Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.27133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68554 | 1.19186 | 0.595930 | − | 0.803037i | \(-0.296784\pi\) | ||||
0.595930 | + | 0.803037i | \(0.296784\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.841058 | 0.420529 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.68554 | 0.688120 | ||||||||
\(7\) | −4.79793 | −1.81345 | −0.906724 | − | 0.421724i | \(-0.861425\pi\) | ||||
−0.906724 | + | 0.421724i | \(0.861425\pi\) | |||||||
\(8\) | −1.95345 | −0.690648 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.98737 | 1.50375 | 0.751874 | − | 0.659307i | \(-0.229150\pi\) | ||||
0.751874 | + | 0.659307i | \(0.229150\pi\) | |||||||
\(12\) | 0.841058 | 0.242793 | ||||||||
\(13\) | 3.91032 | 1.08453 | 0.542264 | − | 0.840208i | \(-0.317567\pi\) | ||||
0.542264 | + | 0.840208i | \(0.317567\pi\) | |||||||
\(14\) | −8.08713 | −2.16138 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.97474 | −1.24368 | ||||||||
\(17\) | −6.51397 | −1.57987 | −0.789935 | − | 0.613191i | \(-0.789886\pi\) | ||||
−0.789935 | + | 0.613191i | \(0.789886\pi\) | |||||||
\(18\) | 1.68554 | 0.397287 | ||||||||
\(19\) | −4.65505 | −1.06794 | −0.533971 | − | 0.845503i | \(-0.679301\pi\) | ||||
−0.533971 | + | 0.845503i | \(0.679301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.79793 | −1.04699 | ||||||||
\(22\) | 8.40643 | 1.79226 | ||||||||
\(23\) | 1.62636 | 0.339119 | 0.169560 | − | 0.985520i | \(-0.445765\pi\) | ||||
0.169560 | + | 0.985520i | \(0.445765\pi\) | |||||||
\(24\) | −1.95345 | −0.398746 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.59102 | 1.29261 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.03534 | −0.762608 | ||||||||
\(29\) | 3.76744 | 0.699596 | 0.349798 | − | 0.936825i | \(-0.386250\pi\) | ||||
0.349798 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.29585 | −1.31037 | −0.655186 | − | 0.755467i | \(-0.727410\pi\) | ||||
−0.655186 | + | 0.755467i | \(0.727410\pi\) | |||||||
\(32\) | −4.47824 | −0.791649 | ||||||||
\(33\) | 4.98737 | 0.868189 | ||||||||
\(34\) | −10.9796 | −1.88298 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.841058 | 0.140176 | ||||||||
\(37\) | −8.07269 | −1.32714 | −0.663571 | − | 0.748113i | \(-0.730960\pi\) | ||||
−0.663571 | + | 0.748113i | \(0.730960\pi\) | |||||||
\(38\) | −7.84629 | −1.27284 | ||||||||
\(39\) | 3.91032 | 0.626153 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.49791 | −1.01480 | −0.507402 | − | 0.861710i | \(-0.669394\pi\) | ||||
−0.507402 | + | 0.861710i | \(0.669394\pi\) | |||||||
\(42\) | −8.08713 | −1.24787 | ||||||||
\(43\) | −11.1463 | −1.69980 | −0.849898 | − | 0.526947i | \(-0.823337\pi\) | ||||
−0.849898 | + | 0.526947i | \(0.823337\pi\) | |||||||
\(44\) | 4.19467 | 0.632370 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.74130 | 0.404183 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | −4.97474 | −0.718042 | ||||||||
\(49\) | 16.0202 | 2.28859 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.51397 | −0.912138 | ||||||||
\(52\) | 3.28881 | 0.456076 | ||||||||
\(53\) | −2.23921 | −0.307580 | −0.153790 | − | 0.988104i | \(-0.549148\pi\) | ||||
−0.153790 | + | 0.988104i | \(0.549148\pi\) | |||||||
\(54\) | 1.68554 | 0.229373 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.37251 | 1.25245 | ||||||||
\(57\) | −4.65505 | −0.616576 | ||||||||
\(58\) | 6.35018 | 0.833820 | ||||||||
\(59\) | −2.49126 | −0.324335 | −0.162167 | − | 0.986763i | \(-0.551848\pi\) | ||||
−0.162167 | + | 0.986763i | \(0.551848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.9137 | −1.90951 | −0.954755 | − | 0.297394i | \(-0.903883\pi\) | ||||
−0.954755 | + | 0.297394i | \(0.903883\pi\) | |||||||
\(62\) | −12.2975 | −1.56178 | ||||||||
\(63\) | −4.79793 | −0.604483 | ||||||||
\(64\) | 2.40120 | 0.300150 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.40643 | 1.03476 | ||||||||
\(67\) | 6.18165 | 0.755209 | 0.377604 | − | 0.925967i | \(-0.376748\pi\) | ||||
0.377604 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(68\) | −5.47863 | −0.664381 | ||||||||
\(69\) | 1.62636 | 0.195791 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.54447 | 1.13272 | 0.566360 | − | 0.824158i | \(-0.308351\pi\) | ||||
0.566360 | + | 0.824158i | \(0.308351\pi\) | |||||||
\(72\) | −1.95345 | −0.230216 | ||||||||
\(73\) | 4.36101 | 0.510417 | 0.255209 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255209 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(74\) | −13.6069 | −1.58177 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.91517 | −0.449101 | ||||||||
\(77\) | −23.9291 | −2.72697 | ||||||||
\(78\) | 6.59102 | 0.746286 | ||||||||
\(79\) | 3.21215 | 0.361395 | 0.180697 | − | 0.983539i | \(-0.442165\pi\) | ||||
0.180697 | + | 0.983539i | \(0.442165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.9525 | −1.20950 | ||||||||
\(83\) | −5.71423 | −0.627219 | −0.313609 | − | 0.949552i | \(-0.601538\pi\) | ||||
−0.313609 | + | 0.949552i | \(0.601538\pi\) | |||||||
\(84\) | −4.03534 | −0.440292 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18.7876 | −2.02592 | ||||||||
\(87\) | 3.76744 | 0.403912 | ||||||||
\(88\) | −9.74256 | −1.03856 | ||||||||
\(89\) | −1.60687 | −0.170328 | −0.0851642 | − | 0.996367i | \(-0.527141\pi\) | ||||
−0.0851642 | + | 0.996367i | \(0.527141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.7615 | −1.96674 | ||||||||
\(92\) | 1.36786 | 0.142610 | ||||||||
\(93\) | −7.29585 | −0.756544 | ||||||||
\(94\) | 1.68554 | 0.173851 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.47824 | −0.457059 | ||||||||
\(97\) | 8.26050 | 0.838727 | 0.419364 | − | 0.907818i | \(-0.362253\pi\) | ||||
0.419364 | + | 0.907818i | \(0.362253\pi\) | |||||||
\(98\) | 27.0027 | 2.72768 | ||||||||
\(99\) | 4.98737 | 0.501249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.38117 | 0.833957 | 0.416979 | − | 0.908916i | \(-0.363089\pi\) | ||||
0.416979 | + | 0.908916i | \(0.363089\pi\) | |||||||
\(102\) | −10.9796 | −1.08714 | ||||||||
\(103\) | −14.1775 | −1.39695 | −0.698474 | − | 0.715635i | \(-0.746137\pi\) | ||||
−0.698474 | + | 0.715635i | \(0.746137\pi\) | |||||||
\(104\) | −7.63861 | −0.749027 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.77429 | −0.366592 | ||||||||
\(107\) | −5.17157 | −0.499955 | −0.249977 | − | 0.968252i | \(-0.580423\pi\) | ||||
−0.249977 | + | 0.968252i | \(0.580423\pi\) | |||||||
\(108\) | 0.841058 | 0.0809309 | ||||||||
\(109\) | −0.928932 | −0.0889756 | −0.0444878 | − | 0.999010i | \(-0.514166\pi\) | ||||
−0.0444878 | + | 0.999010i | \(0.514166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.07269 | −0.766226 | ||||||||
\(112\) | 23.8685 | 2.25536 | ||||||||
\(113\) | 3.66170 | 0.344464 | 0.172232 | − | 0.985056i | \(-0.444902\pi\) | ||||
