Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.254102 | −0.179677 | −0.0898385 | − | 0.995956i | \(-0.528635\pi\) | ||||
−0.0898385 | + | 0.995956i | \(0.528635\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.93543 | −0.967716 | ||||||||
\(5\) | −1.93543 | −0.865552 | −0.432776 | − | 0.901502i | \(-0.642466\pi\) | ||||
−0.432776 | + | 0.901502i | \(0.642466\pi\) | |||||||
\(6\) | 0.254102 | 0.103737 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.491797 | 0.155520 | ||||||||
\(11\) | 3.87086 | 1.16711 | 0.583555 | − | 0.812074i | \(-0.301661\pi\) | ||||
0.583555 | + | 0.812074i | \(0.301661\pi\) | |||||||
\(12\) | 1.93543 | 0.558711 | ||||||||
\(13\) | 5.68133 | 1.57572 | 0.787859 | − | 0.615856i | \(-0.211190\pi\) | ||||
0.787859 | + | 0.615856i | \(0.211190\pi\) | |||||||
\(14\) | 0.254102 | 0.0679115 | ||||||||
\(15\) | 1.93543 | 0.499726 | ||||||||
\(16\) | 3.61676 | 0.904191 | ||||||||
\(17\) | −5.69774 | −1.38190 | −0.690952 | − | 0.722900i | \(-0.742808\pi\) | ||||
−0.690952 | + | 0.722900i | \(0.742808\pi\) | |||||||
\(18\) | −0.254102 | −0.0598923 | ||||||||
\(19\) | 2.31867 | 0.531939 | 0.265970 | − | 0.963981i | \(-0.414308\pi\) | ||||
0.265970 | + | 0.963981i | \(0.414308\pi\) | |||||||
\(20\) | 3.74590 | 0.837608 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −0.983593 | −0.209703 | ||||||||
\(23\) | −3.50820 | −0.731511 | −0.365755 | − | 0.930711i | \(-0.619189\pi\) | ||||
−0.365755 | + | 0.930711i | \(0.619189\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.25410 | −0.250820 | ||||||||
\(26\) | −1.44364 | −0.283120 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.93543 | 0.365762 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −0.491797 | −0.0897894 | ||||||||
\(31\) | −0.826873 | −0.148511 | −0.0742554 | − | 0.997239i | \(-0.523658\pi\) | ||||
−0.0742554 | + | 0.997239i | \(0.523658\pi\) | |||||||
\(32\) | −2.91903 | −0.516016 | ||||||||
\(33\) | −3.87086 | −0.673831 | ||||||||
\(34\) | 1.44780 | 0.248296 | ||||||||
\(35\) | 1.93543 | 0.327148 | ||||||||
\(36\) | −1.93543 | −0.322572 | ||||||||
\(37\) | −3.44364 | −0.566130 | −0.283065 | − | 0.959101i | \(-0.591351\pi\) | ||||
−0.283065 | + | 0.959101i | \(0.591351\pi\) | |||||||
\(38\) | −0.589178 | −0.0955773 | ||||||||
\(39\) | −5.68133 | −0.909741 | ||||||||
\(40\) | −1.93543 | −0.306019 | ||||||||
\(41\) | 2.82687 | 0.441483 | 0.220742 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220742 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(42\) | −0.254102 | −0.0392087 | ||||||||
\(43\) | 3.49180 | 0.532494 | 0.266247 | − | 0.963905i | \(-0.414216\pi\) | ||||
0.266247 | + | 0.963905i | \(0.414216\pi\) | |||||||
\(44\) | −7.49180 | −1.12943 | ||||||||
\(45\) | −1.93543 | −0.288517 | ||||||||
\(46\) | 0.891440 | 0.131436 | ||||||||
\(47\) | −3.66492 | −0.534584 | −0.267292 | − | 0.963616i | \(-0.586129\pi\) | ||||
−0.267292 | + | 0.963616i | \(0.586129\pi\) | |||||||
\(48\) | −3.61676 | −0.522035 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.318669 | 0.0450667 | ||||||||
\(51\) | 5.69774 | 0.797843 | ||||||||
\(52\) | −10.9958 | −1.52485 | ||||||||
\(53\) | −1.27051 | −0.174518 | −0.0872589 | − | 0.996186i | \(-0.527811\pi\) | ||||
−0.0872589 | + | 0.996186i | \(0.527811\pi\) | |||||||
\(54\) | 0.254102 | 0.0345789 | ||||||||
\(55\) | −7.49180 | −1.01019 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.31867 | −0.307115 | ||||||||
\(58\) | −0.762305 | −0.100096 | ||||||||
\(59\) | −10.4876 | −1.36537 | −0.682686 | − | 0.730711i | \(-0.739188\pi\) | ||||
−0.682686 | + | 0.730711i | \(0.739188\pi\) | |||||||
\(60\) | −3.74590 | −0.483593 | ||||||||
\(61\) | 2.38324 | 0.305142 | 0.152571 | − | 0.988292i | \(-0.451245\pi\) | ||||
0.152571 | + | 0.988292i | \(0.451245\pi\) | |||||||
\(62\) | 0.210110 | 0.0266840 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −6.49180 | −0.811475 | ||||||||
\(65\) | −10.9958 | −1.36386 | ||||||||
\(66\) | 0.983593 | 0.121072 | ||||||||
\(67\) | −3.06457 | −0.374397 | −0.187198 | − | 0.982322i | \(-0.559941\pi\) | ||||
−0.187198 | + | 0.982322i | \(0.559941\pi\) | |||||||
\(68\) | 11.0276 | 1.33729 | ||||||||
\(69\) | 3.50820 | 0.422338 | ||||||||
\(70\) | −0.491797 | −0.0587809 | ||||||||
\(71\) | 8.72532 | 1.03551 | 0.517753 | − | 0.855530i | \(-0.326769\pi\) | ||||
0.517753 | + | 0.855530i | \(0.326769\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.55636 | 0.650323 | 0.325162 | − | 0.945658i | \(-0.394581\pi\) | ||||
0.325162 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(74\) | 0.875034 | 0.101721 | ||||||||
\(75\) | 1.25410 | 0.144811 | ||||||||
\(76\) | −4.48763 | −0.514766 | ||||||||
\(77\) | −3.87086 | −0.441126 | ||||||||
\(78\) | 1.44364 | 0.163460 | ||||||||
\(79\) | 8.18953 | 0.921395 | 0.460697 | − | 0.887557i | \(-0.347599\pi\) | ||||
0.460697 | + | 0.887557i | \(0.347599\pi\) | |||||||
\(80\) | −7.00000 | −0.782624 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.718313 | −0.0793244 | ||||||||
\(83\) | −9.69774 | −1.06446 | −0.532232 | − | 0.846598i | \(-0.678647\pi\) | ||||
−0.532232 | + | 0.846598i | \(0.678647\pi\) | |||||||
\(84\) | −1.93543 | −0.211173 | ||||||||
\(85\) | 11.0276 | 1.19611 | ||||||||
\(86\) | −0.887271 | −0.0956769 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 3.87086 | 0.412636 | ||||||||
\(89\) | 3.91903 | 0.415416 | 0.207708 | − | 0.978191i | \(-0.433400\pi\) | ||||
0.207708 | + | 0.978191i | \(0.433400\pi\) | |||||||
\(90\) | 0.491797 | 0.0518399 | ||||||||
\(91\) | −5.68133 | −0.595565 | ||||||||
\(92\) | 6.78989 | 0.707895 | ||||||||
\(93\) | 0.826873 | 0.0857427 | ||||||||
\(94\) | 0.931263 | 0.0960525 | ||||||||
\(95\) | −4.48763 | −0.460421 | ||||||||
\(96\) | 2.91903 | 0.297922 | ||||||||
\(97\) | −10.4548 | −1.06153 | −0.530763 | − | 0.847520i | \(-0.678094\pi\) | ||||
−0.530763 | + | 0.847520i | \(0.678094\pi\) | |||||||
\(98\) | −0.254102 | −0.0256681 | ||||||||
\(99\) | 3.87086 | 0.389037 | ||||||||
\(100\) | 2.42723 | 0.242723 | ||||||||
\(101\) | −0.854458 | −0.0850217 | −0.0425109 | − | 0.999096i | \(-0.513536\pi\) | ||||
−0.0425109 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(102\) | −1.44780 | −0.143354 | ||||||||
\(103\) | 0.491797 | 0.0484582 | 0.0242291 | − | 0.999706i | \(-0.492287\pi\) | ||||
0.0242291 | + | 0.999706i | \(0.492287\pi\) | |||||||
\(104\) | 5.68133 | 0.557100 | ||||||||
\(105\) | −1.93543 | −0.188879 | ||||||||
\(106\) | 0.322838 | 0.0313568 | ||||||||
\(107\) | −15.0440 | −1.45436 | −0.727179 | − | 0.686448i | \(-0.759169\pi\) | ||||
−0.727179 | + | 0.686448i | \(0.759169\pi\) | |||||||
\(108\) | 1.93543 | 0.186237 | ||||||||
\(109\) | −13.0880 | −1.25360 | −0.626801 | − | 0.779180i | \(-0.715636\pi\) | ||||
−0.626801 | + | 0.779180i | \(0.715636\pi\) | |||||||
\(110\) | 1.90368 | 0.181509 | ||||||||
\(111\) | 3.44364 | 0.326855 | ||||||||
\(112\) | −3.61676 | −0.341752 | ||||||||
\(113\) | 4.52461 | 0.425640 | 0.212820 | − | 0.977091i | \(-0.431735\pi\) | ||||
0.212820 | + | 0.977091i | \(0.431735\pi\) | |||||||
\(114\) | 0.589178 | 0.0551816 | ||||||||
\(115\) | 6.78989 | 0.633161 | ||||||||
\(116\) | −5.80630 | −0.539101 | ||||||||
\(117\) | 5.68133 | 0.525239 | ||||||||
\(118\) | 2.66492 | 0.245326 | ||||||||
\(119\) | 5.69774 | 0.522311 | ||||||||
\(120\) | 1.93543 | 0.176680 | ||||||||
\(121\) | 3.98359 | 0.362145 | ||||||||
\(122\) | −0.605585 | −0.0548270 | ||||||||
\(123\) | −2.82687 | −0.254891 | ||||||||
\(124\) | 1.60036 | 0.143716 | ||||||||
\(125\) | 12.1044 | 1.08265 | ||||||||
\(126\) | 0.254102 | 0.0226372 | ||||||||
\(127\) | −9.29392 | −0.824702 | −0.412351 | − | 0.911025i | \(-0.635292\pi\) | ||||
−0.412351 | + | 0.911025i | \(0.635292\pi\) | |||||||
\(128\) | 7.48763 | 0.661819 | ||||||||
\(129\) | −3.49180 | −0.307436 | ||||||||
\(130\) | 2.79406 | 0.245055 | ||||||||
\(131\) | 9.67716 | 0.845498 | 0.422749 | − | 0.906247i | \(-0.361065\pi\) | ||||
0.422749 | + | 0.906247i | \(0.361065\pi\) | |||||||
\(132\) | 7.49180 | 0.652077 | ||||||||
\(133\) | −2.31867 | −0.201054 | ||||||||
\(134\) | 0.778712 | 0.0672705 | ||||||||
\(135\) | 1.93543 | 0.166575 | ||||||||
\(136\) | −5.69774 | −0.488577 | ||||||||
\(137\) | 17.6608 | 1.50886 | 0.754430 | − | 0.656380i | \(-0.227913\pi\) | ||||
0.754430 | + | 0.656380i | \(0.227913\pi\) | |||||||
\(138\) | −0.891440 | −0.0758844 | ||||||||
\(139\) | 12.4876 | 1.05919 | 0.529593 | − | 0.848252i | \(-0.322345\pi\) | ||||
0.529593 | + | 0.848252i | \(0.322345\pi\) | |||||||
\(140\) | −3.74590 | −0.316586 | ||||||||
\(141\) | 3.66492 | 0.308642 | ||||||||
\(142\) | −2.21712 | −0.186057 | ||||||||
\(143\) | 21.9917 | 1.83904 | ||||||||
\(144\) | 3.61676 | 0.301397 | ||||||||
\(145\) | −5.80630 | −0.482187 | ||||||||
\(146\) | −1.41188 | −0.116848 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 6.66492 | 0.547853 | ||||||||
\(149\) | 9.53162 | 0.780861 | 0.390430 | − | 0.920632i | \(-0.372326\pi\) | ||||
0.390430 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(150\) | −0.318669 | −0.0260192 | ||||||||
\(151\) | 18.9313 | 1.54060 | 0.770302 | − | 0.637679i | \(-0.220105\pi\) | ||||
0.770302 | + | 0.637679i | \(0.220105\pi\) | |||||||
\(152\) | 2.31867 | 0.188069 | ||||||||
\(153\) | −5.69774 | −0.460635 | ||||||||
\(154\) | 0.983593 | 0.0792602 | ||||||||
\(155\) | 1.60036 | 0.128544 | ||||||||
\(156\) | 10.9958 | 0.880371 | ||||||||
\(157\) | 1.34625 | 0.107443 | 0.0537214 | − | 0.998556i | \(-0.482892\pi\) | ||||
0.0537214 | + | 0.998556i | \(0.482892\pi\) | |||||||
\(158\) | −2.08097 | −0.165553 | ||||||||
\(159\) | 1.27051 | 0.100758 | ||||||||
\(160\) | 5.64958 | 0.446638 | ||||||||
\(161\) | 3.50820 | 0.276485 | ||||||||
\(162\) | −0.254102 | −0.0199641 | ||||||||
\(163\) | 15.9313 | 1.24783 | 0.623916 | − | 0.781491i | \(-0.285541\pi\) | ||||
0.623916 | + | 0.781491i | \(0.285541\pi\) | |||||||
\(164\) | −5.47122 | −0.427231 | ||||||||
\(165\) | 7.49180 | 0.583236 | ||||||||
\(166\) | 2.46421 | 0.191260 | ||||||||
\(167\) | 14.9630 | 1.15787 | 0.578937 | − | 0.815373i | \(-0.303468\pi\) | ||||
0.578937 | + | 0.815373i | \(0.303468\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 19.2775 | 1.48289 | ||||||||
\(170\) | −2.80213 | −0.214913 | ||||||||
\(171\) | 2.31867 | 0.177313 | ||||||||
\(172\) | −6.75814 | −0.515303 | ||||||||
\(173\) | −24.5358 | −1.86542 | −0.932711 | − | 0.360625i | \(-0.882563\pi\) | ||||
−0.932711 | + | 0.360625i | \(0.882563\pi\) | |||||||
\(174\) | 0.762305 | 0.0577902 | ||||||||
\(175\) | 1.25410 | 0.0948012 | ||||||||
\(176\) | 14.0000 | 1.05529 | ||||||||
\(177\) | 10.4876 | 0.788298 | ||||||||
\(178\) | −0.995831 | −0.0746407 | ||||||||
\(179\) | 9.06457 | 0.677518 | 0.338759 | − | 0.940873i | \(-0.389993\pi\) | ||||
0.338759 | + | 0.940873i | \(0.389993\pi\) | |||||||
\(180\) | 3.74590 | 0.279203 | ||||||||
\(181\) | −3.87503 | −0.288029 | −0.144014 | − | 0.989576i | \(-0.546001\pi\) | ||||
−0.144014 | + | 0.989576i | \(0.546001\pi\) | |||||||
\(182\) | 1.44364 | 0.107009 | ||||||||
\(183\) | −2.38324 | −0.176174 | ||||||||
\(184\) | −3.50820 | −0.258628 | ||||||||
\(185\) | 6.66492 | 0.490015 | ||||||||
\(186\) | −0.210110 | −0.0154060 | ||||||||
\(187\) | −22.0552 | −1.61283 | ||||||||
\(188\) | 7.09321 | 0.517326 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.14031 | 0.0827271 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 6.49180 | 0.468505 | ||||||||
\(193\) | 19.7253 | 1.41986 | 0.709930 | − | 0.704272i | \(-0.248727\pi\) | ||||
0.709930 | + | 0.704272i | \(0.248727\pi\) | |||||||
\(194\) | 2.65659 | 0.190732 | ||||||||
\(195\) | 10.9958 | 0.787428 | ||||||||
\(196\) | −1.93543 | −0.138245 | ||||||||
\(197\) | −7.09215 | −0.505295 | −0.252647 | − | 0.967558i | \(-0.581301\pi\) | ||||
−0.252647 | + | 0.967558i | \(0.581301\pi\) | |||||||
\(198\) | −0.983593 | −0.0699009 | ||||||||
\(199\) | 8.54102 | 0.605457 | 0.302728 | − | 0.953077i | \(-0.402103\pi\) | ||||
0.302728 | + | 0.953077i | \(0.402103\pi\) | |||||||
\(200\) | −1.25410 | −0.0886784 | ||||||||
\(201\) | 3.06457 | 0.216158 | ||||||||
\(202\) | 0.217119 | 0.0152765 | ||||||||
\(203\) | −3.00000 | −0.210559 | ||||||||
\(204\) | −11.0276 | −0.772085 | ||||||||
\(205\) | −5.47122 | −0.382127 | ||||||||
\(206\) | −0.124966 | −0.00870682 | ||||||||
\(207\) | −3.50820 | −0.243837 | ||||||||
\(208\) | 20.5480 | 1.42475 | ||||||||
\(209\) | 8.97526 | 0.620831 | ||||||||
\(210\) | 0.491797 | 0.0339372 | ||||||||
\(211\) | 22.2775 | 1.53365 | 0.766824 | − | 0.641858i | \(-0.221836\pi\) | ||||
0.766824 | + | 0.641858i | \(0.221836\pi\) | |||||||
\(212\) | 2.45898 | 0.168884 | ||||||||
\(213\) | −8.72532 | −0.597849 | ||||||||
\(214\) | 3.82270 | 0.261315 | ||||||||
\(215\) | −6.75814 | −0.460901 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.826873 | 0.0561318 | ||||||||
\(218\) | 3.32568 | 0.225243 | ||||||||
\(219\) | −5.55636 | −0.375464 | ||||||||
\(220\) | 14.4999 | 0.977581 | ||||||||
\(221\) | −32.3707 | −2.17749 | ||||||||
\(222\) | −0.875034 | −0.0587284 | ||||||||
\(223\) | 7.27051 | 0.486869 | 0.243435 | − | 0.969917i | \(-0.421726\pi\) | ||||
0.243435 | + | 0.969917i | \(0.421726\pi\) | |||||||
\(224\) | 2.91903 | 0.195036 | ||||||||
\(225\) | −1.25410 | −0.0836068 | ||||||||
\(226\) | −1.14971 | −0.0764776 | ||||||||
\(227\) | −4.78572 | −0.317639 | −0.158820 | − | 0.987308i | \(-0.550769\pi\) | ||||
−0.158820 | + | 0.987308i | \(0.550769\pi\) | |||||||
\(228\) | 4.48763 | 0.297200 | ||||||||
\(229\) | −5.13614 | −0.339406 | −0.169703 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169703 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(230\) | −1.72532 | −0.113764 | ||||||||
\(231\) | 3.87086 | 0.254684 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 24.7089 | 1.61873 | 0.809367 | − | 0.587303i | \(-0.199810\pi\) | ||||
0.809367 | + | 0.587303i | \(0.199810\pi\) | |||||||
\(234\) | −1.44364 | −0.0943734 | ||||||||
\(235\) | 7.09321 | 0.462710 | ||||||||
\(236\) | 20.2981 | 1.32129 | ||||||||
\(237\) | −8.18953 | −0.531967 | ||||||||
\(238\) | −1.44780 | −0.0938472 | ||||||||
\(239\) | −0.399644 | −0.0258508 | −0.0129254 | − | 0.999916i | \(-0.504114\pi\) | ||||
−0.0129254 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(240\) | 7.00000 | 0.451848 | ||||||||
\(241\) | −14.5962 | −0.940223 | −0.470112 | − | 0.882607i | \(-0.655786\pi\) | ||||
−0.470112 | + | 0.882607i | \(0.655786\pi\) | |||||||
\(242\) | −1.01224 | −0.0650691 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.61259 | −0.295291 | ||||||||
\(245\) | −1.93543 | −0.123650 | ||||||||
\(246\) | 0.718313 | 0.0457980 | ||||||||
\(247\) | 13.1731 | 0.838186 | ||||||||
\(248\) | −0.826873 | −0.0525065 | ||||||||
\(249\) | 9.69774 | 0.614569 | ||||||||
\(250\) | −3.07575 | −0.194527 | ||||||||
\(251\) | −8.63734 | −0.545184 | −0.272592 | − | 0.962130i | \(-0.587881\pi\) | ||||
−0.272592 | + | 0.962130i | \(0.587881\pi\) | |||||||
\(252\) | 1.93543 | 0.121921 | ||||||||
\(253\) | −13.5798 | −0.853753 | ||||||||
\(254\) | 2.36160 | 0.148180 | ||||||||
\(255\) | −11.0276 | −0.690574 | ||||||||
\(256\) | 11.0810 | 0.692561 | ||||||||
\(257\) | 14.5204 | 0.905760 | 0.452880 | − | 0.891571i | \(-0.350397\pi\) | ||||
0.452880 | + | 0.891571i | \(0.350397\pi\) | |||||||
\(258\) | 0.887271 | 0.0552391 | ||||||||
\(259\) | 3.44364 | 0.213977 | ||||||||
\(260\) | 21.2817 | 1.31983 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | −2.45898 | −0.151916 | ||||||||
\(263\) | −12.3749 | −0.763069 | −0.381534 | − | 0.924355i | \(-0.624604\pi\) | ||||
−0.381534 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(264\) | −3.87086 | −0.238235 | ||||||||
\(265\) | 2.45898 | 0.151054 | ||||||||
\(266\) | 0.589178 | 0.0361248 | ||||||||
\(267\) | −3.91903 | −0.239840 | ||||||||
\(268\) | 5.93126 | 0.362310 | ||||||||
\(269\) | 9.26111 | 0.564660 | 0.282330 | − | 0.959317i | \(-0.408893\pi\) | ||||
0.282330 | + | 0.959317i | \(0.408893\pi\) | |||||||
\(270\) | −0.491797 | −0.0299298 | ||||||||
\(271\) | 2.12497 | 0.129083 | 0.0645413 | − | 0.997915i | \(-0.479442\pi\) | ||||
0.0645413 | + | 0.997915i | \(0.479442\pi\) | |||||||
\(272\) | −20.6074 | −1.24951 | ||||||||
\(273\) | 5.68133 | 0.343850 | ||||||||
\(274\) | −4.48763 | −0.271108 | ||||||||
\(275\) | −4.85446 | −0.292735 | ||||||||
\(276\) | −6.78989 | −0.408703 | ||||||||
\(277\) | 14.5522 | 0.874357 | 0.437178 | − | 0.899375i | \(-0.355978\pi\) | ||||
0.437178 | + | 0.899375i | \(0.355978\pi\) | |||||||
\(278\) | −3.17313 | −0.190312 | ||||||||
\(279\) | −0.826873 | −0.0495036 | ||||||||
\(280\) | 1.93543 | 0.115664 | ||||||||
\(281\) | 13.9641 | 0.833027 | 0.416513 | − | 0.909130i | \(-0.363252\pi\) | ||||
0.416513 | + | 0.909130i | \(0.363252\pi\) | |||||||
\(282\) | −0.931263 | −0.0554559 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | −16.8873 | −1.00208 | ||||||||
\(285\) | 4.48763 | 0.265824 | ||||||||
\(286\) | −5.58812 | −0.330432 | ||||||||
\(287\) | −2.82687 | −0.166865 | ||||||||
\(288\) | −2.91903 | −0.172005 | ||||||||
\(289\) | 15.4642 | 0.909659 | ||||||||
\(290\) | 1.47539 | 0.0866379 | ||||||||
\(291\) | 10.4548 | 0.612872 | ||||||||
\(292\) | −10.7540 | −0.629328 | ||||||||
\(293\) | 8.46421 | 0.494485 | 0.247242 | − | 0.968954i | \(-0.420476\pi\) | ||||
0.247242 | + | 0.968954i | \(0.420476\pi\) | |||||||
\(294\) | 0.254102 | 0.0148195 | ||||||||
\(295\) | 20.2981 | 1.18180 | ||||||||
\(296\) | −3.44364 | −0.200157 | ||||||||
\(297\) | −3.87086 | −0.224610 | ||||||||
\(298\) | −2.42200 | −0.140303 | ||||||||
\(299\) | −19.9313 | −1.15265 | ||||||||
\(300\) | −2.42723 | −0.140136 | ||||||||
\(301\) | −3.49180 | −0.201264 | ||||||||
\(302\) | −4.81047 | −0.276811 | ||||||||
\(303\) | 0.854458 | 0.0490873 | ||||||||
\(304\) | 8.38608 | 0.480975 | ||||||||
\(305\) | −4.61259 | −0.264116 | ||||||||
\(306\) | 1.44780 | 0.0827655 | ||||||||
\(307\) | −20.5275 | −1.17156 | −0.585782 | − | 0.810469i | \(-0.699212\pi\) | ||||
−0.585782 | + | 0.810469i | \(0.699212\pi\) | |||||||
\(308\) | 7.49180 | 0.426885 | ||||||||
\(309\) | −0.491797 | −0.0279773 | ||||||||
\(310\) | −0.406653 | −0.0230964 | ||||||||
\(311\) | −12.3103 | −0.698055 | −0.349027 | − | 0.937113i | \(-0.613488\pi\) | ||||
−0.349027 | + | 0.937113i | \(0.613488\pi\) | |||||||
\(312\) | −5.68133 | −0.321642 | ||||||||
\(313\) | −25.5686 | −1.44522 | −0.722611 | − | 0.691254i | \(-0.757058\pi\) | ||||
−0.722611 | + | 0.691254i | \(0.757058\pi\) | |||||||
\(314\) | −0.342086 | −0.0193050 | ||||||||
\(315\) | 1.93543 | 0.109049 | ||||||||
\(316\) | −15.8503 | −0.891648 | ||||||||
\(317\) | −31.3861 | −1.76282 | −0.881409 | − | 0.472354i | \(-0.843404\pi\) | ||||
−0.881409 | + | 0.472354i | \(0.843404\pi\) | |||||||
\(318\) | −0.322838 | −0.0181039 | ||||||||
\(319\) | 11.6126 | 0.650180 | ||||||||
\(320\) | 12.5644 | 0.702373 | ||||||||
\(321\) | 15.0440 | 0.839674 | ||||||||
\(322\) | −0.891440 | −0.0496780 | ||||||||
\(323\) | −13.2112 | −0.735089 | ||||||||
\(324\) | −1.93543 | −0.107524 | ||||||||
\(325\) | −7.12497 | −0.395222 | ||||||||
\(326\) | −4.04816 | −0.224207 | ||||||||
\(327\) | 13.0880 | 0.723767 | ||||||||
\(328\) | 2.82687 | 0.156088 | ||||||||
\(329\) | 3.66492 | 0.202054 | ||||||||
\(330\) | −1.90368 | −0.104794 | ||||||||
\(331\) | 25.3749 | 1.39473 | 0.697365 | − | 0.716716i | \(-0.254356\pi\) | ||||
0.697365 | + | 0.716716i | \(0.254356\pi\) | |||||||
\(332\) | 18.7693 | 1.03010 | ||||||||
\(333\) | −3.44364 | −0.188710 | ||||||||
\(334\) | −3.80213 | −0.208043 | ||||||||
\(335\) | 5.93126 | 0.324060 | ||||||||
\(336\) | 3.61676 | 0.197311 | ||||||||
\(337\) | 28.3913 | 1.54657 | 0.773286 | − | 0.634057i | \(-0.218611\pi\) | ||||
0.773286 | + | 0.634057i | \(0.218611\pi\) | |||||||
\(338\) | −4.89845 | −0.266441 | ||||||||
\(339\) | −4.52461 | −0.245743 | ||||||||
\(340\) | −21.3431 | −1.15749 | ||||||||
\(341\) | −3.20071 | −0.173328 | ||||||||
\(342\) | −0.589178 | −0.0318591 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.49180 | 0.188265 | ||||||||
\(345\) | −6.78989 | −0.365555 | ||||||||
\(346\) | 6.23459 | 0.335173 | ||||||||
\(347\) | −21.9149 | −1.17645 | −0.588226 | − | 0.808697i | \(-0.700173\pi\) | ||||
−0.588226 | + | 0.808697i | \(0.700173\pi\) | |||||||
\(348\) | 5.80630 | 0.311250 | ||||||||
\(349\) | 16.6014 | 0.888653 | 0.444327 | − | 0.895865i | \(-0.353443\pi\) | ||||
0.444327 | + | 0.895865i | \(0.353443\pi\) | |||||||
\(350\) | −0.318669 | −0.0170336 | ||||||||
\(351\) | −5.68133 | −0.303247 | ||||||||
\(352\) | −11.2992 | −0.602247 | ||||||||
\(353\) | −34.7745 | −1.85086 | −0.925431 | − | 0.378916i | \(-0.876297\pi\) | ||||
−0.925431 | + | 0.378916i | \(0.876297\pi\) | |||||||
\(354\) | −2.66492 | −0.141639 | ||||||||
\(355\) | −16.8873 | −0.896283 | ||||||||
\(356\) | −7.58501 | −0.402005 | ||||||||
\(357\) | −5.69774 | −0.301556 | ||||||||
\(358\) | −2.30332 | −0.121734 | ||||||||
\(359\) | −2.22936 | −0.117661 | −0.0588305 | − | 0.998268i | \(-0.518737\pi\) | ||||
−0.0588305 | + | 0.998268i | \(0.518737\pi\) | |||||||
\(360\) | −1.93543 | −0.102006 | ||||||||
\(361\) | −13.6238 | −0.717041 | ||||||||
\(362\) | 0.984653 | 0.0517522 | ||||||||
\(363\) | −3.98359 | −0.209084 | ||||||||
\(364\) | 10.9958 | 0.576338 | ||||||||
\(365\) | −10.7540 | −0.562888 | ||||||||
\(366\) | 0.605585 | 0.0316544 | ||||||||
\(367\) | 20.7100 | 1.08105 | 0.540526 | − | 0.841327i | \(-0.318225\pi\) | ||||
0.540526 | + | 0.841327i | \(0.318225\pi\) | |||||||
\(368\) | −12.6883 | −0.661425 | ||||||||
\(369\) | 2.82687 | 0.147161 | ||||||||
\(370\) | −1.69357 | −0.0880444 | ||||||||
\(371\) | 1.27051 | 0.0659615 | ||||||||
\(372\) | −1.60036 | −0.0829746 | ||||||||
\(373\) | 25.0768 | 1.29843 | 0.649214 | − | 0.760606i | \(-0.275098\pi\) | ||||
0.649214 | + | 0.760606i | \(0.275098\pi\) | |||||||
\(374\) | 5.60426 | 0.289789 | ||||||||
\(375\) | −12.1044 | −0.625068 | ||||||||
\(376\) | −3.66492 | −0.189004 | ||||||||
\(377\) | 17.0440 | 0.877810 | ||||||||
\(378\) | −0.254102 | −0.0130696 | ||||||||
\(379\) | −19.2377 | −0.988174 | −0.494087 | − | 0.869412i | \(-0.664498\pi\) | ||||
−0.494087 | + | 0.869412i | \(0.664498\pi\) | |||||||
\(380\) | 8.68550 | 0.445557 | ||||||||
\(381\) | 9.29392 | 0.476142 | ||||||||
\(382\) | −0.254102 | −0.0130010 | ||||||||
\(383\) | −1.08514 | −0.0554482 | −0.0277241 | − | 0.999616i | \(-0.508826\pi\) | ||||
−0.0277241 | + | 0.999616i | \(0.508826\pi\) | |||||||
\(384\) | −7.48763 | −0.382101 | ||||||||
\(385\) | 7.49180 | 0.381817 | ||||||||
\(386\) | −5.01224 | −0.255116 | ||||||||
\(387\) | 3.49180 | 0.177498 | ||||||||
\(388\) | 20.2346 | 1.02726 | ||||||||
\(389\) | −5.94767 | −0.301559 | −0.150779 | − | 0.988567i | \(-0.548178\pi\) | ||||
−0.150779 | + | 0.988567i | \(0.548178\pi\) | |||||||
\(390\) | −2.79406 | −0.141483 | ||||||||
\(391\) | 19.9888 | 1.01088 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −9.67716 | −0.488148 | ||||||||
\(394\) | 1.80213 | 0.0907899 | ||||||||
\(395\) | −15.8503 | −0.797515 | ||||||||
\(396\) | −7.49180 | −0.376477 | ||||||||
\(397\) | 16.2018 | 0.813144 | 0.406572 | − | 0.913619i | \(-0.366724\pi\) | ||||
0.406572 | + | 0.913619i | \(0.366724\pi\) | |||||||
\(398\) | −2.17029 | −0.108787 | ||||||||
\(399\) | 2.31867 | 0.116079 | ||||||||
\(400\) | −4.53579 | −0.226789 | ||||||||
\(401\) | −0.891440 | −0.0445164 | −0.0222582 | − | 0.999752i | \(-0.507086\pi\) | ||||
−0.0222582 | + | 0.999752i | \(0.507086\pi\) | |||||||
\(402\) | −0.778712 | −0.0388386 | ||||||||
\(403\) | −4.69774 | −0.234011 | ||||||||
\(404\) | 1.65375 | 0.0822769 | ||||||||
\(405\) | −1.93543 | −0.0961724 | ||||||||
\(406\) | 0.762305 | 0.0378326 | ||||||||
\(407\) | −13.3298 | −0.660736 | ||||||||
\(408\) | 5.69774 | 0.282080 | ||||||||
\(409\) | 12.9078 | 0.638252 | 0.319126 | − | 0.947712i | \(-0.396611\pi\) | ||||
0.319126 | + | 0.947712i | \(0.396611\pi\) | |||||||
\(410\) | 1.39025 | 0.0686594 | ||||||||
\(411\) | −17.6608 | −0.871141 | ||||||||
\(412\) | −0.951839 | −0.0468937 | ||||||||
\(413\) | 10.4876 | 0.516062 | ||||||||
\(414\) | 0.891440 | 0.0438119 | ||||||||
\(415\) | 18.7693 | 0.921349 | ||||||||
\(416\) | −16.5839 | −0.813095 | ||||||||
\(417\) | −12.4876 | −0.611522 | ||||||||
\(418\) | −2.28063 | −0.111549 | ||||||||
\(419\) | 1.55220 | 0.0758297 | 0.0379149 | − | 0.999281i | \(-0.487928\pi\) | ||||
0.0379149 | + | 0.999281i | \(0.487928\pi\) | |||||||
\(420\) | 3.74590 | 0.182781 | ||||||||
\(421\) | 33.1414 | 1.61521 | 0.807606 | − | 0.589723i | \(-0.200763\pi\) | ||||
0.807606 | + | 0.589723i | \(0.200763\pi\) | |||||||
\(422\) | −5.66075 | −0.275561 | ||||||||
\(423\) | −3.66492 | −0.178195 | ||||||||
\(424\) | −1.27051 | −0.0617013 | ||||||||
\(425\) | 7.14554 | 0.346610 | ||||||||
\(426\) | 2.21712 | 0.107420 | ||||||||
\(427\) | −2.38324 | −0.115333 | ||||||||
\(428\) | 29.1166 | 1.40741 | ||||||||
\(429\) | −21.9917 | −1.06177 | ||||||||
\(430\) | 1.71725 | 0.0828133 | ||||||||
\(431\) | −41.3449 | −1.99152 | −0.995758 | − | 0.0920163i | \(-0.970669\pi\) | ||||
−0.995758 | + | 0.0920163i | \(0.970669\pi\) | |||||||
\(432\) | −3.61676 | −0.174012 | ||||||||
\(433\) | 3.78288 | 0.181794 | 0.0908968 | − | 0.995860i | \(-0.471027\pi\) | ||||
0.0908968 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(434\) | −0.210110 | −0.0100856 | ||||||||
\(435\) | 5.80630 | 0.278391 | ||||||||
\(436\) | 25.3309 | 1.21313 | ||||||||
\(437\) | −8.13436 | −0.389119 | ||||||||
\(438\) | 1.41188 | 0.0674623 | ||||||||
\(439\) | 9.77454 | 0.466513 | 0.233257 | − | 0.972415i | \(-0.425062\pi\) | ||||
0.233257 | + | 0.972415i | \(0.425062\pi\) | |||||||
\(440\) | −7.49180 | −0.357157 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 8.22546 | 0.391245 | ||||||||
\(443\) | 23.7058 | 1.12630 | 0.563148 | − | 0.826356i | \(-0.309590\pi\) | ||||
0.563148 | + | 0.826356i | \(0.309590\pi\) | |||||||
\(444\) | −6.66492 | −0.316303 | ||||||||
\(445\) | −7.58501 | −0.359564 | ||||||||
\(446\) | −1.84745 | −0.0874792 | ||||||||
\(447\) | −9.53162 | −0.450830 | ||||||||
\(448\) | 6.49180 | 0.306709 | ||||||||
\(449\) | −11.1044 | −0.524049 | −0.262024 | − | 0.965061i | \(-0.584390\pi\) | ||||
−0.262024 | + | 0.965061i | \(0.584390\pi\) | |||||||
\(450\) | 0.318669 | 0.0150222 | ||||||||
\(451\) | 10.9424 | 0.515259 | ||||||||
\(452\) | −8.75708 | −0.411898 | ||||||||
\(453\) | −18.9313 | −0.889468 | ||||||||
\(454\) | 1.21606 | 0.0570725 | ||||||||
\(455\) | 10.9958 | 0.515493 | ||||||||
\(456\) | −2.31867 | −0.108582 | ||||||||
\(457\) | 35.8737 | 1.67810 | 0.839051 | − | 0.544053i | \(-0.183111\pi\) | ||||
0.839051 | + | 0.544053i | \(0.183111\pi\) | |||||||
\(458\) | 1.30510 | 0.0609835 | ||||||||
\(459\) | 5.69774 | 0.265948 | ||||||||
\(460\) | −13.1414 | −0.612720 | ||||||||
\(461\) | 22.5603 | 1.05074 | 0.525368 | − | 0.850875i | \(-0.323928\pi\) | ||||
0.525368 | + | 0.850875i | \(0.323928\pi\) | |||||||
\(462\) | −0.983593 | −0.0457609 | ||||||||
\(463\) | −18.5892 | −0.863912 | −0.431956 | − | 0.901895i | \(-0.642176\pi\) | ||||
−0.431956 | + | 0.901895i | \(0.642176\pi\) | |||||||
\(464\) | 10.8503 | 0.503712 | ||||||||
\(465\) | −1.60036 | −0.0742147 | ||||||||
\(466\) | −6.27858 | −0.290849 | ||||||||
\(467\) | 9.03565 | 0.418120 | 0.209060 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209060 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(468\) | −10.9958 | −0.508282 | ||||||||
\(469\) | 3.06457 | 0.141509 | ||||||||
\(470\) | −1.80240 | −0.0831384 | ||||||||
\(471\) | −1.34625 | −0.0620321 | ||||||||
\(472\) | −10.4876 | −0.482732 | ||||||||
\(473\) | 13.5163 | 0.621479 | ||||||||
\(474\) | 2.08097 | 0.0955823 | ||||||||
\(475\) | −2.90785 | −0.133421 | ||||||||
\(476\) | −11.0276 | −0.505449 | ||||||||
\(477\) | −1.27051 | −0.0581726 | ||||||||
\(478\) | 0.101550 | 0.00464480 | ||||||||
\(479\) | 20.8873 | 0.954364 | 0.477182 | − | 0.878805i | \(-0.341658\pi\) | ||||
0.477182 | + | 0.878805i | \(0.341658\pi\) | |||||||
\(480\) | −5.64958 | −0.257867 | ||||||||
\(481\) | −19.5644 | −0.892061 | ||||||||
\(482\) | 3.70892 | 0.168936 | ||||||||
\(483\) | −3.50820 | −0.159629 | ||||||||
\(484\) | −7.70998 | −0.350453 | ||||||||
\(485\) | 20.2346 | 0.918805 | ||||||||
\(486\) | 0.254102 | 0.0115263 | ||||||||
\(487\) | −8.16195 | −0.369853 | −0.184927 | − | 0.982752i | \(-0.559205\pi\) | ||||
−0.184927 | + | 0.982752i | \(0.559205\pi\) | |||||||
\(488\) | 2.38324 | 0.107884 | ||||||||
\(489\) | −15.9313 | −0.720437 | ||||||||
\(490\) | 0.491797 | 0.0222171 | ||||||||
\(491\) | −18.8175 | −0.849221 | −0.424610 | − | 0.905376i | \(-0.639589\pi\) | ||||
−0.424610 | + | 0.905376i | \(0.639589\pi\) | |||||||
\(492\) | 5.47122 | 0.246662 | ||||||||
\(493\) | −17.0932 | −0.769840 | ||||||||
\(494\) | −3.34731 | −0.150603 | ||||||||
\(495\) | −7.49180 | −0.336731 | ||||||||
\(496\) | −2.99060 | −0.134282 | ||||||||
\(497\) | −8.72532 | −0.391384 | ||||||||
\(498\) | −2.46421 | −0.110424 | ||||||||
\(499\) | 23.2252 | 1.03970 | 0.519851 | − | 0.854257i | \(-0.325987\pi\) | ||||
0.519851 | + | 0.854257i | \(0.325987\pi\) | |||||||
\(500\) | −23.4272 | −1.04770 | ||||||||
\(501\) | −14.9630 | −0.668498 | ||||||||
\(502\) | 2.19476 | 0.0979570 | ||||||||
\(503\) | −4.32568 | −0.192872 | −0.0964362 | − | 0.995339i | \(-0.530744\pi\) | ||||
−0.0964362 | + | 0.995339i | \(0.530744\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 1.65375 | 0.0735907 | ||||||||
\(506\) | 3.45065 | 0.153400 | ||||||||
\(507\) | −19.2775 | −0.856145 | ||||||||
\(508\) | 17.9878 | 0.798078 | ||||||||
\(509\) | −31.7540 | −1.40747 | −0.703735 | − | 0.710463i | \(-0.748486\pi\) | ||||
−0.703735 | + | 0.710463i | \(0.748486\pi\) | |||||||
\(510\) | 2.80213 | 0.124080 | ||||||||
\(511\) | −5.55636 | −0.245799 | ||||||||
\(512\) | −17.7909 | −0.786256 | ||||||||
\(513\) | −2.31867 | −0.102372 | ||||||||
\(514\) | −3.68967 | −0.162744 | ||||||||
\(515\) | −0.951839 | −0.0419430 | ||||||||
\(516\) | 6.75814 | 0.297510 | ||||||||
\(517\) | −14.1864 | −0.623918 | ||||||||
\(518\) | −0.875034 | −0.0384468 | ||||||||
\(519\) | 24.5358 | 1.07700 | ||||||||
\(520\) | −10.9958 | −0.482199 | ||||||||
\(521\) | 9.08514 | 0.398027 | 0.199014 | − | 0.979997i | \(-0.436226\pi\) | ||||
0.199014 | + | 0.979997i | \(0.436226\pi\) | |||||||
\(522\) | −0.762305 | −0.0333652 | ||||||||
\(523\) | −30.3983 | −1.32923 | −0.664613 | − | 0.747188i | \(-0.731403\pi\) | ||||
−0.664613 | + | 0.747188i | \(0.731403\pi\) | |||||||
\(524\) | −18.7295 | −0.818202 | ||||||||
\(525\) | −1.25410 | −0.0547335 | ||||||||
\(526\) | 3.14448 | 0.137106 | ||||||||
\(527\) | 4.71130 | 0.205228 | ||||||||
\(528\) | −14.0000 | −0.609272 | ||||||||
\(529\) | −10.6925 | −0.464892 | ||||||||
\(530\) | −0.624832 | −0.0271410 | ||||||||
\(531\) | −10.4876 | −0.455124 | ||||||||
\(532\) | 4.48763 | 0.194563 | ||||||||
\(533\) | 16.0604 | 0.695653 | ||||||||
\(534\) | 0.995831 | 0.0430938 | ||||||||
\(535\) | 29.1166 | 1.25882 | ||||||||
\(536\) | −3.06457 | −0.132369 | ||||||||
\(537\) | −9.06457 | −0.391165 | ||||||||
\(538\) | −2.35326 | −0.101456 | ||||||||
\(539\) | 3.87086 | 0.166730 | ||||||||
\(540\) | −3.74590 | −0.161198 | ||||||||
\(541\) | 33.8984 | 1.45741 | 0.728704 | − | 0.684829i | \(-0.240123\pi\) | ||||
0.728704 | + | 0.684829i | \(0.240123\pi\) | |||||||
\(542\) | −0.539958 | −0.0231932 | ||||||||
\(543\) | 3.87503 | 0.166294 | ||||||||
\(544\) | 16.6318 | 0.713084 | ||||||||
\(545\) | 25.3309 | 1.08506 | ||||||||
\(546\) | −1.44364 | −0.0617819 | ||||||||
\(547\) | −11.6454 | −0.497922 | −0.248961 | − | 0.968514i | \(-0.580089\pi\) | ||||
−0.248961 | + | 0.968514i | \(0.580089\pi\) | |||||||
\(548\) | −34.1812 | −1.46015 | ||||||||
\(549\) | 2.38324 | 0.101714 | ||||||||
\(550\) | 1.23353 | 0.0525977 | ||||||||
\(551\) | 6.95601 | 0.296336 | ||||||||
\(552\) | 3.50820 | 0.149319 | ||||||||
\(553\) | −8.18953 | −0.348254 | ||||||||
\(554\) | −3.69774 | −0.157102 | ||||||||
\(555\) | −6.66492 | −0.282910 | ||||||||
\(556\) | −24.1690 | −1.02499 | ||||||||
\(557\) | 27.8545 | 1.18023 | 0.590116 | − | 0.807319i | \(-0.299082\pi\) | ||||
0.590116 | + | 0.807319i | \(0.299082\pi\) | |||||||
\(558\) | 0.210110 | 0.00889466 | ||||||||
\(559\) | 19.8381 | 0.839060 | ||||||||
\(560\) | 7.00000 | 0.295804 | ||||||||
\(561\) | 22.0552 | 0.931170 | ||||||||
\(562\) | −3.54830 | −0.149676 | ||||||||
\(563\) | 16.0151 | 0.674955 | 0.337478 | − | 0.941334i | \(-0.390426\pi\) | ||||
0.337478 | + | 0.941334i | \(0.390426\pi\) | |||||||
\(564\) | −7.09321 | −0.298678 | ||||||||
\(565\) | −8.75708 | −0.368413 | ||||||||
\(566\) | −2.03281 | −0.0854455 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 8.72532 | 0.366106 | ||||||||
\(569\) | 5.21117 | 0.218464 | 0.109232 | − | 0.994016i | \(-0.465161\pi\) | ||||
0.109232 | + | 0.994016i | \(0.465161\pi\) | |||||||
\(570\) | −1.14031 | −0.0477625 | ||||||||
\(571\) | 26.3902 | 1.10440 | 0.552199 | − | 0.833713i | \(-0.313789\pi\) | ||||
0.552199 | + | 0.833713i | \(0.313789\pi\) | |||||||
\(572\) | −42.5634 | −1.77966 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 0.718313 | 0.0299818 | ||||||||
\(575\) | 4.39964 | 0.183478 | ||||||||
\(576\) | −6.49180 | −0.270492 | ||||||||
\(577\) | −18.0122 | −0.749859 | −0.374930 | − | 0.927053i | \(-0.622333\pi\) | ||||
−0.374930 | + | 0.927053i | \(0.622333\pi\) | |||||||
\(578\) | −3.92948 | −0.163445 | ||||||||
\(579\) | −19.7253 | −0.819756 | ||||||||
\(580\) | 11.2377 | 0.466620 | ||||||||
\(581\) | 9.69774 | 0.402330 | ||||||||
\(582\) | −2.65659 | −0.110119 | ||||||||
\(583\) | −4.91797 | −0.203681 | ||||||||
\(584\) | 5.55636 | 0.229924 | ||||||||
\(585\) | −10.9958 | −0.454622 | ||||||||
\(586\) | −2.15077 | −0.0888475 | ||||||||
\(587\) | −10.1854 | −0.420395 | −0.210198 | − | 0.977659i | \(-0.567411\pi\) | ||||
−0.210198 | + | 0.977659i | \(0.567411\pi\) | |||||||
\(588\) | 1.93543 | 0.0798159 | ||||||||
\(589\) | −1.91724 | −0.0789987 | ||||||||
\(590\) | −5.15778 | −0.212342 | ||||||||
\(591\) | 7.09215 | 0.291732 | ||||||||
\(592\) | −12.4548 | −0.511890 | ||||||||
\(593\) | 33.3627 | 1.37004 | 0.685020 | − | 0.728524i | \(-0.259793\pi\) | ||||
0.685020 | + | 0.728524i | \(0.259793\pi\) | |||||||
\(594\) | 0.983593 | 0.0403573 | ||||||||
\(595\) | −11.0276 | −0.452087 | ||||||||
\(596\) | −18.4478 | −0.755652 | ||||||||
\(597\) | −8.54102 | −0.349561 | ||||||||
\(598\) | 5.06457 | 0.207106 | ||||||||
\(599\) | −7.12391 | −0.291075 | −0.145537 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145537 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(600\) | 1.25410 | 0.0511985 | ||||||||
\(601\) | 21.4835 | 0.876329 | 0.438164 | − | 0.898895i | \(-0.355629\pi\) | ||||
0.438164 | + | 0.898895i | \(0.355629\pi\) | |||||||
\(602\) | 0.887271 | 0.0361625 | ||||||||
\(603\) | −3.06457 | −0.124799 | ||||||||
\(604\) | −36.6402 | −1.49087 | ||||||||
\(605\) | −7.70998 | −0.313455 | ||||||||
\(606\) | −0.217119 | −0.00881986 | ||||||||
\(607\) | −0.450645 | −0.0182911 | −0.00914556 | − | 0.999958i | \(-0.502911\pi\) | ||||
−0.00914556 | + | 0.999958i | \(0.502911\pi\) | |||||||
\(608\) | −6.76826 | −0.274489 | ||||||||
\(609\) | 3.00000 | 0.121566 | ||||||||
\(610\) | 1.17207 | 0.0474556 | ||||||||
\(611\) | −20.8216 | −0.842354 | ||||||||
\(612\) | 11.0276 | 0.445764 | ||||||||
\(613\) | 43.2130 | 1.74535 | 0.872677 | − | 0.488297i | \(-0.162382\pi\) | ||||
0.872677 | + | 0.488297i | \(0.162382\pi\) | |||||||
\(614\) | 5.21606 | 0.210503 | ||||||||
\(615\) | 5.47122 | 0.220621 | ||||||||
\(616\) | −3.87086 | −0.155962 | ||||||||
\(617\) | 29.4587 | 1.18596 | 0.592982 | − | 0.805216i | \(-0.297951\pi\) | ||||
0.592982 | + | 0.805216i | \(0.297951\pi\) | |||||||
\(618\) | 0.124966 | 0.00502688 | ||||||||
\(619\) | 30.8451 | 1.23977 | 0.619884 | − | 0.784694i | \(-0.287180\pi\) | ||||
0.619884 | + | 0.784694i | \(0.287180\pi\) | |||||||
\(620\) | −3.09738 | −0.124394 | ||||||||
\(621\) | 3.50820 | 0.140779 | ||||||||
\(622\) | 3.12808 | 0.125424 | ||||||||
\(623\) | −3.91903 | −0.157012 | ||||||||
\(624\) | −20.5480 | −0.822579 | ||||||||
\(625\) | −17.1567 | −0.686269 | ||||||||
\(626\) | 6.49702 | 0.259673 | ||||||||
\(627\) | −8.97526 | −0.358437 | ||||||||
\(628\) | −2.60558 | −0.103974 | ||||||||
\(629\) | 19.6209 | 0.782338 | ||||||||
\(630\) | −0.491797 | −0.0195936 | ||||||||
\(631\) | 12.6014 | 0.501654 | 0.250827 | − | 0.968032i | \(-0.419297\pi\) | ||||
0.250827 | + | 0.968032i | \(0.419297\pi\) | |||||||
\(632\) | 8.18953 | 0.325762 | ||||||||
\(633\) | −22.2775 | −0.885452 | ||||||||
\(634\) | 7.97526 | 0.316738 | ||||||||
\(635\) | 17.9878 | 0.713823 | ||||||||
\(636\) | −2.45898 | −0.0975050 | ||||||||
\(637\) | 5.68133 | 0.225103 | ||||||||
\(638\) | −2.95078 | −0.116822 | ||||||||
\(639\) | 8.72532 | 0.345168 | ||||||||
\(640\) | −14.4918 | −0.572839 | ||||||||
\(641\) | −1.76931 | −0.0698837 | −0.0349419 | − | 0.999389i | \(-0.511125\pi\) | ||||
−0.0349419 | + | 0.999389i | \(0.511125\pi\) | |||||||
\(642\) | −3.82270 | −0.150870 | ||||||||
\(643\) | 46.2004 | 1.82197 | 0.910984 | − | 0.412442i | \(-0.135324\pi\) | ||||
0.910984 | + | 0.412442i | \(0.135324\pi\) | |||||||
\(644\) | −6.78989 | −0.267559 | ||||||||
\(645\) | 6.75814 | 0.266101 | ||||||||
\(646\) | 3.35698 | 0.132079 | ||||||||
\(647\) | 1.90679 | 0.0749636 | 0.0374818 | − | 0.999297i | \(-0.488066\pi\) | ||||
0.0374818 | + | 0.999297i | \(0.488066\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −40.5962 | −1.59354 | ||||||||
\(650\) | 1.81047 | 0.0710123 | ||||||||
\(651\) | −0.826873 | −0.0324077 | ||||||||
\(652\) | −30.8339 | −1.20755 | ||||||||
\(653\) | 3.00106 | 0.117441 | 0.0587203 | − | 0.998274i | \(-0.481298\pi\) | ||||
0.0587203 | + | 0.998274i | \(0.481298\pi\) | |||||||
\(654\) | −3.32568 | −0.130044 | ||||||||
\(655\) | −18.7295 | −0.731822 | ||||||||
\(656\) | 10.2241 | 0.399185 | ||||||||
\(657\) | 5.55636 | 0.216774 | ||||||||
\(658\) | −0.931263 | −0.0363044 | ||||||||
\(659\) | −39.3009 | −1.53095 | −0.765474 | − | 0.643467i | \(-0.777495\pi\) | ||||
−0.765474 | + | 0.643467i | \(0.777495\pi\) | |||||||
\(660\) | −14.4999 | −0.564406 | ||||||||
\(661\) | −34.9864 | −1.36081 | −0.680407 | − | 0.732834i | \(-0.738197\pi\) | ||||
−0.680407 | + | 0.732834i | \(0.738197\pi\) | |||||||
\(662\) | −6.44780 | −0.250601 | ||||||||
\(663\) | 32.3707 | 1.25717 | ||||||||
\(664\) | −9.69774 | −0.376345 | ||||||||
\(665\) | 4.48763 | 0.174023 | ||||||||
\(666\) | 0.875034 | 0.0339069 | ||||||||
\(667\) | −10.5246 | −0.407515 | ||||||||
\(668\) | −28.9599 | −1.12049 | ||||||||
\(669\) | −7.27051 | −0.281094 | ||||||||
\(670\) | −1.50714 | −0.0582261 | ||||||||
\(671\) | 9.22519 | 0.356134 | ||||||||
\(672\) | −2.91903 | −0.112604 | ||||||||
\(673\) | −22.8297 | −0.880021 | −0.440010 | − | 0.897993i | \(-0.645025\pi\) | ||||
−0.440010 | + | 0.897993i | \(0.645025\pi\) | |||||||
\(674\) | −7.21428 | −0.277884 | ||||||||
\(675\) | 1.25410 | 0.0482704 | ||||||||
\(676\) | −37.3103 | −1.43501 | ||||||||
\(677\) | 29.7498 | 1.14338 | 0.571689 | − | 0.820471i | \(-0.306288\pi\) | ||||
0.571689 | + | 0.820471i | \(0.306288\pi\) | |||||||
\(678\) | 1.14971 | 0.0441544 | ||||||||
\(679\) | 10.4548 | 0.401219 | ||||||||
\(680\) | 11.0276 | 0.422889 | ||||||||
\(681\) | 4.78572 | 0.183389 | ||||||||
\(682\) | 0.813306 | 0.0311431 | ||||||||
\(683\) | −5.36266 | −0.205197 | −0.102598 | − | 0.994723i | \(-0.532716\pi\) | ||||
−0.102598 | + | 0.994723i | \(0.532716\pi\) | |||||||
\(684\) | −4.48763 | −0.171589 | ||||||||
\(685\) | −34.1812 | −1.30600 | ||||||||
\(686\) | 0.254102 | 0.00970165 | ||||||||
\(687\) | 5.13614 | 0.195956 | ||||||||
\(688\) | 12.6290 | 0.481476 | ||||||||
\(689\) | −7.21818 | −0.274991 | ||||||||
\(690\) | 1.72532 | 0.0656819 | ||||||||
\(691\) | −28.1812 | −1.07206 | −0.536032 | − | 0.844198i | \(-0.680077\pi\) | ||||
−0.536032 | + | 0.844198i | \(0.680077\pi\) | |||||||
\(692\) | 47.4874 | 1.80520 | ||||||||
\(693\) | −3.87086 | −0.147042 | ||||||||
\(694\) | 5.56860 | 0.211381 | ||||||||
\(695\) | −24.1690 | −0.916781 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | −16.1068 | −0.610088 | ||||||||
\(698\) | −4.21845 | −0.159671 | ||||||||
\(699\) | −24.7089 | −0.934577 | ||||||||
\(700\) | −2.42723 | −0.0917406 | ||||||||
\(701\) | 36.4793 | 1.37780 | 0.688902 | − | 0.724855i | \(-0.258093\pi\) | ||||
0.688902 | + | 0.724855i | \(0.258093\pi\) | |||||||
\(702\) | 1.44364 | 0.0544865 | ||||||||
\(703\) | −7.98465 | −0.301147 | ||||||||
\(704\) | −25.1289 | −0.947080 | ||||||||
\(705\) | −7.09321 | −0.267146 | ||||||||
\(706\) | 8.83627 | 0.332557 | ||||||||
\(707\) | 0.854458 | 0.0321352 | ||||||||
\(708\) | −20.2981 | −0.762849 | ||||||||
\(709\) | −9.08798 | −0.341306 | −0.170653 | − | 0.985331i | \(-0.554588\pi\) | ||||
−0.170653 | + | 0.985331i | \(0.554588\pi\) | |||||||
\(710\) | 4.29108 | 0.161042 | ||||||||
\(711\) | 8.18953 | 0.307132 | ||||||||
\(712\) | 3.91903 | 0.146872 | ||||||||
\(713\) | 2.90084 | 0.108637 | ||||||||
\(714\) | 1.44780 | 0.0541827 | ||||||||
\(715\) | −42.5634 | −1.59178 | ||||||||
\(716\) | −17.5439 | −0.655645 | ||||||||
\(717\) | 0.399644 | 0.0149250 | ||||||||
\(718\) | 0.566483 | 0.0211410 | ||||||||
\(719\) | −7.61676 | −0.284057 | −0.142029 | − | 0.989863i | \(-0.545363\pi\) | ||||
−0.142029 | + | 0.989863i | \(0.545363\pi\) | |||||||
\(720\) | −7.00000 | −0.260875 | ||||||||
\(721\) | −0.491797 | −0.0183155 | ||||||||
\(722\) | 3.46182 | 0.128836 | ||||||||
\(723\) | 14.5962 | 0.542838 | ||||||||
\(724\) | 7.49987 | 0.278730 | ||||||||
\(725\) | −3.76231 | −0.139729 | ||||||||
\(726\) | 1.01224 | 0.0375677 | ||||||||
\(727\) | 19.7006 | 0.730654 | 0.365327 | − | 0.930879i | \(-0.380957\pi\) | ||||
0.365327 | + | 0.930879i | \(0.380957\pi\) | |||||||
\(728\) | −5.68133 | −0.210564 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.73260 | 0.101138 | ||||||||
\(731\) | −19.8953 | −0.735856 | ||||||||
\(732\) | 4.61259 | 0.170486 | ||||||||
\(733\) | 29.8726 | 1.10337 | 0.551686 | − | 0.834052i | \(-0.313985\pi\) | ||||
0.551686 | + | 0.834052i | \(0.313985\pi\) | |||||||
\(734\) | −5.26244 | −0.194240 | ||||||||
\(735\) | 1.93543 | 0.0713895 | ||||||||
\(736\) | 10.2405 | 0.377471 | ||||||||
\(737\) | −11.8625 | −0.436962 | ||||||||
\(738\) | −0.718313 | −0.0264415 | ||||||||
\(739\) | 50.0221 | 1.84009 | 0.920046 | − | 0.391810i | \(-0.128151\pi\) | ||||
0.920046 | + | 0.391810i | \(0.128151\pi\) | |||||||
\(740\) | −12.8995 | −0.474195 | ||||||||
\(741\) | −13.1731 | −0.483927 | ||||||||
\(742\) | −0.322838 | −0.0118518 | ||||||||
\(743\) | 17.2077 | 0.631290 | 0.315645 | − | 0.948877i | \(-0.397779\pi\) | ||||
0.315645 | + | 0.948877i | \(0.397779\pi\) | |||||||
\(744\) | 0.826873 | 0.0303146 | ||||||||
\(745\) | −18.4478 | −0.675875 | ||||||||
\(746\) | −6.37206 | −0.233298 | ||||||||
\(747\) | −9.69774 | −0.354822 | ||||||||
\(748\) | 42.6863 | 1.56077 | ||||||||
\(749\) | 15.0440 | 0.549696 | ||||||||
\(750\) | 3.07575 | 0.112310 | ||||||||
\(751\) | −13.7735 | −0.502602 | −0.251301 | − | 0.967909i | \(-0.580858\pi\) | ||||
−0.251301 | + | 0.967909i | \(0.580858\pi\) | |||||||
\(752\) | −13.2552 | −0.483366 | ||||||||
\(753\) | 8.63734 | 0.314762 | ||||||||
\(754\) | −4.33091 | −0.157722 | ||||||||
\(755\) | −36.6402 | −1.33347 | ||||||||
\(756\) | −1.93543 | −0.0703910 | ||||||||
\(757\) | 5.99583 | 0.217922 | 0.108961 | − | 0.994046i | \(-0.465248\pi\) | ||||
0.108961 | + | 0.994046i | \(0.465248\pi\) | |||||||
\(758\) | 4.88833 | 0.177552 | ||||||||
\(759\) | 13.5798 | 0.492915 | ||||||||
\(760\) | −4.48763 | −0.162783 | ||||||||
\(761\) | −45.0838 | −1.63429 | −0.817144 | − | 0.576434i | \(-0.804444\pi\) | ||||
−0.817144 | + | 0.576434i | \(0.804444\pi\) | |||||||
\(762\) | −2.36160 | −0.0855518 | ||||||||
\(763\) | 13.0880 | 0.473817 | ||||||||
\(764\) | −1.93543 | −0.0700215 | ||||||||
\(765\) | 11.0276 | 0.398703 | ||||||||
\(766\) | 0.275737 | 0.00996277 | ||||||||
\(767\) | −59.5837 | −2.15144 | ||||||||
\(768\) | −11.0810 | −0.399850 | ||||||||
\(769\) | 31.2489 | 1.12686 | 0.563432 | − | 0.826163i | \(-0.309481\pi\) | ||||
0.563432 | + | 0.826163i | \(0.309481\pi\) | |||||||
\(770\) | −1.90368 | −0.0686038 | ||||||||
\(771\) | −14.5204 | −0.522941 | ||||||||
\(772\) | −38.1770 | −1.37402 | ||||||||
\(773\) | 3.37490 | 0.121387 | 0.0606933 | − | 0.998156i | \(-0.480669\pi\) | ||||
0.0606933 | + | 0.998156i | \(0.480669\pi\) | |||||||
\(774\) | −0.887271 | −0.0318923 | ||||||||
\(775\) | 1.03698 | 0.0372495 | ||||||||
\(776\) | −10.4548 | −0.375306 | ||||||||
\(777\) | −3.44364 | −0.123540 | ||||||||
\(778\) | 1.51131 | 0.0541832 | ||||||||
\(779\) | 6.55458 | 0.234842 | ||||||||
\(780\) | −21.2817 | −0.762007 | ||||||||
\(781\) | 33.7745 | 1.20855 | ||||||||
\(782\) | −5.07919 | −0.181632 | ||||||||
\(783\) | −3.00000 | −0.107211 | ||||||||
\(784\) | 3.61676 | 0.129170 | ||||||||
\(785\) | −2.60558 | −0.0929973 | ||||||||
\(786\) | 2.45898 | 0.0877090 | ||||||||
\(787\) | −1.01224 | −0.0360824 | −0.0180412 | − | 0.999837i | \(-0.505743\pi\) | ||||
−0.0180412 | + | 0.999837i | \(0.505743\pi\) | |||||||
\(788\) | 13.7264 | 0.488982 | ||||||||
\(789\) | 12.3749 | 0.440558 | ||||||||
\(790\) | 4.02759 | 0.143295 | ||||||||
\(791\) | −4.52461 | −0.160877 | ||||||||
\(792\) | 3.87086 | 0.137545 | ||||||||
\(793\) | 13.5400 | 0.480818 | ||||||||
\(794\) | −4.11690 | −0.146103 | ||||||||
\(795\) | −2.45898 | −0.0872111 | ||||||||
\(796\) | −16.5306 | −0.585910 | ||||||||
\(797\) | 32.0039 | 1.13364 | 0.566818 | − | 0.823843i | \(-0.308174\pi\) | ||||
0.566818 | + | 0.823843i | \(0.308174\pi\) | |||||||
\(798\) | −0.589178 | −0.0208567 | ||||||||
\(799\) | 20.8818 | 0.738744 | ||||||||
\(800\) | 3.66075 | 0.129427 | ||||||||
\(801\) | 3.91903 | 0.138472 | ||||||||
\(802\) | 0.226517 | 0.00799858 | ||||||||
\(803\) | 21.5079 | 0.758999 | ||||||||
\(804\) | −5.93126 | −0.209180 | ||||||||
\(805\) | −6.78989 | −0.239312 | ||||||||
\(806\) | 1.19370 | 0.0420464 | ||||||||
\(807\) | −9.26111 | −0.326007 | ||||||||
\(808\) | −0.854458 | −0.0300597 | ||||||||
\(809\) | 6.40665 | 0.225246 | 0.112623 | − | 0.993638i | \(-0.464075\pi\) | ||||
0.112623 | + | 0.993638i | \(0.464075\pi\) | |||||||
\(810\) | 0.491797 | 0.0172800 | ||||||||
\(811\) | 3.55220 | 0.124734 | 0.0623672 | − | 0.998053i | \(-0.480135\pi\) | ||||
0.0623672 | + | 0.998053i | \(0.480135\pi\) | |||||||
\(812\) | 5.80630 | 0.203761 | ||||||||
\(813\) | −2.12497 | −0.0745258 | ||||||||
\(814\) | 3.38714 | 0.118719 | ||||||||
\(815\) | −30.8339 | −1.08006 | ||||||||
\(816\) | 20.6074 | 0.721402 | ||||||||
\(817\) | 8.09632 | 0.283254 | ||||||||
\(818\) | −3.27991 | −0.114679 | ||||||||
\(819\) | −5.68133 | −0.198522 | ||||||||
\(820\) | 10.5892 | 0.369790 | ||||||||
\(821\) | 13.8737 | 0.484196 | 0.242098 | − | 0.970252i | \(-0.422165\pi\) | ||||
0.242098 | + | 0.970252i | \(0.422165\pi\) | |||||||
\(822\) | 4.48763 | 0.156524 | ||||||||
\(823\) | 15.6126 | 0.544221 | 0.272110 | − | 0.962266i | \(-0.412278\pi\) | ||||
0.272110 | + | 0.962266i | \(0.412278\pi\) | |||||||
\(824\) | 0.491797 | 0.0171325 | ||||||||
\(825\) | 4.85446 | 0.169011 | ||||||||
\(826\) | −2.66492 | −0.0927246 | ||||||||
\(827\) | 31.0992 | 1.08142 | 0.540712 | − | 0.841208i | \(-0.318155\pi\) | ||||
0.540712 | + | 0.841208i | \(0.318155\pi\) | |||||||
\(828\) | 6.78989 | 0.235965 | ||||||||
\(829\) | 28.6137 | 0.993793 | 0.496897 | − | 0.867810i | \(-0.334473\pi\) | ||||
0.496897 | + | 0.867810i | \(0.334473\pi\) | |||||||
\(830\) | −4.76931 | −0.165545 | ||||||||
\(831\) | −14.5522 | −0.504810 | ||||||||
\(832\) | −36.8820 | −1.27865 | ||||||||
\(833\) | −5.69774 | −0.197415 | ||||||||
\(834\) | 3.17313 | 0.109876 | ||||||||
\(835\) | −28.9599 | −1.00220 | ||||||||
\(836\) | −17.3710 | −0.600789 | ||||||||
\(837\) | 0.826873 | 0.0285809 | ||||||||
\(838\) | −0.394415 | −0.0136249 | ||||||||
\(839\) | 4.67716 | 0.161474 | 0.0807368 | − | 0.996735i | \(-0.474273\pi\) | ||||
0.0807368 | + | 0.996735i | \(0.474273\pi\) | |||||||
\(840\) | −1.93543 | −0.0667788 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −8.42128 | −0.290216 | ||||||||
\(843\) | −13.9641 | −0.480948 | ||||||||
\(844\) | −43.1166 | −1.48414 | ||||||||
\(845\) | −37.3103 | −1.28351 | ||||||||
\(846\) | 0.931263 | 0.0320175 | ||||||||
\(847\) | −3.98359 | −0.136878 | ||||||||
\(848\) | −4.59513 | −0.157797 | ||||||||
\(849\) | −8.00000 | −0.274559 | ||||||||
\(850\) | −1.81569 | −0.0622778 | ||||||||
\(851\) | 12.0810 | 0.414130 | ||||||||
\(852\) | 16.8873 | 0.578548 | ||||||||
\(853\) | −21.9341 | −0.751009 | −0.375505 | − | 0.926820i | \(-0.622531\pi\) | ||||
−0.375505 | + | 0.926820i | \(0.622531\pi\) | |||||||
\(854\) | 0.605585 | 0.0207227 | ||||||||
\(855\) | −4.48763 | −0.153474 | ||||||||
\(856\) | −15.0440 | −0.514193 | ||||||||
\(857\) | −42.8807 | −1.46478 | −0.732389 | − | 0.680887i | \(-0.761595\pi\) | ||||
−0.732389 | + | 0.680887i | \(0.761595\pi\) | |||||||
\(858\) | 5.58812 | 0.190775 | ||||||||
\(859\) | −29.7159 | −1.01389 | −0.506947 | − | 0.861977i | \(-0.669226\pi\) | ||||
−0.506947 | + | 0.861977i | \(0.669226\pi\) | |||||||
\(860\) | 13.0799 | 0.446021 | ||||||||
\(861\) | 2.82687 | 0.0963396 | ||||||||
\(862\) | 10.5058 | 0.357829 | ||||||||
\(863\) | 24.4548 | 0.832452 | 0.416226 | − | 0.909261i | \(-0.363353\pi\) | ||||
0.416226 | + | 0.909261i | \(0.363353\pi\) | |||||||
\(864\) | 2.91903 | 0.0993073 | ||||||||
\(865\) | 47.4874 | 1.61462 | ||||||||
\(866\) | −0.961236 | −0.0326641 | ||||||||
\(867\) | −15.4642 | −0.525192 | ||||||||
\(868\) | −1.60036 | −0.0543196 | ||||||||
\(869\) | 31.7006 | 1.07537 | ||||||||
\(870\) | −1.47539 | −0.0500204 | ||||||||
\(871\) | −17.4108 | −0.589943 | ||||||||
\(872\) | −13.0880 | −0.443215 | ||||||||
\(873\) | −10.4548 | −0.353842 | ||||||||
\(874\) | 2.06696 | 0.0699158 | ||||||||
\(875\) | −12.1044 | −0.409203 | ||||||||
\(876\) | 10.7540 | 0.363343 | ||||||||
\(877\) | −17.4559 | −0.589443 | −0.294721 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294721 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(878\) | −2.48373 | −0.0838218 | ||||||||
\(879\) | −8.46421 | −0.285491 | ||||||||
\(880\) | −27.0961 | −0.913408 | ||||||||
\(881\) | 49.4915 | 1.66741 | 0.833706 | − | 0.552209i | \(-0.186215\pi\) | ||||
0.833706 | + | 0.552209i | \(0.186215\pi\) | |||||||
\(882\) | −0.254102 | −0.00855605 | ||||||||
\(883\) | −21.5327 | −0.724632 | −0.362316 | − | 0.932055i | \(-0.618014\pi\) | ||||
−0.362316 | + | 0.932055i | \(0.618014\pi\) | |||||||
\(884\) | 62.6514 | 2.10719 | ||||||||
\(885\) | −20.2981 | −0.682313 | ||||||||
\(886\) | −6.02369 | −0.202370 | ||||||||
\(887\) | −39.2775 | −1.31881 | −0.659405 | − | 0.751788i | \(-0.729192\pi\) | ||||
−0.659405 | + | 0.751788i | \(0.729192\pi\) | |||||||
\(888\) | 3.44364 | 0.115561 | ||||||||
\(889\) | 9.29392 | 0.311708 | ||||||||
\(890\) | 1.92736 | 0.0646054 | ||||||||
\(891\) | 3.87086 | 0.129679 | ||||||||
\(892\) | −14.0716 | −0.471151 | ||||||||
\(893\) | −8.49775 | −0.284366 | ||||||||
\(894\) | 2.42200 | 0.0810038 | ||||||||
\(895\) | −17.5439 | −0.586426 | ||||||||
\(896\) | −7.48763 | −0.250144 | ||||||||
\(897\) | 19.9313 | 0.665486 | ||||||||
\(898\) | 2.82164 | 0.0941595 | ||||||||
\(899\) | −2.48062 | −0.0827332 | ||||||||
\(900\) | 2.42723 | 0.0809076 | ||||||||
\(901\) | 7.23902 | 0.241167 | ||||||||
\(902\) | −2.78049 | −0.0925803 | ||||||||
\(903\) | 3.49180 | 0.116200 | ||||||||
\(904\) | 4.52461 | 0.150486 | ||||||||
\(905\) | 7.49987 | 0.249304 | ||||||||
\(906\) | 4.81047 | 0.159817 | ||||||||
\(907\) | 4.21295 | 0.139889 | 0.0699444 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699444 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(908\) | 9.26244 | 0.307385 | ||||||||
\(909\) | −0.854458 | −0.0283406 | ||||||||
\(910\) | −2.79406 | −0.0926222 | ||||||||
\(911\) | 27.5428 | 0.912534 | 0.456267 | − | 0.889843i | \(-0.349186\pi\) | ||||
0.456267 | + | 0.889843i | \(0.349186\pi\) | |||||||
\(912\) | −8.38608 | −0.277691 | ||||||||
\(913\) | −37.5386 | −1.24235 | ||||||||
\(914\) | −9.11557 | −0.301516 | ||||||||
\(915\) | 4.61259 | 0.152488 | ||||||||
\(916\) | 9.94066 | 0.328449 | ||||||||
\(917\) | −9.67716 | −0.319568 | ||||||||
\(918\) | −1.44780 | −0.0477847 | ||||||||
\(919\) | 55.8584 | 1.84260 | 0.921299 | − | 0.388856i | \(-0.127130\pi\) | ||||
0.921299 | + | 0.388856i | \(0.127130\pi\) | |||||||
\(920\) | 6.78989 | 0.223856 | ||||||||
\(921\) | 20.5275 | 0.676402 | ||||||||
\(922\) | −5.73260 | −0.188793 | ||||||||
\(923\) | 49.5714 | 1.63166 | ||||||||
\(924\) | −7.49180 | −0.246462 | ||||||||
\(925\) | 4.31867 | 0.141997 | ||||||||
\(926\) | 4.72354 | 0.155225 | ||||||||
\(927\) | 0.491797 | 0.0161527 | ||||||||
\(928\) | −8.75708 | −0.287465 | ||||||||
\(929\) | −0.409763 | −0.0134439 | −0.00672194 | − | 0.999977i | \(-0.502140\pi\) | ||||
−0.00672194 | + | 0.999977i | \(0.502140\pi\) | |||||||
\(930\) | 0.406653 | 0.0133347 | ||||||||
\(931\) | 2.31867 | 0.0759913 | ||||||||
\(932\) | −47.8224 | −1.56648 | ||||||||
\(933\) | 12.3103 | 0.403022 | ||||||||
\(934\) | −2.29597 | −0.0751266 | ||||||||
\(935\) | 42.6863 | 1.39599 | ||||||||
\(936\) | 5.68133 | 0.185700 | ||||||||
\(937\) | 26.9149 | 0.879270 | 0.439635 | − | 0.898177i | \(-0.355108\pi\) | ||||
0.439635 | + | 0.898177i | \(0.355108\pi\) | |||||||
\(938\) | −0.778712 | −0.0254258 | ||||||||
\(939\) | 25.5686 | 0.834400 | ||||||||
\(940\) | −13.7284 | −0.447772 | ||||||||
\(941\) | −23.1979 | −0.756229 | −0.378115 | − | 0.925759i | \(-0.623427\pi\) | ||||
−0.378115 | + | 0.925759i | \(0.623427\pi\) | |||||||
\(942\) | 0.342086 | 0.0111457 | ||||||||
\(943\) | −9.91724 | −0.322950 | ||||||||
\(944\) | −37.9313 | −1.23456 | ||||||||
\(945\) | −1.93543 | −0.0629596 | ||||||||
\(946\) | −3.43451 | −0.111665 | ||||||||
\(947\) | −6.05206 | −0.196666 | −0.0983328 | − | 0.995154i | \(-0.531351\pi\) | ||||
−0.0983328 | + | 0.995154i | \(0.531351\pi\) | |||||||
\(948\) | 15.8503 | 0.514793 | ||||||||
\(949\) | 31.5675 | 1.02473 | ||||||||
\(950\) | 0.738889 | 0.0239727 | ||||||||
\(951\) | 31.3861 | 1.01776 | ||||||||
\(952\) | 5.69774 | 0.184665 | ||||||||
\(953\) | 29.4600 | 0.954304 | 0.477152 | − | 0.878821i | \(-0.341669\pi\) | ||||
0.477152 | + | 0.878821i | \(0.341669\pi\) | |||||||
\(954\) | 0.322838 | 0.0104523 | ||||||||
\(955\) | −1.93543 | −0.0626291 | ||||||||
\(956\) | 0.773483 | 0.0250162 | ||||||||
\(957\) | −11.6126 | −0.375382 | ||||||||
\(958\) | −5.30749 | −0.171477 | ||||||||
\(959\) | −17.6608 | −0.570296 | ||||||||
\(960\) | −12.5644 | −0.405515 | ||||||||
\(961\) | −30.3163 | −0.977945 | ||||||||
\(962\) | 4.97136 | 0.160283 | ||||||||
\(963\) | −15.0440 | −0.484786 | ||||||||
\(964\) | 28.2499 | 0.909869 | ||||||||
\(965\) | −38.1770 | −1.22896 | ||||||||
\(966\) | 0.891440 | 0.0286816 | ||||||||
\(967\) | −3.75530 | −0.120762 | −0.0603811 | − | 0.998175i | \(-0.519232\pi\) | ||||
−0.0603811 | + | 0.998175i | \(0.519232\pi\) | |||||||
\(968\) | 3.98359 | 0.128038 | ||||||||
\(969\) | 13.2112 | 0.424404 | ||||||||
\(970\) | −5.14164 | −0.165088 | ||||||||
\(971\) | −16.4600 | −0.528228 | −0.264114 | − | 0.964491i | \(-0.585080\pi\) | ||||
−0.264114 | + | 0.964491i | \(0.585080\pi\) | |||||||
\(972\) | 1.93543 | 0.0620790 | ||||||||
\(973\) | −12.4876 | −0.400335 | ||||||||
\(974\) | 2.07396 | 0.0664541 | ||||||||
\(975\) | 7.12497 | 0.228182 | ||||||||
\(976\) | 8.61960 | 0.275907 | ||||||||
\(977\) | 40.5878 | 1.29852 | 0.649260 | − | 0.760566i | \(-0.275079\pi\) | ||||
0.649260 | + | 0.760566i | \(0.275079\pi\) | |||||||
\(978\) | 4.04816 | 0.129446 | ||||||||
\(979\) | 15.1700 | 0.484836 | ||||||||
\(980\) | 3.74590 | 0.119658 | ||||||||
\(981\) | −13.0880 | −0.417867 | ||||||||
\(982\) | 4.78155 | 0.152585 | ||||||||
\(983\) | −0.858627 | −0.0273859 | −0.0136930 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136930 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(984\) | −2.82687 | −0.0901174 | ||||||||
\(985\) | 13.7264 | 0.437359 | ||||||||
\(986\) | 4.34341 | 0.138322 | ||||||||
\(987\) | −3.66492 | −0.116656 | ||||||||
\(988\) | −25.4957 | −0.811126 | ||||||||
\(989\) | −12.2499 | −0.389525 | ||||||||
\(990\) | 1.90368 | 0.0605029 | ||||||||
\(991\) | −12.8185 | −0.407194 | −0.203597 | − | 0.979055i | \(-0.565263\pi\) | ||||
−0.203597 | + | 0.979055i | \(0.565263\pi\) | |||||||
\(992\) | 2.41366 | 0.0766339 | ||||||||
\(993\) | −25.3749 | −0.805248 | ||||||||
\(994\) | 2.21712 | 0.0703228 | ||||||||
\(995\) | −16.5306 | −0.524054 | ||||||||
\(996\) | −18.7693 | −0.594728 | ||||||||
\(997\) | 6.49180 | 0.205597 | 0.102799 | − | 0.994702i | \(-0.467220\pi\) | ||||
0.102799 | + | 0.994702i | \(0.467220\pi\) | |||||||
\(998\) | −5.90156 | −0.186811 | ||||||||
\(999\) | 3.44364 | 0.108952 |
(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 | 4011.2.a.e.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |