Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17557 | 0.831254 | 0.415627 | − | 0.909535i | \(-0.363562\pi\) | ||||
0.415627 | + | 0.909535i | \(0.363562\pi\) | |||||||
\(3\) | 1.17557 | 0.678716 | 0.339358 | − | 0.940657i | \(-0.389790\pi\) | ||||
0.339358 | + | 0.940657i | \(0.389790\pi\) | |||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.38197 | 0.564185 | ||||||||
\(7\) | −0.236068 | −0.0892253 | −0.0446127 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446127 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(8\) | −3.07768 | −1.08813 | ||||||||
\(9\) | −1.61803 | −0.539345 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.854102 | 0.257521 | 0.128761 | − | 0.991676i | \(-0.458900\pi\) | ||||
0.128761 | + | 0.991676i | \(0.458900\pi\) | |||||||
\(12\) | −0.726543 | −0.209735 | ||||||||
\(13\) | 0.726543 | 0.201507 | 0.100753 | − | 0.994911i | \(-0.467875\pi\) | ||||
0.100753 | + | 0.994911i | \(0.467875\pi\) | |||||||
\(14\) | −0.277515 | −0.0741689 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.38197 | −0.595492 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | −1.90211 | −0.448332 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.277515 | −0.0605586 | ||||||||
\(22\) | 1.00406 | 0.214066 | ||||||||
\(23\) | 7.09017 | 1.47840 | 0.739201 | − | 0.673485i | \(-0.235203\pi\) | ||||
0.739201 | + | 0.673485i | \(0.235203\pi\) | |||||||
\(24\) | −3.61803 | −0.738528 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.854102 | 0.167503 | ||||||||
\(27\) | −5.42882 | −1.04478 | ||||||||
\(28\) | 0.145898 | 0.0275721 | ||||||||
\(29\) | 8.78402 | 1.63115 | 0.815576 | − | 0.578650i | \(-0.196420\pi\) | ||||
0.815576 | + | 0.578650i | \(0.196420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17557 | 0.211139 | 0.105569 | − | 0.994412i | \(-0.466333\pi\) | ||||
0.105569 | + | 0.994412i | \(0.466333\pi\) | |||||||
\(32\) | 3.35520 | 0.593121 | ||||||||
\(33\) | 1.00406 | 0.174784 | ||||||||
\(34\) | −0.898056 | −0.154015 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.78402 | −1.44408 | −0.722042 | − | 0.691849i | \(-0.756796\pi\) | ||||
−0.722042 | + | 0.691849i | \(0.756796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.854102 | 0.136766 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.62460 | −0.253720 | −0.126860 | − | 0.991921i | \(-0.540490\pi\) | ||||
−0.126860 | + | 0.991921i | \(0.540490\pi\) | |||||||
\(42\) | −0.326238 | −0.0503396 | ||||||||
\(43\) | −2.61803 | −0.399246 | −0.199623 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199623 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(44\) | −0.527864 | −0.0795785 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.33499 | 1.22893 | ||||||||
\(47\) | −7.47214 | −1.08992 | −0.544962 | − | 0.838461i | \(-0.683456\pi\) | ||||
−0.544962 | + | 0.838461i | \(0.683456\pi\) | |||||||
\(48\) | −2.80017 | −0.404170 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.898056 | −0.125753 | ||||||||
\(52\) | −0.449028 | −0.0622690 | ||||||||
\(53\) | 1.00406 | 0.137918 | 0.0689589 | − | 0.997620i | \(-0.478032\pi\) | ||||
0.0689589 | + | 0.997620i | \(0.478032\pi\) | |||||||
\(54\) | −6.38197 | −0.868476 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.726543 | 0.0970883 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.3262 | 1.35590 | ||||||||
\(59\) | 11.3067 | 1.47200 | 0.736002 | − | 0.676979i | \(-0.236711\pi\) | ||||
0.736002 | + | 0.676979i | \(0.236711\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9443 | −1.78538 | −0.892691 | − | 0.450670i | \(-0.851185\pi\) | ||||
−0.892691 | + | 0.450670i | \(0.851185\pi\) | |||||||
\(62\) | 1.38197 | 0.175510 | ||||||||
\(63\) | 0.381966 | 0.0481232 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.18034 | 0.145290 | ||||||||
\(67\) | −11.5842 | −1.41523 | −0.707617 | − | 0.706596i | \(-0.750230\pi\) | ||||
−0.707617 | + | 0.706596i | \(0.750230\pi\) | |||||||
\(68\) | 0.472136 | 0.0572549 | ||||||||
\(69\) | 8.33499 | 1.00342 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0373 | −1.54724 | −0.773620 | − | 0.633650i | \(-0.781556\pi\) | ||||
−0.773620 | + | 0.633650i | \(0.781556\pi\) | |||||||
\(72\) | 4.97980 | 0.586875 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | −10.3262 | −1.20040 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.201626 | −0.0229774 | ||||||||
\(78\) | 1.00406 | 0.113687 | ||||||||
\(79\) | −8.50651 | −0.957057 | −0.478528 | − | 0.878072i | \(-0.658830\pi\) | ||||
−0.478528 | + | 0.878072i | \(0.658830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.52786 | −0.169763 | ||||||||
\(82\) | −1.90983 | −0.210905 | ||||||||
\(83\) | 13.2361 | 1.45285 | 0.726424 | − | 0.687247i | \(-0.241181\pi\) | ||||
0.726424 | + | 0.687247i | \(0.241181\pi\) | |||||||
\(84\) | 0.171513 | 0.0187136 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.07768 | −0.331875 | ||||||||
\(87\) | 10.3262 | 1.10709 | ||||||||
\(88\) | −2.62866 | −0.280216 | ||||||||
\(89\) | −8.33499 | −0.883508 | −0.441754 | − | 0.897136i | \(-0.645644\pi\) | ||||
−0.441754 | + | 0.897136i | \(0.645644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.171513 | −0.0179795 | ||||||||
\(92\) | −4.38197 | −0.456852 | ||||||||
\(93\) | 1.38197 | 0.143303 | ||||||||
\(94\) | −8.78402 | −0.906003 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.94427 | 0.402561 | ||||||||
\(97\) | 4.25325 | 0.431853 | 0.215926 | − | 0.976410i | \(-0.430723\pi\) | ||||
0.215926 | + | 0.976410i | \(0.430723\pi\) | |||||||
\(98\) | −8.16348 | −0.824636 | ||||||||
\(99\) | −1.38197 | −0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.7082 | 1.66253 | 0.831264 | − | 0.555878i | \(-0.187618\pi\) | ||||
0.831264 | + | 0.555878i | \(0.187618\pi\) | |||||||
\(102\) | −1.05573 | −0.104533 | ||||||||
\(103\) | 1.34708 | 0.132732 | 0.0663661 | − | 0.997795i | \(-0.478859\pi\) | ||||
0.0663661 | + | 0.997795i | \(0.478859\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.18034 | 0.114645 | ||||||||
\(107\) | 7.77997 | 0.752118 | 0.376059 | − | 0.926596i | \(-0.377279\pi\) | ||||
0.376059 | + | 0.926596i | \(0.377279\pi\) | |||||||
\(108\) | 3.35520 | 0.322854 | ||||||||
\(109\) | −9.23305 | −0.884366 | −0.442183 | − | 0.896925i | \(-0.645796\pi\) | ||||
−0.442183 | + | 0.896925i | \(0.645796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3262 | −0.980123 | ||||||||
\(112\) | 0.562306 | 0.0531329 | ||||||||
\(113\) | 4.35926 | 0.410084 | 0.205042 | − | 0.978753i | \(-0.434267\pi\) | ||||
0.205042 | + | 0.978753i | \(0.434267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.42882 | −0.504054 | ||||||||
\(117\) | −1.17557 | −0.108682 | ||||||||
\(118\) | 13.2918 | 1.22361 | ||||||||
\(119\) | 0.180340 | 0.0165317 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2705 | −0.933683 | ||||||||
\(122\) | −16.3925 | −1.48410 | ||||||||
\(123\) | −1.90983 | −0.172204 | ||||||||
\(124\) | −0.726543 | −0.0652454 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.449028 | 0.0400026 | ||||||||
\(127\) | 2.17963 | 0.193411 | 0.0967053 | − | 0.995313i | \(-0.469170\pi\) | ||||
0.0967053 | + | 0.995313i | \(0.469170\pi\) | |||||||
\(128\) | 3.52671 | 0.311720 | ||||||||
\(129\) | −3.07768 | −0.270975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3820 | −1.16919 | −0.584594 | − | 0.811326i | \(-0.698746\pi\) | ||||
−0.584594 | + | 0.811326i | \(0.698746\pi\) | |||||||
\(132\) | −0.620541 | −0.0540112 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.6180 | −1.17642 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.35114 | 0.201609 | ||||||||
\(137\) | −14.2361 | −1.21627 | −0.608135 | − | 0.793834i | \(-0.708082\pi\) | ||||
−0.608135 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(138\) | 9.79837 | 0.834093 | ||||||||
\(139\) | −10.9098 | −0.925360 | −0.462680 | − | 0.886525i | \(-0.653112\pi\) | ||||
−0.462680 | + | 0.886525i | \(0.653112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.78402 | −0.739748 | ||||||||
\(142\) | −15.3262 | −1.28615 | ||||||||
\(143\) | 0.620541 | 0.0518923 | ||||||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.17557 | 0.0972909 | ||||||||
\(147\) | −8.16348 | −0.673313 | ||||||||
\(148\) | 5.42882 | 0.446247 | ||||||||
\(149\) | −4.09017 | −0.335080 | −0.167540 | − | 0.985865i | \(-0.553582\pi\) | ||||
−0.167540 | + | 0.985865i | \(0.553582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.0171 | −1.46621 | −0.733104 | − | 0.680116i | \(-0.761929\pi\) | ||||
−0.733104 | + | 0.680116i | \(0.761929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.23607 | 0.0999302 | ||||||||
\(154\) | −0.237026 | −0.0191001 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.527864 | −0.0422629 | ||||||||
\(157\) | −17.2705 | −1.37834 | −0.689168 | − | 0.724601i | \(-0.742024\pi\) | ||||
−0.689168 | + | 0.724601i | \(0.742024\pi\) | |||||||
\(158\) | −10.0000 | −0.795557 | ||||||||
\(159\) | 1.18034 | 0.0936070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.67376 | −0.131911 | ||||||||
\(162\) | −1.79611 | −0.141116 | ||||||||
\(163\) | 2.81966 | 0.220853 | 0.110426 | − | 0.993884i | \(-0.464778\pi\) | ||||
0.110426 | + | 0.993884i | \(0.464778\pi\) | |||||||
\(164\) | 1.00406 | 0.0784037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.5599 | 1.20768 | ||||||||
\(167\) | 13.0373 | 1.00885 | 0.504427 | − | 0.863454i | \(-0.331704\pi\) | ||||
0.504427 | + | 0.863454i | \(0.331704\pi\) | |||||||
\(168\) | 0.854102 | 0.0658954 | ||||||||
\(169\) | −12.4721 | −0.959395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.61803 | 0.123374 | ||||||||
\(173\) | −12.8658 | −0.978166 | −0.489083 | − | 0.872237i | \(-0.662668\pi\) | ||||
−0.489083 | + | 0.872237i | \(0.662668\pi\) | |||||||
\(174\) | 12.1392 | 0.920272 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.03444 | −0.153352 | ||||||||
\(177\) | 13.2918 | 0.999073 | ||||||||
\(178\) | −9.79837 | −0.734419 | ||||||||
\(179\) | −12.1392 | −0.907328 | −0.453664 | − | 0.891173i | \(-0.649883\pi\) | ||||
−0.453664 | + | 0.891173i | \(0.649883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6619 | −1.08981 | −0.544904 | − | 0.838498i | \(-0.683434\pi\) | ||||
−0.544904 | + | 0.838498i | \(0.683434\pi\) | |||||||
\(182\) | −0.201626 | −0.0149455 | ||||||||
\(183\) | −16.3925 | −1.21177 | ||||||||
\(184\) | −21.8213 | −1.60869 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.62460 | 0.119121 | ||||||||
\(187\) | −0.652476 | −0.0477138 | ||||||||
\(188\) | 4.61803 | 0.336805 | ||||||||
\(189\) | 1.28157 | 0.0932206 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0000 | 0.940647 | 0.470323 | − | 0.882494i | \(-0.344137\pi\) | ||||
0.470323 | + | 0.882494i | \(0.344137\pi\) | |||||||
\(192\) | 10.2371 | 0.738800 | ||||||||
\(193\) | −6.15537 | −0.443073 | −0.221537 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221537 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(194\) | 5.00000 | 0.358979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.29180 | 0.306557 | ||||||||
\(197\) | 20.8885 | 1.48825 | 0.744124 | − | 0.668042i | \(-0.232867\pi\) | ||||
0.744124 | + | 0.668042i | \(0.232867\pi\) | |||||||
\(198\) | −1.62460 | −0.115455 | ||||||||
\(199\) | −13.4164 | −0.951064 | −0.475532 | − | 0.879698i | \(-0.657744\pi\) | ||||
−0.475532 | + | 0.879698i | \(0.657744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.6180 | −0.960542 | ||||||||
\(202\) | 19.6417 | 1.38198 | ||||||||
\(203\) | −2.07363 | −0.145540 | ||||||||
\(204\) | 0.555029 | 0.0388598 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.58359 | 0.110334 | ||||||||
\(207\) | −11.4721 | −0.797369 | ||||||||
\(208\) | −1.73060 | −0.119995 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2128 | −0.978453 | −0.489226 | − | 0.872157i | \(-0.662721\pi\) | ||||
−0.489226 | + | 0.872157i | \(0.662721\pi\) | |||||||
\(212\) | −0.620541 | −0.0426190 | ||||||||
\(213\) | −15.3262 | −1.05014 | ||||||||
\(214\) | 9.14590 | 0.625201 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | −0.277515 | −0.0188389 | ||||||||
\(218\) | −10.8541 | −0.735133 | ||||||||
\(219\) | 1.17557 | 0.0794377 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.555029 | −0.0373353 | ||||||||
\(222\) | −12.1392 | −0.814731 | ||||||||
\(223\) | −19.7477 | −1.32240 | −0.661201 | − | 0.750209i | \(-0.729953\pi\) | ||||
−0.661201 | + | 0.750209i | \(0.729953\pi\) | |||||||
\(224\) | −0.792055 | −0.0529214 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.12461 | 0.340884 | ||||||||
\(227\) | −18.6376 | −1.23702 | −0.618511 | − | 0.785776i | \(-0.712264\pi\) | ||||
−0.618511 | + | 0.785776i | \(0.712264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.8541 | −1.64241 | −0.821203 | − | 0.570637i | \(-0.806696\pi\) | ||||
−0.821203 | + | 0.570637i | \(0.806696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.237026 | −0.0155951 | ||||||||
\(232\) | −27.0344 | −1.77490 | ||||||||
\(233\) | −6.23607 | −0.408538 | −0.204269 | − | 0.978915i | \(-0.565482\pi\) | ||||
−0.204269 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(234\) | −1.38197 | −0.0903419 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.98791 | −0.454874 | ||||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0.212002 | 0.0137421 | ||||||||
\(239\) | 28.2148 | 1.82506 | 0.912531 | − | 0.409007i | \(-0.134125\pi\) | ||||
0.912531 | + | 0.409007i | \(0.134125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4904 | 0.933406 | 0.466703 | − | 0.884414i | \(-0.345442\pi\) | ||||
0.466703 | + | 0.884414i | \(0.345442\pi\) | |||||||
\(242\) | −12.0737 | −0.776127 | ||||||||
\(243\) | 14.4904 | 0.929557 | ||||||||
\(244\) | 8.61803 | 0.551713 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.24514 | −0.143145 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.61803 | −0.229745 | ||||||||
\(249\) | 15.5599 | 0.986071 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | −0.236068 | −0.0148709 | ||||||||
\(253\) | 6.05573 | 0.380720 | ||||||||
\(254\) | 2.56231 | 0.160773 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.2705 | −0.829407 | ||||||||
\(257\) | −13.7638 | −0.858563 | −0.429282 | − | 0.903171i | \(-0.641233\pi\) | ||||
−0.429282 | + | 0.903171i | \(0.641233\pi\) | |||||||
\(258\) | −3.61803 | −0.225249 | ||||||||
\(259\) | 2.07363 | 0.128849 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.2128 | −0.879753 | ||||||||
\(262\) | −15.7314 | −0.971892 | ||||||||
\(263\) | 6.00000 | 0.369976 | 0.184988 | − | 0.982741i | \(-0.440775\pi\) | ||||
0.184988 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(264\) | −3.09017 | −0.190187 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.79837 | −0.599651 | ||||||||
\(268\) | 7.15942 | 0.437331 | ||||||||
\(269\) | −6.26137 | −0.381762 | −0.190881 | − | 0.981613i | \(-0.561135\pi\) | ||||
−0.190881 | + | 0.981613i | \(0.561135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.38197 | 0.387677 | 0.193838 | − | 0.981033i | \(-0.437906\pi\) | ||||
0.193838 | + | 0.981033i | \(0.437906\pi\) | |||||||
\(272\) | 1.81966 | 0.110333 | ||||||||
\(273\) | −0.201626 | −0.0122030 | ||||||||
\(274\) | −16.7355 | −1.01103 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.15131 | −0.310072 | ||||||||
\(277\) | 28.8328 | 1.73240 | 0.866198 | − | 0.499701i | \(-0.166557\pi\) | ||||
0.866198 | + | 0.499701i | \(0.166557\pi\) | |||||||
\(278\) | −12.8253 | −0.769209 | ||||||||
\(279\) | −1.90211 | −0.113877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7921 | 0.643805 | 0.321902 | − | 0.946773i | \(-0.395678\pi\) | ||||
0.321902 | + | 0.946773i | \(0.395678\pi\) | |||||||
\(282\) | −10.3262 | −0.614919 | ||||||||
\(283\) | −5.27051 | −0.313299 | −0.156650 | − | 0.987654i | \(-0.550069\pi\) | ||||
−0.156650 | + | 0.987654i | \(0.550069\pi\) | |||||||
\(284\) | 8.05748 | 0.478123 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.729490 | 0.0431357 | ||||||||
\(287\) | 0.383516 | 0.0226382 | ||||||||
\(288\) | −5.42882 | −0.319897 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | 0.293105 | ||||||||
\(292\) | −0.618034 | −0.0361677 | ||||||||
\(293\) | 30.8828 | 1.80419 | 0.902097 | − | 0.431533i | \(-0.142027\pi\) | ||||
0.902097 | + | 0.431533i | \(0.142027\pi\) | |||||||
\(294\) | −9.59675 | −0.559694 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 27.0344 | 1.57135 | ||||||||
\(297\) | −4.63677 | −0.269053 | ||||||||
\(298\) | −4.80828 | −0.278536 | ||||||||
\(299\) | 5.15131 | 0.297908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.618034 | 0.0356229 | ||||||||
\(302\) | −21.1803 | −1.21879 | ||||||||
\(303\) | 19.6417 | 1.12838 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.45309 | 0.0830673 | ||||||||
\(307\) | 25.4540 | 1.45274 | 0.726369 | − | 0.687305i | \(-0.241207\pi\) | ||||
0.726369 | + | 0.687305i | \(0.241207\pi\) | |||||||
\(308\) | 0.124612 | 0.00710042 | ||||||||
\(309\) | 1.58359 | 0.0900874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.23607 | −0.410320 | −0.205160 | − | 0.978728i | \(-0.565771\pi\) | ||||
−0.205160 | + | 0.978728i | \(0.565771\pi\) | |||||||
\(312\) | −2.62866 | −0.148818 | ||||||||
\(313\) | 30.2705 | 1.71099 | 0.855495 | − | 0.517811i | \(-0.173253\pi\) | ||||
0.855495 | + | 0.517811i | \(0.173253\pi\) | |||||||
\(314\) | −20.3027 | −1.14575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.25731 | 0.295747 | ||||||||
\(317\) | −26.6296 | −1.49567 | −0.747833 | − | 0.663887i | \(-0.768906\pi\) | ||||
−0.747833 | + | 0.663887i | \(0.768906\pi\) | |||||||
\(318\) | 1.38757 | 0.0778112 | ||||||||
\(319\) | 7.50245 | 0.420057 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.14590 | 0.510474 | ||||||||
\(322\) | −1.96763 | −0.109651 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.944272 | 0.0524596 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.31471 | 0.183585 | ||||||||
\(327\) | −10.8541 | −0.600233 | ||||||||
\(328\) | 5.00000 | 0.276079 | ||||||||
\(329\) | 1.76393 | 0.0972487 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.79611 | −0.0987232 | −0.0493616 | − | 0.998781i | \(-0.515719\pi\) | ||||
−0.0493616 | + | 0.998781i | \(0.515719\pi\) | |||||||
\(332\) | −8.18034 | −0.448954 | ||||||||
\(333\) | 14.2128 | 0.778859 | ||||||||
\(334\) | 15.3262 | 0.838614 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.661030 | 0.0360622 | ||||||||
\(337\) | 3.46120 | 0.188544 | 0.0942718 | − | 0.995547i | \(-0.469948\pi\) | ||||
0.0942718 | + | 0.995547i | \(0.469948\pi\) | |||||||
\(338\) | −14.6619 | −0.797501 | ||||||||
\(339\) | 5.12461 | 0.278331 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.00406 | 0.0543727 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 8.05748 | 0.434430 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.1246 | −0.813104 | ||||||||
\(347\) | −7.52786 | −0.404117 | −0.202058 | − | 0.979373i | \(-0.564763\pi\) | ||||
−0.202058 | + | 0.979373i | \(0.564763\pi\) | |||||||
\(348\) | −6.38197 | −0.342109 | ||||||||
\(349\) | 17.5623 | 0.940089 | 0.470044 | − | 0.882643i | \(-0.344238\pi\) | ||||
0.470044 | + | 0.882643i | \(0.344238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.94427 | −0.210530 | ||||||||
\(352\) | 2.86568 | 0.152741 | ||||||||
\(353\) | −19.3262 | −1.02863 | −0.514316 | − | 0.857601i | \(-0.671954\pi\) | ||||
−0.514316 | + | 0.857601i | \(0.671954\pi\) | |||||||
\(354\) | 15.6254 | 0.830483 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.15131 | 0.273019 | ||||||||
\(357\) | 0.212002 | 0.0112203 | ||||||||
\(358\) | −14.2705 | −0.754220 | ||||||||
\(359\) | 9.61803 | 0.507620 | 0.253810 | − | 0.967254i | \(-0.418316\pi\) | ||||
0.253810 | + | 0.967254i | \(0.418316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −17.2361 | −0.905908 | ||||||||
\(363\) | −12.0737 | −0.633705 | ||||||||
\(364\) | 0.106001 | 0.00555597 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.2705 | −1.00729 | ||||||||
\(367\) | 27.0689 | 1.41298 | 0.706492 | − | 0.707721i | \(-0.250277\pi\) | ||||
0.706492 | + | 0.707721i | \(0.250277\pi\) | |||||||
\(368\) | −16.8885 | −0.880376 | ||||||||
\(369\) | 2.62866 | 0.136842 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.237026 | −0.0123058 | ||||||||
\(372\) | −0.854102 | −0.0442831 | ||||||||
\(373\) | 4.53077 | 0.234594 | 0.117297 | − | 0.993097i | \(-0.462577\pi\) | ||||
0.117297 | + | 0.993097i | \(0.462577\pi\) | |||||||
\(374\) | −0.767031 | −0.0396622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.9969 | 1.18597 | ||||||||
\(377\) | 6.38197 | 0.328688 | ||||||||
\(378\) | 1.50658 | 0.0774900 | ||||||||
\(379\) | −13.2088 | −0.678490 | −0.339245 | − | 0.940698i | \(-0.610172\pi\) | ||||
−0.339245 | + | 0.940698i | \(0.610172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.56231 | 0.131271 | ||||||||
\(382\) | 15.2824 | 0.781916 | ||||||||
\(383\) | −2.62866 | −0.134318 | −0.0671590 | − | 0.997742i | \(-0.521393\pi\) | ||||
−0.0671590 | + | 0.997742i | \(0.521393\pi\) | |||||||
\(384\) | 4.14590 | 0.211569 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.23607 | −0.368306 | ||||||||
\(387\) | 4.23607 | 0.215331 | ||||||||
\(388\) | −2.62866 | −0.133450 | ||||||||
\(389\) | −14.1459 | −0.717226 | −0.358613 | − | 0.933486i | \(-0.616750\pi\) | ||||
−0.358613 | + | 0.933486i | \(0.616750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.41641 | −0.273920 | ||||||||
\(392\) | 21.3723 | 1.07946 | ||||||||
\(393\) | −15.7314 | −0.793546 | ||||||||
\(394\) | 24.5560 | 1.23711 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.854102 | 0.0429202 | ||||||||
\(397\) | −29.8328 | −1.49727 | −0.748633 | − | 0.662985i | \(-0.769289\pi\) | ||||
−0.748633 | + | 0.662985i | \(0.769289\pi\) | |||||||
\(398\) | −15.7719 | −0.790576 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8576 | 0.542205 | 0.271103 | − | 0.962550i | \(-0.412612\pi\) | ||||
0.271103 | + | 0.962550i | \(0.412612\pi\) | |||||||
\(402\) | −16.0090 | −0.798454 | ||||||||
\(403\) | 0.854102 | 0.0425458 | ||||||||
\(404\) | −10.3262 | −0.513750 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.43769 | −0.120981 | ||||||||
\(407\) | −7.50245 | −0.371883 | ||||||||
\(408\) | 2.76393 | 0.136835 | ||||||||
\(409\) | −18.1231 | −0.896128 | −0.448064 | − | 0.894001i | \(-0.647886\pi\) | ||||
−0.448064 | + | 0.894001i | \(0.647886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.7355 | −0.825501 | ||||||||
\(412\) | −0.832544 | −0.0410165 | ||||||||
\(413\) | −2.66914 | −0.131340 | ||||||||
\(414\) | −13.4863 | −0.662816 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.43769 | 0.119518 | ||||||||
\(417\) | −12.8253 | −0.628056 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.81966 | 0.186603 | 0.0933013 | − | 0.995638i | \(-0.470258\pi\) | ||||
0.0933013 | + | 0.995638i | \(0.470258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.98385 | 0.291635 | 0.145818 | − | 0.989311i | \(-0.453419\pi\) | ||||
0.145818 | + | 0.989311i | \(0.453419\pi\) | |||||||
\(422\) | −16.7082 | −0.813343 | ||||||||
\(423\) | 12.0902 | 0.587844 | ||||||||
\(424\) | −3.09017 | −0.150072 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0171 | −0.872930 | ||||||||
\(427\) | 3.29180 | 0.159301 | ||||||||
\(428\) | −4.80828 | −0.232417 | ||||||||
\(429\) | 0.729490 | 0.0352201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.62460 | 0.0782542 | 0.0391271 | − | 0.999234i | \(-0.487542\pi\) | ||||
0.0391271 | + | 0.999234i | \(0.487542\pi\) | |||||||
\(432\) | 12.9313 | 0.622156 | ||||||||
\(433\) | −22.5478 | −1.08358 | −0.541790 | − | 0.840514i | \(-0.682253\pi\) | ||||
−0.541790 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(434\) | −0.326238 | −0.0156599 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.70634 | 0.273284 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.38197 | 0.0660329 | ||||||||
\(439\) | 37.6587 | 1.79735 | 0.898677 | − | 0.438611i | \(-0.144529\pi\) | ||||
0.898677 | + | 0.438611i | \(0.144529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.2361 | 0.535051 | ||||||||
\(442\) | −0.652476 | −0.0310351 | ||||||||
\(443\) | 36.7771 | 1.74733 | 0.873666 | − | 0.486526i | \(-0.161736\pi\) | ||||
0.873666 | + | 0.486526i | \(0.161736\pi\) | |||||||
\(444\) | 6.38197 | 0.302875 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.2148 | −1.09925 | ||||||||
\(447\) | −4.80828 | −0.227424 | ||||||||
\(448\) | −2.05573 | −0.0971240 | ||||||||
\(449\) | 37.6587 | 1.77723 | 0.888613 | − | 0.458658i | \(-0.151670\pi\) | ||||
0.888613 | + | 0.458658i | \(0.151670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.38757 | −0.0653382 | ||||||||
\(452\) | −2.69417 | −0.126723 | ||||||||
\(453\) | −21.1803 | −0.995139 | ||||||||
\(454\) | −21.9098 | −1.02828 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.763932 | −0.0357352 | −0.0178676 | − | 0.999840i | \(-0.505688\pi\) | ||||
−0.0178676 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(458\) | −29.2177 | −1.36526 | ||||||||
\(459\) | 4.14725 | 0.193577 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00000 | −0.372597 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(462\) | −0.278640 | −0.0129635 | ||||||||
\(463\) | −6.85410 | −0.318537 | −0.159269 | − | 0.987235i | \(-0.550914\pi\) | ||||
−0.159269 | + | 0.987235i | \(0.550914\pi\) | |||||||
\(464\) | −20.9232 | −0.971337 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.33094 | −0.339599 | ||||||||
\(467\) | −13.1803 | −0.609913 | −0.304957 | − | 0.952366i | \(-0.598642\pi\) | ||||
−0.304957 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(468\) | 0.726543 | 0.0335844 | ||||||||
\(469\) | 2.73466 | 0.126275 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.3027 | −0.935499 | ||||||||
\(472\) | −34.7984 | −1.60172 | ||||||||
\(473\) | −2.23607 | −0.102815 | ||||||||
\(474\) | −11.7557 | −0.539957 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.111456 | −0.00510859 | ||||||||
\(477\) | −1.62460 | −0.0743853 | ||||||||
\(478\) | 33.1685 | 1.51709 | ||||||||
\(479\) | −31.5623 | −1.44212 | −0.721059 | − | 0.692873i | \(-0.756344\pi\) | ||||
−0.721059 | + | 0.692873i | \(0.756344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.38197 | −0.290993 | ||||||||
\(482\) | 17.0344 | 0.775898 | ||||||||
\(483\) | −1.96763 | −0.0895301 | ||||||||
\(484\) | 6.34752 | 0.288524 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 17.0344 | 0.772698 | ||||||||
\(487\) | 34.0260 | 1.54187 | 0.770933 | − | 0.636916i | \(-0.219790\pi\) | ||||
0.770933 | + | 0.636916i | \(0.219790\pi\) | |||||||
\(488\) | 42.9161 | 1.94272 | ||||||||
\(489\) | 3.31471 | 0.149896 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.72949 | 0.168310 | 0.0841548 | − | 0.996453i | \(-0.473181\pi\) | ||||
0.0841548 | + | 0.996453i | \(0.473181\pi\) | |||||||
\(492\) | 1.18034 | 0.0532138 | ||||||||
\(493\) | −6.71040 | −0.302221 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.80017 | −0.125731 | ||||||||
\(497\) | 3.07768 | 0.138053 | ||||||||
\(498\) | 18.2918 | 0.819675 | ||||||||
\(499\) | −38.4721 | −1.72225 | −0.861125 | − | 0.508394i | \(-0.830239\pi\) | ||||
−0.861125 | + | 0.508394i | \(0.830239\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.3262 | 0.684726 | ||||||||
\(502\) | −3.52671 | −0.157405 | ||||||||
\(503\) | −0.347524 | −0.0154953 | −0.00774767 | − | 0.999970i | \(-0.502466\pi\) | ||||
−0.00774767 | + | 0.999970i | \(0.502466\pi\) | |||||||
\(504\) | −1.17557 | −0.0523641 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.11894 | 0.316475 | ||||||||
\(507\) | −14.6619 | −0.651157 | ||||||||
\(508\) | −1.34708 | −0.0597672 | ||||||||
\(509\) | 10.7516 | 0.476558 | 0.238279 | − | 0.971197i | \(-0.423417\pi\) | ||||
0.238279 | + | 0.971197i | \(0.423417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.236068 | −0.0104430 | ||||||||
\(512\) | −22.6538 | −1.00117 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.1803 | −0.713684 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.90211 | 0.0837359 | ||||||||
\(517\) | −6.38197 | −0.280679 | ||||||||
\(518\) | 2.43769 | 0.107106 | ||||||||
\(519\) | −15.1246 | −0.663897 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.08985 | 0.266801 | 0.133401 | − | 0.991062i | \(-0.457410\pi\) | ||||
0.133401 | + | 0.991062i | \(0.457410\pi\) | |||||||
\(522\) | −16.7082 | −0.731298 | ||||||||
\(523\) | 27.6992 | 1.21120 | 0.605600 | − | 0.795769i | \(-0.292933\pi\) | ||||
0.605600 | + | 0.795769i | \(0.292933\pi\) | |||||||
\(524\) | 8.27051 | 0.361299 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.05342 | 0.307544 | ||||||||
\(527\) | −0.898056 | −0.0391199 | ||||||||
\(528\) | −2.39163 | −0.104082 | ||||||||
\(529\) | 27.2705 | 1.18567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.2946 | −0.793917 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.18034 | −0.0511262 | ||||||||
\(534\) | −11.5187 | −0.498462 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 35.6525 | 1.53995 | ||||||||
\(537\) | −14.2705 | −0.615818 | ||||||||
\(538\) | −7.36068 | −0.317341 | ||||||||
\(539\) | −5.93112 | −0.255471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.5967 | 1.05750 | 0.528748 | − | 0.848779i | \(-0.322662\pi\) | ||||
0.528748 | + | 0.848779i | \(0.322662\pi\) | |||||||
\(542\) | 7.50245 | 0.322258 | ||||||||
\(543\) | −17.2361 | −0.739670 | ||||||||
\(544\) | −2.56314 | −0.109894 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.237026 | −0.0101438 | ||||||||
\(547\) | −13.1433 | −0.561966 | −0.280983 | − | 0.959713i | \(-0.590660\pi\) | ||||
−0.280983 | + | 0.959713i | \(0.590660\pi\) | |||||||
\(548\) | 8.79837 | 0.375848 | ||||||||
\(549\) | 22.5623 | 0.962936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −25.6525 | −1.09184 | ||||||||
\(553\) | 2.00811 | 0.0853937 | ||||||||
\(554\) | 33.8950 | 1.44006 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.74265 | 0.285952 | ||||||||
\(557\) | −27.0689 | −1.14695 | −0.573473 | − | 0.819225i | \(-0.694404\pi\) | ||||
−0.573473 | + | 0.819225i | \(0.694404\pi\) | |||||||
\(558\) | −2.23607 | −0.0946603 | ||||||||
\(559\) | −1.90211 | −0.0804508 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.767031 | −0.0323841 | ||||||||
\(562\) | 12.6869 | 0.535165 | ||||||||
\(563\) | 18.4661 | 0.778253 | 0.389127 | − | 0.921184i | \(-0.372777\pi\) | ||||
0.389127 | + | 0.921184i | \(0.372777\pi\) | |||||||
\(564\) | 5.42882 | 0.228595 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.19586 | −0.260431 | ||||||||
\(567\) | 0.360680 | 0.0151471 | ||||||||
\(568\) | 40.1246 | 1.68359 | ||||||||
\(569\) | 7.71445 | 0.323407 | 0.161703 | − | 0.986839i | \(-0.448301\pi\) | ||||
0.161703 | + | 0.986839i | \(0.448301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.1459 | −0.801231 | −0.400615 | − | 0.916246i | \(-0.631204\pi\) | ||||
−0.400615 | + | 0.916246i | \(0.631204\pi\) | |||||||
\(572\) | −0.383516 | −0.0160356 | ||||||||
\(573\) | 15.2824 | 0.638432 | ||||||||
\(574\) | 0.450850 | 0.0188181 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.0902 | −0.587090 | ||||||||
\(577\) | −17.4721 | −0.727375 | −0.363687 | − | 0.931521i | \(-0.618482\pi\) | ||||
−0.363687 | + | 0.931521i | \(0.618482\pi\) | |||||||
\(578\) | −19.2986 | −0.802718 | ||||||||
\(579\) | −7.23607 | −0.300721 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.12461 | −0.129631 | ||||||||
\(582\) | 5.87785 | 0.243645 | ||||||||
\(583\) | 0.857567 | 0.0355168 | ||||||||
\(584\) | −3.07768 | −0.127355 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.3050 | 1.49974 | ||||||||
\(587\) | −9.58359 | −0.395557 | −0.197779 | − | 0.980247i | \(-0.563373\pi\) | ||||
−0.197779 | + | 0.980247i | \(0.563373\pi\) | |||||||
\(588\) | 5.04531 | 0.208065 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5560 | 1.01010 | ||||||||
\(592\) | 20.9232 | 0.859940 | ||||||||
\(593\) | −7.29180 | −0.299438 | −0.149719 | − | 0.988729i | \(-0.547837\pi\) | ||||
−0.149719 | + | 0.988729i | \(0.547837\pi\) | |||||||
\(594\) | −5.45085 | −0.223651 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.52786 | 0.103545 | ||||||||
\(597\) | −15.7719 | −0.645502 | ||||||||
\(598\) | 6.05573 | 0.247637 | ||||||||
\(599\) | 10.3431 | 0.422608 | 0.211304 | − | 0.977420i | \(-0.432229\pi\) | ||||
0.211304 | + | 0.977420i | \(0.432229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0130 | 0.693975 | 0.346988 | − | 0.937870i | \(-0.387205\pi\) | ||||
0.346988 | + | 0.937870i | \(0.387205\pi\) | |||||||
\(602\) | 0.726543 | 0.0296117 | ||||||||
\(603\) | 18.7436 | 0.763299 | ||||||||
\(604\) | 11.1352 | 0.453083 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23.0902 | 0.937974 | ||||||||
\(607\) | 20.5397 | 0.833682 | 0.416841 | − | 0.908979i | \(-0.363137\pi\) | ||||
0.416841 | + | 0.908979i | \(0.363137\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.43769 | −0.0987803 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.42882 | −0.219627 | ||||||||
\(612\) | −0.763932 | −0.0308801 | ||||||||
\(613\) | −35.4721 | −1.43271 | −0.716353 | − | 0.697738i | \(-0.754190\pi\) | ||||
−0.716353 | + | 0.697738i | \(0.754190\pi\) | |||||||
\(614\) | 29.9230 | 1.20759 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.620541 | 0.0250023 | ||||||||
\(617\) | −19.3820 | −0.780289 | −0.390144 | − | 0.920754i | \(-0.627575\pi\) | ||||
−0.390144 | + | 0.920754i | \(0.627575\pi\) | |||||||
\(618\) | 1.86162 | 0.0748855 | ||||||||
\(619\) | −27.5410 | −1.10697 | −0.553484 | − | 0.832860i | \(-0.686702\pi\) | ||||
−0.553484 | + | 0.832860i | \(0.686702\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −38.4913 | −1.54460 | ||||||||
\(622\) | −8.50651 | −0.341080 | ||||||||
\(623\) | 1.96763 | 0.0788312 | ||||||||
\(624\) | −2.03444 | −0.0814429 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 35.5851 | 1.42227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.6738 | 0.425929 | ||||||||
\(629\) | 6.71040 | 0.267561 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8197 | −0.749199 | −0.374599 | − | 0.927187i | \(-0.622220\pi\) | ||||
−0.374599 | + | 0.927187i | \(0.622220\pi\) | |||||||
\(632\) | 26.1803 | 1.04140 | ||||||||
\(633\) | −16.7082 | −0.664091 | ||||||||
\(634\) | −31.3050 | −1.24328 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.729490 | −0.0289262 | ||||||||
\(637\) | −5.04531 | −0.199902 | ||||||||
\(638\) | 8.81966 | 0.349174 | ||||||||
\(639\) | 21.0948 | 0.834496 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.4508 | −1.51872 | −0.759358 | − | 0.650673i | \(-0.774487\pi\) | ||||
−0.759358 | + | 0.650673i | \(0.774487\pi\) | |||||||
\(642\) | 10.7516 | 0.424334 | ||||||||
\(643\) | 29.5279 | 1.16447 | 0.582233 | − | 0.813022i | \(-0.302179\pi\) | ||||
0.582233 | + | 0.813022i | \(0.302179\pi\) | |||||||
\(644\) | 1.03444 | 0.0407627 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4721 | −0.686901 | −0.343450 | − | 0.939171i | \(-0.611596\pi\) | ||||
−0.343450 | + | 0.939171i | \(0.611596\pi\) | |||||||
\(648\) | 4.70228 | 0.184723 | ||||||||
\(649\) | 9.65706 | 0.379073 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.326238 | −0.0127863 | ||||||||
\(652\) | −1.74265 | −0.0682473 | ||||||||
\(653\) | −10.7984 | −0.422573 | −0.211287 | − | 0.977424i | \(-0.567765\pi\) | ||||
−0.211287 | + | 0.977424i | \(0.567765\pi\) | |||||||
\(654\) | −12.7598 | −0.498946 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.86974 | 0.151088 | ||||||||
\(657\) | −1.61803 | −0.0631255 | ||||||||
\(658\) | 2.07363 | 0.0808384 | ||||||||
\(659\) | 30.7768 | 1.19890 | 0.599448 | − | 0.800414i | \(-0.295387\pi\) | ||||
0.599448 | + | 0.800414i | \(0.295387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4208 | 0.522008 | 0.261004 | − | 0.965338i | \(-0.415946\pi\) | ||||
0.261004 | + | 0.965338i | \(0.415946\pi\) | |||||||
\(662\) | −2.11146 | −0.0820641 | ||||||||
\(663\) | −0.652476 | −0.0253401 | ||||||||
\(664\) | −40.7364 | −1.58088 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.7082 | 0.647430 | ||||||||
\(667\) | 62.2802 | 2.41150 | ||||||||
\(668\) | −8.05748 | −0.311753 | ||||||||
\(669\) | −23.2148 | −0.897535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9098 | −0.459774 | ||||||||
\(672\) | −0.931116 | −0.0359186 | ||||||||
\(673\) | 34.9646 | 1.34779 | 0.673893 | − | 0.738829i | \(-0.264621\pi\) | ||||
0.673893 | + | 0.738829i | \(0.264621\pi\) | |||||||
\(674\) | 4.06888 | 0.156728 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.70820 | 0.296469 | ||||||||
\(677\) | 16.0494 | 0.616830 | 0.308415 | − | 0.951252i | \(-0.400201\pi\) | ||||
0.308415 | + | 0.951252i | \(0.400201\pi\) | |||||||
\(678\) | 6.02434 | 0.231363 | ||||||||
\(679\) | −1.00406 | −0.0385322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.9098 | −0.839587 | ||||||||
\(682\) | 1.18034 | 0.0451976 | ||||||||
\(683\) | 32.6134 | 1.24792 | 0.623959 | − | 0.781457i | \(-0.285523\pi\) | ||||
0.623959 | + | 0.781457i | \(0.285523\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.86974 | 0.147747 | ||||||||
\(687\) | −29.2177 | −1.11473 | ||||||||
\(688\) | 6.23607 | 0.237748 | ||||||||
\(689\) | 0.729490 | 0.0277914 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.76393 | −0.295354 | −0.147677 | − | 0.989036i | \(-0.547180\pi\) | ||||
−0.147677 | + | 0.989036i | \(0.547180\pi\) | |||||||
\(692\) | 7.95148 | 0.302270 | ||||||||
\(693\) | 0.326238 | 0.0123928 | ||||||||
\(694\) | −8.84953 | −0.335924 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −31.7809 | −1.20465 | ||||||||
\(697\) | 1.24108 | 0.0470094 | ||||||||
\(698\) | 20.6457 | 0.781452 | ||||||||
\(699\) | −7.33094 | −0.277282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.0902 | −1.62749 | −0.813747 | − | 0.581220i | \(-0.802576\pi\) | ||||
−0.813747 | + | 0.581220i | \(0.802576\pi\) | |||||||
\(702\) | −4.63677 | −0.175004 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 7.43769 | 0.280319 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.7194 | −0.855054 | ||||||||
\(707\) | −3.94427 | −0.148340 | ||||||||
\(708\) | −8.21478 | −0.308730 | ||||||||
\(709\) | 13.8197 | 0.519008 | 0.259504 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259504 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.7638 | 0.516184 | ||||||||
\(712\) | 25.6525 | 0.961367 | ||||||||
\(713\) | 8.33499 | 0.312148 | ||||||||
\(714\) | 0.249224 | 0.00932696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50245 | 0.280380 | ||||||||
\(717\) | 33.1685 | 1.23870 | ||||||||
\(718\) | 11.3067 | 0.421961 | ||||||||
\(719\) | −42.0902 | −1.56970 | −0.784849 | − | 0.619687i | \(-0.787260\pi\) | ||||
−0.784849 | + | 0.619687i | \(0.787260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.318003 | −0.0118431 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.0344 | 0.633518 | ||||||||
\(724\) | 9.06154 | 0.336769 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.1935 | −0.526770 | ||||||||
\(727\) | 10.3607 | 0.384256 | 0.192128 | − | 0.981370i | \(-0.438461\pi\) | ||||
0.192128 | + | 0.981370i | \(0.438461\pi\) | |||||||
\(728\) | 0.527864 | 0.0195639 | ||||||||
\(729\) | 21.6180 | 0.800668 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.00000 | 0.0739727 | ||||||||
\(732\) | 10.1311 | 0.374456 | ||||||||
\(733\) | 11.0000 | 0.406294 | 0.203147 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203147 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(734\) | 31.8214 | 1.17455 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.7889 | 0.876871 | ||||||||
\(737\) | −9.89408 | −0.364453 | ||||||||
\(738\) | 3.09017 | 0.113751 | ||||||||
\(739\) | −32.2361 | −1.18582 | −0.592911 | − | 0.805268i | \(-0.702022\pi\) | ||||
−0.592911 | + | 0.805268i | \(0.702022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.278640 | −0.0102292 | ||||||||
\(743\) | 11.5842 | 0.424983 | 0.212491 | − | 0.977163i | \(-0.431842\pi\) | ||||
0.212491 | + | 0.977163i | \(0.431842\pi\) | |||||||
\(744\) | −4.25325 | −0.155932 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.32624 | 0.195007 | ||||||||
\(747\) | −21.4164 | −0.783585 | ||||||||
\(748\) | 0.403252 | 0.0147444 | ||||||||
\(749\) | −1.83660 | −0.0671079 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.7000 | 1.52165 | 0.760827 | − | 0.648954i | \(-0.224793\pi\) | ||||
0.760827 | + | 0.648954i | \(0.224793\pi\) | |||||||
\(752\) | 17.7984 | 0.649040 | ||||||||
\(753\) | −3.52671 | −0.128521 | ||||||||
\(754\) | 7.50245 | 0.273223 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.792055 | −0.0288068 | ||||||||
\(757\) | 43.9787 | 1.59843 | 0.799217 | − | 0.601043i | \(-0.205248\pi\) | ||||
0.799217 | + | 0.601043i | \(0.205248\pi\) | |||||||
\(758\) | −15.5279 | −0.563997 | ||||||||
\(759\) | 7.11894 | 0.258401 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.1803 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(762\) | 3.01217 | 0.109119 | ||||||||
\(763\) | 2.17963 | 0.0789078 | ||||||||
\(764\) | −8.03444 | −0.290676 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.09017 | −0.111652 | ||||||||
\(767\) | 8.21478 | 0.296619 | ||||||||
\(768\) | −15.6004 | −0.562932 | ||||||||
\(769\) | 20.2705 | 0.730973 | 0.365487 | − | 0.930817i | \(-0.380903\pi\) | ||||
0.365487 | + | 0.930817i | \(0.380903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.1803 | −0.582721 | ||||||||
\(772\) | 3.80423 | 0.136917 | ||||||||
\(773\) | 6.94742 | 0.249881 | 0.124941 | − | 0.992164i | \(-0.460126\pi\) | ||||
0.124941 | + | 0.992164i | \(0.460126\pi\) | |||||||
\(774\) | 4.97980 | 0.178995 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.0902 | −0.469910 | ||||||||
\(777\) | 2.43769 | 0.0874518 | ||||||||
\(778\) | −16.6295 | −0.596196 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1352 | −0.398447 | ||||||||
\(782\) | −6.36737 | −0.227697 | ||||||||
\(783\) | −47.6869 | −1.70419 | ||||||||
\(784\) | 16.5410 | 0.590751 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.4934 | −0.659639 | ||||||||
\(787\) | −43.9856 | −1.56792 | −0.783959 | − | 0.620812i | \(-0.786803\pi\) | ||||
−0.783959 | + | 0.620812i | \(0.786803\pi\) | |||||||
\(788\) | −12.9098 | −0.459894 | ||||||||
\(789\) | 7.05342 | 0.251109 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.02908 | −0.0365899 | ||||||||
\(792\) | 4.25325 | 0.151133 | ||||||||
\(793\) | −10.1311 | −0.359766 | ||||||||
\(794\) | −35.0706 | −1.24461 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.29180 | 0.293895 | ||||||||
\(797\) | 4.14725 | 0.146903 | 0.0734516 | − | 0.997299i | \(-0.476599\pi\) | ||||
0.0734516 | + | 0.997299i | \(0.476599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.70820 | 0.201942 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4863 | 0.476515 | ||||||||
\(802\) | 12.7639 | 0.450710 | ||||||||
\(803\) | 0.854102 | 0.0301406 | ||||||||
\(804\) | 8.41641 | 0.296824 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00406 | 0.0353664 | ||||||||
\(807\) | −7.36068 | −0.259108 | ||||||||
\(808\) | −51.4226 | −1.80904 | ||||||||
\(809\) | −1.78522 | −0.0627649 | −0.0313825 | − | 0.999507i | \(-0.509991\pi\) | ||||
−0.0313825 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.2663 | −0.746760 | −0.373380 | − | 0.927679i | \(-0.621801\pi\) | ||||
−0.373380 | + | 0.927679i | \(0.621801\pi\) | |||||||
\(812\) | 1.28157 | 0.0449743 | ||||||||
\(813\) | 7.50245 | 0.263122 | ||||||||
\(814\) | −8.81966 | −0.309129 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.13914 | 0.0748848 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −21.3050 | −0.744910 | ||||||||
\(819\) | 0.277515 | 0.00969714 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.4508 | 0.992942 | 0.496471 | − | 0.868053i | \(-0.334629\pi\) | ||||
0.496471 | + | 0.868053i | \(0.334629\pi\) | |||||||
\(822\) | −19.6738 | −0.686201 | ||||||||
\(823\) | 21.2361 | 0.740243 | 0.370121 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370121 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(824\) | −4.14590 | −0.144429 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.13777 | −0.109177 | ||||||||
\(827\) | −2.17963 | −0.0757931 | −0.0378965 | − | 0.999282i | \(-0.512066\pi\) | ||||
−0.0378965 | + | 0.999282i | \(0.512066\pi\) | |||||||
\(828\) | 7.09017 | 0.246400 | ||||||||
\(829\) | −20.7517 | −0.720737 | −0.360369 | − | 0.932810i | \(-0.617349\pi\) | ||||
−0.360369 | + | 0.932810i | \(0.617349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.8950 | 1.17580 | ||||||||
\(832\) | 6.32688 | 0.219345 | ||||||||
\(833\) | 5.30495 | 0.183806 | ||||||||
\(834\) | −15.0770 | −0.522074 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.38197 | −0.220593 | ||||||||
\(838\) | 4.49028 | 0.155114 | ||||||||
\(839\) | −10.4086 | −0.359346 | −0.179673 | − | 0.983726i | \(-0.557504\pi\) | ||||
−0.179673 | + | 0.983726i | \(0.557504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.1591 | 1.66066 | ||||||||
\(842\) | 7.03444 | 0.242423 | ||||||||
\(843\) | 12.6869 | 0.436961 | ||||||||
\(844\) | 8.78402 | 0.302359 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.2128 | 0.488648 | ||||||||
\(847\) | 2.42454 | 0.0833081 | ||||||||
\(848\) | −2.39163 | −0.0821289 | ||||||||
\(849\) | −6.19586 | −0.212641 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −62.2802 | −2.13494 | ||||||||
\(852\) | 9.47214 | 0.324510 | ||||||||
\(853\) | 6.52786 | 0.223510 | 0.111755 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111755 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(854\) | 3.86974 | 0.132420 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.9443 | −0.818398 | ||||||||
\(857\) | 35.5851 | 1.21556 | 0.607782 | − | 0.794104i | \(-0.292059\pi\) | ||||
0.607782 | + | 0.794104i | \(0.292059\pi\) | |||||||
\(858\) | 0.857567 | 0.0292769 | ||||||||
\(859\) | −27.2361 | −0.929283 | −0.464641 | − | 0.885499i | \(-0.653817\pi\) | ||||
−0.464641 | + | 0.885499i | \(0.653817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.450850 | 0.0153649 | ||||||||
\(862\) | 1.90983 | 0.0650491 | ||||||||
\(863\) | 24.8335 | 0.845341 | 0.422671 | − | 0.906283i | \(-0.361093\pi\) | ||||
0.422671 | + | 0.906283i | \(0.361093\pi\) | |||||||
\(864\) | −18.2148 | −0.619679 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.5066 | −0.900730 | ||||||||
\(867\) | −19.2986 | −0.655416 | ||||||||
\(868\) | 0.171513 | 0.00582154 | ||||||||
\(869\) | −7.26543 | −0.246463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.41641 | −0.285179 | ||||||||
\(872\) | 28.4164 | 0.962301 | ||||||||
\(873\) | −6.88191 | −0.232917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.726543 | −0.0245476 | ||||||||
\(877\) | 23.1684 | 0.782341 | 0.391170 | − | 0.920318i | \(-0.372070\pi\) | ||||
0.391170 | + | 0.920318i | \(0.372070\pi\) | |||||||
\(878\) | 44.2705 | 1.49406 | ||||||||
\(879\) | 36.3050 | 1.22454 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.32624 | −0.179446 | −0.0897228 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897228 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(882\) | 13.2088 | 0.444763 | ||||||||
\(883\) | 57.2148 | 1.92543 | 0.962715 | − | 0.270516i | \(-0.0871944\pi\) | ||||
0.962715 | + | 0.270516i | \(0.0871944\pi\) | |||||||
\(884\) | 0.343027 | 0.0115372 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 43.2341 | 1.45248 | ||||||||
\(887\) | 19.3642 | 0.650185 | 0.325092 | − | 0.945682i | \(-0.394605\pi\) | ||||
0.325092 | + | 0.945682i | \(0.394605\pi\) | |||||||
\(888\) | 31.7809 | 1.06650 | ||||||||
\(889\) | −0.514540 | −0.0172571 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.30495 | −0.0437175 | ||||||||
\(892\) | 12.2047 | 0.408645 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −5.65248 | −0.189047 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.832544 | −0.0278133 | ||||||||
\(897\) | 6.05573 | 0.202195 | ||||||||
\(898\) | 44.2705 | 1.47733 | ||||||||
\(899\) | 10.3262 | 0.344399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.767031 | −0.0255535 | ||||||||
\(902\) | −1.63119 | −0.0543127 | ||||||||
\(903\) | 0.726543 | 0.0241778 | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.8990 | −0.827213 | ||||||||
\(907\) | −41.5035 | −1.37810 | −0.689050 | − | 0.724714i | \(-0.741972\pi\) | ||||
−0.689050 | + | 0.724714i | \(0.741972\pi\) | |||||||
\(908\) | 11.5187 | 0.382261 | ||||||||
\(909\) | −27.0344 | −0.896676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.9718 | −0.429774 | −0.214887 | − | 0.976639i | \(-0.568938\pi\) | ||||
−0.214887 | + | 0.976639i | \(0.568938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3050 | 0.374139 | ||||||||
\(914\) | −0.898056 | −0.0297051 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.3607 | 0.507531 | ||||||||
\(917\) | 3.15905 | 0.104321 | ||||||||
\(918\) | 4.87539 | 0.160912 | ||||||||
\(919\) | −37.3607 | −1.23242 | −0.616208 | − | 0.787584i | \(-0.711332\pi\) | ||||
−0.616208 | + | 0.787584i | \(0.711332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.9230 | 0.985996 | ||||||||
\(922\) | −9.40456 | −0.309723 | ||||||||
\(923\) | −9.47214 | −0.311779 | ||||||||
\(924\) | 0.146490 | 0.00481917 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.05748 | −0.264785 | ||||||||
\(927\) | −2.17963 | −0.0715884 | ||||||||
\(928\) | 29.4721 | 0.967470 | ||||||||
\(929\) | 17.4377 | 0.572112 | 0.286056 | − | 0.958213i | \(-0.407656\pi\) | ||||
0.286056 | + | 0.958213i | \(0.407656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.85410 | 0.126245 | ||||||||
\(933\) | −8.50651 | −0.278491 | ||||||||
\(934\) | −15.4944 | −0.506993 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.61803 | 0.118259 | ||||||||
\(937\) | −47.7984 | −1.56150 | −0.780752 | − | 0.624841i | \(-0.785164\pi\) | ||||
−0.780752 | + | 0.624841i | \(0.785164\pi\) | |||||||
\(938\) | 3.21478 | 0.104966 | ||||||||
\(939\) | 35.5851 | 1.16128 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.6013 | 1.29097 | 0.645484 | − | 0.763774i | \(-0.276656\pi\) | ||||
0.645484 | + | 0.763774i | \(0.276656\pi\) | |||||||
\(942\) | −23.8673 | −0.777637 | ||||||||
\(943\) | −11.5187 | −0.375100 | ||||||||
\(944\) | −26.9321 | −0.876566 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.62866 | −0.0854650 | ||||||||
\(947\) | 25.4164 | 0.825922 | 0.412961 | − | 0.910749i | \(-0.364495\pi\) | ||||
0.412961 | + | 0.910749i | \(0.364495\pi\) | |||||||
\(948\) | 6.18034 | 0.200728 | ||||||||
\(949\) | 0.726543 | 0.0235846 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.3050 | −1.01513 | ||||||||
\(952\) | −0.555029 | −0.0179886 | ||||||||
\(953\) | −55.0148 | −1.78210 | −0.891052 | − | 0.453901i | \(-0.850032\pi\) | ||||
−0.891052 | + | 0.453901i | \(0.850032\pi\) | |||||||
\(954\) | −1.90983 | −0.0618330 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.4377 | −0.563975 | ||||||||
\(957\) | 8.81966 | 0.285099 | ||||||||
\(958\) | −37.1037 | −1.19877 | ||||||||
\(959\) | 3.36068 | 0.108522 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6180 | −0.955420 | ||||||||
\(962\) | −7.50245 | −0.241889 | ||||||||
\(963\) | −12.5882 | −0.405651 | ||||||||
\(964\) | −8.95554 | −0.288438 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.31308 | −0.0744222 | ||||||||
\(967\) | 46.9443 | 1.50963 | 0.754813 | − | 0.655940i | \(-0.227728\pi\) | ||||
0.754813 | + | 0.655940i | \(0.227728\pi\) | |||||||
\(968\) | 31.6094 | 1.01596 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.5964 | 0.468420 | 0.234210 | − | 0.972186i | \(-0.424750\pi\) | ||||
0.234210 | + | 0.972186i | \(0.424750\pi\) | |||||||
\(972\) | −8.95554 | −0.287249 | ||||||||
\(973\) | 2.57546 | 0.0825655 | ||||||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.2148 | 1.06318 | ||||||||
\(977\) | 4.31877 | 0.138170 | 0.0690848 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690848 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(978\) | 3.89667 | 0.124602 | ||||||||
\(979\) | −7.11894 | −0.227522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.9394 | 0.476978 | ||||||||
\(982\) | 4.38428 | 0.139908 | ||||||||
\(983\) | −6.26137 | −0.199707 | −0.0998533 | − | 0.995002i | \(-0.531837\pi\) | ||||
−0.0998533 | + | 0.995002i | \(0.531837\pi\) | |||||||
\(984\) | 5.87785 | 0.187379 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.88854 | −0.251222 | ||||||||
\(987\) | 2.07363 | 0.0660043 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.5623 | −0.590247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2500 | 0.547966 | 0.273983 | − | 0.961735i | \(-0.411659\pi\) | ||||
0.273983 | + | 0.961735i | \(0.411659\pi\) | |||||||
\(992\) | 3.94427 | 0.125231 | ||||||||
\(993\) | −2.11146 | −0.0670050 | ||||||||
\(994\) | 3.61803 | 0.114757 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.61657 | −0.304713 | ||||||||
\(997\) | 19.0557 | 0.603501 | 0.301750 | − | 0.953387i | \(-0.402429\pi\) | ||||
0.301750 | + | 0.953387i | \(0.402429\pi\) | |||||||
\(998\) | −45.2267 | −1.43163 | ||||||||
\(999\) | 47.6869 | 1.50875 |
(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 | 9025.2.a.bl.1.3 | 4 | ||
5.4 | even | 2 | 1805.2.a.l.1.2 | ✓ | 4 | ||
19.18 | odd | 2 | inner | 9025.2.a.bl.1.2 | 4 | ||
95.94 | odd | 2 | 1805.2.a.l.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.l.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
1805.2.a.l.1.3 | yes | 4 | 95.94 | odd | 2 | ||
9025.2.a.bl.1.2 | 4 | 19.18 | odd | 2 | inner | ||
9025.2.a.bl.1.3 | 4 | 1.1 | even | 1 | trivial |