Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, 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("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.39605.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.681685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-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 | ||||||||
\(5\) | −0.318315 | −0.142355 | −0.0711774 | − | 0.997464i | \(-0.522676\pi\) | ||||
−0.0711774 | + | 0.997464i | \(0.522676\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.71255 | 1.11938 | 0.559688 | − | 0.828704i | \(-0.310921\pi\) | ||||
0.559688 | + | 0.828704i | \(0.310921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.66749 | −0.739829 | −0.369915 | − | 0.929066i | \(-0.620613\pi\) | ||||
−0.369915 | + | 0.929066i | \(0.620613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.318315 | −0.0821886 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.21699 | 0.537699 | 0.268850 | − | 0.963182i | \(-0.413357\pi\) | ||||
0.268850 | + | 0.963182i | \(0.413357\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.34918 | −0.538938 | −0.269469 | − | 0.963009i | \(-0.586848\pi\) | ||||
−0.269469 | + | 0.963009i | \(0.586848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89868 | −0.979735 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.41527 | 1.00559 | 0.502795 | − | 0.864406i | \(-0.332305\pi\) | ||||
0.502795 | + | 0.864406i | \(0.332305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.21699 | 1.47582 | 0.737908 | − | 0.674902i | \(-0.235814\pi\) | ||||
0.737908 | + | 0.674902i | \(0.235814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.71255 | 0.646272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.318315 | 0.0538051 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.28308 | 1.19733 | 0.598666 | − | 0.800999i | \(-0.295698\pi\) | ||||
0.598666 | + | 0.800999i | \(0.295698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.66749 | −0.427141 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.77864 | 0.746298 | 0.373149 | − | 0.927771i | \(-0.378278\pi\) | ||||
0.373149 | + | 0.927771i | \(0.378278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.59703 | −1.31103 | −0.655517 | − | 0.755180i | \(-0.727549\pi\) | ||||
−0.655517 | + | 0.755180i | \(0.727549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.318315 | −0.0474516 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.63226 | −0.529820 | −0.264910 | − | 0.964273i | \(-0.585342\pi\) | ||||
−0.264910 | + | 0.964273i | \(0.585342\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.21699 | 0.310441 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.615591 | −0.0845580 | −0.0422790 | − | 0.999106i | \(-0.513462\pi\) | ||||
−0.0422790 | + | 0.999106i | \(0.513462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18176 | −0.159348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.34918 | −0.311156 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.81839 | 1.27825 | 0.639123 | − | 0.769105i | \(-0.279298\pi\) | ||||
0.639123 | + | 0.769105i | \(0.279298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9364 | 1.40026 | 0.700130 | − | 0.714015i | \(-0.253125\pi\) | ||||
0.700130 | + | 0.714015i | \(0.253125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.849103 | 0.105318 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.747779 | 0.0913557 | 0.0456778 | − | 0.998956i | \(-0.485455\pi\) | ||||
0.0456778 | + | 0.998956i | \(0.485455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5309 | 1.60583 | 0.802913 | − | 0.596096i | \(-0.203282\pi\) | ||||
0.802913 | + | 0.596096i | \(0.203282\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.84473 | −0.449992 | −0.224996 | − | 0.974360i | \(-0.572237\pi\) | ||||
−0.224996 | + | 0.974360i | \(0.572237\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.89868 | −0.565650 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.71255 | −0.423084 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1797 | 1.70785 | 0.853926 | − | 0.520395i | \(-0.174215\pi\) | ||||
0.853926 | + | 0.520395i | \(0.174215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.11799 | −0.122716 | −0.0613579 | − | 0.998116i | \(-0.519543\pi\) | ||||
−0.0613579 | + | 0.998116i | \(0.519543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.705701 | −0.0765441 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.41527 | 0.580578 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.32814 | 0.670781 | 0.335391 | − | 0.942079i | \(-0.391132\pi\) | ||||
0.335391 | + | 0.942079i | \(0.391132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.66749 | 0.279629 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21699 | 0.852062 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.747779 | 0.0767205 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.1136 | −1.63609 | −0.818045 | − | 0.575154i | \(-0.804942\pi\) | ||||
−0.818045 | + | 0.575154i | \(0.804942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.71255 | 0.373125 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2435 | −1.31778 | −0.658888 | − | 0.752241i | \(-0.728973\pi\) | ||||
−0.658888 | + | 0.752241i | \(0.728973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.12782 | −0.308193 | −0.154097 | − | 0.988056i | \(-0.549247\pi\) | ||||
−0.154097 | + | 0.988056i | \(0.549247\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.318315 | 0.0310644 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6631 | −1.51421 | −0.757106 | − | 0.653292i | \(-0.773387\pi\) | ||||
−0.757106 | + | 0.653292i | \(0.773387\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.75230 | 0.838318 | 0.419159 | − | 0.907913i | \(-0.362325\pi\) | ||||
0.419159 | + | 0.907913i | \(0.362325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.28308 | 0.691280 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8051 | −1.48682 | −0.743411 | − | 0.668835i | \(-0.766793\pi\) | ||||
