Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1261,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1261");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.l (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1261.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1261 |
Dual form | 1710.2.l.n.1531.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44949 | −0.547856 | −0.273928 | − | 0.961750i | \(-0.588323\pi\) | ||||
−0.273928 | + | 0.961750i | \(0.588323\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | + | 4.24264i | −0.679366 | + | 1.17670i | 0.295806 | + | 0.955248i | \(0.404412\pi\) |
−0.975172 | + | 0.221449i | \(0.928921\pi\) | |||||||
\(14\) | −0.724745 | − | 1.25529i | −0.193696 | − | 0.335492i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.775255 | − | 1.34278i | −0.188027 | − | 0.325672i | 0.756565 | − | 0.653918i | \(-0.226876\pi\) |
−0.944592 | + | 0.328246i | \(0.893543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17423 | + | 1.25529i | −0.957635 | + | 0.287984i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | −2.94949 | + | 5.10867i | −0.615011 | + | 1.06523i | 0.375371 | + | 0.926874i | \(0.377515\pi\) |
−0.990383 | + | 0.138356i | \(0.955818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −4.89898 | −0.960769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.724745 | − | 1.25529i | 0.136964 | − | 0.237228i | ||||
\(29\) | 4.67423 | − | 8.09601i | 0.867984 | − | 1.50339i | 0.00392972 | − | 0.999992i | \(-0.498749\pi\) |
0.864054 | − | 0.503399i | \(-0.167918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.898979 | −0.161461 | −0.0807307 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807307 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.775255 | − | 1.34278i | 0.132955 | − | 0.230285i | ||||
\(35\) | −0.724745 | − | 1.25529i | −0.122504 | − | 0.212184i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.89898 | −1.62738 | −0.813691 | − | 0.581298i | \(-0.802545\pi\) | ||||
−0.813691 | + | 0.581298i | \(0.802545\pi\) | |||||||
\(38\) | −3.17423 | − | 2.98735i | −0.514929 | − | 0.484611i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | 2.17423 | + | 3.76588i | 0.339558 | + | 0.588132i | 0.984350 | − | 0.176226i | \(-0.0563890\pi\) |
−0.644791 | + | 0.764359i | \(0.723056\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.89898 | + | 10.2173i | 0.899586 | + | 1.55813i | 0.828024 | + | 0.560692i | \(0.189465\pi\) |
0.0715617 | + | 0.997436i | \(0.477202\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.89898 | −0.869757 | ||||||||
\(47\) | −0.550510 | + | 0.953512i | −0.0803002 | + | 0.139084i | −0.903379 | − | 0.428843i | \(-0.858921\pi\) |
0.823079 | + | 0.567927i | \(0.192255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.44949 | − | 4.24264i | −0.339683 | − | 0.588348i | ||||
\(53\) | −3.72474 | + | 6.45145i | −0.511633 | + | 0.886174i | 0.488276 | + | 0.872689i | \(0.337626\pi\) |
−0.999909 | + | 0.0134852i | \(0.995707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | 1.44949 | 0.193696 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.34847 | 1.22751 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.22474 | + | 10.7816i | −0.796997 | + | 1.38044i | 0.124566 | + | 0.992211i | \(0.460246\pi\) |
−0.921563 | + | 0.388228i | \(0.873087\pi\) | |||||||
\(62\) | −0.449490 | − | 0.778539i | −0.0570853 | − | 0.0988746i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.89898 | −0.607644 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.67423 | − | 6.36396i | 0.448879 | − | 0.777482i | −0.549434 | − | 0.835537i | \(-0.685157\pi\) |
0.998313 | + | 0.0580554i | \(0.0184900\pi\) | |||||||
\(68\) | 1.55051 | 0.188027 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.724745 | − | 1.25529i | 0.0866236 | − | 0.150036i | ||||
\(71\) | −1.67423 | − | 2.89986i | −0.198695 | − | 0.344150i | 0.749410 | − | 0.662106i | \(-0.230337\pi\) |
−0.948106 | + | 0.317956i | \(0.897004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.22474 | − | 9.04952i | −0.611510 | − | 1.05917i | −0.990986 | − | 0.133965i | \(-0.957229\pi\) |
0.379476 | − | 0.925202i | \(-0.376104\pi\) | |||||||
\(74\) | −4.94949 | − | 8.57277i | −0.575366 | − | 0.996564i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | − | 4.24264i | 0.114708 | − | 0.486664i | ||||
\(77\) | −4.34847 | −0.495554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.44949 | − | 5.97469i | −0.388098 | − | 0.672205i | 0.604096 | − | 0.796912i | \(-0.293534\pi\) |
−0.992194 | + | 0.124706i | \(0.960201\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.17423 | + | 3.76588i | −0.240104 | + | 0.415872i | ||||
\(83\) | −11.7980 | −1.29499 | −0.647497 | − | 0.762068i | \(-0.724184\pi\) | ||||
−0.647497 | + | 0.762068i | \(0.724184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.775255 | − | 1.34278i | 0.0840882 | − | 0.145645i | ||||
\(86\) | −5.89898 | + | 10.2173i | −0.636103 | + | 1.10176i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −2.72474 | + | 4.71940i | −0.288822 | + | 0.500255i | −0.973529 | − | 0.228564i | \(-0.926597\pi\) |
0.684707 | + | 0.728819i | \(0.259930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.55051 | − | 6.14966i | 0.372195 | − | 0.644660i | ||||
\(92\) | −2.94949 | − | 5.10867i | −0.307506 | − | 0.532615i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.10102 | −0.113562 | ||||||||
\(95\) | −3.17423 | − | 2.98735i | −0.325670 | − | 0.306495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.22474 | + | 15.9777i | 0.936631 | + | 1.62229i | 0.771699 | + | 0.635987i | \(0.219407\pi\) |
0.164931 | + | 0.986305i | \(0.447260\pi\) | |||||||
\(98\) | −2.44949 | − | 4.24264i | −0.247436 | − | 0.428571i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −0.550510 | + | 0.953512i | −0.0547778 | + | 0.0948780i | −0.892114 | − | 0.451810i | \(-0.850778\pi\) |
0.837336 | + | 0.546688i | \(0.184112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2474 | 1.10824 | 0.554122 | − | 0.832435i | \(-0.313054\pi\) | ||||
0.554122 | + | 0.832435i | \(0.313054\pi\) | |||||||
\(104\) | 2.44949 | − | 4.24264i | 0.240192 | − | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.44949 | −0.723558 | ||||||||
\(107\) | 2.65153 | 0.256333 | 0.128167 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128167 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.674235 | − | 1.16781i | −0.0645800 | − | 0.111856i | 0.831928 | − | 0.554884i | \(-0.187237\pi\) |
−0.896508 | + | 0.443028i | \(0.853904\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.724745 | + | 1.25529i | 0.0684820 | + | 0.118614i | ||||
\(113\) | 9.55051 | 0.898436 | 0.449218 | − | 0.893422i | \(-0.351703\pi\) | ||||
0.449218 | + | 0.893422i | \(0.351703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.89898 | −0.550083 | ||||||||
\(116\) | 4.67423 | + | 8.09601i | 0.433992 | + | 0.751696i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | − | 5.19615i | 0.276172 | − | 0.478345i | ||||
\(119\) | 1.12372 | + | 1.94635i | 0.103012 | + | 0.178421i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −12.4495 | −1.12712 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.449490 | − | 0.778539i | 0.0403654 | − | 0.0699149i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.174235 | − | 0.301783i | 0.0154608 | − | 0.0267789i | −0.858191 | − | 0.513330i | \(-0.828412\pi\) |
0.873652 | + | 0.486551i | \(0.161745\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.44949 | − | 4.24264i | −0.214834 | − | 0.372104i | ||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.05051 | − | 1.81954i | 0.524646 | − | 0.157774i | ||||
\(134\) | 7.34847 | 0.634811 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.775255 | + | 1.34278i | 0.0664776 | + | 0.115143i | ||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.34847 | − | 12.7279i | 0.623289 | − | 1.07957i | −0.365580 | − | 0.930780i | \(-0.619129\pi\) |
0.988869 | − | 0.148788i | \(-0.0475373\pi\) | |||||||
\(140\) | 1.44949 | 0.122504 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.67423 | − | 2.89986i | 0.140499 | − | 0.243351i | ||||
\(143\) | −7.34847 | + | 12.7279i | −0.614510 | + | 1.06436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.34847 | 0.776348 | ||||||||
\(146\) | 5.22474 | − | 9.04952i | 0.432403 | − | 0.748944i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.94949 | − | 8.57277i | 0.406846 | − | 0.704677i | ||||
\(149\) | 6.77526 | + | 11.7351i | 0.555051 | + | 0.961376i | 0.997900 | + | 0.0647795i | \(0.0206344\pi\) |
−0.442849 | + | 0.896596i | \(0.646032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.65153 | −0.378536 | −0.189268 | − | 0.981925i | \(-0.560612\pi\) | ||||
−0.189268 | + | 0.981925i | \(0.560612\pi\) | |||||||
\(152\) | 4.17423 | − | 1.25529i | 0.338575 | − | 0.101818i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.17423 | − | 3.76588i | −0.175205 | − | 0.303464i | ||||
\(155\) | −0.449490 | − | 0.778539i | −0.0361039 | − | 0.0625338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3990 | − | 18.0116i | −0.829929 | − | 1.43748i | −0.898093 | − | 0.439805i | \(-0.855048\pi\) |
0.0681644 | − | 0.997674i | \(-0.478286\pi\) | |||||||
\(158\) | 3.44949 | − | 5.97469i | 0.274427 | − | 0.475321i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.27526 | − | 7.40496i | 0.336937 | − | 0.583593i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6969 | 1.30781 | 0.653903 | − | 0.756579i | \(-0.273131\pi\) | ||||
0.653903 | + | 0.756579i | \(0.273131\pi\) | |||||||
\(164\) | −4.34847 | −0.339558 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.89898 | − | 10.2173i | −0.457850 | − | 0.793019i | ||||
\(167\) | −4.84847 | + | 8.39780i | −0.375186 | + | 0.649841i | −0.990355 | − | 0.138554i | \(-0.955754\pi\) |
0.615169 | + | 0.788395i | \(0.289088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50000 | − | 9.52628i | −0.423077 | − | 0.732791i | ||||
\(170\) | 1.55051 | 0.118919 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.7980 | −0.899586 | ||||||||
\(173\) | −2.27526 | − | 3.94086i | −0.172984 | − | 0.299618i | 0.766477 | − | 0.642271i | \(-0.222008\pi\) |
−0.939462 | + | 0.342653i | \(0.888674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.724745 | − | 1.25529i | 0.0547856 | − | 0.0948914i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.44949 | −0.408457 | ||||||||
\(179\) | 20.7980 | 1.55451 | 0.777256 | − | 0.629184i | \(-0.216611\pi\) | ||||
0.777256 | + | 0.629184i | \(0.216611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.57321 | + | 14.8492i | −0.637242 | + | 1.10374i | 0.348793 | + | 0.937200i | \(0.386591\pi\) |
−0.986035 | + | 0.166536i | \(0.946742\pi\) | |||||||
\(182\) | 7.10102 | 0.526363 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.94949 | − | 5.10867i | 0.217439 | − | 0.376616i | ||||
\(185\) | −4.94949 | − | 8.57277i | −0.363894 | − | 0.630282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.32577 | − | 4.02834i | −0.170077 | − | 0.294582i | ||||
\(188\) | −0.550510 | − | 0.953512i | −0.0401501 | − | 0.0695420i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.00000 | − | 4.24264i | 0.0725476 | − | 0.307794i | ||||
\(191\) | 3.79796 | 0.274811 | 0.137405 | − | 0.990515i | \(-0.456124\pi\) | ||||
0.137405 | + | 0.990515i | \(0.456124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6742 | + | 18.4883i | 0.768348 | + | 1.33082i | 0.938458 | + | 0.345393i | \(0.112254\pi\) |
−0.170110 | + | 0.985425i | \(0.554412\pi\) | |||||||
\(194\) | −9.22474 | + | 15.9777i | −0.662298 | + | 1.14713i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.44949 | − | 4.24264i | 0.174964 | − | 0.303046i | ||||
\(197\) | −6.55051 | −0.466705 | −0.233352 | − | 0.972392i | \(-0.574970\pi\) | ||||
−0.233352 | + | 0.972392i | \(0.574970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.22474 | + | 5.58542i | −0.228596 | + | 0.395940i | −0.957392 | − | 0.288791i | \(-0.906747\pi\) |
0.728796 | + | 0.684731i | \(0.240080\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.10102 | −0.0774675 | ||||||||
\(203\) | −6.77526 | + | 11.7351i | −0.475530 | + | 0.823642i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.17423 | + | 3.76588i | −0.151855 | + | 0.263021i | ||||
\(206\) | 5.62372 | + | 9.74058i | 0.391823 | + | 0.678658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89898 | 0.339683 | ||||||||
\(209\) | −12.5227 | + | 3.76588i | −0.866214 | + | 0.260492i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1742 | + | 22.8184i | 0.906952 | + | 1.57089i | 0.818276 | + | 0.574826i | \(0.194930\pi\) |
0.0886760 | + | 0.996061i | \(0.471736\pi\) | |||||||
\(212\) | −3.72474 | − | 6.45145i | −0.255817 | − | 0.443087i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.32577 | + | 2.29629i | 0.0906275 | + | 0.156971i | ||||
\(215\) | −5.89898 | + | 10.2173i | −0.402307 | + | 0.696816i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.30306 | 0.0884576 | ||||||||
\(218\) | 0.674235 | − | 1.16781i | 0.0456649 | − | 0.0790940i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 7.59592 | 0.510957 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.72474 | + | 2.98735i | 0.115497 | + | 0.200047i | 0.917978 | − | 0.396630i | \(-0.129820\pi\) |
−0.802481 | + | 0.596678i | \(0.796487\pi\) | |||||||
\(224\) | −0.724745 | + | 1.25529i | −0.0484241 | + | 0.0838729i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.77526 | + | 8.27098i | 0.317645 | + | 0.550178i | ||||
\(227\) | 11.3485 | 0.753224 | 0.376612 | − | 0.926371i | \(-0.377089\pi\) | ||||
0.376612 | + | 0.926371i | \(0.377089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.69694 | 0.574710 | 0.287355 | − | 0.957824i | \(-0.407224\pi\) | ||||
0.287355 | + | 0.957824i | \(0.407224\pi\) | |||||||
\(230\) | −2.94949 | − | 5.10867i | −0.194484 | − | 0.336855i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.67423 | + | 8.09601i | −0.306879 | + | 0.531529i | ||||
\(233\) | −13.8990 | − | 24.0737i | −0.910552 | − | 1.57712i | −0.813286 | − | 0.581865i | \(-0.802323\pi\) |
−0.0972668 | − | 0.995258i | \(-0.531010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.10102 | −0.0718227 | ||||||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.12372 | + | 1.94635i | −0.0728402 | + | 0.126163i | ||||
\(239\) | 29.7980 | 1.92747 | 0.963735 | − | 0.266862i | \(-0.0859867\pi\) | ||||
0.963735 | + | 0.266862i | \(0.0859867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.34847 | + | 5.79972i | −0.215694 | + | 0.373593i | −0.953487 | − | 0.301434i | \(-0.902535\pi\) |
0.737793 | + | 0.675027i | \(0.235868\pi\) | |||||||
\(242\) | −1.00000 | − | 1.73205i | −0.0642824 | − | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.22474 | − | 10.7816i | −0.398498 | − | 0.690220i | ||||
\(245\) | −2.44949 | − | 4.24264i | −0.156492 | − | 0.271052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.89898 | − | 20.7846i | 0.311715 | − | 1.32249i | ||||
\(248\) | 0.898979 | 0.0570853 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | −1.10102 | + | 1.90702i | −0.0694958 | + | 0.120370i | −0.898679 | − | 0.438606i | \(-0.855472\pi\) |
0.829184 | + | 0.558976i | \(0.188806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.84847 | + | 15.3260i | −0.556298 | + | 0.963537i | ||||
\(254\) | 0.348469 | 0.0218649 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.89898 | − | 13.6814i | 0.492725 | − | 0.853424i | −0.507240 | − | 0.861805i | \(-0.669334\pi\) |
0.999965 | + | 0.00838040i | \(0.00266760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.3485 | 0.891570 | ||||||||
\(260\) | 2.44949 | − | 4.24264i | 0.151911 | − | 0.263117i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.50000 | − | 2.59808i | 0.0926703 | − | 0.160510i | ||||
\(263\) | 5.05051 | + | 8.74774i | 0.311428 | + | 0.539409i | 0.978672 | − | 0.205431i | \(-0.0658595\pi\) |
−0.667244 | + | 0.744839i | \(0.732526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.44949 | −0.457619 | ||||||||
\(266\) | 4.60102 | + | 4.33013i | 0.282107 | + | 0.265497i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.67423 | + | 6.36396i | 0.224440 | + | 0.388741i | ||||
\(269\) | −12.1237 | − | 20.9989i | −0.739197 | − | 1.28033i | −0.952858 | − | 0.303418i | \(-0.901872\pi\) |
0.213661 | − | 0.976908i | \(-0.431461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.44949 | + | 12.9029i | 0.452524 | + | 0.783795i | 0.998542 | − | 0.0539785i | \(-0.0171903\pi\) |
−0.546018 | + | 0.837774i | \(0.683857\pi\) | |||||||
\(272\) | −0.775255 | + | 1.34278i | −0.0470067 | + | 0.0814181i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8990 | −0.775025 | −0.387512 | − | 0.921865i | \(-0.626666\pi\) | ||||
−0.387512 | + | 0.921865i | \(0.626666\pi\) | |||||||
\(278\) | 14.6969 | 0.881464 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.724745 | + | 1.25529i | 0.0433118 | + | 0.0750182i | ||||
\(281\) | 7.17423 | − | 12.4261i | 0.427979 | − | 0.741281i | −0.568714 | − | 0.822535i | \(-0.692559\pi\) |
0.996693 | + | 0.0812537i | \(0.0258924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.34847 | + | 10.9959i | 0.377377 | + | 0.653637i | 0.990680 | − | 0.136211i | \(-0.0434927\pi\) |
−0.613302 | + | 0.789848i | \(0.710159\pi\) | |||||||
\(284\) | 3.34847 | 0.198695 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.6969 | −0.869048 | ||||||||
\(287\) | −3.15153 | − | 5.45861i | −0.186029 | − | 0.322212i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.29796 | − | 12.6404i | 0.429292 | − | 0.743555i | ||||
\(290\) | 4.67423 | + | 8.09601i | 0.274481 | + | 0.475414i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.4495 | 0.611510 | ||||||||
\(293\) | 11.4495 | 0.668886 | 0.334443 | − | 0.942416i | \(-0.391452\pi\) | ||||
0.334443 | + | 0.942416i | \(0.391452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 9.89898 | 0.575366 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.77526 | + | 11.7351i | −0.392480 | + | 0.679795i | ||||
\(299\) | −14.4495 | − | 25.0273i | −0.835636 | − | 1.44736i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.55051 | − | 14.8099i | −0.492843 | − | 0.853629i | ||||
\(302\) | −2.32577 | − | 4.02834i | −0.133833 | − | 0.231805i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.17423 | + | 2.98735i | 0.182055 | + | 0.171336i | ||||
\(305\) | −12.4495 | −0.712856 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.12372 | + | 8.87455i | 0.292426 | + | 0.506497i | 0.974383 | − | 0.224895i | \(-0.0722040\pi\) |
−0.681957 | + | 0.731393i | \(0.738871\pi\) | |||||||
\(308\) | 2.17423 | − | 3.76588i | 0.123889 | − | 0.214581i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.449490 | − | 0.778539i | 0.0255293 | − | 0.0442180i | ||||
\(311\) | 9.79796 | 0.555591 | 0.277796 | − | 0.960640i | \(-0.410396\pi\) | ||||
0.277796 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.7980 | + | 27.3629i | −0.892953 | + | 1.54664i | −0.0566362 | + | 0.998395i | \(0.518038\pi\) |
−0.836317 | + | 0.548246i | \(0.815296\pi\) | |||||||
\(314\) | 10.3990 | − | 18.0116i | 0.586848 | − | 1.01645i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.89898 | 0.388098 | ||||||||
\(317\) | 4.72474 | − | 8.18350i | 0.265368 | − | 0.459631i | −0.702292 | − | 0.711889i | \(-0.747840\pi\) |
0.967660 | + | 0.252258i | \(0.0811732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0227 | − | 24.2880i | 0.785121 | − | 1.35987i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.55051 | 0.476501 | ||||||||
\(323\) | 4.92168 | + | 4.63191i | 0.273850 | + | 0.257726i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.44949 | − | 4.24264i | −0.135873 | − | 0.235339i | ||||
\(326\) | 8.34847 | + | 14.4600i | 0.462379 | + | 0.800864i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.17423 | − | 3.76588i | −0.120052 | − | 0.207936i | ||||
\(329\) | 0.797959 | − | 1.38211i | 0.0439929 | − | 0.0761979i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3485 | 1.00852 | 0.504262 | − | 0.863551i | \(-0.331765\pi\) | ||||
0.504262 | + | 0.863551i | \(0.331765\pi\) | |||||||
\(332\) | 5.89898 | − | 10.2173i | 0.323749 | − | 0.560749i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.69694 | −0.530593 | ||||||||
\(335\) | 7.34847 | 0.401490 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2474 | + | 22.9453i | 0.721635 | + | 1.24991i | 0.960344 | + | 0.278817i | \(0.0899422\pi\) |
−0.238710 | + | 0.971091i | \(0.576724\pi\) | |||||||
\(338\) | 5.50000 | − | 9.52628i | 0.299161 | − | 0.518161i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.775255 | + | 1.34278i | 0.0420441 | + | 0.0728225i | ||||
\(341\) | −2.69694 | −0.146047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2474 | 0.931275 | ||||||||
\(344\) | −5.89898 | − | 10.2173i | −0.318052 | − | 0.550882i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.27526 | − | 3.94086i | 0.122318 | − | 0.211862i | ||||
\(347\) | 5.89898 | + | 10.2173i | 0.316674 | + | 0.548495i | 0.979792 | − | 0.200020i | \(-0.0641006\pi\) |
−0.663118 | + | 0.748515i | \(0.730767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0454 | −1.07301 | −0.536503 | − | 0.843898i | \(-0.680255\pi\) | ||||
−0.536503 | + | 0.843898i | \(0.680255\pi\) | |||||||
\(350\) | 1.44949 | 0.0774785 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | 35.3485 | 1.88141 | 0.940705 | − | 0.339227i | \(-0.110165\pi\) | ||||
0.940705 | + | 0.339227i | \(0.110165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.67423 | − | 2.89986i | 0.0888591 | − | 0.153909i | ||||
\(356\) | −2.72474 | − | 4.71940i | −0.144411 | − | 0.250128i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.3990 | + | 18.0116i | 0.549603 | + | 0.951941i | ||||
\(359\) | 13.2247 | + | 22.9059i | 0.697975 | + | 1.20893i | 0.969167 | + | 0.246403i | \(0.0792488\pi\) |
−0.271192 | + | 0.962525i | \(0.587418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8485 | − | 10.4798i | 0.834130 | − | 0.551568i | ||||
\(362\) | −17.1464 | −0.901196 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.55051 | + | 6.14966i | 0.186097 | + | 0.322330i | ||||
\(365\) | 5.22474 | − | 9.04952i | 0.273476 | − | 0.473674i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4495 | + | 18.0990i | −0.545459 | + | 0.944763i | 0.453119 | + | 0.891450i | \(0.350311\pi\) |
−0.998578 | + | 0.0533125i | \(0.983022\pi\) | |||||||
\(368\) | 5.89898 | 0.307506 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.94949 | − | 8.57277i | 0.257312 | − | 0.445677i | ||||
\(371\) | 5.39898 | − | 9.35131i | 0.280301 | − | 0.485496i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.89898 | −0.201882 | −0.100941 | − | 0.994892i | \(-0.532185\pi\) | ||||
−0.100941 | + | 0.994892i | \(0.532185\pi\) | |||||||
\(374\) | 2.32577 | − | 4.02834i | 0.120262 | − | 0.208301i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.550510 | − | 0.953512i | 0.0283904 | − | 0.0491736i | ||||
\(377\) | 22.8990 | + | 39.6622i | 1.17936 | + | 2.04271i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.69694 | −0.343999 | −0.171999 | − | 0.985097i | \(-0.555023\pi\) | ||||
−0.171999 | + | 0.985097i | \(0.555023\pi\) | |||||||
\(380\) | 4.17423 | − | 1.25529i | 0.214134 | − | 0.0643953i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.89898 | + | 3.28913i | 0.0971602 | + | 0.168286i | ||||
\(383\) | 15.2474 | + | 26.4094i | 0.779108 | + | 1.34946i | 0.932456 | + | 0.361283i | \(0.117661\pi\) |
−0.153348 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.17423 | − | 3.76588i | −0.110809 | − | 0.191927i | ||||
\(386\) | −10.6742 | + | 18.4883i | −0.543304 | + | 0.941031i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.4495 | −0.936631 | ||||||||
\(389\) | −11.5732 | + | 20.0454i | −0.586785 | + | 1.01634i | 0.407865 | + | 0.913042i | \(0.366273\pi\) |
−0.994650 | + | 0.103300i | \(0.967060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.14643 | 0.462555 | ||||||||
\(392\) | 4.89898 | 0.247436 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.27526 | − | 5.67291i | −0.165005 | − | 0.285797i | ||||
\(395\) | 3.44949 | − | 5.97469i | 0.173563 | − | 0.300619i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.74745 | − | 9.95487i | −0.288456 | − | 0.499621i | 0.684985 | − | 0.728557i | \(-0.259809\pi\) |
−0.973441 | + | 0.228936i | \(0.926475\pi\) | |||||||
\(398\) | −6.44949 | −0.323284 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.89898 | − | 3.28913i | −0.0948305 | − | 0.164251i | 0.814707 | − | 0.579872i | \(-0.196898\pi\) |
−0.909538 | + | 0.415621i | \(0.863564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.20204 | − | 3.81405i | 0.109691 | − | 0.189991i | ||||
\(404\) | −0.550510 | − | 0.953512i | −0.0273889 | − | 0.0474390i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.5505 | −0.672501 | ||||||||
\(407\) | −29.6969 | −1.47202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.74745 | − | 8.22282i | 0.234746 | − | 0.406592i | −0.724453 | − | 0.689325i | \(-0.757907\pi\) |
0.959199 | + | 0.282732i | \(0.0912408\pi\) | |||||||
\(410\) | −4.34847 | −0.214756 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.62372 | + | 9.74058i | −0.277061 | + | 0.479884i | ||||
\(413\) | 4.34847 | + | 7.53177i | 0.213974 | + | 0.370614i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.89898 | − | 10.2173i | −0.289570 | − | 0.501549i | ||||
\(416\) | 2.44949 | + | 4.24264i | 0.120096 | + | 0.208013i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.52270 | − | 8.96204i | −0.465771 | − | 0.438348i | ||||
\(419\) | −21.8990 | −1.06984 | −0.534918 | − | 0.844904i | \(-0.679657\pi\) | ||||
−0.534918 | + | 0.844904i | \(0.679657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32577 | + | 16.1527i | 0.454510 | + | 0.787234i | 0.998660 | − | 0.0517536i | \(-0.0164811\pi\) |
−0.544150 | + | 0.838988i | \(0.683148\pi\) | |||||||
\(422\) | −13.1742 | + | 22.8184i | −0.641312 | + | 1.11078i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.72474 | − | 6.45145i | 0.180890 | − | 0.313310i | ||||
\(425\) | 1.55051 | 0.0752108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.02270 | − | 15.6278i | 0.436639 | − | 0.756281i | ||||
\(428\) | −1.32577 | + | 2.29629i | −0.0640833 | + | 0.110996i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.7980 | −0.568948 | ||||||||
\(431\) | 5.32577 | − | 9.22450i | 0.256533 | − | 0.444328i | −0.708778 | − | 0.705432i | \(-0.750753\pi\) |
0.965311 | + | 0.261104i | \(0.0840864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.67423 | + | 2.89986i | −0.0804586 | + | 0.139358i | −0.903447 | − | 0.428700i | \(-0.858972\pi\) |
0.822988 | + | 0.568058i | \(0.192305\pi\) | |||||||
\(434\) | 0.651531 | + | 1.12848i | 0.0312745 | + | 0.0541690i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.34847 | 0.0645800 | ||||||||
\(437\) | 5.89898 | − | 25.0273i | 0.282186 | − | 1.19722i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.67423 | − | 2.89986i | −0.0799069 | − | 0.138403i | 0.823303 | − | 0.567603i | \(-0.192129\pi\) |
−0.903210 | + | 0.429200i | \(0.858796\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.79796 | + | 6.57826i | 0.180650 | + | 0.312896i | ||||
\(443\) | 0.876276 | − | 1.51775i | 0.0416331 | − | 0.0721107i | −0.844458 | − | 0.535622i | \(-0.820077\pi\) |
0.886091 | + | 0.463511i | \(0.153411\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.44949 | −0.258331 | ||||||||
\(446\) | −1.72474 | + | 2.98735i | −0.0816690 | + | 0.141455i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.44949 | −0.0684820 | ||||||||
\(449\) | −8.75255 | −0.413058 | −0.206529 | − | 0.978440i | \(-0.566217\pi\) | ||||
−0.206529 | + | 0.978440i | \(0.566217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.52270 | + | 11.2977i | 0.307142 | + | 0.531986i | ||||
\(452\) | −4.77526 | + | 8.27098i | −0.224609 | + | 0.389034i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.67423 | + | 9.82806i | 0.266305 | + | 0.461254i | ||||
\(455\) | 7.10102 | 0.332901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0454 | −0.563460 | −0.281730 | − | 0.959494i | \(-0.590908\pi\) | ||||
−0.281730 | + | 0.959494i | \(0.590908\pi\) | |||||||
\(458\) | 4.34847 | + | 7.53177i | 0.203191 | + | 0.351936i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.94949 | − | 5.10867i | 0.137521 | − | 0.238193i | ||||
\(461\) | −13.8990 | − | 24.0737i | −0.647340 | − | 1.12123i | −0.983756 | − | 0.179512i | \(-0.942548\pi\) |
0.336416 | − | 0.941714i | \(-0.390785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6515 | −0.727388 | −0.363694 | − | 0.931518i | \(-0.618485\pi\) | ||||
−0.363694 | + | 0.931518i | \(0.618485\pi\) | |||||||
\(464\) | −9.34847 | −0.433992 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.8990 | − | 24.0737i | 0.643858 | − | 1.11519i | ||||
\(467\) | 40.2474 | 1.86243 | 0.931215 | − | 0.364471i | \(-0.118750\pi\) | ||||
0.931215 | + | 0.364471i | \(0.118750\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.32577 | + | 9.22450i | −0.245921 | + | 0.425948i | ||||
\(470\) | −0.550510 | − | 0.953512i | −0.0253931 | − | 0.0439822i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | 17.6969 | + | 30.6520i | 0.813706 | + | 1.40938i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | − | 4.24264i | 0.0458831 | − | 0.194666i | ||||
\(476\) | −2.24745 | −0.103012 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.8990 | + | 25.8058i | 0.681463 | + | 1.18033i | ||||
\(479\) | 5.02270 | − | 8.69958i | 0.229493 | − | 0.397494i | −0.728165 | − | 0.685402i | \(-0.759626\pi\) |
0.957658 | + | 0.287908i | \(0.0929598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.2474 | − | 41.9978i | 1.10559 | − | 1.91494i | ||||
\(482\) | −6.69694 | −0.305037 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | −9.22474 | + | 15.9777i | −0.418874 | + | 0.725511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.1464 | −1.27544 | −0.637718 | − | 0.770270i | \(-0.720122\pi\) | ||||
−0.637718 | + | 0.770270i | \(0.720122\pi\) | |||||||
\(488\) | 6.22474 | − | 10.7816i | 0.281781 | − | 0.488059i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.44949 | − | 4.24264i | 0.110657 | − | 0.191663i | ||||
\(491\) | −7.60102 | − | 13.1654i | −0.343029 | − | 0.594144i | 0.641964 | − | 0.766734i | \(-0.278120\pi\) |
−0.984994 | + | 0.172590i | \(0.944786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.4949 | −0.652817 | ||||||||
\(494\) | 20.4495 | − | 6.14966i | 0.920066 | − | 0.276686i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.449490 | + | 0.778539i | 0.0201827 | + | 0.0349574i | ||||
\(497\) | 2.42679 | + | 4.20332i | 0.108856 | + | 0.188545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.27526 | − | 9.13701i | −0.236153 | − | 0.409029i | 0.723454 | − | 0.690372i | \(-0.242553\pi\) |
−0.959607 | + | 0.281344i | \(0.909220\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.20204 | −0.0982819 | ||||||||
\(503\) | 1.15153 | − | 1.99451i | 0.0513442 | − | 0.0889308i | −0.839211 | − | 0.543806i | \(-0.816983\pi\) |
0.890555 | + | 0.454875i | \(0.150316\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.10102 | −0.0489948 | ||||||||
\(506\) | −17.6969 | −0.786725 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.174235 | + | 0.301783i | 0.00773041 | + | 0.0133895i | ||||
\(509\) | −1.44949 | + | 2.51059i | −0.0642475 | + | 0.111280i | −0.896360 | − | 0.443327i | \(-0.853798\pi\) |
0.832112 | + | 0.554607i | \(0.187131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.57321 | + | 13.1172i | 0.335019 | + | 0.580270i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.7980 | 0.696818 | ||||||||
\(515\) | 5.62372 | + | 9.74058i | 0.247811 | + | 0.429221i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.65153 | + | 2.86054i | −0.0726342 | + | 0.125806i | ||||
\(518\) | 7.17423 | + | 12.4261i | 0.315218 | + | 0.545973i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.89898 | 0.214834 | ||||||||
\(521\) | −1.10102 | −0.0482366 | −0.0241183 | − | 0.999709i | \(-0.507678\pi\) | ||||
−0.0241183 | + | 0.999709i | \(0.507678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.57321 | + | 2.72489i | −0.0687918 | + | 0.119151i | −0.898370 | − | 0.439240i | \(-0.855248\pi\) |
0.829578 | + | 0.558391i | \(0.188581\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.05051 | + | 8.74774i | −0.220213 | + | 0.381420i | ||||
\(527\) | 0.696938 | + | 1.20713i | 0.0303591 | + | 0.0525835i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.89898 | − | 10.2173i | −0.256477 | − | 0.444232i | ||||
\(530\) | −3.72474 | − | 6.45145i | −0.161793 | − | 0.280233i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.44949 | + | 6.14966i | −0.0628434 | + | 0.266622i | ||||
\(533\) | −21.3031 | −0.922738 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32577 | + | 2.29629i | 0.0573178 | + | 0.0992774i | ||||
\(536\) | −3.67423 | + | 6.36396i | −0.158703 | + | 0.274881i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.1237 | − | 20.9989i | 0.522691 | − | 0.905327i | ||||
\(539\) | −14.6969 | −0.633042 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.55051 | + | 16.5420i | −0.410609 | + | 0.711195i | −0.994956 | − | 0.100308i | \(-0.968017\pi\) |
0.584348 | + | 0.811503i | \(0.301350\pi\) | |||||||
\(542\) | −7.44949 | + | 12.9029i | −0.319983 | + | 0.554227i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.55051 | −0.0664776 | ||||||||
\(545\) | 0.674235 | − | 1.16781i | 0.0288810 | − | 0.0500234i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.65153 | − | 2.86054i | 0.0706144 | − | 0.122308i | −0.828556 | − | 0.559906i | \(-0.810837\pi\) |
0.899171 | + | 0.437598i | \(0.144171\pi\) | |||||||
\(548\) | −6.00000 | − | 10.3923i | −0.256307 | − | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.00000 | −0.127920 | ||||||||
\(551\) | −9.34847 | + | 39.6622i | −0.398258 | + | 1.68967i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.00000 | + | 8.66025i | 0.212622 | + | 0.368271i | ||||
\(554\) | −6.44949 | − | 11.1708i | −0.274013 | − | 0.474604i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.34847 | + | 12.7279i | 0.311645 | + | 0.539784i | ||||
\(557\) | −9.17423 | + | 15.8902i | −0.388725 | + | 0.673291i | −0.992278 | − | 0.124031i | \(-0.960418\pi\) |
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.7980 | −2.44459 | ||||||||
\(560\) | −0.724745 | + | 1.25529i | −0.0306261 | + | 0.0530459i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.3485 | 0.605254 | ||||||||
\(563\) | −29.3939 | −1.23880 | −0.619402 | − | 0.785074i | \(-0.712625\pi\) | ||||
−0.619402 | + | 0.785074i | \(0.712625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.77526 | + | 8.27098i | 0.200896 | + | 0.347963i | ||||
\(566\) | −6.34847 | + | 10.9959i | −0.266846 | + | 0.462191i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.67423 | + | 2.89986i | 0.0702493 | + | 0.121675i | ||||
\(569\) | 7.44949 | 0.312299 | 0.156149 | − | 0.987733i | \(-0.450092\pi\) | ||||
0.156149 | + | 0.987733i | \(0.450092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.20204 | −0.343245 | −0.171622 | − | 0.985163i | \(-0.554901\pi\) | ||||
−0.171622 | + | 0.985163i | \(0.554901\pi\) | |||||||
\(572\) | −7.34847 | − | 12.7279i | −0.307255 | − | 0.532181i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.15153 | − | 5.45861i | 0.131542 | − | 0.227838i | ||||
\(575\) | −2.94949 | − | 5.10867i | −0.123002 | − | 0.213046i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1464 | 0.464032 | 0.232016 | − | 0.972712i | \(-0.425468\pi\) | ||||
0.232016 | + | 0.972712i | \(0.425468\pi\) | |||||||
\(578\) | 14.5959 | 0.607110 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.67423 | + | 8.09601i | −0.194087 | + | 0.336169i | ||||
\(581\) | 17.1010 | 0.709470 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1742 | + | 19.3543i | −0.462790 | + | 0.801575i | ||||
\(584\) | 5.22474 | + | 9.04952i | 0.216201 | + | 0.374472i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.72474 | + | 9.91555i | 0.236487 | + | 0.409608i | ||||
\(587\) | −16.2474 | − | 28.1414i | −0.670604 | − | 1.16152i | −0.977733 | − | 0.209852i | \(-0.932702\pi\) |
0.307129 | − | 0.951668i | \(-0.400632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.75255 | − | 1.12848i | 0.154621 | − | 0.0464984i | ||||
\(590\) | 6.00000 | 0.247016 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.94949 | + | 8.57277i | 0.203423 | + | 0.352339i | ||||
\(593\) | −17.5732 | + | 30.4377i | −0.721645 | + | 1.24993i | 0.238695 | + | 0.971095i | \(0.423281\pi\) |
−0.960340 | + | 0.278832i | \(0.910053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.12372 | + | 1.94635i | −0.0460682 | + | 0.0797925i | ||||
\(596\) | −13.5505 | −0.555051 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.4495 | − | 25.0273i | 0.590884 | − | 1.02344i | ||||
\(599\) | 12.6742 | − | 21.9524i | 0.517855 | − | 0.896951i | −0.481930 | − | 0.876210i | \(-0.660064\pi\) |
0.999785 | − | 0.0207416i | \(-0.00660273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 8.55051 | − | 14.8099i | 0.348493 | − | 0.603607i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.32577 | − | 4.02834i | 0.0946341 | − | 0.163911i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4495 | 1.19532 | 0.597659 | − | 0.801750i | \(-0.296098\pi\) | ||||
0.597659 | + | 0.801750i | \(0.296098\pi\) | |||||||
\(608\) | −1.00000 | + | 4.24264i | −0.0405554 | + | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.22474 | − | 10.7816i | −0.252033 | − | 0.436533i | ||||
\(611\) | −2.69694 | − | 4.67123i | −0.109106 | − | 0.188978i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.74745 | − | 9.95487i | −0.232137 | − | 0.402074i | 0.726300 | − | 0.687378i | \(-0.241239\pi\) |
−0.958437 | + | 0.285305i | \(0.907905\pi\) | |||||||
\(614\) | −5.12372 | + | 8.87455i | −0.206777 | + | 0.358148i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.34847 | 0.175205 | ||||||||
\(617\) | 7.79796 | − | 13.5065i | 0.313934 | − | 0.543750i | −0.665276 | − | 0.746597i | \(-0.731686\pi\) |
0.979210 | + | 0.202848i | \(0.0650196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0454 | 0.926273 | 0.463137 | − | 0.886287i | \(-0.346724\pi\) | ||||
0.463137 | + | 0.886287i | \(0.346724\pi\) | |||||||
\(620\) | 0.898979 | 0.0361039 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.89898 | + | 8.48528i | 0.196431 | + | 0.340229i | ||||
\(623\) | 3.94949 | − | 6.84072i | 0.158233 | − | 0.274068i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −31.5959 | −1.26283 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.7980 | 0.829929 | ||||||||
\(629\) | 7.67423 | + | 13.2922i | 0.305992 | + | 0.529993i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1237 | − | 22.7310i | 0.522447 | − | 0.904905i | −0.477212 | − | 0.878788i | \(-0.658353\pi\) |
0.999659 | − | 0.0261167i | \(-0.00831416\pi\) | |||||||
\(632\) | 3.44949 | + | 5.97469i | 0.137213 | + | 0.237660i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.44949 | 0.375287 | ||||||||
\(635\) | 0.348469 | 0.0138286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | − | 20.7846i | 0.475457 | − | 0.823516i | ||||
\(638\) | 28.0454 | 1.11033 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −5.65153 | − | 9.78874i | −0.223222 | − | 0.386632i | 0.732563 | − | 0.680700i | \(-0.238324\pi\) |
−0.955785 | + | 0.294068i | \(0.904991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1237 | − | 17.5348i | −0.399241 | − | 0.691505i | 0.594392 | − | 0.804176i | \(-0.297393\pi\) |
−0.993632 | + | 0.112670i | \(0.964060\pi\) | |||||||
\(644\) | 4.27526 | + | 7.40496i | 0.168469 | + | 0.291796i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.55051 | + | 6.57826i | −0.0610040 | + | 0.258818i | ||||
\(647\) | −0.101021 | −0.00397153 | −0.00198576 | − | 0.999998i | \(-0.500632\pi\) | ||||
−0.00198576 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 15.5885i | −0.353281 | − | 0.611900i | ||||
\(650\) | 2.44949 | − | 4.24264i | 0.0960769 | − | 0.166410i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.34847 | + | 14.4600i | −0.326951 | + | 0.566296i | ||||
\(653\) | 40.3485 | 1.57896 | 0.789479 | − | 0.613778i | \(-0.210351\pi\) | ||||
0.789479 | + | 0.613778i | \(0.210351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.50000 | − | 2.59808i | 0.0586098 | − | 0.101515i | ||||
\(656\) | 2.17423 | − | 3.76588i | 0.0848896 | − | 0.147033i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.59592 | 0.0622154 | ||||||||
\(659\) | 11.2980 | − | 19.5686i | 0.440106 | − | 0.762286i | −0.557591 | − | 0.830116i | \(-0.688274\pi\) |
0.997697 | + | 0.0678299i | \(0.0216075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.89898 | − | 11.9494i | 0.268339 | − | 0.464777i | −0.700094 | − | 0.714051i | \(-0.746859\pi\) |
0.968433 | + | 0.249274i | \(0.0801919\pi\) | |||||||
\(662\) | 9.17423 | + | 15.8902i | 0.356567 | + | 0.617592i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.7980 | 0.457850 | ||||||||
\(665\) | 4.60102 | + | 4.33013i | 0.178420 | + | 0.167915i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.5732 | + | 47.7582i | 1.06764 | + | 1.84921i | ||||
\(668\) | −4.84847 | − | 8.39780i | −0.187593 | − | 0.324920i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.67423 | + | 6.36396i | 0.141948 | + | 0.245861i | ||||
\(671\) | −18.6742 | + | 32.3447i | −0.720911 | + | 1.24865i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.4949 | −1.56096 | −0.780482 | − | 0.625179i | \(-0.785026\pi\) | ||||
−0.780482 | + | 0.625179i | \(0.785026\pi\) | |||||||
\(674\) | −13.2474 | + | 22.9453i | −0.510273 | + | 0.883818i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | −29.9444 | −1.15086 | −0.575428 | − | 0.817852i | \(-0.695165\pi\) | ||||
−0.575428 | + | 0.817852i | \(0.695165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3712 | − | 23.1596i | −0.513139 | − | 0.888782i | ||||
\(680\) | −0.775255 | + | 1.34278i | −0.0297297 | + | 0.0514933i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.34847 | − | 2.33562i | −0.0516356 | − | 0.0894354i | ||||
\(683\) | 17.7526 | 0.679282 | 0.339641 | − | 0.940555i | \(-0.389694\pi\) | ||||
0.339641 | + | 0.940555i | \(0.389694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 8.62372 | + | 14.9367i | 0.329255 | + | 0.570287i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.89898 | − | 10.2173i | 0.224896 | − | 0.389532i | ||||
\(689\) | −18.2474 | − | 31.6055i | −0.695172 | − | 1.20407i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.4495 | −1.19639 | −0.598197 | − | 0.801349i | \(-0.704116\pi\) | ||||
−0.598197 | + | 0.801349i | \(0.704116\pi\) | |||||||
\(692\) | 4.55051 | 0.172984 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.89898 | + | 10.2173i | −0.223922 | + | 0.387845i | ||||
\(695\) | 14.6969 | 0.557487 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.37117 | − | 5.83904i | 0.127692 | − | 0.221170i | ||||
\(698\) | −10.0227 | − | 17.3598i | −0.379365 | − | 0.657079i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.724745 | + | 1.25529i | 0.0273928 | + | 0.0474457i | ||||
\(701\) | 2.10102 | + | 3.63907i | 0.0793544 | + | 0.137446i | 0.902972 | − | 0.429700i | \(-0.141381\pi\) |
−0.823617 | + | 0.567146i | \(0.808047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.3207 | − | 12.4261i | 1.55844 | − | 0.468661i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.6742 | + | 30.6127i | 0.665179 | + | 1.15212i | ||||
\(707\) | 0.797959 | − | 1.38211i | 0.0300103 | − | 0.0519794i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.4722 | + | 38.9230i | −0.843961 | + | 1.46178i | 0.0425596 | + | 0.999094i | \(0.486449\pi\) |
−0.886521 | + | 0.462689i | \(0.846885\pi\) | |||||||
\(710\) | 3.34847 | 0.125666 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.72474 | − | 4.71940i | 0.102114 | − | 0.176867i | ||||
\(713\) | 2.65153 | − | 4.59259i | 0.0993006 | − | 0.171994i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6969 | −0.549634 | ||||||||
\(716\) | −10.3990 | + | 18.0116i | −0.388628 | + | 0.673124i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.2247 | + | 22.9059i | −0.493543 | + | 0.854842i | ||||
\(719\) | −17.3485 | − | 30.0484i | −0.646989 | − | 1.12062i | −0.983838 | − | 0.179059i | \(-0.942695\pi\) |
0.336850 | − | 0.941558i | \(-0.390639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3031 | −0.607158 | ||||||||
\(722\) | 17.0000 | + | 8.48528i | 0.632674 | + | 0.315789i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.57321 | − | 14.8492i | −0.318621 | − | 0.551868i | ||||
\(725\) | 4.67423 | + | 8.09601i | 0.173597 | + | 0.300678i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.10102 | − | 7.10318i | −0.152098 | − | 0.263442i | 0.779900 | − | 0.625904i | \(-0.215270\pi\) |
−0.931999 | + | 0.362462i | \(0.881936\pi\) | |||||||
\(728\) | −3.55051 | + | 6.14966i | −0.131591 | + | 0.227922i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.4495 | 0.386753 | ||||||||
\(731\) | 9.14643 | − | 15.8421i | 0.338293 | − | 0.585940i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.59592 | −0.0958824 | −0.0479412 | − | 0.998850i | \(-0.515266\pi\) | ||||
−0.0479412 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(734\) | −20.8990 | −0.771395 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.94949 | + | 5.10867i | 0.108720 | + | 0.188308i | ||||
\(737\) | 11.0227 | − | 19.0919i | 0.406027 | − | 0.703259i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9722 | − | 32.8608i | −0.697903 | − | 1.20880i | −0.969192 | − | 0.246306i | \(-0.920783\pi\) |
0.271289 | − | 0.962498i | \(-0.412550\pi\) | |||||||
\(740\) | 9.89898 | 0.363894 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.7980 | 0.396406 | ||||||||
\(743\) | −9.84847 | − | 17.0580i | −0.361305 | − | 0.625799i | 0.626871 | − | 0.779123i | \(-0.284335\pi\) |
−0.988176 | + | 0.153324i | \(0.951002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.77526 | + | 11.7351i | −0.248226 | + | 0.429940i | ||||
\(746\) | −1.94949 | − | 3.37662i | −0.0713759 | − | 0.123627i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.65153 | 0.170077 | ||||||||
\(749\) | −3.84337 | −0.140434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4949 | − | 38.9623i | 0.820850 | − | 1.42175i | −0.0841993 | − | 0.996449i | \(-0.526833\pi\) |
0.905050 | − | 0.425306i | \(-0.139833\pi\) | |||||||
\(752\) | 1.10102 | 0.0401501 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.8990 | + | 39.6622i | −0.833932 | + | 1.44441i | ||||
\(755\) | −2.32577 | − | 4.02834i | −0.0846433 | − | 0.146606i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.19694 | + | 3.80521i | 0.0798491 | + | 0.138303i | 0.903185 | − | 0.429252i | \(-0.141223\pi\) |
−0.823336 | + | 0.567555i | \(0.807889\pi\) | |||||||
\(758\) | −3.34847 | − | 5.79972i | −0.121622 | − | 0.210655i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.17423 | + | 2.98735i | 0.115142 | + | 0.108362i | ||||
\(761\) | −21.4495 | −0.777543 | −0.388772 | − | 0.921334i | \(-0.627101\pi\) | ||||
−0.388772 | + | 0.921334i | \(0.627101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.977296 | + | 1.69273i | 0.0353805 | + | 0.0612808i | ||||
\(764\) | −1.89898 | + | 3.28913i | −0.0687027 | + | 0.118997i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.2474 | + | 26.4094i | −0.550913 | + | 0.954209i | ||||
\(767\) | 29.3939 | 1.06135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8990 | − | 29.2699i | 0.609393 | − | 1.05550i | −0.381948 | − | 0.924184i | \(-0.624747\pi\) |
0.991341 | − | 0.131315i | \(-0.0419201\pi\) | |||||||
\(770\) | 2.17423 | − | 3.76588i | 0.0783540 | − | 0.135713i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.3485 | −0.768348 | ||||||||
\(773\) | −22.5227 | + | 39.0105i | −0.810085 | + | 1.40311i | 0.102718 | + | 0.994710i | \(0.467246\pi\) |
−0.912804 | + | 0.408399i | \(0.866087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.449490 | − | 0.778539i | 0.0161461 | − | 0.0279659i | ||||
\(776\) | −9.22474 | − | 15.9777i | −0.331149 | − | 0.573567i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.1464 | −0.829840 | ||||||||
\(779\) | −13.8031 | − | 12.9904i | −0.494546 | − | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.02270 | − | 8.69958i | −0.179726 | − | 0.311295i | ||||
\(782\) | 4.57321 | + | 7.92104i | 0.163538 | + | 0.283256i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.44949 | + | 4.24264i | 0.0874818 | + | 0.151523i | ||||
\(785\) | 10.3990 | − | 18.0116i | 0.371155 | − | 0.642860i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0454 | 0.714542 | 0.357271 | − | 0.934001i | \(-0.383707\pi\) | ||||
0.357271 | + | 0.934001i | \(0.383707\pi\) | |||||||
\(788\) | 3.27526 | − | 5.67291i | 0.116676 | − | 0.202089i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.89898 | 0.245455 | ||||||||
\(791\) | −13.8434 | −0.492213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.4949 | − | 52.8187i | −1.08291 | − | 1.87565i | ||||
\(794\) | 5.74745 | − | 9.95487i | 0.203969 | − | 0.353285i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.22474 | − | 5.58542i | −0.114298 | − | 0.197970i | ||||
\(797\) | −16.3485 | −0.579092 | −0.289546 | − | 0.957164i | \(-0.593504\pi\) | ||||
−0.289546 | + | 0.957164i | \(0.593504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.70714 | 0.0603944 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.89898 | − | 3.28913i | 0.0670553 | − | 0.116143i | ||||
\(803\) | −15.6742 | − | 27.1486i | −0.553132 | − | 0.958052i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.55051 | 0.301366 | ||||||||
\(806\) | 4.40408 | 0.155127 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.550510 | − | 0.953512i | 0.0193669 | − | 0.0335444i | ||||
\(809\) | −20.4949 | −0.720562 | −0.360281 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360281 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.4217 | + | 18.0509i | −0.365955 | + | 0.633852i | −0.988929 | − | 0.148390i | \(-0.952591\pi\) |
0.622974 | + | 0.782242i | \(0.285924\pi\) | |||||||
\(812\) | −6.77526 | − | 11.7351i | −0.237765 | − | 0.411821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.8485 | − | 25.7183i | −0.520439 | − | 0.901426i | ||||
\(815\) | 8.34847 | + | 14.4600i | 0.292434 | + | 0.506511i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4495 | − | 35.2446i | −1.31019 | − | 1.23305i | ||||
\(818\) | 9.49490 | 0.331981 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.17423 | − | 3.76588i | −0.0759276 | − | 0.131510i | ||||
\(821\) | 11.0000 | − | 19.0526i | 0.383903 | − | 0.664939i | −0.607714 | − | 0.794156i | \(-0.707913\pi\) |
0.991616 | + | 0.129217i | \(0.0412465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.926786 | − | 1.60524i | 0.0323057 | − | 0.0559552i | −0.849421 | − | 0.527717i | \(-0.823048\pi\) |
0.881726 | + | 0.471761i | \(0.156382\pi\) | |||||||
\(824\) | −11.2474 | −0.391823 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.34847 | + | 7.53177i | −0.151303 | + | 0.262064i | ||||
\(827\) | −10.5732 | + | 18.3133i | −0.367667 | + | 0.636817i | −0.989200 | − | 0.146570i | \(-0.953177\pi\) |
0.621534 | + | 0.783388i | \(0.286510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.1010 | 0.802332 | 0.401166 | − | 0.916005i | \(-0.368605\pi\) | ||||
0.401166 | + | 0.916005i | \(0.368605\pi\) | |||||||
\(830\) | 5.89898 | − | 10.2173i | 0.204757 | − | 0.354649i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.44949 | + | 4.24264i | −0.0849208 | + | 0.147087i | ||||
\(833\) | 3.79796 | + | 6.57826i | 0.131591 | + | 0.227923i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.69694 | −0.335576 | ||||||||
\(836\) | 3.00000 | − | 12.7279i | 0.103757 | − | 0.440204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.9495 | − | 18.9651i | −0.378244 | − | 0.655138i | ||||
\(839\) | 27.2474 | + | 47.1940i | 0.940686 | + | 1.62932i | 0.764166 | + | 0.645020i | \(0.223151\pi\) |
0.176520 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.1969 | − | 50.5706i | −1.00679 | − | 1.74381i | ||||
\(842\) | −9.32577 | + | 16.1527i | −0.321387 | + | 0.556659i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.3485 | −0.906952 | ||||||||
\(845\) | 5.50000 | − | 9.52628i | 0.189206 | − | 0.327714i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.89898 | 0.0996101 | ||||||||
\(848\) | 7.44949 | 0.255817 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.775255 | + | 1.34278i | 0.0265910 | + | 0.0460570i | ||||
\(851\) | 29.1969 | − | 50.5706i | 1.00086 | − | 1.73354i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.69694 | + | 13.3315i | 0.263538 | + | 0.456461i | 0.967180 | − | 0.254094i | \(-0.0817772\pi\) |
−0.703641 | + | 0.710555i | \(0.748444\pi\) | |||||||
\(854\) | 18.0454 | 0.617501 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.65153 | −0.0906275 | ||||||||
\(857\) | −21.7980 | − | 37.7552i | −0.744604 | − | 1.28969i | −0.950380 | − | 0.311093i | \(-0.899305\pi\) |
0.205775 | − | 0.978599i | \(-0.434028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.5227 | + | 28.6182i | −0.563747 | + | 0.976439i | 0.433418 | + | 0.901193i | \(0.357308\pi\) |
−0.997165 | + | 0.0752459i | \(0.976026\pi\) | |||||||
\(860\) | −5.89898 | − | 10.2173i | −0.201154 | − | 0.348408i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.6515 | 0.362793 | ||||||||
\(863\) | −29.0000 | −0.987171 | −0.493586 | − | 0.869697i | \(-0.664314\pi\) | ||||
−0.493586 | + | 0.869697i | \(0.664314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.27526 | − | 3.94086i | 0.0773610 | − | 0.133993i | ||||
\(866\) | −3.34847 | −0.113786 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.651531 | + | 1.12848i | −0.0221144 | + | 0.0383033i | ||||
\(869\) | −10.3485 | − | 17.9241i | −0.351048 | − | 0.608033i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0000 | + | 31.1769i | 0.609907 | + | 1.05639i | ||||
\(872\) | 0.674235 | + | 1.16781i | 0.0228325 | + | 0.0395470i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.6237 | − | 7.40496i | 0.832910 | − | 0.250476i | ||||
\(875\) | 1.44949 | 0.0490017 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7474 | − | 29.0074i | −0.565521 | − | 0.979511i | −0.997001 | − | 0.0773888i | \(-0.975342\pi\) |
0.431480 | − | 0.902123i | \(-0.357992\pi\) | |||||||
\(878\) | 1.67423 | − | 2.89986i | 0.0565027 | − | 0.0978655i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | −37.0454 | −1.24809 | −0.624046 | − | 0.781388i | \(-0.714512\pi\) | ||||
−0.624046 | + | 0.781388i | \(0.714512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.4722 | + | 40.6550i | −0.789902 | + | 1.36815i | 0.136124 | + | 0.990692i | \(0.456535\pi\) |
−0.926026 | + | 0.377459i | \(0.876798\pi\) | |||||||
\(884\) | −3.79796 | + | 6.57826i | −0.127739 | + | 0.221251i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.75255 | 0.0588781 | ||||||||
\(887\) | −21.8990 | + | 37.9301i | −0.735296 | + | 1.27357i | 0.219298 | + | 0.975658i | \(0.429623\pi\) |
−0.954593 | + | 0.297912i | \(0.903710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.252551 | + | 0.437432i | −0.00847030 | + | 0.0146710i | ||||
\(890\) | −2.72474 | − | 4.71940i | −0.0913337 | − | 0.158195i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.44949 | −0.115497 | ||||||||
\(893\) | 1.10102 | − | 4.67123i | 0.0368442 | − | 0.156317i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.3990 | + | 18.0116i | 0.347600 | + | 0.602060i | ||||
\(896\) | −0.724745 | − | 1.25529i | −0.0242120 | − | 0.0419365i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.37628 | − | 7.57993i | −0.146038 | − | 0.252946i | ||||
\(899\) | −4.20204 | + | 7.27815i | −0.140146 | + | 0.242740i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.5505 | 0.384803 | ||||||||
\(902\) | −6.52270 | + | 11.2977i | −0.217182 | + | 0.376171i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.55051 | −0.317645 | ||||||||
\(905\) | −17.1464 | −0.569967 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7980 | + | 32.5590i | 0.624176 | + | 1.08110i | 0.988700 | + | 0.149910i | \(0.0478985\pi\) |
−0.364524 | + | 0.931194i | \(0.618768\pi\) | |||||||
\(908\) | −5.67423 | + | 9.82806i | −0.188306 | + | 0.326156i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.55051 | + | 6.14966i | 0.117698 | + | 0.203859i | ||||
\(911\) | 54.0908 | 1.79211 | 0.896054 | − | 0.443944i | \(-0.146421\pi\) | ||||
0.896054 | + | 0.443944i | \(0.146421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.3939 | −1.17137 | ||||||||
\(914\) | −6.02270 | − | 10.4316i | −0.199213 | − | 0.345048i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.34847 | + | 7.53177i | −0.143677 | + | 0.248857i | ||||
\(917\) | 2.17423 | + | 3.76588i | 0.0717996 | + | 0.124360i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.5505 | −0.512964 | −0.256482 | − | 0.966549i | \(-0.582563\pi\) | ||||
−0.256482 | + | 0.966549i | \(0.582563\pi\) | |||||||
\(920\) | 5.89898 | 0.194484 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.8990 | − | 24.0737i | 0.457739 | − | 0.792826i | ||||
\(923\) | 16.4041 | 0.539947 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.94949 | − | 8.57277i | 0.162738 | − | 0.281871i | ||||
\(926\) | −7.82577 | − | 13.5546i | −0.257171 | − | 0.445433i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.67423 | − | 8.09601i | −0.153439 | − | 0.265765i | ||||
\(929\) | 17.2753 | + | 29.9216i | 0.566783 | + | 0.981696i | 0.996881 | + | 0.0789146i | \(0.0251454\pi\) |
−0.430099 | + | 0.902782i | \(0.641521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.4495 | − | 6.14966i | 0.670205 | − | 0.201547i | ||||
\(932\) | 27.7980 | 0.910552 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.1237 | + | 34.8553i | 0.658468 | + | 1.14050i | ||||
\(935\) | 2.32577 | − | 4.02834i | 0.0760607 | − | 0.131741i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.0227 | − | 22.5560i | 0.425433 | − | 0.736872i | −0.571028 | − | 0.820931i | \(-0.693455\pi\) |
0.996461 | + | 0.0840590i | \(0.0267884\pi\) | |||||||
\(938\) | −10.6515 | −0.347785 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.550510 | − | 0.953512i | 0.0179557 | − | 0.0311001i | ||||
\(941\) | −7.77526 | + | 13.4671i | −0.253466 | + | 0.439016i | −0.964478 | − | 0.264164i | \(-0.914904\pi\) |
0.711012 | + | 0.703180i | \(0.248237\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.6515 | −0.835329 | ||||||||
\(944\) | −3.00000 | + | 5.19615i | −0.0976417 | + | 0.169120i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.6969 | + | 30.6520i | −0.575377 | + | 0.996582i | ||||
\(947\) | −12.2247 | − | 21.1739i | −0.397251 | − | 0.688059i | 0.596135 | − | 0.802884i | \(-0.296702\pi\) |
−0.993386 | + | 0.114826i | \(0.963369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.1918 | 1.66176 | ||||||||
\(950\) | 4.17423 | − | 1.25529i | 0.135430 | − | 0.0407271i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.12372 | − | 1.94635i | −0.0364201 | − | 0.0630815i | ||||
\(953\) | −20.6969 | − | 35.8481i | −0.670440 | − | 1.16124i | −0.977780 | − | 0.209636i | \(-0.932772\pi\) |
0.307340 | − | 0.951600i | \(-0.400561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.89898 | + | 3.28913i | 0.0614495 | + | 0.106434i | ||||
\(956\) | −14.8990 | + | 25.8058i | −0.481867 | + | 0.834619i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.0454 | 0.324552 | ||||||||
\(959\) | 8.69694 | − | 15.0635i | 0.280839 | − | 0.486427i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1918 | −0.973930 | ||||||||
\(962\) | 48.4949 | 1.56354 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.34847 | − | 5.79972i | −0.107847 | − | 0.186796i | ||||
\(965\) | −10.6742 | + | 18.4883i | −0.343616 | + | 0.595160i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.44949 | − | 11.1708i | −0.207402 | − | 0.359230i | 0.743494 | − | 0.668743i | \(-0.233167\pi\) |
−0.950895 | + | 0.309513i | \(0.899834\pi\) | |||||||
\(968\) | 2.00000 | 0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.4495 | −0.592377 | ||||||||
\(971\) | 1.65153 | + | 2.86054i | 0.0530001 | + | 0.0917989i | 0.891308 | − | 0.453398i | \(-0.149788\pi\) |
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6515 | + | 18.4490i | −0.341472 | + | 0.591448i | ||||
\(974\) | −14.0732 | − | 24.3755i | −0.450935 | − | 0.781042i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4495 | 0.398498 | ||||||||
\(977\) | 8.94439 | 0.286156 | 0.143078 | − | 0.989711i | \(-0.454300\pi\) | ||||
0.143078 | + | 0.989711i | \(0.454300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.17423 | + | 14.1582i | −0.261250 | + | 0.452498i | ||||
\(980\) | 4.89898 | 0.156492 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.60102 | − | 13.1654i | 0.242558 | − | 0.420123i | ||||
\(983\) | −12.0959 | − | 20.9507i | −0.385800 | − | 0.668225i | 0.606080 | − | 0.795404i | \(-0.292741\pi\) |
−0.991880 | + | 0.127179i | \(0.959408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.27526 | − | 5.67291i | −0.104358 | − | 0.180754i | ||||
\(986\) | −7.24745 | − | 12.5529i | −0.230806 | − | 0.399767i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.5505 | + | 14.6349i | 0.494728 | + | 0.465600i | ||||
\(989\) | −69.5959 | −2.21302 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.6742 | − | 18.4883i | −0.339078 | − | 0.587301i | 0.645181 | − | 0.764029i | \(-0.276782\pi\) |
−0.984260 | + | 0.176729i | \(0.943448\pi\) | |||||||
\(992\) | −0.449490 | + | 0.778539i | −0.0142713 | + | 0.0247186i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.42679 | + | 4.20332i | −0.0769730 | + | 0.133321i | ||||
\(995\) | −6.44949 | −0.204463 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.2980 | + | 21.3007i | −0.389480 | + | 0.674600i | −0.992380 | − | 0.123218i | \(-0.960679\pi\) |
0.602899 | + | 0.797817i | \(0.294012\pi\) | |||||||
\(998\) | 5.27526 | − | 9.13701i | 0.166985 | − | 0.289227i | ||||
\(999\) | 0 | 0 |
(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 | 1710.2.l.n.1261.1 | 4 | ||
3.2 | odd | 2 | 570.2.i.f.121.1 | ✓ | 4 | ||
19.11 | even | 3 | inner | 1710.2.l.n.1531.1 | 4 | ||
57.11 | odd | 6 | 570.2.i.f.391.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.f.121.1 | ✓ | 4 | 3.2 | odd | 2 | ||
570.2.i.f.391.1 | yes | 4 | 57.11 | odd | 6 | ||
1710.2.l.n.1261.1 | 4 | 1.1 | even | 1 | trivial | ||
1710.2.l.n.1531.1 | 4 | 19.11 | even | 3 | inner |