Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.445042 | −0.314692 | −0.157346 | − | 0.987544i | \(-0.550294\pi\) | ||||
−0.157346 | + | 0.987544i | \(0.550294\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.80194 | −0.900969 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −0.445042 | −0.181688 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.69202 | 0.598220 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.445042 | −0.140735 | ||||||||
\(11\) | 0.445042 | 0.134185 | 0.0670926 | − | 0.997747i | \(-0.478628\pi\) | ||||
0.0670926 | + | 0.997747i | \(0.478628\pi\) | |||||||
\(12\) | −1.80194 | −0.520175 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.445042 | 0.118942 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.85086 | 0.712714 | ||||||||
\(17\) | −0.753020 | −0.182634 | −0.0913171 | − | 0.995822i | \(-0.529108\pi\) | ||||
−0.0913171 | + | 0.995822i | \(0.529108\pi\) | |||||||
\(18\) | −0.445042 | −0.104897 | ||||||||
\(19\) | −3.40581 | −0.781347 | −0.390674 | − | 0.920529i | \(-0.627758\pi\) | ||||
−0.390674 | + | 0.920529i | \(0.627758\pi\) | |||||||
\(20\) | −1.80194 | −0.402926 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.198062 | −0.0422270 | ||||||||
\(23\) | −2.64310 | −0.551125 | −0.275563 | − | 0.961283i | \(-0.588864\pi\) | ||||
−0.275563 | + | 0.961283i | \(0.588864\pi\) | |||||||
\(24\) | 1.69202 | 0.345382 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.80194 | 0.340534 | ||||||||
\(29\) | −2.13706 | −0.396843 | −0.198421 | − | 0.980117i | \(-0.563581\pi\) | ||||
−0.198421 | + | 0.980117i | \(0.563581\pi\) | |||||||
\(30\) | −0.445042 | −0.0812532 | ||||||||
\(31\) | 1.24698 | 0.223964 | 0.111982 | − | 0.993710i | \(-0.464280\pi\) | ||||
0.111982 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(32\) | −4.65279 | −0.822505 | ||||||||
\(33\) | 0.445042 | 0.0774718 | ||||||||
\(34\) | 0.335126 | 0.0574736 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.80194 | −0.300323 | ||||||||
\(37\) | 8.20775 | 1.34935 | 0.674673 | − | 0.738117i | \(-0.264285\pi\) | ||||
0.674673 | + | 0.738117i | \(0.264285\pi\) | |||||||
\(38\) | 1.51573 | 0.245884 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.69202 | 0.267532 | ||||||||
\(41\) | 1.51573 | 0.236717 | 0.118359 | − | 0.992971i | \(-0.462237\pi\) | ||||
0.118359 | + | 0.992971i | \(0.462237\pi\) | |||||||
\(42\) | 0.445042 | 0.0686715 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −0.801938 | −0.120897 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.17629 | 0.173435 | ||||||||
\(47\) | −8.07069 | −1.17723 | −0.588615 | − | 0.808413i | \(-0.700327\pi\) | ||||
−0.588615 | + | 0.808413i | \(0.700327\pi\) | |||||||
\(48\) | 2.85086 | 0.411485 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.78017 | 0.251754 | ||||||||
\(51\) | −0.753020 | −0.105444 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.16421 | 0.571998 | 0.285999 | − | 0.958230i | \(-0.407675\pi\) | ||||
0.285999 | + | 0.958230i | \(0.407675\pi\) | |||||||
\(54\) | −0.445042 | −0.0605625 | ||||||||
\(55\) | 0.445042 | 0.0600094 | ||||||||
\(56\) | −1.69202 | −0.226106 | ||||||||
\(57\) | −3.40581 | −0.451111 | ||||||||
\(58\) | 0.951083 | 0.124883 | ||||||||
\(59\) | −10.3840 | −1.35189 | −0.675944 | − | 0.736953i | \(-0.736264\pi\) | ||||
−0.675944 | + | 0.736953i | \(0.736264\pi\) | |||||||
\(60\) | −1.80194 | −0.232629 | ||||||||
\(61\) | −2.14914 | −0.275170 | −0.137585 | − | 0.990490i | \(-0.543934\pi\) | ||||
−0.137585 | + | 0.990490i | \(0.543934\pi\) | |||||||
\(62\) | −0.554958 | −0.0704798 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −3.63102 | −0.453878 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.198062 | −0.0243798 | ||||||||
\(67\) | 0.740939 | 0.0905201 | 0.0452600 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452600 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(68\) | 1.35690 | 0.164548 | ||||||||
\(69\) | −2.64310 | −0.318192 | ||||||||
\(70\) | 0.445042 | 0.0531927 | ||||||||
\(71\) | 1.66487 | 0.197584 | 0.0987921 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987921 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(72\) | 1.69202 | 0.199407 | ||||||||
\(73\) | 5.74094 | 0.671926 | 0.335963 | − | 0.941875i | \(-0.390938\pi\) | ||||
0.335963 | + | 0.941875i | \(0.390938\pi\) | |||||||
\(74\) | −3.65279 | −0.424629 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 6.13706 | 0.703969 | ||||||||
\(77\) | −0.445042 | −0.0507172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.719169 | 0.0809128 | 0.0404564 | − | 0.999181i | \(-0.487119\pi\) | ||||
0.0404564 | + | 0.999181i | \(0.487119\pi\) | |||||||
\(80\) | 2.85086 | 0.318735 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.674563 | −0.0744930 | ||||||||
\(83\) | −0.131687 | −0.0144545 | −0.00722724 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722724 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(84\) | 1.80194 | 0.196608 | ||||||||
\(85\) | −0.753020 | −0.0816765 | ||||||||
\(86\) | 3.56033 | 0.383921 | ||||||||
\(87\) | −2.13706 | −0.229117 | ||||||||
\(88\) | 0.753020 | 0.0802722 | ||||||||
\(89\) | 15.5918 | 1.65273 | 0.826363 | − | 0.563137i | \(-0.190406\pi\) | ||||
0.826363 | + | 0.563137i | \(0.190406\pi\) | |||||||
\(90\) | −0.445042 | −0.0469115 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.76271 | 0.496547 | ||||||||
\(93\) | 1.24698 | 0.129306 | ||||||||
\(94\) | 3.59179 | 0.370465 | ||||||||
\(95\) | −3.40581 | −0.349429 | ||||||||
\(96\) | −4.65279 | −0.474874 | ||||||||
\(97\) | 10.8726 | 1.10395 | 0.551974 | − | 0.833861i | \(-0.313875\pi\) | ||||
0.551974 | + | 0.833861i | \(0.313875\pi\) | |||||||
\(98\) | −0.445042 | −0.0449560 | ||||||||
\(99\) | 0.445042 | 0.0447284 | ||||||||
\(100\) | 7.20775 | 0.720775 | ||||||||
\(101\) | −17.0858 | −1.70010 | −0.850048 | − | 0.526705i | \(-0.823427\pi\) | ||||
−0.850048 | + | 0.526705i | \(0.823427\pi\) | |||||||
\(102\) | 0.335126 | 0.0331824 | ||||||||
\(103\) | −7.11529 | −0.701091 | −0.350545 | − | 0.936546i | \(-0.614004\pi\) | ||||
−0.350545 | + | 0.936546i | \(0.614004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −1.85325 | −0.180003 | ||||||||
\(107\) | −13.3545 | −1.29103 | −0.645514 | − | 0.763748i | \(-0.723357\pi\) | ||||
−0.645514 | + | 0.763748i | \(0.723357\pi\) | |||||||
\(108\) | −1.80194 | −0.173392 | ||||||||
\(109\) | −3.93900 | −0.377288 | −0.188644 | − | 0.982046i | \(-0.560409\pi\) | ||||
−0.188644 | + | 0.982046i | \(0.560409\pi\) | |||||||
\(110\) | −0.198062 | −0.0188845 | ||||||||
\(111\) | 8.20775 | 0.779045 | ||||||||
\(112\) | −2.85086 | −0.269380 | ||||||||
\(113\) | −12.5797 | −1.18340 | −0.591700 | − | 0.806158i | \(-0.701543\pi\) | ||||
−0.591700 | + | 0.806158i | \(0.701543\pi\) | |||||||
\(114\) | 1.51573 | 0.141961 | ||||||||
\(115\) | −2.64310 | −0.246471 | ||||||||
\(116\) | 3.85086 | 0.357543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.62133 | 0.425428 | ||||||||
\(119\) | 0.753020 | 0.0690293 | ||||||||
\(120\) | 1.69202 | 0.154460 | ||||||||
\(121\) | −10.8019 | −0.981994 | ||||||||
\(122\) | 0.956459 | 0.0865938 | ||||||||
\(123\) | 1.51573 | 0.136669 | ||||||||
\(124\) | −2.24698 | −0.201785 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0.445042 | 0.0396475 | ||||||||
\(127\) | −11.3991 | −1.01151 | −0.505754 | − | 0.862678i | \(-0.668786\pi\) | ||||
−0.505754 | + | 0.862678i | \(0.668786\pi\) | |||||||
\(128\) | 10.9215 | 0.965337 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.65279 | 0.231776 | 0.115888 | − | 0.993262i | \(-0.463029\pi\) | ||||
0.115888 | + | 0.993262i | \(0.463029\pi\) | |||||||
\(132\) | −0.801938 | −0.0697997 | ||||||||
\(133\) | 3.40581 | 0.295321 | ||||||||
\(134\) | −0.329749 | −0.0284860 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −1.27413 | −0.109255 | ||||||||
\(137\) | −19.9855 | −1.70748 | −0.853739 | − | 0.520701i | \(-0.825671\pi\) | ||||
−0.853739 | + | 0.520701i | \(0.825671\pi\) | |||||||
\(138\) | 1.17629 | 0.100133 | ||||||||
\(139\) | −5.54527 | −0.470344 | −0.235172 | − | 0.971954i | \(-0.575565\pi\) | ||||
−0.235172 | + | 0.971954i | \(0.575565\pi\) | |||||||
\(140\) | 1.80194 | 0.152292 | ||||||||
\(141\) | −8.07069 | −0.679675 | ||||||||
\(142\) | −0.740939 | −0.0621782 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.85086 | 0.237571 | ||||||||
\(145\) | −2.13706 | −0.177473 | ||||||||
\(146\) | −2.55496 | −0.211450 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −14.7899 | −1.21572 | ||||||||
\(149\) | 17.6015 | 1.44197 | 0.720985 | − | 0.692951i | \(-0.243690\pi\) | ||||
0.720985 | + | 0.692951i | \(0.243690\pi\) | |||||||
\(150\) | 1.78017 | 0.145350 | ||||||||
\(151\) | −3.41550 | −0.277950 | −0.138975 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138975 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(152\) | −5.76271 | −0.467417 | ||||||||
\(153\) | −0.753020 | −0.0608781 | ||||||||
\(154\) | 0.198062 | 0.0159603 | ||||||||
\(155\) | 1.24698 | 0.100160 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1196 | −1.36629 | −0.683147 | − | 0.730281i | \(-0.739389\pi\) | ||||
−0.683147 | + | 0.730281i | \(0.739389\pi\) | |||||||
\(158\) | −0.320060 | −0.0254626 | ||||||||
\(159\) | 4.16421 | 0.330243 | ||||||||
\(160\) | −4.65279 | −0.367836 | ||||||||
\(161\) | 2.64310 | 0.208306 | ||||||||
\(162\) | −0.445042 | −0.0349658 | ||||||||
\(163\) | 3.59419 | 0.281518 | 0.140759 | − | 0.990044i | \(-0.455046\pi\) | ||||
0.140759 | + | 0.990044i | \(0.455046\pi\) | |||||||
\(164\) | −2.73125 | −0.213275 | ||||||||
\(165\) | 0.445042 | 0.0346465 | ||||||||
\(166\) | 0.0586060 | 0.00454871 | ||||||||
\(167\) | 8.47219 | 0.655598 | 0.327799 | − | 0.944748i | \(-0.393693\pi\) | ||||
0.327799 | + | 0.944748i | \(0.393693\pi\) | |||||||
\(168\) | −1.69202 | −0.130542 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.335126 | 0.0257030 | ||||||||
\(171\) | −3.40581 | −0.260449 | ||||||||
\(172\) | 14.4155 | 1.09917 | ||||||||
\(173\) | 19.2500 | 1.46355 | 0.731774 | − | 0.681548i | \(-0.238693\pi\) | ||||
0.731774 | + | 0.681548i | \(0.238693\pi\) | |||||||
\(174\) | 0.951083 | 0.0721014 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 1.26875 | 0.0956356 | ||||||||
\(177\) | −10.3840 | −0.780512 | ||||||||
\(178\) | −6.93900 | −0.520100 | ||||||||
\(179\) | −5.63773 | −0.421384 | −0.210692 | − | 0.977553i | \(-0.567572\pi\) | ||||
−0.210692 | + | 0.977553i | \(0.567572\pi\) | |||||||
\(180\) | −1.80194 | −0.134309 | ||||||||
\(181\) | −14.0368 | −1.04335 | −0.521675 | − | 0.853144i | \(-0.674693\pi\) | ||||
−0.521675 | + | 0.853144i | \(0.674693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14914 | −0.158869 | ||||||||
\(184\) | −4.47219 | −0.329694 | ||||||||
\(185\) | 8.20775 | 0.603446 | ||||||||
\(186\) | −0.554958 | −0.0406915 | ||||||||
\(187\) | −0.335126 | −0.0245068 | ||||||||
\(188\) | 14.5429 | 1.06065 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.51573 | 0.109963 | ||||||||
\(191\) | −19.4252 | −1.40556 | −0.702779 | − | 0.711409i | \(-0.748058\pi\) | ||||
−0.702779 | + | 0.711409i | \(0.748058\pi\) | |||||||
\(192\) | −3.63102 | −0.262046 | ||||||||
\(193\) | 6.49827 | 0.467756 | 0.233878 | − | 0.972266i | \(-0.424858\pi\) | ||||
0.233878 | + | 0.972266i | \(0.424858\pi\) | |||||||
\(194\) | −4.83877 | −0.347404 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.80194 | −0.128710 | ||||||||
\(197\) | −13.8998 | −0.990318 | −0.495159 | − | 0.868802i | \(-0.664890\pi\) | ||||
−0.495159 | + | 0.868802i | \(0.664890\pi\) | |||||||
\(198\) | −0.198062 | −0.0140757 | ||||||||
\(199\) | −0.984935 | −0.0698202 | −0.0349101 | − | 0.999390i | \(-0.511114\pi\) | ||||
−0.0349101 | + | 0.999390i | \(0.511114\pi\) | |||||||
\(200\) | −6.76809 | −0.478576 | ||||||||
\(201\) | 0.740939 | 0.0522618 | ||||||||
\(202\) | 7.60388 | 0.535007 | ||||||||
\(203\) | 2.13706 | 0.149992 | ||||||||
\(204\) | 1.35690 | 0.0950017 | ||||||||
\(205\) | 1.51573 | 0.105863 | ||||||||
\(206\) | 3.16660 | 0.220628 | ||||||||
\(207\) | −2.64310 | −0.183708 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.51573 | −0.104845 | ||||||||
\(210\) | 0.445042 | 0.0307108 | ||||||||
\(211\) | 1.44935 | 0.0997776 | 0.0498888 | − | 0.998755i | \(-0.484113\pi\) | ||||
0.0498888 | + | 0.998755i | \(0.484113\pi\) | |||||||
\(212\) | −7.50365 | −0.515353 | ||||||||
\(213\) | 1.66487 | 0.114075 | ||||||||
\(214\) | 5.94331 | 0.406277 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 1.69202 | 0.115127 | ||||||||
\(217\) | −1.24698 | −0.0846505 | ||||||||
\(218\) | 1.75302 | 0.118730 | ||||||||
\(219\) | 5.74094 | 0.387937 | ||||||||
\(220\) | −0.801938 | −0.0540666 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.65279 | −0.245159 | ||||||||
\(223\) | −13.7832 | −0.922988 | −0.461494 | − | 0.887143i | \(-0.652686\pi\) | ||||
−0.461494 | + | 0.887143i | \(0.652686\pi\) | |||||||
\(224\) | 4.65279 | 0.310878 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 5.59850 | 0.372407 | ||||||||
\(227\) | 0.259061 | 0.0171945 | 0.00859725 | − | 0.999963i | \(-0.497263\pi\) | ||||
0.00859725 | + | 0.999963i | \(0.497263\pi\) | |||||||
\(228\) | 6.13706 | 0.406437 | ||||||||
\(229\) | −24.7265 | −1.63397 | −0.816985 | − | 0.576658i | \(-0.804356\pi\) | ||||
−0.816985 | + | 0.576658i | \(0.804356\pi\) | |||||||
\(230\) | 1.17629 | 0.0775624 | ||||||||
\(231\) | −0.445042 | −0.0292816 | ||||||||
\(232\) | −3.61596 | −0.237399 | ||||||||
\(233\) | 13.5961 | 0.890711 | 0.445355 | − | 0.895354i | \(-0.353077\pi\) | ||||
0.445355 | + | 0.895354i | \(0.353077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.07069 | −0.526474 | ||||||||
\(236\) | 18.7114 | 1.21801 | ||||||||
\(237\) | 0.719169 | 0.0467150 | ||||||||
\(238\) | −0.335126 | −0.0217230 | ||||||||
\(239\) | −16.9269 | −1.09491 | −0.547456 | − | 0.836835i | \(-0.684404\pi\) | ||||
−0.547456 | + | 0.836835i | \(0.684404\pi\) | |||||||
\(240\) | 2.85086 | 0.184022 | ||||||||
\(241\) | −7.91484 | −0.509840 | −0.254920 | − | 0.966962i | \(-0.582049\pi\) | ||||
−0.254920 | + | 0.966962i | \(0.582049\pi\) | |||||||
\(242\) | 4.80731 | 0.309026 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.87263 | 0.247919 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −0.674563 | −0.0430086 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.10992 | 0.133980 | ||||||||
\(249\) | −0.131687 | −0.00834529 | ||||||||
\(250\) | 4.00538 | 0.253322 | ||||||||
\(251\) | 13.7845 | 0.870069 | 0.435034 | − | 0.900414i | \(-0.356736\pi\) | ||||
0.435034 | + | 0.900414i | \(0.356736\pi\) | |||||||
\(252\) | 1.80194 | 0.113511 | ||||||||
\(253\) | −1.17629 | −0.0739528 | ||||||||
\(254\) | 5.07308 | 0.318313 | ||||||||
\(255\) | −0.753020 | −0.0471560 | ||||||||
\(256\) | 2.40150 | 0.150094 | ||||||||
\(257\) | 1.56571 | 0.0976664 | 0.0488332 | − | 0.998807i | \(-0.484450\pi\) | ||||
0.0488332 | + | 0.998807i | \(0.484450\pi\) | |||||||
\(258\) | 3.56033 | 0.221657 | ||||||||
\(259\) | −8.20775 | −0.510005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.13706 | −0.132281 | ||||||||
\(262\) | −1.18060 | −0.0729380 | ||||||||
\(263\) | 16.1371 | 0.995054 | 0.497527 | − | 0.867449i | \(-0.334242\pi\) | ||||
0.497527 | + | 0.867449i | \(0.334242\pi\) | |||||||
\(264\) | 0.753020 | 0.0463452 | ||||||||
\(265\) | 4.16421 | 0.255805 | ||||||||
\(266\) | −1.51573 | −0.0929353 | ||||||||
\(267\) | 15.5918 | 0.954202 | ||||||||
\(268\) | −1.33513 | −0.0815558 | ||||||||
\(269\) | −28.7318 | −1.75181 | −0.875906 | − | 0.482482i | \(-0.839735\pi\) | ||||
−0.875906 | + | 0.482482i | \(0.839735\pi\) | |||||||
\(270\) | −0.445042 | −0.0270844 | ||||||||
\(271\) | 1.18359 | 0.0718978 | 0.0359489 | − | 0.999354i | \(-0.488555\pi\) | ||||
0.0359489 | + | 0.999354i | \(0.488555\pi\) | |||||||
\(272\) | −2.14675 | −0.130166 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.89440 | 0.537330 | ||||||||
\(275\) | −1.78017 | −0.107348 | ||||||||
\(276\) | 4.76271 | 0.286681 | ||||||||
\(277\) | −25.8866 | −1.55538 | −0.777688 | − | 0.628650i | \(-0.783608\pi\) | ||||
−0.777688 | + | 0.628650i | \(0.783608\pi\) | |||||||
\(278\) | 2.46788 | 0.148013 | ||||||||
\(279\) | 1.24698 | 0.0746547 | ||||||||
\(280\) | −1.69202 | −0.101118 | ||||||||
\(281\) | 18.3793 | 1.09641 | 0.548207 | − | 0.836343i | \(-0.315310\pi\) | ||||
0.548207 | + | 0.836343i | \(0.315310\pi\) | |||||||
\(282\) | 3.59179 | 0.213888 | ||||||||
\(283\) | 6.02954 | 0.358419 | 0.179209 | − | 0.983811i | \(-0.442646\pi\) | ||||
0.179209 | + | 0.983811i | \(0.442646\pi\) | |||||||
\(284\) | −3.00000 | −0.178017 | ||||||||
\(285\) | −3.40581 | −0.201743 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51573 | −0.0894707 | ||||||||
\(288\) | −4.65279 | −0.274168 | ||||||||
\(289\) | −16.4330 | −0.966645 | ||||||||
\(290\) | 0.951083 | 0.0558495 | ||||||||
\(291\) | 10.8726 | 0.637365 | ||||||||
\(292\) | −10.3448 | −0.605384 | ||||||||
\(293\) | −23.3575 | −1.36456 | −0.682279 | − | 0.731091i | \(-0.739011\pi\) | ||||
−0.682279 | + | 0.731091i | \(0.739011\pi\) | |||||||
\(294\) | −0.445042 | −0.0259554 | ||||||||
\(295\) | −10.3840 | −0.604582 | ||||||||
\(296\) | 13.8877 | 0.807206 | ||||||||
\(297\) | 0.445042 | 0.0258239 | ||||||||
\(298\) | −7.83340 | −0.453776 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.20775 | 0.416140 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 1.52004 | 0.0874686 | ||||||||
\(303\) | −17.0858 | −0.981551 | ||||||||
\(304\) | −9.70948 | −0.556877 | ||||||||
\(305\) | −2.14914 | −0.123060 | ||||||||
\(306\) | 0.335126 | 0.0191579 | ||||||||
\(307\) | −4.14782 | −0.236728 | −0.118364 | − | 0.992970i | \(-0.537765\pi\) | ||||
−0.118364 | + | 0.992970i | \(0.537765\pi\) | |||||||
\(308\) | 0.801938 | 0.0456946 | ||||||||
\(309\) | −7.11529 | −0.404775 | ||||||||
\(310\) | −0.554958 | −0.0315195 | ||||||||
\(311\) | 23.9584 | 1.35856 | 0.679278 | − | 0.733882i | \(-0.262293\pi\) | ||||
0.679278 | + | 0.733882i | \(0.262293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6920 | −0.943489 | −0.471744 | − | 0.881735i | \(-0.656376\pi\) | ||||
−0.471744 | + | 0.881735i | \(0.656376\pi\) | |||||||
\(314\) | 7.61894 | 0.429962 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −1.29590 | −0.0728999 | ||||||||
\(317\) | 9.70948 | 0.545339 | 0.272669 | − | 0.962108i | \(-0.412093\pi\) | ||||
0.272669 | + | 0.962108i | \(0.412093\pi\) | |||||||
\(318\) | −1.85325 | −0.103925 | ||||||||
\(319\) | −0.951083 | −0.0532504 | ||||||||
\(320\) | −3.63102 | −0.202980 | ||||||||
\(321\) | −13.3545 | −0.745376 | ||||||||
\(322\) | −1.17629 | −0.0655522 | ||||||||
\(323\) | 2.56465 | 0.142701 | ||||||||
\(324\) | −1.80194 | −0.100108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.59956 | −0.0885916 | ||||||||
\(327\) | −3.93900 | −0.217827 | ||||||||
\(328\) | 2.56465 | 0.141609 | ||||||||
\(329\) | 8.07069 | 0.444951 | ||||||||
\(330\) | −0.198062 | −0.0109030 | ||||||||
\(331\) | 13.3207 | 0.732169 | 0.366085 | − | 0.930582i | \(-0.380698\pi\) | ||||
0.366085 | + | 0.930582i | \(0.380698\pi\) | |||||||
\(332\) | 0.237291 | 0.0130230 | ||||||||
\(333\) | 8.20775 | 0.449782 | ||||||||
\(334\) | −3.77048 | −0.206311 | ||||||||
\(335\) | 0.740939 | 0.0404818 | ||||||||
\(336\) | −2.85086 | −0.155527 | ||||||||
\(337\) | 26.8974 | 1.46519 | 0.732597 | − | 0.680663i | \(-0.238308\pi\) | ||||
0.732597 | + | 0.680663i | \(0.238308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5797 | −0.683236 | ||||||||
\(340\) | 1.35690 | 0.0735880 | ||||||||
\(341\) | 0.554958 | 0.0300527 | ||||||||
\(342\) | 1.51573 | 0.0819613 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −13.5362 | −0.729821 | ||||||||
\(345\) | −2.64310 | −0.142300 | ||||||||
\(346\) | −8.56704 | −0.460567 | ||||||||
\(347\) | 18.1860 | 0.976275 | 0.488137 | − | 0.872767i | \(-0.337677\pi\) | ||||
0.488137 | + | 0.872767i | \(0.337677\pi\) | |||||||
\(348\) | 3.85086 | 0.206427 | ||||||||
\(349\) | 21.5623 | 1.15420 | 0.577100 | − | 0.816673i | \(-0.304184\pi\) | ||||
0.577100 | + | 0.816673i | \(0.304184\pi\) | |||||||
\(350\) | −1.78017 | −0.0951540 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.07069 | −0.110368 | ||||||||
\(353\) | −0.997607 | −0.0530973 | −0.0265486 | − | 0.999648i | \(-0.508452\pi\) | ||||
−0.0265486 | + | 0.999648i | \(0.508452\pi\) | |||||||
\(354\) | 4.62133 | 0.245621 | ||||||||
\(355\) | 1.66487 | 0.0883624 | ||||||||
\(356\) | −28.0954 | −1.48906 | ||||||||
\(357\) | 0.753020 | 0.0398541 | ||||||||
\(358\) | 2.50902 | 0.132606 | ||||||||
\(359\) | 14.4983 | 0.765189 | 0.382595 | − | 0.923916i | \(-0.375031\pi\) | ||||
0.382595 | + | 0.923916i | \(0.375031\pi\) | |||||||
\(360\) | 1.69202 | 0.0891774 | ||||||||
\(361\) | −7.40044 | −0.389497 | ||||||||
\(362\) | 6.24698 | 0.328334 | ||||||||
\(363\) | −10.8019 | −0.566955 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.74094 | 0.300494 | ||||||||
\(366\) | 0.956459 | 0.0499949 | ||||||||
\(367\) | −8.33752 | −0.435215 | −0.217607 | − | 0.976036i | \(-0.569825\pi\) | ||||
−0.217607 | + | 0.976036i | \(0.569825\pi\) | |||||||
\(368\) | −7.53511 | −0.392795 | ||||||||
\(369\) | 1.51573 | 0.0789057 | ||||||||
\(370\) | −3.65279 | −0.189900 | ||||||||
\(371\) | −4.16421 | −0.216195 | ||||||||
\(372\) | −2.24698 | −0.116500 | ||||||||
\(373\) | 35.8974 | 1.85870 | 0.929348 | − | 0.369205i | \(-0.120370\pi\) | ||||
0.929348 | + | 0.369205i | \(0.120370\pi\) | |||||||
\(374\) | 0.149145 | 0.00771210 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | −13.6558 | −0.704243 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.445042 | 0.0228905 | ||||||||
\(379\) | −34.6088 | −1.77773 | −0.888867 | − | 0.458166i | \(-0.848507\pi\) | ||||
−0.888867 | + | 0.458166i | \(0.848507\pi\) | |||||||
\(380\) | 6.13706 | 0.314825 | ||||||||
\(381\) | −11.3991 | −0.583994 | ||||||||
\(382\) | 8.64502 | 0.442318 | ||||||||
\(383\) | −9.31037 | −0.475738 | −0.237869 | − | 0.971297i | \(-0.576449\pi\) | ||||
−0.237869 | + | 0.971297i | \(0.576449\pi\) | |||||||
\(384\) | 10.9215 | 0.557338 | ||||||||
\(385\) | −0.445042 | −0.0226814 | ||||||||
\(386\) | −2.89200 | −0.147199 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −19.5918 | −0.994623 | ||||||||
\(389\) | 38.5448 | 1.95430 | 0.977149 | − | 0.212554i | \(-0.0681781\pi\) | ||||
0.977149 | + | 0.212554i | \(0.0681781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.99031 | 0.100654 | ||||||||
\(392\) | 1.69202 | 0.0854600 | ||||||||
\(393\) | 2.65279 | 0.133816 | ||||||||
\(394\) | 6.18598 | 0.311645 | ||||||||
\(395\) | 0.719169 | 0.0361853 | ||||||||
\(396\) | −0.801938 | −0.0402989 | ||||||||
\(397\) | 3.67696 | 0.184541 | 0.0922706 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922706 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(398\) | 0.438337 | 0.0219719 | ||||||||
\(399\) | 3.40581 | 0.170504 | ||||||||
\(400\) | −11.4034 | −0.570171 | ||||||||
\(401\) | 23.9530 | 1.19616 | 0.598078 | − | 0.801438i | \(-0.295931\pi\) | ||||
0.598078 | + | 0.801438i | \(0.295931\pi\) | |||||||
\(402\) | −0.329749 | −0.0164464 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 30.7875 | 1.53173 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −0.951083 | −0.0472014 | ||||||||
\(407\) | 3.65279 | 0.181062 | ||||||||
\(408\) | −1.27413 | −0.0630787 | ||||||||
\(409\) | −28.0344 | −1.38621 | −0.693107 | − | 0.720835i | \(-0.743759\pi\) | ||||
−0.693107 | + | 0.720835i | \(0.743759\pi\) | |||||||
\(410\) | −0.674563 | −0.0333143 | ||||||||
\(411\) | −19.9855 | −0.985813 | ||||||||
\(412\) | 12.8213 | 0.631661 | ||||||||
\(413\) | 10.3840 | 0.510965 | ||||||||
\(414\) | 1.17629 | 0.0578116 | ||||||||
\(415\) | −0.131687 | −0.00646424 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.54527 | −0.271553 | ||||||||
\(418\) | 0.674563 | 0.0329940 | ||||||||
\(419\) | −27.5918 | −1.34795 | −0.673974 | − | 0.738755i | \(-0.735414\pi\) | ||||
−0.673974 | + | 0.738755i | \(0.735414\pi\) | |||||||
\(420\) | 1.80194 | 0.0879256 | ||||||||
\(421\) | −17.6746 | −0.861405 | −0.430703 | − | 0.902494i | \(-0.641734\pi\) | ||||
−0.430703 | + | 0.902494i | \(0.641734\pi\) | |||||||
\(422\) | −0.645023 | −0.0313992 | ||||||||
\(423\) | −8.07069 | −0.392410 | ||||||||
\(424\) | 7.04593 | 0.342181 | ||||||||
\(425\) | 3.01208 | 0.146107 | ||||||||
\(426\) | −0.740939 | −0.0358986 | ||||||||
\(427\) | 2.14914 | 0.104004 | ||||||||
\(428\) | 24.0640 | 1.16318 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.56033 | 0.171695 | ||||||||
\(431\) | 7.59717 | 0.365943 | 0.182971 | − | 0.983118i | \(-0.441428\pi\) | ||||
0.182971 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(432\) | 2.85086 | 0.137162 | ||||||||
\(433\) | 19.3927 | 0.931952 | 0.465976 | − | 0.884797i | \(-0.345703\pi\) | ||||
0.465976 | + | 0.884797i | \(0.345703\pi\) | |||||||
\(434\) | 0.554958 | 0.0266388 | ||||||||
\(435\) | −2.13706 | −0.102464 | ||||||||
\(436\) | 7.09783 | 0.339925 | ||||||||
\(437\) | 9.00192 | 0.430620 | ||||||||
\(438\) | −2.55496 | −0.122081 | ||||||||
\(439\) | −13.9554 | −0.666055 | −0.333027 | − | 0.942917i | \(-0.608070\pi\) | ||||
−0.333027 | + | 0.942917i | \(0.608070\pi\) | |||||||
\(440\) | 0.753020 | 0.0358988 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2271 | 1.15107 | 0.575533 | − | 0.817779i | \(-0.304795\pi\) | ||||
0.575533 | + | 0.817779i | \(0.304795\pi\) | |||||||
\(444\) | −14.7899 | −0.701896 | ||||||||
\(445\) | 15.5918 | 0.739122 | ||||||||
\(446\) | 6.13408 | 0.290457 | ||||||||
\(447\) | 17.6015 | 0.832522 | ||||||||
\(448\) | 3.63102 | 0.171550 | ||||||||
\(449\) | −6.01447 | −0.283841 | −0.141920 | − | 0.989878i | \(-0.545328\pi\) | ||||
−0.141920 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(450\) | 1.78017 | 0.0839179 | ||||||||
\(451\) | 0.674563 | 0.0317639 | ||||||||
\(452\) | 22.6679 | 1.06621 | ||||||||
\(453\) | −3.41550 | −0.160474 | ||||||||
\(454\) | −0.115293 | −0.00541097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.76271 | −0.269864 | ||||||||
\(457\) | −6.64848 | −0.311003 | −0.155501 | − | 0.987836i | \(-0.549699\pi\) | ||||
−0.155501 | + | 0.987836i | \(0.549699\pi\) | |||||||
\(458\) | 11.0043 | 0.514198 | ||||||||
\(459\) | −0.753020 | −0.0351480 | ||||||||
\(460\) | 4.76271 | 0.222062 | ||||||||
\(461\) | 13.5386 | 0.630554 | 0.315277 | − | 0.949000i | \(-0.397903\pi\) | ||||
0.315277 | + | 0.949000i | \(0.397903\pi\) | |||||||
\(462\) | 0.198062 | 0.00921469 | ||||||||
\(463\) | −0.907542 | −0.0421771 | −0.0210885 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210885 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(464\) | −6.09246 | −0.282835 | ||||||||
\(465\) | 1.24698 | 0.0578273 | ||||||||
\(466\) | −6.05084 | −0.280300 | ||||||||
\(467\) | −21.6189 | −1.00041 | −0.500203 | − | 0.865908i | \(-0.666741\pi\) | ||||
−0.500203 | + | 0.865908i | \(0.666741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.740939 | −0.0342134 | ||||||||
\(470\) | 3.59179 | 0.165677 | ||||||||
\(471\) | −17.1196 | −0.788830 | ||||||||
\(472\) | −17.5700 | −0.808726 | ||||||||
\(473\) | −3.56033 | −0.163704 | ||||||||
\(474\) | −0.320060 | −0.0147008 | ||||||||
\(475\) | 13.6233 | 0.625078 | ||||||||
\(476\) | −1.35690 | −0.0621932 | ||||||||
\(477\) | 4.16421 | 0.190666 | ||||||||
\(478\) | 7.53319 | 0.344560 | ||||||||
\(479\) | −27.4064 | −1.25223 | −0.626115 | − | 0.779730i | \(-0.715356\pi\) | ||||
−0.626115 | + | 0.779730i | \(0.715356\pi\) | |||||||
\(480\) | −4.65279 | −0.212370 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.52243 | 0.160442 | ||||||||
\(483\) | 2.64310 | 0.120265 | ||||||||
\(484\) | 19.4644 | 0.884746 | ||||||||
\(485\) | 10.8726 | 0.493700 | ||||||||
\(486\) | −0.445042 | −0.0201875 | ||||||||
\(487\) | −26.1317 | −1.18414 | −0.592070 | − | 0.805887i | \(-0.701689\pi\) | ||||
−0.592070 | + | 0.805887i | \(0.701689\pi\) | |||||||
\(488\) | −3.63640 | −0.164612 | ||||||||
\(489\) | 3.59419 | 0.162535 | ||||||||
\(490\) | −0.445042 | −0.0201049 | ||||||||
\(491\) | 17.6364 | 0.795920 | 0.397960 | − | 0.917403i | \(-0.369718\pi\) | ||||
0.397960 | + | 0.917403i | \(0.369718\pi\) | |||||||
\(492\) | −2.73125 | −0.123134 | ||||||||
\(493\) | 1.60925 | 0.0724771 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.445042 | 0.0200031 | ||||||||
\(496\) | 3.55496 | 0.159622 | ||||||||
\(497\) | −1.66487 | −0.0746798 | ||||||||
\(498\) | 0.0586060 | 0.00262620 | ||||||||
\(499\) | 16.6843 | 0.746890 | 0.373445 | − | 0.927652i | \(-0.378177\pi\) | ||||
0.373445 | + | 0.927652i | \(0.378177\pi\) | |||||||
\(500\) | 16.2174 | 0.725266 | ||||||||
\(501\) | 8.47219 | 0.378509 | ||||||||
\(502\) | −6.13467 | −0.273804 | ||||||||
\(503\) | 41.6373 | 1.85651 | 0.928257 | − | 0.371940i | \(-0.121307\pi\) | ||||
0.928257 | + | 0.371940i | \(0.121307\pi\) | |||||||
\(504\) | −1.69202 | −0.0753686 | ||||||||
\(505\) | −17.0858 | −0.760306 | ||||||||
\(506\) | 0.523499 | 0.0232724 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.5405 | 0.911337 | ||||||||
\(509\) | 16.7356 | 0.741791 | 0.370895 | − | 0.928675i | \(-0.379051\pi\) | ||||
0.370895 | + | 0.928675i | \(0.379051\pi\) | |||||||
\(510\) | 0.335126 | 0.0148396 | ||||||||
\(511\) | −5.74094 | −0.253964 | ||||||||
\(512\) | −22.9119 | −1.01257 | ||||||||
\(513\) | −3.40581 | −0.150370 | ||||||||
\(514\) | −0.696807 | −0.0307349 | ||||||||
\(515\) | −7.11529 | −0.313537 | ||||||||
\(516\) | 14.4155 | 0.634607 | ||||||||
\(517\) | −3.59179 | −0.157967 | ||||||||
\(518\) | 3.65279 | 0.160495 | ||||||||
\(519\) | 19.2500 | 0.844980 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9801 | 0.656292 | 0.328146 | − | 0.944627i | \(-0.393576\pi\) | ||||
0.328146 | + | 0.944627i | \(0.393576\pi\) | |||||||
\(522\) | 0.951083 | 0.0416278 | ||||||||
\(523\) | −43.9754 | −1.92291 | −0.961454 | − | 0.274965i | \(-0.911334\pi\) | ||||
−0.961454 | + | 0.274965i | \(0.911334\pi\) | |||||||
\(524\) | −4.78017 | −0.208823 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −7.18167 | −0.313136 | ||||||||
\(527\) | −0.939001 | −0.0409035 | ||||||||
\(528\) | 1.26875 | 0.0552153 | ||||||||
\(529\) | −16.0140 | −0.696261 | ||||||||
\(530\) | −1.85325 | −0.0804999 | ||||||||
\(531\) | −10.3840 | −0.450629 | ||||||||
\(532\) | −6.13706 | −0.266075 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.93900 | −0.300280 | ||||||||
\(535\) | −13.3545 | −0.577366 | ||||||||
\(536\) | 1.25368 | 0.0541509 | ||||||||
\(537\) | −5.63773 | −0.243286 | ||||||||
\(538\) | 12.7869 | 0.551281 | ||||||||
\(539\) | 0.445042 | 0.0191693 | ||||||||
\(540\) | −1.80194 | −0.0775431 | ||||||||
\(541\) | 16.6485 | 0.715774 | 0.357887 | − | 0.933765i | \(-0.383497\pi\) | ||||
0.357887 | + | 0.933765i | \(0.383497\pi\) | |||||||
\(542\) | −0.526746 | −0.0226257 | ||||||||
\(543\) | −14.0368 | −0.602378 | ||||||||
\(544\) | 3.50365 | 0.150218 | ||||||||
\(545\) | −3.93900 | −0.168728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.8592 | −1.91804 | −0.959021 | − | 0.283336i | \(-0.908559\pi\) | ||||
−0.959021 | + | 0.283336i | \(0.908559\pi\) | |||||||
\(548\) | 36.0127 | 1.53839 | ||||||||
\(549\) | −2.14914 | −0.0917233 | ||||||||
\(550\) | 0.792249 | 0.0337816 | ||||||||
\(551\) | 7.27844 | 0.310072 | ||||||||
\(552\) | −4.47219 | −0.190349 | ||||||||
\(553\) | −0.719169 | −0.0305822 | ||||||||
\(554\) | 11.5206 | 0.489465 | ||||||||
\(555\) | 8.20775 | 0.348400 | ||||||||
\(556\) | 9.99223 | 0.423765 | ||||||||
\(557\) | −2.23596 | −0.0947408 | −0.0473704 | − | 0.998877i | \(-0.515084\pi\) | ||||
−0.0473704 | + | 0.998877i | \(0.515084\pi\) | |||||||
\(558\) | −0.554958 | −0.0234933 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.85086 | −0.120471 | ||||||||
\(561\) | −0.335126 | −0.0141490 | ||||||||
\(562\) | −8.17954 | −0.345033 | ||||||||
\(563\) | 17.0019 | 0.716545 | 0.358273 | − | 0.933617i | \(-0.383366\pi\) | ||||
0.358273 | + | 0.933617i | \(0.383366\pi\) | |||||||
\(564\) | 14.5429 | 0.612366 | ||||||||
\(565\) | −12.5797 | −0.529232 | ||||||||
\(566\) | −2.68340 | −0.112792 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 2.81700 | 0.118199 | ||||||||
\(569\) | 1.81940 | 0.0762731 | 0.0381365 | − | 0.999273i | \(-0.487858\pi\) | ||||
0.0381365 | + | 0.999273i | \(0.487858\pi\) | |||||||
\(570\) | 1.51573 | 0.0634869 | ||||||||
\(571\) | 31.3924 | 1.31373 | 0.656866 | − | 0.754008i | \(-0.271882\pi\) | ||||
0.656866 | + | 0.754008i | \(0.271882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.4252 | −0.811499 | ||||||||
\(574\) | 0.674563 | 0.0281557 | ||||||||
\(575\) | 10.5724 | 0.440900 | ||||||||
\(576\) | −3.63102 | −0.151293 | ||||||||
\(577\) | 14.4752 | 0.602609 | 0.301305 | − | 0.953528i | \(-0.402578\pi\) | ||||
0.301305 | + | 0.953528i | \(0.402578\pi\) | |||||||
\(578\) | 7.31336 | 0.304195 | ||||||||
\(579\) | 6.49827 | 0.270059 | ||||||||
\(580\) | 3.85086 | 0.159898 | ||||||||
\(581\) | 0.131687 | 0.00546328 | ||||||||
\(582\) | −4.83877 | −0.200574 | ||||||||
\(583\) | 1.85325 | 0.0767537 | ||||||||
\(584\) | 9.71379 | 0.401960 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3951 | 0.429416 | ||||||||
\(587\) | 16.9892 | 0.701221 | 0.350611 | − | 0.936521i | \(-0.385974\pi\) | ||||
0.350611 | + | 0.936521i | \(0.385974\pi\) | |||||||
\(588\) | −1.80194 | −0.0743107 | ||||||||
\(589\) | −4.24698 | −0.174994 | ||||||||
\(590\) | 4.62133 | 0.190257 | ||||||||
\(591\) | −13.8998 | −0.571760 | ||||||||
\(592\) | 23.3991 | 0.961697 | ||||||||
\(593\) | 16.1666 | 0.663883 | 0.331941 | − | 0.943300i | \(-0.392296\pi\) | ||||
0.331941 | + | 0.943300i | \(0.392296\pi\) | |||||||
\(594\) | −0.198062 | −0.00812659 | ||||||||
\(595\) | 0.753020 | 0.0308708 | ||||||||
\(596\) | −31.7168 | −1.29917 | ||||||||
\(597\) | −0.984935 | −0.0403107 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.997607 | 0.0407611 | 0.0203806 | − | 0.999792i | \(-0.493512\pi\) | ||||
0.0203806 | + | 0.999792i | \(0.493512\pi\) | |||||||
\(600\) | −6.76809 | −0.276306 | ||||||||
\(601\) | −11.3297 | −0.462150 | −0.231075 | − | 0.972936i | \(-0.574224\pi\) | ||||
−0.231075 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(602\) | −3.56033 | −0.145108 | ||||||||
\(603\) | 0.740939 | 0.0301734 | ||||||||
\(604\) | 6.15452 | 0.250424 | ||||||||
\(605\) | −10.8019 | −0.439161 | ||||||||
\(606\) | 7.60388 | 0.308886 | ||||||||
\(607\) | 32.1027 | 1.30301 | 0.651505 | − | 0.758644i | \(-0.274138\pi\) | ||||
0.651505 | + | 0.758644i | \(0.274138\pi\) | |||||||
\(608\) | 15.8465 | 0.642662 | ||||||||
\(609\) | 2.13706 | 0.0865982 | ||||||||
\(610\) | 0.956459 | 0.0387259 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.35690 | 0.0548493 | ||||||||
\(613\) | 14.5972 | 0.589574 | 0.294787 | − | 0.955563i | \(-0.404751\pi\) | ||||
0.294787 | + | 0.955563i | \(0.404751\pi\) | |||||||
\(614\) | 1.84595 | 0.0744966 | ||||||||
\(615\) | 1.51573 | 0.0611201 | ||||||||
\(616\) | −0.753020 | −0.0303401 | ||||||||
\(617\) | −34.2717 | −1.37973 | −0.689864 | − | 0.723939i | \(-0.742330\pi\) | ||||
−0.689864 | + | 0.723939i | \(0.742330\pi\) | |||||||
\(618\) | 3.16660 | 0.127379 | ||||||||
\(619\) | 13.9202 | 0.559501 | 0.279750 | − | 0.960073i | \(-0.409748\pi\) | ||||
0.279750 | + | 0.960073i | \(0.409748\pi\) | |||||||
\(620\) | −2.24698 | −0.0902409 | ||||||||
\(621\) | −2.64310 | −0.106064 | ||||||||
\(622\) | −10.6625 | −0.427527 | ||||||||
\(623\) | −15.5918 | −0.624672 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 7.42865 | 0.296909 | ||||||||
\(627\) | −1.51573 | −0.0605324 | ||||||||
\(628\) | 30.8485 | 1.23099 | ||||||||
\(629\) | −6.18060 | −0.246437 | ||||||||
\(630\) | 0.445042 | 0.0177309 | ||||||||
\(631\) | 36.4292 | 1.45023 | 0.725113 | − | 0.688630i | \(-0.241788\pi\) | ||||
0.725113 | + | 0.688630i | \(0.241788\pi\) | |||||||
\(632\) | 1.21685 | 0.0484036 | ||||||||
\(633\) | 1.44935 | 0.0576066 | ||||||||
\(634\) | −4.32113 | −0.171614 | ||||||||
\(635\) | −11.3991 | −0.452360 | ||||||||
\(636\) | −7.50365 | −0.297539 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.423272 | 0.0167575 | ||||||||
\(639\) | 1.66487 | 0.0658614 | ||||||||
\(640\) | 10.9215 | 0.431712 | ||||||||
\(641\) | 14.6756 | 0.579652 | 0.289826 | − | 0.957079i | \(-0.406402\pi\) | ||||
0.289826 | + | 0.957079i | \(0.406402\pi\) | |||||||
\(642\) | 5.94331 | 0.234564 | ||||||||
\(643\) | −18.7966 | −0.741264 | −0.370632 | − | 0.928780i | \(-0.620859\pi\) | ||||
−0.370632 | + | 0.928780i | \(0.620859\pi\) | |||||||
\(644\) | −4.76271 | −0.187677 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | −1.14138 | −0.0449068 | ||||||||
\(647\) | −19.7198 | −0.775264 | −0.387632 | − | 0.921814i | \(-0.626707\pi\) | ||||
−0.387632 | + | 0.921814i | \(0.626707\pi\) | |||||||
\(648\) | 1.69202 | 0.0664689 | ||||||||
\(649\) | −4.62133 | −0.181403 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.24698 | −0.0488730 | ||||||||
\(652\) | −6.47650 | −0.253639 | ||||||||
\(653\) | 6.61058 | 0.258692 | 0.129346 | − | 0.991600i | \(-0.458712\pi\) | ||||
0.129346 | + | 0.991600i | \(0.458712\pi\) | |||||||
\(654\) | 1.75302 | 0.0685485 | ||||||||
\(655\) | 2.65279 | 0.103653 | ||||||||
\(656\) | 4.32113 | 0.168712 | ||||||||
\(657\) | 5.74094 | 0.223975 | ||||||||
\(658\) | −3.59179 | −0.140023 | ||||||||
\(659\) | −26.9812 | −1.05104 | −0.525519 | − | 0.850782i | \(-0.676129\pi\) | ||||
−0.525519 | + | 0.850782i | \(0.676129\pi\) | |||||||
\(660\) | −0.801938 | −0.0312154 | ||||||||
\(661\) | −25.6353 | −0.997099 | −0.498549 | − | 0.866861i | \(-0.666134\pi\) | ||||
−0.498549 | + | 0.866861i | \(0.666134\pi\) | |||||||
\(662\) | −5.92825 | −0.230408 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.222816 | −0.00864695 | ||||||||
\(665\) | 3.40581 | 0.132072 | ||||||||
\(666\) | −3.65279 | −0.141543 | ||||||||
\(667\) | 5.64848 | 0.218710 | ||||||||
\(668\) | −15.2664 | −0.590673 | ||||||||
\(669\) | −13.7832 | −0.532887 | ||||||||
\(670\) | −0.329749 | −0.0127393 | ||||||||
\(671\) | −0.956459 | −0.0369237 | ||||||||
\(672\) | 4.65279 | 0.179485 | ||||||||
\(673\) | −34.8122 | −1.34191 | −0.670956 | − | 0.741497i | \(-0.734116\pi\) | ||||
−0.670956 | + | 0.741497i | \(0.734116\pi\) | |||||||
\(674\) | −11.9705 | −0.461085 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.9782 | 0.767826 | 0.383913 | − | 0.923369i | \(-0.374576\pi\) | ||||
0.383913 | + | 0.923369i | \(0.374576\pi\) | |||||||
\(678\) | 5.59850 | 0.215009 | ||||||||
\(679\) | −10.8726 | −0.417253 | ||||||||
\(680\) | −1.27413 | −0.0488605 | ||||||||
\(681\) | 0.259061 | 0.00992725 | ||||||||
\(682\) | −0.246980 | −0.00945734 | ||||||||
\(683\) | −31.5340 | −1.20662 | −0.603308 | − | 0.797508i | \(-0.706151\pi\) | ||||
−0.603308 | + | 0.797508i | \(0.706151\pi\) | |||||||
\(684\) | 6.13706 | 0.234656 | ||||||||
\(685\) | −19.9855 | −0.763608 | ||||||||
\(686\) | 0.445042 | 0.0169918 | ||||||||
\(687\) | −24.7265 | −0.943373 | ||||||||
\(688\) | −22.8068 | −0.869503 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.17629 | 0.0447807 | ||||||||
\(691\) | 32.4805 | 1.23562 | 0.617809 | − | 0.786328i | \(-0.288020\pi\) | ||||
0.617809 | + | 0.786328i | \(0.288020\pi\) | |||||||
\(692\) | −34.6872 | −1.31861 | ||||||||
\(693\) | −0.445042 | −0.0169057 | ||||||||
\(694\) | −8.09352 | −0.307226 | ||||||||
\(695\) | −5.54527 | −0.210344 | ||||||||
\(696\) | −3.61596 | −0.137062 | ||||||||
\(697\) | −1.14138 | −0.0432327 | ||||||||
\(698\) | −9.59611 | −0.363218 | ||||||||
\(699\) | 13.5961 | 0.514252 | ||||||||
\(700\) | −7.20775 | −0.272427 | ||||||||
\(701\) | 33.7904 | 1.27625 | 0.638124 | − | 0.769934i | \(-0.279711\pi\) | ||||
0.638124 | + | 0.769934i | \(0.279711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.9541 | −1.05431 | ||||||||
\(704\) | −1.61596 | −0.0609037 | ||||||||
\(705\) | −8.07069 | −0.303960 | ||||||||
\(706\) | 0.443977 | 0.0167093 | ||||||||
\(707\) | 17.0858 | 0.642576 | ||||||||
\(708\) | 18.7114 | 0.703217 | ||||||||
\(709\) | −27.4499 | −1.03090 | −0.515452 | − | 0.856918i | \(-0.672376\pi\) | ||||
−0.515452 | + | 0.856918i | \(0.672376\pi\) | |||||||
\(710\) | −0.740939 | −0.0278069 | ||||||||
\(711\) | 0.719169 | 0.0269709 | ||||||||
\(712\) | 26.3817 | 0.988694 | ||||||||
\(713\) | −3.29590 | −0.123432 | ||||||||
\(714\) | −0.335126 | −0.0125418 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.1588 | 0.379653 | ||||||||
\(717\) | −16.9269 | −0.632147 | ||||||||
\(718\) | −6.45234 | −0.240799 | ||||||||
\(719\) | 34.0984 | 1.27166 | 0.635828 | − | 0.771830i | \(-0.280659\pi\) | ||||
0.635828 | + | 0.771830i | \(0.280659\pi\) | |||||||
\(720\) | 2.85086 | 0.106245 | ||||||||
\(721\) | 7.11529 | 0.264987 | ||||||||
\(722\) | 3.29350 | 0.122572 | ||||||||
\(723\) | −7.91484 | −0.294356 | ||||||||
\(724\) | 25.2935 | 0.940026 | ||||||||
\(725\) | 8.54825 | 0.317474 | ||||||||
\(726\) | 4.80731 | 0.178416 | ||||||||
\(727\) | −42.3086 | −1.56914 | −0.784569 | − | 0.620042i | \(-0.787116\pi\) | ||||
−0.784569 | + | 0.620042i | \(0.787116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.55496 | −0.0945632 | ||||||||
\(731\) | 6.02416 | 0.222812 | ||||||||
\(732\) | 3.87263 | 0.143136 | ||||||||
\(733\) | 37.6920 | 1.39219 | 0.696093 | − | 0.717951i | \(-0.254920\pi\) | ||||
0.696093 | + | 0.717951i | \(0.254920\pi\) | |||||||
\(734\) | 3.71054 | 0.136959 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 12.2978 | 0.453304 | ||||||||
\(737\) | 0.329749 | 0.0121465 | ||||||||
\(738\) | −0.674563 | −0.0248310 | ||||||||
\(739\) | −28.9353 | −1.06440 | −0.532201 | − | 0.846618i | \(-0.678635\pi\) | ||||
−0.532201 | + | 0.846618i | \(0.678635\pi\) | |||||||
\(740\) | −14.7899 | −0.543686 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85325 | 0.0680349 | ||||||||
\(743\) | −52.3430 | −1.92028 | −0.960139 | − | 0.279521i | \(-0.909824\pi\) | ||||
−0.960139 | + | 0.279521i | \(0.909824\pi\) | |||||||
\(744\) | 2.10992 | 0.0773533 | ||||||||
\(745\) | 17.6015 | 0.644868 | ||||||||
\(746\) | −15.9758 | −0.584917 | ||||||||
\(747\) | −0.131687 | −0.00481816 | ||||||||
\(748\) | 0.603875 | 0.0220799 | ||||||||
\(749\) | 13.3545 | 0.487963 | ||||||||
\(750\) | 4.00538 | 0.146256 | ||||||||
\(751\) | 2.35690 | 0.0860044 | 0.0430022 | − | 0.999075i | \(-0.486308\pi\) | ||||
0.0430022 | + | 0.999075i | \(0.486308\pi\) | |||||||
\(752\) | −23.0084 | −0.839029 | ||||||||
\(753\) | 13.7845 | 0.502334 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.41550 | −0.124303 | ||||||||
\(756\) | 1.80194 | 0.0655358 | ||||||||
\(757\) | −15.2433 | −0.554026 | −0.277013 | − | 0.960866i | \(-0.589344\pi\) | ||||
−0.277013 | + | 0.960866i | \(0.589344\pi\) | |||||||
\(758\) | 15.4024 | 0.559439 | ||||||||
\(759\) | −1.17629 | −0.0426967 | ||||||||
\(760\) | −5.76271 | −0.209035 | ||||||||
\(761\) | 11.9360 | 0.432680 | 0.216340 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216340 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(762\) | 5.07308 | 0.183778 | ||||||||
\(763\) | 3.93900 | 0.142601 | ||||||||
\(764\) | 35.0030 | 1.26636 | ||||||||
\(765\) | −0.753020 | −0.0272255 | ||||||||
\(766\) | 4.14351 | 0.149711 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.40150 | 0.0866567 | ||||||||
\(769\) | 35.0073 | 1.26240 | 0.631198 | − | 0.775622i | \(-0.282564\pi\) | ||||
0.631198 | + | 0.775622i | \(0.282564\pi\) | |||||||
\(770\) | 0.198062 | 0.00713767 | ||||||||
\(771\) | 1.56571 | 0.0563877 | ||||||||
\(772\) | −11.7095 | −0.421433 | ||||||||
\(773\) | 46.0489 | 1.65626 | 0.828132 | − | 0.560533i | \(-0.189404\pi\) | ||||
0.828132 | + | 0.560533i | \(0.189404\pi\) | |||||||
\(774\) | 3.56033 | 0.127974 | ||||||||
\(775\) | −4.98792 | −0.179171 | ||||||||
\(776\) | 18.3967 | 0.660404 | ||||||||
\(777\) | −8.20775 | −0.294451 | ||||||||
\(778\) | −17.1540 | −0.615002 | ||||||||
\(779\) | −5.16229 | −0.184958 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.740939 | 0.0265129 | ||||||||
\(782\) | −0.885772 | −0.0316751 | ||||||||
\(783\) | −2.13706 | −0.0763724 | ||||||||
\(784\) | 2.85086 | 0.101816 | ||||||||
\(785\) | −17.1196 | −0.611025 | ||||||||
\(786\) | −1.18060 | −0.0421107 | ||||||||
\(787\) | 46.4965 | 1.65742 | 0.828710 | − | 0.559678i | \(-0.189075\pi\) | ||||
0.828710 | + | 0.559678i | \(0.189075\pi\) | |||||||
\(788\) | 25.0465 | 0.892245 | ||||||||
\(789\) | 16.1371 | 0.574495 | ||||||||
\(790\) | −0.320060 | −0.0113872 | ||||||||
\(791\) | 12.5797 | 0.447283 | ||||||||
\(792\) | 0.753020 | 0.0267574 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.63640 | −0.0580736 | ||||||||
\(795\) | 4.16421 | 0.147689 | ||||||||
\(796\) | 1.77479 | 0.0629058 | ||||||||
\(797\) | 9.40389 | 0.333103 | 0.166552 | − | 0.986033i | \(-0.446737\pi\) | ||||
0.166552 | + | 0.986033i | \(0.446737\pi\) | |||||||
\(798\) | −1.51573 | −0.0536562 | ||||||||
\(799\) | 6.07739 | 0.215003 | ||||||||
\(800\) | 18.6112 | 0.658004 | ||||||||
\(801\) | 15.5918 | 0.550909 | ||||||||
\(802\) | −10.6601 | −0.376421 | ||||||||
\(803\) | 2.55496 | 0.0901625 | ||||||||
\(804\) | −1.33513 | −0.0470862 | ||||||||
\(805\) | 2.64310 | 0.0931572 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.7318 | −1.01141 | ||||||||
\(808\) | −28.9095 | −1.01703 | ||||||||
\(809\) | −42.9023 | −1.50836 | −0.754182 | − | 0.656665i | \(-0.771966\pi\) | ||||
−0.754182 | + | 0.656665i | \(0.771966\pi\) | |||||||
\(810\) | −0.445042 | −0.0156372 | ||||||||
\(811\) | 51.3411 | 1.80283 | 0.901415 | − | 0.432957i | \(-0.142530\pi\) | ||||
0.901415 | + | 0.432957i | \(0.142530\pi\) | |||||||
\(812\) | −3.85086 | −0.135139 | ||||||||
\(813\) | 1.18359 | 0.0415102 | ||||||||
\(814\) | −1.62565 | −0.0569789 | ||||||||
\(815\) | 3.59419 | 0.125899 | ||||||||
\(816\) | −2.14675 | −0.0751514 | ||||||||
\(817\) | 27.2465 | 0.953235 | ||||||||
\(818\) | 12.4765 | 0.436231 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.73125 | −0.0953794 | ||||||||
\(821\) | 29.4553 | 1.02800 | 0.513999 | − | 0.857791i | \(-0.328164\pi\) | ||||
0.513999 | + | 0.857791i | \(0.328164\pi\) | |||||||
\(822\) | 8.89440 | 0.310228 | ||||||||
\(823\) | 22.8068 | 0.794996 | 0.397498 | − | 0.917603i | \(-0.369878\pi\) | ||||
0.397498 | + | 0.917603i | \(0.369878\pi\) | |||||||
\(824\) | −12.0392 | −0.419406 | ||||||||
\(825\) | −1.78017 | −0.0619775 | ||||||||
\(826\) | −4.62133 | −0.160797 | ||||||||
\(827\) | 28.5512 | 0.992824 | 0.496412 | − | 0.868087i | \(-0.334651\pi\) | ||||
0.496412 | + | 0.868087i | \(0.334651\pi\) | |||||||
\(828\) | 4.76271 | 0.165516 | ||||||||
\(829\) | 48.2887 | 1.67714 | 0.838568 | − | 0.544797i | \(-0.183393\pi\) | ||||
0.838568 | + | 0.544797i | \(0.183393\pi\) | |||||||
\(830\) | 0.0586060 | 0.00203424 | ||||||||
\(831\) | −25.8866 | −0.897997 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.753020 | −0.0260906 | ||||||||
\(834\) | 2.46788 | 0.0854556 | ||||||||
\(835\) | 8.47219 | 0.293192 | ||||||||
\(836\) | 2.73125 | 0.0944623 | ||||||||
\(837\) | 1.24698 | 0.0431019 | ||||||||
\(838\) | 12.2795 | 0.424188 | ||||||||
\(839\) | −37.9191 | −1.30911 | −0.654557 | − | 0.756012i | \(-0.727145\pi\) | ||||
−0.654557 | + | 0.756012i | \(0.727145\pi\) | |||||||
\(840\) | −1.69202 | −0.0583803 | ||||||||
\(841\) | −24.4330 | −0.842516 | ||||||||
\(842\) | 7.86592 | 0.271078 | ||||||||
\(843\) | 18.3793 | 0.633015 | ||||||||
\(844\) | −2.61165 | −0.0898965 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.59179 | 0.123488 | ||||||||
\(847\) | 10.8019 | 0.371159 | ||||||||
\(848\) | 11.8716 | 0.407671 | ||||||||
\(849\) | 6.02954 | 0.206933 | ||||||||
\(850\) | −1.34050 | −0.0459789 | ||||||||
\(851\) | −21.6939 | −0.743659 | ||||||||
\(852\) | −3.00000 | −0.102778 | ||||||||
\(853\) | 10.4679 | 0.358413 | 0.179207 | − | 0.983811i | \(-0.442647\pi\) | ||||
0.179207 | + | 0.983811i | \(0.442647\pi\) | |||||||
\(854\) | −0.956459 | −0.0327294 | ||||||||
\(855\) | −3.40581 | −0.116476 | ||||||||
\(856\) | −22.5961 | −0.772319 | ||||||||
\(857\) | 36.7942 | 1.25686 | 0.628432 | − | 0.777864i | \(-0.283697\pi\) | ||||
0.628432 | + | 0.777864i | \(0.283697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0476 | −0.376939 | −0.188469 | − | 0.982079i | \(-0.560353\pi\) | ||||
−0.188469 | + | 0.982079i | \(0.560353\pi\) | |||||||
\(860\) | 14.4155 | 0.491565 | ||||||||
\(861\) | −1.51573 | −0.0516559 | ||||||||
\(862\) | −3.38106 | −0.115159 | ||||||||
\(863\) | 48.9372 | 1.66584 | 0.832921 | − | 0.553392i | \(-0.186667\pi\) | ||||
0.832921 | + | 0.553392i | \(0.186667\pi\) | |||||||
\(864\) | −4.65279 | −0.158291 | ||||||||
\(865\) | 19.2500 | 0.654518 | ||||||||
\(866\) | −8.63055 | −0.293278 | ||||||||
\(867\) | −16.4330 | −0.558093 | ||||||||
\(868\) | 2.24698 | 0.0762675 | ||||||||
\(869\) | 0.320060 | 0.0108573 | ||||||||
\(870\) | 0.951083 | 0.0322447 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.66487 | −0.225701 | ||||||||
\(873\) | 10.8726 | 0.367983 | ||||||||
\(874\) | −4.00623 | −0.135513 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | −10.3448 | −0.349519 | ||||||||
\(877\) | 2.31203 | 0.0780716 | 0.0390358 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390358 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(878\) | 6.21073 | 0.209602 | ||||||||
\(879\) | −23.3575 | −0.787828 | ||||||||
\(880\) | 1.26875 | 0.0427695 | ||||||||
\(881\) | 39.7351 | 1.33871 | 0.669355 | − | 0.742943i | \(-0.266571\pi\) | ||||
0.669355 | + | 0.742943i | \(0.266571\pi\) | |||||||
\(882\) | −0.445042 | −0.0149853 | ||||||||
\(883\) | 53.9480 | 1.81549 | 0.907747 | − | 0.419519i | \(-0.137801\pi\) | ||||
0.907747 | + | 0.419519i | \(0.137801\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3840 | −0.349056 | ||||||||
\(886\) | −10.7821 | −0.362231 | ||||||||
\(887\) | −7.81727 | −0.262478 | −0.131239 | − | 0.991351i | \(-0.541896\pi\) | ||||
−0.131239 | + | 0.991351i | \(0.541896\pi\) | |||||||
\(888\) | 13.8877 | 0.466040 | ||||||||
\(889\) | 11.3991 | 0.382314 | ||||||||
\(890\) | −6.93900 | −0.232596 | ||||||||
\(891\) | 0.445042 | 0.0149095 | ||||||||
\(892\) | 24.8364 | 0.831584 | ||||||||
\(893\) | 27.4873 | 0.919826 | ||||||||
\(894\) | −7.83340 | −0.261988 | ||||||||
\(895\) | −5.63773 | −0.188448 | ||||||||
\(896\) | −10.9215 | −0.364863 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.67669 | 0.0893224 | ||||||||
\(899\) | −2.66487 | −0.0888785 | ||||||||
\(900\) | 7.20775 | 0.240258 | ||||||||
\(901\) | −3.13574 | −0.104466 | ||||||||
\(902\) | −0.300209 | −0.00999586 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | −21.2851 | −0.707933 | ||||||||
\(905\) | −14.0368 | −0.466600 | ||||||||
\(906\) | 1.52004 | 0.0505000 | ||||||||
\(907\) | 0.554958 | 0.0184271 | 0.00921354 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921354 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(908\) | −0.466812 | −0.0154917 | ||||||||
\(909\) | −17.0858 | −0.566699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.44265 | −0.312849 | −0.156424 | − | 0.987690i | \(-0.549997\pi\) | ||||
−0.156424 | + | 0.987690i | \(0.549997\pi\) | |||||||
\(912\) | −9.70948 | −0.321513 | ||||||||
\(913\) | −0.0586060 | −0.00193958 | ||||||||
\(914\) | 2.95885 | 0.0978701 | ||||||||
\(915\) | −2.14914 | −0.0710485 | ||||||||
\(916\) | 44.5555 | 1.47216 | ||||||||
\(917\) | −2.65279 | −0.0876029 | ||||||||
\(918\) | 0.335126 | 0.0110608 | ||||||||
\(919\) | 22.4862 | 0.741751 | 0.370875 | − | 0.928683i | \(-0.379058\pi\) | ||||
0.370875 | + | 0.928683i | \(0.379058\pi\) | |||||||
\(920\) | −4.47219 | −0.147444 | ||||||||
\(921\) | −4.14782 | −0.136675 | ||||||||
\(922\) | −6.02523 | −0.198430 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.801938 | 0.0263818 | ||||||||
\(925\) | −32.8310 | −1.07948 | ||||||||
\(926\) | 0.403894 | 0.0132728 | ||||||||
\(927\) | −7.11529 | −0.233697 | ||||||||
\(928\) | 9.94331 | 0.326405 | ||||||||
\(929\) | 29.2500 | 0.959660 | 0.479830 | − | 0.877361i | \(-0.340698\pi\) | ||||
0.479830 | + | 0.877361i | \(0.340698\pi\) | |||||||
\(930\) | −0.554958 | −0.0181978 | ||||||||
\(931\) | −3.40581 | −0.111621 | ||||||||
\(932\) | −24.4993 | −0.802502 | ||||||||
\(933\) | 23.9584 | 0.784362 | ||||||||
\(934\) | 9.62133 | 0.314820 | ||||||||
\(935\) | −0.335126 | −0.0109598 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.4679 | −0.439976 | −0.219988 | − | 0.975503i | \(-0.570602\pi\) | ||||
−0.219988 | + | 0.975503i | \(0.570602\pi\) | |||||||
\(938\) | 0.329749 | 0.0107667 | ||||||||
\(939\) | −16.6920 | −0.544724 | ||||||||
\(940\) | 14.5429 | 0.474336 | ||||||||
\(941\) | −15.3418 | −0.500129 | −0.250065 | − | 0.968229i | \(-0.580452\pi\) | ||||
−0.250065 | + | 0.968229i | \(0.580452\pi\) | |||||||
\(942\) | 7.61894 | 0.248239 | ||||||||
\(943\) | −4.00623 | −0.130461 | ||||||||
\(944\) | −29.6034 | −0.963509 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 1.58450 | 0.0515165 | ||||||||
\(947\) | −16.2228 | −0.527171 | −0.263585 | − | 0.964636i | \(-0.584905\pi\) | ||||
−0.263585 | + | 0.964636i | \(0.584905\pi\) | |||||||
\(948\) | −1.29590 | −0.0420888 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.06292 | −0.196707 | ||||||||
\(951\) | 9.70948 | 0.314851 | ||||||||
\(952\) | 1.27413 | 0.0412947 | ||||||||
\(953\) | −1.85218 | −0.0599981 | −0.0299990 | − | 0.999550i | \(-0.509550\pi\) | ||||
−0.0299990 | + | 0.999550i | \(0.509550\pi\) | |||||||
\(954\) | −1.85325 | −0.0600011 | ||||||||
\(955\) | −19.4252 | −0.628584 | ||||||||
\(956\) | 30.5013 | 0.986481 | ||||||||
\(957\) | −0.951083 | −0.0307441 | ||||||||
\(958\) | 12.1970 | 0.394067 | ||||||||
\(959\) | 19.9855 | 0.645366 | ||||||||
\(960\) | −3.63102 | −0.117191 | ||||||||
\(961\) | −29.4450 | −0.949840 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.3545 | −0.430343 | ||||||||
\(964\) | 14.2620 | 0.459350 | ||||||||
\(965\) | 6.49827 | 0.209187 | ||||||||
\(966\) | −1.17629 | −0.0378466 | ||||||||
\(967\) | 13.8030 | 0.443875 | 0.221937 | − | 0.975061i | \(-0.428762\pi\) | ||||
0.221937 | + | 0.975061i | \(0.428762\pi\) | |||||||
\(968\) | −18.2771 | −0.587449 | ||||||||
\(969\) | 2.56465 | 0.0823883 | ||||||||
\(970\) | −4.83877 | −0.155364 | ||||||||
\(971\) | 36.2814 | 1.16433 | 0.582163 | − | 0.813072i | \(-0.302207\pi\) | ||||
0.582163 | + | 0.813072i | \(0.302207\pi\) | |||||||
\(972\) | −1.80194 | −0.0577972 | ||||||||
\(973\) | 5.54527 | 0.177773 | ||||||||
\(974\) | 11.6297 | 0.372639 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.12690 | −0.196117 | ||||||||
\(977\) | −31.5472 | −1.00928 | −0.504642 | − | 0.863329i | \(-0.668375\pi\) | ||||
−0.504642 | + | 0.863329i | \(0.668375\pi\) | |||||||
\(978\) | −1.59956 | −0.0511484 | ||||||||
\(979\) | 6.93900 | 0.221771 | ||||||||
\(980\) | −1.80194 | −0.0575608 | ||||||||
\(981\) | −3.93900 | −0.125763 | ||||||||
\(982\) | −7.84894 | −0.250470 | ||||||||
\(983\) | 26.6547 | 0.850153 | 0.425077 | − | 0.905157i | \(-0.360247\pi\) | ||||
0.425077 | + | 0.905157i | \(0.360247\pi\) | |||||||
\(984\) | 2.56465 | 0.0817580 | ||||||||
\(985\) | −13.8998 | −0.442884 | ||||||||
\(986\) | −0.716185 | −0.0228080 | ||||||||
\(987\) | 8.07069 | 0.256893 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.1448 | 0.672367 | ||||||||
\(990\) | −0.198062 | −0.00629483 | ||||||||
\(991\) | 1.15990 | 0.0368454 | 0.0184227 | − | 0.999830i | \(-0.494136\pi\) | ||||
0.0184227 | + | 0.999830i | \(0.494136\pi\) | |||||||
\(992\) | −5.80194 | −0.184212 | ||||||||
\(993\) | 13.3207 | 0.422718 | ||||||||
\(994\) | 0.740939 | 0.0235012 | ||||||||
\(995\) | −0.984935 | −0.0312245 | ||||||||
\(996\) | 0.237291 | 0.00751885 | ||||||||
\(997\) | −33.2984 | −1.05457 | −0.527286 | − | 0.849688i | \(-0.676790\pi\) | ||||
−0.527286 | + | 0.849688i | \(0.676790\pi\) | |||||||
\(998\) | −7.42519 | −0.235040 | ||||||||
\(999\) | 8.20775 | 0.259682 |
(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 | 3549.2.a.j.1.2 | ✓ | 3 | |
13.12 | even | 2 | 3549.2.a.p.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.j.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3549.2.a.p.1.2 | yes | 3 | 13.12 | even | 2 |