0.172232 | + | 0.985056i | \(0.444902\pi\) | |||||||
\(114\) | −7.84629 | −0.734872 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.16864 | 0.294200 | ||||||||
\(117\) | 3.91032 | 0.361509 | ||||||||
\(118\) | −4.19913 | −0.386561 | ||||||||
\(119\) | 31.2536 | 2.86501 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.8738 | 1.26126 | ||||||||
\(122\) | −25.1378 | −2.27587 | ||||||||
\(123\) | −6.49791 | −0.585897 | ||||||||
\(124\) | −6.13623 | −0.551050 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.08713 | −0.720458 | ||||||||
\(127\) | −14.3633 | −1.27454 | −0.637269 | − | 0.770642i | \(-0.719936\pi\) | ||||
−0.637269 | + | 0.770642i | \(0.719936\pi\) | |||||||
\(128\) | 13.0038 | 1.14939 | ||||||||
\(129\) | −11.1463 | −0.981378 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.04313 | −0.178509 | −0.0892544 | − | 0.996009i | \(-0.528448\pi\) | ||||
−0.0892544 | + | 0.996009i | \(0.528448\pi\) | |||||||
\(132\) | 4.19467 | 0.365099 | ||||||||
\(133\) | 22.3346 | 1.93666 | ||||||||
\(134\) | 10.4194 | 0.900103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.7247 | 1.09113 | ||||||||
\(137\) | −3.45734 | −0.295380 | −0.147690 | − | 0.989034i | \(-0.547184\pi\) | ||||
−0.147690 | + | 0.989034i | \(0.547184\pi\) | |||||||
\(138\) | 2.74130 | 0.233355 | ||||||||
\(139\) | −20.8114 | −1.76520 | −0.882602 | − | 0.470122i | \(-0.844210\pi\) | ||||
−0.882602 | + | 0.470122i | \(0.844210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 16.0876 | 1.35004 | ||||||||
\(143\) | 19.5022 | 1.63086 | ||||||||
\(144\) | −4.97474 | −0.414561 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.35067 | 0.608346 | ||||||||
\(147\) | 16.0202 | 1.32132 | ||||||||
\(148\) | −6.78960 | −0.558102 | ||||||||
\(149\) | −4.76744 | −0.390564 | −0.195282 | − | 0.980747i | \(-0.562562\pi\) | ||||
−0.195282 | + | 0.980747i | \(0.562562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.516523 | 0.0420341 | 0.0210170 | − | 0.999779i | \(-0.493310\pi\) | ||||
0.0210170 | + | 0.999779i | \(0.493310\pi\) | |||||||
\(152\) | 9.09339 | 0.737572 | ||||||||
\(153\) | −6.51397 | −0.526623 | ||||||||
\(154\) | −40.3335 | −3.25016 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.28881 | 0.263315 | ||||||||
\(157\) | −20.5054 | −1.63651 | −0.818256 | − | 0.574854i | \(-0.805059\pi\) | ||||
−0.818256 | + | 0.574854i | \(0.805059\pi\) | |||||||
\(158\) | 5.41421 | 0.430732 | ||||||||
\(159\) | −2.23921 | −0.177581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.80316 | −0.614976 | ||||||||
\(162\) | 1.68554 | 0.132429 | ||||||||
\(163\) | 16.6527 | 1.30434 | 0.652169 | − | 0.758073i | \(-0.273859\pi\) | ||||
0.652169 | + | 0.758073i | \(0.273859\pi\) | |||||||
\(164\) | −5.46512 | −0.426754 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.63159 | −0.747557 | ||||||||
\(167\) | −5.46381 | −0.422802 | −0.211401 | − | 0.977399i | \(-0.567803\pi\) | ||||
−0.211401 | + | 0.977399i | \(0.567803\pi\) | |||||||
\(168\) | 9.37251 | 0.723105 | ||||||||
\(169\) | 2.29061 | 0.176201 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.65505 | −0.355981 | ||||||||
\(172\) | −9.37470 | −0.714814 | ||||||||
\(173\) | 24.6727 | 1.87583 | 0.937914 | − | 0.346869i | \(-0.112755\pi\) | ||||
0.937914 | + | 0.346869i | \(0.112755\pi\) | |||||||
\(174\) | 6.35018 | 0.481406 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.8109 | −1.87019 | ||||||||
\(177\) | −2.49126 | −0.187255 | ||||||||
\(178\) | −2.70846 | −0.203007 | ||||||||
\(179\) | 5.27798 | 0.394495 | 0.197247 | − | 0.980354i | \(-0.436800\pi\) | ||||
0.197247 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0101 | −0.818373 | −0.409186 | − | 0.912451i | \(-0.634187\pi\) | ||||
−0.409186 | + | 0.912451i | \(0.634187\pi\) | |||||||
\(182\) | −31.6233 | −2.34407 | ||||||||
\(183\) | −14.9137 | −1.10246 | ||||||||
\(184\) | −3.17701 | −0.234212 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.2975 | −0.901694 | ||||||||
\(187\) | −32.4876 | −2.37573 | ||||||||
\(188\) | 0.841058 | 0.0613405 | ||||||||
\(189\) | −4.79793 | −0.348998 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.1201 | 1.81763 | 0.908813 | − | 0.417203i | \(-0.136990\pi\) | ||||
0.908813 | + | 0.417203i | \(0.136990\pi\) | |||||||
\(192\) | 2.40120 | 0.173291 | ||||||||
\(193\) | −17.6591 | −1.27113 | −0.635567 | − | 0.772046i | \(-0.719233\pi\) | ||||
−0.635567 | + | 0.772046i | \(0.719233\pi\) | |||||||
\(194\) | 13.9234 | 0.999645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4739 | 0.962421 | ||||||||
\(197\) | 21.5263 | 1.53369 | 0.766844 | − | 0.641833i | \(-0.221826\pi\) | ||||
0.766844 | + | 0.641833i | \(0.221826\pi\) | |||||||
\(198\) | 8.40643 | 0.597419 | ||||||||
\(199\) | 3.98072 | 0.282186 | 0.141093 | − | 0.989996i | \(-0.454938\pi\) | ||||
0.141093 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.18165 | 0.436020 | ||||||||
\(202\) | 14.1268 | 0.993960 | ||||||||
\(203\) | −18.0759 | −1.26868 | ||||||||
\(204\) | −5.47863 | −0.383581 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.8968 | −1.66497 | ||||||||
\(207\) | 1.62636 | 0.113040 | ||||||||
\(208\) | −19.4528 | −1.34881 | ||||||||
\(209\) | −23.2164 | −1.60592 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.12845 | −0.490743 | −0.245371 | − | 0.969429i | \(-0.578910\pi\) | ||||
−0.245371 | + | 0.969429i | \(0.578910\pi\) | |||||||
\(212\) | −1.88331 | −0.129346 | ||||||||
\(213\) | 9.54447 | 0.653976 | ||||||||
\(214\) | −8.71691 | −0.595876 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.95345 | −0.132915 | ||||||||
\(217\) | 35.0050 | 2.37629 | ||||||||
\(218\) | −1.56576 | −0.106046 | ||||||||
\(219\) | 4.36101 | 0.294690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.4717 | −1.71341 | ||||||||
\(222\) | −13.6069 | −0.913234 | ||||||||
\(223\) | 12.7853 | 0.856167 | 0.428084 | − | 0.903739i | \(-0.359189\pi\) | ||||
0.428084 | + | 0.903739i | \(0.359189\pi\) | |||||||
\(224\) | 21.4863 | 1.43561 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.17196 | 0.410553 | ||||||||
\(227\) | −15.7516 | −1.04547 | −0.522735 | − | 0.852495i | \(-0.675088\pi\) | ||||
−0.522735 | + | 0.852495i | \(0.675088\pi\) | |||||||
\(228\) | −3.91517 | −0.259288 | ||||||||
\(229\) | −5.69998 | −0.376665 | −0.188333 | − | 0.982105i | \(-0.560308\pi\) | ||||
−0.188333 | + | 0.982105i | \(0.560308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.9291 | −1.57442 | ||||||||
\(232\) | −7.35949 | −0.483174 | ||||||||
\(233\) | 11.9949 | 0.785812 | 0.392906 | − | 0.919579i | \(-0.371470\pi\) | ||||
0.392906 | + | 0.919579i | \(0.371470\pi\) | |||||||
\(234\) | 6.59102 | 0.430868 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.09530 | −0.136392 | ||||||||
\(237\) | 3.21215 | 0.208651 | ||||||||
\(238\) | 52.6793 | 3.41469 | ||||||||
