Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47214 | 0.567147 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | 1.16243 | 0.581215 | − | 0.813750i | \(-0.302578\pi\) | ||||
0.581215 | + | 0.813750i | \(0.302578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.52786 | −0.198911 | −0.0994555 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994555 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47214 | −0.572598 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000 | 0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9443 | −1.58139 | −0.790697 | − | 0.612207i | \(-0.790282\pi\) | ||||
−0.790697 | + | 0.612207i | \(0.790282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.52786 | 0.881070 | 0.440535 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440535 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4721 | −1.17821 | −0.589104 | − | 0.808057i | \(-0.700519\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9443 | 1.58409 | 0.792045 | − | 0.610463i | \(-0.209017\pi\) | ||||
0.792045 | + | 0.610463i | \(0.209017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47214 | −0.253636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.47214 | 0.454077 | 0.227038 | − | 0.973886i | \(-0.427096\pi\) | ||||
0.227038 | + | 0.973886i | \(0.427096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.47214 | 0.843009 | 0.421505 | − | 0.906826i | \(-0.361502\pi\) | ||||
0.421505 | + | 0.906826i | \(0.361502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4721 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.944272 | −0.0912862 | −0.0456431 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456431 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.52786 | 0.337908 | 0.168954 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168954 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.47214 | 0.603530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.4164 | −1.24035 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.47214 | −0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4721 | 1.61392 | 0.806959 | − | 0.590607i | \(-0.201112\pi\) | ||||
0.806959 | + | 0.590607i | \(0.201112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47214 | −0.214361 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4721 | −0.888235 | −0.444117 | − | 0.895969i | \(-0.646483\pi\) | ||||
−0.444117 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.47214 | 0.373979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.47214 | 0.371391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.472136 | 0.0386789 | 0.0193394 | − | 0.999813i | \(-0.493844\pi\) | ||||
0.0193394 | + | 0.999813i | \(0.493844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.47214 | −0.201180 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.4164 | −1.08465 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.47214 | −0.519854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9443 | 1.19268 | 0.596341 | − | 0.802731i | \(-0.296620\pi\) | ||||
0.596341 | + | 0.802731i | \(0.296620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.47214 | 0.510076 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.9443 | 1.64048 | 0.820241 | − | 0.572018i | \(-0.193839\pi\) | ||||
0.820241 | + | 0.572018i | \(0.193839\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.8885 | 1.38426 | 0.692129 | − | 0.721774i | \(-0.256673\pi\) | ||||
0.692129 | + | 0.721774i | \(0.256673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.41641 | −0.567147 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4721 | 0.948239 | 0.474119 | − | 0.880461i | \(-0.342766\pi\) | ||||
0.474119 | + | 0.880461i | \(0.342766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9443 | 1.11080 | 0.555399 | − | 0.831584i | \(-0.312565\pi\) | ||||
0.555399 | + | 0.831584i | \(0.312565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.47214 | 0.328798 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.47214 | 0.327035 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.8885 | 1.29437 | 0.647185 | − | 0.762333i | \(-0.275946\pi\) | ||||
0.647185 | + | 0.762333i | \(0.275946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.0000 | 1.58359 | 0.791797 | − | 0.610784i | \(-0.209146\pi\) | ||||
0.791797 | + | 0.610784i | \(0.209146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.94427 | 0.494759 | 0.247379 | − | 0.968919i | \(-0.420431\pi\) | ||||
0.247379 | + | 0.968919i | \(0.420431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.52786 | −0.675412 | −0.337706 | − | 0.941252i | \(-0.609651\pi\) | ||||
−0.337706 | + | 0.941252i | \(0.609651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.4164 | 1.34953 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.47214 | 0.171001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.8885 | −1.50687 | −0.753435 | − | 0.657523i | \(-0.771604\pi\) | ||||
−0.753435 | + | 0.657523i | \(0.771604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4721 | −1.23699 | −0.618493 | − | 0.785790i | \(-0.712256\pi\) | ||||
−0.618493 | + | 0.785790i | \(0.712256\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.00000 | 0.530979 | 0.265489 | − | 0.964114i | \(-0.414466\pi\) | ||||
