Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
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: | \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.63325\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.63325 | 1.15488 | 0.577441 | − | 0.816432i | \(-0.304051\pi\) | ||||
0.577441 | + | 0.816432i | \(0.304051\pi\) | |||||||
\(3\) | −0.456743 | −0.263701 | −0.131850 | − | 0.991270i | \(-0.542092\pi\) | ||||
−0.131850 | + | 0.991270i | \(0.542092\pi\) | |||||||
\(4\) | 0.667506 | 0.333753 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.745975 | −0.304543 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.17630 | −0.769437 | ||||||||
\(9\) | −2.79139 | −0.930462 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.335247 | 0.101081 | 0.0505404 | − | 0.998722i | \(-0.483906\pi\) | ||||
0.0505404 | + | 0.998722i | \(0.483906\pi\) | |||||||
\(12\) | −0.304879 | −0.0880109 | ||||||||
\(13\) | −4.58103 | −1.27055 | −0.635274 | − | 0.772287i | \(-0.719113\pi\) | ||||
−0.635274 | + | 0.772287i | \(0.719113\pi\) | |||||||
\(14\) | 1.63325 | 0.436504 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88945 | −1.22236 | ||||||||
\(17\) | 3.39509 | 0.823430 | 0.411715 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411715 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(18\) | −4.55903 | −1.07457 | ||||||||
\(19\) | 2.11764 | 0.485819 | 0.242910 | − | 0.970049i | \(-0.421898\pi\) | ||||
0.242910 | + | 0.970049i | \(0.421898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.456743 | −0.0996694 | ||||||||
\(22\) | 0.547542 | 0.116736 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.994007 | 0.202901 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.48196 | −1.46733 | ||||||||
\(27\) | 2.64517 | 0.509064 | ||||||||
\(28\) | 0.667506 | 0.126147 | ||||||||
\(29\) | 1.10564 | 0.205313 | 0.102656 | − | 0.994717i | \(-0.467266\pi\) | ||||
0.102656 | + | 0.994717i | \(0.467266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.68701 | 0.302996 | 0.151498 | − | 0.988458i | \(-0.451590\pi\) | ||||
0.151498 | + | 0.988458i | \(0.451590\pi\) | |||||||
\(32\) | −3.63310 | −0.642247 | ||||||||
\(33\) | −0.153122 | −0.0266551 | ||||||||
\(34\) | 5.54503 | 0.950965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.86327 | −0.310545 | ||||||||
\(37\) | 6.60823 | 1.08639 | 0.543194 | − | 0.839608i | \(-0.317215\pi\) | ||||
0.543194 | + | 0.839608i | \(0.317215\pi\) | |||||||
\(38\) | 3.45863 | 0.561064 | ||||||||
\(39\) | 2.09235 | 0.335044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.47182 | 1.47925 | 0.739625 | − | 0.673019i | \(-0.235003\pi\) | ||||
0.739625 | + | 0.673019i | \(0.235003\pi\) | |||||||
\(42\) | −0.745975 | −0.115106 | ||||||||
\(43\) | 9.10800 | 1.38896 | 0.694479 | − | 0.719513i | \(-0.255635\pi\) | ||||
0.694479 | + | 0.719513i | \(0.255635\pi\) | |||||||
\(44\) | 0.223779 | 0.0337360 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.63325 | 0.240810 | ||||||||
\(47\) | 2.36690 | 0.345248 | 0.172624 | − | 0.984988i | \(-0.444775\pi\) | ||||
0.172624 | + | 0.984988i | \(0.444775\pi\) | |||||||
\(48\) | 2.23322 | 0.322337 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.55068 | −0.217139 | ||||||||
\(52\) | −3.05786 | −0.424049 | ||||||||
\(53\) | 1.55754 | 0.213944 | 0.106972 | − | 0.994262i | \(-0.465884\pi\) | ||||
0.106972 | + | 0.994262i | \(0.465884\pi\) | |||||||
\(54\) | 4.32023 | 0.587909 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.17630 | −0.290820 | ||||||||
\(57\) | −0.967216 | −0.128111 | ||||||||
\(58\) | 1.80579 | 0.237112 | ||||||||
\(59\) | 10.2206 | 1.33061 | 0.665307 | − | 0.746570i | \(-0.268301\pi\) | ||||
0.665307 | + | 0.746570i | \(0.268301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.04415 | 0.389764 | 0.194882 | − | 0.980827i | \(-0.437568\pi\) | ||||
0.194882 | + | 0.980827i | \(0.437568\pi\) | |||||||
\(62\) | 2.75531 | 0.349925 | ||||||||
\(63\) | −2.79139 | −0.351682 | ||||||||
\(64\) | 3.84513 | 0.480642 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.250086 | −0.0307834 | ||||||||
\(67\) | −0.953507 | −0.116489 | −0.0582447 | − | 0.998302i | \(-0.518550\pi\) | ||||
−0.0582447 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(68\) | 2.26624 | 0.274822 | ||||||||
\(69\) | −0.456743 | −0.0549854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.97877 | −0.828227 | −0.414114 | − | 0.910225i | \(-0.635908\pi\) | ||||
−0.414114 | + | 0.910225i | \(0.635908\pi\) | |||||||
\(72\) | 6.07488 | 0.715932 | ||||||||
\(73\) | 7.24562 | 0.848036 | 0.424018 | − | 0.905654i | \(-0.360619\pi\) | ||||
0.424018 | + | 0.905654i | \(0.360619\pi\) | |||||||
\(74\) | 10.7929 | 1.25465 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41354 | 0.162144 | ||||||||
\(77\) | 0.335247 | 0.0382049 | ||||||||
\(78\) | 3.41733 | 0.386937 | ||||||||
\(79\) | −2.83560 | −0.319030 | −0.159515 | − | 0.987195i | \(-0.550993\pi\) | ||||
−0.159515 | + | 0.987195i | \(0.550993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.16599 | 0.796222 | ||||||||
\(82\) | 15.4699 | 1.70836 | ||||||||
\(83\) | −8.54319 | −0.937737 | −0.468869 | − | 0.883268i | \(-0.655338\pi\) | ||||
−0.468869 | + | 0.883268i | \(0.655338\pi\) | |||||||
\(84\) | −0.304879 | −0.0332650 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.8756 | 1.60408 | ||||||||
\(87\) | −0.504994 | −0.0541410 | ||||||||
\(88\) | −0.729597 | −0.0777753 | ||||||||
\(89\) | −12.2488 | −1.29837 | −0.649186 | − | 0.760630i | \(-0.724890\pi\) | ||||
−0.649186 | + | 0.760630i | \(0.724890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.58103 | −0.480222 | ||||||||
\(92\) | 0.667506 | 0.0695923 | ||||||||
\(93\) | −0.770530 | −0.0799003 | ||||||||
\(94\) | 3.86574 | 0.398721 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.65939 | 0.169361 | ||||||||
\(97\) | −1.59216 | −0.161660 | −0.0808298 | − | 0.996728i | \(-0.525757\pi\) | ||||
−0.0808298 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(98\) | 1.63325 | 0.164983 | ||||||||
\(99\) | −0.935804 | −0.0940518 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.27098 | 0.225971 | 0.112985 | − | 0.993597i | \(-0.463959\pi\) | ||||
0.112985 | + | 0.993597i | \(0.463959\pi\) | |||||||
\(102\) | −2.53265 | −0.250770 | ||||||||
\(103\) | −14.9493 | −1.47300 | −0.736501 | − | 0.676437i | \(-0.763523\pi\) | ||||
−0.736501 | + | 0.676437i | \(0.763523\pi\) | |||||||
\(104\) | 9.96967 | 0.977607 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.54385 | 0.247080 | ||||||||
\(107\) | 4.87423 | 0.471210 | 0.235605 | − | 0.971849i | \(-0.424293\pi\) | ||||
0.235605 | + | 0.971849i | \(0.424293\pi\) | |||||||
\(108\) | 1.76567 | 0.169902 | ||||||||
\(109\) | 1.76579 | 0.169132 | 0.0845661 | − | 0.996418i | \(-0.473050\pi\) | ||||
0.0845661 | + | 0.996418i | \(0.473050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.01826 | −0.286481 | ||||||||
