938i | \(-0.403012\pi\) | ||||
0.300004 | + | 0.953938i | \(0.403012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.01261 | 0.150819 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.83325 | −0.241361 | −0.120680 | − | 0.992691i | \(-0.538508\pi\) | ||||
−0.120680 | + | 0.992691i | \(0.538508\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 63.7755 | 3.17689 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.1605 | 1.10117 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.2461 | −2.19320 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.7528 | −0.927264 | −0.463632 | − | 0.886028i | \(-0.653454\pi\) | ||||
−0.463632 | + | 0.886028i | \(0.653454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.06258 | −0.447024 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.06859 | 0.200202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.1377 | 1.62666 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.58173 | 0.322309 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.75926 | 0.330211 | 0.165106 | − | 0.986276i | \(-0.447203\pi\) | ||||
0.165106 | + | 0.986276i | \(0.447203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.9070 | −1.16515 | −0.582577 | − | 0.812775i | \(-0.697956\pi\) | ||||
−0.582577 | + | 0.812775i | \(0.697956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.08838 | 0.101540 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.8716 | 1.49749 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8346 | 0.669501 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.2010 | −0.733909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.0435 | −1.06180 | −0.530899 | − | 0.847435i | \(-0.678146\pi\) | ||||
−0.530899 | + | 0.847435i | \(0.678146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.78620 | 0.374181 | 0.187090 | − | 0.982343i | \(-0.440094\pi\) | ||||
0.187090 | + | 0.982343i | \(0.440094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.9559 | −0.812974 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.4678 | −1.55314 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7303 | −0.750766 | −0.375383 | − | 0.926870i | \(-0.622489\pi\) | ||||
−0.375383 | + | 0.926870i | \(0.622489\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.2588 | 0.726610 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1674 | 0.768135 | 0.384068 | − | 0.923305i | \(-0.374523\pi\) | ||||
0.384068 | + | 0.923305i | \(0.374523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −51.8204 | −2.45652 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.30546 | 0.156343 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0269 | 1.74741 | 0.873703 | − | 0.486460i | \(-0.161712\pi\) | ||||
0.873703 | + | 0.486460i | \(0.161712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8798 | 0.841926 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.21126 | 0.197862 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.0582 | 1.22163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.144604 | 0.00676429 | 0.00338214 | − | 0.999994i | \(-0.498923\pi\) | ||||
0.00338214 | + | 0.999994i | \(0.498923\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.5429 | −0.538777 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.52018 | −0.303675 | −0.151837 | − | 0.988405i | \(-0.548519\pi\) | ||||
−0.151837 | + | 0.988405i | \(0.548519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.2598 | −1.22039 | −0.610197 | − | 0.792250i | \(-0.708910\pi\) | ||||
−0.610197 | + | 0.792250i | \(0.708910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.6810 | −1.05180 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.3872 | −1.22105 | −0.610527 | − | 0.791996i | \(-0.709042\pi\) | ||||
−0.610527 | + | 0.791996i | \(0.709042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.24247 | −0.426778 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.79064 | −0.405052 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.5541 | −1.68076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.0292 | −1.88255 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.2893 | 1.52421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9251 | −1.04747 | −0.523736 | − | 0.851880i | \(-0.675462\pi\) | ||||
−0.523736 | + | 0.851880i | \(0.675462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 68.5533 | 3.12576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.71611 | −0.214590 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.0873 | 1.22997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.95964 | −0.451314 | −0.225657 | − | 0.974207i | \(-0.572453\pi\) | ||||
−0.225657 | + | 0.974207i | \(0.572453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.36272 | −0.332954 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.65342 | 0.164877 | 0.0824384 | − | 0.996596i | \(-0.473729\pi\) | ||||
0.0824384 | + | 0.996596i | \(0.473729\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.0083 | −1.17135 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.1189 | −1.80321 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3407 | −0.822692 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.8117 | −1.24502 | −0.622511 | − | 0.782611i | \(-0.713887\pi\) | ||||
−0.622511 | + | 0.782611i | \(0.713887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.90805 | −0.219276 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.0442 | −2.04894 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.7926 | 0.701373 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.97937 | −0.0877341 | −0.0438671 | − | 0.999037i | \(-0.513968\pi\) | ||||
−0.0438671 | + | 0.999037i | \(0.513968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4144 | −0.681891 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.3408 | 0.677314 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.9196 | 0.745565 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.20265 | −0.140852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.45185 | −0.107624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.35762 | −0.322343 | −0.161172 | − | 0.986926i | \(-0.551527\pi\) | ||||
