Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,2,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(0.183655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | −3.61803 | −1.47706 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 5.23607 | 1.65579 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 1.38197 | 0.398939 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −7.23607 | −1.86834 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | −3.23607 | −0.762749 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | −2.76393 | −0.603139 | ||||||||
\(22\) | 1.23607 | 0.263531 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 5.00000 | 1.02062 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | −4.85410 | −0.951968 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −0.763932 | −0.144370 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 11.7082 | 2.13762 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | −1.70820 | −0.297360 | ||||||||
\(34\) | −8.47214 | −1.45296 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 1.23607 | 0.206011 | ||||||||
\(37\) | 3.23607 | 0.532006 | 0.266003 | − | 0.963972i | \(-0.414297\pi\) | ||||
0.266003 | + | 0.963972i | \(0.414297\pi\) | |||||||
\(38\) | 3.23607 | 0.524960 | ||||||||
\(39\) | 6.70820 | 1.07417 | ||||||||
\(40\) | −7.23607 | −1.14412 | ||||||||
\(41\) | 5.47214 | 0.854604 | 0.427302 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427302 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(42\) | 4.47214 | 0.690066 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −0.472136 | −0.0711772 | ||||||||
\(45\) | −6.47214 | −0.964809 | ||||||||
\(46\) | −1.61803 | −0.238566 | ||||||||
\(47\) | 2.23607 | 0.326164 | 0.163082 | − | 0.986613i | \(-0.447856\pi\) | ||||
0.163082 | + | 0.986613i | \(0.447856\pi\) | |||||||
\(48\) | −10.8541 | −1.56665 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | −8.85410 | −1.25216 | ||||||||
\(51\) | 11.7082 | 1.63948 | ||||||||
\(52\) | 1.85410 | 0.257118 | ||||||||
\(53\) | −8.47214 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(54\) | 3.61803 | 0.492352 | ||||||||
\(55\) | 2.47214 | 0.333343 | ||||||||
\(56\) | −2.76393 | −0.369346 | ||||||||
\(57\) | −4.47214 | −0.592349 | ||||||||
\(58\) | 4.85410 | 0.637375 | ||||||||
\(59\) | −2.47214 | −0.321845 | −0.160922 | − | 0.986967i | \(-0.551447\pi\) | ||||
−0.160922 | + | 0.986967i | \(0.551447\pi\) | |||||||
\(60\) | −4.47214 | −0.577350 | ||||||||
\(61\) | 10.9443 | 1.40127 | 0.700635 | − | 0.713520i | \(-0.252900\pi\) | ||||
0.700635 | + | 0.713520i | \(0.252900\pi\) | |||||||
\(62\) | 10.8541 | 1.37847 | ||||||||
\(63\) | −2.47214 | −0.311460 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −9.70820 | −1.20415 | ||||||||
\(66\) | 2.76393 | 0.340217 | ||||||||
\(67\) | −7.23607 | −0.884026 | −0.442013 | − | 0.897009i | \(-0.645736\pi\) | ||||
−0.442013 | + | 0.897009i | \(0.645736\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | 2.23607 | 0.269191 | ||||||||
\(70\) | −6.47214 | −0.773568 | ||||||||
\(71\) | 7.76393 | 0.921409 | 0.460705 | − | 0.887554i | \(-0.347597\pi\) | ||||
0.460705 | + | 0.887554i | \(0.347597\pi\) | |||||||
\(72\) | 4.47214 | 0.527046 | ||||||||
\(73\) | 15.4721 | 1.81088 | 0.905438 | − | 0.424478i | \(-0.139542\pi\) | ||||
0.905438 | + | 0.424478i | \(0.139542\pi\) | |||||||
\(74\) | −5.23607 | −0.608681 | ||||||||
\(75\) | 12.2361 | 1.41290 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 0.944272 | 0.107610 | ||||||||
\(78\) | −10.8541 | −1.22899 | ||||||||
\(79\) | 6.94427 | 0.781292 | 0.390646 | − | 0.920541i | \(-0.372252\pi\) | ||||
0.390646 | + | 0.920541i | \(0.372252\pi\) | |||||||
\(80\) | 15.7082 | 1.75623 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −8.85410 | −0.977772 | ||||||||
\(83\) | −13.2361 | −1.45285 | −0.726424 | − | 0.687247i | \(-0.758819\pi\) | ||||
−0.726424 | + | 0.687247i | \(0.758819\pi\) | |||||||
\(84\) | −1.70820 | −0.186380 | ||||||||
\(85\) | −16.9443 | −1.83786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.70820 | −0.719195 | ||||||||
\(88\) | −1.70820 | −0.182095 | ||||||||
\(89\) | −1.52786 | −0.161953 | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809766 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(90\) | 10.4721 | 1.10386 | ||||||||
\(91\) | −3.70820 | −0.388725 | ||||||||
\(92\) | 0.618034 | 0.0644345 | ||||||||
\(93\) | −15.0000 | −1.55543 | ||||||||
\(94\) | −3.61803 | −0.373172 | ||||||||
\(95\) | 6.47214 | 0.664027 | ||||||||
\(96\) | 7.56231 | 0.771825 | ||||||||
\(97\) | 4.29180 | 0.435766 | 0.217883 | − | 0.975975i | \(-0.430085\pi\) | ||||
0.217883 | + | 0.975975i | \(0.430085\pi\) | |||||||
\(98\) | 8.85410 | 0.894399 | ||||||||
\(99\) | −1.52786 | −0.153556 | ||||||||
\(100\) | 3.38197 | 0.338197 | ||||||||
\(101\) | −4.47214 | −0.444994 | −0.222497 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222497 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(102\) | −18.9443 | −1.87576 | ||||||||
\(103\) | 18.1803 | 1.79136 | 0.895681 | − | 0.444697i | \(-0.146689\pi\) | ||||
0.895681 | + | 0.444697i | \(0.146689\pi\) | |||||||
\(104\) | 6.70820 | 0.657794 | ||||||||
\(105\) | 8.94427 | 0.872872 | ||||||||
\(106\) | 13.7082 | 1.33146 | ||||||||
\(107\) | −13.4164 | −1.29701 | −0.648507 | − | 0.761209i | \(-0.724606\pi\) | ||||
−0.648507 | + | 0.761209i | \(0.724606\pi\) | |||||||
\(108\) | −1.38197 | −0.132980 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −4.00000 | −0.381385 | ||||||||
\(111\) | 7.23607 | 0.686817 | ||||||||
\(112\) | 6.00000 | 0.566947 | ||||||||
\(113\) | 13.2361 | 1.24514 | 0.622572 | − | 0.782562i | \(-0.286088\pi\) | ||||
0.622572 | + | 0.782562i | \(0.286088\pi\) | |||||||
\(114\) | 7.23607 | 0.677720 | ||||||||
\(115\) | −3.23607 | −0.301765 | ||||||||
\(116\) | −1.85410 | −0.172149 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | −6.47214 | −0.593300 | ||||||||
\(120\) | −16.1803 | −1.47706 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | −17.7082 | −1.60323 | ||||||||
\(123\) | 12.2361 | 1.10329 | ||||||||
\(124\) | −4.14590 | −0.372313 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | −20.7082 | −1.83756 | −0.918778 | − | 0.394775i | \(-0.870823\pi\) | ||||
−0.918778 | + | 0.394775i | \(0.870823\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.7082 | 1.37770 | ||||||||
\(131\) | 5.29180 | 0.462346 | 0.231173 | − | 0.972913i | \(-0.425744\pi\) | ||||
0.231173 | + | 0.972913i | \(0.425744\pi\) | |||||||
\(132\) | −1.05573 | −0.0918893 | ||||||||
\(133\) | 2.47214 | 0.214361 | ||||||||
\(134\) | 11.7082 | 1.01143 | ||||||||
\(135\) | 7.23607 | 0.622782 | ||||||||
\(136\) | 11.7082 | 1.00397 | ||||||||
\(137\) | 13.8885 | 1.18658 | 0.593289 | − | 0.804989i | \(-0.297829\pi\) | ||||
0.593289 | + | 0.804989i | \(0.297829\pi\) | |||||||
\(138\) | −3.61803 | −0.307988 | ||||||||
\(139\) | 2.70820 | 0.229707 | 0.114853 | − | 0.993382i | \(-0.463360\pi\) | ||||
0.114853 | + | 0.993382i | \(0.463360\pi\) | |||||||
\(140\) | 2.47214 | 0.208934 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | −12.5623 | −1.05421 | ||||||||
\(143\) | −2.29180 | −0.191650 | ||||||||
\(144\) | −9.70820 | −0.809017 | ||||||||
\(145\) | 9.70820 | 0.806222 | ||||||||
\(146\) | −25.0344 | −2.07187 | ||||||||
\(147\) | −12.2361 | −1.00921 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −11.8885 | −0.973947 | −0.486974 | − | 0.873417i | \(-0.661899\pi\) | ||||
−0.486974 | + | 0.873417i | \(0.661899\pi\) | |||||||
\(150\) | −19.7984 | −1.61653 | ||||||||
\(151\) | −0.236068 | −0.0192109 | −0.00960547 | − | 0.999954i | \(-0.503058\pi\) | ||||
−0.00960547 | + | 0.999954i | \(0.503058\pi\) | |||||||
\(152\) | −4.47214 | −0.362738 | ||||||||
\(153\) | 10.4721 | 0.846622 | ||||||||
\(154\) | −1.52786 | −0.123119 | ||||||||
\(155\) | 21.7082 | 1.74364 | ||||||||
\(156\) | 4.14590 | 0.331937 | ||||||||
\(157\) | 15.4164 | 1.23036 | 0.615182 | − | 0.788385i | \(-0.289083\pi\) | ||||
0.615182 | + | 0.788385i | \(0.289083\pi\) | |||||||
\(158\) | −11.2361 | −0.893894 | ||||||||
\(159\) | −18.9443 | −1.50238 | ||||||||
\(160\) | −10.9443 | −0.865221 | ||||||||
\(161\) | −1.23607 | −0.0974158 | ||||||||
\(162\) | 17.7984 | 1.39837 | ||||||||
\(163\) | −10.2361 | −0.801751 | −0.400875 | − | 0.916133i | \(-0.631294\pi\) | ||||
−0.400875 | + | 0.916133i | \(0.631294\pi\) | |||||||
\(164\) | 3.38197 | 0.264087 | ||||||||
\(165\) | 5.52786 | 0.430344 | ||||||||
\(166\) | 21.4164 | 1.66224 | ||||||||
\(167\) | 10.4721 | 0.810358 | 0.405179 | − | 0.914237i | \(-0.367209\pi\) | ||||
0.405179 | + | 0.914237i | \(0.367209\pi\) | |||||||
\(168\) | −6.18034 | −0.476824 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 27.4164 | 2.10274 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.05573 | 0.384380 | 0.192190 | − | 0.981358i | \(-0.438441\pi\) | ||||
0.192190 | + | 0.981358i | \(0.438441\pi\) | |||||||
\(174\) | 10.8541 | 0.822847 | ||||||||
\(175\) | −6.76393 | −0.511305 | ||||||||
\(176\) | 3.70820 | 0.279516 | ||||||||
\(177\) | −5.52786 | −0.415500 | ||||||||
\(178\) | 2.47214 | 0.185294 | ||||||||
\(179\) | −12.7082 | −0.949856 | −0.474928 | − | 0.880025i | \(-0.657526\pi\) | ||||
−0.474928 | + | 0.880025i | \(0.657526\pi\) | |||||||
\(180\) | −4.00000 | −0.298142 | ||||||||
\(181\) | −14.6525 | −1.08911 | −0.544555 | − | 0.838725i | \(-0.683301\pi\) | ||||
−0.544555 | + | 0.838725i | \(0.683301\pi\) | |||||||
\(182\) | 6.00000 | 0.444750 | ||||||||
\(183\) | 24.4721 | 1.80903 | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | −10.4721 | −0.769927 | ||||||||
\(186\) | 24.2705 | 1.77960 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 1.38197 | 0.100790 | ||||||||
\(189\) | 2.76393 | 0.201046 | ||||||||
\(190\) | −10.4721 | −0.759729 | ||||||||
\(191\) | −3.81966 | −0.276381 | −0.138190 | − | 0.990406i | \(-0.544129\pi\) | ||||
−0.138190 | + | 0.990406i | \(0.544129\pi\) | |||||||
\(192\) | 9.47214 | 0.683593 | ||||||||
\(193\) | −7.94427 | −0.571841 | −0.285921 | − | 0.958253i | \(-0.592299\pi\) | ||||
−0.285921 | + | 0.958253i | \(0.592299\pi\) | |||||||
\(194\) | −6.94427 | −0.498570 | ||||||||
\(195\) | −21.7082 | −1.55456 | ||||||||
\(196\) | −3.38197 | −0.241569 | ||||||||
\(197\) | 7.47214 | 0.532368 | 0.266184 | − | 0.963922i | \(-0.414237\pi\) | ||||
0.266184 | + | 0.963922i | \(0.414237\pi\) | |||||||
\(198\) | 2.47214 | 0.175687 | ||||||||
\(199\) | −25.7082 | −1.82241 | −0.911203 | − | 0.411957i | \(-0.864845\pi\) | ||||
−0.911203 | + | 0.411957i | \(0.864845\pi\) | |||||||
\(200\) | 12.2361 | 0.865221 | ||||||||
\(201\) | −16.1803 | −1.14127 | ||||||||
\(202\) | 7.23607 | 0.509128 | ||||||||
\(203\) | 3.70820 | 0.260265 | ||||||||
\(204\) | 7.23607 | 0.506626 | ||||||||
\(205\) | −17.7082 | −1.23679 | ||||||||
\(206\) | −29.4164 | −2.04954 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | −14.5623 | −1.00971 | ||||||||
\(209\) | 1.52786 | 0.105685 | ||||||||
\(210\) | −14.4721 | −0.998672 | ||||||||
\(211\) | 3.41641 | 0.235195 | 0.117598 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117598 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(212\) | −5.23607 | −0.359615 | ||||||||
\(213\) | 17.3607 | 1.18953 | ||||||||
\(214\) | 21.7082 | 1.48394 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 8.29180 | 0.562884 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.5967 | 2.33783 | ||||||||
\(220\) | 1.52786 | 0.103009 | ||||||||
\(221\) | 15.7082 | 1.05665 | ||||||||
\(222\) | −11.7082 | −0.785803 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | −4.18034 | −0.279311 | ||||||||
\(225\) | 10.9443 | 0.729618 | ||||||||
\(226\) | −21.4164 | −1.42460 | ||||||||
\(227\) | 10.1803 | 0.675693 | 0.337846 | − | 0.941201i | \(-0.390302\pi\) | ||||
0.337846 | + | 0.941201i | \(0.390302\pi\) | |||||||
\(228\) | −2.76393 | −0.183046 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 5.23607 | 0.345256 | ||||||||
\(231\) | 2.11146 | 0.138924 | ||||||||
\(232\) | −6.70820 | −0.440415 | ||||||||
\(233\) | −15.4721 | −1.01361 | −0.506807 | − | 0.862060i | \(-0.669174\pi\) | ||||
−0.506807 | + | 0.862060i | \(0.669174\pi\) | |||||||
\(234\) | −9.70820 | −0.634645 | ||||||||
\(235\) | −7.23607 | −0.472029 | ||||||||
\(236\) | −1.52786 | −0.0994555 | ||||||||
\(237\) | 15.5279 | 1.00864 | ||||||||
\(238\) | 10.4721 | 0.678808 | ||||||||
\(239\) | 18.2361 | 1.17959 | 0.589797 | − | 0.807552i | \(-0.299208\pi\) | ||||
0.589797 | + | 0.807552i | \(0.299208\pi\) | |||||||
\(240\) | 35.1246 | 2.26728 | ||||||||
\(241\) | 17.1246 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(242\) | 16.8541 | 1.08342 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | 6.76393 | 0.433016 | ||||||||
\(245\) | 17.7082 | 1.13134 | ||||||||
\(246\) | −19.7984 | −1.26230 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | −29.5967 | −1.87562 | ||||||||
\(250\) | 2.47214 | 0.156352 | ||||||||
\(251\) | 15.7082 | 0.991493 | 0.495747 | − | 0.868467i | \(-0.334895\pi\) | ||||
0.495747 | + | 0.868467i | \(0.334895\pi\) | |||||||
\(252\) | −1.52786 | −0.0962464 | ||||||||
\(253\) | −0.763932 | −0.0480280 | ||||||||
\(254\) | 33.5066 | 2.10239 | ||||||||
\(255\) | −37.8885 | −2.37267 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 1.47214 | 0.0918293 | 0.0459147 | − | 0.998945i | \(-0.485380\pi\) | ||||
0.0459147 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | −8.56231 | −0.528981 | ||||||||
\(263\) | −14.9443 | −0.921503 | −0.460752 | − | 0.887529i | \(-0.652420\pi\) | ||||
−0.460752 | + | 0.887529i | \(0.652420\pi\) | |||||||
\(264\) | −3.81966 | −0.235084 | ||||||||
\(265\) | 27.4164 | 1.68418 | ||||||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | −3.41641 | −0.209081 | ||||||||
\(268\) | −4.47214 | −0.273179 | ||||||||
\(269\) | 9.94427 | 0.606313 | 0.303156 | − | 0.952941i | \(-0.401960\pi\) | ||||
0.303156 | + | 0.952941i | \(0.401960\pi\) | |||||||
\(270\) | −11.7082 | −0.712539 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | −25.4164 | −1.54110 | ||||||||
\(273\) | −8.29180 | −0.501842 | ||||||||
\(274\) | −22.4721 | −1.35759 | ||||||||
\(275\) | −4.18034 | −0.252084 | ||||||||
\(276\) | 1.38197 | 0.0831846 | ||||||||
\(277\) | 6.52786 | 0.392221 | 0.196111 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196111 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(278\) | −4.38197 | −0.262813 | ||||||||
\(279\) | −13.4164 | −0.803219 | ||||||||
\(280\) | 8.94427 | 0.534522 | ||||||||
\(281\) | −13.2361 | −0.789598 | −0.394799 | − | 0.918768i | \(-0.629186\pi\) | ||||
−0.394799 | + | 0.918768i | \(0.629186\pi\) | |||||||
\(282\) | −8.09017 | −0.481763 | ||||||||
\(283\) | 14.2918 | 0.849559 | 0.424780 | − | 0.905297i | \(-0.360352\pi\) | ||||
0.424780 | + | 0.905297i | \(0.360352\pi\) | |||||||
\(284\) | 4.79837 | 0.284731 | ||||||||
\(285\) | 14.4721 | 0.857255 | ||||||||
\(286\) | 3.70820 | 0.219271 | ||||||||
\(287\) | −6.76393 | −0.399262 | ||||||||
\(288\) | 6.76393 | 0.398569 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | −15.7082 | −0.922417 | ||||||||
\(291\) | 9.59675 | 0.562571 | ||||||||
\(292\) | 9.56231 | 0.559592 | ||||||||
\(293\) | −10.4721 | −0.611789 | −0.305894 | − | 0.952065i | \(-0.598955\pi\) | ||||
−0.305894 | + | 0.952065i | \(0.598955\pi\) | |||||||
\(294\) | 19.7984 | 1.15466 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 7.23607 | 0.420588 | ||||||||
\(297\) | 1.70820 | 0.0991200 | ||||||||
\(298\) | 19.2361 | 1.11432 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 7.56231 | 0.436610 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.381966 | 0.0219797 | ||||||||
\(303\) | −10.0000 | −0.574485 | ||||||||
\(304\) | 9.70820 | 0.556804 | ||||||||
\(305\) | −35.4164 | −2.02794 | ||||||||
\(306\) | −16.9443 | −0.968640 | ||||||||
\(307\) | 18.4721 | 1.05426 | 0.527130 | − | 0.849785i | \(-0.323268\pi\) | ||||
0.527130 | + | 0.849785i | \(0.323268\pi\) | |||||||
\(308\) | 0.583592 | 0.0332532 | ||||||||
\(309\) | 40.6525 | 2.31264 | ||||||||
\(310\) | −35.1246 | −1.99494 | ||||||||
\(311\) | −9.18034 | −0.520569 | −0.260285 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260285 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(312\) | 15.0000 | 0.849208 | ||||||||
\(313\) | −20.3607 | −1.15085 | −0.575427 | − | 0.817853i | \(-0.695164\pi\) | ||||
−0.575427 | + | 0.817853i | \(0.695164\pi\) | |||||||
\(314\) | −24.9443 | −1.40769 | ||||||||
\(315\) | 8.00000 | 0.450749 | ||||||||
\(316\) | 4.29180 | 0.241432 | ||||||||
\(317\) | −1.41641 | −0.0795534 | −0.0397767 | − | 0.999209i | \(-0.512665\pi\) | ||||
−0.0397767 | + | 0.999209i | \(0.512665\pi\) | |||||||
\(318\) | 30.6525 | 1.71891 | ||||||||
\(319\) | 2.29180 | 0.128316 | ||||||||
\(320\) | −13.7082 | −0.766312 | ||||||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | 2.00000 | 0.111456 | ||||||||
\(323\) | −10.4721 | −0.582685 | ||||||||
\(324\) | −6.79837 | −0.377687 | ||||||||
\(325\) | 16.4164 | 0.910618 | ||||||||
\(326\) | 16.5623 | 0.917301 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.2361 | 0.675624 | ||||||||
\(329\) | −2.76393 | −0.152381 | ||||||||
\(330\) | −8.94427 | −0.492366 | ||||||||
\(331\) | 11.6525 | 0.640478 | 0.320239 | − | 0.947337i | \(-0.396237\pi\) | ||||
0.320239 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(332\) | −8.18034 | −0.448954 | ||||||||
\(333\) | 6.47214 | 0.354671 | ||||||||
\(334\) | −16.9443 | −0.927149 | ||||||||
\(335\) | 23.4164 | 1.27938 | ||||||||
\(336\) | 13.4164 | 0.731925 | ||||||||
\(337\) | −3.41641 | −0.186104 | −0.0930518 | − | 0.995661i | \(-0.529662\pi\) | ||||
−0.0930518 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(338\) | 6.47214 | 0.352038 | ||||||||
\(339\) | 29.5967 | 1.60747 | ||||||||
\(340\) | −10.4721 | −0.567931 | ||||||||
\(341\) | 5.12461 | 0.277513 | ||||||||
\(342\) | 6.47214 | 0.349973 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.23607 | −0.389577 | ||||||||
\(346\) | −8.18034 | −0.439778 | ||||||||
\(347\) | 25.8885 | 1.38977 | 0.694885 | − | 0.719121i | \(-0.255455\pi\) | ||||
0.694885 | + | 0.719121i | \(0.255455\pi\) | |||||||
\(348\) | −4.14590 | −0.222243 | ||||||||
\(349\) | −2.41641 | −0.129347 | −0.0646737 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646737 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(350\) | 10.9443 | 0.584996 | ||||||||
\(351\) | −6.70820 | −0.358057 | ||||||||
\(352\) | −2.58359 | −0.137706 | ||||||||
\(353\) | −35.3607 | −1.88206 | −0.941030 | − | 0.338324i | \(-0.890140\pi\) | ||||
−0.941030 | + | 0.338324i | \(0.890140\pi\) | |||||||
\(354\) | 8.94427 | 0.475383 | ||||||||
\(355\) | −25.1246 | −1.33348 | ||||||||
\(356\) | −0.944272 | −0.0500463 | ||||||||
\(357\) | −14.4721 | −0.765947 | ||||||||
\(358\) | 20.5623 | 1.08675 | ||||||||
\(359\) | 15.8885 | 0.838565 | 0.419283 | − | 0.907856i | \(-0.362282\pi\) | ||||
0.419283 | + | 0.907856i | \(0.362282\pi\) | |||||||
\(360\) | −14.4721 | −0.762749 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 23.7082 | 1.24608 | ||||||||
\(363\) | −23.2918 | −1.22250 | ||||||||
\(364\) | −2.29180 | −0.120123 | ||||||||
\(365\) | −50.0689 | −2.62073 | ||||||||
\(366\) | −39.5967 | −2.06976 | ||||||||
\(367\) | 18.1803 | 0.949006 | 0.474503 | − | 0.880254i | \(-0.342628\pi\) | ||||
0.474503 | + | 0.880254i | \(0.342628\pi\) | |||||||
\(368\) | −4.85410 | −0.253038 | ||||||||
\(369\) | 10.9443 | 0.569736 | ||||||||
\(370\) | 16.9443 | 0.880891 | ||||||||
\(371\) | 10.4721 | 0.543686 | ||||||||
\(372\) | −9.27051 | −0.480654 | ||||||||
\(373\) | −5.70820 | −0.295560 | −0.147780 | − | 0.989020i | \(-0.547213\pi\) | ||||
−0.147780 | + | 0.989020i | \(0.547213\pi\) | |||||||
\(374\) | 6.47214 | 0.334666 | ||||||||
\(375\) | −3.41641 | −0.176423 | ||||||||
\(376\) | 5.00000 | 0.257855 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | −4.47214 | −0.230022 | ||||||||
\(379\) | −20.3607 | −1.04586 | −0.522929 | − | 0.852376i | \(-0.675161\pi\) | ||||
−0.522929 | + | 0.852376i | \(0.675161\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | −46.3050 | −2.37227 | ||||||||
\(382\) | 6.18034 | 0.316214 | ||||||||
\(383\) | 24.9443 | 1.27459 | 0.637296 | − | 0.770619i | \(-0.280053\pi\) | ||||
0.637296 | + | 0.770619i | \(0.280053\pi\) | |||||||
\(384\) | −30.4508 | −1.55394 | ||||||||
\(385\) | −3.05573 | −0.155734 | ||||||||
\(386\) | 12.8541 | 0.654257 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.65248 | 0.134659 | ||||||||
\(389\) | 34.4721 | 1.74781 | 0.873903 | − | 0.486100i | \(-0.161581\pi\) | ||||
0.873903 | + | 0.486100i | \(0.161581\pi\) | |||||||
\(390\) | 35.1246 | 1.77860 | ||||||||
\(391\) | 5.23607 | 0.264799 | ||||||||
\(392\) | −12.2361 | −0.618015 | ||||||||
\(393\) | 11.8328 | 0.596887 | ||||||||
\(394\) | −12.0902 | −0.609094 | ||||||||
\(395\) | −22.4721 | −1.13070 | ||||||||
\(396\) | −0.944272 | −0.0474514 | ||||||||
\(397\) | 2.41641 | 0.121276 | 0.0606380 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606380 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(398\) | 41.5967 | 2.08506 | ||||||||
\(399\) | 5.52786 | 0.276739 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | 8.18034 | 0.408507 | 0.204253 | − | 0.978918i | \(-0.434523\pi\) | ||||
0.204253 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(402\) | 26.1803 | 1.30576 | ||||||||
\(403\) | −20.1246 | −1.00248 | ||||||||
\(404\) | −2.76393 | −0.137511 | ||||||||
\(405\) | 35.5967 | 1.76882 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | −2.47214 | −0.122539 | ||||||||
\(408\) | 26.1803 | 1.29612 | ||||||||
\(409\) | −23.3607 | −1.15511 | −0.577556 | − | 0.816351i | \(-0.695993\pi\) | ||||
−0.577556 | + | 0.816351i | \(0.695993\pi\) | |||||||
\(410\) | 28.6525 | 1.41504 | ||||||||
\(411\) | 31.0557 | 1.53187 | ||||||||
\(412\) | 11.2361 | 0.553561 | ||||||||
\(413\) | 3.05573 | 0.150363 | ||||||||
\(414\) | −3.23607 | −0.159044 | ||||||||
\(415\) | 42.8328 | 2.10258 | ||||||||
\(416\) | 10.1459 | 0.497444 | ||||||||
\(417\) | 6.05573 | 0.296550 | ||||||||
\(418\) | −2.47214 | −0.120916 | ||||||||
\(419\) | −31.4164 | −1.53479 | −0.767396 | − | 0.641173i | \(-0.778448\pi\) | ||||
−0.767396 | + | 0.641173i | \(0.778448\pi\) | |||||||
\(420\) | 5.52786 | 0.269732 | ||||||||
\(421\) | −23.7082 | −1.15547 | −0.577734 | − | 0.816225i | \(-0.696063\pi\) | ||||
−0.577734 | + | 0.816225i | \(0.696063\pi\) | |||||||
\(422\) | −5.52786 | −0.269092 | ||||||||
\(423\) | 4.47214 | 0.217443 | ||||||||
\(424\) | −18.9443 | −0.920015 | ||||||||
\(425\) | 28.6525 | 1.38985 | ||||||||
\(426\) | −28.0902 | −1.36097 | ||||||||
\(427\) | −13.5279 | −0.654659 | ||||||||
\(428\) | −8.29180 | −0.400799 | ||||||||
\(429\) | −5.12461 | −0.247419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4721 | −1.27512 | −0.637559 | − | 0.770402i | \(-0.720056\pi\) | ||||
−0.637559 | + | 0.770402i | \(0.720056\pi\) | |||||||
\(432\) | 10.8541 | 0.522218 | ||||||||
\(433\) | 40.1803 | 1.93094 | 0.965472 | − | 0.260507i | \(-0.0838897\pi\) | ||||
0.965472 | + | 0.260507i | \(0.0838897\pi\) | |||||||
\(434\) | −13.4164 | −0.644008 | ||||||||
\(435\) | 21.7082 | 1.04083 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | −55.9787 | −2.67477 | ||||||||
\(439\) | −5.29180 | −0.252564 | −0.126282 | − | 0.991994i | \(-0.540304\pi\) | ||||
−0.126282 | + | 0.991994i | \(0.540304\pi\) | |||||||
\(440\) | 5.52786 | 0.263531 | ||||||||
\(441\) | −10.9443 | −0.521156 | ||||||||
\(442\) | −25.4164 | −1.20894 | ||||||||
\(443\) | −2.12461 | −0.100943 | −0.0504717 | − | 0.998725i | \(-0.516072\pi\) | ||||
−0.0504717 | + | 0.998725i | \(0.516072\pi\) | |||||||
\(444\) | 4.47214 | 0.212238 | ||||||||
\(445\) | 4.94427 | 0.234381 | ||||||||
\(446\) | −6.47214 | −0.306465 | ||||||||
\(447\) | −26.5836 | −1.25736 | ||||||||
\(448\) | −5.23607 | −0.247381 | ||||||||
\(449\) | 2.94427 | 0.138949 | 0.0694744 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694744 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(450\) | −17.7082 | −0.834773 | ||||||||
\(451\) | −4.18034 | −0.196845 | ||||||||
\(452\) | 8.18034 | 0.384771 | ||||||||
\(453\) | −0.527864 | −0.0248012 | ||||||||
\(454\) | −16.4721 | −0.773076 | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | −10.0000 | −0.468293 | ||||||||
\(457\) | 35.1246 | 1.64306 | 0.821530 | − | 0.570165i | \(-0.193121\pi\) | ||||
0.821530 | + | 0.570165i | \(0.193121\pi\) | |||||||
\(458\) | 19.4164 | 0.907269 | ||||||||
\(459\) | −11.7082 | −0.546492 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | 7.47214 | 0.348012 | 0.174006 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174006 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(462\) | −3.41641 | −0.158946 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 14.5623 | 0.676038 | ||||||||
\(465\) | 48.5410 | 2.25104 | ||||||||
\(466\) | 25.0344 | 1.15970 | ||||||||
\(467\) | −30.9443 | −1.43193 | −0.715965 | − | 0.698136i | \(-0.754013\pi\) | ||||
−0.715965 | + | 0.698136i | \(0.754013\pi\) | |||||||
\(468\) | 3.70820 | 0.171412 | ||||||||
\(469\) | 8.94427 | 0.413008 | ||||||||
\(470\) | 11.7082 | 0.540059 | ||||||||
\(471\) | 34.4721 | 1.58839 | ||||||||
\(472\) | −5.52786 | −0.254441 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −25.1246 | −1.15401 | ||||||||
\(475\) | −10.9443 | −0.502158 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | −16.9443 | −0.775825 | ||||||||
\(478\) | −29.5066 | −1.34960 | ||||||||
\(479\) | −17.5967 | −0.804016 | −0.402008 | − | 0.915636i | \(-0.631688\pi\) | ||||
−0.402008 | + | 0.915636i | \(0.631688\pi\) | |||||||
\(480\) | −24.4721 | −1.11700 | ||||||||
\(481\) | 9.70820 | 0.442656 | ||||||||
\(482\) | −27.7082 | −1.26207 | ||||||||
\(483\) | −2.76393 | −0.125763 | ||||||||
\(484\) | −6.43769 | −0.292622 | ||||||||
\(485\) | −13.8885 | −0.630646 | ||||||||
\(486\) | 28.9443 | 1.31294 | ||||||||
\(487\) | −1.29180 | −0.0585369 | −0.0292684 | − | 0.999572i | \(-0.509318\pi\) | ||||
−0.0292684 | + | 0.999572i | \(0.509318\pi\) | |||||||
\(488\) | 24.4721 | 1.10780 | ||||||||
\(489\) | −22.8885 | −1.03506 | ||||||||
\(490\) | −28.6525 | −1.29439 | ||||||||
\(491\) | 39.6525 | 1.78949 | 0.894746 | − | 0.446576i | \(-0.147357\pi\) | ||||
0.894746 | + | 0.446576i | \(0.147357\pi\) | |||||||
\(492\) | 7.56231 | 0.340935 | ||||||||
\(493\) | −15.7082 | −0.707462 | ||||||||
\(494\) | 9.70820 | 0.436793 | ||||||||
\(495\) | 4.94427 | 0.222228 | ||||||||
\(496\) | 32.5623 | 1.46209 | ||||||||
\(497\) | −9.59675 | −0.430473 | ||||||||
\(498\) | 47.8885 | 2.14594 | ||||||||
\(499\) | 32.7082 | 1.46422 | 0.732110 | − | 0.681186i | \(-0.238536\pi\) | ||||
0.732110 | + | 0.681186i | \(0.238536\pi\) | |||||||
\(500\) | −0.944272 | −0.0422291 | ||||||||
\(501\) | 23.4164 | 1.04617 | ||||||||
\(502\) | −25.4164 | −1.13439 | ||||||||
\(503\) | −9.05573 | −0.403775 | −0.201887 | − | 0.979409i | \(-0.564708\pi\) | ||||
−0.201887 | + | 0.979409i | \(0.564708\pi\) | |||||||
\(504\) | −5.52786 | −0.246231 | ||||||||
\(505\) | 14.4721 | 0.644002 | ||||||||
\(506\) | 1.23607 | 0.0549499 | ||||||||
\(507\) | −8.94427 | −0.397229 | ||||||||
\(508\) | −12.7984 | −0.567836 | ||||||||
\(509\) | 34.3050 | 1.52054 | 0.760270 | − | 0.649607i | \(-0.225067\pi\) | ||||
0.760270 | + | 0.649607i | \(0.225067\pi\) | |||||||
\(510\) | 61.3050 | 2.71463 | ||||||||
\(511\) | −19.1246 | −0.846023 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 4.47214 | 0.197450 | ||||||||
\(514\) | −2.38197 | −0.105064 | ||||||||
\(515\) | −58.8328 | −2.59248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70820 | −0.0751267 | ||||||||
\(518\) | 6.47214 | 0.284369 | ||||||||
\(519\) | 11.3050 | 0.496232 | ||||||||
\(520\) | −21.7082 | −0.951968 | ||||||||
\(521\) | 4.58359 | 0.200811 | 0.100405 | − | 0.994947i | \(-0.467986\pi\) | ||||
0.100405 | + | 0.994947i | \(0.467986\pi\) | |||||||
\(522\) | 9.70820 | 0.424917 | ||||||||
\(523\) | 0.875388 | 0.0382781 | 0.0191390 | − | 0.999817i | \(-0.493907\pi\) | ||||
0.0191390 | + | 0.999817i | \(0.493907\pi\) | |||||||
\(524\) | 3.27051 | 0.142873 | ||||||||
\(525\) | −15.1246 | −0.660092 | ||||||||
\(526\) | 24.1803 | 1.05431 | ||||||||
\(527\) | −35.1246 | −1.53005 | ||||||||
\(528\) | 8.29180 | 0.360854 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −44.3607 | −1.92690 | ||||||||
\(531\) | −4.94427 | −0.214563 | ||||||||
\(532\) | 1.52786 | 0.0662413 | ||||||||
\(533\) | 16.4164 | 0.711074 | ||||||||
\(534\) | 5.52786 | 0.239214 | ||||||||
\(535\) | 43.4164 | 1.87705 | ||||||||
\(536\) | −16.1803 | −0.698884 | ||||||||
\(537\) | −28.4164 | −1.22626 | ||||||||
\(538\) | −16.0902 | −0.693696 | ||||||||
\(539\) | 4.18034 | 0.180060 | ||||||||
\(540\) | 4.47214 | 0.192450 | ||||||||
\(541\) | −7.58359 | −0.326044 | −0.163022 | − | 0.986622i | \(-0.552124\pi\) | ||||
−0.163022 | + | 0.986622i | \(0.552124\pi\) | |||||||
\(542\) | −12.9443 | −0.556004 | ||||||||
\(543\) | −32.7639 | −1.40603 | ||||||||
\(544\) | 17.7082 | 0.759233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.4164 | 0.574169 | ||||||||
\(547\) | 37.5410 | 1.60514 | 0.802569 | − | 0.596559i | \(-0.203466\pi\) | ||||
0.802569 | + | 0.596559i | \(0.203466\pi\) | |||||||
\(548\) | 8.58359 | 0.366673 | ||||||||
\(549\) | 21.8885 | 0.934180 | ||||||||
\(550\) | 6.76393 | 0.288415 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 5.00000 | 0.212814 | ||||||||
\(553\) | −8.58359 | −0.365011 | ||||||||
\(554\) | −10.5623 | −0.448749 | ||||||||
\(555\) | −23.4164 | −0.993971 | ||||||||
\(556\) | 1.67376 | 0.0709833 | ||||||||
\(557\) | 19.4164 | 0.822700 | 0.411350 | − | 0.911478i | \(-0.365057\pi\) | ||||
0.411350 | + | 0.911478i | \(0.365057\pi\) | |||||||
\(558\) | 21.7082 | 0.918982 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −19.4164 | −0.820493 | ||||||||
\(561\) | −8.94427 | −0.377627 | ||||||||
\(562\) | 21.4164 | 0.903397 | ||||||||
\(563\) | −15.0557 | −0.634523 | −0.317262 | − | 0.948338i | \(-0.602763\pi\) | ||||
−0.317262 | + | 0.948338i | \(0.602763\pi\) | |||||||
\(564\) | 3.09017 | 0.130120 | ||||||||
\(565\) | −42.8328 | −1.80199 | ||||||||
\(566\) | −23.1246 | −0.972000 | ||||||||
\(567\) | 13.5967 | 0.571010 | ||||||||
\(568\) | 17.3607 | 0.728438 | ||||||||
\(569\) | 0.180340 | 0.00756024 | 0.00378012 | − | 0.999993i | \(-0.498797\pi\) | ||||
0.00378012 | + | 0.999993i | \(0.498797\pi\) | |||||||
\(570\) | −23.4164 | −0.980805 | ||||||||
\(571\) | −27.7082 | −1.15955 | −0.579776 | − | 0.814776i | \(-0.696860\pi\) | ||||
−0.579776 | + | 0.814776i | \(0.696860\pi\) | |||||||
\(572\) | −1.41641 | −0.0592230 | ||||||||
\(573\) | −8.54102 | −0.356806 | ||||||||
\(574\) | 10.9443 | 0.456805 | ||||||||
\(575\) | 5.47214 | 0.228204 | ||||||||
\(576\) | 8.47214 | 0.353006 | ||||||||
\(577\) | −12.8885 | −0.536557 | −0.268279 | − | 0.963341i | \(-0.586455\pi\) | ||||
−0.268279 | + | 0.963341i | \(0.586455\pi\) | |||||||
\(578\) | −16.8541 | −0.701038 | ||||||||
\(579\) | −17.7639 | −0.738244 | ||||||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 16.3607 | 0.678755 | ||||||||
\(582\) | −15.5279 | −0.643651 | ||||||||
\(583\) | 6.47214 | 0.268048 | ||||||||
\(584\) | 34.5967 | 1.43162 | ||||||||
\(585\) | −19.4164 | −0.802770 | ||||||||
\(586\) | 16.9443 | 0.699961 | ||||||||
\(587\) | −11.2918 | −0.466062 | −0.233031 | − | 0.972469i | \(-0.574864\pi\) | ||||
−0.233031 | + | 0.972469i | \(0.574864\pi\) | |||||||
\(588\) | −7.56231 | −0.311864 | ||||||||
\(589\) | 13.4164 | 0.552813 | ||||||||
\(590\) | −12.9443 | −0.532907 | ||||||||
\(591\) | 16.7082 | 0.687284 | ||||||||
\(592\) | −15.7082 | −0.645603 | ||||||||
\(593\) | 14.9443 | 0.613688 | 0.306844 | − | 0.951760i | \(-0.400727\pi\) | ||||
0.306844 | + | 0.951760i | \(0.400727\pi\) | |||||||
\(594\) | −2.76393 | −0.113406 | ||||||||
\(595\) | 20.9443 | 0.858631 | ||||||||
\(596\) | −7.34752 | −0.300966 | ||||||||
\(597\) | −57.4853 | −2.35272 | ||||||||
\(598\) | −4.85410 | −0.198499 | ||||||||
\(599\) | −1.88854 | −0.0771638 | −0.0385819 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385819 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(600\) | 27.3607 | 1.11700 | ||||||||
\(601\) | 11.1115 | 0.453246 | 0.226623 | − | 0.973983i | \(-0.427232\pi\) | ||||
0.226623 | + | 0.973983i | \(0.427232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.4721 | −0.589351 | ||||||||
\(604\) | −0.145898 | −0.00593651 | ||||||||
\(605\) | 33.7082 | 1.37043 | ||||||||
\(606\) | 16.1803 | 0.657281 | ||||||||
\(607\) | 17.5279 | 0.711434 | 0.355717 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355717 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(608\) | −6.76393 | −0.274314 | ||||||||
\(609\) | 8.29180 | 0.336001 | ||||||||
\(610\) | 57.3050 | 2.32021 | ||||||||
\(611\) | 6.70820 | 0.271385 | ||||||||
\(612\) | 6.47214 | 0.261621 | ||||||||
\(613\) | −7.70820 | −0.311331 | −0.155666 | − | 0.987810i | \(-0.549752\pi\) | ||||
−0.155666 | + | 0.987810i | \(0.549752\pi\) | |||||||
\(614\) | −29.8885 | −1.20620 | ||||||||
\(615\) | −39.5967 | −1.59669 | ||||||||
\(616\) | 2.11146 | 0.0850730 | ||||||||
\(617\) | −16.4721 | −0.663143 | −0.331572 | − | 0.943430i | \(-0.607579\pi\) | ||||
−0.331572 | + | 0.943430i | \(0.607579\pi\) | |||||||
\(618\) | −65.7771 | −2.64594 | ||||||||
\(619\) | −7.41641 | −0.298091 | −0.149045 | − | 0.988830i | \(-0.547620\pi\) | ||||
−0.149045 | + | 0.988830i | \(0.547620\pi\) | |||||||
\(620\) | 13.4164 | 0.538816 | ||||||||
\(621\) | −2.23607 | −0.0897303 | ||||||||
\(622\) | 14.8541 | 0.595595 | ||||||||
\(623\) | 1.88854 | 0.0756629 | ||||||||
\(624\) | −32.5623 | −1.30354 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 32.9443 | 1.31672 | ||||||||
\(627\) | 3.41641 | 0.136438 | ||||||||
\(628\) | 9.52786 | 0.380203 | ||||||||
\(629\) | 16.9443 | 0.675612 | ||||||||
\(630\) | −12.9443 | −0.515712 | ||||||||
\(631\) | −32.3607 | −1.28826 | −0.644129 | − | 0.764917i | \(-0.722780\pi\) | ||||
−0.644129 | + | 0.764917i | \(0.722780\pi\) | |||||||
\(632\) | 15.5279 | 0.617665 | ||||||||
\(633\) | 7.63932 | 0.303636 | ||||||||
\(634\) | 2.29180 | 0.0910188 | ||||||||
\(635\) | 67.0132 | 2.65934 | ||||||||
\(636\) | −11.7082 | −0.464260 | ||||||||
\(637\) | −16.4164 | −0.650442 | ||||||||
\(638\) | −3.70820 | −0.146809 | ||||||||
\(639\) | 15.5279 | 0.614273 | ||||||||
\(640\) | 44.0689 | 1.74198 | ||||||||
\(641\) | 45.3050 | 1.78944 | 0.894719 | − | 0.446629i | \(-0.147376\pi\) | ||||
0.894719 | + | 0.446629i | \(0.147376\pi\) | |||||||
\(642\) | 48.5410 | 1.91576 | ||||||||
\(643\) | 19.5967 | 0.772820 | 0.386410 | − | 0.922327i | \(-0.373715\pi\) | ||||
0.386410 | + | 0.922327i | \(0.373715\pi\) | |||||||
\(644\) | −0.763932 | −0.0301031 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.9443 | 0.666663 | ||||||||
\(647\) | −6.70820 | −0.263727 | −0.131863 | − | 0.991268i | \(-0.542096\pi\) | ||||
−0.131863 | + | 0.991268i | \(0.542096\pi\) | |||||||
\(648\) | −24.5967 | −0.966252 | ||||||||
\(649\) | 1.88854 | 0.0741318 | ||||||||
\(650\) | −26.5623 | −1.04186 | ||||||||
\(651\) | 18.5410 | 0.726680 | ||||||||
\(652\) | −6.32624 | −0.247755 | ||||||||
\(653\) | 24.3050 | 0.951126 | 0.475563 | − | 0.879682i | \(-0.342244\pi\) | ||||
0.475563 | + | 0.879682i | \(0.342244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1246 | −0.669114 | ||||||||
\(656\) | −26.5623 | −1.03708 | ||||||||
\(657\) | 30.9443 | 1.20725 | ||||||||
\(658\) | 4.47214 | 0.174342 | ||||||||
\(659\) | 20.6525 | 0.804506 | 0.402253 | − | 0.915528i | \(-0.368227\pi\) | ||||
0.402253 | + | 0.915528i | \(0.368227\pi\) | |||||||
\(660\) | 3.41641 | 0.132983 | ||||||||
\(661\) | −5.05573 | −0.196645 | −0.0983225 | − | 0.995155i | \(-0.531348\pi\) | ||||
−0.0983225 | + | 0.995155i | \(0.531348\pi\) | |||||||
\(662\) | −18.8541 | −0.732785 | ||||||||
\(663\) | 35.1246 | 1.36413 | ||||||||
\(664\) | −29.5967 | −1.14858 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | −10.4721 | −0.405787 | ||||||||
\(667\) | −3.00000 | −0.116160 | ||||||||
\(668\) | 6.47214 | 0.250414 | ||||||||
\(669\) | 8.94427 | 0.345806 | ||||||||
\(670\) | −37.8885 | −1.46376 | ||||||||
\(671\) | −8.36068 | −0.322760 | ||||||||
\(672\) | −9.34752 | −0.360589 | ||||||||
\(673\) | 3.00000 | 0.115642 | 0.0578208 | − | 0.998327i | \(-0.481585\pi\) | ||||
0.0578208 | + | 0.998327i | \(0.481585\pi\) | |||||||
\(674\) | 5.52786 | 0.212925 | ||||||||
\(675\) | −12.2361 | −0.470966 | ||||||||
\(676\) | −2.47214 | −0.0950822 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | −47.8885 | −1.83915 | ||||||||
\(679\) | −5.30495 | −0.203585 | ||||||||
\(680\) | −37.8885 | −1.45296 | ||||||||
\(681\) | 22.7639 | 0.872316 | ||||||||
\(682\) | −8.29180 | −0.317509 | ||||||||
\(683\) | −22.5967 | −0.864641 | −0.432320 | − | 0.901720i | \(-0.642305\pi\) | ||||
−0.432320 | + | 0.901720i | \(0.642305\pi\) | |||||||
\(684\) | −2.47214 | −0.0945245 | ||||||||
\(685\) | −44.9443 | −1.71723 | ||||||||
\(686\) | −24.9443 | −0.952377 | ||||||||
\(687\) | −26.8328 | −1.02374 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.4164 | −0.968288 | ||||||||
\(690\) | 11.7082 | 0.445724 | ||||||||
\(691\) | 24.9443 | 0.948925 | 0.474462 | − | 0.880276i | \(-0.342642\pi\) | ||||
0.474462 | + | 0.880276i | \(0.342642\pi\) | |||||||
\(692\) | 3.12461 | 0.118780 | ||||||||
\(693\) | 1.88854 | 0.0717398 | ||||||||
\(694\) | −41.8885 | −1.59007 | ||||||||
\(695\) | −8.76393 | −0.332435 | ||||||||
\(696\) | −15.0000 | −0.568574 | ||||||||
\(697\) | 28.6525 | 1.08529 | ||||||||
\(698\) | 3.90983 | 0.147989 | ||||||||
\(699\) | −34.5967 | −1.30857 | ||||||||
\(700\) | −4.18034 | −0.158002 | ||||||||
\(701\) | −26.1803 | −0.988818 | −0.494409 | − | 0.869229i | \(-0.664615\pi\) | ||||
−0.494409 | + | 0.869229i | \(0.664615\pi\) | |||||||
\(702\) | 10.8541 | 0.409662 | ||||||||
\(703\) | −6.47214 | −0.244101 | ||||||||
\(704\) | −3.23607 | −0.121964 | ||||||||
\(705\) | −16.1803 | −0.609387 | ||||||||
\(706\) | 57.2148 | 2.15331 | ||||||||
\(707\) | 5.52786 | 0.207897 | ||||||||
\(708\) | −3.41641 | −0.128396 | ||||||||
\(709\) | 16.0689 | 0.603480 | 0.301740 | − | 0.953390i | \(-0.402433\pi\) | ||||
0.301740 | + | 0.953390i | \(0.402433\pi\) | |||||||
\(710\) | 40.6525 | 1.52566 | ||||||||
\(711\) | 13.8885 | 0.520861 | ||||||||
\(712\) | −3.41641 | −0.128035 | ||||||||
\(713\) | −6.70820 | −0.251224 | ||||||||
\(714\) | 23.4164 | 0.876337 | ||||||||
\(715\) | 7.41641 | 0.277358 | ||||||||
\(716\) | −7.85410 | −0.293522 | ||||||||
\(717\) | 40.7771 | 1.52285 | ||||||||
\(718\) | −25.7082 | −0.959422 | ||||||||
\(719\) | −20.9443 | −0.781090 | −0.390545 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390545 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(720\) | 31.4164 | 1.17082 | ||||||||
\(721\) | −22.4721 | −0.836906 | ||||||||
\(722\) | 24.2705 | 0.903255 | ||||||||
\(723\) | 38.2918 | 1.42409 | ||||||||
\(724\) | −9.05573 | −0.336553 | ||||||||
\(725\) | −16.4164 | −0.609690 | ||||||||
\(726\) | 37.6869 | 1.39869 | ||||||||
\(727\) | −14.2918 | −0.530053 | −0.265027 | − | 0.964241i | \(-0.585381\pi\) | ||||
−0.265027 | + | 0.964241i | \(0.585381\pi\) | |||||||
\(728\) | −8.29180 | −0.307314 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 81.0132 | 2.99843 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 15.1246 | 0.559022 | ||||||||
\(733\) | −26.7639 | −0.988548 | −0.494274 | − | 0.869306i | \(-0.664566\pi\) | ||||
−0.494274 | + | 0.869306i | \(0.664566\pi\) | |||||||
\(734\) | −29.4164 | −1.08578 | ||||||||
\(735\) | 39.5967 | 1.46055 | ||||||||
\(736\) | 3.38197 | 0.124661 | ||||||||
\(737\) | 5.52786 | 0.203621 | ||||||||
\(738\) | −17.7082 | −0.651848 | ||||||||
\(739\) | 49.1803 | 1.80913 | 0.904564 | − | 0.426338i | \(-0.140197\pi\) | ||||
0.904564 | + | 0.426338i | \(0.140197\pi\) | |||||||
\(740\) | −6.47214 | −0.237920 | ||||||||
\(741\) | −13.4164 | −0.492864 | ||||||||
\(742\) | −16.9443 | −0.622044 | ||||||||
\(743\) | 0.875388 | 0.0321149 | 0.0160574 | − | 0.999871i | \(-0.494889\pi\) | ||||
0.0160574 | + | 0.999871i | \(0.494889\pi\) | |||||||
\(744\) | −33.5410 | −1.22967 | ||||||||
\(745\) | 38.4721 | 1.40951 | ||||||||
\(746\) | 9.23607 | 0.338156 | ||||||||
\(747\) | −26.4721 | −0.968565 | ||||||||
\(748\) | −2.47214 | −0.0903902 | ||||||||
\(749\) | 16.5836 | 0.605951 | ||||||||
\(750\) | 5.52786 | 0.201849 | ||||||||
\(751\) | −44.3607 | −1.61874 | −0.809372 | − | 0.587296i | \(-0.800192\pi\) | ||||
−0.809372 | + | 0.587296i | \(0.800192\pi\) | |||||||
\(752\) | −10.8541 | −0.395808 | ||||||||
\(753\) | 35.1246 | 1.28001 | ||||||||
\(754\) | 14.5623 | 0.530328 | ||||||||
\(755\) | 0.763932 | 0.0278023 | ||||||||
\(756\) | 1.70820 | 0.0621268 | ||||||||
\(757\) | −47.5967 | −1.72993 | −0.864967 | − | 0.501829i | \(-0.832661\pi\) | ||||
−0.864967 | + | 0.501829i | \(0.832661\pi\) | |||||||
\(758\) | 32.9443 | 1.19659 | ||||||||
\(759\) | −1.70820 | −0.0620039 | ||||||||
\(760\) | 14.4721 | 0.524960 | ||||||||
\(761\) | −16.3050 | −0.591054 | −0.295527 | − | 0.955334i | \(-0.595495\pi\) | ||||
−0.295527 | + | 0.955334i | \(0.595495\pi\) | |||||||
\(762\) | 74.9230 | 2.71417 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.36068 | −0.0854064 | ||||||||
\(765\) | −33.8885 | −1.22524 | ||||||||
\(766\) | −40.3607 | −1.45829 | ||||||||
\(767\) | −7.41641 | −0.267791 | ||||||||
\(768\) | 30.3262 | 1.09430 | ||||||||
\(769\) | 17.1246 | 0.617529 | 0.308765 | − | 0.951138i | \(-0.400084\pi\) | ||||
0.308765 | + | 0.951138i | \(0.400084\pi\) | |||||||
\(770\) | 4.94427 | 0.178179 | ||||||||
\(771\) | 3.29180 | 0.118551 | ||||||||
\(772\) | −4.90983 | −0.176709 | ||||||||
\(773\) | −14.4721 | −0.520527 | −0.260263 | − | 0.965538i | \(-0.583809\pi\) | ||||
−0.260263 | + | 0.965538i | \(0.583809\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.7082 | −1.31860 | ||||||||
\(776\) | 9.59675 | 0.344503 | ||||||||
\(777\) | −8.94427 | −0.320874 | ||||||||
\(778\) | −55.7771 | −1.99971 | ||||||||
\(779\) | −10.9443 | −0.392119 | ||||||||
\(780\) | −13.4164 | −0.480384 | ||||||||
\(781\) | −5.93112 | −0.212232 | ||||||||
\(782\) | −8.47214 | −0.302963 | ||||||||
\(783\) | 6.70820 | 0.239732 | ||||||||
\(784\) | 26.5623 | 0.948654 | ||||||||
\(785\) | −49.8885 | −1.78060 | ||||||||
\(786\) | −19.1459 | −0.682912 | ||||||||
\(787\) | 51.4164 | 1.83280 | 0.916399 | − | 0.400267i | \(-0.131083\pi\) | ||||
0.916399 | + | 0.400267i | \(0.131083\pi\) | |||||||
\(788\) | 4.61803 | 0.164511 | ||||||||
\(789\) | −33.4164 | −1.18966 | ||||||||
\(790\) | 36.3607 | 1.29365 | ||||||||
\(791\) | −16.3607 | −0.581719 | ||||||||
\(792\) | −3.41641 | −0.121397 | ||||||||
\(793\) | 32.8328 | 1.16593 | ||||||||
\(794\) | −3.90983 | −0.138755 | ||||||||
\(795\) | 61.3050 | 2.17426 | ||||||||
\(796\) | −15.8885 | −0.563155 | ||||||||
\(797\) | 10.3607 | 0.366994 | 0.183497 | − | 0.983020i | \(-0.441258\pi\) | ||||
0.183497 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(798\) | −8.94427 | −0.316624 | ||||||||
\(799\) | 11.7082 | 0.414206 | ||||||||
\(800\) | 18.5066 | 0.654306 | ||||||||
\(801\) | −3.05573 | −0.107969 | ||||||||
\(802\) | −13.2361 | −0.467382 | ||||||||
\(803\) | −11.8197 | −0.417107 | ||||||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 32.5623 | 1.14696 | ||||||||
\(807\) | 22.2361 | 0.782747 | ||||||||
\(808\) | −10.0000 | −0.351799 | ||||||||
\(809\) | 47.8885 | 1.68367 | 0.841836 | − | 0.539734i | \(-0.181475\pi\) | ||||
0.841836 | + | 0.539734i | \(0.181475\pi\) | |||||||
\(810\) | −57.5967 | −2.02374 | ||||||||
\(811\) | −55.6525 | −1.95422 | −0.977111 | − | 0.212728i | \(-0.931765\pi\) | ||||
−0.977111 | + | 0.212728i | \(0.931765\pi\) | |||||||
\(812\) | 2.29180 | 0.0804263 | ||||||||
\(813\) | 17.8885 | 0.627379 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | 33.1246 | 1.16030 | ||||||||
\(816\) | −56.8328 | −1.98955 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 37.7984 | 1.32159 | ||||||||
\(819\) | −7.41641 | −0.259150 | ||||||||
\(820\) | −10.9443 | −0.382191 | ||||||||
\(821\) | −21.0557 | −0.734850 | −0.367425 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367425 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(822\) | −50.2492 | −1.75264 | ||||||||
\(823\) | 27.5410 | 0.960020 | 0.480010 | − | 0.877263i | \(-0.340633\pi\) | ||||
0.480010 | + | 0.877263i | \(0.340633\pi\) | |||||||
\(824\) | 40.6525 | 1.41620 | ||||||||
\(825\) | −9.34752 | −0.325439 | ||||||||
\(826\) | −4.94427 | −0.172033 | ||||||||
\(827\) | 10.4721 | 0.364152 | 0.182076 | − | 0.983284i | \(-0.441718\pi\) | ||||
0.182076 | + | 0.983284i | \(0.441718\pi\) | |||||||
\(828\) | 1.23607 | 0.0429563 | ||||||||
\(829\) | −40.2492 | −1.39791 | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(830\) | −69.3050 | −2.40561 | ||||||||
\(831\) | 14.5967 | 0.506356 | ||||||||
\(832\) | 12.7082 | 0.440578 | ||||||||
\(833\) | −28.6525 | −0.992749 | ||||||||
\(834\) | −9.79837 | −0.339290 | ||||||||
\(835\) | −33.8885 | −1.17276 | ||||||||
\(836\) | 0.944272 | 0.0326583 | ||||||||
\(837\) | 15.0000 | 0.518476 | ||||||||
\(838\) | 50.8328 | 1.75599 | ||||||||
\(839\) | −0.875388 | −0.0302218 | −0.0151109 | − | 0.999886i | \(-0.504810\pi\) | ||||
−0.0151109 | + | 0.999886i | \(0.504810\pi\) | |||||||
\(840\) | 20.0000 | 0.690066 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 38.3607 | 1.32200 | ||||||||
\(843\) | −29.5967 | −1.01937 | ||||||||
\(844\) | 2.11146 | 0.0726793 | ||||||||
\(845\) | 12.9443 | 0.445296 | ||||||||
\(846\) | −7.23607 | −0.248781 | ||||||||
\(847\) | 12.8754 | 0.442404 | ||||||||
\(848\) | 41.1246 | 1.41222 | ||||||||
\(849\) | 31.9574 | 1.09678 | ||||||||
\(850\) | −46.3607 | −1.59016 | ||||||||
\(851\) | 3.23607 | 0.110931 | ||||||||
\(852\) | 10.7295 | 0.367586 | ||||||||
\(853\) | −37.4164 | −1.28111 | −0.640557 | − | 0.767911i | \(-0.721296\pi\) | ||||
−0.640557 | + | 0.767911i | \(0.721296\pi\) | |||||||
\(854\) | 21.8885 | 0.749011 | ||||||||
\(855\) | 12.9443 | 0.442685 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | −7.47214 | −0.255243 | −0.127622 | − | 0.991823i | \(-0.540734\pi\) | ||||
−0.127622 | + | 0.991823i | \(0.540734\pi\) | |||||||
\(858\) | 8.29180 | 0.283077 | ||||||||
\(859\) | −3.29180 | −0.112315 | −0.0561573 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561573 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.1246 | −0.515445 | ||||||||
\(862\) | 42.8328 | 1.45889 | ||||||||
\(863\) | 45.5410 | 1.55023 | 0.775117 | − | 0.631818i | \(-0.217691\pi\) | ||||
0.775117 | + | 0.631818i | \(0.217691\pi\) | |||||||
\(864\) | −7.56231 | −0.257275 | ||||||||
\(865\) | −16.3607 | −0.556280 | ||||||||
\(866\) | −65.0132 | −2.20924 | ||||||||
\(867\) | 23.2918 | 0.791031 | ||||||||
\(868\) | 5.12461 | 0.173941 | ||||||||
\(869\) | −5.30495 | −0.179958 | ||||||||
\(870\) | −35.1246 | −1.19084 | ||||||||
\(871\) | −21.7082 | −0.735554 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.58359 | 0.290511 | ||||||||
\(874\) | 3.23607 | 0.109462 | ||||||||
\(875\) | 1.88854 | 0.0638444 | ||||||||
\(876\) | 21.3820 | 0.722430 | ||||||||
\(877\) | −27.5279 | −0.929550 | −0.464775 | − | 0.885429i | \(-0.653865\pi\) | ||||
−0.464775 | + | 0.885429i | \(0.653865\pi\) | |||||||
\(878\) | 8.56231 | 0.288964 | ||||||||
\(879\) | −23.4164 | −0.789816 | ||||||||
\(880\) | −12.0000 | −0.404520 | ||||||||
\(881\) | 21.8197 | 0.735123 | 0.367562 | − | 0.929999i | \(-0.380193\pi\) | ||||
0.367562 | + | 0.929999i | \(0.380193\pi\) | |||||||
\(882\) | 17.7082 | 0.596266 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 9.70820 | 0.326522 | ||||||||
\(885\) | 17.8885 | 0.601317 | ||||||||
\(886\) | 3.43769 | 0.115492 | ||||||||
\(887\) | −35.0689 | −1.17750 | −0.588749 | − | 0.808316i | \(-0.700379\pi\) | ||||
−0.588749 | + | 0.808316i | \(0.700379\pi\) | |||||||
\(888\) | 16.1803 | 0.542977 | ||||||||
\(889\) | 25.5967 | 0.858487 | ||||||||
\(890\) | −8.00000 | −0.268161 | ||||||||
\(891\) | 8.40325 | 0.281520 | ||||||||
\(892\) | 2.47214 | 0.0827732 | ||||||||
\(893\) | −4.47214 | −0.149654 | ||||||||
\(894\) | 43.0132 | 1.43858 | ||||||||
\(895\) | 41.1246 | 1.37464 | ||||||||
\(896\) | 16.8328 | 0.562345 | ||||||||
\(897\) | 6.70820 | 0.223980 | ||||||||
\(898\) | −4.76393 | −0.158974 | ||||||||
\(899\) | 20.1246 | 0.671193 | ||||||||
\(900\) | 6.76393 | 0.225464 | ||||||||
\(901\) | −44.3607 | −1.47787 | ||||||||
\(902\) | 6.76393 | 0.225214 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.5967 | 0.984373 | ||||||||
\(905\) | 47.4164 | 1.57617 | ||||||||
\(906\) | 0.854102 | 0.0283756 | ||||||||
\(907\) | 40.2492 | 1.33645 | 0.668227 | − | 0.743958i | \(-0.267054\pi\) | ||||
0.668227 | + | 0.743958i | \(0.267054\pi\) | |||||||
\(908\) | 6.29180 | 0.208801 | ||||||||
\(909\) | −8.94427 | −0.296663 | ||||||||
\(910\) | −19.4164 | −0.643648 | ||||||||
\(911\) | −31.3050 | −1.03718 | −0.518590 | − | 0.855023i | \(-0.673543\pi\) | ||||
−0.518590 | + | 0.855023i | \(0.673543\pi\) | |||||||
\(912\) | 21.7082 | 0.718830 | ||||||||
\(913\) | 10.1115 | 0.334640 | ||||||||
\(914\) | −56.8328 | −1.87986 | ||||||||
\(915\) | −79.1935 | −2.61806 | ||||||||
\(916\) | −7.41641 | −0.245045 | ||||||||
\(917\) | −6.54102 | −0.216003 | ||||||||
\(918\) | 18.9443 | 0.625254 | ||||||||
\(919\) | 0.875388 | 0.0288764 | 0.0144382 | − | 0.999896i | \(-0.495404\pi\) | ||||
0.0144382 | + | 0.999896i | \(0.495404\pi\) | |||||||
\(920\) | −7.23607 | −0.238566 | ||||||||
\(921\) | 41.3050 | 1.36104 | ||||||||
\(922\) | −12.0902 | −0.398169 | ||||||||
\(923\) | 23.2918 | 0.766659 | ||||||||
\(924\) | 1.30495 | 0.0429298 | ||||||||
\(925\) | 17.7082 | 0.582242 | ||||||||
\(926\) | 32.3607 | 1.06344 | ||||||||
\(927\) | 36.3607 | 1.19424 | ||||||||
\(928\) | −10.1459 | −0.333055 | ||||||||
\(929\) | −41.9443 | −1.37615 | −0.688073 | − | 0.725641i | \(-0.741543\pi\) | ||||
−0.688073 | + | 0.725641i | \(0.741543\pi\) | |||||||
\(930\) | −78.5410 | −2.57546 | ||||||||
\(931\) | 10.9443 | 0.358684 | ||||||||
\(932\) | −9.56231 | −0.313224 | ||||||||
\(933\) | −20.5279 | −0.672052 | ||||||||
\(934\) | 50.0689 | 1.63830 | ||||||||
\(935\) | 12.9443 | 0.423323 | ||||||||
\(936\) | 13.4164 | 0.438529 | ||||||||
\(937\) | 11.8197 | 0.386131 | 0.193066 | − | 0.981186i | \(-0.438157\pi\) | ||||
0.193066 | + | 0.981186i | \(0.438157\pi\) | |||||||
\(938\) | −14.4721 | −0.472532 | ||||||||
\(939\) | −45.5279 | −1.48575 | ||||||||
\(940\) | −4.47214 | −0.145865 | ||||||||
\(941\) | −24.6525 | −0.803648 | −0.401824 | − | 0.915717i | \(-0.631624\pi\) | ||||
−0.401824 | + | 0.915717i | \(0.631624\pi\) | |||||||
\(942\) | −55.7771 | −1.81732 | ||||||||
\(943\) | 5.47214 | 0.178197 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | −8.94427 | −0.290957 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.1803 | −1.07822 | −0.539108 | − | 0.842237i | \(-0.681239\pi\) | ||||
−0.539108 | + | 0.842237i | \(0.681239\pi\) | |||||||
\(948\) | 9.59675 | 0.311688 | ||||||||
\(949\) | 46.4164 | 1.50674 | ||||||||
\(950\) | 17.7082 | 0.574530 | ||||||||
\(951\) | −3.16718 | −0.102703 | ||||||||
\(952\) | −14.4721 | −0.469045 | ||||||||
\(953\) | 11.5279 | 0.373424 | 0.186712 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186712 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(954\) | 27.4164 | 0.887639 | ||||||||
\(955\) | 12.3607 | 0.399982 | ||||||||
\(956\) | 11.2705 | 0.364514 | ||||||||
\(957\) | 5.12461 | 0.165655 | ||||||||
\(958\) | 28.4721 | 0.919893 | ||||||||
\(959\) | −17.1672 | −0.554357 | ||||||||
\(960\) | −30.6525 | −0.989304 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | −15.7082 | −0.506453 | ||||||||
\(963\) | −26.8328 | −0.864675 | ||||||||
\(964\) | 10.5836 | 0.340875 | ||||||||
\(965\) | 25.7082 | 0.827576 | ||||||||
\(966\) | 4.47214 | 0.143889 | ||||||||
\(967\) | −39.5410 | −1.27155 | −0.635777 | − | 0.771873i | \(-0.719320\pi\) | ||||
−0.635777 | + | 0.771873i | \(0.719320\pi\) | |||||||
\(968\) | −23.2918 | −0.748627 | ||||||||
\(969\) | −23.4164 | −0.752243 | ||||||||
\(970\) | 22.4721 | 0.721537 | ||||||||
\(971\) | 7.52786 | 0.241581 | 0.120790 | − | 0.992678i | \(-0.461457\pi\) | ||||
0.120790 | + | 0.992678i | \(0.461457\pi\) | |||||||
\(972\) | −11.0557 | −0.354613 | ||||||||
\(973\) | −3.34752 | −0.107317 | ||||||||
\(974\) | 2.09017 | 0.0669734 | ||||||||
\(975\) | 36.7082 | 1.17560 | ||||||||
\(976\) | −53.1246 | −1.70048 | ||||||||
\(977\) | −54.6525 | −1.74849 | −0.874244 | − | 0.485487i | \(-0.838642\pi\) | ||||
−0.874244 | + | 0.485487i | \(0.838642\pi\) | |||||||
\(978\) | 37.0344 | 1.18423 | ||||||||
\(979\) | 1.16718 | 0.0373034 | ||||||||
\(980\) | 10.9443 | 0.349602 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −64.1591 | −2.04740 | ||||||||
\(983\) | −31.5279 | −1.00558 | −0.502791 | − | 0.864408i | \(-0.667694\pi\) | ||||
−0.502791 | + | 0.864408i | \(0.667694\pi\) | |||||||
\(984\) | 27.3607 | 0.872227 | ||||||||
\(985\) | −24.1803 | −0.770450 | ||||||||
\(986\) | 25.4164 | 0.809423 | ||||||||
\(987\) | −6.18034 | −0.196722 | ||||||||
\(988\) | −3.70820 | −0.117974 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −8.00000 | −0.254257 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | −22.6869 | −0.720310 | ||||||||
\(993\) | 26.0557 | 0.826854 | ||||||||
\(994\) | 15.5279 | 0.492514 | ||||||||
\(995\) | 83.1935 | 2.63741 | ||||||||
\(996\) | −18.2918 | −0.579598 | ||||||||
\(997\) | −36.8328 | −1.16651 | −0.583253 | − | 0.812290i | \(-0.698221\pi\) | ||||
−0.583253 | + | 0.812290i | \(0.698221\pi\) | |||||||
\(998\) | −52.9230 | −1.67525 | ||||||||
\(999\) | −7.23607 | −0.228939 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))