Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.00000 | 1.78885 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) | ||||
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.44949 | 1.68175 | 0.840875 | − | 0.541230i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541230i | \(0.182041\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.00000 | 1.26491 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −6.89898 | −1.91343 | −0.956716 | − | 0.291022i | \(-0.906005\pi\) | ||||
−0.956716 | + | 0.291022i | \(0.906005\pi\) | |||||||
\(14\) | 4.44949 | 1.18918 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.44949 | −1.02078 | −0.510391 | − | 0.859942i | \(-0.670499\pi\) | ||||
−0.510391 | + | 0.859942i | \(0.670499\pi\) | |||||||
\(20\) | 4.00000 | 0.894427 | ||||||||
\(21\) | 4.44949 | 0.970958 | ||||||||
\(22\) | 4.89898 | 1.04447 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 11.0000 | 2.20000 | ||||||||
\(26\) | −6.89898 | −1.35300 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.44949 | 0.840875 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.89898 | 0.852803 | ||||||||
\(34\) | −4.89898 | −0.840168 | ||||||||
\(35\) | 17.7980 | 3.00840 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −4.44949 | −0.721803 | ||||||||
\(39\) | −6.89898 | −1.10472 | ||||||||
\(40\) | 4.00000 | 0.632456 | ||||||||
\(41\) | −8.89898 | −1.38979 | −0.694894 | − | 0.719113i | \(-0.744549\pi\) | ||||
−0.694894 | + | 0.719113i | \(0.744549\pi\) | |||||||
\(42\) | 4.44949 | 0.686571 | ||||||||
\(43\) | 12.4495 | 1.89853 | 0.949265 | − | 0.314478i | \(-0.101830\pi\) | ||||
0.949265 | + | 0.314478i | \(0.101830\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 4.00000 | 0.596285 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | 11.0000 | 1.55563 | ||||||||
\(51\) | −4.89898 | −0.685994 | ||||||||
\(52\) | −6.89898 | −0.956716 | ||||||||
\(53\) | −8.89898 | −1.22237 | −0.611184 | − | 0.791488i | \(-0.709307\pi\) | ||||
−0.611184 | + | 0.791488i | \(0.709307\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 19.5959 | 2.64231 | ||||||||
\(56\) | 4.44949 | 0.594588 | ||||||||
\(57\) | −4.44949 | −0.589349 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 4.00000 | 0.516398 | ||||||||
\(61\) | 2.89898 | 0.371176 | 0.185588 | − | 0.982628i | \(-0.440581\pi\) | ||||
0.185588 | + | 0.982628i | \(0.440581\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 4.44949 | 0.560583 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −27.5959 | −3.42285 | ||||||||
\(66\) | 4.89898 | 0.603023 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −4.89898 | −0.594089 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 17.7980 | 2.12726 | ||||||||
\(71\) | −10.8990 | −1.29347 | −0.646735 | − | 0.762714i | \(-0.723866\pi\) | ||||
−0.646735 | + | 0.762714i | \(0.723866\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.89898 | −0.807464 | −0.403732 | − | 0.914877i | \(-0.632287\pi\) | ||||
−0.403732 | + | 0.914877i | \(0.632287\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 11.0000 | 1.27017 | ||||||||
\(76\) | −4.44949 | −0.510391 | ||||||||
\(77\) | 21.7980 | 2.48411 | ||||||||
\(78\) | −6.89898 | −0.781156 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.89898 | −0.982728 | ||||||||
\(83\) | −1.55051 | −0.170191 | −0.0850953 | − | 0.996373i | \(-0.527119\pi\) | ||||
−0.0850953 | + | 0.996373i | \(0.527119\pi\) | |||||||
\(84\) | 4.44949 | 0.485479 | ||||||||
\(85\) | −19.5959 | −2.12548 | ||||||||
\(86\) | 12.4495 | 1.34246 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 4.89898 | 0.522233 | ||||||||
\(89\) | 12.8990 | 1.36729 | 0.683645 | − | 0.729815i | \(-0.260394\pi\) | ||||
0.683645 | + | 0.729815i | \(0.260394\pi\) | |||||||
\(90\) | 4.00000 | 0.421637 | ||||||||
\(91\) | −30.6969 | −3.21791 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 4.00000 | 0.412568 | ||||||||
\(95\) | −17.7980 | −1.82603 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −19.1464 | −1.94403 | −0.972013 | − | 0.234929i | \(-0.924514\pi\) | ||||
−0.972013 | + | 0.234929i | \(0.924514\pi\) | |||||||
\(98\) | 12.7980 | 1.29279 | ||||||||
\(99\) | 4.89898 | 0.492366 | ||||||||
\(100\) | 11.0000 | 1.10000 | ||||||||
\(101\) | −5.10102 | −0.507571 | −0.253785 | − | 0.967261i | \(-0.581676\pi\) | ||||
−0.253785 | + | 0.967261i | \(0.581676\pi\) | |||||||
\(102\) | −4.89898 | −0.485071 | ||||||||
\(103\) | 6.24745 | 0.615579 | 0.307790 | − | 0.951454i | \(-0.400411\pi\) | ||||
0.307790 | + | 0.951454i | \(0.400411\pi\) | |||||||
\(104\) | −6.89898 | −0.676501 | ||||||||
\(105\) | 17.7980 | 1.73690 | ||||||||
\(106\) | −8.89898 | −0.864345 | ||||||||
\(107\) | −9.55051 | −0.923283 | −0.461641 | − | 0.887067i | \(-0.652739\pi\) | ||||
−0.461641 | + | 0.887067i | \(0.652739\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.44949 | −0.426184 | −0.213092 | − | 0.977032i | \(-0.568353\pi\) | ||||
−0.213092 | + | 0.977032i | \(0.568353\pi\) | |||||||
\(110\) | 19.5959 | 1.86840 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 4.44949 | 0.420437 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | −4.44949 | −0.416733 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −6.89898 | −0.637811 | ||||||||
\(118\) | −4.89898 | −0.450988 | ||||||||
\(119\) | −21.7980 | −1.99822 | ||||||||
\(120\) | 4.00000 | 0.365148 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 2.89898 | 0.262461 | ||||||||
\(123\) | −8.89898 | −0.802394 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 4.44949 | 0.396392 | ||||||||
\(127\) | 5.79796 | 0.514486 | 0.257243 | − | 0.966347i | \(-0.417186\pi\) | ||||
0.257243 | + | 0.966347i | \(0.417186\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.4495 | 1.09612 | ||||||||
\(130\) | −27.5959 | −2.42032 | ||||||||
\(131\) | 18.8990 | 1.65121 | 0.825606 | − | 0.564247i | \(-0.190834\pi\) | ||||
0.825606 | + | 0.564247i | \(0.190834\pi\) | |||||||
\(132\) | 4.89898 | 0.426401 | ||||||||
\(133\) | −19.7980 | −1.71670 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | −4.89898 | −0.420084 | ||||||||
\(137\) | −5.79796 | −0.495353 | −0.247677 | − | 0.968843i | \(-0.579667\pi\) | ||||
−0.247677 | + | 0.968843i | \(0.579667\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | 17.7980 | 1.50420 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | −10.8990 | −0.914622 | ||||||||
\(143\) | −33.7980 | −2.82633 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | −6.89898 | −0.570964 | ||||||||
