Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 \) |
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 | 1.6 | ||
Root | \(1.09372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09372 | −0.773374 | −0.386687 | − | 0.922211i | \(-0.626381\pi\) | ||||
−0.386687 | + | 0.922211i | \(0.626381\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.803784 | −0.401892 | ||||||||
\(5\) | −3.36980 | −1.50702 | −0.753510 | − | 0.657436i | \(-0.771641\pi\) | ||||
−0.753510 | + | 0.657436i | \(0.771641\pi\) | |||||||
\(6\) | −1.09372 | −0.446508 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.06655 | 1.08419 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.68561 | 1.16549 | ||||||||
\(11\) | −0.408118 | −0.123052 | −0.0615260 | − | 0.998105i | \(-0.519597\pi\) | ||||
−0.0615260 | + | 0.998105i | \(0.519597\pi\) | |||||||
\(12\) | −0.803784 | −0.232032 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.09372 | −0.292308 | ||||||||
\(15\) | −3.36980 | −0.870079 | ||||||||
\(16\) | −1.74636 | −0.436591 | ||||||||
\(17\) | 0.412077 | 0.0999434 | 0.0499717 | − | 0.998751i | \(-0.484087\pi\) | ||||
0.0499717 | + | 0.998751i | \(0.484087\pi\) | |||||||
\(18\) | −1.09372 | −0.257791 | ||||||||
\(19\) | 1.06384 | 0.244062 | 0.122031 | − | 0.992526i | \(-0.461059\pi\) | ||||
0.122031 | + | 0.992526i | \(0.461059\pi\) | |||||||
\(20\) | 2.70859 | 0.605659 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.446365 | 0.0951653 | ||||||||
\(23\) | 8.83682 | 1.84260 | 0.921302 | − | 0.388847i | \(-0.127126\pi\) | ||||
0.921302 | + | 0.388847i | \(0.127126\pi\) | |||||||
\(24\) | 3.06655 | 0.625956 | ||||||||
\(25\) | 6.35555 | 1.27111 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.803784 | −0.151901 | ||||||||
\(29\) | −3.54528 | −0.658341 | −0.329171 | − | 0.944270i | \(-0.606769\pi\) | ||||
−0.329171 | + | 0.944270i | \(0.606769\pi\) | |||||||
\(30\) | 3.68561 | 0.672896 | ||||||||
\(31\) | −1.89809 | −0.340908 | −0.170454 | − | 0.985366i | \(-0.554523\pi\) | ||||
−0.170454 | + | 0.985366i | \(0.554523\pi\) | |||||||
\(32\) | −4.22306 | −0.746539 | ||||||||
\(33\) | −0.408118 | −0.0710441 | ||||||||
\(34\) | −0.450696 | −0.0772937 | ||||||||
\(35\) | −3.36980 | −0.569600 | ||||||||
\(36\) | −0.803784 | −0.133964 | ||||||||
\(37\) | −4.79988 | −0.789095 | −0.394547 | − | 0.918876i | \(-0.629099\pi\) | ||||
−0.394547 | + | 0.918876i | \(0.629099\pi\) | |||||||
\(38\) | −1.16354 | −0.188751 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.3336 | −1.63389 | ||||||||
\(41\) | −10.0404 | −1.56805 | −0.784025 | − | 0.620729i | \(-0.786837\pi\) | ||||
−0.784025 | + | 0.620729i | \(0.786837\pi\) | |||||||
\(42\) | −1.09372 | −0.168764 | ||||||||
\(43\) | −2.32877 | −0.355135 | −0.177567 | − | 0.984109i | \(-0.556823\pi\) | ||||
−0.177567 | + | 0.984109i | \(0.556823\pi\) | |||||||
\(44\) | 0.328038 | 0.0494536 | ||||||||
\(45\) | −3.36980 | −0.502340 | ||||||||
\(46\) | −9.66498 | −1.42502 | ||||||||
\(47\) | −8.84728 | −1.29051 | −0.645254 | − | 0.763968i | \(-0.723249\pi\) | ||||
−0.645254 | + | 0.763968i | \(0.723249\pi\) | |||||||
\(48\) | −1.74636 | −0.252066 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.95117 | −0.983044 | ||||||||
\(51\) | 0.412077 | 0.0577024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.18910 | −0.575418 | −0.287709 | − | 0.957718i | \(-0.592894\pi\) | ||||
−0.287709 | + | 0.957718i | \(0.592894\pi\) | |||||||
\(54\) | −1.09372 | −0.148836 | ||||||||
\(55\) | 1.37527 | 0.185442 | ||||||||
\(56\) | 3.06655 | 0.409784 | ||||||||
\(57\) | 1.06384 | 0.140909 | ||||||||
\(58\) | 3.87753 | 0.509144 | ||||||||
\(59\) | 11.4506 | 1.49074 | 0.745369 | − | 0.666652i | \(-0.232273\pi\) | ||||
0.745369 | + | 0.666652i | \(0.232273\pi\) | |||||||
\(60\) | 2.70859 | 0.349678 | ||||||||
\(61\) | 11.6354 | 1.48976 | 0.744880 | − | 0.667199i | \(-0.232507\pi\) | ||||
0.744880 | + | 0.667199i | \(0.232507\pi\) | |||||||
\(62\) | 2.07598 | 0.263649 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.11156 | 1.01395 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.446365 | 0.0549437 | ||||||||
\(67\) | −2.39553 | −0.292661 | −0.146330 | − | 0.989236i | \(-0.546746\pi\) | ||||
−0.146330 | + | 0.989236i | \(0.546746\pi\) | |||||||
\(68\) | −0.331221 | −0.0401665 | ||||||||
\(69\) | 8.83682 | 1.06383 | ||||||||
\(70\) | 3.68561 | 0.440514 | ||||||||
\(71\) | −14.6773 | −1.74188 | −0.870939 | − | 0.491391i | \(-0.836489\pi\) | ||||
−0.870939 | + | 0.491391i | \(0.836489\pi\) | |||||||
\(72\) | 3.06655 | 0.361396 | ||||||||
\(73\) | 14.5666 | 1.70489 | 0.852447 | − | 0.522814i | \(-0.175118\pi\) | ||||
0.852447 | + | 0.522814i | \(0.175118\pi\) | |||||||
\(74\) | 5.24970 | 0.610266 | ||||||||
\(75\) | 6.35555 | 0.733876 | ||||||||
\(76\) | −0.855097 | −0.0980864 | ||||||||
\(77\) | −0.408118 | −0.0465093 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.27789 | 0.481300 | 0.240650 | − | 0.970612i | \(-0.422639\pi\) | ||||
0.240650 | + | 0.970612i | \(0.422639\pi\) | |||||||
\(80\) | 5.88489 | 0.657951 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.9814 | 1.21269 | ||||||||
\(83\) | 4.60644 | 0.505623 | 0.252811 | − | 0.967516i | \(-0.418645\pi\) | ||||
0.252811 | + | 0.967516i | \(0.418645\pi\) | |||||||
\(84\) | −0.803784 | −0.0877000 | ||||||||
\(85\) | −1.38862 | −0.150617 | ||||||||
\(86\) | 2.54702 | 0.274652 | ||||||||
\(87\) | −3.54528 | −0.380093 | ||||||||
\(88\) | −1.25151 | −0.133411 | ||||||||
\(89\) | −14.3179 | −1.51769 | −0.758846 | − | 0.651271i | \(-0.774236\pi\) | ||||
−0.758846 | + | 0.651271i | \(0.774236\pi\) | |||||||
\(90\) | 3.68561 | 0.388497 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.10290 | −0.740528 | ||||||||
\(93\) | −1.89809 | −0.196823 | ||||||||
\(94\) | 9.67642 | 0.998046 | ||||||||
\(95\) | −3.58493 | −0.367806 | ||||||||
\(96\) | −4.22306 | −0.431015 | ||||||||
\(97\) | 12.3236 | 1.25127 | 0.625633 | − | 0.780117i | \(-0.284841\pi\) | ||||
0.625633 | + | 0.780117i | \(0.284841\pi\) | |||||||
\(98\) | −1.09372 | −0.110482 | ||||||||
\(99\) | −0.408118 | −0.0410174 | ||||||||
\(100\) | −5.10849 | −0.510849 | ||||||||
\(101\) | −1.21016 | −0.120416 | −0.0602079 | − | 0.998186i | \(-0.519176\pi\) | ||||
−0.0602079 | + | 0.998186i | \(0.519176\pi\) | |||||||
\(102\) | −0.450696 | −0.0446255 | ||||||||
\(103\) | 13.5513 | 1.33525 | 0.667626 | − | 0.744497i | \(-0.267311\pi\) | ||||
0.667626 | + | 0.744497i | \(0.267311\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.36980 | −0.328859 | ||||||||
\(106\) | 4.58169 | 0.445013 | ||||||||
\(107\) | 8.58829 | 0.830261 | 0.415131 | − | 0.909762i | \(-0.363736\pi\) | ||||
0.415131 | + | 0.909762i | \(0.363736\pi\) | |||||||
\(108\) | −0.803784 | −0.0773442 | ||||||||
\(109\) | 19.6808 | 1.88508 | 0.942540 | − | 0.334093i | \(-0.108430\pi\) | ||||
0.942540 | + | 0.334093i | \(0.108430\pi\) | |||||||
\(110\) | −1.50416 | −0.143416 | ||||||||
\(111\) | −4.79988 | −0.455584 | ||||||||
\(112\) | −1.74636 | −0.165016 | ||||||||
\(113\) | 1.36619 | 0.128520 | 0.0642602 | − | 0.997933i | \(-0.479531\pi\) | ||||
0.0642602 | + | 0.997933i | \(0.479531\pi\) | |||||||
\(114\) | −1.16354 | −0.108975 | ||||||||
\(115\) | −29.7783 | −2.77684 | ||||||||
\(116\) | 2.84964 | 0.264582 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5237 | −1.15290 | ||||||||
\(119\) | 0.412077 | 0.0377751 | ||||||||
\(120\) | −10.3336 | −0.943328 | ||||||||
\(121\) | −10.8334 | −0.984858 | ||||||||
\(122\) | −12.7258 | −1.15214 | ||||||||
\(123\) | −10.0404 | −0.905314 | ||||||||
\(124\) | 1.52566 | 0.137008 | ||||||||
\(125\) | −4.56793 | −0.408568 | ||||||||
\(126\) | −1.09372 | −0.0974360 | ||||||||
\(127\) | −16.5831 | −1.47151 | −0.735756 | − | 0.677247i | \(-0.763173\pi\) | ||||
−0.735756 | + | 0.677247i | \(0.763173\pi\) | |||||||
\(128\) | −0.425621 | −0.0376199 | ||||||||
\(129\) | −2.32877 | −0.205037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.76818 | 0.853449 | 0.426725 | − | 0.904382i | \(-0.359667\pi\) | ||||
0.426725 | + | 0.904382i | \(0.359667\pi\) | |||||||
\(132\) | 0.328038 | 0.0285521 | ||||||||
\(133\) | 1.06384 | 0.0922466 | ||||||||
\(134\) | 2.62003 | 0.226336 | ||||||||
\(135\) | −3.36980 | −0.290026 | ||||||||
\(136\) | 1.26365 | 0.108357 | ||||||||
\(137\) | 14.4867 | 1.23768 | 0.618839 | − | 0.785518i | \(-0.287603\pi\) | ||||
0.618839 | + | 0.785518i | \(0.287603\pi\) | |||||||
\(138\) | −9.66498 | −0.822738 | ||||||||
\(139\) | −7.75313 | −0.657612 | −0.328806 | − | 0.944398i | \(-0.606646\pi\) | ||||
−0.328806 | + | 0.944398i | \(0.606646\pi\) | |||||||
\(140\) | 2.70859 | 0.228918 | ||||||||
\(141\) | −8.84728 | −0.745075 | ||||||||
\(142\) | 16.0528 | 1.34712 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.74636 | −0.145530 | ||||||||
\(145\) | 11.9469 | 0.992133 | ||||||||
\(146\) | −15.9318 | −1.31852 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 3.85806 | 0.317131 | ||||||||
\(149\) | −2.67814 | −0.219402 | −0.109701 | − | 0.993965i | \(-0.534989\pi\) | ||||
−0.109701 | + | 0.993965i | \(0.534989\pi\) | |||||||
\(150\) | −6.95117 | −0.567561 | ||||||||
\(151\) | 7.62102 | 0.620190 | 0.310095 | − | 0.950706i | \(-0.399639\pi\) | ||||
0.310095 | + | 0.950706i | \(0.399639\pi\) | |||||||
\(152\) | 3.26231 | 0.264608 | ||||||||
\(153\) | 0.412077 | 0.0333145 | ||||||||
\(154\) | 0.446365 | 0.0359691 | ||||||||
\(155\) | 6.39620 | 0.513755 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1947 | 1.45209 | 0.726047 | − | 0.687645i | \(-0.241355\pi\) | ||||
0.726047 | + | 0.687645i | \(0.241355\pi\) | |||||||
\(158\) | −4.67880 | −0.372225 | ||||||||
\(159\) | −4.18910 | −0.332218 | ||||||||
\(160\) | 14.2309 | 1.12505 | ||||||||
\(161\) | 8.83682 | 0.696439 | ||||||||
\(162\) | −1.09372 | −0.0859305 | ||||||||
\(163\) | 19.5824 | 1.53381 | 0.766905 | − | 0.641760i | \(-0.221796\pi\) | ||||
0.766905 | + | 0.641760i | \(0.221796\pi\) | |||||||
\(164\) | 8.07033 | 0.630187 | ||||||||
\(165\) | 1.37527 | 0.107065 | ||||||||
\(166\) | −5.03814 | −0.391036 | ||||||||
\(167\) | −6.00027 | −0.464315 | −0.232158 | − | 0.972678i | \(-0.574578\pi\) | ||||
−0.232158 | + | 0.972678i | \(0.574578\pi\) | |||||||
\(168\) | 3.06655 | 0.236589 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.51875 | 0.116483 | ||||||||
\(171\) | 1.06384 | 0.0813539 | ||||||||
\(172\) | 1.87183 | 0.142726 | ||||||||
\(173\) | −1.17561 | −0.0893797 | −0.0446899 | − | 0.999001i | \(-0.514230\pi\) | ||||
−0.0446899 | + | 0.999001i | \(0.514230\pi\) | |||||||
\(174\) | 3.87753 | 0.293955 | ||||||||
\(175\) | 6.35555 | 0.480434 | ||||||||
\(176\) | 0.712721 | 0.0537234 | ||||||||
\(177\) | 11.4506 | 0.860678 | ||||||||
\(178\) | 15.6597 | 1.17374 | ||||||||
\(179\) | 0.249567 | 0.0186535 | 0.00932677 | − | 0.999957i | \(-0.497031\pi\) | ||||
0.00932677 | + | 0.999957i | \(0.497031\pi\) | |||||||
\(180\) | 2.70859 | 0.201886 | ||||||||
\(181\) | 0.442464 | 0.0328881 | 0.0164440 | − | 0.999865i | \(-0.494765\pi\) | ||||
0.0164440 | + | 0.999865i | \(0.494765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6354 | 0.860113 | ||||||||
\(184\) | 27.0985 | 1.99773 | ||||||||
\(185\) | 16.1746 | 1.18918 | ||||||||
\(186\) | 2.07598 | 0.152218 | ||||||||
\(187\) | −0.168176 | −0.0122982 | ||||||||
\(188\) | 7.11130 | 0.518645 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 3.92089 | 0.284452 | ||||||||
\(191\) | 15.8545 | 1.14719 | 0.573597 | − | 0.819138i | \(-0.305548\pi\) | ||||
0.573597 | + | 0.819138i | \(0.305548\pi\) | |||||||
\(192\) | 8.11156 | 0.585401 | ||||||||
\(193\) | −4.24322 | −0.305434 | −0.152717 | − | 0.988270i | \(-0.548802\pi\) | ||||
−0.152717 | + | 0.988270i | \(0.548802\pi\) | |||||||
\(194\) | −13.4785 | −0.967698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.803784 | −0.0574131 | ||||||||
\(197\) | −9.13404 | −0.650773 | −0.325387 | − | 0.945581i | \(-0.605494\pi\) | ||||
−0.325387 | + | 0.945581i | \(0.605494\pi\) | |||||||
\(198\) | 0.446365 | 0.0317218 | ||||||||
\(199\) | 9.66460 | 0.685105 | 0.342553 | − | 0.939499i | \(-0.388708\pi\) | ||||
0.342553 | + | 0.939499i | \(0.388708\pi\) | |||||||
\(200\) | 19.4896 | 1.37812 | ||||||||
\(201\) | −2.39553 | −0.168968 | ||||||||
\(202\) | 1.32358 | 0.0931265 | ||||||||
\(203\) | −3.54528 | −0.248830 | ||||||||
\(204\) | −0.331221 | −0.0231901 | ||||||||
\(205\) | 33.8342 | 2.36308 | ||||||||
\(206\) | −14.8213 | −1.03265 | ||||||||
\(207\) | 8.83682 | 0.614202 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.434172 | −0.0300323 | ||||||||
\(210\) | 3.68561 | 0.254331 | ||||||||
\(211\) | −24.0587 | −1.65627 | −0.828135 | − | 0.560528i | \(-0.810598\pi\) | ||||
−0.828135 | + | 0.560528i | \(0.810598\pi\) | |||||||
\(212\) | 3.36714 | 0.231256 | ||||||||
\(213\) | −14.6773 | −1.00567 | ||||||||
\(214\) | −9.39315 | −0.642103 | ||||||||
\(215\) | 7.84750 | 0.535195 | ||||||||
\(216\) | 3.06655 | 0.208652 | ||||||||
\(217\) | −1.89809 | −0.128851 | ||||||||
\(218\) | −21.5252 | −1.45787 | ||||||||
\(219\) | 14.5666 | 0.984321 | ||||||||
\(220\) | −1.10542 | −0.0745276 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.24970 | 0.352337 | ||||||||
\(223\) | 18.1487 | 1.21532 | 0.607662 | − | 0.794196i | \(-0.292108\pi\) | ||||
0.607662 | + | 0.794196i | \(0.292108\pi\) | |||||||
\(224\) | −4.22306 | −0.282165 | ||||||||
\(225\) | 6.35555 | 0.423703 | ||||||||
\(226\) | −1.49423 | −0.0993944 | ||||||||
\(227\) | 16.2228 | 1.07674 | 0.538372 | − | 0.842707i | \(-0.319039\pi\) | ||||
0.538372 | + | 0.842707i | \(0.319039\pi\) | |||||||
\(228\) | −0.855097 | −0.0566302 | ||||||||
\(229\) | −0.980804 | −0.0648134 | −0.0324067 | − | 0.999475i | \(-0.510317\pi\) | ||||
−0.0324067 | + | 0.999475i | \(0.510317\pi\) | |||||||
\(230\) | 32.5690 | 2.14754 | ||||||||
\(231\) | −0.408118 | −0.0268522 | ||||||||
\(232\) | −10.8717 | −0.713765 | ||||||||
\(233\) | −19.4629 | −1.27506 | −0.637528 | − | 0.770427i | \(-0.720043\pi\) | ||||
−0.637528 | + | 0.770427i | \(0.720043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.8136 | 1.94482 | ||||||||
\(236\) | −9.20379 | −0.599116 | ||||||||
\(237\) | 4.27789 | 0.277879 | ||||||||
\(238\) | −0.450696 | −0.0292143 | ||||||||
\(239\) | −18.7859 | −1.21516 | −0.607580 | − | 0.794259i | \(-0.707859\pi\) | ||||
−0.607580 | + | 0.794259i | \(0.707859\pi\) | |||||||
\(240\) | 5.88489 | 0.379868 | ||||||||
\(241\) | 9.08287 | 0.585079 | 0.292540 | − | 0.956253i | \(-0.405500\pi\) | ||||
0.292540 | + | 0.956253i | \(0.405500\pi\) | |||||||
\(242\) | 11.8487 | 0.761664 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.35235 | −0.598723 | ||||||||
\(245\) | −3.36980 | −0.215289 | ||||||||
\(246\) | 10.9814 | 0.700147 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.82059 | −0.369608 | ||||||||
\(249\) | 4.60644 | 0.291921 | ||||||||
\(250\) | 4.99602 | 0.315976 | ||||||||
\(251\) | 11.7323 | 0.740535 | 0.370267 | − | 0.928925i | \(-0.379266\pi\) | ||||
0.370267 | + | 0.928925i | \(0.379266\pi\) | |||||||
\(252\) | −0.803784 | −0.0506336 | ||||||||
\(253\) | −3.60646 | −0.226736 | ||||||||
\(254\) | 18.1372 | 1.13803 | ||||||||
\(255\) | −1.38862 | −0.0869586 | ||||||||
\(256\) | −15.7576 | −0.984851 | ||||||||
\(257\) | 20.0321 | 1.24957 | 0.624784 | − | 0.780797i | \(-0.285187\pi\) | ||||
0.624784 | + | 0.780797i | \(0.285187\pi\) | |||||||
\(258\) | 2.54702 | 0.158570 | ||||||||
\(259\) | −4.79988 | −0.298250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.54528 | −0.219447 | ||||||||
\(262\) | −10.6836 | −0.660036 | ||||||||
\(263\) | −5.06336 | −0.312220 | −0.156110 | − | 0.987740i | \(-0.549895\pi\) | ||||
−0.156110 | + | 0.987740i | \(0.549895\pi\) | |||||||
\(264\) | −1.25151 | −0.0770252 | ||||||||
\(265\) | 14.1164 | 0.867166 | ||||||||
\(266\) | −1.16354 | −0.0713412 | ||||||||
\(267\) | −14.3179 | −0.876239 | ||||||||
\(268\) | 1.92549 | 0.117618 | ||||||||
\(269\) | 4.89625 | 0.298530 | 0.149265 | − | 0.988797i | \(-0.452309\pi\) | ||||
0.149265 | + | 0.988797i | \(0.452309\pi\) | |||||||
\(270\) | 3.68561 | 0.224299 | ||||||||
\(271\) | 27.2537 | 1.65554 | 0.827772 | − | 0.561064i | \(-0.189608\pi\) | ||||
0.827772 | + | 0.561064i | \(0.189608\pi\) | |||||||
\(272\) | −0.719637 | −0.0436344 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.8443 | −0.957189 | ||||||||
\(275\) | −2.59381 | −0.156413 | ||||||||
\(276\) | −7.10290 | −0.427544 | ||||||||
\(277\) | −2.91367 | −0.175066 | −0.0875328 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875328 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(278\) | 8.47972 | 0.508580 | ||||||||
\(279\) | −1.89809 | −0.113636 | ||||||||
\(280\) | −10.3336 | −0.617553 | ||||||||
\(281\) | 25.2705 | 1.50751 | 0.753757 | − | 0.657153i | \(-0.228240\pi\) | ||||
0.753757 | + | 0.657153i | \(0.228240\pi\) | |||||||
\(282\) | 9.67642 | 0.576222 | ||||||||
\(283\) | 18.5059 | 1.10006 | 0.550031 | − | 0.835144i | \(-0.314616\pi\) | ||||
0.550031 | + | 0.835144i | \(0.314616\pi\) | |||||||
\(284\) | 11.7974 | 0.700047 | ||||||||
\(285\) | −3.58493 | −0.212353 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0404 | −0.592667 | ||||||||
\(288\) | −4.22306 | −0.248846 | ||||||||
\(289\) | −16.8302 | −0.990011 | ||||||||
\(290\) | −13.0665 | −0.767291 | ||||||||
\(291\) | 12.3236 | 0.722419 | ||||||||
\(292\) | −11.7084 | −0.685183 | ||||||||
\(293\) | −5.10573 | −0.298280 | −0.149140 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149140 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(294\) | −1.09372 | −0.0637868 | ||||||||
\(295\) | −38.5861 | −2.24657 | ||||||||
\(296\) | −14.7190 | −0.855527 | ||||||||
\(297\) | −0.408118 | −0.0236814 | ||||||||
\(298\) | 2.92912 | 0.169680 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.10849 | −0.294939 | ||||||||
\(301\) | −2.32877 | −0.134228 | ||||||||
\(302\) | −8.33524 | −0.479639 | ||||||||
\(303\) | −1.21016 | −0.0695221 | ||||||||
\(304\) | −1.85785 | −0.106555 | ||||||||
\(305\) | −39.2090 | −2.24510 | ||||||||
\(306\) | −0.450696 | −0.0257646 | ||||||||
\(307\) | 0.145600 | 0.00830986 | 0.00415493 | − | 0.999991i | \(-0.498677\pi\) | ||||
0.00415493 | + | 0.999991i | \(0.498677\pi\) | |||||||
\(308\) | 0.328038 | 0.0186917 | ||||||||
\(309\) | 13.5513 | 0.770908 | ||||||||
\(310\) | −6.99563 | −0.397325 | ||||||||
\(311\) | −27.0891 | −1.53608 | −0.768041 | − | 0.640400i | \(-0.778769\pi\) | ||||
−0.768041 | + | 0.640400i | \(0.778769\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.6140 | 1.67388 | 0.836941 | − | 0.547293i | \(-0.184342\pi\) | ||||
0.836941 | + | 0.547293i | \(0.184342\pi\) | |||||||
\(314\) | −19.8998 | −1.12301 | ||||||||
\(315\) | −3.36980 | −0.189867 | ||||||||
\(316\) | −3.43850 | −0.193431 | ||||||||
\(317\) | 23.9730 | 1.34646 | 0.673229 | − | 0.739434i | \(-0.264907\pi\) | ||||
0.673229 | + | 0.739434i | \(0.264907\pi\) | |||||||
\(318\) | 4.58169 | 0.256929 | ||||||||
\(319\) | 1.44689 | 0.0810102 | ||||||||
\(320\) | −27.3343 | −1.52804 | ||||||||
\(321\) | 8.58829 | 0.479352 | ||||||||
\(322\) | −9.66498 | −0.538608 | ||||||||
\(323\) | 0.438384 | 0.0243924 | ||||||||
\(324\) | −0.803784 | −0.0446547 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.4176 | −1.18621 | ||||||||
\(327\) | 19.6808 | 1.08835 | ||||||||
\(328\) | −30.7894 | −1.70006 | ||||||||
\(329\) | −8.84728 | −0.487766 | ||||||||
\(330\) | −1.50416 | −0.0828013 | ||||||||
\(331\) | −5.54793 | −0.304942 | −0.152471 | − | 0.988308i | \(-0.548723\pi\) | ||||
−0.152471 | + | 0.988308i | \(0.548723\pi\) | |||||||
\(332\) | −3.70258 | −0.203206 | ||||||||
\(333\) | −4.79988 | −0.263032 | ||||||||
\(334\) | 6.56260 | 0.359089 | ||||||||
\(335\) | 8.07247 | 0.441046 | ||||||||
\(336\) | −1.74636 | −0.0952719 | ||||||||
\(337\) | 5.52923 | 0.301196 | 0.150598 | − | 0.988595i | \(-0.451880\pi\) | ||||
0.150598 | + | 0.988595i | \(0.451880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.36619 | 0.0742013 | ||||||||
\(340\) | 1.11615 | 0.0605317 | ||||||||
\(341\) | 0.774646 | 0.0419494 | ||||||||
\(342\) | −1.16354 | −0.0629170 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.14129 | −0.385032 | ||||||||
\(345\) | −29.7783 | −1.60321 | ||||||||
\(346\) | 1.28578 | 0.0691240 | ||||||||
\(347\) | 29.0528 | 1.55964 | 0.779818 | − | 0.626007i | \(-0.215312\pi\) | ||||
0.779818 | + | 0.626007i | \(0.215312\pi\) | |||||||
\(348\) | 2.84964 | 0.152757 | ||||||||
\(349\) | 15.4431 | 0.826652 | 0.413326 | − | 0.910583i | \(-0.364367\pi\) | ||||
0.413326 | + | 0.910583i | \(0.364367\pi\) | |||||||
\(350\) | −6.95117 | −0.371556 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.72351 | 0.0918632 | ||||||||
\(353\) | 18.6976 | 0.995175 | 0.497587 | − | 0.867414i | \(-0.334219\pi\) | ||||
0.497587 | + | 0.867414i | \(0.334219\pi\) | |||||||
\(354\) | −12.5237 | −0.665626 | ||||||||
\(355\) | 49.4596 | 2.62505 | ||||||||
\(356\) | 11.5085 | 0.609948 | ||||||||
\(357\) | 0.412077 | 0.0218094 | ||||||||
\(358\) | −0.272956 | −0.0144262 | ||||||||
\(359\) | −10.9693 | −0.578939 | −0.289470 | − | 0.957187i | \(-0.593479\pi\) | ||||
−0.289470 | + | 0.957187i | \(0.593479\pi\) | |||||||
\(360\) | −10.3336 | −0.544631 | ||||||||
\(361\) | −17.8682 | −0.940434 | ||||||||
\(362\) | −0.483930 | −0.0254348 | ||||||||
\(363\) | −10.8334 | −0.568608 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −49.0866 | −2.56931 | ||||||||
\(366\) | −12.7258 | −0.665190 | ||||||||
\(367\) | 11.8585 | 0.619011 | 0.309505 | − | 0.950898i | \(-0.399837\pi\) | ||||
0.309505 | + | 0.950898i | \(0.399837\pi\) | |||||||
\(368\) | −15.4323 | −0.804464 | ||||||||
\(369\) | −10.0404 | −0.522683 | ||||||||
\(370\) | −17.6905 | −0.919683 | ||||||||
\(371\) | −4.18910 | −0.217487 | ||||||||
\(372\) | 1.52566 | 0.0791017 | ||||||||
\(373\) | 8.62231 | 0.446446 | 0.223223 | − | 0.974767i | \(-0.428342\pi\) | ||||
0.223223 | + | 0.974767i | \(0.428342\pi\) | |||||||
\(374\) | 0.183937 | 0.00951115 | ||||||||
\(375\) | −4.56793 | −0.235887 | ||||||||
\(376\) | −27.1306 | −1.39915 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.09372 | −0.0562547 | ||||||||
\(379\) | −30.5029 | −1.56683 | −0.783413 | − | 0.621501i | \(-0.786523\pi\) | ||||
−0.783413 | + | 0.621501i | \(0.786523\pi\) | |||||||
\(380\) | 2.88151 | 0.147818 | ||||||||
\(381\) | −16.5831 | −0.849578 | ||||||||
\(382\) | −17.3404 | −0.887211 | ||||||||
\(383\) | −25.7592 | −1.31623 | −0.658117 | − | 0.752915i | \(-0.728647\pi\) | ||||
−0.658117 | + | 0.752915i | \(0.728647\pi\) | |||||||
\(384\) | −0.425621 | −0.0217199 | ||||||||
\(385\) | 1.37527 | 0.0700905 | ||||||||
\(386\) | 4.64088 | 0.236215 | ||||||||
\(387\) | −2.32877 | −0.118378 | ||||||||
\(388\) | −9.90547 | −0.502874 | ||||||||
\(389\) | 16.5425 | 0.838737 | 0.419368 | − | 0.907816i | \(-0.362252\pi\) | ||||
0.419368 | + | 0.907816i | \(0.362252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.64145 | 0.184156 | ||||||||
\(392\) | 3.06655 | 0.154884 | ||||||||
\(393\) | 9.76818 | 0.492739 | ||||||||
\(394\) | 9.99005 | 0.503291 | ||||||||
\(395\) | −14.4156 | −0.725329 | ||||||||
\(396\) | 0.328038 | 0.0164845 | ||||||||
\(397\) | −8.82355 | −0.442841 | −0.221421 | − | 0.975178i | \(-0.571069\pi\) | ||||
−0.221421 | + | 0.975178i | \(0.571069\pi\) | |||||||
\(398\) | −10.5703 | −0.529843 | ||||||||
\(399\) | 1.06384 | 0.0532586 | ||||||||
\(400\) | −11.0991 | −0.554955 | ||||||||
\(401\) | 10.8101 | 0.539832 | 0.269916 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269916 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(402\) | 2.62003 | 0.130675 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.972710 | 0.0483941 | ||||||||
\(405\) | −3.36980 | −0.167447 | ||||||||
\(406\) | 3.87753 | 0.192438 | ||||||||
\(407\) | 1.95891 | 0.0970998 | ||||||||
\(408\) | 1.26365 | 0.0625602 | ||||||||
\(409\) | 19.5162 | 0.965015 | 0.482507 | − | 0.875892i | \(-0.339726\pi\) | ||||
0.482507 | + | 0.875892i | \(0.339726\pi\) | |||||||
\(410\) | −37.0050 | −1.82755 | ||||||||
\(411\) | 14.4867 | 0.714574 | ||||||||
\(412\) | −10.8923 | −0.536627 | ||||||||
\(413\) | 11.4506 | 0.563446 | ||||||||
\(414\) | −9.66498 | −0.475008 | ||||||||
\(415\) | −15.5228 | −0.761983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.75313 | −0.379672 | ||||||||
\(418\) | 0.474861 | 0.0232262 | ||||||||
\(419\) | 2.14931 | 0.105001 | 0.0525004 | − | 0.998621i | \(-0.483281\pi\) | ||||
0.0525004 | + | 0.998621i | \(0.483281\pi\) | |||||||
\(420\) | 2.70859 | 0.132166 | ||||||||
\(421\) | −17.1850 | −0.837547 | −0.418774 | − | 0.908091i | \(-0.637540\pi\) | ||||
−0.418774 | + | 0.908091i | \(0.637540\pi\) | |||||||
\(422\) | 26.3134 | 1.28092 | ||||||||
\(423\) | −8.84728 | −0.430169 | ||||||||
\(424\) | −12.8461 | −0.623861 | ||||||||
\(425\) | 2.61898 | 0.127039 | ||||||||
\(426\) | 16.0528 | 0.777762 | ||||||||
\(427\) | 11.6354 | 0.563076 | ||||||||
\(428\) | −6.90313 | −0.333675 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.58294 | −0.413906 | ||||||||
\(431\) | 12.4147 | 0.597997 | 0.298998 | − | 0.954254i | \(-0.403347\pi\) | ||||
0.298998 | + | 0.954254i | \(0.403347\pi\) | |||||||
\(432\) | −1.74636 | −0.0840219 | ||||||||
\(433\) | −1.89315 | −0.0909791 | −0.0454896 | − | 0.998965i | \(-0.514485\pi\) | ||||
−0.0454896 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(434\) | 2.07598 | 0.0996501 | ||||||||
\(435\) | 11.9469 | 0.572808 | ||||||||
\(436\) | −15.8191 | −0.757599 | ||||||||
\(437\) | 9.40096 | 0.449709 | ||||||||
\(438\) | −15.9318 | −0.761249 | ||||||||
\(439\) | −4.57342 | −0.218277 | −0.109139 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109139 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(440\) | 4.21734 | 0.201054 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.3955 | 1.34911 | 0.674556 | − | 0.738224i | \(-0.264335\pi\) | ||||
0.674556 | + | 0.738224i | \(0.264335\pi\) | |||||||
\(444\) | 3.85806 | 0.183096 | ||||||||
\(445\) | 48.2484 | 2.28719 | ||||||||
\(446\) | −19.8495 | −0.939901 | ||||||||
\(447\) | −2.67814 | −0.126672 | ||||||||
\(448\) | 8.11156 | 0.383235 | ||||||||
\(449\) | 35.6530 | 1.68257 | 0.841284 | − | 0.540594i | \(-0.181800\pi\) | ||||
0.841284 | + | 0.540594i | \(0.181800\pi\) | |||||||
\(450\) | −6.95117 | −0.327681 | ||||||||
\(451\) | 4.09767 | 0.192952 | ||||||||
\(452\) | −1.09812 | −0.0516513 | ||||||||
\(453\) | 7.62102 | 0.358067 | ||||||||
\(454\) | −17.7431 | −0.832727 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.26231 | 0.152772 | ||||||||
\(457\) | 31.4697 | 1.47209 | 0.736045 | − | 0.676933i | \(-0.236691\pi\) | ||||
0.736045 | + | 0.676933i | \(0.236691\pi\) | |||||||
\(458\) | 1.07272 | 0.0501250 | ||||||||
\(459\) | 0.412077 | 0.0192341 | ||||||||
\(460\) | 23.9353 | 1.11599 | ||||||||
\(461\) | 21.2279 | 0.988680 | 0.494340 | − | 0.869269i | \(-0.335410\pi\) | ||||
0.494340 | + | 0.869269i | \(0.335410\pi\) | |||||||
\(462\) | 0.446365 | 0.0207668 | ||||||||
\(463\) | −8.12061 | −0.377397 | −0.188698 | − | 0.982035i | \(-0.560427\pi\) | ||||
−0.188698 | + | 0.982035i | \(0.560427\pi\) | |||||||
\(464\) | 6.19134 | 0.287426 | ||||||||
\(465\) | 6.39620 | 0.296617 | ||||||||
\(466\) | 21.2869 | 0.986095 | ||||||||
\(467\) | −26.8288 | −1.24149 | −0.620743 | − | 0.784014i | \(-0.713169\pi\) | ||||
−0.620743 | + | 0.784014i | \(0.713169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.39553 | −0.110615 | ||||||||
\(470\) | −32.6076 | −1.50408 | ||||||||
\(471\) | 18.1947 | 0.838367 | ||||||||
\(472\) | 35.1137 | 1.61624 | ||||||||
\(473\) | 0.950413 | 0.0437000 | ||||||||
\(474\) | −4.67880 | −0.214904 | ||||||||
\(475\) | 6.76129 | 0.310229 | ||||||||
\(476\) | −0.331221 | −0.0151815 | ||||||||
\(477\) | −4.18910 | −0.191806 | ||||||||
\(478\) | 20.5465 | 0.939773 | ||||||||
\(479\) | −9.75257 | −0.445606 | −0.222803 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222803 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(480\) | 14.2309 | 0.649548 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.93409 | −0.452485 | ||||||||
\(483\) | 8.83682 | 0.402089 | ||||||||
\(484\) | 8.70775 | 0.395807 | ||||||||
\(485\) | −41.5279 | −1.88568 | ||||||||
\(486\) | −1.09372 | −0.0496120 | ||||||||
\(487\) | 21.8869 | 0.991791 | 0.495895 | − | 0.868382i | \(-0.334840\pi\) | ||||
0.495895 | + | 0.868382i | \(0.334840\pi\) | |||||||
\(488\) | 35.6805 | 1.61518 | ||||||||
\(489\) | 19.5824 | 0.885546 | ||||||||
\(490\) | 3.68561 | 0.166499 | ||||||||
\(491\) | 33.1640 | 1.49667 | 0.748336 | − | 0.663320i | \(-0.230853\pi\) | ||||
0.748336 | + | 0.663320i | \(0.230853\pi\) | |||||||
\(492\) | 8.07033 | 0.363838 | ||||||||
\(493\) | −1.46093 | −0.0657969 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.37527 | 0.0618140 | ||||||||
\(496\) | 3.31476 | 0.148837 | ||||||||
\(497\) | −14.6773 | −0.658368 | ||||||||
\(498\) | −5.03814 | −0.225764 | ||||||||
\(499\) | −40.6778 | −1.82099 | −0.910494 | − | 0.413522i | \(-0.864298\pi\) | ||||
−0.910494 | + | 0.413522i | \(0.864298\pi\) | |||||||
\(500\) | 3.67163 | 0.164200 | ||||||||
\(501\) | −6.00027 | −0.268072 | ||||||||
\(502\) | −12.8318 | −0.572710 | ||||||||
\(503\) | −35.7797 | −1.59534 | −0.797669 | − | 0.603096i | \(-0.793934\pi\) | ||||
−0.797669 | + | 0.603096i | \(0.793934\pi\) | |||||||
\(504\) | 3.06655 | 0.136595 | ||||||||
\(505\) | 4.07801 | 0.181469 | ||||||||
\(506\) | 3.94445 | 0.175352 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3292 | 0.591389 | ||||||||
\(509\) | 39.4278 | 1.74761 | 0.873803 | − | 0.486279i | \(-0.161646\pi\) | ||||
0.873803 | + | 0.486279i | \(0.161646\pi\) | |||||||
\(510\) | 1.51875 | 0.0672516 | ||||||||
\(511\) | 14.5666 | 0.644389 | ||||||||
\(512\) | 18.0856 | 0.799278 | ||||||||
\(513\) | 1.06384 | 0.0469697 | ||||||||
\(514\) | −21.9095 | −0.966385 | ||||||||
\(515\) | −45.6652 | −2.01225 | ||||||||
\(516\) | 1.87183 | 0.0824027 | ||||||||
\(517\) | 3.61073 | 0.158800 | ||||||||
\(518\) | 5.24970 | 0.230659 | ||||||||
\(519\) | −1.17561 | −0.0516034 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.1536 | −1.62773 | −0.813865 | − | 0.581055i | \(-0.802640\pi\) | ||||
−0.813865 | + | 0.581055i | \(0.802640\pi\) | |||||||
\(522\) | 3.87753 | 0.169715 | ||||||||
\(523\) | −18.8684 | −0.825057 | −0.412529 | − | 0.910945i | \(-0.635354\pi\) | ||||
−0.412529 | + | 0.910945i | \(0.635354\pi\) | |||||||
\(524\) | −7.85150 | −0.342995 | ||||||||
\(525\) | 6.35555 | 0.277379 | ||||||||
\(526\) | 5.53788 | 0.241463 | ||||||||
\(527\) | −0.782162 | −0.0340715 | ||||||||
\(528\) | 0.712721 | 0.0310172 | ||||||||
\(529\) | 55.0894 | 2.39519 | ||||||||
\(530\) | −15.4394 | −0.670644 | ||||||||
\(531\) | 11.4506 | 0.496913 | ||||||||
\(532\) | −0.855097 | −0.0370732 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15.6597 | 0.677661 | ||||||||
\(535\) | −28.9408 | −1.25122 | ||||||||
\(536\) | −7.34601 | −0.317299 | ||||||||
\(537\) | 0.249567 | 0.0107696 | ||||||||
\(538\) | −5.35511 | −0.230875 | ||||||||
\(539\) | −0.408118 | −0.0175789 | ||||||||
\(540\) | 2.70859 | 0.116559 | ||||||||
\(541\) | −34.2960 | −1.47450 | −0.737250 | − | 0.675620i | \(-0.763876\pi\) | ||||
−0.737250 | + | 0.675620i | \(0.763876\pi\) | |||||||
\(542\) | −29.8078 | −1.28036 | ||||||||
\(543\) | 0.442464 | 0.0189879 | ||||||||
\(544\) | −1.74023 | −0.0746117 | ||||||||
\(545\) | −66.3204 | −2.84085 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2529 | 1.29352 | 0.646761 | − | 0.762693i | \(-0.276123\pi\) | ||||
0.646761 | + | 0.762693i | \(0.276123\pi\) | |||||||
\(548\) | −11.6441 | −0.497413 | ||||||||
\(549\) | 11.6354 | 0.496587 | ||||||||
\(550\) | 2.83689 | 0.120966 | ||||||||
\(551\) | −3.77160 | −0.160676 | ||||||||
\(552\) | 27.0985 | 1.15339 | ||||||||
\(553\) | 4.27789 | 0.181914 | ||||||||
\(554\) | 3.18673 | 0.135391 | ||||||||
\(555\) | 16.1746 | 0.686575 | ||||||||
\(556\) | 6.23184 | 0.264289 | ||||||||
\(557\) | −23.7963 | −1.00828 | −0.504141 | − | 0.863622i | \(-0.668191\pi\) | ||||
−0.504141 | + | 0.863622i | \(0.668191\pi\) | |||||||
\(558\) | 2.07598 | 0.0878831 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.88489 | 0.248682 | ||||||||
\(561\) | −0.168176 | −0.00710040 | ||||||||
\(562\) | −27.6388 | −1.16587 | ||||||||
\(563\) | −20.0697 | −0.845839 | −0.422919 | − | 0.906167i | \(-0.638995\pi\) | ||||
−0.422919 | + | 0.906167i | \(0.638995\pi\) | |||||||
\(564\) | 7.11130 | 0.299440 | ||||||||
\(565\) | −4.60379 | −0.193683 | ||||||||
\(566\) | −20.2402 | −0.850760 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −45.0087 | −1.88852 | ||||||||
\(569\) | −35.6422 | −1.49420 | −0.747100 | − | 0.664712i | \(-0.768554\pi\) | ||||
−0.747100 | + | 0.664712i | \(0.768554\pi\) | |||||||
\(570\) | 3.92089 | 0.164228 | ||||||||
\(571\) | 27.9511 | 1.16972 | 0.584859 | − | 0.811135i | \(-0.301150\pi\) | ||||
0.584859 | + | 0.811135i | \(0.301150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.8545 | 0.662333 | ||||||||
\(574\) | 10.9814 | 0.458354 | ||||||||
\(575\) | 56.1629 | 2.34215 | ||||||||
\(576\) | 8.11156 | 0.337982 | ||||||||
\(577\) | −16.1295 | −0.671481 | −0.335741 | − | 0.941954i | \(-0.608987\pi\) | ||||
−0.335741 | + | 0.941954i | \(0.608987\pi\) | |||||||
\(578\) | 18.4075 | 0.765649 | ||||||||
\(579\) | −4.24322 | −0.176342 | ||||||||
\(580\) | −9.60270 | −0.398730 | ||||||||
\(581\) | 4.60644 | 0.191107 | ||||||||
\(582\) | −13.4785 | −0.558701 | ||||||||
\(583\) | 1.70965 | 0.0708063 | ||||||||
\(584\) | 44.6692 | 1.84842 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.58422 | 0.230682 | ||||||||
\(587\) | 25.2546 | 1.04237 | 0.521184 | − | 0.853445i | \(-0.325491\pi\) | ||||
0.521184 | + | 0.853445i | \(0.325491\pi\) | |||||||
\(588\) | −0.803784 | −0.0331475 | ||||||||
\(589\) | −2.01927 | −0.0832025 | ||||||||
\(590\) | 42.2023 | 1.73744 | ||||||||
\(591\) | −9.13404 | −0.375724 | ||||||||
\(592\) | 8.38233 | 0.344512 | ||||||||
\(593\) | 3.67915 | 0.151085 | 0.0755424 | − | 0.997143i | \(-0.475931\pi\) | ||||
0.0755424 | + | 0.997143i | \(0.475931\pi\) | |||||||
\(594\) | 0.446365 | 0.0183146 | ||||||||
\(595\) | −1.38862 | −0.0569278 | ||||||||
\(596\) | 2.15264 | 0.0881758 | ||||||||
\(597\) | 9.66460 | 0.395546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.1745 | −0.987744 | −0.493872 | − | 0.869535i | \(-0.664419\pi\) | ||||
−0.493872 | + | 0.869535i | \(0.664419\pi\) | |||||||
\(600\) | 19.4896 | 0.795659 | ||||||||
\(601\) | −9.85564 | −0.402020 | −0.201010 | − | 0.979589i | \(-0.564422\pi\) | ||||
−0.201010 | + | 0.979589i | \(0.564422\pi\) | |||||||
\(602\) | 2.54702 | 0.103809 | ||||||||
\(603\) | −2.39553 | −0.0975537 | ||||||||
\(604\) | −6.12566 | −0.249249 | ||||||||
\(605\) | 36.5065 | 1.48420 | ||||||||
\(606\) | 1.32358 | 0.0537666 | ||||||||
\(607\) | 4.87139 | 0.197724 | 0.0988619 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988619 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(608\) | −4.49266 | −0.182202 | ||||||||
\(609\) | −3.54528 | −0.143662 | ||||||||
\(610\) | 42.8835 | 1.73630 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.331221 | −0.0133888 | ||||||||
\(613\) | 19.7564 | 0.797954 | 0.398977 | − | 0.916961i | \(-0.369365\pi\) | ||||
0.398977 | + | 0.916961i | \(0.369365\pi\) | |||||||
\(614\) | −0.159246 | −0.00642663 | ||||||||
\(615\) | 33.8342 | 1.36433 | ||||||||
\(616\) | −1.25151 | −0.0504248 | ||||||||
\(617\) | 4.52746 | 0.182269 | 0.0911343 | − | 0.995839i | \(-0.470951\pi\) | ||||
0.0911343 | + | 0.995839i | \(0.470951\pi\) | |||||||
\(618\) | −14.8213 | −0.596200 | ||||||||
\(619\) | 40.5342 | 1.62921 | 0.814604 | − | 0.580017i | \(-0.196954\pi\) | ||||
0.814604 | + | 0.580017i | \(0.196954\pi\) | |||||||
\(620\) | −5.14116 | −0.206474 | ||||||||
\(621\) | 8.83682 | 0.354609 | ||||||||
\(622\) | 29.6278 | 1.18797 | ||||||||
\(623\) | −14.3179 | −0.573633 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3847 | −0.655389 | ||||||||
\(626\) | −32.3893 | −1.29454 | ||||||||
\(627\) | −0.434172 | −0.0173391 | ||||||||
\(628\) | −14.6246 | −0.583585 | ||||||||
\(629\) | −1.97792 | −0.0788648 | ||||||||
\(630\) | 3.68561 | 0.146838 | ||||||||
\(631\) | −9.09532 | −0.362079 | −0.181039 | − | 0.983476i | \(-0.557946\pi\) | ||||
−0.181039 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(632\) | 13.1183 | 0.521819 | ||||||||
\(633\) | −24.0587 | −0.956248 | ||||||||
\(634\) | −26.2197 | −1.04132 | ||||||||
\(635\) | 55.8817 | 2.21760 | ||||||||
\(636\) | 3.36714 | 0.133516 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.58249 | −0.0626512 | ||||||||
\(639\) | −14.6773 | −0.580626 | ||||||||
\(640\) | 1.43426 | 0.0566940 | ||||||||
\(641\) | −27.6571 | −1.09239 | −0.546194 | − | 0.837658i | \(-0.683924\pi\) | ||||
−0.546194 | + | 0.837658i | \(0.683924\pi\) | |||||||
\(642\) | −9.39315 | −0.370718 | ||||||||
\(643\) | 27.7846 | 1.09572 | 0.547859 | − | 0.836571i | \(-0.315443\pi\) | ||||
0.547859 | + | 0.836571i | \(0.315443\pi\) | |||||||
\(644\) | −7.10290 | −0.279893 | ||||||||
\(645\) | 7.84750 | 0.308995 | ||||||||
\(646\) | −0.479468 | −0.0188644 | ||||||||
\(647\) | −42.0045 | −1.65137 | −0.825685 | − | 0.564132i | \(-0.809211\pi\) | ||||
−0.825685 | + | 0.564132i | \(0.809211\pi\) | |||||||
\(648\) | 3.06655 | 0.120465 | ||||||||
\(649\) | −4.67318 | −0.183438 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.89809 | −0.0743922 | ||||||||
\(652\) | −15.7400 | −0.616426 | ||||||||
\(653\) | −6.17528 | −0.241657 | −0.120829 | − | 0.992673i | \(-0.538555\pi\) | ||||
−0.120829 | + | 0.992673i | \(0.538555\pi\) | |||||||
\(654\) | −21.5252 | −0.841703 | ||||||||
\(655\) | −32.9168 | −1.28617 | ||||||||
\(656\) | 17.5342 | 0.684596 | ||||||||
\(657\) | 14.5666 | 0.568298 | ||||||||
\(658\) | 9.67642 | 0.377226 | ||||||||
\(659\) | −16.3984 | −0.638790 | −0.319395 | − | 0.947622i | \(-0.603480\pi\) | ||||
−0.319395 | + | 0.947622i | \(0.603480\pi\) | |||||||
\(660\) | −1.10542 | −0.0430286 | ||||||||
\(661\) | 5.90374 | 0.229629 | 0.114814 | − | 0.993387i | \(-0.463373\pi\) | ||||
0.114814 | + | 0.993387i | \(0.463373\pi\) | |||||||
\(662\) | 6.06786 | 0.235834 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.1259 | 0.548190 | ||||||||
\(665\) | −3.58493 | −0.139018 | ||||||||
\(666\) | 5.24970 | 0.203422 | ||||||||
\(667\) | −31.3290 | −1.21306 | ||||||||
\(668\) | 4.82292 | 0.186605 | ||||||||
\(669\) | 18.1487 | 0.701668 | ||||||||
\(670\) | −8.82899 | −0.341094 | ||||||||
\(671\) | −4.74861 | −0.183318 | ||||||||
\(672\) | −4.22306 | −0.162908 | ||||||||
\(673\) | −1.67667 | −0.0646308 | −0.0323154 | − | 0.999478i | \(-0.510288\pi\) | ||||
−0.0323154 | + | 0.999478i | \(0.510288\pi\) | |||||||
\(674\) | −6.04741 | −0.232937 | ||||||||
\(675\) | 6.35555 | 0.244625 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.3324 | 1.28107 | 0.640535 | − | 0.767929i | \(-0.278713\pi\) | ||||
0.640535 | + | 0.767929i | \(0.278713\pi\) | |||||||
\(678\) | −1.49423 | −0.0573854 | ||||||||
\(679\) | 12.3236 | 0.472934 | ||||||||
\(680\) | −4.25826 | −0.163297 | ||||||||
\(681\) | 16.2228 | 0.621659 | ||||||||
\(682\) | −0.847243 | −0.0324426 | ||||||||
\(683\) | 24.7425 | 0.946746 | 0.473373 | − | 0.880862i | \(-0.343036\pi\) | ||||
0.473373 | + | 0.880862i | \(0.343036\pi\) | |||||||
\(684\) | −0.855097 | −0.0326955 | ||||||||
\(685\) | −48.8171 | −1.86521 | ||||||||
\(686\) | −1.09372 | −0.0417583 | ||||||||
\(687\) | −0.980804 | −0.0374200 | ||||||||
\(688\) | 4.06688 | 0.155048 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 32.5690 | 1.23988 | ||||||||
\(691\) | −48.1772 | −1.83275 | −0.916374 | − | 0.400323i | \(-0.868898\pi\) | ||||
−0.916374 | + | 0.400323i | \(0.868898\pi\) | |||||||
\(692\) | 0.944934 | 0.0359210 | ||||||||
\(693\) | −0.408118 | −0.0155031 | ||||||||
\(694\) | −31.7755 | −1.20618 | ||||||||
\(695\) | 26.1265 | 0.991034 | ||||||||
\(696\) | −10.8717 | −0.412092 | ||||||||
\(697\) | −4.13743 | −0.156716 | ||||||||
\(698\) | −16.8904 | −0.639311 | ||||||||
\(699\) | −19.4629 | −0.736154 | ||||||||
\(700\) | −5.10849 | −0.193083 | ||||||||
\(701\) | 41.5798 | 1.57045 | 0.785224 | − | 0.619212i | \(-0.212548\pi\) | ||||
0.785224 | + | 0.619212i | \(0.212548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.10630 | −0.192588 | ||||||||
\(704\) | −3.31047 | −0.124768 | ||||||||
\(705\) | 29.8136 | 1.12284 | ||||||||
\(706\) | −20.4499 | −0.769642 | ||||||||
\(707\) | −1.21016 | −0.0455129 | ||||||||
\(708\) | −9.20379 | −0.345900 | ||||||||
\(709\) | 35.6206 | 1.33776 | 0.668879 | − | 0.743371i | \(-0.266774\pi\) | ||||
0.668879 | + | 0.743371i | \(0.266774\pi\) | |||||||
\(710\) | −54.0948 | −2.03014 | ||||||||
\(711\) | 4.27789 | 0.160433 | ||||||||
\(712\) | −43.9064 | −1.64546 | ||||||||
\(713\) | −16.7731 | −0.628158 | ||||||||
\(714\) | −0.450696 | −0.0168669 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.200598 | −0.00749671 | ||||||||
\(717\) | −18.7859 | −0.701573 | ||||||||
\(718\) | 11.9973 | 0.447737 | ||||||||
\(719\) | 8.40093 | 0.313302 | 0.156651 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156651 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(720\) | 5.88489 | 0.219317 | ||||||||
\(721\) | 13.5513 | 0.504678 | ||||||||
\(722\) | 19.5428 | 0.727308 | ||||||||
\(723\) | 9.08287 | 0.337796 | ||||||||
\(724\) | −0.355645 | −0.0132175 | ||||||||
\(725\) | −22.5322 | −0.836824 | ||||||||
\(726\) | 11.8487 | 0.439747 | ||||||||
\(727\) | −16.4191 | −0.608950 | −0.304475 | − | 0.952520i | \(-0.598481\pi\) | ||||
−0.304475 | + | 0.952520i | \(0.598481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 53.6868 | 1.98704 | ||||||||
\(731\) | −0.959635 | −0.0354934 | ||||||||
\(732\) | −9.35235 | −0.345673 | ||||||||
\(733\) | 50.9943 | 1.88352 | 0.941759 | − | 0.336288i | \(-0.109171\pi\) | ||||
0.941759 | + | 0.336288i | \(0.109171\pi\) | |||||||
\(734\) | −12.9699 | −0.478727 | ||||||||
\(735\) | −3.36980 | −0.124297 | ||||||||
\(736\) | −37.3185 | −1.37558 | ||||||||
\(737\) | 0.977659 | 0.0360125 | ||||||||
\(738\) | 10.9814 | 0.404230 | ||||||||
\(739\) | 13.3896 | 0.492545 | 0.246272 | − | 0.969201i | \(-0.420794\pi\) | ||||
0.246272 | + | 0.969201i | \(0.420794\pi\) | |||||||
\(740\) | −13.0009 | −0.477923 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.58169 | 0.168199 | ||||||||
\(743\) | −35.2833 | −1.29442 | −0.647209 | − | 0.762313i | \(-0.724064\pi\) | ||||
−0.647209 | + | 0.762313i | \(0.724064\pi\) | |||||||
\(744\) | −5.82059 | −0.213393 | ||||||||
\(745\) | 9.02479 | 0.330643 | ||||||||
\(746\) | −9.43037 | −0.345270 | ||||||||
\(747\) | 4.60644 | 0.168541 | ||||||||
\(748\) | 0.135177 | 0.00494257 | ||||||||
\(749\) | 8.58829 | 0.313809 | ||||||||
\(750\) | 4.99602 | 0.182429 | ||||||||
\(751\) | −17.2150 | −0.628183 | −0.314091 | − | 0.949393i | \(-0.601700\pi\) | ||||
−0.314091 | + | 0.949393i | \(0.601700\pi\) | |||||||
\(752\) | 15.4506 | 0.563424 | ||||||||
\(753\) | 11.7323 | 0.427548 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.6813 | −0.934639 | ||||||||
\(756\) | −0.803784 | −0.0292333 | ||||||||
\(757\) | 25.2096 | 0.916260 | 0.458130 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458130 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(758\) | 33.3615 | 1.21174 | ||||||||
\(759\) | −3.60646 | −0.130906 | ||||||||
\(760\) | −10.9933 | −0.398770 | ||||||||
\(761\) | 5.13105 | 0.186000 | 0.0930001 | − | 0.995666i | \(-0.470354\pi\) | ||||
0.0930001 | + | 0.995666i | \(0.470354\pi\) | |||||||
\(762\) | 18.1372 | 0.657042 | ||||||||
\(763\) | 19.6808 | 0.712493 | ||||||||
\(764\) | −12.7436 | −0.461048 | ||||||||
\(765\) | −1.38862 | −0.0502056 | ||||||||
\(766\) | 28.1733 | 1.01794 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −15.7576 | −0.568604 | ||||||||
\(769\) | 20.5305 | 0.740349 | 0.370174 | − | 0.928962i | \(-0.379298\pi\) | ||||
0.370174 | + | 0.928962i | \(0.379298\pi\) | |||||||
\(770\) | −1.50416 | −0.0542062 | ||||||||
\(771\) | 20.0321 | 0.721439 | ||||||||
\(772\) | 3.41063 | 0.122751 | ||||||||
\(773\) | 10.8128 | 0.388911 | 0.194455 | − | 0.980911i | \(-0.437706\pi\) | ||||
0.194455 | + | 0.980911i | \(0.437706\pi\) | |||||||
\(774\) | 2.54702 | 0.0915507 | ||||||||
\(775\) | −12.0634 | −0.433331 | ||||||||
\(776\) | 37.7907 | 1.35661 | ||||||||
\(777\) | −4.79988 | −0.172195 | ||||||||
\(778\) | −18.0928 | −0.648658 | ||||||||
\(779\) | −10.6814 | −0.382701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.99007 | 0.214342 | ||||||||
\(782\) | −3.98272 | −0.142422 | ||||||||
\(783\) | −3.54528 | −0.126698 | ||||||||
\(784\) | −1.74636 | −0.0623701 | ||||||||
\(785\) | −61.3125 | −2.18834 | ||||||||
\(786\) | −10.6836 | −0.381072 | ||||||||
\(787\) | −30.3280 | −1.08108 | −0.540538 | − | 0.841320i | \(-0.681779\pi\) | ||||
−0.540538 | + | 0.841320i | \(0.681779\pi\) | |||||||
\(788\) | 7.34180 | 0.261541 | ||||||||
\(789\) | −5.06336 | −0.180260 | ||||||||
\(790\) | 15.7666 | 0.560951 | ||||||||
\(791\) | 1.36619 | 0.0485762 | ||||||||
\(792\) | −1.25151 | −0.0444705 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.65047 | 0.342482 | ||||||||
\(795\) | 14.1164 | 0.500659 | ||||||||
\(796\) | −7.76825 | −0.275338 | ||||||||
\(797\) | −18.9162 | −0.670046 | −0.335023 | − | 0.942210i | \(-0.608744\pi\) | ||||
−0.335023 | + | 0.942210i | \(0.608744\pi\) | |||||||
\(798\) | −1.16354 | −0.0411888 | ||||||||
\(799\) | −3.64576 | −0.128978 | ||||||||
\(800\) | −26.8399 | −0.948934 | ||||||||
\(801\) | −14.3179 | −0.505897 | ||||||||
\(802\) | −11.8232 | −0.417492 | ||||||||
\(803\) | −5.94489 | −0.209791 | ||||||||
\(804\) | 1.92549 | 0.0679068 | ||||||||
\(805\) | −29.7783 | −1.04955 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.89625 | 0.172356 | ||||||||
\(808\) | −3.71102 | −0.130553 | ||||||||
\(809\) | 33.8433 | 1.18987 | 0.594934 | − | 0.803774i | \(-0.297178\pi\) | ||||
0.594934 | + | 0.803774i | \(0.297178\pi\) | |||||||
\(810\) | 3.68561 | 0.129499 | ||||||||
\(811\) | −29.5769 | −1.03859 | −0.519293 | − | 0.854596i | \(-0.673805\pi\) | ||||
−0.519293 | + | 0.854596i | \(0.673805\pi\) | |||||||
\(812\) | 2.84964 | 0.100003 | ||||||||
\(813\) | 27.2537 | 0.955829 | ||||||||
\(814\) | −2.14250 | −0.0750945 | ||||||||
\(815\) | −65.9887 | −2.31148 | ||||||||
\(816\) | −0.719637 | −0.0251923 | ||||||||
\(817\) | −2.47744 | −0.0866747 | ||||||||
\(818\) | −21.3452 | −0.746318 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.1954 | −0.949704 | ||||||||
\(821\) | −12.1069 | −0.422533 | −0.211266 | − | 0.977429i | \(-0.567759\pi\) | ||||
−0.211266 | + | 0.977429i | \(0.567759\pi\) | |||||||
\(822\) | −15.8443 | −0.552633 | ||||||||
\(823\) | −55.2074 | −1.92441 | −0.962204 | − | 0.272330i | \(-0.912206\pi\) | ||||
−0.962204 | + | 0.272330i | \(0.912206\pi\) | |||||||
\(824\) | 41.5557 | 1.44766 | ||||||||
\(825\) | −2.59381 | −0.0903049 | ||||||||
\(826\) | −12.5237 | −0.435755 | ||||||||
\(827\) | 30.5277 | 1.06155 | 0.530777 | − | 0.847512i | \(-0.321900\pi\) | ||||
0.530777 | + | 0.847512i | \(0.321900\pi\) | |||||||
\(828\) | −7.10290 | −0.246843 | ||||||||
\(829\) | −2.22089 | −0.0771346 | −0.0385673 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385673 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(830\) | 16.9775 | 0.589299 | ||||||||
\(831\) | −2.91367 | −0.101074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.412077 | 0.0142776 | ||||||||
\(834\) | 8.47972 | 0.293629 | ||||||||
\(835\) | 20.2197 | 0.699732 | ||||||||
\(836\) | 0.348980 | 0.0120697 | ||||||||
\(837\) | −1.89809 | −0.0656077 | ||||||||
\(838\) | −2.35074 | −0.0812050 | ||||||||
\(839\) | 10.0791 | 0.347970 | 0.173985 | − | 0.984748i | \(-0.444336\pi\) | ||||
0.173985 | + | 0.984748i | \(0.444336\pi\) | |||||||
\(840\) | −10.3336 | −0.356545 | ||||||||
\(841\) | −16.4310 | −0.566587 | ||||||||
\(842\) | 18.7955 | 0.647737 | ||||||||
\(843\) | 25.2705 | 0.870363 | ||||||||
\(844\) | 19.3380 | 0.665642 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.67642 | 0.332682 | ||||||||
\(847\) | −10.8334 | −0.372241 | ||||||||
\(848\) | 7.31570 | 0.251222 | ||||||||
\(849\) | 18.5059 | 0.635121 | ||||||||
\(850\) | −2.86442 | −0.0982488 | ||||||||
\(851\) | −42.4157 | −1.45399 | ||||||||
\(852\) | 11.7974 | 0.404172 | ||||||||
\(853\) | −13.2747 | −0.454516 | −0.227258 | − | 0.973835i | \(-0.572976\pi\) | ||||
−0.227258 | + | 0.973835i | \(0.572976\pi\) | |||||||
\(854\) | −12.7258 | −0.435469 | ||||||||
\(855\) | −3.58493 | −0.122602 | ||||||||
\(856\) | 26.3364 | 0.900159 | ||||||||
\(857\) | 24.4586 | 0.835490 | 0.417745 | − | 0.908564i | \(-0.362821\pi\) | ||||
0.417745 | + | 0.908564i | \(0.362821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.20774 | 0.0753272 | 0.0376636 | − | 0.999290i | \(-0.488008\pi\) | ||||
0.0376636 | + | 0.999290i | \(0.488008\pi\) | |||||||
\(860\) | −6.30769 | −0.215091 | ||||||||
\(861\) | −10.0404 | −0.342177 | ||||||||
\(862\) | −13.5782 | −0.462476 | ||||||||
\(863\) | −9.06990 | −0.308743 | −0.154371 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154371 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(864\) | −4.22306 | −0.143672 | ||||||||
\(865\) | 3.96156 | 0.134697 | ||||||||
\(866\) | 2.07057 | 0.0703609 | ||||||||
\(867\) | −16.8302 | −0.571583 | ||||||||
\(868\) | 1.52566 | 0.0517842 | ||||||||
\(869\) | −1.74588 | −0.0592250 | ||||||||
\(870\) | −13.0665 | −0.442995 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 60.3521 | 2.04378 | ||||||||
\(873\) | 12.3236 | 0.417089 | ||||||||
\(874\) | −10.2820 | −0.347793 | ||||||||
\(875\) | −4.56793 | −0.154424 | ||||||||
\(876\) | −11.7084 | −0.395591 | ||||||||
\(877\) | 5.06468 | 0.171022 | 0.0855110 | − | 0.996337i | \(-0.472748\pi\) | ||||
0.0855110 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(878\) | 5.00202 | 0.168810 | ||||||||
\(879\) | −5.10573 | −0.172212 | ||||||||
\(880\) | −2.40173 | −0.0809622 | ||||||||
\(881\) | −10.4132 | −0.350828 | −0.175414 | − | 0.984495i | \(-0.556126\pi\) | ||||
−0.175414 | + | 0.984495i | \(0.556126\pi\) | |||||||
\(882\) | −1.09372 | −0.0368274 | ||||||||
\(883\) | 39.6733 | 1.33511 | 0.667556 | − | 0.744560i | \(-0.267340\pi\) | ||||
0.667556 | + | 0.744560i | \(0.267340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.5861 | −1.29706 | ||||||||
\(886\) | −31.0567 | −1.04337 | ||||||||
\(887\) | −19.9363 | −0.669394 | −0.334697 | − | 0.942326i | \(-0.608634\pi\) | ||||
−0.334697 | + | 0.942326i | \(0.608634\pi\) | |||||||
\(888\) | −14.7190 | −0.493939 | ||||||||
\(889\) | −16.5831 | −0.556179 | ||||||||
\(890\) | −52.7700 | −1.76886 | ||||||||
\(891\) | −0.408118 | −0.0136725 | ||||||||
\(892\) | −14.5876 | −0.488429 | ||||||||
\(893\) | −9.41209 | −0.314964 | ||||||||
\(894\) | 2.92912 | 0.0979646 | ||||||||
\(895\) | −0.840992 | −0.0281113 | ||||||||
\(896\) | −0.425621 | −0.0142190 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.9942 | −1.30125 | ||||||||
\(899\) | 6.72927 | 0.224434 | ||||||||
\(900\) | −5.10849 | −0.170283 | ||||||||
\(901\) | −1.72623 | −0.0575092 | ||||||||
\(902\) | −4.48169 | −0.149224 | ||||||||
\(903\) | −2.32877 | −0.0774967 | ||||||||
\(904\) | 4.18949 | 0.139340 | ||||||||
\(905\) | −1.49101 | −0.0495630 | ||||||||
\(906\) | −8.33524 | −0.276920 | ||||||||
\(907\) | 25.9765 | 0.862535 | 0.431268 | − | 0.902224i | \(-0.358066\pi\) | ||||
0.431268 | + | 0.902224i | \(0.358066\pi\) | |||||||
\(908\) | −13.0396 | −0.432735 | ||||||||
\(909\) | −1.21016 | −0.0401386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.4073 | 0.874911 | 0.437456 | − | 0.899240i | \(-0.355880\pi\) | ||||
0.437456 | + | 0.899240i | \(0.355880\pi\) | |||||||
\(912\) | −1.85785 | −0.0615196 | ||||||||
\(913\) | −1.87997 | −0.0622179 | ||||||||
\(914\) | −34.4189 | −1.13848 | ||||||||
\(915\) | −39.2090 | −1.29621 | ||||||||
\(916\) | 0.788355 | 0.0260480 | ||||||||
\(917\) | 9.76818 | 0.322574 | ||||||||
\(918\) | −0.450696 | −0.0148752 | ||||||||
\(919\) | −24.8301 | −0.819068 | −0.409534 | − | 0.912295i | \(-0.634309\pi\) | ||||
−0.409534 | + | 0.912295i | \(0.634309\pi\) | |||||||
\(920\) | −91.3166 | −3.01062 | ||||||||
\(921\) | 0.145600 | 0.00479770 | ||||||||
\(922\) | −23.2173 | −0.764620 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.328038 | 0.0107917 | ||||||||
\(925\) | −30.5059 | −1.00303 | ||||||||
\(926\) | 8.88164 | 0.291869 | ||||||||
\(927\) | 13.5513 | 0.445084 | ||||||||
\(928\) | 14.9719 | 0.491477 | ||||||||
\(929\) | 18.6678 | 0.612472 | 0.306236 | − | 0.951956i | \(-0.400930\pi\) | ||||
0.306236 | + | 0.951956i | \(0.400930\pi\) | |||||||
\(930\) | −6.99563 | −0.229396 | ||||||||
\(931\) | 1.06384 | 0.0348659 | ||||||||
\(932\) | 15.6439 | 0.512435 | ||||||||
\(933\) | −27.0891 | −0.886858 | ||||||||
\(934\) | 29.3431 | 0.960134 | ||||||||
\(935\) | 0.566719 | 0.0185337 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.93693 | 0.0959453 | 0.0479727 | − | 0.998849i | \(-0.484724\pi\) | ||||
0.0479727 | + | 0.998849i | \(0.484724\pi\) | |||||||
\(938\) | 2.62003 | 0.0855472 | ||||||||
\(939\) | 29.6140 | 0.966416 | ||||||||
\(940\) | −23.9637 | −0.781609 | ||||||||
\(941\) | 50.7259 | 1.65362 | 0.826808 | − | 0.562484i | \(-0.190154\pi\) | ||||
0.826808 | + | 0.562484i | \(0.190154\pi\) | |||||||
\(942\) | −19.8998 | −0.648372 | ||||||||
\(943\) | −88.7254 | −2.88930 | ||||||||
\(944\) | −19.9969 | −0.650842 | ||||||||
\(945\) | −3.36980 | −0.109620 | ||||||||
\(946\) | −1.03948 | −0.0337965 | ||||||||
\(947\) | 25.8256 | 0.839220 | 0.419610 | − | 0.907704i | \(-0.362167\pi\) | ||||
0.419610 | + | 0.907704i | \(0.362167\pi\) | |||||||
\(948\) | −3.43850 | −0.111677 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.39493 | −0.239923 | ||||||||
\(951\) | 23.9730 | 0.777378 | ||||||||
\(952\) | 1.26365 | 0.0409553 | ||||||||
\(953\) | −42.6541 | −1.38170 | −0.690851 | − | 0.722998i | \(-0.742764\pi\) | ||||
−0.690851 | + | 0.722998i | \(0.742764\pi\) | |||||||
\(954\) | 4.58169 | 0.148338 | ||||||||
\(955\) | −53.4266 | −1.72884 | ||||||||
\(956\) | 15.0998 | 0.488363 | ||||||||
\(957\) | 1.44689 | 0.0467713 | ||||||||
\(958\) | 10.6666 | 0.344621 | ||||||||
\(959\) | 14.4867 | 0.467798 | ||||||||
\(960\) | −27.3343 | −0.882212 | ||||||||
\(961\) | −27.3972 | −0.883782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.58829 | 0.276754 | ||||||||
\(964\) | −7.30067 | −0.235139 | ||||||||
\(965\) | 14.2988 | 0.460295 | ||||||||
\(966\) | −9.66498 | −0.310966 | ||||||||
\(967\) | −37.4458 | −1.20418 | −0.602088 | − | 0.798430i | \(-0.705664\pi\) | ||||
−0.602088 | + | 0.798430i | \(0.705664\pi\) | |||||||
\(968\) | −33.2212 | −1.06777 | ||||||||
\(969\) | 0.438384 | 0.0140829 | ||||||||
\(970\) | 45.4197 | 1.45834 | ||||||||
\(971\) | 22.1197 | 0.709855 | 0.354928 | − | 0.934894i | \(-0.384505\pi\) | ||||
0.354928 | + | 0.934894i | \(0.384505\pi\) | |||||||
\(972\) | −0.803784 | −0.0257814 | ||||||||
\(973\) | −7.75313 | −0.248554 | ||||||||
\(974\) | −23.9381 | −0.767026 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.3196 | −0.650415 | ||||||||
\(977\) | −39.8028 | −1.27340 | −0.636702 | − | 0.771110i | \(-0.719702\pi\) | ||||
−0.636702 | + | 0.771110i | \(0.719702\pi\) | |||||||
\(978\) | −21.4176 | −0.684859 | ||||||||
\(979\) | 5.84337 | 0.186755 | ||||||||
\(980\) | 2.70859 | 0.0865228 | ||||||||
\(981\) | 19.6808 | 0.628360 | ||||||||
\(982\) | −36.2720 | −1.15749 | ||||||||
\(983\) | −21.8790 | −0.697832 | −0.348916 | − | 0.937154i | \(-0.613450\pi\) | ||||
−0.348916 | + | 0.937154i | \(0.613450\pi\) | |||||||
\(984\) | −30.7894 | −0.981530 | ||||||||
\(985\) | 30.7799 | 0.980729 | ||||||||
\(986\) | 1.59784 | 0.0508856 | ||||||||
\(987\) | −8.84728 | −0.281612 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.5790 | −0.654373 | ||||||||
\(990\) | −1.50416 | −0.0478054 | ||||||||
\(991\) | 35.6459 | 1.13233 | 0.566164 | − | 0.824293i | \(-0.308427\pi\) | ||||
0.566164 | + | 0.824293i | \(0.308427\pi\) | |||||||
\(992\) | 8.01577 | 0.254501 | ||||||||
\(993\) | −5.54793 | −0.176058 | ||||||||
\(994\) | 16.0528 | 0.509165 | ||||||||
\(995\) | −32.5678 | −1.03247 | ||||||||
\(996\) | −3.70258 | −0.117321 | ||||||||
\(997\) | 46.5398 | 1.47393 | 0.736965 | − | 0.675931i | \(-0.236258\pi\) | ||||
0.736965 | + | 0.675931i | \(0.236258\pi\) | |||||||
\(998\) | 44.4900 | 1.40831 | ||||||||
\(999\) | −4.79988 | −0.151861 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3549.2.a.bg.1.6 | ✓ | 15 | |
13.12 | even | 2 | 3549.2.a.bh.1.10 | yes | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.6 | ✓ | 15 | 1.1 | even | 1 | trivial | |
3549.2.a.bh.1.10 | yes | 15 | 13.12 | even | 2 |