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 | 1.1 | ||
Root | \(1.43959\) 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 | ||||||||
\(7\) | −4.23800 | −1.60182 | −0.800908 | − | 0.598788i | \(-0.795649\pi\) | ||||
−0.800908 | + | 0.598788i | \(0.795649\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.01784 | 0.608403 | 0.304202 | − | 0.952608i | \(-0.401610\pi\) | ||||
0.304202 | + | 0.952608i | \(0.401610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.86299 | −1.07140 | −0.535701 | − | 0.844408i | \(-0.679953\pi\) | ||||
−0.535701 | + | 0.844408i | \(0.679953\pi\) | |||||||
\(14\) | −4.23800 | −1.13265 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.23800 | 1.51294 | 0.756469 | − | 0.654029i | \(-0.226923\pi\) | ||||
0.756469 | + | 0.654029i | \(0.226923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.49220 | −1.71883 | −0.859414 | − | 0.511280i | \(-0.829172\pi\) | ||||
−0.859414 | + | 0.511280i | \(0.829172\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.01784 | 0.430206 | ||||||||
\(23\) | 5.86299 | 1.22252 | 0.611259 | − | 0.791430i | \(-0.290663\pi\) | ||||
0.611259 | + | 0.791430i | \(0.290663\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.86299 | −0.757595 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.23800 | −0.800908 | ||||||||
\(29\) | 0.375011 | 0.0696378 | 0.0348189 | − | 0.999394i | \(-0.488915\pi\) | ||||
0.0348189 | + | 0.999394i | \(0.488915\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.47436 | 1.70164 | 0.850822 | − | 0.525454i | \(-0.176104\pi\) | ||||
0.850822 | + | 0.525454i | \(0.176104\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.23800 | 1.06981 | ||||||||
\(35\) | −4.23800 | −0.716354 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −7.49220 | −1.21540 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.72433 | 1.05016 | 0.525082 | − | 0.851052i | \(-0.324035\pi\) | ||||
0.525082 | + | 0.851052i | \(0.324035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.72433 | 1.33045 | 0.665224 | − | 0.746644i | \(-0.268336\pi\) | ||||
0.665224 | + | 0.746644i | \(0.268336\pi\) | |||||||
\(44\) | 2.01784 | 0.304202 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.86299 | 0.864451 | ||||||||
\(47\) | 11.3195 | 1.65112 | 0.825560 | − | 0.564315i | \(-0.190860\pi\) | ||||
0.825560 | + | 0.564315i | \(0.190860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.9607 | 1.56581 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.86299 | −0.535701 | ||||||||
\(53\) | −0.861339 | −0.118314 | −0.0591570 | − | 0.998249i | \(-0.518841\pi\) | ||||
−0.0591570 | + | 0.998249i | \(0.518841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.01784 | 0.272086 | ||||||||
\(56\) | −4.23800 | −0.566327 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.375011 | 0.0492414 | ||||||||
\(59\) | −4.03569 | −0.525402 | −0.262701 | − | 0.964877i | \(-0.584613\pi\) | ||||
−0.262701 | + | 0.964877i | \(0.584613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.12247 | 0.527828 | 0.263914 | − | 0.964546i | \(-0.414986\pi\) | ||||
0.263914 | + | 0.964546i | \(0.414986\pi\) | |||||||
\(62\) | 9.47436 | 1.20324 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.86299 | −0.479145 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5117 | 1.52855 | 0.764274 | − | 0.644892i | \(-0.223098\pi\) | ||||
0.764274 | + | 0.644892i | \(0.223098\pi\) | |||||||
\(68\) | 6.23800 | 0.756469 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.23800 | −0.506538 | ||||||||
\(71\) | −14.1987 | −1.68507 | −0.842537 | − | 0.538638i | \(-0.818939\pi\) | ||||
−0.842537 | + | 0.538638i | \(0.818939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3714 | −1.21388 | −0.606939 | − | 0.794748i | \(-0.707603\pi\) | ||||
−0.606939 | + | 0.794748i | \(0.707603\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.49220 | −0.859414 | ||||||||
\(77\) | −8.55164 | −0.974549 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1987 | −1.37246 | −0.686230 | − | 0.727385i | \(-0.740736\pi\) | ||||
−0.686230 | + | 0.727385i | \(0.740736\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.72433 | 0.742578 | ||||||||
\(83\) | 1.82730 | 0.200573 | 0.100286 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100286 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.23800 | 0.676607 | ||||||||
\(86\) | 8.72433 | 0.940769 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.01784 | 0.215103 | ||||||||
\(89\) | 13.0890 | 1.38743 | 0.693717 | − | 0.720248i | \(-0.255972\pi\) | ||||
0.693717 | + | 0.720248i | \(0.255972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3714 | 1.71619 | ||||||||
\(92\) | 5.86299 | 0.611259 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.3195 | 1.16752 | ||||||||
\(95\) | −7.49220 | −0.768684 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.59517 | 0.669638 | 0.334819 | − | 0.942282i | \(-0.391325\pi\) | ||||
0.334819 | + | 0.942282i | \(0.391325\pi\) | |||||||
\(98\) | 10.9607 | 1.10720 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.0422 | 1.29775 | 0.648873 | − | 0.760897i | \(-0.275241\pi\) | ||||
0.648873 | + | 0.760897i | \(0.275241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.31950 | −0.918278 | −0.459139 | − | 0.888364i | \(-0.651842\pi\) | ||||
−0.459139 | + | 0.888364i | \(0.651842\pi\) | |||||||
\(104\) | −3.86299 | −0.378798 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.861339 | −0.0836607 | ||||||||
\(107\) | 5.11297 | 0.494290 | 0.247145 | − | 0.968979i | \(-0.420508\pi\) | ||||
0.247145 | + | 0.968979i | \(0.420508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1808 | 1.35828 | 0.679139 | − | 0.734009i | \(-0.262353\pi\) | ||||
0.679139 | + | 0.734009i | \(0.262353\pi\) | |||||||
\(110\) | 2.01784 | 0.192394 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.23800 | −0.400454 | ||||||||
\(113\) | 3.66068 | 0.344368 | 0.172184 | − | 0.985065i | \(-0.444918\pi\) | ||||
0.172184 | + | 0.985065i | \(0.444918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.86299 | 0.546727 | ||||||||
\(116\) | 0.375011 | 0.0348189 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.03569 | −0.371515 | ||||||||
\(119\) | −26.4367 | −2.42345 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.92830 | −0.629846 | ||||||||