−0.161172 | + | 0.986926i | \(0.551527\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.94830 | −0.347555 | −0.173778 | − | 0.984785i | \(-0.555597\pi\) | ||||
−0.173778 | + | 0.984785i | \(0.555597\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.95970 | −0.260103 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.7898 | −1.51547 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8269 | 1.20986 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.70517 | 0.421169 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.7023 | −1.19992 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −62.4026 | −2.69790 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.82933 | −0.294707 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.4003 | −1.00792 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.4451 | −0.836009 | −0.418005 | − | 0.908445i | \(-0.637270\pi\) | ||||
−0.418005 | + | 0.908445i | \(0.637270\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.68882 | −0.0724742 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.99961 | −0.342666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4460 | −0.574907 | −0.287454 | − | 0.957795i | \(-0.592809\pi\) | ||||
−0.287454 | + | 0.957795i | \(0.592809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.0008 | 1.40844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.5657 | 1.47255 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20630 | 0.0512972 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.3801 | −1.03488 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.3211 | −0.861032 | −0.430516 | − | 0.902583i | \(-0.641668\pi\) | ||||
−0.430516 | + | 0.902583i | \(0.641668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.6355 | 2.39543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.29217 | 0.350096 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.8840 | 0.711576 | 0.355788 | − | 0.934567i | \(-0.384212\pi\) | ||||
0.355788 | + | 0.934567i | \(0.384212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9336 | 0.628260 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.56198 | −0.275577 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.8114 | 0.620928 | 0.310464 | − | 0.950585i | \(-0.399516\pi\) | ||||
0.310464 | + | 0.950585i | \(0.399516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4136 | −0.854284 | −0.427142 | − | 0.904185i | \(-0.640480\pi\) | ||||
−0.427142 | + | 0.904185i | \(0.640480\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.08384 | 0.295931 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 64.2294 | 2.67855 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.09712 | 0.170565 | 0.0852827 | − | 0.996357i | \(-0.472821\pi\) | ||||
0.0852827 | + | 0.996357i | \(0.472821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.54171 | 0.0640712 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.81244 | −0.407089 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.0511 | −2.11432 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 62.1588 | 2.56995 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5359 | −0.517412 | −0.258706 | − | 0.965956i | \(-0.583296\pi\) | ||||
−0.258706 | + | 0.965956i | \(0.583296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.2365 | 1.90514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.59116 | 0.394528 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.2115 | 0.706793 | 0.353396 | − | 0.935474i | \(-0.385027\pi\) | ||||
0.353396 | + | 0.935474i | \(0.385027\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.2148 | −0.582751 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.0519 | −0.452325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.04421 | −0.246960 | −0.123480 | − | 0.992347i | \(-0.539405\pi\) | ||||
−0.123480 | + | 0.992347i | \(0.539405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.0009 | 1.75404 | 0.877021 | − | 0.480452i | \(-0.159527\pi\) | ||||
0.877021 | + | 0.480452i | \(0.159527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0469 | −0.897818 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.3529 | 0.827465 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.34473 | −0.379291 | −0.189645 | − | 0.981853i | \(-0.560734\pi\) | ||||
−0.189645 | + | 0.981853i | \(0.560734\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.02084 | 0.203455 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.96207 | 0.200744 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2822 | 0.940360 | 0.470180 | − | 0.882570i | \(-0.344189\pi\) | ||||
0.470180 | + | 0.882570i | \(0.344189\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.85196 | 0.397270 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.8413 | −1.32214 | −0.661071 | − | 0.750324i | \(-0.729898\pi\) | ||||
−0.661071 | + | 0.750324i | \(0.729898\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.26759 | −0.372496 | −0.186248 | − | 0.982503i | \(-0.559633\pi\) | ||||
−0.186248 | + | 0.982503i | \(0.559633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.0154 | −0.963705 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3446 | 0.614768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1200 | 0.444800 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.0205 | −0.440117 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.3961 | −1.49108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.74843 | 0.308460 | 0.154230 | − | 0.988035i | \(-0.450710\pi\) | ||||
0.154230 | + | 0.988035i | \(0.450710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.16917 | −0.284949 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.9028 | 1.58349 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.2555 | 1.43650 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −43.7496 | −1.73071 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.2774 | −1.15639 | −0.578193 | − | 0.815900i | \(-0.696242\pi\) | ||||