\(147\) | 12.7980 | 1.05556 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −18.6969 | −1.53171 | −0.765856 | − | 0.643012i | \(-0.777685\pi\) | ||||
−0.765856 | + | 0.643012i | \(0.777685\pi\) | |||||||
\(150\) | 11.0000 | 0.898146 | ||||||||
\(151\) | −13.7980 | −1.12286 | −0.561431 | − | 0.827524i | \(-0.689749\pi\) | ||||
−0.561431 | + | 0.827524i | \(0.689749\pi\) | |||||||
\(152\) | −4.44949 | −0.360901 | ||||||||
\(153\) | −4.89898 | −0.396059 | ||||||||
\(154\) | 21.7980 | 1.75653 | ||||||||
\(155\) | −24.0000 | −1.92773 | ||||||||
\(156\) | −6.89898 | −0.552360 | ||||||||
\(157\) | −15.7980 | −1.26081 | −0.630407 | − | 0.776265i | \(-0.717112\pi\) | ||||
−0.630407 | + | 0.776265i | \(0.717112\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −8.89898 | −0.705735 | ||||||||
\(160\) | 4.00000 | 0.316228 | ||||||||
\(161\) | −4.44949 | −0.350669 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.898979 | 0.0704135 | 0.0352068 | − | 0.999380i | \(-0.488791\pi\) | ||||
0.0352068 | + | 0.999380i | \(0.488791\pi\) | |||||||
\(164\) | −8.89898 | −0.694894 | ||||||||
\(165\) | 19.5959 | 1.52554 | ||||||||
\(166\) | −1.55051 | −0.120343 | ||||||||
\(167\) | 9.79796 | 0.758189 | 0.379094 | − | 0.925358i | \(-0.376236\pi\) | ||||
0.379094 | + | 0.925358i | \(0.376236\pi\) | |||||||
\(168\) | 4.44949 | 0.343286 | ||||||||
\(169\) | 34.5959 | 2.66122 | ||||||||
\(170\) | −19.5959 | −1.50294 | ||||||||
\(171\) | −4.44949 | −0.340261 | ||||||||
\(172\) | 12.4495 | 0.949265 | ||||||||
\(173\) | −3.10102 | −0.235766 | −0.117883 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117883 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 48.9444 | 3.69985 | ||||||||
\(176\) | 4.89898 | 0.369274 | ||||||||
\(177\) | −4.89898 | −0.368230 | ||||||||
\(178\) | 12.8990 | 0.966819 | ||||||||
\(179\) | 14.6969 | 1.09850 | 0.549250 | − | 0.835658i | \(-0.314913\pi\) | ||||
0.549250 | + | 0.835658i | \(0.314913\pi\) | |||||||
\(180\) | 4.00000 | 0.298142 | ||||||||
\(181\) | −25.3485 | −1.88414 | −0.942068 | − | 0.335421i | \(-0.891122\pi\) | ||||
−0.942068 | + | 0.335421i | \(0.891122\pi\) | |||||||
\(182\) | −30.6969 | −2.27541 | ||||||||
\(183\) | 2.89898 | 0.214299 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | −24.0000 | −1.75505 | ||||||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | 4.44949 | 0.323653 | ||||||||
\(190\) | −17.7980 | −1.29120 | ||||||||
\(191\) | 7.34847 | 0.531717 | 0.265858 | − | 0.964012i | \(-0.414345\pi\) | ||||
0.265858 | + | 0.964012i | \(0.414345\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 21.5959 | 1.55451 | 0.777254 | − | 0.629187i | \(-0.216612\pi\) | ||||
0.777254 | + | 0.629187i | \(0.216612\pi\) | |||||||
\(194\) | −19.1464 | −1.37463 | ||||||||
\(195\) | −27.5959 | −1.97618 | ||||||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | 3.79796 | 0.270593 | 0.135297 | − | 0.990805i | \(-0.456801\pi\) | ||||
0.135297 | + | 0.990805i | \(0.456801\pi\) | |||||||
\(198\) | 4.89898 | 0.348155 | ||||||||
\(199\) | −26.2474 | −1.86063 | −0.930316 | − | 0.366759i | \(-0.880468\pi\) | ||||
−0.930316 | + | 0.366759i | \(0.880468\pi\) | |||||||
\(200\) | 11.0000 | 0.777817 | ||||||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | −5.10102 | −0.358907 | ||||||||
\(203\) | 4.44949 | 0.312293 | ||||||||
\(204\) | −4.89898 | −0.342997 | ||||||||
\(205\) | −35.5959 | −2.48613 | ||||||||
\(206\) | 6.24745 | 0.435280 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −6.89898 | −0.478358 | ||||||||
\(209\) | −21.7980 | −1.50780 | ||||||||
\(210\) | 17.7980 | 1.22818 | ||||||||
\(211\) | 24.8990 | 1.71412 | 0.857058 | − | 0.515220i | \(-0.172290\pi\) | ||||
0.857058 | + | 0.515220i | \(0.172290\pi\) | |||||||
\(212\) | −8.89898 | −0.611184 | ||||||||
\(213\) | −10.8990 | −0.746786 | ||||||||
\(214\) | −9.55051 | −0.652859 | ||||||||
\(215\) | 49.7980 | 3.39619 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −26.6969 | −1.81231 | ||||||||
\(218\) | −4.44949 | −0.301357 | ||||||||
\(219\) | −6.89898 | −0.466190 | ||||||||
\(220\) | 19.5959 | 1.32116 | ||||||||
\(221\) | 33.7980 | 2.27350 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | 13.7980 | 0.923980 | 0.461990 | − | 0.886885i | \(-0.347136\pi\) | ||||
0.461990 | + | 0.886885i | \(0.347136\pi\) | |||||||
\(224\) | 4.44949 | 0.297294 | ||||||||
\(225\) | 11.0000 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.34847 | 0.487735 | 0.243868 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(228\) | −4.44949 | −0.294675 | ||||||||
\(229\) | −12.6969 | −0.839037 | −0.419519 | − | 0.907747i | \(-0.637801\pi\) | ||||
−0.419519 | + | 0.907747i | \(0.637801\pi\) | |||||||
\(230\) | −4.00000 | −0.263752 | ||||||||
\(231\) | 21.7980 | 1.43420 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 16.6969 | 1.09385 | 0.546926 | − | 0.837181i | \(-0.315798\pi\) | ||||
0.546926 | + | 0.837181i | \(0.315798\pi\) | |||||||
\(234\) | −6.89898 | −0.451000 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | −4.89898 | −0.318896 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | −21.7980 | −1.41295 | ||||||||
\(239\) | −1.10102 | −0.0712191 | −0.0356095 | − | 0.999366i | \(-0.511337\pi\) | ||||
−0.0356095 | + | 0.999366i | \(0.511337\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | 20.6969 | 1.33321 | 0.666604 | − | 0.745412i | \(-0.267747\pi\) | ||||
0.666604 | + | 0.745412i | \(0.267747\pi\) | |||||||
\(242\) | 13.0000 | 0.835672 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.89898 | 0.185588 | ||||||||
\(245\) | 51.1918 | 3.27053 | ||||||||
\(246\) | −8.89898 | −0.567378 | ||||||||
\(247\) | 30.6969 | 1.95320 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | −1.55051 | −0.0982596 | ||||||||
\(250\) | 24.0000 | 1.51789 | ||||||||
\(251\) | 3.10102 | 0.195735 | 0.0978673 | − | 0.995199i | \(-0.468798\pi\) | ||||
0.0978673 | + | 0.995199i | \(0.468798\pi\) | |||||||
\(252\) | 4.44949 | 0.280292 | ||||||||
\(253\) | −4.89898 | −0.307996 | ||||||||
\(254\) | 5.79796 | 0.363796 | ||||||||
\(255\) | −19.5959 | −1.22714 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.10102 | −0.0686798 | −0.0343399 | − | 0.999410i | \(-0.510933\pi\) | ||||
−0.0343399 | + | 0.999410i | \(0.510933\pi\) | |||||||
\(258\) | 12.4495 | 0.775071 | ||||||||
\(259\) | −8.89898 | −0.552956 | ||||||||
\(260\) | −27.5959 | −1.71143 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 18.8990 | 1.16758 | ||||||||
\(263\) | 28.2474 | 1.74181 | 0.870906 | − | 0.491449i | \(-0.163533\pi\) | ||||
0.870906 | + | 0.491449i | \(0.163533\pi\) | |||||||
\(264\) | 4.89898 | 0.301511 | ||||||||
