Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1862,2,Mod(1,1862)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1862, 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("1862.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1862 = 2 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1862.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: | \(14.8681448564\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1862.1 |
$q$-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 | ||||||||
\(3\) | 1.30278 | 0.752158 | 0.376079 | − | 0.926588i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.30278 | −1.02983 | −0.514916 | − | 0.857240i | \(-0.672177\pi\) | ||||
−0.514916 | + | 0.857240i | \(0.672177\pi\) | |||||||
\(6\) | 1.30278 | 0.531856 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | −2.30278 | −0.728202 | ||||||||
\(11\) | −0.697224 | −0.210221 | −0.105111 | − | 0.994461i | \(-0.533520\pi\) | ||||
−0.105111 | + | 0.994461i | \(0.533520\pi\) | |||||||
\(12\) | 1.30278 | 0.376079 | ||||||||
\(13\) | −6.60555 | −1.83205 | −0.916025 | − | 0.401121i | \(-0.868621\pi\) | ||||
−0.916025 | + | 0.401121i | \(0.868621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.30278 | −0.307067 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.30278 | −0.514916 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.697224 | −0.148649 | ||||||||
\(23\) | −4.60555 | −0.960324 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(24\) | 1.30278 | 0.265928 | ||||||||
\(25\) | 0.302776 | 0.0605551 | ||||||||
\(26\) | −6.60555 | −1.29546 | ||||||||
\(27\) | −5.60555 | −1.07879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.908327 | 0.168672 | 0.0843360 | − | 0.996437i | \(-0.473123\pi\) | ||||
0.0843360 | + | 0.996437i | \(0.473123\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | 7.21110 | 1.29515 | 0.647576 | − | 0.762001i | \(-0.275783\pi\) | ||||
0.647576 | + | 0.762001i | \(0.275783\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.908327 | −0.158119 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30278 | −0.217129 | ||||||||
\(37\) | −4.90833 | −0.806924 | −0.403462 | − | 0.914996i | \(-0.632193\pi\) | ||||
−0.403462 | + | 0.914996i | \(0.632193\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −8.60555 | −1.37799 | ||||||||
\(40\) | −2.30278 | −0.364101 | ||||||||
\(41\) | −2.30278 | −0.359633 | −0.179817 | − | 0.983700i | \(-0.557550\pi\) | ||||
−0.179817 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.30278 | −0.961164 | −0.480582 | − | 0.876950i | \(-0.659575\pi\) | ||||
−0.480582 | + | 0.876950i | \(0.659575\pi\) | |||||||
\(44\) | −0.697224 | −0.105111 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | −4.60555 | −0.679051 | ||||||||
\(47\) | 3.90833 | 0.570088 | 0.285044 | − | 0.958514i | \(-0.407992\pi\) | ||||
0.285044 | + | 0.958514i | \(0.407992\pi\) | |||||||
\(48\) | 1.30278 | 0.188039 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.302776 | 0.0428189 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.60555 | −0.916025 | ||||||||
\(53\) | −8.51388 | −1.16947 | −0.584736 | − | 0.811224i | \(-0.698802\pi\) | ||||
−0.584736 | + | 0.811224i | \(0.698802\pi\) | |||||||
\(54\) | −5.60555 | −0.762819 | ||||||||
\(55\) | 1.60555 | 0.216492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.30278 | −0.172557 | ||||||||
\(58\) | 0.908327 | 0.119269 | ||||||||
\(59\) | 8.30278 | 1.08093 | 0.540465 | − | 0.841367i | \(-0.318248\pi\) | ||||
0.540465 | + | 0.841367i | \(0.318248\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | 7.90833 | 1.01256 | 0.506279 | − | 0.862370i | \(-0.331021\pi\) | ||||
0.506279 | + | 0.862370i | \(0.331021\pi\) | |||||||
\(62\) | 7.21110 | 0.915811 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.2111 | 1.88671 | ||||||||
\(66\) | −0.908327 | −0.111807 | ||||||||
\(67\) | −0.788897 | −0.0963792 | −0.0481896 | − | 0.998838i | \(-0.515345\pi\) | ||||
−0.0481896 | + | 0.998838i | \(0.515345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.09167 | −0.248236 | −0.124118 | − | 0.992267i | \(-0.539610\pi\) | ||||
−0.124118 | + | 0.992267i | \(0.539610\pi\) | |||||||
\(72\) | −1.30278 | −0.153534 | ||||||||
\(73\) | −12.6056 | −1.47537 | −0.737684 | − | 0.675146i | \(-0.764081\pi\) | ||||
−0.737684 | + | 0.675146i | \(0.764081\pi\) | |||||||
\(74\) | −4.90833 | −0.570581 | ||||||||
\(75\) | 0.394449 | 0.0455470 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.60555 | −0.974387 | ||||||||
\(79\) | 14.9083 | 1.67732 | 0.838659 | − | 0.544657i | \(-0.183340\pi\) | ||||
0.838659 | + | 0.544657i | \(0.183340\pi\) | |||||||
\(80\) | −2.30278 | −0.257458 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | −2.30278 | −0.254299 | ||||||||
\(83\) | 9.21110 | 1.01105 | 0.505525 | − | 0.862812i | \(-0.331299\pi\) | ||||
0.505525 | + | 0.862812i | \(0.331299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.30278 | −0.679646 | ||||||||
\(87\) | 1.18335 | 0.126868 | ||||||||
\(88\) | −0.697224 | −0.0743244 | ||||||||
\(89\) | −15.9083 | −1.68628 | −0.843140 | − | 0.537695i | \(-0.819295\pi\) | ||||
−0.843140 | + | 0.537695i | \(0.819295\pi\) | |||||||
\(90\) | 3.00000 | 0.316228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.60555 | −0.480162 | ||||||||
\(93\) | 9.39445 | 0.974159 | ||||||||
\(94\) | 3.90833 | 0.403113 | ||||||||
\(95\) | 2.30278 | 0.236260 | ||||||||
\(96\) | 1.30278 | 0.132964 | ||||||||
\(97\) | −13.3028 | −1.35069 | −0.675346 | − | 0.737501i | \(-0.736006\pi\) | ||||
−0.675346 | + | 0.737501i | \(0.736006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.908327 | 0.0912903 | ||||||||
\(100\) | 0.302776 | 0.0302776 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.39445 | −0.334465 | −0.167232 | − | 0.985917i | \(-0.553483\pi\) | ||||
−0.167232 | + | 0.985917i | \(0.553483\pi\) | |||||||
\(104\) | −6.60555 | −0.647728 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.51388 | −0.826941 | ||||||||
\(107\) | 13.8167 | 1.33571 | 0.667853 | − | 0.744293i | \(-0.267213\pi\) | ||||
0.667853 | + | 0.744293i | \(0.267213\pi\) | |||||||
\(108\) | −5.60555 | −0.539394 | ||||||||
\(109\) | 17.9083 | 1.71531 | 0.857653 | − | 0.514228i | \(-0.171922\pi\) | ||||
0.857653 | + | 0.514228i | \(0.171922\pi\) | |||||||
\(110\) | 1.60555 | 0.153083 | ||||||||
\(111\) | −6.39445 | −0.606934 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4222 | −1.73302 | −0.866508 | − | 0.499164i | \(-0.833641\pi\) | ||||
−0.866508 | + | 0.499164i | \(0.833641\pi\) | |||||||
\(114\) | −1.30278 | −0.122016 | ||||||||
\(115\) | 10.6056 | 0.988973 | ||||||||
\(116\) | 0.908327 | 0.0843360 | ||||||||
\(117\) | 8.60555 | 0.795583 | ||||||||
\(118\) | 8.30278 | 0.764332 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | −10.5139 | −0.955807 | ||||||||
\(122\) | 7.90833 | 0.715986 | ||||||||
\(123\) | −3.00000 | −0.270501 | ||||||||
\(124\) | 7.21110 | 0.647576 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.30278 | −0.293074 | −0.146537 | − | 0.989205i | \(-0.546813\pi\) | ||||
−0.146537 | + | 0.989205i | \(0.546813\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.21110 | −0.722947 | ||||||||
\(130\) | 15.2111 | 1.33410 | ||||||||
\(131\) | 7.81665 | 0.682944 | 0.341472 | − | 0.939892i | \(-0.389075\pi\) | ||||
0.341472 | + | 0.939892i | \(0.389075\pi\) | |||||||
\(132\) | −0.908327 | −0.0790597 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.788897 | −0.0681504 | ||||||||
\(135\) | 12.9083 | 1.11097 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9083 | −1.10283 | −0.551416 | − | 0.834230i | \(-0.685912\pi\) | ||||
−0.551416 | + | 0.834230i | \(0.685912\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | −17.2111 | −1.45983 | −0.729913 | − | 0.683540i | \(-0.760440\pi\) | ||||
−0.729913 | + | 0.683540i | \(0.760440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.09167 | 0.428796 | ||||||||
\(142\) | −2.09167 | −0.175529 | ||||||||
\(143\) | 4.60555 | 0.385136 | ||||||||
\(144\) | −1.30278 | −0.108565 | ||||||||
\(145\) | −2.09167 | −0.173704 | ||||||||
\(146\) | −12.6056 | −1.04324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.90833 | −0.403462 | ||||||||
\(149\) | 2.78890 | 0.228475 | 0.114238 | − | 0.993453i | \(-0.463557\pi\) | ||||
0.114238 | + | 0.993453i | \(0.463557\pi\) | |||||||
\(150\) | 0.394449 | 0.0322066 | ||||||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6056 | −1.33379 | ||||||||
\(156\) | −8.60555 | −0.688996 | ||||||||
\(157\) | 5.11943 | 0.408575 | 0.204287 | − | 0.978911i | \(-0.434512\pi\) | ||||
0.204287 | + | 0.978911i | \(0.434512\pi\) | |||||||
\(158\) | 14.9083 | 1.18604 | ||||||||
\(159\) | −11.0917 | −0.879627 | ||||||||
\(160\) | −2.30278 | −0.182050 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.39445 | −0.266693 | ||||||||
\(163\) | −13.9083 | −1.08938 | −0.544692 | − | 0.838636i | \(-0.683353\pi\) | ||||
−0.544692 | + | 0.838636i | \(0.683353\pi\) | |||||||
\(164\) | −2.30278 | −0.179817 | ||||||||
\(165\) | 2.09167 | 0.162837 | ||||||||
\(166\) | 9.21110 | 0.714920 | ||||||||
\(167\) | −12.4222 | −0.961259 | −0.480630 | − | 0.876924i | \(-0.659592\pi\) | ||||
−0.480630 | + | 0.876924i | \(0.659592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.6333 | 2.35641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30278 | 0.0996257 | ||||||||
\(172\) | −6.30278 | −0.480582 | ||||||||
\(173\) | −4.60555 | −0.350154 | −0.175077 | − | 0.984555i | \(-0.556017\pi\) | ||||
−0.175077 | + | 0.984555i | \(0.556017\pi\) | |||||||
\(174\) | 1.18335 | 0.0897092 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.697224 | −0.0525553 | ||||||||
\(177\) | 10.8167 | 0.813029 | ||||||||
\(178\) | −15.9083 | −1.19238 | ||||||||
\(179\) | 13.8167 | 1.03271 | 0.516353 | − | 0.856376i | \(-0.327289\pi\) | ||||
0.516353 | + | 0.856376i | \(0.327289\pi\) | |||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | 2.18335 | 0.162287 | 0.0811434 | − | 0.996702i | \(-0.474143\pi\) | ||||
0.0811434 | + | 0.996702i | \(0.474143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3028 | 0.761603 | ||||||||
\(184\) | −4.60555 | −0.339526 | ||||||||
\(185\) | 11.3028 | 0.830997 | ||||||||
\(186\) | 9.39445 | 0.688834 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.90833 | 0.285044 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.30278 | 0.167061 | ||||||||
\(191\) | 4.60555 | 0.333246 | 0.166623 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166623 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(192\) | 1.30278 | 0.0940197 | ||||||||
\(193\) | −24.2389 | −1.74475 | −0.872376 | − | 0.488836i | \(-0.837422\pi\) | ||||
−0.872376 | + | 0.488836i | \(0.837422\pi\) | |||||||
\(194\) | −13.3028 | −0.955084 | ||||||||
\(195\) | 19.8167 | 1.41910 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.21110 | −0.228782 | −0.114391 | − | 0.993436i | \(-0.536492\pi\) | ||||
−0.114391 | + | 0.993436i | \(0.536492\pi\) | |||||||
\(198\) | 0.908327 | 0.0645520 | ||||||||
\(199\) | 4.90833 | 0.347942 | 0.173971 | − | 0.984751i | \(-0.444340\pi\) | ||||
0.173971 | + | 0.984751i | \(0.444340\pi\) | |||||||
\(200\) | 0.302776 | 0.0214095 | ||||||||
\(201\) | −1.02776 | −0.0724923 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.30278 | 0.370362 | ||||||||
\(206\) | −3.39445 | −0.236502 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | −6.60555 | −0.458013 | ||||||||
\(209\) | 0.697224 | 0.0482280 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7889 | 0.742738 | 0.371369 | − | 0.928485i | \(-0.378888\pi\) | ||||
0.371369 | + | 0.928485i | \(0.378888\pi\) | |||||||
\(212\) | −8.51388 | −0.584736 | ||||||||
\(213\) | −2.72498 | −0.186713 | ||||||||
\(214\) | 13.8167 | 0.944487 | ||||||||
\(215\) | 14.5139 | 0.989838 | ||||||||
\(216\) | −5.60555 | −0.381409 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.9083 | 1.21290 | ||||||||
\(219\) | −16.4222 | −1.10971 | ||||||||
\(220\) | 1.60555 | 0.108246 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.39445 | −0.429167 | ||||||||
\(223\) | 9.02776 | 0.604543 | 0.302272 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302272 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.394449 | −0.0262966 | ||||||||
\(226\) | −18.4222 | −1.22543 | ||||||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | −1.30278 | −0.0862784 | ||||||||
\(229\) | −10.3028 | −0.680827 | −0.340413 | − | 0.940276i | \(-0.610567\pi\) | ||||
−0.340413 | + | 0.940276i | \(0.610567\pi\) | |||||||
\(230\) | 10.6056 | 0.699309 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.908327 | 0.0596346 | ||||||||
\(233\) | 19.1194 | 1.25256 | 0.626278 | − | 0.779600i | \(-0.284578\pi\) | ||||
0.626278 | + | 0.779600i | \(0.284578\pi\) | |||||||
\(234\) | 8.60555 | 0.562562 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | 8.30278 | 0.540465 | ||||||||
\(237\) | 19.4222 | 1.26161 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6056 | −1.46223 | −0.731116 | − | 0.682253i | \(-0.761000\pi\) | ||||
−0.731116 | + | 0.682253i | \(0.761000\pi\) | |||||||
\(240\) | −3.00000 | −0.193649 | ||||||||
\(241\) | −14.9083 | −0.960330 | −0.480165 | − | 0.877178i | \(-0.659423\pi\) | ||||
−0.480165 | + | 0.877178i | \(0.659423\pi\) | |||||||
\(242\) | −10.5139 | −0.675858 | ||||||||
\(243\) | 12.3944 | 0.795104 | ||||||||
\(244\) | 7.90833 | 0.506279 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | 6.60555 | 0.420301 | ||||||||
\(248\) | 7.21110 | 0.457905 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 10.8167 | 0.684105 | ||||||||
\(251\) | 4.18335 | 0.264050 | 0.132025 | − | 0.991246i | \(-0.457852\pi\) | ||||
0.132025 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21110 | 0.201880 | ||||||||
\(254\) | −3.30278 | −0.207235 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.4861 | 0.778863 | 0.389431 | − | 0.921055i | \(-0.372672\pi\) | ||||
0.389431 | + | 0.921055i | \(0.372672\pi\) | |||||||
\(258\) | −8.21110 | −0.511201 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.2111 | 0.943353 | ||||||||
\(261\) | −1.18335 | −0.0732473 | ||||||||
\(262\) | 7.81665 | 0.482914 | ||||||||
\(263\) | 7.81665 | 0.481996 | 0.240998 | − | 0.970526i | \(-0.422525\pi\) | ||||
0.240998 | + | 0.970526i | \(0.422525\pi\) | |||||||
\(264\) | −0.908327 | −0.0559037 | ||||||||
\(265\) | 19.6056 | 1.20436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.7250 | −1.26835 | ||||||||
\(268\) | −0.788897 | −0.0481896 | ||||||||
\(269\) | 3.21110 | 0.195784 | 0.0978922 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978922 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(270\) | 12.9083 | 0.785576 | ||||||||
\(271\) | −15.3305 | −0.931263 | −0.465632 | − | 0.884979i | \(-0.654173\pi\) | ||||
−0.465632 | + | 0.884979i | \(0.654173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.9083 | −0.779821 | ||||||||
\(275\) | −0.211103 | −0.0127300 | ||||||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 0.605551 | 0.0363840 | 0.0181920 | − | 0.999835i | \(-0.494209\pi\) | ||||
0.0181920 | + | 0.999835i | \(0.494209\pi\) | |||||||
\(278\) | −17.2111 | −1.03225 | ||||||||
\(279\) | −9.39445 | −0.562431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4222 | 1.09898 | 0.549488 | − | 0.835501i | \(-0.314823\pi\) | ||||
0.549488 | + | 0.835501i | \(0.314823\pi\) | |||||||
\(282\) | 5.09167 | 0.303205 | ||||||||
\(283\) | −23.6333 | −1.40485 | −0.702427 | − | 0.711756i | \(-0.747900\pi\) | ||||
−0.702427 | + | 0.711756i | \(0.747900\pi\) | |||||||
\(284\) | −2.09167 | −0.124118 | ||||||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | 4.60555 | 0.272332 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.30278 | −0.0767668 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −2.09167 | −0.122827 | ||||||||
\(291\) | −17.3305 | −1.01593 | ||||||||
\(292\) | −12.6056 | −0.737684 | ||||||||
\(293\) | 7.81665 | 0.456654 | 0.228327 | − | 0.973585i | \(-0.426675\pi\) | ||||
0.228327 | + | 0.973585i | \(0.426675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.1194 | −1.11318 | ||||||||
\(296\) | −4.90833 | −0.285291 | ||||||||
\(297\) | 3.90833 | 0.226784 | ||||||||
\(298\) | 2.78890 | 0.161556 | ||||||||
\(299\) | 30.4222 | 1.75936 | ||||||||
\(300\) | 0.394449 | 0.0227735 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.4222 | 0.829905 | ||||||||
\(303\) | 7.81665 | 0.449055 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −18.2111 | −1.04276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.1472 | −1.66352 | −0.831759 | − | 0.555137i | \(-0.812666\pi\) | ||||
−0.831759 | + | 0.555137i | \(0.812666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.42221 | −0.251570 | ||||||||
\(310\) | −16.6056 | −0.943132 | ||||||||
\(311\) | 0.275019 | 0.0155949 | 0.00779746 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779746 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(312\) | −8.60555 | −0.487193 | ||||||||
\(313\) | −14.4222 | −0.815191 | −0.407596 | − | 0.913163i | \(-0.633633\pi\) | ||||
−0.407596 | + | 0.913163i | \(0.633633\pi\) | |||||||
\(314\) | 5.11943 | 0.288906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.9083 | 0.838659 | ||||||||
\(317\) | −28.3305 | −1.59120 | −0.795601 | − | 0.605821i | \(-0.792845\pi\) | ||||
−0.795601 | + | 0.605821i | \(0.792845\pi\) | |||||||
\(318\) | −11.0917 | −0.621990 | ||||||||
\(319\) | −0.633308 | −0.0354584 | ||||||||
\(320\) | −2.30278 | −0.128729 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.39445 | −0.188580 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | −13.9083 | −0.770311 | ||||||||
\(327\) | 23.3305 | 1.29018 | ||||||||
\(328\) | −2.30278 | −0.127150 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.09167 | 0.115143 | ||||||||
\(331\) | −16.4222 | −0.902646 | −0.451323 | − | 0.892361i | \(-0.649048\pi\) | ||||
−0.451323 | + | 0.892361i | \(0.649048\pi\) | |||||||
\(332\) | 9.21110 | 0.505525 | ||||||||
\(333\) | 6.39445 | 0.350414 | ||||||||
\(334\) | −12.4222 | −0.679713 | ||||||||
\(335\) | 1.81665 | 0.0992544 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.60555 | 0.359827 | 0.179914 | − | 0.983682i | \(-0.442418\pi\) | ||||
0.179914 | + | 0.983682i | \(0.442418\pi\) | |||||||
\(338\) | 30.6333 | 1.66623 | ||||||||
\(339\) | −24.0000 | −1.30350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.02776 | −0.272268 | ||||||||
\(342\) | 1.30278 | 0.0704460 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.30278 | −0.339823 | ||||||||
\(345\) | 13.8167 | 0.743864 | ||||||||
\(346\) | −4.60555 | −0.247596 | ||||||||
\(347\) | 15.6333 | 0.839240 | 0.419620 | − | 0.907700i | \(-0.362163\pi\) | ||||
0.419620 | + | 0.907700i | \(0.362163\pi\) | |||||||
\(348\) | 1.18335 | 0.0634340 | ||||||||
\(349\) | 3.57779 | 0.191515 | 0.0957575 | − | 0.995405i | \(-0.469473\pi\) | ||||
0.0957575 | + | 0.995405i | \(0.469473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.0278 | 1.97640 | ||||||||
\(352\) | −0.697224 | −0.0371622 | ||||||||
\(353\) | 15.6333 | 0.832077 | 0.416039 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416039 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(354\) | 10.8167 | 0.574899 | ||||||||
\(355\) | 4.81665 | 0.255641 | ||||||||
\(356\) | −15.9083 | −0.843140 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.8167 | 0.730233 | ||||||||
\(359\) | 28.6056 | 1.50974 | 0.754872 | − | 0.655873i | \(-0.227699\pi\) | ||||
0.754872 | + | 0.655873i | \(0.227699\pi\) | |||||||
\(360\) | 3.00000 | 0.158114 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.18335 | 0.114754 | ||||||||
\(363\) | −13.6972 | −0.718918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.0278 | 1.51938 | ||||||||
\(366\) | 10.3028 | 0.538535 | ||||||||
\(367\) | −13.3028 | −0.694399 | −0.347200 | − | 0.937791i | \(-0.612867\pi\) | ||||
−0.347200 | + | 0.937791i | \(0.612867\pi\) | |||||||
\(368\) | −4.60555 | −0.240081 | ||||||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | 11.3028 | 0.587603 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.39445 | 0.487079 | ||||||||
\(373\) | −15.0917 | −0.781417 | −0.390709 | − | 0.920514i | \(-0.627770\pi\) | ||||
−0.390709 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.0917 | 0.727691 | ||||||||
\(376\) | 3.90833 | 0.201557 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.39445 | 0.482560 | 0.241280 | − | 0.970455i | \(-0.422433\pi\) | ||||
0.241280 | + | 0.970455i | \(0.422433\pi\) | |||||||
\(380\) | 2.30278 | 0.118130 | ||||||||
\(381\) | −4.30278 | −0.220438 | ||||||||
\(382\) | 4.60555 | 0.235641 | ||||||||
\(383\) | −37.8167 | −1.93234 | −0.966170 | − | 0.257905i | \(-0.916968\pi\) | ||||
−0.966170 | + | 0.257905i | \(0.916968\pi\) | |||||||
\(384\) | 1.30278 | 0.0664820 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.2389 | −1.23373 | ||||||||
\(387\) | 8.21110 | 0.417394 | ||||||||
\(388\) | −13.3028 | −0.675346 | ||||||||
\(389\) | 21.6333 | 1.09685 | 0.548426 | − | 0.836199i | \(-0.315227\pi\) | ||||
0.548426 | + | 0.836199i | \(0.315227\pi\) | |||||||
\(390\) | 19.8167 | 1.00346 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1833 | 0.513682 | ||||||||
\(394\) | −3.21110 | −0.161773 | ||||||||
\(395\) | −34.3305 | −1.72736 | ||||||||
\(396\) | 0.908327 | 0.0456451 | ||||||||
\(397\) | 10.6972 | 0.536878 | 0.268439 | − | 0.963297i | \(-0.413492\pi\) | ||||
0.268439 | + | 0.963297i | \(0.413492\pi\) | |||||||
\(398\) | 4.90833 | 0.246032 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | −24.8444 | −1.24067 | −0.620335 | − | 0.784337i | \(-0.713003\pi\) | ||||
−0.620335 | + | 0.784337i | \(0.713003\pi\) | |||||||
\(402\) | −1.02776 | −0.0512598 | ||||||||
\(403\) | −47.6333 | −2.37278 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 7.81665 | 0.388413 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.42221 | 0.169632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0917 | −0.795682 | −0.397841 | − | 0.917454i | \(-0.630240\pi\) | ||||
−0.397841 | + | 0.917454i | \(0.630240\pi\) | |||||||
\(410\) | 5.30278 | 0.261885 | ||||||||
\(411\) | −16.8167 | −0.829504 | ||||||||
\(412\) | −3.39445 | −0.167232 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | −21.2111 | −1.04121 | ||||||||
\(416\) | −6.60555 | −0.323864 | ||||||||
\(417\) | −22.4222 | −1.09802 | ||||||||
\(418\) | 0.697224 | 0.0341024 | ||||||||
\(419\) | −12.4222 | −0.606864 | −0.303432 | − | 0.952853i | \(-0.598133\pi\) | ||||
−0.303432 | + | 0.952853i | \(0.598133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.78890 | 0.233397 | 0.116698 | − | 0.993167i | \(-0.462769\pi\) | ||||
0.116698 | + | 0.993167i | \(0.462769\pi\) | |||||||
\(422\) | 10.7889 | 0.525195 | ||||||||
\(423\) | −5.09167 | −0.247566 | ||||||||
\(424\) | −8.51388 | −0.413470 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.72498 | −0.132026 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.8167 | 0.667853 | ||||||||
\(429\) | 6.00000 | 0.289683 | ||||||||
\(430\) | 14.5139 | 0.699921 | ||||||||
\(431\) | −25.5416 | −1.23030 | −0.615149 | − | 0.788411i | \(-0.710904\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(432\) | −5.60555 | −0.269697 | ||||||||
\(433\) | 9.09167 | 0.436918 | 0.218459 | − | 0.975846i | \(-0.429897\pi\) | ||||
0.218459 | + | 0.975846i | \(0.429897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.72498 | −0.130653 | ||||||||
\(436\) | 17.9083 | 0.857653 | ||||||||
\(437\) | 4.60555 | 0.220313 | ||||||||
\(438\) | −16.4222 | −0.784683 | ||||||||
\(439\) | −32.4222 | −1.54743 | −0.773714 | − | 0.633535i | \(-0.781603\pi\) | ||||
−0.773714 | + | 0.633535i | \(0.781603\pi\) | |||||||
\(440\) | 1.60555 | 0.0765417 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.5139 | 0.547041 | 0.273520 | − | 0.961866i | \(-0.411812\pi\) | ||||
0.273520 | + | 0.961866i | \(0.411812\pi\) | |||||||
\(444\) | −6.39445 | −0.303467 | ||||||||
\(445\) | 36.6333 | 1.73659 | ||||||||
\(446\) | 9.02776 | 0.427477 | ||||||||
\(447\) | 3.63331 | 0.171850 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.3944 | 1.19844 | 0.599219 | − | 0.800585i | \(-0.295478\pi\) | ||||
0.599219 | + | 0.800585i | \(0.295478\pi\) | |||||||
\(450\) | −0.394449 | −0.0185945 | ||||||||
\(451\) | 1.60555 | 0.0756025 | ||||||||
\(452\) | −18.4222 | −0.866508 | ||||||||
\(453\) | 18.7889 | 0.882779 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.30278 | −0.0610081 | ||||||||
\(457\) | −36.5139 | −1.70805 | −0.854024 | − | 0.520234i | \(-0.825845\pi\) | ||||
−0.854024 | + | 0.520234i | \(0.825845\pi\) | |||||||
\(458\) | −10.3028 | −0.481417 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.6056 | 0.494486 | ||||||||
\(461\) | −2.51388 | −0.117083 | −0.0585415 | − | 0.998285i | \(-0.518645\pi\) | ||||
−0.0585415 | + | 0.998285i | \(0.518645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.2389 | 1.59121 | 0.795607 | − | 0.605813i | \(-0.207152\pi\) | ||||
0.795607 | + | 0.605813i | \(0.207152\pi\) | |||||||
\(464\) | 0.908327 | 0.0421680 | ||||||||
\(465\) | −21.6333 | −1.00322 | ||||||||
\(466\) | 19.1194 | 0.885690 | ||||||||
\(467\) | 13.8167 | 0.639358 | 0.319679 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319679 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(468\) | 8.60555 | 0.397792 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.00000 | −0.415139 | ||||||||
\(471\) | 6.66947 | 0.307313 | ||||||||
\(472\) | 8.30278 | 0.382166 | ||||||||
\(473\) | 4.39445 | 0.202057 | ||||||||
\(474\) | 19.4222 | 0.892091 | ||||||||
\(475\) | −0.302776 | −0.0138923 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0917 | 0.507853 | ||||||||
\(478\) | −22.6056 | −1.03395 | ||||||||
\(479\) | 26.7250 | 1.22110 | 0.610548 | − | 0.791979i | \(-0.290949\pi\) | ||||
0.610548 | + | 0.791979i | \(0.290949\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | 32.4222 | 1.47833 | ||||||||
\(482\) | −14.9083 | −0.679056 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5139 | −0.477904 | ||||||||
\(485\) | 30.6333 | 1.39099 | ||||||||
\(486\) | 12.3944 | 0.562224 | ||||||||
\(487\) | −9.09167 | −0.411983 | −0.205992 | − | 0.978554i | \(-0.566042\pi\) | ||||
−0.205992 | + | 0.978554i | \(0.566042\pi\) | |||||||
\(488\) | 7.90833 | 0.357993 | ||||||||
\(489\) | −18.1194 | −0.819389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8444 | −1.12121 | −0.560606 | − | 0.828082i | \(-0.689432\pi\) | ||||
−0.560606 | + | 0.828082i | \(0.689432\pi\) | |||||||
\(492\) | −3.00000 | −0.135250 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 6.60555 | 0.297198 | ||||||||
\(495\) | −2.09167 | −0.0940137 | ||||||||
\(496\) | 7.21110 | 0.323788 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | 10.3028 | 0.461216 | 0.230608 | − | 0.973047i | \(-0.425929\pi\) | ||||
0.230608 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(500\) | 10.8167 | 0.483735 | ||||||||
\(501\) | −16.1833 | −0.723019 | ||||||||
\(502\) | 4.18335 | 0.186712 | ||||||||
\(503\) | −18.4861 | −0.824255 | −0.412128 | − | 0.911126i | \(-0.635214\pi\) | ||||
−0.412128 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.8167 | −0.614833 | ||||||||
\(506\) | 3.21110 | 0.142751 | ||||||||
\(507\) | 39.9083 | 1.77239 | ||||||||
\(508\) | −3.30278 | −0.146537 | ||||||||
\(509\) | 38.6611 | 1.71362 | 0.856811 | − | 0.515631i | \(-0.172442\pi\) | ||||
0.856811 | + | 0.515631i | \(0.172442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.60555 | 0.247491 | ||||||||
\(514\) | 12.4861 | 0.550739 | ||||||||
\(515\) | 7.81665 | 0.344443 | ||||||||
\(516\) | −8.21110 | −0.361474 | ||||||||
\(517\) | −2.72498 | −0.119845 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 15.2111 | 0.667051 | ||||||||
\(521\) | −39.2111 | −1.71787 | −0.858935 | − | 0.512085i | \(-0.828873\pi\) | ||||
−0.858935 | + | 0.512085i | \(0.828873\pi\) | |||||||
\(522\) | −1.18335 | −0.0517937 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | 7.81665 | 0.341472 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.81665 | 0.340822 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.908327 | −0.0395299 | ||||||||
\(529\) | −1.78890 | −0.0777781 | ||||||||
\(530\) | 19.6056 | 0.851611 | ||||||||
\(531\) | −10.8167 | −0.469403 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.2111 | 0.658866 | ||||||||
\(534\) | −20.7250 | −0.896858 | ||||||||
\(535\) | −31.8167 | −1.37555 | ||||||||
\(536\) | −0.788897 | −0.0340752 | ||||||||
\(537\) | 18.0000 | 0.776757 | ||||||||
\(538\) | 3.21110 | 0.138440 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.9083 | 0.555486 | ||||||||
\(541\) | −44.6056 | −1.91774 | −0.958871 | − | 0.283841i | \(-0.908391\pi\) | ||||
−0.958871 | + | 0.283841i | \(0.908391\pi\) | |||||||
\(542\) | −15.3305 | −0.658503 | ||||||||
\(543\) | 2.84441 | 0.122065 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.2389 | −1.76648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.1833 | −0.606436 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(548\) | −12.9083 | −0.551416 | ||||||||
\(549\) | −10.3028 | −0.439712 | ||||||||
\(550\) | −0.211103 | −0.00900144 | ||||||||
\(551\) | −0.908327 | −0.0386960 | ||||||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.605551 | 0.0257274 | ||||||||
\(555\) | 14.7250 | 0.625041 | ||||||||
\(556\) | −17.2111 | −0.729913 | ||||||||
\(557\) | 44.6611 | 1.89235 | 0.946175 | − | 0.323655i | \(-0.104912\pi\) | ||||
0.946175 | + | 0.323655i | \(0.104912\pi\) | |||||||
\(558\) | −9.39445 | −0.397699 | ||||||||
\(559\) | 41.6333 | 1.76090 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.4222 | 0.777094 | ||||||||
\(563\) | 27.9083 | 1.17620 | 0.588098 | − | 0.808790i | \(-0.299877\pi\) | ||||
0.588098 | + | 0.808790i | \(0.299877\pi\) | |||||||
\(564\) | 5.09167 | 0.214398 | ||||||||
\(565\) | 42.4222 | 1.78472 | ||||||||
\(566\) | −23.6333 | −0.993382 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.09167 | −0.0877647 | ||||||||
\(569\) | −44.2389 | −1.85459 | −0.927295 | − | 0.374332i | \(-0.877872\pi\) | ||||
−0.927295 | + | 0.374332i | \(0.877872\pi\) | |||||||
\(570\) | 3.00000 | 0.125656 | ||||||||
\(571\) | 42.7527 | 1.78915 | 0.894573 | − | 0.446921i | \(-0.147480\pi\) | ||||
0.894573 | + | 0.446921i | \(0.147480\pi\) | |||||||
\(572\) | 4.60555 | 0.192568 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.39445 | −0.0581525 | ||||||||
\(576\) | −1.30278 | −0.0542823 | ||||||||
\(577\) | 25.6333 | 1.06713 | 0.533564 | − | 0.845760i | \(-0.320852\pi\) | ||||
0.533564 | + | 0.845760i | \(0.320852\pi\) | |||||||
\(578\) | −17.0000 | −0.707107 | ||||||||
\(579\) | −31.5778 | −1.31233 | ||||||||
\(580\) | −2.09167 | −0.0868520 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17.3305 | −0.718374 | ||||||||
\(583\) | 5.93608 | 0.245847 | ||||||||
\(584\) | −12.6056 | −0.521621 | ||||||||
\(585\) | −19.8167 | −0.819318 | ||||||||
\(586\) | 7.81665 | 0.322903 | ||||||||
\(587\) | 10.1833 | 0.420312 | 0.210156 | − | 0.977668i | \(-0.432603\pi\) | ||||
0.210156 | + | 0.977668i | \(0.432603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.21110 | −0.297128 | ||||||||
\(590\) | −19.1194 | −0.787134 | ||||||||
\(591\) | −4.18335 | −0.172080 | ||||||||
\(592\) | −4.90833 | −0.201731 | ||||||||
\(593\) | 13.8167 | 0.567382 | 0.283691 | − | 0.958916i | \(-0.408441\pi\) | ||||
0.283691 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(594\) | 3.90833 | 0.160361 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.78890 | 0.114238 | ||||||||
\(597\) | 6.39445 | 0.261707 | ||||||||
\(598\) | 30.4222 | 1.24406 | ||||||||
\(599\) | 36.6972 | 1.49941 | 0.749704 | − | 0.661773i | \(-0.230196\pi\) | ||||
0.749704 | + | 0.661773i | \(0.230196\pi\) | |||||||
\(600\) | 0.394449 | 0.0161033 | ||||||||
\(601\) | 16.4222 | 0.669876 | 0.334938 | − | 0.942240i | \(-0.391285\pi\) | ||||
0.334938 | + | 0.942240i | \(0.391285\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.02776 | 0.0418535 | ||||||||
\(604\) | 14.4222 | 0.586831 | ||||||||
\(605\) | 24.2111 | 0.984321 | ||||||||
\(606\) | 7.81665 | 0.317530 | ||||||||
\(607\) | −6.60555 | −0.268111 | −0.134056 | − | 0.990974i | \(-0.542800\pi\) | ||||
−0.134056 | + | 0.990974i | \(0.542800\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.2111 | −0.737346 | ||||||||
\(611\) | −25.8167 | −1.04443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.21110 | 0.210474 | 0.105237 | − | 0.994447i | \(-0.466440\pi\) | ||||
0.105237 | + | 0.994447i | \(0.466440\pi\) | |||||||
\(614\) | −29.1472 | −1.17628 | ||||||||
\(615\) | 6.90833 | 0.278571 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.1194 | 1.37360 | 0.686798 | − | 0.726848i | \(-0.259016\pi\) | ||||
0.686798 | + | 0.726848i | \(0.259016\pi\) | |||||||
\(618\) | −4.42221 | −0.177887 | ||||||||
\(619\) | −8.97224 | −0.360625 | −0.180312 | − | 0.983609i | \(-0.557711\pi\) | ||||
−0.180312 | + | 0.983609i | \(0.557711\pi\) | |||||||
\(620\) | −16.6056 | −0.666895 | ||||||||
\(621\) | 25.8167 | 1.03599 | ||||||||
\(622\) | 0.275019 | 0.0110273 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.60555 | −0.344498 | ||||||||
\(625\) | −26.4222 | −1.05689 | ||||||||
\(626\) | −14.4222 | −0.576427 | ||||||||
\(627\) | 0.908327 | 0.0362751 | ||||||||
\(628\) | 5.11943 | 0.204287 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.21110 | −0.0482132 | −0.0241066 | − | 0.999709i | \(-0.507674\pi\) | ||||
−0.0241066 | + | 0.999709i | \(0.507674\pi\) | |||||||
\(632\) | 14.9083 | 0.593021 | ||||||||
\(633\) | 14.0555 | 0.558656 | ||||||||
\(634\) | −28.3305 | −1.12515 | ||||||||
\(635\) | 7.60555 | 0.301817 | ||||||||
\(636\) | −11.0917 | −0.439813 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.633308 | −0.0250729 | ||||||||
\(639\) | 2.72498 | 0.107799 | ||||||||
\(640\) | −2.30278 | −0.0910252 | ||||||||
\(641\) | −1.81665 | −0.0717535 | −0.0358768 | − | 0.999356i | \(-0.511422\pi\) | ||||
−0.0358768 | + | 0.999356i | \(0.511422\pi\) | |||||||
\(642\) | 18.0000 | 0.710403 | ||||||||
\(643\) | 38.0555 | 1.50076 | 0.750381 | − | 0.661005i | \(-0.229870\pi\) | ||||
0.750381 | + | 0.661005i | \(0.229870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.9083 | 0.744515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.7250 | −1.52244 | −0.761218 | − | 0.648496i | \(-0.775398\pi\) | ||||
−0.761218 | + | 0.648496i | \(0.775398\pi\) | |||||||
\(648\) | −3.39445 | −0.133347 | ||||||||
\(649\) | −5.78890 | −0.227234 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.9083 | −0.544692 | ||||||||
\(653\) | 19.8167 | 0.775486 | 0.387743 | − | 0.921768i | \(-0.373255\pi\) | ||||
0.387743 | + | 0.921768i | \(0.373255\pi\) | |||||||
\(654\) | 23.3305 | 0.912296 | ||||||||
\(655\) | −18.0000 | −0.703318 | ||||||||
\(656\) | −2.30278 | −0.0899083 | ||||||||
\(657\) | 16.4222 | 0.640691 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.2111 | −1.76117 | −0.880587 | − | 0.473884i | \(-0.842852\pi\) | ||||
−0.880587 | + | 0.473884i | \(0.842852\pi\) | |||||||
\(660\) | 2.09167 | 0.0814183 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | −16.4222 | −0.638267 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.21110 | 0.357460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.39445 | 0.247780 | ||||||||
\(667\) | −4.18335 | −0.161980 | ||||||||
\(668\) | −12.4222 | −0.480630 | ||||||||
\(669\) | 11.7611 | 0.454712 | ||||||||
\(670\) | 1.81665 | 0.0701835 | ||||||||
\(671\) | −5.51388 | −0.212861 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.81665 | 0.147121 | 0.0735606 | − | 0.997291i | \(-0.476564\pi\) | ||||
0.0735606 | + | 0.997291i | \(0.476564\pi\) | |||||||
\(674\) | 6.60555 | 0.254436 | ||||||||
\(675\) | −1.69722 | −0.0653262 | ||||||||
\(676\) | 30.6333 | 1.17820 | ||||||||
\(677\) | −51.2111 | −1.96820 | −0.984101 | − | 0.177608i | \(-0.943164\pi\) | ||||
−0.984101 | + | 0.177608i | \(0.943164\pi\) | |||||||
\(678\) | −24.0000 | −0.921714 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.2666 | 1.19814 | ||||||||
\(682\) | −5.02776 | −0.192523 | ||||||||
\(683\) | −9.63331 | −0.368608 | −0.184304 | − | 0.982869i | \(-0.559003\pi\) | ||||
−0.184304 | + | 0.982869i | \(0.559003\pi\) | |||||||
\(684\) | 1.30278 | 0.0498129 | ||||||||
\(685\) | 29.7250 | 1.13573 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.4222 | −0.512089 | ||||||||
\(688\) | −6.30278 | −0.240291 | ||||||||
\(689\) | 56.2389 | 2.14253 | ||||||||
\(690\) | 13.8167 | 0.525991 | ||||||||
\(691\) | −36.6056 | −1.39254 | −0.696270 | − | 0.717780i | \(-0.745159\pi\) | ||||
−0.696270 | + | 0.717780i | \(0.745159\pi\) | |||||||
\(692\) | −4.60555 | −0.175077 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6333 | 0.593432 | ||||||||
\(695\) | 39.6333 | 1.50338 | ||||||||
\(696\) | 1.18335 | 0.0448546 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.57779 | 0.135422 | ||||||||
\(699\) | 24.9083 | 0.942119 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8167 | −0.521848 | −0.260924 | − | 0.965359i | \(-0.584027\pi\) | ||||
−0.260924 | + | 0.965359i | \(0.584027\pi\) | |||||||
\(702\) | 37.0278 | 1.39752 | ||||||||
\(703\) | 4.90833 | 0.185121 | ||||||||
\(704\) | −0.697224 | −0.0262776 | ||||||||
\(705\) | −11.7250 | −0.441588 | ||||||||
\(706\) | 15.6333 | 0.588367 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.8167 | 0.406515 | ||||||||
\(709\) | −23.8167 | −0.894453 | −0.447227 | − | 0.894421i | \(-0.647588\pi\) | ||||
−0.447227 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(710\) | 4.81665 | 0.180766 | ||||||||
\(711\) | −19.4222 | −0.728390 | ||||||||
\(712\) | −15.9083 | −0.596190 | ||||||||
\(713\) | −33.2111 | −1.24377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.6056 | −0.396625 | ||||||||
\(716\) | 13.8167 | 0.516353 | ||||||||
\(717\) | −29.4500 | −1.09983 | ||||||||
\(718\) | 28.6056 | 1.06755 | ||||||||
\(719\) | −42.4222 | −1.58208 | −0.791041 | − | 0.611764i | \(-0.790460\pi\) | ||||
−0.791041 | + | 0.611764i | \(0.790460\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −19.4222 | −0.722320 | ||||||||
\(724\) | 2.18335 | 0.0811434 | ||||||||
\(725\) | 0.275019 | 0.0102140 | ||||||||
\(726\) | −13.6972 | −0.508352 | ||||||||
\(727\) | 29.1194 | 1.07998 | 0.539990 | − | 0.841671i | \(-0.318428\pi\) | ||||
0.539990 | + | 0.841671i | \(0.318428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 29.0278 | 1.07437 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 10.3028 | 0.380802 | ||||||||
\(733\) | −3.88057 | −0.143332 | −0.0716661 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716661 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(734\) | −13.3028 | −0.491014 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.60555 | −0.169763 | ||||||||
\(737\) | 0.550039 | 0.0202609 | ||||||||
\(738\) | 3.00000 | 0.110432 | ||||||||
\(739\) | −21.9361 | −0.806932 | −0.403466 | − | 0.914995i | \(-0.632195\pi\) | ||||
−0.403466 | + | 0.914995i | \(0.632195\pi\) | |||||||
\(740\) | 11.3028 | 0.415498 | ||||||||
\(741\) | 8.60555 | 0.316133 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.4861 | −0.458071 | −0.229036 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229036 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(744\) | 9.39445 | 0.344417 | ||||||||
\(745\) | −6.42221 | −0.235291 | ||||||||
\(746\) | −15.0917 | −0.552545 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.0917 | 0.514555 | ||||||||
\(751\) | 1.93608 | 0.0706487 | 0.0353243 | − | 0.999376i | \(-0.488754\pi\) | ||||
0.0353243 | + | 0.999376i | \(0.488754\pi\) | |||||||
\(752\) | 3.90833 | 0.142522 | ||||||||
\(753\) | 5.44996 | 0.198608 | ||||||||
\(754\) | −6.00000 | −0.218507 | ||||||||
\(755\) | −33.2111 | −1.20868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.2111 | −1.35246 | −0.676230 | − | 0.736690i | \(-0.736388\pi\) | ||||
−0.676230 | + | 0.736690i | \(0.736388\pi\) | |||||||
\(758\) | 9.39445 | 0.341222 | ||||||||
\(759\) | 4.18335 | 0.151846 | ||||||||
\(760\) | 2.30278 | 0.0835305 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | −4.30278 | −0.155873 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.60555 | 0.166623 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.8167 | −1.36637 | ||||||||
\(767\) | −54.8444 | −1.98032 | ||||||||
\(768\) | 1.30278 | 0.0470099 | ||||||||
\(769\) | 32.6056 | 1.17579 | 0.587893 | − | 0.808939i | \(-0.299958\pi\) | ||||
0.587893 | + | 0.808939i | \(0.299958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.2666 | 0.585828 | ||||||||
\(772\) | −24.2389 | −0.872376 | ||||||||
\(773\) | −20.2389 | −0.727941 | −0.363971 | − | 0.931410i | \(-0.618579\pi\) | ||||
−0.363971 | + | 0.931410i | \(0.618579\pi\) | |||||||
\(774\) | 8.21110 | 0.295142 | ||||||||
\(775\) | 2.18335 | 0.0784281 | ||||||||
\(776\) | −13.3028 | −0.477542 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.6333 | 0.775592 | ||||||||
\(779\) | 2.30278 | 0.0825055 | ||||||||
\(780\) | 19.8167 | 0.709550 | ||||||||
\(781\) | 1.45837 | 0.0521844 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.09167 | −0.181962 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.7889 | −0.420764 | ||||||||
\(786\) | 10.1833 | 0.363228 | ||||||||
\(787\) | −13.5139 | −0.481718 | −0.240859 | − | 0.970560i | \(-0.577429\pi\) | ||||
−0.240859 | + | 0.970560i | \(0.577429\pi\) | |||||||
\(788\) | −3.21110 | −0.114391 | ||||||||
\(789\) | 10.1833 | 0.362537 | ||||||||
\(790\) | −34.3305 | −1.22143 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.908327 | 0.0322760 | ||||||||
\(793\) | −52.2389 | −1.85506 | ||||||||
\(794\) | 10.6972 | 0.379630 | ||||||||
\(795\) | 25.5416 | 0.905868 | ||||||||
\(796\) | 4.90833 | 0.173971 | ||||||||
\(797\) | 4.60555 | 0.163137 | 0.0815685 | − | 0.996668i | \(-0.474007\pi\) | ||||
0.0815685 | + | 0.996668i | \(0.474007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.302776 | 0.0107047 | ||||||||
\(801\) | 20.7250 | 0.732281 | ||||||||
\(802\) | −24.8444 | −0.877287 | ||||||||
\(803\) | 8.78890 | 0.310153 | ||||||||
\(804\) | −1.02776 | −0.0362462 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −47.6333 | −1.67781 | ||||||||
\(807\) | 4.18335 | 0.147261 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | 38.7250 | 1.36150 | 0.680749 | − | 0.732517i | \(-0.261654\pi\) | ||||
0.680749 | + | 0.732517i | \(0.261654\pi\) | |||||||
\(810\) | 7.81665 | 0.274649 | ||||||||
\(811\) | −44.5694 | −1.56504 | −0.782521 | − | 0.622624i | \(-0.786067\pi\) | ||||
−0.782521 | + | 0.622624i | \(0.786067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9722 | −0.700457 | ||||||||
\(814\) | 3.42221 | 0.119948 | ||||||||
\(815\) | 32.0278 | 1.12188 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.30278 | 0.220506 | ||||||||
\(818\) | −16.0917 | −0.562632 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.30278 | 0.185181 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | −16.8167 | −0.586548 | ||||||||
\(823\) | 14.0000 | 0.488009 | 0.244005 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244005 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(824\) | −3.39445 | −0.118251 | ||||||||
\(825\) | −0.275019 | −0.00957494 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.4500 | −1.44136 | −0.720678 | − | 0.693270i | \(-0.756169\pi\) | ||||
−0.720678 | + | 0.693270i | \(0.756169\pi\) | |||||||
\(828\) | 6.00000 | 0.208514 | ||||||||
\(829\) | −20.0000 | −0.694629 | −0.347314 | − | 0.937749i | \(-0.612906\pi\) | ||||
−0.347314 | + | 0.937749i | \(0.612906\pi\) | |||||||
\(830\) | −21.2111 | −0.736248 | ||||||||
\(831\) | 0.788897 | 0.0273665 | ||||||||
\(832\) | −6.60555 | −0.229006 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −22.4222 | −0.776417 | ||||||||
\(835\) | 28.6056 | 0.989936 | ||||||||
\(836\) | 0.697224 | 0.0241140 | ||||||||
\(837\) | −40.4222 | −1.39720 | ||||||||
\(838\) | −12.4222 | −0.429118 | ||||||||
\(839\) | 6.00000 | 0.207143 | 0.103572 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103572 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1749 | −0.971550 | ||||||||
\(842\) | 4.78890 | 0.165036 | ||||||||
\(843\) | 24.0000 | 0.826604 | ||||||||
\(844\) | 10.7889 | 0.371369 | ||||||||
\(845\) | −70.5416 | −2.42671 | ||||||||
\(846\) | −5.09167 | −0.175055 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.51388 | −0.292368 | ||||||||
\(849\) | −30.7889 | −1.05667 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.6056 | 0.774908 | ||||||||
\(852\) | −2.72498 | −0.0933563 | ||||||||
\(853\) | 21.0917 | 0.722165 | 0.361083 | − | 0.932534i | \(-0.382407\pi\) | ||||
0.361083 | + | 0.932534i | \(0.382407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00000 | −0.102598 | ||||||||
\(856\) | 13.8167 | 0.472244 | ||||||||
\(857\) | −0.422205 | −0.0144223 | −0.00721113 | − | 0.999974i | \(-0.502295\pi\) | ||||
−0.00721113 | + | 0.999974i | \(0.502295\pi\) | |||||||
\(858\) | 6.00000 | 0.204837 | ||||||||
\(859\) | −52.2389 | −1.78237 | −0.891183 | − | 0.453643i | \(-0.850124\pi\) | ||||
−0.891183 | + | 0.453643i | \(0.850124\pi\) | |||||||
\(860\) | 14.5139 | 0.494919 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.5416 | −0.869952 | ||||||||
\(863\) | −40.9638 | −1.39443 | −0.697213 | − | 0.716864i | \(-0.745577\pi\) | ||||
−0.697213 | + | 0.716864i | \(0.745577\pi\) | |||||||
\(864\) | −5.60555 | −0.190705 | ||||||||
\(865\) | 10.6056 | 0.360600 | ||||||||
\(866\) | 9.09167 | 0.308948 | ||||||||
\(867\) | −22.1472 | −0.752158 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3944 | −0.352608 | ||||||||
\(870\) | −2.72498 | −0.0923855 | ||||||||
\(871\) | 5.21110 | 0.176571 | ||||||||
\(872\) | 17.9083 | 0.606452 | ||||||||
\(873\) | 17.3305 | 0.586550 | ||||||||
\(874\) | 4.60555 | 0.155785 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.4222 | −0.554855 | ||||||||
\(877\) | 29.9083 | 1.00993 | 0.504966 | − | 0.863139i | \(-0.331505\pi\) | ||||
0.504966 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(878\) | −32.4222 | −1.09420 | ||||||||
\(879\) | 10.1833 | 0.343476 | ||||||||
\(880\) | 1.60555 | 0.0541231 | ||||||||
\(881\) | 4.18335 | 0.140941 | 0.0704703 | − | 0.997514i | \(-0.477550\pi\) | ||||
0.0704703 | + | 0.997514i | \(0.477550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1194 | −1.18186 | −0.590931 | − | 0.806722i | \(-0.701240\pi\) | ||||
−0.590931 | + | 0.806722i | \(0.701240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.9083 | −0.837284 | ||||||||
\(886\) | 11.5139 | 0.386816 | ||||||||
\(887\) | 2.36669 | 0.0794658 | 0.0397329 | − | 0.999210i | \(-0.487349\pi\) | ||||
0.0397329 | + | 0.999210i | \(0.487349\pi\) | |||||||
\(888\) | −6.39445 | −0.214584 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36.6333 | 1.22795 | ||||||||
\(891\) | 2.36669 | 0.0792872 | ||||||||
\(892\) | 9.02776 | 0.302272 | ||||||||
\(893\) | −3.90833 | −0.130787 | ||||||||
\(894\) | 3.63331 | 0.121516 | ||||||||
\(895\) | −31.8167 | −1.06351 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.6333 | 1.32332 | ||||||||
\(898\) | 25.3944 | 0.847424 | ||||||||
\(899\) | 6.55004 | 0.218456 | ||||||||
\(900\) | −0.394449 | −0.0131483 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.60555 | 0.0534590 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.4222 | −0.612713 | ||||||||
\(905\) | −5.02776 | −0.167128 | ||||||||
\(906\) | 18.7889 | 0.624219 | ||||||||
\(907\) | 12.1833 | 0.404541 | 0.202271 | − | 0.979330i | \(-0.435168\pi\) | ||||
0.202271 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(908\) | 24.0000 | 0.796468 | ||||||||
\(909\) | −7.81665 | −0.259262 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.09167 | 0.168695 | 0.0843473 | − | 0.996436i | \(-0.473119\pi\) | ||||
0.0843473 | + | 0.996436i | \(0.473119\pi\) | |||||||
\(912\) | −1.30278 | −0.0431392 | ||||||||
\(913\) | −6.42221 | −0.212544 | ||||||||
\(914\) | −36.5139 | −1.20777 | ||||||||
\(915\) | −23.7250 | −0.784324 | ||||||||
\(916\) | −10.3028 | −0.340413 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.6056 | −1.47140 | −0.735701 | − | 0.677307i | \(-0.763147\pi\) | ||||
−0.735701 | + | 0.677307i | \(0.763147\pi\) | |||||||
\(920\) | 10.6056 | 0.349655 | ||||||||
\(921\) | −37.9722 | −1.25123 | ||||||||
\(922\) | −2.51388 | −0.0827902 | ||||||||
\(923\) | 13.8167 | 0.454781 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.48612 | −0.0488634 | ||||||||
\(926\) | 34.2389 | 1.12516 | ||||||||
\(927\) | 4.42221 | 0.145244 | ||||||||
\(928\) | 0.908327 | 0.0298173 | ||||||||
\(929\) | 19.8167 | 0.650163 | 0.325082 | − | 0.945686i | \(-0.394608\pi\) | ||||
0.325082 | + | 0.945686i | \(0.394608\pi\) | |||||||
\(930\) | −21.6333 | −0.709384 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.1194 | 0.626278 | ||||||||
\(933\) | 0.358288 | 0.0117298 | ||||||||
\(934\) | 13.8167 | 0.452095 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.60555 | 0.281281 | ||||||||
\(937\) | −34.7889 | −1.13650 | −0.568252 | − | 0.822855i | \(-0.692380\pi\) | ||||
−0.568252 | + | 0.822855i | \(0.692380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.7889 | −0.613152 | ||||||||
\(940\) | −9.00000 | −0.293548 | ||||||||
\(941\) | −6.97224 | −0.227289 | −0.113644 | − | 0.993521i | \(-0.536252\pi\) | ||||
−0.113644 | + | 0.993521i | \(0.536252\pi\) | |||||||
\(942\) | 6.66947 | 0.217303 | ||||||||
\(943\) | 10.6056 | 0.345364 | ||||||||
\(944\) | 8.30278 | 0.270232 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.39445 | 0.142876 | ||||||||
\(947\) | −17.7250 | −0.575984 | −0.287992 | − | 0.957633i | \(-0.592988\pi\) | ||||
−0.287992 | + | 0.957633i | \(0.592988\pi\) | |||||||
\(948\) | 19.4222 | 0.630804 | ||||||||
\(949\) | 83.2666 | 2.70295 | ||||||||
\(950\) | −0.302776 | −0.00982334 | ||||||||
\(951\) | −36.9083 | −1.19683 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.4222 | 0.791113 | 0.395556 | − | 0.918442i | \(-0.370552\pi\) | ||||
0.395556 | + | 0.918442i | \(0.370552\pi\) | |||||||
\(954\) | 11.0917 | 0.359106 | ||||||||
\(955\) | −10.6056 | −0.343188 | ||||||||
\(956\) | −22.6056 | −0.731116 | ||||||||
\(957\) | −0.825058 | −0.0266703 | ||||||||
\(958\) | 26.7250 | 0.863445 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.00000 | −0.0968246 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | 32.4222 | 1.04533 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | −14.9083 | −0.480165 | ||||||||
\(965\) | 55.8167 | 1.79680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.7889 | −0.604210 | −0.302105 | − | 0.953275i | \(-0.597689\pi\) | ||||
−0.302105 | + | 0.953275i | \(0.597689\pi\) | |||||||
\(968\) | −10.5139 | −0.337929 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.6333 | 0.983576 | ||||||||
\(971\) | 18.1472 | 0.582371 | 0.291185 | − | 0.956667i | \(-0.405950\pi\) | ||||
0.291185 | + | 0.956667i | \(0.405950\pi\) | |||||||
\(972\) | 12.3944 | 0.397552 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.09167 | −0.291316 | ||||||||
\(975\) | −2.60555 | −0.0834444 | ||||||||
\(976\) | 7.90833 | 0.253139 | ||||||||
\(977\) | 16.6056 | 0.531259 | 0.265629 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265629 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(978\) | −18.1194 | −0.579395 | ||||||||
\(979\) | 11.0917 | 0.354491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.3305 | −0.744887 | ||||||||
\(982\) | −24.8444 | −0.792817 | ||||||||
\(983\) | 15.6333 | 0.498625 | 0.249313 | − | 0.968423i | \(-0.419795\pi\) | ||||
0.249313 | + | 0.968423i | \(0.419795\pi\) | |||||||
\(984\) | −3.00000 | −0.0956365 | ||||||||
\(985\) | 7.39445 | 0.235607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.60555 | 0.210151 | ||||||||
\(989\) | 29.0278 | 0.923029 | ||||||||
\(990\) | −2.09167 | −0.0664777 | ||||||||
\(991\) | −37.3583 | −1.18673 | −0.593363 | − | 0.804935i | \(-0.702200\pi\) | ||||
−0.593363 | + | 0.804935i | \(0.702200\pi\) | |||||||
\(992\) | 7.21110 | 0.228953 | ||||||||
\(993\) | −21.3944 | −0.678932 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3028 | −0.358322 | ||||||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | 48.7250 | 1.54314 | 0.771568 | − | 0.636147i | \(-0.219473\pi\) | ||||
0.771568 | + | 0.636147i | \(0.219473\pi\) | |||||||
\(998\) | 10.3028 | 0.326129 | ||||||||
\(999\) | 27.5139 | 0.870501 |
(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 | 1862.2.a.l.1.2 | 2 | ||
7.6 | odd | 2 | 266.2.a.c.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 2394.2.a.q.1.1 | 2 | |||
28.27 | even | 2 | 2128.2.a.h.1.2 | 2 | |||
35.34 | odd | 2 | 6650.2.a.bl.1.2 | 2 | |||
56.13 | odd | 2 | 8512.2.a.n.1.2 | 2 | |||
56.27 | even | 2 | 8512.2.a.u.1.1 | 2 | |||
133.132 | even | 2 | 5054.2.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.a.c.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1862.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2128.2.a.h.1.2 | 2 | 28.27 | even | 2 | |||
2394.2.a.q.1.1 | 2 | 21.20 | even | 2 | |||
5054.2.a.e.1.2 | 2 | 133.132 | even | 2 | |||
6650.2.a.bl.1.2 | 2 | 35.34 | odd | 2 | |||
8512.2.a.n.1.2 | 2 | 56.13 | odd | 2 | |||
8512.2.a.u.1.1 | 2 | 56.27 | even | 2 |