Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2415,2,Mod(1,2415)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2415, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2415.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2415.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: | \(19.2838720881\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.42978136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 7x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.27660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2415.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27660 | −0.902694 | −0.451347 | − | 0.892348i | \(-0.649056\pi\) | ||||
−0.451347 | + | 0.892348i | \(0.649056\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.370286 | −0.185143 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.27660 | 0.521171 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.02591 | 1.06982 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.27660 | 0.403697 | ||||||||
\(11\) | 4.90026 | 1.47748 | 0.738742 | − | 0.673988i | \(-0.235420\pi\) | ||||
0.738742 | + | 0.673988i | \(0.235420\pi\) | |||||||
\(12\) | 0.370286 | 0.106892 | ||||||||
\(13\) | 4.50637 | 1.24984 | 0.624922 | − | 0.780687i | \(-0.285131\pi\) | ||||
0.624922 | + | 0.780687i | \(0.285131\pi\) | |||||||
\(14\) | 1.27660 | 0.341186 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −3.12232 | −0.780579 | ||||||||
\(17\) | 3.98364 | 0.966176 | 0.483088 | − | 0.875572i | \(-0.339515\pi\) | ||||
0.483088 | + | 0.875572i | \(0.339515\pi\) | |||||||
\(18\) | −1.27660 | −0.300898 | ||||||||
\(19\) | 8.07358 | 1.85221 | 0.926104 | − | 0.377269i | \(-0.123137\pi\) | ||||
0.926104 | + | 0.377269i | \(0.123137\pi\) | |||||||
\(20\) | 0.370286 | 0.0827984 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −6.25569 | −1.33372 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −3.02591 | −0.617662 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.75285 | −1.12823 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.370286 | 0.0699775 | ||||||||
\(29\) | −7.63580 | −1.41793 | −0.708966 | − | 0.705243i | \(-0.750838\pi\) | ||||
−0.708966 | + | 0.705243i | \(0.750838\pi\) | |||||||
\(30\) | −1.27660 | −0.233075 | ||||||||
\(31\) | −5.07594 | −0.911665 | −0.455832 | − | 0.890066i | \(-0.650658\pi\) | ||||
−0.455832 | + | 0.890066i | \(0.650658\pi\) | |||||||
\(32\) | −2.06587 | −0.365197 | ||||||||
\(33\) | −4.90026 | −0.853026 | ||||||||
\(34\) | −5.08553 | −0.872161 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.370286 | −0.0617143 | ||||||||
\(37\) | 5.24695 | 0.862593 | 0.431296 | − | 0.902210i | \(-0.358056\pi\) | ||||
0.431296 | + | 0.902210i | \(0.358056\pi\) | |||||||
\(38\) | −10.3068 | −1.67198 | ||||||||
\(39\) | −4.50637 | −0.721597 | ||||||||
\(40\) | −3.02591 | −0.478439 | ||||||||
\(41\) | −8.82791 | −1.37869 | −0.689344 | − | 0.724434i | \(-0.742101\pi\) | ||||
−0.689344 | + | 0.724434i | \(0.742101\pi\) | |||||||
\(42\) | −1.27660 | −0.196984 | ||||||||
\(43\) | −4.72888 | −0.721147 | −0.360574 | − | 0.932731i | \(-0.617419\pi\) | ||||
−0.360574 | + | 0.932731i | \(0.617419\pi\) | |||||||
\(44\) | −1.81450 | −0.273546 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.27660 | −0.188225 | ||||||||
\(47\) | 3.44679 | 0.502767 | 0.251383 | − | 0.967888i | \(-0.419115\pi\) | ||||
0.251383 | + | 0.967888i | \(0.419115\pi\) | |||||||
\(48\) | 3.12232 | 0.450668 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.27660 | −0.180539 | ||||||||
\(51\) | −3.98364 | −0.557822 | ||||||||
\(52\) | −1.66865 | −0.231400 | ||||||||
\(53\) | 13.8913 | 1.90811 | 0.954055 | − | 0.299631i | \(-0.0968637\pi\) | ||||
0.954055 | + | 0.299631i | \(0.0968637\pi\) | |||||||
\(54\) | 1.27660 | 0.173724 | ||||||||
\(55\) | −4.90026 | −0.660751 | ||||||||
\(56\) | −3.02591 | −0.404355 | ||||||||
\(57\) | −8.07358 | −1.06937 | ||||||||
\(58\) | 9.74788 | 1.27996 | ||||||||
\(59\) | 11.5380 | 1.50212 | 0.751060 | − | 0.660234i | \(-0.229543\pi\) | ||||
0.751060 | + | 0.660234i | \(0.229543\pi\) | |||||||
\(60\) | −0.370286 | −0.0478037 | ||||||||
\(61\) | −11.6241 | −1.48831 | −0.744155 | − | 0.668007i | \(-0.767148\pi\) | ||||
−0.744155 | + | 0.668007i | \(0.767148\pi\) | |||||||
\(62\) | 6.47995 | 0.822955 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.88193 | 1.11024 | ||||||||
\(65\) | −4.50637 | −0.558947 | ||||||||
\(66\) | 6.25569 | 0.770022 | ||||||||
\(67\) | 0.415644 | 0.0507790 | 0.0253895 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253895 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(68\) | −1.47509 | −0.178881 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.27660 | −0.152583 | ||||||||
\(71\) | −0.0137499 | −0.00163181 | −0.000815905 | − | 1.00000i | \(-0.500260\pi\) | ||||
−0.000815905 | 1.00000i | \(0.500260\pi\) | ||||||||
\(72\) | 3.02591 | 0.356607 | ||||||||
\(73\) | 5.23692 | 0.612935 | 0.306467 | − | 0.951881i | \(-0.400853\pi\) | ||||
0.306467 | + | 0.951881i | \(0.400853\pi\) | |||||||
\(74\) | −6.69827 | −0.778658 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −2.98953 | −0.342923 | ||||||||
\(77\) | −4.90026 | −0.558437 | ||||||||
\(78\) | 5.75285 | 0.651382 | ||||||||
\(79\) | 2.49002 | 0.280149 | 0.140075 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140075 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(80\) | 3.12232 | 0.349086 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.2697 | 1.24453 | ||||||||
\(83\) | 14.6322 | 1.60610 | 0.803048 | − | 0.595914i | \(-0.203210\pi\) | ||||
0.803048 | + | 0.595914i | \(0.203210\pi\) | |||||||
\(84\) | −0.370286 | −0.0404015 | ||||||||
\(85\) | −3.98364 | −0.432087 | ||||||||
\(86\) | 6.03690 | 0.650976 | ||||||||
\(87\) | 7.63580 | 0.818644 | ||||||||
\(88\) | 14.8278 | 1.58064 | ||||||||
\(89\) | 2.83796 | 0.300823 | 0.150412 | − | 0.988623i | \(-0.451940\pi\) | ||||
0.150412 | + | 0.988623i | \(0.451940\pi\) | |||||||
\(90\) | 1.27660 | 0.134566 | ||||||||
\(91\) | −4.50637 | −0.472396 | ||||||||
\(92\) | −0.370286 | −0.0386050 | ||||||||
\(93\) | 5.07594 | 0.526350 | ||||||||
\(94\) | −4.40019 | −0.453845 | ||||||||
\(95\) | −8.07358 | −0.828332 | ||||||||
\(96\) | 2.06587 | 0.210847 | ||||||||
\(97\) | −16.9015 | −1.71609 | −0.858043 | − | 0.513578i | \(-0.828320\pi\) | ||||
−0.858043 | + | 0.513578i | \(0.828320\pi\) | |||||||
\(98\) | −1.27660 | −0.128956 | ||||||||
\(99\) | 4.90026 | 0.492495 | ||||||||
\(100\) | −0.370286 | −0.0370286 | ||||||||
\(101\) | 2.93913 | 0.292454 | 0.146227 | − | 0.989251i | \(-0.453287\pi\) | ||||
0.146227 | + | 0.989251i | \(0.453287\pi\) | |||||||
\(102\) | 5.08553 | 0.503543 | ||||||||
\(103\) | −11.1499 | −1.09863 | −0.549317 | − | 0.835614i | \(-0.685112\pi\) | ||||
−0.549317 | + | 0.835614i | \(0.685112\pi\) | |||||||
\(104\) | 13.6359 | 1.33711 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −17.7336 | −1.72244 | ||||||||
\(107\) | −0.0747441 | −0.00722579 | −0.00361289 | − | 0.999993i | \(-0.501150\pi\) | ||||
−0.00361289 | + | 0.999993i | \(0.501150\pi\) | |||||||
\(108\) | 0.370286 | 0.0356308 | ||||||||
\(109\) | 10.3065 | 0.987186 | 0.493593 | − | 0.869693i | \(-0.335683\pi\) | ||||
0.493593 | + | 0.869693i | \(0.335683\pi\) | |||||||
\(110\) | 6.25569 | 0.596456 | ||||||||
\(111\) | −5.24695 | −0.498018 | ||||||||
\(112\) | 3.12232 | 0.295031 | ||||||||
\(113\) | 4.86844 | 0.457984 | 0.228992 | − | 0.973428i | \(-0.426457\pi\) | ||||
0.228992 | + | 0.973428i | \(0.426457\pi\) | |||||||
\(114\) | 10.3068 | 0.965316 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 2.82743 | 0.262520 | ||||||||
\(117\) | 4.50637 | 0.416614 | ||||||||
\(118\) | −14.7294 | −1.35596 | ||||||||
\(119\) | −3.98364 | −0.365180 | ||||||||
\(120\) | 3.02591 | 0.276227 | ||||||||
\(121\) | 13.0126 | 1.18296 | ||||||||
\(122\) | 14.8393 | 1.34349 | ||||||||
\(123\) | 8.82791 | 0.795985 | ||||||||
\(124\) | 1.87955 | 0.168788 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.27660 | 0.113729 | ||||||||
\(127\) | −17.7348 | −1.57371 | −0.786856 | − | 0.617137i | \(-0.788292\pi\) | ||||
−0.786856 | + | 0.617137i | \(0.788292\pi\) | |||||||
\(128\) | −7.20695 | −0.637011 | ||||||||
\(129\) | 4.72888 | 0.416355 | ||||||||
\(130\) | 5.75285 | 0.504558 | ||||||||
\(131\) | 7.24695 | 0.633169 | 0.316584 | − | 0.948564i | \(-0.397464\pi\) | ||||
0.316584 | + | 0.948564i | \(0.397464\pi\) | |||||||
\(132\) | 1.81450 | 0.157932 | ||||||||
\(133\) | −8.07358 | −0.700069 | ||||||||
\(134\) | −0.530612 | −0.0458379 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 12.0542 | 1.03364 | ||||||||
\(137\) | 18.7017 | 1.59779 | 0.798896 | − | 0.601470i | \(-0.205418\pi\) | ||||
0.798896 | + | 0.601470i | \(0.205418\pi\) | |||||||
\(138\) | 1.27660 | 0.108672 | ||||||||
\(139\) | −16.2333 | −1.37689 | −0.688444 | − | 0.725289i | \(-0.741706\pi\) | ||||
−0.688444 | + | 0.725289i | \(0.741706\pi\) | |||||||
\(140\) | −0.370286 | −0.0312949 | ||||||||
\(141\) | −3.44679 | −0.290272 | ||||||||
\(142\) | 0.0175531 | 0.00147303 | ||||||||
\(143\) | 22.0824 | 1.84662 | ||||||||
\(144\) | −3.12232 | −0.260193 | ||||||||
\(145\) | 7.63580 | 0.634119 | ||||||||
\(146\) | −6.68546 | −0.553293 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.94287 | −0.159703 | ||||||||
\(149\) | 10.1254 | 0.829509 | 0.414755 | − | 0.909933i | \(-0.363867\pi\) | ||||
0.414755 | + | 0.909933i | \(0.363867\pi\) | |||||||
\(150\) | 1.27660 | 0.104234 | ||||||||
\(151\) | −22.3700 | −1.82045 | −0.910224 | − | 0.414116i | \(-0.864091\pi\) | ||||
−0.910224 | + | 0.414116i | \(0.864091\pi\) | |||||||
\(152\) | 24.4300 | 1.98153 | ||||||||
\(153\) | 3.98364 | 0.322059 | ||||||||
\(154\) | 6.25569 | 0.504097 | ||||||||
\(155\) | 5.07594 | 0.407709 | ||||||||
\(156\) | 1.66865 | 0.133599 | ||||||||
\(157\) | 17.8851 | 1.42738 | 0.713692 | − | 0.700460i | \(-0.247022\pi\) | ||||
0.713692 | + | 0.700460i | \(0.247022\pi\) | |||||||
\(158\) | −3.17876 | −0.252889 | ||||||||
\(159\) | −13.8913 | −1.10165 | ||||||||
\(160\) | 2.06587 | 0.163321 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −1.27660 | −0.100299 | ||||||||
\(163\) | 1.25644 | 0.0984119 | 0.0492060 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492060 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(164\) | 3.26885 | 0.255254 | ||||||||
\(165\) | 4.90026 | 0.381485 | ||||||||
\(166\) | −18.6795 | −1.44981 | ||||||||
\(167\) | 11.1566 | 0.863324 | 0.431662 | − | 0.902036i | \(-0.357927\pi\) | ||||
0.431662 | + | 0.902036i | \(0.357927\pi\) | |||||||
\(168\) | 3.02591 | 0.233454 | ||||||||
\(169\) | 7.30741 | 0.562109 | ||||||||
\(170\) | 5.08553 | 0.390042 | ||||||||
\(171\) | 8.07358 | 0.617402 | ||||||||
\(172\) | 1.75104 | 0.133515 | ||||||||
\(173\) | −14.5762 | −1.10821 | −0.554104 | − | 0.832448i | \(-0.686939\pi\) | ||||
−0.554104 | + | 0.832448i | \(0.686939\pi\) | |||||||
\(174\) | −9.74788 | −0.738985 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −15.3002 | −1.15329 | ||||||||
\(177\) | −11.5380 | −0.867249 | ||||||||
\(178\) | −3.62295 | −0.271551 | ||||||||
\(179\) | −19.3754 | −1.44818 | −0.724092 | − | 0.689704i | \(-0.757741\pi\) | ||||
−0.724092 | + | 0.689704i | \(0.757741\pi\) | |||||||
\(180\) | 0.370286 | 0.0275995 | ||||||||
\(181\) | 4.63964 | 0.344862 | 0.172431 | − | 0.985022i | \(-0.444838\pi\) | ||||
0.172431 | + | 0.985022i | \(0.444838\pi\) | |||||||
\(182\) | 5.75285 | 0.426430 | ||||||||
\(183\) | 11.6241 | 0.859276 | ||||||||
\(184\) | 3.02591 | 0.223073 | ||||||||
\(185\) | −5.24695 | −0.385763 | ||||||||
\(186\) | −6.47995 | −0.475133 | ||||||||
\(187\) | 19.5209 | 1.42751 | ||||||||
\(188\) | −1.27630 | −0.0930837 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 10.3068 | 0.747731 | ||||||||
\(191\) | −3.84027 | −0.277872 | −0.138936 | − | 0.990301i | \(-0.544368\pi\) | ||||
−0.138936 | + | 0.990301i | \(0.544368\pi\) | |||||||
\(192\) | −8.88193 | −0.640998 | ||||||||
\(193\) | −5.12537 | −0.368932 | −0.184466 | − | 0.982839i | \(-0.559056\pi\) | ||||
−0.184466 | + | 0.982839i | \(0.559056\pi\) | |||||||
\(194\) | 21.5765 | 1.54910 | ||||||||
\(195\) | 4.50637 | 0.322708 | ||||||||
\(196\) | −0.370286 | −0.0264490 | ||||||||
\(197\) | −8.01081 | −0.570746 | −0.285373 | − | 0.958416i | \(-0.592118\pi\) | ||||
−0.285373 | + | 0.958416i | \(0.592118\pi\) | |||||||
\(198\) | −6.25569 | −0.444572 | ||||||||
\(199\) | −8.69874 | −0.616637 | −0.308319 | − | 0.951283i | \(-0.599766\pi\) | ||||
−0.308319 | + | 0.951283i | \(0.599766\pi\) | |||||||
\(200\) | 3.02591 | 0.213964 | ||||||||
\(201\) | −0.415644 | −0.0293173 | ||||||||
\(202\) | −3.75210 | −0.263997 | ||||||||
\(203\) | 7.63580 | 0.535928 | ||||||||
\(204\) | 1.47509 | 0.103277 | ||||||||
\(205\) | 8.82791 | 0.616568 | ||||||||
\(206\) | 14.2340 | 0.991732 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −14.0703 | −0.975602 | ||||||||
\(209\) | 39.5627 | 2.73661 | ||||||||
\(210\) | 1.27660 | 0.0880939 | ||||||||
\(211\) | 0.133840 | 0.00921393 | 0.00460696 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460696 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(212\) | −5.14373 | −0.353273 | ||||||||
\(213\) | 0.0137499 | 0.000942126 0 | ||||||||
\(214\) | 0.0954186 | 0.00652268 | ||||||||
\(215\) | 4.72888 | 0.322507 | ||||||||
\(216\) | −3.02591 | −0.205887 | ||||||||
\(217\) | 5.07594 | 0.344577 | ||||||||
\(218\) | −13.1573 | −0.891127 | ||||||||
\(219\) | −5.23692 | −0.353878 | ||||||||
\(220\) | 1.81450 | 0.122333 | ||||||||
\(221\) | 17.9518 | 1.20757 | ||||||||
\(222\) | 6.69827 | 0.449558 | ||||||||
\(223\) | 22.5532 | 1.51027 | 0.755136 | − | 0.655568i | \(-0.227571\pi\) | ||||
0.755136 | + | 0.655568i | \(0.227571\pi\) | |||||||
\(224\) | 2.06587 | 0.138032 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.21506 | −0.413419 | ||||||||
\(227\) | 19.3447 | 1.28395 | 0.641976 | − | 0.766725i | \(-0.278115\pi\) | ||||
0.641976 | + | 0.766725i | \(0.278115\pi\) | |||||||
\(228\) | 2.98953 | 0.197987 | ||||||||
\(229\) | 7.01364 | 0.463474 | 0.231737 | − | 0.972778i | \(-0.425559\pi\) | ||||
0.231737 | + | 0.972778i | \(0.425559\pi\) | |||||||
\(230\) | 1.27660 | 0.0841767 | ||||||||
\(231\) | 4.90026 | 0.322413 | ||||||||
\(232\) | −23.1053 | −1.51693 | ||||||||
\(233\) | −18.5301 | −1.21395 | −0.606975 | − | 0.794721i | \(-0.707617\pi\) | ||||
−0.606975 | + | 0.794721i | \(0.707617\pi\) | |||||||
\(234\) | −5.75285 | −0.376076 | ||||||||
\(235\) | −3.44679 | −0.224844 | ||||||||
\(236\) | −4.27236 | −0.278107 | ||||||||
\(237\) | −2.49002 | −0.161744 | ||||||||
\(238\) | 5.08553 | 0.329646 | ||||||||
\(239\) | −16.8314 | −1.08873 | −0.544365 | − | 0.838848i | \(-0.683230\pi\) | ||||
−0.544365 | + | 0.838848i | \(0.683230\pi\) | |||||||
\(240\) | −3.12232 | −0.201545 | ||||||||
\(241\) | −15.3101 | −0.986207 | −0.493104 | − | 0.869971i | \(-0.664138\pi\) | ||||
−0.493104 | + | 0.869971i | \(0.664138\pi\) | |||||||
\(242\) | −16.6119 | −1.06785 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.30423 | 0.275550 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −11.2697 | −0.718532 | ||||||||
\(247\) | 36.3826 | 2.31497 | ||||||||
\(248\) | −15.3593 | −0.975319 | ||||||||
\(249\) | −14.6322 | −0.927280 | ||||||||
\(250\) | 1.27660 | 0.0807394 | ||||||||
\(251\) | −15.5681 | −0.982647 | −0.491324 | − | 0.870977i | \(-0.663487\pi\) | ||||
−0.491324 | + | 0.870977i | \(0.663487\pi\) | |||||||
\(252\) | 0.370286 | 0.0233258 | ||||||||
\(253\) | 4.90026 | 0.308077 | ||||||||
\(254\) | 22.6403 | 1.42058 | ||||||||
\(255\) | 3.98364 | 0.249465 | ||||||||
\(256\) | −8.56344 | −0.535215 | ||||||||
\(257\) | 10.4474 | 0.651688 | 0.325844 | − | 0.945423i | \(-0.394351\pi\) | ||||
0.325844 | + | 0.945423i | \(0.394351\pi\) | |||||||
\(258\) | −6.03690 | −0.375841 | ||||||||
\(259\) | −5.24695 | −0.326029 | ||||||||
\(260\) | 1.66865 | 0.103485 | ||||||||
\(261\) | −7.63580 | −0.472644 | ||||||||
\(262\) | −9.25147 | −0.571558 | ||||||||
\(263\) | 4.47873 | 0.276171 | 0.138085 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138085 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(264\) | −14.8278 | −0.912586 | ||||||||
\(265\) | −13.8913 | −0.853333 | ||||||||
\(266\) | 10.3068 | 0.631948 | ||||||||
\(267\) | −2.83796 | −0.173680 | ||||||||
\(268\) | −0.153907 | −0.00940138 | ||||||||
\(269\) | 21.7194 | 1.32426 | 0.662128 | − | 0.749391i | \(-0.269654\pi\) | ||||
0.662128 | + | 0.749391i | \(0.269654\pi\) | |||||||
\(270\) | −1.27660 | −0.0776916 | ||||||||
\(271\) | 14.1313 | 0.858413 | 0.429206 | − | 0.903206i | \(-0.358793\pi\) | ||||
0.429206 | + | 0.903206i | \(0.358793\pi\) | |||||||
\(272\) | −12.4382 | −0.754177 | ||||||||
\(273\) | 4.50637 | 0.272738 | ||||||||
\(274\) | −23.8746 | −1.44232 | ||||||||
\(275\) | 4.90026 | 0.295497 | ||||||||
\(276\) | 0.370286 | 0.0222886 | ||||||||
\(277\) | −19.7094 | −1.18422 | −0.592111 | − | 0.805856i | \(-0.701705\pi\) | ||||
−0.592111 | + | 0.805856i | \(0.701705\pi\) | |||||||
\(278\) | 20.7234 | 1.24291 | ||||||||
\(279\) | −5.07594 | −0.303888 | ||||||||
\(280\) | 3.02591 | 0.180833 | ||||||||
\(281\) | −19.5815 | −1.16814 | −0.584068 | − | 0.811705i | \(-0.698540\pi\) | ||||
−0.584068 | + | 0.811705i | \(0.698540\pi\) | |||||||
\(282\) | 4.40019 | 0.262027 | ||||||||
\(283\) | 14.6687 | 0.871963 | 0.435981 | − | 0.899956i | \(-0.356401\pi\) | ||||
0.435981 | + | 0.899956i | \(0.356401\pi\) | |||||||
\(284\) | 0.00509138 | 0.000302118 0 | ||||||||
\(285\) | 8.07358 | 0.478238 | ||||||||
\(286\) | −28.1905 | −1.66694 | ||||||||
\(287\) | 8.82791 | 0.521095 | ||||||||
\(288\) | −2.06587 | −0.121732 | ||||||||
\(289\) | −1.13058 | −0.0665046 | ||||||||
\(290\) | −9.74788 | −0.572415 | ||||||||
\(291\) | 16.9015 | 0.990783 | ||||||||
\(292\) | −1.93916 | −0.113481 | ||||||||
\(293\) | 28.1979 | 1.64734 | 0.823670 | − | 0.567070i | \(-0.191923\pi\) | ||||
0.823670 | + | 0.567070i | \(0.191923\pi\) | |||||||
\(294\) | 1.27660 | 0.0744530 | ||||||||
\(295\) | −11.5380 | −0.671769 | ||||||||
\(296\) | 15.8768 | 0.922820 | ||||||||
\(297\) | −4.90026 | −0.284342 | ||||||||
\(298\) | −12.9262 | −0.748793 | ||||||||
\(299\) | 4.50637 | 0.260610 | ||||||||
\(300\) | 0.370286 | 0.0213785 | ||||||||
\(301\) | 4.72888 | 0.272568 | ||||||||
\(302\) | 28.5577 | 1.64331 | ||||||||
\(303\) | −2.93913 | −0.168848 | ||||||||
\(304\) | −25.2083 | −1.44579 | ||||||||
\(305\) | 11.6241 | 0.665592 | ||||||||
\(306\) | −5.08553 | −0.290720 | ||||||||
\(307\) | 26.6887 | 1.52320 | 0.761602 | − | 0.648045i | \(-0.224413\pi\) | ||||
0.761602 | + | 0.648045i | \(0.224413\pi\) | |||||||
\(308\) | 1.81450 | 0.103391 | ||||||||
\(309\) | 11.1499 | 0.634297 | ||||||||
\(310\) | −6.47995 | −0.368037 | ||||||||
\(311\) | −8.65298 | −0.490666 | −0.245333 | − | 0.969439i | \(-0.578897\pi\) | ||||
−0.245333 | + | 0.969439i | \(0.578897\pi\) | |||||||
\(312\) | −13.6359 | −0.771981 | ||||||||
\(313\) | 29.7841 | 1.68350 | 0.841750 | − | 0.539868i | \(-0.181526\pi\) | ||||
0.841750 | + | 0.539868i | \(0.181526\pi\) | |||||||
\(314\) | −22.8321 | −1.28849 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −0.922019 | −0.0518676 | ||||||||
\(317\) | −3.18540 | −0.178910 | −0.0894549 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894549 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(318\) | 17.7336 | 0.994451 | ||||||||
\(319\) | −37.4174 | −2.09497 | ||||||||
\(320\) | −8.88193 | −0.496515 | ||||||||
\(321\) | 0.0747441 | 0.00417181 | ||||||||
\(322\) | 1.27660 | 0.0711423 | ||||||||
\(323\) | 32.1623 | 1.78956 | ||||||||
\(324\) | −0.370286 | −0.0205714 | ||||||||
\(325\) | 4.50637 | 0.249969 | ||||||||
\(326\) | −1.60397 | −0.0888359 | ||||||||
\(327\) | −10.3065 | −0.569952 | ||||||||
\(328\) | −26.7125 | −1.47495 | ||||||||
\(329\) | −3.44679 | −0.190028 | ||||||||
\(330\) | −6.25569 | −0.344364 | ||||||||
\(331\) | 9.03447 | 0.496579 | 0.248290 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248290 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(332\) | −5.41811 | −0.297357 | ||||||||
\(333\) | 5.24695 | 0.287531 | ||||||||
\(334\) | −14.2425 | −0.779317 | ||||||||
\(335\) | −0.415644 | −0.0227091 | ||||||||
\(336\) | −3.12232 | −0.170336 | ||||||||
\(337\) | 15.3133 | 0.834166 | 0.417083 | − | 0.908868i | \(-0.363052\pi\) | ||||
0.417083 | + | 0.908868i | \(0.363052\pi\) | |||||||
\(338\) | −9.32866 | −0.507412 | ||||||||
\(339\) | −4.86844 | −0.264417 | ||||||||
\(340\) | 1.47509 | 0.0799978 | ||||||||
\(341\) | −24.8734 | −1.34697 | ||||||||
\(342\) | −10.3068 | −0.557326 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −14.3092 | −0.771499 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 18.6080 | 1.00037 | ||||||||
\(347\) | −0.274739 | −0.0147488 | −0.00737438 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737438 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(348\) | −2.82743 | −0.151566 | ||||||||
\(349\) | 11.9953 | 0.642094 | 0.321047 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321047 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(350\) | 1.27660 | 0.0682373 | ||||||||
\(351\) | −4.50637 | −0.240532 | ||||||||
\(352\) | −10.1233 | −0.539573 | ||||||||
\(353\) | 20.2066 | 1.07549 | 0.537745 | − | 0.843107i | \(-0.319276\pi\) | ||||
0.537745 | + | 0.843107i | \(0.319276\pi\) | |||||||
\(354\) | 14.7294 | 0.782861 | ||||||||
\(355\) | 0.0137499 | 0.000729767 0 | ||||||||
\(356\) | −1.05086 | −0.0556953 | ||||||||
\(357\) | 3.98364 | 0.210837 | ||||||||
\(358\) | 24.7346 | 1.30727 | ||||||||
\(359\) | 32.6414 | 1.72275 | 0.861373 | − | 0.507973i | \(-0.169605\pi\) | ||||
0.861373 | + | 0.507973i | \(0.169605\pi\) | |||||||
\(360\) | −3.02591 | −0.159480 | ||||||||
\(361\) | 46.1828 | 2.43067 | ||||||||
\(362\) | −5.92298 | −0.311305 | ||||||||
\(363\) | −13.0126 | −0.682982 | ||||||||
\(364\) | 1.66865 | 0.0874609 | ||||||||
\(365\) | −5.23692 | −0.274113 | ||||||||
\(366\) | −14.8393 | −0.775664 | ||||||||
\(367\) | 3.25575 | 0.169949 | 0.0849743 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849743 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(368\) | −3.12232 | −0.162762 | ||||||||
\(369\) | −8.82791 | −0.459562 | ||||||||
\(370\) | 6.69827 | 0.348226 | ||||||||
\(371\) | −13.8913 | −0.721198 | ||||||||
\(372\) | −1.87955 | −0.0974500 | ||||||||
\(373\) | 7.53712 | 0.390257 | 0.195129 | − | 0.980778i | \(-0.437488\pi\) | ||||
0.195129 | + | 0.980778i | \(0.437488\pi\) | |||||||
\(374\) | −24.9204 | −1.28860 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 10.4297 | 0.537871 | ||||||||
\(377\) | −34.4098 | −1.77219 | ||||||||
\(378\) | −1.27660 | −0.0656614 | ||||||||
\(379\) | −18.3325 | −0.941675 | −0.470838 | − | 0.882220i | \(-0.656048\pi\) | ||||
−0.470838 | + | 0.882220i | \(0.656048\pi\) | |||||||
\(380\) | 2.98953 | 0.153360 | ||||||||
\(381\) | 17.7348 | 0.908583 | ||||||||
\(382\) | 4.90250 | 0.250834 | ||||||||
\(383\) | −4.54692 | −0.232337 | −0.116168 | − | 0.993230i | \(-0.537061\pi\) | ||||
−0.116168 | + | 0.993230i | \(0.537061\pi\) | |||||||
\(384\) | 7.20695 | 0.367778 | ||||||||
\(385\) | 4.90026 | 0.249740 | ||||||||
\(386\) | 6.54306 | 0.333033 | ||||||||
\(387\) | −4.72888 | −0.240382 | ||||||||
\(388\) | 6.25838 | 0.317721 | ||||||||
\(389\) | 0.0546609 | 0.00277142 | 0.00138571 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138571 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(390\) | −5.75285 | −0.291307 | ||||||||
\(391\) | 3.98364 | 0.201462 | ||||||||
\(392\) | 3.02591 | 0.152832 | ||||||||
\(393\) | −7.24695 | −0.365560 | ||||||||
\(394\) | 10.2266 | 0.515209 | ||||||||
\(395\) | −2.49002 | −0.125286 | ||||||||
\(396\) | −1.81450 | −0.0911819 | ||||||||
\(397\) | 4.38391 | 0.220022 | 0.110011 | − | 0.993930i | \(-0.464911\pi\) | ||||
0.110011 | + | 0.993930i | \(0.464911\pi\) | |||||||
\(398\) | 11.1048 | 0.556635 | ||||||||
\(399\) | 8.07358 | 0.404185 | ||||||||
\(400\) | −3.12232 | −0.156116 | ||||||||
\(401\) | 28.4337 | 1.41991 | 0.709955 | − | 0.704247i | \(-0.248715\pi\) | ||||
0.709955 | + | 0.704247i | \(0.248715\pi\) | |||||||
\(402\) | 0.530612 | 0.0264645 | ||||||||
\(403\) | −22.8741 | −1.13944 | ||||||||
\(404\) | −1.08832 | −0.0541458 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −9.74788 | −0.483779 | ||||||||
\(407\) | 25.7114 | 1.27447 | ||||||||
\(408\) | −12.0542 | −0.596770 | ||||||||
\(409\) | −6.09312 | −0.301285 | −0.150643 | − | 0.988588i | \(-0.548134\pi\) | ||||
−0.150643 | + | 0.988588i | \(0.548134\pi\) | |||||||
\(410\) | −11.2697 | −0.556572 | ||||||||
\(411\) | −18.7017 | −0.922485 | ||||||||
\(412\) | 4.12866 | 0.203405 | ||||||||
\(413\) | −11.5380 | −0.567748 | ||||||||
\(414\) | −1.27660 | −0.0627416 | ||||||||
\(415\) | −14.6322 | −0.718268 | ||||||||
\(416\) | −9.30958 | −0.456440 | ||||||||
\(417\) | 16.2333 | 0.794947 | ||||||||
\(418\) | −50.5058 | −2.47032 | ||||||||
\(419\) | 28.3838 | 1.38664 | 0.693320 | − | 0.720630i | \(-0.256147\pi\) | ||||
0.693320 | + | 0.720630i | \(0.256147\pi\) | |||||||
\(420\) | 0.370286 | 0.0180681 | ||||||||
\(421\) | −10.2520 | −0.499652 | −0.249826 | − | 0.968291i | \(-0.580373\pi\) | ||||
−0.249826 | + | 0.968291i | \(0.580373\pi\) | |||||||
\(422\) | −0.170860 | −0.00831736 | ||||||||
\(423\) | 3.44679 | 0.167589 | ||||||||
\(424\) | 42.0337 | 2.04134 | ||||||||
\(425\) | 3.98364 | 0.193235 | ||||||||
\(426\) | −0.0175531 | −0.000850451 0 | ||||||||
\(427\) | 11.6241 | 0.562528 | ||||||||
\(428\) | 0.0276767 | 0.00133780 | ||||||||
\(429\) | −22.0824 | −1.06615 | ||||||||
\(430\) | −6.03690 | −0.291125 | ||||||||
\(431\) | −36.1581 | −1.74167 | −0.870836 | − | 0.491573i | \(-0.836422\pi\) | ||||
−0.870836 | + | 0.491573i | \(0.836422\pi\) | |||||||
\(432\) | 3.12232 | 0.150223 | ||||||||
\(433\) | −1.73863 | −0.0835531 | −0.0417766 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417766 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(434\) | −6.47995 | −0.311048 | ||||||||
\(435\) | −7.63580 | −0.366109 | ||||||||
\(436\) | −3.81636 | −0.182771 | ||||||||
\(437\) | 8.07358 | 0.386212 | ||||||||
\(438\) | 6.68546 | 0.319444 | ||||||||
\(439\) | −18.7589 | −0.895311 | −0.447656 | − | 0.894206i | \(-0.647741\pi\) | ||||
−0.447656 | + | 0.894206i | \(0.647741\pi\) | |||||||
\(440\) | −14.8278 | −0.706886 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −22.9173 | −1.09007 | ||||||||
\(443\) | 12.5021 | 0.593991 | 0.296996 | − | 0.954879i | \(-0.404015\pi\) | ||||
0.296996 | + | 0.954879i | \(0.404015\pi\) | |||||||
\(444\) | 1.94287 | 0.0922045 | ||||||||
\(445\) | −2.83796 | −0.134532 | ||||||||
\(446\) | −28.7914 | −1.36331 | ||||||||
\(447\) | −10.1254 | −0.478917 | ||||||||
\(448\) | −8.88193 | −0.419632 | ||||||||
\(449\) | 3.09266 | 0.145952 | 0.0729758 | − | 0.997334i | \(-0.476750\pi\) | ||||
0.0729758 | + | 0.997334i | \(0.476750\pi\) | |||||||
\(450\) | −1.27660 | −0.0601796 | ||||||||
\(451\) | −43.2590 | −2.03699 | ||||||||
\(452\) | −1.80271 | −0.0847925 | ||||||||
\(453\) | 22.3700 | 1.05104 | ||||||||
\(454\) | −24.6955 | −1.15902 | ||||||||
\(455\) | 4.50637 | 0.211262 | ||||||||
\(456\) | −24.4300 | −1.14404 | ||||||||
\(457\) | 9.70083 | 0.453786 | 0.226893 | − | 0.973920i | \(-0.427143\pi\) | ||||
0.226893 | + | 0.973920i | \(0.427143\pi\) | |||||||
\(458\) | −8.95362 | −0.418375 | ||||||||
\(459\) | −3.98364 | −0.185941 | ||||||||
\(460\) | 0.370286 | 0.0172647 | ||||||||
\(461\) | −30.4866 | −1.41990 | −0.709951 | − | 0.704251i | \(-0.751283\pi\) | ||||
−0.709951 | + | 0.704251i | \(0.751283\pi\) | |||||||
\(462\) | −6.25569 | −0.291041 | ||||||||
\(463\) | −33.0357 | −1.53530 | −0.767650 | − | 0.640869i | \(-0.778574\pi\) | ||||
−0.767650 | + | 0.640869i | \(0.778574\pi\) | |||||||
\(464\) | 23.8414 | 1.10681 | ||||||||
\(465\) | −5.07594 | −0.235391 | ||||||||
\(466\) | 23.6556 | 1.09583 | ||||||||
\(467\) | −37.8632 | −1.75210 | −0.876049 | − | 0.482222i | \(-0.839830\pi\) | ||||
−0.876049 | + | 0.482222i | \(0.839830\pi\) | |||||||
\(468\) | −1.66865 | −0.0771332 | ||||||||
\(469\) | −0.415644 | −0.0191927 | ||||||||
\(470\) | 4.40019 | 0.202965 | ||||||||
\(471\) | −17.8851 | −0.824100 | ||||||||
\(472\) | 34.9130 | 1.60700 | ||||||||
\(473\) | −23.1727 | −1.06548 | ||||||||
\(474\) | 3.17876 | 0.146005 | ||||||||
\(475\) | 8.07358 | 0.370441 | ||||||||
\(476\) | 1.47509 | 0.0676105 | ||||||||
\(477\) | 13.8913 | 0.636037 | ||||||||
\(478\) | 21.4870 | 0.982791 | ||||||||
\(479\) | 23.2812 | 1.06375 | 0.531873 | − | 0.846824i | \(-0.321489\pi\) | ||||
0.531873 | + | 0.846824i | \(0.321489\pi\) | |||||||
\(480\) | −2.06587 | −0.0942936 | ||||||||
\(481\) | 23.6447 | 1.07811 | ||||||||
\(482\) | 19.5449 | 0.890244 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −4.81836 | −0.219017 | ||||||||
\(485\) | 16.9015 | 0.767457 | ||||||||
\(486\) | 1.27660 | 0.0579079 | ||||||||
\(487\) | 0.794155 | 0.0359866 | 0.0179933 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179933 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(488\) | −35.1734 | −1.59223 | ||||||||
\(489\) | −1.25644 | −0.0568182 | ||||||||
\(490\) | 1.27660 | 0.0576710 | ||||||||
\(491\) | 2.99262 | 0.135055 | 0.0675274 | − | 0.997717i | \(-0.478489\pi\) | ||||
0.0675274 | + | 0.997717i | \(0.478489\pi\) | |||||||
\(492\) | −3.26885 | −0.147371 | ||||||||
\(493\) | −30.4183 | −1.36997 | ||||||||
\(494\) | −46.4461 | −2.08971 | ||||||||
\(495\) | −4.90026 | −0.220250 | ||||||||
\(496\) | 15.8487 | 0.711627 | ||||||||
\(497\) | 0.0137499 | 0.000616766 0 | ||||||||
\(498\) | 18.6795 | 0.837050 | ||||||||
\(499\) | −2.36763 | −0.105990 | −0.0529948 | − | 0.998595i | \(-0.516877\pi\) | ||||
−0.0529948 | + | 0.998595i | \(0.516877\pi\) | |||||||
\(500\) | 0.370286 | 0.0165597 | ||||||||
\(501\) | −11.1566 | −0.498440 | ||||||||
\(502\) | 19.8742 | 0.887030 | ||||||||
\(503\) | 9.62369 | 0.429099 | 0.214549 | − | 0.976713i | \(-0.431172\pi\) | ||||
0.214549 | + | 0.976713i | \(0.431172\pi\) | |||||||
\(504\) | −3.02591 | −0.134785 | ||||||||
\(505\) | −2.93913 | −0.130789 | ||||||||
\(506\) | −6.25569 | −0.278099 | ||||||||
\(507\) | −7.30741 | −0.324534 | ||||||||
\(508\) | 6.56696 | 0.291362 | ||||||||
\(509\) | 9.45127 | 0.418920 | 0.209460 | − | 0.977817i | \(-0.432829\pi\) | ||||
0.209460 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(510\) | −5.08553 | −0.225191 | ||||||||
\(511\) | −5.23692 | −0.231668 | ||||||||
\(512\) | 25.3460 | 1.12015 | ||||||||
\(513\) | −8.07358 | −0.356457 | ||||||||
\(514\) | −13.3371 | −0.588275 | ||||||||
\(515\) | 11.1499 | 0.491324 | ||||||||
\(516\) | −1.75104 | −0.0770851 | ||||||||
\(517\) | 16.8902 | 0.742830 | ||||||||
\(518\) | 6.69827 | 0.294305 | ||||||||
\(519\) | 14.5762 | 0.639824 | ||||||||
\(520\) | −13.6359 | −0.597974 | ||||||||
\(521\) | 26.6167 | 1.16610 | 0.583049 | − | 0.812437i | \(-0.301860\pi\) | ||||
0.583049 | + | 0.812437i | \(0.301860\pi\) | |||||||
\(522\) | 9.74788 | 0.426653 | ||||||||
\(523\) | −37.0328 | −1.61933 | −0.809666 | − | 0.586891i | \(-0.800352\pi\) | ||||
−0.809666 | + | 0.586891i | \(0.800352\pi\) | |||||||
\(524\) | −2.68344 | −0.117227 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −5.71756 | −0.249298 | ||||||||
\(527\) | −20.2207 | −0.880828 | ||||||||
\(528\) | 15.3002 | 0.665854 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 17.7336 | 0.770299 | ||||||||
\(531\) | 11.5380 | 0.500707 | ||||||||
\(532\) | 2.98953 | 0.129613 | ||||||||
\(533\) | −39.7819 | −1.72314 | ||||||||
\(534\) | 3.62295 | 0.156780 | ||||||||
\(535\) | 0.0747441 | 0.00323147 | ||||||||
\(536\) | 1.25770 | 0.0543245 | ||||||||
\(537\) | 19.3754 | 0.836109 | ||||||||
\(538\) | −27.7270 | −1.19540 | ||||||||
\(539\) | 4.90026 | 0.211069 | ||||||||
\(540\) | −0.370286 | −0.0159346 | ||||||||
\(541\) | 1.13558 | 0.0488224 | 0.0244112 | − | 0.999702i | \(-0.492229\pi\) | ||||
0.0244112 | + | 0.999702i | \(0.492229\pi\) | |||||||
\(542\) | −18.0400 | −0.774884 | ||||||||
\(543\) | −4.63964 | −0.199106 | ||||||||
\(544\) | −8.22969 | −0.352845 | ||||||||
\(545\) | −10.3065 | −0.441483 | ||||||||
\(546\) | −5.75285 | −0.246199 | ||||||||
\(547\) | −21.0464 | −0.899877 | −0.449939 | − | 0.893059i | \(-0.648554\pi\) | ||||
−0.449939 | + | 0.893059i | \(0.648554\pi\) | |||||||
\(548\) | −6.92496 | −0.295820 | ||||||||
\(549\) | −11.6241 | −0.496103 | ||||||||
\(550\) | −6.25569 | −0.266743 | ||||||||
\(551\) | −61.6483 | −2.62630 | ||||||||
\(552\) | −3.02591 | −0.128791 | ||||||||
\(553\) | −2.49002 | −0.105886 | ||||||||
\(554\) | 25.1611 | 1.06899 | ||||||||
\(555\) | 5.24695 | 0.222720 | ||||||||
\(556\) | 6.01095 | 0.254921 | ||||||||
\(557\) | 25.0999 | 1.06351 | 0.531757 | − | 0.846897i | \(-0.321532\pi\) | ||||
0.531757 | + | 0.846897i | \(0.321532\pi\) | |||||||
\(558\) | 6.47995 | 0.274318 | ||||||||
\(559\) | −21.3101 | −0.901321 | ||||||||
\(560\) | −3.12232 | −0.131942 | ||||||||
\(561\) | −19.5209 | −0.824173 | ||||||||
\(562\) | 24.9978 | 1.05447 | ||||||||
\(563\) | 15.6922 | 0.661346 | 0.330673 | − | 0.943745i | \(-0.392724\pi\) | ||||
0.330673 | + | 0.943745i | \(0.392724\pi\) | |||||||
\(564\) | 1.27630 | 0.0537419 | ||||||||
\(565\) | −4.86844 | −0.204817 | ||||||||
\(566\) | −18.7261 | −0.787116 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −0.0416059 | −0.00174575 | ||||||||
\(569\) | 37.1169 | 1.55602 | 0.778011 | − | 0.628250i | \(-0.216229\pi\) | ||||
0.778011 | + | 0.628250i | \(0.216229\pi\) | |||||||
\(570\) | −10.3068 | −0.431703 | ||||||||
\(571\) | 20.0947 | 0.840936 | 0.420468 | − | 0.907307i | \(-0.361866\pi\) | ||||
0.420468 | + | 0.907307i | \(0.361866\pi\) | |||||||
\(572\) | −8.17680 | −0.341889 | ||||||||
\(573\) | 3.84027 | 0.160430 | ||||||||
\(574\) | −11.2697 | −0.470389 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 8.88193 | 0.370080 | ||||||||
\(577\) | −9.32873 | −0.388360 | −0.194180 | − | 0.980966i | \(-0.562205\pi\) | ||||
−0.194180 | + | 0.980966i | \(0.562205\pi\) | |||||||
\(578\) | 1.44330 | 0.0600333 | ||||||||
\(579\) | 5.12537 | 0.213003 | ||||||||
\(580\) | −2.82743 | −0.117403 | ||||||||
\(581\) | −14.6322 | −0.607047 | ||||||||
\(582\) | −21.5765 | −0.894374 | ||||||||
\(583\) | 68.0707 | 2.81920 | ||||||||
\(584\) | 15.8465 | 0.655731 | ||||||||
\(585\) | −4.50637 | −0.186316 | ||||||||
\(586\) | −35.9975 | −1.48704 | ||||||||
\(587\) | −40.7683 | −1.68269 | −0.841343 | − | 0.540502i | \(-0.818235\pi\) | ||||
−0.841343 | + | 0.540502i | \(0.818235\pi\) | |||||||
\(588\) | 0.370286 | 0.0152703 | ||||||||
\(589\) | −40.9810 | −1.68859 | ||||||||
\(590\) | 14.7294 | 0.606402 | ||||||||
\(591\) | 8.01081 | 0.329521 | ||||||||
\(592\) | −16.3826 | −0.673322 | ||||||||
\(593\) | 21.5790 | 0.886143 | 0.443072 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443072 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(594\) | 6.25569 | 0.256674 | ||||||||
\(595\) | 3.98364 | 0.163313 | ||||||||
\(596\) | −3.74931 | −0.153578 | ||||||||
\(597\) | 8.69874 | 0.356016 | ||||||||
\(598\) | −5.75285 | −0.235252 | ||||||||
\(599\) | −30.2136 | −1.23450 | −0.617248 | − | 0.786769i | \(-0.711752\pi\) | ||||
−0.617248 | + | 0.786769i | \(0.711752\pi\) | |||||||
\(600\) | −3.02591 | −0.123532 | ||||||||
\(601\) | 47.4917 | 1.93723 | 0.968613 | − | 0.248572i | \(-0.0799614\pi\) | ||||
0.968613 | + | 0.248572i | \(0.0799614\pi\) | |||||||
\(602\) | −6.03690 | −0.246046 | ||||||||
\(603\) | 0.415644 | 0.0169263 | ||||||||
\(604\) | 8.28331 | 0.337043 | ||||||||
\(605\) | −13.0126 | −0.529035 | ||||||||
\(606\) | 3.75210 | 0.152419 | ||||||||
\(607\) | −35.9283 | −1.45828 | −0.729142 | − | 0.684363i | \(-0.760081\pi\) | ||||
−0.729142 | + | 0.684363i | \(0.760081\pi\) | |||||||
\(608\) | −16.6790 | −0.676421 | ||||||||
\(609\) | −7.63580 | −0.309418 | ||||||||
\(610\) | −14.8393 | −0.600826 | ||||||||
\(611\) | 15.5325 | 0.628380 | ||||||||
\(612\) | −1.47509 | −0.0596269 | ||||||||
\(613\) | 23.8546 | 0.963480 | 0.481740 | − | 0.876314i | \(-0.340005\pi\) | ||||
0.481740 | + | 0.876314i | \(0.340005\pi\) | |||||||
\(614\) | −34.0708 | −1.37499 | ||||||||
\(615\) | −8.82791 | −0.355976 | ||||||||
\(616\) | −14.8278 | −0.597428 | ||||||||
\(617\) | −12.3866 | −0.498667 | −0.249333 | − | 0.968418i | \(-0.580212\pi\) | ||||
−0.249333 | + | 0.968418i | \(0.580212\pi\) | |||||||
\(618\) | −14.2340 | −0.572576 | ||||||||
\(619\) | 24.8467 | 0.998671 | 0.499336 | − | 0.866409i | \(-0.333577\pi\) | ||||
0.499336 | + | 0.866409i | \(0.333577\pi\) | |||||||
\(620\) | −1.87955 | −0.0754844 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 11.0464 | 0.442921 | ||||||||
\(623\) | −2.83796 | −0.113700 | ||||||||
\(624\) | 14.0703 | 0.563264 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −38.0225 | −1.51969 | ||||||||
\(627\) | −39.5627 | −1.57998 | ||||||||
\(628\) | −6.62258 | −0.264270 | ||||||||
\(629\) | 20.9020 | 0.833416 | ||||||||
\(630\) | −1.27660 | −0.0508611 | ||||||||
\(631\) | 26.7079 | 1.06323 | 0.531613 | − | 0.846987i | \(-0.321586\pi\) | ||||
0.531613 | + | 0.846987i | \(0.321586\pi\) | |||||||
\(632\) | 7.53458 | 0.299710 | ||||||||
\(633\) | −0.133840 | −0.00531966 | ||||||||
\(634\) | 4.06649 | 0.161501 | ||||||||
\(635\) | 17.7348 | 0.703785 | ||||||||
\(636\) | 5.14373 | 0.203962 | ||||||||
\(637\) | 4.50637 | 0.178549 | ||||||||
\(638\) | 47.7672 | 1.89112 | ||||||||
\(639\) | −0.0137499 | −0.000543936 0 | ||||||||
\(640\) | 7.20695 | 0.284880 | ||||||||
\(641\) | −16.7496 | −0.661569 | −0.330784 | − | 0.943706i | \(-0.607313\pi\) | ||||
−0.330784 | + | 0.943706i | \(0.607313\pi\) | |||||||
\(642\) | −0.0954186 | −0.00376587 | ||||||||
\(643\) | 37.2806 | 1.47021 | 0.735103 | − | 0.677956i | \(-0.237134\pi\) | ||||
0.735103 | + | 0.677956i | \(0.237134\pi\) | |||||||
\(644\) | 0.370286 | 0.0145913 | ||||||||
\(645\) | −4.72888 | −0.186199 | ||||||||
\(646\) | −41.0585 | −1.61542 | ||||||||
\(647\) | 29.4555 | 1.15802 | 0.579008 | − | 0.815322i | \(-0.303440\pi\) | ||||
0.579008 | + | 0.815322i | \(0.303440\pi\) | |||||||
\(648\) | 3.02591 | 0.118869 | ||||||||
\(649\) | 56.5392 | 2.21936 | ||||||||
\(650\) | −5.75285 | −0.225645 | ||||||||
\(651\) | −5.07594 | −0.198942 | ||||||||
\(652\) | −0.465242 | −0.0182203 | ||||||||
\(653\) | 14.2991 | 0.559567 | 0.279784 | − | 0.960063i | \(-0.409737\pi\) | ||||
0.279784 | + | 0.960063i | \(0.409737\pi\) | |||||||
\(654\) | 13.1573 | 0.514493 | ||||||||
\(655\) | −7.24695 | −0.283162 | ||||||||
\(656\) | 27.5635 | 1.07617 | ||||||||
\(657\) | 5.23692 | 0.204312 | ||||||||
\(658\) | 4.40019 | 0.171537 | ||||||||
\(659\) | 37.4967 | 1.46066 | 0.730332 | − | 0.683092i | \(-0.239365\pi\) | ||||
0.730332 | + | 0.683092i | \(0.239365\pi\) | |||||||
\(660\) | −1.81450 | −0.0706292 | ||||||||
\(661\) | −38.5966 | −1.50123 | −0.750616 | − | 0.660738i | \(-0.770243\pi\) | ||||
−0.750616 | + | 0.660738i | \(0.770243\pi\) | |||||||
\(662\) | −11.5334 | −0.448259 | ||||||||
\(663\) | −17.9518 | −0.697190 | ||||||||
\(664\) | 44.2759 | 1.71824 | ||||||||
\(665\) | 8.07358 | 0.313080 | ||||||||
\(666\) | −6.69827 | −0.259553 | ||||||||
\(667\) | −7.63580 | −0.295659 | ||||||||
\(668\) | −4.13113 | −0.159838 | ||||||||
\(669\) | −22.5532 | −0.871956 | ||||||||
\(670\) | 0.530612 | 0.0204993 | ||||||||
\(671\) | −56.9610 | −2.19895 | ||||||||
\(672\) | −2.06587 | −0.0796926 | ||||||||
\(673\) | −37.2134 | −1.43447 | −0.717235 | − | 0.696831i | \(-0.754593\pi\) | ||||
−0.717235 | + | 0.696831i | \(0.754593\pi\) | |||||||
\(674\) | −19.5489 | −0.752997 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −2.70583 | −0.104070 | ||||||||
\(677\) | −39.7033 | −1.52592 | −0.762960 | − | 0.646446i | \(-0.776255\pi\) | ||||
−0.762960 | + | 0.646446i | \(0.776255\pi\) | |||||||
\(678\) | 6.21506 | 0.238688 | ||||||||
\(679\) | 16.9015 | 0.648620 | ||||||||
\(680\) | −12.0542 | −0.462256 | ||||||||
\(681\) | −19.3447 | −0.741290 | ||||||||
\(682\) | 31.7535 | 1.21590 | ||||||||
\(683\) | −0.378741 | −0.0144921 | −0.00724605 | − | 0.999974i | \(-0.502307\pi\) | ||||
−0.00724605 | + | 0.999974i | \(0.502307\pi\) | |||||||
\(684\) | −2.98953 | −0.114308 | ||||||||
\(685\) | −18.7017 | −0.714554 | ||||||||
\(686\) | 1.27660 | 0.0487409 | ||||||||
\(687\) | −7.01364 | −0.267587 | ||||||||
\(688\) | 14.7651 | 0.562913 | ||||||||
\(689\) | 62.5992 | 2.38484 | ||||||||
\(690\) | −1.27660 | −0.0485994 | ||||||||
\(691\) | 29.4083 | 1.11874 | 0.559372 | − | 0.828917i | \(-0.311042\pi\) | ||||
0.559372 | + | 0.828917i | \(0.311042\pi\) | |||||||
\(692\) | 5.39736 | 0.205177 | ||||||||
\(693\) | −4.90026 | −0.186146 | ||||||||
\(694\) | 0.350732 | 0.0133136 | ||||||||
\(695\) | 16.2333 | 0.615763 | ||||||||
\(696\) | 23.1053 | 0.875803 | ||||||||
\(697\) | −35.1672 | −1.33205 | ||||||||
\(698\) | −15.3132 | −0.579614 | ||||||||
\(699\) | 18.5301 | 0.700874 | ||||||||
\(700\) | 0.370286 | 0.0139955 | ||||||||
\(701\) | −16.8501 | −0.636419 | −0.318210 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318210 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(702\) | 5.75285 | 0.217127 | ||||||||
\(703\) | 42.3617 | 1.59770 | ||||||||
\(704\) | 43.5238 | 1.64036 | ||||||||
\(705\) | 3.44679 | 0.129814 | ||||||||
\(706\) | −25.7958 | −0.970839 | ||||||||
\(707\) | −2.93913 | −0.110537 | ||||||||
\(708\) | 4.27236 | 0.160565 | ||||||||
\(709\) | −12.9703 | −0.487111 | −0.243555 | − | 0.969887i | \(-0.578314\pi\) | ||||
−0.243555 | + | 0.969887i | \(0.578314\pi\) | |||||||
\(710\) | −0.0175531 | −0.000658757 0 | ||||||||
\(711\) | 2.49002 | 0.0933830 | ||||||||
\(712\) | 8.58742 | 0.321827 | ||||||||
\(713\) | −5.07594 | −0.190095 | ||||||||
\(714\) | −5.08553 | −0.190321 | ||||||||
\(715\) | −22.0824 | −0.825835 | ||||||||
\(716\) | 7.17443 | 0.268121 | ||||||||
\(717\) | 16.8314 | 0.628579 | ||||||||
\(718\) | −41.6701 | −1.55511 | ||||||||
\(719\) | −28.5189 | −1.06357 | −0.531787 | − | 0.846878i | \(-0.678479\pi\) | ||||
−0.531787 | + | 0.846878i | \(0.678479\pi\) | |||||||
\(720\) | 3.12232 | 0.116362 | ||||||||
\(721\) | 11.1499 | 0.415245 | ||||||||
\(722\) | −58.9570 | −2.19415 | ||||||||
\(723\) | 15.3101 | 0.569387 | ||||||||
\(724\) | −1.71799 | −0.0638487 | ||||||||
\(725\) | −7.63580 | −0.283586 | ||||||||
\(726\) | 16.6119 | 0.616524 | ||||||||
\(727\) | −47.5256 | −1.76263 | −0.881313 | − | 0.472532i | \(-0.843340\pi\) | ||||
−0.881313 | + | 0.472532i | \(0.843340\pi\) | |||||||
\(728\) | −13.6359 | −0.505380 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.68546 | 0.247440 | ||||||||
\(731\) | −18.8382 | −0.696755 | ||||||||
\(732\) | −4.30423 | −0.159089 | ||||||||
\(733\) | 20.6587 | 0.763046 | 0.381523 | − | 0.924359i | \(-0.375400\pi\) | ||||
0.381523 | + | 0.924359i | \(0.375400\pi\) | |||||||
\(734\) | −4.15629 | −0.153412 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −2.06587 | −0.0761489 | ||||||||
\(737\) | 2.03676 | 0.0750252 | ||||||||
\(738\) | 11.2697 | 0.414844 | ||||||||
\(739\) | 19.6839 | 0.724084 | 0.362042 | − | 0.932162i | \(-0.382080\pi\) | ||||
0.362042 | + | 0.932162i | \(0.382080\pi\) | |||||||
\(740\) | 1.94287 | 0.0714213 | ||||||||
\(741\) | −36.3826 | −1.33655 | ||||||||
\(742\) | 17.7336 | 0.651021 | ||||||||
\(743\) | −23.9674 | −0.879280 | −0.439640 | − | 0.898174i | \(-0.644894\pi\) | ||||
−0.439640 | + | 0.898174i | \(0.644894\pi\) | |||||||
\(744\) | 15.3593 | 0.563101 | ||||||||
\(745\) | −10.1254 | −0.370968 | ||||||||
\(746\) | −9.62190 | −0.352283 | ||||||||
\(747\) | 14.6322 | 0.535365 | ||||||||
\(748\) | −7.22831 | −0.264293 | ||||||||
\(749\) | 0.0747441 | 0.00273109 | ||||||||
\(750\) | −1.27660 | −0.0466149 | ||||||||
\(751\) | −49.9941 | −1.82431 | −0.912156 | − | 0.409843i | \(-0.865583\pi\) | ||||
−0.912156 | + | 0.409843i | \(0.865583\pi\) | |||||||
\(752\) | −10.7620 | −0.392449 | ||||||||
\(753\) | 15.5681 | 0.567332 | ||||||||
\(754\) | 43.9276 | 1.59975 | ||||||||
\(755\) | 22.3700 | 0.814129 | ||||||||
\(756\) | −0.370286 | −0.0134672 | ||||||||
\(757\) | 3.78026 | 0.137396 | 0.0686979 | − | 0.997638i | \(-0.478116\pi\) | ||||
0.0686979 | + | 0.997638i | \(0.478116\pi\) | |||||||
\(758\) | 23.4033 | 0.850045 | ||||||||
\(759\) | −4.90026 | −0.177868 | ||||||||
\(760\) | −24.4300 | −0.886168 | ||||||||
\(761\) | 37.9329 | 1.37507 | 0.687534 | − | 0.726153i | \(-0.258693\pi\) | ||||
0.687534 | + | 0.726153i | \(0.258693\pi\) | |||||||
\(762\) | −22.6403 | −0.820172 | ||||||||
\(763\) | −10.3065 | −0.373121 | ||||||||
\(764\) | 1.42200 | 0.0514461 | ||||||||
\(765\) | −3.98364 | −0.144029 | ||||||||
\(766\) | 5.80461 | 0.209729 | ||||||||
\(767\) | 51.9946 | 1.87741 | ||||||||
\(768\) | 8.56344 | 0.309006 | ||||||||
\(769\) | −17.0955 | −0.616481 | −0.308240 | − | 0.951308i | \(-0.599740\pi\) | ||||
−0.308240 | + | 0.951308i | \(0.599740\pi\) | |||||||
\(770\) | −6.25569 | −0.225439 | ||||||||
\(771\) | −10.4474 | −0.376253 | ||||||||
\(772\) | 1.89785 | 0.0683052 | ||||||||
\(773\) | 20.8751 | 0.750827 | 0.375413 | − | 0.926857i | \(-0.377501\pi\) | ||||
0.375413 | + | 0.926857i | \(0.377501\pi\) | |||||||
\(774\) | 6.03690 | 0.216992 | ||||||||
\(775\) | −5.07594 | −0.182333 | ||||||||
\(776\) | −51.1424 | −1.83591 | ||||||||
\(777\) | 5.24695 | 0.188233 | ||||||||
\(778\) | −0.0697803 | −0.00250174 | ||||||||
\(779\) | −71.2728 | −2.55361 | ||||||||
\(780\) | −1.66865 | −0.0597471 | ||||||||
\(781\) | −0.0673779 | −0.00241097 | ||||||||
\(782\) | −5.08553 | −0.181858 | ||||||||
\(783\) | 7.63580 | 0.272881 | ||||||||
\(784\) | −3.12232 | −0.111511 | ||||||||
\(785\) | −17.8851 | −0.638345 | ||||||||
\(786\) | 9.25147 | 0.329989 | ||||||||
\(787\) | 29.7743 | 1.06134 | 0.530670 | − | 0.847579i | \(-0.321940\pi\) | ||||
0.530670 | + | 0.847579i | \(0.321940\pi\) | |||||||
\(788\) | 2.96629 | 0.105670 | ||||||||
\(789\) | −4.47873 | −0.159447 | ||||||||
\(790\) | 3.17876 | 0.113095 | ||||||||
\(791\) | −4.86844 | −0.173102 | ||||||||
\(792\) | 14.8278 | 0.526882 | ||||||||
\(793\) | −52.3824 | −1.86015 | ||||||||
\(794\) | −5.59652 | −0.198613 | ||||||||
\(795\) | 13.8913 | 0.492672 | ||||||||
\(796\) | 3.22102 | 0.114166 | ||||||||
\(797\) | 23.3339 | 0.826530 | 0.413265 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413265 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(798\) | −10.3068 | −0.364855 | ||||||||
\(799\) | 13.7308 | 0.485761 | ||||||||
\(800\) | −2.06587 | −0.0730395 | ||||||||
\(801\) | 2.83796 | 0.100274 | ||||||||
\(802\) | −36.2985 | −1.28174 | ||||||||
\(803\) | 25.6623 | 0.905601 | ||||||||
\(804\) | 0.153907 | 0.00542789 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | 29.2011 | 1.02856 | ||||||||
\(807\) | −21.7194 | −0.764559 | ||||||||
\(808\) | 8.89354 | 0.312874 | ||||||||
\(809\) | −4.03632 | −0.141909 | −0.0709547 | − | 0.997480i | \(-0.522605\pi\) | ||||
−0.0709547 | + | 0.997480i | \(0.522605\pi\) | |||||||
\(810\) | 1.27660 | 0.0448552 | ||||||||
\(811\) | 1.22018 | 0.0428463 | 0.0214231 | − | 0.999770i | \(-0.493180\pi\) | ||||
0.0214231 | + | 0.999770i | \(0.493180\pi\) | |||||||
\(812\) | −2.82743 | −0.0992233 | ||||||||
\(813\) | −14.1313 | −0.495605 | ||||||||
\(814\) | −32.8232 | −1.15045 | ||||||||
\(815\) | −1.25644 | −0.0440112 | ||||||||
\(816\) | 12.4382 | 0.435424 | ||||||||
\(817\) | −38.1790 | −1.33571 | ||||||||
\(818\) | 7.77849 | 0.271969 | ||||||||
\(819\) | −4.50637 | −0.157465 | ||||||||
\(820\) | −3.26885 | −0.114153 | ||||||||
\(821\) | −15.7740 | −0.550515 | −0.275258 | − | 0.961371i | \(-0.588763\pi\) | ||||
−0.275258 | + | 0.961371i | \(0.588763\pi\) | |||||||
\(822\) | 23.8746 | 0.832722 | ||||||||
\(823\) | −27.2866 | −0.951152 | −0.475576 | − | 0.879675i | \(-0.657760\pi\) | ||||
−0.475576 | + | 0.879675i | \(0.657760\pi\) | |||||||
\(824\) | −33.7387 | −1.17534 | ||||||||
\(825\) | −4.90026 | −0.170605 | ||||||||
\(826\) | 14.7294 | 0.512503 | ||||||||
\(827\) | −22.1178 | −0.769111 | −0.384555 | − | 0.923102i | \(-0.625645\pi\) | ||||
−0.384555 | + | 0.923102i | \(0.625645\pi\) | |||||||
\(828\) | −0.370286 | −0.0128683 | ||||||||
\(829\) | −9.81595 | −0.340922 | −0.170461 | − | 0.985364i | \(-0.554526\pi\) | ||||
−0.170461 | + | 0.985364i | \(0.554526\pi\) | |||||||
\(830\) | 18.6795 | 0.648376 | ||||||||
\(831\) | 19.7094 | 0.683711 | ||||||||
\(832\) | 40.0253 | 1.38763 | ||||||||
\(833\) | 3.98364 | 0.138025 | ||||||||
\(834\) | −20.7234 | −0.717594 | ||||||||
\(835\) | −11.1566 | −0.386090 | ||||||||
\(836\) | −14.6495 | −0.506663 | ||||||||
\(837\) | 5.07594 | 0.175450 | ||||||||
\(838\) | −36.2348 | −1.25171 | ||||||||
\(839\) | 10.5603 | 0.364583 | 0.182291 | − | 0.983245i | \(-0.441649\pi\) | ||||
0.182291 | + | 0.983245i | \(0.441649\pi\) | |||||||
\(840\) | −3.02591 | −0.104404 | ||||||||
\(841\) | 29.3054 | 1.01053 | ||||||||
\(842\) | 13.0877 | 0.451033 | ||||||||
\(843\) | 19.5815 | 0.674424 | ||||||||
\(844\) | −0.0495591 | −0.00170589 | ||||||||
\(845\) | −7.30741 | −0.251383 | ||||||||
\(846\) | −4.40019 | −0.151282 | ||||||||
\(847\) | −13.0126 | −0.447117 | ||||||||
\(848\) | −43.3729 | −1.48943 | ||||||||
\(849\) | −14.6687 | −0.503428 | ||||||||
\(850\) | −5.08553 | −0.174432 | ||||||||
\(851\) | 5.24695 | 0.179863 | ||||||||
\(852\) | −0.00509138 | −0.000174428 0 | ||||||||
\(853\) | 24.5300 | 0.839890 | 0.419945 | − | 0.907550i | \(-0.362049\pi\) | ||||
0.419945 | + | 0.907550i | \(0.362049\pi\) | |||||||
\(854\) | −14.8393 | −0.507791 | ||||||||
\(855\) | −8.07358 | −0.276111 | ||||||||
\(856\) | −0.226169 | −0.00773031 | ||||||||
\(857\) | 10.6203 | 0.362781 | 0.181391 | − | 0.983411i | \(-0.441940\pi\) | ||||
0.181391 | + | 0.983411i | \(0.441940\pi\) | |||||||
\(858\) | 28.1905 | 0.962406 | ||||||||
\(859\) | −13.7045 | −0.467593 | −0.233797 | − | 0.972286i | \(-0.575115\pi\) | ||||
−0.233797 | + | 0.972286i | \(0.575115\pi\) | |||||||
\(860\) | −1.75104 | −0.0597099 | ||||||||
\(861\) | −8.82791 | −0.300854 | ||||||||
\(862\) | 46.1595 | 1.57220 | ||||||||
\(863\) | 35.3808 | 1.20438 | 0.602189 | − | 0.798354i | \(-0.294295\pi\) | ||||
0.602189 | + | 0.798354i | \(0.294295\pi\) | |||||||
\(864\) | 2.06587 | 0.0702823 | ||||||||
\(865\) | 14.5762 | 0.495605 | ||||||||
\(866\) | 2.21954 | 0.0754229 | ||||||||
\(867\) | 1.13058 | 0.0383964 | ||||||||
\(868\) | −1.87955 | −0.0637960 | ||||||||
\(869\) | 12.2017 | 0.413916 | ||||||||
\(870\) | 9.74788 | 0.330484 | ||||||||
\(871\) | 1.87305 | 0.0634658 | ||||||||
\(872\) | 31.1867 | 1.05611 | ||||||||
\(873\) | −16.9015 | −0.572029 | ||||||||
\(874\) | −10.3068 | −0.348631 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 1.93916 | 0.0655180 | ||||||||
\(877\) | −33.2454 | −1.12262 | −0.561308 | − | 0.827607i | \(-0.689702\pi\) | ||||
−0.561308 | + | 0.827607i | \(0.689702\pi\) | |||||||
\(878\) | 23.9476 | 0.808193 | ||||||||
\(879\) | −28.1979 | −0.951092 | ||||||||
\(880\) | 15.3002 | 0.515768 | ||||||||
\(881\) | −3.78991 | −0.127685 | −0.0638427 | − | 0.997960i | \(-0.520336\pi\) | ||||
−0.0638427 | + | 0.997960i | \(0.520336\pi\) | |||||||
\(882\) | −1.27660 | −0.0429854 | ||||||||
\(883\) | −46.0928 | −1.55115 | −0.775573 | − | 0.631258i | \(-0.782539\pi\) | ||||
−0.775573 | + | 0.631258i | \(0.782539\pi\) | |||||||
\(884\) | −6.64730 | −0.223573 | ||||||||
\(885\) | 11.5380 | 0.387846 | ||||||||
\(886\) | −15.9602 | −0.536193 | ||||||||
\(887\) | −7.77075 | −0.260916 | −0.130458 | − | 0.991454i | \(-0.541645\pi\) | ||||
−0.130458 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(888\) | −15.8768 | −0.532791 | ||||||||
\(889\) | 17.7348 | 0.594807 | ||||||||
\(890\) | 3.62295 | 0.121441 | ||||||||
\(891\) | 4.90026 | 0.164165 | ||||||||
\(892\) | −8.35112 | −0.279616 | ||||||||
\(893\) | 27.8280 | 0.931228 | ||||||||
\(894\) | 12.9262 | 0.432316 | ||||||||
\(895\) | 19.3754 | 0.647647 | ||||||||
\(896\) | 7.20695 | 0.240767 | ||||||||
\(897\) | −4.50637 | −0.150463 | ||||||||
\(898\) | −3.94810 | −0.131750 | ||||||||
\(899\) | 38.7588 | 1.29268 | ||||||||
\(900\) | −0.370286 | −0.0123429 | ||||||||
\(901\) | 55.3378 | 1.84357 | ||||||||
\(902\) | 55.2246 | 1.83878 | ||||||||
\(903\) | −4.72888 | −0.157367 | ||||||||
\(904\) | 14.7315 | 0.489961 | ||||||||
\(905\) | −4.63964 | −0.154227 | ||||||||
\(906\) | −28.5577 | −0.948765 | ||||||||
\(907\) | 3.00779 | 0.0998719 | 0.0499360 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499360 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(908\) | −7.16306 | −0.237715 | ||||||||
\(909\) | 2.93913 | 0.0974847 | ||||||||
\(910\) | −5.75285 | −0.190705 | ||||||||
\(911\) | 10.8287 | 0.358769 | 0.179385 | − | 0.983779i | \(-0.442589\pi\) | ||||
0.179385 | + | 0.983779i | \(0.442589\pi\) | |||||||
\(912\) | 25.2083 | 0.834730 | ||||||||
\(913\) | 71.7017 | 2.37298 | ||||||||
\(914\) | −12.3841 | −0.409630 | ||||||||
\(915\) | −11.6241 | −0.384280 | ||||||||
\(916\) | −2.59705 | −0.0858089 | ||||||||
\(917\) | −7.24695 | −0.239315 | ||||||||
\(918\) | 5.08553 | 0.167848 | ||||||||
\(919\) | −18.7216 | −0.617568 | −0.308784 | − | 0.951132i | \(-0.599922\pi\) | ||||
−0.308784 | + | 0.951132i | \(0.599922\pi\) | |||||||
\(920\) | −3.02591 | −0.0997614 | ||||||||
\(921\) | −26.6887 | −0.879422 | ||||||||
\(922\) | 38.9193 | 1.28174 | ||||||||
\(923\) | −0.0619621 | −0.00203951 | ||||||||
\(924\) | −1.81450 | −0.0596926 | ||||||||
\(925\) | 5.24695 | 0.172519 | ||||||||
\(926\) | 42.1735 | 1.38591 | ||||||||
\(927\) | −11.1499 | −0.366212 | ||||||||
\(928\) | 15.7746 | 0.517825 | ||||||||
\(929\) | 37.1627 | 1.21927 | 0.609634 | − | 0.792683i | \(-0.291316\pi\) | ||||
0.609634 | + | 0.792683i | \(0.291316\pi\) | |||||||
\(930\) | 6.47995 | 0.212486 | ||||||||
\(931\) | 8.07358 | 0.264601 | ||||||||
\(932\) | 6.86145 | 0.224754 | ||||||||
\(933\) | 8.65298 | 0.283286 | ||||||||
\(934\) | 48.3362 | 1.58161 | ||||||||
\(935\) | −19.5209 | −0.638402 | ||||||||
\(936\) | 13.6359 | 0.445703 | ||||||||
\(937\) | 55.6539 | 1.81813 | 0.909067 | − | 0.416650i | \(-0.136796\pi\) | ||||
0.909067 | + | 0.416650i | \(0.136796\pi\) | |||||||
\(938\) | 0.530612 | 0.0173251 | ||||||||
\(939\) | −29.7841 | −0.971969 | ||||||||
\(940\) | 1.27630 | 0.0416283 | ||||||||
\(941\) | −17.4038 | −0.567348 | −0.283674 | − | 0.958921i | \(-0.591553\pi\) | ||||
−0.283674 | + | 0.958921i | \(0.591553\pi\) | |||||||
\(942\) | 22.8321 | 0.743910 | ||||||||
\(943\) | −8.82791 | −0.287476 | ||||||||
\(944\) | −36.0253 | −1.17252 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 29.5824 | 0.961806 | ||||||||
\(947\) | 1.49523 | 0.0485884 | 0.0242942 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242942 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(948\) | 0.922019 | 0.0299458 | ||||||||
\(949\) | 23.5995 | 0.766073 | ||||||||
\(950\) | −10.3068 | −0.334395 | ||||||||
\(951\) | 3.18540 | 0.103294 | ||||||||
\(952\) | −12.0542 | −0.390678 | ||||||||
\(953\) | 0.362277 | 0.0117353 | 0.00586765 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586765 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(954\) | −17.7336 | −0.574147 | ||||||||
\(955\) | 3.84027 | 0.124268 | ||||||||
\(956\) | 6.23242 | 0.201571 | ||||||||
\(957\) | 37.4174 | 1.20953 | ||||||||
\(958\) | −29.7208 | −0.960237 | ||||||||
\(959\) | −18.7017 | −0.603908 | ||||||||
\(960\) | 8.88193 | 0.286663 | ||||||||
\(961\) | −5.23488 | −0.168867 | ||||||||
\(962\) | −30.1849 | −0.973200 | ||||||||
\(963\) | −0.0747441 | −0.00240860 | ||||||||
\(964\) | 5.66910 | 0.182589 | ||||||||
\(965\) | 5.12537 | 0.164992 | ||||||||
\(966\) | −1.27660 | −0.0410740 | ||||||||
\(967\) | 29.3252 | 0.943036 | 0.471518 | − | 0.881857i | \(-0.343706\pi\) | ||||
0.471518 | + | 0.881857i | \(0.343706\pi\) | |||||||
\(968\) | 39.3749 | 1.26556 | ||||||||
\(969\) | −32.1623 | −1.03320 | ||||||||
\(970\) | −21.5765 | −0.692779 | ||||||||
\(971\) | −32.0712 | −1.02921 | −0.514607 | − | 0.857426i | \(-0.672062\pi\) | ||||
−0.514607 | + | 0.857426i | \(0.672062\pi\) | |||||||
\(972\) | 0.370286 | 0.0118769 | ||||||||
\(973\) | 16.2333 | 0.520415 | ||||||||
\(974\) | −1.01382 | −0.0324849 | ||||||||
\(975\) | −4.50637 | −0.144319 | ||||||||
\(976\) | 36.2940 | 1.16174 | ||||||||
\(977\) | −15.0727 | −0.482218 | −0.241109 | − | 0.970498i | \(-0.577511\pi\) | ||||
−0.241109 | + | 0.970498i | \(0.577511\pi\) | |||||||
\(978\) | 1.60397 | 0.0512894 | ||||||||
\(979\) | 13.9067 | 0.444461 | ||||||||
\(980\) | 0.370286 | 0.0118283 | ||||||||
\(981\) | 10.3065 | 0.329062 | ||||||||
\(982\) | −3.82038 | −0.121913 | ||||||||
\(983\) | 9.08586 | 0.289794 | 0.144897 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144897 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(984\) | 26.7125 | 0.851563 | ||||||||
\(985\) | 8.01081 | 0.255245 | ||||||||
\(986\) | 38.8321 | 1.23667 | ||||||||
\(987\) | 3.44679 | 0.109713 | ||||||||
\(988\) | −13.4720 | −0.428600 | ||||||||
\(989\) | −4.72888 | −0.150370 | ||||||||
\(990\) | 6.25569 | 0.198819 | ||||||||
\(991\) | −5.52857 | −0.175621 | −0.0878104 | − | 0.996137i | \(-0.527987\pi\) | ||||
−0.0878104 | + | 0.996137i | \(0.527987\pi\) | |||||||
\(992\) | 10.4862 | 0.332938 | ||||||||
\(993\) | −9.03447 | −0.286700 | ||||||||
\(994\) | −0.0175531 | −0.000556751 0 | ||||||||
\(995\) | 8.69874 | 0.275768 | ||||||||
\(996\) | 5.41811 | 0.171679 | ||||||||
\(997\) | −44.5505 | −1.41093 | −0.705464 | − | 0.708746i | \(-0.749261\pi\) | ||||
−0.705464 | + | 0.708746i | \(0.749261\pi\) | |||||||
\(998\) | 3.02252 | 0.0956763 | ||||||||
\(999\) | −5.24695 | −0.166006 |
(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 | 2415.2.a.p.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 7245.2.a.bk.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2415.2.a.p.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7245.2.a.bk.1.5 | 6 | 3.2 | odd | 2 |