0.265489 | + | 0.964114i | \(0.414466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9443 | 0.987545 | 0.493773 | − | 0.869591i | \(-0.335618\pi\) | ||||
0.493773 | + | 0.869591i | \(0.335618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.9443 | −1.50313 | −0.751565 | − | 0.659659i | \(-0.770701\pi\) | ||||
−0.751565 | + | 0.659659i | \(0.770701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4164 | 0.997205 | 0.498602 | − | 0.866831i | \(-0.333847\pi\) | ||||
0.498602 | + | 0.866831i | \(0.333847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0557 | 0.703459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.4164 | 1.73051 | 0.865254 | − | 0.501333i | \(-0.167157\pi\) | ||||
0.865254 | + | 0.501333i | \(0.167157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47214 | −0.406900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.52786 | 0.469575 | 0.234788 | − | 0.972047i | \(-0.424561\pi\) | ||||
0.234788 | + | 0.972047i | \(0.424561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | 0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4164 | 0.830455 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47214 | −0.520439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.9443 | 1.39894 | 0.699468 | − | 0.714663i | \(-0.253420\pi\) | ||||
0.699468 | + | 0.714663i | \(0.253420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8885 | −0.954650 | −0.477325 | − | 0.878727i | \(-0.658394\pi\) | ||||
−0.477325 | + | 0.878727i | \(0.658394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.4164 | −1.16243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8885 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.3607 | −1.07264 | −0.536321 | − | 0.844014i | \(-0.680186\pi\) | ||||
−0.536321 | + | 0.844014i | \(0.680186\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.52786 | 0.0889557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.9443 | −1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214 | 0.256074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.94427 | −0.282185 | −0.141092 | − | 0.989996i | \(-0.545061\pi\) | ||||
−0.141092 | + | 0.989996i | \(0.545061\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.4721 | −0.820640 | −0.410320 | − | 0.911942i | \(-0.634583\pi\) | ||||
−0.410320 | + | 0.911942i | \(0.634583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4164 | 0.984434 | 0.492217 | − | 0.870473i | \(-0.336187\pi\) | ||||
0.492217 | + | 0.870473i | \(0.336187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00000 | −0.169031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.58359 | −0.145109 | −0.0725545 | − | 0.997364i | \(-0.523115\pi\) | ||||
−0.0725545 | + | 0.997364i | \(0.523115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.47214 | −0.250392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.0557 | 0.615157 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.47214 | 0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.47214 | −0.136293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.8328 | 1.47486 | 0.737432 | − | 0.675421i | \(-0.236038\pi\) | ||||
0.737432 | + | 0.675421i | \(0.236038\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.4164 | 0.735215 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9443 | 0.707221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.8328 | 1.57062 | 0.785312 | − | 0.619100i | \(-0.212503\pi\) | ||||
0.785312 | + | 0.619100i | \(0.212503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.47214 | 0.350486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0000 | 1.07366 | 0.536828 | − | 0.843692i | \(-0.319622\pi\) | ||||
0.536828 | + | 0.843692i | \(0.319622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.4164 | −0.932279 | −0.466139 | − | 0.884711i | \(-0.654356\pi\) | ||||
−0.466139 | + | 0.884711i | \(0.654356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3607 | −0.977240 | −0.488620 | − | 0.872497i | \(-0.662500\pi\) | ||||
−0.488620 | + | 0.872497i | \(0.662500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3607 | −1.07460 | −0.537298 | − | 0.843393i | \(-0.680555\pi\) | ||||
−0.537298 | + | 0.843393i | \(0.680555\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.52786 | −0.394026 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4721 | −0.546641 | −0.273321 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273321 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.47214 | −0.439851 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.8328 | 1.70002 | 0.850009 | − | 0.526768i | \(-0.176596\pi\) | ||||
0.850009 | + | 0.526768i | \(0.176596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.94427 | 0.459436 | 0.229718 | − | 0.973257i | \(-0.426220\pi\) | ||||
0.229718 | + | 0.973257i | \(0.426220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.3050 | −1.29302 | −0.646511 | − | 0.762904i | \(-0.723773\pi\) | ||||
−0.646511 | + | 0.762904i | \(0.723773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0000 | 0.609994 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.94427 | −0.352089 | −0.176044 | − | 0.984382i | \(-0.556330\pi\) | ||||
−0.176044 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.9443 | −1.46377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.4721 | 0.526910 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.05573 | 0.253740 | 0.126870 | − | 0.991919i | \(-0.459507\pi\) | ||||
0.126870 | + | 0.991919i | \(0.459507\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9443 | 1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.47214 | −0.221676 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8328 | −1.62348 | −0.811739 | − | 0.584020i | \(-0.801479\pi\) | ||||
−0.811739 | + | 0.584020i | \(0.801479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.52786 | 0.0751813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.41641 | −0.166902 | −0.0834512 | − | 0.996512i | \(-0.526594\pi\) | ||||
−0.0834512 | + | 0.996512i | \(0.526594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.41641 | −0.360598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.47214 | 0.216422 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.58359 | −0.413457 | −0.206729 | − | 0.978398i | \(-0.566282\pi\) | ||||
−0.206729 | + | 0.978398i | \(0.566282\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.3050 | 1.69665 | 0.848324 | − | 0.529478i | \(-0.177612\pi\) | ||||
0.848324 | + | 0.529478i | \(0.177612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.9443 | −0.708426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | −0.0941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.47214 | 0.209657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.8885 | −1.67880 | −0.839398 | − | 0.543518i | \(-0.817092\pi\) | ||||
−0.839398 | + | 0.543518i | \(0.817092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.58359 | 0.306628 | 0.153314 | − | 0.988177i | \(-0.451005\pi\) | ||||
0.153314 | + | 0.988177i | \(0.451005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.41641 | 0.158774 | 0.0793870 | − | 0.996844i | \(-0.474704\pi\) | ||||
0.0793870 | + | 0.996844i | \(0.474704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.11146 | 0.282804 | 0.141402 | − | 0.989952i | \(-0.454839\pi\) | ||||
0.141402 | + | 0.989952i | \(0.454839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9443 | 0.597711 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | −0.183920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47214 | 0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.4164 | −1.16374 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9443 | −1.32250 | −0.661249 | − | 0.750167i | \(-0.729973\pi\) | ||||
−0.661249 | + | 0.750167i | \(0.729973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.47214 | −0.203069 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.4164 | 1.24236 | 0.621178 | − | 0.783669i | \(-0.286654\pi\) | ||||
0.621178 | + | 0.783669i | \(0.286654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.9443 | 1.48675 | 0.743377 | − | 0.668873i | \(-0.233223\pi\) | ||||
0.743377 | + | 0.668873i | \(0.233223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | −0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8885 | 0.621737 | 0.310868 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310868 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.94427 | 0.220454 | 0.110227 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110227 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.47214 | −0.377005 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8328 | −0.568805 | −0.284402 | − | 0.958705i | \(-0.591795\pi\) | ||||
−0.284402 | + | 0.958705i | \(0.591795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.52786 | −0.333013 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4721 | 0.461457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.47214 | 0.108724 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8885 | 0.871333 | 0.435666 | − | 0.900108i | \(-0.356513\pi\) | ||||
0.435666 | + | 0.900108i | \(0.356513\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.8328 | 0.998409 | 0.499205 | − | 0.866484i | \(-0.333626\pi\) | ||||
0.499205 | + | 0.866484i | \(0.333626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9443 | 1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.58359 | 0.198911 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.94427 | −0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.944272 | 0.0408244 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.52786 | 0.151675 | 0.0758374 | − | 0.997120i | \(-0.475837\pi\) | ||||
0.0758374 | + | 0.997120i | \(0.475837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.52786 | −0.151117 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.8885 | 1.62000 | 0.809999 | − | 0.586432i | \(-0.199468\pi\) | ||||
0.809999 | + | 0.586432i | \(0.199468\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.4164 | 0.572598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0557 | −0.470990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.4721 | 0.445321 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8328 | 1.05220 | 0.526100 | − | 0.850423i | \(-0.323654\pi\) | ||||
0.526100 | + | 0.850423i | \(0.323654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.8885 | −0.756605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.9443 | 0.882696 | 0.441348 | − | 0.897336i | \(-0.354500\pi\) | ||||
0.441348 | + | 0.897336i | \(0.354500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0000 | −0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | −0.377964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9443 | −1.46494 | −0.732470 | − | 0.680799i | \(-0.761633\pi\) | ||||
−0.732470 | + | 0.680799i | \(0.761633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8328 | −0.788129 | −0.394064 | − | 0.919083i | \(-0.628931\pi\) | ||||
−0.394064 | + | 0.919083i | \(0.628931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.47214 | −0.269907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3050 | −0.970198 | −0.485099 | − | 0.874459i | \(-0.661216\pi\) | ||||
−0.485099 | + | 0.874459i | \(0.661216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.47214 | 0.350880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.4164 | 0.554700 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.88854 | −0.408144 | −0.204072 | − | 0.978956i | \(-0.565418\pi\) | ||||
−0.204072 | + | 0.978956i | \(0.565418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.4164 | 1.70077 | 0.850384 | − | 0.526163i | \(-0.176370\pi\) | ||||
0.850384 | + | 0.526163i | \(0.176370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.47214 | 0.183340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.8885 | 1.71152 | 0.855760 | − | 0.517373i | \(-0.173090\pi\) | ||||
0.855760 | + | 0.517373i | \(0.173090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8328 | 0.849788 | 0.424894 | − | 0.905243i | \(-0.360311\pi\) | ||||
0.424894 | + | 0.905243i | \(0.360311\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.8328 | 1.58139 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.8328 | −1.57618 | −0.788088 | − | 0.615563i | \(-0.788929\pi\) | ||||
−0.788088 | + | 0.615563i | \(0.788929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0557 | 0.447267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.8885 | 1.77264 | 0.886321 | − | 0.463072i | \(-0.153253\pi\) | ||||
0.886321 | + | 0.463072i | \(0.153253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8328 | 0.677664 | 0.338832 | − | 0.940847i | \(-0.389968\pi\) | ||||
0.338832 | + | 0.940847i | \(0.389968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5836 | −0.505777 | −0.252889 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252889 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.9443 | −0.598730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8885 | −0.712132 | −0.356066 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356066 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.88854 | −0.311579 | −0.155789 | − | 0.987790i | \(-0.549792\pi\) | ||||
−0.155789 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.9443 | 1.14145 | 0.570725 | − | 0.821141i | \(-0.306662\pi\) | ||||
0.570725 | + | 0.821141i | \(0.306662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4721 | 1.04073 | 0.520364 | − | 0.853945i | \(-0.325796\pi\) | ||||
0.520364 | + | 0.853945i | \(0.325796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.52786 | −0.0599739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.47214 | 0.331540 | 0.165770 | − | 0.986164i | \(-0.446989\pi\) | ||||
0.165770 | + | 0.986164i | \(0.446989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.4721 | −0.721766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.5836 | −0.881070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.8885 | −1.47593 | −0.737964 | − | 0.674840i | \(-0.764213\pi\) | ||||
−0.737964 | + | 0.674840i | \(0.764213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8885 | −1.24032 | −0.620160 | − | 0.784475i | \(-0.712932\pi\) | ||||
−0.620160 | + | 0.784475i | \(0.712932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.47214 | 0.0958653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9443 | 1.12073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.47214 | −0.172645 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.8328 | 1.72818 | 0.864089 | − | 0.503339i | \(-0.167895\pi\) | ||||
0.864089 | + | 0.503339i | \(0.167895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.58359 | 0.0992955 | 0.0496478 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496478 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.47214 | −0.171625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7214 | −1.55816 | −0.779080 | − | 0.626925i | \(-0.784313\pi\) | ||||
−0.779080 | + | 0.626925i | \(0.784313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.8885 | 1.44344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.4164 | 0.738635 | 0.369317 | − | 0.929303i | \(-0.379591\pi\) | ||||
0.369317 | + | 0.929303i | \(0.379591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | 0.113961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.4721 | 0.397231 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.94427 | −0.338788 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.41641 | −0.355653 | −0.177826 | − | 0.984062i | \(-0.556907\pi\) | ||||
