Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2672,2,Mod(1,2672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2672, 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("2672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2672 = 2^{4} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2672.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: | \(21.3360274201\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.826865.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 668) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.147687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2672.1 |
$q$-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 | ||||||||
\(3\) | −3.12588 | −1.80472 | −0.902362 | − | 0.430978i | \(-0.858169\pi\) | ||||
−0.902362 | + | 0.430978i | \(0.858169\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.516539 | 0.195233 | 0.0976167 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976167 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.77110 | 2.25703 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.538350 | −0.162319 | −0.0811593 | − | 0.996701i | \(-0.525862\pi\) | ||||
−0.0811593 | + | 0.996701i | \(0.525862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.295373 | −0.0819218 | −0.0409609 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409609 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.25175 | −1.61420 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.99507 | −1.69655 | −0.848277 | − | 0.529553i | \(-0.822360\pi\) | ||||
−0.848277 | + | 0.529553i | \(0.822360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.06647 | 0.932912 | 0.466456 | − | 0.884544i | \(-0.345531\pi\) | ||||
0.466456 | + | 0.884544i | \(0.345531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.61464 | −0.352342 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.781327 | −0.162918 | −0.0814590 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814590 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.7880 | −2.26860 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.811912 | 0.150768 | 0.0753841 | − | 0.997155i | \(-0.475982\pi\) | ||||
0.0753841 | + | 0.997155i | \(0.475982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07629 | −0.552517 | −0.276259 | − | 0.961083i | \(-0.589095\pi\) | ||||
−0.276259 | + | 0.961083i | \(0.589095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.68282 | 0.292941 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.03308 | 0.174622 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.95638 | −0.650424 | −0.325212 | − | 0.945641i | \(-0.605436\pi\) | ||||
−0.325212 | + | 0.945641i | \(0.605436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.923300 | 0.147846 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.743318 | 0.116087 | 0.0580434 | − | 0.998314i | \(-0.481514\pi\) | ||||
0.0580434 | + | 0.998314i | \(0.481514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.590746 | −0.0900880 | −0.0450440 | − | 0.998985i | \(-0.514343\pi\) | ||||
−0.0450440 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.5422 | 2.01875 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.47572 | 0.506986 | 0.253493 | − | 0.967337i | \(-0.418420\pi\) | ||||
0.253493 | + | 0.967337i | \(0.418420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73319 | −0.961884 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.8657 | 3.06181 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.69970 | 0.920274 | 0.460137 | − | 0.887848i | \(-0.347800\pi\) | ||||
0.460137 | + | 0.887848i | \(0.347800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.07670 | −0.145182 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.7113 | −1.68365 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.91427 | 1.16054 | 0.580269 | − | 0.814425i | \(-0.302947\pi\) | ||||
0.580269 | + | 0.814425i | \(0.302947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.63992 | 0.594081 | 0.297041 | − | 0.954865i | \(-0.404000\pi\) | ||||
0.297041 | + | 0.954865i | \(0.404000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.49753 | 0.440648 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.590746 | −0.0732731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55274 | −0.800544 | −0.400272 | − | 0.916396i | \(-0.631084\pi\) | ||||
−0.400272 | + | 0.916396i | \(0.631084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.44233 | 0.294022 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4655 | −1.47938 | −0.739691 | − | 0.672947i | \(-0.765028\pi\) | ||||
−0.739691 | + | 0.672947i | \(0.765028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.77640 | 0.910158 | 0.455079 | − | 0.890451i | \(-0.349611\pi\) | ||||
0.455079 | + | 0.890451i | \(0.349611\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.12588 | 0.360945 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.278079 | −0.0316900 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.88529 | 0.549638 | 0.274819 | − | 0.961496i | \(-0.411382\pi\) | ||||
0.274819 | + | 0.961496i | \(0.411382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.5345 | 1.83716 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.11388 | 0.122264 | 0.0611321 | − | 0.998130i | \(-0.480529\pi\) | ||||
0.0611321 | + | 0.998130i | \(0.480529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.9901 | −1.51744 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.53794 | −0.272095 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.79742 | −0.190527 | −0.0952633 | − | 0.995452i | \(-0.530369\pi\) | ||||
−0.0952633 | + | 0.995452i | \(0.530369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.152572 | −0.0159939 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.61609 | 0.997142 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.13294 | 0.834422 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.1192 | −1.73819 | −0.869097 | − | 0.494641i | \(-0.835300\pi\) | ||||
−0.869097 | + | 0.494641i | \(0.835300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.64522 | −0.366358 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0281 | −1.39585 | −0.697926 | − | 0.716170i | \(-0.745894\pi\) | ||||
−0.697926 | + | 0.716170i | \(0.745894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.7553 | −1.65094 | −0.825472 | − | 0.564443i | \(-0.809091\pi\) | ||||
−0.825472 | + | 0.564443i | \(0.809091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.22927 | −0.315145 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.47360 | −0.915847 | −0.457924 | − | 0.888992i | \(-0.651407\pi\) | ||||
−0.457924 | + | 0.888992i | \(0.651407\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.3467 | 1.94886 | 0.974429 | − | 0.224695i | \(-0.0721384\pi\) | ||||
0.974429 | + | 0.224695i | \(0.0721384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.3671 | 1.17384 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8270 | 1.58295 | 0.791476 | − | 0.611200i | \(-0.209313\pi\) | ||||
0.791476 | + | 0.611200i | \(0.209313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.56265 | −0.145718 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.61322 | −0.331224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7102 | −0.973653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.32352 | −0.209505 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.52781 | −0.845456 | −0.422728 | − | 0.906257i | \(-0.638927\pi\) | ||||
−0.422728 | + | 0.906257i | \(0.638927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.84660 | 0.162584 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5809 | 1.44868 | 0.724339 | − | 0.689444i | \(-0.242145\pi\) | ||||
0.724339 | + | 0.689444i | \(0.242145\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.10049 | 0.182136 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.5760 | −2.02909 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.53903 | 0.302360 | 0.151180 | − | 0.988506i | \(-0.451693\pi\) | ||||
0.151180 | + | 0.988506i | \(0.451693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.40022 | 0.797316 | 0.398658 | − | 0.917100i | \(-0.369476\pi\) | ||||
0.398658 | + | 0.917100i | \(0.369476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8647 | −0.914971 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.159014 | 0.0132974 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.62382 | 0.134851 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.0471 | 1.73594 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.5809 | −1.52221 | −0.761103 | − | 0.648631i | \(-0.775342\pi\) | ||||
−0.761103 | + | 0.648631i | \(0.775342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2644 | −1.40495 | −0.702477 | − | 0.711706i | \(-0.747923\pi\) | ||||
−0.702477 | + | 0.711706i | \(0.747923\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −47.3643 | −3.82918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.15257 | −0.494186 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.19863 | −0.574513 | −0.287256 | − | 0.957854i | \(-0.592743\pi\) | ||||
−0.287256 | + | 0.957854i | \(0.592743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.9424 | −1.66084 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.403586 | −0.0318070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.6948 | −1.85592 | −0.927959 | − | 0.372683i | \(-0.878438\pi\) | ||||
−0.927959 | + | 0.372683i | \(0.878438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.36563 | 0.262014 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9128 | −0.993289 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.5345 | 2.10561 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.5278 | −1.48467 | −0.742336 | − | 0.670028i | \(-0.766282\pi\) | ||||
−0.742336 | + | 0.670028i | \(0.766282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.516539 | −0.0390467 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.8649 | −2.09445 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5038 | 0.785092 | 0.392546 | − | 0.919732i | \(-0.371594\pi\) | ||||
0.392546 | + | 0.919732i | \(0.371594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.36184 | 0.621531 | 0.310765 | − | 0.950487i | \(-0.399415\pi\) | ||||
0.310765 | + | 0.950487i | \(0.399415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.5038 | −1.07215 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.91275 | −0.581757 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.76580 | 0.275382 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.08895 | −0.442906 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.43844 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3291 | −1.17540 | −0.587698 | − | 0.809080i | \(-0.699966\pi\) | ||||
−0.587698 | + | 0.809080i | \(0.699966\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.84660 | 0.132238 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3460 | −1.23585 | −0.617926 | − | 0.786237i | \(-0.712027\pi\) | ||||
−0.617926 | + | 0.786237i | \(0.712027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.46097 | −0.458006 | −0.229003 | − | 0.973426i | \(-0.573547\pi\) | ||||
−0.229003 | + | 0.973426i | \(0.573547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.4830 | 1.44476 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.419384 | 0.0294350 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.48664 | 0.103831 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.29044 | −0.367711 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.18918 | −0.151429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.41035 | 0.165935 | 0.0829677 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829677 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38.9656 | 2.66988 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.18149 | −0.0805771 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.58902 | −0.107870 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.3080 | −1.64259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.06616 | 0.138985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.798106 | 0.0534452 | 0.0267226 | − | 0.999643i | \(-0.491493\pi\) | ||||
0.0267226 | + | 0.999643i | \(0.491493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.77110 | −0.451406 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4979 | 0.696769 | 0.348385 | − | 0.937352i | \(-0.386730\pi\) | ||||
0.348385 | + | 0.937352i | \(0.386730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6916 | 0.772602 | 0.386301 | − | 0.922373i | \(-0.373753\pi\) | ||||
0.386301 | + | 0.922373i | \(0.373753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.869240 | 0.0571918 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.8858 | −1.56481 | −0.782404 | − | 0.622771i | \(-0.786007\pi\) | ||||
−0.782404 | + | 0.622771i | \(0.786007\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.95145 | 0.453462 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.2708 | −0.991946 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.8051 | −1.41046 | −0.705228 | − | 0.708981i | \(-0.749155\pi\) | ||||
−0.705228 | + | 0.708981i | \(0.749155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4951 | 1.12696 | 0.563481 | − | 0.826129i | \(-0.309462\pi\) | ||||
0.563481 | + | 0.826129i | \(0.309462\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.3207 | −1.04697 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.4664 | −0.860335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20113 | −0.0764258 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.48185 | −0.220653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.26889 | 0.0800917 | 0.0400458 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400458 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.420628 | 0.0264446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 43.7314 | 2.73857 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.5168 | 1.65407 | 0.827036 | − | 0.562149i | \(-0.190025\pi\) | ||||
0.827036 | + | 0.562149i | \(0.190025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.04362 | −0.126985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.49753 | 0.340289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.2975 | 0.881622 | 0.440811 | − | 0.897600i | \(-0.354691\pi\) | ||||
0.440811 | + | 0.897600i | \(0.354691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.3994 | 0.823118 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.61852 | 0.343848 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.0183 | −1.09859 | −0.549297 | − | 0.835627i | \(-0.685104\pi\) | ||||
−0.549297 | + | 0.835627i | \(0.685104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.40925 | −0.328589 | −0.164294 | − | 0.986411i | \(-0.552535\pi\) | ||||
−0.164294 | + | 0.986411i | \(0.552535\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.476920 | 0.0288645 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.538350 | 0.0324637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.475355 | 0.0285613 | 0.0142806 | − | 0.999898i | \(-0.495454\pi\) | ||||
0.0142806 | + | 0.999898i | \(0.495454\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.8298 | −1.24705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.23067 | −0.550655 | −0.275328 | − | 0.961350i | \(-0.588786\pi\) | ||||
−0.275328 | + | 0.961350i | \(0.588786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.6333 | −1.34541 | −0.672704 | − | 0.739911i | \(-0.734867\pi\) | ||||
−0.672704 | + | 0.739911i | \(0.734867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.4226 | −1.50590 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.383953 | 0.0226640 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.9310 | 1.87829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 53.5126 | 3.13696 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0171 | −0.585207 | −0.292604 | − | 0.956234i | \(-0.594522\pi\) | ||||
−0.292604 | + | 0.956234i | \(0.594522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.8285 | 1.03802 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.34606 | 0.368236 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.230783 | 0.0133465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.305143 | −0.0175882 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.8502 | 2.51913 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.27984 | 0.531362 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0119 | −0.913849 | −0.456925 | − | 0.889505i | \(-0.651049\pi\) | ||||
−0.456925 | + | 0.889505i | \(0.651049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.3748 | 2.97950 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3613 | 0.587537 | 0.293768 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293768 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.36002 | 0.529059 | 0.264530 | − | 0.964378i | \(-0.414783\pi\) | ||||
0.264530 | + | 0.964378i | \(0.414783\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.99507 | 0.394127 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.8595 | 0.722260 | 0.361130 | − | 0.932515i | \(-0.382391\pi\) | ||||
0.361130 | + | 0.932515i | \(0.382391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.437093 | −0.0244725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.6133 | 1.65285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.4452 | −1.58273 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.295373 | 0.0163844 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −63.6012 | −3.51715 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.79535 | 0.0989806 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.81289 | 0.154611 | 0.0773053 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773053 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.7890 | −1.46803 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.1055 | −0.716029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3021 | 1.05145 | 0.525725 | − | 0.850654i | \(-0.323794\pi\) | ||||
0.525725 | + | 0.850654i | \(0.323794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −52.5992 | −2.85679 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.65612 | 0.0896839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.09373 | −0.383025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.88466 | 0.262981 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4120 | −1.52524 | −0.762618 | − | 0.646849i | \(-0.776086\pi\) | ||||
−0.762618 | + | 0.646849i | \(0.776086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.74264 | 0.414454 | 0.207227 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207227 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.48185 | 0.185847 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3204 | 1.02832 | 0.514161 | − | 0.857694i | \(-0.328104\pi\) | ||||
0.514161 | + | 0.857694i | \(0.328104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.9310 | −1.32320 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.2945 | 0.597768 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.57278 | 0.135786 | 0.0678932 | − | 0.997693i | \(-0.478372\pi\) | ||||
0.0678932 | + | 0.997693i | \(0.478372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46383 | −0.129675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.4787 | 1.75718 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5528 | 0.814070 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.1615 | 1.20902 | 0.604509 | − | 0.796598i | \(-0.293369\pi\) | ||||
0.604509 | + | 0.796598i | \(0.293369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.03308 | 0.262012 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.46065 | 0.179668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9233 | 1.08337 | 0.541684 | − | 0.840582i | \(-0.317787\pi\) | ||||
0.541684 | + | 0.840582i | \(0.317787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 37.5105 | 1.93703 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.239817 | −0.0123512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.4945 | −1.56640 | −0.783198 | − | 0.621773i | \(-0.786413\pi\) | ||||
−0.783198 | + | 0.621773i | \(0.786413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.7827 | 1.52582 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.8997 | −1.42561 | −0.712804 | − | 0.701363i | \(-0.752575\pi\) | ||||
−0.712804 | + | 0.701363i | \(0.752575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.556158 | −0.0283444 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.9087 | 0.958707 | 0.479353 | − | 0.877622i | \(-0.340871\pi\) | ||||
0.479353 | + | 0.877622i | \(0.340871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.46544 | 0.276399 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −51.8298 | −2.61447 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.77058 | 0.491611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.2771 | −1.16824 | −0.584122 | − | 0.811666i | \(-0.698561\pi\) | ||||
−0.584122 | + | 0.811666i | \(0.698561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.56587 | −0.328705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3692 | −1.16700 | −0.583500 | − | 0.812113i | \(-0.698317\pi\) | ||||
−0.583500 | + | 0.812113i | \(0.698317\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.908652 | 0.0452632 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.0689 | 1.64321 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.12992 | 0.105576 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5940 | −0.672178 | −0.336089 | − | 0.941830i | \(-0.609104\pi\) | ||||
−0.336089 | + | 0.941830i | \(0.609104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0626 | −0.545676 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.60456 | 0.226576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.22776 | 0.109356 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.3839 | −1.43894 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.6740 | −1.00999 | −0.504996 | − | 0.863121i | \(-0.668506\pi\) | ||||
−0.504996 | + | 0.863121i | \(0.668506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.9625 | 1.65523 | 0.827614 | − | 0.561297i | \(-0.189698\pi\) | ||||
0.827614 | + | 0.561297i | \(0.189698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.5345 | 1.14428 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.99507 | 0.339311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.39670 | 0.115984 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.497059 | −0.0239982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.35940 | 0.209985 | 0.104992 | − | 0.994473i | \(-0.466518\pi\) | ||||
0.104992 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.95196 | −0.430204 | −0.215102 | − | 0.976592i | \(-0.569008\pi\) | ||||
−0.215102 | + | 0.976592i | \(0.569008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.07587 | −0.243369 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.17724 | −0.151988 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.0473 | −1.43408 | −0.717039 | − | 0.697033i | \(-0.754503\pi\) | ||||
−0.717039 | + | 0.697033i | \(0.754503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −45.5911 | −2.17100 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2252 | 0.675858 | 0.337929 | − | 0.941172i | \(-0.390274\pi\) | ||||
0.337929 | + | 0.941172i | \(0.390274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.59485 | −0.170412 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 58.0815 | 2.74716 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.54334 | −0.261606 | −0.130803 | − | 0.991408i | \(-0.541756\pi\) | ||||
−0.130803 | + | 0.991408i | \(0.541756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.400165 | −0.0188431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.9663 | 2.53556 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.305143 | −0.0143053 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2195 | −0.524826 | −0.262413 | − | 0.964956i | \(-0.584518\pi\) | ||||
−0.262413 | + | 0.964956i | \(0.584518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 82.4577 | 3.84880 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.92450 | −0.0896328 | −0.0448164 | − | 0.998995i | \(-0.514270\pi\) | ||||
−0.0448164 | + | 0.998995i | \(0.514270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.4339 | −1.22849 | −0.614244 | − | 0.789116i | \(-0.710539\pi\) | ||||
−0.614244 | + | 0.789116i | \(0.710539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.2322 | 0.891871 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.5897 | 1.46180 | 0.730898 | − | 0.682486i | \(-0.239101\pi\) | ||||
0.730898 | + | 0.682486i | \(0.239101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.38474 | −0.156293 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.5020 | 1.03684 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.318028 | 0.0146230 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.06647 | −0.186582 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 45.3643 | 2.07709 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8045 | −0.585052 | −0.292526 | − | 0.956258i | \(-0.594496\pi\) | ||||
−0.292526 | + | 0.956258i | \(0.594496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.16861 | 0.0532839 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.26156 | 0.0574029 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.2385 | −1.55469 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.2482 | 1.73319 | 0.866596 | − | 0.499011i | \(-0.166303\pi\) | ||||
0.866596 | + | 0.499011i | \(0.166303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 74.0669 | 3.34942 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4176 | 1.73376 | 0.866881 | − | 0.498514i | \(-0.166121\pi\) | ||||
0.866881 | + | 0.498514i | \(0.166121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.67938 | −0.255786 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.29044 | −0.327681 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.43891 | −0.288825 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.61884 | 0.162001 | 0.0810007 | − | 0.996714i | \(-0.474188\pi\) | ||||
0.0810007 | + | 0.996714i | \(0.474188\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.12588 | −0.139654 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.3565 | 1.39812 | 0.699059 | − | 0.715064i | \(-0.253602\pi\) | ||||
0.699059 | + | 0.715064i | \(0.253602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0563 | −1.24849 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.3637 | 1.79261 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9722 | 1.01822 | 0.509111 | − | 0.860701i | \(-0.329974\pi\) | ||||
0.509111 | + | 0.860701i | \(0.329974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.01681 | 0.177693 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −47.9354 | −2.11640 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −33.5105 | −1.47665 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.87116 | −0.0822934 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 61.0415 | 2.67942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1707 | 0.533210 | 0.266605 | − | 0.963806i | \(-0.414098\pi\) | ||||
0.266605 | + | 0.963806i | \(0.414098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.62991 | −0.289906 | −0.144953 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144953 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.61464 | 0.0704685 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.5188 | 0.937375 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3895 | −0.973458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.3593 | 2.61937 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.219556 | −0.00951003 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.9472 | −0.819159 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.8336 | −1.41688 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.62481 | 0.156132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6963 | −0.631842 | −0.315921 | − | 0.948785i | \(-0.602313\pi\) | ||||
−0.315921 | + | 0.948785i | \(0.602313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1381 | −1.12169 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.6934 | 1.74311 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.9360 | −1.75030 | −0.875148 | − | 0.483856i | \(-0.839236\pi\) | ||||
−0.875148 | + | 0.483856i | \(0.839236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.4174 | 1.34086 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.30162 | 0.140654 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.52344 | 0.107308 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.7343 | 1.04991 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.2803 | 1.74910 | 0.874552 | − | 0.484932i | \(-0.161156\pi\) | ||||
0.874552 | + | 0.484932i | \(0.161156\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.174491 | 0.00738017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.7714 | −0.496989 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.4103 | −0.649467 | −0.324733 | − | 0.945806i | \(-0.605275\pi\) | ||||
−0.324733 | + | 0.945806i | \(0.605275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.6540 | 1.41584 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.54069 | 0.358675 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2870 | 0.473177 | 0.236588 | − | 0.971610i | \(-0.423971\pi\) | ||||
0.236588 | + | 0.971610i | \(0.423971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.50980 | −0.0631830 | −0.0315915 | − | 0.999501i | \(-0.510058\pi\) | ||||
−0.0315915 | + | 0.999501i | \(0.510058\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.5034 | 1.23252 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.781327 | 0.0325836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.9800 | 1.03993 | 0.519966 | − | 0.854187i | \(-0.325945\pi\) | ||||
0.519966 | + | 0.854187i | \(0.325945\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.0428 | 2.12127 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.575363 | 0.0238701 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.60678 | −0.149378 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.9400 | −0.864287 | −0.432144 | − | 0.901805i | \(-0.642243\pi\) | ||||
−0.432144 | + | 0.901805i | \(0.642243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5096 | −0.515450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.2214 | 2.23037 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.8904 | −1.35065 | −0.675323 | − | 0.737522i | \(-0.735996\pi\) | ||||
−0.675323 | + | 0.737522i | \(0.735996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.22645 | −0.296256 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.1962 | 0.826575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.3583 | 0.750098 | 0.375049 | − | 0.927005i | \(-0.377626\pi\) | ||||
0.375049 | + | 0.927005i | \(0.377626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.8253 | −1.86925 | −0.934626 | − | 0.355633i | \(-0.884265\pi\) | ||||
−0.934626 | + | 0.355633i | \(0.884265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.3692 | −1.80685 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.4204 | −0.870861 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6455 | −0.716210 | −0.358105 | − | 0.933681i | \(-0.616577\pi\) | ||||
−0.358105 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.31094 | −0.0531221 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.02664 | −0.0415332 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.27761 | 0.0919919 | 0.0459960 | − | 0.998942i | \(-0.485354\pi\) | ||||
0.0459960 | + | 0.998942i | \(0.485354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.64704 | −0.187387 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.33514 | 0.0537507 | 0.0268753 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268753 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.6808 | −0.670458 | −0.335229 | − | 0.942137i | \(-0.608814\pi\) | ||||
−0.335229 | + | 0.942137i | \(0.608814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.21027 | 0.369595 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.928440 | −0.0371971 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.84312 | 0.273288 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.6751 | 1.10348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.60704 | 0.143594 | 0.0717971 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717971 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.53445 | −0.299468 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.0556 | −0.756199 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.98880 | 0.0787992 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84.4050 | −3.33901 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2139 | 0.403426 | 0.201713 | − | 0.979445i | \(-0.435349\pi\) | ||||
0.201713 | + | 0.979445i | \(0.435349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.82338 | −0.111343 | −0.0556717 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556717 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.69320 | 0.145420 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.4408 | 1.62921 | 0.814604 | − | 0.580018i | \(-0.196954\pi\) | ||||
0.814604 | + | 0.580018i | \(0.196954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.79900 | −0.188377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.96708 | 0.194675 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.7584 | −1.71240 | −0.856200 | − | 0.516645i | \(-0.827181\pi\) | ||||
−0.856200 | + | 0.516645i | \(0.827181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.1618 | 1.29574 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.6547 | 2.05426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.47042 | −0.291006 | −0.145503 | − | 0.989358i | \(-0.546480\pi\) | ||||
−0.145503 | + | 0.989358i | \(0.546480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3065 | 1.10099 | 0.550497 | − | 0.834837i | \(-0.314438\pi\) | ||||
0.550497 | + | 0.834837i | \(0.314438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.45854 | −0.250829 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.20098 | 0.162907 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.634369 | −0.0245629 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.49478 | −0.0964538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.49790 | −0.0964305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.8789 | −1.22884 | −0.614421 | − | 0.788979i | \(-0.710610\pi\) | ||||
−0.614421 | + | 0.788979i | \(0.710610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.7880 | 0.453719 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.6470 | 1.33159 | 0.665797 | − | 0.746133i | \(-0.268092\pi\) | ||||
0.665797 | + | 0.746133i | \(0.268092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.84275 | −0.339354 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.8151 | −1.25748 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.53159 | −0.288188 | −0.144094 | − | 0.989564i | \(-0.546027\pi\) | ||||
−0.144094 | + | 0.989564i | \(0.546027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.07806 | 0.270439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −36.5464 | −1.39433 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.97891 | −0.0753905 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.3094 | 1.30519 | 0.652596 | − | 0.757706i | \(-0.273680\pi\) | ||||
0.652596 | + | 0.757706i | \(0.273680\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.88290 | −0.0715254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.8004 | 0.713141 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.19956 | −0.196947 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 74.6639 | 2.82405 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0251855 | 0.000951242 0 | 0.000475621 | − | 1.00000i | \(-0.499849\pi\) | ||||
0.000475621 | 1.00000i | \(0.499849\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0885 | −0.606789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.7294 | −0.818375 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.24608 | −0.272517 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2131 | −1.05957 | −0.529783 | − | 0.848133i | \(-0.677727\pi\) | ||||
−0.529783 | + | 0.848133i | \(0.677727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.0788 | 1.24055 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.40359 | 0.0900150 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.318028 | 0.0118936 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 68.1600 | 2.54548 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5507 | 0.915585 | 0.457792 | − | 0.889059i | \(-0.348640\pi\) | ||||
0.457792 | + | 0.889059i | \(0.348640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.65474 | −0.322319 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.6877 | −2.03386 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.811912 | −0.0301537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.2103 | −0.601208 | −0.300604 | − | 0.953749i | \(-0.597188\pi\) | ||||
−0.300604 | + | 0.953749i | \(0.597188\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.41315 | 0.0523389 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.13231 | 0.152839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0087 | −0.591296 | −0.295648 | − | 0.955297i | \(-0.595535\pi\) | ||||
−0.295648 | + | 0.955297i | \(0.595535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 42.0942 | 1.55267 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.52767 | 0.129943 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.9536 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.75457 | 0.137928 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.6259 | −1.41705 | −0.708524 | − | 0.705686i | \(-0.750639\pi\) | ||||
−0.708524 | + | 0.705686i | \(0.750639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.1618 | −1.36150 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.54219 | 0.275954 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.89348 | −0.178804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6589 | −0.790346 | −0.395173 | − | 0.918607i | \(-0.629315\pi\) | ||||
−0.395173 | + | 0.918607i | \(0.629315\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.96639 | −0.144543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.5287 | −1.25663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.6016 | 1.58473 | 0.792364 | − | 0.610048i | \(-0.208850\pi\) | ||||
0.792364 | + | 0.610048i | \(0.208850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.31483 | −0.0477253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.5442 | 1.17973 | 0.589863 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589863 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5099 | 0.380482 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −94.7286 | −3.42492 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.63303 | −0.0950734 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9886 | −0.432319 | −0.216159 | − | 0.976358i | \(-0.569353\pi\) | ||||
−0.216159 | + | 0.976358i | \(0.569353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −82.8882 | −2.98515 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.3355 | 1.12706 | 0.563530 | − | 0.826096i | \(-0.309443\pi\) | ||||
0.563530 | + | 0.826096i | \(0.309443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.07629 | 0.110503 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.38811 | 0.229172 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.02268 | 0.108299 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.71080 | 0.240131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.57080 | −0.342032 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.3973 | −0.513860 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.39669 | −0.334956 | −0.167478 | − | 0.985876i | \(-0.553562\pi\) | ||||
−0.167478 | + | 0.985876i | \(0.553562\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −44.6922 | −1.59109 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.69181 | 0.309045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.37051 | −0.0486682 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41.8848 | −1.48550 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.7756 | 0.771330 | 0.385665 | − | 0.922639i | \(-0.373972\pi\) | ||||
0.385665 | + | 0.922639i | \(0.373972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.3129 | −0.860129 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.1705 | −0.430025 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.18642 | −0.147736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.807172 | −0.0284491 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 56.3229 | 1.98266 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.83916 | −0.0646614 | −0.0323307 | − | 0.999477i | \(-0.510293\pi\) | ||||
−0.0323307 | + | 0.999477i | \(0.510293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.27579 | −0.255488 | −0.127744 | − | 0.991807i | \(-0.540774\pi\) | ||||
−0.127744 | + | 0.991807i | \(0.540774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.9087 | 0.593012 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.3895 | −1.65998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.40225 | −0.0840441 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.03308 | −0.0360987 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.0675 | −1.57287 | −0.786434 | − | 0.617674i | \(-0.788075\pi\) | ||||
−0.786434 | + | 0.617674i | \(0.788075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.71724 | 0.303864 | 0.151932 | − | 0.988391i | \(-0.451451\pi\) | ||||
0.151932 | + | 0.988391i | \(0.451451\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.68282 | −0.0585881 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.18072 | 0.284471 | 0.142236 | − | 0.989833i | \(-0.454571\pi\) | ||||
0.142236 | + | 0.989833i | \(0.454571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.1349 | −1.49814 | −0.749068 | − | 0.662493i | \(-0.769498\pi\) | ||||
−0.749068 | + | 0.662493i | \(0.769498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.48590 | −0.0515453 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.0991 | 1.63189 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | 0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.2632 | 1.25344 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.2048 | 1.28445 | 0.642226 | − | 0.766515i | \(-0.278011\pi\) | ||||
0.642226 | + | 0.766515i | \(0.278011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3408 | −0.977269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.8539 | 0.993782 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.8255 | −0.888425 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.53222 | −0.190089 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 70.7488 | 2.42809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.09123 | 0.105966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9553 | 0.409341 | 0.204671 | − | 0.978831i | \(-0.434388\pi\) | ||||
0.204671 | + | 0.978831i | \(0.434388\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 55.0689 | 1.88332 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.28383 | −0.0780142 | −0.0390071 | − | 0.999239i | \(-0.512420\pi\) | ||||
−0.0390071 | + | 0.999239i | \(0.512420\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8387 | 0.574529 | 0.287265 | − | 0.957851i | \(-0.407254\pi\) | ||||
0.287265 | + | 0.957851i | \(0.407254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.20019 | −0.0409023 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.2591 | 1.06407 | 0.532036 | − | 0.846721i | \(-0.321427\pi\) | ||||
0.532036 | + | 0.846721i | \(0.321427\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.0556 | −1.32793 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −99.8123 | −3.38980 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.63000 | −0.0892165 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.93550 | 0.0655820 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −115.916 | −3.92316 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.19847 | −0.209546 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.86671 | −0.231872 | −0.115936 | − | 0.993257i | \(-0.536987\pi\) | ||||
−0.115936 | + | 0.993257i | \(0.536987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.3123 | 1.05614 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.06820 | −0.305515 | −0.152758 | − | 0.988264i | \(-0.548815\pi\) | ||||
−0.152758 | + | 0.988264i | \(0.548815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.28390 | 0.0768594 | 0.0384297 | − | 0.999261i | \(-0.487764\pi\) | ||||
0.0384297 | + | 0.999261i | \(0.487764\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −55.7298 | −1.87334 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.8293 | 1.06872 | 0.534361 | − | 0.845256i | \(-0.320552\pi\) | ||||
0.534361 | + | 0.845256i | \(0.320552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.92148 | −0.165061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.90133 | −0.298206 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1339 | 0.472974 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0076 | 0.702208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.721399 | −0.0240868 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.49767 | −0.0833021 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.8648 | −1.56129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.953840 | 0.0317418 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.7237 | 0.555914 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.0598 | 1.79502 | 0.897512 | − | 0.440989i | \(-0.145372\pi\) | ||||
0.897512 | + | 0.440989i | \(0.145372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −94.9859 | −3.15048 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.19867 | −0.205371 | −0.102686 | − | 0.994714i | \(-0.532744\pi\) | ||||
−0.102686 | + | 0.994714i | \(0.532744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.599658 | −0.0198458 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.0076 | −0.958963 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.56467 | 0.282830 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.53624 | −0.215611 | −0.107805 | − | 0.994172i | \(-0.534382\pi\) | ||||
−0.107805 | + | 0.994172i | \(0.534382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50.0513 | 1.64925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.68197 | 0.121194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.95638 | 0.130085 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −113.451 | −3.72623 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.4372 | 0.703331 | 0.351666 | − | 0.936126i | \(-0.385615\pi\) | ||||
0.351666 | + | 0.936126i | \(0.385615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.3803 | −0.897353 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.3882 | −1.06034 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.53159 | 0.246309 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.58083 | −0.0516434 | −0.0258217 | − | 0.999667i | \(-0.508220\pi\) | ||||
−0.0258217 | + | 0.999667i | \(0.508220\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.2582 | −0.954807 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.6995 | 0.348794 | 0.174397 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174397 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.580775 | −0.0189126 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.1779 | −0.396147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.2664 | −0.951030 | −0.475515 | − | 0.879708i | \(-0.657738\pi\) | ||||
−0.475515 | + | 0.879708i | \(0.657738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.29694 | −0.0745618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.1971 | −1.30348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.0155 | −1.45820 | −0.729098 | − | 0.684410i | \(-0.760060\pi\) | ||||
−0.729098 | + | 0.684410i | \(0.760060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.8769 | −0.610842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.36630 | 0.0441661 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.82805 | 0.0590307 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5365 | −0.694725 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −64.1466 | −2.06710 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.6583 | −1.05131 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.7031 | −1.98424 | −0.992118 | − | 0.125304i | \(-0.960009\pi\) | ||||
−0.992118 | + | 0.125304i | \(0.960009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 88.9162 | 2.85640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.4233 | 0.366590 | 0.183295 | − | 0.983058i | \(-0.441324\pi\) | ||||
0.183295 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.85558 | 0.155663 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.923300 | −0.0295693 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.28909 | −0.105227 | −0.0526137 | − | 0.998615i | \(-0.516755\pi\) | ||||
−0.0526137 | + | 0.998615i | \(0.516755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.967644 | 0.0309260 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 137.769 | 4.39864 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.4572 | −0.493009 | −0.246505 | − | 0.969142i | \(-0.579282\pi\) | ||||
−0.246505 | + | 0.969142i | \(0.579282\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.6920 | −1.10538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.61203 | −0.178633 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.461566 | 0.0146770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3319 | 0.677630 | 0.338815 | − | 0.940853i | \(-0.389974\pi\) | ||||
0.338815 | + | 0.940853i | \(0.389974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.79276 | −0.279030 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.9219 | −0.409653 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.9757 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46.6377 | 1.47555 |
(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 | 2672.2.a.j.1.1 | 5 | ||
4.3 | odd | 2 | 668.2.a.b.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 6012.2.a.d.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.a.b.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
2672.2.a.j.1.1 | 5 | 1.1 | even | 1 | trivial | ||
6012.2.a.d.1.2 | 5 | 12.11 | even | 2 |