Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} - 760 x^{4} - 742 x^{3} + 366 x^{2} + 236 x - 47 \) |
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 | \(-0.805107\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.805107 | −0.569296 | −0.284648 | − | 0.958632i | \(-0.591877\pi\) | ||||
−0.284648 | + | 0.958632i | \(0.591877\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.35180 | −0.675902 | ||||||||
\(5\) | 1.06503 | 0.476298 | 0.238149 | − | 0.971229i | \(-0.423459\pi\) | ||||
0.238149 | + | 0.971229i | \(0.423459\pi\) | |||||||
\(6\) | 0.805107 | 0.328683 | ||||||||
\(7\) | −0.203035 | −0.0767401 | −0.0383701 | − | 0.999264i | \(-0.512217\pi\) | ||||
−0.0383701 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(8\) | 2.69856 | 0.954085 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.857467 | −0.271155 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.35180 | 0.390232 | ||||||||
\(13\) | 0.801491 | 0.222294 | 0.111147 | − | 0.993804i | \(-0.464548\pi\) | ||||
0.111147 | + | 0.993804i | \(0.464548\pi\) | |||||||
\(14\) | 0.163465 | 0.0436879 | ||||||||
\(15\) | −1.06503 | −0.274991 | ||||||||
\(16\) | 0.530979 | 0.132745 | ||||||||
\(17\) | −0.376525 | −0.0913207 | −0.0456603 | − | 0.998957i | \(-0.514539\pi\) | ||||
−0.0456603 | + | 0.998957i | \(0.514539\pi\) | |||||||
\(18\) | −0.805107 | −0.189765 | ||||||||
\(19\) | 2.62261 | 0.601667 | 0.300833 | − | 0.953677i | \(-0.402735\pi\) | ||||
0.300833 | + | 0.953677i | \(0.402735\pi\) | |||||||
\(20\) | −1.43972 | −0.321931 | ||||||||
\(21\) | 0.203035 | 0.0443059 | ||||||||
\(22\) | −0.805107 | −0.171649 | ||||||||
\(23\) | 2.93099 | 0.611154 | 0.305577 | − | 0.952167i | \(-0.401151\pi\) | ||||
0.305577 | + | 0.952167i | \(0.401151\pi\) | |||||||
\(24\) | −2.69856 | −0.550841 | ||||||||
\(25\) | −3.86570 | −0.773140 | ||||||||
\(26\) | −0.645286 | −0.126551 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.274464 | 0.0518688 | ||||||||
\(29\) | 0.907071 | 0.168439 | 0.0842195 | − | 0.996447i | \(-0.473160\pi\) | ||||
0.0842195 | + | 0.996447i | \(0.473160\pi\) | |||||||
\(30\) | 0.857467 | 0.156551 | ||||||||
\(31\) | 2.07822 | 0.373260 | 0.186630 | − | 0.982430i | \(-0.440243\pi\) | ||||
0.186630 | + | 0.982430i | \(0.440243\pi\) | |||||||
\(32\) | −5.82461 | −1.02966 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.303143 | 0.0519885 | ||||||||
\(35\) | −0.216240 | −0.0365512 | ||||||||
\(36\) | −1.35180 | −0.225301 | ||||||||
\(37\) | −2.14816 | −0.353155 | −0.176578 | − | 0.984287i | \(-0.556503\pi\) | ||||
−0.176578 | + | 0.984287i | \(0.556503\pi\) | |||||||
\(38\) | −2.11148 | −0.342527 | ||||||||
\(39\) | −0.801491 | −0.128341 | ||||||||
\(40\) | 2.87406 | 0.454429 | ||||||||
\(41\) | −1.83276 | −0.286229 | −0.143115 | − | 0.989706i | \(-0.545712\pi\) | ||||
−0.143115 | + | 0.989706i | \(0.545712\pi\) | |||||||
\(42\) | −0.163465 | −0.0252232 | ||||||||
\(43\) | −2.25276 | −0.343542 | −0.171771 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171771 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(44\) | −1.35180 | −0.203792 | ||||||||
\(45\) | 1.06503 | 0.158766 | ||||||||
\(46\) | −2.35976 | −0.347928 | ||||||||
\(47\) | −0.685433 | −0.0999806 | −0.0499903 | − | 0.998750i | \(-0.515919\pi\) | ||||
−0.0499903 | + | 0.998750i | \(0.515919\pi\) | |||||||
\(48\) | −0.530979 | −0.0766402 | ||||||||
\(49\) | −6.95878 | −0.994111 | ||||||||
\(50\) | 3.11230 | 0.440146 | ||||||||
\(51\) | 0.376525 | 0.0527240 | ||||||||
\(52\) | −1.08346 | −0.150249 | ||||||||
\(53\) | 14.0454 | 1.92928 | 0.964640 | − | 0.263570i | \(-0.0849002\pi\) | ||||
0.964640 | + | 0.263570i | \(0.0849002\pi\) | |||||||
\(54\) | 0.805107 | 0.109561 | ||||||||
\(55\) | 1.06503 | 0.143609 | ||||||||
\(56\) | −0.547903 | −0.0732166 | ||||||||
\(57\) | −2.62261 | −0.347373 | ||||||||
\(58\) | −0.730289 | −0.0958917 | ||||||||
\(59\) | 7.73715 | 1.00729 | 0.503646 | − | 0.863910i | \(-0.331992\pi\) | ||||
0.503646 | + | 0.863910i | \(0.331992\pi\) | |||||||
\(60\) | 1.43972 | 0.185867 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −1.67319 | −0.212495 | ||||||||
\(63\) | −0.203035 | −0.0255800 | ||||||||
\(64\) | 3.62748 | 0.453435 | ||||||||
\(65\) | 0.853616 | 0.105878 | ||||||||
\(66\) | 0.805107 | 0.0991018 | ||||||||
\(67\) | −7.59429 | −0.927790 | −0.463895 | − | 0.885890i | \(-0.653549\pi\) | ||||
−0.463895 | + | 0.885890i | \(0.653549\pi\) | |||||||
\(68\) | 0.508987 | 0.0617238 | ||||||||
\(69\) | −2.93099 | −0.352850 | ||||||||
\(70\) | 0.174096 | 0.0208085 | ||||||||
\(71\) | −9.23954 | −1.09653 | −0.548266 | − | 0.836304i | \(-0.684712\pi\) | ||||
−0.548266 | + | 0.836304i | \(0.684712\pi\) | |||||||
\(72\) | 2.69856 | 0.318028 | ||||||||
\(73\) | 7.49398 | 0.877104 | 0.438552 | − | 0.898706i | \(-0.355491\pi\) | ||||
0.438552 | + | 0.898706i | \(0.355491\pi\) | |||||||
\(74\) | 1.72950 | 0.201050 | ||||||||
\(75\) | 3.86570 | 0.446373 | ||||||||
\(76\) | −3.54525 | −0.406668 | ||||||||
\(77\) | −0.203035 | −0.0231380 | ||||||||
\(78\) | 0.645286 | 0.0730642 | ||||||||
\(79\) | 7.41703 | 0.834481 | 0.417240 | − | 0.908796i | \(-0.362997\pi\) | ||||
0.417240 | + | 0.908796i | \(0.362997\pi\) | |||||||
\(80\) | 0.565511 | 0.0632260 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.47557 | 0.162949 | ||||||||
\(83\) | −8.55136 | −0.938634 | −0.469317 | − | 0.883030i | \(-0.655500\pi\) | ||||
−0.469317 | + | 0.883030i | \(0.655500\pi\) | |||||||
\(84\) | −0.274464 | −0.0299465 | ||||||||
\(85\) | −0.401012 | −0.0434959 | ||||||||
\(86\) | 1.81371 | 0.195577 | ||||||||
\(87\) | −0.907071 | −0.0972483 | ||||||||
\(88\) | 2.69856 | 0.287667 | ||||||||
\(89\) | −2.97849 | −0.315719 | −0.157860 | − | 0.987462i | \(-0.550459\pi\) | ||||
−0.157860 | + | 0.987462i | \(0.550459\pi\) | |||||||
\(90\) | −0.857467 | −0.0903849 | ||||||||
\(91\) | −0.162731 | −0.0170588 | ||||||||
\(92\) | −3.96212 | −0.413080 | ||||||||
\(93\) | −2.07822 | −0.215502 | ||||||||
\(94\) | 0.551846 | 0.0569186 | ||||||||
\(95\) | 2.79317 | 0.286573 | ||||||||
\(96\) | 5.82461 | 0.594472 | ||||||||
\(97\) | 17.8193 | 1.80928 | 0.904638 | − | 0.426181i | \(-0.140141\pi\) | ||||
0.904638 | + | 0.426181i | \(0.140141\pi\) | |||||||
\(98\) | 5.60256 | 0.565944 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 5.22567 | 0.522567 | ||||||||
\(101\) | −4.50884 | −0.448646 | −0.224323 | − | 0.974515i | \(-0.572017\pi\) | ||||
−0.224323 | + | 0.974515i | \(0.572017\pi\) | |||||||
\(102\) | −0.303143 | −0.0300156 | ||||||||
\(103\) | 19.8815 | 1.95898 | 0.979489 | − | 0.201499i | \(-0.0645812\pi\) | ||||
0.979489 | + | 0.201499i | \(0.0645812\pi\) | |||||||
\(104\) | 2.16287 | 0.212087 | ||||||||
\(105\) | 0.216240 | 0.0211028 | ||||||||
\(106\) | −11.3080 | −1.09833 | ||||||||
\(107\) | 6.58861 | 0.636945 | 0.318472 | − | 0.947932i | \(-0.396830\pi\) | ||||
0.318472 | + | 0.947932i | \(0.396830\pi\) | |||||||
\(108\) | 1.35180 | 0.130077 | ||||||||
\(109\) | 19.1473 | 1.83398 | 0.916990 | − | 0.398910i | \(-0.130612\pi\) | ||||
0.916990 | + | 0.398910i | \(0.130612\pi\) | |||||||
\(110\) | −0.857467 | −0.0817562 | ||||||||
\(111\) | 2.14816 | 0.203894 | ||||||||
\(112\) | −0.107807 | −0.0101868 | ||||||||
\(113\) | −2.84072 | −0.267232 | −0.133616 | − | 0.991033i | \(-0.542659\pi\) | ||||
−0.133616 | + | 0.991033i | \(0.542659\pi\) | |||||||
\(114\) | 2.11148 | 0.197758 | ||||||||
\(115\) | 3.12161 | 0.291091 | ||||||||
\(116\) | −1.22618 | −0.113848 | ||||||||
\(117\) | 0.801491 | 0.0740979 | ||||||||
\(118\) | −6.22923 | −0.573447 | ||||||||
\(119\) | 0.0764478 | 0.00700796 | ||||||||
\(120\) | −2.87406 | −0.262365 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.805107 | 0.0728909 | ||||||||
\(123\) | 1.83276 | 0.165255 | ||||||||
\(124\) | −2.80935 | −0.252287 | ||||||||
\(125\) | −9.44228 | −0.844543 | ||||||||
\(126\) | 0.163465 | 0.0145626 | ||||||||
\(127\) | 5.00348 | 0.443987 | 0.221993 | − | 0.975048i | \(-0.428744\pi\) | ||||
0.221993 | + | 0.975048i | \(0.428744\pi\) | |||||||
\(128\) | 8.72872 | 0.771517 | ||||||||
\(129\) | 2.25276 | 0.198344 | ||||||||
\(130\) | −0.687252 | −0.0602760 | ||||||||
\(131\) | −19.0550 | −1.66485 | −0.832423 | − | 0.554140i | \(-0.813047\pi\) | ||||
−0.832423 | + | 0.554140i | \(0.813047\pi\) | |||||||
\(132\) | 1.35180 | 0.117659 | ||||||||
\(133\) | −0.532481 | −0.0461720 | ||||||||
\(134\) | 6.11422 | 0.528188 | ||||||||
\(135\) | −1.06503 | −0.0916636 | ||||||||
\(136\) | −1.01607 | −0.0871277 | ||||||||
\(137\) | 18.4521 | 1.57647 | 0.788237 | − | 0.615372i | \(-0.210994\pi\) | ||||
0.788237 | + | 0.615372i | \(0.210994\pi\) | |||||||
\(138\) | 2.35976 | 0.200876 | ||||||||
\(139\) | 14.6161 | 1.23972 | 0.619861 | − | 0.784711i | \(-0.287189\pi\) | ||||
0.619861 | + | 0.784711i | \(0.287189\pi\) | |||||||
\(140\) | 0.292313 | 0.0247050 | ||||||||
\(141\) | 0.685433 | 0.0577238 | ||||||||
\(142\) | 7.43882 | 0.624252 | ||||||||
\(143\) | 0.801491 | 0.0670241 | ||||||||
\(144\) | 0.530979 | 0.0442482 | ||||||||
\(145\) | 0.966063 | 0.0802271 | ||||||||
\(146\) | −6.03345 | −0.499332 | ||||||||
\(147\) | 6.95878 | 0.573950 | ||||||||
\(148\) | 2.90389 | 0.238698 | ||||||||
\(149\) | −4.26078 | −0.349057 | −0.174528 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174528 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(150\) | −3.11230 | −0.254118 | ||||||||
\(151\) | 19.9980 | 1.62741 | 0.813707 | − | 0.581276i | \(-0.197446\pi\) | ||||
0.813707 | + | 0.581276i | \(0.197446\pi\) | |||||||
\(152\) | 7.07726 | 0.574041 | ||||||||
\(153\) | −0.376525 | −0.0304402 | ||||||||
\(154\) | 0.163465 | 0.0131724 | ||||||||
\(155\) | 2.21338 | 0.177783 | ||||||||
\(156\) | 1.08346 | 0.0867461 | ||||||||
\(157\) | 0.492192 | 0.0392812 | 0.0196406 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196406 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(158\) | −5.97150 | −0.475067 | ||||||||
\(159\) | −14.0454 | −1.11387 | ||||||||
\(160\) | −6.20342 | −0.490423 | ||||||||
\(161\) | −0.595095 | −0.0469000 | ||||||||
\(162\) | −0.805107 | −0.0632552 | ||||||||
\(163\) | −1.93731 | −0.151742 | −0.0758708 | − | 0.997118i | \(-0.524174\pi\) | ||||
−0.0758708 | + | 0.997118i | \(0.524174\pi\) | |||||||
\(164\) | 2.47753 | 0.193463 | ||||||||
\(165\) | −1.06503 | −0.0829129 | ||||||||
\(166\) | 6.88476 | 0.534361 | ||||||||
\(167\) | 14.8338 | 1.14788 | 0.573938 | − | 0.818899i | \(-0.305415\pi\) | ||||
0.573938 | + | 0.818899i | \(0.305415\pi\) | |||||||
\(168\) | 0.547903 | 0.0422716 | ||||||||
\(169\) | −12.3576 | −0.950586 | ||||||||
\(170\) | 0.322857 | 0.0247620 | ||||||||
\(171\) | 2.62261 | 0.200556 | ||||||||
\(172\) | 3.04529 | 0.232201 | ||||||||
\(173\) | −10.3859 | −0.789623 | −0.394812 | − | 0.918762i | \(-0.629190\pi\) | ||||
−0.394812 | + | 0.918762i | \(0.629190\pi\) | |||||||
\(174\) | 0.730289 | 0.0553631 | ||||||||
\(175\) | 0.784874 | 0.0593309 | ||||||||
\(176\) | 0.530979 | 0.0400240 | ||||||||
\(177\) | −7.73715 | −0.581560 | ||||||||
\(178\) | 2.39800 | 0.179738 | ||||||||
\(179\) | 16.9049 | 1.26353 | 0.631765 | − | 0.775160i | \(-0.282331\pi\) | ||||
0.631765 | + | 0.775160i | \(0.282331\pi\) | |||||||
\(180\) | −1.43972 | −0.107310 | ||||||||
\(181\) | 2.91712 | 0.216828 | 0.108414 | − | 0.994106i | \(-0.465423\pi\) | ||||
0.108414 | + | 0.994106i | \(0.465423\pi\) | |||||||
\(182\) | 0.131016 | 0.00971154 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 7.90945 | 0.583093 | ||||||||
\(185\) | −2.28787 | −0.168207 | ||||||||
\(186\) | 1.67319 | 0.122684 | ||||||||
\(187\) | −0.376525 | −0.0275342 | ||||||||
\(188\) | 0.926570 | 0.0675771 | ||||||||
\(189\) | 0.203035 | 0.0147686 | ||||||||
\(190\) | −2.24880 | −0.163145 | ||||||||
\(191\) | 10.8546 | 0.785410 | 0.392705 | − | 0.919664i | \(-0.371539\pi\) | ||||
0.392705 | + | 0.919664i | \(0.371539\pi\) | |||||||
\(192\) | −3.62748 | −0.261791 | ||||||||
\(193\) | 9.85294 | 0.709230 | 0.354615 | − | 0.935012i | \(-0.384612\pi\) | ||||
0.354615 | + | 0.935012i | \(0.384612\pi\) | |||||||
\(194\) | −14.3464 | −1.03001 | ||||||||
\(195\) | −0.853616 | −0.0611287 | ||||||||
\(196\) | 9.40690 | 0.671921 | ||||||||
\(197\) | 1.58403 | 0.112857 | 0.0564286 | − | 0.998407i | \(-0.482029\pi\) | ||||
0.0564286 | + | 0.998407i | \(0.482029\pi\) | |||||||
\(198\) | −0.805107 | −0.0572164 | ||||||||
\(199\) | 25.5545 | 1.81151 | 0.905756 | − | 0.423799i | \(-0.139304\pi\) | ||||
0.905756 | + | 0.423799i | \(0.139304\pi\) | |||||||
\(200\) | −10.4318 | −0.737641 | ||||||||
\(201\) | 7.59429 | 0.535660 | ||||||||
\(202\) | 3.63010 | 0.255413 | ||||||||
\(203\) | −0.184168 | −0.0129260 | ||||||||
\(204\) | −0.508987 | −0.0356363 | ||||||||
\(205\) | −1.95196 | −0.136330 | ||||||||
\(206\) | −16.0067 | −1.11524 | ||||||||
\(207\) | 2.93099 | 0.203718 | ||||||||
\(208\) | 0.425575 | 0.0295083 | ||||||||
\(209\) | 2.62261 | 0.181409 | ||||||||
\(210\) | −0.174096 | −0.0120138 | ||||||||
\(211\) | 16.1904 | 1.11460 | 0.557298 | − | 0.830313i | \(-0.311838\pi\) | ||||
0.557298 | + | 0.830313i | \(0.311838\pi\) | |||||||
\(212\) | −18.9866 | −1.30400 | ||||||||
\(213\) | 9.23954 | 0.633083 | ||||||||
\(214\) | −5.30453 | −0.362610 | ||||||||
\(215\) | −2.39927 | −0.163629 | ||||||||
\(216\) | −2.69856 | −0.183614 | ||||||||
\(217\) | −0.421952 | −0.0286440 | ||||||||
\(218\) | −15.4156 | −1.04408 | ||||||||
\(219\) | −7.49398 | −0.506396 | ||||||||
\(220\) | −1.43972 | −0.0970657 | ||||||||
\(221\) | −0.301781 | −0.0203000 | ||||||||
\(222\) | −1.72950 | −0.116076 | ||||||||
\(223\) | −4.93169 | −0.330250 | −0.165125 | − | 0.986273i | \(-0.552803\pi\) | ||||
−0.165125 | + | 0.986273i | \(0.552803\pi\) | |||||||
\(224\) | 1.18260 | 0.0790159 | ||||||||
\(225\) | −3.86570 | −0.257713 | ||||||||
\(226\) | 2.28708 | 0.152134 | ||||||||
\(227\) | −2.59452 | −0.172204 | −0.0861022 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861022 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(228\) | 3.54525 | 0.234790 | ||||||||
\(229\) | −6.75414 | −0.446326 | −0.223163 | − | 0.974781i | \(-0.571638\pi\) | ||||
−0.223163 | + | 0.974781i | \(0.571638\pi\) | |||||||
\(230\) | −2.51323 | −0.165717 | ||||||||
\(231\) | 0.203035 | 0.0133587 | ||||||||
\(232\) | 2.44779 | 0.160705 | ||||||||
\(233\) | −27.8481 | −1.82439 | −0.912195 | − | 0.409757i | \(-0.865614\pi\) | ||||
−0.912195 | + | 0.409757i | \(0.865614\pi\) | |||||||
\(234\) | −0.645286 | −0.0421837 | ||||||||
\(235\) | −0.730010 | −0.0476206 | ||||||||
\(236\) | −10.4591 | −0.680830 | ||||||||
\(237\) | −7.41703 | −0.481788 | ||||||||
\(238\) | −0.0615487 | −0.00398961 | ||||||||
\(239\) | 16.9202 | 1.09448 | 0.547240 | − | 0.836976i | \(-0.315679\pi\) | ||||
0.547240 | + | 0.836976i | \(0.315679\pi\) | |||||||
\(240\) | −0.565511 | −0.0365036 | ||||||||
\(241\) | −1.06455 | −0.0685739 | −0.0342869 | − | 0.999412i | \(-0.510916\pi\) | ||||
−0.0342869 | + | 0.999412i | \(0.510916\pi\) | |||||||
\(242\) | −0.805107 | −0.0517542 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.35180 | 0.0865403 | ||||||||
\(245\) | −7.41134 | −0.473493 | ||||||||
\(246\) | −1.47557 | −0.0940788 | ||||||||
\(247\) | 2.10199 | 0.133747 | ||||||||
\(248\) | 5.60821 | 0.356121 | ||||||||
\(249\) | 8.55136 | 0.541920 | ||||||||
\(250\) | 7.60204 | 0.480795 | ||||||||
\(251\) | −3.19791 | −0.201850 | −0.100925 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100925 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(252\) | 0.274464 | 0.0172896 | ||||||||
\(253\) | 2.93099 | 0.184270 | ||||||||
\(254\) | −4.02833 | −0.252760 | ||||||||
\(255\) | 0.401012 | 0.0251124 | ||||||||
\(256\) | −14.2825 | −0.892657 | ||||||||
\(257\) | −12.0296 | −0.750388 | −0.375194 | − | 0.926946i | \(-0.622424\pi\) | ||||
−0.375194 | + | 0.926946i | \(0.622424\pi\) | |||||||
\(258\) | −1.81371 | −0.112917 | ||||||||
\(259\) | 0.436152 | 0.0271012 | ||||||||
\(260\) | −1.15392 | −0.0715631 | ||||||||
\(261\) | 0.907071 | 0.0561463 | ||||||||
\(262\) | 15.3413 | 0.947791 | ||||||||
\(263\) | −3.98169 | −0.245521 | −0.122761 | − | 0.992436i | \(-0.539175\pi\) | ||||
−0.122761 | + | 0.992436i | \(0.539175\pi\) | |||||||
\(264\) | −2.69856 | −0.166085 | ||||||||
\(265\) | 14.9588 | 0.918912 | ||||||||
\(266\) | 0.428704 | 0.0262855 | ||||||||
\(267\) | 2.97849 | 0.182281 | ||||||||
\(268\) | 10.2660 | 0.627095 | ||||||||
\(269\) | 2.20633 | 0.134522 | 0.0672611 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672611 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(270\) | 0.857467 | 0.0521838 | ||||||||
\(271\) | 10.9268 | 0.663754 | 0.331877 | − | 0.943323i | \(-0.392318\pi\) | ||||
0.331877 | + | 0.943323i | \(0.392318\pi\) | |||||||
\(272\) | −0.199927 | −0.0121223 | ||||||||
\(273\) | 0.162731 | 0.00984893 | ||||||||
\(274\) | −14.8559 | −0.897480 | ||||||||
\(275\) | −3.86570 | −0.233111 | ||||||||
\(276\) | 3.96212 | 0.238492 | ||||||||
\(277\) | 7.40923 | 0.445177 | 0.222589 | − | 0.974912i | \(-0.428549\pi\) | ||||
0.222589 | + | 0.974912i | \(0.428549\pi\) | |||||||
\(278\) | −11.7675 | −0.705770 | ||||||||
\(279\) | 2.07822 | 0.124420 | ||||||||
\(280\) | −0.583535 | −0.0348729 | ||||||||
\(281\) | −0.155459 | −0.00927391 | −0.00463696 | − | 0.999989i | \(-0.501476\pi\) | ||||
−0.00463696 | + | 0.999989i | \(0.501476\pi\) | |||||||
\(282\) | −0.551846 | −0.0328620 | ||||||||
\(283\) | −11.9494 | −0.710316 | −0.355158 | − | 0.934806i | \(-0.615573\pi\) | ||||
−0.355158 | + | 0.934806i | \(0.615573\pi\) | |||||||
\(284\) | 12.4900 | 0.741148 | ||||||||
\(285\) | −2.79317 | −0.165453 | ||||||||
\(286\) | −0.645286 | −0.0381565 | ||||||||
\(287\) | 0.372115 | 0.0219653 | ||||||||
\(288\) | −5.82461 | −0.343219 | ||||||||
\(289\) | −16.8582 | −0.991661 | ||||||||
\(290\) | −0.777784 | −0.0456730 | ||||||||
\(291\) | −17.8193 | −1.04459 | ||||||||
\(292\) | −10.1304 | −0.592836 | ||||||||
\(293\) | 16.9701 | 0.991404 | 0.495702 | − | 0.868493i | \(-0.334911\pi\) | ||||
0.495702 | + | 0.868493i | \(0.334911\pi\) | |||||||
\(294\) | −5.60256 | −0.326748 | ||||||||
\(295\) | 8.24034 | 0.479771 | ||||||||
\(296\) | −5.79694 | −0.336940 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 3.43038 | 0.198717 | ||||||||
\(299\) | 2.34916 | 0.135856 | ||||||||
\(300\) | −5.22567 | −0.301704 | ||||||||
\(301\) | 0.457390 | 0.0263635 | ||||||||
\(302\) | −16.1005 | −0.926480 | ||||||||
\(303\) | 4.50884 | 0.259026 | ||||||||
\(304\) | 1.39255 | 0.0798681 | ||||||||
\(305\) | −1.06503 | −0.0609837 | ||||||||
\(306\) | 0.303143 | 0.0173295 | ||||||||
\(307\) | 13.3520 | 0.762041 | 0.381021 | − | 0.924567i | \(-0.375573\pi\) | ||||
0.381021 | + | 0.924567i | \(0.375573\pi\) | |||||||
\(308\) | 0.274464 | 0.0156390 | ||||||||
\(309\) | −19.8815 | −1.13102 | ||||||||
\(310\) | −1.78201 | −0.101211 | ||||||||
\(311\) | −12.6506 | −0.717352 | −0.358676 | − | 0.933462i | \(-0.616772\pi\) | ||||
−0.358676 | + | 0.933462i | \(0.616772\pi\) | |||||||
\(312\) | −2.16287 | −0.122448 | ||||||||
\(313\) | 8.15405 | 0.460894 | 0.230447 | − | 0.973085i | \(-0.425981\pi\) | ||||
0.230447 | + | 0.973085i | \(0.425981\pi\) | |||||||
\(314\) | −0.396267 | −0.0223627 | ||||||||
\(315\) | −0.216240 | −0.0121837 | ||||||||
\(316\) | −10.0264 | −0.564027 | ||||||||
\(317\) | −22.7512 | −1.27784 | −0.638918 | − | 0.769274i | \(-0.720618\pi\) | ||||
−0.638918 | + | 0.769274i | \(0.720618\pi\) | |||||||
\(318\) | 11.3080 | 0.634122 | ||||||||
\(319\) | 0.907071 | 0.0507863 | ||||||||
\(320\) | 3.86339 | 0.215970 | ||||||||
\(321\) | −6.58861 | −0.367740 | ||||||||
\(322\) | 0.479115 | 0.0267000 | ||||||||
\(323\) | −0.987476 | −0.0549446 | ||||||||
\(324\) | −1.35180 | −0.0751002 | ||||||||
\(325\) | −3.09832 | −0.171864 | ||||||||
\(326\) | 1.55974 | 0.0863860 | ||||||||
\(327\) | −19.1473 | −1.05885 | ||||||||
\(328\) | −4.94582 | −0.273087 | ||||||||
\(329\) | 0.139167 | 0.00767253 | ||||||||
\(330\) | 0.857467 | 0.0472020 | ||||||||
\(331\) | 2.47607 | 0.136097 | 0.0680486 | − | 0.997682i | \(-0.478323\pi\) | ||||
0.0680486 | + | 0.997682i | \(0.478323\pi\) | |||||||
\(332\) | 11.5598 | 0.634424 | ||||||||
\(333\) | −2.14816 | −0.117718 | ||||||||
\(334\) | −11.9428 | −0.653481 | ||||||||
\(335\) | −8.08819 | −0.441905 | ||||||||
\(336\) | 0.107807 | 0.00588138 | ||||||||
\(337\) | −11.8667 | −0.646419 | −0.323210 | − | 0.946327i | \(-0.604762\pi\) | ||||
−0.323210 | + | 0.946327i | \(0.604762\pi\) | |||||||
\(338\) | 9.94920 | 0.541165 | ||||||||
\(339\) | 2.84072 | 0.154287 | ||||||||
\(340\) | 0.542089 | 0.0293989 | ||||||||
\(341\) | 2.07822 | 0.112542 | ||||||||
\(342\) | −2.11148 | −0.114176 | ||||||||
\(343\) | 2.83412 | 0.153028 | ||||||||
\(344\) | −6.07920 | −0.327769 | ||||||||
\(345\) | −3.12161 | −0.168062 | ||||||||
\(346\) | 8.36174 | 0.449530 | ||||||||
\(347\) | 33.4479 | 1.79558 | 0.897789 | − | 0.440426i | \(-0.145173\pi\) | ||||
0.897789 | + | 0.440426i | \(0.145173\pi\) | |||||||
\(348\) | 1.22618 | 0.0657303 | ||||||||
\(349\) | −19.7785 | −1.05872 | −0.529359 | − | 0.848398i | \(-0.677567\pi\) | ||||
−0.529359 | + | 0.848398i | \(0.677567\pi\) | |||||||
\(350\) | −0.631907 | −0.0337768 | ||||||||
\(351\) | −0.801491 | −0.0427804 | ||||||||
\(352\) | −5.82461 | −0.310453 | ||||||||
\(353\) | −15.2833 | −0.813448 | −0.406724 | − | 0.913551i | \(-0.633329\pi\) | ||||
−0.406724 | + | 0.913551i | \(0.633329\pi\) | |||||||
\(354\) | 6.22923 | 0.331080 | ||||||||
\(355\) | −9.84043 | −0.522276 | ||||||||
\(356\) | 4.02633 | 0.213395 | ||||||||
\(357\) | −0.0764478 | −0.00404605 | ||||||||
\(358\) | −13.6102 | −0.719324 | ||||||||
\(359\) | 10.2459 | 0.540759 | 0.270380 | − | 0.962754i | \(-0.412851\pi\) | ||||
0.270380 | + | 0.962754i | \(0.412851\pi\) | |||||||
\(360\) | 2.87406 | 0.151476 | ||||||||
\(361\) | −12.1219 | −0.637997 | ||||||||
\(362\) | −2.34859 | −0.123439 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0.219980 | 0.0115301 | ||||||||
\(365\) | 7.98135 | 0.417763 | ||||||||
\(366\) | −0.805107 | −0.0420836 | ||||||||
\(367\) | 11.5481 | 0.602807 | 0.301403 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301403 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(368\) | 1.55629 | 0.0811274 | ||||||||
\(369\) | −1.83276 | −0.0954098 | ||||||||
\(370\) | 1.84198 | 0.0957598 | ||||||||
\(371\) | −2.85171 | −0.148053 | ||||||||
\(372\) | 2.80935 | 0.145658 | ||||||||
\(373\) | −26.2319 | −1.35824 | −0.679119 | − | 0.734028i | \(-0.737638\pi\) | ||||
−0.679119 | + | 0.734028i | \(0.737638\pi\) | |||||||
\(374\) | 0.303143 | 0.0156751 | ||||||||
\(375\) | 9.44228 | 0.487597 | ||||||||
\(376\) | −1.84968 | −0.0953900 | ||||||||
\(377\) | 0.727010 | 0.0374429 | ||||||||
\(378\) | −0.163465 | −0.00840774 | ||||||||
\(379\) | 11.1404 | 0.572245 | 0.286123 | − | 0.958193i | \(-0.407634\pi\) | ||||
0.286123 | + | 0.958193i | \(0.407634\pi\) | |||||||
\(380\) | −3.77581 | −0.193695 | ||||||||
\(381\) | −5.00348 | −0.256336 | ||||||||
\(382\) | −8.73910 | −0.447131 | ||||||||
\(383\) | 37.6696 | 1.92483 | 0.962413 | − | 0.271590i | \(-0.0875494\pi\) | ||||
0.962413 | + | 0.271590i | \(0.0875494\pi\) | |||||||
\(384\) | −8.72872 | −0.445436 | ||||||||
\(385\) | −0.216240 | −0.0110206 | ||||||||
\(386\) | −7.93266 | −0.403762 | ||||||||
\(387\) | −2.25276 | −0.114514 | ||||||||
\(388\) | −24.0882 | −1.22289 | ||||||||
\(389\) | −10.9370 | −0.554527 | −0.277263 | − | 0.960794i | \(-0.589427\pi\) | ||||
−0.277263 | + | 0.960794i | \(0.589427\pi\) | |||||||
\(390\) | 0.687252 | 0.0348004 | ||||||||
\(391\) | −1.10359 | −0.0558110 | ||||||||
\(392\) | −18.7787 | −0.948466 | ||||||||
\(393\) | 19.0550 | 0.961200 | ||||||||
\(394\) | −1.27531 | −0.0642492 | ||||||||
\(395\) | 7.89939 | 0.397461 | ||||||||
\(396\) | −1.35180 | −0.0679307 | ||||||||
\(397\) | 33.2094 | 1.66673 | 0.833365 | − | 0.552722i | \(-0.186411\pi\) | ||||
0.833365 | + | 0.552722i | \(0.186411\pi\) | |||||||
\(398\) | −20.5741 | −1.03129 | ||||||||
\(399\) | 0.532481 | 0.0266574 | ||||||||
\(400\) | −2.05260 | −0.102630 | ||||||||
\(401\) | −18.7562 | −0.936640 | −0.468320 | − | 0.883559i | \(-0.655141\pi\) | ||||
−0.468320 | + | 0.883559i | \(0.655141\pi\) | |||||||
\(402\) | −6.11422 | −0.304949 | ||||||||
\(403\) | 1.66568 | 0.0829733 | ||||||||
\(404\) | 6.09506 | 0.303241 | ||||||||
\(405\) | 1.06503 | 0.0529220 | ||||||||
\(406\) | 0.148274 | 0.00735874 | ||||||||
\(407\) | −2.14816 | −0.106480 | ||||||||
\(408\) | 1.01607 | 0.0503032 | ||||||||
\(409\) | 5.97380 | 0.295385 | 0.147693 | − | 0.989033i | \(-0.452815\pi\) | ||||
0.147693 | + | 0.989033i | \(0.452815\pi\) | |||||||
\(410\) | 1.57153 | 0.0776125 | ||||||||
\(411\) | −18.4521 | −0.910177 | ||||||||
\(412\) | −26.8758 | −1.32408 | ||||||||
\(413\) | −1.57091 | −0.0772997 | ||||||||
\(414\) | −2.35976 | −0.115976 | ||||||||
\(415\) | −9.10750 | −0.447069 | ||||||||
\(416\) | −4.66838 | −0.228886 | ||||||||
\(417\) | −14.6161 | −0.715754 | ||||||||
\(418\) | −2.11148 | −0.103276 | ||||||||
\(419\) | −21.7376 | −1.06195 | −0.530976 | − | 0.847387i | \(-0.678174\pi\) | ||||
−0.530976 | + | 0.847387i | \(0.678174\pi\) | |||||||
\(420\) | −0.292313 | −0.0142634 | ||||||||
\(421\) | −16.2177 | −0.790402 | −0.395201 | − | 0.918595i | \(-0.629325\pi\) | ||||
−0.395201 | + | 0.918595i | \(0.629325\pi\) | |||||||
\(422\) | −13.0350 | −0.634535 | ||||||||
\(423\) | −0.685433 | −0.0333269 | ||||||||
\(424\) | 37.9023 | 1.84070 | ||||||||
\(425\) | 1.45553 | 0.0706037 | ||||||||
\(426\) | −7.43882 | −0.360412 | ||||||||
\(427\) | 0.203035 | 0.00982557 | ||||||||
\(428\) | −8.90650 | −0.430512 | ||||||||
\(429\) | −0.801491 | −0.0386964 | ||||||||
\(430\) | 1.93167 | 0.0931532 | ||||||||
\(431\) | −31.0756 | −1.49686 | −0.748430 | − | 0.663214i | \(-0.769192\pi\) | ||||
−0.748430 | + | 0.663214i | \(0.769192\pi\) | |||||||
\(432\) | −0.530979 | −0.0255467 | ||||||||
\(433\) | 37.4627 | 1.80034 | 0.900171 | − | 0.435536i | \(-0.143441\pi\) | ||||
0.900171 | + | 0.435536i | \(0.143441\pi\) | |||||||
\(434\) | 0.339717 | 0.0163069 | ||||||||
\(435\) | −0.966063 | −0.0463192 | ||||||||
\(436\) | −25.8834 | −1.23959 | ||||||||
\(437\) | 7.68683 | 0.367711 | ||||||||
\(438\) | 6.03345 | 0.288290 | ||||||||
\(439\) | 15.0607 | 0.718809 | 0.359405 | − | 0.933182i | \(-0.382980\pi\) | ||||
0.359405 | + | 0.933182i | \(0.382980\pi\) | |||||||
\(440\) | 2.87406 | 0.137015 | ||||||||
\(441\) | −6.95878 | −0.331370 | ||||||||
\(442\) | 0.242966 | 0.0115567 | ||||||||
\(443\) | 7.50403 | 0.356527 | 0.178264 | − | 0.983983i | \(-0.442952\pi\) | ||||
0.178264 | + | 0.983983i | \(0.442952\pi\) | |||||||
\(444\) | −2.90389 | −0.137813 | ||||||||
\(445\) | −3.17220 | −0.150376 | ||||||||
\(446\) | 3.97054 | 0.188010 | ||||||||
\(447\) | 4.26078 | 0.201528 | ||||||||
\(448\) | −0.736506 | −0.0347966 | ||||||||
\(449\) | 13.5424 | 0.639103 | 0.319552 | − | 0.947569i | \(-0.396468\pi\) | ||||
0.319552 | + | 0.947569i | \(0.396468\pi\) | |||||||
\(450\) | 3.11230 | 0.146715 | ||||||||
\(451\) | −1.83276 | −0.0863014 | ||||||||
\(452\) | 3.84009 | 0.180623 | ||||||||
\(453\) | −19.9980 | −0.939587 | ||||||||
\(454\) | 2.08887 | 0.0980353 | ||||||||
\(455\) | −0.173314 | −0.00812509 | ||||||||
\(456\) | −7.07726 | −0.331423 | ||||||||
\(457\) | 10.1840 | 0.476388 | 0.238194 | − | 0.971218i | \(-0.423445\pi\) | ||||
0.238194 | + | 0.971218i | \(0.423445\pi\) | |||||||
\(458\) | 5.43780 | 0.254092 | ||||||||
\(459\) | 0.376525 | 0.0175747 | ||||||||
\(460\) | −4.21980 | −0.196749 | ||||||||
\(461\) | −14.0649 | −0.655067 | −0.327533 | − | 0.944840i | \(-0.606217\pi\) | ||||
−0.327533 | + | 0.944840i | \(0.606217\pi\) | |||||||
\(462\) | −0.163465 | −0.00760508 | ||||||||
\(463\) | −27.3090 | −1.26916 | −0.634578 | − | 0.772859i | \(-0.718826\pi\) | ||||
−0.634578 | + | 0.772859i | \(0.718826\pi\) | |||||||
\(464\) | 0.481636 | 0.0223594 | ||||||||
\(465\) | −2.21338 | −0.102643 | ||||||||
\(466\) | 22.4207 | 1.03862 | ||||||||
\(467\) | 16.1833 | 0.748875 | 0.374437 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374437 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(468\) | −1.08346 | −0.0500829 | ||||||||
\(469\) | 1.54191 | 0.0711988 | ||||||||
\(470\) | 0.587736 | 0.0271102 | ||||||||
\(471\) | −0.492192 | −0.0226790 | ||||||||
\(472\) | 20.8792 | 0.961041 | ||||||||
\(473\) | −2.25276 | −0.103582 | ||||||||
\(474\) | 5.97150 | 0.274280 | ||||||||
\(475\) | −10.1382 | −0.465173 | ||||||||
\(476\) | −0.103342 | −0.00473669 | ||||||||
\(477\) | 14.0454 | 0.643093 | ||||||||
\(478\) | −13.6226 | −0.623083 | ||||||||
\(479\) | −19.5798 | −0.894623 | −0.447311 | − | 0.894378i | \(-0.647618\pi\) | ||||
−0.447311 | + | 0.894378i | \(0.647618\pi\) | |||||||
\(480\) | 6.20342 | 0.283146 | ||||||||
\(481\) | −1.72173 | −0.0785042 | ||||||||
\(482\) | 0.857078 | 0.0390389 | ||||||||
\(483\) | 0.595095 | 0.0270777 | ||||||||
\(484\) | −1.35180 | −0.0614456 | ||||||||
\(485\) | 18.9782 | 0.861754 | ||||||||
\(486\) | 0.805107 | 0.0365204 | ||||||||
\(487\) | −25.6857 | −1.16393 | −0.581966 | − | 0.813213i | \(-0.697716\pi\) | ||||
−0.581966 | + | 0.813213i | \(0.697716\pi\) | |||||||
\(488\) | −2.69856 | −0.122158 | ||||||||
\(489\) | 1.93731 | 0.0876081 | ||||||||
\(490\) | 5.96692 | 0.269558 | ||||||||
\(491\) | 30.0246 | 1.35499 | 0.677497 | − | 0.735526i | \(-0.263065\pi\) | ||||
0.677497 | + | 0.735526i | \(0.263065\pi\) | |||||||
\(492\) | −2.47753 | −0.111696 | ||||||||
\(493\) | −0.341535 | −0.0153820 | ||||||||
\(494\) | −1.69233 | −0.0761415 | ||||||||
\(495\) | 1.06503 | 0.0478698 | ||||||||
\(496\) | 1.10349 | 0.0495482 | ||||||||
\(497\) | 1.87595 | 0.0841480 | ||||||||
\(498\) | −6.88476 | −0.308513 | ||||||||
\(499\) | 16.6668 | 0.746109 | 0.373054 | − | 0.927810i | \(-0.378311\pi\) | ||||
0.373054 | + | 0.927810i | \(0.378311\pi\) | |||||||
\(500\) | 12.7641 | 0.570828 | ||||||||
\(501\) | −14.8338 | −0.662726 | ||||||||
\(502\) | 2.57466 | 0.114912 | ||||||||
\(503\) | −27.2800 | −1.21635 | −0.608176 | − | 0.793802i | \(-0.708099\pi\) | ||||
−0.608176 | + | 0.793802i | \(0.708099\pi\) | |||||||
\(504\) | −0.547903 | −0.0244055 | ||||||||
\(505\) | −4.80207 | −0.213689 | ||||||||
\(506\) | −2.35976 | −0.104904 | ||||||||
\(507\) | 12.3576 | 0.548821 | ||||||||
\(508\) | −6.76372 | −0.300092 | ||||||||
\(509\) | −21.2805 | −0.943243 | −0.471622 | − | 0.881801i | \(-0.656331\pi\) | ||||
−0.471622 | + | 0.881801i | \(0.656331\pi\) | |||||||
\(510\) | −0.322857 | −0.0142964 | ||||||||
\(511\) | −1.52154 | −0.0673091 | ||||||||
\(512\) | −5.95850 | −0.263331 | ||||||||
\(513\) | −2.62261 | −0.115791 | ||||||||
\(514\) | 9.68514 | 0.427193 | ||||||||
\(515\) | 21.1744 | 0.933057 | ||||||||
\(516\) | −3.04529 | −0.134061 | ||||||||
\(517\) | −0.685433 | −0.0301453 | ||||||||
\(518\) | −0.351149 | −0.0154286 | ||||||||
\(519\) | 10.3859 | 0.455889 | ||||||||
\(520\) | 2.30353 | 0.101017 | ||||||||
\(521\) | −25.1670 | −1.10258 | −0.551292 | − | 0.834312i | \(-0.685865\pi\) | ||||
−0.551292 | + | 0.834312i | \(0.685865\pi\) | |||||||
\(522\) | −0.730289 | −0.0319639 | ||||||||
\(523\) | 20.0188 | 0.875362 | 0.437681 | − | 0.899130i | \(-0.355800\pi\) | ||||
0.437681 | + | 0.899130i | \(0.355800\pi\) | |||||||
\(524\) | 25.7587 | 1.12527 | ||||||||
\(525\) | −0.784874 | −0.0342547 | ||||||||
\(526\) | 3.20568 | 0.139774 | ||||||||
\(527\) | −0.782502 | −0.0340863 | ||||||||
\(528\) | −0.530979 | −0.0231079 | ||||||||
\(529\) | −14.4093 | −0.626491 | ||||||||
\(530\) | −12.0434 | −0.523134 | ||||||||
\(531\) | 7.73715 | 0.335764 | ||||||||
\(532\) | 0.719810 | 0.0312077 | ||||||||
\(533\) | −1.46894 | −0.0636270 | ||||||||
\(534\) | −2.39800 | −0.103772 | ||||||||
\(535\) | 7.01710 | 0.303376 | ||||||||
\(536\) | −20.4936 | −0.885191 | ||||||||
\(537\) | −16.9049 | −0.729500 | ||||||||
\(538\) | −1.77633 | −0.0765830 | ||||||||
\(539\) | −6.95878 | −0.299736 | ||||||||
\(540\) | 1.43972 | 0.0619556 | ||||||||
\(541\) | 33.9981 | 1.46169 | 0.730847 | − | 0.682541i | \(-0.239125\pi\) | ||||
0.730847 | + | 0.682541i | \(0.239125\pi\) | |||||||
\(542\) | −8.79722 | −0.377873 | ||||||||
\(543\) | −2.91712 | −0.125186 | ||||||||
\(544\) | 2.19311 | 0.0940289 | ||||||||
\(545\) | 20.3926 | 0.873521 | ||||||||
\(546\) | −0.131016 | −0.00560696 | ||||||||
\(547\) | −17.6728 | −0.755636 | −0.377818 | − | 0.925880i | \(-0.623325\pi\) | ||||
−0.377818 | + | 0.925880i | \(0.623325\pi\) | |||||||
\(548\) | −24.9437 | −1.06554 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 3.11230 | 0.132709 | ||||||||
\(551\) | 2.37889 | 0.101344 | ||||||||
\(552\) | −7.90945 | −0.336649 | ||||||||
\(553\) | −1.50592 | −0.0640381 | ||||||||
\(554\) | −5.96522 | −0.253438 | ||||||||
\(555\) | 2.28787 | 0.0971145 | ||||||||
\(556\) | −19.7581 | −0.837931 | ||||||||
\(557\) | 40.6753 | 1.72347 | 0.861734 | − | 0.507360i | \(-0.169379\pi\) | ||||
0.861734 | + | 0.507360i | \(0.169379\pi\) | |||||||
\(558\) | −1.67319 | −0.0708318 | ||||||||
\(559\) | −1.80557 | −0.0763673 | ||||||||
\(560\) | −0.114819 | −0.00485197 | ||||||||
\(561\) | 0.376525 | 0.0158969 | ||||||||
\(562\) | 0.125161 | 0.00527961 | ||||||||
\(563\) | 43.3214 | 1.82578 | 0.912890 | − | 0.408207i | \(-0.133846\pi\) | ||||
0.912890 | + | 0.408207i | \(0.133846\pi\) | |||||||
\(564\) | −0.926570 | −0.0390156 | ||||||||
\(565\) | −3.02546 | −0.127282 | ||||||||
\(566\) | 9.62051 | 0.404380 | ||||||||
\(567\) | −0.203035 | −0.00852668 | ||||||||
\(568\) | −24.9335 | −1.04618 | ||||||||
\(569\) | −26.7783 | −1.12260 | −0.561302 | − | 0.827611i | \(-0.689699\pi\) | ||||
−0.561302 | + | 0.827611i | \(0.689699\pi\) | |||||||
\(570\) | 2.24880 | 0.0941917 | ||||||||
\(571\) | 29.9130 | 1.25182 | 0.625910 | − | 0.779896i | \(-0.284728\pi\) | ||||
0.625910 | + | 0.779896i | \(0.284728\pi\) | |||||||
\(572\) | −1.08346 | −0.0453017 | ||||||||
\(573\) | −10.8546 | −0.453457 | ||||||||
\(574\) | −0.299593 | −0.0125048 | ||||||||
\(575\) | −11.3303 | −0.472508 | ||||||||
\(576\) | 3.62748 | 0.151145 | ||||||||
\(577\) | −19.3583 | −0.805897 | −0.402948 | − | 0.915223i | \(-0.632015\pi\) | ||||
−0.402948 | + | 0.915223i | \(0.632015\pi\) | |||||||
\(578\) | 13.5727 | 0.564549 | ||||||||
\(579\) | −9.85294 | −0.409474 | ||||||||
\(580\) | −1.30593 | −0.0542257 | ||||||||
\(581\) | 1.73623 | 0.0720309 | ||||||||
\(582\) | 14.3464 | 0.594679 | ||||||||
\(583\) | 14.0454 | 0.581700 | ||||||||
\(584\) | 20.2230 | 0.836832 | ||||||||
\(585\) | 0.853616 | 0.0352927 | ||||||||
\(586\) | −13.6627 | −0.564402 | ||||||||
\(587\) | −33.1146 | −1.36679 | −0.683394 | − | 0.730050i | \(-0.739497\pi\) | ||||
−0.683394 | + | 0.730050i | \(0.739497\pi\) | |||||||
\(588\) | −9.40690 | −0.387934 | ||||||||
\(589\) | 5.45036 | 0.224578 | ||||||||
\(590\) | −6.63435 | −0.273132 | ||||||||
\(591\) | −1.58403 | −0.0651581 | ||||||||
\(592\) | −1.14063 | −0.0468795 | ||||||||
\(593\) | −11.3857 | −0.467555 | −0.233778 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233778 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(594\) | 0.805107 | 0.0330339 | ||||||||
\(595\) | 0.0814196 | 0.00333788 | ||||||||
\(596\) | 5.75974 | 0.235928 | ||||||||
\(597\) | −25.5545 | −1.04588 | ||||||||
\(598\) | −1.89133 | −0.0773421 | ||||||||
\(599\) | 14.0221 | 0.572927 | 0.286463 | − | 0.958091i | \(-0.407520\pi\) | ||||
0.286463 | + | 0.958091i | \(0.407520\pi\) | |||||||
\(600\) | 10.4318 | 0.425877 | ||||||||
\(601\) | 1.14648 | 0.0467660 | 0.0233830 | − | 0.999727i | \(-0.492556\pi\) | ||||
0.0233830 | + | 0.999727i | \(0.492556\pi\) | |||||||
\(602\) | −0.368247 | −0.0150086 | ||||||||
\(603\) | −7.59429 | −0.309263 | ||||||||
\(604\) | −27.0333 | −1.09997 | ||||||||
\(605\) | 1.06503 | 0.0432998 | ||||||||
\(606\) | −3.63010 | −0.147463 | ||||||||
\(607\) | −15.6771 | −0.636315 | −0.318157 | − | 0.948038i | \(-0.603064\pi\) | ||||
−0.318157 | + | 0.948038i | \(0.603064\pi\) | |||||||
\(608\) | −15.2757 | −0.619510 | ||||||||
\(609\) | 0.184168 | 0.00746284 | ||||||||
\(610\) | 0.857467 | 0.0347178 | ||||||||
\(611\) | −0.549368 | −0.0222251 | ||||||||
\(612\) | 0.508987 | 0.0205746 | ||||||||
\(613\) | 18.6826 | 0.754584 | 0.377292 | − | 0.926094i | \(-0.376855\pi\) | ||||
0.377292 | + | 0.926094i | \(0.376855\pi\) | |||||||
\(614\) | −10.7498 | −0.433827 | ||||||||
\(615\) | 1.95196 | 0.0787104 | ||||||||
\(616\) | −0.547903 | −0.0220756 | ||||||||
\(617\) | 3.28234 | 0.132142 | 0.0660709 | − | 0.997815i | \(-0.478954\pi\) | ||||
0.0660709 | + | 0.997815i | \(0.478954\pi\) | |||||||
\(618\) | 16.0067 | 0.643883 | ||||||||
\(619\) | −20.4789 | −0.823116 | −0.411558 | − | 0.911383i | \(-0.635015\pi\) | ||||
−0.411558 | + | 0.911383i | \(0.635015\pi\) | |||||||
\(620\) | −2.99205 | −0.120164 | ||||||||
\(621\) | −2.93099 | −0.117617 | ||||||||
\(622\) | 10.1851 | 0.408386 | ||||||||
\(623\) | 0.604738 | 0.0242283 | ||||||||
\(624\) | −0.425575 | −0.0170366 | ||||||||
\(625\) | 9.27215 | 0.370886 | ||||||||
\(626\) | −6.56488 | −0.262385 | ||||||||
\(627\) | −2.62261 | −0.104737 | ||||||||
\(628\) | −0.665347 | −0.0265502 | ||||||||
\(629\) | 0.808836 | 0.0322504 | ||||||||
\(630\) | 0.174096 | 0.00693615 | ||||||||
\(631\) | −21.1120 | −0.840454 | −0.420227 | − | 0.907419i | \(-0.638050\pi\) | ||||
−0.420227 | + | 0.907419i | \(0.638050\pi\) | |||||||
\(632\) | 20.0153 | 0.796165 | ||||||||
\(633\) | −16.1904 | −0.643512 | ||||||||
\(634\) | 18.3172 | 0.727468 | ||||||||
\(635\) | 5.32888 | 0.211470 | ||||||||
\(636\) | 18.9866 | 0.752867 | ||||||||
\(637\) | −5.57740 | −0.220985 | ||||||||
\(638\) | −0.730289 | −0.0289124 | ||||||||
\(639\) | −9.23954 | −0.365511 | ||||||||
\(640\) | 9.29639 | 0.367472 | ||||||||
\(641\) | −28.2912 | −1.11743 | −0.558717 | − | 0.829358i | \(-0.688706\pi\) | ||||
−0.558717 | + | 0.829358i | \(0.688706\pi\) | |||||||
\(642\) | 5.30453 | 0.209353 | ||||||||
\(643\) | −20.9767 | −0.827238 | −0.413619 | − | 0.910450i | \(-0.635736\pi\) | ||||
−0.413619 | + | 0.910450i | \(0.635736\pi\) | |||||||
\(644\) | 0.804451 | 0.0316998 | ||||||||
\(645\) | 2.39927 | 0.0944710 | ||||||||
\(646\) | 0.795024 | 0.0312798 | ||||||||
\(647\) | 20.5640 | 0.808456 | 0.404228 | − | 0.914658i | \(-0.367540\pi\) | ||||
0.404228 | + | 0.914658i | \(0.367540\pi\) | |||||||
\(648\) | 2.69856 | 0.106009 | ||||||||
\(649\) | 7.73715 | 0.303710 | ||||||||
\(650\) | 2.49448 | 0.0978416 | ||||||||
\(651\) | 0.421952 | 0.0165376 | ||||||||
\(652\) | 2.61886 | 0.102562 | ||||||||
\(653\) | 3.95699 | 0.154849 | 0.0774246 | − | 0.996998i | \(-0.475330\pi\) | ||||
0.0774246 | + | 0.996998i | \(0.475330\pi\) | |||||||
\(654\) | 15.4156 | 0.602799 | ||||||||
\(655\) | −20.2943 | −0.792963 | ||||||||
\(656\) | −0.973158 | −0.0379954 | ||||||||
\(657\) | 7.49398 | 0.292368 | ||||||||
\(658\) | −0.112044 | −0.00436794 | ||||||||
\(659\) | −13.5419 | −0.527519 | −0.263759 | − | 0.964589i | \(-0.584962\pi\) | ||||
−0.263759 | + | 0.964589i | \(0.584962\pi\) | |||||||
\(660\) | 1.43972 | 0.0560409 | ||||||||
\(661\) | −37.6849 | −1.46577 | −0.732886 | − | 0.680351i | \(-0.761827\pi\) | ||||
−0.732886 | + | 0.680351i | \(0.761827\pi\) | |||||||
\(662\) | −1.99350 | −0.0774797 | ||||||||
\(663\) | 0.301781 | 0.0117202 | ||||||||
\(664\) | −23.0764 | −0.895536 | ||||||||
\(665\) | −0.567111 | −0.0219916 | ||||||||
\(666\) | 1.72950 | 0.0670167 | ||||||||
\(667\) | 2.65862 | 0.102942 | ||||||||
\(668\) | −20.0524 | −0.775851 | ||||||||
\(669\) | 4.93169 | 0.190670 | ||||||||
\(670\) | 6.51185 | 0.251575 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −1.18260 | −0.0456199 | ||||||||
\(673\) | 46.2878 | 1.78427 | 0.892133 | − | 0.451774i | \(-0.149209\pi\) | ||||
0.892133 | + | 0.451774i | \(0.149209\pi\) | |||||||
\(674\) | 9.55394 | 0.368004 | ||||||||
\(675\) | 3.86570 | 0.148791 | ||||||||
\(676\) | 16.7051 | 0.642502 | ||||||||
\(677\) | 26.6561 | 1.02448 | 0.512239 | − | 0.858843i | \(-0.328816\pi\) | ||||
0.512239 | + | 0.858843i | \(0.328816\pi\) | |||||||
\(678\) | −2.28708 | −0.0878348 | ||||||||
\(679\) | −3.61795 | −0.138844 | ||||||||
\(680\) | −1.08215 | −0.0414987 | ||||||||
\(681\) | 2.59452 | 0.0994222 | ||||||||
\(682\) | −1.67319 | −0.0640698 | ||||||||
\(683\) | 27.7294 | 1.06104 | 0.530519 | − | 0.847673i | \(-0.321997\pi\) | ||||
0.530519 | + | 0.847673i | \(0.321997\pi\) | |||||||
\(684\) | −3.54525 | −0.135556 | ||||||||
\(685\) | 19.6522 | 0.750871 | ||||||||
\(686\) | −2.28177 | −0.0871185 | ||||||||
\(687\) | 6.75414 | 0.257687 | ||||||||
\(688\) | −1.19617 | −0.0456034 | ||||||||
\(689\) | 11.2572 | 0.428867 | ||||||||
\(690\) | 2.51323 | 0.0956769 | ||||||||
\(691\) | −14.4148 | −0.548365 | −0.274183 | − | 0.961678i | \(-0.588407\pi\) | ||||
−0.274183 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(692\) | 14.0397 | 0.533708 | ||||||||
\(693\) | −0.203035 | −0.00771267 | ||||||||
\(694\) | −26.9291 | −1.02222 | ||||||||
\(695\) | 15.5667 | 0.590477 | ||||||||
\(696\) | −2.44779 | −0.0927831 | ||||||||
\(697\) | 0.690080 | 0.0261387 | ||||||||
\(698\) | 15.9238 | 0.602724 | ||||||||
\(699\) | 27.8481 | 1.05331 | ||||||||
\(700\) | −1.06099 | −0.0401018 | ||||||||
\(701\) | −21.9567 | −0.829295 | −0.414647 | − | 0.909982i | \(-0.636095\pi\) | ||||
−0.414647 | + | 0.909982i | \(0.636095\pi\) | |||||||
\(702\) | 0.645286 | 0.0243547 | ||||||||
\(703\) | −5.63378 | −0.212482 | ||||||||
\(704\) | 3.62748 | 0.136716 | ||||||||
\(705\) | 0.730010 | 0.0274938 | ||||||||
\(706\) | 12.3047 | 0.463093 | ||||||||
\(707\) | 0.915453 | 0.0344292 | ||||||||
\(708\) | 10.4591 | 0.393077 | ||||||||
\(709\) | −5.41410 | −0.203331 | −0.101665 | − | 0.994819i | \(-0.532417\pi\) | ||||
−0.101665 | + | 0.994819i | \(0.532417\pi\) | |||||||
\(710\) | 7.92260 | 0.297330 | ||||||||
\(711\) | 7.41703 | 0.278160 | ||||||||
\(712\) | −8.03763 | −0.301223 | ||||||||
\(713\) | 6.09125 | 0.228119 | ||||||||
\(714\) | 0.0615487 | 0.00230340 | ||||||||
\(715\) | 0.853616 | 0.0319234 | ||||||||
\(716\) | −22.8521 | −0.854023 | ||||||||
\(717\) | −16.9202 | −0.631898 | ||||||||
\(718\) | −8.24906 | −0.307852 | ||||||||
\(719\) | 34.7613 | 1.29638 | 0.648188 | − | 0.761480i | \(-0.275527\pi\) | ||||
0.648188 | + | 0.761480i | \(0.275527\pi\) | |||||||
\(720\) | 0.565511 | 0.0210753 | ||||||||
\(721\) | −4.03664 | −0.150332 | ||||||||
\(722\) | 9.75946 | 0.363209 | ||||||||
\(723\) | 1.06455 | 0.0395911 | ||||||||
\(724\) | −3.94337 | −0.146554 | ||||||||
\(725\) | −3.50647 | −0.130227 | ||||||||
\(726\) | 0.805107 | 0.0298803 | ||||||||
\(727\) | 34.1852 | 1.26786 | 0.633930 | − | 0.773390i | \(-0.281441\pi\) | ||||
0.633930 | + | 0.773390i | \(0.281441\pi\) | |||||||
\(728\) | −0.439139 | −0.0162756 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.42584 | −0.237831 | ||||||||
\(731\) | 0.848220 | 0.0313725 | ||||||||
\(732\) | −1.35180 | −0.0499641 | ||||||||
\(733\) | −21.4554 | −0.792474 | −0.396237 | − | 0.918148i | \(-0.629684\pi\) | ||||
−0.396237 | + | 0.918148i | \(0.629684\pi\) | |||||||
\(734\) | −9.29746 | −0.343176 | ||||||||
\(735\) | 7.41134 | 0.273371 | ||||||||
\(736\) | −17.0719 | −0.629278 | ||||||||
\(737\) | −7.59429 | −0.279739 | ||||||||
\(738\) | 1.47557 | 0.0543164 | ||||||||
\(739\) | 33.6003 | 1.23601 | 0.618004 | − | 0.786175i | \(-0.287942\pi\) | ||||
0.618004 | + | 0.786175i | \(0.287942\pi\) | |||||||
\(740\) | 3.09274 | 0.113692 | ||||||||
\(741\) | −2.10199 | −0.0772187 | ||||||||
\(742\) | 2.29593 | 0.0842862 | ||||||||
\(743\) | 3.15148 | 0.115617 | 0.0578083 | − | 0.998328i | \(-0.481589\pi\) | ||||
0.0578083 | + | 0.998328i | \(0.481589\pi\) | |||||||
\(744\) | −5.60821 | −0.205607 | ||||||||
\(745\) | −4.53788 | −0.166255 | ||||||||
\(746\) | 21.1195 | 0.773240 | ||||||||
\(747\) | −8.55136 | −0.312878 | ||||||||
\(748\) | 0.508987 | 0.0186104 | ||||||||
\(749\) | −1.33772 | −0.0488792 | ||||||||
\(750\) | −7.60204 | −0.277587 | ||||||||
\(751\) | −21.1165 | −0.770551 | −0.385276 | − | 0.922802i | \(-0.625894\pi\) | ||||
−0.385276 | + | 0.922802i | \(0.625894\pi\) | |||||||
\(752\) | −0.363950 | −0.0132719 | ||||||||
\(753\) | 3.19791 | 0.116538 | ||||||||
\(754\) | −0.585320 | −0.0213161 | ||||||||
\(755\) | 21.2986 | 0.775134 | ||||||||
\(756\) | −0.274464 | −0.00998215 | ||||||||
\(757\) | 25.3065 | 0.919779 | 0.459890 | − | 0.887976i | \(-0.347889\pi\) | ||||
0.459890 | + | 0.887976i | \(0.347889\pi\) | |||||||
\(758\) | −8.96923 | −0.325777 | ||||||||
\(759\) | −2.93099 | −0.106388 | ||||||||
\(760\) | 7.53752 | 0.273415 | ||||||||
\(761\) | −26.3449 | −0.955000 | −0.477500 | − | 0.878632i | \(-0.658457\pi\) | ||||
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(762\) | 4.02833 | 0.145931 | ||||||||
\(763\) | −3.88758 | −0.140740 | ||||||||
\(764\) | −14.6733 | −0.530860 | ||||||||
\(765\) | −0.401012 | −0.0144986 | ||||||||
\(766\) | −30.3280 | −1.09580 | ||||||||
\(767\) | 6.20126 | 0.223914 | ||||||||
\(768\) | 14.2825 | 0.515375 | ||||||||
\(769\) | −0.854669 | −0.0308202 | −0.0154101 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154101 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(770\) | 0.174096 | 0.00627398 | ||||||||
\(771\) | 12.0296 | 0.433237 | ||||||||
\(772\) | −13.3192 | −0.479370 | ||||||||
\(773\) | 14.3339 | 0.515555 | 0.257778 | − | 0.966204i | \(-0.417010\pi\) | ||||
0.257778 | + | 0.966204i | \(0.417010\pi\) | |||||||
\(774\) | 1.81371 | 0.0651925 | ||||||||
\(775\) | −8.03378 | −0.288582 | ||||||||
\(776\) | 48.0864 | 1.72620 | ||||||||
\(777\) | −0.436152 | −0.0156469 | ||||||||
\(778\) | 8.80543 | 0.315690 | ||||||||
\(779\) | −4.80661 | −0.172215 | ||||||||
\(780\) | 1.15392 | 0.0413170 | ||||||||
\(781\) | −9.23954 | −0.330617 | ||||||||
\(782\) | 0.888508 | 0.0317730 | ||||||||
\(783\) | −0.907071 | −0.0324161 | ||||||||
\(784\) | −3.69496 | −0.131963 | ||||||||
\(785\) | 0.524202 | 0.0187096 | ||||||||
\(786\) | −15.3413 | −0.547208 | ||||||||
\(787\) | 46.4807 | 1.65686 | 0.828430 | − | 0.560093i | \(-0.189235\pi\) | ||||
0.828430 | + | 0.560093i | \(0.189235\pi\) | |||||||
\(788\) | −2.14129 | −0.0762804 | ||||||||
\(789\) | 3.98169 | 0.141752 | ||||||||
\(790\) | −6.35985 | −0.226273 | ||||||||
\(791\) | 0.576766 | 0.0205074 | ||||||||
\(792\) | 2.69856 | 0.0958891 | ||||||||
\(793\) | −0.801491 | −0.0284618 | ||||||||
\(794\) | −26.7371 | −0.948864 | ||||||||
\(795\) | −14.9588 | −0.530534 | ||||||||
\(796\) | −34.5447 | −1.22440 | ||||||||
\(797\) | −13.5176 | −0.478817 | −0.239409 | − | 0.970919i | \(-0.576954\pi\) | ||||
−0.239409 | + | 0.970919i | \(0.576954\pi\) | |||||||
\(798\) | −0.428704 | −0.0151760 | ||||||||
\(799\) | 0.258082 | 0.00913030 | ||||||||
\(800\) | 22.5162 | 0.796068 | ||||||||
\(801\) | −2.97849 | −0.105240 | ||||||||
\(802\) | 15.1007 | 0.533226 | ||||||||
\(803\) | 7.49398 | 0.264457 | ||||||||
\(804\) | −10.2660 | −0.362054 | ||||||||
\(805\) | −0.633797 | −0.0223384 | ||||||||
\(806\) | −1.34105 | −0.0472364 | ||||||||
\(807\) | −2.20633 | −0.0776665 | ||||||||
\(808\) | −12.1674 | −0.428046 | ||||||||
\(809\) | 44.3814 | 1.56037 | 0.780183 | − | 0.625551i | \(-0.215126\pi\) | ||||
0.780183 | + | 0.625551i | \(0.215126\pi\) | |||||||
\(810\) | −0.857467 | −0.0301283 | ||||||||
\(811\) | −2.02464 | −0.0710946 | −0.0355473 | − | 0.999368i | \(-0.511317\pi\) | ||||
−0.0355473 | + | 0.999368i | \(0.511317\pi\) | |||||||
\(812\) | 0.248958 | 0.00873672 | ||||||||
\(813\) | −10.9268 | −0.383219 | ||||||||
\(814\) | 1.72950 | 0.0606189 | ||||||||
\(815\) | −2.06330 | −0.0722743 | ||||||||
\(816\) | 0.199927 | 0.00699883 | ||||||||
\(817\) | −5.90810 | −0.206698 | ||||||||
\(818\) | −4.80954 | −0.168162 | ||||||||
\(819\) | −0.162731 | −0.00568628 | ||||||||
\(820\) | 2.63866 | 0.0921460 | ||||||||
\(821\) | 26.4603 | 0.923472 | 0.461736 | − | 0.887017i | \(-0.347227\pi\) | ||||
0.461736 | + | 0.887017i | \(0.347227\pi\) | |||||||
\(822\) | 14.8559 | 0.518161 | ||||||||
\(823\) | −40.6265 | −1.41615 | −0.708075 | − | 0.706137i | \(-0.750436\pi\) | ||||
−0.708075 | + | 0.706137i | \(0.750436\pi\) | |||||||
\(824\) | 53.6513 | 1.86903 | ||||||||
\(825\) | 3.86570 | 0.134586 | ||||||||
\(826\) | 1.26475 | 0.0440064 | ||||||||
\(827\) | −39.7573 | −1.38250 | −0.691248 | − | 0.722617i | \(-0.742939\pi\) | ||||
−0.691248 | + | 0.722617i | \(0.742939\pi\) | |||||||
\(828\) | −3.96212 | −0.137693 | ||||||||
\(829\) | −8.76395 | −0.304385 | −0.152192 | − | 0.988351i | \(-0.548633\pi\) | ||||
−0.152192 | + | 0.988351i | \(0.548633\pi\) | |||||||
\(830\) | 7.33251 | 0.254515 | ||||||||
\(831\) | −7.40923 | −0.257023 | ||||||||
\(832\) | 2.90739 | 0.100796 | ||||||||
\(833\) | 2.62015 | 0.0907829 | ||||||||
\(834\) | 11.7675 | 0.407476 | ||||||||
\(835\) | 15.7985 | 0.546731 | ||||||||
\(836\) | −3.54525 | −0.122615 | ||||||||
\(837\) | −2.07822 | −0.0718339 | ||||||||
\(838\) | 17.5011 | 0.604565 | ||||||||
\(839\) | −0.750852 | −0.0259223 | −0.0129611 | − | 0.999916i | \(-0.504126\pi\) | ||||
−0.0129611 | + | 0.999916i | \(0.504126\pi\) | |||||||
\(840\) | 0.583535 | 0.0201339 | ||||||||
\(841\) | −28.1772 | −0.971628 | ||||||||
\(842\) | 13.0570 | 0.449973 | ||||||||
\(843\) | 0.155459 | 0.00535430 | ||||||||
\(844\) | −21.8863 | −0.753357 | ||||||||
\(845\) | −13.1613 | −0.452762 | ||||||||
\(846\) | 0.551846 | 0.0189729 | ||||||||
\(847\) | −0.203035 | −0.00697637 | ||||||||
\(848\) | 7.45779 | 0.256102 | ||||||||
\(849\) | 11.9494 | 0.410101 | ||||||||
\(850\) | −1.17186 | −0.0401944 | ||||||||
\(851\) | −6.29624 | −0.215832 | ||||||||
\(852\) | −12.4900 | −0.427902 | ||||||||
\(853\) | 27.3127 | 0.935168 | 0.467584 | − | 0.883949i | \(-0.345124\pi\) | ||||
0.467584 | + | 0.883949i | \(0.345124\pi\) | |||||||
\(854\) | −0.163465 | −0.00559366 | ||||||||
\(855\) | 2.79317 | 0.0955243 | ||||||||
\(856\) | 17.7798 | 0.607699 | ||||||||
\(857\) | −8.31434 | −0.284012 | −0.142006 | − | 0.989866i | \(-0.545355\pi\) | ||||
−0.142006 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(858\) | 0.645286 | 0.0220297 | ||||||||
\(859\) | 27.0139 | 0.921703 | 0.460852 | − | 0.887477i | \(-0.347544\pi\) | ||||
0.460852 | + | 0.887477i | \(0.347544\pi\) | |||||||
\(860\) | 3.24334 | 0.110597 | ||||||||
\(861\) | −0.372115 | −0.0126817 | ||||||||
\(862\) | 25.0192 | 0.852157 | ||||||||
\(863\) | −7.54619 | −0.256875 | −0.128438 | − | 0.991718i | \(-0.540996\pi\) | ||||
−0.128438 | + | 0.991718i | \(0.540996\pi\) | |||||||
\(864\) | 5.82461 | 0.198157 | ||||||||
\(865\) | −11.0613 | −0.376096 | ||||||||
\(866\) | −30.1615 | −1.02493 | ||||||||
\(867\) | 16.8582 | 0.572535 | ||||||||
\(868\) | 0.570397 | 0.0193605 | ||||||||
\(869\) | 7.41703 | 0.251605 | ||||||||
\(870\) | 0.777784 | 0.0263693 | ||||||||
\(871\) | −6.08676 | −0.206242 | ||||||||
\(872\) | 51.6702 | 1.74977 | ||||||||
\(873\) | 17.8193 | 0.603092 | ||||||||
\(874\) | −6.18872 | −0.209337 | ||||||||
\(875\) | 1.91712 | 0.0648104 | ||||||||
\(876\) | 10.1304 | 0.342274 | ||||||||
\(877\) | −40.4243 | −1.36503 | −0.682515 | − | 0.730871i | \(-0.739114\pi\) | ||||
−0.682515 | + | 0.730871i | \(0.739114\pi\) | |||||||
\(878\) | −12.1255 | −0.409215 | ||||||||
\(879\) | −16.9701 | −0.572387 | ||||||||
\(880\) | 0.565511 | 0.0190634 | ||||||||
\(881\) | −24.8846 | −0.838383 | −0.419191 | − | 0.907898i | \(-0.637686\pi\) | ||||
−0.419191 | + | 0.907898i | \(0.637686\pi\) | |||||||
\(882\) | 5.60256 | 0.188648 | ||||||||
\(883\) | 43.2827 | 1.45658 | 0.728289 | − | 0.685270i | \(-0.240316\pi\) | ||||
0.728289 | + | 0.685270i | \(0.240316\pi\) | |||||||
\(884\) | 0.407949 | 0.0137208 | ||||||||
\(885\) | −8.24034 | −0.276996 | ||||||||
\(886\) | −6.04154 | −0.202970 | ||||||||
\(887\) | 10.2272 | 0.343396 | 0.171698 | − | 0.985150i | \(-0.445075\pi\) | ||||
0.171698 | + | 0.985150i | \(0.445075\pi\) | |||||||
\(888\) | 5.79694 | 0.194533 | ||||||||
\(889\) | −1.01588 | −0.0340716 | ||||||||
\(890\) | 2.55396 | 0.0856088 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 6.66667 | 0.223217 | ||||||||
\(893\) | −1.79762 | −0.0601550 | ||||||||
\(894\) | −3.43038 | −0.114729 | ||||||||
\(895\) | 18.0043 | 0.601817 | ||||||||
\(896\) | −1.77224 | −0.0592063 | ||||||||
\(897\) | −2.34916 | −0.0784363 | ||||||||
\(898\) | −10.9030 | −0.363839 | ||||||||
\(899\) | 1.88510 | 0.0628715 | ||||||||
\(900\) | 5.22567 | 0.174189 | ||||||||
\(901\) | −5.28843 | −0.176183 | ||||||||
\(902\) | 1.47557 | 0.0491311 | ||||||||
\(903\) | −0.457390 | −0.0152210 | ||||||||
\(904\) | −7.66584 | −0.254962 | ||||||||
\(905\) | 3.10683 | 0.103275 | ||||||||
\(906\) | 16.1005 | 0.534904 | ||||||||
\(907\) | −34.3774 | −1.14148 | −0.570741 | − | 0.821130i | \(-0.693344\pi\) | ||||
−0.570741 | + | 0.821130i | \(0.693344\pi\) | |||||||
\(908\) | 3.50728 | 0.116393 | ||||||||
\(909\) | −4.50884 | −0.149549 | ||||||||
\(910\) | 0.139536 | 0.00462559 | ||||||||
\(911\) | −20.2548 | −0.671072 | −0.335536 | − | 0.942027i | \(-0.608917\pi\) | ||||
−0.335536 | + | 0.942027i | \(0.608917\pi\) | |||||||
\(912\) | −1.39255 | −0.0461118 | ||||||||
\(913\) | −8.55136 | −0.283009 | ||||||||
\(914\) | −8.19921 | −0.271206 | ||||||||
\(915\) | 1.06503 | 0.0352090 | ||||||||
\(916\) | 9.13027 | 0.301673 | ||||||||
\(917\) | 3.86885 | 0.127761 | ||||||||
\(918\) | −0.303143 | −0.0100052 | ||||||||
\(919\) | −26.9266 | −0.888227 | −0.444114 | − | 0.895970i | \(-0.646481\pi\) | ||||
−0.444114 | + | 0.895970i | \(0.646481\pi\) | |||||||
\(920\) | 8.42384 | 0.277726 | ||||||||
\(921\) | −13.3520 | −0.439965 | ||||||||
\(922\) | 11.3237 | 0.372927 | ||||||||
\(923\) | −7.40541 | −0.243752 | ||||||||
\(924\) | −0.274464 | −0.00902919 | ||||||||
\(925\) | 8.30415 | 0.273039 | ||||||||
\(926\) | 21.9866 | 0.722526 | ||||||||
\(927\) | 19.8815 | 0.652993 | ||||||||
\(928\) | −5.28334 | −0.173434 | ||||||||
\(929\) | 13.1495 | 0.431421 | 0.215711 | − | 0.976457i | \(-0.430793\pi\) | ||||
0.215711 | + | 0.976457i | \(0.430793\pi\) | |||||||
\(930\) | 1.78201 | 0.0584343 | ||||||||
\(931\) | −18.2501 | −0.598124 | ||||||||
\(932\) | 37.6452 | 1.23311 | ||||||||
\(933\) | 12.6506 | 0.414163 | ||||||||
\(934\) | −13.0293 | −0.426332 | ||||||||
\(935\) | −0.401012 | −0.0131145 | ||||||||
\(936\) | 2.16287 | 0.0706957 | ||||||||
\(937\) | 19.9881 | 0.652981 | 0.326491 | − | 0.945200i | \(-0.394134\pi\) | ||||
0.326491 | + | 0.945200i | \(0.394134\pi\) | |||||||
\(938\) | −1.24140 | −0.0405332 | ||||||||
\(939\) | −8.15405 | −0.266097 | ||||||||
\(940\) | 0.986829 | 0.0321868 | ||||||||
\(941\) | 24.3479 | 0.793720 | 0.396860 | − | 0.917879i | \(-0.370100\pi\) | ||||
0.396860 | + | 0.917879i | \(0.370100\pi\) | |||||||
\(942\) | 0.396267 | 0.0129111 | ||||||||
\(943\) | −5.37181 | −0.174930 | ||||||||
\(944\) | 4.10826 | 0.133713 | ||||||||
\(945\) | 0.216240 | 0.00703428 | ||||||||
\(946\) | 1.81371 | 0.0589688 | ||||||||
\(947\) | −33.4192 | −1.08598 | −0.542989 | − | 0.839740i | \(-0.682707\pi\) | ||||
−0.542989 | + | 0.839740i | \(0.682707\pi\) | |||||||
\(948\) | 10.0264 | 0.325641 | ||||||||
\(949\) | 6.00636 | 0.194975 | ||||||||
\(950\) | 8.16234 | 0.264821 | ||||||||
\(951\) | 22.7512 | 0.737760 | ||||||||
\(952\) | 0.206299 | 0.00668619 | ||||||||
\(953\) | −1.05530 | −0.0341847 | −0.0170923 | − | 0.999854i | \(-0.505441\pi\) | ||||
−0.0170923 | + | 0.999854i | \(0.505441\pi\) | |||||||
\(954\) | −11.3080 | −0.366111 | ||||||||
\(955\) | 11.5605 | 0.374089 | ||||||||
\(956\) | −22.8728 | −0.739761 | ||||||||
\(957\) | −0.907071 | −0.0293215 | ||||||||
\(958\) | 15.7638 | 0.509305 | ||||||||
\(959\) | −3.74644 | −0.120979 | ||||||||
\(960\) | −3.86339 | −0.124690 | ||||||||
\(961\) | −26.6810 | −0.860677 | ||||||||
\(962\) | 1.38618 | 0.0446922 | ||||||||
\(963\) | 6.58861 | 0.212315 | ||||||||
\(964\) | 1.43907 | 0.0463492 | ||||||||
\(965\) | 10.4937 | 0.337805 | ||||||||
\(966\) | −0.479115 | −0.0154153 | ||||||||
\(967\) | 15.5418 | 0.499791 | 0.249895 | − | 0.968273i | \(-0.419604\pi\) | ||||
0.249895 | + | 0.968273i | \(0.419604\pi\) | |||||||
\(968\) | 2.69856 | 0.0867350 | ||||||||
\(969\) | 0.987476 | 0.0317223 | ||||||||
\(970\) | −15.2795 | −0.490594 | ||||||||
\(971\) | −27.9120 | −0.895738 | −0.447869 | − | 0.894099i | \(-0.647817\pi\) | ||||
−0.447869 | + | 0.894099i | \(0.647817\pi\) | |||||||
\(972\) | 1.35180 | 0.0433591 | ||||||||
\(973\) | −2.96759 | −0.0951365 | ||||||||
\(974\) | 20.6797 | 0.662622 | ||||||||
\(975\) | 3.09832 | 0.0992258 | ||||||||
\(976\) | −0.530979 | −0.0169962 | ||||||||
\(977\) | 10.2968 | 0.329423 | 0.164712 | − | 0.986342i | \(-0.447331\pi\) | ||||
0.164712 | + | 0.986342i | \(0.447331\pi\) | |||||||
\(978\) | −1.55974 | −0.0498750 | ||||||||
\(979\) | −2.97849 | −0.0951929 | ||||||||
\(980\) | 10.0187 | 0.320035 | ||||||||
\(981\) | 19.1473 | 0.611327 | ||||||||
\(982\) | −24.1730 | −0.771393 | ||||||||
\(983\) | −53.4728 | −1.70552 | −0.852759 | − | 0.522304i | \(-0.825073\pi\) | ||||
−0.852759 | + | 0.522304i | \(0.825073\pi\) | |||||||
\(984\) | 4.94582 | 0.157667 | ||||||||
\(985\) | 1.68704 | 0.0537537 | ||||||||
\(986\) | 0.274972 | 0.00875689 | ||||||||
\(987\) | −0.139167 | −0.00442973 | ||||||||
\(988\) | −2.84148 | −0.0903996 | ||||||||
\(989\) | −6.60282 | −0.209957 | ||||||||
\(990\) | −0.857467 | −0.0272521 | ||||||||
\(991\) | −22.7926 | −0.724031 | −0.362015 | − | 0.932172i | \(-0.617911\pi\) | ||||
−0.362015 | + | 0.932172i | \(0.617911\pi\) | |||||||
\(992\) | −12.1048 | −0.384329 | ||||||||
\(993\) | −2.47607 | −0.0785758 | ||||||||
\(994\) | −1.51034 | −0.0479051 | ||||||||
\(995\) | 27.2165 | 0.862820 | ||||||||
\(996\) | −11.5598 | −0.366285 | ||||||||
\(997\) | 53.2933 | 1.68782 | 0.843908 | − | 0.536488i | \(-0.180249\pi\) | ||||
0.843908 | + | 0.536488i | \(0.180249\pi\) | |||||||
\(998\) | −13.4186 | −0.424757 | ||||||||
\(999\) | 2.14816 | 0.0679648 |
(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 | 2013.2.a.e.1.6 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.8 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.6 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.8 | 13 | 3.2 | odd | 2 |