−0.177826 | + | 0.984062i | \(0.556907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.0557 | −0.416975 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.47214 | −0.318627 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8328 | −0.632170 | −0.316085 | − | 0.948731i | \(-0.602368\pi\) | ||||
−0.316085 | + | 0.948731i | \(0.602368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.4164 | 1.17821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.8885 | −1.56874 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.47214 | −0.167248 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.5836 | −0.469289 | −0.234644 | − | 0.972081i | \(-0.575393\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4721 | 0.390003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.47214 | −0.166091 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.4164 | 0.571763 | 0.285881 | − | 0.958265i | \(-0.407714\pi\) | ||||
0.285881 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.3607 | −0.678167 | −0.339084 | − | 0.940756i | \(-0.610117\pi\) | ||||
−0.339084 | + | 0.940756i | \(0.610117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.9443 | −0.476808 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.88854 | 0.0692840 | 0.0346420 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346420 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.472136 | −0.0172977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.944272 | 0.0345029 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.88854 | −0.360838 | −0.180419 | − | 0.983590i | \(-0.557745\pi\) | ||||
−0.180419 | + | 0.983590i | \(0.557745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.47214 | 0.0899702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.5279 | −1.43666 | −0.718332 | − | 0.695700i | \(-0.755094\pi\) | ||||
−0.718332 | + | 0.695700i | \(0.755094\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9443 | 0.686729 | 0.343365 | − | 0.939202i | \(-0.388433\pi\) | ||||
0.343365 | + | 0.939202i | \(0.388433\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.52786 | −0.127717 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.4164 | 0.485071 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.83282 | −0.246719 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.7771 | −0.785302 | −0.392651 | − | 0.919688i | \(-0.628442\pi\) | ||||
−0.392651 | + | 0.919688i | \(0.628442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.9443 | −0.393638 | −0.196819 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.47214 | 0.232486 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.94427 | −0.177147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.9443 | −0.533384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.05573 | 0.108925 | 0.0544625 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544625 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0000 | −0.355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.9443 | 1.09610 | 0.548051 | − | 0.836445i | \(-0.315370\pi\) | ||||
0.548051 | + | 0.836445i | \(0.315370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0557 | 0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.8328 | −1.58409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.52786 | 0.265653 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.47214 | −0.228113 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.8328 | 1.71687 | 0.858435 | − | 0.512922i | \(-0.171437\pi\) | ||||
0.858435 | + | 0.512922i | \(0.171437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4721 | 1.21048 | 0.605240 | − | 0.796043i | \(-0.293077\pi\) | ||||
0.605240 | + | 0.796043i | \(0.293077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.9443 | −0.733646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.88854 | −0.345956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.4164 | 0.468807 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4721 | −0.993684 | −0.496842 | − | 0.867841i | \(-0.665507\pi\) | ||||
−0.496842 | + | 0.867841i | \(0.665507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.4164 | −1.23454 | −0.617269 | − | 0.786752i | \(-0.711761\pi\) | ||||
−0.617269 | + | 0.786752i | \(0.711761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.944272 | 0.0328356 | 0.0164178 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164178 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.47214 | 0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.8885 | −0.619059 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.2492 | 1.73480 | 0.867398 | − | 0.497615i | \(-0.165791\pi\) | ||||
0.867398 | + | 0.497615i | \(0.165791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.00000 | −0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.9443 | 0.992197 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.3607 | 1.58736 | 0.793680 | − | 0.608336i | \(-0.208163\pi\) | ||||
0.793680 | + | 0.608336i | \(0.208163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.41641 | 0.253636 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.3050 | 0.659445 | 0.329722 | − | 0.944078i | \(-0.393045\pi\) | ||||
0.329722 | + | 0.944078i | \(0.393045\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.3050 | 0.726916 | 0.363458 | − | 0.931611i | \(-0.381596\pi\) | ||||
0.363458 | + | 0.931611i | \(0.381596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4721 | 1.58193 | 0.790965 | − | 0.611861i | \(-0.209579\pi\) | ||||
0.790965 | + | 0.611861i | \(0.209579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4721 | −0.424065 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4721 | −0.355243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.8885 | −1.96148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.4164 | −0.454077 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.8885 | −1.61708 | −0.808541 | − | 0.588440i | \(-0.799742\pi\) | ||||
−0.808541 | + | 0.588440i | \(0.799742\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0557 | −1.11368 | −0.556838 | − | 0.830621i | \(-0.687986\pi\) | ||||
−0.556838 | + | 0.830621i | \(0.687986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.94427 | −0.166388 | −0.0831940 | − | 0.996533i | \(-0.526512\pi\) | ||||
−0.0831940 | + | 0.996533i | \(0.526512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8328 | 1.03526 | 0.517632 | − | 0.855603i | \(-0.326814\pi\) | ||||
0.517632 | + | 0.855603i | \(0.326814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | 0.301511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.11146 | 0.204512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.94427 | −0.298974 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.9443 | −0.965346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8885 | 1.26225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.9443 | −0.496764 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0000 | 1.06254 | 0.531271 | − | 0.847202i | \(-0.321714\pi\) | ||||
0.531271 | + | 0.847202i | \(0.321714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.4164 | −0.843009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.7771 | −1.45040 | −0.725200 | − | 0.688538i | \(-0.758253\pi\) | ||||
−0.725200 | + | 0.688538i | \(0.758253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.4721 | −0.610004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5279 | −0.446243 | −0.223122 | − | 0.974791i | \(-0.571625\pi\) | ||||
−0.223122 | + | 0.974791i | \(0.571625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.47214 | −0.147043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.4164 | 1.03185 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.00000 | 0.0656179 | 0.0328089 | − | 0.999462i | \(-0.489555\pi\) | ||||
0.0328089 | + | 0.999462i | \(0.489555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.47214 | 0.0810210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.47214 | −0.146254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.4164 | −1.74504 | −0.872519 | − | 0.488580i | \(-0.837515\pi\) | ||||
−0.872519 | + | 0.488580i | \(0.837515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.4164 | 0.437362 | 0.218681 | − | 0.975796i | \(-0.429825\pi\) | ||||
0.218681 | + | 0.975796i | \(0.429825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.9443 | 0.421523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.05573 | 0.0992978 | 0.0496489 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496489 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.6656 | 1.09283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0000 | 1.23094 | 0.615470 | − | 0.788160i | \(-0.288966\pi\) | ||||
0.615470 | + | 0.788160i | \(0.288966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8885 | −0.578860 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00000 | −0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.83282 | 0.0912862 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.0000 | −0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0557 | −0.870054 | −0.435027 | − | 0.900418i | \(-0.643261\pi\) | ||||
−0.435027 | + | 0.900418i | \(0.643261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.63932 | 0.245157 | 0.122579 | − | 0.992459i | \(-0.460884\pi\) | ||||
0.122579 | + | 0.992459i | \(0.460884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4721 | 0.335721 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.111456 | 0.00356580 | 0.00178290 | − | 0.999998i | \(-0.499432\pi\) | ||||
0.00178290 | + | 0.999998i | \(0.499432\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.9443 | 0.477621 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5836 | −0.337908 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4721 | −0.334009 | −0.167005 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.94427 | −0.221263 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.8885 | 0.823208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0557 | −0.859454 | −0.429727 | − | 0.902959i | \(-0.641390\pi\) | ||||
−0.429727 | + | 0.902959i | \(0.641390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.52786 | 0.302054 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.58359 | 0.0818232 | 0.0409116 | − | 0.999163i | \(-0.486974\pi\) | ||||
0.0409116 | + | 0.999163i | \(0.486974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6160.2.a.w.1.2 | 2 | ||
4.3 | odd | 2 | 3080.2.a.f.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.f.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
6160.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial |