Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [352,2,Mod(351,352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("352.351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(2.81073415115\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.12 | ||
Root | \(-0.892524 - 1.09700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.351 |
Dual form | 352.2.e.a.351.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/352\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(287\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.81361i | 1.62444i | 0.583354 | + | 0.812218i | \(0.301740\pi\) | ||||
−0.583354 | + | 0.812218i | \(0.698260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.289169 | 0.129320 | 0.0646601 | − | 0.997907i | \(-0.479404\pi\) | ||||
0.0646601 | + | 0.997907i | \(0.479404\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.38799 | 1.65850 | 0.829252 | − | 0.558876i | \(-0.188767\pi\) | ||||
0.829252 | + | 0.558876i | \(0.188767\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.91638 | −1.63879 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56483 | + | 2.10278i | 0.773324 | + | 0.634011i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55956i | 0.432544i | 0.976333 | + | 0.216272i | \(0.0693898\pi\) | ||||
−0.976333 | + | 0.216272i | \(0.930610\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.813607i | 0.210072i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.57009i | − | 0.865875i | −0.901424 | − | 0.432938i | \(-0.857477\pi\) | ||
0.901424 | − | 0.432938i | \(-0.142523\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.39852 | −1.46792 | −0.733961 | − | 0.679192i | \(-0.762330\pi\) | ||||
−0.733961 | + | 0.679192i | \(0.762330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3461i | 2.69413i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.39194i | − | 0.707269i | −0.935384 | − | 0.353635i | \(-0.884946\pi\) | ||
0.935384 | − | 0.353635i | \(-0.115054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.91638 | −0.983276 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.39194i | − | 1.03768i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.64632i | − | 0.677104i | −0.940948 | − | 0.338552i | \(-0.890063\pi\) | ||
0.940948 | − | 0.338552i | \(-0.109937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.01916i | 1.61989i | 0.586507 | + | 0.809944i | \(0.300503\pi\) | ||||
−0.586507 | + | 0.809944i | \(0.699497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.91638 | + | 7.21641i | −1.02991 | + | 1.25622i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26887 | 0.214478 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.289169 | 0.0475390 | 0.0237695 | − | 0.999717i | \(-0.492433\pi\) | ||||
0.0237695 | + | 0.999717i | \(0.492433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.38799 | −0.702640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.68921i | − | 1.04468i | −0.852737 | − | 0.522340i | \(-0.825059\pi\) | ||
0.852737 | − | 0.522340i | \(-0.174941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12965 | 0.782265 | 0.391132 | − | 0.920334i | \(-0.372083\pi\) | ||||
0.391132 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.42166 | −0.211929 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.04888i | − | 1.02818i | −0.857735 | − | 0.514092i | \(-0.828129\pi\) | ||
0.857735 | − | 0.514092i | \(-0.171871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2544 | 1.75063 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0448 | 1.40656 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.25443 | 1.27119 | 0.635597 | − | 0.772021i | \(-0.280754\pi\) | ||||
0.635597 | + | 0.772021i | \(0.280754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.741667 | + | 0.608056i | 0.100006 | + | 0.0819903i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 18.0029i | − | 2.38455i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.440820i | − | 0.0573898i | −0.999588 | − | 0.0286949i | \(-0.990865\pi\) | ||
0.999588 | − | 0.0286949i | \(-0.00913513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.7865i | − | 1.38107i | −0.723299 | − | 0.690535i | \(-0.757375\pi\) | ||
0.723299 | − | 0.690535i | \(-0.242625\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.5730 | −2.71794 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.450976i | 0.0559366i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.97028i | 0.485047i | 0.970146 | + | 0.242523i | \(0.0779751\pi\) | ||||
−0.970146 | + | 0.242523i | \(0.922025\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.54359 | 1.14891 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.76473i | 0.684148i | 0.939673 | + | 0.342074i | \(0.111129\pi\) | ||||
−0.939673 | + | 0.342074i | \(0.888871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.68921i | 0.782913i | 0.920197 | + | 0.391457i | \(0.128029\pi\) | ||||
−0.920197 | + | 0.391457i | \(0.871971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 13.8328i | − | 1.59727i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.2544 | + | 9.22695i | 1.28256 | + | 1.05151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.421663 | 0.0468514 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.9056 | −1.52634 | −0.763170 | − | 0.646197i | \(-0.776358\pi\) | ||||
−0.763170 | + | 0.646197i | \(0.776358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.03236i | − | 0.111975i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2593 | 1.09991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5925 | 1.33480 | 0.667400 | − | 0.744700i | \(-0.267407\pi\) | ||||
0.667400 | + | 0.744700i | \(0.267407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.84333i | 0.717375i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.3764 | −2.63141 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85025 | −0.189832 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.75971 | −0.889414 | −0.444707 | − | 0.895676i | \(-0.646692\pi\) | ||||
−0.444707 | + | 0.895676i | \(0.646692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.6097 | − | 10.3380i | −1.26732 | − | 1.03901i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.8733i | − | 1.28094i | −0.767984 | − | 0.640469i | \(-0.778740\pi\) | ||
0.767984 | − | 0.640469i | \(-0.221260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.2056i | − | 1.59678i | −0.602140 | − | 0.798390i | \(-0.705685\pi\) | ||
0.602140 | − | 0.798390i | \(-0.294315\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.57009i | 0.348406i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6912 | −1.32357 | −0.661787 | − | 0.749692i | \(-0.730202\pi\) | ||||
−0.661787 | + | 0.749692i | \(0.730202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.527200i | 0.0504966i | 0.999681 | + | 0.0252483i | \(0.00803764\pi\) | ||||
−0.999681 | + | 0.0252483i | \(0.991962\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.813607i | 0.0772241i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.49472 | 0.234683 | 0.117342 | − | 0.993092i | \(-0.462563\pi\) | ||||
0.117342 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.980843i | − | 0.0914641i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.66739i | − | 0.708850i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 15.6655i | − | 1.43606i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.15667 | + | 10.7865i | 0.196061 | + | 0.980592i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.8208 | 1.69702 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.86751 | −0.256478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.90465 | 0.257746 | 0.128873 | − | 0.991661i | \(-0.458864\pi\) | ||||
0.128873 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.4328i | 1.27074i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39852 | −0.559041 | −0.279521 | − | 0.960140i | \(-0.590176\pi\) | ||||
−0.279521 | + | 0.960140i | \(0.590176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.0766 | −2.43455 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.55918i | − | 0.134193i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.33804 | 0.114317 | 0.0571584 | − | 0.998365i | \(-0.481796\pi\) | ||||
0.0571584 | + | 0.998365i | \(0.481796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.37745 | −0.201653 | −0.100826 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100826 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.8328 | 1.67022 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.27940 | + | 4.00000i | −0.274237 | + | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.05440i | − | 0.0875632i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 34.4791i | 2.84379i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.55956i | − | 0.127764i | −0.997957 | − | 0.0638820i | \(-0.979652\pi\) | ||
0.997957 | − | 0.0638820i | \(-0.0203481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.72157 | 0.628373 | 0.314186 | − | 0.949361i | \(-0.398268\pi\) | ||||
0.314186 | + | 0.949361i | \(0.398268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.5519i | 1.41899i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.60806i | 0.209484i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.12193 | −0.328966 | −0.164483 | − | 0.986380i | \(-0.552596\pi\) | ||||
−0.164483 | + | 0.986380i | \(0.552596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.0383i | 2.06497i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 14.8838i | − | 1.17301i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7144i | 1.46583i | 0.680323 | + | 0.732913i | \(0.261840\pi\) | ||||
−0.680323 | + | 0.732913i | \(0.738160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.71083 | + | 2.08676i | −0.133188 | + | 0.162454i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.92572 | 0.535928 | 0.267964 | − | 0.963429i | \(-0.413649\pi\) | ||||
0.267964 | + | 0.963429i | \(0.413649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5678 | 0.812906 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.4576 | 2.40562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0791i | 1.37453i | 0.726406 | + | 0.687266i | \(0.241189\pi\) | ||||
−0.726406 | + | 0.687266i | \(0.758811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5730 | −1.63077 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.24029 | 0.0932261 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 11.6952i | − | 0.874144i | −0.899427 | − | 0.437072i | \(-0.856016\pi\) | ||
0.899427 | − | 0.437072i | \(-0.143984\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.96526 | −0.220406 | −0.110203 | − | 0.993909i | \(-0.535150\pi\) | ||||
−0.110203 | + | 0.993909i | \(0.535150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.3490 | 2.24346 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0836184 | 0.00614775 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50711 | − | 9.15667i | 0.548974 | − | 0.669602i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 23.6598i | − | 1.72100i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.98084i | − | 0.505116i | −0.967582 | − | 0.252558i | \(-0.918728\pi\) | ||
0.967582 | − | 0.252558i | \(-0.0812719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.17352i | − | 0.300417i | −0.988654 | − | 0.150208i | \(-0.952006\pi\) | ||
0.988654 | − | 0.150208i | \(-0.0479944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.26887 | −0.0908655 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.9056i | − | 0.990735i | −0.868684 | − | 0.495367i | \(-0.835033\pi\) | ||
0.868684 | − | 0.495367i | \(-0.164967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4600i | 1.09593i | 0.836502 | + | 0.547964i | \(0.184597\pi\) | ||||
−0.836502 | + | 0.547964i | \(0.815403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1708 | −0.787928 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 16.0000i | − | 1.12298i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.93431i | − | 0.135098i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.6761i | 1.15907i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.4111 | − | 13.4547i | −1.13518 | − | 0.930678i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18405 | 0.425728 | 0.212864 | − | 0.977082i | \(-0.431721\pi\) | ||||
0.212864 | + | 0.977082i | \(0.431721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.2197 | −1.11135 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.48333 | 0.101163 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 39.5759i | 2.68659i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.8208 | −1.27179 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.56777 | 0.374529 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.98084i | − | 0.467472i | −0.972300 | − | 0.233736i | \(-0.924905\pi\) | ||
0.972300 | − | 0.233736i | \(-0.0750951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.1708 | 1.61139 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6912 | 0.908714 | 0.454357 | − | 0.890820i | \(-0.349869\pi\) | ||||
0.454357 | + | 0.890820i | \(0.349869\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2786 | −1.40613 | −0.703065 | − | 0.711126i | \(-0.748186\pi\) | ||||
−0.703065 | + | 0.711126i | \(0.748186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.9610 | + | 31.6655i | −1.70811 | + | 2.08344i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.8113i | 1.82198i | 0.412433 | + | 0.910988i | \(0.364679\pi\) | ||||
−0.412433 | + | 0.910988i | \(0.635321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.03831i | − | 0.132965i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.8323i | 2.06773i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.50440 | 0.356050 | 0.178025 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178025 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4118i | 0.670680i | 0.942097 | + | 0.335340i | \(0.108851\pi\) | ||||
−0.942097 | + | 0.335340i | \(0.891149\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 14.9894i | − | 0.961573i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.54359 | 0.226392 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.97887i | − | 0.634941i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 39.1250i | − | 2.47944i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.2841i | − | 0.964727i | −0.875971 | − | 0.482363i | \(-0.839778\pi\) | ||
0.875971 | − | 0.482363i | \(-0.160222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.13249 | − | 8.69975i | 0.448416 | − | 0.546948i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.90465 | 0.181896 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5678 | −0.721578 | −0.360789 | − | 0.932647i | \(-0.617493\pi\) | ||||
−0.360789 | + | 0.932647i | \(0.617493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26887 | 0.0788436 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.9267i | 1.10963i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.4443 | −1.69229 | −0.846145 | − | 0.532952i | \(-0.821082\pi\) | ||||
−0.846145 | + | 0.532952i | \(0.821082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67609 | 0.164391 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.4303i | 2.16830i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.25443 | 0.0764837 | 0.0382419 | − | 0.999269i | \(-0.487824\pi\) | ||||
0.0382419 | + | 0.999269i | \(0.487824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.9610 | −1.57702 | −0.788509 | − | 0.615023i | \(-0.789147\pi\) | ||||
−0.788509 | + | 0.615023i | \(0.789147\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.2544 | −1.16533 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.6097 | − | 10.3380i | −0.760392 | − | 0.623408i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.527200i | − | 0.0316764i | −0.999875 | − | 0.0158382i | \(-0.994958\pi\) | ||
0.999875 | − | 0.0158382i | \(-0.00504167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 44.3416i | − | 2.65466i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.2593i | − | 0.612019i | −0.952028 | − | 0.306009i | \(-0.901006\pi\) | ||
0.952028 | − | 0.306009i | \(-0.0989939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.59192 | 0.154074 | 0.0770368 | − | 0.997028i | \(-0.475454\pi\) | ||||
0.0770368 | + | 0.997028i | \(0.475454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 5.20588i | − | 0.308370i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 29.3522i | − | 1.73260i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.25443 | 0.250260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 24.6464i | − | 1.44480i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.73308i | − | 0.334930i | −0.985878 | − | 0.167465i | \(-0.946442\pi\) | ||
0.985878 | − | 0.167465i | \(-0.0535581\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.127471i | − | 0.00742166i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.3380 | − | 13.8294i | 0.657900 | − | 0.802463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.28994 | 0.305925 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.5089 | 1.29739 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.2203 | 2.08080 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.11912i | − | 0.178600i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.1745 | −0.866054 | −0.433027 | − | 0.901381i | \(-0.642555\pi\) | ||||
−0.433027 | + | 0.901381i | \(0.642555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 45.5960 | 2.59387 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1466i | 0.745477i | 0.927936 | + | 0.372738i | \(0.121581\pi\) | ||||
−0.927936 | + | 0.372738i | \(0.878419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6030 | −0.881936 | −0.440968 | − | 0.897523i | \(-0.645365\pi\) | ||||
−0.440968 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.23824 | −0.351485 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.44584 | 0.0812066 | 0.0406033 | − | 0.999175i | \(-0.487072\pi\) | ||||
0.0406033 | + | 0.999175i | \(0.487072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.66739 | − | 9.35218i | 0.429291 | − | 0.523621i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.5215i | − | 2.15006i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.8433i | 1.27104i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7.66739i | − | 0.425310i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.48333 | −0.0820286 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 30.9304i | − | 1.70525i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0680i | 0.773249i | 0.922237 | + | 0.386624i | \(0.126359\pi\) | ||||
−0.922237 | + | 0.386624i | \(0.873641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.42166 | −0.0779066 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.14808i | 0.0627263i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.66814i | − | 0.145343i | −0.997356 | − | 0.0726715i | \(-0.976848\pi\) | ||
0.997356 | − | 0.0726715i | \(-0.0231525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.01916i | 0.381228i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9653 | + | 23.1326i | −1.02703 | + | 1.25270i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23.0564 | 1.24493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.75971 | 0.148578 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.9294 | −1.06987 | −0.534933 | − | 0.844894i | \(-0.679663\pi\) | ||||
−0.534933 | + | 0.844894i | \(0.679663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.60170i | 0.513967i | 0.966416 | + | 0.256984i | \(0.0827286\pi\) | ||||
−0.966416 | + | 0.256984i | \(0.917271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.40906 | 0.448842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.24029 | 0.385362 | 0.192681 | − | 0.981261i | \(-0.438282\pi\) | ||||
0.192681 | + | 0.981261i | \(0.438282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.66698i | 0.0884740i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.0766 | 2.33278 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.35466 | −0.388164 | −0.194082 | − | 0.980985i | \(-0.562173\pi\) | ||||
−0.194082 | + | 0.980985i | \(0.562173\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.9411 | 1.15479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.3490 | + | 6.06803i | −1.59291 | + | 0.318489i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.93431i | 0.101246i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5280i | 0.810555i | 0.914194 | + | 0.405278i | \(0.132825\pi\) | ||||
−0.914194 | + | 0.405278i | \(0.867175\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.8867i | 1.71201i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.6083 | 2.10828 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.3919i | − | 1.72897i | −0.502662 | − | 0.864483i | \(-0.667646\pi\) | ||
0.502662 | − | 0.864483i | \(-0.332354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 8.06803i | − | 0.416631i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.68665 | 0.292877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.1275i | − | 0.725679i | −0.931852 | − | 0.362840i | \(-0.881807\pi\) | ||
0.931852 | − | 0.362840i | \(-0.118193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.17255i | 0.418692i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.3713i | 1.96068i | 0.197307 | + | 0.980342i | \(0.436781\pi\) | ||||
−0.197307 | + | 0.980342i | \(0.563219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.25443 | + | 2.66814i | 0.165861 | + | 0.135981i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.2193 | −1.28197 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.3658 | 1.43820 | 0.719101 | − | 0.694905i | \(-0.244554\pi\) | ||||
0.719101 | + | 0.694905i | \(0.244554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1096 | −0.612407 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.0029i | − | 0.908127i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.27157 | 0.164610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2544 | −1.06673 | −0.533365 | − | 0.845885i | \(-0.679073\pi\) | ||||
−0.533365 | + | 0.845885i | \(0.679073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 78.9966i | − | 3.95478i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0766 | −0.902704 | −0.451352 | − | 0.892346i | \(-0.649058\pi\) | ||||
−0.451352 | + | 0.892346i | \(0.649058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0659 | −0.700673 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.121932 | 0.00605883 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.741667 | + | 0.608056i | 0.0367631 | + | 0.0301402i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.4328i | − | 0.713657i | −0.934170 | − | 0.356829i | \(-0.883858\pi\) | ||
0.934170 | − | 0.356829i | \(-0.116142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.76473i | 0.185700i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.93431i | − | 0.0951812i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.02107 | −0.197387 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.68921i | − | 0.327572i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.61665i | − | 0.225538i | −0.993621 | − | 0.112769i | \(-0.964028\pi\) | ||
0.993621 | − | 0.112769i | \(-0.0359720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2544 | −0.645981 | −0.322991 | − | 0.946402i | \(-0.604688\pi\) | ||||
−0.322991 | + | 0.946402i | \(0.604688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.6550i | 1.68498i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.5519i | 0.851394i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 47.3311i | − | 2.29051i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.2544 | − | 9.22695i | −0.543369 | − | 0.445481i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.33359 | 0.160573 | 0.0802866 | − | 0.996772i | \(-0.474416\pi\) | ||||
0.0802866 | + | 0.996772i | \(0.474416\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.759707 | −0.0365092 | −0.0182546 | − | 0.999833i | \(-0.505811\pi\) | ||||
−0.0182546 | + | 0.999833i | \(0.505811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.96667 | 0.142241 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.7034i | 1.03822i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2593 | 0.489650 | 0.244825 | − | 0.969567i | \(-0.421269\pi\) | ||||
0.244825 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −60.2474 | −2.86893 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7336i | 1.41268i | 0.707871 | + | 0.706342i | \(0.249656\pi\) | ||||
−0.707871 | + | 0.706342i | \(0.750344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.64135 | 0.172616 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.38799 | 0.207545 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0036 | 0.802448 | 0.401224 | − | 0.915980i | \(-0.368585\pi\) | ||||
0.401224 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0659 | − | 17.1567i | 0.662338 | − | 0.807876i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.7255i | 1.02075i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97887i | 0.0927711i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.3348i | − | 0.717331i | −0.933466 | − | 0.358665i | \(-0.883232\pi\) | ||
0.933466 | − | 0.358665i | \(-0.116768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.2497 | −0.898501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2841i | 1.27075i | 0.772206 | + | 0.635373i | \(0.219153\pi\) | ||||
−0.772206 | + | 0.635373i | \(0.780847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8625i | 0.737192i | 0.929590 | + | 0.368596i | \(0.120161\pi\) | ||||
−0.929590 | + | 0.368596i | \(0.879839\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.33804 | −0.340294 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.32246i | 0.0611961i | 0.999532 | + | 0.0305980i | \(0.00974118\pi\) | ||||
−0.999532 | + | 0.0305980i | \(0.990259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.4215i | 0.804452i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.5975i | − | 0.534384i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.1567 | + | 10.7865i | 0.604945 | + | 0.495964i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.4576 | 1.44337 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −45.4983 | −2.08322 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.2747 | −1.70313 | −0.851563 | − | 0.524253i | \(-0.824345\pi\) | ||||
−0.851563 | + | 0.524253i | \(0.824345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.450976i | 0.0205627i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 41.8772 | 1.90548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.53303 | −0.115019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.43026i | 0.246068i | 0.992402 | + | 0.123034i | \(0.0392625\pi\) | ||||
−0.992402 | + | 0.123034i | \(0.960738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −52.6550 | −2.38114 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.374751 | −0.0169123 | −0.00845613 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845613 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.0177 | −0.586288 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.64632 | − | 2.98944i | −0.163890 | − | 0.134365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.2956i | 1.13466i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.61665i | − | 0.206670i | −0.994647 | − | 0.103335i | \(-0.967049\pi\) | ||
0.994647 | − | 0.103335i | \(-0.0329513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.4863i | 0.870582i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.48333 | −0.0661386 | −0.0330693 | − | 0.999453i | \(-0.510528\pi\) | ||||
−0.0330693 | + | 0.999453i | \(0.510528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.72254i | − | 0.165651i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.7336i | 1.32051i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4458 | 0.773273 | 0.386637 | − | 0.922232i | \(-0.373637\pi\) | ||||
0.386637 | + | 0.922232i | \(0.373637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.3522i | 1.29846i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.5005i | 1.52323i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.68614i | − | 0.206496i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.8222 | − | 18.0791i | 0.651880 | − | 0.795120i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −50.8676 | −2.23284 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3663 | −1.46180 | −0.730902 | − | 0.682482i | \(-0.760901\pi\) | ||||
−0.730902 | + | 0.682482i | \(0.760901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9838 | 0.917557 | 0.458779 | − | 0.888551i | \(-0.348287\pi\) | ||||
0.458779 | + | 0.888551i | \(0.348287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 60.6980i | − | 2.64908i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.1992 | 1.40262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4947 | 0.499770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.16724i | 0.0940501i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.4322 | 0.451870 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.95905 | −0.171165 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.9058 | 1.41999 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.4305 | + | 25.7683i | 1.35381 | + | 1.10992i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.2850i | 1.00110i | 0.865707 | + | 0.500551i | \(0.166869\pi\) | ||||
−0.865707 | + | 0.500551i | \(0.833131\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.34307i | − | 0.358035i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.152450i | 0.00653023i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6816 | −0.969795 | −0.484898 | − | 0.874571i | \(-0.661143\pi\) | ||||
−0.484898 | + | 0.874571i | \(0.661143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53.0306i | 2.26329i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.3311i | 0.993936i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 49.6444 | 2.11109 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.235269i | 0.00998663i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 40.6845i | − | 1.72386i | −0.507029 | − | 0.861929i | \(-0.669256\pi\) | ||
0.507029 | − | 0.861929i | \(-0.330744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.7633 | + | 21.1220i | 1.08773 | + | 0.891773i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0895 | 0.804525 | 0.402262 | − | 0.915524i | \(-0.368224\pi\) | ||||
0.402262 | + | 0.915524i | \(0.368224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.721394 | 0.0303493 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.85025 | 0.0777032 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.6485i | − | 1.11716i | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||
0.829450 | − | 0.558581i | \(-0.188654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6605 | −0.780919 | −0.390459 | − | 0.920620i | \(-0.627684\pi\) | ||||
−0.390459 | + | 0.920620i | \(0.627684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.6413 | 0.820529 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6761i | 0.695441i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5230 | −0.771122 | −0.385561 | − | 0.922682i | \(-0.625992\pi\) | ||||
−0.385561 | + | 0.922682i | \(0.625992\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7426 | 0.488008 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −61.0177 | −2.53144 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7360 | + | 19.4600i | 0.983045 | + | 0.805950i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.21717i | − | 0.0916686i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3622i | 0.551518i | 0.961227 | + | 0.275759i | \(0.0889292\pi\) | ||||
−0.961227 | + | 0.275759i | \(0.911071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 57.7093i | − | 2.37787i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.1250 | 1.60939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.24899i | − | 0.379811i | −0.981802 | − | 0.189905i | \(-0.939182\pi\) | ||
0.981802 | − | 0.189905i | \(-0.0608181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.52998i | − | 0.185711i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.4983 | −1.78027 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7733i | 1.37994i | 0.723838 | + | 0.689970i | \(0.242376\pi\) | ||||
−0.723838 | + | 0.689970i | \(0.757624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.4901i | 1.36609i | 0.730375 | + | 0.683046i | \(0.239345\pi\) | ||||
−0.730375 | + | 0.683046i | \(0.760655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 19.5194i | − | 0.794892i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.623642 | + | 3.11912i | 0.0253547 | + | 0.126810i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.5519 | −0.712412 | −0.356206 | − | 0.934408i | \(-0.615930\pi\) | ||||
−0.356206 | + | 0.934408i | \(0.615930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.0177 | 1.82421 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.9931 | 0.444735 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 35.3262i | − | 1.42681i | −0.700751 | − | 0.713406i | \(-0.747152\pi\) | ||
0.700751 | − | 0.713406i | \(-0.252848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.44239 | 0.219458 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.2544 | −1.01670 | −0.508352 | − | 0.861149i | \(-0.669745\pi\) | ||||
−0.508352 | + | 0.861149i | \(0.669745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7547i | 0.794008i | 0.917817 | + | 0.397004i | \(0.129950\pi\) | ||||
−0.917817 | + | 0.397004i | \(0.870050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.2892 | −0.733919 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.2556 | 2.21377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.7527 | 0.950109 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 37.8561 | − | 46.1744i | 1.51183 | − | 1.84403i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.03236i | − | 0.0411628i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.0575i | − | 0.758666i | −0.925260 | − | 0.379333i | \(-0.876154\pi\) | ||
0.925260 | − | 0.379333i | \(-0.123846\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.3995i | 0.691568i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.839934 | 0.0333318 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.1115i | 0.757225i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 28.3416i | − | 1.12118i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.3275 | −0.881883 | −0.440941 | − | 0.897536i | \(-0.645355\pi\) | ||||
−0.440941 | + | 0.897536i | \(0.645355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.9703i | 0.472062i | 0.971746 | + | 0.236031i | \(0.0758467\pi\) | ||||
−0.971746 | + | 0.236031i | \(0.924153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.17352i | 0.164332i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 10.2353i | − | 0.402390i | −0.979551 | − | 0.201195i | \(-0.935518\pi\) | ||
0.979551 | − | 0.201195i | \(-0.0644825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.926944 | − | 1.13063i | 0.0363857 | − | 0.0443809i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −111.351 | −4.36419 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.1325 | 0.592180 | 0.296090 | − | 0.955160i | \(-0.404317\pi\) | ||||
0.296090 | + | 0.955160i | \(0.404317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.85025 | −0.0722953 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 32.8867i | − | 1.28303i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.374751 | 0.0145982 | 0.00729911 | − | 0.999973i | \(-0.497677\pi\) | ||||
0.00729911 | + | 0.999973i | \(0.497677\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.6202 | 1.85221 | 0.926106 | − | 0.377263i | \(-0.123135\pi\) | ||||
0.926106 | + | 0.377263i | \(0.123135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.6655i | 0.608399i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.11888 | −0.314837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3681 | −0.478895 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.6413 | 0.759378 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.6816 | − | 27.6655i | 0.875613 | − | 1.06802i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.8745i | 1.53705i | 0.639821 | + | 0.768524i | \(0.279008\pi\) | ||||
−0.639821 | + | 0.768524i | \(0.720992\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.5089i | 1.02033i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.9380i | − | 0.574113i | −0.957914 | − | 0.287057i | \(-0.907323\pi\) | ||
0.957914 | − | 0.287057i | \(-0.0926768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.4375 | −1.47510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.5215i | 1.47615i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2056i | 0.467032i | 0.972353 | + | 0.233516i | \(0.0750232\pi\) | ||||
−0.972353 | + | 0.233516i | \(0.924977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.386920 | 0.0147835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 59.8696i | − | 2.28417i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4328i | 0.549847i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.1658i | 1.22364i | 0.790995 | + | 0.611822i | \(0.209563\pi\) | ||||
−0.790995 | + | 0.611822i | \(0.790437\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −55.3311 | − | 45.3632i | −2.10185 | − | 1.72321i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.687484 | −0.0260778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.8811 | −0.904562 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −78.2499 | −2.95968 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.657608i | 0.0248375i | 0.999923 | + | 0.0124188i | \(0.00395312\pi\) | ||||
−0.999923 | + | 0.0124188i | \(0.996047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.85025 | −0.0697835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.73501 | 0.215993 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 56.4877i | − | 2.12444i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.2302 | 1.24799 | 0.623994 | − | 0.781429i | \(-0.285509\pi\) | ||||
0.623994 | + | 0.781429i | \(0.285509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −55.6225 | −2.08601 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.5925 | 1.14570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.948300 | + | 1.15667i | −0.0354644 | + | 0.0432572i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.4872i | 0.578381i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 18.1164i | − | 0.675627i | −0.941213 | − | 0.337814i | \(-0.890313\pi\) | ||
0.941213 | − | 0.337814i | \(-0.109687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 71.1097i | − | 2.64826i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.2946 | −1.08948 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.9267i | 0.665781i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.3708i | − | 0.792600i | −0.918121 | − | 0.396300i | \(-0.870294\pi\) | ||
0.918121 | − | 0.396300i | \(-0.129706\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.4394 | 1.60887 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 18.3133i | − | 0.677344i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.4683i | 1.27312i | 0.771229 | + | 0.636558i | \(0.219643\pi\) | ||||
−0.771229 | + | 0.636558i | \(0.780357\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.97028i | 0.367759i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.34861 | + | 10.1831i | −0.307525 | + | 0.375099i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.15072 | 0.336615 | 0.168307 | − | 0.985735i | \(-0.446170\pi\) | ||||
0.168307 | + | 0.985735i | \(0.446170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.0766 | 1.03142 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.98774 | −0.256355 | −0.128178 | − | 0.991751i | \(-0.540913\pi\) | ||||
−0.128178 | + | 0.991751i | \(0.540913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.450976i | − | 0.0165225i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 68.3654 | 2.50136 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −60.0766 | −2.19515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 40.5285i | − | 1.47891i | −0.673208 | − | 0.739453i | \(-0.735084\pi\) | ||
0.673208 | − | 0.739453i | \(-0.264916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.0036 | 1.56714 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.23284 | 0.0812612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.74557 | −0.245172 | −0.122586 | − | 0.992458i | \(-0.539119\pi\) | ||||
−0.122586 | + | 0.992458i | \(0.539119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.4777 | + | 20.0680i | 0.888483 | + | 0.728423i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0363i | 0.545064i | 0.962147 | + | 0.272532i | \(0.0878610\pi\) | ||||
−0.962147 | + | 0.272532i | \(0.912139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.31335i | 0.0837488i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.07547i | 0.183504i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.687484 | 0.0248236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.66814i | − | 0.0962157i | −0.998842 | − | 0.0481079i | \(-0.984681\pi\) | ||
0.998842 | − | 0.0481079i | \(-0.0153191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 32.5472i | − | 1.17216i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.3311 | −1.48657 | −0.743287 | − | 0.668972i | \(-0.766734\pi\) | ||||
−0.743287 | + | 0.668972i | \(0.766734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 44.3416i | − | 1.59280i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.57009i | 0.128076i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.8011i | 1.53351i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1219 | + | 14.7855i | −0.433757 | + | 0.529068i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.6607 | −0.702618 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.19193 | −0.0425419 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3346 | −0.510972 | −0.255486 | − | 0.966813i | \(-0.582235\pi\) | ||||
−0.255486 | + | 0.966813i | \(0.582235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 77.2176i | − | 2.74902i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9468 | 0.389223 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8222 | 0.597374 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.52946i | 0.267042i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.0313 | 1.27629 | 0.638147 | − | 0.769914i | \(-0.279701\pi\) | ||||
0.638147 | + | 0.769914i | \(0.279701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.1652 | −0.890279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −61.9094 | −2.18746 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0659 | + | 17.1567i | −0.496375 | + | 0.605446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 4.30393i | − | 0.151694i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.52946i | 0.124243i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.7705i | 1.67952i | 0.542956 | + | 0.839761i | \(0.317305\pi\) | ||||
−0.542956 | + | 0.839761i | \(0.682695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9620 | 1.29791 | 0.648955 | − | 0.760827i | \(-0.275206\pi\) | ||||
0.648955 | + | 0.760827i | \(0.275206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 73.0440i | − | 2.56177i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.41162i | 0.189561i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.8222 | −1.14830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 33.6444i | − | 1.17563i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 14.8076i | − | 0.516788i | −0.966040 | − | 0.258394i | \(-0.916807\pi\) | ||
0.966040 | − | 0.258394i | \(-0.0831933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.4096i | − | 1.12973i | −0.825184 | − | 0.564865i | \(-0.808928\pi\) | ||
0.825184 | − | 0.564865i | \(-0.191072\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.0872 | − | 35.4786i | 1.01269 | − | 1.23521i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9573 | −0.450570 | −0.225285 | − | 0.974293i | \(-0.572331\pi\) | ||||
−0.225285 | + | 0.974293i | \(0.572331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5542 | −0.505487 | −0.252743 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252743 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.48333 | 0.0514563 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 43.7495i | − | 1.51583i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00270 | 0.0693063 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.6308 | 1.68093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.7436i | 1.37210i | 0.727554 | + | 0.686051i | \(0.240657\pi\) | ||||
−0.727554 | + | 0.686051i | \(0.759343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.7044 | 0.541530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.8657 | 0.994186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.05587 | 0.105125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.46346 | + | 47.3311i | 0.325168 | + | 1.62631i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.29264i | 0.250283i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.980843i | − | 0.0336229i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.7429i | − | 0.436307i | −0.975914 | − | 0.218154i | \(-0.929997\pi\) | ||
0.975914 | − | 0.218154i | \(-0.0700034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.09654 | 0.311095 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 11.1613i | − | 0.381261i | −0.981662 | − | 0.190631i | \(-0.938947\pi\) | ||
0.981662 | − | 0.190631i | \(-0.0610533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 54.6152i | − | 1.86345i | −0.363169 | − | 0.931723i | \(-0.618305\pi\) | ||
0.363169 | − | 0.931723i | \(-0.381695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 82.5855 | 2.81451 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.9688i | 1.29247i | 0.763137 | + | 0.646237i | \(0.223658\pi\) | ||||
−0.763137 | + | 0.646237i | \(0.776342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.22792i | 0.177755i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9703i | 0.406532i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.0177 | + | 23.7902i | 0.984358 | + | 0.807027i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.19189 | −0.209804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.0661 | 1.45757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.5826 | −0.425369 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3919i | 1.12756i | 0.825924 | + | 0.563782i | \(0.190654\pi\) | ||||
−0.825924 | + | 0.563782i | \(0.809346\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.1306 | 0.544073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4358 | 1.46339 | 0.731695 | − | 0.681633i | \(-0.238730\pi\) | ||||
0.731695 | + | 0.681633i | \(0.238730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.7733i | − | 0.463509i | −0.972774 | − | 0.231755i | \(-0.925553\pi\) | ||
0.972774 | − | 0.231755i | \(-0.0744466\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.358654 | 0.0120560 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.6627 | −1.39890 | −0.699448 | − | 0.714683i | \(-0.746571\pi\) | ||||
−0.699448 | + | 0.714683i | \(0.746571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7456 | 0.427473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.08149 | + | 0.886662i | 0.0362314 | + | 0.0297043i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.1024i | 1.50929i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.38190i | − | 0.113044i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8838i | 0.496956i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.8867 | 1.09683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 33.0392i | − | 1.10069i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 63.3311i | 2.10753i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.857459 | −0.0285029 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2056i | 0.405279i | 0.979253 | + | 0.202639i | \(0.0649519\pi\) | ||||
−0.979253 | + | 0.202639i | \(0.935048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 63.2899i | 2.09919i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.36222i | − | 0.310184i | −0.987900 | − | 0.155092i | \(-0.950433\pi\) | ||
0.987900 | − | 0.155092i | \(-0.0495675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.6655 | − | 29.2404i | −1.18036 | − | 0.967716i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.77597 | 0.290125 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.0766 | −0.927172 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.8113 | 0.917409 | 0.458704 | − | 0.888589i | \(-0.348314\pi\) | ||||
0.458704 | + | 0.888589i | \(0.348314\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 42.6951i | − | 1.40685i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.99044 | −0.295924 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42166 | −0.0467440 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 79.6727i | 2.61679i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.76328 | −0.254705 | −0.127352 | − | 0.991858i | \(-0.540648\pi\) | ||||
−0.127352 | + | 0.991858i | \(0.540648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78.4102 | −2.56979 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.9894 | −1.21098 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.17082 | − | 2.64782i | 0.0709934 | − | 0.0865930i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.4882i | − | 1.35536i | −0.735357 | − | 0.677680i | \(-0.762985\pi\) | ||
0.735357 | − | 0.677680i | \(-0.237015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 43.9008i | − | 1.43265i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.1439i | 0.656671i | 0.944561 | + | 0.328336i | \(0.106488\pi\) | ||||
−0.944561 | + | 0.328336i | \(0.893512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.6894 | −0.738870 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 6.84166i | − | 0.222559i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.3225i | 1.34280i | 0.741095 | + | 0.671400i | \(0.234307\pi\) | ||||
−0.741095 | + | 0.671400i | \(0.765693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4322 | −0.338644 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.06803i | 0.131915i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.1098i | 0.910565i | 0.890347 | + | 0.455283i | \(0.150462\pi\) | ||||
−0.890347 | + | 0.455283i | \(0.849538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.01864i | − | 0.0653217i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.3133 | + | 21.5730i | 0.850590 | + | 0.697357i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.87132 | 0.189595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.3452 | −1.62404 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 67.3110 | 2.16907 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.20685i | − | 0.0388499i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5730 | 0.693741 | 0.346871 | − | 0.937913i | \(-0.387244\pi\) | ||||
0.346871 | + | 0.937913i | \(0.387244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −64.2721 | −2.06472 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17.9320i | − | 0.575464i | −0.957711 | − | 0.287732i | \(-0.907099\pi\) | ||
0.957711 | − | 0.287732i | \(-0.0929013\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4322 | −0.334442 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.5730 | 0.690889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8953 | −1.40433 | −0.702167 | − | 0.712012i | \(-0.747784\pi\) | ||||
−0.702167 | + | 0.712012i | \(0.747784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.2975 | + | 26.4791i | 1.03223 | + | 0.846277i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.59192i | − | 0.0827536i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 21.7053i | − | 0.692291i | −0.938181 | − | 0.346146i | \(-0.887490\pi\) | ||
0.938181 | − | 0.346146i | \(-0.112510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.02107i | − | 0.128122i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 87.0259 | 2.77006 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 17.3995i | − | 0.553272i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 54.3799i | − | 1.72744i | −0.503976 | − | 0.863718i | \(-0.668130\pi\) | ||
0.503976 | − | 0.863718i | \(-0.331870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.5819 | −1.25609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.47054i | 0.141726i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.1384i | 1.87293i | 0.350758 | + | 0.936466i | \(0.385924\pi\) | ||||
−0.350758 | + | 0.936466i | \(0.614076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.55918i | − | 0.0493303i |
(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 | 352.2.e.a.351.12 | yes | 12 | |
3.2 | odd | 2 | 3168.2.o.e.703.7 | 12 | |||
4.3 | odd | 2 | inner | 352.2.e.a.351.1 | ✓ | 12 | |
8.3 | odd | 2 | 704.2.e.d.703.11 | 12 | |||
8.5 | even | 2 | 704.2.e.d.703.2 | 12 | |||
11.10 | odd | 2 | inner | 352.2.e.a.351.11 | yes | 12 | |
12.11 | even | 2 | 3168.2.o.e.703.6 | 12 | |||
16.3 | odd | 4 | 2816.2.g.i.1407.10 | 12 | |||
16.5 | even | 4 | 2816.2.g.i.1407.11 | 12 | |||
16.11 | odd | 4 | 2816.2.g.d.1407.4 | 12 | |||
16.13 | even | 4 | 2816.2.g.d.1407.1 | 12 | |||
33.32 | even | 2 | 3168.2.o.e.703.5 | 12 | |||
44.43 | even | 2 | inner | 352.2.e.a.351.2 | yes | 12 | |
88.21 | odd | 2 | 704.2.e.d.703.1 | 12 | |||
88.43 | even | 2 | 704.2.e.d.703.12 | 12 | |||
132.131 | odd | 2 | 3168.2.o.e.703.8 | 12 | |||
176.21 | odd | 4 | 2816.2.g.i.1407.12 | 12 | |||
176.43 | even | 4 | 2816.2.g.d.1407.3 | 12 | |||
176.109 | odd | 4 | 2816.2.g.d.1407.2 | 12 | |||
176.131 | even | 4 | 2816.2.g.i.1407.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.e.a.351.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
352.2.e.a.351.2 | yes | 12 | 44.43 | even | 2 | inner | |
352.2.e.a.351.11 | yes | 12 | 11.10 | odd | 2 | inner | |
352.2.e.a.351.12 | yes | 12 | 1.1 | even | 1 | trivial | |
704.2.e.d.703.1 | 12 | 88.21 | odd | 2 | |||
704.2.e.d.703.2 | 12 | 8.5 | even | 2 | |||
704.2.e.d.703.11 | 12 | 8.3 | odd | 2 | |||
704.2.e.d.703.12 | 12 | 88.43 | even | 2 | |||
2816.2.g.d.1407.1 | 12 | 16.13 | even | 4 | |||
2816.2.g.d.1407.2 | 12 | 176.109 | odd | 4 | |||
2816.2.g.d.1407.3 | 12 | 176.43 | even | 4 | |||
2816.2.g.d.1407.4 | 12 | 16.11 | odd | 4 | |||
2816.2.g.i.1407.9 | 12 | 176.131 | even | 4 | |||
2816.2.g.i.1407.10 | 12 | 16.3 | odd | 4 | |||
2816.2.g.i.1407.11 | 12 | 16.5 | even | 4 | |||
2816.2.g.i.1407.12 | 12 | 176.21 | odd | 4 | |||
3168.2.o.e.703.5 | 12 | 33.32 | even | 2 | |||
3168.2.o.e.703.6 | 12 | 12.11 | even | 2 | |||
3168.2.o.e.703.7 | 12 | 3.2 | odd | 2 | |||
3168.2.o.e.703.8 | 12 | 132.131 | odd | 2 |