\(239\) | 3.78623 | 0.244911 | 0.122455 | − | 0.992474i | \(-0.460923\pi\) | ||||
0.122455 | + | 0.992474i | \(0.460923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4642 | 0.674058 | 0.337029 | − | 0.941494i | \(-0.390578\pi\) | ||||
0.337029 | + | 0.941494i | \(0.390578\pi\) | |||||||
\(242\) | 23.3850 | 1.50324 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.5433 | −0.803005 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.9525 | −0.698307 | ||||||||
\(247\) | −18.2027 | −1.15821 | ||||||||
\(248\) | 14.2520 | 0.905006 | ||||||||
\(249\) | −5.71423 | −0.362125 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.7981 | −0.681572 | −0.340786 | − | 0.940141i | \(-0.610693\pi\) | ||||
−0.340786 | + | 0.940141i | \(0.610693\pi\) | |||||||
\(252\) | −4.03534 | −0.254203 | ||||||||
\(253\) | 8.11126 | 0.509950 | ||||||||
\(254\) | −24.2100 | −1.51907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.1161 | 1.06976 | ||||||||
\(257\) | −4.55112 | −0.283891 | −0.141945 | − | 0.989874i | \(-0.545336\pi\) | ||||
−0.141945 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(258\) | −18.7876 | −1.16966 | ||||||||
\(259\) | 38.7322 | 2.40670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.76744 | 0.233199 | ||||||||
\(262\) | −3.44378 | −0.212757 | ||||||||
\(263\) | −5.18258 | −0.319572 | −0.159786 | − | 0.987152i | \(-0.551080\pi\) | ||||
−0.159786 | + | 0.987152i | \(0.551080\pi\) | |||||||
\(264\) | −9.74256 | −0.599613 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 37.6460 | 2.30822 | ||||||||
\(267\) | −1.60687 | −0.0983391 | ||||||||
\(268\) | 5.19913 | 0.317587 | ||||||||
\(269\) | 11.2816 | 0.687851 | 0.343925 | − | 0.938997i | \(-0.388243\pi\) | ||||
0.343925 | + | 0.938997i | \(0.388243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.4302 | 1.90925 | 0.954625 | − | 0.297811i | \(-0.0962565\pi\) | ||||
0.954625 | + | 0.297811i | \(0.0962565\pi\) | |||||||
\(272\) | 32.4053 | 1.96486 | ||||||||
\(273\) | −18.7615 | −1.13550 | ||||||||
\(274\) | −5.82750 | −0.352052 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.36786 | 0.0823357 | ||||||||
\(277\) | 16.2654 | 0.977290 | 0.488645 | − | 0.872483i | \(-0.337491\pi\) | ||||
0.488645 | + | 0.872483i | \(0.337491\pi\) | |||||||
\(278\) | −35.0786 | −2.10387 | ||||||||
\(279\) | −7.29585 | −0.436791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.17157 | −0.129545 | −0.0647726 | − | 0.997900i | \(-0.520632\pi\) | ||||
−0.0647726 | + | 0.997900i | \(0.520632\pi\) | |||||||
\(282\) | 1.68554 | 0.100373 | ||||||||
\(283\) | 8.61050 | 0.511841 | 0.255921 | − | 0.966698i | \(-0.417621\pi\) | ||||
0.255921 | + | 0.966698i | \(0.417621\pi\) | |||||||
\(284\) | 8.02745 | 0.476342 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32.8718 | 1.94375 | ||||||||
\(287\) | 31.1765 | 1.84029 | ||||||||
\(288\) | −4.47824 | −0.263883 | ||||||||
\(289\) | 25.4318 | 1.49599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.26050 | 0.484239 | ||||||||
\(292\) | 3.66786 | 0.214645 | ||||||||
\(293\) | 19.7701 | 1.15498 | 0.577491 | − | 0.816397i | \(-0.304032\pi\) | ||||
0.577491 | + | 0.816397i | \(0.304032\pi\) | |||||||
\(294\) | 27.0027 | 1.57483 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.7696 | 0.916588 | ||||||||
\(297\) | 4.98737 | 0.289396 | ||||||||
\(298\) | −8.03573 | −0.465497 | ||||||||
\(299\) | 6.35959 | 0.367785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 53.4792 | 3.08249 | ||||||||
\(302\) | 0.870623 | 0.0500987 | ||||||||
\(303\) | 8.38117 | 0.481485 | ||||||||
\(304\) | 23.1576 | 1.32818 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.9796 | −0.627661 | ||||||||
\(307\) | −6.07107 | −0.346494 | −0.173247 | − | 0.984878i | \(-0.555426\pi\) | ||||
−0.173247 | + | 0.984878i | \(0.555426\pi\) | |||||||
\(308\) | −20.1257 | −1.14677 | ||||||||
\(309\) | −14.1775 | −0.806528 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.8681 | 1.69366 | 0.846831 | − | 0.531861i | \(-0.178507\pi\) | ||||
0.846831 | + | 0.531861i | \(0.178507\pi\) | |||||||
\(312\) | −7.63861 | −0.432451 | ||||||||
\(313\) | −2.93236 | −0.165747 | −0.0828734 | − | 0.996560i | \(-0.526410\pi\) | ||||
−0.0828734 | + | 0.996560i | \(0.526410\pi\) | |||||||
\(314\) | −34.5628 | −1.95049 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.70160 | 0.151977 | ||||||||
\(317\) | 19.6247 | 1.10224 | 0.551118 | − | 0.834428i | \(-0.314202\pi\) | ||||
0.551118 | + | 0.834428i | \(0.314202\pi\) | |||||||
\(318\) | −3.77429 | −0.211652 | ||||||||
\(319\) | 18.7896 | 1.05202 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.17157 | −0.288649 | ||||||||
\(322\) | −13.1526 | −0.732964 | ||||||||
\(323\) | 30.3229 | 1.68721 | ||||||||
\(324\) | 0.841058 | 0.0467255 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 28.0688 | 1.55459 | ||||||||
\(327\) | −0.928932 | −0.0513701 | ||||||||
\(328\) | 12.6933 | 0.700872 | ||||||||
\(329\) | −4.79793 | −0.264519 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0609889 | −0.00335226 | −0.00167613 | − | 0.999999i | \(-0.500534\pi\) | ||||
−0.00167613 | + | 0.999999i | \(0.500534\pi\) | |||||||
\(332\) | −4.80600 | −0.263764 | ||||||||
\(333\) | −8.07269 | −0.442381 | ||||||||
\(334\) | −9.20949 | −0.503921 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 23.8685 | 1.30213 | ||||||||
\(337\) | 24.9920 | 1.36140 | 0.680699 | − | 0.732563i | \(-0.261676\pi\) | ||||
0.680699 | + | 0.732563i | \(0.261676\pi\) | |||||||
\(338\) | 3.86093 | 0.210007 | ||||||||
\(339\) | 3.66170 | 0.198876 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.3871 | −1.97047 | ||||||||
\(342\) | −7.84629 | −0.424279 | ||||||||
\(343\) | −43.2781 | −2.33680 | ||||||||
\(344\) | 21.7737 | 1.17396 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 41.5868 | 2.23572 | ||||||||
\(347\) | −18.5427 | −0.995422 | −0.497711 | − | 0.867343i | \(-0.665826\pi\) | ||||
−0.497711 | + | 0.867343i | \(0.665826\pi\) | |||||||
\(348\) | 3.16864 | 0.169857 | ||||||||
\(349\) | −26.9141 | −1.44068 | −0.720340 | − | 0.693621i | \(-0.756014\pi\) | ||||
−0.720340 | + | 0.693621i | \(0.756014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.91032 | 0.208718 | ||||||||
\(352\) | −22.3347 | −1.19044 | ||||||||
\(353\) | −27.1201 | −1.44346 | −0.721729 | − | 0.692176i | \(-0.756652\pi\) | ||||
−0.721729 | + | 0.692176i | \(0.756652\pi\) | |||||||
\(354\) | −4.19913 | −0.223181 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.35147 | −0.0716280 | ||||||||
\(357\) | 31.2536 | 1.65412 | ||||||||
\(358\) | 8.89627 | 0.470183 | ||||||||
\(359\) | −0.427902 | −0.0225838 | −0.0112919 | − | 0.999936i | \(-0.503594\pi\) | ||||
−0.0112919 | + | 0.999936i | \(0.503594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.66949 | 0.140499 | ||||||||
\(362\) | −18.5580 | −0.975385 | ||||||||
\(363\) | 13.8738 | 0.728188 | ||||||||
\(364\) | −15.7795 | −0.827070 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −25.1378 | −1.31397 | ||||||||
\(367\) | 8.41744 | 0.439387 | 0.219693 | − | 0.975569i | \(-0.429494\pi\) | ||||
0.219693 | + | 0.975569i | \(0.429494\pi\) | |||||||
\(368\) | −8.09071 | −0.421758 | ||||||||
\(369\) | −6.49791 | −0.338268 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.7436 | 0.557780 | ||||||||
\(372\) | −6.13623 | −0.318149 | ||||||||
\(373\) | 30.4169 | 1.57493 | 0.787464 | − | 0.616361i | \(-0.211394\pi\) | ||||
0.787464 | + | 0.616361i | \(0.211394\pi\) | |||||||
\(374\) | −54.7592 | −2.83153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.95345 | −0.100741 | ||||||||
\(377\) | 14.7319 | 0.758731 | ||||||||
\(378\) | −8.08713 | −0.415957 | ||||||||
\(379\) | −14.7694 | −0.758655 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3633 | −0.735854 | ||||||||
\(382\) | 42.3410 | 2.16636 | ||||||||
\(383\) | 1.84361 | 0.0942041 | 0.0471021 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471021 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(384\) | 13.0038 | 0.663598 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −29.7653 | −1.51501 | ||||||||
\(387\) | −11.1463 | −0.566599 | ||||||||
\(388\) | 6.94757 | 0.352709 | ||||||||
\(389\) | 5.63577 | 0.285745 | 0.142872 | − | 0.989741i | \(-0.454366\pi\) | ||||
0.142872 | + | 0.989741i | \(0.454366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5941 | −0.535765 | ||||||||
\(392\) | −31.2945 | −1.58061 | ||||||||
\(393\) | −2.04313 | −0.103062 | ||||||||
\(394\) | 36.2836 | 1.82794 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.19467 | 0.210790 | ||||||||
\(397\) | −2.13528 | −0.107167 | −0.0535833 | − | 0.998563i | \(-0.517064\pi\) | ||||
−0.0535833 | + | 0.998563i | \(0.517064\pi\) | |||||||
\(398\) | 6.70967 | 0.336326 | ||||||||
\(399\) | 22.3346 | 1.11813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0880 | 0.603646 | 0.301823 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301823 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(402\) | 10.4194 | 0.519675 | ||||||||
\(403\) | −28.5291 | −1.42114 | ||||||||
\(404\) | 7.04905 | 0.350703 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.4677 | −1.51209 | ||||||||
\(407\) | −40.2615 | −1.99569 | ||||||||
\(408\) | 12.7247 | 0.629966 | ||||||||
\(409\) | −23.7490 | −1.17431 | −0.587156 | − | 0.809473i | \(-0.699753\pi\) | ||||
−0.587156 | + | 0.809473i | \(0.699753\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.45734 | −0.170538 | ||||||||
\(412\) | −11.9241 | −0.587458 | ||||||||
\(413\) | 11.9529 | 0.588164 | ||||||||
\(414\) | 2.74130 | 0.134728 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −17.5114 | −0.858566 | ||||||||
\(417\) | −20.8114 | −1.01914 | ||||||||
\(418\) | −39.1323 | −1.91403 | ||||||||
\(419\) | −16.3513 | −0.798815 | −0.399408 | − | 0.916773i | \(-0.630784\pi\) | ||||
−0.399408 | + | 0.916773i | \(0.630784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0036 | 0.682494 | 0.341247 | − | 0.939974i | \(-0.389151\pi\) | ||||
0.341247 | + | 0.939974i | \(0.389151\pi\) | |||||||
\(422\) | −12.0153 | −0.584896 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 4.37418 | 0.212429 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.0876 | 0.779448 | ||||||||
\(427\) | 71.5552 | 3.46280 | ||||||||
\(428\) | −4.34959 | −0.210246 | ||||||||
\(429\) | 19.5022 | 0.941576 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.1248 | −1.30655 | −0.653277 | − | 0.757119i | \(-0.726606\pi\) | ||||
−0.653277 | + | 0.757119i | \(0.726606\pi\) | |||||||
\(432\) | −4.97474 | −0.239347 | ||||||||
\(433\) | 35.8832 | 1.72444 | 0.862218 | − | 0.506537i | \(-0.169075\pi\) | ||||
0.862218 | + | 0.506537i | \(0.169075\pi\) | |||||||
\(434\) | 59.0024 | 2.83221 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.781286 | −0.0374168 | ||||||||
\(437\) | −7.57079 | −0.362160 | ||||||||
\(438\) | 7.35067 | 0.351229 | ||||||||
\(439\) | 10.8236 | 0.516581 | 0.258291 | − | 0.966067i | \(-0.416841\pi\) | ||||
0.258291 | + | 0.966067i | \(0.416841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.0202 | 0.762865 | ||||||||
\(442\) | −42.9337 | −2.04215 | ||||||||
\(443\) | −9.79216 | −0.465239 | −0.232620 | − | 0.972568i | \(-0.574730\pi\) | ||||
−0.232620 | + | 0.972568i | \(0.574730\pi\) | |||||||
\(444\) | −6.78960 | −0.322220 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.5502 | 1.02043 | ||||||||
\(447\) | −4.76744 | −0.225492 | ||||||||
\(448\) | −11.5208 | −0.544306 | ||||||||
\(449\) | −4.80409 | −0.226719 | −0.113360 | − | 0.993554i | \(-0.536161\pi\) | ||||
−0.113360 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.4075 | −1.52601 | ||||||||
\(452\) | 3.07970 | 0.144857 | ||||||||
\(453\) | 0.516523 | 0.0242684 | ||||||||
\(454\) | −26.5500 | −1.24605 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.09339 | 0.425837 | ||||||||
\(457\) | 2.97891 | 0.139348 | 0.0696738 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696738 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(458\) | −9.60757 | −0.448932 | ||||||||
\(459\) | −6.51397 | −0.304046 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2372 | 1.26856 | 0.634280 | − | 0.773103i | \(-0.281297\pi\) | ||||
0.634280 | + | 0.773103i | \(0.281297\pi\) | |||||||
\(462\) | −40.3335 | −1.87648 | ||||||||
\(463\) | −4.17841 | −0.194187 | −0.0970935 | − | 0.995275i | \(-0.530955\pi\) | ||||
−0.0970935 | + | 0.995275i | \(0.530955\pi\) | |||||||
\(464\) | −18.7420 | −0.870076 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.2179 | 0.936577 | ||||||||
\(467\) | 16.5287 | 0.764858 | 0.382429 | − | 0.923985i | \(-0.375088\pi\) | ||||
0.382429 | + | 0.923985i | \(0.375088\pi\) | |||||||
\(468\) | 3.28881 | 0.152025 | ||||||||
\(469\) | −29.6591 | −1.36953 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.5054 | −0.944841 | ||||||||
\(472\) | 4.86655 | 0.224001 | ||||||||
\(473\) | −55.5908 | −2.55607 | ||||||||
\(474\) | 5.41421 | 0.248683 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.2861 | 1.20482 | ||||||||
\(477\) | −2.23921 | −0.102527 | ||||||||
\(478\) | 6.38186 | 0.291899 | ||||||||
\(479\) | −39.9123 | −1.82364 | −0.911820 | − | 0.410589i | \(-0.865323\pi\) | ||||
−0.911820 | + | 0.410589i | \(0.865323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.5668 | −1.43932 | ||||||||
\(482\) | 17.6379 | 0.803382 | ||||||||
\(483\) | −7.80316 | −0.355056 | ||||||||
\(484\) | 11.6687 | 0.530396 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.68554 | 0.0764578 | ||||||||
\(487\) | −5.78169 | −0.261993 | −0.130997 | − | 0.991383i | \(-0.541818\pi\) | ||||
−0.130997 | + | 0.991383i | \(0.541818\pi\) | |||||||
\(488\) | 29.1332 | 1.31880 | ||||||||
\(489\) | 16.6527 | 0.753060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.4871 | −0.789181 | −0.394591 | − | 0.918857i | \(-0.629114\pi\) | ||||
−0.394591 | + | 0.918857i | \(0.629114\pi\) | |||||||
\(492\) | −5.46512 | −0.246387 | ||||||||
\(493\) | −24.5410 | −1.10527 | ||||||||
\(494\) | −30.6815 | −1.38043 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.2949 | 1.62969 | ||||||||
\(497\) | −45.7937 | −2.05413 | ||||||||
\(498\) | −9.63159 | −0.431602 | ||||||||
\(499\) | 11.6687 | 0.522364 | 0.261182 | − | 0.965290i | \(-0.415888\pi\) | ||||
0.261182 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.46381 | −0.244105 | ||||||||
\(502\) | −18.2007 | −0.812338 | ||||||||
\(503\) | 3.96440 | 0.176764 | 0.0883819 | − | 0.996087i | \(-0.471830\pi\) | ||||
0.0883819 | + | 0.996087i | \(0.471830\pi\) | |||||||
\(504\) | 9.37251 | 0.417485 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.6719 | 0.607789 | ||||||||
\(507\) | 2.29061 | 0.101730 | ||||||||
\(508\) | −12.0804 | −0.535980 | ||||||||
\(509\) | −25.3225 | −1.12240 | −0.561199 | − | 0.827681i | \(-0.689660\pi\) | ||||
−0.561199 | + | 0.827681i | \(0.689660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.9238 | −0.925616 | ||||||||
\(512\) | 2.84232 | 0.125614 | ||||||||
\(513\) | −4.65505 | −0.205525 | ||||||||
\(514\) | −7.67111 | −0.338358 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.37470 | −0.412698 | ||||||||
\(517\) | 4.98737 | 0.219344 | ||||||||
\(518\) | 65.2849 | 2.86845 | ||||||||
\(519\) | 24.6727 | 1.08301 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5284 | −0.680313 | −0.340156 | − | 0.940369i | \(-0.610480\pi\) | ||||
−0.340156 | + | 0.940369i | \(0.610480\pi\) | |||||||
\(522\) | 6.35018 | 0.277940 | ||||||||
\(523\) | −10.4599 | −0.457379 | −0.228690 | − | 0.973499i | \(-0.573444\pi\) | ||||
−0.228690 | + | 0.973499i | \(0.573444\pi\) | |||||||
\(524\) | −1.71839 | −0.0750681 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.73547 | −0.380885 | ||||||||
\(527\) | 47.5249 | 2.07022 | ||||||||
\(528\) | −24.8109 | −1.07975 | ||||||||
\(529\) | −20.3550 | −0.884998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.49126 | −0.108112 | ||||||||
\(532\) | 18.7847 | 0.814421 | ||||||||
\(533\) | −25.4089 | −1.10058 | ||||||||
\(534\) | −2.70846 | −0.117206 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.0755 | −0.521583 | ||||||||
\(537\) | 5.27798 | 0.227762 | ||||||||
\(538\) | 19.0156 | 0.819822 | ||||||||
\(539\) | 79.8984 | 3.44147 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.9025 | −1.71554 | −0.857770 | − | 0.514033i | \(-0.828151\pi\) | ||||
−0.857770 | + | 0.514033i | \(0.828151\pi\) | |||||||
\(542\) | 52.9770 | 2.27556 | ||||||||
\(543\) | −11.0101 | −0.472488 | ||||||||
\(544\) | 29.1712 | 1.25070 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −31.6233 | −1.35335 | ||||||||
\(547\) | 4.54952 | 0.194523 | 0.0972616 | − | 0.995259i | \(-0.468992\pi\) | ||||
0.0972616 | + | 0.995259i | \(0.468992\pi\) | |||||||
\(548\) | −2.90782 | −0.124216 | ||||||||
\(549\) | −14.9137 | −0.636503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.5376 | −0.747127 | ||||||||
\(552\) | −3.17701 | −0.135222 | ||||||||
\(553\) | −15.4117 | −0.655370 | ||||||||
\(554\) | 27.4160 | 1.16479 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.5036 | −0.742319 | ||||||||
\(557\) | −18.7945 | −0.796346 | −0.398173 | − | 0.917310i | \(-0.630356\pi\) | ||||
−0.398173 | + | 0.917310i | \(0.630356\pi\) | |||||||
\(558\) | −12.2975 | −0.520593 | ||||||||
\(559\) | −43.5857 | −1.84348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.4876 | −1.37163 | ||||||||
\(562\) | −3.66028 | −0.154400 | ||||||||
\(563\) | −15.0257 | −0.633257 | −0.316628 | − | 0.948550i | \(-0.602551\pi\) | ||||
−0.316628 | + | 0.948550i | \(0.602551\pi\) | |||||||
\(564\) | 0.841058 | 0.0354149 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.5134 | 0.610043 | ||||||||
\(567\) | −4.79793 | −0.201494 | ||||||||
\(568\) | −18.6446 | −0.782310 | ||||||||
\(569\) | −4.97891 | −0.208727 | −0.104363 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104363 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.3235 | −1.52009 | −0.760046 | − | 0.649870i | \(-0.774823\pi\) | ||||
−0.760046 | + | 0.649870i | \(0.774823\pi\) | |||||||
\(572\) | 16.4025 | 0.685823 | ||||||||
\(573\) | 25.1201 | 1.04941 | ||||||||
\(574\) | 52.5494 | 2.19337 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.40120 | 0.100050 | ||||||||
\(577\) | 36.7158 | 1.52850 | 0.764249 | − | 0.644921i | \(-0.223110\pi\) | ||||
0.764249 | + | 0.644921i | \(0.223110\pi\) | |||||||
\(578\) | 42.8664 | 1.78301 | ||||||||
\(579\) | −17.6591 | −0.733889 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.4165 | 1.13743 | ||||||||
\(582\) | 13.9234 | 0.577145 | ||||||||
\(583\) | −11.1678 | −0.462522 | ||||||||
\(584\) | −8.51900 | −0.352519 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.3234 | 1.37658 | ||||||||
\(587\) | 14.7577 | 0.609117 | 0.304559 | − | 0.952494i | \(-0.401491\pi\) | ||||
0.304559 | + | 0.952494i | \(0.401491\pi\) | |||||||
\(588\) | 13.4739 | 0.555654 | ||||||||
\(589\) | 33.9625 | 1.39940 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5263 | 0.885475 | ||||||||
\(592\) | 40.1595 | 1.65055 | ||||||||
\(593\) | −32.3786 | −1.32963 | −0.664815 | − | 0.747008i | \(-0.731490\pi\) | ||||
−0.664815 | + | 0.747008i | \(0.731490\pi\) | |||||||
\(594\) | 8.40643 | 0.344920 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.00969 | −0.164243 | ||||||||
\(597\) | 3.98072 | 0.162920 | ||||||||
\(598\) | 10.7194 | 0.438348 | ||||||||
\(599\) | −31.3206 | −1.27972 | −0.639862 | − | 0.768490i | \(-0.721008\pi\) | ||||
−0.639862 | + | 0.768490i | \(0.721008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.2791 | 0.623246 | 0.311623 | − | 0.950206i | \(-0.399127\pi\) | ||||
0.311623 | + | 0.950206i | \(0.399127\pi\) | |||||||
\(602\) | 90.1416 | 3.67390 | ||||||||
\(603\) | 6.18165 | 0.251736 | ||||||||
\(604\) | 0.434426 | 0.0176766 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.1268 | 0.573863 | ||||||||
\(607\) | −13.8748 | −0.563160 | −0.281580 | − | 0.959538i | \(-0.590858\pi\) | ||||
−0.281580 | + | 0.959538i | \(0.590858\pi\) | |||||||
\(608\) | 20.8464 | 0.845435 | ||||||||
\(609\) | −18.0759 | −0.732473 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.91032 | 0.158195 | ||||||||
\(612\) | −5.47863 | −0.221460 | ||||||||
\(613\) | −5.67042 | −0.229026 | −0.114513 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114513 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(614\) | −10.2331 | −0.412972 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 46.7442 | 1.88338 | ||||||||
\(617\) | 26.7059 | 1.07514 | 0.537570 | − | 0.843219i | \(-0.319343\pi\) | ||||
0.537570 | + | 0.843219i | \(0.319343\pi\) | |||||||