\(265\) | −35.5959 | −2.18664 | ||||||||
\(266\) | −19.7980 | −1.21389 | ||||||||
\(267\) | 12.8990 | 0.789405 | ||||||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 1.10102 | 0.0671304 | 0.0335652 | − | 0.999437i | \(-0.489314\pi\) | ||||
0.0335652 | + | 0.999437i | \(0.489314\pi\) | |||||||
\(270\) | 4.00000 | 0.243432 | ||||||||
\(271\) | 5.79796 | 0.352201 | 0.176100 | − | 0.984372i | \(-0.443652\pi\) | ||||
0.176100 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(272\) | −4.89898 | −0.297044 | ||||||||
\(273\) | −30.6969 | −1.85786 | ||||||||
\(274\) | −5.79796 | −0.350268 | ||||||||
\(275\) | 53.8888 | 3.24962 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −4.69694 | −0.282212 | −0.141106 | − | 0.989995i | \(-0.545066\pi\) | ||||
−0.141106 | + | 0.989995i | \(0.545066\pi\) | |||||||
\(278\) | 6.00000 | 0.359856 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 17.7980 | 1.06363 | ||||||||
\(281\) | −21.5505 | −1.28560 | −0.642798 | − | 0.766036i | \(-0.722226\pi\) | ||||
−0.642798 | + | 0.766036i | \(0.722226\pi\) | |||||||
\(282\) | 4.00000 | 0.238197 | ||||||||
\(283\) | 17.5959 | 1.04597 | 0.522984 | − | 0.852342i | \(-0.324819\pi\) | ||||
0.522984 | + | 0.852342i | \(0.324819\pi\) | |||||||
\(284\) | −10.8990 | −0.646735 | ||||||||
\(285\) | −17.7980 | −1.05426 | ||||||||
\(286\) | −33.7980 | −1.99852 | ||||||||
\(287\) | −39.5959 | −2.33727 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 4.00000 | 0.234888 | ||||||||
\(291\) | −19.1464 | −1.12238 | ||||||||
\(292\) | −6.89898 | −0.403732 | ||||||||
\(293\) | 25.1464 | 1.46907 | 0.734535 | − | 0.678571i | \(-0.237400\pi\) | ||||
0.734535 | + | 0.678571i | \(0.237400\pi\) | |||||||
\(294\) | 12.7980 | 0.746392 | ||||||||
\(295\) | −19.5959 | −1.14092 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 4.89898 | 0.284268 | ||||||||
\(298\) | −18.6969 | −1.08308 | ||||||||
\(299\) | 6.89898 | 0.398978 | ||||||||
\(300\) | 11.0000 | 0.635085 | ||||||||
\(301\) | 55.3939 | 3.19285 | ||||||||
\(302\) | −13.7980 | −0.793983 | ||||||||
\(303\) | −5.10102 | −0.293046 | ||||||||
\(304\) | −4.44949 | −0.255196 | ||||||||
\(305\) | 11.5959 | 0.663980 | ||||||||
\(306\) | −4.89898 | −0.280056 | ||||||||
\(307\) | −22.6969 | −1.29538 | −0.647691 | − | 0.761903i | \(-0.724265\pi\) | ||||
−0.647691 | + | 0.761903i | \(0.724265\pi\) | |||||||
\(308\) | 21.7980 | 1.24205 | ||||||||
\(309\) | 6.24745 | 0.355405 | ||||||||
\(310\) | −24.0000 | −1.36311 | ||||||||
\(311\) | −2.69694 | −0.152929 | −0.0764647 | − | 0.997072i | \(-0.524363\pi\) | ||||
−0.0764647 | + | 0.997072i | \(0.524363\pi\) | |||||||
\(312\) | −6.89898 | −0.390578 | ||||||||
\(313\) | −21.5959 | −1.22067 | −0.610337 | − | 0.792142i | \(-0.708966\pi\) | ||||
−0.610337 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(314\) | −15.7980 | −0.891530 | ||||||||
\(315\) | 17.7980 | 1.00280 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 10.8990 | 0.612148 | 0.306074 | − | 0.952008i | \(-0.400985\pi\) | ||||
0.306074 | + | 0.952008i | \(0.400985\pi\) | |||||||
\(318\) | −8.89898 | −0.499030 | ||||||||
\(319\) | 4.89898 | 0.274290 | ||||||||
\(320\) | 4.00000 | 0.223607 | ||||||||
\(321\) | −9.55051 | −0.533058 | ||||||||
\(322\) | −4.44949 | −0.247960 | ||||||||
\(323\) | 21.7980 | 1.21287 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −75.8888 | −4.20955 | ||||||||
\(326\) | 0.898979 | 0.0497899 | ||||||||
\(327\) | −4.44949 | −0.246057 | ||||||||
\(328\) | −8.89898 | −0.491364 | ||||||||
\(329\) | 17.7980 | 0.981233 | ||||||||
\(330\) | 19.5959 | 1.07872 | ||||||||
\(331\) | −11.1010 | −0.610167 | −0.305084 | − | 0.952326i | \(-0.598684\pi\) | ||||
−0.305084 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(332\) | −1.55051 | −0.0850953 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 9.79796 | 0.536120 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 4.44949 | 0.242740 | ||||||||
\(337\) | 20.4495 | 1.11395 | 0.556977 | − | 0.830528i | \(-0.311961\pi\) | ||||
0.556977 | + | 0.830528i | \(0.311961\pi\) | |||||||
\(338\) | 34.5959 | 1.88177 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.5959 | −1.06274 | ||||||||
\(341\) | −29.3939 | −1.59177 | ||||||||
\(342\) | −4.44949 | −0.240601 | ||||||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | 12.4495 | 0.671232 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | −3.10102 | −0.166712 | ||||||||
\(347\) | −19.5959 | −1.05196 | −0.525982 | − | 0.850496i | \(-0.676302\pi\) | ||||
−0.525982 | + | 0.850496i | \(0.676302\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 48.9444 | 2.61619 | ||||||||
\(351\) | −6.89898 | −0.368240 | ||||||||
\(352\) | 4.89898 | 0.261116 | ||||||||
\(353\) | −3.79796 | −0.202145 | −0.101072 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101072 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(354\) | −4.89898 | −0.260378 | ||||||||
\(355\) | −43.5959 | −2.31383 | ||||||||
\(356\) | 12.8990 | 0.683645 | ||||||||
\(357\) | −21.7980 | −1.15367 | ||||||||
\(358\) | 14.6969 | 0.776757 | ||||||||
\(359\) | −10.4495 | −0.551503 | −0.275751 | − | 0.961229i | \(-0.588927\pi\) | ||||
−0.275751 | + | 0.961229i | \(0.588927\pi\) | |||||||
\(360\) | 4.00000 | 0.210819 | ||||||||
\(361\) | 0.797959 | 0.0419978 | ||||||||
\(362\) | −25.3485 | −1.33229 | ||||||||
\(363\) | 13.0000 | 0.682323 | ||||||||
\(364\) | −30.6969 | −1.60896 | ||||||||
\(365\) | −27.5959 | −1.44444 | ||||||||
\(366\) | 2.89898 | 0.151532 | ||||||||
\(367\) | −30.0000 | −1.56599 | −0.782994 | − | 0.622030i | \(-0.786308\pi\) | ||||
−0.782994 | + | 0.622030i | \(0.786308\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −8.89898 | −0.463262 | ||||||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | −39.5959 | −2.05572 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 24.0454 | 1.24502 | 0.622512 | − | 0.782610i | \(-0.286112\pi\) | ||||
0.622512 | + | 0.782610i | \(0.286112\pi\) | |||||||
\(374\) | −24.0000 | −1.24101 | ||||||||
\(375\) | 24.0000 | 1.23935 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | −6.89898 | −0.355316 | ||||||||
\(378\) | 4.44949 | 0.228857 | ||||||||
\(379\) | 2.65153 | 0.136200 | 0.0681000 | − | 0.997679i | \(-0.478306\pi\) | ||||
0.0681000 | + | 0.997679i | \(0.478306\pi\) | |||||||
\(380\) | −17.7980 | −0.913016 | ||||||||
\(381\) | 5.79796 | 0.297038 | ||||||||
\(382\) | 7.34847 | 0.375980 | ||||||||
\(383\) | 9.79796 | 0.500652 | 0.250326 | − | 0.968162i | \(-0.419462\pi\) | ||||
0.250326 | + | 0.968162i | \(0.419462\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 87.1918 | 4.44371 | ||||||||
\(386\) | 21.5959 | 1.09920 | ||||||||
\(387\) | 12.4495 | 0.632843 | ||||||||
\(388\) | −19.1464 | −0.972013 | ||||||||
\(389\) | 16.6515 | 0.844266 | 0.422133 | − | 0.906534i | \(-0.361281\pi\) | ||||
0.422133 | + | 0.906534i | \(0.361281\pi\) | |||||||
\(390\) | −27.5959 | −1.39737 | ||||||||
\(391\) | 4.89898 | 0.247752 | ||||||||
\(392\) | 12.7980 | 0.646395 | ||||||||
\(393\) | 18.8990 | 0.953327 | ||||||||
\(394\) | 3.79796 | 0.191338 | ||||||||
\(395\) | 40.0000 | 2.01262 | ||||||||
\(396\) | 4.89898 | 0.246183 | ||||||||
\(397\) | 25.5959 | 1.28462 | 0.642311 | − | 0.766444i | \(-0.277976\pi\) | ||||
0.642311 | + | 0.766444i | \(0.277976\pi\) | |||||||
\(398\) | −26.2474 | −1.31567 | ||||||||
\(399\) | −19.7980 | −0.991138 | ||||||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | 7.75255 | 0.387144 | 0.193572 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193572 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | 41.3939 | 2.06198 | ||||||||
\(404\) | −5.10102 | −0.253785 | ||||||||
\(405\) | 4.00000 | 0.198762 | ||||||||
\(406\) | 4.44949 | 0.220824 | ||||||||
\(407\) | −9.79796 | −0.485667 | ||||||||
\(408\) | −4.89898 | −0.242536 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | −35.5959 | −1.75796 | ||||||||
\(411\) | −5.79796 | −0.285992 | ||||||||
\(412\) | 6.24745 | 0.307790 | ||||||||
\(413\) | −21.7980 | −1.07261 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −6.20204 | −0.304446 | ||||||||
\(416\) | −6.89898 | −0.338250 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | −21.7980 | −1.06617 | ||||||||
\(419\) | −7.75255 | −0.378737 | −0.189368 | − | 0.981906i | \(-0.560644\pi\) | ||||
−0.189368 | + | 0.981906i | \(0.560644\pi\) | |||||||
\(420\) | 17.7980 | 0.868451 | ||||||||
\(421\) | 34.4949 | 1.68118 | 0.840589 | − | 0.541673i | \(-0.182209\pi\) | ||||
0.840589 | + | 0.541673i | \(0.182209\pi\) | |||||||
\(422\) | 24.8990 | 1.21206 | ||||||||
\(423\) | 4.00000 | 0.194487 | ||||||||
\(424\) | −8.89898 | −0.432173 | ||||||||
\(425\) | −53.8888 | −2.61399 | ||||||||
\(426\) | −10.8990 | −0.528057 | ||||||||
\(427\) | 12.8990 | 0.624225 | ||||||||
\(428\) | −9.55051 | −0.461641 | ||||||||
\(429\) | −33.7980 | −1.63178 | ||||||||
\(430\) | 49.7980 | 2.40147 | ||||||||
\(431\) | −12.4949 | −0.601858 | −0.300929 | − | 0.953647i | \(-0.597297\pi\) | ||||
−0.300929 | + | 0.953647i | \(0.597297\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 1.75255 | 0.0842222 | 0.0421111 | − | 0.999113i | \(-0.486592\pi\) | ||||
0.0421111 | + | 0.999113i | \(0.486592\pi\) | |||||||
\(434\) | −26.6969 | −1.28149 | ||||||||
\(435\) | 4.00000 | 0.191785 | ||||||||
\(436\) | −4.44949 | −0.213092 | ||||||||
\(437\) | 4.44949 | 0.212848 | ||||||||
\(438\) | −6.89898 | −0.329646 | ||||||||
\(439\) | 2.20204 | 0.105098 | 0.0525488 | − | 0.998618i | \(-0.483265\pi\) | ||||
0.0525488 | + | 0.998618i | \(0.483265\pi\) | |||||||
\(440\) | 19.5959 | 0.934199 | ||||||||
\(441\) | 12.7980 | 0.609427 | ||||||||
\(442\) | 33.7980 | 1.60760 | ||||||||
\(443\) | 9.10102 | 0.432403 | 0.216201 | − | 0.976349i | \(-0.430633\pi\) | ||||
0.216201 | + | 0.976349i | \(0.430633\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 51.5959 | 2.44588 | ||||||||
\(446\) | 13.7980 | 0.653352 | ||||||||
\(447\) | −18.6969 | −0.884335 | ||||||||
\(448\) | 4.44949 | 0.210219 | ||||||||
\(449\) | 28.4949 | 1.34476 | 0.672379 | − | 0.740207i | \(-0.265273\pi\) | ||||
0.672379 | + | 0.740207i | \(0.265273\pi\) | |||||||
\(450\) | 11.0000 | 0.518545 | ||||||||
\(451\) | −43.5959 | −2.05285 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.7980 | −0.648285 | ||||||||
\(454\) | 7.34847 | 0.344881 | ||||||||
\(455\) | −122.788 | −5.75638 | ||||||||
\(456\) | −4.44949 | −0.208366 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | −12.6969 | −0.593289 | ||||||||
\(459\) | −4.89898 | −0.228665 | ||||||||
\(460\) | −4.00000 | −0.186501 | ||||||||
\(461\) | −20.6969 | −0.963953 | −0.481976 | − | 0.876184i | \(-0.660081\pi\) | ||||
−0.481976 | + | 0.876184i | \(0.660081\pi\) | |||||||
\(462\) | 21.7980 | 1.01413 | ||||||||
\(463\) | −10.2020 | −0.474129 | −0.237065 | − | 0.971494i | \(-0.576185\pi\) | ||||
−0.237065 | + | 0.971494i | \(0.576185\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −24.0000 | −1.11297 | ||||||||
\(466\) | 16.6969 | 0.773471 | ||||||||
\(467\) | −1.79796 | −0.0831996 | −0.0415998 | − | 0.999134i | \(-0.513245\pi\) | ||||
−0.0415998 | + | 0.999134i | \(0.513245\pi\) | |||||||
\(468\) | −6.89898 | −0.318905 | ||||||||
\(469\) | 8.89898 | 0.410917 | ||||||||
\(470\) | 16.0000 | 0.738025 | ||||||||
\(471\) | −15.7980 | −0.727932 | ||||||||
\(472\) | −4.89898 | −0.225494 | ||||||||
\(473\) | 60.9898 | 2.80431 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | −48.9444 | −2.24572 | ||||||||
\(476\) | −21.7980 | −0.999108 | ||||||||
\(477\) | −8.89898 | −0.407456 | ||||||||
\(478\) | −1.10102 | −0.0503595 | ||||||||
\(479\) | −0.247449 | −0.0113062 | −0.00565311 | − | 0.999984i | \(-0.501799\pi\) | ||||
−0.00565311 | + | 0.999984i | \(0.501799\pi\) | |||||||
\(480\) | 4.00000 | 0.182574 | ||||||||
\(481\) | 13.7980 | 0.629133 | ||||||||
\(482\) | 20.6969 | 0.942720 | ||||||||
\(483\) | −4.44949 | −0.202459 | ||||||||
\(484\) | 13.0000 | 0.590909 | ||||||||
\(485\) | −76.5857 | −3.47758 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | 2.89898 | 0.131231 | ||||||||
\(489\) | 0.898979 | 0.0406533 | ||||||||
\(490\) | 51.1918 | 2.31261 | ||||||||
\(491\) | −14.8990 | −0.672382 | −0.336191 | − | 0.941794i | \(-0.609139\pi\) | ||||
−0.336191 | + | 0.941794i | \(0.609139\pi\) | |||||||
\(492\) | −8.89898 | −0.401197 | ||||||||
\(493\) | −4.89898 | −0.220639 | ||||||||
\(494\) | 30.6969 | 1.38112 | ||||||||
\(495\) | 19.5959 | 0.880771 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | −48.4949 | −2.17529 | ||||||||
\(498\) | −1.55051 | −0.0694800 | ||||||||
\(499\) | −15.7980 | −0.707214 | −0.353607 | − | 0.935394i | \(-0.615045\pi\) | ||||
−0.353607 | + | 0.935394i | \(0.615045\pi\) | |||||||
\(500\) | 24.0000 | 1.07331 | ||||||||
\(501\) | 9.79796 | 0.437741 | ||||||||
\(502\) | 3.10102 | 0.138405 | ||||||||
\(503\) | 20.6515 | 0.920806 | 0.460403 | − | 0.887710i | \(-0.347705\pi\) | ||||
0.460403 | + | 0.887710i | \(0.347705\pi\) | |||||||
\(504\) | 4.44949 | 0.198196 | ||||||||
\(505\) | −20.4041 | −0.907970 | ||||||||
\(506\) | −4.89898 | −0.217786 | ||||||||
\(507\) | 34.5959 | 1.53646 | ||||||||
\(508\) | 5.79796 | 0.257243 | ||||||||
\(509\) | 3.10102 | 0.137450 | 0.0687252 | − | 0.997636i | \(-0.478107\pi\) | ||||
0.0687252 | + | 0.997636i | \(0.478107\pi\) | |||||||
\(510\) | −19.5959 | −0.867722 | ||||||||
\(511\) | −30.6969 | −1.35795 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.44949 | −0.196450 | ||||||||
\(514\) | −1.10102 | −0.0485639 | ||||||||
\(515\) | 24.9898 | 1.10118 | ||||||||
\(516\) | 12.4495 | 0.548058 | ||||||||
\(517\) | 19.5959 | 0.861827 | ||||||||
\(518\) | −8.89898 | −0.390999 | ||||||||
\(519\) | −3.10102 | −0.136120 | ||||||||
\(520\) | −27.5959 | −1.21016 | ||||||||
\(521\) | 13.5505 | 0.593659 | 0.296829 | − | 0.954931i | \(-0.404071\pi\) | ||||
0.296829 | + | 0.954931i | \(0.404071\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 0.202041 | 0.00883464 | 0.00441732 | − | 0.999990i | \(-0.498594\pi\) | ||||
0.00441732 | + | 0.999990i | \(0.498594\pi\) | |||||||
\(524\) | 18.8990 | 0.825606 | ||||||||
\(525\) | 48.9444 | 2.13611 | ||||||||
\(526\) | 28.2474 | 1.23165 | ||||||||
\(527\) | 29.3939 | 1.28042 | ||||||||
\(528\) | 4.89898 | 0.213201 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −35.5959 | −1.54619 | ||||||||
\(531\) | −4.89898 | −0.212598 | ||||||||
\(532\) | −19.7980 | −0.858350 | ||||||||
\(533\) | 61.3939 | 2.65926 | ||||||||
\(534\) | 12.8990 | 0.558193 | ||||||||
\(535\) | −38.2020 | −1.65162 | ||||||||
\(536\) | 2.00000 | 0.0863868 | ||||||||
\(537\) | 14.6969 | 0.634220 | ||||||||
\(538\) | 1.10102 | 0.0474684 | ||||||||
\(539\) | 62.6969 | 2.70055 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 21.7980 | 0.937167 | 0.468584 | − | 0.883419i | \(-0.344764\pi\) | ||||
0.468584 | + | 0.883419i | \(0.344764\pi\) | |||||||
\(542\) | 5.79796 | 0.249044 | ||||||||
\(543\) | −25.3485 | −1.08781 | ||||||||
\(544\) | −4.89898 | −0.210042 | ||||||||
\(545\) | −17.7980 | −0.762381 | ||||||||
\(546\) | −30.6969 | −1.31371 | ||||||||
\(547\) | 8.20204 | 0.350694 | 0.175347 | − | 0.984507i | \(-0.443895\pi\) | ||||
0.175347 | + | 0.984507i | \(0.443895\pi\) | |||||||
\(548\) | −5.79796 | −0.247677 | ||||||||
\(549\) | 2.89898 | 0.123725 | ||||||||
\(550\) | 53.8888 | 2.29783 | ||||||||
\(551\) | −4.44949 | −0.189555 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 44.4949 | 1.89212 | ||||||||
\(554\) | −4.69694 | −0.199554 | ||||||||
\(555\) | −8.00000 | −0.339581 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | 37.3939 | 1.58443 | 0.792215 | − | 0.610242i | \(-0.208928\pi\) | ||||
0.792215 | + | 0.610242i | \(0.208928\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | −85.8888 | −3.63271 | ||||||||
\(560\) | 17.7980 | 0.752101 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | −21.5505 | −0.909053 | ||||||||
\(563\) | 16.8990 | 0.712207 | 0.356104 | − | 0.934447i | \(-0.384105\pi\) | ||||
0.356104 | + | 0.934447i | \(0.384105\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.5959 | 0.739612 | ||||||||
\(567\) | 4.44949 | 0.186861 | ||||||||
\(568\) | −10.8990 | −0.457311 | ||||||||
\(569\) | −17.7980 | −0.746129 | −0.373065 | − | 0.927805i | \(-0.621693\pi\) | ||||
−0.373065 | + | 0.927805i | \(0.621693\pi\) | |||||||
\(570\) | −17.7980 | −0.745474 | ||||||||
\(571\) | −25.1010 | −1.05045 | −0.525223 | − | 0.850965i | \(-0.676018\pi\) | ||||
−0.525223 | + | 0.850965i | \(0.676018\pi\) | |||||||
\(572\) | −33.7980 | −1.41316 | ||||||||
\(573\) | 7.34847 | 0.306987 | ||||||||
\(574\) | −39.5959 | −1.65270 | ||||||||
\(575\) | −11.0000 | −0.458732 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 7.00000 | 0.291162 | ||||||||
\(579\) | 21.5959 | 0.897496 | ||||||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | −6.89898 | −0.286218 | ||||||||
\(582\) | −19.1464 | −0.793645 | ||||||||
\(583\) | −43.5959 | −1.80556 | ||||||||
\(584\) | −6.89898 | −0.285482 | ||||||||
\(585\) | −27.5959 | −1.14095 | ||||||||
\(586\) | 25.1464 | 1.03879 | ||||||||
\(587\) | −31.1918 | −1.28742 | −0.643712 | − | 0.765267i | \(-0.722607\pi\) | ||||
−0.643712 | + | 0.765267i | \(0.722607\pi\) | |||||||
\(588\) | 12.7980 | 0.527779 | ||||||||
\(589\) | 26.6969 | 1.10003 | ||||||||
\(590\) | −19.5959 | −0.806751 | ||||||||
\(591\) | 3.79796 | 0.156227 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 21.5959 | 0.886838 | 0.443419 | − | 0.896314i | \(-0.353765\pi\) | ||||
0.443419 | + | 0.896314i | \(0.353765\pi\) | |||||||
\(594\) | 4.89898 | 0.201008 | ||||||||
\(595\) | −87.1918 | −3.57452 | ||||||||
\(596\) | −18.6969 | −0.765856 | ||||||||
\(597\) | −26.2474 | −1.07424 | ||||||||
\(598\) | 6.89898 | 0.282120 | ||||||||
\(599\) | 22.6969 | 0.927372 | 0.463686 | − | 0.886000i | \(-0.346527\pi\) | ||||
0.463686 | + | 0.886000i | \(0.346527\pi\) | |||||||
\(600\) | 11.0000 | 0.449073 | ||||||||
\(601\) | 39.3939 | 1.60691 | 0.803455 | − | 0.595366i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595366i | \(0.202993\pi\) | |||||||
\(602\) | 55.3939 | 2.25769 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | −13.7980 | −0.561431 | ||||||||
\(605\) | 52.0000 | 2.11410 | ||||||||
\(606\) | −5.10102 | −0.207215 | ||||||||
\(607\) | 15.7980 | 0.641219 | 0.320610 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320610 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(608\) | −4.44949 | −0.180451 | ||||||||
\(609\) | 4.44949 | 0.180302 | ||||||||
\(610\) | 11.5959 | 0.469505 | ||||||||
\(611\) | −27.5959 | −1.11641 | ||||||||
\(612\) | −4.89898 | −0.198030 | ||||||||
\(613\) | −8.04541 | −0.324951 | −0.162475 | − | 0.986713i | \(-0.551948\pi\) | ||||
−0.162475 | + | 0.986713i | \(0.551948\pi\) | |||||||
\(614\) | −22.6969 | −0.915974 | ||||||||
\(615\) | −35.5959 | −1.43537 | ||||||||
\(616\) | 21.7980 | 0.878265 | ||||||||
\(617\) | 19.5959 | 0.788902 | 0.394451 | − | 0.918917i | \(-0.370935\pi\) | ||||
0.394451 | + | 0.918917i | \(0.370935\pi\) | |||||||
\(618\) | 6.24745 | 0.251309 | ||||||||
\(619\) | 20.0454 | 0.805693 | 0.402846 | − | 0.915268i | \(-0.368021\pi\) | ||||
0.402846 | + | 0.915268i | \(0.368021\pi\) | |||||||
\(620\) | −24.0000 | −0.963863 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −2.69694 | −0.108137 | ||||||||
\(623\) | 57.3939 | 2.29944 | ||||||||
\(624\) | −6.89898 | −0.276180 | ||||||||
\(625\) | 41.0000 | 1.64000 | ||||||||
\(626\) | −21.5959 | −0.863146 | ||||||||
\(627\) | −21.7980 | −0.870527 | ||||||||
\(628\) | −15.7980 | −0.630407 | ||||||||
\(629\) | 9.79796 | 0.390670 | ||||||||
\(630\) | 17.7980 | 0.709088 | ||||||||
\(631\) | −3.55051 | −0.141344 | −0.0706718 | − | 0.997500i | \(-0.522514\pi\) | ||||
−0.0706718 | + | 0.997500i | \(0.522514\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | 24.8990 | 0.989646 | ||||||||
\(634\) | 10.8990 | 0.432854 | ||||||||
\(635\) | 23.1918 | 0.920340 | ||||||||
\(636\) | −8.89898 | −0.352867 | ||||||||
\(637\) | −88.2929 | −3.49829 | ||||||||
\(638\) | 4.89898 | 0.193952 | ||||||||
\(639\) | −10.8990 | −0.431157 | ||||||||
\(640\) | 4.00000 | 0.158114 | ||||||||
\(641\) | −39.5959 | −1.56394 | −0.781972 | − | 0.623313i | \(-0.785786\pi\) | ||||
−0.781972 | + | 0.623313i | \(0.785786\pi\) | |||||||
\(642\) | −9.55051 | −0.376929 | ||||||||
\(643\) | −28.2020 | −1.11218 | −0.556090 | − | 0.831122i | \(-0.687699\pi\) | ||||
−0.556090 | + | 0.831122i | \(0.687699\pi\) | |||||||
\(644\) | −4.44949 | −0.175334 | ||||||||
\(645\) | 49.7980 | 1.96079 | ||||||||
\(646\) | 21.7980 | 0.857629 | ||||||||
\(647\) | −5.10102 | −0.200542 | −0.100271 | − | 0.994960i | \(-0.531971\pi\) | ||||
−0.100271 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | −75.8888 | −2.97660 | ||||||||
\(651\) | −26.6969 | −1.04634 | ||||||||
\(652\) | 0.898979 | 0.0352068 | ||||||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | −4.44949 | −0.173989 | ||||||||
\(655\) | 75.5959 | 2.95378 | ||||||||
\(656\) | −8.89898 | −0.347447 | ||||||||
\(657\) | −6.89898 | −0.269155 | ||||||||
\(658\) | 17.7980 | 0.693837 | ||||||||
\(659\) | −4.40408 | −0.171559 | −0.0857793 | − | 0.996314i | \(-0.527338\pi\) | ||||
−0.0857793 | + | 0.996314i | \(0.527338\pi\) | |||||||
\(660\) | 19.5959 | 0.762770 | ||||||||
\(661\) | −18.6515 | −0.725460 | −0.362730 | − | 0.931894i | \(-0.618155\pi\) | ||||
−0.362730 | + | 0.931894i | \(0.618155\pi\) | |||||||
\(662\) | −11.1010 | −0.431453 | ||||||||
\(663\) | 33.7980 | 1.31260 | ||||||||
\(664\) | −1.55051 | −0.0601715 | ||||||||
\(665\) | −79.1918 | −3.07093 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 9.79796 | 0.379094 | ||||||||
\(669\) | 13.7980 | 0.533460 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | 14.2020 | 0.548264 | ||||||||
\(672\) | 4.44949 | 0.171643 | ||||||||
\(673\) | −2.40408 | −0.0926706 | −0.0463353 | − | 0.998926i | \(-0.514754\pi\) | ||||
−0.0463353 | + | 0.998926i | \(0.514754\pi\) | |||||||
\(674\) | 20.4495 | 0.787685 | ||||||||
\(675\) | 11.0000 | 0.423390 | ||||||||
\(676\) | 34.5959 | 1.33061 | ||||||||
\(677\) | −19.3485 | −0.743622 | −0.371811 | − | 0.928308i | \(-0.621263\pi\) | ||||
−0.371811 | + | 0.928308i | \(0.621263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −85.1918 | −3.26936 | ||||||||
\(680\) | −19.5959 | −0.751469 | ||||||||
\(681\) | 7.34847 | 0.281594 | ||||||||
\(682\) | −29.3939 | −1.12555 | ||||||||
\(683\) | 19.5959 | 0.749817 | 0.374908 | − | 0.927062i | \(-0.377674\pi\) | ||||
0.374908 | + | 0.927062i | \(0.377674\pi\) | |||||||
\(684\) | −4.44949 | −0.170130 | ||||||||
\(685\) | −23.1918 | −0.886115 | ||||||||
\(686\) | 25.7980 | 0.984971 | ||||||||
\(687\) | −12.6969 | −0.484418 | ||||||||
\(688\) | 12.4495 | 0.474632 | ||||||||
\(689\) | 61.3939 | 2.33892 | ||||||||
\(690\) | −4.00000 | −0.152277 | ||||||||
\(691\) | −29.3939 | −1.11820 | −0.559098 | − | 0.829102i | \(-0.688852\pi\) | ||||
−0.559098 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(692\) | −3.10102 | −0.117883 | ||||||||
\(693\) | 21.7980 | 0.828036 | ||||||||
\(694\) | −19.5959 | −0.743851 | ||||||||
\(695\) | 24.0000 | 0.910372 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 43.5959 | 1.65131 | ||||||||
\(698\) | 14.0000 | 0.529908 | ||||||||
\(699\) | 16.6969 | 0.631536 | ||||||||
\(700\) | 48.9444 | 1.84992 | ||||||||
\(701\) | 25.7980 | 0.974375 | 0.487188 | − | 0.873297i | \(-0.338023\pi\) | ||||
0.487188 | + | 0.873297i | \(0.338023\pi\) | |||||||
\(702\) | −6.89898 | −0.260385 | ||||||||
\(703\) | 8.89898 | 0.335631 | ||||||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | −3.79796 | −0.142938 | ||||||||
\(707\) | −22.6969 | −0.853606 | ||||||||
\(708\) | −4.89898 | −0.184115 | ||||||||
\(709\) | 6.24745 | 0.234628 | 0.117314 | − | 0.993095i | \(-0.462572\pi\) | ||||
0.117314 | + | 0.993095i | \(0.462572\pi\) | |||||||
\(710\) | −43.5959 | −1.63613 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | 12.8990 | 0.483410 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −21.7980 | −0.815768 | ||||||||
\(715\) | −135.192 | −5.05589 | ||||||||
\(716\) | 14.6969 | 0.549250 | ||||||||
\(717\) | −1.10102 | −0.0411184 | ||||||||
\(718\) | −10.4495 | −0.389971 | ||||||||
\(719\) | −21.3939 | −0.797857 | −0.398928 | − | 0.916982i | \(-0.630618\pi\) | ||||
−0.398928 | + | 0.916982i | \(0.630618\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | 27.7980 | 1.03525 | ||||||||
\(722\) | 0.797959 | 0.0296970 | ||||||||
\(723\) | 20.6969 | 0.769727 | ||||||||
\(724\) | −25.3485 | −0.942068 | ||||||||
\(725\) | 11.0000 | 0.408530 | ||||||||
\(726\) | 13.0000 | 0.482475 | ||||||||
\(727\) | 19.7980 | 0.734266 | 0.367133 | − | 0.930169i | \(-0.380339\pi\) | ||||
0.367133 | + | 0.930169i | \(0.380339\pi\) | |||||||
\(728\) | −30.6969 | −1.13770 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.5959 | −1.02137 | ||||||||
\(731\) | −60.9898 | −2.25579 | ||||||||
\(732\) | 2.89898 | 0.107149 | ||||||||
\(733\) | −19.7980 | −0.731254 | −0.365627 | − | 0.930761i | \(-0.619145\pi\) | ||||
−0.365627 | + | 0.930761i | \(0.619145\pi\) | |||||||
\(734\) | −30.0000 | −1.10732 | ||||||||
\(735\) | 51.1918 | 1.88824 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 9.79796 | 0.360912 | ||||||||
\(738\) | −8.89898 | −0.327576 | ||||||||
\(739\) | −33.7980 | −1.24328 | −0.621639 | − | 0.783304i | \(-0.713533\pi\) | ||||
−0.621639 | + | 0.783304i | \(0.713533\pi\) | |||||||
\(740\) | −8.00000 | −0.294086 | ||||||||
\(741\) | 30.6969 | 1.12768 | ||||||||
\(742\) | −39.5959 | −1.45361 | ||||||||
\(743\) | 33.1464 | 1.21602 | 0.608012 | − | 0.793928i | \(-0.291967\pi\) | ||||
0.608012 | + | 0.793928i | \(0.291967\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −74.7878 | −2.74001 | ||||||||
\(746\) | 24.0454 | 0.880365 | ||||||||
\(747\) | −1.55051 | −0.0567302 | ||||||||
\(748\) | −24.0000 | −0.877527 | ||||||||
\(749\) | −42.4949 | −1.55273 | ||||||||
\(750\) | 24.0000 | 0.876356 | ||||||||
\(751\) | 7.79796 | 0.284552 | 0.142276 | − | 0.989827i | \(-0.454558\pi\) | ||||
0.142276 | + | 0.989827i | \(0.454558\pi\) | |||||||
\(752\) | 4.00000 | 0.145865 | ||||||||
\(753\) | 3.10102 | 0.113007 | ||||||||
\(754\) | −6.89898 | −0.251246 | ||||||||
\(755\) | −55.1918 | −2.00864 | ||||||||
\(756\) | 4.44949 | 0.161826 | ||||||||
\(757\) | 6.49490 | 0.236061 | 0.118031 | − | 0.993010i | \(-0.462342\pi\) | ||||
0.118031 | + | 0.993010i | \(0.462342\pi\) | |||||||
\(758\) | 2.65153 | 0.0963079 | ||||||||
\(759\) | −4.89898 | −0.177822 | ||||||||
\(760\) | −17.7980 | −0.645600 | ||||||||
\(761\) | 11.3939 | 0.413028 | 0.206514 | − | 0.978444i | \(-0.433788\pi\) | ||||
0.206514 | + | 0.978444i | \(0.433788\pi\) | |||||||
\(762\) | 5.79796 | 0.210038 | ||||||||
\(763\) | −19.7980 | −0.716734 | ||||||||
\(764\) | 7.34847 | 0.265858 | ||||||||
\(765\) | −19.5959 | −0.708492 | ||||||||
\(766\) | 9.79796 | 0.354015 | ||||||||
\(767\) | 33.7980 | 1.22037 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 9.75255 | 0.351686 | 0.175843 | − | 0.984418i | \(-0.443735\pi\) | ||||
0.175843 | + | 0.984418i | \(0.443735\pi\) | |||||||
\(770\) | 87.1918 | 3.14218 | ||||||||
\(771\) | −1.10102 | −0.0396523 | ||||||||
\(772\) | 21.5959 | 0.777254 | ||||||||
\(773\) | 49.5505 | 1.78221 | 0.891104 | − | 0.453799i | \(-0.149932\pi\) | ||||
0.891104 | + | 0.453799i | \(0.149932\pi\) | |||||||
\(774\) | 12.4495 | 0.447488 | ||||||||
\(775\) | −66.0000 | −2.37079 | ||||||||
\(776\) | −19.1464 | −0.687317 | ||||||||
\(777\) | −8.89898 | −0.319249 | ||||||||
\(778\) | 16.6515 | 0.596986 | ||||||||
\(779\) | 39.5959 | 1.41867 | ||||||||
\(780\) | −27.5959 | −0.988092 | ||||||||
\(781\) | −53.3939 | −1.91058 | ||||||||
\(782\) | 4.89898 | 0.175187 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 12.7980 | 0.457070 | ||||||||
\(785\) | −63.1918 | −2.25541 | ||||||||
\(786\) | 18.8990 | 0.674104 | ||||||||
\(787\) | 34.0000 | 1.21197 | 0.605985 | − | 0.795476i | \(-0.292779\pi\) | ||||
0.605985 | + | 0.795476i | \(0.292779\pi\) | |||||||
\(788\) | 3.79796 | 0.135297 | ||||||||
\(789\) | 28.2474 | 1.00564 | ||||||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.89898 | 0.174078 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 25.5959 | 0.908365 | ||||||||
\(795\) | −35.5959 | −1.26246 | ||||||||
\(796\) | −26.2474 | −0.930316 | ||||||||
\(797\) | 23.8434 | 0.844575 | 0.422288 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422288 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(798\) | −19.7980 | −0.700840 | ||||||||
\(799\) | −19.5959 | −0.693254 | ||||||||
\(800\) | 11.0000 | 0.388909 | ||||||||
\(801\) | 12.8990 | 0.455763 | ||||||||
\(802\) | 7.75255 | 0.273752 | ||||||||
\(803\) | −33.7980 | −1.19270 | ||||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | −17.7980 | −0.627296 | ||||||||
\(806\) | 41.3939 | 1.45804 | ||||||||
\(807\) | 1.10102 | 0.0387578 | ||||||||
\(808\) | −5.10102 | −0.179453 | ||||||||
\(809\) | −28.4949 | −1.00183 | −0.500914 | − | 0.865497i | \(-0.667003\pi\) | ||||
−0.500914 | + | 0.865497i | \(0.667003\pi\) | |||||||
\(810\) | 4.00000 | 0.140546 | ||||||||
\(811\) | −6.40408 | −0.224878 | −0.112439 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112439 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(812\) | 4.44949 | 0.156146 | ||||||||
\(813\) | 5.79796 | 0.203343 | ||||||||
\(814\) | −9.79796 | −0.343418 | ||||||||
\(815\) | 3.59592 | 0.125960 | ||||||||
\(816\) | −4.89898 | −0.171499 | ||||||||
\(817\) | −55.3939 | −1.93799 | ||||||||
\(818\) | −6.00000 | −0.209785 | ||||||||
\(819\) | −30.6969 | −1.07264 | ||||||||
\(820\) | −35.5959 | −1.24306 | ||||||||
\(821\) | 23.1010 | 0.806231 | 0.403116 | − | 0.915149i | \(-0.367927\pi\) | ||||
0.403116 | + | 0.915149i | \(0.367927\pi\) | |||||||
\(822\) | −5.79796 | −0.202227 | ||||||||
\(823\) | −45.7980 | −1.59642 | −0.798208 | − | 0.602382i | \(-0.794219\pi\) | ||||
−0.798208 | + | 0.602382i | \(0.794219\pi\) | |||||||
\(824\) | 6.24745 | 0.217640 | ||||||||
\(825\) | 53.8888 | 1.87617 | ||||||||
\(826\) | −21.7980 | −0.758448 | ||||||||
\(827\) | −31.5959 | −1.09870 | −0.549349 | − | 0.835593i | \(-0.685124\pi\) | ||||
−0.549349 | + | 0.835593i | \(0.685124\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −6.20204 | −0.215276 | ||||||||
\(831\) | −4.69694 | −0.162935 | ||||||||
\(832\) | −6.89898 | −0.239179 | ||||||||
\(833\) | −62.6969 | −2.17232 | ||||||||
\(834\) | 6.00000 | 0.207763 | ||||||||
\(835\) | 39.1918 | 1.35629 | ||||||||
\(836\) | −21.7980 | −0.753898 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −7.75255 | −0.267807 | ||||||||
\(839\) | −20.7423 | −0.716105 | −0.358053 | − | 0.933701i | \(-0.616559\pi\) | ||||
−0.358053 | + | 0.933701i | \(0.616559\pi\) | |||||||
\(840\) | 17.7980 | 0.614088 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 34.4949 | 1.18877 | ||||||||
\(843\) | −21.5505 | −0.742239 | ||||||||
\(844\) | 24.8990 | 0.857058 | ||||||||
\(845\) | 138.384 | 4.76054 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | 57.8434 | 1.98752 | ||||||||
\(848\) | −8.89898 | −0.305592 | ||||||||
\(849\) | 17.5959 | 0.603890 | ||||||||
\(850\) | −53.8888 | −1.84837 | ||||||||
\(851\) | 2.00000 | 0.0685591 | ||||||||
\(852\) | −10.8990 | −0.373393 | ||||||||
\(853\) | 53.1918 | 1.82125 | 0.910627 | − | 0.413230i | \(-0.135599\pi\) | ||||
0.910627 | + | 0.413230i | \(0.135599\pi\) | |||||||
\(854\) | 12.8990 | 0.441394 | ||||||||
\(855\) | −17.7980 | −0.608677 | ||||||||
\(856\) | −9.55051 | −0.326430 | ||||||||
\(857\) | 25.1010 | 0.857435 | 0.428717 | − | 0.903439i | \(-0.358966\pi\) | ||||
0.428717 | + | 0.903439i | \(0.358966\pi\) | |||||||
\(858\) | −33.7980 | −1.15384 | ||||||||
\(859\) | −35.5959 | −1.21452 | −0.607259 | − | 0.794504i | \(-0.707731\pi\) | ||||
−0.607259 | + | 0.794504i | \(0.707731\pi\) | |||||||
\(860\) | 49.7980 | 1.69810 | ||||||||
\(861\) | −39.5959 | −1.34943 | ||||||||
\(862\) | −12.4949 | −0.425578 | ||||||||
\(863\) | −1.79796 | −0.0612032 | −0.0306016 | − | 0.999532i | \(-0.509742\pi\) | ||||
−0.0306016 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −12.4041 | −0.421751 | ||||||||
\(866\) | 1.75255 | 0.0595541 | ||||||||
\(867\) | 7.00000 | 0.237732 | ||||||||
\(868\) | −26.6969 | −0.906153 | ||||||||
\(869\) | 48.9898 | 1.66186 | ||||||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | −13.7980 | −0.467526 | ||||||||
\(872\) | −4.44949 | −0.150679 | ||||||||
\(873\) | −19.1464 | −0.648008 | ||||||||
\(874\) | 4.44949 | 0.150506 | ||||||||
\(875\) | 106.788 | 3.61008 | ||||||||
\(876\) | −6.89898 | −0.233095 | ||||||||
\(877\) | −16.6969 | −0.563816 | −0.281908 | − | 0.959442i | \(-0.590967\pi\) | ||||
−0.281908 | + | 0.959442i | \(0.590967\pi\) | |||||||
\(878\) | 2.20204 | 0.0743153 | ||||||||
\(879\) | 25.1464 | 0.848168 | ||||||||
\(880\) | 19.5959 | 0.660578 | ||||||||
\(881\) | −20.8990 | −0.704105 | −0.352052 | − | 0.935980i | \(-0.614516\pi\) | ||||
−0.352052 | + | 0.935980i | \(0.614516\pi\) | |||||||
\(882\) | 12.7980 | 0.430930 | ||||||||
\(883\) | 1.79796 | 0.0605061 | 0.0302531 | − | 0.999542i | \(-0.490369\pi\) | ||||
0.0302531 | + | 0.999542i | \(0.490369\pi\) | |||||||
\(884\) | 33.7980 | 1.13675 | ||||||||
\(885\) | −19.5959 | −0.658710 | ||||||||
\(886\) | 9.10102 | 0.305755 | ||||||||
\(887\) | 4.89898 | 0.164492 | 0.0822458 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822458 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | 25.7980 | 0.865236 | ||||||||
\(890\) | 51.5959 | 1.72950 | ||||||||
\(891\) | 4.89898 | 0.164122 | ||||||||
\(892\) | 13.7980 | 0.461990 | ||||||||
\(893\) | −17.7980 | −0.595586 | ||||||||
\(894\) | −18.6969 | −0.625319 | ||||||||
\(895\) | 58.7878 | 1.96506 | ||||||||
\(896\) | 4.44949 | 0.148647 | ||||||||
\(897\) | 6.89898 | 0.230350 | ||||||||
\(898\) | 28.4949 | 0.950887 | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 11.0000 | 0.366667 | ||||||||
\(901\) | 43.5959 | 1.45239 | ||||||||
\(902\) | −43.5959 | −1.45159 | ||||||||
\(903\) | 55.3939 | 1.84339 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −101.394 | −3.37045 | ||||||||
\(906\) | −13.7980 | −0.458406 | ||||||||
\(907\) | 10.6515 | 0.353678 | 0.176839 | − | 0.984240i | \(-0.443413\pi\) | ||||
0.176839 | + | 0.984240i | \(0.443413\pi\) | |||||||
\(908\) | 7.34847 | 0.243868 | ||||||||
\(909\) | −5.10102 | −0.169190 | ||||||||
\(910\) | −122.788 | −4.07037 | ||||||||
\(911\) | 35.8434 | 1.18754 | 0.593772 | − | 0.804633i | \(-0.297638\pi\) | ||||
0.593772 | + | 0.804633i | \(0.297638\pi\) | |||||||
\(912\) | −4.44949 | −0.147337 | ||||||||
\(913\) | −7.59592 | −0.251388 | ||||||||
\(914\) | −22.0000 | −0.727695 | ||||||||
\(915\) | 11.5959 | 0.383349 | ||||||||
\(916\) | −12.6969 | −0.419519 | ||||||||
\(917\) | 84.0908 | 2.77692 | ||||||||
\(918\) | −4.89898 | −0.161690 | ||||||||
\(919\) | −1.75255 | −0.0578113 | −0.0289057 | − | 0.999582i | \(-0.509202\pi\) | ||||
−0.0289057 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(920\) | −4.00000 | −0.131876 | ||||||||
\(921\) | −22.6969 | −0.747890 | ||||||||
\(922\) | −20.6969 | −0.681617 | ||||||||
\(923\) | 75.1918 | 2.47497 | ||||||||
\(924\) | 21.7980 | 0.717100 | ||||||||
\(925\) | −22.0000 | −0.723356 | ||||||||
\(926\) | −10.2020 | −0.335260 | ||||||||
\(927\) | 6.24745 | 0.205193 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 26.0000 | 0.853032 | 0.426516 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426516 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(930\) | −24.0000 | −0.786991 | ||||||||
\(931\) | −56.9444 | −1.86628 | ||||||||
\(932\) | 16.6969 | 0.546926 | ||||||||
\(933\) | −2.69694 | −0.0882938 | ||||||||
\(934\) | −1.79796 | −0.0588310 | ||||||||
\(935\) | −96.0000 | −3.13954 | ||||||||
\(936\) | −6.89898 | −0.225500 | ||||||||
\(937\) | −11.7980 | −0.385423 | −0.192711 | − | 0.981256i | \(-0.561728\pi\) | ||||
−0.192711 | + | 0.981256i | \(0.561728\pi\) | |||||||
\(938\) | 8.89898 | 0.290562 | ||||||||
\(939\) | −21.5959 | −0.704756 | ||||||||
\(940\) | 16.0000 | 0.521862 | ||||||||
\(941\) | −43.1918 | −1.40801 | −0.704007 | − | 0.710193i | \(-0.748608\pi\) | ||||
−0.704007 | + | 0.710193i | \(0.748608\pi\) | |||||||
\(942\) | −15.7980 | −0.514725 | ||||||||
\(943\) | 8.89898 | 0.289791 | ||||||||
\(944\) | −4.89898 | −0.159448 | ||||||||
\(945\) | 17.7980 | 0.578968 | ||||||||
\(946\) | 60.9898 | 1.98295 | ||||||||
\(947\) | 18.8990 | 0.614134 | 0.307067 | − | 0.951688i | \(-0.400652\pi\) | ||||
0.307067 | + | 0.951688i | \(0.400652\pi\) | |||||||
\(948\) | 10.0000 | 0.324785 | ||||||||
\(949\) | 47.5959 | 1.54503 | ||||||||
\(950\) | −48.9444 | −1.58797 | ||||||||
\(951\) | 10.8990 | 0.353424 | ||||||||
\(952\) | −21.7980 | −0.706476 | ||||||||
\(953\) | −1.05561 | −0.0341947 | −0.0170973 | − | 0.999854i | \(-0.505443\pi\) | ||||
−0.0170973 | + | 0.999854i | \(0.505443\pi\) | |||||||
\(954\) | −8.89898 | −0.288115 | ||||||||
\(955\) | 29.3939 | 0.951164 | ||||||||
\(956\) | −1.10102 | −0.0356095 | ||||||||
\(957\) | 4.89898 | 0.158362 | ||||||||
\(958\) | −0.247449 | −0.00799471 | ||||||||
\(959\) | −25.7980 | −0.833060 | ||||||||
\(960\) | 4.00000 | 0.129099 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 13.7980 | 0.444864 | ||||||||
\(963\) | −9.55051 | −0.307761 | ||||||||
\(964\) | 20.6969 | 0.666604 | ||||||||
\(965\) | 86.3837 | 2.78079 | ||||||||
\(966\) | −4.44949 | −0.143160 | ||||||||
\(967\) | −1.39388 | −0.0448241 | −0.0224120 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224120 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(968\) | 13.0000 | 0.417836 | ||||||||
\(969\) | 21.7980 | 0.700251 | ||||||||
\(970\) | −76.5857 | −2.45902 | ||||||||
\(971\) | −30.2929 | −0.972144 | −0.486072 | − | 0.873919i | \(-0.661571\pi\) | ||||
−0.486072 | + | 0.873919i | \(0.661571\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 26.6969 | 0.855865 | ||||||||
\(974\) | −32.0000 | −1.02535 | ||||||||
\(975\) | −75.8888 | −2.43039 | ||||||||
\(976\) | 2.89898 | 0.0927941 | ||||||||
\(977\) | 28.7423 | 0.919549 | 0.459775 | − | 0.888036i | \(-0.347930\pi\) | ||||
0.459775 | + | 0.888036i | \(0.347930\pi\) | |||||||
\(978\) | 0.898979 | 0.0287462 | ||||||||
\(979\) | 63.1918 | 2.01962 | ||||||||
\(980\) | 51.1918 | 1.63526 | ||||||||
\(981\) | −4.44949 | −0.142061 | ||||||||
\(982\) | −14.8990 | −0.475446 | ||||||||
\(983\) | 38.9444 | 1.24213 | 0.621067 | − | 0.783758i | \(-0.286700\pi\) | ||||
0.621067 | + | 0.783758i | \(0.286700\pi\) | |||||||
\(984\) | −8.89898 | −0.283689 | ||||||||
\(985\) | 15.1918 | 0.484052 | ||||||||
\(986\) | −4.89898 | −0.156015 | ||||||||
\(987\) | 17.7980 | 0.566515 | ||||||||
\(988\) | 30.6969 | 0.976600 | ||||||||
\(989\) | −12.4495 | −0.395871 | ||||||||
\(990\) | 19.5959 | 0.622799 | ||||||||
\(991\) | −52.8990 | −1.68039 | −0.840196 | − | 0.542283i | \(-0.817560\pi\) | ||||
−0.840196 | + | 0.542283i | \(0.817560\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | −11.1010 | −0.352280 | ||||||||
\(994\) | −48.4949 | −1.53816 | ||||||||
\(995\) | −104.990 | −3.32840 | ||||||||
\(996\) | −1.55051 | −0.0491298 | ||||||||
\(997\) | 37.5959 | 1.19067 | 0.595337 | − | 0.803476i | \(-0.297018\pi\) | ||||
0.595337 | + | 0.803476i | \(0.297018\pi\) | |||||||
\(998\) | −15.7980 | −0.500076 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 4002.2.a.x.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.x.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |