Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.57500224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 12x^{3} + 11x^{2} - 18x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.94641\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 2.94641 | 1.70111 | 0.850555 | − | 0.525887i | \(-0.176266\pi\) | ||||
0.850555 | + | 0.525887i | \(0.176266\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.26823 | −1.46160 | −0.730798 | − | 0.682594i | \(-0.760852\pi\) | ||||
−0.730798 | + | 0.682594i | \(0.760852\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.50474 | 1.70263 | 0.851315 | − | 0.524654i | \(-0.175805\pi\) | ||||
0.851315 | + | 0.524654i | \(0.175805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.68132 | 1.89377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.39613 | 1.49662 | 0.748308 | − | 0.663351i | \(-0.230867\pi\) | ||||
0.748308 | + | 0.663351i | \(0.230867\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.62953 | −2.48633 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.19596 | 0.775135 | 0.387567 | − | 0.921841i | \(-0.373315\pi\) | ||||
0.387567 | + | 0.921841i | \(0.373315\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.2728 | 2.89636 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.01938 | −0.212556 | −0.106278 | − | 0.994336i | \(-0.533893\pi\) | ||||
−0.106278 | + | 0.994336i | \(0.533893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.68132 | 1.13626 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.90025 | 1.52040 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22036 | 0.783701 | 0.391851 | − | 0.920029i | \(-0.371835\pi\) | ||||
0.391851 | + | 0.920029i | \(0.371835\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.59076 | −0.644920 | −0.322460 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322460 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.94641 | −0.512904 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.7225 | −2.48856 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.26094 | −1.52249 | −0.761245 | − | 0.648465i | \(-0.775411\pi\) | ||||
−0.761245 | + | 0.648465i | \(0.775411\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.8992 | 2.54591 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.49030 | −1.48214 | −0.741068 | − | 0.671430i | \(-0.765680\pi\) | ||||
−0.741068 | + | 0.671430i | \(0.765680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.64397 | 1.47069 | 0.735346 | − | 0.677692i | \(-0.237020\pi\) | ||||
0.735346 | + | 0.677692i | \(0.237020\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.5678 | −2.76793 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3221 | −1.50563 | −0.752815 | − | 0.658232i | \(-0.771305\pi\) | ||||
−0.752815 | + | 0.658232i | \(0.771305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.2927 | 1.89895 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.41661 | 1.31859 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.95945 | −0.681233 | −0.340617 | − | 0.940202i | \(-0.610636\pi\) | ||||
−0.340617 | + | 0.940202i | \(0.610636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.26823 | 0.440688 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.94641 | 0.390261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.15410 | −0.280440 | −0.140220 | − | 0.990120i | \(-0.544781\pi\) | ||||
−0.140220 | + | 0.990120i | \(0.544781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.38751 | 0.817837 | 0.408918 | − | 0.912571i | \(-0.365906\pi\) | ||||
0.408918 | + | 0.912571i | \(0.365906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25.5928 | 3.22439 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.6358 | −2.18745 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.37994 | 0.657265 | 0.328632 | − | 0.944458i | \(-0.393412\pi\) | ||||
0.328632 | + | 0.944458i | \(0.393412\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00352 | −0.361581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.48606 | 0.769754 | 0.384877 | − | 0.922968i | \(-0.374244\pi\) | ||||
0.384877 | + | 0.922968i | \(0.374244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4644 | 1.69293 | 0.846466 | − | 0.532442i | \(-0.178726\pi\) | ||||
0.846466 | + | 0.532442i | \(0.178726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.7395 | 1.93291 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.50474 | −0.513362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.5586 | −1.86299 | −0.931494 | − | 0.363757i | \(-0.881494\pi\) | ||||
−0.931494 | + | 0.363757i | \(0.881494\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.23341 | 0.692601 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7606 | 1.29090 | 0.645448 | − | 0.763804i | \(-0.276671\pi\) | ||||
0.645448 | + | 0.763804i | \(0.276671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4451 | −1.13293 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.4349 | 1.33316 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.92706 | 0.840266 | 0.420133 | − | 0.907462i | \(-0.361983\pi\) | ||||
0.420133 | + | 0.907462i | \(0.361983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.3081 | 2.54818 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5799 | −1.09708 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.26823 | −0.335313 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.72448 | −0.276629 | −0.138315 | − | 0.990388i | \(-0.544169\pi\) | ||||
−0.138315 | + | 0.990388i | \(0.544169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.68132 | −0.570994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3275 | 1.02762 | 0.513812 | − | 0.857903i | \(-0.328233\pi\) | ||||
0.513812 | + | 0.857903i | \(0.328233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9528 | −1.17774 | −0.588871 | − | 0.808227i | \(-0.700427\pi\) | ||||
−0.588871 | + | 0.808227i | \(0.700427\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −43.3785 | −4.23331 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.0324 | 1.93660 | 0.968301 | − | 0.249786i | \(-0.0803604\pi\) | ||||
0.968301 | + | 0.249786i | \(0.0803604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.28509 | 0.314654 | 0.157327 | − | 0.987547i | \(-0.449712\pi\) | ||||
0.157327 | + | 0.987547i | \(0.449712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.2865 | −2.58992 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.73871 | −0.539853 | −0.269926 | − | 0.962881i | \(-0.586999\pi\) | ||||
−0.269926 | + | 0.962881i | \(0.586999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.33158 | 0.310671 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.6571 | 2.83425 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.3970 | 1.31977 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.9623 | −2.52127 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.22670 | −0.199162 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.64208 | −0.766860 | −0.383430 | − | 0.923570i | \(-0.625257\pi\) | ||||
−0.383430 | + | 0.923570i | \(0.625257\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.4151 | 2.50181 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.40471 | 0.297471 | 0.148735 | − | 0.988877i | \(-0.452480\pi\) | ||||
0.148735 | + | 0.988877i | \(0.452480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50474 | 0.390610 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −25.8198 | −2.22222 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.4467 | −1.57600 | −0.788002 | − | 0.615672i | \(-0.788885\pi\) | ||||
−0.788002 | + | 0.615672i | \(0.788885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9534 | 1.60761 | 0.803803 | − | 0.594896i | \(-0.202807\pi\) | ||||
0.803803 | + | 0.594896i | \(0.202807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.4131 | −2.56124 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.39613 | −0.451247 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.7931 | −1.14545 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 39.1656 | 3.23032 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.63702 | −0.297956 | −0.148978 | − | 0.988840i | \(-0.547598\pi\) | ||||
−0.148978 | + | 0.988840i | \(0.547598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1036 | −1.14774 | −0.573869 | − | 0.818947i | \(-0.694558\pi\) | ||||
−0.573869 | + | 0.818947i | \(0.694558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.1573 | 1.46793 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.7354 | 0.942613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.99943 | 0.478807 | 0.239403 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239403 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6126 | −1.15885 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.59206 | −0.361905 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.872118 | 0.0683096 | 0.0341548 | − | 0.999417i | \(-0.489126\pi\) | ||||
0.0341548 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.62953 | 0.749658 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.735620 | 0.0569239 | 0.0284620 | − | 0.999595i | \(-0.490939\pi\) | ||||
0.0284620 | + | 0.999595i | \(0.490939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.1182 | 1.23986 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.68132 | 0.434461 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.13245 | −0.694327 | −0.347164 | − | 0.937805i | \(-0.612855\pi\) | ||||
−0.347164 | + | 0.937805i | \(0.612855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25.5928 | 1.93464 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.34687 | −0.477060 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4332 | −0.929303 | −0.464652 | − | 0.885494i | \(-0.653820\pi\) | ||||
−0.464652 | + | 0.885494i | \(0.653820\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.710184 | 0.0527875 | 0.0263938 | − | 0.999652i | \(-0.491598\pi\) | ||||
0.0263938 | + | 0.999652i | \(0.491598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.8202 | 1.39123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30.2669 | 2.22526 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.19596 | −0.233712 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35.5886 | 2.58869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.7000 | 1.06366 | 0.531828 | − | 0.846852i | \(-0.321505\pi\) | ||||
0.531828 | + | 0.846852i | \(0.321505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.13566 | −0.369673 | −0.184836 | − | 0.982769i | \(-0.559176\pi\) | ||||
−0.184836 | + | 0.982769i | \(0.559176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −51.9622 | −3.72109 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.12832 | 0.365378 | 0.182689 | − | 0.983171i | \(-0.441520\pi\) | ||||
0.182689 | + | 0.983171i | \(0.441520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.98380 | 0.707733 | 0.353866 | − | 0.935296i | \(-0.384867\pi\) | ||||
0.353866 | + | 0.935296i | \(0.384867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.8515 | 1.11808 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.0116 | 1.33435 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.0165 | 2.16628 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.79144 | −0.402533 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8722 | 1.23037 | 0.615186 | − | 0.788382i | \(-0.289081\pi\) | ||||
0.615186 | + | 0.788382i | \(0.289081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.1106 | 1.30944 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.5187 | −2.14956 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.1755 | −1.09806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.6181 | 2.87986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.2458 | 1.16008 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5866 | 0.909824 | 0.454912 | − | 0.890536i | \(-0.349671\pi\) | ||||
0.454912 | + | 0.890536i | \(0.349671\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32.2774 | 2.15182 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.15739 | −0.342308 | −0.171154 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171154 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.6083 | −1.16359 | −0.581794 | − | 0.813336i | \(-0.697649\pi\) | ||||
−0.581794 | + | 0.813336i | \(0.697649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.2728 | −0.873286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.8393 | −1.49625 | −0.748125 | − | 0.663558i | \(-0.769046\pi\) | ||||
−0.748125 | + | 0.663558i | \(0.769046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.7349 | 2.20062 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −48.7884 | −3.16914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.9219 | 0.835848 | 0.417924 | − | 0.908482i | \(-0.362758\pi\) | ||||
0.417924 | + | 0.908482i | \(0.362758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5380 | −0.936477 | −0.468238 | − | 0.883602i | \(-0.655111\pi\) | ||||
−0.468238 | + | 0.883602i | \(0.655111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.33460 | −0.342215 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −43.4434 | −2.77550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.39613 | 0.343347 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.6516 | 2.19595 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5156 | −1.42117 | −0.710586 | − | 0.703611i | \(-0.751570\pi\) | ||||
−0.710586 | + | 0.703611i | \(0.751570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.01938 | 0.0640881 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −30.7756 | −1.92724 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.75995 | −0.546431 | −0.273215 | − | 0.961953i | \(-0.588087\pi\) | ||||
−0.273215 | + | 0.961953i | \(0.588087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.7181 | −2.59224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.9772 | 1.48415 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.97342 | 0.368337 | 0.184169 | − | 0.982895i | \(-0.441041\pi\) | ||||
0.184169 | + | 0.982895i | \(0.441041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2086 | 0.995688 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.3563 | 1.42938 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5163 | −0.824103 | −0.412051 | − | 0.911161i | \(-0.635188\pi\) | ||||
−0.412051 | + | 0.911161i | \(0.635188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.13822 | 0.433616 | 0.216808 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216808 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 71.6217 | 4.33474 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.68132 | −0.342596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.01233 | −0.301162 | −0.150581 | − | 0.988598i | \(-0.548114\pi\) | ||||
−0.150581 | + | 0.988598i | \(0.548114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.4003 | −1.22133 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.6480 | −1.53003 | −0.765016 | − | 0.644012i | \(-0.777269\pi\) | ||||
−0.765016 | + | 0.644012i | \(0.777269\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2620 | 0.907234 | 0.453617 | − | 0.891197i | \(-0.350133\pi\) | ||||
0.453617 | + | 0.891197i | \(0.350133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.62953 | −0.570404 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.7513 | −2.52353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.78582 | −0.399166 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.02744 | −0.470577 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.5905 | −1.20291 | −0.601456 | − | 0.798906i | \(-0.705412\pi\) | ||||
−0.601456 | + | 0.798906i | \(0.705412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.04010 | 0.409891 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.90025 | −0.458419 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.50072 | −0.318115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.4436 | 2.50404 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.4290 | 1.74810 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.8758 | −1.19535 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.1808 | −1.83666 | −0.918329 | − | 0.395818i | \(-0.870461\pi\) | ||||
−0.918329 | + | 0.395818i | \(0.870461\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.2178 | −2.00347 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.8839 | −1.41103 | −0.705517 | − | 0.708693i | \(-0.749285\pi\) | ||||
−0.705517 | + | 0.708693i | \(0.749285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.40539 | 0.135961 | 0.0679805 | − | 0.997687i | \(-0.478344\pi\) | ||||
0.0679805 | + | 0.997687i | \(0.478344\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −83.6432 | −4.71276 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4338 | −1.03535 | −0.517673 | − | 0.855579i | \(-0.673201\pi\) | ||||
−0.517673 | + | 0.855579i | \(0.673201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.22036 | −0.236295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 59.0235 | 3.29437 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.19596 | 0.177828 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.6571 | 1.70055 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.67921 | 0.535261 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −46.4983 | −2.56353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0397 | −1.65113 | −0.825566 | − | 0.564306i | \(-0.809144\pi\) | ||||
−0.825566 | + | 0.564306i | \(0.809144\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −52.6143 | −2.88325 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.5829 | −0.960655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02468 | 0.0558176 | 0.0279088 | − | 0.999610i | \(-0.491115\pi\) | ||||
0.0279088 | + | 0.999610i | \(0.491115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.9086 | −0.918348 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.59076 | 0.194451 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 28.3468 | 1.53058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.81619 | 0.528486 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.70510 | 0.0915345 | 0.0457673 | − | 0.998952i | \(-0.485427\pi\) | ||||
0.0457673 | + | 0.998952i | \(0.485427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7500 | −1.37837 | −0.689183 | − | 0.724587i | \(-0.742031\pi\) | ||||
−0.689183 | + | 0.724587i | \(0.742031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 42.6307 | 2.27546 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.23845 | −0.332039 | −0.166020 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166020 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.1979 | −1.12507 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 42.4193 | 2.24507 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.3958 | −0.865335 | −0.432668 | − | 0.901554i | \(-0.642428\pi\) | ||||
−0.432668 | + | 0.901554i | \(0.642428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.94641 | 0.154646 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.2730 | −2.47438 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.9944 | −1.14810 | −0.574048 | − | 0.818821i | \(-0.694628\pi\) | ||||
−0.574048 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −53.9174 | −2.80683 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.3410 | −1.15989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.0023 | 1.60524 | 0.802618 | − | 0.596493i | \(-0.203440\pi\) | ||||
0.802618 | + | 0.596493i | \(0.203440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.56076 | −0.338796 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.7736 | 1.17290 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7850 | −1.27312 | −0.636559 | − | 0.771228i | \(-0.719643\pi\) | ||||
−0.636559 | + | 0.771228i | \(0.719643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.4631 | −1.30451 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.4303 | 1.35052 | 0.675261 | − | 0.737578i | \(-0.264031\pi\) | ||||
0.675261 | + | 0.737578i | \(0.264031\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7225 | 0.750329 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 54.7904 | 2.78515 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.4198 | 1.59304 | 0.796522 | − | 0.604609i | \(-0.206671\pi\) | ||||
0.796522 | + | 0.604609i | \(0.206671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.25791 | −0.164760 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.0317 | 0.506030 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 54.1173 | 2.72294 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.38831 | −0.370809 | −0.185404 | − | 0.982662i | \(-0.559359\pi\) | ||||
−0.185404 | + | 0.982662i | \(0.559359\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.2728 | 0.664471 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.5903 | 0.928355 | 0.464178 | − | 0.885742i | \(-0.346350\pi\) | ||||
0.464178 | + | 0.885742i | \(0.346350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.3762 | −0.965198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.3722 | −1.01230 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.26094 | 0.459048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.10092 | 0.450011 | 0.225006 | − | 0.974357i | \(-0.427760\pi\) | ||||
0.225006 | + | 0.974357i | \(0.427760\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.3514 | −2.68096 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.70367 | −0.477486 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.4364 | −1.88677 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 55.8444 | 2.73471 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.42443 | 0.118441 | 0.0592205 | − | 0.998245i | \(-0.481138\pi\) | ||||
0.0592205 | + | 0.998245i | \(0.481138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.88486 | −0.433022 | −0.216511 | − | 0.976280i | \(-0.569468\pi\) | ||||
−0.216511 | + | 0.976280i | \(0.569468\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −58.6430 | −2.85132 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.1573 | 0.880757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.7740 | 1.39247 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.8992 | −0.767620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.7567 | −0.566299 | −0.283150 | − | 0.959076i | \(-0.591379\pi\) | ||||
−0.283150 | + | 0.959076i | \(0.591379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5262 | 1.17865 | 0.589326 | − | 0.807895i | \(-0.299393\pi\) | ||||
0.589326 | + | 0.807895i | \(0.299393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.6401 | −1.94854 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.01938 | −0.0487637 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6164 | −0.745330 | −0.372665 | − | 0.927966i | \(-0.621556\pi\) | ||||
−0.372665 | + | 0.927966i | \(0.621556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 75.5198 | 3.59618 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.0999 | 1.52511 | 0.762557 | − | 0.646921i | \(-0.223944\pi\) | ||||
0.762557 | + | 0.646921i | \(0.223944\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.9074 | −1.22813 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.7161 | −0.506856 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5155 | −0.543450 | −0.271725 | − | 0.962375i | \(-0.587594\pi\) | ||||
−0.271725 | + | 0.962375i | \(0.587594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.49030 | 0.446881 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.5551 | −1.95243 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −79.4445 | −3.72442 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0593 | 0.470554 | 0.235277 | − | 0.971928i | \(-0.424400\pi\) | ||||
0.235277 | + | 0.971928i | \(0.424400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.2489 | 1.17852 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.67074 | −0.357262 | −0.178631 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178631 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7119 | 1.00904 | 0.504518 | − | 0.863401i | \(-0.331670\pi\) | ||||
0.504518 | + | 0.863401i | \(0.331670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 34.5774 | 1.60349 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.0457 | −0.788783 | −0.394391 | − | 0.918943i | \(-0.629045\pi\) | ||||
−0.394391 | + | 0.918943i | \(0.629045\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.2352 | 1.11908 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.6768 | 0.814503 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.64397 | −0.443430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.68132 | 0.260677 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.1762 | −1.29010 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6568 | 1.03521 | 0.517607 | − | 0.855618i | \(-0.326823\pi\) | ||||
0.517607 | + | 0.855618i | \(0.326823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.9732 | −2.27858 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.5301 | −0.615639 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.90423 | 0.404320 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.82492 | 0.309267 | 0.154633 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154633 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.56962 | 0.116202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.6416 | 1.20232 | 0.601160 | − | 0.799129i | \(-0.294706\pi\) | ||||
0.601160 | + | 0.799129i | \(0.294706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4881 | 0.607474 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.5678 | 0.834562 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.2180 | 1.31061 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7582 | 1.15309 | 0.576547 | − | 0.817064i | \(-0.304400\pi\) | ||||
0.576547 | + | 0.817064i | \(0.304400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.16743 | 0.0968338 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.2458 | 1.52694 | 0.763472 | − | 0.645841i | \(-0.223493\pi\) | ||||
0.763472 | + | 0.645841i | \(0.223493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.7526 | −1.50197 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 47.4907 | 2.10914 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.26071 | 0.410474 | 0.205237 | − | 0.978712i | \(-0.434203\pi\) | ||||
0.205237 | + | 0.978712i | \(0.434203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65.1584 | 2.88244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.90025 | 0.348805 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.0644 | 1.72138 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3221 | 0.453965 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.9079 | −1.18113 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0560 | −1.22916 | −0.614579 | − | 0.788855i | \(-0.710674\pi\) | ||||
−0.614579 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.2887 | −1.89288 | −0.946441 | − | 0.322877i | \(-0.895350\pi\) | ||||
−0.946441 | + | 0.322877i | \(0.895350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 75.4069 | 3.29103 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.4759 | −0.499900 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9609 | −0.954820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.2381 | −0.531090 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −51.2109 | −2.21819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −65.4703 | −2.83053 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.6334 | −1.58085 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2927 | −0.572555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.9827 | −1.93396 | −0.966979 | − | 0.254858i | \(-0.917971\pi\) | ||||
−0.966979 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.09249 | 0.0897974 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.7364 | −0.459898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.53568 | 0.322202 | 0.161101 | − | 0.986938i | \(-0.448495\pi\) | ||||
0.161101 | + | 0.986938i | \(0.448495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.2895 | 1.54880 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.22036 | 0.179793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −74.5921 | −3.17198 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 89.1785 | 3.78542 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.6924 | 0.537794 | 0.268897 | − | 0.963169i | \(-0.413341\pi\) | ||||
0.268897 | + | 0.963169i | \(0.413341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.0401 | 2.20106 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.41661 | −0.397569 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.6269 | 0.574305 | 0.287152 | − | 0.957885i | \(-0.407291\pi\) | ||||
0.287152 | + | 0.957885i | \(0.407291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.7554 | 0.789046 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.0799 | 1.17924 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.90870 | 0.205783 | 0.102892 | − | 0.994693i | \(-0.467190\pi\) | ||||
0.102892 | + | 0.994693i | \(0.467190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.3597 | −0.642782 | −0.321391 | − | 0.946947i | \(-0.604150\pi\) | ||||
−0.321391 | + | 0.946947i | \(0.604150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.3123 | 1.80940 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.79144 | −0.241520 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4960 | 0.894892 | 0.447446 | − | 0.894311i | \(-0.352334\pi\) | ||||
0.447446 | + | 0.894311i | \(0.352334\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.1318 | −0.628854 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.9785 | 2.19792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.95945 | 0.205400 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −100.194 | −4.14253 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.6383 | 1.47095 | 0.735475 | − | 0.677552i | \(-0.236959\pi\) | ||||
0.735475 | + | 0.677552i | \(0.236959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.59076 | −0.147955 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1101 | 0.621547 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.3396 | −1.73868 | −0.869340 | − | 0.494215i | \(-0.835455\pi\) | ||||
−0.869340 | + | 0.494215i | \(0.835455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.0526 | −1.92897 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.4163 | 1.20393 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.73689 | 0.234403 | 0.117201 | − | 0.993108i | \(-0.462608\pi\) | ||||
0.117201 | + | 0.993108i | \(0.462608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.2015 | 0.742453 | 0.371226 | − | 0.928542i | \(-0.378937\pi\) | ||||
0.371226 | + | 0.928542i | \(0.378937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.5652 | 1.24471 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.26823 | −0.132872 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.56532 | −0.307067 | −0.153533 | − | 0.988143i | \(-0.549065\pi\) | ||||
−0.153533 | + | 0.988143i | \(0.549065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 56.0160 | 2.26988 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.6993 | −2.25335 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4648 | −0.584230 | −0.292115 | − | 0.956383i | \(-0.594359\pi\) | ||||
−0.292115 | + | 0.956383i | \(0.594359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 91.3871 | 3.68509 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.4446 | 0.541259 | 0.270630 | − | 0.962684i | \(-0.412768\pi\) | ||||
0.270630 | + | 0.962684i | \(0.412768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7907 | −1.27777 | −0.638887 | − | 0.769300i | \(-0.720605\pi\) | ||||
−0.638887 | + | 0.769300i | \(0.720605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.05339 | −0.323171 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.7093 | 1.43066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1292 | −0.845169 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.94641 | −0.117668 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.5976 | −1.18013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.35280 | 0.252901 | 0.126451 | − | 0.991973i | \(-0.459641\pi\) | ||||
0.126451 | + | 0.991973i | \(0.459641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 52.6588 | 2.09300 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2443 | 1.12084 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 71.7289 | 2.84200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.8494 | 1.45774 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.26589 | −0.365981 | −0.182990 | − | 0.983115i | \(-0.558578\pi\) | ||||
−0.182990 | + | 0.983115i | \(0.558578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.8530 | 0.940670 | 0.470335 | − | 0.882488i | \(-0.344133\pi\) | ||||
0.470335 | + | 0.882488i | \(0.344133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −92.8669 | −3.65663 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.4001 | 0.448182 | 0.224091 | − | 0.974568i | \(-0.428059\pi\) | ||||
0.224091 | + | 0.974568i | \(0.428059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.15410 | 0.0845559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −47.6595 | −1.86792 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1919 | −0.555371 | −0.277685 | − | 0.960672i | \(-0.589567\pi\) | ||||
−0.277685 | + | 0.960672i | \(0.589567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.1274 | −0.434782 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 82.1770 | 3.20603 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.69991 | −0.0662191 | −0.0331095 | − | 0.999452i | \(-0.510541\pi\) | ||||
−0.0331095 | + | 0.999452i | \(0.510541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.4577 | −0.679025 | −0.339513 | − | 0.940601i | \(-0.610262\pi\) | ||||
−0.339513 | + | 0.940601i | \(0.610262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50.8132 | 1.97342 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.7225 | −0.570914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.30217 | −0.166581 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.0316 | 1.54771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.38751 | −0.246587 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7235 | −0.529003 | −0.264502 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 44.8838 | 1.72758 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.7204 | −0.604186 | −0.302093 | − | 0.953278i | \(-0.597685\pi\) | ||||
−0.302093 | + | 0.953278i | \(0.597685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2731 | −0.470998 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1958 | −0.582303 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.7965 | −1.17840 | −0.589198 | − | 0.807989i | \(-0.700556\pi\) | ||||
−0.589198 | + | 0.807989i | \(0.700556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60.2879 | 2.30348 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −51.8812 | −1.97939 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.7618 | −1.01954 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.21888 | 0.198536 | 0.0992678 | − | 0.995061i | \(-0.468350\pi\) | ||||
0.0992678 | + | 0.995061i | \(0.468350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.5928 | −0.972192 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −61.9440 | −2.34967 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.3306 | −1.14885 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −67.2938 | −2.54528 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.56839 | 0.0970069 | 0.0485034 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485034 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.26094 | −0.349283 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 99.3969 | 3.74350 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.5226 | 1.74966 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0388 | 1.16569 | 0.582843 | − | 0.812585i | \(-0.301940\pi\) | ||||
0.582843 | + | 0.812585i | \(0.301940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −94.0746 | −3.52807 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.66037 | 0.137082 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6358 | 0.659540 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.0732 | 1.42187 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.3524 | −1.35571 | −0.677857 | − | 0.735193i | \(-0.737091\pi\) | ||||
−0.677857 | + | 0.735193i | \(0.737091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.8441 | −2.00526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.8350 | −1.59305 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.9772 | 0.890491 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.2802 | 1.56808 | 0.784042 | − | 0.620707i | \(-0.213154\pi\) | ||||
0.784042 | + | 0.620707i | \(0.213154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.4181 | −1.27474 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.8218 | 1.13998 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.52920 | 0.130354 | 0.0651770 | − | 0.997874i | \(-0.479239\pi\) | ||||
0.0651770 | + | 0.997874i | \(0.479239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −128.002 | −4.72143 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.37994 | −0.198173 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2076 | −0.596207 | −0.298103 | − | 0.954534i | \(-0.596354\pi\) | ||||
−0.298103 | + | 0.954534i | \(0.596354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8992 | 0.584071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.3207 | 0.928928 | 0.464464 | − | 0.885592i | \(-0.346247\pi\) | ||||
0.464464 | + | 0.885592i | \(0.346247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8866 | 0.435492 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 66.8158 | 2.44466 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 90.2406 | 3.29732 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1631 | 0.772253 | 0.386127 | − | 0.922446i | \(-0.373813\pi\) | ||||
0.386127 | + | 0.922446i | \(0.373813\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −66.3401 | −2.41757 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.0939 | 1.67753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.5117 | −1.76319 | −0.881595 | − | 0.472007i | \(-0.843530\pi\) | ||||
−0.881595 | + | 0.472007i | \(0.843530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00352 | 0.109021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.42681 | −0.232972 | −0.116486 | − | 0.993192i | \(-0.537163\pi\) | ||||
−0.116486 | + | 0.993192i | \(0.537163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.7985 | 0.535740 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −59.3421 | −2.14552 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.6238 | −0.419712 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.22562 | −0.224501 | −0.112251 | − | 0.993680i | \(-0.535806\pi\) | ||||
−0.112251 | + | 0.993680i | \(0.535806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.8104 | −0.929539 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.5482 | −1.53035 | −0.765177 | − | 0.643820i | \(-0.777349\pi\) | ||||
−0.765177 | + | 0.643820i | \(0.777349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.4003 | −0.732799 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −122.919 | −4.40968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.49030 | −0.340025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.48606 | −0.232090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.3419 | 1.19154 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.6075 | −0.699822 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.8477 | 1.06396 | 0.531978 | − | 0.846758i | \(-0.321449\pi\) | ||||
0.531978 | + | 0.846758i | \(0.321449\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.6001 | 0.626582 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.8514 | −0.919170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.4678 | 1.22399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.7572 | 1.69377 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.403408 | −0.0142894 | −0.00714472 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714472 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9890 | −1.16707 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.0361 | 1.59127 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4644 | −0.510438 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0079 | 0.528959 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −39.8245 | −1.40189 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.2101 | 0.851183 | 0.425592 | − | 0.904915i | \(-0.360066\pi\) | ||||
0.425592 | + | 0.904915i | \(0.360066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.48323 | −0.122313 | −0.0611563 | − | 0.998128i | \(-0.519479\pi\) | ||||
−0.0611563 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.0321 | 0.737628 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.85028 | −0.0998410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.64397 | 0.337400 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 138.102 | 4.82568 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.8355 | 1.00637 | 0.503183 | − | 0.864180i | \(-0.332162\pi\) | ||||
0.503183 | + | 0.864180i | \(0.332162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0923 | −0.491227 | −0.245613 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245613 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.7395 | −0.582794 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0724 | 1.25436 | 0.627180 | − | 0.778874i | \(-0.284209\pi\) | ||||
0.627180 | + | 0.778874i | \(0.284209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6519 | −0.439418 | −0.219709 | − | 0.975565i | \(-0.570511\pi\) | ||||
−0.219709 | + | 0.975565i | \(0.570511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.7684 | −0.512309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.4828 | 1.47194 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.40417 | −0.0831998 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.3679 | −0.980539 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9119 | 1.61958 | 0.809789 | − | 0.586721i | \(-0.199582\pi\) | ||||
0.809789 | + | 0.586721i | \(0.199582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1886 | −0.385813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −75.5694 | −2.60275 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −52.6779 | −1.81217 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.50474 | 0.154785 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.9682 | 1.54330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.44045 | 0.323614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.48291 | 0.290449 | 0.145225 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145225 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.5678 | −0.635007 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4016 | 0.867702 | 0.433851 | − | 0.900985i | \(-0.357154\pi\) | ||||
0.433851 | + | 0.900985i | \(0.357154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6944 | 0.774323 | 0.387162 | − | 0.922012i | \(-0.373456\pi\) | ||||
0.387162 | + | 0.922012i | \(0.373456\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −125.963 | −4.29280 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.4235 | −0.593103 | −0.296552 | − | 0.955017i | \(-0.595837\pi\) | ||||
−0.296552 | + | 0.955017i | \(0.595837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.8469 | 1.01483 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.9938 | −0.679025 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.5586 | 0.561712 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.0309 | 0.983673 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.4787 | −0.523873 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.0307 | −0.339099 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.7462 | 1.84865 | 0.924325 | − | 0.381607i | \(-0.124629\pi\) | ||||
0.924325 | + | 0.381607i | \(0.124629\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −60.6681 | −2.04628 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.3479 | −0.651848 | −0.325924 | − | 0.945396i | \(-0.605675\pi\) | ||||
−0.325924 | + | 0.945396i | \(0.605675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.2313 | 0.579879 | 0.289939 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289939 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.7430 | 0.697268 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.30136 | −0.312309 | −0.156155 | − | 0.987733i | \(-0.549910\pi\) | ||||
−0.156155 | + | 0.987733i | \(0.549910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.9303 | −1.30568 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.23341 | −0.208827 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.3221 | −0.345415 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.6346 | 1.35827 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.2074 | −0.541148 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.1543 | −0.505425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8502 | −0.528048 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 128.002 | 4.25965 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.32104 | −0.0771541 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.8731 | −0.991921 | −0.495961 | − | 0.868345i | \(-0.665184\pi\) | ||||
−0.495961 | + | 0.868345i | \(0.665184\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.6738 | 1.94609 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.3876 | 0.377288 | 0.188644 | − | 0.982046i | \(-0.439591\pi\) | ||||
0.188644 | + | 0.982046i | \(0.439591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.7606 | −0.389220 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −61.5087 | −2.03342 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3373 | 0.506483 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8388 | −1.21520 | −0.607599 | − | 0.794244i | \(-0.707867\pi\) | ||||
−0.607599 | + | 0.794244i | \(0.707867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −94.8179 | −3.12436 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.9996 | 1.15203 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.6143 | −1.72995 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −67.9075 | −2.23038 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8374 | −0.519608 | −0.259804 | − | 0.965661i | \(-0.583658\pi\) | ||||
−0.259804 | + | 0.965661i | \(0.583658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.2927 | 0.435649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −73.3180 | −2.40032 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.4451 | 0.341592 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7080 | 0.937849 | 0.468924 | − | 0.883238i | \(-0.344642\pi\) | ||||
0.468924 | + | 0.883238i | \(0.344642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.08727 | 0.231284 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.5074 | −0.929316 | −0.464658 | − | 0.885490i | \(-0.653823\pi\) | ||||
−0.464658 | + | 0.885490i | \(0.653823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.67426 | 0.315037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −116.312 | −3.78361 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3550 | −0.726439 | −0.363219 | − | 0.931704i | \(-0.618322\pi\) | ||||
−0.363219 | + | 0.931704i | \(0.618322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 78.0518 | 2.53367 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.3135 | −1.76124 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.7765 | 1.06173 | 0.530867 | − | 0.847455i | \(-0.321866\pi\) | ||||
0.530867 | + | 0.847455i | \(0.321866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.0430 | −1.55464 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.4349 | −0.401963 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −83.0974 | −2.68335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1064 | −0.584078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 113.810 | 3.66748 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.7845 | 0.540313 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.984453 | −0.0316579 | −0.0158289 | − | 0.999875i | \(-0.505039\pi\) | ||||
−0.0158289 | + | 0.999875i | \(0.505039\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.41661 | 0.302505 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.2522 | −1.00293 | −0.501465 | − | 0.865178i | \(-0.667205\pi\) | ||||
−0.501465 | + | 0.865178i | \(0.667205\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 85.3801 | 2.73716 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 90.3283 | 2.89282 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.4218 | −0.781322 | −0.390661 | − | 0.920535i | \(-0.627754\pi\) | ||||
−0.390661 | + | 0.920535i | \(0.627754\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.92706 | −0.253350 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6636 | 0.595884 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.8832 | 1.14450 | 0.572248 | − | 0.820080i | \(-0.306071\pi\) | ||||
0.572248 | + | 0.820080i | \(0.306071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.7605 | −0.534034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −137.003 | −4.36085 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.83091 | −0.312605 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1779 | 0.386845 | 0.193422 | − | 0.981116i | \(-0.438041\pi\) | ||||
0.193422 | + | 0.981116i | \(0.438041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −88.5092 | −2.80875 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.6293 | −1.03442 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.61391 | −0.304476 | −0.152238 | − | 0.988344i | \(-0.548648\pi\) | ||||
−0.152238 | + | 0.988344i | \(0.548648\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −73.1637 | −2.31480 |
(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 | 3344.2.a.y.1.6 | 6 | ||
4.3 | odd | 2 | 1672.2.a.h.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.h.1.1 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.y.1.6 | 6 | 1.1 | even | 1 | trivial |