\(112\) | −4.88945 | −0.462009 | ||||||||
\(113\) | 2.36111 | 0.222114 | 0.111057 | − | 0.993814i | \(-0.464576\pi\) | ||||
0.111057 | + | 0.993814i | \(0.464576\pi\) | |||||||
\(114\) | −1.57970 | −0.147953 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.738023 | 0.0685237 | ||||||||
\(117\) | 12.7874 | 1.18220 | ||||||||
\(118\) | 16.6929 | 1.53670 | ||||||||
\(119\) | 3.39509 | 0.311227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8876 | −0.989783 | ||||||||
\(122\) | 4.97186 | 0.450131 | ||||||||
\(123\) | −4.32619 | −0.390079 | ||||||||
\(124\) | 1.12609 | 0.101126 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.55903 | −0.406151 | ||||||||
\(127\) | 15.9550 | 1.41578 | 0.707890 | − | 0.706322i | \(-0.249647\pi\) | ||||
0.707890 | + | 0.706322i | \(0.249647\pi\) | |||||||
\(128\) | 13.5463 | 1.19733 | ||||||||
\(129\) | −4.16001 | −0.366269 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4772 | −0.915396 | −0.457698 | − | 0.889108i | \(-0.651326\pi\) | ||||
−0.457698 | + | 0.889108i | \(0.651326\pi\) | |||||||
\(132\) | −0.102210 | −0.00889620 | ||||||||
\(133\) | 2.11764 | 0.183622 | ||||||||
\(134\) | −1.55732 | −0.134532 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.38872 | −0.633577 | ||||||||
\(137\) | 0.0798775 | 0.00682440 | 0.00341220 | − | 0.999994i | \(-0.498914\pi\) | ||||
0.00341220 | + | 0.999994i | \(0.498914\pi\) | |||||||
\(138\) | −0.745975 | −0.0635016 | ||||||||
\(139\) | 9.20759 | 0.780978 | 0.390489 | − | 0.920608i | \(-0.372306\pi\) | ||||
0.390489 | + | 0.920608i | \(0.372306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.08107 | −0.0910421 | ||||||||
\(142\) | −11.3981 | −0.956505 | ||||||||
\(143\) | −1.53578 | −0.128428 | ||||||||
\(144\) | 13.6483 | 1.13736 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.8339 | 0.979382 | ||||||||
\(147\) | −0.456743 | −0.0376715 | ||||||||
\(148\) | 4.41104 | 0.362585 | ||||||||
\(149\) | 19.3465 | 1.58493 | 0.792464 | − | 0.609919i | \(-0.208798\pi\) | ||||
0.792464 | + | 0.609919i | \(0.208798\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.19693 | −0.178784 | −0.0893918 | − | 0.995997i | \(-0.528492\pi\) | ||||
−0.0893918 | + | 0.995997i | \(0.528492\pi\) | |||||||
\(152\) | −4.60861 | −0.373807 | ||||||||
\(153\) | −9.47701 | −0.766171 | ||||||||
\(154\) | 0.547542 | 0.0441222 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.39666 | 0.111822 | ||||||||
\(157\) | −3.64204 | −0.290666 | −0.145333 | − | 0.989383i | \(-0.546425\pi\) | ||||
−0.145333 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(158\) | −4.63125 | −0.368442 | ||||||||
\(159\) | −0.711393 | −0.0564171 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 11.7039 | 0.919542 | ||||||||
\(163\) | 21.5685 | 1.68938 | 0.844689 | − | 0.535258i | \(-0.179785\pi\) | ||||
0.844689 | + | 0.535258i | \(0.179785\pi\) | |||||||
\(164\) | 6.32250 | 0.493704 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.9532 | −1.08298 | ||||||||
\(167\) | 15.3534 | 1.18809 | 0.594043 | − | 0.804433i | \(-0.297531\pi\) | ||||
0.594043 | + | 0.804433i | \(0.297531\pi\) | |||||||
\(168\) | 0.994007 | 0.0766893 | ||||||||
\(169\) | 7.98581 | 0.614293 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.91114 | −0.452037 | ||||||||
\(172\) | 6.07965 | 0.463569 | ||||||||
\(173\) | 21.6642 | 1.64710 | 0.823548 | − | 0.567246i | \(-0.191991\pi\) | ||||
0.823548 | + | 0.567246i | \(0.191991\pi\) | |||||||
\(174\) | −0.824781 | −0.0625265 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.63917 | −0.123557 | ||||||||
\(177\) | −4.66820 | −0.350884 | ||||||||
\(178\) | −20.0054 | −1.49947 | ||||||||
\(179\) | −11.2083 | −0.837745 | −0.418873 | − | 0.908045i | \(-0.637575\pi\) | ||||
−0.418873 | + | 0.908045i | \(0.637575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.20726 | 0.312723 | 0.156362 | − | 0.987700i | \(-0.450023\pi\) | ||||
0.156362 | + | 0.987700i | \(0.450023\pi\) | |||||||
\(182\) | −7.48196 | −0.554600 | ||||||||
\(183\) | −1.39039 | −0.102781 | ||||||||
\(184\) | −2.17630 | −0.160439 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.25847 | −0.0922754 | ||||||||
\(187\) | 1.13819 | 0.0832330 | ||||||||
\(188\) | 1.57992 | 0.115228 | ||||||||
\(189\) | 2.64517 | 0.192408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4542 | 0.756439 | 0.378219 | − | 0.925716i | \(-0.376537\pi\) | ||||
0.378219 | + | 0.925716i | \(0.376537\pi\) | |||||||
\(192\) | −1.75624 | −0.126746 | ||||||||
\(193\) | −0.207193 | −0.0149141 | −0.00745706 | − | 0.999972i | \(-0.502374\pi\) | ||||
−0.00745706 | + | 0.999972i | \(0.502374\pi\) | |||||||
\(194\) | −2.60040 | −0.186698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.667506 | 0.0476790 | ||||||||
\(197\) | −4.58568 | −0.326716 | −0.163358 | − | 0.986567i | \(-0.552233\pi\) | ||||
−0.163358 | + | 0.986567i | \(0.552233\pi\) | |||||||
\(198\) | −1.52840 | −0.108619 | ||||||||
\(199\) | −17.2299 | −1.22140 | −0.610698 | − | 0.791863i | \(-0.709111\pi\) | ||||
−0.610698 | + | 0.791863i | \(0.709111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.435507 | 0.0307183 | ||||||||
\(202\) | 3.70908 | 0.260970 | ||||||||
\(203\) | 1.10564 | 0.0776009 | ||||||||
\(204\) | −1.03509 | −0.0724708 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −24.4160 | −1.70114 | ||||||||
\(207\) | −2.79139 | −0.194015 | ||||||||
\(208\) | 22.3987 | 1.55307 | ||||||||
\(209\) | 0.709932 | 0.0491070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1367 | −1.59280 | −0.796399 | − | 0.604772i | \(-0.793264\pi\) | ||||
−0.796399 | + | 0.604772i | \(0.793264\pi\) | |||||||
\(212\) | 1.03966 | 0.0714044 | ||||||||
\(213\) | 3.18750 | 0.218404 | ||||||||
\(214\) | 7.96084 | 0.544192 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.75668 | −0.391692 | ||||||||
\(217\) | 1.68701 | 0.114522 | ||||||||
\(218\) | 2.88398 | 0.195328 | ||||||||
\(219\) | −3.30939 | −0.223628 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5530 | −1.04621 | ||||||||
\(222\) | −4.92958 | −0.330852 | ||||||||
\(223\) | −14.2056 | −0.951278 | −0.475639 | − | 0.879641i | \(-0.657783\pi\) | ||||
−0.475639 | + | 0.879641i | \(0.657783\pi\) | |||||||
\(224\) | −3.63310 | −0.242747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.85628 | 0.256516 | ||||||||
\(227\) | −15.8588 | −1.05258 | −0.526291 | − | 0.850304i | \(-0.676418\pi\) | ||||
−0.526291 | + | 0.850304i | \(0.676418\pi\) | |||||||
\(228\) | −0.645622 | −0.0427574 | ||||||||
\(229\) | −1.17836 | −0.0778683 | −0.0389341 | − | 0.999242i | \(-0.512396\pi\) | ||||
−0.0389341 | + | 0.999242i | \(0.512396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.153122 | −0.0100747 | ||||||||
\(232\) | −2.40620 | −0.157975 | ||||||||
\(233\) | 15.3627 | 1.00644 | 0.503220 | − | 0.864158i | \(-0.332148\pi\) | ||||
0.503220 | + | 0.864158i | \(0.332148\pi\) | |||||||
\(234\) | 20.8850 | 1.36530 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.82234 | 0.444097 | ||||||||
\(237\) | 1.29514 | 0.0841284 | ||||||||
\(238\) | 5.54503 | 0.359431 | ||||||||
\(239\) | 11.5814 | 0.749135 | 0.374568 | − | 0.927200i | \(-0.377791\pi\) | ||||
0.374568 | + | 0.927200i | \(0.377791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.18147 | 0.527015 | 0.263508 | − | 0.964657i | \(-0.415121\pi\) | ||||
0.263508 | + | 0.964657i | \(0.415121\pi\) | |||||||
\(242\) | −17.7822 | −1.14308 | ||||||||
\(243\) | −11.2085 | −0.719028 | ||||||||
\(244\) | 2.03199 | 0.130085 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.06575 | −0.450495 | ||||||||
\(247\) | −9.70096 | −0.617257 | ||||||||
\(248\) | −3.67144 | −0.233137 | ||||||||
\(249\) | 3.90204 | 0.247282 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0243 | 0.758964 | 0.379482 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379482 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(252\) | −1.86327 | −0.117375 | ||||||||
\(253\) | 0.335247 | 0.0210768 | ||||||||
\(254\) | 26.0586 | 1.63506 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.4342 | 0.902136 | ||||||||
\(257\) | 6.13850 | 0.382909 | 0.191455 | − | 0.981501i | \(-0.438680\pi\) | ||||
0.191455 | + | 0.981501i | \(0.438680\pi\) | |||||||
\(258\) | −6.79434 | −0.422997 | ||||||||
\(259\) | 6.60823 | 0.410616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.08627 | −0.191036 | ||||||||
\(262\) | −17.1119 | −1.05717 | ||||||||
\(263\) | 14.1956 | 0.875338 | 0.437669 | − | 0.899136i | \(-0.355804\pi\) | ||||
0.437669 | + | 0.899136i | \(0.355804\pi\) | |||||||
\(264\) | 0.333238 | 0.0205094 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.45863 | 0.212062 | ||||||||
\(267\) | 5.59456 | 0.342381 | ||||||||
\(268\) | −0.636472 | −0.0388787 | ||||||||
\(269\) | −7.12319 | −0.434309 | −0.217154 | − | 0.976137i | \(-0.569677\pi\) | ||||
−0.217154 | + | 0.976137i | \(0.569677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.98249 | −0.606393 | −0.303197 | − | 0.952928i | \(-0.598054\pi\) | ||||
−0.303197 | + | 0.952928i | \(0.598054\pi\) | |||||||
\(272\) | −16.6001 | −1.00653 | ||||||||
\(273\) | 2.09235 | 0.126635 | ||||||||
\(274\) | 0.130460 | 0.00788137 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.304879 | −0.0183515 | ||||||||
\(277\) | 23.5355 | 1.41411 | 0.707054 | − | 0.707159i | \(-0.250024\pi\) | ||||
0.707054 | + | 0.707159i | \(0.250024\pi\) | |||||||
\(278\) | 15.0383 | 0.901937 | ||||||||
\(279\) | −4.70910 | −0.281927 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.22319 | −0.251934 | −0.125967 | − | 0.992034i | \(-0.540203\pi\) | ||||
−0.125967 | + | 0.992034i | \(0.540203\pi\) | |||||||
\(282\) | −1.76565 | −0.105143 | ||||||||
\(283\) | 6.96407 | 0.413971 | 0.206985 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206985 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(284\) | −4.65837 | −0.276423 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.50831 | −0.148319 | ||||||||
\(287\) | 9.47182 | 0.559104 | ||||||||
\(288\) | 10.1414 | 0.597587 | ||||||||
\(289\) | −5.47337 | −0.321963 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.727208 | 0.0426297 | ||||||||
\(292\) | 4.83650 | 0.283035 | ||||||||
\(293\) | −6.40853 | −0.374390 | −0.187195 | − | 0.982323i | \(-0.559940\pi\) | ||||
−0.187195 | + | 0.982323i | \(0.559940\pi\) | |||||||
\(294\) | −0.745975 | −0.0435061 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.3815 | −0.835906 | ||||||||
\(297\) | 0.886786 | 0.0514566 | ||||||||
\(298\) | 31.5977 | 1.83041 | ||||||||
\(299\) | −4.58103 | −0.264928 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.10800 | 0.524977 | ||||||||
\(302\) | −3.58813 | −0.206474 | ||||||||
\(303\) | −1.03725 | −0.0595886 | ||||||||
\(304\) | −10.3541 | −0.593847 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.4783 | −0.884837 | ||||||||
\(307\) | −4.62513 | −0.263970 | −0.131985 | − | 0.991252i | \(-0.542135\pi\) | ||||
−0.131985 | + | 0.991252i | \(0.542135\pi\) | |||||||
\(308\) | 0.223779 | 0.0127510 | ||||||||
\(309\) | 6.82800 | 0.388431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.86816 | −0.162638 | −0.0813191 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813191 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(312\) | −4.55357 | −0.257795 | ||||||||
\(313\) | −16.9889 | −0.960267 | −0.480133 | − | 0.877195i | \(-0.659412\pi\) | ||||
−0.480133 | + | 0.877195i | \(0.659412\pi\) | |||||||
\(314\) | −5.94836 | −0.335685 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.89278 | −0.106477 | ||||||||
\(317\) | −3.78249 | −0.212446 | −0.106223 | − | 0.994342i | \(-0.533876\pi\) | ||||
−0.106223 | + | 0.994342i | \(0.533876\pi\) | |||||||
\(318\) | −1.16188 | −0.0651551 | ||||||||
\(319\) | 0.370663 | 0.0207532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.22627 | −0.124258 | ||||||||
\(322\) | 1.63325 | 0.0910175 | ||||||||
\(323\) | 7.18957 | 0.400038 | ||||||||
\(324\) | 4.78335 | 0.265741 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.2268 | 1.95103 | ||||||||
\(327\) | −0.806513 | −0.0446003 | ||||||||
\(328\) | −20.6135 | −1.13819 | ||||||||
\(329\) | 2.36690 | 0.130492 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6540 | −0.970349 | −0.485175 | − | 0.874417i | \(-0.661244\pi\) | ||||
−0.485175 | + | 0.874417i | \(0.661244\pi\) | |||||||
\(332\) | −5.70263 | −0.312973 | ||||||||
\(333\) | −18.4461 | −1.01084 | ||||||||
\(334\) | 25.0760 | 1.37210 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.23322 | 0.121832 | ||||||||
\(337\) | 25.4009 | 1.38367 | 0.691837 | − | 0.722054i | \(-0.256802\pi\) | ||||
0.691837 | + | 0.722054i | \(0.256802\pi\) | |||||||
\(338\) | 13.0428 | 0.709436 | ||||||||
\(339\) | −1.07842 | −0.0585716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.565566 | 0.0306271 | ||||||||
\(342\) | −9.65438 | −0.522049 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −19.8217 | −1.06872 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.3830 | 1.90220 | ||||||||
\(347\) | 6.36913 | 0.341913 | 0.170957 | − | 0.985279i | \(-0.445314\pi\) | ||||
0.170957 | + | 0.985279i | \(0.445314\pi\) | |||||||
\(348\) | −0.337087 | −0.0180697 | ||||||||
\(349\) | −19.9299 | −1.06682 | −0.533411 | − | 0.845856i | \(-0.679090\pi\) | ||||
−0.533411 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.1176 | −0.646790 | ||||||||
\(352\) | −1.21799 | −0.0649189 | ||||||||
\(353\) | 12.6504 | 0.673314 | 0.336657 | − | 0.941627i | \(-0.390704\pi\) | ||||
0.336657 | + | 0.941627i | \(0.390704\pi\) | |||||||
\(354\) | −7.62434 | −0.405229 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.17616 | −0.433336 | ||||||||
\(357\) | −1.55068 | −0.0820708 | ||||||||
\(358\) | −18.3059 | −0.967497 | ||||||||
\(359\) | 15.6866 | 0.827907 | 0.413954 | − | 0.910298i | \(-0.364148\pi\) | ||||
0.413954 | + | 0.910298i | \(0.364148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5156 | −0.763980 | ||||||||
\(362\) | 6.87151 | 0.361159 | ||||||||
\(363\) | 4.97284 | 0.261006 | ||||||||
\(364\) | −3.05786 | −0.160276 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.27086 | −0.118700 | ||||||||
\(367\) | 16.0954 | 0.840171 | 0.420085 | − | 0.907485i | \(-0.362000\pi\) | ||||
0.420085 | + | 0.907485i | \(0.362000\pi\) | |||||||
\(368\) | −4.88945 | −0.254880 | ||||||||
\(369\) | −26.4395 | −1.37639 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.55754 | 0.0808632 | ||||||||
\(372\) | −0.514334 | −0.0266670 | ||||||||
\(373\) | 29.3402 | 1.51918 | 0.759590 | − | 0.650403i | \(-0.225400\pi\) | ||||
0.759590 | + | 0.650403i | \(0.225400\pi\) | |||||||
\(374\) | 1.85895 | 0.0961243 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.15108 | −0.265647 | ||||||||
\(377\) | −5.06498 | −0.260860 | ||||||||
\(378\) | 4.32023 | 0.222209 | ||||||||
\(379\) | −3.56915 | −0.183335 | −0.0916675 | − | 0.995790i | \(-0.529220\pi\) | ||||
−0.0916675 | + | 0.995790i | \(0.529220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.28735 | −0.373342 | ||||||||
\(382\) | 17.0743 | 0.873598 | ||||||||
\(383\) | 14.5600 | 0.743983 | 0.371992 | − | 0.928236i | \(-0.378675\pi\) | ||||
0.371992 | + | 0.928236i | \(0.378675\pi\) | |||||||
\(384\) | −6.18716 | −0.315737 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.338399 | −0.0172240 | ||||||||
\(387\) | −25.4240 | −1.29237 | ||||||||
\(388\) | −1.06278 | −0.0539544 | ||||||||
\(389\) | −27.7276 | −1.40584 | −0.702922 | − | 0.711266i | \(-0.748122\pi\) | ||||
−0.702922 | + | 0.711266i | \(0.748122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.39509 | 0.171697 | ||||||||
\(392\) | −2.17630 | −0.109920 | ||||||||
\(393\) | 4.78538 | 0.241390 | ||||||||
\(394\) | −7.48957 | −0.377319 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.624655 | −0.0313901 | ||||||||
\(397\) | 26.1295 | 1.31140 | 0.655702 | − | 0.755020i | \(-0.272373\pi\) | ||||
0.655702 | + | 0.755020i | \(0.272373\pi\) | |||||||
\(398\) | −28.1408 | −1.41057 | ||||||||
\(399\) | −0.967216 | −0.0484213 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.78796 | −0.139224 | −0.0696121 | − | 0.997574i | \(-0.522176\pi\) | ||||
−0.0696121 | + | 0.997574i | \(0.522176\pi\) | |||||||
\(402\) | 0.711293 | 0.0354761 | ||||||||
\(403\) | −7.72825 | −0.384972 | ||||||||
\(404\) | 1.51589 | 0.0754184 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.80579 | 0.0896199 | ||||||||
\(407\) | 2.21539 | 0.109813 | ||||||||
\(408\) | 3.37474 | 0.167075 | ||||||||
\(409\) | −22.9895 | −1.13676 | −0.568380 | − | 0.822766i | \(-0.692430\pi\) | ||||
−0.568380 | + | 0.822766i | \(0.692430\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0364835 | −0.00179960 | ||||||||
\(412\) | −9.97877 | −0.491619 | ||||||||
\(413\) | 10.2206 | 0.502925 | ||||||||
\(414\) | −4.55903 | −0.224064 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.6433 | 0.816006 | ||||||||
\(417\) | −4.20550 | −0.205944 | ||||||||
\(418\) | 1.15950 | 0.0567128 | ||||||||
\(419\) | −39.9990 | −1.95408 | −0.977038 | − | 0.213064i | \(-0.931656\pi\) | ||||
−0.977038 | + | 0.213064i | \(0.931656\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.4910 | 0.852458 | 0.426229 | − | 0.904615i | \(-0.359842\pi\) | ||||
0.426229 | + | 0.904615i | \(0.359842\pi\) | |||||||
\(422\) | −37.7881 | −1.83949 | ||||||||
\(423\) | −6.60694 | −0.321240 | ||||||||
\(424\) | −3.38966 | −0.164616 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.20599 | 0.252231 | ||||||||
\(427\) | 3.04415 | 0.147317 | ||||||||
\(428\) | 3.25358 | 0.157268 | ||||||||
\(429\) | 0.701454 | 0.0338665 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.5444 | 1.61578 | 0.807889 | − | 0.589335i | \(-0.200610\pi\) | ||||
0.807889 | + | 0.589335i | \(0.200610\pi\) | |||||||
\(432\) | −12.9334 | −0.622260 | ||||||||
\(433\) | −32.2856 | −1.55155 | −0.775773 | − | 0.631012i | \(-0.782640\pi\) | ||||
−0.775773 | + | 0.631012i | \(0.782640\pi\) | |||||||
\(434\) | 2.75531 | 0.132259 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.17868 | 0.0564484 | ||||||||
\(437\) | 2.11764 | 0.101300 | ||||||||
\(438\) | −5.40505 | −0.258263 | ||||||||
\(439\) | 14.0359 | 0.669899 | 0.334950 | − | 0.942236i | \(-0.391281\pi\) | ||||
0.334950 | + | 0.942236i | \(0.391281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.79139 | −0.132923 | ||||||||
\(442\) | −25.4019 | −1.20825 | ||||||||
\(443\) | 8.02107 | 0.381093 | 0.190546 | − | 0.981678i | \(-0.438974\pi\) | ||||
0.190546 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(444\) | −2.01471 | −0.0956138 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.2013 | −1.09861 | ||||||||
\(447\) | −8.83638 | −0.417946 | ||||||||
\(448\) | 3.84513 | 0.181666 | ||||||||
\(449\) | 34.1493 | 1.61161 | 0.805803 | − | 0.592183i | \(-0.201734\pi\) | ||||
0.805803 | + | 0.592183i | \(0.201734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17540 | 0.149524 | ||||||||
\(452\) | 1.57605 | 0.0741313 | ||||||||
\(453\) | 1.00343 | 0.0471453 | ||||||||
\(454\) | −25.9013 | −1.21561 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.10495 | 0.0985732 | ||||||||
\(457\) | 29.6565 | 1.38727 | 0.693637 | − | 0.720325i | \(-0.256007\pi\) | ||||
0.693637 | + | 0.720325i | \(0.256007\pi\) | |||||||
\(458\) | −1.92456 | −0.0899287 | ||||||||
\(459\) | 8.98060 | 0.419179 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4444 | −0.533017 | −0.266509 | − | 0.963833i | \(-0.585870\pi\) | ||||
−0.266509 | + | 0.963833i | \(0.585870\pi\) | |||||||
\(462\) | −0.250086 | −0.0116350 | ||||||||
\(463\) | 38.4089 | 1.78501 | 0.892507 | − | 0.451033i | \(-0.148944\pi\) | ||||
0.892507 | + | 0.451033i | \(0.148944\pi\) | |||||||
\(464\) | −5.40598 | −0.250966 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0911 | 1.16232 | ||||||||
\(467\) | −4.43064 | −0.205026 | −0.102513 | − | 0.994732i | \(-0.532688\pi\) | ||||
−0.102513 | + | 0.994732i | \(0.532688\pi\) | |||||||
\(468\) | 8.53568 | 0.394562 | ||||||||
\(469\) | −0.953507 | −0.0440289 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.66347 | 0.0766488 | ||||||||
\(472\) | −22.2431 | −1.02382 | ||||||||
\(473\) | 3.05343 | 0.140397 | ||||||||
\(474\) | 2.11529 | 0.0971584 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.26624 | 0.103873 | ||||||||
\(477\) | −4.34768 | −0.199067 | ||||||||
\(478\) | 18.9152 | 0.865163 | ||||||||
\(479\) | 0.713525 | 0.0326018 | 0.0163009 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0163009 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.2725 | −1.38031 | ||||||||
\(482\) | 13.3624 | 0.608640 | ||||||||
\(483\) | −0.456743 | −0.0207825 | ||||||||
\(484\) | −7.26755 | −0.330343 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.3063 | −0.830393 | ||||||||
\(487\) | 8.82567 | 0.399929 | 0.199965 | − | 0.979803i | \(-0.435917\pi\) | ||||
0.199965 | + | 0.979803i | \(0.435917\pi\) | |||||||
\(488\) | −6.62497 | −0.299898 | ||||||||
\(489\) | −9.85127 | −0.445490 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.73916 | −0.259005 | −0.129502 | − | 0.991579i | \(-0.541338\pi\) | ||||
−0.129502 | + | 0.991579i | \(0.541338\pi\) | |||||||
\(492\) | −2.88776 | −0.130190 | ||||||||
\(493\) | 3.75375 | 0.169061 | ||||||||
\(494\) | −15.8441 | −0.712859 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.24856 | −0.370371 | ||||||||
\(497\) | −6.97877 | −0.313040 | ||||||||
\(498\) | 6.37301 | 0.285581 | ||||||||
\(499\) | 10.5018 | 0.470123 | 0.235062 | − | 0.971980i | \(-0.424471\pi\) | ||||
0.235062 | + | 0.971980i | \(0.424471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.01258 | −0.313299 | ||||||||
\(502\) | 19.6386 | 0.876515 | ||||||||
\(503\) | −0.988754 | −0.0440864 | −0.0220432 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220432 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(504\) | 6.07488 | 0.270597 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.547542 | 0.0243412 | ||||||||
\(507\) | −3.64746 | −0.161989 | ||||||||
\(508\) | 10.6501 | 0.472521 | ||||||||
\(509\) | −30.2168 | −1.33934 | −0.669668 | − | 0.742661i | \(-0.733564\pi\) | ||||
−0.669668 | + | 0.742661i | \(0.733564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.24562 | 0.320528 | ||||||||
\(512\) | −3.51792 | −0.155472 | ||||||||
\(513\) | 5.60152 | 0.247313 | ||||||||
\(514\) | 10.0257 | 0.442215 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.77683 | −0.122243 | ||||||||
\(517\) | 0.793497 | 0.0348980 | ||||||||
\(518\) | 10.7929 | 0.474213 | ||||||||
\(519\) | −9.89495 | −0.434340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.7415 | 1.04014 | 0.520068 | − | 0.854125i | \(-0.325907\pi\) | ||||
0.520068 | + | 0.854125i | \(0.325907\pi\) | |||||||
\(522\) | −5.04066 | −0.220624 | ||||||||
\(523\) | 30.1770 | 1.31955 | 0.659774 | − | 0.751464i | \(-0.270652\pi\) | ||||
0.659774 | + | 0.751464i | \(0.270652\pi\) | |||||||
\(524\) | −6.99359 | −0.305516 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.1850 | 1.01091 | ||||||||
\(527\) | 5.72756 | 0.249496 | ||||||||
\(528\) | 0.748680 | 0.0325821 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.5298 | −1.23809 | ||||||||
\(532\) | 1.41354 | 0.0612846 | ||||||||
\(533\) | −43.3907 | −1.87946 | ||||||||
\(534\) | 9.13731 | 0.395410 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.07511 | 0.0896313 | ||||||||
\(537\) | 5.11929 | 0.220914 | ||||||||
\(538\) | −11.6340 | −0.501575 | ||||||||
\(539\) | 0.335247 | 0.0144401 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.5534 | 1.35658 | 0.678292 | − | 0.734792i | \(-0.262720\pi\) | ||||
0.678292 | + | 0.734792i | \(0.262720\pi\) | |||||||
\(542\) | −16.3039 | −0.700313 | ||||||||
\(543\) | −1.92164 | −0.0824653 | ||||||||
\(544\) | −12.3347 | −0.528846 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.41733 | 0.146248 | ||||||||
\(547\) | 21.1299 | 0.903449 | 0.451724 | − | 0.892158i | \(-0.350809\pi\) | ||||
0.451724 | + | 0.892158i | \(0.350809\pi\) | |||||||
\(548\) | 0.0533187 | 0.00227766 | ||||||||
\(549\) | −8.49740 | −0.362660 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.34135 | 0.0997448 | ||||||||
\(552\) | 0.994007 | 0.0423078 | ||||||||
\(553\) | −2.83560 | −0.120582 | ||||||||
\(554\) | 38.4393 | 1.63313 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.14612 | 0.260654 | ||||||||
\(557\) | −16.2800 | −0.689807 | −0.344903 | − | 0.938638i | \(-0.612088\pi\) | ||||
−0.344903 | + | 0.938638i | \(0.612088\pi\) | |||||||
\(558\) | −7.69114 | −0.325592 | ||||||||
\(559\) | −41.7240 | −1.76474 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.519862 | −0.0219486 | ||||||||
\(562\) | −6.89752 | −0.290954 | ||||||||
\(563\) | 35.8486 | 1.51084 | 0.755420 | − | 0.655241i | \(-0.227433\pi\) | ||||
0.755420 | + | 0.655241i | \(0.227433\pi\) | |||||||
\(564\) | −0.721618 | −0.0303856 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.3741 | 0.478087 | ||||||||
\(567\) | 7.16599 | 0.300943 | ||||||||
\(568\) | 15.1879 | 0.637269 | ||||||||
\(569\) | −24.9388 | −1.04549 | −0.522745 | − | 0.852489i | \(-0.675092\pi\) | ||||
−0.522745 | + | 0.852489i | \(0.675092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.7684 | −1.45501 | −0.727507 | − | 0.686101i | \(-0.759321\pi\) | ||||
−0.727507 | + | 0.686101i | \(0.759321\pi\) | |||||||
\(572\) | −1.02514 | −0.0428632 | ||||||||
\(573\) | −4.77487 | −0.199473 | ||||||||
\(574\) | 15.4699 | 0.645699 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.7333 | −0.447219 | ||||||||
\(577\) | 5.46961 | 0.227703 | 0.113851 | − | 0.993498i | \(-0.463681\pi\) | ||||
0.113851 | + | 0.993498i | \(0.463681\pi\) | |||||||
\(578\) | −8.93938 | −0.371829 | ||||||||
\(579\) | 0.0946341 | 0.00393286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.54319 | −0.354431 | ||||||||
\(582\) | 1.18771 | 0.0492323 | ||||||||
\(583\) | 0.522159 | 0.0216256 | ||||||||
\(584\) | −15.7686 | −0.652510 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.4667 | −0.432377 | ||||||||
\(587\) | −38.6017 | −1.59326 | −0.796631 | − | 0.604467i | \(-0.793386\pi\) | ||||
−0.796631 | + | 0.604467i | \(0.793386\pi\) | |||||||
\(588\) | −0.304879 | −0.0125730 | ||||||||
\(589\) | 3.57248 | 0.147202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.09448 | 0.0861553 | ||||||||
\(592\) | −32.3106 | −1.32796 | ||||||||
\(593\) | −30.2591 | −1.24259 | −0.621296 | − | 0.783576i | \(-0.713394\pi\) | ||||
−0.621296 | + | 0.783576i | \(0.713394\pi\) | |||||||
\(594\) | 1.44834 | 0.0594263 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9139 | 0.528975 | ||||||||
\(597\) | 7.86964 | 0.322083 | ||||||||
\(598\) | −7.48196 | −0.305960 | ||||||||
\(599\) | −16.9792 | −0.693752 | −0.346876 | − | 0.937911i | \(-0.612758\pi\) | ||||
−0.346876 | + | 0.937911i | \(0.612758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.8894 | 0.484979 | 0.242490 | − | 0.970154i | \(-0.422036\pi\) | ||||
0.242490 | + | 0.970154i | \(0.422036\pi\) | |||||||
\(602\) | 14.8756 | 0.606286 | ||||||||
\(603\) | 2.66161 | 0.108389 | ||||||||
\(604\) | −1.46646 | −0.0596695 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.69409 | −0.0688178 | ||||||||
\(607\) | 22.2307 | 0.902315 | 0.451158 | − | 0.892444i | \(-0.351011\pi\) | ||||
0.451158 | + | 0.892444i | \(0.351011\pi\) | |||||||
\(608\) | −7.69359 | −0.312016 | ||||||||
\(609\) | −0.504994 | −0.0204634 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8428 | −0.438655 | ||||||||
\(612\) | −6.32596 | −0.255712 | ||||||||
\(613\) | 23.5668 | 0.951854 | 0.475927 | − | 0.879485i | \(-0.342113\pi\) | ||||
0.475927 | + | 0.879485i | \(0.342113\pi\) | |||||||
\(614\) | −7.55399 | −0.304854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.729597 | −0.0293963 | ||||||||
\(617\) | −26.9361 | −1.08441 | −0.542204 | − | 0.840247i | \(-0.682410\pi\) | ||||
−0.542204 | + | 0.840247i | \(0.682410\pi\) | |||||||
\(618\) | 11.1518 | 0.448592 | ||||||||
\(619\) | −16.7211 | −0.672078 | −0.336039 | − | 0.941848i | \(-0.609087\pi\) | ||||
−0.336039 | + | 0.941848i | \(0.609087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.64517 | 0.106147 | ||||||||
\(622\) | −4.68442 | −0.187828 | ||||||||
\(623\) | −12.2488 | −0.490738 | ||||||||
\(624\) | −10.2304 | −0.409545 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.7470 | −1.10900 | ||||||||
\(627\) | −0.324256 | −0.0129495 | ||||||||
\(628\) | −2.43108 | −0.0970107 | ||||||||
\(629\) | 22.4355 | 0.894564 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.7787 | −1.06604 | −0.533021 | − | 0.846102i | \(-0.678943\pi\) | ||||
−0.533021 | + | 0.846102i | \(0.678943\pi\) | |||||||
\(632\) | 6.17111 | 0.245474 | ||||||||
\(633\) | 10.5675 | 0.420022 | ||||||||
\(634\) | −6.17775 | −0.245350 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.474859 | −0.0188294 | ||||||||
\(637\) | −4.58103 | −0.181507 | ||||||||
\(638\) | 0.605386 | 0.0239675 | ||||||||
\(639\) | 19.4804 | 0.770634 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.6757 | 1.96207 | 0.981036 | − | 0.193825i | \(-0.0620893\pi\) | ||||
0.981036 | + | 0.193825i | \(0.0620893\pi\) | |||||||
\(642\) | −3.63605 | −0.143504 | ||||||||
\(643\) | −36.3622 | −1.43399 | −0.716993 | − | 0.697080i | \(-0.754482\pi\) | ||||
−0.716993 | + | 0.697080i | \(0.754482\pi\) | |||||||
\(644\) | 0.667506 | 0.0263034 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.7424 | 0.461997 | ||||||||
\(647\) | 10.2239 | 0.401943 | 0.200971 | − | 0.979597i | \(-0.435590\pi\) | ||||
0.200971 | + | 0.979597i | \(0.435590\pi\) | |||||||
\(648\) | −15.5953 | −0.612642 | ||||||||
\(649\) | 3.42644 | 0.134500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.770530 | −0.0301995 | ||||||||
\(652\) | 14.3971 | 0.563835 | ||||||||
\(653\) | 6.87794 | 0.269155 | 0.134577 | − | 0.990903i | \(-0.457032\pi\) | ||||
0.134577 | + | 0.990903i | \(0.457032\pi\) | |||||||
\(654\) | −1.31724 | −0.0515080 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −46.3120 | −1.80818 | ||||||||
\(657\) | −20.2253 | −0.789065 | ||||||||
\(658\) | 3.86574 | 0.150702 | ||||||||
\(659\) | −14.2426 | −0.554812 | −0.277406 | − | 0.960753i | \(-0.589475\pi\) | ||||
−0.277406 | + | 0.960753i | \(0.589475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1642 | 0.628714 | 0.314357 | − | 0.949305i | \(-0.398211\pi\) | ||||
0.314357 | + | 0.949305i | \(0.398211\pi\) | |||||||
\(662\) | −28.8333 | −1.12064 | ||||||||
\(663\) | 7.10372 | 0.275886 | ||||||||
\(664\) | 18.5925 | 0.721530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −30.1272 | −1.16740 | ||||||||
\(667\) | 1.10564 | 0.0428106 | ||||||||
\(668\) | 10.2485 | 0.396527 | ||||||||
\(669\) | 6.48831 | 0.250853 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.02054 | 0.0393976 | ||||||||
\(672\) | 1.65939 | 0.0640124 | ||||||||
\(673\) | −1.76184 | −0.0679140 | −0.0339570 | − | 0.999423i | \(-0.510811\pi\) | ||||
−0.0339570 | + | 0.999423i | \(0.510811\pi\) | |||||||
\(674\) | 41.4860 | 1.59798 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.33058 | 0.205022 | ||||||||
\(677\) | 4.98819 | 0.191712 | 0.0958560 | − | 0.995395i | \(-0.469441\pi\) | ||||
0.0958560 | + | 0.995395i | \(0.469441\pi\) | |||||||
\(678\) | −1.76133 | −0.0676433 | ||||||||
\(679\) | −1.59216 | −0.0611016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.24337 | 0.277567 | ||||||||
\(682\) | 0.923710 | 0.0353707 | ||||||||
\(683\) | −22.5273 | −0.861983 | −0.430992 | − | 0.902356i | \(-0.641836\pi\) | ||||
−0.430992 | + | 0.902356i | \(0.641836\pi\) | |||||||
\(684\) | −3.94572 | −0.150869 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.63325 | 0.0623578 | ||||||||
\(687\) | 0.538208 | 0.0205339 | ||||||||
\(688\) | −44.5331 | −1.69781 | ||||||||
\(689\) | −7.13511 | −0.271826 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.35936 | −0.203880 | −0.101940 | − | 0.994791i | \(-0.532505\pi\) | ||||
−0.101940 | + | 0.994791i | \(0.532505\pi\) | |||||||
\(692\) | 14.4610 | 0.549723 | ||||||||
\(693\) | −0.935804 | −0.0355482 | ||||||||
\(694\) | 10.4024 | 0.394869 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.09902 | 0.0416581 | ||||||||
\(697\) | 32.1577 | 1.21806 | ||||||||
\(698\) | −32.5505 | −1.23205 | ||||||||
\(699\) | −7.01678 | −0.265399 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.7698 | −1.53985 | −0.769927 | − | 0.638132i | \(-0.779707\pi\) | ||||
−0.769927 | + | 0.638132i | \(0.779707\pi\) | |||||||
\(702\) | −19.7911 | −0.746967 | ||||||||
\(703\) | 13.9938 | 0.527788 | ||||||||
\(704\) | 1.28907 | 0.0485837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.6613 | 0.777598 | ||||||||
\(707\) | 2.27098 | 0.0854089 | ||||||||
\(708\) | −3.11605 | −0.117109 | ||||||||
\(709\) | −4.52746 | −0.170032 | −0.0850161 | − | 0.996380i | \(-0.527094\pi\) | ||||
−0.0850161 | + | 0.996380i | \(0.527094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.91526 | 0.296845 | ||||||||
\(712\) | 26.6570 | 0.999015 | ||||||||
\(713\) | 1.68701 | 0.0631791 | ||||||||
\(714\) | −2.53265 | −0.0947821 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.48159 | −0.279600 | ||||||||
\(717\) | −5.28970 | −0.197547 | ||||||||
\(718\) | 25.6201 | 0.956135 | ||||||||
\(719\) | −14.6162 | −0.545092 | −0.272546 | − | 0.962143i | \(-0.587866\pi\) | ||||
−0.272546 | + | 0.962143i | \(0.587866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.9493 | −0.556742 | ||||||||
\(722\) | −23.7076 | −0.882306 | ||||||||
\(723\) | −3.73683 | −0.138974 | ||||||||
\(724\) | 2.80837 | 0.104372 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.12189 | 0.301431 | ||||||||
\(727\) | 4.65173 | 0.172523 | 0.0862616 | − | 0.996273i | \(-0.472508\pi\) | ||||
0.0862616 | + | 0.996273i | \(0.472508\pi\) | |||||||
\(728\) | 9.96967 | 0.369501 | ||||||||
\(729\) | −16.3786 | −0.606614 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.9225 | 1.14371 | ||||||||
\(732\) | −0.928096 | −0.0343034 | ||||||||
\(733\) | −44.5812 | −1.64664 | −0.823321 | − | 0.567575i | \(-0.807882\pi\) | ||||
−0.823321 | + | 0.567575i | \(0.807882\pi\) | |||||||
\(734\) | 26.2877 | 0.970298 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.63310 | −0.133918 | ||||||||
\(737\) | −0.319660 | −0.0117748 | ||||||||
\(738\) | −43.1824 | −1.58956 | ||||||||
\(739\) | 2.50482 | 0.0921412 | 0.0460706 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460706 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.43084 | 0.162771 | ||||||||
\(742\) | 2.54385 | 0.0933875 | ||||||||
\(743\) | −8.92060 | −0.327265 | −0.163632 | − | 0.986521i | \(-0.552321\pi\) | ||||
−0.163632 | + | 0.986521i | \(0.552321\pi\) | |||||||
\(744\) | 1.67690 | 0.0614782 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 47.9199 | 1.75447 | ||||||||
\(747\) | 23.8474 | 0.872529 | ||||||||
\(748\) | 0.759751 | 0.0277793 | ||||||||
\(749\) | 4.87423 | 0.178100 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.3798 | 1.76540 | 0.882701 | − | 0.469934i | \(-0.155722\pi\) | ||||
0.882701 | + | 0.469934i | \(0.155722\pi\) | |||||||
\(752\) | −11.5728 | −0.422018 | ||||||||
\(753\) | −5.49199 | −0.200139 | ||||||||
\(754\) | −8.27237 | −0.301262 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.76567 | 0.0642168 | ||||||||
\(757\) | 11.2483 | 0.408825 | 0.204412 | − | 0.978885i | \(-0.434472\pi\) | ||||
0.204412 | + | 0.978885i | \(0.434472\pi\) | |||||||
\(758\) | −5.82931 | −0.211730 | ||||||||
\(759\) | −0.153122 | −0.00555796 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.84600 | 0.211917 | 0.105959 | − | 0.994371i | \(-0.466209\pi\) | ||||
0.105959 | + | 0.994371i | \(0.466209\pi\) | |||||||
\(762\) | −11.9021 | −0.431166 | ||||||||
\(763\) | 1.76579 | 0.0639260 | ||||||||
\(764\) | 6.97824 | 0.252464 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.7802 | 0.859213 | ||||||||
\(767\) | −46.8210 | −1.69061 | ||||||||
\(768\) | −6.59270 | −0.237894 | ||||||||
\(769\) | −31.2618 | −1.12733 | −0.563664 | − | 0.826004i | \(-0.690609\pi\) | ||||
−0.563664 | + | 0.826004i | \(0.690609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.80371 | −0.100973 | ||||||||
\(772\) | −0.138303 | −0.00497763 | ||||||||
\(773\) | −37.3451 | −1.34321 | −0.671605 | − | 0.740910i | \(-0.734395\pi\) | ||||
−0.671605 | + | 0.740910i | \(0.734395\pi\) | |||||||
\(774\) | −41.5237 | −1.49254 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.46502 | 0.124387 | ||||||||
\(777\) | −3.01826 | −0.108280 | ||||||||
\(778\) | −45.2861 | −1.62359 | ||||||||
\(779\) | 20.0579 | 0.718649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.33961 | −0.0837179 | ||||||||
\(782\) | 5.54503 | 0.198290 | ||||||||
\(783\) | 2.92461 | 0.104517 | ||||||||
\(784\) | −4.88945 | −0.174623 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.81572 | 0.278778 | ||||||||
\(787\) | 16.6878 | 0.594856 | 0.297428 | − | 0.954744i | \(-0.403871\pi\) | ||||
0.297428 | + | 0.954744i | \(0.403871\pi\) | |||||||
\(788\) | −3.06097 | −0.109043 | ||||||||
\(789\) | −6.48373 | −0.230827 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.36111 | 0.0839513 | ||||||||
\(792\) | 2.03659 | 0.0723669 | ||||||||
\(793\) | −13.9453 | −0.495213 | ||||||||
\(794\) | 42.6761 | 1.51452 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5011 | −0.407645 | ||||||||
\(797\) | −49.9631 | −1.76978 | −0.884892 | − | 0.465796i | \(-0.845768\pi\) | ||||
−0.884892 | + | 0.465796i | \(0.845768\pi\) | |||||||
\(798\) | −1.57970 | −0.0559209 | ||||||||
\(799\) | 8.03585 | 0.284288 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.1912 | 1.20809 | ||||||||
\(802\) | −4.55344 | −0.160788 | ||||||||
\(803\) | 2.42907 | 0.0857201 | ||||||||
\(804\) | 0.290704 | 0.0102523 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.6222 | −0.444597 | ||||||||
\(807\) | 3.25347 | 0.114527 | ||||||||
\(808\) | −4.94232 | −0.173870 | ||||||||
\(809\) | −26.2425 | −0.922635 | −0.461318 | − | 0.887235i | \(-0.652623\pi\) | ||||
−0.461318 | + | 0.887235i | \(0.652623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.59171 | −0.0910074 | −0.0455037 | − | 0.998964i | \(-0.514489\pi\) | ||||
−0.0455037 | + | 0.998964i | \(0.514489\pi\) | |||||||
\(812\) | 0.738023 | 0.0258995 | ||||||||
\(813\) | 4.55943 | 0.159906 | ||||||||
\(814\) | 3.61829 | 0.126821 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.58198 | 0.265422 | ||||||||
\(817\) | 19.2875 | 0.674783 | ||||||||
\(818\) | −37.5477 | −1.31282 | ||||||||
\(819\) | 12.7874 | 0.446828 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.49572 | 0.226702 | 0.113351 | − | 0.993555i | \(-0.463842\pi\) | ||||
0.113351 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(822\) | −0.0595866 | −0.00207832 | ||||||||
\(823\) | 8.51260 | 0.296731 | 0.148365 | − | 0.988933i | \(-0.452599\pi\) | ||||
0.148365 | + | 0.988933i | \(0.452599\pi\) | |||||||
\(824\) | 32.5342 | 1.13338 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.6929 | 0.580819 | ||||||||
\(827\) | 4.09417 | 0.142368 | 0.0711842 | − | 0.997463i | \(-0.477322\pi\) | ||||
0.0711842 | + | 0.997463i | \(0.477322\pi\) | |||||||
\(828\) | −1.86327 | −0.0647530 | ||||||||
\(829\) | −24.1706 | −0.839481 | −0.419740 | − | 0.907644i | \(-0.637879\pi\) | ||||
−0.419740 | + | 0.907644i | \(0.637879\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.7496 | −0.372901 | ||||||||
\(832\) | −17.6147 | −0.610679 | ||||||||
\(833\) | 3.39509 | 0.117633 | ||||||||
\(834\) | −6.86863 | −0.237841 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.473884 | 0.0163896 | ||||||||
\(837\) | 4.46244 | 0.154244 | ||||||||
\(838\) | −65.3283 | −2.25673 | ||||||||
\(839\) | 22.7688 | 0.786066 | 0.393033 | − | 0.919524i | \(-0.371426\pi\) | ||||
0.393033 | + | 0.919524i | \(0.371426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7776 | −0.957847 | ||||||||
\(842\) | 28.5671 | 0.984489 | ||||||||
\(843\) | 1.92891 | 0.0664352 | ||||||||
\(844\) | −15.4439 | −0.531601 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.7908 | −0.370995 | ||||||||
\(847\) | −10.8876 | −0.374103 | ||||||||
\(848\) | −7.61549 | −0.261517 | ||||||||
\(849\) | −3.18079 | −0.109164 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.60823 | 0.226527 | ||||||||
\(852\) | 2.12768 | 0.0728930 | ||||||||
\(853\) | −43.9698 | −1.50550 | −0.752749 | − | 0.658308i | \(-0.771273\pi\) | ||||
−0.752749 | + | 0.658308i | \(0.771273\pi\) | |||||||
\(854\) | 4.97186 | 0.170134 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6078 | −0.362566 | ||||||||
\(857\) | 6.03103 | 0.206016 | 0.103008 | − | 0.994681i | \(-0.467153\pi\) | ||||
0.103008 | + | 0.994681i | \(0.467153\pi\) | |||||||
\(858\) | 1.14565 | 0.0391119 | ||||||||
\(859\) | −20.2416 | −0.690636 | −0.345318 | − | 0.938486i | \(-0.612229\pi\) | ||||
−0.345318 | + | 0.938486i | \(0.612229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.32619 | −0.147436 | ||||||||
\(862\) | 54.7864 | 1.86603 | ||||||||
\(863\) | −41.6744 | −1.41861 | −0.709307 | − | 0.704900i | \(-0.750992\pi\) | ||||
−0.709307 | + | 0.704900i | \(0.750992\pi\) | |||||||
\(864\) | −9.61018 | −0.326945 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −52.7304 | −1.79185 | ||||||||
\(867\) | 2.49992 | 0.0849017 | ||||||||
\(868\) | 1.12609 | 0.0382220 | ||||||||
\(869\) | −0.950627 | −0.0322478 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.36804 | 0.148005 | ||||||||
\(872\) | −3.84289 | −0.130137 | ||||||||
\(873\) | 4.44434 | 0.150418 | ||||||||
