Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8040,2,Mod(1,8040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8040.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 3x^{4} + 43x^{3} - 6x^{2} - 29x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.922407\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.52856 | 1.71163 | 0.855817 | − | 0.517279i | \(-0.173055\pi\) | ||||
0.855817 | + | 0.517279i | \(0.173055\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.01746 | 0.909798 | 0.454899 | − | 0.890543i | \(-0.349675\pi\) | ||||
0.454899 | + | 0.890543i | \(0.349675\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.99509 | −1.38539 | −0.692695 | − | 0.721231i | \(-0.743577\pi\) | ||||
−0.692695 | + | 0.721231i | \(0.743577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.07157 | 0.987501 | 0.493751 | − | 0.869603i | \(-0.335626\pi\) | ||||
0.493751 | + | 0.869603i | \(0.335626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78959 | 0.410559 | 0.205280 | − | 0.978703i | \(-0.434190\pi\) | ||||
0.205280 | + | 0.978703i | \(0.434190\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.52856 | 0.988212 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.12194 | 0.859485 | 0.429742 | − | 0.902951i | \(-0.358604\pi\) | ||||
0.429742 | + | 0.902951i | \(0.358604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.71175 | 0.503560 | 0.251780 | − | 0.967785i | \(-0.418984\pi\) | ||||
0.251780 | + | 0.967785i | \(0.418984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.66138 | 0.837208 | 0.418604 | − | 0.908169i | \(-0.362519\pi\) | ||||
0.418604 | + | 0.908169i | \(0.362519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.01746 | 0.525272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.52856 | −0.765466 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.96844 | 0.816807 | 0.408403 | − | 0.912802i | \(-0.366086\pi\) | ||||
0.408403 | + | 0.912802i | \(0.366086\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.99509 | −0.799855 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.66138 | −0.415638 | −0.207819 | − | 0.978167i | \(-0.566636\pi\) | ||||
−0.207819 | + | 0.978167i | \(0.566636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.11704 | −1.39034 | −0.695168 | − | 0.718848i | \(-0.744670\pi\) | ||||
−0.695168 | + | 0.718848i | \(0.744670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.72945 | −0.398131 | −0.199066 | − | 0.979986i | \(-0.563791\pi\) | ||||
−0.199066 | + | 0.979986i | \(0.563791\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.5078 | 1.92969 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.07157 | 0.570134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.311159 | 0.0427409 | 0.0213705 | − | 0.999772i | \(-0.493197\pi\) | ||||
0.0213705 | + | 0.999772i | \(0.493197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.01746 | −0.406874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.78959 | 0.237036 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.27322 | −0.295948 | −0.147974 | − | 0.988991i | \(-0.547275\pi\) | ||||
−0.147974 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.999758 | −0.128006 | −0.0640030 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640030 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.52856 | 0.570545 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.99509 | 0.619565 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.12194 | 0.496224 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.73447 | −0.443200 | −0.221600 | − | 0.975138i | \(-0.571128\pi\) | ||||
−0.221600 | + | 0.975138i | \(0.571128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6689 | 1.59982 | 0.799912 | − | 0.600117i | \(-0.204879\pi\) | ||||
0.799912 | + | 0.600117i | \(0.204879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6647 | 1.55724 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.72419 | −0.306495 | −0.153248 | − | 0.988188i | \(-0.548973\pi\) | ||||
−0.153248 | + | 0.988188i | \(0.548973\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.69329 | −0.954213 | −0.477106 | − | 0.878846i | \(-0.658314\pi\) | ||||
−0.477106 | + | 0.878846i | \(0.658314\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.07157 | −0.441624 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.71175 | 0.290730 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8698 | −1.25820 | −0.629098 | − | 0.777326i | \(-0.716576\pi\) | ||||
−0.629098 | + | 0.777326i | \(0.716576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.6206 | −2.37128 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.66138 | 0.483362 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.78959 | −0.183608 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.55597 | 0.868727 | 0.434363 | − | 0.900738i | \(-0.356973\pi\) | ||||
0.434363 | + | 0.900738i | \(0.356973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.01746 | 0.303266 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4184 | 1.03667 | 0.518335 | − | 0.855178i | \(-0.326552\pi\) | ||||
0.518335 | + | 0.855178i | \(0.326552\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.83575 | −0.772079 | −0.386040 | − | 0.922482i | \(-0.626157\pi\) | ||||
−0.386040 | + | 0.922482i | \(0.626157\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.52856 | −0.441942 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.7245 | 1.03678 | 0.518388 | − | 0.855146i | \(-0.326532\pi\) | ||||
0.518388 | + | 0.855146i | \(0.326532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1961 | −1.16818 | −0.584088 | − | 0.811690i | \(-0.698548\pi\) | ||||
−0.584088 | + | 0.811690i | \(0.698548\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.96844 | 0.471584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.55298 | 0.334237 | 0.167118 | − | 0.985937i | \(-0.446554\pi\) | ||||
0.167118 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.12194 | −0.384373 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.99509 | −0.461796 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.4384 | 1.69024 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.89494 | −0.172268 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.66138 | −0.239968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7682 | 1.75415 | 0.877073 | − | 0.480357i | \(-0.159493\pi\) | ||||
