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 | 1.10 | ||
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 | \(-0.373619\pi\) | ||||
0.386687 | + | 0.922211i | \(0.373619\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.803784 | −0.401892 | ||||||||
\(5\) | 3.36980 | 1.50702 | 0.753510 | − | 0.657436i | \(-0.228359\pi\) | ||||
0.753510 | + | 0.657436i | \(0.228359\pi\) | |||||||
\(6\) | 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 | \(-0.480403\pi\) | ||||
0.0615260 | + | 0.998105i | \(0.480403\pi\) | |||||||
\(12\) | −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 | \(-0.538941\pi\) | ||||
−0.122031 | + | 0.992526i | \(0.538941\pi\) | |||||||
\(20\) | −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 | \(-0.445477\pi\) | ||||
0.170454 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(32\) | 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 | \(-0.370901\pi\) | ||||
0.394547 | + | 0.918876i | \(0.370901\pi\) | |||||||
\(38\) | −1.16354 | −0.188751 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.3336 | −1.63389 | ||||||||
\(41\) | 10.0404 | 1.56805 | 0.784025 | − | 0.620729i | \(-0.213163\pi\) | ||||
0.784025 | + | 0.620729i | \(0.213163\pi\) | |||||||
\(42\) | −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 | \(-0.276751\pi\) | ||||
0.645254 | + | 0.763968i | \(0.276751\pi\) | |||||||
\(48\) | −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 | \(-0.767727\pi\) | ||||
−0.745369 | + | 0.666652i | \(0.767727\pi\) | |||||||
\(60\) | −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 | \(-0.453254\pi\) | ||||
0.146330 | + | 0.989236i | \(0.453254\pi\) | |||||||
\(68\) | −0.331221 | −0.0401665 | ||||||||
\(69\) | 8.83682 | 1.06383 | ||||||||
\(70\) | −3.68561 | −0.440514 | ||||||||
\(71\) | 14.6773 | 1.74188 | 0.870939 | − | 0.491391i | \(-0.163511\pi\) | ||||
0.870939 | + | 0.491391i | \(0.163511\pi\) | |||||||
\(72\) | −3.06655 | −0.361396 | ||||||||
\(73\) | −14.5666 | −1.70489 | −0.852447 | − | 0.522814i | \(-0.824882\pi\) | ||||
−0.852447 | + | 0.522814i | \(0.824882\pi\) | |||||||
\(74\) | 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 | \(-0.581355\pi\) | ||||
−0.252811 | + | 0.967516i | \(0.581355\pi\) | |||||||
\(84\) | 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 | \(-0.225764\pi\) | ||||
0.758846 | + | 0.651271i | \(0.225764\pi\) | |||||||
\(90\) | 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 | \(-0.715159\pi\) | ||||
−0.625633 | + | 0.780117i | \(0.715159\pi\) | |||||||
\(98\) | 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 | \(-0.891570\pi\) | ||||
−0.942540 | + | 0.334093i | \(0.891570\pi\) | |||||||
\(110\) | 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 | \(-0.712397\pi\) | ||||
−0.618839 | + | 0.785518i | \(0.712397\pi\) | |||||||
\(138\) | 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 | \(-0.465011\pi\) | ||||
0.109701 | + | 0.993965i | \(0.465011\pi\) | |||||||
\(150\) | 6.95117 | 0.567561 | ||||||||
\(151\) | −7.62102 | −0.620190 | −0.310095 | − | 0.950706i | \(-0.600361\pi\) | ||||
−0.310095 | + | 0.950706i | \(0.600361\pi\) | |||||||
\(152\) | 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 | \(-0.778204\pi\) | ||||
−0.766905 | + | 0.641760i | \(0.778204\pi\) | |||||||
\(164\) | −8.07033 | −0.630187 | ||||||||
\(165\) | 1.37527 | 0.107065 | ||||||||
\(166\) | −5.03814 | −0.391036 | ||||||||
\(167\) | 6.00027 | 0.464315 | 0.232158 | − | 0.972678i | \(-0.425422\pi\) | ||||
0.232158 | + | 0.972678i | \(0.425422\pi\) | |||||||
\(168\) | 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 | \(-0.451198\pi\) | ||||
0.152717 | + | 0.988270i | \(0.451198\pi\) | |||||||
\(194\) | −13.4785 | −0.967698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.803784 | −0.0574131 | ||||||||
\(197\) | 9.13404 | 0.650773 | 0.325387 | − | 0.945581i | \(-0.394506\pi\) | ||||
0.325387 | + | 0.945581i | \(0.394506\pi\) | |||||||
\(198\) | 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 | \(-0.707892\pi\) | ||||
−0.607662 | + | 0.794196i | \(0.707892\pi\) | |||||||
\(224\) | −4.22306 | −0.282165 | ||||||||
\(225\) | 6.35555 | 0.423703 | ||||||||
\(226\) | 1.49423 | 0.0993944 | ||||||||
\(227\) | −16.2228 | −1.07674 | −0.538372 | − | 0.842707i | \(-0.680961\pi\) | ||||
−0.538372 | + | 0.842707i | \(0.680961\pi\) | |||||||
\(228\) | 0.855097 | 0.0566302 | ||||||||
\(229\) | 0.980804 | 0.0648134 | 0.0324067 | − | 0.999475i | \(-0.489683\pi\) | ||||
0.0324067 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(230\) | 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 | \(-0.292141\pi\) | ||||
0.607580 | + | 0.794259i | \(0.292141\pi\) | |||||||
\(240\) | −5.88489 | −0.379868 | ||||||||
\(241\) | −9.08287 | −0.585079 | −0.292540 | − | 0.956253i | \(-0.594500\pi\) | ||||
−0.292540 | + | 0.956253i | \(0.594500\pi\) | |||||||
\(242\) | −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 | \(-0.810392\pi\) | ||||
−0.827772 | + | 0.561064i | \(0.810392\pi\) | |||||||
\(272\) | −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 | \(-0.771760\pi\) | ||||
−0.753757 | + | 0.657153i | \(0.771760\pi\) | |||||||
\(282\) | 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 | \(-0.452350\pi\) | ||||
0.149140 | + | 0.988816i | \(0.452350\pi\) | |||||||
\(294\) | 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 | \(-0.501323\pi\) | ||||
−0.00415493 | + | 0.999991i | \(0.501323\pi\) | |||||||
\(308\) | 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 | \(-0.735093\pi\) | ||||
−0.673229 | + | 0.739434i | \(0.735093\pi\) | |||||||
\(318\) | −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 | \(-0.451277\pi\) | ||||
0.152471 | + | 0.988308i | \(0.451277\pi\) | |||||||
\(332\) | 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 | \(-0.635633\pi\) | ||||
−0.413326 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(350\) | −6.95117 | −0.371556 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.72351 | 0.0918632 | ||||||||
\(353\) | −18.6976 | −0.995175 | −0.497587 | − | 0.867414i | \(-0.665781\pi\) | ||||
−0.497587 | + | 0.867414i | \(0.665781\pi\) | |||||||
\(354\) | −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 | \(-0.406521\pi\) | ||||
0.289470 | + | 0.957187i | \(0.406521\pi\) | |||||||
\(360\) | −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 | \(-0.213477\pi\) | ||||
0.783413 | + | 0.621501i | \(0.213477\pi\) | |||||||
\(380\) | 2.88151 | 0.147818 | ||||||||
\(381\) | −16.5831 | −0.849578 | ||||||||
\(382\) | 17.3404 | 0.887211 | ||||||||
\(383\) | 25.7592 | 1.31623 | 0.658117 | − | 0.752915i | \(-0.271353\pi\) | ||||
0.658117 | + | 0.752915i | \(0.271353\pi\) | |||||||
\(384\) | 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 | \(-0.428931\pi\) | ||||
0.221421 | + | 0.975178i | \(0.428931\pi\) | |||||||
\(398\) | 10.5703 | 0.529843 | ||||||||
\(399\) | 1.06384 | 0.0532586 | ||||||||
\(400\) | −11.0991 | −0.554955 | ||||||||
\(401\) | −10.8101 | −0.539832 | −0.269916 | − | 0.962884i | \(-0.586996\pi\) | ||||
−0.269916 | + | 0.962884i | \(0.586996\pi\) | |||||||
\(402\) | 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 | \(-0.660274\pi\) | ||||
−0.482507 | + | 0.875892i | \(0.660274\pi\) | |||||||
\(410\) | 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 | \(-0.362460\pi\) | ||||
0.418774 | + | 0.908091i | \(0.362460\pi\) | |||||||
\(422\) | −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 | \(-0.596653\pi\) | ||||
−0.298998 | + | 0.954254i | \(0.596653\pi\) | |||||||
\(432\) | −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 | \(-0.818200\pi\) | ||||
−0.841284 | + | 0.540594i | \(0.818200\pi\) | |||||||
\(450\) | 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 | \(-0.763309\pi\) | ||||
−0.736045 | + | 0.676933i | \(0.763309\pi\) | |||||||
\(458\) | 1.07272 | 0.0501250 | ||||||||
\(459\) | 0.412077 | 0.0192341 | ||||||||
\(460\) | −23.9353 | −1.11599 | ||||||||
\(461\) | −21.2279 | −0.988680 | −0.494340 | − | 0.869269i | \(-0.664590\pi\) | ||||
−0.494340 | + | 0.869269i | \(0.664590\pi\) | |||||||
\(462\) | −0.446365 | −0.0207668 | ||||||||
\(463\) | 8.12061 | 0.377397 | 0.188698 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188698 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(464\) | 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 | \(-0.428479\pi\) | ||||
0.222803 | + | 0.974863i | \(0.428479\pi\) | |||||||
\(480\) | 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 | \(-0.665160\pi\) | ||||
−0.495895 | + | 0.868382i | \(0.665160\pi\) | |||||||
\(488\) | −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 | \(-0.135702\pi\) | ||||
0.910494 | + | 0.413522i | \(0.135702\pi\) | |||||||
\(500\) | −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 | \(-0.838354\pi\) | ||||
−0.873803 | + | 0.486279i | \(0.838354\pi\) | |||||||
\(510\) | 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 | \(-0.236124\pi\) | ||||
0.737250 | + | 0.675620i | \(0.236124\pi\) | |||||||
\(542\) | −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 | \(-0.331809\pi\) | ||||
0.504141 | + | 0.863622i | \(0.331809\pi\) | |||||||
\(558\) | 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 | \(-0.391013\pi\) | ||||
0.335741 | + | 0.941954i | \(0.391013\pi\) | |||||||
\(578\) | −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 | \(-0.674509\pi\) | ||||
−0.521184 | + | 0.853445i | \(0.674509\pi\) | |||||||
\(588\) | −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 | \(-0.524069\pi\) | ||||
−0.0755424 | + | 0.997143i | \(0.524069\pi\) | |||||||
\(594\) | 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 | \(-0.630635\pi\) | ||||
−0.398977 | + | 0.916961i | \(0.630635\pi\) | |||||||
\(614\) | −0.159246 | −0.00642663 | ||||||||
\(615\) | 33.8342 | 1.36433 | ||||||||
\(616\) | 1.25151 | 0.0504248 | ||||||||
\(617\) | −4.52746 | −0.182269 | −0.0911343 | − | 0.995839i | \(-0.529049\pi\) | ||||
−0.0911343 | + | 0.995839i | \(0.529049\pi\) | |||||||
\(618\) | 14.8213 | 0.596200 | ||||||||
\(619\) | −40.5342 | −1.62921 | −0.814604 | − | 0.580017i | \(-0.803046\pi\) | ||||
−0.814604 | + | 0.580017i | \(0.803046\pi\) | |||||||
\(620\) | −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 | \(-0.442054\pi\) | ||||
0.181039 | + | 0.983476i | \(0.442054\pi\) | |||||||
\(632\) | −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 | \(-0.684557\pi\) | ||||
−0.547859 | + | 0.836571i | \(0.684557\pi\) | |||||||
\(644\) | 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 | \(-0.536627\pi\) | ||||
−0.114814 | + | 0.993387i | \(0.536627\pi\) | |||||||
\(662\) | 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 | \(-0.656964\pi\) | ||||
−0.473373 | + | 0.880862i | \(0.656964\pi\) | |||||||
\(684\) | 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 | \(-0.131102\pi\) | ||||
0.916374 | + | 0.400323i | \(0.131102\pi\) | |||||||
\(692\) | 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 | \(-0.733226\pi\) | ||||
−0.668879 | + | 0.743371i | \(0.733226\pi\) | |||||||
\(710\) | 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 | \(-0.890829\pi\) | ||||
−0.941759 | + | 0.336288i | \(0.890829\pi\) | |||||||
\(734\) | 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 | \(-0.579206\pi\) | ||||
−0.246272 | + | 0.969201i | \(0.579206\pi\) | |||||||
\(740\) | −13.0009 | −0.477923 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.58169 | 0.168199 | ||||||||
\(743\) | 35.2833 | 1.29442 | 0.647209 | − | 0.762313i | \(-0.275936\pi\) | ||||
0.647209 | + | 0.762313i | \(0.275936\pi\) | |||||||
\(744\) | −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 | \(-0.529646\pi\) | ||||
−0.0930001 | + | 0.995666i | \(0.529646\pi\) | |||||||
\(762\) | −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 | \(-0.620702\pi\) | ||||
−0.370174 | + | 0.928962i | \(0.620702\pi\) | |||||||
\(770\) | −1.50416 | −0.0542062 | ||||||||
\(771\) | 20.0321 | 0.721439 | ||||||||
\(772\) | −3.41063 | −0.122751 | ||||||||
\(773\) | −10.8128 | −0.388911 | −0.194455 | − | 0.980911i | \(-0.562294\pi\) | ||||
−0.194455 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(774\) | −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 | \(-0.318221\pi\) | ||||
0.540538 | + | 0.841320i | \(0.318221\pi\) | |||||||
\(788\) | −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 | \(-0.326195\pi\) | ||||
0.519293 | + | 0.854596i | \(0.326195\pi\) | |||||||
\(812\) | −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 | \(-0.432241\pi\) | ||||
0.211266 | + | 0.977429i | \(0.432241\pi\) | |||||||
\(822\) | −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 | \(-0.678100\pi\) | ||||
−0.530777 | + | 0.847512i | \(0.678100\pi\) | |||||||
\(828\) | −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 | \(-0.555664\pi\) | ||||
−0.173985 | + | 0.984748i | \(0.555664\pi\) | |||||||
\(840\) | 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 | \(-0.427024\pi\) | ||||
0.227258 | + | 0.973835i | \(0.427024\pi\) | |||||||
\(854\) | −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 | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(864\) | 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 | \(-0.527252\pi\) | ||||
−0.0855110 | + | 0.996337i | \(0.527252\pi\) | |||||||
\(878\) | −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 | \(-0.599070\pi\) | ||||
−0.306236 | + | 0.951956i | \(0.599070\pi\) | |||||||
\(930\) | 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 | \(-0.809846\pi\) | ||||
−0.826808 | + | 0.562484i | \(0.809846\pi\) | |||||||
\(942\) | 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 | \(-0.637833\pi\) | ||||
−0.419610 | + | 0.907704i | \(0.637833\pi\) | |||||||
\(948\) | −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 | \(-0.294336\pi\) | ||||
0.602088 | + | 0.798430i | \(0.294336\pi\) | |||||||
\(968\) | 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 | \(-0.280298\pi\) | ||||
0.636702 | + | 0.771110i | \(0.280298\pi\) | |||||||
\(978\) | −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 | \(-0.386550\pi\) | ||||
0.348916 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(984\) | −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.bh.1.10 | yes | 15 | |
13.12 | even | 2 | 3549.2.a.bg.1.6 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.6 | ✓ | 15 | 13.12 | even | 2 | ||
3549.2.a.bh.1.10 | yes | 15 | 1.1 | even | 1 | trivial |