−0.743411 | + | 0.668835i | \(0.766793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.318315 | 0.0296830 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.66749 | −0.246610 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.21699 | −0.203231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.78301 | 0.253001 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.77864 | 0.430876 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.15090 | 0.281825 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.92706 | 0.525942 | 0.262971 | − | 0.964804i | \(-0.415298\pi\) | ||||
0.262971 | + | 0.964804i | \(0.415298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.59703 | −0.756926 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.78316 | 0.767388 | 0.383694 | − | 0.923460i | \(-0.374652\pi\) | ||||
0.383694 | + | 0.923460i | \(0.374652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.34918 | 0.203700 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.318315 | −0.0273962 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1333 | 1.54923 | 0.774615 | − | 0.632433i | \(-0.217944\pi\) | ||||
0.774615 | + | 0.632433i | \(0.217944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.884483 | −0.0750209 | −0.0375104 | − | 0.999296i | \(-0.511943\pi\) | ||||
−0.0375104 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.63226 | −0.305892 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.90319 | −0.828147 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72376 | −0.143151 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7690 | 1.61954 | 0.809768 | − | 0.586750i | \(-0.199593\pi\) | ||||
0.809768 | + | 0.586750i | \(0.199593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.7930 | 1.69211 | 0.846054 | − | 0.533096i | \(-0.178972\pi\) | ||||
0.846054 | + | 0.533096i | \(0.178972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.21699 | 0.179233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.61559 | −0.210089 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3350 | 0.904630 | 0.452315 | − | 0.891858i | \(-0.350598\pi\) | ||||
0.452315 | + | 0.891858i | \(0.350598\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.615591 | −0.0488196 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.1534 | 1.81351 | 0.906756 | − | 0.421655i | \(-0.138551\pi\) | ||||
0.906756 | + | 0.421655i | \(0.138551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.18176 | −0.0919999 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.34918 | −0.181785 | −0.0908924 | − | 0.995861i | \(-0.528972\pi\) | ||||
−0.0908924 | + | 0.995861i | \(0.528972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.88448 | −0.452653 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.34918 | −0.179646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.74589 | −0.740966 | −0.370483 | − | 0.928839i | \(-0.620808\pi\) | ||||
−0.370483 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.89868 | 0.370305 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.81839 | 0.737995 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.0168 | −1.94459 | −0.972294 | − | 0.233761i | \(-0.924897\pi\) | ||||
−0.972294 | + | 0.233761i | \(0.924897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.8449 | 1.40073 | 0.700365 | − | 0.713785i | \(-0.253021\pi\) | ||||
0.700365 | + | 0.713785i | \(0.253021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9364 | 0.808441 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.31832 | −0.170446 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.23068 | 0.601887 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1939 | 0.737606 | 0.368803 | − | 0.929508i | \(-0.379768\pi\) | ||||
0.368803 | + | 0.929508i | \(0.379768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7361 | 0.844780 | 0.422390 | − | 0.906414i | \(-0.361191\pi\) | ||||
0.422390 | + | 0.906414i | \(0.361191\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.849103 | 0.0608055 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4560 | 1.10119 | 0.550596 | − | 0.834772i | \(-0.314401\pi\) | ||||
0.550596 | + | 0.834772i | \(0.314401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8424 | 1.19393 | 0.596963 | − | 0.802269i | \(-0.296374\pi\) | ||||
0.596963 | + | 0.802269i | \(0.296374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.747779 | 0.0527442 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.41527 | −0.380078 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.52111 | −0.106239 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.72143 | −0.603274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6842 | 1.21743 | 0.608714 | − | 0.793390i | \(-0.291686\pi\) | ||||
0.608714 | + | 0.793390i | \(0.291686\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.5309 | 0.927125 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.73656 | 0.186632 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.21699 | −0.557806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.84473 | −0.259803 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.91381 | −0.397806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.90850 | −0.395662 | −0.197831 | − | 0.980236i | \(-0.563390\pi\) | ||||
−0.197831 | + | 0.980236i | \(0.563390\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.89868 | −0.326578 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0500 | 1.26439 | 0.632197 | − | 0.774808i | \(-0.282153\pi\) | ||||
0.632197 | + | 0.774808i | \(0.282153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1819 | −1.46582 | −0.732911 | − | 0.680325i | \(-0.761839\pi\) | ||||
−0.732911 | + | 0.680325i | \(0.761839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.71255 | −0.244268 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.8712 | −0.974247 | −0.487123 | − | 0.873333i | \(-0.661954\pi\) | ||||
−0.487123 | + | 0.873333i | \(0.661954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.15620 | 0.0754224 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1797 | 0.986029 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.8008 | −0.957382 | −0.478691 | − | 0.877983i | \(-0.658889\pi\) | ||||
−0.478691 | + | 0.877983i | \(0.658889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6887 | −1.78358 | −0.891792 | − | 0.452445i | \(-0.850552\pi\) | ||||