0.877073 | + | 0.480357i | \(0.159493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.11704 | −0.802710 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.62342 | −0.316580 | −0.158290 | − | 0.987393i | \(-0.550598\pi\) | ||||
−0.158290 | + | 0.987393i | \(0.550598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.10424 | 0.702727 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4342 | −1.23320 | −0.616598 | − | 0.787278i | \(-0.711489\pi\) | ||||
−0.616598 | + | 0.787278i | \(0.711489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.13358 | 0.180968 | 0.0904839 | − | 0.995898i | \(-0.471159\pi\) | ||||
0.0904839 | + | 0.995898i | \(0.471159\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.72945 | −0.229861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0725 | −1.26042 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.71175 | −0.225199 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.5078 | 1.11411 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0243 | 1.14892 | 0.574458 | − | 0.818534i | \(-0.305213\pi\) | ||||
0.574458 | + | 0.818534i | \(0.305213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1469 | 1.15126 | 0.575631 | − | 0.817710i | \(-0.304757\pi\) | ||||
0.575631 | + | 0.817710i | \(0.304757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.07157 | 0.329167 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.66138 | −0.374411 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.9743 | 1.67393 | 0.836965 | − | 0.547256i | \(-0.184328\pi\) | ||||
0.836965 | + | 0.547256i | \(0.184328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.311159 | 0.0246765 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.6665 | 1.47112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.2727 | −1.58788 | −0.793941 | − | 0.607995i | \(-0.791974\pi\) | ||||
−0.793941 | + | 0.607995i | \(0.791974\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.01746 | −0.234909 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.04113 | 0.467476 | 0.233738 | − | 0.972300i | \(-0.424904\pi\) | ||||
0.233738 | + | 0.972300i | \(0.424904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9509 | 0.919304 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.78959 | 0.136853 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.61707 | −0.275001 | −0.137500 | − | 0.990502i | \(-0.543907\pi\) | ||||
−0.137500 | + | 0.990502i | \(0.543907\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.52856 | 0.342327 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.27322 | −0.170866 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.97723 | −0.222529 | −0.111264 | − | 0.993791i | \(-0.535490\pi\) | ||||
−0.111264 | + | 0.993791i | \(0.535490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.47802 | 0.258519 | 0.129260 | − | 0.991611i | \(-0.458740\pi\) | ||||
0.129260 | + | 0.991611i | \(0.458740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.999758 | −0.0739043 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.96844 | −0.365287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.2858 | 0.898427 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.52856 | 0.329404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.48662 | 0.686428 | 0.343214 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343214 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.7833 | 1.13610 | 0.568052 | − | 0.822992i | \(-0.307697\pi\) | ||||
0.568052 | + | 0.822992i | \(0.307697\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.99509 | 0.357706 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.46333 | −0.460493 | −0.230247 | − | 0.973132i | \(-0.573953\pi\) | ||||
−0.230247 | + | 0.973132i | \(0.573953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.52523 | 0.675226 | 0.337613 | − | 0.941285i | \(-0.390381\pi\) | ||||
0.337613 | + | 0.941285i | \(0.390381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2803 | 0.861910 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.66138 | 0.185879 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.12194 | 0.286495 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.40000 | 0.373526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4972 | −1.27340 | −0.636702 | − | 0.771110i | \(-0.719702\pi\) | ||||
−0.636702 | + | 0.771110i | \(0.719702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.73447 | −0.255882 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.11704 | 0.621777 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.1093 | 1.43299 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6689 | 0.923659 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.3379 | −1.36807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.4186 | −0.965542 | −0.482771 | − | 0.875747i | \(-0.660370\pi\) | ||||
−0.482771 | + | 0.875747i | \(0.660370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.4412 | −1.82134 | −0.910668 | − | 0.413139i | \(-0.864432\pi\) | ||||
−0.910668 | + | 0.413139i | \(0.864432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.95040 | 0.261050 | 0.130525 | − | 0.991445i | \(-0.458334\pi\) | ||||
0.130525 | + | 0.991445i | \(0.458334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6647 | 0.899074 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2038 | −1.19257 | −0.596285 | − | 0.802773i | \(-0.703357\pi\) | ||||
−0.596285 | + | 0.802773i | \(0.703357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.72945 | 0.178050 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.72419 | −0.176955 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.17999 | −0.399750 | −0.199875 | − | 0.979821i | \(-0.564054\pi\) | ||||
−0.199875 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9358 | 0.833270 | 0.416635 | − | 0.909074i | \(-0.363209\pi\) | ||||