\(874\) | 3.45863 | 0.116990 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.20904 | −0.0746364 | ||||||||
\(877\) | 56.0744 | 1.89350 | 0.946749 | − | 0.321973i | \(-0.104346\pi\) | ||||
0.946749 | + | 0.321973i | \(0.104346\pi\) | |||||||
\(878\) | 22.9242 | 0.773655 | ||||||||
\(879\) | 2.92705 | 0.0987269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.7638 | 1.00277 | 0.501385 | − | 0.865225i | \(-0.332824\pi\) | ||||
0.501385 | + | 0.865225i | \(0.332824\pi\) | |||||||
\(882\) | −4.55903 | −0.153511 | ||||||||
\(883\) | −10.5038 | −0.353482 | −0.176741 | − | 0.984257i | \(-0.556555\pi\) | ||||
−0.176741 | + | 0.984257i | \(0.556555\pi\) | |||||||
\(884\) | −10.3817 | −0.349175 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.1004 | 0.440117 | ||||||||
\(887\) | −48.7845 | −1.63802 | −0.819012 | − | 0.573777i | \(-0.805478\pi\) | ||||
−0.819012 | + | 0.573777i | \(0.805478\pi\) | |||||||
\(888\) | 6.56863 | 0.220429 | ||||||||
\(889\) | 15.9550 | 0.535115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.40238 | 0.0804827 | ||||||||
\(892\) | −9.48233 | −0.317492 | ||||||||
\(893\) | 5.01224 | 0.167728 | ||||||||
\(894\) | −14.4320 | −0.482679 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.5463 | 0.452549 | ||||||||
\(897\) | 2.09235 | 0.0698616 | ||||||||
\(898\) | 55.7744 | 1.86122 | ||||||||
\(899\) | 1.86523 | 0.0622090 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.28797 | 0.176168 | ||||||||
\(902\) | 5.18622 | 0.172682 | ||||||||
\(903\) | −4.16001 | −0.138437 | ||||||||
\(904\) | −5.13846 | −0.170903 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.63885 | 0.0544473 | ||||||||
\(907\) | −1.62527 | −0.0539664 | −0.0269832 | − | 0.999636i | \(-0.508590\pi\) | ||||
−0.0269832 | + | 0.999636i | \(0.508590\pi\) | |||||||
\(908\) | −10.5858 | −0.351303 | ||||||||
\(909\) | −6.33918 | −0.210257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8739 | −0.393401 | −0.196700 | − | 0.980464i | \(-0.563023\pi\) | ||||
−0.196700 | + | 0.980464i | \(0.563023\pi\) | |||||||
\(912\) | 4.72915 | 0.156598 | ||||||||
\(913\) | −2.86408 | −0.0947872 | ||||||||
\(914\) | 48.4365 | 1.60214 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.786563 | −0.0259888 | ||||||||
\(917\) | −10.4772 | −0.345987 | ||||||||
\(918\) | 14.6676 | 0.484102 | ||||||||
\(919\) | −18.9944 | −0.626568 | −0.313284 | − | 0.949659i | \(-0.601429\pi\) | ||||
−0.313284 | + | 0.949659i | \(0.601429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.11249 | 0.0696090 | ||||||||
\(922\) | −18.6915 | −0.615572 | ||||||||
\(923\) | 31.9699 | 1.05230 | ||||||||
\(924\) | −0.102210 | −0.00336245 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 62.7314 | 2.06148 | ||||||||
\(927\) | 41.7294 | 1.37057 | ||||||||
\(928\) | −4.01691 | −0.131861 | ||||||||
\(929\) | 56.1778 | 1.84313 | 0.921567 | − | 0.388218i | \(-0.126909\pi\) | ||||
0.921567 | + | 0.388218i | \(0.126909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.11764 | 0.0694028 | ||||||||
\(932\) | 10.2547 | 0.335903 | ||||||||
\(933\) | 1.31001 | 0.0428878 | ||||||||
\(934\) | −7.23635 | −0.236781 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −27.8292 | −0.909626 | ||||||||
\(937\) | 50.1197 | 1.63734 | 0.818669 | − | 0.574266i | \(-0.194712\pi\) | ||||
0.818669 | + | 0.574266i | \(0.194712\pi\) | |||||||
\(938\) | −1.55732 | −0.0508482 | ||||||||
\(939\) | 7.75953 | 0.253223 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.0121 | 0.521979 | 0.260989 | − | 0.965342i | \(-0.415951\pi\) | ||||
0.260989 | + | 0.965342i | \(0.415951\pi\) | |||||||
\(942\) | 2.71687 | 0.0885203 | ||||||||
\(943\) | 9.47182 | 0.308445 | ||||||||
\(944\) | −49.9733 | −1.62649 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.98702 | 0.162142 | ||||||||
\(947\) | 47.0892 | 1.53019 | 0.765097 | − | 0.643915i | \(-0.222691\pi\) | ||||
0.765097 | + | 0.643915i | \(0.222691\pi\) | |||||||
\(948\) | 0.864514 | 0.0280781 | ||||||||
\(949\) | −33.1924 | −1.07747 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.72762 | 0.0560220 | ||||||||
\(952\) | −7.38872 | −0.239470 | ||||||||
\(953\) | −38.3796 | −1.24324 | −0.621618 | − | 0.783320i | \(-0.713524\pi\) | ||||
−0.621618 | + | 0.783320i | \(0.713524\pi\) | |||||||
\(954\) | −7.10085 | −0.229899 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.73062 | 0.250026 | ||||||||
\(957\) | −0.169298 | −0.00547262 | ||||||||
\(958\) | 1.16536 | 0.0376512 | ||||||||
\(959\) | 0.0798775 | 0.00257938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.1540 | −0.908193 | ||||||||
\(962\) | −49.4426 | −1.59409 | ||||||||
\(963\) | −13.6059 | −0.438443 | ||||||||
\(964\) | 5.46118 | 0.175893 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.745975 | −0.0240014 | ||||||||
\(967\) | 14.8104 | 0.476272 | 0.238136 | − | 0.971232i | \(-0.423464\pi\) | ||||
0.238136 | + | 0.971232i | \(0.423464\pi\) | |||||||
\(968\) | 23.6947 | 0.761575 | ||||||||
\(969\) | −3.28378 | −0.105490 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.1730 | 0.936205 | 0.468102 | − | 0.883674i | \(-0.344938\pi\) | ||||
0.468102 | + | 0.883674i | \(0.344938\pi\) | |||||||
\(972\) | −7.48177 | −0.239978 | ||||||||
\(973\) | 9.20759 | 0.295182 | ||||||||
\(974\) | 14.4145 | 0.461871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.8842 | −0.476432 | ||||||||
\(977\) | −49.0835 | −1.57032 | −0.785161 | − | 0.619292i | \(-0.787420\pi\) | ||||
−0.785161 | + | 0.619292i | \(0.787420\pi\) | |||||||
\(978\) | −16.0896 | −0.514488 | ||||||||
\(979\) | −4.10638 | −0.131240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.92901 | −0.157371 | ||||||||
\(982\) | −9.37348 | −0.299120 | ||||||||
\(983\) | 27.9923 | 0.892815 | 0.446408 | − | 0.894830i | \(-0.352703\pi\) | ||||
0.446408 | + | 0.894830i | \(0.352703\pi\) | |||||||
\(984\) | 9.41506 | 0.300141 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.13082 | 0.195245 | ||||||||
\(987\) | −1.08107 | −0.0344107 | ||||||||
\(988\) | −6.47545 | −0.206011 | ||||||||
\(989\) | 9.10800 | 0.289618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.1269 | 1.68763 | 0.843816 | − | 0.536633i | \(-0.180304\pi\) | ||||
0.843816 | + | 0.536633i | \(0.180304\pi\) | |||||||
\(992\) | −6.12908 | −0.194599 | ||||||||
\(993\) | 8.06332 | 0.255882 | ||||||||
\(994\) | −11.3981 | −0.361525 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.60464 | 0.0825311 | ||||||||
\(997\) | −28.9207 | −0.915928 | −0.457964 | − | 0.888971i | \(-0.651421\pi\) | ||||
−0.457964 | + | 0.888971i | \(0.651421\pi\) | |||||||
\(998\) | 17.1520 | 0.542937 | ||||||||
\(999\) | 17.4799 | 0.553040 |
(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 | 4025.2.a.bc.1.11 | yes | 14 | |
5.4 | even | 2 | 4025.2.a.z.1.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.z.1.4 | ✓ | 14 | 5.4 | even | 2 | ||
4025.2.a.bc.1.11 | yes | 14 | 1.1 | even | 1 | trivial |