Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [794,2,Mod(1,794)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(794, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("794.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 794 = 2 \cdot 397 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 794.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: | \(6.34012192049\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 32 x^{12} + 33 x^{11} + 399 x^{10} - 423 x^{9} - 2413 x^{8} + 2601 x^{7} + 7136 x^{6} + \cdots - 1498 \) |
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 | 1.7 | ||
Root | \(-0.447625\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 794.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.447625 | −0.258436 | −0.129218 | − | 0.991616i | \(-0.541247\pi\) | ||||
−0.129218 | + | 0.991616i | \(0.541247\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.34910 | 0.603335 | 0.301667 | − | 0.953413i | \(-0.402457\pi\) | ||||
0.301667 | + | 0.953413i | \(0.402457\pi\) | |||||||
\(6\) | −0.447625 | −0.182742 | ||||||||
\(7\) | 4.95731 | 1.87369 | 0.936843 | − | 0.349750i | \(-0.113733\pi\) | ||||
0.936843 | + | 0.349750i | \(0.113733\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.79963 | −0.933211 | ||||||||
\(10\) | 1.34910 | 0.426622 | ||||||||
\(11\) | 2.19805 | 0.662737 | 0.331368 | − | 0.943501i | \(-0.392490\pi\) | ||||
0.331368 | + | 0.943501i | \(0.392490\pi\) | |||||||
\(12\) | −0.447625 | −0.129218 | ||||||||
\(13\) | 0.925316 | 0.256636 | 0.128318 | − | 0.991733i | \(-0.459042\pi\) | ||||
0.128318 | + | 0.991733i | \(0.459042\pi\) | |||||||
\(14\) | 4.95731 | 1.32490 | ||||||||
\(15\) | −0.603889 | −0.155924 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.56127 | −1.10627 | −0.553135 | − | 0.833092i | \(-0.686569\pi\) | ||||
−0.553135 | + | 0.833092i | \(0.686569\pi\) | |||||||
\(18\) | −2.79963 | −0.659880 | ||||||||
\(19\) | −3.63175 | −0.833181 | −0.416590 | − | 0.909094i | \(-0.636775\pi\) | ||||
−0.416590 | + | 0.909094i | \(0.636775\pi\) | |||||||
\(20\) | 1.34910 | 0.301667 | ||||||||
\(21\) | −2.21901 | −0.484229 | ||||||||
\(22\) | 2.19805 | 0.468626 | ||||||||
\(23\) | 7.58553 | 1.58169 | 0.790847 | − | 0.612015i | \(-0.209641\pi\) | ||||
0.790847 | + | 0.612015i | \(0.209641\pi\) | |||||||
\(24\) | −0.447625 | −0.0913710 | ||||||||
\(25\) | −3.17994 | −0.635987 | ||||||||
\(26\) | 0.925316 | 0.181469 | ||||||||
\(27\) | 2.59606 | 0.499612 | ||||||||
\(28\) | 4.95731 | 0.936843 | ||||||||
\(29\) | −5.05344 | −0.938401 | −0.469200 | − | 0.883092i | \(-0.655458\pi\) | ||||
−0.469200 | + | 0.883092i | \(0.655458\pi\) | |||||||
\(30\) | −0.603889 | −0.110255 | ||||||||
\(31\) | −0.162725 | −0.0292263 | −0.0146132 | − | 0.999893i | \(-0.504652\pi\) | ||||
−0.0146132 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.983901 | −0.171275 | ||||||||
\(34\) | −4.56127 | −0.782251 | ||||||||
\(35\) | 6.68789 | 1.13046 | ||||||||
\(36\) | −2.79963 | −0.466605 | ||||||||
\(37\) | 5.61399 | 0.922934 | 0.461467 | − | 0.887157i | \(-0.347323\pi\) | ||||
0.461467 | + | 0.887157i | \(0.347323\pi\) | |||||||
\(38\) | −3.63175 | −0.589148 | ||||||||
\(39\) | −0.414194 | −0.0663241 | ||||||||
\(40\) | 1.34910 | 0.213311 | ||||||||
\(41\) | 8.67270 | 1.35445 | 0.677224 | − | 0.735777i | \(-0.263183\pi\) | ||||
0.677224 | + | 0.735777i | \(0.263183\pi\) | |||||||
\(42\) | −2.21901 | −0.342401 | ||||||||
\(43\) | −1.17630 | −0.179384 | −0.0896918 | − | 0.995970i | \(-0.528588\pi\) | ||||
−0.0896918 | + | 0.995970i | \(0.528588\pi\) | |||||||
\(44\) | 2.19805 | 0.331368 | ||||||||
\(45\) | −3.77698 | −0.563038 | ||||||||
\(46\) | 7.58553 | 1.11843 | ||||||||
\(47\) | −8.70886 | −1.27032 | −0.635159 | − | 0.772382i | \(-0.719065\pi\) | ||||
−0.635159 | + | 0.772382i | \(0.719065\pi\) | |||||||
\(48\) | −0.447625 | −0.0646091 | ||||||||
\(49\) | 17.5749 | 2.51070 | ||||||||
\(50\) | −3.17994 | −0.449711 | ||||||||
\(51\) | 2.04174 | 0.285900 | ||||||||
\(52\) | 0.925316 | 0.128318 | ||||||||
\(53\) | 4.17360 | 0.573288 | 0.286644 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286644 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(54\) | 2.59606 | 0.353279 | ||||||||
\(55\) | 2.96538 | 0.399852 | ||||||||
\(56\) | 4.95731 | 0.662448 | ||||||||
\(57\) | 1.62566 | 0.215324 | ||||||||
\(58\) | −5.05344 | −0.663549 | ||||||||
\(59\) | −7.77000 | −1.01157 | −0.505784 | − | 0.862660i | \(-0.668797\pi\) | ||||
−0.505784 | + | 0.862660i | \(0.668797\pi\) | |||||||
\(60\) | −0.603889 | −0.0779618 | ||||||||
\(61\) | −10.8481 | −1.38896 | −0.694480 | − | 0.719512i | \(-0.744366\pi\) | ||||
−0.694480 | + | 0.719512i | \(0.744366\pi\) | |||||||
\(62\) | −0.162725 | −0.0206661 | ||||||||
\(63\) | −13.8786 | −1.74854 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.24834 | 0.154838 | ||||||||
\(66\) | −0.983901 | −0.121110 | ||||||||
\(67\) | 11.0660 | 1.35193 | 0.675964 | − | 0.736935i | \(-0.263727\pi\) | ||||
0.675964 | + | 0.736935i | \(0.263727\pi\) | |||||||
\(68\) | −4.56127 | −0.553135 | ||||||||
\(69\) | −3.39547 | −0.408767 | ||||||||
\(70\) | 6.68789 | 0.799356 | ||||||||
\(71\) | −11.6965 | −1.38812 | −0.694058 | − | 0.719919i | \(-0.744179\pi\) | ||||
−0.694058 | + | 0.719919i | \(0.744179\pi\) | |||||||
\(72\) | −2.79963 | −0.329940 | ||||||||
\(73\) | 9.21305 | 1.07831 | 0.539153 | − | 0.842208i | \(-0.318744\pi\) | ||||
0.539153 | + | 0.842208i | \(0.318744\pi\) | |||||||
\(74\) | 5.61399 | 0.652613 | ||||||||
\(75\) | 1.42342 | 0.164362 | ||||||||
\(76\) | −3.63175 | −0.416590 | ||||||||
\(77\) | 10.8964 | 1.24176 | ||||||||
\(78\) | −0.414194 | −0.0468983 | ||||||||
\(79\) | −4.73532 | −0.532766 | −0.266383 | − | 0.963867i | \(-0.585829\pi\) | ||||
−0.266383 | + | 0.963867i | \(0.585829\pi\) | |||||||
\(80\) | 1.34910 | 0.150834 | ||||||||
\(81\) | 7.23684 | 0.804093 | ||||||||
\(82\) | 8.67270 | 0.957740 | ||||||||
\(83\) | −3.16799 | −0.347732 | −0.173866 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173866 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(84\) | −2.21901 | −0.242114 | ||||||||
\(85\) | −6.15359 | −0.667451 | ||||||||
\(86\) | −1.17630 | −0.126843 | ||||||||
\(87\) | 2.26205 | 0.242517 | ||||||||
\(88\) | 2.19805 | 0.234313 | ||||||||
\(89\) | −8.78993 | −0.931731 | −0.465865 | − | 0.884856i | \(-0.654257\pi\) | ||||
−0.465865 | + | 0.884856i | \(0.654257\pi\) | |||||||
\(90\) | −3.77698 | −0.398128 | ||||||||
\(91\) | 4.58707 | 0.480856 | ||||||||
\(92\) | 7.58553 | 0.790847 | ||||||||
\(93\) | 0.0728398 | 0.00755314 | ||||||||
\(94\) | −8.70886 | −0.898250 | ||||||||
\(95\) | −4.89958 | −0.502687 | ||||||||
\(96\) | −0.447625 | −0.0456855 | ||||||||
\(97\) | −3.24337 | −0.329314 | −0.164657 | − | 0.986351i | \(-0.552652\pi\) | ||||
−0.164657 | + | 0.986351i | \(0.552652\pi\) | |||||||
\(98\) | 17.5749 | 1.77533 | ||||||||
\(99\) | −6.15373 | −0.618473 | ||||||||
\(100\) | −3.17994 | −0.317994 | ||||||||
\(101\) | −5.99714 | −0.596738 | −0.298369 | − | 0.954451i | \(-0.596443\pi\) | ||||
−0.298369 | + | 0.954451i | \(0.596443\pi\) | |||||||
\(102\) | 2.04174 | 0.202162 | ||||||||
\(103\) | 8.61138 | 0.848504 | 0.424252 | − | 0.905544i | \(-0.360537\pi\) | ||||
0.424252 | + | 0.905544i | \(0.360537\pi\) | |||||||
