Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.148347072.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 29x^{4} + 223x^{2} + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.2 | ||
Root | \(-3.41374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.s.271.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.663404 | + | 1.14905i | −0.234549 | + | 0.406251i | −0.959141 | − | 0.282927i | \(-0.908695\pi\) |
0.724593 | + | 0.689177i | \(0.242028\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.11979 | + | 5.40363i | 0.389974 | + | 0.675454i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0521 | − | 20.8749i | 0.650754 | − | 1.12714i | −0.332186 | − | 0.943214i | \(-0.607786\pi\) |
0.982940 | − | 0.183925i | \(-0.0588804\pi\) | |||||||
\(8\) | −18.8932 | −0.834969 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.63404 | −0.209787 | ||||||||
\(11\) | 4.13810 | − | 7.16739i | 0.113426 | − | 0.196459i | −0.803724 | − | 0.595003i | \(-0.797151\pi\) |
0.917149 | + | 0.398544i | \(0.130484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −43.5573 | − | 75.4434i | −0.929278 | − | 1.60956i | −0.784533 | − | 0.620087i | \(-0.787097\pi\) |
−0.144745 | − | 0.989469i | \(-0.546236\pi\) | |||||||
\(14\) | 15.9909 | + | 27.6970i | 0.305267 | + | 0.528738i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.4245 | + | 21.5198i | −0.194133 | + | 0.336248i | ||||
\(17\) | −51.9166 | −0.740684 | −0.370342 | − | 0.928895i | \(-0.620760\pi\) | ||||
−0.370342 | + | 0.928895i | \(0.620760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −88.5107 | −1.06872 | −0.534362 | − | 0.845256i | \(-0.679448\pi\) | ||||
−0.534362 | + | 0.845256i | \(0.679448\pi\) | |||||||
\(20\) | −15.5989 | + | 27.0182i | −0.174402 | + | 0.302072i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.49046 | + | 9.50976i | 0.0532077 | + | 0.0921585i | ||||
\(23\) | −64.6224 | − | 111.929i | −0.585856 | − | 1.01473i | −0.994768 | − | 0.102159i | \(-0.967425\pi\) |
0.408912 | − | 0.912574i | \(-0.365908\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 115.584 | 0.871844 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 150.400 | 1.01511 | ||||||||
\(29\) | −135.554 | + | 234.787i | −0.867993 | + | 1.50341i | −0.00394885 | + | 0.999992i | \(0.501257\pi\) |
−0.864044 | + | 0.503416i | \(0.832076\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −112.273 | − | 194.463i | −0.650481 | − | 1.12667i | −0.983006 | − | 0.183571i | \(-0.941234\pi\) |
0.332526 | − | 0.943094i | \(-0.392099\pi\) | |||||||
\(32\) | −92.0577 | − | 159.449i | −0.508552 | − | 0.880837i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 34.4417 | − | 59.6548i | 0.173727 | − | 0.300903i | ||||
\(35\) | 120.521 | 0.582052 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.5268 | −0.313366 | −0.156683 | − | 0.987649i | \(-0.550080\pi\) | ||||
−0.156683 | + | 0.987649i | \(0.550080\pi\) | |||||||
\(38\) | 58.7184 | − | 101.703i | 0.250668 | − | 0.434169i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −47.2330 | − | 81.8099i | −0.186705 | − | 0.323382i | ||||
\(41\) | 183.469 | + | 317.778i | 0.698855 | + | 1.21045i | 0.968864 | + | 0.247594i | \(0.0796401\pi\) |
−0.270009 | + | 0.962858i | \(0.587027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 97.7736 | − | 169.349i | 0.346752 | − | 0.600592i | −0.638918 | − | 0.769274i | \(-0.720618\pi\) |
0.985670 | + | 0.168682i | \(0.0539512\pi\) | |||||||
\(44\) | 51.6399 | 0.176932 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 171.483 | 0.549648 | ||||||||
\(47\) | −179.596 | + | 311.069i | −0.557378 | + | 0.965407i | 0.440336 | + | 0.897833i | \(0.354859\pi\) |
−0.997714 | + | 0.0675743i | \(0.978474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −119.008 | − | 206.128i | −0.346962 | − | 0.600955i | ||||
\(50\) | −16.5851 | − | 28.7262i | −0.0469098 | − | 0.0812501i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 271.779 | − | 470.735i | 0.724788 | − | 1.25537i | ||||
\(53\) | −29.4890 | −0.0764270 | −0.0382135 | − | 0.999270i | \(-0.512167\pi\) | ||||
−0.0382135 | + | 0.999270i | \(0.512167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 41.3810 | 0.101451 | ||||||||
\(56\) | −227.703 | + | 394.394i | −0.543360 | + | 0.941126i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −179.855 | − | 311.517i | −0.407174 | − | 0.705245i | ||||
\(59\) | −429.052 | − | 743.140i | −0.946743 | − | 1.63981i | −0.752224 | − | 0.658908i | \(-0.771019\pi\) |
−0.194519 | − | 0.980899i | \(-0.562315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 278.406 | − | 482.213i | 0.584364 | − | 1.01215i | −0.410591 | − | 0.911820i | \(-0.634677\pi\) |
0.994954 | − | 0.100328i | \(-0.0319892\pi\) | |||||||
\(62\) | 297.931 | 0.610278 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 45.4941 | 0.0888557 | ||||||||
\(65\) | 217.786 | − | 377.217i | 0.415586 | − | 0.719815i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.9493 | + | 36.2853i | 0.0381995 | + | 0.0661635i | 0.884493 | − | 0.466553i | \(-0.154504\pi\) |
−0.846294 | + | 0.532717i | \(0.821171\pi\) | |||||||
\(68\) | −161.969 | − | 280.538i | −0.288847 | − | 0.500298i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −79.9544 | + | 138.485i | −0.136520 | + | 0.236459i | ||||
\(71\) | 549.163 | 0.917939 | 0.458970 | − | 0.888452i | \(-0.348219\pi\) | ||||
0.458970 | + | 0.888452i | \(0.348219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −185.505 | −0.297420 | −0.148710 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148710 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(74\) | 46.7878 | − | 81.0388i | 0.0734996 | − | 0.127305i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −276.135 | − | 478.279i | −0.416774 | − | 0.721874i | ||||
\(77\) | −99.7458 | − | 172.765i | −0.147624 | − | 0.255693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.2456 | + | 69.7075i | −0.0573163 | + | 0.0992748i | −0.893260 | − | 0.449541i | \(-0.851588\pi\) |
0.835944 | + | 0.548815i | \(0.184921\pi\) | |||||||
\(80\) | −124.245 | −0.173637 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −486.857 | −0.655663 | ||||||||
\(83\) | −288.377 | + | 499.483i | −0.381367 | + | 0.660547i | −0.991258 | − | 0.131939i | \(-0.957880\pi\) |
0.609891 | + | 0.792485i | \(0.291213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −129.792 | − | 224.806i | −0.165622 | − | 0.286866i | ||||
\(86\) | 129.727 | + | 224.694i | 0.162661 | + | 0.281736i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −78.1818 | + | 135.415i | −0.0947070 | + | 0.164037i | ||||
\(89\) | −224.516 | −0.267401 | −0.133700 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133700 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2099.83 | −2.41893 | ||||||||
\(92\) | 403.216 | − | 698.391i | 0.456937 | − | 0.791438i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −238.290 | − | 412.730i | −0.261465 | − | 0.452870i | ||||
\(95\) | −221.277 | − | 383.263i | −0.238974 | − | 0.413915i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 277.508 | − | 480.658i | 0.290481 | − | 0.503128i | −0.683442 | − | 0.730005i | \(-0.739518\pi\) |
0.973924 | + | 0.226876i | \(0.0728513\pi\) | |||||||
\(98\) | 315.801 | 0.325518 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −155.989 | −0.155989 | ||||||||
\(101\) | 113.500 | − | 196.587i | 0.111818 | − | 0.193675i | −0.804685 | − | 0.593702i | \(-0.797666\pi\) |
0.916503 | + | 0.400027i | \(0.130999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −191.762 | − | 332.142i | −0.183446 | − | 0.317737i | 0.759606 | − | 0.650383i | \(-0.225392\pi\) |
−0.943052 | + | 0.332646i | \(0.892058\pi\) | |||||||
\(104\) | 822.936 | + | 1425.37i | 0.775918 | + | 1.34393i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.5632 | − | 33.8844i | 0.0179259 | − | 0.0310485i | ||||
\(107\) | 1775.32 | 1.60399 | 0.801993 | − | 0.597334i | \(-0.203773\pi\) | ||||
0.801993 | + | 0.597334i | \(0.203773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1530.50 | 1.34491 | 0.672454 | − | 0.740139i | \(-0.265240\pi\) | ||||
0.672454 | + | 0.740139i | \(0.265240\pi\) | |||||||
\(110\) | −27.4523 | + | 47.5488i | −0.0237952 | + | 0.0412145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 299.483 | + | 518.720i | 0.252665 | + | 0.437629i | ||||
\(113\) | −420.391 | − | 728.138i | −0.349974 | − | 0.606173i | 0.636271 | − | 0.771466i | \(-0.280476\pi\) |
−0.986244 | + | 0.165293i | \(0.947143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 323.112 | − | 559.646i | 0.262003 | − | 0.453802i | ||||
\(116\) | −1691.60 | −1.35398 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1138.54 | 0.888230 | ||||||||
\(119\) | −625.706 | + | 1083.75i | −0.482003 | + | 0.834854i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 631.252 | + | 1093.36i | 0.474269 | + | 0.821458i | ||||
\(122\) | 369.391 | + | 639.804i | 0.274124 | + | 0.474796i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 700.539 | − | 1213.37i | 0.507341 | − | 0.878740i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1038.45 | 0.725572 | 0.362786 | − | 0.931873i | \(-0.381826\pi\) | ||||
0.362786 | + | 0.931873i | \(0.381826\pi\) | |||||||
\(128\) | 706.281 | − | 1223.31i | 0.487711 | − | 0.844740i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 288.961 | + | 500.495i | 0.194950 | + | 0.337664i | ||||
\(131\) | −401.705 | − | 695.774i | −0.267917 | − | 0.464046i | 0.700407 | − | 0.713744i | \(-0.253002\pi\) |
−0.968324 | + | 0.249698i | \(0.919669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1066.74 | + | 1847.65i | −0.695476 | + | 1.20460i | ||||
\(134\) | −55.5915 | −0.0358386 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 980.871 | 0.618449 | ||||||||
\(137\) | 434.576 | − | 752.707i | 0.271010 | − | 0.469402i | −0.698111 | − | 0.715990i | \(-0.745976\pi\) |
0.969121 | + | 0.246587i | \(0.0793091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 98.1990 | + | 170.086i | 0.0599218 | + | 0.103788i | 0.894430 | − | 0.447208i | \(-0.147582\pi\) |
−0.834508 | + | 0.550995i | \(0.814248\pi\) | |||||||
\(140\) | 376.001 | + | 651.253i | 0.226985 | + | 0.393150i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −364.317 | + | 631.016i | −0.215302 | + | 0.372913i | ||||
\(143\) | −720.976 | −0.421616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1355.54 | −0.776357 | ||||||||
\(146\) | 123.065 | − | 213.154i | 0.0697596 | − | 0.120827i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −220.029 | − | 381.101i | −0.122204 | − | 0.211664i | ||||
\(149\) | 377.142 | + | 653.228i | 0.207360 | + | 0.359158i | 0.950882 | − | 0.309553i | \(-0.100180\pi\) |
−0.743522 | + | 0.668711i | \(0.766846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1028.82 | + | 1781.96i | −0.554464 | + | 0.960359i | 0.443481 | + | 0.896284i | \(0.353743\pi\) |
−0.997945 | + | 0.0640756i | \(0.979590\pi\) | |||||||
\(152\) | 1672.25 | 0.892351 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 264.687 | 0.138501 | ||||||||
\(155\) | 561.367 | − | 972.316i | 0.290904 | − | 0.503860i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1679.29 | + | 2908.62i | 0.853644 | + | 1.47855i | 0.877897 | + | 0.478849i | \(0.158946\pi\) |
−0.0242531 | + | 0.999706i | \(0.507721\pi\) | |||||||
\(158\) | −53.3983 | − | 92.4885i | −0.0268869 | − | 0.0465696i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 460.289 | − | 797.243i | 0.227431 | − | 0.393922i | ||||
\(161\) | −3115.35 | −1.52499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −710.376 | −0.341356 | −0.170678 | − | 0.985327i | \(-0.554596\pi\) | ||||
−0.170678 | + | 0.985327i | \(0.554596\pi\) | |||||||
\(164\) | −1144.77 | + | 1982.80i | −0.545070 | + | 0.944089i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −382.621 | − | 662.718i | −0.178898 | − | 0.309861i | ||||
\(167\) | −574.134 | − | 994.430i | −0.266035 | − | 0.460786i | 0.701799 | − | 0.712375i | \(-0.252380\pi\) |
−0.967834 | + | 0.251589i | \(0.919047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2695.97 | + | 4669.56i | −1.22711 | + | 2.12542i | ||||
\(170\) | 344.417 | 0.155386 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1220.13 | 0.540897 | ||||||||
\(173\) | −1462.64 | + | 2533.37i | −0.642790 | + | 1.11335i | 0.342017 | + | 0.939694i | \(0.388890\pi\) |
−0.984807 | + | 0.173652i | \(0.944443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 301.303 | + | 521.873i | 0.130151 | + | 0.225428i | ||||
\(176\) | 102.827 | + | 178.102i | 0.0440393 | + | 0.0762782i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 148.945 | − | 257.980i | 0.0627185 | − | 0.108632i | ||||
\(179\) | −3422.02 | −1.42890 | −0.714452 | − | 0.699685i | \(-0.753324\pi\) | ||||
−0.714452 | + | 0.699685i | \(0.753324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1151.58 | −0.472907 | −0.236454 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236454 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(182\) | 1393.04 | − | 2412.81i | 0.567356 | − | 0.982690i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1220.92 | + | 2114.70i | 0.489172 | + | 0.847271i | ||||
\(185\) | −176.317 | − | 305.390i | −0.0700707 | − | 0.121366i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −214.836 | + | 372.107i | −0.0840126 | + | 0.145514i | ||||
\(188\) | −2241.21 | −0.869451 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 587.184 | 0.224204 | ||||||||
\(191\) | 466.060 | − | 807.240i | 0.176560 | − | 0.305811i | −0.764140 | − | 0.645050i | \(-0.776836\pi\) |
0.940700 | + | 0.339240i | \(0.110170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2136.41 | + | 3700.36i | 0.796797 | + | 1.38009i | 0.921692 | + | 0.387923i | \(0.126807\pi\) |
−0.124894 | + | 0.992170i | \(0.539859\pi\) | |||||||
\(194\) | 368.200 | + | 637.742i | 0.136264 | + | 0.236016i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 742.559 | − | 1286.15i | 0.270612 | − | 0.468713i | ||||
\(197\) | 1924.15 | 0.695888 | 0.347944 | − | 0.937515i | \(-0.386880\pi\) | ||||
0.347944 | + | 0.937515i | \(0.386880\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1738.84 | 0.619414 | 0.309707 | − | 0.950832i | \(-0.399769\pi\) | ||||
0.309707 | + | 0.950832i | \(0.399769\pi\) | |||||||
\(200\) | 236.165 | − | 409.050i | 0.0834969 | − | 0.144621i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 150.593 | + | 260.834i | 0.0524537 | + | 0.0908525i | ||||
\(203\) | 3267.44 | + | 5659.37i | 1.12970 | + | 1.95670i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −917.345 | + | 1588.89i | −0.312537 | + | 0.541331i | ||||
\(206\) | 508.864 | 0.172108 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2164.71 | 0.721613 | ||||||||
\(209\) | −366.266 | + | 634.391i | −0.121221 | + | 0.209960i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1601.17 | − | 2773.32i | −0.522414 | − | 0.904848i | −0.999660 | − | 0.0260782i | \(-0.991698\pi\) |
0.477246 | − | 0.878770i | \(-0.341635\pi\) | |||||||
\(212\) | −91.9996 | − | 159.348i | −0.0298045 | − | 0.0516229i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1177.75 | + | 2039.93i | −0.376213 | + | 0.651620i | ||||
\(215\) | 977.736 | 0.310144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5412.54 | −1.69321 | ||||||||
\(218\) | −1015.34 | + | 1758.62i | −0.315447 | + | 0.546370i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 129.100 | + | 223.608i | 0.0395632 | + | 0.0685255i | ||||
\(221\) | 2261.35 | + | 3916.77i | 0.688301 | + | 1.19217i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 702.494 | − | 1216.76i | 0.210953 | − | 0.365381i | −0.741060 | − | 0.671439i | \(-0.765677\pi\) |
0.952013 | + | 0.306058i | \(0.0990100\pi\) | |||||||
\(224\) | −4437.97 | −1.32377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1115.56 | 0.328344 | ||||||||
\(227\) | 3119.17 | − | 5402.57i | 0.912012 | − | 1.57965i | 0.100794 | − | 0.994907i | \(-0.467862\pi\) |
0.811218 | − | 0.584744i | \(-0.198805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3315.15 | − | 5742.01i | −0.956644 | − | 1.65696i | −0.730560 | − | 0.682848i | \(-0.760741\pi\) |
−0.226084 | − | 0.974108i | \(-0.572592\pi\) | |||||||
\(230\) | 428.708 | + | 742.543i | 0.122905 | + | 0.212878i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2561.05 | − | 4435.88i | 0.724747 | − | 1.25530i | ||||
\(233\) | −2453.48 | −0.689840 | −0.344920 | − | 0.938632i | \(-0.612094\pi\) | ||||
−0.344920 | + | 0.938632i | \(0.612094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1795.96 | −0.498534 | ||||||||
\(236\) | 2677.10 | − | 4636.88i | 0.738410 | − | 1.27896i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −830.192 | − | 1437.94i | −0.226107 | − | 0.391628i | ||||
\(239\) | −3474.87 | − | 6018.65i | −0.940463 | − | 1.62893i | −0.764590 | − | 0.644517i | \(-0.777058\pi\) |
−0.175873 | − | 0.984413i | \(-0.556275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3167.60 | + | 5486.44i | −0.846651 | + | 1.46644i | 0.0375294 | + | 0.999296i | \(0.488051\pi\) |
−0.884180 | + | 0.467146i | \(0.845282\pi\) | |||||||
\(242\) | −1675.10 | −0.444957 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3474.27 | 0.911546 | ||||||||
\(245\) | 595.039 | − | 1030.64i | 0.155166 | − | 0.268755i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3855.28 | + | 6677.55i | 0.993141 | + | 1.72017i | ||||
\(248\) | 2121.20 | + | 3674.03i | 0.543131 | + | 0.940731i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 82.9255 | − | 143.631i | 0.0209787 | − | 0.0363362i | ||||
\(251\) | 4022.65 | 1.01158 | 0.505792 | − | 0.862656i | \(-0.331200\pi\) | ||||
0.505792 | + | 0.862656i | \(0.331200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1069.65 | −0.265805 | ||||||||
\(254\) | −688.913 | + | 1193.23i | −0.170182 | + | 0.294764i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1119.08 | + | 1938.30i | 0.273212 | + | 0.473217i | ||||
\(257\) | −2498.87 | − | 4328.17i | −0.606519 | − | 1.05052i | −0.991809 | − | 0.127726i | \(-0.959232\pi\) |
0.385291 | − | 0.922795i | \(-0.374101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −849.998 | + | 1472.24i | −0.203924 | + | 0.353207i | ||||
\(260\) | 2717.79 | 0.648270 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1065.97 | 0.251359 | ||||||||
\(263\) | −1996.24 | + | 3457.58i | −0.468035 | + | 0.810660i | −0.999333 | − | 0.0365251i | \(-0.988371\pi\) |
0.531298 | + | 0.847185i | \(0.321704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −73.7226 | − | 127.691i | −0.0170896 | − | 0.0296000i | ||||
\(266\) | −1415.36 | − | 2451.48i | −0.326246 | − | 0.565075i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −130.715 | + | 226.405i | −0.0297936 | + | 0.0516041i | ||||
\(269\) | 2188.89 | 0.496131 | 0.248065 | − | 0.968743i | \(-0.420205\pi\) | ||||
0.248065 | + | 0.968743i | \(0.420205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4280.26 | 0.959437 | 0.479718 | − | 0.877423i | \(-0.340739\pi\) | ||||
0.479718 | + | 0.877423i | \(0.340739\pi\) | |||||||
\(272\) | 645.038 | − | 1117.24i | 0.143791 | − | 0.249053i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 576.599 | + | 998.699i | 0.127130 | + | 0.220196i | ||||
\(275\) | 103.452 | + | 179.185i | 0.0226851 | + | 0.0392918i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1939.98 | − | 3360.15i | 0.420803 | − | 0.728852i | −0.575215 | − | 0.818002i | \(-0.695082\pi\) |
0.996018 | + | 0.0891502i | \(0.0284151\pi\) | |||||||
\(278\) | −260.583 | −0.0562184 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2277.03 | −0.485996 | ||||||||
\(281\) | −3198.72 | + | 5540.34i | −0.679072 | + | 1.17619i | 0.296188 | + | 0.955130i | \(0.404284\pi\) |
−0.975261 | + | 0.221058i | \(0.929049\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 171.435 | + | 296.933i | 0.0360096 | + | 0.0623705i | 0.883469 | − | 0.468490i | \(-0.155202\pi\) |
−0.847459 | + | 0.530861i | \(0.821869\pi\) | |||||||
\(284\) | 1713.27 | + | 2967.48i | 0.357972 | + | 0.620026i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 478.299 | − | 828.438i | 0.0988895 | − | 0.171282i | ||||
\(287\) | 8844.78 | 1.81913 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2217.66 | −0.451387 | ||||||||
\(290\) | 899.273 | − | 1557.59i | 0.182094 | − | 0.315395i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −578.735 | − | 1002.40i | −0.115986 | − | 0.200894i | ||||
\(293\) | −3666.71 | − | 6350.94i | −0.731098 | − | 1.26630i | −0.956414 | − | 0.292013i | \(-0.905675\pi\) |
0.225316 | − | 0.974286i | \(-0.427659\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2145.26 | − | 3715.70i | 0.423396 | − | 0.733344i | ||||
\(296\) | 1332.48 | 0.261651 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1000.79 | −0.194544 | ||||||||
\(299\) | −5629.55 | + | 9750.66i | −1.08885 | + | 1.88594i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2356.76 | − | 4082.03i | −0.451300 | − | 0.781675i | ||||
\(302\) | −1365.04 | − | 2364.33i | −0.260098 | − | 0.450502i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1099.70 | − | 1904.74i | 0.207474 | − | 0.359356i | ||||
\(305\) | 2784.06 | 0.522671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7965.33 | −1.48080 | −0.740399 | − | 0.672167i | \(-0.765364\pi\) | ||||
−0.740399 | + | 0.672167i | \(0.765364\pi\) | |||||||
\(308\) | 622.372 | − | 1077.98i | 0.115139 | − | 0.199427i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 744.827 | + | 1290.08i | 0.136462 | + | 0.236360i | ||||
\(311\) | −1093.10 | − | 1893.30i | −0.199305 | − | 0.345206i | 0.748998 | − | 0.662572i | \(-0.230535\pi\) |
−0.948303 | + | 0.317366i | \(0.897202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.3152 | + | 33.4549i | −0.00348805 | + | 0.00604147i | −0.867764 | − | 0.496976i | \(-0.834444\pi\) |
0.864276 | + | 0.503018i | \(0.167777\pi\) | |||||||
\(314\) | −4456.20 | −0.800885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −502.232 | −0.0894074 | ||||||||
\(317\) | 4767.91 | − | 8258.25i | 0.844770 | − | 1.46319i | −0.0410499 | − | 0.999157i | \(-0.513070\pi\) |
0.885820 | − | 0.464028i | \(-0.153596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1121.87 | + | 1943.14i | 0.196905 | + | 0.341050i | ||||
\(320\) | 113.735 | + | 196.995i | 0.0198687 | + | 0.0344137i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2066.74 | − | 3579.69i | 0.357686 | − | 0.619530i | ||||
\(323\) | 4595.18 | 0.791587 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2177.86 | 0.371711 | ||||||||
\(326\) | 471.267 | − | 816.258i | 0.0800645 | − | 0.138676i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3466.32 | − | 6003.84i | −0.583522 | − | 1.01069i | ||||
\(329\) | 4329.03 | + | 7498.10i | 0.725432 | + | 1.25649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1505.29 | − | 2607.24i | 0.249964 | − | 0.432951i | −0.713551 | − | 0.700603i | \(-0.752914\pi\) |
0.963516 | + | 0.267652i | \(0.0862477\pi\) | |||||||
\(332\) | −3598.70 | −0.594892 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1523.53 | 0.249593 | ||||||||
\(335\) | −104.747 | + | 181.427i | −0.0170833 | + | 0.0295892i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1406.36 | − | 2435.89i | −0.227327 | − | 0.393742i | 0.729688 | − | 0.683780i | \(-0.239665\pi\) |
−0.957015 | + | 0.290038i | \(0.906332\pi\) | |||||||
\(338\) | −3577.04 | − | 6195.61i | −0.575637 | − | 0.997032i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 809.845 | − | 1402.69i | 0.129176 | − | 0.223740i | ||||
\(341\) | −1858.39 | −0.295125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2530.57 | 0.398361 | ||||||||
\(344\) | −1847.26 | + | 3199.54i | −0.289527 | + | 0.501476i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1940.65 | − | 3361.30i | −0.301531 | − | 0.522268i | ||||
\(347\) | −69.6769 | − | 120.684i | −0.0107794 | − | 0.0186705i | 0.860585 | − | 0.509306i | \(-0.170098\pi\) |
−0.871365 | + | 0.490636i | \(0.836765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2605.14 | − | 4512.24i | 0.399571 | − | 0.692077i | −0.594102 | − | 0.804390i | \(-0.702493\pi\) |
0.993673 | + | 0.112313i | \(0.0358259\pi\) | |||||||
\(350\) | −799.544 | −0.122107 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1523.77 | −0.230731 | ||||||||
\(353\) | −1705.23 | + | 2953.55i | −0.257112 | + | 0.445330i | −0.965467 | − | 0.260526i | \(-0.916104\pi\) |
0.708355 | + | 0.705856i | \(0.249437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1372.91 | + | 2377.95i | 0.205257 | + | 0.355516i | ||||
\(356\) | −700.443 | − | 1213.20i | −0.104279 | − | 0.180617i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2270.18 | − | 3932.07i | 0.335148 | − | 0.580493i | ||||
\(359\) | −8131.85 | −1.19549 | −0.597747 | − | 0.801685i | \(-0.703937\pi\) | ||||
−0.597747 | + | 0.801685i | \(0.703937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 975.143 | 0.142170 | ||||||||
\(362\) | 763.963 | − | 1323.22i | 0.110920 | − | 0.192119i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6551.03 | − | 11346.7i | −0.943317 | − | 1.63387i | ||||
\(365\) | −463.762 | − | 803.259i | −0.0665052 | − | 0.115190i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −66.0757 | + | 114.447i | −0.00939816 | + | 0.0162781i | −0.870686 | − | 0.491839i | \(-0.836325\pi\) |
0.861288 | + | 0.508117i | \(0.169658\pi\) | |||||||
\(368\) | 3211.60 | 0.454935 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 467.878 | 0.0657400 | ||||||||
\(371\) | −355.406 | + | 615.581i | −0.0497352 | + | 0.0861438i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4674.44 | − | 8096.37i | −0.648883 | − | 1.12390i | −0.983390 | − | 0.181505i | \(-0.941903\pi\) |
0.334507 | − | 0.942393i | \(-0.391430\pi\) | |||||||
\(374\) | −285.046 | − | 493.715i | −0.0394101 | − | 0.0682603i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3393.14 | − | 5877.10i | 0.465394 | − | 0.806085i | ||||
\(377\) | 23617.5 | 3.22643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6164.17 | 0.835441 | 0.417720 | − | 0.908576i | \(-0.362829\pi\) | ||||
0.417720 | + | 0.908576i | \(0.362829\pi\) | |||||||
\(380\) | 1380.67 | − | 2391.40i | 0.186387 | − | 0.322832i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 618.373 | + | 1071.05i | 0.0828238 | + | 0.143455i | ||||
\(383\) | −1300.64 | − | 2252.77i | −0.173523 | − | 0.300551i | 0.766126 | − | 0.642690i | \(-0.222182\pi\) |
−0.939649 | + | 0.342139i | \(0.888849\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 498.729 | − | 863.824i | 0.0660197 | − | 0.114349i | ||||
\(386\) | −5669.20 | −0.747552 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3463.07 | 0.453120 | ||||||||
\(389\) | −2125.29 | + | 3681.10i | −0.277008 | + | 0.479793i | −0.970640 | − | 0.240537i | \(-0.922676\pi\) |
0.693631 | + | 0.720330i | \(0.256010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3354.98 | + | 5810.99i | 0.433935 | + | 0.751597i | ||||
\(392\) | 2248.44 | + | 3894.41i | 0.289702 | + | 0.501779i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1276.49 | + | 2210.94i | −0.163220 | + | 0.282705i | ||||
\(395\) | −402.456 | −0.0512653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6088.35 | −0.769687 | −0.384843 | − | 0.922982i | \(-0.625745\pi\) | ||||
−0.384843 | + | 0.922982i | \(0.625745\pi\) | |||||||
\(398\) | −1153.56 | + | 1998.02i | −0.145283 | + | 0.251637i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −310.612 | − | 537.996i | −0.0388265 | − | 0.0672495i | ||||
\(401\) | −3862.90 | − | 6690.73i | −0.481057 | − | 0.833215i | 0.518707 | − | 0.854952i | \(-0.326414\pi\) |
−0.999764 | + | 0.0217370i | \(0.993080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9780.64 | + | 16940.6i | −1.20895 | + | 2.09397i | ||||
\(404\) | 1416.38 | 0.174425 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8670.53 | −1.05988 | ||||||||
\(407\) | −291.847 | + | 505.493i | −0.0355437 | + | 0.0615635i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8160.57 | − | 14134.5i | −0.986588 | − | 1.70882i | −0.634657 | − | 0.772794i | \(-0.718859\pi\) |
−0.351930 | − | 0.936026i | \(-0.614475\pi\) | |||||||
\(410\) | −1217.14 | − | 2108.15i | −0.146611 | − | 0.253937i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1196.52 | − | 2072.43i | 0.143078 | − | 0.247818i | ||||
\(413\) | −20684.0 | −2.46439 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2883.77 | −0.341105 | ||||||||
\(416\) | −8019.56 | + | 13890.3i | −0.945172 | + | 1.63709i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −485.964 | − | 841.715i | −0.0568644 | − | 0.0984920i | ||||
\(419\) | −576.228 | − | 998.055i | −0.0671851 | − | 0.116368i | 0.830476 | − | 0.557054i | \(-0.188068\pi\) |
−0.897661 | + | 0.440686i | \(0.854735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1765.61 | − | 3058.13i | 0.204396 | − | 0.354024i | −0.745544 | − | 0.666456i | \(-0.767810\pi\) |
0.949940 | + | 0.312432i | \(0.101144\pi\) | |||||||
\(422\) | 4248.91 | 0.490127 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 557.142 | 0.0638142 | ||||||||
\(425\) | 648.958 | − | 1124.03i | 0.0740684 | − | 0.128290i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6710.76 | − | 11623.4i | −0.760554 | − | 1.31732i | ||||
\(428\) | 5538.62 | + | 9593.17i | 0.625512 | + | 1.08342i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −648.634 | + | 1123.47i | −0.0727440 | + | 0.125996i | ||||
\(431\) | 10230.6 | 1.14337 | 0.571683 | − | 0.820475i | \(-0.306291\pi\) | ||||
0.571683 | + | 0.820475i | \(0.306291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7311.31 | −0.811453 | −0.405726 | − | 0.913995i | \(-0.632981\pi\) | ||||
−0.405726 | + | 0.913995i | \(0.632981\pi\) | |||||||
\(434\) | 3590.70 | − | 6219.27i | 0.397141 | − | 0.687868i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4774.83 | + | 8270.24i | 0.524479 | + | 0.908424i | ||||
\(437\) | 5719.77 | + | 9906.94i | 0.626119 | + | 1.08447i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3526.59 | + | 6108.23i | −0.383405 | + | 0.664077i | −0.991547 | − | 0.129751i | \(-0.958582\pi\) |
0.608141 | + | 0.793829i | \(0.291915\pi\) | |||||||
\(440\) | −781.818 | −0.0847085 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6000.75 | −0.645761 | ||||||||
\(443\) | 83.8952 | − | 145.311i | 0.00899770 | − | 0.0155845i | −0.861491 | − | 0.507772i | \(-0.830469\pi\) |
0.870489 | + | 0.492188i | \(0.163803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −561.290 | − | 972.183i | −0.0597926 | − | 0.103564i | ||||
\(446\) | 932.076 | + | 1614.40i | 0.0989575 | + | 0.171399i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 548.301 | − | 949.685i | 0.0578232 | − | 0.100153i | ||||
\(449\) | 3949.94 | 0.415165 | 0.207582 | − | 0.978218i | \(-0.433440\pi\) | ||||
0.207582 | + | 0.978218i | \(0.433440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3036.85 | 0.317072 | ||||||||
\(452\) | 2623.06 | − | 4543.28i | 0.272961 | − | 0.472783i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4138.55 | + | 7168.17i | 0.427823 | + | 0.741011i | ||||
\(455\) | −5249.58 | − | 9092.54i | −0.540888 | − | 0.936846i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3723.80 | − | 6449.81i | 0.381164 | − | 0.660195i | −0.610065 | − | 0.792351i | \(-0.708857\pi\) |
0.991229 | + | 0.132156i | \(0.0421900\pi\) | |||||||
\(458\) | 8797.15 | 0.897519 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4032.16 | 0.408697 | ||||||||
\(461\) | −5443.82 | + | 9428.98i | −0.549987 | + | 0.952606i | 0.448287 | + | 0.893889i | \(0.352034\pi\) |
−0.998275 | + | 0.0587164i | \(0.981299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1585.63 | + | 2746.40i | 0.159159 | + | 0.275672i | 0.934566 | − | 0.355791i | \(-0.115788\pi\) |
−0.775407 | + | 0.631462i | \(0.782455\pi\) | |||||||
\(464\) | −3368.39 | − | 5834.21i | −0.337012 | − | 0.583721i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1627.65 | − | 2819.17i | 0.161801 | − | 0.280248i | ||||
\(467\) | −16348.5 | −1.61996 | −0.809978 | − | 0.586461i | \(-0.800521\pi\) | ||||
−0.809978 | + | 0.586461i | \(0.800521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1009.94 | 0.0994340 | ||||||||
\(470\) | 1191.45 | − | 2063.65i | 0.116931 | − | 0.202530i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8106.17 | + | 14040.3i | 0.790501 | + | 1.36919i | ||||
\(473\) | −809.193 | − | 1401.56i | −0.0786612 | − | 0.136245i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1106.38 | − | 1916.31i | 0.106872 | − | 0.185108i | ||||
\(476\) | −7808.29 | −0.751874 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9220.98 | 0.882338 | ||||||||
\(479\) | −4706.84 | + | 8152.49i | −0.448980 | + | 0.777655i | −0.998320 | − | 0.0579433i | \(-0.981546\pi\) |
0.549340 | + | 0.835599i | \(0.314879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3071.95 | + | 5320.78i | 0.291204 | + | 0.504380i | ||||
\(482\) | −4202.79 | − | 7279.45i | −0.397162 | − | 0.687905i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3938.75 | + | 6822.11i | −0.369905 | + | 0.640694i | ||||
\(485\) | 2775.08 | 0.259814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13482.3 | 1.25450 | 0.627250 | − | 0.778818i | \(-0.284180\pi\) | ||||
0.627250 | + | 0.778818i | \(0.284180\pi\) | |||||||
\(488\) | −5259.97 | + | 9110.54i | −0.487926 | + | 0.845112i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 789.503 | + | 1367.46i | 0.0727880 | + | 0.126073i | ||||
