Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55848 | −1.80912 | −0.904558 | − | 0.426350i | \(-0.859799\pi\) | ||||
−0.904558 | + | 0.426350i | \(0.859799\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.54580 | 2.27290 | ||||||||
\(5\) | 3.55238 | 1.58867 | 0.794337 | − | 0.607477i | \(-0.207818\pi\) | ||||
0.794337 | + | 0.607477i | \(0.207818\pi\) | |||||||
\(6\) | 2.55848 | 1.04449 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.51338 | −2.30283 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.08869 | −2.87410 | ||||||||
\(11\) | −1.59905 | −0.482132 | −0.241066 | − | 0.970509i | \(-0.577497\pi\) | ||||
−0.241066 | + | 0.970509i | \(0.577497\pi\) | |||||||
\(12\) | −4.54580 | −1.31226 | ||||||||
\(13\) | 3.71849 | 1.03132 | 0.515661 | − | 0.856793i | \(-0.327546\pi\) | ||||
0.515661 | + | 0.856793i | \(0.327546\pi\) | |||||||
\(14\) | −2.55848 | −0.683782 | ||||||||
\(15\) | −3.55238 | −0.917222 | ||||||||
\(16\) | 7.57272 | 1.89318 | ||||||||
\(17\) | 2.71431 | 0.658317 | 0.329159 | − | 0.944275i | \(-0.393235\pi\) | ||||
0.329159 | + | 0.944275i | \(0.393235\pi\) | |||||||
\(18\) | −2.55848 | −0.603039 | ||||||||
\(19\) | 1.03969 | 0.238522 | 0.119261 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119261 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(20\) | 16.1484 | 3.61090 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 4.09113 | 0.872232 | ||||||||
\(23\) | 3.04813 | 0.635579 | 0.317790 | − | 0.948161i | \(-0.397059\pi\) | ||||
0.317790 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(24\) | 6.51338 | 1.32954 | ||||||||
\(25\) | 7.61944 | 1.52389 | ||||||||
\(26\) | −9.51366 | −1.86578 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.54580 | 0.859076 | ||||||||
\(29\) | 7.73676 | 1.43668 | 0.718340 | − | 0.695692i | \(-0.244902\pi\) | ||||
0.718340 | + | 0.695692i | \(0.244902\pi\) | |||||||
\(30\) | 9.08869 | 1.65936 | ||||||||
\(31\) | 8.27017 | 1.48537 | 0.742683 | − | 0.669643i | \(-0.233553\pi\) | ||||
0.742683 | + | 0.669643i | \(0.233553\pi\) | |||||||
\(32\) | −6.34787 | −1.12216 | ||||||||
\(33\) | 1.59905 | 0.278359 | ||||||||
\(34\) | −6.94450 | −1.19097 | ||||||||
\(35\) | 3.55238 | 0.600463 | ||||||||
\(36\) | 4.54580 | 0.757634 | ||||||||
\(37\) | 6.82052 | 1.12129 | 0.560643 | − | 0.828057i | \(-0.310554\pi\) | ||||
0.560643 | + | 0.828057i | \(0.310554\pi\) | |||||||
\(38\) | −2.66003 | −0.431514 | ||||||||
\(39\) | −3.71849 | −0.595434 | ||||||||
\(40\) | −23.1380 | −3.65844 | ||||||||
\(41\) | 0.500993 | 0.0782420 | 0.0391210 | − | 0.999234i | \(-0.487544\pi\) | ||||
0.0391210 | + | 0.999234i | \(0.487544\pi\) | |||||||
\(42\) | 2.55848 | 0.394782 | ||||||||
\(43\) | 11.4404 | 1.74464 | 0.872319 | − | 0.488937i | \(-0.162615\pi\) | ||||
0.872319 | + | 0.488937i | \(0.162615\pi\) | |||||||
\(44\) | −7.26897 | −1.09584 | ||||||||
\(45\) | 3.55238 | 0.529558 | ||||||||
\(46\) | −7.79857 | −1.14984 | ||||||||
\(47\) | −6.65378 | −0.970553 | −0.485277 | − | 0.874361i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874361i | \(0.661281\pi\) | |||||||
\(48\) | −7.57272 | −1.09303 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −19.4942 | −2.75689 | ||||||||
\(51\) | −2.71431 | −0.380080 | ||||||||
\(52\) | 16.9035 | 2.34409 | ||||||||
\(53\) | 13.8620 | 1.90409 | 0.952044 | − | 0.305960i | \(-0.0989773\pi\) | ||||
0.952044 | + | 0.305960i | \(0.0989773\pi\) | |||||||
\(54\) | 2.55848 | 0.348165 | ||||||||
\(55\) | −5.68044 | −0.765951 | ||||||||
\(56\) | −6.51338 | −0.870387 | ||||||||
\(57\) | −1.03969 | −0.137711 | ||||||||
\(58\) | −19.7943 | −2.59912 | ||||||||
\(59\) | −7.73203 | −1.00663 | −0.503313 | − | 0.864104i | \(-0.667886\pi\) | ||||
−0.503313 | + | 0.864104i | \(0.667886\pi\) | |||||||
\(60\) | −16.1484 | −2.08475 | ||||||||
\(61\) | 6.96622 | 0.891933 | 0.445966 | − | 0.895050i | \(-0.352860\pi\) | ||||
0.445966 | + | 0.895050i | \(0.352860\pi\) | |||||||
\(62\) | −21.1590 | −2.68720 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.09544 | 0.136930 | ||||||||
\(65\) | 13.2095 | 1.63844 | ||||||||
\(66\) | −4.09113 | −0.503584 | ||||||||
\(67\) | −10.4775 | −1.28003 | −0.640015 | − | 0.768363i | \(-0.721072\pi\) | ||||
−0.640015 | + | 0.768363i | \(0.721072\pi\) | |||||||
\(68\) | 12.3387 | 1.49629 | ||||||||
\(69\) | −3.04813 | −0.366952 | ||||||||
\(70\) | −9.08869 | −1.08631 | ||||||||
\(71\) | 15.8202 | 1.87751 | 0.938755 | − | 0.344586i | \(-0.111981\pi\) | ||||
0.938755 | + | 0.344586i | \(0.111981\pi\) | |||||||
\(72\) | −6.51338 | −0.767609 | ||||||||
\(73\) | 1.90550 | 0.223022 | 0.111511 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111511 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(74\) | −17.4501 | −2.02854 | ||||||||
\(75\) | −7.61944 | −0.879817 | ||||||||
\(76\) | 4.72624 | 0.542137 | ||||||||
\(77\) | −1.59905 | −0.182229 | ||||||||
\(78\) | 9.51366 | 1.07721 | ||||||||
\(79\) | −7.08096 | −0.796670 | −0.398335 | − | 0.917240i | \(-0.630412\pi\) | ||||
−0.398335 | + | 0.917240i | \(0.630412\pi\) | |||||||
\(80\) | 26.9012 | 3.00765 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.28178 | −0.141549 | ||||||||
\(83\) | −16.1031 | −1.76755 | −0.883773 | − | 0.467916i | \(-0.845005\pi\) | ||||
−0.883773 | + | 0.467916i | \(0.845005\pi\) | |||||||
\(84\) | −4.54580 | −0.495988 | ||||||||
\(85\) | 9.64228 | 1.04585 | ||||||||
\(86\) | −29.2699 | −3.15625 | ||||||||
\(87\) | −7.73676 | −0.829468 | ||||||||
\(88\) | 10.4152 | 1.11027 | ||||||||
\(89\) | −3.81355 | −0.404236 | −0.202118 | − | 0.979361i | \(-0.564782\pi\) | ||||
−0.202118 | + | 0.979361i | \(0.564782\pi\) | |||||||
\(90\) | −9.08869 | −0.958032 | ||||||||
\(91\) | 3.71849 | 0.389803 | ||||||||
\(92\) | 13.8562 | 1.44461 | ||||||||
\(93\) | −8.27017 | −0.857577 | ||||||||
\(94\) | 17.0235 | 1.75584 | ||||||||
\(95\) | 3.69339 | 0.378934 | ||||||||
\(96\) | 6.34787 | 0.647877 | ||||||||
\(97\) | −11.7860 | −1.19668 | −0.598341 | − | 0.801242i | \(-0.704173\pi\) | ||||
−0.598341 | + | 0.801242i | \(0.704173\pi\) | |||||||
\(98\) | −2.55848 | −0.258445 | ||||||||
\(99\) | −1.59905 | −0.160711 | ||||||||
\(100\) | 34.6365 | 3.46365 | ||||||||
\(101\) | −3.13057 | −0.311504 | −0.155752 | − | 0.987796i | \(-0.549780\pi\) | ||||
−0.155752 | + | 0.987796i | \(0.549780\pi\) | |||||||
\(102\) | 6.94450 | 0.687608 | ||||||||
\(103\) | 1.97999 | 0.195094 | 0.0975470 | − | 0.995231i | \(-0.468900\pi\) | ||||
0.0975470 | + | 0.995231i | \(0.468900\pi\) | |||||||
\(104\) | −24.2199 | −2.37496 | ||||||||
\(105\) | −3.55238 | −0.346677 | ||||||||
\(106\) | −35.4655 | −3.44472 | ||||||||
\(107\) | −16.7934 | −1.62348 | −0.811738 | − | 0.584022i | \(-0.801478\pi\) | ||||
−0.811738 | + | 0.584022i | \(0.801478\pi\) | |||||||
\(108\) | −4.54580 | −0.437420 | ||||||||
\(109\) | 15.5866 | 1.49292 | 0.746461 | − | 0.665430i | \(-0.231752\pi\) | ||||
0.746461 | + | 0.665430i | \(0.231752\pi\) | |||||||
\(110\) | 14.5333 | 1.38569 | ||||||||
\(111\) | −6.82052 | −0.647375 | ||||||||
\(112\) | 7.57272 | 0.715555 | ||||||||
\(113\) | −8.79725 | −0.827576 | −0.413788 | − | 0.910373i | \(-0.635794\pi\) | ||||
−0.413788 | + | 0.910373i | \(0.635794\pi\) | |||||||
\(114\) | 2.66003 | 0.249135 | ||||||||
\(115\) | 10.8281 | 1.00973 | ||||||||
\(116\) | 35.1698 | 3.26543 | ||||||||
\(117\) | 3.71849 | 0.343774 | ||||||||
\(118\) | 19.7822 | 1.82110 | ||||||||
\(119\) | 2.71431 | 0.248820 | ||||||||
\(120\) | 23.1380 | 2.11220 | ||||||||
\(121\) | −8.44304 | −0.767549 | ||||||||
\(122\) | −17.8229 | −1.61361 | ||||||||
\(123\) | −0.500993 | −0.0451731 | ||||||||
\(124\) | 37.5946 | 3.37609 | ||||||||
\(125\) | 9.30525 | 0.832287 | ||||||||
\(126\) | −2.55848 | −0.227927 | ||||||||
\(127\) | 13.6682 | 1.21286 | 0.606429 | − | 0.795138i | \(-0.292601\pi\) | ||||
0.606429 | + | 0.795138i | \(0.292601\pi\) | |||||||
\(128\) | 9.89308 | 0.874433 | ||||||||
\(129\) | −11.4404 | −1.00727 | ||||||||
\(130\) | −33.7962 | −2.96412 | ||||||||
\(131\) | 5.20953 | 0.455159 | 0.227580 | − | 0.973759i | \(-0.426919\pi\) | ||||
0.227580 | + | 0.973759i | \(0.426919\pi\) | |||||||
\(132\) | 7.26897 | 0.632682 | ||||||||
\(133\) | 1.03969 | 0.0901528 | ||||||||
\(134\) | 26.8064 | 2.31572 | ||||||||
\(135\) | −3.55238 | −0.305741 | ||||||||
\(136\) | −17.6793 | −1.51599 | ||||||||
\(137\) | 11.0237 | 0.941814 | 0.470907 | − | 0.882183i | \(-0.343927\pi\) | ||||
0.470907 | + | 0.882183i | \(0.343927\pi\) | |||||||
\(138\) | 7.79857 | 0.663859 | ||||||||
\(139\) | −4.31470 | −0.365968 | −0.182984 | − | 0.983116i | \(-0.558576\pi\) | ||||
−0.182984 | + | 0.983116i | \(0.558576\pi\) | |||||||
\(140\) | 16.1484 | 1.36479 | ||||||||
\(141\) | 6.65378 | 0.560349 | ||||||||
\(142\) | −40.4756 | −3.39663 | ||||||||
\(143\) | −5.94605 | −0.497233 | ||||||||
\(144\) | 7.57272 | 0.631060 | ||||||||
\(145\) | 27.4840 | 2.28242 | ||||||||
\(146\) | −4.87519 | −0.403473 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 31.0047 | 2.54857 | ||||||||
\(149\) | −2.30263 | −0.188638 | −0.0943192 | − | 0.995542i | \(-0.530067\pi\) | ||||
−0.0943192 | + | 0.995542i | \(0.530067\pi\) | |||||||
\(150\) | 19.4942 | 1.59169 | ||||||||
\(151\) | −8.87322 | −0.722093 | −0.361046 | − | 0.932548i | \(-0.617580\pi\) | ||||
−0.361046 | + | 0.932548i | \(0.617580\pi\) | |||||||
\(152\) | −6.77191 | −0.549275 | ||||||||
\(153\) | 2.71431 | 0.219439 | ||||||||
\(154\) | 4.09113 | 0.329673 | ||||||||
\(155\) | 29.3788 | 2.35976 | ||||||||
\(156\) | −16.9035 | −1.35336 | ||||||||
\(157\) | 7.81294 | 0.623540 | 0.311770 | − | 0.950158i | \(-0.399078\pi\) | ||||
0.311770 | + | 0.950158i | \(0.399078\pi\) | |||||||
\(158\) | 18.1165 | 1.44127 | ||||||||
\(159\) | −13.8620 | −1.09933 | ||||||||
\(160\) | −22.5501 | −1.78274 | ||||||||
\(161\) | 3.04813 | 0.240226 | ||||||||
\(162\) | −2.55848 | −0.201013 | ||||||||
\(163\) | 20.7196 | 1.62288 | 0.811441 | − | 0.584434i | \(-0.198683\pi\) | ||||
0.811441 | + | 0.584434i | \(0.198683\pi\) | |||||||
\(164\) | 2.27742 | 0.177836 | ||||||||
\(165\) | 5.68044 | 0.442222 | ||||||||
\(166\) | 41.1994 | 3.19770 | ||||||||
\(167\) | −15.1567 | −1.17286 | −0.586429 | − | 0.810001i | \(-0.699467\pi\) | ||||
−0.586429 | + | 0.810001i | \(0.699467\pi\) | |||||||
\(168\) | 6.51338 | 0.502518 | ||||||||
\(169\) | 0.827139 | 0.0636261 | ||||||||
\(170\) | −24.6695 | −1.89207 | ||||||||
\(171\) | 1.03969 | 0.0795073 | ||||||||
\(172\) | 52.0056 | 3.96539 | ||||||||
\(173\) | −12.2564 | −0.931839 | −0.465920 | − | 0.884827i | \(-0.654276\pi\) | ||||
−0.465920 | + | 0.884827i | \(0.654276\pi\) | |||||||
\(174\) | 19.7943 | 1.50060 | ||||||||
\(175\) | 7.61944 | 0.575975 | ||||||||
\(176\) | −12.1092 | −0.912762 | ||||||||
\(177\) | 7.73203 | 0.581175 | ||||||||
\(178\) | 9.75689 | 0.731310 | ||||||||
\(179\) | −5.31786 | −0.397476 | −0.198738 | − | 0.980053i | \(-0.563684\pi\) | ||||
−0.198738 | + | 0.980053i | \(0.563684\pi\) | |||||||
\(180\) | 16.1484 | 1.20363 | ||||||||
\(181\) | 4.35552 | 0.323743 | 0.161872 | − | 0.986812i | \(-0.448247\pi\) | ||||
0.161872 | + | 0.986812i | \(0.448247\pi\) | |||||||
\(182\) | −9.51366 | −0.705199 | ||||||||
\(183\) | −6.96622 | −0.514958 | ||||||||
\(184\) | −19.8536 | −1.46363 | ||||||||
\(185\) | 24.2291 | 1.78136 | ||||||||
\(186\) | 21.1590 | 1.55146 | ||||||||
\(187\) | −4.34032 | −0.317396 | ||||||||
\(188\) | −30.2468 | −2.20597 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −9.44945 | −0.685535 | ||||||||
\(191\) | 4.76255 | 0.344606 | 0.172303 | − | 0.985044i | \(-0.444879\pi\) | ||||
0.172303 | + | 0.985044i | \(0.444879\pi\) | |||||||
\(192\) | −1.09544 | −0.0790566 | ||||||||
\(193\) | 6.87865 | 0.495136 | 0.247568 | − | 0.968871i | \(-0.420369\pi\) | ||||
0.247568 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(194\) | 30.1541 | 2.16494 | ||||||||
\(195\) | −13.2095 | −0.945951 | ||||||||
\(196\) | 4.54580 | 0.324700 | ||||||||
\(197\) | −18.3570 | −1.30789 | −0.653943 | − | 0.756544i | \(-0.726886\pi\) | ||||
−0.653943 | + | 0.756544i | \(0.726886\pi\) | |||||||
\(198\) | 4.09113 | 0.290744 | ||||||||
\(199\) | −1.30520 | −0.0925235 | −0.0462618 | − | 0.998929i | \(-0.514731\pi\) | ||||
−0.0462618 | + | 0.998929i | \(0.514731\pi\) | |||||||
\(200\) | −49.6283 | −3.50925 | ||||||||
\(201\) | 10.4775 | 0.739025 | ||||||||
\(202\) | 8.00950 | 0.563546 | ||||||||
\(203\) | 7.73676 | 0.543014 | ||||||||
\(204\) | −12.3387 | −0.863883 | ||||||||
\(205\) | 1.77972 | 0.124301 | ||||||||
\(206\) | −5.06575 | −0.352948 | ||||||||
\(207\) | 3.04813 | 0.211860 | ||||||||
\(208\) | 28.1591 | 1.95248 | ||||||||
\(209\) | −1.66252 | −0.114999 | ||||||||
\(210\) | 9.08869 | 0.627179 | ||||||||
\(211\) | −17.4286 | −1.19984 | −0.599918 | − | 0.800061i | \(-0.704800\pi\) | ||||
−0.599918 | + | 0.800061i | \(0.704800\pi\) | |||||||
\(212\) | 63.0138 | 4.32781 | ||||||||
\(213\) | −15.8202 | −1.08398 | ||||||||
\(214\) | 42.9654 | 2.93706 | ||||||||
\(215\) | 40.6406 | 2.77166 | ||||||||
\(216\) | 6.51338 | 0.443179 | ||||||||
\(217\) | 8.27017 | 0.561416 | ||||||||
\(218\) | −39.8778 | −2.70087 | ||||||||
\(219\) | −1.90550 | −0.128762 | ||||||||
\(220\) | −25.8222 | −1.74093 | ||||||||
\(221\) | 10.0931 | 0.678937 | ||||||||
\(222\) | 17.4501 | 1.17118 | ||||||||
\(223\) | 3.53637 | 0.236813 | 0.118407 | − | 0.992965i | \(-0.462221\pi\) | ||||
0.118407 | + | 0.992965i | \(0.462221\pi\) | |||||||
\(224\) | −6.34787 | −0.424135 | ||||||||
\(225\) | 7.61944 | 0.507963 | ||||||||
\(226\) | 22.5076 | 1.49718 | ||||||||
\(227\) | −1.71958 | −0.114133 | −0.0570663 | − | 0.998370i | \(-0.518175\pi\) | ||||
−0.0570663 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(228\) | −4.72624 | −0.313003 | ||||||||
\(229\) | −7.53757 | −0.498097 | −0.249048 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249048 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(230\) | −27.7035 | −1.82672 | ||||||||
\(231\) | 1.59905 | 0.105210 | ||||||||
\(232\) | −50.3924 | −3.30843 | ||||||||
\(233\) | 11.8519 | 0.776447 | 0.388223 | − | 0.921565i | \(-0.373089\pi\) | ||||
0.388223 | + | 0.921565i | \(0.373089\pi\) | |||||||
\(234\) | −9.51366 | −0.621927 | ||||||||
\(235\) | −23.6368 | −1.54189 | ||||||||
\(236\) | −35.1483 | −2.28796 | ||||||||
\(237\) | 7.08096 | 0.459958 | ||||||||
\(238\) | −6.94450 | −0.450145 | ||||||||
\(239\) | 2.29552 | 0.148485 | 0.0742425 | − | 0.997240i | \(-0.476346\pi\) | ||||
0.0742425 | + | 0.997240i | \(0.476346\pi\) | |||||||
\(240\) | −26.9012 | −1.73647 | ||||||||
\(241\) | −9.25898 | −0.596424 | −0.298212 | − | 0.954500i | \(-0.596390\pi\) | ||||
−0.298212 | + | 0.954500i | \(0.596390\pi\) | |||||||
\(242\) | 21.6013 | 1.38859 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 31.6671 | 2.02728 | ||||||||
\(245\) | 3.55238 | 0.226954 | ||||||||
\(246\) | 1.28178 | 0.0817233 | ||||||||
\(247\) | 3.86608 | 0.245993 | ||||||||
\(248\) | −53.8667 | −3.42054 | ||||||||
\(249\) | 16.1031 | 1.02049 | ||||||||
\(250\) | −23.8073 | −1.50570 | ||||||||
\(251\) | −20.0498 | −1.26553 | −0.632765 | − | 0.774344i | \(-0.718080\pi\) | ||||
−0.632765 | + | 0.774344i | \(0.718080\pi\) | |||||||
\(252\) | 4.54580 | 0.286359 | ||||||||
\(253\) | −4.87411 | −0.306433 | ||||||||
\(254\) | −34.9698 | −2.19420 | ||||||||
\(255\) | −9.64228 | −0.603823 | ||||||||
\(256\) | −27.5021 | −1.71888 | ||||||||
\(257\) | −10.3896 | −0.648084 | −0.324042 | − | 0.946043i | \(-0.605042\pi\) | ||||
−0.324042 | + | 0.946043i | \(0.605042\pi\) | |||||||
\(258\) | 29.2699 | 1.82226 | ||||||||
\(259\) | 6.82052 | 0.423806 | ||||||||
\(260\) | 60.0478 | 3.72400 | ||||||||
\(261\) | 7.73676 | 0.478893 | ||||||||
\(262\) | −13.3285 | −0.823436 | ||||||||
\(263\) | −26.4874 | −1.63328 | −0.816640 | − | 0.577147i | \(-0.804166\pi\) | ||||
−0.816640 | + | 0.577147i | \(0.804166\pi\) | |||||||
\(264\) | −10.4152 | −0.641012 | ||||||||
\(265\) | 49.2431 | 3.02498 | ||||||||
\(266\) | −2.66003 | −0.163097 | ||||||||
\(267\) | 3.81355 | 0.233386 | ||||||||
\(268\) | −47.6286 | −2.90938 | ||||||||
\(269\) | −28.3791 | −1.73030 | −0.865151 | − | 0.501511i | \(-0.832778\pi\) | ||||
−0.865151 | + | 0.501511i | \(0.832778\pi\) | |||||||
\(270\) | 9.08869 | 0.553120 | ||||||||
\(271\) | −26.8832 | −1.63304 | −0.816520 | − | 0.577317i | \(-0.804100\pi\) | ||||
−0.816520 | + | 0.577317i | \(0.804100\pi\) | |||||||
\(272\) | 20.5547 | 1.24631 | ||||||||
\(273\) | −3.71849 | −0.225053 | ||||||||
\(274\) | −28.2038 | −1.70385 | ||||||||
\(275\) | −12.1839 | −0.734715 | ||||||||
\(276\) | −13.8562 | −0.834046 | ||||||||
\(277\) | 19.2208 | 1.15487 | 0.577434 | − | 0.816437i | \(-0.304054\pi\) | ||||
0.577434 | + | 0.816437i | \(0.304054\pi\) | |||||||
\(278\) | 11.0391 | 0.662079 | ||||||||
\(279\) | 8.27017 | 0.495122 | ||||||||
\(280\) | −23.1380 | −1.38276 | ||||||||
\(281\) | 16.0403 | 0.956887 | 0.478443 | − | 0.878118i | \(-0.341201\pi\) | ||||
0.478443 | + | 0.878118i | \(0.341201\pi\) | |||||||
\(282\) | −17.0235 | −1.01374 | ||||||||
\(283\) | 28.0068 | 1.66483 | 0.832415 | − | 0.554153i | \(-0.186958\pi\) | ||||
0.832415 | + | 0.554153i | \(0.186958\pi\) | |||||||
\(284\) | 71.9154 | 4.26739 | ||||||||
\(285\) | −3.69339 | −0.218777 | ||||||||
\(286\) | 15.2128 | 0.899553 | ||||||||
\(287\) | 0.500993 | 0.0295727 | ||||||||
\(288\) | −6.34787 | −0.374052 | ||||||||
\(289\) | −9.63252 | −0.566619 | ||||||||
\(290\) | −70.3170 | −4.12916 | ||||||||
\(291\) | 11.7860 | 0.690905 | ||||||||
\(292\) | 8.66204 | 0.506908 | ||||||||
\(293\) | 9.16667 | 0.535523 | 0.267761 | − | 0.963485i | \(-0.413716\pi\) | ||||
0.267761 | + | 0.963485i | \(0.413716\pi\) | |||||||
\(294\) | 2.55848 | 0.149213 | ||||||||
\(295\) | −27.4672 | −1.59920 | ||||||||
\(296\) | −44.4246 | −2.58213 | ||||||||
\(297\) | 1.59905 | 0.0927863 | ||||||||
\(298\) | 5.89121 | 0.341269 | ||||||||
\(299\) | 11.3344 | 0.655487 | ||||||||
\(300\) | −34.6365 | −1.99974 | ||||||||
\(301\) | 11.4404 | 0.659411 | ||||||||
\(302\) | 22.7019 | 1.30635 | ||||||||
\(303\) | 3.13057 | 0.179847 | ||||||||
\(304\) | 7.87330 | 0.451565 | ||||||||
\(305\) | 24.7467 | 1.41699 | ||||||||
\(306\) | −6.94450 | −0.396991 | ||||||||
\(307\) | −10.7189 | −0.611759 | −0.305880 | − | 0.952070i | \(-0.598951\pi\) | ||||
−0.305880 | + | 0.952070i | \(0.598951\pi\) | |||||||
\(308\) | −7.26897 | −0.414188 | ||||||||
\(309\) | −1.97999 | −0.112638 | ||||||||
\(310\) | −75.1650 | −4.26909 | ||||||||
\(311\) | 31.7612 | 1.80101 | 0.900506 | − | 0.434844i | \(-0.143197\pi\) | ||||
0.900506 | + | 0.434844i | \(0.143197\pi\) | |||||||
\(312\) | 24.2199 | 1.37118 | ||||||||
\(313\) | 13.1052 | 0.740747 | 0.370374 | − | 0.928883i | \(-0.379230\pi\) | ||||
0.370374 | + | 0.928883i | \(0.379230\pi\) | |||||||
\(314\) | −19.9892 | −1.12806 | ||||||||
\(315\) | 3.55238 | 0.200154 | ||||||||
\(316\) | −32.1886 | −1.81075 | ||||||||
\(317\) | −33.1956 | −1.86445 | −0.932224 | − | 0.361882i | \(-0.882134\pi\) | ||||
−0.932224 | + | 0.361882i | \(0.882134\pi\) | |||||||
\(318\) | 35.4655 | 1.98881 | ||||||||
\(319\) | −12.3715 | −0.692669 | ||||||||
\(320\) | 3.89143 | 0.217537 | ||||||||
\(321\) | 16.7934 | 0.937314 | ||||||||
\(322\) | −7.79857 | −0.434597 | ||||||||
\(323\) | 2.82205 | 0.157023 | ||||||||
\(324\) | 4.54580 | 0.252545 | ||||||||
\(325\) | 28.3328 | 1.57162 | ||||||||
\(326\) | −53.0106 | −2.93598 | ||||||||
\(327\) | −15.5866 | −0.861939 | ||||||||
\(328\) | −3.26316 | −0.180178 | ||||||||
\(329\) | −6.65378 | −0.366835 | ||||||||
\(330\) | −14.5333 | −0.800031 | ||||||||
\(331\) | −0.00736511 | −0.000404823 0 | −0.000202411 | − | 1.00000i | \(-0.500064\pi\) | ||||
−0.000202411 | 1.00000i | \(0.500064\pi\) | ||||||||
\(332\) | −73.2016 | −4.01746 | ||||||||
\(333\) | 6.82052 | 0.373762 | ||||||||
\(334\) | 38.7779 | 2.12184 | ||||||||
\(335\) | −37.2201 | −2.03355 | ||||||||
\(336\) | −7.57272 | −0.413126 | ||||||||
\(337\) | 14.7457 | 0.803252 | 0.401626 | − | 0.915804i | \(-0.368445\pi\) | ||||
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(338\) | −2.11622 | −0.115107 | ||||||||
\(339\) | 8.79725 | 0.477801 | ||||||||
\(340\) | 43.8319 | 2.37712 | ||||||||
\(341\) | −13.2244 | −0.716142 | ||||||||
\(342\) | −2.66003 | −0.143838 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −74.5154 | −4.01760 | ||||||||
\(345\) | −10.8281 | −0.582967 | ||||||||
\(346\) | 31.3578 | 1.68581 | ||||||||
\(347\) | −13.1170 | −0.704155 | −0.352077 | − | 0.935971i | \(-0.614525\pi\) | ||||
−0.352077 | + | 0.935971i | \(0.614525\pi\) | |||||||
\(348\) | −35.1698 | −1.88530 | ||||||||
\(349\) | −25.6281 | −1.37184 | −0.685919 | − | 0.727678i | \(-0.740600\pi\) | ||||
−0.685919 | + | 0.727678i | \(0.740600\pi\) | |||||||
\(350\) | −19.4942 | −1.04201 | ||||||||
\(351\) | −3.71849 | −0.198478 | ||||||||
\(352\) | 10.1506 | 0.541027 | ||||||||
\(353\) | −24.1173 | −1.28364 | −0.641818 | − | 0.766857i | \(-0.721819\pi\) | ||||
−0.641818 | + | 0.766857i | \(0.721819\pi\) | |||||||
\(354\) | −19.7822 | −1.05141 | ||||||||
\(355\) | 56.1994 | 2.98275 | ||||||||
\(356\) | −17.3357 | −0.918788 | ||||||||
\(357\) | −2.71431 | −0.143657 | ||||||||
\(358\) | 13.6056 | 0.719079 | ||||||||
\(359\) | −6.48500 | −0.342265 | −0.171133 | − | 0.985248i | \(-0.554743\pi\) | ||||
−0.171133 | + | 0.985248i | \(0.554743\pi\) | |||||||
\(360\) | −23.1380 | −1.21948 | ||||||||
\(361\) | −17.9190 | −0.943107 | ||||||||
\(362\) | −11.1435 | −0.585689 | ||||||||
\(363\) | 8.44304 | 0.443145 | ||||||||
\(364\) | 16.9035 | 0.885984 | ||||||||
\(365\) | 6.76908 | 0.354310 | ||||||||
\(366\) | 17.8229 | 0.931618 | ||||||||
\(367\) | 24.8129 | 1.29522 | 0.647610 | − | 0.761972i | \(-0.275769\pi\) | ||||
0.647610 | + | 0.761972i | \(0.275769\pi\) | |||||||
\(368\) | 23.0826 | 1.20327 | ||||||||
\(369\) | 0.500993 | 0.0260807 | ||||||||
\(370\) | −61.9896 | −3.22269 | ||||||||
\(371\) | 13.8620 | 0.719678 | ||||||||
\(372\) | −37.5946 | −1.94919 | ||||||||
\(373\) | −5.45384 | −0.282389 | −0.141195 | − | 0.989982i | \(-0.545094\pi\) | ||||
−0.141195 | + | 0.989982i | \(0.545094\pi\) | |||||||
\(374\) | 11.1046 | 0.574205 | ||||||||
\(375\) | −9.30525 | −0.480521 | ||||||||
\(376\) | 43.3386 | 2.23502 | ||||||||
\(377\) | 28.7690 | 1.48168 | ||||||||
\(378\) | 2.55848 | 0.131594 | ||||||||
\(379\) | −5.84207 | −0.300087 | −0.150043 | − | 0.988679i | \(-0.547941\pi\) | ||||
−0.150043 | + | 0.988679i | \(0.547941\pi\) | |||||||
\(380\) | 16.7894 | 0.861279 | ||||||||
\(381\) | −13.6682 | −0.700244 | ||||||||
\(382\) | −12.1849 | −0.623433 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | −9.89308 | −0.504854 | ||||||||
\(385\) | −5.68044 | −0.289502 | ||||||||
\(386\) | −17.5989 | −0.895758 | ||||||||
\(387\) | 11.4404 | 0.581546 | ||||||||
\(388\) | −53.5766 | −2.71994 | ||||||||
\(389\) | −30.8769 | −1.56552 | −0.782760 | − | 0.622324i | \(-0.786189\pi\) | ||||
−0.782760 | + | 0.622324i | \(0.786189\pi\) | |||||||
\(390\) | 33.7962 | 1.71134 | ||||||||
\(391\) | 8.27358 | 0.418413 | ||||||||
\(392\) | −6.51338 | −0.328975 | ||||||||
\(393\) | −5.20953 | −0.262786 | ||||||||
\(394\) | 46.9661 | 2.36612 | ||||||||
\(395\) | −25.1543 | −1.26565 | ||||||||
\(396\) | −7.26897 | −0.365279 | ||||||||
\(397\) | 29.9851 | 1.50491 | 0.752455 | − | 0.658644i | \(-0.228870\pi\) | ||||
0.752455 | + | 0.658644i | \(0.228870\pi\) | |||||||
\(398\) | 3.33934 | 0.167386 | ||||||||
\(399\) | −1.03969 | −0.0520497 | ||||||||
\(400\) | 57.6999 | 2.88499 | ||||||||
\(401\) | −34.5655 | −1.72612 | −0.863060 | − | 0.505102i | \(-0.831455\pi\) | ||||
−0.863060 | + | 0.505102i | \(0.831455\pi\) | |||||||
\(402\) | −26.8064 | −1.33698 | ||||||||
\(403\) | 30.7525 | 1.53189 | ||||||||
\(404\) | −14.2310 | −0.708017 | ||||||||
\(405\) | 3.55238 | 0.176519 | ||||||||
\(406\) | −19.7943 | −0.982376 | ||||||||
\(407\) | −10.9064 | −0.540608 | ||||||||
\(408\) | 17.6793 | 0.875257 | ||||||||
\(409\) | −9.10775 | −0.450349 | −0.225175 | − | 0.974318i | \(-0.572295\pi\) | ||||
−0.225175 | + | 0.974318i | \(0.572295\pi\) | |||||||
\(410\) | −4.55338 | −0.224875 | ||||||||
\(411\) | −11.0237 | −0.543757 | ||||||||
\(412\) | 9.00064 | 0.443430 | ||||||||
\(413\) | −7.73203 | −0.380468 | ||||||||
\(414\) | −7.79857 | −0.383279 | ||||||||
\(415\) | −57.2044 | −2.80806 | ||||||||
\(416\) | −23.6045 | −1.15730 | ||||||||
\(417\) | 4.31470 | 0.211292 | ||||||||
\(418\) | 4.25352 | 0.208046 | ||||||||
\(419\) | 2.57151 | 0.125626 | 0.0628132 | − | 0.998025i | \(-0.479993\pi\) | ||||
0.0628132 | + | 0.998025i | \(0.479993\pi\) | |||||||
\(420\) | −16.1484 | −0.787963 | ||||||||
\(421\) | −12.9324 | −0.630288 | −0.315144 | − | 0.949044i | \(-0.602053\pi\) | ||||
−0.315144 | + | 0.949044i | \(0.602053\pi\) | |||||||
\(422\) | 44.5907 | 2.17064 | ||||||||
\(423\) | −6.65378 | −0.323518 | ||||||||
\(424\) | −90.2883 | −4.38479 | ||||||||
\(425\) | 20.6815 | 1.00320 | ||||||||
\(426\) | 40.4756 | 1.96105 | ||||||||
\(427\) | 6.96622 | 0.337119 | ||||||||
\(428\) | −76.3393 | −3.69000 | ||||||||
\(429\) | 5.94605 | 0.287078 | ||||||||
\(430\) | −103.978 | −5.01426 | ||||||||
\(431\) | −15.9417 | −0.767887 | −0.383944 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383944 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(432\) | −7.57272 | −0.364343 | ||||||||
\(433\) | 35.1364 | 1.68855 | 0.844274 | − | 0.535912i | \(-0.180032\pi\) | ||||
0.844274 | + | 0.535912i | \(0.180032\pi\) | |||||||
\(434\) | −21.1590 | −1.01567 | ||||||||
\(435\) | −27.4840 | −1.31775 | ||||||||
\(436\) | 70.8534 | 3.39326 | ||||||||
\(437\) | 3.16912 | 0.151600 | ||||||||
\(438\) | 4.87519 | 0.232945 | ||||||||
\(439\) | −24.8569 | −1.18636 | −0.593178 | − | 0.805071i | \(-0.702127\pi\) | ||||
−0.593178 | + | 0.805071i | \(0.702127\pi\) | |||||||
\(440\) | 36.9989 | 1.76385 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −25.8230 | −1.22828 | ||||||||
\(443\) | 17.9854 | 0.854511 | 0.427255 | − | 0.904131i | \(-0.359480\pi\) | ||||
0.427255 | + | 0.904131i | \(0.359480\pi\) | |||||||
\(444\) | −31.0047 | −1.47142 | ||||||||
\(445\) | −13.5472 | −0.642199 | ||||||||
\(446\) | −9.04773 | −0.428422 | ||||||||
\(447\) | 2.30263 | 0.108910 | ||||||||
\(448\) | 1.09544 | 0.0517547 | ||||||||
\(449\) | 17.2059 | 0.811997 | 0.405998 | − | 0.913874i | \(-0.366924\pi\) | ||||
0.405998 | + | 0.913874i | \(0.366924\pi\) | |||||||
\(450\) | −19.4942 | −0.918963 | ||||||||
\(451\) | −0.801114 | −0.0377230 | ||||||||
\(452\) | −39.9906 | −1.88100 | ||||||||
\(453\) | 8.87322 | 0.416900 | ||||||||
\(454\) | 4.39950 | 0.206479 | ||||||||
\(455\) | 13.2095 | 0.619271 | ||||||||
\(456\) | 6.77191 | 0.317124 | ||||||||
\(457\) | −21.5416 | −1.00767 | −0.503836 | − | 0.863800i | \(-0.668078\pi\) | ||||
−0.503836 | + | 0.863800i | \(0.668078\pi\) | |||||||
\(458\) | 19.2847 | 0.901115 | ||||||||
\(459\) | −2.71431 | −0.126693 | ||||||||
\(460\) | 49.2226 | 2.29501 | ||||||||
\(461\) | −5.20012 | −0.242194 | −0.121097 | − | 0.992641i | \(-0.538641\pi\) | ||||
−0.121097 | + | 0.992641i | \(0.538641\pi\) | |||||||
\(462\) | −4.09113 | −0.190337 | ||||||||
\(463\) | −0.961649 | −0.0446916 | −0.0223458 | − | 0.999750i | \(-0.507113\pi\) | ||||
−0.0223458 | + | 0.999750i | \(0.507113\pi\) | |||||||
\(464\) | 58.5883 | 2.71989 | ||||||||
\(465\) | −29.3788 | −1.36241 | ||||||||
\(466\) | −30.3229 | −1.40468 | ||||||||
\(467\) | 8.56194 | 0.396199 | 0.198100 | − | 0.980182i | \(-0.436523\pi\) | ||||
0.198100 | + | 0.980182i | \(0.436523\pi\) | |||||||
\(468\) | 16.9035 | 0.781365 | ||||||||
\(469\) | −10.4775 | −0.483806 | ||||||||
\(470\) | 60.4741 | 2.78946 | ||||||||
\(471\) | −7.81294 | −0.360001 | ||||||||
\(472\) | 50.3617 | 2.31808 | ||||||||
\(473\) | −18.2937 | −0.841146 | ||||||||
\(474\) | −18.1165 | −0.832117 | ||||||||
\(475\) | 7.92187 | 0.363480 | ||||||||
\(476\) | 12.3387 | 0.565544 | ||||||||
\(477\) | 13.8620 | 0.634696 | ||||||||
\(478\) | −5.87304 | −0.268627 | ||||||||
\(479\) | −28.6941 | −1.31107 | −0.655534 | − | 0.755166i | \(-0.727556\pi\) | ||||
−0.655534 | + | 0.755166i | \(0.727556\pi\) | |||||||
\(480\) | 22.5501 | 1.02927 | ||||||||
\(481\) | 25.3620 | 1.15641 | ||||||||
\(482\) | 23.6889 | 1.07900 | ||||||||
\(483\) | −3.04813 | −0.138695 | ||||||||
\(484\) | −38.3804 | −1.74456 | ||||||||
\(485\) | −41.8682 | −1.90114 | ||||||||
\(486\) | 2.55848 | 0.116055 | ||||||||
\(487\) | 43.2664 | 1.96059 | 0.980295 | − | 0.197541i | \(-0.0632956\pi\) | ||||
0.980295 | + | 0.197541i | \(0.0632956\pi\) | |||||||
\(488\) | −45.3736 | −2.05397 | ||||||||
\(489\) | −20.7196 | −0.936972 | ||||||||
\(490\) | −9.08869 | −0.410585 | ||||||||
\(491\) | −6.20509 | −0.280032 | −0.140016 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140016 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(492\) | −2.27742 | −0.102674 | ||||||||
\(493\) | 21.0000 | 0.945791 | ||||||||
\(494\) | −9.89128 | −0.445030 | ||||||||
\(495\) | −5.68044 | −0.255317 | ||||||||
\(496\) | 62.6277 | 2.81207 | ||||||||
\(497\) | 15.8202 | 0.709632 | ||||||||
\(498\) | −41.1994 | −1.84619 | ||||||||
\(499\) | −29.3188 | −1.31249 | −0.656244 | − | 0.754549i | \(-0.727856\pi\) | ||||
−0.656244 | + | 0.754549i | \(0.727856\pi\) | |||||||
\(500\) | 42.2998 | 1.89171 | ||||||||
\(501\) | 15.1567 | 0.677149 | ||||||||
\(502\) | 51.2968 | 2.28949 | ||||||||
\(503\) | 10.4901 | 0.467732 | 0.233866 | − | 0.972269i | \(-0.424862\pi\) | ||||
0.233866 | + | 0.972269i | \(0.424862\pi\) | |||||||
\(504\) | −6.51338 | −0.290129 | ||||||||
\(505\) | −11.1210 | −0.494878 | ||||||||
\(506\) | 12.4703 | 0.554373 | ||||||||
\(507\) | −0.827139 | −0.0367345 | ||||||||
\(508\) | 62.1330 | 2.75671 | ||||||||
\(509\) | −20.4149 | −0.904872 | −0.452436 | − | 0.891797i | \(-0.649445\pi\) | ||||
−0.452436 | + | 0.891797i | \(0.649445\pi\) | |||||||
\(510\) | 24.6695 | 1.09239 | ||||||||
\(511\) | 1.90550 | 0.0842945 | ||||||||
\(512\) | 50.5773 | 2.23522 | ||||||||
\(513\) | −1.03969 | −0.0459036 | ||||||||
\(514\) | 26.5815 | 1.17246 | ||||||||
\(515\) | 7.03368 | 0.309941 | ||||||||
\(516\) | −52.0056 | −2.28942 | ||||||||
\(517\) | 10.6397 | 0.467934 | ||||||||
\(518\) | −17.4501 | −0.766715 | ||||||||
\(519\) | 12.2564 | 0.537998 | ||||||||
\(520\) | −86.0384 | −3.77303 | ||||||||
\(521\) | 0.789813 | 0.0346024 | 0.0173012 | − | 0.999850i | \(-0.494493\pi\) | ||||
0.0173012 | + | 0.999850i | \(0.494493\pi\) | |||||||
\(522\) | −19.7943 | −0.866374 | ||||||||
\(523\) | −1.35522 | −0.0592596 | −0.0296298 | − | 0.999561i | \(-0.509433\pi\) | ||||
−0.0296298 | + | 0.999561i | \(0.509433\pi\) | |||||||
\(524\) | 23.6815 | 1.03453 | ||||||||
\(525\) | −7.61944 | −0.332540 | ||||||||
\(526\) | 67.7673 | 2.95479 | ||||||||
\(527\) | 22.4478 | 0.977842 | ||||||||
\(528\) | 12.1092 | 0.526983 | ||||||||
\(529\) | −13.7089 | −0.596039 | ||||||||
\(530\) | −125.987 | −5.47254 | ||||||||
\(531\) | −7.73203 | −0.335542 | ||||||||
\(532\) | 4.72624 | 0.204908 | ||||||||
\(533\) | 1.86294 | 0.0806928 | ||||||||
\(534\) | −9.75689 | −0.422222 | ||||||||
\(535\) | −59.6565 | −2.57918 | ||||||||
\(536\) | 68.2439 | 2.94769 | ||||||||
\(537\) | 5.31786 | 0.229483 | ||||||||
\(538\) | 72.6072 | 3.13032 | ||||||||
\(539\) | −1.59905 | −0.0688760 | ||||||||
\(540\) | −16.1484 | −0.694918 | ||||||||
\(541\) | −3.61096 | −0.155247 | −0.0776236 | − | 0.996983i | \(-0.524733\pi\) | ||||
−0.0776236 | + | 0.996983i | \(0.524733\pi\) | |||||||
\(542\) | 68.7801 | 2.95436 | ||||||||
\(543\) | −4.35552 | −0.186913 | ||||||||
\(544\) | −17.2301 | −0.738734 | ||||||||
\(545\) | 55.3694 | 2.37177 | ||||||||
\(546\) | 9.51366 | 0.407147 | ||||||||
\(547\) | 14.8002 | 0.632810 | 0.316405 | − | 0.948624i | \(-0.397524\pi\) | ||||
0.316405 | + | 0.948624i | \(0.397524\pi\) | |||||||
\(548\) | 50.1114 | 2.14065 | ||||||||
\(549\) | 6.96622 | 0.297311 | ||||||||
\(550\) | 31.1721 | 1.32918 | ||||||||
\(551\) | 8.04385 | 0.342680 | ||||||||
\(552\) | 19.8536 | 0.845027 | ||||||||
\(553\) | −7.08096 | −0.301113 | ||||||||
\(554\) | −49.1761 | −2.08929 | ||||||||
\(555\) | −24.2291 | −1.02847 | ||||||||
\(556\) | −19.6138 | −0.831810 | ||||||||
\(557\) | 13.9396 | 0.590639 | 0.295319 | − | 0.955399i | \(-0.404574\pi\) | ||||
0.295319 | + | 0.955399i | \(0.404574\pi\) | |||||||
\(558\) | −21.1590 | −0.895733 | ||||||||
\(559\) | 42.5408 | 1.79929 | ||||||||
\(560\) | 26.9012 | 1.13678 | ||||||||
\(561\) | 4.34032 | 0.183248 | ||||||||
\(562\) | −41.0388 | −1.73112 | ||||||||
\(563\) | 38.2550 | 1.61226 | 0.806128 | − | 0.591741i | \(-0.201559\pi\) | ||||
0.806128 | + | 0.591741i | \(0.201559\pi\) | |||||||
\(564\) | 30.2468 | 1.27362 | ||||||||
\(565\) | −31.2512 | −1.31475 | ||||||||
\(566\) | −71.6547 | −3.01187 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −103.043 | −4.32358 | ||||||||
\(569\) | 17.7973 | 0.746102 | 0.373051 | − | 0.927811i | \(-0.378312\pi\) | ||||
0.373051 | + | 0.927811i | \(0.378312\pi\) | |||||||
\(570\) | 9.44945 | 0.395794 | ||||||||
\(571\) | −41.8234 | −1.75026 | −0.875128 | − | 0.483892i | \(-0.839223\pi\) | ||||
−0.875128 | + | 0.483892i | \(0.839223\pi\) | |||||||
\(572\) | −27.0296 | −1.13016 | ||||||||
\(573\) | −4.76255 | −0.198959 | ||||||||
\(574\) | −1.28178 | −0.0535005 | ||||||||
\(575\) | 23.2250 | 0.968551 | ||||||||
\(576\) | 1.09544 | 0.0456434 | ||||||||
\(577\) | 1.37013 | 0.0570394 | 0.0285197 | − | 0.999593i | \(-0.490921\pi\) | ||||
0.0285197 | + | 0.999593i | \(0.490921\pi\) | |||||||
\(578\) | 24.6446 | 1.02508 | ||||||||
\(579\) | −6.87865 | −0.285867 | ||||||||
\(580\) | 124.937 | 5.18771 | ||||||||
\(581\) | −16.1031 | −0.668070 | ||||||||
\(582\) | −30.1541 | −1.24993 | ||||||||
\(583\) | −22.1660 | −0.918022 | ||||||||
\(584\) | −12.4113 | −0.513582 | ||||||||
\(585\) | 13.2095 | 0.546145 | ||||||||
\(586\) | −23.4527 | −0.968822 | ||||||||
\(587\) | −9.80599 | −0.404737 | −0.202368 | − | 0.979309i | \(-0.564864\pi\) | ||||
−0.202368 | + | 0.979309i | \(0.564864\pi\) | |||||||
\(588\) | −4.54580 | −0.187466 | ||||||||
\(589\) | 8.59843 | 0.354292 | ||||||||
\(590\) | 70.2741 | 2.89314 | ||||||||
\(591\) | 18.3570 | 0.755108 | ||||||||
\(592\) | 51.6499 | 2.12280 | ||||||||
\(593\) | −46.1043 | −1.89328 | −0.946639 | − | 0.322296i | \(-0.895545\pi\) | ||||
−0.946639 | + | 0.322296i | \(0.895545\pi\) | |||||||
\(594\) | −4.09113 | −0.167861 | ||||||||
\(595\) | 9.64228 | 0.395295 | ||||||||
\(596\) | −10.4673 | −0.428757 | ||||||||
\(597\) | 1.30520 | 0.0534185 | ||||||||
\(598\) | −28.9989 | −1.18585 | ||||||||
\(599\) | 28.8668 | 1.17947 | 0.589734 | − | 0.807598i | \(-0.299233\pi\) | ||||
0.589734 | + | 0.807598i | \(0.299233\pi\) | |||||||
\(600\) | 49.6283 | 2.02607 | ||||||||
\(601\) | 29.7081 | 1.21182 | 0.605909 | − | 0.795534i | \(-0.292810\pi\) | ||||
0.605909 | + | 0.795534i | \(0.292810\pi\) | |||||||
\(602\) | −29.2699 | −1.19295 | ||||||||
\(603\) | −10.4775 | −0.426676 | ||||||||
\(604\) | −40.3359 | −1.64125 | ||||||||
\(605\) | −29.9929 | −1.21939 | ||||||||
\(606\) | −8.00950 | −0.325364 | ||||||||
\(607\) | 1.97026 | 0.0799704 | 0.0399852 | − | 0.999200i | \(-0.487269\pi\) | ||||
0.0399852 | + | 0.999200i | \(0.487269\pi\) | |||||||
\(608\) | −6.59983 | −0.267659 | ||||||||
\(609\) | −7.73676 | −0.313509 | ||||||||
\(610\) | −63.3138 | −2.56350 | ||||||||
\(611\) | −24.7420 | −1.00095 | ||||||||
\(612\) | 12.3387 | 0.498763 | ||||||||
\(613\) | −10.8390 | −0.437783 | −0.218892 | − | 0.975749i | \(-0.570244\pi\) | ||||
−0.218892 | + | 0.975749i | \(0.570244\pi\) | |||||||
\(614\) | 27.4240 | 1.10674 | ||||||||
\(615\) | −1.77972 | −0.0717653 | ||||||||
\(616\) | 10.4152 | 0.419641 | ||||||||
\(617\) | −29.8250 | −1.20071 | −0.600354 | − | 0.799734i | \(-0.704974\pi\) | ||||
−0.600354 | + | 0.799734i | \(0.704974\pi\) | |||||||
\(618\) | 5.06575 | 0.203775 | ||||||||
\(619\) | −40.0962 | −1.61160 | −0.805802 | − | 0.592185i | \(-0.798266\pi\) | ||||
−0.805802 | + | 0.592185i | \(0.798266\pi\) | |||||||
\(620\) | 133.550 | 5.36351 | ||||||||
\(621\) | −3.04813 | −0.122317 | ||||||||
\(622\) | −81.2602 | −3.25824 | ||||||||
\(623\) | −3.81355 | −0.152787 | ||||||||
\(624\) | −28.1591 | −1.12726 | ||||||||
\(625\) | −5.04135 | −0.201654 | ||||||||
\(626\) | −33.5292 | −1.34010 | ||||||||
\(627\) | 1.66252 | 0.0663947 | ||||||||
\(628\) | 35.5161 | 1.41725 | ||||||||
\(629\) | 18.5130 | 0.738162 | ||||||||
\(630\) | −9.08869 | −0.362102 | ||||||||
\(631\) | 36.5753 | 1.45604 | 0.728020 | − | 0.685556i | \(-0.240441\pi\) | ||||
0.728020 | + | 0.685556i | \(0.240441\pi\) | |||||||
\(632\) | 46.1210 | 1.83459 | ||||||||
\(633\) | 17.4286 | 0.692726 | ||||||||
\(634\) | 84.9301 | 3.37300 | ||||||||
\(635\) | 48.5548 | 1.92684 | ||||||||
\(636\) | −63.0138 | −2.49866 | ||||||||
\(637\) | 3.71849 | 0.147332 | ||||||||
\(638\) | 31.6521 | 1.25312 | ||||||||
\(639\) | 15.8202 | 0.625837 | ||||||||
\(640\) | 35.1440 | 1.38919 | ||||||||
\(641\) | 2.55550 | 0.100936 | 0.0504680 | − | 0.998726i | \(-0.483929\pi\) | ||||
0.0504680 | + | 0.998726i | \(0.483929\pi\) | |||||||
\(642\) | −42.9654 | −1.69571 | ||||||||
\(643\) | 15.2678 | 0.602102 | 0.301051 | − | 0.953608i | \(-0.402663\pi\) | ||||
0.301051 | + | 0.953608i | \(0.402663\pi\) | |||||||
\(644\) | 13.8562 | 0.546011 | ||||||||
\(645\) | −40.6406 | −1.60022 | ||||||||
\(646\) | −7.22015 | −0.284073 | ||||||||
\(647\) | 12.9048 | 0.507340 | 0.253670 | − | 0.967291i | \(-0.418362\pi\) | ||||
0.253670 | + | 0.967291i | \(0.418362\pi\) | |||||||
\(648\) | −6.51338 | −0.255870 | ||||||||
\(649\) | 12.3639 | 0.485326 | ||||||||
\(650\) | −72.4887 | −2.84324 | ||||||||
\(651\) | −8.27017 | −0.324133 | ||||||||
\(652\) | 94.1871 | 3.68865 | ||||||||
\(653\) | 11.3501 | 0.444164 | 0.222082 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222082 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(654\) | 39.8778 | 1.55935 | ||||||||
\(655\) | 18.5063 | 0.723100 | ||||||||
\(656\) | 3.79388 | 0.148126 | ||||||||
\(657\) | 1.90550 | 0.0743408 | ||||||||
\(658\) | 17.0235 | 0.663646 | ||||||||
\(659\) | −26.1746 | −1.01962 | −0.509809 | − | 0.860287i | \(-0.670284\pi\) | ||||
−0.509809 | + | 0.860287i | \(0.670284\pi\) | |||||||
\(660\) | 25.8222 | 1.00513 | ||||||||
\(661\) | 19.3722 | 0.753493 | 0.376746 | − | 0.926316i | \(-0.377043\pi\) | ||||
0.376746 | + | 0.926316i | \(0.377043\pi\) | |||||||
\(662\) | 0.0188435 | 0.000732372 0 | ||||||||
\(663\) | −10.0931 | −0.391985 | ||||||||
\(664\) | 104.886 | 4.07035 | ||||||||
\(665\) | 3.69339 | 0.143223 | ||||||||
\(666\) | −17.4501 | −0.676179 | ||||||||
\(667\) | 23.5827 | 0.913124 | ||||||||
\(668\) | −68.8992 | −2.66579 | ||||||||
\(669\) | −3.53637 | −0.136724 | ||||||||
\(670\) | 95.2267 | 3.67893 | ||||||||
\(671\) | −11.1393 | −0.430029 | ||||||||
\(672\) | 6.34787 | 0.244874 | ||||||||
\(673\) | 40.0119 | 1.54235 | 0.771173 | − | 0.636626i | \(-0.219670\pi\) | ||||
0.771173 | + | 0.636626i | \(0.219670\pi\) | |||||||
\(674\) | −37.7267 | −1.45318 | ||||||||
\(675\) | −7.61944 | −0.293272 | ||||||||
\(676\) | 3.76001 | 0.144616 | ||||||||
\(677\) | 29.8781 | 1.14831 | 0.574154 | − | 0.818747i | \(-0.305331\pi\) | ||||
0.574154 | + | 0.818747i | \(0.305331\pi\) | |||||||
\(678\) | −22.5076 | −0.864398 | ||||||||
\(679\) | −11.7860 | −0.452303 | ||||||||
\(680\) | −62.8038 | −2.40842 | ||||||||
\(681\) | 1.71958 | 0.0658944 | ||||||||
\(682\) | 33.8344 | 1.29558 | ||||||||
\(683\) | 34.2084 | 1.30895 | 0.654475 | − | 0.756084i | \(-0.272890\pi\) | ||||
0.654475 | + | 0.756084i | \(0.272890\pi\) | |||||||
\(684\) | 4.72624 | 0.180712 | ||||||||
\(685\) | 39.1603 | 1.49624 | ||||||||
\(686\) | −2.55848 | −0.0976831 | ||||||||
\(687\) | 7.53757 | 0.287576 | ||||||||
\(688\) | 86.6346 | 3.30291 | ||||||||
\(689\) | 51.5456 | 1.96373 | ||||||||
\(690\) | 27.7035 | 1.05466 | ||||||||
\(691\) | −3.38017 | −0.128588 | −0.0642938 | − | 0.997931i | \(-0.520479\pi\) | ||||
−0.0642938 | + | 0.997931i | \(0.520479\pi\) | |||||||
\(692\) | −55.7153 | −2.11798 | ||||||||
\(693\) | −1.59905 | −0.0607429 | ||||||||
\(694\) | 33.5594 | 1.27390 | ||||||||
\(695\) | −15.3275 | −0.581405 | ||||||||
\(696\) | 50.3924 | 1.91012 | ||||||||
\(697\) | 1.35985 | 0.0515081 | ||||||||
\(698\) | 65.5688 | 2.48182 | ||||||||
\(699\) | −11.8519 | −0.448282 | ||||||||
\(700\) | 34.6365 | 1.30914 | ||||||||
\(701\) | 41.8071 | 1.57903 | 0.789516 | − | 0.613729i | \(-0.210331\pi\) | ||||
0.789516 | + | 0.613729i | \(0.210331\pi\) | |||||||
\(702\) | 9.51366 | 0.359070 | ||||||||
\(703\) | 7.09124 | 0.267451 | ||||||||
\(704\) | −1.75166 | −0.0660183 | ||||||||
\(705\) | 23.6368 | 0.890213 | ||||||||
\(706\) | 61.7036 | 2.32225 | ||||||||
\(707\) | −3.13057 | −0.117737 | ||||||||
\(708\) | 35.1483 | 1.32095 | ||||||||
\(709\) | −46.8010 | −1.75765 | −0.878823 | − | 0.477147i | \(-0.841671\pi\) | ||||
−0.878823 | + | 0.477147i | \(0.841671\pi\) | |||||||
\(710\) | −143.785 | −5.39615 | ||||||||
\(711\) | −7.08096 | −0.265557 | ||||||||
\(712\) | 24.8391 | 0.930885 | ||||||||
\(713\) | 25.2086 | 0.944068 | ||||||||
\(714\) | 6.94450 | 0.259891 | ||||||||
\(715\) | −21.1226 | −0.789942 | ||||||||
\(716\) | −24.1739 | −0.903423 | ||||||||
\(717\) | −2.29552 | −0.0857279 | ||||||||
\(718\) | 16.5917 | 0.619197 | ||||||||
\(719\) | −38.3986 | −1.43203 | −0.716013 | − | 0.698087i | \(-0.754035\pi\) | ||||
−0.716013 | + | 0.698087i | \(0.754035\pi\) | |||||||
\(720\) | 26.9012 | 1.00255 | ||||||||
\(721\) | 1.97999 | 0.0737386 | ||||||||
\(722\) | 45.8454 | 1.70619 | ||||||||
\(723\) | 9.25898 | 0.344345 | ||||||||
\(724\) | 19.7993 | 0.735836 | ||||||||
\(725\) | 58.9498 | 2.18934 | ||||||||
\(726\) | −21.6013 | −0.801700 | ||||||||
\(727\) | −50.5319 | −1.87412 | −0.937061 | − | 0.349165i | \(-0.886465\pi\) | ||||
−0.937061 | + | 0.349165i | \(0.886465\pi\) | |||||||
\(728\) | −24.2199 | −0.897649 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.3185 | −0.640988 | ||||||||
\(731\) | 31.0527 | 1.14853 | ||||||||
\(732\) | −31.6671 | −1.17045 | ||||||||
\(733\) | −37.5500 | −1.38694 | −0.693471 | − | 0.720485i | \(-0.743919\pi\) | ||||
−0.693471 | + | 0.720485i | \(0.743919\pi\) | |||||||
\(734\) | −63.4831 | −2.34320 | ||||||||
\(735\) | −3.55238 | −0.131032 | ||||||||
\(736\) | −19.3491 | −0.713219 | ||||||||
\(737\) | 16.7540 | 0.617143 | ||||||||
\(738\) | −1.28178 | −0.0471830 | ||||||||
\(739\) | 14.6248 | 0.537983 | 0.268992 | − | 0.963143i | \(-0.413310\pi\) | ||||
0.268992 | + | 0.963143i | \(0.413310\pi\) | |||||||
\(740\) | 110.141 | 4.04885 | ||||||||
\(741\) | −3.86608 | −0.142024 | ||||||||
\(742\) | −35.4655 | −1.30198 | ||||||||
\(743\) | 46.2516 | 1.69681 | 0.848403 | − | 0.529351i | \(-0.177565\pi\) | ||||
0.848403 | + | 0.529351i | \(0.177565\pi\) | |||||||
\(744\) | 53.8667 | 1.97485 | ||||||||
\(745\) | −8.17981 | −0.299685 | ||||||||
\(746\) | 13.9535 | 0.510875 | ||||||||
\(747\) | −16.1031 | −0.589182 | ||||||||
\(748\) | −19.7302 | −0.721409 | ||||||||
\(749\) | −16.7934 | −0.613616 | ||||||||
\(750\) | 23.8073 | 0.869319 | ||||||||
\(751\) | 31.0900 | 1.13449 | 0.567245 | − | 0.823549i | \(-0.308009\pi\) | ||||
0.567245 | + | 0.823549i | \(0.308009\pi\) | |||||||
\(752\) | −50.3872 | −1.83743 | ||||||||
\(753\) | 20.0498 | 0.730654 | ||||||||
\(754\) | −73.6049 | −2.68053 | ||||||||
\(755\) | −31.5211 | −1.14717 | ||||||||
\(756\) | −4.54580 | −0.165329 | ||||||||
\(757\) | 42.2710 | 1.53637 | 0.768184 | − | 0.640230i | \(-0.221161\pi\) | ||||
0.768184 | + | 0.640230i | \(0.221161\pi\) | |||||||
\(758\) | 14.9468 | 0.542892 | ||||||||
\(759\) | 4.87411 | 0.176919 | ||||||||
\(760\) | −24.0564 | −0.872619 | ||||||||
\(761\) | −8.40649 | −0.304735 | −0.152368 | − | 0.988324i | \(-0.548690\pi\) | ||||
−0.152368 | + | 0.988324i | \(0.548690\pi\) | |||||||
\(762\) | 34.9698 | 1.26682 | ||||||||
\(763\) | 15.5866 | 0.564271 | ||||||||
\(764\) | 21.6496 | 0.783256 | ||||||||
\(765\) | 9.64228 | 0.348617 | ||||||||
\(766\) | 2.55848 | 0.0924415 | ||||||||
\(767\) | −28.7515 | −1.03816 | ||||||||
\(768\) | 27.5021 | 0.992397 | ||||||||
\(769\) | −26.7663 | −0.965217 | −0.482608 | − | 0.875836i | \(-0.660311\pi\) | ||||
−0.482608 | + | 0.875836i | \(0.660311\pi\) | |||||||
\(770\) | 14.5333 | 0.523743 | ||||||||
\(771\) | 10.3896 | 0.374171 | ||||||||
\(772\) | 31.2690 | 1.12539 | ||||||||
\(773\) | 12.0509 | 0.433441 | 0.216721 | − | 0.976234i | \(-0.430464\pi\) | ||||
0.216721 | + | 0.976234i | \(0.430464\pi\) | |||||||
\(774\) | −29.2699 | −1.05208 | ||||||||
\(775\) | 63.0140 | 2.26353 | ||||||||
\(776\) | 76.7664 | 2.75575 | ||||||||
\(777\) | −6.82052 | −0.244685 | ||||||||
\(778\) | 78.9978 | 2.83221 | ||||||||
\(779\) | 0.520879 | 0.0186624 | ||||||||
\(780\) | −60.0478 | −2.15005 | ||||||||
\(781\) | −25.2973 | −0.905207 | ||||||||
\(782\) | −21.1678 | −0.756957 | ||||||||
\(783\) | −7.73676 | −0.276489 | ||||||||
\(784\) | 7.57272 | 0.270454 | ||||||||
\(785\) | 27.7546 | 0.990603 | ||||||||
\(786\) | 13.3285 | 0.475411 | ||||||||
\(787\) | 1.12847 | 0.0402256 | 0.0201128 | − | 0.999798i | \(-0.493597\pi\) | ||||
0.0201128 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(788\) | −83.4475 | −2.97270 | ||||||||
\(789\) | 26.4874 | 0.942975 | ||||||||
\(790\) | 64.3567 | 2.28971 | ||||||||
\(791\) | −8.79725 | −0.312794 | ||||||||
\(792\) | 10.4152 | 0.370089 | ||||||||
\(793\) | 25.9038 | 0.919870 | ||||||||
\(794\) | −76.7162 | −2.72256 | ||||||||
\(795\) | −49.2431 | −1.74647 | ||||||||
\(796\) | −5.93320 | −0.210297 | ||||||||
\(797\) | 40.2066 | 1.42419 | 0.712095 | − | 0.702083i | \(-0.247746\pi\) | ||||
0.712095 | + | 0.702083i | \(0.247746\pi\) | |||||||
\(798\) | 2.66003 | 0.0941640 | ||||||||
\(799\) | −18.0604 | −0.638932 | ||||||||
\(800\) | −48.3672 | −1.71004 | ||||||||
\(801\) | −3.81355 | −0.134745 | ||||||||
\(802\) | 88.4350 | 3.12275 | ||||||||
\(803\) | −3.04700 | −0.107526 | ||||||||
\(804\) | 47.6286 | 1.67973 | ||||||||
\(805\) | 10.8281 | 0.381642 | ||||||||
\(806\) | −78.6796 | −2.77137 | ||||||||
\(807\) | 28.3791 | 0.998991 | ||||||||
\(808\) | 20.3906 | 0.717339 | ||||||||
\(809\) | 46.7869 | 1.64494 | 0.822469 | − | 0.568809i | \(-0.192596\pi\) | ||||
0.822469 | + | 0.568809i | \(0.192596\pi\) | |||||||
\(810\) | −9.08869 | −0.319344 | ||||||||
\(811\) | 30.5910 | 1.07419 | 0.537097 | − | 0.843520i | \(-0.319521\pi\) | ||||
0.537097 | + | 0.843520i | \(0.319521\pi\) | |||||||
\(812\) | 35.1698 | 1.23422 | ||||||||
\(813\) | 26.8832 | 0.942836 | ||||||||
\(814\) | 27.9036 | 0.978022 | ||||||||
\(815\) | 73.6039 | 2.57823 | ||||||||
\(816\) | −20.5547 | −0.719559 | ||||||||
\(817\) | 11.8945 | 0.416134 | ||||||||
\(818\) | 23.3020 | 0.814734 | ||||||||
\(819\) | 3.71849 | 0.129934 | ||||||||
\(820\) | 8.09026 | 0.282524 | ||||||||
\(821\) | −48.7632 | −1.70185 | −0.850924 | − | 0.525289i | \(-0.823957\pi\) | ||||
−0.850924 | + | 0.525289i | \(0.823957\pi\) | |||||||
\(822\) | 28.2038 | 0.983719 | ||||||||
\(823\) | −1.88548 | −0.0657237 | −0.0328619 | − | 0.999460i | \(-0.510462\pi\) | ||||
−0.0328619 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(824\) | −12.8964 | −0.449268 | ||||||||
\(825\) | 12.1839 | 0.424188 | ||||||||
\(826\) | 19.7822 | 0.688312 | ||||||||
\(827\) | −43.7034 | −1.51972 | −0.759859 | − | 0.650088i | \(-0.774732\pi\) | ||||
−0.759859 | + | 0.650088i | \(0.774732\pi\) | |||||||
\(828\) | 13.8562 | 0.481536 | ||||||||
\(829\) | −21.0053 | −0.729543 | −0.364771 | − | 0.931097i | \(-0.618853\pi\) | ||||
−0.364771 | + | 0.931097i | \(0.618853\pi\) | |||||||
\(830\) | 146.356 | 5.08010 | ||||||||
\(831\) | −19.2208 | −0.666764 | ||||||||
\(832\) | 4.07338 | 0.141219 | ||||||||
\(833\) | 2.71431 | 0.0940453 | ||||||||
\(834\) | −11.0391 | −0.382252 | ||||||||
\(835\) | −53.8423 | −1.86329 | ||||||||
\(836\) | −7.55749 | −0.261381 | ||||||||
\(837\) | −8.27017 | −0.285859 | ||||||||
\(838\) | −6.57915 | −0.227273 | ||||||||
\(839\) | 48.9656 | 1.69048 | 0.845240 | − | 0.534388i | \(-0.179458\pi\) | ||||
0.845240 | + | 0.534388i | \(0.179458\pi\) | |||||||
\(840\) | 23.1380 | 0.798338 | ||||||||
\(841\) | 30.8575 | 1.06405 | ||||||||
\(842\) | 33.0873 | 1.14026 | ||||||||
\(843\) | −16.0403 | −0.552459 | ||||||||
\(844\) | −79.2271 | −2.72711 | ||||||||
\(845\) | 2.93832 | 0.101081 | ||||||||
\(846\) | 17.0235 | 0.585281 | ||||||||
\(847\) | −8.44304 | −0.290106 | ||||||||
\(848\) | 104.973 | 3.60478 | ||||||||
\(849\) | −28.0068 | −0.961190 | ||||||||
\(850\) | −52.9132 | −1.81491 | ||||||||
\(851\) | 20.7898 | 0.712666 | ||||||||
\(852\) | −71.9154 | −2.46378 | ||||||||
\(853\) | −23.3560 | −0.799694 | −0.399847 | − | 0.916582i | \(-0.630937\pi\) | ||||
−0.399847 | + | 0.916582i | \(0.630937\pi\) | |||||||
\(854\) | −17.8229 | −0.609887 | ||||||||
\(855\) | 3.69339 | 0.126311 | ||||||||
\(856\) | 109.382 | 3.73858 | ||||||||
\(857\) | 11.4905 | 0.392506 | 0.196253 | − | 0.980553i | \(-0.437123\pi\) | ||||
0.196253 | + | 0.980553i | \(0.437123\pi\) | |||||||
\(858\) | −15.2128 | −0.519357 | ||||||||
\(859\) | −14.7448 | −0.503087 | −0.251544 | − | 0.967846i | \(-0.580938\pi\) | ||||
−0.251544 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(860\) | 184.744 | 6.29972 | ||||||||
\(861\) | −0.500993 | −0.0170738 | ||||||||
\(862\) | 40.7866 | 1.38920 | ||||||||
\(863\) | −19.3803 | −0.659712 | −0.329856 | − | 0.944031i | \(-0.607000\pi\) | ||||
−0.329856 | + | 0.944031i | \(0.607000\pi\) | |||||||
\(864\) | 6.34787 | 0.215959 | ||||||||
\(865\) | −43.5396 | −1.48039 | ||||||||
\(866\) | −89.8957 | −3.05478 | ||||||||
\(867\) | 9.63252 | 0.327137 | ||||||||
\(868\) | 37.5946 | 1.27604 | ||||||||
\(869\) | 11.3228 | 0.384100 | ||||||||
\(870\) | 70.3170 | 2.38397 | ||||||||
\(871\) | −38.9604 | −1.32012 | ||||||||
\(872\) | −101.521 | −3.43794 | ||||||||
\(873\) | −11.7860 | −0.398894 | ||||||||
\(874\) | −8.10812 | −0.274261 | ||||||||
\(875\) | 9.30525 | 0.314575 | ||||||||
\(876\) | −8.66204 | −0.292663 | ||||||||
\(877\) | 18.5870 | 0.627639 | 0.313820 | − | 0.949483i | \(-0.398391\pi\) | ||||
0.313820 | + | 0.949483i | \(0.398391\pi\) | |||||||
\(878\) | 63.5959 | 2.14626 | ||||||||
\(879\) | −9.16667 | −0.309184 | ||||||||
\(880\) | −43.0164 | −1.45008 | ||||||||
\(881\) | 13.9901 | 0.471337 | 0.235669 | − | 0.971833i | \(-0.424272\pi\) | ||||
0.235669 | + | 0.971833i | \(0.424272\pi\) | |||||||
\(882\) | −2.55848 | −0.0861484 | ||||||||
\(883\) | −37.2229 | −1.25265 | −0.626325 | − | 0.779562i | \(-0.715442\pi\) | ||||
−0.626325 | + | 0.779562i | \(0.715442\pi\) | |||||||
\(884\) | 45.8814 | 1.54316 | ||||||||
\(885\) | 27.4672 | 0.923298 | ||||||||
\(886\) | −46.0152 | −1.54591 | ||||||||
\(887\) | 23.2403 | 0.780333 | 0.390166 | − | 0.920744i | \(-0.372417\pi\) | ||||
0.390166 | + | 0.920744i | \(0.372417\pi\) | |||||||
\(888\) | 44.4246 | 1.49079 | ||||||||
\(889\) | 13.6682 | 0.458417 | ||||||||
\(890\) | 34.6602 | 1.16181 | ||||||||
\(891\) | −1.59905 | −0.0535702 | ||||||||
\(892\) | 16.0757 | 0.538253 | ||||||||
\(893\) | −6.91788 | −0.231498 | ||||||||
\(894\) | −5.89121 | −0.197032 | ||||||||
\(895\) | −18.8911 | −0.631459 | ||||||||
\(896\) | 9.89308 | 0.330505 | ||||||||
\(897\) | −11.3344 | −0.378446 | ||||||||
\(898\) | −44.0209 | −1.46900 | ||||||||
\(899\) | 63.9843 | 2.13400 | ||||||||
\(900\) | 34.6365 | 1.15455 | ||||||||
\(901\) | 37.6257 | 1.25349 | ||||||||
\(902\) | 2.04963 | 0.0682452 | ||||||||
\(903\) | −11.4404 | −0.380711 | ||||||||
\(904\) | 57.2998 | 1.90576 | ||||||||
\(905\) | 15.4725 | 0.514323 | ||||||||
\(906\) | −22.7019 | −0.754221 | ||||||||
\(907\) | −16.7305 | −0.555528 | −0.277764 | − | 0.960649i | \(-0.589593\pi\) | ||||
−0.277764 | + | 0.960649i | \(0.589593\pi\) | |||||||
\(908\) | −7.81687 | −0.259412 | ||||||||
\(909\) | −3.13057 | −0.103835 | ||||||||
\(910\) | −33.7962 | −1.12033 | ||||||||
\(911\) | −53.5197 | −1.77319 | −0.886593 | − | 0.462551i | \(-0.846934\pi\) | ||||
−0.886593 | + | 0.462551i | \(0.846934\pi\) | |||||||
\(912\) | −7.87330 | −0.260711 | ||||||||
\(913\) | 25.7497 | 0.852190 | ||||||||
\(914\) | 55.1136 | 1.82299 | ||||||||
\(915\) | −24.7467 | −0.818100 | ||||||||
\(916\) | −34.2643 | −1.13213 | ||||||||
\(917\) | 5.20953 | 0.172034 | ||||||||
\(918\) | 6.94450 | 0.229203 | ||||||||
\(919\) | −20.7607 | −0.684833 | −0.342416 | − | 0.939548i | \(-0.611245\pi\) | ||||
−0.342416 | + | 0.939548i | \(0.611245\pi\) | |||||||
\(920\) | −70.5277 | −2.32523 | ||||||||
\(921\) | 10.7189 | 0.353199 | ||||||||
\(922\) | 13.3044 | 0.438157 | ||||||||
\(923\) | 58.8271 | 1.93632 | ||||||||
\(924\) | 7.26897 | 0.239131 | ||||||||
\(925\) | 51.9685 | 1.70871 | ||||||||
\(926\) | 2.46036 | 0.0808523 | ||||||||
\(927\) | 1.97999 | 0.0650313 | ||||||||
\(928\) | −49.1120 | −1.61218 | ||||||||
\(929\) | −41.9540 | −1.37647 | −0.688233 | − | 0.725489i | \(-0.741614\pi\) | ||||
−0.688233 | + | 0.725489i | \(0.741614\pi\) | |||||||
\(930\) | 75.1650 | 2.46476 | ||||||||
\(931\) | 1.03969 | 0.0340746 | ||||||||
\(932\) | 53.8766 | 1.76479 | ||||||||
\(933\) | −31.7612 | −1.03981 | ||||||||
\(934\) | −21.9055 | −0.716771 | ||||||||
\(935\) | −15.4185 | −0.504238 | ||||||||
\(936\) | −24.2199 | −0.791652 | ||||||||
\(937\) | −43.6871 | −1.42719 | −0.713597 | − | 0.700556i | \(-0.752935\pi\) | ||||
−0.713597 | + | 0.700556i | \(0.752935\pi\) | |||||||
\(938\) | 26.8064 | 0.875261 | ||||||||
\(939\) | −13.1052 | −0.427671 | ||||||||
\(940\) | −107.448 | −3.50457 | ||||||||
\(941\) | −7.98130 | −0.260183 | −0.130091 | − | 0.991502i | \(-0.541527\pi\) | ||||
−0.130091 | + | 0.991502i | \(0.541527\pi\) | |||||||
\(942\) | 19.9892 | 0.651284 | ||||||||
\(943\) | 1.52709 | 0.0497290 | ||||||||
\(944\) | −58.5525 | −1.90572 | ||||||||
\(945\) | −3.55238 | −0.115559 | ||||||||
\(946\) | 46.8040 | 1.52173 | ||||||||
\(947\) | −47.8121 | −1.55368 | −0.776842 | − | 0.629695i | \(-0.783180\pi\) | ||||
−0.776842 | + | 0.629695i | \(0.783180\pi\) | |||||||
\(948\) | 32.1886 | 1.04544 | ||||||||
\(949\) | 7.08559 | 0.230008 | ||||||||
\(950\) | −20.2679 | −0.657578 | ||||||||
\(951\) | 33.1956 | 1.07644 | ||||||||
\(952\) | −17.6793 | −0.572990 | ||||||||
\(953\) | −29.0952 | −0.942484 | −0.471242 | − | 0.882004i | \(-0.656194\pi\) | ||||
−0.471242 | + | 0.882004i | \(0.656194\pi\) | |||||||
\(954\) | −35.4655 | −1.14824 | ||||||||
\(955\) | 16.9184 | 0.547467 | ||||||||
\(956\) | 10.4350 | 0.337492 | ||||||||
\(957\) | 12.3715 | 0.399913 | ||||||||
\(958\) | 73.4132 | 2.37187 | ||||||||
\(959\) | 11.0237 | 0.355972 | ||||||||
\(960\) | −3.89143 | −0.125595 | ||||||||
\(961\) | 37.3957 | 1.20631 | ||||||||
\(962\) | −64.8881 | −2.09208 | ||||||||
\(963\) | −16.7934 | −0.541159 | ||||||||
\(964\) | −42.0895 | −1.35561 | ||||||||
\(965\) | 24.4356 | 0.786610 | ||||||||
\(966\) | 7.79857 | 0.250915 | ||||||||
\(967\) | −4.60559 | −0.148106 | −0.0740529 | − | 0.997254i | \(-0.523593\pi\) | ||||
−0.0740529 | + | 0.997254i | \(0.523593\pi\) | |||||||
\(968\) | 54.9927 | 1.76753 | ||||||||
\(969\) | −2.82205 | −0.0906573 | ||||||||
\(970\) | 107.119 | 3.43938 | ||||||||
\(971\) | −30.6355 | −0.983139 | −0.491570 | − | 0.870838i | \(-0.663577\pi\) | ||||
−0.491570 | + | 0.870838i | \(0.663577\pi\) | |||||||
\(972\) | −4.54580 | −0.145807 | ||||||||
\(973\) | −4.31470 | −0.138323 | ||||||||
\(974\) | −110.696 | −3.54693 | ||||||||
\(975\) | −28.3328 | −0.907375 | ||||||||
\(976\) | 52.7532 | 1.68859 | ||||||||
\(977\) | 16.5895 | 0.530746 | 0.265373 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265373 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(978\) | 53.0106 | 1.69509 | ||||||||
\(979\) | 6.09806 | 0.194895 | ||||||||
\(980\) | 16.1484 | 0.515843 | ||||||||
\(981\) | 15.5866 | 0.497640 | ||||||||
\(982\) | 15.8756 | 0.506610 | ||||||||
\(983\) | 15.3648 | 0.490060 | 0.245030 | − | 0.969515i | \(-0.421202\pi\) | ||||
0.245030 | + | 0.969515i | \(0.421202\pi\) | |||||||
\(984\) | 3.26316 | 0.104026 | ||||||||
\(985\) | −65.2113 | −2.07780 | ||||||||
\(986\) | −53.7279 | −1.71105 | ||||||||
\(987\) | 6.65378 | 0.211792 | ||||||||
\(988\) | 17.5745 | 0.559118 | ||||||||
\(989\) | 34.8717 | 1.10886 | ||||||||
\(990\) | 14.5333 | 0.461898 | ||||||||
\(991\) | 28.3203 | 0.899625 | 0.449813 | − | 0.893123i | \(-0.351491\pi\) | ||||
0.449813 | + | 0.893123i | \(0.351491\pi\) | |||||||
\(992\) | −52.4980 | −1.66681 | ||||||||
\(993\) | 0.00736511 | 0.000233725 0 | ||||||||
\(994\) | −40.4756 | −1.28381 | ||||||||
\(995\) | −4.63659 | −0.146990 | ||||||||
\(996\) | 73.2016 | 2.31948 | ||||||||
\(997\) | −14.4552 | −0.457800 | −0.228900 | − | 0.973450i | \(-0.573513\pi\) | ||||
−0.228900 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(998\) | 75.0114 | 2.37444 | ||||||||
\(999\) | −6.82052 | −0.215792 |
(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 | 8043.2.a.t.1.4 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.4 | ✓ | 52 | 1.1 | even | 1 | trivial |