−0.891792 | + | 0.452445i | \(0.850552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.318315 | −0.0203364 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.26641 | 0.398722 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.11799 | −0.0708500 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.1895 | −1.58995 | −0.794975 | − | 0.606642i | \(-0.792516\pi\) | ||||
−0.794975 | + | 0.606642i | \(0.792516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.71255 | −0.233406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.705701 | −0.0441927 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.89227 | 0.305171 | 0.152586 | − | 0.988290i | \(-0.451240\pi\) | ||||
0.152586 | + | 0.988290i | \(0.451240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.28308 | −0.452549 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.41527 | 0.335197 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.1755 | 1.42906 | 0.714531 | − | 0.699603i | \(-0.246640\pi\) | ||||
0.714531 | + | 0.699603i | \(0.246640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.195952 | 0.0120372 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.32814 | 0.387276 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.3811 | −1.48654 | −0.743272 | − | 0.668990i | \(-0.766727\pi\) | ||||
−0.743272 | + | 0.668990i | \(0.766727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.42853 | 0.329759 | 0.164880 | − | 0.986314i | \(-0.447276\pi\) | ||||
0.164880 | + | 0.986314i | \(0.447276\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.66749 | 0.161444 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.1866 | −1.09669 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5730 | −0.935692 | −0.467846 | − | 0.883810i | \(-0.654970\pi\) | ||||
−0.467846 | + | 0.883810i | \(0.654970\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.21699 | 0.491938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.05736 | 0.182387 | 0.0911933 | − | 0.995833i | \(-0.470932\pi\) | ||||
0.0911933 | + | 0.995833i | \(0.470932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.24334 | 0.252240 | 0.126120 | − | 0.992015i | \(-0.459748\pi\) | ||||
0.126120 | + | 0.992015i | \(0.459748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.747779 | 0.0442946 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.77864 | −0.282074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0850 | −0.710880 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.1136 | −0.944598 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.6984 | −1.09237 | −0.546185 | − | 0.837665i | \(-0.683920\pi\) | ||||
−0.546185 | + | 0.837665i | \(0.683920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.12534 | −0.181964 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.71255 | 0.215424 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.66749 | 0.154265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.59703 | 0.495525 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.2435 | −0.760818 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.48122 | −0.199334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.3448 | 1.44650 | 0.723252 | − | 0.690584i | \(-0.242646\pi\) | ||||
0.723252 | + | 0.690584i | \(0.242646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.12782 | −0.177935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5221 | 0.823470 | 0.411735 | − | 0.911304i | \(-0.364923\pi\) | ||||
0.411735 | + | 0.911304i | \(0.364923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.53778 | 0.256491 | 0.128245 | − | 0.991742i | \(-0.459066\pi\) | ||||
0.128245 | + | 0.991742i | \(0.459066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.318315 | 0.0179350 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.61996 | 0.203317 | 0.101659 | − | 0.994819i | \(-0.467585\pi\) | ||||
0.101659 | + | 0.994819i | \(0.467585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1045 | 1.12563 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6631 | −0.874230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.20810 | −0.289787 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0672 | 0.724837 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.75230 | 0.484003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.63226 | 0.200253 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5749 | 0.691179 | 0.345590 | − | 0.938386i | \(-0.387679\pi\) | ||||
0.345590 | + | 0.938386i | \(0.387679\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.28308 | 0.399111 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.238029 | −0.0130049 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.07265 | 0.0584310 | 0.0292155 | − | 0.999573i | \(-0.490699\pi\) | ||||
0.0292155 | + | 0.999573i | \(0.490699\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.8051 | −0.858417 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.5060 | 1.65199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.318315 | 0.0171375 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.3732 | −0.610545 | −0.305273 | − | 0.952265i | \(-0.598748\pi\) | ||||
−0.305273 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.3580 | 1.73209 | 0.866043 | − | 0.499969i | \(-0.166655\pi\) | ||||
0.866043 | + | 0.499969i | \(0.166655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.66749 | −0.142380 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.3447 | −0.657040 | −0.328520 | − | 0.944497i | \(-0.606550\pi\) | ||||
−0.328520 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.30710 | −0.228597 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.21699 | −0.117336 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7239 | 1.51599 | 0.757995 | − | 0.652260i | \(-0.226179\pi\) | ||||
0.757995 | + | 0.652260i | \(0.226179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4814 | −0.709546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.78301 | 0.146070 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.22384 | 0.0640585 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4365 | −0.649178 | −0.324589 | − | 0.945855i | \(-0.605226\pi\) | ||||
−0.324589 | + | 0.945855i | \(0.605226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.77864 | 0.248766 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.615591 | 0.0319599 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.97692 | −0.309473 | −0.154737 | − | 0.987956i | \(-0.549453\pi\) | ||||
−0.154737 | + | 0.987956i | \(0.549453\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.15090 | 0.162712 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.4452 | −0.743965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1369 | −0.982994 | −0.491497 | − | 0.870879i | \(-0.663550\pi\) | ||||
−0.491497 | + | 0.870879i | \(0.663550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.92706 | 0.303652 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4482 | −0.789365 | −0.394682 | − | 0.918818i | \(-0.629145\pi\) | ||||
−0.394682 | + | 0.918818i | \(0.629145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.18176 | 0.0602280 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.59703 | −0.437012 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.9065 | −1.21211 | −0.606053 | − | 0.795424i | \(-0.707248\pi\) | ||||
−0.606053 | + | 0.795424i | \(0.707248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.21699 | −0.112118 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.78316 | 0.443052 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.83193 | −0.243121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.8551 | −1.74933 | −0.874665 | − | 0.484728i | \(-0.838919\pi\) | ||||
−0.874665 | + | 0.484728i | \(0.838919\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34918 | 0.117606 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.481365 | −0.0240382 | −0.0120191 | − | 0.999928i | \(-0.503826\pi\) | ||||
−0.0120191 | + | 0.999928i | \(0.503826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.9188 | −1.09185 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.318315 | −0.0158172 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.0388 | 1.34026 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1621 | 1.49142 | 0.745710 | − | 0.666271i | \(-0.232111\pi\) | ||||
0.745710 | + | 0.666271i | \(0.232111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.1333 | 0.894448 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.81839 | −0.483131 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.355874 | 0.0174692 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.884483 | −0.0433133 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.7390 | 1.20858 | 0.604291 | − | 0.796764i | \(-0.293457\pi\) | ||||
0.604291 | + | 0.796764i | \(0.293457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4452 | −0.801490 | −0.400745 | − | 0.916190i | \(-0.631249\pi\) | ||||
−0.400745 | + | 0.916190i | \(0.631249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.63226 | −0.176607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8603 | −0.526803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9364 | −0.529249 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.90319 | −0.478131 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.6061 | −1.95593 | −0.977963 | − | 0.208780i | \(-0.933051\pi\) | ||||
−0.977963 | + | 0.208780i | \(0.933051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.36789 | 0.257964 | 0.128982 | − | 0.991647i | \(-0.458829\pi\) | ||||
0.128982 | + | 0.991647i | \(0.458829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.72376 | −0.0826481 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.34918 | 0.112376 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.7655 | −1.13427 | −0.567134 | − | 0.823626i | \(-0.691948\pi\) | ||||
−0.567134 | + | 0.823626i | \(0.691948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6655 | 0.791800 | 0.395900 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395900 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.01434 | −0.0954890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.7690 | 0.935040 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6910 | 0.693312 | 0.346656 | − | 0.937992i | \(-0.387317\pi\) | ||||
0.346656 | + | 0.937992i | \(0.387317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7409 | 0.835388 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.7930 | 0.976940 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.849103 | −0.0398066 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.2346 | 0.852979 | 0.426489 | − | 0.904493i | \(-0.359750\pi\) | ||||
0.426489 | + | 0.904493i | \(0.359750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.21699 | 0.103480 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.1200 | −0.983658 | −0.491829 | − | 0.870692i | \(-0.663671\pi\) | ||||
−0.491829 | + | 0.870692i | \(0.663671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.75026 | 0.406659 | 0.203329 | − | 0.979110i | \(-0.434824\pi\) | ||||
0.203329 | + | 0.979110i | \(0.434824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.61559 | −0.121295 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2743 | −1.53975 | −0.769877 | − | 0.638193i | \(-0.779682\pi\) | ||||
−0.769877 | + | 0.638193i | \(0.779682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.747779 | −0.0345292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.3350 | 0.522289 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.9169 | −1.46754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.5079 | 0.528017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.615591 | −0.0281860 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.9155 | −0.635815 | −0.317908 | − | 0.948122i | \(-0.602980\pi\) | ||||
−0.317908 | + | 0.948122i | \(0.602980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4276 | −0.885821 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.12921 | 0.232905 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.9306 | −1.26566 | −0.632829 | − | 0.774292i | \(-0.718106\pi\) | ||||
−0.632829 | + | 0.774292i | \(0.718106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.1534 | 1.04703 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.3047 | 1.09686 | 0.548428 | − | 0.836198i | \(-0.315226\pi\) | ||||