\(491\) | 4609.87 | + | 7984.53i | 0.423708 | + | 0.733883i | 0.996299 | − | 0.0859577i | \(-0.0273950\pi\) |
−0.572591 | + | 0.819841i | \(0.694062\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7037.52 | − | 12189.3i | 0.642909 | − | 1.11355i | ||||
\(494\) | −10230.4 | −0.931760 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5579.76 | 0.505118 | ||||||||
\(497\) | 6618.59 | − | 11463.7i | 0.597353 | − | 1.03465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −52.1731 | − | 90.3665i | −0.00468054 | − | 0.00810693i | 0.863676 | − | 0.504048i | \(-0.168157\pi\) |
−0.868356 | + | 0.495941i | \(0.834823\pi\) | |||||||
\(500\) | −389.974 | − | 675.454i | −0.0348803 | − | 0.0604145i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2668.64 | + | 4622.23i | −0.237266 | + | 0.410956i | ||||
\(503\) | 490.652 | 0.0434933 | 0.0217466 | − | 0.999764i | \(-0.493077\pi\) | ||||
0.0217466 | + | 0.999764i | \(0.493077\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1135.00 | 0.100013 | ||||||||
\(506\) | 709.613 | − | 1229.09i | 0.0623442 | − | 0.107983i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3239.75 | + | 5611.41i | 0.282954 | + | 0.490090i | ||||
\(509\) | 1706.40 | + | 2955.58i | 0.148595 | + | 0.257375i | 0.930709 | − | 0.365762i | \(-0.119192\pi\) |
−0.782113 | + | 0.623136i | \(0.785858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2235.73 | + | 3872.39i | −0.193547 | + | 0.335234i | ||||
\(512\) | 8330.89 | 0.719095 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6631.05 | 0.569033 | ||||||||
\(515\) | 958.811 | − | 1660.71i | 0.0820393 | − | 0.142096i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1486.37 | + | 2574.47i | 0.126442 | + | 0.219004i | ||||
\(518\) | −1127.79 | − | 1953.38i | −0.0956603 | − | 0.165688i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4114.68 | + | 7126.83i | −0.347001 | + | 0.601024i | ||||
\(521\) | −3486.31 | −0.293163 | −0.146582 | − | 0.989199i | \(-0.546827\pi\) | ||||
−0.146582 | + | 0.989199i | \(0.546827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14465.6 | 1.20943 | 0.604717 | − | 0.796440i | \(-0.293286\pi\) | ||||
0.604717 | + | 0.796440i | \(0.293286\pi\) | |||||||
\(524\) | 2506.47 | − | 4341.34i | 0.208961 | − | 0.361932i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2648.62 | − | 4587.55i | −0.219554 | − | 0.380279i | ||||
\(527\) | 5828.86 | + | 10095.9i | 0.481801 | + | 0.834503i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2268.60 | + | 3929.34i | −0.186456 | + | 0.322950i | ||||
\(530\) | 195.632 | 0.0160334 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13312.1 | −1.08487 | ||||||||
\(533\) | 15982.8 | − | 27683.1i | 1.29886 | − | 2.24969i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4438.29 | + | 7687.35i | 0.358662 | + | 0.621221i | ||||
\(536\) | −395.800 | − | 685.545i | −0.0318954 | − | 0.0552445i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1452.12 | + | 2515.15i | −0.116367 | + | 0.201553i | ||||
\(539\) | −1969.86 | −0.157417 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6602.78 | 0.524724 | 0.262362 | − | 0.964970i | \(-0.415499\pi\) | ||||
0.262362 | + | 0.964970i | \(0.415499\pi\) | |||||||
\(542\) | −2839.54 | + | 4918.23i | −0.225035 | + | 0.389772i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4779.33 | + | 8278.03i | 0.376676 | + | 0.652422i | ||||
\(545\) | 3826.24 | + | 6627.24i | 0.300731 | + | 0.520881i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3179.28 | + | 5506.67i | −0.248512 | + | 0.430436i | −0.963113 | − | 0.269096i | \(-0.913275\pi\) |
0.714601 | + | 0.699532i | \(0.246608\pi\) | |||||||
\(548\) | 5423.14 | 0.422746 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −274.523 | −0.0212831 | ||||||||
\(551\) | 11998.0 | − | 20781.2i | 0.927645 | − | 1.60673i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 970.092 | + | 1680.25i | 0.0745976 | + | 0.129207i | ||||
\(554\) | 2573.99 | + | 4458.28i | 0.197398 | + | 0.341903i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −612.720 | + | 1061.26i | −0.0467359 | + | 0.0809489i | ||||
\(557\) | −20782.3 | −1.58092 | −0.790461 | − | 0.612513i | \(-0.790159\pi\) | ||||
−0.790461 | + | 0.612513i | \(0.790159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17035.0 | −1.28892 | ||||||||
\(560\) | −1497.42 | + | 2593.60i | −0.112995 | + | 0.195714i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4244.08 | − | 7350.97i | −0.318551 | − | 0.551747i | ||||
\(563\) | −8234.98 | − | 14263.4i | −0.616453 | − | 1.06773i | −0.990128 | − | 0.140168i | \(-0.955236\pi\) |
0.373675 | − | 0.927560i | \(-0.378098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2101.95 | − | 3640.69i | 0.156513 | − | 0.271089i | ||||
\(566\) | −454.922 | −0.0337841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10375.4 | −0.766451 | ||||||||
\(569\) | −2712.69 | + | 4698.52i | −0.199863 | + | 0.346173i | −0.948484 | − | 0.316825i | \(-0.897383\pi\) |
0.748621 | + | 0.662998i | \(0.230716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7344.86 | + | 12721.7i | 0.538306 | + | 0.932374i | 0.998995 | + | 0.0448121i | \(0.0142689\pi\) |
−0.460689 | + | 0.887561i | \(0.652398\pi\) | |||||||
\(572\) | −2249.29 | − | 3895.89i | −0.164419 | − | 0.284782i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5867.66 | + | 10163.1i | −0.426675 | + | 0.739023i | ||||
\(575\) | 3231.12 | 0.234343 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17933.1 | −1.29387 | −0.646935 | − | 0.762545i | \(-0.723949\pi\) | ||||
−0.646935 | + | 0.762545i | \(0.723949\pi\) | |||||||
\(578\) | 1471.21 | − | 2548.21i | 0.105872 | − | 0.183376i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4229.01 | − | 7324.86i | −0.302759 | − | 0.524393i | ||||
\(581\) | 6951.11 | + | 12039.7i | 0.496352 | + | 0.859707i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −122.028 | + | 211.359i | −0.00866878 | + | 0.0150148i | ||||
\(584\) | 3504.78 | 0.248337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9730.06 | 0.685913 | ||||||||
\(587\) | −2400.58 | + | 4157.92i | −0.168795 | + | 0.292361i | −0.937996 | − | 0.346645i | \(-0.887321\pi\) |
0.769202 | + | 0.639006i | \(0.220654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9937.40 | + | 17212.1i | 0.695184 | + | 1.20409i | ||||
\(590\) | 2846.35 | + | 4930.02i | 0.198614 | + | 0.344010i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 876.259 | − | 1517.73i | 0.0608345 | − | 0.105368i | ||||
\(593\) | −16803.8 | −1.16366 | −0.581830 | − | 0.813311i | \(-0.697663\pi\) | ||||
−0.581830 | + | 0.813311i | \(0.697663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6257.06 | −0.431117 | ||||||||
\(596\) | −2353.20 | + | 4075.87i | −0.161730 | + | 0.280124i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7469.33 | − | 12937.3i | −0.510775 | − | 0.884689i | ||||
\(599\) | 8610.08 | + | 14913.1i | 0.587310 | + | 1.01725i | 0.994583 | + | 0.103944i | \(0.0331462\pi\) |
−0.407274 | + | 0.913306i | \(0.633520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10768.3 | + | 18651.3i | −0.730865 | + | 1.26590i | 0.225649 | + | 0.974209i | \(0.427550\pi\) |
−0.956514 | + | 0.291687i | \(0.905784\pi\) | |||||||
\(602\) | 6253.94 | 0.423408 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12838.8 | −0.864905 | ||||||||
\(605\) | −3156.26 | + | 5466.81i | −0.212100 | + | 0.367367i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12025.5 | + | 20828.7i | 0.804117 | + | 1.39277i | 0.916886 | + | 0.399150i | \(0.130695\pi\) |
−0.112769 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(608\) | 8148.09 | + | 14112.9i | 0.543501 | + | 0.941372i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1846.96 | + | 3199.02i | −0.122592 | + | 0.212335i | ||||
\(611\) | 31290.8 | 2.07184 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3554.49 | −0.234200 | −0.117100 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117100 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(614\) | 5284.23 | − | 9152.56i | 0.347320 | − | 0.601575i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1884.52 | + | 3264.08i | 0.123262 | + | 0.213496i | ||||
\(617\) | −4873.71 | − | 8441.51i | −0.318003 | − | 0.550798i | 0.662068 | − | 0.749444i | \(-0.269679\pi\) |
−0.980071 | + | 0.198646i | \(0.936346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10382.6 | − | 17983.2i | 0.674171 | − | 1.16770i | −0.302540 | − | 0.953137i | \(-0.597835\pi\) |
0.976711 | − | 0.214561i | \(-0.0688321\pi\) | |||||||
\(620\) | 7005.39 | 0.453779 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2900.66 | 0.186987 | ||||||||
\(623\) | −2705.90 | + | 4686.75i | −0.174012 | + | 0.301398i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −25.6275 | − | 44.3882i | −0.00163623 | − | 0.00283404i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10478.1 | + | 18148.6i | −0.665797 | + | 1.15320i | ||||
\(629\) | 3661.51 | 0.232105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23740.6 | 1.49778 | 0.748890 | − | 0.662694i | \(-0.230587\pi\) | ||||
0.748890 | + | 0.662694i | \(0.230587\pi\) | |||||||
\(632\) | 760.369 | − | 1317.00i | 0.0478574 | − | 0.0828914i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6326.10 | + | 10957.1i | 0.396280 | + | 0.686377i | ||||
\(635\) | 2596.13 | + | 4496.62i | 0.162243 | + | 0.281013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10367.3 | + | 17956.7i | −0.644848 | + | 1.11691i | ||||
\(638\) | −2977.02 | −0.184736 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7062.81 | 0.436222 | ||||||||
\(641\) | 13054.4 | − | 22610.8i | 0.804394 | − | 1.39325i | −0.112306 | − | 0.993674i | \(-0.535824\pi\) |
0.916700 | − | 0.399577i | \(-0.130843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12008.9 | + | 20800.1i | 0.736526 | + | 1.27570i | 0.954051 | + | 0.299646i | \(0.0968685\pi\) |
−0.217525 | + | 0.976055i | \(0.569798\pi\) | |||||||
\(644\) | −9719.24 | − | 16834.2i | −0.594707 | − | 1.03006i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3048.46 | + | 5280.09i | −0.185666 | + | 0.321582i | ||||
\(647\) | −18588.3 | −1.12949 | −0.564747 | − | 0.825264i | \(-0.691026\pi\) | ||||
−0.564747 | + | 0.825264i | \(0.691026\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7101.83 | −0.429540 | ||||||||
\(650\) | −1444.80 | + | 2502.47i | −0.0871844 | + | 0.151008i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2216.22 | − | 3838.61i | −0.133120 | − | 0.230570i | ||||
\(653\) | 6085.97 | + | 10541.2i | 0.364721 | + | 0.631714i | 0.988731 | − | 0.149701i | \(-0.0478312\pi\) |
−0.624011 | + | 0.781416i | \(0.714498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2008.53 | − | 3478.87i | 0.119816 | − | 0.207528i | ||||
\(656\) | −9118.04 | −0.542682 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11487.6 | −0.680597 | ||||||||
\(659\) | 4294.82 | − | 7438.84i | 0.253873 | − | 0.439721i | −0.710716 | − | 0.703479i | \(-0.751629\pi\) |
0.964589 | + | 0.263758i | \(0.0849621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12497.7 | − | 21646.6i | −0.735405 | − | 1.27376i | −0.954545 | − | 0.298066i | \(-0.903659\pi\) |
0.219140 | − | 0.975693i | \(-0.429675\pi\) | |||||||
\(662\) | 1997.23 | + | 3459.31i | 0.117258 | + | 0.203096i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5448.36 | − | 9436.83i | 0.318430 | − | 0.551536i | ||||
\(665\) | −10667.4 | −0.622053 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35039.4 | 2.03408 | ||||||||
\(668\) | 3582.36 | − | 6204.82i | 0.207493 | − | 0.359389i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −138.979 | − | 240.718i | −0.00801376 | − | 0.0138802i | ||||
\(671\) | −2304.14 | − | 3990.88i | −0.132564 | − | 0.229607i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1270.08 | − | 2199.85i | 0.0727461 | − | 0.126000i | −0.827358 | − | 0.561675i | \(-0.810157\pi\) |
0.900104 | + | 0.435675i | \(0.143490\pi\) | |||||||
\(674\) | 3731.94 | 0.213277 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33643.4 | −1.91417 | ||||||||
\(677\) | 2098.89 | − | 3635.39i | 0.119154 | − | 0.206380i | −0.800279 | − | 0.599628i | \(-0.795315\pi\) |
0.919433 | + | 0.393248i | \(0.128649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6689.13 | − | 11585.9i | −0.378064 | − | 0.654826i | ||||
\(680\) | 2452.18 | + | 4247.30i | 0.138289 | + | 0.239524i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1232.87 | − | 2135.39i | 0.0692212 | − | 0.119895i | ||||
\(683\) | −8523.02 | −0.477488 | −0.238744 | − | 0.971083i | \(-0.576736\pi\) | ||||
−0.238744 | + | 0.971083i | \(0.576736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4345.76 | 0.242398 | ||||||||
\(686\) | −1678.79 | + | 2907.75i | −0.0934352 | + | 0.161834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2429.57 | + | 4208.15i | 0.134632 | + | 0.233189i | ||||
\(689\) | 1284.46 | + | 2224.75i | 0.0710219 | + | 0.123014i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10146.0 | − | 17573.4i | 0.558571 | − | 0.967473i | −0.439045 | − | 0.898465i | \(-0.644683\pi\) |
0.997616 | − | 0.0690084i | \(-0.0219835\pi\) | |||||||
\(692\) | −18252.6 | −1.00269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 184.896 | 0.0101132 | ||||||||
\(695\) | −490.995 | + | 850.428i | −0.0267978 | + | 0.0464152i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9525.10 | − | 16498.0i | −0.517631 | − | 0.896563i | ||||
\(698\) | 3456.53 | + | 5986.88i | 0.187438 | + | 0.324652i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1880.01 | + | 3256.27i | −0.101511 | + | 0.175822i | ||||
\(701\) | −11223.6 | −0.604721 | −0.302361 | − | 0.953194i | \(-0.597775\pi\) | ||||
−0.302361 | + | 0.953194i | \(0.597775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6242.38 | 0.334901 | ||||||||
\(704\) | 188.259 | − | 326.074i | 0.0100785 | − | 0.0174565i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2262.52 | − | 3918.79i | −0.120610 | − | 0.208903i | ||||
\(707\) | −2735.83 | − | 4738.60i | −0.145533 | − | 0.252070i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9965.49 | − | 17260.7i | 0.527873 | − | 0.914302i | −0.471600 | − | 0.881813i | \(-0.656323\pi\) |
0.999472 | − | 0.0324893i | \(-0.0103435\pi\) | |||||||
\(710\) | −3643.17 | −0.192572 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4241.83 | 0.223271 | ||||||||
\(713\) | −14510.7 | + | 25133.4i | −0.762177 | + | 1.32013i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1802.44 | − | 3121.92i | −0.0942762 | − | 0.163291i | ||||
\(716\) | −10676.0 | − | 18491.3i | −0.557235 | − | 0.965159i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5394.70 | − | 9343.90i | 0.280402 | − | 0.485670i | ||||
\(719\) | −3186.13 | −0.165261 | −0.0826305 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826305 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9244.58 | −0.477512 | ||||||||
\(722\) | −646.914 | + | 1120.49i | −0.0333458 | + | 0.0577566i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3592.69 | − | 6222.72i | −0.184421 | − | 0.319427i | ||||
\(725\) | −3388.86 | − | 5869.67i | −0.173599 | − | 0.300682i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11544.1 | − | 19995.0i | 0.588923 | − | 1.02004i | −0.405451 | − | 0.914117i | \(-0.632886\pi\) |
0.994374 | − | 0.105927i | \(-0.0337810\pi\) | |||||||
\(728\) | 39672.5 | 2.01973 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1230.65 | 0.0623949 | ||||||||
\(731\) | −5076.08 | + | 8792.02i | −0.256834 | + | 0.444849i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14900.7 | + | 25808.8i | 0.750846 | + | 1.30050i | 0.947413 | + | 0.320013i | \(0.103687\pi\) |
−0.196567 | + | 0.980490i | \(0.562979\pi\) | |||||||
\(734\) | −87.6698 | − | 151.849i | −0.00440866 | − | 0.00763602i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11898.0 | + | 20607.9i | −0.595877 | + | 1.03209i | ||||
\(737\) | 346.761 | 0.0173312 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39741.5 | 1.97823 | 0.989117 | − | 0.147134i | \(-0.0470047\pi\) | ||||
0.989117 | + | 0.147134i | \(0.0470047\pi\) | |||||||
\(740\) | 1100.14 | − | 1905.50i | 0.0546515 | − | 0.0946591i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −471.555 | − | 816.758i | −0.0233307 | − | 0.0404099i | ||||
\(743\) | −4856.77 | − | 8412.17i | −0.239808 | − | 0.415360i | 0.720851 | − | 0.693090i | \(-0.243751\pi\) |
−0.960659 | + | 0.277730i | \(0.910418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1885.71 | + | 3266.14i | −0.0927342 | + | 0.160620i | ||||
\(746\) | 12404.2 | 0.608779 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2680.97 | −0.131051 | ||||||||
\(749\) | 21396.4 | − | 37059.6i | 1.04380 | − | 1.80791i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1254.64 | + | 2173.10i | 0.0609619 | + | 0.105589i | 0.894896 | − | 0.446275i | \(-0.147250\pi\) |
−0.833934 | + | 0.551865i | \(0.813917\pi\) | |||||||
\(752\) | −4462.78 | − | 7729.76i | −0.216411 | − | 0.374834i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15667.9 | + | 27137.7i | −0.756755 | + | 1.31074i | ||||
\(755\) | −10288.2 | −0.495927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9705.73 | 0.465998 | 0.232999 | − | 0.972477i | \(-0.425146\pi\) | ||||
0.232999 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(758\) | −4089.34 | + | 7082.94i | −0.195952 | + | 0.339398i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4180.62 | + | 7241.05i | 0.199536 | + | 0.345606i | ||||
\(761\) | 3889.22 | + | 6736.33i | 0.185262 | + | 0.320883i | 0.943665 | − | 0.330903i | \(-0.107353\pi\) |
−0.758403 | + | 0.651786i | \(0.774020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18445.7 | − | 31949.0i | 0.875204 | − | 1.51590i | ||||
\(764\) | 5816.04 | 0.275415 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3451.39 | 0.162799 | ||||||||
\(767\) | −37376.7 | + | 64738.3i | −1.75957 | + | 3.04767i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −693.951 | − | 1201.96i | −0.0325416 | − | 0.0563638i | 0.849296 | − | 0.527917i | \(-0.177027\pi\) |
−0.881838 | + | 0.471553i | \(0.843693\pi\) | |||||||
\(770\) | 661.718 | + | 1146.13i | 0.0309697 | + | 0.0536410i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13330.3 | + | 23088.7i | −0.621460 | + | 1.07640i | ||||
\(773\) | 20692.0 | 0.962796 | 0.481398 | − | 0.876502i | \(-0.340129\pi\) | ||||
0.481398 | + | 0.876502i | \(0.340129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5613.67 | 0.260192 | ||||||||
\(776\) | −5243.02 | + | 9081.17i | −0.242543 | + | 0.420097i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2819.85 | − | 4884.12i | −0.129944 | − | 0.225070i | ||||
\(779\) | −16239.0 | − | 28126.7i | −0.746883 | − | 1.29364i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2272.49 | − | 3936.07i | 0.104118 | − | 0.180338i | ||||
\(782\) | −8902.82 | −0.407115 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5914.45 | 0.269426 | ||||||||
\(785\) | −8396.46 | + | 14543.1i | −0.381761 | + | 0.661230i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16948.4 | − | 29355.5i | −0.767655 | − | 1.32962i | −0.938831 | − | 0.344377i | \(-0.888090\pi\) |
0.171176 | − | 0.985240i | \(-0.445243\pi\) | |||||||
\(788\) | 6002.94 | + | 10397.4i | 0.271378 | + | 0.470041i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 266.991 | − | 462.443i | 0.0120242 | − | 0.0208265i | ||||
\(791\) | −20266.4 | −0.910988 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48506.4 | −2.17215 | ||||||||
\(794\) | 4039.04 | − | 6995.82i | 0.180529 | − | 0.312686i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5424.83 | + | 9396.07i | 0.241555 | + | 0.418386i | ||||
\(797\) | 5977.27 | + | 10352.9i | 0.265653 | + | 0.460125i | 0.967735 | − | 0.251972i | \(-0.0810790\pi\) |
−0.702081 | + | 0.712097i | \(0.747746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9324.02 | − | 16149.7i | 0.412841 | − | 0.715062i | ||||
\(800\) | 4602.89 | 0.203421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10250.7 | 0.451325 | ||||||||
\(803\) | −767.636 | + | 1329.58i | −0.0337351 | + | 0.0584309i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7788.38 | − | 13489.9i | −0.340999 | − | 0.590628i | ||||
\(806\) | −12977.0 | − | 22476.9i | −0.567118 | − | 0.982277i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2144.37 | + | 3714.17i | −0.0933649 | + | 0.161713i | ||||
\(809\) | 27377.3 | 1.18978 | 0.594891 | − | 0.803807i | \(-0.297195\pi\) | ||||
0.594891 | + | 0.803807i | \(0.297195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −713.034 | −0.0308730 | −0.0154365 | − | 0.999881i | \(-0.504914\pi\) | ||||
−0.0154365 | + | 0.999881i | \(0.504914\pi\) | |||||||
\(812\) | −20387.4 | + | 35312.1i | −0.881107 | + | 1.52612i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −387.225 | − | 670.693i | −0.0166735 | − | 0.0288793i | ||||
\(815\) | −1775.94 | − | 3076.02i | −0.0763294 | − | 0.132206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8654.01 | + | 14989.2i | −0.370582 | + | 0.641867i | ||||
\(818\) | 21655.0 | 0.925612 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11447.7 | −0.487526 | ||||||||
\(821\) | −3192.06 | + | 5528.81i | −0.135693 | + | 0.235026i | −0.925862 | − | 0.377862i | \(-0.876659\pi\) |
0.790169 | + | 0.612889i | \(0.209993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9818.14 | − | 17005.5i | −0.415843 | − | 0.720261i | 0.579674 | − | 0.814849i | \(-0.303180\pi\) |
−0.995517 | + | 0.0945876i | \(0.969847\pi\) | |||||||
\(824\) | 3623.00 | + | 6275.22i | 0.153171 | + | 0.265301i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13721.8 | − | 23766.9i | 0.578019 | − | 1.00116i | ||||
\(827\) | 43578.4 | 1.83237 | 0.916185 | − | 0.400756i | \(-0.131253\pi\) | ||||
0.916185 | + | 0.400756i | \(0.131253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20418.8 | −0.855458 | −0.427729 | − | 0.903907i | \(-0.640686\pi\) | ||||
−0.427729 | + | 0.903907i | \(0.640686\pi\) | |||||||
\(830\) | 1913.10 | − | 3313.59i | 0.0800058 | − | 0.138574i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1981.60 | − | 3432.23i | −0.0825716 | − | 0.143018i | ||||
\(833\) | 6178.49 | + | 10701.5i | 0.256989 | + | 0.445118i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2870.67 | − | 4972.15i | 0.118974 | − | 0.206070i | ||||
\(836\) | −4570.69 | −0.189092 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1529.09 | 0.0630328 | ||||||||
\(839\) | 5480.99 | − | 9493.36i | 0.225536 | − | 0.390640i | −0.730944 | − | 0.682438i | \(-0.760920\pi\) |
0.956480 | + | 0.291797i | \(0.0942533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24555.4 | − | 42531.3i | −1.00682 | − | 1.74387i | ||||
\(842\) | 2342.63 | + | 4057.56i | 0.0958817 | + | 0.166072i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9990.66 | − | 17304.3i | 0.407456 | − | 0.705734i | ||||
\(845\) | −26959.7 | −1.09756 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30431.8 | 1.23453 | ||||||||
\(848\) | 366.386 | − | 634.599i | 0.0148370 | − | 0.0256984i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 861.043 | + | 1491.37i | 0.0347453 | + | 0.0601807i | ||||
\(851\) | 4557.61 | + | 7894.01i | 0.183587 | + | 0.317983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2623.20 | − | 4543.52i | 0.105295 | − | 0.182377i | −0.808564 | − | 0.588409i | \(-0.799755\pi\) |
0.913859 | + | 0.406032i | \(0.133088\pi\) | |||||||
\(854\) | 17807.8 | 0.713548 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33541.4 | −1.33928 | ||||||||
\(857\) | 13641.5 | − | 23627.8i | 0.543741 | − | 0.941787i | −0.454944 | − | 0.890520i | \(-0.650341\pi\) |
0.998685 | − | 0.0512671i | \(-0.0163260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1790.52 | − | 3101.28i | −0.0711198 | − | 0.123183i | 0.828273 | − | 0.560325i | \(-0.189324\pi\) |
−0.899392 | + | 0.437142i | \(0.855991\pi\) | |||||||
\(860\) | 3050.33 | + | 5283.33i | 0.120948 | + | 0.209488i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6787.02 | + | 11755.5i | −0.268175 | + | 0.464493i | ||||
\(863\) | −41710.9 | −1.64526 | −0.822629 | − | 0.568579i | \(-0.807493\pi\) | ||||
−0.822629 | + | 0.568579i | \(0.807493\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14626.4 | −0.574929 | ||||||||
\(866\) | 4850.35 | − | 8401.06i | 0.190325 | − | 0.329653i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16886.0 | − | 29247.4i | −0.660308 | − | 1.14369i | ||||
\(869\) | 333.081 | + | 576.913i | 0.0130023 | + | 0.0225206i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1824.99 | − | 3160.98i | 0.0709959 | − | 0.122969i | ||||
\(872\) | −28916.0 | −1.12296 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15178.1 | −0.587422 | ||||||||
\(875\) | −1506.52 | + | 2609.36i | −0.0582052 | + | 0.100814i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10766.8 | − | 18648.6i | −0.414560 | − | 0.718038i | 0.580822 | − | 0.814030i | \(-0.302731\pi\) |
−0.995382 | + | 0.0959919i | \(0.969398\pi\) | |||||||
\(878\) | −4679.11 | − | 8104.45i | −0.179855 | − | 0.311517i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −514.137 | + | 890.512i | −0.0196950 | + | 0.0341127i | ||||
\(881\) | −30919.1 | −1.18240 | −0.591199 | − | 0.806526i | \(-0.701345\pi\) | ||||
−0.591199 | + | 0.806526i | \(0.701345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5341.72 | 0.203582 | 0.101791 | − | 0.994806i | \(-0.467543\pi\) | ||||
0.101791 | + | 0.994806i | \(0.467543\pi\) | |||||||
\(884\) | −14109.8 | + | 24439.0i | −0.536839 | + | 0.929832i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 111.313 | + | 192.799i | 0.00422080 | + | 0.00731064i | ||||
\(887\) | 5605.16 | + | 9708.42i | 0.212179 | + | 0.367505i | 0.952396 | − | 0.304863i | \(-0.0986107\pi\) |
−0.740217 | + | 0.672368i | \(0.765277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12515.5 | − | 21677.6i | 0.472169 | − | 0.817820i | ||||
\(890\) | 1489.45 | 0.0560972 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8766.54 | 0.329064 | ||||||||
\(893\) | 15896.2 | − | 27533.0i | 0.595683 | − | 1.03175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8555.05 | − | 14817.8i | −0.319513 | − | 0.553412i | ||||
\(896\) | −17024.4 | − | 29487.1i | −0.634760 | − | 1.09944i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2620.41 | + | 4538.68i | −0.0973765 | + | 0.168661i | ||||
\(899\) | 60876.6 | 2.25845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1530.97 | 0.0566083 | ||||||||
\(902\) | −2014.66 | + | 3489.49i | −0.0743690 | + | 0.128811i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7942.53 | + | 13756.9i | 0.292217 | + | 0.506135i | ||||
\(905\) | −2878.95 | − | 4986.49i | −0.105745 | − | 0.183156i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10345.4 | + | 17918.8i | −0.378737 | + | 0.655991i | −0.990879 | − | 0.134757i | \(-0.956975\pi\) |
0.612142 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(908\) | 38924.6 | 1.42264 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13930.4 | 0.507459 | ||||||||
\(911\) | 9735.79 | − | 16862.9i | 0.354073 | − | 0.613273i | −0.632885 | − | 0.774245i | \(-0.718130\pi\) |
0.986959 | + | 0.160972i | \(0.0514629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2386.66 | + | 4133.82i | 0.0865136 | + | 0.149846i | ||||
\(914\) | 4940.77 | + | 8557.66i | 0.178803 | + | 0.309696i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20685.2 | − | 35827.8i | 0.746132 | − | 1.29234i | ||||
\(917\) | −19365.6 | −0.697393 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30002.0 | −1.07690 | −0.538452 | − | 0.842656i | \(-0.680991\pi\) | ||||
−0.538452 | + | 0.842656i | \(0.680991\pi\) | |||||||
\(920\) | −6104.62 | + | 10573.5i | −0.218764 | + | 0.378911i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7222.91 | − | 12510.5i | −0.257998 | − | 0.446865i | ||||
\(923\) | −23920.0 | − | 41430.7i | −0.853021 | − | 1.47747i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 881.585 | − | 1526.95i | 0.0313366 | − | 0.0542765i | ||||
\(926\) | −4207.66 | −0.149322 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49915.3 | 1.76568 | ||||||||
\(929\) | 11131.4 | − | 19280.1i | 0.393121 | − | 0.680905i | −0.599739 | − | 0.800196i | \(-0.704729\pi\) |
0.992859 | + | 0.119291i | \(0.0380621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10533.5 | + | 18244.5i | 0.370806 | + | 0.642255i | ||||
\(932\) | −7654.33 | − | 13257.7i | −0.269019 | − | 0.465955i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10845.7 | − | 18785.3i | 0.379959 | − | 0.658108i | ||||
\(935\) | −2148.36 | −0.0751432 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23361.5 | 0.814500 | 0.407250 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407250 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(938\) | −669.996 | + | 1160.47i | −0.0233221 | + | 0.0403951i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5603.02 | − | 9704.71i | −0.194415 | − | 0.336737i | ||||
\(941\) | 19665.5 | + | 34061.6i | 0.681271 | + | 1.18000i | 0.974593 | + | 0.223982i | \(0.0719058\pi\) |
−0.293322 | + | 0.956014i | \(0.594761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23712.4 | − | 41071.1i | 0.818857 | − | 1.41830i | ||||
\(944\) | 21323.0 | 0.735175 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2147.29 | 0.0737995 | ||||||||
\(947\) | −13434.9 | + | 23270.0i | −0.461011 | + | 0.798494i | −0.999012 | − | 0.0444504i | \(-0.985846\pi\) |
0.538001 | + | 0.842944i | \(0.319180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8080.07 | + | 13995.1i | 0.276386 | + | 0.478715i | ||||
\(950\) | 1467.96 | + | 2542.58i | 0.0501336 | + | 0.0868339i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11821.6 | − | 20475.6i | 0.402458 | − | 0.697078i | ||||
\(953\) | −16422.6 | −0.558218 | −0.279109 | − | 0.960259i | \(-0.590039\pi\) | ||||
−0.279109 | + | 0.960259i | \(0.590039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4660.60 | 0.157920 | ||||||||
\(956\) | 21681.7 | − | 37553.9i | 0.733512 | − | 1.27048i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6245.08 | − | 10816.8i | −0.210615 | − | 0.364796i | ||||
\(959\) | −10475.1 | − | 18143.5i | −0.352721 | − | 0.610931i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10315.1 | + | 17866.3i | −0.346250 | + | 0.599723i | ||||
\(962\) | −8151.79 | −0.273206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −39528.9 | −1.32069 | ||||||||
\(965\) | −10682.0 | + | 18501.8i | −0.356339 | + | 0.617197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5152.22 | − | 8923.91i | −0.171339 | − | 0.296767i | 0.767550 | − | 0.640990i | \(-0.221476\pi\) |
−0.938888 | + | 0.344223i | \(0.888143\pi\) | |||||||
\(968\) | −11926.4 | − | 20657.1i | −0.396000 | − | 0.685892i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1841.00 | + | 3188.71i | −0.0609392 | + | 0.105550i | ||||
\(971\) | 44153.1 | 1.45926 | 0.729630 | − | 0.683842i | \(-0.239692\pi\) | ||||
0.729630 | + | 0.683842i | \(0.239692\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4734.03 | 0.155977 | ||||||||
\(974\) | −8944.22 | + | 15491.9i | −0.294242 | + | 0.509642i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6918.10 | + | 11982.5i | 0.226888 | + | 0.392982i | ||||
\(977\) | 8057.81 | + | 13956.5i | 0.263861 | + | 0.457021i | 0.967265 | − | 0.253770i | \(-0.0816706\pi\) |
−0.703403 | + | 0.710791i | \(0.748337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −929.069 | + | 1609.20i | −0.0303301 | + | 0.0525333i | ||||
\(980\) | 7425.59 | 0.242043 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12232.8 | −0.397521 | ||||||||
\(983\) | 19374.3 | − | 33557.2i | 0.628630 | − | 1.08882i | −0.359197 | − | 0.933262i | \(-0.616949\pi\) |
0.987827 | − | 0.155558i | \(-0.0497174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4810.37 | + | 8331.81i | 0.155605 | + | 0.269516i | ||||
\(986\) | 9337.44 | + | 16172.9i | 0.301587 | + | 0.522364i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24055.3 | + | 41665.1i | −0.774598 | + | 1.34164i | ||||
\(989\) | −25273.5 | −0.812587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42906.4 | −1.37534 | −0.687672 | − | 0.726022i | \(-0.741367\pi\) | ||||
−0.687672 | + | 0.726022i | \(0.741367\pi\) | |||||||
\(992\) | −20671.3 | + | 35803.7i | −0.661606 | + | 1.14594i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8781.60 | + | 15210.2i | 0.280217 | + | 0.485350i | ||||
\(995\) | 4347.11 | + | 7529.41i | 0.138505 | + | 0.239898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9697.66 | − | 16796.8i | 0.308052 | − | 0.533562i | −0.669884 | − | 0.742466i | \(-0.733656\pi\) |
0.977936 | + | 0.208904i | \(0.0669895\pi\) | |||||||
\(998\) | 138.447 | 0.00439126 | ||||||||
\(999\) | 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 | 405.4.e.s.136.2 | 6 | ||
3.2 | odd | 2 | 405.4.e.u.136.2 | 6 | |||
9.2 | odd | 6 | 405.4.a.g.1.2 | ✓ | 3 | ||
9.4 | even | 3 | inner | 405.4.e.s.271.2 | 6 | ||
9.5 | odd | 6 | 405.4.e.u.271.2 | 6 | |||
9.7 | even | 3 | 405.4.a.i.1.2 | yes | 3 | ||
45.29 | odd | 6 | 2025.4.a.r.1.2 | 3 | |||
45.34 | even | 6 | 2025.4.a.p.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.g.1.2 | ✓ | 3 | 9.2 | odd | 6 | ||
405.4.a.i.1.2 | yes | 3 | 9.7 | even | 3 | ||
405.4.e.s.136.2 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.s.271.2 | 6 | 9.4 | even | 3 | inner | ||
405.4.e.u.136.2 | 6 | 3.2 | odd | 2 | |||
405.4.e.u.271.2 | 6 | 9.5 | odd | 6 | |||
2025.4.a.p.1.2 | 3 | 45.34 | even | 6 | |||
2025.4.a.r.1.2 | 3 | 45.29 | odd | 6 |