\(618\) | −23.8968 | −0.961269 | ||||||||
\(619\) | −27.6770 | −1.11243 | −0.556217 | − | 0.831037i | \(-0.687747\pi\) | ||||
−0.556217 | + | 0.831037i | \(0.687747\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.62636 | 0.0652636 | ||||||||
\(622\) | 50.3439 | 2.01861 | ||||||||
\(623\) | 7.70967 | 0.308882 | ||||||||
\(624\) | −19.4528 | −0.778736 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.94262 | −0.197547 | ||||||||
\(627\) | −23.2164 | −0.927176 | ||||||||
\(628\) | −17.2463 | −0.688201 | ||||||||
\(629\) | 52.5853 | 2.09671 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.12386 | 0.124359 | 0.0621794 | − | 0.998065i | \(-0.480195\pi\) | ||||
0.0621794 | + | 0.998065i | \(0.480195\pi\) | |||||||
\(632\) | −6.27476 | −0.249596 | ||||||||
\(633\) | −7.12845 | −0.283330 | ||||||||
\(634\) | 33.0784 | 1.31371 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.88331 | −0.0746781 | ||||||||
\(637\) | 62.6440 | 2.48204 | ||||||||
\(638\) | 31.6707 | 1.25386 | ||||||||
\(639\) | 9.54447 | 0.377573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4431 | −0.728459 | −0.364229 | − | 0.931309i | \(-0.618668\pi\) | ||||
−0.364229 | + | 0.931309i | \(0.618668\pi\) | |||||||
\(642\) | −8.71691 | −0.344029 | ||||||||
\(643\) | 2.57676 | 0.101618 | 0.0508088 | − | 0.998708i | \(-0.483820\pi\) | ||||
0.0508088 | + | 0.998708i | \(0.483820\pi\) | |||||||
\(644\) | −6.56292 | −0.258615 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 51.1105 | 2.01092 | ||||||||
\(647\) | −28.1876 | −1.10817 | −0.554084 | − | 0.832461i | \(-0.686931\pi\) | ||||
−0.554084 | + | 0.832461i | \(0.686931\pi\) | |||||||
\(648\) | −1.95345 | −0.0767386 | ||||||||
\(649\) | −12.4248 | −0.487718 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.0050 | 1.37195 | ||||||||
\(652\) | 14.0059 | 0.548512 | ||||||||
\(653\) | 36.2208 | 1.41743 | 0.708715 | − | 0.705495i | \(-0.249275\pi\) | ||||
0.708715 | + | 0.705495i | \(0.249275\pi\) | |||||||
\(654\) | −1.56576 | −0.0612259 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.3254 | 1.26210 | ||||||||
\(657\) | 4.36101 | 0.170139 | ||||||||
\(658\) | −8.08713 | −0.315269 | ||||||||
\(659\) | −15.3532 | −0.598077 | −0.299038 | − | 0.954241i | \(-0.596666\pi\) | ||||
−0.299038 | + | 0.954241i | \(0.596666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.4276 | 1.45577 | 0.727883 | − | 0.685701i | \(-0.240504\pi\) | ||||
0.727883 | + | 0.685701i | \(0.240504\pi\) | |||||||
\(662\) | −0.102800 | −0.00399542 | ||||||||
\(663\) | −25.4717 | −0.989240 | ||||||||
\(664\) | 11.1625 | 0.433187 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.6069 | −0.527256 | ||||||||
\(667\) | 6.12721 | 0.237247 | ||||||||
\(668\) | −4.59538 | −0.177801 | ||||||||
\(669\) | 12.7853 | 0.494308 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −74.3804 | −2.87142 | ||||||||
\(672\) | 21.4863 | 0.828853 | ||||||||
\(673\) | −5.37091 | −0.207033 | −0.103517 | − | 0.994628i | \(-0.533009\pi\) | ||||
−0.103517 | + | 0.994628i | \(0.533009\pi\) | |||||||
\(674\) | 42.1250 | 1.62260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.92654 | 0.0740977 | ||||||||
\(677\) | −22.3546 | −0.859157 | −0.429578 | − | 0.903030i | \(-0.641338\pi\) | ||||
−0.429578 | + | 0.903030i | \(0.641338\pi\) | |||||||
\(678\) | 6.17196 | 0.237033 | ||||||||
\(679\) | −39.6333 | −1.52099 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.7516 | −0.603602 | ||||||||
\(682\) | −61.3320 | −2.34852 | ||||||||
\(683\) | −1.43893 | −0.0550592 | −0.0275296 | − | 0.999621i | \(-0.508764\pi\) | ||||
−0.0275296 | + | 0.999621i | \(0.508764\pi\) | |||||||
\(684\) | −3.91517 | −0.149700 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −72.9472 | −2.78514 | ||||||||
\(687\) | −5.69998 | −0.217468 | ||||||||
\(688\) | 55.4500 | 2.11401 | ||||||||
\(689\) | −8.75604 | −0.333579 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.4432 | −0.853780 | −0.426890 | − | 0.904304i | \(-0.640391\pi\) | ||||
−0.426890 | + | 0.904304i | \(0.640391\pi\) | |||||||
\(692\) | 20.7511 | 0.788840 | ||||||||
\(693\) | −23.9291 | −0.908990 | ||||||||
\(694\) | −31.2545 | −1.18640 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.35949 | −0.278961 | ||||||||
\(697\) | 42.3272 | 1.60326 | ||||||||
\(698\) | −45.3650 | −1.71709 | ||||||||
\(699\) | 11.9949 | 0.453689 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.2203 | −0.990329 | −0.495164 | − | 0.868799i | \(-0.664892\pi\) | ||||
−0.495164 | + | 0.868799i | \(0.664892\pi\) | |||||||
\(702\) | 6.59102 | 0.248762 | ||||||||
\(703\) | 37.5788 | 1.41731 | ||||||||
\(704\) | 11.9757 | 0.451350 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.7121 | −1.72040 | ||||||||
\(707\) | −40.2123 | −1.51234 | ||||||||
\(708\) | −2.09530 | −0.0787460 | ||||||||
\(709\) | −5.85921 | −0.220047 | −0.110024 | − | 0.993929i | \(-0.535093\pi\) | ||||
−0.110024 | + | 0.993929i | \(0.535093\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.21215 | 0.120465 | ||||||||
\(712\) | 3.13894 | 0.117637 | ||||||||
\(713\) | −11.8657 | −0.444373 | ||||||||
\(714\) | 52.6793 | 1.97147 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.43909 | 0.165897 | ||||||||
\(717\) | 3.78623 | 0.141399 | ||||||||
\(718\) | −0.721248 | −0.0269167 | ||||||||
\(719\) | −13.3431 | −0.497613 | −0.248807 | − | 0.968553i | \(-0.580038\pi\) | ||||
−0.248807 | + | 0.968553i | \(0.580038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 68.0226 | 2.53329 | ||||||||
\(722\) | 4.49954 | 0.167455 | ||||||||
\(723\) | 10.4642 | 0.389168 | ||||||||
\(724\) | −9.26012 | −0.344150 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.3850 | 0.867898 | ||||||||
\(727\) | −38.3618 | −1.42276 | −0.711380 | − | 0.702807i | \(-0.751930\pi\) | ||||
−0.711380 | + | 0.702807i | \(0.751930\pi\) | |||||||
\(728\) | 36.6495 | 1.35832 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72.6067 | 2.68546 | ||||||||
\(732\) | −12.5433 | −0.463615 | ||||||||
\(733\) | 39.4542 | 1.45728 | 0.728638 | − | 0.684899i | \(-0.240154\pi\) | ||||
0.728638 | + | 0.684899i | \(0.240154\pi\) | |||||||
\(734\) | 14.1880 | 0.523687 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.28324 | −0.268464 | ||||||||
\(737\) | 30.8302 | 1.13564 | ||||||||
\(738\) | −10.9525 | −0.403168 | ||||||||
\(739\) | 11.3133 | 0.416168 | 0.208084 | − | 0.978111i | \(-0.433277\pi\) | ||||
0.208084 | + | 0.978111i | \(0.433277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.2027 | −0.668694 | ||||||||
\(742\) | 18.1088 | 0.664795 | ||||||||
\(743\) | 22.4849 | 0.824891 | 0.412445 | − | 0.910982i | \(-0.364675\pi\) | ||||
0.412445 | + | 0.910982i | \(0.364675\pi\) | |||||||
\(744\) | 14.2520 | 0.522505 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 51.2690 | 1.87709 | ||||||||
\(747\) | −5.71423 | −0.209073 | ||||||||
\(748\) | −27.3239 | −0.999062 | ||||||||
\(749\) | 24.8129 | 0.906642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.8715 | −1.41844 | −0.709220 | − | 0.704987i | \(-0.750953\pi\) | ||||
−0.709220 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(752\) | −4.97474 | −0.181410 | ||||||||
\(753\) | −10.7981 | −0.393506 | ||||||||
\(754\) | 24.8313 | 0.904301 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.03534 | −0.146764 | ||||||||
\(757\) | 36.6789 | 1.33312 | 0.666559 | − | 0.745453i | \(-0.267767\pi\) | ||||
0.666559 | + | 0.745453i | \(0.267767\pi\) | |||||||
\(758\) | −24.8945 | −0.904211 | ||||||||
\(759\) | 8.11126 | 0.294420 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.6063 | 1.36323 | 0.681614 | − | 0.731712i | \(-0.261278\pi\) | ||||
0.681614 | + | 0.731712i | \(0.261278\pi\) | |||||||
\(762\) | −24.2100 | −0.877035 | ||||||||
\(763\) | 4.45695 | 0.161353 | ||||||||
\(764\) | 21.1275 | 0.764365 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.10749 | 0.112278 | ||||||||
\(767\) | −9.74163 | −0.351750 | ||||||||
\(768\) | 17.1161 | 0.617624 | ||||||||
\(769\) | 23.4609 | 0.846023 | 0.423012 | − | 0.906124i | \(-0.360973\pi\) | ||||
0.423012 | + | 0.906124i | \(0.360973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.55112 | −0.163904 | ||||||||
\(772\) | −14.8524 | −0.534549 | ||||||||
\(773\) | −31.0435 | −1.11656 | −0.558279 | − | 0.829653i | \(-0.688538\pi\) | ||||
−0.558279 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(774\) | −18.7876 | −0.675306 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.1365 | −0.579265 | ||||||||
\(777\) | 38.7322 | 1.38951 | ||||||||
\(778\) | 9.49933 | 0.340568 | ||||||||
\(779\) | 30.2481 | 1.08375 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.6018 | 1.70333 | ||||||||
\(782\) | −17.8568 | −0.638556 | ||||||||
\(783\) | 3.76744 | 0.134637 | ||||||||
\(784\) | −79.6961 | −2.84629 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.44378 | −0.122835 | ||||||||
\(787\) | −25.9324 | −0.924391 | −0.462195 | − | 0.886778i | \(-0.652938\pi\) | ||||
−0.462195 | + | 0.886778i | \(0.652938\pi\) | |||||||
\(788\) | 18.1049 | 0.644961 | ||||||||
\(789\) | −5.18258 | −0.184505 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5686 | −0.624667 | ||||||||
\(792\) | −9.74256 | −0.346187 | ||||||||
\(793\) | −58.3175 | −2.07092 | ||||||||
\(794\) | −3.59911 | −0.127728 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.34802 | 0.118667 | ||||||||
\(797\) | −17.3135 | −0.613274 | −0.306637 | − | 0.951827i | \(-0.599204\pi\) | ||||
−0.306637 | + | 0.951827i | \(0.599204\pi\) | |||||||
\(798\) | 37.6460 | 1.33265 | ||||||||
\(799\) | −6.51397 | −0.230448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60687 | −0.0567761 | ||||||||
\(802\) | 20.3749 | 0.719461 | ||||||||
\(803\) | 21.7500 | 0.767539 | ||||||||
\(804\) | 5.19913 | 0.183359 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −48.0871 | −1.69379 | ||||||||
\(807\) | 11.2816 | 0.397131 | ||||||||
\(808\) | −16.3722 | −0.575971 | ||||||||
\(809\) | −4.16229 | −0.146338 | −0.0731692 | − | 0.997320i | \(-0.523311\pi\) | ||||
−0.0731692 | + | 0.997320i | \(0.523311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.28938 | 0.0803909 | 0.0401954 | − | 0.999192i | \(-0.487202\pi\) | ||||
0.0401954 | + | 0.999192i | \(0.487202\pi\) | |||||||
\(812\) | −15.2029 | −0.533517 | ||||||||
\(813\) | 31.4302 | 1.10231 | ||||||||
\(814\) | −67.8625 | −2.37858 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 32.4053 | 1.13441 | ||||||||
\(817\) | 51.8866 | 1.81528 | ||||||||
\(818\) | −40.0300 | −1.39962 | ||||||||
\(819\) | −18.7615 | −0.655578 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0108 | −0.558780 | −0.279390 | − | 0.960178i | \(-0.590132\pi\) | ||||
−0.279390 | + | 0.960178i | \(0.590132\pi\) | |||||||
\(822\) | −5.82750 | −0.203257 | ||||||||
\(823\) | −21.2463 | −0.740598 | −0.370299 | − | 0.928913i | \(-0.620745\pi\) | ||||
−0.370299 | + | 0.928913i | \(0.620745\pi\) | |||||||
\(824\) | 27.6950 | 0.964799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.1471 | 0.701009 | ||||||||
\(827\) | −45.9564 | −1.59806 | −0.799030 | − | 0.601292i | \(-0.794653\pi\) | ||||
−0.799030 | + | 0.601292i | \(0.794653\pi\) | |||||||
\(828\) | 1.36786 | 0.0475365 | ||||||||
\(829\) | 14.4412 | 0.501564 | 0.250782 | − | 0.968044i | \(-0.419312\pi\) | ||||
0.250782 | + | 0.968044i | \(0.419312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2654 | 0.564239 | ||||||||
\(832\) | 9.38945 | 0.325521 | ||||||||
\(833\) | −104.355 | −3.61568 | ||||||||
\(834\) | −35.0786 | −1.21467 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.5264 | −0.675334 | ||||||||
\(837\) | −7.29585 | −0.252181 | ||||||||
\(838\) | −27.5609 | −0.952076 | ||||||||
\(839\) | −31.8243 | −1.09870 | −0.549348 | − | 0.835594i | \(-0.685124\pi\) | ||||
−0.549348 | + | 0.835594i | \(0.685124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8064 | −0.510566 | ||||||||
\(842\) | 23.6037 | 0.813437 | ||||||||
\(843\) | −2.17157 | −0.0747929 | ||||||||
\(844\) | −5.99544 | −0.206372 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.68554 | 0.0579502 | ||||||||
\(847\) | −66.5658 | −2.28723 | ||||||||
\(848\) | 11.1395 | 0.382532 | ||||||||
\(849\) | 8.61050 | 0.295512 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1291 | −0.450060 | ||||||||
\(852\) | 8.02745 | 0.275016 | ||||||||
\(853\) | 1.12254 | 0.0384351 | 0.0192176 | − | 0.999815i | \(-0.493882\pi\) | ||||
0.0192176 | + | 0.999815i | \(0.493882\pi\) | |||||||
\(854\) | 120.609 | 4.12717 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1024 | 0.345293 | ||||||||
\(857\) | −14.2433 | −0.486543 | −0.243271 | − | 0.969958i | \(-0.578221\pi\) | ||||
−0.243271 | + | 0.969958i | \(0.578221\pi\) | |||||||
\(858\) | 32.8718 | 1.12223 | ||||||||
\(859\) | 57.3669 | 1.95733 | 0.978666 | − | 0.205458i | \(-0.0658683\pi\) | ||||
0.978666 | + | 0.205458i | \(0.0658683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.1765 | 1.06249 | ||||||||
\(862\) | −45.7200 | −1.55723 | ||||||||
\(863\) | 48.0449 | 1.63547 | 0.817734 | − | 0.575597i | \(-0.195230\pi\) | ||||
0.817734 | + | 0.575597i | \(0.195230\pi\) | |||||||
\(864\) | −4.47824 | −0.152353 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 60.4827 | 2.05529 | ||||||||
\(867\) | 25.4318 | 0.863710 | ||||||||
\(868\) | 29.4412 | 0.999300 | ||||||||
\(869\) | 16.0202 | 0.543447 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.1722 | 0.819045 | ||||||||
\(872\) | 1.81462 | 0.0614508 | ||||||||
\(873\) | 8.26050 | 0.279576 | ||||||||
\(874\) | −12.7609 | −0.431644 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.66786 | 0.123926 | ||||||||
\(877\) | −41.0548 | −1.38632 | −0.693161 | − | 0.720783i | \(-0.743782\pi\) | ||||
−0.693161 | + | 0.720783i | \(0.743782\pi\) | |||||||
\(878\) | 18.2436 | 0.615692 | ||||||||
\(879\) | 19.7701 | 0.666830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.1361 | −1.48698 | −0.743492 | − | 0.668745i | \(-0.766832\pi\) | ||||
−0.743492 | + | 0.668745i | \(0.766832\pi\) | |||||||
\(882\) | 27.0027 | 0.909228 | ||||||||
\(883\) | −48.2632 | −1.62419 | −0.812093 | − | 0.583528i | \(-0.801672\pi\) | ||||
−0.812093 | + | 0.583528i | \(0.801672\pi\) | |||||||
\(884\) | −21.4232 | −0.720540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.5051 | −0.554500 | ||||||||
\(887\) | −45.5980 | −1.53103 | −0.765515 | − | 0.643418i | \(-0.777516\pi\) | ||||
−0.765515 | + | 0.643418i | \(0.777516\pi\) | |||||||
\(888\) | 15.7696 | 0.529192 | ||||||||
\(889\) | 68.9142 | 2.31131 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.98737 | 0.167083 | ||||||||
\(892\) | 10.7532 | 0.360043 | ||||||||
\(893\) | −4.65505 | −0.155775 | ||||||||
\(894\) | −8.03573 | −0.268755 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −62.3914 | −2.08435 | ||||||||
\(897\) | 6.35959 | 0.212341 | ||||||||
\(898\) | −8.09751 | −0.270217 | ||||||||
\(899\) | −27.4866 | −0.916731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.5862 | 0.485936 | ||||||||
\(902\) | −54.6242 | −1.81879 | ||||||||
\(903\) | 53.4792 | 1.77968 | ||||||||
\(904\) | −7.15294 | −0.237903 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.870623 | 0.0289245 | ||||||||
\(907\) | 45.2934 | 1.50394 | 0.751972 | − | 0.659195i | \(-0.229103\pi\) | ||||
0.751972 | + | 0.659195i | \(0.229103\pi\) | |||||||
\(908\) | −13.2480 | −0.439650 | ||||||||
\(909\) | 8.38117 | 0.277986 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.7491 | −1.21755 | −0.608775 | − | 0.793343i | \(-0.708339\pi\) | ||||
−0.608775 | + | 0.793343i | \(0.708339\pi\) | |||||||
\(912\) | 23.1576 | 0.766826 | ||||||||
\(913\) | −28.4990 | −0.943179 | ||||||||
\(914\) | 5.02109 | 0.166083 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.79402 | −0.158399 | ||||||||
\(917\) | 9.80278 | 0.323716 | ||||||||
\(918\) | −10.9796 | −0.362380 | ||||||||
\(919\) | −7.84168 | −0.258673 | −0.129337 | − | 0.991601i | \(-0.541285\pi\) | ||||
−0.129337 | + | 0.991601i | \(0.541285\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.07107 | −0.200048 | ||||||||
\(922\) | 45.9094 | 1.51195 | ||||||||
\(923\) | 37.3219 | 1.22847 | ||||||||
\(924\) | −20.1257 | −0.662088 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.04289 | −0.231444 | ||||||||
\(927\) | −14.1775 | −0.465649 | ||||||||
\(928\) | −16.8715 | −0.553834 | ||||||||
\(929\) | −49.0920 | −1.61066 | −0.805329 | − | 0.592829i | \(-0.798011\pi\) | ||||
−0.805329 | + | 0.592829i | \(0.798011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −74.5746 | −2.44408 | ||||||||
\(932\) | 10.0884 | 0.330457 | ||||||||
\(933\) | 29.8681 | 0.977837 | ||||||||
\(934\) | 27.8599 | 0.911603 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.63861 | −0.249676 | ||||||||
\(937\) | −41.1403 | −1.34399 | −0.671997 | − | 0.740554i | \(-0.734563\pi\) | ||||
−0.671997 | + | 0.740554i | \(0.734563\pi\) | |||||||
\(938\) | −49.9918 | −1.63229 | ||||||||
\(939\) | −2.93236 | −0.0956939 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.0325 | 0.555245 | 0.277622 | − | 0.960690i | \(-0.410454\pi\) | ||||
0.277622 | + | 0.960690i | \(0.410454\pi\) | |||||||
\(942\) | −34.5628 | −1.12612 | ||||||||
\(943\) | −10.5679 | −0.344140 | ||||||||
\(944\) | 12.3934 | 0.403370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −93.7007 | −3.04647 | ||||||||
\(947\) | 0.0239474 | 0.000778184 0 | 0.000389092 | − | 1.00000i | \(-0.499876\pi\) | ||||
0.000389092 | 1.00000i | \(0.499876\pi\) | ||||||||
\(948\) | 2.70160 | 0.0877440 | ||||||||
\(949\) | 17.0529 | 0.553562 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.6247 | 0.636376 | ||||||||
\(952\) | −61.0522 | −1.97871 | ||||||||
\(953\) | −23.8427 | −0.772340 | −0.386170 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386170 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(954\) | −3.77429 | −0.122197 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.18444 | 0.102992 | ||||||||
\(957\) | 18.7896 | 0.607382 | ||||||||
\(958\) | −67.2740 | −2.17352 | ||||||||
\(959\) | 16.5881 | 0.535657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.2294 | 0.717076 | ||||||||
\(962\) | −53.2073 | −1.71547 | ||||||||
\(963\) | −5.17157 | −0.166652 | ||||||||
\(964\) | 8.80100 | 0.283461 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.1526 | −0.423177 | ||||||||
\(967\) | 17.2054 | 0.553290 | 0.276645 | − | 0.960972i | \(-0.410777\pi\) | ||||
0.276645 | + | 0.960972i | \(0.410777\pi\) | |||||||
\(968\) | −27.1018 | −0.871086 | ||||||||
\(969\) | 30.3229 | 0.974111 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.9206 | 0.575100 | 0.287550 | − | 0.957766i | \(-0.407159\pi\) | ||||
0.287550 | + | 0.957766i | \(0.407159\pi\) | |||||||
\(972\) | 0.841058 | 0.0269770 | ||||||||
\(973\) | 99.8519 | 3.20110 | ||||||||
\(974\) | −9.74530 | −0.312259 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 74.1920 | 2.37483 | ||||||||
\(977\) | −3.19742 | −0.102295 | −0.0511473 | − | 0.998691i | \(-0.516288\pi\) | ||||
−0.0511473 | + | 0.998691i | \(0.516288\pi\) | |||||||
\(978\) | 28.0688 | 0.897542 | ||||||||
\(979\) | −8.01407 | −0.256131 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.928932 | −0.0296585 | ||||||||
\(982\) | −29.4753 | −0.940593 | ||||||||
\(983\) | −41.4880 | −1.32326 | −0.661631 | − | 0.749830i | \(-0.730135\pi\) | ||||
−0.661631 | + | 0.749830i | \(0.730135\pi\) | |||||||
\(984\) | 12.6933 | 0.404649 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.3649 | −1.31733 | ||||||||
\(987\) | −4.79793 | −0.152720 | ||||||||
\(988\) | −15.3096 | −0.487062 | ||||||||
\(989\) | −18.1279 | −0.576434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.51931 | −0.238859 | −0.119429 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119429 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(992\) | 32.6726 | 1.03736 | ||||||||
\(993\) | −0.0609889 | −0.00193543 | ||||||||
\(994\) | −77.1873 | −2.44823 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.80600 | −0.152284 | ||||||||
\(997\) | 26.0695 | 0.825630 | 0.412815 | − | 0.910815i | \(-0.364546\pi\) | ||||
0.412815 | + | 0.910815i | \(0.364546\pi\) | |||||||
\(998\) | 19.6682 | 0.622585 | ||||||||
\(999\) | −8.07269 | −0.255409 |
(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 | 3525.2.a.t.1.4 | 4 | ||
5.4 | even | 2 | 705.2.a.k.1.1 | ✓ | 4 | ||
15.14 | odd | 2 | 2115.2.a.o.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.a.k.1.1 | ✓ | 4 | 5.4 | even | 2 | ||
2115.2.a.o.1.4 | 4 | 15.14 | odd | 2 | |||
3525.2.a.t.1.4 | 4 | 1.1 | even | 1 | trivial |