Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
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: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.38197 | 0.564185 | ||||||||
\(7\) | 0.236068 | 0.0892253 | 0.0446127 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446127 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(8\) | −3.07768 | −1.08813 | ||||||||
\(9\) | −1.61803 | −0.539345 | ||||||||
\(10\) | −1.17557 | −0.371748 | ||||||||
\(11\) | 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 | ||||||||
\(15\) | −1.17557 | −0.303531 | ||||||||
\(16\) | −2.38197 | −0.595492 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | −1.90211 | −0.448332 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | 0.277515 | 0.0605586 | ||||||||
\(22\) | 1.00406 | 0.214066 | ||||||||
\(23\) | −7.09017 | −1.47840 | −0.739201 | − | 0.673485i | \(-0.764797\pi\) | ||||
−0.739201 | + | 0.673485i | \(0.764797\pi\) | |||||||
\(24\) | −3.61803 | −0.738528 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.854102 | 0.167503 | ||||||||
\(27\) | −5.42882 | −1.04478 | ||||||||
\(28\) | −0.145898 | −0.0275721 | ||||||||
\(29\) | −8.78402 | −1.63115 | −0.815576 | − | 0.578650i | \(-0.803580\pi\) | ||||
−0.815576 | + | 0.578650i | \(0.803580\pi\) | |||||||
\(30\) | −1.38197 | −0.252311 | ||||||||
\(31\) | −1.17557 | −0.211139 | −0.105569 | − | 0.994412i | \(-0.533667\pi\) | ||||
−0.105569 | + | 0.994412i | \(0.533667\pi\) | |||||||
\(32\) | 3.35520 | 0.593121 | ||||||||
\(33\) | 1.00406 | 0.174784 | ||||||||
\(34\) | 0.898056 | 0.154015 | ||||||||
\(35\) | −0.236068 | −0.0399028 | ||||||||
\(36\) | 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 | ||||||||
\(40\) | 3.07768 | 0.486624 | ||||||||
\(41\) | 1.62460 | 0.253720 | 0.126860 | − | 0.991921i | \(-0.459510\pi\) | ||||
0.126860 | + | 0.991921i | \(0.459510\pi\) | |||||||
\(42\) | 0.326238 | 0.0503396 | ||||||||
\(43\) | 2.61803 | 0.399246 | 0.199623 | − | 0.979873i | \(-0.436028\pi\) | ||||
0.199623 | + | 0.979873i | \(0.436028\pi\) | |||||||
\(44\) | −0.527864 | −0.0795785 | ||||||||
\(45\) | 1.61803 | 0.241202 | ||||||||
\(46\) | −8.33499 | −1.22893 | ||||||||
\(47\) | 7.47214 | 1.08992 | 0.544962 | − | 0.838461i | \(-0.316544\pi\) | ||||
0.544962 | + | 0.838461i | \(0.316544\pi\) | |||||||
\(48\) | −2.80017 | −0.404170 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 1.17557 | 0.166251 | ||||||||
\(51\) | 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 | ||||||||
\(55\) | −0.854102 | −0.115167 | ||||||||
\(56\) | −0.726543 | −0.0970883 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.3262 | −1.35590 | ||||||||
\(59\) | −11.3067 | −1.47200 | −0.736002 | − | 0.676979i | \(-0.763289\pi\) | ||||
−0.736002 | + | 0.676979i | \(0.763289\pi\) | |||||||
\(60\) | 0.726543 | 0.0937962 | ||||||||
\(61\) | −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 | ||||||||
\(65\) | −0.726543 | −0.0901165 | ||||||||
\(66\) | 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 | ||||||||
\(70\) | −0.277515 | −0.0331693 | ||||||||
\(71\) | 13.0373 | 1.54724 | 0.773620 | − | 0.633650i | \(-0.218444\pi\) | ||||
0.773620 | + | 0.633650i | \(0.218444\pi\) | |||||||
\(72\) | 4.97980 | 0.586875 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −10.3262 | −1.20040 | ||||||||
\(75\) | 1.17557 | 0.135743 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.201626 | 0.0229774 | ||||||||
\(78\) | 1.00406 | 0.113687 | ||||||||
\(79\) | 8.50651 | 0.957057 | 0.478528 | − | 0.878072i | \(-0.341170\pi\) | ||||
0.478528 | + | 0.878072i | \(0.341170\pi\) | |||||||
\(80\) | 2.38197 | 0.266312 | ||||||||
\(81\) | −1.52786 | −0.169763 | ||||||||
\(82\) | 1.90983 | 0.210905 | ||||||||
\(83\) | −13.2361 | −1.45285 | −0.726424 | − | 0.687247i | \(-0.758819\pi\) | ||||
−0.726424 | + | 0.687247i | \(0.758819\pi\) | |||||||
\(84\) | −0.171513 | −0.0187136 | ||||||||
\(85\) | −0.763932 | −0.0828601 | ||||||||
\(86\) | 3.07768 | 0.331875 | ||||||||
\(87\) | −10.3262 | −1.10709 | ||||||||
\(88\) | −2.62866 | −0.280216 | ||||||||
\(89\) | 8.33499 | 0.883508 | 0.441754 | − | 0.897136i | \(-0.354356\pi\) | ||||
0.441754 | + | 0.897136i | \(0.354356\pi\) | |||||||
\(90\) | 1.90211 | 0.200500 | ||||||||
\(91\) | 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 | ||||||||
\(100\) | −0.618034 | −0.0618034 | ||||||||
\(101\) | 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 | ||||||||
\(105\) | −0.277515 | −0.0270826 | ||||||||
\(106\) | 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 | \(-0.354204\pi\) | ||||
0.442183 | + | 0.896925i | \(0.354204\pi\) | |||||||
\(110\) | −1.00406 | −0.0957331 | ||||||||
\(111\) | −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 | ||||||||
\(115\) | 7.09017 | 0.661162 | ||||||||
\(116\) | 5.42882 | 0.504054 | ||||||||
\(117\) | −1.17557 | −0.108682 | ||||||||
\(118\) | −13.2918 | −1.22361 | ||||||||
\(119\) | 0.180340 | 0.0165317 | ||||||||
\(120\) | 3.61803 | 0.330280 | ||||||||
\(121\) | −10.2705 | −0.933683 | ||||||||
\(122\) | −16.3925 | −1.48410 | ||||||||
\(123\) | 1.90983 | 0.172204 | ||||||||
\(124\) | 0.726543 | 0.0652454 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −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 | ||||||||
\(130\) | −0.854102 | −0.0749097 | ||||||||
\(131\) | −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 | ||||||||
\(135\) | 5.42882 | 0.467239 | ||||||||
\(136\) | −2.35114 | −0.201609 | ||||||||
\(137\) | 14.2361 | 1.21627 | 0.608135 | − | 0.793834i | \(-0.291918\pi\) | ||||
0.608135 | + | 0.793834i | \(0.291918\pi\) | |||||||
\(138\) | −9.79837 | −0.834093 | ||||||||
\(139\) | −10.9098 | −0.925360 | −0.462680 | − | 0.886525i | \(-0.653112\pi\) | ||||
−0.462680 | + | 0.886525i | \(0.653112\pi\) | |||||||
\(140\) | 0.145898 | 0.0123306 | ||||||||
\(141\) | 8.78402 | 0.739748 | ||||||||
\(142\) | 15.3262 | 1.28615 | ||||||||
\(143\) | 0.620541 | 0.0518923 | ||||||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | 8.78402 | 0.729473 | ||||||||
\(146\) | −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 | \(0.553582\pi\) | |||||||
\(150\) | 1.38197 | 0.112837 | ||||||||
\(151\) | 18.0171 | 1.46621 | 0.733104 | − | 0.680116i | \(-0.238071\pi\) | ||||
0.733104 | + | 0.680116i | \(0.238071\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.23607 | −0.0999302 | ||||||||
\(154\) | 0.237026 | 0.0191001 | ||||||||
\(155\) | 1.17557 | 0.0944241 | ||||||||
\(156\) | −0.527864 | −0.0422629 | ||||||||
\(157\) | 17.2705 | 1.37834 | 0.689168 | − | 0.724601i | \(-0.257976\pi\) | ||||
0.689168 | + | 0.724601i | \(0.257976\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | 1.18034 | 0.0936070 | ||||||||
\(160\) | −3.35520 | −0.265252 | ||||||||
\(161\) | −1.67376 | −0.131911 | ||||||||
\(162\) | −1.79611 | −0.141116 | ||||||||
\(163\) | −2.81966 | −0.220853 | −0.110426 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110426 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(164\) | −1.00406 | −0.0784037 | ||||||||
\(165\) | −1.00406 | −0.0781657 | ||||||||
\(166\) | −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 | ||||||||
\(170\) | −0.898056 | −0.0688777 | ||||||||
\(171\) | 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 | ||||||||
\(175\) | 0.236068 | 0.0178451 | ||||||||
\(176\) | −2.03444 | −0.153352 | ||||||||
\(177\) | −13.2918 | −0.999073 | ||||||||
\(178\) | 9.79837 | 0.734419 | ||||||||
\(179\) | 12.1392 | 0.907328 | 0.453664 | − | 0.891173i | \(-0.350117\pi\) | ||||
0.453664 | + | 0.891173i | \(0.350117\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 14.6619 | 1.08981 | 0.544904 | − | 0.838498i | \(-0.316566\pi\) | ||||
0.544904 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(182\) | 0.201626 | 0.0149455 | ||||||||
\(183\) | −16.3925 | −1.21177 | ||||||||
\(184\) | 21.8213 | 1.60869 | ||||||||
\(185\) | 8.78402 | 0.645814 | ||||||||
\(186\) | −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 | ||||||||
\(195\) | −0.854102 | −0.0611635 | ||||||||
\(196\) | 4.29180 | 0.306557 | ||||||||
\(197\) | −20.8885 | −1.48825 | −0.744124 | − | 0.668042i | \(-0.767133\pi\) | ||||
−0.744124 | + | 0.668042i | \(0.767133\pi\) | |||||||
\(198\) | −1.62460 | −0.115455 | ||||||||
\(199\) | −13.4164 | −0.951064 | −0.475532 | − | 0.879698i | \(-0.657744\pi\) | ||||
−0.475532 | + | 0.879698i | \(0.657744\pi\) | |||||||
\(200\) | −3.07768 | −0.217625 | ||||||||
\(201\) | −13.6180 | −0.960542 | ||||||||
\(202\) | 19.6417 | 1.38198 | ||||||||
\(203\) | −2.07363 | −0.145540 | ||||||||
\(204\) | −0.555029 | −0.0388598 | ||||||||
\(205\) | −1.62460 | −0.113467 | ||||||||
\(206\) | 1.58359 | 0.110334 | ||||||||
\(207\) | 11.4721 | 0.797369 | ||||||||
\(208\) | −1.73060 | −0.119995 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.326238 | −0.0225126 | ||||||||
\(211\) | 14.2128 | 0.978453 | 0.489226 | − | 0.872157i | \(-0.337279\pi\) | ||||
0.489226 | + | 0.872157i | \(0.337279\pi\) | |||||||
\(212\) | −0.620541 | −0.0426190 | ||||||||
\(213\) | 15.3262 | 1.05014 | ||||||||
\(214\) | 9.14590 | 0.625201 | ||||||||
\(215\) | −2.61803 | −0.178548 | ||||||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | −0.277515 | −0.0188389 | ||||||||
\(218\) | 10.8541 | 0.735133 | ||||||||
\(219\) | −1.17557 | −0.0794377 | ||||||||
\(220\) | 0.527864 | 0.0355886 | ||||||||
\(221\) | 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 | ||||||||
\(225\) | −1.61803 | −0.107869 | ||||||||
\(226\) | 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 | \(0.806696\pi\) | |||||||
\(230\) | 8.33499 | 0.549593 | ||||||||
\(231\) | 0.237026 | 0.0155951 | ||||||||
\(232\) | 27.0344 | 1.77490 | ||||||||
\(233\) | 6.23607 | 0.408538 | 0.204269 | − | 0.978915i | \(-0.434518\pi\) | ||||
0.204269 | + | 0.978915i | \(0.434518\pi\) | |||||||
\(234\) | −1.38197 | −0.0903419 | ||||||||
\(235\) | −7.47214 | −0.487428 | ||||||||
\(236\) | 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 | \(0.134125\pi\) | |||||||
\(240\) | 2.80017 | 0.180750 | ||||||||
\(241\) | −14.4904 | −0.933406 | −0.466703 | − | 0.884414i | \(-0.654558\pi\) | ||||
−0.466703 | + | 0.884414i | \(0.654558\pi\) | |||||||
\(242\) | −12.0737 | −0.776127 | ||||||||
\(243\) | 14.4904 | 0.929557 | ||||||||
\(244\) | 8.61803 | 0.551713 | ||||||||
\(245\) | 6.94427 | 0.443653 | ||||||||
\(246\) | 2.24514 | 0.143145 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.61803 | 0.229745 | ||||||||
\(249\) | −15.5599 | −0.986071 | ||||||||
\(250\) | −1.17557 | −0.0743496 | ||||||||
\(251\) | −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 | ||||||||
\(255\) | −0.898056 | −0.0562384 | ||||||||
\(256\) | −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 | ||||||||
\(260\) | 0.449028 | 0.0278475 | ||||||||
\(261\) | 14.2128 | 0.879753 | ||||||||
\(262\) | −15.7314 | −0.971892 | ||||||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | −3.09017 | −0.190187 | ||||||||
\(265\) | −1.00406 | −0.0616787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.79837 | 0.599651 | ||||||||
\(268\) | 7.15942 | 0.437331 | ||||||||
\(269\) | 6.26137 | 0.381762 | 0.190881 | − | 0.981613i | \(-0.438865\pi\) | ||||
0.190881 | + | 0.981613i | \(0.438865\pi\) | |||||||
\(270\) | 6.38197 | 0.388394 | ||||||||
\(271\) | 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 | ||||||||
\(275\) | 0.854102 | 0.0515043 | ||||||||
\(276\) | 5.15131 | 0.310072 | ||||||||
\(277\) | −28.8328 | −1.73240 | −0.866198 | − | 0.499701i | \(-0.833443\pi\) | ||||
−0.866198 | + | 0.499701i | \(0.833443\pi\) | |||||||
\(278\) | −12.8253 | −0.769209 | ||||||||
\(279\) | 1.90211 | 0.113877 | ||||||||
\(280\) | 0.726543 | 0.0434192 | ||||||||
\(281\) | −10.7921 | −0.643805 | −0.321902 | − | 0.946773i | \(-0.604322\pi\) | ||||
−0.321902 | + | 0.946773i | \(0.604322\pi\) | |||||||
\(282\) | 10.3262 | 0.614919 | ||||||||
\(283\) | 5.27051 | 0.313299 | 0.156650 | − | 0.987654i | \(-0.449931\pi\) | ||||
0.156650 | + | 0.987654i | \(0.449931\pi\) | |||||||
\(284\) | −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 | ||||||||
\(290\) | 10.3262 | 0.606378 | ||||||||
\(291\) | 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 | ||||||||
\(295\) | 11.3067 | 0.658300 | ||||||||
\(296\) | 27.0344 | 1.57135 | ||||||||
\(297\) | −4.63677 | −0.269053 | ||||||||
\(298\) | −4.80828 | −0.278536 | ||||||||
\(299\) | −5.15131 | −0.297908 | ||||||||
\(300\) | −0.726543 | −0.0419470 | ||||||||
\(301\) | 0.618034 | 0.0356229 | ||||||||
\(302\) | 21.1803 | 1.21879 | ||||||||
\(303\) | 19.6417 | 1.12838 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9443 | 0.798447 | ||||||||
\(306\) | −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 | ||||||||
\(310\) | 1.38197 | 0.0784904 | ||||||||
\(311\) | −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 | \(-0.826747\pi\) | ||||
−0.855495 | + | 0.517811i | \(0.826747\pi\) | |||||||
\(314\) | 20.3027 | 1.14575 | ||||||||
\(315\) | 0.381966 | 0.0215213 | ||||||||
\(316\) | −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 | ||||||||
\(320\) | −8.70820 | −0.486803 | ||||||||
\(321\) | 9.14590 | 0.510474 | ||||||||
\(322\) | −1.96763 | −0.109651 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.944272 | 0.0524596 | ||||||||
\(325\) | 0.726543 | 0.0403013 | ||||||||
\(326\) | −3.31471 | −0.183585 | ||||||||
\(327\) | 10.8541 | 0.600233 | ||||||||
\(328\) | −5.00000 | −0.276079 | ||||||||
\(329\) | 1.76393 | 0.0972487 | ||||||||
\(330\) | −1.18034 | −0.0649756 | ||||||||
\(331\) | 1.79611 | 0.0987232 | 0.0493616 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493616 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(332\) | 8.18034 | 0.448954 | ||||||||
\(333\) | 14.2128 | 0.778859 | ||||||||
\(334\) | 15.3262 | 0.838614 | ||||||||
\(335\) | 11.5842 | 0.632912 | ||||||||
\(336\) | −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 | ||||||||
\(340\) | 0.472136 | 0.0256052 | ||||||||
\(341\) | −1.00406 | −0.0543727 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.29180 | −0.177740 | ||||||||
\(344\) | −8.05748 | −0.434430 | ||||||||
\(345\) | 8.33499 | 0.448741 | ||||||||
\(346\) | −15.1246 | −0.813104 | ||||||||
\(347\) | 7.52786 | 0.404117 | 0.202058 | − | 0.979373i | \(-0.435237\pi\) | ||||
0.202058 | + | 0.979373i | \(0.435237\pi\) | |||||||
\(348\) | 6.38197 | 0.342109 | ||||||||
\(349\) | 17.5623 | 0.940089 | 0.470044 | − | 0.882643i | \(-0.344238\pi\) | ||||
0.470044 | + | 0.882643i | \(0.344238\pi\) | |||||||
\(350\) | 0.277515 | 0.0148338 | ||||||||
\(351\) | −3.94427 | −0.210530 | ||||||||
\(352\) | 2.86568 | 0.152741 | ||||||||
\(353\) | 19.3262 | 1.02863 | 0.514316 | − | 0.857601i | \(-0.328046\pi\) | ||||
0.514316 | + | 0.857601i | \(0.328046\pi\) | |||||||
\(354\) | −15.6254 | −0.830483 | ||||||||
\(355\) | −13.0373 | −0.691947 | ||||||||
\(356\) | −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 | \(0.418316\pi\) | |||||||
\(360\) | −4.97980 | −0.262458 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.2361 | 0.905908 | ||||||||
\(363\) | −12.0737 | −0.633705 | ||||||||
\(364\) | −0.106001 | −0.00555597 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −19.2705 | −1.00729 | ||||||||
\(367\) | −27.0689 | −1.41298 | −0.706492 | − | 0.707721i | \(-0.749723\pi\) | ||||
−0.706492 | + | 0.707721i | \(0.749723\pi\) | |||||||
\(368\) | 16.8885 | 0.880376 | ||||||||
\(369\) | −2.62866 | −0.136842 | ||||||||
\(370\) | 10.3262 | 0.536836 | ||||||||
\(371\) | 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 | ||||||||
\(375\) | −1.17557 | −0.0607062 | ||||||||
\(376\) | −22.9969 | −1.18597 | ||||||||
\(377\) | −6.38197 | −0.328688 | ||||||||
\(378\) | −1.50658 | −0.0774900 | ||||||||
\(379\) | 13.2088 | 0.678490 | 0.339245 | − | 0.940698i | \(-0.389828\pi\) | ||||
0.339245 | + | 0.940698i | \(0.389828\pi\) | |||||||
\(380\) | 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 | ||||||||
\(385\) | −0.201626 | −0.0102758 | ||||||||
\(386\) | −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 | \(0.616750\pi\) | |||||||
\(390\) | −1.00406 | −0.0508424 | ||||||||
\(391\) | −5.41641 | −0.273920 | ||||||||
\(392\) | 21.3723 | 1.07946 | ||||||||
\(393\) | −15.7314 | −0.793546 | ||||||||
\(394\) | −24.5560 | −1.23711 | ||||||||
\(395\) | −8.50651 | −0.428009 | ||||||||
\(396\) | 0.854102 | 0.0429202 | ||||||||
\(397\) | 29.8328 | 1.49727 | 0.748633 | − | 0.662985i | \(-0.230711\pi\) | ||||
0.748633 | + | 0.662985i | \(0.230711\pi\) | |||||||
\(398\) | −15.7719 | −0.790576 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.38197 | −0.119098 | ||||||||
\(401\) | −10.8576 | −0.542205 | −0.271103 | − | 0.962550i | \(-0.587388\pi\) | ||||
−0.271103 | + | 0.962550i | \(0.587388\pi\) | |||||||
\(402\) | −16.0090 | −0.798454 | ||||||||
\(403\) | −0.854102 | −0.0425458 | ||||||||
\(404\) | −10.3262 | −0.513750 | ||||||||
\(405\) | 1.52786 | 0.0759202 | ||||||||
\(406\) | −2.43769 | −0.120981 | ||||||||
\(407\) | −7.50245 | −0.371883 | ||||||||
\(408\) | −2.76393 | −0.136835 | ||||||||
\(409\) | 18.1231 | 0.896128 | 0.448064 | − | 0.894001i | \(-0.352114\pi\) | ||||
0.448064 | + | 0.894001i | \(0.352114\pi\) | |||||||
\(410\) | −1.90983 | −0.0943198 | ||||||||
\(411\) | 16.7355 | 0.825501 | ||||||||
\(412\) | −0.832544 | −0.0410165 | ||||||||
\(413\) | −2.66914 | −0.131340 | ||||||||
\(414\) | 13.4863 | 0.662816 | ||||||||
\(415\) | 13.2361 | 0.649733 | ||||||||
\(416\) | 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 | \(0.470258\pi\) | |||||||
\(420\) | 0.171513 | 0.00836900 | ||||||||
\(421\) | −5.98385 | −0.291635 | −0.145818 | − | 0.989311i | \(-0.546581\pi\) | ||||
−0.145818 | + | 0.989311i | \(0.546581\pi\) | |||||||
\(422\) | 16.7082 | 0.813343 | ||||||||
\(423\) | −12.0902 | −0.587844 | ||||||||
\(424\) | −3.09017 | −0.150072 | ||||||||
\(425\) | 0.763932 | 0.0370561 | ||||||||
\(426\) | 18.0171 | 0.872930 | ||||||||
\(427\) | −3.29180 | −0.159301 | ||||||||
\(428\) | −4.80828 | −0.232417 | ||||||||
\(429\) | 0.729490 | 0.0352201 | ||||||||
\(430\) | −3.07768 | −0.148419 | ||||||||
\(431\) | −1.62460 | −0.0782542 | −0.0391271 | − | 0.999234i | \(-0.512458\pi\) | ||||
−0.0391271 | + | 0.999234i | \(0.512458\pi\) | |||||||
\(432\) | 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 | ||||||||
\(435\) | 10.3262 | 0.495105 | ||||||||
\(436\) | −5.70634 | −0.273284 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.38197 | −0.0660329 | ||||||||
\(439\) | −37.6587 | −1.79735 | −0.898677 | − | 0.438611i | \(-0.855471\pi\) | ||||
−0.898677 | + | 0.438611i | \(0.855471\pi\) | |||||||
\(440\) | 2.62866 | 0.125316 | ||||||||
\(441\) | 11.2361 | 0.535051 | ||||||||
\(442\) | 0.652476 | 0.0310351 | ||||||||
\(443\) | −36.7771 | −1.74733 | −0.873666 | − | 0.486526i | \(-0.838264\pi\) | ||||
−0.873666 | + | 0.486526i | \(0.838264\pi\) | |||||||
\(444\) | 6.38197 | 0.302875 | ||||||||
\(445\) | −8.33499 | −0.395117 | ||||||||
\(446\) | −23.2148 | −1.09925 | ||||||||
\(447\) | −4.80828 | −0.227424 | ||||||||
\(448\) | 2.05573 | 0.0971240 | ||||||||
\(449\) | −37.6587 | −1.77723 | −0.888613 | − | 0.458658i | \(-0.848330\pi\) | ||||
−0.888613 | + | 0.458658i | \(0.848330\pi\) | |||||||
\(450\) | −1.90211 | −0.0896665 | ||||||||
\(451\) | 1.38757 | 0.0653382 | ||||||||
\(452\) | −2.69417 | −0.126723 | ||||||||
\(453\) | 21.1803 | 0.995139 | ||||||||
\(454\) | −21.9098 | −1.02828 | ||||||||
\(455\) | −0.171513 | −0.00804067 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.763932 | 0.0357352 | 0.0178676 | − | 0.999840i | \(-0.494312\pi\) | ||||
0.0178676 | + | 0.999840i | \(0.494312\pi\) | |||||||
\(458\) | −29.2177 | −1.36526 | ||||||||
\(459\) | −4.14725 | −0.193577 | ||||||||
\(460\) | −4.38197 | −0.204310 | ||||||||
\(461\) | −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 | \(-0.449086\pi\) | ||||
0.159269 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(464\) | 20.9232 | 0.971337 | ||||||||
\(465\) | 1.38197 | 0.0640871 | ||||||||
\(466\) | 7.33094 | 0.339599 | ||||||||
\(467\) | 13.1803 | 0.609913 | 0.304957 | − | 0.952366i | \(-0.401358\pi\) | ||||
0.304957 | + | 0.952366i | \(0.401358\pi\) | |||||||
\(468\) | 0.726543 | 0.0335844 | ||||||||
\(469\) | −2.73466 | −0.126275 | ||||||||
\(470\) | −8.78402 | −0.405177 | ||||||||
\(471\) | 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 | \(0.756344\pi\) | |||||||
\(480\) | −3.94427 | −0.180031 | ||||||||
\(481\) | −6.38197 | −0.290993 | ||||||||
\(482\) | −17.0344 | −0.775898 | ||||||||
\(483\) | −1.96763 | −0.0895301 | ||||||||
\(484\) | 6.34752 | 0.288524 | ||||||||
\(485\) | −4.25325 | −0.193130 | ||||||||
\(486\) | 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 | ||||||||
\(490\) | 8.16348 | 0.368788 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | 1.38197 | 0.0621148 | ||||||||
\(496\) | 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 | \(0.830239\pi\) | |||||||
\(500\) | 0.618034 | 0.0276393 | ||||||||
\(501\) | 15.3262 | 0.684726 | ||||||||
\(502\) | −3.52671 | −0.157405 | ||||||||
\(503\) | 0.347524 | 0.0154953 | 0.00774767 | − | 0.999970i | \(-0.497534\pi\) | ||||
0.00774767 | + | 0.999970i | \(0.497534\pi\) | |||||||
\(504\) | 1.17557 | 0.0523641 | ||||||||
\(505\) | −16.7082 | −0.743505 | ||||||||
\(506\) | −7.11894 | −0.316475 | ||||||||
\(507\) | −14.6619 | −0.651157 | ||||||||
\(508\) | −1.34708 | −0.0597672 | ||||||||
\(509\) | −10.7516 | −0.476558 | −0.238279 | − | 0.971197i | \(-0.576583\pi\) | ||||
−0.238279 | + | 0.971197i | \(0.576583\pi\) | |||||||
\(510\) | −1.05573 | −0.0467484 | ||||||||
\(511\) | −0.236068 | −0.0104430 | ||||||||
\(512\) | −22.6538 | −1.00117 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.1803 | −0.713684 | ||||||||
\(515\) | −1.34708 | −0.0593596 | ||||||||
\(516\) | −1.90211 | −0.0837359 | ||||||||
\(517\) | 6.38197 | 0.280679 | ||||||||
\(518\) | −2.43769 | −0.107106 | ||||||||
\(519\) | −15.1246 | −0.663897 | ||||||||
\(520\) | 2.23607 | 0.0980581 | ||||||||
\(521\) | −6.08985 | −0.266801 | −0.133401 | − | 0.991062i | \(-0.542590\pi\) | ||||
−0.133401 | + | 0.991062i | \(0.542590\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | 0.277515 | 0.0121117 | ||||||||
\(526\) | −7.05342 | −0.307544 | ||||||||
\(527\) | −0.898056 | −0.0391199 | ||||||||
\(528\) | −2.39163 | −0.104082 | ||||||||
\(529\) | 27.2705 | 1.18567 | ||||||||
\(530\) | −1.18034 | −0.0512707 | ||||||||
\(531\) | 18.2946 | 0.793917 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.18034 | 0.0511262 | ||||||||
\(534\) | 11.5187 | 0.498462 | ||||||||
\(535\) | −7.77997 | −0.336357 | ||||||||
\(536\) | 35.6525 | 1.53995 | ||||||||
\(537\) | 14.2705 | 0.615818 | ||||||||
\(538\) | 7.36068 | 0.317341 | ||||||||
\(539\) | −5.93112 | −0.255471 | ||||||||
\(540\) | −3.35520 | −0.144385 | ||||||||
\(541\) | 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 | ||||||||
\(545\) | −9.23305 | −0.395500 | ||||||||
\(546\) | 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 | ||||||||
\(550\) | 1.00406 | 0.0428131 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 25.6525 | 1.09184 | ||||||||
\(553\) | 2.00811 | 0.0853937 | ||||||||
\(554\) | −33.8950 | −1.44006 | ||||||||
\(555\) | 10.3262 | 0.438324 | ||||||||
\(556\) | 6.74265 | 0.285952 | ||||||||
\(557\) | 27.0689 | 1.14695 | 0.573473 | − | 0.819225i | \(-0.305596\pi\) | ||||
0.573473 | + | 0.819225i | \(0.305596\pi\) | |||||||
\(558\) | 2.23607 | 0.0946603 | ||||||||
\(559\) | 1.90211 | 0.0804508 | ||||||||
\(560\) | 0.562306 | 0.0237618 | ||||||||
\(561\) | 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 | ||||||||
\(565\) | −4.35926 | −0.183395 | ||||||||
\(566\) | 6.19586 | 0.260431 | ||||||||
\(567\) | −0.360680 | −0.0151471 | ||||||||
\(568\) | −40.1246 | −1.68359 | ||||||||
\(569\) | −7.71445 | −0.323407 | −0.161703 | − | 0.986839i | \(-0.551699\pi\) | ||||
−0.161703 | + | 0.986839i | \(0.551699\pi\) | |||||||
\(570\) | 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 | ||||||||
\(575\) | −7.09017 | −0.295681 | ||||||||
\(576\) | −14.0902 | −0.587090 | ||||||||
\(577\) | 17.4721 | 0.727375 | 0.363687 | − | 0.931521i | \(-0.381518\pi\) | ||||
0.363687 | + | 0.931521i | \(0.381518\pi\) | |||||||
\(578\) | −19.2986 | −0.802718 | ||||||||
\(579\) | −7.23607 | −0.300721 | ||||||||
\(580\) | −5.42882 | −0.225420 | ||||||||
\(581\) | −3.12461 | −0.129631 | ||||||||
\(582\) | 5.87785 | 0.243645 | ||||||||
\(583\) | 0.857567 | 0.0355168 | ||||||||
\(584\) | 3.07768 | 0.127355 | ||||||||
\(585\) | 1.17557 | 0.0486039 | ||||||||
\(586\) | 36.3050 | 1.49974 | ||||||||
\(587\) | 9.58359 | 0.395557 | 0.197779 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197779 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(588\) | 5.04531 | 0.208065 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 13.2918 | 0.547215 | ||||||||
\(591\) | −24.5560 | −1.01010 | ||||||||
\(592\) | 20.9232 | 0.859940 | ||||||||
\(593\) | 7.29180 | 0.299438 | 0.149719 | − | 0.988729i | \(-0.452163\pi\) | ||||
0.149719 | + | 0.988729i | \(0.452163\pi\) | |||||||
\(594\) | −5.45085 | −0.223651 | ||||||||
\(595\) | −0.180340 | −0.00739321 | ||||||||
\(596\) | 2.52786 | 0.103545 | ||||||||
\(597\) | −15.7719 | −0.645502 | ||||||||
\(598\) | −6.05573 | −0.247637 | ||||||||
\(599\) | −10.3431 | −0.422608 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(600\) | −3.61803 | −0.147706 | ||||||||
\(601\) | −17.0130 | −0.693975 | −0.346988 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346988 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(602\) | 0.726543 | 0.0296117 | ||||||||
\(603\) | 18.7436 | 0.763299 | ||||||||
\(604\) | −11.1352 | −0.453083 | ||||||||
\(605\) | 10.2705 | 0.417556 | ||||||||
\(606\) | 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 | ||||||||
\(610\) | 16.3925 | 0.663712 | ||||||||
\(611\) | 5.42882 | 0.219627 | ||||||||
\(612\) | 0.763932 | 0.0308801 | ||||||||
\(613\) | 35.4721 | 1.43271 | 0.716353 | − | 0.697738i | \(-0.245810\pi\) | ||||
0.716353 | + | 0.697738i | \(0.245810\pi\) | |||||||
\(614\) | 29.9230 | 1.20759 | ||||||||
\(615\) | −1.90983 | −0.0770118 | ||||||||
\(616\) | −0.620541 | −0.0250023 | ||||||||
\(617\) | 19.3820 | 0.780289 | 0.390144 | − | 0.920754i | \(-0.372425\pi\) | ||||
0.390144 | + | 0.920754i | \(0.372425\pi\) | |||||||
\(618\) | 1.86162 | 0.0748855 | ||||||||
\(619\) | −27.5410 | −1.10697 | −0.553484 | − | 0.832860i | \(-0.686702\pi\) | ||||
−0.553484 | + | 0.832860i | \(0.686702\pi\) | |||||||
\(620\) | −0.726543 | −0.0291787 | ||||||||
\(621\) | 38.4913 | 1.54460 | ||||||||
\(622\) | −8.50651 | −0.341080 | ||||||||
\(623\) | 1.96763 | 0.0788312 | ||||||||
\(624\) | −2.03444 | −0.0814429 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.5851 | −1.42227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.6738 | −0.425929 | ||||||||
\(629\) | −6.71040 | −0.267561 | ||||||||
\(630\) | 0.449028 | 0.0178897 | ||||||||
\(631\) | −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 | ||||||||
\(635\) | −2.17963 | −0.0864959 | ||||||||
\(636\) | −0.729490 | −0.0289262 | ||||||||
\(637\) | −5.04531 | −0.199902 | ||||||||
\(638\) | −8.81966 | −0.349174 | ||||||||
\(639\) | −21.0948 | −0.834496 | ||||||||
\(640\) | −3.52671 | −0.139406 | ||||||||
\(641\) | 38.4508 | 1.51872 | 0.759358 | − | 0.650673i | \(-0.225513\pi\) | ||||
0.759358 | + | 0.650673i | \(0.225513\pi\) | |||||||
\(642\) | 10.7516 | 0.424334 | ||||||||
\(643\) | −29.5279 | −1.16447 | −0.582233 | − | 0.813022i | \(-0.697821\pi\) | ||||
−0.582233 | + | 0.813022i | \(0.697821\pi\) | |||||||
\(644\) | 1.03444 | 0.0407627 | ||||||||
\(645\) | −3.07768 | −0.121184 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4721 | 0.686901 | 0.343450 | − | 0.939171i | \(-0.388404\pi\) | ||||
0.343450 | + | 0.939171i | \(0.388404\pi\) | |||||||
\(648\) | 4.70228 | 0.184723 | ||||||||
\(649\) | −9.65706 | −0.379073 | ||||||||
\(650\) | 0.854102 | 0.0335006 | ||||||||
\(651\) | −0.326238 | −0.0127863 | ||||||||
\(652\) | 1.74265 | 0.0682473 | ||||||||
\(653\) | 10.7984 | 0.422573 | 0.211287 | − | 0.977424i | \(-0.432235\pi\) | ||||
0.211287 | + | 0.977424i | \(0.432235\pi\) | |||||||
\(654\) | 12.7598 | 0.498946 | ||||||||
\(655\) | 13.3820 | 0.522877 | ||||||||
\(656\) | −3.86974 | −0.151088 | ||||||||
\(657\) | 1.61803 | 0.0631255 | ||||||||
\(658\) | 2.07363 | 0.0808384 | ||||||||
\(659\) | −30.7768 | −1.19890 | −0.599448 | − | 0.800414i | \(-0.704613\pi\) | ||||
−0.599448 | + | 0.800414i | \(0.704613\pi\) | |||||||
\(660\) | 0.620541 | 0.0241545 | ||||||||
\(661\) | −13.4208 | −0.522008 | −0.261004 | − | 0.965338i | \(-0.584054\pi\) | ||||
−0.261004 | + | 0.965338i | \(0.584054\pi\) | |||||||
\(662\) | 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 | ||||||||
\(670\) | 13.6180 | 0.526111 | ||||||||
\(671\) | −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 | ||||||||
\(675\) | −5.42882 | −0.208956 | ||||||||
\(676\) | 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 | ||||||||
\(680\) | 2.35114 | 0.0901621 | ||||||||
\(681\) | −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 | ||||||||
\(685\) | −14.2361 | −0.543932 | ||||||||
\(686\) | −3.86974 | −0.147747 | ||||||||
\(687\) | −29.2177 | −1.11473 | ||||||||
\(688\) | −6.23607 | −0.237748 | ||||||||
\(689\) | 0.729490 | 0.0277914 | ||||||||
\(690\) | 9.79837 | 0.373018 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | 10.9098 | 0.413833 | ||||||||
\(696\) | 31.7809 | 1.20465 | ||||||||
\(697\) | 1.24108 | 0.0470094 | ||||||||
\(698\) | 20.6457 | 0.781452 | ||||||||
\(699\) | 7.33094 | 0.277282 | ||||||||
\(700\) | −0.145898 | −0.00551443 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | −8.78402 | −0.330825 | ||||||||
\(706\) | 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 | \(0.416441\pi\) | |||||||
\(710\) | −15.3262 | −0.575183 | ||||||||
\(711\) | −13.7638 | −0.516184 | ||||||||
\(712\) | −25.6525 | −0.961367 | ||||||||
\(713\) | 8.33499 | 0.312148 | ||||||||
\(714\) | 0.249224 | 0.00932696 | ||||||||
\(715\) | −0.620541 | −0.0232069 | ||||||||
\(716\) | −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 | \(0.787260\pi\) | |||||||
\(720\) | −3.85410 | −0.143634 | ||||||||
\(721\) | 0.318003 | 0.0118431 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.0344 | −0.633518 | ||||||||
\(724\) | −9.06154 | −0.336769 | ||||||||
\(725\) | −8.78402 | −0.326230 | ||||||||
\(726\) | −14.1935 | −0.526770 | ||||||||
\(727\) | −10.3607 | −0.384256 | −0.192128 | − | 0.981370i | \(-0.561539\pi\) | ||||
−0.192128 | + | 0.981370i | \(0.561539\pi\) | |||||||
\(728\) | −0.527864 | −0.0195639 | ||||||||
\(729\) | 21.6180 | 0.800668 | ||||||||
\(730\) | 1.17557 | 0.0435098 | ||||||||
\(731\) | 2.00000 | 0.0739727 | ||||||||
\(732\) | 10.1311 | 0.374456 | ||||||||
\(733\) | −11.0000 | −0.406294 | −0.203147 | − | 0.979148i | \(-0.565117\pi\) | ||||
−0.203147 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(734\) | −31.8214 | −1.17455 | ||||||||
\(735\) | 8.16348 | 0.301115 | ||||||||
\(736\) | −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 | \(0.702022\pi\) | |||||||
\(740\) | −5.42882 | −0.199568 | ||||||||
\(741\) | 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 | ||||||||
\(745\) | 4.09017 | 0.149852 | ||||||||
\(746\) | 5.32624 | 0.195007 | ||||||||
\(747\) | 21.4164 | 0.783585 | ||||||||
\(748\) | −0.403252 | −0.0147444 | ||||||||
\(749\) | 1.83660 | 0.0671079 | ||||||||
\(750\) | −1.38197 | −0.0504623 | ||||||||
\(751\) | −41.7000 | −1.52165 | −0.760827 | − | 0.648954i | \(-0.775207\pi\) | ||||
−0.760827 | + | 0.648954i | \(0.775207\pi\) | |||||||
\(752\) | −17.7984 | −0.649040 | ||||||||
\(753\) | −3.52671 | −0.128521 | ||||||||
\(754\) | −7.50245 | −0.273223 | ||||||||
\(755\) | −18.0171 | −0.655708 | ||||||||
\(756\) | 0.792055 | 0.0288068 | ||||||||
\(757\) | −43.9787 | −1.59843 | −0.799217 | − | 0.601043i | \(-0.794752\pi\) | ||||
−0.799217 | + | 0.601043i | \(0.794752\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 1.23607 | 0.0446901 | ||||||||
\(766\) | −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 | \(0.380903\pi\) | |||||||
\(770\) | −0.237026 | −0.00854181 | ||||||||
\(771\) | −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 | ||||||||
\(775\) | −1.17557 | −0.0422277 | ||||||||
\(776\) | −13.0902 | −0.469910 | ||||||||
\(777\) | −2.43769 | −0.0874518 | ||||||||
\(778\) | −16.6295 | −0.596196 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.527864 | 0.0189006 | ||||||||
\(781\) | 11.1352 | 0.398447 | ||||||||
\(782\) | −6.36737 | −0.227697 | ||||||||
\(783\) | 47.6869 | 1.70419 | ||||||||
\(784\) | 16.5410 | 0.590751 | ||||||||
\(785\) | −17.2705 | −0.616411 | ||||||||
\(786\) | −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 | ||||||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | 1.02908 | 0.0365899 | ||||||||
\(792\) | 4.25325 | 0.151133 | ||||||||
\(793\) | −10.1311 | −0.359766 | ||||||||
\(794\) | 35.0706 | 1.24461 | ||||||||
\(795\) | −1.18034 | −0.0418623 | ||||||||
\(796\) | 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 | ||||||||
\(800\) | 3.35520 | 0.118624 | ||||||||
\(801\) | −13.4863 | −0.476515 | ||||||||
\(802\) | −12.7639 | −0.450710 | ||||||||
\(803\) | −0.854102 | −0.0301406 | ||||||||
\(804\) | 8.41641 | 0.296824 | ||||||||
\(805\) | 1.67376 | 0.0589924 | ||||||||
\(806\) | −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 | \(0.509991\pi\) | |||||||
\(810\) | 1.79611 | 0.0631089 | ||||||||
\(811\) | 21.2663 | 0.746760 | 0.373380 | − | 0.927679i | \(-0.378199\pi\) | ||||
0.373380 | + | 0.927679i | \(0.378199\pi\) | |||||||
\(812\) | 1.28157 | 0.0449743 | ||||||||
\(813\) | 7.50245 | 0.263122 | ||||||||
\(814\) | −8.81966 | −0.309129 | ||||||||
\(815\) | 2.81966 | 0.0987684 | ||||||||
\(816\) | −2.13914 | −0.0748848 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 21.3050 | 0.744910 | ||||||||
\(819\) | −0.277515 | −0.00969714 | ||||||||
\(820\) | 1.00406 | 0.0350632 | ||||||||
\(821\) | 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 | \(-0.620684\pi\) | ||||
−0.370121 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(824\) | −4.14590 | −0.144429 | ||||||||
\(825\) | 1.00406 | 0.0349568 | ||||||||
\(826\) | −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 | \(-0.382651\pi\) | ||||
0.360369 | + | 0.932810i | \(0.382651\pi\) | |||||||
\(830\) | 15.5599 | 0.540093 | ||||||||
\(831\) | −33.8950 | −1.17580 | ||||||||
\(832\) | 6.32688 | 0.219345 | ||||||||
\(833\) | −5.30495 | −0.183806 | ||||||||
\(834\) | −15.0770 | −0.522074 | ||||||||
\(835\) | −13.0373 | −0.451174 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.38197 | 0.220593 | ||||||||
\(838\) | 4.49028 | 0.155114 | ||||||||
\(839\) | 10.4086 | 0.359346 | 0.179673 | − | 0.983726i | \(-0.442496\pi\) | ||||
0.179673 | + | 0.983726i | \(0.442496\pi\) | |||||||
\(840\) | 0.854102 | 0.0294693 | ||||||||
\(841\) | 48.1591 | 1.66066 | ||||||||
\(842\) | −7.03444 | −0.242423 | ||||||||
\(843\) | −12.6869 | −0.436961 | ||||||||
\(844\) | −8.78402 | −0.302359 | ||||||||
\(845\) | 12.4721 | 0.429055 | ||||||||
\(846\) | −14.2128 | −0.488648 | ||||||||
\(847\) | −2.42454 | −0.0833081 | ||||||||
\(848\) | −2.39163 | −0.0821289 | ||||||||
\(849\) | 6.19586 | 0.212641 | ||||||||
\(850\) | 0.898056 | 0.0308031 | ||||||||
\(851\) | 62.2802 | 2.13494 | ||||||||
\(852\) | −9.47214 | −0.324510 | ||||||||
\(853\) | −6.52786 | −0.223510 | −0.111755 | − | 0.993736i | \(-0.535647\pi\) | ||||
−0.111755 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(854\) | −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 | \(0.653817\pi\) | |||||||
\(860\) | 1.61803 | 0.0551745 | ||||||||
\(861\) | 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 | ||||||||
\(865\) | 12.8658 | 0.437449 | ||||||||
\(866\) | −26.5066 | −0.900730 | ||||||||
\(867\) | −19.2986 | −0.655416 | ||||||||
\(868\) | 0.171513 | 0.00582154 | ||||||||
\(869\) | 7.26543 | 0.246463 | ||||||||
\(870\) | 12.1392 | 0.411558 | ||||||||
\(871\) | −8.41641 | −0.285179 | ||||||||
\(872\) | −28.4164 | −0.962301 | ||||||||
\(873\) | −6.88191 | −0.232917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.236068 | −0.00798055 | ||||||||
\(876\) | 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 | ||||||||
\(880\) | 2.03444 | 0.0685810 | ||||||||
\(881\) | −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 | \(-0.912806\pi\) | ||||
−0.962715 | + | 0.270516i | \(0.912806\pi\) | |||||||
\(884\) | −0.343027 | −0.0115372 | ||||||||
\(885\) | 13.2918 | 0.446799 | ||||||||
\(886\) | −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 | ||||||||
\(890\) | −9.79837 | −0.328442 | ||||||||
\(891\) | −1.30495 | −0.0437175 | ||||||||
\(892\) | 12.2047 | 0.408645 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −5.65248 | −0.189047 | ||||||||
\(895\) | −12.1392 | −0.405769 | ||||||||
\(896\) | 0.832544 | 0.0278133 | ||||||||
\(897\) | −6.05573 | −0.202195 | ||||||||
\(898\) | −44.2705 | −1.47733 | ||||||||
\(899\) | 10.3262 | 0.344399 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0.767031 | 0.0255535 | ||||||||
\(902\) | 1.63119 | 0.0543127 | ||||||||
\(903\) | 0.726543 | 0.0241778 | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | −14.6619 | −0.487377 | ||||||||
\(906\) | 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 | ||||||||
\(910\) | −0.201626 | −0.00668384 | ||||||||
\(911\) | 12.9718 | 0.429774 | 0.214887 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214887 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3050 | −0.374139 | ||||||||
\(914\) | 0.898056 | 0.0297051 | ||||||||
\(915\) | 16.3925 | 0.541918 | ||||||||
\(916\) | 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 | \(0.711332\pi\) | |||||||
\(920\) | −21.8213 | −0.719427 | ||||||||
\(921\) | 29.9230 | 0.985996 | ||||||||
\(922\) | −9.40456 | −0.309723 | ||||||||
\(923\) | 9.47214 | 0.311779 | ||||||||
\(924\) | −0.146490 | −0.00481917 | ||||||||
\(925\) | −8.78402 | −0.288817 | ||||||||
\(926\) | 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 | \(0.407656\pi\) | |||||||
\(930\) | 1.62460 | 0.0532727 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.85410 | −0.126245 | ||||||||
\(933\) | −8.50651 | −0.278491 | ||||||||
\(934\) | 15.4944 | 0.506993 | ||||||||
\(935\) | −0.652476 | −0.0213382 | ||||||||
\(936\) | 3.61803 | 0.118259 | ||||||||
\(937\) | 47.7984 | 1.56150 | 0.780752 | − | 0.624841i | \(-0.214836\pi\) | ||||
0.780752 | + | 0.624841i | \(0.214836\pi\) | |||||||
\(938\) | −3.21478 | −0.104966 | ||||||||
\(939\) | −35.5851 | −1.16128 | ||||||||
\(940\) | 4.61803 | 0.150624 | ||||||||
\(941\) | −39.6013 | −1.29097 | −0.645484 | − | 0.763774i | \(-0.723344\pi\) | ||||
−0.645484 | + | 0.763774i | \(0.723344\pi\) | |||||||
\(942\) | 23.8673 | 0.777637 | ||||||||
\(943\) | −11.5187 | −0.375100 | ||||||||
\(944\) | 26.9321 | 0.876566 | ||||||||
\(945\) | 1.28157 | 0.0416895 | ||||||||
\(946\) | 2.62866 | 0.0854650 | ||||||||
\(947\) | −25.4164 | −0.825922 | −0.412961 | − | 0.910749i | \(-0.635505\pi\) | ||||
−0.412961 | + | 0.910749i | \(0.635505\pi\) | |||||||
\(948\) | −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 | ||||||||
\(955\) | −13.0000 | −0.420670 | ||||||||
\(956\) | −17.4377 | −0.563975 | ||||||||
\(957\) | −8.81966 | −0.285099 | ||||||||
\(958\) | −37.1037 | −1.19877 | ||||||||
\(959\) | 3.36068 | 0.108522 | ||||||||
\(960\) | −10.2371 | −0.330401 | ||||||||
\(961\) | −29.6180 | −0.955420 | ||||||||
\(962\) | −7.50245 | −0.241889 | ||||||||
\(963\) | −12.5882 | −0.405651 | ||||||||
\(964\) | 8.95554 | 0.288438 | ||||||||
\(965\) | 6.15537 | 0.198148 | ||||||||
\(966\) | −2.31308 | −0.0744222 | ||||||||
\(967\) | −46.9443 | −1.50963 | −0.754813 | − | 0.655940i | \(-0.772272\pi\) | ||||
−0.754813 | + | 0.655940i | \(0.772272\pi\) | |||||||
\(968\) | 31.6094 | 1.01596 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | −0.160540 | ||||||||
\(971\) | −14.5964 | −0.468420 | −0.234210 | − | 0.972186i | \(-0.575250\pi\) | ||||
−0.234210 | + | 0.972186i | \(0.575250\pi\) | |||||||
\(972\) | −8.95554 | −0.287249 | ||||||||
\(973\) | −2.57546 | −0.0825655 | ||||||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | 0.854102 | 0.0273532 | ||||||||
\(976\) | 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 | ||||||||
\(980\) | −4.29180 | −0.137096 | ||||||||
\(981\) | −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 | ||||||||
\(985\) | 20.8885 | 0.665564 | ||||||||
\(986\) | −7.88854 | −0.251222 | ||||||||
\(987\) | 2.07363 | 0.0660043 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.5623 | −0.590247 | ||||||||
\(990\) | 1.62460 | 0.0516331 | ||||||||
\(991\) | −17.2500 | −0.547966 | −0.273983 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273983 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(992\) | −3.94427 | −0.125231 | ||||||||
\(993\) | 2.11146 | 0.0670050 | ||||||||
\(994\) | 3.61803 | 0.114757 | ||||||||
\(995\) | 13.4164 | 0.425329 | ||||||||
\(996\) | 9.61657 | 0.304713 | ||||||||
\(997\) | −19.0557 | −0.603501 | −0.301750 | − | 0.953387i | \(-0.597571\pi\) | ||||
−0.301750 | + | 0.953387i | \(0.597571\pi\) | |||||||
\(998\) | −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 | 1805.2.a.l.1.3 | yes | 4 | |
5.4 | even | 2 | 9025.2.a.bl.1.2 | 4 | |||
19.18 | odd | 2 | inner | 1805.2.a.l.1.2 | ✓ | 4 | |
95.94 | odd | 2 | 9025.2.a.bl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.l.1.2 | ✓ | 4 | 19.18 | odd | 2 | inner | |
1805.2.a.l.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
9025.2.a.bl.1.2 | 4 | 5.4 | even | 2 | |||
9025.2.a.bl.1.3 | 4 | 95.94 | odd | 2 |