Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.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: | \(29.9439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.61803 | −0.989524 | −0.494762 | − | 0.869029i | \(-0.664745\pi\) | ||||
−0.494762 | + | 0.869029i | \(0.664745\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.61803 | 1.09088 | 0.545439 | − | 0.838150i | \(-0.316363\pi\) | ||||
0.545439 | + | 0.838150i | \(0.316363\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.47214 | 1.79505 | 0.897524 | − | 0.440966i | \(-0.145364\pi\) | ||||
0.897524 | + | 0.440966i | \(0.145364\pi\) | |||||||
\(14\) | 2.61803 | 0.699699 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.23607 | −0.299791 | −0.149895 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149895 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −5.70820 | −1.30955 | −0.654776 | − | 0.755823i | \(-0.727237\pi\) | ||||
−0.654776 | + | 0.755823i | \(0.727237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61803 | −0.571302 | ||||||||
\(22\) | −3.61803 | −0.771367 | ||||||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.47214 | −1.26929 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.61803 | −0.494762 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61803 | 1.18863 | 0.594317 | − | 0.804231i | \(-0.297422\pi\) | ||||
0.594317 | + | 0.804231i | \(0.297422\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.61803 | 0.629819 | ||||||||
\(34\) | 1.23607 | 0.211984 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 5.70820 | 0.925993 | ||||||||
\(39\) | 6.47214 | 1.03637 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.70820 | 0.891472 | 0.445736 | − | 0.895165i | \(-0.352942\pi\) | ||||
0.445736 | + | 0.895165i | \(0.352942\pi\) | |||||||
\(42\) | 2.61803 | 0.403971 | ||||||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | 3.61803 | 0.545439 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.47214 | 0.659380 | ||||||||
\(47\) | −1.70820 | −0.249167 | −0.124584 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124584 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | 6.47214 | 0.897524 | ||||||||
\(53\) | 2.09017 | 0.287107 | 0.143553 | − | 0.989643i | \(-0.454147\pi\) | ||||
0.143553 | + | 0.989643i | \(0.454147\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61803 | 0.349850 | ||||||||
\(57\) | −5.70820 | −0.756070 | ||||||||
\(58\) | −8.47214 | −1.11245 | ||||||||
\(59\) | −3.61803 | −0.471028 | −0.235514 | − | 0.971871i | \(-0.575677\pi\) | ||||
−0.235514 | + | 0.971871i | \(0.575677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76393 | 0.353885 | 0.176943 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176943 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(62\) | −6.61803 | −0.840491 | ||||||||
\(63\) | −2.61803 | −0.329841 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.61803 | −0.445349 | ||||||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | −4.47214 | −0.538382 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.52786 | 0.656037 | 0.328018 | − | 0.944671i | \(-0.393619\pi\) | ||||
0.328018 | + | 0.944671i | \(0.393619\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.52786 | −0.412905 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.70820 | −0.654776 | ||||||||
\(77\) | −9.47214 | −1.07945 | ||||||||
\(78\) | −6.47214 | −0.732825 | ||||||||
\(79\) | −5.61803 | −0.632078 | −0.316039 | − | 0.948746i | \(-0.602353\pi\) | ||||
−0.316039 | + | 0.948746i | \(0.602353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.70820 | −0.630366 | ||||||||
\(83\) | −2.14590 | −0.235543 | −0.117771 | − | 0.993041i | \(-0.537575\pi\) | ||||
−0.117771 | + | 0.993041i | \(0.537575\pi\) | |||||||
\(84\) | −2.61803 | −0.285651 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.70820 | −0.831197 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | −3.61803 | −0.385684 | ||||||||
\(89\) | 3.52786 | 0.373953 | 0.186976 | − | 0.982364i | \(-0.440131\pi\) | ||||
0.186976 | + | 0.982364i | \(0.440131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.9443 | −1.77624 | ||||||||
\(92\) | −4.47214 | −0.466252 | ||||||||
\(93\) | 6.61803 | 0.686258 | ||||||||
\(94\) | 1.70820 | 0.176188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.38197 | 0.343387 | 0.171693 | − | 0.985150i | \(-0.445076\pi\) | ||||
0.171693 | + | 0.985150i | \(0.445076\pi\) | |||||||
\(98\) | 0.145898 | 0.0147379 | ||||||||
\(99\) | 3.61803 | 0.363626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38197 | 0.436022 | 0.218011 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218011 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(102\) | 1.23607 | 0.122389 | ||||||||
\(103\) | −14.3262 | −1.41161 | −0.705803 | − | 0.708408i | \(-0.749414\pi\) | ||||
−0.705803 | + | 0.708408i | \(0.749414\pi\) | |||||||
\(104\) | −6.47214 | −0.634645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.09017 | −0.203015 | ||||||||
\(107\) | 11.6180 | 1.12316 | 0.561579 | − | 0.827423i | \(-0.310194\pi\) | ||||
0.561579 | + | 0.827423i | \(0.310194\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 17.2361 | 1.65092 | 0.825458 | − | 0.564464i | \(-0.190917\pi\) | ||||
0.825458 | + | 0.564464i | \(0.190917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | −2.61803 | −0.247381 | ||||||||
\(113\) | 19.2361 | 1.80958 | 0.904789 | − | 0.425861i | \(-0.140029\pi\) | ||||
0.904789 | + | 0.425861i | \(0.140029\pi\) | |||||||
\(114\) | 5.70820 | 0.534622 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.47214 | 0.786618 | ||||||||
\(117\) | 6.47214 | 0.598349 | ||||||||
\(118\) | 3.61803 | 0.333067 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | −2.76393 | −0.250235 | ||||||||
\(123\) | 5.70820 | 0.514691 | ||||||||
\(124\) | 6.61803 | 0.594317 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | −13.6180 | −1.20841 | −0.604203 | − | 0.796831i | \(-0.706508\pi\) | ||||
−0.604203 | + | 0.796831i | \(0.706508\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.70820 | 0.678670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.8885 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(132\) | 3.61803 | 0.314909 | ||||||||
\(133\) | 14.9443 | 1.29583 | ||||||||
\(134\) | −1.52786 | −0.131987 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.23607 | 0.105992 | ||||||||
\(137\) | 12.1803 | 1.04064 | 0.520318 | − | 0.853972i | \(-0.325813\pi\) | ||||
0.520318 | + | 0.853972i | \(0.325813\pi\) | |||||||
\(138\) | 4.47214 | 0.380693 | ||||||||
\(139\) | 10.4721 | 0.888235 | 0.444117 | − | 0.895969i | \(-0.353517\pi\) | ||||
0.444117 | + | 0.895969i | \(0.353517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.70820 | −0.143857 | ||||||||
\(142\) | −5.52786 | −0.463888 | ||||||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.52786 | 0.291968 | ||||||||
\(147\) | −0.145898 | −0.0120335 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 22.0902 | 1.80970 | 0.904849 | − | 0.425733i | \(-0.139984\pi\) | ||||
0.904849 | + | 0.425733i | \(0.139984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3262 | 1.49137 | 0.745684 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745684 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(152\) | 5.70820 | 0.462996 | ||||||||
\(153\) | −1.23607 | −0.0999302 | ||||||||
\(154\) | 9.47214 | 0.763286 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.47214 | 0.518186 | ||||||||
\(157\) | −8.65248 | −0.690543 | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||||
−0.345271 | + | 0.938503i | \(0.612213\pi\) | |||||||
\(158\) | 5.61803 | 0.446947 | ||||||||
\(159\) | 2.09017 | 0.165761 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.7082 | 0.922736 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 0.472136 | 0.0369805 | 0.0184903 | − | 0.999829i | \(-0.494114\pi\) | ||||
0.0184903 | + | 0.999829i | \(0.494114\pi\) | |||||||
\(164\) | 5.70820 | 0.445736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.14590 | 0.166554 | ||||||||
\(167\) | −11.7082 | −0.906008 | −0.453004 | − | 0.891508i | \(-0.649648\pi\) | ||||
−0.453004 | + | 0.891508i | \(0.649648\pi\) | |||||||
\(168\) | 2.61803 | 0.201986 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.70820 | −0.436517 | ||||||||
\(172\) | 7.70820 | 0.587745 | ||||||||
\(173\) | −5.09017 | −0.386998 | −0.193499 | − | 0.981100i | \(-0.561984\pi\) | ||||
−0.193499 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(174\) | −8.47214 | −0.642271 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.61803 | 0.272720 | ||||||||
\(177\) | −3.61803 | −0.271948 | ||||||||
\(178\) | −3.52786 | −0.264425 | ||||||||
\(179\) | 9.85410 | 0.736530 | 0.368265 | − | 0.929721i | \(-0.379952\pi\) | ||||
0.368265 | + | 0.929721i | \(0.379952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.65248 | −0.494475 | −0.247237 | − | 0.968955i | \(-0.579523\pi\) | ||||
−0.247237 | + | 0.968955i | \(0.579523\pi\) | |||||||
\(182\) | 16.9443 | 1.25599 | ||||||||
\(183\) | 2.76393 | 0.204316 | ||||||||
\(184\) | 4.47214 | 0.329690 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.61803 | −0.485258 | ||||||||
\(187\) | −4.47214 | −0.327035 | ||||||||
\(188\) | −1.70820 | −0.124584 | ||||||||
\(189\) | −2.61803 | −0.190434 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.29180 | 0.310543 | 0.155272 | − | 0.987872i | \(-0.450375\pi\) | ||||
0.155272 | + | 0.987872i | \(0.450375\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −17.8541 | −1.28517 | −0.642583 | − | 0.766216i | \(-0.722137\pi\) | ||||
−0.642583 | + | 0.766216i | \(0.722137\pi\) | |||||||
\(194\) | −3.38197 | −0.242811 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.145898 | −0.0104213 | ||||||||
\(197\) | 17.0902 | 1.21762 | 0.608812 | − | 0.793314i | \(-0.291646\pi\) | ||||
0.608812 | + | 0.793314i | \(0.291646\pi\) | |||||||
\(198\) | −3.61803 | −0.257122 | ||||||||
\(199\) | 19.5066 | 1.38278 | 0.691392 | − | 0.722480i | \(-0.256998\pi\) | ||||
0.691392 | + | 0.722480i | \(0.256998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52786 | 0.107767 | ||||||||
\(202\) | −4.38197 | −0.308314 | ||||||||
\(203\) | −22.1803 | −1.55675 | ||||||||
\(204\) | −1.23607 | −0.0865421 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.3262 | 0.998156 | ||||||||
\(207\) | −4.47214 | −0.310835 | ||||||||
\(208\) | 6.47214 | 0.448762 | ||||||||
\(209\) | −20.6525 | −1.42856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.41641 | −0.235195 | −0.117598 | − | 0.993061i | \(-0.537519\pi\) | ||||
−0.117598 | + | 0.993061i | \(0.537519\pi\) | |||||||
\(212\) | 2.09017 | 0.143553 | ||||||||
\(213\) | 5.52786 | 0.378763 | ||||||||
\(214\) | −11.6180 | −0.794192 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −17.3262 | −1.17618 | ||||||||
\(218\) | −17.2361 | −1.16737 | ||||||||
\(219\) | −3.52786 | −0.238391 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 8.00000 | 0.536925 | ||||||||
\(223\) | 8.09017 | 0.541758 | 0.270879 | − | 0.962613i | \(-0.412686\pi\) | ||||
0.270879 | + | 0.962613i | \(0.412686\pi\) | |||||||
\(224\) | 2.61803 | 0.174925 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.2361 | −1.27956 | ||||||||
\(227\) | 22.2705 | 1.47815 | 0.739073 | − | 0.673626i | \(-0.235264\pi\) | ||||
0.739073 | + | 0.673626i | \(0.235264\pi\) | |||||||
\(228\) | −5.70820 | −0.378035 | ||||||||
\(229\) | −5.52786 | −0.365292 | −0.182646 | − | 0.983179i | \(-0.558466\pi\) | ||||
−0.182646 | + | 0.983179i | \(0.558466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.47214 | −0.623221 | ||||||||
\(232\) | −8.47214 | −0.556223 | ||||||||
\(233\) | −18.6525 | −1.22196 | −0.610982 | − | 0.791644i | \(-0.709225\pi\) | ||||
−0.610982 | + | 0.791644i | \(0.709225\pi\) | |||||||
\(234\) | −6.47214 | −0.423097 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.61803 | −0.235514 | ||||||||
\(237\) | −5.61803 | −0.364931 | ||||||||
\(238\) | −3.23607 | −0.209763 | ||||||||
\(239\) | 12.2918 | 0.795090 | 0.397545 | − | 0.917583i | \(-0.369862\pi\) | ||||
0.397545 | + | 0.917583i | \(0.369862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.56231 | 0.615962 | 0.307981 | − | 0.951392i | \(-0.400347\pi\) | ||||
0.307981 | + | 0.951392i | \(0.400347\pi\) | |||||||
\(242\) | −2.09017 | −0.134361 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.76393 | 0.176943 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.70820 | −0.363942 | ||||||||
\(247\) | −36.9443 | −2.35071 | ||||||||
\(248\) | −6.61803 | −0.420246 | ||||||||
\(249\) | −2.14590 | −0.135991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5623 | 0.856045 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(252\) | −2.61803 | −0.164921 | ||||||||
\(253\) | −16.1803 | −1.01725 | ||||||||
\(254\) | 13.6180 | 0.854471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | −7.70820 | −0.479892 | ||||||||
\(259\) | 20.9443 | 1.30141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.47214 | 0.524412 | ||||||||
\(262\) | 17.8885 | 1.10516 | ||||||||
\(263\) | 11.7082 | 0.721959 | 0.360979 | − | 0.932574i | \(-0.382442\pi\) | ||||
0.360979 | + | 0.932574i | \(0.382442\pi\) | |||||||
\(264\) | −3.61803 | −0.222675 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.9443 | −0.916292 | ||||||||
\(267\) | 3.52786 | 0.215902 | ||||||||
\(268\) | 1.52786 | 0.0933292 | ||||||||
\(269\) | −9.09017 | −0.554237 | −0.277119 | − | 0.960836i | \(-0.589380\pi\) | ||||
−0.277119 | + | 0.960836i | \(0.589380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0344 | −1.09551 | −0.547757 | − | 0.836637i | \(-0.684518\pi\) | ||||
−0.547757 | + | 0.836637i | \(0.684518\pi\) | |||||||
\(272\) | −1.23607 | −0.0749476 | ||||||||
\(273\) | −16.9443 | −1.02551 | ||||||||
\(274\) | −12.1803 | −0.735841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | −16.9443 | −1.01808 | −0.509041 | − | 0.860742i | \(-0.670000\pi\) | ||||
−0.509041 | + | 0.860742i | \(0.670000\pi\) | |||||||
\(278\) | −10.4721 | −0.628077 | ||||||||
\(279\) | 6.61803 | 0.396211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.88854 | 0.351281 | 0.175641 | − | 0.984454i | \(-0.443800\pi\) | ||||
0.175641 | + | 0.984454i | \(0.443800\pi\) | |||||||
\(282\) | 1.70820 | 0.101722 | ||||||||
\(283\) | −4.58359 | −0.272466 | −0.136233 | − | 0.990677i | \(-0.543500\pi\) | ||||
−0.136233 | + | 0.990677i | \(0.543500\pi\) | |||||||
\(284\) | 5.52786 | 0.328018 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.4164 | −1.38464 | ||||||||
\(287\) | −14.9443 | −0.882132 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.4721 | −0.910126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.38197 | 0.198254 | ||||||||
\(292\) | −3.52786 | −0.206453 | ||||||||
\(293\) | 22.0902 | 1.29052 | 0.645261 | − | 0.763962i | \(-0.276749\pi\) | ||||
0.645261 | + | 0.763962i | \(0.276749\pi\) | |||||||
\(294\) | 0.145898 | 0.00850895 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.00000 | 0.464991 | ||||||||
\(297\) | 3.61803 | 0.209940 | ||||||||
\(298\) | −22.0902 | −1.27965 | ||||||||
\(299\) | −28.9443 | −1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1803 | −1.16318 | ||||||||
\(302\) | −18.3262 | −1.05456 | ||||||||
\(303\) | 4.38197 | 0.251737 | ||||||||
\(304\) | −5.70820 | −0.327388 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.23607 | 0.0706613 | ||||||||
\(307\) | −10.0000 | −0.570730 | −0.285365 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285365 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(308\) | −9.47214 | −0.539725 | ||||||||
\(309\) | −14.3262 | −0.814991 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.05573 | −0.0598648 | −0.0299324 | − | 0.999552i | \(-0.509529\pi\) | ||||
−0.0299324 | + | 0.999552i | \(0.509529\pi\) | |||||||
\(312\) | −6.47214 | −0.366413 | ||||||||
\(313\) | 16.2705 | 0.919664 | 0.459832 | − | 0.888006i | \(-0.347910\pi\) | ||||
0.459832 | + | 0.888006i | \(0.347910\pi\) | |||||||
\(314\) | 8.65248 | 0.488287 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.61803 | −0.316039 | ||||||||
\(317\) | 20.5623 | 1.15489 | 0.577447 | − | 0.816428i | \(-0.304049\pi\) | ||||
0.577447 | + | 0.816428i | \(0.304049\pi\) | |||||||
\(318\) | −2.09017 | −0.117211 | ||||||||
\(319\) | 30.6525 | 1.71621 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6180 | 0.648455 | ||||||||
\(322\) | −11.7082 | −0.652473 | ||||||||
\(323\) | 7.05573 | 0.392591 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.472136 | −0.0261492 | ||||||||
\(327\) | 17.2361 | 0.953157 | ||||||||
\(328\) | −5.70820 | −0.315183 | ||||||||
\(329\) | 4.47214 | 0.246557 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0000 | −0.989369 | −0.494685 | − | 0.869072i | \(-0.664716\pi\) | ||||
−0.494685 | + | 0.869072i | \(0.664716\pi\) | |||||||
\(332\) | −2.14590 | −0.117771 | ||||||||
\(333\) | −8.00000 | −0.438397 | ||||||||
\(334\) | 11.7082 | 0.640644 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.61803 | −0.142825 | ||||||||
\(337\) | −0.909830 | −0.0495616 | −0.0247808 | − | 0.999693i | \(-0.507889\pi\) | ||||
−0.0247808 | + | 0.999693i | \(0.507889\pi\) | |||||||
\(338\) | −28.8885 | −1.57133 | ||||||||
\(339\) | 19.2361 | 1.04476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.9443 | 1.29666 | ||||||||
\(342\) | 5.70820 | 0.308664 | ||||||||
\(343\) | 18.7082 | 1.01015 | ||||||||
\(344\) | −7.70820 | −0.415599 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.09017 | 0.273649 | ||||||||
\(347\) | −20.5623 | −1.10384 | −0.551921 | − | 0.833896i | \(-0.686105\pi\) | ||||
−0.551921 | + | 0.833896i | \(0.686105\pi\) | |||||||
\(348\) | 8.47214 | 0.454154 | ||||||||
\(349\) | −27.8885 | −1.49284 | −0.746420 | − | 0.665475i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665475i | \(0.768229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.47214 | 0.345457 | ||||||||
\(352\) | −3.61803 | −0.192842 | ||||||||
\(353\) | 13.2361 | 0.704485 | 0.352242 | − | 0.935909i | \(-0.385419\pi\) | ||||
0.352242 | + | 0.935909i | \(0.385419\pi\) | |||||||
\(354\) | 3.61803 | 0.192296 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.52786 | 0.186976 | ||||||||
\(357\) | 3.23607 | 0.171271 | ||||||||
\(358\) | −9.85410 | −0.520805 | ||||||||
\(359\) | 22.1803 | 1.17063 | 0.585317 | − | 0.810805i | \(-0.300970\pi\) | ||||
0.585317 | + | 0.810805i | \(0.300970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5836 | 0.714926 | ||||||||
\(362\) | 6.65248 | 0.349646 | ||||||||
\(363\) | 2.09017 | 0.109705 | ||||||||
\(364\) | −16.9443 | −0.888121 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.76393 | −0.144473 | ||||||||
\(367\) | 30.6180 | 1.59825 | 0.799124 | − | 0.601166i | \(-0.205297\pi\) | ||||
0.799124 | + | 0.601166i | \(0.205297\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | 5.70820 | 0.297157 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.47214 | −0.284099 | ||||||||
\(372\) | 6.61803 | 0.343129 | ||||||||
\(373\) | 11.5279 | 0.596890 | 0.298445 | − | 0.954427i | \(-0.403532\pi\) | ||||
0.298445 | + | 0.954427i | \(0.403532\pi\) | |||||||
\(374\) | 4.47214 | 0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.70820 | 0.0880939 | ||||||||
\(377\) | 54.8328 | 2.82403 | ||||||||
\(378\) | 2.61803 | 0.134657 | ||||||||
\(379\) | −20.1803 | −1.03659 | −0.518297 | − | 0.855201i | \(-0.673434\pi\) | ||||
−0.518297 | + | 0.855201i | \(0.673434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6180 | −0.697673 | ||||||||
\(382\) | −4.29180 | −0.219587 | ||||||||
\(383\) | 20.0000 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.8541 | 0.908750 | ||||||||
\(387\) | 7.70820 | 0.391830 | ||||||||
\(388\) | 3.38197 | 0.171693 | ||||||||
\(389\) | −12.3820 | −0.627791 | −0.313895 | − | 0.949458i | \(-0.601634\pi\) | ||||
−0.313895 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.52786 | 0.279556 | ||||||||
\(392\) | 0.145898 | 0.00736896 | ||||||||
\(393\) | −17.8885 | −0.902358 | ||||||||
\(394\) | −17.0902 | −0.860990 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.61803 | 0.181813 | ||||||||
\(397\) | 30.7639 | 1.54400 | 0.771999 | − | 0.635624i | \(-0.219257\pi\) | ||||
0.771999 | + | 0.635624i | \(0.219257\pi\) | |||||||
\(398\) | −19.5066 | −0.977776 | ||||||||
\(399\) | 14.9443 | 0.748149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.7082 | 1.28381 | 0.641903 | − | 0.766786i | \(-0.278145\pi\) | ||||
0.641903 | + | 0.766786i | \(0.278145\pi\) | |||||||
\(402\) | −1.52786 | −0.0762029 | ||||||||
\(403\) | 42.8328 | 2.13365 | ||||||||
\(404\) | 4.38197 | 0.218011 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.1803 | 1.10079 | ||||||||
\(407\) | −28.9443 | −1.43471 | ||||||||
\(408\) | 1.23607 | 0.0611945 | ||||||||
\(409\) | 5.79837 | 0.286711 | 0.143356 | − | 0.989671i | \(-0.454211\pi\) | ||||
0.143356 | + | 0.989671i | \(0.454211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.1803 | 0.600812 | ||||||||
\(412\) | −14.3262 | −0.705803 | ||||||||
\(413\) | 9.47214 | 0.466093 | ||||||||
\(414\) | 4.47214 | 0.219793 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.47214 | −0.317323 | ||||||||
\(417\) | 10.4721 | 0.512823 | ||||||||
\(418\) | 20.6525 | 1.01015 | ||||||||
\(419\) | −3.09017 | −0.150965 | −0.0754823 | − | 0.997147i | \(-0.524050\pi\) | ||||
−0.0754823 | + | 0.997147i | \(0.524050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7639 | −1.10945 | −0.554723 | − | 0.832035i | \(-0.687176\pi\) | ||||
−0.554723 | + | 0.832035i | \(0.687176\pi\) | |||||||
\(422\) | 3.41641 | 0.166308 | ||||||||
\(423\) | −1.70820 | −0.0830557 | ||||||||
\(424\) | −2.09017 | −0.101508 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.52786 | −0.267826 | ||||||||
\(427\) | −7.23607 | −0.350178 | ||||||||
\(428\) | 11.6180 | 0.561579 | ||||||||
\(429\) | 23.4164 | 1.13055 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8328 | 0.810808 | 0.405404 | − | 0.914138i | \(-0.367131\pi\) | ||||
0.405404 | + | 0.914138i | \(0.367131\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −15.5066 | −0.745199 | −0.372599 | − | 0.927992i | \(-0.621533\pi\) | ||||
−0.372599 | + | 0.927992i | \(0.621533\pi\) | |||||||
\(434\) | 17.3262 | 0.831686 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.2361 | 0.825458 | ||||||||
\(437\) | 25.5279 | 1.22116 | ||||||||
\(438\) | 3.52786 | 0.168568 | ||||||||
\(439\) | −23.5066 | −1.12191 | −0.560954 | − | 0.827847i | \(-0.689566\pi\) | ||||
−0.560954 | + | 0.827847i | \(0.689566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.145898 | −0.00694753 | ||||||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −16.6180 | −0.789547 | −0.394773 | − | 0.918779i | \(-0.629177\pi\) | ||||
−0.394773 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(444\) | −8.00000 | −0.379663 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.09017 | −0.383081 | ||||||||
\(447\) | 22.0902 | 1.04483 | ||||||||
\(448\) | −2.61803 | −0.123690 | ||||||||
\(449\) | −27.7082 | −1.30763 | −0.653815 | − | 0.756654i | \(-0.726833\pi\) | ||||
−0.653815 | + | 0.756654i | \(0.726833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6525 | 0.972487 | ||||||||
\(452\) | 19.2361 | 0.904789 | ||||||||
\(453\) | 18.3262 | 0.861042 | ||||||||
\(454\) | −22.2705 | −1.04521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70820 | 0.267311 | ||||||||
\(457\) | 4.09017 | 0.191330 | 0.0956650 | − | 0.995414i | \(-0.469502\pi\) | ||||
0.0956650 | + | 0.995414i | \(0.469502\pi\) | |||||||
\(458\) | 5.52786 | 0.258300 | ||||||||
\(459\) | −1.23607 | −0.0576947 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.56231 | 0.352212 | 0.176106 | − | 0.984371i | \(-0.443650\pi\) | ||||
0.176106 | + | 0.984371i | \(0.443650\pi\) | |||||||
\(462\) | 9.47214 | 0.440684 | ||||||||
\(463\) | 22.8328 | 1.06113 | 0.530565 | − | 0.847644i | \(-0.321980\pi\) | ||||
0.530565 | + | 0.847644i | \(0.321980\pi\) | |||||||
\(464\) | 8.47214 | 0.393309 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.6525 | 0.864059 | ||||||||
\(467\) | −10.6738 | −0.493923 | −0.246961 | − | 0.969025i | \(-0.579432\pi\) | ||||
−0.246961 | + | 0.969025i | \(0.579432\pi\) | |||||||
\(468\) | 6.47214 | 0.299175 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.65248 | −0.398685 | ||||||||
\(472\) | 3.61803 | 0.166534 | ||||||||
\(473\) | 27.8885 | 1.28232 | ||||||||
\(474\) | 5.61803 | 0.258045 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.23607 | 0.148325 | ||||||||
\(477\) | 2.09017 | 0.0957023 | ||||||||
\(478\) | −12.2918 | −0.562214 | ||||||||
\(479\) | −29.1246 | −1.33074 | −0.665369 | − | 0.746515i | \(-0.731726\pi\) | ||||
−0.665369 | + | 0.746515i | \(0.731726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.7771 | −2.36083 | ||||||||
\(482\) | −9.56231 | −0.435551 | ||||||||
\(483\) | 11.7082 | 0.532742 | ||||||||
\(484\) | 2.09017 | 0.0950077 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.7984 | −0.806521 | −0.403261 | − | 0.915085i | \(-0.632123\pi\) | ||||
−0.403261 | + | 0.915085i | \(0.632123\pi\) | |||||||
\(488\) | −2.76393 | −0.125117 | ||||||||
\(489\) | 0.472136 | 0.0213507 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.2705 | −1.14044 | −0.570221 | − | 0.821491i | \(-0.693142\pi\) | ||||
−0.570221 | + | 0.821491i | \(0.693142\pi\) | |||||||
\(492\) | 5.70820 | 0.257346 | ||||||||
\(493\) | −10.4721 | −0.471641 | ||||||||
\(494\) | 36.9443 | 1.66220 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.61803 | 0.297158 | ||||||||
\(497\) | −14.4721 | −0.649164 | ||||||||
\(498\) | 2.14590 | 0.0961600 | ||||||||
\(499\) | 35.5967 | 1.59353 | 0.796765 | − | 0.604290i | \(-0.206543\pi\) | ||||
0.796765 | + | 0.604290i | \(0.206543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7082 | −0.523084 | ||||||||
\(502\) | −13.5623 | −0.605315 | ||||||||
\(503\) | −23.8885 | −1.06514 | −0.532569 | − | 0.846387i | \(-0.678773\pi\) | ||||
−0.532569 | + | 0.846387i | \(0.678773\pi\) | |||||||
\(504\) | 2.61803 | 0.116617 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.1803 | 0.719304 | ||||||||
\(507\) | 28.8885 | 1.28299 | ||||||||
\(508\) | −13.6180 | −0.604203 | ||||||||
\(509\) | −17.5066 | −0.775965 | −0.387983 | − | 0.921667i | \(-0.626828\pi\) | ||||
−0.387983 | + | 0.921667i | \(0.626828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.23607 | 0.408580 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.70820 | −0.252023 | ||||||||
\(514\) | −22.0000 | −0.970378 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.70820 | 0.339335 | ||||||||
\(517\) | −6.18034 | −0.271811 | ||||||||
\(518\) | −20.9443 | −0.920238 | ||||||||
\(519\) | −5.09017 | −0.223434 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1803 | 0.621252 | 0.310626 | − | 0.950532i | \(-0.399461\pi\) | ||||
0.310626 | + | 0.950532i | \(0.399461\pi\) | |||||||
\(522\) | −8.47214 | −0.370815 | ||||||||
\(523\) | −11.0557 | −0.483433 | −0.241717 | − | 0.970347i | \(-0.577710\pi\) | ||||
−0.241717 | + | 0.970347i | \(0.577710\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.7082 | −0.510502 | ||||||||
\(527\) | −8.18034 | −0.356341 | ||||||||
\(528\) | 3.61803 | 0.157455 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.61803 | −0.157009 | ||||||||
\(532\) | 14.9443 | 0.647916 | ||||||||
\(533\) | 36.9443 | 1.60023 | ||||||||
\(534\) | −3.52786 | −0.152666 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.52786 | −0.0659937 | ||||||||
\(537\) | 9.85410 | 0.425236 | ||||||||
\(538\) | 9.09017 | 0.391905 | ||||||||
\(539\) | −0.527864 | −0.0227367 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.1803 | −1.12558 | −0.562790 | − | 0.826600i | \(-0.690272\pi\) | ||||
−0.562790 | + | 0.826600i | \(0.690272\pi\) | |||||||
\(542\) | 18.0344 | 0.774646 | ||||||||
\(543\) | −6.65248 | −0.285485 | ||||||||
\(544\) | 1.23607 | 0.0529960 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.9443 | 0.725148 | ||||||||
\(547\) | −9.70820 | −0.415093 | −0.207546 | − | 0.978225i | \(-0.566548\pi\) | ||||
−0.207546 | + | 0.978225i | \(0.566548\pi\) | |||||||
\(548\) | 12.1803 | 0.520318 | ||||||||
\(549\) | 2.76393 | 0.117962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.3607 | −2.06023 | ||||||||
\(552\) | 4.47214 | 0.190347 | ||||||||
\(553\) | 14.7082 | 0.625456 | ||||||||
\(554\) | 16.9443 | 0.719893 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.4721 | 0.444117 | ||||||||
\(557\) | 18.3262 | 0.776508 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(558\) | −6.61803 | −0.280164 | ||||||||
\(559\) | 49.8885 | 2.11006 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.47214 | −0.188814 | ||||||||
\(562\) | −5.88854 | −0.248393 | ||||||||
\(563\) | −21.2705 | −0.896445 | −0.448223 | − | 0.893922i | \(-0.647943\pi\) | ||||
−0.448223 | + | 0.893922i | \(0.647943\pi\) | |||||||
\(564\) | −1.70820 | −0.0719284 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.58359 | 0.192663 | ||||||||
\(567\) | −2.61803 | −0.109947 | ||||||||
\(568\) | −5.52786 | −0.231944 | ||||||||
\(569\) | −27.7771 | −1.16448 | −0.582238 | − | 0.813018i | \(-0.697823\pi\) | ||||
−0.582238 | + | 0.813018i | \(0.697823\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.88854 | 0.330125 | 0.165063 | − | 0.986283i | \(-0.447217\pi\) | ||||
0.165063 | + | 0.986283i | \(0.447217\pi\) | |||||||
\(572\) | 23.4164 | 0.979089 | ||||||||
\(573\) | 4.29180 | 0.179292 | ||||||||
\(574\) | 14.9443 | 0.623762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.97871 | −0.373789 | −0.186894 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186894 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(578\) | 15.4721 | 0.643556 | ||||||||
\(579\) | −17.8541 | −0.741991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.61803 | 0.233075 | ||||||||
\(582\) | −3.38197 | −0.140187 | ||||||||
\(583\) | 7.56231 | 0.313199 | ||||||||
\(584\) | 3.52786 | 0.145984 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.0902 | −0.912537 | ||||||||
\(587\) | 0.965558 | 0.0398528 | 0.0199264 | − | 0.999801i | \(-0.493657\pi\) | ||||
0.0199264 | + | 0.999801i | \(0.493657\pi\) | |||||||
\(588\) | −0.145898 | −0.00601673 | ||||||||
\(589\) | −37.7771 | −1.55658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.0902 | 0.702996 | ||||||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −3.61803 | −0.148450 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.0902 | 0.904849 | ||||||||
\(597\) | 19.5066 | 0.798351 | ||||||||
\(598\) | 28.9443 | 1.18362 | ||||||||
\(599\) | 0.472136 | 0.0192910 | 0.00964548 | − | 0.999953i | \(-0.496930\pi\) | ||||
0.00964548 | + | 0.999953i | \(0.496930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.72949 | −0.315292 | −0.157646 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157646 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(602\) | 20.1803 | 0.822489 | ||||||||
\(603\) | 1.52786 | 0.0622194 | ||||||||
\(604\) | 18.3262 | 0.745684 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.38197 | −0.178005 | ||||||||
\(607\) | −6.56231 | −0.266356 | −0.133178 | − | 0.991092i | \(-0.542518\pi\) | ||||
−0.133178 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(608\) | 5.70820 | 0.231498 | ||||||||
\(609\) | −22.1803 | −0.898793 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0557 | −0.447267 | ||||||||
\(612\) | −1.23607 | −0.0499651 | ||||||||
\(613\) | −48.2492 | −1.94877 | −0.974384 | − | 0.224891i | \(-0.927797\pi\) | ||||
−0.974384 | + | 0.224891i | \(0.927797\pi\) | |||||||
\(614\) | 10.0000 | 0.403567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.47214 | 0.381643 | ||||||||
\(617\) | −2.11146 | −0.0850040 | −0.0425020 | − | 0.999096i | \(-0.513533\pi\) | ||||
−0.0425020 | + | 0.999096i | \(0.513533\pi\) | |||||||
\(618\) | 14.3262 | 0.576286 | ||||||||
\(619\) | −9.41641 | −0.378477 | −0.189239 | − | 0.981931i | \(-0.560602\pi\) | ||||
−0.189239 | + | 0.981931i | \(0.560602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.47214 | −0.179461 | ||||||||
\(622\) | 1.05573 | 0.0423308 | ||||||||
\(623\) | −9.23607 | −0.370035 | ||||||||
\(624\) | 6.47214 | 0.259093 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2705 | −0.650300 | ||||||||
\(627\) | −20.6525 | −0.824780 | ||||||||
\(628\) | −8.65248 | −0.345271 | ||||||||
\(629\) | 9.88854 | 0.394282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.4721 | 1.85003 | 0.925013 | − | 0.379935i | \(-0.124054\pi\) | ||||
0.925013 | + | 0.379935i | \(0.124054\pi\) | |||||||
\(632\) | 5.61803 | 0.223473 | ||||||||
\(633\) | −3.41641 | −0.135790 | ||||||||
\(634\) | −20.5623 | −0.816633 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.09017 | 0.0828806 | ||||||||
\(637\) | −0.944272 | −0.0374134 | ||||||||
\(638\) | −30.6525 | −1.21354 | ||||||||
\(639\) | 5.52786 | 0.218679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8197 | −0.545844 | −0.272922 | − | 0.962036i | \(-0.587990\pi\) | ||||
−0.272922 | + | 0.962036i | \(0.587990\pi\) | |||||||
\(642\) | −11.6180 | −0.458527 | ||||||||
\(643\) | −21.8885 | −0.863200 | −0.431600 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431600 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(644\) | 11.7082 | 0.461368 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.05573 | −0.277604 | ||||||||
\(647\) | 22.9443 | 0.902032 | 0.451016 | − | 0.892516i | \(-0.351062\pi\) | ||||
0.451016 | + | 0.892516i | \(0.351062\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −13.0902 | −0.513834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3262 | −0.679069 | ||||||||
\(652\) | 0.472136 | 0.0184903 | ||||||||
\(653\) | 3.85410 | 0.150823 | 0.0754113 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754113 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(654\) | −17.2361 | −0.673984 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.70820 | 0.222868 | ||||||||
\(657\) | −3.52786 | −0.137635 | ||||||||
\(658\) | −4.47214 | −0.174342 | ||||||||
\(659\) | −20.6180 | −0.803165 | −0.401582 | − | 0.915823i | \(-0.631540\pi\) | ||||
−0.401582 | + | 0.915823i | \(0.631540\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.4721 | −1.18523 | −0.592614 | − | 0.805486i | \(-0.701904\pi\) | ||||
−0.592614 | + | 0.805486i | \(0.701904\pi\) | |||||||
\(662\) | 18.0000 | 0.699590 | ||||||||
\(663\) | −8.00000 | −0.310694 | ||||||||
\(664\) | 2.14590 | 0.0832770 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | −37.8885 | −1.46705 | ||||||||
\(668\) | −11.7082 | −0.453004 | ||||||||
\(669\) | 8.09017 | 0.312784 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 2.61803 | 0.100993 | ||||||||
\(673\) | 31.4508 | 1.21234 | 0.606171 | − | 0.795335i | \(-0.292705\pi\) | ||||
0.606171 | + | 0.795335i | \(0.292705\pi\) | |||||||
\(674\) | 0.909830 | 0.0350453 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | −29.0902 | −1.11803 | −0.559013 | − | 0.829159i | \(-0.688820\pi\) | ||||
−0.559013 | + | 0.829159i | \(0.688820\pi\) | |||||||
\(678\) | −19.2361 | −0.738757 | ||||||||
\(679\) | −8.85410 | −0.339789 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.2705 | 0.853408 | ||||||||
\(682\) | −23.9443 | −0.916874 | ||||||||
\(683\) | −33.5066 | −1.28209 | −0.641047 | − | 0.767502i | \(-0.721500\pi\) | ||||
−0.641047 | + | 0.767502i | \(0.721500\pi\) | |||||||
\(684\) | −5.70820 | −0.218259 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.7082 | −0.714283 | ||||||||
\(687\) | −5.52786 | −0.210901 | ||||||||
\(688\) | 7.70820 | 0.293873 | ||||||||
\(689\) | 13.5279 | 0.515371 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2361 | 0.427440 | 0.213720 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213720 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(692\) | −5.09017 | −0.193499 | ||||||||
\(693\) | −9.47214 | −0.359817 | ||||||||
\(694\) | 20.5623 | 0.780534 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.47214 | −0.321135 | ||||||||
\(697\) | −7.05573 | −0.267255 | ||||||||
\(698\) | 27.8885 | 1.05560 | ||||||||
\(699\) | −18.6525 | −0.705501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8328 | 1.54223 | 0.771117 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771117 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(702\) | −6.47214 | −0.244275 | ||||||||
\(703\) | 45.6656 | 1.72231 | ||||||||
\(704\) | 3.61803 | 0.136360 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.2361 | −0.498146 | ||||||||
\(707\) | −11.4721 | −0.431454 | ||||||||
\(708\) | −3.61803 | −0.135974 | ||||||||
\(709\) | −43.7082 | −1.64150 | −0.820748 | − | 0.571290i | \(-0.806443\pi\) | ||||
−0.820748 | + | 0.571290i | \(0.806443\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.61803 | −0.210693 | ||||||||
\(712\) | −3.52786 | −0.132212 | ||||||||
\(713\) | −29.5967 | −1.10841 | ||||||||
\(714\) | −3.23607 | −0.121107 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.85410 | 0.368265 | ||||||||
\(717\) | 12.2918 | 0.459046 | ||||||||
\(718\) | −22.1803 | −0.827763 | ||||||||
\(719\) | −16.5836 | −0.618464 | −0.309232 | − | 0.950987i | \(-0.600072\pi\) | ||||
−0.309232 | + | 0.950987i | \(0.600072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.5066 | 1.39682 | ||||||||
\(722\) | −13.5836 | −0.505529 | ||||||||
\(723\) | 9.56231 | 0.355626 | ||||||||
\(724\) | −6.65248 | −0.247237 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.09017 | −0.0775735 | ||||||||
\(727\) | 8.58359 | 0.318348 | 0.159174 | − | 0.987251i | \(-0.449117\pi\) | ||||
0.159174 | + | 0.987251i | \(0.449117\pi\) | |||||||
\(728\) | 16.9443 | 0.627996 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.52786 | −0.352401 | ||||||||
\(732\) | 2.76393 | 0.102158 | ||||||||
\(733\) | 35.8885 | 1.32557 | 0.662787 | − | 0.748808i | \(-0.269374\pi\) | ||||
0.662787 | + | 0.748808i | \(0.269374\pi\) | |||||||
\(734\) | −30.6180 | −1.13013 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.47214 | 0.164845 | ||||||||
\(737\) | 5.52786 | 0.203621 | ||||||||
\(738\) | −5.70820 | −0.210122 | ||||||||
\(739\) | −48.1803 | −1.77234 | −0.886171 | − | 0.463358i | \(-0.846644\pi\) | ||||
−0.886171 | + | 0.463358i | \(0.846644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.9443 | −1.35718 | ||||||||
\(742\) | 5.47214 | 0.200888 | ||||||||
\(743\) | 39.0132 | 1.43125 | 0.715627 | − | 0.698483i | \(-0.246141\pi\) | ||||
0.715627 | + | 0.698483i | \(0.246141\pi\) | |||||||
\(744\) | −6.61803 | −0.242629 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.5279 | −0.422065 | ||||||||
\(747\) | −2.14590 | −0.0785143 | ||||||||
\(748\) | −4.47214 | −0.163517 | ||||||||
\(749\) | −30.4164 | −1.11139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7984 | 0.904906 | 0.452453 | − | 0.891788i | \(-0.350549\pi\) | ||||
0.452453 | + | 0.891788i | \(0.350549\pi\) | |||||||
\(752\) | −1.70820 | −0.0622918 | ||||||||
\(753\) | 13.5623 | 0.494238 | ||||||||
\(754\) | −54.8328 | −1.99689 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.61803 | −0.0952170 | ||||||||
\(757\) | 17.1246 | 0.622405 | 0.311202 | − | 0.950344i | \(-0.399268\pi\) | ||||
0.311202 | + | 0.950344i | \(0.399268\pi\) | |||||||
\(758\) | 20.1803 | 0.732983 | ||||||||
\(759\) | −16.1803 | −0.587309 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41641 | 0.0513447 | 0.0256724 | − | 0.999670i | \(-0.491827\pi\) | ||||
0.0256724 | + | 0.999670i | \(0.491827\pi\) | |||||||
\(762\) | 13.6180 | 0.493329 | ||||||||
\(763\) | −45.1246 | −1.63362 | ||||||||
\(764\) | 4.29180 | 0.155272 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0000 | −0.722629 | ||||||||
\(767\) | −23.4164 | −0.845517 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 24.6869 | 0.890233 | 0.445117 | − | 0.895473i | \(-0.353162\pi\) | ||||
0.445117 | + | 0.895473i | \(0.353162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | 0.792311 | ||||||||
\(772\) | −17.8541 | −0.642583 | ||||||||
\(773\) | 1.14590 | 0.0412151 | 0.0206075 | − | 0.999788i | \(-0.493440\pi\) | ||||
0.0206075 | + | 0.999788i | \(0.493440\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.38197 | −0.121406 | ||||||||
\(777\) | 20.9443 | 0.751372 | ||||||||
\(778\) | 12.3820 | 0.443915 | ||||||||
\(779\) | −32.5836 | −1.16743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | 0.715656 | ||||||||
\(782\) | −5.52786 | −0.197676 | ||||||||
\(783\) | 8.47214 | 0.302769 | ||||||||
\(784\) | −0.145898 | −0.00521064 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.8885 | 0.638063 | ||||||||
\(787\) | −28.0689 | −1.00055 | −0.500274 | − | 0.865867i | \(-0.666767\pi\) | ||||
−0.500274 | + | 0.865867i | \(0.666767\pi\) | |||||||
\(788\) | 17.0902 | 0.608812 | ||||||||
\(789\) | 11.7082 | 0.416823 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.3607 | −1.79062 | ||||||||
\(792\) | −3.61803 | −0.128561 | ||||||||
\(793\) | 17.8885 | 0.635241 | ||||||||
\(794\) | −30.7639 | −1.09177 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.5066 | 0.691392 | ||||||||
\(797\) | −1.50658 | −0.0533657 | −0.0266829 | − | 0.999644i | \(-0.508494\pi\) | ||||
−0.0266829 | + | 0.999644i | \(0.508494\pi\) | |||||||
\(798\) | −14.9443 | −0.529021 | ||||||||
\(799\) | 2.11146 | 0.0746979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.52786 | 0.124651 | ||||||||
\(802\) | −25.7082 | −0.907788 | ||||||||
\(803\) | −12.7639 | −0.450429 | ||||||||
\(804\) | 1.52786 | 0.0538836 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.8328 | −1.50872 | ||||||||
\(807\) | −9.09017 | −0.319989 | ||||||||
\(808\) | −4.38197 | −0.154157 | ||||||||
\(809\) | −30.8328 | −1.08402 | −0.542012 | − | 0.840371i | \(-0.682337\pi\) | ||||
−0.542012 | + | 0.840371i | \(0.682337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.70820 | −0.200442 | −0.100221 | − | 0.994965i | \(-0.531955\pi\) | ||||
−0.100221 | + | 0.994965i | \(0.531955\pi\) | |||||||
\(812\) | −22.1803 | −0.778377 | ||||||||
\(813\) | −18.0344 | −0.632495 | ||||||||
\(814\) | 28.9443 | 1.01450 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.23607 | −0.0432710 | ||||||||
\(817\) | −44.0000 | −1.53937 | ||||||||
\(818\) | −5.79837 | −0.202735 | ||||||||
\(819\) | −16.9443 | −0.592081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.0902 | −1.57366 | −0.786829 | − | 0.617171i | \(-0.788279\pi\) | ||||
−0.786829 | + | 0.617171i | \(0.788279\pi\) | |||||||
\(822\) | −12.1803 | −0.424838 | ||||||||
\(823\) | −2.96556 | −0.103373 | −0.0516864 | − | 0.998663i | \(-0.516460\pi\) | ||||
−0.0516864 | + | 0.998663i | \(0.516460\pi\) | |||||||
\(824\) | 14.3262 | 0.499078 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.47214 | −0.329578 | ||||||||
\(827\) | −44.1033 | −1.53362 | −0.766811 | − | 0.641872i | \(-0.778158\pi\) | ||||
−0.766811 | + | 0.641872i | \(0.778158\pi\) | |||||||
\(828\) | −4.47214 | −0.155417 | ||||||||
\(829\) | 25.8885 | 0.899146 | 0.449573 | − | 0.893244i | \(-0.351576\pi\) | ||||
0.449573 | + | 0.893244i | \(0.351576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9443 | −0.587790 | ||||||||
\(832\) | 6.47214 | 0.224381 | ||||||||
\(833\) | 0.180340 | 0.00624841 | ||||||||
\(834\) | −10.4721 | −0.362620 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.6525 | −0.714281 | ||||||||
\(837\) | 6.61803 | 0.228753 | ||||||||
\(838\) | 3.09017 | 0.106748 | ||||||||
\(839\) | 6.36068 | 0.219595 | 0.109798 | − | 0.993954i | \(-0.464980\pi\) | ||||
0.109798 | + | 0.993954i | \(0.464980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 22.7639 | 0.784497 | ||||||||
\(843\) | 5.88854 | 0.202812 | ||||||||
\(844\) | −3.41641 | −0.117598 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.70820 | 0.0587293 | ||||||||
\(847\) | −5.47214 | −0.188025 | ||||||||
\(848\) | 2.09017 | 0.0717767 | ||||||||
\(849\) | −4.58359 | −0.157308 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7771 | 1.22642 | ||||||||
\(852\) | 5.52786 | 0.189382 | ||||||||
\(853\) | 43.5967 | 1.49272 | 0.746362 | − | 0.665540i | \(-0.231799\pi\) | ||||
0.746362 | + | 0.665540i | \(0.231799\pi\) | |||||||
\(854\) | 7.23607 | 0.247613 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.6180 | −0.397096 | ||||||||
\(857\) | 16.0689 | 0.548903 | 0.274451 | − | 0.961601i | \(-0.411504\pi\) | ||||
0.274451 | + | 0.961601i | \(0.411504\pi\) | |||||||
\(858\) | −23.4164 | −0.799423 | ||||||||
\(859\) | −2.29180 | −0.0781951 | −0.0390975 | − | 0.999235i | \(-0.512448\pi\) | ||||
−0.0390975 | + | 0.999235i | \(0.512448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9443 | −0.509299 | ||||||||
\(862\) | −16.8328 | −0.573328 | ||||||||
\(863\) | 10.1803 | 0.346543 | 0.173271 | − | 0.984874i | \(-0.444566\pi\) | ||||
0.173271 | + | 0.984874i | \(0.444566\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.5066 | 0.526935 | ||||||||
\(867\) | −15.4721 | −0.525461 | ||||||||
\(868\) | −17.3262 | −0.588091 | ||||||||
\(869\) | −20.3262 | −0.689520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.88854 | 0.335061 | ||||||||
\(872\) | −17.2361 | −0.583687 | ||||||||
\(873\) | 3.38197 | 0.114462 | ||||||||
\(874\) | −25.5279 | −0.863493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.52786 | −0.119195 | ||||||||
\(877\) | 37.1246 | 1.25361 | 0.626805 | − | 0.779177i | \(-0.284362\pi\) | ||||
0.626805 | + | 0.779177i | \(0.284362\pi\) | |||||||
\(878\) | 23.5066 | 0.793309 | ||||||||
\(879\) | 22.0902 | 0.745083 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.5967 | −0.794995 | −0.397497 | − | 0.917603i | \(-0.630121\pi\) | ||||
−0.397497 | + | 0.917603i | \(0.630121\pi\) | |||||||
\(882\) | 0.145898 | 0.00491264 | ||||||||
\(883\) | 30.0689 | 1.01190 | 0.505949 | − | 0.862563i | \(-0.331142\pi\) | ||||
0.505949 | + | 0.862563i | \(0.331142\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.6180 | 0.558294 | ||||||||
\(887\) | −23.4164 | −0.786246 | −0.393123 | − | 0.919486i | \(-0.628605\pi\) | ||||
−0.393123 | + | 0.919486i | \(0.628605\pi\) | |||||||
\(888\) | 8.00000 | 0.268462 | ||||||||
\(889\) | 35.6525 | 1.19575 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.61803 | 0.121209 | ||||||||
\(892\) | 8.09017 | 0.270879 | ||||||||
\(893\) | 9.75078 | 0.326297 | ||||||||
\(894\) | −22.0902 | −0.738806 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.61803 | 0.0874624 | ||||||||
\(897\) | −28.9443 | −0.966421 | ||||||||
\(898\) | 27.7082 | 0.924635 | ||||||||
\(899\) | 56.0689 | 1.87000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.58359 | −0.0860719 | ||||||||
\(902\) | −20.6525 | −0.687652 | ||||||||
\(903\) | −20.1803 | −0.671560 | ||||||||
\(904\) | −19.2361 | −0.639782 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.3262 | −0.608848 | ||||||||
\(907\) | −30.4721 | −1.01181 | −0.505905 | − | 0.862589i | \(-0.668841\pi\) | ||||
−0.505905 | + | 0.862589i | \(0.668841\pi\) | |||||||
\(908\) | 22.2705 | 0.739073 | ||||||||
\(909\) | 4.38197 | 0.145341 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1803 | 0.602342 | 0.301171 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(912\) | −5.70820 | −0.189018 | ||||||||
\(913\) | −7.76393 | −0.256949 | ||||||||
\(914\) | −4.09017 | −0.135291 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.52786 | −0.182646 | ||||||||
\(917\) | 46.8328 | 1.54656 | ||||||||
\(918\) | 1.23607 | 0.0407963 | ||||||||
\(919\) | −40.7214 | −1.34327 | −0.671637 | − | 0.740881i | \(-0.734408\pi\) | ||||
−0.671637 | + | 0.740881i | \(0.734408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | −0.329511 | ||||||||
\(922\) | −7.56231 | −0.249051 | ||||||||
\(923\) | 35.7771 | 1.17762 | ||||||||
\(924\) | −9.47214 | −0.311610 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.8328 | −0.750333 | ||||||||
\(927\) | −14.3262 | −0.470535 | ||||||||
\(928\) | −8.47214 | −0.278111 | ||||||||
\(929\) | −19.0132 | −0.623801 | −0.311901 | − | 0.950115i | \(-0.600966\pi\) | ||||
−0.311901 | + | 0.950115i | \(0.600966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.832816 | 0.0272944 | ||||||||
\(932\) | −18.6525 | −0.610982 | ||||||||
\(933\) | −1.05573 | −0.0345630 | ||||||||
\(934\) | 10.6738 | 0.349256 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.47214 | −0.211548 | ||||||||
\(937\) | 8.68692 | 0.283789 | 0.141895 | − | 0.989882i | \(-0.454681\pi\) | ||||
0.141895 | + | 0.989882i | \(0.454681\pi\) | |||||||
\(938\) | 4.00000 | 0.130605 | ||||||||
\(939\) | 16.2705 | 0.530968 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.43769 | −0.144665 | −0.0723323 | − | 0.997381i | \(-0.523044\pi\) | ||||
−0.0723323 | + | 0.997381i | \(0.523044\pi\) | |||||||
\(942\) | 8.65248 | 0.281913 | ||||||||
\(943\) | −25.5279 | −0.831302 | ||||||||
\(944\) | −3.61803 | −0.117757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.8885 | −0.906735 | ||||||||
\(947\) | 33.5623 | 1.09063 | 0.545314 | − | 0.838232i | \(-0.316410\pi\) | ||||
0.545314 | + | 0.838232i | \(0.316410\pi\) | |||||||
\(948\) | −5.61803 | −0.182465 | ||||||||
\(949\) | −22.8328 | −0.741185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | −3.23607 | −0.104882 | ||||||||
\(953\) | −5.30495 | −0.171844 | −0.0859221 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859221 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(954\) | −2.09017 | −0.0676718 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.2918 | 0.397545 | ||||||||
\(957\) | 30.6525 | 0.990854 | ||||||||
\(958\) | 29.1246 | 0.940973 | ||||||||
\(959\) | −31.8885 | −1.02973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7984 | 0.412851 | ||||||||
\(962\) | 51.7771 | 1.66936 | ||||||||
\(963\) | 11.6180 | 0.374386 | ||||||||
\(964\) | 9.56231 | 0.307981 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.7082 | −0.376705 | ||||||||
\(967\) | −10.9098 | −0.350836 | −0.175418 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175418 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(968\) | −2.09017 | −0.0671806 | ||||||||
\(969\) | 7.05573 | 0.226663 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.2148 | −0.456174 | −0.228087 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228087 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −27.4164 | −0.878930 | ||||||||
\(974\) | 17.7984 | 0.570297 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76393 | 0.0884713 | ||||||||
\(977\) | 0.763932 | 0.0244404 | 0.0122202 | − | 0.999925i | \(-0.496110\pi\) | ||||
0.0122202 | + | 0.999925i | \(0.496110\pi\) | |||||||
\(978\) | −0.472136 | −0.0150972 | ||||||||
\(979\) | 12.7639 | 0.407937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.2361 | 0.550305 | ||||||||
\(982\) | 25.2705 | 0.806414 | ||||||||
\(983\) | −40.1803 | −1.28155 | −0.640777 | − | 0.767727i | \(-0.721388\pi\) | ||||
−0.640777 | + | 0.767727i | \(0.721388\pi\) | |||||||
\(984\) | −5.70820 | −0.181971 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.4721 | 0.333501 | ||||||||
\(987\) | 4.47214 | 0.142350 | ||||||||
\(988\) | −36.9443 | −1.17535 | ||||||||
\(989\) | −34.4721 | −1.09615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4508 | 0.935537 | 0.467769 | − | 0.883851i | \(-0.345058\pi\) | ||||
0.467769 | + | 0.883851i | \(0.345058\pi\) | |||||||
\(992\) | −6.61803 | −0.210123 | ||||||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | 14.4721 | 0.459028 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.14590 | −0.0679954 | ||||||||
\(997\) | 5.59675 | 0.177251 | 0.0886254 | − | 0.996065i | \(-0.471753\pi\) | ||||
0.0886254 | + | 0.996065i | \(0.471753\pi\) | |||||||
\(998\) | −35.5967 | −1.12680 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(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 | 3750.2.a.d.1.1 | 2 | ||
5.2 | odd | 4 | 3750.2.c.b.1249.1 | 4 | |||
5.3 | odd | 4 | 3750.2.c.b.1249.4 | 4 | |||
5.4 | even | 2 | 3750.2.a.f.1.2 | 2 | |||
25.3 | odd | 20 | 750.2.h.b.49.2 | 8 | |||
25.4 | even | 10 | 150.2.g.a.91.1 | yes | 4 | ||
25.6 | even | 5 | 750.2.g.b.301.1 | 4 | |||
25.8 | odd | 20 | 750.2.h.b.199.1 | 8 | |||
25.17 | odd | 20 | 750.2.h.b.199.2 | 8 | |||
25.19 | even | 10 | 150.2.g.a.61.1 | ✓ | 4 | ||
25.21 | even | 5 | 750.2.g.b.451.1 | 4 | |||
25.22 | odd | 20 | 750.2.h.b.49.1 | 8 | |||
75.29 | odd | 10 | 450.2.h.c.91.1 | 4 | |||
75.44 | odd | 10 | 450.2.h.c.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.61.1 | ✓ | 4 | 25.19 | even | 10 | ||
150.2.g.a.91.1 | yes | 4 | 25.4 | even | 10 | ||
450.2.h.c.91.1 | 4 | 75.29 | odd | 10 | |||
450.2.h.c.361.1 | 4 | 75.44 | odd | 10 | |||
750.2.g.b.301.1 | 4 | 25.6 | even | 5 | |||
750.2.g.b.451.1 | 4 | 25.21 | even | 5 | |||
750.2.h.b.49.1 | 8 | 25.22 | odd | 20 | |||
750.2.h.b.49.2 | 8 | 25.3 | odd | 20 | |||
750.2.h.b.199.1 | 8 | 25.8 | odd | 20 | |||
750.2.h.b.199.2 | 8 | 25.17 | odd | 20 | |||
3750.2.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3750.2.a.f.1.2 | 2 | 5.4 | even | 2 | |||
3750.2.c.b.1249.1 | 4 | 5.2 | odd | 4 | |||
3750.2.c.b.1249.4 | 4 | 5.3 | odd | 4 |