Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.23544108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 20x^{3} + 39x^{2} + 9x - 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.892002\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.647226 | 0.244629 | 0.122314 | − | 0.992491i | \(-0.460968\pi\) | ||||
0.122314 | + | 0.992491i | \(0.460968\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.68293 | 1.11045 | 0.555223 | − | 0.831702i | \(-0.312633\pi\) | ||||
0.555223 | + | 0.831702i | \(0.312633\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.22455 | −0.894330 | −0.447165 | − | 0.894451i | \(-0.647566\pi\) | ||||
−0.447165 | + | 0.894451i | \(0.647566\pi\) | |||||||
\(14\) | 0.647226 | 0.172979 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.35277 | 0.328096 | 0.164048 | − | 0.986452i | \(-0.447545\pi\) | ||||
0.164048 | + | 0.986452i | \(0.447545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.30301 | 1.44601 | 0.723005 | − | 0.690843i | \(-0.242760\pi\) | ||||
0.723005 | + | 0.690843i | \(0.242760\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.68293 | 0.785204 | ||||||||
\(23\) | 5.22455 | 1.08939 | 0.544697 | − | 0.838633i | \(-0.316645\pi\) | ||||
0.544697 | + | 0.838633i | \(0.316645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.22455 | −0.632387 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.647226 | 0.122314 | ||||||||
\(29\) | −3.87178 | −0.718972 | −0.359486 | − | 0.933151i | \(-0.617048\pi\) | ||||
−0.359486 | + | 0.933151i | \(0.617048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.98594 | −1.07511 | −0.537553 | − | 0.843230i | \(-0.680651\pi\) | ||||
−0.537553 | + | 0.843230i | \(0.680651\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.35277 | 0.231999 | ||||||||
\(35\) | 0.647226 | 0.109401 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 6.30301 | 1.02248 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −0.242382 | −0.0378537 | −0.0189269 | − | 0.999821i | \(-0.506025\pi\) | ||||
−0.0189269 | + | 0.999821i | \(0.506025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75762 | 0.268034 | 0.134017 | − | 0.990979i | \(-0.457212\pi\) | ||||
0.134017 | + | 0.990979i | \(0.457212\pi\) | |||||||
\(44\) | 3.68293 | 0.555223 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.22455 | 0.770318 | ||||||||
\(47\) | −6.44432 | −0.940001 | −0.470000 | − | 0.882666i | \(-0.655746\pi\) | ||||
−0.470000 | + | 0.882666i | \(0.655746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58110 | −0.940157 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.22455 | −0.447165 | ||||||||
\(53\) | 5.46694 | 0.750941 | 0.375471 | − | 0.926834i | \(-0.377481\pi\) | ||||
0.375471 | + | 0.926834i | \(0.377481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.68293 | 0.496606 | ||||||||
\(56\) | 0.647226 | 0.0864893 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.87178 | −0.508390 | ||||||||
\(59\) | −7.36586 | −0.958954 | −0.479477 | − | 0.877555i | \(-0.659174\pi\) | ||||
−0.479477 | + | 0.877555i | \(0.659174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4755 | 1.85340 | 0.926699 | − | 0.375805i | \(-0.122634\pi\) | ||||
0.926699 | + | 0.375805i | \(0.122634\pi\) | |||||||
\(62\) | −5.98594 | −0.760215 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.22455 | −0.399957 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.07141 | 0.741741 | 0.370870 | − | 0.928685i | \(-0.379059\pi\) | ||||
0.370870 | + | 0.928685i | \(0.379059\pi\) | |||||||
\(68\) | 1.35277 | 0.164048 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.647226 | 0.0773583 | ||||||||
\(71\) | 8.22832 | 0.976522 | 0.488261 | − | 0.872698i | \(-0.337631\pi\) | ||||
0.488261 | + | 0.872698i | \(0.337631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.08702 | 0.946514 | 0.473257 | − | 0.880924i | \(-0.343078\pi\) | ||||
0.473257 | + | 0.880924i | \(0.343078\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.30301 | 0.723005 | ||||||||
\(77\) | 2.38369 | 0.271647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2283 | 1.15078 | 0.575388 | − | 0.817880i | \(-0.304851\pi\) | ||||
0.575388 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.242382 | −0.0267666 | ||||||||
\(83\) | −2.14131 | −0.235039 | −0.117520 | − | 0.993071i | \(-0.537494\pi\) | ||||
−0.117520 | + | 0.993071i | \(0.537494\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.35277 | 0.146729 | ||||||||
\(86\) | 1.75762 | 0.189529 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.68293 | 0.392602 | ||||||||
\(89\) | −5.81346 | −0.616225 | −0.308113 | − | 0.951350i | \(-0.599697\pi\) | ||||
−0.308113 | + | 0.951350i | \(0.599697\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.08702 | −0.218779 | ||||||||
\(92\) | 5.22455 | 0.544697 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.44432 | −0.664681 | ||||||||
\(95\) | 6.30301 | 0.646675 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.20194 | −0.426642 | −0.213321 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213321 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(98\) | −6.58110 | −0.664791 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.3782 | −1.72919 | −0.864597 | − | 0.502465i | \(-0.832426\pi\) | ||||
−0.864597 | + | 0.502465i | \(0.832426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.44432 | 0.832044 | 0.416022 | − | 0.909355i | \(-0.363424\pi\) | ||||
0.416022 | + | 0.909355i | \(0.363424\pi\) | |||||||
\(104\) | −3.22455 | −0.316194 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.46694 | 0.530996 | ||||||||
\(107\) | 12.9681 | 1.25367 | 0.626837 | − | 0.779150i | \(-0.284349\pi\) | ||||
0.626837 | + | 0.779150i | \(0.284349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.91126 | −0.949326 | −0.474663 | − | 0.880168i | \(-0.657430\pi\) | ||||
−0.474663 | + | 0.880168i | \(0.657430\pi\) | |||||||
\(110\) | 3.68293 | 0.351154 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.647226 | 0.0611571 | ||||||||
\(113\) | 11.2376 | 1.05715 | 0.528574 | − | 0.848887i | \(-0.322727\pi\) | ||||
0.528574 | + | 0.848887i | \(0.322727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.22455 | 0.487192 | ||||||||
\(116\) | −3.87178 | −0.359486 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.36586 | −0.678083 | ||||||||
\(119\) | 0.875551 | 0.0802616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.56398 | 0.233089 | ||||||||
