Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(1,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.15883 | −1.41267 | −0.706337 | − | 0.707876i | \(-0.749654\pi\) | ||||
−0.706337 | + | 0.707876i | \(0.749654\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.69202 | −1.77342 | −0.886709 | − | 0.462329i | \(-0.847014\pi\) | ||||
−0.886709 | + | 0.462329i | \(0.847014\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.15883 | 0.998911 | ||||||||
\(11\) | 0.137063 | 0.0413262 | 0.0206631 | − | 0.999786i | \(-0.493422\pi\) | ||||
0.0206631 | + | 0.999786i | \(0.493422\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.69202 | 1.25400 | ||||||||
\(15\) | 3.15883 | 0.815607 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.60388 | −1.35914 | −0.679570 | − | 0.733611i | \(-0.737833\pi\) | ||||
−0.679570 | + | 0.733611i | \(0.737833\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.98792 | −1.14431 | −0.572153 | − | 0.820147i | \(-0.693892\pi\) | ||||
−0.572153 | + | 0.820147i | \(0.693892\pi\) | |||||||
\(20\) | −3.15883 | −0.706337 | ||||||||
\(21\) | 4.69202 | 1.02388 | ||||||||
\(22\) | −0.137063 | −0.0292220 | ||||||||
\(23\) | −6.09783 | −1.27149 | −0.635743 | − | 0.771901i | \(-0.719306\pi\) | ||||
−0.635743 | + | 0.771901i | \(0.719306\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.97823 | 0.995646 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.69202 | −0.886709 | ||||||||
\(29\) | −0.850855 | −0.158000 | −0.0789999 | − | 0.996875i | \(-0.525173\pi\) | ||||
−0.0789999 | + | 0.996875i | \(0.525173\pi\) | |||||||
\(30\) | −3.15883 | −0.576721 | ||||||||
\(31\) | 6.23490 | 1.11982 | 0.559910 | − | 0.828553i | \(-0.310836\pi\) | ||||
0.559910 | + | 0.828553i | \(0.310836\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.137063 | −0.0238597 | ||||||||
\(34\) | 5.60388 | 0.961057 | ||||||||
\(35\) | 14.8213 | 2.50526 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.7017 | 1.92375 | 0.961875 | − | 0.273491i | \(-0.0881783\pi\) | ||||
0.961875 | + | 0.273491i | \(0.0881783\pi\) | |||||||
\(38\) | 4.98792 | 0.809147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.15883 | 0.499455 | ||||||||
\(41\) | −4.27413 | −0.667506 | −0.333753 | − | 0.942660i | \(-0.608315\pi\) | ||||
−0.333753 | + | 0.942660i | \(0.608315\pi\) | |||||||
\(42\) | −4.69202 | −0.723995 | ||||||||
\(43\) | −2.09783 | −0.319917 | −0.159958 | − | 0.987124i | \(-0.551136\pi\) | ||||
−0.159958 | + | 0.987124i | \(0.551136\pi\) | |||||||
\(44\) | 0.137063 | 0.0206631 | ||||||||
\(45\) | −3.15883 | −0.470891 | ||||||||
\(46\) | 6.09783 | 0.899077 | ||||||||
\(47\) | 4.98792 | 0.727563 | 0.363781 | − | 0.931484i | \(-0.381486\pi\) | ||||
0.363781 | + | 0.931484i | \(0.381486\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 15.0151 | 2.14501 | ||||||||
\(50\) | −4.97823 | −0.704028 | ||||||||
\(51\) | 5.60388 | 0.784700 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.82908 | −0.251244 | −0.125622 | − | 0.992078i | \(-0.540093\pi\) | ||||
−0.125622 | + | 0.992078i | \(0.540093\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.432960 | −0.0583804 | ||||||||
\(56\) | 4.69202 | 0.626998 | ||||||||
\(57\) | 4.98792 | 0.660666 | ||||||||
\(58\) | 0.850855 | 0.111723 | ||||||||
\(59\) | −5.89977 | −0.768085 | −0.384042 | − | 0.923315i | \(-0.625468\pi\) | ||||
−0.384042 | + | 0.923315i | \(0.625468\pi\) | |||||||
\(60\) | 3.15883 | 0.407804 | ||||||||
\(61\) | 4.39612 | 0.562866 | 0.281433 | − | 0.959581i | \(-0.409190\pi\) | ||||
0.281433 | + | 0.959581i | \(0.409190\pi\) | |||||||
\(62\) | −6.23490 | −0.791833 | ||||||||
\(63\) | −4.69202 | −0.591139 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.137063 | 0.0168713 | ||||||||
\(67\) | −4.71379 | −0.575881 | −0.287941 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287941 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(68\) | −5.60388 | −0.679570 | ||||||||
\(69\) | 6.09783 | 0.734093 | ||||||||
\(70\) | −14.8213 | −1.77149 | ||||||||
\(71\) | −0.0978347 | −0.0116108 | −0.00580542 | − | 0.999983i | \(-0.501848\pi\) | ||||
−0.00580542 | + | 0.999983i | \(0.501848\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.32304 | −0.271892 | −0.135946 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135946 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(74\) | −11.7017 | −1.36030 | ||||||||
\(75\) | −4.97823 | −0.574836 | ||||||||
\(76\) | −4.98792 | −0.572153 | ||||||||
\(77\) | −0.643104 | −0.0732885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5157 | 1.63315 | 0.816574 | − | 0.577241i | \(-0.195871\pi\) | ||||
0.816574 | + | 0.577241i | \(0.195871\pi\) | |||||||
\(80\) | −3.15883 | −0.353168 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.27413 | 0.471998 | ||||||||
\(83\) | −9.85623 | −1.08186 | −0.540931 | − | 0.841067i | \(-0.681928\pi\) | ||||
−0.540931 | + | 0.841067i | \(0.681928\pi\) | |||||||
\(84\) | 4.69202 | 0.511942 | ||||||||
\(85\) | 17.7017 | 1.92002 | ||||||||
\(86\) | 2.09783 | 0.226215 | ||||||||
\(87\) | 0.850855 | 0.0912212 | ||||||||
\(88\) | −0.137063 | −0.0146110 | ||||||||
\(89\) | 17.0858 | 1.81109 | 0.905543 | − | 0.424254i | \(-0.139464\pi\) | ||||
0.905543 | + | 0.424254i | \(0.139464\pi\) | |||||||
\(90\) | 3.15883 | 0.332970 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.09783 | −0.635743 | ||||||||
\(93\) | −6.23490 | −0.646529 | ||||||||
\(94\) | −4.98792 | −0.514465 | ||||||||
\(95\) | 15.7560 | 1.61653 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 2.12737 | 0.216002 | 0.108001 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108001 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(98\) | −15.0151 | −1.51675 | ||||||||
\(99\) | 0.137063 | 0.0137754 | ||||||||
\(100\) | 4.97823 | 0.497823 | ||||||||
\(101\) | −9.18598 | −0.914039 | −0.457020 | − | 0.889457i | \(-0.651083\pi\) | ||||
−0.457020 | + | 0.889457i | \(0.651083\pi\) | |||||||
\(102\) | −5.60388 | −0.554866 | ||||||||
\(103\) | 0.225209 | 0.0221905 | 0.0110953 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110953 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.8213 | −1.44641 | ||||||||
\(106\) | 1.82908 | 0.177656 | ||||||||
\(107\) | 11.2838 | 1.09085 | 0.545424 | − | 0.838160i | \(-0.316369\pi\) | ||||
0.545424 | + | 0.838160i | \(0.316369\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.195669 | −0.0187417 | −0.00937086 | − | 0.999956i | \(-0.502983\pi\) | ||||
−0.00937086 | + | 0.999956i | \(0.502983\pi\) | |||||||
\(110\) | 0.432960 | 0.0412811 | ||||||||
\(111\) | −11.7017 | −1.11068 | ||||||||
\(112\) | −4.69202 | −0.443354 | ||||||||
\(113\) | −0.439665 | −0.0413602 | −0.0206801 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206801 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(114\) | −4.98792 | −0.467161 | ||||||||
\(115\) | 19.2620 | 1.79619 | ||||||||
\(116\) | −0.850855 | −0.0789999 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.89977 | 0.543118 | ||||||||
\(119\) | 26.2935 | 2.41032 | ||||||||
\(120\) | −3.15883 | −0.288361 | ||||||||
\(121\) | −10.9812 | −0.998292 | ||||||||
\(122\) | −4.39612 | −0.398006 | ||||||||
\(123\) | 4.27413 | 0.385385 | ||||||||
\(124\) | 6.23490 | 0.559910 | ||||||||
\(125\) | 0.0687686 | 0.00615085 | ||||||||
\(126\) | 4.69202 | 0.417998 | ||||||||
\(127\) | −7.87263 | −0.698583 | −0.349291 | − | 0.937014i | \(-0.613578\pi\) | ||||
−0.349291 | + | 0.937014i | \(0.613578\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.09783 | 0.184704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.621334 | −0.0542862 | −0.0271431 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271431 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(132\) | −0.137063 | −0.0119298 | ||||||||
\(133\) | 23.4034 | 2.02933 | ||||||||
\(134\) | 4.71379 | 0.407210 | ||||||||
\(135\) | 3.15883 | 0.271869 | ||||||||
\(136\) | 5.60388 | 0.480528 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | −6.09783 | −0.519082 | ||||||||
\(139\) | −13.6582 | −1.15847 | −0.579235 | − | 0.815160i | \(-0.696649\pi\) | ||||
−0.579235 | + | 0.815160i | \(0.696649\pi\) | |||||||
\(140\) | 14.8213 | 1.25263 | ||||||||
\(141\) | −4.98792 | −0.420059 | ||||||||
\(142\) | 0.0978347 | 0.00821010 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.68771 | 0.223202 | ||||||||
\(146\) | 2.32304 | 0.192256 | ||||||||
\(147\) | −15.0151 | −1.23842 | ||||||||
\(148\) | 11.7017 | 0.961875 | ||||||||
\(149\) | 16.0586 | 1.31557 | 0.657786 | − | 0.753205i | \(-0.271493\pi\) | ||||
0.657786 | + | 0.753205i | \(0.271493\pi\) | |||||||
\(150\) | 4.97823 | 0.406471 | ||||||||
\(151\) | −21.8823 | −1.78076 | −0.890379 | − | 0.455221i | \(-0.849560\pi\) | ||||
−0.890379 | + | 0.455221i | \(0.849560\pi\) | |||||||
\(152\) | 4.98792 | 0.404574 | ||||||||
\(153\) | −5.60388 | −0.453046 | ||||||||
\(154\) | 0.643104 | 0.0518228 | ||||||||
\(155\) | −19.6950 | −1.58194 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.90217 | −0.630661 | −0.315331 | − | 0.948982i | \(-0.602115\pi\) | ||||
−0.315331 | + | 0.948982i | \(0.602115\pi\) | |||||||
\(158\) | −14.5157 | −1.15481 | ||||||||
\(159\) | 1.82908 | 0.145056 | ||||||||
\(160\) | 3.15883 | 0.249728 | ||||||||
\(161\) | 28.6112 | 2.25488 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 8.01938 | 0.628126 | 0.314063 | − | 0.949402i | \(-0.398310\pi\) | ||||
0.314063 | + | 0.949402i | \(0.398310\pi\) | |||||||
\(164\) | −4.27413 | −0.333753 | ||||||||
\(165\) | 0.432960 | 0.0337059 | ||||||||
\(166\) | 9.85623 | 0.764992 | ||||||||
\(167\) | −17.0858 | −1.32214 | −0.661068 | − | 0.750326i | \(-0.729896\pi\) | ||||
−0.661068 | + | 0.750326i | \(0.729896\pi\) | |||||||
\(168\) | −4.69202 | −0.361997 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −17.7017 | −1.35766 | ||||||||
\(171\) | −4.98792 | −0.381436 | ||||||||
\(172\) | −2.09783 | −0.159958 | ||||||||
\(173\) | −15.3448 | −1.16664 | −0.583322 | − | 0.812241i | \(-0.698248\pi\) | ||||
−0.583322 | + | 0.812241i | \(0.698248\pi\) | |||||||
\(174\) | −0.850855 | −0.0645032 | ||||||||
\(175\) | −23.3580 | −1.76570 | ||||||||
\(176\) | 0.137063 | 0.0103315 | ||||||||
\(177\) | 5.89977 | 0.443454 | ||||||||
\(178\) | −17.0858 | −1.28063 | ||||||||
\(179\) | 0.523499 | 0.0391282 | 0.0195641 | − | 0.999809i | \(-0.493772\pi\) | ||||
0.0195641 | + | 0.999809i | \(0.493772\pi\) | |||||||
\(180\) | −3.15883 | −0.235446 | ||||||||
\(181\) | 8.89008 | 0.660795 | 0.330397 | − | 0.943842i | \(-0.392817\pi\) | ||||
0.330397 | + | 0.943842i | \(0.392817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.39612 | −0.324971 | ||||||||
\(184\) | 6.09783 | 0.449538 | ||||||||
\(185\) | −36.9638 | −2.71763 | ||||||||
\(186\) | 6.23490 | 0.457165 | ||||||||
\(187\) | −0.768086 | −0.0561680 | ||||||||
\(188\) | 4.98792 | 0.363781 | ||||||||
\(189\) | 4.69202 | 0.341294 | ||||||||
\(190\) | −15.7560 | −1.14306 | ||||||||
\(191\) | −7.03146 | −0.508779 | −0.254389 | − | 0.967102i | \(-0.581874\pi\) | ||||
−0.254389 | + | 0.967102i | \(0.581874\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −17.7560 | −1.27811 | −0.639053 | − | 0.769163i | \(-0.720673\pi\) | ||||
−0.639053 | + | 0.769163i | \(0.720673\pi\) | |||||||
\(194\) | −2.12737 | −0.152737 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0151 | 1.07250 | ||||||||
\(197\) | 18.6571 | 1.32926 | 0.664632 | − | 0.747171i | \(-0.268588\pi\) | ||||
0.664632 | + | 0.747171i | \(0.268588\pi\) | |||||||
\(198\) | −0.137063 | −0.00974067 | ||||||||
\(199\) | 7.66248 | 0.543179 | 0.271589 | − | 0.962413i | \(-0.412451\pi\) | ||||
0.271589 | + | 0.962413i | \(0.412451\pi\) | |||||||
\(200\) | −4.97823 | −0.352014 | ||||||||
\(201\) | 4.71379 | 0.332485 | ||||||||
\(202\) | 9.18598 | 0.646323 | ||||||||
\(203\) | 3.99223 | 0.280200 | ||||||||
\(204\) | 5.60388 | 0.392350 | ||||||||
\(205\) | 13.5013 | 0.942969 | ||||||||
\(206\) | −0.225209 | −0.0156911 | ||||||||
\(207\) | −6.09783 | −0.423829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.683661 | −0.0472898 | ||||||||
\(210\) | 14.8213 | 1.02277 | ||||||||
\(211\) | 11.1642 | 0.768576 | 0.384288 | − | 0.923213i | \(-0.374447\pi\) | ||||
0.384288 | + | 0.923213i | \(0.374447\pi\) | |||||||
\(212\) | −1.82908 | −0.125622 | ||||||||
\(213\) | 0.0978347 | 0.00670352 | ||||||||
\(214\) | −11.2838 | −0.771346 | ||||||||
\(215\) | 6.62671 | 0.451938 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −29.2543 | −1.98591 | ||||||||
\(218\) | 0.195669 | 0.0132524 | ||||||||
\(219\) | 2.32304 | 0.156977 | ||||||||
\(220\) | −0.432960 | −0.0291902 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.7017 | 0.785367 | ||||||||
\(223\) | −24.6353 | −1.64970 | −0.824852 | − | 0.565349i | \(-0.808742\pi\) | ||||
−0.824852 | + | 0.565349i | \(0.808742\pi\) | |||||||
\(224\) | 4.69202 | 0.313499 | ||||||||
\(225\) | 4.97823 | 0.331882 | ||||||||
\(226\) | 0.439665 | 0.0292461 | ||||||||
\(227\) | 7.47650 | 0.496233 | 0.248116 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248116 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(228\) | 4.98792 | 0.330333 | ||||||||
\(229\) | 19.2271 | 1.27056 | 0.635282 | − | 0.772280i | \(-0.280884\pi\) | ||||
0.635282 | + | 0.772280i | \(0.280884\pi\) | |||||||
\(230\) | −19.2620 | −1.27010 | ||||||||
\(231\) | 0.643104 | 0.0423131 | ||||||||
\(232\) | 0.850855 | 0.0558614 | ||||||||
\(233\) | 3.70171 | 0.242507 | 0.121254 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121254 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7560 | −1.02781 | ||||||||
\(236\) | −5.89977 | −0.384042 | ||||||||
\(237\) | −14.5157 | −0.942898 | ||||||||
\(238\) | −26.2935 | −1.70435 | ||||||||
\(239\) | −8.51334 | −0.550682 | −0.275341 | − | 0.961347i | \(-0.588791\pi\) | ||||
−0.275341 | + | 0.961347i | \(0.588791\pi\) | |||||||
\(240\) | 3.15883 | 0.203902 | ||||||||
\(241\) | −17.4330 | −1.12296 | −0.561478 | − | 0.827492i | \(-0.689767\pi\) | ||||
−0.561478 | + | 0.827492i | \(0.689767\pi\) | |||||||
\(242\) | 10.9812 | 0.705899 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.39612 | 0.281433 | ||||||||
\(245\) | −47.4301 | −3.03020 | ||||||||
\(246\) | −4.27413 | −0.272508 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.23490 | −0.395916 | ||||||||
\(249\) | 9.85623 | 0.624613 | ||||||||
\(250\) | −0.0687686 | −0.00434931 | ||||||||
\(251\) | −3.48427 | −0.219925 | −0.109963 | − | 0.993936i | \(-0.535073\pi\) | ||||
−0.109963 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(252\) | −4.69202 | −0.295570 | ||||||||
\(253\) | −0.835790 | −0.0525456 | ||||||||
\(254\) | 7.87263 | 0.493972 | ||||||||
\(255\) | −17.7017 | −1.10852 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.6039 | −0.848586 | −0.424293 | − | 0.905525i | \(-0.639477\pi\) | ||||
−0.424293 | + | 0.905525i | \(0.639477\pi\) | |||||||
\(258\) | −2.09783 | −0.130605 | ||||||||
\(259\) | −54.9047 | −3.41161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.850855 | −0.0526666 | ||||||||
\(262\) | 0.621334 | 0.0383861 | ||||||||
\(263\) | 11.4577 | 0.706513 | 0.353256 | − | 0.935527i | \(-0.385074\pi\) | ||||
0.353256 | + | 0.935527i | \(0.385074\pi\) | |||||||
\(264\) | 0.137063 | 0.00843567 | ||||||||
\(265\) | 5.77777 | 0.354926 | ||||||||
\(266\) | −23.4034 | −1.43496 | ||||||||
\(267\) | −17.0858 | −1.04563 | ||||||||
\(268\) | −4.71379 | −0.287941 | ||||||||
\(269\) | 22.3666 | 1.36371 | 0.681857 | − | 0.731485i | \(-0.261172\pi\) | ||||
0.681857 | + | 0.731485i | \(0.261172\pi\) | |||||||
\(270\) | −3.15883 | −0.192240 | ||||||||
\(271\) | 3.87263 | 0.235245 | 0.117623 | − | 0.993058i | \(-0.462473\pi\) | ||||
0.117623 | + | 0.993058i | \(0.462473\pi\) | |||||||
\(272\) | −5.60388 | −0.339785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | 0.682333 | 0.0411462 | ||||||||
\(276\) | 6.09783 | 0.367047 | ||||||||
\(277\) | 28.7090 | 1.72496 | 0.862478 | − | 0.506094i | \(-0.168911\pi\) | ||||
0.862478 | + | 0.506094i | \(0.168911\pi\) | |||||||
\(278\) | 13.6582 | 0.819163 | ||||||||
\(279\) | 6.23490 | 0.373274 | ||||||||
\(280\) | −14.8213 | −0.885743 | ||||||||
\(281\) | −29.0858 | −1.73511 | −0.867555 | − | 0.497341i | \(-0.834310\pi\) | ||||
−0.867555 | + | 0.497341i | \(0.834310\pi\) | |||||||
\(282\) | 4.98792 | 0.297026 | ||||||||
\(283\) | 13.7560 | 0.817710 | 0.408855 | − | 0.912599i | \(-0.365928\pi\) | ||||
0.408855 | + | 0.912599i | \(0.365928\pi\) | |||||||
\(284\) | −0.0978347 | −0.00580542 | ||||||||
\(285\) | −15.7560 | −0.933305 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0543 | 1.18377 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 14.4034 | 0.847260 | ||||||||
\(290\) | −2.68771 | −0.157828 | ||||||||
\(291\) | −2.12737 | −0.124709 | ||||||||
\(292\) | −2.32304 | −0.135946 | ||||||||
\(293\) | 27.7362 | 1.62036 | 0.810182 | − | 0.586179i | \(-0.199368\pi\) | ||||
0.810182 | + | 0.586179i | \(0.199368\pi\) | |||||||
\(294\) | 15.0151 | 0.875696 | ||||||||
\(295\) | 18.6364 | 1.08505 | ||||||||
\(296\) | −11.7017 | −0.680148 | ||||||||
\(297\) | −0.137063 | −0.00795322 | ||||||||
\(298\) | −16.0586 | −0.930250 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.97823 | −0.287418 | ||||||||
\(301\) | 9.84309 | 0.567346 | ||||||||
\(302\) | 21.8823 | 1.25919 | ||||||||
\(303\) | 9.18598 | 0.527721 | ||||||||
\(304\) | −4.98792 | −0.286077 | ||||||||
\(305\) | −13.8866 | −0.795146 | ||||||||
\(306\) | 5.60388 | 0.320352 | ||||||||
\(307\) | −12.4590 | −0.711075 | −0.355538 | − | 0.934662i | \(-0.615702\pi\) | ||||
−0.355538 | + | 0.934662i | \(0.615702\pi\) | |||||||
\(308\) | −0.643104 | −0.0366443 | ||||||||
\(309\) | −0.225209 | −0.0128117 | ||||||||
\(310\) | 19.6950 | 1.11860 | ||||||||
\(311\) | −6.09783 | −0.345776 | −0.172888 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172888 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7385 | −0.720025 | −0.360013 | − | 0.932947i | \(-0.617228\pi\) | ||||
−0.360013 | + | 0.932947i | \(0.617228\pi\) | |||||||
\(314\) | 7.90217 | 0.445945 | ||||||||
\(315\) | 14.8213 | 0.835087 | ||||||||
\(316\) | 14.5157 | 0.816574 | ||||||||
\(317\) | 14.8140 | 0.832038 | 0.416019 | − | 0.909356i | \(-0.363425\pi\) | ||||
0.416019 | + | 0.909356i | \(0.363425\pi\) | |||||||
\(318\) | −1.82908 | −0.102570 | ||||||||
\(319\) | −0.116621 | −0.00652952 | ||||||||
\(320\) | −3.15883 | −0.176584 | ||||||||
\(321\) | −11.2838 | −0.629801 | ||||||||
\(322\) | −28.6112 | −1.59444 | ||||||||
\(323\) | 27.9517 | 1.55527 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.01938 | −0.444152 | ||||||||
\(327\) | 0.195669 | 0.0108205 | ||||||||
\(328\) | 4.27413 | 0.235999 | ||||||||
\(329\) | −23.4034 | −1.29027 | ||||||||
\(330\) | −0.432960 | −0.0238337 | ||||||||
\(331\) | 7.70171 | 0.423324 | 0.211662 | − | 0.977343i | \(-0.432112\pi\) | ||||
0.211662 | + | 0.977343i | \(0.432112\pi\) | |||||||
\(332\) | −9.85623 | −0.540931 | ||||||||
\(333\) | 11.7017 | 0.641250 | ||||||||
\(334\) | 17.0858 | 0.934891 | ||||||||
\(335\) | 14.8901 | 0.813532 | ||||||||
\(336\) | 4.69202 | 0.255971 | ||||||||
\(337\) | 26.5961 | 1.44878 | 0.724391 | − | 0.689389i | \(-0.242121\pi\) | ||||
0.724391 | + | 0.689389i | \(0.242121\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.439665 | 0.0238793 | ||||||||
\(340\) | 17.7017 | 0.960010 | ||||||||
\(341\) | 0.854576 | 0.0462779 | ||||||||
\(342\) | 4.98792 | 0.269716 | ||||||||
\(343\) | −37.6069 | −2.03058 | ||||||||
\(344\) | 2.09783 | 0.113108 | ||||||||
\(345\) | −19.2620 | −1.03703 | ||||||||
\(346\) | 15.3448 | 0.824942 | ||||||||
\(347\) | 0.911854 | 0.0489509 | 0.0244754 | − | 0.999700i | \(-0.492208\pi\) | ||||
0.0244754 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(348\) | 0.850855 | 0.0456106 | ||||||||
\(349\) | −17.7211 | −0.948588 | −0.474294 | − | 0.880366i | \(-0.657297\pi\) | ||||
−0.474294 | + | 0.880366i | \(0.657297\pi\) | |||||||
\(350\) | 23.3580 | 1.24854 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.137063 | −0.00730550 | ||||||||
\(353\) | −26.4349 | −1.40699 | −0.703493 | − | 0.710702i | \(-0.748378\pi\) | ||||
−0.703493 | + | 0.710702i | \(0.748378\pi\) | |||||||
\(354\) | −5.89977 | −0.313569 | ||||||||
\(355\) | 0.309043 | 0.0164023 | ||||||||
\(356\) | 17.0858 | 0.905543 | ||||||||
\(357\) | −26.2935 | −1.39160 | ||||||||
\(358\) | −0.523499 | −0.0276678 | ||||||||
\(359\) | 7.76941 | 0.410054 | 0.205027 | − | 0.978756i | \(-0.434272\pi\) | ||||
0.205027 | + | 0.978756i | \(0.434272\pi\) | |||||||
\(360\) | 3.15883 | 0.166485 | ||||||||
\(361\) | 5.87933 | 0.309438 | ||||||||
\(362\) | −8.89008 | −0.467252 | ||||||||
\(363\) | 10.9812 | 0.576364 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.33811 | 0.384094 | ||||||||
\(366\) | 4.39612 | 0.229789 | ||||||||
\(367\) | −13.3274 | −0.695682 | −0.347841 | − | 0.937553i | \(-0.613085\pi\) | ||||
−0.347841 | + | 0.937553i | \(0.613085\pi\) | |||||||
\(368\) | −6.09783 | −0.317872 | ||||||||
\(369\) | −4.27413 | −0.222502 | ||||||||
\(370\) | 36.9638 | 1.92165 | ||||||||
\(371\) | 8.58211 | 0.445561 | ||||||||
\(372\) | −6.23490 | −0.323264 | ||||||||
\(373\) | 6.70304 | 0.347070 | 0.173535 | − | 0.984828i | \(-0.444481\pi\) | ||||
0.173535 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(374\) | 0.768086 | 0.0397168 | ||||||||
\(375\) | −0.0687686 | −0.00355120 | ||||||||
\(376\) | −4.98792 | −0.257232 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.69202 | −0.241332 | ||||||||
\(379\) | 2.41550 | 0.124076 | 0.0620380 | − | 0.998074i | \(-0.480240\pi\) | ||||
0.0620380 | + | 0.998074i | \(0.480240\pi\) | |||||||
\(380\) | 15.7560 | 0.808266 | ||||||||
\(381\) | 7.87263 | 0.403327 | ||||||||
\(382\) | 7.03146 | 0.359761 | ||||||||
\(383\) | 10.0978 | 0.515975 | 0.257988 | − | 0.966148i | \(-0.416941\pi\) | ||||
0.257988 | + | 0.966148i | \(0.416941\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.03146 | 0.103533 | ||||||||
\(386\) | 17.7560 | 0.903757 | ||||||||
\(387\) | −2.09783 | −0.106639 | ||||||||
\(388\) | 2.12737 | 0.108001 | ||||||||
\(389\) | 25.1336 | 1.27432 | 0.637162 | − | 0.770730i | \(-0.280108\pi\) | ||||
0.637162 | + | 0.770730i | \(0.280108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.1715 | 1.72813 | ||||||||
\(392\) | −15.0151 | −0.758375 | ||||||||
\(393\) | 0.621334 | 0.0313421 | ||||||||
\(394\) | −18.6571 | −0.939931 | ||||||||
\(395\) | −45.8528 | −2.30710 | ||||||||
\(396\) | 0.137063 | 0.00688769 | ||||||||
\(397\) | 20.8358 | 1.04572 | 0.522859 | − | 0.852419i | \(-0.324865\pi\) | ||||
0.522859 | + | 0.852419i | \(0.324865\pi\) | |||||||
\(398\) | −7.66248 | −0.384085 | ||||||||
\(399\) | −23.4034 | −1.17164 | ||||||||
\(400\) | 4.97823 | 0.248911 | ||||||||
\(401\) | −5.95646 | −0.297451 | −0.148726 | − | 0.988878i | \(-0.547517\pi\) | ||||
−0.148726 | + | 0.988878i | \(0.547517\pi\) | |||||||
\(402\) | −4.71379 | −0.235103 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9.18598 | −0.457020 | ||||||||
\(405\) | −3.15883 | −0.156964 | ||||||||
\(406\) | −3.99223 | −0.198131 | ||||||||
\(407\) | 1.60388 | 0.0795012 | ||||||||
\(408\) | −5.60388 | −0.277433 | ||||||||
\(409\) | −1.80194 | −0.0891001 | −0.0445500 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445500 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(410\) | −13.5013 | −0.666779 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 0.225209 | 0.0110953 | ||||||||
\(413\) | 27.6819 | 1.36214 | ||||||||
\(414\) | 6.09783 | 0.299692 | ||||||||
\(415\) | 31.1342 | 1.52832 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6582 | 0.668843 | ||||||||
\(418\) | 0.683661 | 0.0334389 | ||||||||
\(419\) | −28.4499 | −1.38987 | −0.694935 | − | 0.719072i | \(-0.744567\pi\) | ||||
−0.694935 | + | 0.719072i | \(0.744567\pi\) | |||||||
\(420\) | −14.8213 | −0.723206 | ||||||||
\(421\) | 13.9323 | 0.679019 | 0.339509 | − | 0.940603i | \(-0.389739\pi\) | ||||
0.339509 | + | 0.940603i | \(0.389739\pi\) | |||||||
\(422\) | −11.1642 | −0.543465 | ||||||||
\(423\) | 4.98792 | 0.242521 | ||||||||
\(424\) | 1.82908 | 0.0888282 | ||||||||
\(425\) | −27.8974 | −1.35322 | ||||||||
\(426\) | −0.0978347 | −0.00474011 | ||||||||
\(427\) | −20.6267 | −0.998196 | ||||||||
\(428\) | 11.2838 | 0.545424 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62671 | −0.319568 | ||||||||
\(431\) | −15.9022 | −0.765980 | −0.382990 | − | 0.923752i | \(-0.625106\pi\) | ||||
−0.382990 | + | 0.923752i | \(0.625106\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.77718 | 0.229577 | 0.114788 | − | 0.993390i | \(-0.463381\pi\) | ||||
0.114788 | + | 0.993390i | \(0.463381\pi\) | |||||||
\(434\) | 29.2543 | 1.40425 | ||||||||
\(435\) | −2.68771 | −0.128866 | ||||||||
\(436\) | −0.195669 | −0.00937086 | ||||||||
\(437\) | 30.4155 | 1.45497 | ||||||||
\(438\) | −2.32304 | −0.110999 | ||||||||
\(439\) | −33.6316 | −1.60515 | −0.802575 | − | 0.596552i | \(-0.796537\pi\) | ||||
−0.802575 | + | 0.596552i | \(0.796537\pi\) | |||||||
\(440\) | 0.432960 | 0.0206406 | ||||||||
\(441\) | 15.0151 | 0.715003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3749 | −1.68071 | −0.840357 | − | 0.542033i | \(-0.817655\pi\) | ||||
−0.840357 | + | 0.542033i | \(0.817655\pi\) | |||||||
\(444\) | −11.7017 | −0.555339 | ||||||||
\(445\) | −53.9711 | −2.55847 | ||||||||
\(446\) | 24.6353 | 1.16652 | ||||||||
\(447\) | −16.0586 | −0.759546 | ||||||||
\(448\) | −4.69202 | −0.221677 | ||||||||
\(449\) | 18.0629 | 0.852442 | 0.426221 | − | 0.904619i | \(-0.359845\pi\) | ||||
0.426221 | + | 0.904619i | \(0.359845\pi\) | |||||||
\(450\) | −4.97823 | −0.234676 | ||||||||
\(451\) | −0.585826 | −0.0275855 | ||||||||
\(452\) | −0.439665 | −0.0206801 | ||||||||
\(453\) | 21.8823 | 1.02812 | ||||||||
\(454\) | −7.47650 | −0.350890 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.98792 | −0.233581 | ||||||||
\(457\) | 15.4668 | 0.723507 | 0.361753 | − | 0.932274i | \(-0.382178\pi\) | ||||
0.361753 | + | 0.932274i | \(0.382178\pi\) | |||||||
\(458\) | −19.2271 | −0.898425 | ||||||||
\(459\) | 5.60388 | 0.261567 | ||||||||
\(460\) | 19.2620 | 0.898097 | ||||||||
\(461\) | 18.8092 | 0.876033 | 0.438017 | − | 0.898967i | \(-0.355681\pi\) | ||||
0.438017 | + | 0.898967i | \(0.355681\pi\) | |||||||
\(462\) | −0.643104 | −0.0299199 | ||||||||
\(463\) | 15.8431 | 0.736291 | 0.368145 | − | 0.929768i | \(-0.379993\pi\) | ||||
0.368145 | + | 0.929768i | \(0.379993\pi\) | |||||||
\(464\) | −0.850855 | −0.0395000 | ||||||||
\(465\) | 19.6950 | 0.913334 | ||||||||
\(466\) | −3.70171 | −0.171478 | ||||||||
\(467\) | 22.0006 | 1.01807 | 0.509033 | − | 0.860747i | \(-0.330003\pi\) | ||||
0.509033 | + | 0.860747i | \(0.330003\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.1172 | 1.02128 | ||||||||
\(470\) | 15.7560 | 0.726770 | ||||||||
\(471\) | 7.90217 | 0.364113 | ||||||||
\(472\) | 5.89977 | 0.271559 | ||||||||
\(473\) | −0.287536 | −0.0132209 | ||||||||
\(474\) | 14.5157 | 0.666730 | ||||||||
\(475\) | −24.8310 | −1.13932 | ||||||||
\(476\) | 26.2935 | 1.20516 | ||||||||
\(477\) | −1.82908 | −0.0837480 | ||||||||
\(478\) | 8.51334 | 0.389391 | ||||||||
\(479\) | 21.3491 | 0.975466 | 0.487733 | − | 0.872993i | \(-0.337824\pi\) | ||||
0.487733 | + | 0.872993i | \(0.337824\pi\) | |||||||
\(480\) | −3.15883 | −0.144180 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 17.4330 | 0.794050 | ||||||||
\(483\) | −28.6112 | −1.30185 | ||||||||
\(484\) | −10.9812 | −0.499146 | ||||||||
\(485\) | −6.72002 | −0.305141 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 31.6394 | 1.43372 | 0.716859 | − | 0.697219i | \(-0.245579\pi\) | ||||
0.716859 | + | 0.697219i | \(0.245579\pi\) | |||||||
\(488\) | −4.39612 | −0.199003 | ||||||||
\(489\) | −8.01938 | −0.362649 | ||||||||
\(490\) | 47.4301 | 2.14267 | ||||||||
\(491\) | −1.39911 | −0.0631409 | −0.0315704 | − | 0.999502i | \(-0.510051\pi\) | ||||
−0.0315704 | + | 0.999502i | \(0.510051\pi\) | |||||||
\(492\) | 4.27413 | 0.192693 | ||||||||
\(493\) | 4.76809 | 0.214744 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.432960 | −0.0194601 | ||||||||
\(496\) | 6.23490 | 0.279955 | ||||||||
\(497\) | 0.459042 | 0.0205909 | ||||||||
\(498\) | −9.85623 | −0.441668 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0.0687686 | 0.00307543 | ||||||||
\(501\) | 17.0858 | 0.763335 | ||||||||
\(502\) | 3.48427 | 0.155511 | ||||||||
\(503\) | −18.3827 | −0.819645 | −0.409822 | − | 0.912165i | \(-0.634409\pi\) | ||||
−0.409822 | + | 0.912165i | \(0.634409\pi\) | |||||||
\(504\) | 4.69202 | 0.208999 | ||||||||
\(505\) | 29.0170 | 1.29124 | ||||||||
\(506\) | 0.835790 | 0.0371554 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.87263 | −0.349291 | ||||||||
\(509\) | −0.132751 | −0.00588411 | −0.00294205 | − | 0.999996i | \(-0.500936\pi\) | ||||
−0.00294205 | + | 0.999996i | \(0.500936\pi\) | |||||||
\(510\) | 17.7017 | 0.783845 | ||||||||
\(511\) | 10.8998 | 0.482178 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.98792 | 0.220222 | ||||||||
\(514\) | 13.6039 | 0.600041 | ||||||||
\(515\) | −0.711399 | −0.0313480 | ||||||||
\(516\) | 2.09783 | 0.0923520 | ||||||||
\(517\) | 0.683661 | 0.0300674 | ||||||||
\(518\) | 54.9047 | 2.41237 | ||||||||
\(519\) | 15.3448 | 0.673563 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0508 | 1.62323 | 0.811613 | − | 0.584195i | \(-0.198590\pi\) | ||||
0.811613 | + | 0.584195i | \(0.198590\pi\) | |||||||
\(522\) | 0.850855 | 0.0372409 | ||||||||
\(523\) | −3.15346 | −0.137891 | −0.0689455 | − | 0.997620i | \(-0.521963\pi\) | ||||
−0.0689455 | + | 0.997620i | \(0.521963\pi\) | |||||||
\(524\) | −0.621334 | −0.0271431 | ||||||||
\(525\) | 23.3580 | 1.01942 | ||||||||
\(526\) | −11.4577 | −0.499580 | ||||||||
\(527\) | −34.9396 | −1.52199 | ||||||||
\(528\) | −0.137063 | −0.00596492 | ||||||||
\(529\) | 14.1836 | 0.616678 | ||||||||
\(530\) | −5.77777 | −0.250970 | ||||||||
\(531\) | −5.89977 | −0.256028 | ||||||||
\(532\) | 23.4034 | 1.01467 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 17.0858 | 0.739373 | ||||||||
\(535\) | −35.6437 | −1.54101 | ||||||||
\(536\) | 4.71379 | 0.203605 | ||||||||
\(537\) | −0.523499 | −0.0225907 | ||||||||
\(538\) | −22.3666 | −0.964292 | ||||||||
\(539\) | 2.05802 | 0.0886450 | ||||||||
\(540\) | 3.15883 | 0.135935 | ||||||||
\(541\) | 4.07846 | 0.175347 | 0.0876733 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876733 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(542\) | −3.87263 | −0.166344 | ||||||||
\(543\) | −8.89008 | −0.381510 | ||||||||
\(544\) | 5.60388 | 0.240264 | ||||||||
\(545\) | 0.618087 | 0.0264759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0508 | −0.985583 | −0.492791 | − | 0.870148i | \(-0.664023\pi\) | ||||
−0.492791 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(548\) | 4.00000 | 0.170872 | ||||||||
\(549\) | 4.39612 | 0.187622 | ||||||||
\(550\) | −0.682333 | −0.0290948 | ||||||||
\(551\) | 4.24400 | 0.180800 | ||||||||
\(552\) | −6.09783 | −0.259541 | ||||||||
\(553\) | −68.1081 | −2.89625 | ||||||||
\(554\) | −28.7090 | −1.21973 | ||||||||
\(555\) | 36.9638 | 1.56902 | ||||||||
\(556\) | −13.6582 | −0.579235 | ||||||||
\(557\) | 20.4155 | 0.865033 | 0.432516 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432516 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(558\) | −6.23490 | −0.263944 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.8213 | 0.626315 | ||||||||
\(561\) | 0.768086 | 0.0324286 | ||||||||
\(562\) | 29.0858 | 1.22691 | ||||||||
\(563\) | 21.5609 | 0.908685 | 0.454342 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454342 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(564\) | −4.98792 | −0.210029 | ||||||||
\(565\) | 1.38883 | 0.0584285 | ||||||||
\(566\) | −13.7560 | −0.578208 | ||||||||
\(567\) | −4.69202 | −0.197046 | ||||||||
\(568\) | 0.0978347 | 0.00410505 | ||||||||
\(569\) | 8.98792 | 0.376793 | 0.188397 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188397 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(570\) | 15.7560 | 0.659946 | ||||||||
\(571\) | 13.5603 | 0.567482 | 0.283741 | − | 0.958901i | \(-0.408424\pi\) | ||||
0.283741 | + | 0.958901i | \(0.408424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.03146 | 0.293743 | ||||||||
\(574\) | −20.0543 | −0.837050 | ||||||||
\(575\) | −30.3564 | −1.26595 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.2825 | 0.677849 | 0.338924 | − | 0.940814i | \(-0.389937\pi\) | ||||
0.338924 | + | 0.940814i | \(0.389937\pi\) | |||||||
\(578\) | −14.4034 | −0.599103 | ||||||||
\(579\) | 17.7560 | 0.737914 | ||||||||
\(580\) | 2.68771 | 0.111601 | ||||||||
\(581\) | 46.2457 | 1.91859 | ||||||||
\(582\) | 2.12737 | 0.0881825 | ||||||||
\(583\) | −0.250700 | −0.0103830 | ||||||||
\(584\) | 2.32304 | 0.0961282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.7362 | −1.14577 | ||||||||
\(587\) | 47.5706 | 1.96345 | 0.981725 | − | 0.190307i | \(-0.0609482\pi\) | ||||
0.981725 | + | 0.190307i | \(0.0609482\pi\) | |||||||
\(588\) | −15.0151 | −0.619211 | ||||||||
\(589\) | −31.0992 | −1.28142 | ||||||||
\(590\) | −18.6364 | −0.767248 | ||||||||
\(591\) | −18.6571 | −0.767451 | ||||||||
\(592\) | 11.7017 | 0.480937 | ||||||||
\(593\) | 31.0267 | 1.27411 | 0.637056 | − | 0.770817i | \(-0.280152\pi\) | ||||
0.637056 | + | 0.770817i | \(0.280152\pi\) | |||||||
\(594\) | 0.137063 | 0.00562378 | ||||||||
\(595\) | −83.0568 | −3.40500 | ||||||||
\(596\) | 16.0586 | 0.657786 | ||||||||
\(597\) | −7.66248 | −0.313604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3263 | 0.912228 | 0.456114 | − | 0.889921i | \(-0.349241\pi\) | ||||
0.456114 | + | 0.889921i | \(0.349241\pi\) | |||||||
\(600\) | 4.97823 | 0.203235 | ||||||||
\(601\) | −8.18060 | −0.333694 | −0.166847 | − | 0.985983i | \(-0.553359\pi\) | ||||
−0.166847 | + | 0.985983i | \(0.553359\pi\) | |||||||
\(602\) | −9.84309 | −0.401174 | ||||||||
\(603\) | −4.71379 | −0.191960 | ||||||||
\(604\) | −21.8823 | −0.890379 | ||||||||
\(605\) | 34.6878 | 1.41026 | ||||||||
\(606\) | −9.18598 | −0.373155 | ||||||||
\(607\) | 3.30798 | 0.134267 | 0.0671334 | − | 0.997744i | \(-0.478615\pi\) | ||||
0.0671334 | + | 0.997744i | \(0.478615\pi\) | |||||||
\(608\) | 4.98792 | 0.202287 | ||||||||
\(609\) | −3.99223 | −0.161773 | ||||||||
\(610\) | 13.8866 | 0.562253 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.60388 | −0.226523 | ||||||||
\(613\) | −10.8853 | −0.439653 | −0.219827 | − | 0.975539i | \(-0.570549\pi\) | ||||
−0.219827 | + | 0.975539i | \(0.570549\pi\) | |||||||
\(614\) | 12.4590 | 0.502806 | ||||||||
\(615\) | −13.5013 | −0.544423 | ||||||||
\(616\) | 0.643104 | 0.0259114 | ||||||||
\(617\) | −34.5676 | −1.39164 | −0.695820 | − | 0.718216i | \(-0.744959\pi\) | ||||
−0.695820 | + | 0.718216i | \(0.744959\pi\) | |||||||
\(618\) | 0.225209 | 0.00905925 | ||||||||
\(619\) | 2.86592 | 0.115191 | 0.0575955 | − | 0.998340i | \(-0.481657\pi\) | ||||
0.0575955 | + | 0.998340i | \(0.481657\pi\) | |||||||
\(620\) | −19.6950 | −0.790970 | ||||||||
\(621\) | 6.09783 | 0.244698 | ||||||||
\(622\) | 6.09783 | 0.244501 | ||||||||
\(623\) | −80.1667 | −3.21181 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1084 | −1.00434 | ||||||||
\(626\) | 12.7385 | 0.509135 | ||||||||
\(627\) | 0.683661 | 0.0273028 | ||||||||
\(628\) | −7.90217 | −0.315331 | ||||||||
\(629\) | −65.5749 | −2.61464 | ||||||||
\(630\) | −14.8213 | −0.590495 | ||||||||
\(631\) | −42.6631 | −1.69839 | −0.849195 | − | 0.528079i | \(-0.822912\pi\) | ||||
−0.849195 | + | 0.528079i | \(0.822912\pi\) | |||||||
\(632\) | −14.5157 | −0.577405 | ||||||||
\(633\) | −11.1642 | −0.443738 | ||||||||
\(634\) | −14.8140 | −0.588340 | ||||||||
\(635\) | 24.8683 | 0.986869 | ||||||||
\(636\) | 1.82908 | 0.0725279 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.116621 | 0.00461707 | ||||||||
\(639\) | −0.0978347 | −0.00387028 | ||||||||
\(640\) | 3.15883 | 0.124864 | ||||||||
\(641\) | 41.3927 | 1.63491 | 0.817456 | − | 0.575991i | \(-0.195384\pi\) | ||||
0.817456 | + | 0.575991i | \(0.195384\pi\) | |||||||
\(642\) | 11.2838 | 0.445337 | ||||||||
\(643\) | 13.7125 | 0.540767 | 0.270383 | − | 0.962753i | \(-0.412850\pi\) | ||||
0.270383 | + | 0.962753i | \(0.412850\pi\) | |||||||
\(644\) | 28.6112 | 1.12744 | ||||||||
\(645\) | −6.62671 | −0.260926 | ||||||||
\(646\) | −27.9517 | −1.09974 | ||||||||
\(647\) | 18.0086 | 0.707992 | 0.353996 | − | 0.935247i | \(-0.384823\pi\) | ||||
0.353996 | + | 0.935247i | \(0.384823\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.808643 | −0.0317420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.2543 | 1.14657 | ||||||||
\(652\) | 8.01938 | 0.314063 | ||||||||
\(653\) | 46.5652 | 1.82224 | 0.911119 | − | 0.412143i | \(-0.135220\pi\) | ||||
0.911119 | + | 0.412143i | \(0.135220\pi\) | |||||||
\(654\) | −0.195669 | −0.00765128 | ||||||||
\(655\) | 1.96269 | 0.0766887 | ||||||||
\(656\) | −4.27413 | −0.166877 | ||||||||
\(657\) | −2.32304 | −0.0906306 | ||||||||
\(658\) | 23.4034 | 0.912360 | ||||||||
\(659\) | 13.8562 | 0.539762 | 0.269881 | − | 0.962894i | \(-0.413016\pi\) | ||||
0.269881 | + | 0.962894i | \(0.413016\pi\) | |||||||
\(660\) | 0.432960 | 0.0168530 | ||||||||
\(661\) | −43.1051 | −1.67660 | −0.838298 | − | 0.545213i | \(-0.816449\pi\) | ||||
−0.838298 | + | 0.545213i | \(0.816449\pi\) | |||||||
\(662\) | −7.70171 | −0.299335 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.85623 | 0.382496 | ||||||||
\(665\) | −73.9275 | −2.86679 | ||||||||
\(666\) | −11.7017 | −0.453432 | ||||||||
\(667\) | 5.18837 | 0.200895 | ||||||||
\(668\) | −17.0858 | −0.661068 | ||||||||
\(669\) | 24.6353 | 0.952457 | ||||||||
\(670\) | −14.8901 | −0.575254 | ||||||||
\(671\) | 0.602548 | 0.0232611 | ||||||||
\(672\) | −4.69202 | −0.180999 | ||||||||
\(673\) | 30.7415 | 1.18500 | 0.592499 | − | 0.805571i | \(-0.298141\pi\) | ||||
0.592499 | + | 0.805571i | \(0.298141\pi\) | |||||||
\(674\) | −26.5961 | −1.02444 | ||||||||
\(675\) | −4.97823 | −0.191612 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5894 | 0.637582 | 0.318791 | − | 0.947825i | \(-0.396723\pi\) | ||||
0.318791 | + | 0.947825i | \(0.396723\pi\) | |||||||
\(678\) | −0.439665 | −0.0168852 | ||||||||
\(679\) | −9.98169 | −0.383062 | ||||||||
\(680\) | −17.7017 | −0.678830 | ||||||||
\(681\) | −7.47650 | −0.286500 | ||||||||
\(682\) | −0.854576 | −0.0327234 | ||||||||
\(683\) | −34.9885 | −1.33880 | −0.669399 | − | 0.742903i | \(-0.733448\pi\) | ||||
−0.669399 | + | 0.742903i | \(0.733448\pi\) | |||||||
\(684\) | −4.98792 | −0.190718 | ||||||||
\(685\) | −12.6353 | −0.482771 | ||||||||
\(686\) | 37.6069 | 1.43584 | ||||||||
\(687\) | −19.2271 | −0.733561 | ||||||||
\(688\) | −2.09783 | −0.0799792 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19.2620 | 0.733294 | ||||||||
\(691\) | 14.0871 | 0.535898 | 0.267949 | − | 0.963433i | \(-0.413654\pi\) | ||||
0.267949 | + | 0.963433i | \(0.413654\pi\) | |||||||
\(692\) | −15.3448 | −0.583322 | ||||||||
\(693\) | −0.643104 | −0.0244295 | ||||||||
\(694\) | −0.911854 | −0.0346135 | ||||||||
\(695\) | 43.1439 | 1.63654 | ||||||||
\(696\) | −0.850855 | −0.0322516 | ||||||||
\(697\) | 23.9517 | 0.907234 | ||||||||
\(698\) | 17.7211 | 0.670753 | ||||||||
\(699\) | −3.70171 | −0.140012 | ||||||||
\(700\) | −23.3580 | −0.882848 | ||||||||
\(701\) | 48.6112 | 1.83602 | 0.918009 | − | 0.396559i | \(-0.129796\pi\) | ||||
0.918009 | + | 0.396559i | \(0.129796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58.3672 | −2.20136 | ||||||||
\(704\) | 0.137063 | 0.00516577 | ||||||||
\(705\) | 15.7560 | 0.593405 | ||||||||
\(706\) | 26.4349 | 0.994890 | ||||||||
\(707\) | 43.1008 | 1.62097 | ||||||||
\(708\) | 5.89977 | 0.221727 | ||||||||
\(709\) | 17.2862 | 0.649197 | 0.324599 | − | 0.945852i | \(-0.394771\pi\) | ||||
0.324599 | + | 0.945852i | \(0.394771\pi\) | |||||||
\(710\) | −0.309043 | −0.0115982 | ||||||||
\(711\) | 14.5157 | 0.544382 | ||||||||
\(712\) | −17.0858 | −0.640316 | ||||||||
\(713\) | −38.0194 | −1.42384 | ||||||||
\(714\) | 26.2935 | 0.984010 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.523499 | 0.0195641 | ||||||||
\(717\) | 8.51334 | 0.317936 | ||||||||
\(718\) | −7.76941 | −0.289952 | ||||||||
\(719\) | 29.1207 | 1.08602 | 0.543009 | − | 0.839727i | \(-0.317285\pi\) | ||||
0.543009 | + | 0.839727i | \(0.317285\pi\) | |||||||
\(720\) | −3.15883 | −0.117723 | ||||||||
\(721\) | −1.05669 | −0.0393531 | ||||||||
\(722\) | −5.87933 | −0.218806 | ||||||||
\(723\) | 17.4330 | 0.648339 | ||||||||
\(724\) | 8.89008 | 0.330397 | ||||||||
\(725\) | −4.23575 | −0.157312 | ||||||||
\(726\) | −10.9812 | −0.407551 | ||||||||
\(727\) | 45.5666 | 1.68997 | 0.844985 | − | 0.534790i | \(-0.179609\pi\) | ||||
0.844985 | + | 0.534790i | \(0.179609\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.33811 | −0.271596 | ||||||||
\(731\) | 11.7560 | 0.434812 | ||||||||
\(732\) | −4.39612 | −0.162485 | ||||||||
\(733\) | −21.7995 | −0.805185 | −0.402592 | − | 0.915379i | \(-0.631891\pi\) | ||||
−0.402592 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(734\) | 13.3274 | 0.491922 | ||||||||
\(735\) | 47.4301 | 1.74949 | ||||||||
\(736\) | 6.09783 | 0.224769 | ||||||||
\(737\) | −0.646088 | −0.0237990 | ||||||||
\(738\) | 4.27413 | 0.157333 | ||||||||
\(739\) | −41.5663 | −1.52904 | −0.764521 | − | 0.644599i | \(-0.777024\pi\) | ||||
−0.764521 | + | 0.644599i | \(0.777024\pi\) | |||||||
\(740\) | −36.9638 | −1.35881 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.58211 | −0.315059 | ||||||||
\(743\) | 28.8224 | 1.05739 | 0.528695 | − | 0.848812i | \(-0.322681\pi\) | ||||
0.528695 | + | 0.848812i | \(0.322681\pi\) | |||||||
\(744\) | 6.23490 | 0.228582 | ||||||||
\(745\) | −50.7265 | −1.85847 | ||||||||
\(746\) | −6.70304 | −0.245416 | ||||||||
\(747\) | −9.85623 | −0.360621 | ||||||||
\(748\) | −0.768086 | −0.0280840 | ||||||||
\(749\) | −52.9439 | −1.93453 | ||||||||
\(750\) | 0.0687686 | 0.00251108 | ||||||||
\(751\) | 16.6203 | 0.606482 | 0.303241 | − | 0.952914i | \(-0.401931\pi\) | ||||
0.303241 | + | 0.952914i | \(0.401931\pi\) | |||||||
\(752\) | 4.98792 | 0.181891 | ||||||||
\(753\) | 3.48427 | 0.126974 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 69.1226 | 2.51563 | ||||||||
\(756\) | 4.69202 | 0.170647 | ||||||||
\(757\) | −40.3913 | −1.46805 | −0.734024 | − | 0.679123i | \(-0.762360\pi\) | ||||
−0.734024 | + | 0.679123i | \(0.762360\pi\) | |||||||
\(758\) | −2.41550 | −0.0877350 | ||||||||
\(759\) | 0.835790 | 0.0303372 | ||||||||
\(760\) | −15.7560 | −0.571530 | ||||||||
\(761\) | −3.29483 | −0.119438 | −0.0597188 | − | 0.998215i | \(-0.519020\pi\) | ||||
−0.0597188 | + | 0.998215i | \(0.519020\pi\) | |||||||
\(762\) | −7.87263 | −0.285195 | ||||||||
\(763\) | 0.918085 | 0.0332369 | ||||||||
\(764\) | −7.03146 | −0.254389 | ||||||||
\(765\) | 17.7017 | 0.640007 | ||||||||
\(766\) | −10.0978 | −0.364850 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −2.35258 | −0.0848363 | −0.0424182 | − | 0.999100i | \(-0.513506\pi\) | ||||
−0.0424182 | + | 0.999100i | \(0.513506\pi\) | |||||||
\(770\) | −2.03146 | −0.0732087 | ||||||||
\(771\) | 13.6039 | 0.489932 | ||||||||
\(772\) | −17.7560 | −0.639053 | ||||||||
\(773\) | −20.3937 | −0.733512 | −0.366756 | − | 0.930317i | \(-0.619532\pi\) | ||||
−0.366756 | + | 0.930317i | \(0.619532\pi\) | |||||||
\(774\) | 2.09783 | 0.0754051 | ||||||||
\(775\) | 31.0388 | 1.11494 | ||||||||
\(776\) | −2.12737 | −0.0763683 | ||||||||
\(777\) | 54.9047 | 1.96969 | ||||||||
\(778\) | −25.1336 | −0.901083 | ||||||||
\(779\) | 21.3190 | 0.763832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0134095 | −0.000479831 0 | ||||||||
\(782\) | −34.1715 | −1.22197 | ||||||||
\(783\) | 0.850855 | 0.0304071 | ||||||||
\(784\) | 15.0151 | 0.536252 | ||||||||
\(785\) | 24.9616 | 0.890919 | ||||||||
\(786\) | −0.621334 | −0.0221622 | ||||||||
\(787\) | 19.6775 | 0.701429 | 0.350714 | − | 0.936482i | \(-0.385939\pi\) | ||||
0.350714 | + | 0.936482i | \(0.385939\pi\) | |||||||
\(788\) | 18.6571 | 0.664632 | ||||||||
\(789\) | −11.4577 | −0.407905 | ||||||||
\(790\) | 45.8528 | 1.63137 | ||||||||
\(791\) | 2.06292 | 0.0733489 | ||||||||
\(792\) | −0.137063 | −0.00487033 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.8358 | −0.739435 | ||||||||
\(795\) | −5.77777 | −0.204917 | ||||||||
\(796\) | 7.66248 | 0.271589 | ||||||||
\(797\) | −45.8689 | −1.62476 | −0.812380 | − | 0.583128i | \(-0.801828\pi\) | ||||
−0.812380 | + | 0.583128i | \(0.801828\pi\) | |||||||
\(798\) | 23.4034 | 0.828472 | ||||||||
\(799\) | −27.9517 | −0.988859 | ||||||||
\(800\) | −4.97823 | −0.176007 | ||||||||
\(801\) | 17.0858 | 0.603695 | ||||||||
\(802\) | 5.95646 | 0.210330 | ||||||||
\(803\) | −0.318404 | −0.0112362 | ||||||||
\(804\) | 4.71379 | 0.166243 | ||||||||
\(805\) | −90.3779 | −3.18540 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.3666 | −0.787341 | ||||||||
\(808\) | 9.18598 | 0.323162 | ||||||||
\(809\) | 38.1414 | 1.34098 | 0.670490 | − | 0.741919i | \(-0.266084\pi\) | ||||
0.670490 | + | 0.741919i | \(0.266084\pi\) | |||||||
\(810\) | 3.15883 | 0.110990 | ||||||||
\(811\) | 46.6983 | 1.63980 | 0.819899 | − | 0.572509i | \(-0.194030\pi\) | ||||
0.819899 | + | 0.572509i | \(0.194030\pi\) | |||||||
\(812\) | 3.99223 | 0.140100 | ||||||||
\(813\) | −3.87263 | −0.135819 | ||||||||
\(814\) | −1.60388 | −0.0562158 | ||||||||
\(815\) | −25.3319 | −0.887337 | ||||||||
\(816\) | 5.60388 | 0.196175 | ||||||||
\(817\) | 10.4638 | 0.366083 | ||||||||
\(818\) | 1.80194 | 0.0630033 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5013 | 0.471484 | ||||||||
\(821\) | 32.6950 | 1.14106 | 0.570532 | − | 0.821276i | \(-0.306737\pi\) | ||||
0.570532 | + | 0.821276i | \(0.306737\pi\) | |||||||
\(822\) | 4.00000 | 0.139516 | ||||||||
\(823\) | −21.6799 | −0.755715 | −0.377858 | − | 0.925864i | \(-0.623339\pi\) | ||||
−0.377858 | + | 0.925864i | \(0.623339\pi\) | |||||||
\(824\) | −0.225209 | −0.00784554 | ||||||||
\(825\) | −0.682333 | −0.0237558 | ||||||||
\(826\) | −27.6819 | −0.963175 | ||||||||
\(827\) | −13.9172 | −0.483950 | −0.241975 | − | 0.970283i | \(-0.577795\pi\) | ||||
−0.241975 | + | 0.970283i | \(0.577795\pi\) | |||||||
\(828\) | −6.09783 | −0.211914 | ||||||||
\(829\) | −16.4047 | −0.569760 | −0.284880 | − | 0.958563i | \(-0.591954\pi\) | ||||
−0.284880 | + | 0.958563i | \(0.591954\pi\) | |||||||
\(830\) | −31.1342 | −1.08068 | ||||||||
\(831\) | −28.7090 | −0.995904 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84.1426 | −2.91537 | ||||||||
\(834\) | −13.6582 | −0.472944 | ||||||||
\(835\) | 53.9711 | 1.86775 | ||||||||
\(836\) | −0.683661 | −0.0236449 | ||||||||
\(837\) | −6.23490 | −0.215510 | ||||||||
\(838\) | 28.4499 | 0.982787 | ||||||||
\(839\) | 11.6146 | 0.400982 | 0.200491 | − | 0.979696i | \(-0.435746\pi\) | ||||
0.200491 | + | 0.979696i | \(0.435746\pi\) | |||||||
\(840\) | 14.8213 | 0.511384 | ||||||||
\(841\) | −28.2760 | −0.975036 | ||||||||
\(842\) | −13.9323 | −0.480139 | ||||||||
\(843\) | 29.0858 | 1.00177 | ||||||||
\(844\) | 11.1642 | 0.384288 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.98792 | −0.171488 | ||||||||
\(847\) | 51.5241 | 1.77039 | ||||||||
\(848\) | −1.82908 | −0.0628110 | ||||||||
\(849\) | −13.7560 | −0.472105 | ||||||||
\(850\) | 27.8974 | 0.956872 | ||||||||
\(851\) | −71.3551 | −2.44602 | ||||||||
\(852\) | 0.0978347 | 0.00335176 | ||||||||
\(853\) | 26.2983 | 0.900436 | 0.450218 | − | 0.892919i | \(-0.351346\pi\) | ||||
0.450218 | + | 0.892919i | \(0.351346\pi\) | |||||||
\(854\) | 20.6267 | 0.705832 | ||||||||
\(855\) | 15.7560 | 0.538844 | ||||||||
\(856\) | −11.2838 | −0.385673 | ||||||||
\(857\) | −48.6305 | −1.66119 | −0.830594 | − | 0.556879i | \(-0.811999\pi\) | ||||
−0.830594 | + | 0.556879i | \(0.811999\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6185 | 1.14705 | 0.573524 | − | 0.819189i | \(-0.305576\pi\) | ||||
0.573524 | + | 0.819189i | \(0.305576\pi\) | |||||||
\(860\) | 6.62671 | 0.225969 | ||||||||
\(861\) | −20.0543 | −0.683449 | ||||||||
\(862\) | 15.9022 | 0.541630 | ||||||||
\(863\) | −5.78879 | −0.197053 | −0.0985264 | − | 0.995134i | \(-0.531413\pi\) | ||||
−0.0985264 | + | 0.995134i | \(0.531413\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 48.4717 | 1.64809 | ||||||||
\(866\) | −4.77718 | −0.162335 | ||||||||
\(867\) | −14.4034 | −0.489166 | ||||||||
\(868\) | −29.2543 | −0.992955 | ||||||||
\(869\) | 1.98957 | 0.0674917 | ||||||||
\(870\) | 2.68771 | 0.0911219 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.195669 | 0.00662620 | ||||||||
\(873\) | 2.12737 | 0.0720007 | ||||||||
\(874\) | −30.4155 | −1.02882 | ||||||||
\(875\) | −0.322664 | −0.0109080 | ||||||||
\(876\) | 2.32304 | 0.0784884 | ||||||||
\(877\) | 9.50604 | 0.320996 | 0.160498 | − | 0.987036i | \(-0.448690\pi\) | ||||
0.160498 | + | 0.987036i | \(0.448690\pi\) | |||||||
\(878\) | 33.6316 | 1.13501 | ||||||||
\(879\) | −27.7362 | −0.935517 | ||||||||
\(880\) | −0.432960 | −0.0145951 | ||||||||
\(881\) | −46.7875 | −1.57631 | −0.788155 | − | 0.615477i | \(-0.788963\pi\) | ||||
−0.788155 | + | 0.615477i | \(0.788963\pi\) | |||||||
\(882\) | −15.0151 | −0.505584 | ||||||||
\(883\) | 3.03146 | 0.102017 | 0.0510084 | − | 0.998698i | \(-0.483756\pi\) | ||||
0.0510084 | + | 0.998698i | \(0.483756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.6364 | −0.626456 | ||||||||
\(886\) | 35.3749 | 1.18844 | ||||||||
\(887\) | 37.0180 | 1.24294 | 0.621472 | − | 0.783436i | \(-0.286535\pi\) | ||||
0.621472 | + | 0.783436i | \(0.286535\pi\) | |||||||
\(888\) | 11.7017 | 0.392684 | ||||||||
\(889\) | 36.9385 | 1.23888 | ||||||||
\(890\) | 53.9711 | 1.80911 | ||||||||
\(891\) | 0.137063 | 0.00459179 | ||||||||
\(892\) | −24.6353 | −0.824852 | ||||||||
\(893\) | −24.8793 | −0.832555 | ||||||||
\(894\) | 16.0586 | 0.537080 | ||||||||
\(895\) | −1.65365 | −0.0552753 | ||||||||
\(896\) | 4.69202 | 0.156749 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0629 | −0.602767 | ||||||||
\(899\) | −5.30499 | −0.176931 | ||||||||
\(900\) | 4.97823 | 0.165941 | ||||||||
\(901\) | 10.2500 | 0.341476 | ||||||||
\(902\) | 0.585826 | 0.0195059 | ||||||||
\(903\) | −9.84309 | −0.327557 | ||||||||
\(904\) | 0.439665 | 0.0146230 | ||||||||
\(905\) | −28.0823 | −0.933487 | ||||||||
\(906\) | −21.8823 | −0.726991 | ||||||||
\(907\) | 19.0965 | 0.634089 | 0.317045 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317045 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(908\) | 7.47650 | 0.248116 | ||||||||
\(909\) | −9.18598 | −0.304680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3142 | −1.03749 | −0.518743 | − | 0.854930i | \(-0.673600\pi\) | ||||
−0.518743 | + | 0.854930i | \(0.673600\pi\) | |||||||
\(912\) | 4.98792 | 0.165166 | ||||||||
\(913\) | −1.35093 | −0.0447092 | ||||||||
\(914\) | −15.4668 | −0.511597 | ||||||||
\(915\) | 13.8866 | 0.459078 | ||||||||
\(916\) | 19.2271 | 0.635282 | ||||||||
\(917\) | 2.91531 | 0.0962721 | ||||||||
\(918\) | −5.60388 | −0.184955 | ||||||||
\(919\) | 30.3967 | 1.00270 | 0.501348 | − | 0.865246i | \(-0.332838\pi\) | ||||
0.501348 | + | 0.865246i | \(0.332838\pi\) | |||||||
\(920\) | −19.2620 | −0.635051 | ||||||||
\(921\) | 12.4590 | 0.410539 | ||||||||
\(922\) | −18.8092 | −0.619449 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.643104 | 0.0211566 | ||||||||
\(925\) | 58.2538 | 1.91537 | ||||||||
\(926\) | −15.8431 | −0.520636 | ||||||||
\(927\) | 0.225209 | 0.00739685 | ||||||||
\(928\) | 0.850855 | 0.0279307 | ||||||||
\(929\) | −40.5810 | −1.33142 | −0.665710 | − | 0.746210i | \(-0.731871\pi\) | ||||
−0.665710 | + | 0.746210i | \(0.731871\pi\) | |||||||
\(930\) | −19.6950 | −0.645825 | ||||||||
\(931\) | −74.8939 | −2.45455 | ||||||||
\(932\) | 3.70171 | 0.121254 | ||||||||
\(933\) | 6.09783 | 0.199634 | ||||||||
\(934\) | −22.0006 | −0.719881 | ||||||||
\(935\) | 2.42626 | 0.0793470 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7047 | −0.611056 | −0.305528 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305528 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(938\) | −22.1172 | −0.722153 | ||||||||
\(939\) | 12.7385 | 0.415707 | ||||||||
\(940\) | −15.7560 | −0.513904 | ||||||||
\(941\) | −4.04998 | −0.132026 | −0.0660128 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660128 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(942\) | −7.90217 | −0.257466 | ||||||||
\(943\) | 26.0629 | 0.848725 | ||||||||
\(944\) | −5.89977 | −0.192021 | ||||||||
\(945\) | −14.8213 | −0.482137 | ||||||||
\(946\) | 0.287536 | 0.00934861 | ||||||||
\(947\) | 11.5356 | 0.374856 | 0.187428 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187428 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(948\) | −14.5157 | −0.471449 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.8310 | 0.805624 | ||||||||
\(951\) | −14.8140 | −0.480377 | ||||||||
\(952\) | −26.2935 | −0.852177 | ||||||||
\(953\) | −9.57109 | −0.310038 | −0.155019 | − | 0.987911i | \(-0.549544\pi\) | ||||
−0.155019 | + | 0.987911i | \(0.549544\pi\) | |||||||
\(954\) | 1.82908 | 0.0592188 | ||||||||
\(955\) | 22.2112 | 0.718738 | ||||||||
\(956\) | −8.51334 | −0.275341 | ||||||||
\(957\) | 0.116621 | 0.00376982 | ||||||||
\(958\) | −21.3491 | −0.689759 | ||||||||
\(959\) | −18.7681 | −0.606053 | ||||||||
\(960\) | 3.15883 | 0.101951 | ||||||||
\(961\) | 7.87395 | 0.253998 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2838 | 0.363616 | ||||||||
\(964\) | −17.4330 | −0.561478 | ||||||||
\(965\) | 56.0883 | 1.80555 | ||||||||
\(966\) | 28.6112 | 0.920549 | ||||||||
\(967\) | −61.2073 | −1.96829 | −0.984147 | − | 0.177357i | \(-0.943245\pi\) | ||||
−0.984147 | + | 0.177357i | \(0.943245\pi\) | |||||||
\(968\) | 10.9812 | 0.352950 | ||||||||
\(969\) | −27.9517 | −0.897937 | ||||||||
\(970\) | 6.72002 | 0.215767 | ||||||||
\(971\) | −28.8595 | −0.926145 | −0.463072 | − | 0.886320i | \(-0.653253\pi\) | ||||
−0.463072 | + | 0.886320i | \(0.653253\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 64.0844 | 2.05445 | ||||||||
\(974\) | −31.6394 | −1.01379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.39612 | 0.140717 | ||||||||
\(977\) | −46.6305 | −1.49184 | −0.745922 | − | 0.666034i | \(-0.767991\pi\) | ||||
−0.745922 | + | 0.666034i | \(0.767991\pi\) | |||||||
\(978\) | 8.01938 | 0.256431 | ||||||||
\(979\) | 2.34183 | 0.0748452 | ||||||||
\(980\) | −47.4301 | −1.51510 | ||||||||
\(981\) | −0.195669 | −0.00624724 | ||||||||
\(982\) | 1.39911 | 0.0446473 | ||||||||
\(983\) | −55.6883 | −1.77618 | −0.888090 | − | 0.459669i | \(-0.847968\pi\) | ||||
−0.888090 | + | 0.459669i | \(0.847968\pi\) | |||||||
\(984\) | −4.27413 | −0.136254 | ||||||||
\(985\) | −58.9347 | −1.87782 | ||||||||
\(986\) | −4.76809 | −0.151847 | ||||||||
\(987\) | 23.4034 | 0.744939 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7922 | 0.406770 | ||||||||
\(990\) | 0.432960 | 0.0137604 | ||||||||
\(991\) | −9.32172 | −0.296114 | −0.148057 | − | 0.988979i | \(-0.547302\pi\) | ||||
−0.148057 | + | 0.988979i | \(0.547302\pi\) | |||||||
\(992\) | −6.23490 | −0.197958 | ||||||||
\(993\) | −7.70171 | −0.244406 | ||||||||
\(994\) | −0.459042 | −0.0145599 | ||||||||
\(995\) | −24.2045 | −0.767334 | ||||||||
\(996\) | 9.85623 | 0.312307 | ||||||||
\(997\) | 46.0253 | 1.45764 | 0.728819 | − | 0.684707i | \(-0.240070\pi\) | ||||
0.728819 | + | 0.684707i | \(0.240070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.7017 | −0.370226 |
(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 | 1014.2.a.l.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 3042.2.a.bh.1.3 | 3 | |||
4.3 | odd | 2 | 8112.2.a.cj.1.1 | 3 | |||
13.2 | odd | 12 | 1014.2.i.h.823.3 | 12 | |||
13.3 | even | 3 | 1014.2.e.n.529.1 | 6 | |||
13.4 | even | 6 | 1014.2.e.l.991.3 | 6 | |||
13.5 | odd | 4 | 1014.2.b.f.337.6 | 6 | |||
13.6 | odd | 12 | 1014.2.i.h.361.6 | 12 | |||
13.7 | odd | 12 | 1014.2.i.h.361.1 | 12 | |||
13.8 | odd | 4 | 1014.2.b.f.337.1 | 6 | |||
13.9 | even | 3 | 1014.2.e.n.991.1 | 6 | |||
13.10 | even | 6 | 1014.2.e.l.529.3 | 6 | |||
13.11 | odd | 12 | 1014.2.i.h.823.4 | 12 | |||
13.12 | even | 2 | 1014.2.a.n.1.3 | yes | 3 | ||
39.5 | even | 4 | 3042.2.b.o.1351.1 | 6 | |||
39.8 | even | 4 | 3042.2.b.o.1351.6 | 6 | |||
39.38 | odd | 2 | 3042.2.a.ba.1.1 | 3 | |||
52.51 | odd | 2 | 8112.2.a.cm.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1014.2.a.n.1.3 | yes | 3 | 13.12 | even | 2 | ||
1014.2.b.f.337.1 | 6 | 13.8 | odd | 4 | |||
1014.2.b.f.337.6 | 6 | 13.5 | odd | 4 | |||
1014.2.e.l.529.3 | 6 | 13.10 | even | 6 | |||
1014.2.e.l.991.3 | 6 | 13.4 | even | 6 | |||
1014.2.e.n.529.1 | 6 | 13.3 | even | 3 | |||
1014.2.e.n.991.1 | 6 | 13.9 | even | 3 | |||
1014.2.i.h.361.1 | 12 | 13.7 | odd | 12 | |||
1014.2.i.h.361.6 | 12 | 13.6 | odd | 12 | |||
1014.2.i.h.823.3 | 12 | 13.2 | odd | 12 | |||
1014.2.i.h.823.4 | 12 | 13.11 | odd | 12 | |||
3042.2.a.ba.1.1 | 3 | 39.38 | odd | 2 | |||
3042.2.a.bh.1.3 | 3 | 3.2 | odd | 2 | |||
3042.2.b.o.1351.1 | 6 | 39.5 | even | 4 | |||
3042.2.b.o.1351.6 | 6 | 39.8 | even | 4 | |||
8112.2.a.cj.1.1 | 3 | 4.3 | odd | 2 | |||
8112.2.a.cm.1.3 | 3 | 52.51 | odd | 2 |