Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.42 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36215 | 1.67029 | 0.835145 | − | 0.550029i | \(-0.185383\pi\) | ||||
0.835145 | + | 0.550029i | \(0.185383\pi\) | |||||||
\(3\) | −2.05253 | −1.18503 | −0.592515 | − | 0.805559i | \(-0.701865\pi\) | ||||
−0.592515 | + | 0.805559i | \(0.701865\pi\) | |||||||
\(4\) | 3.57974 | 1.78987 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.84838 | −1.97934 | ||||||||
\(7\) | −3.07728 | −1.16310 | −0.581551 | − | 0.813510i | \(-0.697554\pi\) | ||||
−0.581551 | + | 0.813510i | \(0.697554\pi\) | |||||||
\(8\) | 3.73158 | 1.31931 | ||||||||
\(9\) | 1.21289 | 0.404296 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.942447 | 0.284159 | 0.142079 | − | 0.989855i | \(-0.454621\pi\) | ||||
0.142079 | + | 0.989855i | \(0.454621\pi\) | |||||||
\(12\) | −7.34753 | −2.12105 | ||||||||
\(13\) | 1.99403 | 0.553046 | 0.276523 | − | 0.961007i | \(-0.410818\pi\) | ||||
0.276523 | + | 0.961007i | \(0.410818\pi\) | |||||||
\(14\) | −7.26899 | −1.94272 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.65507 | 0.413766 | ||||||||
\(17\) | 3.11539 | 0.755592 | 0.377796 | − | 0.925889i | \(-0.376682\pi\) | ||||
0.377796 | + | 0.925889i | \(0.376682\pi\) | |||||||
\(18\) | 2.86502 | 0.675291 | ||||||||
\(19\) | −6.33222 | −1.45271 | −0.726355 | − | 0.687320i | \(-0.758787\pi\) | ||||
−0.726355 | + | 0.687320i | \(0.758787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.31621 | 1.37831 | ||||||||
\(22\) | 2.22620 | 0.474627 | ||||||||
\(23\) | 7.91084 | 1.64952 | 0.824762 | − | 0.565479i | \(-0.191309\pi\) | ||||
0.824762 | + | 0.565479i | \(0.191309\pi\) | |||||||
\(24\) | −7.65919 | −1.56343 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.71020 | 0.923747 | ||||||||
\(27\) | 3.66811 | 0.705927 | ||||||||
\(28\) | −11.0159 | −2.08180 | ||||||||
\(29\) | −1.63432 | −0.303485 | −0.151742 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151742 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.96040 | 1.25012 | 0.625062 | − | 0.780575i | \(-0.285074\pi\) | ||||
0.625062 | + | 0.780575i | \(0.285074\pi\) | |||||||
\(32\) | −3.55366 | −0.628203 | ||||||||
\(33\) | −1.93440 | −0.336736 | ||||||||
\(34\) | 7.35900 | 1.26206 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.34182 | 0.723637 | ||||||||
\(37\) | −0.864280 | −0.142087 | −0.0710434 | − | 0.997473i | \(-0.522633\pi\) | ||||
−0.0710434 | + | 0.997473i | \(0.522633\pi\) | |||||||
\(38\) | −14.9576 | −2.42645 | ||||||||
\(39\) | −4.09282 | −0.655375 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70732 | 0.266639 | 0.133319 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133319 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(42\) | 14.9198 | 2.30218 | ||||||||
\(43\) | −10.2266 | −1.55953 | −0.779767 | − | 0.626069i | \(-0.784663\pi\) | ||||
−0.779767 | + | 0.626069i | \(0.784663\pi\) | |||||||
\(44\) | 3.37372 | 0.508607 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.6866 | 2.75519 | ||||||||
\(47\) | −6.49786 | −0.947811 | −0.473905 | − | 0.880576i | \(-0.657156\pi\) | ||||
−0.473905 | + | 0.880576i | \(0.657156\pi\) | |||||||
\(48\) | −3.39707 | −0.490326 | ||||||||
\(49\) | 2.46965 | 0.352807 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.39443 | −0.895399 | ||||||||
\(52\) | 7.13813 | 0.989880 | ||||||||
\(53\) | 2.20905 | 0.303436 | 0.151718 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151718 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(54\) | 8.66461 | 1.17910 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.4831 | −1.53450 | ||||||||
\(57\) | 12.9971 | 1.72150 | ||||||||
\(58\) | −3.86050 | −0.506908 | ||||||||
\(59\) | −7.69694 | −1.00206 | −0.501028 | − | 0.865431i | \(-0.667045\pi\) | ||||
−0.501028 | + | 0.865431i | \(0.667045\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.70322 | −0.474149 | −0.237075 | − | 0.971491i | \(-0.576189\pi\) | ||||
−0.237075 | + | 0.971491i | \(0.576189\pi\) | |||||||
\(62\) | 16.4415 | 2.08807 | ||||||||
\(63\) | −3.73239 | −0.470237 | ||||||||
\(64\) | −11.7044 | −1.46305 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.56935 | −0.562448 | ||||||||
\(67\) | −7.96470 | −0.973043 | −0.486521 | − | 0.873669i | \(-0.661734\pi\) | ||||
−0.486521 | + | 0.873669i | \(0.661734\pi\) | |||||||
\(68\) | 11.1523 | 1.35241 | ||||||||
\(69\) | −16.2373 | −1.95474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.02031 | −0.833157 | −0.416579 | − | 0.909100i | \(-0.636771\pi\) | ||||
−0.416579 | + | 0.909100i | \(0.636771\pi\) | |||||||
\(72\) | 4.52599 | 0.533393 | ||||||||
\(73\) | −6.13583 | −0.718144 | −0.359072 | − | 0.933310i | \(-0.616907\pi\) | ||||
−0.359072 | + | 0.933310i | \(0.616907\pi\) | |||||||
\(74\) | −2.04156 | −0.237326 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.6677 | −2.60016 | ||||||||
\(77\) | −2.90017 | −0.330505 | ||||||||
\(78\) | −9.66784 | −1.09467 | ||||||||
\(79\) | −14.0583 | −1.58168 | −0.790842 | − | 0.612021i | \(-0.790357\pi\) | ||||
−0.790842 | + | 0.612021i | \(0.790357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1676 | −1.24084 | ||||||||
\(82\) | 4.03294 | 0.445364 | ||||||||
\(83\) | 3.98789 | 0.437728 | 0.218864 | − | 0.975755i | \(-0.429765\pi\) | ||||
0.218864 | + | 0.975755i | \(0.429765\pi\) | |||||||
\(84\) | 22.6104 | 2.46700 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −24.1566 | −2.60488 | ||||||||
\(87\) | 3.35449 | 0.359639 | ||||||||
\(88\) | 3.51682 | 0.374894 | ||||||||
\(89\) | −11.7782 | −1.24849 | −0.624245 | − | 0.781229i | \(-0.714593\pi\) | ||||
−0.624245 | + | 0.781229i | \(0.714593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.13620 | −0.643249 | ||||||||
\(92\) | 28.3188 | 2.95244 | ||||||||
\(93\) | −14.2864 | −1.48144 | ||||||||
\(94\) | −15.3489 | −1.58312 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.29399 | 0.744440 | ||||||||
\(97\) | −17.6694 | −1.79405 | −0.897026 | − | 0.441978i | \(-0.854277\pi\) | ||||
−0.897026 | + | 0.441978i | \(0.854277\pi\) | |||||||
\(98\) | 5.83367 | 0.589290 | ||||||||
\(99\) | 1.14308 | 0.114884 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.05634 | 0.901140 | 0.450570 | − | 0.892741i | \(-0.351221\pi\) | ||||
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(102\) | −15.1046 | −1.49558 | ||||||||
\(103\) | 2.20110 | 0.216881 | 0.108440 | − | 0.994103i | \(-0.465414\pi\) | ||||
0.108440 | + | 0.994103i | \(0.465414\pi\) | |||||||
\(104\) | 7.44090 | 0.729641 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.21809 | 0.506826 | ||||||||
\(107\) | −7.08595 | −0.685024 | −0.342512 | − | 0.939513i | \(-0.611278\pi\) | ||||
−0.342512 | + | 0.939513i | \(0.611278\pi\) | |||||||
\(108\) | 13.1309 | 1.26352 | ||||||||
\(109\) | −7.57661 | −0.725708 | −0.362854 | − | 0.931846i | \(-0.618198\pi\) | ||||
−0.362854 | + | 0.931846i | \(0.618198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.77396 | 0.168377 | ||||||||
\(112\) | −5.09310 | −0.481253 | ||||||||
\(113\) | 17.7967 | 1.67418 | 0.837088 | − | 0.547069i | \(-0.184256\pi\) | ||||
0.837088 | + | 0.547069i | \(0.184256\pi\) | |||||||
\(114\) | 30.7010 | 2.87541 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.85043 | −0.543199 | ||||||||
\(117\) | 2.41854 | 0.223594 | ||||||||
\(118\) | −18.1813 | −1.67373 | ||||||||
\(119\) | −9.58691 | −0.878831 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1118 | −0.919254 | ||||||||
\(122\) | −8.74756 | −0.791967 | ||||||||
\(123\) | −3.50433 | −0.315975 | ||||||||
\(124\) | 24.9164 | 2.23756 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.81646 | −0.785433 | ||||||||
\(127\) | 19.4716 | 1.72782 | 0.863912 | − | 0.503642i | \(-0.168007\pi\) | ||||
0.863912 | + | 0.503642i | \(0.168007\pi\) | |||||||
\(128\) | −20.5402 | −1.81551 | ||||||||
\(129\) | 20.9903 | 1.84810 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.30848 | −0.725915 | −0.362958 | − | 0.931806i | \(-0.618233\pi\) | ||||
−0.362958 | + | 0.931806i | \(0.618233\pi\) | |||||||
\(132\) | −6.92466 | −0.602714 | ||||||||
\(133\) | 19.4860 | 1.68965 | ||||||||
\(134\) | −18.8138 | −1.62526 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.6253 | 0.996863 | ||||||||
\(137\) | −4.26661 | −0.364521 | −0.182261 | − | 0.983250i | \(-0.558341\pi\) | ||||
−0.182261 | + | 0.983250i | \(0.558341\pi\) | |||||||
\(138\) | −38.3548 | −3.26498 | ||||||||
\(139\) | −4.25699 | −0.361073 | −0.180537 | − | 0.983568i | \(-0.557783\pi\) | ||||
−0.180537 | + | 0.983568i | \(0.557783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3371 | 1.12318 | ||||||||
\(142\) | −16.5830 | −1.39162 | ||||||||
\(143\) | 1.87927 | 0.157153 | ||||||||
\(144\) | 2.00741 | 0.167284 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.4937 | −1.19951 | ||||||||
\(147\) | −5.06903 | −0.418086 | ||||||||
\(148\) | −3.09390 | −0.254317 | ||||||||
\(149\) | 6.80166 | 0.557214 | 0.278607 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278607 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.11661 | −0.335005 | −0.167503 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167503 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(152\) | −23.6292 | −1.91658 | ||||||||
\(153\) | 3.77861 | 0.305483 | ||||||||
\(154\) | −6.85064 | −0.552040 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.6512 | −1.17304 | ||||||||
\(157\) | 19.2876 | 1.53931 | 0.769657 | − | 0.638457i | \(-0.220427\pi\) | ||||
0.769657 | + | 0.638457i | \(0.220427\pi\) | |||||||
\(158\) | −33.2078 | −2.64187 | ||||||||
\(159\) | −4.53414 | −0.359580 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.3439 | −1.91857 | ||||||||
\(162\) | −26.3794 | −2.07256 | ||||||||
\(163\) | −1.77142 | −0.138749 | −0.0693743 | − | 0.997591i | \(-0.522100\pi\) | ||||
−0.0693743 | + | 0.997591i | \(0.522100\pi\) | |||||||
\(164\) | 6.11176 | 0.477249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.41999 | 0.731133 | ||||||||
\(167\) | 0.0398907 | 0.00308683 | 0.00154342 | − | 0.999999i | \(-0.499509\pi\) | ||||
0.00154342 | + | 0.999999i | \(0.499509\pi\) | |||||||
\(168\) | 23.5695 | 1.81842 | ||||||||
\(169\) | −9.02383 | −0.694141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.68027 | −0.587325 | ||||||||
\(172\) | −36.6084 | −2.79137 | ||||||||
\(173\) | 16.1574 | 1.22842 | 0.614210 | − | 0.789142i | \(-0.289475\pi\) | ||||
0.614210 | + | 0.789142i | \(0.289475\pi\) | |||||||
\(174\) | 7.92379 | 0.600701 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.55981 | 0.117575 | ||||||||
\(177\) | 15.7982 | 1.18747 | ||||||||
\(178\) | −27.8219 | −2.08534 | ||||||||
\(179\) | 0.727604 | 0.0543837 | 0.0271918 | − | 0.999630i | \(-0.491344\pi\) | ||||
0.0271918 | + | 0.999630i | \(0.491344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7237 | 1.02008 | 0.510039 | − | 0.860151i | \(-0.329631\pi\) | ||||
0.510039 | + | 0.860151i | \(0.329631\pi\) | |||||||
\(182\) | −14.4946 | −1.07441 | ||||||||
\(183\) | 7.60098 | 0.561881 | ||||||||
\(184\) | 29.5200 | 2.17624 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −33.7467 | −2.47443 | ||||||||
\(187\) | 2.93609 | 0.214708 | ||||||||
\(188\) | −23.2607 | −1.69646 | ||||||||
\(189\) | −11.2878 | −0.821066 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2809 | −0.888612 | −0.444306 | − | 0.895875i | \(-0.646550\pi\) | ||||
−0.444306 | + | 0.895875i | \(0.646550\pi\) | |||||||
\(192\) | 24.0236 | 1.73376 | ||||||||
\(193\) | −9.92702 | −0.714563 | −0.357281 | − | 0.933997i | \(-0.616296\pi\) | ||||
−0.357281 | + | 0.933997i | \(0.616296\pi\) | |||||||
\(194\) | −41.7376 | −2.99659 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.84070 | 0.631478 | ||||||||
\(197\) | 12.1160 | 0.863229 | 0.431614 | − | 0.902058i | \(-0.357944\pi\) | ||||
0.431614 | + | 0.902058i | \(0.357944\pi\) | |||||||
\(198\) | 2.70013 | 0.191890 | ||||||||
\(199\) | 13.7540 | 0.974995 | 0.487498 | − | 0.873124i | \(-0.337910\pi\) | ||||
0.487498 | + | 0.873124i | \(0.337910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.3478 | 1.15308 | ||||||||
\(202\) | 21.3924 | 1.50517 | ||||||||
\(203\) | 5.02925 | 0.352984 | ||||||||
\(204\) | −22.8904 | −1.60265 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.19932 | 0.362254 | ||||||||
\(207\) | 9.59496 | 0.666896 | ||||||||
\(208\) | 3.30026 | 0.228832 | ||||||||
\(209\) | −5.96778 | −0.412800 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0235 | −1.24079 | −0.620396 | − | 0.784289i | \(-0.713028\pi\) | ||||
−0.620396 | + | 0.784289i | \(0.713028\pi\) | |||||||
\(212\) | 7.90781 | 0.543111 | ||||||||
\(213\) | 14.4094 | 0.987316 | ||||||||
\(214\) | −16.7381 | −1.14419 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.6878 | 0.931339 | ||||||||
\(217\) | −21.4191 | −1.45402 | ||||||||
\(218\) | −17.8971 | −1.21214 | ||||||||
\(219\) | 12.5940 | 0.851022 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.21219 | 0.417877 | ||||||||
\(222\) | 4.19036 | 0.281239 | ||||||||
\(223\) | −27.9985 | −1.87492 | −0.937458 | − | 0.348098i | \(-0.886828\pi\) | ||||
−0.937458 | + | 0.348098i | \(0.886828\pi\) | |||||||
\(224\) | 10.9356 | 0.730665 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 42.0385 | 2.79636 | ||||||||
\(227\) | 12.7878 | 0.848755 | 0.424378 | − | 0.905485i | \(-0.360493\pi\) | ||||
0.424378 | + | 0.905485i | \(0.360493\pi\) | |||||||
\(228\) | 46.5262 | 3.08127 | ||||||||
\(229\) | −15.9201 | −1.05203 | −0.526015 | − | 0.850475i | \(-0.676314\pi\) | ||||
−0.526015 | + | 0.850475i | \(0.676314\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.95270 | 0.391659 | ||||||||
\(232\) | −6.09859 | −0.400392 | ||||||||
\(233\) | −20.1234 | −1.31833 | −0.659165 | − | 0.751999i | \(-0.729090\pi\) | ||||
−0.659165 | + | 0.751999i | \(0.729090\pi\) | |||||||
\(234\) | 5.71295 | 0.373467 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.5531 | −1.79355 | ||||||||
\(237\) | 28.8551 | 1.87434 | ||||||||
\(238\) | −22.6457 | −1.46790 | ||||||||
\(239\) | 4.68343 | 0.302946 | 0.151473 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151473 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −23.8855 | −1.53542 | ||||||||
\(243\) | 11.9175 | 0.764506 | ||||||||
\(244\) | −13.2566 | −0.848665 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.27774 | −0.527770 | ||||||||
\(247\) | −12.6267 | −0.803415 | ||||||||
\(248\) | 25.9733 | 1.64931 | ||||||||
\(249\) | −8.18528 | −0.518721 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.0713 | −1.45625 | −0.728123 | − | 0.685447i | \(-0.759607\pi\) | ||||
−0.728123 | + | 0.685447i | \(0.759607\pi\) | |||||||
\(252\) | −13.3610 | −0.841664 | ||||||||
\(253\) | 7.45555 | 0.468727 | ||||||||
\(254\) | 45.9948 | 2.88597 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −25.1102 | −1.56939 | ||||||||
\(257\) | 11.6020 | 0.723715 | 0.361857 | − | 0.932233i | \(-0.382143\pi\) | ||||
0.361857 | + | 0.932233i | \(0.382143\pi\) | |||||||
\(258\) | 49.5822 | 3.08686 | ||||||||
\(259\) | 2.65963 | 0.165261 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.98224 | −0.122698 | ||||||||
\(262\) | −19.6259 | −1.21249 | ||||||||
\(263\) | 15.3744 | 0.948024 | 0.474012 | − | 0.880518i | \(-0.342805\pi\) | ||||
0.474012 | + | 0.880518i | \(0.342805\pi\) | |||||||
\(264\) | −7.21838 | −0.444261 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 46.0288 | 2.82221 | ||||||||
\(267\) | 24.1752 | 1.47950 | ||||||||
\(268\) | −28.5116 | −1.74162 | ||||||||
\(269\) | 9.03287 | 0.550744 | 0.275372 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275372 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.0727 | −1.52306 | −0.761528 | − | 0.648132i | \(-0.775550\pi\) | ||||
−0.761528 | + | 0.648132i | \(0.775550\pi\) | |||||||
\(272\) | 5.15617 | 0.312639 | ||||||||
\(273\) | 12.5947 | 0.762269 | ||||||||
\(274\) | −10.0784 | −0.608856 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −58.1252 | −3.49873 | ||||||||
\(277\) | −10.5495 | −0.633855 | −0.316928 | − | 0.948450i | \(-0.602651\pi\) | ||||
−0.316928 | + | 0.948450i | \(0.602651\pi\) | |||||||
\(278\) | −10.0556 | −0.603097 | ||||||||
\(279\) | 8.44218 | 0.505420 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2094 | 0.966971 | 0.483485 | − | 0.875352i | \(-0.339371\pi\) | ||||
0.483485 | + | 0.875352i | \(0.339371\pi\) | |||||||
\(282\) | 31.5041 | 1.87604 | ||||||||
\(283\) | −8.03684 | −0.477741 | −0.238870 | − | 0.971051i | \(-0.576777\pi\) | ||||
−0.238870 | + | 0.971051i | \(0.576777\pi\) | |||||||
\(284\) | −25.1309 | −1.49124 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.43912 | 0.262491 | ||||||||
\(287\) | −5.25390 | −0.310128 | ||||||||
\(288\) | −4.31018 | −0.253980 | ||||||||
\(289\) | −7.29437 | −0.429081 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.2669 | 2.12600 | ||||||||
\(292\) | −21.9647 | −1.28539 | ||||||||
\(293\) | 26.1918 | 1.53014 | 0.765072 | − | 0.643945i | \(-0.222703\pi\) | ||||
0.765072 | + | 0.643945i | \(0.222703\pi\) | |||||||
\(294\) | −11.9738 | −0.698326 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.22513 | −0.187457 | ||||||||
\(297\) | 3.45700 | 0.200595 | ||||||||
\(298\) | 16.0665 | 0.930709 | ||||||||
\(299\) | 15.7745 | 0.912262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.4700 | 1.81390 | ||||||||
\(302\) | −9.72405 | −0.559556 | ||||||||
\(303\) | −18.5884 | −1.06788 | ||||||||
\(304\) | −10.4802 | −0.601083 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.92564 | 0.510245 | ||||||||
\(307\) | 4.41238 | 0.251828 | 0.125914 | − | 0.992041i | \(-0.459814\pi\) | ||||
0.125914 | + | 0.992041i | \(0.459814\pi\) | |||||||
\(308\) | −10.3819 | −0.591562 | ||||||||
\(309\) | −4.51783 | −0.257010 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2563 | −0.751693 | −0.375847 | − | 0.926682i | \(-0.622648\pi\) | ||||
−0.375847 | + | 0.926682i | \(0.622648\pi\) | |||||||
\(312\) | −15.2727 | −0.864646 | ||||||||
\(313\) | 22.1456 | 1.25174 | 0.625871 | − | 0.779927i | \(-0.284744\pi\) | ||||
0.625871 | + | 0.779927i | \(0.284744\pi\) | |||||||
\(314\) | 45.5601 | 2.57110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.3251 | −2.83101 | ||||||||
\(317\) | 3.01320 | 0.169238 | 0.0846190 | − | 0.996413i | \(-0.473033\pi\) | ||||
0.0846190 | + | 0.996413i | \(0.473033\pi\) | |||||||
\(318\) | −10.7103 | −0.600604 | ||||||||
\(319\) | −1.54026 | −0.0862378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5441 | 0.811774 | ||||||||
\(322\) | −57.5038 | −3.20456 | ||||||||
\(323\) | −19.7273 | −1.09766 | ||||||||
\(324\) | −39.9770 | −2.22094 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.18436 | −0.231750 | ||||||||
\(327\) | 15.5512 | 0.859985 | ||||||||
\(328\) | 6.37101 | 0.351780 | ||||||||
\(329\) | 19.9957 | 1.10240 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.41939 | 0.517736 | 0.258868 | − | 0.965913i | \(-0.416650\pi\) | ||||
0.258868 | + | 0.965913i | \(0.416650\pi\) | |||||||
\(332\) | 14.2756 | 0.783477 | ||||||||
\(333\) | −1.04827 | −0.0574451 | ||||||||
\(334\) | 0.0942276 | 0.00515591 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.4537 | 0.570299 | ||||||||
\(337\) | −17.0177 | −0.927011 | −0.463505 | − | 0.886094i | \(-0.653409\pi\) | ||||
−0.463505 | + | 0.886094i | \(0.653409\pi\) | |||||||
\(338\) | −21.3156 | −1.15942 | ||||||||
\(339\) | −36.5284 | −1.98395 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.55981 | 0.355234 | ||||||||
\(342\) | −18.1419 | −0.981003 | ||||||||
\(343\) | 13.9412 | 0.752752 | ||||||||
\(344\) | −38.1612 | −2.05752 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.1661 | 2.05182 | ||||||||
\(347\) | 23.6966 | 1.27210 | 0.636049 | − | 0.771649i | \(-0.280568\pi\) | ||||
0.636049 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(348\) | 12.0082 | 0.643707 | ||||||||
\(349\) | 4.05897 | 0.217272 | 0.108636 | − | 0.994082i | \(-0.465352\pi\) | ||||
0.108636 | + | 0.994082i | \(0.465352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.31433 | 0.390410 | ||||||||
\(352\) | −3.34913 | −0.178509 | ||||||||
\(353\) | 15.8788 | 0.845144 | 0.422572 | − | 0.906329i | \(-0.361127\pi\) | ||||
0.422572 | + | 0.906329i | \(0.361127\pi\) | |||||||
\(354\) | 37.3177 | 1.98342 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −42.1630 | −2.23463 | ||||||||
\(357\) | 19.6774 | 1.04144 | ||||||||
\(358\) | 1.71871 | 0.0908366 | ||||||||
\(359\) | −4.02791 | −0.212585 | −0.106293 | − | 0.994335i | \(-0.533898\pi\) | ||||
−0.106293 | + | 0.994335i | \(0.533898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.0970 | 1.11037 | ||||||||
\(362\) | 32.4175 | 1.70383 | ||||||||
\(363\) | 20.7548 | 1.08934 | ||||||||
\(364\) | −21.9660 | −1.15133 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 17.9546 | 0.938504 | ||||||||
\(367\) | −38.1519 | −1.99151 | −0.995757 | − | 0.0920267i | \(-0.970665\pi\) | ||||
−0.995757 | + | 0.0920267i | \(0.970665\pi\) | |||||||
\(368\) | 13.0930 | 0.682518 | ||||||||
\(369\) | 2.07079 | 0.107801 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.79785 | −0.352927 | ||||||||
\(372\) | −51.1418 | −2.65158 | ||||||||
\(373\) | −20.3518 | −1.05377 | −0.526887 | − | 0.849935i | \(-0.676641\pi\) | ||||
−0.526887 | + | 0.849935i | \(0.676641\pi\) | |||||||
\(374\) | 6.93547 | 0.358625 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.2473 | −1.25046 | ||||||||
\(377\) | −3.25888 | −0.167841 | ||||||||
\(378\) | −26.6634 | −1.37142 | ||||||||
\(379\) | −30.2111 | −1.55184 | −0.775919 | − | 0.630833i | \(-0.782713\pi\) | ||||
−0.775919 | + | 0.630833i | \(0.782713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.9661 | −2.04752 | ||||||||
\(382\) | −29.0092 | −1.48424 | ||||||||
\(383\) | 23.4619 | 1.19885 | 0.599425 | − | 0.800431i | \(-0.295396\pi\) | ||||
0.599425 | + | 0.800431i | \(0.295396\pi\) | |||||||
\(384\) | 42.1594 | 2.15144 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.4491 | −1.19353 | ||||||||
\(387\) | −12.4037 | −0.630513 | ||||||||
\(388\) | −63.2517 | −3.21112 | ||||||||
\(389\) | 0.990019 | 0.0501959 | 0.0250980 | − | 0.999685i | \(-0.492010\pi\) | ||||
0.0250980 | + | 0.999685i | \(0.492010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.6453 | 1.24637 | ||||||||
\(392\) | 9.21569 | 0.465463 | ||||||||
\(393\) | 17.0534 | 0.860231 | ||||||||
\(394\) | 28.6198 | 1.44184 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.09194 | 0.205628 | ||||||||
\(397\) | −4.90685 | −0.246268 | −0.123134 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123134 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(398\) | 32.4890 | 1.62853 | ||||||||
\(399\) | −39.9956 | −2.00229 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.6157 | −1.52888 | −0.764439 | − | 0.644696i | \(-0.776984\pi\) | ||||
−0.764439 | + | 0.644696i | \(0.776984\pi\) | |||||||
\(402\) | 38.6159 | 1.92599 | ||||||||
\(403\) | 13.8793 | 0.691376 | ||||||||
\(404\) | 32.4194 | 1.61292 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.8798 | 0.589586 | ||||||||
\(407\) | −0.814538 | −0.0403752 | ||||||||
\(408\) | −23.8613 | −1.18131 | ||||||||
\(409\) | −4.00516 | −0.198043 | −0.0990213 | − | 0.995085i | \(-0.531571\pi\) | ||||
−0.0990213 | + | 0.995085i | \(0.531571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.75735 | 0.431968 | ||||||||
\(412\) | 7.87937 | 0.388189 | ||||||||
\(413\) | 23.6856 | 1.16549 | ||||||||
\(414\) | 22.6647 | 1.11391 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.08611 | −0.347425 | ||||||||
\(417\) | 8.73761 | 0.427883 | ||||||||
\(418\) | −14.0968 | −0.689496 | ||||||||
\(419\) | 31.4086 | 1.53441 | 0.767206 | − | 0.641401i | \(-0.221646\pi\) | ||||
0.767206 | + | 0.641401i | \(0.221646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.1136 | 1.90628 | 0.953141 | − | 0.302526i | \(-0.0978298\pi\) | ||||
0.953141 | + | 0.302526i | \(0.0978298\pi\) | |||||||
\(422\) | −42.5743 | −2.07248 | ||||||||
\(423\) | −7.88117 | −0.383196 | ||||||||
\(424\) | 8.24323 | 0.400327 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 34.0372 | 1.64911 | ||||||||
\(427\) | 11.3958 | 0.551484 | ||||||||
\(428\) | −25.3659 | −1.22610 | ||||||||
\(429\) | −3.85727 | −0.186231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.68918 | 0.370375 | 0.185188 | − | 0.982703i | \(-0.440711\pi\) | ||||
0.185188 | + | 0.982703i | \(0.440711\pi\) | |||||||
\(432\) | 6.07096 | 0.292089 | ||||||||
\(433\) | −4.67921 | −0.224869 | −0.112434 | − | 0.993659i | \(-0.535865\pi\) | ||||
−0.112434 | + | 0.993659i | \(0.535865\pi\) | |||||||
\(434\) | −50.5951 | −2.42864 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.1223 | −1.29892 | ||||||||
\(437\) | −50.0932 | −2.39628 | ||||||||
\(438\) | 29.7488 | 1.42145 | ||||||||
\(439\) | 14.7770 | 0.705270 | 0.352635 | − | 0.935761i | \(-0.385286\pi\) | ||||
0.352635 | + | 0.935761i | \(0.385286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.99540 | 0.142638 | ||||||||
\(442\) | 14.6741 | 0.697976 | ||||||||
\(443\) | 3.71495 | 0.176503 | 0.0882513 | − | 0.996098i | \(-0.471872\pi\) | ||||
0.0882513 | + | 0.996098i | \(0.471872\pi\) | |||||||
\(444\) | 6.35033 | 0.301373 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −66.1365 | −3.13165 | ||||||||
\(447\) | −13.9606 | −0.660315 | ||||||||
\(448\) | 36.0177 | 1.70168 | ||||||||
\(449\) | −23.6261 | −1.11498 | −0.557492 | − | 0.830183i | \(-0.688236\pi\) | ||||
−0.557492 | + | 0.830183i | \(0.688236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.60906 | 0.0757676 | ||||||||
\(452\) | 63.7077 | 2.99656 | ||||||||
\(453\) | 8.44948 | 0.396991 | ||||||||
\(454\) | 30.2066 | 1.41767 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 48.4997 | 2.27120 | ||||||||
\(457\) | −16.0363 | −0.750146 | −0.375073 | − | 0.926995i | \(-0.622382\pi\) | ||||
−0.375073 | + | 0.926995i | \(0.622382\pi\) | |||||||
\(458\) | −37.6056 | −1.75720 | ||||||||
\(459\) | 11.4276 | 0.533393 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.0734 | 1.07464 | 0.537319 | − | 0.843379i | \(-0.319437\pi\) | ||||
0.537319 | + | 0.843379i | \(0.319437\pi\) | |||||||
\(462\) | 14.0612 | 0.654184 | ||||||||
\(463\) | −34.0986 | −1.58470 | −0.792349 | − | 0.610068i | \(-0.791142\pi\) | ||||
−0.792349 | + | 0.610068i | \(0.791142\pi\) | |||||||
\(464\) | −2.70490 | −0.125572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.5345 | −2.20199 | ||||||||
\(467\) | −15.2453 | −0.705467 | −0.352734 | − | 0.935724i | \(-0.614748\pi\) | ||||
−0.352734 | + | 0.935724i | \(0.614748\pi\) | |||||||
\(468\) | 8.65774 | 0.400204 | ||||||||
\(469\) | 24.5096 | 1.13175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.5883 | −1.82413 | ||||||||
\(472\) | −28.7218 | −1.32203 | ||||||||
\(473\) | −9.63798 | −0.443155 | ||||||||
\(474\) | 68.1601 | 3.13070 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −34.3187 | −1.57299 | ||||||||
\(477\) | 2.67932 | 0.122678 | ||||||||
\(478\) | 11.0630 | 0.506008 | ||||||||
\(479\) | 41.7622 | 1.90816 | 0.954082 | − | 0.299546i | \(-0.0968351\pi\) | ||||
0.954082 | + | 0.299546i | \(0.0968351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.72340 | −0.0785805 | ||||||||
\(482\) | 2.36215 | 0.107593 | ||||||||
\(483\) | 49.9666 | 2.27356 | ||||||||
\(484\) | −36.1976 | −1.64535 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.1508 | 1.27695 | ||||||||
\(487\) | −33.0645 | −1.49830 | −0.749148 | − | 0.662402i | \(-0.769537\pi\) | ||||
−0.749148 | + | 0.662402i | \(0.769537\pi\) | |||||||
\(488\) | −13.8189 | −0.625551 | ||||||||
\(489\) | 3.63590 | 0.164421 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6839 | −0.572415 | −0.286208 | − | 0.958168i | \(-0.592395\pi\) | ||||
−0.286208 | + | 0.958168i | \(0.592395\pi\) | |||||||
\(492\) | −12.5446 | −0.565554 | ||||||||
\(493\) | −5.09153 | −0.229311 | ||||||||
\(494\) | −29.8260 | −1.34194 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.5199 | 0.517260 | ||||||||
\(497\) | 21.6035 | 0.969047 | ||||||||
\(498\) | −19.3348 | −0.866415 | ||||||||
\(499\) | −15.4405 | −0.691213 | −0.345606 | − | 0.938380i | \(-0.612327\pi\) | ||||
−0.345606 | + | 0.938380i | \(0.612327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0818768 | −0.00365799 | ||||||||
\(502\) | −54.4977 | −2.43235 | ||||||||
\(503\) | −26.3951 | −1.17690 | −0.588450 | − | 0.808534i | \(-0.700262\pi\) | ||||
−0.588450 | + | 0.808534i | \(0.700262\pi\) | |||||||
\(504\) | −13.9277 | −0.620390 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.6111 | 0.782910 | ||||||||
\(507\) | 18.5217 | 0.822577 | ||||||||
\(508\) | 69.7033 | 3.09258 | ||||||||
\(509\) | 13.4761 | 0.597318 | 0.298659 | − | 0.954360i | \(-0.403461\pi\) | ||||
0.298659 | + | 0.954360i | \(0.403461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8817 | 0.835275 | ||||||||
\(512\) | −18.2336 | −0.805817 | ||||||||
\(513\) | −23.2272 | −1.02551 | ||||||||
\(514\) | 27.4057 | 1.20881 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 75.1399 | 3.30785 | ||||||||
\(517\) | −6.12389 | −0.269328 | ||||||||
\(518\) | 6.28244 | 0.276035 | ||||||||
\(519\) | −33.1635 | −1.45572 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7045 | −1.03851 | −0.519256 | − | 0.854619i | \(-0.673791\pi\) | ||||
−0.519256 | + | 0.854619i | \(0.673791\pi\) | |||||||
\(522\) | −4.68235 | −0.204941 | ||||||||
\(523\) | 3.98543 | 0.174271 | 0.0871354 | − | 0.996196i | \(-0.472229\pi\) | ||||
0.0871354 | + | 0.996196i | \(0.472229\pi\) | |||||||
\(524\) | −29.7422 | −1.29929 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.3165 | 1.58348 | ||||||||
\(527\) | 21.6843 | 0.944584 | ||||||||
\(528\) | −3.20156 | −0.139330 | ||||||||
\(529\) | 39.5814 | 1.72093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.33553 | −0.405127 | ||||||||
\(532\) | 69.7548 | 3.02426 | ||||||||
\(533\) | 3.40445 | 0.147463 | ||||||||
\(534\) | 57.1053 | 2.47119 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −29.7209 | −1.28375 | ||||||||
\(537\) | −1.49343 | −0.0644463 | ||||||||
\(538\) | 21.3370 | 0.919902 | ||||||||
\(539\) | 2.32751 | 0.100253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3140 | 0.615405 | 0.307703 | − | 0.951483i | \(-0.400440\pi\) | ||||
0.307703 | + | 0.951483i | \(0.400440\pi\) | |||||||
\(542\) | −59.2253 | −2.54394 | ||||||||
\(543\) | −28.1684 | −1.20882 | ||||||||
\(544\) | −11.0710 | −0.474666 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 29.7506 | 1.27321 | ||||||||
\(547\) | −25.1893 | −1.07702 | −0.538508 | − | 0.842621i | \(-0.681012\pi\) | ||||
−0.538508 | + | 0.842621i | \(0.681012\pi\) | |||||||
\(548\) | −15.2734 | −0.652446 | ||||||||
\(549\) | −4.49159 | −0.191696 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3488 | 0.440876 | ||||||||
\(552\) | −60.5907 | −2.57891 | ||||||||
\(553\) | 43.2613 | 1.83966 | ||||||||
\(554\) | −24.9194 | −1.05872 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2389 | −0.646275 | ||||||||
\(557\) | 16.4450 | 0.696798 | 0.348399 | − | 0.937346i | \(-0.386725\pi\) | ||||
0.348399 | + | 0.937346i | \(0.386725\pi\) | |||||||
\(558\) | 19.9417 | 0.844199 | ||||||||
\(559\) | −20.3921 | −0.862494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.02641 | −0.254435 | ||||||||
\(562\) | 38.2890 | 1.61512 | ||||||||
\(563\) | −14.8796 | −0.627100 | −0.313550 | − | 0.949572i | \(-0.601518\pi\) | ||||
−0.313550 | + | 0.949572i | \(0.601518\pi\) | |||||||
\(564\) | 47.7433 | 2.01035 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.9842 | −0.797966 | ||||||||
\(567\) | 34.3657 | 1.44322 | ||||||||
\(568\) | −26.1969 | −1.09920 | ||||||||
\(569\) | −37.4832 | −1.57138 | −0.785689 | − | 0.618622i | \(-0.787691\pi\) | ||||
−0.785689 | + | 0.618622i | \(0.787691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58161 | 0.0661885 | 0.0330943 | − | 0.999452i | \(-0.489464\pi\) | ||||
0.0330943 | + | 0.999452i | \(0.489464\pi\) | |||||||
\(572\) | 6.72731 | 0.281283 | ||||||||
\(573\) | 25.2069 | 1.05303 | ||||||||
\(574\) | −12.4105 | −0.518004 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.1961 | −0.591504 | ||||||||
\(577\) | 37.7122 | 1.56998 | 0.784990 | − | 0.619508i | \(-0.212668\pi\) | ||||
0.784990 | + | 0.619508i | \(0.212668\pi\) | |||||||
\(578\) | −17.2304 | −0.716689 | ||||||||
\(579\) | 20.3755 | 0.846778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.2719 | −0.509123 | ||||||||
\(582\) | 85.6678 | 3.55105 | ||||||||
\(583\) | 2.08191 | 0.0862238 | ||||||||
\(584\) | −22.8963 | −0.947457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.8690 | 2.55578 | ||||||||
\(587\) | 27.6567 | 1.14151 | 0.570756 | − | 0.821120i | \(-0.306650\pi\) | ||||
0.570756 | + | 0.821120i | \(0.306650\pi\) | |||||||
\(588\) | −18.1458 | −0.748321 | ||||||||
\(589\) | −44.0748 | −1.81607 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.8685 | −1.02295 | ||||||||
\(592\) | −1.43044 | −0.0587907 | ||||||||
\(593\) | −18.1987 | −0.747329 | −0.373665 | − | 0.927564i | \(-0.621899\pi\) | ||||
−0.373665 | + | 0.927564i | \(0.621899\pi\) | |||||||
\(594\) | 8.16593 | 0.335052 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.3482 | 0.997341 | ||||||||
\(597\) | −28.2305 | −1.15540 | ||||||||
\(598\) | 37.2617 | 1.52374 | ||||||||
\(599\) | −7.12390 | −0.291075 | −0.145537 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145537 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.3425 | 0.462672 | 0.231336 | − | 0.972874i | \(-0.425690\pi\) | ||||
0.231336 | + | 0.972874i | \(0.425690\pi\) | |||||||
\(602\) | 74.3367 | 3.02974 | ||||||||
\(603\) | −9.66028 | −0.393397 | ||||||||
\(604\) | −14.7364 | −0.599616 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −43.9086 | −1.78367 | ||||||||
\(607\) | 9.88248 | 0.401117 | 0.200559 | − | 0.979682i | \(-0.435724\pi\) | ||||
0.200559 | + | 0.979682i | \(0.435724\pi\) | |||||||
\(608\) | 22.5025 | 0.912598 | ||||||||
\(609\) | −10.3227 | −0.418297 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.9570 | −0.524182 | ||||||||
\(612\) | 13.5265 | 0.546775 | ||||||||
\(613\) | −6.32265 | −0.255369 | −0.127685 | − | 0.991815i | \(-0.540755\pi\) | ||||
−0.127685 | + | 0.991815i | \(0.540755\pi\) | |||||||
\(614\) | 10.4227 | 0.420626 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.8222 | −0.436040 | ||||||||
\(617\) | 28.4003 | 1.14335 | 0.571676 | − | 0.820480i | \(-0.306293\pi\) | ||||
0.571676 | + | 0.820480i | \(0.306293\pi\) | |||||||
\(618\) | −10.6718 | −0.429282 | ||||||||
\(619\) | 14.3962 | 0.578633 | 0.289316 | − | 0.957234i | \(-0.406572\pi\) | ||||
0.289316 | + | 0.957234i | \(0.406572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.0178 | 1.16444 | ||||||||
\(622\) | −31.3132 | −1.25555 | ||||||||
\(623\) | 36.2449 | 1.45212 | ||||||||
\(624\) | −6.77388 | −0.271172 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 52.3111 | 2.09077 | ||||||||
\(627\) | 12.2491 | 0.489180 | ||||||||
\(628\) | 69.0445 | 2.75517 | ||||||||
\(629\) | −2.69257 | −0.107360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.4378 | −0.654379 | −0.327190 | − | 0.944959i | \(-0.606102\pi\) | ||||
−0.327190 | + | 0.944959i | \(0.606102\pi\) | |||||||
\(632\) | −52.4597 | −2.08674 | ||||||||
\(633\) | 36.9939 | 1.47038 | ||||||||
\(634\) | 7.11761 | 0.282677 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.2310 | −0.643602 | ||||||||
\(637\) | 4.92456 | 0.195118 | ||||||||
\(638\) | −3.63831 | −0.144042 | ||||||||
\(639\) | −8.51484 | −0.336842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.38495 | 0.370683 | 0.185342 | − | 0.982674i | \(-0.440661\pi\) | ||||
0.185342 | + | 0.982674i | \(0.440661\pi\) | |||||||
\(642\) | 34.3554 | 1.35590 | ||||||||
\(643\) | 2.90484 | 0.114556 | 0.0572778 | − | 0.998358i | \(-0.481758\pi\) | ||||
0.0572778 | + | 0.998358i | \(0.481758\pi\) | |||||||
\(644\) | −87.1448 | −3.43399 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.5988 | −1.83341 | ||||||||
\(647\) | 16.2707 | 0.639667 | 0.319833 | − | 0.947474i | \(-0.396373\pi\) | ||||
0.319833 | + | 0.947474i | \(0.396373\pi\) | |||||||
\(648\) | −41.6727 | −1.63706 | ||||||||
\(649\) | −7.25396 | −0.284743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43.9634 | 1.72306 | ||||||||
\(652\) | −6.34124 | −0.248342 | ||||||||
\(653\) | 11.7812 | 0.461035 | 0.230517 | − | 0.973068i | \(-0.425958\pi\) | ||||
0.230517 | + | 0.973068i | \(0.425958\pi\) | |||||||
\(654\) | 36.7343 | 1.43643 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.82573 | 0.110326 | ||||||||
\(657\) | −7.44207 | −0.290343 | ||||||||
\(658\) | 47.2329 | 1.84133 | ||||||||
\(659\) | 47.0426 | 1.83252 | 0.916260 | − | 0.400583i | \(-0.131193\pi\) | ||||
0.916260 | + | 0.400583i | \(0.131193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.3779 | −1.45383 | −0.726916 | − | 0.686726i | \(-0.759047\pi\) | ||||
−0.726916 | + | 0.686726i | \(0.759047\pi\) | |||||||
\(662\) | 22.2500 | 0.864770 | ||||||||
\(663\) | −12.7507 | −0.495197 | ||||||||
\(664\) | 14.8812 | 0.577501 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.47618 | −0.0959500 | ||||||||
\(667\) | −12.9288 | −0.500606 | ||||||||
\(668\) | 0.142798 | 0.00552503 | ||||||||
\(669\) | 57.4678 | 2.22183 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.49009 | −0.134733 | ||||||||
\(672\) | −22.4456 | −0.865860 | ||||||||
\(673\) | −37.3014 | −1.43786 | −0.718931 | − | 0.695081i | \(-0.755368\pi\) | ||||
−0.718931 | + | 0.695081i | \(0.755368\pi\) | |||||||
\(674\) | −40.1982 | −1.54838 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −32.3030 | −1.24242 | ||||||||
\(677\) | 21.0921 | 0.810636 | 0.405318 | − | 0.914176i | \(-0.367161\pi\) | ||||
0.405318 | + | 0.914176i | \(0.367161\pi\) | |||||||
\(678\) | −86.2854 | −3.31377 | ||||||||
\(679\) | 54.3735 | 2.08667 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.2473 | −1.00580 | ||||||||
\(682\) | 15.4952 | 0.593343 | ||||||||
\(683\) | −30.1078 | −1.15204 | −0.576022 | − | 0.817434i | \(-0.695396\pi\) | ||||
−0.576022 | + | 0.817434i | \(0.695396\pi\) | |||||||
\(684\) | −27.4934 | −1.05124 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.9311 | 1.25731 | ||||||||
\(687\) | 32.6765 | 1.24669 | ||||||||
\(688\) | −16.9256 | −0.645283 | ||||||||
\(689\) | 4.40491 | 0.167814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.9001 | −0.871162 | −0.435581 | − | 0.900149i | \(-0.643457\pi\) | ||||
−0.435581 | + | 0.900149i | \(0.643457\pi\) | |||||||
\(692\) | 57.8391 | 2.19871 | ||||||||
\(693\) | −3.51758 | −0.133622 | ||||||||
\(694\) | 55.9748 | 2.12477 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.5175 | 0.474476 | ||||||||
\(697\) | 5.31896 | 0.201470 | ||||||||
\(698\) | 9.58790 | 0.362907 | ||||||||
\(699\) | 41.3040 | 1.56226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7502 | −0.481567 | −0.240784 | − | 0.970579i | \(-0.577404\pi\) | ||||
−0.240784 | + | 0.970579i | \(0.577404\pi\) | |||||||
\(702\) | 17.2775 | 0.652098 | ||||||||
\(703\) | 5.47281 | 0.206411 | ||||||||
\(704\) | −11.0308 | −0.415738 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.5081 | 1.41164 | ||||||||
\(707\) | −27.8689 | −1.04812 | ||||||||
\(708\) | 56.5536 | 2.12541 | ||||||||
\(709\) | −30.5429 | −1.14706 | −0.573531 | − | 0.819184i | \(-0.694427\pi\) | ||||
−0.573531 | + | 0.819184i | \(0.694427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.0511 | −0.639468 | ||||||||
\(712\) | −43.9514 | −1.64715 | ||||||||
\(713\) | 55.0626 | 2.06211 | ||||||||
\(714\) | 46.4810 | 1.73951 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.60463 | 0.0973398 | ||||||||
\(717\) | −9.61289 | −0.359000 | ||||||||
\(718\) | −9.51453 | −0.355079 | ||||||||
\(719\) | −4.70422 | −0.175438 | −0.0877190 | − | 0.996145i | \(-0.527958\pi\) | ||||
−0.0877190 | + | 0.996145i | \(0.527958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.77340 | −0.252255 | ||||||||
\(722\) | 49.8342 | 1.85464 | ||||||||
\(723\) | −2.05253 | −0.0763345 | ||||||||
\(724\) | 49.1275 | 1.82581 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 49.0259 | 1.81952 | ||||||||
\(727\) | 34.0042 | 1.26114 | 0.630572 | − | 0.776130i | \(-0.282820\pi\) | ||||
0.630572 | + | 0.776130i | \(0.282820\pi\) | |||||||
\(728\) | −22.8977 | −0.848646 | ||||||||
\(729\) | 9.04171 | 0.334878 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.8597 | −1.17837 | ||||||||
\(732\) | 27.2096 | 1.00569 | ||||||||
\(733\) | 16.4990 | 0.609406 | 0.304703 | − | 0.952447i | \(-0.401443\pi\) | ||||
0.304703 | + | 0.952447i | \(0.401443\pi\) | |||||||
\(734\) | −90.1204 | −3.32641 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.1124 | −1.03624 | ||||||||
\(737\) | −7.50631 | −0.276498 | ||||||||
\(738\) | 4.89150 | 0.180059 | ||||||||
\(739\) | 41.0735 | 1.51091 | 0.755456 | − | 0.655199i | \(-0.227415\pi\) | ||||
0.755456 | + | 0.655199i | \(0.227415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.9166 | 0.952071 | ||||||||
\(742\) | −16.0575 | −0.589490 | ||||||||
\(743\) | 6.32830 | 0.232163 | 0.116081 | − | 0.993240i | \(-0.462967\pi\) | ||||
0.116081 | + | 0.993240i | \(0.462967\pi\) | |||||||
\(744\) | −53.3110 | −1.95448 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −48.0739 | −1.76011 | ||||||||
\(747\) | 4.83687 | 0.176972 | ||||||||
\(748\) | 10.5104 | 0.384299 | ||||||||
\(749\) | 21.8054 | 0.796753 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.2850 | 1.94440 | 0.972199 | − | 0.234157i | \(-0.0752331\pi\) | ||||
0.972199 | + | 0.234157i | \(0.0752331\pi\) | |||||||
\(752\) | −10.7544 | −0.392172 | ||||||||
\(753\) | 47.3545 | 1.72569 | ||||||||
\(754\) | −7.69796 | −0.280343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −40.4074 | −1.46960 | ||||||||
\(757\) | 38.5378 | 1.40068 | 0.700340 | − | 0.713810i | \(-0.253032\pi\) | ||||
0.700340 | + | 0.713810i | \(0.253032\pi\) | |||||||
\(758\) | −71.3630 | −2.59202 | ||||||||
\(759\) | −15.3028 | −0.555455 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.2682 | −0.589723 | −0.294861 | − | 0.955540i | \(-0.595273\pi\) | ||||
−0.294861 | + | 0.955540i | \(0.595273\pi\) | |||||||
\(762\) | −94.4057 | −3.41996 | ||||||||
\(763\) | 23.3153 | 0.844072 | ||||||||
\(764\) | −43.9623 | −1.59050 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 55.4206 | 2.00243 | ||||||||
\(767\) | −15.3480 | −0.554183 | ||||||||
\(768\) | 51.5394 | 1.85977 | ||||||||
\(769\) | −35.5516 | −1.28202 | −0.641012 | − | 0.767531i | \(-0.721485\pi\) | ||||
−0.641012 | + | 0.767531i | \(0.721485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8135 | −0.857623 | ||||||||
\(772\) | −35.5362 | −1.27898 | ||||||||
\(773\) | −0.807556 | −0.0290458 | −0.0145229 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145229 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(774\) | −29.2993 | −1.05314 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −65.9347 | −2.36692 | ||||||||
\(777\) | −5.45898 | −0.195840 | ||||||||
\(778\) | 2.33857 | 0.0838418 | ||||||||
\(779\) | −10.8111 | −0.387349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.61627 | −0.236749 | ||||||||
\(782\) | 58.2159 | 2.08180 | ||||||||
\(783\) | −5.99484 | −0.214238 | ||||||||
\(784\) | 4.08743 | 0.145980 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 40.2827 | 1.43684 | ||||||||
\(787\) | −13.8726 | −0.494504 | −0.247252 | − | 0.968951i | \(-0.579528\pi\) | ||||
−0.247252 | + | 0.968951i | \(0.579528\pi\) | |||||||
\(788\) | 43.3721 | 1.54507 | ||||||||
\(789\) | −31.5564 | −1.12344 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54.7655 | −1.94724 | ||||||||
\(792\) | 4.26551 | 0.151568 | ||||||||
\(793\) | −7.38435 | −0.262226 | ||||||||
\(794\) | −11.5907 | −0.411338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 49.2358 | 1.74512 | ||||||||
\(797\) | −3.24320 | −0.114880 | −0.0574400 | − | 0.998349i | \(-0.518294\pi\) | ||||
−0.0574400 | + | 0.998349i | \(0.518294\pi\) | |||||||
\(798\) | −94.4756 | −3.34440 | ||||||||
\(799\) | −20.2433 | −0.716158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2857 | −0.504759 | ||||||||
\(802\) | −72.3189 | −2.55367 | ||||||||
\(803\) | −5.78269 | −0.204067 | ||||||||
\(804\) | 58.5209 | 2.06387 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.7849 | 1.15480 | ||||||||
\(807\) | −18.5403 | −0.652648 | ||||||||
\(808\) | 33.7945 | 1.18889 | ||||||||
\(809\) | 54.4503 | 1.91437 | 0.957184 | − | 0.289479i | \(-0.0934819\pi\) | ||||
0.957184 | + | 0.289479i | \(0.0934819\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6483 | −0.725059 | −0.362530 | − | 0.931972i | \(-0.618087\pi\) | ||||
−0.362530 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(812\) | 18.0034 | 0.631796 | ||||||||
\(813\) | 51.4624 | 1.80487 | ||||||||
\(814\) | −1.92406 | −0.0674383 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.5832 | −0.370486 | ||||||||
\(817\) | 64.7567 | 2.26555 | ||||||||
\(818\) | −9.46079 | −0.330789 | ||||||||
\(819\) | −7.44252 | −0.260063 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0000 | 0.698006 | 0.349003 | − | 0.937122i | \(-0.386520\pi\) | ||||
0.349003 | + | 0.937122i | \(0.386520\pi\) | |||||||
\(822\) | 20.6862 | 0.721513 | ||||||||
\(823\) | −25.3107 | −0.882277 | −0.441138 | − | 0.897439i | \(-0.645425\pi\) | ||||
−0.441138 | + | 0.897439i | \(0.645425\pi\) | |||||||
\(824\) | 8.21359 | 0.286134 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 55.9490 | 1.94671 | ||||||||
\(827\) | −28.9282 | −1.00593 | −0.502966 | − | 0.864306i | \(-0.667758\pi\) | ||||
−0.502966 | + | 0.864306i | \(0.667758\pi\) | |||||||
\(828\) | 34.3475 | 1.19366 | ||||||||
\(829\) | 10.9469 | 0.380201 | 0.190100 | − | 0.981765i | \(-0.439119\pi\) | ||||
0.190100 | + | 0.981765i | \(0.439119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.6531 | 0.751137 | ||||||||
\(832\) | −23.3390 | −0.809133 | ||||||||
\(833\) | 7.69390 | 0.266578 | ||||||||
\(834\) | 20.6395 | 0.714689 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −21.3631 | −0.738859 | ||||||||
\(837\) | 25.5315 | 0.882497 | ||||||||
\(838\) | 74.1918 | 2.56291 | ||||||||
\(839\) | 16.6348 | 0.574298 | 0.287149 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287149 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3290 | −0.907897 | ||||||||
\(842\) | 92.3922 | 3.18405 | ||||||||
\(843\) | −33.2703 | −1.14589 | ||||||||
\(844\) | −64.5196 | −2.22086 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.6165 | −0.640048 | ||||||||
\(847\) | 31.1168 | 1.06919 | ||||||||
\(848\) | 3.65611 | 0.125552 | ||||||||
\(849\) | 16.4959 | 0.566137 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.83719 | −0.234376 | ||||||||
\(852\) | 51.5820 | 1.76717 | ||||||||
\(853\) | 1.31481 | 0.0450182 | 0.0225091 | − | 0.999747i | \(-0.492835\pi\) | ||||
0.0225091 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(854\) | 26.9187 | 0.921138 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.4418 | −0.903762 | ||||||||
\(857\) | 51.6669 | 1.76491 | 0.882454 | − | 0.470399i | \(-0.155890\pi\) | ||||
0.882454 | + | 0.470399i | \(0.155890\pi\) | |||||||
\(858\) | −9.11143 | −0.311059 | ||||||||
\(859\) | −39.7084 | −1.35483 | −0.677417 | − | 0.735599i | \(-0.736901\pi\) | ||||
−0.677417 | + | 0.735599i | \(0.736901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7838 | 0.367511 | ||||||||
\(862\) | 18.1630 | 0.618634 | ||||||||
\(863\) | −28.5307 | −0.971196 | −0.485598 | − | 0.874182i | \(-0.661398\pi\) | ||||
−0.485598 | + | 0.874182i | \(0.661398\pi\) | |||||||
\(864\) | −13.0352 | −0.443466 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0530 | −0.375596 | ||||||||
\(867\) | 14.9719 | 0.508473 | ||||||||
\(868\) | −76.6748 | −2.60251 | ||||||||
\(869\) | −13.2492 | −0.449449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.8819 | −0.538137 | ||||||||
\(872\) | −28.2727 | −0.957436 | ||||||||
\(873\) | −21.4309 | −0.725327 | ||||||||
\(874\) | −118.327 | −4.00249 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 45.0832 | 1.52322 | ||||||||
\(877\) | −4.60926 | −0.155644 | −0.0778219 | − | 0.996967i | \(-0.524797\pi\) | ||||
−0.0778219 | + | 0.996967i | \(0.524797\pi\) | |||||||
\(878\) | 34.9055 | 1.17801 | ||||||||
\(879\) | −53.7596 | −1.81327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.5627 | −0.490630 | −0.245315 | − | 0.969443i | \(-0.578891\pi\) | ||||
−0.245315 | + | 0.969443i | \(0.578891\pi\) | |||||||
\(882\) | 7.07559 | 0.238247 | ||||||||
\(883\) | 4.65262 | 0.156573 | 0.0782866 | − | 0.996931i | \(-0.475055\pi\) | ||||
0.0782866 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(884\) | 22.2380 | 0.747946 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.77526 | 0.294810 | ||||||||
\(887\) | −8.77283 | −0.294563 | −0.147281 | − | 0.989095i | \(-0.547052\pi\) | ||||
−0.147281 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(888\) | 6.61969 | 0.222142 | ||||||||
\(889\) | −59.9195 | −2.00964 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.5248 | −0.352595 | ||||||||
\(892\) | −100.227 | −3.35586 | ||||||||
\(893\) | 41.1459 | 1.37689 | ||||||||
\(894\) | −32.9771 | −1.10292 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 63.2079 | 2.11163 | ||||||||
\(897\) | −32.3776 | −1.08106 | ||||||||
\(898\) | −55.8083 | −1.86235 | ||||||||
\(899\) | −11.3755 | −0.379394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.88203 | 0.229274 | ||||||||
\(902\) | 3.80083 | 0.126554 | ||||||||
\(903\) | −64.5931 | −2.14952 | ||||||||
\(904\) | 66.4100 | 2.20876 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.9589 | 0.663091 | ||||||||
\(907\) | 17.5415 | 0.582457 | 0.291229 | − | 0.956653i | \(-0.405936\pi\) | ||||
0.291229 | + | 0.956653i | \(0.405936\pi\) | |||||||
\(908\) | 45.7770 | 1.51916 | ||||||||
\(909\) | 10.9843 | 0.364327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.2299 | −0.869034 | −0.434517 | − | 0.900664i | \(-0.643081\pi\) | ||||
−0.434517 | + | 0.900664i | \(0.643081\pi\) | |||||||
\(912\) | 21.5110 | 0.712301 | ||||||||
\(913\) | 3.75838 | 0.124384 | ||||||||
\(914\) | −37.8801 | −1.25296 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −56.9898 | −1.88300 | ||||||||
\(917\) | 25.5675 | 0.844314 | ||||||||
\(918\) | 26.9936 | 0.890921 | ||||||||
\(919\) | −26.0740 | −0.860101 | −0.430051 | − | 0.902805i | \(-0.641504\pi\) | ||||
−0.430051 | + | 0.902805i | \(0.641504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.05655 | −0.298424 | ||||||||
\(922\) | 54.5029 | 1.79496 | ||||||||
\(923\) | −13.9987 | −0.460774 | ||||||||
\(924\) | 21.3091 | 0.701019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −80.5460 | −2.64691 | ||||||||
\(927\) | 2.66969 | 0.0876840 | ||||||||
\(928\) | 5.80780 | 0.190650 | ||||||||
\(929\) | 22.2068 | 0.728582 | 0.364291 | − | 0.931285i | \(-0.381311\pi\) | ||||
0.364291 | + | 0.931285i | \(0.381311\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.6383 | −0.512526 | ||||||||
\(932\) | −72.0367 | −2.35964 | ||||||||
\(933\) | 27.2089 | 0.890779 | ||||||||
\(934\) | −36.0116 | −1.17834 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.02498 | 0.294991 | ||||||||
\(937\) | 39.4539 | 1.28890 | 0.644452 | − | 0.764645i | \(-0.277086\pi\) | ||||
0.644452 | + | 0.764645i | \(0.277086\pi\) | |||||||
\(938\) | 57.8953 | 1.89035 | ||||||||
\(939\) | −45.4545 | −1.48335 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.12527 | 0.232277 | 0.116139 | − | 0.993233i | \(-0.462948\pi\) | ||||
0.116139 | + | 0.993233i | \(0.462948\pi\) | |||||||
\(942\) | −93.5135 | −3.04683 | ||||||||
\(943\) | 13.5063 | 0.439827 | ||||||||
\(944\) | −12.7389 | −0.414617 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7663 | −0.740198 | ||||||||
\(947\) | −47.2038 | −1.53392 | −0.766959 | − | 0.641696i | \(-0.778231\pi\) | ||||
−0.766959 | + | 0.641696i | \(0.778231\pi\) | |||||||
\(948\) | 103.294 | 3.35483 | ||||||||
\(949\) | −12.2350 | −0.397166 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.18468 | −0.200552 | ||||||||
\(952\) | −35.7744 | −1.15945 | ||||||||
\(953\) | 6.73058 | 0.218025 | 0.109013 | − | 0.994040i | \(-0.465231\pi\) | ||||
0.109013 | + | 0.994040i | \(0.465231\pi\) | |||||||
\(954\) | 6.32896 | 0.204908 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.7655 | 0.542234 | ||||||||
\(957\) | 3.16143 | 0.102194 | ||||||||
\(958\) | 98.6485 | 3.18719 | ||||||||
\(959\) | 13.1296 | 0.423975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.4472 | 0.562812 | ||||||||
\(962\) | −4.07094 | −0.131252 | ||||||||
\(963\) | −8.59446 | −0.276952 | ||||||||
\(964\) | 3.57974 | 0.115296 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 118.028 | 3.79750 | ||||||||
\(967\) | −51.9356 | −1.67014 | −0.835069 | − | 0.550146i | \(-0.814572\pi\) | ||||
−0.835069 | + | 0.550146i | \(0.814572\pi\) | |||||||
\(968\) | −37.7330 | −1.21278 | ||||||||
\(969\) | 40.4909 | 1.30076 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5150 | 0.690451 | 0.345225 | − | 0.938520i | \(-0.387803\pi\) | ||||
0.345225 | + | 0.938520i | \(0.387803\pi\) | |||||||
\(972\) | 42.6615 | 1.36837 | ||||||||
\(973\) | 13.1000 | 0.419965 | ||||||||
\(974\) | −78.1033 | −2.50259 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.12908 | −0.196187 | ||||||||
\(977\) | −1.00409 | −0.0321238 | −0.0160619 | − | 0.999871i | \(-0.505113\pi\) | ||||
−0.0160619 | + | 0.999871i | \(0.505113\pi\) | |||||||
\(978\) | 8.58854 | 0.274631 | ||||||||
\(979\) | −11.1004 | −0.354769 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.18958 | −0.293401 | ||||||||
\(982\) | −29.9612 | −0.956100 | ||||||||
\(983\) | −29.7602 | −0.949203 | −0.474601 | − | 0.880201i | \(-0.657408\pi\) | ||||
−0.474601 | + | 0.880201i | \(0.657408\pi\) | |||||||
\(984\) | −13.0767 | −0.416870 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0269 | −0.383016 | ||||||||
\(987\) | −41.0419 | −1.30638 | ||||||||
\(988\) | −45.2002 | −1.43801 | ||||||||
\(989\) | −80.9007 | −2.57249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2504 | −0.547976 | −0.273988 | − | 0.961733i | \(-0.588343\pi\) | ||||
−0.273988 | + | 0.961733i | \(0.588343\pi\) | |||||||
\(992\) | −24.7349 | −0.785333 | ||||||||
\(993\) | −19.3336 | −0.613533 | ||||||||
\(994\) | 51.0305 | 1.61859 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −29.3012 | −0.928444 | ||||||||
\(997\) | −36.3908 | −1.15251 | −0.576254 | − | 0.817271i | \(-0.695486\pi\) | ||||
−0.576254 | + | 0.817271i | \(0.695486\pi\) | |||||||
\(998\) | −36.4728 | −1.15453 | ||||||||
\(999\) | −3.17027 | −0.100303 |
(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 | 6025.2.a.p.1.42 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.42 | yes | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.5 | ✓ | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.5 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.5 | ✓ | 46 | 5.3 | odd | 4 | ||
1205.2.b.c.724.42 | yes | 46 | 5.2 | odd | 4 | ||
6025.2.a.p.1.5 | 46 | 5.4 | even | 2 | inner | ||
6025.2.a.p.1.42 | 46 | 1.1 | even | 1 | trivial |