Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 \) |
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 | \(1.44008\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44008 | −1.01829 | −0.509145 | − | 0.860681i | \(-0.670038\pi\) | ||||
−0.509145 | + | 0.860681i | \(0.670038\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.0738306 | 0.0369153 | ||||||||
\(5\) | 0.734622 | 0.328533 | 0.164266 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164266 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(6\) | −1.44008 | −0.587910 | ||||||||
\(7\) | 3.73618 | 1.41214 | 0.706071 | − | 0.708141i | \(-0.250466\pi\) | ||||
0.706071 | + | 0.708141i | \(0.250466\pi\) | |||||||
\(8\) | 2.77384 | 0.980700 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.05791 | −0.334542 | ||||||||
\(11\) | −2.70213 | −0.814723 | −0.407361 | − | 0.913267i | \(-0.633551\pi\) | ||||
−0.407361 | + | 0.913267i | \(0.633551\pi\) | |||||||
\(12\) | 0.0738306 | 0.0213131 | ||||||||
\(13\) | −2.87193 | −0.796531 | −0.398265 | − | 0.917270i | \(-0.630388\pi\) | ||||
−0.398265 | + | 0.917270i | \(0.630388\pi\) | |||||||
\(14\) | −5.38039 | −1.43797 | ||||||||
\(15\) | 0.734622 | 0.189678 | ||||||||
\(16\) | −4.14221 | −1.03555 | ||||||||
\(17\) | −2.75120 | −0.667263 | −0.333632 | − | 0.942704i | \(-0.608274\pi\) | ||||
−0.333632 | + | 0.942704i | \(0.608274\pi\) | |||||||
\(18\) | −1.44008 | −0.339430 | ||||||||
\(19\) | −5.54463 | −1.27202 | −0.636012 | − | 0.771679i | \(-0.719417\pi\) | ||||
−0.636012 | + | 0.771679i | \(0.719417\pi\) | |||||||
\(20\) | 0.0542376 | 0.0121279 | ||||||||
\(21\) | 3.73618 | 0.815300 | ||||||||
\(22\) | 3.89128 | 0.829625 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.77384 | 0.566207 | ||||||||
\(25\) | −4.46033 | −0.892066 | ||||||||
\(26\) | 4.13581 | 0.811099 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.275844 | 0.0521296 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.05791 | −0.193148 | ||||||||
\(31\) | −10.2606 | −1.84285 | −0.921425 | − | 0.388557i | \(-0.872974\pi\) | ||||
−0.921425 | + | 0.388557i | \(0.872974\pi\) | |||||||
\(32\) | 0.417438 | 0.0737933 | ||||||||
\(33\) | −2.70213 | −0.470380 | ||||||||
\(34\) | 3.96194 | 0.679468 | ||||||||
\(35\) | 2.74468 | 0.463935 | ||||||||
\(36\) | 0.0738306 | 0.0123051 | ||||||||
\(37\) | −11.4951 | −1.88978 | −0.944888 | − | 0.327394i | \(-0.893829\pi\) | ||||
−0.944888 | + | 0.327394i | \(0.893829\pi\) | |||||||
\(38\) | 7.98471 | 1.29529 | ||||||||
\(39\) | −2.87193 | −0.459877 | ||||||||
\(40\) | 2.03772 | 0.322192 | ||||||||
\(41\) | −1.81028 | −0.282718 | −0.141359 | − | 0.989958i | \(-0.545147\pi\) | ||||
−0.141359 | + | 0.989958i | \(0.545147\pi\) | |||||||
\(42\) | −5.38039 | −0.830212 | ||||||||
\(43\) | 0.181163 | 0.0276271 | 0.0138136 | − | 0.999905i | \(-0.495603\pi\) | ||||
0.0138136 | + | 0.999905i | \(0.495603\pi\) | |||||||
\(44\) | −0.199500 | −0.0300757 | ||||||||
\(45\) | 0.734622 | 0.109511 | ||||||||
\(46\) | −1.44008 | −0.212328 | ||||||||
\(47\) | −6.02453 | −0.878768 | −0.439384 | − | 0.898299i | \(-0.644803\pi\) | ||||
−0.439384 | + | 0.898299i | \(0.644803\pi\) | |||||||
\(48\) | −4.14221 | −0.597877 | ||||||||
\(49\) | 6.95901 | 0.994144 | ||||||||
\(50\) | 6.42323 | 0.908382 | ||||||||
\(51\) | −2.75120 | −0.385245 | ||||||||
\(52\) | −0.212037 | −0.0294042 | ||||||||
\(53\) | −0.662081 | −0.0909438 | −0.0454719 | − | 0.998966i | \(-0.514479\pi\) | ||||
−0.0454719 | + | 0.998966i | \(0.514479\pi\) | |||||||
\(54\) | −1.44008 | −0.195970 | ||||||||
\(55\) | −1.98504 | −0.267663 | ||||||||
\(56\) | 10.3635 | 1.38489 | ||||||||
\(57\) | −5.54463 | −0.734404 | ||||||||
\(58\) | 1.44008 | 0.189092 | ||||||||
\(59\) | −0.174372 | −0.0227013 | −0.0113506 | − | 0.999936i | \(-0.503613\pi\) | ||||
−0.0113506 | + | 0.999936i | \(0.503613\pi\) | |||||||
\(60\) | 0.0542376 | 0.00700204 | ||||||||
\(61\) | −5.37843 | −0.688637 | −0.344318 | − | 0.938853i | \(-0.611890\pi\) | ||||
−0.344318 | + | 0.938853i | \(0.611890\pi\) | |||||||
\(62\) | 14.7760 | 1.87656 | ||||||||
\(63\) | 3.73618 | 0.470714 | ||||||||
\(64\) | 7.68328 | 0.960410 | ||||||||
\(65\) | −2.10978 | −0.261686 | ||||||||
\(66\) | 3.89128 | 0.478984 | ||||||||
\(67\) | 15.9959 | 1.95421 | 0.977106 | − | 0.212754i | \(-0.0682432\pi\) | ||||
0.977106 | + | 0.212754i | \(0.0682432\pi\) | |||||||
\(68\) | −0.203123 | −0.0246322 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −3.95255 | −0.472420 | ||||||||
\(71\) | 12.0047 | 1.42469 | 0.712347 | − | 0.701828i | \(-0.247632\pi\) | ||||
0.712347 | + | 0.701828i | \(0.247632\pi\) | |||||||
\(72\) | 2.77384 | 0.326900 | ||||||||
\(73\) | 0.990842 | 0.115969 | 0.0579847 | − | 0.998317i | \(-0.481533\pi\) | ||||
0.0579847 | + | 0.998317i | \(0.481533\pi\) | |||||||
\(74\) | 16.5538 | 1.92434 | ||||||||
\(75\) | −4.46033 | −0.515035 | ||||||||
\(76\) | −0.409363 | −0.0469572 | ||||||||
\(77\) | −10.0956 | −1.15050 | ||||||||
\(78\) | 4.13581 | 0.468288 | ||||||||
\(79\) | −2.96323 | −0.333390 | −0.166695 | − | 0.986009i | \(-0.553309\pi\) | ||||
−0.166695 | + | 0.986009i | \(0.553309\pi\) | |||||||
\(80\) | −3.04296 | −0.340213 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.60694 | 0.287889 | ||||||||
\(83\) | 1.08995 | 0.119638 | 0.0598189 | − | 0.998209i | \(-0.480948\pi\) | ||||
0.0598189 | + | 0.998209i | \(0.480948\pi\) | |||||||
\(84\) | 0.275844 | 0.0300971 | ||||||||
\(85\) | −2.02109 | −0.219218 | ||||||||
\(86\) | −0.260889 | −0.0281324 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −7.49527 | −0.798999 | ||||||||
\(89\) | 5.21337 | 0.552617 | 0.276308 | − | 0.961069i | \(-0.410889\pi\) | ||||
0.276308 | + | 0.961069i | \(0.410889\pi\) | |||||||
\(90\) | −1.05791 | −0.111514 | ||||||||
\(91\) | −10.7300 | −1.12481 | ||||||||
\(92\) | 0.0738306 | 0.00769737 | ||||||||
\(93\) | −10.2606 | −1.06397 | ||||||||
\(94\) | 8.67580 | 0.894841 | ||||||||
\(95\) | −4.07320 | −0.417902 | ||||||||
\(96\) | 0.417438 | 0.0426046 | ||||||||
\(97\) | −3.97122 | −0.403217 | −0.201608 | − | 0.979466i | \(-0.564617\pi\) | ||||
−0.201608 | + | 0.979466i | \(0.564617\pi\) | |||||||
\(98\) | −10.0215 | −1.01233 | ||||||||
\(99\) | −2.70213 | −0.271574 | ||||||||
\(100\) | −0.329309 | −0.0329309 | ||||||||
\(101\) | 18.4855 | 1.83938 | 0.919688 | − | 0.392650i | \(-0.128442\pi\) | ||||
0.919688 | + | 0.392650i | \(0.128442\pi\) | |||||||
\(102\) | 3.96194 | 0.392291 | ||||||||
\(103\) | −2.24948 | −0.221648 | −0.110824 | − | 0.993840i | \(-0.535349\pi\) | ||||
−0.110824 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(104\) | −7.96627 | −0.781157 | ||||||||
\(105\) | 2.74468 | 0.267853 | ||||||||
\(106\) | 0.953449 | 0.0926072 | ||||||||
\(107\) | −12.9231 | −1.24932 | −0.624660 | − | 0.780897i | \(-0.714762\pi\) | ||||
−0.624660 | + | 0.780897i | \(0.714762\pi\) | |||||||
\(108\) | 0.0738306 | 0.00710435 | ||||||||
\(109\) | 16.2725 | 1.55863 | 0.779313 | − | 0.626635i | \(-0.215568\pi\) | ||||
0.779313 | + | 0.626635i | \(0.215568\pi\) | |||||||
\(110\) | 2.85862 | 0.272559 | ||||||||
\(111\) | −11.4951 | −1.09106 | ||||||||
\(112\) | −15.4760 | −1.46235 | ||||||||
\(113\) | −11.3227 | −1.06515 | −0.532573 | − | 0.846384i | \(-0.678775\pi\) | ||||
−0.532573 | + | 0.846384i | \(0.678775\pi\) | |||||||
\(114\) | 7.98471 | 0.747836 | ||||||||
\(115\) | 0.734622 | 0.0685038 | ||||||||
\(116\) | −0.0738306 | −0.00685500 | ||||||||
\(117\) | −2.87193 | −0.265510 | ||||||||
\(118\) | 0.251109 | 0.0231165 | ||||||||
\(119\) | −10.2790 | −0.942270 | ||||||||
\(120\) | 2.03772 | 0.186018 | ||||||||
\(121\) | −3.69849 | −0.336227 | ||||||||
\(122\) | 7.74536 | 0.701232 | ||||||||
\(123\) | −1.81028 | −0.163227 | ||||||||
\(124\) | −0.757543 | −0.0680294 | ||||||||
\(125\) | −6.94976 | −0.621606 | ||||||||
\(126\) | −5.38039 | −0.479323 | ||||||||
\(127\) | −9.54485 | −0.846968 | −0.423484 | − | 0.905903i | \(-0.639193\pi\) | ||||
−0.423484 | + | 0.905903i | \(0.639193\pi\) | |||||||
\(128\) | −11.8994 | −1.05177 | ||||||||
\(129\) | 0.181163 | 0.0159505 | ||||||||
\(130\) | 3.03826 | 0.266473 | ||||||||
\(131\) | 15.3632 | 1.34229 | 0.671146 | − | 0.741326i | \(-0.265803\pi\) | ||||
0.671146 | + | 0.741326i | \(0.265803\pi\) | |||||||
\(132\) | −0.199500 | −0.0173642 | ||||||||
\(133\) | −20.7157 | −1.79628 | ||||||||
\(134\) | −23.0354 | −1.98995 | ||||||||
\(135\) | 0.734622 | 0.0632262 | ||||||||
\(136\) | −7.63137 | −0.654385 | ||||||||
\(137\) | 15.4197 | 1.31739 | 0.658697 | − | 0.752408i | \(-0.271108\pi\) | ||||
0.658697 | + | 0.752408i | \(0.271108\pi\) | |||||||
\(138\) | −1.44008 | −0.122588 | ||||||||
\(139\) | −16.2808 | −1.38092 | −0.690461 | − | 0.723370i | \(-0.742592\pi\) | ||||
−0.690461 | + | 0.723370i | \(0.742592\pi\) | |||||||
\(140\) | 0.202641 | 0.0171263 | ||||||||
\(141\) | −6.02453 | −0.507357 | ||||||||
\(142\) | −17.2877 | −1.45075 | ||||||||
\(143\) | 7.76033 | 0.648952 | ||||||||
\(144\) | −4.14221 | −0.345184 | ||||||||
\(145\) | −0.734622 | −0.0610070 | ||||||||
\(146\) | −1.42689 | −0.118090 | ||||||||
\(147\) | 6.95901 | 0.573969 | ||||||||
\(148\) | −0.848687 | −0.0697617 | ||||||||
\(149\) | −11.2442 | −0.921159 | −0.460580 | − | 0.887618i | \(-0.652358\pi\) | ||||
−0.460580 | + | 0.887618i | \(0.652358\pi\) | |||||||
\(150\) | 6.42323 | 0.524455 | ||||||||
\(151\) | −13.0268 | −1.06011 | −0.530053 | − | 0.847965i | \(-0.677828\pi\) | ||||
−0.530053 | + | 0.847965i | \(0.677828\pi\) | |||||||
\(152\) | −15.3799 | −1.24747 | ||||||||
\(153\) | −2.75120 | −0.222421 | ||||||||
\(154\) | 14.5385 | 1.17155 | ||||||||
\(155\) | −7.53762 | −0.605436 | ||||||||
\(156\) | −0.212037 | −0.0169765 | ||||||||
\(157\) | 5.40186 | 0.431116 | 0.215558 | − | 0.976491i | \(-0.430843\pi\) | ||||
0.215558 | + | 0.976491i | \(0.430843\pi\) | |||||||
\(158\) | 4.26729 | 0.339488 | ||||||||
\(159\) | −0.662081 | −0.0525064 | ||||||||
\(160\) | 0.306659 | 0.0242435 | ||||||||
\(161\) | 3.73618 | 0.294452 | ||||||||
\(162\) | −1.44008 | −0.113143 | ||||||||
\(163\) | 5.91249 | 0.463102 | 0.231551 | − | 0.972823i | \(-0.425620\pi\) | ||||
0.231551 | + | 0.972823i | \(0.425620\pi\) | |||||||
\(164\) | −0.133654 | −0.0104366 | ||||||||
\(165\) | −1.98504 | −0.154535 | ||||||||
\(166\) | −1.56962 | −0.121826 | ||||||||
\(167\) | −0.341562 | −0.0264308 | −0.0132154 | − | 0.999913i | \(-0.504207\pi\) | ||||
−0.0132154 | + | 0.999913i | \(0.504207\pi\) | |||||||
\(168\) | 10.3635 | 0.799565 | ||||||||
\(169\) | −4.75201 | −0.365539 | ||||||||
\(170\) | 2.91053 | 0.223227 | ||||||||
\(171\) | −5.54463 | −0.424008 | ||||||||
\(172\) | 0.0133754 | 0.00101986 | ||||||||
\(173\) | 13.8093 | 1.04990 | 0.524950 | − | 0.851133i | \(-0.324084\pi\) | ||||
0.524950 | + | 0.851133i | \(0.324084\pi\) | |||||||
\(174\) | 1.44008 | 0.109172 | ||||||||
\(175\) | −16.6646 | −1.25972 | ||||||||
\(176\) | 11.1928 | 0.843688 | ||||||||
\(177\) | −0.174372 | −0.0131066 | ||||||||
\(178\) | −7.50768 | −0.562724 | ||||||||
\(179\) | 15.3349 | 1.14619 | 0.573093 | − | 0.819490i | \(-0.305743\pi\) | ||||
0.573093 | + | 0.819490i | \(0.305743\pi\) | |||||||
\(180\) | 0.0542376 | 0.00404263 | ||||||||
\(181\) | −4.64338 | −0.345139 | −0.172570 | − | 0.984997i | \(-0.555207\pi\) | ||||
−0.172570 | + | 0.984997i | \(0.555207\pi\) | |||||||
\(182\) | 15.4521 | 1.14539 | ||||||||
\(183\) | −5.37843 | −0.397585 | ||||||||
\(184\) | 2.77384 | 0.204490 | ||||||||
\(185\) | −8.44452 | −0.620853 | ||||||||
\(186\) | 14.7760 | 1.08343 | ||||||||
\(187\) | 7.43409 | 0.543635 | ||||||||
\(188\) | −0.444795 | −0.0324400 | ||||||||
\(189\) | 3.73618 | 0.271767 | ||||||||
\(190\) | 5.86574 | 0.425545 | ||||||||
\(191\) | 9.85469 | 0.713060 | 0.356530 | − | 0.934284i | \(-0.383960\pi\) | ||||
0.356530 | + | 0.934284i | \(0.383960\pi\) | |||||||
\(192\) | 7.68328 | 0.554493 | ||||||||
\(193\) | −21.2787 | −1.53167 | −0.765837 | − | 0.643035i | \(-0.777675\pi\) | ||||
−0.765837 | + | 0.643035i | \(0.777675\pi\) | |||||||
\(194\) | 5.71888 | 0.410592 | ||||||||
\(195\) | −2.10978 | −0.151085 | ||||||||
\(196\) | 0.513788 | 0.0366991 | ||||||||
\(197\) | 9.61747 | 0.685216 | 0.342608 | − | 0.939478i | \(-0.388690\pi\) | ||||
0.342608 | + | 0.939478i | \(0.388690\pi\) | |||||||
\(198\) | 3.89128 | 0.276542 | ||||||||
\(199\) | 4.39951 | 0.311873 | 0.155936 | − | 0.987767i | \(-0.450161\pi\) | ||||
0.155936 | + | 0.987767i | \(0.450161\pi\) | |||||||
\(200\) | −12.3722 | −0.874849 | ||||||||
\(201\) | 15.9959 | 1.12826 | ||||||||
\(202\) | −26.6206 | −1.87302 | ||||||||
\(203\) | −3.73618 | −0.262228 | ||||||||
\(204\) | −0.203123 | −0.0142214 | ||||||||
\(205\) | −1.32987 | −0.0928821 | ||||||||
\(206\) | 3.23944 | 0.225702 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 11.8961 | 0.824849 | ||||||||
\(209\) | 14.9823 | 1.03635 | ||||||||
\(210\) | −3.95255 | −0.272752 | ||||||||
\(211\) | 1.95120 | 0.134326 | 0.0671630 | − | 0.997742i | \(-0.478605\pi\) | ||||
0.0671630 | + | 0.997742i | \(0.478605\pi\) | |||||||
\(212\) | −0.0488818 | −0.00335722 | ||||||||
\(213\) | 12.0047 | 0.822547 | ||||||||
\(214\) | 18.6103 | 1.27217 | ||||||||
\(215\) | 0.133086 | 0.00907641 | ||||||||
\(216\) | 2.77384 | 0.188736 | ||||||||
\(217\) | −38.3352 | −2.60236 | ||||||||
\(218\) | −23.4337 | −1.58713 | ||||||||
\(219\) | 0.990842 | 0.0669549 | ||||||||
\(220\) | −0.146557 | −0.00988087 | ||||||||
\(221\) | 7.90125 | 0.531495 | ||||||||
\(222\) | 16.5538 | 1.11102 | ||||||||
\(223\) | 5.60600 | 0.375406 | 0.187703 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(224\) | 1.55962 | 0.104207 | ||||||||
\(225\) | −4.46033 | −0.297355 | ||||||||
\(226\) | 16.3055 | 1.08463 | ||||||||
\(227\) | −5.99730 | −0.398055 | −0.199027 | − | 0.979994i | \(-0.563778\pi\) | ||||
−0.199027 | + | 0.979994i | \(0.563778\pi\) | |||||||
\(228\) | −0.409363 | −0.0271107 | ||||||||
\(229\) | −14.2127 | −0.939199 | −0.469599 | − | 0.882880i | \(-0.655602\pi\) | ||||
−0.469599 | + | 0.882880i | \(0.655602\pi\) | |||||||
\(230\) | −1.05791 | −0.0697568 | ||||||||
\(231\) | −10.0956 | −0.664244 | ||||||||
\(232\) | −2.77384 | −0.182111 | ||||||||
\(233\) | −28.3893 | −1.85985 | −0.929923 | − | 0.367755i | \(-0.880126\pi\) | ||||
−0.929923 | + | 0.367755i | \(0.880126\pi\) | |||||||
\(234\) | 4.13581 | 0.270366 | ||||||||
\(235\) | −4.42575 | −0.288704 | ||||||||
\(236\) | −0.0128740 | −0.000838024 0 | ||||||||
\(237\) | −2.96323 | −0.192483 | ||||||||
\(238\) | 14.8025 | 0.959504 | ||||||||
\(239\) | 20.3486 | 1.31624 | 0.658121 | − | 0.752912i | \(-0.271352\pi\) | ||||
0.658121 | + | 0.752912i | \(0.271352\pi\) | |||||||
\(240\) | −3.04296 | −0.196422 | ||||||||
\(241\) | 19.2101 | 1.23743 | 0.618715 | − | 0.785615i | \(-0.287654\pi\) | ||||
0.618715 | + | 0.785615i | \(0.287654\pi\) | |||||||
\(242\) | 5.32613 | 0.342376 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.397093 | −0.0254212 | ||||||||
\(245\) | 5.11224 | 0.326609 | ||||||||
\(246\) | 2.60694 | 0.166213 | ||||||||
\(247\) | 15.9238 | 1.01321 | ||||||||
\(248\) | −28.4611 | −1.80728 | ||||||||
\(249\) | 1.08995 | 0.0690729 | ||||||||
\(250\) | 10.0082 | 0.632975 | ||||||||
\(251\) | −1.27973 | −0.0807761 | −0.0403880 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403880 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(252\) | 0.275844 | 0.0173765 | ||||||||
\(253\) | −2.70213 | −0.169881 | ||||||||
\(254\) | 13.7453 | 0.862460 | ||||||||
\(255\) | −2.02109 | −0.126565 | ||||||||
\(256\) | 1.76955 | 0.110597 | ||||||||
\(257\) | −21.5611 | −1.34494 | −0.672472 | − | 0.740123i | \(-0.734767\pi\) | ||||
−0.672472 | + | 0.740123i | \(0.734767\pi\) | |||||||
\(258\) | −0.260889 | −0.0162423 | ||||||||
\(259\) | −42.9475 | −2.66863 | ||||||||
\(260\) | −0.155767 | −0.00966023 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −22.1243 | −1.36684 | ||||||||
\(263\) | 14.7781 | 0.911258 | 0.455629 | − | 0.890170i | \(-0.349414\pi\) | ||||
0.455629 | + | 0.890170i | \(0.349414\pi\) | |||||||
\(264\) | −7.49527 | −0.461302 | ||||||||
\(265\) | −0.486379 | −0.0298780 | ||||||||
\(266\) | 29.8323 | 1.82913 | ||||||||
\(267\) | 5.21337 | 0.319053 | ||||||||
\(268\) | 1.18099 | 0.0721403 | ||||||||
\(269\) | 9.78238 | 0.596442 | 0.298221 | − | 0.954497i | \(-0.403607\pi\) | ||||
0.298221 | + | 0.954497i | \(0.403607\pi\) | |||||||
\(270\) | −1.05791 | −0.0643826 | ||||||||
\(271\) | 1.60503 | 0.0974985 | 0.0487492 | − | 0.998811i | \(-0.484476\pi\) | ||||
0.0487492 | + | 0.998811i | \(0.484476\pi\) | |||||||
\(272\) | 11.3960 | 0.690986 | ||||||||
\(273\) | −10.7300 | −0.649412 | ||||||||
\(274\) | −22.2056 | −1.34149 | ||||||||
\(275\) | 12.0524 | 0.726787 | ||||||||
\(276\) | 0.0738306 | 0.00444408 | ||||||||
\(277\) | 2.04019 | 0.122583 | 0.0612917 | − | 0.998120i | \(-0.480478\pi\) | ||||
0.0612917 | + | 0.998120i | \(0.480478\pi\) | |||||||
\(278\) | 23.4457 | 1.40618 | ||||||||
\(279\) | −10.2606 | −0.614283 | ||||||||
\(280\) | 7.61328 | 0.454981 | ||||||||
\(281\) | −6.40945 | −0.382356 | −0.191178 | − | 0.981555i | \(-0.561231\pi\) | ||||
−0.191178 | + | 0.981555i | \(0.561231\pi\) | |||||||
\(282\) | 8.67580 | 0.516636 | ||||||||
\(283\) | −6.25421 | −0.371774 | −0.185887 | − | 0.982571i | \(-0.559516\pi\) | ||||
−0.185887 | + | 0.982571i | \(0.559516\pi\) | |||||||
\(284\) | 0.886313 | 0.0525930 | ||||||||
\(285\) | −4.07320 | −0.241276 | ||||||||
\(286\) | −11.1755 | −0.660821 | ||||||||
\(287\) | −6.76351 | −0.399238 | ||||||||
\(288\) | 0.417438 | 0.0245978 | ||||||||
\(289\) | −9.43092 | −0.554760 | ||||||||
\(290\) | 1.05791 | 0.0621228 | ||||||||
\(291\) | −3.97122 | −0.232797 | ||||||||
\(292\) | 0.0731545 | 0.00428104 | ||||||||
\(293\) | −16.3014 | −0.952338 | −0.476169 | − | 0.879354i | \(-0.657975\pi\) | ||||
−0.476169 | + | 0.879354i | \(0.657975\pi\) | |||||||
\(294\) | −10.0215 | −0.584467 | ||||||||
\(295\) | −0.128097 | −0.00745811 | ||||||||
\(296\) | −31.8854 | −1.85330 | ||||||||
\(297\) | −2.70213 | −0.156793 | ||||||||
\(298\) | 16.1925 | 0.938008 | ||||||||
\(299\) | −2.87193 | −0.166088 | ||||||||
\(300\) | −0.329309 | −0.0190127 | ||||||||
\(301\) | 0.676857 | 0.0390134 | ||||||||
\(302\) | 18.7596 | 1.07949 | ||||||||
\(303\) | 18.4855 | 1.06196 | ||||||||
\(304\) | 22.9670 | 1.31725 | ||||||||
\(305\) | −3.95111 | −0.226240 | ||||||||
\(306\) | 3.96194 | 0.226489 | ||||||||
\(307\) | 6.13524 | 0.350157 | 0.175078 | − | 0.984555i | \(-0.443982\pi\) | ||||
0.175078 | + | 0.984555i | \(0.443982\pi\) | |||||||
\(308\) | −0.745367 | −0.0424712 | ||||||||
\(309\) | −2.24948 | −0.127969 | ||||||||
\(310\) | 10.8548 | 0.616510 | ||||||||
\(311\) | −0.302171 | −0.0171346 | −0.00856728 | − | 0.999963i | \(-0.502727\pi\) | ||||
−0.00856728 | + | 0.999963i | \(0.502727\pi\) | |||||||
\(312\) | −7.96627 | −0.451001 | ||||||||
\(313\) | 21.6672 | 1.22471 | 0.612353 | − | 0.790585i | \(-0.290223\pi\) | ||||
0.612353 | + | 0.790585i | \(0.290223\pi\) | |||||||
\(314\) | −7.77912 | −0.439001 | ||||||||
\(315\) | 2.74468 | 0.154645 | ||||||||
\(316\) | −0.218777 | −0.0123072 | ||||||||
\(317\) | −7.71514 | −0.433326 | −0.216663 | − | 0.976247i | \(-0.569517\pi\) | ||||
−0.216663 | + | 0.976247i | \(0.569517\pi\) | |||||||
\(318\) | 0.953449 | 0.0534668 | ||||||||
\(319\) | 2.70213 | 0.151290 | ||||||||
\(320\) | 5.64430 | 0.315526 | ||||||||
\(321\) | −12.9231 | −0.721295 | ||||||||
\(322\) | −5.38039 | −0.299837 | ||||||||
\(323\) | 15.2544 | 0.848775 | ||||||||
\(324\) | 0.0738306 | 0.00410170 | ||||||||
\(325\) | 12.8098 | 0.710558 | ||||||||
\(326\) | −8.51446 | −0.471573 | ||||||||
\(327\) | 16.2725 | 0.899873 | ||||||||
\(328\) | −5.02142 | −0.277261 | ||||||||
\(329\) | −22.5087 | −1.24094 | ||||||||
\(330\) | 2.85862 | 0.157362 | ||||||||
\(331\) | −15.6398 | −0.859642 | −0.429821 | − | 0.902914i | \(-0.641423\pi\) | ||||
−0.429821 | + | 0.902914i | \(0.641423\pi\) | |||||||
\(332\) | 0.0804719 | 0.00441647 | ||||||||
\(333\) | −11.4951 | −0.629925 | ||||||||
\(334\) | 0.491876 | 0.0269143 | ||||||||
\(335\) | 11.7509 | 0.642023 | ||||||||
\(336\) | −15.4760 | −0.844286 | ||||||||
\(337\) | 22.0539 | 1.20135 | 0.600675 | − | 0.799493i | \(-0.294898\pi\) | ||||
0.600675 | + | 0.799493i | \(0.294898\pi\) | |||||||
\(338\) | 6.84327 | 0.372225 | ||||||||
\(339\) | −11.3227 | −0.614962 | ||||||||
\(340\) | −0.149218 | −0.00809249 | ||||||||
\(341\) | 27.7253 | 1.50141 | ||||||||
\(342\) | 7.98471 | 0.431764 | ||||||||
\(343\) | −0.153162 | −0.00826999 | ||||||||
\(344\) | 0.502517 | 0.0270939 | ||||||||
\(345\) | 0.734622 | 0.0395507 | ||||||||
\(346\) | −19.8865 | −1.06910 | ||||||||
\(347\) | −3.22284 | −0.173011 | −0.0865055 | − | 0.996251i | \(-0.527570\pi\) | ||||
−0.0865055 | + | 0.996251i | \(0.527570\pi\) | |||||||
\(348\) | −0.0738306 | −0.00395774 | ||||||||
\(349\) | 12.2805 | 0.657362 | 0.328681 | − | 0.944441i | \(-0.393396\pi\) | ||||
0.328681 | + | 0.944441i | \(0.393396\pi\) | |||||||
\(350\) | 23.9983 | 1.28276 | ||||||||
\(351\) | −2.87193 | −0.153292 | ||||||||
\(352\) | −1.12797 | −0.0601211 | ||||||||
\(353\) | 23.4425 | 1.24772 | 0.623860 | − | 0.781536i | \(-0.285564\pi\) | ||||
0.623860 | + | 0.781536i | \(0.285564\pi\) | |||||||
\(354\) | 0.251109 | 0.0133463 | ||||||||
\(355\) | 8.81890 | 0.468058 | ||||||||
\(356\) | 0.384907 | 0.0204000 | ||||||||
\(357\) | −10.2790 | −0.544020 | ||||||||
\(358\) | −22.0835 | −1.16715 | ||||||||
\(359\) | −3.94790 | −0.208362 | −0.104181 | − | 0.994558i | \(-0.533222\pi\) | ||||
−0.104181 | + | 0.994558i | \(0.533222\pi\) | |||||||
\(360\) | 2.03772 | 0.107397 | ||||||||
\(361\) | 11.7429 | 0.618047 | ||||||||
\(362\) | 6.68683 | 0.351452 | ||||||||
\(363\) | −3.69849 | −0.194121 | ||||||||
\(364\) | −0.792206 | −0.0415229 | ||||||||
\(365\) | 0.727894 | 0.0380997 | ||||||||
\(366\) | 7.74536 | 0.404857 | ||||||||
\(367\) | −8.80947 | −0.459850 | −0.229925 | − | 0.973208i | \(-0.573848\pi\) | ||||
−0.229925 | + | 0.973208i | \(0.573848\pi\) | |||||||
\(368\) | −4.14221 | −0.215928 | ||||||||
\(369\) | −1.81028 | −0.0942393 | ||||||||
\(370\) | 12.1608 | 0.632209 | ||||||||
\(371\) | −2.47365 | −0.128426 | ||||||||
\(372\) | −0.757543 | −0.0392768 | ||||||||
\(373\) | 15.8227 | 0.819267 | 0.409634 | − | 0.912250i | \(-0.365657\pi\) | ||||
0.409634 | + | 0.912250i | \(0.365657\pi\) | |||||||
\(374\) | −10.7057 | −0.553578 | ||||||||
\(375\) | −6.94976 | −0.358884 | ||||||||
\(376\) | −16.7111 | −0.861807 | ||||||||
\(377\) | 2.87193 | 0.147912 | ||||||||
\(378\) | −5.38039 | −0.276737 | ||||||||
\(379\) | 10.4466 | 0.536605 | 0.268302 | − | 0.963335i | \(-0.413537\pi\) | ||||
0.268302 | + | 0.963335i | \(0.413537\pi\) | |||||||
\(380\) | −0.300727 | −0.0154270 | ||||||||
\(381\) | −9.54485 | −0.488997 | ||||||||
\(382\) | −14.1915 | −0.726102 | ||||||||
\(383\) | −8.85503 | −0.452471 | −0.226236 | − | 0.974073i | \(-0.572642\pi\) | ||||
−0.226236 | + | 0.974073i | \(0.572642\pi\) | |||||||
\(384\) | −11.8994 | −0.607239 | ||||||||
\(385\) | −7.41647 | −0.377978 | ||||||||
\(386\) | 30.6430 | 1.55969 | ||||||||
\(387\) | 0.181163 | 0.00920903 | ||||||||
\(388\) | −0.293198 | −0.0148849 | ||||||||
\(389\) | 18.5823 | 0.942158 | 0.471079 | − | 0.882091i | \(-0.343865\pi\) | ||||
0.471079 | + | 0.882091i | \(0.343865\pi\) | |||||||
\(390\) | 3.03826 | 0.153848 | ||||||||
\(391\) | −2.75120 | −0.139134 | ||||||||
\(392\) | 19.3032 | 0.974957 | ||||||||
\(393\) | 15.3632 | 0.774972 | ||||||||
\(394\) | −13.8499 | −0.697749 | ||||||||
\(395\) | −2.17685 | −0.109529 | ||||||||
\(396\) | −0.199500 | −0.0100252 | ||||||||
\(397\) | −21.6225 | −1.08520 | −0.542602 | − | 0.839990i | \(-0.682561\pi\) | ||||
−0.542602 | + | 0.839990i | \(0.682561\pi\) | |||||||
\(398\) | −6.33564 | −0.317577 | ||||||||
\(399\) | −20.7157 | −1.03708 | ||||||||
\(400\) | 18.4756 | 0.923781 | ||||||||
\(401\) | −25.2586 | −1.26135 | −0.630677 | − | 0.776045i | \(-0.717223\pi\) | ||||
−0.630677 | + | 0.776045i | \(0.717223\pi\) | |||||||
\(402\) | −23.0354 | −1.14890 | ||||||||
\(403\) | 29.4676 | 1.46789 | ||||||||
\(404\) | 1.36480 | 0.0679011 | ||||||||
\(405\) | 0.734622 | 0.0365036 | ||||||||
\(406\) | 5.38039 | 0.267024 | ||||||||
\(407\) | 31.0611 | 1.53964 | ||||||||
\(408\) | −7.63137 | −0.377809 | ||||||||
\(409\) | 2.31715 | 0.114576 | 0.0572878 | − | 0.998358i | \(-0.481755\pi\) | ||||
0.0572878 | + | 0.998358i | \(0.481755\pi\) | |||||||
\(410\) | 1.91512 | 0.0945809 | ||||||||
\(411\) | 15.4197 | 0.760598 | ||||||||
\(412\) | −0.166081 | −0.00818221 | ||||||||
\(413\) | −0.651483 | −0.0320574 | ||||||||
\(414\) | −1.44008 | −0.0707761 | ||||||||
\(415\) | 0.800703 | 0.0393050 | ||||||||
\(416\) | −1.19885 | −0.0587787 | ||||||||
\(417\) | −16.2808 | −0.797276 | ||||||||
\(418\) | −21.5757 | −1.05530 | ||||||||
\(419\) | −6.36432 | −0.310917 | −0.155459 | − | 0.987842i | \(-0.549686\pi\) | ||||
−0.155459 | + | 0.987842i | \(0.549686\pi\) | |||||||
\(420\) | 0.202641 | 0.00988787 | ||||||||
\(421\) | −5.84235 | −0.284739 | −0.142369 | − | 0.989814i | \(-0.545472\pi\) | ||||
−0.142369 | + | 0.989814i | \(0.545472\pi\) | |||||||
\(422\) | −2.80988 | −0.136783 | ||||||||
\(423\) | −6.02453 | −0.292923 | ||||||||
\(424\) | −1.83651 | −0.0891886 | ||||||||
\(425\) | 12.2712 | 0.595243 | ||||||||
\(426\) | −17.2877 | −0.837592 | ||||||||
\(427\) | −20.0947 | −0.972453 | ||||||||
\(428\) | −0.954118 | −0.0461190 | ||||||||
\(429\) | 7.76033 | 0.374672 | ||||||||
\(430\) | −0.191655 | −0.00924242 | ||||||||
\(431\) | −17.3297 | −0.834744 | −0.417372 | − | 0.908736i | \(-0.637049\pi\) | ||||
−0.417372 | + | 0.908736i | \(0.637049\pi\) | |||||||
\(432\) | −4.14221 | −0.199292 | ||||||||
\(433\) | −13.9592 | −0.670835 | −0.335417 | − | 0.942070i | \(-0.608877\pi\) | ||||
−0.335417 | + | 0.942070i | \(0.608877\pi\) | |||||||
\(434\) | 55.2058 | 2.64996 | ||||||||
\(435\) | −0.734622 | −0.0352224 | ||||||||
\(436\) | 1.20141 | 0.0575371 | ||||||||
\(437\) | −5.54463 | −0.265236 | ||||||||
\(438\) | −1.42689 | −0.0681795 | ||||||||
\(439\) | 14.7239 | 0.702733 | 0.351367 | − | 0.936238i | \(-0.385717\pi\) | ||||
0.351367 | + | 0.936238i | \(0.385717\pi\) | |||||||
\(440\) | −5.50619 | −0.262497 | ||||||||
\(441\) | 6.95901 | 0.331381 | ||||||||
\(442\) | −11.3784 | −0.541217 | ||||||||
\(443\) | −39.8806 | −1.89479 | −0.947393 | − | 0.320073i | \(-0.896293\pi\) | ||||
−0.947393 | + | 0.320073i | \(0.896293\pi\) | |||||||
\(444\) | −0.848687 | −0.0402769 | ||||||||
\(445\) | 3.82986 | 0.181553 | ||||||||
\(446\) | −8.07309 | −0.382272 | ||||||||
\(447\) | −11.2442 | −0.531832 | ||||||||
\(448\) | 28.7061 | 1.35623 | ||||||||
\(449\) | 13.8427 | 0.653277 | 0.326639 | − | 0.945149i | \(-0.394084\pi\) | ||||
0.326639 | + | 0.945149i | \(0.394084\pi\) | |||||||
\(450\) | 6.42323 | 0.302794 | ||||||||
\(451\) | 4.89160 | 0.230337 | ||||||||
\(452\) | −0.835958 | −0.0393202 | ||||||||
\(453\) | −13.0268 | −0.612052 | ||||||||
\(454\) | 8.63659 | 0.405335 | ||||||||
\(455\) | −7.88252 | −0.369538 | ||||||||
\(456\) | −15.3799 | −0.720230 | ||||||||
\(457\) | 16.5018 | 0.771924 | 0.385962 | − | 0.922515i | \(-0.373870\pi\) | ||||
0.385962 | + | 0.922515i | \(0.373870\pi\) | |||||||
\(458\) | 20.4674 | 0.956377 | ||||||||
\(459\) | −2.75120 | −0.128415 | ||||||||
\(460\) | 0.0542376 | 0.00252884 | ||||||||
\(461\) | 32.0920 | 1.49468 | 0.747338 | − | 0.664445i | \(-0.231332\pi\) | ||||
0.747338 | + | 0.664445i | \(0.231332\pi\) | |||||||
\(462\) | 14.5385 | 0.676393 | ||||||||
\(463\) | 1.18030 | 0.0548530 | 0.0274265 | − | 0.999624i | \(-0.491269\pi\) | ||||
0.0274265 | + | 0.999624i | \(0.491269\pi\) | |||||||
\(464\) | 4.14221 | 0.192297 | ||||||||
\(465\) | −7.53762 | −0.349549 | ||||||||
\(466\) | 40.8829 | 1.89386 | ||||||||
\(467\) | 18.8983 | 0.874507 | 0.437254 | − | 0.899338i | \(-0.355951\pi\) | ||||
0.437254 | + | 0.899338i | \(0.355951\pi\) | |||||||
\(468\) | −0.212037 | −0.00980139 | ||||||||
\(469\) | 59.7635 | 2.75962 | ||||||||
\(470\) | 6.37343 | 0.293984 | ||||||||
\(471\) | 5.40186 | 0.248905 | ||||||||
\(472\) | −0.483679 | −0.0222631 | ||||||||
\(473\) | −0.489526 | −0.0225084 | ||||||||
\(474\) | 4.26729 | 0.196003 | ||||||||
\(475\) | 24.7309 | 1.13473 | ||||||||
\(476\) | −0.758901 | −0.0347842 | ||||||||
\(477\) | −0.662081 | −0.0303146 | ||||||||
\(478\) | −29.3036 | −1.34032 | ||||||||
\(479\) | 15.2872 | 0.698490 | 0.349245 | − | 0.937031i | \(-0.386438\pi\) | ||||
0.349245 | + | 0.937031i | \(0.386438\pi\) | |||||||
\(480\) | 0.306659 | 0.0139970 | ||||||||
\(481\) | 33.0130 | 1.50526 | ||||||||
\(482\) | −27.6641 | −1.26006 | ||||||||
\(483\) | 3.73618 | 0.170002 | ||||||||
\(484\) | −0.273062 | −0.0124119 | ||||||||
\(485\) | −2.91735 | −0.132470 | ||||||||
\(486\) | −1.44008 | −0.0653234 | ||||||||
\(487\) | −22.1203 | −1.00237 | −0.501183 | − | 0.865341i | \(-0.667102\pi\) | ||||
−0.501183 | + | 0.865341i | \(0.667102\pi\) | |||||||
\(488\) | −14.9189 | −0.675346 | ||||||||
\(489\) | 5.91249 | 0.267372 | ||||||||
\(490\) | −7.36203 | −0.332583 | ||||||||
\(491\) | −33.8069 | −1.52568 | −0.762842 | − | 0.646585i | \(-0.776197\pi\) | ||||
−0.762842 | + | 0.646585i | \(0.776197\pi\) | |||||||
\(492\) | −0.133654 | −0.00602558 | ||||||||
\(493\) | 2.75120 | 0.123908 | ||||||||
\(494\) | −22.9315 | −1.03174 | ||||||||
\(495\) | −1.98504 | −0.0892211 | ||||||||
\(496\) | 42.5014 | 1.90837 | ||||||||
\(497\) | 44.8516 | 2.01187 | ||||||||
\(498\) | −1.56962 | −0.0703363 | ||||||||
\(499\) | 25.1393 | 1.12539 | 0.562695 | − | 0.826664i | \(-0.309764\pi\) | ||||
0.562695 | + | 0.826664i | \(0.309764\pi\) | |||||||
\(500\) | −0.513105 | −0.0229468 | ||||||||
\(501\) | −0.341562 | −0.0152599 | ||||||||
\(502\) | 1.84292 | 0.0822535 | ||||||||
\(503\) | −40.7380 | −1.81642 | −0.908209 | − | 0.418518i | \(-0.862550\pi\) | ||||
−0.908209 | + | 0.418518i | \(0.862550\pi\) | |||||||
\(504\) | 10.3635 | 0.461629 | ||||||||
\(505\) | 13.5798 | 0.604295 | ||||||||
\(506\) | 3.89128 | 0.172989 | ||||||||
\(507\) | −4.75201 | −0.211044 | ||||||||
\(508\) | −0.704702 | −0.0312661 | ||||||||
\(509\) | 25.6947 | 1.13890 | 0.569450 | − | 0.822026i | \(-0.307156\pi\) | ||||
0.569450 | + | 0.822026i | \(0.307156\pi\) | |||||||
\(510\) | 2.91053 | 0.128880 | ||||||||
\(511\) | 3.70196 | 0.163765 | ||||||||
\(512\) | 21.2505 | 0.939149 | ||||||||
\(513\) | −5.54463 | −0.244801 | ||||||||
\(514\) | 31.0497 | 1.36954 | ||||||||
\(515\) | −1.65252 | −0.0728187 | ||||||||
\(516\) | 0.0133754 | 0.000588818 0 | ||||||||
\(517\) | 16.2791 | 0.715952 | ||||||||
\(518\) | 61.8479 | 2.71744 | ||||||||
\(519\) | 13.8093 | 0.606160 | ||||||||
\(520\) | −5.85220 | −0.256636 | ||||||||
\(521\) | −38.8339 | −1.70134 | −0.850671 | − | 0.525698i | \(-0.823804\pi\) | ||||
−0.850671 | + | 0.525698i | \(0.823804\pi\) | |||||||
\(522\) | 1.44008 | 0.0630306 | ||||||||
\(523\) | 27.7980 | 1.21552 | 0.607762 | − | 0.794119i | \(-0.292068\pi\) | ||||
0.607762 | + | 0.794119i | \(0.292068\pi\) | |||||||
\(524\) | 1.13428 | 0.0495511 | ||||||||
\(525\) | −16.6646 | −0.727302 | ||||||||
\(526\) | −21.2817 | −0.927925 | ||||||||
\(527\) | 28.2288 | 1.22967 | ||||||||
\(528\) | 11.1928 | 0.487104 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.700425 | 0.0304245 | ||||||||
\(531\) | −0.174372 | −0.00756709 | ||||||||
\(532\) | −1.52945 | −0.0663102 | ||||||||
\(533\) | 5.19899 | 0.225193 | ||||||||
\(534\) | −7.50768 | −0.324889 | ||||||||
\(535\) | −9.49356 | −0.410443 | ||||||||
\(536\) | 44.3701 | 1.91650 | ||||||||
\(537\) | 15.3349 | 0.661751 | ||||||||
\(538\) | −14.0874 | −0.607351 | ||||||||
\(539\) | −18.8041 | −0.809952 | ||||||||
\(540\) | 0.0542376 | 0.00233401 | ||||||||
\(541\) | −34.1038 | −1.46624 | −0.733118 | − | 0.680101i | \(-0.761936\pi\) | ||||
−0.733118 | + | 0.680101i | \(0.761936\pi\) | |||||||
\(542\) | −2.31137 | −0.0992818 | ||||||||
\(543\) | −4.64338 | −0.199266 | ||||||||
\(544\) | −1.14845 | −0.0492396 | ||||||||
\(545\) | 11.9541 | 0.512059 | ||||||||
\(546\) | 15.4521 | 0.661290 | ||||||||
\(547\) | 9.35076 | 0.399810 | 0.199905 | − | 0.979815i | \(-0.435937\pi\) | ||||
0.199905 | + | 0.979815i | \(0.435937\pi\) | |||||||
\(548\) | 1.13845 | 0.0486320 | ||||||||
\(549\) | −5.37843 | −0.229546 | ||||||||
\(550\) | −17.3564 | −0.740080 | ||||||||
\(551\) | 5.54463 | 0.236209 | ||||||||
\(552\) | 2.77384 | 0.118062 | ||||||||
\(553\) | −11.0712 | −0.470793 | ||||||||
\(554\) | −2.93804 | −0.124826 | ||||||||
\(555\) | −8.44452 | −0.358450 | ||||||||
\(556\) | −1.20202 | −0.0509772 | ||||||||
\(557\) | −12.7997 | −0.542341 | −0.271170 | − | 0.962531i | \(-0.587411\pi\) | ||||
−0.271170 | + | 0.962531i | \(0.587411\pi\) | |||||||
\(558\) | 14.7760 | 0.625519 | ||||||||
\(559\) | −0.520288 | −0.0220058 | ||||||||
\(560\) | −11.3690 | −0.480429 | ||||||||
\(561\) | 7.43409 | 0.313868 | ||||||||
\(562\) | 9.23012 | 0.389349 | ||||||||
\(563\) | 24.8909 | 1.04903 | 0.524513 | − | 0.851402i | \(-0.324247\pi\) | ||||
0.524513 | + | 0.851402i | \(0.324247\pi\) | |||||||
\(564\) | −0.444795 | −0.0187292 | ||||||||
\(565\) | −8.31786 | −0.349935 | ||||||||
\(566\) | 9.00656 | 0.378574 | ||||||||
\(567\) | 3.73618 | 0.156905 | ||||||||
\(568\) | 33.2990 | 1.39720 | ||||||||
\(569\) | −36.1179 | −1.51414 | −0.757072 | − | 0.653332i | \(-0.773371\pi\) | ||||
−0.757072 | + | 0.653332i | \(0.773371\pi\) | |||||||
\(570\) | 5.86574 | 0.245689 | ||||||||
\(571\) | −24.7666 | −1.03645 | −0.518226 | − | 0.855244i | \(-0.673407\pi\) | ||||
−0.518226 | + | 0.855244i | \(0.673407\pi\) | |||||||
\(572\) | 0.572950 | 0.0239563 | ||||||||
\(573\) | 9.85469 | 0.411686 | ||||||||
\(574\) | 9.74000 | 0.406540 | ||||||||
\(575\) | −4.46033 | −0.186009 | ||||||||
\(576\) | 7.68328 | 0.320137 | ||||||||
\(577\) | 21.4822 | 0.894315 | 0.447157 | − | 0.894455i | \(-0.352436\pi\) | ||||
0.447157 | + | 0.894455i | \(0.352436\pi\) | |||||||
\(578\) | 13.5813 | 0.564907 | ||||||||
\(579\) | −21.2787 | −0.884312 | ||||||||
\(580\) | −0.0542376 | −0.00225209 | ||||||||
\(581\) | 4.07225 | 0.168946 | ||||||||
\(582\) | 5.71888 | 0.237055 | ||||||||
\(583\) | 1.78903 | 0.0740940 | ||||||||
\(584\) | 2.74844 | 0.113731 | ||||||||
\(585\) | −2.10978 | −0.0872288 | ||||||||
\(586\) | 23.4753 | 0.969756 | ||||||||
\(587\) | 47.2043 | 1.94833 | 0.974164 | − | 0.225840i | \(-0.0725127\pi\) | ||||
0.974164 | + | 0.225840i | \(0.0725127\pi\) | |||||||
\(588\) | 0.513788 | 0.0211882 | ||||||||
\(589\) | 56.8909 | 2.34415 | ||||||||
\(590\) | 0.184470 | 0.00759452 | ||||||||
\(591\) | 9.61747 | 0.395610 | ||||||||
\(592\) | 47.6149 | 1.95696 | ||||||||
\(593\) | −30.4167 | −1.24906 | −0.624532 | − | 0.780999i | \(-0.714710\pi\) | ||||
−0.624532 | + | 0.780999i | \(0.714710\pi\) | |||||||
\(594\) | 3.89128 | 0.159661 | ||||||||
\(595\) | −7.55114 | −0.309567 | ||||||||
\(596\) | −0.830165 | −0.0340049 | ||||||||
\(597\) | 4.39951 | 0.180060 | ||||||||
\(598\) | 4.13581 | 0.169126 | ||||||||
\(599\) | 3.07961 | 0.125829 | 0.0629147 | − | 0.998019i | \(-0.479960\pi\) | ||||
0.0629147 | + | 0.998019i | \(0.479960\pi\) | |||||||
\(600\) | −12.3722 | −0.505094 | ||||||||
\(601\) | −22.7054 | −0.926171 | −0.463086 | − | 0.886314i | \(-0.653258\pi\) | ||||
−0.463086 | + | 0.886314i | \(0.653258\pi\) | |||||||
\(602\) | −0.974728 | −0.0397269 | ||||||||
\(603\) | 15.9959 | 0.651404 | ||||||||
\(604\) | −0.961776 | −0.0391341 | ||||||||
\(605\) | −2.71699 | −0.110461 | ||||||||
\(606\) | −26.6206 | −1.08139 | ||||||||
\(607\) | 23.3283 | 0.946868 | 0.473434 | − | 0.880829i | \(-0.343014\pi\) | ||||
0.473434 | + | 0.880829i | \(0.343014\pi\) | |||||||
\(608\) | −2.31454 | −0.0938670 | ||||||||
\(609\) | −3.73618 | −0.151397 | ||||||||
\(610\) | 5.68991 | 0.230378 | ||||||||
\(611\) | 17.3020 | 0.699965 | ||||||||
\(612\) | −0.203123 | −0.00821074 | ||||||||
\(613\) | −10.1942 | −0.411739 | −0.205869 | − | 0.978579i | \(-0.566002\pi\) | ||||
−0.205869 | + | 0.978579i | \(0.566002\pi\) | |||||||
\(614\) | −8.83524 | −0.356561 | ||||||||
\(615\) | −1.32987 | −0.0536255 | ||||||||
\(616\) | −28.0036 | −1.12830 | ||||||||
\(617\) | −35.5944 | −1.43298 | −0.716489 | − | 0.697599i | \(-0.754252\pi\) | ||||
−0.716489 | + | 0.697599i | \(0.754252\pi\) | |||||||
\(618\) | 3.23944 | 0.130309 | ||||||||
\(619\) | 24.9632 | 1.00336 | 0.501678 | − | 0.865055i | \(-0.332716\pi\) | ||||
0.501678 | + | 0.865055i | \(0.332716\pi\) | |||||||
\(620\) | −0.556507 | −0.0223499 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0.435151 | 0.0174480 | ||||||||
\(623\) | 19.4781 | 0.780373 | ||||||||
\(624\) | 11.8961 | 0.476227 | ||||||||
\(625\) | 17.1962 | 0.687848 | ||||||||
\(626\) | −31.2026 | −1.24711 | ||||||||
\(627\) | 14.9823 | 0.598336 | ||||||||
\(628\) | 0.398823 | 0.0159148 | ||||||||
\(629\) | 31.6252 | 1.26098 | ||||||||
\(630\) | −3.95255 | −0.157473 | ||||||||
\(631\) | −47.0960 | −1.87486 | −0.937431 | − | 0.348172i | \(-0.886802\pi\) | ||||
−0.937431 | + | 0.348172i | \(0.886802\pi\) | |||||||
\(632\) | −8.21953 | −0.326955 | ||||||||
\(633\) | 1.95120 | 0.0775531 | ||||||||
\(634\) | 11.1104 | 0.441251 | ||||||||
\(635\) | −7.01185 | −0.278257 | ||||||||
\(636\) | −0.0488818 | −0.00193829 | ||||||||
\(637\) | −19.9858 | −0.791866 | ||||||||
\(638\) | −3.89128 | −0.154057 | ||||||||
\(639\) | 12.0047 | 0.474898 | ||||||||
\(640\) | −8.74156 | −0.345541 | ||||||||
\(641\) | −21.9528 | −0.867084 | −0.433542 | − | 0.901133i | \(-0.642736\pi\) | ||||
−0.433542 | + | 0.901133i | \(0.642736\pi\) | |||||||
\(642\) | 18.6103 | 0.734488 | ||||||||
\(643\) | −40.4333 | −1.59454 | −0.797268 | − | 0.603626i | \(-0.793722\pi\) | ||||
−0.797268 | + | 0.603626i | \(0.793722\pi\) | |||||||
\(644\) | 0.275844 | 0.0108698 | ||||||||
\(645\) | 0.133086 | 0.00524027 | ||||||||
\(646\) | −21.9675 | −0.864300 | ||||||||
\(647\) | 7.21645 | 0.283708 | 0.141854 | − | 0.989888i | \(-0.454694\pi\) | ||||
0.141854 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(648\) | 2.77384 | 0.108967 | ||||||||
\(649\) | 0.471175 | 0.0184952 | ||||||||
\(650\) | −18.4471 | −0.723554 | ||||||||
\(651\) | −38.3352 | −1.50248 | ||||||||
\(652\) | 0.436523 | 0.0170956 | ||||||||
\(653\) | 13.4765 | 0.527377 | 0.263689 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263689 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(654\) | −23.4337 | −0.916332 | ||||||||
\(655\) | 11.2862 | 0.440987 | ||||||||
\(656\) | 7.49855 | 0.292769 | ||||||||
\(657\) | 0.990842 | 0.0386564 | ||||||||
\(658\) | 32.4143 | 1.26364 | ||||||||
\(659\) | 37.3480 | 1.45487 | 0.727435 | − | 0.686177i | \(-0.240712\pi\) | ||||
0.727435 | + | 0.686177i | \(0.240712\pi\) | |||||||
\(660\) | −0.146557 | −0.00570472 | ||||||||
\(661\) | 50.2592 | 1.95486 | 0.977428 | − | 0.211268i | \(-0.0677592\pi\) | ||||
0.977428 | + | 0.211268i | \(0.0677592\pi\) | |||||||
\(662\) | 22.5226 | 0.875366 | ||||||||
\(663\) | 7.90125 | 0.306859 | ||||||||
\(664\) | 3.02335 | 0.117329 | ||||||||
\(665\) | −15.2182 | −0.590137 | ||||||||
\(666\) | 16.5538 | 0.641447 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −0.0252177 | −0.000975703 0 | ||||||||
\(669\) | 5.60600 | 0.216740 | ||||||||
\(670\) | −16.9223 | −0.653765 | ||||||||
\(671\) | 14.5332 | 0.561048 | ||||||||
\(672\) | 1.55962 | 0.0601637 | ||||||||
\(673\) | −32.0250 | −1.23447 | −0.617236 | − | 0.786778i | \(-0.711748\pi\) | ||||
−0.617236 | + | 0.786778i | \(0.711748\pi\) | |||||||
\(674\) | −31.7593 | −1.22332 | ||||||||
\(675\) | −4.46033 | −0.171678 | ||||||||
\(676\) | −0.350844 | −0.0134940 | ||||||||
\(677\) | 47.4069 | 1.82200 | 0.910998 | − | 0.412412i | \(-0.135314\pi\) | ||||
0.910998 | + | 0.412412i | \(0.135314\pi\) | |||||||
\(678\) | 16.3055 | 0.626210 | ||||||||
\(679\) | −14.8372 | −0.569399 | ||||||||
\(680\) | −5.60617 | −0.214987 | ||||||||
\(681\) | −5.99730 | −0.229817 | ||||||||
\(682\) | −39.9267 | −1.52887 | ||||||||
\(683\) | −6.12035 | −0.234189 | −0.117094 | − | 0.993121i | \(-0.537358\pi\) | ||||
−0.117094 | + | 0.993121i | \(0.537358\pi\) | |||||||
\(684\) | −0.409363 | −0.0156524 | ||||||||
\(685\) | 11.3276 | 0.432807 | ||||||||
\(686\) | 0.220566 | 0.00842126 | ||||||||
\(687\) | −14.2127 | −0.542247 | ||||||||
\(688\) | −0.750415 | −0.0286093 | ||||||||
\(689\) | 1.90145 | 0.0724395 | ||||||||
\(690\) | −1.05791 | −0.0402741 | ||||||||
\(691\) | −46.8351 | −1.78169 | −0.890845 | − | 0.454307i | \(-0.849887\pi\) | ||||
−0.890845 | + | 0.454307i | \(0.849887\pi\) | |||||||
\(692\) | 1.01955 | 0.0387574 | ||||||||
\(693\) | −10.0956 | −0.383501 | ||||||||
\(694\) | 4.64114 | 0.176175 | ||||||||
\(695\) | −11.9603 | −0.453678 | ||||||||
\(696\) | −2.77384 | −0.105142 | ||||||||
\(697\) | 4.98043 | 0.188647 | ||||||||
\(698\) | −17.6850 | −0.669386 | ||||||||
\(699\) | −28.3893 | −1.07378 | ||||||||
\(700\) | −1.23036 | −0.0465031 | ||||||||
\(701\) | −8.62132 | −0.325623 | −0.162811 | − | 0.986657i | \(-0.552056\pi\) | ||||
−0.162811 | + | 0.986657i | \(0.552056\pi\) | |||||||
\(702\) | 4.13581 | 0.156096 | ||||||||
\(703\) | 63.7358 | 2.40384 | ||||||||
\(704\) | −20.7612 | −0.782468 | ||||||||
\(705\) | −4.42575 | −0.166683 | ||||||||
\(706\) | −33.7591 | −1.27054 | ||||||||
\(707\) | 69.0651 | 2.59746 | ||||||||
\(708\) | −0.0128740 | −0.000483834 0 | ||||||||
\(709\) | −23.5240 | −0.883463 | −0.441731 | − | 0.897147i | \(-0.645636\pi\) | ||||
−0.441731 | + | 0.897147i | \(0.645636\pi\) | |||||||
\(710\) | −12.6999 | −0.476619 | ||||||||
\(711\) | −2.96323 | −0.111130 | ||||||||
\(712\) | 14.4611 | 0.541951 | ||||||||
\(713\) | −10.2606 | −0.384261 | ||||||||
\(714\) | 14.8025 | 0.553970 | ||||||||
\(715\) | 5.70091 | 0.213202 | ||||||||
\(716\) | 1.13219 | 0.0423118 | ||||||||
\(717\) | 20.3486 | 0.759932 | ||||||||
\(718\) | 5.68529 | 0.212173 | ||||||||
\(719\) | −14.1926 | −0.529294 | −0.264647 | − | 0.964345i | \(-0.585255\pi\) | ||||
−0.264647 | + | 0.964345i | \(0.585255\pi\) | |||||||
\(720\) | −3.04296 | −0.113404 | ||||||||
\(721\) | −8.40447 | −0.312999 | ||||||||
\(722\) | −16.9107 | −0.629351 | ||||||||
\(723\) | 19.2101 | 0.714431 | ||||||||
\(724\) | −0.342823 | −0.0127409 | ||||||||
\(725\) | 4.46033 | 0.165653 | ||||||||
\(726\) | 5.32613 | 0.197671 | ||||||||
\(727\) | −4.28230 | −0.158822 | −0.0794108 | − | 0.996842i | \(-0.525304\pi\) | ||||
−0.0794108 | + | 0.996842i | \(0.525304\pi\) | |||||||
\(728\) | −29.7634 | −1.10310 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.04823 | −0.0387966 | ||||||||
\(731\) | −0.498415 | −0.0184345 | ||||||||
\(732\) | −0.397093 | −0.0146770 | ||||||||
\(733\) | 12.6104 | 0.465774 | 0.232887 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232887 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(734\) | 12.6863 | 0.468261 | ||||||||
\(735\) | 5.11224 | 0.188568 | ||||||||
\(736\) | 0.417438 | 0.0153870 | ||||||||
\(737\) | −43.2230 | −1.59214 | ||||||||
\(738\) | 2.60694 | 0.0959629 | ||||||||
\(739\) | −14.4588 | −0.531874 | −0.265937 | − | 0.963990i | \(-0.585681\pi\) | ||||
−0.265937 | + | 0.963990i | \(0.585681\pi\) | |||||||
\(740\) | −0.623464 | −0.0229190 | ||||||||
\(741\) | 15.9238 | 0.584975 | ||||||||
\(742\) | 3.56225 | 0.130774 | ||||||||
\(743\) | −52.1742 | −1.91409 | −0.957044 | − | 0.289944i | \(-0.906363\pi\) | ||||
−0.957044 | + | 0.289944i | \(0.906363\pi\) | |||||||
\(744\) | −28.4611 | −1.04343 | ||||||||
\(745\) | −8.26022 | −0.302631 | ||||||||
\(746\) | −22.7859 | −0.834252 | ||||||||
\(747\) | 1.08995 | 0.0398793 | ||||||||
\(748\) | 0.548864 | 0.0200684 | ||||||||
\(749\) | −48.2828 | −1.76422 | ||||||||
\(750\) | 10.0082 | 0.365448 | ||||||||
\(751\) | −29.7393 | −1.08520 | −0.542602 | − | 0.839990i | \(-0.682561\pi\) | ||||
−0.542602 | + | 0.839990i | \(0.682561\pi\) | |||||||
\(752\) | 24.9549 | 0.910010 | ||||||||
\(753\) | −1.27973 | −0.0466361 | ||||||||
\(754\) | −4.13581 | −0.150617 | ||||||||
\(755\) | −9.56976 | −0.348279 | ||||||||
\(756\) | 0.275844 | 0.0100324 | ||||||||
\(757\) | 1.08267 | 0.0393504 | 0.0196752 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196752 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(758\) | −15.0439 | −0.546419 | ||||||||
\(759\) | −2.70213 | −0.0980811 | ||||||||
\(760\) | −11.2984 | −0.409836 | ||||||||
\(761\) | −24.7614 | −0.897599 | −0.448799 | − | 0.893633i | \(-0.648148\pi\) | ||||
−0.448799 | + | 0.893633i | \(0.648148\pi\) | |||||||
\(762\) | 13.7453 | 0.497941 | ||||||||
\(763\) | 60.7970 | 2.20100 | ||||||||
\(764\) | 0.727578 | 0.0263228 | ||||||||
\(765\) | −2.02109 | −0.0730726 | ||||||||
\(766\) | 12.7520 | 0.460747 | ||||||||
\(767\) | 0.500784 | 0.0180823 | ||||||||
\(768\) | 1.76955 | 0.0638531 | ||||||||
\(769\) | 38.2442 | 1.37912 | 0.689560 | − | 0.724229i | \(-0.257804\pi\) | ||||
0.689560 | + | 0.724229i | \(0.257804\pi\) | |||||||
\(770\) | 10.6803 | 0.384892 | ||||||||
\(771\) | −21.5611 | −0.776504 | ||||||||
\(772\) | −1.57102 | −0.0565422 | ||||||||
\(773\) | −4.36196 | −0.156889 | −0.0784444 | − | 0.996918i | \(-0.524995\pi\) | ||||
−0.0784444 | + | 0.996918i | \(0.524995\pi\) | |||||||
\(774\) | −0.260889 | −0.00937747 | ||||||||
\(775\) | 45.7655 | 1.64394 | ||||||||
\(776\) | −11.0155 | −0.395435 | ||||||||
\(777\) | −42.9475 | −1.54073 | ||||||||
\(778\) | −26.7599 | −0.959390 | ||||||||
\(779\) | 10.0373 | 0.359624 | ||||||||
\(780\) | −0.155767 | −0.00557734 | ||||||||
\(781\) | −32.4382 | −1.16073 | ||||||||
\(782\) | 3.96194 | 0.141679 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −28.8257 | −1.02949 | ||||||||
\(785\) | 3.96833 | 0.141636 | ||||||||
\(786\) | −22.1243 | −0.789147 | ||||||||
\(787\) | −54.5403 | −1.94415 | −0.972076 | − | 0.234666i | \(-0.924600\pi\) | ||||
−0.972076 | + | 0.234666i | \(0.924600\pi\) | |||||||
\(788\) | 0.710064 | 0.0252950 | ||||||||
\(789\) | 14.7781 | 0.526115 | ||||||||
\(790\) | 3.13485 | 0.111533 | ||||||||
\(791\) | −42.3034 | −1.50414 | ||||||||
\(792\) | −7.49527 | −0.266333 | ||||||||
\(793\) | 15.4465 | 0.548520 | ||||||||
\(794\) | 31.1382 | 1.10505 | ||||||||
\(795\) | −0.486379 | −0.0172501 | ||||||||
\(796\) | 0.324818 | 0.0115129 | ||||||||
\(797\) | −14.1584 | −0.501518 | −0.250759 | − | 0.968050i | \(-0.580680\pi\) | ||||
−0.250759 | + | 0.968050i | \(0.580680\pi\) | |||||||
\(798\) | 29.8323 | 1.05605 | ||||||||
\(799\) | 16.5747 | 0.586369 | ||||||||
\(800\) | −1.86191 | −0.0658286 | ||||||||
\(801\) | 5.21337 | 0.184206 | ||||||||
\(802\) | 36.3744 | 1.28442 | ||||||||
\(803\) | −2.67738 | −0.0944829 | ||||||||
\(804\) | 1.18099 | 0.0416502 | ||||||||
\(805\) | 2.74468 | 0.0967371 | ||||||||
\(806\) | −42.4357 | −1.49473 | ||||||||
\(807\) | 9.78238 | 0.344356 | ||||||||
\(808\) | 51.2758 | 1.80388 | ||||||||
\(809\) | −7.90499 | −0.277925 | −0.138962 | − | 0.990298i | \(-0.544377\pi\) | ||||
−0.138962 | + | 0.990298i | \(0.544377\pi\) | |||||||
\(810\) | −1.05791 | −0.0371713 | ||||||||
\(811\) | −22.0093 | −0.772853 | −0.386426 | − | 0.922320i | \(-0.626291\pi\) | ||||
−0.386426 | + | 0.922320i | \(0.626291\pi\) | |||||||
\(812\) | −0.275844 | −0.00968023 | ||||||||
\(813\) | 1.60503 | 0.0562908 | ||||||||
\(814\) | −44.7305 | −1.56780 | ||||||||
\(815\) | 4.34345 | 0.152144 | ||||||||
\(816\) | 11.3960 | 0.398941 | ||||||||
\(817\) | −1.00448 | −0.0351424 | ||||||||
\(818\) | −3.33688 | −0.116671 | ||||||||
\(819\) | −10.7300 | −0.374938 | ||||||||
\(820\) | −0.0981850 | −0.00342877 | ||||||||
\(821\) | 1.48851 | 0.0519495 | 0.0259747 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259747 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(822\) | −22.2056 | −0.774509 | ||||||||
\(823\) | 10.8193 | 0.377138 | 0.188569 | − | 0.982060i | \(-0.439615\pi\) | ||||
0.188569 | + | 0.982060i | \(0.439615\pi\) | |||||||
\(824\) | −6.23970 | −0.217370 | ||||||||
\(825\) | 12.0524 | 0.419611 | ||||||||
\(826\) | 0.938188 | 0.0326437 | ||||||||
\(827\) | −11.1086 | −0.386285 | −0.193142 | − | 0.981171i | \(-0.561868\pi\) | ||||
−0.193142 | + | 0.981171i | \(0.561868\pi\) | |||||||
\(828\) | 0.0738306 | 0.00256579 | ||||||||
\(829\) | 37.1704 | 1.29098 | 0.645490 | − | 0.763769i | \(-0.276653\pi\) | ||||
0.645490 | + | 0.763769i | \(0.276653\pi\) | |||||||
\(830\) | −1.15308 | −0.0400239 | ||||||||
\(831\) | 2.04019 | 0.0707736 | ||||||||
\(832\) | −22.0658 | −0.764996 | ||||||||
\(833\) | −19.1456 | −0.663355 | ||||||||
\(834\) | 23.4457 | 0.811858 | ||||||||
\(835\) | −0.250919 | −0.00868340 | ||||||||
\(836\) | 1.10615 | 0.0382571 | ||||||||
\(837\) | −10.2606 | −0.354657 | ||||||||
\(838\) | 9.16513 | 0.316604 | ||||||||
\(839\) | −32.0230 | −1.10556 | −0.552778 | − | 0.833328i | \(-0.686432\pi\) | ||||
−0.552778 | + | 0.833328i | \(0.686432\pi\) | |||||||
\(840\) | 7.61328 | 0.262683 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 8.41345 | 0.289947 | ||||||||
\(843\) | −6.40945 | −0.220753 | ||||||||
\(844\) | 0.144058 | 0.00495869 | ||||||||
\(845\) | −3.49093 | −0.120092 | ||||||||
\(846\) | 8.67580 | 0.298280 | ||||||||
\(847\) | −13.8182 | −0.474800 | ||||||||
\(848\) | 2.74248 | 0.0941771 | ||||||||
\(849\) | −6.25421 | −0.214644 | ||||||||
\(850\) | −17.6716 | −0.606130 | ||||||||
\(851\) | −11.4951 | −0.394045 | ||||||||
\(852\) | 0.886313 | 0.0303646 | ||||||||
\(853\) | −34.0427 | −1.16560 | −0.582799 | − | 0.812616i | \(-0.698043\pi\) | ||||
−0.582799 | + | 0.812616i | \(0.698043\pi\) | |||||||
\(854\) | 28.9380 | 0.990239 | ||||||||
\(855\) | −4.07320 | −0.139301 | ||||||||
\(856\) | −35.8465 | −1.22521 | ||||||||
\(857\) | −8.43886 | −0.288266 | −0.144133 | − | 0.989558i | \(-0.546039\pi\) | ||||
−0.144133 | + | 0.989558i | \(0.546039\pi\) | |||||||
\(858\) | −11.1755 | −0.381525 | ||||||||
\(859\) | 9.83616 | 0.335605 | 0.167803 | − | 0.985821i | \(-0.446333\pi\) | ||||
0.167803 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(860\) | 0.00982584 | 0.000335058 0 | ||||||||
\(861\) | −6.76351 | −0.230500 | ||||||||
\(862\) | 24.9562 | 0.850012 | ||||||||
\(863\) | −42.6331 | −1.45125 | −0.725624 | − | 0.688092i | \(-0.758449\pi\) | ||||
−0.725624 | + | 0.688092i | \(0.758449\pi\) | |||||||
\(864\) | 0.417438 | 0.0142015 | ||||||||
\(865\) | 10.1446 | 0.344926 | ||||||||
\(866\) | 20.1023 | 0.683104 | ||||||||
\(867\) | −9.43092 | −0.320291 | ||||||||
\(868\) | −2.83031 | −0.0960671 | ||||||||
\(869\) | 8.00704 | 0.271620 | ||||||||
\(870\) | 1.05791 | 0.0358666 | ||||||||
\(871\) | −45.9392 | −1.55659 | ||||||||
\(872\) | 45.1374 | 1.52854 | ||||||||
\(873\) | −3.97122 | −0.134406 | ||||||||
\(874\) | 7.98471 | 0.270087 | ||||||||
\(875\) | −25.9655 | −0.877795 | ||||||||
\(876\) | 0.0731545 | 0.00247166 | ||||||||
\(877\) | 43.1875 | 1.45834 | 0.729170 | − | 0.684333i | \(-0.239906\pi\) | ||||
0.729170 | + | 0.684333i | \(0.239906\pi\) | |||||||
\(878\) | −21.2036 | −0.715587 | ||||||||
\(879\) | −16.3014 | −0.549832 | ||||||||
\(880\) | 8.22247 | 0.277179 | ||||||||
\(881\) | 5.46060 | 0.183972 | 0.0919861 | − | 0.995760i | \(-0.470678\pi\) | ||||
0.0919861 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(882\) | −10.0215 | −0.337442 | ||||||||
\(883\) | 17.9095 | 0.602703 | 0.301352 | − | 0.953513i | \(-0.402562\pi\) | ||||
0.301352 | + | 0.953513i | \(0.402562\pi\) | |||||||
\(884\) | 0.583354 | 0.0196203 | ||||||||
\(885\) | −0.128097 | −0.00430594 | ||||||||
\(886\) | 57.4313 | 1.92944 | ||||||||
\(887\) | −36.8826 | −1.23840 | −0.619198 | − | 0.785235i | \(-0.712542\pi\) | ||||
−0.619198 | + | 0.785235i | \(0.712542\pi\) | |||||||
\(888\) | −31.8854 | −1.07000 | ||||||||
\(889\) | −35.6612 | −1.19604 | ||||||||
\(890\) | −5.51530 | −0.184873 | ||||||||
\(891\) | −2.70213 | −0.0905248 | ||||||||
\(892\) | 0.413894 | 0.0138582 | ||||||||
\(893\) | 33.4038 | 1.11781 | ||||||||
\(894\) | 16.1925 | 0.541559 | ||||||||
\(895\) | 11.2654 | 0.376560 | ||||||||
\(896\) | −44.4583 | −1.48525 | ||||||||
\(897\) | −2.87193 | −0.0958910 | ||||||||
\(898\) | −19.9346 | −0.665226 | ||||||||
\(899\) | 10.2606 | 0.342209 | ||||||||
\(900\) | −0.329309 | −0.0109770 | ||||||||
\(901\) | 1.82151 | 0.0606834 | ||||||||
\(902\) | −7.04430 | −0.234550 | ||||||||
\(903\) | 0.676857 | 0.0225244 | ||||||||
\(904\) | −31.4072 | −1.04459 | ||||||||
\(905\) | −3.41112 | −0.113390 | ||||||||
\(906\) | 18.7596 | 0.623247 | ||||||||
\(907\) | −38.3059 | −1.27193 | −0.635964 | − | 0.771719i | \(-0.719397\pi\) | ||||
−0.635964 | + | 0.771719i | \(0.719397\pi\) | |||||||
\(908\) | −0.442784 | −0.0146943 | ||||||||
\(909\) | 18.4855 | 0.613125 | ||||||||
\(910\) | 11.3515 | 0.376297 | ||||||||
\(911\) | −21.4837 | −0.711787 | −0.355894 | − | 0.934526i | \(-0.615823\pi\) | ||||
−0.355894 | + | 0.934526i | \(0.615823\pi\) | |||||||
\(912\) | 22.9670 | 0.760514 | ||||||||
\(913\) | −2.94519 | −0.0974717 | ||||||||
\(914\) | −23.7640 | −0.786042 | ||||||||
\(915\) | −3.95111 | −0.130620 | ||||||||
\(916\) | −1.04933 | −0.0346708 | ||||||||
\(917\) | 57.3997 | 1.89550 | ||||||||
\(918\) | 3.96194 | 0.130764 | ||||||||
\(919\) | −22.6683 | −0.747759 | −0.373880 | − | 0.927477i | \(-0.621973\pi\) | ||||
−0.373880 | + | 0.927477i | \(0.621973\pi\) | |||||||
\(920\) | 2.03772 | 0.0671817 | ||||||||
\(921\) | 6.13524 | 0.202163 | ||||||||
\(922\) | −46.2151 | −1.52201 | ||||||||
\(923\) | −34.4766 | −1.13481 | ||||||||
\(924\) | −0.745367 | −0.0245208 | ||||||||
\(925\) | 51.2718 | 1.68581 | ||||||||
\(926\) | −1.69972 | −0.0558563 | ||||||||
\(927\) | −2.24948 | −0.0738828 | ||||||||
\(928\) | −0.417438 | −0.0137031 | ||||||||
\(929\) | −21.5525 | −0.707115 | −0.353558 | − | 0.935413i | \(-0.615028\pi\) | ||||
−0.353558 | + | 0.935413i | \(0.615028\pi\) | |||||||
\(930\) | 10.8548 | 0.355942 | ||||||||
\(931\) | −38.5851 | −1.26458 | ||||||||
\(932\) | −2.09600 | −0.0686568 | ||||||||
\(933\) | −0.302171 | −0.00989265 | ||||||||
\(934\) | −27.2150 | −0.890502 | ||||||||
\(935\) | 5.46124 | 0.178602 | ||||||||
\(936\) | −7.96627 | −0.260386 | ||||||||
\(937\) | 53.7168 | 1.75485 | 0.877425 | − | 0.479713i | \(-0.159259\pi\) | ||||
0.877425 | + | 0.479713i | \(0.159259\pi\) | |||||||
\(938\) | −86.0643 | −2.81010 | ||||||||
\(939\) | 21.6672 | 0.707084 | ||||||||
\(940\) | −0.326756 | −0.0106576 | ||||||||
\(941\) | 33.2298 | 1.08326 | 0.541631 | − | 0.840617i | \(-0.317807\pi\) | ||||
0.541631 | + | 0.840617i | \(0.317807\pi\) | |||||||
\(942\) | −7.77912 | −0.253457 | ||||||||
\(943\) | −1.81028 | −0.0589507 | ||||||||
\(944\) | 0.722284 | 0.0235084 | ||||||||
\(945\) | 2.74468 | 0.0892843 | ||||||||
\(946\) | 0.704957 | 0.0229201 | ||||||||
\(947\) | 6.93643 | 0.225404 | 0.112702 | − | 0.993629i | \(-0.464050\pi\) | ||||
0.112702 | + | 0.993629i | \(0.464050\pi\) | |||||||
\(948\) | −0.218777 | −0.00710556 | ||||||||
\(949\) | −2.84563 | −0.0923731 | ||||||||
\(950\) | −35.6144 | −1.15548 | ||||||||
\(951\) | −7.71514 | −0.250181 | ||||||||
\(952\) | −28.5121 | −0.924084 | ||||||||
\(953\) | 34.3469 | 1.11261 | 0.556303 | − | 0.830979i | \(-0.312219\pi\) | ||||
0.556303 | + | 0.830979i | \(0.312219\pi\) | |||||||
\(954\) | 0.953449 | 0.0308691 | ||||||||
\(955\) | 7.23947 | 0.234264 | ||||||||
\(956\) | 1.50235 | 0.0485895 | ||||||||
\(957\) | 2.70213 | 0.0873475 | ||||||||
\(958\) | −22.0148 | −0.711266 | ||||||||
\(959\) | 57.6107 | 1.86035 | ||||||||
\(960\) | 5.64430 | 0.182169 | ||||||||
\(961\) | 74.2789 | 2.39609 | ||||||||
\(962\) | −47.5414 | −1.53280 | ||||||||
\(963\) | −12.9231 | −0.416440 | ||||||||
\(964\) | 1.41829 | 0.0456801 | ||||||||
\(965\) | −15.6318 | −0.503205 | ||||||||
\(966\) | −5.38039 | −0.173111 | ||||||||
\(967\) | 22.8151 | 0.733685 | 0.366843 | − | 0.930283i | \(-0.380439\pi\) | ||||
0.366843 | + | 0.930283i | \(0.380439\pi\) | |||||||
\(968\) | −10.2590 | −0.329737 | ||||||||
\(969\) | 15.2544 | 0.490041 | ||||||||
\(970\) | 4.20121 | 0.134893 | ||||||||
\(971\) | −43.7200 | −1.40304 | −0.701521 | − | 0.712649i | \(-0.747495\pi\) | ||||
−0.701521 | + | 0.712649i | \(0.747495\pi\) | |||||||
\(972\) | 0.0738306 | 0.00236812 | ||||||||
\(973\) | −60.8280 | −1.95006 | ||||||||
\(974\) | 31.8550 | 1.02070 | ||||||||
\(975\) | 12.8098 | 0.410241 | ||||||||
\(976\) | 22.2786 | 0.713120 | ||||||||
\(977\) | −0.346127 | −0.0110736 | −0.00553679 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553679 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(978\) | −8.51446 | −0.272263 | ||||||||
\(979\) | −14.0872 | −0.450229 | ||||||||
\(980\) | 0.377440 | 0.0120569 | ||||||||
\(981\) | 16.2725 | 0.519542 | ||||||||
\(982\) | 48.6846 | 1.55359 | ||||||||
\(983\) | −3.49735 | −0.111548 | −0.0557741 | − | 0.998443i | \(-0.517763\pi\) | ||||
−0.0557741 | + | 0.998443i | \(0.517763\pi\) | |||||||
\(984\) | −5.02142 | −0.160077 | ||||||||
\(985\) | 7.06520 | 0.225116 | ||||||||
\(986\) | −3.96194 | −0.126174 | ||||||||
\(987\) | −22.5087 | −0.716459 | ||||||||
\(988\) | 1.17566 | 0.0374028 | ||||||||
\(989\) | 0.181163 | 0.00576065 | ||||||||
\(990\) | 2.85862 | 0.0908529 | ||||||||
\(991\) | −21.4825 | −0.682414 | −0.341207 | − | 0.939988i | \(-0.610836\pi\) | ||||
−0.341207 | + | 0.939988i | \(0.610836\pi\) | |||||||
\(992\) | −4.28315 | −0.135990 | ||||||||
\(993\) | −15.6398 | −0.496315 | ||||||||
\(994\) | −64.5899 | −2.04867 | ||||||||
\(995\) | 3.23197 | 0.102460 | ||||||||
\(996\) | 0.0804719 | 0.00254985 | ||||||||
\(997\) | 15.2460 | 0.482845 | 0.241422 | − | 0.970420i | \(-0.422386\pi\) | ||||
0.241422 | + | 0.970420i | \(0.422386\pi\) | |||||||
\(998\) | −36.2026 | −1.14597 | ||||||||
\(999\) | −11.4951 | −0.363687 |
(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 | 2001.2.a.i.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 6003.2.a.j.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.i.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
6003.2.a.j.1.5 | 7 | 3.2 | odd | 2 |