\(122\) | 14.4755 | 1.31055 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.98594 | −0.537553 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9020 | 1.76602 | 0.883008 | − | 0.469358i | \(-0.155515\pi\) | ||||
0.883008 | + | 0.469358i | \(0.155515\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.22455 | −0.282812 | ||||||||
\(131\) | 1.95477 | 0.170789 | 0.0853944 | − | 0.996347i | \(-0.472785\pi\) | ||||
0.0853944 | + | 0.996347i | \(0.472785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.07948 | 0.353735 | ||||||||
\(134\) | 6.07141 | 0.524490 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.35277 | 0.115999 | ||||||||
\(137\) | 1.78400 | 0.152418 | 0.0762089 | − | 0.997092i | \(-0.475718\pi\) | ||||
0.0762089 | + | 0.997092i | \(0.475718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00932 | −0.0856092 | −0.0428046 | − | 0.999083i | \(-0.513629\pi\) | ||||
−0.0428046 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(140\) | 0.647226 | 0.0547006 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.22832 | 0.690506 | ||||||||
\(143\) | −11.8758 | −0.993105 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.87178 | −0.321534 | ||||||||
\(146\) | 8.08702 | 0.669286 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | −20.4614 | −1.67627 | −0.838133 | − | 0.545466i | \(-0.816353\pi\) | ||||
−0.838133 | + | 0.545466i | \(0.816353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1964 | −1.07391 | −0.536955 | − | 0.843611i | \(-0.680426\pi\) | ||||
−0.536955 | + | 0.843611i | \(0.680426\pi\) | |||||||
\(152\) | 6.30301 | 0.511242 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.38369 | 0.192083 | ||||||||
\(155\) | −5.98594 | −0.480802 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24948 | −0.658380 | −0.329190 | − | 0.944264i | \(-0.606776\pi\) | ||||
−0.329190 | + | 0.944264i | \(0.606776\pi\) | |||||||
\(158\) | 10.2283 | 0.813722 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.38147 | 0.266497 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7785 | −1.15754 | −0.578771 | − | 0.815490i | \(-0.696467\pi\) | ||||
−0.578771 | + | 0.815490i | \(0.696467\pi\) | |||||||
\(164\) | −0.242382 | −0.0189269 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.14131 | −0.166198 | ||||||||
\(167\) | −5.22455 | −0.404288 | −0.202144 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202144 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.60225 | −0.200173 | ||||||||
\(170\) | 1.35277 | 0.103753 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.75762 | 0.134017 | ||||||||
\(173\) | −20.9541 | −1.59311 | −0.796554 | − | 0.604568i | \(-0.793346\pi\) | ||||
−0.796554 | + | 0.604568i | \(0.793346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.647226 | 0.0489257 | ||||||||
\(176\) | 3.68293 | 0.277611 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.81346 | −0.435737 | ||||||||
\(179\) | −9.77922 | −0.730933 | −0.365466 | − | 0.930824i | \(-0.619091\pi\) | ||||
−0.365466 | + | 0.930824i | \(0.619091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.92859 | 0.292010 | 0.146005 | − | 0.989284i | \(-0.453358\pi\) | ||||
0.146005 | + | 0.989284i | \(0.453358\pi\) | |||||||
\(182\) | −2.08702 | −0.154700 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.22455 | 0.385159 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.98217 | 0.364332 | ||||||||
\(188\) | −6.44432 | −0.470000 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.30301 | 0.457269 | ||||||||
\(191\) | −6.86801 | −0.496952 | −0.248476 | − | 0.968638i | \(-0.579930\pi\) | ||||
−0.248476 | + | 0.968638i | \(0.579930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.5537 | 1.69544 | 0.847718 | − | 0.530448i | \(-0.177976\pi\) | ||||
0.847718 | + | 0.530448i | \(0.177976\pi\) | |||||||
\(194\) | −4.20194 | −0.301682 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.58110 | −0.470078 | ||||||||
\(197\) | 15.2960 | 1.08979 | 0.544896 | − | 0.838504i | \(-0.316569\pi\) | ||||
0.544896 | + | 0.838504i | \(0.316569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.78879 | −0.268580 | −0.134290 | − | 0.990942i | \(-0.542875\pi\) | ||||
−0.134290 | + | 0.990942i | \(0.542875\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.3782 | −1.22273 | ||||||||
\(203\) | −2.50592 | −0.175881 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.242382 | −0.0169287 | ||||||||
\(206\) | 8.44432 | 0.588344 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.22455 | −0.223583 | ||||||||
\(209\) | 23.2136 | 1.60572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4778 | 0.996693 | 0.498347 | − | 0.866978i | \(-0.333941\pi\) | ||||
0.498347 | + | 0.866978i | \(0.333941\pi\) | |||||||
\(212\) | 5.46694 | 0.375471 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.9681 | 0.886482 | ||||||||
\(215\) | 1.75762 | 0.119869 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.87426 | −0.263002 | ||||||||
\(218\) | −9.91126 | −0.671275 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.68293 | 0.248303 | ||||||||
\(221\) | −4.36209 | −0.293426 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.06209 | 0.606843 | 0.303421 | − | 0.952857i | \(-0.401871\pi\) | ||||
0.303421 | + | 0.952857i | \(0.401871\pi\) | |||||||
\(224\) | 0.647226 | 0.0432446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2376 | 0.747517 | ||||||||
\(227\) | 7.94319 | 0.527208 | 0.263604 | − | 0.964631i | \(-0.415089\pi\) | ||||
0.263604 | + | 0.964631i | \(0.415089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.0099 | 1.52054 | 0.760268 | − | 0.649609i | \(-0.225067\pi\) | ||||
0.760268 | + | 0.649609i | \(0.225067\pi\) | |||||||
\(230\) | 5.22455 | 0.344497 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.87178 | −0.254195 | ||||||||
\(233\) | 11.3707 | 0.744916 | 0.372458 | − | 0.928049i | \(-0.378515\pi\) | ||||
0.372458 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.44432 | −0.420381 | ||||||||
\(236\) | −7.36586 | −0.479477 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.875551 | 0.0567535 | ||||||||
\(239\) | −16.1453 | −1.04436 | −0.522178 | − | 0.852837i | \(-0.674880\pi\) | ||||
−0.522178 | + | 0.852837i | \(0.674880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.4871 | 1.89943 | 0.949716 | − | 0.313112i | \(-0.101372\pi\) | ||||
0.949716 | + | 0.313112i | \(0.101372\pi\) | |||||||
\(242\) | 2.56398 | 0.164819 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.4755 | 0.926699 | ||||||||
\(245\) | −6.58110 | −0.420451 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.3244 | −1.29321 | ||||||||
\(248\) | −5.98594 | −0.380108 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −7.85063 | −0.495527 | −0.247764 | − | 0.968821i | \(-0.579696\pi\) | ||||
−0.247764 | + | 0.968821i | \(0.579696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2417 | 1.20971 | ||||||||
\(254\) | 19.9020 | 1.24876 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.1846 | −1.38384 | −0.691919 | − | 0.721975i | \(-0.743234\pi\) | ||||
−0.691919 | + | 0.721975i | \(0.743234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.647226 | 0.0402167 | ||||||||
\(260\) | −3.22455 | −0.199978 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.95477 | 0.120766 | ||||||||
\(263\) | −17.3395 | −1.06920 | −0.534599 | − | 0.845106i | \(-0.679537\pi\) | ||||
−0.534599 | + | 0.845106i | \(0.679537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.46694 | 0.335831 | ||||||||
\(266\) | 4.07948 | 0.250129 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.07141 | 0.370870 | ||||||||
\(269\) | 12.8235 | 0.781864 | 0.390932 | − | 0.920419i | \(-0.372153\pi\) | ||||
0.390932 | + | 0.920419i | \(0.372153\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8886 | 1.26889 | 0.634447 | − | 0.772966i | \(-0.281228\pi\) | ||||
0.634447 | + | 0.772966i | \(0.281228\pi\) | |||||||
\(272\) | 1.35277 | 0.0820239 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.78400 | 0.107776 | ||||||||
\(275\) | 3.68293 | 0.222089 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.17932 | −0.311195 | −0.155598 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155598 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(278\) | −1.00932 | −0.0605349 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.647226 | 0.0386792 | ||||||||
\(281\) | −2.99623 | −0.178740 | −0.0893700 | − | 0.995998i | \(-0.528485\pi\) | ||||
−0.0893700 | + | 0.995998i | \(0.528485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8306 | −0.703255 | −0.351627 | − | 0.936140i | \(-0.614372\pi\) | ||||
−0.351627 | + | 0.936140i | \(0.614372\pi\) | |||||||
\(284\) | 8.22832 | 0.488261 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.8758 | −0.702231 | ||||||||
\(287\) | −0.156876 | −0.00926010 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1700 | −0.892353 | ||||||||
\(290\) | −3.87178 | −0.227359 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.08702 | 0.473257 | ||||||||
\(293\) | 8.55018 | 0.499507 | 0.249753 | − | 0.968309i | \(-0.419650\pi\) | ||||
0.249753 | + | 0.968309i | \(0.419650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.36586 | −0.428857 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.4614 | −1.18530 | ||||||||
\(299\) | −16.8469 | −0.974279 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13758 | 0.0655688 | ||||||||
\(302\) | −13.1964 | −0.759370 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.30301 | 0.361502 | ||||||||
\(305\) | 14.4755 | 0.828864 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3659 | −0.648684 | −0.324342 | − | 0.945940i | \(-0.605143\pi\) | ||||
−0.324342 | + | 0.945940i | \(0.605143\pi\) | |||||||
\(308\) | 2.38369 | 0.135823 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.98594 | −0.339979 | ||||||||
\(311\) | −17.3231 | −0.982306 | −0.491153 | − | 0.871073i | \(-0.663424\pi\) | ||||
−0.491153 | + | 0.871073i | \(0.663424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4777 | 0.761806 | 0.380903 | − | 0.924615i | \(-0.375613\pi\) | ||||
0.380903 | + | 0.924615i | \(0.375613\pi\) | |||||||
\(314\) | −8.24948 | −0.465545 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2283 | 0.575388 | ||||||||
\(317\) | −4.96505 | −0.278865 | −0.139432 | − | 0.990232i | \(-0.544528\pi\) | ||||
−0.139432 | + | 0.990232i | \(0.544528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.2595 | −0.798379 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.38147 | 0.188442 | ||||||||
\(323\) | 8.52655 | 0.474430 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.22455 | −0.178866 | ||||||||
\(326\) | −14.7785 | −0.818506 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.242382 | −0.0133833 | ||||||||
\(329\) | −4.17093 | −0.229951 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.97432 | 0.383343 | 0.191672 | − | 0.981459i | \(-0.438609\pi\) | ||||
0.191672 | + | 0.981459i | \(0.438609\pi\) | |||||||
\(332\) | −2.14131 | −0.117520 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.22455 | −0.285875 | ||||||||
\(335\) | 6.07141 | 0.331717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.46916 | −0.134504 | −0.0672518 | − | 0.997736i | \(-0.521423\pi\) | ||||
−0.0672518 | + | 0.997736i | \(0.521423\pi\) | |||||||
\(338\) | −2.60225 | −0.141544 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.35277 | 0.0733645 | ||||||||
\(341\) | −22.0458 | −1.19385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.79004 | −0.474618 | ||||||||
\(344\) | 1.75762 | 0.0947644 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.9541 | −1.12650 | ||||||||
\(347\) | −5.03801 | −0.270455 | −0.135227 | − | 0.990815i | \(-0.543176\pi\) | ||||
−0.135227 | + | 0.990815i | \(0.543176\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.64168 | −0.462578 | −0.231289 | − | 0.972885i | \(-0.574294\pi\) | ||||
−0.231289 | + | 0.972885i | \(0.574294\pi\) | |||||||
\(350\) | 0.647226 | 0.0345957 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.68293 | 0.196301 | ||||||||
\(353\) | 6.98120 | 0.371572 | 0.185786 | − | 0.982590i | \(-0.440517\pi\) | ||||
0.185786 | + | 0.982590i | \(0.440517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.22832 | 0.436714 | ||||||||
\(356\) | −5.81346 | −0.308113 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.77922 | −0.516848 | ||||||||
\(359\) | −34.4753 | −1.81954 | −0.909768 | − | 0.415117i | \(-0.863741\pi\) | ||||
−0.909768 | + | 0.415117i | \(0.863741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7280 | 1.09094 | ||||||||
\(362\) | 3.92859 | 0.206482 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.08702 | −0.109389 | ||||||||
\(365\) | 8.08702 | 0.423294 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.1515 | −1.36510 | −0.682548 | − | 0.730841i | \(-0.739128\pi\) | ||||
−0.682548 | + | 0.730841i | \(0.739128\pi\) | |||||||
\(368\) | 5.22455 | 0.272349 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | 3.53835 | 0.183702 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.7488 | −1.38500 | −0.692501 | − | 0.721417i | \(-0.743491\pi\) | ||||
−0.692501 | + | 0.721417i | \(0.743491\pi\) | |||||||
\(374\) | 4.98217 | 0.257622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.44432 | −0.332340 | ||||||||
\(377\) | 12.4848 | 0.642998 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.74130 | 0.346277 | 0.173139 | − | 0.984897i | \(-0.444609\pi\) | ||||
0.173139 | + | 0.984897i | \(0.444609\pi\) | |||||||
\(380\) | 6.30301 | 0.323338 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.86801 | −0.351398 | ||||||||
\(383\) | −28.9354 | −1.47853 | −0.739264 | − | 0.673415i | \(-0.764827\pi\) | ||||
−0.739264 | + | 0.673415i | \(0.764827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.38369 | 0.121484 | ||||||||
\(386\) | 23.5537 | 1.19885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.20194 | −0.213321 | ||||||||
\(389\) | −28.0458 | −1.42198 | −0.710990 | − | 0.703203i | \(-0.751753\pi\) | ||||
−0.710990 | + | 0.703203i | \(0.751753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.06764 | 0.357426 | ||||||||
\(392\) | −6.58110 | −0.332396 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.2960 | 0.770599 | ||||||||
\(395\) | 10.2283 | 0.514643 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0551 | −1.45824 | −0.729118 | − | 0.684388i | \(-0.760069\pi\) | ||||
−0.729118 | + | 0.684388i | \(0.760069\pi\) | |||||||
\(398\) | −3.78879 | −0.189915 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 11.3131 | 0.564948 | 0.282474 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282474 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.3020 | 0.961501 | ||||||||
\(404\) | −17.3782 | −0.864597 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.50592 | −0.124367 | ||||||||
\(407\) | 3.68293 | 0.182556 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.29973 | 0.410395 | 0.205198 | − | 0.978721i | \(-0.434216\pi\) | ||||
0.205198 | + | 0.978721i | \(0.434216\pi\) | |||||||
\(410\) | −0.242382 | −0.0119704 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.44432 | 0.416022 | ||||||||
\(413\) | −4.76738 | −0.234587 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.14131 | −0.105113 | ||||||||
\(416\) | −3.22455 | −0.158097 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.2136 | 1.13541 | ||||||||
\(419\) | 13.3083 | 0.650153 | 0.325076 | − | 0.945688i | \(-0.394610\pi\) | ||||
0.325076 | + | 0.945688i | \(0.394610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7840 | 0.769265 | 0.384633 | − | 0.923070i | \(-0.374328\pi\) | ||||
0.384633 | + | 0.923070i | \(0.374328\pi\) | |||||||
\(422\) | 14.4778 | 0.704768 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.46694 | 0.265498 | ||||||||
\(425\) | 1.35277 | 0.0656192 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.36892 | 0.453394 | ||||||||
\(428\) | 12.9681 | 0.626837 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.75762 | 0.0847599 | ||||||||
\(431\) | −27.7551 | −1.33692 | −0.668459 | − | 0.743749i | \(-0.733046\pi\) | ||||
−0.668459 | + | 0.743749i | \(0.733046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5190 | −0.601625 | −0.300813 | − | 0.953683i | \(-0.597258\pi\) | ||||
−0.300813 | + | 0.953683i | \(0.597258\pi\) | |||||||
\(434\) | −3.87426 | −0.185970 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.91126 | −0.474663 | ||||||||
\(437\) | 32.9304 | 1.57528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.4946 | −1.59861 | −0.799306 | − | 0.600925i | \(-0.794799\pi\) | ||||
−0.799306 | + | 0.600925i | \(0.794799\pi\) | |||||||
\(440\) | 3.68293 | 0.175577 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.36209 | −0.207484 | ||||||||
\(443\) | −20.7131 | −0.984109 | −0.492054 | − | 0.870565i | \(-0.663754\pi\) | ||||
−0.492054 | + | 0.870565i | \(0.663754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.81346 | −0.275584 | ||||||||
\(446\) | 9.06209 | 0.429102 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.647226 | 0.0305786 | ||||||||
\(449\) | −9.08325 | −0.428665 | −0.214332 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214332 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.892676 | −0.0420345 | ||||||||
\(452\) | 11.2376 | 0.528574 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.94319 | 0.372792 | ||||||||
\(455\) | −2.08702 | −0.0978408 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.8532 | −0.507691 | −0.253845 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253845 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(458\) | 23.0099 | 1.07518 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.22455 | 0.243596 | ||||||||
\(461\) | 34.3455 | 1.59963 | 0.799816 | − | 0.600246i | \(-0.204930\pi\) | ||||
0.799816 | + | 0.600246i | \(0.204930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4087 | 0.855523 | 0.427762 | − | 0.903892i | \(-0.359302\pi\) | ||||
0.427762 | + | 0.903892i | \(0.359302\pi\) | |||||||
\(464\) | −3.87178 | −0.179743 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.3707 | 0.526735 | ||||||||
\(467\) | 28.2570 | 1.30758 | 0.653789 | − | 0.756677i | \(-0.273178\pi\) | ||||
0.653789 | + | 0.756677i | \(0.273178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.92958 | 0.181451 | ||||||||
\(470\) | −6.44432 | −0.297254 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.36586 | −0.339041 | ||||||||
\(473\) | 6.47319 | 0.297637 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.30301 | 0.289202 | ||||||||
\(476\) | 0.875551 | 0.0401308 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.1453 | −0.738471 | ||||||||
\(479\) | −24.5642 | −1.12237 | −0.561184 | − | 0.827691i | \(-0.689654\pi\) | ||||
−0.561184 | + | 0.827691i | \(0.689654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.22455 | −0.147027 | ||||||||
\(482\) | 29.4871 | 1.34310 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.56398 | 0.116545 | ||||||||
\(485\) | −4.20194 | −0.190800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.22128 | 0.417856 | 0.208928 | − | 0.977931i | \(-0.433003\pi\) | ||||
0.208928 | + | 0.977931i | \(0.433003\pi\) | |||||||
\(488\) | 14.4755 | 0.655275 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.58110 | −0.297304 | ||||||||
\(491\) | −27.2415 | −1.22939 | −0.614696 | − | 0.788764i | \(-0.710721\pi\) | ||||
−0.614696 | + | 0.788764i | \(0.710721\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.23764 | −0.235892 | ||||||||
\(494\) | −20.3244 | −0.914438 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.98594 | −0.268777 | ||||||||
\(497\) | 5.32559 | 0.238885 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.3083 | 0.685293 | 0.342647 | − | 0.939464i | \(-0.388677\pi\) | ||||
0.342647 | + | 0.939464i | \(0.388677\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.85063 | −0.350391 | ||||||||
\(503\) | −39.1979 | −1.74775 | −0.873875 | − | 0.486151i | \(-0.838401\pi\) | ||||
−0.873875 | + | 0.486151i | \(0.838401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3782 | −0.773319 | ||||||||
\(506\) | 19.2417 | 0.855397 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.9020 | 0.883008 | ||||||||
\(509\) | 23.6951 | 1.05026 | 0.525132 | − | 0.851021i | \(-0.324016\pi\) | ||||
0.525132 | + | 0.851021i | \(0.324016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.23413 | 0.231544 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.1846 | −0.978521 | ||||||||
\(515\) | 8.44432 | 0.372101 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.7340 | −1.04382 | ||||||||
\(518\) | 0.647226 | 0.0284375 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.22455 | −0.141406 | ||||||||
\(521\) | −39.0672 | −1.71157 | −0.855784 | − | 0.517334i | \(-0.826925\pi\) | ||||
−0.855784 | + | 0.517334i | \(0.826925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.9867 | −1.35496 | −0.677478 | − | 0.735543i | \(-0.736927\pi\) | ||||
−0.677478 | + | 0.735543i | \(0.736927\pi\) | |||||||
\(524\) | 1.95477 | 0.0853944 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3395 | −0.756037 | ||||||||
\(527\) | −8.09763 | −0.352738 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.29596 | 0.186781 | ||||||||
\(530\) | 5.46694 | 0.237469 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.07948 | 0.176868 | ||||||||
\(533\) | 0.781574 | 0.0338537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.9681 | 0.560660 | ||||||||
\(536\) | 6.07141 | 0.262245 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.8235 | 0.552862 | ||||||||
\(539\) | −24.2377 | −1.04399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7069 | 0.804272 | 0.402136 | − | 0.915580i | \(-0.368268\pi\) | ||||
0.402136 | + | 0.915580i | \(0.368268\pi\) | |||||||
\(542\) | 20.8886 | 0.897244 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.35277 | 0.0579997 | ||||||||
\(545\) | −9.91126 | −0.424552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.79186 | 0.162128 | 0.0810641 | − | 0.996709i | \(-0.474168\pi\) | ||||
0.0810641 | + | 0.996709i | \(0.474168\pi\) | |||||||
\(548\) | 1.78400 | 0.0762089 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.68293 | 0.157041 | ||||||||
\(551\) | −24.4039 | −1.03964 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.62004 | 0.281513 | ||||||||
\(554\) | −5.17932 | −0.220048 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00932 | −0.0428046 | ||||||||
\(557\) | 25.2588 | 1.07025 | 0.535125 | − | 0.844773i | \(-0.320265\pi\) | ||||
0.535125 | + | 0.844773i | \(0.320265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.66753 | −0.239711 | ||||||||
\(560\) | 0.647226 | 0.0273503 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.99623 | −0.126388 | ||||||||
\(563\) | −13.3774 | −0.563792 | −0.281896 | − | 0.959445i | \(-0.590963\pi\) | ||||
−0.281896 | + | 0.959445i | \(0.590963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2376 | 0.472771 | ||||||||
\(566\) | −11.8306 | −0.497276 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.22832 | 0.345253 | ||||||||
\(569\) | −26.1303 | −1.09544 | −0.547720 | − | 0.836662i | \(-0.684504\pi\) | ||||
−0.547720 | + | 0.836662i | \(0.684504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.60048 | −0.192524 | −0.0962621 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962621 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(572\) | −11.8758 | −0.496553 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.156876 | −0.00654788 | ||||||||
\(575\) | 5.22455 | 0.217879 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7107 | 0.903826 | 0.451913 | − | 0.892062i | \(-0.350742\pi\) | ||||
0.451913 | + | 0.892062i | \(0.350742\pi\) | |||||||
\(578\) | −15.1700 | −0.630989 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.87178 | −0.160767 | ||||||||
\(581\) | −1.38591 | −0.0574973 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.1343 | 0.833879 | ||||||||
\(584\) | 8.08702 | 0.334643 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.55018 | 0.353205 | ||||||||
\(587\) | −42.5925 | −1.75798 | −0.878990 | − | 0.476839i | \(-0.841782\pi\) | ||||
−0.878990 | + | 0.476839i | \(0.841782\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.7295 | −1.55462 | ||||||||
\(590\) | −7.36586 | −0.303248 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | 19.7915 | 0.812741 | 0.406371 | − | 0.913708i | \(-0.366794\pi\) | ||||
0.406371 | + | 0.913708i | \(0.366794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.875551 | 0.0358941 | ||||||||
\(596\) | −20.4614 | −0.838133 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.8469 | −0.688919 | ||||||||
\(599\) | −10.0714 | −0.411507 | −0.205753 | − | 0.978604i | \(-0.565964\pi\) | ||||
−0.205753 | + | 0.978604i | \(0.565964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1677 | −0.455542 | −0.227771 | − | 0.973715i | \(-0.573144\pi\) | ||||
−0.227771 | + | 0.973715i | \(0.573144\pi\) | |||||||
\(602\) | 1.13758 | 0.0463642 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.1964 | −0.536955 | ||||||||
\(605\) | 2.56398 | 0.104241 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8653 | 0.441009 | 0.220505 | − | 0.975386i | \(-0.429230\pi\) | ||||
0.220505 | + | 0.975386i | \(0.429230\pi\) | |||||||
\(608\) | 6.30301 | 0.255621 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.4755 | 0.586096 | ||||||||
\(611\) | 20.7801 | 0.840671 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8057 | 0.921112 | 0.460556 | − | 0.887631i | \(-0.347650\pi\) | ||||
0.460556 | + | 0.887631i | \(0.347650\pi\) | |||||||
\(614\) | −11.3659 | −0.458689 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.38369 | 0.0960416 | ||||||||
\(617\) | 23.6860 | 0.953562 | 0.476781 | − | 0.879022i | \(-0.341803\pi\) | ||||
0.476781 | + | 0.879022i | \(0.341803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.7962 | −1.88090 | −0.940448 | − | 0.339936i | \(-0.889595\pi\) | ||||
−0.940448 | + | 0.339936i | \(0.889595\pi\) | |||||||
\(620\) | −5.98594 | −0.240401 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.3231 | −0.694595 | ||||||||
\(623\) | −3.76262 | −0.150746 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.4777 | 0.538678 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.24948 | −0.329190 | ||||||||
\(629\) | 1.35277 | 0.0539386 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.1459 | −1.12047 | −0.560235 | − | 0.828334i | \(-0.689289\pi\) | ||||
−0.560235 | + | 0.828334i | \(0.689289\pi\) | |||||||
\(632\) | 10.2283 | 0.406861 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.96505 | −0.197187 | ||||||||
\(635\) | 19.9020 | 0.789786 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.2211 | 0.840811 | ||||||||
\(638\) | −14.2595 | −0.564539 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −1.48254 | −0.0585569 | −0.0292785 | − | 0.999571i | \(-0.509321\pi\) | ||||
−0.0292785 | + | 0.999571i | \(0.509321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.3845 | −1.39543 | −0.697715 | − | 0.716376i | \(-0.745800\pi\) | ||||
−0.697715 | + | 0.716376i | \(0.745800\pi\) | |||||||
\(644\) | 3.38147 | 0.133249 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.52655 | 0.335473 | ||||||||
\(647\) | 8.03717 | 0.315974 | 0.157987 | − | 0.987441i | \(-0.449500\pi\) | ||||
0.157987 | + | 0.987441i | \(0.449500\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1280 | −1.06487 | ||||||||
\(650\) | −3.22455 | −0.126477 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7785 | −0.578771 | ||||||||
\(653\) | −14.4135 | −0.564042 | −0.282021 | − | 0.959408i | \(-0.591005\pi\) | ||||
−0.282021 | + | 0.959408i | \(0.591005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.95477 | 0.0763791 | ||||||||
\(656\) | −0.242382 | −0.00946343 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.17093 | −0.162600 | ||||||||
\(659\) | 13.4995 | 0.525864 | 0.262932 | − | 0.964814i | \(-0.415311\pi\) | ||||
0.262932 | + | 0.964814i | \(0.415311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.6005 | −1.30691 | −0.653454 | − | 0.756966i | \(-0.726681\pi\) | ||||
−0.653454 | + | 0.756966i | \(0.726681\pi\) | |||||||
\(662\) | 6.97432 | 0.271064 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.14131 | −0.0830989 | ||||||||
\(665\) | 4.07948 | 0.158195 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.2283 | −0.783244 | ||||||||
\(668\) | −5.22455 | −0.202144 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.07141 | 0.234559 | ||||||||
\(671\) | 53.3122 | 2.05810 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.8396 | 0.533479 | 0.266739 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266739 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(674\) | −2.46916 | −0.0951084 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.60225 | −0.100087 | ||||||||
\(677\) | 42.1987 | 1.62183 | 0.810914 | − | 0.585166i | \(-0.198970\pi\) | ||||
0.810914 | + | 0.585166i | \(0.198970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.71960 | −0.104369 | ||||||||
\(680\) | 1.35277 | 0.0518765 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.0458 | −0.844178 | ||||||||
\(683\) | 35.4303 | 1.35570 | 0.677852 | − | 0.735199i | \(-0.262911\pi\) | ||||
0.677852 | + | 0.735199i | \(0.262911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.78400 | 0.0681633 | ||||||||
\(686\) | −8.79004 | −0.335605 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.75762 | 0.0670086 | ||||||||
\(689\) | −17.6284 | −0.671590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8740 | −0.413668 | −0.206834 | − | 0.978376i | \(-0.566316\pi\) | ||||
−0.206834 | + | 0.978376i | \(0.566316\pi\) | |||||||
\(692\) | −20.9541 | −0.796554 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.03801 | −0.191240 | ||||||||
\(695\) | −1.00932 | −0.0382856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.327888 | −0.0124196 | ||||||||
\(698\) | −8.64168 | −0.327092 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.647226 | 0.0244629 | ||||||||
\(701\) | 8.30629 | 0.313724 | 0.156862 | − | 0.987621i | \(-0.449862\pi\) | ||||
0.156862 | + | 0.987621i | \(0.449862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.30301 | 0.237723 | ||||||||
\(704\) | 3.68293 | 0.138806 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.98120 | 0.262741 | ||||||||
\(707\) | −11.2476 | −0.423010 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5550 | −0.396400 | −0.198200 | − | 0.980162i | \(-0.563510\pi\) | ||||
−0.198200 | + | 0.980162i | \(0.563510\pi\) | |||||||
\(710\) | 8.22832 | 0.308804 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.81346 | −0.217869 | ||||||||
\(713\) | −31.2739 | −1.17122 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.8758 | −0.444130 | ||||||||
\(716\) | −9.77922 | −0.365466 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.4753 | −1.28661 | ||||||||
\(719\) | −24.4400 | −0.911460 | −0.455730 | − | 0.890118i | \(-0.650622\pi\) | ||||
−0.455730 | + | 0.890118i | \(0.650622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.46539 | 0.203542 | ||||||||
\(722\) | 20.7280 | 0.771415 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.92859 | 0.146005 | ||||||||
\(725\) | −3.87178 | −0.143794 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8748 | 0.477500 | 0.238750 | − | 0.971081i | \(-0.423262\pi\) | ||||
0.238750 | + | 0.971081i | \(0.423262\pi\) | |||||||
\(728\) | −2.08702 | −0.0773500 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.08702 | 0.299314 | ||||||||
\(731\) | 2.37766 | 0.0879409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.5230 | −0.979651 | −0.489825 | − | 0.871821i | \(-0.662939\pi\) | ||||
−0.489825 | + | 0.871821i | \(0.662939\pi\) | |||||||
\(734\) | −26.1515 | −0.965268 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.22455 | 0.192580 | ||||||||
\(737\) | 22.3606 | 0.823663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8599 | −0.767345 | −0.383673 | − | 0.923469i | \(-0.625341\pi\) | ||||
−0.383673 | + | 0.923469i | \(0.625341\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.53835 | 0.129897 | ||||||||
\(743\) | 12.8794 | 0.472498 | 0.236249 | − | 0.971693i | \(-0.424082\pi\) | ||||
0.236249 | + | 0.971693i | \(0.424082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4614 | −0.749649 | ||||||||
\(746\) | −26.7488 | −0.979345 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.98217 | 0.182166 | ||||||||
\(749\) | 8.39331 | 0.306685 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.20367 | −0.153394 | −0.0766970 | − | 0.997054i | \(-0.524437\pi\) | ||||
−0.0766970 | + | 0.997054i | \(0.524437\pi\) | |||||||
\(752\) | −6.44432 | −0.235000 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.4848 | 0.454668 | ||||||||
\(755\) | −13.1964 | −0.480268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.46623 | −0.307710 | −0.153855 | − | 0.988093i | \(-0.549169\pi\) | ||||
−0.153855 | + | 0.988093i | \(0.549169\pi\) | |||||||
\(758\) | 6.74130 | 0.244855 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.30301 | 0.228634 | ||||||||
\(761\) | 10.3993 | 0.376974 | 0.188487 | − | 0.982076i | \(-0.439642\pi\) | ||||
0.188487 | + | 0.982076i | \(0.439642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.41483 | −0.232232 | ||||||||
\(764\) | −6.86801 | −0.248476 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.9354 | −1.04548 | ||||||||
\(767\) | 23.7516 | 0.857621 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.18083 | 0.114704 | 0.0573519 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573519 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(770\) | 2.38369 | 0.0859022 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.5537 | 0.847718 | ||||||||
\(773\) | −35.7481 | −1.28577 | −0.642885 | − | 0.765962i | \(-0.722263\pi\) | ||||
−0.642885 | + | 0.765962i | \(0.722263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.98594 | −0.215021 | ||||||||
\(776\) | −4.20194 | −0.150841 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.0458 | −1.00549 | ||||||||
\(779\) | −1.52774 | −0.0547368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.3044 | 1.08437 | ||||||||
\(782\) | 7.06764 | 0.252738 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.58110 | −0.235039 | ||||||||
\(785\) | −8.24948 | −0.294437 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1474 | −0.860763 | −0.430382 | − | 0.902647i | \(-0.641621\pi\) | ||||
−0.430382 | + | 0.902647i | \(0.641621\pi\) | |||||||
\(788\) | 15.2960 | 0.544896 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.2283 | 0.363907 | ||||||||
\(791\) | 7.27330 | 0.258609 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.6770 | −1.65755 | ||||||||
\(794\) | −29.0551 | −1.03113 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.78879 | −0.134290 | ||||||||
\(797\) | 28.4753 | 1.00865 | 0.504323 | − | 0.863515i | \(-0.331742\pi\) | ||||
0.504323 | + | 0.863515i | \(0.331742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.71771 | −0.308410 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.3131 | 0.399479 | ||||||||
\(803\) | 29.7839 | 1.05105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.38147 | 0.119181 | ||||||||
\(806\) | 19.3020 | 0.679884 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −17.3782 | −0.611363 | ||||||||
\(809\) | 25.9825 | 0.913494 | 0.456747 | − | 0.889597i | \(-0.349014\pi\) | ||||
0.456747 | + | 0.889597i | \(0.349014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2360 | 0.991499 | 0.495749 | − | 0.868466i | \(-0.334893\pi\) | ||||
0.495749 | + | 0.868466i | \(0.334893\pi\) | |||||||
\(812\) | −2.50592 | −0.0879405 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.68293 | 0.129087 | ||||||||
\(815\) | −14.7785 | −0.517668 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0783 | 0.387580 | ||||||||
\(818\) | 8.29973 | 0.290193 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.242382 | −0.00846435 | ||||||||
\(821\) | 31.8087 | 1.11013 | 0.555065 | − | 0.831807i | \(-0.312693\pi\) | ||||
0.555065 | + | 0.831807i | \(0.312693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3169 | −0.359623 | −0.179812 | − | 0.983701i | \(-0.557549\pi\) | ||||
−0.179812 | + | 0.983701i | \(0.557549\pi\) | |||||||
\(824\) | 8.44432 | 0.294172 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.76738 | −0.165878 | ||||||||
\(827\) | 22.6487 | 0.787574 | 0.393787 | − | 0.919202i | \(-0.371165\pi\) | ||||
0.393787 | + | 0.919202i | \(0.371165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.8071 | −1.38256 | −0.691279 | − | 0.722588i | \(-0.742952\pi\) | ||||
−0.691279 | + | 0.722588i | \(0.742952\pi\) | |||||||
\(830\) | −2.14131 | −0.0743259 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.22455 | −0.111791 | ||||||||
\(833\) | −8.90274 | −0.308462 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.22455 | −0.180803 | ||||||||
\(836\) | 23.2136 | 0.802858 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.3083 | 0.459727 | ||||||||
\(839\) | 3.37544 | 0.116533 | 0.0582665 | − | 0.998301i | \(-0.481443\pi\) | ||||
0.0582665 | + | 0.998301i | \(0.481443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0093 | −0.483080 | ||||||||
\(842\) | 15.7840 | 0.543953 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.4778 | 0.498347 | ||||||||
\(845\) | −2.60225 | −0.0895202 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.65948 | 0.0570203 | ||||||||
\(848\) | 5.46694 | 0.187735 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.35277 | 0.0463998 | ||||||||
\(851\) | 5.22455 | 0.179095 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.2417 | 1.13817 | 0.569087 | − | 0.822278i | \(-0.307297\pi\) | ||||
0.569087 | + | 0.822278i | \(0.307297\pi\) | |||||||
\(854\) | 9.36892 | 0.320598 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9681 | 0.443241 | ||||||||
\(857\) | 23.0465 | 0.787253 | 0.393626 | − | 0.919270i | \(-0.371220\pi\) | ||||
0.393626 | + | 0.919270i | \(0.371220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6123 | −1.38567 | −0.692837 | − | 0.721094i | \(-0.743640\pi\) | ||||
−0.692837 | + | 0.721094i | \(0.743640\pi\) | |||||||
\(860\) | 1.75762 | 0.0599343 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.7551 | −0.945344 | ||||||||
\(863\) | −30.4021 | −1.03490 | −0.517451 | − | 0.855713i | \(-0.673119\pi\) | ||||
−0.517451 | + | 0.855713i | \(0.673119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9541 | −0.712459 | ||||||||
\(866\) | −12.5190 | −0.425413 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.87426 | −0.131501 | ||||||||
\(869\) | 37.6702 | 1.27787 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.5776 | −0.663361 | ||||||||
\(872\) | −9.91126 | −0.335637 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.9304 | 1.11389 | ||||||||
\(875\) | 0.647226 | 0.0218802 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.9721 | −1.65367 | −0.826836 | − | 0.562443i | \(-0.809861\pi\) | ||||
−0.826836 | + | 0.562443i | \(0.809861\pi\) | |||||||
\(878\) | −33.4946 | −1.13039 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.68293 | 0.124152 | ||||||||
\(881\) | 9.31809 | 0.313934 | 0.156967 | − | 0.987604i | \(-0.449828\pi\) | ||||
0.156967 | + | 0.987604i | \(0.449828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.5555 | 0.658094 | 0.329047 | − | 0.944314i | \(-0.393273\pi\) | ||||
0.329047 | + | 0.944314i | \(0.393273\pi\) | |||||||
\(884\) | −4.36209 | −0.146713 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.7131 | −0.695870 | ||||||||
\(887\) | −9.95507 | −0.334259 | −0.167129 | − | 0.985935i | \(-0.553450\pi\) | ||||
−0.167129 | + | 0.985935i | \(0.553450\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8811 | 0.432018 | ||||||||
\(890\) | −5.81346 | −0.194868 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.06209 | 0.303421 | ||||||||
\(893\) | −40.6186 | −1.35925 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.77922 | −0.326883 | ||||||||
\(896\) | 0.647226 | 0.0216223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.08325 | −0.303112 | ||||||||
\(899\) | 23.1763 | 0.772971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.39553 | 0.246381 | ||||||||
\(902\) | −0.892676 | −0.0297229 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2376 | 0.373758 | ||||||||
\(905\) | 3.92859 | 0.130591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.2797 | 1.66951 | 0.834755 | − | 0.550622i | \(-0.185609\pi\) | ||||
0.834755 | + | 0.550622i | \(0.185609\pi\) | |||||||
\(908\) | 7.94319 | 0.263604 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.08702 | −0.0691839 | ||||||||
\(911\) | 23.0456 | 0.763533 | 0.381767 | − | 0.924259i | \(-0.375316\pi\) | ||||
0.381767 | + | 0.924259i | \(0.375316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.88629 | −0.260998 | ||||||||
\(914\) | −10.8532 | −0.358992 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.0099 | 0.760268 | ||||||||
\(917\) | 1.26518 | 0.0417798 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.3252 | −0.637481 | −0.318741 | − | 0.947842i | \(-0.603260\pi\) | ||||
−0.318741 | + | 0.947842i | \(0.603260\pi\) | |||||||
\(920\) | 5.22455 | 0.172248 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.3455 | 1.13111 | ||||||||
\(923\) | −26.5327 | −0.873334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 18.4087 | 0.604946 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.87178 | −0.127097 | ||||||||
\(929\) | −20.3013 | −0.666064 | −0.333032 | − | 0.942916i | \(-0.608072\pi\) | ||||
−0.333032 | + | 0.942916i | \(0.608072\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.4807 | −1.35948 | ||||||||
\(932\) | 11.3707 | 0.372458 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.2570 | 0.924598 | ||||||||
\(935\) | 4.98217 | 0.162934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.08786 | 0.166213 | 0.0831066 | − | 0.996541i | \(-0.473516\pi\) | ||||
0.0831066 | + | 0.996541i | \(0.473516\pi\) | |||||||
\(938\) | 3.92958 | 0.128305 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.44432 | −0.210191 | ||||||||
\(941\) | −28.8079 | −0.939111 | −0.469556 | − | 0.882903i | \(-0.655586\pi\) | ||||
−0.469556 | + | 0.882903i | \(0.655586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.26634 | −0.0412376 | ||||||||
\(944\) | −7.36586 | −0.239738 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.47319 | 0.210461 | ||||||||
\(947\) | 35.4303 | 1.15133 | 0.575665 | − | 0.817686i | \(-0.304743\pi\) | ||||
0.575665 | + | 0.817686i | \(0.304743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.0770 | −0.846496 | ||||||||
\(950\) | 6.30301 | 0.204497 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.875551 | 0.0283768 | ||||||||
\(953\) | 14.8501 | 0.481043 | 0.240521 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240521 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.86801 | −0.222244 | ||||||||
\(956\) | −16.1453 | −0.522178 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.5642 | −0.793635 | ||||||||
\(959\) | 1.15465 | 0.0372858 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.83151 | 0.155855 | ||||||||
\(962\) | −3.22455 | −0.103964 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.4871 | 0.949716 | ||||||||
\(965\) | 23.5537 | 0.758222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.593694 | 0.0190919 | 0.00954595 | − | 0.999954i | \(-0.496961\pi\) | ||||
0.00954595 | + | 0.999954i | \(0.496961\pi\) | |||||||
\(968\) | 2.56398 | 0.0824095 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.20194 | −0.134916 | ||||||||
\(971\) | 31.8152 | 1.02100 | 0.510499 | − | 0.859878i | \(-0.329461\pi\) | ||||
0.510499 | + | 0.859878i | \(0.329461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.653257 | −0.0209425 | ||||||||
\(974\) | 9.22128 | 0.295469 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.4755 | 0.463349 | ||||||||
\(977\) | −7.05606 | −0.225743 | −0.112872 | − | 0.993610i | \(-0.536005\pi\) | ||||
−0.112872 | + | 0.993610i | \(0.536005\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.4106 | −0.684285 | ||||||||
\(980\) | −6.58110 | −0.210225 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.2415 | −0.869311 | ||||||||
\(983\) | 4.73957 | 0.151169 | 0.0755844 | − | 0.997139i | \(-0.475918\pi\) | ||||
0.0755844 | + | 0.997139i | \(0.475918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2960 | 0.487370 | ||||||||
\(986\) | −5.23764 | −0.166801 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.3244 | −0.646605 | ||||||||
\(989\) | 9.18277 | 0.291995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.2404 | 0.960619 | 0.480310 | − | 0.877099i | \(-0.340524\pi\) | ||||
0.480310 | + | 0.877099i | \(0.340524\pi\) | |||||||
\(992\) | −5.98594 | −0.190054 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.32559 | 0.168917 | ||||||||
\(995\) | −3.78879 | −0.120113 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.4939 | 1.78918 | 0.894590 | − | 0.446888i | \(-0.147468\pi\) | ||||
0.894590 | + | 0.446888i | \(0.147468\pi\) | |||||||
\(998\) | 15.3083 | 0.484576 | ||||||||
\(999\) | 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 | 3330.2.a.bl.1.3 | yes | 5 | |
3.2 | odd | 2 | 3330.2.a.bk.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3330.2.a.bk.1.3 | ✓ | 5 | 3.2 | odd | 2 | ||
3330.2.a.bl.1.3 | yes | 5 | 1.1 | even | 1 | trivial |