\(104\) | 0.925316 | 0.0907347 | ||||||||
\(105\) | −2.99366 | −0.292152 | ||||||||
\(106\) | 4.17360 | 0.405376 | ||||||||
\(107\) | −17.2040 | −1.66317 | −0.831585 | − | 0.555397i | \(-0.812566\pi\) | ||||
−0.831585 | + | 0.555397i | \(0.812566\pi\) | |||||||
\(108\) | 2.59606 | 0.249806 | ||||||||
\(109\) | 0.289805 | 0.0277583 | 0.0138791 | − | 0.999904i | \(-0.495582\pi\) | ||||
0.0138791 | + | 0.999904i | \(0.495582\pi\) | |||||||
\(110\) | 2.96538 | 0.282738 | ||||||||
\(111\) | −2.51296 | −0.238520 | ||||||||
\(112\) | 4.95731 | 0.468422 | ||||||||
\(113\) | 8.25002 | 0.776096 | 0.388048 | − | 0.921639i | \(-0.373149\pi\) | ||||
0.388048 | + | 0.921639i | \(0.373149\pi\) | |||||||
\(114\) | 1.62566 | 0.152257 | ||||||||
\(115\) | 10.2336 | 0.954290 | ||||||||
\(116\) | −5.05344 | −0.469200 | ||||||||
\(117\) | −2.59054 | −0.239496 | ||||||||
\(118\) | −7.77000 | −0.715286 | ||||||||
\(119\) | −22.6116 | −2.07280 | ||||||||
\(120\) | −0.603889 | −0.0551273 | ||||||||
\(121\) | −6.16858 | −0.560780 | ||||||||
\(122\) | −10.8481 | −0.982143 | ||||||||
\(123\) | −3.88212 | −0.350039 | ||||||||
\(124\) | −0.162725 | −0.0146132 | ||||||||
\(125\) | −11.0355 | −0.987048 | ||||||||
\(126\) | −13.8786 | −1.23641 | ||||||||
\(127\) | −17.9409 | −1.59200 | −0.795999 | − | 0.605298i | \(-0.793054\pi\) | ||||
−0.795999 | + | 0.605298i | \(0.793054\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.526539 | 0.0463592 | ||||||||
\(130\) | 1.24834 | 0.109487 | ||||||||
\(131\) | 14.1561 | 1.23682 | 0.618410 | − | 0.785856i | \(-0.287777\pi\) | ||||
0.618410 | + | 0.785856i | \(0.287777\pi\) | |||||||
\(132\) | −0.983901 | −0.0856376 | ||||||||
\(133\) | −18.0037 | −1.56112 | ||||||||
\(134\) | 11.0660 | 0.955957 | ||||||||
\(135\) | 3.50234 | 0.301433 | ||||||||
\(136\) | −4.56127 | −0.391125 | ||||||||
\(137\) | −1.08012 | −0.0922810 | −0.0461405 | − | 0.998935i | \(-0.514692\pi\) | ||||
−0.0461405 | + | 0.998935i | \(0.514692\pi\) | |||||||
\(138\) | −3.39547 | −0.289042 | ||||||||
\(139\) | −15.8941 | −1.34812 | −0.674058 | − | 0.738678i | \(-0.735450\pi\) | ||||
−0.674058 | + | 0.738678i | \(0.735450\pi\) | |||||||
\(140\) | 6.68789 | 0.565230 | ||||||||
\(141\) | 3.89830 | 0.328296 | ||||||||
\(142\) | −11.6965 | −0.981546 | ||||||||
\(143\) | 2.03389 | 0.170082 | ||||||||
\(144\) | −2.79963 | −0.233303 | ||||||||
\(145\) | −6.81758 | −0.566169 | ||||||||
\(146\) | 9.21305 | 0.762477 | ||||||||
\(147\) | −7.86696 | −0.648856 | ||||||||
\(148\) | 5.61399 | 0.461467 | ||||||||
\(149\) | −18.9510 | −1.55252 | −0.776262 | − | 0.630411i | \(-0.782886\pi\) | ||||
−0.776262 | + | 0.630411i | \(0.782886\pi\) | |||||||
\(150\) | 1.42342 | 0.116222 | ||||||||
\(151\) | −5.65661 | −0.460328 | −0.230164 | − | 0.973152i | \(-0.573926\pi\) | ||||
−0.230164 | + | 0.973152i | \(0.573926\pi\) | |||||||
\(152\) | −3.63175 | −0.294574 | ||||||||
\(153\) | 12.7699 | 1.03238 | ||||||||
\(154\) | 10.8964 | 0.878057 | ||||||||
\(155\) | −0.219532 | −0.0176332 | ||||||||
\(156\) | −0.414194 | −0.0331621 | ||||||||
\(157\) | 20.6012 | 1.64415 | 0.822077 | − | 0.569376i | \(-0.192815\pi\) | ||||
0.822077 | + | 0.569376i | \(0.192815\pi\) | |||||||
\(158\) | −4.73532 | −0.376722 | ||||||||
\(159\) | −1.86821 | −0.148158 | ||||||||
\(160\) | 1.34910 | 0.106655 | ||||||||
\(161\) | 37.6038 | 2.96360 | ||||||||
\(162\) | 7.23684 | 0.568580 | ||||||||
\(163\) | 22.4091 | 1.75522 | 0.877608 | − | 0.479378i | \(-0.159138\pi\) | ||||
0.877608 | + | 0.479378i | \(0.159138\pi\) | |||||||
\(164\) | 8.67270 | 0.677224 | ||||||||
\(165\) | −1.32738 | −0.103336 | ||||||||
\(166\) | −3.16799 | −0.245884 | ||||||||
\(167\) | −18.0954 | −1.40027 | −0.700133 | − | 0.714013i | \(-0.746876\pi\) | ||||
−0.700133 | + | 0.714013i | \(0.746876\pi\) | |||||||
\(168\) | −2.21901 | −0.171201 | ||||||||
\(169\) | −12.1438 | −0.934138 | ||||||||
\(170\) | −6.15359 | −0.471959 | ||||||||
\(171\) | 10.1676 | 0.777533 | ||||||||
\(172\) | −1.17630 | −0.0896918 | ||||||||
\(173\) | −2.17952 | −0.165706 | −0.0828528 | − | 0.996562i | \(-0.526403\pi\) | ||||
−0.0828528 | + | 0.996562i | \(0.526403\pi\) | |||||||
\(174\) | 2.26205 | 0.171485 | ||||||||
\(175\) | −15.7639 | −1.19164 | ||||||||
\(176\) | 2.19805 | 0.165684 | ||||||||
\(177\) | 3.47804 | 0.261426 | ||||||||
\(178\) | −8.78993 | −0.658833 | ||||||||
\(179\) | −15.7330 | −1.17594 | −0.587969 | − | 0.808883i | \(-0.700072\pi\) | ||||
−0.587969 | + | 0.808883i | \(0.700072\pi\) | |||||||
\(180\) | −3.77698 | −0.281519 | ||||||||
\(181\) | 10.4414 | 0.776103 | 0.388052 | − | 0.921638i | \(-0.373148\pi\) | ||||
0.388052 | + | 0.921638i | \(0.373148\pi\) | |||||||
\(182\) | 4.58707 | 0.340017 | ||||||||
\(183\) | 4.85589 | 0.358958 | ||||||||
\(184\) | 7.58553 | 0.559213 | ||||||||
\(185\) | 7.57382 | 0.556838 | ||||||||
\(186\) | 0.0728398 | 0.00534087 | ||||||||
\(187\) | −10.0259 | −0.733166 | ||||||||
\(188\) | −8.70886 | −0.635159 | ||||||||
\(189\) | 12.8695 | 0.936116 | ||||||||
\(190\) | −4.89958 | −0.355453 | ||||||||
\(191\) | 11.1156 | 0.804299 | 0.402150 | − | 0.915574i | \(-0.368263\pi\) | ||||
0.402150 | + | 0.915574i | \(0.368263\pi\) | |||||||
\(192\) | −0.447625 | −0.0323045 | ||||||||
\(193\) | 3.89523 | 0.280385 | 0.140193 | − | 0.990124i | \(-0.455228\pi\) | ||||
0.140193 | + | 0.990124i | \(0.455228\pi\) | |||||||
\(194\) | −3.24337 | −0.232860 | ||||||||
\(195\) | −0.558788 | −0.0400156 | ||||||||
\(196\) | 17.5749 | 1.25535 | ||||||||
\(197\) | 1.50902 | 0.107513 | 0.0537565 | − | 0.998554i | \(-0.482881\pi\) | ||||
0.0537565 | + | 0.998554i | \(0.482881\pi\) | |||||||
\(198\) | −6.15373 | −0.437326 | ||||||||
\(199\) | 11.9161 | 0.844712 | 0.422356 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422356 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(200\) | −3.17994 | −0.224856 | ||||||||
\(201\) | −4.95342 | −0.349387 | ||||||||
\(202\) | −5.99714 | −0.421957 | ||||||||
\(203\) | −25.0515 | −1.75827 | ||||||||
\(204\) | 2.04174 | 0.142950 | ||||||||
\(205\) | 11.7003 | 0.817186 | ||||||||
\(206\) | 8.61138 | 0.599983 | ||||||||
\(207\) | −21.2367 | −1.47605 | ||||||||
\(208\) | 0.925316 | 0.0641591 | ||||||||
\(209\) | −7.98277 | −0.552180 | ||||||||
\(210\) | −2.99366 | −0.206583 | ||||||||
\(211\) | −0.999252 | −0.0687913 | −0.0343957 | − | 0.999408i | \(-0.510951\pi\) | ||||
−0.0343957 | + | 0.999408i | \(0.510951\pi\) | |||||||
\(212\) | 4.17360 | 0.286644 | ||||||||
\(213\) | 5.23563 | 0.358739 | ||||||||
\(214\) | −17.2040 | −1.17604 | ||||||||
\(215\) | −1.58694 | −0.108228 | ||||||||
\(216\) | 2.59606 | 0.176639 | ||||||||
\(217\) | −0.806679 | −0.0547609 | ||||||||
\(218\) | 0.289805 | 0.0196281 | ||||||||
\(219\) | −4.12399 | −0.278673 | ||||||||
\(220\) | 2.96538 | 0.199926 | ||||||||
\(221\) | −4.22061 | −0.283909 | ||||||||
\(222\) | −2.51296 | −0.168659 | ||||||||
\(223\) | 1.01101 | 0.0677022 | 0.0338511 | − | 0.999427i | \(-0.489223\pi\) | ||||
0.0338511 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(224\) | 4.95731 | 0.331224 | ||||||||
\(225\) | 8.90265 | 0.593510 | ||||||||
\(226\) | 8.25002 | 0.548783 | ||||||||
\(227\) | −17.8679 | −1.18593 | −0.592967 | − | 0.805227i | \(-0.702043\pi\) | ||||
−0.592967 | + | 0.805227i | \(0.702043\pi\) | |||||||
\(228\) | 1.62566 | 0.107662 | ||||||||
\(229\) | 0.979883 | 0.0647525 | 0.0323763 | − | 0.999476i | \(-0.489693\pi\) | ||||
0.0323763 | + | 0.999476i | \(0.489693\pi\) | |||||||
\(230\) | 10.2336 | 0.674785 | ||||||||
\(231\) | −4.87750 | −0.320916 | ||||||||
\(232\) | −5.05344 | −0.331775 | ||||||||
\(233\) | 7.29869 | 0.478153 | 0.239076 | − | 0.971001i | \(-0.423155\pi\) | ||||
0.239076 | + | 0.971001i | \(0.423155\pi\) | |||||||
\(234\) | −2.59054 | −0.169349 | ||||||||
\(235\) | −11.7491 | −0.766426 | ||||||||
\(236\) | −7.77000 | −0.505784 | ||||||||
\(237\) | 2.11965 | 0.137686 | ||||||||
\(238\) | −22.6116 | −1.46569 | ||||||||
\(239\) | 23.0334 | 1.48991 | 0.744953 | − | 0.667117i | \(-0.232472\pi\) | ||||
0.744953 | + | 0.667117i | \(0.232472\pi\) | |||||||
\(240\) | −0.603889 | −0.0389809 | ||||||||
\(241\) | −15.8573 | −1.02146 | −0.510728 | − | 0.859742i | \(-0.670624\pi\) | ||||
−0.510728 | + | 0.859742i | \(0.670624\pi\) | |||||||
\(242\) | −6.16858 | −0.396531 | ||||||||
\(243\) | −11.0276 | −0.707419 | ||||||||
\(244\) | −10.8481 | −0.694480 | ||||||||
\(245\) | 23.7103 | 1.51479 | ||||||||
\(246\) | −3.88212 | −0.247515 | ||||||||
\(247\) | −3.36052 | −0.213825 | ||||||||
\(248\) | −0.162725 | −0.0103331 | ||||||||
\(249\) | 1.41807 | 0.0898666 | ||||||||
\(250\) | −11.0355 | −0.697948 | ||||||||
\(251\) | −7.97624 | −0.503456 | −0.251728 | − | 0.967798i | \(-0.580999\pi\) | ||||
−0.251728 | + | 0.967798i | \(0.580999\pi\) | |||||||
\(252\) | −13.8786 | −0.874272 | ||||||||
\(253\) | 16.6734 | 1.04825 | ||||||||
\(254\) | −17.9409 | −1.12571 | ||||||||
\(255\) | 2.75450 | 0.172493 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.87093 | 0.303840 | 0.151920 | − | 0.988393i | \(-0.451454\pi\) | ||||
0.151920 | + | 0.988393i | \(0.451454\pi\) | |||||||
\(258\) | 0.526539 | 0.0327809 | ||||||||
\(259\) | 27.8303 | 1.72929 | ||||||||
\(260\) | 1.24834 | 0.0774188 | ||||||||
\(261\) | 14.1478 | 0.875725 | ||||||||
\(262\) | 14.1561 | 0.874564 | ||||||||
\(263\) | 31.5063 | 1.94276 | 0.971382 | − | 0.237525i | \(-0.0763360\pi\) | ||||
0.971382 | + | 0.237525i | \(0.0763360\pi\) | |||||||
\(264\) | −0.983901 | −0.0605549 | ||||||||
\(265\) | 5.63059 | 0.345884 | ||||||||
\(266\) | −18.0037 | −1.10388 | ||||||||
\(267\) | 3.93459 | 0.240793 | ||||||||
\(268\) | 11.0660 | 0.675964 | ||||||||
\(269\) | 5.70493 | 0.347836 | 0.173918 | − | 0.984760i | \(-0.444357\pi\) | ||||
0.173918 | + | 0.984760i | \(0.444357\pi\) | |||||||
\(270\) | 3.50234 | 0.213145 | ||||||||
\(271\) | 6.23357 | 0.378662 | 0.189331 | − | 0.981913i | \(-0.439368\pi\) | ||||
0.189331 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(272\) | −4.56127 | −0.276567 | ||||||||
\(273\) | −2.05329 | −0.124271 | ||||||||
\(274\) | −1.08012 | −0.0652525 | ||||||||
\(275\) | −6.98966 | −0.421492 | ||||||||
\(276\) | −3.39547 | −0.204383 | ||||||||
\(277\) | 12.3348 | 0.741129 | 0.370564 | − | 0.928807i | \(-0.379164\pi\) | ||||
0.370564 | + | 0.928807i | \(0.379164\pi\) | |||||||
\(278\) | −15.8941 | −0.953262 | ||||||||
\(279\) | 0.455571 | 0.0272743 | ||||||||
\(280\) | 6.68789 | 0.399678 | ||||||||
\(281\) | 23.8730 | 1.42415 | 0.712073 | − | 0.702105i | \(-0.247756\pi\) | ||||
0.712073 | + | 0.702105i | \(0.247756\pi\) | |||||||
\(282\) | 3.89830 | 0.232140 | ||||||||
\(283\) | −28.8683 | −1.71604 | −0.858022 | − | 0.513614i | \(-0.828307\pi\) | ||||
−0.858022 | + | 0.513614i | \(0.828307\pi\) | |||||||
\(284\) | −11.6965 | −0.694058 | ||||||||
\(285\) | 2.19318 | 0.129912 | ||||||||
\(286\) | 2.03389 | 0.120266 | ||||||||
\(287\) | 42.9933 | 2.53781 | ||||||||
\(288\) | −2.79963 | −0.164970 | ||||||||
\(289\) | 3.80516 | 0.223833 | ||||||||
\(290\) | −6.81758 | −0.400342 | ||||||||
\(291\) | 1.45181 | 0.0851068 | ||||||||
\(292\) | 9.21305 | 0.539153 | ||||||||
\(293\) | −22.9256 | −1.33933 | −0.669663 | − | 0.742665i | \(-0.733562\pi\) | ||||
−0.669663 | + | 0.742665i | \(0.733562\pi\) | |||||||
\(294\) | −7.86696 | −0.458811 | ||||||||
\(295\) | −10.4825 | −0.610313 | ||||||||
\(296\) | 5.61399 | 0.326307 | ||||||||
\(297\) | 5.70626 | 0.331111 | ||||||||
\(298\) | −18.9510 | −1.09780 | ||||||||
\(299\) | 7.01901 | 0.405920 | ||||||||
\(300\) | 1.42342 | 0.0821811 | ||||||||
\(301\) | −5.83126 | −0.336108 | ||||||||
\(302\) | −5.65661 | −0.325501 | ||||||||
\(303\) | 2.68447 | 0.154219 | ||||||||
\(304\) | −3.63175 | −0.208295 | ||||||||
\(305\) | −14.6352 | −0.838008 | ||||||||
\(306\) | 12.7699 | 0.730005 | ||||||||
\(307\) | 23.8143 | 1.35915 | 0.679576 | − | 0.733605i | \(-0.262164\pi\) | ||||
0.679576 | + | 0.733605i | \(0.262164\pi\) | |||||||
\(308\) | 10.8964 | 0.620880 | ||||||||
\(309\) | −3.85466 | −0.219284 | ||||||||
\(310\) | −0.219532 | −0.0124686 | ||||||||
\(311\) | −10.7820 | −0.611394 | −0.305697 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305697 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(312\) | −0.414194 | −0.0234491 | ||||||||
\(313\) | 19.5918 | 1.10739 | 0.553696 | − | 0.832719i | \(-0.313217\pi\) | ||||
0.553696 | + | 0.832719i | \(0.313217\pi\) | |||||||
\(314\) | 20.6012 | 1.16259 | ||||||||
\(315\) | −18.7236 | −1.05496 | ||||||||
\(316\) | −4.73532 | −0.266383 | ||||||||
\(317\) | −22.5910 | −1.26884 | −0.634418 | − | 0.772990i | \(-0.718760\pi\) | ||||
−0.634418 | + | 0.772990i | \(0.718760\pi\) | |||||||
\(318\) | −1.86821 | −0.104764 | ||||||||
\(319\) | −11.1077 | −0.621912 | ||||||||
\(320\) | 1.34910 | 0.0754168 | ||||||||
\(321\) | 7.70092 | 0.429824 | ||||||||
\(322\) | 37.6038 | 2.09558 | ||||||||
\(323\) | 16.5654 | 0.921723 | ||||||||
\(324\) | 7.23684 | 0.402046 | ||||||||
\(325\) | −2.94245 | −0.163218 | ||||||||
\(326\) | 22.4091 | 1.24113 | ||||||||
\(327\) | −0.129724 | −0.00717374 | ||||||||
\(328\) | 8.67270 | 0.478870 | ||||||||
\(329\) | −43.1725 | −2.38018 | ||||||||
\(330\) | −1.32738 | −0.0730698 | ||||||||
\(331\) | 12.2636 | 0.674070 | 0.337035 | − | 0.941492i | \(-0.390576\pi\) | ||||
0.337035 | + | 0.941492i | \(0.390576\pi\) | |||||||
\(332\) | −3.16799 | −0.173866 | ||||||||
\(333\) | −15.7171 | −0.861292 | ||||||||
\(334\) | −18.0954 | −0.990137 | ||||||||
\(335\) | 14.9291 | 0.815665 | ||||||||
\(336\) | −2.21901 | −0.121057 | ||||||||
\(337\) | 1.44495 | 0.0787114 | 0.0393557 | − | 0.999225i | \(-0.487469\pi\) | ||||
0.0393557 | + | 0.999225i | \(0.487469\pi\) | |||||||
\(338\) | −12.1438 | −0.660535 | ||||||||
\(339\) | −3.69291 | −0.200571 | ||||||||
\(340\) | −6.15359 | −0.333725 | ||||||||
\(341\) | −0.357678 | −0.0193693 | ||||||||
\(342\) | 10.1676 | 0.549799 | ||||||||
\(343\) | 52.4231 | 2.83058 | ||||||||
\(344\) | −1.17630 | −0.0634216 | ||||||||
\(345\) | −4.58082 | −0.246623 | ||||||||
\(346\) | −2.17952 | −0.117172 | ||||||||
\(347\) | 3.24257 | 0.174070 | 0.0870352 | − | 0.996205i | \(-0.472261\pi\) | ||||
0.0870352 | + | 0.996205i | \(0.472261\pi\) | |||||||
\(348\) | 2.26205 | 0.121258 | ||||||||
\(349\) | −24.2741 | −1.29936 | −0.649682 | − | 0.760206i | \(-0.725098\pi\) | ||||
−0.649682 | + | 0.760206i | \(0.725098\pi\) | |||||||
\(350\) | −15.7639 | −0.842617 | ||||||||
\(351\) | 2.40217 | 0.128219 | ||||||||
\(352\) | 2.19805 | 0.117156 | ||||||||
\(353\) | 22.5168 | 1.19845 | 0.599224 | − | 0.800581i | \(-0.295476\pi\) | ||||
0.599224 | + | 0.800581i | \(0.295476\pi\) | |||||||
\(354\) | 3.47804 | 0.184856 | ||||||||
\(355\) | −15.7797 | −0.837498 | ||||||||
\(356\) | −8.78993 | −0.465865 | ||||||||
\(357\) | 10.1215 | 0.535687 | ||||||||
\(358\) | −15.7330 | −0.831514 | ||||||||
\(359\) | −3.03152 | −0.159998 | −0.0799988 | − | 0.996795i | \(-0.525492\pi\) | ||||
−0.0799988 | + | 0.996795i | \(0.525492\pi\) | |||||||
\(360\) | −3.77698 | −0.199064 | ||||||||
\(361\) | −5.81038 | −0.305810 | ||||||||
\(362\) | 10.4414 | 0.548788 | ||||||||
\(363\) | 2.76121 | 0.144926 | ||||||||
\(364\) | 4.58707 | 0.240428 | ||||||||
\(365\) | 12.4293 | 0.650579 | ||||||||
\(366\) | 4.85589 | 0.253821 | ||||||||
\(367\) | −13.9669 | −0.729067 | −0.364534 | − | 0.931190i | \(-0.618772\pi\) | ||||
−0.364534 | + | 0.931190i | \(0.618772\pi\) | |||||||
\(368\) | 7.58553 | 0.395423 | ||||||||
\(369\) | −24.2804 | −1.26399 | ||||||||
\(370\) | 7.57382 | 0.393744 | ||||||||
\(371\) | 20.6898 | 1.07416 | ||||||||
\(372\) | 0.0728398 | 0.00377657 | ||||||||
\(373\) | 22.7430 | 1.17759 | 0.588794 | − | 0.808283i | \(-0.299603\pi\) | ||||
0.588794 | + | 0.808283i | \(0.299603\pi\) | |||||||
\(374\) | −10.0259 | −0.518426 | ||||||||
\(375\) | 4.93978 | 0.255089 | ||||||||
\(376\) | −8.70886 | −0.449125 | ||||||||
\(377\) | −4.67603 | −0.240828 | ||||||||
\(378\) | 12.8695 | 0.661934 | ||||||||
\(379\) | 23.3257 | 1.19816 | 0.599081 | − | 0.800688i | \(-0.295533\pi\) | ||||
0.599081 | + | 0.800688i | \(0.295533\pi\) | |||||||
\(380\) | −4.89958 | −0.251343 | ||||||||
\(381\) | 8.03079 | 0.411430 | ||||||||
\(382\) | 11.1156 | 0.568726 | ||||||||
\(383\) | −15.7808 | −0.806359 | −0.403180 | − | 0.915121i | \(-0.632095\pi\) | ||||
−0.403180 | + | 0.915121i | \(0.632095\pi\) | |||||||
\(384\) | −0.447625 | −0.0228428 | ||||||||
\(385\) | 14.7003 | 0.749197 | ||||||||
\(386\) | 3.89523 | 0.198262 | ||||||||
\(387\) | 3.29320 | 0.167403 | ||||||||
\(388\) | −3.24337 | −0.164657 | ||||||||
\(389\) | −19.9086 | −1.00941 | −0.504703 | − | 0.863293i | \(-0.668398\pi\) | ||||
−0.504703 | + | 0.863293i | \(0.668398\pi\) | |||||||
\(390\) | −0.558788 | −0.0282953 | ||||||||
\(391\) | −34.5996 | −1.74978 | ||||||||
\(392\) | 17.5749 | 0.887667 | ||||||||
\(393\) | −6.33660 | −0.319639 | ||||||||
\(394\) | 1.50902 | 0.0760232 | ||||||||
\(395\) | −6.38841 | −0.321436 | ||||||||
\(396\) | −6.15373 | −0.309236 | ||||||||
\(397\) | −1.00000 | −0.0501886 | ||||||||
\(398\) | 11.9161 | 0.597301 | ||||||||
\(399\) | 8.05891 | 0.403450 | ||||||||
\(400\) | −3.17994 | −0.158997 | ||||||||
\(401\) | 12.0474 | 0.601617 | 0.300809 | − | 0.953685i | \(-0.402743\pi\) | ||||
0.300809 | + | 0.953685i | \(0.402743\pi\) | |||||||
\(402\) | −4.95342 | −0.247054 | ||||||||
\(403\) | −0.150572 | −0.00750053 | ||||||||
\(404\) | −5.99714 | −0.298369 | ||||||||
\(405\) | 9.76319 | 0.485137 | ||||||||
\(406\) | −25.0515 | −1.24328 | ||||||||
\(407\) | 12.3398 | 0.611662 | ||||||||
\(408\) | 2.04174 | 0.101081 | ||||||||
\(409\) | 35.2892 | 1.74494 | 0.872470 | − | 0.488668i | \(-0.162517\pi\) | ||||
0.872470 | + | 0.488668i | \(0.162517\pi\) | |||||||
\(410\) | 11.7003 | 0.577837 | ||||||||
\(411\) | 0.483489 | 0.0238488 | ||||||||
\(412\) | 8.61138 | 0.424252 | ||||||||
\(413\) | −38.5183 | −1.89536 | ||||||||
\(414\) | −21.2367 | −1.04373 | ||||||||
\(415\) | −4.27393 | −0.209799 | ||||||||
\(416\) | 0.925316 | 0.0453673 | ||||||||
\(417\) | 7.11458 | 0.348402 | ||||||||
\(418\) | −7.98277 | −0.390450 | ||||||||
\(419\) | −4.51542 | −0.220593 | −0.110296 | − | 0.993899i | \(-0.535180\pi\) | ||||
−0.110296 | + | 0.993899i | \(0.535180\pi\) | |||||||
\(420\) | −2.99366 | −0.146076 | ||||||||
\(421\) | 18.3797 | 0.895771 | 0.447885 | − | 0.894091i | \(-0.352177\pi\) | ||||
0.447885 | + | 0.894091i | \(0.352177\pi\) | |||||||
\(422\) | −0.999252 | −0.0486428 | ||||||||
\(423\) | 24.3816 | 1.18547 | ||||||||
\(424\) | 4.17360 | 0.202688 | ||||||||
\(425\) | 14.5045 | 0.703574 | ||||||||
\(426\) | 5.23563 | 0.253667 | ||||||||
\(427\) | −53.7775 | −2.60248 | ||||||||
\(428\) | −17.2040 | −0.831585 | ||||||||
\(429\) | −0.910419 | −0.0439554 | ||||||||
\(430\) | −1.58694 | −0.0765289 | ||||||||
\(431\) | −7.46835 | −0.359738 | −0.179869 | − | 0.983691i | \(-0.557567\pi\) | ||||
−0.179869 | + | 0.983691i | \(0.557567\pi\) | |||||||
\(432\) | 2.59606 | 0.124903 | ||||||||
\(433\) | 4.02751 | 0.193550 | 0.0967750 | − | 0.995306i | \(-0.469147\pi\) | ||||
0.0967750 | + | 0.995306i | \(0.469147\pi\) | |||||||
\(434\) | −0.806679 | −0.0387218 | ||||||||
\(435\) | 3.05172 | 0.146319 | ||||||||
\(436\) | 0.289805 | 0.0138791 | ||||||||
\(437\) | −27.5488 | −1.31784 | ||||||||
\(438\) | −4.12399 | −0.197052 | ||||||||
\(439\) | −8.00670 | −0.382139 | −0.191069 | − | 0.981577i | \(-0.561196\pi\) | ||||
−0.191069 | + | 0.981577i | \(0.561196\pi\) | |||||||
\(440\) | 2.96538 | 0.141369 | ||||||||
\(441\) | −49.2033 | −2.34301 | ||||||||
\(442\) | −4.22061 | −0.200754 | ||||||||
\(443\) | −17.6097 | −0.836664 | −0.418332 | − | 0.908294i | \(-0.637385\pi\) | ||||
−0.418332 | + | 0.908294i | \(0.637385\pi\) | |||||||
\(444\) | −2.51296 | −0.119260 | ||||||||
\(445\) | −11.8585 | −0.562145 | ||||||||
\(446\) | 1.01101 | 0.0478727 | ||||||||
\(447\) | 8.48292 | 0.401228 | ||||||||
\(448\) | 4.95731 | 0.234211 | ||||||||
\(449\) | −7.33333 | −0.346081 | −0.173041 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173041 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(450\) | 8.90265 | 0.419675 | ||||||||
\(451\) | 19.0630 | 0.897643 | ||||||||
\(452\) | 8.25002 | 0.388048 | ||||||||
\(453\) | 2.53204 | 0.118965 | ||||||||
\(454\) | −17.8679 | −0.838581 | ||||||||
\(455\) | 6.18841 | 0.290117 | ||||||||
\(456\) | 1.62566 | 0.0761286 | ||||||||
\(457\) | 35.9698 | 1.68260 | 0.841298 | − | 0.540571i | \(-0.181792\pi\) | ||||
0.841298 | + | 0.540571i | \(0.181792\pi\) | |||||||
\(458\) | 0.979883 | 0.0457869 | ||||||||
\(459\) | −11.8413 | −0.552705 | ||||||||
\(460\) | 10.2336 | 0.477145 | ||||||||
\(461\) | −16.5204 | −0.769434 | −0.384717 | − | 0.923035i | \(-0.625701\pi\) | ||||
−0.384717 | + | 0.923035i | \(0.625701\pi\) | |||||||
\(462\) | −4.87750 | −0.226922 | ||||||||
\(463\) | 23.9280 | 1.11203 | 0.556015 | − | 0.831172i | \(-0.312330\pi\) | ||||
0.556015 | + | 0.831172i | \(0.312330\pi\) | |||||||
\(464\) | −5.05344 | −0.234600 | ||||||||
\(465\) | 0.0982680 | 0.00455707 | ||||||||
\(466\) | 7.29869 | 0.338105 | ||||||||
\(467\) | −13.9916 | −0.647454 | −0.323727 | − | 0.946150i | \(-0.604936\pi\) | ||||
−0.323727 | + | 0.946150i | \(0.604936\pi\) | |||||||
\(468\) | −2.59054 | −0.119748 | ||||||||
\(469\) | 54.8576 | 2.53309 | ||||||||
\(470\) | −11.7491 | −0.541945 | ||||||||
\(471\) | −9.22161 | −0.424909 | ||||||||
\(472\) | −7.77000 | −0.357643 | ||||||||
\(473\) | −2.58556 | −0.118884 | ||||||||
\(474\) | 2.11965 | 0.0973587 | ||||||||
\(475\) | 11.5487 | 0.529893 | ||||||||
\(476\) | −22.6116 | −1.03640 | ||||||||
\(477\) | −11.6845 | −0.534998 | ||||||||
\(478\) | 23.0334 | 1.05352 | ||||||||
\(479\) | 16.6626 | 0.761333 | 0.380666 | − | 0.924712i | \(-0.375695\pi\) | ||||
0.380666 | + | 0.924712i | \(0.375695\pi\) | |||||||
\(480\) | −0.603889 | −0.0275636 | ||||||||
\(481\) | 5.19471 | 0.236859 | ||||||||
\(482\) | −15.8573 | −0.722279 | ||||||||
\(483\) | −16.8324 | −0.765901 | ||||||||
\(484\) | −6.16858 | −0.280390 | ||||||||
\(485\) | −4.37562 | −0.198687 | ||||||||
\(486\) | −11.0276 | −0.500220 | ||||||||
\(487\) | 22.1080 | 1.00181 | 0.500904 | − | 0.865503i | \(-0.333001\pi\) | ||||
0.500904 | + | 0.865503i | \(0.333001\pi\) | |||||||
\(488\) | −10.8481 | −0.491072 | ||||||||
\(489\) | −10.0309 | −0.453612 | ||||||||
\(490\) | 23.7103 | 1.07112 | ||||||||
\(491\) | 41.9288 | 1.89222 | 0.946109 | − | 0.323848i | \(-0.104977\pi\) | ||||
0.946109 | + | 0.323848i | \(0.104977\pi\) | |||||||
\(492\) | −3.88212 | −0.175019 | ||||||||
\(493\) | 23.0501 | 1.03812 | ||||||||
\(494\) | −3.36052 | −0.151197 | ||||||||
\(495\) | −8.30198 | −0.373146 | ||||||||
\(496\) | −0.162725 | −0.00730658 | ||||||||
\(497\) | −57.9830 | −2.60089 | ||||||||
\(498\) | 1.41807 | 0.0635453 | ||||||||
\(499\) | 27.7340 | 1.24154 | 0.620772 | − | 0.783991i | \(-0.286819\pi\) | ||||
0.620772 | + | 0.783991i | \(0.286819\pi\) | |||||||
\(500\) | −11.0355 | −0.493524 | ||||||||
\(501\) | 8.09995 | 0.361879 | ||||||||
\(502\) | −7.97624 | −0.355997 | ||||||||
\(503\) | −15.6652 | −0.698478 | −0.349239 | − | 0.937034i | \(-0.613560\pi\) | ||||
−0.349239 | + | 0.937034i | \(0.613560\pi\) | |||||||
\(504\) | −13.8786 | −0.618204 | ||||||||
\(505\) | −8.09072 | −0.360032 | ||||||||
\(506\) | 16.6734 | 0.741222 | ||||||||
\(507\) | 5.43586 | 0.241415 | ||||||||
\(508\) | −17.9409 | −0.795999 | ||||||||
\(509\) | 26.4941 | 1.17433 | 0.587165 | − | 0.809467i | \(-0.300244\pi\) | ||||
0.587165 | + | 0.809467i | \(0.300244\pi\) | |||||||
\(510\) | 2.75450 | 0.121971 | ||||||||
\(511\) | 45.6719 | 2.02041 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.42824 | −0.416267 | ||||||||
\(514\) | 4.87093 | 0.214848 | ||||||||
\(515\) | 11.6176 | 0.511932 | ||||||||
\(516\) | 0.526539 | 0.0231796 | ||||||||
\(517\) | −19.1425 | −0.841886 | ||||||||
\(518\) | 27.8303 | 1.22279 | ||||||||
\(519\) | 0.975606 | 0.0428244 | ||||||||
\(520\) | 1.24834 | 0.0547434 | ||||||||
\(521\) | 41.6071 | 1.82284 | 0.911420 | − | 0.411477i | \(-0.134987\pi\) | ||||
0.911420 | + | 0.411477i | \(0.134987\pi\) | |||||||
\(522\) | 14.1478 | 0.619231 | ||||||||
\(523\) | −23.2913 | −1.01846 | −0.509229 | − | 0.860631i | \(-0.670069\pi\) | ||||
−0.509229 | + | 0.860631i | \(0.670069\pi\) | |||||||
\(524\) | 14.1561 | 0.618410 | ||||||||
\(525\) | 7.05632 | 0.307963 | ||||||||
\(526\) | 31.5063 | 1.37374 | ||||||||
\(527\) | 0.742233 | 0.0323322 | ||||||||
\(528\) | −0.983901 | −0.0428188 | ||||||||
\(529\) | 34.5403 | 1.50175 | ||||||||
\(530\) | 5.63059 | 0.244577 | ||||||||
\(531\) | 21.7531 | 0.944005 | ||||||||
\(532\) | −18.0037 | −0.780560 | ||||||||
\(533\) | 8.02499 | 0.347601 | ||||||||
\(534\) | 3.93459 | 0.170266 | ||||||||
\(535\) | −23.2098 | −1.00345 | ||||||||
\(536\) | 11.0660 | 0.477979 | ||||||||
\(537\) | 7.04248 | 0.303905 | ||||||||
\(538\) | 5.70493 | 0.245957 | ||||||||
\(539\) | 38.6305 | 1.66393 | ||||||||
\(540\) | 3.50234 | 0.150717 | ||||||||
\(541\) | −32.1227 | −1.38106 | −0.690531 | − | 0.723303i | \(-0.742623\pi\) | ||||
−0.690531 | + | 0.723303i | \(0.742623\pi\) | |||||||
\(542\) | 6.23357 | 0.267755 | ||||||||
\(543\) | −4.67383 | −0.200573 | ||||||||
\(544\) | −4.56127 | −0.195563 | ||||||||
\(545\) | 0.390975 | 0.0167475 | ||||||||
\(546\) | −2.05329 | −0.0878726 | ||||||||
\(547\) | −15.8786 | −0.678922 | −0.339461 | − | 0.940620i | \(-0.610245\pi\) | ||||
−0.339461 | + | 0.940620i | \(0.610245\pi\) | |||||||
\(548\) | −1.08012 | −0.0461405 | ||||||||
\(549\) | 30.3708 | 1.29619 | ||||||||
\(550\) | −6.98966 | −0.298040 | ||||||||
\(551\) | 18.3528 | 0.781857 | ||||||||
\(552\) | −3.39547 | −0.144521 | ||||||||
\(553\) | −23.4745 | −0.998236 | ||||||||
\(554\) | 12.3348 | 0.524057 | ||||||||
\(555\) | −3.39023 | −0.143907 | ||||||||
\(556\) | −15.8941 | −0.674058 | ||||||||
\(557\) | 36.1116 | 1.53010 | 0.765049 | − | 0.643972i | \(-0.222715\pi\) | ||||
0.765049 | + | 0.643972i | \(0.222715\pi\) | |||||||
\(558\) | 0.455571 | 0.0192858 | ||||||||
\(559\) | −1.08845 | −0.0460363 | ||||||||
\(560\) | 6.68789 | 0.282615 | ||||||||
\(561\) | 4.48784 | 0.189477 | ||||||||
\(562\) | 23.8730 | 1.00702 | ||||||||
\(563\) | −12.7816 | −0.538679 | −0.269339 | − | 0.963045i | \(-0.586805\pi\) | ||||
−0.269339 | + | 0.963045i | \(0.586805\pi\) | |||||||
\(564\) | 3.89830 | 0.164148 | ||||||||
\(565\) | 11.1301 | 0.468246 | ||||||||
\(566\) | −28.8683 | −1.21343 | ||||||||
\(567\) | 35.8752 | 1.50662 | ||||||||
\(568\) | −11.6965 | −0.490773 | ||||||||
\(569\) | 6.77043 | 0.283831 | 0.141916 | − | 0.989879i | \(-0.454674\pi\) | ||||
0.141916 | + | 0.989879i | \(0.454674\pi\) | |||||||
\(570\) | 2.19318 | 0.0918620 | ||||||||
\(571\) | −17.6287 | −0.737739 | −0.368870 | − | 0.929481i | \(-0.620255\pi\) | ||||
−0.368870 | + | 0.929481i | \(0.620255\pi\) | |||||||
\(572\) | 2.03389 | 0.0850412 | ||||||||
\(573\) | −4.97563 | −0.207860 | ||||||||
\(574\) | 42.9933 | 1.79450 | ||||||||
\(575\) | −24.1215 | −1.00594 | ||||||||
\(576\) | −2.79963 | −0.116651 | ||||||||
\(577\) | 14.6547 | 0.610083 | 0.305042 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305042 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(578\) | 3.80516 | 0.158274 | ||||||||
\(579\) | −1.74360 | −0.0724617 | ||||||||
\(580\) | −6.81758 | −0.283085 | ||||||||
\(581\) | −15.7047 | −0.651541 | ||||||||
\(582\) | 1.45181 | 0.0601796 | ||||||||
\(583\) | 9.17377 | 0.379939 | ||||||||
\(584\) | 9.21305 | 0.381239 | ||||||||
\(585\) | −3.49489 | −0.144496 | ||||||||
\(586\) | −22.9256 | −0.947047 | ||||||||
\(587\) | −26.5437 | −1.09557 | −0.547787 | − | 0.836618i | \(-0.684530\pi\) | ||||
−0.547787 | + | 0.836618i | \(0.684530\pi\) | |||||||
\(588\) | −7.86696 | −0.324428 | ||||||||
\(589\) | 0.590977 | 0.0243508 | ||||||||
\(590\) | −10.4825 | −0.431557 | ||||||||
\(591\) | −0.675474 | −0.0277853 | ||||||||
\(592\) | 5.61399 | 0.230734 | ||||||||
\(593\) | 15.6534 | 0.642808 | 0.321404 | − | 0.946942i | \(-0.395845\pi\) | ||||
0.321404 | + | 0.946942i | \(0.395845\pi\) | |||||||
\(594\) | 5.70626 | 0.234131 | ||||||||
\(595\) | −30.5053 | −1.25059 | ||||||||
\(596\) | −18.9510 | −0.776262 | ||||||||
\(597\) | −5.33395 | −0.218304 | ||||||||
\(598\) | 7.01901 | 0.287029 | ||||||||
\(599\) | 28.6057 | 1.16880 | 0.584398 | − | 0.811467i | \(-0.301331\pi\) | ||||
0.584398 | + | 0.811467i | \(0.301331\pi\) | |||||||
\(600\) | 1.42342 | 0.0581108 | ||||||||
\(601\) | 39.4979 | 1.61115 | 0.805577 | − | 0.592491i | \(-0.201855\pi\) | ||||
0.805577 | + | 0.592491i | \(0.201855\pi\) | |||||||
\(602\) | −5.83126 | −0.237665 | ||||||||
\(603\) | −30.9807 | −1.26163 | ||||||||
\(604\) | −5.65661 | −0.230164 | ||||||||
\(605\) | −8.32201 | −0.338338 | ||||||||
\(606\) | 2.68447 | 0.109049 | ||||||||
\(607\) | 33.1804 | 1.34675 | 0.673376 | − | 0.739300i | \(-0.264844\pi\) | ||||
0.673376 | + | 0.739300i | \(0.264844\pi\) | |||||||
\(608\) | −3.63175 | −0.147287 | ||||||||
\(609\) | 11.2137 | 0.454400 | ||||||||
\(610\) | −14.6352 | −0.592561 | ||||||||
\(611\) | −8.05844 | −0.326010 | ||||||||
\(612\) | 12.7699 | 0.516191 | ||||||||
\(613\) | 3.06851 | 0.123936 | 0.0619680 | − | 0.998078i | \(-0.480262\pi\) | ||||
0.0619680 | + | 0.998078i | \(0.480262\pi\) | |||||||
\(614\) | 23.8143 | 0.961065 | ||||||||
\(615\) | −5.23735 | −0.211190 | ||||||||
\(616\) | 10.8964 | 0.439029 | ||||||||
\(617\) | 3.64432 | 0.146715 | 0.0733573 | − | 0.997306i | \(-0.476629\pi\) | ||||
0.0733573 | + | 0.997306i | \(0.476629\pi\) | |||||||
\(618\) | −3.85466 | −0.155057 | ||||||||
\(619\) | −3.14773 | −0.126518 | −0.0632590 | − | 0.997997i | \(-0.520149\pi\) | ||||
−0.0632590 | + | 0.997997i | \(0.520149\pi\) | |||||||
\(620\) | −0.219532 | −0.00881662 | ||||||||
\(621\) | 19.6925 | 0.790232 | ||||||||
\(622\) | −10.7820 | −0.432321 | ||||||||
\(623\) | −43.5744 | −1.74577 | ||||||||
\(624\) | −0.414194 | −0.0165810 | ||||||||
\(625\) | 1.01169 | 0.0404675 | ||||||||
\(626\) | 19.5918 | 0.783044 | ||||||||
\(627\) | 3.57328 | 0.142703 | ||||||||
\(628\) | 20.6012 | 0.822077 | ||||||||
\(629\) | −25.6069 | −1.02101 | ||||||||
\(630\) | −18.7236 | −0.745967 | ||||||||
\(631\) | −1.09172 | −0.0434607 | −0.0217304 | − | 0.999764i | \(-0.506918\pi\) | ||||
−0.0217304 | + | 0.999764i | \(0.506918\pi\) | |||||||
\(632\) | −4.73532 | −0.188361 | ||||||||
\(633\) | 0.447290 | 0.0177782 | ||||||||
\(634\) | −22.5910 | −0.897202 | ||||||||
\(635\) | −24.2040 | −0.960507 | ||||||||
\(636\) | −1.86821 | −0.0740792 | ||||||||
\(637\) | 16.2623 | 0.644337 | ||||||||
\(638\) | −11.1077 | −0.439759 | ||||||||
\(639\) | 32.7458 | 1.29540 | ||||||||
\(640\) | 1.34910 | 0.0533277 | ||||||||
\(641\) | −20.6028 | −0.813763 | −0.406881 | − | 0.913481i | \(-0.633384\pi\) | ||||
−0.406881 | + | 0.913481i | \(0.633384\pi\) | |||||||
\(642\) | 7.70092 | 0.303931 | ||||||||
\(643\) | −10.7036 | −0.422110 | −0.211055 | − | 0.977474i | \(-0.567690\pi\) | ||||
−0.211055 | + | 0.977474i | \(0.567690\pi\) | |||||||
\(644\) | 37.6038 | 1.48180 | ||||||||
\(645\) | 0.710353 | 0.0279701 | ||||||||
\(646\) | 16.5654 | 0.651756 | ||||||||
\(647\) | −45.6576 | −1.79498 | −0.897492 | − | 0.441031i | \(-0.854613\pi\) | ||||
−0.897492 | + | 0.441031i | \(0.854613\pi\) | |||||||
\(648\) | 7.23684 | 0.284290 | ||||||||
\(649\) | −17.0788 | −0.670403 | ||||||||
\(650\) | −2.94245 | −0.115412 | ||||||||
\(651\) | 0.361089 | 0.0141522 | ||||||||
\(652\) | 22.4091 | 0.877608 | ||||||||
\(653\) | −22.1323 | −0.866103 | −0.433051 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433051 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(654\) | −0.129724 | −0.00507260 | ||||||||
\(655\) | 19.0979 | 0.746216 | ||||||||
\(656\) | 8.67270 | 0.338612 | ||||||||
\(657\) | −25.7932 | −1.00629 | ||||||||
\(658\) | −43.1725 | −1.68304 | ||||||||
\(659\) | 0.699095 | 0.0272329 | 0.0136164 | − | 0.999907i | \(-0.495666\pi\) | ||||
0.0136164 | + | 0.999907i | \(0.495666\pi\) | |||||||
\(660\) | −1.32738 | −0.0516681 | ||||||||
\(661\) | 25.4178 | 0.988637 | 0.494319 | − | 0.869281i | \(-0.335418\pi\) | ||||
0.494319 | + | 0.869281i | \(0.335418\pi\) | |||||||
\(662\) | 12.2636 | 0.476639 | ||||||||
\(663\) | 1.88925 | 0.0733724 | ||||||||
\(664\) | −3.16799 | −0.122942 | ||||||||
\(665\) | −24.2888 | −0.941877 | ||||||||
\(666\) | −15.7171 | −0.609025 | ||||||||
\(667\) | −38.3330 | −1.48426 | ||||||||
\(668\) | −18.0954 | −0.700133 | ||||||||
\(669\) | −0.452553 | −0.0174967 | ||||||||
\(670\) | 14.9291 | 0.576762 | ||||||||
\(671\) | −23.8447 | −0.920515 | ||||||||
\(672\) | −2.21901 | −0.0856003 | ||||||||
\(673\) | −34.1269 | −1.31549 | −0.657747 | − | 0.753239i | \(-0.728490\pi\) | ||||
−0.657747 | + | 0.753239i | \(0.728490\pi\) | |||||||
\(674\) | 1.44495 | 0.0556574 | ||||||||
\(675\) | −8.25530 | −0.317747 | ||||||||
\(676\) | −12.1438 | −0.467069 | ||||||||
\(677\) | −31.1955 | −1.19894 | −0.599471 | − | 0.800397i | \(-0.704622\pi\) | ||||
−0.599471 | + | 0.800397i | \(0.704622\pi\) | |||||||
\(678\) | −3.69291 | −0.141825 | ||||||||
\(679\) | −16.0784 | −0.617032 | ||||||||
\(680\) | −6.15359 | −0.235979 | ||||||||
\(681\) | 7.99811 | 0.306488 | ||||||||
\(682\) | −0.357678 | −0.0136962 | ||||||||
\(683\) | −39.4692 | −1.51025 | −0.755124 | − | 0.655582i | \(-0.772423\pi\) | ||||
−0.755124 | + | 0.655582i | \(0.772423\pi\) | |||||||
\(684\) | 10.1676 | 0.388767 | ||||||||
\(685\) | −1.45719 | −0.0556763 | ||||||||
\(686\) | 52.4231 | 2.00152 | ||||||||
\(687\) | −0.438620 | −0.0167344 | ||||||||
\(688\) | −1.17630 | −0.0448459 | ||||||||
\(689\) | 3.86190 | 0.147127 | ||||||||
\(690\) | −4.58082 | −0.174389 | ||||||||
\(691\) | −10.4221 | −0.396477 | −0.198239 | − | 0.980154i | \(-0.563522\pi\) | ||||
−0.198239 | + | 0.980154i | \(0.563522\pi\) | |||||||
\(692\) | −2.17952 | −0.0828528 | ||||||||
\(693\) | −30.5059 | −1.15882 | ||||||||
\(694\) | 3.24257 | 0.123086 | ||||||||
\(695\) | −21.4426 | −0.813365 | ||||||||
\(696\) | 2.26205 | 0.0857426 | ||||||||
\(697\) | −39.5585 | −1.49839 | ||||||||
\(698\) | −24.2741 | −0.918789 | ||||||||
\(699\) | −3.26707 | −0.123572 | ||||||||
\(700\) | −15.7639 | −0.595821 | ||||||||
\(701\) | 0.766152 | 0.0289372 | 0.0144686 | − | 0.999895i | \(-0.495394\pi\) | ||||
0.0144686 | + | 0.999895i | \(0.495394\pi\) | |||||||
\(702\) | 2.40217 | 0.0906642 | ||||||||
\(703\) | −20.3886 | −0.768971 | ||||||||
\(704\) | 2.19805 | 0.0828421 | ||||||||
\(705\) | 5.25919 | 0.198072 | ||||||||
\(706\) | 22.5168 | 0.847431 | ||||||||
\(707\) | −29.7297 | −1.11810 | ||||||||
\(708\) | 3.47804 | 0.130713 | ||||||||
\(709\) | −16.5164 | −0.620288 | −0.310144 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310144 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(710\) | −15.7797 | −0.592201 | ||||||||
\(711\) | 13.2572 | 0.497183 | ||||||||
\(712\) | −8.78993 | −0.329417 | ||||||||
\(713\) | −1.23436 | −0.0462270 | ||||||||
\(714\) | 10.1215 | 0.378788 | ||||||||
\(715\) | 2.74391 | 0.102617 | ||||||||
\(716\) | −15.7330 | −0.587969 | ||||||||
\(717\) | −10.3103 | −0.385046 | ||||||||
\(718\) | −3.03152 | −0.113135 | ||||||||
\(719\) | −7.50127 | −0.279750 | −0.139875 | − | 0.990169i | \(-0.544670\pi\) | ||||
−0.139875 | + | 0.990169i | \(0.544670\pi\) | |||||||
\(720\) | −3.77698 | −0.140760 | ||||||||
\(721\) | 42.6892 | 1.58983 | ||||||||
\(722\) | −5.81038 | −0.216240 | ||||||||
\(723\) | 7.09810 | 0.263981 | ||||||||
\(724\) | 10.4414 | 0.388052 | ||||||||
\(725\) | 16.0696 | 0.596811 | ||||||||
\(726\) | 2.76121 | 0.102478 | ||||||||
\(727\) | −12.6957 | −0.470858 | −0.235429 | − | 0.971892i | \(-0.575650\pi\) | ||||
−0.235429 | + | 0.971892i | \(0.575650\pi\) | |||||||
\(728\) | 4.58707 | 0.170008 | ||||||||
\(729\) | −16.7743 | −0.621270 | ||||||||
\(730\) | 12.4293 | 0.460029 | ||||||||
\(731\) | 5.36540 | 0.198447 | ||||||||
\(732\) | 4.85589 | 0.179479 | ||||||||
\(733\) | 8.89614 | 0.328586 | 0.164293 | − | 0.986412i | \(-0.447466\pi\) | ||||
0.164293 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(734\) | −13.9669 | −0.515528 | ||||||||
\(735\) | −10.6133 | −0.391477 | ||||||||
\(736\) | 7.58553 | 0.279606 | ||||||||
\(737\) | 24.3236 | 0.895972 | ||||||||
\(738\) | −24.2804 | −0.893773 | ||||||||
\(739\) | 48.6678 | 1.79027 | 0.895137 | − | 0.445792i | \(-0.147078\pi\) | ||||
0.895137 | + | 0.445792i | \(0.147078\pi\) | |||||||
\(740\) | 7.57382 | 0.278419 | ||||||||
\(741\) | 1.50425 | 0.0552600 | ||||||||
\(742\) | 20.6898 | 0.759547 | ||||||||
\(743\) | 3.83348 | 0.140637 | 0.0703184 | − | 0.997525i | \(-0.477598\pi\) | ||||
0.0703184 | + | 0.997525i | \(0.477598\pi\) | |||||||
\(744\) | 0.0728398 | 0.00267044 | ||||||||
\(745\) | −25.5667 | −0.936691 | ||||||||
\(746\) | 22.7430 | 0.832681 | ||||||||
\(747\) | 8.86921 | 0.324507 | ||||||||
\(748\) | −10.0259 | −0.366583 | ||||||||
\(749\) | −85.2854 | −3.11626 | ||||||||
\(750\) | 4.93978 | 0.180375 | ||||||||
\(751\) | 6.09920 | 0.222563 | 0.111281 | − | 0.993789i | \(-0.464504\pi\) | ||||
0.111281 | + | 0.993789i | \(0.464504\pi\) | |||||||
\(752\) | −8.70886 | −0.317579 | ||||||||
\(753\) | 3.57036 | 0.130111 | ||||||||
\(754\) | −4.67603 | −0.170291 | ||||||||
\(755\) | −7.63131 | −0.277732 | ||||||||
\(756\) | 12.8695 | 0.468058 | ||||||||
\(757\) | 32.1732 | 1.16936 | 0.584678 | − | 0.811266i | \(-0.301221\pi\) | ||||
0.584678 | + | 0.811266i | \(0.301221\pi\) | |||||||
\(758\) | 23.3257 | 0.847229 | ||||||||
\(759\) | −7.46341 | −0.270905 | ||||||||
\(760\) | −4.89958 | −0.177727 | ||||||||
\(761\) | 2.33017 | 0.0844686 | 0.0422343 | − | 0.999108i | \(-0.486552\pi\) | ||||
0.0422343 | + | 0.999108i | \(0.486552\pi\) | |||||||
\(762\) | 8.03079 | 0.290925 | ||||||||
\(763\) | 1.43665 | 0.0520103 | ||||||||
\(764\) | 11.1156 | 0.402150 | ||||||||
\(765\) | 17.2278 | 0.622872 | ||||||||
\(766\) | −15.7808 | −0.570182 | ||||||||
\(767\) | −7.18970 | −0.259605 | ||||||||
\(768\) | −0.447625 | −0.0161523 | ||||||||
\(769\) | 14.2764 | 0.514819 | 0.257409 | − | 0.966302i | \(-0.417131\pi\) | ||||
0.257409 | + | 0.966302i | \(0.417131\pi\) | |||||||
\(770\) | 14.7003 | 0.529762 | ||||||||
\(771\) | −2.18035 | −0.0785234 | ||||||||
\(772\) | 3.89523 | 0.140193 | ||||||||
\(773\) | 12.3992 | 0.445969 | 0.222984 | − | 0.974822i | \(-0.428420\pi\) | ||||
0.222984 | + | 0.974822i | \(0.428420\pi\) | |||||||
\(774\) | 3.29320 | 0.118372 | ||||||||
\(775\) | 0.517456 | 0.0185876 | ||||||||
\(776\) | −3.24337 | −0.116430 | ||||||||
\(777\) | −12.4575 | −0.446911 | ||||||||
\(778\) | −19.9086 | −0.713758 | ||||||||
\(779\) | −31.4971 | −1.12850 | ||||||||
\(780\) | −0.558788 | −0.0200078 | ||||||||
\(781\) | −25.7094 | −0.919955 | ||||||||
\(782\) | −34.5996 | −1.23728 | ||||||||
\(783\) | −13.1190 | −0.468836 | ||||||||
\(784\) | 17.5749 | 0.627675 | ||||||||
\(785\) | 27.7930 | 0.991975 | ||||||||
\(786\) | −6.33660 | −0.226019 | ||||||||
\(787\) | −44.3249 | −1.58001 | −0.790006 | − | 0.613099i | \(-0.789923\pi\) | ||||
−0.790006 | + | 0.613099i | \(0.789923\pi\) | |||||||
\(788\) | 1.50902 | 0.0537565 | ||||||||
\(789\) | −14.1030 | −0.502080 | ||||||||
\(790\) | −6.38841 | −0.227290 | ||||||||
\(791\) | 40.8979 | 1.45416 | ||||||||
\(792\) | −6.15373 | −0.218663 | ||||||||
\(793\) | −10.0379 | −0.356458 | ||||||||
\(794\) | −1.00000 | −0.0354887 | ||||||||
\(795\) | −2.52039 | −0.0893890 | ||||||||
\(796\) | 11.9161 | 0.422356 | ||||||||
\(797\) | 2.94940 | 0.104473 | 0.0522365 | − | 0.998635i | \(-0.483365\pi\) | ||||
0.0522365 | + | 0.998635i | \(0.483365\pi\) | |||||||
\(798\) | 8.05891 | 0.285282 | ||||||||
\(799\) | 39.7234 | 1.40531 | ||||||||
\(800\) | −3.17994 | −0.112428 | ||||||||
\(801\) | 24.6086 | 0.869501 | ||||||||
\(802\) | 12.0474 | 0.425408 | ||||||||
\(803\) | 20.2507 | 0.714633 | ||||||||
\(804\) | −4.95342 | −0.174694 | ||||||||
\(805\) | 50.7312 | 1.78804 | ||||||||
\(806\) | −0.150572 | −0.00530368 | ||||||||
\(807\) | −2.55367 | −0.0898933 | ||||||||
\(808\) | −5.99714 | −0.210979 | ||||||||
\(809\) | 3.40440 | 0.119692 | 0.0598461 | − | 0.998208i | \(-0.480939\pi\) | ||||
0.0598461 | + | 0.998208i | \(0.480939\pi\) | |||||||
\(810\) | 9.76319 | 0.343044 | ||||||||
\(811\) | −51.6006 | −1.81194 | −0.905970 | − | 0.423341i | \(-0.860857\pi\) | ||||
−0.905970 | + | 0.423341i | \(0.860857\pi\) | |||||||
\(812\) | −25.0515 | −0.879134 | ||||||||
\(813\) | −2.79030 | −0.0978601 | ||||||||
\(814\) | 12.3398 | 0.432511 | ||||||||
\(815\) | 30.2321 | 1.05898 | ||||||||
\(816\) | 2.04174 | 0.0714751 | ||||||||
\(817\) | 4.27202 | 0.149459 | ||||||||
\(818\) | 35.2892 | 1.23386 | ||||||||
\(819\) | −12.8421 | −0.448740 | ||||||||
\(820\) | 11.7003 | 0.408593 | ||||||||
\(821\) | −0.954654 | −0.0333177 | −0.0166588 | − | 0.999861i | \(-0.505303\pi\) | ||||
−0.0166588 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(822\) | 0.483489 | 0.0168636 | ||||||||
\(823\) | 51.8997 | 1.80911 | 0.904556 | − | 0.426355i | \(-0.140203\pi\) | ||||
0.904556 | + | 0.426355i | \(0.140203\pi\) | |||||||
\(824\) | 8.61138 | 0.299991 | ||||||||
\(825\) | 3.12874 | 0.108929 | ||||||||
\(826\) | −38.5183 | −1.34022 | ||||||||
\(827\) | 26.4333 | 0.919175 | 0.459588 | − | 0.888132i | \(-0.347997\pi\) | ||||
0.459588 | + | 0.888132i | \(0.347997\pi\) | |||||||
\(828\) | −21.2367 | −0.738026 | ||||||||
\(829\) | 21.5046 | 0.746887 | 0.373444 | − | 0.927653i | \(-0.378177\pi\) | ||||
0.373444 | + | 0.927653i | \(0.378177\pi\) | |||||||
\(830\) | −4.27393 | −0.148350 | ||||||||
\(831\) | −5.52138 | −0.191534 | ||||||||
\(832\) | 0.925316 | 0.0320795 | ||||||||
\(833\) | −80.1638 | −2.77751 | ||||||||
\(834\) | 7.11458 | 0.246358 | ||||||||
\(835\) | −24.4125 | −0.844828 | ||||||||
\(836\) | −7.98277 | −0.276090 | ||||||||
\(837\) | −0.422444 | −0.0146018 | ||||||||
\(838\) | −4.51542 | −0.155983 | ||||||||
\(839\) | −18.5077 | −0.638958 | −0.319479 | − | 0.947593i | \(-0.603508\pi\) | ||||
−0.319479 | + | 0.947593i | \(0.603508\pi\) | |||||||
\(840\) | −2.99366 | −0.103291 | ||||||||
\(841\) | −3.46273 | −0.119404 | ||||||||
\(842\) | 18.3797 | 0.633405 | ||||||||
\(843\) | −10.6862 | −0.368051 | ||||||||
\(844\) | −0.999252 | −0.0343957 | ||||||||
\(845\) | −16.3832 | −0.563598 | ||||||||
\(846\) | 24.3816 | 0.838257 | ||||||||
\(847\) | −30.5796 | −1.05073 | ||||||||
\(848\) | 4.17360 | 0.143322 | ||||||||
\(849\) | 12.9222 | 0.443488 | ||||||||
\(850\) | 14.5045 | 0.497502 | ||||||||
\(851\) | 42.5851 | 1.45980 | ||||||||
\(852\) | 5.23563 | 0.179370 | ||||||||
\(853\) | −24.8092 | −0.849451 | −0.424725 | − | 0.905322i | \(-0.639629\pi\) | ||||
−0.424725 | + | 0.905322i | \(0.639629\pi\) | |||||||
\(854\) | −53.7775 | −1.84023 | ||||||||
\(855\) | 13.7170 | 0.469113 | ||||||||
\(856\) | −17.2040 | −0.588020 | ||||||||
\(857\) | 46.1840 | 1.57762 | 0.788808 | − | 0.614639i | \(-0.210698\pi\) | ||||
0.788808 | + | 0.614639i | \(0.210698\pi\) | |||||||
\(858\) | −0.910419 | −0.0310812 | ||||||||
\(859\) | −9.54974 | −0.325833 | −0.162916 | − | 0.986640i | \(-0.552090\pi\) | ||||
−0.162916 | + | 0.986640i | \(0.552090\pi\) | |||||||
\(860\) | −1.58694 | −0.0541141 | ||||||||
\(861\) | −19.2448 | −0.655863 | ||||||||
\(862\) | −7.46835 | −0.254373 | ||||||||
\(863\) | −24.1830 | −0.823200 | −0.411600 | − | 0.911365i | \(-0.635030\pi\) | ||||
−0.411600 | + | 0.911365i | \(0.635030\pi\) | |||||||
\(864\) | 2.59606 | 0.0883197 | ||||||||
\(865\) | −2.94038 | −0.0999760 | ||||||||
\(866\) | 4.02751 | 0.136860 | ||||||||
\(867\) | −1.70328 | −0.0578465 | ||||||||
\(868\) | −0.806679 | −0.0273805 | ||||||||
\(869\) | −10.4085 | −0.353083 | ||||||||
\(870\) | 3.05172 | 0.103463 | ||||||||
\(871\) | 10.2395 | 0.346954 | ||||||||
\(872\) | 0.289805 | 0.00981403 | ||||||||
\(873\) | 9.08024 | 0.307320 | ||||||||
\(874\) | −27.5488 | −0.931851 | ||||||||
\(875\) | −54.7065 | −1.84942 | ||||||||
\(876\) | −4.12399 | −0.139337 | ||||||||
\(877\) | 15.4877 | 0.522981 | 0.261491 | − | 0.965206i | \(-0.415786\pi\) | ||||
0.261491 | + | 0.965206i | \(0.415786\pi\) | |||||||
\(878\) | −8.00670 | −0.270213 | ||||||||
\(879\) | 10.2621 | 0.346131 | ||||||||
\(880\) | 2.96538 | 0.0999630 | ||||||||
\(881\) | 19.1469 | 0.645076 | 0.322538 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322538 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(882\) | −49.2033 | −1.65676 | ||||||||
\(883\) | 0.0844106 | 0.00284064 | 0.00142032 | − | 0.999999i | \(-0.499548\pi\) | ||||
0.00142032 | + | 0.999999i | \(0.499548\pi\) | |||||||
\(884\) | −4.22061 | −0.141955 | ||||||||
\(885\) | 4.69222 | 0.157727 | ||||||||
\(886\) | −17.6097 | −0.591611 | ||||||||
\(887\) | 43.5197 | 1.46125 | 0.730624 | − | 0.682780i | \(-0.239229\pi\) | ||||
0.730624 | + | 0.682780i | \(0.239229\pi\) | |||||||
\(888\) | −2.51296 | −0.0843294 | ||||||||
\(889\) | −88.9386 | −2.98290 | ||||||||
\(890\) | −11.8585 | −0.397497 | ||||||||
\(891\) | 15.9069 | 0.532902 | ||||||||
\(892\) | 1.01101 | 0.0338511 | ||||||||
\(893\) | 31.6284 | 1.05840 | ||||||||
\(894\) | 8.48292 | 0.283711 | ||||||||
\(895\) | −21.2253 | −0.709485 | ||||||||
\(896\) | 4.95731 | 0.165612 | ||||||||
\(897\) | −3.14188 | −0.104904 | ||||||||
\(898\) | −7.33333 | −0.244716 | ||||||||
\(899\) | 0.822322 | 0.0274260 | ||||||||
\(900\) | 8.90265 | 0.296755 | ||||||||
\(901\) | −19.0369 | −0.634211 | ||||||||
\(902\) | 19.0630 | 0.634729 | ||||||||
\(903\) | 2.61022 | 0.0868626 | ||||||||
\(904\) | 8.25002 | 0.274392 | ||||||||
\(905\) | 14.0865 | 0.468250 | ||||||||
\(906\) | 2.53204 | 0.0841213 | ||||||||
\(907\) | −11.2618 | −0.373943 | −0.186971 | − | 0.982365i | \(-0.559867\pi\) | ||||
−0.186971 | + | 0.982365i | \(0.559867\pi\) | |||||||
\(908\) | −17.8679 | −0.592967 | ||||||||
\(909\) | 16.7898 | 0.556882 | ||||||||
\(910\) | 6.18841 | 0.205144 | ||||||||
\(911\) | −43.5635 | −1.44332 | −0.721661 | − | 0.692247i | \(-0.756621\pi\) | ||||
−0.721661 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(912\) | 1.62566 | 0.0538310 | ||||||||
\(913\) | −6.96340 | −0.230455 | ||||||||
\(914\) | 35.9698 | 1.18978 | ||||||||
\(915\) | 6.55107 | 0.216572 | ||||||||
\(916\) | 0.979883 | 0.0323763 | ||||||||
\(917\) | 70.1759 | 2.31741 | ||||||||
\(918\) | −11.8413 | −0.390822 | ||||||||
\(919\) | −26.5306 | −0.875162 | −0.437581 | − | 0.899179i | \(-0.644165\pi\) | ||||
−0.437581 | + | 0.899179i | \(0.644165\pi\) | |||||||
\(920\) | 10.2336 | 0.337392 | ||||||||
\(921\) | −10.6599 | −0.351254 | ||||||||
\(922\) | −16.5204 | −0.544072 | ||||||||
\(923\) | −10.8229 | −0.356241 | ||||||||
\(924\) | −4.87750 | −0.160458 | ||||||||
\(925\) | −17.8521 | −0.586975 | ||||||||
\(926\) | 23.9280 | 0.786324 | ||||||||
\(927\) | −24.1087 | −0.791833 | ||||||||
\(928\) | −5.05344 | −0.165887 | ||||||||
\(929\) | −23.4384 | −0.768989 | −0.384494 | − | 0.923127i | \(-0.625624\pi\) | ||||
−0.384494 | + | 0.923127i | \(0.625624\pi\) | |||||||
\(930\) | 0.0982680 | 0.00322233 | ||||||||
\(931\) | −63.8277 | −2.09187 | ||||||||
\(932\) | 7.29869 | 0.239076 | ||||||||
\(933\) | 4.82631 | 0.158006 | ||||||||
\(934\) | −13.9916 | −0.457819 | ||||||||
\(935\) | −13.5259 | −0.442344 | ||||||||
\(936\) | −2.59054 | −0.0846746 | ||||||||
\(937\) | −41.7500 | −1.36391 | −0.681957 | − | 0.731392i | \(-0.738871\pi\) | ||||
−0.681957 | + | 0.731392i | \(0.738871\pi\) | |||||||
\(938\) | 54.8576 | 1.79116 | ||||||||
\(939\) | −8.76976 | −0.286190 | ||||||||
\(940\) | −11.7491 | −0.383213 | ||||||||
\(941\) | 28.8674 | 0.941051 | 0.470525 | − | 0.882386i | \(-0.344064\pi\) | ||||
0.470525 | + | 0.882386i | \(0.344064\pi\) | |||||||
\(942\) | −9.22161 | −0.300456 | ||||||||
\(943\) | 65.7871 | 2.14232 | ||||||||
\(944\) | −7.77000 | −0.252892 | ||||||||
\(945\) | 17.3622 | 0.564791 | ||||||||
\(946\) | −2.58556 | −0.0840637 | ||||||||
\(947\) | 18.6445 | 0.605865 | 0.302933 | − | 0.953012i | \(-0.402034\pi\) | ||||
0.302933 | + | 0.953012i | \(0.402034\pi\) | |||||||
\(948\) | 2.11965 | 0.0688430 | ||||||||
\(949\) | 8.52498 | 0.276733 | ||||||||
\(950\) | 11.5487 | 0.374691 | ||||||||
\(951\) | 10.1123 | 0.327913 | ||||||||
\(952\) | −22.6116 | −0.732846 | ||||||||
\(953\) | −47.1351 | −1.52685 | −0.763427 | − | 0.645894i | \(-0.776485\pi\) | ||||
−0.763427 | + | 0.645894i | \(0.776485\pi\) | |||||||
\(954\) | −11.6845 | −0.378301 | ||||||||
\(955\) | 14.9961 | 0.485262 | ||||||||
\(956\) | 23.0334 | 0.744953 | ||||||||
\(957\) | 4.97209 | 0.160725 | ||||||||
\(958\) | 16.6626 | 0.538344 | ||||||||
\(959\) | −5.35449 | −0.172906 | ||||||||
\(960\) | −0.603889 | −0.0194904 | ||||||||
\(961\) | −30.9735 | −0.999146 | ||||||||
\(962\) | 5.19471 | 0.167484 | ||||||||
\(963\) | 48.1648 | 1.55209 | ||||||||
\(964\) | −15.8573 | −0.510728 | ||||||||
\(965\) | 5.25505 | 0.169166 | ||||||||
\(966\) | −16.8324 | −0.541574 | ||||||||
\(967\) | 19.5434 | 0.628475 | 0.314237 | − | 0.949344i | \(-0.398251\pi\) | ||||
0.314237 | + | 0.949344i | \(0.398251\pi\) | |||||||
\(968\) | −6.16858 | −0.198266 | ||||||||
\(969\) | −7.41508 | −0.238207 | ||||||||
\(970\) | −4.37562 | −0.140493 | ||||||||
\(971\) | −2.05287 | −0.0658796 | −0.0329398 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329398 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(972\) | −11.0276 | −0.353709 | ||||||||
\(973\) | −78.7918 | −2.52595 | ||||||||
\(974\) | 22.1080 | 0.708385 | ||||||||
\(975\) | 1.31711 | 0.0421813 | ||||||||
\(976\) | −10.8481 | −0.347240 | ||||||||
\(977\) | 49.2010 | 1.57408 | 0.787040 | − | 0.616902i | \(-0.211613\pi\) | ||||
0.787040 | + | 0.616902i | \(0.211613\pi\) | |||||||
\(978\) | −10.0309 | −0.320752 | ||||||||
\(979\) | −19.3207 | −0.617492 | ||||||||
\(980\) | 23.7103 | 0.757396 | ||||||||
\(981\) | −0.811347 | −0.0259043 | ||||||||
\(982\) | 41.9288 | 1.33800 | ||||||||
\(983\) | 5.60019 | 0.178618 | 0.0893091 | − | 0.996004i | \(-0.471534\pi\) | ||||
0.0893091 | + | 0.996004i | \(0.471534\pi\) | |||||||
\(984\) | −3.88212 | −0.123757 | ||||||||
\(985\) | 2.03581 | 0.0648663 | ||||||||
\(986\) | 23.0501 | 0.734065 | ||||||||
\(987\) | 19.3251 | 0.615124 | ||||||||
\(988\) | −3.36052 | −0.106912 | ||||||||
\(989\) | −8.92284 | −0.283730 | ||||||||
\(990\) | −8.30198 | −0.263854 | ||||||||
\(991\) | 13.6582 | 0.433867 | 0.216934 | − | 0.976186i | \(-0.430394\pi\) | ||||
0.216934 | + | 0.976186i | \(0.430394\pi\) | |||||||
\(992\) | −0.162725 | −0.00516653 | ||||||||
\(993\) | −5.48950 | −0.174204 | ||||||||
\(994\) | −57.9830 | −1.83911 | ||||||||
\(995\) | 16.0760 | 0.509644 | ||||||||
\(996\) | 1.41807 | 0.0449333 | ||||||||
\(997\) | 55.2248 | 1.74899 | 0.874493 | − | 0.485037i | \(-0.161194\pi\) | ||||
0.874493 | + | 0.485037i | \(0.161194\pi\) | |||||||
\(998\) | 27.7340 | 0.877905 | ||||||||
\(999\) | 14.5742 | 0.461109 |
(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 | 794.2.a.h.1.7 | ✓ | 14 | |
3.2 | odd | 2 | 7146.2.a.be.1.7 | 14 | |||
4.3 | odd | 2 | 6352.2.a.t.1.8 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
794.2.a.h.1.7 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6352.2.a.t.1.8 | 14 | 4.3 | odd | 2 | |||
7146.2.a.be.1.7 | 14 | 3.2 | odd | 2 |