0.548428 | + | 0.836198i | \(0.315226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0056 | 0.540705 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.18176 | −0.0531161 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.5309 | −0.606945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7763 | 0.616712 | 0.308356 | − | 0.951271i | \(-0.400221\pi\) | ||||
0.308356 | + | 0.951271i | \(0.400221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.34918 | −0.104954 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.2572 | −0.858635 | −0.429318 | − | 0.903154i | \(-0.641246\pi\) | ||||
−0.429318 | + | 0.903154i | \(0.641246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.21560 | 0.187592 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.88448 | −0.261339 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.18503 | −0.229822 | −0.114911 | − | 0.993376i | \(-0.536658\pi\) | ||||
−0.114911 | + | 0.993376i | \(0.536658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.84473 | 0.170081 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.34918 | −0.103719 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.995632 | 0.0438728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4849 | −0.593067 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.74589 | −0.427797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.1520 | −1.45241 | −0.726207 | − | 0.687476i | \(-0.758719\pi\) | ||||
−0.726207 | + | 0.687476i | \(0.758719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1323 | 0.486783 | 0.243392 | − | 0.969928i | \(-0.421740\pi\) | ||||
0.243392 | + | 0.969928i | \(0.421740\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.89868 | 0.213796 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.2170 | 0.793545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.81839 | 0.426082 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7470 | −0.552133 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.98581 | 0.215555 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.0168 | −1.12271 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.71255 | 0.159911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6192 | −0.456553 | −0.228277 | − | 0.973596i | \(-0.573309\pi\) | ||||
−0.228277 | + | 0.973596i | \(0.573309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.8449 | 0.808711 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.78599 | −0.119339 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.1819 | 1.54703 | 0.773513 | − | 0.633780i | \(-0.218498\pi\) | ||||
0.773513 | + | 0.633780i | \(0.218498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.9364 | 0.466754 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7214 | −0.541951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1797 | −0.645507 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.31832 | −0.0984070 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.524091 | 0.0222065 | 0.0111032 | − | 0.999938i | \(-0.496466\pi\) | ||||
0.0111032 | + | 0.999938i | \(0.496466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9325 | 0.969942 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.23068 | 0.347500 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.30427 | 0.181403 | 0.0907017 | − | 0.995878i | \(-0.471089\pi\) | ||||
0.0907017 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.03101 | 0.211656 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.2318 | 1.51891 | 0.759457 | − | 0.650557i | \(-0.225465\pi\) | ||||
0.759457 | + | 0.650557i | \(0.225465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5480 | 1.27840 | 0.639198 | − | 0.769042i | \(-0.279266\pi\) | ||||
0.639198 | + | 0.769042i | \(0.279266\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1939 | 0.425857 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.89868 | 0.204289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.3878 | −1.26506 | −0.632531 | − | 0.774535i | \(-0.717984\pi\) | ||||
−0.632531 | + | 0.774535i | \(0.717984\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7361 | 0.487734 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.11799 | 0.0463822 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.28541 | −0.0946521 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.849103 | 0.0351061 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.4654 | 1.62891 | 0.814456 | − | 0.580225i | \(-0.197035\pi\) | ||||
0.814456 | + | 0.580225i | \(0.197035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3032 | −0.795373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.4560 | 0.635773 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.7930 | −0.935996 | −0.467998 | − | 0.883730i | \(-0.655024\pi\) | ||||
−0.467998 | + | 0.883730i | \(0.655024\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.705701 | 0.0289309 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.8424 | 0.689314 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.8287 | −1.46392 | −0.731960 | − | 0.681348i | \(-0.761394\pi\) | ||||
−0.731960 | + | 0.681348i | \(0.761394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3669 | −1.60581 | −0.802905 | − | 0.596106i | \(-0.796714\pi\) | ||||
−0.802905 | + | 0.596106i | \(0.796714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.747779 | 0.0304519 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.885874 | −0.0360159 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4076 | 1.23421 | 0.617104 | − | 0.786882i | \(-0.288306\pi\) | ||||
0.617104 | + | 0.786882i | \(0.288306\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.41527 | −0.219438 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.68903 | 0.391976 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.5252 | −1.55602 | −0.778009 | − | 0.628254i | \(-0.783770\pi\) | ||||
−0.778009 | + | 0.628254i | \(0.783770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.52111 | −0.0613372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.9032 | −0.479205 | −0.239602 | − | 0.970871i | \(-0.577017\pi\) | ||||
−0.239602 | + | 0.970871i | \(0.577017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8522 | 0.436188 | 0.218094 | − | 0.975928i | \(-0.430016\pi\) | ||||
0.218094 | + | 0.975928i | \(0.430016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.32814 | −0.253532 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4904 | 0.939616 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.72143 | −0.348301 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.1465 | 0.643804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3250 | −0.848936 | −0.424468 | − | 0.905443i | \(-0.639539\pi\) | ||||
−0.424468 | + | 0.905443i | \(0.639539\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6842 | 0.702882 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.88667 | −0.0748703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.66749 | −0.105690 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5309 | 0.535276 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.33251 | −0.131626 | −0.0658131 | − | 0.997832i | \(-0.520964\pi\) | ||||
−0.0658131 | + | 0.997832i | \(0.520964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.0776 | 1.77769 | 0.888844 | − | 0.458211i | \(-0.151509\pi\) | ||||
0.888844 | + | 0.458211i | \(0.151509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.73656 | 0.107752 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7616 | 0.619653 | 0.309827 | − | 0.950793i | \(-0.399729\pi\) | ||||
0.309827 | + | 0.950793i | \(0.399729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.4512 | 1.43084 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.21699 | −0.322049 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.9836 | 1.60381 | 0.801907 | − | 0.597449i | \(-0.203819\pi\) | ||||
0.801907 | + | 0.597449i | \(0.203819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.79581 | −0.109241 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.84473 | −0.149997 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.1376 | −0.589679 | −0.294839 | − | 0.955547i | \(-0.595266\pi\) | ||||
−0.294839 | + | 0.955547i | \(0.595266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.2700 | −1.79969 | −0.899847 | − | 0.436206i | \(-0.856322\pi\) | ||||
−0.899847 | + | 0.436206i | \(0.856322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.91381 | −0.229673 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.747779 | −0.0289976 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.41527 | −0.209680 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.90850 | −0.228436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.6018 | 1.56742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1177 | −0.390009 | −0.195004 | − | 0.980802i | \(-0.562472\pi\) | ||||
−0.195004 | + | 0.980802i | \(0.562472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.89868 | −0.188550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0373 | −0.616362 | −0.308181 | − | 0.951328i | \(-0.599720\pi\) | ||||
−0.308181 | + | 0.951328i | \(0.599720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.1136 | 0.618384 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0500 | 0.729998 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.6137 | −1.51578 | −0.757888 | − | 0.652385i | \(-0.773769\pi\) | ||||
−0.757888 | + | 0.652385i | \(0.773769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.77209 | −0.220540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.1819 | −0.846293 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.64209 | 0.0625585 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.69210 | 0.254579 | 0.127290 | − | 0.991866i | \(-0.459372\pi\) | ||||
0.127290 | + | 0.991866i | \(0.459372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.71255 | −0.141028 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.281544 | 0.0106796 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.5942 | 0.401284 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8712 | −0.562482 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.1778 | −1.59303 | −0.796517 | − | 0.604616i | \(-0.793327\pi\) | ||||
−0.796517 | + | 0.604616i | \(0.793327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1093 | −0.645288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.15620 | 0.0435451 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.2435 | 0.498073 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.18707 | 0.345028 | 0.172514 | − | 0.985007i | \(-0.444811\pi\) | ||||
0.172514 | + | 0.985007i | \(0.444811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.1797 | 0.569284 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.21699 | −0.307729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.15234 | 0.117891 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.8008 | −0.552745 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.1883 | 0.566429 | 0.283214 | − | 0.959057i | \(-0.408599\pi\) | ||||
0.283214 | + | 0.959057i | \(0.408599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.12782 | 0.116486 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.6887 | −1.02975 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.5277 | −0.985212 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7830 | 0.659535 | 0.329768 | − | 0.944062i | \(-0.393030\pi\) | ||||
0.329768 | + | 0.944062i | \(0.393030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.0595 | −0.704942 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.6564 | −0.504412 | −0.252206 | − | 0.967674i | \(-0.581156\pi\) | ||||
−0.252206 | + | 0.967674i | \(0.581156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.318315 | −0.0117412 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.77616 | 0.102261 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.7127 | −0.835500 | −0.417750 | − | 0.908562i | \(-0.637181\pi\) | ||||
−0.417750 | + | 0.908562i | \(0.637181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.26641 | 0.230202 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.81824 | −0.250137 | −0.125068 | − | 0.992148i | \(-0.539915\pi\) | ||||
−0.125068 | + | 0.992148i | \(0.539915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.29276 | −0.230549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.11799 | −0.0409053 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.6631 | 0.572318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.78505 | −0.284080 | −0.142040 | − | 0.989861i | \(-0.545366\pi\) | ||||
−0.142040 | + | 0.989861i | \(0.545366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.1895 | −0.917958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.61872 | −0.240880 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.1096 | 1.49415 | 0.747076 | − | 0.664738i | \(-0.231457\pi\) | ||||
0.747076 | + | 0.664738i | \(0.231457\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.71255 | −0.134757 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8485 | −1.08201 | −0.541003 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541003 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.75230 | −0.316854 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.705701 | −0.0255147 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.1905 | −0.945683 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6148 | −1.21218 | −0.606090 | − | 0.795396i | \(-0.707263\pi\) | ||||
−0.606090 | + | 0.795396i | \(0.707263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.89227 | 0.176191 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.3212 | 0.515099 | 0.257549 | − | 0.966265i | \(-0.417085\pi\) | ||||
0.257549 | + | 0.966265i | \(0.417085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.2524 | −1.44591 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.28308 | −0.261279 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2259 | −0.402209 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.2342 | 1.79752 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.41527 | 0.193526 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.60810 | −0.128778 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.71066 | −0.239209 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.1755 | 0.825070 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8051 | 0.561966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.1727 | −1.03595 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.195952 | 0.00694970 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.4248 | −0.652640 | −0.326320 | − | 0.945259i | \(-0.605809\pi\) | ||||
−0.326320 | + | 0.945259i | \(0.605809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.05269 | −0.284884 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.32814 | 0.223594 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.2738 | −0.503710 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.318315 | −0.0112191 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3811 | −0.858256 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.6917 | 0.657164 | 0.328582 | − | 0.944475i | \(-0.393429\pi\) | ||||
0.328582 | + | 0.944475i | \(0.393429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7543 | 0.869242 | 0.434621 | − | 0.900613i | \(-0.356882\pi\) | ||||
0.434621 | + | 0.900613i | \(0.356882\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.42853 | 0.190387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.37007 | −0.258162 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.1960 | 0.706567 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.66749 | 0.0932097 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.24866 | 0.252980 | 0.126490 | − | 0.991968i | \(-0.459629\pi\) | ||||
0.126490 | + | 0.991968i | \(0.459629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1352 | 0.388147 | 0.194074 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194074 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.1866 | −0.633175 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7059 | −0.824333 | −0.412167 | − | 0.911108i | \(-0.635228\pi\) | ||||
−0.412167 | + | 0.911108i | \(0.635228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.28250 | −0.287663 | −0.143832 | − | 0.989602i | \(-0.545942\pi\) | ||||
−0.143832 | + | 0.989602i | \(0.545942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5730 | −0.540222 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.21699 | 0.0768142 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.747779 | 0.0258779 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.21699 | 0.284021 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.7672 | −1.58006 | −0.790030 | − | 0.613068i | \(-0.789935\pi\) | ||||
−0.790030 | + | 0.613068i | \(0.789935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.325161 | 0.0112125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.05736 | 0.105301 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.87312 | 0.0644373 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.78301 | −0.0956253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.24334 | 0.145631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.28308 | −0.249661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.8222 | −1.87708 | −0.938539 | − | 0.345173i | \(-0.887820\pi\) | ||||
−0.938539 | + | 0.345173i | \(0.887820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.747779 | 0.0255735 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.7841 | −1.56395 | −0.781977 | − | 0.623307i | \(-0.785789\pi\) | ||||
−0.781977 | + | 0.623307i | \(0.785789\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8351 | −0.983840 | −0.491920 | − | 0.870641i | \(-0.663705\pi\) | ||||
−0.491920 | + | 0.870641i | \(0.663705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.77864 | −0.162856 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.1744 | −0.720785 | −0.360393 | − | 0.932801i | \(-0.617357\pi\) | ||||
−0.360393 | + | 0.932801i | \(0.617357\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.10226 | 0.105480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0850 | −0.410427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.3554 | 1.91173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.99469 | −0.0675876 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.1136 | −0.545364 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.15090 | −0.106520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.55728 | 0.255191 | 0.127596 | − | 0.991826i | \(-0.459274\pi\) | ||||
0.127596 | + | 0.991826i | \(0.459274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.6984 | −0.630680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0422 | 0.372022 | 0.186011 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186011 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.5381 | −1.66709 | −0.833544 | − | 0.552453i | \(-0.813692\pi\) | ||||
−0.833544 | + | 0.552453i | \(0.813692\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.12534 | −0.105057 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.4475 | 1.22379 | 0.611894 | − | 0.790940i | \(-0.290408\pi\) | ||||
0.611894 | + | 0.790940i | \(0.290408\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.92706 | −0.198787 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.71255 | 0.124375 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.53283 | 0.285540 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.28154 | 0.276821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.66749 | 0.0890650 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.4972 | 1.48407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.36476 | −0.0454668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.59703 | 0.286091 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.99861 | −0.199401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5496 | 0.350295 | 0.175148 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175148 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.2435 | −0.439259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6343 | −0.882433 | −0.441217 | − | 0.897401i | \(-0.645453\pi\) | ||||
−0.441217 | + | 0.897401i | \(0.645453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.15061 | −0.137365 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.48122 | −0.115085 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.78316 | −0.290045 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8918 | 0.458247 | 0.229124 | − | 0.973397i | \(-0.426414\pi\) | ||||
0.229124 | + | 0.973397i | \(0.426414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.3448 | 0.835140 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.0937 | −1.18804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.6775 | −1.17307 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.12782 | −0.102731 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.69538 | −0.318095 | −0.159048 | − | 0.987271i | \(-0.550842\pi\) | ||||
−0.159048 | + | 0.987271i | \(0.550842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.34918 | −0.0769912 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.5221 | 0.475431 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.61995 | −0.0856815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.3715 | −0.796181 | −0.398091 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398091 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.53778 | 0.148085 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.1171 | −0.460203 | −0.230101 | − | 0.973167i | \(-0.573906\pi\) | ||||
−0.230101 | + | 0.973167i | \(0.573906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.77864 | −0.155614 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.318315 | 0.0103548 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.6097 | 0.474751 | 0.237375 | − | 0.971418i | \(-0.423713\pi\) | ||||
0.237375 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2558 | 0.332917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.61996 | 0.117385 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.5328 | 0.567944 | 0.283972 | − | 0.958833i | \(-0.408348\pi\) | ||||
0.283972 | + | 0.958833i | \(0.408348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.24488 | −0.105002 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.1045 | 0.649885 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1333 | −0.585554 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.5189 | 1.17803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.6631 | −0.504737 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.73577 | −0.120259 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.8221 | 1.50570 | 0.752849 | − | 0.658194i | \(-0.228679\pi\) | ||||
0.752849 | + | 0.658194i | \(0.228679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.20810 | −0.167308 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.9608 | −1.79587 | −0.897934 | − | 0.440129i | \(-0.854933\pi\) | ||||
−0.897934 | + | 0.440129i | \(0.854933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.884483 | 0.0283552 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.0672 | 0.418485 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7251 | 0.407113 | 0.203557 | − | 0.979063i | \(-0.434750\pi\) | ||||
0.203557 | + | 0.979063i | \(0.434750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.4935 | 0.750856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.75230 | 0.279439 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.5147 | −0.909478 | −0.454739 | − | 0.890625i | \(-0.650267\pi\) | ||||
−0.454739 | + | 0.890625i | \(0.650267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.91986 | −0.156760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.63226 | 0.115616 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.59703 | 0.273370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.993154 | 0.0315486 | 0.0157743 | − | 0.999876i | \(-0.494979\pi\) | ||||
0.0157743 | + | 0.999876i | \(0.494979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.5749 | 0.399053 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.36119 | −0.169961 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8410 | 1.26178 | 0.630888 | − | 0.775874i | \(-0.282691\pi\) | ||||
0.630888 | + | 0.775874i | \(0.282691\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.28308 | 0.230427 |
(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 | 3864.2.a.t.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 7728.2.a.bz.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.t.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7728.2.a.bz.1.3 | 4 | 4.3 | odd | 2 |