0.416635 | + | 0.909074i | \(0.363209\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5078 | −0.862984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.93915 | −0.568784 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.69329 | −0.550915 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4636 | 0.660457 | 0.330228 | − | 0.943901i | \(-0.392874\pi\) | ||||
0.330228 | + | 0.943901i | \(0.392874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4378 | 0.781958 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.07157 | −0.254972 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.77262 | −0.422464 | −0.211232 | − | 0.977436i | \(-0.567748\pi\) | ||||
−0.211232 | + | 0.977436i | \(0.567748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4999 | 1.39807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.71175 | 0.167853 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.2916 | −1.62121 | −0.810606 | − | 0.585592i | \(-0.800862\pi\) | ||||
−0.810606 | + | 0.585592i | \(0.800862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.311159 | −0.0191143 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8698 | −0.726420 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.6254 | −1.68435 | −0.842175 | − | 0.539204i | \(-0.818725\pi\) | ||||
−0.842175 | + | 0.539204i | \(0.818725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4445 | 1.30266 | 0.651330 | − | 0.758795i | \(-0.274211\pi\) | ||||
0.651330 | + | 0.758795i | \(0.274211\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.6206 | −1.36906 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.01746 | 0.181960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.90868 | −0.355018 | −0.177509 | − | 0.984119i | \(-0.556804\pi\) | ||||
−0.177509 | + | 0.984119i | \(0.556804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.66138 | 0.279069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4143 | −0.919537 | −0.459769 | − | 0.888039i | \(-0.652068\pi\) | ||||
−0.459769 | + | 0.888039i | \(0.652068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1098 | 0.898186 | 0.449093 | − | 0.893485i | \(-0.351747\pi\) | ||||
0.449093 | + | 0.893485i | \(0.351747\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.78959 | −0.106006 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0522 | −0.711419 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.422296 | −0.0248410 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.55597 | 0.501560 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3820 | −0.606526 | −0.303263 | − | 0.952907i | \(-0.598076\pi\) | ||||
−0.303263 | + | 0.952907i | \(0.598076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.27322 | 0.132352 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.01746 | 0.175091 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.5895 | −1.19072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.2870 | −2.37975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.4184 | 0.598522 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.999758 | 0.0572460 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6699 | 1.06555 | 0.532773 | − | 0.846258i | \(-0.321150\pi\) | ||||
0.532773 | + | 0.846258i | \(0.321150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.83575 | −0.445760 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1111 | 0.743461 | 0.371730 | − | 0.928341i | \(-0.378765\pi\) | ||||
0.371730 | + | 0.928341i | \(0.378765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.29921 | −0.412576 | −0.206288 | − | 0.978491i | \(-0.566138\pi\) | ||||
−0.206288 | + | 0.978491i | \(0.566138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.52856 | −0.255155 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.4771 | 1.76793 | 0.883964 | − | 0.467556i | \(-0.154865\pi\) | ||||
0.883964 | + | 0.467556i | \(0.154865\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.18260 | 0.458137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.7245 | 0.598583 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.28643 | 0.405428 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.99509 | −0.277078 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1961 | −0.674447 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3605 | −0.681455 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.29632 | −0.401042 | −0.200521 | − | 0.979689i | \(-0.564264\pi\) | ||||
−0.200521 | + | 0.979689i | \(0.564264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.96844 | 0.272269 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.70904 | −0.256518 | −0.128259 | − | 0.991741i | \(-0.540939\pi\) | ||||
−0.128259 | + | 0.991741i | \(0.540939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.55298 | 0.192972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.0655 | 0.761690 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 29.4711 | 1.59129 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.12194 | −0.221918 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.5439 | −0.941805 | −0.470902 | − | 0.882185i | \(-0.656072\pi\) | ||||
−0.470902 | + | 0.882185i | \(0.656072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5530 | 1.04665 | 0.523323 | − | 0.852134i | \(-0.324692\pi\) | ||||
0.523323 | + | 0.852134i | \(0.324692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.99509 | −0.266618 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20618 | 0.330322 | 0.165161 | − | 0.986267i | \(-0.447186\pi\) | ||||
0.165161 | + | 0.986267i | \(0.447186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.73447 | 0.198205 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.4384 | 0.975861 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.8531 | 0.572804 | 0.286402 | − | 0.958110i | \(-0.407541\pi\) | ||||
0.286402 | + | 0.958110i | \(0.407541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7974 | −0.831441 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.89494 | −0.0994588 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.6689 | −0.715463 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.31956 | −0.329878 | −0.164939 | − | 0.986304i | \(-0.552743\pi\) | ||||
−0.164939 | + | 0.986304i | \(0.552743\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.66138 | −0.138546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.40910 | 0.0731568 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.30921 | −0.0677885 | −0.0338943 | − | 0.999425i | \(-0.510791\pi\) | ||||
−0.0338943 | + | 0.999425i | \(0.510791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.5454 | −0.697626 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6595 | 0.958472 | 0.479236 | − | 0.877686i | \(-0.340914\pi\) | ||||
0.479236 | + | 0.877686i | \(0.340914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.7682 | 1.01276 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.1748 | 1.08198 | 0.540990 | − | 0.841029i | \(-0.318050\pi\) | ||||
0.540990 | + | 0.841029i | \(0.318050\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6647 | −0.696419 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.11704 | −0.463445 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.6516 | −0.590760 | −0.295380 | − | 0.955380i | \(-0.595446\pi\) | ||||
−0.295380 | + | 0.955380i | \(0.595446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7828 | 0.848743 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.62342 | −0.182777 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.72419 | 0.137069 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4764 | 1.57976 | 0.789879 | − | 0.613263i | \(-0.210143\pi\) | ||||
0.789879 | + | 0.613263i | \(0.210143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.10424 | 0.405720 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.6154 | 1.92836 | 0.964181 | − | 0.265246i | \(-0.0854532\pi\) | ||||
0.964181 | + | 0.265246i | \(0.0854532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.2840 | −1.15986 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9921 | 0.743129 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5356 | 1.26266 | 0.631328 | − | 0.775516i | \(-0.282510\pi\) | ||||
0.631328 | + | 0.775516i | \(0.282510\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4342 | −0.711986 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2944 | −0.506555 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.69329 | 0.426737 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.13358 | 0.104482 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7202 | −1.01225 | −0.506124 | − | 0.862461i | \(-0.668922\pi\) | ||||
−0.506124 | + | 0.862461i | \(0.668922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5622 | −0.758454 | −0.379227 | − | 0.925304i | \(-0.623810\pi\) | ||||
−0.379227 | + | 0.925304i | \(0.623810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.72945 | −0.132710 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.07157 | 0.197500 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.52746 | −0.219099 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0725 | −0.727706 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.7281 | −1.52829 | −0.764144 | − | 0.645046i | \(-0.776838\pi\) | ||||
−0.764144 | + | 0.645046i | \(0.776838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.49421 | 0.215978 | 0.107989 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107989 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.71175 | −0.130019 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.37658 | 0.352869 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8257 | 0.755321 | 0.377660 | − | 0.925944i | \(-0.376729\pi\) | ||||
0.377660 | + | 0.925944i | \(0.376729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5078 | 0.643230 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.8635 | 0.848719 | 0.424360 | − | 0.905494i | \(-0.360499\pi\) | ||||
0.424360 | + | 0.905494i | \(0.360499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.8698 | 0.562683 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0243 | 0.663327 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.122541 | −0.00578308 | −0.00289154 | − | 0.999996i | \(-0.500920\pi\) | ||||
−0.00289154 | + | 0.999996i | \(0.500920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.03060 | −0.378146 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.1469 | 0.664681 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.6206 | 1.06047 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.4200 | 1.09554 | 0.547771 | − | 0.836628i | \(-0.315477\pi\) | ||||
0.547771 | + | 0.836628i | \(0.315477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.07157 | 0.190045 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.6749 | −1.42867 | −0.714337 | − | 0.699802i | \(-0.753272\pi\) | ||||
−0.714337 | + | 0.699802i | \(0.753272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1660 | 0.472455 | 0.236227 | − | 0.971698i | \(-0.424089\pi\) | ||||
0.236227 | + | 0.971698i | \(0.424089\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.66138 | −0.216166 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.90183 | 0.319378 | 0.159689 | − | 0.987167i | \(-0.448951\pi\) | ||||
0.159689 | + | 0.987167i | \(0.448951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.52856 | 0.209109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.9743 | 0.966444 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5103 | −1.26492 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.78959 | 0.0821118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.311159 | 0.0142470 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.66608 | −0.350272 | −0.175136 | − | 0.984544i | \(-0.556037\pi\) | ||||
−0.175136 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.8178 | −1.13160 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.6665 | 0.849354 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.55597 | −0.388506 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8798 | 0.764895 | 0.382447 | − | 0.923977i | \(-0.375081\pi\) | ||||
0.382447 | + | 0.923977i | \(0.375081\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.2727 | −0.916764 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.1301 | −1.35975 | −0.679875 | − | 0.733328i | \(-0.737966\pi\) | ||||
−0.679875 | + | 0.733328i | \(0.737966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0411 | 0.497266 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.01746 | −0.135625 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.9118 | −0.758597 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.5501 | 1.86004 | 0.930019 | − | 0.367511i | \(-0.119790\pi\) | ||||
0.930019 | + | 0.367511i | \(0.119790\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.04113 | 0.269898 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.2858 | 1.61790 | 0.808951 | − | 0.587876i | \(-0.200036\pi\) | ||||
0.808951 | + | 0.587876i | \(0.200036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4184 | −0.463613 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9509 | 0.530760 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.7617 | −1.31916 | −0.659582 | − | 0.751633i | \(-0.729267\pi\) | ||||
−0.659582 | + | 0.751633i | \(0.729267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 61.9004 | 2.73831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.78959 | 0.0790122 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.83575 | 0.345284 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.23601 | −0.362219 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.61707 | −0.158772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.5559 | 0.462461 | 0.231230 | − | 0.972899i | \(-0.425725\pi\) | ||||
0.231230 | + | 0.972899i | \(0.425725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1314 | 0.924013 | 0.462006 | − | 0.886877i | \(-0.347130\pi\) | ||||
0.462006 | + | 0.886877i | \(0.347130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.52856 | 0.197642 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.9791 | 0.826744 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.00957 | −0.261286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27322 | −0.0986495 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2938 | 0.575820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7245 | −0.463660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.97723 | −0.128477 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.7593 | 1.75563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.65064 | 0.414913 | 0.207457 | − | 0.978244i | \(-0.433481\pi\) | ||||
0.207457 | + | 0.978244i | \(0.433481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.47802 | 0.149256 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1961 | 0.522424 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2906 | −1.59443 | −0.797216 | − | 0.603694i | \(-0.793695\pi\) | ||||
−0.797216 | + | 0.603694i | \(0.793695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.999758 | −0.0426686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.85291 | 0.206741 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3366 | −0.524607 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.96844 | −0.210899 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.0909 | 0.936020 | 0.468010 | − | 0.883723i | \(-0.344971\pi\) | ||||
0.468010 | + | 0.883723i | \(0.344971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.5404 | 1.92616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.2858 | 0.518707 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.4094 | 0.902300 | 0.451150 | − | 0.892448i | \(-0.351014\pi\) | ||||
0.451150 | + | 0.892448i | \(0.351014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.55298 | −0.149475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.52856 | 0.190182 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.6142 | 0.906116 | 0.453058 | − | 0.891481i | \(-0.350333\pi\) | ||||
0.453058 | + | 0.891481i | \(0.350333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2151 | 1.05522 | 0.527609 | − | 0.849487i | \(-0.323089\pi\) | ||||
0.527609 | + | 0.849487i | \(0.323089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.48662 | 0.396309 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.12194 | 0.171897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.50017 | −0.395497 | −0.197749 | − | 0.980253i | \(-0.563363\pi\) | ||||
−0.197749 | + | 0.980253i | \(0.563363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.7833 | 0.655930 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.3681 | −1.63326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.938908 | 0.0388856 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.99509 | 0.206522 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.1639 | −1.36882 | −0.684409 | − | 0.729098i | \(-0.739940\pi\) | ||||
−0.684409 | + | 0.729098i | \(0.739940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.34194 | 0.343724 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.46333 | −0.265866 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.3144 | 1.12167 | 0.560835 | − | 0.827928i | \(-0.310480\pi\) | ||||
0.560835 | + | 0.827928i | \(0.310480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.4384 | −0.755899 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.52523 | 0.389842 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.42693 | 0.385174 | 0.192587 | − | 0.981280i | \(-0.438312\pi\) | ||||
0.192587 | + | 0.981280i | \(0.438312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.1898 | −1.35384 | −0.676920 | − | 0.736057i | \(-0.736686\pi\) | ||||
−0.676920 | + | 0.736057i | \(0.736686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.89494 | 0.0770404 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1532 | 0.412106 | 0.206053 | − | 0.978541i | \(-0.433938\pi\) | ||||
0.206053 | + | 0.978541i | \(0.433938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.2803 | 0.497624 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.6339 | 0.551567 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0912 | −0.932646 | −0.466323 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466323 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.66138 | 0.107317 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.52338 | −0.0613288 | −0.0306644 | − | 0.999530i | \(-0.509762\pi\) | ||||
−0.0306644 | + | 0.999530i | \(0.509762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.3184 | −1.62053 | −0.810266 | − | 0.586062i | \(-0.800677\pi\) | ||||
−0.810266 | + | 0.586062i | \(0.800677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.12194 | 0.165408 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −53.7531 | −2.15357 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.40000 | 0.215655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.2294 | 0.806598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.363697 | 0.0144785 | 0.00723927 | − | 0.999974i | \(-0.497696\pi\) | ||||
0.00723927 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.4972 | −0.735200 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.7682 | −0.784478 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −67.4729 | −2.67337 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.73447 | −0.147733 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.1645 | 0.993937 | 0.496968 | − | 0.867769i | \(-0.334447\pi\) | ||||
0.496968 | + | 0.867769i | \(0.334447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.18919 | −0.244078 | −0.122039 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122039 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.11704 | 0.358983 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.3079 | −1.03427 | −0.517135 | − | 0.855904i | \(-0.673002\pi\) | ||||
−0.517135 | + | 0.855904i | \(0.673002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.85936 | −0.269253 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.1093 | 0.827340 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.9711 | 0.977196 | 0.488598 | − | 0.872509i | \(-0.337509\pi\) | ||||
0.488598 | + | 0.872509i | \(0.337509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.62342 | 0.141579 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.6689 | 0.533275 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.8149 | 1.31724 | 0.658621 | − | 0.752474i | \(-0.271140\pi\) | ||||
0.658621 | + | 0.752474i | \(0.271140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.02483 | −0.351025 | −0.175513 | − | 0.984477i | \(-0.556158\pi\) | ||||
−0.175513 | + | 0.984477i | \(0.556158\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.3379 | −0.789858 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.10424 | −0.314269 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1777 | 0.432802 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.4186 | −0.557456 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.01673 | −0.116460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0138 | −1.07985 | −0.539927 | − | 0.841712i | \(-0.681548\pi\) | ||||
−0.539927 | + | 0.841712i | \(0.681548\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.97519 | −0.268078 | −0.134039 | − | 0.990976i | \(-0.542795\pi\) | ||||
−0.134039 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.7462 | 1.48694 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.4412 | −1.05155 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.0960 | −1.30465 | −0.652324 | − | 0.757940i | \(-0.726206\pi\) | ||||
−0.652324 | + | 0.757940i | \(0.726206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4342 | 0.551502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.95040 | 0.150717 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.55427 | −0.0592128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2338 | 1.56861 | 0.784304 | − | 0.620377i | \(-0.213020\pi\) | ||||
0.784304 | + | 0.620377i | \(0.213020\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.6647 | 0.519080 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.13358 | −0.0809312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8360 | −0.410443 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.2038 | −0.688530 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.11548 | 0.117670 | 0.0588350 | − | 0.998268i | \(-0.481261\pi\) | ||||
0.0588350 | + | 0.998268i | \(0.481261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.89145 | 0.335347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.72945 | 0.102797 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.1804 | 1.77440 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.97845 | 0.374749 | 0.187374 | − | 0.982289i | \(-0.440002\pi\) | ||||
0.187374 | + | 0.982289i | \(0.440002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.72419 | −0.102165 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.2139 | 0.719568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0725 | 0.563679 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.17999 | −0.230796 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.0440 | 1.60527 | 0.802635 | − | 0.596471i | \(-0.203431\pi\) | ||||
0.802635 | + | 0.596471i | \(0.203431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.4846 | −1.32152 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.9358 | 0.481089 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.71175 | 0.100712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.8439 | −1.03267 | −0.516336 | − | 0.856386i | \(-0.672704\pi\) | ||||
−0.516336 | + | 0.856386i | \(0.672704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.1207 | −1.37296 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8584 | 0.733486 | 0.366743 | − | 0.930322i | \(-0.380473\pi\) | ||||
0.366743 | + | 0.930322i | \(0.380473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5078 | −0.498244 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.01746 | 0.111150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.1107 | −1.03407 | −0.517035 | − | 0.855964i | \(-0.672964\pi\) | ||||
−0.517035 | + | 0.855964i | \(0.672964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.93915 | −0.328388 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.81336 | 0.249958 | 0.124979 | − | 0.992159i | \(-0.460114\pi\) | ||||
0.124979 | + | 0.992159i | \(0.460114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0243 | −0.513811 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.69329 | −0.318071 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.5665 | 1.77458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.45304 | 0.308456 | 0.154228 | − | 0.988035i | \(-0.450711\pi\) | ||||
0.154228 | + | 0.988035i | \(0.450711\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.4636 | 0.381315 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.1469 | −0.514860 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.50624 | 0.345510 | 0.172755 | − | 0.984965i | \(-0.444733\pi\) | ||||
0.172755 | + | 0.984965i | \(0.444733\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.4378 | 0.451463 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.3448 | −0.628747 | −0.314374 | − | 0.949299i | \(-0.601794\pi\) | ||||
−0.314374 | + | 0.949299i | \(0.601794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −55.2308 | −1.99949 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.07157 | −0.147208 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.3550 | 0.410004 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.8263 | 1.32799 | 0.663995 | − | 0.747737i | \(-0.268860\pi\) | ||||
0.663995 | + | 0.747737i | \(0.268860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.77262 | −0.243910 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.48691 | −0.197351 | −0.0986753 | − | 0.995120i | \(-0.531461\pi\) | ||||
−0.0986753 | + | 0.995120i | \(0.531461\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.66138 | 0.167442 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.4999 | 0.807178 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.76277 | −0.170644 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2686 | −0.403223 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.71175 | 0.0969101 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.9743 | −0.748604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.7969 | 1.48990 | 0.744949 | − | 0.667121i | \(-0.232474\pi\) | ||||
0.744949 | + | 0.667121i | \(0.232474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.2916 | −0.936007 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.0899 | 0.572091 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.99389 | 0.177338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.311159 | −0.0110357 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.99894 | −0.247915 | −0.123958 | − | 0.992288i | \(-0.539559\pi\) | ||||
−0.123958 | + | 0.992288i | \(0.539559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.1132 | −0.393155 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.8698 | −0.419399 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.2454 | 1.45552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.6665 | −0.657907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.6254 | −0.972460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.7908 | 0.801282 | 0.400641 | − | 0.916235i | \(-0.368787\pi\) | ||||
0.400641 | + | 0.916235i | \(0.368787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.2680 | −0.922395 | −0.461197 | − | 0.887298i | \(-0.652580\pi\) | ||||
−0.461197 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.4445 | 0.752091 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.2727 | 0.710123 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.3157 | −0.570815 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.6206 | −0.790427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.8917 | −1.04323 | −0.521614 | − | 0.853182i | \(-0.674670\pi\) | ||||
−0.521614 | + | 0.853182i | \(0.674670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.2087 | 1.57587 | 0.787937 | − | 0.615755i | \(-0.211149\pi\) | ||||
0.787937 | + | 0.615755i | \(0.211149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.01746 | 0.105054 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.5552 | −0.853868 | −0.426934 | − | 0.904283i | \(-0.640406\pi\) | ||||
−0.426934 | + | 0.904283i | \(0.640406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0885 | −0.906090 | −0.453045 | − | 0.891488i | \(-0.649662\pi\) | ||||
−0.453045 | + | 0.891488i | \(0.649662\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.90868 | −0.204970 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 54.9982 | 1.90557 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.04113 | −0.209062 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.66138 | 0.161121 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.3367 | −0.874720 | −0.437360 | − | 0.899286i | \(-0.644086\pi\) | ||||
−0.437360 | + | 0.899286i | \(0.644086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6464 | −0.746428 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.4143 | −0.530895 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.9509 | −0.411125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.58136 | −0.294859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1098 | 0.518568 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.4796 | 0.702033 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.49921 | −0.154050 | −0.0770250 | − | 0.997029i | \(-0.524542\pi\) | ||||
−0.0770250 | + | 0.997029i | \(0.524542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.78959 | −0.0612026 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.5055 | −1.07621 | −0.538103 | − | 0.842879i | \(-0.680859\pi\) | ||||
−0.538103 | + | 0.842879i | \(0.680859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2301 | 0.485524 | 0.242762 | − | 0.970086i | \(-0.421947\pi\) | ||||
0.242762 | + | 0.970086i | \(0.421947\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0522 | −0.410738 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.2066 | −1.26653 | −0.633263 | − | 0.773936i | \(-0.718285\pi\) | ||||
−0.633263 | + | 0.773936i | \(0.718285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.61707 | 0.122984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.422296 | −0.0143419 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.22012 | −0.278849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.99509 | −0.169252 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.55597 | 0.289576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.52856 | −0.153093 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2708 | −0.718262 | −0.359131 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359131 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3820 | −0.350178 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.8417 | −1.37599 | −0.687996 | − | 0.725714i | \(-0.741509\pi\) | ||||
−0.687996 | + | 0.725714i | \(0.741509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0760 | 0.541000 | 0.270500 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270500 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.27322 | 0.0764136 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.5466 | −0.790617 | −0.395308 | − | 0.918548i | \(-0.629362\pi\) | ||||
−0.395308 | + | 0.918548i | \(0.629362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 89.5216 | 3.00246 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.01746 | 0.101089 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.88459 | −0.163457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.97723 | 0.0995179 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.5895 | −0.687463 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.6405 | 0.421584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26690 | 0.0422067 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −41.2870 | −1.37395 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.47802 | −0.115613 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.8507 | −1.42283 | −0.711416 | − | 0.702771i | \(-0.751946\pi\) | ||||
−0.711416 | + | 0.702771i | \(0.751946\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.4184 | 0.345557 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3201 | −0.971419 | −0.485709 | − | 0.874120i | \(-0.661439\pi\) | ||||
−0.485709 | + | 0.874120i | \(0.661439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2317 | −0.868141 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.999758 | 0.0330510 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.4089 | −0.541869 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.77825 | 0.289568 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6699 | 0.615193 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6540 | 0.614005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.96844 | 0.163361 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.83575 | −0.257360 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.6432 | 0.775709 | 0.387855 | − | 0.921721i | \(-0.373216\pi\) | ||||
0.387855 | + | 0.921721i | \(0.373216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1734 | 0.792253 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1111 | 0.429237 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.2858 | −0.401789 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.80530 | 0.124314 | 0.0621568 | − | 0.998066i | \(-0.480202\pi\) | ||||
0.0621568 | + | 0.998066i | \(0.480202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.29921 | −0.238201 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8919 | 0.355067 | 0.177534 | − | 0.984115i | \(-0.443188\pi\) | ||||
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9701 | −0.357234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.52856 | −0.147314 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.9819 | −1.75418 | −0.877089 | − | 0.480329i | \(-0.840517\pi\) | ||||
−0.877089 | + | 0.480329i | \(0.840517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −68.2775 | −2.21638 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.4771 | 1.02071 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.1294 | −1.23513 | −0.617566 | − | 0.786519i | \(-0.711881\pi\) | ||||
−0.617566 | + | 0.786519i | \(0.711881\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.48662 | −0.306980 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.18260 | 0.264506 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −65.3660 | −2.11078 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.27155 | −0.299082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.7245 | 0.345592 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.7833 | −0.508081 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.32514 | −0.299876 | −0.149938 | − | 0.988695i | \(-0.547907\pi\) | ||||
−0.149938 | + | 0.988695i | \(0.547907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.28643 | 0.234074 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4385 | 0.784268 | 0.392134 | − | 0.919908i | \(-0.371737\pi\) | ||||
0.392134 | + | 0.919908i | \(0.371737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.66203 | 0.309751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.99509 | −0.159971 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.1127 | −0.835419 | −0.417710 | − | 0.908581i | \(-0.637167\pi\) | ||||
−0.417710 | + | 0.908581i | \(0.637167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.8166 | −1.14470 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1961 | −0.389392 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5111 | 0.877468 | 0.438734 | − | 0.898617i | \(-0.355427\pi\) | ||||
0.438734 | + | 0.898617i | \(0.355427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.46333 | 0.205939 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.3605 | −0.393438 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.5799 | −1.19497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.5897 | −1.47997 | −0.739985 | − | 0.672623i | \(-0.765167\pi\) | ||||
−0.739985 | + | 0.672623i | \(0.765167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.29632 | −0.231542 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.52523 | −0.301970 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.9541 | −1.55039 | −0.775196 | − | 0.631721i | \(-0.782349\pi\) | ||||
−0.775196 | + | 0.631721i | \(0.782349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.96844 | 0.157195 |
(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 | 8040.2.a.t.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8040.2.a.t.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial |