Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.76052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76052 | −1.95198 | −0.975992 | − | 0.217808i | \(-0.930109\pi\) | ||||
−0.975992 | + | 0.217808i | \(0.930109\pi\) | |||||||
\(3\) | −0.148409 | −0.0856839 | −0.0428420 | − | 0.999082i | \(-0.513641\pi\) | ||||
−0.0428420 | + | 0.999082i | \(0.513641\pi\) | |||||||
\(4\) | 5.62048 | 2.81024 | ||||||||
\(5\) | 2.53457 | 1.13349 | 0.566747 | − | 0.823892i | \(-0.308202\pi\) | ||||
0.566747 | + | 0.823892i | \(0.308202\pi\) | |||||||
\(6\) | 0.409686 | 0.167254 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.99440 | −3.53355 | ||||||||
\(9\) | −2.97797 | −0.992658 | ||||||||
\(10\) | −6.99673 | −2.21256 | ||||||||
\(11\) | 1.58351 | 0.477447 | 0.238724 | − | 0.971088i | \(-0.423271\pi\) | ||||
0.238724 | + | 0.971088i | \(0.423271\pi\) | |||||||
\(12\) | −0.834129 | −0.240792 | ||||||||
\(13\) | −6.17112 | −1.71156 | −0.855780 | − | 0.517340i | \(-0.826922\pi\) | ||||
−0.855780 | + | 0.517340i | \(0.826922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.376152 | −0.0971221 | ||||||||
\(16\) | 16.3488 | 4.08720 | ||||||||
\(17\) | 3.03303 | 0.735617 | 0.367809 | − | 0.929902i | \(-0.380108\pi\) | ||||
0.367809 | + | 0.929902i | \(0.380108\pi\) | |||||||
\(18\) | 8.22076 | 1.93765 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 14.2455 | 3.18539 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.37132 | −0.931969 | ||||||||
\(23\) | 6.07217 | 1.26614 | 0.633068 | − | 0.774096i | \(-0.281795\pi\) | ||||
0.633068 | + | 0.774096i | \(0.281795\pi\) | |||||||
\(24\) | 1.48326 | 0.302769 | ||||||||
\(25\) | 1.42404 | 0.284807 | ||||||||
\(26\) | 17.0355 | 3.34094 | ||||||||
\(27\) | 0.887185 | 0.170739 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.46356 | 0.271776 | 0.135888 | − | 0.990724i | \(-0.456611\pi\) | ||||
0.135888 | + | 0.990724i | \(0.456611\pi\) | |||||||
\(30\) | 1.03838 | 0.189581 | ||||||||
\(31\) | 7.46482 | 1.34072 | 0.670361 | − | 0.742035i | \(-0.266139\pi\) | ||||
0.670361 | + | 0.742035i | \(0.266139\pi\) | |||||||
\(32\) | −25.1424 | −4.44459 | ||||||||
\(33\) | −0.235007 | −0.0409095 | ||||||||
\(34\) | −8.37274 | −1.43591 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.7376 | −2.78961 | ||||||||
\(37\) | −0.493725 | −0.0811678 | −0.0405839 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405839 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(38\) | −2.76052 | −0.447816 | ||||||||
\(39\) | 0.915849 | 0.146653 | ||||||||
\(40\) | −25.3315 | −4.00526 | ||||||||
\(41\) | 6.46929 | 1.01033 | 0.505166 | − | 0.863022i | \(-0.331431\pi\) | ||||
0.505166 | + | 0.863022i | \(0.331431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.636828 | 0.0971153 | 0.0485576 | − | 0.998820i | \(-0.484538\pi\) | ||||
0.0485576 | + | 0.998820i | \(0.484538\pi\) | |||||||
\(44\) | 8.90010 | 1.34174 | ||||||||
\(45\) | −7.54788 | −1.12517 | ||||||||
\(46\) | −16.7624 | −2.47148 | ||||||||
\(47\) | −3.56543 | −0.520072 | −0.260036 | − | 0.965599i | \(-0.583734\pi\) | ||||
−0.260036 | + | 0.965599i | \(0.583734\pi\) | |||||||
\(48\) | −2.42631 | −0.350207 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.93108 | −0.555939 | ||||||||
\(51\) | −0.450128 | −0.0630306 | ||||||||
\(52\) | −34.6846 | −4.80989 | ||||||||
\(53\) | 11.0835 | 1.52244 | 0.761219 | − | 0.648495i | \(-0.224601\pi\) | ||||
0.761219 | + | 0.648495i | \(0.224601\pi\) | |||||||
\(54\) | −2.44909 | −0.333279 | ||||||||
\(55\) | 4.01352 | 0.541183 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.148409 | −0.0196572 | ||||||||
\(58\) | −4.04019 | −0.530502 | ||||||||
\(59\) | 13.7225 | 1.78652 | 0.893260 | − | 0.449539i | \(-0.148412\pi\) | ||||
0.893260 | + | 0.449539i | \(0.148412\pi\) | |||||||
\(60\) | −2.11416 | −0.272936 | ||||||||
\(61\) | 3.53613 | 0.452754 | 0.226377 | − | 0.974040i | \(-0.427312\pi\) | ||||
0.226377 | + | 0.974040i | \(0.427312\pi\) | |||||||
\(62\) | −20.6068 | −2.61707 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.7086 | 4.58857 | ||||||||
\(65\) | −15.6411 | −1.94004 | ||||||||
\(66\) | 0.648743 | 0.0798547 | ||||||||
\(67\) | −4.76008 | −0.581537 | −0.290768 | − | 0.956793i | \(-0.593911\pi\) | ||||
−0.290768 | + | 0.956793i | \(0.593911\pi\) | |||||||
\(68\) | 17.0471 | 2.06726 | ||||||||
\(69\) | −0.901165 | −0.108487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.975752 | −0.115800 | −0.0579002 | − | 0.998322i | \(-0.518441\pi\) | ||||
−0.0579002 | + | 0.998322i | \(0.518441\pi\) | |||||||
\(72\) | 29.7631 | 3.50761 | ||||||||
\(73\) | −1.26338 | −0.147868 | −0.0739339 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739339 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(74\) | 1.36294 | 0.158438 | ||||||||
\(75\) | −0.211340 | −0.0244034 | ||||||||
\(76\) | 5.62048 | 0.644713 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.52822 | −0.286264 | ||||||||
\(79\) | −16.2898 | −1.83275 | −0.916373 | − | 0.400327i | \(-0.868897\pi\) | ||||
−0.916373 | + | 0.400327i | \(0.868897\pi\) | |||||||
\(80\) | 41.4372 | 4.63282 | ||||||||
\(81\) | 8.80226 | 0.978029 | ||||||||
\(82\) | −17.8586 | −1.97215 | ||||||||
\(83\) | 0.284058 | 0.0311794 | 0.0155897 | − | 0.999878i | \(-0.495037\pi\) | ||||
0.0155897 | + | 0.999878i | \(0.495037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.68741 | 0.833817 | ||||||||
\(86\) | −1.75798 | −0.189567 | ||||||||
\(87\) | −0.217205 | −0.0232868 | ||||||||
\(88\) | −15.8263 | −1.68709 | ||||||||
\(89\) | 6.16563 | 0.653556 | 0.326778 | − | 0.945101i | \(-0.394037\pi\) | ||||
0.326778 | + | 0.945101i | \(0.394037\pi\) | |||||||
\(90\) | 20.8361 | 2.19632 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 34.1285 | 3.55814 | ||||||||
\(93\) | −1.10785 | −0.114878 | ||||||||
\(94\) | 9.84245 | 1.01517 | ||||||||
\(95\) | 2.53457 | 0.260041 | ||||||||
\(96\) | 3.73136 | 0.380830 | ||||||||
\(97\) | 13.9410 | 1.41549 | 0.707747 | − | 0.706466i | \(-0.249712\pi\) | ||||
0.707747 | + | 0.706466i | \(0.249712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.71566 | −0.473942 | ||||||||
\(100\) | 8.00376 | 0.800376 | ||||||||
\(101\) | 16.2153 | 1.61348 | 0.806740 | − | 0.590907i | \(-0.201230\pi\) | ||||
0.806740 | + | 0.590907i | \(0.201230\pi\) | |||||||
\(102\) | 1.24259 | 0.123035 | ||||||||
\(103\) | 7.62785 | 0.751595 | 0.375797 | − | 0.926702i | \(-0.377369\pi\) | ||||
0.375797 | + | 0.926702i | \(0.377369\pi\) | |||||||
\(104\) | 61.6766 | 6.04789 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30.5963 | −2.97177 | ||||||||
\(107\) | 2.72492 | 0.263428 | 0.131714 | − | 0.991288i | \(-0.457952\pi\) | ||||
0.131714 | + | 0.991288i | \(0.457952\pi\) | |||||||
\(108\) | 4.98640 | 0.479817 | ||||||||
\(109\) | 2.84550 | 0.272549 | 0.136275 | − | 0.990671i | \(-0.456487\pi\) | ||||
0.136275 | + | 0.990671i | \(0.456487\pi\) | |||||||
\(110\) | −11.0794 | −1.05638 | ||||||||
\(111\) | 0.0732731 | 0.00695478 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.07066 | −0.571080 | −0.285540 | − | 0.958367i | \(-0.592173\pi\) | ||||
−0.285540 | + | 0.958367i | \(0.592173\pi\) | |||||||
\(114\) | 0.409686 | 0.0383706 | ||||||||
\(115\) | 15.3903 | 1.43516 | ||||||||
\(116\) | 8.22590 | 0.763756 | ||||||||
\(117\) | 18.3774 | 1.69899 | ||||||||
\(118\) | −37.8813 | −3.48726 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.75942 | 0.343186 | ||||||||
\(121\) | −8.49249 | −0.772044 | ||||||||
\(122\) | −9.76155 | −0.883769 | ||||||||
\(123\) | −0.960100 | −0.0865693 | ||||||||
\(124\) | 41.9559 | 3.76775 | ||||||||
\(125\) | −9.06353 | −0.810666 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4368 | −1.01485 | −0.507426 | − | 0.861695i | \(-0.669403\pi\) | ||||
−0.507426 | + | 0.861695i | \(0.669403\pi\) | |||||||
\(128\) | −51.0499 | −4.51222 | ||||||||
\(129\) | −0.0945109 | −0.00832122 | ||||||||
\(130\) | 43.1776 | 3.78693 | ||||||||
\(131\) | −11.9389 | −1.04311 | −0.521554 | − | 0.853218i | \(-0.674647\pi\) | ||||
−0.521554 | + | 0.853218i | \(0.674647\pi\) | |||||||
\(132\) | −1.32085 | −0.114966 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.1403 | 1.13515 | ||||||||
\(135\) | 2.24863 | 0.193531 | ||||||||
\(136\) | −30.3133 | −2.59934 | ||||||||
\(137\) | −9.26003 | −0.791138 | −0.395569 | − | 0.918436i | \(-0.629453\pi\) | ||||
−0.395569 | + | 0.918436i | \(0.629453\pi\) | |||||||
\(138\) | 2.48768 | 0.211766 | ||||||||
\(139\) | 6.14306 | 0.521048 | 0.260524 | − | 0.965467i | \(-0.416105\pi\) | ||||
0.260524 | + | 0.965467i | \(0.416105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.529142 | 0.0445618 | ||||||||
\(142\) | 2.69358 | 0.226040 | ||||||||
\(143\) | −9.77204 | −0.817179 | ||||||||
\(144\) | −48.6863 | −4.05719 | ||||||||
\(145\) | 3.70949 | 0.308056 | ||||||||
\(146\) | 3.48759 | 0.288635 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.77497 | −0.228101 | ||||||||
\(149\) | 12.0740 | 0.989141 | 0.494571 | − | 0.869138i | \(-0.335325\pi\) | ||||
0.494571 | + | 0.869138i | \(0.335325\pi\) | |||||||
\(150\) | 0.583407 | 0.0476350 | ||||||||
\(151\) | 6.45109 | 0.524983 | 0.262491 | − | 0.964934i | \(-0.415456\pi\) | ||||
0.262491 | + | 0.964934i | \(0.415456\pi\) | |||||||
\(152\) | −9.99440 | −0.810653 | ||||||||
\(153\) | −9.03228 | −0.730217 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9201 | 1.51970 | ||||||||
\(156\) | 5.14751 | 0.412130 | ||||||||
\(157\) | 4.02184 | 0.320977 | 0.160489 | − | 0.987038i | \(-0.448693\pi\) | ||||
0.160489 | + | 0.987038i | \(0.448693\pi\) | |||||||
\(158\) | 44.9683 | 3.57749 | ||||||||
\(159\) | −1.64489 | −0.130448 | ||||||||
\(160\) | −63.7252 | −5.03792 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −24.2988 | −1.90910 | ||||||||
\(163\) | −11.9800 | −0.938346 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(164\) | 36.3605 | 2.83928 | ||||||||
\(165\) | −0.595642 | −0.0463707 | ||||||||
\(166\) | −0.784147 | −0.0608616 | ||||||||
\(167\) | 15.1250 | 1.17041 | 0.585204 | − | 0.810886i | \(-0.301015\pi\) | ||||
0.585204 | + | 0.810886i | \(0.301015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.0827 | 1.92944 | ||||||||
\(170\) | −21.2213 | −1.62760 | ||||||||
\(171\) | −2.97797 | −0.227731 | ||||||||
\(172\) | 3.57927 | 0.272917 | ||||||||
\(173\) | 14.8273 | 1.12730 | 0.563649 | − | 0.826014i | \(-0.309397\pi\) | ||||
0.563649 | + | 0.826014i | \(0.309397\pi\) | |||||||
\(174\) | 0.599600 | 0.0454555 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.8885 | 1.95142 | ||||||||
\(177\) | −2.03655 | −0.153076 | ||||||||
\(178\) | −17.0204 | −1.27573 | ||||||||
\(179\) | −16.2947 | −1.21792 | −0.608961 | − | 0.793200i | \(-0.708414\pi\) | ||||
−0.608961 | + | 0.793200i | \(0.708414\pi\) | |||||||
\(180\) | −42.4227 | −3.16200 | ||||||||
\(181\) | 1.03994 | 0.0772982 | 0.0386491 | − | 0.999253i | \(-0.487695\pi\) | ||||
0.0386491 | + | 0.999253i | \(0.487695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.524792 | −0.0387938 | ||||||||
\(184\) | −60.6878 | −4.47396 | ||||||||
\(185\) | −1.25138 | −0.0920032 | ||||||||
\(186\) | 3.05823 | 0.224240 | ||||||||
\(187\) | 4.80284 | 0.351218 | ||||||||
\(188\) | −20.0394 | −1.46153 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.99673 | −0.507596 | ||||||||
\(191\) | 3.77831 | 0.273389 | 0.136694 | − | 0.990613i | \(-0.456352\pi\) | ||||
0.136694 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(192\) | −5.44788 | −0.393167 | ||||||||
\(193\) | 10.4678 | 0.753491 | 0.376746 | − | 0.926317i | \(-0.377043\pi\) | ||||
0.376746 | + | 0.926317i | \(0.377043\pi\) | |||||||
\(194\) | −38.4844 | −2.76302 | ||||||||
\(195\) | 2.32128 | 0.166230 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4885 | −0.961014 | −0.480507 | − | 0.876991i | \(-0.659547\pi\) | ||||
−0.480507 | + | 0.876991i | \(0.659547\pi\) | |||||||
\(198\) | 13.0177 | 0.925126 | ||||||||
\(199\) | −17.9294 | −1.27098 | −0.635491 | − | 0.772109i | \(-0.719202\pi\) | ||||
−0.635491 | + | 0.772109i | \(0.719202\pi\) | |||||||
\(200\) | −14.2324 | −1.00638 | ||||||||
\(201\) | 0.706439 | 0.0498284 | ||||||||
\(202\) | −44.7626 | −3.14949 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.52994 | −0.177131 | ||||||||
\(205\) | 16.3968 | 1.14521 | ||||||||
\(206\) | −21.0568 | −1.46710 | ||||||||
\(207\) | −18.0828 | −1.25684 | ||||||||
\(208\) | −100.890 | −6.99549 | ||||||||
\(209\) | 1.58351 | 0.109534 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.90422 | 0.544149 | 0.272074 | − | 0.962276i | \(-0.412290\pi\) | ||||
0.272074 | + | 0.962276i | \(0.412290\pi\) | |||||||
\(212\) | 62.2946 | 4.27841 | ||||||||
\(213\) | 0.144810 | 0.00992223 | ||||||||
\(214\) | −7.52221 | −0.514208 | ||||||||
\(215\) | 1.61408 | 0.110080 | ||||||||
\(216\) | −8.86688 | −0.603315 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.85506 | −0.532012 | ||||||||
\(219\) | 0.187497 | 0.0126699 | ||||||||
\(220\) | 22.5579 | 1.52085 | ||||||||
\(221\) | −18.7172 | −1.25905 | ||||||||
\(222\) | −0.202272 | −0.0135756 | ||||||||
\(223\) | 4.22024 | 0.282608 | 0.141304 | − | 0.989966i | \(-0.454870\pi\) | ||||
0.141304 | + | 0.989966i | \(0.454870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.24074 | −0.282716 | ||||||||
\(226\) | 16.7582 | 1.11474 | ||||||||
\(227\) | −16.1145 | −1.06956 | −0.534778 | − | 0.844993i | \(-0.679605\pi\) | ||||
−0.534778 | + | 0.844993i | \(0.679605\pi\) | |||||||
\(228\) | −0.834129 | −0.0552415 | ||||||||
\(229\) | 13.2448 | 0.875240 | 0.437620 | − | 0.899160i | \(-0.355821\pi\) | ||||
0.437620 | + | 0.899160i | \(0.355821\pi\) | |||||||
\(230\) | −42.4854 | −2.80140 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.6274 | −0.960336 | ||||||||
\(233\) | 16.9074 | 1.10764 | 0.553821 | − | 0.832636i | \(-0.313169\pi\) | ||||
0.553821 | + | 0.832636i | \(0.313169\pi\) | |||||||
\(234\) | −50.7313 | −3.31641 | ||||||||
\(235\) | −9.03683 | −0.589498 | ||||||||
\(236\) | 77.1272 | 5.02055 | ||||||||
\(237\) | 2.41755 | 0.157037 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.77655 | −0.438338 | −0.219169 | − | 0.975687i | \(-0.570335\pi\) | ||||
−0.219169 | + | 0.975687i | \(0.570335\pi\) | |||||||
\(240\) | −6.14964 | −0.396958 | ||||||||
\(241\) | 22.6252 | 1.45742 | 0.728708 | − | 0.684824i | \(-0.240121\pi\) | ||||
0.728708 | + | 0.684824i | \(0.240121\pi\) | |||||||
\(242\) | 23.4437 | 1.50702 | ||||||||
\(243\) | −3.96789 | −0.254540 | ||||||||
\(244\) | 19.8747 | 1.27235 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.65038 | 0.168982 | ||||||||
\(247\) | −6.17112 | −0.392659 | ||||||||
\(248\) | −74.6064 | −4.73751 | ||||||||
\(249\) | −0.0421567 | −0.00267157 | ||||||||
\(250\) | 25.0201 | 1.58241 | ||||||||
\(251\) | 11.3603 | 0.717053 | 0.358527 | − | 0.933520i | \(-0.383279\pi\) | ||||
0.358527 | + | 0.933520i | \(0.383279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.61537 | 0.604513 | ||||||||
\(254\) | 31.5715 | 1.98097 | ||||||||
\(255\) | −1.14088 | −0.0714447 | ||||||||
\(256\) | 67.5073 | 4.21921 | ||||||||
\(257\) | −17.5409 | −1.09417 | −0.547085 | − | 0.837077i | \(-0.684263\pi\) | ||||
−0.547085 | + | 0.837077i | \(0.684263\pi\) | |||||||
\(258\) | 0.260899 | 0.0162429 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −87.9105 | −5.45198 | ||||||||
\(261\) | −4.35844 | −0.269781 | ||||||||
\(262\) | 32.9576 | 2.03613 | ||||||||
\(263\) | −15.3999 | −0.949596 | −0.474798 | − | 0.880095i | \(-0.657479\pi\) | ||||
−0.474798 | + | 0.880095i | \(0.657479\pi\) | |||||||
\(264\) | 2.34876 | 0.144556 | ||||||||
\(265\) | 28.0919 | 1.72567 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.915035 | −0.0559992 | ||||||||
\(268\) | −26.7539 | −1.63426 | ||||||||
\(269\) | 7.92775 | 0.483363 | 0.241682 | − | 0.970356i | \(-0.422301\pi\) | ||||
0.241682 | + | 0.970356i | \(0.422301\pi\) | |||||||
\(270\) | −6.20739 | −0.377770 | ||||||||
\(271\) | −8.75327 | −0.531723 | −0.265862 | − | 0.964011i | \(-0.585656\pi\) | ||||
−0.265862 | + | 0.964011i | \(0.585656\pi\) | |||||||
\(272\) | 49.5864 | 3.00662 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.5625 | 1.54429 | ||||||||
\(275\) | 2.25498 | 0.135980 | ||||||||
\(276\) | −5.06498 | −0.304876 | ||||||||
\(277\) | 18.4795 | 1.11032 | 0.555162 | − | 0.831742i | \(-0.312656\pi\) | ||||
0.555162 | + | 0.831742i | \(0.312656\pi\) | |||||||
\(278\) | −16.9581 | −1.01708 | ||||||||
\(279\) | −22.2300 | −1.33088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.48167 | −0.207699 | −0.103850 | − | 0.994593i | \(-0.533116\pi\) | ||||
−0.103850 | + | 0.994593i | \(0.533116\pi\) | |||||||
\(282\) | −1.46071 | −0.0869839 | ||||||||
\(283\) | −11.3181 | −0.672791 | −0.336395 | − | 0.941721i | \(-0.609208\pi\) | ||||
−0.336395 | + | 0.941721i | \(0.609208\pi\) | |||||||
\(284\) | −5.48419 | −0.325427 | ||||||||
\(285\) | −0.376152 | −0.0222813 | ||||||||
\(286\) | 26.9759 | 1.59512 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 74.8735 | 4.41196 | ||||||||
\(289\) | −7.80074 | −0.458867 | ||||||||
\(290\) | −10.2401 | −0.601321 | ||||||||
\(291\) | −2.06897 | −0.121285 | ||||||||
\(292\) | −7.10081 | −0.415544 | ||||||||
\(293\) | −15.0868 | −0.881381 | −0.440691 | − | 0.897659i | \(-0.645266\pi\) | ||||
−0.440691 | + | 0.897659i | \(0.645266\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.7807 | 2.02501 | ||||||||
\(296\) | 4.93448 | 0.286811 | ||||||||
\(297\) | 1.40487 | 0.0815187 | ||||||||
\(298\) | −33.3305 | −1.93079 | ||||||||
\(299\) | −37.4721 | −2.16707 | ||||||||
\(300\) | −1.18783 | −0.0685793 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.8084 | −1.02476 | ||||||||
\(303\) | −2.40649 | −0.138249 | ||||||||
\(304\) | 16.3488 | 0.937668 | ||||||||
\(305\) | 8.96255 | 0.513194 | ||||||||
\(306\) | 24.9338 | 1.42537 | ||||||||
\(307\) | −6.07516 | −0.346728 | −0.173364 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173364 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.13204 | −0.0643996 | ||||||||
\(310\) | −52.2293 | −2.96643 | ||||||||
\(311\) | 18.5023 | 1.04917 | 0.524586 | − | 0.851358i | \(-0.324220\pi\) | ||||
0.524586 | + | 0.851358i | \(0.324220\pi\) | |||||||
\(312\) | −9.15336 | −0.518207 | ||||||||
\(313\) | −11.8582 | −0.670263 | −0.335131 | − | 0.942171i | \(-0.608781\pi\) | ||||
−0.335131 | + | 0.942171i | \(0.608781\pi\) | |||||||
\(314\) | −11.1024 | −0.626543 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −91.5564 | −5.15045 | ||||||||
\(317\) | −2.28430 | −0.128299 | −0.0641495 | − | 0.997940i | \(-0.520433\pi\) | ||||
−0.0641495 | + | 0.997940i | \(0.520433\pi\) | |||||||
\(318\) | 4.54076 | 0.254633 | ||||||||
\(319\) | 2.31756 | 0.129759 | ||||||||
\(320\) | 93.0404 | 5.20111 | ||||||||
\(321\) | −0.404403 | −0.0225716 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.03303 | 0.168762 | ||||||||
\(324\) | 49.4729 | 2.74849 | ||||||||
\(325\) | −8.78789 | −0.487464 | ||||||||
\(326\) | 33.0710 | 1.83163 | ||||||||
\(327\) | −0.422297 | −0.0233531 | ||||||||
\(328\) | −64.6567 | −3.57007 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.64428 | 0.0905148 | ||||||||
\(331\) | 21.2867 | 1.17002 | 0.585011 | − | 0.811026i | \(-0.301090\pi\) | ||||
0.585011 | + | 0.811026i | \(0.301090\pi\) | |||||||
\(332\) | 1.59654 | 0.0876215 | ||||||||
\(333\) | 1.47030 | 0.0805719 | ||||||||
\(334\) | −41.7529 | −2.28462 | ||||||||
\(335\) | −12.0648 | −0.659168 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1088 | 0.931978 | 0.465989 | − | 0.884791i | \(-0.345699\pi\) | ||||
0.465989 | + | 0.884791i | \(0.345699\pi\) | |||||||
\(338\) | −69.2413 | −3.76623 | ||||||||
\(339\) | 0.900941 | 0.0489324 | ||||||||
\(340\) | 43.2069 | 2.34323 | ||||||||
\(341\) | 11.8206 | 0.640124 | ||||||||
\(342\) | 8.22076 | 0.444528 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.36471 | −0.343162 | ||||||||
\(345\) | −2.28406 | −0.122970 | ||||||||
\(346\) | −40.9311 | −2.20047 | ||||||||
\(347\) | 10.7992 | 0.579729 | 0.289865 | − | 0.957068i | \(-0.406390\pi\) | ||||
0.289865 | + | 0.957068i | \(0.406390\pi\) | |||||||
\(348\) | −1.22080 | −0.0654416 | ||||||||
\(349\) | −20.7117 | −1.10867 | −0.554336 | − | 0.832293i | \(-0.687028\pi\) | ||||
−0.554336 | + | 0.832293i | \(0.687028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.47492 | −0.292230 | ||||||||
\(352\) | −39.8133 | −2.12206 | ||||||||
\(353\) | 16.9047 | 0.899749 | 0.449874 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449874 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(354\) | 5.62193 | 0.298802 | ||||||||
\(355\) | −2.47311 | −0.131259 | ||||||||
\(356\) | 34.6538 | 1.83665 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 44.9819 | 2.37736 | ||||||||
\(359\) | 15.5071 | 0.818433 | 0.409217 | − | 0.912437i | \(-0.365802\pi\) | ||||
0.409217 | + | 0.912437i | \(0.365802\pi\) | |||||||
\(360\) | 75.4366 | 3.97586 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −2.87078 | −0.150885 | ||||||||
\(363\) | 1.26036 | 0.0661518 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.20213 | −0.167607 | ||||||||
\(366\) | 1.44870 | 0.0757248 | ||||||||
\(367\) | 2.71781 | 0.141869 | 0.0709343 | − | 0.997481i | \(-0.477402\pi\) | ||||
0.0709343 | + | 0.997481i | \(0.477402\pi\) | |||||||
\(368\) | 99.2728 | 5.17495 | ||||||||
\(369\) | −19.2654 | −1.00292 | ||||||||
\(370\) | 3.45446 | 0.179589 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.22662 | −0.322835 | ||||||||
\(373\) | −16.3916 | −0.848727 | −0.424364 | − | 0.905492i | \(-0.639502\pi\) | ||||
−0.424364 | + | 0.905492i | \(0.639502\pi\) | |||||||
\(374\) | −13.2583 | −0.685572 | ||||||||
\(375\) | 1.34511 | 0.0694611 | ||||||||
\(376\) | 35.6344 | 1.83770 | ||||||||
\(377\) | −9.03179 | −0.465161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4759 | −1.35998 | −0.679988 | − | 0.733223i | \(-0.738015\pi\) | ||||
−0.679988 | + | 0.733223i | \(0.738015\pi\) | |||||||
\(380\) | 14.2455 | 0.730778 | ||||||||
\(381\) | 1.69732 | 0.0869565 | ||||||||
\(382\) | −10.4301 | −0.533650 | ||||||||
\(383\) | −8.97673 | −0.458689 | −0.229345 | − | 0.973345i | \(-0.573658\pi\) | ||||
−0.229345 | + | 0.973345i | \(0.573658\pi\) | |||||||
\(384\) | 7.57627 | 0.386625 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.8967 | −1.47080 | ||||||||
\(387\) | −1.89646 | −0.0964023 | ||||||||
\(388\) | 78.3551 | 3.97788 | ||||||||
\(389\) | −22.0155 | −1.11623 | −0.558115 | − | 0.829763i | \(-0.688475\pi\) | ||||
−0.558115 | + | 0.829763i | \(0.688475\pi\) | |||||||
\(390\) | −6.40794 | −0.324479 | ||||||||
\(391\) | 18.4171 | 0.931391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.77184 | 0.0893775 | ||||||||
\(394\) | 37.2352 | 1.87588 | ||||||||
\(395\) | −41.2876 | −2.07740 | ||||||||
\(396\) | −26.5043 | −1.33189 | ||||||||
\(397\) | −3.35484 | −0.168374 | −0.0841872 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841872 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(398\) | 49.4945 | 2.48093 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.2813 | 1.16406 | ||||||||
\(401\) | −20.1098 | −1.00423 | −0.502117 | − | 0.864800i | \(-0.667445\pi\) | ||||
−0.502117 | + | 0.864800i | \(0.667445\pi\) | |||||||
\(402\) | −1.95014 | −0.0972641 | ||||||||
\(403\) | −46.0663 | −2.29472 | ||||||||
\(404\) | 91.1376 | 4.53426 | ||||||||
\(405\) | 22.3099 | 1.10859 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.781819 | −0.0387533 | ||||||||
\(408\) | 4.49876 | 0.222722 | ||||||||
\(409\) | −2.44826 | −0.121059 | −0.0605294 | − | 0.998166i | \(-0.519279\pi\) | ||||
−0.0605294 | + | 0.998166i | \(0.519279\pi\) | |||||||
\(410\) | −45.2638 | −2.23542 | ||||||||
\(411\) | 1.37427 | 0.0677878 | ||||||||
\(412\) | 42.8722 | 2.11216 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 49.9179 | 2.45333 | ||||||||
\(415\) | 0.719963 | 0.0353416 | ||||||||
\(416\) | 155.157 | 7.60719 | ||||||||
\(417\) | −0.911685 | −0.0446454 | ||||||||
\(418\) | −4.37132 | −0.213808 | ||||||||
\(419\) | −36.0307 | −1.76022 | −0.880108 | − | 0.474774i | \(-0.842530\pi\) | ||||
−0.880108 | + | 0.474774i | \(0.842530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2289 | −1.03463 | −0.517316 | − | 0.855795i | \(-0.673069\pi\) | ||||
−0.517316 | + | 0.855795i | \(0.673069\pi\) | |||||||
\(422\) | −21.8198 | −1.06217 | ||||||||
\(423\) | 10.6178 | 0.516254 | ||||||||
\(424\) | −110.773 | −5.37962 | ||||||||
\(425\) | 4.31914 | 0.209509 | ||||||||
\(426\) | −0.399752 | −0.0193680 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.3154 | 0.740297 | ||||||||
\(429\) | 1.45026 | 0.0700191 | ||||||||
\(430\) | −4.45571 | −0.214873 | ||||||||
\(431\) | −11.3811 | −0.548208 | −0.274104 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274104 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(432\) | 14.5044 | 0.697844 | ||||||||
\(433\) | 23.1101 | 1.11060 | 0.555300 | − | 0.831650i | \(-0.312604\pi\) | ||||
0.555300 | + | 0.831650i | \(0.312604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.550521 | −0.0263955 | ||||||||
\(436\) | 15.9931 | 0.765929 | ||||||||
\(437\) | 6.07217 | 0.290471 | ||||||||
\(438\) | −0.517590 | −0.0247314 | ||||||||
\(439\) | −27.9702 | −1.33494 | −0.667472 | − | 0.744635i | \(-0.732624\pi\) | ||||
−0.667472 | + | 0.744635i | \(0.732624\pi\) | |||||||
\(440\) | −40.1127 | −1.91230 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 51.6691 | 2.45765 | ||||||||
\(443\) | 28.6352 | 1.36050 | 0.680249 | − | 0.732981i | \(-0.261872\pi\) | ||||
0.680249 | + | 0.732981i | \(0.261872\pi\) | |||||||
\(444\) | 0.411830 | 0.0195446 | ||||||||
\(445\) | 15.6272 | 0.740801 | ||||||||
\(446\) | −11.6501 | −0.551646 | ||||||||
\(447\) | −1.79189 | −0.0847535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.51721 | 0.0716016 | 0.0358008 | − | 0.999359i | \(-0.488602\pi\) | ||||
0.0358008 | + | 0.999359i | \(0.488602\pi\) | |||||||
\(450\) | 11.7067 | 0.551857 | ||||||||
\(451\) | 10.2442 | 0.482380 | ||||||||
\(452\) | −34.1200 | −1.60487 | ||||||||
\(453\) | −0.957400 | −0.0449826 | ||||||||
\(454\) | 44.4844 | 2.08776 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.48326 | 0.0694599 | ||||||||
\(457\) | 8.02405 | 0.375349 | 0.187675 | − | 0.982231i | \(-0.439905\pi\) | ||||
0.187675 | + | 0.982231i | \(0.439905\pi\) | |||||||
\(458\) | −36.5625 | −1.70845 | ||||||||
\(459\) | 2.69086 | 0.125598 | ||||||||
\(460\) | 86.5010 | 4.03313 | ||||||||
\(461\) | 19.3393 | 0.900719 | 0.450360 | − | 0.892847i | \(-0.351296\pi\) | ||||
0.450360 | + | 0.892847i | \(0.351296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2738 | 1.49989 | 0.749946 | − | 0.661499i | \(-0.230080\pi\) | ||||
0.749946 | + | 0.661499i | \(0.230080\pi\) | |||||||
\(464\) | 23.9274 | 1.11080 | ||||||||
\(465\) | −2.80791 | −0.130214 | ||||||||
\(466\) | −46.6733 | −2.16210 | ||||||||
\(467\) | 32.1680 | 1.48856 | 0.744278 | − | 0.667870i | \(-0.232794\pi\) | ||||
0.744278 | + | 0.667870i | \(0.232794\pi\) | |||||||
\(468\) | 103.290 | 4.77458 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.9464 | 1.15069 | ||||||||
\(471\) | −0.596876 | −0.0275026 | ||||||||
\(472\) | −137.148 | −6.31277 | ||||||||
\(473\) | 1.00842 | 0.0463674 | ||||||||
\(474\) | −6.67370 | −0.306533 | ||||||||
\(475\) | 1.42404 | 0.0653392 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −33.0064 | −1.51126 | ||||||||
\(478\) | 18.7068 | 0.855629 | ||||||||
\(479\) | −7.81799 | −0.357213 | −0.178606 | − | 0.983921i | \(-0.557159\pi\) | ||||
−0.178606 | + | 0.983921i | \(0.557159\pi\) | |||||||
\(480\) | 9.45738 | 0.431669 | ||||||||
\(481\) | 3.04683 | 0.138924 | ||||||||
\(482\) | −62.4573 | −2.84485 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −47.7318 | −2.16963 | ||||||||
\(485\) | 35.3344 | 1.60445 | ||||||||
\(486\) | 10.9534 | 0.496858 | ||||||||
\(487\) | −29.7980 | −1.35027 | −0.675137 | − | 0.737692i | \(-0.735916\pi\) | ||||
−0.675137 | + | 0.737692i | \(0.735916\pi\) | |||||||
\(488\) | −35.3415 | −1.59983 | ||||||||
\(489\) | 1.77794 | 0.0804011 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8290 | 0.894872 | 0.447436 | − | 0.894316i | \(-0.352337\pi\) | ||||
0.447436 | + | 0.894316i | \(0.352337\pi\) | |||||||
\(492\) | −5.39622 | −0.243280 | ||||||||
\(493\) | 4.43901 | 0.199923 | ||||||||
\(494\) | 17.0355 | 0.766463 | ||||||||
\(495\) | −11.9522 | −0.537210 | ||||||||
\(496\) | 122.041 | 5.47980 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.116374 | 0.00521486 | ||||||||
\(499\) | −30.6722 | −1.37308 | −0.686539 | − | 0.727093i | \(-0.740871\pi\) | ||||
−0.686539 | + | 0.727093i | \(0.740871\pi\) | |||||||
\(500\) | −50.9413 | −2.27817 | ||||||||
\(501\) | −2.24468 | −0.100285 | ||||||||
\(502\) | −31.3602 | −1.39968 | ||||||||
\(503\) | −36.5009 | −1.62750 | −0.813748 | − | 0.581218i | \(-0.802576\pi\) | ||||
−0.813748 | + | 0.581218i | \(0.802576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.0987 | 1.82887 | ||||||||
\(506\) | −26.5434 | −1.18000 | ||||||||
\(507\) | −3.72249 | −0.165322 | ||||||||
\(508\) | −64.2802 | −2.85197 | ||||||||
\(509\) | 4.95937 | 0.219820 | 0.109910 | − | 0.993942i | \(-0.464944\pi\) | ||||
0.109910 | + | 0.993942i | \(0.464944\pi\) | |||||||
\(510\) | 3.14943 | 0.139459 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −84.2554 | −3.72360 | ||||||||
\(513\) | 0.887185 | 0.0391702 | ||||||||
\(514\) | 48.4220 | 2.13580 | ||||||||
\(515\) | 19.3333 | 0.851928 | ||||||||
\(516\) | −0.531196 | −0.0233846 | ||||||||
\(517\) | −5.64591 | −0.248307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.20050 | −0.0965914 | ||||||||
\(520\) | 156.324 | 6.85524 | ||||||||
\(521\) | −33.8799 | −1.48431 | −0.742153 | − | 0.670231i | \(-0.766195\pi\) | ||||
−0.742153 | + | 0.670231i | \(0.766195\pi\) | |||||||
\(522\) | 12.0316 | 0.526608 | ||||||||
\(523\) | −25.7088 | −1.12417 | −0.562083 | − | 0.827081i | \(-0.690000\pi\) | ||||
−0.562083 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(524\) | −67.1024 | −2.93138 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.5116 | 1.85360 | ||||||||
\(527\) | 22.6410 | 0.986258 | ||||||||
\(528\) | −3.84209 | −0.167206 | ||||||||
\(529\) | 13.8713 | 0.603100 | ||||||||
\(530\) | −77.5483 | −3.36848 | ||||||||
\(531\) | −40.8653 | −1.77340 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.9227 | −1.72924 | ||||||||
\(534\) | 2.52597 | 0.109310 | ||||||||
\(535\) | 6.90651 | 0.298594 | ||||||||
\(536\) | 47.5742 | 2.05489 | ||||||||
\(537\) | 2.41828 | 0.104356 | ||||||||
\(538\) | −21.8847 | −0.943517 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.6384 | 0.543869 | ||||||||
\(541\) | 21.7172 | 0.933697 | 0.466849 | − | 0.884337i | \(-0.345389\pi\) | ||||
0.466849 | + | 0.884337i | \(0.345389\pi\) | |||||||
\(542\) | 24.1636 | 1.03791 | ||||||||
\(543\) | −0.154336 | −0.00662321 | ||||||||
\(544\) | −76.2576 | −3.26952 | ||||||||
\(545\) | 7.21211 | 0.308933 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1501 | 1.11810 | 0.559049 | − | 0.829135i | \(-0.311166\pi\) | ||||
0.559049 | + | 0.829135i | \(0.311166\pi\) | |||||||
\(548\) | −52.0458 | −2.22329 | ||||||||
\(549\) | −10.5305 | −0.449430 | ||||||||
\(550\) | −6.22492 | −0.265431 | ||||||||
\(551\) | 1.46356 | 0.0623497 | ||||||||
\(552\) | 9.00660 | 0.383346 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −51.0130 | −2.16733 | ||||||||
\(555\) | 0.185716 | 0.00788319 | ||||||||
\(556\) | 34.5269 | 1.46427 | ||||||||
\(557\) | −17.5350 | −0.742983 | −0.371492 | − | 0.928436i | \(-0.621154\pi\) | ||||
−0.371492 | + | 0.928436i | \(0.621154\pi\) | |||||||
\(558\) | 61.3665 | 2.59785 | ||||||||
\(559\) | −3.92994 | −0.166219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.712784 | −0.0300938 | ||||||||
\(562\) | 9.61123 | 0.405425 | ||||||||
\(563\) | −23.0311 | −0.970644 | −0.485322 | − | 0.874335i | \(-0.661298\pi\) | ||||
−0.485322 | + | 0.874335i | \(0.661298\pi\) | |||||||
\(564\) | 2.97403 | 0.125229 | ||||||||
\(565\) | −15.3865 | −0.647315 | ||||||||
\(566\) | 31.2438 | 1.31328 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.75205 | 0.409187 | ||||||||
\(569\) | −41.3636 | −1.73405 | −0.867027 | − | 0.498261i | \(-0.833972\pi\) | ||||
−0.867027 | + | 0.498261i | \(0.833972\pi\) | |||||||
\(570\) | 1.03838 | 0.0434928 | ||||||||
\(571\) | −28.2907 | −1.18393 | −0.591964 | − | 0.805965i | \(-0.701647\pi\) | ||||
−0.591964 | + | 0.805965i | \(0.701647\pi\) | |||||||
\(572\) | −54.9235 | −2.29647 | ||||||||
\(573\) | −0.560734 | −0.0234250 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.64699 | 0.360604 | ||||||||
\(576\) | −109.317 | −4.55488 | ||||||||
\(577\) | 29.7398 | 1.23808 | 0.619041 | − | 0.785359i | \(-0.287521\pi\) | ||||
0.619041 | + | 0.785359i | \(0.287521\pi\) | |||||||
\(578\) | 21.5341 | 0.895701 | ||||||||
\(579\) | −1.55352 | −0.0645621 | ||||||||
\(580\) | 20.8491 | 0.865712 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.71143 | 0.236746 | ||||||||
\(583\) | 17.5509 | 0.726883 | ||||||||
\(584\) | 12.6268 | 0.522499 | ||||||||
\(585\) | 46.5788 | 1.92580 | ||||||||
\(586\) | 41.6475 | 1.72044 | ||||||||
\(587\) | 7.21249 | 0.297691 | 0.148846 | − | 0.988860i | \(-0.452444\pi\) | ||||
0.148846 | + | 0.988860i | \(0.452444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.46482 | 0.307583 | ||||||||
\(590\) | −96.0128 | −3.95278 | ||||||||
\(591\) | 2.00181 | 0.0823435 | ||||||||
\(592\) | −8.07181 | −0.331749 | ||||||||
\(593\) | 5.16126 | 0.211948 | 0.105974 | − | 0.994369i | \(-0.466204\pi\) | ||||
0.105974 | + | 0.994369i | \(0.466204\pi\) | |||||||
\(594\) | −3.87817 | −0.159123 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 67.8617 | 2.77972 | ||||||||
\(597\) | 2.66088 | 0.108903 | ||||||||
\(598\) | 103.442 | 4.23008 | ||||||||
\(599\) | 32.8017 | 1.34024 | 0.670121 | − | 0.742252i | \(-0.266242\pi\) | ||||
0.670121 | + | 0.742252i | \(0.266242\pi\) | |||||||
\(600\) | 2.11221 | 0.0862307 | ||||||||
\(601\) | −24.6906 | −1.00715 | −0.503576 | − | 0.863951i | \(-0.667983\pi\) | ||||
−0.503576 | + | 0.863951i | \(0.667983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.1754 | 0.577267 | ||||||||
\(604\) | 36.2582 | 1.47533 | ||||||||
\(605\) | −21.5248 | −0.875107 | ||||||||
\(606\) | 6.64317 | 0.269860 | ||||||||
\(607\) | −17.4222 | −0.707146 | −0.353573 | − | 0.935407i | \(-0.615033\pi\) | ||||
−0.353573 | + | 0.935407i | \(0.615033\pi\) | |||||||
\(608\) | −25.1424 | −1.01966 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.7413 | −1.00175 | ||||||||
\(611\) | 22.0027 | 0.890134 | ||||||||
\(612\) | −50.7657 | −2.05208 | ||||||||
\(613\) | −28.0331 | −1.13225 | −0.566123 | − | 0.824321i | \(-0.691557\pi\) | ||||
−0.566123 | + | 0.824321i | \(0.691557\pi\) | |||||||
\(614\) | 16.7706 | 0.676806 | ||||||||
\(615\) | −2.43344 | −0.0981257 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.79442 | −0.313791 | −0.156896 | − | 0.987615i | \(-0.550149\pi\) | ||||
−0.156896 | + | 0.987615i | \(0.550149\pi\) | |||||||
\(618\) | 3.12502 | 0.125707 | ||||||||
\(619\) | −21.1086 | −0.848424 | −0.424212 | − | 0.905563i | \(-0.639449\pi\) | ||||
−0.424212 | + | 0.905563i | \(0.639449\pi\) | |||||||
\(620\) | 106.340 | 4.27072 | ||||||||
\(621\) | 5.38714 | 0.216178 | ||||||||
\(622\) | −51.0761 | −2.04797 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.9730 | 0.599401 | ||||||||
\(625\) | −30.0923 | −1.20369 | ||||||||
\(626\) | 32.7347 | 1.30834 | ||||||||
\(627\) | −0.235007 | −0.00938529 | ||||||||
\(628\) | 22.6046 | 0.902023 | ||||||||
\(629\) | −1.49748 | −0.0597084 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8768 | 1.10976 | 0.554880 | − | 0.831931i | \(-0.312764\pi\) | ||||
0.554880 | + | 0.831931i | \(0.312764\pi\) | |||||||
\(632\) | 162.807 | 6.47611 | ||||||||
\(633\) | −1.17306 | −0.0466248 | ||||||||
\(634\) | 6.30585 | 0.250437 | ||||||||
\(635\) | −28.9873 | −1.15033 | ||||||||
\(636\) | −9.24507 | −0.366591 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.39769 | −0.253287 | ||||||||
\(639\) | 2.90576 | 0.114950 | ||||||||
\(640\) | −129.390 | −5.11457 | ||||||||
\(641\) | 22.5527 | 0.890780 | 0.445390 | − | 0.895337i | \(-0.353065\pi\) | ||||
0.445390 | + | 0.895337i | \(0.353065\pi\) | |||||||
\(642\) | 1.11636 | 0.0440593 | ||||||||
\(643\) | 16.1900 | 0.638472 | 0.319236 | − | 0.947675i | \(-0.396574\pi\) | ||||
0.319236 | + | 0.947675i | \(0.396574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.239544 | −0.00943205 | ||||||||
\(646\) | −8.37274 | −0.329421 | ||||||||
\(647\) | −29.3233 | −1.15282 | −0.576408 | − | 0.817162i | \(-0.695546\pi\) | ||||
−0.576408 | + | 0.817162i | \(0.695546\pi\) | |||||||
\(648\) | −87.9733 | −3.45592 | ||||||||
\(649\) | 21.7298 | 0.852969 | ||||||||
\(650\) | 24.2592 | 0.951522 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −67.3333 | −2.63697 | ||||||||
\(653\) | −6.28876 | −0.246098 | −0.123049 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123049 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(654\) | 1.16576 | 0.0455849 | ||||||||
\(655\) | −30.2600 | −1.18236 | ||||||||
\(656\) | 105.765 | 4.12943 | ||||||||
\(657\) | 3.76232 | 0.146782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.10004 | −0.315533 | −0.157766 | − | 0.987476i | \(-0.550429\pi\) | ||||
−0.157766 | + | 0.987476i | \(0.550429\pi\) | |||||||
\(660\) | −3.34779 | −0.130313 | ||||||||
\(661\) | −9.95412 | −0.387170 | −0.193585 | − | 0.981083i | \(-0.562012\pi\) | ||||
−0.193585 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(662\) | −58.7623 | −2.28386 | ||||||||
\(663\) | 2.77779 | 0.107881 | ||||||||
\(664\) | −2.83899 | −0.110174 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.05879 | −0.157275 | ||||||||
\(667\) | 8.88699 | 0.344105 | ||||||||
\(668\) | 85.0097 | 3.28912 | ||||||||
\(669\) | −0.626321 | −0.0242150 | ||||||||
\(670\) | 33.3050 | 1.28668 | ||||||||
\(671\) | 5.59950 | 0.216166 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.7331 | −1.37741 | −0.688704 | − | 0.725042i | \(-0.741820\pi\) | ||||
−0.688704 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(674\) | −47.2293 | −1.81920 | ||||||||
\(675\) | 1.26338 | 0.0486276 | ||||||||
\(676\) | 140.977 | 5.42218 | ||||||||
\(677\) | 5.43480 | 0.208876 | 0.104438 | − | 0.994531i | \(-0.466696\pi\) | ||||
0.104438 | + | 0.994531i | \(0.466696\pi\) | |||||||
\(678\) | −2.48707 | −0.0955152 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −76.8311 | −2.94634 | ||||||||
\(681\) | 2.39153 | 0.0916437 | ||||||||
\(682\) | −32.6311 | −1.24951 | ||||||||
\(683\) | 20.9587 | 0.801963 | 0.400982 | − | 0.916086i | \(-0.368669\pi\) | ||||
0.400982 | + | 0.916086i | \(0.368669\pi\) | |||||||
\(684\) | −16.7376 | −0.639980 | ||||||||
\(685\) | −23.4702 | −0.896749 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.96564 | −0.0749940 | ||||||||
\(688\) | 10.4114 | 0.396930 | ||||||||
\(689\) | −68.3976 | −2.60574 | ||||||||
\(690\) | 6.30520 | 0.240035 | ||||||||
\(691\) | 41.0627 | 1.56210 | 0.781049 | − | 0.624470i | \(-0.214685\pi\) | ||||
0.781049 | + | 0.624470i | \(0.214685\pi\) | |||||||
\(692\) | 83.3365 | 3.16798 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.8113 | −1.13162 | ||||||||
\(695\) | 15.5700 | 0.590604 | ||||||||
\(696\) | 2.17084 | 0.0822853 | ||||||||
\(697\) | 19.6215 | 0.743218 | ||||||||
\(698\) | 57.1751 | 2.16411 | ||||||||
\(699\) | −2.50921 | −0.0949071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.6574 | −1.49784 | −0.748920 | − | 0.662661i | \(-0.769427\pi\) | ||||
−0.748920 | + | 0.662661i | \(0.769427\pi\) | |||||||
\(702\) | 15.1136 | 0.570427 | ||||||||
\(703\) | −0.493725 | −0.0186212 | ||||||||
\(704\) | 58.1285 | 2.19080 | ||||||||
\(705\) | 1.34115 | 0.0505105 | ||||||||
\(706\) | −46.6659 | −1.75629 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.4464 | −0.430180 | ||||||||
\(709\) | −38.7028 | −1.45351 | −0.726757 | − | 0.686894i | \(-0.758973\pi\) | ||||
−0.726757 | + | 0.686894i | \(0.758973\pi\) | |||||||
\(710\) | 6.82707 | 0.256215 | ||||||||
\(711\) | 48.5106 | 1.81929 | ||||||||
\(712\) | −61.6218 | −2.30937 | ||||||||
\(713\) | 45.3277 | 1.69754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.7679 | −0.926267 | ||||||||
\(716\) | −91.5840 | −3.42265 | ||||||||
\(717\) | 1.00570 | 0.0375585 | ||||||||
\(718\) | −42.8077 | −1.59757 | ||||||||
\(719\) | 25.4944 | 0.950781 | 0.475390 | − | 0.879775i | \(-0.342307\pi\) | ||||
0.475390 | + | 0.879775i | \(0.342307\pi\) | |||||||
\(720\) | −123.399 | −4.59880 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.76052 | −0.102736 | ||||||||
\(723\) | −3.35778 | −0.124877 | ||||||||
\(724\) | 5.84496 | 0.217226 | ||||||||
\(725\) | 2.08416 | 0.0774038 | ||||||||
\(726\) | −3.47925 | −0.129127 | ||||||||
\(727\) | 22.6721 | 0.840860 | 0.420430 | − | 0.907325i | \(-0.361879\pi\) | ||||
0.420430 | + | 0.907325i | \(0.361879\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8179 | −0.956219 | ||||||||
\(730\) | 8.83955 | 0.327166 | ||||||||
\(731\) | 1.93152 | 0.0714397 | ||||||||
\(732\) | −2.94958 | −0.109020 | ||||||||
\(733\) | −9.50433 | −0.351050 | −0.175525 | − | 0.984475i | \(-0.556162\pi\) | ||||
−0.175525 | + | 0.984475i | \(0.556162\pi\) | |||||||
\(734\) | −7.50258 | −0.276925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −152.669 | −5.62746 | ||||||||
\(737\) | −7.53765 | −0.277653 | ||||||||
\(738\) | 53.1825 | 1.95767 | ||||||||
\(739\) | 14.2287 | 0.523410 | 0.261705 | − | 0.965148i | \(-0.415715\pi\) | ||||
0.261705 | + | 0.965148i | \(0.415715\pi\) | |||||||
\(740\) | −7.03334 | −0.258551 | ||||||||
\(741\) | 0.915849 | 0.0336445 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.0267 | −1.17494 | −0.587472 | − | 0.809244i | \(-0.699877\pi\) | ||||
−0.587472 | + | 0.809244i | \(0.699877\pi\) | |||||||
\(744\) | 11.0723 | 0.405929 | ||||||||
\(745\) | 30.6024 | 1.12118 | ||||||||
\(746\) | 45.2495 | 1.65670 | ||||||||
\(747\) | −0.845916 | −0.0309505 | ||||||||
\(748\) | 26.9942 | 0.987007 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.71320 | −0.135587 | ||||||||
\(751\) | −7.55357 | −0.275634 | −0.137817 | − | 0.990458i | \(-0.544009\pi\) | ||||
−0.137817 | + | 0.990458i | \(0.544009\pi\) | |||||||
\(752\) | −58.2906 | −2.12564 | ||||||||
\(753\) | −1.68596 | −0.0614399 | ||||||||
\(754\) | 24.9325 | 0.907986 | ||||||||
\(755\) | 16.3507 | 0.595064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.3179 | −0.920193 | −0.460097 | − | 0.887869i | \(-0.652185\pi\) | ||||
−0.460097 | + | 0.887869i | \(0.652185\pi\) | |||||||
\(758\) | 73.0873 | 2.65465 | ||||||||
\(759\) | −1.42701 | −0.0517970 | ||||||||
\(760\) | −25.3315 | −0.918870 | ||||||||
\(761\) | 5.14945 | 0.186667 | 0.0933337 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933337 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(762\) | −4.68549 | −0.169738 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.2359 | 0.768287 | ||||||||
\(765\) | −22.8929 | −0.827696 | ||||||||
\(766\) | 24.7804 | 0.895354 | ||||||||
\(767\) | −84.6833 | −3.05774 | ||||||||
\(768\) | −10.0187 | −0.361518 | ||||||||
\(769\) | −30.5976 | −1.10338 | −0.551689 | − | 0.834050i | \(-0.686017\pi\) | ||||
−0.551689 | + | 0.834050i | \(0.686017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.60322 | 0.0937528 | ||||||||
\(772\) | 58.8342 | 2.11749 | ||||||||
\(773\) | 49.6897 | 1.78721 | 0.893606 | − | 0.448851i | \(-0.148167\pi\) | ||||
0.893606 | + | 0.448851i | \(0.148167\pi\) | |||||||
\(774\) | 5.23521 | 0.188176 | ||||||||
\(775\) | 10.6302 | 0.381847 | ||||||||
\(776\) | −139.332 | −5.00173 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 60.7743 | 2.17886 | ||||||||
\(779\) | 6.46929 | 0.231786 | ||||||||
\(780\) | 13.0467 | 0.467147 | ||||||||
\(781\) | −1.54512 | −0.0552886 | ||||||||
\(782\) | −50.8407 | −1.81806 | ||||||||
\(783\) | 1.29845 | 0.0464027 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.1936 | 0.363826 | ||||||||
\(786\) | −4.89120 | −0.174463 | ||||||||
\(787\) | 13.4645 | 0.479957 | 0.239978 | − | 0.970778i | \(-0.422860\pi\) | ||||
0.239978 | + | 0.970778i | \(0.422860\pi\) | |||||||
\(788\) | −75.8117 | −2.70068 | ||||||||
\(789\) | 2.28548 | 0.0813651 | ||||||||
\(790\) | 113.975 | 4.05506 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 47.1302 | 1.67470 | ||||||||
\(793\) | −21.8218 | −0.774916 | ||||||||
\(794\) | 9.26110 | 0.328664 | ||||||||
\(795\) | −4.16909 | −0.147862 | ||||||||
\(796\) | −100.772 | −3.57176 | ||||||||
\(797\) | 10.9902 | 0.389293 | 0.194647 | − | 0.980873i | \(-0.437644\pi\) | ||||
0.194647 | + | 0.980873i | \(0.437644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8141 | −0.382574 | ||||||||
\(800\) | −35.8037 | −1.26585 | ||||||||
\(801\) | −18.3611 | −0.648757 | ||||||||
\(802\) | 55.5134 | 1.96025 | ||||||||
\(803\) | −2.00058 | −0.0705990 | ||||||||
\(804\) | 3.97052 | 0.140030 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 127.167 | 4.47926 | ||||||||
\(807\) | −1.17655 | −0.0414165 | ||||||||
\(808\) | −162.062 | −5.70132 | ||||||||
\(809\) | 20.0635 | 0.705396 | 0.352698 | − | 0.935737i | \(-0.385264\pi\) | ||||
0.352698 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(810\) | −61.5870 | −2.16395 | ||||||||
\(811\) | 1.57184 | 0.0551948 | 0.0275974 | − | 0.999619i | \(-0.491214\pi\) | ||||
0.0275974 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.29906 | 0.0455601 | ||||||||
\(814\) | 2.15823 | 0.0756459 | ||||||||
\(815\) | −30.3641 | −1.06361 | ||||||||
\(816\) | −7.35906 | −0.257619 | ||||||||
\(817\) | 0.636828 | 0.0222798 | ||||||||
\(818\) | 6.75848 | 0.236305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 92.1581 | 3.21830 | ||||||||
\(821\) | 3.08159 | 0.107548 | 0.0537742 | − | 0.998553i | \(-0.482875\pi\) | ||||
0.0537742 | + | 0.998553i | \(0.482875\pi\) | |||||||
\(822\) | −3.79370 | −0.132321 | ||||||||
\(823\) | 49.4005 | 1.72199 | 0.860996 | − | 0.508612i | \(-0.169841\pi\) | ||||
0.860996 | + | 0.508612i | \(0.169841\pi\) | |||||||
\(824\) | −76.2358 | −2.65580 | ||||||||
\(825\) | −0.334659 | −0.0116513 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.8375 | 0.689817 | 0.344909 | − | 0.938636i | \(-0.387910\pi\) | ||||
0.344909 | + | 0.938636i | \(0.387910\pi\) | |||||||
\(828\) | −101.634 | −3.53202 | ||||||||
\(829\) | 40.6536 | 1.41196 | 0.705979 | − | 0.708233i | \(-0.250507\pi\) | ||||
0.705979 | + | 0.708233i | \(0.250507\pi\) | |||||||
\(830\) | −1.98747 | −0.0689862 | ||||||||
\(831\) | −2.74252 | −0.0951369 | ||||||||
\(832\) | −226.533 | −7.85361 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.51673 | 0.0871471 | ||||||||
\(835\) | 38.3353 | 1.32665 | ||||||||
\(836\) | 8.90010 | 0.307816 | ||||||||
\(837\) | 6.62268 | 0.228913 | ||||||||
\(838\) | 99.4635 | 3.43591 | ||||||||
\(839\) | 21.7950 | 0.752448 | 0.376224 | − | 0.926529i | \(-0.377222\pi\) | ||||
0.376224 | + | 0.926529i | \(0.377222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8580 | −0.926138 | ||||||||
\(842\) | 58.6027 | 2.01958 | ||||||||
\(843\) | 0.516711 | 0.0177965 | ||||||||
\(844\) | 44.4255 | 1.52919 | ||||||||
\(845\) | 63.5737 | 2.18700 | ||||||||
\(846\) | −29.3106 | −1.00772 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 181.202 | 6.22251 | ||||||||
\(849\) | 1.67971 | 0.0576474 | ||||||||
\(850\) | −11.9231 | −0.408958 | ||||||||
\(851\) | −2.99798 | −0.102769 | ||||||||
\(852\) | 0.813902 | 0.0278838 | ||||||||
\(853\) | 52.6727 | 1.80348 | 0.901740 | − | 0.432280i | \(-0.142291\pi\) | ||||
0.901740 | + | 0.432280i | \(0.142291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.54788 | −0.258132 | ||||||||
\(856\) | −27.2340 | −0.930839 | ||||||||
\(857\) | 25.9375 | 0.886007 | 0.443003 | − | 0.896520i | \(-0.353913\pi\) | ||||
0.443003 | + | 0.896520i | \(0.353913\pi\) | |||||||
\(858\) | −4.00347 | −0.136676 | ||||||||
\(859\) | −41.6061 | −1.41958 | −0.709791 | − | 0.704413i | \(-0.751210\pi\) | ||||
−0.709791 | + | 0.704413i | \(0.751210\pi\) | |||||||
\(860\) | 9.07191 | 0.309350 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.4178 | 1.07009 | ||||||||
\(863\) | 26.6445 | 0.906990 | 0.453495 | − | 0.891259i | \(-0.350177\pi\) | ||||
0.453495 | + | 0.891259i | \(0.350177\pi\) | |||||||
\(864\) | −22.3060 | −0.758864 | ||||||||
\(865\) | 37.5808 | 1.27779 | ||||||||
\(866\) | −63.7959 | −2.16787 | ||||||||
\(867\) | 1.15770 | 0.0393175 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.7951 | −0.875039 | ||||||||
\(870\) | 1.51973 | 0.0515235 | ||||||||
\(871\) | 29.3750 | 0.995335 | ||||||||
\(872\) | −28.4391 | −0.963068 | ||||||||
\(873\) | −41.5159 | −1.40510 | ||||||||
\(874\) | −16.7624 | −0.566995 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.05382 | 0.0356054 | ||||||||
\(877\) | −21.6320 | −0.730461 | −0.365230 | − | 0.930917i | \(-0.619010\pi\) | ||||
−0.365230 | + | 0.930917i | \(0.619010\pi\) | |||||||
\(878\) | 77.2123 | 2.60579 | ||||||||
\(879\) | 2.23902 | 0.0755202 | ||||||||
\(880\) | 65.6163 | 2.21192 | ||||||||
\(881\) | −36.3647 | −1.22516 | −0.612579 | − | 0.790409i | \(-0.709868\pi\) | ||||
−0.612579 | + | 0.790409i | \(0.709868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.8156 | −1.54182 | −0.770908 | − | 0.636946i | \(-0.780197\pi\) | ||||
−0.770908 | + | 0.636946i | \(0.780197\pi\) | |||||||
\(884\) | −105.199 | −3.53824 | ||||||||
\(885\) | −5.16176 | −0.173511 | ||||||||
\(886\) | −79.0479 | −2.65567 | ||||||||
\(887\) | −20.6252 | −0.692526 | −0.346263 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346263 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(888\) | −0.732321 | −0.0245751 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −43.1393 | −1.44603 | ||||||||
\(891\) | 13.9385 | 0.466957 | ||||||||
\(892\) | 23.7198 | 0.794196 | ||||||||
\(893\) | −3.56543 | −0.119313 | ||||||||
\(894\) | 4.94655 | 0.165437 | ||||||||
\(895\) | −41.3000 | −1.38051 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.56119 | 0.185683 | ||||||||
\(898\) | −4.18829 | −0.139765 | ||||||||
\(899\) | 10.9252 | 0.364376 | ||||||||
\(900\) | −23.8350 | −0.794500 | ||||||||
\(901\) | 33.6166 | 1.11993 | ||||||||
\(902\) | −28.2793 | −0.941599 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 60.6727 | 2.01794 | ||||||||
\(905\) | 2.63580 | 0.0876169 | ||||||||
\(906\) | 2.64292 | 0.0878052 | ||||||||
\(907\) | 8.54091 | 0.283596 | 0.141798 | − | 0.989896i | \(-0.454712\pi\) | ||||
0.141798 | + | 0.989896i | \(0.454712\pi\) | |||||||
\(908\) | −90.5711 | −3.00571 | ||||||||
\(909\) | −48.2887 | −1.60163 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6287 | −1.44548 | −0.722742 | − | 0.691118i | \(-0.757119\pi\) | ||||
−0.722742 | + | 0.691118i | \(0.757119\pi\) | |||||||
\(912\) | −2.42631 | −0.0803431 | ||||||||
\(913\) | 0.449809 | 0.0148865 | ||||||||
\(914\) | −22.1505 | −0.732675 | ||||||||
\(915\) | −1.33012 | −0.0439725 | ||||||||
\(916\) | 74.4420 | 2.45963 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.42816 | −0.245166 | ||||||||
\(919\) | −49.8066 | −1.64297 | −0.821484 | − | 0.570231i | \(-0.806854\pi\) | ||||
−0.821484 | + | 0.570231i | \(0.806854\pi\) | |||||||
\(920\) | −153.817 | −5.07120 | ||||||||
\(921\) | 0.901607 | 0.0297090 | ||||||||
\(922\) | −53.3864 | −1.75819 | ||||||||
\(923\) | 6.02148 | 0.198199 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.703081 | −0.0231172 | ||||||||
\(926\) | −89.0926 | −2.92776 | ||||||||
\(927\) | −22.7156 | −0.746077 | ||||||||
\(928\) | −36.7974 | −1.20793 | ||||||||
\(929\) | 44.5895 | 1.46293 | 0.731467 | − | 0.681876i | \(-0.238836\pi\) | ||||
0.731467 | + | 0.681876i | \(0.238836\pi\) | |||||||
\(930\) | 7.75130 | 0.254175 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 95.0277 | 3.11274 | ||||||||
\(933\) | −2.74591 | −0.0898971 | ||||||||
\(934\) | −88.8004 | −2.90564 | ||||||||
\(935\) | 12.1731 | 0.398104 | ||||||||
\(936\) | −183.671 | −6.00349 | ||||||||
\(937\) | −52.7172 | −1.72219 | −0.861097 | − | 0.508440i | \(-0.830222\pi\) | ||||
−0.861097 | + | 0.508440i | \(0.830222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.75986 | 0.0574307 | ||||||||
\(940\) | −50.7913 | −1.65663 | ||||||||
\(941\) | 15.0751 | 0.491436 | 0.245718 | − | 0.969341i | \(-0.420976\pi\) | ||||
0.245718 | + | 0.969341i | \(0.420976\pi\) | |||||||
\(942\) | 1.64769 | 0.0536846 | ||||||||
\(943\) | 39.2826 | 1.27922 | ||||||||
\(944\) | 224.347 | 7.30187 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.78378 | −0.0905084 | ||||||||
\(947\) | −12.9216 | −0.419895 | −0.209948 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209948 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(948\) | 13.5878 | 0.441311 | ||||||||
\(949\) | 7.79648 | 0.253085 | ||||||||
\(950\) | −3.93108 | −0.127541 | ||||||||
\(951\) | 0.339010 | 0.0109932 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.3314 | −0.529026 | −0.264513 | − | 0.964382i | \(-0.585211\pi\) | ||||
−0.264513 | + | 0.964382i | \(0.585211\pi\) | |||||||
\(954\) | 91.1149 | 2.94995 | ||||||||
\(955\) | 9.57638 | 0.309884 | ||||||||
\(956\) | −38.0874 | −1.23184 | ||||||||
\(957\) | −0.343947 | −0.0111182 | ||||||||
\(958\) | 21.5817 | 0.697274 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.8080 | −0.445652 | ||||||||
\(961\) | 24.7236 | 0.797534 | ||||||||
\(962\) | −8.41084 | −0.271176 | ||||||||
\(963\) | −8.11476 | −0.261494 | ||||||||
\(964\) | 127.164 | 4.09569 | ||||||||
\(965\) | 26.5314 | 0.854077 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.7625 | 1.82536 | 0.912679 | − | 0.408678i | \(-0.134010\pi\) | ||||
0.912679 | + | 0.408678i | \(0.134010\pi\) | |||||||
\(968\) | 84.8773 | 2.72806 | ||||||||
\(969\) | −0.450128 | −0.0144602 | ||||||||
\(970\) | −97.5414 | −3.13187 | ||||||||
\(971\) | −6.73556 | −0.216154 | −0.108077 | − | 0.994143i | \(-0.534469\pi\) | ||||
−0.108077 | + | 0.994143i | \(0.534469\pi\) | |||||||
\(972\) | −22.3014 | −0.715318 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 82.2579 | 2.63571 | ||||||||
\(975\) | 1.30420 | 0.0417679 | ||||||||
\(976\) | 57.8114 | 1.85050 | ||||||||
\(977\) | 21.3172 | 0.681997 | 0.340999 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340999 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(978\) | −4.90804 | −0.156942 | ||||||||
\(979\) | 9.76336 | 0.312038 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.47382 | −0.270548 | ||||||||
\(982\) | −54.7385 | −1.74678 | ||||||||
\(983\) | −21.2637 | −0.678206 | −0.339103 | − | 0.940749i | \(-0.610124\pi\) | ||||
−0.339103 | + | 0.940749i | \(0.610124\pi\) | |||||||
\(984\) | 9.59562 | 0.305897 | ||||||||
\(985\) | −34.1875 | −1.08930 | ||||||||
\(986\) | −12.2540 | −0.390247 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −34.6846 | −1.10346 | ||||||||
\(989\) | 3.86693 | 0.122961 | ||||||||
\(990\) | 32.9942 | 1.04862 | ||||||||
\(991\) | −43.6356 | −1.38613 | −0.693065 | − | 0.720875i | \(-0.743740\pi\) | ||||
−0.693065 | + | 0.720875i | \(0.743740\pi\) | |||||||
\(992\) | −187.684 | −5.95896 | ||||||||
\(993\) | −3.15913 | −0.100252 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.4433 | −1.44065 | ||||||||
\(996\) | −0.236941 | −0.00750775 | ||||||||
\(997\) | 51.7772 | 1.63980 | 0.819901 | − | 0.572506i | \(-0.194029\pi\) | ||||
0.819901 | + | 0.572506i | \(0.194029\pi\) | |||||||
\(998\) | 84.6714 | 2.68023 | ||||||||
\(999\) | −0.438025 | −0.0138585 |
(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 | 931.2.a.q.1.1 | yes | 10 | |
3.2 | odd | 2 | 8379.2.a.cs.1.10 | 10 | |||
7.2 | even | 3 | 931.2.f.q.704.10 | 20 | |||
7.3 | odd | 6 | 931.2.f.r.324.10 | 20 | |||
7.4 | even | 3 | 931.2.f.q.324.10 | 20 | |||
7.5 | odd | 6 | 931.2.f.r.704.10 | 20 | |||
7.6 | odd | 2 | 931.2.a.p.1.1 | ✓ | 10 | ||
21.20 | even | 2 | 8379.2.a.ct.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.p.1.1 | ✓ | 10 | 7.6 | odd | 2 | ||
931.2.a.q.1.1 | yes | 10 | 1.1 | even | 1 | trivial | |
931.2.f.q.324.10 | 20 | 7.4 | even | 3 | |||
931.2.f.q.704.10 | 20 | 7.2 | even | 3 | |||
931.2.f.r.324.10 | 20 | 7.3 | odd | 6 | |||
931.2.f.r.704.10 | 20 | 7.5 | odd | 6 | |||
8379.2.a.cs.1.10 | 10 | 3.2 | odd | 2 | |||
8379.2.a.ct.1.10 | 10 | 21.20 | even | 2 |