\(122\) | 4.12247 | 0.373231 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.47436 | 0.850822 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.609707 | −0.0541028 | −0.0270514 | − | 0.999634i | \(-0.508612\pi\) | ||||
−0.0270514 | + | 0.999634i | \(0.508612\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.86299 | −0.338807 | ||||||||
\(131\) | −20.9163 | −1.82747 | −0.913734 | − | 0.406313i | \(-0.866814\pi\) | ||||
−0.913734 | + | 0.406313i | \(0.866814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.7520 | 2.75325 | ||||||||
\(134\) | 12.5117 | 1.08085 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.23800 | 0.534904 | ||||||||
\(137\) | −2.87918 | −0.245985 | −0.122993 | − | 0.992408i | \(-0.539249\pi\) | ||||
−0.122993 | + | 0.992408i | \(0.539249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8594 | −1.34517 | −0.672587 | − | 0.740018i | \(-0.734817\pi\) | ||||
−0.672587 | + | 0.740018i | \(0.734817\pi\) | |||||||
\(140\) | −4.23800 | −0.358177 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.1987 | −1.19153 | ||||||||
\(143\) | −7.79492 | −0.651844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.375011 | 0.0311430 | ||||||||
\(146\) | −10.3714 | −0.858342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | 5.35189 | 0.438444 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0857 | 1.39042 | 0.695208 | − | 0.718809i | \(-0.255312\pi\) | ||||
0.695208 | + | 0.718809i | \(0.255312\pi\) | |||||||
\(152\) | −7.49220 | −0.607698 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.55164 | −0.689110 | ||||||||
\(155\) | 9.47436 | 0.760999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.16072 | 0.0926358 | 0.0463179 | − | 0.998927i | \(-0.485251\pi\) | ||||
0.0463179 | + | 0.998927i | \(0.485251\pi\) | |||||||
\(158\) | −12.1987 | −0.970475 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −24.8474 | −1.95825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.36973 | 0.733894 | 0.366947 | − | 0.930242i | \(-0.380403\pi\) | ||||
0.366947 | + | 0.930242i | \(0.380403\pi\) | |||||||
\(164\) | 6.72433 | 0.525082 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.82730 | 0.141826 | ||||||||
\(167\) | −5.86299 | −0.453692 | −0.226846 | − | 0.973931i | \(-0.572841\pi\) | ||||
−0.226846 | + | 0.973931i | \(0.572841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.92272 | 0.147901 | ||||||||
\(170\) | 6.23800 | 0.478433 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.72433 | 0.665224 | ||||||||
\(173\) | 2.36138 | 0.179533 | 0.0897663 | − | 0.995963i | \(-0.471388\pi\) | ||||
0.0897663 | + | 0.995963i | \(0.471388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.23800 | −0.320363 | ||||||||
\(176\) | 2.01784 | 0.152101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.0890 | 0.981064 | ||||||||
\(179\) | 13.9247 | 1.04078 | 0.520390 | − | 0.853929i | \(-0.325787\pi\) | ||||
0.520390 | + | 0.853929i | \(0.325787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.51170 | −0.186693 | −0.0933466 | − | 0.995634i | \(-0.529756\pi\) | ||||
−0.0933466 | + | 0.995634i | \(0.529756\pi\) | |||||||
\(182\) | 16.3714 | 1.21353 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.86299 | 0.432226 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.5873 | 0.920476 | ||||||||
\(188\) | 11.3195 | 0.825560 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.49220 | −0.543541 | ||||||||
\(191\) | −25.6867 | −1.85862 | −0.929311 | − | 0.369298i | \(-0.879598\pi\) | ||||
−0.929311 | + | 0.369298i | \(0.879598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.03384 | −0.434325 | −0.217163 | − | 0.976135i | \(-0.569680\pi\) | ||||
−0.217163 | + | 0.976135i | \(0.569680\pi\) | |||||||
\(194\) | 6.59517 | 0.473506 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.9607 | 0.782906 | ||||||||
\(197\) | 22.3747 | 1.59413 | 0.797065 | − | 0.603893i | \(-0.206385\pi\) | ||||
0.797065 | + | 0.603893i | \(0.206385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1663 | −1.28778 | −0.643888 | − | 0.765120i | \(-0.722680\pi\) | ||||
−0.643888 | + | 0.765120i | \(0.722680\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.0422 | 0.917645 | ||||||||
\(203\) | −1.58930 | −0.111547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.72433 | 0.469648 | ||||||||
\(206\) | −9.31950 | −0.649321 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.86299 | −0.267850 | ||||||||
\(209\) | −15.1181 | −1.04574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3594 | −1.19507 | −0.597536 | − | 0.801842i | \(-0.703853\pi\) | ||||
−0.597536 | + | 0.801842i | \(0.703853\pi\) | |||||||
\(212\) | −0.861339 | −0.0591570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.11297 | 0.349516 | ||||||||
\(215\) | 8.72433 | 0.594995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.1524 | −2.72572 | ||||||||
\(218\) | 14.1808 | 0.960448 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.01784 | 0.136043 | ||||||||
\(221\) | −24.0974 | −1.62096 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.652333 | 0.0436834 | 0.0218417 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218417 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(224\) | −4.23800 | −0.283164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.66068 | 0.243505 | ||||||||
\(227\) | 10.1367 | 0.672796 | 0.336398 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336398 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.1747 | −1.72968 | −0.864838 | − | 0.502051i | \(-0.832579\pi\) | ||||
−0.864838 | + | 0.502051i | \(0.832579\pi\) | |||||||
\(230\) | 5.86299 | 0.386594 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.375011 | 0.0246207 | ||||||||
\(233\) | 27.0812 | 1.77415 | 0.887074 | − | 0.461628i | \(-0.152735\pi\) | ||||
0.887074 | + | 0.461628i | \(0.152735\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3195 | 0.738403 | ||||||||
\(236\) | −4.03569 | −0.262701 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.4367 | −1.71364 | ||||||||
\(239\) | −12.3426 | −0.798378 | −0.399189 | − | 0.916869i | \(-0.630708\pi\) | ||||
−0.399189 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | 0.805193 | 0.402596 | − | 0.915378i | \(-0.368108\pi\) | ||||
0.402596 | + | 0.915378i | \(0.368108\pi\) | |||||||
\(242\) | −6.92830 | −0.445368 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.12247 | 0.263914 | ||||||||
\(245\) | 10.9607 | 0.700252 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9423 | 1.84156 | ||||||||
\(248\) | 9.47436 | 0.601622 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 9.41298 | 0.594142 | 0.297071 | − | 0.954855i | \(-0.403990\pi\) | ||||
0.297071 | + | 0.954855i | \(0.403990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.8306 | 0.743784 | ||||||||
\(254\) | −0.609707 | −0.0382564 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.26431 | 0.390757 | 0.195379 | − | 0.980728i | \(-0.437406\pi\) | ||||
0.195379 | + | 0.980728i | \(0.437406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.23800 | −0.263337 | ||||||||
\(260\) | −3.86299 | −0.239573 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9163 | −1.29222 | ||||||||
\(263\) | −25.6392 | −1.58098 | −0.790491 | − | 0.612474i | \(-0.790174\pi\) | ||||
−0.790491 | + | 0.612474i | \(0.790174\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.861339 | −0.0529117 | ||||||||
\(266\) | 31.7520 | 1.94684 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.5117 | 0.764274 | ||||||||
\(269\) | 6.74549 | 0.411280 | 0.205640 | − | 0.978628i | \(-0.434072\pi\) | ||||
0.205640 | + | 0.978628i | \(0.434072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6390 | −0.889256 | −0.444628 | − | 0.895715i | \(-0.646664\pi\) | ||||
−0.444628 | + | 0.895715i | \(0.646664\pi\) | |||||||
\(272\) | 6.23800 | 0.378235 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.87918 | −0.173938 | ||||||||
\(275\) | 2.01784 | 0.121681 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0533 | 1.02464 | 0.512318 | − | 0.858796i | \(-0.328787\pi\) | ||||
0.512318 | + | 0.858796i | \(0.328787\pi\) | |||||||
\(278\) | −15.8594 | −0.951182 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.23800 | −0.253269 | ||||||||
\(281\) | −26.0617 | −1.55471 | −0.777355 | − | 0.629062i | \(-0.783439\pi\) | ||||
−0.777355 | + | 0.629062i | \(0.783439\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1214 | 0.898874 | 0.449437 | − | 0.893312i | \(-0.351625\pi\) | ||||
0.449437 | + | 0.893312i | \(0.351625\pi\) | |||||||
\(284\) | −14.1987 | −0.842537 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.79492 | −0.460923 | ||||||||
\(287\) | −28.4978 | −1.68217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9127 | 1.28898 | ||||||||
\(290\) | 0.375011 | 0.0220214 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.3714 | −0.606939 | ||||||||
\(293\) | 6.82896 | 0.398952 | 0.199476 | − | 0.979903i | \(-0.436076\pi\) | ||||
0.199476 | + | 0.979903i | \(0.436076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.03569 | −0.234967 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.35189 | 0.310026 | ||||||||
\(299\) | −22.6487 | −1.30981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.9738 | −2.13113 | ||||||||
\(302\) | 17.0857 | 0.983173 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.49220 | −0.429707 | ||||||||
\(305\) | 4.12247 | 0.236052 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.03569 | −0.458621 | −0.229311 | − | 0.973353i | \(-0.573647\pi\) | ||||
−0.229311 | + | 0.973353i | \(0.573647\pi\) | |||||||
\(308\) | −8.55164 | −0.487275 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.47436 | 0.538107 | ||||||||
\(311\) | 25.5614 | 1.44945 | 0.724727 | − | 0.689036i | \(-0.241966\pi\) | ||||
0.724727 | + | 0.689036i | \(0.241966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4182 | 1.15411 | 0.577053 | − | 0.816707i | \(-0.304203\pi\) | ||||
0.577053 | + | 0.816707i | \(0.304203\pi\) | |||||||
\(314\) | 1.16072 | 0.0655034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.1987 | −0.686230 | ||||||||
\(317\) | 0.280705 | 0.0157660 | 0.00788298 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788298 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.756714 | 0.0423679 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.8474 | −1.38469 | ||||||||
\(323\) | −46.7364 | −2.60048 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.86299 | −0.214280 | ||||||||
\(326\) | 9.36973 | 0.518941 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.72433 | 0.371289 | ||||||||
\(329\) | −47.9721 | −2.64479 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.85184 | −0.101786 | −0.0508932 | − | 0.998704i | \(-0.516207\pi\) | ||||
−0.0508932 | + | 0.998704i | \(0.516207\pi\) | |||||||
\(332\) | 1.82730 | 0.100286 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.86299 | −0.320809 | ||||||||
\(335\) | 12.5117 | 0.683587 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4344 | −0.731819 | −0.365910 | − | 0.930650i | \(-0.619242\pi\) | ||||
−0.365910 | + | 0.930650i | \(0.619242\pi\) | |||||||
\(338\) | 1.92272 | 0.104582 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.23800 | 0.338303 | ||||||||
\(341\) | 19.1178 | 1.03529 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.7854 | −0.906326 | ||||||||
\(344\) | 8.72433 | 0.470384 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.36138 | 0.126949 | ||||||||
\(347\) | 13.2260 | 0.710011 | 0.355005 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355005 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.1591 | 1.82849 | 0.914246 | − | 0.405159i | \(-0.132784\pi\) | ||||
0.914246 | + | 0.405159i | \(0.132784\pi\) | |||||||
\(350\) | −4.23800 | −0.226531 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.01784 | 0.107551 | ||||||||
\(353\) | −9.08934 | −0.483777 | −0.241888 | − | 0.970304i | \(-0.577767\pi\) | ||||
−0.241888 | + | 0.970304i | \(0.577767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.1987 | −0.753588 | ||||||||
\(356\) | 13.0890 | 0.693717 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.9247 | 0.735942 | ||||||||
\(359\) | −19.3214 | −1.01974 | −0.509871 | − | 0.860251i | \(-0.670307\pi\) | ||||
−0.509871 | + | 0.860251i | \(0.670307\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.1331 | 1.95437 | ||||||||
\(362\) | −2.51170 | −0.132012 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.3714 | 0.858094 | ||||||||
\(365\) | −10.3714 | −0.542863 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.77043 | 0.196815 | 0.0984074 | − | 0.995146i | \(-0.468625\pi\) | ||||
0.0984074 | + | 0.995146i | \(0.468625\pi\) | |||||||
\(368\) | 5.86299 | 0.305630 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | 3.65036 | 0.189517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0390 | −0.623356 | −0.311678 | − | 0.950188i | \(-0.600891\pi\) | ||||
−0.311678 | + | 0.950188i | \(0.600891\pi\) | |||||||
\(374\) | 12.5873 | 0.650875 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.3195 | 0.583759 | ||||||||
\(377\) | −1.44867 | −0.0746101 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.1624 | 1.96027 | 0.980134 | − | 0.198334i | \(-0.0635532\pi\) | ||||
0.980134 | + | 0.198334i | \(0.0635532\pi\) | |||||||
\(380\) | −7.49220 | −0.384342 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.6867 | −1.31424 | ||||||||
\(383\) | −33.1280 | −1.69276 | −0.846381 | − | 0.532577i | \(-0.821224\pi\) | ||||
−0.846381 | + | 0.532577i | \(0.821224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.55164 | −0.435832 | ||||||||
\(386\) | −6.03384 | −0.307114 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.59517 | 0.334819 | ||||||||
\(389\) | 13.1178 | 0.665098 | 0.332549 | − | 0.943086i | \(-0.392091\pi\) | ||||
0.332549 | + | 0.943086i | \(0.392091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.5734 | 1.84960 | ||||||||
\(392\) | 10.9607 | 0.553598 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.3747 | 1.12722 | ||||||||
\(395\) | −12.1987 | −0.613783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.74159 | −0.137596 | −0.0687982 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687982 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(398\) | −18.1663 | −0.910595 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 10.3423 | 0.516470 | 0.258235 | − | 0.966082i | \(-0.416859\pi\) | ||||
0.258235 | + | 0.966082i | \(0.416859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.5994 | −1.82314 | ||||||||
\(404\) | 13.0422 | 0.648873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.58930 | −0.0788756 | ||||||||
\(407\) | 2.01784 | 0.100021 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.68699 | −0.380097 | −0.190049 | − | 0.981775i | \(-0.560865\pi\) | ||||
−0.190049 | + | 0.981775i | \(0.560865\pi\) | |||||||
\(410\) | 6.72433 | 0.332091 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.31950 | −0.459139 | ||||||||
\(413\) | 17.1033 | 0.841597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.82730 | 0.0896988 | ||||||||
\(416\) | −3.86299 | −0.189399 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.1181 | −0.739450 | ||||||||
\(419\) | −6.70318 | −0.327472 | −0.163736 | − | 0.986504i | \(-0.552354\pi\) | ||||
−0.163736 | + | 0.986504i | \(0.552354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1208 | 0.541995 | 0.270998 | − | 0.962580i | \(-0.412646\pi\) | ||||
0.270998 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(422\) | −17.3594 | −0.845043 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.861339 | −0.0418303 | ||||||||
\(425\) | 6.23800 | 0.302588 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4710 | −0.845483 | ||||||||
\(428\) | 5.11297 | 0.247145 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.72433 | 0.420725 | ||||||||
\(431\) | 26.7035 | 1.28626 | 0.643130 | − | 0.765757i | \(-0.277635\pi\) | ||||
0.643130 | + | 0.765757i | \(0.277635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.38698 | −0.162768 | −0.0813840 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813840 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(434\) | −40.1524 | −1.92737 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.1808 | 0.679139 | ||||||||
\(437\) | −43.9267 | −2.10130 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.5847 | −1.31655 | −0.658274 | − | 0.752779i | \(-0.728713\pi\) | ||||
−0.658274 | + | 0.752779i | \(0.728713\pi\) | |||||||
\(440\) | 2.01784 | 0.0961970 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0974 | −1.14620 | ||||||||
\(443\) | 15.6474 | 0.743428 | 0.371714 | − | 0.928347i | \(-0.378770\pi\) | ||||
0.371714 | + | 0.928347i | \(0.378770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0890 | 0.620479 | ||||||||
\(446\) | 0.652333 | 0.0308888 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.23800 | −0.200227 | ||||||||
\(449\) | −13.6903 | −0.646085 | −0.323043 | − | 0.946384i | \(-0.604706\pi\) | ||||
−0.323043 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5687 | 0.638923 | ||||||||
\(452\) | 3.66068 | 0.172184 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.1367 | 0.475738 | ||||||||
\(455\) | 16.3714 | 0.767502 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.66324 | 0.218137 | 0.109069 | − | 0.994034i | \(-0.465213\pi\) | ||||
0.109069 | + | 0.994034i | \(0.465213\pi\) | |||||||
\(458\) | −26.1747 | −1.22307 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.86299 | 0.273363 | ||||||||
\(461\) | −22.8048 | −1.06212 | −0.531062 | − | 0.847333i | \(-0.678207\pi\) | ||||
−0.531062 | + | 0.847333i | \(0.678207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8551 | 0.736851 | 0.368426 | − | 0.929657i | \(-0.379897\pi\) | ||||
0.368426 | + | 0.929657i | \(0.379897\pi\) | |||||||
\(464\) | 0.375011 | 0.0174095 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.0812 | 1.25451 | ||||||||
\(467\) | −27.2841 | −1.26256 | −0.631278 | − | 0.775556i | \(-0.717469\pi\) | ||||
−0.631278 | + | 0.775556i | \(0.717469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.0246 | −2.44845 | ||||||||
\(470\) | 11.3195 | 0.522130 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.03569 | −0.185758 | ||||||||
\(473\) | 17.6044 | 0.809449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.49220 | −0.343766 | ||||||||
\(476\) | −26.4367 | −1.21172 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.3426 | −0.564539 | ||||||||
\(479\) | −38.3033 | −1.75012 | −0.875062 | − | 0.484012i | \(-0.839179\pi\) | ||||
−0.875062 | + | 0.484012i | \(0.839179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.86299 | −0.176137 | ||||||||
\(482\) | 12.5000 | 0.569357 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.92830 | −0.314923 | ||||||||
\(485\) | 6.59517 | 0.299471 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.66820 | 0.347480 | 0.173740 | − | 0.984792i | \(-0.444415\pi\) | ||||
0.173740 | + | 0.984792i | \(0.444415\pi\) | |||||||
\(488\) | 4.12247 | 0.186615 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.9607 | 0.495153 | ||||||||
\(491\) | 42.1786 | 1.90350 | 0.951748 | − | 0.306882i | \(-0.0992856\pi\) | ||||
0.951748 | + | 0.306882i | \(0.0992856\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.33932 | 0.105358 | ||||||||
\(494\) | 28.9423 | 1.30218 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.47436 | 0.425411 | ||||||||
\(497\) | 60.1741 | 2.69918 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.70318 | −0.210543 | −0.105272 | − | 0.994444i | \(-0.533571\pi\) | ||||
−0.105272 | + | 0.994444i | \(0.533571\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.41298 | 0.420122 | ||||||||
\(503\) | −25.7650 | −1.14880 | −0.574402 | − | 0.818573i | \(-0.694765\pi\) | ||||
−0.574402 | + | 0.818573i | \(0.694765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0422 | 0.580369 | ||||||||
\(506\) | 11.8306 | 0.525935 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.609707 | −0.0270514 | ||||||||
\(509\) | −9.86114 | −0.437087 | −0.218544 | − | 0.975827i | \(-0.570131\pi\) | ||||
−0.218544 | + | 0.975827i | \(0.570131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.9540 | 1.94441 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.26431 | 0.276307 | ||||||||
\(515\) | −9.31950 | −0.410666 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.8410 | 1.00455 | ||||||||
\(518\) | −4.23800 | −0.186207 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.86299 | −0.169403 | ||||||||
\(521\) | 19.1374 | 0.838425 | 0.419212 | − | 0.907888i | \(-0.362306\pi\) | ||||
0.419212 | + | 0.907888i | \(0.362306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9313 | −1.39626 | −0.698129 | − | 0.715972i | \(-0.745984\pi\) | ||||
−0.698129 | + | 0.715972i | \(0.745984\pi\) | |||||||
\(524\) | −20.9163 | −0.913734 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.6392 | −1.11792 | ||||||||
\(527\) | 59.1011 | 2.57448 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3747 | 0.494552 | ||||||||
\(530\) | −0.861339 | −0.0374142 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 31.7520 | 1.37662 | ||||||||
\(533\) | −25.9761 | −1.12515 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.11297 | 0.221053 | ||||||||
\(536\) | 12.5117 | 0.540423 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.74549 | 0.290819 | ||||||||
\(539\) | 22.1170 | 0.952645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6825 | −0.717238 | −0.358619 | − | 0.933484i | \(-0.616752\pi\) | ||||
−0.358619 | + | 0.933484i | \(0.616752\pi\) | |||||||
\(542\) | −14.6390 | −0.628799 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.23800 | 0.267452 | ||||||||
\(545\) | 14.1808 | 0.607441 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5600 | 0.665297 | 0.332648 | − | 0.943051i | \(-0.392058\pi\) | ||||
0.332648 | + | 0.943051i | \(0.392058\pi\) | |||||||
\(548\) | −2.87918 | −0.122993 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.01784 | 0.0860412 | ||||||||
\(551\) | −2.80966 | −0.119695 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.6981 | 2.19843 | ||||||||
\(554\) | 17.0533 | 0.724527 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.8594 | −0.672587 | ||||||||
\(557\) | 30.6986 | 1.30074 | 0.650372 | − | 0.759616i | \(-0.274613\pi\) | ||||
0.650372 | + | 0.759616i | \(0.274613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7020 | −1.42544 | ||||||||
\(560\) | −4.23800 | −0.179088 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.0617 | −1.09935 | ||||||||
\(563\) | 15.0173 | 0.632905 | 0.316452 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316452 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.66068 | 0.154006 | ||||||||
\(566\) | 15.1214 | 0.635600 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.1987 | −0.595764 | ||||||||
\(569\) | 16.8084 | 0.704645 | 0.352322 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352322 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0050 | 1.67416 | 0.837079 | − | 0.547082i | \(-0.184261\pi\) | ||||
0.837079 | + | 0.547082i | \(0.184261\pi\) | |||||||
\(572\) | −7.79492 | −0.325922 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.4978 | −1.18947 | ||||||||
\(575\) | 5.86299 | 0.244504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.7442 | −1.52968 | −0.764841 | − | 0.644219i | \(-0.777182\pi\) | ||||
−0.764841 | + | 0.644219i | \(0.777182\pi\) | |||||||
\(578\) | 21.9127 | 0.911448 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.375011 | 0.0155715 | ||||||||
\(581\) | −7.74412 | −0.321280 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.73805 | −0.0719826 | ||||||||
\(584\) | −10.3714 | −0.429171 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.82896 | 0.282102 | ||||||||
\(587\) | 7.28472 | 0.300673 | 0.150336 | − | 0.988635i | \(-0.451964\pi\) | ||||
0.150336 | + | 0.988635i | \(0.451964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −70.9838 | −2.92484 | ||||||||
\(590\) | −4.03569 | −0.166147 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −31.0025 | −1.27312 | −0.636561 | − | 0.771226i | \(-0.719644\pi\) | ||||
−0.636561 | + | 0.771226i | \(0.719644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.4367 | −1.08380 | ||||||||
\(596\) | 5.35189 | 0.219222 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.6487 | −0.926174 | ||||||||
\(599\) | −16.5117 | −0.674650 | −0.337325 | − | 0.941388i | \(-0.609522\pi\) | ||||
−0.337325 | + | 0.941388i | \(0.609522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9997 | −0.571059 | −0.285529 | − | 0.958370i | \(-0.592169\pi\) | ||||
−0.285529 | + | 0.958370i | \(0.592169\pi\) | |||||||
\(602\) | −36.9738 | −1.50694 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.0857 | 0.695208 | ||||||||
\(605\) | −6.92830 | −0.281676 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.5422 | −1.48320 | −0.741602 | − | 0.670841i | \(-0.765933\pi\) | ||||
−0.741602 | + | 0.670841i | \(0.765933\pi\) | |||||||
\(608\) | −7.49220 | −0.303849 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.12247 | 0.166914 | ||||||||
\(611\) | −43.7272 | −1.76901 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.90231 | 0.238392 | 0.119196 | − | 0.992871i | \(-0.461968\pi\) | ||||
0.119196 | + | 0.992871i | \(0.461968\pi\) | |||||||
\(614\) | −8.03569 | −0.324294 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.55164 | −0.344555 | ||||||||
\(617\) | 19.4115 | 0.781478 | 0.390739 | − | 0.920501i | \(-0.372219\pi\) | ||||
0.390739 | + | 0.920501i | \(0.372219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6723 | −1.15244 | −0.576219 | − | 0.817295i | \(-0.695473\pi\) | ||||
−0.576219 | + | 0.817295i | \(0.695473\pi\) | |||||||
\(620\) | 9.47436 | 0.380499 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.5614 | 1.02492 | ||||||||
\(623\) | −55.4713 | −2.22241 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 20.4182 | 0.816076 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.16072 | 0.0463179 | ||||||||
\(629\) | 6.23800 | 0.248726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5167 | −0.697327 | −0.348664 | − | 0.937248i | \(-0.613364\pi\) | ||||
−0.348664 | + | 0.937248i | \(0.613364\pi\) | |||||||
\(632\) | −12.1987 | −0.485238 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.280705 | 0.0111482 | ||||||||
\(635\) | −0.609707 | −0.0241955 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42.3410 | −1.67761 | ||||||||
\(638\) | 0.756714 | 0.0299586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 29.7444 | 1.17483 | 0.587417 | − | 0.809284i | \(-0.300145\pi\) | ||||
0.587417 | + | 0.809284i | \(0.300145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.3541 | 0.644944 | 0.322472 | − | 0.946579i | \(-0.395486\pi\) | ||||
0.322472 | + | 0.946579i | \(0.395486\pi\) | |||||||
\(644\) | −24.8474 | −0.979124 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.7364 | −1.83882 | ||||||||
\(647\) | 9.67605 | 0.380405 | 0.190202 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190202 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.14340 | −0.319656 | ||||||||
\(650\) | −3.86299 | −0.151519 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.36973 | 0.366947 | ||||||||
\(653\) | −30.9006 | −1.20924 | −0.604618 | − | 0.796516i | \(-0.706674\pi\) | ||||
−0.604618 | + | 0.796516i | \(0.706674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9163 | −0.817269 | ||||||||
\(656\) | 6.72433 | 0.262541 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −47.9721 | −1.87015 | ||||||||
\(659\) | −30.5779 | −1.19115 | −0.595573 | − | 0.803301i | \(-0.703075\pi\) | ||||
−0.595573 | + | 0.803301i | \(0.703075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4749 | 0.524115 | 0.262057 | − | 0.965052i | \(-0.415599\pi\) | ||||
0.262057 | + | 0.965052i | \(0.415599\pi\) | |||||||
\(662\) | −1.85184 | −0.0719738 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.82730 | 0.0709131 | ||||||||
\(665\) | 31.7520 | 1.23129 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.19869 | 0.0851335 | ||||||||
\(668\) | −5.86299 | −0.226846 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.5117 | 0.483369 | ||||||||
\(671\) | 8.31851 | 0.321132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.4937 | −0.828519 | −0.414260 | − | 0.910159i | \(-0.635959\pi\) | ||||
−0.414260 | + | 0.910159i | \(0.635959\pi\) | |||||||
\(674\) | −13.4344 | −0.517474 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.92272 | 0.0739507 | ||||||||
\(677\) | −27.9981 | −1.07605 | −0.538027 | − | 0.842927i | \(-0.680830\pi\) | ||||
−0.538027 | + | 0.842927i | \(0.680830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.9504 | −1.07264 | ||||||||
\(680\) | 6.23800 | 0.239217 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.1178 | 0.732058 | ||||||||
\(683\) | 20.6366 | 0.789639 | 0.394820 | − | 0.918759i | \(-0.370807\pi\) | ||||
0.394820 | + | 0.918759i | \(0.370807\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.87918 | −0.110008 | ||||||||
\(686\) | −16.7854 | −0.640869 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.72433 | 0.332612 | ||||||||
\(689\) | 3.32735 | 0.126762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2874 | 1.26631 | 0.633156 | − | 0.774024i | \(-0.281759\pi\) | ||||
0.633156 | + | 0.774024i | \(0.281759\pi\) | |||||||
\(692\) | 2.36138 | 0.0897663 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.2260 | 0.502053 | ||||||||
\(695\) | −15.8594 | −0.601580 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.9464 | 1.58883 | ||||||||
\(698\) | 34.1591 | 1.29294 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.23800 | −0.160182 | ||||||||
\(701\) | −3.29741 | −0.124542 | −0.0622708 | − | 0.998059i | \(-0.519834\pi\) | ||||
−0.0622708 | + | 0.998059i | \(0.519834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.49220 | −0.282574 | ||||||||
\(704\) | 2.01784 | 0.0760504 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.08934 | −0.342082 | ||||||||
\(707\) | −55.2728 | −2.07875 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.8744 | −1.04685 | −0.523423 | − | 0.852073i | \(-0.675345\pi\) | ||||
−0.523423 | + | 0.852073i | \(0.675345\pi\) | |||||||
\(710\) | −14.1987 | −0.532867 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.0890 | 0.490532 | ||||||||
\(713\) | 55.5481 | 2.08029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.79492 | −0.291514 | ||||||||
\(716\) | 13.9247 | 0.520390 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.3214 | −0.721067 | ||||||||
\(719\) | −34.0982 | −1.27165 | −0.635825 | − | 0.771833i | \(-0.719340\pi\) | ||||
−0.635825 | + | 0.771833i | \(0.719340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.4961 | 1.47091 | ||||||||
\(722\) | 37.1331 | 1.38195 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.51170 | −0.0933466 | ||||||||
\(725\) | 0.375011 | 0.0139276 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3122 | −1.23548 | −0.617741 | − | 0.786381i | \(-0.711952\pi\) | ||||
−0.617741 | + | 0.786381i | \(0.711952\pi\) | |||||||
\(728\) | 16.3714 | 0.606764 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.3714 | −0.383862 | ||||||||
\(731\) | 54.4224 | 2.01289 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.5569 | −0.648480 | −0.324240 | − | 0.945975i | \(-0.605108\pi\) | ||||
−0.324240 | + | 0.945975i | \(0.605108\pi\) | |||||||
\(734\) | 3.77043 | 0.139169 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.86299 | 0.216113 | ||||||||
\(737\) | 25.2467 | 0.929973 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.4464 | −0.678561 | −0.339281 | − | 0.940685i | \(-0.610184\pi\) | ||||
−0.339281 | + | 0.940685i | \(0.610184\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.65036 | 0.134009 | ||||||||
\(743\) | −19.0679 | −0.699532 | −0.349766 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349766 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.35189 | 0.196078 | ||||||||
\(746\) | −12.0390 | −0.440779 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.5873 | 0.460238 | ||||||||
\(749\) | −21.6688 | −0.791761 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.9571 | −1.31209 | −0.656046 | − | 0.754721i | \(-0.727772\pi\) | ||||
−0.656046 | + | 0.754721i | \(0.727772\pi\) | |||||||
\(752\) | 11.3195 | 0.412780 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.44867 | −0.0527573 | ||||||||
\(755\) | 17.0857 | 0.621813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5940 | −0.821194 | −0.410597 | − | 0.911817i | \(-0.634680\pi\) | ||||
−0.410597 | + | 0.911817i | \(0.634680\pi\) | |||||||
\(758\) | 38.1624 | 1.38612 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.49220 | −0.271771 | ||||||||
\(761\) | −25.4347 | −0.922008 | −0.461004 | − | 0.887398i | \(-0.652511\pi\) | ||||
−0.461004 | + | 0.887398i | \(0.652511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −60.0985 | −2.17571 | ||||||||
\(764\) | −25.6867 | −0.929311 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.1280 | −1.19696 | ||||||||
\(767\) | 15.5898 | 0.562917 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.20263 | −0.0794290 | −0.0397145 | − | 0.999211i | \(-0.512645\pi\) | ||||
−0.0397145 | + | 0.999211i | \(0.512645\pi\) | |||||||
\(770\) | −8.55164 | −0.308180 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.03384 | −0.217163 | ||||||||
\(773\) | −20.5939 | −0.740713 | −0.370356 | − | 0.928890i | \(-0.620764\pi\) | ||||
−0.370356 | + | 0.928890i | \(0.620764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.47436 | 0.340329 | ||||||||
\(776\) | 6.59517 | 0.236753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1178 | 0.470295 | ||||||||
\(779\) | −50.3800 | −1.80505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.6508 | −1.02520 | ||||||||
\(782\) | 36.5734 | 1.30786 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.9607 | 0.391453 | ||||||||
\(785\) | 1.16072 | 0.0414280 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.94036 | 0.211751 | 0.105876 | − | 0.994379i | \(-0.466235\pi\) | ||||
0.105876 | + | 0.994379i | \(0.466235\pi\) | |||||||
\(788\) | 22.3747 | 0.797065 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.1987 | −0.434010 | ||||||||
\(791\) | −15.5140 | −0.551613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9251 | −0.565516 | ||||||||
\(794\) | −2.74159 | −0.0972953 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.1663 | −0.643888 | ||||||||
\(797\) | 13.3214 | 0.471867 | 0.235933 | − | 0.971769i | \(-0.424185\pi\) | ||||
0.235933 | + | 0.971769i | \(0.424185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.6111 | 2.49804 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.3423 | 0.365200 | ||||||||
\(803\) | −20.9278 | −0.738528 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.8474 | −0.875756 | ||||||||
\(806\) | −36.5994 | −1.28916 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.0422 | 0.458822 | ||||||||
\(809\) | 3.52974 | 0.124099 | 0.0620496 | − | 0.998073i | \(-0.480236\pi\) | ||||
0.0620496 | + | 0.998073i | \(0.480236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.46105 | −0.121534 | −0.0607669 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607669 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(812\) | −1.58930 | −0.0557735 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.01784 | 0.0707254 | ||||||||
\(815\) | 9.36973 | 0.328207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.3644 | −2.28681 | ||||||||
\(818\) | −7.68699 | −0.268769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.72433 | 0.234824 | ||||||||
\(821\) | −6.13452 | −0.214096 | −0.107048 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107048 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.18104 | −0.250315 | −0.125158 | − | 0.992137i | \(-0.539944\pi\) | ||||
−0.125158 | + | 0.992137i | \(0.539944\pi\) | |||||||
\(824\) | −9.31950 | −0.324660 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.1033 | 0.595099 | ||||||||
\(827\) | 34.6127 | 1.20360 | 0.601801 | − | 0.798646i | \(-0.294450\pi\) | ||||
0.601801 | + | 0.798646i | \(0.294450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.3225 | −0.740561 | −0.370281 | − | 0.928920i | \(-0.620738\pi\) | ||||
−0.370281 | + | 0.928920i | \(0.620738\pi\) | |||||||
\(830\) | 1.82730 | 0.0634266 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.86299 | −0.133925 | ||||||||
\(833\) | 68.3728 | 2.36898 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.86299 | −0.202897 | ||||||||
\(836\) | −15.1181 | −0.522870 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.70318 | −0.231557 | ||||||||
\(839\) | 38.1267 | 1.31628 | 0.658139 | − | 0.752896i | \(-0.271344\pi\) | ||||
0.658139 | + | 0.752896i | \(0.271344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8594 | −0.995151 | ||||||||
\(842\) | 11.1208 | 0.383249 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.3594 | −0.597536 | ||||||||
\(845\) | 1.92272 | 0.0661435 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.3622 | 1.00890 | ||||||||
\(848\) | −0.861339 | −0.0295785 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.23800 | 0.213962 | ||||||||
\(851\) | 5.86299 | 0.200981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8306 | 0.884423 | 0.442212 | − | 0.896911i | \(-0.354194\pi\) | ||||
0.442212 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(854\) | −17.4710 | −0.597847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.11297 | 0.174758 | ||||||||
\(857\) | 39.5354 | 1.35050 | 0.675252 | − | 0.737587i | \(-0.264035\pi\) | ||||
0.675252 | + | 0.737587i | \(0.264035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.9118 | −1.66885 | −0.834424 | − | 0.551122i | \(-0.814200\pi\) | ||||
−0.834424 | + | 0.551122i | \(0.814200\pi\) | |||||||
\(860\) | 8.72433 | 0.297497 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.7035 | 0.909523 | ||||||||
\(863\) | 33.7426 | 1.14861 | 0.574305 | − | 0.818641i | \(-0.305272\pi\) | ||||
0.574305 | + | 0.818641i | \(0.305272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.36138 | 0.0802895 | ||||||||
\(866\) | −3.38698 | −0.115094 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −40.1524 | −1.36286 | ||||||||
\(869\) | −24.6151 | −0.835009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.3326 | −1.63769 | ||||||||
\(872\) | 14.1808 | 0.480224 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −43.9267 | −1.48584 | ||||||||
\(875\) | −4.23800 | −0.143271 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.2829 | −1.39402 | −0.697012 | − | 0.717059i | \(-0.745488\pi\) | ||||
−0.697012 | + | 0.717059i | \(0.745488\pi\) | |||||||
\(878\) | −27.5847 | −0.930940 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.01784 | 0.0680215 | ||||||||
\(881\) | 53.0893 | 1.78862 | 0.894312 | − | 0.447443i | \(-0.147665\pi\) | ||||
0.894312 | + | 0.447443i | \(0.147665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6180 | 0.390976 | 0.195488 | − | 0.980706i | \(-0.437371\pi\) | ||||
0.195488 | + | 0.980706i | \(0.437371\pi\) | |||||||
\(884\) | −24.0974 | −0.810482 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.6474 | 0.525683 | ||||||||
\(887\) | −28.7458 | −0.965189 | −0.482595 | − | 0.875844i | \(-0.660306\pi\) | ||||
−0.482595 | + | 0.875844i | \(0.660306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.58394 | 0.0866627 | ||||||||
\(890\) | 13.0890 | 0.438745 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.652333 | 0.0218417 | ||||||||
\(893\) | −84.8080 | −2.83799 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.9247 | 0.465451 | ||||||||
\(896\) | −4.23800 | −0.141582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.6903 | −0.456851 | ||||||||
\(899\) | 3.55299 | 0.118499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.37304 | −0.179002 | ||||||||
\(902\) | 13.5687 | 0.451787 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.66068 | 0.121752 | ||||||||
\(905\) | −2.51170 | −0.0834917 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6046 | 0.816982 | 0.408491 | − | 0.912762i | \(-0.366055\pi\) | ||||
0.408491 | + | 0.912762i | \(0.366055\pi\) | |||||||
\(908\) | 10.1367 | 0.336398 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.3714 | 0.542706 | ||||||||
\(911\) | −41.3494 | −1.36997 | −0.684983 | − | 0.728559i | \(-0.740191\pi\) | ||||
−0.684983 | + | 0.728559i | \(0.740191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.68722 | 0.122029 | ||||||||
\(914\) | 4.66324 | 0.154246 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.1747 | −0.864838 | ||||||||
\(917\) | 88.6435 | 2.92727 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.8444 | 1.64422 | 0.822108 | − | 0.569332i | \(-0.192798\pi\) | ||||
0.822108 | + | 0.569332i | \(0.192798\pi\) | |||||||
\(920\) | 5.86299 | 0.193297 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.8048 | −0.751035 | ||||||||
\(923\) | 54.8494 | 1.80539 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 15.8551 | 0.521033 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.375011 | 0.0123103 | ||||||||
\(929\) | 15.1440 | 0.496859 | 0.248429 | − | 0.968650i | \(-0.420086\pi\) | ||||
0.248429 | + | 0.968650i | \(0.420086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −82.1196 | −2.69136 | ||||||||
\(932\) | 27.0812 | 0.887074 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.2841 | −0.892763 | ||||||||
\(935\) | 12.5873 | 0.411650 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.2735 | −1.08700 | −0.543498 | − | 0.839410i | \(-0.682901\pi\) | ||||
−0.543498 | + | 0.839410i | \(0.682901\pi\) | |||||||
\(938\) | −53.0246 | −1.73132 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.3195 | 0.369201 | ||||||||
\(941\) | −47.6286 | −1.55265 | −0.776323 | − | 0.630335i | \(-0.782918\pi\) | ||||
−0.776323 | + | 0.630335i | \(0.782918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.4247 | 1.28385 | ||||||||
\(944\) | −4.03569 | −0.131351 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.6044 | 0.572367 | ||||||||
\(947\) | 20.6366 | 0.670601 | 0.335300 | − | 0.942111i | \(-0.391162\pi\) | ||||
0.335300 | + | 0.942111i | \(0.391162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0646 | 1.30055 | ||||||||
\(950\) | −7.49220 | −0.243079 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.4367 | −0.856818 | ||||||||
\(953\) | 22.8435 | 0.739973 | 0.369987 | − | 0.929037i | \(-0.379362\pi\) | ||||
0.369987 | + | 0.929037i | \(0.379362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.6867 | −0.831201 | ||||||||
\(956\) | −12.3426 | −0.399189 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.3033 | −1.23752 | ||||||||
\(959\) | 12.2020 | 0.394023 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.7634 | 1.89559 | ||||||||
\(962\) | −3.86299 | −0.124548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.5000 | 0.402596 | ||||||||
\(965\) | −6.03384 | −0.194236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0934721 | 0.00300586 | 0.00150293 | − | 0.999999i | \(-0.499522\pi\) | ||||
0.00150293 | + | 0.999999i | \(0.499522\pi\) | |||||||
\(968\) | −6.92830 | −0.222684 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.59517 | 0.211758 | ||||||||
\(971\) | 34.5628 | 1.10917 | 0.554586 | − | 0.832126i | \(-0.312877\pi\) | ||||
0.554586 | + | 0.832126i | \(0.312877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.2121 | 2.15472 | ||||||||
\(974\) | 7.66820 | 0.245705 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.12247 | 0.131957 | ||||||||
\(977\) | −61.6264 | −1.97160 | −0.985802 | − | 0.167915i | \(-0.946297\pi\) | ||||
−0.985802 | + | 0.167915i | \(0.946297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.4116 | 0.844119 | ||||||||
\(980\) | 10.9607 | 0.350126 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.1786 | 1.34597 | ||||||||
\(983\) | −6.38987 | −0.203805 | −0.101903 | − | 0.994794i | \(-0.532493\pi\) | ||||
−0.101903 | + | 0.994794i | \(0.532493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3747 | 0.712917 | ||||||||
\(986\) | 2.33932 | 0.0744992 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.9423 | 0.920778 | ||||||||
\(989\) | 51.1507 | 1.62650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0777 | −0.764852 | −0.382426 | − | 0.923986i | \(-0.624911\pi\) | ||||
−0.382426 | + | 0.923986i | \(0.624911\pi\) | |||||||
\(992\) | 9.47436 | 0.300811 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 60.1741 | 1.90861 | ||||||||
\(995\) | −18.1663 | −0.575911 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.1397 | 1.58794 | 0.793970 | − | 0.607957i | \(-0.208011\pi\) | ||||
0.793970 | + | 0.607957i | \(0.208011\pi\) | |||||||
\(998\) | −4.70318 | −0.148877 | ||||||||
\(999\) | 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.1.1 | yes | 5 | |
3.2 | odd | 2 | 3330.2.a.bk.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3330.2.a.bk.1.1 | ✓ | 5 | 3.2 | odd | 2 | ||
3330.2.a.bl.1.1 | yes | 5 | 1.1 | even | 1 | trivial |