−0.578193 | + | 0.815900i | \(0.696242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5922 | 0.969824 | 0.484912 | − | 0.874563i | \(-0.338852\pi\) | ||||
0.484912 | + | 0.874563i | \(0.338852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.1417 | −0.793079 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5557 | 0.886758 | 0.443379 | − | 0.896334i | \(-0.353780\pi\) | ||||
0.443379 | + | 0.896334i | \(0.353780\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8835 | −0.584227 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.71609 | 0.263224 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.45203 | 0.291621 | 0.145810 | − | 0.989313i | \(-0.453421\pi\) | ||||
0.145810 | + | 0.989313i | \(0.453421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.5858 | 1.31231 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.7692 | −1.43450 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.23818 | −0.0482326 | −0.0241163 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241163 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7457 | 1.50703 | 0.753517 | − | 0.657428i | \(-0.228356\pi\) | ||||
0.753517 | + | 0.657428i | \(0.228356\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.8476 | −0.498959 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.8919 | 0.732595 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.1111 | −2.09519 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.70502 | 0.104582 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.6086 | −1.95372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.29534 | −0.0884788 | −0.0442394 | − | 0.999021i | \(-0.514086\pi\) | ||||
−0.0442394 | + | 0.999021i | \(0.514086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.3480 | −1.16810 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.9949 | 1.19123 | 0.595615 | − | 0.803270i | \(-0.296908\pi\) | ||||
0.595615 | + | 0.803270i | \(0.296908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.02086 | −0.307812 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.23884 | −0.200753 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6566 | 0.484290 | 0.242145 | − | 0.970240i | \(-0.422149\pi\) | ||||
0.242145 | + | 0.970240i | \(0.422149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56.8308 | −2.17139 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.9907 | −0.495625 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 79.0966 | 3.01334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.5327 | 1.80823 | 0.904114 | − | 0.427291i | \(-0.140532\pi\) | ||||
0.904114 | + | 0.427291i | \(0.140532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.8797 | 0.451271 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.2736 | 1.56560 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.1117 | 0.572396 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.21431 | 0.348517 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.1521 | −1.55429 | −0.777147 | − | 0.629319i | \(-0.783334\pi\) | ||||
−0.777147 | + | 0.629319i | \(0.783334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.7004 | 1.87449 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.76470 | −0.0664623 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.6342 | 0.512767 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.55047 | 0.208452 | 0.104226 | − | 0.994554i | \(-0.466763\pi\) | ||||
0.104226 | + | 0.994554i | \(0.466763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.87750 | 0.107915 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −72.3813 | −2.71070 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −95.3242 | −3.56492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.51908 | −0.131422 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0126 | −0.522583 | −0.261291 | − | 0.965260i | \(-0.584148\pi\) | ||||
−0.261291 | + | 0.965260i | \(0.584148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.01007 | −0.186585 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.5123 | 0.390958 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −68.3796 | −2.53956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.112833 | 0.00418476 | 0.00209238 | − | 0.999998i | \(-0.499334\pi\) | ||||
0.00209238 | + | 0.999998i | \(0.499334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.62118 | −0.356340 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.8949 | −1.14269 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0094 | 0.812935 | 0.406467 | − | 0.913665i | \(-0.366760\pi\) | ||||
0.406467 | + | 0.913665i | \(0.366760\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.8938 | −0.475596 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.8102 | 1.24541 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.05841 | 0.149291 | 0.0746455 | − | 0.997210i | \(-0.476217\pi\) | ||||
0.0746455 | + | 0.997210i | \(0.476217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.0748 | 0.627258 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.6795 | −0.685283 | −0.342642 | − | 0.939466i | \(-0.611322\pi\) | ||||
−0.342642 | + | 0.939466i | \(0.611322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7283 | 0.759426 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.4065 | −0.856398 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.4781 | 0.675175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.8836 | 1.38239 | 0.691196 | − | 0.722667i | \(-0.257084\pi\) | ||||
0.691196 | + | 0.722667i | \(0.257084\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.8764 | 0.396359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.4085 | 0.961105 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3896 | −0.959146 | −0.479573 | − | 0.877502i | \(-0.659208\pi\) | ||||
−0.479573 | + | 0.877502i | \(0.659208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.2521 | 0.626213 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.4889 | 1.72147 | 0.860736 | − | 0.509052i | \(-0.170004\pi\) | ||||
0.860736 | + | 0.509052i | \(0.170004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.36878 | 0.0857554 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.9078 | −1.22594 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.0599 | 0.832644 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1250 | −0.797849 | −0.398924 | − | 0.916984i | \(-0.630616\pi\) | ||||
−0.398924 | + | 0.916984i | \(0.630616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19889 | 0.0431769 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.70020 | −0.169054 | −0.0845272 | − | 0.996421i | \(-0.526938\pi\) | ||||
−0.0845272 | + | 0.996421i | \(0.526938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −91.4675 | −3.28561 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.21923 | 0.258988 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0838 | −0.719578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.0926 | 2.40076 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.5672 | 0.913696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.1255 | −1.96751 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.97274 | 0.212905 | 0.106453 | − | 0.994318i | \(-0.466051\pi\) | ||||
0.106453 | + | 0.994318i | \(0.466051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.5413 | 0.553284 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.42200 | −0.157228 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 78.4111 | 2.78446 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.1297 | −0.997658 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.7237 | −0.486120 | −0.243060 | − | 0.970011i | \(-0.578151\pi\) | ||||
−0.243060 | + | 0.970011i | \(0.578151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.70682 | −0.0957605 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.6028 | 1.29330 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.3878 | 1.98988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.5744 | −1.04236 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3461 | 0.540209 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.2563 | −1.55597 | −0.777985 | − | 0.628283i | \(-0.783758\pi\) | ||||
−0.777985 | + | 0.628283i | \(0.783758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.3816 | −1.66379 | −0.831896 | − | 0.554932i | \(-0.812744\pi\) | ||||
−0.831896 | + | 0.554932i | \(0.812744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.3324 | 0.467589 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.1712 | −1.61730 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.0601 | 1.43651 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.4059 | −0.643155 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.7955 | −0.411666 | −0.205833 | − | 0.978587i | \(-0.565990\pi\) | ||||
−0.205833 | + | 0.978587i | \(0.565990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.96953 | −0.103511 | −0.0517557 | − | 0.998660i | \(-0.516482\pi\) | ||||
−0.0517557 | + | 0.998660i | \(0.516482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.8014 | 0.759026 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7782 | −0.826850 | −0.413425 | − | 0.910538i | \(-0.635668\pi\) | ||||
−0.413425 | + | 0.910538i | \(0.635668\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.6100 | −0.507426 | −0.253713 | − | 0.967280i | \(-0.581652\pi\) | ||||
−0.253713 | + | 0.967280i | \(0.581652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.17613 | 0.248937 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.7775 | −0.685250 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.7781 | −1.06512 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.1997 | 1.18211 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.2987 | 0.769836 | 0.384918 | − | 0.922951i | \(-0.374230\pi\) | ||||
0.384918 | + | 0.922951i | \(0.374230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6075 | 0.986465 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0988443 | −0.00340438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 99.0342 | 3.40688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.02674 | −0.207081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.43693 | 0.186595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −77.8038 | −2.66708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6780 | 0.879199 | 0.439599 | − | 0.898194i | \(-0.355120\pi\) | ||||
0.439599 | + | 0.898194i | \(0.355120\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45.0644 | 1.54117 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.639804 | −0.0218553 | −0.0109276 | − | 0.999940i | \(-0.503478\pi\) | ||||
−0.0109276 | + | 0.999940i | \(0.503478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2690 | −0.520973 | −0.260486 | − | 0.965478i | \(-0.583883\pi\) | ||||
−0.260486 | + | 0.965478i | \(0.583883\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.91728 | −0.0994206 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.05247 | −0.308150 | −0.154075 | − | 0.988059i | \(-0.549240\pi\) | ||||
−0.154075 | + | 0.988059i | \(0.549240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.3754 | −0.522778 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.13827 | −0.106581 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.41281 | −0.149694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.3843 | −1.77497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.1329 | −0.647549 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.6314 | −0.562245 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7534 | −0.700793 | −0.350397 | − | 0.936601i | \(-0.613953\pi\) | ||||
−0.350397 | + | 0.936601i | \(0.613953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.39177 | −0.0806725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1931 | −1.05092 | −0.525461 | − | 0.850818i | \(-0.676107\pi\) | ||||
−0.525461 | + | 0.850818i | \(0.676107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1829 | −0.376333 | −0.188167 | − | 0.982137i | \(-0.560255\pi\) | ||||
−0.188167 | + | 0.982137i | \(0.560255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.20095 | −0.275672 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.12495 | 0.306386 | 0.153193 | − | 0.988196i | \(-0.451044\pi\) | ||||
0.153193 | + | 0.988196i | \(0.451044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8157 | −0.396285 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.0046 | 0.804184 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.59744 | 0.120384 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.8263 | −1.43152 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.7298 | −0.892483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 77.0582 | 2.57003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.1475 | −1.43745 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.96419 | 0.198476 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.5905 | −0.352039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.2911 | −1.43746 | −0.718728 | − | 0.695291i | \(-0.755275\pi\) | ||||
−0.718728 | + | 0.695291i | \(0.755275\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.5229 | 1.07872 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.88679 | 0.195038 | 0.0975190 | − | 0.995234i | \(-0.468909\pi\) | ||||
0.0975190 | + | 0.995234i | \(0.468909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.8952 | 1.18796 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.8859 | −0.921880 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.94515 | −0.328418 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.5637 | 1.73392 | 0.866958 | − | 0.498380i | \(-0.166072\pi\) | ||||
0.866958 | + | 0.498380i | \(0.166072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.16374 | 0.104249 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −103.951 | −3.42158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −98.3199 | −3.23274 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.9510 | −0.392521 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.5702 | 1.26545 | 0.632724 | − | 0.774378i | \(-0.281937\pi\) | ||||
0.632724 | + | 0.774378i | \(0.281937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.2848 | 0.861451 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.14557 | −0.233935 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.9997 | 1.70057 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.6182 | 1.58829 | 0.794144 | − | 0.607729i | \(-0.207919\pi\) | ||||
0.794144 | + | 0.607729i | \(0.207919\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9335 | −0.389436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3489 | 0.989346 | 0.494673 | − | 0.869079i | \(-0.335288\pi\) | ||||
0.494673 | + | 0.869079i | \(0.335288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.4404 | 1.02384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.9737 | 0.454565 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.4765 | −1.64027 | −0.820133 | − | 0.572172i | \(-0.806101\pi\) | ||||
−0.820133 | + | 0.572172i | \(0.806101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −87.3651 | −2.83599 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.64795 | −0.183147 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.77733 | 0.187146 | 0.0935731 | − | 0.995612i | \(-0.470171\pi\) | ||||
0.0935731 | + | 0.995612i | \(0.470171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.4223 | 1.43747 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.3669 | −0.593717 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.8282 | 0.543412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.0763 | 2.32504 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44.0774 | 1.42038 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.66795 | 0.311222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2393 | 0.393588 | 0.196794 | − | 0.980445i | \(-0.436947\pi\) | ||||
0.196794 | + | 0.980445i | \(0.436947\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.31436 | −0.299220 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9154 | 0.414476 | 0.207238 | − | 0.978291i | \(-0.433553\pi\) | ||||
0.207238 | + | 0.978291i | \(0.433553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2216 | −0.391806 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.7782 | −1.08177 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.5065 | 0.560084 | 0.280042 | − | 0.959988i | \(-0.409652\pi\) | ||||
0.280042 | + | 0.959988i | \(0.409652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.1325 | −1.79400 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.65045 | 0.180405 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.14983 | −0.228044 | −0.114022 | − | 0.993478i | \(-0.536373\pi\) | ||||
−0.114022 | + | 0.993478i | \(0.536373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60.1455 | 1.91640 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.522546 | 0.0166328 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.2778 | −2.04392 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8989 | −1.36273 | −0.681364 | − | 0.731945i | \(-0.738613\pi\) | ||||
−0.681364 | + | 0.731945i | \(0.738613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.61713 | −0.241722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −69.3058 | −2.19714 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1968 | −1.01968 | −0.509842 | − | 0.860268i | \(-0.670296\pi\) | ||||
−0.509842 | + | 0.860268i | \(0.670296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.7618 | 1.16309 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8048.2.a.v.1.17 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.12 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.17 | 28 | 1.1 | even | 1 | trivial |